diff --git "a/config.json" "b/config.json" new file mode 100644--- /dev/null +++ "b/config.json" @@ -0,0 +1,10043 @@ +{ + "_name_or_path": "thewordsmiths/llama_sciq", + "architectures": [ + "LlamaForCausalLM" + ], + "attention_bias": false, + "attention_dropout": 0.0, + "bos_token_id": 128000, + "eos_token_id": 128001, + "hidden_act": "silu", + "hidden_size": 4096, + "initializer_range": 0.02, + "intermediate_size": 14336, + "max_position_embeddings": 8192, + "mlp_bias": false, + "model_type": "llama", + "num_attention_heads": 32, + "num_hidden_layers": 32, + "num_key_value_heads": 8, + "pad_token_id": 128255, + "pretraining_tp": 1, + "quantization_config": { + "bits": 8, + "damp_percent": 0.1, + "dataset": [ + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average of five consecutive odd numbers is 61. What is the difference between the highest and lowest numbers?\n\n### Options:\nA. 6\nB. 7\nC. 8\nD. 4\nE. 1\n\n### Answer:\nLet the numbers x, x + 2, x + 4, x + 6 and x + 8\nThen, [x + (x + 2) + (x + 4) + (x + 6) + (x + 8)]5 = 61\nor 5x + 20 = 305 => x = 57\nSo, required difference = (57 + 8) - 57 = 8.\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the function Q is defined by the formula Q = 5w/(4vf(z^2)), by what factor will Q be multiplied if w is quadrupled, f is doubled, and z is tripled?\n\n### Options:\nA. 1/9\nB. 2/9\nC. 4/9\nD. 3/9\nE. 2/27\n\n### Answer:\nWe just need to find the factor thats all,\nw -> quadrupled -> 4w\nf-> doubled -> 2f\nz-> tripled -> 3Z\nHence, Z^2 = 9Z^2\nW is in numerator, and f*z in denominator.\nHence,\nAdditional factor being introduced = 4/2*9\n=4/18 = 2/9 = B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nhe distance from town A to town B is five miles. C is six miles from B. Which of the following could be the maximum distance from A to C?\n\n### Options:\nA. 11\nB. 77\nC. 51\nD. 16\nE. 12\n\n### Answer:\nExplanation:\nDo not assume that AB and C are on a straight line. Make a diagram with A and B marked 5 miles apart. Draw a circle centered on B, with radius 6. C could be anywhere on this circle. The minimum distance will be 1, and maximum 11\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA family has two children. find the probability that both the children are girls given that at least\none of them is a girl?\n\n### Options:\nA. 2/5\nB. 1/3\nC. 2/7\nD. 3/5\nE. 1/7\n\n### Answer:\nLet b stand for boy and g for girl. The sample space of the experiment is\nS = {(g, g), (g, b), (b, g), (b, b)}\nLet E and F denote the following events :\nE : \u2018both the children are girls\u2019\nF : \u2018at least one of the child is a girl\u2019\nThen E = {(g,g)} and F = {(g,g), (g,b), (b,g)}\nNow E n F = {(g,g)}\nThus P(F) = 3/4\nand P (E n F )= 1/4\nTherefore P(E|F) = P(E \u2229 F)/P(F) = (1/4)/(3/4) = 1/3\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train 1500 m long can cross an electric pole in 50 sec and then find the speed of the train?\n\n### Options:\nA. 106\nB. 107\nC. 108\nD. 109\nE. 110\n\n### Answer:\nLength = Speed * time\nSpeed = L/T\nS = 1500/50\nS = 30 M/Sec\nSpeed= 30*18/5 (To convert M/Sec in to Kmph multiply by 18/5)\nSpeed = 108 Kmph\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOn average, activated yeast cells divide once every 120 minutes; that is, each individual cell divides into two individual cells over that time span. Given that a certain yeast colony consisted of 300,000 cells two hours ago, approximately how many cells will be populating the colony six hours from now?\n\n### Options:\nA. 77,500\nB. 1,860,000\nC. 2,480,000\nD. 3,720,000\nE. 4,800,000\n\n### Answer:\n300,000 \u00d7 2 \u00d7 2\u00d72\u00d72 = 300,000 \u00d7 16 = E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo pipes P and Q can fill a cistern in 12 and 15 minutes respectively. Both are opened together, but at the end of 3 minutes the first is turned off. How much longer will the cistern take to fill?\n\n### Options:\nA. 11 1/2 min\nB. 11 1/4 min\nC. 11 2/4 min\nD. 11 1/5 min\nE. 11 7/4 min\n\n### Answer:\n3/12 + x/15 = 1\nx= 11 1/4\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA recycling facility is staffed by 10 floor workers and one manager. All of the floor workers are paid equal wages, but the manager is paid n times as much as a floor worker. If the manager\u2019s wages account for 1/10 of all wages paid at the facility, what is the value of n?\n\n### Options:\nA. 5/4\nB. 10/9\nC. 3/2\nD. 5/3\nE. 5\n\n### Answer:\nSay each floor worker is paid $x, then the manager is paid $xn.\nTotal salary would be 10x+xn and we are told that it equals to 10xn:\n10x+xn=10xn --> reduce by x:10+n=10n -->9n= 10\nn = 10/9\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJohnson has a corporate proposal. The probability that vice-president Adams will approve the proposal is 0.6. If VP Adams approves the proposal, then the probability that vice-president Baker will approve the proposal is 0.4. If VP Adams doesn\u2019t approve the proposal, then the probability that vice-president Baker will approve the proposal is 0.3. What is the probability that at least one of the two VPs, approves Johnson\u2019s proposal?\n\n### Options:\nA. 0.12\nB. 0.24\nC. 0.28\nD. 0.48\nE. 0.72\n\n### Answer:\n(1at approves * second rejects ) + (1st rejects * 2nd approves ) + (both approves )\n=0.6*0.2+0.4*0.3+0.6*0.4\n= 0.12+0.12+0.24\n=0.48\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how many ways, a committee of 5 members can be selected from 4 men and 5 ladies, consisting of 3 men and 2 ladies?\n\n### Options:\nA. 40\nB. 152\nC. 175\nD. 200\nE. 212\n\n### Answer:\n(3 men out 4) and (2 ladies out of 5) are to be chosen\nRequired number of ways = (4C3 * 5C2) = 40\nAnswer is A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the greatest positive integer E such that 3^E is a factor of 9^10?\n\n### Options:\nA. E=5\nB. E=9\nC. E=10\nD. E=20\nE. 30\n\n### Answer:\nWhat is the greatest positive integer E such that 3^E is a factor of 9^10?\n9^10 = (3^2)^10 = 3^20\nD. 20\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nBy selling a watch for Rs.400/-, a man loses 20% what is that watch cost price?\n\n### Options:\nA. s. 600/-\nB. s. 700/-\nC. s. 800/-\nD. s. 500/-\nE. s. 900/-\n\n### Answer:\n80 % ------> 400 (80 * 5 = 400)\n100 % ------>500 (100 * 5 = 500)\nCost price = Rs. 500/-\nD)\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 4XZ + YW = 10 and XW + YZ = 20, what is the value of the expression (2X + Y)(2Z + W)?\n\n### Options:\nA. 9.\nB. 12.\nC. 15.\nD. 50.\nE. 18.\n\n### Answer:\n(2x+y)*(2z+w) = 10+2(20) =50\nAnswer : D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average of first 7 prime numbers is?\n\n### Options:\nA. 10.11\nB. 11.11\nC. 8.29\nD. 13.11\nE. 14.11\n\n### Answer:\nSum of 7 prime no. = 58\nAverage = 58/7 = 8.29\nANSWER: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf x is an odd integer and y and z are even integers, which of the following CANNOT be an integer?\n\n### Options:\nA. y/z\nB. x/y\nC. z/x\nD. yx/z\nE. zx/y\n\n### Answer:\nx = Odd\ny = Even\nz = Even\nChecking Options:\nA. y/z Even/Even may be an Integer e.g. 4/2=2 Hence Incorrect Option\nB. x/y Odd/Even CAN NEVER be an Integer Hence Correct Option\nAnswer : B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA boy was asked to multiply a number by 22. He instead multiplied the number by 44 and got the answer 308 more than the correct answer. What was the number to be multiplied?\n\n### Options:\nA. 16\nB. 10\nC. 14\nD. 12\nE. 13\n\n### Answer:\nLet required number\n=x\n=22x+308=44x\n\u21d222x=308\n\u21d2x=308/22\n=154/11\n=14\nAnswer :C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 sec. The speed of the train is?\n\n### Options:\nA. 40\nB. 50\nC. 60\nD. 70\nE. 80\n\n### Answer:\nSpeed of the train relative to man = 125/10 = 25/2 m/sec.\n= 25/2 * 18/5 = 45 km/hr\nLet the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr.\nx - 5 = 45 => x = 50 km/hr.\nAnswer: Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nConvert the 13/36 m/s into kilometers per hour?\n\n### Options:\nA. 2.9 kmph\nB. 9.9 kmph\nC. 1.3 kmph\nD. 1.2 kmph\nE. 5.7 kmph\n\n### Answer:\n13/36 m/s = 13/36 * 18/5 = 13/10\n= 1.3 kmph.\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe difference between a 8 digit number and the number formed by reversing its digit is not a multiple of\n\n### Options:\nA. 3\nB. 5\nC. 296297\nD. 888891\nE. 2666673\n\n### Answer:\nAnother approach is to TEST a number.\nLet's say the original number is 12000002\nSo, the REVERSED number is 20000021\nThe DIFFERENCE = 20000021-12000002 = 8000019\nNo check the answer choices\n8000019 is a multiple of 3,296297,888891,2666673\n5 is NOT a multiple of 8000019\nAnswer ; B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n1,000^2 + 1,001^2 +1,002^2 =\n\n### Options:\nA. 6,030,053\nB. 6,030,054\nC. 6,006,005\nD. 6,030,056\nE. 6,030,057\n\n### Answer:\nInteresting problem.\nI think key is to notice that all the given answer choices differs in last two digits. Therefore, our entire focus should be to figure out how the given terms contribute to last two digits of total.\n1000^2 -> 00\n1001^1 -> 01\n.\n.\n.\n1002^2 -> 5\nTotal -> *5\nAnswer C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJoshua and Jose work at an auto repair center with 5 other workers. For a survey on health care insurance, 2 of the 6 workers will be randomly chosen to be interviewed. What is the probability that Joshua and Jose will both be chosen?\n\n### Options:\nA. 1/21\nB. 1/12\nC. 1/9\nD. 1/6\nE. 1/3\n\n### Answer:\nTwo Methods\n1) Probability of chosing Josh first = 1/7\nProbability of chosing Jose second = 1/6\ntotal = 1/42\nProbability of chosing Jose first = 1/7\nProbability of chosing Josh second = 1/6\nTotal = 1/42\nFinal = 1/42 + 1/42 = 1/21\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA and B complete a work in 6 days. A alone can do it in 10 days. If both together can do the work in how many days?\n\n### Options:\nA. 3.75 days\nB. 4 days\nC. 5 days\nD. 6 days\nE. 7 days\n\n### Answer:\nExplanation:\n1/6 + 1/10 = 8/30 = 4/15\n15/4 = 3.75 days\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOut of four numbers ,the average of first three is 16 and that of the last three is 15. If the last number is 21,the first number is :\n\n### Options:\nA. 22\nB. 21\nC. 77\nD. 99\nE. 24\n\n### Answer:\nExplanation:\nLet the numbers be a,b,c,d\nGiven, a + b + c = 48, b + c + d = 45\nNow, d = 21\nthus, b + c + 21 = 45 \u21d2 b + c = 24\nPutting the value of b + c in a + b + c = 48\na + 24 = 48 \u21d2 a = 24\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n9 friends went to a super market, and everyone decided to contribute equally to the total bill of $900. If one of the friends had a coupon for 10% off the total bill, and if each friend still contributed equally after the coupon was applied to the bill, how much did each friend pay?\n\n### Options:\nA. 30\nB. 60\nC. 80\nD. 90\nE. 95\n\n### Answer:\nAt the non-discounted price, each friend would pay $100, as $900 divided by 9 friends is $100 per friend. But if the bill is 10% off, then each friend would pay 10% less. 10% of $100 is $10, so each friend saves $10 and pays the remaining $90\nCORRECT OPTION:OPTION D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf X,Y is 20%,25% greater than Z then how much percentage is X smaller than Y?\n\n### Options:\nA. 2\nB. 4\nC. 6\nD. 7\nE. 1\n\n### Answer:\nX=120%\nY=125%\nZ=100%\nX-Y/Y*100 = 5/125*100\n==>4%\nANSWER B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAccording to the directions on a can of frozen orange juice concentrate, 1 can of concentrate is to be mixed with 4 cans of water to make orange juice. How many 12 ounce cans of concentrate are required to prepare 140 six-ounce servings of orange juice?\n\n### Options:\nA. 12\nB. 14\nC. 16\nD. 18\nE. 20\n\n### Answer:\n1 X 12 ounce can of concentrate + 4 X 12 ounce cans of water = 60 ounces of the mixture.\n60 ounces of mixture gives (60 / 6 ) = 10 servings.\nThus 1 x 12 ounce can of concentrate is used to produce 10 servings of the mixture.\nTo make 140 servings of the mixture, we need 140 / 10 = 14 cans of the concentrate.\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSudhir started a business with Rs.30,000 and after 8 months Ravi joined him with Rs.60,000. If they get a profit of Rs.28000 then ratio of their shares will be\n\n### Options:\nA. 3:2\nB. 2:3\nC. 4:3\nD. 3:4\nE. 3:5\n\n### Answer:\n30000*12:60000*(12-8)\n=360000 :240000\n=3:2\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average age of M boys is \u2018b\u2019 years and of \u2018n\u2019 girls \u2018c\u2019 years. The average age of all together is?\n\n### Options:\nA. (mb + nc)/ (m + b) years\nB. (mb + bc)/ (m + n) years\nC. (mb + nc)/ (m + n) years\nD. (nb + nc)/ (m + n) years\nE. (mb + nb)/ (m + n) years\n\n### Answer:\n(mb + nc) / (m+ n).nswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nExcluding stoppages, the speed of a train is 48 kmph and including stoppages it is 36 kmph. Of how many minutes does the train stop per hour?\n\n### Options:\nA. 16\nB. 17\nC. 15\nD. 18\nE. 12\n\n### Answer:\nT = 12/48 * 60\n= 15\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAn assembly line produces 90 cogs per hour until an initial order of 60 cogs is completed. The speed of the assembly line is then immediately decreased so that it only produces 60 cogs per hour until another 60 cogs are produced. What is the overall average output, in cogs per hour, for the assembly line during this whole time?\n\n### Options:\nA. 68\nB. 69\nC. 70\nD. 71\nE. 72\n\n### Answer:\nThe time to produce the first 60 cogs is 60/90 = 2/3 hours.\nThe time to produce the next 60 cogs is 60/60 = 1 hour.\nThe average output is 120 cogs / (5/3) hours = 72 cogs per hour.\nThe answer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf r < y < -1, which of the following is true?\n\n### Options:\nA. r/y > ry\nB. y/r > r+y\nC. y/r > ry\nD. y/r < r+y\nE. y/r > r/y\n\n### Answer:\nConsider :\nr= -3\ny= -2\nthen put for every option. U'll get ans B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA pump can fill a tank with water in 2 hours. Because of a leak, it took 7 hours to fill the tank. The leak can drain all the water in ?\n\n### Options:\nA. 15hr 10min\nB. 16hr 20min\nC. 2hr 48min\nD. 15hr\nE. 14hr 25min\n\n### Answer:\nWork done by the leak in 1 hour = 1/2 - 1/7 = 5/14\nLeak will empty the tank in 14/5 hrs = 2hr 48min\nAnswer is C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOn a certain test, Bill scored 20 more points than John, but half as many points as Sue. If the sum of the scores of the three students was 220 points, how many points did Bill receive?\n\n### Options:\nA. 30\nB. 40\nC. 50\nD. 60\nE. 100\n\n### Answer:\nconsider john's points as x\nso bill's points are x +20\nSo sue's points are 2x +40\ntotal of all three students is 4x +60, but this total is given as 220\nx = 40\nso bill's points = 40 +20 = 60\ncorrect answer option D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe cross-section of a water channel is a trapezium in shape. If the channel is 12 meters wide at the top and 8 meters wide at the bottom and the area of cross-section is 700 square meters, what is the depth of the channel (in meters)?\n\n### Options:\nA. 50\nB. 60\nC. 70\nD. 80\nE. 90\n\n### Answer:\n1/2 * d * (12 + 8) = 700\nd = 70\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a certain sequence, each term except for the first term is one less than twice the previous term. If the first term is 1.75, then the 3rd term is which of the following?\n\n### Options:\nA. \u22121.5\nB. \u22121\nC. 0\nD. 0.5\nE. 4\n\n### Answer:\nFirst = 1.75\nSecond = 2*1.75-1 = 2.5\nSecond = 2*2.5-1 = 4\nAnswer: option E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?\n\n### Options:\nA. 40\nB. 28\nC. 27\nD. 17\nE. 21\n\n### Answer:\nSpeed = 45 * 5/18 = 25/2 m/sec\nTotal distance covered = 360 + 140 = 500 m\nRequired time = 500 * 2/25\n= 40 sec\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the average of three tenths and five thousandths\n\n### Options:\nA. 0.2022\nB. 0.3325\nC. 0.1525\nD. 0.2012\nE. 0.2114\n\n### Answer:\nExplanation:\nthree tenths = 0.3\nFive thousandths = 0.005\nThe average is (0.3 + 0.005)/2 = 0.1525\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train covers a distance of 1000 km in 10hrs. Find the speed of the train?\n\n### Options:\nA. 100km/hr\nB. 120km/hr\nC. 150km/hr\nD. 50km/hr\nE. 75km/hr\n\n### Answer:\nSpeed = 1000/10 = 100km/hr\nAnswer is A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA box is in the shape of a semicircle with a radius of 12. What is the approximate perimeter of the semicircle?\n\n### Options:\nA. 54\nB. 62\nC. 25\nD. 34\nE. 60\n\n### Answer:\nperimeter of a circle =2pi*r\nperimeter of a semicircle = pi*r + 2r\naprox perimiter = 3.14*12 + 2*12 = 61.68 approximately 62\nanswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe probabilities of solving a question by 3students A, B & C are 1/2,1/3 &1/4, respectively. The probability that the problem will be solved is?\n\n### Options:\nA. 1/5\nB. 3/4\nC. 3/7\nD. 3/5\nE. 3/7\n\n### Answer:\nSol. First, we find the probability of not solving the problem x PTO x = (1 \u2014 D x - D x - D\n1 2 3 1 =iXiX71=4;\n1 3 Required probability 3/4\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe ratio of male to female in a class is 6:6. the career preference of the students in the class are to be represented in a circle graph. If the area of the graph allocated to each career preference is to be proportional to the number of students who have that career preference, how many degrees of the circle should be used to represent a career that is preferred by one third of the males and two-third of the females in the class?\n\n### Options:\nA. a)180 degree\nB. b) 168 degree\nC. c)191 degree\nD. d)192 degree\nE. e)204 degree\n\n### Answer:\nhere is my approach => males => 6x and females =6x => total =12x\nnow 12x=> 360\ntherefore 6x => 180 degree .\nP.S => 6x is nothing but total number of students with the given preference\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA number which is divided by 13 and 26 yields same remainder?\n\n### Options:\nA. 108\nB. 61\nC. 86\nD. 78\nE. 92\n\n### Answer:\nWe can find it with the help of option\n108=108/13 and 108/26 not gives the remainder 6 and 3\n61=61/13 and 61/26 not gives the remainder 6 and 3\n86=86/13 and 86/26 not gives the remainder 6 and 3\n78=78/13 and 78/26 gives same remainder 0\nOption D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a certain corporation, there are 300 male employees and 150 female employees. It is known that 30% of the male employees have advanced degrees and 40% of the females have advanced degrees. If one of the 450 employees is chosen at random, what is the probability this employee has an advanced degree or is female?\n\n### Options:\nA. 2/3\nB. 3/5\nC. 3/10\nD. 8/15\nE. 11/30\n\n### Answer:\nP(female) = 150/450 = 1/3\nP(male with advanced degree) = 0.3*300/450 = 90/450 = 1/5\nThe sum of the probabilities is 8/15\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf each day a tree loses half its remaining leaves, what fraction of its leaves will it have lost after 5 days ?\n\n### Options:\nA. 1/32\nB. 1/16\nC. 9/10\nD. 15/16\nE. 31/32\n\n### Answer:\nAt the end of each day, the tree has 1212 it's remaining leaves.\nIf initially the tree has x leaves.\nAfter day 1: 1/2x\nAfter day 2: 1/2x\u22171/2=1/^2 x and so on ....\nAfter day 5: 1/2^5x=1/32x\nSo leaves lost = Initial amount of leaves - Leaves remaining = x\u22121/32x=31/32x\nAnswer:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the principle on a certain sum of money at 5% per annum for 2 2/5 years if the amount being Rs.2120?\n\n### Options:\nA. Rs.1000.15\nB. Rs.1100.95\nC. Rs.1892.85\nD. Rs.1050.85\nE. Rs.1200.25\n\n### Answer:\n2120 = P [1 + (5*12/5)/100]\nP= 1892.85\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA, B and C are partners. A receives 2/3 of profits, B and C dividing the remainder equally. A's income is increased by Rs.400 when the rate to profit rises from 5 to 7 percent. Find the Capital of C?\n\n### Options:\nA. 3377\nB. 2899\nC. 5000\nD. 2778\nE. 1991\n\n### Answer:\nA:B:C = 2/3:1/6:1/6 = 4:1:1\nx * 2/100 * 2/3 = 400\nC's capital = 30000*1/6 = 5000\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn the xy-plane, a triangle has vertices (0,0), (4,0) and (4,9). If a point (a,b) is selected at random from the triangular region, What is the probability that a-b>0?\n\n### Options:\nA. 1/5\nB. 1/3\nC. 1/2\nD. 2/9\nE. 4/5\n\n### Answer:\nThe area of the right triangle is (1/2)*4*9 = 18.\nOnly the points (a,b) below the line y=x satisfy a - b > 0.\nThe part of the triangle which is below the line y=x has an area of (1/2)(4)(4) = 8.\nP(a - b > 0) = 8/18 = 2/9\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the sum of 7 consecutive negative integers is -70, what is the value of the 2nd number in the sequence?\n\n### Options:\nA. 8\nB. -9\nC. -8\nD. 9\nE. 6\n\n### Answer:\nif sum is -70, the average = median = -70/7 = -10 = which is the middle in the sequence.\n7/2 = 3.5. When rounded up = 4. So -10 is the 4th in the sequence.\n4th - 2nd = 2 numbers away.\n-10 + 2= -8\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf x-y=10, which of the following must be true?\nI. Both x and y are positive\nII. If x is negative, y must be negative\nIII.If x is positive, y must be positive\n\n### Options:\nA. I only\nB. II only\nC. III only\nD. I and II\nE. II and III\n\n### Answer:\nThe best way to approach such questions is to plug in values for x and y\nGiven: x-y=10\nI. Both x and y are positive:\nLet x=12 and y=2\nx-y=10\nBut,\nLet x=6 and y=-4\nx-y=8\nTherefore, NOT TRUE\nIII. If x is positive, y must be positive\nLet x=12 and y=2\nx-y=10\nBut,\nLet x = 6 and y=-4\nx-y=10\nTherefore, NOT TRUE\nII. If x is negative, y must be negative\nIf x is negative, for the expression x-y=8 to be true, y must be a -ve number. Otherwise, the sum of two negative numbers will yield another negative number!\nTherefore, TRUE\nAns: 'B'\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 9x^2-16y^2=3x+4y,then what will give the answer?\n\n### Options:\nA. 3x-4y=0\nB. 3x-4y=2\nC. 3x-4y=1\nD. 3x+4y=0\nE. 3x+4y=1\n\n### Answer:\n9x^2-16y^2=3x+4y\n(3x+4y)(3x-4y)=3x+4y\n3x-4y=(3x+4y)/(3x+4y)\n3x-4y=1\nAnswer is option C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA library contains 90671 books in English and 405063 books in other languages. What is the total number of books available in the library?\n\n### Options:\nA. 494947\nB. 494044\nC. 495734\nD. 493734\nE. 493923\n\n### Answer:\nNumber of English Books = 90671\nNumber of in other Language Books = 405063\ntotal number of books 90671 + 405063 = 495734 books\nanswer :C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a rectangular coordinate system, what is the area of a rectangle whose vertices have the coordinates (-5, 1), (1, 1), (1, -4) and (-5, -4)?\n\n### Options:\nA. 20\nB. 30\nC. 40\nD. 55\nE. 48\n\n### Answer:\nLength of side 1= 5+1=6\nLength of side 2= 4+1= 5\nArea of rectangle= 6*5= 30\nB is the answer\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf p(x)=ax^4+bx^3+cx^2+dx+e has roots at x=1,2,3,4 and p(0)=48, what is p(5)\n\n### Options:\nA. 48\nB. 24\nC. 0\nD. 50\nE. 40\n\n### Answer:\np(x)=ax^4+bx^3+cx^2+dx+e\nit can be written as\np(x)=a*(x-1)*(x-2)*(x-3)*(x-4) ----(1)\nput x=0 in(1), we get\np(0)=a*(-1)(-2)(-3)(-4)\n=> 48=a*24\n=> a=2\nso, p(x)=2*(x-1)*(x-2)*(x-3)*(x-4)\n=> p(5)=2*(5-1)*(5-2)*(5-3)*(5-4)=2*4*3*2*1=48\np(5) = 48\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nEach of the 26 members in a high school class is required to sign up for a minimum of one and a maximum of three academic clubs. The three clubs to choose from are the poetry club, the history club, and the writing club. A total of 11 students sign up for the poetry club, 17 students for the history club, and 15 students for the writing club. If 5 students sign up for exactly two clubs, how many students sign up for all three clubs?\n\n### Options:\nA. 2\nB. 3\nC. 4\nD. 5\nE. 6\n\n### Answer:\nThe total number in the three clubs is 11+17+15=43.\nAll 26 students signed up for at least one club.\n5 of those students signed up for exactly one more club.\n43 - 31 = 12 so 6 students must have signed up for exactly three clubs.\nThe answer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the value of a piece of property decreases by 10% while the new tax rate on the property represent 110% of the original tax rate, what is the effect on the taxes?\n\n### Options:\nA. taxes increase by 10%\nB. taxes increase by 1%\nC. there is no change in taxes\nD. taxes decrease by 1%\nE. taxes decrease by 10%\n\n### Answer:\nConsider the value of property = 100, Original tax rate 10%, hence tax value = 100*10% = 10.\nDecreased value of property = 90, New tax rate = 110% of 10 = 11%, hence tax value = 90*11% = 9.9\n10-9.9 = decrease by 1%.\nAnswer D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA box contains 25 electric bulbs, out of which 4 are defective. Two bulbs are chosen at random from this box. The probability that at least one of these is defective is\n\n### Options:\nA. 3/10\nB. 7/19\nC. 12/19\nD. 21/95\nE. None\n\n### Answer:\nSolution\nP( None is defective)\n= 21C2 / 25C2\n= 7/10\nP( at least one is defective)\n= (1- 7/10)\n=3/10.\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThis topic is locked. If you want to discuss this question please re-post it in the respective forum.\nMatt and Peter can do together a piece of work in 20 days. After they have worked together for 12 days Matt stops and Peter completes the remaining work in 16 days. In how many days Peter complete the work separately.\n\n### Options:\nA. 26 days\nB. 27 days\nC. 23 days\nD. 35 days\nE. 40 days\n\n### Answer:\nTogether they complete the job in 20 days means they complete 12/20 of the job after 12 days.\nPeter completes the remaining (8/20) of the job in 16 days which means that the whole job(1) can be completed in X days.\n<=> 8/20->16 <=> X=16/(8/20)=40 Thus the answer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe difference between the place value and the face value of 8 in the numeral 856973 is\n\n### Options:\nA. 973\nB. 6973\nC. 5994\nD. 6084\nE. None of these\n\n### Answer:\n(Place value of 8) - (Face value of 8) = (800000 - 8) = 799992\nAnswer: Option E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe difference between the ages of two persons is 30 years. Fifteen years ago, the elder one was twice as old as the younger one. The present age of the younger person is?\n\n### Options:\nA. 30yr\nB. 25yr\nC. 45yr\nD. 40yr\nE. 50yr\n\n### Answer:\nLet their ages be x years and (x+30) years\nThen, (x+30) - 15 = 2(x-15)\nx +15 = 2x-30\nx = 45\nAnswer is C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn an examination 65% failed in Math and 35% failed in French. If 22% failed in both. What % of students passed in both.\n\n### Options:\nA. 22%\nB. 15%\nC. 20%\nD. 30%\nE. 10%\n\n### Answer:\nPassed in Math = 100 - 65 = 35%\nPassed in French = 100 - 35 = 65%\nStudents who passed Math or French = 100 -22 = 78%\nStudents passed in Math and French = (Passed in Math) + (Passed in French) - (Students who passed Math or French) = 35+65-78 =22%\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe value of ((x \u2013 y)\u00b3 + (y - z)\u00b3 + (z \u2013 x)\u00b3)/(21 (x \u2013 y) (y \u2013 z) (z \u2013 x))\nis equal to :\n\n### Options:\nA. 0\nB. 1/12\nC. 1/7\nD. 1/4\nE. 1/3\n\n### Answer:\nSince (x \u2013 y) + (y \u2013 z) + (z \u2013 x) = 0,\nso (x \u2013 y)\u00b3 + (y \u2013 z)\u00b3 + (z \u2013 x)\u00b3= 3 (x \u2013 y) (y \u2013 z) (z \u2013 x).\n(3 (x \u2013 y) (y \u2013 z) (z \u2013 x))/(21(x \u2013 y) (y \u2013 z) (z \u2013 x)) = 1/7.\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf y \u2260 3 and 2 x/y is a prime integer greater than 2, which of the following must be true?\nI. x = y\nII. y = 1\nIII. x and y are prime integers.\n\n### Options:\nA. None\nB. I only\nC. II only\nD. III only\nE. I and II\n\n### Answer:\nLet 2 x/Y = K , Where k is a prime number > 2 ( 3, 5, 7, 11 ...etc)\nso 2x = Ky --> ( 3y or 5y or 7y or 11y etc...)\nWhich implies always X > Y\nSo answer is (A)\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain club has exactly 5 new members at the end of its first week. Every subsequent week, each of the previous week's new members (and only these members) brings exactly M new members into the club. If y is the number of new members brought into the club during the twelfth week, which of the following could be y?\n\n### Options:\nA. 5^1/12\nB. 3^11 * 5^11\nC. 3^12 * 5^12\nD. 3^11 * 5^12\nE. 60^12\n\n### Answer:\nAt the end of the first week, there are 5 new members;\nAt the end of the second week, there are 5M new members (since each 5 new members from the previous week brings M new members);\nAt the end of the third week, there are 5M^2 new members (since each 5M new members from the previous week brings M new members);\n...\nAt the end of the twelfth week, there are 5M^11 new members (since each 5M^10 new members from the previous week brings M new members).\nWe are given that 5M^11=y. Out of the answers only D yields integer value for M: 5M^11=3^11 * 5^12 --> M=3*5=15.\nAnswer: D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe sum of first four prime numbers is?\n\n### Options:\nA. 17\nB. 23\nC. 24\nD. 28\nE. 30\n\n### Answer:\nRequired sum = (2 + 3 + 5 + 7) = 17.\nNote: 1 is not a prime number.\nDefinition: A prime number (or a prime) is a natural number that has exactly two distinct natural number divisors: 1 and itself.\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe set S has 36 different subsets each of which contains exactly two elements. How many subsets of S could contain exactly six elements each?\n\n### Options:\nA. 96\nB. 80\nC. 84\nD. 88\nE. 92\n\n### Answer:\nnC2 = 36\n=> n*(n-1)/2 = 36 by middle term factor and n cannot be negative\n=> n = 9\nnC3 = 9C6 = 9!/6!*(9-6)!= 9*8*7*6!/6!*3*2 =84\nSo, Answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a vessel, there are 10 litres of alcohol. An operation is defined as taking out five litres of what is present in the vessel and adding 10 litres of pure water to it. What is the ratio of alcohol to water after two operations?\n\n### Options:\nA. 1 : 0\nB. 1 : 5\nC. 1 : 1\nD. 1 : 2\nE. 1 : 9\n\n### Answer:\nFinal concentration = Initial concentration (1\u2212replacement quantityfinal volume)(1\u2212replacement quantityfinal volume)\nFinal concentration = =1\u00d7(1\u22121015)=13=1\u00d7(1\u22121015)=13\nFinal concentration = 13\u00d7(1\u22121020)=1613\u00d7(1\u22121020)=16\nSo ratio of alcohol : water = 1 : 5\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average weight of a group of boys is 30 kg. After a boy of weight 36 kg joins the group, the average weight of the group goes up by 1 kg. Find the number of boys in the group originally ?\n\n### Options:\nA. A)5\nB. B)8\nC. C)6\nD. D)2\nE. E)1\n\n### Answer:\nLet the number off boys in the group originally be x.\nTotal weight of the boys = 30x\nAfter the boy weighing 36 kg joins the group, total weight of boys = 30x + 36\nSo 30x + 36 = 31(x + 1) = > x = 5.\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many words can be formed by using all letters of the word \u2018DAUGHTER\u2019 so that the vowels always come together?\n\n### Options:\nA. 1214\nB. 4320\nC. 1254\nD. 3265\nE. 4512\n\n### Answer:\nGiven word contains 8 different letters. When the vowels AUE are always together, we may suppose them to form an entity, treated as one letter.\nThen, the letters to be arranged are DGNTR (AUE).\nThen 6 letters to be arranged in 6p6 = 6! = 720 ways.\nThe vowels in the group (AUE) may be arranged in 3! = 6 ways.\nRequired number of words = (720x6) = 4320.\nAns: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf x is positive integer,y is negative integer, and 5x+2y=4, which of the following could be the value of x ?\n\n### Options:\nA. 0\nB. 1\nC. 2\nD. 3\nE. 4\n\n### Answer:\nUse answer options to solve this problem -\nPut x = 2\nSo, 5x+2y=4\nOr, 5(2)+2y=4\nOr, 10+2y=4\nOr, 2y=4-10;2y=-6\nOr, y=-3(y is negative integer)\nAnswer will be (C)\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf X gets 25% more than Y and Y gets 20% more than Z, the share of Z out of Rs. 1110 will be:\n\n### Options:\nA. Rs. 300\nB. Rs. 200\nC. Rs. 240\nD. Rs. 350\nE. None of these\n\n### Answer:\nZ share = Z,\nY = 1.2Z\nX = 1.25\u00c3\u20141.2Z,\nX+Y+Z =111\n(1.25\u00c3\u2014 1.2+1.2+1)Z=1110\n3.7Z=1110, Z=300\nAnswer: . A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo goods trains each 720 m long are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one?\n\n### Options:\nA. 22 sec\nB. 88 sec\nC. 48 sec\nD. 18 sec\nE. 72 sec\n\n### Answer:\nRelative speed = 45 + 30 = 75 km/hr.\n75 * 5/18 = 125/6 m/sec.\nDistance covered = 750 + 750 = 1500 m.\nRequired time = 1500 * 6/125 = 72 sec.\nAnswer:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the price of a book is first decreased by 50% and then increased by 60%, then the net change in the price will be?\n\n### Options:\nA. 20% decrease\nB. 10% increase\nC. 10% decrease\nD. 15% increase\nE. 25% decrease\n\n### Answer:\nLet the original price be $100\nNew final price = 160% of (50% of $100)\n= 160/100 * 50/100 *100 = $80\nDecrease is 20%\nAnswer is A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe standard deviation of a normal distribution of data is 2, and 3 standard deviations below the mean is greater than 44. What is a possible value for the mean of the distribution?\n\n### Options:\nA. 46\nB. 47\nC. 48\nD. 49\nE. 51\n\n### Answer:\nThe standard deviation ({SD}) = 2;\n3 standard deviations below the mean is greater than 44:\n{Mean} - 3*{SD} > 44;\n{Mean} - 6 > 44;\n{Mean} > 50.\nAnswer: E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAt present, the ratio between the ages of Arun and Deepak is 4:3. After 2 years, Arun's age will be 26 years. What is the age of Deepak at present?\n\n### Options:\nA. 16\nB. 17\nC. 10\nD. 18\nE. 15\n\n### Answer:\nLet the present ages of Arun and Deepak be 4x and 3x years respectively.\nThen, 4x + 2 = 26 => x = 8\nDeepak's age = 3x = 18 years.\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn 2008, the profits of Company N were 10 percent of revenues. In 2009, the revenues of Company N fell by 20 percent, but profits were 18 percent of revenues. The profits in 2009 were what percent of the profits in 2008?\n\n### Options:\nA. 80%\nB. 105%\nC. 120%\nD. 144%\nE. 138%\n\n### Answer:\nx = profits\nr= revenue\nx/r = 0,1\nx= 10\nr=100\n2009:\nr=80\nx/80 = 0,18 = 18/100\nx= 80*18/100\nx= 14.4\n14.4/10 = 1,44 = 144%, Answer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA shopkeeper buys two articles for Rs.1000 each and then sells them, making 30% profit on the first article and 30% loss on second article. Find the net profit or loss percent?\n\n### Options:\nA. 200\nB. 768\nC. 276\nD. 300\nE. 279\n\n### Answer:\nProfit on first article = 30% of 1000 = 300.\nThis is equal to the loss he makes on the second article. That, is he makes neither profit nor loss.\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average score in an examination of 10 students of a class is 60. If the scores of the top five students are not considered, the average score of the remaining students falls by 5. The pass mark was 50 and the maximum mark was 100. It is also known that none of the students failed. If each of the top five scorers had distinct integral scores, the maximum possible score of the topper is\n\n### Options:\nA. 99\nB. 95\nC. 98\nD. 97\nE. 100\n\n### Answer:\nThe average score in an examination of 10 students of a class is 60 --> the total score = 10*60 = 600;\nThe 5 smallest scores have an average of 55 --> the total score of the 5 smallest scores = 275.\nFrom above, the total score of the 5 largest scores = 600 - 275 = 325.\nSay the 5 largest scores are a, b, c, d, and e (where a", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn an increasing sequence of 8 consecutive integers, the sum of the first 4 integers is 570. What is the sum of the last 4 integers in the sequence?\n\n### Options:\nA. 585\nB. 580\nC. 586\nD. 587\nE. 589\n\n### Answer:\nSolution:\nIn solving this problem we must first remember that when we have 8 consecutive integers we can display them in terms of just 1 variable. Thus, we have the following:\nInteger 1: x\nInteger 2: x + 1\nInteger 3: x + 2\nInteger 4: x + 3\nInteger 5: x + 4\nInteger 6: x + 5\nInteger 7: x + 6\nInteger 8: x + 7\nWe are given that the sum of the first 4 integers is 570. This means that:\nx + x+1 + x+2 + x+3 = 570\n4x + 6 = 570\n4x = 564\nx = 141\nThe sum of the last 4 integers can be expressed and simplified as:\nx+4 + x+5 + x+6+ x+7 = 4x + 22\nSubstituting 141 for x yields:\n(4)(141) + 22 = 586\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain high school has 500 students. Of these students, 50 are taking music, 20 are taking art, and 10 are taking both music and art. How many students are taking neither music nor art?\n\n### Options:\nA. 430\nB. 440\nC. 450\nD. 460\nE. 470\n\n### Answer:\nWe're given a series of facts to work with:\n1) A certain high school has 500 students.\n2) Of these students:\nX are taking music,\nY are taking art, and\nZ are taking BOTH music and art.\nWe're asked how many students are taking NEITHER music nor art?\nLet's TEST\nX = 50\nY = 20\nZ = 10\nSo, we have 50 students taking music, 20 taking art and 10 taking BOTH music and art.\n40 student taking JUST music\n10 student taking JUST art\n10 student taking BOTH music and art\nTotal = 60 students\nWe're asked for the total number of students who are taking NEITHER Course. That is 500 - 60 = 440.\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is?\n\n### Options:\nA. 13 km/hr\nB. 50 km/hr\nC. 17 km/hr\nD. 18 km/hr\nE. 12 km/hr\n\n### Answer:\nSpeed of the train relative to man = (125/10) m/sec\n= (25/2) m/sec. [(25/2) * (18/5)] km/hr\n= 45 km/hr. Let the speed of the train be x km/hr. Then, relative speed\n= (x - 5) km/hr. x - 5 = 45 ==> x\n= 50 km/hr.\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf X,Y is 20%,25% greater than Z then how much percentage is X smaller than Y?\n\n### Options:\nA. 3 1/13%\nB. 3%\nC. 3 11/13%\nD. 4%\nE. None of these\n\n### Answer:\nExplanation:\nX = 125%\nY = 130%\nZ = 100%\nX-Y/Y * 100 = 5/130 * 100\n= 500/130 %\n= 3 11/13% smaller than Y\nAnswer: Option C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn the xy-plane, line e passes through point (3,-2) and intersect perpendicularly with line n that passes through points (0,3) and (3,5). What is the equation of line e?\n\n### Options:\nA. 3x+2y-5=0\nB. 3x+2y+5=0\nC. 2x-3y-12=0\nD. 2x+3y=0\nE. 4x+3y-6=0\n\n### Answer:\nIf two lines intersect perpendicularly, we get -1 when we multiply two slopes together. The slope of a line n is (5-3)/(3-0)=2/3. Hence, the slope of a line e should be -3/2. Since it crosses (3,-2), if we calculate we get 3x+2y=5. Hence, the correct answer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWalking at 6/7th of his usual speed, a man is 25 mins too late. His usual time is\n\n### Options:\nA. 7.5 hrs\nB. 1.5 hrs\nC. 2.5 hrs\nD. 1.67 hrs\nE. 2.67 hrs\n\n### Answer:\nAs the distance is same s*t=6/7s*(t+25)\nsolving this we get t=150 sec\n150/60=2.5 hrs\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a competitive examination in State A, 6% candidates got selected from the total appeared candidates. State B had an equal number of candidates appeared and 7% candidates got selected with 80 more candidates got selected than A. What was the number of candidates appeared from each State ?\n\n### Options:\nA. 2438\nB. 8000\nC. 2379\nD. 2988\nE. 2791\n\n### Answer:\nExplanation:\nLet the number of candidates appeared from each state be x.\nIn state A, 6% candidates got selected from the total appeared candidates\nIn state B, 7% candidates got selected from the total appeared candidates\nBut in State B, 80 more candidates got selected than State A\nFrom these, it is clear that 1% of the total appeared candidates in State B = 80\n=> total appeared candidates in State B = 80 x 100 = 8000\n=> total appeared candidates in State A = total appeared candidates in State B = 8000\nAnswer: B) 8000\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhen she chooses a password, Eloise\nalways uses exactly ten different\ncharacters: five letters (A, B, C, D, and E)\nand five numbers (2, 3, 4, 5, and 6).\nAdditionally, she always ensures that no\npair of letters is consecutive and that no\npair of numbers is consecutive. How many\ndifferent passwords conform to these rules?\n\n### Options:\nA. fewer than 1,000\nB. between 1,000 and 10,000\nC. between 10,000 and 100,000\nD. between 100,000 and 1,000,000\nE. more than 1,000,000\n\n### Answer:\nThe first character of the password can be any letter or number, so Eloise has ten\noptions. Her second choice must be from the set (letter or number) not yet used, so she\nhas five options. Choice 3 is from the same set as Choice 1, and she has four options left.\nChoice 4 is the second item from the same set as Choice 2, so she has four options.\nChoices 5 and 6 are from different sets, each with three options; Choices 7 and 8 are from\ndifferent sets, each with two options; Choices 9 and 10 are from different sets, each with\nonly one option remaining. You can see this information in the following chart:\n1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th\n10 5 4 4 3 3 2 2 1 1\nTo find the total number of possible passwords, multiply these numbers together:\n10 \u00d7 5 \u00d7 4 \u00d7 4 \u00d7 3 \u00d7 3 \u00d7 2 \u00d7 2 \u00d7 1 \u00d7 1 = 28,800\ncorrect anser C)between 10,000 and 100,000\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf m is a positive integer and m^2 is divisible by 33, then the largest positive integer that must divide m is?\n\n### Options:\nA. 3\nB. 6\nC. 8\nD. 11\nE. 16\n\n### Answer:\nM^2 is divisible by 33 so M^2 must be multiple of 48.\nIf the value of M is Multiples of 11 then it will satisfy the condition. If we If M is 12 or 24 or 36 then it ans is D but if M = 33 then answer should be 16.\nIs the question right? Or am i missing some thing?\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo trains are moving in opposite directions with speed of 70 km/hr and 90 km/hr respectively. Their lengths are 1.10 km and 0.9 km respectively. the slower train cross the faster train in --- seconds\n\n### Options:\nA. 56\nB. 45\nC. 47\nD. 26\nE. 25\n\n### Answer:\nExplanation:\nRelative speed = 70+90 = 160 km/hr (Since both trains are moving in opposite directions)\nTotal distance = 1.1+.9 = 2km\nTime = 2/160 hr = 1/80 hr = 3600/80 seconds = = 45 seconds\nAnswer: Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many prime numbers exist between 1 and 20?\n\n### Options:\nA. 7\nB. 6\nC. 5\nD. 8\nE. 9\n\n### Answer:\nE)\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJolene entered an 18-month investment contract that guarantees to pay 2 percent interest at the end of 4 months, another 3 percent interest at the end of 12 months, and 4 percent interest at the end of the 18 month contract. If each interest payment is reinvested in the contract, and Jolene invested $10,000 initially, what will be the total amount of interest paid during the 18-month contract?\n\n### Options:\nA. $506.00\nB. $726.24\nC. $900.00\nD. $920.24\nE. $926.24\n\n### Answer:\nIf interest were not compounded in every six months (so if interest were not earned on interest) then we would have (2+3+4)=9% simple interest earned on $10,000, which is $900. So, you can rule out A, B and C right away.\nInterest earned after the first time interval: $10,000*2%=$200;\nInterest earned after the second time interval: ($10,000+$200)*3%=$300+$6=$306;\nInterest earned after the third time interval: ($10,000+$200+$306)*4%=$400+$8+(~$12)=~$420;\nTotal: 200+306+(~420)=~$920.24\nAnswer: D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a survey of 350 employees, 104 of them are uninsured, 54 work part time, and 12.5 percent of employees who are uninsured work part time. If a person is to be randomly selected from those surveyed, what is the probability that the person will neither work part time nor be uninsured?\n\n### Options:\nA. 7/12\nB. 8/41\nC. 9/348\nD. 1/8\nE. 41/70\n\n### Answer:\n---------UI----------------NUI-------Total\nPT----(12.5/100)*104 = 13----------- --54\nNPT---104-13-------------- x--------296\nTotal--104----------------------------350\nwe have to find not part time and not uninsured . in other words not part time and insured = x/350 = (296-104+13)/350\n= 41/70\nAnswer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe value of (2.502+0.064)^2 - (2.502-0.064)^2/2.502*0.064\n\n### Options:\nA. .25\nB. .235\nC. 4\nD. 3\nE. 2\n\n### Answer:\n(2.502+0.064)2 - (2.502-0.064)2/2.502*0.064 = (a+b)2 - (a-b)/ab\n= 4ab/ab\n= 4\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOn flipping 2 coins together what is the outcomes for at least two heads?\n\n### Options:\nA. {HH}\nB. {TT}\nC. {HT}\nD. {TH}\nE. None\n\n### Answer:\nSample space, S = {HH, TH, TH, TT}\nFavorable outcomes for at least two heads\n= favorable outcomes for exactly two heads and favorable outcomes for more than two heads\n= {HH}\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe difference between simple and compound interest on Rs. 1600 for one year at 10% per annum reckoned half-yearly is?\n\n### Options:\nA. 8\nB. 3\nC. 9\nD. 4\nE. 2\n\n### Answer:\nS.I. = (1600 * 10 * 1)/100 = Rs. 160\nC.I. = [1600 * (1 + 5/100)2 - 1600]\n= Rs. 164 Difference = (164 - 160)\n= Rs.4.\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo cars cover the same distance at the speed of 50 and 45 kmps respectively. Find the distance traveled by them if the slower car takes 1 hour more than the faster car?\n\n### Options:\nA. 278\nB. 277\nC. 960\nD. 600\nE. 261\n\n### Answer:\n50(x + 1) = 45 x\nX = 10\n60 * 10 = 600 km\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIncome and expenditure of a person are in the ratio 5 : 4. If the income of the person is Rs. 20000, then find his savings?\n\n### Options:\nA. Rs.3600\nB. Rs.4000\nC. Rs.3639\nD. Rs.3632\nE. Rs.3602\n\n### Answer:\nLet the income and the expenditure of the person be Rs. 5x and Rs. 4x respectively.\nIncome, 5x = 20000 => x = 4000\nSavings = Income - expenditure = 5x - 4x = x\nSo, savings = Rs.4000\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nDhoni spent 40 percent of his earning last month on rent and 20 percent less than what he spent on rent to purchase a new dishwasher. What percent of last month's earning did Dhoni have left over?\n\n### Options:\nA. 30%\nB. 28%\nC. 32%\nD. 33%\nE. 34%\n\n### Answer:\nSay Dhoni's earning last month was $100.\nDhoni spent 40 percent of his earning last month on rent --> $40 on rent;\n20 percent less than what he spent on rent to purchase a new dishwasher --> $40*0.8=$32 on the dishwasher.\nLeft over amount 100 - (40 + 32) = $28\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe equal amounts of money are deposited in two banks each at 15% per annum for 3.5 years and 5 years respectively. If the difference between their interests is Rs.144, find the each sum?\n\n### Options:\nA. 299\nB. 100\nC. 270\nD. 278\nE. 213\n\n### Answer:\n(P*5*15)/100 - (P*3.5*15)/100 = 144\n75P/100 \u2013 52.5P/100 = 144\n22.5P = 144 * 100\n=> P = Rs.640.Answer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOf three numbers, the third is twice the second and the second is 4 times the first. If their average is 78, the smallest of the three numbers is:\n\n### Options:\nA. 18\nB. 19\nC. 20\nD. 21\nE. 22\n\n### Answer:\nExplanation:\nLet first number be x.\nSo,2nd no. = 4x & 3rd no.=8x.\nSo,x+4x+8x=78 \u00d7 3 = 234.\n13x = 234\nx = 234/13\nHence,smallest Number x=18.\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf two numbers, a and b, are to be chosen from a set of 4 consecutive integers starting with 1 and a set of three consecutive even integers starting with 6, respectively, what is the probability that b/a will not be an integer?\n\n### Options:\nA. 1/6\nB. 1/4\nC. 1/3\nD. 1/2\nE. 2/3\n\n### Answer:\na is from the following set {1,2,3,4}\nb is from the following set {6,8,10}\nThe total number of ways of choosing 2 integers, one from each set is 4*3 = 12 ways.\nThe possibilities where b/a is not an integer is for the following outcomes:\n{b,a} = {6,4},{8,3},{10,3},{10,4} = 4 ways\nThus the probability is 4/12 = 1/3\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA and B working separately can complete a piece of work in 9 and 12 days respectively. If they work alternatively starting from A in how many days will the work be completed?\n\n### Options:\nA. 10.21 days\nB. 10.23 days\nC. 18.25 days\nD. 10.25 days\nE. 40.25 days\n\n### Answer:\nExplanation:\nA takes 9 days to complete a piece of work. B takes 12 days to complete a piece of work.\n=> In one day A came complete 1/9th of the task(x/9)\n=> In one day B can complete 1/12th of the job.(x/12)\nFirst day x/9th work will be done next day x/12th and so on:\nTogether A and B can do x/9 + x/12 work.\n=>(x/9) + (x/12) = 7/36th work done\nIn 10 days 35/36th of the work will be done.\nOn 11th day it will be A\u2019s chance. It takes A 1 day to complete 1/9th work.\nSo, 1/36th work will be done in 1/4 days.\n=>10.25 days\nANSWER: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nLook at this series: 439,404, 369, 334, 299, 264 ... What number should come next?\n\n### Options:\nA. 206\nB. 208\nC. 206\nD. 229\nE. 204\n\n### Answer:\n229\nThis is a simple subtraction series. Each number is 35 less than the previous number.\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man can row three - quarters of a kilometer against the stream in 11\u00bcminutes. The speed(in km/hr) of the man in still water is\n\n### Options:\nA. 2\nB. 3\nC. 4\nD. 5\nE. 6\n\n### Answer:\nSolution\nRate upstream\t= (750 / 675)m/sec\n= (10 / 9) m/ sec.\nRate downstream\t= (750 / 450)\n=(5 / 3) m/sec\nRate in still water\t= 1/2(10 /9 + 5/3)\n= (25/18x18/5)km/hr\n= 5 km/hr.\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAmit Kumar invested an amount of 15,000 at compound interest rate of 10 pcpa for a period of two years. What amount will he receive at the end of two years?\n\n### Options:\nA. 18,000\nB. 18,500\nC. 17,000\nD. 17,500\nE. None of these\n\n### Answer:\nAmount = 15000 (1 + 10\u2044100)2\n= 15000 \u00d7 11\u204410 \u00d7 11\u204410 = 18150\nAnswer E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOut of 15 students in a class, 7 are from Maharashtra, 5 are from Karnataka, and 3 are from Goa. Four students are to be selected at random. What are the chances that at least one is from Karnataka?\n\n### Options:\nA. 12/13\nB. 11/13\nC. 10/15\nD. 1/15\nE. 4/14\n\n### Answer:\nTotal possible ways of selecting 4students out of 15 = 15C4 = (15*14*13*12)/(4*3*2*1) =1365\nThe number of ways of selecting a 4 students in which no student belongs to Karnataka = 10C4\nNumber of ways of selecting atleast one student from Karnataka = 15C4-10C4 = 1155\nProbability = 1155/1365 = 11/13\nAnswer is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn the last set of tests, a student scored marks in each of 5 subjects in the ratio 4:5:6:7:8 and got an overall average score of 54%. If a mark of 50% in a subject is a pass and the maximum marks of each subject is the same, how many subjects did the student pass?\n\n### Options:\nA. 1\nB. 2\nC. 3\nD. 4\nE. 5\n\n### Answer:\nThe tests scores are 4k, 5k, 6k, 7k, and 8k.\nThe sum of the test scores is 30k.\nThe average test score is 30k/5 = 54. Then k = 9.\nThe test scores are 36, 45, 54, 63, and 72.\nThe student passed 3 subjects.\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nLarry and Daniel are partners in a business, they invested Rs. 50,000 and Rs. 39,000 respectively.If the business yielded a total profit of Rs. 21,000, what is Daniel's share?\n\n### Options:\nA. 9402.25\nB. 9272.25\nC. 9982.25\nD. 9211.25\nE. 9202.25\n\n### Answer:\nExplanation:\nRatio of their shares = 50,000 : 39,000 = 50 : 39.\nDaniel's share = Rs. (21000 * 39/89) = Rs. 9202.25.\nAnswer: E) 9202.25\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRs.385 were divided among X,Y,Z in such a way that X had Rs.20 more than Y and Z had Rs 15 more than X . How much was Y\u2019s share?\n\n### Options:\nA. Rs.110\nB. Rs.145\nC. Rs.150\nD. Rs.176\nE. Rs.181\n\n### Answer:\nLet Y gets Rs x. Then We can say X gets Rs (x + 20 ) and Y gets Rs ( x + 35) .\nx + 20 + x + x + 35 = 385\n3x = 330\nx = 110 .\nR\u2019s share = Rs ( 110 + 35 ) = Rs.145\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a, b, and c are consecutive integers such that a < b < c and a is an even prime number, which of the following is true?\nI. a \u00d7 b \u00d7 c < a^3\nII. 5b > 5c\nIII.a + b + c > a^3\n\n### Options:\nA. I only\nB. II only\nC. III only\nD. II and III\nE. I, II, and III\n\n### Answer:\nOnly 'A' is possible solution. If a is even prime number i.e 2, b is 3 and c is 4\nPutting the values in the answers only 'A' seems valid.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nKurt, a French painter, has 9 jars of paint: 4 jars of yellow paint, 2 jars of red paint, and 3 jars of brown paint. Kurt pours the contents of 3 jars of paint into a new container to make a new color, which he will name according to the following conditions:\nThe paint will be namedBrun Yif it contains 2 jars of brown paint and no yellow.\nThe paint will be namedBrun Xif the paint contains 3 jars of brown paint.\nThe paint will be namedJaune Xif the paint contains at least 2 jars of yellow.\nThe paint will be namedJaune Yif the paint contains exactly 1 jar of yellow.\nWhat is the probability Q that the new color will be one of theJaunecolors?\n\n### Options:\nA. 5/42\nB. 37/42\nC. 1/21\nD. 4/9\nE. 5/9\n\n### Answer:\nI get B.\nJaune Y = (4 choose 1)*(5 choose 2) = 4*10 = 40\nJaune X = (4 choose 2)*(5 choose 1) + (4 choose 3) = 6*5 + 4 = 34\nTotal combinations = 9 choose 3 = 84\nProbability of Jaune Q= (40 + 34)/84 = 37/42\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA can do a piece of work in 6days of 9 hours each and B alone can do it in 12 days of 9 hours each.how long will they take it to do working together\n4 1/2 hours a day?\n\n### Options:\nA. 8 days\nB. 9 days\nC. 7 days\nD. 6 days\nE. 10 days\n\n### Answer:\nA's work per hour=1/54\nB's work per hour=1/108\nA & B's work per hour together=(1/54)+(1/108)=3/108=1/36\nso A & B together complete the work in 36 hours...\nif they work 4 1/2=9/2 hours a day,\nit will take (36)/(9/2) days=8 days...\nANSWER: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich of the following is the Highest Common Factor of 49, 63 and 77?\n\n### Options:\nA. 8\nB. 10\nC. 7\nD. 14\nE. 12\n\n### Answer:\nTHE HIGHEST COMMON FACTOR IS 7\rAns is :C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a dairy farm, 20 cows eat 20 bags of husk in 20 days. In how many days one cow will eat one bag of husk?\n\n### Options:\nA. 1\nB. 40\nC. 20\nD. 26\nE. 30\n\n### Answer:\nExplanation :\nOne bag of husk = 20 cows per day\n\u21d2 20 \u00d7 1 \u00d7 20 = 1 \u00d7 20 \u00d7 x\nFor one cow = 20 days\nAnswer : C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a survey of 340 employees, 104 of them are uninsured, 54 work part time, and 12.5 percent of employees who are uninsured work part time. If a person is to be randomly selected from those surveyed, what is the probability that the person will neither work part time nor be uninsured?\n\n### Options:\nA. 7/12\nB. 8/41\nC. 39/68\nD. 1/8\nE. 41/91\n\n### Answer:\n---------UI----------------NUI-------Total\nPT----(12.5/100)*104 = 13----------- --54\nNPT---104-13-------------- x--------286\nTotal--104----------------------------340\nwe have to find not part time and not uninsured . in other words not part time and insured = x/340 = (286-104+13)/340\n= 39/68\nAnswer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n1. X and Y invest Rs.21000 and Rs.17500 respectively in a business. At the end of the year, they make a profit of Rs.26400. What is the share of X in the profit?\n\n### Options:\nA. Rs.14400\nB. Rs.26400\nC. Rs.12000\nD. Rs.12500\nE. Rs.13000\n\n### Answer:\nExplanation:\nRatio of the investment\n=21000:17500=210:175=21000:17500=210:175 =42:35=6:5=42:35=6:5\nShare of X in the profit\n=26400\u00c3\u2014611=2400\u00c3\u20146=14400\nANSWER IS A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man started his journey from Lucknow to Kolkata, which is 200 km, at the speed of 40 kmph then he went to Banglore which is 300 km, at the speed of 20 kmph. Further he went to Ahmedabad which is 500 km, at the speed of 10 kmph. The average speed of the man is :\n\n### Options:\nA. 14(2/7) kmph\nB. 14(5/7) Kmph\nC. 15.6 kmph\nD. 16.1 kmph\nE. None\n\n### Answer:\nSolution: Average speed,\n= (Total distance /Total time)\n= [(200+300+500)/{(200/40)+(300/20)+(500/10)}]\n= 1000/70\n= 14(2/7) kmph.\nAnswer: Option A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe age of the two friends were in the ration of 6:5. If the sum of their ages is 55. Then after how many years their ratio will become 8:7?\n\n### Options:\nA. 11\nB. 7\nC. 10\nD. 12\nE. 13\n\n### Answer:\nsince given ratio is 6:5 of their ages.\n6x+5x=55(given)\n11x=55\nx=5. so present ages are: 6*5=30 and 5*5=25\nafter few yrs ratio becomes 8:5.\nso,their ages will become 8x and 7x respectively, ie. 40 and 35 respectively.\nnw difference of their current ages and further ages is clear from above... ie. 10 yrs.\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe sum of a number and its reciprocal is one-eighth of 34. What is the product of the number and its square root?\n\n### Options:\nA. 8\nB. 27\nC. 32\nD. 42\nE. 52\n\n### Answer:\nLet the number be x. Then,\nx + 1/x = 34/8\n8x2 - 34x + 8 = 0\n4x2 - 17x + 4 = 0\n(4x - 1)(x - 4) = 0\nx = 4\nrequired number = 4 * \u221a4 = 4 * 2 = 8.\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man can row 9 kmph in still water. When the river is running at 3.1 kmph, it takes him 1 hour to row to a place and black. What is the total distance traveled by the man?\n\n### Options:\nA. 2.21\nB. 2.48\nC. 9.24\nD. 7.29\nE. 7.94\n\n### Answer:\nM = 9\nS = 3.1\nDS = 12.1\nUS = 5.9\nx/12.1 + x/5.9 = 1\nx = 3.97\nD = 3.97 * 2 = 7.94\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA, B, C, D, E are the five electronic shops in the Naza market, which have 20, 30, 60, 80 and 50 T. V . sets with them respectively, then the average number of T. V. sets in each shop is\n\n### Options:\nA. 24\nB. 48\nC. 50\nD. 60\nE. None\n\n### Answer:\nAnswer\nAverage number of T. V. sets\n= ( 20 + 30 + 60 + 80 + 50 ) / 5\n= 48\nCorrect Option: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train 260 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?\n\n### Options:\nA. 40\nB. 32\nC. 26\nD. 21\nE. 14\n\n### Answer:\nSpeed = 45 * 5/18 = 25/2 m/sec\nTotal distance covered = 260 + 140 = 400 m\nRequired time = 400 * 2/25 = 32 sec\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the sixth digit to the right of the decimal point, in the decimal expansion of (3/5)^6?\n\n### Options:\nA. 2\nB. 4\nC. 6\nD. 8\nE. 0\n\n### Answer:\nStep 1 Convert fraction to decimal with two decimal places 3/5 = 0.60 then convert to scientific number = 6*10^-1\nStep 2 Multiply 6^6 by 10^-6\nStep 3 6 has the sequence 6, 36, 216\nAnswer is C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMichelle deposited a certain sum of money in a savings account on July 1st, 2007. She earns an 14% interest compounded semiannually. The sum of money in the account on December 31st, 2009 is approximately what percent of the initial deposit?\n\n### Options:\nA. 117%\nB. 120%\nC. 121%\nD. 138%\nE. 145%\n\n### Answer:\nSince Michelle earns 14% interest compounded semiannually, then she earns 7% interest every 6 months.\nNow, the simple interest earned in 5 periods (30 months = 5*6 months) would be 7%*5=35%. But, since the interest iscompoundedevery 6 months, then there would be interest earned on interest (very small amount) thus the actual interest earned would be a little bit more than 35%, only answer choice D fits.\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo people measure each other's height, the height of the taller person is H and the height of the other person is L. If the difference in their heights is equal to the average height, what is the Value of H/L\n\n### Options:\nA. 1/3.\nB. 3.\nC. 2.\nD. 1/2.\nE. 6.\n\n### Answer:\nDifference = Average\nH - L = (H + L)/2,\nSolving for H/L gives 3. A quick check, H be 18 and L be 6, 18 - 6 = (18 + 6)/2\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA,B,C invested some money such that capital of C is half of B and capital of B is half of A. If they get a profit of Rs.7000 then profit share of B is\n\n### Options:\nA. Rs.3000\nB. Rs.2000\nC. Rs.2500\nD. Rs.3500\nE. Rs.3600\n\n### Answer:\nRatio of their capital ie c:b:a=1:2:4\nHence b's share of profit =2/(7) *7000=2000\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nExpress a speed of 90 kmph in meters per second?\n\n### Options:\nA. 25mps\nB. 20 mps\nC. 35 mps\nD. 19 mps\nE. 21 mps\n\n### Answer:\n90 * 5/18 = 25 mps\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJohn weighs twice as much as Susan. Susan's weight is 60% of Sam's weight. Mark weighs 50% of Lynn's weight. Lynn weighs 180% of John's weight. Which of these 5 people weighs the least?\n\n### Options:\nA. John\nB. Susan\nC. Sam\nD. Mark\nE. Lynn\n\n### Answer:\nJohn weighs twice as much as Susan --> J=2S --> John cannot weigh the least;\nSusan's weight is 60% of Sam's weight --> S=0.6*Sam --> Sam cannot weigh the least;\nMark weighs 50% of Lynn's weight --> M=0.5*L --> Lynn cannot weigh the least;\nLynn weighs 180% of John's weight --> L=1.8*J --> John cannot weigh the least (we already know that);\nAs you can see the answer is either Susan (S) or Mark (M). To compare their weights we should express their weights in regards of the same person: M=0.5*L=0.5*(1.8*J)=0.9*J and from J=2S, S=0.5*J --> Susan weights the least: Susan's weight is 50% of that of John and Mark's weight is more than 50%of that of John.\nAnswer: B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\na survey of n people in the town of badaville found that 50% of them prefer brand A.another survey of 100 people in the town of Chotaville found that 60% prefer brand A.In total 55% of all the people surveyed prefer brand A.What is the total number of people surveyed?\n\n### Options:\nA. 100\nB. 200\nC. 300\nD. 400\nE. 500\n\n### Answer:\n.5*n+.6*100=.55*(n+100)\nn=100\ntotal people surveyed=n+100\n=100+100\n=200\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the average of the first 20 natural numbers?\n\n### Options:\nA. 18.5\nB. 10.0\nC. 10.4\nD. 10.5\nE. 10.2\n\n### Answer:\nAverage of the first 'n' natural numbers = (n + 1)/2\nWe get (20 + 1)/2 = 10.5.Answer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA jar full of whiskey contains 40% alcohol. A part of this whisky is replaced by another containing 19% alcohol and now the percentage of alcohol was found to be 26%. The quantity of whisky replaced is\n\n### Options:\nA. 1/3\nB. 2/3\nC. 2/5\nD. 1/4\nE. 1/2\n\n### Answer:\n1 st jar (alchohol) = 40%\n2nd jar = 19%\nafter mix = 26%\nmean = 7:14=1:2=>2/1+2=2/3\nANSWER B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA manufacturer of a certain type of screw rejects any screw whose length is less than 2.5 \u2014 0.03 centimeters or greater than 2.53 centimeters. If k represents the length of a screw, in centimeters, which of the following inequalities specifies all the lengths of screws that are acceptable?\n\n### Options:\nA. |k + 0.03| > 2.5\nB. |k \u2014 0.03| <= 2.5\nC. |k \u2014 2.5| > 0.03\nD. |2k \u2014 5| <= 0.06\nE. |k \u2014 2.5| >= 0.09\n\n### Answer:\nSo, let's go through this step by step:\nrejects any screw whose length is less than 2.5 \u2014 0.03 centimeters or greater than 2.5 + 0.03 centimeters.\nIn other words, any screw that is less than: 2.50 - 0.03 =2.47or greater than 2.53 will be rejected.\nIf k represents the length of a screw\nIn other words,Kis an acceptable screw that must fall within the acceptable range of 2.47 to 2.53, So:\n2.47 \u2264 K \u2264 2.53\nYou can rule out answers with < or > as opposed to \u2264 or \u2265 because the length cannot be LESS than 2.47 or GREATER than 2.53. In other words, 2.47 and 2.53 are acceptable lengths.\nLet's look at (D): |2k \u2014 5| <= 0.06 or dividing by 2\n|k \u2014 2.5| <= 0.03\nFor the positive case: k - 2.5 \u2264 0.03 ===>k \u2264 2.53\nFor the negative case: -(k - 2.5) \u2264 0.03 ===> -k +2.5 \u2264 0.03 ===> - k \u2264 -2.47 ===>k \u2265 2.47\n2.47 \u2264\u00a0k \u2264 2.53\n(D)\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nDivide $600 among A,B in the ratio 1:2. How many $ that A get?\n\n### Options:\nA. $50\nB. $500\nC. $150\nD. $250\nE. $600\n\n### Answer:\nSum of ratio terms = 1+2 = 3\nA = 600*1/3 = $200\nAnswer is E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA recycling facility is staffed by 7 floor workers and one manager. All of the floor workers are paid equal wages, but the manager is paid n times as much as a floor worker. If the manager\u2019s wages account for 1/7 of all wages paid at the facility, what is the value of n?\n\n### Options:\nA. 3/7\nB. 4/5\nC. 7/5\nD. 7/6\nE. 7/4\n\n### Answer:\nSay each floor worker is paid $x, then the manager is paid $xn.\nTotal salary would be 7x+xn and we are told that it equals to 7xn:\n7x+xn=7xn --> reduce by x: 7+n=7n -->6n= 7\nn = 7/6\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many such pairs of letters are there in the word EXPRESSION which have as many letters between them in the word as in the alphabet ?\n\n### Options:\nA. 4\nB. 5\nC. 3\nD. 2\nE. 1\n\n### Answer:\n(E,N)\n(P,S)\n(O.N)\n(X,S)\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAmy\u2019s retirement portfolio contains only stocks and bonds. At the beginning of 2016, her portfolio had an allocation of 60% stocks and 40% bonds. Over the course of 2016, the total value of her portfolio increased by 8%, with the value of her stock holdings increasing by 10%. By what percent did the value of her bond holdings increase?\n\n### Options:\nA. 4%\nB. 5%\nC. 6%\nD. 7%\nE. 7.5%\n\n### Answer:\nThus total value of Bond at the end of 2016 is 420 ( ie, 1080 - 660 )\nSo, Per unit value of Bond at the end of 2016 is 420/40=10.50\nHence, percentage increase is 0.50/10\u2217100=5%, answer will be (B)\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?\n\n### Options:\nA. 120 metres\nB. 180 metres\nC. 324 metres\nD. 150 metres\nE. 175 metres\n\n### Answer:\nExplanation:\nSpeed= 60 x\t5/18\tm/sec\t= 50/3\tm/sec.\nLength of the train = (Speed x Time).\nLength of the train = 50/3\tx 9\tm = 150 m.\nANSWER IS D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIntegers 3n+2 and 8n+6 are divisible by an integer p. If p is not equal to 1, then p equals to?\n\n### Options:\nA. 2\nB. 3\nC. 5\nD. 7\nE. 11\n\n### Answer:\nIf p divides 3n+2, then p divides 24n+16.\nIf p divides 8n+6, then p divides 24n+18.\nThen p must equal 2.\nThe answer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nCompound interest earned on a sum for the second and the third years are Rs.12000 and Rs.13800 respectively. Find the rate of interest?\n\n### Options:\nA. 15% p.a.\nB. 22% p.a.\nC. 20% p.a.\nD. 24% p.a.\nE. None of these.\n\n### Answer:\nRs.13800 - 12000 = Rs.1800 is the interest on Rs.12000 for one year.\nRate of interest = (1800/12000) * 100 = 15% p.a\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nBy selling an article at Rs.1000, a shopkeeper makes a profit of 25%. At what price should he sell the article so as to make a loss of 25%?\n\n### Options:\nA. s.600\nB. s.480\nC. s.500\nD. s.450\nE. s.550\n\n### Answer:\nSP = 1000\nProfit = 25%\nCP = (SP)*[100/(100+P)]\n= 1000 * [100/125]\n= 800\nLoss = 25% = 25% of 800 = Rs.200\nSP = CP - Loss = 800 - 200 = Rs.600\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhen a number is divided by 6 &then multiply by 12 the answer is 9 what is the no.?\n\n### Options:\nA. 4.5\nB. 5\nC. 5.6\nD. 7\nE. 7.2\n\n### Answer:\nif $x$ is the number, x/6 * 12 = 9\n=> 2x = 9\n=> x = 4.5\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nExpress of the following as a fraction: 4%\n\n### Options:\nA. 2/25\nB. 1/25\nC. 4/25\nD. 7/25\nE. None of them\n\n### Answer:\n4% =4/100 =1/25.\nAnswer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe smallest 3 digit prime number is\n\n### Options:\nA. A)103\nB. B)101\nC. C)109\nD. D)113\nE. E)None\n\n### Answer:\nThe smallest 3-digit number is 100, which is divisible by 2.\n100 is not a prime number.\n101 < 11 and 101 is not divisible by any of the prime numbers 2, 3, 5, 7, 11.\n101 is a prime number.\nHence 101 is the smallest 3-digit prime number.\nB)\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA tap can fill a tank in 4 hours. After half the tank is filled, two more similar taps are opened. What is the total time taken to fill the tank completely?\n\n### Options:\nA. 1 hr 20 min\nB. 4 hr\nC. 3 hr\nD. 2 hr 40 min\nE. 2 hr 50 min\n\n### Answer:\nExplanation:\n1 tap can fill the tank in 4 hours.\nTherefore\n1 tap can fill half tank in 2 hours.\n3 taps can fill the tank in 4/3 hour.\nTherefore\n3 taps can fill half tank in 4/6 hour =40 minutes.\nTotal time taken=2 hour 40 minutes\nAnswer: Option D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are 5 boxes of different weights. They are weighed in pairs taken 2 at a time and the weights obtained are 110, 112, 113, 114, 115, 116, 117, 118, 120 and 121. What is the sum of the weights of the 5 boxes ?\n\n### Options:\nA. 250\nB. 289\nC. 290\nD. 295\nE. 305\n\n### Answer:\nLet the 5 boxes be a, b, c, d and e. The ten weights correspond to all the possible combinations of 2 weights out of 5.\nOn adding all the given weights, each boxes weight gets added 4 times:\na+b, a+c, a+d, a+e.\nSimilarly for b:\nb+c, b+d, b+e and a+b (already included above)\nSimilarly for c, d and e.\nTherefore, 110+112+113+114 .....+120+121 = 4* (a+b+c+d+e)\nor, 4* (a+b+c+d+e) = 1156\nor, (a+b+c+d+e) = 1156/4 = 289\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 5^r is a factor of 30!, which of the following is the maximum possible value of r?\n\n### Options:\nA. 4\nB. 5\nC. 6\nD. 7\nE. 8\n\n### Answer:\n5^r is a factor of 30! We need the maximum value of r\nOr in other words, we need the maximum power of 5 in 30!\nPowers of 5 in 30! = [30/5] + [30/25] = 7, where [x] is the integral part of x\nOther way is to calculate the number of 5's in 30!\nIn the multiplication upto 30, we will encounter: 5, 10, 15, 20,25, 30\nEach of 5, 10, 15, 20, 30 contain one power of 5\n25 contains 2 powers of 5.\nHence total powers of 5 in 30!= 5 + 2 = 7\nCorrect option: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nCarrey rented a car for Rs.20 plus Rs.0.25 per kilometer driven. Samuel rented a car for Rs.24 plus Rs.0.16 per kilometer driven. If each drove d km. and each was charged exactly the same amount for the rental, then d equals ?\n\n### Options:\nA. 44.4\nB. 44.8\nC. 1\nD. 19\nE. 44.11\n\n### Answer:\nExplanation:\n20 + 0.25 \u00d7 d = 24 + 0.16d\nSolving we get d = 44.4\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFresh grapes contain 85% water by weight and raisins obtained by drying fresh grapes contain 25% water by weight. How many kgs of fresh grapes are needed to get 20kgs of raisins?\n\n### Options:\nA. 75 kgs\nB. 64kgs\nC. 100 kgs\nD. 65 kgs\nE. 70 kgs\n\n### Answer:\nThe weight of non-water in 20 kg of dried grapes (which is 100-25=75% of whole weight) will be the same as the weight of non-water in x kg of fresh grapes (which is 100-85=15% of whole weight), so 20*0.75 = x*0.15\n--> x =100.\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAdding 30% of x to x is equivalent to multiplying x by which of the following?\n\n### Options:\nA. 12.5\nB. 1.05\nC. 1.15\nD. 1.3\nE. 1.25\n\n### Answer:\n130x/100= 1.3*x\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many different pairs of positive integers (a, b) satisfy the equation 1/a+1/b=34/57 ?\n\n### Options:\nA. 6\nB. 3\nC. 2\nD. 1\nE. 5\n\n### Answer:\nThere is no certain way to solve 2 unknown with 1 equation. The best way is to look at the question and retrospect the most efficient way. In this question, a and b are only positive integers. So that is a big relief. Now, we can start with putting a=1,2,.. and so on till the time we are confident about one of the options.\nSo, we start with\na=1, we get b as -ve. out\na=2, we get b as 6. Yes (Now (a,b) = (2,6). We can directly see that (a,b)=(6,2) will also satisfy. So we have 2 possible solutions)\na=3, we get b as 3. Yes (Now we have 3 possible solutions)\na=4, we get b as fraction. Out\na=5, we get b again as some fraction. Out\na=6 already taken.\nWe have A,B options left. C,D,E are out.\nA is 6. To have 6 as the answer, we will need one more pair like2,6and one more solution where a=b.\nWhen a=b, we have only 1 solution = 5. So, one more solution, where a=b is not possible.\nSo, answer will be E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe cost price of a radio is Rs.1500 and it was sold for Rs.1230, find the loss %?\n\n### Options:\nA. 18%\nB. 12%\nC. 22%\nD. 24%\nE. 21\n\n### Answer:\n1500 ---- 270\n100 ---- ? => 18%\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nif m>0 and a is m percent of b, then, in terms of m, b is what percent of a?\n\n### Options:\nA. a)100m\nB. b)1/10^-4m\nC. c)1/m\nD. d)10/m\nE. e)10,000/m\n\n### Answer:\nGiven (m*b)/100=a\nto find (b/a)*100\nRearranging first equation\nb/a*100 = 100*100/m\n=10000/m\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhen a number is divided by 13, the remainder is 11. When the same number is divided by 17, then remainder is 9. What is the number ?\n\n### Options:\nA. 300\nB. 349\nC. 500\nD. 550\nE. 370\n\n### Answer:\nx = 13p + 11 and x = 17q + 9\n13p + 11 = 17q + 9\n17q - 13p = 2 => q = 2+13p/17\nleast value of p for which q = 2+13p/17 is whole no is p = 26\nx = (13*26+11) = 349\nANSWER B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA woman has two blouses of different colors, three skirts of different colors, and two different pairs of shoes. She refuses to wear her pink blouse with her green skirt. How many different blouseskirt-shoe combinations could she wear?\n\n### Options:\nA. 8\nB. 10\nC. 16\nD. 17\nE. 18\n\n### Answer:\ntotal ways = 2*3*2=12..\nnow its better to find the ways in which the pink blose and green skirty are together and subtract from total to get the answer..\nthe ways in which the pink blose and green skirty are together=1*1*2=2..\ntotal ways =12-2=10..\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA number when divided by a divisor leaves a remainder of 24.\nWhen twice the original number is divided by the same divisor, the remainder is 11. What is the value of the divisor?\n\n### Options:\nA. 37\nB. 39\nC. 42\nD. 44\nE. 45\n\n### Answer:\nLet the original number be 'a'\nLet the divisor be 'd'\nLet the quotient of the division of aa by dd be 'x'\nTherefore, we can write the relation as a/d = x and the remainder is 24.\ni.e., a=dx+24 When twice the original number is divided by d, 2a is divided by d.\nWe know that a=dx+24. Therefore, 2a = 2dx + 48\nThe problem states that (2dx+48)/d leaves a remainder of 11.\n2dx2dx is perfectly divisible by d and will therefore, not leave a remainder.\nThe remainder of 11 was obtained by dividing 48 by d.\nWhen 48 is divided by 37, the remainder that one will obtain is 11.\nHence, the divisor is 37.\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo trains 300 m and 450 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is?\n\n### Options:\nA. 10.6\nB. 27\nC. 10.4\nD. 10.8\nE. 10.1\n\n### Answer:\nRelative speed = 60 + 40 = 100 km/hr.\n= 100 * 5/18 = 250/9 m/sec.\nDistance covered in crossing each other = 300 + 450 = 750 m.\nRequired time = 700 * 9/250 = 27 sec.\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 3 and 5 are prime numbers, which of the following CANNOT be the sum of 3 and 5?\n\n### Options:\nA. 9\nB. 11\nC. 13\nD. 8\nE. 19\n\n### Answer:\nans : A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA tradesman by means of his false balance defrauds to the extent of 20%? in buying goods as well as by selling the goods. What percent does he gain on his outlay?\n\n### Options:\nA. 49%\nB. 47%\nC. 44%\nD. 46%\nE. 43%\n\n### Answer:\ng% = 20 + 20 + (20*20)/100\n= 44%\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn measuring the sides of a rectangle, one side is taken 6% in excess, and the other 5% in deficit. Find the error percent in the area calculated from these measurements.\n\n### Options:\nA. 0.11%\nB. 0.7%\nC. 0.4%\nD. 0.6%\nE. 0.8%\n\n### Answer:\nLet x and y be the sides of the rectangle. Then, Correct area = xy.\nCalculated area = (53/50) x (19/20) y = (144/143)(xy)\nError In measurement = (144/143)xy- xy = (1/143)xy\nError percentage = [(1/143)xy (1/xy)100] % = (7/10) % = 0.7%.\nAnswer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat percent of 120 are 90?\n\n### Options:\nA. 33\nB. 66\nC. 75\nD. 44\nE. 31\n\n### Answer:\n(?% /100) * 120 = 90\n? = 75%\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe ratio of the length and the breadth of a rectangle is 4 : 3 and the area of the rectangle is 6912 sq cm. Find the ratio of the breadth and the area of the rectangle?\n\n### Options:\nA. 1:96\nB. 2:96\nC. 1:86\nD. 1:94\nE. 2:96\n\n### Answer:\nLet the length and the breadth of the rectangle be 4x cm and 3x respectively.\n(4x)(3x) = 6912\n12x2 = 6912\nx2 = 576 = 4 * 144 = 22 * 122 (x > 0)\n=> x = 2 * 12 = 24\nRatio of the breadth and the areas = 3x : 12x2 = 1 : 4x = 1: 96.\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAn error 4% in excess is made while measuring the side of a square. The percentage of error in the calculated area of the square is:\n\n### Options:\nA. 4.16\nB. 5.16\nC. 7.16\nD. 8.16\nE. 9.16\n\n### Answer:\nExplanation:\n100 cm is read as 104 cm.\nA1 =(100 \u00d7 100)cm2 = 10000\nand A2= (104 \u00d7 104)cm2= 10816\n(A2 - A1) = 10816-10000 = 816\n=> 816/10000*100 =8.16\nAnswer : D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo unbiased coins are tossed. What is probability of getting at most one tail ?\n\n### Options:\nA. 12\nB. 13\nC. 32\nD. 34\nE. None of these\n\n### Answer:\nExplanation:\nTotal 4 cases = [HH, TT, TH, HT]\nFavourable cases = [HH, TH, HT]\nPlease note we need atmost one tail, not atleast one tail.\nSo probability = 3/4\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe slant height of a cone is 13 cm and radius of the base is 9 cm, find the curved surface of the cone?\n\n### Options:\nA. 367\nB. 378\nC. 365\nD. 26\nE. 28\n\n### Answer:\n\u03c0 * 13 * 9\n= 367\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe perimeter of a semi circle is 144 cm then the radius is?\n\n### Options:\nA. 88\nB. 28\nC. 61\nD. 86\nE. 21\n\n### Answer:\n36/7 r = 144\n=> r = 28\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA box contains 12 mangoes out of which 4 are spoilt. If four mangoes are chosen at random, find the probability that A number is selected at random from first thirty natural numbers. What is the chance that it is a multiple of either 3 or 13?\n\n### Options:\nA. 17/30\nB. 2/5\nC. 11/30\nD. 4/15\nE. 7/15\n\n### Answer:\nThe probability that the number is a multiple of 3 is 10/30. (Since 3*10 = 30).\nSimilarly the probability that the number is a multiple of 13 is 2/30. {Since 13*2 =\n26).\nNeither 3 nor 13 has common multiple from 1 to 30. Hence these events are mutually exclusive events. Therefore chance that the selected number is a multiple of 3 or 13 is (10+2)/30 = 2/5.\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?\n\n### Options:\nA. 380\nB. 384\nC. 356\nD. 324\nE. 314\n\n### Answer:\nSpeed = (54 * 5/18) m/sec = 15 m/sec. Length of the train = (15 x 20)m = 300 m. Let the length of the platform be x meters. Then, (x + 300)/36 = 15 ==> x + 300 = 540 ==> x = 240 m.\nAnswer: Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average weight of 8 girls increases by 3 kg when a new girl comes in place of one of them weighing 70 kg. What might be the weight of the new girl?\n\n### Options:\nA. 94 kg\nB. 95 kg\nC. 96 kg\nD. 97 kg\nE. 98 kg\n\n### Answer:\nTotal weight increased = 8 x 3 kg = 24 kg.\nWeight of new person = 70 + 24 kg = 94 kg\nAnswer : A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nseven balls of different colors are to be placed in three different boxes such that any box contains at least 1 ball . What is the maximum number of different ways in which this can be done?\n\n### Options:\nA. 60\nB. 90\nC. 240\nD. 150\nE. 180\n\n### Answer:\nSince the balls are all of different colors, let's permute them and then decide how many balls we put in each box.\nFor example, arrange in a row the balls, then decide: two balls go into the first box, next two in the second box, and the last ball goes to the third box.\nSince in each box there must be at least one ball, we have the possibilities of (2,2,1), (2,1,2), (1,2,2) OR (3,1,1), (1,3,1), (1,1,3) balls in the three boxes.\nFor the 2,2,1 type arrangements, we have [5!/(2!2!1!)]*3 = 90 possibilities. Inside a box, it doesn't matter the order of the balls.\nFor the 3,1,1 type arrangements, we have [5!/(3!1!1!)]*3 = 60 possibilities.\nTotal of 150 + 90 =240 possibilities.\nAnswer C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe time it took car P to travel 900 miles was 2 hours less than the time it took car R to travel the same distance. If car P\u2019s average speed was 10 miles per hour greater than that of car R, what was car R\u2019s average speed, in miles per hour?\n\n### Options:\nA. 40\nB. 54\nC. 62\nD. 70\nE. 80\n\n### Answer:\nLet speed of car R be=x\nThen speed of car P= x+10\nA/Q,\n(900/x)-(900/(x+10))=2\nSolving for x=62 miles\\hr.\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich of the following statements must be true?\nI)The product of first 100 prime numbers is even\nII)The sum of first 100 prime numbers is odd.\nIII)The sum of first five non-negative even numbers is divisible by both 4 and 5\n\n### Options:\nA. I only\nB. II only\nC. I and II only\nD. I and III only\nE. I, II and III\n\n### Answer:\nFirst look at some Odd & Even Rules:-\nMultiplication\nE x E = E\nO x O = O\nE x O = E = O x O\nAddition\nE + E = E\nE + O = O = O + E\nO + O = E\nNow coming to the statements:-\nI. The product of first 100 prime numbers is even\nFirst 100 prime nos. includes 2 which is the ONLY even no. Hence, any no. multiplied by even no will give an Even No.\nII. The sum of first 100 prime numbers is odd\nWe can figure this out through Cyclicity Rule. Ignore the First TWO Prime Nos. and let us start with 5, which is Odd.\nO + O = E (Sum of two primes)\nE + O = O (Even is carried over and added to 3rd prime)\nO + O = E (Carry over and 4th prime)\nE + O = O (5th prime)\nO + O = E (6th prime)\nThrough Cyclicity, we can find out that the sum of any Even No of ODDS will always be EVEN. Since 98th no is Even, the answer will also be EVEN. Now, include the first two prime nos. i.e. 2 & 3.\nE + 2(E) + 3(O) = O\nHence, the statement is TRUE.\nIII. The sum of first five non-negative even numbers is divisible by both 4 and 5\nFirst five non negative even nos. = 0, 2, 4, 6 and 8\nSum = 20. Divisible by both 4 AND 5\nAnswer : E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe ratio of the earnings of P and Q is 9:10. If the earnings of P increases by one-fourth and the earnings of Q decreases by one-fourth, then find the new ratio of their earnings?\n\n### Options:\nA. 4/7\nB. 3/2\nC. 3/5\nD. 9/4\nE. 3/1\n\n### Answer:\nLet the earnings of P and Q be 9x and 10x respectively.\nNew ratio = [9x + 1/4 (9x)]/[10x - 1/4 (10x)]\n=> 9*(1 + 1/4)/10*(1 - 1/4)\n=> 9/10 * (5/4)/(3/4) = 3/2\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are an average of 117 jellybeans in each of 34 bags of various sizes. After adding another bag, the average number of jellybeans per bag increases by 7. How many jellybeans are in the new bag?\n\n### Options:\nA. 124\nB. 97\nC. 117\nD. 229\nE. 362\n\n### Answer:\nTotal jellybeans in 34 bags = 34*117 = 3978\nTotal jellybeans in 35 bags = 35*124 = 4340\nNumber of jellybeans in new bag = 3978-4340 = 362 jellybeans\nAnswer is E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA basket has 5 apples and 4 oranges. Three fruits are picked at random. The probability that at least 2 apples are picked is ?\n\n### Options:\nA. 25/42\nB. 25/49\nC. 25/47\nD. 25/44\nE. 25/41\n\n### Answer:\nTotal fruits = 9\nSince there must be at least two apples,\n= 25/42.\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWorking alone at its constant rate, pump P pumped out \u00bc of the water in a tank in 2 hours. Then pumps Q and R started working and the three pumps, working simultaneously at their respective constant rates, pumped out the rest of the water in 3 hours. If pump Q, working alone at its constant rate, would have taken 18 hours to pump out the rest of the water, how many hours would it have taken pump R, working alone at its constant rate, to pump out all of the water that was pumped out of the tank?\n\n### Options:\nA. 6\nB. 12\nC. 15\nD. 18\nE. 24\n\n### Answer:\nRate of pump P = 1/8\n3 hours are required to pump out the remaining (3/4)ths of tank --> 1 hr to pump out 1/4\nRate of P + Rate of Q + Rate of R = 1/4\nRate of Q + Rate of R = 1/4 - 1/8 = 1/8\nQ takes 18 hours to pump out the remaining (3/4)ths of tank --> 6 hrs per (1/4)ths --> 24 hrs to pump out fully.\nRate of Q = 1/24\n1/24 + Rate of R = 1/8\nRate of R = 1/8 - 1/24 = 1/12\nTime required to pump out all the water by R = 12 hrs\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTo celebrate a colleague's retirement, the T coworkers in an office agreed to share equally the cost of a catered lunch. If the lunch costs a total of R dollars and S of the coworkers fail to pay their share, which of the following represents the additional amount, in dollars, that each of the remaining coworkers would have to contribute so that the cost of the lunch is completely paid?\n\n### Options:\nA. R/T\nB. R/(T-S)\nC. SR/(T-S)\nD. SR/T(T-S)\nE. R(T-S)/T\n\n### Answer:\nSince no absolute values are given in the question we can replace the given parameters with assumed numbers,\nLet Total colleagues be 100 (T)\nLet total contribution be 500 (R) (point to note is that its total cost not per person)\nThose who dont pay are S (30)\nPer person cost = R/T = 800/100 = 8\nSo cost for those who failed to pay = (R/T) * S = SR/T = 30*8=240\nThe equation for people who would bear the total cost after S people fail = (T-S)=70\nThere fore the solution is (SR/T)/ (T-S) = SR/T(T-S) = 240/70\nAnswer D\nHope this helps !!!\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA lady gives a dinner party to 5 guests to be selected from nine friends. The number of ways of forming the party of 5, given that two of the friends will not attend the party together is\n\n### Options:\nA. 56\nB. 126\nC. 91\nD. 94\nE. None of these\n\n### Answer:\nNumber of ways of selecting 5 guests from nine friends = 9C5\nOut of these, 7C3 ways are those in which two of the friends occur together [3 more persons to be selected out of remaining 7]\n\u2234 Number of ways, in which two of the friends will not attend the party together = 9C5 \u2013 7C3 = 91.\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich of the following describes all values of x for which 1\u2013x^2 >0?\n\n### Options:\nA. x >= 1\nB. x <= \u20131\nC. 0 <= x <= 1\nD. x <= \u20131 or x >= 1\nE. \u20131 < x < 1\n\n### Answer:\nWhich of the following describes all values of x for which 1\u2013x^2 >= 0?\n(A) x >= 1\nPlugged in 2. 1\u2013(2)^2 >= 0 -3>=0? NO. Wrong\n(B) x <= \u20131\nPlugged in -2. 1\u2013(-2)^2 >= 0 -3>=0? NO. Wrong\n(C) 0 <= x <= 1\nPlugged in 0, 1, and 1/2. All of them work. But E is better because it describes all the values of x\n(D) x <= \u20131 or x >= 1\nA and B answer this. Wrong.\n(E) \u20131 < x < 1\nX is a positive or negative fraction.\nx = -1/2 x = 1/2 x = 0\nPlug all of them. They work.\nAnswer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is 2 2/3 - 1 1/4 divided by 1/2 - 1/5 ?\n\n### Options:\nA. 17/36\nB. 36/17\nC. 17/6\nD. 17/4\nE. 85/18\n\n### Answer:\n2 2/3 - 1 1/4 = 8/3 - 5/4 = (32 - 15 )/12 = 17/12\n1/2 - 1/5 = (5-2)/10 = 3/10\nSo 17/12/3/10 = 17/12 *10/ 3 = 85/18\nAnswer - E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n5/9 of the part of the population in a villagae are males.if 30 % of the males are married.the percentage of unmarried females in the total population is..\n\n### Options:\nA. 250/9%\nB. 150/9%\nC. 350/9%\nD. 450/9%\nE. 550/9%\n\n### Answer:\nLet total population = p\nno. of males =5p/9\nno. of females =(p-5p/9)=4p/9\nmarried males = 30% of 5p/9=30*5p/100*9 =p/6\nmarried females = p/6\nunmarried females =(4p/9-p/6)=5p/18\n%age of unmarried females in the total population = {(5p/18)/p}*100= 250/9%\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man walks at a speed of 5 km/hr and runs at a speed of 10 km/hr. How much time will the man require to cover a distance of 10 km, if he completes half of the distance, i.e., (5 1/4) km on foot and the other half by running?\n\n### Options:\nA. 2.5\nB. 3.5\nC. 4\nD. 2\nE. 1.5\n\n### Answer:\nRequired time = (5)/5 + (5)/10 = 1.5 hours.\nAnswer:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man can row upstream at 37 kmph and downstream at 53 kmph, and then find the speed of the man in still water?\n\n### Options:\nA. 29\nB. 92\nC. 30\nD. 32\nE. 45\n\n### Answer:\nUS = 37\nDS = 53\nM = (53 + 37)/2 = 45\nAnswer:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 30% of a number is equal to one-fourth of another number, what is the ratio of first number to the second number?\n\n### Options:\nA. 4:7\nB. 6:5\nC. 1:2\nD. 2:3\nE. 5:6\n\n### Answer:\nLet 30% of A = 1/4 B. Then,\n30A/100 = 1B/4 => 3A/10 = 1B/4\nA/B = (1/4 * 10/3) = 5/6\nA:B = 5:6.\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA, B and C started a business with a total investment of Rs. 90000. A invests Rs. 6000 more than B and B invests Rs. 3000 less than C. If the total profit at the end of a year is Rs. 8640, Find B's share.\n\n### Options:\nA. Rs. 2592\nB. Rs. 2520\nC. Rs. 2880\nD. Rs. 3360\nE. None of these\n\n### Answer:\nExplanation:\nLet C's investment = Rs. x\nB's investment = Rs. (x - 3000)\nA's investment = Rs. (x - 3000 + 6000) = Rs. (x + 3000)\nNow, (A + B + C)'s investment = Rs. 90000\n=> x + (x - 3000) + (x + 3000) = 90000\n=> 3x = 90000\n=> x = 30000\nHence, A's investment = Rs. 33000\nB's investment = Rs. 27000\nC's investment = Rs. 30000\nRatio of the capitals of A, B and C\n= 33000 : 27000 : 30000\n= 11 : 9 : 10\nA's share = Rs. [(9/30) \u00c3\u2014 8640] = Rs. 2592\nAnswer: Option A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a group of 6 boys and 4 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be there\n\n### Options:\nA. 109\nB. 128\nC. 138\nD. 209\nE. 176\n\n### Answer:\nExplanation:\nIn a group of 6 boys and 4 girls, four children are to be selected such that\nat least one boy should be there.\nSo we can have\n(four boys) or (three boys and one girl) or (two boys and two girls) or (one boy and three gils)\nThis combination question can be solved as\n(6C4)+(6C3\u22174C1)++(6C2\u22174C2)+(6C1\u22174C3)\n=[6\u00d75/2\u00d71]+[(6\u00d75\u00d74/3\u00d72\u00d71)\u00d74]+[(6\u00d75/2\u00d71)(4\u00d73/2\u00d71)]+[6\u00d74]\n=15+80+90+24=209\nOption D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is?\n\n### Options:\nA. 3/7\nB. 3/2\nC. 3/1\nD. 3/9\nE. 3/4\n\n### Answer:\nLet the speeds of the two trains be x m/sec and y m/sec respectively. Then, length of the first train = 27 x meters, and length of the second train = 17 y meters. (27 x + 17 y) / (x + y)\n= 23 ==> 27 x + 17 y = 23 x + 23 y\n==> 4 x = 6 y\n==> x/y\n= 3/2.\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf x is an integer, which of the following is a possible value of H=(x^2 +2x \u2013 7)/9?\n\n### Options:\nA. -2.4\nB. 0.268\nC. 1.166 repeating\nD. 4.555 repeating\nE. 8.125\n\n### Answer:\nx is an integer, which of the following is a possible value of H=(x^2 +2x \u2013 7)/9?\nUsed process of elimination\nA. -2.4\nwhen this is multiplied by 9, x is not an integer\nB. 0.268\nwhen this is multiplied by 9, x is not an integer\nC. 1.166 repeating\nwhen this is multiplied by 9, x is not an integer\nD. 4.555 repeating\nE. 8.125\nwhen this is multiplied by 9, x is not an integer\nAnswer choice D seems to fit\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nVishal invested 10% more than Trishul. Trishul invested 10% less than Raghu. If the total sum of their investments is Rs. 6069, how much amount did Raghu invest ?\n\n### Options:\nA. 1287\nB. 2887\nC. 2100\nD. 1129\nE. 1192\n\n### Answer:\nLet money invested by Raghu = Rs. x\nMoney invested by Trishul = 9/10 x = 0.9x\nMoney invested by Vishal = 9/10x * 110/100 = 0.99x\nAlso, x+0.9x+0.99x = 6069\n= x= 6069/2.89 = 2100\nTherefore, amount invested by Raghu is Rs. 2100.\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA bag contains 4 white, 5 red and 6 blue balls. Three balls are drawn at random from the bag. The probability that all of them are red, is:\n\n### Options:\nA. 3/21\nB. 2/91\nC. 4/91\nD. 8/81\nE. 9/72\n\n### Answer:\nLet S be the sample space.\nThen, n(S)\t= number of ways of drawing 3 balls out of 15\n= 15C3\n= (15*14*13)/(3*2*1)\n= 455\nLet E = event of getting all the 3 red balls\nn(E) = 5C3 = 5C2 =(5*4)/(2*1)\n= 10\nP(E) =n(E)/n(S)\n= 10/455\n= 2/91\nAnswer should be B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average of 20 numbers is zero. Of them, How many of them may be greater than zero, at the most?\n\n### Options:\nA. 1\nB. 20\nC. 0\nD. 19\nE. 18\n\n### Answer:\nExplanation:\nAverage of 20 numbers = 0\n=>Sum of 20 numbers/20=0\nHence at the most, there can be 19 positive numbers.\n(Such that if the sum of these 19 positive numbers is x, 20th number will be -x)\nANSWER IS D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf f(x) = 6x^4 - 4x^3 - 3x^2 + 6x , then f(-1) =\n\n### Options:\nA. -2\nB. -1\nC. 0\nD. 1\nE. 2\n\n### Answer:\nf(-1) = 6(-1)^4 - 4(-1)^3 - 3(-1)^2 + 6(-1) = 6+4-3-6 = 1\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA cricket bat is sold for $850, making a profit of $255. The profit percentage would be\n\n### Options:\nA. 24%\nB. 25%\nC. 30%\nD. 36%\nE. 43%\n\n### Answer:\n255/(850 - 255) = 255/595 = 51/119=43% .\nAnswer: E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf s and t are positive integers such that s/t = 64.12, which of the following could be the remainder when s is divided by t ?\n\n### Options:\nA. 2\nB. 4\nC. 8\nD. 20\nE. 45\n\n### Answer:\ns/t = 64.12\n= 64+12/100\n= 64+3/25\ni got 3, and in the options the multiple of is 45\nAnswer - E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average salary of all the workers in a workshop is Rs. 8000. The average salary of 10 technicians is Rs. 12000 and the average salary of the rest is Rs. 6000. The total number of workers in the workshop is :\n\n### Options:\nA. 22\nB. 21\nC. 88\nD. 30\nE. 29\n\n### Answer:\nExplanation:\nLot the total number of workers be v Then,\n8OOOv = (12000 * 10) + 6000 (v - 10) <=> 2000v = 60000 <=> v = 30\nAnswer: D) 30\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAt noon, ship A is 100km west of ship B. Ship A is sailing east at 35 km/hr and ship B is sailing north at 25km/hr. How fast is the distance between the ships changing at 4.00pm.\n\n### Options:\nA. 35.21 km/hr.\nB. 36.21 km/hr.\nC. 37.21 km/hr.\nD. 39.21 km/hr.\nE. 32.21 km/hr.\n\n### Answer:\nLet the position of ship B at noon be at the origin\n=>ship A has x-coordinate = -100km and B has x-coordinate =0km\nAt 4.00 p.m., ship A is at x = -100+4*35=40km\nand B is at x = 0 and y = 4 * 25 = 100 km\nDistance between them at 4.00 p.m. = \u221a[(100)^2 + (40)^2] = 20\u221a(29) km\nDistance between the ships,\ns^2 = x^2 + y^2\n=> 2s ds/dt = 2x dx/dt + 2y dy/dt\n=> rate of change of distance between the ships, ds/dt\n= (x dx/dt + y dy/dt) / s\n= [40 * 35 + 100 * 25] / [20\u221a(29)] km/hr\n= (1400 + 2500) / [20\u221a(29)] km/hr\n= 195/\u221a(29) km/hr\n\u2248 36.21 km/hr.\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow long does a train 110 m long running at the speed of 54 km/hr takes to cross a bridge 132 m length?\n\n### Options:\nA. 12.9 sec\nB. 12.1 sec\nC. 17.9 sec\nD. 16.13 sec\nE. 14.9 sec\n\n### Answer:\nSpeed = 54 * 5/18 = 15 m/sec\nTotal distance covered = 110 + 132 = 242 m.\nRequired time = 242/15 = 16.13 sec.\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow long will it take a sum of money invested at 5% p.a. S.I. to increase its value by 50%?\n\n### Options:\nA. 10 years.\nB. 4 years.\nC. 8 years.\nD. 12 years.\nE. 14 years.\n\n### Answer:\nSol.\nLet the sum be x. Then, S.I. = 50% of x = x/2; Rate =5%.\n\u00e2\u02c6\u00b4 Time = [100 * x/2 * 1/x*5] = 10 years.\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn Arun's opinion, his weight is greater than 65 kg but leas than 72 kg. His brother does not agree with Arun and he thinks that Arun's weight is greater than 60 kg but less than 70 kg. His mother's view is that his weight cannot be greater than 68 kg. If all of them are correct in their estimation, what is the average of diferent probable weights of Arun ?\n\n### Options:\nA. 66.9 kg\nB. 66.5 kg\nC. 66.6 kg\nD. 86.5 kg\nE. 66.7 kg\n\n### Answer:\nLet Arun's weight be X kg.\nAccording to Arun, 65 < X < 72.\nAccording to Arun's brother, 60 < X < 70.\nAccording to Arun's mother, X < 68.\nThe values satisfying all the above conditions are 66 and 67.\nRequired average = (66 + 67) / 2 = 66.5 kg\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFrom a pack of 52 cards, one card is drawn. What is the probability that the card drawn is a face card (Jack, Queen and King only)?\n\n### Options:\nA. 1/13\nB. 3/13\nC. 13/13\nD. 8/13\nE. 6/13\n\n### Answer:\nAnswer:\tSolution\nLet S be the sample space. Then,\nn(S) = 52C1\t= 52.\nLet E = event of getting 1 face card.\nn(E) = number of ways of choosing 1 face card out of 12\n=12C1 = 12\nP(E) = n(E) / n(S)\t= 12 / 52\n= 3/13.\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the distance covered by a man walking for 30min at a speed of 5km/hr?\n\n### Options:\nA. 1km\nB. 3km\nC. 4km\nD. 2.5 km\nE. 6km\n\n### Answer:\nDistance = 5*30/60 =2.5 km\nAnswer is D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a man lost 4% by selling oranges at the rate of 12 a rupee at how many a rupee must he sell them to gain 44%?\n\n### Options:\nA. 9\nB. 8\nC. 7\nD. 6\nE. 65\n\n### Answer:\n96% ---- 12\n144% ---- ?\n96/144 * 12 = 8\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nEach week, Harry is paid x dollars per hour for the first 30 hours and 1.5x dollars for each additional hour worked that week. Each week, James is paid x dollars per per hour for the first 40 hours and 2x dollars for each additional hour worked that week. Last week James worked a total of 42 hours If Harry and James were paid the same amount last week, how many hours did Harry work last week ?\n\n### Options:\nA. 35\nB. 36\nC. 37\nD. 38\nE. 39\n\n### Answer:\nJames worked for 41 hours hence he earned 40*x+2*2x=44x dollars;\nWe know that Harry also earned the same 44x dollars, out of which he earned 30x dollars for thefirst 30 hoursplus 14x additional dollars. Since for each additional hour he gets 1.5x dollars then he worked for 14x/1.5x=9 additional hours, so Harry worked for total of 30+9=39 hours.\nAnswer: E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTownville has 100 residents, and 20 of them are females. If half of Townville\u2019s male residents are smokers, and 1/2 of the female residents are smokers, which of the following represents the total number of Townville\u2019s residents who are NOT smokers?\n\n### Options:\nA. 40\nB. 45\nC. 50\nD. 55\nE. 60\n\n### Answer:\nNumber of people =100\nFemales = 20\nmen = 100-20=80\nHalf of the men are smoker80/2=40, that means the remaining men 80-40=40 are non smokers.\n1/2 females are smoker. i.e 1/2*20 = 10\n20-10=10 females are non smokers\nSo, total number of non smokers in the town are 40+10 =50\nAnswer : C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a and b are digits, and the number a,11b is evenly divisible by 88, what are the values of a and b?\n\n### Options:\nA. a = b = 9\nB. a = b = 7\nC. a = b = 5\nD. a = b = 2\nE. a = b = 1\n\n### Answer:\na,11b, divisible by 88.\nFactors of 88 = (8)(11)\nDivisible by 8: if the last 3 digits of the number are divisible by 8.\n11b/8 => 112/8 = 14 => b = 2\nDivisibe by 11: subtract the last digit from the number, over and over again, as necessary. If the remaining number is divisible by 11, the original number is divisible by 11.\na11-2 => a09 => 209/11 = 19.\nSo a = 2.\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA person is traveling at 25km/hr and reached his destiny in 6hr find the distance?\n\n### Options:\nA. A)100km\nB. B)95km\nC. C)135km\nD. D)150km\nE. E)125km\n\n### Answer:\nspeed = 25km/hr\ntime = 6hr\ndistance = 25*6 = 150km\nAnswer is D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat will come in place of the x in the following Number series? 46080, 3840, 384, 48, 8, 2, x\n\n### Options:\nA. 1\nB. 3\nC. 5\nD. 6\nE. 8\n\n### Answer:\n46080 /12 = 3840\n3840 /10 = 384\n384 /8 = 48\n48 /6 = 8\n8/4 = 2\n2 /2 = 1\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA baseball card decreased in value 60% in its first year and 10% in its second year. What was the total percent decrease of the card's value over the two years?\n\n### Options:\nA. 28%\nB. 30%\nC. 32%\nD. 36%\nE. 64%\n\n### Answer:\nLet the initial value of baseball card = 100\nAfter first year , value of baseball card = (1- 60/100)* 100 = 40\nAfter second year , value of baseball card =(1 - 10/100)* 40 = 36\ntotal percent decrease of the card's value over the two years = (100-36)/100 *100%\n=64%\nAnswer E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf two numbers are in the ratio 2:3. If 10 is added to both of the numbers then the ratio becomes 5:7 then find the largest number?\n\n### Options:\nA. 30\nB. 34\nC. 38\nD. 40\nE. 42\n\n### Answer:\n2:3\n2x + 10 : 3x + 10 = 5 : 7\n7[2x + 10] = 5[3x + 10]\n14x + 70 = 15x + 50\n15x - 14x = 70 - 50\nx = 20\nThen the first number is = 2\n2x = 40\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf (-4)^(6x) = 4^(30 + x) and x is an integer, what is the value of x ?\n\n### Options:\nA. 5\nB. 4\nC. 3\nD. 2\nE. 6\n\n### Answer:\nSince x is an integer, (-4)^(6x) is always positive.\nSo, 4^6x = 4^(30 + x)\n6x = 30 + x\n5x = 30\nx = 6\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAfter decreasing 50% in the price of an article costs Rs.620. Find the actual cost of an article?\n\n### Options:\nA. 1400\nB. 1240\nC. 1200\nD. 1100\nE. 1500\n\n### Answer:\nCP* (50/100) = 620\nCP= 12.4 * 100 => CP = 1240\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man rows his boat 80 km downstream and 38 km upstream, taking 3 hours each time. Find the speed of the stream?\n\n### Options:\nA. 6\nB. 9\nC. 7\nD. 8\nE. 2\n\n### Answer:\nSpeed downstream = d/t = 80/(3) = 27 kmph\nSpeed upstream = d/t = 38/(3) = 9 kmph\nThe speed of the stream = (27 - 9)/2 = 9 kmph\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA chocolate has 12 equal piece. Monju gave 1/4th of it to Anju, 1/3rd of it to Sujata and 1/6th of it to Fiza. The number of piece of chocolate left with Manju is?\n\n### Options:\nA. 1\nB. 2\nC. 3\nD. 4\nE. 5\n\n### Answer:\nAnswer\nThe number of pieces of chocolate left with Manju\n= 1- [(1/4) + (1/3) + (1/6)\n= 1 - (3 + 4 + 2)/12\n= 1 - 9/12 = (12 - 9) / 12\n= 3/12\nOption: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA 16% stock yielding 10% is quoted at :\n\n### Options:\nA. 83.33\nB. 110\nC. 112\nD. 120\nE. 160\n\n### Answer:\nSolution\nTo earn Rs. 10, money invested = Rs. 100.\nTo earn Rs. 16, money invested = Rs.(100/10X16) = Rs. 160.\n\u00e2\u02c6\u00b4 Market value of Rs. 100 stock =Rs. 160\nAnswer E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n180 candies are distributed to children with the same number of candies for each child. What can\u2019t be the range which includes the number of children?\n\n### Options:\nA. 1~10\nB. 10~20\nC. 35~45\nD. 65~75\nE. 85~95\n\n### Answer:\n180 = 2^2*3^3*5\nThere are factors in each range except for 65~75\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average age of 20 men in the class is 14.6 years. Five new men join and the new average becomes 15.56 years. What was the average age of five new men?\n\n### Options:\nA. 15.5\nB. 19.4\nC. 15.25\nD. 15.3\nE. 15.6\n\n### Answer:\nTotal age of 20 men = 14.6 x 20 = 292\nNow, total age of 25 men = 389.\nTotal age of five men added later = 389 - 292 = 97.\nHence, the total average of five men = 97/5 = 19.4\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nPakistan, India and Srilanka are engaged in a missile war, such that they fire one after the other, in a sequence, the sequence selected by draw of lots. The rules of war are such that the 3 countries keep on shooting at each other until they hit with the missile. This goes on until there is one last country left unhit, and then the war ends. The chances that Pakistan hits its target is 100%, Srilanka hits the target is 80% and India hits the target is 50%.\nWho has the highest chance of winning the war?\n\n### Options:\nA. India\nB. Pakistan\nC. Srilanka\nD. None of these\nE. Cannot be determined\n\n### Answer:\nSolution:\nIndia has the highest chances of winning the war (47/90)\nMissile Firing order:\nChances of Remaining Unhit - Pakistan:\nChances of Remaining Unhit - Srilanka:\nChances of Remaining Unhit - India\nPakistan - Srilanka - India\n1/2 0 1/2\nPakistan - India - Srilanka\n1/2 0 1/2\nIndia - Pakistan - Srilanka\n1/10 16/45 49/90\nSrilanka- Pakistan - India\n1/2 0 1/2\nSrilanka - India - Pakistan\n1/10 16/45 49/90\nIndia - Srilanka - Pakistan\n1/10 16/45 49/90\nTotal chances of being unhit (sum of the probabilities divided by 6):\n27/90 16/90 47/90\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOn rainy mornings, Mo drinks exactly N cups of hot chocolate (assume that N is an integer). On mornings that are not rainy, Mo drinks exactly 5 cups of tea. Last week Mo drank a total of 22 cups of tea and hot chocolate together. If during that week Mo drank 8 more tea cups than hot chocolate cups, then how many rainy days were there last week?\n\n### Options:\nA. 2\nB. 4\nC. 3\nD. 5\nE. 6\n\n### Answer:\nT= the number of cups of tea\nC= the number of cups of hot chocolate\nT+C = 22 T-C=8 -> T= 15. C=7.\nMo drinks 5 cups of tea a day then number of days that are not rainy = 15/5 = 3\nSo number of rainy days = 7-3 = 4\nB is the answer.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe speed at which a man can row a boat in still water is 15 kmph. If he rows downstream, where the speed of current is 3 kmph, what time will he take to cover 60 metres?\n\n### Options:\nA. 28\nB. 27\nC. 12\nD. 99\nE. 14\n\n### Answer:\nSpeed of the boat downstream = 15 + 3 = 18 kmph\n= 18 * 5/18 = 5 m/s\nHence time taken to cover 60 m = 60/5\n= 12 seconds.\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA fair price shopkeeper takes 10% profit on his goods. He lost 70% goods during theft. His loss percent is:\n\n### Options:\nA. 72%\nB. 42%\nC. 32%\nD. 67%\nE. 22%\n\n### Answer:\nExplanation:\nSuppose he has 100 items. Let C.P. of each item be Re. 1.\nTotal cost = Rs. 100. Number of items left after theft = 30.\nS.P. of each item = Rs. 1.10\nTotal sale = 1.10 * 30 = Rs. 33\nHence, loss % = 67/100 * 100 = 67%\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the ones digit of 73^356\n\n### Options:\nA. 1\nB. 5\nC. 6\nD. 7\nE. 9\n\n### Answer:\nThe units digit of 73^356 will be the same as the units digit of 3^356.\n3^1=3 --> the units digit is 3;\n3^2=9 --> the units digit is 9;\n3^3=27 --> the units digit is 7;\n3^4=81 --> the units digit is 1;\n3^5=243 --> the units digit is 3 AGAIN;\n...\nSo, as you can see the units digit repeats in blocks of 4: {3, 9, 7, 1}, {3, 9, 7, 1}, ... Now, since 356=356+0=(multiple of 4)+0, then the units digit of 3^356 will be thus 1.\nAnswer: A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average of 11 results is 46, if the average of first six results is 49 and that of the last six is 52. Find the sixth result?\n\n### Options:\nA. 21\nB. 56\nC. 100\nD. 25\nE. 23\n\n### Answer:\n1 to 11 = 11 * 46 = 506\n1 to 6 = 6 * 49 = 294\n6 to 11 = 6 * 52 = 312\n6th = 294 + 312 \u00e2\u20ac\u201c 506 = 100\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf x^2=x-2, then x^3=?\n\n### Options:\nA. 3x+2\nB. 3x-2\nC. 2x+1\nD. -x-2\nE. 3x+4\n\n### Answer:\nGiven X^2 = X-2\nX^3 = X*X^2 = x*(X-2)-- Substituted from above.\n= X^2 - 2X = X-2-2X = -X-2.\nHence D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat percent of a day is 5 hours?\n\n### Options:\nA. 20%\nB. 20.23%\nC. 20.5%\nD. 20.67%\nE. 20.83%\n\n### Answer:\nTotal hours in a day = 24\nRequired percent =5/24\u00d7100=20.83 %\nanswer :E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nPoint (g,h) is on the circle represented by g^2+h^2=10, and g, h are integers. How many such points are possible?\n\n### Options:\nA. 0\nB. 2\nC. 4\nD. 6\nE. 8\n\n### Answer:\ng^2+h^2=10 and g, h are integers means that 10 is the sum of two perfect squares.\n10 is the sum of only one pair of perfect squares 1 and 9.\nSo, there can be 8 such points, 4 in each quadrant:\n(1, 3);\n(1, -3);\n(-1, 3);\n(-1, -3);\n(3, 1);\n(3, -1);\n(-3, 1);\n(-3, -1).\nAnswer: E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf it would take one machine 15 minutes to fill a large production order and another machine 20 minutes to fill the same order, how many minutes would it take both machines working together, at their respective rates, to fill the order?\n\n### Options:\nA. 4 1/60\nB. 5\nC. 5 5/11\nD. 5 1/2\nE. 8 4/11\n\n### Answer:\nSince , Machine 1-M1 take 15 mins to fill the order\nThe work done by M1 in a min = 1/15\nMachine 2- M2 take 20 mins to fill the same order\nand work done by M2 in a min = 1/20\nTotal work done by M1 and M2 in a min = 1/15 + 1/20 = 7/60\nTime needed for M1 and M2 to complete the order = 60/7 = 8 4/11\nAnswer E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMurali travelled from city A to city B at a speed of 70 kmph and from city B to city C at 30 kmph. What is the average speed of Murali from A to C given that the ratio of distances between A to B and B to C is 2 : 3?\n\n### Options:\nA. kmph\nB. kmph\nC. kmph\nD. kmph\nE. kmph\n\n### Answer:\nLet the distances between city A to B and B to C be 2x km and 3x km respectively.\nTotal time taken to cover from A to C\n= (2x)/70 + (3x)/30\n= (6x + 21x)/210 = 27x/210\n= x/10 Average speed\n= (2x + 3x)/(27x/210) = 38.9 kmph.\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe unit digit in the product (784 x 618 x 917 x 463) is:\n\n### Options:\nA. 4\nB. 2\nC. 9\nD. 1\nE. 8\n\n### Answer:\nUnit digit in the given product = Unit digit in (4 x 8 x 7 x 3) = (672) = 2\nAnswer B) 2.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nCalculate the time it will take for a train that is 120 meter long to pass a bridge of 160 meter length, if the speed of the train is 40 km/hour ?\n\n### Options:\nA. 21.2 seconds\nB. 25.2 seconds\nC. 29.2 seconds\nD. 35.2 seconds\nE. 11.2 seconds\n\n### Answer:\nSpeed = 40 Km/hr = 40*(5/18) m/sec = 11.1111 m/sec\nTotal distance = 120+160 = 280 meter\nTime = Distance/speed\n= 280 * (1/11.1111) = 25.2 seconds\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the least number which when divided by 5, 6, 7 and 8 leaves a remainder 3, but when divided by 9 leaves no remainder?\n\n### Options:\nA. 1108\nB. 1683\nC. 2007\nD. 3363\nE. 3567\n\n### Answer:\nLCM of 5, 6, 7 and 8 = 840\nHence the number can be written in the form (840k + 3) which is divisible by 9.\nIf k = 1, number = (840 \u00d7 1) + 3 = 843 which is not divisible by 9.\nIf k = 2, number = (840 \u00d7 2) + 3 = 1683 which is divisible by 9.\nHence 1683 is the least number which when divided by 5, 6, 7 and 8 leaves a remainder 3, but when divided by 9 leaves no remainder.\nAnswer: Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo pipes A and B can separately fill a tank in 2 minutes and 15 minutes respectively. Both the pipes are opened together but 4 minutes after the start the pipe A is turned off. How much time will it take to fill the tank?\n\n### Options:\nA. 22\nB. 10\nC. 88\nD. 566\nE. 222\n\n### Answer:\n4/12 + x/15 = 1\nx = 10.Answer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the units' digit of the following expression (10)^5*(12)^5*(18)^5?\n\n### Options:\nA. 0\nB. 1\nC. 3\nD. 5\nE. 9\n\n### Answer:\nWe do not have to do any calculations or find units digit of remaining numbers...\nall three terms - 10,12,18 - are EVEN and since the PRODUCT contains 0, the units digit of the product will remain 0\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA 6% stock yields 8%. The market value of the stock is\n\n### Options:\nA. 33\nB. 75\nC. 44\nD. 27\nE. 91\n\n### Answer:\nFor an income of Rs. 8, investment = Rs. 100.\nFor an income of Rs. 6, investment = Rs. 100\tx 6 = Rs. 75.\n8\nMarket value of Rs. 100 stock = Rs. 75.\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn an election between the two candidates, the candidates who gets 70% of votes polled is winned by 160 vote\u2019s majority. What is the total number of votes polled?\n\n### Options:\nA. 750\nB. 400\nC. 800\nD. 850\nE. None of these\n\n### Answer:\nExplanation:\nNote: majority (40 %) = difference in votes polled to win (70 %) & defeated candidates (30 %)\n40 % = 70 % - 30 %\n40% -----> 160 (40*4 = 160)\n100% -----> 400 (100*4 = 400)\nAnswer: Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain candy manufacturer reduced the weight of Candy Bar M by 5 percent buy left the price unchanged. What was the resulting percent increase in the price per ounce of Candy Bar M?\n\n### Options:\nA. 5.5\nB. 5.4\nC. 5.3\nD. 5.2\nE. 5.1\n\n### Answer:\nassume 1oz candy cost $1 before.\nnow price remain same $1 but weight of candy reduces to 0.95 oz\nnew price of candy = 1/0.95 =1.052\nprice increase 5.2 %\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA test has a mean of 220 and a standard deviation of 10, find the corresponding z score for: a) a test score of 232?\n\n### Options:\nA. A)1.2\nB. B)2.4\nC. C)5\nD. D)5.6\nE. E)7\n\n### Answer:\nA test has a mean of 220 and a standard deviation of 10,\nfind the corresponding z score for:\na) a test score of 232,\nz(232) = (232-220)/10 = 12/10 = 1.2\nOption A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train leaves Mumabai at 9 am at a speed of 40 kmph. After one hour, another train leaves Mumbai in the same direction as that of the first train at a speed of 80 kmph. When and at what distance from Mumbai do the two trains meet?\n\n### Options:\nA. 87\nB. 279\nC. 80\nD. 278\nE. 379\n\n### Answer:\nWhen the second train leaves Mumbai the first train covers 40 * 1 = 40 km\nSo, the distance between first train and second train is 40 km at 10.00am\nTime taken by the trains to meet\n= Distance / relative speed = 40 / (80 -40) = 1 hours\nSo, the two trains meet at 11 a.m. The two trains meet 1 * 80 = 80 km away from Mumbai.\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nCalculate the different number of ways 7 boys and 2 girls can sit on a bench?\n\n### Options:\nA. 362881\nB. 362880\nC. 311880\nD. 362280\nE. 362810\n\n### Answer:\nnpn = n!\n9p9 = 9 \u00d7 8 \u00d7 7 \u00d7 6 \u00d7 5 \u00d7 4 \u00d7 3 \u00d7 2 \u00d7 1 = 362880\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the value of a piece of house decreases by 10% while the new tax rate on the house represent 110% of the original tax rate, what is the effect on the taxes?\n\n### Options:\nA. a - taxes increase by 10%\nB. b- taxes increase by 1%\nC. c- there is no change in taxes\nD. d- taxes decrease by 1%\nE. c- taxes decrease by 10%\n\n### Answer:\nCansider the value of house = 100, Original tax rate 10%, hence tax value = 100*10% = 10.\nDecreased value of house = 90, New tax rate = 110% of 10 = 11%, hence tax value = 90*11% = 9.9\n10-9.9 = decrease by 1%.\nAnswer D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nPositive Integer A gives the remainder of 12 when divided by another positive Integer B. If A/B = 47.24, what is the value of B?\n\n### Options:\nA. 96\nB. 75\nC. 48\nD. 25\nE. 50\n\n### Answer:\n.24 of B = Remainder\n.24 of B = 12\nB = (12 *100) / 24 = 50.\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a company of 16 employees, 8 employees earn $38,000, 4 employees earn $42,000, and the 4 highest-paid employees earn the same amount. If the average annual salary for the 16 employees is $44,000, what is the annual salary for each of the highest-paid employees?\n\n### Options:\nA. $54,000\nB. $55,000\nC. $56,000\nD. $57,000\nE. $58,000\n\n### Answer:\n8*38,000+4*42,000+4x=16*44,000\n4x=704,000-304,000-168,000\n4x=232,000\nx=58,000\nThe answer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe positive value of x that satisfies the equation (1 + 2x)^5 = (1 + 3x)^6 is between\nBunuel, can you please explain this one?\n\n### Options:\nA. 0 and 0.5\nB. 0.5 and 1\nC. 1 and 1.5\nD. 1.5 and 2\nE. 2 and 2.5\n\n### Answer:\nTrial and error would probably be the easiest way to solve this problem. When x is large enough positive number, then because of the exponents (5>4), LHS will be more than RHS (as you increase the positive value of x the distance between the values of LHS and RHS will increase).\nTry x=1 --> LHS=3^5=81*3=243 and RHS=4^4=64*4=256, so (1 + 2x)^5 < (1 + 3x)^4. As you can see LHS is still slightly less than than RHS. So, the value of x for which (1 + 2x)^5 = (1 + 3x)^4 is slightly more than 1.\nAnswer: E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average of four positive integers is 69. The highest integer is 93 and the least integer is 39. The difference between the remaining two integers is 28. Which of the following integers is the higher of the remaining two integers?\n\n### Options:\nA. 22\nB. 86\nC. 68\nD. 55\nE. 23\n\n### Answer:\nLet the four integers be A, B, C and D where A > B > C > D.\n(A + B + C + D)/4 = 69 => A + B + C + D = 276 ---> (1)\nA = 93, D = 39 and B - C = 28\n(1) => B + C = 276 - (A + D) = 276 - 132 = 144.\nB + B -28 = 144\nB = (144 + 28)/2 = 86\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe banker's discount on a certain sum due 2 years hence is 11/10 of the true discount.The rate percent is\n\n### Options:\nA. 11%\nB. 10%\nC. 5%\nD. 5.5%\nE. 6%\n\n### Answer:\nSolution\nLet T.D be Rs 1.Then, B.D\t=Rs.11 / 10\n= Rs.1.10.\nSum\t=Rs.(1.10 x 1/ 1.10-1)\n= Rs.(110 / 10)\n= Rs. 11.\nS.I on Rs.11 for 2 years is Rs.1.10.\nRate\t=(100 x 1.10 / 11 x 2)%\n= 5%\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA rectangular plot measuring 90 meters by 50 meters is to be enclosed by wire fencing. If the poles of the fence are kept 5 meters apart. How many poles will be needed?\n\n### Options:\nA. 46m\nB. 66m\nC. 26m\nD. 56m\nE. 25m\n\n### Answer:\nPerimeter of the plot = 2(90+50) = 280m\nno of poles =280/5 =56m\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\no mow a grass field a team of mowers planned to cover 15 hectares a day. After 4 working days they increased the daily productivity by 33\u00d713%33\u00d713%, and finished the work 1 day earlier than it was planned.\nA) What is the area of the grass field?\nB) How many days did it take to mow the whole field?\nC) How many days were scheduled initially for this job?\n\n### Options:\nA. 387\nB. 39\nC. 37\nD. 20\nE. 28\n\n### Answer:\nHint: See problem 20 and solve by yourself.\nAnswer: A) 120 hectares; B) 7 days; C) 8 days.\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn 1995, the Johnsons spent $800 on the family\u2019s water bills. Anticipating that water rates would increase in 1996 by 50%, the Johnsons cut back their water usage. By how much must the Johnsons have reduced their 1996 water usage to pay exactly the same amount Q in 1996 as they paid in 1995?\n\n### Options:\nA. 33 1\u20443%\nB. 40%\nC. 50%\nD. 66 2\u20443%\nE. 100%\n\n### Answer:\nwater rate increases by 50 % in 1996 means 150% of rate in 1995. to pay exactly the same amount in 1996 as they paid in 1995, water use should decrease in the same ratio\nQ=150-> 100 means 1/3 rd= 33(1/3) %=A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJohn purchased some shirts and trousers for $1100. He paid $550 less for the shirts than he did for the trousers. If he bought 5 shirts and the cost of a shirt is $20 less than that of a trouser, how many trousers did he buy?\n\n### Options:\nA. 4\nB. 5\nC. 6\nD. 7\nE. 11\n\n### Answer:\nGiven that the total purchase of two items cost 1100.\nSo the average purchase of one item will cost 1100/2 = 550.\nIts given as total shirt cost 100$ less. Hence Total Shirt cost = 550 - 275 and Total trouser cost = 300 + 275\n5 shirts = 275$ ==> One shirt = 55$\nOne trouser = 55 + 20 = 75$\nTotal trousers = 825 / 75 = 11.\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMolly is rolling a number cube with faces numbered 1 to 6 repeatedly. When she receives a 1, she will stop rolling the cube. What is the probability that Molly will roll the die less than 3 times before stopping?\n\n### Options:\nA. 11/180\nB. 125/216\nC. 25/216\nD. 11/216\nE. 27/128\n\n### Answer:\nThe probability that Molly will roll the die less than 4 times before stopping is the sum of the following:\nThe probability that Molly will roll the die once: P=1/6 (she gets 1 on the first roll);\nThe probability that Molly will roll the die twice: P=5/6*1/6 (not 1, 1);\nP = 1/6 + 5/6*1/6 = 11/216.\nAnswer: D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAt what rate percent on simple interest will Rs.750 amount to Rs.900 in 5 years?\n\n### Options:\nA. 2\nB. 3\nC. 4\nD. 5\nE. 6\n\n### Answer:\n150 = (750*5*R)/100\nR = 4%.Answer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nfind the number of 6 digit numbers that can be formed using digits 1,2,3,4,5,6 once such that the 6digit number is divisible by its unit digit.\n\n### Options:\nA. 648\nB. 649\nC. 650\nD. 651\nE. 652\n\n### Answer:\nwhen unit digit 1,2,3,5,6 then no. formed will be divisible by the digit at the unit place.\n=> 5*5p5 numbers\nwhen unit place is 4, tenth place should be 2 or 6\n=> 2*4p4 numbers\ntotal = 5*5p5 + 2*4p4 = 5*5! + 2*4! = 648\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA boy wants to go abroad by boat and return by flight. He has a choice of 2 different boat to go and 8 flight to return. In how many ways, can the boy perform his journey?\n\n### Options:\nA. 20\nB. 16\nC. 45\nD. 18\nE. 70\n\n### Answer:\nAns.(B)\nSol. Number of choices to go by ship = 2 Number of choices to return by airline = 8 From, fundamental principle, total number of ways of performing the journey = 2 x 8 = 16 ways\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf x is 50 percent greater than 88, then x =\n\n### Options:\nA. 68\nB. 132\nC. 86\nD. 105.6\nE. 108\n\n### Answer:\nx=88*1.5=132\nSo the answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf x is an integer, then x(x - 1)(x - b) must be evenly divisible by three when b is any of the following values EXCEPT\n\n### Options:\nA. -4\nB. -2\nC. -1\nD. 2\nE. 5\n\n### Answer:\nhere's another approach\nx(x - 1)(x - b)\nall three are consecutive, so the product MUST be a multiple of 3\nwe don't know the value of b just yet ... so let's extend the series ... the extension itself reveals the answers\n..(x-5)..(x-2)(x-1)x(x+1)..(x+4)..\nwe can see the possible values of b too from the series\nb = 2 OR 2+3n [25]\nb = -1 OR -1+3n [-1-4]\nB i.e. -2 does not fit in any value of b\nso B it is\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe present ratio of students to teachers at a certain school is 70 to 1. If the student enrollment were to increase by 50 students and the number of teachers were to increase by 5, the ratio of students to teachers would then be 25 to 1. What is the present number of teachers?\n\n### Options:\nA. 2\nB. 8\nC. 10\nD. 12\nE. 15\n\n### Answer:\nWe are given that the ratio of students to teacher is 70 to 1. We can rewrite this using variable multipliers.\nstudents : teachers = 70x : x\nWe are next given that student enrollment increases by 50 and the number of teachers increases by 5. With this change the new ratio becomes 25 to 1. We can put all this into an equation:\nStudents/Teachers \uf0e0 25/1 = (70x + 50)/(x + 5)\nIf we cross multiply we have:\n25(x + 5) =70x + 50\n25x + 125 = 70x + 50\n1.667 = x\nx~2\nSince x is the present number of teachers, currently there are 2 teachers.\nAnswer A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many days will there be from 29th January,1996 to 15th May,1996(both days included)?\n\n### Options:\nA. 102\nB. 103\nC. 111\nD. 120\nE. 108\n\n### Answer:\nExplanation:\nNumber of days from 29-Jan-1996 to 15-May-1996 (both days included)\n= 3(Jan) + 29(Feb) + 31 (Mar) + 30(Apr)+ 15(May) = 108\nAnswer: Option E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train crosses a platform of 150 m in 15 sec, same train crosses another platform of length 250 m in 20 sec. then find the length of the train?\n\n### Options:\nA. 150m\nB. 120m\nC. 186m\nD. 167m\nE. 189m\n\n### Answer:\nLength of the train be \u2018X\u2019\nX + 150/15 = X + 250/20\n4X + 600 = 3X + 750\nX = 150m\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average temperature of a city in the first four days of a month was 36\u00b0. The average for the 2nd, 3rd, 4th and 5th day was 38\u00b0. If the temperature of the 1st and 5th day were in the ratio 4 : 5, then what is the temperature on the fifth day ?\n\n### Options:\nA. 32\u00b0\nB. 35\u00b0\nC. 38\u00b0\nD. 40\u00b0\nE. None of these\n\n### Answer:\nExplanation:\nThe temperature for first 4 days = 4 * 36 = 144\nThe temperature for last 4 days = 4 * 38 = 152\nThe difference between the temperatures is (152 \u2013 144) = 8\nThe ratio of temperature between first and fifth day is 4 : 5\nThe temperature on fifth day is 5*8 = 40\nANSWER D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRead the following three equations:\n5 ~ 4 ~ 3 ~ 9 = 4215\n6 ~ 9 ~ 2 ~ 6 = 3816\n4 ~ 7 ~ 3 ~ 3 = 1122\nNow based on the rule that has been used, solve the following equation:\n6 ~ 2 ~ 7 ~ 4 = ____\n\n### Options:\nA. 2414\nB. 2910\nC. 2940\nD. 3749\nE. 4470\n\n### Answer:\nA\n2414\n2414\nThe rule that is being followed here is\nP ~ Q ~ R ~ S = [first digit of (P * S)] [last digit of (Q * R)] [first digit of (Q * R)] [last digit of (P * S)]\nUsing the same rule in the incomplete equation,\n6 ~ 2 ~ 7 ~ 4 = [first digit of (6 * 4)] [last digit of (2 * 7)] [first digit of (2 * 7)] [last digit of (6 * 4)]\n= 2414\nThus 2414 is the missing number.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOn rainy mornings, Mo drinks exactly N cups of hot chocolate (assume that N is an integer). On mornings that are not rainy, Mo drinks exactly 4 cups of tea. Last week Mo drank a total of 42 cups of tea and hot chocolate together. If during that week Mo drank 14 more tea cups than hot chocolate cups, then how many rainy days were there last week?\n\n### Options:\nA. 0\nB. 4\nC. 5\nD. 6\nE. 7\n\n### Answer:\nT= the number of cups of tea\nC= the number of cups of hot chocolate\nT+C = 42 T-C=14 -> T= 28. C=14.\nMo drinks 4 cups of tea a day then number of days that are not rainy = 28/4= 7\nSo number of rainy days = 7-7 = 0\nA is the answer.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf y is 40 percent greater than x, then x is what percent less than y?\n\n### Options:\nA. 18%\nB. 21%\nC. 25%\nD. 29%\nE. 35%\n\n### Answer:\ny = 1.4x\nx = y/1.4 = 10y/14 = y - (2/7)*y\n2/7 is about 29%.\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA sum of money place at compound interest doubles itself in 6 years. In how many years will it amount to eight times itself?\n\n### Options:\nA. 15 years\nB. 11 years\nC. 12 years\nD. 18 years\nE. 19 years\n\n### Answer:\n100 ---- 200 ---- 6\n400 ---- 6\n800 ---- 6\n------\n18 years\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA company has two types of machines, type R and type S. Operating at a constant rate, a machine of type R does a certain job in 18 hrs and a machine of type S does the same job in 9 hours. If the company used the same number of each type of machine to do the job in 2 hours, how many machines of type R were used?\n\n### Options:\nA. A)3\nB. B)4\nC. C)6\nD. D)9\nE. E)12\n\n### Answer:\nRate of machine R =1/18\nRate of machine S =1/9\nsince same no of machines used for R and S to do the same work in 2 hrs\nSo collective rate needed to finish the work in 2 hrs= 1/2\nLet the no of machine be x\nSo, x/18 +x/9 =1/2\n3x/18=1/2\nx=18/6=3\nSo no of machine R is 3\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many two digit numbers are there such that the product of their digits after reducing it to the smallest form is a prime number? for example if we take 98 then 9*8=72, 72=7*2=14, 14=1*4=4. Consider only 4 prime no.s (2,3,5,7)\n\n### Options:\nA. 16\nB. 17\nC. 18\nD. 19\nE. 20\n\n### Answer:\nwe know prime no. are 2 ,3 , 5, 7\nmulply by 1 is prime no\n2 = 21(2*1)=73(7*3)\n2 = 21 (2*1)=37(3*7)\n2= 12(1*2)=43(4*3)or34(3*4)\nor26(2*6)or62(6*2)\n.\n.\n.similarly for all prime no then u will got it....\n12,13,15,17,21,26,31,34,35,37,43,51,53,57,62,71,73,75\nans is 18\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOn a sum of money, simple interest for 2 years is Rs 660 and compound interest is Rs 696.30, the rate of interest being the same in both cases.\n\n### Options:\nA. 8%\nB. 9%\nC. 10%\nD. 11%\nE. 12%\n\n### Answer:\nExplanation:\nDifference between C.I and S.I for 2 years = 36.30\nS.I. for one year = 330.\nS.I. on Rs 330 for one year = 36.30\nSo R% = \\frac{100*36.30}{330*1} = 11%\nOption D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n50 men took a dip in a water tank 40 m long and 20 m broad on a religious day. If the average displacement of water by a man is 5m3 , then the rise in the water level in the tank will be:\n\n### Options:\nA. 31.25 cm\nB. 25 cm\nC. 35 cm\nD. 50 cm\nE. None of these\n\n### Answer:\nExplanation:\nTotal volume of water displaced =(5 x 50) m3 = 250 m3\nRise in water level = 250/40\u00c3\u201420= 0.3125m = 31.25cm\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nExcluding stoppages, the speed of a bus is 54 kmph and including stoppages, it is 45 kmph. For how many minutes does the bus stop per hour?\n\n### Options:\nA. 9\nB. 10\nC. 12\nD. 20\nE. 14\n\n### Answer:\nDue to stoppages, it covers 9 km less.\nTime taken to cover 9 km =(9* 60)/54min\t= 10 min.\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe sale price sarees listed for Rs.175 after successive discount is 20% and 5% is?\n\n### Options:\nA. 187\nB. 133\nC. 142\nD. 178\nE. 175\n\n### Answer:\n175*(80/100)*(95/100)\n= 133\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf an item that originally sold for A dollars was marked up by x percent and then discounted by M percent, which of the following expressions represents the final price of the item?\n\n### Options:\nA. (10,000z + 100z(x \u2013 y) \u2013 xyz)/10,000\nB. (10,000z + 100z(y \u2013 x) \u2013 xyz)/10,000\nC. (100z(x \u2013 y) \u2013 xyz)/10000\nD. (A+ Ax/100) - M/100 ( A +Ax/100)\nE. 10000 /(x \u2013 y)\n\n### Answer:\nvalue of item =A ..marked up by x% = Ax/100\ntotal value = A +ax/100 .discounted by L% on Total M/100 * ( A+Ax/100)\nFinal price =(A+ Ax/100) - M/100 ( A +Ax/100)\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJane makes toy bears. When she works with an assistant, she makes 100 percent more bears per week and works 10 percent fewer hours each week. Having an assistant increases Jane\u2019s output of toy bears per hour by what percent?\n\n### Options:\nA. 20%\nB. 80%\nC. 100%\nD. 180%\nE. 200%\n\n### Answer:\nWe can use fractional equivalents here to solve the problem\n80% = 4/5; this means that in 1st case if she prepares 5 bears, in 2nd case she prepares 9 bears\n10% = 1/10; this means that in 1st case if she needs 10 hours, in 2nd case she needs 9 hours\nNow we come to productivity\nBased on above fractional values the productivity in 1st case is 0.5 bears / hour and in the 2nd case it is 1 bear / hour\nHence the productivity is double with the assistant i.e. the increase in productivity is 200%\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train 420 m long is running at a speed of 48 km/hr. In what time will it pass a bridge 60 m long?\n\n### Options:\nA. 40 sec\nB. 36sec\nC. 60 sec\nD. 48 sec\nE. 18 sec\n\n### Answer:\ntotal length= 420+60=480\nspeed=48km/h=(48*5)/18= 40/3 m/s\ntime=(480*3)/40=36 sec.\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHockey Stick and ball cost $50. If the Stick cost $49 more than the ball.\nwhat is the cost of each ?\n\n### Options:\nA. Hockey Stick $48.50 & ball $1.50\nB. Hockey Stick $49.00 & ball $1.00\nC. Hockey Stick $48.00 & ball $2.00\nD. Hockey Stick $49.50 & ball $0.50\nE. Hockey Stick $41.50 & ball $8.50\n\n### Answer:\nD\nHockey Stick $49.50 & ball $0.50\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo twins sisters Sita and Geeta were standing back to back and suddenly they started running in opposite directions for 6 km each. Then they turned left and ran for another 4.5 km.\nWhat is the distance (in kilometers) between the the two twins when they stop?\n\n### Options:\nA. 12\nB. 15\nC. 18\nD. 21\nE. 24\n\n### Answer:\nThe distance between them is the hypotenuse of a right angle triangle with sides 9 km and 12 km.\nhypotenuse = sqrt(9^2 + 12^2) = 15\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAnand and Deepak started a business investing Rs. 22,500 and Rs. 35,000 respectively. Out of a total profit of Rs. 16,100, Deepak's share is:?\n\n### Options:\nA. s.8467\nB. s.8428\nC. s.8400\nD. s.9800\nE. s.8420\n\n### Answer:\nRatio of their shares\n= 22500 : 35000\n= 9:14\nDeepak's share\n= 16100 * 14/23\n= Rs.9800.\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe ages of X and Y are in the proportion of 6:5 and total of their ages is 44 years. The proportion of their ages after 8 years will be\n\n### Options:\nA. 3:6\nB. 6:3\nC. 8:7\nD. 9:5\nE. None of these\n\n### Answer:\nExplanation:\nLet current ages of X and Y correspondingly, is 6A & 5A\nGiven: 6A + 5A = 44\n=> A = 4\nProportion of ages after 0.8 decades will be\n6A + 8 : 5A + 8 32:28 (or) 8:7 . Answer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhen Rahul was born, his father was 35 years older than his brother and his mother was 25 years older than his sister. If Rahul's brother is 5 years older than him and his mother is 3 years younger than his father, how old was Rahul's sister when he was born ?\n\n### Options:\nA. 11 years\nB. 10 years\nC. 12 years\nD. 9 years\nE. 8 years\n\n### Answer:\nWhen Rahul was born, his brother's age = 5 years; his father's age = (5 + 35) years = 40 years,\nhis mother's age = (40 - 3) years = 37 years;\nhis sister's age = (37 - 25) years = 12 years.\nAnswer: Option C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSam invested Rs. 15000 @ 10% per annum for one year. If the interest is compounded half-yearly, then the amount received by Sam at the end of the year will be?\n\n### Options:\nA. Rs.16,537.58\nB. Rs.16,537.52\nC. Rs.16,537.50\nD. Rs.16,537.22\nE. Rs.16,537.21\n\n### Answer:\nP = Rs. 15000; R = 10% p.a. = 5% per half-year; T = 1 year = 2 half-year\nAmount = [15000 * (1 + 5/100)2]\n= (15000 * 21/20 * 21/20)\n= Rs. 16537.50\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nEvaluate the expression\nm - (m - n) : (-2) \u22c5 (-5) when m = -4, n = -6\n\n### Options:\nA. 8\nB. 9\nC. 5\nD. 7\nE. 6\n\n### Answer:\nSolution:\nm - (m - n) : (-2) \u22c5 (-5) = (-4) - [-4 - (-6)] : (-2) \u22c5 (-5) = -4 - 2 : (-2) \u22c5 (-5) = -4 - (-1) \u22c5 (-5) = -4 - (+5) = -9\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n20-3*4^2+53 = ?\n\n### Options:\nA. 25\nB. -13\nC. -73\nD. 13\nE. None\n\n### Answer:\n20-3*4^2+53= 20-3*16+53=20-48+53=25..\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA tradesman by means of his false balance defrauds to the extent of 14%? in buying goods as well as by selling the goods. What percent does he gain on his outlay?\n\n### Options:\nA. 54.6%\nB. 29.96%\nC. 24.45%\nD. 24%\nE. 45%\n\n### Answer:\ng% = 14 + 14 + (14*14)/100\n= 29.96%\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe positive two-digit integers s and t have the same digits, but in reverse order. Which of the following must be a factor of s + t?\n\n### Options:\nA. 6\nB. 9\nC. 44\nD. 12\nE. 14\n\n### Answer:\nRemember: When you take the difference between the two, it will always be 9. e.g 23-32=9, 89-98=9\nand when you add both integers, the sum will always be a multiple of 11 e.g 23+32=55, 89+98= 187\n44 is multiple of 11\nAnswer : C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat value of K gives the equation,3k-2=2k-1?\n\n### Options:\nA. ONE\nB. TWO\nC. THREE\nD. FOUR\nE. NONE\n\n### Answer:\n3k-2=2k-1\nIf k=1\n3(1)-2=2(1)-1\n3-2=2-1\n1=1\nOption A is answer\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAjay pays Rs 8.0 per litre of spirit. He adds water and sells the mixture at Rs 9 per litre, thereby making 40 % profit. The proportion of water to spirit received by the customers is\n\n### Options:\nA. 45:11\nB. 11:45\nC. 2:45\nD. 45:2\nE. None of these\n\n### Answer:\nSuppose the quantity of spirit purchased = X lites\nSuppose quantity of water mixed = Y litres\nRequired ratio of the water and the spirit in the mixture = Y:X\nC.P. of x litres of spirit = Rs 8.0X\nS.P of x litres of spirit = 9(X + Y)\nThus,C.P = S.P x 100/(100 + gain% )\n=> 64 = (9X+9Y) x 100/100 + 40\n=> 1120X =900X +900Y\n=> 220X= 900Y\n=> Y/X = 220/900 = 11/45\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRamesh can finish a piece of work in 22 days. Rohan is twice as efficient as Ramesh. If they work together how many days will they need to finish the same amount of work?\n\n### Options:\nA. 22/3 days\nB. 9/3 days\nC. 10/3 days\nD. 11/3 days\nE. 7/3 days\n\n### Answer:\nRamesh can finish a piece of work in 22 days. Rohan is twice as efficient as Ramesh.\nSo Rohan can finish a piece of work in 11 days.\ndays needed to finish the same amount of work = 1/(1/11+1/22)=22/3 days\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a and b are the two values of t that satisfy\nthe equation t^2 \u00e2\u20ac\u201c 12t + 20 = 0, with a > b, what is the value of a \u00e2\u20ac\u201c b?\n\n### Options:\nA. 2\nB. 4\nC. 6\nD. 8\nE. 10\n\n### Answer:\nFactor the left side of the equation:\nt^2 \u00e2\u20ac\u201c 12t + 20 = 0\n(t \u00e2\u20ac\u201c 2)(t \u00e2\u20ac\u201c 10) = 0\nt = 2, t = 10\nThus, a = 10 and b = 2. So a \u00e2\u20ac\u201c b = 10 \u00e2\u20ac\u201c 2 = 8.\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA car travels at a speed of 65 miles per hour. How far will it travel in 4 hours?\n\n### Options:\nA. 125 miles\nB. 225 miles\nC. 260 miles\nD. 425 miles\nE. 525 miles\n\n### Answer:\nDuring each hour, the car travels 65 miles. For 4 hours it will travel\n65 + 65 + 65 + 65 = 4 \u00d7 65 = 260 miles\ncorrect answer is C) 260 miles\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAn investor receives a total combined return of 7% on his two different investments. On his $20,000 investment he receives a return of 6%. What is the return on his $20,000 investment?\n\n### Options:\nA. 7.25%\nB. 4.9%\nC. 8%\nD. 8.5%\nE. 9%\n\n### Answer:\n0.06 * 20000 + 20000x = 0.07(40000)\nsolving for x give x = 8%\noption C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a Express Train passengers traveling in A.C. Sleeper Class, First Class and Sleeper Class are in the ratio 1:2:3, and fare to each class in the ratio 5:4:2. If the income from this train is Rs. 57000, the income of A.C. Sleeper Class is\n\n### Options:\nA. Rs. 8000\nB. Rs. 12000\nC. Rs. 15000\nD. Rs. 6000\nE. None\n\n### Answer:\nIncome is divided in the ratio 1\u00d75:2\u00d74:3\u00d72= 5:8:6.\nNow 5x + 8x + 6x = 19x = 57000.\n\u2234 x =3000.\nTherefore income from A.C. Sleeper Class = 30005=15000.\nAnswer:C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOn a certain day, Tim invested $500 at 10 percent annual interest, compounded annually, and Lana invested 1,000 at 5 percent annual interest, compounded annually.The total amount of interest earned by Tim\u2019s investment in the first 2 years was how much greater than the total amount of interest earned by Lana\u2019s investment in the first 2 years?\n\n### Options:\nA. $2.5\nB. $15\nC. $50\nD. $100\nE. $105\n\n### Answer:\nCompounded annually means that the interest is applied once per year. One can have 10% annual interest compounded monthly - in this case 10%/12 would be applied each month, or 10% annual interest compounded daily etc.\nWith respect to the problem at hand, at the end of two years, Tim would have\n500(1.10)^2 = 500(1.21) = 605\nand Lana would have\n1,000(1.05)^2 = 1,000(1.1025) =1102.5\nThus, Tim earned 105 dollars, while Lana earned 102.5 dollars\nThe difference is $2.5 and the answer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn covering a distance of 60 km, A takes 2 hours more than B. If A doubles his speed, then he would take 1 hour less than B. A's speed is:\n\n### Options:\nA. 5 km/h\nB. 8 km/h\nC. 10 km/h\nD. 15 km/h\nE. 20 km/h\n\n### Answer:\nLet A's speed be X km/hr.\nThen, 60/x - 60/2x = 3\n30/x = 3\nx = 10 km/hr.\nAnswer : C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe length of a room is 5.5 m and width is 3.75 m. Find the cost of paying the floor by slabs at the rate of Rs. 1000 per sq.metre.\n\n### Options:\nA. Rs. 15,000\nB. Rs. 15,500\nC. Rs. 15,600\nD. Rs. 20,625\nE. None\n\n### Answer:\nSolution\nArea of the floor\t= (5.5 x 3.75)m\u00b2\n= 20.635m \u00b2\nCost of paying\t= Rs. (1000 x 20.625)\n= Rs.20625.\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many positive integers less than 200 are there such that they are multiples of 13 or multiples of 14?\n\n### Options:\nA. 25\nB. 26\nC. 27\nD. 28\nE. 29\n\n### Answer:\n200/13 = 15 (plus remainder) so there are 15 multiples of 13\n200/14 = 14 (plus remainder) so there are 14 multiples of 14\nWe need to subtract 1 because 13*14 is a multiple of both so it was counted twice.\nThe total is 15+14-1 = 28\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn your classes you counted 126 hands. How many students were at the class?\n\n### Options:\nA. 63\nB. 61\nC. 85\nD. 86\nE. 88\n\n### Answer:\nTotal number of hands = 126\nWe have 2 hands.\nTo find how many students were at the class, divide the total number of hands by the number of hands we have.\nWe get, divide 126 by 2\n126 \u00f7 2 = 63\nTherefore, there were 63 students at the class.\nANSWER IS A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn an examination, 5% of the applicants were found ineligible and 85% of the eligible candidates belonged to the general category. If 4275 eligible candidates belonged to other categories, then how many candidates applied for the examination?\n\n### Options:\nA. 28000\nB. 30000\nC. 32000\nD. 33000\nE. None of these\n\n### Answer:\nExplanation :\nLet the number of candidates applied for the examination = x\nGiven that 5% of the applicants were found ineligible.\nIt means that 95% of the applicants were eligible (\u2234 100% - 5% = 95%)\nHence total eligible candidates = 95x/100\nGiven that 85% of the eligible candidates belonged to the general category\nIt means 15% of the eligible candidates belonged to other categories(\u2234 100% - 85% = 15%)\nHence Total eligible candidates belonged to other categories\n= total eligible candidates \u00d7 (15/100) = (95x/100) \u00d7 (15/100)\n= (95x \u00d7 15)/(100 \u00d7 100)\nGiven that Total eligible candidates belonged to other categories = 4275\n\u21d2 (95x \u00d7 15)/(100 \u00d7 100) = 4275\n\u21d2 (19x \u00d7 15)/(100 \u00d7 100) = 855\n\u21d2 (19x \u00d7 3)/(100 \u00d7 100) = 171\n\u21d2 (x \u00d7 3)/(100 \u00d7 100) = 9\n\u21d2 x/(100 \u00d7 100) = 3\n\u21d2 x = 3 \u00d7 100 \u00d7 100 = 30000\nAnswer : Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many meters are there in 660 centimeters?\n\n### Options:\nA. 6.6 meters\nB. 660 meters\nC. 600 meters\nD. 6.5 meters\nE. 6 meter\n\n### Answer:\nSolution:\n1 meter = 100 centimeters\nJust divide 660 by 100\n660 \u00c3\u00b7 100 = 6.6, so there are 6.6 meters in 660 centimeters\nOption A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf k = 2n - 1, where n is an integer, what is the remainder of k^2/8?\n\n### Options:\nA. 1\nB. 3\nC. 5\nD. 7\nE. Cannot be determined from the information given.\n\n### Answer:\nLet us assume that k = 4(n)(n-1)\nThis is divisible by 8.\nSo k+1 when divided by 8 will give reminder 1.\nFor example, consider n = 2\nWe have 4*2*1 + 1 = 9\nWhen we divide this by 8 we get reminder 1.\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA person goes to his office at 1/3rd of the speed at which he returns from his office. If the avg speed during the whole trip is 15m/h. what is the speedof the person while he was going to his office?\n\n### Options:\nA. 8km/h\nB. 10km/h\nC. 12km/h\nD. 13km/h\nE. 14km/h\n\n### Answer:\nu = k , v= 3k\n\\inline \\therefore \\frac{2uv}{u+v}\\: \\: \\Rightarrow \\frac{2\\times k\\times 3k}{(k+3k)}=15\n\\inline \\Rightarrow 1.5k = 15\n\\inline \\Rightarrow k=10km/h\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA started a business with an investment of Rs. 70000 and after 6 months B joined him investing Rs. 120000. If the profit at the end of a year is Rs. 52000, then the share of B is?\n\n### Options:\nA. 24029\nB. 24000\nC. 24028\nD. 24014\nE. 24012\n\n### Answer:\nRatio of investments of A and B is (70000 * 12) : (120000 * 6) = 7 : 6\nTotal profit = Rs. 52000\nShare of B = 6/13 (52000) = Rs. 24000\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe value of 5 in the number 357.21 is\n\n### Options:\nA. 5 tenths\nB. 5 ones\nC. 5 tens\nD. 5 hundreds\nE. 5 twentys\n\n### Answer:\nAns: C\nThe number 357.21 consists of: 3 hundreds, 5 tens, 7 ones, 2 tenths and 1 hundredth =>the value of 5 in 357.21\tis 5 tens\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwenty people at a meeting were born during the month of September, which has 30 days. The probability that at least two of the people in the room share the same birthday is closest to which of the following?\n\n### Options:\nA. 10%\nB. 33%\nC. 67%\nD. 90%\nE. 99%\n\n### Answer:\nThe probability that at least two people sharing the same birthday = 1 - the probability that none of them sharing the same birthday\nA = The number of ways of none of them sharing the same birthday = 30P20 = 30!/(30-20)! = 30!/10! = 11*12*...*29*30\nB = The total number of possible ways of 20 people born in September = 20*20*....*20*20 = 20^30 ( each day has 20 options)\nA/B = the probability that none of them sharing the same birthday\nsince B is much greater than A, A/B may equal 1%\n--> The probability that at least two people sharing the same birthday = 1 - 1% = 99%\nAnswer E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWorkers decided to raise Rs.3lacs by equal contribution from each. Had they contributed Rs.50 eachextra, the contribution would have been Rs.3.25lacs. How many workers were they?\n\n### Options:\nA. 350\nB. 400\nC. 500\nD. 550\nE. 590\n\n### Answer:\nN * 50 = (325000 - 300000) = 25000\nN = 25000 / 50\n= 500\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the difference between the place value and the face value of 8 in the numeral 296487?\n\n### Options:\nA. None of these\nB. 82\nC. 78\nD. 52\nE. 72\n\n### Answer:\nExplanation:\nPlace value of 8 = 80\nFace value of 8 = 8\nDifference = 80 - 8 = 72\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSolve below question 4x + 1 = 37\n\n### Options:\nA. -8\nB. -9\nC. -5\nD. 9\nE. 1\n\n### Answer:\n1. Subtract 1 from both sides: 4x + 1 - 1 = 37 - 1 2. Simplify both sides: 4x = 36 3. Divide both sides by 4: 4. Simplify both sides: x = 9 D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAdding two non multiples of R always results in a multiple of R; which of the following must be the value of R ?\n\n### Options:\nA. [A] two\nB. [B] three\nC. [C] five\nD. [D] ten\nE. [E] hundred\n\n### Answer:\nNON- multiples of 2 would always be ODD and sum of two odd would be EVEN.\nso irrespective of value of non-multiples, sum of two them would always be even and thus multiple of 2..\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA salesperson gets a 15% commission on each sale he makes. How many sales of $270 each must he make in order to reach a salary of at least $1000?\n\n### Options:\nA. 15\nB. 24\nC. 25\nD. 26\nE. 52\n\n### Answer:\nSoln:-\n10% of 270 = 27.\n5% of 270 = 13.5.\nso,\n15 % of 270 = 40.5\ntotal salary required 1000\nearning from single sale 40.5\n# of sale = 1000/40.5 = 24.62\nApprox 25 sale\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe tax on a commodity is diminished by 20% and its consumption increased by 15%. The effect on revenue is?\n\n### Options:\nA. It increases by 8%\nB. It decreases by 8%\nC. No change in revenue\nD. It increases by 10%\nE. None\n\n### Answer:\nExplanation:\n100 * 100 = 10000\n80 * 115 = 9200\n-----------\n10000-----------800\n100-----------? => 8% decrease\nANSWER IS B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMary's income is 60% more Than Tim's income and Tim's income is 20% less than Juan's income.What % of Juan's income is Mary's income.\n\n### Options:\nA. 128%\nB. B.120%\nC. 96%\nD. 80%\nE. 64%\n\n### Answer:\nEven I got 96%\nJ = 100\nT = 100*0.8 = 80\nM = 80*1.6 = 128\nIf Mary's income is x percent of J\nM = J*x/100\nx = M*100/J = 128*100/100 = 128\nAns:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThree persons invested Rs.9000 in a joint business. The second person invested Rs.1000 more than the first and the third Rs.1000 more than second. After two years, they gained Rs.3600. How much third person will get?\n\n### Options:\nA. 1600\nB. 2878\nC. 2699\nD. 2662\nE. 1821\n\n### Answer:\nFirst persons investment = x\nSecond persons investment = x + 1000\nThird persons investments = x + 2000\nx + x + 1000 + x + 2000 = 9000\n3x = 6000\nx = 2000\nRatio = 2000 : 3000 : 4000\n2:3:4\n4/9 * 3600 = 1600\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the probability that the position in which the consonants appear remain unchanged when the letters of the word \"Math\" are re-arranged?\n\n### Options:\nA. 1/4\nB. 1/6\nC. 1/3\nD. 1/24\nE. 1/12\n\n### Answer:\nExplanatory Answer\nStep 1: Compute denominator\nIn any probability question, the denominator represents the total number of outcomes for an event. The numerator represents the number of favorable outcomes.\nThe total number of ways in which the word MATH can be re-arranged = 4! = 4*3*2*1 = 24 ways.\nStep 2: Compute numerator and the probability\nIf the positions in which the consonants appear do not change, the first, third and the fourth positions are reserved for consonants and the vowel A remains at the second position.\nThe consonants M, T and H can be re-arranged in the first, third and fourth positions in 3! = 6 ways so that the positions in which the positions in which the consonants appear remain unchanged.\nTherefore, the required probability 6/24=/14\nChoice A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a graduating class of 232 students, 144 took geometry and 119 took biology. What is the difference between the greatest possible number P and the smallest possible number of students that could have taken both geometry and biology?\n\n### Options:\nA. 144\nB. 119\nC. 113\nD. 88\nE. 31\n\n### Answer:\nOFFICIAL SOLUTION:\nFirst of all, notice that since 144 took geometry and 119 took biology, then the number of students who took both geometry and biology cannot be greater than 119.\n{Total} = {geometry} + {biology} - {both} + {neither};\n232 = 144 + 119 - {both} + {neither};\n{both} = 31 + {neither}.\n{both} is minimized when {neither} is 0. In this case {both} = 31.\nThe greatest possible number of students P that could have taken both geometry and biology, is 119.\nThus, the answer is 119 - 31 = 88.\nAnswer: D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA retailer bought a machine at a wholesale price of $90 and later on sold it after a 10% discount of the retail price. If the retailer made a profit equivalent to 20% of the whole price, what is the retail price r of the machine?\n\n### Options:\nA. 81\nB. 100\nC. 120\nD. 135\nE. 160\n\n### Answer:\nSince the wholesale price was $90 and the profit was 20% of the wholesale price ([.2][90] = $18), the retail price would have to be above $108, but not that much greater than that.\nLet's start by TESTing Answer C: $120....\nIf.....\nRetail Price r= $120\n10% discount off = $120 - (.1)(120) = 120 - 12 = 108\n20% profit on wholesale price = 90 + (.2)(90) = 90 + 18 = 108\nThese two numbers MATCH, so this MUST be the answer!\nFinal Answer:\n[Reveal]Spoiler:\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n10 men and 15 women together can complete a work in 8 days. It takes 100 days for one man alone to complete the same work. How many days will be required for one woman alone to complete the same work?\n\n### Options:\nA. 127 days\nB. 667 days\nC. 177 days\nD. 187 days\nE. 600 days\n\n### Answer:\n1 man's 1 day work = 1/100\n(10 men + 15 women)'s 1 day work = 1/8\n15 women's 1 day work = (1/8 - 10/100) = 1/40\n1 woman's 1 day work = 1/600\n1 woman alone can complete the work in 600 days.\nAnswer:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTom drives from town Q to town B, driving at a constant speed of 60 miles per hour. From town B Tom immediately continues to town C. The distance between Q and B is twice the distance between B and C. If the average speed of the whole journey was 36 mph, then what is Tom's speed driving from B to C in miles per hour?\n\n### Options:\nA. 12\nB. 20\nC. 24\nD. 30\nE. 36\n\n### Answer:\nLet's assume that it takes 4 hours to go from point Q to B. Then the distance between them becomes 240 which makes distance between B and C 120. (240+120)/(4+x) gives us the average speed which is 36. You find x=6. So the question simplifies itself to 120/6=20\nHence the answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 4 persons can do 4 times of a particular work in 4 days, then, 7 persons can do 7 times of that work in?\n\n### Options:\nA. 3 days\nB. 4 days\nC. 6 days\nD. 7 days\nE. 8 days\n\n### Answer:\nThat is, 1 person can do one time of the work in 4 days.\nTherefore, 7 persons can do 7 times work in the same 4 days itself\nB)\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nsue has 3 apples. Billy has 5 apples. If billy steals all of sues apples and eats 1 how many does he have left?\n\n### Options:\nA. 2\nB. 5\nC. 6\nD. 7\nE. 8\n\n### Answer:\n7 D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the sum of three consecutive positive odd integers is A, then the sum of the next three consecutive odd integers in terms of A is:\n\n### Options:\nA. A+3\nB. A+9\nC. A+18\nD. 2A + 3\nE. 3A\n\n### Answer:\nIn Case of Consecutive Integers or Integers in Arithmetic Progression Mean = Median\nI.e. Median = A/3 = Mean = Second Integer\nFirst Integer = A/3 - 2\nSecond Integer = A/3\nThird Integer = A/3 + 2\ni.e.\nFourth Integer = A/3 + 4\nFifth Integer = A/3 + 6\nSixth Integer = A/3 + 8\nNow Mean of next 3 Integers = Median = A/3 + 6\ni.e. Sum of Next 3 integers = (A/3 + 6)*3 = A+18\nAnswer: option C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe effective annual rate of interest corresponding to a nominal rate of 6% per annum payable half-yearly is?\n\n### Options:\nA. 6.06%\nB. 6.07%\nC. 6.08%\nD. 6.09%\nE. 6.19%\n\n### Answer:\nAmount of Rs. 100 for 1 year when compounded half-yearly = [100 * (1 + 3/100)2] = Rs. 106.09 Effective rate = (106.09 - 100) = 6.09%\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo different types of tea are mixed, at 6 Kg of type 1 and 4 Kg of type 2. One Kg of type 1 is Rs. 6 and that of type 2 is Rs. 7. The seller get 10% profit, by this action. Find at what price, he had sold the mixture/Kg?\n\n### Options:\nA. Rs 5.04\nB. Rs 7.04\nC. Rs 6.04\nD. Rs 8.04\nE. Rs 9.04\n\n### Answer:\nCP of 6 kg tea of type 1= 6*6=36 Rs.\nCP of 4 kg tea of type 2= 4*7=Rs 28\nCP of 10 kg mixed tea = Rs Rs 64\nSP of mixture for 10% profit = 64*1.1= Rs 70.4\nSP of 1kg mixed tea = Rs 7.04\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train 640 meters long is running with a speed of 64 kmph. The time taken by it to cross a tunnel 140 meters long is?\n\n### Options:\nA. 44 sec\nB. 49 sec\nC. 48 sec\nD. 16 sec\nE. 17 sec\n\n### Answer:\nD = 640 + 140 = 780\nS = 64 * 5/18 = 17.7 mps\nT = 780/17.7 = 44 sec\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe cost price of a radio is Rs.1800 and it was sold for Rs.1430, find the loss %?\n\n### Options:\nA. 18%\nB. 20.5%\nC. 30%\nD. 45%\nE. 12%\n\n### Answer:\n1800 ---- 370\n100 ---- ? => 20.5%\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA and B walk around a circular track. They start at 8 a.m. from the same point in the opposite directions. A and B walk at a speed of 2 rounds per hour and 2 rounds per hour respectively. How many times shall they cross each other before 9.30 a.m. ?\n\n### Options:\nA. A)5\nB. B)61\nC. C)8\nD. D)6\nE. E)9\n\n### Answer:\nRelative speed = 2 + 2 = 4 rounds per hour.\nSo, they cross each other 4 times in an hour and 2 times in half an hour.\nHence, they cross each other 6 times before 9.30 a.m.\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man bought 40 shares of Rs. 60 at 5 discount, the rate of dividend being 12%The rate of interest obtained is\n\n### Options:\nA. 13.09%\nB. 15.5%\nC. 14%\nD. 14.25%\nE. 14.95%\n\n### Answer:\nExplanation :\nFace Value of a share = Rs.60\nHe bought each share at Rs.60 - Rs.5 = Rs.55\nNumber of shares = 40\nDividend = 12 %\nDividend per share = 60\u00d712\u00d7100=Rs.7 1/5\nTotal dividend = (40 \u00d7 7 1/5)\nie, He got a dividend of (40 \u00d7 7 1/5) for an investment of Rs.(40 \u00d7 55)\nInterest obtained = 40\u00d77 1/5\u00d7100/40\u00d755=13.09%\nAnswer : Option A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nPipe A can fill a tank in 6 hours. Due to a leak at the bottom, it takes 9 hours for the pipe A to fill the tank. In what time can the leak alone empty the full tank?\n\n### Options:\nA. 33\nB. 77\nC. 18\nD. 99\nE. 66\n\n### Answer:\nLet the leak can empty the full tank in x hours 1/6 - 1/x = 1/9\n=> 1/x = 1/6 - 1/9 = (3 - 2)/18 = 1/18\n=> x = 18.\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n342\n\n### Options:\nA. 9\nB. 8\nC. 6\nD. 5\nE. 4\n\n### Answer:\nOne day's work of A and B = 1/9 + 1/8 = (2+1)/18\n= 1/6 So, the time taken to complete the work is 6 days.\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn what ratio must rice at Rs.7.10 be mixed with rice at Rs.9.20 so that the mixture may be worth\nRs.8 per Kg?\n\n### Options:\nA. 5 : 4\nB. 2 : 1\nC. 3 : 2\nD. 4 : 3\nE. None of these\n\n### Answer:\nExplanation :\nBy the rule of alligation, we have\nCP of 1 kg Rice of 1st kind CP of 1 kg Rice of 2nd kind\n7.1 9.2\nMean Price\n8\n9.2 - 8 = 1.2 8 - 7.1 = .9\nRequired ratio = 1.2 : .9 = 12 : 9 = 4 : 3\nAnswer : Option D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA tea expert claims that he can easily find out whether milk or tea leaves were added first to water just by tasting the cup of tea. In order to check this claims 12 cups of tea are prepared, 6 in one way and 6 in other. Find the different possible ways of presenting these 12 cups to the expert.\n\n### Options:\nA. 252\nB. 240\nC. 300\nD. 924\nE. None\n\n### Answer:\nSolution:\nSince, there are 6 cups of each kind, prepared with milk or tea leaves added first, are identical hence, total number of different people ways of presenting the cups to the expert is,\n[12!/(6!x 6!)]= 924\nAnswer: Option D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAll the students of class are told to sit in circle shape. Here the boy at the 10 th position is exactly opposite to 40 th boy. Total number of boys in the class?\n\n### Options:\nA. 50\nB. 45\nC. 60\nD. 55\nE. 53\n\n### Answer:\nAs half the circle shape consist of 40-10=30 boys,\nSo total number of boys in full circle=2*30=60\nANSWER: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo trains each 190m in length each, are running on two parallel lines in opposite directions. If one goes at the speed of 65km/h while the other travels at 50km/h. how long will it take for them to pass each other completely.\n\n### Options:\nA. 10.7 sec\nB. 2.7 sec\nC. 11.9 sec\nD. 12.7 sec\nE. 25.7 sec\n\n### Answer:\nExplanation:\nD = 190 m + 190 m = 380 m\nRS = 65 + 50 = 115 * 5/18 = 319/10\nT = 380 * 10/319 = 11.9 sec\nAnswer: Option C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n25 binders can bind 1400 books in 21 days. How many binders will be required to bind 1600 books in 20 days?\n\n### Options:\nA. 87\nB. 18\nC. 17\nD. 16\nE. 30\n\n### Answer:\nBinders Books Days\n25 1400 21\nx 1600 20\nx/25 = (1600/1400) * (21/20) => x = 30\nAnswer:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe lenght of a room is 5.5 m and width is 4 m. Find the cost of paving the floor by slabs at the rate of Rs. 750 per sq. metre.\n\n### Options:\nA. s. 15,550\nB. s. 15,600\nC. s. 16,500\nD. s. 17,600\nE. s. 17,900\n\n### Answer:\nArea of the floor = (5.5 \u00c3\u2014 4) m2 = 22 m2.\nCost of paving = Rs. (750 \u00c3\u2014 22) = Rs. 16500\n.\nAnswer: Option C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe ratio of the length and the breadth of a rectangle is 4 : 3 and the area of the rectangle is 6912 sq cm. Find the ratio of the breadth and the area of the rectangle?\n\n### Options:\nA. 1 : 96\nB. 1 : 48\nC. 1 : 84\nD. 1 : 68\nE. None of these\n\n### Answer:\nLet the length and the breadth of the rectangle be 4x cm and 3x respectively.\n(4x)(3x) = 6912\n12x2 = 6912\nx2 = 576 = 4 * 144 = 22 * 122 (x > 0)\n=> x = 2 * 12 = 24\nRatio of the breadth and the areas = 3x : 12x2 = 1 : 4x = 1: 96.\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n9 - 3 \u00f7 1/3 + 4 = ?\n\n### Options:\nA. 4\nB. 3\nC. 6\nD. 9\nE. 12\n\n### Answer:\n9 - 3 1/3 + 4\n=9-3\u00f71/3+4\n=9-(3X3) +4\n=9-9+4\n=4\nCORRECT ANSWER : A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe product of first twelve positive integers is divisible by all of the the following EXCEPT?\n\n### Options:\nA. 210\nB. 88\nC. 75\nD. 60\nE. 34\n\n### Answer:\nThe product of the first twelve positive integers, 12!12! contains only the primes less than 12 (2, 3, 5, 7, 11), which means that the product won't be divisible by any number containing higher prime number.\nNow, you can notice that 34=2*17 --> 12! is not divisible by 17 (prime >11), thus 12! is not divisible by 2*17=34 too.\nAnswer: E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAnil and suresh started a business with Rs.50,000 and 40,000 respectively. After 6 months Rakesh joined them with capital of Rs.60,000 They got a profit of Rs.6000, then profit of Rakesh is\n\n### Options:\nA. Rs.1500\nB. Rs.3000\nC. Rs.2000\nD. Rs.1000\nE. Rs.4000\n\n### Answer:\nRatio of investments of Anil, Suresh & Rakesh=(50000*12) : (40000*12) : (60000*6)=5 : 4 : 3\nProfit of Rakesh in Rs. 6000 = 3*6000/(5+4+3) =1500\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nBy selling 150 mangoes, a fruit-seller gains the selling price of 5 mangoes. Find the gain percent?\n\n### Options:\nA. 3.4%\nB. 2.5%\nC. 2.1%\nD. 8.5%\nE. 2.4%\n\n### Answer:\nSP = CP + g\n150 SP = 150 CP + 5 SP\n145 SP = 150 CP\n145 --- 5 CP\n100 --- ? => 3.4%\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the odd man out. 9,18,23,36,99\n\n### Options:\nA. 9\nB. 18\nC. 23\nD. 36\nE. 99\n\n### Answer:\nAll except 23 are multiples of 9\nAnswer is C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nP, Q and R have $7000 among themselves. R has two-thirds of the total amount with P and Q. Find the amount with R?\n\n### Options:\nA. 2800\nB. 2403\nC. 3998\nD. 2539\nE. 1930\n\n### Answer:\nA\n2800\nLet the amount with R be $ r\nr = 2/3 (total amount with P and Q)\nr = 2/3(7000 - r) => 3r = 14000 - 2r\n=> 5r = 14000 => r = 2800.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe jogging track in a sports complex is 726 m in circumference. Suresh and his wife start from the same point and walk in opposite direction at 4.5 km/hr and 3.75 km/hr respectively. They will meet for the first time in?\n\n### Options:\nA. 5.2 minutes\nB. 5.21 minutes\nC. 5.25 minutes\nD. 5.28 minutes\nE. 6 minutes\n\n### Answer:\nLet both of them meet after TT min\n4500 m are covered by Suresh in 60 m.\nIn TT min he will cover 4500T604500T60\nLikewise, In TT min Suresh's wife will cover 3750T603750T60\nGiven,\n4500T60+3750T60=7264500T60+3750T60=726\nTT = 5.28 minutes\nOption(D) is correct\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a fair coin is tossed six times, what is the probability of getting exactly five heads in a row?\n\n### Options:\nA. 1/64\nB. 1/32\nC. 1/16\nD. 3/64\nE. 3/32\n\n### Answer:\nP(HHHHHT) = 1/64\nP(THHHHH) = 1/64\nThe sum of these probabilities is 2/64 = 1/32\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAt an election 2 candidates are participated and a candidate got 30% of votes and defeated by 1000. and 100 votes are invalid. Find the total polled votes?\n\n### Options:\nA. 2150\nB. 2600\nC. 3120\nD. 1500\nE. 1895\n\n### Answer:\nWinner votes = 100-30 = 70\npolled votes = [(100*1000)/2*70-100]+100 = 2600\nAnswer is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nExpress 35 mps in kmph?\n\n### Options:\nA. 122\nB. 188\nC. 126\nD. 140\nE. 124\n\n### Answer:\n35 * 18/5 = 126 kmph\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA batch of cookies was divided amomg 3 tins: 3/4 of all the cookies were placed in either the blue or the green tin, and the rest were placed in the red tin. If 1/4 of all the cookies were placed in the blue tin, what fraction of the cookies that were placed in the other tins were placed in the green tin\n\n### Options:\nA. 15/2\nB. 9/4\nC. 5/9\nD. 3/5\nE. 9/7\n\n### Answer:\nThis will help reduce the number of variables you have to deal with:\nG + B = 3/4\nR = 1/3\nB = 1/4\nWe can solve for G which is 1/2\nWhat fraction (let it equal X) of the cookies that were placed in the other tins were placed in the green tin?\nSo..\nX*(G+R)=G\nX*(1/2 + 1/3) = 1/2\nX = 3/5\nANSWER: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe CI on Rs. 30,000 at 7% per year is Rs. 4347. The period is?\n\n### Options:\nA. 1 year\nB. 2 years\nC. 3 years\nD. 4 years\nE. 5 years\n\n### Answer:\nAmount = Rs. (30000 + 4347) = Rs. 34347.\nLet the time be n years.\nThen, 30000 1 +\t7 n\t= 34347\n100\n107 n\t=\t34347\t=\t11449\t= 107 2\n100\t30000\t10000\t100\nn = 2 years\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA candidate got 30% of the votes polled and he lost to his rival by 1760 votes. How many votes were cast?\n\n### Options:\nA. 4000\nB. 4100\nC. 4200\nD. 4300\nE. 4400\n\n### Answer:\nLet x be the total number of votes.\n0.3x + 1760 = 0.7x\n0.4x = 1760\nx = 1760/0.4 = 4400\nThe answer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the units digit of 33^2 * 17^3 * 49^3?\n\n### Options:\nA. 1\nB. 3\nC. 5\nD. 7\nE. 9\n\n### Answer:\nThe units digit of 33^2 is the units digit of 3*3 = 9 which is 9.\nThe units digit of 17^3 is the units digit of 7*7*7 = 343 which is 3.\nThe units digit of 49^3 is the units digit of 9*9*9 = 729 which is 9.\nThe units digit of 9*3*9 = 243 is 3.\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nM is 30% of Q. Q is 20% of P. N is 50% of P. Find M:N ratio\n\n### Options:\nA. 1:25\nB. 2:25\nC. 3:25\nD. 4:25\nE. 5:25\n\n### Answer:\nLet p be 100\nN = 50% of 100 (P=100) = 50\nQ= 20% of 100 (P=100) = 20\nM = 30% of 20 (Q=20) = 6\nM:N = 6:50\nM:N = 3:25\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA sum was put at simple interest at a certain rate for 5 years Had it been put at 6% higher rate, it would have fetched 90 more. Find the sum.\n\n### Options:\nA. 90\nB. 100\nC. 200\nD. 300\nE. 400\n\n### Answer:\nDifference in S.I. = P\u00d7T/100(R1\u2212R2)\n\u21d2 90 = P\u00d75x6/100(\u2235 R1 - R2 = 2)\n\u21d2 P = 90\u00d7100/5x6=300\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average salary of all the workers in a workshop is Rs. 8000. The average salary of 7 technicians is Rs. 12000 and the average salary of the rest is Rs. 6000. The total number of workers in the workshop is:\n\n### Options:\nA. 21\nB. 20\nC. 22\nD. 25\nE. 40\n\n### Answer:\nLet the total number of workers be x. Then,\n8000x = (12000 * 7) + 6000(x - 7)\n= 2000x = 42000\n= x = 21.\nANSWER A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe largest 5 digit number exactly divisible by 91 is:\n\n### Options:\nA. 25698\nB. 581396\nC. 369741\nD. 99918\nE. 1258\n\n### Answer:\nExplanation:\nLargest 5-digit number = 99999\n91) 99999 (1098\n91\n---\n899\n819\n----\n809\n728\n---\n81\n---\nRequired number = (99999 - 81)\n= 99918.\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf y > 0, (2y)/5 + (3y)/10 is what percent of y?\n\n### Options:\nA. 40%\nB. 50%\nC. 60%\nD. 70%\nE. 80%\n\n### Answer:\ncan be reduced to 2y/5+3y/10 =2y/5=70%\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are n cities. What is the number of airlines that connected 4 different cities (airline from city A to city B is different with airline from city B to city A)?\n\n### Options:\nA. n(n-1)\nB. n(n-3)\nC. n(n-1)/2\nD. n(n+1)/2\nE. n2\n\n### Answer:\nFirst of all, the possible number of airlines is n. Then, the possible number of airlines departing from one city to another becomes (n-3). Hence, the answer is n(n-3), which makes A an answer choice.\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain basketball team that has played 2/3 of its games has a record of 18 wins and 2 losses. What is the greatest number of the remaining games that the team can lose and still win at least 3/4 of all of its games?\n\n### Options:\nA. 7\nB. 6\nC. 5\nD. 4\nE. 3\n\n### Answer:\n18 wins, 2 losses - total 20 games played.\nThe team has played 2/3rd of all games so total number of games = 30\n3/4th of 30 is 22.5 so the team must win 23 games and can afford to lose at most 7 total games. It has already lost 2 games so it can lose another 5 at most.\nAnswer (C)\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn August,a cricket team that played 120 matches won 24% of the games it played.After a continuous winning streak,this team raised its average to 52%.How many matches did the team win to attain this average?\n\n### Options:\nA. 40\nB. 52\nC. 68\nD. 70\nE. 98\n\n### Answer:\nlet the no of matches played more=x\nso,\n(120+x)*52/100=28.8+x\nby solving we get x=70\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how many ways can 6 people be seated at a round table if one of those seated cannot sit next to 2 of the other 5?\n\n### Options:\nA. 720\nB. 120\nC. 108\nD. 84\nE. 48\n\n### Answer:\n6 People in a round table can be seated in (6 - 1) ! ways = 120.\nNow we need to subtract the number of cases when one of those is sitting next to 2 of the other 5.\nWe can consider as if 5 people are sitting in a row because it is round table.\nAgain consider 3 people, those who can not sit together, as a single unit \u00e2\u20ac\u201c\nSo the possible arrangements among remaining people 5 \u00e2\u20ac\u201c 3 + 1 Unit are = 3 !\nAnd the 3 people unit can arrange among themselves in 3 ! ways.\nSo the possible cases when one of those is sitting next to 2 of the other 5 = 3 ! * 3 ! = 36\nTotal possible cases = 120 -36 = 84 ANS:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA father said to his son, \"I was as old as you are at the present at the time of your birth\". If the father's age is 38 years now, the son's age five years back was:\n\n### Options:\nA. 14\nB. 17\nC. 19\nD. 22\nE. 24\n\n### Answer:\nLet the son's present age be x years. Then, (38 - x) = x\n2x = 38.\nx = 19.\nSon's age 5 years back (19 - 5) = 14 years.\nAnswer : A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many kg of pure salt must be added to 100kg of 10% solution of salt and water to increase it to a 35% solution?\n\n### Options:\nA. A)6.7\nB. B)38.5\nC. C)9.6\nD. D)12.5\nE. E)7.9\n\n### Answer:\nAmount salt in 100kg solution = 10*100/100 = 10 kg\nLet x kg of pure salt be added\nthen(10+x)/(100+x)=35/100\n200+20x=700+7x\n13x = 500\nx = 28.5\nAnswer is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nLagaan is levied on the 60 percent of the cultivated land. The revenue department collected total Rs. 3,84,000 through the lagaan from the village of Mettur. Mettur, a very rich farmer , paid only Rs.480 as lagaan. The percentage of total land of Mettur over the total taxable land of the village is:\n\n### Options:\nA. 0.20833\nB. 0.35424\nC. 0.10982\nD. 0.20933\nE. 0.10984\n\n### Answer:\nTotal land of Sukhiya = \\inline \\frac{480x}{0.6} = 800x\n\\therefore Cultivated land of village = 384000x\n\\therefore Required percentage = \\inline \\frac{800x}{384000}\\times 100 = 0.20833\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA sum of money is divided among A, B, C & D in the ratio 3:5:8:9 respectively. If the share of D Rs.1872 more than the share of A, then what is the total amount of money of B & C together?\n\n### Options:\nA. 3456\nB. 4056\nC. 4156\nD. 4567\nE. 6532\n\n### Answer:\nSol. Share of B + C = -3 x (5 + 8) = Rs. 4056\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA father said his son , \" I was as old as you are at present at the time of your birth. \" If the father age is 38 now, the son age 5 years back was\n\n### Options:\nA. 14\nB. 17\nC. 11\nD. 19\nE. 99\n\n### Answer:\nLet the son's present age be x years .Then, (38 - x) = x x= 19.\nSon's age 5 years back = (19 - 5) = 14 years\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n1/2, 1/4, 1/8, 1/16, 1/32, ....\nIn the sequence above each term after after the first one-half the previous term. If x is the FOURTH term of the sequence, then x satisfies which of the following inequalities?\n\n### Options:\nA. 0.0625\nB. 0.625\nC. 0.1\nD. 1\nE. 1.1\n\n### Answer:\nIn the Sequence notice that the sequence is just the 1/(2^n) ...\nso for 1st term=1/2^1=1/2\n2nd term=1/(2^2)1/4, 3rd term=1/(2^3)=1/8 and so on...\nThus the 4th term will be 1/(2^4)=1/16 =0.0625\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhen positive integer B is divided by 6 the remainder is 3. Which of the following CANNOT be an even integer?\n\n### Options:\nA. a. k + 1\nB. b. k -11\nC. c. 4k + 2\nD. d. (k-3)/3 +2\nE. e. B/3\n\n### Answer:\nWhen positive integer B is divided by 6 the remainder is 3\nSo, B could equal 3, 9, 15, 21, etc\nlet's TEST B =3\na.3+ 1 = 4 (EVEN)\nb.3-11 = -8 (EVEN)\nc. 4(3) + 2 = 14 (EVEN)\nd. (3-3)/3 +2 = 2 (EVEN)\nAt this point, we can already see the answer must be E.\nLet's check E forfun\ne.3/3 = 1 (ODD)\nGreat!\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA store reduced the price of all items in the store by 8% on the first day and by another 10% on the second day. The price of items on the second day was what percent of the price before the first reduction took place?\n\n### Options:\nA. 80.0\nB. 80.9\nC. 81.0\nD. 81.1\nE. 82.8\n\n### Answer:\nconsider price of the all items as $100\nafter a initial reduction of 8% price becomes = 0.92 *100 = $ 92\nafter the final reduction of 10% price becomes = 0.9* 92 = $ 82.8\nprice of all items on second day is 82.8% of price on first day\ncorrect answer option E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA machine puts c caps on bottles in m minutes. How many R hours will it take to put caps on b bottles?\n\n### Options:\nA. 60bm/c\nB. R=bm/60c\nC. bc/60m\nD. 60b/cm\nE. b/60cm\n\n### Answer:\nThe machine puts c caps in m minutes or c caps in m/60 hours.\nRate = c/m/60 = 60c/m.\nTo put b caps the machine will take:-\nTime = Work/Rate\nT = b/60c/m = bm/60c\nAnswer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA pipe can fill a cistern in 20 minutes whereas the cistern when fill can be emptied by a leak in 28 minutes. When both pipes are opened, find when the cistern will be full?\n\n### Options:\nA. 22 minutes\nB. 88 minutes\nC. 70 minutes\nD. 77 minutes\nE. 48 minutes\n\n### Answer:\n1/20 - 1/28 = 1/70\n70 minutes\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe product of two numbers is 4107. If the H.C.F of these numbers is 37, then the greater number is?\n\n### Options:\nA. 377\nB. 126\nC. 111\nD. 727\nE. 121\n\n### Answer:\nLet the numbers be 37a and 37b.\nThen, 37a * 37 b = 4107 => ab = 3\nNow, co-primes with product 3 are (1, 3).\nSo, the required numbers are (37 * 1, 37 * 3) i.e., (1, 111).\nGreater number = 111.\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA carpenter worked alone for 1 day on a job that would take him 6 more days to finish. He and another carpenter completed the job in 6 more days. How many days would it have taken the second carpenter to do the complete job working alone?\n\n### Options:\nA. 4 2/3\nB. 7\nC. 9\nD. 24\nE. 21\n\n### Answer:\nA carpenter worked only 1 day on something that takes him 6 MORE days.\nMeans;\nCarpenter finishes his work in 7 days.\nLet his buddy finish the same task in x days.\nRespective rates per day:\n1/7 AND 1/x\nTo complete 1 work:\nFirst guy worked for 5 days @ rate=1/7 per day.\nSecond one worked for 6 days @ rate=1/x per day\nExpression:\nDays*Rate=Work\n5*1/7+6*1/x=1\n5x+42=7x\n2x=42\nx=21 days.\nAns:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many ways can you arrange 16 people into 4 rows of 4 desks each?\n\n### Options:\nA. 14!\nB. 15!\nC. 16!\nD. 17!\nE. 18!\n\n### Answer:\nfor 1st person there are 16 places\nfor 2nd person there are 15 places\nfor 3rd ..... 14 places\nno. of ways will be = 16*15*14......3*2*1\n= 16!\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe distance that light travels in one year is approximately 5,870,000,000,000 miles. The distance light travels in 100 years is:\n\n### Options:\nA. 111 \u00d7 1827 miles\nB. 999\u00d7 1238 miles\nC. 346 \u00d7 1012 miles\nD. 247 \u00d7 1012 miles\nE. 587 \u00d7 1012 miles\n\n### Answer:\nThe distance of the light travels in 100 years is:\n5,870,000,000,000 \u00d7 100 miles.\n= 587,000,000,000,000 miles.\n= 587 \u00d7 1012 miles.\nAnswer :E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n50% of the population of a village is 23040. The total population of the village is ?\n\n### Options:\nA. 32256\nB. 24000\nC. 44936\nD. 46080\nE. None\n\n### Answer:\nAnswer\n\u2235 50% of P = 23040\n\u2234 P = (23040 x 100) / 50 = 46080\nCorrect Option: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe cost price of an article is 55% of the marked price. Calculate the gain percent after allowing a discount of 15%.\n\n### Options:\nA. 40.5 %\nB. 48.7 %\nC. 54.5%\nD. 55.6% %\nE. none\n\n### Answer:\nSol.\nLet marked price = Rs. 100. Then, C.P. = Rs. 55. S.P = Rs. 85.\n\u00e2\u02c6\u00b4 Gain % = [30/55 * 100]% = 54.5%.\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat two-digit number is less than the sum of the square of its digits by 13 and exceeds their doubled product by 5?\n\n### Options:\nA. 95\nB. 99\nC. 26\nD. 73\nE. None of the Above\n\n### Answer:\nLet the digits be x and y. The number would be 10x + y.\nWe are given that 2xy + 5 = 10x +y = x^2 y^2 -13\nThus 2xy +5 = x^2 + y^2 - 13\nx^2 + y^2 -2xy = 16\n(x-y)^2 = 16\n(x-y) = 4 or -4\nSubstituting the values of (x-y) in the equation 2xy +5 = 10x + y\nx comes out to be 1 or 9... thus the two numbers can be 15 or 99\nThus the answer is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nDavid obtained 70, 60, 78, 60 and 65 marks (out of 100) in English, Mathematics,Physics, Chemistry and Biology What are his average marks ?\n\n### Options:\nA. 75\nB. 27.6\nC. 66.6\nD. 16.5\nE. 11\n\n### Answer:\nExplanation:\nAverage = (70+ 60+ 78+ 60+ 65 )/ 5 = 333/5 = 66.6.\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe cost of Type 1 material is Rs. 15 per kg and Type 2 material is Rs.20 per kg. If both Type 1 and Type 2 are mixed in the ratio of 2 : 3, then what is the price per kg of the mixed variety of material?\n\n### Options:\nA. 18\nB. 20\nC. 25\nD. 30\nE. 35\n\n### Answer:\nType 1 cost = 15\ntype 2 cost = 20\n=>2:3\nhence cost the mixture= (15*2)+(20*3) /(2+3) = 18\nANSWER A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe speed of a boat in upstream is 45 kmph and the speed of the boat downstream is 90 kmph. Find the speed of the boat in still water and the speed of the stream?\n\n### Options:\nA. 70,10 kmph\nB. 67.5,22.5 kmph\nC. 70.5,70.5 kmph\nD. 78.6,10.25 kmph\nE. 70,12 kmph\n\n### Answer:\nSpeed of the boat in still water\n= (45+90)/2\n= 67.5 kmph. Speed of the stream\n= (90-45)/2\n= 22.5 kmph.\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a St.Johns college students, 50 percent are third year students and 80 percent are not second-year students. What fraction of those students who are not third-year students are second-year students?\n\n### Options:\nA. 3/4\nB. 2/5\nC. 4/7\nD. 1/2\nE. 3/7\n\n### Answer:\n= 20/50. = 2/5\nmy answer is B too\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n3 candidates in an election and received 1136, 7636 and 11628 votes respectively. What % of the total votes did the winningcandidate got in that election?\n\n### Options:\nA. 45%\nB. 50%\nC. 57%\nD. 60%\nE. 65%\n\n### Answer:\nTotal number of votes polled = (1136 + 7636 + 11628) = 20400\nSo, Required percentage = 11628/20400 * 100 = 57%\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe speed of a boat in upstream is 50 kmph and the speed of the boat downstream is 90 kmph. Find the speed of the boat in still water and the speed of the stream?\n\n### Options:\nA. 10\nB. 40\nC. 88\nD. 66\nE. 23\n\n### Answer:\nSpeed of the boat in still water = (50+90)/2 = 70 kmph. Speed of the stream = (90-50)/2 = 20 kmph. Answer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFrom the given equation find the value of c: c\u00c2\u00b2-3c-10\n\n### Options:\nA. 1\nB. 3\nC. 5\nD. 2\nE. -5\n\n### Answer:\n(c - 5)(c + 2)\nC = -2 or 5\nAnswer is C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSolution X is 10 percent alcohol by volume, and solution Y is 30 percent alcohol by volume. How many milliliters of solution Y must be added to 200 milliliters of solution X to create a solution that is 25 percent alcohol by volume?\n\n### Options:\nA. 250/3\nB. 500/3\nC. 400\nD. 480\nE. 600\n\n### Answer:\nwe know that X is 10% , Y is 30% and W.Avg = 25% . what does this mean with respect to W.Avg technique ?\nW.Avg is 1 portion away from Y and 3 portion away from X so for every 1 portion of X we will have to add 3 portions of Y.\nIf X = 200 then Y = 600\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many three letter words are formed using the letters of the word THREE?\n\n### Options:\nA. A)117\nB. B)118\nC. C)119\nD. D)120\nE. E)121\n\n### Answer:\nThe number of letters in the given word is five.\nThe number of three letter words that can be formed using these four letters is 5P4\n= 5 * 4 * 3*2 = 120.\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe least number which when divided by 5, 6, 7 and 8 leaves a remainder 3, but when divided by 9 leaves no remainder, is\n\n### Options:\nA. 1677\nB. 1683\nC. 2523\nD. 3363\nE. None of these\n\n### Answer:\nExplanation:\nL.C.M of 5, 6, 7, 8 = 840\ntherefore Required Number is of the form 840k+3.\nLeast value of k for which (840k+3) is divisible by 9 is k = 2\ntherefore Required Number = (840 x 2+3)=1683. Answer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf (2)^n=(1/2)^2, what is the value of n?\n\n### Options:\nA. -2\nB. -1\nC. 0\nD. 1\nE. 2\n\n### Answer:\n(2)^n = (1/2)^2\n= (2)^-2\nn = -2 (Answer = A)\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAverage of money that group of 4 friends pay for rent each month is $800.After one persons rent is increased by 20% the new mean is $860.What was original rent of friend whose rent is increased?\n\n### Options:\nA. 800\nB. 900\nC. 1000\nD. 1100\nE. 1200\n\n### Answer:\n0.2X = 4(860-800)\n0.2X = 240\nX = 1200\nAnswer E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRose went to a shop and bought things worth Rs. 25, out of which 30 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?\n\n### Options:\nA. 19\nB. 19.7\nC. 19.9\nD. 20.1\nE. 20.4\n\n### Answer:\nTotal cost of the items he purchased = Rs.25\nGiven that out of this Rs.25, 30 Paise is given as tax\n=> Total tax incurred = 30 Paise = Rs.30/100\nLet the cost of the tax free items = x\nGiven that tax rate = 6%\n\u2234 (25\u221230/100\u2212x)6/100 = 30/100\n\u21d2 6(25 \u22120.3 \u2212x) = 30\n\u21d2 (25 \u2212 0.3 \u2212 x) = 5\n\u21d2 x = 25 \u2212 0.3 \u2212 5 = 19.7\nB)\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA cube of edge 16cm is immersed completely in a rectangular vessel containing water. If the dimensions of the base of vessel are 20cm * 15cm , find the rise in water level?\n\n### Options:\nA. 6cm\nB. 8.25cm\nC. 13.65cm\nD. 15.12cm\nE. 20.62cm\n\n### Answer:\nIncrease in volume = volume of the cube = 16*16*16 cm^3\nRise in water level = volume / area = 16*16*16/20*15 = 13.65cm\nAnswer is C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf P represents the product of the first 14 positive integers, then P is NOT a multiple of\n\n### Options:\nA. 99\nB. 84\nC. 72\nD. 65\nE. 34\n\n### Answer:\nAnswer is E.\nSince prime factor of 57 is 2x17. 17 is a prime number and not part of the first 14 positive integers.\nA) 9 x 11\nB) 12 x 7\nC) 12 x 6\nD) 13 x 5\nE) 2 x 17\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain kind of necklace is made from 9 yellow, 6 blue, and 3 silver beads. What is the maximum number of these necklaces that can be made from 63 beads of each color ?\n\n### Options:\nA. 7\nB. 6\nC. 5\nD. 4\nE. 3\n\n### Answer:\nAtleast 9 yellow breads are needed to make a necklace, so irrespective of the combinations of blue and silver beads, the number of necklaces that can be formed will be\n63/9 =7\nAnswer:- A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA single discount equivalent to the discount series of 20%, 10% and 5% is?\n\n### Options:\nA. 31.7\nB. 31.2\nC. 31.6\nD. 31.1\nE. 31.3\n\n### Answer:\n100*(80/100)*(90/100)*(95/100) = 68.4\n100 - 68.4 = 31.6\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA grocer has a sale of Rs. 5400, Rs. 9000, Rs. 6300, Rs. 7200 and Rs.4500 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 5600?\n\n### Options:\nA. s. 1200\nB. s. 5400\nC. s. 5400\nD. s. 4999\nE. s. 5000\n\n### Answer:\nTotal sale for 5 months = Rs. (5400 + 9000 + 6300+ 7200 + 4500) = Rs. 32400.\nRequired sale = Rs. [ (5600 x 6) - 32400 ]\n= Rs. (33600 - 32400)\n= Rs.1200.\nOption A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many positive integers less than 256 are multiple of 4 but NOT multiples of 6?\n\n### Options:\nA. 20\nB. 31\nC. 42\nD. 53\nE. 44\n\n### Answer:\n248/4=64\nMultiples of 4 which are a multiple of 6 will be of the form 2*2*3=12n where n>0\n240/12=20\n64-20=44\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe area of a base of a cone is 30 cm2. If the height of the cone is 6cm, find its volume?\n\n### Options:\nA. 87\nB. 16\nC. 17\nD. 60\nE. 18\n\n### Answer:\n\u03c0r2 = 30 h = 6\n1/3 * 30 * 6 = 60\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA bullet train leaves Kyoto for Tokyo traveling 240 miles per hour at 12 noon. Ten minutes later, a train leaves Tokyo for Kyoto traveling 160 miles per hour. If Tokyo and Kyoto are 400 miles apart, at what time will the trains pass each other?\n\n### Options:\nA. 12:40pm\nB. 12:49pm\nC. 12:55pm\nD. 1:00pm\nE. 1:04pm\n\n### Answer:\nTrain A: going from K to T\nTrain B: going from T to K\nFirst I calculated how far Train A will have travelled by the time Train B starts at 12:10:\n10 minutes at 240 mph\n1/6*240=40miles\nThey have 400-40=360 miles to travel to meet each other.\nI found the combined rate of the two trains\nRate(A) + Rate(B) = 400mph\nDivide Distance/Rate to find total time each will travel:\n360/400>>> 54 Minutes to meet\n12:10+54 minutes = 01:04 or Answer E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe product of all the prime numbers less than 22 is closest to which of the following powers of 10?\n\n### Options:\nA. 10^9\nB. 10^8\nC. 1*10^7\nD. 10^6\nE. 10^5\n\n### Answer:\nQuickly approximate\n2, 3, 5, 7, 11, 13, 17, 19\n=2.1x10^2*1.3*1.7*1.9\n=9.69* 10^6\n=1*10^7\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA retailer buys a radio for Rs 225. His overhead expenses are Rs 20. He sellis the radio for Rs 300. The profit percent of the retailer is\n\n### Options:\nA. 22.4%\nB. 50%\nC. 25%\nD. 52%\nE. None of these\n\n### Answer:\nExplanation:\ncost price = (225 + 20) = 245 sell price = 300\ngain = (55/245)*100 = 22.4%. Answer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTATA company plans to assign identification numbers to its employees. Each number is to consist of four different digits from 0 to 9, inclusive, except that the first digit cannot be 0. How many different identification numbers are possible?\n\n### Options:\nA. 3,024\nB. 4,536\nC. 5,040\nD. 9,000\nE. 10,000\n\n### Answer:\nTATA company plans to assign identification numbers to its employeeS.The first digit can take 9 values from 1 to 9 inclusive;\nThe second digit can also take 9 values (9 digits minus the one we used for the first digit plus 0);\nThe third digit can take 8 values;\nThe fourth digit can take 7 values.\nTotal = 9*9*8*7 = something with the units digit if 6.\nAnswer: B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOf the 20,210 employees of the anvil factory, 2/7 are journeymen. If half of the journeymen were laid off, what percentage of the total remaining employees would be journeymen?\n\n### Options:\nA. 14.3%\nB. 16.67%\nC. 33%\nD. 28.6%\nE. 49.67%\n\n### Answer:\nThe exam gives us a number that is easily divisible by 7 to pique our curiosity and tempt us into calculating actual numbers (also because otherwise the ratio would be incorrect). Since the question is about percentages, the actual numbers will be meaningless, as only the ratio of that number versus others will be meaningful. Nonetheless, for those who are curious, each 1/7 portion represents (14210/7) 2,030 employees. This in turn means that 4,060 employees are journeymen and the remaining 10,150 are full time workers.\nIf half the journeymen were laid off, that would mean 1/7 of the total current workforce would be removed. This statistic is what leads many students to think that since half the journeymen are left, the remaining journeymen would represent half of what they used to be, which means 1/7 of the total workforce. If 1/7 of the workforce is journeymen, and 1/7 is roughly 14.3%, then answer choice A should be the right answer. In this case, though, it is merely the tempting trap answer choice.\nWhat changed between the initial statement and the final tally? Well, you let go of 1/7 of the workforce, so the total number of workers went down. The remaining workers are still 1/7 of the initial workers, but the group has changed. The new workforce is smaller than the original group, specifically 6/7 of it because 1/7 was eliminated. The remaining workers now account for 1/7 out of 6/7 of the force, which if we multiply by 7 gives us 1 out of 6. This number as a percentage is answer choice B, 49.67%.\nUsing the absolute numbers we calculated before, there were 4,060 journeymen employees out of 14,210 total. If 2,030 of them are laid off, then there are 2,030 journeyman employees left, but now out of a total of (14,210-2,030) 12,180 employees. 2,030/12,180 is exactly 1/6, or 16.67%. The answer will work with either percentages or absolute numbers, but the percentage calculation will be significantly faster and applicable to any similar situation.\nThe underlying principle of percentages (and, on a related note, ratios) can be summed up in the brainteaser I like to ask my students: If you\u2019re running a race and you overtake the 2nd place runner just before the end, what position do you end up in?\nThe correct answer is 2nd place.\nPercentages, like ratios and other concepts of relative math, depend entirely on the context. Whether 100% more of something is better than 50% more of something else depends on the context much more than the percentages quoted. When it comes to percentages on the GMAT, the goal is to understand them enough to instinctively not fall into the traps laid out for you.E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe length of the bridge, which a train 130 meters long and travelling at 45 km/hr can cross in 30 seconds, is?\n\n### Options:\nA. 178\nB. 169\nC. 245\nD. 178\nE. 119\n\n### Answer:\nSpeed = (45 * 5/18) m/sec = (25/2) m/sec. Time = 30 sec. Let the length of bridge be x meters. Then, (130 + X)/30\n= 25/2 ==> 2(130 + X) = 750 ==> X\n= 245 m.\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 2x + y = 7 and x + 2y = 5, then 5xy/3 =?\n\n### Options:\nA. A) 5\nB. B) 2\nC. C) 17/5\nD. D) 18/5\nE. E) 4\n\n### Answer:\n2*(x+2y = 5) equals 2x+4y=10\n2x+4y=10\n- 2x + y= 7\n= 3y=3\nTherefore Y = 1\nPlug and solve...\n2x + 1 = 7\n2x=6\nx=3\n(5*3*1)/3\n= 15/3\n=5\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOn the xy-plane, each point on circle C has coordinates such\nthat x 0 and y 0. If the center of circle C is the point (3; 12),\nwhat is the maximum possible area of C?\n\n### Options:\nA. 6\nB. 9\nC. 24\nD. 32\nE. 64\n\n### Answer:\nI think that theintentof this question is that the circle will have NO CO-ORDINATES that fit the following 2 forms: (0, Y) or (X, 0). In real basic terms, this circle will NEITHER touch (nor cross) the X-axis NOR will it touch (nor cross) the Y-axis.\nWith a center at (3,8), the longest possible radius would ALMOST touch the X-axis, so the radius would be a little less than 3.\nIf the radius WAS 3 exactly, then the area would be 9pi, which is approximately 28.26\nSince the circle CAN'T touch the X-axis, the area has to be LESS than approximately 28.26\nAs it's written, none of the answers is clearly the correct one.\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA rectangular room has the rectangular shaped rug shown as above figure such that the rug\u2019s area is 160 square feet and its length is 6 feet longer than its width. If the uniform width between the rug and room is 6 feet, what is the area of the region uncovered by the rug (shaded region), in square feet?\n\n### Options:\nA. 32\nB. 456\nC. 40\nD. 46\nE. 104\n\n### Answer:\nRug's area = 160\nwhich is (x) x (6+x) = 160\nso x= 10\nrug maintains a uniform distance of 6 feet\nso room has dimension 10+12 and 16+12 i.e. 22 and 28\narea of room 22x28 = 616\narea covered is 160\nso uncovered area is 616-160=456 (ANSWER B)\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA merchant gains or loses, in a bargain, a certain sum. In a second bargain, he gains 550 dollars, and, in a third, loses 120. In the end he finds he has gained 300 dollars, by the three together. How much did he gain or lose bv the first ?\n\n### Options:\nA. -130\nB. 120\nC. 130\nD. -80\nE. None\n\n### Answer:\nIn this sum, as the profit and loss are opposite in their nature, they must be distinguished by contrary signs. If the profit is marked +, the loss must be -.\nLet x = the sum required.\nThen according to the statement x + 550 - 120 = 300\nAnd x = -130.\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the greatest possible (straight line) distance, between any two points on a hemisphere of radius 5?\n\n### Options:\nA. 0.1\nB. 10\nC. \u03c0/10\nD. 8\nE. \u03c0\n\n### Answer:\nMaximum distance straight line is diameter\nd = 2r = 10..\nANS option B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFive drainage pipes, each draining water from a pool at the same constant rate, together can drain a certain pool in 16 days. How many additional pipes, each draining water at the same constant rate, will be needed to drain the pool in 4 days?\n\n### Options:\nA. 6\nB. 9\nC. 10\nD. 12\nE. 15\n\n### Answer:\nThis is an inverse proportional problem......\n5 pipes in 16 days; So for 4 days, it will be = 16 x 5 / 4 = 20\nSo, 20-5 = 15\nAnswer E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA bag consists of 1 rupee, 50 paise and 25p coins and their total value in rupees is Rs 1120 .These three types of coins are in the ratio 3:20:4. How may 25 paisa coins are there?\n\n### Options:\nA. 30 coins\nB. 330 coins\nC. 320 coins\nD. 32 coins\nE. 10 coins\n\n### Answer:\nThe ratio is 100p: 50 p : 25 p =4 : 2: 1\nThe coins are in the ratio = 3 :20: 4\nThe ratio of their values in rupees=> 12 :40 :4\nThe value of 25 p coins in total Rs 1120 = 1120 x 4/56= 80 rupees\nNumber of 25 p coins are = 80x4 = 320 coins\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n16.02 \u00d7 0.001 = ?\n\n### Options:\nA. 0.1602\nB. 0.001602\nC. 1.6021\nD. 0.01602\nE. None of these\n\n### Answer:\n16.02 \u00d7 0.001 = ?\nor,? = 0.01602\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train 200 m long running at 54 kmph crosses a platform in 25 sec. What is the length of the platform?\n\n### Options:\nA. 175\nB. 266\nC. 350\nD. 277\nE. 232\n\n### Answer:\nLength of the platform= 54 * 5/18 * 25 = 375 \u2013 200\n= 175\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nx - y =2\n2x = 2y + 4\nThe system of equations above has how many solutions?\n\n### Options:\nA. None\nB. Exactly one\nC. Exactly two\nD. Infinitely many\nE. Exactly three\n\n### Answer:\nx-y=2 ---------------1\n2x=2y+4 ---------------2\nDivide equation 2 by 2:\n2x/2=(2y+4)/2\nx=y+2\nx-y=2----------------3\nEquation 1 and 3 are equal and thus have infinitely many solutions:\nx-y=2\nx=4, y=2\nx=6, y=4\nx=7, y=5\nAns:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRs. 6000 is lent out in two parts. One part is lent at 7% p.a simple interest and the other is lent at 10% p.a simple interest. The total interest at the end of one year was Rs. 450. Find the ratio of the amounts lent at the lower rate and higher rate of interest?\n\n### Options:\nA. 5:1\nB. 6:3\nC. 5:3\nD. 9:3\nE. 9:1\n\n### Answer:\nLet the amount lent at 7% be Rs. x\nAmount lent at 10% is Rs. (6000 - x)\nTotal interest for one year on the two sums lent\n= 7/100 x + 10/100 (6000 - x) = 600 - 3x/100\n=> 600 - 3/100 x = 450 => x = 5000\nAmount lent at 10% = 1000\nRequired ratio = 5000 : 1000 = 5 : 1\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are two positive numbers in the ratio 5:8. If the larger number exceeds the smaller by 36, then find the smaller number?\n\n### Options:\nA. 25\nB. 66\nC. 77\nD. 60\nE. 44\n\n### Answer:\nLet the two positive numbers be 5x and 8x respectively.\n8x - 5x = 36\n3x = 36 => x = 12\n=> Smaller number = 5x = 60.\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nGuna has 8 flavors of ice cream in him parlor. How many options are there for Thilak to pick a one-flavor, two-flavor, three-flavor, four-flavor, five-flavor, six-flavor,seven-flavor or eight-flavor order?\n\n### Options:\nA. 223\nB. 395\nC. 448\nD. 774\nE. 835\n\n### Answer:\n8C1 + 8C2+ 8C3+8C4+8C5+8C6+8C7+8C8 = 395.\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nCity A to city B, Andrew drove for 1hr at 48 mph and for 3 hours at 60 mph. What was the average speed for the whole trip?\n\n### Options:\nA. 57\nB. 57.5\nC. 61\nD. 61.5\nE. 62.5\n\n### Answer:\nThe total distance is 1\u00d748+3\u00d760=228\nAnd the total time is 4 hours. Hence,\nAverage Speed=(Total Distance/Total Time)\n=228/4=57\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many of the following numbers are divisible by 3 but not by 9 ?\n2133, 2343, 3474, 4131, 5286, 5340, 6336, 7347, 8115, 9276\n\n### Options:\nA. 5\nB. 6\nC. 7\nD. 8\nE. None of these\n\n### Answer:\nExplanation:\nMarking (/) those which are are divisible by 3 by not by 9 and the others by (X), by taking the sum of digits, we get:s\n2133 -> 9 (X)\n2343 -> 12 (/)\n3474 -> 18 (X)\n4131 -> 9 (X)\n5286 ->21 (/)\n5340 -> 12 (/)\n6336 -> 18 (X)\n7347 -> 21 (/)\n8115 -> 15 (/)\n9276 -> 24 (/)\nRequired number of numbers = 6.\nANSWER IS B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the probability that when a hand of 5 cards is drawn from a well shuffled deck of 52 cards,\nit contains all Queens?\n\n### Options:\nA. 192/3790\nB. 192/379015\nC. 193\nD. Cannot be determined\nE. None\n\n### Answer:\nnCr = n!/(n-r)!r!\nTotal number of possible hands = 52C5\n52C5 = 2274090\nNumber of hands with 4 Queens = 4C4 \u00d7 48C1\n4C4 = 24\n48C1 = 48\n(other 1 card must be chosen from the rest 48 cards)\nHence P (a hand will have 4 Queens) = (4C4 \u00d7 48C1)/52C5 = 192/379015.\nOption is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man is standing on a railway bridge which is 165 m long. He finds that a train crosses the bridge in 20 seconds but himself in 8 seconds. Find the length of the train and its speed.\n\n### Options:\nA. 10 m/sec\nB. 13.75 m/sec\nC. 18 m/sec\nD. 19 m/sec\nE. 25 m/sec\n\n### Answer:\nIf length of train is l and speed of train is s, then\nl/s = 8\n(l+165)/s = 20\n(l+165)/l = 20/8 =5/2\n2l+330 =5*l\n3*l= 330\nl=110 mtrs\ns= l/8 = 110/8 = 13.75 m/sec\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA bag contains 12 white &18 black balls. 2balls are drawn in succession. What is the probability that first is white and second is black?\n\n### Options:\nA. 31/113\nB. 36/145\nC. 30/117\nD. 31/213\nE. 1/412\n\n### Answer:\nThe probability that first ball is white:\n=12C130C1=12C130C1\n=1230=1230\n=25=25\nSince, the ball is not replaced; hence the number of balls left in bag is 29.\nHence, the probability the second ball is black:\n=18C129C1=18C129C1\n=1829=1829\nRequired probability,\n=(25)\u00d7(1829)=(25)\u00d7(1829)\n=36/145\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 47, then how old is B?\n\n### Options:\nA. 17 years\nB. 19 years\nC. 18 years\nD. 10 years\nE. 12 years\n\n### Answer:\nLet C's age be x years.\nThen, B's age = 2x years.\nA's age = (2x + 2) years.\n(2x + 2) + 2x + x = 47\n5x = 45 => x = 9\nHence, B's age = 2x = 18 years.\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA can do a certain job in 18 days. B is 60% more efficient than A. How many days does B alone take to do the same job?\n\n### Options:\nA. 11 1/4 days\nB. 8 days\nC. 5 days\nD. 9 days\nE. None of them\n\n### Answer:\nRatio of times taken by A and B = 160 : 100 = 8 : 5.\nSuppose B alone takes x days to do the job.\nThen, 8 : 5 :: 18 : x = 8x = 5 x 18 =x = 11 1/4 days.\nAnswer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA sun is divided among X, Y and Z in such a way that for each three rupees X gets, Y gets two rupees and Z gets 80 paisa. If the share of Y is RS. 55, what is the total amount of X and Y?\n\n### Options:\nA. 120\nB. 124.5\nC. 104.5\nD. 114.5\nE. 100\n\n### Answer:\nx:y:z = 300:200:80\n15:10:4\n10 --- 55\n19 --- ? => 104.5\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nExactly 36% of the numbers in set W are even multiples of 3. If 40% of the even integers in set W are not multiples of 3, what percent of the numbers in set W are not even integers?\n\n### Options:\nA. 76%\nB. 60%\nC. 50%\nD. 40%\nE. 24%\n\n### Answer:\nEverything is correct except the red part with a typo: it should be N=0.6W --> even numbers are 60% of W --> 40% of W are not even integers.\nAnswer: D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA, Band C can do a piece of work in 11 days, 20 days and 20 days respectively, working alone. How soon can the work be done if A is assisted by Band C on alternate days?\n\n### Options:\nA. 7 days\nB. 8 days\nC. 9 days\nD. 10 days\nE. 11 days\n\n### Answer:\n(A+B)'s 1 day's work = 1/11+1/20 = 31/220\n(A+C)'s 1 day's work = 1/11+1/20 = 31/220\nwork done in 2 day's = 31/220+31/220= 31/110\n31/110th work done in 2 days\nwork done= 110/31*2 = 7 days (approx)\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nBill made a profit of 10% by selling a product. If he had purchased that product for 10% less and sold it at a profit of 30%, he would have received $28 more. What was his original selling price?\n\n### Options:\nA. $200\nB. $260\nC. $320\nD. $380\nE. $440\n\n### Answer:\nLet P be the original purchase price of the product.\nBill originally sold the product for 1.1*P.\nIn the second scenario, the purchase price is 0.9*P.\nA 30% profit means the selling price would be 1.3*0.9*P = 1.17*P\nThus, according to the information in the question, 1.17P - 1.1P = 28\n0.07 = 28\nP = 400\nThe original selling price was 400*1.1 = 440.\nThe correct answer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nI bought two books; for Rs.480. I sold one at a loss of 15% and other at a gain of 19% and then I found each book was sold at the same price. Find the cost of the book sold at a loss?\n\n### Options:\nA. 657\nB. 280\nC. 438\nD. 289\nE. 427\n\n### Answer:\nx*(85/100)\n= (480 - x)119/100\nx = 280\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe letters D, G, I, I , and T can be used to form 5-letter strings as DIGIT or DGIIT. Using these letters, how many 5-letter strings can be formed in which the two occurrences of the letter I are separated by at least one other letter?\n\n### Options:\nA. 12\nB. 18\nC. 24\nD. 36\nE. 48\n\n### Answer:\nTotal no of ways arranging 5 letter with one letter redundant is 5!/2!=60\nNo of ways two I's can be together 4!=24\nno of ways at least one alpha is between two I's =60-24=36\nANS:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe sides of a square region, measured to the nearest centimeter, are 10 centimeters long. The least possible value of the actual area of the square region is\n\n### Options:\nA. 96.25 sq cm\nB. 98.25 sq cm\nC. 92.25 sq cm\nD. 100.25 sq cm\nE. 90.25 sq cm\n\n### Answer:\nThough there might be some technicalities concerning the termnearest(as 9.5 is equidistant from both 9 and 10) the answer still should be : 9.5^2=90.25.\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA monkey ascends a greased pole 22 meters high. He ascends 2 meters in the first minute and then slips down 1 meter in the alternate minute. If this pattern continues until he climbs the pole , in how many minutes would he reach at the top of the pole ?\n\n### Options:\nA. 40th minute\nB. 41st minute\nC. 43rd minute\nD. 42nd minute\nE. 45th minute\n\n### Answer:\nThe money is climbing 1meter in 2min. This pattern will go on till he reaches 20meters. I mean this will continue for first 20*2=40mins. he would have reached 20meters. After that he will climb 2meters and he will reach the pole. So total time taken = 40 + 1 = 41mins.\nSo, asnwer will be B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn an office, totally there are 5200 employees and 45% of the total employees are males. 50% of the males in the office are at-least 50 years old. Find the number of males aged below 50 years?\n\n### Options:\nA. 1040\nB. 1170\nC. 1150\nD. 4160\nE. None of these\n\n### Answer:\nNumber of male employees = 5200* 45/100 = 2340\nRequired number of male employees who are less than 50 years old = 4160 * (100 - 50)%\n= 2340* 50/100 = 1170.\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe value of (9x10^8)(5x10^9) is closest to which of the following?\n\n### Options:\nA. 10^19\nB. 10^15\nC. 10^16\nD. 10^14\nE. 10^12\n\n### Answer:\nmultiplying these we get,\n45 x 10^8 x 10^9\n= 4.5 x 10^18\nwhich is closer to 10^19\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nVirginia, Adrienne, and Dennis have taught history for a combined total of 102 years. If Virginia has taught for 9 more years than Adrienne and for 9 fewer years than Dennis, for how many years has Dennis taught?\n\n### Options:\nA. 23\nB. 32\nC. 35\nD. 43\nE. 44\n\n### Answer:\nLet number of years taught by Virginia = V\nnumber of years taught by Adrienne = A\nnumber of years taught by Dennis = D\nV+A+D = 96\nV= A+9\n=>A = V-9\nV= D-9\n=> A = (D-9)-9 = D-18\nD-9 + D-18 + D =102\n=> 3D = 102 + 27 = 129\n=> D = 43\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo trains travel in opposite directions at 36 kmph and 45 kmph and a man sitting in slower train passes the faster train in 8 seconds. The length of the faster train is\n\n### Options:\nA. 80 m\nB. 100 m\nC. 120 m\nD. 180 m\nE. None\n\n### Answer:\nSolution\nRelative Speed\t= (36 + 45) km/hr\n= (81 x 5/18) m/sec\n= (45/2) m/sec\nLength of the train\t= (45 / 2 x 8) m\n= 180 m.\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMrs. Rodger got a weekly raise of $147. If she gets paid every other week, write an integer describing how the raise will affect her paycheck.\n\n### Options:\nA. $140\nB. $141\nC. $142\nD. $147\nE. $145\n\n### Answer:\nLet the 1st paycheck be x (integer).\nMrs. Rodger got a weekly raise of $ 147.\nSo after completing the 1st week she will get $ (x+147).\nSimilarly after completing the 2nd week she will get $ (x + 147) + $ 147.\n= $ (x + 147 + 147)\n= $ (x + 294)\nSo in this way end of every week her salary will increase by $ 147.\ncorrect answer D)$147\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf fy > 0 and yz < 0, which of the following must be negative:\n\n### Options:\nA. fyz\nB. fy(z^2)\nC. f(y^2)z\nD. x(y^2)(z^2)\nE. (x^2)(y^2)(z^2)\n\n### Answer:\nfy > 0 means that fy is positive.\nyz < 0 means that yz is negative.\nf(y^2)z = (fy)(yz) = positive*negative = negative. Thus option C is always negative.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA car covers a distance of 660 km in 6 hours. Find its speed?\n\n### Options:\nA. 104\nB. 7778\nC. 266\nD. 110\nE. 121\n\n### Answer:\n660/6 = 110 kmph\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the value of (70+ 28/100) \u00d7 100\n\n### Options:\nA. 7028\nB. 4028\nC. 3128\nD. 3256\nE. 5264\n\n### Answer:\n(7000 +28)/100 * 100 = 7028\nAnswer : A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a queue if 30 children were made to stand in a column, 16 columns could be formed. If 24 children were made to stand in a column, how many columns could be formed?\n\n### Options:\nA. 10\nB. 20\nC. 25\nD. 36\nE. 40\n\n### Answer:\nSol. Required number = 16 *^30 = 20\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how many ways can the letters of the word 'LEADER' be arranged?\n\n### Options:\nA. 72\nB. 144\nC. 360\nD. 720\nE. None of these\n\n### Answer:\nExplanation:\nThe word 'LEADER' contains 6 letters, namely 1L, 2E, 1A, 1D and 1R.\nRequired number of ways =\t6! / (1!)(2!)(1!)(1!)(1!) =360.\nANSWER IS C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 144/0.144 = 14.4/x, then the value of x is:\n\n### Options:\nA. 2.\nB. 1.\nC. -1.\nD. -2.\nE. 0\n\n### Answer:\nGiven Expression\n=[a(Power2) - b(Power 2)]/(a + b)(a - b)\n=[a(Power 2 - b(Power 2)]/[a(Power 2) - b(Power 2)]\n= 1.\nAnswer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA and B can do a work in 6 days, B and C in 2 days and C and A in 8 days. In how many days will the work be completed, if all three of them work together?\n\n### Options:\nA. 12/24\nB. 48/63\nC. 45/56\nD. 48/19\nE. 28/12\n\n### Answer:\nOne day work of A and B = 1/6\nOne day work of B and C = 1/2\nOne day work of C and A = 1/8\n2(A + B + C) = 1/6 + 1/2 + 1/8\n2(A + B + C) = 19/24\n(A + B + C) = 19/48\nNumber of days required = 48/19 days.\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe length of the longest rod that can fit in a cubical room of 4 m side is?\n\n### Options:\nA. 100%\nB. 108%\nC. 120%\nD. 110%\nE. 101%\n\n### Answer:\n100%\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRavi's brother is 3 years senior to him. His father was 28 years of age when his sister was born while his mother was 26 years of age when he was born. If his sister was 4 years of age when his brother was born, what were the ages of Ravi's father and mother respectively when his brother was born ?\n\n### Options:\nA. 32 years, 23 years\nB. 32 years, 29 years\nC. 35 years, 29 years\nD. 35 years, 33 years\nE. 36 years, 33 years\n\n### Answer:\nExplanation:\nWhen Ravi's brother was born, let Ravi's father's age = x years and mother's age = y years.\nThen, sister's age = (x - 28) years. So, x - 28 = 4 or x = 32.\nRavi's age = (y - 26) years.\nAge of Ravi's brother = (y - 26 + 3) years = (y - 23) years.\nNow, when Ravi's brother was born, his age = 0 i.e. y - 23 = 0 or y = 23.\nAnswer: A) 32 years, 23 years\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAfter replacing an old member by a new member, it was found that the average age of five members of a club is the same as it was 3 years ago. What is the difference between the ages of the replaced and the new member ?\n\n### Options:\nA. 37\nB. 29\nC. 11\nD. 15\nE. 12\n\n### Answer:\nExplanation:\ni) Let the ages of the five members at present be a, b, c, d & e years.\nAnd the age of the new member be f years.\nii) So the new average of five members' age = (a + b + c + d + f)/5 ------- (1)\niii) Their corresponding ages 3 years ago = (a-3), (b-3), (c-3), (d-3) & (e-3) years\nSo their average age 3 years ago = (a + b + c + d + e - 15)/5 = x ----- (2)\n==> a + b + c + d + e = 5x + 15\n==> a + b + c + d = 5x + 15 - e ------ (3)\niv) Substituting this value of a + b + c + d = 5x + 15 - e in (1) above,\nThe new average is: (5x + 15 - e + f)/5\nEquating this to the average age of x years, 3 yrs, ago as in (2) above,\n(5x + 15 - e + f)/5 = x\n==> (5x + 15 - e + f) = 5x\nSolving e - f = 15 years.\nThus the difference of ages between replaced and new member = 15 years.\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA and B put in Rs.300 and Rs.400 respectively into a business. A reinvests into the business his share of the first year's profit of Rs.238 where as B does not. In what ratio should they divide the second year's profit?\n\n### Options:\nA. 220:113\nB. 201:200\nC. 210:201\nD. 100:99\nE. 113:77\n\n### Answer:\nExplanation:\n3: 4\nA = 3/7*238 = 102\n402: 400\n201:200\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train of length 250 metres takes 45 seconds to cross a tunnel of length 350metres. What is the speed of the train in km/hr?\n\n### Options:\nA. 10 km/hr.\nB. 240 km/hr.\nC. 30 km/hr.\nD. 24 km/hr.\nE. None\n\n### Answer:\nSol.\nSpeed = [250 + 350/ 45] m/sec = [600 / 45 * 18/5] km/hr = 24 km/hr.\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAfter 10% of the inhabitants of a village disappeared, a panic set in during which 25% of the remaining inhabitants left the village. At that time, the population was reduced to 5130. What was the number of original inhabitants?\n\n### Options:\nA. 7300\nB. 7600\nC. 7900\nD. 8200\nE. 8500\n\n### Answer:\nLet the total number of original inhabitants be x.\n(75/100) * (90/100) * x = 5130\n(27/40) * x = 5130\nx = 5130 * 40 / 27 = 7600\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhen x is divided by 3, the quotient is y and the remainder is 1. When x is divided by 5, the quotient is z and the remainder is 6. Which of the following is the value of y in terms of z?\n\n### Options:\nA. 4z/7 + 5\nB. (7z + 5) / 6\nC. (6z + 7) / 4\nD. (5z + 5) / 3\nE. (4z + 6) / 7\n\n### Answer:\nWhen x is divided by 3, the quotient is y and the remainder is 1: x = 3y + 1.\nWhen x is divided by 5, the quotient is z and the remainder is 6: x = 5z + 6.\nEquate those two:\n3y + 1 = 5z + 6;\ny = (5z + 5)/3.\nAnswer: D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man can row a boat at 20 kmph in still water. If the speed of the stream is 6 kmph, what is the time taken to row a distance of 72 km downstream?\n\n### Options:\nA. 30/16 hours\nB. 36/13 hours\nC. 30/73 hours\nD. 30/13 hours\nE. 50/13 hours\n\n### Answer:\nSpeed downstream = 20 + 6 = 26 kmph.\nTime required to cover 60 km downstream\n= d/s = 72/26\n= 36/13 hours.\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe overall age of X and Y is 12 year greater than the overall age of Y and Z. Z is how many decades younger that X?\n\n### Options:\nA. 11\nB. 15\nC. 12\nD. 17\nE. 19\n\n### Answer:\nC\n12\n(X + Y) \u2013 (Y + Z) = 12\nX \u2013 Z = 12\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwelve years ago, P was half of Q in age. If the ratio of their present ages is 3:4, what will be the total of their present ages\n\n### Options:\nA. A)35\nB. B)34\nC. C)42\nD. D)25\nE. E)26\n\n### Answer:\nExplanation:\nLet the present age of P and Q be 3x and 4x respectively.\nTwelve years ago, P was half of Q in age\n=> 2(3x \u2013 12) = (4x \u2013 12)\n=> 6x \u2013 24 = 4x \u2013 12\n=> 2x = 12\n=> x = 6\n7x = 7*6 = 42\nAnswer: Option C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n10 friends went to a hotel and decided to pay the bill amount equally. But 9 of them could pay Rs. 50 each as a result 10th has to pay Rs. 180 extra than his share. Find the amount paid by him.\n\n### Options:\nA. 130\nB. 140\nC. 110\nD. 120\nE. None\n\n### Answer:\nExplanation:\nAverage amount paid by 9 persons = Rs. 50\nIncrease in average due to Rs. 50 paid extra by the 10th men = Rs. 180/9= Rs. 20\nTherefore, Average expenditure of 10 friends = Rs. 50 + Rs. 20 = Rs. 70\nTherefore, Amount paid by the 10th men = Rs. 70 + Rs. 50 = Rs. 120\nCorrect Option: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average age of husband, wife and their child 3 years ago was 27 years and that of wife and the child 5 years ago was 20 years. The present age of the husband is?\n\n### Options:\nA. 65 years\nB. 40 years\nC. 54 years\nD. 46 years\nE. 13 years\n\n### Answer:\nSum of the present ages of husband, wife and child\n= (27 * 3 + 3 * 3) = 90 years.\nSum of the present age of wife and child\n= (20 * 2 + 5 * 2) = 50 years.\nHusband's present age\n(90 - 50) = 40 years.\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo pipes A and B can separately fill a tank in 20 minutes and 15 minutes respectively. Both the pipes are opened together but 4 minutes after the start the pipe A is turned off. How much time will it take to fill the tank?\n\n### Options:\nA. 12min\nB. 14min\nC. 15min\nD. 13min\nE. 10min\n\n### Answer:\n4/20 + x/15 = 1\nx = 12\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man saves a certain portion of his income during a year and spends the remaining portion on his personal expenses. Next year his income increases by 35% but his savings increase by 100%. If his total expenditure in 2 years is double his expenditure in 1st year, What %age of his income in the first year did he save?\n\n### Options:\nA. 25%\nB. 28%\nC. 30%\nD. 32.5%\nE. 35%\n\n### Answer:\n1st year Income= I\n1st year savings= S\n1st year Expense= E1\n2nd year Income = 1.35I\n2nd year savings= 2S (100% increase)\n2nd Year expense= E2\nE1+ E2= 2E1\nE2=E1\nThat means Expenses are same during both years. With increase of 35% income the savings increased by 100%.\nor S= .35I\nor S= 35% of Income\nE is the answer\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nx+(1/x) = 4 find x^2 + (1/x^2)\n\n### Options:\nA. 2.25\nB. 3.25\nC. 4.25\nD. 14\nE. 6.25\n\n### Answer:\nsquaring on both sides (x+1/x)^2=4^2\nx^2+1/X^2=16-2\nx^2+1/X^2=14\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nDuring a clearance sale, a retailer discounted the original price of its TVs by 24% for the first two weeks of the month, then for the remainder of the month further reduced the price by taking 20% off the sale price. For those who purchased TVs during the last week of the month, what percent of the original price did they have to pay?\n\n### Options:\nA. 40%\nB. 45%\nC. 55%\nD. 60%\nE. 62%\n\n### Answer:\nVERITAS PREPOFFICIAL SOLUTION:\nD. With percent problems, the key is often to make sure that you take the percent of the correct value. In this case, the initial 25% off means that customers will pay 75% of the original price. Then for the second discount, keep in mind that the discount is taken off of the sale price, not of the original price. So that's 20% off of the 75% that they did pay, which can be made easier by looking at what the customer does pay: 80% of the 75% sale price. Using fractions, that means they pay: 4/5*(3/4) of the original price, which nets to 3/5 of the original price, or 62%.\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 2994 \u00f7 14.5 = 172, then 29.94 \u00f7 1.45 = ?\n\n### Options:\nA. 17.2\nB. 18.2\nC. 19.2\nD. 15.2\nE. 16.2\n\n### Answer:\n29.94/ 1.45 = 299.4/14.5\n= (2994/14.5) x 1/10) [ Here, Substitute 172 in the place of 2994/14.5 ]\n= 172/10\n= 17.2\nAnswer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the solution of the equations x - y = 0.1 and 1(x + y)-1 = 2 ?\n\n### Options:\nA. x = 0.3, y = -0.2\nB. x = 1, y = 0.1\nC. x = 2, y = 1.1\nD. x = 1.2, y = 0.3\nE. None\n\n### Answer:\nAnswer\nx - y = 0.1 ...(i)\nand 1(x + y)-1=2\n\u21d2 1/ (x + y) = 2\n\u21d2 2(x + y) =1\n\u21d2 x + y = 1/2 ...(ii)\nOn solving Eqs.(i) and (ii),we get\nx = 0.3\nand y = -0.2\nCorrect Option: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nCarrie likes to buy t-shirts at the local clothing store. They cost $8.75 each. One day, she bought 18 t-shirts. How much money did she spend?\n\n### Options:\nA. $150\nB. $70\nC. $200\nD. $171.6\nE. $190\n\n### Answer:\n$8.75*18=$70. Answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many words can be formed using the letters of the word \u201cCORPORBTION\u201d?\n\n### Options:\nA. 32441\nB. 24334\nC. 23335\nD. 45566\nE. 50400\n\n### Answer:\nIn the word 'CORPORATION', we treat the vowels OOAIO as one letter.\nThus, we have CRPRTN (OOAIO).\nThis has 7 (6 + 1) letters of which R occurs 2 times and the rest are different.\nNumber of ways arranging these letters =\t7!\t= 2520.\n2!\nNow, 5 vowels in which O occurs 3 times and the rest are different, can be arranged\nin\t5!\t= 20 ways.\n3!\nRequired number of ways = (2520 x 20) = 50400.\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA doctor prescribed 18 cubic centimeters of a certain drug to a patient whose body weight was 75 pounds. If the typical dosage is 2 cubic centimeters per 15 pounds of the body weight, by what percent was the prescribed dosage greater than the typical dosage?\n\n### Options:\nA. 8%\nB. 9%\nC. 11%\nD. 12.5%\nE. 20%\n\n### Answer:\nTypical dosage is Dose : weight :: 2: 15.\nNow if weight is 75 :(75/15)) then typical dosage would be 2 *5 = 10 cc.\nDosage = 18 cc. Dosage is greater by 2 cc.\n% dosage is greater: (2 / 10)*100 = 20 %\nE is the answer.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA confectioner decides to sell all of his pastry due to the coming holiday. His pastry goods are equally divided among a group of 35 regular customers. If only 49 customers come to the bakery, each one will receive 6 less pastry goods. How much pastry does the confectioner needs to sell?\n\n### Options:\nA. 525.\nB. 412.\nC. 432.\nD. 502.\nE. 522.\n\n### Answer:\nPastry is divided in 35 customers equally. So,total number of pastry must be a multiple of 35\nOnly option A satisfies the condition, and hence is the answer\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a and b are nonzero integers such that 2a+1 = 5b+1, then each of the following must be true EXCEPT\n\n### Options:\nA. 0 < b/a < 1\nB. ab is positive.\nC. On the number line, b lies between 0 and a.\nD. The ratio of a to b is equivalent to 10/4.\nE. a \u2013 b is positive.\n\n### Answer:\nThis question can be solved by TESTing VALUES. Based on its wording, you would likely need to do 2 TESTs to get to the correct answer though.\nWe're told that A and B are NONZERO INTEGERS and that 2a+1 = 5b+1 or 2A = 5b. We're told that each of the answer is always true EXCEPT for one of them...\nBefore we get to the actual work, it's important to note a few details:\n1) We are NOT told that A and B are positive - we're just told that they're NONZERO - that's interesting - it means that we have to consider the possibility that they're both NEGATIVE...\n2) 4 of the answers will always be true, while one of them will EITHER be sometimes true OR never true. We'll have to keep working until we find 1 answer that is not true (for whatever reason) - that will be the solution to this question.\nSince 2A = 5B, I'm going to run 2 pairs of TESTs at the same time...\nA = 5\nB = 2\nAND\nA = -5\nB = -2\nAnswer A: 0 < B/A < 1\n2/5 and -2/-5 both = 2/5. Answer A appears true.\nAnswer B: AB is positive\n(2)(5) and (-2)(-5) both = +10. Answer B appears true.\nAnswer C: B is between 0 and A on the number line\n0....2....5\n-5....-2....0\nAnswer C appears true.\nAnswer D: A/B = 10/4\n5/2 = -5/-2\n10/4 = 5/2\nAnswer D appears true.\nAnswer E: A - B is positive\n5 - 2 = 3\n-5 - (-2) = -3 *****This is NOT always true.\nFinal Answer:\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJanuary 1, 2008 is Saturday. What day of the week lies on Jan 1, 2009?\n\n### Options:\nA. Saturday\nB. Wednesday\nC. Thursday\nD. Tuesday\nE. Monday\n\n### Answer:\nExplanation:\nNumber of odd days in 2008 = 2 (since it is a leap year)\n(we have taken the complete year 2008 because we need to find out the odd days from 01-Jan-2008 to 31-Dec-2008, that is the whole year 2008)\nGiven that January 1, 2008 is Saturday.\nHence January 1, 2009 = (Saturday+ 2 odd days) = Monday\nAnswer: Option E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nLook at this series: 28, 25, 30, 27, 32, 29, ... What number should come next?\n\n### Options:\nA. 32\nB. 34\nC. 30\nD. 31\nE. 36\n\n### Answer:\nExplanation:\nIn this simple alternating subtraction and addition series; 3 is subtracted, then 5 is added, and so on.\nAnswer: Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA is half good a work man as B and together they finish a job in 14 days. In how many days working alone B finish the job?\n\n### Options:\nA. 76 days\nB. 21 days\nC. 97 days\nD. 45 days\nE. 97 days\n\n### Answer:\nWC = 1:2\n2x + x = 1/14 => x = 1/42\n2x = 1/21 => 21 days\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nX can do a piece of work in 40 days; Y can do the same in 30 days. X started alone but left the work after 10 days, then Y worked at it for 10 days. Z finished the remaining work in 10 days. Z alone can do the whole work in?\n\n### Options:\nA. days\nB. days\nC. days\nD. 1/2 days\nE. days\n\n### Answer:\nExplanation:\n10/40 + 10/30 + 10/x = 1\nx = 24 days\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the number that fits somewhere into the middle of the series. Some of the items involve both numbers and letters\nLook at this series: VI, 10, V, 11, __, 12, III, ... What number should fill the blank?\n\n### Options:\nA. IV\nB. X\nC. VI\nD. V\nE. III\n\n### Answer:\nA\nIV\nThis is an alternating addition and subtraction series. Roman numbers alternate with Arabic numbers. In the Roman numeral pattern, each number decreases by 1. In the Arabic numeral pattern, each number increases by 1.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nBy selling 11 pencils for a rupee a man loses 30%. How many for a rupee should he sell in order to gain 30%?\n\n### Options:\nA. 8\nB. 7\nC. 6\nD. 11\nE. 9\n\n### Answer:\n70% --- 12\n130% --- ?\n70/130 * 11\n= 6\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA cube of side one meter length is cut into small cubes of side 10 cm each. How many such small cubes can be obtained?\n\n### Options:\nA. 288\nB. 2889\nC. 1000\nD. 2770\nE. 27912\n\n### Answer:\nAlong one edge, the number of small cubes that can be cut\n= 100/10 = 10\nAlong each edge 10 cubes can be cut. (Along length, breadth and height). Total number of small cubes that can be cut = 10 * 10 * 10 = 1000\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRichard has to paint a mural with seven horizontal stripes. He only has enough paint for four red stripes, four blue stripes, four white stripes, four black stripes, and four yellow stripes. If his patron wants at most two different colors in the mural, how many different ways can he paint the wall?\n\n### Options:\nA. 120\nB. 350\nC. 700\nD. 2,520\nE. 5,040\n\n### Answer:\nNumber of ways to choose 2 colors among 5 - 5c2\nNumber of ways that the chosen colors can be painted for 7 horizontal stripes - 2 (either (4,3) or (3,4))\nNow the order,\nthe number of ways in which a particular color among the 2 chosen colors can be painted for 4 stripes is - 7c4\n[Note: We don't need to calculate the ways for the remaining 3 stripes as they are obvious and already counted under this]\nTotal number of combinations - 5c2 * 2* 7c4 = 700 ANS:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are 18 balls in a jar. You take out 3 blue balls without putting them back inside, and now the probability of pulling out a blue ball is 1/5. How many blue balls were there in the beginning?\n\n### Options:\nA. 12\nB. 9\nC. 8\nD. 7\nE. 6\n\n### Answer:\nThere are 18 balls in a jar. You take out 3 blue balls without putting\n3 blue balls + 15 / 5 =6\nAnswer:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a kilometer race, If Abhishek gives Bharti a 40 m start, Abhishek wins by 19 sec. But if Abhishek gives Bharti a 30 sec start, Bharti wins by 40 m. Find the time taken by Bharti to run 5,000 m?\n\n### Options:\nA. 150 sec\nB. 750 sec\nC. 450 sec\nD. 825 sec\nE. 920 sec\n\n### Answer:\nIf Abhishek takes x seconds and Bharti takes y seconds to run 1 km, then:\n=>y=150 sec and x=125 sec\n=>x+19=960y/1000 and\n=(960x/1000)+30=y\n=>y=150 sec and x=125 sec\nAnswer =(150/1000)\u00d7500\n= 750 sec Answer : B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf n is a positive integer, which of the following is a possible value of |46 - 5n| ?\n\n### Options:\nA. 7\nB. 2\nC. 11\nD. 15\nE. 20\n\n### Answer:\nWhen 46>5n, then |46- 5n| = 46- 5n = (45-5n) + 1 = {multiple of 5} + 1\nWhen 46<=5n, then |46- 5n| = -(46- 5n) = (5n-45) - 1 = {multiple of 5} - 1\nSo, the correct answer must be 1 greater or 1 less than a multiple of 5. Only C fits.\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA and B entered into a partnership investing Rs.25000 and Rs.30000 respectively. After 4 months C also joined the business with an investment of Rs.35000. What is the share of C in an annual profit of Rs.47000?\n\n### Options:\nA. 14020\nB. 11289\nC. 68928\nD. 14000\nE. 16881\n\n### Answer:\n25*12: 30*12: 35*8\n15:18:14\n14/47 * 47000\n= 14000\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the numerator of a fraction is increased by 20% and its denominator is diminished by 25% value of the fraction is 2/15. Find the original fraction?\n\n### Options:\nA. 1/12\nB. 1/18\nC. 1/42\nD. 1/15\nE. 1/17\n\n### Answer:\nX * (120/100)\n---------------- = 2/15\nY * (75/100)\nX/Y = 1/12\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n16! is equal to which of the following?\n\n### Options:\nA. 20,922,789,888,321\nB. 20,922,789,888,000\nC. 20,922,789,888,525\nD. 20,922,789,888,416\nE. 20,922,789,888,928\n\n### Answer:\nAfter 4!, the units digit of every factorial is 0.\n5!=120\n6!=720\netc...\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n6x \u2013 5y + 3z = 23\n4x + 8y \u2013 11z = 7\n5x \u2013 6y + 2z = 11\nGiven the equations above, x + y + z = ?\n\n### Options:\nA. 11\nB. 12\nC. 13\nD. 14\nE. 15\n\n### Answer:\n(6x \u2013 5y + 3z) - (5x \u2013 6y + 2z ) = 23-11\nor, x+y+z = 12\nOption B is the ans\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA committee has 5 men and 6 women. What are the number of ways of selecting 2 men and 3 women from the given committee?\n\n### Options:\nA. 187\nB. 200\nC. 827\nD. 289\nE. 270\n\n### Answer:\nThe number of ways to select two men and three women\n= \u2075C\u2082 * \u2076C\u2083\n= (5 *4 )/(2 * 1) * (6 * 5 * 4)/(3 * 2)\n= 200\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe ratio between the present ages of A and B is 5:3 respectively. The ratio between A's age 4 years ago and B's age 4 years hence is 1:1. What is the ratio between A's age 4 years hence and B's age 4 years ago?\n\n### Options:\nA. 1:3\nB. 2:1\nC. 3:1\nD. 4:1\nE. None of these\n\n### Answer:\nLet the present ages of A and B be 5x and 3x years respectively.\nThen, (5x - 4)/(3x + 4) = 1/1\n2x = 8 => x = 4\nRequired ratio = (5x + 4):(3x - 4) = 24:8 = 3:1\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many such letter-pairs are there in the word SERVANT having the same no. of letters left between them in the word as they have in the series?\n\n### Options:\nA. 2\nB. 3\nC. 4\nD. 5\nE. 6\n\n### Answer:\n1 pair is S & V\n1 pair is N &S\ntotal 2 pair\nANSWER: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain company that sells only cars and trucks reported that revenues from car sales in 1997 were down 11 percent from 1996 and revenues from truck sales were up 7 percent from 1996. If total revenues from car sales and truck sales in 1997 were up 1 percent from 1996, what is the ratio W of revenue from car sales in 1996 to revenue from truck sales in 1996?\n\n### Options:\nA. 1:2\nB. 4:5\nC. 1:1\nD. 3:2\nE. 5:3\n\n### Answer:\nA.. I have probably solved this question 3-4 times by now.. Remember the answer.. 1:2\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf (x/y)=(7/5), find the value (x^2+y^2)/(x^2-y^2)\n\n### Options:\nA. 37/12\nB. 59/11\nC. 51/77\nD. 41/11\nE. None of them\n\n### Answer:\n= (x^2+y^2)/(x^2-y^2) = ( x^2 /y^2+ 1)/ ( x^2 /y^2-1) = [(7/5)^2+1] / [(7/5)^2-1]\n= [(49/25)+1] / [(49/25)-1] = 37/12\nAnswer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTea worth Rs. 126 per kg and Rs. 135 per kg are mixed with a third variety in the ratio 1 : 1 : 2. If the mixture is worth Rs. 153 per kg, the price of the third variety per kg will be:\n\n### Options:\nA. 175.5\nB. 170\nC. 169.5\nD. 180\nE. 190\n\n### Answer:\nSince first and second varieties are mixed in equal proportions.\naverage price = 126+135/2 = 130.50\no, the mixture is formed by mixing two varieties, one at Rs. 130.50 per kg and the other at say, Rs. x per kg in the ratio 2 : 2, i.e., 1 : 1. We have to find x.\nx - 153 = 22.50\nx = 175.50\nANSWER A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the smallest number that must be added to 1780 to make it a perfect\nsquare.\n\n### Options:\nA. 17\nB. 42\nC. 69\nD. 47\nE. 52\n\n### Answer:\n4 1780 (42\n16\n82\t180\n164\n16\nNumber to be added = (43)2 - 1780 = 1849 - 1780 = 69.\nANSWER C 69\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a camp, there is a meal for 110 men or 200 children. If 140 children have taken the meal, how many men will be catered to with remaining meal?\n\n### Options:\nA. 41\nB. 30\nC. 35\nD. 33\nE. 36\n\n### Answer:\nD\n33\nThere is a meal for 200 children.\n140 children have taken the meal.\nRemaining meal is to be catered to 60 children.\nNow, 200 children 110 men.\n60 children = (110/200)x 60= 33 men.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSet A: 3, e, 8, 10\nSet B: 4, y, 9, 11\nThe terms of each set above are given in ascending order. If the median of Set A is equal to the median of Set B, what is the value of y \u2013 e?\n\n### Options:\nA. -2\nB. -1\nC. 0\nD. 1\nE. 2\n\n### Answer:\nSo we have even no. of elements in the Set\nSo median is the average of Middle two numbers\n(e+8)/2= (y+9)/2\ny - e= -1\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA technician makes a round-trip to and from a certain service center by the same route. If the technician completes the drive to the center and then completes 40 percent of the drive from the center, what percent of the round-trip has the technician completed?\n\n### Options:\nA. 30\nB. 40\nC. 70\nD. 80\nE. 60\n\n### Answer:\nround trip means 2 trips i.e.to and fro. He has completed one i.e 50% completed. then he traveled another 40% of 50% i.e 20%. so he completed 50 +20 =70 % of total trip\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe banker\u2019s gain on a sum due 3 years hence at 12% per annum is Rs. 270. The banker\u2019s discount is\n\n### Options:\nA. Rs.960\nB. Rs.840\nC. Rs.1020\nD. Rs.760\nE. None\n\n### Answer:\nSolution\nT.D\t=(B.G x 100 / R x T)\n= Rs.(270x100/12 x 3)\n= Rs.750.\nB.D\n=Rs(750 + 270)\n= Rs.1020.\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain university will select 1 of 8 candidates eligible to fill a position in the mathematics department and 2 of 12 candidates eligible to fill 2 identical positions in the computer science department. If none of the candidates is eligible for a position in both departments, how many different sets of 3 candidates are there to fill the 3 positions?\n\n### Options:\nA. 340\nB. 380\nC. 472\nD. 528\nE. 630\n\n### Answer:\n1C8*2C12 = 8*66 = 528\nthe answer is (D)\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the line L passes through the point (3,n) and (n,3), where n is not equal to 3, which of the following must be true?\n1. The slope of L is negative\n2. Line L does pass the origin.\n3. Line L must passes through the first quadrant\n\n### Options:\nA. I only\nB. II only\nC. III only\nD. I and II\nE. II and III\n\n### Answer:\nSlope of the given line= 3-n/n-3\nGiven information is that n is not equal to 3, that means n <3 or n>3. In both these conditions the slope will be negative.\n1) n<3 (n=2)\n3-2/2-3= -1\n2) n<3 (n= 0)\n3-0/0-3= -1\n3) n<3 (n=-3)\n3+3/ -3-3= -2/3\n4) n>3\n3-4/4-3= -1\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train with 120 wagons crosses John who is going in the same direction, in 36 seconds. It travels for half an hour from the time it starts overtaking the John ( he is riding on the horse) before it starts overtaking the Mike(who is also riding on his horse) coming from the opposite direction in 24 seconds. In how much time (in secs) after the train has crossed the Mike do the John meets to Mike?\n\n### Options:\nA. 3476 s\nB. 3500 s\nC. 3650 s\nD. 3670 s\nE. 3576 s\n\n### Answer:\nLet the length of the train be L metres and speeds of the train Arun and Sriram be R, A and S respectively, then\n---------- (i)\nand ---------(ii)\nFrom eq.(i) and (ii)\n3(R - A ) = 2 (R + K)\nR = 3A + 2K\nIn 30 minutes (i.e 1800 seconds), the train covers 1800R (distance) but the Arun also covers 1800 A (distance) in the same time. Therefore distance between Arun and Sriram, when the train has just crossed Sriram\n= 1800 ( R - A) - 24 ( A + K)\nTime required =\n= (3600 - 24) = 3576 s\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n1/2+[(2/3*3/8)+4]-7/16=\n\n### Options:\nA. 29/16\nB. 19/16\nC. 69/16\nD. 9/13\nE. 0\n\n### Answer:\n1/2+[(2/3*3/8)+4]-7/16=\n1/2+[(1/4)+4]-7/16=\n1/2+[17/4]-7/16=\n8/16 + 68/16 - 7/16 = 69/16\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat should come in the place of the question mark(?) in the following equation?\n45(2)\u00d727(2)/135(2)=?\n\n### Options:\nA. 81\nB. 1\nC. 243\nD. 9\nE. None of these\n\n### Answer:\n? = 45\u00d745\u00d727\u00d727 /135\u00d7135=81\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSides of a rectangular park are in the ratio 3: 2 and its area is 2460sq m, the cost of fencing it at 50 ps per meter is?\n\n### Options:\nA. s.122\nB. s.129\nC. s.129.76\nD. s.120\nE. s.121\n\n### Answer:\n3x * 2x = 2460 => x = 20.24\n2(79.76 + 50) = 259.52 m\n259.52 * 1/2 = Rs.129.76\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe length of a rectangular plot is thrice its breadth. If the area of the rectangular plot is 867 sq m, then what is the breadth of the rectangular plot?\n\n### Options:\nA. 19 m\nB. 17 m\nC. 18 m\nD. 14 m\nE. 12 m\n\n### Answer:\nLet the breadth of the plot be b m.\nLength of the plot = 3 b m\n(3b)(b) = 867\n3b2 = 867\nb2 = 289 = 172 (b > 0)\nb = 17 m.\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA can finish a work in 48days, B in 9days and C in 2days, B and C start the work but are forced to leave after 3 days. The remaining work was done by A in?\n\n### Options:\nA. 10days\nB. 12days\nC. 6days\nD. 20days\nE. 8days\n\n### Answer:\nB+C 1day work = 1/9 + 1/12 = 7/36\nwork done by B and C in 3days = 7/36 * 3 = 7/12\nRemaining work = 1 - 7/12 = 5/12\n1/48 work is done by A in 1day\n5/12 work is done by A in 48*5/12 = 20days\nAnswer is D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the L.C.M of two numbers is 660 and their product is 18480, find the H.C.F of the numbers.\n\n### Options:\nA. 50\nB. 30\nC. 125\nD. 25\nE. None of these\n\n### Answer:\nH.C.F = (Product of the numbers) / (Their L.C.M) = 18480/660 = 28.\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA batsman makes a score of 87 runs in the 17th inning and thus increases his average by 3. Find his average after 17th inning?\n\n### Options:\nA. 15\nB. 88\nC. 44\nD. 54\nE. 23\n\n### Answer:\nLet the average after 7th inning = x\nThen average after 16th inning = x - 3\n16(x-3)+87 = 17x\nx = 87 - 48 = 39\nANSWER=B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThree cannons are firing at a target. If their individual probabilities to hit the target are 0.6, 0.7, and 0.8 respectively, what is the probability that none of the cannons will hit the target after one round of fire?\nprob. that all the cannons will hit the target = .06\nprob. that none of the cannons will hit = 1 - .06 = .94\n\n### Options:\nA. 0.006\nB. 0.012\nC. 0.024\nD. 0.029\nE. 0.904\n\n### Answer:\nThe probability that eachdoesn'thit is: 0.4, 0.3, and 0.2. When we have multiple independent events, we multiply the probabilities:\n.4*.3*.2 = 0.024.\nOption: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the product 4864 x 9 P 2 is divisible by 12, then the value of P is:\n\n### Options:\nA. 1\nB. 5\nC. 8\nD. 6\nE. 4\n\n### Answer:\nExplanation:\nClearly, 4864 is divisible by 4.\nSo, 9P2 must be divisible by 3. So, (9 + P + 2) must be divisible by 3.\nP = 1.\nANSWER A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe percentage increase in the area of a rectangle, if each of its sides is increased by 20% is:\n\n### Options:\nA. 40%\nB. 44%\nC. 50%\nD. 54%\nE. 60%\n\n### Answer:\nLet original length = x metres and original breadth = y metres.\nOriginal area = (xy) m2.\nNew length = 120 x m = 6 x m.\n100 5\nNew breadth = 120 y m = 6 y m.\n100 5\nNew Area = 6 x x 6 y m2 = 36 xy m2.\n5 5 25\nThe difference between the original area = xy and new-area 36/25 xy is\n= (36/25)xy - xy\n= xy(36/25 - 1)\n= xy(11/25) or (11/25)xy\nIncrease % = 11 xy x 1 x 100 % = 44%.\n25 xy\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man can swim in still water at 9 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is?\n\n### Options:\nA. 3.9\nB. 4.2\nC. 5.3\nD. 1.5\nE. 3\n\n### Answer:\nM = 9\nS = x\nDS = 9 + x\nUS = 9 - x\n9 + x = (9 - x)2\n9 + x = 18 -2x\n3x = 9\nx = 3\nAnswer:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the value of X, Y by solving the below equations\nX + Y = 12\nX - Y = 4\n\n### Options:\nA. 5, 7\nB. 8, 4\nC. 6, 6\nD. 7, 5\nE. 9, 3\n\n### Answer:\nX + Y = 12 ---(I)\nX - Y = 4 -----(II) by adding (I) and (II)\n------------\n2X = 16 ==> X = 16/2 = 8\nBy Replacing the value of X in (I) we get 8 + Y = 12 ==> Y = 12-8=4.\nSo, X = 8, Y = 4\nAnswer B) 8, 4\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTo deliver an order on time, a company has to make 25 parts a day. After making 25 parts per day for 3 days, the company started to produce 5 more parts per day, and by the last day of work 100 more parts than planned were produced. Find how many parts the company made and how many days this took.\n\n### Options:\nA. 475 pieces.\nB. 575 pieces.\nC. 675 pieces.\nD. 775 pieces.\nE. None of these\n\n### Answer:\nSolution:\nLet xx be the number of days the company worked. Then 25x is the number of parts they planned to make. At the new production rate they made:\n3\u22c525+(x\u22123)\u22c530=75+30(x\u22123)\nTherefore: 25x=75+30(x\u22123)\u2212100\n25x=75+30x\u221290\u2212100\n190\u221275=30x\u221225\n115=5x\nx=23\nSo the company worked 23 days and they made 23\u22c525+100=675 pieces.\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf (A+B) = 4, (B+C) = 8 and (C+D) = 3, what is the value of (A+D)?\n\n### Options:\nA. 16.\nB. 8.\nC. 7.\nD. 2.\nE. -1.\n\n### Answer:\nGiven A+B = 4\nB+C = 8\nC+D = 3\nThen (A+B)-(B+C)+(C+D)=4-8+3=-1\nOption E...\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA clothing store prices jeans at 30% above the wholesale price of $50. They have a sale for 25% off all jeans. How much would a customer pay for 2 pairs of jeans during the sale?\n\n### Options:\nA. $98.5\nB. $97.25\nC. $48.75\nD. $97.50\nE. $95\n\n### Answer:\nWholesale cost of jeans = $50\nJeans were priced at 30% above $50 = $65\n% discount given by sale = 25%\nCustomer paid = .75 * 65 = $48.75\nCost of 2 pairs of jeans = 48.75 * 2 = $97.5\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn what ratio must rice of Rs.16 per kg be mixed with rice of Rs.24 per kg so that cost of mixture is Rs.18 per kg?\n\n### Options:\nA. 4:1\nB. 2:1\nC. 3:1\nD. 4:3\nE. 4:5\n\n### Answer:\n(18-24)/(16-18)=6/2=3:1\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average of seven numbers is 18. The average of first three numbers is 16 and the average of last three numbers is 20. What is the middle number?\n\n### Options:\nA. 20\nB. 22\nC. 25\nD. 18\nE. 24\n\n### Answer:\nThe total of seven numbers = 7X18 = 126\nThe total of first 3 and last 3 numbers is = 3 X 16+3 X 20 = 108\nSo, the middle number is (126 - 108 ) = 18\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nLook at this series: 53, 53, 39, 39, 25, 25, ... What number should come next?\n\n### Options:\nA. A)12\nB. B)11\nC. C)27\nD. D)53\nE. E)86\n\n### Answer:\nIn this series, each number is repeated, then 14 is subtracted to arrive at the next number.\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n240 candies are distributed to children with the same number of candies for each child. What can\u2019t be the range which includes the number of children?\n\n### Options:\nA. 1~10\nB. 10~20\nC. 20~30\nD. 55~65\nE. 65~75\n\n### Answer:\n240 = 2^4*3*5\nThere are factors in each range except for 65~75\nThe answer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train of length 250 m crosses a bridge of length 180m in 20 seconds. What is the speed of train?\n\n### Options:\nA. 33\nB. 77.4\nC. 25\nD. 22\nE. 72\n\n### Answer:\nSol : (length of train+ length of bridge) = speed of train x Time\n(250+180) = 20 x Speed\nSpeed = 430/20= 21.5 m/s =77.4 km/h\nANSWER=B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAn investment yields an interest payment of $228 each month. If the simple annual interest rate is 9%, what is the amount of the investment?\n\n### Options:\nA. $28,300\nB. $30,400\nC. $31,300\nD. $32,500\nE. $35,100\n\n### Answer:\nLet the principal amount = P\nSimple annual interest = 9%\nSimple monthly interest = (9/12) = (3/4)%\n(3/4)*(P/100) = 228\n=>P = (228 *4 * 10^2 )/3\n= 76*4*10^2\n= 304 * 10^2\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 25 toys cost Rs, 234, what do 35 toys cost?\n\n### Options:\nA. 327.6\nB. 564.6\nC. 546.6\nD. 654.6\nE. None of them\n\n### Answer:\nLet the required cost be Rs. x. Then,\nMore toys, More cost\t(Direct Proportion)\nx=(35 X 234)/25 =327.60\nAnswer is A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA company\u2019s four cars running 8 hrs a day consume 1200 lts of fuel in 10 days. In the next 6 days, the company will need to run 9 cars for 12 hrs each so it rents 5 more cars which consume 20% less fuel than the company\u2019s four cars. How many lts of fuel will be consumed in the next 6 days?\n\n### Options:\nA. 1200 lt\nB. 1555 lt\nC. 1664 lt\nD. 1728 lt\nE. 2160 lt\n\n### Answer:\nGiven that\n4 cars running 8 hrs a day consume 1200 lts. of fuel in 10 days.\n1 car consumption per hour per day = 1200 /4 *8 *10 = 3.75 litre\nNow question say new car consume 20% less fuel than the company\u2019s four cars = 80/100 of 3.75 = 3 ( 20 percent less than 3.75)\nHence we calculate total consumption for next 6 days, the company will need to run 5 new cars for 12 hrs = 3*12 *6*5 =1080\nsimilarly = old 4 car consumption for next 6 days for 12 hrs = 3.75*6*12*4 = 1080\nhence total is = 1080+1080 = 2160 lt\nAns is E .\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nI bought two books; for Rs.480. I sold one at a loss of 15% and other at a gain of 19% and then I found each book was sold at the same price. Find the cost of the book sold at a loss?\n\n### Options:\nA. 327\nB. 280\nC. 277\nD. 216\nE. 287\n\n### Answer:\nx*(85/100) = (480 - x)119/100\nx = 280\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe time on a clock is 20 minutes past 7. What is the angle between the hands of the clock?\n\n### Options:\nA. 60 degrees\nB. 100 degrees\nC. 80 degrees\nD. 50 degrees\nE. 120 degrees\n\n### Answer:\nThe hour hand rotates 360 degrees in twelve hours.\nThe hour hand rotates 30 degrees in one hour.\nThe hour hand rotates 5 degrees in ten minutes.\nAt this time, the hour hand has rotated 220 degrees.\nThe minute hand rotates 360 degrees in 60 minutes, or 60 degrees in ten minutes.\nAt this time, the minute hand has rotated 120 degrees.\nThe difference is 220 - 120 = 100 degrees.\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn what ratio must rice of Rs.16 per kg be mixed with rice of Rs.10 per kg so that cost of mixture is Rs.12 per kg?\n\n### Options:\nA. 2:3\nB. 5:8\nC. 5:6\nD. 3:4\nE. 1:2\n\n### Answer:\n(12-10)/(16-12)=2/4=1:2\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n(1/4 + 1/4 \u00f7 5/4) / (1/4 x 1/4 + 2 1/4) = ?\n\n### Options:\nA. 16/25\nB. 32/185\nC. 36/185\nD. None of these\nE. Cannot be determined\n\n### Answer:\nAnswer\nGiven expression = (1/4 + 1/4 x 4/5) / (1/16 + 9/4)\n= (1/4 + 1/5) / (37/16)\n= 9/20 x 16/37\n= 36/185\nCorrect Option: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe T train leaves station A moving at a constant speed, and passes by stations B and C, in this order. It takes the T train 7 hours to reach station B, and 5 additional hours to reach station C. The distance between stations A and B is m kilometers longer than the distance between stations B and C. What is the distance between stations A and C in terms of m?\n\n### Options:\nA. 1.8m\nB. 6m\nC. 7m\nD. 9m\nE. 12m\n\n### Answer:\nThe reason it is failing for you is that you chose incorrect numbers. If the question says T it took 7 hrs to reach from A to B and 5 hrs to reach from B to C at a constant speed. It shows that distance AB and BC should be in ratio of 7/5.\nIf you take such numbers you can solve problem.\nAB = 7, BC=5\nTherefore\nAB-BC = 2\nBut from question, AB-BC =m\n=> m=2\nNow total distance = AB+BC= 12\nSubstitute 12 to get answer in terms of m\nTotal distance =12 =6m\nAns B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAngelina walked 1200 meters from her home to the grocery at a constant speed. She then walked 480 meters to the gym at double the speed. She spent 40 seconds less on her way from the grocery to the gym than on her way from home to the grocery. What was Angelina's speed, in meters per second, from the grocery to the gym?\n\n### Options:\nA. 12\nB. 23\nC. 34\nD. 48\nE. 52\n\n### Answer:\nlet the speed be X...\nso time taken from home to grocery= 1200/x..\nthe speed to gym = 2x..\nso time taken = 480/2x=240/x..\nits given 1200/x-240/x=40..\n960/x=40..\nx=24m/secs..\nso grocery to gym=2*24=48m/s...\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOn 4th Jan, 2009 Sunday falls. What day of the week was it on 4th Jan, 2008?\n\n### Options:\nA. Wednesday\nB. Thursday\nC. Friday\nD. Saturday\nE. Sunday\n\n### Answer:\nExplanation:\n4th Jan 2009 \u2013 4th Jan 2008 = 52 weeks 1 day. So Jan 4th 2008 is behind one day = Saturday\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the 4 digit no.in which the 1st digit is 1/3 of the second, the 3rd is the sum of the 1st and 2nd, and the last is three times the second?\n\n### Options:\nA. 1200\nB. 1256\nC. 1349\nD. 1456\nE. 1590\n\n### Answer:\nFirst digit is 1/3 second digit => The numbers can be 1 & 3, 2& 6, 3 & 9.\nFirst + second = third => we can eliminate 3 & 9 since 3 + 9 = 12.\nLast is 3 times the second => we can eliminate option 2 & 6 since 3 * 6 = 18.\nHence the number is 1349\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are a lot of houses such that the numbers of their doorplates are odd numbers and the first number of the doorplates is 545, the last number of the doorplates is 715. How many houses are there?\n\n### Options:\nA. 86\nB. 71\nC. 81\nD. 91\nE. 101\n\n### Answer:\nSo it starts from 545 and goes like 547, 549,...... 715. and both first and last number are inclusive. Since every other number is odd, it's just 1/2 of the numbers and since it starts with an odd and ends with an odd inclusive add one to the result.\ni.e., ([715-545][/2]+1 = 86\nAns A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind 80 / ? = ? / 20\n\n### Options:\nA. 40\nB. 400\nC. 800\nD. 1600\nE. None\n\n### Answer:\nAnswer\nLet 80/y = y/20\nThen, y 2 = 80 x 20 = 1600\n\u2234 y = \u221a1600 = 40.\nOption: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a basketball game, Tim scored 20 points more than Joe, but only half as many points as Ken. If the three players scored a combined total of 100 points, how many points did Tim score?\n\n### Options:\nA. 15\nB. 20\nC. 25\nD. 30\nE. 45\n\n### Answer:\nLet Joe scored point = x\nThen Tim Scored = x+20\nKen Scored = 2*(x+20) = 2x+40\nAs given, x+x+20+2x+40 = 100 points\n4x+60 = 100\nx = 100-60/4 = 10\nSo Tim Scored = x +20 i.e) 10+20 = 30\nAnswer : D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average (arithmetic mean) of eight numbers is 43.2. If the sum of half of these numbers is 156.4, what is the average of the other half?\n\n### Options:\nA. 47.3\nB. 51.5\nC. 55.8\nD. 59.2\nE. 63.7\n\n### Answer:\nThe average of this half is 156.4/4 = 39.1\nThis is 4.1 below the overall average, thus the average of the other half of the numbers must be 4.1 above the overall age, that is 43.2+4.1 = 47.3\nThe answer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA person took some amount with some interest for 5 years, but increase the interest for 1%, he paid Rs.250/- extra, then how much amount he took?\n\n### Options:\nA. Rs.5500/-\nB. Rs.6000/-\nC. Rs.4000/-\nD. Rs.5000/-\nE. None of these\n\n### Answer:\nExplanation:\r5 years = Rs.250/-\ryear = 250/5\rRate of Interest = 1%\r100/1% \u00d7 250/5 = Rs.5000/-\rP = Rs.5000/- Answer: Option D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n10 camels cost as much as 24 horses, 16 horses cost as much as 4 oxen and 6 oxen as much as 4 elephants. If the cost of 10 elephants is Rs.150000, find the cost of a camel?\n\n### Options:\nA. s.9800\nB. s.3800\nC. s.9800\nD. s.6000\nE. s.6880\n\n### Answer:\nCost of the camel = P\n10 camels = 24 horses\n16 horses = 4 oxen\n6 oxen = 4 elephants\n10 elephants = Rs.150000\nP = Rs.[(24 * 4 * 4 * 150000)/(10 * 16 * 6 * 10)]\nP = Rs.(57600000/9600) => P = Rs.6000\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf air is called green , green is called blue, blue is called blue, sky is called yellow, yellow is called water and water is called pink, then what is the color of clear sky ?\n\n### Options:\nA. Blue\nB. Sky\nC. Water\nD. Yellow\nE. Black\n\n### Answer:\nExplanation:\rThe colour of clear sky is 'blue' and as given, 'blue' is called 'blue'.\rSo, the colour of clear sky is 'blue'.\rAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many different subsets of the set {0, 1, 2} do not contain 0?\n\n### Options:\nA. A.6\nB. B.7\nC. C.1\nD. D.4\nE. E.2\n\n### Answer:\nNumber of subset\nSince we have 2 digits other than 0, we can take any numbers from the set of 2 to make a subset. Also it is a matter of selection and not arrangement.So we will consider combinations.\n2c1+2c2=3\nAnd one set is the NULL set having no elements in it so\n3+1=4.\nANSWER D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA = {1, 2, 3} and B = {4, 5, 6}.Find A-B\n\n### Options:\nA. {2,8,4}\nB. {1,3,5}\nC. {1,2,3}\nD. {5,10,15}\nE. {8,9,10}\n\n### Answer:\nA = {1, 2, 3}\nB = {4, 5, 6}\ncorrect answer :A - B = {1, 2, 3}\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a, b are integers and |a-b|=6, which of the following is the smallest possible value of ab?\n\n### Options:\nA. -16\nB. 0\nC. 16\nD. -9\nE. 40\n\n### Answer:\na=3, b=-3. Hence, the answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how many different ways can the letters of the word \u2018PREPTY\u2019 be arranged?\n\n### Options:\nA. 120\nB. 230\nC. 330\nD. 340\nE. 360\n\n### Answer:\nNumber of ways = 61/21 6X5X4X3X2X1 - 360\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the least integer greater than \u20133+0.5?\n\n### Options:\nA. \u20132\nB. \u20131\nC. 0\nD. 1\nE. 2\n\n### Answer:\nThis question is just about doing careful Arithmetic and remembering what makes a numberbiggerorsmallercompared to another number.\nFirst, let's take care of the Arithmetic:\n(-3) + (0.5) = -2.5\nOn a number line, since we're ADDING +.5 to a number, the total moves to the RIGHT (so we're moving from -3 to -2.5).\nNext, the question asks for the LEAST integer that is GREATER than -2.5\nAgain, we can use a number line. Numbers become greater as you move to the RIGHT. The first INTEGER to the right of -2.5 is -2.\nFinal Answer:\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe edge of three cubes of metal is 3 dm, 4 dm and 5 dm. They are melted and formed into a single cube. Find the edge of the new cube?\n\n### Options:\nA. 8\nB. 2\nC. 4\nD. 6\nE. 5\n\n### Answer:\n33 + 43 + 53\n= a3\n=> a = 6\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the next number in the series?\n2,4,7,10,15,18,....\n\n### Options:\nA. 23\nB. 24\nC. 25\nD. 26\nE. 27\n\n### Answer:\nAdding (0,1,2,3,4,5,6,7) to the prime numbers.\n2+0=2\n3+1=4\n5+2=7\n7+3=10\n11+4=15\n13+5=18\n17+6=23\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nLet the polynomials be:\nP1(x)=3x2\u22127x+3,\nP2(x)=\u22125x2\u22124x+2,\nP1(x)+P2(x)=\n\n### Options:\nA. 2x2 + 11x - 7\nB. -2x2 - 11x + 5\nC. -2x2 - 11x + 6\nD. 2x2 - 9x + 7\nE. None of these\n\n### Answer:\nSolution:\nP1(x)+P2(x)=(3x2\u22127x+3)+(\u22125x2\u22124x+2)=P1(x)+P2(x)=(3x2\u22127x+3)+(\u22125x2\u22124x+2)=\n3x2\u22127x+3\u22125x2\u22124x+2=3x2\u22127x+3\u22125x2\u22124x+2=\n\u22122x2\u221211x+5\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat least no. must be subtracted from 427398 so that remaining no.is divisible by 15?\n\n### Options:\nA. 344545629\nB. 723437481\nC. 354595321\nD. 964564944\nE. 458449909\n\n### Answer:\nExplanation:\nOn dividing 427398 by 15 we get the remainder 3, so 3 should be subtracted\nOption B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn the coordinate plane, points (x, 6) and (10, y) are on line k. If line k passes through the origin and has slope 1/2, then x * y =\n\n### Options:\nA. 52\nB. 46\nC. 60\nD. 50\nE. 35\n\n### Answer:\nLine k passes through the origin and has slope 1/2 means that its equation is y=1/2*x.\nThus: (x, 6)=(12, 6) and (10, y) = (10,5) --> x*y=12*5=60.\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a dairy farm, 40 cows eat 40 bags of husk in 40 days. In how many days one cow will eat one bag of husk?\n\n### Options:\nA. 1\nB. 1/40\nC. 40\nD. 80\nE. 1/80\n\n### Answer:\nAssume that in x days, one cow will eat one bag of husk.\nMore cows, less days (Indirect proportion)\nMore bags, more days (direct proportion)\nHence we can write as\nCowsBags40:11:40\u23ab\u23ad\u23ac::x:40\n\u21d240\u00d71\u00d740=1\u00d740\u00d7x\n\u21d2x=40\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nwhich of the following is correct formula for divisor rule ?\n\n### Options:\nA. dividend = divisor * quotient + remainder\nB. quotient = divisor * dividend + remainder\nC. dividend = divisor * quotient - remainder\nD. dividend = divisor * remainder + quotient\nE. dividend = divisor * remainder - quotient\n\n### Answer:\noption A is correct\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA popular website requires users to create a password consisting of the digits {1,2,3,4,5,6,7,8,9}. If no digit may be repeated and each password must be at least 8 digits long, how many passwords are possible?\n\n### Options:\nA. 8! + 9!\nB. 2 x 9!\nC. 8! x 9!\nD. 17!\nE. 18!\n\n### Answer:\nIf we choose the 9 different digits then they can be arranged in 9! ways.\nThe number of possible 8-digit passwords is 9*8*...*2 = 9!\nThe total number of passwords is 9! + 9! = 2*9!\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA car driver travels from the plains to the hill station, which are 200 km apart at an average speed of 50km/hr. in return trip, he covers the same distance at an average speed of 20km/hr. the average speed of the car over the entire distance of 400 km is\n\n### Options:\nA. 8.95km/hr\nB. 26.7km/hr\nC. 27.8km/hr\nD. 28.5km/hr\nE. 8.45km/hr\n\n### Answer:\naverage speed = (2*50*20)/50+20 km/hr\n=28.5 km/hr\nAnswer (D)\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA coin is tossed live times. What is the probability that there is at the least one tail?\n\n### Options:\nA. 31/32\nB. 31/36\nC. 31/27\nD. 31/28\nE. 31/18\n\n### Answer:\nLet P(T) be the probability of getting least one tail when the coin is tossed five times.\n= There is not even a single tail.\ni.e. all the outcomes are heads.\n= 1/32 ; P(T)\n= 1 - 1/32\n= 31/32\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJohn completes a piece of work in 10 days, Rose completes the same work in 40 days. If both of them work together, then the number of days required to complete the work is?\n\n### Options:\nA. 5 days\nB. 8 days\nC. 10 days\nD. 12 days\nE. 14 days\n\n### Answer:\nIf A can complete a work in x days and B can complete the same work in y days, then, both\nof them together can complete the work in x y/ x+ y days.\nThat is, the required No. of days = 10 \u00d7 40/50 = 8 days\nB)\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the invalid no.from the following series 13, 18, 25, 30, 37, 40\n\n### Options:\nA. 13\nB. 18\nC. 40\nD. 30\nE. 37\n\n### Answer:\nThe differences between two successive terms from the beginning are 7, 5, 7, 5, 7, 5. So, 40 is wrong.\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nConvert the 13/48 m/s into kilometers per hour?\n\n### Options:\nA. 1.5 kmph.\nB. 0.91 kmph.\nC. 1.2 kmph.\nD. 1.5 kmph.\nE. 0.98 kmph.\n\n### Answer:\n13/48 m/s = 13/48 * 18/5 = 49/50 = 0.98 kmph.\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe sum of three prime numbers is 100. If one of them exceeds another by 36, then one of the numbers is:\n\n### Options:\nA. 7\nB. 29\nC. 41\nD. 67\nE. 89\n\n### Answer:\nx+(x+36)+y=100 => 2x+y=64\nTherefore y must be even prime, which is 2.\nTherefore 2x+2=64 => x=31\nThird prime number= (x+36)= (31+36)= 67.\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the odd man out. 125, 127, 130, 135, 142, 153, 165\n\n### Options:\nA. 165\nB. 142\nC. 153\nD. 130\nE. None of these\n\n### Answer:\nExplanation :\nPrime numbers 2, 3, 5, 7, 11, 13 are added successively. Hence, 165 is wrong. Answer : Option A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA computer manufacturer produces a certain electronic component at a cost of $80 per component. Shipping costs for delivering the components are $4 per unit. Further, the manufacturer has costs of $16,500 a month related to the electronic component regardless of how many it produces. If the manufacturer produces and sells 150 components a month, what is the lowest price it can sell them for such that the costs don't exceed the revenues?\n\n### Options:\nA. $28\nB. $82\nC. $110\nD. $138\nE. $194\n\n### Answer:\nby the question, the equation would be 150 p - 84*150 - 16500 = 0\np being the price we want to find and equation resulting zero means revenue and costs are equal so we can get the minimum price of the component.\nsolving the equation, we get p = $ 194. Answer E for me.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average of 6 observations is 12. A new seventh observation is included and the new average is decreased by 1. The seventh observation is :\n\n### Options:\nA. 1\nB. 3\nC. 5\nD. 6\nE. 8\n\n### Answer:\nExplanation:\nSeventh observation = (7\u00d7\u00d711-6\u00d7\u00d712)=5\nCorrect Option: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nif 105 is represented as 253 in base 6,how is 253 represented in base 6?\n\n### Options:\nA. 1100\nB. 1101\nC. 1111\nD. 1011\nE. 1010\n\n### Answer:\n(105)base6=253\nthen (253)base6=1101\nbecause 253%6=1 and 253/6=42\nthen 42%6=0 and 42/6=7\nthen7%6=1 and 7/6 = 1\nand then 1%6=1 and 1/6=0\nwe see remainder part in reverse order that is 1101\nso ans is 1101\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n5 percent of 255 =\n\n### Options:\nA. 5\nB. 12.5\nC. 14.5\nD. 12.75\nE. 25\n\n### Answer:\n255/100=2.55\r1% =2.55\r5%= 2.55*5 = 12.75 ANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThree persons invested Rs.9000 in a joint business. The second person invested Rs.1000 more than the first and the third Rs.1000 more than second. After two years, they gained Rs.5400. How much third person will get?\n\n### Options:\nA. 2400\nB. 2429\nC. 2428\nD. 2421\nE. 2408\n\n### Answer:\nFirst persons investment = x\nSecond persons investment = x + 1000\nThird persons investments = x + 2000\nx + x + 1000 + x + 2000 = 9000\n3x = 6000\nx = 2000\nRatio = 2000 : 3000 : 4000\n2:3:4\n4/9 * 54000 = 2400\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA 6 litre sol is 20% alcohol .How many litres of pure alcohol must be added to produce a sol that is 50% alcohol ?\n\n### Options:\nA. A.0.6\nB. B.1\nC. C.2.1\nD. D.3.6\nE. E.5.4\n\n### Answer:\n20% of 6 = 1.2\n50% of 6 = 3\nshortage is 1.8\nso we need to have 1.8/50% to get 50% alcohol content.\n= 3.6 D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf log10 2 = 0.3010, the value of log10 80 is:\n\n### Options:\nA. 2.65\nB. 1.903\nC. 3.05\nD. 6.487\nE. 5.98\n\n### Answer:\nExplanation:\nlog10 80\t= log10 (8 x 10)\n= log10 8 + log10 10\n= log10 (23 ) + 1\n= 3 log10 2 + 1\n= (3 x 0.3010) + 1\n= 1.9030.\nanswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA pump can fill a tank with a water in 2 hours. Because of a leak, it took 2x1/3 hours to fill the tank. The leak can drain all the water of the tank in\n\n### Options:\nA. 5 hrs\nB. 7 hrs\nC. 12 hrs\nD. 14 hrs\nE. None\n\n### Answer:\nSol.\nWork done by the leak in 1 hour = (1/2 - 3/7) = 1/14.\n\u2234 Leak will empty the tank in 14 hrs.\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf YWVSQ is 25 - 23 - 21 - 19 - 11, Then MKIGF\n\n### Options:\nA. 13 - 11 - 9 - 7 - 9\nB. 13 - 11 - 9 - 7 - 6\nC. 13 - 11 - 9 - 7 - 7\nD. 13 - 11 - 9 - 7 - 3\nE. 11 - 11 - 9 - 7 - 1\n\n### Answer:\nMKIGF = 11 - 11 - 9 - 7 - 1\nNote: this is a dummy question. Dont answer these questions\nAnswer:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the length of an edge of cube P is thrice the length of an edge of cube Q, what is the ratio of the volume of cube Q to the volume of cube P?\n\n### Options:\nA. 1/4\nB. 1/5\nC. 1/6\nD. 1/27\nE. 1/9\n\n### Answer:\nThe length of cube Q = 1;\nThe length of cube P = 3;\nThe ratio of the volume of cube Q to the volume of cube P = 1^3/3^3 = 1/27\nAnswer : D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHaving received his weekly allowance, a student spent 3/5 of his allowance at the arcade. The next day he spent one third of his remaining allowance at the toy store, and then spent his last $1.20 at the candy store. What is this student\u2019s weekly allowance?\n\n### Options:\nA. $3.50\nB. $4.00\nC. $4.25\nD. $4.50\nE. $5.00\n\n### Answer:\nLet x be the value of the weekly allowance.\n(2/3)(2/5)x = 120 cents\n(4/15)x = 120\nx = $4.50\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe inner circumference of a circular race track, 14 m wide, is 440 m. Find radius of the outer circle.\n\n### Options:\nA. 84\nB. 86\nC. 82\nD. 80\nE. None of them\n\n### Answer:\nLet inner radius be r metres. Then, 2(22/7)r = 440 = r = (440 x (7/44))= 70 m.\nRadius of outer circle = (70 + 14) m = 84 m.\nAnswer is A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many minutes does it take James to type 8 words if he types at the rate of 4 words per minute?\n\n### Options:\nA. 4\nB. 1\nC. 2\nD. 6\nE. 3\n\n### Answer:\ntime*rate=job --> time*4=8 --> time=8/4=2.\nAnswer: C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a group of 28 junior high school students, 7 take French, 10 take Spanish, and 4 take both languages. The students taking both French and Spanish are not counted with the 7 taking French or the 10 taking Spanish. How many students are not taking either French or Spanish?\n\n### Options:\nA. 7\nB. 6\nC. 9\nD. 4\nE. 8\n\n### Answer:\nA\n7\nAdd 7 + 10 + 4 to get 21.\nThen subtract 21 from the total students \u21d2 28 \u2013 21 = 7.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe sum of the even numbers between 1 and n is 89*90, where n is an odd number, then n=?\n\n### Options:\nA. 167\nB. 173\nC. 179\nD. 185\nE. 193\n\n### Answer:\nLet n-1 = 2a.\n2+4+...+2a = 2*(1+2+...+a) = 2*(a)(a+1)/2 = (a)(a+1) = 89*90\nThen a = 89 and n = 179.\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how many different ways can a group of 8 people be divided into 4 teams of 2 people each?\n\n### Options:\nA. 90\nB. 105\nC. 168\nD. 420\nE. 2520\n\n### Answer:\nYou need to choose 4 groups of 2 from 8 people: That's 8/!2!2!2!2!, then divided by 4!, since any ordering of these 4 groups is the same.\nTotal = 8/2!2!2!2!4!=8!/8\u22172\u22174!=7!/2\u22174!=7\u22176\u22175\u22174\u22173\u22172/4\u22173\u22172\u22172=7\u22176\u22175/2=35\u22173=105.\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow long will it take a sum of money invested at 6 % p.a. S.I. to increase its value by 60%?\n\n### Options:\nA. 11 years\nB. 12 years\nC. 10 years\nD. 15 years\nE. 8 years\n\n### Answer:\nSol.\nLet the sum be x. Then, S.I. = 60% of x = 3x/5; Rate = 6%.\n\u00e2\u02c6\u00b4 Time = [100 * 3x/5 * 1/x*6] = 10 years\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe sum of the present age of Henry and Jill is 43. What is their present ages if 5 years ago Henry was twice the age of Jill?\n\n### Options:\nA. and 27\nB. and 24\nC. and 22\nD. and 29\nE. of these\n\n### Answer:\nLet the age of Jill 5 years ago be x, age of Henry be 2x\nx+5 + 2x+5 = 43\nx = 11\nPresent ages will be 16 and 27\nAnswer : A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA necklace is made by stringing N individual beads together in the repeating pattern red bead, green bead, white bead, blue bead and yellow bead. If the necklace begins with a red bead and ends with a white bead, then N could be:\n\n### Options:\nA. 38\nB. 77\nC. 68\nD. 29\nE. 112\n\n### Answer:\nThe pattern is R G W B Y R G W B Y R .......\nSo, White bead comes at these positions 3rd, 8th, 13th, 18th...\nIf we take this as a arithmetic progression, then this series can be expressed as 3 + (n - 1) 5. ( From the formula for general term of AP = a + (n-1)d).\nThis can be expressed as 5n - 2\nWe check the answer options so only 68 satisfy the condition.\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn Smithtown, the ratio of right-handed people to left-handed people is 3 to 1 and the ratio of men to women is 3 to 2. If the number of right-handed men is maximized, then what q percent of all the people in Smithtown are left-handed women?\n\n### Options:\nA. 50%\nB. 40%\nC. 25%\nD. 20%\nE. 10%\n\n### Answer:\nlooking at the ratio we can take total number of people q=20..\nans 5/20 or 25% C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf $30,000 interest is invested in x percent simple annual interest for n years, which of the following represents the total amount of interest, in dollars, that will be earned by this investment in the n years?\n\n### Options:\nA. 10,000(x^n)\nB. 30,000n(x/100)\nC. 10,000(1 + x/100)^n\nD. 30,000(x/100)^n\nE. 10,000n(1 + x/100)\n\n### Answer:\nPrincipal * no.of years * percentage of interest\nAnswer : B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWith a uniform speed a car covers the distance in 8 hours. Had the speed been increased by 4 km/hr, the same distance could have been covered in 7 1/2 hours. What is the distance covered?\n\n### Options:\nA. 400 km\nB. 480 km\nC. 490 km\nD. 380 km\nE. 330 km\n\n### Answer:\nB\n480 km\nLet the distance be x km. Then,\nx/(7 1/2) - x/8 = 4\n2x/15 - x/8 = 4 => x = 480 km.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n(1+0.0001)/(0.00004+1)\nThe value of the expression above is closet to which of the following?\n\n### Options:\nA. 0.0001\nB. 0.001\nC. 0.1\nD. 1\nE. 10\n\n### Answer:\nNotice that we need approximate value of the fraction.\nNow, the nominator is very close to 1 and the denominator is very close to 1, hence the value of the fraction is very close to 1/1=1.\nAnswer: D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nGoldenrod and No Hope are in a horse race with 6 contestants. How many different L arrangements of finishes are there if No Hope always finishes before Goldenrod and if all of the horses finish the race?\n\n### Options:\nA. 720\nB. 360\nC. 120\nD. 24\nE. 21\n\n### Answer:\nno hope finishing before goldenrod= 1/2 of the times\ntherefore the different L arrangements are 1/2* 6! = 360 = B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the number 872,152,24x is divisible by 11, what must be the value of x?\n\n### Options:\nA. 1\nB. 2\nC. 3\nD. 4\nE. 5\n\n### Answer:\nMultiplication rule of 11: (Sum of digits at odd places - Sum of digits at even places) should be divisible by 11\nGiven number: 872,152,24x\nSum of digits at odd places = 8 + 2 + 5 + 2 + x = 17 + x (i)\nSum of digits at even places = 7 + 1 + 2 + 4 = 14 (ii)\n(i) - (ii) = 17 + x - 14 = x - 3\nHence x should be = 3 to make this a multiple of 11 (0) Option C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn order to complete a reading assignment on time, Terry planned to read 120 pages per day. However, she read only 60 pages per day at first, leaving 840 pages to be read during the last 6 days before the assignment was to be completed. How many days in all did Terry have to complete the assignment on time?\n\n### Options:\nA. 4\nB. 6\nC. 8\nD. 10\nE. 12\n\n### Answer:\nD=120*X - according to the plan, assignment to be completed on time reading 120 pages per day for next X days. But, Terry's plans changed so she read as follow:\n60 pages for first Y days and 780 pages for last 6 days, we get these equations:\n60*Y+840=120*X\nX-Y=6 --------->>X planned number of days, Y - actually used reading 60 pages per day and 6 leftover days used to complete a lump 780 pages\nFrom above we find that X=Y+6 and 60Y+840=120Y+720 or 60Y=120 --->>>>> Y=2, hence X=8\nAnswer : C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA and B started a business investing Rs. 75,000 and Rs 20,000 respectively. In what ratio the profit earned after 2 years be divided between A and B respectively?\n\n### Options:\nA. 9:2\nB. 3:2\nC. 18:20\nD. 18:4\nE. 13:4\n\n### Answer:\nA: B = 75000 : 20000\n= 75 : 20\n= 13 : 4\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nPoint X is located on line segment AB and point Y is located on line segment CD. If AB = CD and AX < CY, then\n\n### Options:\nA. XB > YD\nB. XB < YD\nC. AX > XB\nD. AX > CY\nE. AX > AB\n\n### Answer:\nA--X------B\nC----Y----D\nXB > YD.\nAnswer: A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the sum which earned interest?\nI. The total simple interest was Rs. 7000 after 7 years.\nII. The total of sum and simple interest was double of the sum after 5 years.\n\n### Options:\nA. I alone sufficient while II alone not sufficient to answer\nB. II alone sufficient while I alone not sufficient to answer\nC. Either I or II alone sufficient to answer\nD. Both I and II are necessary to answer\nE. None of these\n\n### Answer:\nExplanation:\nLet the sum be Rs. x.\nI gives, S.I. = Rs. 7000 and T = 7 years.\nII gives, Sum + S.I. for 5 years = 2 x Sum Sum = S.I. for 5 years.\nNow, S.I. for 7 years = Rs. 7000.\ntherefore, S.I. for 1 year = Rs. 1000.\nThus, I and II both are needed to get the answer.\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf r and s are positive integers and r-s=6, which of the following has the greatest value M?\n\n### Options:\nA. 2r\nB. 2s\nC. r +s\nD. 2r-s\nE. 2s-r\n\n### Answer:\nYou can answer this question by using Number Properties and logic or by TESTing VALUES.\nWe're told that R and S are POSITIVE INTEGERS and that R-S = 6. We're asked which of the 5 answers has the GREATEST value.\nIF....\nR = 8\nS = 2\nAnswer A: 2R = 2(8) = 16\nAnswer B: 2S = 2(2) = 4\nAnswer C: R+S = 8+2 = 10\nAnswer D: 2R-S = 2(8) - 2 = 14\nAnswer E: 2S-R = 2(2) - 8 = -4\nFinal Answer:\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man buys Rs. 20 shares paying 9 % dividend. The man wants to have an interest of 12% on his money.The market value of each share is :\n\n### Options:\nA. Rs. 12\nB. Rs. 15\nC. Rs. 18\nD. Rs. 21\nE. None\n\n### Answer:\nSolution\nDividend on Rs. 20 = Rs.(9/100x20) = Rs.9/5\nRs. 12 is an income on Rs. 100.\n\u2234 Rs.9/5 is an income on Rs. (100/12 X9/5)= Rs.15\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn an exam, Amar scored 64 percent, Bhavan scored 36 percent and Chetan 44 percent. The maximum score awarded in the exam is 500. Find the average mark scored by all the three boys?\n\n### Options:\nA. 384\nB. 826\nC. 240\nD. 269\nE. 208\n\n### Answer:\nAverage mark scored by all the three boys =\n[64/100 (500) + 36/100 (500) + 44/100 (500)] / 3\n= 240\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n\" I am eight times as old as you were when I was as old as you are \" , said a man to his son. Find out their present ages if the sum of the their ages is 75 years.\n\n### Options:\nA. 23\nB. 24\nC. 25\nD. 26\nE. 27\n\n### Answer:\npresent age of boy x and previous age of boy y\nso present age of dad : 8y and previous age is x\nso the gap between duration must be same\nso 8y-x=x-y --> x=9y/2\nand x+8y = 75 (given) --> 9y/2 + y=75 so y=6 and and x=27\ntherefore fathers age is 8y = 8*6 = 48\nand child's age = x=27\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n2 log10 5 + log10 8 \u2013 \u00bd log10 4 = ?\n\n### Options:\nA. 2\nB. 4\nC. 2 + 2 log10 2\nD. 4 - 4 log10 2\nE. 6\n\n### Answer:\n2 log10 5 + log10 8 \u2013 \u00bd log10 4\n= log10 (52) + log10 8 - log10 (41/2)\n= log10 25 + log10 8 - log10 2 = log10 (25*8)/2\n= log10 100 = 2\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf Jos\u00e9 reads at a constant rate of 2 pages every 5 minutes, how many seconds will it take him to read N pages?\n\n### Options:\nA. 2/5*N\nB. 2N\nC. 5/2*N\nD. 24N\nE. 150N\n\n### Answer:\nJose would read 1 page in 5/2 min\nJose would read N page in (5/2)*N min i.e. (5/2)*N*60 Seconds = 150N Seconds.\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man buys 54 pens at marked price of 46 pens from a whole seller. If he sells these pens giving a discount of 1% , what is the profit percent?\n\n### Options:\nA. 7.6 %\nB. 7.7 %\nC. 16.21 %\nD. 13.6 %\nE. 7.8 %\n\n### Answer:\nExplanation:\nLet Marked price be Re. 1 each\nC.P. of 54 pens = Rs. 46\nS.P. of 54 pens = 99% of Rs. 54= Rs. 53.46\nProfit % = (Profit /C.P.) x 100\nProfit% = (7.46/46) x 100 = 16.21 %\nANSWER: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a group of 5 boys and 5 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be selected?\n\n### Options:\nA. 100\nB. 110\nC. 179\nD. 205\nE. 219\n\n### Answer:\nNumber of ways to select four children is 10C4 = 210\nNumber of ways to choose only girls is 5C4 = 5\nNumber of ways that at least one boy is selected is 210 - 5 = 205\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are 5 marbles in a bag - 2 are orange and 3 are blue. If two marbles are pulled from the bag, what is the probability R that at least one will be orange?\n\n### Options:\nA. R=7/10\nB. R=3/5\nC. R=2/5\nD. R=3/10\nE. 1/10\n\n### Answer:\nMethod 1\nProbability R that at least one out of two marbles will be orange = 1 - Probability that both marbles are blue = 1- P(First marble is blue) * P (Second Marble is Blue) = 1- (3/5)(2/4) = 7/10\nMethod 2\nProbability that at least one marble will be orange = P( First Marble is Orange)*P(Second Marble is Blue) + P (First Marble is Blue)*P(Second Marble is Orange) + P(First Marble is Orange) *P(Second Marble is Orange) = (2/5)*(3/4)*2 + (2/5)*(1/4) = 7/10\nMethod 3\nProbabilty that at least one marble will be orange = 1 - Probability that both marbles are blue\n= 1 - (Number of ways 2 blue marbles out of 3 can be pulled)/(Number of ways 2 marbles out of 5 can be pulled)\n= 1 - 3C2/5C2\n= 1-(3/10) = 7/10\nAnswer :A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nUsing all the letters of the word \"NOKIA\", how many words can be formed, which begin with N and end with A?\n\n### Options:\nA. 8\nB. 6\nC. 9\nD. 3\nE. 1\n\n### Answer:\nThere are five letters in the given word.\nConsider 5 blanks ....\nThe first blank and last blank must be filled with N and A all the remaining three blanks can be filled with the remaining 3 letters in 3! ways.\nThe number of words = 3! = 6.\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average (arithmetic mean) of the even integers from 0 to 60 inclusive is how much greater than the average (arithmetic mean) of the even integers from 0 to 30 inclusive?\n\n### Options:\nA. 10\nB. 15\nC. 20\nD. 25\nE. 30\n\n### Answer:\nThe sum of even numbers from 0 to N is 2 + 4 +...+ N\n= 2(1 + 2 + ...+ N/2)\n= 2(N/2)(N/2+1)/2 = (N/2)(N/2+1)\nThe average is (N/2)(N/2+1)/(N/2+1) = N/2\nThe average of the even numbers from 0 to 60 is 60/2 = 30\nThe average of the even numbers from 0 to 30 is 30/2 = 15\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nhe ratio between the sale price and the cost price of an article is 5:6. What is the ratio between the profit and the cost price of that article?\n\n### Options:\nA. 2:6\nB. 1:8\nC. 1:6\nD. 2:1\nE. 2:5\n\n### Answer:\nLet C.P. = Rs. 6x and S.P. = Rs. 5x.\nThen, Gain = Rs. x\nRequired ratio = x : 6x = 1:6.\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf there are 664,579 prime numbers among the first 10 million positive integers, approximately what percent of the first 10 million positive integers are prime numbers?\n\n### Options:\nA. 0.0066%\nB. 0.066%\nC. 0.66%\nD. 6.6%\nE. 66%\n\n### Answer:\n664,579 = (x/100) * 10^7;\n664, 579 = x * 10^5\n=> x = 664, 579/10^5\n= 6.64579 ~ 6.6%\nAns is (D).\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe data A and B are equal to the data subtracted C; The data B is three times the data A; If the data A is equal to 12 What is the sum of the data A, B and C?\n\n### Options:\nA. 86\nB. 92\nC. 84\nD. 102\nE. 96\n\n### Answer:\nThe equations raised.\nA + B = C\nB = 3A\nA = 12 then\nB = 36 and C = 48\nA + B + C = 96\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\ntotal dinning bill of 7 people was $139.00 and 10% tip divided the bill evenly ?what is the bill amount each person shared .\n\n### Options:\nA. 21.84\nB. 22.84\nC. 23.84\nD. 24.84\nE. 25.84\n\n### Answer:\ndinner bill of 7 person = 139 + 10% tip\nso,\n10% of 139 = (139*10)/100 = 13.9\nSo, the actual total amount = 139+13.9 = $ 152.9\nso per head bill = 152.9/7 = $ 21.84\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA cistern of capacity 8000 litres measures externally 3.3 m by 2.6 m by 1.5 m and its walls are 5 cm thick. The thickness of the bottom is:\n\n### Options:\nA. 90 cm\nB. 5 dm\nC. 1 m\nD. 1.1 cm\nE. None of these\n\n### Answer:\nExplanation:\nLet the thickness of the bottom be x cm.\nThen , [(330 - 10) \u00d7 (260 - 10) \u00d7 (150 - x)] = 8000 \u00d7 1000\n=> 320 \u00d7 250 \u00d7 (150 - x) = 8000 \u00d7 1000\n=> (150 - x) = 8000\u00d71000/320=\n100\n=> x = 50 cm = 5 dm.\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a, b, c, and d are integers; w, x, y, and z are prime numbers; w < x < y < z; and (wa)(xb)(yc)(zd)=660(wa)(xb)(yc)(zd)=660, what is the value of (a + b) \u2013 (c + d)?\n\n### Options:\nA. \u20131\nB. 0\nC. 1\nD. 2\nE. 3\n\n### Answer:\n660660= 2^2 x 3^1 x 5^1 x 11^1\nw < x < y < z = 2 < 3 < 5 < 11\nSo, can can say -\nw = 2\nx = 3\ny = 5\nz = 11\nHence a = 2 , b = c = d = 1\n(a + b) \u2013 (c + d) will be (2 + 1) \u2013 (1 + 1) = 1\nAnswer will be (C)\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA, B and C invest in the ratio of 3 : 4: 5. The percentage of return on their investments are in the ratio of 6 : 5 : 4. Find the total earnings, If B earns Rs. 350 more than A :\n\n### Options:\nA. 10150\nB. 7250\nC. 2767\nD. 1998\nE. 2771\n\n### Answer:\nExplanation:\nA B C\ninvestment 3x 4x 5x\nRate of return 6y% 5y% 4y%\nReturn \\inline \\frac{18xy}{100} \\inline \\frac{20xy}{100} \\inline \\frac{20xy}{100}\nTotal = (18+20+20) = \\inline \\frac{58xy}{100}\nB's earnings - A's earnings = \\inline \\frac{2xy}{100} = 350\nTotal earning = \\inline \\frac{58xy}{100} = 10150\nAnswer: A) Rs.10150\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA basket of 1430 apples is divided equally among a group of apple lovers. If 45 people join the group, each apple lover would receive 9 apples less. How many W apples did each person get before 45 people joined the feast?\n\n### Options:\nA. 20.\nB. 21.\nC. 22.\nD. 23.\nE. 24.\n\n### Answer:\nBefore solving it algebraically, let us prime factorize 1430 = 2*5*11*13.\nSince number of apples per person * total persons W= 1430, the answer should be a factor of 1430. Only C is. And that's your answer.C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA snail, climbing a 20 feet high wall, climbs up 4 feet on the first day but slides down 2 feet on the second. It climbs 4 feet on the third day and slides down again 2 feet on the fourth day. If this pattern continues, how many days will it take the snail to reach the top of the wall?\n\n### Options:\nA. 12\nB. 16\nC. 17\nD. 20\nE. 21\n\n### Answer:\ntotal transaction in two days = 4-2 = 2 feet\nin 16 days it will climb 16 feet\non the 17th day , the snail will climb 4 feet , thus reaching the top\ntherefore , total no of days required =17\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA starts business with Rs.3500 and after 10 months, B joins with A as his partner. After a year, the profit is divided in the ratio 2 : 3. What is B\u00e2\u20ac\u2122s contribution in the Capital ?\n\n### Options:\nA. 24887\nB. 20778\nC. 23788\nD. 31500\nE. 2811\n\n### Answer:\nExplanation:\nA invested Rs.3500 for 12 months.\nLet B joined with investment x. And he invested for 12 - 10 = 2 months.\nSo there profit ratio = (3500 \u00c3\u2014 12) : (2x) = 2 : 3\n\u00e2\u2021\u2019 x = 31500\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich of the following are divisible by both 2 and 3?\nI. 234,124,422\nII. 88,865,544,264\nIII. 5,555,554,678\n\n### Options:\nA. I\u200b only\nB. I and II\u200b\nC. II and III\nD. II Only\nE. I\u200b and III\n\n### Answer:\nIII. is not divisible by 2 & 3\nI. is divisible by 3 since sum of the digits is 24 , which is divisible by 3\nII. is divisible by 3 since sum of the digits is 60 , which is divisible by 3\nThus among the given options only (B) holds true.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf six persons sit in a row, then the probability that three particular persons are always together is?\n\n### Options:\nA. 1/6\nB. 1/1\nC. 1/5\nD. 1/9\nE. 1/2\n\n### Answer:\nSix persons can be arranged in a row in 6! ways. Treat the three persons to sit together as one unit then there four persons and they can be arranged in 4! ways. Again three persons can be arranged among them selves in 3! ways. Favourable outcomes\n= 3!4! Required probability\n= 3!4!/6!\n= 1/5\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n35.62 + 408.926 + 48.2 = ?\n\n### Options:\nA. 622.441\nB. 492.243\nC. 492.746\nD. 622.443\nE. None of these\n\n### Answer:\nExplanation :\n35.62 + 408.926 + 48.2 = 492.746. Answer : Option C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOn rainy mornings, Mo drinks exactly N cups of hot chocolate (assume that N is an integer). On mornings that are not rainy, Mo drinks exactly 3 cups of tea. Last week Mo drank a total of 26 cups of tea and hot chocolate together. If during that week Mo drank 10 more tea cups than hot chocolate cups, then how many rainy days were there last week?\n\n### Options:\nA. 0\nB. 1\nC. 4\nD. 5\nE. 6\n\n### Answer:\nT= the number of cups of tea\nC= the number of cups of hot chocolate\nT+C = 26 T-C=10 -> T= 18. C=8.\nMo drinks 3 cups of tea a day then number of days that are not rainy = 18/3 = 6\nSo number of rainy days = 7-6 = 1\nB is the answer.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the are of an equilateral triangle of side 16 cm?\n\n### Options:\nA. 64\u221a5\nB. 64\u221a9\nC. 64\u221a4\nD. 64\u221a3\nE. 64\u221a2\n\n### Answer:\nArea of an equilateral triangle = \u221a3/4 S2\nIf S = 16, Area of triangle = \u221a3/4 * 16 * 16 = 64\u221a3 cm2;\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA farmer grows Broccoli in his farm that is in the shape of a square. Each Broccoli takes 1 square foot of area in his garden. This year, he has increased his output by 101 Broccoli when compared to last year. The shape of the area used for growing the Broccoli has remained a square in both these years. How many Broccoli did he produce this year?\n\n### Options:\nA. 2400\nB. 2601\nC. 1987\nD. 2000\nE. Cannot be determined\n\n### Answer:\nExplanatory Answer\nThe shape of the area used for growing Broccoli has remained a square in both the years.\nLet the side of the square area used for growing Broccoli this year be X ft.\nTherefore, the area of the ground used for cultivation this year = X2 sq.ft.\nLet the side of the square area used for growing Broccoli last year be Y ft.\nTherefore, the area of the ground used for cultivation last year = Y2 sq.ft.\nAs the number of Broccoli grown has increased by 101, the area would have increased by 101 sq ft because each Broccoli takes 1 sq ft space.\nHence, X2 - Y2 = 101\n(X + Y)(X - Y) = 101.\n101 is a prime number and hence it will have only two factors. i.e., 101and 1.\nTherefore, 101 can be expressed as product of 2 numbers in only way = 101 * 1\ni.e., (X + Y)(X - Y) = 101* 1\nSo, (X + Y) should be 101 and (X - Y) should be 1.\nSolving the two equations we get X = 51 and Y = 50.\nTherefore, number of Broccoli produced this year = X2 = 512 = 2601.\nAlternative Approach : Use answer choices\nThe area in both the years are squares of two numbers.\nThat rules out choice A,C and D. as 2400,1987 and 2000 are not the square of any number.\nCheck Choice B: If this year's produce is 2601, last year's produce would have been 2601 - 101 = 2500\n2500 is the square of 50.\nSo, 2601 is the answer.\nChoice B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA group of students decided to collect as many paise from each member of group as is the number of members. If the total collection amounts to Rs. 59.29, the number of the member is the group is:\n\n### Options:\nA. 57\nB. 67\nC. 77\nD. 87\nE. 97\n\n### Answer:\nMoney collected = (59.29 x 100) paise = 5929 paise.\nNumber of members = 5929 = 77.\nAnswer: Option C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf x > 5 and y < -5, then which of the following must be true ?\n\n### Options:\nA. x/y > 1\nB. x/y < -1\nC. x/y < 0\nD. x + y > 0\nE. xy > 0\n\n### Answer:\nPick x=3, y = -3\nA) x/y > 1 - Incorrect as x/y = -1\nB) x/y < -1 - Incorrect as x/y = -1\nC) x/y < 0 -Correct. It will hold for all values x > 2 and y < -2 as x/y = -1 < 0\nD) x + y > 0 - Incorrect. x + y = 0\nE) xy > 0 - Incorrect. XY = -9 which is less than zero.\nA should be the answer.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA technician makes a round-trip to and from a certain service center by the same route. If the technician completes the drive to the center and then completes 30 percent of the drive from the center, what percent of the round-trip has the technician completed?\n\n### Options:\nA. 60\nB. 65\nC. 55\nD. 50\nE. 55\n\n### Answer:\nround trip means 2 trips i.e.to and fro. He has completed one i.e 50% completed. then he traveled another 30% of 50% i.e 15%. so he completed 50 +15 =65 % of total trip.\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man can row at 5 kmph in still water. If the velocity of current is 3 kmph and it takes him 1 hour to row to a place and come back, how far is the place?\n\n### Options:\nA. 2.4 km\nB. 2.9 km\nC. 3.4 km\nD. 4.4 km\nE. 1.6 km\n\n### Answer:\nExplanation:\nSpeed in still water = 5 kmph\nSpeed of the current = 3 kmph\nSpeed downstream = (5+3) = 8 kmph\nSpeed upstream = (5-3) = 2 kmph\nLet the required distance be x km\nTotal time taken = 1 hour\n\u00e2\u2021\u2019 x/8+x/2=1\n\u00e2\u2021\u2019x+4x=8\n\u00e2\u2021\u20195x=8\n\u00e2\u2021\u2019x=1.6 km\nAnswer: Option E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many digits are required to write numbers between 1 to 100.\n\n### Options:\nA. 196\nB. 158\nC. 192\nD. 200\nE. None\n\n### Answer:\nExplanation:\nSingle digits are from 1 to 9 = 9 digits\nDoubt digits are from 10 to 99 = 90 x 2 = 180 digits\n100 needs 3 digits. Total 192 digits\nCorrect Option: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe respective ages of father and his son are 47 and 16 years. In how many years will the father be twice as old as his son ?\n\n### Options:\nA. 19 years\nB. 9 years\nC. 10 years\nD. 15 years\nE. 12 years\n\n### Answer:\nSuppose x years later the father will be twice as old as his son.\nx + 47 = 2 (x + 16)\nx = 47 - 32 = 15 years\nanswer : D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain company employs 6 senior officers and 4 junior officers. If a committee is to be created, that is made up of 3 senior officers and 1 junior officer, how many different committee are possible?\n\n### Options:\nA. 8\nB. 24\nC. 58\nD. 80\nE. 210\n\n### Answer:\n6!/3!(6-3)! = 20\n4!/1!(4-1)!=4\nso number of different committees equals 20*4=80\nANS:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo goods trains each 680 m long are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one?\n\n### Options:\nA. 228\nB. 65.28\nC. 48.32\nD. 27\nE. 21.1\n\n### Answer:\nRelative speed = 45 + 30 = 75 km/hr.\n75 * 5/18 = 125/6 m/sec.\nDistance covered = 680 + 680 = 1360 m.\nRequired time = 1360 * 6/125 = 65.28 sec.\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAjay and Sasi start walking towards each other at 6am at speed of 4kmph and 5kmph. They were initially 20km apart. At what time do they meet?\n\n### Options:\nA. 6am\nB. 8am\nC. 10am\nD. 9am\nE. 12pm\n\n### Answer:\nTime of meeting = distance / relative speed = 20/6+4 = 20/10 = 2 hrs after 6am = 8am\nAnswer is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a class,30 students pass in english and 20 students in maths,while some students among these pass in both.how many students do only english as compared to those doing only maths?\n\n### Options:\nA. 10\nB. 15\nC. 4\nD. 12\nE. indeterminate\n\n### Answer:\nFor doing Union or Intersection we would need three values. In this question the missing information in this question is Total no.of Students in the class.\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe sum of the squares of three numbers is 138, while the sum of their products taken two at a time is 131. Their sum is:\n\n### Options:\nA. 20\nB. 30\nC. 40\nD. 50\nE. 60\n\n### Answer:\nLet the numbers be a, b and c.\nThen, a2 + b2 + c2 = 138 and (ab + bc + ca) = 131.\n(a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca) = 138+2x131= 400.\n(a + b + c) = square root of 400 = 20\nanswer :A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA towel, when bleached, was found to have lost 20% of its length and 10% of its breadth. The percentage of decrease in area is ?\n\n### Options:\nA. 88%\nB. 38%\nC. 68%\nD. 28%\nE. 24%\n\n### Answer:\nLet original length = x\nand original width = y\nDecrease in area will be\n=xy\u2212(80x100\u00d790y100)=(xy\u22121825xy)=725xyDecrease = (7xy25xy\u00d7100)%=28%\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf R is between (4) and (-4), which of the following can be greatest?\n\n### Options:\nA. (7/(R+1))\nB. R^2\nC. R^3\nD. R^4\nE. 100^7\n\n### Answer:\n7/(R+1) - can be as large as possible.\nfor eg. if R = -1.000001 => 7/(R+1) = 7000000\nAns A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf c is 25% of a and 10% of b, what percent of a is b?\n\n### Options:\nA. 2.5%\nB. 15%\nC. 25%\nD. 35%\nE. 250%\n\n### Answer:\nc is 25% of a --> c=a/4;\nc is 10% of b --> c=b/10;\nThus a/4=b/10 --> b=5/2*a=2.5a. Therefore, b is 250% of a.\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat number comes next?\n452, 693, 714, 526, 937, ?\n\n### Options:\nA. 113\nB. 231\nC. 145\nD. 148\nE. 123\n\n### Answer:\nC\n145\nThe numbers 45269371 are being repeated in the same sequence.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nthere are sixty markings on a clock, minutes hand was exactly on one of those markings. nine markings away from the minutes hand was hours hand. what could be the time.\n\n### Options:\nA. 5:14\nB. 6:20\nC. 7:48\nD. 3:09\nE. 3:19\n\n### Answer:\ngiven angle diff=9mins\nwe know\n1min=6 deg\ntherefore 9mins=9*6=54 deg\nso the angle diff must be 54 deg\nbetter to go through the options\nlet us consider\nA.5hrs 14mins\nfind angle\nangle traced by hour hand=(5*30)+(14/2)=157\nangle traced by minute hand=(14*6)=84\nangle diff=157-84=73\nsimilarly for option C.\nangle traced by hour hand=(7*30)+(48/2)=234\nangle traced by minute hand=(48*6)=288\nangle diff=(288-234)=54\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA, B, and C were to be paid in proportion to the part of work they did while working on the same piece of work. A and B individually can finish the piece of work in 12 days and 10 days respectively. They worked together for five days and then C completed the remaining work all alone. If $720 was the net sum to be paid for the entire work, what was the average daily wage of B?\n\n### Options:\nA. $144\nB. $90\nC. $72\nD. $54\nE. $48\n\n### Answer:\nThe correct answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe cost of 14 packets of sugar, each weighing 900 grams is Rs. 28. What will be the cost of 27 packets, if each packet weighs 1 kg?\n\n### Options:\nA. Rs 52.50\nB. Rs 56\nC. Rs 58.50\nD. Rs 60\nE. None of these\n\n### Answer:\nExplanation :\nLet the required cost be Rs. x. Then,\nMore packets, More cost (Direct Proportion)\nMore weight, More cost (Direct Proportion)\nPackets 14 : 27\nWeight 900 : 1000 :: 28 : x\n(14 x 900 x x) = (27 x 1000 x 28)\nx = (27 x 1000 x 28) /14 x 900\n=60\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA technician makes a round-trip to and from a certain service center by the same route. If the technician completes the drive to the center and then completes 40 percent of the drive from the center, what percent of the round-trip has the technician completed?\n\n### Options:\nA. 5%\nB. 70%\nC. 25%\nD. 40%\nE. 55%\n\n### Answer:\nThe complete round trip consists of driving to the service center and then back home again.\nSo, once the technician drives to the service center he/she has already competed 50% of the entire trip.\nSince the technician completes a portion of the trip back home,the correct answer must be greater than 50%\nso 0.5+0.5*0.4=0.70\nAnswer:\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA bicyclist's wheel has a circumference of 9 meters. if the bicyclist covers 180 meters in 5 hours at a constant speed, how many rotations does the wheel make per hour at that speed?\n\n### Options:\nA. 2\nB. 3\nC. 4\nD. 5\nE. 6\n\n### Answer:\nThe bicyclist covers y meters in t hrs. So he covers y/t meters in one hour.\nTo cover y/t meters, the bicycle's wheel went round and round that is, multiple times, the wheel completed one circumference on the road. How many times did it complete one full rotation. Since the circumference is x, the number of times it completes the circumference is y/xt.=180/9*5=4\nAnswer (C)\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man can reach certain place in 50hours. If he reduces his speed by 1/10th, he goes 450km less in time. Find his speed?\n\n### Options:\nA. 20km/hr\nB. 30km/hr\nC. 40km/hr\nD. 50km/hr\nE. 90km/hr\n\n### Answer:\nLet the speed be x km/hr\n50x-50* 9/10 *x = 450\n50x - 45x = 450\nx = 90km/hr\nAnswer is E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA part-time employee whose hourly wage was decreased by 20 percent decided to increase the number of hours worked per week so that the employee's total income did not change. By what percent T should the number of hours worked be increased?\n\n### Options:\nA. 12.5%\nB. 20%\nC. 25%\nD. 50%\nE. 100%\n\n### Answer:\nCorrect Answer: C\nSolution: C. We can set up equations for income before and after the wage reduction. Initially, the employee earns W wage and works H hours per week. After the reduction, the employee earns .8W wage and works X hours. By setting these equations equal to each other, we can determine the increase in hours worked: WH = .8WX (divide both sides by .8W) 1.25H = X We know that the new number of hours worked T will be 25% greater than the original number. The answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA, B and C are entered into a partnership. A invested Rs.6500 for 6 months, B invested Rs.8400 for 5 months and C invested for Rs.10000 for 3 months. A is a working partner and gets 5% of the total profit for the same. Find the share of C in a total profit of Rs.7400.\n\n### Options:\nA. 2997\nB. 1900\nC. 2887\nD. 2898\nE. 27912\n\n### Answer:\n65 * 6 : 84 * 5 : 100 * 3\n26:28:20\nC share = 74000 * 95/100 = 7030 * 20/74 => 1900.Answer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe list price of an article is Rs.65. A customer pays Rs.56.16 for it. He was given two successive discounts, one of them being 10%. The other discount is?\n\n### Options:\nA. 9%\nB. 4%\nC. 2%\nD. 1%\nE. 6%\n\n### Answer:\n65*(90/100)*((100-x)/100) = 56.16\nx = 4%\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train travels from Albany to Syracuse, a distance of 120 miles, at the average rate of 30 miles per hour. The train then travels back to Albany from Syracuse. The total travelling time of the train is 6 hours . What was the average rate of speed of the train on the return trip to Albany?\n\n### Options:\nA. 31\nB. 38\nC. 60\nD. 50\nE. 40\n\n### Answer:\n30*T =120 THEREFORE T = 120/30 =4\nON RETURN SPEED * ( 6 -4) =120 THEREFORE T = 120/2 =60\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich of the following CANNOT be a product of two distinct positive integers X and Y?\n\n### Options:\nA. X\nB. Y\nC. 3Y + 2X\nD. Y - X\nE. YX\n\n### Answer:\nIn these questions it is best to take an example as if something is true for all positive integers than it as to be true for the smallest and the easiest integers to work with\ntake X = 1 and Y = 2 and work with the options\nXY = 2\nA) X take X =2, Y = 1\nB) Y take X = 1 Y = 2\nC) 3Y + 2X Seems tricky, lets see other options and then come back to it.\nD) Y - X take Y = 1 and X = 2 --> Y - X = -1 .. How the hell can product of two positive integers be negative ?? or less than each of them?\nE) YX Always true\nYou don't even have to worry what C is !\nans D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo girls started running simultaneously around a circular track of length 500 m from the same point at speeds of 30 km/hr and 20 km/hr. When will they meet for the first time any where on the track if they are moving in opposite directions?\n\n### Options:\nA. 35\nB. 36\nC. 37\nD. 38\nE. 39\n\n### Answer:\nTime taken to meet for the first time anywhere on the track\n= length of the track / relative speed\n= 500 / (30 + 20)5/18 = 500* 18 / 50 * 5 = 36 seconds.\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how much time will a train of length 100 m, moving at 36 kmph cross an electric pole?\n\n### Options:\nA. 33\nB. 787\nC. 18\nD. 10\nE. 87\n\n### Answer:\nConvert kmph to mps. 36 kmph = 36 * 5/18 = 10 mps.\nThe distance to be covered is equal to the length of the train.\nRequired time t = d/s = 100/10 = 10 sec.\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo men start together to walk a certain distance, one at 4 kmph and another at 3 kmph.The former arrives half an hour before the latter. Find the distance.\n\n### Options:\nA. 6 kilometre\nB. 7 km\nC. 8 km\nD. 9 km\nE. None of these\n\n### Answer:\nLet the distance be x km. Then,\nx/3 - x/4 = 1/2\n(4x - 3x)/12 = 1/2\nx = 6 km\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhen 242 is divided by a certain divisor the remainder obtained is 6. When 698 is divided by the same divisor the remainder obtained is 13. However, when the sum of the two numbers 242 and 698 is divided by the divisor, the remainder obtained is 5. What is the value of the divisor?\n\n### Options:\nA. 11\nB. 14\nC. 18\nD. 23\nE. None of these\n\n### Answer:\nlet that divisor be x\nsince remainder is 6 or 13 it means divisor is greater than 13.\nnow 242-6=236 =kx (k is an integer and 234 is divisble by x)\nsimilarly 698-13=685 = lx (l is an integer and 689 is divisible by x)\nadding both 698 and 242\n= (236+685)+6+13\n=x(k+l) + 19\nwhen we divide this number by x then remainder will be equal to remainder of (19 divided by x) = 5 hence x = 19-5 = 14\nhence B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 15% of 30% of 50% of a number is 90, then what is the number?\n\n### Options:\nA. 4000\nB. 3050\nC. 4400\nD. 4500\nE. None of these\n\n### Answer:\nLet the number be a\nGiven, 15/100 * 30/100 * 50/100 * a = 90\n=> 3/20 * 3/10 * 1/2 * a = 90\n=> a = 10 * 20 * 10 * 2 = 4000.\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man can row upstream at 7 kmph and downstream at 10kmph.find man\u2019s rate in still water and the rate of current.\n\n### Options:\nA. 1.5 km/hr\nB. 2.5 km/hr\nC. 3.5 km/hr\nD. 4.5 km/hr\nE. 5.5 km/hr\n\n### Answer:\nRate in still water=1/2(10+7)km/hr=8.5 km/hr.\nRate of current=1/2(10-7)km/hr=1.5 km/hr.\nANSWER A 1.5 km/hr\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nNine men went to a hotel. Eight of them spent Rs.1 each over their meals and the ninth spent Rs.2 more than the average expenditure of all the nine. Determine the total money spent by them?\n\n### Options:\nA. 19.28\nB. 10.28\nC. 11.28\nD. 14.28\nE. 17.28\n\n### Answer:\nAverage of 9 = x\n9x = 8 * 1 + x * 2\nx = 1.14\nTotal = 9 * 3.25 = 10.28\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOne pipe can fill a pool three times faster than a second pipe. When both pipes are opened, they fill the pool in seven hours. How long would it take to fill the pool if only the slower pipe is used?\n\n### Options:\nA. 10 hr\nB. 12 hr\nC. 15 hr\nD. 20 hr\nE. 28 hr\n\n### Answer:\nfast pipe + slow pipe = together\nOne pipe fills the pool three times faster than the other pipe so,\nhourly fill rates:\n1/x + 1/3x = 1/7\nLet x = number of hours it would take the fast pipe to fill the pool thus,\nx=9.3 hours\n9.3*3 = 28 hours\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAnnika hikes at a constant rate of 10 minutes per kilometer. She has hiked 2.75 kilometers east from the start of a hiking trail when she realizes that she has to be back at the start of the trail in 45 minutes. If Annika continues east, then turns around and retraces her path to reach the start of the trail in exactly 45 minutes, for how many kilometers total did she hike east?\n\n### Options:\nA. 3.625\nB. 3.5\nC. 4\nD. 4.5\nE. 5\n\n### Answer:\nSet up two R x T =D cases.\n1. 1/10 km/ min x T = 2.75\nfrom which T= 27.5 mins.\nWe know total journey time now is 45 +27.5 = 72.5\nThe rate is the same ie 1/10km/min.\nset up second R x T =D case.\n1/10 km/min x 72.5 = 7.25 km\nNow the total journey would be halved as distance would be same in each direction. 7.25/2 =3.625.\nA.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average of temperatures at noontime from Monday to Friday is 30; the lowest one is 20, what is the possible maximum range of the temperatures?\n\n### Options:\nA. 20\nB. 25\nC. 40\nD. 45\nE. 10\n\n### Answer:\nAverage=30, Sum of temperatures=30*5=150\nAs the min temperature is 20, max would be 150-4*20=30 --> The range=30(max)-20(min)=10\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nP is able to do a piece of work in 5 days and Q can do the same work in 10 days. If they can work together for 3 days, what is the fraction of work completed?\n\n### Options:\nA. 13/10\nB. 4/5\nC. 11/10\nD. 7/10\nE. 9/10\n\n### Answer:\nExplanation :\nAmount of work P can do in 1 day = 1/5\nAmount of work Q can do in 1 day = 1/10\nAmount of work P and Q can do in 1 day = 1/5 + 1/10 = 3/10\nAmount of work P and Q can together do in 3 days = 3 \u00d7 (3/10) = 9/10\nAnswer : Option E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain auto manufacturer sold 6% fewer vehicles in 2007 than in 2006. If the manufacturer sold 2.1 million vehicles in 2006, how many vehicles, to the nearest 10,000, did the manufacturer sell in 2007?\n\n### Options:\nA. 63,000\nB. 1,980,000\nC. 2,030,000\nD. 2,040,000\nE. 2,300,000\n\n### Answer:\nLet's assume in 2006 the manufacturer sold X.\nIn 2007 he sold X-6/100(X)\nIf sales in 2006,X= 2.1 million find X-6/100(X)\n(2.1 x 10^6)-6/100(2.1 x 10^6)\n2100000-126000=1,974,000-----> 1,980,000(approx)\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 250!/10^n is an integer, what is the largest possible value of n?\n\n### Options:\nA. 65\nB. 66\nC. 62\nD. 69\nE. 97\n\n### Answer:\nThe question actually asks the highest power of 10 which divides 250! ( For a number to be an integer - Without any remainder all the trailing zeroe's must be divided by the denominator)\n10 = 2 x 5\n250 factorial will have 62 as -\n250/5 = 50\n50/5 = 10\n10/5 =2\nSo answer will be (C) 62\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how many years, Rs. 150 will produce the same interest at 6% as Rs. 800 produce in 2 years at 4\u00bd% ?\n\n### Options:\nA. 4 years\nB. 6 years\nC. 8 years\nD. 9 years\nE. 12 years\n\n### Answer:\nExplanation :\nLet Simple Interest for Rs.150 at 6% for n years = Simple Interest for Rs.800 at 4\u00bd % for 2 years\n150\u00d76\u00d7n/100=800\u00d79/2\u00d72/100\n150\u00d76\u00d7n=800\u00d79/2\u00d72\n150\u00d76\u00d7n=800\u00d79\n3\u00d76\u00d7n=16\u00d79\n6\u00d7n=16\u00d73\n2\u00d7n=16\nn=8 years\nAnswer : Option C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA motorcyclist started riding at highway marker A, drove 120 miles to highway marker B, and then, without pausing, continued to highway marker C, where she stopped. The average speed of the motorcyclist, over the course of the entire trip, was 25 miles per hour. If the ride from marker A to marker B lasted 3 times as many hours as the rest of the ride, and the distance from marker B to marker C was half of the distance from marker A to marker B, what was the average speed, in miles per hour, of the motorcyclist while driving from marker B to marker C?\n\n### Options:\nA. 40\nB. 45\nC. 108\nD. 55\nE. 60\n\n### Answer:\nA- B = 120 Miles\nB - C = 60 Miles\nAvg Speed = 25 Miles\nTime taken for A-B 3t and B-C be t\navg speed = (120+60) / Total time\n25 = 180/4t\nt = 108\nB-C = 108mph\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how many different number of ways 5 men and 3 women can sit on a shopa which can accommodate persons?\n\n### Options:\nA. 200\nB. 210\nC. 230\nD. 56\nE. 270\n\n### Answer:\n8p2 = 8 X 7 = 56\nD)\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf rupee one produces rupees nine over a period of 40 years, find the rate of simple interest?\n\n### Options:\nA. 22 1/6 %\nB. 22 8/2 %\nC. 25 1/2 %\nD. 22 1/2 %\nE. 22 5/2 %\n\n### Answer:\n9 = (1*40*R)/100\nR = 22 1/2 %\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFour persons enter the lift of a six storey building at the ground floor. In how many ways can they get out of lift on any floor other than ground floor\n\n### Options:\nA. 625\nB. 1296\nC. 1540\nD. 1478\nE. 360\n\n### Answer:\nEach person out of 4 has 5 floors (options) to get out of (since no one gets out on the ground floor), hence total ways is 5*5*5*5=5^4=625.\nAnswer: A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRon begins reading a book at 4: 30 p.m. and reads at a steady pace of 40 pages per hour. Michelle begins reading a copy of the same book at 6: 00 p.m. If Michelle started 5 pages behind the page that Ron started on and reads at an average pace of 50 pages per hour, at what time would Ron and Michelle be reading the same page?\n\n### Options:\nA. 7: 00 a.m.\nB. 12: 30 a.m.\nC. 7: 45 p.m.\nD. 8: 00 p.m.\nE. 8: 30 p.m.\n\n### Answer:\nM gains 50-40=10 pages per hour on R\nat 6pm R has read 60 pages and M is 60+5=65 pages behind him\ntime=65/10=6.5 hours\nthey are on the same page at 12:30 a.m.\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nx and y are integers. a+ b< 11 , and a> 6. What is the smallest possible value of a- b?\n\n### Options:\nA. 1\nB. 2\nC. 4\nD. -2\nE. -4\n\n### Answer:\nFocus on the transition points and plug in the values.\na> 6 so a could be 7, 8, 9, 10, 11 etc\nLook at a= 7\n7 + b< 11\nb< 4\nb could be 3, 2, 1, 0, -1 etc\nWhen b is 3, we get a- b= 4\nThis must be the smallest value because as a increases, b reduces so a- b increases.\nTake another example. a= 11 so b< 0.\na- b will give a value greater than 11.\nAnswer (C).\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA shopkeeper increases the price of an article by X% and then decreases it by X%. As a result the price of the article is reduced by $180. After one more such change the price is further reduced by $153 Find the original price of the article.\n\n### Options:\nA. $1200\nB. $1100\nC. $1400\nD. $1000\nE. $1500\n\n### Answer:\nGiven:\nAfter a% decrease the price of the article is reduced by $180 --> pa=180;\nAfter one more such change the price is further reduced by $153. After the first decrease the price became $(p\u2212180), thus (p\u2212180)a=153--> pa\u2212180a=153a=15--->a=15 --> p\u22170.15=180--> p=1,200\nAnswer: A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the sub-triplicate ratio of 27:125\n\n### Options:\nA. 3:5\nB. 3:9\nC. 3:6\nD. 3:1\nE. 3:2\n\n### Answer:\nThe sub-triplicate ration of 27 : 125 = 3:5\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nGasoline varies in cost from $0.93 to $1.13 per gallon. If a car\u2019s mileage varies from 16 to 24 miles per gallon, what is the difference between the most and least that the gasoline for a 480-mile trip will cost?\n\n### Options:\nA. $15.13\nB. $15.30\nC. $15.72\nD. $16.01\nE. $16.23\n\n### Answer:\nSolution:\nWe know that the per gallon cost of gasoline varies from $0.93 - $1.13.\nNow we want to find the MAXIMUM difference between the least amount of money spent on gasoline and the largest amount of money spent i.e. to calculate max. trip cost - min. trip cost.\nMileage is given to be 16 to 24 miles per gallon, thus to travel 480 miles you will need gasoline in the range 480/24 to 480/16 which is 20 to 30 gallons.\nSo, for these 20 gallons and 30 gallons of gasoline the cost is as follows: (divide this task into 2 parts, 1 for 30 gallons and 2nd one for 20 gallons).\nCase 1: for 30 gallons the cost is 30*0.93 to 30*1.13 which is $27.90 to $33.90\nCase 2: for 20 gallons the cost is 20*0.93 to 20*1.13 which is $18.60 to $22.60\nThus, the maximum cost of the 480 mile trip is $33.90 and minimum is $18.60\nso the difference is $33.90 - $18.60 = $15.30\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain company employs 8 senior officers and 4 junior officers. If a committee is to be created, that is made up of 3 senior officers and 1 junior officer, how many different committee are possible?\n\n### Options:\nA. 8\nB. 24\nC. 58\nD. 224\nE. 210\n\n### Answer:\nNumber of ways to select 3 senior officers from 8 of them = 8C3 = 56 ways\nNext we can determine the number of ways to select 1 junior officer.\nnumber of ways to select 1 junior officer from 4 of them = 4C1 = 4 ways\nThus the number of ways to select 3 senior officers and 1 junior officer is 56 x 4 = 224 ways.\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n9 - 3 \u00f7 1/3 + 5 = ?\n\n### Options:\nA. 5\nB. 3\nC. 6\nD. 9\nE. 12\n\n### Answer:\n9 - 3 1/3 + 5\n=9-3\u00f71/3+5\n=9-(3X3) +5\n=9-9+5\n=5\nCORRECT ANSWER : A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nVictor gets 92 % marks in examinations. If these are 184 marks, find the maximum marks.\n\n### Options:\nA. 334\nB. 500\nC. 200\nD. 288\nE. 271\n\n### Answer:\nLet the maximum marks be m\nThen 92 % of m = 184\n\u21d2 92/100 \u00d7 m = 184\n\u21d2 m = (184 \u00d7 100)/92\n\u21d2 m = 18400/92\n\u21d2 m = 200\nTherefore, maximum marks in the examinations are 200.\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA basket contains 5 apples of which one is rotten. If Henry is to select 2 apples from the basket simultaneously and at random what is the probability that the 2 apples selected will include the rotten apple?\n\n### Options:\nA. 1/5\nB. 3/10\nC. 2/5\nD. 1/2\nE. 3/5\n\n### Answer:\nDirect probability approach:\nP=15\u221744+45\u221714=25P=15\u221744+45\u221714=25: probability of {first apple rotten, second apple good} plus the probability of {first apple good, second apple rotten}.\nReverse probability approach:\nAgain 1- the probability of the opposite event --> P=1\u221245\u221734=25P=1\u221245\u221734=25.\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man cycling along the road noticed that every 15 minutes a bus overtakes him and every 5 minutes he meets an oncoming bus. If all buses and the cyclist move at a constant speed, what is the time interval between consecutive buses?\n\n### Options:\nA. 5 minutes\nB. 6 minutes\nC. 8 minutes\nD. 9 minutes\nE. 15/2 minutes\n\n### Answer:\nLet's say the distance between the buses is d. We want to determine Interval=\\frac{d}{b}, where b is the speed of bus.\nLet the speed of cyclist be c.\nEvery 15 minutes a bus overtakes cyclist: \\frac{d}{b-c}=15, d=15b-15c;\nEvery 5 minutes cyclist meets an oncoming bus: \\frac{d}{b+c}=4, d=4b+4c;\nd=15b-15c=5b+5c, --> b=2c, --> d=15b-15b/2=15b/2.\nInterval=\\frac{d}{b}=\\frac{15/2b}{b}=15/2\nAnswer: E (15/2 minutes).\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nBy selling an umbrella for Rs. 300, a shop keeper gains 20%. During a clearance sale, the shopkeeper allows a discount of 5% on the marked price. His gain percent during the sale is?\n\n### Options:\nA. 6%\nB. 2%\nC. 8%\nD. 3%\nE. 4%\n\n### Answer:\nMarked price = Rs. 300\nC.P. = 100/120 * 300 = Rs. 250\nSale price = 95% of Rs. 300 = Rs. 285\nRequired gain % = 15/250 * 100 =6%.\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n18 times a positive integer is more than its square by 80, then the positive integer is\n\n### Options:\nA. 13\nB. 10\nC. 11\nD. 12\nE. 14\n\n### Answer:\nExplanation:\nLet the number be x. Then,\n18x = x2 + 80\n=> x2 - 18x + 80 = 0\n=>(x - 10)(x - 8) = 0\n=> x = 10 or 8\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe side of a rhombus is 26 m and length of one of its diagonals is 20 m. The area of the rhombus is?\n\n### Options:\nA. 299\nB. 278\nC. 278\nD. 480\nE. 281\n\n### Answer:\n262 \u2013 102 = 242\nd1 = 20 d2 = 48\n1/2 * 20 * 48 = 480\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe perimeter of a triangle is 36 cm and the inradius of the triangle is 2.5 cm. What is the area of the triangle?\n\n### Options:\nA. 87 cm2\nB. 28 cm2\nC. 98 cm2\nD. 26 cm2\nE. 45 cm2\n\n### Answer:\nArea of a triangle = r * s\nWhere r is the inradius and s is the semi perimeter of the triangle.\nArea of triangle\n= 2.5 * 36/2\n= 45 cm2\nAnswer:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA bag contains 2 yellow, 3 green and 2 blue balls. Two balls are drawn at random. What is the probability that none of the balls drawn is blue?\n\n### Options:\nA. 1/2\nB. 10/21\nC. 9/11\nD. 7/11\nE. 5/11\n\n### Answer:\nTotal number of balls = 2 + 3 + 2 = 7\nLet S be the sample space.\nn(S) = Total number of ways of drawing 2 balls out of 7 = 7C2\nLet E = Event of drawing 2 balls , none of them is blue.\nn(E) = Number of ways of drawing 2 balls , none of them is blue\n= Number of ways of drawing 2 balls from the total 5 (=7-2) balls = 5C2\n(\u2235 There are two blue balls in the total 7 balls. Total number of non-blue balls = 7 - 2 = 5)\nP(E) = n(E)/n(S)=5C2/7C2=(5\u00d74/2\u00d71)/(7\u00d76/2\u00d71)=5\u00d74/7\u00d76=10/21\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe standard serial numbers for a bill are 2 letters followed by 5 digits. How many bills are possible if letters and digits can be repeated?\n\n### Options:\nA. 26 \u00d7 26 \u00d7 100 000\nB. 24\u00b3 \u00d7 10 \u00d710 000\nC. 26\u00b3 \u00d7 10 000\nD. 26 \u00d7 25 \u00d7 24 \u00d7 10\nE. 26 x 26 x 10 000\n\n### Answer:\nOFFICIAL SOLUTION:\n(A) The formula for permutations of events is the product of the number of ways each event can occur. There are 26 letters and 10 digits. So there are 26 \u00d7 26 options for the two letters, and 10 \u00d7 10 \u00d7 10 \u00d7 10 x 10 for the five digits. The number of bills is 26 \u00d7 26 \u00d7 10 \u00d7 10 \u00d7 10 \u00d7 10 x 10 = 26 x 26 x 100 000.\nThe correct answer is choice (A).\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nGeorge takes 30 days to do a piece of work and Mark takes 45 days for the same work. For the first 15 days only George works. Then Mark also joins him. Find the time taken to complete the entire work.\n\n### Options:\nA. 24 days\nB. 25 days\nC. 26 days\nD. 27 days\nE. 28 days\n\n### Answer:\nGeorge 1 day work= 1/30\nMark 1 day work= 1/45\nGeorge 15 day work= 15*1/30 =1/2\nWork remaining= 1-1/2 =1/2\nGeorge + Mark 1 day work= 1/30 + 1/45 =1/18\nNumber of day required to complete 1/2 work= (1/2)/(1/18)= 9 days\nSo total days required to complete the work is 15+9= 24 days.\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man can row upstream at 25 kmph and downstream at 35 kmph, and then find the speed of the man in still water?\n\n### Options:\nA. 18 kmph\nB. 20 kmph\nC. 30 kmph\nD. 19 kmph\nE. 10 kmph\n\n### Answer:\nUS = 25\nDS = 35\nM = (35 + 25)/2 = 30\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn what ratio should water and wine be mixed so that after selling the mixture at the cost price a profit of 33.33% is made?\n\n### Options:\nA. 1:0\nB. 1:3\nC. 1:9\nD. 1:6\nE. 1:5\n\n### Answer:\nExplanation:\n33.33% profit means there is one part water and 3 part is pure wine. so the required ratio of water and wine in the mixture is 1:3\nAnswer: B) 1:3\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA person lent a certain sum of money at 4% per annum at simple interest and in 8 years the interest amounted to Rs.204 less than the sum lent. What was the sum lent?\n\n### Options:\nA. 228\nB. 278\nC. 300\nD. 500\nE. 821\n\n### Answer:\nP - 204 = (P*4*8)/100\nP = 300\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nEqual amount of water were poured into two empty jars of different capacities, which made one jar 1/5 full and other jar 1/4 full. If the water in the jar with lesser capacity is then poured into the jar with greater capacity, what fraction of the larger jar will be filled with water?\n\n### Options:\nA. 1/7\nB. 2/5\nC. 1/2\nD. 7/12\nE. 2/3\n\n### Answer:\nSame amount of water made bigger jar 1/5 full, then the same amount of water(stored for a while in smaller jar) were added to bigger jar, so bigger jar is 1/5+1/5=2/5 full.\nAnswer: B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOf the 800 employees of Company P, 60 percent have been with the company for at least ten years. If q of theselong-termmembers were to retire and no other employee changes were to occur, what value of q would reduce the percent oflong-termemployees in the company to 50 percent ?\n\n### Options:\nA. 200\nB. 160\nC. 112\nD. 80\nE. 56\n\n### Answer:\nThe # oflong-termemployees is 60%*800=480.\nAfter q of them retire new # oflong-termemployees would become 480-q.\nTotal # of employees would become 800-q.\nWe want 480-q to be 50% of 800-q --> 480-q=(800 -q)*50% --> q = 160.\nAnswer: B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA Cuban cigar would cost 4 dollar less than 1.5 times a French cigar, had the French cigar cost 0.7 dollar less than it does now. An Arabian cigar costs 50 cents more than 1.5 times the Cuban cigar. The three cigars together cost 74.7 dollars. What is the price of the French cigar?\n\n### Options:\nA. 11.8$.\nB. 23$.\nC. 13.7$.\nD. 35$.\nE. 37.4$.\n\n### Answer:\nThe three cigars together cost 74.7 dollars. If each cost the same , they would have cost a little less than 25 dollars each.\nFrom the given data we know French cigar < Cuban cigar < Arabic cigar\nand each is more expensive 1.5 times. Therefore eliminate options A,D,E straightaway . Since French cigar is at least 1.5 times cheaper we know B cannot be the answer.\nTherefore C is the answer.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average age of a husband and a wife is 23 years when they were married five years ago but now the average age of the husband, wife and child is 21 years(the child was born during the interval). What is the present age of the child?\n\n### Options:\nA. 7\nB. 5\nC. 8\nD. 4\nE. 2\n\n### Answer:\n28 * 2 = 56\n21 * 3 = 63\n-----------\n7 years.Answer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a person walks at 14 km/hr instead of 10 km/hr, he would have walked 20 km more. The actual distance traveled by him is:\n\n### Options:\nA. 50 km\nB. 56 km\nC. 60 km\nD. 70 km\nE. 80 km\n\n### Answer:\nLet the actual distance travelled be x km.\nx/10 = (x+20)/14\n14x = 10x + 200\n4x = 200\nx = 50 km.\nanswer :A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe length of rectangle is thrice its breadth and its perimeter is 96 m, find the area of the rectangle?\n\n### Options:\nA. 432\nB. 288\nC. 278\nD. 269\nE. 271\n\n### Answer:\n2(3x + x) = 96\nl = 36 b = 12\nlb = 36 * 12 = 432\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe original price of a certain TV set is discounted by g percent, and the reduced price is then discounted by 2g percent. If P is the original price of the TV Set, which of the following represents the price of the television set after the two successive discounts?\n\n### Options:\nA. P(1 - 0.03x + 0.02x^2)\nB. P(1 - 0.03g + 0.0002g^2)\nC. P(1 - 0.03x + 0.002x^2)\nD. P(1 - 2x^2)\nE. P(1 - 3x + 2x^2)\n\n### Answer:\nYoucansolve this problem with number plugging.\nSay the original price was $10 and g=50. Then after the first reduction the price would become $5 and after the second reduction of 2*50=100% the rprice would become $0.\nNow, since P is not zero, then the expression in the brackets must be zero for g=50. Only answer choice B works.\nAnswer: B.\nOn this problem - number pluggin is not giving me the answer.. I initially used g = 10, then g = 20 and P = 100. Answer should after both consecutive discounts = 72. I plug in the respective values and I keep getting 68. Can you double check my math.\n100 (1-0.03(10) + 0.0002 (10)^2)\n100 (1-0.3 + 0.0002 (100))\n100 (0.7 + 0.02)\n100 (0.68) = 68????\ndouble check my math. Am I missing something? I also plugged in your numbers and still did not get zero as final answer with choice B..\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain junior class has 1000 students and a certain senior class has 800 students. Among these students, there are 60 siblings pairs each consisting of 1 junior and 1 senior. If 1 student is to be selected at random from each class, what is the probability that the 2 students selected will be a sibling pair?\n\n### Options:\nA. 3/40000\nB. 1/3600\nC. 9/2000\nD. 1/60\nE. 1/15\n\n### Answer:\nThere are 60 siblings in junior class and 60 their pair siblings in the senior class. We want to determine probability of choosing one sibling from junior class and its pair from senior.\nWhat is the probability of choosing ANY sibling from junior class? 60/1000 (as there are 60 of them).\nWhat is the probability of choosing PAIR OF CHOSEN SIBLING in senior class? As in senior class there is only one pair of chosen sibling it would be 1/800 (as there is only one sibling pair of chosen one).\nSo the probability of that the 2 students selected will be a sibling pair is: 60/1000\u22171/800=3/40000\nAnswer: A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe length of a rectangular field is 7/5 its width. If the perimeter of the field is 240 meters, what is the width of the field?\n\n### Options:\nA. 50\nB. 60\nC. 70\nD. 80\nE. 90\n\n### Answer:\nLet L be the length and W be the width. L = (7/5)W\nPerimeter: 2L + 2W = 240, 2(7/5)W + 2W = 240\nSolve the above equation to find: W = 50 m and L = 70 m.\ncorrect answer A)50\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA watch was sold at a loss of 10%. If it was sold for Rs.140 more, there would have been a gain of 4%. What is the cost price?\n\n### Options:\nA. 1000\nB. 2777\nC. 2667\nD. 2908\nE. 2712\n\n### Answer:\n90%\n104%\n--------\n14% ---- 140\n100% ---- ? => Rs.1000\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA room is 12 meters long, 10 meters wide 8 meters in height. The longest possible rod which can be placed in the room is\n\n### Options:\nA. 16.95 meters\nB. 16.80 meters\nC. 16.75 meters\nD. 16.55 meters\nE. 17.55 meters\n\n### Answer:\nSquare root of 12^2+10^2+8^2...(Diognal) which is square root of 308 that lies 17<\u221a308<18. Hence the answer should be E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average of 30 numbers is 48. If three numbers namely 45, 55 and 43 are discarded, the average of remaining numbers is?\n\n### Options:\nA. 47\nB. 47.03\nC. 48.03\nD. 48\nE. 49\n\n### Answer:\nExplanation:\nTotal of 30 numbers = 30 * 48 = 1440\nAverage o 27 numbers = 1440 - (45 + 55 + 43) / 27\n= 48.03\nAnswer: Option C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nCalculate the effect changes in dimension of a rectangle will have on its area, if length is increased by 40% and its breadth is decreased by 25%?\n\n### Options:\nA. 5% increase\nB. 7% increase\nC. 6% increase\nD. 4% increase\nE. 3% increase\n\n### Answer:\nlet L and B be 100 each\n100 * 100 = 10000\nL increase by 40% = 140\nB decrease by 25% = 75\n140 * 75 = 10500\n5% increase\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nGiven that a is the average (arithmetic mean) of the first six positive multiples of six and b is the median of the first twelve positive multiples of six, what is the ratio of a to b?\n\n### Options:\nA. 3:4\nB. 10:13\nC. 5:6\nD. 13:10\nE. 7:13\n\n### Answer:\nThe first nine positive multiples of six are {6, 12, 18, 24,30, 36}\nThe first twelve positive multiples of six are {6, 12, 18, 24, 30,36,42, 48, 54, 60, 66, 72}\nBoth sets are evenly spaced, thus their median=mean:\na=21 and b=(36+42)/2=39 --> a/b=21/39=7/13.\nAnswer: E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a boat goes 5km upstream in 25 minutes and the speed of the stream is 7 kmph, then the speed of the boat in still water is ?\n\n### Options:\nA. 18\nB. 19\nC. 20\nD. 21\nE. 22\n\n### Answer:\nRate upsteram =(5/25*60)kmph=12kmph.\nspeed of the stream =7kmph let speed in still water be xkm/hr. then speed upstream=(x-7)km/hr. x-7=12==>x=19km/hr Answer(B)\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn Town X, 120 percent of the population are employed, and 80 percent of the population are employed males. What percent of the employed people in Town X are females?\n\n### Options:\nA. 16%\nB. 25%\nC. 33%\nD. 40%\nE. 52%\n\n### Answer:\nTotal employed people 12%, out of which 80 are employed males, hence 40% are employed females.\n(employed females)/(total employed people)=40/120=1/3=33%\nAnswer: C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe amount of water (in ml) that should be added to reduce 21 ml. Lotion, containing 50% alcohol, to a lotion containing 30% alcohol, is?\n\n### Options:\nA. 8 ml\nB. 5 ml\nC. 14.5 ml\nD. 6 ml\nE. 1 ml\n\n### Answer:\n10.5 10.5\n30% 70%\n30% ----- 10.5\n70% ------? => 24.5 - 10.5 = 14.5 ml\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man invested Rs. 1552 in a stock at 97 to obtain an income of Rs. 160. The dividend from the stock is :\n\n### Options:\nA. 7.5 %\nB. 8 %\nC. 10 %\nD. None of these\nE. Cannot be determined\n\n### Answer:\nSolution\nBy investing Rs. 1552,income = Rs. 128.\nBy investing Rs. 97, income = Rs. (160/1552x97)= Rs.10\n\u00e2\u02c6\u00b4 Dividend =10%.\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man arranges to pay off a debt of Rs 3600 by 40 annual installments which are in A.P. When 30 of the installments are paid he dies leaving one-third of the debt unpaid.\nThe value of the 8th installment is:\n\n### Options:\nA. Rs 35\nB. Rs 50\nC. Rs 65\nD. Rs 70\nE. Rs 80\n\n### Answer:\nExplanation :\nLet the first installment be 'a' and the common difference between any two consecutive installments be 'd'\nUsing the formula for the sum of an A.P :-\nS=n/2[2a+(n\u22121)d].\nWe have,\n3600=40/2[2a+(40-1)d].\n3600=20[2a+39d].\n180 =2a+39d. ----(i)\nSimilarly,\n2400=30/2[2a+(30-1)d].\n160=2a+29d. ----(ii)\nOn solving both the equations we get:\nd=2 and a=51\nHence, the Value of 8th installment is :-\n=51+(8\u22121)2.\n=65.\nAnswer : C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nExcluding stoppages, the speed of a train is 45 kmph and including stoppages it is 36 kmph. Of how many minutes does the train stop per hour?\n\n### Options:\nA. 18\nB. 77\nC. 12\nD. 99\nE. 12\n\n### Answer:\nT = 9/45 * 60\n= 12\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA reduction of 20% in the price of salt enables a lady to obtain 10kgs more for Rs.100, find the original price per kg?\n\n### Options:\nA. 2.9\nB. 2.6\nC. 2.5\nD. 2.4\nE. 2.1\n\n### Answer:\n100*(20/100) = 20 --- 10\n? --- 1 => Rs.2\n100 --- 80\n? --- 2 => Rs.2.5\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMike's age is 48 years. If he is 4 more than twice the age of his son, find the age of his son.\n\n### Options:\nA. 20 years\nB. 22 years\nC. 16 years\nD. 18 years\nE. 19 years\n\n### Answer:\nLet Mike's son age be x.\n4 + 2 x = 48\nx = 22\nHence Mike's son age is 22 years\nAnswer : B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train speeds past a pole in 15 seconds and a platform 110 meters long in 25 seconds. What is the length of the train?\n\n### Options:\nA. 100 m\nB. 125 m\nC. 130 m\nD. 150 m\nE. 165 m\n\n### Answer:\nLet the length of the train be x meters.\nThe speed of the train is x / 15.\nThen, x + 110 = 25*(x / 15)\n10x = 1650\nx = 165 meters\nThe answer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n30 square stone slabs of equal size were needed to cover a floor area of 67.5 sq.m. Find the length of each stone slab?\n\n### Options:\nA. 150cm\nB. 767cm\nC. 88cm\nD. 666cm\nE. 776cm\n\n### Answer:\nArea of each slab\n=67.5/30m2=2.25m2\nLength of each slab \u221a2.25=1.5m=150cm\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n120 is what percent of 80?\n\n### Options:\nA. 0.2%\nB. 2%\nC. 5%\nD. 150%\nE. 500%\n\n### Answer:\n120= x*80/100\nx = 150%\nAns; D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n39! is divided by 41. Then what is the remainder?\n\n### Options:\nA. 1\nB. 3\nC. 4\nD. 5\nE. 6\n\n### Answer:\nSubstituting p = 41 in the wilson's theorem, we get\n40!+141=0\n40\u00d739!+141=0\n\u22121\u00d739!41=\u22121\nCancelling -1 on both sides,\n39!41=1\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nCost is expressed by the formula tb^4. If b is doubled, the new cost is what percent of the original cost?\n\n### Options:\nA. 200\nB. 600\nC. 800\nD. 1600\nE. 50\n\n### Answer:\nOriginal Cost C1=t1*b1^4\nNew Cost C2=t2*b2^4....only b is doubled so t2=t1 and b2=2b1\nC2=t2*(2b1)^4\n=16(t1*b1^4)\n=16C1\n16 times C1=>1600% of C1\nAns D=1600\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA class contains five juniors and five seniors. If one member of the class is assigned at random to present a paper on a certain subject, and another member of the class is randomly assigned to assist him, what is the probability R that both will be juniors?\n\n### Options:\nA. 1/10\nB. 1/5\nC. 2/9\nD. 2/5\nE. 1/2\n\n### Answer:\nI think you're right. The other way to do it (but the long way) is to figure out the probability that it is not two Juniors.\n2 seniors = P(Senior) * P(Senior) = 2/9\n1 Senior and 1 Junior = (1/2) *(5/9)*2 = 5/9\nProbability that it is not two Juniors is 5/9+2/9 = 7/9 so the probability R that it is two juniors is 1- (7/9) = 2/9.C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA merchant sells an item at a 20% discount, but still makes a gross profit of 50 percent of the cost. What percent of the cost would the gross profit on the item have been if it had been sold without the discount?\n\n### Options:\nA. 20%\nB. 40%\nC. 87.5%\nD. 60%\nE. 75%\n\n### Answer:\noriginal SP = X\nCost =C\ncurrent selling price = .8x ( 20% discount)\n.8x = 1.5C (50% profit)\nx= 1.5/.8 *C\nx= 15/8 C\nOriginal selling price is 1.875C which is 87.5% profit\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n2 pipes function simultaneously the reservoir will be filled in 12 hrs. One pipe fills reservoir 10 hrs faster thanthe other. How many hours does the faster pipe take to fill the reservoir?\n\n### Options:\nA. 12\nB. 20\nC. 24\nD. 26\nE. 29\n\n### Answer:\n1/x + 1/(x + 10) = 1/12\nx = 20\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the area of a circle is 36pi square feet, find its circumference.\n\n### Options:\nA. 12 pi feet\nB. 28 pi feet\nC. 38 pi feet\nD. 48 pi feet\nE. 58 pi feet\n\n### Answer:\nThe area is given by pi *r* r. Hence\npi * r *r = 36 pi\nr * r = 36; hence r = 36 feet\nThe circumference is given by\n2 * pi * r = 2 * pi * 6 = 12 pi feet\ncorrect answer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a number N is chosen at random from the set of two-digit integers whose digits are both prime numbers, what is the probability R that N is divisible by 3?\n\n### Options:\nA. 1/3\nB. \u00bc\nC. 9/25\nD. 5/16\nE. 0\n\n### Answer:\nPrime digits are: 2, 3, 5, 7\nTotal number of 2 digit #s with both digits prime are: 4*4 = 16\nout of these numbers divisible by 3 = 33, 27, 57, 72 and 75. I had to find the numbers manually using the 4 numbers above.\n=> prob = 5/16.\nAns D. Took me 3:20 mins.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average age of 8 men increases by 2 years when two women are included in place of two men of ages 20 and 24 years. Find the average age of the women?\n\n### Options:\nA. 11\nB. 12\nC. 30\nD. 98\nE. 15\n\n### Answer:\n20 + 24 + 8 * 2 = 60/2 = 30\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe price of an item changed from $120 to $100. Then later the price decreased again from $100 to $80. Which of the two decreases was larger in percentage term?\n\n### Options:\nA. 10%\nB. 20%\nC. 30%\nD. 40%\nE. 50%\n\n### Answer:\nFirst decrease in percent\npart / whole = (120 - 100) / 120 = 0.17 = 17%\nSecond decrease in percent\npart / whole = (100 - 80) / 100 = 0.20 = 20%\nThe second decrease was larger in percent term. The part were the same in both cases but the whole was smaller in the second decrease.\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA polygon has 44 diagonals, then the number of its sides are\n\n### Options:\nA. 11\nB. 9\nC. 7\nD. 5\nE. 3\n\n### Answer:\nLet the number of sides be n.\nThe number of diagonals is given by nC2 - n\nTherefore, nC2 - n = 44, n>0\nn(n - 1) / 2 - n = 44\nn2 - 3n - 88 = 0\nn2 -11n + 8n - 88 = 0\nn(n - 11) + 8(n - 11) = 0\nn = -8 or n = 11.\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 0 < x < 1 and x \u2260 0, which of the following inequalities must be true?\nI. x^3 < x\nII. x^2 < |x|\nIII. x^4 \u2013 x^5 > x^3 \u2013 x^2\n\n### Options:\nA. I only\nB. II only\nC. III only\nD. II and III only\nE. I, II, and III\n\n### Answer:\nAnswer is D. Let's look at the statements one by one\nStmt I. x^3 < x\nif 0x\nSo this statement is not always true\nStmt II. x^2 < |x|\nBecause we know that x is a number less than one but not equal to zero then x^2 will always be less than |x|.\nWhy? think of positive fractions (and you can think in terms of positive fractions because the inequality is in regards to |x|). Lets set x = 1/2, then x^2 = 1/4 and 1/4<1/2\nSo Stmt II is always true\nStmt III. x^4 \u2013 x^5 > x^3 \u2013 x^2\nThis one may seem tricky but lets break it down. x^4 \u2013 x^5 > x^3 \u2013 x^2 = x^4(1-x)>x^2(x-1).\nBecause lets concentrate on (1-x) and (x-1). We are given that -10 and (x-1)<0. x^4 will always be positive and x^2 will always be positive so without doing any math we are looking at positive > negative... which is always true.\nSo Stmt III is always true\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA 240 meter long train crosses a man standing on the platform in 6 sec. What is the speed of the train?\n\n### Options:\nA. 228\nB. 144\nC. 1266\nD. 188\nE. 211\n\n### Answer:\nS = 240/6 * 18/5 = 144 kmph\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJalal weighs twice as much as Meena. Meena's weight is 60% of Bahar's weight. Dolly weighs 50% of Laila's weight. Laila weighs 19% of Jalal's weight. Who among these 5 persons weighs the least?\n\n### Options:\nA. Bahar\nB. Dolly\nC. Jalal\nD. Laila\nE. Meena\n\n### Answer:\nLet Jalal weigh 100 kg.\nThen Meena = 50 kg, Bahar = 83.33 kg, Laila = 19 kg, Dolly = 9.5 kg\nTherefore clearly Dolly is the lightest.\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many 4 digit numbers can be formed with the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 and 9?\n\n### Options:\nA. a. 220\nB. b. 249\nC. c. 432\nD. d. 216\nE. e. 288\n\n### Answer:\nTaking Question with it's same language as given\nTo make number divisible by 5, the unit digit should be either 0 or 5 only\nCase 1: If unit digit is fixed as zero\nWith two6s The choice to fill the remaining three digits = 3C2 x 5 = 15\nWith all remaining 3 digits different, The choice to fill the remaining three digits = 6 x 5 x 4= 120\nTotal Such cases = 120+15 = 135\nCase 2: If unit digit is fixed as Five\nWith two6s and one0The choice to fill the remaining three digits = 2 [6605 or 6065]\nWith two6s and without0The choice to fill the remaining three digits = 3C2 x 4 = 12\nWith all remaining 3 digits different, and one0The choice to fill the remaining three digits = 2 (ways to place zero) x 5 x 4= 40\nWith all remaining 3 digits different, and without0The choice to fill the remaining three digits = 3 x 5 x 4= 60\nTotal Such cases = 2+12+40+60 = 114\nTotal numbers = 135+114 = 432\nANSWER OPTION E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf x/y is an integer, which of the following must also be an integer?\nI. xy\nII. y/x\nIII. x\n\n### Options:\nA. I alone\nB. II alone\nC. III alone\nD. I and III\nE. None of the above\n\n### Answer:\nLet's take X = 4/3 and Y = 2/3\nThen X/Y = 2 which is an integer.\nBut XY = 4/3 * 2/3 = 8/9 --> Not an integer.\nY/X = 2/3 divided by 4/3 = 2/4 = 1/2 Not an integer.\nX alone is 4/3. Not an integer.\nHence E.\nNone of the above.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nCountry X imported approximately $1.44 billion of goods in 1996. If Country X imported $420 million of goods in the first two months of 1997 and continued to import goods at the same rate for the rest of the year, by how much would Country Xs 1997 imports exceed those of 1996?\n\n### Options:\nA. $214 million\nB. $1120 million\nC. $1144 million\nD. $1240 million\nE. $1080 million\n\n### Answer:\nConvert units to millions as answer is in millions\n1996 Imports = $1.44 bill = $1440 mill\ni.e. 1440/12 = $120 mill/month\n1997 Imports = $420 mill/2 month\ni.e. $210 mill/month\nDifference/month = 210-120 = 90\nDifference/year = $90 mill * 12 = $1080 mill\nANSWER: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA watch which gains uniformly is 2 minutes low at noon on Monday and is 4 min. 48 sec. fast at 2 p.m. on the following Monday. When was it correct?\n\n### Options:\nA. 2 p.m. on Tuesday\nB. 2 p.m. on Wednesday\nC. 3 p.m. on Thursday\nD. 1 p.m. on Friday\nE. None of these\n\n### Answer:\nTime from 12 p.m. on Monday to 2 p.m. on the following Monday = 7 days 2 hours = 170 hours.\n\u2234 The watch gains (2 + 44\u20445) min.\nor 34\u20445 min. in 170 hrs.\nNow, 34\u20445 min. are gained in 170 hrs.\n\u2234 2 min. are gained in (170 \u00d7 5\u204434 \u00d7 2)hrs. = 50 hrs\n\u2234 Watch is correct 2 days 2 hrs. after 12 p.m. on Monday i.e. it will be correct at 2 p.m. on Wednesday.\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the smallest five digit number that is divisible by 15, 24, 36, and 54?\n\n### Options:\nA. 10320\nB. 10800\nC. 10030\nD. 10380\nE. 10460\n\n### Answer:\n15 = 3 * 5\n24 = 2^3 * 3\n36 = 2^2 * 3^2\n54 = 2 * 3^3\nLCM = 2^3 * 3^3 * 5 = 1080\nThe smallest five-digit number that is a multiple of 1080 is 10*1080 = 10,800\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how many different number of ways 4 boys and 3 girls can sit on a bench such that girls always sit together?\n\n### Options:\nA. 720\nB. 740\nC. 760\nD. 790\nE. 800\n\n### Answer:\nOption 'A'\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA dealer purchased an article at 3/4 of its list price and sold 50% more than the list price. Find his gain percent\n\n### Options:\nA. 90%\nB. 40%\nC. 100%\nD. 75%\nE. 25%\n\n### Answer:\nMP = 100\nCP = 75\nSP = 150\n------\n75 ---- 75\n100 ---- ? => 100%\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRose is two years older than Bruce who is twice as old as Chris. If the total of the age of Rose, B and Chris be 37 years, then how old is Chris ?\n\n### Options:\nA. 7 years\nB. 10 years\nC. 12 years\nD. 13 years\nE. 14 years\n\n### Answer:\nLet Chris's age be x years. Then, Bruce's age = 2x years.Rose's age = (2x + 2) years.\n(2x + 2) + 2x + x = 37\n5x = 35\nx = 7\nHence, Chris's age =7 years.\nAnswer : A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe banker's discount on Rs.1150 due a certain time hence is Rs.115. Find the true discount and the banker's gain.\n\n### Options:\nA. 10\nB. 15\nC. 18\nD. 21\nE. None\n\n### Answer:\nSolution\nSum\t=B.D x T.D/ B.D - T.D\n= B.D x T.D/ B.G\nT.D / B. G\t=Sum / B.D\n= 1650 / 165\n= 10 / 1\nIf B.D is Rs. 11,T.D= Rs.10.\nIf B.D is Rs.165,\nT.D\t= Rs.(10 / 11 x 165)\n= Rs.150.\nAnd, B.G\t= Rs(165 - 150)\n= Rs.15.\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA lady builds 12cm length, 16cm width, and 6cm height box using 3cubic cm cubes. What is the minimum number of cubes required to build the box?\n\n### Options:\nA. 345\nB. 384\nC. 378\nD. 398\nE. 300\n\n### Answer:\nNumber of cubes required = Volume of box/Volume of cube\n= 12*16*6/3\n=384 cubes\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRichard has to paint a mural with seven horizontal stripes. He only has enough paint for four red stripes, four blue stripes, four white stripes. If his patron wants at most two different colors in the mural, how many different ways can he paint the wall?\n\n### Options:\nA. 210\nB. 350\nC. 700\nD. 2,520\nE. 5,040\n\n### Answer:\nNumber of ways to choose 2 colors among 3 - 3c2\nNumber of ways that the chosen colors can be painted for 7 horizontal stripes - 2 (either (4,3) or (3,4))\nNow the order,\nthe number of ways in which a particular color among the 2 chosen colors can be painted for 4 stripes is - 7c4\n[Note: We don't need to calculate the ways for the remaining 3 stripes as they are obvious and already counted under this]\nTotal number of combinations - 3c2 * 2* 7c4 = 210\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average (arithmetic mean) of 24, 35, and 58 is 6 more than the average of 19, 51, and x. What is x?\n\n### Options:\nA. 26\nB. 27\nC. 28\nD. 29\nE. 30\n\n### Answer:\nThe average of 24, 35, and 58 is 39.\nThe average of 19, 51 and x is 33.\nThen 19 + 51 + x = 99.\nx = 29.\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf three numbers are added in pairs, the sums equal 10,19 and 21. Find the numbers?\n\n### Options:\nA. 5, 10, 15\nB. 6, 4, 15\nC. 2, 4, 8\nD. 15, 20, 25\nE. None\n\n### Answer:\nSol.\nLet the numbers be x, y and z.\nThen, x + y = 10 ............(i) and\ny + z = 19 ....................(II) and\nx + z =21 ...............(III)\nAdding (i),(ii) and (iii), we get : 2(x+y+z) = 50 or (x+y+z) = 25.\nThus, x = (25 - 19) = 6;\ny = (25 - 21) = 4;\nz = (25 - 10) = 15.\nHence, the required numbers are 6, 4 and 15.\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many 5's are there preceded by 2 but not followed by 6?\n5 9 3 2 1 2 6 7 4 9 2 5 2 1 3 2 8 2 5 1 3 8 3 2 5 6 2 5 3 9 5 8 2 0 1 8 7 4 6 3\n\n### Options:\nA. 4\nB. 5\nC. 6\nD. 8\nE. 3\n\n### Answer:\n2 5 2\n2 5 3\n2 5 1\nOnly at these places 3 is preceded by 2 but not followed by 6\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a sports club with 30 members, 16 play badminton and 19 play tennis and 2 do not play either. How many members play both badminton and tennis?\n\n### Options:\nA. 7\nB. 8\nC. 9\nD. 10\nE. 11\n\n### Answer:\nLet x play both badminton and tennis so 16-x play only badminton and 19-x play only tennis. 2 play none and there are total 30 students. hence,\n(16-x)+(19-x)+x+2=30\n37-2x+x=30\n37-x=30\nx=7\nSo 7 members play both badminton and tennis.\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFor any positive integer n, the sum of the first n positive integers equals n(n+1)/2. What is the sum of all the integers between 100 and 200?\n\n### Options:\nA. 4545\nB. 5050\nC. 6525\nD. 4352\nE. 4652\n\n### Answer:\nsum = 100*101/2 = 50*101 = 5050\nAnswer is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n3/4 of a number is 19 less than the original number. The number is ?\n\n### Options:\nA. 84\nB. 64\nC. 76\nD. 72\nE. None\n\n### Answer:\nAnswer\nLet the original number be N.\nSo from question N - 3N/4 = 19\n\u21d2 4N - 3N = 76\n\u2234 N = 76\nOption: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA dishonest dealer professes to sell goods at the cost price but uses a weight of 880 grams per kg, what is his percent?\n\n### Options:\nA. 2%\nB. 25%\nC. 22%\nD. 13.63%\nE. 45%\n\n### Answer:\n880 --- 120\n100 --- ? => 13.63%\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOn 8th Feb, 2005 it was Tuesday. What was the day of the week on 8th Feb, 2004?\n\n### Options:\nA. Tuesday\nB. Monday\nC. Sunday\nD. Wednesday\nE. Friday\n\n### Answer:\nThe year 2004 is a leap year. It has 2 odd days.\nThe day on 8th Feb, 2004 is 2 days before the day on 8th Feb, 2005.\nHence, this day is Sunday.\nAnswer: Option C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA work which could be finished in 9 days was finished 3 days earlier after 10 more men joined. The number of men employed was?\n\n### Options:\nA. 24\nB. 27\nC. 20\nD. 35\nE. 25\n\n### Answer:\nC\n20\nx ------- 9\n(x + 10) ---- 6\nx * 9 = (x + 10)6\nx = 20\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn certain year in Country C, x sets of twins and y sets of triplets were born. If there were z total babies born in Country C in this year, and x and y were both greater than 0, which of the following represents the fraction Q of all babies born who were NOT part of a set of twins or triplets?\n\n### Options:\nA. z - 2x - 3y\nB. (2x+3y)/z\nC. (x+y)/z\nD. 1 - (2x+3y)/z\nE. 1 - (x+y)/z\n\n### Answer:\nX set of twins implies 2x babies of twin category.\nY set of triplets means 3y babies of triplet category.\nLet K be the babies other than twin or triplet category.\nTotal babies = z = 2x+3y+k.\nor K=Z-(2x+3y)\n=> Fraction of babies other than twin or triplet categories = K/Z = Z-(2x+3y)/Z.\nQ= 1- (2x+3y)/Z. Hence answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average wages of a worker during a fortnight comprising 15 consecutive working days was $90 per day. During the first 7 days, his average wages was $87 per day and the average wages during the last 7 days was $94 per day. What was his wage on the 8th day?\n\n### Options:\nA. $83\nB. $90\nC. $92\nD. $97\nE. $104\n\n### Answer:\nAverage daily wage of a worker for 15 consecutive working days = 90$\nDuring the first 7 days , the daily average daily wage = 87$\nDuring the last 7 days , the daily average daily wage = 94$\nWage on 8th day = 90*15 -( 87*7 + 94 *7)\n= 1350 - (609 + 658)\n=1350 - 1267\n= 83\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTake number 1000 and then add 20 to it. Now add 1000 one more time. Now add 30. Now add 1000 one more time. Now add 40. Now add 1000 one more time. Now add 10. What is the total?\n\n### Options:\nA. 4100\nB. 3590\nC. 2800\nD. 3700\nE. 3600\n\n### Answer:\nA\n4100\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA can give B 100 meters start and C 200 meters start in a kilometer race. How much start can B give C in a kilometer race?\n\n### Options:\nA. 111.12\nB. 111.18\nC. 131.12\nD. 211.12\nE. 111.17\n\n### Answer:\nA runs 1000 m while B runs 900 m and C runs 800 m.\nThe number of meters that C runs when B runs 1000 m,\n= (1000 * 800)/900 = 8000/9 = 888.88 m.\nB can give C = 1000 - 888.88 = 111.12 m.\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSelect Odd number:\n6, 9, 15, 21, 24, 28, 30\n\n### Options:\nA. 20\nB. 21\nC. 24\nD. 28\nE. 30\n\n### Answer:\nEach of the numbers except 28, is a multiple of 3.\nanswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA truck owner will refuel his vehicle at a rate of 2 gallons of diesel fuel every 5 seconds. If diesel fuel costs $ 2 per gallon, how long will it take for the truck owner to refuel his vehicle with $ 50 worth of diesel fuel?\n\n### Options:\nA. 50 seconds\nB. 1 minute\nC. 1 minute 20 seconds\nD. 20 minutes\nE. 1 hour 20 minutes\n\n### Answer:\n2 gal / 5 sec\n$2 / gal\n$40/$2 = 20 gal\n2 gal / 5 sec with 20 gal = 50 sec\nA. 50 seconds\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n9. On level farmland, two runners leave at the same time from the intersection of two country roads. One runner jogs due north at a constant rate of 6 miles per hour while the second runner jogs due east at a constant rate that is 2 miles per hour faster than the first runner's rate. How far apart, to the nearest mile, will they be after 1/2 hour ?\n\n### Options:\nA. 6\nB. 7\nC. 5\nD. 12\nE. 14\n\n### Answer:\nIf runner 1 is going north and runner 2 is going east they are like two sides of a 90 degree triangle.\nSide 1 = 6 m/h --> 3 m in 1/2 hr\nSide 2 = 8 m/h --> 4 m in 1/2 hr\nto complete this right angle triangle\nd^2 = 4^2 + 3^2\nd^2 = 25\n= 5\nAnswer option C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 sec. The speed of the train is?\n\n### Options:\nA. 22\nB. 50\nC. 888\nD. 277\nE. 21\n\n### Answer:\nSpeed of the train relative to man = 125/10 = 25/2 m/sec.\n= 25/2 * 18/5 = 45 km/hr\nLet the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr.\nx - 5 = 45 => x = 50 km/hr.\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn an election only two candidates contested. A candidate secured 70% of the valid votes and won by a majority of 172 votes. Find the total number of valid votes?\n\n### Options:\nA. 430\nB. 437\nC. 435\nD. 431\nE. 433\n\n### Answer:\nLet the total number of valid votes be x.\n70% of x = 70/100 * x = 7x/10\nNumber of votes secured by the other candidate = x - 7x/100 = 3x/10\nGiven, 7x/10 - 3x/10 = 172 => 4x/10 = 172\n=> 4x = 1720 => x = 430.\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA tailor trims 6 feet from opposite edges of a square piece of cloth, and 5 feet from the other two edges. If 120 square feet of cloth remain, what was the length of a side of the original piece of cloth?\n\n### Options:\nA. 20\nB. 22\nC. 24\nD. 26\nE. 28\n\n### Answer:\nLet the original side of the square be x.\n(x-12)*(x-10) = 120 = 10*12\nx = 22\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhen processing flower-nectar into honey bees' extract, a considerable amount of water gets reduced. How much flower-nectar must be processed to yield 1kg of honey, if nectar contains 50% water, and the honey obtained from this nectar contains 35% water?\n\n### Options:\nA. 1.3 kg\nB. 1.5 kg\nC. 1.7 kg\nD. 1.9 kg\nE. None of these\n\n### Answer:\nExplanation :\nFlower-nectar contains 50% of non-water part.\nIn honey this non-water part constitutes 65% (100-35).\nTherefore 0.5 X Amount of flower-nectar = 0.65 X Amount of honey = 0.65 X 1 kg\nTherefore amount of flower-nectar needed =\n(0.65/0.51)kg=1.3 kgs\nAnswer : A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how many years, Rs. 200 will produce the same interest @ 5 % as Rs. 900 produce in 2 years @ 3 \u00bd %?\n\n### Options:\nA. 6.3 years\nB. 8.2 years\nC. 9 years\nD. 12 years\nE. None of these\n\n### Answer:\nExplanation:\nP = Rs 900, R = 3 \u00bd % = 7/2 %, T = 2 years.\nTherefore,\nS.I. = PRT/100\nS.I. = Rs. (900 x 7/2 x 2/100) = Rs. 63\nNow, P = Rs. 200, S.I. = Rs. 63, R = 5 %\nTime = ((100 x 63) / (200 x 5) ) years = 6.3 years\nANSWER A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the 11th term in this sequence?\n1,4,5,11,18,29,49,80,129,211,\n\n### Options:\nA. 352\nB. 442\nC. 345\nD. 342\nE. 362\n\n### Answer:\n1+4 =5 +0 =5\n5+4 =9+2 =11\n11+5 =16+2 =18\n18+11=29+0 =29\n29+18=47+2 =49\n49+29=78+2 =80\n80+49=129+0=129\n129+80=209+2=211\n211+129=340+2=342\nso 11th term is 342\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA factory producing tennis balls stores them in either big boxes, 25 balls per box, or small boxes, with 17 balls per box. If 94 freshly manufactured balls are to be stored, what is the least number of balls that can be left unboxed?\n\n### Options:\nA. 0\nB. 1\nC. 2\nD. 3\nE. 4\n\n### Answer:\nThere is no way to store 94 balls without leftovers: 94\u22120\u221725=94- 94\u22122\u221725=44 ,94\u22123\u221725=19 are not divisible by 17\n.93 balls can be stored successfully: 93\u22121\u221725=68 is divisible by 17. Thus, 93=1\u221725+4\u221717 and we need 1 big box and 4 small boxes.\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe music class consists of 4 girls and 7 boys. How many ways can a group of 3 be formed if it has to include at least one boy?\n\n### Options:\nA. 155\nB. 158\nC. 161\nD. 165\nE. 172\n\n### Answer:\nClassic combination problem\nAt least 1 boy = Total - all girls\nAll girls = C(4,3) = 4\nTotal combination = C(11,3) = 165\nAns = 165-4 = 161\nANS:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA boatman goes 2 km against the current of the stream in 1 hour and goes 1 km along the current in 10 minutes.How long will it take to go 5 km in stationary water ?\n\n### Options:\nA. 40 minutes\nB. 1 hour\nC. 1 hr 15 min\nD. 1 hr 20 min\nE. None of these\n\n### Answer:\nSolution\nRate downstream =(1/10x60) km/hr = 6 km/hr, Rate upstream = 2 km/hr.\nSpeed in still water =1/2(6 + 2) km/hr = 4 km/hr.\n\u2234 Required time =(5/4)hrs = 1 1/4hrs = 1 hr 15 min. Answer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nCity X has a population 5 times as great as the population of City Y, which has a population twice as great as the population of City Z. What is the ratio of the population of City X to the population of City Z?\n\n### Options:\nA. 1:8\nB. 1:4\nC. 2:1\nD. 4:1\nE. 10:1\n\n### Answer:\nx= 5y, y= 2*z\nX : Y , Y : Z\n5 : 1 , 2 : 1\n10 : 2 , 2 : 1\nSo, X : Z = 10 : 1\n(E)\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds. Its length is\n\n### Options:\nA. 100\nB. 120\nC. 130\nD. 150\nE. 140\n\n### Answer:\nLet the length of the train be x meters and its speed be y m/sec.\nThey, x / y = 15 => y = x/15\nx + 100 / 25 = x / 15\nx = 150 m.\nAnswer: Option D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA snooker tournament charges $40.00 for VIP seats and $15.00 for general admission (\u201cregular\u201d seats). On a certain night, a total of 320 tickets were sold, for a total cost of $7,500. How many fewer tickets were sold that night for VIP seats than for general admission seats?\n\n### Options:\nA. 212\nB. 200\nC. 220\nD. 230\nE. 240\n\n### Answer:\nlet no of sits in vip enclosure is x then x*40 +15( 320-x) =7500 or 25x = 7500 -4800 , x = 2700/25 =108\nvip =108 general 212\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA person spends 40% of his salary on food, 25% on house rent, 15% on entertainment and 5% on conveyance. If his savings at the end of the month is Rs. 1500, then his salary per month in rupees is:\n\n### Options:\nA. 4000\nB. 6000\nC. 8000\nD. 10000\nE. None of these\n\n### Answer:\nTotal expenditure = 40 + 25 + 15 + 5 = 85%\nSaving = (100 - 85) = 15%\n15/100 \u00d7 Salary = 1500, Salary = 10000 Rs.\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAn article is bought for Rs.675 and sold for Rs.775, find the gain percent?\n\n### Options:\nA. 73%\nB. 14.8%\nC. 33 1/3%\nD. 93 1/3%\nE. 33 1/3%\n\n### Answer:\nExplanation:\n675 ---- 100\n100 ---- ? => 14.8%\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRavi and sunil are partners in a business. Ravi invests Rs.15,000 for 8 months and Sunil invested Rs.8000 for 10 months then after one year ratio of their profits will be\n\n### Options:\nA. 1:3\nB. 2:3\nC. 3:2\nD. 3:1\nE. 3:4\n\n### Answer:\n=(15000*8):(8000*10)\n=120000:80000\n=3:2\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a race where 10 cars are running, the chance that car X will win is 1/7, that Y will win is 1/3 and that Z will win is 1/5. Assuming that a dead heat is impossible, find the chance that one of them will win.\n\n### Options:\nA. 1/140\nB. 1/180\nC. 71/105\nD. 21/113\nE. 57/120\n\n### Answer:\nRequired probability = P(X) + P(Y) + P(Z) (all the events are mutually exclusive).\n= 1/7 + 1/3 + 1/5\n= 71/105\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nYou forgot the three digit code of your safe. But you have written some hints to calculate the code if you forgot the code.\nBelow are the hints that you have written\nHint-1 : One of the numbers is correct and is placed in its correct position\n5 4 7\nHint-2: Nothing is correct\n5 3 0\nHint-3: Two numbers are correct but not placed at its correct position.\n2 5 9\nHint-4: One number is correct but not placed at its correct position.\n7 0 6\nHint-5: One number is correct but not placed at its correct position.\n6 4 9\nWhat's is the code.\n\n### Options:\nA. 827\nB. 728\nC. 923\nD. 323\nE. 927\n\n### Answer:\nE\n927\n1) 5 4 7 : 7 is placed correctly\n2) 5 3 0 : None of the numbers is in the code\n3) 2 5 9 : 2 & 9 are correct number of code but placed at wrong position\n4) 7 0 6: Number 7 is there but placed at wrong position\n5) 6 4 9: Number 9 is there but placed at wrong position\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average of 11 numbers is 12.8. If the average of the first six numbers is 12.4 and that of the last six numbers is 12.2,then the middle number is?\n\n### Options:\nA. 7.8\nB. 7.9\nC. 7.1\nD. 7.2\nE. 6.8\n\n### Answer:\nMiddle number = 12.4*6 + 12.2*6 - 12.8*11 = 147.6-140.8=6.8\nAnswer is E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average runs scored by a batsman in 20 matches is 40. In the next 10 matches the batsman scored an average of 30 runs. Find his average in all the 30 matches?\n\n### Options:\nA. 31\nB. 36.67\nC. 88\nD. 13\nE. 12\n\n### Answer:\nTotal score of the batsman in 20 matches = 800.\nTotal score of the batsman in the next 10 matches = 300.\nTotal score of the batsman in the 30 matches = 1100.\nAverage score of the batsman = 1100/30 = 36.67.\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf two positive numbers are in the ratio 1/8 : 1/5, then by what percent is the second number more than the first?\n\n### Options:\nA. 40%\nB. 33 1/3%\nC. 60%\nD. 66 2/3%\nE. None of these\n\n### Answer:\nGiven ratio = 1/8 : 1/5 = 5 : 8\nLet first number be 5x and the second number be 8x.\nThe second number is more than first number by 3x.\nRequired percentage = 3x/5x * 100 = 60%.\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n7 + 7+ 7 + 7 \u00d7 7^2 + 7 \u00d7 7^3 + 7 \u00d7 7^4 + 7 \u00d7 7^5 + 7 \u00d7 7^6 + 7 \u00d7 7^7 =\n\n### Options:\nA. 7^3\nB. 7^8\nC. 7^2\nD. 7^7\nE. 7^11\n\n### Answer:\nWe have the sum of 9 terms. Now, if all terms were equal to the largest term 7*7^7 we would have: sum=9*(7*7^7)=63*7^7=~7^9, so the actual sum is less than 7^9 and more than 7^7 (option D) as the last term is already more than that. So the answer is clearly B.\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man buys an article and sells it at a profit of 20%. If he had bought it at 20% less and sold it for Rs.75 less, he could have gained 25%. What is the cost price?\n\n### Options:\nA. 288\nB. 375\nC. 267\nD. 298\nE. 121\n\n### Answer:\nCP1 = 100 SP1 = 120\nCP2 = 80 SP2 = 80 * (125/100) = 100\n20 ----- 100\n75 ----- ? => 375\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe ratio of the area of a square to that of the square drawn on its diagonal is?\n\n### Options:\nA. 4/16\nB. 4/13\nC. 4/11\nD. 4/19\nE. 4/12\n\n### Answer:\nP(S\u1d1cK)\n= P(S) + P(K) - P(S\u2229K), where S denotes spade and K denotes king.\nP(S\u1d1cK)\n= 13/52 + 4/52 - 1/52\n= 4/13\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo cars, Car1 and Car2 move towards each other from Q and Y respectively with respective speeds of 20 m/s and 15 m/s. After meeting each other Car1 reaches Y in 10 seconds. In how many seconds does Car 2 reach Q starting from Y?\n\n### Options:\nA. 15.5 sec\nB. 8.4 sec\nC. 33.6 sec\nD. 31.11 sec\nE. 16.8 sec\n\n### Answer:\nQ--------------------------------------|----------------------------Y\nCar A(20mps)------------------------->P<---------------Car B(15mps)\nLet 2 cars meet each other at point P in t seconds.\nCar1 covers distance= 20t. Car2 covers distance=15t. So, total distance QY= 35t.\nFrom P, Car 1 reaches onto Y in 10 secs. So it covers 15t further.\nso, 15t/20 = 10\nSo t=40/3 sec and total distance = (35*40)/3\nHence Car2 will cover total distance in (35*40)/(3*15) = 31.11 sec approx.\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n108.\tTriangle A\u2019s base is 20% greater than the base of triangle B, and A\u2019s height is 20% less than the height of triangle B. The area of triangle A is what percent less or more than the area of triangle B?\n\n### Options:\nA. 0.25 % less\nB. 1 % less\nC. Equal to each other\nD. 1 % more\nE. 9 % more\n\n### Answer:\nWish the question specified that we are talking about corresponding height.\nBase of A = 21/20 * Base of B\nHeight of A = 19/20 * Height of B\nArea of A = (1/2) * Base of A * Height of A = 21/20 * 19/20 * Area of B = 399/400 * Area of B\nArea of A is 0.25% less than the area of B.\nAnswer (A)\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe speed of a boat in upstream is 50 kmph and the speed of the boat downstream is 60 kmph. Find the speed of the boat in still water and the speed of the stream?\n\n### Options:\nA. 5 kmph\nB. 4 kmph\nC. 9 kmph\nD. 8 kmph\nE. 6 kmph\n\n### Answer:\nSpeed of the boat in still water = (50+60)/2 = 55 kmph. Speed of the stream\n= (60-50)/2\n= 5 kmph.\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOf the goose eggs laid at a certain pond, 1/3 hatched and 4/5 of the geese that hatched from those eggs survived the first month. Of the geese that survived the first month, 3/5 did not survive the first year. If 120 geese survived the first year and if no more than one goose hatched from each egg, how many goose eggs were laid at the pond?\n\n### Options:\nA. 1025\nB. 1075\nC. 1125\nD. 1175\nE. 1225\n\n### Answer:\nLet x be the number of eggs that were laid.\n(2/5)(4/5)(1/3)x = 120\n(8/75)x = 120\nx = 1125\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n50 men took a dip in a water tank 40 m long and 20 m broad on a religious day. If the average displacement of water by a man is 4 m3, then the rise in the water level in the tank will be:\n\n### Options:\nA. 20 cm\nB. 23 cm\nC. 25 cm\nD. 30 cm\nE. 32 cm\n\n### Answer:\nL*b*h=Total water displaced=200(given)\nTo find height i.e rise in the water level\nh=200/L*B\nH=25cm\nanswer :C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA meal cost $ 35.50 and there was no tax. If the tip was more than 10 pc but less than 15pc of the price, then the total amount paid should be:\n\n### Options:\nA. 40-42\nB. 39-41\nC. 38-40\nD. 37-39\nE. 36-37\n\n### Answer:\n10%(35.5) = 3.55\n15%(35.5) = 5.325\ntotal amount could have been 35.5+3.55 and 35.5+5.325\n=> could have been between 39.05 and 40.625\n=> approximately between 39 and 41\nAnswer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA woman says, \"If you reverse my own age, the figures represent my husband's age. He is, of course, senior to me and the difference between our ages is one-eleventh of their sum.\" The woman's age is\n\n### Options:\nA. 23 years\nB. 34 years\nC. 45 years\nD. 54 years\nE. None of these\n\n### Answer:\nExplanation:\nLet x and y be the ten's and unit's digits respectively of the numeral denoting the woman's age.\nThen, woman's age = (10X + y) years; husband's age = (10y + x) years.\nTherefore (10y + x)- (10X + y) = (1/11) (10y + x + 10x + y)\n(9y-9x) = (1/11)(11y + 11x) = (x + y) 10x = 8y x = (4/5)y\nClearly, y should be a single-digit multiple of 5, which is 5.\nSo, x = 4, y = 5.\nHence, woman's age = 10x + y = 45 years.\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a man lost 4% by selling oranges at the rate of 24 a rupee at how many a rupee must he sell them to gain 44%?\n\n### Options:\nA. 16\nB. 8\nC. 9\nD. 4\nE. 3\n\n### Answer:\n96% ---- 24\n144% ---- ?\n96/144 * 24 = 16\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average salary/head of all the workers in a workshop is Rs.1100, if the average salary/head of 9 technician is Rs.1300 and the average salary/head of the rest is Rs.880, the total no. of workers in the work-shop is ?\n\n### Options:\nA. 18\nB. 20\nC. 22\nD. 17\nE. 26\n\n### Answer:\nLet the total number of workers be y.\rSo sum of salary for all workers = sum of salary of 9 technician + sum of salary for other y -9 workers.\r9 x 1300 + 880(y -9) = 1100 y\r\u21d2 11700 + 880y - 7920 = 1100y\r\u21d2 220y = 3780\r\u2234 y = 17 So total number of workers = 17 D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain sum of money at simple interest amounted Rs.840 in 10 years at 3% per annum, find the sum?\n\n### Options:\nA. 277\nB. 262\nC. 298\nD. 646\nE. 267\n\n### Answer:\n840 = P [1 + (10*3)/100]\nP = 646\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nGiven distinct positive integers 1, 12, 3, x, 2, and 9, which of the following could be the median?\n\n### Options:\nA. 1\nB. 3\nC. 6\nD. 8\nE. 9\n\n### Answer:\nThe median of a set with even number of terms is the average of two middle terms when arranged in ascending (or descending) order.\nArrange numbers in ascending order: 1, 2, 3, 9, 11, and x.\nNow, x can not possibly be less than 3 as given that all integers are positive and distinct (and we already have 1, 2, and 3).\nNext, if x is 3 not among answer choices;\nIf x=7, then median=(3+7)/2=5 --> not among answer choices;;\nIf x is more than 9 so 10 or more then the median will be the average of 3 and 9 so (3+9)/2=6 (the maximum median possible).\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a positive integer n is divisible by both 3 and 5, then n must also be divisible by which of the following?\nI. 15\nII. 8\nIII. 45\n\n### Options:\nA. None\nB. I only\nC. II only\nD. I and II\nE. II and III\n\n### Answer:\nA multiple of 3 and 5 is also a multiple of 15, but not necessarily a multiple of 8 or 45.\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe length of rectangle is thrice its breadth and its perimeter is 96 m, find the area of the rectangle?\n\n### Options:\nA. 432 sq m\nB. 356 sq m\nC. 452 sq m\nD. 428 sq m\nE. 528 sq m\n\n### Answer:\n2(3x + x) = 96\nl = 36 b = 12\nlb = 36 * 12 = 432\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man sells a horse for Rs.800 and loses something, if he had sold it for Rs.980, his gain would have been double the former loss. Find the cost price of the horse?\n\n### Options:\nA. 337\nB. 278\nC. 288\nD. 860\nE. 721\n\n### Answer:\nCP = SP + 1CP = SP - g\n800 + x = 980 - 2x\n3x = 180 => x = 60\nCP = 800 + 60 = 860\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a friendship gang Andrew has 8 gang, in how many ways can he invite one or more of the gang to his house?\n\n### Options:\nA. 243\nB. 255\nC. 256\nD. 287\nE. 300\n\n### Answer:\nAndrew can select one or more than one of his 8 gang.\n=> Required number of ways = 28 \u2013 1= 255.\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If two marbles are drawn at random, what is the probability that at least one is green?\n\n### Options:\nA. 23/35\nB. 23/37\nC. 23/39\nD. 23/32\nE. 23/31\n\n### Answer:\nGiven that there are three blue marbles, four red marbles, six green marbles and two yellow marbles.\nProbability that at least one green marble can be picked in the random draw of two marbles = Probability that one is green + Probability that both are green\n= (6 * 9 * 2)/(15 * 14) + (6 * 5)/(15 * 14) = 36/70 + 1/7\n= 46/70 = 23/35\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe expression rs+r is odd when the r and s are integers. Which of the following expressions must be even?\n\n### Options:\nA. r\nB. s\nC. r + s\nD. rs - r\nE. r + s^2\n\n### Answer:\nrs+r is odd\nr and s are integers\nIf r were even rs+r would be even despite any value of s.\ns can't be odd, so s must be even.\nAns : B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJohn is three times as old as Sam. If John will be twice as old as Sam in five years, how old was Sam two years ago?\n\n### Options:\nA. 2\nB. 4\nC. 6\nD. 3\nE. 16\n\n### Answer:\nj= 3s\nafter 5 years\nj +5 = 2(s+5)\nj= 2s+5\n2s +5 = 3s\ns= 5\ntwo years ago\ns= 5-2= 3\nD is the answer\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo trains 140 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is?\n\n### Options:\nA. 17.9 sec\nB. 11.8 sec\nC. 27.7 sec\nD. 10.8 sec\nE. 17.8 sec\n\n### Answer:\nRelative speed = 60 + 40 = 100 km/hr.\n= 100 * 5/18 = 250/9 m/sec.\nDistance covered in crossing each other = 140 + 160 = 300 m.\nRequired time = 300 * 9/250 = 54/5 = 10.8 sec.\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA alone can finish a work in 10 days which B alone can finish in 15 days. If they work together and finish it, then out of a total wages of Rs.3400, A will get:\n\n### Options:\nA. Rs.1200\nB. Rs.1500\nC. Rs. 2040\nD. Rs.2000\nE. None of these\n\n### Answer:\nExplanation:\nRatio of working days of A : B = 10 : 15\nTherefore, their wages ratio = reverse ratio = 15 : 10\nTherefore, A will get 15 units of ratio\nTotal ratio = 25\n1 unit of ratio =3000/25 = 136\nSo, A\u2019s amount = 120 \u00d7 15 = Rs.2040.\nAnswer: Option C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the value of 27^2 + 28^2 + 29^2 + 30^2 + 31^2 + 32^2 + 33^2 ?\n\n### Options:\nA. 6298\nB. 6308\nC. 6318\nD. 6328\nE. 6338\n\n### Answer:\nthe method would seem to be lengthy as it is being explained but is very short actually\nsecond would be to take advantage of proximity to 30 and a set of two numbers giving us 60 as sum..\n(27^2 + 33^2) + (29^2 + 31^2) + (32^2 + 28^2)+ 30^2\n(60^2-2*27*33) +(60^2-2*29*31)+ (60^2-2*28*32)+ 30^2\n3*60^2+30^2-2(27*33+29*31+28*32)\n3*60^2+30^2-2((30-3)*(30+3)+(30-1)*(30+1)+(30-2)*(30+2))\n3*60^2+30^2-2((30^2-3^2)+(30^2-1^2)+(30^2-2^2))\n3*60^2+30^2-6(30^2)+2(3^2+1^2+2^2)\nwe are interested only in terms where square of multiple of 10 is not involved..\n2(9+1+4)=28 so the answer should be something*100+28....this gives us the answer as 6328\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA motorist travel to a place 150 km away at an average speed of 90 km/hr and returns at 30 km/hr.His average speed for the whole journey in km/hr is\n\n### Options:\nA. 36km/hr\nB. 37 km/hr\nC. 35 km/hr\nD. 45 km/hr\nE. None of these\n\n### Answer:\nExplanation:\nAverage speed will be\n2xy/x+y km/hr\n= {2(90)(30)}/{90+30} km/hr\n= 45 km/hr\nAnswer: Option D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere is food for 760 men for 22 days. How many more men should join after two days so that the same food may last for 19 days more?\n\n### Options:\nA. 38\nB. 40\nC. 83\nD. 87\nE. 81\n\n### Answer:\n760 ---- 22\n760 ---- 20\nx ----- 19\nx*19 = 760*20\nx = 800\n760\n-------\n40\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the circus were to sell all of its 220 tickets for this month's performance at its usual price, the revenue from sales would be 10% greater than that collected last month. If the circus raised the ticket price by 7% and sold only 200 tickets as a result, what percent less would last month's revenue be compared to this month's revenue?\n\n### Options:\nA. 2\nB. 5\nC. 700/107\nD. 110/20\nE. 9/4\n\n### Answer:\nLet price be 10/ticket\nthen 220 tickets for this month's performance at its usual price=2200\nwhich is 10%greater than last month(let X)---->x(1+10/100)=2200----->x=2000\nnow new revenue this month=200*10.7=2140\nas per question asked 2000=2140(1-A/100)----->A=700/107%\nAns C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a certain store, the profit is 320% of the cost. If the cost increases by 25% but the selling price remains constant, approximately what percentage of the selling price is the profit?\n\n### Options:\nA. 30%\nB. 70%\nC. 100%\nD. 120%\nE. None\n\n### Answer:\nSolution\nLet C.P. = Rs. 100.\tThen, Profit = Rs.320,\nS.P. = 420.\nLet C.P. = Rs. 125% of Rs. 100\t= Rs.125.\nNew S.P. = Rs.420.\nProfit = Rs. (420 - 125)\t= Rs.295.\n\u2234 Required percentage\t= (295 / 420 x 100)%\n= 1475 / 21%\n= 70%.\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe sale price of an article including the sales tax is Rs. 616. The rate of sales tax is 10%. If the shopkeeper has made a profit of 12%, then the cost price of the article is:\n\n### Options:\nA. 500\nB. 277\nC. 222\nD. 297\nE. 111\n\n### Answer:\nExplanation:\n110% of S.P. = 616\nS.P. = (616 * 100)/110 = Rs. 560\nC.P = (110 * 560)/112 = Rs. 500\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSeven children \u2014 A, B, C, D, E, F, and G \u2014 are going to sit in seven chairs in a row. Child A has to sit next to both B & G, with these two children immediately adjacent to Child A on either side. The other four children can sit in any order in any of the remaining seats. How many possible configurations are there for the children?\n\n### Options:\nA. 240\nB. 480\nC. 720\nD. 1440\nE. 3600\n\n### Answer:\nFirst we can imagine the trio ABG as one item to arrange along with four other items: C , D, E, F.\nThis can be done in 5! = 120 ways\nHowever the trio can be arranged in 2 ways: BAG or GAB.\nSo, total number of ways to sit the seven children is equal to 2*120 = 240 (option A)\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA 300 m long train crosses a platform in 39 sec while it crosses a signal pole in 18 sec. What is the length of the platform?\n\n### Options:\nA. 288\nB. 350\nC. 889\nD. 276\nE. 234\n\n### Answer:\nSpeed = 300/18 = 50/3 m/sec.\nLet the length of the platform be x meters.\nThen, (x + 300)/39 = 50/3\n3x + 900 = 1950 => x = 350 m.\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n(128.5 x 25) + (13.8 x 50) = ? x 50\n\n### Options:\nA. 78.05\nB. 556.02\nC. 574.36\nD. 585.64\nE. 595.46\n\n### Answer:\nExplanation :\n? = (128.5 x 25) + (13.8 x 50)/50\n= 3212.5 + 690/50 = 78.05\nAnswer : Option A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nReplace X with the appropriate number in\n4 , 5 , 14 , 15 , 24 , 25 , X\n\n### Options:\nA. 30\nB. 29\nC. 34\nD. 21\nE. 20\n\n### Answer:\nC\nlist of consecutive numbers that has an 'f' in the spelling\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train running at the speed of 54 km/hr crosses a pole in 9 sec. What is the length of the train?\n\n### Options:\nA. 135 m\nB. 786 m\nC. 566 m\nD. 546 m\nE. 445 m\n\n### Answer:\nSpeed = 54 * 5/18 = 15 m/sec\nLength of the train = speed * time = 15 * 9\n= 135 m\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA fair coin is tossed 3 times. What is the probability of getting at least 2 heads?\n\n### Options:\nA. 3/4\nB. 3/2\nC. 1/4\nD. 1/2\nE. 1/5\n\n### Answer:\nLet's find the probability of 2 heads , 3 heads\nP(HHH)=((1/2)^3=1/8.\nP(HHT)=(3!/2!)*(1/2)^3=3/8\nTotal Probablity = 1/8 + 3/8\n=1/2\nAnswer(D)\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat percentage of numbers from 1 to 70 have 1 or 9 in the unit's digit?\n\n### Options:\nA. 12 %\nB. 16 %\nC. 18 %\nD. 20 %\nE. 22 %\n\n### Answer:\nClearly, the numbers which have 1 or 9 in the unit's digit, have squares that end in the digit 1. Such numbers from 1 to 70 are 1, 9, 11, 19, 21, 29, 31, 39, 41, 49, 51, 59, 61, 69.\nNumber of such number =14\nRequired % = (14/70)x100 % =20 %\nanswer : D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a sports club with 40 members, 20 play badminton and 18 play tennis and 5 do not play either. How many members play both badminton and tennis?\n\n### Options:\nA. 3\nB. 5\nC. 6\nD. 7\nE. 3\n\n### Answer:\n20+18=38\nbut where as total number is 40-5=35\ntherefore answer is 38-35=3\nHence Answer is E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that all the four bulbs are defective.\n\n### Options:\nA. 1/127\nB. 1/191\nC. 1/138\nD. 1/132\nE. 1/126\n\n### Answer:\nOut of nine, five are good and four are defective. Required probability\n= \u2074C\u2084/\u2079C\u2084 = 1/126\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe tax on a commodity is diminished by 20% and its consumption increased by 15%. The effect on revenue is?\n\n### Options:\nA. 6%\nB. 8%\nC. 9%\nD. 2%\nE. 1%\n\n### Answer:\n100 * 100 = 10000\n80 * 115 = 9200\n-----------\n10000-----------800\n100-----------? => 8% decrease\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nup to 20,how many no. are odd and prime both?\n\n### Options:\nA. 9\nB. 5\nC. 6\nD. 7\nE. 8\n\n### Answer:\nwe have to calculate it manually.\nodd 1,3,5,7,9,11,13,15,17,19\nprime 2,3,5,7,11,13,17,19\ncommon 3,5,7,11,13,17,19\ntotal no. 7\nanswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA child must place 2 different toys in 4 different bins. If any of the toys can go in any of the bins, in how many ways can the child place the toys into the bins?\n\n### Options:\nA. 6^6\nB. 6^4\nC. 4^6\nD. 4^4\nE. 4^2\n\n### Answer:\nthere are 4 different bins and each of the toy can go to any of these bins..\nso answer 4\u00e2\u02c6\u20144=4^2\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n1398 x 1398\n\n### Options:\nA. 1954404\nB. 1981709\nC. 18362619\nD. 2031719\nE. None of these\n\n### Answer:\n1398 x 1398 = (1398)2\n= (1400 - 2)2\n= (1400)2 + (2)2 - (2 x 1400 x 2)\n= 1954404.\nAnswer: Option A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nArun, Kamal and Vinay invested Rs. 8000, Rs. 4000 and Rs. 8000 respectively in a business. Arun left after six months. If after eight months, there was a gain of Rs. 4005, then what will be the share of Kamal?\n\n### Options:\nA. Rs 870\nB. Rs 880\nC. Rs 890\nD. Rs 900\nE. None of these\n\n### Answer:\nExplanation:\nArun : Kamal : Vinay = (8,000 x 6) : (4,000 x 8) : (8,000 x 8)\n= 48 : 32 : 64\n= 3 : 2 : 4\nKamal's share=4005\u22172/9=Rs890\nOption C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn an exam, students need to answer 120 multiple choice questions. If the question paper is divided into 10 sections, how many questions are there in a section?\n\n### Options:\nA. 6\nB. 12\nC. 10\nD. 4\nE. 50\n\n### Answer:\n120 questions divided into 10 sections means each section containing 120/10=12 questions. Answer B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJerry\u2019s average (arithmetic mean) score on the first 3 of 4 tests is 85. If Jerry wants to raise his average by 3 points, what score must he earn on the fourth test?\n\n### Options:\nA. 97\nB. 89\nC. 90\nD. 93\nE. 95\n\n### Answer:\nTotal score on 3 tests = 85*3 = 255\nJerry wants the average to be = 88\nHence total score on 4 tests should be = 88*4 = 352\nScore required on the fourth test = 352 - 255 = 97\nOption A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe area of the maximum size of the circle described from the 10 inch square?\n\n### Options:\nA. 75.5 sq inch\nB. 76.5 sq inch\nC. 77.5 sq inch\nD. 78.5 sq inch\nE. 79.5 sq inch\n\n### Answer:\n10 inch square means sides of sq are 10inch\nthen circle is within square so diameter would be 10 inch maximum and radius is 5inch\nso area of the circle is = pi*r*r=3.14*5*5=78.5 sq inch\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe cost of water in the area where the Jones family lives is scheduled to increase by 35% next year. Since the Jones family cannot afford an increase in their water bill, how much will they have to reduce consumption to keep their cost the same?\n\n### Options:\nA. None\nB. 25.9%\nC. 10.2%\nD. 45%\nE. 15.5%\n\n### Answer:\nSolution: Let the current water expense be represented by Rs. 100.\nThe cost of water rises 35%. So, to buy same amount of water, they need to increase their expense,\n= (100 + 35% of 100) = Rs. 135.\nBut, they want to keep water expense the same, so they have to cut Rs. by 35 to keep it to Rs. =100.\nThe % decrease in consumption is,\n(35/135)*100 = 25.9%.\nMental Calculation Method;\n100-----35%\u2191---\u2192135------X%\u2193---\u2192100.\nHere, X = (35/135)*100 = 25.9%.\nAnswer: Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf r and s are positive integers and r-s=6, which of the following has the greatest value T?\n\n### Options:\nA. 2r\nB. 2s\nC. r +s\nD. 2r-s\nE. 2s-r\n\n### Answer:\nThe simplest way to do this is to assume values.\nWe are told that r and s are positive integers T.\nAlso, r-s = 6 => r = 6+s\nHence r is 6 more than s.\nLet s be 10. Hence r = 16.\nOption A: 2r = 2*16 = 32\nOption B: 2s = 2 * 10 = 20\nOption C: r + s = 16 + 10 = 26\nOption D: 2r - s = 2(16) - 10 = 32 - 10 = 22\nOption E: 2s - r = 2(10) - 16 = 20 - 16 = 4\nHence option A is the greatest.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn the manufacture of a certain product, 8 percent of the units produced are defective and 4 percent of the defective units are shipped for sale. What percent of the units produced are defective units that are shipped for sale?\n\n### Options:\nA. 0.125%\nB. 0.32%\nC. 0.8%\nD. 1.25%\nE. 2.0%\n\n### Answer:\nPercent of defective produced = 8%\nPercent of the defective units that are shipped for sale = 4%\nPercent of units produced are defective units that are shipped for sale = (4/100)*(8/100)*100%\n= (32/10000)*100%\n= (32/100)%\n= .32 %\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA departmental store has 6 managers and 36 associates. The 6 managers have an average salary of $700. The 36 associates have an average salary of $1500. What is the average salary for the departmental store?\n\n### Options:\nA. $1400\nB. $1385.71\nC. $1500.25\nD. $1466.58\nE. $1650.56\n\n### Answer:\nNumber of managers is 6\nTheir average salary is $700\nNumber of associates is 36\nTheir average salary is $1500\nTotal salary of managers is 6*700=$4200\nTotal salary of associates is 36*1500=$54,000\nTotal salary for the departmental store is 54000+4200=58200\nAverage salary for the departmental store is 58200/6+36=1385.71\nAnswer is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a camp,there is a meal for 120 men or 200 children.If 120 children have taken the meal,how many men will be catered to with the remaining meal ?\n\n### Options:\nA. 20\nB. 30\nC. 40\nD. 48\nE. 60\n\n### Answer:\nSolution\nThere is a metal for 200 children. 120 children have taken the meal.\nRemaining meal is to be catered to 80 children.\nNow, 200 children = 120 men\n80 children =( 120/200x80)men= 48 men. Answer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA tree is 12 m tall and casts an an 8 m long shadow. At the same time, a flag pole caste a 100 m long shadow. How long is the flag pole ?\n\n### Options:\nA. 150 m\nB. 200 m\nC. 125 m\nD. 115 m\nE. None\n\n### Answer:\nAnswer\n\u2235 8 m shadow means original height = 12 m\n\u2234 1 m shadow means original height = 12/8 m\n\u2234 100 m shadow means original height = (12/8) x 100 m\n= (6/4) x 100 = 6 x 25 = 150 m\nCorrect Option: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe area of a square is equal to five times the area of a rectangle of dimensions 125 cm * 64 cm. What is the perimeter of the square?\n\n### Options:\nA. 377\nB. 800\nC. 278\nD. 277\nE. 281\n\n### Answer:\nArea of the square = s * s = 5(125 * 64)\n=> s = 25 * 8 = 200 cm\nPerimeter of the square = 4 * 200 = 800 cm.\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat will be the remainder when 8-3 + 3^5 + 2^10 is divided by 4?\n\n### Options:\nA. 12\nB. 3\nC. 16\nD. 0\nE. 9\n\n### Answer:\nThe multiplication(e.g. 2^10) is done first and then the sum(e.g. 15+20) and\nsubtraction (e.g. 8-3), and after all this expression it should be divided by 4 and the answer is 0, option D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many quarters are equal to 2 dollars?\n\n### Options:\nA. 1\nB. 8\nC. 12\nD. 9\nE. 7\n\n### Answer:\nB. 8 quarters\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nInsert the missing number.\n2, 6, 12, 20, 30, 42, 56,72, 90, 110 (....)\n\n### Options:\nA. 22\nB. 132\nC. 72\nD. 66\nE. 19\n\n### Answer:\nExplanation:\nThe pattern is 1 x 2, 2 x 3, 3 x 4, 4 x 5, 5 x 6, 6 x 7, 7 x 8,8 x 9, 9 x 10,10 x 11.\nSo, the next number is 11 x 12 = 132.\nAnswer: B) 132\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the principle on a certain sum of money at 5% per annum for 2 2/5 years if the amount being Rs.1120?\n\n### Options:\nA. 1000\nB. 2877\nC. 2769\nD. 2776\nE. 9871\n\n### Answer:\n1120 = P [1 + (5*12/5)/100]\nP= 1000\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a2 - b2 = 10 and a*b = 5, find a4 + b4.\n\n### Options:\nA. 50\nB. 100\nC. 150\nD. 92\nE. 25\n\n### Answer:\na2 - b2 = 10 : given\na4 + b4 - 2a2b2 = 102 : square both sides and expand.\na*b = 5 : given\na2b2 = 52 : square both sides.\na4 + b4 - 2(25) = 100 : substitute\na4 + b4 = 150\ncorrect answer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain deck of cards contains 2 white cards, 2 red cards, 2 yellow cards, and 2 green cards. If two cards are randomly drawn from the deck, what is the probability that they will both be not white?\n\n### Options:\nA. 15/28\nB. 1/4\nC. 9/16\nD. 1/32\nE. 1/16\n\n### Answer:\nThe question asks they will both be not white. Considering that these are draws without replacement there are following possibilities :\ndraw 1, draw 2\n===== =====\n1) Not white, white;\n2) white, Not white;\n3) white, white;\n4) Not white, not white;\nThe answer has to be either P(4) OR all exclusion of the 3 previous conditions i.e. 1- [P(1) + P(2) + P(3)] => neither of the draws are white\nP(4) = 6/8*5/7=15/28\n1- [P(1) + P(2) + P(3)] = 1 - [ (6/8 * 2/7) + (2/8*6/7) + (2/8*1/7)] = 1 - [26/8*7] = 1 - [13/28] = 15/28\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf x is a positive, single-digit integer such that 4/3*x, 2x, x, and x + 2, and 5x \u2013 2 form a non-ordered list of consecutive integers, which of the following could be the median of that list?\n\n### Options:\nA. 3\nB. 4\nC. 5\nD. 6\nE. 8\n\n### Answer:\nThe big hints are thatx is a 1-digit integerAND (4/3)x, 2x, x, and x + 2, and 5x \u2013 2 are ALLintegers\nFor (4/3)x to be an integer, x MUST BE A MULTIPLE OF 3. So, x can equal 3, 6, or 9.\nNow let's plug each possible value of x into the terms and see which one yields a list ofconsecutive integers\nWhen x =3, we get the following terms: (4/3)(3), 2(3),3,3+ 2, and 5(3) \u2013 2.\nWhen we evaluate these terms we get: 4, 6, 3, 5 and 13\nRearrange to get: 3, 4, 5, 6, 13. So, when x = 3, we get consecutive integers.\nIn this case, the MEDIAN = 5\nSince 5 is among the answer choices, we need not test the other 2 values of x (i.e., x = 6 and x = 9)\nAnswer:\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train passes a station platform in 42 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?\n\n### Options:\nA. 180 m\nB. 240 m\nC. 330 m\nD. 280 m\nE. 380 m\n\n### Answer:\nSpeed = 54 x 5/18 = 15 m/s\nLength of the train = (15 x 20)m = 300 m.\nLet the length of the platform be x metres.\nThen, (x + 300)/42 = 15\n--> x + 300 = 630\nx = 330m.\nAnswer : C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWHEN A PERSON SELLS TWO ITEMS $800 each, ONE AT A GAIN OF 20% AND OTHER AT A LOSS OF 20%.THEN THE SELLER INCURES A LOSS OR GAIN OF:\n\n### Options:\nA. no loss no gain\nB. 4% loss\nC. 5% gain\nD. 2% gain\nE. 1% loss\n\n### Answer:\nWhen two items are sold at the same price, one at a profit of a% and other at a loss of a% (which means the cost price of one item was lower than the selling price and the cost price of the other item was higher than the selling price), there will always be a loss of (a^2)/100 %. e.g. Here a = 20, so loss % = (20)^2/100 % = 4%.\nAnswer : B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA tortoise is making its way to eat a piece of lettuce at a constant speed. On its way to the lettuce, it takes 10 seconds to walk past a grain of sand. It then passes a piece of wood 20 cm long in 30 seconds to get to the lettuce. What is the length of the tortoise?\n\n### Options:\nA. 4 cm\nB. 5 cm\nC. 7.5 cm\nD. 9 cm\nE. 10 cm\n\n### Answer:\nSol.\rLet the length of the tortoise be x centimetres and its speed be y cm/sec. Then, x / y = 10 \u21d2 y = x / 10\r\u2234 (x + 20) / 30 = x / 10 \u21d4 x = 10 cm. Answer E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA boy bought a pen at 40% discount on its original price. He sold it at a 70% increase on the price he bought it. What percent of profit did he make on the original price?\n\n### Options:\nA. 10%\nB. 8%\nC. 6%\nD. 2%\nE. 4%\n\n### Answer:\nOriginal price = 100\nCP = 60\nS = 60*(170/100) = 102\n100 - 102 = 2%\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA boat running downstream covers a distance of 16 km in 2 hours while for covering the same distance upstream,it takes 4 hour.What is the speed of the boat in still water ?\n\n### Options:\nA. 4 km/hr\nB. 6 km/hr\nC. 8 km/hr\nD. Data inadequate\nE. None of these\n\n### Answer:\nSolution\nRate downstream =(16/2) kmph = 8 kmph,Rate upstream = (16/4) kmph = 4 kmph.\n\u2234 Speed in still water =1/2(8+4) kmph = 6 kmph. Answer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo machines, Y and Z, work at constant rates producing identical items. Machine Y produces 23 items in the same time Machine Z produces 21 items. If machine Y takes 21 minutes to produce a batch of items, how many minutes does it take for machine Z to produce the same number of items?\n\n### Options:\nA. 6\nB. 9\nC. 9 1/2\nD. 12\nE. 23\n\n### Answer:\nrate z/rate y=21/23\ntime z/time y=23/21\n(23/21)*21=23 minutes\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA is half good a work man as B and together they finish a job in 20 days. In how many days working alone B finish the job?\n\n### Options:\nA. 98 days\nB. 30 days\nC. 17 days\nD. 18 days\nE. 19 days\n\n### Answer:\nWC = 1:2\n2x + x = 1/20 => x = 1/60\n2x = 1/60 => 30 days\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMr Yadav spends 60% of his monthly salary on consumable items and 50% of the remaining on clothes and transport. He saves the remaining amount. If his savings at the end of the year were 24000, how much amount per month would he have spent on clothes and transport?\n\n### Options:\nA. 2000\nB. 8076\nC. 9691.2\nD. 4845.6\nE. None of these\n\n### Answer:\n\u2235 Amount, he have spent in 1 month on clothes transport = Amount spent on saving per month\n\u2235 Amount, spent on clothes and transport\n= 24000\u204412 = 2000\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man purchased a grinder for Rs. 660 and sold it at a profit of 10%. The selling price is:\n\n### Options:\nA. Rs. 736\nB. Rs. 812\nC. Rs. 660\nD. None of these\nE. Cannot be determined\n\n### Answer:\ns.p.=110/100 \u00d7 600 = 660\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFrom a pack of cards two cards are drawn one after the other, with replacement. The probability that the first card is a black and the second card is a spade is?\n\n### Options:\nA. 1/16\nB. 1/8\nC. 1/13\nD. 1/26\nE. 1/52\n\n### Answer:\nProbability of a black card= 26/52 = 1/12\nProbability of a jack = 13/52 = 1/4\nProbability of both = P1*P2 = 1/(2*4) = 1/8\nAnswer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA cube is divided into 729 identical cubelets. Each cut is made parallel to some surface of the cube . But before doing that the cube is coloured with green colour on one set of adjacent faces ,red on the other set of adjacent faces, blue on the third set. So, how many cubelets are there which are painted with exactly one colour?\n\n### Options:\nA. 293\nB. 294\nC. 295\nD. 296\nE. 298\n\n### Answer:\ntotal cubes created are 729\nso a plane of big cube has 9*9 cubes\nout of that(n-2)*(n-2)=7*7=49 are painted only one side\nand a cube has six sides=6*49=294\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe diagonals of two squares are in the ratio of 2 : 5. Find the ratio of their areas.\n\n### Options:\nA. 5:20\nB. 5:25\nC. 4:25\nD. 3:15\nE. 3:20\n\n### Answer:\nLet the diagonals of the squares be 2x and 5x respectively.\nRatio of their areas = (1/2)*(2x) 2:(1/2)*(5x) 2= 4x2: 25x2= 4 : 25.\nOption C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nArrange the following in a logical order:\n1. Birth\n2. College\n3. Marriage\n4. School\n5. Employment\n\n### Options:\nA. 1, 3, 5, 4, 2\nB. 1, 4, 2, 5, 3\nC. 2, 5, 3, 1, 4\nD. 2, 4, 1, 5, 3\nE. None of these\n\n### Answer:\nExplanation:\nThe given words when arranged in the order of various events as they occur in man's life, the sequence is : Birth, School, College, Employment, Marriage.\nSequence is : 1, 4, 2, 5, 3.\nANSWER B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe compound interest on Rs.2800 for 1 1/2years at 10% per annum is\n\n### Options:\nA. Rs.441.35\nB. Rs.436.75\nC. Rs.434\nD. Rs.420\nE. None\n\n### Answer:\nExplanation:\nAmount = Rs.[[2800\u00d7(1+10/100)](1+5/100)]\n= Rs.[2800\u00d711/100\u00d721/20]= Rs.3234\nC.I = Rs.(3234-2800)= Rs.434\nCorrect Option: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAt the store opening, Larry's Grocery had 50 Lemons and 60 Oranges. By closing, the store at 20 Lemons and 40 Oranges left. By approximately what percent did the ratio of Lemons to Orange decrease from opening to closing.\n\n### Options:\nA. 50.0%\nB. 40.0%\nC. 30.0%\nD. 20.0%\nE. 10.0%\n\n### Answer:\nOpening: Lemons/Oranges = 50/60 =100/120\nClosing: Lemons/Oranges = 20/40 =60/120\nASIDE: It's useful to write both ratios with the same denominator. This allows us to IGNORE the denominator and focus solely on the numerators.\nSo, our ratio went from 100/120 to 60/120\nIgnoring the denominators, we went from 100 to 60\nThe percent change = 100(difference in values)/(original value)\n= (100)(100-60)/100\n= (100)(40)/100)\n= 40\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA and B rent a pasture for 10 months. A put in 80 cows for 7 months. How many can B put in for the remaining 3 months, if he pays half as much again as A?\n\n### Options:\nA. 299\nB. 297\nC. 261\nD. 280\nE. 172\n\n### Answer:\n80* 7: x* 3 = 1:1 1/2\n560: 3x = 2: 3\nx = 280\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTough and Tricky questions: Number Properties.\nWhat is the smallest positive integer x such that 225x is the cube of a positive integer?\n\n### Options:\nA. 5\nB. 15\nC. 30\nD. 60\nE. 90\n\n### Answer:\nWe want to know the smallest x that will make 225x a CUBE of some number. Let's call that number y.\nLet's first figure out what we're working with. The prime factorization of 225 can be visualized:\n...........225\n......../.......\\\n......25.......9\n...../..\\....../...\\\n...5....5...3.....3\nSo, we have 5 * 5 * 3 * 3 that can be multiplied together to get 225. Now we need to figure out what we need to make 225 * x into a cube of y (y^3=225*x).\nWe have two 5s and two 3s. To arrange these numbers in identical sets (3,5), we need at least one more 5 and one 3. Each of these numbers will give us the value of y (3*5=15), which, multiplied by itself three times, gives us 225 * x.\nLooking at the factors we need to complete the triples, we get 5 * 3 = 15. We know this is the smallest number possible because prime factors by definition cannot be broken down any further.\nTherefore, we can go with answer choice B.\nIf time permits, we can do a sanity check. We calculated that y should be 3 * 5, or 15. 15 * 15 * 15 = 3375. Also, 225 * 15 = 3375.\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf |20x-10| = 190, then find the product of the values of x?\n\n### Options:\nA. -45\nB. 50\nC. -62\nD. 35\nE. -90\n\n### Answer:\n|20x-10| = 190\n20x-10 = 190 or 20x-10 = -190\n20x = 200 or 20x = -180\nx = 10 or x = -9\nproduct = -9*10 = -90\nAnswer is E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a number is formed by writing integers 1 to 150 one after another, like 12345...150. How many Q digits does this integer consists of?\n\n### Options:\nA. 150\nB. 339\nC. 342\nD. 359\nE. 362\n\n### Answer:\nNumber of single digit integers = 9\nNumber of 2 digit integers = 99 - 10 + 1 = 90\nNumber of 3 digit integers = 150 - 100 + 1 = 51\nNumber of digits in the integer Q= 1*9 + 2*90 + 3*51 = 9 + 180 + 153 = 342\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a mixture of 60 litres, the ratio of acid to base is 2 : 1. If this ratio is to be 1 : 2, then the quantity of base (in litres) to be further added is\n\n### Options:\nA. 20\nB. 30\nC. 40\nD. 50\nE. 60\n\n### Answer:\nAcid = 40 lts\nBase = 20 lts\nto make the ratio A:B = 1:2 ,\n60 lts of base should be added\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf integers e and b are distinct factors of 30, which of the following CANNOT be a factor of 30?\nI. eb + b^2\nII. (e + b)^2\nIII. e + b\n\n### Options:\nA. I only\nB. II only\nC. III only\nD. I and II only\nE. I, II, and III\n\n### Answer:\nFactors of 30 are: 1, 2, 3, 5, 6, 10, 15, and 30.\nI. eb + b^2 --> if e=1 and b=2 then eb + b^2=6, which is a factor of 30. OK;\nII. (e + b)^2 --> (e + b)^2 is a perfect square, no perfect square (but 1) is a factor of 30. DISCARD;\nIII. e + b --> if e=1 and b=2 then e + b=3, which is a factor of 30. OK.\nAnswer: B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nthe cyclist walking at a constant rate of 15 miles per hour is passed by a car traveling in the same direction along the same path at 60 miles per hour. the car stops to wait for the cyclist for 6 minutes after passing her, while the cyclist continues to go at her constant rate, how many minutes must the car wait until the cyclist catches up?\n\n### Options:\nA. 9\nB. 10\nC. 12\nD. 15\nE. 18\n\n### Answer:\nFor the 6 minutes the car continues to overtake the cyclist, she is going at 45 miles per hour faster than the cyclist.\nOnce the car stops, the cyclist is going at 15 miles per hour while the car is at rest\nSo the amount of time the cyclist will take to cover the distance between them is going to be in the ratio of the relative speeds. 45/15 * 6 or 18 minutes\nAnswer is (E)\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n5 blue marbles, 3 red marbles and 4 purple marbles are placed in a bag. If 4 marbles are drawn without replacement, what is the probability that the resu lt will not be 2 blue and 2 purple marbles?\n\n### Options:\nA. 4/33\nB. (5/36)^2\nC. 1/2\nD. (31/36)^2\nE. 29/33\n\n### Answer:\nAnswer is 29/33.\nThe probability of 2 blue and 2 purple marbles selected is 5C2.4C2/12C4 =4/33.\nSubtracting the above from 1 we get 29/33 E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average of 11 observations is 60. If the average of first five observations is 58 and that of the last five is 56, then the sixth observation is.\n\n### Options:\nA. 85\nB. 90\nC. 100\nD. 110\nE. None of these\n\n### Answer:\nExplanation :\nSixth observation=[60*11 - (58*5 + 56*5)] = 90.\nAnswer : B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the sum of a number and its square is 182, What is the number?\n\n### Options:\nA. 16\nB. 77\nC. 25\nD. 87\nE. 13\n\n### Answer:\nExplanation:\nLet the integer be x.\nThen, x + x2 = 182\nx2 + x - 182 = 0\n(x + 14) (x \u2013 13) = 0\nx = 13\nANSWER: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nE=\u221a[2\u221a63 + 2/(8+3\u221a7)] =\n\n### Options:\nA. 8 + 3\u221a7\nB. 4 + 3\u221a7\nC. 8\nD. 4\nE. \u221a7\n\n### Answer:\nIn these type of question u multiply the nominator and denominator with conjugate...Conjugate of 8 +3sqrt(7) is 8 -3sqrt(7)\nsqrt[2sqrt(63) + 2 { 8 - 3sqrt(7)}/{64 - 63}]\nE=sqrt[2sqrt(63) +16 - 2sqrt(63)] =4\nAnswer is 4.D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe marks obtained by Vijay and Amith are in the ratio 6:5 and those obtained by Amith and Abhishek in the ratio of 3:2. The marks obtained by Vijay and Abhishek are in the ratio of?\n\n### Options:\nA. 1:5\nB. 4:5\nC. 9:5\nD. 9:8\nE. 9:7\n\n### Answer:\n6:5\n3:2\n-------\n18:15:10\n18:10\n9:5\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe speed of a boat in still water in 22 km/hr and the rate of current is 4 km/hr. The distance travelled downstream in 24 minutes is:\n\n### Options:\nA. 10.4 km\nB. 10.6 km\nC. 11.4 km\nD. 11 km\nE. 12 km\n\n### Answer:\nExplanation:\nSpeed downstream = (22 + 4) = 26 kmph\nTime = 24 minutes = 24/60 hour = 2/5 hour\nDistance travelled = Time \u00d7 speed = (2/5)\u00d726 = 10.4 km\nAnswer: Option A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhen 0.232323..... is converted into a fraction, then the result is\n\n### Options:\nA. 23/99\nB. 2/9\nC. 1/5\nD. 23/100\nE. 23/98\n\n### Answer:\n0.232323... = 0.23\n=\t23/99\nAnswer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nnd the area of trapezium whose parallel sides are 20 cm and 18 cm long, and the distance between them is 12 cm?\n\n### Options:\nA. 243cm2\nB. 239cm2\nC. 267cm2\nD. 230cm2\nE. 228cm2\n\n### Answer:\nArea of a trapezium = 1/2 (sum of parallel sides) * (perpendicular distance between them)\n= 1/2 (20 + 18) * (12)\n= 228 cm2\nAnswer:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a particular is never chosen, in how many ways can a cricketbe chosen out of 15 players?\n\n### Options:\nA. 345\nB. 350\nC. 364\nD. 370\nE. 354\n\n### Answer:\nA particular players is never chosen, it means that 11 players are selected out of 14 players.\n=> Required number of ways = 14C11\n= 14!/11!x3! = 364\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nGuadalupe owns 2 rectangular tracts of land. One is 300 m by 500 m and the other is 250 m by 630 m. The combined area of these 2 tracts is how many square meters?\n\n### Options:\nA. 3,360\nB. 307,500\nC. 621,500\nD. 704,000\nE. 2,816,000\n\n### Answer:\nOne is 300 m by 500 m and the other is 250 m by 630 m :\n(300*500)+(250*630) = 150000+157500\n307500\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe dimensions of a rectangular solid are 4 inches, 5 inches, and 12 inches. If a cube, a side of which is equal to one of the dimensions of the rectangular solid, is placed entirely within thespherejust large enough to hold the cube, what the ratio of the volume of the cube to the volume within thespherethat is not occupied by the cube?\n\n### Options:\nA. 10:17\nB. 2:5\nC. 5:16\nD. 25:7\nE. 10:21\n\n### Answer:\nAnswer: E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n14 men make 1400 toy in 5 days 1 day after work 14 more worker join now how may days work can finish\n\n### Options:\nA. 1 day\nB. 2 days\nC. 3 days\nD. 4 days\nE. 5 days\n\n### Answer:\n14 men make toy in 5 days\nafter 1 day 14 more worker join\nm1/m2=d2/d1\n14/28=d2/4\n=2 day\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAt a party, there were five times as many girls as boys and three times as many adults as children. Which of the following could NOT be the number of people at the party?\n\n### Options:\nA. 258\nB. 259\nC. 216\nD. 120\nE. 72\n\n### Answer:\nFive times as many girls as boys --> F = 5M.\nThree times as many adults as children --> (F + M) = 3C.\nThe number of people at the party = F + M + C = 3C + C = 4C.\nThe number of people at the party must be a multiple of 4. The only answer choice which is NOT a multiple of 4 is A.\nAnswer: A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe length of a rectangle is two - fifths of the radius of a circle. The radius of the circle is equal to the side of the square, whose area is 1225 sq.units. What is the area (in sq.units) of the rectangle if the rectangle if the breadth is 10 units?\n\n### Options:\nA. 140\nB. 156\nC. 175\nD. 214\nE. None of these\n\n### Answer:\nExplanation:\nGiven that the area of the square = 1225 sq.units\n=> Side of square = \u00e2\u02c6\u01611225 = 35 units\nThe radius of the circle = side of the square = 35 units Length of the rectangle = 2/5 * 35 = 14 units\nGiven that breadth = 10 units\nArea of the rectangle = lb = 14 * 10 = 140 sq.units\nANSWER IS A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAn article costs Rs. 600. What should be the marked price of an article so that after 10% discount, the trader makes 20% profit?\n\n### Options:\nA. Rs. 800\nB. Rs. 950\nC. Rs. 1100\nD. Rs. 1040\nE. None of these\n\n### Answer:\nExplanation:\nCost price of article = Rs. 600\nProfit % = 20%\nTherefore,\nselling price of article = 120% of C.P.\n= (120 / 100) * 600 = Rs. 720\nMarked price = ?\nDiscount % = 10%\nS.P. = Rs. 720\n90% of M.P. = S.P.\n90/100 * M.P. = 720\nM.P. = 720 * (100/90) = Rs. 800\nANSWER A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhen all the students in a school are made to stand in rows of 46, 36 such rows are formed. If the students are made to stand in rows of 42, how many such rows will be formed ?\n\n### Options:\nA. 31\nB. 36\nC. 38\nD. 39\nE. 21\n\n### Answer:\nExplanation:\nTotal number of students = 46 x 36\nWhen arranged in rows of 42, number of rows formed are,\n= 39.\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the arithmetic mean of seventy five numbers is calculated, it is 35. If each number is increased by 5, then mean of new number is?\n\n### Options:\nA. 43\nB. 40\nC. 87\nD. 77\nE. 22\n\n### Answer:\nA.M. of 75 numbers = 35\nSum of 75 numbers = 75 * 35 = 2625\nTotal increase = 75 * 5 = 375\nIncreased sum = 2625 + 375 = 3000\nIncreased average = 3000/75 = 40.\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain football coach allows his quarterback to call three plays in a row. If the quarterback can choose from 3 passing plays, 4 running plays, and 2 trick plays, how many different R arrangements of plays can be run, if the same play can\u2019t be run more than once?\n\n### Options:\nA. 24\nB. 125\nC. 243\nD. 504\nE. 729\n\n### Answer:\nNumber of R ways to choose the first play: 9\nSecond play: 8\nThird:7\n9*8*7= 504.D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThree years ago, the ratio of ages of P and Q was 4:3. Six years from now, the ratio of their ages will be 7:6. What is P's age at present?\n\n### Options:\nA. 9\nB. 12\nC. 15\nD. 18\nE. 21\n\n### Answer:\n3(P-3)/4 = (Q-3). Then Q = 3(P-3)/4 + 3\n6(P+6)/7 = Q+6\n6(P+6)/7 = 3(P-3)/4 + 9\n24P+144 = 21P + 189\n3P = 45\nP = 15\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAt an examination in which full marks were 500. A got 10% less than B, B got 25% more than C and C got 20% less than D. If A got 360marks, what percentage of full marks was obtained by D?\n\n### Options:\nA. 48%\nB. 30%\nC. 12%\nD. 80%\nE. 28%\n\n### Answer:\nA B C D\n90 100 80 100\nA D\n90 ----- 100\n360 ------ ? = 400\n500 ------ 400\n100 ------- ? => 80%\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJerry, an electrician, worked 8 months out of the year. What percent\nof the year did he work? (round answer to the nearest hundredth)\nWhat percent 12 is 8? 12 months = 1 year\n\n### Options:\nA. 58.33%\nB. 66.67%\nC. 78.33%\nD. 88.33%\nE. 98.33%\n\n### Answer:\n1. Multiply the opposites\n8 x 100 = 800\n100=8/12\nDivide by the remaining number\n66.67% (rounded to hundredth)\ncorrect answer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn six successive games, a baseball team scored 1 runs once, 4 runs twice, and 5 runs three times.\nWhat was the average (arithmetic mean) number of runs the team scored per game over the six-game period?\n\n### Options:\nA. 8\nB. 7\nC. 6\nD. 5\nE. 4\n\n### Answer:\n1 runs once (one game)\n4 runs twice (two game)\n5 runs three times (three games)\nSO we have (1*1 + 4*2 + 5*3)/6 = 24/6 = 4.\nANS: E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the maximum number of pieces that a circular pie can be divided into by four linear cuts?\n\n### Options:\nA. 6\nB. 8\nC. 9\nD. 10\nE. 11\n\n### Answer:\nSuch kind of combinations problems are always about a pattern recognition.\nMaximum pieces:\n0 line gives 1 whole piece;\n1 line will gives 2 pieces: 1+1=2;\n2 lines will give 4 pieces: 2+2=4;\n3 lines will give 7 pieces: 4+3=7;\n4 lines will give 7+4=11 pieces.\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n852.68 \u00e2\u02c6\u2019 4.5 + 288.98 = ? \u00e2\u02c6\u2019 2132.54\n\n### Options:\nA. 6078.58\nB. 5225.9\nC. 6258.58\nD. 6088.58\nE. None\n\n### Answer:\nOption 'C'\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe sum of the present ages of two persons A and B is 60. If the age of A is twice that of B, find the sum of their ages 5 years hence?\n\n### Options:\nA. 70\nB. 65\nC. 25\nD. 30\nE. 40\n\n### Answer:\nA + B = 60, A = 2B\n2B + B = 60 => B = 20 then A = 40.\n5 years, their ages will be 45 and 25.\nSum of their ages = 45 + 25 = 70.\nANSWER A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat percent of the different arrangements of the letters of the word AKACUL are those in which the vowels appear together?\n\n### Options:\nA. 50%\nB. 40%\nC. 30%\nD. 25%\nE. 20%\n\n### Answer:\nlet's determine the number of total possibilities in arranging the letters. There are six spaces, so the total number of arrangements is 6!, or 360.\nNext, we need to figure out how to determine the number of ways that we can arrange the 3 vowels together - simply place them together (as in AAU) and call that a single place.\nNext, we must determine the number of ways to arrange the now 4 units (i.e., AAU, B, C, S). Like above, there are 4 units and 4 places so the number of arrangements is 4!, or 24.\nFinally, we need to account for the number of ways we can arrange AAU. We can either write out each unique iteration (AAU, AUA and UAA) or calculate as 3!/2! and get 3.\nPutting this all together, we get the number of ways to arrange the letters so that the vowels are together is 4! x 3 ==> 72\nthe number of total arrangements of all the letters is 6! ==> 360\n72/360 = 1/5, or 20%\nCorrect answer is E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFour friends, Patricia, Melyssa, Tania, and Cassandra, are pooling their money to buy a $1100 item. Patricia has twice as much money as Melyssa. Tania has $10 more than Patricia. Cassandra has 20% more than Tania. If they put all their money together and spend the $1100, they will have $32 left. How much money does Patricia have?\n\n### Options:\nA. $200\nB. $420\nC. $300\nD. $315\nE. $280\n\n### Answer:\nP= 2M ; T= P+10 ; C= 1.2(T)\nP+M+T+C-1100=32\nP+0.5P+P+10+1.2(P+10) = 1132\nP+0.5P+P+10+1.2P+12=1132\nP+0.5P+P+1.2P+22=1132\nP+0.5P+P+1.2P=1110\n3.7P=1110\nP=300\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSanjay invested an amount of ` 16,000 for two years on compound interest and received an amount of ` 17,640 on maturity. What is the rate of interest per annum?\n\n### Options:\nA. 4%\nB. 5%\nC. 8%\nD. 9%\nE. None of these\n\n### Answer:\nThe extra money for two years is 1,640. This can be broken up as 800 + (800 + 40). Since 40 = 5% of 800 and 800 = 5% of 16000\nSo, r = 5%.\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe S.I. on a certain sum of money for 4 years at 12% per annum is half the C.I. on Rs. 6000 for 2 years at 15% per annum. The sum placed on S.I. is?\n\n### Options:\nA. 2019.625\nB. 2017.625\nC. 2013.625\nD. 2015.625\nE. 2011.625\n\n### Answer:\nC.I. = [6000 * (1 + 15/100)2 - 6000]\r= (6000 * 23/20 * 23/20 - 6000) = Rs. 1935.\rSum = (967.5 * 100)/(4 * 12)\r= Rs.2015.625\rAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a certain parking lot, 3% of the cars are towed for parking illegally. However 80% of the cars which are parked illegally are not towed. What % of cars in the parking lot are parked illegally.'\n\n### Options:\nA. 11\nB. 13\nC. 15\nD. 60\nE. 75\n\n### Answer:\nSo Total no. of cars parked illegally: 300\nTotal no. of cars: 2000\n300/2000*100, So 15%\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA rectangular-shaped carpet that measures x feet by y feet is priced at $46. What is the cost of the carpet, in dollars per square yard? (1 square yard = 9 square feet)\n\n### Options:\nA. xy/360\nB. 9xy/40\nC. 40xy/9\nD. 414xy\nE. 414/(xy)\n\n### Answer:\nThe area of the carpet in feet is xy.\nThe area in square yards is xy / 9.\nThe price per square yard is 46 / (xy/9) = 414/(xy).\nThe answer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA number x is multiplied by 3, and this product is then divided by 7. If the positive square root of the result of these two operations equals x, what is the value of x if x\u22600 ?\n\n### Options:\nA. 25/9\nB. 3/7\nC. 5/3\nD. 3/5\nE. 9/25\n\n### Answer:\nsqrt(3x/7) to be perfect square x has to 3/7\nAns: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA dishonest dealer professes to sell his goods at Cost Price but still gets 20% profit by using a false weight. What weight does he substitute for a kilogram?\n\n### Options:\nA. 833 1/3 grams\nB. 850 1/3 grams\nC. 825 1/3 grams\nD. 810 1/3 grams\nE. 870 1/3 grams\n\n### Answer:\nA\n833 1/3 grams\nIf the cost price is Rs.100, then to get a profit of 20%, the selling price should be Rs.120.\nIf 120kg are to be sold, and the dealer gives only 100kg, to get a profit of 20%.\nHow many grams he has to give instead of one kilogram(1000 gm).\n120 gm ------ 100 gm\n1000 gm ------ ?\n(1000 * 100)/120 = 2500/3 = 833 1/3 grams.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 7^k + 7^k = (7^9)^(7^9) - 7^k, then k = ?\n\n### Options:\nA. 11/3\nB. 11/2\nC. 242\nD. 3^10\nE. 7^11 - 1\n\n### Answer:\n7^k + 7^k = (7^9)^7^9 - 7^k\n7*(7^k) = 7 ^ (49 * 7^9 ) = 7^(7^2 * 7^9) = 7^(7^11)\n7^k+1 = 7^(7^11)\nSo k+1 = 7^11\nSo k = 7^11 -1\nAnswer is E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nP alone can complete a job in 12 days. The work done by Q alone in one day is equal to one-half of the work done by P alone in one day. In how many days can the work be completed if P and Q work together?\n\n### Options:\nA. 5\nB. 6\nC. 7\nD. 8\nE. 9\n\n### Answer:\nP's rate is 1/12\nQ's rate is 1/24\nThe combined rate is 1/12 + 1/24 = 1/8\nIf they work together, the job will take 8 days.\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA straight line has a slope of 1/2 and a y-intercept of -2. On this line, what is the x-coordinate of the point whose y-coordinate is 10?\n\n### Options:\nA. (8)\nB. (12)\nC. (13)\nD. (16)\nE. (24)\n\n### Answer:\nFor the point intercept form of a line y=mx+b ; m is the slope and (b=y when x=0)\nSlope=y2\u2212y1/ x2\u2212x1\nwe are given slope =1/2\ny intercept is always equal to b when x = 0 (therefore at origin we can always write any (x,y) pair as (0,b)\ny intercept hence (b) is given -2\nnow we have got all the values that we want to calculate slope\n1/2=10\u2212(\u22122)/x\u22120\n1/2=10+2/x==>1/2=12/x==>x=24\nCORRECT ANSWER IS E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe sum of the mean, the median, and the range of the set {1, 2, 9} equals which one of the following values?\n\n### Options:\nA. 12\nB. 14\nC. 16\nD. 8\nE. 10\n\n### Answer:\nset {1, 2, 9}\nMean = (1+2+9)/3 = 4\nMeadian = Middle term = 2\nRange = Highest - Lowest = 9-1 = 8\nMean+Median+Range = 4+2+8 = 14\nAnswer: Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSimran started a software business by investing Rs.50,000. After six months, Nanda joined her with a capital of Rs.80,000. After 3 years , they earned a profit of Rs.24,500. What was Simran's share in the profit?\n\n### Options:\nA. Rs.9423\nB. Rs.10,250\nC. Rs.10,500\nD. Rs.14,000\nE. None\n\n### Answer:\nSolution\nSimran : Nanda\t=(5000x36):(80000x30)\n= 3 : 4.\nSimran's share\t= Rs.(24500x3/7)\n= Rs.10,500.\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA watch which gains uniformly ,is 5 min,slow at 8 o'clock in the morning on sunday and it is 5 min 48 sec.fast at 8 p.m on following sunday. when was it correct?\n\n### Options:\nA. 10 min past 7pm on wednesday\nB. 20 min past 7pm on wednesday\nC. 20 min past 9pm on wednesday\nD. 26 min past 7pm on wednesday\nE. 20 min past 4pm on wednesday\n\n### Answer:\nThis sunday morning at 8:00 AM, the watch is 5 min. Slow, and the next sunday at 8:00PM it becomes 5 min 48 sec fast. The watch gains min in a time of (7\u00d724)+12 = 180 hours.\nTo show the correct time, it has to gain 5 min.\nSo the correct time will be shown on wednesday at 7:20 PM\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many three letter words are formed using the letters of the word GAMER?\n\n### Options:\nA. 60\nB. 45\nC. 67\nD. 98\nE. 29\n\n### Answer:\nThe number of letters in the given word is four.\nThe number of three letter words that can be formed using these four letters is 5P3\n= 5 * 4 *3 = 60.\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a triangle, one side is 6 Cm and another side is 8 Cm. which of the following can be the perimeter of the triangle?\n\n### Options:\nA. 22.\nB. 25.\nC. 30.\nD. 32.\nE. 34.\n\n### Answer:\nGiven : one side is 6 Cm and another side is 8 Cm. So the 3rd side will be > 3 and < 15. Thus the perimeter will be : 18 < perimeter < 30. Only option satisfying this condition is 22. Hence A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA motor car starts with a speed of 70km/hr with its speed increasing every 2hours by 10kmph. In how many hours will it cover 345kms?\n\n### Options:\nA. 3hours\nB. 2hours 30mnts\nC. 4hours\nD. 4hours 30mnts\nE. 5hours\n\n### Answer:\nDistance covered in first 2hours = 70*2 = 140km\nDistance covered in next 2hours = 80*2 = 160km\nremaining distance = 345- (140+160) = 45km\nspeed in the fifth hour = 90km/hr\ntotal time to cover 45km = 45/90 = 1/2 hr\ntotal time taken = 4+(1/2) = 4hours 30minutes.\ncorrect option is D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe salary of a worker is first increased by 30% and afterwards reduced by 30%. What is net change in his salary?\n\n### Options:\nA. 910% increase\nB. 10% increase\nC. 9% decrease\nD. 12% decrease\nE. 15% increase\n\n### Answer:\n(30 * 30)/100 = 9% decrease\nANSWER C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many five-digit numbers exist such that the product of their digits is 400?\n\n### Options:\nA. 60\nB. 120\nC. 180\nD. 30\nE. 75\n\n### Answer:\nWe're asked to name all of the 5-digit numbers whose product-of-digits is 400. We can use prime-factorization to figure out the digits, BUT this comes with a \"twist\".....NOT ALL of the digits have to be primes....\n400 = (25)(16)\nThe 25 = (5)(5) and there's no way around that. Every option MUST have two 5s as two of the digits.\nThe 16 can be broken down in a few different ways though:\n16 = (1)(2)(8)\n16 = (1)(4)(4)\n16 = (2)(2)(4)\nEach of those options has to be accounted for.\nSo, we have 3 sets of 5 digits:\n1) 1, 2, 8, 5, 5 --> This gives us 5!/2! arrangements = 120/2 = 60 different 5-digit numbers.\n2) 1, 4, 4, 5, 5 --> This gives us 5!/(2!2!) arrangements = 120/4 = 30 different 5-digit numbers.\n3) 2, 2, 4, 5, 5 --> This gives us 5!/(2!2!) arrangements = 120/4 = 30 different 5-digit numbers.\n60 + 30 + 30 = 120 different 5-digit numbers\nFinal Answer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo trains of length 120 m and 280 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively. In what time will they be clear of each other from the moment they meet?\n\n### Options:\nA. 22 sec\nB. 88 sec\nC. 99 sec\nD. 20 sec\nE. 17 sec\n\n### Answer:\nRelative speed = (42 + 30) * 5/18 = 4 * 5 = 20 mps.\nDistance covered in passing each other = 120 + 280 = 400 m.\nThe time required = d/s = 400/20 = 20 sec.Answer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nCalculate f(3), given that f(x) = x3 + f0(-1)x2 + f00(1)x + f0(-1)f(-1).\n\n### Options:\nA. 198\nB. 197\nC. 196\nD. 195\nE. 194\n\n### Answer:\nDifferentiating, we compute\nf0(x) = 3x2 + 2f0(-1)x + f00(1)\nf00(x) = 6x + 2f0(-1):\nPlugging in x = -1 into the first equation and x = 1 into the second, we obtain a system of\nequations in f0(-1) and f00(1):\nf0(-1) = 3 - 2f0(-1) + f00(1);\nf00(1) = 6 + 2f0(-1):\nDenoting f0(-1) and f00(1) by a and b respectively, we have\na = 3 - 2a + b\nb = 6 + 2a:\nPlugging the second equation into the first, we get\na = 3 - 2a + (6 + 2a) = 9:\nThus, b = 6 + 2a = 24, so\nf(x) = x3 + ax2 + bx + af(-1) = x3 + 9x2 + 24x + 9f(-1):\nFinally, plugging x = -\udbc0\udc001 into this equation, we get\nf(-1) =-1 + 9-24 + 9f(-1)\n-8f(-1) = -16\nf(-1) = -2\nWe conclude that\nf(x) = x3 + 9x2 + 24x + 18\nf(3) = 33 + 9* 32 + 24 *3 + 18\n= 27 + 81 + 72 + 18 = 198\ncorrect answer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average weight of A, B and C is 60 kg. If the average weight of A and B be 70 kg and that of B and C be 50 kg, then the weight of B is:\n\n### Options:\nA. 50 kg\nB. 60 kg\nC. 55 kg\nD. 57 kg\nE. 62 kg\n\n### Answer:\nEXPLANATION\nLet A, B, C represent their respective weights. Then, we have:\nA + B + C = (60 x 3) = 180 \u00e2\u20ac\u00a6. (i)\nA + B = (70 x 2) = 140 \u00e2\u20ac\u00a6. (ii)\nB + C = (50 x 2) = 100 \u00e2\u20ac\u00a6.(iii)\nAdding (ii) and (iii), we get: A + 2B + C = 240 \u00e2\u20ac\u00a6. (iv)\nSubtracting (i) from (iv), we get : B = 60.\nB\u00e2\u20ac\u2122s weight = 60 kg.\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe letters in the word ADOPTS are permuted in all possible ways and arranged in alphabetical order then find the word at position 42 in the permuted alphabetical order?\n\n### Options:\nA. AOTDSP\nB. AOTPDS\nC. AOTDPS\nD. AOSTPD\nE. None of these\n\n### Answer:\nExplanation :\nIn alphabetical order : A D O P S T\nA _ _ _ _ _ : the places filled in 5! ways = 120, But we need a rank less than 120. So the word starts with A.\nA D _ _ _ _ : empty places can be filled in 4!=24\nA O _ _ _ _ : the places filled with 4! ways = 24. If we add 24 + 24\nthis total crosses 42. So We should not consider all the words starting with AO.\nA O D _ _ _ : 3!= 6\nA O P _ _ _ : 3!=6\nTill this 36 words are obtained, we need the 42nd word.\nAOS _ _ _ : 3!= 6\nExactly we are getting the sum 42. So last 3 letters in the descending order are TPD.\nSo given word is AOSTPD\nAnswer : D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA person can row upstream 2 kmph and downstream 8 kmph. Find the rate of the stream and person rate in still water.\n\n### Options:\nA. 1,5\nB. 2,5\nC. 5,5\nD. 3,5\nE. 5,1\n\n### Answer:\nExplanation:\nPlease remember,\nIf a is rate downstream and b is rate upstream\nRate of current = 1/2(a-b)\nRate in still water = 1/2(a+b)\n=> Rate of current = 1/2(8-2) = 3 kmph\n=> Rate in still water = 1/2(8+2) = 5 kmph\nOption D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the value of * in the following\n(1 5/3) \u00f7 3/11 \u00d7 */11 = (2 2/3 \u00d7 7/5 \u00d7 6/7)\n\n### Options:\nA. 3.1\nB. 3.4\nC. 3.6\nD. 4\nE. 4.5\n\n### Answer:\n3.6\nOption 'C'\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA can do a piece of work in 10 days and B in 20 days. They began the work together but 5 days before the completion of the work, A leaves. The work was completed in?\n\n### Options:\nA. 15 days\nB. 10 days\nC. 12 days\nD. 19 days\nE. 13 days\n\n### Answer:\nB\n(x \u00e2\u20ac\u201c 5)/10 + x/20 = 1\nx = 10 days\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nArun has 13 boxes of chocolates with him, with an average of 17 chocolates per box. If each box has at least 11 chocolates and no two boxes have equal number of chocolates, then what can be the maximum possible number of chocolates in any box?\n\n### Options:\nA. 23\nB. 25\nC. 29\nD. Can't be determined\nE. None of these\n\n### Answer:\nDETAILED SOLUTION\nTotal number of chocolates = 13 x 17 = 221\nFor one box to have maximum number of chocolates, the other boxes need to have minimum number of chocolates i.e. 11, 12, \u2026\u2026\u2026\u2026\u2026\u2026\u2026.., 22\nTotal = 11 x 12 + (0+1+2+\u2026\u2026\u2026\u2026\u2026+11)\n= 132 + 66 = 198\nTherefore, maximum possible chocolates = 221 \u2013 198 = 23\nCORRECT ANSWER A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many seconds will a train 70 meters long take to cross a bridge 80 meters long if the speed of the train is 36 kmph?\n\n### Options:\nA. 22 sec\nB. 27 sec\nC. 25 sec\nD. 15 sec\nE. 11 sec\n\n### Answer:\nExplanation:\nD = 70 + 80 = 150\nS = 36 * 5/18 = 10 mps\nT = 150/10 = 15 sec\nAnswer: Option D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe \u2018moving walkway\u2019 is a 300-foot long walkway consisting of a conveyor belt that moves continuously at 3 feet per second. When Bill steps on the walkway, a group of people that are also on the walkway stands 120 feet in front of him. He walks toward the group at a rate of 3 feet per second. Once Bill reaches the group of people, he stops walking and stands with them until the walkway ends. What is Bill\u2019s average rate Y of movement for his trip along the moving walkway?\n\n### Options:\nA. 2 feet per second\nB. 2.5 feet per second\nC. 3 feet per second\nD. 4 feet per second\nE. 5 feet per second\n\n### Answer:\nA, B, and C don't make ANY sense! we know for some time...(a majority of the 300ft) Bill will walk at a pace of 6ft per second...and then at some later time he will stop and move at 3 ft per second... The average Y MUST bebetween3-6 ft per second or the Earth is FLAT!!!.\nSo we are down to DE, D doesn't make sense on a weighted averages level because we know when Bill gets on the walkway the patrons are already 40% of the way down the 300ft walkway AND they are still moving at half the rate of Bill!! So for Bill to average 4 ft per second he would have had to spend a majority of the 300 ft at 3ft per second because 4 is much closer (when you factor in the size of the values we're dealing with 2 is double 1) to 3 than to 6. We know from the information that isn't possible. Billmust havespent the majority of his time at 6 ft per second before he stopped walking. That leaves only answer E as plausible.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a apartment, 30% of the people speak English, 20% speak Hindi and 10% speak both. If a people is selected at random, what is the probability that he has speak English or Hindi?\n\n### Options:\nA. 1/3\nB. 2/3\nC. 2/5\nD. 2/7\nE. 3/7\n\n### Answer:\nP (E) = 30 / 100 = 3 / 10 , P (H) = 20 / 100 = 1 / 5 and P (E \u2229 H) = 10 / 100 = 1 / 10\nP (E or H) = P (E U H)\n= P (E) + P (H) - P (E \u2229 H)\n= (3 / 10) + (1 / 5) - (1 / 10) = 4 / 10 = 2/5\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe \u201clength of integer x\u201d refers to the number of prime factors, not necessarily distinct, that x has. (If x = 60, the length of x would be 4 because 60 = 2 \u00d7 2 \u00d7 3 \u00d7 5.) What is the greatest possible length of integer z if z < 2500?\n\n### Options:\nA. 7\nB. 9\nC. 11\nD. 13\nE. 15\n\n### Answer:\nTo maximize the length of z, we should minimize its prime base. The smallest prime is 2 and since 2^11 = 2048 < 2500, then the greatest possible length of integer z is 11.\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMane and Thomas are among the 8 people from which a committee of 4 people is to be selected. How many different possible committees of 4 people can be selected from these 8 people if at least one of either Mane or Thomas is to be selected?\n\n### Options:\nA. 28\nB. 46\nC. 55\nD. 63\nE. 70\n\n### Answer:\nAns:C\nSolution:\nM+T+6 = total 8 ,\nwe need to select at least one of the M and T or both= total 4 out of 8 - 4 out of 6\n8C4 - 6C4\n=55\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a*b*c=195, b*c*d = 65, c*d*e=1000 and d*e*f=250 the (a*f)/(c*d) = ?\n\n### Options:\nA. 1/2\nB. 1/4\nC. 3/4\nD. 2/3\nE. None of these\n\n### Answer:\nExplanation :\na\u00e2\u02c6\u2014b\u00e2\u02c6\u2014c/b\u00e2\u02c6\u2014c\u00e2\u02c6\u2014d= 195/65 => a/d = 3\nd\u00e2\u02c6\u2014e\u00e2\u02c6\u2014f/c\u00e2\u02c6\u2014d\u00e2\u02c6\u2014e= 250/1000 => f/c = 1/4\na/d* f/c = 3 * 1/4 = 3/4\nAnswer : C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA soft drink company had 6000 small and 15000 big bottles in storage. If 12% of small 14% of big bottles have been sold, then the total bottles remaining in storage is\n\n### Options:\nA. 15360\nB. 16010\nC. 18180\nD. 14930\nE. 16075\n\n### Answer:\n6000 + 15000 - (0.12*6000 + 0.14*15000) = 18180.\nAnswer: C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nP, Q and R can do a piece of work in 20, 30 and 60 days respectively. In how many days can P do the work if he is assisted by Q and R on every third day?\n\n### Options:\nA. 15 DAYS\nB. 12 DAYS\nC. 10 DAYS\nD. 18 DAYS\nE. 20 DAYS\n\n### Answer:\nP's 2 day's work =\t1/20*2=1/10\nP+Q+R)'S 1 DAY'S WORK = 1/20+1/30+1/60 = 6/60 = 1/10\nWORK IN DAYS = 1/5\nNOW 1/5 DONE IN 3 DAYS\nWHOLE WORK WILL BE DONE IN(3*5) = 15 DAYS\nANSWER A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nCalculate the HCF of 64, 592, 960\n\n### Options:\nA. 15\nB. 16\nC. 13\nD. 14\nE. 12\n\n### Answer:\nExplanation:\nLets solve this question by factorization method.\nThe factors of 64 are: 1, 2, 4, 8, 16, 32, 64\nThe factors of 592 are: 1, 2, 4, 8, 16, 37, 74, 148, 296, 592\nThe factors of 960 are: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 160, 192, 240, 320, 480, 960\nThen the greatest common factor is 16.\nAnswer: Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA watch was sold at a loss of 36%. If it was sold for Rs.140 more, there would have been a gain of 4%. What is the cost price?\n\n### Options:\nA. 350\nB. 288\nC. 799\nD. 778\nE. 901\n\n### Answer:\n64%\n104%\n--------\n40% ---- 140\n100% ---- ? => Rs.350\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a number 105 divides into n with no remainder, which of the following must be a factor of n?\n\n### Options:\nA. 2\nB. 4\nC. 6\nD. 7\nE. 11\n\n### Answer:\n105 / n = k (with k an integer)\n(7)(5)(3) / n = k\nn must have a 7 in his prime factorization to divide 105 without remainder.\nanswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the rate percent when the simple interest on Rs.800 amount to Rs.160 in 3 Years?\n\n### Options:\nA. 5%\nB. 6.6%\nC. 9%\nD. 2%\nE. 4%\n\n### Answer:\n160 = (800*3*R)/100\nR = 6.6%\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow much interest can a person get on Rs. 8200 at 10.5% p.a. simple interest for a period of six years and six months?\n\n### Options:\nA. 5596.5\nB. 5596.55\nC. 5596.54\nD. 3587.51\nE. 3587.57\n\n### Answer:\nI = (8200 * 6.5 * 10.5)/100\n= (8200 * 13 * 21)/(100 * 2 * 2)\n= Rs. 5596.5\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf |5x-20| = 100, then find the sum of the values of x?\n\n### Options:\nA. 1\nB. -2\nC. 8\nD. -3\nE. 4\n\n### Answer:\n|5x-20| = 100\n5x-20 = 100 or 5x-20 = -100\n5x = 120 or 5x = -80\nx = 24 or x = -16\nsum = 24-16 = 8\nAnswer is C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA reduction of 20% in the price of salt enables a lady to obtain 10kgs more for Rs.100, find the original price per kg?\n\n### Options:\nA. Rs.2.7\nB. Rs.2.4\nC. Rs.2.5\nD. Rs.2.1\nE. Rs.2.9\n\n### Answer:\n100*(20/100) = 20 --- 10\n? --- 1 => Rs.2\n100 --- 80\n? --- 2 => Rs.2.5\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA group of students decided to collect as many paise from each member of group as is the number of members. If the total collection amounts to Rs. 20.25, the number of the member is the group is:\n\n### Options:\nA. 57\nB. 67\nC. 45\nD. 47\nE. 97\n\n### Answer:\nMoney collected =(20.25 x 100) paise = 2025 paise\nnumbers of members = 2025 squareroot = 45\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSalesperson A's compensation for any week is $300 plus 6 percent of the portion of A's total sales above $1,000 for that week. Salesperson B's compensation for any week is 8 percent of B's total sales for that week. For what amount of total weekly sales would both salespeople earn the same compensation?\n\n### Options:\nA. $21,000\nB. $18,000\nC. $12,000\nD. $8000\nE. $4000\n\n### Answer:\n300+0.06(x-1000) = 0.08x\n0.02x = 240\nx = $12,000\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man swims downstream 72 km and upstream 45 km taking 9 hours each time; what is the speed of the current?\n\n### Options:\nA. 1.9\nB. 1.5\nC. 1.1\nD. 1.3\nE. 1.2\n\n### Answer:\n72 --- 9 DS = 8\n? ---- 1\n45 ---- 9 US = 5\n? ---- 1 S = ?\nS = (8 - 5)/2 = 1.5\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nwhich number need to add to 859622 to get a number exactly divisible by 456?\n\n### Options:\nA. 389999\nB. 543248\nC. 798790\nD. 795320\nE. 859622\n\n### Answer:\nDividend = Quotient * Divisor + Reminder\n859622 / 456 gives quotient = 1885 and reminder = 62.\nSo, the next number divisible by 456 is 456 places infront of 456 * 1885\nWhich means 456 \u2013 62 = 394 should be added to 859622.\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJohn bought a total of 12 Mangoes and Oranges. Each Mango costs 80 cents and each orange costs 50 cents. If the average price of the 12 mangoes and oranges that John originally purchased was 65 cents, then how many oranges needs to return to raise the average price of his purchase to 72 cents?\n\n### Options:\nA. 4\nB. 5\nC. 6\nD. 7\nE. 8\n\n### Answer:\nLet number of mangoes be x, number of oranges be 12-x\n0.80x +(12-x)0.50/12 = 0.65\nsolving for x, we get x = 6 --> Mangoes 6, Oranges 6\nNow, number of oranges to be returned be y\n[0.80*6 + (6-y)*0.50]/12-y = 0.72\nsolving for y, y = 4\nAns: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA committee has 5 men and 6 women. What are the number of ways of selecting 2 men and 3 women from the given committee?\n\n### Options:\nA. 202\nB. 200\nC. 209\nD. 207\nE. 201\n\n### Answer:\nThe number of ways to select two men and three women = \u2075C\u2082 * \u2076C\u2083\n= (5 *4 )/(2 * 1) * (6 * 5 * 4)/(3 * 2)\n= 200\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the selling price is doubled,the profit is tripled,what is the percentage of profit??\n\n### Options:\nA. 50%\nB. 100%\nC. 150%\nD. 200%\nE. 250%\n\n### Answer:\nLet the profit be 10, then\nSP-CP=10 and 2SP-CP=30\nSolving the above equations we get SP=20 and CP=10, so CP=Profit\nHence the answer is B (100%)\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA Private Limited company have 20 staffs and they celebrated one festival. Director gives Rs.10000/- to his accountant and told him to 4500/- to each staff Rs. 2000/- each to cleaning staff and cooking staff and balance for you. Then how much amount accountant received?\n\n### Options:\nA. 10500\nB. 20000\nC. 4500\nD. 6500\nE. 5000\n\n### Answer:\nTotal amount paid for 20 Staffs : 4500 * 19= 85500/-\nPaid to Cleaning & Cooking Staff : 2000/- * 2 = 4000/-\nTotal amount paid for both : 85500/- + 4000/- =89500/-\nBalance with Accountant : 100000 - 89500 = 10500/-\nAnswer is (A)\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf both 112 and 33 are factors of the number a * 43 * 62 * 1311, then what is the smallest possible value of a?\n\n### Options:\nA. 121\nB. 3267\nC. 363\nD. 33\nE. None of the above\n\n### Answer:\nExplanatory Answer\nStep 1: Prime factorize the given expression\na * 43 * 62 * 1311 can be expressed in terms of its prime factors as a * 28 * 32 * 1311\nStep 2: Find factors missing after excluding 'a' to make the number divisible by both 112 and 33\n112 is a factor of the given number.\nIf we do not include 'a', 11 is not a prime factor of the given number.\nIf 112 is a factor of the number, 112 should have been in 'a'\n33 is a factor of the given number.\nIf we do not include 'a', the number has only 32 in it.\nTherefore, if 33 has to be a factor of the given number 'a' has to contain 31 in it.\nTherefore, 'a' should be at least 112 * 3 = 363 if the given number has 112 and 33 as its factors.\nThe smallest value that \"a\" can take is 363.\nChoice C is the correct answer.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe simple interest on 200 for 7 months at 5 paise per rupee per month is\n\n### Options:\nA. 70\nB. 7\nC. 35\nD. 30.5\nE. None of these\n\n### Answer:\n\u2235 Rate = 5 paise per rupee = 5%\n\u2234 S.I. = 200\u00d75\u00d77/100=70\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWorking simultaneously at their respective constant rates, Machines A and B produce 800 nails in x hours. Working alone at its constant rate, Machine A produces 800 nails in q hours. In terms of x and q, how many hours does it take Machine B, working alone at its constant rate, to produce 800 nails?\n\n### Options:\nA. x/(x+y)\nB. y/(x+y)\nC. xy/(x+y)\nD. xy/(x-y)\nE. xq/(q-x)\n\n### Answer:\nPick some smart numbers for x and q.\nSay x=1 hour and q=2 hours (notice that q must be greater than x, since the time for machine A to do the job, which is q hours, must be more than the time for machines A and B working together to do the same job, which is x hours).\nIn this case, the time needed for machine B to do the job must also be 2 hours: 1/2+1/2=1.\nNow, plug x=1 and q=2 in the options to see which one yields 2. Only option E fits.\nAnswer: E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFor a particular American football game, the probability of a team's quarterback throwing a completed pass on each throw is 3/10. What is the least number of times that the quarterback should throw the ball that will increase the probability of getting a completed pass at least once to more than 50%.\n\n### Options:\nA. 10\nB. 5\nC. 2\nD. 3\nE. 1\n\n### Answer:\nRule of Subtraction: P(A) = 1 - P(A')\nRule of Multiplication: P(A \u2229 B) = P(A) P(B)\nThe probability that the quarterback throws a completed pass at least once in 2 throws is 1- (7/10)^2 = 1 - 49/100 = 51/100 > 50%\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn 1998 the profits of company N were 10 percent of revenues. In 1999, the revenues of company N fell by 30 percent, but profits were 16 percent of revenues. The profits in 1999 were what percent of the profits in 1998?\n\n### Options:\nA. 80%\nB. 105%\nC. 120%\nD. 112%\nE. 138%\n\n### Answer:\n0,112R = x/100*0.1R\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA rectangular field has area equal to 150 sq m and perimeter 50 m. Its length and breadth must be?\n\n### Options:\nA. 11\nB. 99\nC. 89\nD. 10\nE. 12\n\n### Answer:\nlb = 150\n2(l + b) = 50 => l + b = 25\nl \u2013 b = 5\nl = 15 b = 10\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIt takes Avery 2 hours to build a brick wall while Tom can do it in 4 hour. If the two start working together and after an hour Avery leaves, how much time will it take Tom to complete the wall on his own?\n\n### Options:\nA. 70\nB. 20\nC. 50\nD. 60\nE. 30\n\n### Answer:\nAvery takes 2 hours\nTom takes 4 hours\nEfficiency of Avery is 1/2 units/hr\nEfficiency of Tom is 1/4 units/hr\nCombined efficiency of Tom and Avery is 1/2 +1/4 = 3/4 units/hr\nSince they worked for 1 hour they completed 3/4 units of work and 1/4 units of work is left which is to be completed by Tom ( Since Avery left )\nSo Time taken by Tom to complete the remaining work will be 1/4/1/4 hours => 1*60 = 60 minutes...\nAnswer will be (D)\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 20 men can build a water fountain 56 metres long in 7 days, what length of a similar water fountain can be built by 35 men in 3 days?\n\n### Options:\nA. 40 m\nB. 42 m\nC. 47 m\nD. 49 m\nE. 50 m\n\n### Answer:\nExplanation :\nLet the required length be x metres\nMore men, More length built (Direct Proportion)\nLess days, Less length built (Direct Proportion)\nMen 20: 35\nDays 7: 3 : : 56 : x\nTherefore (20 x 7 x x)=(35 x 3 x 56)\nx=(35 x 3 x 56)/140=42\nHence, the required length is 42 m.\nAnswer : B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOn Saturday morning, John will begin a camping vacation and he will return home at the end of the first day on which it rains. If on the first three days of the vacation the probability of rain on each day is 0.3, what is the probability that Malachi will return home at the end of the day on the following Monday?\n\n### Options:\nA. 0.008\nB. 0.125\nC. 0.147\nD. 0.512\nE. 0.64\n\n### Answer:\nRe-phrasing the question:\nWhat is the probability of: Saturday: No rain, Sunday: No rain, Monday: Rain\nProbability of rain = 0.3\nTherefore, probability of no rain = 0.7\n0.7*0.7*0.3 = 0.147\nHence C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nM and N invested in a shop. The profits were divided in the ratio of 4 : 5 respectively. If M invested Rs. 40,000, the amount invested by N is:\n\n### Options:\nA. 35000\nB. 40000\nC. 50000\nD. 60000\nE. None\n\n### Answer:\nSuppose N invested Rs. x. Then, 40000/x = 4/5 or y = [40000 x 5/ 4] = 50000.\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe ratio between a and y is 7/9; a and y are increased by 4, what is the ratio between the new values of a and y?\n\n### Options:\nA. 7/9\nB. 14/9\nC. 7/18\nD. 11/13\nE. It Cannot Be Determined\n\n### Answer:\nRatio = 7k/9k = 7/9, 14/18, etc.\na and y are increased by 4 --> (7k + 4)/(9k + 4)\nNew ratio can be 11/13, 18/22, etc.\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe cross-section of a cannel is a trapezium in shape. If the cannel is 15 m wide at the top and 4 m wide at the bottom and the area of cross-section is 1900 sq m, the depth of cannel is?\n\n### Options:\nA. 150\nB. 200\nC. 140\nD. 240\nE. 145\n\n### Answer:\n1/2 * d (15 + 4) = 1900\nd = 200\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind a sum for first 4 prime no's from number series?\n\n### Options:\nA. 24\nB. 28\nC. 30\nD. 17\nE. 36\n\n### Answer:\nRequired sum = (2 + 3 + 5 + 7 ) = 17\nNote: 1 is not a prime number\nOption D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA rectangular photograph is surrounded by a border that is 1 inch wide on each side. The total area of the photograph and the border is M square inches. If the border had been 3 inches wide on each side, the total area would have been (M + 64) square inches. What is the perimeter of the photograph, in inches?\n\n### Options:\nA. 16\nB. 24\nC. 32\nD. 40\nE. 48\n\n### Answer:\nLet x and y be the width and length of the photograph.\n(x+2)(y+2)=M and so (1) xy + 2x + 2y + 4 = M\n(x+6)(y+6)=M and so (2) xy + 6x + 6y + 36 = M+64\nLet's subtract equation (1) from equation (2).\n4x + 4y + 32 = 64\n2x + 2y = 16, which is the perimeter of the photograph.\nThe answer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the average (arithmetic mean) of a and b is 40 and the average of b and c is 60, what is the value of c \u2212 a?\n\n### Options:\nA. 25\nB. 40\nC. 90\nD. 140\nE. It cannot be determined from the information given.\n\n### Answer:\n-(a + b = 80)\nb + c=120\nc-a=40\nB. 40\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA person can walk at a constant rate of 8mph and can bike at a rate of 32mph. If he wants to travel 80 miles in 4 hours using bike and walking at their constant rates, how much distance would he require to walk?\n\n### Options:\nA. 20\nB. 30\nC. 48\nD. 60\nE. 72\n\n### Answer:\nTotal distance = 80\nDistance = Speed * Time\nWalking speed = s1 = 8\nWalking time = t1\nBike speed = s2 = 32\nTime traveled in bike = t2\nd1 + d2 = 80\ns1t1 + s2t2 = 80\n8*t1 + 32*t2 = 80\nt1 + 4*t2 = 10 ----- (1)\nGiven: t1 + t2 =4 ----- (2)\n(1) - (2) -->3 t2 = 6 , t2=2 and t1 = 8 - 2 = 6\nWalking distance = s1*t1 = 8*6 = 48\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the sales tax reduced from 3 1/2 % to 3 1/3%, then what difference does it make to a person who purchases an article with market price of Rs. 8400 ?\n\n### Options:\nA. Rs.10\nB. Rs.12\nC. Rs.14\nD. Rs.16\nE. Rs.18\n\n### Answer:\nRequired difference = [3 \u00bd % of Rs.8400] \u2013 [3 1/3 % of Rs.8400]\n= [(7/20-(10/3)]% of Rs.8400 =1/6 % of Rs.8400\n= Rs. [(1/6)8(1/100)*8400] = Rs. 14.\nOption C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo trains are traveling from point A to point B such that the speed of first train is 65 kmph and the speed of 2 train is 29 kmph. Where is the distance b/w A and B such that the slower train reached 5 hrs late compared to the faster?\n\n### Options:\nA. 3\nB. 65\nC. 9\nD. 5\nE. 31\n\n### Answer:\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich of the following can be a perimeter r of a triangle inscribed in a circle of radius 1?\nI. 0.001\nII. 0.010\nIII. 0.100\n\n### Options:\nA. I only\nB. III only\nC. II and III only\nD. I, II, and III\nE. Not I, II, or III\n\n### Answer:\nYes,the length of any side of a triangle must be larger than the positive difference of the other two sides, but smaller than the sum of the other two sides.\nBut how do you use the above property to solve the question?\nThe lower limit of the perimeter of an inscribed triangle in a circle of ANY radius is 0: r>0.\nAnswer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n1,3,6,10,15,?\n\n### Options:\nA. 17\nB. 18\nC. 19\nD. 20\nE. 21\n\n### Answer:\n1 =1\n1+2 = 3\n3+3 = 6\n6+4 = 10\n10+5 = 15\n15+6 = 21\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSolve the following quadratic equation by factoring.\nx2-5x-14=0\n\n### Options:\nA. -2,7\nB. 2,-7\nC. 1,8\nD. 1,-8\nE. 2,6\n\n### Answer:\nWe already have zero on one side of the equation, which we need to proceed with this problem. Therefore, all we need to do is actually factor the quadratic.\n(x+2)(x-7)=0\nx=-2 and x=7\nANSWER A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn what time will a train 80 m long cross an electric pole, it its speed be 144 km/hr?\n\n### Options:\nA. 2.0 sec\nB. 2.8 sec\nC. 7.5 sec\nD. 2.3 sec\nE. 1.5 sec\n\n### Answer:\nSpeed = 144 * 5/18\n= 40 m/sec\nTime taken = 80/40\n= 2.0 sec.\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe sum of the ages of 4 children born at the intervals of 1 years each is 12 years. what is the age of the youngest child ?\n\n### Options:\nA. 2.5\nB. 1.5\nC. 1\nD. 3.5\nE. 4.5\n\n### Answer:\nLet x = the youngest child. Each of the other four children will then be x+1, x+2, x+3\nWe know that the sum of their ages is 12\nso, x+(x+1)+(x+2)+(x+3) = 12\ntherefore The youngest child is 1.5 years old\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA, B and C enter into partnership. A invests some money at the beginning, B invests double the amount after 6 months, and C invests thrice the amount after 8 months. If the annual gain be Rs.21000. A's share is?\n\n### Options:\nA. 2999\nB. 2778\nC. 7000\nD. 2889\nE. 6612\n\n### Answer:\nx* 12 : 2x* 6: 3x* 4\n1:1:1\n1/3 * 21000 = 7000\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA merchant has selected two items to be placed on sale, one of which currently sells for 45 percent less than the other. If he wishes to raise the price of the cheaper item so that the two items are equally priced, by what percentage must he raise the price of the less expensive item?\n\n### Options:\nA. 100 %\nB. 90%\nC. 80%\nD. 70%\nE. 60%\n\n### Answer:\nExpensive item = $100;\nCheap item = $55;\nWe must increase $55 to $100, so by $45, which is approximately 80% increase: (100-55)/55 = 3/7 = ~0.81.\nAnswer: C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe age of man is three times the sum of the ages of his two sons.Five years hence,his age will be double of the sum of the ages of his sons.The father\u2019s present age is :\n\n### Options:\nA. 40 years\nB. 45 years\nC. 50 years\nD. 55 years\nE. 75 years\n\n### Answer:\nSolution\nLet the sum of present ages of the two sons be x years.\nThen,father's present age = 3x years.\n\u2234 (3x + 5)=2 (x +10) \u21d4 3x + 5 = 2x + 20 \u21d4 x =15.\nHence,father's present age = 45 years. Answer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nCurrent ages of Rahim and Thomas are in the ratio of 5 : 4 correspondingly. 0.5 decades hence, the ratio of their ages will become 11 : 9 correspondingly, What is Thomas\u00e2\u20ac\u2122s current age in years?\n\n### Options:\nA. 24 years\nB. 44 years\nC. 34 years\nD. 40 years\nE. 84 years\n\n### Answer:\n40 years\nIf current ages of Rahim and Thomas be 5A years and 4A years correspondingly\nThen, 5A + 5 = 11\n4A + 5 = 9\n9(5A + 5)=11(4A + 5)\nA = 10\nThomas\u00e2\u20ac\u2122s current age = 4A\n= 40 years.\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThree students appear at an examination of Mathematics. The probability of their success are 1/3, 3/4, 1/5 respectively. Find the probability of success of at least two.\n\n### Options:\nA. 11/30\nB. 12/50\nC. 13/30\nD. 3/50\nE. 4/50\n\n### Answer:\nThe probability of success of at least two students will involve the following possibilities.\nThe first two students are successful, the last two students are successful, the first and third students are successful and all the three students are successful.\nTherefore, the required probability = 1/3 x 3/4 x 4/5 + 3/4 x 1/5 x 2/3 + 1/3 x 1/5 x 1/4 + 1/3 x 3/4 x 1/5 = 11/30\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA group consists of 4 men, 6 women and 4 children. In how many ways can 2 men , 3 women and 1 child selected from the given group?\n\n### Options:\nA. 400\nB. 480\nC. 287\nD. 278\nE. 281\n\n### Answer:\nExplanation:\nTwo men, three women and one child can be selected in \u00e2\u00b4C\u00e2\u201a\u201a * \u00e2\u00b6C\u00e2\u201a\u0192 * \u00e2\u00b5C\u00e2\u201a ways\n= (4 * 3)/(2 * 1) * (6 * 5 * 4)/(3 * 2) * 4\n= 480 ways.\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 893 \u00d7 78 = p, which of the following is equal to 893 \u00d7 79?\n\n### Options:\nA. p + 1\nB. p + 78\nC. p + 79\nD. p + 893\nE. p + 894\n\n### Answer:\nSince 893 \u00d7 78 = p and 79=78+1, we have 893 \u00d7 79 = 893 \u00d7(78+1)=893\u00d778 + 893 \u00d71 = p + 893.\nThe answer is (D).\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe compounded ratio of (2 : 3), (6: 11) and (11 :2) is :\n\n### Options:\nA. 1:2\nB. 5:9\nC. 2:1\nD. 11:24\nE. None\n\n### Answer:\nAnswer: Option C\n2/3 : 6/11 : 11/2 = 2:1\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA person borrows 20000 for 6 years at 8% p.a. simple interest. He immediately lends it to another person at 9 % p.a. for 6 years. Find his gain in the transaction per year.\n\n### Options:\nA. 200\nB. 250\nC. 210\nD. 190\nE. 180\n\n### Answer:\nGain in 6 years\n= [(20000\u00c3\u20149\u00c3\u20146/100)\u00e2\u02c6\u2019(20000\u00c3\u20146\u00c3\u20148/100)]\n= (10800 \u00e2\u20ac\u201c 9600) = 1200\n\u00e2\u02c6\u00b4 Gain in 6 year = (1200/6) = 200\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAfter spending Rs. 5000 on rent, Rs. 1500 on milk, Rs. 4500 on groceries, Rs.2500 On childrens education Rs. 2000 on petrol and Rs. 2500 on miscellaneous expenses, Mr. Kishore saved 10% of his monthly salary. How much did he save in Rs. ?\n\n### Options:\nA. 2160\nB. 2350\nC. 2000\nD. 2300\nE. None of these\n\n### Answer:\nExplanation :\nTotal Exp = 5000+1500+4500+2500+2000+2500 = 18000\nExp in % = 100-10 = 90%, 18000 = 90%\nSaving = 10 % = 18000 X 10/90 = Rs. 2000\nAnswer : C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the simple interest on a sum of money at thirteen percent per annum for two years is Rs.22400, compound interest on the same sum for the same period at the same rate of interest is\n\n### Options:\nA. 28,356.00\nB. 25,638.00\nC. 23,856.00\nD. 23,685.00\nE. 25,865.00\n\n### Answer:\nS I for 2 years = 22400 ie for one year =11200\nThe compound interest for Rs.11200 for the second year = 11200*13/100 = 1456\nThe CI for two years 22400+1456 = 23,856.00\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n24 oz of juice P and 25 oz of juice E are mixed to make smothies X and Y . The ratio of p to E in smothie X is 4 is to 1 and that in Y is 1is to 5.How many ounces of juice P are contained in the smothie X?\n\n### Options:\nA. 5\nB. 10\nC. 15\nD. 20\nE. 25\n\n### Answer:\nEasy way to solve this question is start from the answer and then conform the information provided in the question.\nwe can start from option D i.e 20 ... as a quantity of juice P in X because it is the only one option that gets divided by 4 is 20 ... since in the X the juice P to E ratio is 4:1\nthis gives us that quantity of juice P in X = 20 therefore quantity of Juice E will be 5 ... hence ratio = 4:1\nThis will lead to quantity of juice P in X = 4 and quantity of Juice E = 20 ... hence ratio 1:5\nif we calculate total Juice P = 24 and total of juice V = 25\nit fits because totals are same as what mentioned in the question ...\nthus ans is D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n240 is increased by 20%. Find the final number.\n\n### Options:\nA. 200\nB. 210\nC. 180\nD. 288\nE. 220\n\n### Answer:\nExplanation\rFinal number = Initial number + 20%(original number) = 240 + 20%(240) = 240 + 48 = 288.\rAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn some quantity of ghee, 60% of pure ghee and 40% of is vanaspati. If 10kg of pure ghee is added, then the strength of vanaspati ghee becomes 20%. The original quantity was?\n\n### Options:\nA. 5kg\nB. 10kg\nC. 15kg\nD. 20kg\nE. 25kg\n\n### Answer:\nLet the original quantity be x kg\nvanaspati ghee in x kg = 40/100 *x = 2x/5 kg\n(2x/5)/(x+10) = 20/100\n2x/(5x+50) = 1/5\n5x = 50\nx = 10kg\nAnswer is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFrom a container having pure milk, 10% is replaced by water and the process is repeated twice. At the end of the second operation, the milk is?\n\n### Options:\nA. 50%\nB. 60%\nC. 55%\nD. 75%\nE. 81%\n\n### Answer:\nLet the total quantity of original milk = 1000gm\nMilk after 1st operation = 90% of 1000 = 900gm\nMilk after second operation = 90% of 900 = 810gm\nStrength of final mixture = 81%\nAnswer is E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nCalculate the fourth proportional to 5.2, 6.6 and 9.1?\n\n### Options:\nA. 19.55\nB. 10.55\nC. 11.55\nD. 10.2\nE. 12.5\n\n### Answer:\nExplanation:\nFormula = Fourth propotional = (b \u00d7 c)/a\nA = 5.2 , B = 6.6 and C = 9.1\n(6.6 \u00d7 9.1)/5.2 = 11.55\nAnswer: Option C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA leak in the bottom of a tank can empty the full tank in 6 hours. An inlet pipe fills water at the rate of 4 liters per minute. When the tank is full in inlet is opened and due to the leak the tank is empties in 8 hours. The capacity of the tank is?\n\n### Options:\nA. 5768\nB. 5760\nC. 5762\nD. 5766\nE. 5712\n\n### Answer:\n1/x - 1/6 = -1/8\nx = 24 hrs\n24 * 60 * 4 = 5760\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man counted his animals, 80 heads and 270 legs (ducks and goats). how many goats are there?\n\n### Options:\nA. 30\nB. 40\nC. 50\nD. 60\nE. 55\n\n### Answer:\nlet no of ducks=d and no of goat=g\nd+g=80(heads)----------> eq 1\neach duck has 2 legs and goat has 4 legs\n2d+4g=270 and divide 2d+4g=270 by 2 we get d+2g=135 -----------> eq2\nsubtract eq1 from eq2\nwe get no of goats=55\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nDifference between the length &breadth of a rectangle is 23 m. If its perimeter is 206 m, then its area is?\n\n### Options:\nA. 2400 m^2\nB. 2500 m^2\nC. 2520 m^2\nD. 2560 m^2\nE. 2580 m^2\n\n### Answer:\nSolving the two equations, we get: l = 63 and b = 40.\nArea = (l x b) = (63 x 40) m2 = 2520 m^2\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA chair is bought for Rs.600/- and sold at a loss of 10% find its selling price\n\n### Options:\nA. Rs.500/-\nB. Rs.540/-\nC. Rs.600/-\nD. Rs.640/-\nE. Rs.660/-\n\n### Answer:\n100 % ------> 600 (100 * 6 = 600)\n90 % ------> 540 (90 * 6 = 540)\nSelling price = Rs.540/-\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo trains start simultaneously from opposite ends of a 160-km route and travel toward each other on parallel tracks. Train X, traveling at a constant rate, completes the 160-km trip in 5 hours. Train Y, travelling at a constant rate, completes the 160-km trip in 3 hours. How many kilometers had Train X traveled when it met Train Y?\n\n### Options:\nA. 56\nB. 58\nC. 60\nD. 62\nE. 64\n\n### Answer:\nIf the two trains cover a total distance D, then Train X travels (3/8)*D while Train Y travels (5/8)*D. If the trains travel 160 km to the meeting point, then Train X travels (3/8)*160 = 60 km. The answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe diagonal of the floor of a rectangular closet is 7 feet. The shorter side of the closet is 4 feet. What is the area of the closet in square feet?\n\n### Options:\nA. 26\nB. 27\nC. 28\nD. 29\nE. 32\n\n### Answer:\nOther side =\n15 2 - 9 2\n2 2\nft\n=\n225 - 81\n4 4\nft\n=\n144\n4\nft\n= 6 ft.\nArea of closet = (6 x 4.5) sq. ft = 27 sq. ft.\nB)\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nDoug, who runs track for his high school,\nwas challenged to a race by his younger\nbrother, Matt. Matt started running first,\nand Doug didn\u2019t start running until Matt\nhad finished a quarter-mile lap on the\nschool track. Doug passed Matt as they\nboth finished their sixth lap. If both boys\nran at a constant speed, with Doug running\n2 miles an hour faster than Matt, what was\nMatt\u2019s speed?\n\n### Options:\nA. 10.5 miles per hour\nB. 10 miles per hour\nC. 9 miles per hour\nD. 8 miles per hour\nE. 7.5 miles per hour\n\n### Answer:\nDoug runs 2 miles an hour faster than Matt, so let Matt\u2019s speed equal x miles per hour.\nThen Doug\u2019s speed equals x + 2 miles per hour. Each lap is one-quarter of a mile, so Doug\nruns 1.5 miles in the time it takes Matt to run 1.25 miles. Place this information in a chart:\nDOUGH RATE:x-2 TIME:1.5/1 DISTANCE:1.5\nMATT RATE:X TIME:1.25/X DISTANCE:1.25\nThe two boys took the same amount of time from the time Doug started, so make an\nequation by setting the two times in the chart equal to each other, and then solve for x:\n1.5/X+2=1.25/X\n1.5X=1.25(X+2)\n1.5X=1.25X+2.5\n0.25X=2.5\nX=10\nSo Matt ran at 10 miles per hour.\ncorrect answer B)10 miles per hour\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nCurrently apples cost 60 cents/pound. Due to a disease affecting the apple trees it is expected that next month apples will cost 200% more than they do currently. How much are apples expected to cost next month?\n\n### Options:\nA. 200 cents /pound\nB. 150 cents /pound\nC. 160 cents /pound\nD. 180 cents /pound\nE. 170 cents /pound\n\n### Answer:\nIf a new cost is p percent greater than the old cost, then (new cost) = (old cost) + (p/100)(old cost).\nIn this case, (new cost) = 60 cents/pound + (200/100)(60 cents/pound)\n= 60 cents/pound + 120 cents/pound\n= 180 cents /pound\nAnswer : D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA candidate appearing for an examination has to secure 42% marks to pass paper I. But he secured only 60 marks and failed by 20 marks. What is the maximum mark for paper I?\n\n### Options:\nA. 110\nB. 120\nC. 130\nD. 140\nE. 190\n\n### Answer:\nhe secured 60 marks nd fail by 20 marks so\ntotal marks for pass the examinatn=80\nlet toal marks x\nx*42/100=80\nx=190\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf each side of a square is increased by 25%, find the percentage change in its area.\n\n### Options:\nA. 26.25%\nB. 36.25%\nC. 46.25%\nD. 56.25%\nE. 66.25%\n\n### Answer:\nLet each side of the square be a. Then, area = a2.\nNew side =(125a/100) =(5a/4). New area = (5a/4) 2=(25a2)/16.\nIncrease in area = ((25 a2)/16)-a2=(9a2)/16.\nIncrease% = [((9a2)/16)*(1/a2)*100] % = 56.25%.\nOption D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA garrison of 2000 men has provisions for 54 days. At the end of 18 days, a reinforcement arrives, and it is now found that the provisions will last only for 20 days more. What is the reinforcement?\n\n### Options:\nA. 1977\nB. 1600\nC. 1979\nD. 1900\nE. 1278\n\n### Answer:\n2000 ---- 54\n2000 ---- 36\nx ----- 20\nx*20 = 2000*36\nx = 3600\n2000\n-------\n1600\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSum of the squares of three numbers is 138 and the sum of their products taken two at a time is 131. Find the sum?\n\n### Options:\nA. 20\nB. 21\nC. 23\nD. 25\nE. 27\n\n### Answer:\n(a + b + c)2 = a2 + b2 + c2 + 2(ab +bc + ca) = 138 + 2* 131\na + b + c = \u221a400 = 20\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many numbers from 10 to 1000 are exactly divisible by 9?\n\n### Options:\nA. 100\nB. 10\nC. 11\nD. 12\nE. 14\n\n### Answer:\n10/9 = 1 and 1000/9 = 111 ==> 111 - 1 = 100. Therefore 100\nAnswer : A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf it takes 6 identical printing presses exactly 4 hours E to print 5,000 newspapers, how long would it take 3 of these presses to print 3,000 newspapers?\n\n### Options:\nA. 3 hours, 20 minutes\nB. 4 hours, 20 minutes\nC. 4 hours, 48 minutes\nD. 5 hours, 48 minutes\nE. 6 hours, 50 minutes\n\n### Answer:\n6 presses - 5,000 newspapers - 4 hours ;\n3 presses - 2,500 newspapers - 4 hours ;\n3 presses - 3,000 newspapers - 4 hours + 1/5*4 hours = 4 hours, 48 minutes (since 2,500+1/5*2,500=3,000) = E.\nAnswer: C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a(a + 5) = 6 and b(b + 5) = 6, where a \u2260 b, then a + b =\n\n### Options:\nA. \u22125\nB. \u22122\nC. 2\nD. 46\nE. 48\n\n### Answer:\na(a + 5) = 6 and b(b + 5) = 6\n=> a, b must be integers and if a is -6 or 1, b will be 1 and -6 respectively\n=> a+b = -5\nAns: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA teacher will pick a group of 5 students from a group of 9 students that includes Bart Lisa and john. If one of all the possible 5-student groups is picked at random, what is the probability of picking a group that includes john Bart and Lisa?\n\n### Options:\nA. 5/97\nB. 3/41\nC. 7/41\nD. 5/42\nE. 2/21\n\n### Answer:\nProbability = Favorable Outcomes / Total Outcomes\nTotal Outcomes= Total No. of ways of Picking Group of 5 out of 9 = 9C5 = 9! / (5! * 4!) = 126\nFavorable Outcomes= Total No. of ways of Picking Group of 5 out of 9 such that J, B and L are always in the group (i.e. we only have to pick remaining 2 out of remaining 6 as J, B and L must be there is group) = 6C2 = 15\nHence,Probability=15/126=5/42\nAnswer: Option D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn Township K each property is taxed at 10 percent of its assessed value. If the assessed value of a property in Township K is increased from $20,000 to $28,000, by how much will the property tax increase?\n\n### Options:\nA. $800\nB. $1000\nC. $600\nD. $400\nE. $500\n\n### Answer:\nIncrease in house value = $28,000 - $20,000 =$8000\nSo, tax increase = 10% of$8000=$800\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a, b and c are even integers, which of the following could be the value of a^2 + b^2 + c^2?\n\n### Options:\nA. a)82\nB. b)84\nC. c)85\nD. d)87\nE. e)90\n\n### Answer:\na, b and c are even integers which means that, supposing that x, y and z are integers, then a=2x, b=2y and c=2z\nTherefore we have: a^2+b^2+c^2=2^2*x^2+2^2*y+2^2*z=4x^2+4y^2+4z^2=4(x^2+y^2+z^2).\nWhich means that the total a^2+b^2+c^2 must be divisible by 4.\nThe only choice which is divisible by 4 is: B)\n84=8^2+4^2+2^2\nAnswer: B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn an election between two candidates, the winner has a margin of 20% of the votes polled. If 1000 people change their mind and vote for the loser, the loser would have won by a margin of 20% of the votes polled. Find the total number of votes polled in the election?\n\n### Options:\nA. 10000\nB. 5000\nC. 15000\nD. 20000\nE. 6000\n\n### Answer:\nWinner - Looser\n60% - 40%\nIf 1000 people change their mind and vote for the loser:\nWinner - Looser\n40% - 60%\nThus 1,000 people compose 20% of all voters, which means that the total number of votes is 5,000.\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe size of a flat-screen television is given as the length of the screen\u2019s diagonal. How many square inches greater is the screen of a square 24-inch flat-screen television than a square 17-inch flat-screen television?\n\n### Options:\nA. 143.5\nB. 154\nC. 160\nD. 148.75\nE. 142.25\n\n### Answer:\nIf we take a square with side length x and draw a diagonal, we get two isosceles right triangles.\nIf we focus on one such right triangle, we see that the legs have length x.\nsquare 24-inch flat-screen television\nThe diagonal (hypotenuse) = 24\nSo, we can apply the Pythagorean Theorem to get x\u00b2 + x\u00b2 = 24\u00b2\nSimplify: 2x\u00b2 = 24\u00b2\nDivide both sides by 2 to get: x\u00b2 = 24\u00b2/2\nSince the area of the square = x\u00b2, we can see that the area of this square is 24\u00b2/2\nsquare 17-inch flat-screen television\nThe diagonal (hypotenuse) = 17\nSo, we can apply the Pythagorean Theorem to get x\u00b2 + x\u00b2 = 17\u00b2\nSimplify: 2x\u00b2 = 17\u00b2\nDivide both sides by 2 to get: x\u00b2 = 17\u00b2/2\nSince the area of the square = x\u00b2, we can see that the area of this square is 17\u00b2/2\nDIFFERENCE IN AREAS =24\u00b2/2-17\u00b2/2\n= 288 -144.5 i.e = 143.5\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo trains of length 100 m and 200 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 54 kmph and 36 kmph. In how much time will the trains cross each other?\n\n### Options:\nA. 12 sec\nB. 13 sec\nC. 15 sec\nD. 16 sec\nE. 17 sec\n\n### Answer:\nD\nRelative speed = (54 + 36)* 5/18 = 5 * 5 = 25 mps.\nThe time required = d/s = (100 + 100 + 200)/25\n= 400/25 = 16 sec.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man invested Rs. 14,400 in Rs. 100 shares of a company at 20% premium.If the company declares 6% dividend at the end of the year,then how much does he get ?\n\n### Options:\nA. Rs. 500\nB. Rs. 600\nC. Rs. 650\nD. Rs. 720\nE. None\n\n### Answer:\nSolution\nNumber of shares = (14400/120) = 120.\nFace value = Rs. (100x120 ) = Rs. 12000.\nAnnual income = Rs.(6/100x12000) = Rs. 720.\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe probability of Sam passing the exam is 1/4. The probability of Sam passing the exam and Michael passing the driving test is 1/3. What is the probability of Michael passing his driving test?\n\n### Options:\nA. 1/24.\nB. 1/2.\nC. 1/3.\nD. 2/3.\nE. 2/5\n\n### Answer:\n1/3 *1/m= 1/6 , 1/m = 1/2\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFrom 6 positive numbers and 6 negative numbers, how many groups S of 4 numbers, yielding a positive product, can be formed?\n\n### Options:\nA. 720\nB. 625\nC. 30\nD. 960\nE. 255\n\n### Answer:\nPotential combinations of 4 numbers that will yield positive product\n++++ 4C6\n---- 4C6\n++-- 2C6*2C6\n4C6 + 4C6 + 2C6*2C6\nS=15 +15 + 15*15 = 255=E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA 300 meter long train crosses a platform in 39 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform?\n\n### Options:\nA. 350\nB. 289\nC. 208\nD. 270\nE. 287\n\n### Answer:\nSpeed = [300 / 18] m/sec = 50/3 m/sec.\nLet the length of the platform be x meters.\nThen, x + 300 / 39 = 50/3\n3(x + 300) = 1950 \u00e8 x\n= 350m.\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average temperature of Monday, Tuesday, Wednesday and Thursday was 38\u2218 and that of Tuesday, Wednesday, Thursday and Friday was 40\u2218. If the temperature on Monday was 36\u2218, the temperature of Friday was :\n\n### Options:\nA. 44\u2218\nB. 40\u2218\nC. 38\u2218\nD. 30\u2218\nE. None of these\n\n### Answer:\nExplanation:\nM+T+W+Th=(4\u00d738)=152\nMonday temperature is 36. So T+W+Th=(152-36)=116\nT+W+Th+F=(4\u00d740)=160\nF = (160-116)=44\u2218\nCorrect Option: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the value of * in the following\n(1 5/3) \u00f7 3/11 \u00d7 */11 = (2 2/3 \u00d7 7/5 \u00d7 6/7)\n\n### Options:\nA. 2.7\nB. 3\nC. 3.6\nD. 4.5\nE. 4.7\n\n### Answer:\nOption 'C'\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFrom the integer n, if n*n is odd, then what is true from below options?\n\n### Options:\nA. n is odd\nB. n*n*n is even\nC. n is even and n*n*n is even\nD. n is even\nE. All of the above\n\n### Answer:\nn is odd\nOption A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA, B and C completed a piece of work, A worked for 6 days, B for 9 days and C for 4 days. Their daily wages were in the ratio of 3:4:5. Find the daily wages of C, if their total earning was Rs.1628?\n\n### Options:\nA. s.109\nB. s.108\nC. s.110\nD. s.103\nE. s.102\n\n### Answer:\n3x 4x 5x\n6 9 4\n18x + 36x + 20x = 1628\n74x = 1628 => x = 22\n5x = 110 Rs.\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA drawer has six loose blue socks and six loose white socks. If four socks are removed from the drawer at random and without replacement. What is the probability that one pair of each color was selected?\n\n### Options:\nA. 2/33\nB. 5/66\nC. 5/33\nD. 5/11\nE. 1/2\n\n### Answer:\nNo of Loose blue socks = 6 (3 pairs)\nNo. of Loose white Socks = 6 (3 pairs)\ntotal no. of blue and white socks = 12\nTotal no. of socks to be selected = 4\nSo we have C (12,4) = no of ways the socks can be selected = 495\nNo of ways One pair of blue socks is selected ( 2 blue socks) , C (6,2) , No of ways one pair of white socks can be selected C (6,2) ..Because we have to find a scenario where EXACTLY one pair of Blue socks and ONE pair of WHITE socks is selected we will multiply the two .. ie 15 x 15 ..\nFilling the information in the Probability formula we get P (A) = (15 x 15) / 495 = 5 /11\nANSWER : (D)\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train 330 m long is running with a speed of 60 km/hr. In what time will it pass a man who is running at 6 km/hr in the direction opposite to that in which the train is going?\n\n### Options:\nA. 5\nB. 6\nC. 7\nD. 18\nE. 9\n\n### Answer:\nSpeed of train relative to man = 60 + 6 = 66 km/hr.\n= 66 * 5/18 = 55/3 m/sec.\nTime taken to pass the men = 330 * 3/55 = 18 sec.\nAnswer: Option D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe length and breadth of a rectangular courtyard is 75 m and 32 m. Find the cost of leveling it at the rate of $3 per m2. Also, find the distance covered by a boy to take 4 rounds of the courtyard.\n\n### Options:\nA. 3573\nB. 3455\nC. 8600\nD. 7000\nE. 7200\n\n### Answer:\nLength of the courtyard = 75 m\nBreadth of the courtyard = 32 m\nPerimeter of the courtyard = 2 (75 + 32) m\n= 2 \u00d7 107 m\n= 214 m\nDistance covered by the boy in taking 4 rounds = 4 \u00d7 perimeter of courtyard = 4 \u00d7 214 = 856 m\nWe know that area of the courtyard = length \u00d7 breadth\n= 75 \u00d7 32 m2\n= 2400 m2\nFor 1 m2, the cost of levelling = $3\nFor 2400 m2, the cost of levelling = $3 \u00d7 2400 = $7200 ANSWER : E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSuppose you have access to a large vat of distilled water, several gallons large. You have two precise measuring pipettes, one to measure exactly 1/5 of an ounce and one to measure exactly 1/6 of an ounce. You can pour precisely measured amounts into a beaker, which initially is empty. You can use either pipette to remove distilled water from the vat or from the beaker and use either pipette to dispense water into either of those receptacles, but you cannot use either pipette to take any quantity of distilled water other than the amount for which it is designed. Which of the following represents, in ounces, a precise amount of distilled water you can transfer from the vat to the beaker?\nI. 1/6\nII. 1/7\nIII. 1/12\n\n### Options:\nA. I only\nB. III only\nC. 1/30 and 11/30\nD. II and III only\nE. I, II, and III\n\n### Answer:\n1/5-1/6=1/30\n1/5+1/6=11/30\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich of the following are roots of an equation (x^-2)-(2x^-1)-35=0\n\n### Options:\nA. 1/5 and -1/7\nB. -1/5 and 1/7\nC. 1/5 and 1/7\nD. -1/5 and -1/7\nE. -5/2 and -1/7\n\n### Answer:\nGiven: (x^-2) - (2x^-1) - 35 = 0\nRewrite as: 1/(x\u00b2) - 2/x - 35 = 0\nRemove fractions by multiplying both sides by x\u00b2 to get: 1 - 2x - 35x\u00b2 = 0\nRearrange to get: 35x\u00b2 + 2x - 1 = 0\nFactor to get: (5x + 1)(7x - 1) = 0\nSo, EITHER 5x + 1 OR 7x - 1 = 0\nIf 5x + 1 = 0, then x = -1/5\nIf 7x - 1 = 0, then x = 1/7\nSo, the roots (solutions) are -1/5 and 1/7\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nChristine selects an item at a 25% off ticket price sale. The item is ticket priced at $25. How much should Christine expect to pay at the register?\n\n### Options:\nA. 22.5\nB. 20.0\nC. 18.75\nD. 12.5\nE. 10.0\n\n### Answer:\nR.P.=$25.00\nSale%=25\nS.P.=R.P.*(1-(Sale%/100))=25*(1-(25/100))=18.75\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the compound interest on $ 10,000 in 2 years at 4% per annum, the interest being compounded half-yearly\n\n### Options:\nA. 824\nB. 824.36\nC. 824.32\nD. 824.24\nE. 824.26\n\n### Answer:\nPrincipal = $ 10000; Rate = 2% per half-year; Time = 2 years = 4 half-years.\nAmount = $ [10000 * (1+(2/100))4] = $(10000 * (51/50) * (51/50) * (51/50) * (51/50))\n= $ 10824.32.\n:. C.I. = $ (10824.32 - 10000) = $ 824.32.\nAnswer C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAn alloy is to contain copper and zinc in the ratio 9:4. The zinc required to be melted with 24kg of copper is?\n\n### Options:\nA. 12kg\nB. 8.3kg\nC. 10.7kg\nD. 15.5kg\nE. 7kg\n\n### Answer:\nLet the required quantity of copper be x kg\n9:4::24:x\n9x = 4*24\nx = 10 2/3 kg = 32/3 = 10.7kg\nAnswer is C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the probability of flipping a fair coin three times and the coin landing on heads on exactly one flip?\n\n### Options:\nA. 3/8\nB. 5/8\nC. 7/8\nD. 1/8\nE. 1/4\n\n### Answer:\nProbability = (Favorable combination)/(Total combination)\nFavorable combination = (HTT, TTH, THT) ==> 3\nTotal combination = 8 (2^3)\nProbability = (3)/(8)\n(A)\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhen a certain number X is divided by 66, the remainder is 14. What is the remainder when X is divided by 11?\n\n### Options:\nA. 2\nB. 3\nC. 7\nD. 9\nE. 10\n\n### Answer:\nLet possible value of x is 80\nleast possible value of x/11 is 80/11 =>7 quotient with remainder 3\nThus answer is (B) 3\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe area of a square is equal to 2 times the area of a rectangle of dimensions 8 cm * 64 cm. What is the perimeter of the square?\n\n### Options:\nA. 482\nB. 268\nC. 800\nD. 128\nE. 632\n\n### Answer:\nArea of the square = s * s = 2(8 * 64)\n=> s = 4 * 8 = 32 cm\nPerimeter of the square = 4 * 32 = 128 cm.\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA boat crossed a lake from North to East at the speed of 7 km/h, entered a river and covered twice as much distance going upstream at 6 km/h. It then turned around and stopped at the south shore of the lake. If it averaged 3.8 km/h that day, what was its approximate downstream speed?\n\n### Options:\nA. 4\nB. 5\nC. 6\nD. 7\nE. 8\n\n### Answer:\nOne way of solving this is:\nSpeed of boat on still water (lake)=7kmph\nSpeed upstream = 6kmph = speed in still water - speed of river => speed of river = 1kmph\n=>Speed downstream = speed in still water + speed of river = 7+1 =8kmph\nAns is E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain country had a total annual expenditure of $1.2x10^12. If the population of the country was 240 million last year, what was the per capita expenditure?\n\n### Options:\nA. $500\nB. $1000\nC. $2000\nD. $3000\nE. $5000\n\n### Answer:\nExplanation:\nIn scientific notation 240 million is 2.4x10^8. So the per capita expenditure was:\n($1.2x10^12)/(2.4x10^8)=($1.2)/(2.4)x10^12-8=$0.5x10^4=$5000\nAnswer: Option E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nEvaluate 20% of 450 + 45% of 200\n\n### Options:\nA. 232\nB. 242\nC. 252\nD. 262\nE. 180\n\n### Answer:\nExplanation:\n= (20/100) * 450 + (45/100) * 200\n= 180\nOption E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA farmer has an apple orchard consisting of Fuji and Gala apple trees. Due to high winds this year 10% of his trees cross pollinated. The number of his trees that are pure Fuji plus the cross-pollinated ones totals 170, while 3/4 of all his trees are pure Fuji. How many of his trees are pure Gala?\n\n### Options:\nA. 30\nB. 33\nC. 55\nD. 77\nE. 88\n\n### Answer:\nLet f = pure fuji , g = pure gala and c - cross pollinated.\nc = 10% of x where x is total trees.\nc = .1x\nalso 3x/4 = f and c+f = 170 => .1x + 3/4x = 170 => x = 200\n200 - 170 = pure gala = 30.\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAn industrial loom weaves 1.14 meters of cloth every second. Approximately, how much time will it take to weave 52 meters of cloth ?\n\n### Options:\nA. 29.32 sec\nB. 42.51 sec\nC. 39.25 sec\nD. 45.61 sec\nE. None of these\n\n### Answer:\nExplanation:\nGiven loom weaves 1.14 mts of cloth in one second then 52 mts of cloth can be weaved by loom in,\n1.14 ----- 1\n52.0 ------?\n=> 52/1.14 = 45.61 sec\nAnswer IS D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA motorcyclist goes from Bombay to Pune, a distance of 160 kms at an average of 32 kmph speed. Another man starts from Bombay by car 2 \u00bd hours after the first, and reaches Pune \u00bd hour earlier. What is the ratio of the speed of the motorcycle and the car?\n\n### Options:\nA. 1:2\nB. 2:5\nC. 1:4\nD. 1:1\nE. 1:6\n\n### Answer:\nT = 160/32 = 5 h\nT = 5 - 3 = 2\nTime Ratio = 5:2 = 5:2\nSpeed Ratio = 2:5\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA = {0, 1, 3, 6, -8}\nB = {-1, 2, -4, 7,-5}\nIf a is a number that is randomly selected from Set A, and b is a number that is randomly selected from Set B, what is the probability that ab > 0?\n\n### Options:\nA. 1/4\nB. 1/3\nC. 2/5\nD. 9/25\nE. 1/2\n\n### Answer:\nFor the product of 2 numbers to be positive either both of them must be positive or both of them must be negative:\nP(positive, positive) = 3/5*2/5 = 6/25;\nP(negative, negative) = 1/5*3/5 = 3/25.\nP = 6/25 + 3/25\n= 9/25\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAyesha's father was 38 years of age when she was born while her mother was 36 years old when her brother three years younger to her was born. What is the difference between the ages of her parents?\n\n### Options:\nA. 2 years\nB. 4 years\nC. 5 years\nD. 7 years\nE. 8 years\n\n### Answer:\nMother's age when Ayesha's brother was born = 36 years.\nFather's age when Ayesha's brother was born = (38 + 3) years = 41 years.\nRequired difference = (41 - 36) years = 5 years.\nAnswer: Option C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA class of 40 students has an average height of 120 cm. four students whose average height is 160 cm, left the class and four others whose average height is 124 cm, joined. Calculate the new average height of the students of the class (in cm) is?\n\n### Options:\nA. 292.4 cm\nB. 296.4 cm\nC. 206.4 cm\nD. 294.4 cm\nE. 236.4 cm\n\n### Answer:\nTotal height = 120 * 40 = 4800 cm.\nTotal height of those who left = 160 * 4 = 640\nTotal height of those who joined = 124 * 4 = 496\nNew average\n= [12000 - 640 + 496 ] / 40 = 11856/40 cm.\n= 296.4 cm\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA and B are two multiples of 14, and Q is the set of consecutive integers between A and B, inclusive. If Q contains 10 multiples of 14, how many multiples of 7 are there in Q?\n\n### Options:\nA. 20\nB. 19\nC. 18\nD. 17\nE. 16\n\n### Answer:\nHalfway between the multiples of 14, there will be another multiple of 7.\nThe total number of multiples of 7 is 10+9 = 19.\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a coconut grove, (x + 2) trees yield 40 nuts per year, x trees yield 120 nuts per year and (x \u2013 2) trees yield 180 nuts per year. If the average yield per year per tree be 100, find x.\n\n### Options:\nA. 3\nB. 4\nC. 5\nD. 6\nE. 7\n\n### Answer:\n(x+2)\u00d740+x\u00d7120+(x\u22122)\u00d7180/(x+2)+x+(x\u22122)=100\n\u21d2 340x\u2212280/3x = 100\n\u21d2 40x = 280 \u21d2 x = 7\nAnswer E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat percent of 30 is 80?\n\n### Options:\nA. 133 1\u20443\nB. 75\nC. 266.66\nD. 33 1\u20443\nE. 25\n\n### Answer:\nTo find out the % of 80 in 30\nDo 80/30 = 266.66%\nAnswer C)\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how many different number of ways 5 men and 2 women can sit on a shopa which can accommodate persons?\n\n### Options:\nA. 210\nB. 220\nC. 230\nD. 240\nE. 250\n\n### Answer:\n7p3 = 7 \u00d7 6 \u00d7 5 = 210\nA)\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is:\n\n### Options:\nA. 40\nB. 50\nC. 60\nD. 70\nE. 80\n\n### Answer:\nSpeed of the train relative to man = (125/10) m/sec = (25/2) m/sec. [(25/2) * (18/5)] km/hr = 45 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 45 ==> x = 50 km/hr.\nAnswer: Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average of 25 result is 18.The average of 1st 12 of them is 14 & that of last 12 is 17.Find the 13th result.\n\n### Options:\nA. 68\nB. 80\nC. 78\nD. 60\nE. 87\n\n### Answer:\nClearly 13th result=(sum of 25 results)-(sum of 24 results)\n=(18*25)-(14*12)+(17*12)\n=450-(168+204)\n=450-372\n=78.\nAnswer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA corporation seven times its annual bonus to 5 of its employees. What percent of the employees\u2019 new bonus is the increase?\n\n### Options:\nA. 1.35%\nB. 85.71%\nC. 3.12%\nD. 4.78%\nE. 3.69%\n\n### Answer:\nLet the annual bonus be X.\nA corporation triples its annual bonus.\nSo new bonus = 7X.\nIncrease = 7X-X =6X\nThe increase is what percent of the employees\u2019 new bonus\n= (6X/7X)*100\n= 85.71%\nHence B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA fair coin is to be tossed twice and an integer is to be selected at random from one of the integers 3, 8, and 10. What is the probability that at least one head is tossed and an even integer is selected?\n\n### Options:\nA. 1/6\nB. 1/4\nC. 1/3\nD. 1/2\nE. 7/12\n\n### Answer:\n1) Let us simply state the possibilities. This method works for this problem due to the limited number of possibilities\nWays of getting at least a head and an even number =6\nHT8\nTH8\nHT10\nTH10\nHH8\nHH10\nWays of not getting at least one head and an even number=6\nTT8\nTT10\nHT3\nTH3\nHH3\nTT3\nTotal probability=6/12=1/2\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nStuart bought a sweater on sale for 30% off the original price and another 25% off the discounted price. If the original price of the sweater was $30, what was the final price of the sweater?\n\n### Options:\nA. $25.75\nB. $35.75\nC. $15.75\nD. $ 45.75\nE. $15.75\n\n### Answer:\nThe price with 30% off\n30 - 30% of 30 = 30 - (30 / 100) *30 = 30 - 9 = 21\nThe price with another 25% off\n21 - 25% of 21 = 21 - (25/100)* 21\n= 21 - (525 / 100) = 21 - 5.25 = $15.75\ncorrect answer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nEvery year Taylor goes to the same carnival, and he attempts to shoot a basketball into a small hoop, hoping that he will win a ten-foot tall teddy bear. If the probability that Taylor does not make a basket is 2/5, what is the probability that Taylor makes exactly one basket in three tries?\n\n### Options:\nA. 36/125\nB. 36/120\nC. 30/125\nD. 30/140\nE. 36/140\n\n### Answer:\nProbability of basket = 3/5\nProbability of no basket = 2/5\nRequired probability=3* 3/5*2/5*2/5\n=36/125\nA is the answer .\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA cistern which could be filled in 7 hours takes one hour more to be filled owing to a leak in its bottom. If the cistern is full in what time will the leak empty it?\n\n### Options:\nA. 76 hrs\nB. 70/3 hrs\nC. 55 hrs\nD. 90 hrs\nE. 11 hrs\n\n### Answer:\n1/7 - 1/x = 1/10\n=> 70/3 hrs\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe cost of 3 kg of sugar is $12. What will the cost of 8 kg of sugar be?\n\n### Options:\nA. 32\nB. 48\nC. 64\nD. 120\nE. 180\n\n### Answer:\n3 kg costs $12\n1 kg costs $4\n8 kg costs $32\nThe answer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nEach of the three people individually can complete a certain job in 4, 5, and 8 hours, respectively. What is the lowest fraction of the job that can be done in 1 hour by 2 of the people working together at their respective rates?\n\n### Options:\nA. 9/20\nB. 11/20\nC. 11/32\nD. 13/40\nE. 17/40\n\n### Answer:\nThe two slowest people work at rates of 1/5 and 1/8 of the job per hour.\nThe sum of these rates is 1/5 + 1/8 = 13/40 of the job per hour.\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSet J consists of the terms {a, b, c, d, e}, where e > d > c > b > a > 3. Which of the following operations would decrease the standard deviation of Set J?\n\n### Options:\nA. Multiply each term by e/d\nB. Divide each term by b/c\nC. Multiply each term by \u22121/2\nD. Divide each term by d/e\nE. Multiply each term by c/e\n\n### Answer:\nCONCEPT: Standard Deviation is Defined as Average Deviation of Terms in the set from the Mean value of the set. i.e.\n1) It depends on the separation between the successive terms of the set\n2) If a Constant Value is Added/Subtracted in every terms of set then the Separation between successive terms does NOT change Hence S.D. remains Constant\n3) If a Constant Value is Multiplied in every terms then the Separation between succesive terms gets multiplied by the constant Hence S.D. remains gets multiplied by same Number\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how many different ways can 4 identical blue pants and 4 identical red pants be shared among 8 children such that each child receives a pant?\n\n### Options:\nA. 10320\nB. 42320\nC. 40320\nD. 20320\nE. 50320\n\n### Answer:\nBBB RRR\nTherefore total number of ways is\n6! but there are two groups of 3 identical things.\nTherefore total number of \"different\" ways is\n8!/ (4!) (4!) = 40320 ANS:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf athul rows 16 km upstream and 24 km down steam taking 4 hours each, then the speed of the stream\n\n### Options:\nA. 1kmph\nB. 2 kmph\nC. 1.5 kmph\nD. 12 kmph\nE. 15 kmph\n\n### Answer:\nSpeed upstream = 16/4 = 4 kmph\nSpeed down stream = 24/4 = 6 kmph\nSpeed of stream = \u00bd (6-4) = 1 kmph\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOn a sum of money, the simple interest for 2 years is Rs. 660,while the compound interest is Rs.696.30,the rate of interest being the same in both the cases. The rate of interest is\n\n### Options:\nA. 23\nB. 11\nC. 378\nD. 36\nE. 29\n\n### Answer:\nExplanation:\nDifference in C.I and S.I for 2 years\n= Rs(696.30-660)\n=Rs. 36.30.\nS.I for one years = Rs330.\nS.I on Rs.330 for 1 year =Rs. 36.30\nRate\n= (100x36.30/330x1)%\n= 11%\nAnswer: B) 11%\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf (4x + 7)(x + 2) = 8x^2 + x, what is a possible value of x?\n\n### Options:\nA. 12\nB. -7\nC. 7\nD. -1\nE. -14\n\n### Answer:\nRearranging the given expression:\n(4x + 7)(x + 2) = 8x^2 + x\ni.e. 8x^2 + 15x + 14 = 8x^2 + x\ni.e. 14x = -14\ni.e. x = -14/14 = -1\nAnswer: Option D\nHad it been a difficult expression to solve further, then we could have used options to check which on esatisfies the expression after solving it as further as possible\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a division sum, the divisor is ten times the quotient and five times the remainder. If the remainder is 20, the dividend is:\n\n### Options:\nA. 1000\nB. 1200\nC. 1020\nD. 100\nE. 120\n\n### Answer:\nDivisor = (5 * 20) = 100\n= 10 * Quotient = Divisor\n=> Quotient = 100/10 = 10\nDividend = (Divisor * Quotient) + Remainder\nDividend = (100* 10) + 20 = 1020.\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a friendship gang Raja has 9 gang, in how many ways can he invite one or more of the gang to his house?\n\n### Options:\nA. 124\nB. 587\nC. 987\nD. 511\nE. 263\n\n### Answer:\nRaja can select one or more than one of his 8 gang.\n=> Required number of ways = 2^9 \u2013 1= 511.\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow long does a vehicle 150 m long traveling at 50 kmph takes to cross a bridge of 150 m in length?\n\n### Options:\nA. 16.7\nB. 21.6\nC. 26.5\nD. 26.1\nE. 56.2\n\n### Answer:\nD = 150 + 150 = 300 m\nS = 50 * 5/18 = 125/9\nT = 300 * 9/125 = 21.6 sec\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a garment industry, 12 men working 9 hours per day complete a piece of work in 10 days. To complete the same work in 12 days, working 15 hours a day, the number of men required is:\n\n### Options:\nA. 4\nB. 5\nC. 6\nD. 7\nE. 9\n\n### Answer:\nExplanation :\nLet the required number of men be x.\nLess days, More men (Indirect Proportion)\nMore working hrs per day, Less men (Indirect Proportion)\nDays 8 : 10\nWorking Hrs 15 : 9 :: 12 : x\n=> 12 x 15 x x = 10 x 8 x 12\n=> x = 10 x 9 x 12 / (12 x 15)\n=> x = 7\nAnswer : D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe equation x/y - 2/5 = 0 is equivalent to each of the following EXCEPT\n\n### Options:\nA. (x - y)/y = -3/5\nB. (5x - 3y)/y = 21/5\nC. (x + 3y)/y = 17/5\nD. (x + y)/x = 7/2\nE. x/y + 1 = 7/5\n\n### Answer:\nx/y - 2/5 = 0\n5x=2y\nx= 2/5 * y or y = 5/2 *x\nplug in x or y depending on the equation. all expressions are true except for\nB. (5x - 3y)/y = 21/5\nwhere y=-21\nB. (5x - 3y)/y = 21/5\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn an IT company 35% of employees are given Development Department and 40% of employees are given Testing Department and 20% are given both.What is the probability for an employee is given Development or testing department\n\n### Options:\nA. 95%\nB. 85%\nC. 55%\nD. 5%\nE. none of these\n\n### Answer:\n(dUt)=d(n)+t(n)-dnt\n=35+40-20\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n23, 29, 31, 37, 41, 43, 47, 53, 59, (...)\n\n### Options:\nA. 53\nB. 47\nC. 61\nD. 59\nE. 45\n\n### Answer:\nExplanation :\nAll are prime numbers in their order, starting from 23\nHence, next number is 61\nAnswer : C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo cars start at the same time from opposite ends of a highway that is 500 miles long. One car is riding at 40 mph and the second car is riding at 60 mph. How long after they begin will they meet?\n\n### Options:\nA. 1\nB. 2\nC. 3\nD. 4\nE. 5\n\n### Answer:\nAs cars are moving in opposite directions their speeds will be added. So their relative speeds: 60+40 = 100 mph\nTotal distance to be covered = 500 miles.\nTime taken would be: 500 miles/100 mph = 5 hours\nE is the answer.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n8873 + x = 13200, then x is ?\n\n### Options:\nA. 3327\nB. 4327\nC. 3337\nD. 2337\nE. None of these\n\n### Answer:\nAnswer\nx = 13200 - 8873 = 4327\nOption: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf c<0, which of the following represents a positive number?\n\n### Options:\nA. |c|/c\nB. |c|c\nC. -c|c|\nD. c/ |c|\nE. c|c|\n\n### Answer:\nAnswer : C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n1804 x 1804 = ?\n\n### Options:\nA. A)3254416\nB. B)3624216\nC. C)3624316\nD. D)3625116\nE. E)3625216\n\n### Answer:\n1804 x 1804 = (1804)2\n= (1800 + 4)2\n= (1800)2 + (4)2 + (2 x 1800 x 4)\n= 3240000 + 16 + 14400.\n= 3254416.\nA)\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFrom a group of 3 boys and 3 girls, 2 children are to be randomly selected. What is the probability that 1 boy and 1 girl will be selected?\n\n### Options:\nA. 1/10\nB. 4/9\nC. 1/2\nD. 9/15\nE. 2/3\n\n### Answer:\nThe total number of ways to choose 2 children from 6 is 6C2 = 15\nThe number of ways to choose 1 boy and 1 girl is 3*3 = 9\nP(1 boy and 1 girl) = 9/15\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRodrick mixes a martini that has a volume of 'n' ounces having 40% Vermouth and 60% Gin by volume. He wants to change it so that the martini is 10% Vermouth by volume. How many ounces of Gin must he add?\n\n### Options:\nA. n/6\nB. n/3\nC. 3n/5\nD. 5n/6\nE. 8n/4\n\n### Answer:\n4 ounces is vermouth\n6 ounces of gin...\nTotal volume 10.\nTo make vermouth account for 10% of total volume the new volume must be....\nx*0.1=4\nx=40 ounces....\nSo now you see that he must add 30 ounces of gin...\nPlug in 15 for n in the answer choices and look for answer 30\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nDropbox charges $3.10 for first 1/5 of a month for 500 GB storage, plus $0.40 for each additional 1/5 of a month. What would Dropbox charge for a data storage of 500 GB for 8 months ?\n\n### Options:\nA. $15.60\nB. $16.00\nC. $17.80\nD. $18.70\nE. $19.10\n\n### Answer:\nfirst 1/5 month charge = $3.10\nrest of the months = 8 - (1/5) = 39/5\ncharge for the rest of the months = 39 *0.4 = 15.6\ntotal charge = 3.10+15.6 = 18.7\nAnswer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind number which is 70% less than 60.\n\n### Options:\nA. 18\nB. 22\nC. 28\nD. 26\nE. 98\n\n### Answer:\nExplanation:\n70% less is 30% of the given number\nTherefore, 30% of 60 is 18.\nANSWER: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the perimeter and area of a square of side 11 cm.\n\n### Options:\nA. 11 cm\u00b2\nB. 21 cm\u00b2\nC. 22 cm\u00b2\nD. 113 cm\u00b2\nE. 121 cm\u00b2\n\n### Answer:\nWe know that the perimeter of square = 4 \u00d7 side\nSide= 11 cm\nTherefore, perimeter = 4 \u00d7 11 cm = 44 cm\nNow, area of the square = (side \u00d7 side) sq. units\n= 11 \u00d7 11 cm\u00b2\n= 121 cm\u00b2\nANSWER : OPTION E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man's speed with the current is 16km/hr and the speed of the current is 2km/hr. The man's speed against the current is:\n\n### Options:\nA. 8 km/hr\nB. 9 km/hr\nC. 12 km/hr\nD. 15 km/hr\nE. 17 km/hr\n\n### Answer:\nMan's rate in still water = (16 - 2) km/hr = 14 km/hr.\nMan's rate against the current = (14 - 2) km/hr = 12 km/hr\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe food in a camp lasts for 30 men for 40 days. If ten more men join, how many days will the food last?\n\n### Options:\nA. 40 days\nB. 20 days\nC. 30 days\nD. 50 days\nE. 45 days\n\n### Answer:\none man can consume the same food in 30*40 = 1200 days.\n10 more men join, the total number of men = 40\nThe number of days the food will last = 1200/40 = 30 days.\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a 100 m race, A runs at 8km per hour. If A gives B a start of 8 m and still him by 15 seconds, what is the speed of B ?\n\n### Options:\nA. 5.52 km/hr.\nB. 5.06 km/hr.\nC. 5.76 km/hr.\nD. 6.76 km/hr.\nE. 5.72 km/hr.\n\n### Answer:\nTime taken by A to cover 100 m =(60 X 60 / 8000)\tx 100 sec = 45 sec.\nB covers (100 - 8) m = 92 m in (45 + 15) sec = 60 sec.\nB's speed = (92 x 60 x 60)/(60 x 1000)km/hr = 5.52 km/hr.\nAnswer is A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nBy walking at 3/4th of his usual speed, a man reaches office 5 minutes later than usual. What is his usual time?\n\n### Options:\nA. 15min\nB. 50min\nC. 65min\nD. 60min\nE. 70min\n\n### Answer:\nlet T be the usual time.\ntime spent=4T/3\ntherefore, 4T/3=T+5\n4T=3T+15...therefor T=15min\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain company reported that the revenue on sales increased 15 % from 2000 to 2003, and increased 30 % from 2000 to 2005. What was the approximate percent increase in revenue for this store from 2003 to 2005?\n\n### Options:\nA. 50 %\nB. 40 %\nC. 35 %\nD. 32 %\nE. 13 %\n\n### Answer:\nAssume the revenue in 2000 to be 100. Then in 2003 it would be 115 and and in 2005 130, so from 2003 to 2005 it increased by (130-115)/115=15/115=13%.\nAnswer: E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA person covered one-fourth of the total distance at 26 kmph and remaining distance at 24 kmph. What is the average speed for the total distance?\n\n### Options:\nA. 91 (1/3) kmph\nB. 21 (1/3) kmph\nC. 81 (1/3) kmph\nD. 21 (1/7) kmph\nE. 23 (1/3) kmph\n\n### Answer:\nLet the total distance be x km\ntotal time taken\n= (x/4)/16 + (3x/4)/24\n= x/64 + x/32 = 3x/64\nAverage speed = x/(3x/64)\n= 64/3kmph = 21 (1/3)kmph.\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJim drove 768 miles of a 1200 miles journey. How many more miles does he need to drive to finish his journey?\n\n### Options:\nA. 432 miles\nB. 651 miles\nC. 387 miles\nD. 954 miles\nE. 556 miles\n\n### Answer:\nThe number of miles to drive to finish his journey is given by\n1200 - 768 = 432 miles\ncorrect answer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRiya and Priya set on a journey. Riya moves eastward at a speed of 25kmph and Priya moves westward at a speed of 40 kmph.How far will be priya from Riya after 15 minutes\n\n### Options:\nA. 18kms\nB. 16kms\nC. 50kms\nD. 30kms\nE. 40kms\n\n### Answer:\ntotal eastward distance= 25kmph*1/4hr=6.25 km\ntotal westward distance= 40kmph*1/4hr=10 km\ntotal distn betn them= 6.25+10=16.25km\nans 16km\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nPresent ages of X and Y are in the ratio 4:5 respectively. 6 years hence this ratio will become 5:6 respectively. What is X's present age in years?\n\n### Options:\nA. 35\nB. 24\nC. 37\nD. 39\nE. 40\n\n### Answer:\nLet the present ages of X and Y be 4x and 5x years respectively.\nThen, (4x + 6)/(5x + 6) = 5/6\n6(4x + 6) = 5(5x + 6) => 24x+36 = 25x+30 => x=6\nX's present age = 4x = 4*6 = 24\nANSWER: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA single discount equal to a discount series of 10% and 20% is\n\n### Options:\nA. 25%\nB. 28%\nC. 30%\nD. 35%\nE. None of these\n\n### Answer:\nEquivalent discount = 10 + 20 - 10\u00d720/100\n= 30 \u2013 2 = 28%\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn the junior basketball league there are 18 teams, 2/3 of them are bad and \u00bd are rich. What can't be the number of teams that are rich and bad\n\n### Options:\nA. 4.\nB. 6.\nC. 7.\nD. 10.\nE. 8.\n\n### Answer:\ntotal teams =18\nbad teams=(2/3)*18=12\nrich teams=9\nso maximum value that the both rich and bad can take will be 9. so E= 10 can not be that value.\nans D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAfter 6 games, team B had an average of 65 points per game. If it got only 47 points in game 7, how many more points does it need to score to get its total above 500?\n\n### Options:\nA. 85\nB. 74\nC. 67\nD. 63\nE. 28\n\n### Answer:\n(6*65) + 47 +x >500\n390+47+x > 500\n437+x >500\n=> x>63\nOption D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nCalculate the time it will take for a full tank to become completely empty due to a leak given that\nthe tank could be filled in 7 hours, but due to the leak in its bottom it takes 8 hours to be filled ?\n\n### Options:\nA. 59 hours\nB. 54 hours\nC. 59 hours\nD. 56 hours\nE. 26 hours\n\n### Answer:\nPart filled without leak in 1 hour = 1/7\nPart filled with leak in 1 hour = 1/8\nWork done by leak in 1 hour\n=1/7\u00e2\u02c6\u20191/8=56 hours\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo cars P and Q start at the same time from A and B which are 120 km apart. If the two cars travel in opposite directions, they meet after one hour and if they travel in same direction (from A towards B), then P meets Q after 6 hours. What is the speed of car P?\n\n### Options:\nA. 75 km/hr\nB. 71 km/hr\nC. 72 km/hr\nD. 70 km/hr\nE. 78 km/hr\n\n### Answer:\nD\n70 km/hr\nLet their speed be x km/hr and y km/he respectively.\nThen, 120/(x + y) = 1 => x + y = 120 --- (i)\nNow, when they move in same direction:\n(Distance traveled by P in 6 hrs) - (Distance traveled by Q in 6 hrs) = 120 km\n6x - 6y = 120 => x - y = 20 --- (ii)\nSloving (i) and (ii), we get x = 70, y = 50\nP's speed = 70 km/hr.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich of the following functions does not intersect with R = 3x^2 + 2x + 1\n\n### Options:\nA. R = 3x^2 + 3x + 1\nB. R = 2x^2 + 3x + 1\nC. R = 3x^2 + 2x + 3\nD. R = 4x^2 + 2x - 3\nE. R = x^2 + 2x + 3\n\n### Answer:\nLet\u2019s find the actual intersecting point of given function and each choice R\nA. 3x^2 + 2x + 1 = 3x^2 + 3x + 1 --> x=0\nB. 3x^2 + 2x + 1 = 2x^2 + 3x + 1 --> x^2 \u2013 x =0 --> x=0 or 1\nC. 3x^2 + 2x + 1 = 3x^2 + 2x + 3 --> 1=3(X) --> they don\u2019t have any intersect.\nD. 3x^2 + 2x + 1 = 4x^2 + 2x - 3 --> x^2 \u20134=0 --> x= 2 or -2\nE. 3x^2 + 2x + 1 = x^2 + 2x + 3 --> 2x^2 \u20132 =0 --> x= 1 or \u20131.\nSo only choice (C) has no intersecting point. The answer is (C).\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nif the price of a book is first decreased by 20% and then increased by 20%, then the net change in the price will be :\n\n### Options:\nA. 10\nB. 388\nC. 4\nD. 29\nE. 22\n\n### Answer:\nExplanation:\nLet the original price be Rs. 100.\nDecreased by 20% = 80\nThen increased 20% on Rs 80 = 80 + 16 = 96\nNet change in price = 100 - 96 = 4\nAnswer : C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how many different ways can the letters of the word 'MATHEMATICS' be arranged so that the vowels always come together?\n\n### Options:\nA. 10080\nB. 4989600\nC. 120960\nD. 180960\nE. None of these\n\n### Answer:\nThe given words contain 8 letter MTHMTCS(AEAT), so 8!.\nThen the 4 vowels can be formed differently, 4!.\nBut there are three words have repeated in the given words. So it should be divided by 2!*2!*2!.\nHence the solution is (8! * 4!) / (2! * 2! * 2!) = 120960\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe speed of a car is 98 km in the first hour and 60 km in the second hour. What is the average speed of the car?\n\n### Options:\nA. 76 kmph\nB. 75 kmph\nC. 87 kmph\nD. 79 kmph\nE. 86 kmph\n\n### Answer:\nS = (98 + 60)/2\n= 79 kmph\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\na dealer buys 4 varieties of rice costing rs. 40,rs.42,rs.54 and rs.50 per kg in the ratio 6:5:10:9 and mixes all the four varieties and sells at 50% profit. What is the selling price per kg of rice?\n\n### Options:\nA. 68\nB. 70\nC. 72\nD. 75\nE. 77\n\n### Answer:\nCP = 40*6+42*5+54*10+50*9=1440\nSP = 1.5*1440=2160\nTotal no.of kgs=6+5+10+9=30\nSP per kg=2160/30=72\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThree years ago the average age of a class of six members was 20 years. A boy have been added, the average age of the class is the same today. What is the age of the boy?\n\n### Options:\nA. A)1\nB. B)2\nC. C)3\nD. D)4\nE. E)5\n\n### Answer:\n6 * 23 = 138\n7 * 20 = 140\n`2\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf (n+2)!/n!=156, n=?\n\n### Options:\nA. 2/131\nB. 9\nC. 10\nD. 11\nE. 12\n\n### Answer:\n(n+2)!/n!= 156\nRewrite as:[(n+2)(n+1)(n)(n-1)(n-2)....(3)(2)(1)]/[(n)(n-1)(n-2)....(3)(2)(1)]= 132\nCancel out terms: (n+2)(n+1) = 156\nFrom here, we might just TEST the answer choices.\nSince (13)(12) = 156, we can see that n = 11\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf Yury has been writing programming code for 13 hours at a rate of 5 lines of code per 20 seconds, how many lines of code has he written?\n\n### Options:\nA. 117(10^2)\nB. 126(10^3)\nC. 12.6(10^5)\nD. 1.26(10^7)\nE. .126(10^9)\n\n### Answer:\n5 LINES IN 20 SECONDS\nSO FOR 1 MINUTE ( 5 X 3 = 15 LINES )\nI HOUR = 60 MINUTES\n15 X 60 = 900 LINES IN AN HOUR\n13 HOURS = 900 X 13 = 117(10^2)\nANSWER A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAverage between two sets of numbers is closer to the set withmore numbers?\n\n### Options:\nA. 70\nB. 80\nC. 90\nD. 95\nE. 98\n\n### Answer:\nIf on a test three people answered 90% of the questions correctly and two people answered 80% correctly, then the average for the group is not 85% but rather 3\u00d790+2\u00d7805=4305=86.3\u00d790+2\u00d7805=4305=86.\nHere, 90 has a weight of 3 => it occurs 3 times.\nWhereas 80 has a weight of 2 => it occurs 2 times.\nSo the average is closer to 90 than to 80 as we have just calculated.\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n45 is the product of two negative numbers. If the greater number is doubled, it is 1 more than the lesser number. What is the greater number?\n\n### Options:\nA. -6\nB. -5\nC. -8\nD. -1\nE. -2\n\n### Answer:\nTest the options.\n(B) - 5\nDouble of -5 is -10 and 1 less is -9.\n-9 * -5 = 45 (Correct)\nCorrect\nAnswer (B)\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nf, b, and c are positive integers. If f, b, and c are assembled into the six-digit number fbcfbc, which one of the following must be a factor of fbcfbc?\n\n### Options:\nA. 16\nB. 13\nC. 5\nD. 3\nE. none of the above\n\n### Answer:\nPlug in some values and check -\nfbcfbc = 123123\nNot divisible by 16 and 5\nlet fbcfbc = 125125\nNot divisible by 3\nOnly option (B) and (E) is left in both the cases...\nCheck once more to marke (B) as correct answer\nlet fbcfbc = 135135\nAgain divisible by 13\nSo, mark answer as (B) 13\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe distance between 2 cities A and B is 1000km. A train starts from A at 12 p.m. and travels towards B at 100 km/hr. Another starts from B at 1 p.m. and travels towards A at 150 km/hr. At what time do they meet?\n\n### Options:\nA. 11am.\nB. 12p.m.\nC. 5pm.\nD. 2p.m.\nE. 1p.m.\n\n### Answer:\nSuppose they meet x hrs after 12 p.m.\nDistance moved by first in x hrs + Distance moved by second in (x-1)hrs = 1000\n100x + 150 (x-1) = 1000\nx = 4.60 = 5 hrs\nThey meet at 10+5 = 5 p.m.\nAnswer is C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere have 12 basket,7 red balls and 5 white balls,find the probability of getting at least 1 red ball and 1 blue ball, if 8 balls are to be drawn ?\n\n### Options:\nA. 505\nB. 495\nC. 425\nD. 548\nE. 525\n\n### Answer:\n(7c3*5c5)+(7c4*5c4)+(7c5*5c3)+(7c6)5c2)+(7c1*5c1)=495\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many 2 digit number contain number 3 ?\n\n### Options:\nA. 18\nB. 28\nC. 38\nD. 68\nE. 58\n\n### Answer:\ntotal 2 digit no. = 9*10* = 90\nnot containing 3 = 8*9 = 72\ntotal 2 digit number contain 3 = 90 - 72 = 18\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nLamp A flashes every 6 seconds, Lamp B flashes every 8 seconds, Lamp C flashes every 10 seconds. At a certain instant of time all three lamps flash simultaneously. During the period of 4 minutes after that how many times will exactly two lamps flash? (Please include any flash of exactly two lights which occurs at the 4 minute mark.)\n\n### Options:\nA. 16\nB. 17\nC. 18\nD. 19\nE. 20\n\n### Answer:\n4 minutes is 240 seconds.\nLamp A and Lamp B will flash together every 24 seconds.\n240/24=10.\nIn the time period, Lamp A and Lamp B will flash together 10 times.\nLamp A and Lamp C will flash together every 30 seconds.\n240/30=8.\nIn the time period, Lamp A and Lamp C will flash together 8 times.\nLamp B and Lamp C will flash together every 40 seconds.\n240/40=6.\nIn the time period, Lamp B and Lamp C will flash together 6 times.\nAll three lights will flash together every 2*2*2*3*5=120 seconds.\n240/120=2.\nWe have counted these triple flashes three times, so we need to subtract three times the number of times that all three lights flash together.\nThe number of times that exactly two lights flash together is 10+8+6-6=18 times.\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA rectangular grass field is 75 m * 55 m, it has a path of 2.5 m wide all round it on the outside. Find the area of the path and the cost of constructing it at Rs.1 per sq m?\n\n### Options:\nA. 675, Rs.1350\nB. 575, Rs.675\nC. 1350, Rs.675\nD. 1450, Rs.775\nE. 1550, Rs.875\n\n### Answer:\nArea = (l + b +2d) 2d\n= (75 + 55 +2.5 * 2) 2*2.5 => 675\n675 * 1 = Rs. 675\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are 5 boys and 3 girls. In how many ways can they be seated in a row so that all the three girls do not sit together?\n\n### Options:\nA. 24000\nB. 36000\nC. 54200\nD. 32560\nE. 45100\n\n### Answer:\nTotal number of persons = 5+3 = 8\nthey can be seated in a row in 8! ways\nTreat 3 girls as 1 so we have 6 people can be arranged in 6! ways\nThree girls can be arranged among themselves in 3! ways\nRequired number of ways = 8!-6!*3! = 36000\nAnswer is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe first photo shoot takes 3 minutes long and then the following shoots are taken at a rate of 23 seconds/shoot as the model is already at the scene. What is the maximum number of photo shoots taken under 10 minutes ?\n\n### Options:\nA. 13\nB. 14\nC. 15\nD. 16\nE. 19\n\n### Answer:\na must be an integer as it is the number shoots at a rate of 23sec/shoot\n3*60 + 23a = 10*60\n23a = 420\na = 18\nThe total number of shoots -->1 +18 = 19 and\n20th shoot will be taken at 617 seconds which is above 10 minutes\nANSWER: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nNicky and Cristina are running a 100 meter race. Since Cristina is faster than Nicky, she gives him a 12 second head start. If Cristina runs at a pace of 5 meters per second and Nicky runs at a pace of only 3 meters per second, how many seconds will Nicky have run before Cristina catches up to him?\n\n### Options:\nA. 30\nB. 35\nC. 40\nD. 25\nE. 60\n\n### Answer:\nThe distance traveled by both of them is the same at the time of overtaking.\n3(t+12) = 5t\nt=18.\nCristina will catch up Nicky in 18 seconds.\nSo in 18 seconds Cristina would cover = 18*5 = 90 meter.\nNow Time taken my Nicky to cover 90 meter = 90/3 = 30 Seconds.\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA grocery store bought some mangoes at a rate of 5 for a dollar. They were separated into two stacks, one of which was sold at a rate of 4 for a dollar and the other at a rate of 6 for a dollar. What was the ratio of the number of mangoes in the two stacks if the store broke even after having sold all of its mangoes?\n\n### Options:\nA. 1:4\nB. 1:5\nC. 2:3\nD. 3:2\nE. 2:5\n\n### Answer:\nThe cost price of a mango = 1/5 dollars.\nThe selling price of a mango from the first stack = 1/4 dollars --> the profit from one mango = 1/4 - 1/5 = 1/20 dollars.\nThe selling price of a mango from the second stack = 1/6 dollars --> the loss from one mango = 1/5 - 1/6 = 1/30 dollars.\nThe profit from one mango from the first stack is 4 times the loss from one mango from the second stack. the ratio is\n1/20*30/1= 3:2\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSachin is younger than Rahul by 18 years. If the ratio of their ages is 7:9, find the age of Sachin\n\n### Options:\nA. 24.5\nB. 63\nC. 65\nD. 36\nE. 24.19\n\n### Answer:\nExplanation:\nIf Rahul age is x, then Sachin age is x - 18,\nso,\n9x - 162 = 7x\n2x = 162\nx = 81\nSo Sachin age is 81 - 18 = 63\nAnswer: B) 63\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA batsman makes a score of 87 runs in the 17th inning and thus increases his avg by 3. Find his average after 17th inning.\n\n### Options:\nA. 24\nB. 52\nC. 39\nD. 36\nE. 85\n\n### Answer:\nSol. Let the average after 17th inning = x.\nThen, average after 16th inning = (x - 3).\n16 (x - 3) + 87 = 17x or x = (87 - 48) = 39.\nAns: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo pipes A and B fill at a certain rate.B is filled at 10,20,40,80(10 in 1 hour,20 in 2 hours,40 in 3 hrs and so on). if 1/16 of B is filled in 17 hrs,what time it will take to get completely filled?\n\n### Options:\nA. 20 hrs\nB. 21 hrs\nC. 22 hrs\nD. 23 hrs\nE. 24 hrs\n\n### Answer:\n1/16 in 17 hrs\nso 1/8 in 18 hrs\n1/4 in 19 hrs\n1/2 in 20 hrs\nand complete tank in 21 hrs\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA password for a computer uses five digits from 0 to 9, inclusive. What is the probability that the digits of the password solely consist of prime numbers or zero?\n\n### Options:\nA. A)1/32\nB. B)1/16\nC. C)1/8\nD. D)2/5\nE. E)1/2\n\n### Answer:\nFavorable outcomes will be obtained by making Password using {0, 2, 3, 5, 7} i.e. 5 digits\nTotal Such Passwords = 5*5*5*5*5 = 5^5\nTotal Possible Password = 10*10*10*10*10 = 10^5\nProbability = (5^5) / (10^5) = 1/2^5 = 1/32\nAnswer: option A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRamesh can finish a piece of work in 10 days. Rohan is twice as efficient as Ramesh.If they work together how many days will they need to finish the same amount of work?\n\n### Options:\nA. 8/3 days\nB. 9/3 days\nC. 10/3 days\nD. 11/3 days\nE. 7/3 days\n\n### Answer:\nRamesh can finish a piece of work in 10 days. Rohan is twice as efficient as Ramesh.\nSo Rohan can finish a piece of work in 5 days.\ndays needed to finish the same amount of work = 1/(1/5+1/10)=10/3 days\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many perfect squares less than 1000 end with the digit 6?\n\n### Options:\nA. 3\nB. 4\nC. 5\nD. 6\nE. 7\n\n### Answer:\n4:16\n6:36\n14:196\n16:256\n24:576\n26:676\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA 6% stock yields 9%. The market value of the stock is:\n\n### Options:\nA. Rs 66.55\nB. Rs 68.55\nC. Rs 69.55\nD. Rs 65.55\nE. Rs 66.66\n\n### Answer:\nExplanation:\nFor an income of Rs. 9, investment = Rs. 100.\nFor an income of Rs 6, investment =Rs.100/9 X6 =Rs 66.66\nMarket value of Rs. 100 stock = Rs. 66.66\nAnswer is E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTom planted vegetables in a rectangular garden that was 25 feet long and 15 feet wide. He used\n1/3 of the area for corn and 1/5 of it for peas. How many square feet are left for other vegetables?\n\n### Options:\nA. 175 sq. ft.\nB. 176 sq. ft.\nC. 177 sq. ft.\nD. 178 sq. ft.\nE. 179 sq. ft.\n\n### Answer:\narea of garden is 25 x 15 = 375 sq. ft.\n1/3 x 375 = 125 sq. ft. for corn\n1/5 x 375 = 75 sq. ft. for peas\n125 + 75 = 200 sq. ft. used\n375 - 200 = 175 sq. ft. left over\ncorrect answer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIt is being given that (2^32 + 1) is completely divisible by a whole number. Which of the following numbers is completely divisible by this number?\n\n### Options:\nA. 16^2+1\nB. 12\nC. (2^96+1)\nD. 24\nE. 4^4+6\n\n### Answer:\nExplanation:\nLet 2^32 = x. Then, (2^32 + 1) = (x + 1).\nLet (x + 1) be completely divisible by the natural number N. Then,\n(296 + 1) = [(2^32)3 + 1] = (x^3 + 1) = (x + 1)(x^2 - x + 1), which is completely divisible by N, since (x + 1) is divisible by N.\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a and b are different positive integers and a + b = a(a + b), then which of the following must be true?\nI. a = 1\nII. b = 1\nIII. a < b\n\n### Options:\nA. I only\nB. II only\nC. III only\nD. I and II\nE. I and III\n\n### Answer:\na+b=a(a+b)a+b=a(a+b) --> a(a+b)\u2212(a+b)=0a(a+b)\u2212(a+b)=0 --> (a+b)(a\u22121)=0(a+b)(a\u22121)=0 --> as aa and bb are positive the a+b\u22600a+b\u22600, so a\u22121=0a\u22121=0 --> a=1a=1. Also as aa and bb are different positive integers then bb must be more than a=1a=1 --> a true;\nII. b = 1 --> not true;\nIII. a < b --> true.\nAnswer: E (I and II only).\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nLet exp(m,n) = m to the power n. If exp(10, m) = n exp(2, 2) where to and n are integers then n =\n\n### Options:\nA. 27\nB. 272\nC. 98\nD. 25\nE. 72\n\n### Answer:\nGiven 10m=n.2210m=n.22\n\u21d2\u21d2 2m\u00d75m=n.22\u21d22m\u22122\u00d75m=n2m\u00d75m=n.22\u21d22m\u22122\u00d75m=n\nFor m = 2 we get least value of n = 25, and for m > 2 we get infinite values are possible for n.\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a shop 90% of the articles are sold at a profit of 20% and the remaining at a loss of 40%.what is the overall profit/loss?\n\n### Options:\nA. 14% profit\nB. 10% loss\nC. 18% profit\nD. 7% loss\nE. 2% Profit\n\n### Answer:\n90*1.05+10*0.6/100=1.14\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhen Usha was thrice as old as Nisha, her sister Asha was 25, When Nisha was half as old as Asha, then sister Usha was 34. their ages add to 100. How old is Usha?\n\n### Options:\nA. 40\nB. 41\nC. 42\nD. 43\nE. 45\n\n### Answer:\nLet the age of Usha is 3x then Nisha is x and Asha is 25\nAlso Usha 34, Nisha y, and Asha 2y.\nWe know that 3x - 34 = x - 2y = 25 - 2y\nSolving above three equations we get x = 9, y = 16\nTheir ages are 34, 16, 32. whose sum = 82. So after 18 years their ages will be equal to 100. So Usha age is 34 + 6 = 40\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA boy was asked to find 7/9 of a number. But he divided the number by 7/9, Thus he got 32 more than the correct answer. Find the number.\n\n### Options:\nA. 61\nB. 63\nC. 62\nD. 54\nE. 34\n\n### Answer:\nExplanation:\nLet the number be x.\nx/7/9 = 9x/7 = 32 + y\nActualy he should do 7x/9 = y\ny = (9x/7) - 32\ny = (9x - 224)/7\n(9x - 224)/7 = 7x/9\n81x - 2016 = 49x\n81x - 49x = 2016\n32x = 2016\nx = 63\nAnswer: Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA wheel has a diameter of x inches and a second wheel has a diameter of y inches. The first wheel covers a distance of D feet in 100 revolutions. How many revolutions does the second wheel make in covering d feet?\n\n### Options:\nA. 100xy\nB. 100y - x\nC. 100x/y\nD. 100y/x\nE. 100x - y\n\n### Answer:\nFirst Wheel with diameter x inches ----> So the circumference = x*pi --------- (1)\nSecond Wheel with diameter y inches ----> So the circumference = y*pi --------- (2)\nRevolutions = distance/circumference\nSo, from equation (1)\n100 = D/(x*pi)\nD = 100 * x * pi ---------- (3)\nFrom equation (2)\nRevolutions = D/(y*pi) = (100 * x * pi) / (y*pi) = 100x/y\nAnswer (C)\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 24 men can do a piece of work in 25 hours, in how many hours will 15 men\ndo it ?\n\n### Options:\nA. 40 hours\nB. 45 hours\nC. 50 hours\nD. 55 hours\nE. 60 hours\n\n### Answer:\nLet the required number of hours be x. Then,\nLess men, More hours\t(Indirect Proportion)\n15 : 24 : : 25 : x<=>(15 x x) =(24 x 25)<=>(24 x 25)/15 = 40\nHence, 15 men can do it in 60 hours\nAnswer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn one hour, a boat goes 11 km along the stream and 5 km against the stream. the sped of the boat in still water (in km/hr) is :\n\n### Options:\nA. 3\nB. 5\nC. 8\nD. 9\nE. 10\n\n### Answer:\nSolution\nSpeed in still water= 1/2(11+5) km/hr= 8kmph. Answer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich of the following is the highest fraction?\n\n### Options:\nA. 5\u20447\nB. 3\u20444\nC. 2\u20443\nD. 6\u20447\nE. 7\u20448\n\n### Answer:\nNote : If the difference between the numerator and the denominator is constant, then the fraction which has larger value in the numerator is the larger fraction.\nUsing the above, among the options (a), (c), (d) and (e), (e) has the larger value. Now, compared to option(a), (e) has the larger value.\nAnswer E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nPointing to an old man, Kailash said, \"His son is my son's uncle.\" How is the old man related to Kailash ?\n\n### Options:\nA. Brother\nB. Uncle\nC. Father\nD. Grandfather\nE. Sister\n\n### Answer:\nExplanation:\nKailash's son's uncle \u2014 Kailash's brother. So. the old man's son is Kailash's brother\ni.e., the old man is Kailash's father.\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train speeds past a pole in 20 seconds and passes through a tunnel 500 m long in 40 seconds. Its length is :\n\n### Options:\nA. 200 m\nB. 400 m\nC. 500 m\nD. 700 m\nE. None of the above\n\n### Answer:\nSol.\rLet the length of the train be x metres and its speed be y m/sec. Then, x / y = 20 \u21d2 y = x / 20\r\u2234 (x + 500) / 40 = x / 20 \u21d4 x = 500 m. Answer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSum of two numbers is 15. Two times of the first exceeds by 5 from the three times of the other. Then the numbers will be?\n\n### Options:\nA. 6, 9\nB. 10, 5\nC. 7, 8\nD. 9, 6\nE. 8, 5\n\n### Answer:\nExplanation:\nx + y = 15\n2x \u2013 3y = 5\nx = 10 y = 5\nANSWER IS B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe total of company C's assets in 1994 was 200% greater than the total in 1993, which in turn was 400% greater than the total in 1992. If the total of company C's assets in in 1992 was N dollars, which one of the following represents company C's assets in 1994:\n\n### Options:\nA. 7N\nB. 8N\nC. 9N\nD. 15\nE. 20\n\n### Answer:\nLet's use actual numbers. Starting in 1992, let's say company C had $100 in assets.\nIn 1993, the total assets were 400% GREATER, which means 1992 PLUS 400% of 1992:\n$100 + 4x$100 = $100 + $400 =$500\nIn 1994, the total assets were 200% GREATER than they were in 1993, which means 1993 PLUS 200% of 1993:\n$500 + 2x$500 = $500 + $1000 =$1500\nThis is 15 times the 1992 number, so the correct answer is 15N.\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf four coins are tossed, the probability of getting two heads and two tails i\n\n### Options:\nA. 3/8\nB. 3/6\nC. 3/9\nD. 3/1\nE. 3/2\n\n### Answer:\nSince four coins are tossed, sample space = 24\nGetting two heads and two tails can happen in six ways.\nn(E) = six ways\np(E) = 6/24 = 3/8\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSushil got thrice as many marks in English as in Science. His total marks in English, Science and Maths are 162. If the ratio of his marks in English and Maths is 3:5, find his marks in Science?\n\n### Options:\nA. 18\nB. 77\nC. 66\nD. 55\nE. 41\n\n### Answer:\nS:E = 1:3\nE:M = 3:5\n------------\nS:E:M = 3:9:15\n3/27 * 162 = 18\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSome persons can do a piece of work in 16 days. Two times the number of these people will do half of that work in?\n\n### Options:\nA. 3\nB. 4\nC. 5\nD. 6\nE. 8\n\n### Answer:\n16/ (2 * 2) = 4 days\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 50! \u00d7 50!/50^n is an integer, what is the largest possible value of n?\n\n### Options:\nA. 36\nB. 24\nC. 8\nD. 4\nE. 2\n\n### Answer:\n50! \u00d7 50!/50^n is an integer.\nOr 50! \u00d7 50!/(5^2n*5^n)\nThis means we need to find the power of 5 in the numerator. We can safely say that the number of powers of 5 will be lower than the number of powers of 4 in the numerator.\nLargest power of 5 in 50! = [50/5] + [50/25] = 12\nSince there are 2 20!'s, power of 12 in the numerator = 2*12 = 24\nHence the largest value of b for which 50! \u00d7 50!/50^n is integer = 24\nCorrect Option : B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFor any positive integer n, the sum of the first n positive integers equals n(n+1)/2. What is the sum of odd all the integers between 10 and 100?\n\n### Options:\nA. 1345\nB. 1576\nC. 2475\nD. 2578\nE. 1895\n\n### Answer:\nnumbers are 11,13,15-------,97,99\nAverage of the set: (largest+smallest)/2=(99+11)/2=55;\n# of terms: (largest-smallest)/2+1=(99-11)/2+1=45\nThe sum = 45*55= 2475\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are 17 teams in the hockey league, and each team faces all the other teams 10 times each. How many games are played in the season?\n\n### Options:\nA. 980\nB. 1150\nC. 1360\nD. 1540\nE. 1720\n\n### Answer:\nThe number of ways to choose two teams is 17C2 = 17*16/2 = 136\nThe total number of games in the season is 10*136 = 1360.\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRaj invested an amount of Rs.17400 for two years. Find the rate of compound interest that will fetch him an amount of Rs.1783.50 at the end of two years?\n\n### Options:\nA. 7\nB. 6\nC. 8\nD. 5\nE. 4\n\n### Answer:\nLet the rate of interest be R% p.a.\n17400[1 + R/100]2 = 17400 + 1783.50\n[1 + R/100]2 = (17400 + 1783.50)/17400\n= 1 + 1025/10000 = 1 + 41/400\n= 441/400 = [21/20]2\n[1 + R/100] = 21/20\nR/100 = 1/20\nTherefore R = 5.Answer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf x and y are positive integers, and x^3*y^4 = 648, which of the following is the value of xy?\n\n### Options:\nA. 6\nB. 10\nC. 14\nD. 15\nE. 21\n\n### Answer:\n648 = 2*324 = 2^2*162 = 2^3*81 = 2^3*3^4\nxy = 2*3 = 6\nThe answer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe least number which should be added to 3218 so that the sum is exactly divisible by 5, 6, 4 and 3 is?\n\n### Options:\nA. 10\nB. 20\nC. 30\nD. 40\nE. 50\n\n### Answer:\nL.C.M. of 5, 6, 4 and 3 = 60.\nOn dividing 3220 by 60, the remainder is 40.\nNumber to be added = (60 - 40) = 20\nB)\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOut of 8 consonants and 4 vowels, how many words of 3 consonants and 1 vowels can be formed?\n\n### Options:\nA. 21005\nB. 10500\nC. 25200\nD. 5376\nE. None of these\n\n### Answer:\nSolution\nNumber of ways of selecting (3 consonants out of 8) and (1 vowels out of 4)\n8c3 x 4c1= (8x7x6/3x2x1)x(4/1) =224\nNumber of group,each having 3 consonants and 1 vowels = 224 .\nEach group contains 4 letter.\nNumber of ways of arranging 5 letters among themselves\n= 4 ! = (4 \u00d7 3 \u00d7 2 \u00d7 1) = 24 .\nSo, Required number of words = (24 \u00d7 224) = 5376 .Answer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA 60 cm long wire is to be cut into two pieces so that one piece will be 2/5th of the other, how many centimeters will the shorter piece be?\n\n### Options:\nA. A)73\nB. B)20\nC. C)83\nD. D)17.1\nE. E)52\n\n### Answer:\nExplanation:\n1: 2/5 = 5: 2\n2/7 * 60 = 20\nAnswer: Option D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many positive integers r less than 30 have no common prime factor with 30?\n\n### Options:\nA. 5\nB. 6\nC. 7\nD. 8\nE. 9\n\n### Answer:\nr=30=2*3*5. So, the number must be less than 30 and not have primes 2, 3, or 5.\nThis means that the number could be: 1, 7, 11, 13, 17, 19, 23, or 29. Total of 8 numbers.\nAnswer: D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMirun travels the first 3 hours of her journey at 20 mph speed and the remaining 2 hours at 40 mph speed. What is the average speed of Mirun 's travel in mph?\n\n### Options:\nA. 26mph\nB. 27mph\nC. 22mph\nD. 28mph\nE. 23mph\n\n### Answer:\nExplanation :\nAverage speed=Total Distance/Time.\nTotal distance travelled by Mirun = Distance covered in the first 3 hours + Distance covered in the next 2 hours.\nDistance covered in the first 3 hours = 3\u00c3\u201420=60 miles\nDistance covered in the next 2 hours= 2\u00c3\u201440=80 miles\nTherefore, total distance travelled = 60+80=140 miles.\nThe total time taken = 3+2=5hours.\nHence, the average speed =140/5= 28mph.\nAnswer : D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA fires 5 shots to B's 3 but A kills only once in 3 shots while B kills once in 2 shots. When B has missed 30 times, A has killed:\n\n### Options:\nA. 60 birds\nB. 72 birds\nC. 33 birds\nD. 80 birds\nE. 20 birds\n\n### Answer:\nLet the total number of shots be x. Then,\nShots fired by A =(5/8)x\nShots fired by B =(3/8)x\nKilling shots by A =(1/3)of\t(5/8)x=(5/24)x\nShots missed by B =(1/2) of (3/8)x\t=(3/16)x\n3x/16= 30 or x =(30 x 16)/3= 160.\nBirds killed by A =(5x/24)\t=(5/24*160)= 33.\nAnswer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train running at the speed of 60 km/hr crosses a pole in 9 seconds. Find the length of the train?\n\n### Options:\nA. 150 meter\nB. 166 meter\nC. 154 meter\nD. 146 meter\nE. 141 meter\n\n### Answer:\nSpeed = 60*(5/18) m/sec = 50/3 m/sec\nLength of Train (Distance) = Speed * Time\n(50/3) * 9 = 150 meter\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nX starts a business with Rs.45000. Y joins in the business after 7 months with Rs.30000. What will be the ratio in which they should share the profit at the end of the year?\n\n### Options:\nA. 1:2\nB. 18:5\nC. 1:5\nD. 3:1\nE. 1:1\n\n### Answer:\nExplanation:\nRatio in which they should share the profit\n= Ratio of the investments multiplied by the time period\n=45000\u00c3\u201412:30000\u00c3\u20145\n=45\u00c3\u201412:30\u00c3\u20145\n=3\u00c3\u201412:2\u00c3\u20145\n=18:5\nAnswer: Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe football association pays $2000 out of $8000 it owes to refrees. Then it pays $6000 out of the $12000 owes for the year to players.\nHow much did the ratio of payments made to monies owed increase?\n\n### Options:\nA. A) 75%\nB. B)100 %\nC. C)1%\nD. D) 50%\nE. E) 25%\n\n### Answer:\nRatio in 1st case 2000:8000(1/4)\nRatio in second case 6000/12000 (2/4)\npercentage increase is (difference/initial quantity)*100\n(1/4)/(2/4 )* 100= 100%\nCorrect option is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nApproximately what percentage of the world\u2019s forested area is represented by Finland given that Finland has 53.42 million hectares of forested land of the world\u2019s 8.076 billion hectares of forested land.\n\n### Options:\nA. 0.0066%\nB. 0.066%\nC. 0.66PERCENT\nD. 6.6%\nE. 66%\n\n### Answer:\nApproximation is a strategy that helps us arrive at less than an exact number and the inclusion in this problem of the word \u201capproximately\u201d is an obvious clue. First, 8.076 billion is 8,076 million. Next, 8,076 million rounds to 8,000 million and 53.42 million rounds to 53 million. Dividing 53 million by 8,000 million we arrive at 0.0066 (53M/8,000M). We convert this decimal figure to a percentage by multiplying by 100 (or moving the decimal point two places to the right) and adding a percent sign in order to obtain our answer of 0.66%. Note that the shortcut method involves comparing 53 million to 1% of 8,000 million or 80 million. Since 53 million is approximately two-thirds of 80 million then the answer is some two-thirds of 1% or 0.66%.\nAnswer: C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n10 men can complete a piece of work in 15 days and 15 women can complete the same work in 12 days. If all the 10 men and 15 women work together, in how many days will the work get completed?\n\n### Options:\nA. 6\nB. 6 1\u20443\nC. 6 2\u20443\nD. 7 2\u20443\nE. None of these\n\n### Answer:\n10 men\u2019s 1 day\u2019s work = 1\u204415\n15 women\u2019s 1 day\u2019s work = 1\u204412\n(10 men + 15 women)\u2019s 1 day\u2019s work\n= (1\u204415 + 1\u204412) = 9\u204460 = 3\u204420\n\u2234 10 men and 15 women will complete the work in 20\u20443 = 62\u20443 days.\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how many ways can the letters of the word FINISHED be arranged?\n\n### Options:\nA. 20155\nB. 1643\nC. 2520\nD. 20152\nE. 20160\n\n### Answer:\nFINISHED has 8 words, but I is repeated two times. Thus ways = 8! / 2! = 20160 ways\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe value of x + x(x^x) when x = 5 is\n\n### Options:\nA. 15630\nB. 14000\nC. 15400\nD. 15560\nE. 15605\n\n### Answer:\nSolution:\nx + x(x^x)\nPut the value of x = 5 in the above expression we get,\n5 + 5(5^5)\n= 5 + 5(5 \u00c3\u2014 5 x 5 x 5 x 5 )\n= 5 + 2(3125)\n= 5 + 15625\n= 15630\nAnswer: (a)\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA courtyard is 18 meter long and 12 meter board is to be paved with bricks of dimensions 12 cm by 6 cm. The total number of bricks required is :\n\n### Options:\nA. 16000\nB. 18000\nC. 20000\nD. 30000\nE. None of these\n\n### Answer:\nExplanation:\nNumber of bricks =Courtyard area /1 brick area\n=(1800\u00c3\u20141200 /12\u00c3\u20146)=30000\nOption D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how many ways can five girls stand in line if Maggie and Lisa cannot stand next to each other?\n\n### Options:\nA. 112\nB. 96\nC. 84\nD. 72\nE. 60\n\n### Answer:\n1. the total number of permutations: 5! = 120\n2. Let's consider Maggie and Lisa as one object, then the total number of permutations with Maggie and Lisa together: 4! = 24.\n3. Take into account that [Maggie, Lisa] and [Lisa, Maggie] are different.\n4. Maggie and Lisa cannot stand next to each other in: 120 - 2*24 = 72 ways.\nANS:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe triplicate ratio of 1:4 is?\n\n### Options:\nA. 1:64\nB. 1:8\nC. 1:7\nD. 1:2\nE. 1:1\n\n### Answer:\n13: 43 = 1:64\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the perimeter of a rectangular garden is 500 m, its length when its breadth is 100 m is?\n\n### Options:\nA. 299 m\nB. 777 m\nC. 200 m\nD. 167 m\nE. 150 m\n\n### Answer:\n2(l + 100) = 500 => l\n= 150 m\nAnswer:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA car runs 10,000 miles using 5 tyres interchangeably. to have equal worn out by all tyres,how many miles each tyre should have run?\n\n### Options:\nA. 5000\nB. 8000\nC. 4000\nD. 3000\nE. 2000\n\n### Answer:\nfor 5 tyres running interchangeably 10,000 miles the car runs\nfor 1 tyre=10000/5=2000\nas you all know i suppose the car has 4 tyre\nto have equal worn out by 4 tyres we need=2000*4=8000\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a class, there are 21 boys who are over 160 cm tall. If these constitute three-fourths of the boys and the total number of boys is two-thirds of the total number of students in the class, what is the number of girls in the class ?\n\n### Options:\nA. 8\nB. 14\nC. 18\nD. 24\nE. 26\n\n### Answer:\nExplanation:\nLet the number of boys be x. Then, (3/4)x = 21 or x = 21 x(4/3) = 28.\nIf total number of students is y, then (2/3) y = 28 or y = 28 x (3/2) = 42.\nTherefore Number of girls in the class = (42 - 28) = 14.\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA tank is filled in eight hours by three pipes A, B and C. Pipe A is twice as fast as pipe B, and B is twice as fast as C. How much time will pipe B alone take to fill the tank?\n\n### Options:\nA. 28\nB. 24\nC. 22\nD. 20\nE. 30\n\n### Answer:\n1/A + 1/B + 1/C = 1/8 (Given)\nAlso given that A = 2B and B = 2C\n=> 1/2B + 1/B + 2/B = 1/8\n=> (1 + 2 + 4)/2B = 1/8\n=> 2B/7 = 8\n=> B = 28 hours.\nANSWER A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf f > x > y > z on the number line, y is halfway between x and z, and x is halfway between w and z, then (y - x)/(y - f) =\n\n### Options:\nA. 1/4\nB. 1/3\nC. 1/2\nD. 3/4\nE. 1\n\n### Answer:\nLet y-z=t ---> since y is halfway between x and z and x>y we have x-y=t. Moreover x-z=(x-y)+(y-z)=2t. Similarly since x is halfway between w and z, we have f-x=2t. So y-x=-t, y-f=-3t. ---> (y - x)/(y - f) = 1/3.\nThe answer is (B).\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe sum of two consecutive number is 67. Which is the larger number?\n\n### Options:\nA. 34\nB. 43\nC. 44\nD. 45\nE. 46\n\n### Answer:\nLet consecutive number be x, x+1\nTherefore sum of the consecutive number is x + x+1=67\n2x+1=67\n2x=66\nx=33\nTherefore larger number is x+1=34\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nNine pens are in the table.To create three pens in each group like as three group. How many ways are there to create these 3 teams?\n\n### Options:\nA. 27\nB. 45\nC. 90\nD. 175\nE. 280\n\n### Answer:\nArrange the 6 pen in a straight line in 6! ways.\nThe first three form team 1, next three form team 2 and last three form team 3. But in each team, the boys are arranged in first, second third positions so you need to un-arrange them by dividing by 3! three times (once for each team). You get 6!/(2! * 2! * 2!)\nAlso, there are no distinct teams - team1, team2 and team3. You just have three teams. So you also need to un-arrange the three teams by dividing by another 3!.\nYou get 6!/(2! * 2! * 2!) * 2! = 45\nAnswer (B)\nYou get 6!/(2! * 2! * 2!) * 2!\nAnswer : B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 2 pounds of dried apricots that cost x dollars per pound are mixed with 2 pounds of prunes that cost y dollars per pound, what is the cost, in dollars, per pound of the mixture?\n\n### Options:\nA. (2x + 2y)/5\nB. (2x + 2y)/(x + y)\nC. (2x + 2y)/(xy)\nD. 5(2x + 2y)\nE. 2x + 2y\n\n### Answer:\nTotal Cost = Weight(in pounds) * Price/pound;\nTo find Total cost/pound, Divide by total pounds.\nCost of Dried apricots = 2x;\nCost of prunes = 2y;\nCost per pound = (2x + 2y)/5;\nAns is (A).\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a question on division with zero remainder, a candidate took 22 as divisor instead of 11. The quotient obtained by him was 35. The correct quotient is?\n\n### Options:\nA. A)70\nB. B)24\nC. C)28\nD. D)29\nE. E)30\n\n### Answer:\nNumber = (35 * 22) = 770\nCorrect quotient = 770/11 = 70\nA)\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThree cubes of metal whose edges are 9, 12 and 24 cm respectively, are melted and one new cube is made. Find the edge of the new cube?\n\n### Options:\nA. 28\nB. 77\nC. 66\nD. 18\nE. 25.3\n\n### Answer:\n93 + 123 + 243 = a3 => a\n= 25.3\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nPam and Stanley packed several boxes with reams of paper. While both packed, Pam packed 20% of the boxes. After Pam stopped, Stanley packed the same number of boxes that he had packed while working with Pam. What is the ratio of the number of boxes Pam packed to the number of boxes Stanley packed?\n\n### Options:\nA. 1 to 4\nB. 1 to 8\nC. 3 to 5\nD. 3 to 4\nE. 3 to 2\n\n### Answer:\nCorrect Answer: B\nSolution: B. We know that when Pam and Stanley were both working, the ratio was 1 boxes by Pam to 4 boxes by Stanley. We also know that Stanley continued working after Pam stopped. He packed as many boxes alone as he had packed whlie working with Pam, effectively doubling his number of boxes. Thus, the ratio of Pam's boxes to Stanley's boxes is 1 to 8. Answer B is correct.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe price of 2 sarees and 4 shirts is Rs. 1600. With the same money one can buy 1 saree and 6 shirts. If one wants to buy 12 shirts, how much shall he have to pay ?\n\n### Options:\nA. 1800\nB. 2000\nC. 2200\nD. 2400\nE. 2600\n\n### Answer:\nLet the price of a saree and a shirt be Rs. x and Rs. y respectively.\nThen, 2x + 4y = 1600 .... (i)\nand x + 6y = 1600 .... (ii)\nDivide equation (i) by 2, we get the below equation.\n= x + 2y = 800. --- (iii)\nNow subtract (iii) from (ii)\nx + 6y = 1600 (-)\nx + 2y = 800\n----------------\n4y = 800\n----------------\nTherefore, y = 200.\nNow apply value of y in (iii)\n= x + 2 x 200 = 800\n= x + 400 = 800\nTherefore x = 400\nSolving (i) and (ii) we get x = 400, y = 200.\nCost of 12 shirts = Rs. (12 x 200) = Rs. 2400.\nanswer : D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA started a business with an investment of Rs. 70000 and after 6 months B joined him investing Rs. 120000. If the profit at the end of a year is Rs. 50000, then the share of B is?\n\n### Options:\nA. 23077\nB. 24000\nC. 24005\nD. 24009\nE. 24002\n\n### Answer:\nRatio of investments of A and B is (70000 * 12) : (120000 * 6) = 7 : 6\nTotal profit = Rs. 50000\nShare of B = 6/13 (50000) = Rs. 23076.92~ 23077\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe probability of a team winning a match given Matt is playing the match is 0.75. The probability of the team winning a match given Matt is not playing the match is 0.35. The probability of Matt playing any match is 0.8.\nIf it is known that the team has won the last match, what is the probability that Matt played the match?\n\n### Options:\nA. A)0.8321\nB. B)0.7\nC. C)0.895\nD. D)0.7531\nE. E)0.8213\n\n### Answer:\nOut of 100 matches:\nMatt is plays in 80 and not plays in 20.\nOut of 80 matches Matt plays in, team wins 0.75*80 = 60.\nOut of 20 matches Matt does not play in, team wins 0.35*20 = 7.\nSo, out of 100 matches 60 + 7 = 67 are won.\nIt is known that the team has won the last match. Out of 67 matches won, Matt is in 60: 60/67 = 0.895...\nAnswer: C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man can row 18 kmph in still water.it takes him thrice as long to row up as to row down the river.find the rate of stream.\n\n### Options:\nA. 2 km/hr\nB. 3 km/hr\nC. 7 km/hr\nD. 9 km/hr\nE. 5 km/hr\n\n### Answer:\nLet man\u2019s rate upstream be x kmph.then ,his rate downstream=3xkmph.\nSo,2x=18 or x=9.\nRate upstream=9 km/hr,rate downstream=27 km/hr.\nHence,rate of stream=1/2(27-9)km/hr=9 km/hr.\nANSWER D 9 km/hr\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA batsman makes a score of 92 runs in the 17th inning and thus increases his average by 3. Find his average after 17th inning.\n\n### Options:\nA. 36\nB. 39\nC. 42\nD. 44\nE. None of the above\n\n### Answer:\nLet the average after 17th inning = x.\nThen, average after 16th inning = (x \u2013 3).\n\u2234 16(x \u2013 3) + 92 = 17x or x = (92 \u2013 48) = 44.\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how many ways can the letters of the word CREATION be arranged such that all the vowels always appear together?\n\n### Options:\nA. 5!*4!\nB. 8!\nC. 8!*4!\nD. 4!*4!\nE. 8!*5!\n\n### Answer:\nThe 8 letters can be grouped into 4 consonants and one set of 4 vowels.\nThe number of ways to arrange 5 units is 5!\nThen, for each arrangement, the 4 vowels can be arranged in 4! ways.\nThe total number of arrangements is 5!*4!\nThe answer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nlist of salaries of 8 employees are listed below. What is the median salary? $40,000, $29,000, $35,500, $31,000, $43,000, $30,000, $27,000, $32,000\n\n### Options:\nA. $15,000\nB. $23,540\nC. $23,550\nD. $30,590\nE. $31,500\n\n### Answer:\nOrdering the data from least to greatest, we get:\n$27,000, $29,000, $30,000, $31,000, $32,000, $35,500, $40,000, $43,000\nSince there is an even number of items in the data set, we compute the median by taking the mean of the two middlemost numbers.\n$31,000 + $32,000 = $63,000\nThe median salary is $31,500.\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nCan you find the missing number in the sequence given below\n11 19 27 12 20 ? 13 21 29 14 22 30\n\n### Options:\nA. 21\nB. 20\nC. 28\nD. 23\nE. 24\n\n### Answer:\nSolution:\n28\nExplanation :\nThe sequence is given in the puzzle is :\n11 19 27 12 20 ? 13 21 29 14 22 30\nLet's break the given series as below:\n11 19 27\n12 20 ?\n13 21 29\n14 22 30\nNow read the number from left hand side from top to bottom as :\nSo the number that will replace '?' is 28.\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAt what rate percent on simple interest will Rs.750 amount to Rs.900 in 5 years?\n\n### Options:\nA. 4%\nB. 9%\nC. 3%\nD. 6%\nE. 8%\n\n### Answer:\n150 = (750*5*R)/100\nR = 4%\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n5357 x 51 = ?\n\n### Options:\nA. 273232\nB. 273243\nC. 273247\nD. 273250\nE. 273207\n\n### Answer:\n5357 x 51\t= 5357 x (50 + 1)\n= 5357 x 50 + 5357 x 1\n= 267850 + 5357\n= 273207\nE)\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how many ways Chief Minister and Minister be elected from a team of 6 members?\n\n### Options:\nA. 28\nB. 20\nC. 36\nD. 30\nE. 32\n\n### Answer:\nTo do this, if captain is elected first, then we have 6 ways of doing this.\nFor election of vice-captain, we have only 5 ways left, coz 1 way is already consumed. (Situations like this is called dependent situation. One selection depends upon other selection.)\nSo, the ans is 6*5 = 30 ways.\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nExpress 25 mps in kmph?\n\n### Options:\nA. 77 kmph\nB. 55 kmph\nC. 90 kmph\nD. 56 kmph\nE. 17 kmph\n\n### Answer:\n25 * 18/5 = 90 kmph\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAccording to a recent survey report issued by the Commerce Ministry, Government of India, 30% of the total FDI goes to Gujarat and 20% of this goes to rural areas. If the FDI in Gujarat, which goes to urban areas, is $72 m, then find the size of FDI in rural Andhra Pradesh, which attracts 50% of the FDI that comes to Andhra Pradesh, which accounts For 20% of the total FDI?\n\n### Options:\nA. 30m\nB. 40m\nC. 35m\nD. 38m\nE. 50m\n\n### Answer:\n30% of total FDI given to Gujarat is $90m.\nso,100% is $300m.\n20%of 300m=60m.\n50%of 60m=30m.\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man swims downstream 65 km and upstream 35 km taking 5 hours each time; what is the speed of the current?\n\n### Options:\nA. 2\nB. 3\nC. 5\nD. 7\nE. 9\n\n### Answer:\n65 --- 5 DS = 13\n? ---- 1\n35 ---- 5 US = 7\n? ---- 1 S = ?\nS = (13 - 7)/2 = 3\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n5862 is to 714\nand 3498 is to 1113\nand 9516 is to 156\ntherefore 8257 is to ?\n\n### Options:\nA. 157\nB. 236\nC. 274\nD. 123\nE. 234\n\n### Answer:\nA\n157\n7 + 8 = 15,\n2 + 5 = 7;\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFrank is 15 years younger then John. In 3 years John will be twice as old as Frank. How old will Frank be in four years?\n\n### Options:\nA. 8\nB. 10\nC. 12\nD. 14\nE. 16\n\n### Answer:\nFrank is 15 years younger then John --> F+15=J;\nIn 5 years John will be twice as old as Frank (in 3 year John will be J+3 years old and Frank will be F+3 years old) --> J+3=2*(F+3) --> (F+15)+3=2*(F+3) --> F=12;\nIn 4 years Frank will be 12+4=16 years old.\nAnswer: E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average height of 50 pupils in a class is 150 cm. Five of them whose height is 146 cm, leave the class and five others whose average height is 156 cm, join. The new average height of the pupils of the class (in cm) is?\n\n### Options:\nA. 718 cm\nB. 151 cm\nC. 627 cm\nD. 282 cm\nE. 636 cm\n\n### Answer:\nTotal height = 150 * 50 = 7500 cm.\nNew average\n= [7500 - 5 * 146 + 5 * 156 ] / 50 = 151 cm.\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf x is a positive integer, and two sides of a certain triangle have lengths x+2 and x+2 respectively, which of the following could be the length of the third side of the triangle?\nI. x + 1\nII. x + 5\nIII. 2x + 1\n\n### Options:\nA. I only\nB. II only\nC. I and II only\nD. I and III only\nE. I, II and III\n\n### Answer:\nLet the third side of triangle be AB.\nTriangle rule states that:\nDifference of other 2 sides < any side < sum of other two sides\nSo x+2 - (x+2) < AB < x+2 + (x+2)\ni.e. 0 < AB < 2x + 4\nLet's take x =1 :\nSo 0 < AB < 6\nCheck if any of the answers are between 0 and 4.\nI: x+1 = 2 ; could be a possible value.\nII: x+5 = 6 ; could not be a possible value.\nIII: 2x+1 = 3; could be a possible value.\nI, II and III could not be a possible value.\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nInsert the missing number\n2, 4, 8, 16, 32, ..., 128, 256\n\n### Options:\nA. 46\nB. 65\nC. 64\nD. 63\nE. 68\n\n### Answer:\nseries is 2* Previous Number.\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo stations A and B are 110 km apart on a straight line. One train starts from A at 8 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet?\n\n### Options:\nA. 11\nB. 10\nC. 8\nD. 12\nE. 15\n\n### Answer:\nSuppose they meet x hours after 8 a.m.\nDistance covered by A in x hours = 20x km.\nDistance covered by B in (x - 1) hours = 25(x - 1) km.\nTherefore 20x + 25(x - 1) = 110\n45x = 135\nx = 3.\nSo, they meet at 11 a.m.\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain series is defined by the following recursive rule: Sm=K(Sm-1) , where k is a constant. If the 1st term of this series is 64 and the 25th term is 192, what is the 9th term?\n\n### Options:\nA. ROOT 2\nB. ROOT 3\nC. 64*ROOT 3\nD. 64*3^1/3\nE. 64*3^24\n\n### Answer:\nAns...D\nNo need for any GP formula here\nThe rule is that mth term is K times the (m-1)th term.\n1st = 64\n2nd = k.64\n3rd = k^2.64\n.\n.\n.\n9th term = k^8 *64\n.\n.\n.\nso 25th = k^24*64\nUsing this solve for k and substitute k in the equation for the 9th term\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA garrison of 400 men had a provision for 31 days. After 28 days 280 persons re-enforcement leave the garrison. Find the number of days for which the remaining ration will be sufficient?\n\n### Options:\nA. 22\nB. 28\nC. 10\nD. 66\nE. 23\n\n### Answer:\n400 --- 31\n400 --- 3\n120 --- ?\n400*3 = 120*x => x =10 days\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn one alloy there is 12% chromium while in another alloy it is 8%. 15 kg of the first alloy was melted together with 40 kg of the second one to form a third alloy. Find the percentage of chromium in the new alloy.\n\n### Options:\nA. 8.8%\nB. 9%\nC. 9.2%\nD. 9.1%\nE. 8.4%\n\n### Answer:\nThe amount of chromium in the new 15+40=55 kg alloy is 0.12*15+0.08*40=5 kg, so the percentage is 5/55*100=9.1%.\nAnswer: D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf A:B = 1/2: 1/5 B:C = 1/2:1/5 then A:B:C?\n\n### Options:\nA. 12:24:36\nB. 1:2:3\nC. 25:10:4\nD. 14:12:16\nE. 4:\n\n### Answer:\nA:B = 1/2:1/5 = 5:2\nB:C = 1/2:1/5 = 5:2\n--------------------\nA:B:C = 8:12\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe list price of an article is Rs.67. A customer pays Rs.56.16 for it. He was given two successive discounts, one of them being 10%. The other discount is?\n\n### Options:\nA. 3.86%\nB. 4.86%\nC. 5.86%\nD. 6.86%\nE. 7.86%\n\n### Answer:\n67*(90/100)*((100-x)/100) = 56.16\nx = 6.86%\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMane can make a handcrafted drum in 4 weeks. Zane can make a similar handcrafted drum in 6 weeks. If they both work together, how many weeks will it take for them to produce 15 handcrafted drums?\n\n### Options:\nA. 30\nB. 36\nC. 70\nD. 80\nE. 150\n\n### Answer:\nMethod I: the rates solution\n\u201cMane can make a handcrafted drum in 4 weeks. Zane can make a similar handcrafted drum in 6 weeks.\u201d Mane\u2019s rate is (1 drum)/(4 weeks) = 1/4. Zane\u2019s rate is (1 drum)/(6 weeks) = 1/6. The combined rate of Mane + Zane is\nR = 1/4 + 1/6 = 3/12 + 2/12 = 5/12\nThat\u2019s the combined rate. We need to make 15 drums \u2014 we have a rate and we have an amount, so use the \u201cart\u201d equation to solve for time:\nT = A/R = 15/(5/12) = 15*(12/5) = (15/5)*12 = 3*12 = 36\nBTW, notice in the penultimate step, the universal fraction strategy: cancelbeforeyou multiply (Tip #3:http://magoosh.com/gmat/2012/can-i-use- ... -the-gmat/. Mane and Zane need 36 weeks to make 15 drums.\nAnswer = B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man sitting in a train which is traveling at 70 kmph observes that a goods train, traveling in opposite direction, takes 9 seconds to pass him. If the goods train is 280 m long, find its speed.?\n\n### Options:\nA. 50 kmph\nB. 58 kmph\nC. 62 kmph\nD. 65 kmph\nE. 42 kmph\n\n### Answer:\nRelative speed = 280/9 m / sec = ((280/9)*(18/5)) kmph = 112 kmph.\nSpeed of goods train = (112 - 70) kmph = 42 kmph.\nAnswer : E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAshok secured average of 74 marks in 6 subjects. If the average of marks in 5 subjects is 74, how many marks did he secure in the 6th subject?\n\n### Options:\nA. 66\nB. 74\nC. 78\nD. 80\nE. None of these\n\n### Answer:\nExplanation:\nNumber of subjects = 6\nAverage of marks in 6 subjects = 74\nTherefore total marks in 6 subjects = 74 * 6 = 444\nNow, No. of subjects = 5\nTotal marks in 5 subjects = 74 * 5 = 370\nTherefore marks in 6th subject = 444 \u2013 370 = 74\nANSWER B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how many ways Chief Minister and Minister be elected from a team of 14 members?\n\n### Options:\nA. 162 ways\nB. 192 ways\nC. 182 ways\nD. 172 ways\nE. 152 ways\n\n### Answer:\nTo do this, if captain is elected first, then we have 14 ways of doing this.\nFor election of vice-captain, we have only 13 ways left, Bcoz 1 way is already consumed. (Situations like this is called dependent situation. One selection depends upon other selection.)\nSo, the ans is 14*13= 182 ways.\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man can row his boat with the stream at 6 km/h and against the stream in 4 km/h. The man's rate is?\n\n### Options:\nA. 1 kmph\nB. 2 kmph\nC. 7 kmph\nD. 8 kmph\nE. 9 kmph\n\n### Answer:\nDS = 6\nUS = 4\nS = ?\nS = (6 - 4)/2 = 1 kmph\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the smallest number which when increased by 3 is divisible by 18, 70, 100 and 84?\n\n### Options:\nA. 5307\nB. 5647\nC. 5927\nD. 6297\nE. 6557\n\n### Answer:\nWhen increased by 3, the number must include at least 2^2*3^2*5^2*7 = 6300\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe \"prime sum\" of an integer n greater than 1 is the sum of all the prime factors of n, including repetitions. For example , the prime sum of 12 is 7, since 12 = 2 x 2 x 3 and 2 +2 + 3 = 7. For which of the following integers is the prime sum greater than 35 ?\n\n### Options:\nA. 440\nB. 512\nC. 620\nD. 700\nE. 750\n\n### Answer:\nSolved it the prime factorization way\n440= 2*2*2*5*11 Sum=22\n512= 2^6 Sum=2*6=12\n620=2*2*5*31 Sum=40>35\nHence correct.\nAns is C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhen a whole no. n is divided by 4,we will get 3 as remainder. What will be the remainder if 2n is divided by 4?\n\n### Options:\nA. 1\nB. 4\nC. 2\nD. 6\nE. 7\n\n### Answer:\nLet n \u00f7 4 = p , remainder = 3\n=> n = 4p + 3\n2n = 2(4p + 3)\n= 8p + 6\n= 8p + 4 + 2\n= 4(2p + 1) + 2\nHence, if 2n is divided by 4, we will get 2 as remainder.\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat number comes next in the following number series? 12, 50, 202, 810, 3242, _____\n\n### Options:\nA. 12400\nB. 12800\nC. 12970\nD. 13015\nE. 16000\n\n### Answer:\n12\r12 \u00d7 4 + 2 = 50\r50 \u00d7 4 + 2 = 202\r202 \u00d7 4 + 2 = 810\r810 \u00d7 4 + 2 = 3242\r3242 \u00d7 4 + 2 = 12970 C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAn examiner rejects 0.16% of the meters as defective. How many will be examine to reject 4?\n\n### Options:\nA. 500\nB. 4000\nC. 2500\nD. 5500\nE. None of these\n\n### Answer:\nExplanation :\nSolution: let the number of meters to be examined be x. then, 0.16% of x = 4\n=>(16/100 * 1/100 * x) = 4\n=>x = (4*100*100)/16 = 2500.\nAnswer : C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA team of eleven footballers has an average height of 170 cm. Four footballers whose average height is 140 cm, left the team and four new others whose average height is 124 cm, joined. Calculate the new average height of the footballers (in cm) is?\n\n### Options:\nA. 166.2 cm\nB. 154.2 cm\nC. 364.2 cm\nD. 124.2 cm\nE. 164.2 cm\n\n### Answer:\nTotal height = 170 * 11 = 1870 cm.\nTotal height of those who left = 140 * 4 = 560\nTotal height of those who joined = 124 * 4 = 496\nNew average\n= [1870 - 560 + 496 ] / 11 = 1806/11 cm.\n= 164.2 cm\nAnswer:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo numbers are in the ratio of 5:7. If 33 is subtracted from each number, they are in the ratio of 1:2. What are the two numbers?\n\n### Options:\nA. 45, 63\nB. 50, 70\nC. 55, 77\nD. 60, 84\nE. 65, 91\n\n### Answer:\n(5x-33):(7x-33) = 1y:2y\n5x - 33 = y\n7x - 33 = 2y\n231-165 = 10y - 7y\n66 = 3y\ny = 22\n5x-33 = 22\nx = 11\nThe two numbers are 5x and 7x which are 55 and 77.\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a randomly selected positive single digit multiple of 3 is multiplied by a randomly selected prime number less than 20, what is the probability T that this product will be a multiple of 45?\n\n### Options:\nA. 1/32\nB. 1/28\nC. 1/24\nD. 1/16\nE. 1/14\n\n### Answer:\nThere are 3 single digit multiple of 3, that is, 3,6,9.\nThere are 8 prime nos less than 20 - 2,3,5,7,11,13,17,19\nTotal outcome - 8*3 = 24\nFavourable outcome = 1 (9*5)\nHence required probability T= 1/24. Answer C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf x, y, and z are consecutive odd integers, with x < y < z, then which of the following must be true?\nI. x + y is even\nII. (x+z)/y is an integer\nIII. xz is even\n\n### Options:\nA. I only\nB. II only\nC. III only\nD. I and II only\nE. I, II, and III\n\n### Answer:\nx, y, and z are consecutive integers \u21d2\nY = X+2\nZ = X+4\n1- x+y is even - Correct: sum of any 2 odd integers is even\n2- (x+z)/y is an integer - Correct: x+z = x+x+4 = 2x+4 = 2(x+2)\nand x+z/y = 2(x+2)/x+2 = 2 \u21d2 integer\n3- xz is even - Not Correct: multiplication of any 2 odd integers is always odd\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSpecial codes are designated by either a 2-letter or a 3-letter code that is created by using the 26 letters of the alphabet. Which of the following gives the maximum number of different codes that can be designated with this system?\n\n### Options:\nA. 2(26)^3\nB. 26(26)^2\nC. 27(26)^2\nD. 26(26)^3\nE. 27(26)^3\n\n### Answer:\n26^2+26^3 = 26^2(1+26)=27*26^2\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nExcluding stoppages, the average speed of a bus is 50 km/hr and including stoppages, the average speed of the bus is 40 km/hr. For how many minutes does the bus stop per hour?\n\n### Options:\nA. 12 min\nB. 18 min\nC. 16 min\nD. 20 min\nE. 26 min\n\n### Answer:\nIn 1hr, the bus covers 50 km without stoppages and 40 km with stoppages.\nStoppage time = time take to travel (50 - 40) km i.e 10 km at 50 km/hr.\nstoppage time = 10/50 hrs\n= 12 min\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo vertical poles 2 meter and 8 meter high stand apart on a horizontal plane. find the height in meters of the point of intersection of the lines joining the top of each pole to the bottom of the other pole.\n\n### Options:\nA. 1.8\nB. 1.9\nC. 1.6\nD. 1.7\nE. 56\n\n### Answer:\nLet A be the point of the top of the 2m pole.\nLet B be the point of the foot of the 2m pole.\nLet C be the point of the top of the 8m pole.\nLet D be the point of the foot of the 8m pole.\nLet E be the point of intersection of the line segments AD and BC.\nFrom E drop a perpendicular to the ground.\nLet F be the point on the ground where perpendicular from E meets the ground.\nLet X be the distance from E to F.\nLet P be the distance from B to F.\nLet Q be the distance from F to D.\nTriangles BEF and BCD are similar so we get Equation 1:\nX/P = 8/(P+Q)\nTriangles DEF and DAB are similar so we get:\nX/Q = 2/(P+Q)\nMultiplying both sides by 4 we get Equation 2:\n(4X)/Q = 8/(P+Q)\nCombining Equations 1 and 2 we get:\nX/P = (4X)/Q\nSimplifying this we get:\n1/P = 4/Q\nAnd then we get:\nQ = 4P\nSubstituting Q=4P into Equation 1 we get:\nX/P = 8/(P+4P)\nSimplifying this we get:\nX/P = 8/(5P)\nX = (8P)/(5P)\nX = 8/5\nX = 1.6\nTherefore, the desired height is 1.6 meters.\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhen throwing 2 dices, and looking at the sum of numbers on the dices - what is the probability to have a sum which is smaller than 5?\n\n### Options:\nA. 1/9\nB. 1/6\nC. 1/2\nD. 1/3\nE. 32/36\n\n### Answer:\na dice is composed of 6 numbers - 1,2,3,4,5,6.\nWhen trowing 2 dices - there are 36 options (6X6=36).\nIf we want the sum of two dices to be< 5 there are those options: (1,1), (1,2), (2,1), (1,3), (3,1), (2,2) - total of 6 options.\nTherefore - the probability to have a sum which is smaller than 5 is 6/36=1/6.\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train 110 meters long completely crosses a 280 meters long bridge in 38 seconds. What is the speed of the train is?\n\n### Options:\nA. 32\nB. 45\nC. 40\nD. 66\nE. 09\n\n### Answer:\nS = (110 + 280 /38 = 390/38 * 18/5 = 40\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe lengths of the legs of a right triangle are x and y, while the length of the hypotenuse is\nx + y- 4. What is the maximum radius of a circle inscribed in this triangle?\n\n### Options:\nA. 1\nB. 2\nC. 4\nD. 22\nE. cannot be determined from the information given\n\n### Answer:\nLength of hypotenuse: x + y-4 = a + b. Hence x + y = a + b + 4.\nSum of lengths of legs: x + y = a + b + 2r.\nTherefore 2r = 4, so r = 2.\ncorrect answer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nExpress of the following as a fraction:\n42%\n\n### Options:\nA. 20/55\nB. 21/50\nC. 34/27\nD. 17/25\nE. None of them\n\n### Answer:\n42% = 42/100= 21/50.\nAnswer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn 10 years,A will be twice as old as B was 10 years ago.If A is now 9 years older than B,the present age of B is :\n\n### Options:\nA. 19 Years\nB. 29 Years\nC. 39 Years\nD. 49 Years\nE. 59 Years\n\n### Answer:\nSolution\nLet B's present age = x years.Then,A's present age =(x +9) years.\n\u2234 (x + 9)+ 10 = 2 (x - 10) \u21d4 x + 19 = 2x- 20 \u21d4 x = 39.Answer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind four consecutive even integers so that the sum of the first two added to twice the sum of the last two is equal to 766.\n\n### Options:\nA. 124 ,126, 128, 130\nB. 120 ,122 , 124 ,128\nC. 120 ,121 , 122 ,123\nD. 123 ,125 , 127 ,129\nE. None of these\n\n### Answer:\nLet x, x + 2, x + 4 and x + 6 be the four integers. The sum of the first two\nx + (x + 2)\ntwice the sum of the last two is written as\n2 ((x + 4) + (x + 6)) = 4 x + 20\nsum of the first two added to twice the sum of the last two is equal to 766 is written as\nx + (x + 2) + 4 x + 20 = 766\nSolve for x and find all four numbers\nx = 124 , x + 2 = 126 , x + 4 = 128 , x + 6 = 130\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe ratio of the length and the breadth of a rectangle is 4 : 3 and the area of the rectangle is 6912 sq cm. Find the ratio of the breadth and the area of the rectangle?\n\n### Options:\nA. 1:96\nB. 1:92\nC. 1:98\nD. 1:94\nE. 1:99\n\n### Answer:\nLet the length and the breadth of the rectangle be 4x cm and 3x respectively.\n(4x)(3x) = 6912\n12x2 = 6912\nx2 = 576 = 4 * 144 = 22 * 122 (x > 0)\n=> x = 2 * 12 = 24\nRatio of the breadth and the areas = 3x : 12x2 = 1 : 4x\n= 1:96.\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAn error 2%in excess is made while measuring the side of a square. What is the percentage of error in the calculated area of the square?\n\n### Options:\nA. 4.04 %\nB. 2.02 %\nC. 4 %\nD. 2 %\nE. 2.40 %\n\n### Answer:\nExplanation:\nError =2% while measuring the side of a square.\nLet correct value of the side of the square =100\nThen, measured value =100+2=102 (\u2235 2 is 2%of 100)\nCorrect area of the square =100\u00d7100=10000\nCalculated area of the square =102\u00d7102=10404\nError =10404\u221210000=404\nPercentage error =error /actual value\u00d7100\n=404/10000\u00d7100=4.04%\nAnswer: Option A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf f(a)=2a+6, what is the value of (f(2a)+f(a)) ?\n\n### Options:\nA. 2a-4\nB. 8a-7\nC. 9a+5\nD. 6a+12\nE. 3a+5\n\n### Answer:\nf(a)=2a+6\nf(2a)= 4a+6\n(f(2a)+f(a)) = 4a+6+2a+6 = 6a+12\nAnswer is D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n1!+2!+3!+4!+5!+..100! is divided by 24. Find the remainder?\n\n### Options:\nA. 2\nB. 5\nC. 9\nD. 10\nE. 12\n\n### Answer:\nBy applying rule 2, we divide the terms of the above expression individually, and add them to get the final remainder. But from 4! onwards all the terms leave a remainder 0 when divided by 24.\nSo the remainder = 1 + 2 + 6 + 0 + 0....... =\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man has a certain number of small boxes to pack into parcles. If he packs 3, 4, 5 or 6 in a parcel, he is left with one over; if he packs 7 in a parcle, none is left over. What is the number of boxes, he may have to pack?\n\n### Options:\nA. 106\nB. 301\nC. 309\nD. 400\nE. 450\n\n### Answer:\nExplanation:\nClearly, the required number would be such that it leaves a remainder of 1 when divided by 3, 4, 5, or 6 and no remainder when divided by 7. Thus, the number must be of the form (L.C.M of 3, 4, 5, 6) x + 1 i.e., (60x + 1 ) and a multiple of 7. Clearly, for x = 5, the number is a multiple of 7. So the number is 301.\nAnswer: B) 301\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAt a certain stage of a soccer tournament, the score ratio of teams A, B and C was 3:4:5. Eventually, the score ratio of A to B has doubled while the score ratio of A to C has halved. If the final score of team C was 40, what was the final score A of team B?\n\n### Options:\nA. 1)8\nB. 2)10\nC. 3)20\nD. 4)40\nE. 5)80\n\n### Answer:\nA to B = 3 : 4\nSo, on doubling we get 6 : 4\nA to C = 3 : 5\nSo, on halving we get 1.5 : 5 or 3 : 10 or 6 : 20\nSo final ratio = 6 : 4 : 20.\nIf 20x = 40\n4x = 8\nHence, answer is A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average age of a group of persons going for tour is 16 years. Twenty new persons with an average age of 15 years join the group on the spot due to which their average age becomes 15.5 years. The number of persons initially going for tour is:\n\n### Options:\nA. 5\nB. 10\nC. 20\nD. 30\nE. 40\n\n### Answer:\nExplanation :\nLet the initial number of persons be x. Then,\n=> 16x + 20 x 15 -15.5 (x + 20)\n=> 0.5x = 10\n=> x = 20\nAnswer : C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich of the following could be the value of x, if |4x \u2013 2| = 10?\n\n### Options:\nA. \u20133\nB. \u20132\nC. 1\nD. 2\nE. 4\n\n### Answer:\n|4x \u2013 2| = 10\n=> 4x - 2 = 10\nor 4x - 2 = -10\n=> 4x = 12 or 4x = -8\n=> x = 3 or x = -2\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe product of all the prime numbers less than 12 is closest to which of the following powers of 10 ?\n\n### Options:\nA. 10^9\nB. 10^3\nC. 10^7\nD. 10^6\nE. 10^5\n\n### Answer:\nP = 2*3*5*7*11\n~ 10^ 3\nAnswer : B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man swims downstream 72 km and upstream 45 km taking 9 hours each time; what is the speed of the current?\n\n### Options:\nA. 1.9\nB. 1.5\nC. 1.2\nD. 1.6\nE. 1.1\n\n### Answer:\n72 --- 9 DS = 8\n? ---- 1\n45 ---- 9 US = 5\n? ---- 1 S = ?\nS = (8 - 5)/2 = 1.5\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHaving scored 96 runs in the 19th inning, a cricketer increases his average score by 4. What will be his average score after 19 innings?\n\n### Options:\nA. 28\nB. 27\nC. 26\nD. 22\nE. 24\n\n### Answer:\nExplanation :\nLet the average score of the first 18 innings be n\n18n + 96 = 19(n+4)=> n = 20\nSo, Average score after 19th innings = x+4 =24.\nAnswer : E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average age of a group of 10 persons was decreased by 3 years when one person, whose age was 42 years, was replaced by a new person. Find the age of the new person?\n\n### Options:\nA. 17\nB. 19\nC. 12\nD. 28\nE. 32\n\n### Answer:\nInitial average age of the 10 persons be P.\nAge of the new person Q.\nSum of the ages of the initial 10 persons = 10P\nNew average = (P-3) 10(P-3) = 10P - 42 + Q => Q = 12\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe edge of a cube is 4a cm. Find its surface?\n\n### Options:\nA. 24a8\nB. 24a4\nC. 96a2\nD. 24a2\nE. 24a7\n\n### Answer:\n6a2 = 6 * 4a * 4a = 96a2\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the integer p is rounded to the nearest hundred, the result represents a 66 2/3 % increase over the value obtained when p is rounded to the nearest ten. which of the following is a possible value of p?\n\n### Options:\nA. 64\nB. 67\nC. 99\nD. 133\nE. 147\n\n### Answer:\nWe have to check options 1 by 1.\n64 rounded to nearest hundred = 100\n64 rounded to nearest ten = 60\nnow difference = 40\nthe result represents a 66 2/3 % increase over the value obtained when x is rounded to the nearest ten.\ntherefore 40/60)*100 = 66 2/3 ==>this is the answer.\n99 rounded to nearest ten = 100\n133 rounded to nearest ten = 130\n133 rounded to nearest hundred p= 100=A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThree unbiased coins are tossed. What is the probability of getting at most 2 heads?\n\n### Options:\nA. 7/8\nB. 5/8\nC. 3/8\nD. 7/5\nE. 3/5\n\n### Answer:\nHere S={TTT, TTH, THT, HTT, THH, HTH, HHT, HHH}\nLet E=event of getting at least two heads ={TTT, TTH, THT, HTT, THH, HTH, HHT}\nP(E) = n(E)/n(S) = 7/8.\nAnswer A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSahil purchased a machine at Rs 9000, then got it repaired at Rs 5000, then gave its transportation charges Rs 1000. Then he sold it with 50% of profit. At what price he actually sold it.\n\n### Options:\nA. Rs. 22500\nB. Rs. 24500\nC. Rs. 26500\nD. Rs. 28500\nE. None of these\n\n### Answer:\nExplanation:\nQuestion seems a bit tricky, but it is very simple.\nJust calculate all Cost price, then get 150% of CP.\nC.P. = 9000 + 5000 + 1000 = 15000\n150% of 15000 = 150/100 * 15000 = 22500\nOption A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA, B and C invests Rs.2000, Rs.3000 and Rs.4000 in a business. After one year A removed his money; B and C continued the business for one more year. If the net profit after 2 years be Rs.3200, then A's share in the profit is?\n\n### Options:\nA. 197\nB. 127\nC. 189\nD. 400\nE. 198\n\n### Answer:\n2*12 : 3*12 : 4*24\n1: 3: 4\n1/8 * 3200 = 400\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA sum is divided among P, Q and R in such a way that for each rupee P gets, Q gets 25 paisa and R gets 15 paisa. If the share of P is RS. 70, what is the total amount?\n\n### Options:\nA. 48\nB. 84\nC. 74\nD. 47\nE. 64\n\n### Answer:\np:q:r = 100:25:15\n20:5:3\n20 --- 70\n28 --- ? => 84\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe traffic lights at three different road crossings change after every 48 sec., 72 sec and 108 sec. respectively .If they all change simultaneously at 8:20:00 hours, then at what time they again change simultaneously .\n\n### Options:\nA. 8:27:12\nB. 8:25:12\nC. 8:26:12\nD. 8:24:12\nE. None of them\n\n### Answer:\nInterval of change = (L.C.M of 48,72,108)sec.=432sec.\nSo, the lights will agin change simultaneously after every 432 seconds i.e,7 min.12sec\nHence , next simultaneous change will take place at 8:27:12 hrs.\nAnswer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nPavan travelled for 11 hours. He covered the first half of the distance at 30 kmph and remaining half of the distance at 25 kmph. Find the distance travelled by Pavan.\n\n### Options:\nA. 240 km\nB. 225 km\nC. 452 km\nD. 300 km\nE. 290 km\n\n### Answer:\nD\n300 km\nLet the distance travelled be x km.\nTotal time = (x/2)/30 + (x/2)/25 = 11 => x/60 + x/50 = 11 => (5x + 6x)/300 = 11 => x = 300 km\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train moves with a speed of 189 kmph. Its speed in metres per second is\n\n### Options:\nA. 60.8\nB. 18\nC. 30\nD. 52.5\nE. None\n\n### Answer:\nSolution\nSpeed\t= 189 Kmph\n= (189 x 5/18)m/sec\n= 52.5 m/sec.\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf cost of sugar increases by 12%. How much percent consumption of sugar should be decreased in order to keep expenditure fixed?\n\n### Options:\nA. 7.5\nB. 9.2\nC. 10.7\nD. 15.3\nE. 18.6\n\n### Answer:\n100\n112\n-----\n112 ----- 12\n100 ------ ? => 10.7%\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain club has 10 members, including Harry. One of the 10 members is to be chosen at random to be the president, one of the remaining 9 members is to be chosen at random to be the secretary, and one of the remaining 8 members is to be chosen at random to be the treasurer. What is the probability that Harry will be either the member chosen to be the president or the member chosen to be the treasurer?\n\n### Options:\nA. 1/720\nB. 1/80\nC. 2/10\nD. 1/9\nE. 1/6\n\n### Answer:\nThis question is much easier than it appears.\nEach member out of 10, including Harry, has equal chances to be selected for any of the positions (the sequence of the selection is given just to confuse us). The probability that Harry will be selected to be the president is 1/10 and the probability that Harry will be selected to be the treasurer is also 1/10. So, the probability that Harry will be selected to be either the president or the the treasurer is 1/10+1/10=2/10.\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTotal of ages of A,B and C at present is 80 years. If ratio of this ages is 2 : 2 : 4 what will be the age of C after 3 years?\n\n### Options:\nA. 43 years\nB. 42 years\nC. 40 years\nD. 37 years\nE. None of the above\n\n### Answer:\n2+2+4=9\n4*(80/8)=40yrs\nafter 5yrs=43\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo brothers took the GMAT exam, the higher score is X and the lower one is Y. If the difference between the two scores is 1/5, what is the value of X/Y ?\n\n### Options:\nA. 3.\nB. 5\nC. 1/2.\nD. 1/3.\nE. There isn't enough data to answer the question.\n\n### Answer:\nAnswer is B : 5\nX - Y = (X + Y)/2\nSolving for X/Y = 5\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA bicycle wheel has a diameter of 0.81m. How many complete revolutions does it make in 1km?\n\n### Options:\nA. 246\nB. 448\nC. 393\nD. 710\nE. 223\n\n### Answer:\n1 revolution = 3.14 * diameter.\nNumber of revolutions in 1km = 1000m / ( 3.14 * 0.81m ) = 393.2. Hence 393 complete revolutions.\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many odd numbers are possible between 1 to 10000000? find out the number of odd number of digits?\n\n### Options:\nA. 2999\nB. 3500\nC. 4000\nD. 4599\nE. 4999999\n\n### Answer:\nThere are always one odd and one even no. And the question is odd no. Between 1 to 10000000\nSo we have to find no. Between 1 to 10000 so we should not includes 1\n10000000/2 -1=4999999\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nCole drove from home to work at an average speed of 75 kmh. He then returned home at an average speed of 105 kmh. If the round trip took a total of 4 hours, how many minutes did it take Cole to drive to work?\n\n### Options:\nA. 66\nB. 70\nC. 95\nD. 112\nE. 140\n\n### Answer:\nFirst round distance travelled (say) = d\nSpeed = 75 k/h\nTime taken, T2 = d/75 hr\nSecond round distance traveled = d (same distance)\nSpeed = 105 k/h\nTime taken, T2 = d/105 hr\nTotal time taken = 4 hrs\nTherefore , 4 = d/75 + d/105\nLCM of 75 and 105 = 525\n4= d/75 + d/105\n=> 4 = 7d/525 + 5d/525\n=> d = 525 / 3 Km\nTherefore, T1= d/75\n=> T1 = 525 / (3 x 75)\n=> T1 = (7 x 60) / 3 -- in minutes\n=> T1 = 140 minutes.\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train 700 m long can cross an electric pole in 20 sec and then find the speed of the train?\n\n### Options:\nA. 72\nB. 67\nC. 28\nD. 126\nE. 27\n\n### Answer:\nLength = Speed * time\nSpeed = L/T\nS = 700/20\nS = 35 M/Sec\nSpeed= 35*18/5 (To convert M/Sec in to Kmph multiply by 18/5)\nSpeed = 126 Kmph\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nP software has coding line 5% more than N, N software has coding line 1/3 more than M. M software has 90 lines of coding. find P lines.\n\n### Options:\nA. 106\nB. 107\nC. 126\nD. 109\nE. 110\n\n### Answer:\nM s/w has 90 line of code\nN s/w has = 90+90*1/3= 120 line of code\nP s/w 5% more N' code 120+6=126\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the average (arithmetic mean) of all multiples of 10 from 10 to 100 inclusive?\n\n### Options:\nA. 190\nB. 195\nC. 200\nD. 205\nE. 55\n\n### Answer:\nThis question can be solved with the Average Formula and 'bunching.'\nWe're asked for the average of all of the multiples of 10 from 10 to 100, inclusive.\nTo start, we can figure out the total number of terms rather easily:\n1(10) = 10\n2(10) = 20\n...\n10(10) = 100\nSo we know that there are 10 total numbers.\nWe can now figure out the SUM of those numbers with 'bunching':\n10 + 100 = 110\n20 + 90 = 110\n30 + 80 = 110\nEtc.\nSince there are 10 total terms, this pattern will create 5 'pairs' of 110.\nThus, since the average = (Sum of terms)/(Number of terms), we have...\n(5)(110)/(10) =55\nAnswer : E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf q is a positive integer and q^2 is divisible by 12, then the largest positive integer that must divide q ^3 is\n\n### Options:\nA. 2^3\nB. 2^6\nC. 3^3\nD. 6^3\nE. 12^2\n\n### Answer:\nSince q is an integer so q cannot have a 2 and sqrt 3 (because squaring this will give us a 2^2 and 3 (making the product as 12, and making q^2 as a multiple of 12))\nq^2 is divisible by 12 (12 = 2*2*3), So, q should have at least one 2 and one 3 so that q^2 has a 2^2 and two 3\nSo, q will have a 2 and a 3. Or q will be a multiple of 6\nSo, largest possible integer than should divide q^3 is 6^3\nSo, Answer will be D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how many different ways can the letters of the word RUMOUR be arranged?\n\n### Options:\nA. 180\nB. 720\nC. 30\nD. 90\nE. None of these\n\n### Answer:\nReqd. number of ways\n6!/2!\u00d72!=6\u00d75\u00d74\u00d73/1\u00d72=180\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich of the following is equal to 1(1/7)%?\n\n### Options:\nA. 0.012/100\nB. 0.12/100\nC. 1.14/100\nD. 12/100\nE. 12/10\n\n### Answer:\nThis notation may be confusing for some, since it looks like we're multiplying 1 and 1/7\nHow about adding a space:Which of the following is equal to (1 1/7)%\n(1 1/7)% = 1.14% = 1.14/100\nAnswer:\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA box contains 6 black, 8 red and 4 green marbles. 2 marbles are drawn from the box at random. What is the probability that both the marbles are of the same color?\n\n### Options:\nA. 49/153\nB. 18/153\nC. 49/153\nD. 40/153\nE. 24/72\n\n### Answer:\nExplanation:\nTotal marbles in a box = 6 black + 8 red +4 green marbles = 18 marbles\n2 marbles are drawn from 18 marbles at random. Therefore,\nn(S) = 18C2 = 153 ways\nLet A be the event that 2 marbles drawn at random are of the same color. Number of cases favorable to the event A is\nn(A) = 6C2 + 8C2 + 4C2 = 15+28+6= 49\nTherefore, by definition of probability of event A,\nP(A) = n(A)/n(S) = 49/153\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf each term in the sum a1+ a2+a3+.....+an is either 7 or 77 and the sum equals 350, which of the following could be equal to n?\n\n### Options:\nA. 38\nB. 39\nC. 40\nD. 41\nE. 42\n\n### Answer:\nFor example: as units digit of 350 is zero then # of terms must be multiple of 10. Only answer choice which is multiple of 10 is C (40).\nTo illustrate consider adding:\n*7\n*7\n...\n77\n77\n----\n=350\nSo, several 7's and several 77's, note that the # of rows equals to the # of terms. Now, to get 0 for the units digit of the sum the # of rows (# of terms) must be multiple of 10. Only answer choice which is multiple of 10 is C (40).\nAnswer: C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nPeter must choose a lab partner by picking a name out of a bag. If the bag has 9 male names and F female names, what is the least number of female names in the bag if the probability of choosing a male lab partner is less than 3 out of 7?\n\n### Options:\nA. 11\nB. 12\nC. 13\nD. 14\nE. 16\n\n### Answer:\nMale Names in the bag = 9\nFemale Names in the bag = F\nProbability of selecting a male name is = P = 9/(9+F)\nThe question asked is \"what is the least number of female names in the bag if the probability of choosing a male lab partner is less than 3 out of 7?\"\nso, we need to find out the minimum value of F for which P<3/7\n9/(9+F) < 3/7\nSolving for F gives the equation;\nF>12\nSince the question asked is the minimum value F should be 13\n( F should be an integer).\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nBy selling a house for Rs.45000, it was found that 1/8 of the outlay was gained, what ought the selling to price to have been in order to have lost 7 p.c?\n\n### Options:\nA. 28000\nB. 29000\nC. 37000\nD. 37200\nE. 40000\n\n### Answer:\nOption B\nExplanation:\nCP + CP/8 = 45000\nCP = 40000\nSP = 40000*(93/100) = 37200\nOption D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe sum of two numbers is twice their difference. If one of the numbers is 10, the other number is\n\n### Options:\nA. 3 1/3\nB. 30\nC. \u22123 1/3\nD. a or b\nE. None\n\n### Answer:\nExplanation:\nLet the other number be a.\nGiven that, 10+a=2(a\u221210)\u21d2a=30\nor if the other number is less than 10, 10+a=2(10\u2212a)\u21d2a=10/3=3 1/3\nCorrect Option: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many such letter-pairs are there in the word SMUGGLER having same no.of letters left between them as they have in the series?\n\n### Options:\nA. 2\nB. 3\nC. 4\nD. 1\nE. 5\n\n### Answer:\nS,U\nAnd E,G\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe length of the bridge, which a train 160 metres long and travelling at 45 km/hr can cross in 30 seconds, is:\n\n### Options:\nA. 200 m\nB. 215 m\nC. 245 m\nD. 250 m\nE. 270 m\n\n### Answer:\nLet the length of the bridge:L\nThe equation now is L+160/12.5m/s(45km/hr or12.5m/s)=30\nSolving, L =215m\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe area of a square is subtracted from one of its sides, and the perimeter is then added to this total, the result is 4. What is the length of one side?\n\n### Options:\nA. 1\nB. 2\nC. 3\nD. 4\nE. 5\n\n### Answer:\nThe equation is; side - Area + Perimeter = s - A + P = s - s^2 + 4s = s(1 - s + 4).\nBy plugging in the answers we can test the answers quickly; then, 4 is the only possible answer.\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA sum of Rs.1550 was lent partly at 8% p.a. simple interest. The total interest received after 3 years was Rs.300. The ratio of the money lent at 5% to that lent at 8% is :\n\n### Options:\nA. 16:18\nB. 16:10\nC. 16:15\nD. 16:11\nE. 16:12\n\n### Answer:\nlet the sum lent at 5% be Rs.x and that lent at 8% be Rs.(1550-x). then,\nInterest on x at 5% for 3 years + interest on (1550-x) at 8% for 3 years = 300\nRequired ratio = x : (1550-x) = 800 : (1550-800) = 800 : 750 = 16 : 15\nAnswer: C) 16:15\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSix computers, each working at the same constant rate, together can process a certain amount of data in 15 days. How many additional computers, each working at the same constant rate, will be needed to process the same amount of data in 5 days?\n\n### Options:\nA. 3\nB. 5\nC. 6\nD. 9\nE. 12\n\n### Answer:\nExplanation: If six computers require 15 days to process the data, thats\na total of 90 computer-days the product of 6 and 15. If you change the number\nof computers or the number of days, 90 will have to remain the product, whether\nthat means 90 days of one computer or one day with 90 computers.\nIn 5 days, the number of computers is:\n5c = 90\nc = 18\n18 computers is 12 more than the 6 that it took to do the job in 15 days, so\nthe correct choice is (E).\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nDivide Rs. 3364 between A and B, so that A's Share at the end of 5 years may equal to B's share at the end of 7 years, compound interest being at 5 percent.\n\n### Options:\nA. Rs. 1764 and Rs.1600\nB. Rs. 1756 and Rs.1608\nC. Rs. 1722 and Rs.1642\nD. Rs. 1732 and Rs.1842\nE. None of these\n\n### Answer:\nExplanation: A's share after 5 years = B's share after 7 years\n(A's present share)(1+5100)5 = (B's present share)(1+5100)7\n=>(A's present share)/(B's present share) = (1+5/100)7/(1+5/100)5 = (1+5/100)(7\u22125) = (1+5/100)2 =(21/20)2 =441/400\ni.e, A's present share : B's present share = 441 : 400\nSince the total present amount is Rs.3364, A's share = 3364 \u00d7 441/(441 + 400)\n= (3364 \u00d7 441)/841 = 4 \u00d7 441 = Rs. 1764\nB's present share = 3364 - 1764 = Rs.1600\nAnswer: Option A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 11.25 m of a uniform steel rod weighs 42.75 kg. what will be the weight of 9 m of the same rod?\n\n### Options:\nA. 22.8 kg\nB. 34.2 kg\nC. 28 kg\nD. 26.5 kg\nE. None of these\n\n### Answer:\nExplanation :\nLet the required weight be x kg. Then, Less length, Less weight (Direct Proportion)\n=> 11.25 : 9 :: 42.75 : x\n=> 11.25 x x = 9 x 42.75\n=> x = (9 x 42.75) / 11.25\n=> x = 34.2\nAnswer : B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOn a Monday in a certain restaurant, 30 percent of the 180 customers ordered the daily special. On Tuesday, only 10 percent of the 120 customers ordered the special. For the two days combined, what percent of the customers ordered the daily special?\n\n### Options:\nA. 15%\nB. 16%\nC. 18%\nD. 22%\nE. 30%\n\n### Answer:\n30% of 180= 54\n10% of 120=12\nTotal =66\npercent for 2 days combined =66/300=0.22. so it should be less than 0.22 so it is 22%\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the value of n if the sum of the consecutive odd intergers W from 1 to n equals 169?\n\n### Options:\nA. 47\nB. 25\nC. 37\nD. 33\nE. 29\n\n### Answer:\nBefore you tackle this question you must first understand that the question is comprised of two key parts, 1st is finding out how manytermsis in that sequence and 2nd whatactual number valuethat term is. In an arithmetic progression, in this case consecutive odd integers 1, 3, 5, ...., there are two set of rules.\nRule #1 (Arithmetic Sequence): xn = a + d(n-1) Identifies what the actual # in the sequence would be. Each number in the sequence has a term such as 1(is the first term), 3(is the second term) and so on. So if I were to ask you to find out what the 10th term is of that sequence you would use that formula to find that value.\na=1 (first term)\nd=2 (the common difference) remember in the sequence 1, 3, 5, 7 the common difference is always 2\n*On a side note we use n-1 because we don't have d in the first term, therefore if we were solving for the first term we would get 0 as n-1 and 0 times d would give us 0, leaving only the first term. This works regardless what your first term is in any sequence.\nBut remember the question asksWhat is thevalueof n if the sum of the consecutive odd integers from 1 to n equals 169?which means we first need a consecutive sequence that sums up to 169 and than find what the value of the n is, in this case it would be the last number in that sequence. In order to find that we first need to knowhow many terms(how many of the n there is) in order to be able to plug n in this formula given we know what the sum is. For that to happen we need to use Rule #2.\nRule #2 (Summing an arithmetic series): 169 = n/2(2a+(n-1)d). Given the question gives us what the sum is (169 in this case) we would simply use this formula to solve for n. Once we solve for n (13 in this case) we can simply plug n into the first formula (rule 1) and find the value.\nIt feels very confusing and difficult at first, but once you identify the steps all you need to do is plug and play. We have the sum (169) of a sequence, the number of terms in that sequence is (unknown). Rule #2 tells us how many numbers there are in that sequence and Rule #1 gives us what that last term is.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average temperature of the town in the first four days of a month was 58 degrees. The average for the second, third, fourth and fifth days was 60 degrees. If the temperatures of the first and fifth days were in the ratio 7 : 8, then what is the temperature on the fifth day ?\n\n### Options:\nA. 22 degrees\nB. 64 degrees\nC. 77 degrees\nD. 26 degrees\nE. 18 degrees\n\n### Answer:\nSum of temperatures on 1st, 2nd, 3rd and 4th days = (58 * 4) = 232 degrees ... (1)\nSum of temperatures on 2nd, 3rd, 4th and 5th days - (60 * 4) = 240 degrees ....(2)\nSubtracting (1) From (2), we get :\nTemp, on 5th day - Temp on 1st day = 8 degrees.\nLet the temperatures on 1st and 5th days be 7x and 8x degrees respectively.\nThen, 8x - 7x = 8 or x = 8.\nTemperature on the 5th day = 8x = 64 degrees.\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA boat goes 100 km downstream in 10 hours, and 75 m upstream in 15 hours. The speed of the stream is?\n\n### Options:\nA. 2 8 \u00bd kmph\nB. 8 2 \u00bd kmph\nC. 2 9 \u00bd kmph\nD. 2 2 \u00bd kmph\nE. 3 2 \u00bd kmph\n\n### Answer:\n100 --- 10 DS = 10\n? ---- 1\n75 ---- 15 US = 5\n? ----- 1 S = (10 - 5)/2\n= 2 2 \u00bd kmph\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe price of a certain product increased by the same percent from 1960 to 1970 as from 1970 to 1980. If its price of $2.00 in 1970 was 150 percent of its price in 1960, what was its price in 1980?\n\n### Options:\nA. a) $ 1.80\nB. b) $ 2.00\nC. c) $ 2.40\nD. d) $ 2.70\nE. e) $ 3.00\n\n### Answer:\nThe price in 1970 was 150 percent of its price in 1960, means that the percent increase was 50% from 1960 to 1970 (and from 1970 to 1980).\nTherefore the price in 1980 = $2.0*1.5 = $3.00.\nAnswer: E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA 300 metre long train crosses a platform in 39 seconds while it crosses a post in 18 seconds. What is the length of the platform?\n\n### Options:\nA. 150 m\nB. 350 m\nC. 420 m\nD. 600 m\nE. 700 m\n\n### Answer:\nExplanation:\nLength of the train = distance covered in crossing the post = speed \u00d7 time = speed \u00d7 18\nSpeed of the train = 300/18 m/s = 50/3 m/s\nTime taken to cross the platform = 39 s\n(300+x)/(50/3) = 39 s where x is the length of the platform\n300+x = (39 \u00d7 50) / 3 = 650 meter\nx = 650-300 = 350 meter\nAnswer: Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn what time will a train 100 m long cross an electric pole, it its speed be 144 km/hr?\n\n### Options:\nA. 2.5 sec\nB. 4.25 sec\nC. 5 sec\nD. 12.5 sec\nE. 6 sec\n\n### Answer:\nSpeed = 144 * 5/18 = 40 m/sec\nTime taken = 100/40 = 2.5 sec.\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the greatest number of four digits which is perfectly divisible by 3 and when divided by 5, 7 and 9 leaves a remainder 3 in each case.\n\n### Options:\nA. 1128\nB. 1659\nC. 2687\nD. 1667\nE. 1891\n\n### Answer:\nLCM of 3, 5, 7, 9 = 315. Greatest number of four digits which is divisible by 315 is 9765. The required number = 9765 + 3 = 9768. Ask doubt with Question Id: 1658 13) Find greatest number of four digits which when increased by 3568 is exactly divisible by 6, 8, 12, 20. a) 9992 b) 9785 c) 9840 d) None Explanation: Greatest number of 4 digits = 9999. 9999 + 3568 = 13567. LCM of 6, 8, 12 and 20 is 120.\n\u2234 Required number of 4 digits = 9999 \u2013 7 = 9992 i.e. 9992 is the number to which if 3568 is added, then it is exactly divisible by 6, 8, 12, 20. Ask doubt with Question Id: 1659\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe circulation for magazine P in 1971 was 4 times the average (arithmetic mean) yearly circulation for magazine P for the years 1972-1980. What is the ratio of the circulation in 1971 to the total circulation during 1971-1980 for magazine P ?\n\n### Options:\nA. 4/7\nB. 5/7\nC. 3/7\nD. 2/7\nE. 1/7\n\n### Answer:\nThere are 9 years from 1972-1980, inclusive. Let's say the average circulation every year between 1972-1980 inclusive is x.\nSo the total circulation is 9x from 1972-1980, inclusive.\nIn 1971, the circulation is 4x.\nSo total circulation for 1971-1980 is 4x + 9x = 13x.\nRatio of circulation in 1971 to total circulation during 1971-1980 is 4x to 14x or 4/14=2/7\nAnswer : D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA boatman goes 2 km against the current of the stream in 1 hour and goes 1 km along the current in 10 minutes. How long will it take to go 6 km in stationary water?\n\n### Options:\nA. 40 minutes\nB. 1 hour\nC. 1 hour 15 min\nD. 1 hour 30 min\nE. 1 hour 10 min\n\n### Answer:\nspeed (upstream) =2/1 = 2 kmhr\nspeed (downstream)=1/(10/60)= 6 kmhr\nspeed in still water = 1/2 (2+6) = 4 kmhr\ntime taken in stationary = 6/4 = 1 hrs 30 min\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the expenditure on digging a well 14m deep and of 3m diameter at Rs.18 per cubic meter?\n\n### Options:\nA. 2998\nB. 2799\nC. 1782\nD. 1485\nE. 2780\n\n### Answer:\n22/7 * 14 * 3/2 * 3/2\n= 99 m2\n99 * 18\n= 1782\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average of 11 numbers is 10.9. If the average of first six is 10.5 and that of the last six is 11.4 the sixth number is?\n\n### Options:\nA. 9.5\nB. 10\nC. 10.5\nD. 11.5\nE. 12\n\n### Answer:\nExplanation:\n1 to 11 = 11 * 10.9 = 119.9\n1 to 6 = 6 * 10.5 = 63\n6 to 11 = 6 * 11.4 = 68.4\n63 + 68.4 = 131.4 \u2013 119.9 = 11.5\n6th number = 11.5\nOption D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average mark of a class of twenty five students is 66. If five students whose marks are 32,28, 30, 26 and 34 are removed , then find the average mark of the remaining students of the class.\n\n### Options:\nA. 75\nB. 74\nC. 57\nD. 70\nE. 80\n\n### Answer:\nExp. Total mark of 25 students = 66*25 = 1650,\nTotal mark after the removal of 5 students = 1650 \u2013(32 +28+30+26+34 )\n= 1650 \u2013 150 = 1500\nAverage mark = 1500/(25-5) = 1500/ 20 = 75\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n35 liters of a mixture is created by mixing Liquid P and Liquid Q in the ratio 4:3. How many liters of Liquid Q must be added to make the ratio 5:7?\n\n### Options:\nA. 10\nB. 11\nC. 12\nD. 13\nE. 14\n\n### Answer:\nLet x be the amount of liquid Q to be added.\n(3/7)*35 + x = (7/12)*(35+x)\n1260 + 84x = 1715 + 49x\n35x = 455\nx = 13\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA cylinder of radius R and height H is reshaped. Which of the following changes results in the cylinder of greatest volume?\n\n### Options:\nA. a 20% decrease in H and a 50% increase in R.\nB. a 500% increase in H and a 50% decrease in R.\nC. a 300% increase in H and a 30% decrease in R\nD. a 70% decrease in H and a 100% increase in R\nE. a 100% increase in H and a 10% decrease in R\n\n### Answer:\nVolume of a cylinder = Pi. R^2.H\nCheck for options as per given Q.\nA. (1.5)^2 * (0.8) = 2.25 * 0.8 = 1.8 (Since 20% decrease in H and a 50% increase in R.)\nB. (0.5)^2 * (6) = 0.25 * 6 = 1.5 (Since 500% increase in H and a 50% decrease in R)\nC. (0.7)^2 * (4) = 0.49 * 4 = 1.96 (Since 300% increase in H and a 30% decrease in R )\nD. (2)^2 * (0.3) = 4 * 0.3 = 1.2 (Since 70% decrease in H and a 100% increase in R. )\nE. (0.9)^2 * (2) = 0.81 * 2 = 1.62 (Since 100% increase in H and a 10% decrease in R. )\nMaximum value is 1.96\nOption C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man can row downstream at 18 kmph and upstream at 10 kmph. Find the speed of the man in still water and the speed of stream respectively?\n\n### Options:\nA. 7\nB. 6\nC. 9\nD. 4\nE. 2\n\n### Answer:\nLet the speed of the man in still water and speed of stream be x kmph and y kmph respectively.\nGiven x + y = 18 --- (1)\nand x - y = 10 --- (2)\nFrom (1) & (2) 2x = 28 => x = 14, y = 4.\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFrom the word 'ASTOUNDER', how many independent words can be made with-out changing the order of the letters and using each letter only once ?\n\n### Options:\nA. 5\nB. 8\nC. 3\nD. 2\nE. 9\n\n### Answer:\nExplanation:\nThe words formed are\nAT and UNDER, AS and UNDER (or) AT and SOUND\nAnswer: D) 2\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSandy walked 20 meters towards south. Then Sandy turned to her left and walked 20 meters. She then turned to her left and walked 20 meters. She then turned to her right and walked 25 meters. What distance is she from the starting point and in which direction?\n\n### Options:\nA. 35 m East\nB. 35 m North\nC. 30 m West\nD. 45 m West\nE. 45 m East\n\n### Answer:\nThe net distance is 20 + 25 = 45 meters to the east.\nThe answer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the greatest integer that will always evenly divide the sum of three consecutive integers?\n\n### Options:\nA. 2\nB. 3\nC. 4\nD. 6\nE. 12\n\n### Answer:\nLet the three consecutive integers be x , x + 1 , x + 2\nSum = x + x + 1 + x + 2\n= 3x+3 = 3(x+1)\nTherefore , 3 will always be a factor .\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many positive three-digit integers are divisible by both 3 and 5?\n\n### Options:\nA. 50\nB. 60\nC. 65\nD. 70\nE. 80\n\n### Answer:\nA number to be divisible by both 3 and 5 should be divisible by the least common multiple of 3 and 5 so by 15.\nMultiples of 15 between 100 and 999, inclusive is\n(last-first)/multiple+1=(990-105)/15+1=59+1=60\nAnswer: B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nYou buy a piece of land with an area of \u221a900, how long is one side of the land plot?\n\n### Options:\nA. 28\nB. 29\nC. 30\nD. 31\nE. 32\n\n### Answer:\nTry filling the numbers into the answer y x y =\nFind the closest to 900.\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man can row downstream at the rate of 16 Km/hr and upstream at 6 Km/hr. Find man's rate in still water and the rate of current?\n\n### Options:\nA. 9,6\nB. 11,5\nC. 9,3\nD. 6,6\nE. None of these\n\n### Answer:\nExplanation:\nRate of still water = 1/2 (16 + 6) = 11 Km/hr\nRate of current = 1/2 (16-6) = 5 Km/hr\nAnswer: Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe New York Classical Group is designing the liner notes for an upcoming CD release. There are 10 soloists featured on the album, but the liner notes are only 5 pages long, and therefore only have room for 5 of the soloists. The soloists are fighting over which of them will appear in the liner notes, though not about which page they appear on. How many different combinations Q of soloists can appear in the liner notes?\n\n### Options:\nA. 5!\nB. 10!/(5!5!)\nC. 10!/5!\nD. 10!\nE. 10!*5!\n\n### Answer:\nTotal Soloists to choose from = 10\nSoloist Required = 5\nQuestion : How many different combinations Q of soloists can appear in the liner notes?\nThe language of the question clearly mentions that only the combinations need to be calculated\ni.e. Arrangement of the Soloists does NOT matter(Refer theHighlightedpart of the question)\nMethod-1:\nTotal Ways to Choose 5 out of 10 soloists = 10C5 = 10! / (5!*5!)\nMethod-2:\nNo. of ways to select and arrange 5 soloist on 5 Page = 10*9*8*7*6\nSince the arrangement of 5 selected Notes (which can happen in 5! ways) doesn't NOT matter,\nTherefore total ways to pick 5 out of 10 soloists = 10*9*8*7*6 / 5! = 10*9*8*7*6 *5! / (5!*5!) = 10! / (5!*5!)\nAnswer: Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man can row at 6 kmph in still water. If the velocity of current is 2 kmph and it takes him 2 hour to row to a place and come back, how far is the place?\n\n### Options:\nA. 5.33 km\nB. 6.33 km\nC. 5.63 km\nD. 7.33 km\nE. 5.93 km\n\n### Answer:\nSpeed in still water = 6 kmph\nSpeed of the current = 2 kmph\nSpeed downstream = (6+2) = 8 kmph\nSpeed upstream = (6-2) = 4 kmph\nLet the required distance be x km\nTotal time taken = 2 hour\nx/8 +x/4 =2\nx+2x/8 =2\n3x/8=2\n3x=16\nx=5.33 km\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 60 percent of 600 is 50 percent of x, then x=?\n\n### Options:\nA. 600\nB. 720\nC. 820\nD. 800\nE. 920\n\n### Answer:\n0.6 * 600 = 0.5 * x\nx = 6/5 * 600 = 720\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n5 x 1.6 - 2 x 1.4/1.3 = ?\n\n### Options:\nA. 0.2\nB. 0.9\nC. 1.4\nD. 4\nE. None of them\n\n### Answer:\nGiven Expression\n= (8 - 2.8)/1.3\n= 5.2/1.3\n= 52/1.3\n= 4.\nAnswer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAn oil cylinder was 3/4th full. When ONE bottles of oil is poured into it, it is 4/5th full. How many bottles of oil\ncan the full cylinder hold?\n\n### Options:\nA. 20\nB. 15\nC. 40\nD. 30\nE. 35\n\n### Answer:\n(4/5 -3/4) cylinder is filled by 1 bottles\n0.8 -0.75 = 0.05 cylinder is filled by 1 bottles\n1 cylinder is filled by 1/0.05 = 20 bottles\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many minutes does it take John to type u words if he types at the rate of x words per minute?\n\n### Options:\nA. x/y\nB. u/x\nC. xy\nD. 60x/y\nE. y/(60x)\n\n### Answer:\ntime*rate=job --> time*x=u --> time=u/x.\nAnswer: B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA student must answer 7 out of 10 questions on an examination. If at least 3 of the first 5 questions must be answered, how many possible combinations of 7 questions are available to the student?\n.\n\n### Options:\nA. 50\nB. 80\nC. 110\nD. 220\nE. 360\n\n### Answer:\n1) preferred one\nas there is ONLY one possiblity of choosing 7 out of 10, while choosing less than 3 in first five\nchoose 2 in first 5 and all 5 from later half..\nways = 5C2 = 10..\ntotal ways = 10C3 = 120\nans = 120-10 = 110\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA completes a work in 6 days and B complete the same work in 12 days. If both of them work together, then the number of days required to complete the work will be?\n\n### Options:\nA. 4 days\nB. 11 days\nC. 21 days\nD. 22 days\nE. 24 days\n\n### Answer:\nIf A can complete a work in x days and B can complete the same work in y days, then, both\nof them together can complete the work in x y/ x+ y days\nTherefore, here, the required number of days = 6 \u00c3\u2014 12/ 18 = 4 days.\nOption 'A'\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If two marbles are drawn at random, what is the probability that at least one is green?\n\n### Options:\nA. 23/35\nB. 23/38\nC. 23/29\nD. 23/12\nE. 23/11\n\n### Answer:\nGiven that there are three blue marbles, four red marbles, six green marbles and two yellow marbles.\nProbability that at least one green marble can be picked in the random draw of two marbles = Probability that one is green + Probability that both are green\n= (\u2076C\u2081 * \u2079C\u2081)/\u00b9\u2075C\u2082 + \u2076C\u2082/\u00b9\u2075C\u2082\n= (6 * 9 * 2)/(15 * 14) + (6 * 5)/(15 * 14) = 36/70 + 1/7\n= 46/70 = 23/35\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA vessel of capacity 2 litre has 35% of alcohol and another vessel of capacity 6 litre had 50% alcohol. The total liquid of 8 litre was poured out in a vessel of capacity 10 litre and thus the rest part of the vessel was filled with the water. What is the new concentration of Mixture?\n\n### Options:\nA. 31%.\nB. 71%.\nC. 49%.\nD. 29%.\nE. 37%.\n\n### Answer:\n35% of 2 litres = 0.7 litres\n50% of 6 litres = 3 litres\nTherefore, total quantity of alcohol is 3.7 litres.\nThis mixture is in a 10 litre vessel. Hence, the concentration of alcohol in this 10 litre vessel is 37%\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nLamp A flashes every 6 seconds, Lamp B flashes every 8 seconds, Lamp C flashes every 10 seconds. At a certain instant of time all three lamps flash simultaneously. During the period of 2 minutes after that how many times will exactly two lamps flash?\n\n### Options:\nA. 5\nB. 6\nC. 9\nD. 12\nE. 15\n\n### Answer:\nlamp A flashes every 6 secs,\nb flashes every 8 secs,\nc flashes every 10 secs.\nAt certain time three flashes simultaneously.\nafter that calculate when the three lamps flashes simultaneously in 2 minutes.\ntake a L.C.M of three 6,8,10 sec then it is 120 secs.\nso exactly after 2 minutes it flashes simultaneoulsy.\nquestion stem asks exactly two lamps falshes .\ntake lcm of a and b .6 and 8 is 24 secs. so two lamp flashes 5times in 2minutes.\nlcm of b and c . 8 and 10 secs is 40 secs. so both flashes 3times in 2minutes.\nlcm of c and a ,6 and 10 secs is 30 secs . pair flashes 4times..\nall three pairs flashes simultaenoulsy at 2 minutes. we have to minus one from all three pairs.\nthen 12-3=9.\nso option C is correct\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRs. 6000 is lent out in two parts. One part is lent at 7% p.a simple interest and the other is lent at 10% p.a simple interest. The total interest at the end of one year was Rs. 450. Find the ratio of the amounts lent at the lower rate and higher rate of interest?\n\n### Options:\nA. 5:1\nB. 5:6\nC. 5:2\nD. 5:8\nE. 5:2\n\n### Answer:\nLet the amount lent at 7% be Rs. x\nAmount lent at 10% is Rs. (6000 - x)\nTotal interest for one year on the two sums lent\n= 7/100 x + 10/100 (6000 - x) = 600 - 3x/100\n=> 600 - 3/100 x = 450 => x = 5000\nAmount lent at 10% = 1000\nRequired ratio = 5000 : 1000 = 5:1\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe area of the square formed on the diagonal of a rectangle as its side is 108 1/3 % more than the area of the rectangle. If the perimeter of the rectangle is 28 units, find the difference between the sides of the rectangle?\n\n### Options:\nA. 5M\nB. 4M\nC. 9M\nD. 2M\nE. 6M\n\n### Answer:\nExplanation:\nLet the sides of the rectangle be l and b respectively.\nFrom the given data,\n(\u221al2 + b2) = (1 + 108 1/3 %)lb\n=> l2 + b2 = (1 + 325/3 * 1/100)lb\n= (1 + 13/12)lb\n= 25/12 lb\n=> (l2 + b2)/lb = 25/12\n12(l2 + b2) = 25lb\nAdding 24lb on both sides\n12l2 + 12b2 + 24lb = 49lb\n12(l2 + b2 + 2lb) = 49lb\nbut 2(l + b) = 28 => l + b = 14\n12(l + b)2 = 49lb\n=> 12(14)2 = 49lb\n=> lb = 48\nSince l + b = 14, l = 8 and b = 6\nl - b = 8 - 6 = 2m.\nAnswer: Option D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHCF and LCM two numbers are 20 and 396 respectively. If one of the numbers is 36, then the other number is?\n\n### Options:\nA. 36\nB. 66\nC. 132\nD. 264\nE. 220\n\n### Answer:\n20 * 396 = 36 * x\nx = 220\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a rectangular axis system, what is the area of a parallelogram with the coordinates: (2,2), (8,2), (3,5), (9,5) ?\n\n### Options:\nA. 18.\nB. 28.\nC. 35.\nD. 49.\nE. 52.\n\n### Answer:\nDelta x will give us the dimension of one side of the parallelogram = 8-2= 6 unit\nDelta y will give us the dimension of the other side of parallelogram = 5-2=3 unit\nArea of parallelogram = 6*3 = 18\nANSWER IS A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAccording to the directions on a packet of smoothie mix, 1 3-ounce packet of smoothie mix is to be combined with 19 ounces of water to make a smoothie. How many 3-ounce packets of smoothie mix are required to prepare 150 12-ounce smoothies?\n\n### Options:\nA. 120\nB. 150\nC. 180\nD. 240\nE. 600\n\n### Answer:\nThis question wasn't particularly grueling, but I think it's the first where I had the opportunity to solve it via theory andinspectionthat many on this board suggest as strategy on the GMAT. It actually came to me by accident. Basically, if we thought that the 3 packets of powder were included in the 12 ounces of water, that would mean we would need 150 packets of smoothie mix (along with 12(150) ounces of water for a total of 150 packets. However, we know, after a more careful reading of the stimulus, that the 3 ounces are NOT included in the 12 ounces. As such, the answer has to be LESS than 150 packets, since 150 would be too much powder considering you already have 150(12) ounces of water and need less packets than water to make a smoothie. As such, the only answer less than 150 is 120, A. Does this make sense? Or am I way off base?\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf S is the sum of the reciprocals of the consecutive integers from 91 to 100, inclusive, which of the following is less than S?\nI. 1/10\nII. 1/9\nIII. 1/8\n\n### Options:\nA. None\nB. I only\nC. III only\nD. II and III only\nE. I, II, and III\n\n### Answer:\nSince we summarize the reciprocals from 100 to 91, we can say also that we add ten numbers who are all (with one exception 1/100) greater than 1/100, so that the sum must be greater than 1/10.\nOn the other side we can say that we add the reciprocals from 91 to 100, so that the sum has to be less than the sum of ten times 1/91.\nWe can conclude that the sum has to be less than 1/9 but more than 1/10. That leaves us B as the only possible answer.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA mathematics teacher tabulated the marks secured by 35 students of 8th class. The average of their marks was 72. If the marks secured by Reema was written as 35 instead of 99 then find the correct average marks up to two decimal places.\n\n### Options:\nA. 73.41\nB. 74.31\nC. 72.43\nD. 73.43\nE. 73.82\n\n### Answer:\nTotal marks = 35 x 72 =2520\nCorrected total marks = 2520 - 35 + 99 =2584\nCorrect Average = 2584/35 = 73.82\nAnswer : E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf (2x + 2)(x + 3) = 2x^2 + x, what is a possible value of x?\n\n### Options:\nA. -6/7\nB. -6/8\nC. -5/7\nD. 8/7\nE. 6/8\n\n### Answer:\nRearranging the given expression:\n(2x + 2)(x + 3) = 2x^2 + x\ni.e. 2x^2 + 8x + 6 = 2x^2 + x\ni.e. 7x = -6\ni.e. x = -6/7\nAnswer: Option A\nHad it been a difficult expression to solve further, then we could have used options to check which one satisfies the expression after solving it as further as possible.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the one which does not belong to that group ?\n\n### Options:\nA. 16\nB. 28\nC. 36\nD. 64\nE. 4\n\n### Answer:\nExplanation:\n16, 36, 64 and 4 are perfect squares but not 28.\nANSWER IS C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe captain of a cricket team of 11 members is 24 years old and the wicket keeper is 3 years older. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. What is the average age of the team?\n\n### Options:\nA. 20 years\nB. 21 years\nC. 22 years\nD. 23 years\nE. 24 years\n\n### Answer:\nExplanation:\nLet the average age of the whole team by x years.\n11x \u00e2\u20ac\u201c (24 + 27) = 9(x -1)\n11x \u00e2\u20ac\u201c 9x = 42\n2x = 42\nx = 21.\nSo, average age of the team is 21 years.\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAlbert borrowed a total of $ 6000 from Brian and Charlie. He paid simple interest at the rate of 7 % Per yr and 9 % per yr respectively.At the end of three years he paid $ 1400 as total interest. What is the interest paid to Brian at the end of three years?\n\n### Options:\nA. 825\nB. 790\nC. 795\nD. 785\nE. 770\n\n### Answer:\nLet x be the amount borrowed form Brian. So amount borrowed form Charlie = 6000-x.\n1400 = 21/100x + 27/100(6000-x)\n=>x = 22000/6.\nInterest paid = 3*7/100*22000/6 = 770.\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA number when successively divided by 3,5 and 8 leaves remainders 1,4 and 7 respectively. Find the respective remainders W when the order of the divisors is reversed.\n\n### Options:\nA. 8,5,3\nB. 4,2,1\nC. W=3,2,1\nD. W=6,4,2\nE. None of above\n\n### Answer:\nMy approach would be\nThree Divisors : 3, 5, 8\nThree Remain: 1, 4, 7\nStart from the bottom of the last column i.e. from the third remainder:\nGo up diagonally and multiply by the second divisor: 5*7 = 35\nGo down and add the second remainder: 35 + 4 = 39\nGo up diagonally and multiply by the first divisor: 39* 3 = 117\nGo down and add the first remainder: 117 + 1 = 118\nDivide 118 by 8, 5, 3\n118/8 gives quotient = 14 and remainder = 6\n14/5 gives quotient = 2 and remainder = 4\n2/3 gives quotient = 0 and remainder = 2\nAns is D i.e. 6,4,2\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat inequality represents the condition 1", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train travelled from station P to Q in 8 hours and came back from station Q to P is 6 hours. What would be the ratio of the speed of the train while traveling from station P to Q to that from station Q to P?\n\n### Options:\nA. 3 : 9\nB. 3 : 0\nC. 3 : 3\nD. 3 : 4\nE. 3 : 1\n\n### Answer:\nSince S # 1/t\nS1 : S2 = 1/t1 : 1/t2 = 1/8 : 1/6 = 3 : 4\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA hiker walked for 3 days. She walked 18 miles on the first day, walking 6 miles per hour. On the second day she walked for one less hour but she walked one mile per hour, faster than on the first day. On the third day she walked the same number of hours as on the first day, but at the same speed as on the second day. How many miles in total did she walk?\n\n### Options:\nA. 24\nB. 44\nC. 53\nD. 60\nE. 62\n\n### Answer:\nShe walked 18 miles on the first day, walking 6 miles per hour i.e. total time of walk on Day-1 = 18/6 = 3 Hours\nSecond day time of walk = 3-1 = 2 hours and Speed = 6+1=7 miles per hour i.e. Distance walked on second day = 2*7 = 14 miles\nThird day time of walk = 3 hours and Speed = 7 miles per hour i.e. Distance walked on second day = 3*7 = 21 miles\nTotal Distance travelled on three days = 18+14+21 = 53\nAnswer: Option C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many positive even integers less than 100 contain digits 5 or 9?\n\n### Options:\nA. 16\nB. 10\nC. 18\nD. 19\nE. 20\n\n### Answer:\nTwo digit numbers:\n5 at tens place: 50,52,54,56,58\n9 at tens place: 90,92,94,96,98\nIf 5 and 9 is at units place, the number cant be even\nTotal:5+5= 10\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many times thekeys of a writter have to bepressed in order to write first 400 counting no's?\n\n### Options:\nA. 900\nB. 980\nC. 1000\nD. 1092\nE. 1200\n\n### Answer:\n1 to 9 = 9 * 1 = 9\n10 to 99 = 90 * 2 = 180\n100 to 400 = 301 * 3 = 903\n-----------\n1092\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA meeting has to be conducted with 5 managers. Find the number of ways in which the managers may be selected from among 7 managers, if there are 2 managers who refuse to attend the meeting together.\n\n### Options:\nA. 6\nB. 8\nC. 10\nD. 11\nE. 15\n\n### Answer:\nThe total number of ways to choose 5 managers is 7C5 = 21\nWe need to subtract the number of groups which include the two managers, which is 5C3 = 10.\n21 - 10 = 11\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a certain growth fund, 3/5 of the investment capital is invested in stocks, and of that portion, 1/3 is invested in preferred stocks. If the mutual fund has $843,000 invested in preferred stocks, what is the total amount of money invested in the fund?\n\n### Options:\nA. $1,974,000\nB. $2,538,000\nC. $3,264,000\nD. $3,826,000\nE. $4,215,000\n\n### Answer:\nPortion invested in preferred stock = 3/5 * 1/3 = 1/5\n1/5 of fund = 843---\nFund = 5 * 843---\nHere, we can avoid the math and simply look at 5 * 3 -> 15. Only option E has 15 in it.\nAnswer (E).\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA began business with 12500 and is joined afterwards by B with 50000. When did B join, if the profits at the end of the year are divided equally?\n\n### Options:\nA. 3 months\nB. 9 months\nC. 10 months\nD. 7 months\nE. None of these\n\n### Answer:\nLet B join after x months of the start of the business so that B\u2019s money is invested for (12 \u2013 x) months.\n\u2234 Profit ratio is 12 \u00d7 12500 : (12 \u2013 x) \u00d7 50000\nor 12 : 4(12 \u2013 x)\nSince profit is equally divided so\n12 = 4(12 \u2013 x) or x = 3. Thus B joined after 8 months.\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe ratio of the ages of Anil and his son at present is 7 : 3. Six years hence, the ratio of the ages of the Anil's wife and the son will be 2 : 1. Find the ratio of the present ages of Anil and his wife?\n\n### Options:\nA. 3:2\nB. 4:1\nC. 3:2\nD. Cannot be determined\nE. None of these\n\n### Answer:\nAnswer: Option D\nExplanation:\nLet the present ages of Anil and his son be 7x and 3x years respectively.\nLet the present age of the son's mother be m years.\n(m + 6) / (3x + 6) = 2/1\nm + 6 = 6x + 12 => m = 6x + 6\nRatio of the present ages of Anil and the son's mother = 7x / (6x + 6).\nThis cannot be found uniquely.\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA diagonal of a polygon is an segment between two non-adjacent vertices of the polygon. How many diagonals does a regular 20-sided polygon have?\n\n### Options:\nA. 875\nB. 170\nC. 1425\nD. 2025\nE. 2500\n\n### Answer:\nThere's a direct formula for this.\nNumber of diagonals in a regular polygon = [n*(n-3)] / 2, n = number of sides of the regular polygon.\nHere, n = 20.\nPlugging it in, we get 170 diagonals!\nAnswer (B).\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nGiven two sets A = {1,1,4,4,5,5} and B = {0,1}, if one number is chosen from each set at random, what is the probability that the sum of both numbers is an even number\n\n### Options:\nA. 1/4\nB. 1/8\nC. 1/7\nD. 1/2\nE. 3\n\n### Answer:\nOne way to look at it:\nThe number from set A can be ANYTHING.\nThe number selected from set B will determine whether the sum is odd or even.\nFor example, if a 4 is selected from set A, we need a 0 from set B to get an even sum.\nIf a 5 is selected from set A, we need a 1 from set B to get an even sum.\nAnd so on.\nSo, P(sum is even) = P(select ANY number from set AANDselect the number from set B that makes the sum even)\n= P(select ANY number from set A)xP(select the number from set B that makes the sum even)\n= 1x1/2\n= 1/2\n= D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain sum is invested at simple interest at 18% p.a. for two years instead of investing at 12% p.a. for the same time period. Therefore the interest received is more by Rs. 600. Find the sum?\n\n### Options:\nA. 7000\nB. 7029\nC. 2778\nD. 2800\nE. 5000\n\n### Answer:\nLet the sum be Rs. x.\n(x * 18 * 2)/100 - (x * 12 * 2)/100 = 600 => 36x/100 - 24x/100 =600\n=> 12x/100 = 600 => x = 5000.Answer:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many numbers with 2 different digits can be formed using only the odd digits?\n\n### Options:\nA. 10\nB. 20\nC. 40\nD. 60\nE. 120\n\n### Answer:\nOdd digits are 1, 3, 5, 7, 9.\nWe want 3 different digits.\nFirst digit can be chosen in 5 ways.\nSecond digit can be chosen in 4 ways.\nTotal ways = 5*4\n= 20\nHence option (B).\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA math teacher has 27 cards, each of which is in the shape of a geometric figure. Half of the cards are rectangles, and a third of the cards are rhombuses. If 8 cards are squares, what is the maximum possible number of cards that re circles.\n\n### Options:\nA. 9\nB. 10\nC. 11\nD. 12\nE. 13\n\n### Answer:\na square is a special kind of rhombus (sides are perpendicular)\na square is a special kind of rectangles (sides with same length)\nAmong the 27 cards with have:\n15 rectangles\n10 rhombus\n8 squares\nAmong the 15 rectangles, there could be 8 special ones (with sides of same length) that are squares. That lets at least 7 rectangles that are not square.\nAmong the 10 rectangles, there could be 8 special ones (with sides perpendicular) that are squares. That lets at least 2 rhombus that are not square.\nWe have 8 squares.\nSo the minimum different cards that represent a square, a rhombus or a rectangle is 2 + 7 + 8 = 17\nWhich means that the maximum number of circles that you could have is 27 - 17 = 10\nAnswer (B)\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nBy selling 175 apples, a shopkeeper gains the price of 25 apples. His gain per cent is\n\n### Options:\nA. 18.66%\nB. 17.66%\nC. 16.66%\nD. 15.66%\nE. 14.66%\n\n### Answer:\nSuppose S.P of 175 apples = Rs 175\nTherefore, Gain = Rs 25 => C.P = Rs 150\nGain % = 25/150 x 100 = 16.66%\nGain = 16.66%\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich number need to add to 172835 to get a number exactly divisible by 136?\n\n### Options:\nA. 27\nB. 25\nC. 26\nD. 21\nE. 24\n\n### Answer:\n172835 / 136 = 1270 and reminder = 115.\n136-115 = 21\nSo, the next number divisible by 115 is 21 places in front of 172835\nWhich means 21 + 172835 =172856\n21 should be added to 172835\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train speeds past a pole in 15 sec and a platform 100 m long in 25 sec, its length is?\n\n### Options:\nA. 228 m\nB. 150 m\nC. 276 m\nD. 255 m\nE. 212 m\n\n### Answer:\nLet the length of the train be x m and its speed be y m/sec.\nThen, x/y = 15 => y = x/15\n(x + 100)/25 = x/15 => x\n= 150 m.\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA salesman sold twice as much pears in the afternoon than in the morning. If he sold 360 kilograms of pears that day, how many kilograms did he sell in the morning and how many in the afternoon?\n\n### Options:\nA. 120\nB. 140\nC. 240\nD. 320\nE. 100\n\n### Answer:\nLet x be the number of kilograms he sold in the morning.Then in the afternoon he sold 2x kilograms. So, the total is\nx+2x=3x. This must be equal to 360.\n3x=360\nx=360/3\nx=120\nTherefore, the salesman sold 120 kg in the morning and 2*120=240 kg in the afternoon.\nAnswer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn the manufacture of a certain product, 4 percent of the units produced are defective and 4 percent of the defective units are shipped for sale. What percent of the units produced are defective units that are shipped for sale?\n\n### Options:\nA. 0.125%\nB. 0.2%\nC. 0.16%\nD. 1.25%\nE. 2.0%\n\n### Answer:\nPercent of defective produced = 4%\nPercent of the defective units that are shipped for sale = 4%\nPercent of units produced are defective units that are shipped for sale = (4/100)*(4/100)*100%\n= (16/10000)*100%\n= (16/100)%\n= .16 %\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf p and r are integers, and p^2 = 20r, then r must be divisible by which of the following?\n\n### Options:\nA. 2\nB. 4\nC. 5\nD. 7\nE. 14\n\n### Answer:\nAns: D\nSolution: for p to be an int 20 r must be whole square of a number.\n20r= 5*2*2*r\nto make it whole square we need 5\nso r can must be divisible by 5y where y is itself a whole square.\nso C is the ans\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average age of 30 boys of a class is equal to 14 yrs. When the age of the class teacher is included the average becomes 15 yrs. Find the age of the class teacher.\n\n### Options:\nA. 40 yrs\nB. 42 yrs\nC. 45 yrs\nD. 46 yrs\nE. 47 yrs\n\n### Answer:\nThe average age of 30 boys of a class is equal to 14 yrs:\ni.e Sum of all boys:30*14\ninclude class teacher:31 candidates in a class\n& avg age is:15 yr\ni.e. sum of all:31*15(include class teacher)=465\nso,the age of the class teacher:465-420=45yr\nanswer will be 45 yrs\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nCalculate 85184 \u00f7 ? = 352\n\n### Options:\nA. 241\nB. 242\nC. 244\nD. 247\nE. 240\n\n### Answer:\nAnswer\nLet 85184 \u00f7 X = 242\nThen X = 85184/242 = 352.\nOption: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train 240 m long passed a pole in 24 sec. How long will it take to pass a platform 750 m long?\n\n### Options:\nA. 78sec\nB. 83sec\nC. 95sec\nD. 99sec\nE. 100sec\n\n### Answer:\nSpeed = 240/24 = 10 m/sec.\nRequired time = (240 + 750)/10 = 99 sec.\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nEach child has 2 pencils and 13 Skittles. If there are 8 children, how many pencils are there in total?\n\n### Options:\nA. 16\nB. 12\nC. 18\nD. 22\nE. 08\n\n### Answer:\n2*8=16.Answer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAvinash covers a distance of 8km in 50 minutes. If he covers 3km distance in 2/5th of time then, What speed should he maintain to cover the remaining distance in the remaining time?\n\n### Options:\nA. 15 Kmph\nB. 17 Kmph\nC. 18 Kmph\nD. 19 Kmph\nE. 20 Kmph\n\n### Answer:\nTotal distance = 8 Km\nTotal time = 50 Km\nTime taken to cover the distence of 3 Km = 50*2/5 = 20 min = 1/3 hours\nRemaining distance = 8 - 3 = 5 Km\nRequired speed = 5/1/3 = 15 Kmph\nA)\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 18 is 15 percent of 20 percent of a certain number, what is the number?\n\n### Options:\nA. 9\nB. 36\nC. 40\nD. 600\nE. 400\n\n### Answer:\nLet the certain number be x.\n=> (15/100)*(20/100)*x = 18;\n300x=18*10000;\n3x = 1800;\nx=1800/3\n=> x=600;\nAns is (D).\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man spends Rs. 1600 per month on an average for the first three months, Rs 1550 for next four months and Rs. 1800 per month for the last five months and saves Rs . 7600 a year. What is his average monthly income?\n\n### Options:\nA. 2000\nB. 2010\nC. 2100\nD. 2200\nE. 2300\n\n### Answer:\nTotal expenditure for the first 3 months = 3 \u00d7 1600 = 4800\nTotal expenditure for 4 months = 4 \u00d7 1550 = 6200\nTotal expenditure for 5 months = 5 \u00d7 1800 = 9000\nTotal expenditure and saving (which is income for one year)\n= 4800 + 6200 + 9000 + 7600 = Rs. 27600\nSo, Average monthly income = 27600/12 = Rs. 2300\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\na, b, c, d, and e are five consecutive numbers in increasing order of size. Deleting one of the five\nnumbers from the set decreased the sum of the remaining numbers in the set by 20%. Which one of\nthe following numbers R was deleted?\n\n### Options:\nA. a\nB. b\nC. c\nD. d\nE. e\n\n### Answer:\na+b+c+d+e => 1+2+3+4+5=15\n20%*15= 3 =>C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA and B invests Rs.6000 and Rs.12000 in a business. After 4 months, A withdraws half of his capital and 2 months later, B withdraws one-third of his capital. In what ratio should they share the profits at the end of the year?\n\n### Options:\nA. 32:99\nB. 8:21\nC. 32:45\nD. 34:89\nE. 35:21\n\n### Answer:\nA : B\n(6000*4)+(3000*8) : (12000*6)+(9000*6)\n48000 : 126000\n8 : 21\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nConvert 30miles into yards?\n\n### Options:\nA. 25630 yards\nB. 35200 yards\nC. 52800 yards\nD. 42560 yards\nE. 41520 yards\n\n### Answer:\n1 mile = 1760 yards\n30 miles = 30*1760 = 52800 yards\nAnswer is C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFor integers U and V, when U is divided by V, the remainder is odd. Which of the following must be true?\n\n### Options:\nA. At least one of U and V is odd\nB. The sum U + V is odd\nC. U and V share no common factors other than 1\nD. UV is odd.\nE. U is odd\n\n### Answer:\nAt least one of U and V is odd\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf A:B = 1/2: 1/3 B:C = 1/2:1/3 then A:B:C?\n\n### Options:\nA. 9:6:6\nB. 9:6:8\nC. 9:6:2\nD. 9:6:4\nE. 9:6:1\n\n### Answer:\nA:B = 1/2:1/3 = 3:2\nB:C = 1/2:1/3 = 3:2\n--------------------\nA:B:C = 9:6:4\nAnswer:D:\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA car covers a distance of 624 km in 4 hours. Find its speed?\n\n### Options:\nA. 104\nB. 277\nC. 156\nD. 269\nE. 213\n\n### Answer:\n624/4 = 156 kmph\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train covers a certain distance at a speed of 150kmph in 4 hours. To cover the same distance in 2 hours, it must travel at a speed of\n\n### Options:\nA. 700km/hr\nB. 600km/hr\nC. 500km/hr\nD. 400km/hr\nE. 300km/hr\n\n### Answer:\nExplanation:\nDistance = 150\u00d74 = 600km\nRequired speed = (600/2) = 300km/hr\nAnswer: Option E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe parameter of a square is equal to the perimeter of a rectangle of length 18 cm and breadth 10 cm. Find the circumference of a semicircle whose diameter is equal to the side of the square. (Round off your answer to two decimal places)?\n\n### Options:\nA. 22.51\nB. 22.0\nC. 22.15\nD. 22.17\nE. 22.63\n\n### Answer:\nLet the side of the square be a cm.\nParameter of the rectangle = 2(18 + 10) = 56 cm Parameter of the square = 56 cm\ni.e. 4a = 56\na = 14\nDiameter of the semicircle = 15 cm\nCircimference of the semicircle\n= 1/2(\u00e2\u02c6\u008f)(14)\n= 1/2(22/7)(14) = 308/14 = 22 cm to two decimal places\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAn old man distributed all the gold coins he had to his two sons into two different numbers such that the difference between the squares of the two numbers is 25 times the difference between the two numbers. How many coins did the old man have?\n\n### Options:\nA. 24\nB. 26\nC. 30\nD. 25\nE. 40\n\n### Answer:\nLet the number of coins one son got be x and the number of coins another got be y. Total = x + y.\nx^2 - y^2 = 25(x - y) --> x + y = 25.\nAnswer: D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn the first 10 overs of a cricket game, the run rate was only 4.6. What should be the run rate in the remaining 40 overs to reach the target of 282 runs?\n\n### Options:\nA. 4.25\nB. 5.9\nC. 6.25\nD. 7\nE. 7.5\n\n### Answer:\nRequired run rate = 282 - (4.6x 10) =\t236 236/40= 5.9\nB)\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSum of 24 odd numbers is?\n\n### Options:\nA. 572\nB. 573\nC. 574\nD. 575\nE. 576\n\n### Answer:\nsum of 1st n odd no.s = 1+3+5+7+... = n^2\nso, Sum of 1st 24 odd numbers = 24^2 = 576\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nKanul spent $80000 in buying raw materials, $30000 in buying machinery and 20% of the total amount he had as cash with him. What was the total amount?\n\n### Options:\nA. $135656\nB. $137500\nC. $134446\nD. $123265\nE. $124564\n\n### Answer:\nLet the total amount be x\nthen, (100-20)% of x = 80000+30000\n80% of x = 110000\n80x/100 = 110000\nx = $1100000/8\nx = $137500\nAnswer is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere is one highland where planes get fuel. A plan can cover the half of the world with full tank. A plane can transfer fuel from one plane to the other in the air. How many planes are required to make one plane cover the entire world once. Starting point of the travel is the Highland and coming back to the same Highland. All the other planes giving fuels to this Plane should also come back to the same highland and they don't have to cover the entire world.\n\n### Options:\nA. 2\nB. 3\nC. 4\nD. 5\nE. 6\n\n### Answer:\nDivide the world as 6 parts.\nTo cover 1/6 th of the distance 1/3 rd of fuel is required.\n1 plane, B, can start in same direction of target flight say A.\nIt can travel 1/6 th of the distance and give 1/3rd of fuel to A and return home with 1/3rd fuel. Now A can cover 4/6th world with that full tank.\nLet C and D start from home at opposite direction.\nLet C cover 1/6th dist and give 1/3rd fuel to D. Now D travels 1/3 rd more distance and meets A and gives 1/3rd fuel. Both are now 1/6th distance away from home. Let E take fuel and bring one plane home and F take fuel and bring home A. Now excluding A.. 5 supporting planes are required.\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\na printer number the page of a book starting with 1 and uses 3189 digits in all How many pages dose the book have ?\n\n### Options:\nA. 1000\nB. 1074\nC. 1075\nD. 1080\nE. None of these\n\n### Answer:\nSolution\nNo of digits in 1-digit page nos. = 1 * 9 = 9 .\nNo of digits in 2-digit page nos. = 2 * 90 = 180.\nNo of digits in 3-digit page nos. = 3 * 900 = 2700 .\nNo of digits in 4-digit page nos. = 3189 - (9 + 180 + 2700) = 3189 - 2889 = 300.\n\u2234 N0. of pages with 4-digit page nos. = (300/4) =75\nHence, total number of pages = (999 + 75) = 1074 .\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many numbers from 10 to 10000 are exactly divisible by 9?\n\n### Options:\nA. 900\nB. 1000\nC. 1110\nD. 1200\nE. 1400\n\n### Answer:\n10/9 = 1 and 10000/9 = 1111 ==> 1111 - 1 = 1110. Therefore 1110\nAnswer : C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf w is three times larger than n , and if 2n+3 is 20% of 25, what is the value of ?\n\n### Options:\nA. 1\nB. 2\nC. 3\nD. 6\nE. 12\n\n### Answer:\nThen the wordings of question are misleading. Moreover, it'd also be a bad way to convey w=4n, if it really wanted to convey so.\nFrom other questions that I have seen, proper wordings could be:\nIf w is three times as large as n\nOR simply,\nIf w is three times n.C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA survey was sent to 60 customers, 7 of whom responded. Then the survey was redesigned and sent to another 72 customers, 9 of whom responded. By approximately what percent did the response rate increase from the original survey to the redesigned survey?\n\n### Options:\nA. 2%\nB. 7%\nC. 14%\nD. 28%\nE. 63%\n\n### Answer:\nRate of first survey = 7/60\nRate of second survey = 9/72\n% Response rate increase (9/72-7/60)/(7/60) = 7%\nAnswer is B = 7%\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nDivide Rs.32000 in the ratio 1:9?\n\n### Options:\nA. 12000, 20000\nB. 12000, 200098\nC. 12000, 20007\nD. 3200, 28800\nE. 12000, 20001\n\n### Answer:\n1/10 * 32000 = 3200\n9/10 * 32000 = 28800\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf {g} denote the remainder when 3g is divided by 2 then which of the following is equal to 1 for all positive integers g?\nI. {2g+1}\nII. {2g}+1\nIII. 2{g+1}\n\n### Options:\nA. I only\nB. II only\nC. I and II\nD. III only\nE. II and III\n\n### Answer:\nC - I and II\n3g/2 = 0 or 1\nI just substituted 1 in the equations and solved.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe function f is defined for all positive integers n by the following rule. f(n) is the number of positive integers each of which is less than n and has no positive factor in common with n other than 1. If p is any prime, number then f(p)=\n\n### Options:\nA. p-1\nB. p-2\nC. (p+1)/2\nD. (p-1)/2\nE. 2\n\n### Answer:\np is a prime, all positive numbers less than p have no common factors with p (except common factor 1). So there would be p-1 such numbers (as we are looking number of integers less than p).\nFor example: if p=7 how many numbers are less than 7 having no common factors with 7: 1, 2, 3, 4, 5, 6 --> 7-1=6.\nAnswer: A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat would be the local minimum for the function represented as f(x,y) = x2 +ay+y2 -3x ?\n\n### Options:\nA. (1,1)\nB. (2,-1)\nC. (-1,1)\nD. (2,2)\nE. (3,2)\n\n### Answer:\nf(x,y) = x2 + ay + y2 - 3x\n= 4 - a + 1 - 6\n= -a-1\nSo the above value will be the minimum if u check for all other options also. therefore, the answer is (2,-1)\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are 3 bags, in 1st there are 9 Mangoes, in 2nd 8 apples & in 3rd 6 bananas. There are how many ways you can buy one fruit if all the mangoes are identical, all the apples are identical, & also all the Bananas are identical?\n\n### Options:\nA. 648\nB. 432\nC. 23\nD. 2 to the power(23)-1\nE. 25\n\n### Answer:\nSince bags are different so it should be 9+8+6=23\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nNew town is straight to the north of New york. A high way M runs from newtown making an angle of 61 degree south east. from newyork there is also an high way N which runs Northeast 61 degrees. If high ways M and N are straight then findout the acute angle made at their intersection point.\n\n### Options:\nA. 56degree\nB. 57degree\nC. 58degree\nD. 59degree\nE. 50degree\n\n### Answer:\nthe acute angle must be 58 degree . taking north-south as reference axis . from center M is at an angle of 61degree near south and N is at an angle of 61degree from north .therefore, 180-61-61 gives 58degree\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich of the following is a prime number ?\n\n### Options:\nA. 33\nB. 81\nC. 97\nD. 93\nE. none\n\n### Answer:\nClearly, 97 is a prime number\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat number should replace the question mark?\n100, 93, 79, 53, ?.\n\n### Options:\nA. 30\nB. 36\nC. 32\nD. 41\nE. 44\n\n### Answer:\nA\n30\nThe sequence progresses \u20137, \u201314, \u201321, \u201328.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n1 Decade ago, Karthik\u2019s mother was quadrice older than her son. After one decade, the mother will be two times older than her son. The current age of Karthik is?\n[Decade = 10 Years; quadrice= 4 times]\n\n### Options:\nA. 20 years\nB. 60 years\nC. 80 years\nD. 40 years\nE. 10 years\n\n### Answer:\nA\n20 years\nLet Karthikh\u2019s age 10 years ago be A year\nHis mother\u2019s age 1 decade ago = 4A\n(4A + 10) + 10 = 2 (A + 10 +10)\n2A = 20 or A =10\nCurrent age of Karthikh = (A + 10)\n= 20 years\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTanks A and E are each in the shape of a right circular cylinder. The interior of tank A has a height of 10 meters and a circumference of 8 meters, and the interior of tank E has a height of 8 meters and a circumference of 10 meters. The capacity of tank A is what percent of the capacity of tank E?\n\n### Options:\nA. 75%\nB. 80%\nC. 100%\nD. 120%\nE. 125%\n\n### Answer:\nB.\nFor A, r=8/2pi. Its capacity = (4pi)^2 * 10= 160pi\nFor E, r=10/pi. Its capacity = (5pi)^2 *8 = 200pi\nA/E = 160pi/200pi = 0.8=B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nToday John is 3 times older than Mark. If in 13 years, John will be one year younger than twice the age of Mark on that day, how old is Mark today?\n\n### Options:\nA. 12\nB. 33\nC. 36\nD. 38\nE. 39\n\n### Answer:\ntoday +13yrs\nJ =3M 3M+13\nM M+13\nGiven after 13yrs john will be 1 year younger than twice mark's age\ni.e 3M+13 = 2(M+13)-1\nM=12\nAnswer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 20 men can build a wall 56 meters long in 6 days , what length of a similar wall can be built by 35 men in 3 days?\n\n### Options:\nA. 44\nB. 48\nC. 45\nD. 47\nE. 49\n\n### Answer:\nLet the required length be x meters\nMore men, More length built (Direct proportion)\nLess days, Less length built (Direct Proportion)\nMen 20:35 and Days 6:3::56:x\nTherefore (20 x 6 x (X))=(35 x 3 x 56)\nx=(35x3x56)/120=49\nHence, the required length is 49 m.\nAnswer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nEvaluate: 6502.5 + 650.25 + 65.025 + 6.5025 + 0.65025\n\n### Options:\nA. 6819.59775\nB. 6981.59775\nC. 7224.92775\nD. 6198.59775\nE. 6891.59775\n\n### Answer:\n6502.5\n650.25\n65.025\n6.5025\n+ 0.65025\n---------------\n7224.92775\nAnswer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJava House charges $4.25 for a cup of coffee that costs a total of $3.85 to make. Cup'O'Joe charges $4.80 for a cup that costs $4.65 to make. If Java House sells 55,000 cups of coffee, how many must Cup'O'Joe sell to make at least as much in total gross profit as its competitor does?\n\n### Options:\nA. 7,858\nB. 8,301\nC. 14,667\nD. 63,840\nE. 146,667\n\n### Answer:\nJava: Profit/Cup = 4.25-3.85 = 0.4\n: No of Cups = 55,000\n: Gross Profit = 55,000*0.4 = 22,000\nJoe: Profit/Cup = 0.15\n: Gross Profit = 22,000\n: No of Cups = 22,000/0.15 = 220,000/1.5 (only closes is 146,667)\nAnswer E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe speed at which a man can row a boat in still water is 15 kmph. If he rows downstream, where the speed of current is 3 kmph, what time will he take to cover 120 metres?\n\n### Options:\nA. 22 seconds\nB. 65 seconds\nC. 24 seconds\nD. 12 seconds\nE. 21 seconds\n\n### Answer:\nSpeed of the boat downstream\n= 15 + 3 = 18 kmph\n= 18 * 5/18 = 5 m/s\nHence time taken to cover 60 m\n= 120/5 = 24 seconds.\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 854 in 4 years. The sum is?\n\n### Options:\nA. 299\nB. 217\nC. 698\nD. 277\nE. 161\n\n### Answer:\nS.I. for 1 year = (854 - 815) = Rs. 39\nS.I. for 3 years = 39 * 3 = Rs. 117\nPrincipal = (815 - 117) = Rs. 698.Answer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA, B and C started a business with capitals of Rs. 8000, Rs. 10000 and Rs. 12000 respectively. At the end of the year, the profit share of B is Rs. 3500. The difference between the profit shares of A and C is?\n\n### Options:\nA. 621\nB. 1400\nC. 236\nD. 600\nE. 211\n\n### Answer:\nExplanation:\nRatio of investments of A, B and C is 8000 : 10000 : 12000 = 4 : 5 : 6\nAnd also given that, profit share of B is Rs. 3500\n=> 5 parts out of 15 parts is Rs. 3500\nNow, required difference is 6 - 4 = 2 parts\nRequired difference = 2/5 (3500) = Rs. 1400\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n150 is increased by 40%. Find the final number.\n\n### Options:\nA. 200\nB. 210\nC. 180\nD. 190\nE. 220\n\n### Answer:\nFinal number = Initial number + 40%(original number) = 150 + 40%(150) = 150 + 60 = 210.\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTom, who has 50 math questions, will get 7 points per question if he chooses a correct answer. If he chooses a wrong answer to a question or skips one, he will lose 3 points per question. Then, which of the following can be the score if he solves all the 50 questions?\n\n### Options:\nA. 190\nB. 193\nC. 194\nD. 195\nE. 196\n\n### Answer:\nLet x be the correctly answered questions. y be the wrongly answered/ skipped ones.\nWe have x + y = 50;\nScore = 7x-3y\n3x+3y = 150; 7x-3y = Score;\n==> 10x = 150+Score;\ncheck for answer choices where 150+Score is divisible by 10\nChoice (A) 190 fits the equation !\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe first three terms of a proportion are 4, 12 and 16. The fourth term is?\n\n### Options:\nA. 22\nB. 28\nC. 27\nD. 36\nE. 48\n\n### Answer:\n(12*16)/4 = 48\nAnswer:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the price of gold increases by 50%, find by how much the quantity of ornaments must be reduced, so that the expenditure may remain the same as before?\n\n### Options:\nA. 331/3%\nB. 332\nC. 333\nD. 335\nE. 400\n\n### Answer:\nExplanation:\n100\n150\n------\n150-------50\n100-------? => 331/3%\nA)\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA jeep takes 9 hours to cover a distance of 480 Km. how much should the speed in Kmph be maintained to cover the same direction in 3/2th of the previous time?\n\n### Options:\nA. 48 Kmph\nB. 52 Kmph\nC. 35 Kmph\nD. 63 Kmph\nE. 65 Kmph\n\n### Answer:\nTime = 9\nDistance = 480\n3/2 of 9 hours = 9 * 3/2 = 13.5 Hours\nRequired speed = 480/13.5 = 35 Kmph\nC)\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe area of a parallelogram is 288sq m and its altitude is twice the corresponding base. Then the length of the base is?\n\n### Options:\nA. 15\nB. 9\nC. 16\nD. 14\nE. 12\n\n### Answer:\n2x * x = 288 => x\n= 12\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a man lost 4% by selling oranges at the rate of 72 a rupee at how many a rupee must he sell them to gain 44%?\n\n### Options:\nA. 41\nB. 48\nC. 49\nD. 44\nE. 43\n\n### Answer:\n96% ---- 72\n144% ---- ?\n96/144 * 72 = 48\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nCuboid volume and Base area are 144 m^3 and 18m^3 respectively.Find the height of a cuboid?\n\n### Options:\nA. 5m\nB. 12m\nC. 6m\nD. 8m\nE. 10m\n\n### Answer:\nHeight of the cuboid=Volume* Base area\n=144/18\n=8 metre\nAnswer is option D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA, B and C enter into a partnership by investing Rs. 15000, Rs.21000 and Rs.27000 respectively. At the end of 8 months, B receives Rs.1260 as his share. Find the share of A.\n\n### Options:\nA. Rs. 600\nB. Rs. 1620\nC. Rs. 1080\nD. Rs. 900\nE. None of these\n\n### Answer:\nExplanation:\nRatio of capital of A, B and C\n= 15000 : 21000 : 27000\n= 5 : 7 : 9\nLet the total profit be Rs. x.\nThen, B's share = Rs. 7x/21 = Rs. x/3\nBut x/3 = 1260\n=> x = 3780\nHence, the total profit = Rs. 3780\nA's share = Rs.[(5/21) \u00d7 3780] = Rs. 900\nAnswer: Option D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the sum of all possible solutions to |x + 3|^2 + |x + 3| = 20 ?\n\n### Options:\nA. -1\nB. 6\nC. 7\nD. 12\nE. 14\n\n### Answer:\nDenote |x + 3| as y: y^2 + y = 20 --> y = -5 or y = 4. Discard the first solution since y = |x + 3|, so it's an absolute value and thus cannot be negative.\ny = |x + 3| = 4 --> x = 7 . The sum = 7.\nAnswer: C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average (arithmetic mean) of 8 numbers is Z, and one of the numbers is 14. If 14 is replaced with 28, then what is the new average (arithmetic mean) in terms of Z?\n\n### Options:\nA. Z + 1/2\nB. Z + 7/4\nC. Z + 2\nD. Z + 4\nE. 2Z + 1\n\n### Answer:\n(8z\u221214+28)/8\nOr, (8z+14)/8\nOr, (4z+7)/4\nOr, z+7/4\nSo, correct answer will be (B) z+7/4\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a recent election, Ms. Robbins received 7,000 votes cast by independent voters, that is, voters not registered with a specific political party. She also received 20 percent of the votes cast by those voters registered with a political party. If N is the total number of votes cast in the election and 50 percent of the votes cast were cast by independent voters, which of the following represents the number of votes that Ms. Robbins received?\n\n### Options:\nA. 0.06N + 3,200\nB. 0.1N + 7,000\nC. 0.4N + 7,200\nD. 0.1N + 8,000\nE. 0.06N + 8,000\n\n### Answer:\nI will go with option B\nAccording to question 50 percent of total votes (N) cas were cast by independent voters. This implies 50 percent of N are voters that belong to political party. And she received 7000 votes from independent voters and 20 percent from registered voters (i.e 0.2 * 0.5 * N = 0.1N). Hence total votes = 7000 + 0.1N ....option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe sum of first five prime numbers is:\n\n### Options:\nA. 11\nB. 18\nC. 26\nD. 28\nE. 35\n\n### Answer:\nExplanation:\nRequired sum = (2 + 3 + 5 + 7 + 11) = 28.\nNote: 1 is not a prime number.\nDefinition: A prime number (or a prime) is a natural number that has exactly two distinct natural number divisors: 1 and itself.\nANSWER IS D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf x > 0.3, which of the following could be the value of x?\n\n### Options:\nA. \u221a0.005\nB. \u221a0.0005\nC. \u221a0.3\nD. \u221a0.006\nE. \u221a0.007\n\n### Answer:\nAnswer : C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich one of the following is the common factor of (47^43 + 43^43) and (47^47 + 43^47) ?\n\n### Options:\nA. (2+56)\nB. (47+43)\nC. (3+7)\nD. (4+9)\nE. (12+19)\n\n### Answer:\nExplanation:\nWhen n is odd, (x^ + a^n) is always divisible by (x + a).\nEach one of (47^43 + 43^43) and (47^47 + 43^47) is divisible by (47 + 43).\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA number is doubled and 5 is added. If the resultant is trebled, it becomes 105. What is that number?\n\n### Options:\nA. 12\nB. 29\nC. 27\nD. 15\nE. 99\n\n### Answer:\nExplanation:\nLet the number be x.\nTherefore,\n3(2x + 5) = 105\n6x + 15 = 105\n6x = 90\nx = 15\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA, B and C rent a pasture. If A puts 10 oxen for 7 months, B puts 12 oxen for 5 months and C puts 15 oxen for 3 months for grazing and the rent of the pasture is Rs. 210, then how much amount should C pay as his share of rent?\n\n### Options:\nA. 54\nB. 45\nC. 25\nD. 15\nE. 55\n\n### Answer:\nA : B : C\n=10\u00d77:12\u00d75:15\u00d73\n=2\u00d77:12\u00d71:3\u00d73\n=14:12:9\nAmount that C should pay\n=210\u00d79/35=6\u00d79=54\nAnswer is A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA reduction of 30% in the price of oil enables a house wife to obtain 5kgs more for Rs.800, what is the reduced price for kg?\n\n### Options:\nA. s.42\nB. s.46\nC. s.48\nD. s.41\nE. s.34\n\n### Answer:\n800*(25/100) = 240 ---- 5\n? ---- 1 => Rs.48\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhen a number is divided by 13, the remainder is 6. When the same number is divided by 7, then remainder is 1. What is the number ?\n\n### Options:\nA. 243\nB. 253\nC. 312\nD. 432\nE. None of these\n\n### Answer:\nExplanation:\nTake 243\n243 \u00f7 7 = 34, remainder = 5\nHence this is not the answer\nTake 312\n312 \u00f7 7 = 44, remainder = 4\nHence this is not the answer\nTake 253\n253 \u00f7 7 = 36, remainder = 1.\n253 \u00f7 13 = 19, remainder = 6\nThis satisfies both the conditions given in the question. Hence it is the answer.\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nBoth Robert and Alice leave from the same location at 7:00 a.m. driving in the same direction, but in separate cars. Robert drives 30 miles per hour while Alice drives 50 miles per hour. After 6 hours, Alice\u2019s car stops. At what time will Robert\u2019s car reach Alice\u2019s car?\n\n### Options:\nA. 1 p.m.\nB. 3 p.m.\nC. 4 p.m.\nD. 7 p.m.\nE. 9 p.m.\n\n### Answer:\n7:00 am so 6 hours later is 1:00 pm\nIn six hours, Robert will have driven 6*30 = 180 miles\nIn six hours, Alive will have driven 6*50 = 300 miles\nSo Robert needs 300-180 = 120 miles do catch Alice up.\nSo at 30 mph, he will need 2 hours\n1:00 pm + 6 hours = 7:00 pm\nANS : D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many ways are there to award a gold, silver and bronze medal to 15 contending teams?\n\n### Options:\nA. 15 \u00d7 14 \u00d7 13\nB. 10!/(3!7!)\nC. 10!/3!\nD. 360\nE. 300\n\n### Answer:\nwe clearly know that there can be only one winning team which deserves the gold medal. we can do the selection in 15 ways\nif gold medal is given to 1 of the teams then only possible 14 teams can be considered for silver medal. we can do selection in 14 ways\nsimilarly if gold and silver medals are awarded then only remaining 13 teams can be considered for a bronze medal. we can do the selection in 13 ways\nTotal number of ways to select the 3 possible medal winners = 15 * 14 * 13\nCorrect answer - A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMANO,INC recently conducted a survey and found that 100,000 of its customers live in rural areas. if the number of it customers who live in urban areas is 200 percents grater than the numbers of customers who live in rural areas, how many of MANO,INC customers live in urban areas ?\n\n### Options:\nA. 200,000\nB. 216,000\nC. 360,000\nD. 300,000\nE. 540.0\n\n### Answer:\nLet's say that we have a starting value of X...\n100% of X = X\n100% MORE than X = X + X = 2X\n200% MORE than X = X + 2X = 3X\n300% MORE than X = X + 3X = 4X\nEtc.\nHere, we're told that 100,000 customers live in rural areas and the number who live in urban areas is 200% GREATER than the number who live in rural areas. That means that the number who are in urban areas is 3 times the number in rural areas...\n3(100,000) = 300,000\nFinal Answer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA sells a bicycle to B at a profit of 50% and B sells it to C at a loss of 40%. Find the resultant profit or loss.\n\n### Options:\nA. -4%\nB. 5%\nC. -5%\nD. 6%\nE. -10%\n\n### Answer:\nThe resultant profit or loss = 50 - 40 - (50*40)/100 = -10%\nloss = 10%\nAnswer is E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe sum of money at compound interest amounts to thrice itself in 5 years. In how many years will it be 15 times itself?\n\n### Options:\nA. 8 years\nB. 9 years\nC. 10 years\nD. 25 years\nE. 3 years\n\n### Answer:\n100 ---- 300 --- 5\n600 --- 5\n900 ---5\n1200 ---5\n1500--- 5\n25 years\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe number of the members of a club is more than 50 and less than 80. When 5 people sit at a table, other people exactly divided to 8-people groups (8 people sit at a table) or 7-people groups (7 people sit at a table). If the members are divided to 9-people groups, how many people will be left?\n\n### Options:\nA. 4\nB. 5\nC. 6\nD. 7\nE. 8\n\n### Answer:\nThe number of members is 7k+5 = 8j+5\nThe only number in this range which satisfies this is 61.\n61/9 = 6(9) + 7\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe ratio of investments of two partners P and Q is 7:5 and the ratio of their profits is 7:10. If P invested the money for 8 months, find for how much time did Q invest the money?\n\n### Options:\nA. 11\nB. 10\nC. 18\nD. 16\nE. 12\n\n### Answer:\n7*5: 8*x = 7:10\nx = 16\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nBirbal is a witty trader who trade of a mystical fruit grown far in north. He travels from one place to another with three sacks which can hold 30 fruits each. None of the sack can hold more than 30 fruits. On his way, he has to pass through thirty check points and at each check point, he has to give one fruit for each sack to the authorities.\nHow many mystical fruits remain after he goes through all the thirty check points?\n\n### Options:\nA. 25 Fruits\nB. 20 Fruits\nC. 23 Fruits\nD. 21 Fruits\nE. 27 Fr5uits\n\n### Answer:\nA\n25 Fruits\nRemember we told you that Birbal is a witty trader. So his sole motive is to get rid of the sacks as fast as he can.\nFor the first sack:\nHe must be able to fill fruits from one sack to other two sacks. Assume that he is able to do that after M check points. Now to find M,\n(Space in first sack) M + (Space in second sack) M = (Remaining fruits in Third Sack) 30 \u2013 M\nM = 10\nThus after 10 checkpoints, Birbal will be left with only 2 sacks containing 30 fruits each.\nNow he must get rid of the second sack.\nFor that, he must fill the fruits from second sack to the first sack. Assume that he manages to do that after N checkpoints.\n(Space in First Sack) N = (Remaining fruits in second sack) 30 \u2013 N\nN = 15\nThus after he has crossed 25 checkpoints, he will be left be one sack with 30 fruits in it. He has to pass five more checkpoints where he will have to give five fruits and he will be left with twenty five fruits once he has crossed all thirty check points.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn the xy-coordinate system, if (m,n) and (m+2, n+k) are two points on the line perpendicular to x=2y+5, then k=?\n\n### Options:\nA. -5\nB. -8\nC. 2\nD. -4\nE. 1\n\n### Answer:\nthe slope= k/2\nthe line perpendicular to x=2y+5 or y=1/2x-5/2 has\na slope= -1/ (1/2) =-2 --->k/2=-2 --> k=-4\nAnswer is D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the rate percent when the simple interest on Rs.800 amount to Rs.160 in 4 Years?\n\n### Options:\nA. 5%\nB. 7%\nC. 8%\nD. 2%\nE. 1%\n\n### Answer:\n160 = (180*4*R)/100\nR = 5%\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nEach shelf of a bookcase contained 12 books. If the librarian took out 21 books and rearranged the remaining books so that all shelves but the last one contained 8 books and that last shelf contained 15 books, how many shelves does the bookcase have?\n\n### Options:\nA. 5\nB. 6\nC. 7\nD. 8\nE. 9\n\n### Answer:\nLet x be the number of shelves.\n12x - 21 = 8(x-1) + 15\n4x = 28\nx= 7\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the total number of prime numbers less than 60?\n\n### Options:\nA. 17\nB. 18\nC. 19\nD. 20\nE. 21\n\n### Answer:\nSolution\nPrime numbers less than 60 are\t=17.\n2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59\nTheir number is 17.\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf x/|y| = -2 which of the following must be true?\n\n### Options:\nA. x = -y\nB. x = y\nC. x = y^2\nD. x^2 =4* y^2\nE. x^3 = y^3\n\n### Answer:\nx/|y| = -2\nx= -2 |y|\nSquaring both sides\nx^2= (-2 |y|) ^2= 4*y^2\nD is the answer\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHCF of two numbers is 11 and the product of these numbers is 363, what is the the greater number?\n\n### Options:\nA. 28\nB. 31\nC. 33\nD. 35\nE. 38\n\n### Answer:\nThe numbers be 11a and 11b\n11a \u00d7 11b = 363\nab = 3\nco-primes with product 3 are (1, 3)\nHence the numbers with HCF 11 and product 363\n= (11 \u00d7 1, 11 \u00d7 3)\n= (11, 33)\nNumbers are 11 and 33\nThe greater number = 33\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the difference between the place value of 2 in the numeral 7889?\n\n### Options:\nA. 160\nB. 165\nC. 180\nD. 190\nE. 720\n\n### Answer:\nAnswer: Option 'E'\n800 - 80 = 720\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn the storage room of a certain bakery, the ratio of sugar to flour is 5 to 6, and the ratio of flour to baking soda is 10 to 1. If there were 60 more pounds of baking soda in the room, the ratio of flour to baking soda would be 8 to 1. How many pounds of sugar are stored in the room?\n\n### Options:\nA. 600\nB. 1200\nC. 1500\nD. 1600\nE. 2000\n\n### Answer:\nSugar:Flour = 5:6 = 25:30;\nFlour:Soda = 10:1 = 30:3;\nThus we have that Sugar:Flour:Soda = 25x:30x:3x.\nAlso given that 30x/(3x+60) = 8/1 --> x=80 --> Sugar = 25x = 2,000.\nAnswer: E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA child has 36 blue marbles and 10 red marbles, and he kept they into a bag. If he asks you to pick up 3 marbles, what is the probability that all the 3 marbles will be red?\n\n### Options:\nA. 1/253\nB. 2/253\nC. 3/253\nD. 1/153\nE. 2/153\n\n### Answer:\nThere are 10 red marbles in a group of 36 + 10 that is 46. Thus the probability of picking all 3 red marbles is: (10/46)(9/45)(8/44) = 2/253. The correct answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTo be undaunted is to be impervious, undisturbed and \u2018fearless\u2019.\n\n### Options:\nA. 2\nB. HH\nC. 28\nD. 28J\nE. 9J\n\n### Answer:\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn the set of positive integers from 1 to 60, what is the sum of all the odd multiples of 5?\n\n### Options:\nA. 180\nB. 185\nC. 190\nD. 160\nE. 165\n\n### Answer:\n1 - 60\n5 - 15 - 25 - 35 - 45 are valid multiples of 5. Add them\n5+15+25+35+45+55 =180\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are 24 students in Chad\u00e2\u20ac\u2122s class. He brought 26 cookies to pass out\nfor his birthday. How many cookies will each student get? Will there be\nany cookies left over?\n\n### Options:\nA. 1-9\nB. 1-7\nC. 2-8\nD. 1-2\nE. 3-10\n\n### Answer:\n26/24 = 1 R 2 Chad will give each student 1 cookie and there will be 2\ncookies left over\ncorrect answer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n23 people are there, they are shaking hands together, How many hand shakes possible, if they are in pair of cyclic sequence ?\n\n### Options:\nA. 20\nB. 77\nC. 66\nD. 88\nE. 11\n\n### Answer:\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe length of the bridge, which a train 150 metres long and travelling at 45 km/hr can cross in 30 seconds, is?\n\n### Options:\nA. 76 m\nB. 178 m\nC. 225 m\nD. 187 m\nE. 176 m\n\n### Answer:\nSpeed = [45 X 5/18] m/sec\n= [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (150 + x)/30 = 25/2\n=> 2(150 + x)= 750 => x = 225 m.\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the sum of natural numbers between 20 and 100\n\n### Options:\nA. 4800\nB. 4860\nC. 5000\nD. 5500\nE. 5550\n\n### Answer:\na = first number\nl = last number\nSn = n/2[a + l]\nbetween 20 and 100 numbers = 81 => 100 - 20 = 80 + 1 = 81\nSn = 81/2 \u00d7 120 = 81 \u00d7 60 = 4860\nB)\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average marks in mathematics scored by the pupils of a school at the public examination were 39. If four of these pupils who actually scored 5, 12, 15 and 19 marks at the examination had not been sent up, the average marks for the school would have been 44. Find the number of pupils sent up for examination from the school?\n\n### Options:\nA. 10\nB. 25\nC. 30\nD. 35\nE. 40\n\n### Answer:\n39x = 5 + 12 + 15 + 19 + (x \u00e2\u20ac\u201c 4)44\nx = 25\nANSWER B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA and B started a partnership business investing Rs. 20,000 and Rs. 15,000 respectively. C joined them with Rs. 20,000 after six months. Calculate B's share in total profit of Rs. 25,000 earned at the end of 2 years from the starting of the business?\n\n### Options:\nA. 7500\nB. 8500\nC. 9000\nD. 8000\nE. 9500\n\n### Answer:\nExplanation:\nA : B : C\n=20000\u00c3\u201424:15000\u00c3\u201424:20000\u00c3\u201418=20\u00c3\u20144:15\u00c3\u20144:20\u00c3\u20143=4\u00c3\u20144:3\u00c3\u20144:4\u00c3\u20143=4:3:3=20000\u00c3\u201424:15000\u00c3\u201424:20000\u00c3\u201418=20\u00c3\u20144:15\u00c3\u20144:20\u00c3\u20143=4\u00c3\u20144:3\u00c3\u20144:4\u00c3\u20143=4:3:3\nB's share = 25000\u00c3\u2014310=7500\nANSWER IS A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a class ,there are 15 boys and 10 girls .one student is selected at random. The probability that one girl is selected,is:\n\n### Options:\nA. 10/25\nB. 2/5\nC. 15/25\nD. 3/25\nE. 1/25\n\n### Answer:\nTotal number of students = 10+15= 25\nno.of girls in a class = 10\nprobability of one girl is selected = 10/25= 2/5\nAnswer is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA jogger running at 9 kmph along side a railway track is 240 metres ahead of the engine of a 120 metre long train running at 45 kmph in the same direction. In how much time will the train pass the jogger?\n\n### Options:\nA. 3.6 sec\nB. 18 sec\nC. 36 sec\nD. 72 sec\nE. None\n\n### Answer:\nCATEGORY\nFormulae\nExamples\nDIRECTIONS : Problems based on Trains.\n11.\tA train 280 m long, running with a speed of 63 km/hr will pass a tree in\nA. 15 sec.\nB. 16 sec.\nC. 18 sec.\nD. 20 sec.\nSolution\nSpeed\t= (63 x 5/18) m/sec\n= 35/2 msec\nTime taken\t= (280 x 2 /35)m/sec\n= 16 sec.\n12.\tA train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is ihe length of the train?\nA. 120 metres\nB. 180 metres\nC. 324 metres\nD. None of these\nSolution\n13.\tA jogger running at 9 kmph alongside a railway track is 240 metres ahead of the engine of a 120 metre long train running at 45 kmph in the same direction. In how much time will the train pass the jogger?\nA. 3.6 sec\nB. 18 sec\nC. 36 sec\nD. 72 sec\nSolution\nSpeed of train relative to jogger\t= (45 - 9) km/hr\n= 36 km/hr\n= (36 x 5/18) m/sec\n= 10 m/sec\nDistance covered\t= (240+120) m\n= 360 m\nTime taken\t= (360 / 10)sec\n= 36 sec.\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA shop owner professes to sell his articles at certain cost price but he uses false weights with which he cheats by 50% while buying and by 10% while selling. What is his percentage profit?\n\n### Options:\nA. 10.22%\nB. 20.22%\nC. 21.22%\nD. 50%\nE. Can't be calculated\n\n### Answer:\nThe owner buys 100kg but actually gets 150kg;\nThe owner sells 100kg but actually gives 90kg;\nProfit: (150-90)/90*100=50%\nAnswer: D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nI. x2 - x - 42 = 0,\nII. y2 - 17y + 72 = 0 to solve both the equations to find the values of x and y?\n\n### Options:\nA. If x < y\nB. If x > y\nC. If x \u2264 y\nD. If x \u2265 y\nE. If x = y or the relationship between x and y cannot be established.\n\n### Answer:\nI. x2 - 7x + 6x - 42 = 0\n=> (x - 7)(x + 6) = 0 => x = 7, -6\nII. y2 - 8y - 9y + 72 = 0\n=> (y - 8)(y - 9) = 0 => y = 8, 9\n=> x < y\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n225 metres long yard, 26 trees are palnted at equal distances, one tree being at each end of the yard. What is the distance between 2consecutive trees\n\n### Options:\nA. 10\nB. 12\nC. 14\nD. 16\nE. 18\n\n### Answer:\n26 trees have 25 gaps between them,\nRequired distance (225/25) = 10\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRs.630/- distributed among A,B and C such that on decreasing their shares by RS.10,RS.5 and RS.15 respectively, The balance money would be divided among them in the ratio 3:4:5. Then, A\u2019s share is:?\n\n### Options:\nA. Rs.160/-\nB. Rs.170/-\nC. Rs.180/-\nD. Rs.190/-\nE. Rs.200/-\n\n### Answer:\nA:B:C = 3:4:5\nTotal parts = 12\nA's share is = 3 parts\n12 -----> Rs.600/-\n3 -----> Rs.150/-\nA's total = 150 + 10 = Rs.160/-\nA)\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe length of a rectangle is reduced by 15%. By what % would the width have to be increased to maintain the original area?\n\n### Options:\nA. 10%\nB. 20%\nC. 17.6%\nD. 30%\nE. 35%\n\n### Answer:\nSol. Required change = (15*100)/(100-15)=17.6%\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nUse distributive property to solve the problem below:\nMaria bought 10 notebooks and 5 pens costing 3 dollars each.How much did Maria pay?\n\n### Options:\nA. 30 dollars\nB. 40 dollars\nC. 45 dollars\nD. 60 dollars\nE. 70 dollars\n\n### Answer:\nSolution\n3 \u00d7 (10 + 5) = 3 \u00d7 10 + 3 \u00d7 5 = 30 + 15 = 45 dollars\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOut of 9 persons, 8 persons spent Rs. 30 each for their meals. The ninth one spent Rs. 20 more than the average expenditure of all the nine. The total money spent by all of them was ?\n\n### Options:\nA. Rs.292.50\nB. Rs.292.56\nC. Rs.292.12\nD. Rs.292.27\nE. Rs.292.11\n\n### Answer:\nLet the average expenditure be Rs. x Then,\nTotal money spent = 9x = Rs. (9 x 32.5O) = Rs 292. 50\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJancy decided to save a certain amount of her monthly salary each month and her salary was unchanged from month to month. If Jancy s savings by the end of the year from these monthly savings were five times the amount she spent per month, what should be the fraction of her salary that she spent each month?\n\n### Options:\nA. 15/17\nB. 17/12\nC. 10/17\nD. 13/17\nE. 12/17\n\n### Answer:\nLet Jancy's monthly savings = S\nJancy's monthly pay = P\nJancy's monthly expenditure = P-S\nJancy's savings by the end of the year from these monthly savings were Five times the amount she spent per month\n12S = 5*(P-S)\n=>12/5 S = P-S\n=> P = 17/5 S\nJancy's monthly expenditure = P-S = 17/5S-S = 12/5S\nfraction of her salary that Jancy spent each month = 12/5S / 17/5S=P-S/P = 12/17. Answer is E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train running at the speed of 60 km/hr crosses a pole in 6 sec. What is the length of the train?\n\n### Options:\nA. 356\nB. 278\nC. 127\nD. 100\nE. 150\n\n### Answer:\nSpeed = 60 * 5/18 = 50/3 m/sec\nLength of the train = speed * time = 50/3 * 6 = 100 m\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA box contains 5 yellow balls and 6 black balls. One by one, every ball is selected at random without replacement. What is the probability that the fourth ball selected is black?\n\n### Options:\nA. 3/4\nB. 4/7\nC. 5/8\nD. 7/9\nE. 6/11\n\n### Answer:\nEach ball has an equal chance (1/11) of being selected fourth.\nThe probability that a black ball is selected fourth is 6/11.\nThe answer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJosh spends a total of $6.50 buying N items in the convenience store. If each of the items is either a 5 cents single bubblegum, or a 50 cents bubblegum pack, then N may be which of the following?\n\n### Options:\nA. 99\nB. 100\nC. 121\nD. 109\nE. 140\n\n### Answer:\nLet x be 0.05$ single bubblegum and y be the total 0.5$ packs ---> 0.05x+0.5y=6.5 ---> x+10y=130 ...(1)\nAlso, x+y=N ...(2)\nSolving 1 and 2 , we get, N = 130-9y ---> only value satisfied is when y = 1---> N = 130-9=121. C is the correct answer. Other options are not equal to multiples of 9 removed from 130.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA sum of money is to be distributed among A, B, C, D in the proportion of 6 : 2 : 4 : 3. If C gets $500 more than D, what is D's share?\n\n### Options:\nA. $2000\nB. $2500\nC. $3000\nD. $3600\nE. $4200\n\n### Answer:\nLet the shares of A, B, C and D be 6x, 2x, 4x and 3x respectively.\nThen, 4x - 3x = 500\nx = $500\nA's share = 6x = 6*$500 = $3000\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 5400 mn = k^4, where m, n, and k are positive integers, what is the least possible value of 3m + n?\n\n### Options:\nA. 11\nB. 18\nC. 20\nD. 45\nE. 33\n\n### Answer:\nk^4=5400\u2217mn\nk^4=3^3.2^3.5^2.mn\nIn order to make RHS a perfect power of 4, we require it to be multiplied by 3, 2 & 5^2\nmn=3.2.5^2\nmn = 150 = 10 * 15 (Least possible)\nAnswer = 3*10 + 15 = 45\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a,b ,and c are positive real numbers such that a(b+c) = 152, b(c+a) =162 , and c(a+b) = 170, then abc is\n\n### Options:\nA. a) 672\nB. b) 688\nC. c) 704\nD. d) 720\nE. e) 750\n\n### Answer:\nab+bc = 152 --------------------------------------1)\nbc+ba = 162---------------------------------------2)\nac+ab = 170---------------------------------------3)\nRe-writing equation 3 as follows:\nac+cb = 162 + 8\nac+cb = bc+ba + 8\nac = ba + 8 ............... (4)\nAdding (1)(4)\n2ac = 160\nac= 80\nabc has to be multiple of 80, only 720 fits in\nAnswer = D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the length of the longest pole which can be kept in a room 12 m long, 4 m broad and 3 m high?\n\n### Options:\nA. 22\nB. 17\nC. 66\nD. 13\nE. 57\n\n### Answer:\nd2 = 122 + 42 + 32 = 13\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n19 5 17 = x\n65 8 10 = y\nWhat will be the value of x + y?\n\n### Options:\nA. 189\nB. 129\nC. 69\nD. 169\nE. 179\n\n### Answer:\naccording to options units digit is 9\n7+1+1=9\n10 's place +10's place+ unit place=1+1+7=9\naccording to this 5+1+6=12\nso over all answer =129\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA, B and C enter into a partnership. They invest Rs. 40,000, Rs. 80,000 and Rs. 1,20,000 respectively. At the end of the first year, B withdraws Rs. 40,000, while at the end of the second year, C withdraws Rs. 80,000. IN what ratio will the profit be shared at the end of 3 years?\n\n### Options:\nA. 3:4:4\nB. 3:4:7\nC. 3:4:3\nD. 3:4:9\nE. 3:4:1\n\n### Answer:\nA:B:C = (40000 * 36) : (80000 * 12 + 40000 * 24) : (120000 * 24 + 40000 * 12)\n= 144:192:336\n= 3:4:7\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n3 friends A,B,C went for week end party to McDonald's restaurant and there they measure there weights in some order in 7 rounds. A, B, C, AB, BC, AC, ABC. Final round measure is 155 kg, then find the average weight of all the 7 rounds?\n\n### Options:\nA. 56\nB. 66\nC. 77\nD. 88\nE. 99\n\n### Answer:\nIts finally a easy one..haha\n(A+B+C+AB+BC+CA+ABC)/7 ...as given ABC=155\nso A+B+C also equal to 155 and AB+BC+CA=2ABC=(2*155)\nfinally..(155+2*155+155)/7=88.57\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich of the following will divide evenly into 347,406,520?\n\n### Options:\nA. 4\nB. 11\nC. 9\nD. 3\nE. 13\n\n### Answer:\nRule:\n4: Last two digits should be divisible by 4\nthe last two digits are 00, which are divisible by 4\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA palindrome is a number that reads the same front-to-back as it does back-to-front (e.g. 202, 575, 1991, etc.) p is the smallest integer greater than 300 that is both a prime and a palindrome. What is the sum of the digits of p?\n\n### Options:\nA. 3\nB. 4\nC. 5\nD. 6\nE. 7\n\n### Answer:\nGiven that p is smallest integer greater than 300 - assume there is a 3-digit that satisfies the above conditions. Let the number be xyx ; question asks us the values of 2x+y\nWe can straight away cross out options A) and D) - sum of digits 3 or 6 implies it is divisible by 3 ---> we know that p is a prime number\nComing to option B) 2x + y = 4 --> only x = 2 and y = 0 satisfy this equation ( x> 2 will never give sum of digits = 4) ; but 202 is divisible by 2 ; we know that p is a prime number\nSimilarly option C) 2x+y = 5 --> only x = 2 and y = 1 satisfy this equation ( x> 2 will never give sum of digits = 5) ; but 212 is divisible by 2 ; we know that p is a prime number\nTherefore answer option should be E ---> can be verified by taking 2x+y = 7 ---> x = 3 and y = 1 ; gives 313\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA cargo ship carrying four kinds of items, doohickies, geegaws, widgets, and yamyams, arrives at the port. Each item weighs 2, 11, 5, and 7 pounds, respectively, and each item is weighed as it is unloaded. If, in the middle of the unloading process, the product of the individual weights of the unloaded items equals 1,043,504,000 pounds, how many widgets have been unloaded?\n\n### Options:\nA. 2\nB. 3\nC. 4\nD. 625\nE. 208,700,800\n\n### Answer:\nWe need to know the number of widgets (which weigh 5 pounds each). The number of times that 5 divides the number is related to the number of times that 10 divides the number.\nWhen we divide 1,043,504,000 by 1000, we get 1,043,504,000 = 1,043,504 * 5^3 *2^3.\n1,043,504 is not divisible by 5, thus there are 3 widgets.\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere were 35 students in a hostel. If the number of students increases by 7, the expenses of the mess increase by Rs. 42 per day while the average expenditure per head diminishes by Re 1. Find the original expenditure of the mess.\n\n### Options:\nA. Rs. 480\nB. Rs. 520\nC. Rs. 420\nD. Rs. 460\nE. None of these\n\n### Answer:\nLet d be the average daily expenditure\nOriginal expenditure = 35 \u00d7 d\nNew expenditure = 35 \u00d7 d + 42\nNew average expenditure will be :\n(35 \u00d7 d + 42)/42 = d - 1\nOn solving, we get d = 12\nTherefore original expenditure = 35 \u00d7 12 = 420\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA started a business with an investment of Rs. 70000 and after 6 months B joined him investing Rs. 120000. If the profit at the end of a year is Rs. 52000, then the share of B is?\n\n### Options:\nA. 34500\nB. 24000\nC. 24098\nD. 23007\nE. 24098\n\n### Answer:\nRatio of investments of A and B is (70000 * 12) : (120000 * 6) = 7 : 6\nTotal profit = Rs. 52000\nShare of B = 6/13 (52000)\n= Rs. 24000\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSeven years ago the average age of a family of 2 members was 21 years. A child has been born. due to Which the average age of the family is 23 years today. What is the present age of the child?\n\n### Options:\nA. 10years\nB. 13years\nC. 15years\nD. 17years\nE. 20years\n\n### Answer:\nExplanation:\nAverage of the family of two numbers\n7 years ago = 21\n= (21+ 7) * 2 = 56 years\nAverage age of the family of three members at present = 23 years\n= 23 * 3 = 69 YEARS\nAge of child = 69 - 56 = 13 years\nAnswer: Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nCalculate the circumference of a circular field whose radius is 5 centimeters.\n\n### Options:\nA. 30 \u03c0 cm\nB. 80 \u03c0 cm\nC. 70 \u03c0 cm\nD. 50 \u03c0 cm\nE. 10 \u03c0 cm\n\n### Answer:\nCircumference C is given by\nC = 2\u03c0r = 2\u03c0*5 = 10 \u03c0 cm\ncorrect answer E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAjay marked the price of his goods 30% more than his C.P. He then sells 1/4th of his stock at a discount of 15%, and half of the stock at the marked price, and the rest at a discount of 30%. Find his gain percentage.\n\n### Options:\nA. 16.5%\nB. 15.375%\nC. 14.20%\nD. 13.37%\nE. None of these\n\n### Answer:\nIf C.P = 100, M.P = 130\nS.P = (1/4) x 110.5 + (1/2) x 130 + (1/4) x 91\nS.P = 27.625 + 65 + 22.75 = 115.375\nHence , Profit = 15.375%\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how many ways letters of the word CORPORATION be arranged?\n\n### Options:\nA. 125879\nB. 3326400\nC. 369\nD. 1698\nE. 8723\n\n### Answer:\nCORPORATION has 11 letters, out of which O repeated 3 times, R repeated 2 times. Hence total ways = 11! / (3!*2!) = 3326400 ways\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA student took 6 courses last year and received an average (arithmetic mean) grade of 100 points. The year before, the student took 5 courses and received an average grade of 80 points. To the nearest tenth of a point, what was the student\u2019s average grade for the entire two-year period?\n\n### Options:\nA. 79\nB. 89\nC. 95\nD. 90.91\nE. 97.2\n\n### Answer:\nLet the 6 courses that were taken last year be A1 , A2, A3 , A4 , A5 , A6\nA1+A2+A3+A4+A5+A6 = 100*6 = 600\nThe year before , the 5 courses be B1, B2 , B3 , B4 , B5\nB1+B2+B3+B4+B5 = 80*5 = 400\nStudent's average = (600+400)/11 = 90.91\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAccording to the direction on a can of frozen orange juice concentrate is to be mixed with 3 cans of water to make orange juice . How many 15 - ounce cans of the concentrate are required to prepare 200 6-ounce servings of orange juice?\n\n### Options:\nA. 20\nB. 34\nC. 50\nD. 67\nE. 100\n\n### Answer:\nOrange juice concentrate: water::1:3\ntotal quantity of orange juice = 200*6 = 1200 oz\nso Orange juice concentrate: water :: 300 oz:900 oz\nno. of 15 oz can = 300 oz/15 oz = 20\nAnswer A, 20 cans\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 20 men can build a wall 66 metres long in 4 days, what length of a similar can be built by 86 men in 8 days?\n\n### Options:\nA. 278.4 mtrs\nB. 378.4 mtrs\nC. 478.4 mtrs\nD. 488.4 mtrs\nE. 567.6 mtrs\n\n### Answer:\nIf 20 men can build a wall 66 metres long in 4 days,\nlength of a similar wall that can be built by 86 men in 8 days = (66*86*8)/(4*20) = 567.6 mtrs\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA number is increased by 20% and then decreased by 20%, the final value of the number is ?\n\n### Options:\nA. does not change\nB. decreases by 2%\nC. increases by 4%\nD. decreases by 4%\nE. None of these\n\n### Answer:\nHere, x = 20 and y = - 20\nTherefore, the net % change in value\n= ( x + y + xy/100)%\n= [20 - 20 + (20x - 20)/100]% or - 4%\nSince the sign is negative, there is a decrease in value by 4%.\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many keyboards do you need if you have to place 1024 keys into keyboards that each hold 32 keys?\n\n### Options:\nA. A)28\nB. B)30\nC. C)32\nD. D)34\nE. E)None of the above\n\n### Answer:\nSol.\n1024 keys of 32 each\n= 1024 / 32\n= 32\nAnswer : C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a certain mathematical activity, we start with seven cards, each with a different prime number written on it. These seven cards are randomly put into three boxes in the following way: one box must get four cards, one must get two, and one gets only one. Then, for each box, we find the product of all the cards in the box, and that\u2019s the \u201cnumber\u201d of the box. Then, we put those three numbers in order, from lowest to highest, and that is our set. How many different sets T can be created from this process?\n\n### Options:\nA. 35\nB. 105\nC. 210\nD. 420\nE. 630\n\n### Answer:\nT=7C4 * 3C2 = 105 Answer B.\n7C4 ways to choose 4 numbers for Box 1\n3C2 ways to choose 2 numbers for Box2\n1 way for Box 3 .\nevery combination will give a different product and can be arranged least to highest only in one way .B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA car averages 30 miles per hour for the first 5 hours of a trip and averages 42 miles per hour for the rest of the trip. If the average speed for the entire trip is 34 miles per hour, how many hours long is the trip?\n\n### Options:\nA. 6.5\nB. 7.5\nC. 8.5\nD. 9.5\nE. 10.5\n\n### Answer:\nLet T be the total time of the trip.\n30*5 + 42(T-5) = 34T\n8T = 210-150\nT = 7.5\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nCalculate 469158 x 9999 = ?\n\n### Options:\nA. 4586970843\nB. 4686970743\nC. 4691100843\nD. 4586870843\nE. 4691110842\n\n### Answer:\nAnswer\n469158 x 9999 = 469157 x (10000-1)\n= 4691580000 - 469158\n= 4691110842.\nOption: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAt what price must an article costing Rs.47.50 be marked in order that after deducting 10% from the list price. It may be sold at a profit of 25% on the cost price?\n\n### Options:\nA. 60.5\nB. 65.9\nC. 67.5\nD. 62.5\nE. 22.5\n\n### Answer:\nCP = 47.50\nSP = 47.50*(125/100) = 59.375\nMP*(90/100) = 59.375\nMP = 65.9\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 2^y = 4^(5x + 3) and 3^(x - 7) = 9^y, what is the value of x + y ?\n\n### Options:\nA. -10\nB. -5\nC. -4\nD. 3\nE. 7\n\n### Answer:\n2^y = 4^(5x + 3)\n2^y=2^2(5x+3)\ny=10x+6 ........... 1\n3^(x - 7) = 9^y\n3^(x-7)=3^2y\nx-7=2y ............. 2\nput value of y=10x+6 in eq 2\nx-7=2(10x+6)\nx-7=20x+12\n19x=-19\nx=-1\ntherefore, y= -10+6\ny=-4\nx+y= -1-4= -5\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man taking the census walks up to the apartment of a mathematician and asks him if he has any children and how old they are. The mathematician says \"I have three daughters and the product of their ages is 72.\" The man tells the mathematician that he needs more information, so the mathematician tells him \"The sum of their ages is equal to our apartment number.\" The man still needs more information so the mathematician tells him \"My oldest daughter has her own bed and the other two share bunk beds.\"\nHow old are his daughters?\n\n### Options:\nA. 5-2-3\nB. 6-4-4\nC. 9-5-4\nD. 8-3-3\nE. 7-2-2\n\n### Answer:\nHis daughters are 8, 3, and 3. The prime factorization of 72 is 2 * 2 * 2 * 3 * 3, so the possible ages are 2, 3, 4, 6, 8, 9, 12, and 18. Using the prime factorization and these numbers the only combinations of numbers that work for the first clue are:\n18, 2 and 2.\n9, 4 and 2.\n6, 6 and 2.\n6, 4 and 3.\n8, 3, and 3.\nSince he doesn't know the ages after this piece of information the sum of the three numbers must not be unique. The sum of 8, 3, and 3; and 6, 6, and 2 are the same. Now the final clue comes in handy. Since we know that the oldest daughter has her own bed it is likely that she has the bed to herself and is older than the other two so there ages are 8, 3, and 3 rather than 2, 6 and 6.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train covers a distance in 50 minutes, if it runs at a speed of 48kmph on an average. Find the speed at which the train must run to reduce the time of journey to 40 minutes.\n\n### Options:\nA. 70 km/hr\nB. 60 km/hr\nC. 10 km/hr\nD. 20 km/hr\nE. 30 km/hr\n\n### Answer:\nExplanation:\nWe are having time and speed given, so first we will calculate the distance. Then we can get new speed for given time and distance.\nLets solve it.\nTime = 50/60 hr = 5/6 hr\nSpeed = 48 mph\nDistance = S*T = 48 * 5/6 = 40 km\nNew time will be 40 minutes so,\nTime = 40/60 hr = 2/3 hr\nNow we know,\nSpeed = Distance/Time\nNew speed = 40*3/2 kmph = 60kmph\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the compound interest accrued on an amount of Rs.14,800 at 13.5% p.a at the end of two years. (Round off your answer to nearest integer?\n\n### Options:\nA. Rs.4268\nB. Rs.4290\nC. Rs.4566\nD. Rs.4266\nE. Rs.4208\n\n### Answer:\nCI = 14800{ [ 1 + 13.5/100]2 - 1 }\n= 14800 { [1 + 27/200]2 - 1\n= 14800 { 2 + 27/200}{27/200}\n= (74)[2 + 27/200](27) =\n1998[2 + 27/200] = 3996 + 269.73 = Rs.4266\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf (4x + y)/(x + 4y) = 2/3, then find the value of (x + 4y)/(4x + y).\n\n### Options:\nA. 3/8\nB. 3/4\nC. 3/2\nD. 3/6\nE. 3/8\n\n### Answer:\nExplanation:\nGiven, (4x + y)/(x + 4y) = 2/3\n=> 3(4x + y) = 2(x + 4y)\n=> 2x = y\n.: (x + 4y)/(4x + y) = x + 4(2x)/(4x + 2x) = 9x/6x = 3/2\nAnswer: Option C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA bus covers a distance of 12 km in 5 min. If it takes 5 sec to pass a telegraph post, then the length of the bus is?\n\n### Options:\nA. 120m\nB. 180m\nC. 240m\nD. 200m\nE. 280m\n\n### Answer:\nSpeed = (12/5 * 60) km/hr = (144 * 5/18) m/sec = 40 m/sec.\nLength of the bus = 40 * 5 = 200 m.\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA car covers a distance of 424 km in 6 \u00bd hours. Find its speed?\n\n### Options:\nA. 65.9 kmph\nB. 75.2 kmph\nC. 65.2 kmph\nD. 66.2 kmph\nE. 55.2 kmph\n\n### Answer:\n424/(13/2) = 424*2/13\n=65.2 kmph\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA computer program assigns consecutive numbers to the days of the week. Sunday is 1, Monday is 2, ..... and Saturday is 7. Every day, the computer program calculates the value of parameter D according to the following definition: D is the number of the day times the value of D on the previous day. If the computer calculated D to be 12 on Wednesday, what would be the value of D calculated on the following Saturday?\n\n### Options:\nA. 2140\nB. 2520\nC. 2960\nD. 3360\nE. 3710\n\n### Answer:\nOn Saturday, the value would be 7*6*5*12 = 2520\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the amount on Rs.8000 in 9 months at 20% per annum, if the interest being compounded quarterly?\n\n### Options:\nA. 1323\nB. 9261\nC. 2788\nD. 2999\nE. 1722\n\n### Answer:\nA = 8000(21/20)3 = 9261\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a flight of 600 km, an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by 200 km/hr and the time of flight increased by 30 minutes. The duration of the flight is?\n\n### Options:\nA. 1 hr\nB. 2 hr\nC. 6 hr\nD. 8 hr\nE. 7 hr\n\n### Answer:\nLet the duration of the flight be x hours. Then,\n600/x - 600/(x + 1/2) = 200\nx(2x + 1) = 3 2x2 + x - 3 = 0\n(2x + 3)(x - 1) = 0\nx = 1 hr.\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAt a certain restaurant, the ratio of the number of cooks to the number of waiters is 3 to 10. When 12 more waiters are hired, the ratio of the number of cooks to the number of waiters changes to 3 to 13. How many cooks does the restaurant have?\n\n### Options:\nA. 4\nB. 6\nC. 9\nD. 12\nE. 15\n\n### Answer:\nOriginally there were 3k cooks and 10k waiters.\n13k = 10k+12\nk=4\nThere are 12 cooks.\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf r and s are two different prime numbers, which of the following cannot be true?\n\n### Options:\nA. rs is odd.\nB. r + s is even.\nC. r + s is odd.\nD. rs is even.\nE. r/s is an integer\n\n### Answer:\nA prime number is a positive integer with exactly two distinct positive divisors: 1 and itself. So, a prime number cannot be a multiple of another prime number. Which makes option E not possible (r/s=integer means that r is a multiple of s).\n.\nAll other options are possible:\nA. rs is odd --> r=3 and s=5;\nB. r + s is even --> r=3 and s=5;\nC. r + s is odd --> r=2 and s=3;\nD. rs is even --> r=2 and s=3;\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRamu rides his bike at an average speed of 45 km/hr and reaches his desitination in four hours. Somu covers the same distance in five hours. If Ramu covered his journey at an average speed which was 9 km/hr less and Somu covered his journey at an average speed which was 10 km/hr more, then the difference in their times taken to reach the destination would be (in minutes).\n\n### Options:\nA. 65 minutes\nB. 66 minutes\nC. 56 minutes\nD. 69 minutes\nE. 46 minutes\n\n### Answer:\nDistance travelled by Ramu = 45 * 4 = 180 km\nSomu travelled the same distance in 5 hours.\nHis speed = 180/5 = 36 km/hr\nHence in the conditional case, Ramu's speed = 45 - 9 = 36 km/hr and Somu's speed = 36 + 10 = 46km/hr.\nTherefore travel time of Ramu and Somu would be 5 hours and 3.9 hours respectively. Hence difference in the time taken = 1.1 hours = 66 minutes.\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe maximum number of students among them 1001 pens and 910 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is:\n\n### Options:\nA. 91\nB. 37\nC. 99\nD. 277\nE. 19\n\n### Answer:\nExplanation:\nRequired number of students = H.C.F of 1001 and 910 = 9\nAnswer: A) 91\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhen the stock market opened yesterday, the price of a share of stock X was 10 1/2. When the market closed, the price was 11 1/4. Of the following, which is closest to the percent increase in the price of stock X?\n\n### Options:\nA. 0.5%\nB. 1.0%\nC. 6.7%\nD. 7.1%\nE. 7.5%\n\n### Answer:\nGeneral formula for percent increase or decrease, (percent change):\npercent=Change/Original\u2217100\nSo, the percent increase in the price of stock X is (45/4\u221221/2)/(2/12)\u2217100=50/7\nAnswer: D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSara's mother is 6 times older than Sara. Next year, however, she will be only 5 times older than her daughter. How old is Sara's mother.\n\n### Options:\nA. 24 years\nB. 25 years\nC. 26 years\nD. 27 years\nE. 28 years\n\n### Answer:\nAt the present,\nSara's age is x.\nSara's mother's age is y=6x.\nNext year,\nSara's age will be x+1.\nSara's mother's age will be y+1=5(x+1).\nFrom the two equations, we can calculate Sara's age:\ny=6x\ny+1=5 (x+1)\n6x+1=5x+5\n6x-5x=5-1\nx=4\nIf Sara is currently 4 years old, and her mother is 6 times older, then her age is\n6x=6\u00d74=24.\nANSWER: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train running at the speed of 70 km/hr crosses a pole in 9 sec. What is the length of the train?\n\n### Options:\nA. 227 m\nB. 150 m\nC. 167 m\nD. 175 m\nE. 187 m\n\n### Answer:\nSpeed = 70 * 5/18 = 175/9 m/sec\nLength of the train = speed * time = 175/9 * 9\n= 175 m\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA began business with Rs.45000 and was joined afterwards by B with Rs.27000. When did B join if the profits at the end of the year were divided in the ratio of 2:1?\n\n### Options:\nA. 1\nB. 6\nC. 7\nD. 8\nE. 2\n\n### Answer:\n45*12 : 27*x = 2: 1\nx = 10\n12 -10 = 2\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe number of new words that can be formed by rearranging the letters of the word 'ALIVE' is\n\n### Options:\nA. 277\nB. 668\nC. 119\nD. 177\nE. 121\n\n### Answer:\nNumber of words which can be formed\n= 5! - 1 = 120 - 1 = 119.\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOne copy machine can make 20 copies a minute, and a second copy machine makes 10 copies a minute. If the two copiers work together, how long would it take them to make 900 copies?\n\n### Options:\nA. 10 minutes\nB. 20 minutes\nC. 25 minutes\nD. 30 minutes\nE. 35 minutes\n\n### Answer:\nTotal work done by both machines in a minute = 20 + 10 = 30 copies\nTotal number of copies required = 900\nTime = 900/30 = 30 mins\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nhe two trains of lengths 400 m, 600 m respectively, running at same directions. The faster train can cross the slower train in 180 sec, the speed of the slower train is 48 km. then find the speed of the faster train?\n\n### Options:\nA. 76 Kmph\nB. 68 Kmph\nC. 87 Kmph\nD. 56 Kmph\nE. 10 Kmph\n\n### Answer:\nLength of the two trains = 600m + 400m\nSpeed of the first train = X\nSpeed of the second train= 48 Kmph\n1000/X - 48 = 180\n1000/x - 48 * 5/18 = 180\n50 = 9X - 120\nX = 68 Kmph\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the next number in this sequence, 1, 11, 21, 1211, 111221 , 312211 ?\n\n### Options:\nA. 1332123\nB. 1112321\nC. 2221313\nD. 1311222\nE. 3321233\n\n### Answer:\nD\nNext in sequence is 13112221.\nThis series describes each number that came before it:\n1 [One]\n11 [One One]\n21 [Two One(s)]\n1211 [One Two and One One(s)]\n111221 [One One, One Two, and Two One(s)]\n312211 [Three One(s), Two Two(s), and One One]\nThe next number in the series is:\n13112221 [One Three, One One, Two Two(s), Two One(s)]\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind avrg speed if a man travels at speed of 15km/hr up and 28km/hr dawn at an altitude of 230m.\n\n### Options:\nA. 25.8\nB. 19.5\nC. 18.0\nD. 12.2\nE. 29.8\n\n### Answer:\navg speed=2*x*y/(x+y)\n=2*15*28/(15+28)=19.5\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA trained covered x km at 30 kmph and another 2x km at 20 kmph. Find the average speed of the train in covering the entire 3x km.\n\n### Options:\nA. 22.5\nB. 99\nC. 24\nD. 66\nE. 887\n\n### Answer:\nTotal time taken = x/30 + 2x/20 hours\n= 2x/15 hours\nAverage speed = 3x/(2x/15) = 22.5 kmph\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n(0.76)(power 3) - (0.1)(power 3)/ (0.76)(power 2) + 0.076 + (0.1)(power 2) is:\n\n### Options:\nA. 0.66\nB. 0.68\nC. 0.96\nD. 0.69\nE. 0.76\n\n### Answer:\nGiven expression\n= (0.76) (power 3) - (0.1)(power 3) / (0.76)(power 2) + (0.76 x 0.1) + (0.1)(power 2)\n= a (power 3) - b(power 3) / a(power 2) + ab + b(power 2)\n= (a - b)\n= (0.76 - 0.1)\n= 0.66\nAnswer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJosh spends a total of $5.5 buying A items in the convenience store. If each of the items is either a 5 cents single bubblegum, or a 50 cents bubblegum pack, then A may be which of the following?\n\n### Options:\nA. 99\nB. 100\nC. 101\nD. 112\nE. 113\n\n### Answer:\nA items in the convenience store$5.5 = 550 cents\n550 = 50a + 5b\n=>110 = 10a + b\nb = 110 - 10a = 10(11-a)\nHence b is even and multiple of 10.\nPossible values of b:\nb = 10,20,30,40,50,60,70,80,90,100\na = 11,9,8,7,6,5,4,3,2,1\nThe total (a+b) is 21,29,38,47,56,65,74,83,92,101\nThe only option is 101. Hence C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf \"PROMPT\" is coded as QSPLOS ,then \"PLAYER\" should be\n\n### Options:\nA. FKSKJH\nB. DSKUIW\nC. SHOUSA\nD. QMBXDQ\nE. SUISDUH\n\n### Answer:\nExplanation:\n1st 3 letters are denoted by its next alphabet and the next 3 letters are denoted by its previous alphabets.\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA company produces 60000 bottles of water everyday. If a case can hold 5 bottles of water .How many cases are required by the company to hold its one day production\n\n### Options:\nA. 12000\nB. 4500\nC. 5000\nD. 8000\nE. 9000\n\n### Answer:\nNumber of bottles that can be held in a case = 5\nNumber of cases required to hold 60000 bottles = 60000/5=12000 cases.\nSo the answer is A =12000\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n16 men can do a piece of work in 16 days .4 days after they started the work, 8 more men joined them. How many days will they now take to complete the remaining work\n\n### Options:\nA. 7 days\nB. 8 days\nC. 9 days\nD. 10 days\nE. None of these\n\n### Answer:\nSolution:Work done by 1 man in 1 day=1/(16*16)\nWork completed by 16 men in 4 days= 4[1/(16*16)]*16=1/4\nRemaining work= 1- 1/4= 3/4\nTotal men now= 16+ 8=24\n24 men do 3/4 work\n=>24*number of days*Work done by 1 man in 1 day=3/4\n=>24*number of days* 1/(16*16)=3/4\n=>number of days=8 days\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThis topic is locked. If you want to discuss this question please re-post it in the respective forum.\nMatt and Peter can do together a piece of work in 20 days. After they have worked together for 12 days Matt stops and Peter completes the remaining work in 14 days. In how many days Peter complete the work separately.\n\n### Options:\nA. 26 days\nB. 27 days\nC. 23 days\nD. 35 days\nE. 24 days\n\n### Answer:\nTogether they complete the job in 20 days means they complete 12/20 of the job after 12 days.\nPeter completes the remaining (8/20) of the job in 14 days which means that the whole job(1) can be completed in X days.\n<=> 8/20->14 <=> X=14/(8/20)=35Thus the answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAverage of 13 results is 65. If the average of first six results is 61 and average of last six results is 59 Then find the seventh result?\n\n### Options:\nA. 120\nB. 123\nC. 125\nD. 128\nE. 130\n\n### Answer:\n125\nOption 'C'\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain school supplies store arranges pencils on display such that each of the six different colors of pencils, yellow, orange, green, red, blue, and purple are consecutive in a repeating pattern. If seven consecutively displayed pencils are purchased, what is the probability that two of the pencils\nare purple?\n\n### Options:\nA. 1/6\nB. 1/36\nC. 1/20\nD. 2/3\nE. 2/5\n\n### Answer:\nAfter yellow, orange, green, red, blue, and purple, the next pencil can be of any given six colours, therefore we have total six possibilites, out of which we need purple i.e. 1 therefore prob is 1/6.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA graph may be defined as a set of points connected by lines called edges. Every edge connects a pair of points. Thus, a triangle is a graph of 3 edges and 3 points. The degree of a point is the number of edges connected to it. For, example, a triangle is a graph with 3 points of degree 2 each. Consider a graph with 12 points. It is possible to reach any point from any through sequence of edges. The number of edges 'e' in the graph must satisfy the condition\n\n### Options:\nA. 11 \u2264 e \u2264 66\nB. 10 \u2264 e \u2264 66\nC. 11 \u2264 e \u2264 65\nD. 0 \u2264 e \u2264 11\nE. None\n\n### Answer:\nExplanation :\nThe least number of edges will be when one point is connected to each of the other 11 points, giving a total of 11 lines. One can move from any point to any other point via the common point.\nThe maximum edges will be when a line exists between any two points. Two points can be selected from 12 points in 12C2 i.e. 66 lines.\nAnswer : A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe remainder when A=1+3+3^2+3^3+..........+3^200 is divided 13.\n\n### Options:\nA. 12\nB. 7\nC. 0\nD. 5\nE. 3\n\n### Answer:\nA=1+3+3^2+3^3+..................+3^200\nIs a Geometric progression having common ratio as '3' and number of terms as '201'.\nSince Sum to n terms in GP = a(r^n-1)/(r-1)\nwhere a=First term and r =common ration\nHence,\n1*(3^201 -1 )/(3-1)\nRem of (3^201-1)/2 divided by 13\n3^201 -1 /26\nWKT, 3^3 = 27 = 26+1\n{(26+1)^67 - 1}/26\n{1-1}/26\n=>0.C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nPatrick is an avid star gazer and wants to make his own constellation. He is using a star chart that has 7 stars on it and decides that he will draw a continuous line using 3 of those 7 stars to make his constellation. There will be no closed shapes in his constellation. How many possible paths could his contstellation follow?\n\n### Options:\nA. 15\nB. 21\nC. 97\nD. 210\nE. 980\n\n### Answer:\nThis is a simple permutation calc\rPermutation calc is: n P r = n! / (n-r)! 4 P 3 = 7!/(7-3)! = 7x6x5x(4x3x2x1)/4!=7X6X5=210 Correct answer is D (210)\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSometime after 10:00 PM a murder took place. A witness claimed that the clock must have stopped at the time of the shooting. It was later found that the postion of both the hands were the same but their positions had interchanged. Tell the time of the shooting (both actual and claimed).\n\n### Options:\nA. 10:59 PM\nB. 11:59 PM\nC. 10:50 PM\nD. 10:52 PM\nE. 10:55 PM\n\n### Answer:\nActual time of shooting = 11:54 PM\nClaimed Time = 10:59 PM\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSix family members are seated around their circular dinner table. If only arrangements that are considered distinct are those where family members are seated in different locations relative to each other, and Michael and Bobby insist on sitting next to one another, then how many distinct arrangements around the table are possible?\n\n### Options:\nA. 48\nB. 56\nC. 64\nD. 72\nE. 80\n\n### Answer:\nLet's consider Michael and Bobby as one unit.\nThere are 5! possible arrangements of 5 units.\nAround a table, there would be repetitions of each arrangement, so we divide by 5.\nThen there are 4! arrangements around a circular table.\nFor each arrangement, Michael and Bobby can switch places, so we multiply by 2.\nThe number of arrangements is 4!*2 = 48.\nThe answer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average weight of a group of boys is 30 kg. After a boy of weight 39 kg joins the group, the average weight of the group goes up by 1 kg. Find the number of boys in the group originally ?\n\n### Options:\nA. 4\nB. 8\nC. 5\nD. 2\nE. 9\n\n### Answer:\nLet the number off boys in the group originally be x.\nTotal weight of the boys = 30x\nAfter the boy weighing 39 kg joins the group, total weight of boys = 30x + 39\nSo 30x + 39 + 31(x + 1) = > x = 8.\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo pipes A and B can separately fill a cistern in 10 and 15 minutes respectively. A person opens both the pipes together when the cistern should have been was full he finds the waste pipe open. He then closes the waste pipe and in another 4 minutes the cistern was full. In what time can the waste pipe empty the cistern when fill?\n\n### Options:\nA. 1/4\nB. 1/7\nC. 2/4\nD. 2/3\nE. 1/3\n\n### Answer:\n1/10 + 1/15 = 1/6 * 4 = 2/3\n1 - 2/3 = 1/3\n1/10 + 1/15 - 1/x = 1/3\nx = 8\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThree unbased coins are tossed. the probability of getting at most three T is ?\n\n### Options:\nA. 1/2\nB. 7/8\nC. 3/4\nD. 1/8\nE. 2/3\n\n### Answer:\nS={TTT,TTH,THT,HTT,THH,HTH,HHT,HHH}\nE be the event of getting at least two head is {TTT}\nP(E)=n(E)/n(S)=1/8\nAnswer(D)\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich of the following is equal to the value of 2^4 + 2^4 + 3^4 + 3^4 + 3^4 ?\n\n### Options:\nA. 2^5 + 3^10\nB. 2^5 + 3^9\nC. 2^5 + 3^8\nD. 2^5 + 3^5\nE. 2^5 + 3^7\n\n### Answer:\n2^4 + 2^4 + 3^4 + 3^4 + 3^4\n= 2 (2^4) + 3 (3^4)\n= 2^1 (2^4) + 3^1 (3^4)\n= 2^(1+4) + 3^(1+4)\n= 2^5 + 3^5\nAns: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nKamal bought a house, whose sale price was Rs. 8 lakh. He availed 20% discount as an early bird offer and then 10% discount due to cash payment. After that he spent 10% of the cost price in interior decoration and lawn of the house. At what price should he sell the house to earn a profit of 25%?\n\n### Options:\nA. Rs. 9 lakh\nB. Rs. 7.99 lakh\nC. Rs. 7.92 lakh\nD. Rs. 7 lakh\nE. None of These\n\n### Answer:\nSolution: Let the marked price be 100.\n100 == 20% \u2193(discount)==> 80 == 10% \u2193(discount)==> 72(CP) == 10% \u2191(interior)==> 79.2(Total CP)\nNow, selling price would be 25% above the Total cost price.\nSP = 79.2 + 25% of 79.2\nSP = 99\nNow, On comparing,\n100 ==> 800000\n99 ==> (800000/100) *99 ==> 7, 92,000\nSo,\nSP = Rs. 7, 92, 000.\nAnswer: Option C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nPresent ages of Abi and Suji are in the ratio of 5:4 respectively. Three years hence, the ratio of their ages will become 11:9 respectively. What is Suji's present age in years?\n\n### Options:\nA. 20\nB. 21\nC. 22\nD. 23\nE. 24\n\n### Answer:\npresent ages = 5x:4x\nThree hence =5x+3:4x+3\n5x+3:4x+3=11:9\nweget x=6\nsuji age is =4x=4*6=24\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the least number must be subtracted from 105829 so that remaining no.is divisible by 21?\n\n### Options:\nA. 7\nB. 10\nC. 20\nD. 32\nE. 35\n\n### Answer:\nOn dividing 105829 by 21 we get the remainder 10, so 10 should be subtracted\nAnswer is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nNine carpenters can individually complete a particular task in 3, 4, 5, and 7 hours, respectively. What is the maximum fraction of the task that can be completed in forty-five minutes if eight of the carpenters work together at their respective rates ?\n\n### Options:\nA. 11/15\nB. 3/5\nC. 11/30\nD. 47/135\nE. 5/9\n\n### Answer:\nFarmer A, B, C, and D\nA's rate: 1/3 job/hour\nB's rate: 1/4 job/hour\nC's rate: 1/5 job/hour\nD's rate: 1/7 job/hour\nBy intuition we know that the three fastest farmers are A B and C.\nAs such\n(1/3 + 1/4 + 1/5)*(8/9) = ?\n47/135 or (D)\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a camp, there is a meal for 120 men or 200 children. If 110 children have taken the meal, how many men will be catered to with remaining meal?\n\n### Options:\nA. 30\nB. 20\nC. 40\nD. 57\nE. 54\n\n### Answer:\nThere is a meal for 200 children.\n110 children have taken the meal.\nRemaining meal is to be catered to 90 children.\nNow, 200 children 120 men.\n90 children = (120/200)x 90 = 54 men.\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 sec. The speed of the train is?\n\n### Options:\nA. 28\nB. 50\nC. 99\nD. 121\nE. 81\n\n### Answer:\nSpeed of the train relative to man = 125/10 = 25/2 m/sec.\n= 25/2 * 18/5 = 45 km/hr\nLet the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr.\nx - 5 = 45 => x = 50 km/hr.\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWorking alone at their respective constant rates, A can complete a task in \u2018a\u2019 days and B in \u2018b\u2019 days. They take turns in doing the task with each working 2 days at a time. If A starts they finish the task in exactly 14 days. If B starts, they take a day more. How long does it take to complete the task if they both work together?\n\n### Options:\nA. 12\nB. 14\nC. 10\nD. 11\nE. 13\n\n### Answer:\nWork done by AB in a day = xy respectively.\nWhen A starts:\nNo. of days when A works = 8No. of days when B works = 6 \u2192 8x + 6y = 1\nWhen B starts:\nNo. of days when A works = 7No. of days when A works = 7 \u2192 7x + 7y = 1\nSolving the above two equations for xy\nx = 1/14 y = 1/14\n\u2192 Total work done by AB in a day = 1/14 + 1/14 = 2/28= 1/14\n\u2192 No. of days to complete the work when both work together =14\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMr X, a businessman, had income in the year 1995 such that he earned a profit of 20% on his investment in the business. In the year 1996 his investment was less by 2000 but still had the same income (Income = Investment + Profit) as that in 1995. Thus the per cent profit earned in 1996 increased by 6%. What was his investment in 1995?\n\n### Options:\nA. 100000\nB. 12500\nC. 42000\nD. Data inadequate\nE. None of these\n\n### Answer:\nLet the investment of X in 1995 be x.\n\u2234 Profit = x\u20445\n\u2234 Income = (x + x\u20445) = 6\u20445x\nInvestment of company X in 1996 would be (x \u2013 2000) From the question,\n(x - 2000) \u00d7 126\u2044100 = 6\u20445x \u21d2 x = 42000\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train travels at an average of 40 miles per hour for 4 hours and then travels at a speed of 60miles per hour for 2hours. How far did the train travel in the entire 6 hours?\n\n### Options:\nA. 100miles\nB. 150miles\nC. 200miles\nD. 250miles\nE. 300miles\n\n### Answer:\nTotal distance traveled = (40*4)+(70*2) = 160+140 = 300 miles\nAnswer is E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a sequence, each term is obtained by adding 7 to the preceding one. If the sum of the first 30 terms is equal to 705, what is the result of the addition of the first 40 terms?\n\n### Options:\nA. 2000\nB. 2250\nC. 2340\nD. 2400\nE. 2440\n\n### Answer:\na is first term and d = 7 since the preceding number is always greater than the previous one..\nNow 30th term is a+29(7).\nSum of n terms is n/2(first term + last term)and here we have to get sum of 30 terms , we get 30/2 ( a + a+203) = 705 ( given sum of 30 terms is 705)\n=> 15(2a+203) = 705\n=> 2a+203 = 47\n=> 2a=-156\n=> a = -78\nNow to get sum of first 40 terms , we need to get 40th term value i.e. -78+39(7) = 195.\nSum of first 40 terms = 40/2( -78 + 195) =2340 .\nHence option C is correct answer..\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn what time a sum of money double itself at 4% per annum simple interest?\n\n### Options:\nA. 33 1/8%\nB. 33 1/3%\nC. 33 7/3%\nD. 32 1/3%\nE. 25 %\n\n### Answer:\nP = (P*4*R)/100\nR = 25%\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain city with a population of 60,000 is to be divided into 11 voting districts , and no district is to have a population that is more than 10 percent greater than the population of any other district What is the minimum possible population that the least populated district could have ?\n\n### Options:\nA. a) 10,700\nB. b) 10,800\nC. c) 10,900\nD. d) 11,000\nE. e) 5,000\n\n### Answer:\nLet x = number of people in smallest district\nx*1.1 = number of people in largest district\nx will be minimised when the number of people in largest district is maximised\n10*x*1.1 = 11x = total number of people in other districts\nSo we have 11x + x = 60k\nx = 5,000\nAnswer : E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a tennis match if the first serve is not legal, that means a fault a second serve is allowed. Normally, 20 to 40 serves are required in a set of tennis match. At the end of a set, set summary stats reveal that first serves percentage was 63%. If m out of n were first serves then m + n is equal to\n\n### Options:\nA. 1.43n\nB. 1.53n\nC. 1.63n\nD. 2.63n\nE. 3.63n\n\n### Answer:\nm=n*(63/100)=63n/100\nso,\nm+n= 63n/100 + n\n= 163n/100\n= 1.63n\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf selling price is doubled, the profit triples. Find the profit percent:\n\n### Options:\nA. 66 2/3\nB. 100\nC. 105 1/3\nD. 120\nE. 150\n\n### Answer:\nLet C.P. be Rs. x and S.P. be Rx. y.\nThen, 3(y - x) = (2y - x) => y = 2x\nProfit = (y - x) = Rs. (2x - x) = Rs. x\nProfit % = x/x * 100 = 100%.\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf P is a prime number greater than 3, find the remainder when P^2 + 15 is divided by 12.\n\n### Options:\nA. 6\nB. 4\nC. 0\nD. 8\nE. 7\n\n### Answer:\nEvery prime number greater than 3 can be written 6N+1 or 6N-1.\nIf P = 6N+1, then P^2 + 15 = 36N^2 + 12N + 1 + 15 = 36N^2 + 12N + 12 + 4\nIf P = 6N-1, then P^2 + 15 = 36N^2 - 12N + 1 + 15 = 36N^2 - 12N + 12 + 4\nWhen divided by 12, it must leave a remainder of 4.\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the sum of all possible solutions to |x - 4|^2 + |x - 4| = 12 ?\n\n### Options:\nA. 3\nB. 4\nC. 5\nD. 6\nE. 7\n\n### Answer:\nDenote |x - 4| as y: y^2 + y = 12 --> y = -4 or y = 3. Discard the first solution since y = |x - 4|, so it's an absolute value and thus cannot be negative.\ny = |x - 4| = 3 --> x = 7 or x = 0. The sum = 7.\nAnswer: E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo trains are running in opposite directions with the same speed. If the length of each train is 120 m and they cross each other in 6 sec, then the speed of each train is?\n\n### Options:\nA. 30\nB. 31\nC. 72\nD. 25\nE. 24\n\n### Answer:\nLet the speed of each train be x m/sec.\nThen, relative speed of the two trains = 2x m/sec.\nSo, 2x = (120 + 120)/6 => x = 20\nSpeed of each train = 20 m/sec.\n= 20 * 18/5 =72km/hr.\nAnswer: Option C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA cistern can be filled by a tap in 4 hours while it can be emptied by another tap in 8 hours. If both the taps are opened simultaneously, then after how much time will the cistern get filled?\n\n### Options:\nA. 7.5\nB. 7.4\nC. 7.9\nD. 7.2\nE. 8.0\n\n### Answer:\nNet part filled in 1 hour = (1/4 - 1/9) = 1/8\nThe cistern will be filled in 8/1 hrs i.e., 8 hrs.Answer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA boy was asked to multiply a number by 22. He instead multiplied the number by 44 and got the answer 308 more than the correct answer. What was the number to be multiplied?\n\n### Options:\nA. 16\nB. 10\nC. 14\nD. 12\nE. 8\n\n### Answer:\nExplanation :\nLet the number be x\n22x + 308 = 44x\n=> 44x - 22x = 308\n=> 22x = 308\n=> x = 308/22 = 154/11 = 14\nAnswer : C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA 150 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train?\n\n### Options:\nA. 220 meter\nB. 225 meter\nC. 230 meter\nD. 350 meter\nE. None of these\n\n### Answer:\nExplanation:\nAs trains are running in opposite directions so their relative speed will get added\nSo, Relative speed = 120 +80 = 200 kmph\n= 200*(5/18) = 500/9 m/sec\nLet the length of other train is x meter then\nx+150 /9=500 /9\n=>x+150=500\n=>x=350\nSo the length of the train is 350 meters\nOption D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAn article is bought for Rs.675 and sold for Rs.900, find the gain percent?\n\n### Options:\nA. 33 1/8%\nB. 33 3/3%\nC. 33 1/3%\nD. 39 1/3%\nE. 33 4/3%\n\n### Answer:\n675 ---- 225\n100 ---- ? => 33 1/3%\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThree candidates contested an election and received 1136, 7636 and 12000 votes respectively. What percentage of the total votes did the winning candidate get?\n\n### Options:\nA. 46%\nB. 58%\nC. 74%\nD. 63%\nE. 68%\n\n### Answer:\nB\n12000/(1136 + 7636 + 12000) = 58%.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nCan you solve the alphametic?\nENLIST + SILENT + LISTEN = ANAGRAM\n\n### Options:\nA. 1816412\nB. 1416312\nC. 1516312\nD. 1216312\nE. 1116312\n\n### Answer:\nCorrect Answer : B\nassume numeric values for alphabetics. like a=0, b=1, c=2, c=3, d=4, e=5,...\nsolution\n547809+087549+780954 = 1416312\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average salary of all the workers in a workshop is Rs.8000. The average salary of 7 technicians is Rs.10000 and the average salary of the rest is Rs.6000. The total number of workers in the workshop is\n\n### Options:\nA. 20\nB. 21\nC. 22\nD. 23\nE. 14\n\n### Answer:\nSolution\nLet the toatl number of workers be x.\nThen 8000x=(10000 x 7) + 6000 (x -7)\nx= 14.\nAnswer E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA five-digit number divisible by 3 is to be formed using numerical 0, 1, 2, 3, 4 and 5 without repetition. The total number E of ways this can be done is:\n\n### Options:\nA. 122\nB. 210\nC. 216\nD. 217\nE. 225\n\n### Answer:\nWe should determine which 5 digits from given 6, would form the 5 digit number divisible by 3.\nWe have six digits: 0, 1, 2, 3, 4, 5. Their sum=15.\nFor a number to be divisible by 3 the sum of the digits must be divisible by 3. As the sum of the six given numbers is 15 (divisible by 3) only 5 digits good to form our 5 digit number would be 15-0={1, 2, 3, 4, 5} and 15-3={0, 1, 2, 4, 5}. Meaning that no other 5 from given six will total the number divisible by 3.\nSecond step:\nWe have two set of numbers:\n1, 2, 3, 4, 5 and 0, 1, 2, 4, 5. How many 5 digit numbers can be formed using these two sets:\n1, 2, 3, 4, 5 --> 5! as any combination of these digits would give us 5 digit number divisible by 3. 5!=120.\n0, 1, 2, 4, 5 --> here we can not use 0 as the first digit, otherwise number won't be any more 5 digit and become 4 digit. So, desired # would be total combinations 5!, minus combinations with 0 as the first digit (combination of 4) 4! --> 5!-4!=4!(5-1)=4!*4=96\n120+96=216=E\nAnswer: C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe ratio of the earnings of P and Q is 9 : 10. If the earnings of P increases by one-fourth and the earnings of Q decreases by one-fourth, then find the new ratio of their earnings?\n\n### Options:\nA. 3/6\nB. 3/2\nC. 3/9\nD. 3/1\nE. 3/5\n\n### Answer:\nLet the earnings of P and Q be Rs. 9x and Rs. 10x respectively.\nNew ration = [9x + 1/4(9x)]/[10x - 1/4(10x)]\n=> [9x(1 + 1/4)]/[10x(1 - 1/4)] = 9/10 * (5/4)/(3/4)\n=> 3/2.\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many of the positive divisors Q of 120 are also multiples of 4 not including 120?\n\n### Options:\nA. 3.\nB. 4.\nC. 5.\nD. 7.\nE. 8.\n\n### Answer:\n4,8,12,20,24,40,60. (7) is the answer\nOther way : factors of 120 = 2^3 * 3*5\nSeparate 2^2 ( which means 4)\nNow, calculate the number of other factors.\nQ=2*3*5 = total positive factors are 2*2*2 = 8\nThis 8 factors include 120\nSo subtract 1 from 8\nAns is 7=D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n25% of a number is more than 20% of 650 by 190. Find the number?\n\n### Options:\nA. 288\nB. 278\nC. 800\nD. 267\nE. 1280\n\n### Answer:\n(25/100) * X \u00e2\u20ac\u201c (20/100) * 650 = 190\n1/4 X = 320\nX = 1280\nAnswer:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn what time will a train 175 m long cross an electric pole, it its speed be 180 km/hr?\n\n### Options:\nA. 7.5\nB. 6.5\nC. 5.5\nD. 4.5\nE. 3.5\n\n### Answer:\nSpeed = 180 * 5/18 = 50 m/sec\nTime taken = 175/50 = 3.5 sec.\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA teacher will pick a group of 4 students from a group of 8 students that includes Lisa. If one of all the possible four-student groups is picked at random, what is the probability of picking a group that includes Lisa?\n\n### Options:\nA. 1/7\nB. 3/14\nC. 1/2\nD. 1/3\nE. 3/7\n\n### Answer:\nProbability = Favorable Outcomes / Total Outcomes\nTotal Outcomes= Total No. of ways of Picking Group of 4 out of 8 = 8C4 = 8! / (4! * 4!) = 70\nFavorable Outcomes= Total No. of ways of Picking Group of 4 out of 8 such that L is always in the group (i.e. we only have to pick remaining 3 out of remaining 7 as L must be there in group) = 7C3 = 35\nHence,Probability=35/70=1/2\nAnswer: Option C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf s,u, and v are positive integers and 2s=u+2v, which of the following must be true?\ni. u>v\nii. u is not equal to v\niii. s=u\n\n### Options:\nA. None\nB. I only\nC. II only\nD. III only\nE. II and III\n\n### Answer:\nNotice two things: 1. we are asked to find out which of the following MUST be true, not COULD be true and 2. s, u, and v are positive integers.\nGiven: 2s=2u+2v --> s=u+v. Now, since s, u, and v are positive integers then s is more than either u or v, so I is never true and III is always true. As for II: it's not necessarily true, for example 4=2+2. So, we have that only option I must be true.\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n90% of the population of a village is 36000. The total population of the village is?\n\n### Options:\nA. 26799\nB. 24000\nC. 26682\nD. 29973\nE. 40000\n\n### Answer:\nX * (90/100) = 36000\nX = 400 * 100\nX = 40000\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf n is a positive integer and the product of all integers from 1 to n, inclusive, is a multiple of 440, what is the least possible value of n?\n\n### Options:\nA. 10\nB. 11\nC. 12\nD. 13\nE. 14\n\n### Answer:\nis it 11 ?\n440 = 2 * 2 * 2 * 5 * 11\nso the least value forNcan be 11.\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are three places P, Q and R such that 3 roads connects P and Q and 4 roads connects Q and R. In how many ways can one travel from P to R?\n\n### Options:\nA. 32\nB. 75\nC. 12\nD. 51\nE. 47\n\n### Answer:\nNumber of ways in which one can travel from P to R\n=3\u00d74=12=3\u00d74=12\nAns: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how many different ways could couples be picked from 8 men and 5 women?\n\n### Options:\nA. 8\nB. 5\nC. 13\nD. 40\nE. 20\n\n### Answer:\nNumber of mens = 8\nNumber of womens = 5\nDifferent ways could couples be picked = 8c1 * 5c1 = 8 * 5 = 40 ways\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA boy goes to his school from his house at a speed of 3 km/hr and returns at a speed of 2 km/hr. If he takes 5 hours in going and coming. The distance between his house and school is?\n\n### Options:\nA. 7 km\nB. 3 km\nC. 6 km\nD. 9 km\nE. 2 km\n\n### Answer:\nAverage speed = (2 * 3 * 2) / (3 + 2)\n= 12/5 km/hr.\nDistance traveled = 12/5 * 5 = 12 km.\nDistance between house and school\n= 12/2\n= 6 km.\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nLine J has a y-intercept of 7 and passes through point (a,b). What is the slope of Line J in terms of a and b?\n\n### Options:\nA. (b-7)/a\nB. (a\u2212b)/6\nC. (6\u2212a)/b\nD. (6\u2212b)/a\nE. (b\u22126)/a\n\n### Answer:\nYou know that the line goes through point (a,b) and the y-intercept of 7 tells you that the line also goes through point (0,7).\nslope m = (y-y1)/(x-x1) = (b-7)/(a-0)\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe ages of 2 persons differ by 16 years. If 6 years ago the elder one be 3 times as old as the younger one, find the present age of younger person.\n\n### Options:\nA. 10\nB. 14\nC. 20\nD. 15\nE. 32\n\n### Answer:\nage of the younger person = x\nage of the elder person = x+16\n3(x-6) = x+16-6\nx= 14\nAnswer is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOf the 100 athletes at a soccer club, 40 play defense and 64 play midfield. If at least 20 of the athletes play neither midfield nor defense, the number of athletes that play both midfield and defense could be any number between\n\n### Options:\nA. 10 to 20\nB. 10 to 40\nC. 24 to 40\nD. 30 to 70\nE. 40 to 70\n\n### Answer:\nFirst of all notice that since only 40 athletes play defense, then the number of athletes that play both midfield and defense cannot possibly be greater than 40.Eliminate D and E.\n{Total} = {defense} + {midfield} - {both} + {neither}\n100 = 40 + 64 - {both} + {neither}\n{both} = {neither} + 4.\nSince the least value of {neither} is given to be 20, then the least value of {both} is 20+4=24.Eliminate A and B.\nAnswer: C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe sector of a circle has radius of 21 cm and central angle 135o. Find its perimeter?\n\n### Options:\nA. 23.9 cm\nB. 62.9 cm\nC. 91.5 cm\nD. 26.8 cm\nE. 16.8 cm\n\n### Answer:\nPerimeter of the sector = length of the arc + 2(radius)\n= (135/360 * 2 * 22/7 * 21) + 2(21)\n= 49.5 + 42\n= 91.5 cm\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn particular old age home, 60% are suffering from diabetic and at the same time 80% are suffering from blood pressure.If suppose 75% are suffering from diabetic,what percentage of old people suffering from blood pressure at the same old age home?\n\n### Options:\nA. 23\nB. 16\nC. 26\nD. 36\nE. 20\n\n### Answer:\ngiven : % of people suffering from diabetics = 60%; % of people suffering from blood pressure = 80% (ie ) 0.8\ntotal =75*100; Those who are suffering from diabetics= 75 - 60 = 15; Those who are suffering from blood pressure =\n100 - 80=20; so those who are suffering from blood pressure =0.8*20=16; Total number of people suffering from blood pressure = 20+16 = 36. Answer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe wages earned by Robin is 30% more than that earned by Erica. The wages earned by Charles is 60% more than that earned by Erica. How much percent is the wages earned by Charles more than that earned by Robin?\n\n### Options:\nA. 18.75%\nB. 23%\nC. 30%\nD. 50%\nE. 100%\n\n### Answer:\nLet wage of Erica = 10\nWage of Robin = 1.3*10 = 13\nWage of Charles = 1.6 *10 = 16\nPercentage by which wage earned by Charles is more than that earned by Robin = (16-13)/13 * 100%\n= 3/13 * 100%\n=23%\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the invalid no.from the following series 15, 17, 34, 105, 424, 2124, 12756\n\n### Options:\nA. 17\nB. 34\nC. 105\nD. 424\nE. 2124\n\n### Answer:\n2nd term = (1st term) * 1 + 1 = 15 *1 + 1 = 16.\n3rd term = (2nd term) * 2 + 2 = 16 * 2 + 2 = 34\n4th term = (3th term) *3 + 3 = 34 * 3 + 3 = 105\n5th term = (4th term) * 4 + 4 = 105 * 4 + 4 = 424\n6th term = (5th term) * 5 + 5 = 424 * 5 + 5 = 2125\n2nd term should 16 instead of 17.\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the odd man out\n1,25, 31,37, 127, 503,\n\n### Options:\nA. 503\nB. 37\nC. 31\nD. 1\nE. 25\n\n### Answer:\n25 is square of 5 which is a square number where as all others are prime numbers.\nANSWER:E\nCorrect Option:\tC) E . Answer : E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many minutes does it take John to type z words if he types at the rate of y words per minute?\n\n### Options:\nA. z/y\nB. y/x\nC. xy\nD. 60x/y\nE. y/(60x)\n\n### Answer:\ntime*rate=job --> time*y=z --> time=z/y.\nAnswer: A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many times the keys of a typewriter have to be pressed in order to write first 400 counting numbers?\n\n### Options:\nA. 2388\nB. 1092\nC. 2788\nD. 1192\nE. 1901\n\n### Answer:\nExplanation:\n1 to 9 = 9 * 1 = 9\n10 to 99 = 90 * 2 = 180\n100 to 400 = 301 * 3 = 903\n-----------\n1092\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average weight of 10 girls increases by 5 kg when a new girl comes in place of one of them weighing 50 kg. What might be the weight of the new girl?\n\n### Options:\nA. 90 kg\nB. 100 kg\nC. 95 kg\nD. 85 kg\nE. 92 kg\n\n### Answer:\nTotal weight increased = 10 x 5 kg = 50 kg.\nWeight of new person = 50 + 50 kg =100 kg\nAnswer : B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhen positive integer m is divided by positive integer x, the reminder is 7 and when positive integer n is divided by positive integer y, the reminder is 11. Which of the following E is a possible value for x + y?\nI. 18\nII. 19\nIII. 20\n\n### Options:\nA. I only\nB. II only\nC. E=III only\nD. II and III only\nE. None\n\n### Answer:\nTIP FOR SUCH QUESTIONS:Make Algebraic Equation in the beginning to understand how to proceed further. Then Start thinking the possible values of variables asked about\ni.e.When positive integer m is divided by positive integer x, the reminder is 7can be understood as\nm = ax +7which means thevalue of x must be greater than 7as the remainder 7 is possible only when the Divisor is bigger than the Remainder 7\ni.e. Min Value of x = 8\nAND\ni.e.When positive integer n is divided by positive integer y, the reminder is 11can be understood as\nn = by +11which means thevalue of y must be greater than 11as the remainder 11 is possible only when the Divisor is bigger than the Remainder 11\ni.e. Min Value of y = 12\ni.e. Minimum Value of x+y = 8+12 = 20\nHence III only can be True\nAnswer: Option\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSolve:-\n666 x 666 x 666 + 555 x 555 x 555 = ?(666 x 666 - 666 x 555 + 555 x 555)\n\n### Options:\nA. 888\nB. 333\nC. 555\nD. 1221\nE. 889\n\n### Answer:\nGiven Exp. = (a3 + b3) = (a + b) = (666 + 555) = 1221(a2 - ab + b2)\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a,b, and c are consecutive positive integers and a>b>c, what can be the value of (a^2-b^2)(b^2-c^2)?\n\n### Options:\nA. 100\nB. 110\nC. 121\nD. 132\nE. 143\n\n### Answer:\n(a^2-b^2)(b^2-c^2) = (a+b)*(a-b)*(b+c)*(b-c) = (a+b)*(-1)*(b+c)*(-1) = (a+b)*(b+c)\nTherefore, the product should have factors with a difference of 2.\n143 = 11*13, so this is a possible value for the original expression.\nThe answer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe smallest ratio out of 1:1, 2:1, 1:3,4:1 and 3:1 is?\n\n### Options:\nA. 1:1\nB. 1:3\nC. 2:1\nD. 3:1\nE. 4:1\n\n### Answer:\n1/1=1\n1/3=0.333\n2/1=2\n3/1=3\n4/1=4\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA, B and C play a cricket match. The ratio of the runs scored by them in the match is A:B = 2:4 and B:C = 2:5. If the total runs scored by all of them are 100, the runs scored by B are?\n\n### Options:\nA. 20.23\nB. 20.13\nC. 30.93\nD. 25\nE. 10.93\n\n### Answer:\nA:B = 2:4\nB:C = 2:5\nA:B:C = 4:8:20\n8/32 *100 = 25\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThree people (1 couple and 1 single) are seated at random in a row of 6 chairs. What is the probability that the couple does not sit together?\n\n### Options:\nA. 2/3\nB. 4/5\nC. 2/7\nD. 3/5\nE. 5/12\n\n### Answer:\nThe total number of arrangements of 3 people is 6*5*4 = 120\nLet's think of the couple as a single unit.\nThe number of arrangements when the couple sits together is 5*4*2 = 40.\nNote that we multiply by 2 because the couple can switch places with each other.\nThe number of ways the couple won't sit together is 120 - 40 = 80\nP(couple won't sit together) = 80/120 = 2/3\nThe answer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAn employee\u2019s annual salary was increased 30%. If her old annual salary equals $30,000 , what was the new salary?\n\n### Options:\nA. $28,000\nB. $25,000\nC. $20,000\nD. $35,000\nE. $39,000\n\n### Answer:\nOld annual salary = $30,000\nSalary increase = 30%.\nOriginal salary = $30,000 *30/100\n= $9000\nnew salary = $30,000+$9000\n=$39,000\nHence E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAt a local supermarket, a box of cereal usually costs 22 dollars. This week, the supermarket sells the box of cereal for 11 dollars. How much money will you save if you buy this cereal at this supermarket?\n\n### Options:\nA. 11 dollars\nB. 13 dollars\nC. 14 dollars\nD. 12 dollars\nE. 10 dollar\n\n### Answer:\nSolution:\nIn this situation, there is a decrease in the price.\nSaving = 22 - 11 = 11 dollars\nOption A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA customer asks the clerk for a paintbrush and a bucket of whitewash for a total price of B dollars. If the paintbrush costs 700 cents less than twice the price of a bucket of whitewash, what is the price of half a bucket of whitewash in dollars?\n\n### Options:\nA. (B + 200)/2.\nB. (B + 2)/6.\nC. (2B + 200)/3.\nD. (B + 2)/3.\nE. (B - 2)/6.\n\n### Answer:\nP = 2w - 200\nthus total price in cents as given should be\n2w-200 +w = 100B\n3w - 200 = 100 B\n3w = 100 B+200\n3w =b+2 (in dollars)\nw/2 = (b+2)/6\nAns:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how many different ways can the letters of the word 'OPTICAL' be arranged so that the vowels always come together?\n\n### Options:\nA. 520\nB. 720\nC. 890\nD. 870\nE. 1098\n\n### Answer:\nThe word 'OPTICAL' contains 7 different letters.\nWhen the vowels OIA are always together, they can be supposed to form one letter.\nThen, we have to arrange the letters PTCL (OIA).\nNow, 5 letters can be arranged in 5! = 120 ways.\nThe vowels (OIA) can be arranged among themselves in 3! = 6 ways.\nRequired number of ways = (120 x 6) = 720.\nANSWER B 72\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo numbers are in the ratio 3 : 4. If their L.C.M. is 72. what is sum of the numbers?\n\n### Options:\nA. 42\nB. 56\nC. 76\nD. 84\nE. 85\n\n### Answer:\nExplanation:\nLet the numbers be 3x and 4x\nLCM of 3x and 4x = 12x (Since LCM of 3 and 4 is 12. Hence LCM of 3x and 4x is 12x)\nGiven that LCM of 3x and 4x is 72\n=> 12x = 72\n=> x = 72/12 = 6\nSum of the numbers\n= 3x + 4x\n= 7x\n= 7 x 6 = 42\nAnswer: Option A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf sushi rows 27 km upstream and 81 km down steam taking 9 hours each, then the speed of the stream\n\n### Options:\nA. 12 kmph\nB. 13 kmph\nC. 22 kmph\nD. 20 kmph\nE. 15 kmph\n\n### Answer:\nSpeed upstream = 27/9 = 3 kmph\nSpeed down stream = 81/3 = 27 kmph\nSpeed of stream = \u00bd (27-3) = 12 kmph\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA student took 6 courses last year and received an average (arithmetic mean) grade of 100 points. The year before, the student took 5 courses and received an average grade of 60 points. To the nearest tenth of a point, what was the student\u2019s average grade for the entire two-year period?\n\n### Options:\nA. 79\nB. 89\nC. 95\nD. 81.81\nE. 97.2\n\n### Answer:\nLet the 6 courses that were taken last year be A1 , A2, A3 , A4 , A5 , A6\nA1+A2+A3+A4+A5+A6 = 100*6 = 600\nThe year before , the 5 courses be B1, B2 , B3 , B4 , B5\nB1+B2+B3+B4+B5 = 60*5 = 300\nStudent's average = (600+300)/11 = 81.81\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA computer program generates a sequence of numbers a1, a2, a3,... such that a1=1, a2=2, and ak = a(k-1) + 3ak-2 for 2 < k < n for n=20. Find a5.\n\n### Options:\nA. 10\nB. 24\nC. 28\nD. 32\nE. 38\n\n### Answer:\na1=1\na2=2\na3=3*2-2=4\na4=3*4-2=10\na5=3*10-2=28\n28\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n3 boys and 7 girls can complete John work in 10 days . But 4 boys and 6 girls need 8 days to complete the same work . In how many days will 10 girls complete the same work?\n\n### Options:\nA. 30 days\nB. 35 days\nC. 40 days\nD. 50 days\nE. 60 days\n\n### Answer:\nWork done by 4 boys and 6 girls in 1 day = 1/8\nWork done by 3 boys and 7 girls in 1 day = 1/10\nLet 1 man does m work in 1 day and 1 woman does w work in 1 day. The above equations can be written as\n4m + 6w = 1/8 ---(1)\n3m + 7w = 1/10 ---(2)\nSolving equation (1) and (2) , we get m=11/400 and w=1/400\nAmount of work 10 girls can do in John day = 10 \u00d7 (1/400) = 1/40\nIe, 10 girls can complete the work in 40 days\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA tank contains 10,000 gallons of a solution that is 6 percent sodium chloride by volume. If 6,000 gallons of water evaporate from the tank, the remaining solution will be approximately what percent sodium chloride?\n\n### Options:\nA. 1.25%\nB. 3.75%\nC. 6.25%\nD. 6.67%\nE. 15%\n\n### Answer:\nThe remaining solution will be approximately what percent sodium chloride?means:what percent of the remaining solution is sodium chloride. Now, since the remaining solution is 10,000-6,000=4,000 gallons and sodium chloride is 600 gallons (6% of initial solution of 10,000 gallons) then sodium chloride is 600/4,000*100=15% of the remaining solution of 4,000 gallons.\nAnswer: E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich of the following is closest to (9!-8!)/(9!+8!)?\n\n### Options:\nA. 0.01\nB. 0.8\nC. 0.2\nD. 1\nE. 10\n\n### Answer:\n(9!-8!)/(9!+8!)\n8! (9-1)/8! (9+1)\n8/9 = 0.8\nB is the answer\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA rope of which a calf is tied is increased from 12 m to 23 m, how much additional grassy ground shall it graze?\n\n### Options:\nA. 1298\nB. 1228\nC. 1210\nD. 1782\nE. 1762\n\n### Answer:\n\u03c0 (232 \u2013 122)\n= 1210\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a renowned city, the average birth rate is 7 people every two seconds and the death rate is 3 people every two seconds. Estimate the size of the population net increase that occurs in one day.\n\n### Options:\nA. 172,700\nB. 172,800\nC. 172,900\nD. 173,000\nE. 173,100\n\n### Answer:\nThis question can be modified so that the birth rate is given every m seconds and the death rate is given every n seconds.\nFor this particular question : Increase in the population every 2 seconds = 7-3 = 4 people.\nTotal 2 second interval in a day = 24*60*60/2 = 43,200\nPopulation increase = 43,200 * 4 = 172,800. Hence B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe investment of A, B, and C in a business are in the ratio 3:1:4. The total investment is Rs. 60,000. Find the investment made by each.\n\n### Options:\nA. 22500, 7500, 30000\nB. 22000, 8000, 30000\nC. 23500, 7500, 29000\nD. 23000, 8500, 28500\nE. 23000, 8000, 29000\n\n### Answer:\nratio of the investment is 3:1:4\nTotal investment =60000\nso, 8x = 60000 ie)x =7500\nso the investment of A, B,C are : A's investment 3x = 22500 B's investment x = 7500 C's investment 4x =30000\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n10 books are placed at random in a shelf. The probability that a pair of books will always be together is?\n\n### Options:\nA. 1/0\nB. 1/3\nC. 1/5\nD. 1/2\nE. 1/1\n\n### Answer:\n10 books can be rearranged in 10! ways consider the two books taken as a pair then number of favourable ways of getting these two books together is 9! 2!\nRequired probability = 1/5\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nKaty worked for h hours each day for d consecutive days. If she earns $3.5 per hour, what is the total amount she earned?\n\n### Options:\nA. 3.50/d + h\nB. 3.50 + d + h\nC. 3.50 + dh\nD. 3.50h + d\nE. 3.50dh\n\n### Answer:\nH hours for d days.\nIncome each day = 3.5*h\nTotal income = 3.5*h*d\nCorrect option: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTrain X departs from station A at 11 a.m. for station B, which is 180 km so far. Train Y departs from station B at 11 a.m. for station A. Train X travels at an average speed of 70 km/hr and does not stop anywhere until it arrives at station B. Train Y travels at an average speed of 50 km/hr, but has to stop for 15 min at station C, which is 60 km away from station B enroute to station A. Ignoring the lengths of the trains, what is the distance, to the nearest kilometre, from station A to the point where the trains cross each other?\n\n### Options:\nA. 112 km\nB. 118 km\nC. 120 km\nD. None of these\nE. Cannot be determined\n\n### Answer:\nExplanation :\nTotal time taken by B to cover 60 km\n60/50 hr i.e 6/5 hr.\nIt stops at station C for 1/4 hr\nNow , in (6/5 + 1/4) hr , train X travels 70 x (29/20) = 101.5 km.\nThis means they do not cross each other by the time train Y finishes it stops at station C.\nLet they meet after t hour.\nThen, 70t + 50(t- 1/4) = 180.\nt = 192.5/120 hr.\nDistance from A will be 70 x 192.5/120 km i.e 112 km approximately.\nAnswer : A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThree candidates contested an election and received 1136, 7636 and 11628 votes respectively. What percentage of the total votes did the winning candidate get?\n\n### Options:\nA. 57%\nB. 50%\nC. 52%\nD. 60%\nE. None of these\n\n### Answer:\nExplanation :\nVotes received by the winning candidate = 11628\nTotal votes = 1136 + 7636 + 11628 = 20400\nRequired percentage = (11628/20400) \u00d7 100 = 11628/204 = 2907/51 = 969/17 = 57%\nAnswer : Option A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the remainder of Q= 3^19 when divided by 10?\n\n### Options:\nA. 0\nB. 1\nC. 5\nD. 7\nE. 9\n\n### Answer:\nI looked for patterns:\n^2 - units digit 9\n^3 - units digit 7\n^4 - units digit 1\n^5 - units digit 3\nhence, we can see that when raised to a power which is multiple of 4, the units digit is 1, and when to an even power not multiple of 4, the units digit is 9\nand we can then see:\n^16 - units digit 1, or\n^18 - units digit 9\nand ^19 - units digit 7\ntherefore, Q=when divided by 10, the remainder must be 7.D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA and B complete a job in 6 days. A alone can do the job in 8 days. If B works alone, how many days will it take to complete the job?\n\n### Options:\nA. 12\nB. 16\nC. 20\nD. 24\nE. 28\n\n### Answer:\nThe rate of A and B is 1/6\nA's rate is 1/8\nB's rate is 1/6 - 1/8 = 1/24\nB can complete the job in 24 days.\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the area of the quadrilateral of one of its diagonals is 20 cm and its off sets 9 cm and 6 cm?\n\n### Options:\nA. 128\nB. 150\nC. 278\nD. 268\nE. 261\n\n### Answer:\n1/2 * 20(9 + 6)\n= 150 cm2\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man walking at the rate of 5 km/hr crosses a bridge in 15 minutes. What is the length of the bridge (in metres)?\n\n### Options:\nA. 1280\nB. 1250\nC. 1320\nD. 1340\nE. 1350\n\n### Answer:\nSpeed = 5 km/hr\nTime = 15 minutes = 1/4 hour\nLength of the bridge = Distance Travelled by the man = Speed \u00d7 Time = 5\u00d71/4 km=5\u00d7(1/4)\u00d71000 metre=1250 metre\nAnswer is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the place value of 7 in the numeral 51468?\n\n### Options:\nA. 100\nB. 10\nC. 1\nD. 1000\nE. 11\n\n### Answer:\nplace value of 1 = 1 * 1000 = 1000\nAnswer is D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man can row downstream at 18 kmph and upstream at 10 kmph. Find the speed of the man in still water and the speed of stream respectively?\n\n### Options:\nA. 3\nB. 5\nC. 6\nD. 4\nE. 9\n\n### Answer:\nLet the speed of the man in still water and speed of stream be x kmph and y kmph respectively.\nGiven x + y = 18 --- (1)\nand x - y = 10 --- (2)\nFrom (1) & (2) 2x = 28 => x = 14, y = 4. Answer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf x^2 - 1 = 0 and x < 0, which of the following must be equal to 0 ?\n\n### Options:\nA. x^2 - 9x\nB. x^2 - 9x + 20\nC. x^2 - 2x + 3\nD. x^2 + 2x + 1\nE. x^2 + 5x + 6\n\n### Answer:\nx^2-1 = 0\nx= +1 or x = -1\nif we substitute x= -1 in the equation x^2 +2x+1 = 1-2+1 = 0\nD is also the answer\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are 14 people in a room. If each person shakes hands with exactly 3 other people, what is the total number of handshakes?\n\n### Options:\nA. 18\nB. 21\nC. 35\nD. 42\nE. 56\n\n### Answer:\nNote that each handshake includes two people.\nThe total number of handshakes is 14*3/2 = 21\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf (x^2 + 1)y=8, which of the following is not a possible value for y?\n\n### Options:\nA. 8/2\nB. 2/5\nC. 18/3\nD. 3\nE. 17/2\n\n### Answer:\nIts simple\nequation is (x^2 +1)y = 8 ===> x^2 = (8/y) - 1 . As , in LHS, it is x^2 the value has to be positive or zero in RHS.\nHence, (8/y) - 1>= 0 ===> y =< 8. Now only option E has greater value of 'y' than 8.\nThus, correct ans is E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many seconds will a 700 meter long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?\n\n### Options:\nA. 287\nB. 288\nC. 600\nD. 277\nE. 121\n\n### Answer:\nLet length of tunnel is x meter\nDistance = 700+x meter\nTime = 1 minute = 60 seconds\nSpeed = 78 km/hr = 78*5/18 m/s = 65/3 m/s\nDistance = Speed*Time\n700+x = (65/3) * 60\n700+x = 20 * 65 = 1300\nx = 1300 - 700 = 600 meters\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe population of a bacteria colony doubles every day. If it was started 3 days ago with 3 bacteria and each bacteria lives for 12 days, how large is the colony today?\n\n### Options:\nA. 512\nB. 1024\nC. 768\nD. 2048\nE. 4096\n\n### Answer:\n9 days ago- 2\n8 days ago- 4\n7 days ago- 8\n6 days ago- 16\n5 days ago- 32\n4 days ago- 64\n3 days ago- 128\n2 days ago- 256\nYesterday- 512\nToday- 1024\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n7 men, 5 women and 8 children were given as assignment of distributing 2000 books to students in a school over a period of 3 days. All of them distributed books on the 1st day. One of the 2nd day 2 women and 3 children remained absent and on the 3rd day 3 men and 5 children remained absent. If the ratio of the no. of books distributed in a day by a man, a woman & a child was 5 : 4 : 2 respectively, a total of approximately how many books were distributed on the second day?\n\n### Options:\nA. 450\nB. 500\nC. 560\nD. 650\nE. 700\n\n### Answer:\nSol. Let the books distributed by man, a woman and a child be 5x, 4x and 2x respectively.\n\u2234 No. of books distributed in 1st day\n= 7\u00d75x+5\u00d74x+8\u00d72x=71x\nNo. of books distributed in 1Ind day\n=7\u00d75x+3\u00d74x+5\u00d72x=57x\nAnd no. of books distributed in IIIrd day\n=4\u00d75x+5\u00d74x+3\u00d72x=46x\n71x + 57x + 46x = 2000, x = 2000/174\n57x=2000/174\u00d757=650\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the invalid no.from the following series 3, 7, 15, 31 , 63, 127, 257\n\n### Options:\nA. 3\nB. 7\nC. 257\nD. 63\nE. 31\n\n### Answer:\nGo on multiplying the number by 2 and adding 1 to it to get the next number.So, 257 is wrong.\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a, b, and c are consecutive positive even integers and a > b > c, which of the following could be equal to a + b + c ?\n\n### Options:\nA. 18\nB. 2\nC. -1\nD. -3\nE. -4\n\n### Answer:\nconsectutive even , X , X + 2 , X + 4 where X = Even\nnow subtract X + (X+2) + (X+4)\ndoing this leaves us with 3X + 6\nwhat even number can we substitute in X to yield an answer choice\nA works 18 (plug in 4 for X)\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAn equity analyst needs to select 4 stocks for the upcoming year and rank these securities in terms of their investment potential. If the analyst has narrowed down the list of potential stocks to 8, in how many ways can she choose and rank her top 4 picks?\n\n### Options:\nA. 1200\nB. 1680\nC. 2102\nD. 4020\nE. 1840\n\n### Answer:\nNumber of ways of choosing 4 stocks = 8C4\nNumber of ways of ranking the chosen stocks = 4!\nHence total ways of chosing and ranking = 8C4 * 4! = 1680\nCorrect Option: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAnup start a bike at 6am. and rides it at 60kmph. Raghu started at 7pm with his car at 70kmph. When will Raghu overtake Anup?\n\n### Options:\nA. 8:30am\nB. 9:40am\nC. 10:00am\nD. 01:00pm\nE. 11:10am\n\n### Answer:\nSuppose bike is overtaken by car xhrs after 6am\nDistance covered by the bike in x hrs = distance covered by the car in x-1 hr\n60x = 70(x-1)\n10x = 70\nx = 7 hrs\nRequired time = 6+7 = 01:00Pm\nAnswer is D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA number when divided successively by 4 and 5 leaves remainders 1 and 4 respectively. When it is successively divided by 5 and 4, then the remainders will be.\n\n### Options:\nA. 1,2\nB. 2,3\nC. 3,2\nD. 4,1\nE. 5,1\n\n### Answer:\n4 l X\n--l---\n5 l Y - 1 Therefore Y = (5 x 1 + 4) = 9\n--l------ X = (4 x Y + 1) = (4 x 9 + 1) = 37\nl 1 - 4\nNow 37 divided successively by 5 and 4, we get\n5 l 37\n--l---\n4 l 7 - 2 Therefore Y = (5 x 1 + 4) = 9\n--l------ X = (4 x Y + 1) = (4 x 9 + 1) = 37\nl 1 - 3\nso the respective remainders are 2 and 3.\nAnswer B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSandy purchased 20 dozen toys at the rate of $360 per dozen. Sandy sold each toy at the rate of $31.50. What was the percentage profit?\n\n### Options:\nA. 3%\nB. 5%\nC. 7%\nD. 9%\nE. 11%\n\n### Answer:\nA dozen toys cost $360, so each toy cost $30.\nselling price / cost price = 31.50 / 30 = 1.05\nThe percentage profit is 5%.\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf (0.2)x = 2 and log 2 = 0.3010, then the value of x to the nearest tenth is:\n\n### Options:\nA. -0.5\nB. -0.2\nC. -0.4\nD. 10.0\nE. -10.0\n\n### Answer:\n(0.2)x = 2.\nTaking log on both sides\nlog (0.2)x = log 2.\nx log (0.2) = 0.3010, [since log 2 = 0.3010].\nx log (2/10) = 0.3010.\nx [log 2 - log 10] = 0.3010.\nx [log 2 - 1] = 0.3010,[since log 10=1].\nx [0.3010 -1] = 0.3010, [since log 2 = 0.3010].\nx[-0.699] = 0.3010.\nx = 0.3010/-0.699.\nx = -0.4306\u2026.\nx = -0.4 (nearest tenth)\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are 600 students in a school. The ratio of boys and girls in this school is 3:5. Find the total of girls & boys are there in this school?\n\n### Options:\nA. 225\nB. 257\nC. 375\nD. 380\nE. 390\n\n### Answer:\nIn order to obtain a ratio of boys to girls equal to 3:5, the number of boys has to be written as 3 x and the number of girls as 5 x where x is a common factor to the number of girls and the number of boys. The total number of boys and girls is 600. Hence\n3x + 5x = 600\nSolve for x\n8x = 600\nx = 75\nNumber of boys\n3x = 3 \u00d7 75 = 225\nNumber of girls\n5x = 5 \u00d7 75 = 375\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n1/x+1/y=1/z where x=12 and y,z positive integer how many possible value of y and z ?\n\n### Options:\nA. 4\nB. 7\nC. 12\nD. 15\nE. infinite\n\n### Answer:\n1/12 = 1/z - 1/y\ny = 12 * z / ( 12 - z )\n0 < z < 12\nOnly for z = 3 ,4 ,6 ,8 , 9 ,10 and 11 , y is intiger\nHence seven solutions\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nPipe A can fill a tank in 4 hours, pipe B in 8 hours, and pipe C in 24 hours. If all the pipes are open, in how many hours will the tank be filled?\n\n### Options:\nA. 2.4 hours\nB. 2.8 hours\nC. 3.2 hours\nD. 4.8 hours\nE. 5.2 hours\n\n### Answer:\nThe part filled by A + B + C in 1 hour\n= 1/4 + 1/8 + 1/24\n= 10/24\nAll the three pipes together will fill the tank in 24/10 = 2.4 hours.\nThe answer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the greatest power that 7 can be raised to so that the resulting number is a factor of 21!?\n\n### Options:\nA. 2\nB. 3\nC. 4\nD. 5\nE. 6\n\n### Answer:\nthe number of 7s in 21!= 21/7=3..\nans B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTea worth Rs.126 per kg are mixed with a third variety in the ratio 1: 1 : 2. If the mixture is worth Rs.143 per kg, the price of the third variety per kg will be\n\n### Options:\nA. Rs.165.50\nB. Rs.1700\nC. Rs. 175.50\nD. Rs. 180\nE. None\n\n### Answer:\nSolution\nSince first second varieties are mixed in equal proportions, so their average price = Rs.(126+135/2) = Rs.130.50\nSo, the mixture is formed by mixing two varieties, one at Rs. 130.50 per kg and the other at say, Rs. x per kg in the ratio 2 : 2, i.e., 1 : 1. We have to find x.\nx-143/22.50 = 1 =\u00e2\u20ac\u00ba x - 143 = 22.50 =\u00e2\u20ac\u00ba x=165.50.\nHence, price of the third variety = Rs.165.50 per kg.\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nVictor gets 80 % marks in examinations. If these are 240 marks, find the maximum marks.\n\n### Options:\nA. 334\nB. 300\nC. 376\nD. 288\nE. 271\n\n### Answer:\nLet the maximum marks be m\nThen 80 % of m = 240\n\u21d2 80/100 \u00d7 m = 240\n\u21d2 m = (240 \u00d7 100)/80\n\u21d2 m = 24000/80\n\u21d2 m = 300\nTherefore, maximum marks in the examinations are 300\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe difference between the compound interest and simple interest on a certain sum of money at 5% per annum for 2 years is 45. Then the original sum is?\n\n### Options:\nA. 17000\nB. 12000\nC. 19000\nD. 14000\nE. 18000\n\n### Answer:\nFor 2 years = (100(power 2)D)/R(power 2)\n= (100(power 2) \u00d7 45)/(5 \u00d7 5) = (10000 \u00d7 45)/25 = Rs.18000/-\nAnswer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThree unbiased coins are tossed. What is the probability of getting 1 heads, 1 Tail?\n\n### Options:\nA. 3/4\nB. 1/4\nC. 3/8\nD. 7/8\nE. 2/8\n\n### Answer:\nLet, H --> Head , T --> Tail\nHere S = {TTT, TTH, THT, HTT, THH, HTH, HHT, HHH}\nLet E = event of getting 3 heads\nThen E = {THT, HTH}\nP(E) = n(E)/n(S) =2/8\nAnswer is E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a game of billiards, A can give B 20 points in 60 and he can give C 30 points in 60. How many points can B give C in a game of 100?\n\n### Options:\nA. 14\nB. 61\nC. 25\nD. 72\nE. 62\n\n### Answer:\nA scores 60 while B score 40 and C scores 30.\nThe number of points that C scores when B scores 100 = (100 * 30)/40 = 25 * 3 = 75.\nIn a game of 100 points, B gives (100 - 75) = 25 points to C.\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the difference between the place values of two sevens in the numeral 54179759 ?\n\n### Options:\nA. 699990\nB. 99990\nC. 99980\nD. 69300\nE. None of these\n\n### Answer:\nExplanation:\nRequired Difference\n= 70000 - 700 = 69300\nAnswer is D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA boat moves upstream at the rate of 1 km in 25 minutes and down stream 1 km in 12 minutes. Then the speed of the current is :\n\n### Options:\nA. 1 kmph\nB. 2 kmph\nC. 3 kmph\nD. 1.3 kmph\nE. 3.5 kmph\n\n### Answer:\nRate upstream = (1/25 *60) = 2.4 kmph\nRate dowm stream = 1/12 * 60 = 5 kmph\nRate of the current = \u00bd (5-2.4) = 1.3 kmph\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe simple interest accrued on an amount of Rs.49500 at he end of three is Rs.17820. What would be the compound interest accured on the same amount at teh same rate in the same period? (Round off your answer to two decimal places)\n\n### Options:\nA. 20043.94\nB. 20043.948\nC. 20043.93\nD. 20043.92\nE. 20043.91\n\n### Answer:\nLet the rate of interest be R% p.a.\n(49500)(3)(R)/100 = 17820\n495R = 5940\nR = 12\nCI on Rs.49500 at 12% p.a. for three years\n= 49500{[1 + 12/100]3 - 1} = 69543.936 - 49500 = Rs.20043.94\nwhen rounded off to two decimal places.\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train covers a distance in 50 min, if it runs at a speed of 48kmph on an average. The speed at which the train must run to reduce the time of journey to 50min will be.\n\n### Options:\nA. 60 km/h\nB. 55 km/h\nC. 48 km/h\nD. 70 km/h\nE. 65 km/h\n\n### Answer:\nTime=50/60 hr=5/6hr\nSpeed=48mph\ndistance=S*T=48*5/6=40km\ntime=50/60hr=5/6hr\nNew speed = 40* 6/5 kmph= 48kmph\nAnswer : C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA wheel rotates 10 times every minute and moves 20 cm during each rotation. How many metres does\nthe wheel move in one hour?\n\n### Options:\nA. 6 metre\nB. 12 metre\nC. 120 metre\nD. 1200 metre\nE. 2200 metre\n\n### Answer:\nExpl : Number of times wheel moves in 1 hour = 10 * 60 = 600\n:. Distance moves = (600 *20) cms = 12000 cms\nIn metres = 120 metre\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf all the sides of a right triangle increase in length by 8%, then by what percentage does the area of the triangle increase?\n\n### Options:\nA. 8%\nB. 16.64%\nC. 24.32%\nD. 32.84%\nE. 36.16%\n\n### Answer:\nLet B be the base and H be the height of the original triangle.\nThe original area is (1/2)BH.\nThe area of the expanded triangle is (1/2)(1.08B)(1.08H) = (1.08)(1.08)(1/2)BH = 1.1664(1/2)BH\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man spends 20% of his income in house rent, 10% of the rest on his children\u2019s education, 15% of the rest miscellaneous causes. If he now posses Rs. 6352 then his income is?\n\n### Options:\nA. A)Rs.10379\nB. B)Rs.40598\nC. C)Rs.45699\nD. D)Rs.30379\nE. E)Rs.59879\n\n### Answer:\nX * (80/100) * (90/100) * (85/100) = 6352\nX * 0.8 * 0.9 * 0.85=6352\nX = 6352/0.612\nX = 10379\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nramesh,ram,kareem and Mohan collected coins of different countries. they collected 100 together. none collected less than 10.each collected an even number. each collected a different number. based on these, we can say that the number of coins collected by the boy who collected the most could not have exceeded\n\n### Options:\nA. 54\nB. 64\nC. 58\nD. 60\nE. 62\n\n### Answer:\nas other three must have collected atleast 10+12+14=36 coins\nthe number of coins collected by the boy who collected the most could not have exceeded\n100-36=64\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a and b are the roots of the equation x2 - 5x + 5 = 0, then the value of a2 + b2 is:\n\n### Options:\nA. 36\nB. 24\nC. 15\nD. 6\nE. 5\n\n### Answer:\nSol.(b) The sum of roots = a+ b = 5\nProduct of roots = ab = 5\nNow, a2 + b2 = (a + b)2 - 2ab = 25 - 10 = 15\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA and B go around a circular track of length 300 m on a cycle at speeds of 34 kmph and 50 kmph. After how much time will they meet for the first time at the starting point?\n\n### Options:\nA. 120 sec\nB. 60 sec\nC. 186 sec\nD. 167 sec\nE. 168 sec\n\n### Answer:\nTime taken to meet for the first time at the starting point\n= LCM { length of the track / speed of A , length of the track / speed of B}\n= LCM { 300/ (36 * 5/18) , 300/ (54 * 5 /18) }\n= LCM (30, 20)\n=60 sec.\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n21, 9, 21, 11, 21, 13, 21, ?\n\n### Options:\nA. 11\nB. 17\nC. 19\nD. 15\nE. 20\n\n### Answer:\nD\n15\nIn this alternating repetition series, the number 21 is interpolated. If you exclude 21, the series increases by 2, beginning with the number 9.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf an item that originally sold for z dollars was marked up by x percent and then discounted by y percent, which of the following expressions W represents the final price of the item?\n\n### Options:\nA. W=(10,000z + 100z(x \u2013 y) \u2013 xyz)/10,000\nB. W=(10,000z + 100z(y \u2013 x) \u2013 xyz)/10,000\nC. W=(100z(x \u2013 y) \u2013 xyz)/10000\nD. (100z(y \u2013 x) \u2013 xyz)/10000\nE. 10000 /(x \u2013 y)\n\n### Answer:\n-A-\nz=Original Price\nx=MU\ny= MD\nNew price with MU:\nz(x/100+1)\nNew price with MD:\nz[(x/100+1)(-y/100+1)]\nSolving\u00e2\u20ac\u00a6\n=z[((x+100)/100)((-y+100)/100)]\n=z(x100-xy+10000-100y)/10000\n=(zx100-xyz+10000z-100yz)/10000 --> similar to A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMr. Sam's car gets him 50 miles per gallons of gas. If Mr Sam get a full tank with 14 gallons of gas, How far can Mr Sam go?\n\n### Options:\nA. 52 miles\nB. 1400 miles\nC. 700 miles\nD. 1000 miles\nE. 100 miles\n\n### Answer:\nSolution\nNumber of miles per gallon = 50 miles\nNumber of miles 14 gallons = x\nx = 50 \u00c3\u2014 14 = 700 miles.\nSo, Number of miles Sam gets with 14 gallons = 700 miles.\nOption C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA reduction of 12% in the price of oil enables a house wife to obtain 6kgs more for Rs.1200, what is the reduced price for kg?\n\n### Options:\nA. 24\nB. 27\nC. 40\nD. 28\nE. 20\n\n### Answer:\n1200*(12/100) = 144 ---- 6\n? ---- 1 => Rs.24\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe rate of spin of a certain gyroscope doubled every 15 seconds from the moment a particular stopwatch started. If after a minute and a half the gyroscope reached a speed of 400 meters per second, what was the speed, in meters per second, when the stopwatch was started?\n\n### Options:\nA. 25/2\nB. 25/4\nC. 25/8\nD. 25/16\nE. 25/32\n\n### Answer:\nLet x be the original speed when the stopwatch was started.\nIn 90 seconds, the speed doubled 6 times.\n2^6 * x = 400\nx = (2^4 * 25) / 2^6 = 25/4\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe ratio of the number of students appearing for examination in the year 1998 in the states A, Band C was 3 : 5 : 6. Next year if the number of students in these states increases by 20%, 10% and 20% respectively, the ratio in states A and C would be 1 : 2. What was the number of students who appeared for the examination in the state A in 1998?\n\n### Options:\nA. 7200\nB. 6000\nC. 7500\nD. Data inadequate\nE. None of these\n\n### Answer:\nLet the number of students appearing for examination in the year 1998 in the states A, B and C be 3x, 5x and 6x respectively.\nAccording to the question,\n3x\u00d7120/100 /6x\u00d7120/100=12\nHence data inadequate.\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAn investor bought a 1-year $6,000 certificate of deposit that paid interest at an annual rate of 8 percent compounded semiannually. What was the total amount of interest paid on this certificate at maturity?\n\n### Options:\nA. $480\nB. $489.60\nC. $634.64\nD. $800.32\nE. $240\n\n### Answer:\n1.04*1.04*6000 = $6489.60\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThree printing presses, L, S, and T, working together at their respective constant rates, can do a certain printing job in 4 hours. S and T, working together at their respective constant rates, can do the same job in 5 hours. How many hours would it take L, working alone at its constant rate, to do the same job?\n\n### Options:\nA. 8\nB. 10\nC. 12\nD. 15\nE. 20\n\n### Answer:\n=1/4-1/5=1/20\nL can do 1/20 job in 1 hour\nL can do the whole job in 20 hours=E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nI forgot the last digit of a 7-digit telephone number. If 1 randomly dial the final 3 digits after correctly dialing the first four, then what is the chance of dialing the correct number?\n\n### Options:\nA. 1/1002\nB. 1/1028\nC. 1/1000\nD. 1/1287\nE. 1/1289\n\n### Answer:\nExplanation:\nIt is given that last three digits are randomly dialled. then each of the digit can be selected out of 10 digits in 10 ways.\nHence required probability = = 1/1000\nAnswer: C) 1/1000\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhen positive integer N is divided by positive integer J, the remainder is 28. If N/J = 142.07, what is value of J?\n\n### Options:\nA. 300\nB. 375\nC. 400\nD. 460\nE. 500\n\n### Answer:\nWhen a number is divided by another number, we can represent it as : Dividend = Quotient * Divisor + Remainder\nSo, Dividend/Divisor = Quotient + Remainder/Divisor\nGiven that N/J = 142.07\nHere 142 is the quotient.\nGiven that Remainder = 28\nSo, 142.07= 142 + 28/J\nSo, J = 400\nAnswer- C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSam taken a loan Rs.15000/- from Co-operative Society with an interest @ 11.5% per month. At the same time he deposited Rs. 10000/- as Fixed Deposit with an interest @ 9.5% per month. After one week sam asked the manager to calculate the interest to be paid. What is the interest amount for 7 days?\n\n### Options:\nA. A)165\nB. B)220\nC. C)310\nD. D)185\nE. E)181\n\n### Answer:\nLoan amount : Rs.15000/- @ 11.5%\nInterest per month = 15000/- * 11.5% =Rs.1725\nInterest for one day = 1725/30=57.50\nInterest for 7 days is = 57.50*7 =403\nFD amount is = Rs.10000/- @ 9.5%\nInterest per month = 10000 * 9.5% = 950/-\nInterest for 7 days = 950/30*7 = 222\nInterest amount to be paid by Sam = 403-222 =181/- for 7 days\nAnswer is E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n(5!+6!+4!)/4!*0!*5*6=?\n\n### Options:\nA. 4/5\nB. 6/5\nC. 5/6\nD. 4/3\nE. 9/8\n\n### Answer:\n4!(5+30+1)/4!*1*5*6\n36/30=6/5\nanswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf each term in the sum Q=a1+a2+a3+...+an either 2 or 22 and the sum equals 100, which of the following could be equal to n?\n\n### Options:\nA. 38\nB. 39\nC. 40\nD. 41\nE. 42\n\n### Answer:\nMin value of 'n' can be 10 i.e 4*22+6*12 =Q=> 22+22+22+22+2+2+2+2+2+2 = 100\nSince we don't have 10 in the options proceed further, (10-1)+22/2 => 20 digits, which is again not in the options\n(20-1) + 22/2 = 30 digits ( not in options)\n(30-1) + 22/2 = 40 digits\nHence C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe avearge score of a cricketer for ten matches is 38.9 runs. If the average for the first six matches is 45. Then find the average for the last four matches?\n\n### Options:\nA. 33.25\nB. 33.5\nC. 34.25\nD. 29.75\nE. none\n\n### Answer:\nSolution\nRequired average\t=(38.9 x 10)-(45 x 6)/ 4\n= 119 / 4.\n= 29.75\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA+B+C+D=D+E+F+G=G+H+I=17 given A=4. Find value of G and H?\n\n### Options:\nA. 2,9\nB. 3,9\nC. 1,9\nD. 4,9\nE. 5,9\n\n### Answer:\nA+B+C+D=17\n4+2+6+5=17\nD=5\nD+E+F+G=17\n5+3+8+1=17\nG=1\nG+H+I=17\n1+9+7=17\nG=1,H=9.\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the mean proportional between 81 & 100?\n\n### Options:\nA. A)59\nB. B)61\nC. C)63\nD. D)65\nE. E)90\n\n### Answer:\nFormula = \u221aa\u00d7b\nA = 81 and B = 100\n\u221a81\u00d7100 = 9 \u00d7 10 = 90\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn 100 m race, A covers the distance in 36 seconds and B in 45 seconds. In this race A beats B by:\n\n### Options:\nA. 20\nB. 99\nC. 88\nD. 27\nE. 21\n\n### Answer:\nDistance covered by B in 9 sec. = \\inline \\fn_jvn {\\color{Black} \\left ( \\frac{100}{45}\\times 9 \\right )m} = 20m\n\\fn_jvn {\\color{Black} \\therefore } A beats B by 20 metres.\nAnswer: A) 20m\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are 10 books on a shelf: 6 English books, 3 Spanish books and 2 Portuguese books. What is the probability of choosing 2 books in different languages?\n\n### Options:\nA. 31/90\nB. 3/10\nC. 4/5\nD. 31/45\nE. 28/90\n\n### Answer:\nProbability = Favourable outcome / Total Outcome = 1- (Unfavourable outcome / Total Outcome)\nFavourable Outcomes\nCase-1: One book is English (out of 6 English books) and one book is Spanish (out of 3 Spanish books) i.e. 6C1*3C1\nCase-2: One book is Spanish (out of 3 Spanish books) and one book is Portuguese (out of 2 Portuguese books) i.e. 3C1*2C1\nCase-3: One book is English (out of 6 English books) and one book is Portuguese (out of 2 Portuguese books) i.e. 6C1*2C1\nTotal favourable Outcomes = 6C1*3C1+3C1*2C1+6C1*2C1 = 18+6+12 = 36\nTotal Possible Outcomes = 10C2 = 45\ni.e. Probability = 36/45=4/5\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a group containing 6 cows and 4 buffalos, 4 livestock are to be selected in such a way that at least 1 cow should always be present. How many way of doing that are possible?\n\n### Options:\nA. 209\nB. 277\nC. 297\nD. 161\nE. 108\n\n### Answer:\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA dealer purchases 15 articles for Rs. 25 and sells 12 articles for Rs. 33. Find the profit percentage?\n\n### Options:\nA. 65%\nB. 50%\nC. 59%\nD. 40%\nE. 53%\n\n### Answer:\nL.C.M of 15 and 12\n= 60\nCP of 60 articles\n= Rs. 100 (25 * 4)\nSP of 60 articles\n= Rs. 165 (33 * 5)\nProfit percentage\n= (165 - 100)/100 * 100 = 65%\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn what time will a railway train 60 m long moving at the rate of 36 kmph pass a telegraph post on its way?\n\n### Options:\nA. 9\nB. 8\nC. 7\nD. 6\nE. 5\n\n### Answer:\nT = 60/36 * 18/5\n= 6 sec\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n2 trains starting at the same time from 2 stations 200km\napart and going in opposite direction cross each other ata\ndistance of 110km from one of the stations.what is the ratio of\ntheir speeds.\n\n### Options:\nA. 10:9\nB. 11:9\nC. 9:9\nD. 9:10\nE. 5:6\n\n### Answer:\nIn same time ,they cover 110km & 90 km respectively\nso ratio of their speed =110:90 = 11:9\nAnswer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nB completes a work in 3 days. A alone can do it in 10 days. If both work together, the work can be completed in how many days?\n\n### Options:\nA. 2.31 days\nB. 4.31 days\nC. 5.31 days\nD. 6.31 days\nE. 7.31 days\n\n### Answer:\n1/3 + 1/10 = 13/30\n30/13 = 2.31 days\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe sale price at which a store sells an article is 25% more than its cost price. If the sale price is an integer, which of the following cannot be the cost price?\n\n### Options:\nA. $64\nB. $80\nC. $96\nD. $112\nE. $123\n\n### Answer:\nSale Price = (5/4)*(Cost Price)\nIf the sale price is an integer, then the cost price must be divisible by 4.\nThe answer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf \u20132 < x < 2 and x \u2260 0, which of the following inequalities must be true?\nI. x^3 < x\nII. x^2 < |x|\nIII. x^4 \u2013 x^5 > x^3 \u2013 x^2\n\n### Options:\nA. I only\nB. II only\nC. III only\nD. II and III only\nE. I, II, and III\n\n### Answer:\nAnswer is D. Let's look at the statements one by one\nStmt I. x^3 < x\nif 0x\nSo this statement is not always true\nStmt II. x^2 < |x|\nBecause we know that x is a number less than one but not equal to zero then x^2 will always be less than |x|.\nWhy? think of positive fractions (and you can think in terms of positive fractions because the inequality is in regards to |x|). Lets set x = 1/2, then x^2 = 1/4 and 1/4<1/2\nSo Stmt II is always true\nStmt III. x^4 \u2013 x^5 > x^3 \u2013 x^2\nThis one may seem tricky but lets break it down. x^4 \u2013 x^5 > x^3 \u2013 x^2 = x^4(1-x)>x^2(x-1).\nBecause lets concentrate on (1-x) and (x-1). We are given that -10 and (x-1)<0. x^4 will always be positive and x^2 will always be positive so without doing any math we are looking at positive > negative... which is always true.\nSo Stmt III is always true\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nVolume of a hemisphere is 19404 cu. cm. Its radius is :\n\n### Options:\nA. 19 cm\nB. 20 cm\nC. 21 cm\nD. 30 cm\nE. None\n\n### Answer:\nSol.\nLet the radius be R cm. Then,\n2/3 * 22/7 * R\u00b3 = 19404 \u21d4 R\u00b3\n= [19404 * 21/44] = (21)\u00b3 \u21d4 R = 21 cm.\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA wheel makes 1000 revolutions in covering a distance of 88 km. Find the radius of the wheel.\n\n### Options:\nA. 14\nB. 11\nC. 28\nD. 26\nE. 18\n\n### Answer:\nExplanation:\nDistance covered in one revolution = = 88m.\nAnswer: A) 14\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nlexus car agency has 162 cars.he sold some cars at 9% profit and rest at 36% profit thus he gains 17% on the sale of all his cars.the no. of cars sold at 36% profit is?\n\n### Options:\nA. 36\nB. 37\nC. 48\nD. 39\nE. 40\n\n### Answer:\nratio of 36% profit cars to 9% profit cars = 8:19\nso no. of cars sold at 36% profit = 162*8/27= 48 cars\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe number of positive integer solutions for the equation x +y +z + t = 10 is\n\n### Options:\nA. 60\nB. 74\nC. 84\nD. 54\nE. 104\n\n### Answer:\nThe number of positive integer solutions for the equatio fx1+x2+\u22ef+xn=k\n(k-1)C(n-1)- where k is the number and n is number of variable in the equation.\n10-1 C 4-1 = 9C3 = 84\nAnswer : C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a:b=2:8 and b:c=3:4 find a:b:c?\n\n### Options:\nA. 3:12:16\nB. 12:3:6\nC. 6:12:3\nD. 4:3:14\nE. 5:2:6\n\n### Answer:\na:b = 2:8, b:c = 3:4\n2:8\n3:4\n(a = a \u00d7 b, b = b \u00d7 b and c = b \u00d7 c)\na:b:c = 3:12:16\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the area of a triangle with the following vertices L(1, 3), M(5, 1), and N(2, 5) ?\n\n### Options:\nA. 3\nB. 4\nC. 5\nD. 6\nE. 7\n\n### Answer:\nThere is a direct formula to calculate the are of a triangle based on coordinates of its vertices and one could use it to solve this problem.\nThough if you make a diagram minimum simple calculations will be needed:\nAnswer: C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOn a certain day, Tim invested $500 at 10 percent annual interest, compounded annually, and Lana invested 800 at 5 percent annual interest, compounded annually.The total amount of interest earned by Tim\u2019s investment in the first 2 years was how much greater than the total amount of interest earned by Lana\u2019s investment in the first 2 years?\n\n### Options:\nA. $5\nB. $15\nC. $23\nD. $100\nE. $105\n\n### Answer:\nCompounded annually means that the interest is applied once per year. One can have 10% annual interest compounded monthly - in this case 10%/12 would be applied each month, or 10% annual interest compounded daily etc.\nWith respect to the problem at hand, at the end of two years, Tim would have\n500(1.10)^2 = 500(1.21) = 605\nand Lana would have\n800(1.05)^2 = 800(1.1025) = 882\nThus, Tim earned 105 dollars, while Lana earned 82 dollars\nThe difference is $23 and the answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo trains A and B starting from two points and travelling in opposite directions, reach their destinations 9 hours and 4 hours respectively after meeting each other. If the train A travels at 60kmph, find the rate at which the train B runs.\n\n### Options:\nA. 40\nB. 90\nC. 120\nD. 80\nE. 100\n\n### Answer:\nIf two objects A and B start simultaneously from opposite points and, after meeting, reach their destinations in \u2018a\u2019 and \u2018b\u2019 hours respectively (i.e. A takes \u2018a hrs\u2019 to travel from the meeting point to his destination and B takes \u2018b hrs\u2019 to travel from the meeting point to his destination), then the ratio of their speeds is given by:\nSa/Sb = \u221a(b/a)\ni.e. Ratio of speeds is given by the square root of the inverse ratio of time taken.\nSa/Sb = \u221a(4/9) = 2/3\nThis gives us that the ratio of the speed of A : speed of B as 2:3.\nSince speed of A is 60 kmph, speed of B must be 60*(3/2) = 90 kmph\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a, b, and c are consecutive odd positive integers and a < b < c, which of the following could be equal to c - b - a+3 ?\n\n### Options:\nA. 4\nB. -4\nC. -1\nD. -2\nE. -3\n\n### Answer:\nlet we put values. a=1, b=3, c=5\n5-3-1=1\n1+3 =4\nAnswer :A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhen you multiply a number by 4 and\nthen subtract 8, the result is the same as\nif you first subtracted 4 from the same\nnumber and then multiplied by 12. What\nis the number?\n\n### Options:\nA. A)5\nB. B)13\nC. C)19\nD. D)31\nE. E)10\n\n### Answer:\nLet x equal the number and then change the words into an equation and solve for x:\n4x \u2013 8 = 12(x \u2013 4)\n4x \u2013 8 = 12x \u2013 48\n40 = 8x\n5 = x\ncorrect answer A)5\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo trains 120 meters and 165 meters in length respectively are running in opposite directions, one at the rate of 80 km and the other at the rate of 65 kmph. In what time will they be completely clear of each other from the moment they meet?\n\n### Options:\nA. 7.16\nB. 7.16\nC. 7.07\nD. 7.15\nE. 7.11\n\n### Answer:\nT = (120 + 165)/ (80 + 65) * 18/5\nT = 7.07\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA part of certain sum of money is invested at 9% per annum and the rest at 12% per annum, if the interest earned in each case for the same period is equal, then ratio of the sums invested is?\n\n### Options:\nA. 7:3\nB. 4:9\nC. 4:3\nD. 2:3\nE. 4:9\n\n### Answer:\n12:9\n= 4:3\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nPipe A can fill a tank in 6 hours, pipe B in 4 hours, and pipe C in 12 hours. If all the pipes are open, in how many hours will the tank be filled?\n\n### Options:\nA. 1.5\nB. 2\nC. 2.5\nD. 3\nE. 3.5\n\n### Answer:\nThe part filled by A + B + C in 1 hour\n= 1/6 + 1/4 + 1/12\n= 12/24 = 1/2\nAll the three pipes together will fill the tank in 2 hours.\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMike needs 30% to pass. If he scored 212 marks and falls short by 28 marks, what was the maximum marks he could have got?\n\n### Options:\nA. 343\nB. 677\nC. 800\nD. 867\nE. 932\n\n### Answer:\nIf Mike had scored 28 marks more, he could have scored 30%\nTherefore, Mike required 212 + 28 = 240 marks\nLet the maximum marks be m.\nThen 30 % of m = 240\n(30/100) \u00d7 m = 240\nm = (240 \u00d7 100)/30\nm = 24000/30\nm = 800\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the sum of n consecutive positive integers is 33, what of the following could be the value of n?\nI. 3\nII. 6\nIII. 11\n\n### Options:\nA. I only\nB. II only\nC. III only\nD. I and II\nE. I, II and III\n\n### Answer:\nsolved it the way bunuel explained, although took some time to arrive to the answer choice.\n3 -> 10+11+12=33.\n6 ->3+4+5+6+7+8=33.\n11 -> since we are told that we have a set of n consecutive POSITIVE numbers, we can have the smallest possible numbers:\n1+2+3+4+5+6+7+8+9+10+11 - the sum is way over 33, it is actually 11*12/2 = 11*6=66.\nthus, only I and II works. the answer is D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average of the marks of 11 students in a class is 36. If the marks of each student are doubled, find the new average?\n\n### Options:\nA. 69\nB. 70\nC. 71\nD. 72\nE. 75\n\n### Answer:\nSum of the marks for the 11 students = 11 * 36 = 396. The marks of each student are doubled, the sum also will be doubled.\nThe new sum = 396 * 2 = 792. So, the new average = 792/11 = 72.\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAnand and Deepak started a business investing Rs. 22,500 and Rs. 35,000 respectively. Out of a total profit of Rs. 14,950, Deepak's share is:?\n\n### Options:\nA. s.8467\nB. s.9100\nC. s.8400\nD. s.8429\nE. s.8420\n\n### Answer:\nRatio of their shares\n= 22500 : 35000\n= 9:14\nDeepak's share\n= 14950 * 14/23\n= Rs.9100.\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nDivide 71 into 2 parts such that 1 part exceeds the other by 8. What are the 2 no.'s in that part?\n\n### Options:\nA. 17\nB. 21\nC. 31\nD. 45\nE. 47\n\n### Answer:\nLet $let n$ be the smaller and 71 - n be the larger number. Now, since the larger number exceeds the smaller number by 7, we can form the equation\nlarger number \u2013 smaller number = 7\nwhich is equivalent to\nSimplifying, we have 71 - 2n = 7. This gives us 2n = 78 which implies that the larger number is . The smaller is 71-39=31.\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train 350 m long, running with a speed of 63 km/hr will pass a tree in?\n\n### Options:\nA. 18 sec\nB. 20 sec\nC. 76 sec\nD. 15 sec\nE. 17 sec\n\n### Answer:\nSpeed = 63 * 5/18 = 35/2 m/sec\nTime taken = 350 * 2/35 = 20 sec\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhen a metallic ball bearing is placed inside a cylindrical container, of radius 2 cm, the height of the water, inside the container, increases by 0.6 cm. The radius, to the nearest tenth of a centimeter, of the ball bearing is\n\n### Options:\nA. 1 cm\nB. 1.2 cm\nC. 2 cm\nD. 0.6 cm\nE. None\n\n### Answer:\nSolution\nWhen the ball was put in water, the volume of water increased by.\npi*22*0.6 = 2.4 pi cubic cm\nThe above volume is equal to the volume of the ball with radius r to find. Hence\n(4/3)*pi*r3 = 2.4 pi\nSolve the above for r\nr = 1.2 cm\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA person travels from A to B at a speed of 40 km/hr and returns by increasing his speed by 50%. What is his average speed for both the trips?\n\n### Options:\nA. 48 km/hr\nB. 56 km/hr\nC. 60 km/hr\nD. 52 km/hr\nE. None of these\n\n### Answer:\nExplanation:\nMethod : 1\nIf a car covers a certain distance atxkmph and an equal distance at y kmph,\nthe average speed of the whole journey = 2xy/x+y kmph.\nBy using the same formula, we can find out the average speed quickly\nSpeed with which he travels from A to B = x = 40 km/hr\nSpeed with which he travels from B to A = x = 40\u00d7(100+50)/100 = 60 km/hr\naverage speed = (2\u00d740\u00d760)/(40+60) = 48 km/hr\nAssume that distance from A to B = x km\nSpeed with which he travels from A to B = x = 40 km/hr\nTime to travel from A to B = distance/speed = x/40 hr\nSpeed with which he travels from B to A = 40\u00d7(100+50)/100 = 60 km/hr\nTime to travel from B to A = distance/speed = x/60\nTotal distance traveled = x+x = 2x\nTotal time taken = x/40 + x/60\nAverage speed = Total distance traveled/Total time taken = 2x/(x/44)+(x/60)\n= 2/[(1/60)+(1/40)] = (2\u00d72400)/(40+60) = 2\u00d724 = 48 km/hr\nAnswer: Option A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man invests Rs.5000 for 3 years at 5% p.a. compound interest reckoned yearly. Income tax at the rate of 20% on the interest earned is deducted at the end of each year. Find the amount at the end of the third year\n\n### Options:\nA. 5624.32\nB. 5624.39\nC. 5654.32\nD. 5624.38\nE. 5624.35\n\n### Answer:\nExplanation:\n5% is the rate of interest. 20% of the interest amount is paid as tax.\ni.e 80% of the interest amount stays back.\nif we compute the rate of interest as 80% of 5% = 4% p.a., we will get the same value.\nThe interest accrued for 3 years in compound interest = 3 x simple interest on principal + 3 x interest on simple interest + 1 x interest on interest on interest.\n= 3 x (200) + 3 x (8) + 1 x 0.32 =600 + 24 + 0.32 = 624.32\nThe amount at the end of 3 years = 5000 + 624.32 = 5624.32\nAnswer: A) Rs.5624.32\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\na pizza which is thin is cut into 'x' pieces by 4 straight lines then the lowest possible value of x is?\n\n### Options:\nA. 3\nB. 4\nC. 5\nD. 6\nE. 7\n\n### Answer:\n4 parallel lines will give minimum number of pieces.\n5 pieces.\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train is 360 meter long is running at a speed of 30 km/hour. In what time will it pass a bridge of 140 meter length?\n\n### Options:\nA. 87\nB. 69\nC. 60\nD. 72\nE. 21\n\n### Answer:\nSpeed = 30 Km/hr = 30*(5/18) m/sec = 25/3 m/sec\nTotal distance = 360+140 = 500 meter\nTime = Distance/speed\n= 500 * (3/25) = 60 seconds\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWorking alone, Tom finishes cleaning half the house in a third of the time it takes Nick to clean the entire house alone. Tom alone cleans the entire house in 6 hours. How many hours will it take Nick and Tom to clean the entire house if they work together?\n\n### Options:\nA. 1.5\nB. 2\nC. 2.4\nD. 3\nE. 3.6\n\n### Answer:\nAnswer is 3.6 hours.\nTom does the complete house in 6 hours while Nick does it in 9 hours. 1/ (1/6+1/9)= 3.6\nanswer is E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a division sum, the divisor is ten times the quotient and five times the remainder. If the remainder is 54, the dividend is:\n\n### Options:\nA. 6324\nB. 7344\nC. 8336\nD. 9356\nE. 9400\n\n### Answer:\nDivisor = (5 * 54) = 270\n= 10 * Quotient = Divisor\n=> Quotient = 270/10 = 27\nDividend = (Divisor * Quotient) + Remainder\nDividend = (270 * 27) + 54 = 7344.\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is 0.05 percent of 12,356?\n\n### Options:\nA. 0.6178\nB. 61.78\nC. 6.178\nD. 0.06178\nE. 0.006178\n\n### Answer:\nSince, Percent=1/100, what=something(s), and is:=. We can write the question as s=0.05(1/100)12,356. The answer is 6.178. Hence, the correct answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhen Professor Wang looked at the rosters for this term's classes, she saw that the roster for her economics class (E) had 26 names, the roster for her marketing class (M) had 28, and the roster for her statistics class (S) had 18. When she compared the rosters, she saw that E and M had 9 names in common, E and S had 7, and M and S had 10. She also saw that 9 names were on all 3 rosters. If the rosters for Professor Wang's 3 classes are combined with no student's name listed more than once, how many names will be on the combined roster?\n\n### Options:\nA. 30\nB. 34\nC. 42\nD. 46\nE. 55\n\n### Answer:\nTotal # of students 26+28+18-(9+7+10)+9=55.\nAnswer: E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFour people need to cross a dark river at night.\n* They have only one torch and the river is too risky to cross without the torch.\n* If all people cross simultaneously then torch light wont be sufficient.\n* Speed of each person of crossing the river is different.cross time for each person is 1 min, 2 minutes, 7 minutes and 10 minutes.\nWhat is the shortest time needed for all four of them to cross the river ?\n\n### Options:\nA. 16 minutes\nB. 17 minutes\nC. 18 minutes\nD. 19 minutes\nE. 20 minutes\n\n### Answer:\nSolution:\n17 min\nThe initial solution most people will think of is to use the fastest person as an usher to guide everyone across. How long would that take? 10 + 1 + 7 + 1 + 2 = 21 minutes. Is that it? No. That would make this question too simple even as a warm up question.\nLet's brainstorm a little further. To reduce the amount of time, we should find a way for 10 and 7 to go together. If they cross together, then we need one of them to come back to get the others. That would not be ideal. How do we get around that? Maybe we can have 1 waiting on the other side to bring the torch back. Ahaa, we are getting closer. The fastest way to get 1 across and be back is to use 2 to usher 1 across. So let's put all this together.\n1 and 2 go cross\n2 comes back\n7 and 10 go across\n1 comes back\n1 and 2 go across (done)\nTotal time = 2 + 2 + 10 + 1 + 2 = 17 minutes\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA dishonest dealer professes to sell goods at the cost price but uses a weight of 800 grams per kg, what is his percent?\n\n### Options:\nA. 75%\nB. 25%\nC. 28%\nD. 85%\nE. 28%\n\n### Answer:\n800 --- 200\n100 --- ? => 25%\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn the formula V = 1/(2r)^3, if r is halved, then V is multiplied by?\n\n### Options:\nA. 16\nB. 8\nC. 1\nD. 1/8\nE. 1/64\n\n### Answer:\nSay r=1 => V1 = 1/8\nwhen r=1/2; V2 = 1\nV2 = 1*V1.\nAnswer : B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAt what price must an article costing Rs.47.50 be marked in order that after deducting 9% from the list price. It may be sold at a profit of 25% on the cost price?\n\n### Options:\nA. 65.25\nB. 62.6\nC. 62.1\nD. 62.7\nE. 62.2\n\n### Answer:\nCP = 47.50\nSP = 47.50*(125/100) = 59.375\nMP*(91/100) = 59.375\nMP = 65.25\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich of the following inequalities is equivalent to \u20132 < x < 4 ?\n\n### Options:\nA. | x \u2013 2 | < 4\nB. | x \u2013 1 | < 3\nC. | x + 1 | < 3\nD. | x + 2 | < 4\nE. None of the above\n\n### Answer:\nFirst remove the mod\nthen set the expression to 0\nthen get a value of X\nthen add and subtract the value from the given number on the RHS\nLets try with an example (B) --------------> | x \u2013 1 | < 3\nFirst remove the mod -------------------> x-1\nthen set the expression to 0--------------> x-1=0\nthen get a value of x---------------------> x=1\nthen add and subtract the value from the given number on the RHS 1+3=4 and 1-3= -2\nthe range become -2 to 4 correct answer\nNow try its with an incorrect option (C) | ----------> |x + 1 | < 3\nFirst remove the mod --------------------------> x+1\nthen set the expression to 0----------------------> x+1=0\nthen get a value of x------------------------------> x=-1\nthen add and subtract the value from the given number on the RHS -1+3=2 and -1-3= -4\nthe range become -4 to 2 Incorrect\nTHE CORRECT ANSWER IS B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many of the positive divisors of 600 are also multiples of 4 not including 600?\n\n### Options:\nA. 6\nB. 8\nC. 9\nD. 11\nE. 12\n\n### Answer:\n600 = 2^6 * 3 * 5 = (4) * 2 * 3 * 5^2\nBesides (4), the exponents of 2, 3, and 5 are 1, 1, and 2.\nThere are (1+1)(1+1)(2+1) = 12 ways to make multiples of 4.\nWe must subtract 1 because one of these multiples is 600.\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the sides of a cube are in the ratio 5:4. What is the ratio of their diagonals?\n\n### Options:\nA. 4:3\nB. 5:4\nC. 4:7\nD. 3:4\nE. 4:5\n\n### Answer:\nExplanation:\nDiagonal of a Cube=a\u221a3 where a is side\na1:a2 = 5:4\nd1:d2 = 5:4 where\u221a3 cancelled both side\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe L.C.M. of two numbers is 54. The numbers are in the ratio 2 : 3. Then sum of the number is:\n\n### Options:\nA. 28\nB. 32\nC. 40\nD. 45\nE. 54\n\n### Answer:\nLet the numbers be 2x and 3x.\nThen, their L.C.M. = 6x.\nSo, 6x = 54 or x = 9.\nThe numbers are 18 and 27.\nHence, required sum = (18 + 27) = 45.\nAnswer: Option D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe list price of an article is Rs.70. A customer pays Rs.61.74 for it. He was given two successive discounts, one of them being 10%. The other discount is?\n\n### Options:\nA. 8%\nB. 7%\nC. 10%\nD. 2%\nE. 4%\n\n### Answer:\nExplanation:\n70*(90/100)*((100-x)/100) = 61.74\nx = 2%\nOption D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA trader bought a car at 20% discount on its original price. He sold it at a 30% increase on the price he bought it. What percent of profit did he make on the original price?\n\n### Options:\nA. A)4%\nB. B)12%\nC. C)14%\nD. D)20%\nE. E)22%\n\n### Answer:\nOriginal price = 100\nCP = 80\nS = 80*(130/100) = 104\n100 - 104 = 4%\nA)\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn 1995, the Johnsons spent $800 on the family\u2019s water bills. Anticipating that water rates would increase in 1996 by 50%, the Johnsons cut back their water usage. By how much must the Johnsons have reduced their 1996 water usage to pay exactly the same amount R in 1996 as they paid in 1995?\n\n### Options:\nA. 33 1\u20443%\nB. 40%\nC. 50%\nD. 66 2\u20443%\nE. 100%\n\n### Answer:\nwater rate increases by 50 % in 1996 means 150% of rate in 1995. to pay exactly the same amount R in 1996 as they paid in 1995, water use should decrease in the same ratio\n150-> 100 means 1/3 rd= 33(1/3) %.A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf x, y, and z are consecutive positive integers greater than 1, not necessarily in that order, then which of the following is (are) true?\nI. x > z\nII. 2(x+ y) > 2z\nIII. yz > xz\nIV. xy > y + z\n\n### Options:\nA. I only\nB. II only\nC. II and III only\nD. II and IV only\nE. III and IV only\n\n### Answer:\nwe do not know the values or the relative values but that the three are consecutive..\nso the max difference in any two number is 2 and min 1..\nlets see the choices..\nI. x > z...\nwe do not know the values or the relative values... need not be true..\nII. 2(x+ y) > 2z or x+ y > z\nwe take the worst case that z is teh largest and x and y are lowest possible..... so 2+3>4.. 5>4.. always true\nIII. yz > xz\nwe do not know the values or the relative values between x and y..need not be true\nIV. xy > y + z\nxy-y>z or y(x-1)>z...\nagain lets take the worst scenario..\nwe take the worst case that z is the largest and x and y are lowest possible..... so (2-1)3>4.. 3>4.. not true\nonly ii is true\nans B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA chair is bought for Rs.900/- and sold at Rs.810/- find the loss percentage\n\n### Options:\nA. 10% Gain\nB. 10% Loss\nC. 20% Loss\nD. 25% Loss\nE. 30% Loss\n\n### Answer:\nFormula = (Selling price ~ Cost price)/Cost price * 100\n= (810 ~ 900)/900 = 10% Loss\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSimran started a software business by investing Rs. 50,000. After six months, Nanda joined her with a capital of Rs. 80,000. After 3 years, they earned a profit of Rs. 28,000. What was Simran's share in the profit?\n\n### Options:\nA. Rs. 9423\nB. Rs. 10,250\nC. Rs. 12,000\nD. Rs. 14,000\nE. None of these\n\n### Answer:\nSimran : Nanda = (50000 * 36) : (80000 * 30) = 3:4\nSimran's share = 28000 * 3/7 = Rs. 12000\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are two numbers. If 20% of the first number is added to the second number, then the second number increases to its five-fourth. Find the ratio of the first number to the second number?\n\n### Options:\nA. 5/4\nB. 5/7\nC. 5/3\nD. 5/8\nE. 5/1\n\n### Answer:\nLet the two numbers be x and y.\n20/100 * x + y = 5/4y\n=> 1/5 x = 1/4 y => x/y\n= 5/4\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAlfred started a business investing Rs. 45,000. After 3 months, Peter joined him with a capital of Rs. 60,000. After another 6 months, Ronald joined them with a capital of Rs. 90,000. At the end of the year, they made a profit of Rs. 16,500. Find the lire of each.\n\n### Options:\nA. 2300\nB. 3300\nC. 4300\nD. 1300\nE. None of them\n\n### Answer:\nClearly, Alfred invested his capital for 12 months, Peter for 9 months and Ronald for 3 months.\nSo, ratio of their capitals = (45000 x 12) : (60000 x 9) : (90000 x 3)\n= 540000 : 540000 : 270000 = 2 : 2 : 1.\nAlfred's share = Rs. (16500 x (2/5)) = Rs. 6600\nPeter's share = Rs. (16500 x (2/5)) = Rs. 6600\nRonald's share = Rs. (16500 x (1/5)) = Rs. 3300.\nAnswer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA girl has 7 jeans and 12 shirts. In how many different ways can she select a jeans and a shirts?\n\n### Options:\nA. A)100\nB. B)102\nC. C)108\nD. D)110\nE. E)84\n\n### Answer:\nThe girl can select one jeans in 7 ways.\nThe girl can select one shirt in 12 ways.\nThe number of ways in which he can select one jeans and one shirt is 7 * 12 = 84 ways.\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA disease has infected an ant colony that consists ofworkersandsoldiers: 30% of the soldiers and 14% of theworkerswere infected. If that colony is inhabited by 7000 ants, out of which 1620 are infected, how manyworkersinhabit the colony?\n\n### Options:\nA. 1500\nB. 2500\nC. 2750\nD. 3000\nE. 3250\n\n### Answer:\nFrom two question we get wo equations:\n(1) 0,3s + 0,14w = 1620\n(2) s + w = 7000\nFrom (2) we get w=7000-s\nIn (1) 0,3s + 980-0,14s= 1620\n0,16s=640\n64000:16= 4000 =s\nIn (2) 4000 + w = 7000\nw= 3000 D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nLakshmi went to the stationers and bought things worth Rs. 200, out of which 50 paise went on sales tax on taxable purchases. If the tax rate was 20%. then what was the cost of the tax free items?\n\n### Options:\nA. Rs. 197\nB. Rs. 190\nC. Rs. 187\nD. Rs. 167\nE. Rs. 191\n\n### Answer:\nSolution\nLet the amount of taxable purchases be Rs.x.\nThen, 20% of x\t= 50/100\nx \u2039=\u203a (50/100\u00d7100/20)\n= 2.50\nCost of tax free items\t= Rs.[200 - (2.50 + 0.50)]\n= Rs. 197\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man can row with a speed of 12 kmph in still water. If the stream flows at 11 kmph, then the speed in downstream is?\n\n### Options:\nA. 22\nB. 28\nC. 20\nD. 82\nE. 23\n\n### Answer:\nM = 12\nS = 11\nDS = 12 + 11 = 23. Answer:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf |x + 10| = 10 what is the sum of all the values of x.\n\n### Options:\nA. 20\nB. 40\nC. -20\nD. 0\nE. -40\n\n### Answer:\nThere will be two cases\nx+10 = 10 and x+10 = -10\nSolve for x => x=10-10=> x=0 or x= -10 - 10 => x= -20\nThe sum of both values will be 0 + -20 =-20\nAnswer is C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nCertain stocks in January were 40% less than they were in February and 15% greater than they were in March. What was the percentage decrease in the stocks from February to March?\n\n### Options:\nA. 50.81%\nB. 15.11%\nC. 20.7%\nD. 48.8%\nE. 40%\n\n### Answer:\nLet stocks value in Feb = 100 => In Jan = 60 and March = 60 * 100/115 = 51.2%\nThus, percent decrease in stocks from Feb to March = 100 - 51.2 = 48.8%\nHence Answer is D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich of the following is closer to \u221a0.8+\u221a0.1?\n\n### Options:\nA. 0.5\nB. 0.7\nC. 0.9\nD. 1.1\nE. 1.2\n\n### Answer:\n\u221a0.8+\u221a0.1=approximately \u221a0.81+\u221a0.09=0.9+0.3=1.2. Hence, the correct answer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe sum of the first 80 positive even integers is 2,550. What is the sum of the odd integers from 101 to 200, inclusive?\n\n### Options:\nA. 5,050\nB. 7,500\nC. 10,500\nD. 15,000\nE. 19,600\n\n### Answer:\n101+103+.......199\nIf we remove 100 from each of these it will be sum of 1st 100 odd numbers.\nso 101+103+.......199 = 80 * 100 + (1+3+5+7+......)\nsum of 1st 100 natural numbers = (100 * 101) / 2 = 5050\nSum of 1st 80 positive even integers = 2550\nsum of 1st 100 odd numbers = 5050 - 2550 = 2500\nso 101+103+.......199 = 80 * 100 + (1+3+5+7+......) = 8000 + 2500 =10500\nC is the answer.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nShreyas bought an article and sold it for 105% of its cost price. What was the cost price of the article, if Shreyas sold it for Rs.42000/-?\n\n### Options:\nA. Rs.40000\nB. Rs.45640\nC. Rs.44250/-\nD. Rs.43200\nE. None of these\n\n### Answer:\nExplanation:\n105% of CP = Rs.42000\n:. CP = Rs.42000x100/105 = Rs.40000.\nAnswer: Option A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA batsman in his 17th innings makes a score of 85 and their by increasing his average by 3. What is his average after the 17th innings ?\n\n### Options:\nA. 22\nB. 27\nC. 19\nD. 37\nE. 21\n\n### Answer:\n16x + 85 = 17(x + 3)\nx = 34 + 3 = 37\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA gambler has won 40% of his 20 poker games for the week so far. If, all of a sudden, his luck changes and he begins winning 80% of the time, how many more games must he play to end up winning 60% of all his games for the week?\n\n### Options:\nA. 20\nB. 25\nC. 30\nD. 35\nE. 40\n\n### Answer:\nLet x be the number of additional games the gambler needs to play.\n0.4(20) + 0.8x = 0.6(x+20)\n0.2x = 4\nx = 20\nThe answer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a, b, c are integers; a\u00b2 + b\u00b2 = 45 and b\u00b2 + c\u00b2 = 40, then the values of a, b and c respectively are :\n\n### Options:\nA. 2, 6, 3\nB. 3, 2, 6\nC. 5, 4, 3\nD. 4,5,3\nE. None of these\n\n### Answer:\na\u00b2 + b\u00b2 = 45 \u2026.(1) and b\u00b2 + c\u00b2 = 40\nSubtracting, we get: a\u00b2 - c\u00b2 = 5 => (a + c) (a \u2013 c) = 5.\n(a + c) = 5 and (a \u2013 c) = 1.\nSolving we get: a = 3, c = 2. Putting c = 2 in (ii), we get b = 6.\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the diagonal of a square field whose perimeter is 24m?\n\n### Options:\nA. 8 m\nB. 2 m\nC. 7 m\nD. 10 m\nE. 6\u221a2 m\n\n### Answer:\nSol:\nLet the side of the square be x meters.\nTherefore,\n4x=24\nx=6\nDiagonal of the square is= \u221a2*(6)^2=6\u221a2\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA garrison of 400 men had a provision for 31 days. After 28 days 300 persons re-enforcement leave the garrison. Find the number of days for which the remaining ration will be sufficient?\n\n### Options:\nA. 65 days\nB. 45 days\nC. 10 days\nD. 16 days\nE. 12 days\n\n### Answer:\n400 --- 31\n400 --- 3\n100 --- ?\n400*3 = 100*x => x =12 days.\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA, B, C, D, E, F are the only six families in Indira Nagar. A, B, C, D, E and F has 7, 8, 10, 13, 6, and 10 member in their families respectively. If 1 member from all the six families left their respective families to accommodate themselves in the hostel of IIM Lucknow, then the average number of member now in each family of Indira nagar is\n\n### Options:\nA. 8\nB. 9\nC. 10\nD. 13\nE. 15\n\n### Answer:\nAnswer\nRequired average\n= (( 7 - 1 ) + ( 8 - 1 ) + ( 10 - 1 ) + ( 13 - 1 ) + (6 - 1) +( 10 - 1 ) )/ 6\n= ( 7 + 8 +10 + 13 + 6 + 10 ) / 6 - ( 6 x 1 ) / 6\n=9 - 1 = 8\nCorrect Option: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain car dealership sells economy cars, luxury cars, and sport utility vehicles. The ratio of economy to luxury cars is 3:1. The ratio of economy cars to sport utility vehicles is 4:3. What is the ratio of luxury cars to sport utility vehicles?\n\n### Options:\nA. 9:8\nB. 8:9\nC. 4:9\nD. 2:3\nE. 1:2\n\n### Answer:\nThe ratio of economy to luxury cars is 3:1 --> E:L = 3:1 = 12:4.\nThe ratio of economy cars to sport utility vehicles is 4:3 --> E:S = 4:3 = 12:9.\nThus, L:S = 4:9.\nAnswer: C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nUsing all the letters of the word \"HEAD\", how many words can be formed, which begin with H and end with D?\n\n### Options:\nA. 8\nB. 4\nC. 2\nD. 7\nE. 9\n\n### Answer:\nThere are five letters in the given word.\nConsider 4 blanks ....\nThe first blank and last blank must be filled with H and D all the remaining three blanks can be filled with the remaining 2 letters in 2! ways.\nThe number of words = 2! = 2.\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many arrangements of the letters of the word BEGIN can be made, without changing the place of the vowels in the word?\n\n### Options:\nA. 6 ways\nB. 7 ways\nC. 9 ways\nD. 11 ways\nE. 13 ways\n\n### Answer:\nE,I fixed. Consonants can be arrangements in 3P3 = 3! = 6 ways\nA)\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat percent of a day is nine hours?\n\n### Options:\nA. 20.83%\nB. 16x1/2%\nC. 18x2/3%\nD. 37.5%\nE. None of these\n\n### Answer:\nExplanation :\nRequired percentage = (9/24100)%\n= 37.5%.\nAnswer : D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe sum of five consecutive odd numbers of set p is 435. What is the sum of five consecutive numbers of another set q. Whose largest number is 45 more than the largest number of set p?\n\n### Options:\nA. 530\nB. 670\nC. 730\nD. 770\nE. None of these\n\n### Answer:\nLet the five consecutive odd numbers of set p be 2n - 3, 2n - 1, 2n + 1, 2n + 3, 2n + 5.\nSum of these five numbers\n= 2n - 3 + 2n - 1 + 2n + 1 + 2n + 3 + 2n + 5\n= 10n + 5 = 435 => n = 43\nLargest number of set p = 2(43) + 5 = 91\nThe largest number of set q = 91 + 45 = 136\n=> The five numbers of set q are 132, 133, 134, 135, 136.\nSum of above numbers = 132 + 133 + 134 + 135 + 136 = 670.\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn the line xy plane line m has the equation y = 3x - 9, then the line m passes through which of the following points?\n\n### Options:\nA. (3, 1)\nB. (3, 4)\nC. (4, 2)\nD. (6, 9)\nE. (6, 15)\n\n### Answer:\nYes it is y=3x-8....extremely sorry for mistake....\nIF that's the case then answer is D\ny=3x-8\n9=3X6-9\n9=18-9\n9=9 (satisfied)\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n39 persons can repair a road in 12 days, working 5 hours a day. In how many days will 30 persons, working 6 hours a day, complete the work?\n\n### Options:\nA. 11\nB. 12\nC. 13\nD. 15\nE. 14\n\n### Answer:\nFirst codition=total hours to complete the work=39 persons * 12 days * 5 hr\nSecond codition=total hours to complete the work=30 persons * x days * 6 hr\nsince the work is still the same so\n39*12*5=30*x*6\nx=13\nanswer :C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA and B can do a piece of work in 10 days. With the help of C they finish the work in 5 days. C alone can do that piece of work in?\n\n### Options:\nA. 40 days\nB. 20 days\nC. 10 days\nD. 60 days\nE. 40 days\n\n### Answer:\nC\n10 days\nC = 1/5 \u2013 1/10 = 1/10 => 10 days\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man bought some mangoes at Rs12 per dozen and bought the same number of at Rs 10 per kg. He sold these mangoes at Rs 13 per dozen and gained Rs 160.The total number of mangos bought by him are\n\n### Options:\nA. 40dozens\nB. 60dozens\nC. 70dozens\nD. 80dozens\nE. 90dozens\n\n### Answer:\nlet total no of mangoes is 2x..\nthen we profit=sp-cp\n160=13*2x-(12x+10x)\n160=4x\nx=40\nhence 2x=80\nso total no are 80dozens\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a class, the teacher wrote a set of consecutive integers beginning with 1 on the blackboard. Little Johnny came and erased one number. The average of the remaining numbers was 2741327413. What was the number that Little Johnny erased?\n\n### Options:\nA. 7\nB. 9\nC. 11\nD. 13\nE. 15\n\n### Answer:\nWe have S = the sum of all integer from 1 to N\nx = the missing integer\nSo as sum = average * Nb of terms\nS-x= 27(4/13) * (N-1) (A)\nAs S-x should be an integer N-1 should be a multiple of 13.\nSo we have some possible scenario\nN-1= 13 => N=14\nN-1= 26 => N=17\nN-1= 39 => N=40\nN-1= 52 => N=53\n....\nBack to our formula (A)\nx = S - 27(4/13)*(N-1)\nx = (N(N+1))/2 - 27(4/13)*(N-1)\nAs x>0\n(N(N+1))/2 > 27(4/13)*(N-1)\napprox 27(4/13) by 27\n(N(N+1))/2 > 27*(N-1)\nN(N+1) > 54*(N-1)\nSo we see than N=53 is working (indeed 53*54>54*52)\nSo if N=53:\nx = (53(54))/2 - 27(4/13)*(52)\nx = (53(54))/2 - (27+4/13)*(52)\nx = (53(54))/2 - 27*52-(4/13)*52\nx = 53*27 - 27*52-(4/13)*52\nx = 53*27 - 27*52-4*4\nx = 27*(53-52) - 16\nx = 27 - 16\nx=11\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA series of boxes are placed on a conveyor belt at one end and unloaded at the other. The boxes are each 0.5 meters on each side and are placed immediately adjacent to one another as they are loaded. If the conveyor belt is 30 meters long and moves the boxes at a speed of 0.25 m/s, how long does it take for 100 boxes to be loaded and unloaded?\n\n### Options:\nA. 4 min 30 sec\nB. 4 min 50 sec\nC. 5 min 20 sec\nD. 5 min 40 sec\nE. 6 min 10 sec\n\n### Answer:\nC\n5 min 20 sec\nd = 100 * 0.5 m +30 m = 80 m\nT = 80 m / 0.25 m/s = 320 s = 5 min 20 sec\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe speed at which a man can row a boat in still water is 15 kmph. If he rows downstream, where the speed of current is 5 kmph, what time will he take to cover 60 metres?\n\n### Options:\nA. 16 seconds\nB. 76 seconds\nC. 10.8 seconds\nD. 12 seconds\nE. 18 seconds\n\n### Answer:\nSpeed of the boat downstream = 15 + 5\n= 20 kmph\n= 20 * 5/18 = 50/9 m/s\nHence time taken to cover 60 m\n= 60*9/50\n= 10.8 seconds.\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA group of men decided to do a work in 50days, but 10 of them became absent. If the rest of the group did the work in 60days, Find the original number of men?\n\n### Options:\nA. 60\nB. 50\nC. 40\nD. 100\nE. 25\n\n### Answer:\nOriginal number of men = 10*60 / (60-50) = 60\nAnswer is A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAn engineer designed a ball so that when it was dropped, it rose with each bounce exactly one-half as high as it had fallen. The engineer dropped the ball from a 20-meter platform and caught it after it had traveled 55 meters. How many times did the ball bounce?\n\n### Options:\nA. 5\nB. 6\nC. 3\nD. 8\nE. 9\n\n### Answer:\nGoing down = 20 m\nGoing Up = 10 --> Total = 30\nGoing down = 10 --> Total = 40\nGoing Up = 5 --> Total = 45\nGoing down = 5 --> Total = 50\nGoing up = 2.5 --> Total = 52.5\nGoing down = 2.5 --> Total =55(Caught)\nNo of bouncing = 3\nAnswer : C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSides of a rectangular park are in the ratio 4: 3 and its area is 3750 sq m, the cost of fencing it at 50 ps per meter is?\n\n### Options:\nA. s.132.3\nB. s.129\nC. s.125\nD. s.120\nE. s.121\n\n### Answer:\n4x * 3x = 3750 => x = 17.7\n2(82.3 + 50) = 264.6 m\n264.6 * 1/2 = Rs.132.3\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA chair is bought for Rs.1000/- and sold at a loss of 20% find its selling price\n\n### Options:\nA. Rs.800/-\nB. Rs.510/-\nC. Rs.515/-\nD. Rs.530/-\nE. Rs.540/-\n\n### Answer:\nLoss = 1000*20/100 = 200\nS.P = C.P - Loss\n= 1000- 200\n=Rs.800/-\nAnswer :A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n33 1/3% of 36?\n\n### Options:\nA. 16\nB. 21\nC. 18\nD. 12 number\nE. 18\n\n### Answer:\nExplanation:\n33 1/3 % = 1/3\n1/3 * 36 = 12\nAnswer: Option D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere exists exactly one positive value of k such that the line y = kx intersects the parabola\ny = x2 + x + 4 at exactly one point. Compute the intersection point.\n\n### Options:\nA. (2,10)\nB. (5,10)\nC. (7,10)\nD. (3,10)\nE. (1,10)\n\n### Answer:\nIf the line is tangent, then we must have that x2 + x + 4 = kx has a unique solution\nin x, or x2 + (1 - k)x + 4 = 0 has a unique solution. Thus, (1 - k)2- 16 = 0, or (1- k) = 4.\nTherefore, k = -3 or k = 5.\nTaking k = 5, we have that y = 5x intersects y = x2 + x + 4 when x = 2, and the intersection\npoint is (2, 10) .\ncorrect answer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are two circles of different radii. The are of a square is 784 sq cm and its side is twice the radius of the larger circle. The radius of the larger circle is seven - third that of the smaller circle. Find the circumference of the smaller circle?\n\n### Options:\nA. 6\nB. 5\nC. 8\nD. 6\nE. 3\n\n### Answer:\nLet the radii of the larger and the smaller circles be l cm and s cm respectively. Let the side of the square be a cm.\na2 = 784 = (4)(196) = (22).(142)\na = (2)(14) = 28\na = 2l, l = a/2 = 14\nl = (7/3)s\nTherefore s = (3/7)(l) = 6 Circumference of the smaller circle\n= 2\u220fs = 12\u220f cm.\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMarsha and Wenbao picked strawberries one afternoon. They combined all of their strawberries together and divided them evenly (50/50). If Marsha picked an odd number of strawberries which of the following is true?\n\n### Options:\nA. Wenbao picked 50 strawberries.\nB. Wenbao picked 49 strawberries.\nC. Wenbao picked 52 strawberries.\nD. Wenbao picked 40 strawberries.\nE. Wenbao picked 56 strawberries.\n\n### Answer:\nFrom Parity Mathematics Rule: The sum of two odd numbers is even. The sum of and odd number and an even number is odd.\nMarsha and Wenbao divided their strawberries evenly (50/50) after adding them together.\nMarsha picked an odd number of strawberries, so Wenbao had to have picked an odd number of strawberries.\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSet Y consists of the following unique integers: -2, 17, 3, n, 2, 15, -3, and -27; which of the following could be the median of set Y?\n\n### Options:\nA. 767\nB. 76\nC. 7\nD. 5\nE. 1\n\n### Answer:\nWhenever a question asks you to deal with the MEDIAN of a group of numbers, you MUST put the numbers in order from least to greatest (or at the very least,group offthe numbers so that you can restrict the potential value of the median).\nHere, we have 8 values (one of the values is the variable N). We're told that the values are UNIQUE, so N CANNOT be any of the other 7 values listed. We're asked which of the following answers COULD be the median, so if we determine that one of the answer choices is a POSSIBLE median, then we can stop working....\nSince the group includes 8 values, the median will be the AVERAGE of the 4th and 5th values...\nPutting the 7 numbers in order, we have:\n-27, -3, -2, 2, 3, 15, 17\nThis means that the2will either be the 4th term or the 5th term (depending on the value of N).\nIF....\nN is REALLY BIG, then the 4th and 5th terms will be 2 and 3, so the median will = 2.5\nN is REALLY SMALL, then the 4th and 5th terms will be -2 and 2, so the median will = 0\nNeither of those answers is among the choices though, so N must be something relativelycloseto 2.....\nIF....\nN = 0, then the 4th and 5th terms will be 0 and 2, so the median will = 1. That answer IS among the choices, so we're done.\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMohan purchased 10 kgs of rice at the rate of Rs.26 per kg and 10 kgs of pulses at the rate of Rs.26 per kg. Whaat is the total amount that he paid to the shopkeeper?\n\n### Options:\nA. A)Rs.520\nB. B)Rs.594\nC. C)Rs.596\nD. D)Rs.595\nE. None of these\n\n### Answer:\nExplanation:\nPrice of 10 kgs of rice at Rs.26/kg = 10x26 = Rs.260\nPrice of 8 kgs of pulses at Rs.26/kg = 10x26 = Rs.260\nTherefore, Total amount = Rs.260+Rs.260 = Rs.520.\nAnswer: Option A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 16 kmph and 22 kmph respectively. When they meet, it is found that one train has traveled 60 km more than the other one. The distance between the two stations is?\n\n### Options:\nA. 565\nB. 444\nC. 676\nD. 456\nE. 663\n\n### Answer:\n1h ----- 6\n? ------ 60\n12 h\nRS = 16 + 22 = 38\nT = 12\nD = 38 * 12 =456\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a bag there are a certain number of blue balls and white balls. The probability of picking up exactly 1 white ball when 2 balls are randomly drawn, is 1/2. Which of the following is the ratio of the number of blue balls to white balls in the bag\n\n### Options:\nA. 1:1\nB. 1:2\nC. 1:5\nD. 1:4\nE. 1:6\n\n### Answer:\nsince the probability of drawing a white ball out of two picks is 1/2.\nthe ratio of the white ball to blue balls should be 1:1\nAnswer : A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average of 13 numbers is 60. Average of the first 7 of them is 57 and that of the last 7 is 61. Find the 8th number?\n\n### Options:\nA. 46\nB. 83\nC. 45\nD. 53\nE. 64\n\n### Answer:\nSum of all the 13 numbers = 13 * 60 = 780\nSum of the first 7 of them = 7 * 57 = 399\nSum of the last 7 of them = 7 * 61 = 427\nSo, the 8th number = 427 + 399 - 780 = 46.\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf two projectiles are launched at the same moment from 1998 km apart and travel directly towards each other at 444 km per hour and 555 km per hour respectively, how many minutes will it take for them to meet?\n\n### Options:\nA. 90\nB. 100\nC. 110\nD. 120\nE. 130\n\n### Answer:\nThe projectiles travel a total of 999 km per hour.\nThe time to meet is 1998/999=2 hours = 120 minutes\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA radio station has to choose one day of the seven in a week to broadcast a certain program, and that set will repeat each week. The program can be broadcast equally on any of the seven weekdays \u2014- weekdays vs. weekends don\u2019t matter at all \u2014- nor does it matter whether the days the program airs are adjacent or not. Absolutely any three of the seven weekdays can be chosen. How many different three-day combinations of the seven weekdays can be constructed?\n\n### Options:\nA. 7\nB. 15\nC. 21\nD. 35\nE. 56\n\n### Answer:\nBehind the story, we are really being asked to evaluate 7C1. We could use the factorial formula, but above we conveniently happen to have Pascal\u2019s Triangle written out to the seventh row. We see that 7C1, the third entry of the seventh row, is 7. Answer = A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe grocer ordered deliveries of apples on each weekday. The numbers of apples he ordered per day were 80, 30, 100, 90 and x. If the median apple delivery was 10 apples larger than the average (arithmetic mean) number of apples delivered, which of the following could be x?\n\n### Options:\nA. 50\nB. 55\nC. 60\nD. 65\nE. 70\n\n### Answer:\nLook at the options available\nValue of x seems to 50 < = x < = 70\nA. 50\nB. 55\nC. 60\nD. 65\nE. 70\nSo position of x is second\n30 , x , 80 , 90 , 100\nMedian = 80\nMedian number of apples was 10 points higher than the average, so average = 70\n30 + x + 80 + 90 + 100 = 350\nx = 50 = Answer = A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA and B are mixed together in the ratio 9 : 11. What is the weight of mixture, if 26.1 kg of A has been consumed in it?\n\n### Options:\nA. 56\nB. 45\nC. 58.2\nD. 58\nE. 46\n\n### Answer:\nExplanation :\nFor 9 kg A, mixture = (9 + 11) kg.\nFor 26.1 kg A, mixture = ((20/9) x 26.1)kg = 58 kg.\nAnswer : D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich one the following fractions has the Lowest value?\n\n### Options:\nA. A)488/850\nB. B)499/850\nC. C)477/850\nD. D)511/850\nE. E)501/850\n\n### Answer:\nAll options have the same denominator 850. If denominator is same, the fraction with the lowest value will be the one with the Lowest numerator.\nAnswer (C).\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHealth insurance Plan A requires the insured to pay $1000 or 50% of total cost, whichever is lower. Plan B requires the insured to pay the initial $300, but then pays 80% of the cost over $300. Which of the following is a cost level for which both insurance plans pay out the same amount?\n\n### Options:\nA. $600\nB. $1000\nC. $3800\nD. $5300\nE. $6200\n\n### Answer:\nPay out for plan A: Cost-$1,000 or Cost-0.5*Cost=0.5*Cost, when 0.5*Cost<$1,000;\nPay out for plan B: 0.8(Cost-$300);\nThe question is: for which of the following costs the pay outs are the same.\nC-1,000=0.8(C-300) --> for C=3,800 and 0.5C=0.8(C-300) --> for C=800. As we have only $3,800 listed then it must be a correct answer.\nOr you can use backsolving for this question:\nA. C=$600: pay out for plan A will be 0.5*600=300 (as 0.5*600<1,000) and pay out for plan B will be 0.8*(600-300)=240;\nB. C=$1000: pay out for plan A will be 0.5*1,00=500 (as 0.5*1,000<1,000) and pay out for plan B will be 0.8*(1,000-300)=560;\nC. C=$3800: pay out for plan A will be 3,800-1,000=2,800 (as 0.5*3,800>1,000) and pay out for plan B will be 0.8*(3,800-300)=2,800 --> 2,800=2,800;\nD. C=$5300: pay out for plan A will be 5,300-1,000=4,300 (as 0.5*5,300>1,000) and pay out for plan B will be 0.8*(5,300-300)=4,000;\nE. C=$6200:pay out for plan A will be 6,200-1,000=5,200 (as 0.5*6,200>1,000) and pay out for plan B will be 0.8*(6,200-300)=4,720.\nAnswer: C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOf the mutual funds on a \u201cselect list,\u201d 2/3 have 5-star ratings, and 2/5 of the remaining funds have 4-star ratings. If the remaining 100 funds on the list have 3-star ratings, how many funds are on the list?\n\n### Options:\nA. 500\nB. 750\nC. 1,000\nD. 1,200\nE. 1,500\n\n### Answer:\nA\nFraction of 5- and 4-star funds: 2/3 + (2/5)*(1/3) = 2/3 + 2/15 = 12/15=4/5\nFraction of 3-star funds = 1 - 4/5 = 1/5\n(1/5)*Total = 100\nTotal = 500\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe citizens of planet nigiet are 8 fingered and have thus developed their decimal system in base 8. A certain street in nigiet contains 1000 buildings numbered 1 to 1000 in base 8. How many 3s are used in numbering these buildings?Express your answer in base 10\n\n### Options:\nA. 192\nB. 200\nC. 196\nD. 198\nE. None\n\n### Answer:\nExplanation :\nNumber 3 in 1-100 comes 20 times.\n101-200-> 20 times\n201-300-> 20 times\n301-400->120 times\n401-500-> 20 times\n501-600-> 20 times\n601-700-> 20 times\n701-800-> 20 times\n801-900-> 20 times\n901-1000-> 20 times\nTotal times: 300 times (any no. from 1 to 9 except 0 will occur 300 times)\n8 based planet.. then\n3*8(2) + 0*8(1) + 0*8(0) = 192\nAnswer : A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo trains of equal lengths take 10 sec and 12 sec respectively to cross a telegraph post. If the length of each train be 120 m, in what time will they cross other travelling in opposite direction?\n\n### Options:\nA. 11 sec\nB. 12 sec\nC. 17 sec\nD. 21 sec\nE. 23 sec\n\n### Answer:\nSpeed of the first train = 120/10 = 12 m/sec.\nSpeed of the second train = 120/12 = 10 m/sec.\nRelative speed = 12 + 10 = 22 m/sec.\nRequired time = (120 + 120)/22 = 11 sec.\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n8,27,64,125,216,???,512\n\n### Options:\nA. 346\nB. 343\nC. 348\nD. 339\nE. 340\n\n### Answer:\nit is a series of cubes of numbers....\n8=2^3\n27=3^3\n64=4^3\n125=5^3\n216=6^3\n512=8^3\nSo, 7^3=343 is the missing number.\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are 50 doors marked with numbers 1 to 50. There are 50 individuals marked 1 to 50.\nAn operation on a door is defined as changing the status of the door from open to closed or vice versa. All the doors are closed to start with. One at a time, one randomly chosen individual goes and operates the doors. The individual however operates only those doors which are a multiple of the number he/she is carrying. For example, the individual marked with number 5 operates the doors marked with 5, 10, 15, 20, 25, 30, 35, 40, 45, and 50. If every individual in the group gets one turn, then how many doors are open at the end?\n\n### Options:\nA. 0\nB. 2\nC. 5\nD. 7\nE. 9\n\n### Answer:\nIf a door is closed at the start, it requires an odd number of people to operate to be open at the end. Only the perfect squares have an odd number of factors.\nThe doors which are open at the end are: 1, 4, 9, 16, 25, 36, 49 for a total of 7 doors.\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the length of the sides of two cubes are in the ratio 6:1, what is the ratio of their total surface area?\n\n### Options:\nA. 6:1\nB. 12:1\nC. 24:1\nD. 36:1\nE. 72:1\n\n### Answer:\nLet x be the length of the small cube's side.\nThe total surface area of the small cube is 6x^2.\nThe total surface area of the large cube is 6(6x)^2=216x^2.\nThe ratio of surface areas is 36:1.\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the average marks of three batches of 62, 60 and 45 students respectively is 50, 55, 60, then the\naverage marks of all the students is\n\n### Options:\nA. 54.48\nB. 54.68\nC. 54.6\nD. 54.49\nE. None of these\n\n### Answer:\nExplanation:\n(62\u00c3\u201450)+(60\u00c3\u201455)+(45\u00c3\u201460)/(62+60+45)=54.49\nAnswer: Option D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many positive integers less than 120 are there such that they are multiples of 13 or multiples of 12 but not both?\n\n### Options:\nA. 13\nB. 19\nC. 15\nD. 16\nE. 17\n\n### Answer:\nfor 13: 13...117=13*9 = 117\nfor 12: 12...120=12*10 =120\nbut there is one integer 13*12. so\nN=(9)+(10)=19\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe ratio of two numbers is 4 : 5 and their H.C.F. is 4. Their L.C.M. is\n\n### Options:\nA. 48\nB. 22\nC. 80\nD. 27\nE. 35\n\n### Answer:\nExplanation:\nLet the numbers be 4x and 5x. Then, their H.C.F. = x. So, x = 4.\nSo, the numbers 16 and 20.\nL.C.M. of 16 and 20 = 80.\nAnswer: Option C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe percentage profit earned by selling an article for Rs. 1920 is equal to the percentage loss incurred by selling the same article for Rs. 1280. At what price should the article be sold to make 35% profit?\n\n### Options:\nA. 2000\nB. 2160\nC. 2299\nD. 2778\nE. 2771\n\n### Answer:\nLet C.P. be Rs. x.\nThen, (1920 - x)/x * 100 = (x - 1280)/x * 100\n1920 - x = x - 1280\n2x = 3200 => x = 1600\nRequired S.P. = 135 % of Rs. 1600 = 135/100 * 1600 = Rs. 2160.\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAn urn contains 5 black and 3 white balls. Two balls are drawn from the urn one after the other\nwithout replacement. What is the probability that both drawn balls are black?\n\n### Options:\nA. 1/5\nB. 3/7\nC. 2/5\nD. 5/14\nE. 2/7\n\n### Answer:\nLet E and F denote respectively the events that first and second ball drawn\nare black. We have to find P(E n F) or P (EF).\nNow P(E) = P (black ball in first draw) = 5/8\nAlso given that the first ball drawn is black, i.e., event E has occurred, now there are 4 black balls and three white balls left in the urn. Therefore, the probability that the second ball drawn is black, given that the ball in the first draw is black, is nothing but the conditional probability of F given that E has occurred.\nThat is P(F|E) = 4/7\nBy multiplication rule of probability, we have\nP (E n F) = P(E) P(F|E)\n= 5/8 \u00d7 4/7 = 5/14\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain sum earns simple interest of Rs. 800 in 2 years at a certain rate of interest. If the same sum earns compound interest of Rs.900in the same period of 2 years, What must be the rate of interest?\n\n### Options:\nA. 25%\nB. 10%\nC. 15%\nD. 20%\nE. 30%\n\n### Answer:\nExplanation:\nGiven: 800 = (P * R * 2) / 100\nS.I. For 1 year = Rs. 400\nThus, (900 \u2013 800) = S.I. on Rs. 400 for 1 year\n100 = (400 * R * 1) / 100\nR = 25% p.a.\nANSWER: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThree dice are thrown together, Find the probability of getting a total of atmost 5?\n\n### Options:\nA. 2/35\nB. 1/8\nC. 3/31\nD. 2/9\nE. 5/108\n\n### Answer:\nThree different dice are thrown at the same time.\nTherefore, total number of possible outcomes will be 63 = (6 \u00d7 6 \u00d7 6) = 216.\nNumber of events of getting a total of atmost 5 = 10\ni.e. (1, 1, 1), (1, 1, 2), (1, 2, 1), (2, 1, 1), (1, 1, 3), (1, 3, 1), (3, 1, 1), (2, 2, 1) and (1, 2, 2).\nTherefore, probability of getting a total of atmost 5\nP(E) = Number of favorable outcomes/Total number of possible outcome\n= 10/216\n= 5/108\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA no.when divided by 221 gives a remainder 43, what remainder will beobtained by dividingthe same no.17?\n\n### Options:\nA. 3\nB. 6\nC. 9\nD. 10\nE. 12\n\n### Answer:\n221 + 43 = 264/17 = 9 (Remainder)\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nNicole cycles at a constant rate of 10 kilometers per hour, and is passed by Jessica, who cycles at a constant rate of 20 kilometers per hour. If Jessica cycles at her constant rate for x minutes after passing Nicole, then stops to wait for her, how many minutes will Jessica have to wait for Nicole to catch up to her?\n\n### Options:\nA. a) x minutes\nB. b) x/2 minutes\nC. c) 2x/3 minutes\nD. d) 3x/2 minutes\nE. e) 2x minutes\n\n### Answer:\nSpeed of nicole = 20km/h or 20/60 km/min = 1/3 km/min.\nOnce jessica passed the nicole, the distance between the nicole and jessica will increase at the rate of (30-20) = 10km/h or 1/6 km/min\nnow jessica is cycling for x minutes after passing the nicole, so in those x minutes distance between jessica and nicole would be (1/6)*x = x/6 km.\nSo, the time taken by nicole to travel x/6 km = (x/6)/(1/3) = x/2. hence answer should be\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSix years hence,a fathers age will be three times his son's age and three years ago the fathers age is nine times as old as his son. the fathers present age is\n\n### Options:\nA. 24 years\nB. 28 years\nC. 30 years\nD. 40 years\nE. 45 years\n\n### Answer:\nLet \"f\" nd \"s\" be the father's nd son's present age respectively\n(f+6) = 3(s+6)\nf=3s+18-6\nf=3s+12\nf-3 = 9(s-3)\nf = 9s-27+3\nf=9s-24\nEquate \"f\"\n9s-24 = 3s+12\n6s = 36\ns=6\nf=3(6)+12\nf=30\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf x and y are distinct prime numbers less than ten, what must be true about the product of x and y?\n\n### Options:\nA. xy is even\nB. xy is odd\nC. xy < 0\nD. xy < 36\nE. xy > 6\n\n### Answer:\nPrime numbers less than 10 = 2, 3, 5, 7. x and y can take any oth the values\nOn checking the options\nA. xy is even\nxy can be even or odd both\nB. xy is odd\nxy can be even or odd both\nC. xy < 0\nProduct of two prime numbers can never be < 0\nPrime numbers are always positive\nD. xy < 36\nThe maximum value of multiplication can be 5*7 = 35.\nHence this is true always\nE. xy > 6\nx = 2, y = 3\nIn this case, xy = 6. FALSE\nCorrect Option: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAt Jefferson Elementary School, the number of teachers and students (kindergarten through sixth grade) totals 510. The ratio of students to teachers is 16 to 1. Kindergarten students make up 1/3 of the student population and fifth and sixth graders account for 1/3 of the remainder. Students in first and second grades account for 1/4 of all the students. If there are an equal number of students in the third and fourth grades, then the number of students in third grade is how many greater or fewer than the number of students in kindergarten?\n\n### Options:\nA. 12 greater\nB. 17 fewer\nC. 92 fewer\nD. 36 fewer\nE. 44 fewer\n\n### Answer:\nSoln>> from the given ratio of 16:1 u can derive that ter are 480 students\nKG= 1/3* 480 =160\n5th and 6th graders = 1/3 * 384= 128 (1/3 of remainder)\n1st and 2nd grade = 1/4 * 480 =120 ( 1/4 of all students)\nequal number of students in 3rd and 4th => 480 - 344= 136 and 136/2=68 each since equal number\n(344 is the sum of remaining students)\nthus 160-68 =92>>> therfore answer is 92 fewer\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAn aeroplane covers a certain distance at a speed of 240 kmph in 5 hours. To cover the same distance in 1 hours, it must travel at a speed of:\n\n### Options:\nA. 300 kmph\nB. 360 kmph\nC. 600 kmph\nD. 720 kmph\nE. 750 kmph\n\n### Answer:\nExplanation:\nDistance = (240 x 5) = 1200 km.\nSpeed = Distance/Time\nSpeed = 1200/(5/3) km/hr.\nRequired speed =(1200 X 3/5)km/hr\t= 720 km/hr.\nANSWER IS D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the remainder when 3^30 is divided by 5?\n\n### Options:\nA. 0\nB. 1\nC. 2\nD. 3\nE. 4\n\n### Answer:\nThe units digit of powers of 3 follow a repeating cycle of four: {3, 9, 7, 1}\n30 has the form 4k+2, so the units digit of 3^30 is 9.\nThe remainder when dividing by 5 is 4.\nThe answer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIfaequals the sum of the even integers from 2 to 20, inclusive, andbequals the sum of the odd integers from 1 to 19, inclusive, what is the value of a + b ?\n\n### Options:\nA. 110\nB. 100\nC. 190\nD. 200\nE. 210\n\n### Answer:\nAnswer is 10\nYes! there is really a faster way to solve it.\nSum of consecutive odd or even integers = (no. of odd or even ints) * (first int + last int) / 2\nHere A = sum of even ints from 2 to 20, inclusive\nnumber of even ints = 10,\nfirst int + last int = 2+20 = 22\nA = 10*22 / 2 = 110\nB = sum of odd ints from 1 to 19, inclusive\nnumber of odd ints = 10,\nfirst int + last int = 1+19 = 20\nA = 10*20 / 2 = 100\nA+B = 110 + 100 = 210\nAns :E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a club there are no more than 20 persons. What is the smallest number of fruits that must be brought to the club so that each person receives the same number of fruits?\n\n### Options:\nA. 26\nB. 75\nC. 80\nD. 45\nE. 33\n\n### Answer:\nThe number of persons is not specified. We are just given that there are no more than 20 persons.\nIf we assume that number of persons is 15 then answer will be B.\nIf we assume that number of persons is 20 then answer will be C because only 80 is divisible by 20.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich of the following is closest to (-2/3)^199\uff1f\n\n### Options:\nA. -1\nB. -1/2\nC. 0\nD. 1\nE. 2\n\n### Answer:\n(-2/3)^4 = 16/81 which is already less than 1/2.\nFor larger exponents, the expression will get closer and closer to zero.\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nX, Y, W and Z are intezers and the expressing X - Y - Z is even and Y - W - Z is odd. If X is even then which of\n\n### Options:\nA. W must be odd\nB. J must be odd\nC. Y must be odd\nD. Z must be odd\nE. F must be odd\n\n### Answer:\nAns. If X is even and X - Y - Z is even then Y and Z both should be odd or both should be even.\nIf Y - W - Z is odd, and Y and Z are also odd W should be odd\nIf Y - W - Z is even, and Y and Z are even then W should be odd.\nW must be ODD\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOn the x-y coordinate plane there is a parabola, y=x(6-x). Which of the following points is in the region that is enclosed by this parabola and the x-axis?\nI. (1, 6) II. (3, 11) III. (5, 4)\n\n### Options:\nA. I only\nB. II only\nC. III only\nD. I and II\nE. I, II, and III\n\n### Answer:\nSince co-efficient of x^2 is negative, the parabola will be downward facing. So the parabola and the x axis will enclose some points where the y-values of the parabola are positive.\nWhen x = 1, y = 5 lies on the parabola, so (1, 6) will not be enclosed by the parabola and x axis.\nWhen x = 3, y = 9 lies on the parabola, so (3, 11) will not be enclosed by the parabola and x axis.\nWhen x = 5, y = 5 lies on the parabola, so (5, 4) will be enclosed by the parabola and x axis.\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe parameter of a square is double the perimeter of a rectangle. The area of the rectangle is 480 sq cm. Find the area of the square.\n\n### Options:\nA. 290 sq cm\nB. 800 sq cm\nC. 209 sq cm\nD. Cannot be determined\nE. 200 sq cm\n\n### Answer:\nExplanation:\nLet the side of the square be a cm. Let the length and the breadth of the rectangle be l cm and b cm respectively.\n4a = 2(l + b)\n2a = l + b\nl . b = 480\nWe cannot find ( l + b) only with the help of l . b. Therefore a cannot be found .\nArea of the square cannot be found.\nAnswer: Option D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFive fencers participate in a fencing championship. Assuming all competitors have an equal chance of winning, how many possibilities are there with respect to how a first-place and second-place medal can be awarded?\n\n### Options:\nA. 6\nB. 8\nC. 12\nD. 16\nE. 20\n\n### Answer:\n5*4 = 20\nThe answer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAbhijit started a business investing 70000. Anuja joined him after 4 months with an amount of 105000 and Sunil joined them with 1.4 lakhs after another six months. The amount of profit earned should be distributed in what ratio among Abhijit, Anuja and Sunil respectively, three years after Abhijit started the business?\n\n### Options:\nA. 9: 13: 26\nB. 9 :12 :13\nC. 8 :14: 24\nD. 12:14:16\nE. 8 :15: 12\n\n### Answer:\nRatio of their investments\n= 70 \u00d7 36 : 105 \u00d7 32: 140 \u00d7 26 = 9 : 12 : 13\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf w,x,y and z are distinct odd positive integers,then the maximum value of the expression (w^2+x^2)*(y^2+z^2) can be divisible by?\n\n### Options:\nA. 2\nB. 3\nC. 5\nD. 8\nE. 10\n\n### Answer:\nANY ODD NUMBER SQUARE WILL GIVE ODD NUMBER ONLY..\nSIMILARLY WEN WE ADD 2 ODD NUMBERS WE WILL GET EVEN NUMBER..\nWEN WE MULTIPLY 2 EVEN OWE WILL GET EVEN NUBER..\nSO THE RESULT OF THE ABOVE EXPRESSION IS AN EVEN NUMBER ONLY..\nHENCE IT IS DIVISIBLE BY 2...\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe difference of two numbers is 20% of the larger number. If the smaller number is 12, the larger one is :\n\n### Options:\nA. 15\nB. 16\nC. 18\nD. 20\nE. None of these\n\n### Answer:\nLet the larger number be x.\nThen, x -12 = 20% of x<>x-(x/5)=12\n4x/5=12<=> x=(12\u22175)/5=15.\nAnswer :A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhen 6 fair coins are tossed simultaneously, in how many outcomes will the first and the last coin turn up heads?\n\n### Options:\nA. 1\nB. 3\nC. 16\nD. 31\nE. 30\n\n### Answer:\nTotal outcome is 2^6 = 64\nFavourable cases = H_ _ _ _ H\nThe second, third, fourth and fifth places can be occupied by either H or T\nThere are 2^4 =16 ways that can be done.\nHence, the correct option is C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTough and Tricky questions: Word Problems.\nIn a rare coin collection, one in six coins is gold, and all coins are either gold or silver. If 10 silver coins were to be subsequently traded for an additional 10 gold coins, the ratio of gold coins to silver coins would be 1 to 5. Based on this information, how many gold coins would there be in this collection after the proposed trade?\n\n### Options:\nA. 50\nB. 60\nC. 180\nD. 200\nE. 300\n\n### Answer:\nThe correct answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf Ram and Gohul can do a job in 10 days and 15 days independently. How many days would they take to complete the same job working simultaneously?\n\n### Options:\nA. 5\nB. 8\nC. 4\nD. 7\nE. 6\n\n### Answer:\nIf Total Work is X.\nRam rate of working=X/10 per day.\nGohul rate of working=X/15 per day.\nRate of work=(x/10)+(x/15)=30X/5X\n=6 days\nAnswer is option E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train 125 m long passes a man running at 5 km/hr in the same direction in which the train is going in 10 sec. The speed of the train is?\n\n### Options:\nA. 33 km/hr\nB. 50 km/hr\nC. 77 km/hr\nD. 65 km/hr\nE. 99 km/hr\n\n### Answer:\nSpeed of the train relative to man = 125/10 = 25/2 m/sec.\n= 25/2 * 18/5 = 45 km/hr\nLet the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr.\nx - 5 = 45 => x = 50 km/hr.\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe population of a town is 45000; 5/9th of them are males and the rest females 40% of the males are married. What is the percentage of married females?\n\n### Options:\nA. 56%\nB. 50%\nC. 57%\nD. 10%\nE. 80%\n\n### Answer:\nMale = 45,000* 5/9 = 25,000\nFemale = 45,000* 4/9 = 20,000\nMarried Male = 25,000* 40/100 = 10,000\nMarried Female = 10,000\n20,000 ------------ 10,000\n100 ------------- ? => 50%\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf x \u2260 0 and x^3 - (2- x^3)/x^3 = y/x^2, then y =\n\n### Options:\nA. -2-x\nB. -2+x\nC. -(x+2)\nD. -2/x\nE. 1/x\n\n### Answer:\nx^3 - (2- x^3)/x^3 = y/x^2\n-2/x^3 = y/x^2\ny = -2/x\nAnswer : D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA group of medical interns at Bohemus Medical School want to go on dates. There are 5 girls and 5 guys. Assuming girls go on dates with guys, how many possible ways can these 10 medical interns date each other?\n\n### Options:\nA. 10\nB. 25\nC. 60\nD. 90\nE. 120\n\n### Answer:\n1st girl can go with 5 guys\n2nd girl can go with remaining 4\n3rd girl can go with remaining 3 and so on\nso the total ways are 5!= 120\nE should be the answer\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n0, 2, 4, 8, 12, 18, 24, 32, ?\rWhat number should replace the question mark?\n\n### Options:\nA. 24\nB. 20\nC. 40\nD. 26\nE. 47\n\n### Answer:\nC 40\radd 2, 2, 4, 4,6, 6,.....\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA no. when divided by 35leaves a remainder 20, what is the remainder if the same no.be divided by 15?\n\n### Options:\nA. 2\nB. 4\nC. 7\nD. 8\nE. 9\n\n### Answer:\nExplanation:\n35 + 25 = 60/15 = 4 (Remainder)\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nW is an even integer greater than 300,000 and smaller than 1,000,000. How many numbers can W be?\n\n### Options:\nA. 300,000\nB. 349,999\nC. 350,000\nD. 399,999\nE. 400,000\n\n### Answer:\nW 1,000,000-300,000=700,000 integers\n700,000/2= 350,000 even integers.\n350,000+1 inclusive. But since 1,000,000 and 300,000 are not included.\n350,001-2=349,999\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 5/2 artists make 5/2 paintings using 5/2 canvases in 5/2 days then how many artists r required to make 25 paintings using 25 canvases in 25 days?\n\n### Options:\nA. 3/2\nB. 5/2\nC. 7/2\nD. 11/2\nE. 1/2\n\n### Answer:\n5/2 artists make 5/2 paintings using 5/2 canvases in 5/2 days. So, 1 artist make 1 painting using 1 canvas in 5/2 days. So, 1/10 artist make 1 painting using 1 canvas in 25 days.\nSo, 25/10 (=5/2) artists make 25 paintings using 25 canvases in 25 days.\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n1600 men have provisions for 28 days in the temple. If after 4 days, 400 men leave the temple, how long will the food last now?\n\n### Options:\nA. 76 days\nB. 98 days\nC. 32 days\nD. 45 days\nE. 24 days\n\n### Answer:\n1600 ---- 28 days\n1600 ---- 24\n1200 ---- ?\n1600*24 = 1200*x\nx = 32 days\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a1 = 1 and an+1= 2an + 5, n = 1, 2 .. , then a10 is equal to ?\n\n### Options:\nA. a. 6*2^9 -5\nB. b. 5*2^99+6\nC. c. 6*2^99+5\nD. d. 6*2^99-5\nE. e. 6*2^99-6\n\n### Answer:\nHere is solution:\nan+1=2an+5............(1)\nlets ADD 5 to both sides....\nso (an+1) + 5= 2 (an+5)....................taking 2 as common factor\nnow a1=1. so for n=1, an+5=6.......\nputting n=1. we get both sides as,\na2 + 5= 2 * 6 ..............as ( an+5=6 .......(for n=1)..)\na2= 2 *6 - 5\na2= 2 * 2 *3 - 5\na2= 2^2 *3 - 5................. so with same progression\na10= 2^10 * 3 - 5\na10=2* 2^9 * 3 - 5\na10= 6 * 2^9 - 5\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn the coordinate plane, points (x, 1) and (10, y) are on line k. If line k passes through the origin and has slope 1/4, then x + y =\n\n### Options:\nA. 6.5\nB. 7\nC. 8\nD. 11\nE. 12\n\n### Answer:\nLine k passes through the origin and has slope 1/4 means that its equation is y=1/4*x.\nThus: (x, 1)=(4, 1) and (10, y) = (10,2.5) --> x+y=4+2.5=6.5\nAnswer: A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the price of petrol increases by 25% and Bill intends to spend only an additional 15% on petrol, by how much % will he reduce the quantity of petrol purchased?\n\n### Options:\nA. A)8%\nB. B)7%\nC. C)10%\nD. D)6%\nE. E)9%\n\n### Answer:\nExplanation:\nAssume that the initial price of 1 Litre petrol = Rs.100 ,Bill spends Rs.100 for petrol,\nsuch that Bill buys 1 litre of petrol\nAfter the increase by 25%, price of 1 Litre petrol = 100 \u00d7 (100+25)/100 = Rs.125\nSince Bill spends additional 15% on petrol,\namount spent by Bill = 100\u00d7 (100+15)/100 = Rs.115\nHence Quantity of petrol that he can purchase = 115/125 Litre\nQuantity of petrol reduced = (1\u2212115/125) Litre\nPercentage Quantity of reduction = (1\u2212115125)/1 \u00d7 100 = 10/125 \u00d7 100 = 105 \u00d7 4 = 2 \u00d7 4 = 8%\nAnswer: Option A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train has a length of 150 meters . it is passing a man who is moving at 3 km/hr in the same direction of the train, in 3 seconds. Find out the speed of the train.\n\n### Options:\nA. 182 km/hr\nB. 180 km/hr\nC. 152 km/hr\nD. 169 km/hr\nE. 183 km/hr\n\n### Answer:\nExplanation:\nLength of the train, l = 150m\nSpeed of the man , Vm= 3 km/hr\nRelative speed, Vr = total distance/time = (150/3) m/s = (150/3) \u00d7 (18/5) = 180 km/hr\nRelative Speed = Speed of train, Vt - Speed of man (As both are moving in the same direction)\n=> 180 = Vt - 3\n=> Vt = 180 + 3 = 183 km/hr\nAnswer: Option E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFive years ago the average of the ages of A and B was 40 years and now the average of the ages of B and C is 49 years. What will be the age of the B ten years hence?\n\n### Options:\nA. 39\nB. 23\nC. 28\nD. 98\nE. 26\n\n### Answer:\nLet the present ages of A, B and C be a, b and c respectively.\nGiven, [(a - 5) + (b - 5)] / 2 = 40 => a + b = 90 --- (1)\n(b + c)/2 = 49 => b + c = 98 --- (2)\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhen the integer n is divided by 8, the remainder is 5. Which of the following is NOT an even number?\n\n### Options:\nA. n + 3\nB. n/2 + 3.5\nC. n \u2013 3\nD. 3n + 1\nE. 5n + 2\n\n### Answer:\nGiven number = N =8p+5 ---> the number N is odd.\nThus ,\nA. n + 3\nn+3 = odd + odd = even. Thus not correct.\nB. n/2 + 3.5\nAs n is odd, thus n/2 = abc.5 (where c = even) ---> abc.5+3.5 = abc+3+0.5+0.5 = even+odd+1= odd+1=even. Thus not correct.\nC. n \u2013 3\nn-3 = odd - odd = even. Thus not correct.\nD. 3n + 1\nAs n =odd, 3n=odd and 3n+1 = odd + odd = even. Thus not correct.\nE. 5n + 2\nAs n =odd, 5n= odd --->5n+2 = odd + even = odd. Thus correct. ANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA grocer has a sale of Rs. 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 6500?\n\n### Options:\nA. Rs. 4991\nB. Rs. 5991\nC. Rs. 6991\nD. Rs. 6001\nE. None of these\n\n### Answer:\nExplanation:\nTotal sale for 5 months = Rs. (6435 + 6927 + 6855 + 7230 + 6562) = Rs. 34009.\nRequired sale = Rs. [ (6500 x 6) - 34009 ]\n= Rs. (39000 - 34009)\n= Rs. 4991.\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average of 10 numbers is calculated as 5. It is discovered later on that while calculating the average, one number namely 36 was wrongly read as 26. The correct average is?\n\n### Options:\nA. 2\nB. 3\nC. 4\nD. 5\nE. 6\n\n### Answer:\n10 * 5 + 36 \u2013 26 = 60/10 = 6\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the 101st digit after the decimal point in the decimal representation of 1/3 + 1/9 + 1/27 + 1/37?\n\n### Options:\nA. 0\nB. 1\nC. 5\nD. 7\nE. 8\n\n### Answer:\n1/3 + 1/9 + 1/27 = 13/27. = .481481\u2026\n1/37=.027027\u2026\n13/27 + 1/27 = .508508..\nHence 101st digit is 0.(3*33 +2=> hence the second digit of the recurring decimal which is 0)\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n2, 5, 10, 17, 26, ?\n\n### Options:\nA. 35\nB. 36\nC. 48\nD. 49\nE. 37\n\n### Answer:\nThe sequence is a series of squares+1,\n1*1+1, 2*2+1, 3*3+1, 4*4+1, 5*5+1, 6*6+1=37\nAnswer : E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the sum of all the prime numbers greater than 30 but less than 50?\n\n### Options:\nA. 126\nB. 199\nC. 198\nD. 188\nE. 122\n\n### Answer:\nRequired sum = (31 + 37 + 41 + 43 + 47) = 199\nNote: 1 is not a prime number\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn expressing a length 81.475 km as nearly as possible with three significant digits, find the percentage error?\n\n### Options:\nA. 0.075%\nB. 0.156%\nC. 0.031%\nD. 0.048%\nE. 0.152%\n\n### Answer:\nError = 81.5-81.475 = 0.028\nRequired percentage = (0.028/81.475)*100 = 0.031%\nAnswer is C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRectangle ABCD is constructed in the coordinate plane parallel to the x- and y-axes. If the x- and y-coordinates of each of the points are integers which satisfy 6 \u2264 x \u2264 11 and -5 \u2264 y \u2264 5, how many possible ways are there to construct rectangle ABCD?\n\n### Options:\nA. 396\nB. 1260\nC. 825\nD. 7920\nE. 15840\n\n### Answer:\nAs the rectangle is parallel to coordinate axes, the coordinates of the points of the rectangle would be\n(X1, Y1), (X2, Y1), (X2, Y2), (X1,Y2)\ngiven that X1, X2 lie between 6 and 11..ie., 6 possible numbers\nPossible combinations for X1,X2 would be 6C2 = 15\nSimilarly, Possible combinations for Y1, Y2 would be 11C2 = 55\nPossible ways of constructing rectangle is by selecting any of the combination of X1,X2 and Y1,Y2\n= 15 * 55 = 825\nAns. C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMr.Jones gave 40% of the money he had to his wife. he also gave 20% of the remaining amount to his 3 sons. half of the amount now left was spent on miscellaneous items and the remaining amount of Rs.12000 was deposited in the bank. how much money did Mr.jones have initially?\n\n### Options:\nA. 100000\nB. 12000\nC. 15000\nD. 13000\nE. 65000\n\n### Answer:\nLet the initial amount with Mr.Jones be Rs.x\nThen, (1/2)[100-(3*20)]% of x=12000\n\uf0f3 (1/2)*(40/100)*(60/100)*x=12000\n\uf0f3x=((12000*25)/3)=100000\nANSWER A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a single throw of a die what is the probability of getting a number greater than 2 ?\n\n### Options:\nA. 2/3\nB. 1/4\nC. 2/5\nD. 1/3\nE. 1/5\n\n### Answer:\nwhen a die is thrown S={1,2,3,4,5,6}\nE = event of getting a number greater than 2 = {3,4,5,6}\nP(E) = n(E)/n(S) = 4/6 = 2/3\nAnswer is A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nPrinter P can print one lakh books in 8 hours. Printer Q can print the same number of books in 10 hours while Printer R can print the same in 12 hours. All the Printers started printing at 9 A.M. Printer P is stopped at 11 A.M. and the remaining 2printers complete work. Approximately at what time will the printing of 1 lac books be completed?\n\n### Options:\nA. 10 pm\nB. 1 pm\nC. 12 pm\nD. 2 pm\nE. 3 pm\n\n### Answer:\nWork done by P in 1 hour = 1/8\nWork done by Q in 1 hour = 1/10\nWork done by R in 1 hour = 1/12\nWork done by P,Q and R in 1 hour = 1/8 + 1/10 + 1/12 = 37/120\nWork done by Q and R in 1 hour = 1/10 + 1/12 = 22/120 = 11/60\nFrom 9 am to 11 am, all the Printer were operating.\nIe, they all operated for 2 hours and work completed = 2 \u00d7 (37/120) = 37/60\nPending work = 1- 37/60 = 23/60\nHours taken by Q an R to complete the pending work = (23/60) / (11/60) = 23/11\nwhich is approximately equal to 2\nHence the work will be completed approximately 2 hours after 11 am ; ie around 1 pm\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many liters of pure alcohol is in a 5 liter bottle where the alcohol is at 30 percent?\n\n### Options:\nA. 2.5\nB. 2\nC. 1\nD. 3\nE. 1.5\n\n### Answer:\n5/10 = .5\n.5 x 3 = 1.5\nAnswer is E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\na and b are two numbers selected randomly from 1,2,3.... 25 what is the probability of a and b are not equal.\n\n### Options:\nA. 1/25\nB. 24/25\nC. 13/25\nD. 2/25\nE. 3/25\n\n### Answer:\nNo of events=625((1,1),(1,2).......(25,25))\nProbability of getting a&b are equal=(25/625)[(1,1),(2,2),(3,3).....(25,25)]\nProbability of a and b or not equal=1-(25/625)\n=600/625\n=24/25\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nConsider the sets Tn = {n, n + 1, n + 2, n + 3, n + 4}, where n = 1, 2, 3,...., 78. How many of these sets contain 6 or any integral multiple thereof (i.e., any one of the numbers 6, 12, 18, ...)?\n\n### Options:\nA. (a) 80\nB. (b) 81\nC. (c) 82\nD. (d) 65\nE. (e) 84\n\n### Answer:\nT1: 1,2,3,4,5\nT2: 2,3,4,5,6\nT3: 3,4,5,6,7\netc.\nmeans that every multiple of 6 will be involved in 5 sets. We have (78-6)/6+1=13 such multiples.\nSo, final number of sets is 13*5=65\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA contractor undertakes to do a job within 100 days and hires 10 people to do it. After 20 days, he realizes that one fourth of the work is done so he fires 2 people. In how many more days W will the work get over?\n\n### Options:\nA. 60\nB. W=70\nC. W=75\nD. W=80\nE. W=100\n\n### Answer:\nWe can also use the concept of man-days here\n100 days -->10men so the job includes 100*10=1000 man-days\nAfter 20 days\n1/4 of Job is completed so 1/4 X 1000 man-days=250 man-days Job is done\nNow the Balance Job=1000-250=750 man-days worth of Job\nSince 2 men are fired so B/L men=8\nTherefore Total no. of days of Job=750 man-day/8 days = 375/4=94 days (approx.)\nNow since this is total and Ques. is asking for additional no. of days,\nSo 94-20=74 days\nThe nearest approx. to answer is 75\nAns: C (75 days)\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the 2nd greatest number of five digits which is exactly divisible by 12, 15 and 18?\n\n### Options:\nA. A)13050\nB. B)12960\nC. C)14090\nD. D)16200\nE. E)12080\n\n### Answer:\nThe largest five digit numbers are\n16200,14090,13050,12960,12080,\n16200 is divisible by 12, 15 and 18 ------(1st largest no)\n14090 is not divisible by 12\n13050 is not divisible by 12\n12960 is divisible by 18, 12 and 15 -------(2nd largest)\n12080 is not divisible by 12\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA seller of used cars has 10 cars to sell and each of his clients selected 2 cars that he liked most. If each car was selected exactly thrice, how many clients visited the garage?\n\n### Options:\nA. 8\nB. 10\nC. 15\nD. 14\nE. 16\n\n### Answer:\nIfNo caris selected more than once then the number of clients = 10/2 =5\nBut since every car is being selected three times so No. of Clients must be thrice as well =5*3 = 15\nAnswer: option C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nx and y are positive integers. When x is divided by 6, the remainder is 3, and when x is divided by 16, the remainder is 5. When y is divided by 9, the remainder is 5, and when y is divided by 7, the remainder is 4. What is the least possible value of x / y?\n\n### Options:\nA. 2.5\nB. 3\nC. 2\nD. 1.3\nE. 1.5\n\n### Answer:\nWhen x is divided by 6, the remainder is 3: So, the possible values of x are: 3, 9, 15, 21, etc.\nWhen x is divided by 16, the remainder is 5: So, the possible values of x are: 5,21... STOP. Since both lists include 21, the smallest possible value of x is 21.\nWhen y is divided by 9, the remainder is 5: So, the possible values of y are: 5, 14, 23,32 etc.\nWhen y is divided by 7, the remainder is 4: So, the possible values of y are: 6, 14, ...STOP. Since both lists include 14, the smallest possible value of y is 14\nSince the smallest possible values of x and y are 21 and 14 respectively, the smallest possible value of x / y is 1.5. So,E is the correct answer to the original question.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n88% OF 370+24% OF 210-?=118\n\n### Options:\nA. 256\nB. 258\nC. 268\nD. 358\nE. NONE OF THESE\n\n### Answer:\nLET 88% OF 370+240% OF 210-X=118\nTHEN, X=(88/100*370)+(24/100*210)-118-325.60+50.40-118=376-118=258\nCORRECT OPTION: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average height of 60 pupils in a class is 150 cm. Five of them whose height is 146 cm, leave the class and five others whose average height is 156 cm, join. The new average height of the pupils of the class (in cm) is ?\n\n### Options:\nA. 287 cm\nB. 150.8 cm\nC. 276 cm\nD. 287 cm\nE. 297 cm\n\n### Answer:\nTotal height = 150 * 60 = 9000 cm.\nNew average = [9000 - 5 * 146 + 5 * 156 ] / 60\n= 150.8 cm.\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man can row his boat with the stream at 6 km/h and against the stream in 4 km/h. The man's rate is?\n\n### Options:\nA. 1 kmph\nB. 7 kmph\nC. 98 kmph\nD. 6 kmph\nE. 4 kmph\n\n### Answer:\nDS = 6\nUS = 4\nS = ?\nS = (6 - 4)/2 = 1 kmph\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMohan purchased 15 kgs of rice at the rate of Rs.26 per kg and 8 kgs of pulses at the rate of Rs.26 per kg. Whaat is the total amount that he paid to the shopkeeper?\n\n### Options:\nA. Rs.598\nB. Rs.594\nC. Rs.596\nD. Rs. 595\nE. None of these\n\n### Answer:\nExplanation:\nPrice of 15 kgs of rice at Rs.26/kg = 15x26 = Rs.390\nPrice of 8 kgs of pulses at Rs.26/kg = 8x26 = Rs.208\nTherefore, Total amount = Rs.390+Rs.208 = Rs.598.\nAnswer: Option A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a apartment, 30% of the people speak English, 20% speak Hindi and 10% speak both. If a people is selected at random, what is the probability that he has speak English or Hindi?\n\n### Options:\nA. 1/3\nB. 2/3\nC. 2/5\nD. 2/7\nE. 2/9\n\n### Answer:\nP (E) = 30 / 100 = 3 / 10 , P (H) = 20 / 100 = 1 / 5 and P (E \u2229 H) = 10 / 100 = 1 / 10\nP (E or H) = P (E U H)\n= P (E) + P (H) - P (E \u2229 H)\n= (3 / 10) + (1 / 5) - (1 / 10) = 4 / 10 = 2/5\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe sum of the smallest six digit number and the greatest five digit number is\n\n### Options:\nA. 201110\nB. 199999\nC. 211110\nD. 1099999\nE. None\n\n### Answer:\nSolution\nRequires sum\t=(100000 + 99999)\n=199999.\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nP is a prime number. If 6p is between 15 and 95, which of the following T can be a value of 7p + 2?\n\n### Options:\nA. T=15\nB. T=79\nC. 121\nD. 65\nE. 21\n\n### Answer:\n[3,5,7,11,13] are prime numbers that fits this equation 15< 6X <95. Afterwards subtract 2 from all the answer n see if it's divisible by 7. Therefore A and E are out. Leaves out with B C D.\nB =11\nC =17\nD = 9\nOnly 11 is the set of prime numbers that fit between 15 and 95. Therefore 79 is the answer.B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man's speed with the current is 22 km / hr and the speed of the current is 4 km / hr. The man's speed against the current is\n\n### Options:\nA. 8.5 km / hr\nB. 9 km / hr\nC. 10 km / hr\nD. 14 km / hr\nE. None\n\n### Answer:\nSol.\nMan's rate in still in water = (22 - 4) km / hr = 18 km / hr.\nMan's rate against the current = (18 - 4) km / hr = 14 km / hr.\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe area of a square field is 4802 m(power)2 the length of its diagonal is:\n\n### Options:\nA. 98m\nB. 102m\nC. 95m\nD. 105m\nE. 96m\n\n### Answer:\nLet the diagonal be d metres,\nThen 1/2 d(power)2 = 4802\nd2 = 9604\nd = \u221a9604\nd = 98 m\nAnswer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 20% of a class averages 80% on a test, 50% of the class averages 60% on the test, and the remainder of the class averages 40% on the test, what is the overall class average?\n\n### Options:\nA. 80%\nB. 74%\nC. 58%\nD. 56%\nE. 50%\n\n### Answer:\n2 students scored 80%\n5 students scored 60%\n3 students scored 40%\n(2)(80) + 5(60) + 3(40) =\n160 + 300 + 120 =\n580\n580/10 students = 58 --> 58% average\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a games hour 4 different types of players came to the ground? cricket 15, hokey 12, football 13, softball 15. How many players are present in the ground?\n\n### Options:\nA. 70\nB. 52\nC. 55\nD. 49\nE. 50\n\n### Answer:\ntotal number of players= 15+12+13+15= 55\nAnswer is C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRs.590 is divided amongst A, B, C so that 5 times A's share, six times B's share and eight times C's share are all equal. Find C's share?\n\n### Options:\nA. Rs.157\nB. Rs.150\nC. Rs.289\nD. Rs.128\nE. Rs.129\n\n### Answer:\nA+B+C = 590\n5A = 6B = 8C = x\nA:B:C = 1/5:1/6:1/8\n= 24:20:15\n15/59 * 590 = Rs.150\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the average of all the numbers between 6 and 30 which are divisible by 4.\n\n### Options:\nA. 15\nB. 18\nC. 20\nD. 22\nE. None\n\n### Answer:\nSol.\nAverage = (8+12+16+20+24+28 / 6) = 108 / 6 = 18\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a function they are distributing noble prize. In how many ways can 2 prizes be distributed among 5 boys when a boy gets any no. of prizes?\n\n### Options:\nA. 25\nB. 30\nC. 64\nD. 70\nE. 80\n\n### Answer:\nAns.(A)\nSol. In this case, repetitions are allowed, so all the two prizes can be given in 5 ways, i.e. (5 x 5) ways = 52 ways = 25 ways Or nr ways = 52 ways = 25 ways\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe set X = {7,8,9,10}. The set Y = {2,3,4,5}. We will randomly choose one element x from set X and one element y from set Y. What is the probability that x / y will be an integer?\n\n### Options:\nA. 7/16\nB. 5/16\nC. 3/16\nD. 7/8\nE. 5/8\n\n### Answer:\nThe total number of x and y pairs is 4*4=16.\nThere are five pairs such that x / y is an integer.\nThe probability that x / y is an integer is 5/16.\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA sum of money triples itself in ten years at simple interest. Find the rate of interest?\n\n### Options:\nA. 12 1/2 % p.a.\nB. 14 1/2 % p.a.\nC. 20 % p.a.\nD. 22 % p.a.\nE. 25 % p.a.\n\n### Answer:\nLet the pricipal be Rs. x, then amount = 3x(where R = rate of interest) => Interest = 3x - x = Rs. 2x\nR = (100 * 2x)/(x * 10) = 20 %\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo men Amar and Bhuvan have the ratio of their monthly incomes as 6 : 5. The ratio of their monthly expenditures is 3 : 2. If Bhuvan saves one-fourth of his income, find the ratio of their monthly savings?\nA. 3 : 5\n\n### Options:\nA. 3:9\nB. 3:10\nC. 3:21\nD. 3:12\nE. 3:14\n\n### Answer:\nLet the monthly incomes of Amar and Bhuvan be 6x and 5x respectively.\nLet the monthly expenditure of Amar and Bhuvan be 3y and 2y respectively.\nSavings of Bhuvan every month = 1/4(5x)\n= (His income) - (His expenditure) = 5x - 2y.\n=> 5x = 20x - 8y => y = 15x/8.\nRatio of savings of Amar and Bhuvan\n= 6x - 3y : 1/4(5x) = 6x - 3(15x/8) : 5x/4 = 3x/8 : 5x/4\n= 3 : 10.\nAnswer: Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nwhat is the sum of all 5 digits numbers which can be formed with the digits 0,1,2,3,4 without repetition\n\n### Options:\nA. 2599980\nB. 2699980\nC. 2799980\nD. 2509980\nE. 2499980\n\n### Answer:\nThere is a simplest formula for solving these type of questions when we are using numbers along with 0 for finding sum.\ni,e........(sum of numbers)*{(n-1)!*(111...........n times)-(n-2)!*(111..........(n-1)times) }\nso,here by putting the values as,\n(0+1+2+3+4){(5-1)!*(11111)-(5-2)!*1111}\n= 10{(4!*11111)-(3!*1111)}\n= 10{266664-6666}\n= 2599980\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the scope including 1/31+1/32+1/33+......+1/40?\n\n### Options:\nA. 1/6~1/5\nB. 1/5~1/4\nC. 1/4~1/3\nD. 1/3~1/2\nE. 1/2~1\n\n### Answer:\nFor Maximum value : It should be less than 1/31 + 1/31 +1/31... 10 times = 10/31 ~ 1/3\nFor Minimum Value : It should be greater than 1/40+ 1/40+ 1/40 .. 10 times = 10/40 = 1/4.\nThus, the answer should lie between 1/4 and 1/3. Correct ans : C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nf n = 3^5 - 2^5, which of the following is NOT a factor of n?\n\n### Options:\nA. 211\nB. 422\nC. 633\nD. 100\nE. 844\n\n### Answer:\n=243-32 =211 is prime number.any number not a factor of 211\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA retailer sells products that belong to different categories, A to F, in alphabetical order. The number of products sold in each category is distinct and in ascending order. If at-least 2 products are sold in any category and a total of 27 products were sold last week, what is the probability that a product sold last week belonged to Category D?\n\n### Options:\nA. 2/27\nB. 4/27\nC. 5/27\nD. 8/27\nE. 15/27\n\n### Answer:\nthere are 6 distinct categories..\nSince each category has to have at least 2 products..\nlet A have 2 and each thereafter has ONE more than previous..\nso A,B,C,D,E, and F will have minimum 2+3+4+5+6+7 = 7*8/2 -1 = 28-1 =27..\ntherefore ONLY possibility of products in each due to restriction of TOTAL as 27 is 2,3,4,5,6,7 so D will have 5 products..\nProbability = 5/27\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA cistern is filled by pipe A in 16 hours and the full cistern can be leaked out by an exhaust pipe B in 20 hours. If both the pipes are opened, in what time the cistern is full?\n\n### Options:\nA. 50hrs\nB. 60hrs\nC. 70hrs\nD. 80hrs\nE. 90hrs\n\n### Answer:\ntime taken to full the cistern=(1/16-1/20)hrs\n=1/80\n=80hrs\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n2 pipes A and B can separately fill a cistern in 10 and 15 mins respectively. A person opens both the pipes together when the cistern should have been was full he findsthe waste pipe open. He then closes the waste pipe and in another 4 mins the cistern was full. In what time can the waste pipe empty the cistern when fill?\n\n### Options:\nA. 6\nB. 8\nC. 10\nD. 12\nE. 14\n\n### Answer:\n1/10 + 1/15 = 1/6 * 4 = 2/3\n1 - 2/3 = 1/3\n1/10 + 1/15 - 1/x = 1/3\nx = 8\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many words can be formed using the letters of the word \u201cCOMPANY\u201d?\n\n### Options:\nA. 1224\nB. 2434\nC. 3243\nD. 3435\nE. 5040\n\n### Answer:\nThere are \u20187\u2019 different letters of the word \u201cCOMPANY\u201d\nNumber of Permutations taking all the letters at a time = 7P7\n7!= 5040\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average expenditure of a man for the first five months is Rs.120 and for the next seven months it is Rs.130. If he saves Rs.290 in that year, his monthly average income is :\n\n### Options:\nA. Rs.140\nB. Rs.150\nC. Rs.160\nD. Rs.170\nE. none\n\n### Answer:\nExplanation:\nTotal income = Rs.(120\u00d75+130\u00d77+290)=Rs.1800\nAverage monthly income\n= Rs. (1800/12)=Rs.150\nCorrect Option: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFor any integer p, *p is equal to the product of all the integers between 1 and p, inclusive. How many prime numbers are there between *5 + 3 and *5 + 5, inclusive?\n\n### Options:\nA. None\nB. One\nC. Two\nD. Three\nE. Four\n\n### Answer:\nGenerally *p or p! will be divisible by ALL numbers from 1 to p. Therefore, *5 would be divisible by all numbers from 1 to 5.\n=> *5+3 would give me a number which is a multiple of 3 and therefore divisible (since *5 is divisible by 3)\nIn fact adding anyprimenumber between 1 to 5 to *5 will definitely be divisible.\nSo the answer is none (A)!\nSupposing if the question had asked for prime numbers between *5 + 3 and *5 + 11 then the answer would be 1. For *5 +3 and *5 + 13, it is 2 and so on...\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nLottery balls numbered consecutively from one through one hundred are placed in a spinner. If one ball is drawn at random, what is the probability that it will have the number 1 on it exactly once?\n\n### Options:\nA. 9/100\nB. 1/10\nC. 11/100\nD. 19/100\nE. 1/5\n\n### Answer:\nProbability = No of balls with exactly one 1 / total number of balls\n= {1,10,12 to 19, 21,31,41,51,61,71,81,91,100}/100\n= 19/100\nAnswer is D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA cylindrical water filter is filled with water at a rate of 11 cubic meters per hour, the level of water in the filter rises at a rate of 0.4 meters per hour. Which of the following best approximates the radius of the filter in meters?\n\n### Options:\nA. \u221a10/2\nB. \u221a10\nC. 4.183\nD. 5\nE. 10\n\n### Answer:\nHere's my re-worked solution:\nvolume = 11 = pi (r^2)(0.4)\n22 = 22/7 (4/10)(r^2)\n70/4 = r^2\nr = sqrt(70/4)\nAns: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n196, 144, 100, 64, 36, ?\n\n### Options:\nA. 16\nB. 8\nC. 18\nD. 12\nE. 6\n\n### Answer:\nExplanation :\nThe pattern is 14^2, 12^2, 10^2, 8^2, 6^2, ...\nSo next number is 4^2 = 16\nAnswer : Option A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If two marbles are picked at random, what is the probability that they are either blue or yellow?\n\n### Options:\nA. 2/29\nB. 2/20\nC. 2/21\nD. 2/28\nE. 2/23\n\n### Answer:\nGiven that there are three blue marbles, four red marbles, six green marbles and two yellow marbles. Probability that both marbles are blue = \u00b3C\u2082/\u00b9\u2075C\u2082 = (3 * 2)/(15 * 14) = 1/35\nProbability that both are yellow = \u00b2C\u2082/\u00b9\u2075C\u2082\n= (2 * 1)/(15 * 14) = 1/105\nProbability that one blue and other is yellow\n= (\u00b3C\u2081 * \u00b2C\u2081)/\u00b9\u2075C\u2082 = (2 * 3 * 2)/(15 * 14)\n= 2/35\nRequired probability = 1/35 + 1/105 + 2/35\n= 3/35 + 1/105 = 1/35(3 + 1/3)\n= 10/(3 * 35)\n= 2/21\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTough and Tricky questions: Percents.\nOver the course of a year, a certain microbrewery increased its beer output by 60 percent. At the same time, it decreased its total working hours by 30 percent. By what percent did this factory increase its output per hour?\n\n### Options:\nA. 228.5\nB. 228\nC. 229.5\nD. 220\nE. 229\n\n### Answer:\nLets assume the initial production was 100 litres of beer for 100 hr.\nWith the 60% increase the total amount of beer production will be 160 litres and with 30 % decrease in total hours will be reduced to 70 hr.\n100hr ----> 100 lts\n1hr -----> 1 lts\n70hr -----> 160 lts\n1hr -----> 2.28 lts\nTotal Increase in production for 1 hr = 228%\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA can complete a project in 20 days while B can complete same project in 30 days. If A and B start working together and A leaves the work 5 days before completion of project, then in how many days the project will be completed?\n\n### Options:\nA. 15\nB. 19\nC. 20\nD. 21\nE. 22\n\n### Answer:\nA's 1day work=1/20;\nB's 1day work=1/30;\n(A+B) 1day work=(1/20+1/30)=1/12;\nIt is given that A leaves the work 5 days before completion of the project..\nThus,B alone does the remaining job in 5 days.\nSo,In 5 days ,B can do 1/6 w ..\nThus,(A+B) have worked (1-1/6)=5/6 w..\n(A+B)can do 1/12 work in 1 day...\nThey did 5/6 w in 10 days.\nTotal days=(10+5) = 15\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe ratio between the length and the breadth of a rectangular park is 5 : 3. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 8 min, then thearea of the park (in sq. m) is?\n\n### Options:\nA. 124545 m\nB. 134561 m\nC. 156787 m\nD. 15450 m\nE. 150000 m\n\n### Answer:\nPerimeter = Distance covered in 8 min. = 12000 x 8 m = 1600 m.\n60\nLet length = 5x metres and breadth = 3x metres.\nThen, 2(5x + 3x) = 1600 or x = 100.\nLength = 500 m and Breadth = 300 m.\nArea = (500 x 300) m2 = 150000 m\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe length of a rectangular garden is three times its width. If the area of the rectangular garden is 675 square meters, then what is the width of the rectangular garden?\n\n### Options:\nA. 14\nB. 15\nC. 16\nD. 17\nE. 18\n\n### Answer:\nLet x be the width of the garden.\n3x^2 = 675\nx^2 = 225\nx = 15\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo stations A and B are 110 km apart on a straight line. One train starts from A at 7 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet?\n\n### Options:\nA. 11\nB. 10\nC. 8\nD. 12\nE. 15\n\n### Answer:\nSuppose they meet x hours after 7 a.m.\nDistance covered by A in x hours = 20x km.\nDistance covered by B in (x - 1) hours = 25(x - 1) km.\nTherefore 20x + 25(x - 1) = 110\n45x = 135\nx = 3.\nSo, they meet at 10 a.m.\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn an election between two candidates, the winner has a margin of 10% of the votes polled. If 3000 people change their mind and vote for the loser, the loser would have won by a margin of 10% of the votes polled. Find the total number of votes polled in the election?\n\n### Options:\nA. 23000\nB. 22000\nC. 20000\nD. 25000\nE. 30000\n\n### Answer:\nWinner - Looser\n55% - 45%\nIf 3000 people change their mind and vote for the loser:\nWinner - Looser\n45% - 55%\nThus 3,000 people compose 10% of all voters, which means that the total number of votes is 30,000.\nAnswer: E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich of the following is closest to 10^170 \u2013 10^30 ?\n\n### Options:\nA. 10^210\nB. 10^180\nC. 10^170\nD. 10^90\nE. 10^6\n\n### Answer:\n10^170 \u2013 10^30\n10^30 * (10^140 \u2013 1)\nas we know 10^2 - 1 means 100-1 and we get 99, which is approximately 100. hence (10^140 \u2013 1) would remain as 10^140.\nand 10^30 * 10^150 = 10^180. Answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n9 spheres of the same size are made from melting a solid cylinder of 16 cm diameter and 12 cm height. What is the diameter of each sphere?\n\n### Options:\nA. 4 cm\nB. 6 cm\nC. 8 cm\nD. 10 cm\nE. 12 cm\n\n### Answer:\nVolume of cylinder = pi*r^2*h\nVolume of a sphere = 4*pi*R^3 / 3\n9*4*pi*R^3 / 3 = pi*r^2*h\nR^3 = r^2*h / 12 = 64 cm^3\nR = 4 cm\nD = 8 cm\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRamu bought an old car for Rs. 42000. He spent Rs. 13000 on repairs and sold it for Rs. 66900. What is his profit percent?\n\n### Options:\nA. 17%\nB. 19%\nC. 18%\nD. 21.6%\nE. 16%\n\n### Answer:\nTotal CP = Rs. 42000 + Rs. 13000\n= Rs. 55000 and SP\n= Rs. 66900\nProfit(%) = (66900 - 55000)/55000 * 100\n= 21.6%\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how many ways can a committee consisting of 4 men and 5 women be formed from a group of 7 men and 10 women?\n\n### Options:\nA. 7C4 10C5\nB. 4C7 5C10\nC. 7C5 9C4\nD. 9C4 7C5\nE. NONE\n\n### Answer:\nGroup consisting of 7 men and 10 women\n4 men can be selected from 7 men in 7C4 ways\n5 women can be selected from 10 women in 10C5 ways\nTherefore, Total number of ways= 7C4 10C5\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a sample of data has mean of 20 and SD of 3, which of the following values is more than 2.7 SDs from the mean?\n\n### Options:\nA. 12.5\nB. 13\nC. 14\nD. 11.8\nE. 15\n\n### Answer:\n2.7 SD's mean is equal to: +/- 2.7*3 = +/- 8.1\nie. 11.9 to 28.1\nAnswer is: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the least number when successively divided by 2, 3 and 7 leaves remainders 1, 2 and 3 respectively?\n\n### Options:\nA. 22\nB. 65\nC. 28\nD. 27\nE. 19\n\n### Answer:\nExplanation:\n2) 65 (32 3) 32 (10 7) 10 (1\n64 30 7\n-------- -------- - -----\n1 2 3\n=> 65\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhen Alice entered the Forest of Forgetfulness, she forgot the day of\nthe week. She met the Lion and the Unicorn resting under a tree. The\nLion lies on Mondays, Tuesdays and Wednesdays and tells the truth\non the other days of the week. The Unicorn, on the other hand, lies\non Thursdays, Fridays, and Saturdays, but tells the truth on the other\ndays of the week. They made the following statements:\nLion: \\Yesterday was one of my lying days.\"\nUnicorn: \\Yesterday was one of my lying days.\"\nFrom these two statements, Alice was able to deduce the day of the\nweek. What day was it?\n\n### Options:\nA. Monday\nB. Wednesday\nC. Thursday\nD. Friday\nE. Sunday\n\n### Answer:\nIf the Lion is telling the truth, the day of the week must be Thursday. If he\nis lying, then the day of the week must be Monday. So the day of the week must be\neither Thursday or Monday. If the Unicorn is telling the truth, the day of the week must\nbe Sunday. If he is lying, then the day of the week must be Thursday. The day of the\nweek cannot be Sunday (since we have already said that it must be Thursday or Monday).\nTherefore, it must be Thursday\ncorrect answer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how many ways Chief Minister and Minister be elected from a team of 6 members?\n\n### Options:\nA. 124\nB. 29\nC. 30\nD. 154\nE. 165\n\n### Answer:\nTo do this, if captain is elected first, then we have 6 ways of doing this.\nFor election of vice-captain, we have only 5 ways left, coz 1 way is already consumed. (Situations like this is called dependent situation. One selection depends upon other selection.)\nSo, the ans is 6*5 = 30 ways.\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA sum was put at simple interest at certain rate for 3 years. Had it been put at 1% higher rate it would have fetched Rs. 78 more. The sum is: A. Rs. 2,400 B. Rs. 2,100 C. Rs. 2,200 D.Rs. 2,480\n\n### Options:\nA. 2000\nB. 2600\nC. 2200\nD. 2300\nE. 2400\n\n### Answer:\n1 percent for 3 years= 78\n1 percent for 1 year = 26\n=> 100 percent = 2600\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf XY denotes X is raised to the power Y, Find the last two digits of 19413843+ 19614181\n\n### Options:\nA. 12\nB. 22\nC. 42\nD. 82\nE. 92\n\n### Answer:\n1941^3843\nunit digit= 1^3=1\n10th digit=4*3=12=2 means last two digit =21\nand 1961^4181\nunit digit=1\n10th digit=6*1=6 mean last two digit= 61\nhence,\n21+61= 82\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSeven children \u2014 A, B, C, D, E,\u2014 are going to sit in seven chairs in a row. The children CE have to sit next to each other, and the others can sit in any order in any remaining chairs. How many possible configurations are there for the children?\n\n### Options:\nA. 600\nB. 720\nC. 48\nD. 4320\nE. 4800\n\n### Answer:\nfor such questions , we can treat both as one then total person=4..\nthese 4 can be arranged in 4! ways.. but within these 4, one consists of two people who can be arranged in 2 ways CF or FC.. so ans =4!*2=48\nans C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOn June 1 a bicycle dealer noted that the number of bicycles in stock had decreased by 3 for each of the past 5 months. If the stock continues to decrease at the same rate for the rest of the year, how many fewer bicycles will be in stock on September 1 than were in stock on January 1?\n\n### Options:\nA. 8\nB. 12\nC. 24\nD. 32\nE. 36\n\n### Answer:\nJan 1 = C\nFeb 1 = C - 3\nMarch 1 = C - 6\nApril 1 = C - 9\nMay 1 = C - 12\nJune 1 = C - 15\nJuly 1 = C - 18\nAug 1 = C - 21\nSept 1 = C - 24\nDifference between stock on September 1 than were in stock on January 1 will be -\nC - ( C - 24 )= 24\nHence answer will be (C)\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJohn bought 2 shares and sold them for $95 each. If he had a profit of 20% on the sale of one of the shares but a loss of 20% on the sale of the other share, then on the sale of both shares John had\n\n### Options:\nA. a profit of $10\nB. a profit of $8\nC. a loss of $8\nD. a loss of $10\nE. neither a profit nor a loss\n\n### Answer:\n$ Profit of the share sold at 20% profit =\n120-95\n20-?\n$15 profit on the sale of 1 share.\n$ Loss of the share sold at 20% loss=\n80-95\n20-?\n$25 loss on the sale of 1 share.\n15-25=Loss of $10\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA completes a work in 12 days and B complete the same work in 24 days. If both of them work together, then the number of days required to complete the work will be?\n\n### Options:\nA. 8 days\nB. 11 days\nC. 21 days\nD. 22 days\nE. 24 days\n\n### Answer:\nIf A can complete a work in x days and B can complete the same work in y days, then, both\nof them together can complete the work in x y/ x+ y days\nTherefore, here, the required number of days = 12 \u00d7 24/ 36 = 8 days.\nOption 'A'\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nLast year, Company Z made q dollars in profit. Half of the profit went to the company\u2019s founder. The rest was split evenly among his two other partners. In terms of q, how much did each of the other partners receive?\n\n### Options:\nA. q/4\nB. q/5\nC. q/6\nD. q/7\nE. q/8\n\n### Answer:\nProfit = q\nProfit to company founder = q/2\nProfit to other partners = q/2\nNumber of other partners = 2\nProfit to each partner = (q/2)/2 = q/4\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA rectangular farm has to be fenced one long side, one short side and the diagonal. If the cost of fencing is Rs.10 per meter. The area of farm is 1200 m2 and the short side is 30 m long. How much would the job cost?\n\n### Options:\nA. 2387\nB. 1298\nC. 1128\nD. 1237\nE. 1200\n\n### Answer:\nl * 30 = 1200 l = 40\n40 + 30 + 50 = 120\n120 * 10 = 1200\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat will be the least number which when doubled will be exactly divisible by 12, 18, 21 and 30?\n\n### Options:\nA. 228\nB. 630\nC. 998\nD. 267\nE. 212\n\n### Answer:\nL.C.M of 12, 18, 21, 30\n= 2 * 3 * 2 * 3 * 7 * 5 = 1260\nRequired number = 1260/2 = 630.\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIdentify the next two numbers in this Sequence ?\n101, 112, 131, 415, 161, 718, ???, ???\n\n### Options:\nA. 123005\nB. 456804\nC. 545788\nD. 342678\nE. 192021\n\n### Answer:\nE\n192 021\nIf you look at it as two-digit numbers you'll see:10 11 12 13 14 15 16 17 18 19 20 21\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIncreasing the original price of an article by 15 percent and then increasing the new price by 15 percent is equivalent to increasing the original price by\n\n### Options:\nA. 32.25%\nB. 31.00%\nC. 30.25%\nD. 30.00%\nE. 22.50%\n\n### Answer:\nYou can do this by approximation, or with straight math by calculating 100*1.15^2.\nOr step by step: if you increase 100 by 15% you'll get 115, then if you increase 115=100+15 by 15% again, 100 will gain 15 again and 15 will gain its 15% which is 2.25, so total gain is 15+2.25=17.25 --> 115+17.25=132.25.\nAnswer: A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA person spends 1/3rd of the money with him on clothes, 1/5th of the remaining on food and 1/4th of the remaining on travel. Now, he is left with Rs 300. How much did he have with him in the beginning?\n\n### Options:\nA. s 200\nB. s 750\nC. s 300\nD. s 450\nE. s 550\n\n### Answer:\nSuppose the amount in the beginning was Rs \u2019x\u2019\nMoney spent on clothes = Rs 1x/3 Balance = Rs 2x/3\nMoney spent on food = 1/5 of 2x/3 = Rs 2x/15\nBalance = 2x/3 - 2x/15 = Rs 8x/15\nMoney spent on travel = 1/4 of 8x/15 = Rs 2x/15 = 8x/15 - 2x/15 = 6x/15 = Rs2x/5\nTherefore 2x/5 = 300 = 750\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe speed of a subway train is represented by the equation z=s^2+2s for all situations where 0\u2264s\u22647, where z is the rate of speed in kilometers per hour and s is the time in seconds from the moment the train starts moving. In kilometers per hour, how much faster is the subway train moving after 7 seconds than it was moving after 5 seconds?\n\n### Options:\nA. 4\nB. 28\nC. 15\nD. 48\nE. 63\n\n### Answer:\nGiven: z=s^2+2s for 0\u2264s\u22647\nz(5) = 5^2 + 2*5 = 35\nz(7) = 7^2 + 2*7 = 63\nTherefore z(7) - z(3) = 63 - 35 = 28 km/hr\nOption B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo cars cover the same distance at the speed of 32 and 64 kmps respectively. Find the distance traveled by them if the slower car takes 1 hour more than the faster car.\n\n### Options:\nA. 73\nB. 38\nC. 64\nD. 83\nE. 93\n\n### Answer:\nExplanation:\n32(x + 1) = 64x\nX = 1\n32 * 2 = 64 km\nAnswer: Option C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA, B and C shared the profit in a business in the ratio 5 : 7 : 8. They had partnered for 14 months, 10 months and 7 months respectively. What was the ratio of their investments?\n\n### Options:\nA. 10:12:14\nB. 12:24:28\nC. 20:22:12\nD. 25:49:80\nE. None of these\n\n### Answer:\nExplanation :\nRatio in which A,B and C shared the profit = 5 : 7 : 8\nAssume that the ratio of their investment = a:b:c\nThen 14a : 10b : 7c = 5 : 7 : 8\nGood to go, we got the equation. Now it's a matter of time to find a, b and c\n14a/10b = 5/7\n=> 98a = 50b\n=> b = 98a/50 = 49a/25 ---(1)\n14a/7c =5/8\n=> 2a/c =5/8\n=> 16a = 5c\n=> c = 16a/5 ---(2)\na : b : c = a : 49a/25 : 16a/5 = 1 : 49/25 : 16/5 = 25 : 49 : 80. Answer : Option D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the greatest value of positive integer x such that 2^x is a factor of 100^70?\n\n### Options:\nA. 120\nB. 140\nC. 130\nD. 150\nE. 160\n\n### Answer:\nPut in simple words, we need to find the highest power of 2 in 100^70\n100 = 2^2*5^2\nTherefore 100^70 = (2^2*5^2)^70 = 2^140*5^140\nAnswer : B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo trains of equal lengths take 10 sec and 15 sec respectively to cross a telegraph post. If the length of each train be 140 m, in what time will they cross other travelling in opposite direction?\n\n### Options:\nA. 17 sec\nB. 12 sec\nC. 16 sec\nD. 14 sec\nE. 18 sec\n\n### Answer:\nSpeed of the first train = 120/10 = 12 m/sec.\nSpeed of the second train = 120/5 = 8 m/sec.\nRelative speed = 12 + 8 = 20 m/sec.\nRequired time = (140 + 140)/20 = 14 sec.\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe greatest number by which the product of three consecutive multiples of 4 is always\n\n### Options:\nA. 384\nB. 81\nC. 162\nD. 243\nE. None of these\n\n### Answer:\nExplanation:\n4*8*12 = 384\nOption A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nCindy paddles her kayak upstream at x kilometers per hour, and then returns downstream the same distance at n kilometers per hour. How many kilometers upstream did she travel if she spent a total of p hours for the round trip?\n\n### Options:\nA. mnp\nB. mn/p\nC. (x + n)/p\nD. xnp/(x + n)\nE. px/n- pn/x\n\n### Answer:\nlet t1 and t2 be the time taken to row upstream and downstream respectively\nnow,\nt1=distance/speed=d/x\nsimilarly,\nt2=d/n (as same distance has to be rowed)\nalso,\nt1+t2=p\ntherefore,\np=(d/x)+(d/n)\n=d(x+n)/xn\nd=pxn/(x+n)=D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRs.8000 become Rs.9261 in a certain interval of time at the rate of 5% per annum of C.I. Find the time?\n\n### Options:\nA. 2\nB. 9\nC. 8\nD. 3\nE. 5\n\n### Answer:\nn:\n9261 = 8000(21/20)N\n(21/20)3 = (21/20)N => N = 3\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOn dividing 109 by a number, the quotient is 9 and the remainder is 1. Find the divisor?\n\n### Options:\nA. 10\nB. 12\nC. 14\nD. 16\nE. 18\n\n### Answer:\nd = (D-R)/Q\n= (109 - 1)/9\n= 108/9 = 12\nB)\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA single discount equivalent to the discount series of 20%, 10% and 5% is?\n\n### Options:\nA. 31.9\nB. 31.2\nC. 31.6\nD. 71.2\nE. 31.1\n\n### Answer:\n100*(80/100)*(90/100)*(95/100) = 68.4\n100 - 68.4 = 31.6'\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo water pumps, working simultaneously at their respective constant rates, took exactly 9 hours to fill a swimming pool. If the constant rate of one pump was 1.5 times the constant rate of the other, how many hours would it have taken the faster pump to fill the pool if it had worked alone at its constant rate?\n\n### Options:\nA. 12\nB. 14\nC. 15\nD. 16\nE. 18\n\n### Answer:\nLet the rate of the slow pump be x. Then the rate of the fast pump is 1.5x.\n(x+1.5x) = 2.5x = 1/9 of the capacity of the whole pool per hour.\nThe rate of the fast pump is (1.5/2.5)*1/9 = 1/15 of the whole pool per hour.\nThe time it takes the faster pump to fill the pool would be 15 hours.\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the set S is composed of the following numbers {99, 100, 100, 105, 106, 111, 128}, which of the following is largest?\n\n### Options:\nA. The average (arithmetic mean) of set S\nB. The median of set S\nC. The mode of set S\nD. The range of set S\nE. The standard deviation of set S\n\n### Answer:\nA) 99, 100, 100, 105, 106, 111, 128 = 749 and its mean is 749/7 = 107.\nB) The list is of 7 numbers and median is 105.\nC) Mode is number of repetition of a number in the list , here it is 100.\nD) Range = Max value - min value = 128 -99 = 29.\nE) SD = square root of (sum of ( mean of series - number)^2 ) / n =>< 100\nIMO option A is correct answer..\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nPeter invested a certain sum of money in a simple interest bond whose value grew to $400 at the end of 3 years and to $ 600 at the end of another 2 years. What was the rate of interest in which he invested his sum?\n\n### Options:\nA. 100%\nB. 12.5%\nC. 67%\nD. 25%\nE. 33%\n\n### Answer:\nLets assume the Principal Amount (initial amount invested) to be P\nrate of interest to beRand time as T. We need to find R\nNow After a time of 3years the principal P amounts to $400 and after a time of 5years ( question says after another 5years so 3+2) P becomes $600.\nFormulating the above data\nAmount (A1) at end of 3years\nA1= P(1 + 3R/100) = 400\nAmount (A2) at end of 8years\nA2 = P(1 + 5R/100) = 600\nDividing A2 by A1 we get\n(1 + 5R/100)/(1 + 3R/100) = 6/8\nafter cross multiplication we are left with R =100\nOption: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a rectangular coordinate system, points O (2,2), P (2,12), and Q (10,2) represent the sites of three proposed housing developments. If a fire station can be built at any point in the coordinate system, at which point would it be equidistant from all three developments?\n\n### Options:\nA. (5,6)\nB. (8,7)\nC. (5,8)\nD. (6,6)\nE. (6,7)\n\n### Answer:\nAll points equidistant from O and Q lie on the line x = 6, so the fire station should lie on this line.\nAll points equidistant from O and P lie on the line y = 7, so the fire station should lie on this line.\nThese two intersect at (6,7) and that will be the point equidistant from all 3 points.\nThe answer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat was the day of the week on, 19th July, 1776?\n\n### Options:\nA. Friday\nB. Wednesday\nC. Monday\nD. Saturday\nE. SUNDAY\n\n### Answer:\n16th July, 1776 = (1775 years + Period from 1st Jan, 1776 to 16th July, 1776)\nCounting of odd days :\n1600 years have 0 odd day.\n100 years have 5 odd days.\n75 years = (18 leap years + 57 ordinary years) = [(18 x 2) + (57 x 1)] = 93 (13 weeks + 2 days) = 2 odd days.\n1775 years have (0 + 5 + 2) odd days = 7 odd days = 0 odd day.\nJan Feb Mar Apr May Jun Jul\n31 + 29 + 31 + 30 + 31 + 30 + 16 = 198 days= (28 weeks + 5 days)\nTotal number of odd days = (0 + 5) = 5.\nRequired day was 'Friday'.\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe price of a coat in a certain store is $500. If the price of the coat is to be reduced by $150, by what percent is the price to be reduced?\n\n### Options:\nA. 10%\nB. 15%\nC. 20%\nD. 25%\nE. 30%\n\n### Answer:\nprice of a coat in a certain store = $500\nthe price of the coat is to be reduced by $150\n% change = (Final Value - Initial Value)*100 / Initial Value\n% Reduction= (Reduction in Price)*100 / Initial Value\ni.e. % Reduction= (150)*100 / 500 = 30%\nAnswer: Option E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA fort had provision of food for 150 men for 45 days. After 10 days, 30 men left the fort. The number of days for which the remaining food will last, is:\n\n### Options:\nA. 29 1/5\nB. 37 1/4\nC. 43 3/4\nD. 54\nE. 48\n\n### Answer:\nAfter 10 days : 150 men had food for 35 days.\nSuppose 120 men had food for x days.\nNow, Less men, More days (Indirect Proportion)\nTherefore 120 : 150 :: 35 : x <=> 120 x x = 150 x 35\n=> x =150 x 35/120\n=> x = 43 3/4.\nCorrect answer is C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSahil purchased a machine at Rs 10000, then got it repaired at Rs 5000, then gave its transporta\u019fon\ncharges Rs 1000. Then he sold it with 50% of profit. At what price he actually sold it\n\n### Options:\nA. Rs. 22000\nB. Rs. 24000\nC. Rs. 26000\nD. Rs. 28000\nE. None of these\n\n### Answer:\nExplanation:\nQuestion seems a bit tricky, but it is very simple.\nJust calculate all Cost price, then get 150% of CP.\nC.P. = 10000 + 5000 + 1000 = 16000\n150% of 16000 = 150/100 * 16000 = 24000\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA sum was put at simple interest at certain rate for 3 years. Had it been put at 1% higher rate it would have fetched Rs. 72 more. The sum is: A. Rs. 2,400 B. Rs. 2,100 C. Rs. 2,200 D.Rs. 2,480\n\n### Options:\nA. 2000\nB. 2100\nC. 2200\nD. 2300\nE. 2400\n\n### Answer:\n1 percent for 3 years= 72\n1 percent for 1 year = 24\n=> 100 percent = 2400\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA does half as much work as Band C does half as much work as A and B together. If C alone can finish the work in 80 days, then together ,all will finish the work in :\n\n### Options:\nA. 13 1/3 days\nB. 16 days\nC. 15 days\nD. 20 days\nE. 30 days\n\n### Answer:\nC alone can finish the work in 80 days.\n(A + B)can do it in 20 days\n(A + B)s 1 days wok = 1/20.\nAs 1 days work : Bs 1 days Work = 1/2 : 1 = 1:2.\nA\u00e2\u20ac\u2122s 1 day\u00e2\u20ac\u2122s work = (1/20) * (1/3) = (1/60). [Divide 1/20 in the raio 1:2] Bs 1 days work = (1/20) * (2/3) = 1/30\n(A+B+c)S 1 day\u00e2\u20ac\u2122s work = (1/60) + (1/30) + (1/80) = 1/16\nAll the three together will finish it in 16 days.\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nReena took a loan of Rs. 1200 with simple interest for as many years as the rate of interest. If she paid Rs. 432 as interest at the end of the loan period, what was the rate of interest?\n\n### Options:\nA. 7\nB. 6\nC. 5\nD. 4\nE. 3\n\n### Answer:\nLet rate = R% and time = R years.\nThen, (1200 * R * R) / 100 = 432\n12R2 = 432\nR2 = 36 => R = 6.\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSet C consists of the following unique integers: -2, 17, 3, n, 2, 15, -3, and -27; which of the following could be the median of set C?\n\n### Options:\nA. 5\nB. 6\nC. 7\nD. 1\nE. 766\n\n### Answer:\nWhenever a question asks you to deal with the MEDIAN of a group of numbers, you MUST put the numbers in order from least to greatest (or at the very least,group offthe numbers so that you can restrict the potential value of the median).\nHere, we have 8 values (one of the values is the variable N). We're told that the values are UNIQUE, so N CANNOT be any of the other 7 values listed. We're asked which of the following answers COULD be the median, so if we determine that one of the answer choices is a POSSIBLE median, then we can stop working....\nSince the group includes 8 values, the median will be the AVERAGE of the 4th and 5th values...\nPutting the 7 numbers in order, we have:\n-27, -3, -2, 2, 3, 15, 17\nThis means that the2will either be the 4th term or the 5th term (depending on the value of N).\nIF....\nN is REALLY BIG, then the 4th and 5th terms will be 2 and 3, so the median will = 2.5\nN is REALLY SMALL, then the 4th and 5th terms will be -2 and 2, so the median will = 0\nNeither of those answers is among the choices though, so N must be something relativelycloseto 2.....\nIF....\nN = 0, then the 4th and 5th terms will be 0 and 2, so the median will = 1. That answer IS among the choices, so we're done.\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a:b=3:1 and b:c=1:4 find a:b:c?\n\n### Options:\nA. 1:6:2\nB. 3:1:4\nC. 2:3:4\nD. 2:3:3\nE. 1:4:2\n\n### Answer:\na:b = 3:1, b:c = 1:4\n3:1\n1:4\n(a = a \u00d7 b, b = b \u00d7 b and c = b \u00d7 c)\na:b:c = 3:1:4\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo trains each 150m in length each, are running on two parallel lines in opposite directions. If one goes at the speed of 95km/h while the other travels at 85km/h. how long will it take for them to pass each other completely.\n\n### Options:\nA. 25 sec\nB. 23 sec\nC. 34 sec\nD. 22 sec\nE. 6 sec\n\n### Answer:\nExplanation:\nD = 150 m + 150 m = 300 m\nRS = 95 + 85 = 180 * 5/18 = 50\nT = 300 * 1/50 = 6 sec\nAnswer: Option E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn Cliff\u2019s impressive rock collection, there are half as many igneous rocks as sedimentary rocks. Of the igneous rocks, 1/3 are shiny and the rest are matte, while 1/5 of the sedimentary rocks are shiny. If there are 30 shiny igneous rocks, how many total rocks does Cliff have?\n\n### Options:\nA. 30\nB. 45\nC. 270\nD. 90\nE. 135\n\n### Answer:\nWe can start with the known quantity and then go on to find the others.\nShiny igneous ricks are 30. These are (1/3) of total igneous rocks.\n(1/3)*Total igneous rocks = 30\nTotal igneous rocks = 30 * (3) = 90\nTotal sedimentary rocks = 2*Total igneous rocks = 2*90 = 180\nTotal number of rocks = 90 + 180 = 270\nAnswer (C)\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average earning of a mechanic for the first-four days of a week is Rs. 18 and for the last four days is Rs. 22. If he earns Rs . 41 on the fourth day, his average earning for the whole week is ?\n\n### Options:\nA. Rs . 18.95\nB. Rs 16\nC. Rs. 17\nD. Rs. 25.71\nE. None of these\n\n### Answer:\nAnswer\nTotal earning for the week = Sum of earning of first four days + Sum of earning of last four days - Earning of 4th day\n= 4 x18 + 4 x 22 -41\n= Rs. 119\n\u00e2\u02c6\u00b4 Average earning = 119 / 7\n= Rs. 17\nCorrect Option: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTotal number of 4 digit number do not having the digit 3 or 6.\n\n### Options:\nA. 22\nB. 28\nC. 27\nD. 19\nE. 11\n\n### Answer:\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man can row upstream at 25 kmph and downstream at 35 kmph, and then find the speed of the man in still water?\n\n### Options:\nA. 11\nB. 77\nC. 30\nD. 88\nE. 34\n\n### Answer:\nUS = 25\nDS = 35\nM = (35 + 25)/2 = 30\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe dimensions of a room are 25 feet * 15 feet * 12 feet. What is the cost of white washing the four walls of the room at Rs. 6 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each?\n\n### Options:\nA. s.4538\nB. s.4518\nC. s.4518\nD. s.4530\nE. s.5436\n\n### Answer:\nArea of the four walls = 2h(l + b)\nSince there are doors and windows, area of the walls = 2 * 12 (15 + 25) - (6 * 3) - 3(4 * 3) = 906 sq.ft.\nTotal cost = 906 * 6 = Rs.5436\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 6 parallel lines in a plane is intersected by a family of another 8 parallel lines, how many parallelograms are there in the network thus formed?\n\n### Options:\nA. 80\nB. 63\nC. 420\nD. 160\nE. 1260\n\n### Answer:\nparallelogram can formed by 2 horizontal and 2 vertical lines\nfor horizontal 6c2\nfor vertical 8c2\ntotal parallelogram is 6 c2*8c2=15*28\n=420\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nDimitri weighs 4x-3x pounds more than Allen weighs. Together, Allen and Dimitri weigh a total of y pounds. Which of the following represents Allen\u2019s weight?\n\n### Options:\nA. y - x/2\nB. 2x - y/2\nC. (y - x)/2\nD. y - 2x\nE. 2x - y\n\n### Answer:\nThese type of multi-variable story problems are usually perfect for TESTing VALUES.\nHere, we're told that Dimitri weighs 4X-3X or X pounds more than Allen weighs and that they weight a combined TOTAL of Y pounds.\nIF....\nDimitri = 30\nAllen = 20\nX = 10\nY = 50\nWe're asked for Allen's weight, so we're looking for an answer that equals 20 when X = 10 and Y = 50.\nAnswer A: 50 - (10/2) = 45 NOT a match\nAnswer B: 20 - (50/2) = -5 NOT a match\nAnswer C: (50-10)/2 = 20 This IS a match\nAnswer D: 50 - 20 = 30 NOT a match\nAnswer E: 20 - 50 = -30 NOT a match\nFinal Answer:\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA customer pays 40 dollars for a coffee maker after a discount of 20 dollars\nWhat is the original price of the coffe maker?\n\n### Options:\nA. 50\nB. 40\nC. 70\nD. 60\nE. 20\n\n### Answer:\nLet x be the original price.\nx - 20 = 40\nx - 20 + 20 = 40 + 20\nx + 0 = 60\nx = 60\nAnswer is D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA CAN FINISH A WORK IN 9 DAYS AND B CAN DO THE SAME WORK IN15 DAYS. B WORKED FOR 10 DAYS AND LEFT THE JOB. IN HOW MANY DAYS, A ALONE CAN FINISH THE REMAINING WORK?\n\n### Options:\nA. 3\nB. 5 1/2\nC. 6\nD. 8\nE. NONE OF THESE\n\n### Answer:\nB'S 10 DAY'S WORK=(1/15*10)=2/3 REMAINING WORK = (1-2/3)=1/3\nNOW, 1/18 WORK IS DONE BY A IN 1 DAY\n1/3 WORK IS DONE BY A IN (9*1/3)=3 DAYS.\nCORRECT OPTION:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA local bank that has 15 branches uses a two-digit code to represent each of its branches. The same integer can be used for both digits of a code, and a pair of two-digit numbers that are the reverse of each other (such as 17 and 71) are considered as two separate codes. What is the fewest number of different integers required for the 15 codes?\n\n### Options:\nA. 3\nB. 4\nC. 5\nD. 6\nE. 7\n\n### Answer:\nConsider the code XY. If there are nn digits available then X can take nn values and Y can also take nn values, thus from nn digits we can form n2n2 different 2-digit codes: this is the same as from 10 digits (0, 1, 2, 3, ..., 9) we can form 10^2=100 different 2-digit numbers (00, 01, 02, ..., 99).\nWe want # of codes possible from nn digit to be at least 15 --> n2\u226515n2\u226515 --> n\u22654n\u22654, hence min 4 digits are required.\nAnswer: B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nif 12401 is divided by any no. then quotient is 76 and remainder is 13.what is divisor?\n\n### Options:\nA. 154\nB. 124\nC. 153\nD. 163\nE. 183\n\n### Answer:\ndivisor=(dividend-remainder)/quotient=(12401-13)/76=12388/76=163\ndivisor = 163\nanswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRoger can read a book in k minutes. What part of the book can he read in 6 minutes? (k>8)\n\n### Options:\nA. 8+k\nB. 8/k\nC. k/8\nD. (k+ 8)/k\nE. (k-8) / k\n\n### Answer:\nLet's sayk = 24\nThat is, it takes 24 minutes to read the entire book.\nSo, in 8 minutes, Roger can read1/3of the book\nSo, we're looking for the answer choice that yields an OUTPUT of1/3whenk = 24\nA) 8+24=32ELIMINATE\nB) 8/24=1/3KEEP\nC)24/8 =3ELIMINATE\nD) (24+ 8)/24=32/24 = 4/3ELIMINATE\nE) (24-8) /24=16/24 = 2/3ELIMINATE\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average of 5 quantities is 10. The average of 3 of them is 4. What is the average of remaining 2 numbers?\n\n### Options:\nA. 19\nB. 14\nC. 8\nD. 9.5\nE. None of these\n\n### Answer:\nANSWER: A\n(5x10-3x4)/2=19\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nEach of the following numbers has a remainder of 3 when divided by 8 except:\n\n### Options:\nA. 11\nB. 19\nC. 3\nD. 83\nE. 26\n\n### Answer:\nIt's E\n26 = 8*3+2\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe population of a town has increased from 133575 to 138918. The percent increase in population is :\n\n### Options:\nA. 2.5\nB. 3\nC. 4.5\nD. 4\nE. 3.5\n\n### Answer:\n(133575-138918)/138918*100=4\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe ratio of boys to girls in Class A is 3 to 5. The ratio of boys to girls in Class B is 4 to 5. If the two classes were combined, the ratio of boys to girls in the combined class would be 17 to 22. If Class A has one more boy and two more girls than class B, how many girls are in Class A?\n\n### Options:\nA. 8\nB. 9\nC. 10\nD. 11\nE. 12\n\n### Answer:\nSince it is given that the ratio of boys to girls in Class A is 3 to 4 - so we can quickly eliminate the answer choices which are not multiples of 4.\nso ans can either be 8 0r 12.\nWith 8 as answer - no of girls = 8\nWith 12 as answer - no of girls = 12\nNow Class A has one more boy and two more girls than class B and also the ratio of boys to girls in Class B is 4 to 5.\nSo we are looking for number of girls in B to be divisible by 5.\nWith 8 as answer -> Girls = 8-2 = 6. (Not possible)\nWith 12 as answer -> Girls = 12-2 = 5.\nSo, answer = 10. ( C)\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf two positive numbers are in the ratio 1/8 : 1/7, then by what percent is the second number more than the first?\n\n### Options:\nA. 14.3%.\nB. 70%.\nC. 60%.\nD. 68%.\nE. 80%.\n\n### Answer:\nGiven ratio = 1/8 : 1/7 = 7 : 8\nLet first number be 7x and the second number be 8x.\nThe second number is more than first number by 1x.\nRequired percentage = 1x/7x * 100 = 14.3%.\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe length of a rectangular plot is thrice its width. If the area of the rectangular plot is 675 sq meters, then what is the width (in meters) of the rectangular plot?\n\n### Options:\nA. 12\nB. 15\nC. 18\nD. 21\nE. 24\n\n### Answer:\nArea = L*W = 3W^2 = 675\nW^2 = 225\nW = 15\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA thief goes away with a SANTRO car at a speed of 40 kmph. The theft has been discovered after half an hour and the owner sets off in a bike at 55 kmph when will the owner over take the thief from the start?\n\n### Options:\nA. A)1.33\nB. B)5\nC. C)7\nD. D)5\nE. E)8\n\n### Answer:\nExplanation:\n|-----------20--------------------|\n55 40\nD = 20\nRS = 55 \u2013 40 = 15\nT = 20/15 = 1.33 hours\nAnswer: Option A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average (arithmetic mean) of five numbers is 5. If 2 is subtracted from each of four of the numbers, what is the new average?\n\n### Options:\nA. 3.4\nB. 4.5\nC. 6.2\nD. 5.7\nE. 6.9\n\n### Answer:\nLet the numbers be a , b, c , d , e ,f\nSo, Total of these 5 numbers must be 25\nOr, a + b + c + d + e = 25\nSo, 12 must be subtracted from the total sum\ni.e a + b + c + d + e - 8\nOr, 25 - 8 = 17\nHence average of the 5 numbers now is 17/5 =>3.4\nSo, Answer will be A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nZinc and copper are melted together in the ratio 9 : 11. What is the weight of melted mixture, if 26.1 kg of zinc has been consumed in it?\n\n### Options:\nA. 58 kg\nB. 60 kg\nC. 64 kg\nD. 70 kg\nE. None\n\n### Answer:\nSol.\nFor 9 kg Zinc, mixture melted = (9+11) kg.\nFor 26.1 kg Zinc, mixture, melted = [20/9 x 26.1] kg\n= 58 kg.\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJar X is 1/5 full of water. Jar Y, which has half the capacity of Jar X, is 1/2 full of water. If the water in Jar Y is poured into Jar X, then Jar X will be filled to what fraction of its capacity?\n\n### Options:\nA. 2/5\nB. 3/5\nC. 7/10\nD. 7/20\nE. 9/20\n\n### Answer:\nLet P be the capacity of Jar X.\nThe amount of water in Jar Y is 1/2*P/2=P/4\nThen the total amount in Jar X is P/5+P/4=9/20\nThe answer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo trains are running at 40 kmph and 20 kmph respectively in the same direction.Fast train completely passes a man sitting in the slower train in 4 seconds.What is the length of the fast train?\n\n### Options:\nA. 23 m\nB. 22 2/9 m\nC. 27m\nD. 27 7/9m\nE. 29 7/9m\n\n### Answer:\nrelative speed=20kmph=50/9m/sec\nlength of the train=50/9*4= 22 2/9m\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRunning at the same rate, 8 identical machines can produce 560 paperclips a minute. At this rate, how many paperclips could 30 machines produce in 6 minutes?\n\n### Options:\nA. 1344\nB. 3360\nC. 8400\nD. 12600\nE. 67200\n\n### Answer:\n8 machines produce 560 in 1 min\n8 machines produce 560* 6 in 6 min\n30 machine produce 560*6*(30/8) in 6 minutes\n560*6*30/8=12600 answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf (2 to the x) - (2 to the (x-2)) = 3 (2 to the 5), what is the value of x?\n\n### Options:\nA. 7\nB. 11\nC. 13\nD. 15\nE. 17\n\n### Answer:\n(2 to the power x) - (2 to the power (x-2)) = 3 (2 to the power 5)\n2^x - 2^(x-2) = 3. 2^5\nHence x = 7.\nAnswer is A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhile flying over the Pacific, an airplane makes a 25\u00b0 turn to the right to avoid a storm. If, as a result, the airplane is traveling in a direction 8\u00b0 east of north, in what direction was it originally flying?\n\n### Options:\nA. (a) 30\u00b0 west of north\nB. (b) 30\u00b0 east of north\nC. (c) 17\u00b0 west of north\nD. (d) 17\u00b0 east of north\nE. (e) 5\u00b0 west of north\n\n### Answer:\nIf after a turn of 25\u00b0 you are 8\u00b0NEast, with a 17\u00b0 turn you would be perfectly pointing at north. So you were, before the turn, 17\u00b0 to the other side (West).\nAnswer C)\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA discount of 10 percent on an order of goods followed by a discount of 40 percent amounts to\n\n### Options:\nA. the same as one 46 percent discount\nB. the same as one 40 percent discount\nC. the same as one 36 percent discount\nD. the same as one 30 percent discount\nE. the same as one 25 percent discount\n\n### Answer:\n0.9*0.6*x=0.54x from initial value, meaning 0.46 or 46% discount\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nthe present average age of a couple and their daughter is 35 years. Fifteen years from now, the age of the mother will be equal to the sum of present ages of the father and the daughter. Find the present age of mother?\n\n### Options:\nA. 38\nB. 49\nC. 55\nD. 45\nE. 50\n\n### Answer:\nD\n45\n(f + m + d)/3 = 35\n=> f + m + d = 105 --- (1)\nm + 15 = f + d\nSubstituting f + d as m + 15 in (1), we get\n2m + 15 = 105\n2m = 90 => m = 45 years.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhen positive integer n is divided by 5, the remainder is 1. When n is divided by 7, the remainder is 3. What is the smallest positive integer k such that k+n is a multiple of 38?\n\n### Options:\nA. 3\nB. 4\nC. 7\nD. 32\nE. 35\n\n### Answer:\nn = 5p + 1 = 6,11,16,21,26,31\nn = 7q + 3 = 3,10,17,24,31\n=>n = 38m + 31\nTo get this, we need to take LCM of co-efficients of p and q and first common number in series.\nSo we need to add 7 more to make it\n38m + 38\nAnswer - C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA, B and C enter into partnership. A invests some money at the beginning, B invests double the amount after 6 months, and C invests thrice the amount after 8 months. If the annual gain be Rs.18300. A's share is?\n\n### Options:\nA. 8876\nB. 2765\nC. 6000\nD. 1298\nE. 6100\n\n### Answer:\nx* 12 : 2x* 6: 3x* 4\n1:1:1\n1/3 * 18300 = 6100\nAnswer:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat should come in place of the question mark(?) in the following equation?\n4 1\u20442 \u00d7 4 1\u20443 - 8 1\u20443 \u00f7 5 2\u20443 = ?\n\n### Options:\nA. 8\nB. 18 1\u204434\nC. 1 33\u204434\nD. 7\u204417\nE. None of these\n\n### Answer:\n? = 9\u20442 \u00d7 13\u20443 - 25\u20443 \u00d7 3\u204417\n= 39\u20442 - 25\u204417 = 663\u221250/34=61334=18 1/34\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nV is the volume of a cylinder; the radius of the cylinder is 3.5. The height of the cylinder is 650% more than the radius. Which of the following is true?\n\n### Options:\nA. 100 < V < 300\nB. 300 < V < 500\nC. 500 < V < 700\nD. 700 < V < 900\nE. 900 < V < 1100\n\n### Answer:\nAs we see the answers are in form of range we can use approximation\nVolume of cylinder is \u03c0r^2h\nGiven \u03c0= 22/7 and r = 3.5 so r^2 ~ 12 and h = 6.5 * 3.5 ~ 23\nSo 22/7 * 12 * 23 ~ 868\nso answer should be\nD. 700 < V < 900\nAnswer : D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?\n\n### Options:\nA. 199\nB. 87\nC. 120\nD. 150\nE. 388\n\n### Answer:\nSpeed=(60 * 5/18) m/sec = (50/3) m/sec Length of the train = (Speed x Time) = (50/3 * 9) m = 150 m.Answer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTough and Tricky questions: Percents.\nOver the course of a year, a certain microbrewery increased its beer output by 90 percent. At the same time, it decreased its total working hours by 5 percent. By what percent did this factory increase its output per hour?\n\n### Options:\nA. 200\nB. 100\nC. 300\nD. 400\nE. 500\n\n### Answer:\nLets assume the initial production was 100 litres of beer for 100 hr.\nWith the 90% increase the total amount of beer production will be 190 litres and with 5 % decrease in total hours will be reduced to 95 hr.\n100hr ----> 100 lts\n1hr -----> 1 lts\n95hr -----> 190 lts\n1hr -----> 2 lts\nTotal Increase in production for 1 hr = 200%\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a coin is tossed three times, what is the probability that on the first toss the coin lands on heads and then lands on tails the next two tosses?\n\n### Options:\nA. 1/8\nB. 1/3\nC. 1/4\nD. 1/2\nE. 1\n\n### Answer:\nP(HTT) = 1/2*1/2*1/2=1/8\nThe answer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich of the following numbers is divisible by 11?\n\n### Options:\nA. 4424\nB. 2232\nC. 1522\nD. 8524\nE. 9515\n\n### Answer:\n9515. This is the only option with last two digits divisible by 11\nAnswer:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAlice deposited Rs 2 million in bank at 4 % simple interest per year. After 10 year how many Rs she will get from bank?\n\n### Options:\nA. 75000\nB. 90000\nC. 10000\nD. 80000\nE. 60000\n\n### Answer:\ni = (200000*10*4)/100\ni = 80000\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a 8*8 chess board, what is the total number of squares refer model?\n\n### Options:\nA. 201\nB. 202\nC. 203\nD. 204\nE. 205\n\n### Answer:\n1x1 8 8 64\n2x2 7 7 49\n3x3 6 6 36\n4x4 5 5 25\n5x5 4 4 16\n6x6 3 3 9\n7x7 2 2 4\n8x8 1 1 1\ntotal 204\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf one-seventh of a number exceeds its eleventh part by 100 then the number is\u2026\n\n### Options:\nA. 770\nB. 870\nC. 1825\nD. 1925\nE. 925\n\n### Answer:\nlet no be :x\n1/7x-1/11x=100\n4x/77=100\nx=7700/4=1925\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nCountry C imposes a two-tiered tax on imported cars: the first tier imposes a tax of 10% of the car's price up to a certain price level. If the car's price is higher than the first tier's level, the tax on the portion of the price that exceeds this value is 8%. If Ron imported a $14,000 imported car and ended up paying $1440 in taxes, what is the first tier's price level?\n\n### Options:\nA. $1600\nB. $6000\nC. $6050\nD. $7050\nE. $8000\n\n### Answer:\nLet T be the tier price, P be total price = 14000\nPer the given conditions:\n0.10T + 0.08(P-T) = 1440 ----> T= 1600. A is the correct answer.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOne out of every 500 light bulbs are defected. If 2 out of every 10 defected light bulbs have a broken glass and there are 16 broken glass light bulbs in the shipment, how many light bulbs total are there in the shipment?\n\n### Options:\nA. 2,000\nB. 5,000\nC. 10,000\nD. 40,000\nE. 52,000\n\n### Answer:\nout of 500 only 1 bulb is defective.So for 10 defective bulbs, we must have 5000 bulbs\nNow out of these 10 bulbs, 2 bulbs, have broken glass\ni.e 2 broken glass out of 5000 bulbs\n16 broken glass will be from 40000 bulbs\nAnswer is D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe bankers discount and the true discount of a sum at 20% per annum simple interest for the same time are Rs.200 and Rs.150 respectively. What is the sum and the time?\n\n### Options:\nA. Sum = Rs.600 and Time = 1.6 years\nB. Sum = Rs.500 and Time = 1.6 years\nC. Sum = Rs.400 and Time = 1.6 years\nD. Sum = Rs.600 and Time = 3 years\nE. None of these\n\n### Answer:\nExplanation :\nBD = Rs.200\nTD = Rs.150\nR = 20%\nF = BD \u00d7TD/(BD \u2013 TD)=200\u00d7150/(200\u2013150)=200\u00d7150/50=Rs. 600\nBD = Simple Interest on the face value of the bill for unexpired time =FTR/100\n\u21d2200 = (600\u00d7T\u00d720)/100\n\u21d2200 = 6 \u00d7 T \u00d7 20 \u21d220 = 12 \u00d7 T\n\u21d2 T = 20/12 = 1.6 years Answer : Option A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nLook at this series: 53, 53, 48, 48, 43, 43, ... What number should come next?\n\n### Options:\nA. A)12\nB. B)14\nC. C)38\nD. D)53\nE. E)86\n\n### Answer:\nIn this series, each number is repeated, then 5 is subtracted to arrive at the next number.\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 16% of 40% of a number is 8, then the number is\n\n### Options:\nA. 200\nB. 225\nC. 125\nD. 320\nE. None of these\n\n### Answer:\nExplanation:\nLet 16/100\u00d740/100\u00d7a=8\na = 8\u00d7100\u00d7100/16\u00d740=125\nCorrect Option: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA shopkeeper sells two articles at Rs.1000 each, making a profit of 20% on the first article and a loss of 20% on the second article. Find the net profit or loss that he makes?\n\n### Options:\nA. neither profit nor loss\nB. 3%\nC. 5%\nD. 4%\nE. 6%\n\n### Answer:\nSP of first article = 1000\nProfit = 20%\nCP = (SP)*[100/(100+P)] = 5000/6 = 2500/3\nSP of second article = 1000\nLoss = 20%\nCP = (SP)*[100/(100-L)] = 5000/4 = 1250\nTotal SP = 2000\nTotal CP = 2500/3 + 1250 = 6250/3\nCP is more than SP, he makes a loss.\nLoss = CP-SP = (6250/3)- 2000 = 250/3\nLoss Percent = [(250/3)/(6250/3)]*100 =\n0.04 * 100 = 4%\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nKiran travels from A to B by car and returns from B to A by cycle in 7 hours. If he travels both ways by car he saves 3 hours. What is the time taken to cover both ways by cycle?\n\n### Options:\nA. 10\nB. 76\nC. 88\nD. 55\nE. 12\n\n### Answer:\nLet the time taken to cover from A to B in car and cycle be x hours and y hours respectively.\nx + y = 7 --- (1) ; 2x = 4 --- (2)\nsolving both the equations, we get y = 5\nSo, time taken to cover both ways by cycle = 2y hours = 10 hours.\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average of ten numbers is 7. If each number is multiplied by 12 ,then the average of new set of numbers is :\n\n### Options:\nA. 22\nB. 29\nC. 27\nD. 84\nE. 19\n\n### Answer:\nThe avg will be = 12\u00d77= 84\nAnswer:\tD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn an office in Singapore there are 60% female employees. 50 % of all the male employees are computer literate. If there are total 62% employees computer literate out of total 1600 employees, then the no. of female employees who are computer literate ?\n\n### Options:\nA. 690\nB. 674\nC. 672\nD. 960\nE. None\n\n### Answer:\nSolution: Total employees,\n= 1600\nFemale employees, 60% of 1600.\n= (60 *1600) /100 = 960.\nThen male employees,\n= 640\n50 % of male are computer literate,\n= 320 male computer literate.\n62 % of total employees are computer literate,\n= (62 *1600) /100 = 992 computer literate.\nThus, Female computer literate = 992 - 320\n= 672.\nAnswer: Option C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA person purchased a TV set for Rs. 12000 and a DVD player for Rs. 6250. He sold both the items together for Rs. 31150. What percentage of profit did he make?\n\n### Options:\nA. 16.68%\nB. 87.68%\nC. 70.68%\nD. 17.68%\nE. 18.68%\n\n### Answer:\nThe total CP = Rs. 12000 + Rs. 6250 = Rs. 18250 and SP\n= Rs. 31150\nProfit(%) = (31150 - 18250)/18250 * 100\n= 70.68%\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIt takes 1.5 hours for Tim to mow the lawn. Linda can mow the same lawn in 2 hours. How long will it take John and Linda, work together, to mow the lawn?\n\n### Options:\nA. 51.1 minutes\nB. 51.3 minutes\nC. 51.5 minutes\nD. 51.7 minutes\nE. 51.9 minutes\n\n### Answer:\nWe first calculate the rate of work of John and Linda\nJohn: 1 / 1.5 and Linda 1 / 2\nLet t be the time for John and Linda to mow the Lawn. The work done by John alone is given by\nt * (1 / 1.5)\nThe work done by Linda alone is given by\nt * (1 / 2)\nWhen the two work together, their work will be added. Hence\nt * (1 / 1.5) + t * (1 / 2) = 1\nMultiply all terms by 6\n6 (t * (1 / 1.5) + t * (1 / 2) ) = 6\nand simplify\n4 t + 3 t = 6\nSolve for t\nt = 6 / 7 hours = 51.5 minutes.\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n5\u20447 of 4\u204415 of a number is 8 more than 2\u20445 of 4\u20449 of the same number. What is half of that number?\n\n### Options:\nA. 630\nB. 315\nC. 210\nD. 105\nE. None of these\n\n### Answer:\nLet the number be x.\n\u2234 5\u20447 \u00d7 4\u204415 \u00d7 x - 2\u20445 \u00d7 4\u20449 \u00d7 x = 8\nor, x = 8\u00d731512=2108\u00d731512=210\n\u2234 Half of the number = 105\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat percentage of numbers from 1 to 100 have cube that end in the digit 5?\n\n### Options:\nA. 1\nB. 10.5\nC. 25\nD. 20\nE. 22\n\n### Answer:\nClearly, the numbers which have 1 or 9 in the unit's digit, have squares that end in the digit 1. Such numbers from 1 to 95 are 5,15,25,35,45,55,65,75,85,95.\nNumber of such numbers = 95.\nRequired percentage = (10/95 * 100) = 10.5%\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOf all the players in a professional baseball league, 1/2 are foreign-born, including 1/3 of the pitchers. If 3/4 of the players are pitchers, what percentage of the players who are not pitchers are foreign-born?\n\n### Options:\nA. 100%\nB. 75%\nC. 66 2/3%\nD. 50%\nE. 25%\n\n### Answer:\nAssume that the total number of players is 100.\n1/2 are foreign born, so 50 are foreign born. 75 players are pitchers out of which 1/3 are foreign born. 25 players are foreign born and pitchers. The other 25 who are foreign born are thus not pitchers.\nThus out of 25 non pitchers, 25 are foreign born. Answer: A - 100%\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf f(2, 3) = 17 and f(2, 4) = 24, what is the value of f(2, 5)?\n\n### Options:\nA. 107\nB. 127\nC. 147\nD. 33\nE. Cannot be determined\n\n### Answer:\nSolution:\nThe function f(a, b) = a3 + b2\nf(2, 3) therefore is = 17 and\nf(2, 4) = 24\nTherefore, f(2, 5) = 33\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf (m-8) is a factor of m^2-sm-24, then s=\n\n### Options:\nA. 3\nB. 5\nC. 6\nD. 11\nE. 16\n\n### Answer:\n(m-8)(m-a)=m^2-sm-24\nA=-3\ns=8+a=5=D=B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a train, travelling at a speed of 160 kmph, crosses a pole in 9 sec, then the length of train is?\n\n### Options:\nA. 281\nB. 125\nC. 288\nD. 266\nE. 400\n\n### Answer:\nD = 160 * 5/18 * 9\n= 400 m\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA FIVE DIGIT NUMBER IS FORMED BY USING THE DIGITS 1,2,3,4,5 WITH OUT REPETITIONS . WHAT IS THE PROBABILITY THE NUMBER IS DIVISIBLE BY5?\n\n### Options:\nA. 12/15\nB. 5/6\nC. 4/5\nD. 7/3\nE. 2/7\n\n### Answer:\nIf a number is divisible by 5 the last 1 digits of the number has 5.\nIf the number ends with 15: Number of possibilities = 4*3 * 2 * 1 = 24\nnumber ends with 25: Possibilities = 4*3 * 2 * 1 = 24\nnumber ends with 35: Possibilities =24\nnumber ends with 45: Possibilities =24\nTotal number of possibilities with restriction = 24*4= 96\nTotal number of possibilities without restriction = 5! = 120\nProbability = 96/120 = 12/15\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRashmi can do a piece of work in 16 days. Ravina can do the same work in 12 days while Gitika can do it in 32 days. All of them started to work together but Rashmi leaves after 4 days. Ravina leaves the job 3 days before the completion of the work. How long the work last?\n\n### Options:\nA. 14\nB. 15\nC. 16\nD. 17\nE. 18\n\n### Answer:\nx/3=x/6+3\nx=18.\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how many different number of ways 4 men and 2 women can sit on a shopa which can accommodate persons?\n\n### Options:\nA. 17\nB. 18\nC. 20\nD. 21\nE. 30\n\n### Answer:\n6p2 = 6 x 5 = 30\nAnswer : E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a class there are 10 boys and 15 girls. In how many ways can a boy and a girl be selected?\n\n### Options:\nA. 150\nB. 500\nC. 600\nD. 530\nE. 630\n\n### Answer:\nExplanation:\nWe can select one boy from 10 boys in 10 ways.\nWe select one girl from 15 girls in 15 ways\nWe select a boy and girl in 10 * 15 ways i.e., = 150 ways.\nAnswer: Option A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man could buy a certain number of notebooks for Rs.300. If each notebook cost is Rs.5 more, he could have bought 10 notebooks less for the same amount. Find the price of each notebook?\n\n### Options:\nA. 10\nB. 8\nC. 6\nD. 4\nE. 2\n\n### Answer:\nLet the price of each note book be Rs.x.\nLet the number of note books which can be brought for Rs.300 each at a price of Rs.x be y.\nHence xy = 300\n=> y = 300/x\n(x + 5)(y - 10) = 300 => xy + 5y - 10x - 50 = xy\n=>5(300/x) - 10x - 50 = 0 => -150 + x2 + 5x = 0\nmultiplying both sides by -1/10x\n=> x2 + 15x - 10x - 150 = 0\n=> x(x + 15) - 10(x + 15) = 0\n=> x = 10 or -15\nAs x>0, x = 10.\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nof polynomial for degree of x>+1 where f(x2)=f(x)2=f(f(x))\n\n### Options:\nA. 0\nB. 1\nC. 2\nD. 3\nE. 4\n\n### Answer:\nLet f(x) = x2\nf(x2)=[x2]2=x4\n(f(x))2=[x2]2=x4\nf(f(x))=f(x2)=[x2]2=x4\nOnly 1\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nBruno and Sacha are running in the same direction around a stadium. Sacha runs at a constant speed of 8 meters per second, and Bruno runs at a constant speed of 5 meters per second. At a certain point Sacha overtakes Bruno. If one minute afterward, Sacha stops and waits for Bruno to reach him, then how many seconds does he have to wait?\n\n### Options:\nA. 12\nB. 24\nC. 36\nD. 60\nE. 72\n\n### Answer:\nthe difference of the speed is 3m per second so in one minute Sacha will be 180 m ahead of Bruno..\nBruno will cover this in 180/5=36 secs..\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n39! is divided by 41. Then what is the remainder?\n\n### Options:\nA. 1\nB. 2\nC. 3\nD. 5\nE. 7\n\n### Answer:\nSubstituting p = 41 in the wilson's theorem, we get\n40!+141=0\n40\u00d739!+141=0\n\u22121\u00d739!41=\u22121\nCancelling -1 on both sides,\n39!41=1\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain characteristic in a large population has a distribution that is symmetric about the mean m. If 68 percent of the distribution lies within one standard deviation d of the mean, what percent Q of the distribution is less than m +d ?\n\n### Options:\nA. 16%\nB. 32%\nC. 48%\nD. 84%\nE. 92%\n\n### Answer:\nD\nThe prompt says that 68% of the population lies between m-d and m+d.\nThus, 32% of the population is less than m-d or greater than m+d.\nSince the population is symmetric, half of this 32% is less than m-d and half is greater than m+d.\nThus, Q=(68+16)% or (100-16)% of the population is less than m+d.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA person travels equal distances with speeds of 4 km/hr, 5 km/hr and 6 km/hr and takes a total time of 47 minutes. The total distance is?\n\n### Options:\nA. 2 km\nB. 4 km\nC. 7 km\nD. 9 km\nE. 5 km\n\n### Answer:\nLet the total distance be 3x km.\nThen, x/4 + x/5 + x/6 = 47/60\n37x/60 = 47/60 => x = 1.27\nTotal distance = 3 * 1.27 = 3.81 km.\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nCost of an item is Rs 12.60 & profit is 10% over selling price what is the selling price\n\n### Options:\nA. 12.86\nB. 13.86\nC. 14.86\nD. 15.86\nE. 16.86\n\n### Answer:\nProfit=( SP-CP/CP )*100\nCP=12.60\n(SP-12.60)/12.60*100 =10\nSP=13.86\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nExcluding stoppages, the speed of a bus is 58 kmph and including stoppages, it is 40 kmph. For how many minutes does the bus stop per hour?\n\n### Options:\nA. 19\nB. 19.13\nC. 10.5\nD. 11.35\nE. None of these\n\n### Answer:\nDue to stoppages, it covers 18 km less.\nTime taken to cover 18 km = ((18/58)\u00c3\u201460) = 19 min.\nOption(A) is correct\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the product of the integers w, x, y and z is 840, and if 1 < w < x < y < z, what is the value of w + z?\n\n### Options:\nA. 10\nB. 11\nC. 16\nD. 18\nE. 21\n\n### Answer:\n840= 4* 5 * 6* 7\nSo w = 4, x = 5, y = 6, z = 7\nw + z = 4+ 7= 11\nAnswer - B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThree coins are tossed. What is the probability of getting at most two tails\n\n### Options:\nA. 4/8\nB. 7/8\nC. 6/8\nD. 9/8\nE. 2/4\n\n### Answer:\nSince three coins are tossed, sample space = 8\nGetting at most two tails=7\np(E) =7/8\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA vendor sells 60 percent of apples he had and throws away 15 percent of the remainder. Next day he sells 50 percent of the remainder and throws away the rest. What percent of his apples does the vendor throw?\n\n### Options:\nA. 17\nB. 23\nC. 75\nD. 77\nE. None of these\n\n### Answer:\nLet the number of apples= 100\nsold 60% = 60 apples...remaining =40\nThrown away 15%= 6 apples\nRemaining =40-6=34\nsold 50 % of remaining = 34/2=17\nRemaining thrown away = 17 apples\nTotal thrown away =6+17=23\nPercentage thrown = 23/100=23%\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n2,300 has how many positive divisors?\n\n### Options:\nA. 12\nB. 15\nC. 18\nD. 24\nE. 30\n\n### Answer:\nBy factorization, we can write 2300 as 2300=2^2*5^2*23.\nThe number of factors is (2+1)(2+1)(1+1) = 18\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nPipes A and B can fill a tank in 5 and 6 hours respectively. Pipe C can empty it in 12 hours. If all the three pipes are opened together, then the tank will be filled in:\n\n### Options:\nA. 3 9 /17 hours\nB. 1 13 /17 hours\nC. 2 8 /11 hours\nD. 4 1 /2 hours\nE. None of these\n\n### Answer:\nExplanation:\nSolution 1\nPipes A and B can fill the tank in 5 and 6 hours respectively. Therefore,\npart filled by pipe A in 1 hour =1/5\npart filled by pipe B in 1 hour =1/6\nPipe C can empty the tank in 12 hours. Therefore,\npart emptied by pipe C in 1 hour =1/12\nNet part filled by Pipes A,B,C together in 1 hour =1/5 +1/6+1/12 =17/60\ni.e., the tank can be filled in 60/17=3 9/17 hours.\nANSWER IS A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a regular week, there are 5 working days and for each day, the working hours are 8. A man gets Rs. 2.40 per hour for regular work and Rs. 3.20 per hours for overtime. If he earns Rs. 432 in 4 weeks, then how many hours does he work for ?\n\n### Options:\nA. 160\nB. 175\nC. 180\nD. 195\nE. 200\n\n### Answer:\nExplanation:\nSuppose the man works overtime for x hours.\nNow, working hours in 4 weeks = (5 x 8 x 4) = 160.\n160 x 2.40 + x x 3.20 = 432\n3.20x = 432 - 384 = 48\nx = 15.\nHence, total hours of work = (160 + 15) = 175.\nANSWER IS B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how many years will a sum of money doubles itself at 25% per annum on simple interest?\n\n### Options:\nA. 4%\nB. 8%\nC. 10%\nD. 12%\nE. 15%\n\n### Answer:\nP = (P*25*R)/100\nR = 4%\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRs.8000 become Rs.8487.20 in a certain interval of time at the rate of 3% per annum of C.I. Find the time?\n\n### Options:\nA. 6 years\nB. 8 years\nC. 9 years\nD. 3 years\nE. 2 years\n\n### Answer:\n8487.20 = 8000(34/30)N\n(34/30)^2 = (34/30)N => N = 2\nAt the end of three years what will be the comp.Answer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo boats are heading towards each other at constant speeds of 5 miles/hr and 23 miles/hr respectively. They begin at a distance 20 miles from each other. How far are they (in miles) one minute before they collide ?\n\n### Options:\nA. 1/12\nB. 7/12\nC. 1/6\nD. 1/3\nE. 1/5\n\n### Answer:\nThe question asks: how far apart will they be 1 minute=1/60 hours before they collide?\nSince the combined rate of the boats is 5+23=25 mph then 1/60 hours before they collide they'll be rate*time=distance --> 28*1/60=7/15 miles apart.\nAnswer: B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are 7 identical pens and 9 identical books. In how many different ways can a person select at least one object from this set?\n\n### Options:\nA. 16\nB. 31\nC. 48\nD. 79\nE. 90\n\n### Answer:\nWe can select from 0 to 7 pens and from 0 to 9 books.\nThus the total possible ways to select objects is 8*10 = 80\nWe must subtract 1 for the case with 0 pens and 0 books.\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJeni has 7 flavors of cake in his bakery. How many options are there for Sheera to pick a one-flavor, two-flavor,three-flavor, four-flavor, five-flavor, six-flavor or seven-flavor order?\n\n### Options:\nA. 423\nB. 325\nC. 142\nD. 171\nE. 127\n\n### Answer:\n7C1 + 7C2+ 7C3+7C4+7C5+7C6+7C7 =127 .\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the probability of getting exactly 4 heads in a single throw of five fair coins?\n\n### Options:\nA. 1/4\nB. 3/8\nC. 3/16\nD. 5/32\nE. 7/32\n\n### Answer:\nOne possible case is HHHHT.\nP(HHHHT) = 1/2*1/2*1/2*1/2*1/2 = 1/32\nThere are 5C4 = 5 possible cases.\nP(4 heads) = 5*1/32 = 5/32\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf |x| = 7x - 5, then x = ?\n\n### Options:\nA. 1\nB. 1/2\nC. 1 and 1/2\nD. 2\nE. -1\n\n### Answer:\nAnswer: A\nApproach:\nSubstituted option A i.e x=1. Inequality satisfied.\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nX can do a piece of work in 15 days. If he is joined by Y who is 50% more efficient, in what time will X and Y together finish the work?\n\n### Options:\nA. 10 days\nB. 6 days\nC. 18 days\nD. Data insufficient\nE. None of these\n\n### Answer:\nX\u2019s one day\u2019s work = 1\u204415 th work.\nY\u2019s one day\u2019s work = 1\u204415 + 50% of 1\u204415 = 1\u204410 th work.\n\u2234 (X + Y)\u2019s one day\u2019s work = 1\u204415 + 1\u204410 = 1\u20446 th work.\nHence, they together finish the work in 6 days.\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOn dividing a number by 357, we get 38 as remainder.On dividing the same number by 17, what will be the remainder ?\n\n### Options:\nA. 4\nB. 5\nC. 8\nD. 7\nE. 2\n\n### Answer:\nLet x be the number and y be the quotient.Then,\nx=357*y+38\n=(17*21*y)+(17*2)+4\n=17*(21y+2)+4.\nRequired number =4.\nAnswer is A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train traveling with constant speed crosses a 90m long platform in 12 seconds and a 120m long platform in 15 seconds.Find the length of the train and its speed.\n\n### Options:\nA. 30\nB. 40\nC. 60\nD. 50\nE. NOne\n\n### Answer:\nLet the length of the train be x m and its speed be y m/sec.\nThen, x/y = 12 => y = x/12\n(x + 90)/12 = x+120/15 => x = 30 m.\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe area of a parallelogram is 72 sq m and its altitude is twice the corresponding base. Then the length of the base is?\n\n### Options:\nA. 6\nB. 16\nC. 8\nD. 36\nE. none\n\n### Answer:\n2x * x = 72 => x\n= 6\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe sector of a circle has radius of 21 cm and central angle 135o. Find its perimeter?\n\n### Options:\nA. 91.5 cm\nB. 91.8 cm\nC. 61.8 cm\nD. 91.6 cm\nE. 92.5 cm\n\n### Answer:\nPerimeter of the sector = length of the arc + 2(radius)\n= (135/360 * 2 * 22/7 * 21) + 2(21)\n= 49.5 + 42 = 91.5 cm\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo trains started at the same time, one from A to B and the other from B to A . If they arrived at B and A respectively 16 hours and 49 hours after they passed each other the ratio of the speeds of the two trains was\n\n### Options:\nA. 2:1\nB. 3:2\nC. 4:3\nD. 7:4\nE. 1:2\n\n### Answer:\nExplanation:\nNote : If two trains (or bodies) start at the same time from points A and B towards each other and after crossing they take a and b sec in reaching B and A respectively, then: (A's speed) : (B's speed) = (b : a)\nTherefore, Ratio of the speeds of two trains = = 7 : 4. Answer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train covers a certain distance at a speed of 300kmph in 4 hours. To cover the same distance in 2 hours, it must travel at a speed of\n\n### Options:\nA. 600km/hr\nB. 700km/hr\nC. 800km/hr\nD. 900km/hr\nE. 1000km/hr\n\n### Answer:\nExplanation:\nDistance = 300\u00d74 = 1200km\nRequired speed = (1200/2) = 600km/hr\nAnswer: Option A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRobert is traveling on his cycle and has calculated to reach point A at 2 p.m. if he travels at 10 km/hr; he will reach there at 12 noon if he travels at 15 km/hr. At what speed must he travel to reach A at 1 p.m.?\n\n### Options:\nA. 22\nB. 88\nC. 12\nD. 77\nE. 99\n\n### Answer:\nLet the distance traveled be x km.\nThen, x/10 - x/15 = 2\n3x - 2x = 60 => x = 60 km.\nTime taken to travel 60 km at 10 km/hr = 60/10 = 6 hrs.\nSo, Robert started 6 hours before 2. p.m. i.e., at 8 a.m.\nRequired speed = 60/5 = 12 kmph.\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere is a 100 pound watermelon laying out in the sun. 99 percent of the watermelon's weight is water. After laying out for a few hours 98 percent of the watermelon's weight is water.\nHow much water evaporated?\n\n### Options:\nA. 20\nB. 30\nC. 40\nD. 50\nE. 10\n\n### Answer:\nIn the beginning it is 99 pounds water and 1 pound other stuff. At the end the 1 pound other stuff is 2 percent so the total weight is 50 pounds. 50 pounds - 1 pound other stuff = 49 pounds water. So 99 pounds - 49 pounds = 50 pounds water lost.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain sum is invested at simple interest at 15% p.a. for two years instead of investing at 12% p.a. for the same time period. Therefore the interest received is more by Rs. 420. Find the sum?\n\n### Options:\nA. s. 5000\nB. s. 7000\nC. s. 14000\nD. s. 17000\nE. s. 27000\n\n### Answer:\nLet the sum be Rs. x.\n(x * 15 * 2)/100 - (x * 12 * 2)/100 = 420\n=> 30x/100 - 24x/100 =420\n=> 6x/100 = 420\n=> x = 7000.\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average mark of a class of twenty students is 64. If three students whose marks are 32,28 and 34 are removed , then find the approximate average mark of the remaining students of the class.\n\n### Options:\nA. 71\nB. 74\nC. 57\nD. 70\nE. 72\n\n### Answer:\nTotal mark of 20 students = 64*20 = 1280,\nTotal mark after the removal of 3 students = 1280 \u2013(32 +28+34 )\n= 1280 \u2013 94 = 1186\nApproximate average mark = 1186/(20-3)\n= 1186/ 17\n= 70\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nCalculate the amount that an investor needs to be invest to earn $460 in interest in 12 months if the investor plans to invest x dollars in a savings account that pays interest at an annual rate of 9% compounded semi-annually?\n\n### Options:\nA. 7,000\nB. 4,000\nC. 6,000\nD. 5,000\nE. 8,000\n\n### Answer:\nthe approach is substitution,\nour interest requirement is 460 after 12 months, 2 compounding period.\ncalculate the compound interest on each option and find out the one that yields 460 in 12 months\n5,000 yielded $460\nusing the formula\nA = P(1 + r/n)nt\nhence answer is D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the area of circle whose radius is 7m?\n\n### Options:\nA. 138\nB. 154\nC. 288\nD. 280\nE. 371\n\n### Answer:\n22/7 * 7 * 7\n= 154\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nDue to construction, the speed limit along an 5-mile section of highway is reduced from 40 miles per hour to 22 miles per hour. Approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ?\n\n### Options:\nA. A) 3.12\nB. B) 8\nC. C) 10\nD. D) 15\nE. E) 6.13\n\n### Answer:\nOld time in minutes to cross 5 miles stretch = 5*60/40 = 5*3/2 = 7.5\nNew time in minutes to cross 5 miles stretch = 5*60/22 = 5*30/11 = 13.63\nTime difference = 6.13\nAns:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the sum of all the multiples of 10 between 0 and 85?\n\n### Options:\nA. 500\nB. 620\nC. 450\nD. 360\nE. 440\n\n### Answer:\nThe multiples of 10 between 0 and 85 are 10, 20, 30, 40, 50, 60, 70, 80. If these are all added together, the result is 360.\nFinal Answer:\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how many different ways can the letters of the word 'MATHEMATICS' be arranged so that the vowels always come together ?\n\n### Options:\nA. 120960\nB. 135650\nC. 115850\nD. 142560\nE. 185260\n\n### Answer:\nIn the word 'MATHEMATICS' we treat the two vowels AEAI as one letter. Thus,we have MTHMTCS (AEAI)\nNow, we have to arranged 8 letters, out of which M occurs twice, T occurs twice and the rest are different.\nNumber of ways of arranging these letters= 8!/(2!)(2!)=10080.\nNow AEAI has 4 letters in which A occurs 2 times and the rest are different.\nnumber of ways of arranging these letters =4!/2!=12.\nRequired number of ways =(10080*12)=120960.\nAnswer is A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA number when divided by 100 leaves 11 as a remainder. What will be the remainder if the number is divided by 11?\n\n### Options:\nA. 11\nB. 1\nC. 2\nD. 3\nE. 21\n\n### Answer:\nLet 100+11=111\n111 divided evenly by eleven leaves a remainder of one.\nCorrect answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the sum of all possible 3-digit numbers that can be constructed using the digits 1, 3, and 4 if each digit can be used only once in each number?\n\n### Options:\nA. 1443\nB. 1554\nC. 1665\nD. 1776\nE. 1887\n\n### Answer:\nThere are 6 possible arrangements of the three numbers.\nThen each number will be in the hundreds, tens, and ones place two times each.\nThe sum is 2(111) + 2(333) + 2(444) = 1776\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the average (arithmetic mean) of the four numbers K, 2K + 3, 3K \u2013 4 and 5K + 1 is 63, what is the value of K?\n\n### Options:\nA. 22 10/11\nB. 15 3/4\nC. 22\nD. 23\nE. 25 3/10\n\n### Answer:\nK + 2K +3 + 3K - 4 + 5K +1 = 11K\n(11K -1)/4 = 63\n11K = 63 * 4 = 252\nK = 252 / 11 = 22 10/11\nAnswer A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain company\u2019s profit in 1996 was 15 percent greater than its profit in 1995, and its profit in 1997 was 20 percent greater than its profit in 1996. The company\u2019s profit in 1997 was what percent greater than its profit in 1995?\n\n### Options:\nA. 5%\nB. 18%\nC. 33%\nD. 35%\nE. 38%\n\n### Answer:\nSoln:-\nProfit in 1995 - 100\nProfit in 1996 - 115\n%increase Profit in 1997 in comparison to 1995 = 15 + 115*20%= 38%\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich of the following integers is a divisor of(15!+15)?\n\n### Options:\nA. 15\nB. 14\nC. 13\nD. 7\nE. 2\n\n### Answer:\nWhen we say 15!, it just means 1*2*3*4*5*...*13*14*15\nSo you need to find the integer which is a divisor of\n(1*2*3*4*5*...*13*14*15 + 15) = 15 (1*2*3*4*5*...*12*13*14 + 1) We obtain this by taking 15 common.\nHence 15 is definitely a divisor of (15! + 15).\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf A lends Rs.2000 to B at 15% per annum and B lends the same sum to C at 17% per annum then the gain of B in a period of 4 years is?\n\n### Options:\nA. 155\nB. 162\nC. 157.5\nD. 160\nE. 157.12\n\n### Answer:\n(2000*2*4)/100\n=> 160\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe population of a town is 176400. If it increase at the rate of 5% per annum. What was its population 2years ago?\n\n### Options:\nA. 152460\nB. 214560\nC. 160000\nD. 210000\nE. 200000\n\n### Answer:\npopulation 2 years ago = 176400/(1 + 5/100)^2\n= 176400* 20/21 * 20/21\n=160000\nAnswer is C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how many years will a sum of money doubles itself at 5% per annum on simple interest?\n\n### Options:\nA. 20\nB. 25\nC. 15\nD. 10\nE. 30\n\n### Answer:\nP = (P*5*R)/100\nR = 20%\nANSWER A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are 13 stamps from which two stamps will be selected. We have five stamps which are the same as five of the stamps which could be selected. What is the probability that the two stamps selected will be different from the stamps that we have?\n\n### Options:\nA. 17/52\nB. 14/39\nC. 12/31\nD. 9/23\nE. 7/17\n\n### Answer:\nP(first stamp is different) = 8/13\nP(second stamp is different) = 7/12\nP(both stamps are different) = 8/13*7/12 = 14/39\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n1=5,2=10,3=253,4=254,5=255,6=256,7=257,8=258 then 10=?\n\n### Options:\nA. 2\nB. 255\nC. 345\nD. 445\nE. 235\n\n### Answer:\n1=5,2=10,3=253,4=254,5=255,6=256,7=257,8=258 then 10=?\n10=2\ncheck the first eqn.\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA part of certain sum of money is invested at 6% per annum and the rest at 15% per annum, if the interest earned in each case for the same period is equal, then ratio of the sums invested is?\n\n### Options:\nA. 4:6\nB. 4:9\nC. 4:3\nD. 5:2\nE. 4:2\n\n### Answer:\n15:6\n= 5:2\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man took some money for borrowed, for 3 years the total will be Rs.5000 and 5 years it will be Rs.6000/-. Then how much amount he borrowed?\n\n### Options:\nA. s.2000/-\nB. s.2500/-\nC. s.2770/-\nD. s.2800/-\nE. s.3500/-\n\n### Answer:\n3 years --------> Rs.5000/-\n5 years --------> Rs.6000/-\n~ ~\n------------------------------\n2 years ---------> Rs.1000/-\n1 year ----------> Rs.500/-\n3years * Rs.500/- = Rs.1500/-\nP = Rs.5000/- - Rs.1500/- = Rs.3500/-\nP = Rs.3500/-\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf x+y=20, x-y=36, for integers of x and y, x=?\n\n### Options:\nA. 20\nB. 25\nC. 28\nD. 20\nE. 42\n\n### Answer:\nx+y = 20\nx-y = 36\n2x =56\nx = 28\nAnswer is C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a 300 m race A beats B by 22.5 m or 6 seconds. B's time over the course is:\n\n### Options:\nA. 86 sec\nB. 80 sec\nC. 76 sec\nD. 96 sec\nE. None of these\n\n### Answer:\nruns 45/2m in 6 sec.\nB covers 300 m in 6 x\t2/45 x 300sec\t= 80 sec.\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA and B began business with Rs.3000 and Rs.4000 after 8 months, A withdraws Rs.1000 and B advances Rs.1000 more. At the end of the year, their profits amounted to Rs.630 find the share of A.\n\n### Options:\nA. 240\nB. 88\nC. 77\nD. 266\nE. 121\n\n### Answer:\n(3*8 + 2*4):(4*8 + 5*4)\n8:13\n8/21 * 630 = 240.\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA dishonest dealer professes to sell goods at the cost price but uses a weight of 800 grams per kg, what is his percent?\n\n### Options:\nA. 65%\nB. 67%\nC. 45%\nD. 78%\nE. 25%\n\n### Answer:\nE\n800 --- 200\n100 --- ? => 25%\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWe made a down payment of $100 and borrowed the balance on a new piano which cost $1000. The balance with interest was paid in 23 monthly payments of $40 each and a final payment of $70. The amount of interest paid was what percent of the amount borrowed?\n\n### Options:\nA. 6%\nB. 7%\nC. 8%\nD. 9%\nE. 10%\n\n### Answer:\nWe borrowed $900.\nTo pay back this loan, we paid 23*$40 + $70=$990.\nThe interest was $990-$900=$90.\nThe percentage was $90/$900=0.1=10%.\nThe answer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf c\u2260d and c\u00b7d\u22600, which of the following may be true?\n\n### Options:\nA. c.d =0\nB. c-d=0\nC. c+d=2\nD. (c+d)(c-d)=0\nE. c\u2212d=d\u2212c\n\n### Answer:\nexcept D all conditions are not as per question\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the area of a parallelogram with base 30 cm and height 12 cm?\n\n### Options:\nA. 290 cm2\nB. 360 cm2\nC. 270 cm2\nD. 280 cm2\nE. 260 cm2\n\n### Answer:\nArea of a parallelogram = base * height = 30 * 12\n= 360 cm2\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf one-third of one-fourth of a number is 15, then three-tenth of that number is\n\n### Options:\nA. 35\nB. 36\nC. 45\nD. 54\nE. 57\n\n### Answer:\nLet the number be x. then 1/3 of \u00bc of x=15\nX=15x12=180\nThe required number=(3/10)*180=54\nANSWER D 54\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nLet y = 2m + x^2 and m = 5x + 2. If m^2 =49, then which of the following can be a value of 2y + 3m?\n\n### Options:\nA. 48\nB. 56\nC. 61\nD. 51\nE. 71\n\n### Answer:\nm^2 = 49 => m=7\n7= 5x+2 => x=1\ny= 2*7+1^2 = 15\n2y+3m = 2*15+3*7 = 51\nAnswer : D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOf the 90 house in a development, 50 have a two-car garage, 40 have an in-the-ground swimming pool, and 35 have both a two-car garage and an in-the-ground swimming pool. How many houses in the development have neither a two-car garage nor an in-the-ground swimming pool?\n\n### Options:\nA. 10\nB. 15\nC. 20\nD. 25\nE. 35\n\n### Answer:\nNeither Car nor Garage\n= Total - Garage - (Swim - Common)\n= 90 - 50 - (40-35) = 90-55 = 35\nAnswer E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nDivide $1000 among A,B in the ratio 1:4. How many $ that B get?\n\n### Options:\nA. $500\nB. $800\nC. $1000\nD. $200\nE. $750\n\n### Answer:\nSum of ratio terms = 1+4 = 5\nA = 1000*4/5 = $800\nAnswer is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n(51+52+53+\u2026\u2026\u2026+100) is equal to:\n\n### Options:\nA. 2525\nB. 2975\nC. 3225\nD. 3775\nE. 3875\n\n### Answer:\n(51+52+53+\u2026\u2026\u2026+100) = (1+2+3+\u2026\u2026.+100)- (1+2+3+4+\u2026\u2026+50)\n= (100*101)/2 - (50*51)/2\n= (5050-1275)= 3775.\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average (arithmetic mean) of all scores on a certain algebra test was 90. If the average of the 8 male students\u2019 grades was 82, and the average of the female students\u2019 grades was 92, how many female students took the test?\n\n### Options:\nA. 8\nB. 9\nC. 10\nD. 21\nE. 32\n\n### Answer:\nTotal Marks of male = M\nTotal Marks of female = F\nNumber of males = 8\nNumber of females = f\nGiven: (M+F)/(8+f) = 90 -------------1\nAlso given, M/8 = 82 Thus M = 656 ---------2\nAlso, F/f = 92 thus F = 92 F - --------3\nPut 2 and 3 in 1: we get\n(656+92f)/(8+f) = 90\nsolving this we get f = 32\nAns: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe mean of set A does not exceed mean of any subset of set A. Which of the following must be true about set A?\nI. Set A contains only one element\nII. All elements in set A are equal\nIII. The median of set A equals the mean of set A\n\n### Options:\nA. of the three qualities is necessary\nB. II only\nC. III only\nD. II and III only\nE. I, II, and III\n\n### Answer:\nThe only necessary condition seems to be II.\nIf all nos are equal.... them mean of any subset is the same.\nI is obviously ruled out ( e.g. A = {1,1,1} )\nBut III, what about 3?\nIt is not necessary in itself, rather, is automatically implied by II.\nAll sets that satsify II satisfy III=D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nLet C represent a set of four distinct prime numbers. If the sum of the numbers in C is even and x is a member of C, then what is the least possible value that x can be?\n\n### Options:\nA. 1\nB. 2\nC. 3\nD. 5\nE. 7\n\n### Answer:\nWe are told that C is a set of four distinct prime numbers, and the sum of the numbers in C is even. Since the question involves odds, evens and the smallest possible prime, you should immediately think of 2, the smallest prime number and the only even prime number.\nIf 2 were a member of the set, then we would have one even number and three odd numbers. Since such sum would always be odd, 2 cannot be a member of the set. Thus, all the members of C must be odd to yield an even sum.\nSince all the members of the set must be odd prime numbers, the answer is the smallest odd prime number, which is 3.\nThe correct answer is choice (C).\nNote:1 is not a prime number.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train speeds past a pole in 15 sec and a platform 120 m long in 25 sec, its length is?\n\n### Options:\nA. 238\nB. 180\nC. 988\nD. 177\nE. 171\n\n### Answer:\nLet the length of the train be x m and its speed be y m/sec.\nThen, x/y = 15 => y = x/15\n(x + 120)/25 = x/15 => x = 180 m.\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRaj invested an amount of Rs.17400 for two years. Find the rate of compound interest that will fetch him an amount of Rs.1783.50 at the end of two years?\n\n### Options:\nA. 4\nB. 3\nC. 2\nD. 5\nE. 6\n\n### Answer:\nLet the rate of interest be R% p.a.\n17400[1 + R/100]2 = 17400 + 1783.50\n[1 + R/100]2 = (17400 + 1783.50)/17400\n= 1 + 1025/10000 = 1 + 41/400\n= 441/400 = [21/20]2\n[1 + R/100] = 21/20\nR/100 = 1/20\nTherefore R = 5\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train 400 m long can cross an electric pole in 20 sec and then find the speed of the train?\n\n### Options:\nA. 65 Kmph\nB. 70 Kmph\nC. 72 Kmph\nD. 75 Kmph\nE. 78 Kmph\n\n### Answer:\nLength = Speed * time\nSpeed = L/T\nS = 400/20\nS = 20 M/Sec\nSpeed= 20*18/5 (To convert M/Sec in to Kmph multiply by 18/5)\nSpeed = 72 Kmph\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA palindrome is a number that reads the same forward and backward. For example. 2442 and 111 are palindromes. If 5-digit palindromes are formed using one or more of the digits, 1, 2, 3, how many such palindromes are possible?\n\n### Options:\nA. 12\nB. 15\nC. 18\nD. 24\nE. 27\n\n### Answer:\nXYZYX\nX can be 1, 2, or 3, thus 3 options.\nY can be 1, 2, or 3, thus 3 options.\nZ can be 1, 2, or 3, thus 3 options.\nTotal 3^3=27.\nAnswer: E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFor 1rs 4p interest\nwat will be for 2000rs?\n\n### Options:\nA. 45Rs\nB. 80Rs\nC. 40Rs\nD. 30Rs\nE. 48Rs\n\n### Answer:\nFor 1rs , 4p interest\nfor 2000rs, x\nx= 2000/1 * 4p ==> 8000 paise\nTo express in rs, 8000/100 = 80rs\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf s, t, and u are distinct positive prime numbers, then (s^3)(t)(u) has how many different positive factors greater than 1?\n\n### Options:\nA. a. 8\nB. b. 9\nC. c. 12\nD. d. 7\nE. e. 27\n\n### Answer:\nLet Number is (s^3)(t)(u) = (1^3)(5)(6) = 30\nWe can write 30 as product of two numbers in following ways\n1*30\n2*15\n3*10\n5*6\n4 cases = 4*2 i.e. 8 factors (including 1)\nFactors greater than 1 = 7\nAnswer: Option D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA rectangular lawn of dimensions 80 m * 60 m has two roads each 10 m wide running in the middle of the lawn, one parallel to the length and the other parallel to the breadth. What is the cost of traveling the two roads at Rs.3 per sq m?\n\n### Options:\nA. Rs.3948\nB. Rs.3929\nC. Rs.3927\nD. Rs.3900\nE. Rs.3928\n\n### Answer:\nArea = (l + b \u2013 d) d\n(80 + 60 \u2013 10)10 => 1300 m2\n1300 * 3 = Rs.3900\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMr. LISA invested in Fund X and Fund Y. The total amount she invested, in both funds combined, was $200,000. In one year, Fund X paid 41% and Fund Y paid 14%. The interest earned in Fund Y was exactly $200 greater than the interest earned in Fund X. How much did Ms. Tom invest in Fund X?\n\n### Options:\nA. 60,545.56\nB. 570,545.56\nC. 50,545.45\nD. 80,545.23\nE. 90,545.78\n\n### Answer:\nX+Y=200,000\n0.14Y=0.41A+200\nTake away decimals first: 14Y+41X+20,000\nIsolate first equation to solve for X (your goal): Y=200,000-Y\nPlug in for B:\n14(200,000-X)=41X+20,000\n2,800,000-14X=41X+20,000\n2,780,000=55X\n2,780,000/55=X\nX=50,545.45=Answer Choice C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMeg and Bob are among the 5 participants in a cycling race. If each participant finishes the race and no two participants finish at the same time, in how many different possible orders can the participants finish the race so that Meg finishes ahead of Bob?\n\n### Options:\nA. 24\nB. 30\nC. 60\nD. 90\nE. 120\n\n### Answer:\nLet me redeem myself:\nJXXXX => Bob can be in any X...Total 4! = 24\nXJXXX => Bob can be in the last 3 Xs...Total 3! = 6. However, since the first person can change too and it cannot be Bob, it can only be 3 other people. So Total = 6*3 = 18\nXXJBX => 3! = 6 total\nXXJXB => 3! = 6 total\nSo this yields total of 12\nXXXJB => 3! = 6\nAns = 24+18+12+6 = 60\nanswer is C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man spends Rs. 1600 per month on an average for the first three months, Rs 1550 for next four months and Rs. 1800 per month for the last five months and saves Rs . 4120 a year. What is his average monthly income?\n\n### Options:\nA. 2000\nB. 2010\nC. 2100\nD. 2200\nE. 2300\n\n### Answer:\nTotal expenditure for the first 3 months = 3 \u00d7 1600 = 4800\nTotal expenditure for 4 months = 4 \u00d7 1550 = 6200\nTotal expenditure for 5 months = 5 \u00d7 1800 = 9000\nTotal expenditure and saving (which is income for one year)\n= 4800 + 6200 + 9000 + 4120 = Rs. 24120\nSo, Average monthly income = 24120/12 = Rs. 2010\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the banker's discount if the true discount on a bill of Rs.540 is Rs.90 ?\n\n### Options:\nA. Rs. 108\nB. Rs. 120\nC. Rs. 102\nD. Rs. 106\nE. None of these\n\n### Answer:\nExplanation :\nPresent Worth, PW = F - TD = 540 - 90 = Rs. 450\nSimple Interest on the Present Worth = True Discount\nHence Simple Interest on 450 = 90 ------(Equation 1)\nSimple Interest on the face value = Bankers Discount\n=> Simple Interest on 540 = Bankers Discount\nFrom Equation 1, Simple Interest on 450 = 90\nHence, Simple Interest on 540 = 90/450\u00d7540=540/5 = Rs. 108\n=> Bankers Discount = Rs. 108 Answer : Option A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nYou collect coins. Suppose you start out with 11. Since his mother makes coins, Miguel decides to double your coins. Since you're nice, you give Mary 12 coins. How many coins do you have at the end?\n\n### Options:\nA. 9\nB. 10\nC. 11\nD. 12\nE. 13\n\n### Answer:\nSolution\nStart with 11 coins.\nMiguel doubles the number of coins you have: 11 \u00d7 2 = 22 coins.\nMary takes 12 coins from you: 22 - 12 = 10 coins.\nSo you have 10 at the end.\nCorrect answer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe ratio of Laxmi's age to the age of her mother is 3:11. The difference of their ages is 24 years. The ratio of their ages after 3 years will be?\n\n### Options:\nA. 1 : 9\nB. 1 : 3\nC. 1 : 2\nD. 1 : 1\nE. 3 : 3\n\n### Answer:\nSuppose age of Laxmi is x years.\nThe difference of their ages\n\\inline \\therefore Ratio of their ages after 3 years = =\n= 12 : 36 = 1 : 3\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA group of three women and three men have tickets for seven adjacent seats in one row of a theatre. If the three men will not sit in three adjacent seats, how many possible different seating arrangements are there for these 7 theatre-goers?\n\n### Options:\nA. 7! \u2013 2!3!2!\nB. 6! \u2013 4!3!\nC. 7! \u2013 5!3!\nD. 7 \u00d7 2!3!2!\nE. 2!3!2!\n\n### Answer:\n6 people can sit in 6! different ways. But because 3 men cannot sit together, we take them as a unit.\nThis unit of men, among themselves can sit in 3! ways.\nHence, 6! - 3!.\nThis unit of men along with3 women can sit in 4! different ways which also needs to be eliminated.\nHence 6! - 4!3!\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a and b are positive integers, and a=3b+12, the greatest common divisor of a and b CANNOT be\n\n### Options:\nA. 1\nB. 3\nC. 2\nD. 5\nE. 4\n\n### Answer:\nIf b is 1, 2, 3, or 4, then GCD of a and b is 1, 2, 3, and 4 respectively. So, by POE the answer must be D.\nStill: if b is a multiple of 5, then a is 12 greater than a multiple of 5, so not a multiple of 5, so both of them cannot be divisive by 5.\nAnswer: D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train 125 m long pass a telegraph pole in 5 seconds. Find the speed of the train\n\n### Options:\nA. 90 km/hr\nB. 68.4 km/hr\nC. 72 km/hr\nD. 79.2 km/hr\nE. None\n\n### Answer:\nSol.\nSpeed = [125/5] m/sec = [25 * 18/5] km/hr = 90 km/hr.\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAmber works 8 days a month at d dollars per day for m months out of the year. Which of the following represents her monthly pay?\n\n### Options:\nA. 8d\nB. 20d\nC. 10md/6\nD. 20d/m\nE. 20md\n\n### Answer:\nANSWER: A The passage states that she works 8 days a month at d dollars per day, so 8 d is her monthly pay\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nNitin ranks 23th in a class of 60 students. What is rank from the last ?\n\n### Options:\nA. 33\nB. 38\nC. 32\nD. 28\nE. 19\n\n### Answer:\nExplanation:\nNumber students behind the nitin in rank = (60 - 23) = 37\nNitin is 38nd from the last\nAnswer: B) 38\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If two marbles are drawn at random, what is the probability that at least one is green?\n\n### Options:\nA. 23/35\nB. 29/35\nC. 47/70\nD. 43/70\nE. None of these\n\n### Answer:\nGiven that there are three blue marbles, four red marbles, six green marbles and two yellow marbles.\nProbability that at least one green marble can be picked in the random draw of two marbles = Probability that one is green + Probability that both are green\n= (\u2076C\u2081 * \u2079C\u2081)/\u00b9\u2075C\u2082 + \u2076C\u2082/\u00b9\u2075C\u2082\n= (6 * 9 * 2)/(15 * 14) + (6 * 5)/(15 * 14) = 36/70 + 1/7\n= 46/70 = 23/35\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA and B can do a piece of work in 40 days and 40 days respectively. They work together for 10 days and B leaves. In how many days the whole work is completed?\n\n### Options:\nA. 30days\nB. 35days\nC. 40days\nD. 45days\nE. 50days\n\n### Answer:\nExplanation:\n(A+B)\u2019s 10 days work = 10[1/40+1/40]=10[1+1/40]= 1/2\nA complete remaining work in 1/2*40 = 20\nTotal work = 10+20 = 30days\nAnswer: Option A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat percent of 60 is 90?\n\n### Options:\nA. 133 1\u20443\nB. 150\nC. 60\nD. 33 1\u20443\nE. 25\n\n### Answer:\n% of 60 is 90?\n= 90/60 = 3/2 = 150%\nThus B is the correct answer.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOf the three-digit integers greater than 400, how many have two digits that are equal to each other and the remaining digit different from the other two?\n\n### Options:\nA. 90\nB. 82\nC. 80\nD. 45\nE. 36\n\n### Answer:\nTo satify the given condition,\nrequired no. of cases = total numbers - numbers with all digits different - numbers when all three digits are same,\nnumber greater than 700;\ntotal numbers = 1*10*10 = 100\nnumbers with all digits different = 1*9*8 = 72\nnumbers when all three digits are same (777) = 1\nreq. = 100- 72 - 1 = 27\nconsidering the numbers between 700999 = 27*3=37\nAnswer is 36('cause 700 can't be included)\nAnswer (E).\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train covers a distance of 12 km in 10 min. If it takes 9 sec to pass a telegraph post, then the length of the train is?\n\n### Options:\nA. 177 m\nB. 189 m\nC. 120 m\nD. 178 m\nE. 180 m\n\n### Answer:\nSpeed = (12/10 * 60) km/hr = (72 * 5/18) m/sec\n= 20 m/sec.\nLength of the train = 20 * 9\n= 180 m.\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nCompound interest of Rs.1000 at 10% per annum for 1 1/2years will be (interest compounded half yearly).\n\n### Options:\nA. Rs.473\nB. Rs.374\nC. Rs.495\nD. Rs.157\nE. None of the above\n\n### Answer:\n10% interest per annum will be 5% interest half yearly for 3 terms( 1 1/2 years)\nSo compound interest=3000[1+(5/100)]^3 - 1000=1000[(21/20)^3 -1]\n=1000(9261-8000)/8000\n=1*1261/8\n=157\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a - b = 3, a^2 + b^2 = 29 ,find the value of ab.\n\n### Options:\nA. 10\nB. 12\nC. 15\nD. 18\nE. 19\n\n### Answer:\nExplanation:\n2ab = (a^2 + b^2) - (a - b)^2 = 29 - 9 = 20 => ab = 10..\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man can row downstream at 26 kmph and upstream at 22 kmph. Find the speed of the man in still water and the speed of stream respectively?\n\n### Options:\nA. 24, 2\nB. 12, 6\nC. 15, 3\nD. 14, 4\nE. None of these\n\n### Answer:\nExplanation:\nLet the speed of the man in still water and speed of stream be x kmph and y kmph respectively.\nGiven x + y = 26 --- (1)\nand x - y = 22 --- (2)\nFrom (1) & (2) 2x = 48 => x = 24, y = 2.\nAnswer: Option A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTommy has a lot of Lego blocks, but only green and red blocks. There are four times as many green blocks as there are red blocks. If Tommy has Y Lego blocks, how many red blocks are there, in terms of Y.\n\n### Options:\nA. 3*Y\nB. Y/3\nC. Y/5\nD. Y/4\nE. Y/6\n\n### Answer:\nSince Y equals the number of blocks, then Y = Green + Red\nSince there are four times green blocks as red blocks, then Green = 4*Red\nThus Y = 4*Red + Red, which simplifies to Y=5*Red\nTherefore the Red = Y/5\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA person buys an article at Rs.500. At what price should he sell the article so as to make a profit of 20%?\n\n### Options:\nA. Rs.600\nB. Rs.500\nC. Rs.250\nD. Rs.700\nE. Rs.800\n\n### Answer:\nCost price = Rs.500\nprofit = 20% of 500 = Rs.100\nSelling price = Cost price + Profit\n= 500 + 100 = 600\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe speed at which a man can row a boat in still water is 6.5 kmph. If he rows downstream, where the speed of current is 2.5 kmph, what time will he take to cover 90 metres?\n\n### Options:\nA. 90 seconds\nB. 36seconds\nC. 26 seconds\nD. 18 seconds\nE. 6.5 seconds\n\n### Answer:\nSpeed of the boat downstream = 6.5 + 2.5\n= 9 kmph\n= 9 * 5/18 = 2.5 m/s\nHence time taken to cover 90m =90/2.5\n= 36 seconds.\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nDepartments A, B, and C have 4 employees each, and department D has 20 employees. Departments A, B, C, and D have no employees in common. A task force is to be formed by selecting 1 employee from each of departments A, B, and C and 2 employees from department D. How many different task forces are possible?\n\n### Options:\nA. 12,610\nB. 40,000\nC. 100,000\nD. 190,000\nE. 400,000\n\n### Answer:\n4c1 * 4c1* 4c1*20c2 = 10*10*10*190=12,610. Hence A is the correct answer.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA number Y is chosen at random from the numbers 1, -3, -1, 0, 1, 2, 3. What is the probability that |X|<3?\n\n### Options:\nA. 1/3\nB. 2/3\nC. 3/7\nD. 3/11\nE. None\n\n### Answer:\n|X||X| can take 7 values.\nTo get |X|<2|X|<2 ( i.e., \u22122", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nLet's say in a lottery Samuel have a 4% chance of winning the jackpot.\nAll lined up and 1st four people on the line lose. Samuel is 5th in the row.\nWhat's the chance of Samuel winning now?\n\n### Options:\nA. 2%\nB. 3%\nC. 4%\nD. 5%\nE. 6%\n\n### Answer:\nSolution:\n4%\nExplanation:\nThe winning chance probability is still 4% as the outcome of Samuel winning the lottery is a separate event from the 1st four losing it.\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe train travels at an average speed of 25km/h, to the top of the hill where the midpoint of the trip is. Going down hill, train travels at an average speed of 5km/h. Which of the following is the closest approximation of train's average speed, in kilometers per hour, for the round trip?\n\n### Options:\nA. 8.5\nB. 8.3\nC. 2.6\nD. 4.2\nE. 6.5\n\n### Answer:\nSince we're not given a distance to work with, we can TEST any distance that we like. Here, since the speeds are 25 km/hour and 5 km/hour, using a multiple of both 25 and 5 would make the math easiest.\nLet's set the Distance up the hill at 50 km.\nSo, going uphill, we have....\nD = (R)(T)\n50 = (25)(T)\n50/25 = 2 = T\n2 hours to go uphill\nGoing downhill, we have....\nD = (R)(T)\n50 = (5)(T)\n50/5 = 10 = T\n10 hours to go downhill\nTotal Distance = 100 km\nTotal Time = 10+2 = 12 hours\nAverage Speed = 100/12 = 8.3 km/hour\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man can row upstream at 25 kmph and downstream at 35 kmph, and then find the speed of the man in still water?\n\n### Options:\nA. 32 kmph\nB. 34 kmph\nC. 30 kmph\nD. 45 kmph\nE. 65 kmph\n\n### Answer:\nUS = 25\nDS = 35\nM = (35 + 25)/2 = 30\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train passes a station platform in 36 sec and a man standing on the platform in 20 sec. If the speed of the train is 54 km/hr. What is the length of the platform?\n\n### Options:\nA. 200\nB. 240\nC. 250\nD. 260\nE. 270\n\n### Answer:\nSpeed = 54 * 5/18 = 15 m/sec.\nLength of the train = 15 * 20 = 300 m.\nLet the length of the platform be x m . Then,\n(x + 300)/36 = 15 => x = 240 m.\nAnswer: Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA and B complete a job in 6 days. A alone can do the job in 15 days. If B works alone, how many days will it take to complete the job?\n\n### Options:\nA. 8\nB. 10\nC. 12\nD. 14\nE. 16\n\n### Answer:\nThe rate of A and B is 1/6\nA's rate is 1/15\nB's rate is 1/6 - 1/15 = 1/10\nB can complete the job in 10 days.\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average score of a cricketer for seven matches is 56 runs. If the average for first four matches is 46, then average for last three matches is\n\n### Options:\nA. 33.25\nB. 32.25\nC. 65\nD. 67\nE. 69\n\n### Answer:\nExplanation:\n=(56\u00d77)\u2212(46\u00d74)/3\n=(392\u2212184)/3=69\nAnswer: Option E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a T.V. factory, an average of 60TVs are produced per day for the fist 25days of the months. A few workers fellill for the next five daysreducing the daily avg for the month to58 sets/day . The average production per day for day last 5days is ?\n\n### Options:\nA. 35\nB. 39\nC. 48\nD. 50\nE. 52\n\n### Answer:\nProduction during these 5 days = Total production in a month - production in first 25 days.\n= 30 x 58 - 25 x 60\n= 240\n\u2234 Average for last 5 days = 240 / 5\n= 48\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf Bill can buy 3 pairs of jeans and 2 shirts for $69 or 2 pairs of jeans and 3 shirts for $76, how much does one shirt cost?\n\n### Options:\nA. $10\nB. $12\nC. $13.20\nD. $15\nE. $18\n\n### Answer:\n3J + 2S = 69\n2J + 3S = 76\n----------------\n5J + 5S = 145 ----(divide by 5)---> J + S = 29\n3J + 2S = J + 2(J + S) = J + 58 = 69 ---> J = 11\n3*11 + 2S = 69\n33 + 2S = 69\n2S = 36\nS = 18\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average age of 4 men is increased by years when two of them whose ages are 21 years and 23 years are replaced by two new men. The average age of the two new men is\n\n### Options:\nA. 22\nB. 30\nC. 99\nD. 26\nE. 27\n\n### Answer:\ntotal age increased = (8 * 2) years = 8 years.\nSum of ages of two new men = (21 + 23 + 8) years = 52 years\nAverage age of two new men = (52/2) years = 26 years.\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA bag contains 7 white balls, 5 black balls, and 4 red balls. One by one, three balls are drawn out without replacement. What is the probability that the third ball is red?\n\n### Options:\nA. 1/2\nB. 1/4\nC. 3/8\nD. 5/12\nE. 2/5\n\n### Answer:\nThe probability for each ball to be drawn third is equal.\nThen the probability a red ball is drawn third is 4/16 = 1/4.\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a man buys 10 lollipops for $90 and sold them for $2 dollars determine his loss.\n\n### Options:\nA. 50\nB. 60\nC. 70\nD. 80\nE. 90\n\n### Answer:\nCost of 10 lollipops = $90\nSold each lollipop for $2\nSo he sold 10 lollipops for $(10 \u00d7 2) = $20\nLoss = $(90 \u2013 20) = $70\nanswer :C\nTherefore, loss = $ 70.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a is a positive integer, then 2^a + 2^(a + 1)+ 2^(a + 2)+ 2^(a + 3)+ 2^(a + 4)+ 2^(a + 5) =\n\n### Options:\nA. 3^(a + 1)\nB. 2^(a + 1)\nC. 2a\nD. 2a^(a + 1)\nE. 63(2^a)\n\n### Answer:\nIf a is a positive integer, then 2^a + 2^(a + 1)+ 2^(a + 2)+ 2^(a + 3)+ 2^(a + 4)+ 2^(a + 5) =\n2^a(1+2+4+8+16+32)\n2^a(63)\nE. 63(2^a)\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many words can be formed from the letters of the word \"SIGNATURE\" so that vowels always come together.\n\n### Options:\nA. 17280\nB. 4320\nC. 720\nD. 80\nE. None of thsee\n\n### Answer:\nExplanation:\nword SIGNATURE contains total 9 letters.\nThere are four vowels in this word, I, A, U and E\nMake it as, SGNTR(IAUE), consider all vowels as 1 letter for now\nSo total letter are 6.\n6 letters can be arranged in 6! ways = 720 ways\nVowels can be arranged in themselves in 4! ways = 24 ways\nRequired number of ways = 720*24 = 17280\nOption A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhen N is divided by 10 the remainder is 1 and when N is divided by 3 the remainder is 2. What is the remainder Q when N is divided by 30?\n\n### Options:\nA. (a) 4\nB. (b) 7\nC. (c) 11\nD. (d) 13\nE. (e) 17\n\n### Answer:\nN ends in the digit 1 because when N is divided by 10, the remainder is 1. Since N ends in 1, the remainder Q when N is divided by 30 also ends in a 1. 11 is the only choice which ends in a 1.C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA person can row at 9 kmph and still water. He takes 4 1/2 hours to row from A to B and back. What is the distance between A and B if the speed of the stream is 1 kmph?\n\n### Options:\nA. 28\nB. 27\nC. 29\nD. 24\nE. 20\n\n### Answer:\nLet the distance between A and B be x km.\nTotal time = x/(9 + 1) + x/(9 - 1) = 4.5\n=> x/10 + x/8 = 9/2 => (4x + 5x)/40\n= 9/2 => x\n= 20 km.\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nk, l, m together started a business. k invested Rs.6000 for 5 months l invested Rs.3600 for 6 months and m Rs.7500 for 3 months. If they get a total profit of Rs.7410. Find the share of l ?\n\n### Options:\nA. Rs. 1640\nB. Rs. 2500\nC. Rs. 2160\nD. Rs. 3000\nE. None of these\n\n### Answer:\nExplanation:\n=> 60x5 : 36x6 : 75x3\n=> 100 : 72 : 75\n=> 72/247 x 7410 = Rs. 2160\nANSWER IS C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA tradesman by means of his false balance defrauds to the extent of 40%? in buying goods as well as by selling the goods. What percent does he gain on his outlay?\n\n### Options:\nA. 80%\nB. 96%\nC. 92%\nD. 84%\nE. 86%\n\n### Answer:\ng% = 40 + 40 + (40*40)/100\n= 96%\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf x and y are integers and 2x\u2013y= 11, then 4x+ y CANNOT be\n\n### Options:\nA. \u20135\nB. 1\nC. 13\nD. 17\nE. 55\n\n### Answer:\n2x-y=11\n2x=11+y\n4x=22+2y\nnow we need to check the value of 4x+4 => 22+2y+y=22+3y\nhence 22+3y=value(in the options)\nso y=value-22/3\nso checking the options only D is unfit\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFor any real number x, the operatoris defined as:\n(x) = x(3 \u2212 x)\nIf p + 1 =(p + 1), then p =\n\n### Options:\nA. \u22123\nB. 0\nC. 1\nD. 2\nE. 3\n\n### Answer:\n(x) = x(1 \u2212 x)\n(p + 1) = (p + 1)(3 - p - 1) =(2 -p)(p+1)\nWe are given that p + 1 =(p + 1)\nTherefore (2-p)(p+1) = (p + 1)\nOr (p + 1) + (p-2)(p+1) = 0\n(p + 1)(p-2) = 0\np = -1,p=2\nOption D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFor any positive integer n, the sum of the first n positive integers equals n(n+1)/2. What is the sum of all the even integers between 99 and 171?\n\n### Options:\nA. 2820\nB. 3440\nC. 4860\nD. 5560\nE. 6720\n\n### Answer:\n100 + 102 + ... + 170 =\n100*36 + (2+4+...+70) =\n100*36 + 2*(1+2+...+35) =\n100*36 + 2(35)(36)/2 =\n100*36 + 35*36 = 135(36) = 4860\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA boat has a speed of 14kmph in standing water. The stream has a speed of 1.2kmph. What time does the boat take to go to a distance of 4864 km and come back? (hours)\n\n### Options:\nA. 700\nB. 378\nC. 2696\nD. 1207\nE. 1712\n\n### Answer:\nExplanation:\nA boat travels at the speed of 14 km/hr in still water.\n=> Speed of stream = 1.2 kmph\n=> Speed of boat downstream becomes 14 + 1.2 = 15.2 kmph\n=> Speed of boat upstream becomes 14 - 1.2 = 12.8 kmph\nTotal time taken in the journey = Journey downstream + Journey upstream\nTherefore, 4864(1/12.8 + 1/15.2) = 700 hours\nANSWER: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMike works at a science lab that conducts experiments on bacteria. The population of the bacteria multiplies at a constant rate, and his job is to notate the population of a certain group of bacteria each hour. At 1 p.m. on a certain day, he noted that the population was 500 and then he left the lab. He returned in time to take a reading at 4 p.m., by which point the population had grown to 62,500. Now he has to fill in the missing data for 2 p.m. and 3 p.m. What was the population at 3 p.m.?\n\n### Options:\nA. 13000\nB. 12500\nC. 13500\nD. 14000\nE. 15000\n\n### Answer:\nlet the rate be x, then population of the bacteria after each hour can be given as 500,500x, 500(x^2), 500(x^3)\nnow population at 4pm =62,500\nthus we have 500(x^3) = 62,500 =125\nthus x=5\ntherefore population at 3pm = 500(25) = 12500\nAnswer : B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA total of 30 percent of the geese included in a certain migration study were male. If some of the geese migrated during the study and 25 percent of the migrating geese were male, what was the ratio of the migration rate for the male geese to the migration rate for the female geese? [Migration rate for geese of a certain sex = (number of geese of that sex migrating) / (total number of geese of that sex)]\n\n### Options:\nA. 1/4\nB. 7/12\nC. 2/3\nD. 7/8\nE. 9/7\n\n### Answer:\nLet' take the Number of geese to be 100.\nMale = 30. Female = 70.\nNow the second part of the Q, Let's take the Number migrated to be 20.\nSo we have 20 geese that migrated and out of that 25% are male i.e 25/100 *20 = 5 Geese (Males)\nAnd now we know out of the total 20 geese , 5 are male , then 15 have to be female.\nNow the ratio part , Male Geese Ratios = 5/30 = 1/6. - A\nFemale Geese Ratios =15/70=3/14 - B\nCross Multiply Equations A and B and you get =9/7 .\nAns E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA focus group is currently made up of x men and y women. If 3 men and 7 women are added to the group, and if one person is selected at random from the larger focus group, then what is the probability that a man is selected?\n\n### Options:\nA. x/(x + 7)\nB. x/(x + y)\nC. (y + 3)/(x + y + 7)\nD. (y + 4)/(x + y + 10)\nE. (x + 3)/(x + y + 10)\n\n### Answer:\nx men\ny women\nx+3+y+7 is the total\n=x+y+10\nx+3 is the number of men\nso (x + 3)/(x + y + 10)\nE. (x + 3)/(x + y + 10)\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSolution Y is 30 percent liquid X and 70 percent water. If 2 kilograms of water evaporate from 10 kilograms of solution Y and 2 kilograms of solution Y are added to the remaining 6 kilograms of liquid, what percent of this new solution is liquid X?\n\n### Options:\nA. 34\nB. 35\nC. 36\nD. 37 1/25\nE. 40\n\n### Answer:\nIn 8 kilograms of solution Y there are 0.3*10=3 kilograms of solution X;\nAfter 2 kilograms of water are replaced by 2 kilograms of solution Y, to the existing 2.4 kilograms of solution X, 0.3*2=0.6 kilograms of solution X are added, so in the new solution of 8 kilograms there are 3+0.6=3.6 kilograms of solution X, which is 3.6/10*100=36% of this new solution.\nAnswer: C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 4 (A's capital) = 6 (B's capital) = 10 (C's capital), then out of a profit of Rs. 930, C will receive\n\n### Options:\nA. 233\nB. 180\nC. 900\nD. 287\nE. 271\n\n### Answer:\nExplanation:\nLet 4A = 6B = 1OC = k. Then, A = k/4, B = k/6, and C =k/10 .\nA : B :C = k/4 : k/6 : k/10 = 15 : 10 : 6.\nHence, C's share (930 * 6/31) = Rs, 180.\nAnswer: B) Rs.180\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe cost of the paint is rs.20 per kg. if 1kg of paint covers 15 sq.ft, how much will it cost to paint outside of a cube having 5 feet each side\n\n### Options:\nA. Rs.200\nB. Rs.672\nC. Rs.546\nD. Rs.876\nE. None of these\n\n### Answer:\nExplanation:\nsurface area of a cube= 6 x 5^2 = 150 sq.ft\nquantity of paint required=(150/15)=10 kg\ncost of painting= 20 x 10 = Rs.200\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMangala completes a piece of work in 10 days, Raju completes the same work in 40 days. If both of them work together, then the number of days required to complete the work is\n\n### Options:\nA. 6 days\nB. 7 days\nC. 8 days\nD. 9 days\nE. 11 days\n\n### Answer:\nIf A can complete a work in x days and B can complete the same work in y days, then, both\nof them together can complete the work in x y/ x+ y days.\nThat is, the required No. of days = 10 \u00d7 40/50 = 8 days.\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n33\na3\n+4b\n___\n88\nIf a and b represent positive single digits in the correctly worked computation above, what is the value of the two digit integer ab?\n\n### Options:\nA. 12\nB. 10\nC. 13\nD. 24\nE. 34\n\n### Answer:\n3+3+b=8\nb=2\n3+a+4=8\na=1\nab=12\nans=A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf i is a positive integer and i^2 is divisible by 12, then the largest positive integer that must divide i ^3 is\n\n### Options:\nA. 2^3\nB. 2^6\nC. 3^3\nD. 6^3\nE. 12^2\n\n### Answer:\nSince i is an integer so i cannot have a 2 and sqrt 3 (because squaring this will give us a 2^2 and 3 (making the product as 12, and making i^2 as a multiple of 12))\ni^2 is divisible by 12 (12 = 2*2*3), So, i should have at least one 2 and one 3 so that i^2 has a 2^2 and two 3\nSo, i will have a 2 and a 3. Or i will be a multiple of 6\nSo, largest possible integer than should divide i^3 is 6^3\nSo, Answer will be D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere is a 5% chance that Tigers will not win at all during the whole season. There is a 5% chance that Federer will not play at all in the whole season. What is the greatest possible probability that the Tigers will win and Federer will play during the season?\n\n### Options:\nA. 55%\nB. 60%\nC. 70%\nD. 72%\nE. 95%\n\n### Answer:\nThere is a 5% chance that Tigers will not win at all during the whole season\nWe can infer that there is 95% chance Tigers will win .\nSimilarly There is a 5% chance that Federer will not play at all in the whole season\nWe can also infer that there is 95% chance that Federer will play.\nAnswer E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA company has two types of machines, type R and type S. Operating at a constant rate, a machine of type R does a certain job in 21 hrs and a machine of type S does the same job in 42 hours. If the company used the same number of each type of machine to do the job in 2 hours, how many machines of type R were used?\n\n### Options:\nA. 6\nB. 7\nC. 8\nD. 9\nE. 10\n\n### Answer:\nType R completes 1/21 of the job each hour.\nType S completes 1/42 of the job each hour.\nTogether R and S complete 1/21 +1/42 = 1/14 of the job each hour.\nLet n be the number of each type of machine.\n2*n*(1/14) = 1 job completed\nn = 7\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe area of circle O is added to its diameter. If the circumference of circle O is then subtracted from this total, the result is 10. What is the radius of circle O?\n\n### Options:\nA. \u20132/pi\nB. 2\nC. 3\nD. 4\nE. 5\n\n### Answer:\npi*r^2 + 2r -2*pi*r = 10\nSimplifying the equation: pi*r(r-2)+2r=10\nWithout much algebraic: We can Test the answers quickly, then 5 is the only possible answer that will eliminate pi from equation.\nAnswer is E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAlicia lives in a town whose streets are on a grid system, with all streets running east-west or north-south without breaks. Her school, located on a corner, lies three blocks south and three blocks east of her home, also located on a corner. If Alicia s equally likely to choose any possible path from home to school, and if she only walks south or east, what is the probability she will walk south for the first two blocks?\n\n### Options:\nA. 1/3\nB. 1/5\nC. 1/6\nD. 1/7\nE. 2/5\n\n### Answer:\nTotal number of ways to go home, considering that the order order matters =\nOptions: SSSEEE\nSlots : ------\ntotal permutations of 6 options in 6 slots: 6P6 = 6! = 6*5*4*3*2\nTotal ways to select \"South\" in the first 2 positions and anything else in the subsequent 4 positions =\nOptions: SS ????\nSlots: -- ----\nPermutations of 3 \"S\" in 2 slots AND Permutations of 4 Choices in 4 slots =\n3P2 * 4P4 = 3! * 4! = 3*2*4*3*2\nThe probability is therefore:\n3P2 * 4P4 = 6P6\n3*2*4*3*2= 1/5\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe price of a T.V. set worth Rs. 40000 is to be paid in 20 installments of Rs. 1000 each. If the rate of interest be 6% per annum, and the first installment be paid at the time of purchase, then the value of the last installment covering the interest as well will be?\n\n### Options:\nA. 22678\nB. 26699\nC. 26788\nD. 19000\nE. 39000\n\n### Answer:\nMoney paid in cash = Rs. 1000\nBalance payment = (40000 - 1000) = Rs. 39000\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe parameter of a square is equal to the perimeter of a rectangle of length 16 cm and breadth 14 cm. Find the circumference of a semicircle whose diameter is equal to the side of the square. (Round off your answer to two decimal places)?\n\n### Options:\nA. 23.58\nB. 23.56\nC. 23.54\nD. 23.57\nE. 23.51\n\n### Answer:\nLet the side of the square be a cm.\nParameter of the rectangle = 2(16 + 14) = 60 cm Parameter of the square = 60 cm\ni.e. 4a = 60\nA = 15\nDiameter of the semicircle = 15 cm\nCircimference of the semicircle\n= 1/2(\u220f)(15)\n= 1/2(22/7)(15) = 330/14 = 23.57 cm to two decimal places\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain car averages 25 miles per gallon of gasoline when driven in the city and 45 miles per gallon when driving on the highway. According to these rates, which of the following is closest to the number of miles per gallon that the car averages when it is driven 10 miles in the city and then 50 miles on the highway?\n\n### Options:\nA. 28\nB. 30\nC. 33\nD. 36\nE. 40\n\n### Answer:\n10*1/25 gpm+50*1/45 gpm=1.6=1.5 total gallons\n60 total miles/1.5 total gallons=40 average mpg\nE. 40\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA car covers a distance of 624 km in 6 \u00bd hours. Find its speed?\n\n### Options:\nA. 104 kmph\nB. 187 kmph\nC. 164 kmph\nD. 175 kmph\nE. 106 kmph\n\n### Answer:\n624/6\n= 104 kmph\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf x is an integer and 2.134 \u00d7 10^x is less than 21000, what is the greatest possible value for x?\n\n### Options:\nA. 7\nB. 6\nC. 5\nD. 4\nE. 3\n\n### Answer:\nIf x=4\n2.134 \u00d7 10^4 = 21340 > 21000\nSo, x = 3\nAnswer : E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTo mail a package, the rate is 20 cents for the first pound and 5 cents for each additional pound. Two packages weighing 5 pounds and 10 pounds, respectively can be mailed seperately or combined as one package. Which method is cheaper and how much money is saved?\n\n### Options:\nA. Combined, with a saving of 10 cents\nB. Separately, with a saving of 10 cents\nC. Combined, with a saving of 15 cents\nD. Separately, with a saving of 15 cents\nE. Combined, with a saving of 5 cents\n\n### Answer:\n5 pounds = 1*20+4*5 = 40\n10 pounds = 1*20+9*5 =65\ntotal = 105\n15 pound = 1*20+14*5 = 90\ndif. 15\nAnswer : C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n|9 - 4| - |12 - 14| = ?\n\n### Options:\nA. 3\nB. 2\nC. 1\nD. 0\nE. 4\n\n### Answer:\n|9 - 4| - |12 - 14| = | 5 | - | -2 | = 5 - 2 = 3\ncorrect answer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nEvaluate :\n28% of 400 + 45 % of 250\n\n### Options:\nA. 220.3\nB. 224.5\nC. 190.3\nD. 150\nE. None of these\n\n### Answer:\nExplanation:\n28% of 400 + 45 % of 250\n= (28/100 *400 + 45/100 * 250)\n= (112 + 112.5)\n= 224.5\nANSWER B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMeg and Bob are among the 4 participants in a cycling race. If each participant finishes the race and no two participants finish at the same time, in how many different possible orders can the participants finish the race so that Meg finishes ahead of Bob?\n\n### Options:\nA. 24\nB. 30\nC. 12\nD. 90\nE. 120\n\n### Answer:\nTotal # of ways the race can be finished is 4!. In half of the cases Meg finishes ahead of Bob and in other half Bob finishes ahead of Meg. So, ways Meg to finish ahead of Bob is 4!/2=12.\nAnswer: C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA batsman scored 120 runs whichincluded 3 boundaries and 8sixes. What % of his total score did he make by running between the wickets\n\n### Options:\nA. 40%\nB. 50%\nC. 65%\nD. 70%\nE. 75%\n\n### Answer:\nNumber of runs made by running = 110 - (3 x 4 + 8 x 6)\n= 120 - (60)\n= 60\nNow, we need to calculate 60 is what percent of 120.\n=> 60/120 * 100 = 50 %\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe length of a rectangular plot is 20 metres more than its breadth. If the cost of fencing the plot @Rs.26.50 per metre is Rs.5300, what is the length of the plot in metres?\n\n### Options:\nA. 55\nB. 60\nC. 65\nD. 70\nE. 75\n\n### Answer:\nLength of the fence =530026.50=200 m\n\u21d2 2(length + breadth)=200 m\n\u21d2 2(breadth + 20 + breadth)=200 m (\u2235 length = breadth+20)\n\u21d2 breadth + 20 + breadth =100 m\n\u21d2 breadth =40 m\nlength =40+20=60 m\nAnswer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA person covered one-fourth of the total distance at 26 kmph and remaining distance at 24 kmph. What is the average speed for the total distance?\n\n### Options:\nA. 27 (1/3)kmph\nB. 21 (1/3)kmph\nC. 21 (1/7)kmph\nD. 26 (1/3)kmph\nE. 31 (1/3)kmph\n\n### Answer:\nLet the total distance be x km\ntotal time taken = (x/4)/16 + (3x/4)/24 = x/64 + x/32 = 3x/64\nAverage speed = x/(3x/64) = 64/3kmph = 21 (1/3)kmph.\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAn empty wooden vessel weighs 20% of its total weight when filled with paint. If the weight of a partially filled vessel is one half that of a completely filled vessel, what fraction of the vessel is filled.\n\n### Options:\nA. 3/5\nB. 5/9\nC. 1/24\nD. 9/19\nE. 2/5\n\n### Answer:\nAn empty wooden vessel weighs 20% of its total weight when filled with paint:\nVessel = 0.2(Vessel + Paint);\n20V = V + P (so the weight of completely filled vessel is 10V)\nP = 19V (so the weight of the paint when the vessels is completely filled is 19V).\nThe weight of a partially filled vessel is one half that of a completely filled vessel:\nV + P' = 1/2*20V;\nP' = 9V (so the weight of the paint when the vessels is partially filled is 9V).\nWhat fraction of the vessel is filled?\nSo, we need to find the ratio of the weight of the paint when the vessel iscompletely filledto the weight of the paint when the vessel ispartially filled:\nP'/P = 9V/19V = 9/19.\nAnswer: D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 30\u00b0 and 45\u00b0 respectively. If the lighthouse is 100 m high, the distance between the two ships is:\n\n### Options:\nA. 173 m\nB. 200 m\nC. 273 m\nD. 300 m\nE. 373 m\n\n### Answer:\nLet AB be the lighthouse and C and D be the positions of the ships.\nThen, AB = 100 m, ACB = 30\u00b0 and ADB = 45\u00b0.\nAB\t= tan 30\u00b0 =\t1 AC = AB x 3 = 1003 m.\nAC\t3\nAB\t= tan 45\u00b0 = 1 AD = AB = 100 m.\nAD\nCD = (AC + AD)\t= (1003 + 100) m\n= 100(3 + 1)\n= (100 x 2.73) m\n= 273 m.\nAnswer = C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf S is the sum of the reciprocals of the consecutive integers from 81 to 90, inclusive, which of the following is less than S?\nI. 1/8\nII. 1/9\nIII. 1/10\nIV. 1/5\nV. 1/8>S >1/9\n\n### Options:\nA. V\nB. I\nC. II\nD. III\nE. IV\n\n### Answer:\nSince we summarize the reciprocals from 90 to 81, we can say also that we add ten numbers who are all (with one exception 1/90) greater than 1/90, so that the sum must be greater than 1/9.\nOn the other side we can say that we add the reciprocals from 91 to 100, so that the sum has to be less than the sum of ten times 1/91.\nsum has to be greater than 1/9 and less than 1/8\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n2 + 2^2 + 2^3 + ... + 2^8 = ?\n\n### Options:\nA. 510\nB. 310\nC. 210\nD. 410\nE. None of them\n\n### Answer:\nGiven series is a G.P. with a = 2, r = 2 and n = 8.\nsum = a(r^n-1)/(r-1) = 2 x (2^8 \u20131)/(2-1)= (2 x 255) =510\nAnswer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain sum is invested at simple interest at 18% p.a. for two years instead of investing at 12% p.a. for the same time period. Therefore the interest received is more by Rs. 300. Find the sum?\n\n### Options:\nA. 7000\nB. 2500\nC. 2778\nD. 2800\nE. 2791\n\n### Answer:\nLet the sum be Rs. x.\n(x * 18 * 2)/100 - (x * 12 * 2)/100 = 300 => 36x/100 - 24x/100 =300\n=> 12x/100 = 300 => x = 2500.Answer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf Q is a negative integer, which of the following must be a negative integer?\n\n### Options:\nA. Q + 1\nB. Q/2+3\nC. Q^4\nD. Q \u2013 y\nE. Q^11\n\n### Answer:\nWe need to check each option here:\nA. Q + 1\nThis will depend on the value of Q. Nothing can be said\nB. Q/2+3\nThis will depend on the value of Q. Nothing can be said\nC. Q^4\nThis will always be positive. Even powers of negative numbers are positive and odd powers are negative\nD. Q \u2013 y\nThis will depend on the value of Q. Nothing can be said\nE. Q^11\nThis will always be negative. Even powers of negative numbers are positive and odd powers are negative\nCorrect Option: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFor a certain set, the value range of its members is 108.4. A new set is created from the members of the old set as follows: 12 is subtracted from a member of the old set, and the result is divided by 4. The resulting value is a member of the new set. If this operation is done for each member of the old set, what is the range of values of the members of the new set?\n\n### Options:\nA. 24.1\nB. 27.1\nC. 54.4\nD. 98.4\nE. 108.4\n\n### Answer:\nLet x and z be the smallest and largest of the original set, respectively.\nz - x = 108.4\nThe smallest and largest members of the new set will be (x-12) / 4 and (z-12) / 4.\nThen the range is (z-12) / 4 - (x-12) / 4 = (z-x) / 4 = 108.4 / 4 = 27.1\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nBy selling 8 pencils for a rupee a man loses 60%. How many for a rupee should he sell in order to gain 60%?\n\n### Options:\nA. 8\nB. 9\nC. 2\nD. 6\nE. 4\n\n### Answer:\n40% --- 8\n160% --- ?\n40/160 * 12 = 2\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe area of a circular field is 17.56 hectares. Find the cost of fencing it at the rate of Rs. 5 per metre approximately\n\n### Options:\nA. 4457\nB. 4567\nC. 4235\nD. 4547\nE. 7429\n\n### Answer:\nExplanation:\nArea = (17.56 x 10000) m2= 175600 m2.\n\u03a0R2 = 175600 \u21d4 (R)2 = (175600 x (7/22)) \u21d4 R = 236.37 m.\nCircumference = 2\u03a0R = (2 x (22/7) x 236.37) m =1485.78 m.\nCost of fencing = Rs. (1485.78 x 5) = Rs. 7429.\nAnswer: Option E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain telescope increases the visual range at a particular location from 50 kilometers to 150 kilometers. By what percent is the visual range increased by using the telescope ?\n\n### Options:\nA. 30%\nB. 33 1/2%\nC. 40%\nD. 60%\nE. 200%\n\n### Answer:\nOriginal visual range = 50 km\nNew visual range = 150 km\nPercent increase in the visual range by using the telescope\n= (150-50)/50 * 100%\n= 2 * 100%\n= 200 %\nAnswer E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA box has 12 shapes; 3 circles, 5 squares, and 4 triangles. How many groups of 3 shapes can be made with at least 1 triangle?\n\n### Options:\nA. 46\nB. 64\nC. 164\nD. 146\nE. 56\n\n### Answer:\nThe problem asks for a combination, since order doesn't matter. Now, selecting r items from a set of n gives the Combination Formula: nCr= n!/r!(n-r)!\nn = 12\nr = 3\nSo, total groups is 12C3 = 12!/(3!(12 - 3)!) = 220, and\nn = 12 - 4 = 8\nr = 3\nfor groups without a triangle is 8C3 = 8!/(3!(8 - 3)!) = 56,\nso, groups with at least 1 triangle = 220 - 56 = 164\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are two examinations rooms A and B. If 10 students are sent from A to B, then the number of students in each room is the same. If 20 candidates are sent from B to A, then the number of students in A is double the number of students in B. The number of students in room A is:\n\n### Options:\nA. 20\nB. 80\nC. 100\nD. 200\nE. None\n\n### Answer:\nEXPLANATION\nLet the number of students in rooms A and B be x and y respectively.\nThen, x \u2013 10 = y + 10 x \u2013 y = 20 \u2026. (i)\nand x + 20 = 2(y \u2013 20) x \u2013 2y = -60 \u2026. (ii)\nSolving (i) and (ii) we get: x = 100 , y = 80.\nThe required answer A = 100.\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn an election between two candidates, the winner has a margin of 10% of the votes polled. If 4000 people change their mind and vote for the loser, the loser would have won by a margin of 10% of the votes polled. Find the total number of votes polled in the election?\n\n### Options:\nA. 16000\nB. 10000\nC. 40000\nD. 12000\nE. 5000\n\n### Answer:\nWinner - Looser\n55% - 45%\nIf 4000 people change their mind and vote for the loser:\nWinner - Looser\n45% - 55%\nThus 4,000 people compose 25% of all voters, which means that the total number of votes is\n40,000\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA boat goes 100 km downstream in 10 hours, and 75 m upstream in 15 hours. The speed of the stream is?\n\n### Options:\nA. 22 1/7\nB. 22 1/4\nC. 22 1/2\nD. 22 1/1\nE. 22 1/3\n\n### Answer:\n100 --- 10 DS = 10\n? ---- 1\n75 ---- 15 US = 5\n? ----- 1 S = (10 - 5)/2\n= 22 1/2 kmp Answer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nwhich of the following inequalities indicates the set of all values of d for which the lengths R of the three sides of a triangle can be 3,4, and d?\n\n### Options:\nA. 0 1", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nListed below are the mean temperatures measured in the Tokharian desert in a certain month. What is the median temperature E in that particular month?\nMean Temp (C\u00b0) No. of days\n29 --------------------> 5\n30 --------------------> 11\n31 --------------------> 8\n32 --------------------> 6\n\n### Options:\nA. 29\nB. 30\nC. 30.5\nD. 31\nE. 32\n\n### Answer:\nto find out median===>they must be arranged in ascending order.\n29 29 29...(5 times)30 30 30 30.....(11 times)31 31 31.....(8 times)32 32 32 .....(6 times)\ntotal days=5+11+8+6=30\ntherefore 30 numbers ...median E will be==>mean of 15 and 16 th place temperature===>(30+30)/2=30\nhence B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA and B began business with Rs.7000 and Rs.15000 after 6 months, A advances Rs.3000 and B withdraws Rs.5000. At the end of the year, their profits amounted to Rs.2940 find the share of A and B respectively.\n\n### Options:\nA. 1100, 1750\nB. 1140, 1800\nC. 940, 2000\nD. 1190, 1750\nE. 1000: 1690\n\n### Answer:\n7*6 + 10*6):(15*6 + 10*6) =102 : 150 = 51 : 75 = 17 : 25\n17 : 25\nA's Share = 17/42 * 2940 = 1190.\nB's Share = 25/42 * 2940 = 1750.\nA and B shares respectively 1190 and 1750 . Answer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA person earns 15% on investment but loses 10% on another investment. If the ratio of the two investments be 3:5, what is the gain or loss on the two investments taken together?\n\n### Options:\nA. 0.63 %\nB. 0.64 %\nC. 0.65 %\nD. 0.66 %\nE. None\n\n### Answer:\nSol.\nSuppose he invested 300 & 500 respectively profit : 15% of 300 = 45 loss =\n500 *10 = 50 net loss = - 5 5/800 *100 = 0.63 %\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nN and M are each 3-digit integers. Each of the numbers 1, 2, 3,4,5 and 6 is a digit of either N or M. What is the smallest possible positive difference between N and M?\n\n### Options:\nA. 59\nB. 49\nC. 58\nD. 113\nE. 131\n\n### Answer:\nYou have 6 digits: 1,2, 3, 4, 5, 6\nEach digit needs to be used to make two 3 digit numbers. This means that we will use each of the digits only once and in only one of the numbers. The numbers need to be as close to each other as possible. The numbers cannot be equal so the greater number needs to be as small as possible and the smaller number needs to be as large as possible to be close to each other.\nThe first digit (hundreds digit) of both numbers should be consecutive integers\nNow let's think about the next digit (the tens digit). To minimize the difference between the numbers, the tens digit of the greater number should be as small as possible and the tens digit of the smaller number should be as large as possible . So let's not use 1 and 6 in the hundreds places and reserve them for the tens places Now what are the options?\nTry and make a pair with (2** and 3**). Make the 2** number as large as possible and make the 3** number as small as possible.\n265 and 314 (difference is 49) or\nTry and make a pair with (4** and 5**). Make the 4** number as large as possible and make the 5** number as small as possible. We get 463 and 512 (difference is 49)\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe ratio of the length and the breadth of a rectangle is 4 : 3 and the area of the rectangle is 6912 sq cm. Find the ratio of the breadth and the area of the rectangle?\n\n### Options:\nA. 1 : 96\nB. 1 : 97\nC. 1 : 98\nD. 1 : 99\nE. 1 : 93\n\n### Answer:\nLet the length and the breadth of the rectangle be 4x cm and 3x respectively.\n(4x)(3x) = 6912\n12x2 = 6912\nx2 = 576 = 4 * 144 = 22 * 122 (x > 0)\n=> x = 2 * 12 = 24\nRatio of the breadth and the areas = 3x : 12x2 = 1 : 4x = 1: 96.\nAnswer: Option A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOn a baseball team, 4 players including Alice want to play 1st base, 2nd base, or 3rd base. Before every game, the coach chooses a name randomly from a bag and this person plays 1st base. Then the coach chooses the next name randomly and this person plays 2nd base. The coach then chooses a third name randomly and this person plays 3rd base. What is the probability that Alice plays 1st, 2nd, or 3rd base?\n\n### Options:\nA. 3/4\nB. 5/6\nC. 7/8\nD. 9/16\nE. 11/16\n\n### Answer:\nThe total number of ways to choose three players is 4C3=4.\nExcluding Alice, the number of ways to choose three players is 3C3=1.\nP(Alice is not chosen)=1/4.\nP(Alice is chosen)=1 - 1/4 = 3/4.\nThe answer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nUse distributive property to solve the problem below:\nMaria bought 15 notebooks and 6 pens costing 2 dollars each.How much did Maria pay?\n\n### Options:\nA. 30 dollars\nB. 40 dollars\nC. 50 dollars\nD. 42 dollars\nE. 70 dollars\n\n### Answer:\nSolution\n2 \u00d7 (15 + 6) = 2 \u00d7 15 + 2 \u00d7 6 = 30 + 12 = 42 dollars\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf log1087.5 = 2.9421, then the number of digits in (875)10 is?\n\n### Options:\nA. 30\nB. 28\nC. 27\nD. 26\nE. 40\n\n### Answer:\nX = (875)10 = (87.5 x 10)10\nTherefore, log10X = 10(log2087.5 + 1)\n= 10(2.9421 + 1)\n= 10(3.9421) = 39.421\nX = antilog(39.421)\nTherefore, number of digits in X = 40.\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRice weighing 25/4 pounds was divided equally and placed in 4 containers. How many ounces of rice were in each container? (Note that 1 pound = 16 ounces)\n\n### Options:\nA. 22\nB. 25\nC. 28\nD. 31\nE. 34\n\n### Answer:\n25/4 \u00f7 4 = 25/16 pounds in each container\n25/16 pounds * 16 ounces / pound = 25 ounces in each container\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere was two trains from calcutta to kanyakumari one train is fast service travels with a speed 75km per hour another travels with a speed of 44km per hour the time taken to reach from calcutta to kanyakumari is 4hours less than the first train...find the distance b/w calcatta to kanyakumari\n\n### Options:\nA. 415.8 km\nB. 425.8 km\nC. 435.8 km\nD. 445.8 km\nE. 455.8 km\n\n### Answer:\nlet distance b/w calcutta to kanyakumari is = x km\nthen eqn is\nx/44 - x/75 = 4\n=> x*(75-44)=4*75*44\n=> x = 425.8 km\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA began business with 12500 and is joined afterwards by B with 25000. When did B join, if the profits at the end of the year are divided equally?\n\n### Options:\nA. 8 months\nB. 9 months\nC. 6 months\nD. 5 months\nE. None of these\n\n### Answer:\nLet B join after x months of the start of the business so that B\u2019s money is invested for (12 \u2013 x) months.\n\u2234 Profit ratio is 12 \u00d7 12500 : (12 \u2013 x) \u00d7 25000\nor 12 : 2(12 \u2013 x)\nSince profit is equally divided so\n12 = 2(12 \u2013 x) or x = 6. Thus B joined after 8 months.\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe ratio of two quantities is 2 to 5. If each of the quantities is increased by 7, what is the ratio of these two new quantities?\n\n### Options:\nA. 2/5\nB. 5/8\nC. 7/13\nD. 22/25\nE. It cannot be determined from the information given.\n\n### Answer:\nCorrect Answer: E\nLet x and y be the two quantities such that x/y = 2/5. There is no algebraic operation that can be used to increase x and y each by 3 and determine what happens to the ratio 2/5.\nFor example, if x = 2 and y = 5, then (x+7)/(y+7) = (2+7)/(5+7) = 9/12 =3/4. However, if x = 4 and y = 10 (which would still set x/y = 2/5), then (x+3)/(y+3) = (4+7)/(10+7) = 11/17. The ratio of the two new quantities cannot be uniquely determined from the information given, and the correct answer is (E).\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo trains of equal length are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. If the faster train passes the slower train in 36 seconds,what is the length of each train?\n\n### Options:\nA. 50 m\nB. 80 m\nC. 76 m\nD. 58 m\nE. 90 m\n\n### Answer:\nlet length of each train = x m\ntotal distance while passing the slower train = (x+x) = 2x m\nrelative speed = (46-36) = 10 km/hr\n=10*5/18 = 50/18 m/s\ntime = 36 sec\n2x/36 = 50/18 => x=50\nANSWER A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn Kaya's teacher's desk there are 4 pink highlighters, 2 yellow highlighters, and 5 blue highlighters. How many highlighters are there in all?\n\n### Options:\nA. 11\nB. 22\nC. 77\nD. 33\nE. 88\n\n### Answer:\nAdd the numbers of highlighters.\n4 + 2 + 5 =11.\nAnswer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat no. should be subtracted from x^3+4x^2\u22127x+12x^3+4x^2\u22127x+12, if it is to be perfectly divisible by x+3x+3?\n\n### Options:\nA. 40\nB. 42\nC. 44\nD. 48\nE. 52\n\n### Answer:\nAccording to remainder theorem when dfracf(x)x+adfracf(x)x+a, then the remainder is f(\u2212a)f(\u2212a).\nIn this case, as x+3x+3 divides x3+4x2\u22127x+12\u2013kx3+4x2\u22127x+12\u2013k perfectly (kk being the number to be subtracted), the remainder is 0 when the value of xx is substituted by -3.\ni.e., (\u22123)3+4(\u22123)2\u22127(\u22123)+12\u2212k=0(\u22123)3+4(\u22123)2\u22127(\u22123)+12\u2212k=0\nor \u221227+36+21+12=k\u221227+36+21+12=k\nor k=k= 42\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nEighteen years ago, a father was three times as old as his son. Now the father is only twice as old his son. Then the sum of the present ages of the son and the father is:\n\n### Options:\nA. 54\nB. 72\nC. 105\nD. 108\nE. 51\n\n### Answer:\nAnswer: Option D\nLet the present ages of the father and son be 2x and x years respectively.\nThen, (2x - 18) = 3(x - 18) => x = 36\nRequired sum = (2x + x) = 108 years.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAt a meeting of 5 Chiefs of Staff, the Chief of Naval Operations does not want to sit next to the Chief of the National Guard Bureau. How many ways can the Chiefs of Staff be seated around a circular table?\n\n### Options:\nA. 9\nB. 12\nC. 15\nD. 18\nE. 21\n\n### Answer:\n5 people can be arranged around a table in 4! ways.\nConsider the two chiefs who will not sit together as a single unit.\nThe number of ways to arrange 4 units around a table is 3!\nWe need to multiply this by 2 as the two people can be switched in each arrangement.\nThe total number of ways to arrange the chiefs is 4! - 2*3! = 2*3! = 12\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the HCF of 2/3, 4/9 and 6/18\n\n### Options:\nA. 7/45\nB. 2/45\nC. 1/9\nD. 8/45\nE. 9/45\n\n### Answer:\nExplanation:\nHCF of Fractions = HCF of Numerators/LCM of Denominators\n= (HCF of 2, 4, 6)/(LCM of 3, 9, 18) = 2/18 = 1/9\nAnswer: Option C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many 7-letter words can be formed using the letters of the English alphabet that contain 3 different vowels and 4 different consonants?\n\n### Options:\nA. 5!*5c2 *21c2\nB. 4!*5c2 *21c2\nC. 4!*5c3 *21c2\nD. 6!*5c3 *21c2\nE. 7!*5c3 *21c4\n\n### Answer:\ncombination for 3 vowels out of 5 = 5c3 ways\ncombination for 4 consonants of 21 = 21c4 ways\nAdditionally the arrangement can be = 7!\ntotal arrangements =7!*5c3 *21c4\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe price of a certain product increased by the same percent from 1960 to 1970 as from 1970 to 1980. If its price of $1.60 in 1970 was 150 percent of its price in 1960, what was its price in 1980?\n\n### Options:\nA. a) $ 1.80\nB. b) $ 2.00\nC. c) $ 2.40\nD. d) $ 2.70\nE. e) $ 3.00\n\n### Answer:\nThe price in 1970 was 150 percent of its price in 1960, means that the percent increase was 50% from 1960 to 1970 (and from 1970 to 1980).\nTherefore the price in 1980 = $1.6*1.5 = $2.4.\nAnswer: C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA parking space have 10 different slots. 10 cars has to arrange in 8 slots. But there are exactly 4 cars between 6 specified cars. In how many ways cars can be arranged?\n\n### Options:\nA. 17280\nB. 65000\nC. 1500\nD. 1640\nE. 1440\n\n### Answer:\nwe arranged 2 specified cars in 4 slots = 4!\nremaining 6 cars in 6 slots = 6!\nnumber of ways = 4!*6! = 17280\ncorrect option is A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train covers a distance of 11 km in 10 min. If it takes 6 sec to pass a telegraph post, then the length of the train is?\n\n### Options:\nA. m\nB. m\nC. m\nD. m\nE. m\n\n### Answer:\nSpeed = (11/10 * 60) km/hr\n= (66 * 5/18) m/sec = 55/3 m/sec.\nLength of the train = 55/3 * 6\n= 110 m.\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train of length 560 metres takes 90 seconds to cross a tunnel of length 340 metres. What is the speed of the train in km/hr?\n\n### Options:\nA. 36 km/hr.\nB. 46 km/hr.\nC. 30 km/hr.\nD. 48 km/hr.\nE. None\n\n### Answer:\nSol.\nSpeed = [560+340 / 90] m/sec = [900 / 90 * 18/5] km/hr = 36km/hr.\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA person borrows Rs. 5000 for 2 years at 4% p.a. simple interest. He immediately lends it to another person at 6 p.a for 2 years. Find his gain in the transaction per year.\n\n### Options:\nA. 100 rs\nB. 150 rs\nC. 160 rs\nD. 180 rs\nE. 200 rs\n\n### Answer:\nGain in 2 years =\n[(5000*6*2)/100]-[(5000*4*2)/100]\n600-400=200\nGain in 1 year =(200/2)=100 rs\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n3889 + 12.952 - ? = 3854.002\n\n### Options:\nA. 47.95\nB. 49.75\nC. 45.97\nD. 47.59\nE. 45.79\n\n### Answer:\nLet 3889 + 12.952 - x = 3854.002.\nThen x = (3889 + 12.952) - 3854.002\n= 3901.952 - 3854.002\n= 47.95.\nAnswer is A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA person is 24 years older than his daughter. In 2 years, the person\u2019s age will be 2 times the age of his daughter. Then, the current age of the daughter is:\n\n### Options:\nA. 22\nB. 42\nC. 32\nD. 41\nE. 56\n\n### Answer:\nLet the daughter\u2019s current age be A years. Then, the person\u2019s current age = (A +24) years.\n(A + 24) + 2 = 2 (A + 2)\nA + 26 = 2A + 4\nA = 22\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nReena took a loan of 1000 with simple interest for as many years as the rate of interest. If she paid 40 as interest at the end of the loan period, what was the rate of interest?\n\n### Options:\nA. 3.8\nB. 2\nC. 6\nD. Cannot be determined\nE. None\n\n### Answer:\nExplanation: Let rate = R% and time = R years.\nThen, (1000 x R x R)/100 = 40\n10R\u00c2\u00b2 = 40\nR\u00c2\u00b2 = 4\nR = 2.\nAnswer: Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nGiven the following factorials (x+3)!, (x-2)!, and (x+4)! what is the value of x if the greatest common divisor is 720?\n\n### Options:\nA. 8\nB. 9\nC. 7\nD. 6\nE. 10\n\n### Answer:\nGCD of (x+3)!, (x-2)!, and (x+4)! is 720. Find x.\nBest way to find n is substitute each of the answer and find out the correct one.\nI started with A.\nTry 8 and find GCD or 11!, 6! and 12!. 6! itself is 720 and 6! which is contained in the other two factorials. This satisfies the condition, hence answer is 7. Also, we can eliminate all other answers as they are less than 7 and n-2 turns out to be less than 5! and hence cannot have a divisor of 120.\nAnswer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train 125 m long passes a man, running at 7 km/hr in the same direction in which the train is going, in 10 sec. The speed of the train is?\n\n### Options:\nA. 52 km/hr\nB. 17 km/hr\nC. 76 km/hr\nD. 50 km/hr\nE. 15 km/hr\n\n### Answer:\nSpeed of the train relative to man = 125/10 = 25/2 m/sec.\n= 25/2 * 18/5 = 45 km/hr\nLet the speed of the train be x km/hr. Then, relative speed = (x - 7) km/hr.\nx - 7 = 45 => x = 52 km/hr.\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nP and Q invested in a business. They earned some profit which they divided in the ratio of 2:3. If P invested Rs.50, 000, the amount invested by Q is:\n\n### Options:\nA. Rs. 65,000\nB. Rs. 70,000\nC. Rs. 75,000\nD. Rs. 90,000\nE. Rs. 60,000\n\n### Answer:\nQ invested = 50000/2*3 = 75000\nAnswer : C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo trains start from A & B and travel towards each other at\nspeed of 50kmph and 60kmph resp. At the time of the meeting the\nsecond train has traveled 100km more than the first.the distance\nbetween them.\n\n### Options:\nA. 800 km\nB. 900 km\nC. 1000 km\nD. 1100 km\nE. 1200 km\n\n### Answer:\nLet the distance traveled by the first train be x km\nthen distance covered by the second train is x + 100km\nx/50 = x+100 / 60\nx= 500\nso the distance between A & B is x + x + 100 = 1100 km\nAnswer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n16 meters of wire is available to fence off a flower bed in the form of a circular sector. What must the radius of the circle in meters be, if we wish to have a flower bed with the greatest possible surface area?\n\n### Options:\nA. 2\u221a2\nB. 4\nC. 5\nD. 4\u221a2\nE. none of these\n\n### Answer:\nArea of Sector, A = x/360*pi*r^2\nCircumference of the sector = 16\n=> x/360*2*pi*r +2r= 16\n=> 2A/r+2r=16\n=> A=(r16- 2r^2)/2\n= r8-r^2\nWe will now max using derivations\nMax value of A will found at A=0\ni.e 8-2r=0\nr=4\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf (5^13)(9^7)=3(15^x), what is the value of x?\n\n### Options:\nA. 7\nB. 9\nC. 11\nD. 13\nE. 15\n\n### Answer:\n(5^13)(9^7)=3(15^x)\n=> 5^13 * 3^14 = 3 * 3^x * 5^x\n=> 5^13 * 3^14 = 3^(x+1) * 5^x\nValue of x = 13\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 1/2 of a pencil is blue, 1/8 of the remaining is red and the remaining 3/8 is white, what is the total length of the pencil?\n\n### Options:\nA. 5\nB. 3\nC. 1\nD. 4\nE. 2\n\n### Answer:\nBlue is 1/2 but can also be written as 4/8\rRed is 1/8\rWhite is 3/8\r4/8+1/8+3/8= 8/8=1\rAnswer is C) 1\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn what time will a train 320 m long cross an electric pole, it its speed be 144 km/hr?\n\n### Options:\nA. 2.5 sec\nB. 8.0 sec\nC. 3.5 sec\nD. 2.9 sec\nE. 9.5 sec\n\n### Answer:\nSpeed = 144 * 5/18 = 40 m/sec\nTime taken = 320/40\n= 8.0 sec.\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 400 resolutions?\n\n### Options:\nA. 563.2 m\nB. 704 m\nC. 287 m\nD. 278 m\nE. 927 m\n\n### Answer:\nIn one resolution, the distance covered by the wheel is its own circumference. Distance covered in 400 resolutions.\n= 400 * 2 * 22/7 * 22.4 = 56320 cm\n= 563.2 m\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nConsider the sets Tn = {n, n + 1, n + 2, n + 3, n + 4}, where n = 1, 2, 3,...., 120. How many of these sets contain 6 or any integral multiple thereof (i.e., any one of the numbers 6, 12, 18, ...)?\n\n### Options:\nA. (a)100\nB. (b) 81\nC. (c) 82\nD. (d) 83\nE. (e) 84\n\n### Answer:\nT1: 1,2,3,4,5\nT2: 2,3,4,5,6\nT3: 3,4,5,6,7\netc.\nmeans that every multiple of 6 will be involved in 5 sets. We have (120-6)/6+1=20 such multiples.\nSo, final number of sets is 20*5=100\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n20 men can dig a tunnel in 30 days. If after 10 days, 20 more men are deployed to dig the tunnel, how many more days it will take to dig the whole tunnel?\n\n### Options:\nA. 10\nB. 15\nC. 20\nD. 25\nE. 30\n\n### Answer:\nA\nRemaining work can be completed by 20 men in 30-10 = 20 days.\nIf 20 men can do X work in 20 days, and let us say 40 men take N days to do the same work.\nNow, more men, less number of days (inversely proportion)\n20 : 40 :: N : 20\nN = 20 X 20 / 40 = 10 days.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA dishonest milkman professes to sell his milk at cost price but he mixes it with water and thereby gains 25%. The percentage of water in the mixture is:\n\n### Options:\nA. 4%\nB. 61/4%\nC. 20%\nD. 25%\nE. 30%\n\n### Answer:\nLet C.P. of 1 litre milk be Re. 1\nThen, S.P. of 1 litre of mixture = Re. 1, Gain = 25%.\nCP of 1 lr = 100/125*1 = 4/5\nRatio of milk to water = 4/5:1/5 = 4:1\n=20%\nANSWER C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAbby and Bobby type at constant rates of 80 words per minute and 60 words per minute, respectively. Bobby begins typing before Abby and has typed 600 words when Abby begins typing at 1:30 pm. If they continue typing at their respective rates, at what time will Abby have typed exactly 400 more words than Bobby?\n\n### Options:\nA. 1:40 PM\nB. 1:50 PM\nC. 2:00 PM\nD. 2:10 PM\nE. 2:20 PM\n\n### Answer:\nSay time needed for Abby to type 200 more words than Bobby is t. In that time she would type 80t words and Bobby would type 60t words.\nNow, total words typed by Bobby would be 600+60t and we want that number to be 200 less than 80t: 600+60t=80t-400 --> t=50.\n1:30 PM + 50 minutes = 2:20 PM.\nAnswer: E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the total cost of 2 sandwiches at $2.49 each and 4 sodas at $1.87 each?\n\n### Options:\nA. $3.36\nB. $6.85\nC. $8.46\nD. $10.08\nE. $12.46\n\n### Answer:\nAnswer = E\n2 * 2.49 + 4 * 1.87\n= 2 (2.50 - 0.01) + 4 (2.00 - 0.13)\n= 5 + 8 - 0.02 - 0.52\n= 13 - 0.54\n= 12.46\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf six machines working at the same rate can do 3/4 of a job in 30 minutes, how many minutes would it take two machines working at the same rate to do 3/5 of the job?\n\n### Options:\nA. 45\nB. 60\nC. 72\nD. 80\nE. 100\n\n### Answer:\nusing the std formula\nm1d1h1/w1=m2d2h2/w2\nsubstituting the values we have\n6*1/2*4/3=2*5/3*x (converted 30 min into hours =1/2)\n4=10/3*x\nx=6/5 hour\nso 72 minutes\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average of seven numbers is 4. The average of first three numbers is 2 and the average of last three numbers is 6. What is the middle number?\n\n### Options:\nA. 3\nB. 4\nC. 6\nD. 7\nE. 8\n\n### Answer:\nThe total of seven numbers = 7X4 = 28\nThe total of first 3 and last 3 numbers is = 3 X 2+3 X 6 = 24\nSo, the middle number is (28 - 24 ) = 4\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain animal in the zoo has consumed 39 pounds of food in six days. If it continues to eat at the same rate, in how many more days will its total consumption be 156 pounds?\n\n### Options:\nA. 18\nB. 7\nC. 12\nD. 9\nE. none of the above\n\n### Answer:\nAns is A:\n39 pounds --> 6 days\n91 pounds --> x days\nx = 156*6/39 = 24\nthe animal has already consumed food in 6 days so the the number of\ndays for it's total consumption be 156 pounds is 24-6 = 18\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhen a train travels at a speed of 80kmph,it reaches the destination on time.when the same train travels at a speed of 50kmph,it reaches its destination 15min late.what is the length of journey?\n\n### Options:\nA. 25km\nB. 50km\nC. 60km\nD. 85km\nE. 95km\n\n### Answer:\nLet x be the time reached with the speed 80km/h\n50km/h ----> x+15\nDistance is equal so\n80(km/h)\u00d7 xhr = 50(km/h) \u00d7 (x+15) hr\nSo\n80 x = 50x + 750\nSo the would be in km\nAnd x = 25\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn what ratio must a grocer mix two varieties of pulses costing Rs. 15 and Rs. 20 per kg respectively so as to get a mixture worth Rs. 16.50 kg?\n\n### Options:\nA. 4:7\nB. 3:7\nC. 4:3\nD. 7:3\nE. 2:3\n\n### Answer:\nCost of 1 kg pulses of 1st kind=Rs. 15\nCost of 1 kg pulses of 2nd kind=Rs. 20\nMean Price=Rs. 16.50\nCost of 1 kg pulses of 1st kind - Mean Price=15-16.50=Rs 1.50\nCost of 1 kg pulses of 2nd kind - Mean Price=20-16.50=Rs 3.50\nRequired rate = 3.50 : 1.50 = 7 : 3.\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man can row downstream at the rate of 45 Kmph and upstream at 23 Kmph. Find the man\u2019s rate in still water and rate of current?\n\n### Options:\nA. 8.5\nB. 10.0\nC. 12.5\nD. 11.0\nE. 8.25\n\n### Answer:\nRate of still water = 1/2 (down stream + upstream)\n= 1/2 (45 + 23) = 34 Kmph\nrate of current = 1/2 (down stream - upstream)\n= 1/2 (45 - 23)\n= 1/2 (22)\n= 11 kmph\nAnswer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRs 50000 is divided into two parts One part is given to a person with 10% interest and another part is given to a person with 20 % interest. At the end of first year he gets profit 8000 Find money given by 10%?\n\n### Options:\nA. 20000\nB. 40000\nC. 50000\nD. 60000\nE. 70000\n\n### Answer:\nlet first parrt is x and second part is y then x+y=50000----------eq1\ntotal profit=profit on x +profit on y\n8000=(x*10*1)/100 + (y*20*1)/100\n80000=x+2y-----------------------------------eq2\n80000=50000+y\nso y=30000 then x =50000-30000=20000\nfirst part =20000\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow much tea worth $0.93 per pound must be mixed with tea worth $0.75 per pound to produce 10 pounds worth $0.85 per pound?\n\n### Options:\nA. 2 2\u20449\nB. 3 1\u20442\nC. 4 4\u20449\nD. 5 5\u20449\nE. 9 1\u20442\n\n### Answer:\nLet weight of tea worth .75 $ = w1\nand weight of tea worth .93 $ = w2\nw1 + w2 = 10 --- equation 1\n.85 = ( w1*.75 + w2* .93 )/(w1+ w2 )\n=> .85 w1 + .85 w2 = .75 w1 + .93 w2\n=> .10 w1 -.08 w2 = 0\n=> 10 w1 - 8 w2 = 0 --- equation 2\nFrom 1 ,\n8 w1 + 8 w2 = 80 --- equation 3\nFrom equations 2 and 3 , we get\n18 w1 = 80\n=> w1 = 40/9\nand w2 = 50/9\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train crosses a platform of 120 m in 15 sec, same train crosses another platform of length 180 m in 18 sec. then find the length of the train?\n\n### Options:\nA. 145\nB. 180\nC. 181\nD. 184\nE. 150\n\n### Answer:\nLength of the train be \u2018X\u2019\nX + 120/15 = X + 180/18\n6X + 720 = 5X + 900\nX = 180m\nAnswer: Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 20 % of certain quantity of work is done by A and the rest 80% by B, the work is completed in 20 days. If 80% of the work is done by A and the remaining 20% by B, then the work is completed in 30 days. How many days are required to complete the work , if A and B work together.\n\n### Options:\nA. 11 1/9\nB. 10 1/9\nC. 12\nD. 15\nE. Source: TIME material.\n\n### Answer:\nUse algebra :\n0.2/A + 0.8/B = 20\n1/A + 4/B = 100\n0.8/A + 0.2/B = 30\n4/A+ 1/B = 150\n15/B = 250\nB = 3/50 work per day\nA = 3/100 work per day\nCombined rate = 3/40 + 3/100 = 9/100\nTime taken when working together = 100/9 = 11(1/9) days\nAnswer (A)\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a car went the first third of the distance at 80 kmh, the second third at 18 kmh, and the last third at 48 kmh, what was the average speed of the car for the entire trip?\n\n### Options:\nA. 34 kmh\nB. 40 kmh\nC. 42 kmh\nD. 44 kmh\nE. 50 kmh\n\n### Answer:\nAssume D/3 = 720 (this number is convenient because it is divisible by 80, 18 and 48)\nSo:\n720 = 80*T1 = 9 hrs\n720 = 18*T2 = 40 hrs\n720 = 48*T3 = 15 hrs\nT = T1 + T2 + T3 = 64 hrs\nD = RT\n(720*3) = R*64\nR = 33.75\nANSWER: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAn error 2% in excess is made while measuring the side of a square. What is the percentage of error in the calculated area of the square?\n\n### Options:\nA. 4.04\nB. 4.02\nC. 4.01\nD. 4.05\nE. 4.06\n\n### Answer:\nFormula for Calculation of Percentage error is:\n=(x\u2212y\u2212(xy)/100)%\n=(2+2+(2\u00d72)/100)%=4.04%\nAnswer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 2^k = 4, then 2^(2K+2) =\n\n### Options:\nA. 29\nB. 45\nC. 81\nD. 64\nE. 18\n\n### Answer:\n2^k=4\n2^2k=4^2\n2^2k=16\n2^(2k+2)\n=2^2k*2^2\n=16*4\n=64\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA photograph measuring 2 1''\u20442 \u00d7 1 7''\u20448 is to be enlarged so that the length will be 4\u201d. How many inches will the enlarged breadth be?\n\n### Options:\nA. 1 1\u20442\nB. 2 1\u20448\nC. 3\nD. 3 3\u20448\nE. None of these\n\n### Answer:\nLet enlarged breadth be x inches. Then,\n5\u20442 : 4 :: 15\u20448 : x\n\u21d2 5\u20442x = 4 \u00d7 15\u20448 \u21d2 x = 3 inches.\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSalesperson A's compensation for any week is $350 plus 6 percent of the portion of A's total sales above $1,000 for that week. Salesperson B's compensation for any week is 8 percent of A's total sales for that week. For what amount of total weekly sales would both salepeople earn the same compensation?\n\n### Options:\nA. $21,000\nB. $18,000\nC. $15,000\nD. $ 14,500\nE. $4,000\n\n### Answer:\nsometime, setting up an equation is an easy way to go with:\n350 + 0.06 (x - 1000) = 0.08 x\nx = 14,500\nAns : D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are 7 players in a bowling team with an average weight of 85 Kg. If two new players join the team, one weighs 110 Kg and the second weighs 60 Kg, what will be the new average weight?\n.\n\n### Options:\nA. 75 Kg\nB. 80 Kg\nC. 85 Kg.\nD. 90 Kg\nE. 92 Kg\n\n### Answer:\nNew average weight= 110+60/2= 85 kgs\nSince avg weight of 85 is added to avg weight of 85, the average will remain the same, i.e 85\nC is the answer\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are 5 bags three of which each contains 5 white and 2 black balls, and remaining 2 bags each contains 1 white and 4 black ball; a black ball has been drawn, find the chance that it came from second group.\n\n### Options:\nA. 2/7\nB. 6/35\nC. 8/25\nD. 28/43\nE. 3/5\n\n### Answer:\nPlease go through my solution and suggest any mistake.\nChances of selecting a black ball from group 1: 2/7----------------------Chances of selecting a black ball from group 2: 4/5\nThus combined probability of section of black ball from group 1:\n3/5 x 2/7 = 6/35\nThus combined probability of section of black ball from group 2:\n2/5 x 4/5 = 8/25\nOut of these chances, chance of occurrence of first case : (8/25) / (6/35 + 8/25) = 28/43\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man complete a journey in 10 hrs. He travels first half of the journey at the rate of 21 km/hr and second half at the rate of 24 km/hr. Find the total journey in km?\n\n### Options:\nA. 271 km\nB. 224 km\nC. 243 km\nD. 222 km\nE. 215 km\n\n### Answer:\nB\n224 km\nLet the total distance be x km.\nThen, [(1/2 x) / 21 + (1/2 x) / 24] = 10\n15x = 168 * 20 => x = 224 km.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf goods be purchased for Rs.840 and one-fourth be sold at a loss of 20% at what gain percent should the remainder be sold so as to gain 20% on the whole transaction?\n\n### Options:\nA. 33 1/7%\nB. 33 6/3%\nC. 33 1/3%\nD. 39 1/3%\nE. 33 1/4%\n\n### Answer:\n1/4 CP = 210 SP = 21*(80/100) = 168\nSP = 840*(120/100) = 1008\n1008 - 168 = 840\n3/4 SP = 630\nGain = 210\n630 --- 210\n100 --- ? => 33 1/3%\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe length of a rectangle is halved, while its breadth is tripled. Watis the % change in area?\n\n### Options:\nA. 30%\nB. 40%\nC. 50%\nD. 60%\nE. 65%\n\n### Answer:\nLet original length = x and original breadth = y.\nOriginal area = xy.\nNew length = x .\n2\nNew breadth = 3y.\nNew area = x x 3y = 3 xy.\n2 2\nIncrease % = 1 xy x 1 x 100 % = 50%.\n2 xy\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMike and Fritz ran a 30-mile Marathon. Mike ran 10 miles at 10 miles per hour and then ran at 5 miles per hour for the remaining 20 miles.Fritz ran the first one-third (by time) of the run at 10 miles per hour and the remaining two-thirds of the run at 5 miles per hour. How much time in hours did Fritz take to complete the Marathon?\n\n### Options:\nA. 3\nB. 3.5\nC. 4\nD. 4.5\nE. 5\n\n### Answer:\nLet total time= t\nF travelled at rate 10mph for t/3 time and 5mph for 2t/3 time\nd= s1t1+s2t2\n30= 10*t/3 + 5*2t/3\n30= 20t/3\nt= 4.5\nD is the answer\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThree-fourth of two-third of three-seventh of a number is 27. what is 10% of that number?\n\n### Options:\nA. 12.6%\nB. 6.3%\nC. 27%\nD. 25.2%\nE. None of these\n\n### Answer:\nExplanation :\nSolution: Assume the number be x. then, 3/4 of 2/3 of 3/7 of x = 27.\nx = 27 * 7/3 *3/2 * 4/3.\nx = 126\n.'. 10% of 126 = 10/100 * 126 = 12.6\nAnswer : A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA, B, C subscribe Rs. 50,000 for a business. A subscribes Rs. 4000 more than B and B Rs. 5000 more than C. Out of a total profit of Rs. 35,000, B receives:\n\n### Options:\nA. s. 11,000\nB. s. 11,300\nC. s. 11,500\nD. s. 11,700\nE. s. 11,900\n\n### Answer:\nLet C = x.\nThen, B = x + 5000 and A = x + 5000 + 4000 = x + 9000.\nSo, x + x + 5000 + x + 9000 = 50000\n3x = 36000\nx = 12000\nA : B : C = 21000 : 17000 : 12000 = 21 : 17 : 12.\nB's share = Rs. (35000 x 17/50) = Rs. 11,900.\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are k-2 members in a certain band, including Jim and Ellen. Two members are to be selected to attend the Grammy awards ceremony. If there are 15 possible combinations in which Jim and Ellen are not selected, what is the value of k?\n\n### Options:\nA. 8\nB. 9\nC. 10\nD. 11\nE. 12\n\n### Answer:\nThere are k-2 members in the band, and k-4 members without Jim and Ellen.\n(k-4)C2 = 15\n(k-4)(k-5)/2 = 15\n(k-4)(k-5) = 30 = 6*5\nk = 10\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average of any 5 consecutive odd natural numbers is k . If two more such numbers , just next to the previous 5 numbers are added , the new average becomes\n\n### Options:\nA. k+8\nB. k+1\nC. k+9\nD. k+2\nE. k+4\n\n### Answer:\nExplanation:\nThe 5 consecutive odd numbers whose average is k are (k-4), (k-2), k, (k+2), (k+4)\nAgain the average of (k-4), (k-2), k, (k+2), (k+4), (k+6), (k+8) is (k+2)\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man invests some money partly in 9% stock at 96 and partly in 12% stock at 120. To obtain equal dividends from both, he must invest the money in the ratio:\n\n### Options:\nA. 16:15\nB. 15:16\nC. 12:11\nD. 11:13\nE. 13:18\n\n### Answer:\nLet the Face Value of Stock giving dividend 9% be Rs. x, whose Market Value is Rs.96.\nLet the Face Value of Stock giving dividend 12% be Rs. y, whose Market Value is Rs.120.\nBy given formula,\nFace Value * Dividend % / Market Value = Annual income.\nAnnual Income from 1st Stock = 9x/96.\nAnnual Income from 2nd Stock = 12y/120.\nTo obtain equal dividends from both,\nAnnual Income from 1st Stock = Annual Income from 2nd Stock.\n= 9x/96 = 12y/120.\n= x/y = 96/90.\nWe find GCD of 96, 90 = 6.\n= x/y = 16*6 / 15*6.\n= Required ratio = x:y = 16:15.\nanswer : A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSophia finished 2/3 of a book. She calculated that she finished 90 more pages than she has yet to read. How long is her book?\n\n### Options:\nA. 270\nB. 150\nC. 130\nD. 90\nE. 210\n\n### Answer:\nLet x be the total number of pages in the book, then she finished 2/3*x pages.\nThen she has x\u22122/3*x=1/3*x pages left.\n2/3*x\u22121/3*x=90\n1/3*x=90\nx=270\nSo the book is 270 pages long.\nAnswer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a class, the number of girls is 20% more than that of the boys. The strength of the class is 66. If 4 more girls are admitted to the class, the ratio of the number of boys to that of the girls is\n\n### Options:\nA. 1:2\nB. 3:4\nC. 1:4\nD. 3:5\nE. None\n\n### Answer:\nSolution: Girls:boys = 6:5;\nHence, girls = 6*66/11 = 36;\nBoys = 30;\nNew ratio, 30:(36+4) = 3:4.\nAnswer: Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA boat goes 100 km downstream in 10 hours, and 75 m upstream in 15 hours. The speed of the stream is?\n\n### Options:\nA. 2 (1/9) km/h\nB. 2 (1/5) km/h\nC. 2 (3/2) km/h\nD. 2 (1/2) km/h\nE. 2 (1/1) km/h\n\n### Answer:\n:100 --- 10 DS = 10\n? ---- 1\n75 ---- 15 US = 5\n? ----- 1 S = (10 - 5)/2\n= 2 2 \u00bd kmph\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the difference between the place values of two sevens in the numeral 54707429 ?\n\n### Options:\nA. 699990\nB. 693000\nC. 99980\nD. 699930\nE. None of these\n\n### Answer:\nExplanation:\nRequired Difference\n= 700000 - 7000 = 693000\nAnswer is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many of the positive factors of 85 , 105 and how many common factors are there in numbers?\n\n### Options:\nA. 5\nB. 4\nC. 2\nD. 3\nE. 1\n\n### Answer:\nfactors of 85 - 1, 5, 17, 85\nfactors of 105 - 1, 3, 5, 7, 15, 21, 35, 105\nComparing both, we have two common factors of 85 and 105- 1,5\nAnswer(C)\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n120 +520 \u00f7 5.00 = ?\n\n### Options:\nA. 100\nB. 150\nC. 120\nD. 520\nE. None\n\n### Answer:\nAnswer\nGiven expression = 120 +520 \u00f7 5.00\n= 120 + 104\n= 224\nCorrect Option: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a*b*c=130, b*c*d = 65, c*d*e=1000 and d*e*f=150 the (a*f)/(c*d) = ?\n\n### Options:\nA. 1/2\nB. 1/4\nC. 3/4\nD. 1/3\nE. None of these\n\n### Answer:\nExplanation :\na\u00e2\u02c6\u2014b\u00e2\u02c6\u2014c/b\u00e2\u02c6\u2014c\u00e2\u02c6\u2014d= 130/65 => a/d = 2\nd\u00e2\u02c6\u2014e\u00e2\u02c6\u2014f/c\u00e2\u02c6\u2014d\u00e2\u02c6\u2014e= 150/1000 => f/c = 1/4\na/d* f/c = 2 * 15/10 = 1/3\nAnswer : D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo cards are drawn at random from a pack of 52 cards.what is the probability that either both are black or both are queen?\n\n### Options:\nA. 55/228\nB. 55/228\nC. 55/221\nD. 55/212\nE. 55/2234\n\n### Answer:\nWe have n(s) = \\inline {\\color{Black}52C_{2}} = = 1326.\nLet A = event of getting both black cards\nB = event of getting both queens\nA\u2229B = event of getting queen of black cards\nn(A) = \\inline {\\color{Black}26C_{2}} = = 325, n(B)= \\inline {\\color{Black}4C_{2}} = = 6 and n(A\u2229B) = \\inline {\\color{Black}2C_{2}} = 1\nP(A) = n(A)/n(S) = 325/1326;\nP(B) = n(B)/n(S) = 6/1326 and\nP(A\u2229B) = n(A\u2229B)/n(S) = 1/1326\nP(A\u222aB) = P(A) + P(B) - P(A\u2229B) = (325+6-1) / 1326 = 330/1326 = 55/221\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train 120 m long is running with a speed of 54 km per hour. In what time will it pass a telegraph post?\n\n### Options:\nA. 11 s\nB. 10 s\nC. 8 s\nD. 12 s\nE. None of these\n\n### Answer:\nWe know from the formula Time = Distance/ Speed\nThus, Time = 120/ 54 x 5/18\nor, Time = 8 sec.\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nLet A be the event that a randomly selected two digit number is divisible by 2 and let B be the event that a randomly selected two digit number is divisible by 10. What is P(A and B)?\n\n### Options:\nA. 1/20\nB. 1/15\nC. 1/12\nD. 1/8\nE. 1/2\n\n### Answer:\nP(A and B) = 1/2*1/10 = 1/20\nThe answer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA jogger running at 9 km/hr along side a railway track is 250 m ahead of the engine of a 100 m long train running at 99 km/hr in the same direction. In how much time will the train pass the jogger?\n\n### Options:\nA. 14 sec\nB. 67 sec\nC. 98 sec\nD. 36 sec\nE. 23 sec\n\n### Answer:\nSpeed of train relative to jogger =99 - 9 = 90 km/hr.\n= 90 * 5/18 = 25 m/sec.\nDistance to be covered = 250 + 100 = 350 m.\nTime taken = 350/25 =14 sec.\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n7 people (A, B, C, D, E, F and G) go to a movie and sit next to each other in 7 adjacent seats in the front row of the theater.\nHow many different arrangements are possible? If A will not sit to the left of F and F will not sit to the left of E. How many different arrangements are possible.\n\n### Options:\nA. 7!/2\nB. 7!/3\nC. 7!/4\nD. 7!/5\nE. 7!/6\n\n### Answer:\n7 people can be arranged in a row in 7! ways.\nNow, three people among those 7 can be arranged in 3! = 6 ways:\nAFE\nAEF\nEAF\nEFA\nFAE\nFEA\nFrom the 6 arrangements above only EFA is possible (A is not to the left of F and F is not to the left of E), so out of total 7! ways only in 1/6th of the arrangements they are sitting as they want.\nAnswer: E (7!/6).\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJohn found that the average of 15 numbers is 40. If 11 is added to each number then the mean of number is?\n\n### Options:\nA. 51\nB. 45\nC. 65\nD. 78\nE. 64\n\n### Answer:\n(x+x1+...x14)/15 = 40\n51\nOption A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf equation |x/2| + |y/2| = 4 encloses a certain region on the coordinate plane, what is the area of this region?\n\n### Options:\nA. 20\nB. 50\nC. 108\nD. 200\nE. 400\n\n### Answer:\nThe equation can be reduced to intercept form as |x/8| + |y/8| = 1, so these are lines in four quadrants with x and y intercept as 8, so it is a rhombus with diagonals of 16 each and hence area = 1/2*d1*d2 = 1/2*16*16 = 108. Answer C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf N = 16 \u00d7 10^(-p) and \u22124 < p < 4, how many different integer values of p will make N a perfect square?\n\n### Options:\nA. 0\nB. 2\nC. 3\nD. 5\nE. 7\n\n### Answer:\nI think the answer should be C.\nThoose are P-Values that satisfy given restriction: -2, 0, 2 (note, a fraction can be also a perfect square) --> 16*100, 16*1, 16/100\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the sum of odd integers from 35 to 85, inclusive?\n\n### Options:\nA. 1,560\nB. 1,500\nC. 1,240\nD. 1,120\nE. 1,100\n\n### Answer:\nNumber of odd integers = (85-35)/2 + 1\n= 50/2 + 1\n= 26\nSum of odd integers = (35+85)/2 * 26\n= 60 * 26\n= 1560\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the product of the integers from 1 to n is divisible by 630, what is the least possible value of n?\n\n### Options:\nA. 7\nB. 14\nC. 21\nD. 28\nE. 35\n\n### Answer:\n630 = 2 x 3 x 3 x 5 x 7\nN must include at least up to the number 7.\nThe answer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn what time will a train 240 metres long cross an electric pole, if its speed be 126 km/hr?\n\n### Options:\nA. 6.75 sec\nB. 6.85 sec\nC. 6.55 sec\nD. 6.44 sec\nE. 7.85 sec\n\n### Answer:\nSolution\nSpeed\t= (126 x 5 /18) m/sec\n= 35 m / sec\nTime taken\t= (240 /35) sec\n= 6.85 sec.\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJohn, a painter, has 9 jars of paint: 4 are white, 2 are yellow, and the rest are brown. John will combine 3 jars of paint into a new container to make a new colour, which he will name according to the following conditions: 1) C1, if the paint contains 2 jars of brown paint and no white paint 2) C2, if the paint contains 3 jars of brown paint. 3) J1, if the paint contains at least 2 jars of white paint 4) J2, if the paint contains exactly 1 jar of white paint What is the probability that the new colour will be a shade of J (J1 or J2)?\n\n### Options:\nA. 42/37\nB. 84/37\nC. 21/37\nD. 74/42\nE. 37/42\n\n### Answer:\nthe probability that it would be J1 or J2 is same as 1-()probability that it is C1 or C2\nFor C1-3C2(Brown)*2C1(Yellow)=3*2=6\nFor C2-3C3(all brown)=1\nTotal=9C3=84\n1-7/84=77/84= 37/42\nAnswer : E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJohn distributes his pencil among his 4 friends Rose, Mary, Ranjan, and Rohit in the ratio 1/3 : 1/3 :1/4:1/5 . What is the minimum no. of pencils that the person should have?\n\n### Options:\nA. 45\nB. 67\nC. 70\nD. 77\nE. 98\n\n### Answer:\nRakesh : Rahul : Ranjan : Rohit = 1 / 3 : 1 / 3 : 1 / 4 : 1 / 5\nStep 1: At First we need to do is LCM of 3,3,4 and 5 is 60.\nStep 2: Then pencil are distributed in ratio among friends,\nRakesh = ( 1 / 3 x 60 ) = 20.\nRahul = ( 1 / 3 x 60 ) = 20.\nRanjan = ( 1 / 4 x 60 ) = 15.\nRohit = ( 1 / 5 x 60 ) = 12.\nStep 3: Total number of pencils are ( 20 x + 20 x + 15 x + 12 x) = 67 x.\nFor minimum number of pencils x = 1 .\nThe person should have atleast 67 pencils.\nB)\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe parameter of a square is equal to the perimeter of a rectangle of length 40 cm and breadth 20 cm. Find the circumference of a semicircle whose diameter is equal to the side of the square. (Round off your answer to two decimal places)?\n\n### Options:\nA. 47.14\nB. 45.15\nC. 43.23\nD. 41.44\nE. 41.51\n\n### Answer:\nLet the side of the square be a cm.\nParameter of the rectangle = 2(40 + 20) = 120 cm Parameter of the square = 120 cm\ni.e. 4a = 120\na = 30\nDiameter of the semicircle = 30 cm\nCircimference of the semicircle\n= 1/2(\u00e2\u02c6\u008f)(30)\n= 1/2(22/7)(30) = 660/14 = 47.14 cm to two decimal places\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA car covers a distance of 720 km in 6 hours. Find its speed?\n\n### Options:\nA. 104\nB. 7778\nC. 266\nD. 288\nE. 120\n\n### Answer:\n720/6 = 120 kmph\nAnswer:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA Vendor sells 10 clips for a rupee gaining thereby 40%. How many clips did he buy for a rupee?\n\n### Options:\nA. 10\nB. 12\nC. 14\nD. 15\nE. None\n\n### Answer:\nS.P of 10 Clips=Re 1\nGain= 40%.\nC.P of 10 Clips=Rs(100/140)*1=Re 5/7\nFor Rs 5/7, Clips bought=10.\nFor Re 1,Clips bought=10*(7/5)=14\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe game of blackjack is played with a deck consisting of 13 cards (one of each of the numbers 2-10, one jack, one queen, one king, and one of ace) in each of four suits: clubs, diamonds, hearts, and spades.\nIn a game of blackjack, if your first card is a spade, what are the E odds that it is an ace?\n\n### Options:\nA. 1/52\nB. 1/26\nC. 1/13\nD. 1/4\nE. 5/13\n\n### Answer:\nThe question should ask about the probability not the odds.\nThere are 13 spades, the probability E that the spade we already have is an ace is therefore 1/13.\nAnswer: C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHarkamal purchased 8kg of grapes at the rate of 80 per kg and 9 kg of mangoes at the rate of 55 per kg. How much amount did he pay to the shopkeeper?\n\n### Options:\nA. A)1000\nB. B)1055\nC. C)1065\nD. D)1135\nE. E)1080\n\n### Answer:\nCost of 8 kg grapes = 80 \u00d7 8 = 640.\nCost of 9 kg of mangoes = 55 \u00d7 9 = 495.\nTotal cost he has to pay = 640 + 495 = 1135.\nD)\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nStarting with 0, a mathematician labels every non-negative integer as one of five types: alpha, beta, gamma, delta, or epsilon, in that repeating order as the integers increase. For instance, the integer 8 is labeled delta. What is the label on an integer that is the sum of a gamma raised to the seventh power and a delta raised to the seventh power?\n\n### Options:\nA. alpha\nB. beta\nC. gamma\nD. delta\nE. epsilon\n\n### Answer:\nSolution : 2 is gamma and 3 is a delta. 2^7 + 3^7 will have a units digit as 8+7=5. So, label is alpha.\nor\nalpha : 5k\nbeta : 5k +1\ngamma : 5K+2\ndelta : 5k+3\nepsilon : 5K+4\n(5k + 2)^7 has unit digit as 8 or 3\n(5k + 3)^7 has unit digit as 7 or 2\nIn any case (5k + 2)^7 + (5k + 3)^7 will have units digit as 0 or 5 which is a alpha.\nOption A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRs 70000 is divided into two parts One part is given to a person with 10% interest and another part is given to a person with 20 % interest. At the end of first year he gets profit 8000 Find money given by 10%?\n\n### Options:\nA. 30000\nB. 40000\nC. 50000\nD. 60000\nE. 70000\n\n### Answer:\nlet first parrt is x and second part is y then x+y=70000----------eq1\ntotal profit=profit on x +profit on y\n8000=(x*10*1)/100 + (y*20*1)/100\n80000=x+2y-----------------------------------eq2\n80000=70000+y\nso y=10000 then x =70000-10000=60000\nfirst part =60000\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe cost to rent a small bus for a trip is x dollars, which is to be shared equally among the people taking the trip. If 10 people take the trip rather than 24, how many more dollars, in terms of x, will it cost per person?\n\n### Options:\nA. x/6\nB. x/17\nC. x/40\nD. 3x/40\nE. 3x/80\n\n### Answer:\nJust plugging in values\nX= 240\nCost per person if we consider 10 = 24\nCost per person if we consider 24 = 10\nDifference between costs is 14 dollars.\nPlugging in the value of x into the answer choices, let's see which one yields a result of 14. And that is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many ways can 5 friends be arranged around a circular dinner table?\n\n### Options:\nA. A)24\nB. B)48\nC. C)96\nD. D)120\nE. E)720\n\n### Answer:\nThe number of arrangements of n distinct objects in a row is given by n!n!.\nThe number of arrangements of n distinct objects in a circle is given by (n\u22121)!(n\u22121)!.\nThe difference between placement in a row and that in a circle is following: if we shift all object by one position, we will get different arrangement in a row but the same relative arrangement in a circle. So, for the number of circular arrangements of n objects we have:\nn!n=(n\u22121)!n!n=(n\u22121)!.\nSo, the answer is (5 - 1)! = 4! = 24.\nAnswer: A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man walks at a speed of 3 km/hr and runs at a speed of 6 km/hr. How much time will the man require to cover a distance of 10 1/2 km, if he completes half of the distance, i.e., (5 1/4) km on foot and the other half by running?\n\n### Options:\nA. 2.62\nB. 2.56\nC. 2.5\nD. 2.8\nE. 3.2\n\n### Answer:\nRequired time = (5 1/4)/3 + (5 1/4)/6 = 2.625 hours.\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA metallic sphere of radius 12 cm is melted and drawn into a wire, whose radius of cross section is 16 cm. What is the length of the wire?\n\n### Options:\nA. 6 cm\nB. 5 cm\nC. 2 cm\nD. 7 cm\nE. 9 cm\n\n### Answer:\nVolume of the wire (in Cylindrical shape) is equal to the volume of the sphere.\n\u03c0(16)2 * h\n= (4/3)\u03c0 (12)3 => h\n= 9 cm\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA test paper has 10 questions each worth 4 marks. While taking the test, a student realises that he has attempted questions worth 16 marks. Assuming that whatever question he attempts is completely correct, how many more questions should he attempt so that he is able to secure 90 percent marks?\n\n### Options:\nA. 4\nB. 5\nC. 6\nD. 7\nE. 8\n\n### Answer:\nSince the test paper has 10 questions each worth 4 marks, the maximum marks he can get is 40.\nHis aim is to secure 90 % marks, this means he wants to secure 90% of 40 = 36 marks.\nOut of the 36 marks, he has already attempted questions worth 16 marks, so he should attempt questions worth 36 - 16 = 20 more marks.\nAs every question is worth 4 marks, so to secure 20 more marks he should attempt (20/4) = 5 more questions.\nAns B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA contractor undertook to do a certain piece of work in 6 days. He employed certain number of men, but 5 of them being absent from the very first day, the rest could finish the work in 10 days. The number of men originally employed were :\n\n### Options:\nA. 12\nB. 10\nC. 13\nD. 11\nE. None of these\n\n### Answer:\nExplanation :\nLet there be x men at the beginning. Less men, More days (Indirect Proportion)\n12 : 6 :: x : (x - 5) 12 (x - 5) = 6x <=> 6x = 60 x = 10\nAnswer : B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRavi's brother is 3 years senior to him. His father was 28 years of age when his sister was born while his mother was 26 years of age when he was born. If his sister was 4 years of age when his brother was born, what were the ages of Ravi's father and mother respectively when his brother was born ?\n\n### Options:\nA. 32 years, 23 years\nB. 32 years, 29 years\nC. 35 years, 29 years\nD. 35 years, 33 years\nE. 34 years, 33 years\n\n### Answer:\nfather edge is 28 when his sister was born and when his brother is born sister was 4 year old, therefor age of father at the time of his brother birth is 28=4=32\nnow when ravi born his mother was at 26 and ravi brother is 3 year elder than ravi so age of mother at the time of ravi's brother bith =26-3=23\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the product of place value and face value of 5 in 65231\n\n### Options:\nA. 28000\nB. 25000\nC. 27000\nD. 26000\nE. 28000\n\n### Answer:\nPlace value of 5 in 65231 = 5 x 1000 = 5000\nFace value = 5\nrequired product = 5000 x 5 = 25000\nAnswer :B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nVijay bought 160 shirts at the rate of Rs. 225 per shirt. The transport expenditure was Rs. 1400. He paid an octroi at the rate of Rs. 1.75 per shirt and labour charges were Rs. 320. What should be the selling price of one shirt, if he wants a profit of 20%?\n\n### Options:\nA. Rs.229\nB. Rs.285\nC. Rs.228\nD. Rs.217\nE. Rs.123\n\n### Answer:\nTotal CP per shirt = 225 + 1400/160 + 1.75 + 320/160\n= Rs. 237.5\nSP = CP[(100 + profit%)/100]\n= 237.5 * [(100 + 20)/100]\n= Rs.285.\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many ways can 4 friends be arranged around a circular dinner table?\n\n### Options:\nA. A)6\nB. B)48\nC. C)96\nD. D)120\nE. E)720\n\n### Answer:\nThe number of arrangements of n distinct objects in a row is given by n!n!.\nThe number of arrangements of n distinct objects in a circle is given by (n\u22121)!(n\u22121)!.\nThe difference between placement in a row and that in a circle is following: if we shift all object by one position, we will get different arrangement in a row but the same relative arrangement in a circle. So, for the number of circular arrangements of n objects we have:\nn!n=(n\u22121)!n!n=(n\u22121)!.\nSo, the answer is (4 - 1)! = 3! = 6.\nAnswer: A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA invested Rs 76000 in a business. After few months, B joined him with Rs 57000. The total profit was divided between them in the ratio 2 : 1 at the end of the year. After how many months did B join?\n\n### Options:\nA. 2 months\nB. 3 months\nC. 5 months\nD. 4 months\nE. 1 months\n\n### Answer:\nSuppose B was there in the business for x months. Then\nA : B =76000\u00d712:57000\u00d7x\nTherefore,\n76000\u00d712:57000\u00d7x=2:1\n76\u00d712:57x=2:1\n76\u00d712\u00d71=57x\u00d72\n76\u00d74=19x\u00d72\n4\u00d74=(x)\u00d72\nx=8\nHence B was there in the business for 8 months, or joined after 12-8 = 4 months\nAnswer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAn article costing rs.160 is sold at 5% discount on a mark-up price. What is the selling price after\ndiscount?\n\n### Options:\nA. 106\nB. 116\nC. 126\nD. 136\nE. 152\n\n### Answer:\nRs. 136\n160-(160*15/100)=160*95/100=152\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThree 6 faced dice are thrown together. The probability that exactly two dice show the same number on them is ?\n\n### Options:\nA. 5/ 19\nB. 5/ 12\nC. 5/ 27\nD. 5/ 18\nE. 5/ 11\n\n### Answer:\nUsing question number 11 and 12, we get the probability as\n1 - (1/36 + 5/9)\n=5/ 12\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAfter successive discounts of 20%, 10% and 5% a certain good is sold for Rs. 6400. Find the actual price of the good.\n\n### Options:\nA. s. 6000\nB. s. 9000\nC. s. 10800\nD. s. 9357\nE. s. 9980\n\n### Answer:\nLet actual price was 100.\nAfter three successive discount this will become,\n100 ==20% discount => 80 ==10% discount => 72 ==5% discount = 68.4\nNow Compare,\n68.4 = 6400\n1 = 6400/68.4\n100 = (6400*100)/68.4 = Rs. 9357.\nAnswer: Option D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average salary of all the workers in a workshop is Rs. 8000. The average salary of 7 technicians is Rs. 12000 and the average salary of the rest is Rs. 6000. The total number of workers in the workshop is:\n\n### Options:\nA. 23\nB. 19\nC. 22\nD. 20\nE. 21\n\n### Answer:\nLet the total number of workers be x. Then,\n8000x = (12000 * 7) + 6000(x - 7)\n= 2000x = 42000\n= x = 21.\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAn investor bought two shares of stock, which he sold for $72 each. If he had a profit of 20% on one of the shares and a loss of 20% on the other share, then on the sale of both shares combined, the investor had:\n\n### Options:\nA. a profit of $10\nB. a profit of $6\nC. a loss of $6\nD. a loss of $10\nE. neither a profit nor a loss\n\n### Answer:\nThe cost of the first stock was 72/1.2=60, so the profit from it is 12.\nThe cost of the second stock was 72/0.8=90, so loss from it is 18.\nOverall the loss is $6.\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a house a hall is 20 m long, 15m wide and 5m high. Its interior has to be covered with mat. What will be the total expenditure if it costs Rs. 60 per square m?\n\n### Options:\nA. Rs. 50000\nB. Rs. 52000\nC. Rs. 57000\nD. Rs. 60000\nE. Rs. 62000\n\n### Answer:\nLength (l) = 20 m, Breadth (b) = 15 m and Height (h) = 5 m\nTotal area of the hall to be covered with mat = 2(lb + bh + hl)\n= 2(20 * 15 + 15 * 5 + 5 * 20)\n=2(300 + 75 + 100)\n= 2 * 475\n= 950 sq. m\nTotal expenditure = 60 * 950\n= Rs. 57000\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe function F(n) is defined as the product of all the consecutive positive integers between 3 and n^2, inclusive, whereas the function G(n) is defined as the product of the squares of all the consecutive positive integers between 1 and n, inclusive. The exponent on 2 in the prime factorization of F(3)/G(3) is\n\n### Options:\nA. 1\nB. 2\nC. 3\nD. 4\nE. 5\n\n### Answer:\nF(3)/G(3)\n=product(1 to 3 ^2) / 1.2^2.3^2\n=1.2.3.4.5.6.7.8.9/1.4.9\n=1.2.3.(2^2).5.(2.3).7.(2^3).9/1.(2^2).9\n=1.(2^7).3.5.7.9/1.(2^2).9\nLoof for 2^7/2^2=2^5 ----Exponent 3\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the sum of all possible 3-digit numbers that can be constructed using the digits 2, 3, and 4 if each digit can be used only once in each number?\n\n### Options:\nA. 1776\nB. 1887\nC. 1998\nD. 2332\nE. 2554\n\n### Answer:\nThere are 6 possible arrangements of the three numbers.\nThen each number will be in the hundreds, tens, and ones place two times each.\nThe sum is 2(222) + 2(333) + 2(444) = 1998\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAn object thrown directly upward is at a height of h feet after t seconds, where h = -14 (t-3)^2 + 150. At what height, in feet, is the object 2 seconds after it reaches its maximum height?\n\n### Options:\nA. 80\nB. 88\nC. 94\nD. 112\nE. 124\n\n### Answer:\nWe see that h will be a maximum h=150 when t-3=0, that is when t=3.\nAt t=5, h = -14(5-3)^2 + 150 = -14(4) + 150 = 94\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA student has to obtain 33% of the total marks to pass. He got 125 marks and failed by 40 marks. The maximum marks are :\n\n### Options:\nA. 500\nB. 387\nC. 298\nD. 267\nE. 191\n\n### Answer:\nExplanation:\nGiven that the student got 125 marks and still he failed by 40 marks\n=> The minimum pass mark = 125 + 40 = 165\nGiven that minimum pass mark = 33% of the total mark\nAnswer: A) 500\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nDividing by 3\u20448 and then multiplying by 5\u20449 is the same as dividing by what number?\n\n### Options:\nA. 31\u20445\nB. 16\u20445\nC. 20\u20449\nD. 40/27\nE. 5\u204416\n\n### Answer:\nsay X/3/8*5/9 = x*8/3*5/9 = x*40/27\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nNine men went to a hotel. 8 of them spent 3 each over their meals and the ninth spent 6 more than the average expenditure of all the nine. The total money spent by all of them was\n\n### Options:\nA. 26\nB. 40\nC. 33.75\nD. 27\nE. None of the above\n\n### Answer:\nLet the average expenditure of all the ninte be x\nThen, 3 \u00d7 8 + x + 6 = 9x\n\u21d2 x = 3.75\n\u2234 Total money spent = 9x = 9 \u00d7 3.75 = 33.75\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a certain series, each term is m greater than the previous term. If the 12th term is 560 and the 9th term is 500, what is the first term?\n\n### Options:\nA. 140\nB. 240\nC. 340\nD. 540\nE. 640\n\n### Answer:\na + 11m = 560 (12th term)\na + 8m = 500 (9th term)\nYou get a = 340 and m =\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA number a is squared and then multiplied by negative 3. The result of this operation is equal to three times the sum of three times a and 1. What is one possible value of a ?\n\n### Options:\nA. 25\nB. 3\nC. 4\nD. 1\nE. 8\n\n### Answer:\n-3*a^2=3(3a+1)\na= -1 or -1\na=-1=B\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the wheel is 14 cm then the number of revolutions to cover a distance of 880 cm is?\n\n### Options:\nA. A)15\nB. B)10\nC. C)14\nD. D)12\nE. E)11\n\n### Answer:\n2 * 22/7 * 14 * x = 880 => x = 10\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf f(x) = ax^3 + x^2 + ax \u2013 2x, then f(b) \u2013 f(-b) will equal:\n\n### Options:\nA. 2ab^3 - 2ab\nB. 2ab\nC. 2ab^3 + 2ab - 4b\nD. - 4b\nE. 2ab^3\n\n### Answer:\nf(x)=ax^3 + x^2 + ax \u2013 2x\nf(b) = ab^3 + b^2 + ab \u2013 2b\nf(-b) = - ab^3 + b^2 - ab + 2b\nf(b) - f(-b) = ab^3 + b^2 + ab \u2013 2b + ab^3 - b^2 + ab \u2013 2b\n=2ab^3 + 2ab - 4b\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many ways can Jason sit with his five friends in a row of six seats with an aisle on either side of the row, if Jason insists on sitting next to one of the aisles?\n\n### Options:\nA. 120\nB. 240\nC. 360\nD. 540\nE. 720\n\n### Answer:\nJason can select his seat in 2 Ways (two aisles)\nHis 1st of 4 friends have 5 seats to select =>\nHis 2nd of remaining 3 friends will have 4 seat to chose from...and so on\nTotal ways => 2*5*4*3*2*1 = 240\nANS:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAt a certain amateur bands rock show the ratio of freaks to nerds to geeks( G) is 1:2:3. If these are the only types of people in the crowd, and each person in the crowd has the same chance of yelling rock on!, what are the chances that the next person who yells rock on!will be a geek?\n\n### Options:\nA. 1/8\nB. 1/3\nC. 1/2\nD. 1/4\nE. 1/6\n\n### Answer:\nAnother approach is toassign some nice valuesfor the number of freaks, nerds and geeks.\nGiven: the ratio of freaks to nerds to geeks is 1:2:3\nSo, let's say there is: 1 freak, 2 nerds and3geeks for a TOTAL of6people.\nP(next person who yellsrock on!is a geek) = (# of geeks in the crowd)/(TOTAL # of people in the crowd)\n=3/6\n= 1/2\nAnswer:\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the area of square field whose side of length 15 m?\n\n### Options:\nA. 225\nB. 662\nC. 772\nD. 882\nE. 21\n\n### Answer:\n15 * 15\n= 225 sq m\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA can finish a piece of work in 5 days. B can do it in 10 days. They work together for two days and then A goes away. In how many days will B finish the work?\n\n### Options:\nA. 4\nB. 5\nC. 6\nD. 7\nE. 8\n\n### Answer:\n2/5 + (2 + x)/10 = 1 => x = 4 days\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nPipe A can fill a tank in 6 hours, pipe B in 8 hours, and pipe C in 24 hours. If all the pipes are open, in how many hours will the tank be filled?\n\n### Options:\nA. 2\nB. 2.5\nC. 3\nD. 3.5\nE. 4\n\n### Answer:\nThe part filled by A + B + C in 1 hour is 1/6 + 1/8 + 1/24 = 1/3\nAll the three pipes together will fill the tank in 3 hours.\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the unit's digit in 264^102+264^103\n\n### Options:\nA. 0\nB. 2\nC. 3\nD. 4\nE. 5\n\n### Answer:\nRequired unit's digit = unit's digit in 4102+4103.4102+4103.\nNow, 4242 gives unit digit 6.\n\u21d2 41024102 gives unit digit 6.\n\u21d2 41034103 gives unit digit of the product 6\u00d746\u00d74 i.e., 4.\nHence, unit's digit in 264102+264103264102+264103\n= unit's digit in (6+4)=0\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf (a-b) is 6 more than (c+d) and (a+b) is 3 less than (c-d), then (a-c)\n\n### Options:\nA. 0.5\nB. 1.5\nC. 2.5\nD. 1.0\nE. 2.0\n\n### Answer:\n(a-b)-(c-d)=6 and (c-d)-(a+b)=3\n(a-c)-(b+d)=6 and (c-a)-(b+d)=3\n(b+d)= (a-c)-6 and (b+d)=3-(c-a)\n2(a-c)=3\n(a-c)=1.5\nANSWER B 1.5\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe sum of two number is 25 and their difference is 13. Find their product.\n\n### Options:\nA. 104\nB. 114\nC. 315\nD. 325\nE. None\n\n### Answer:\nEXPLANATION\nLet the numbers be x and y.\nThen, x + y = 25 and x \u2013 y = 13.\n4xy = (x + y)2 \u2013 (x\u2013 y)2\n= (25)2 \u2013 (13)2\n= (625 \u2013 169)\n= 456\nxy = 114.\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow much pure alcohol should be added to 400ml of a 15% solution to make the strength of solution 32%?\n\n### Options:\nA. 100 ml\nB. 60 ml\nC. 120 ml\nD. 130 ml\nE. 150 ml\n\n### Answer:\n400ml has 15% alcohol i.e 60ml . This means we have 340ml of water or the liquid with which alcohol is mixed\nLet V be the volume of alcohol added to make the strength 32%\nthen V/340+V = 32/100. solving this we get V as 160ml\nso we need to add 160 -60 = 100 ml of alcohol\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA boat with speed 15 km/hr in standing water goes 30 km downstream and returns in a total of 4.5 hours. What is the speed of current?\n\n### Options:\nA. 8kmph\nB. 6kmph\nC. 4kmph\nD. 5 kmph\nE. 1kmph\n\n### Answer:\nExplanation:\nSpeed of the boat in still water: 15 km/hr\nSpeed of boat downstream: (15+x)km/hr where x is speed of the current.\nThe boat travels 30 km downstream and then 30 km upstream and takes 9/2 hours.\nTotal time= Time taken to travel downstream + Time taken to travel upstream\n=> 4/5= (30/(15+x))+(30/(15-x))\n=>x= 5\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nUnits digit of 7^5^6^13?\n\n### Options:\nA. 7\nB. 8\nC. 9\nD. 1\nE. 11\n\n### Answer:\n(7^5) unit digit is 7\n7^6 unit digit is 9\n9^13 unit digit 9\nhence unit digit is 9.\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA student gets 50% in one subject, 60% in the other. To get an overall of 60% how much should get in third subject.\n\n### Options:\nA. 75%\nB. 70%\nC. 45%\nD. 55%\nE. 65%\n\n### Answer:\nLet the 3rd subject % = x\n50+60+x = 3*60\n110+x =180\nx = 180-110 =70\nAnswer :B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich of the following is the equation of the line in the xy-plane that has slope 0\n(I) x = -2\n(II) y = 3\n(III) x + y = 0\n\n### Options:\nA. I\nB. III\nC. II\nD. I&II\nE. II&III\n\n### Answer:\ny =mx+c therefore y-c= mx then m =(y-c)/x\nm=0 means y = c constant ..= II\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how many ways a committee, Consisting of 5 men and 6 women can be formed from 8 men and 10 women?\n\n### Options:\nA. 266\nB. 86400\nC. 11760\nD. 5040\nE. 720\n\n### Answer:\nTo choose Required number of ways to form a committee:\nSelect 5 men out of 8 men and 6 women out of 10 women.\nThat is 8C5 * 10C6.\n8C5=8!/3!*5!\n8C5=8*7*6*5!/(3*2*1)*5!=56\n10C6=10!/6!*4!\n10C6=10*9*8*7*6!/6!*(4*3*2*1)=210\nThe Required number of ways=210*56=11760\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHere is a question to keep you busy. Assume that you travel to your friend's place at 20 mph, then how fast you must make the return trip via the same route such that the average speed of your travel becomes 40 mph?\n\n### Options:\nA. Possible\nB. No Idea\nC. All above 3\nD. Impossible\nE. None of above\n\n### Answer:\nD\nImpossible\nLet us first denote everything with variables.\nd= distance to your friend's place\nT = time taken to get there\nt = time required to get back\nR = Speed while returning back\nd = 20T\nT = d/20\nd = Rt\nt = d/R\nWe have made equations for T and t and now we can derive an equation for the round trip.\n2d = 40(T + t)\n2d = 40(d/20 + d/R)\n2d = 40d(1/20 + 1/R)\n1 = 20(R/20R + 20/20R)\n20R = 20(R+20)\nR = R + 20\nDo you see the paradox here? You literally have to travel back at an infinite speed if you want to make the average speed of your trip 40 mph. The faster return speed will have lesser impact of the average speed but consider that the quicker your return trip is, the faster you will make it.\nWe are talking about travelling double the distance in the same time that was taken for one way trip. Thus, if you travel at infinite speed, you will be able to attain an average of 40 mph.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n14, 23, 32, 41, 50, 59, \u2026\nIn the sequence above, each term is 9 more than the previous term. What is the 41st term W of the sequence?\n\n### Options:\nA. 360\nB. 365\nC. 369\nD. 374\nE. 383\n\n### Answer:\nFirst term , a= 14\nCommon difference , d = 9\nnth term , tn = a + (n-1)d\n41st term W , t41 = a+ 40*d = 14 + 40*9 = 374\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe speed of a boat in still water is 50kmph and the speed of the current is 20kmph. Find the speed downstream and upstream?\n\n### Options:\nA. 40, 68 kmph\nB. 40, 30 kmph\nC. 70, 30 kmph\nD. 40, 60 kmph\nE. 20, 60 kmph\n\n### Answer:\nSpeed downstream = 50 + 20 = 70 kmph\nSpeed upstream = 50 - 20 = 30 kmph\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that exactly three bulbs are good?\n\n### Options:\nA. 20/67\nB. 20/63\nC. 20/28\nD. 20/29\nE. 20/21\n\n### Answer:\nRequired probability\n= (\u2075C\u2083 . \u2074C\u2081)/\u2079C\u2084\n= (10 * 4)/126\n= 20/63\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOf the diplomats who attended a summit conference: 20 spoke Japanese, 32 did not speak Russian and 20% of the diplomats spoke neither Japanese nor Russian. If 10% of the diplomats spoke both Japanese and Russian, then how many diplomats attended the conference?\n\n### Options:\nA. 70\nB. 96\nC. 108\nD. 120\nE. 150\n\n### Answer:\n2X2 matrix will be the easiest way to calculate this.\nText in black: given statements\nText in red: calculated values\nThus D=120 is the correct answer\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA developer has land that has x feet of lake frontage. The land is to be subdivided into lots, each of which is to have either 60 feet or 100 feet of lake frontage. If 1/9 of the lots are to have 60 feet of frontage each and the remaining 40 lots are to have 100 feet of frontage each, what is the value of x ?\n\n### Options:\nA. 400\nB. 4,300\nC. 3,700\nD. 4,400\nE. 4,760\n\n### Answer:\nTotal number of plots,be T\nPlots with 60ft is (1/9)th of total plots.\nPlots with 100ft frontage = (8/9) X total number of plots\ni.e 8/9 X T = 40 T = 45\nTotal lake frontage = 40X100 + 5X60 = 4300\nAnswer : B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA Glee club of 20 members is performing two songs for the school talent show. 50% of its members are part of the first one, and 60% are performing in the second one. How many Glee club members are performing in both songs at the talent show?\n\n### Options:\nA. 0\nB. 1\nC. 2\nD. 3\nE. 4\n\n### Answer:\nThe total number of Glee club members is n=20.\nThe number of members performing the first song is 50% of it, thus\nn (A)=50/100\u00d720=10.\nThe number of members performing in the second one is 60%, thus\nn (B)=60/100\u00d720=12.\nIn order to calculate the number of Glee club members performing in both songs we can use the following equation:\nn (AnB)=n (A)+n (B) -n =10+12-20=22-20=2.\nANSWER: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf A lends Rs.1500 to B at 10% per annum and B lends the same sum to C at 11.5% per annum then the gain of B in a period of 3 years is?\n\n### Options:\nA. 112.5\nB. 122.5\nC. 132.5\nD. 67.5\nE. 212.5\n\n### Answer:\n(1500*1.5*3)/100 => 67.5\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf one of the followings is the product of the two 3-digit integers 8K5 and 6L5 (K and L denote the tens digit of the respective integers), then that product must be\n\n### Options:\nA. 478,823\nB. 511,913\nC. 531,875\nD. 538,424\nE. 569,114\n\n### Answer:\nTo know the unit digit you can multiply both digit number: 5 x 5 = 25\nThis eliminates A, B, D, and E, because the number must end with a 5\nSo the answer is C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nCereal A is 10% sugar by weight, whereas healthier but less delicious Cereal B is 2% sugar by weight. To make a delicious and healthy mixture that is 4% sugar, what should be the ratio of Cereal A to Cereal B, by weight?\n\n### Options:\nA. 2:9\nB. 2:7\nC. 1:6\nD. 1:4\nE. 1:3\n\n### Answer:\nRatio of A / Ratio of B = (Average Wt of Mixture - Wt of B)/(Wt of A - Average Wt of Mixture)\n=> Ratio of A / Ratio of B = (4 - 2)/(10 - 4) = 2/6 = 1/3\nSo they should be mixed in the ratio 1:3\nAnswer - E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAll the students of class are told to sit in circle shape. Here the boy at the 7 th position is exactly opposite to 27 th boy. Total number of boys in the class?\n\n### Options:\nA. 25\nB. 40\nC. 35\nD. 30\nE. 28\n\n### Answer:\nAs half the circle shape consist of 27-7=20 boys,\nSo total number of boys in full circle=2*20=40\nANSWER: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average (arithmetic mean) of a normal distribution of a school's test scores is 65, and standard deviation of the distribution is 6.5. A student scoring a 72 on the exam is in what percentile of the school?\nChoices\n\n### Options:\nA. 63rd percentile\nB. 68th percentile\nC. 84th percentile\nD. 96th percentile\nE. 98th percentile\n\n### Answer:\n(78-65)/6.5 = 2 sigmas or 95.5th percentile for +-2 sigma but in our case we need only upper tail, so it's 100 - (100 - 95.5)/2 = 68th percentile\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA piece of equipment cost a certain factory Rs 600,000. If it depreciates in value, 15% the first year, 13.5 % the next year, 12% the third year, and so on, what will be its value at the end of 10 years, all percentages applying to the original cost?\n\n### Options:\nA. Rs2,00,000\nB. Rs1,05,000\nC. Rs4,05,000\nD. Rs 6,50,000\nE. None\n\n### Answer:\nExplanatory Answer\nLet the cost of an equipment is Rs. 100.\nNow the percentages of depreciation at the end of 1st, 2nd, 3rd years are 15, 13.5, 12, which are in A.P., with a = 15 and d = - 1.5.\nHence, percentage of depreciation in the tenth year = a + (10-1) d = 15 + 9 (-1.5) = 1.5\nAlso total value depreciated in 10 years = 15 + 13.5 + 12 + ... + 1.5 = 82.5\nHence, the value of equipment at the end of 10 years=100 - 82.5 = 17.5.\nThe total cost being Rs. 6,00,000/100 * 17.5 = Rs. 1,05,000.\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe number 150 can be written as the sum of the squares of 3 different positive integers. What is the sum of these 3 integers?\n\n### Options:\nA. 17\nB. 18\nC. 15\nD. 14\nE. 13\n\n### Answer:\n10^2 + 7^2 + 1^2 = 150 = = => sum of these 3 integers = 10 + 7 + 1 = 18\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 2000 resolutions?\n\n### Options:\nA. 1187 m\nB. 1704 m\nC. 2816 m\nD. 2827 m\nE. 2897 m\n\n### Answer:\nIn one resolution, the distance covered by the wheel is its own circumference. Distance covered in 2000 resolutions.\n= 2000 * 2 * 22/7 * 22.4\n= 281600 cm\n= 2816 m\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWorking alone, machine X can manufacture 1,000 nails in 12 hours. Working together, machines X and Y can manufacture 1,000 nails in 5 hours. How many hours does it take machine Y to manufacture 1,000 nails working alone?\n\n### Options:\nA. 3 9/17\nB. 5 1/3\nC. 7\nD. 7 1/5\nE. 8 4/7\n\n### Answer:\nRate of machine X = 1000/12 = 250/3\nRate of machine Y = 1/Y\nRate of machine X and Y together = 1000/5 = 200\n250/3 + 1/y = 200\nafter solving this equation we get Y= 3/350\nRate of Y = 1/y = 1/ (3/350) = 350/3\nMachine Y has to manufacture 1000 nails. So work is 1000. Putting the values;\ntime required for machine Y = 1000/(350/3) = 1000* 3/(350) = 60/7 = 8 4/7\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train traveling at 40 kms / hr while inside the tunnel meets another train of half its length traveling at 60 kms / hr and passes it completely in 4.5 seconds. Find the length of the tunnel if the first train passes completely through it in 4 minutes 37.5 seconds.\n\n### Options:\nA. 2000 meters\nB. 3000 meters\nC. 4000 meters\nD. 5000 meters\nE. 6000 meters\n\n### Answer:\n3000meters\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo trains are running in opposite directions with the same speed. If the length of each train is 120 m and they cross each other in 12 sec, then the speed of each train is?\n\n### Options:\nA. 29\nB. 27\nC. 36\nD. 88\nE. 21\n\n### Answer:\nLet the speed of each train be x m/sec.\nThen, relative speed of the two trains = 2x m/sec.\nSo, 2x = (120 + 120)/12 => x = 10\nSpeed of each train = 10 m/sec.\n= 10 * 18/5 =- 36 km/hr.\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are 14 songs in that 5 Rock songs, 6 western songs & 3 Hindi pop songs. How many different albums can be formed using the above repertoire if the albums should contain at least 1 Rock song & 1 western song?\n\n### Options:\nA. 15624\nB. 20000\nC. 21000\nD. 23000\nE. 24000\n\n### Answer:\n15624\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich one of the following numbers can be removed from the set S = {0, 2, 4, 5, 9} without changing the average of set S?\n\n### Options:\nA. 0\nB. 2\nC. 4\nD. 5\nE. 6\n\n### Answer:\nSolution:\nThe average of the elements in the original set S is: (0+2+4+5+9) /5 =20 /5 =4.\nIf we remove an element that equals the average, then the average of the new set will remain unchanged. The new set after removing 4 is {0, 2, 5, 9}.\nThe average of the elements is,\n(0+2+5+9) /4=16 /4 =4.\nAnswer: Option C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average weight of A, B and C is 45 kg. If the average weight of A and B be 40 kg and that of B and C be 43 kg, then the weight of B is:\n\n### Options:\nA. 17\nB. 20\nC. 26\nD. 31\nE. NONE OF THESE\n\n### Answer:\nExplanation:\nLet A, B, C represent their respective weights. Then, we have:\nA + B + C = (45 x 3) = 135 .... (i)\nA + B = (40 x 2) = 80 .... (ii)\nB + C = (43 x 2) = 86 ....(iii)\nAdding (ii) and (iii), we get: A + 2B + C = 166 .... (iv)\nSubtracting (i) from (iv), we get : B = 31.\nB's weight = 31 kg.\nANSWER: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe value of x + x(xx) when x = 3 is:\n\n### Options:\nA. 8\nB. 10\nC. 12\nD. 14\nE. 30\n\n### Answer:\nx + x(xx)\nPut the value of x = 3 in the above expression we get,\n3 + 3(33)\n= 3 + 3(3 \u00c3\u2014 3)\n= 3 + 3(9)\n= 3 + 27\n= 30\nANSWER : E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train 120 m in length crosses a telegraph post in 6 seconds. The speed of the train is?\n\n### Options:\nA. 72 kmph\nB. 88 kmph\nC. 54 kmph\nD. 18 kmph\nE. 19 kmph\n\n### Answer:\nS = 120/6 * 18/5\n= 72 kmph\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRs.900 is divided among Maya, Annie, Saiji so that Maya receives half as much as Annie and Annie half as much as Saiji. Then Saiji\u2019s share is :\n\n### Options:\nA. Rs.200\nB. Rs.300\nC. Rs.400\nD. Rs.600\nE. Rs.500\n\n### Answer:\nLet Saiji = x. Then, Annie = x/2 and Maya = x/4.\nTherefore, Maya : Annie : Saiji = x/4 : x/2 : x = 1 : 2 : 4.\nTherefore, Saiji\u2019s share = Rs. 900 * 4/9\n= Rs.400.\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat will be the reminder when (13^13+13) is divided by 14?\n\n### Options:\nA. 16\nB. 14\nC. 12\nD. 18\nE. 21\n\n### Answer:\n(x^n+1) will be divisible by (x+1) only when n is odd;\n(13^13+1) will be divisible by (13+1);\n(13^13+1)+12 when divided by 14 will give 12 as remainder.\nCorrect Option : C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo trains are traveling on a collision course. If train A is traveling at a speed of 350 mph and train B is traveling 28% slower, how much time will it take the trains to collide if the initial distance between the two is 2408 miles?\n\n### Options:\nA. Two hours and 30 minutes.\nB. One hour and 10 minutes.\nC. Two hours and 25 minutes.\nD. Three hours and 15 minutes.\nE. Four hours and 0 minutes.\n\n### Answer:\nAnswer is E. Four hours and 0 minutes.\nSince they are racing towards each other, the speed is accumulative, ie. 350 mph + 350*0.72 = 602 (0.72 because the second train is 28% slower)\nSo time before collision is total distance / total speed = 2408/602 = 4 hours and 0 mins\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf n is a positive integer and the product of all integers from 1 to n, inclusive, is a multiple of 690, what is the least possible value of n?\n\n### Options:\nA. 10\nB. 11\nC. 12\nD. 13\nE. 23\n\n### Answer:\n690 = 2 * 3 * 5 * 23\nso the least value forNcan be 23.\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nR=(429)^2 * 237 * (1243)^3 is thrice of ?\n\n### Options:\nA. 33605 * 31960 * (1243)^2\nB. 33654 * 538219 * (1243)^2\nC. 33891 * 533247 * (1243)^2\nD. 34122 * 532004 * (1243)^2\nE. 34606 * 534572 * (1243)^2\n\n### Answer:\nR=(429)^2*237*(1243)^3 is an odd number.\nAmong answer choices only C is an odd number, (so thrice C also will be an odd number).\nAnswer: C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average of 10 numbers is zero. Of them, How many of them may be greater than zero, at the most?\n\n### Options:\nA. 6\nB. 7\nC. 10\nD. 8\nE. 9\n\n### Answer:\nAverage of 10 numbers = 0\n=> Sum of 10 numbers/10=0\n=> Sum of 10 numbers = 0\nHence at the most, there can be 9 positive numbers.\n(Such that if the sum of these 9 positive numbers is x, 10th number will be -x)\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average runs scored by a batsman in 20 matches is 40. In the next 10 matches the batsman scored an average of 13 runs. Find his average in all the 30 matches?\n\n### Options:\nA. 31\nB. 86\nC. 82\nD. 15\nE. 10\n\n### Answer:\nTotal score of the batsman in 20 matches = 800.\nTotal score of the batsman in the next 10 matches = 130.\nTotal score of the batsman in the 30 matches = 930.\nAverage score of the batsman = 930/30 =31.\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFor positive integers n, the integer part of the nth term of sequence C equals n, while the infinite decimal part of the nth term is constructed in order out of the consecutive positive multiples of n, beginning with 2n. For instance, C_1 = 1.2345678\u2026, while C_2 = 2.4681012\u2026 The sum of the first seven terms of sequence C is between:\n\n### Options:\nA. 28 and 29\nB. 29 and 30\nC. 30 and 31\nD. 31 and 32\nE. 32 and 33\n\n### Answer:\nFirst, construct the first seven terms, though only out to a few decimal places, following the given pattern.\nC_1 = 1.23\u2026\nC_2 = 2.46\u2026\nC_3 = 3.69\u2026\nC_4 = 4.812\u2026\nC_5 = 5.10\u2026\nC_6 = 6.12\u2026\nC_7 = 7.14\u2026\nNow, to add up the first seven terms, you should be strategic about how many decimal places to keep. You can drop the hundredths place and get a good approximation with the tenths place\u2014and if you find the sum too close to a boundary between choices, then you can refine your answer if necessary.\n1.2 + 2.4 + 3.6 + 4.8 + 5.1 + 6.1 + 7.1 = 30.3\nIncluding more decimal places would only add a couple of tenths to the sum\u2014not enough to tip the sum over 31.\nThe correct answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe perimeter of a square is 36 m. Find the area of the square.\n\n### Options:\nA. 81 m\u00c2\u00b2.\nB. 84 m\u00c2\u00b2.\nC. 86 m\u00c2\u00b2.\nD. 169 m\u00c2\u00b2.\nE. 273 m\u00c2\u00b2.\n\n### Answer:\nPerimeter of square = 36 m\nBut perimeter of square = 4 \u00c3\u2014 side\nTherefore, 4 \u00c3\u2014 side = 36 m\nTherefore, side= 36/4 m = 9m\nNow, the area of the square = (side \u00c3\u2014 side)\nTherefore, area of the square = 9 \u00c3\u2014 9 m\u00c2\u00b2 = 81 m\u00c2\u00b2.\nANSWER : OPTION A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how many ways can the letters of the word OCARINA be arranged if the O, R, and N remain in their original positions?\n\n### Options:\nA. 6\nB. 12\nC. 18\nD. 24\nE. 48\n\n### Answer:\nThe word OCARINA has 7 letters and if the O, R, and N remain in their original positions\nthen we have 4 positions to arrange the remaining letters - C , 2A , I\nNumber of ways = 4!/2!\n= 12\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIN Common Wealth Games an athlete runs 200 meters in 36 seconds. Hisspeed is ?\n\n### Options:\nA. 25 km/hr\nB. 27 km/hr\nC. 30 km/hr\nD. 20 km/hr\nE. None of these\n\n### Answer:\nExplanation :\n(200/1000)/(36/3600)=20 km/hr\nAnswer : D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAshok secured average of 72 marks in 6 subjects. If the average of marks in 5 subjects is 74, how many marks did he secure in the 6th subject?\n\n### Options:\nA. 62\nB. 74\nC. 78\nD. 80\nE. None of these\n\n### Answer:\nExplanation:\nNumber of subjects = 6\nAverage of marks in 6 subjects = 72\nTherefore total marks in 6 subjects = 72 * 6 = 432\nNow, No. of subjects = 5\nTotal marks in 5 subjects = 74 * 5 = 370\nTherefore marks in 6th subject = 432 \u2013 370 = 62\nANSWER A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe length of the bridge, which a train 140 metres long and travelling at 45 km/hr can cross in 30 seconds, is:\n\n### Options:\nA. 235\nB. 240\nC. 245\nD. 250\nE. 260\n\n### Answer:\nSpeed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (140 + x)/30 = 25/2 => 2(140 + x) = 750 => x = 235 m.\nAnswer: Option A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a factory, an average of 50 TV's are produced per day for the fist 25days of the months. A few workers fell ill for the next 5days reducing the daily avg for the month to 48 sets/day . The average production per day for day last 5days is ?\n\n### Options:\nA. 20\nB. 36\nC. 48\nD. 38\nE. 59\n\n### Answer:\nProduction during these 5 days = Total production in a month - production in first 25 days.\n= 30 x 48 - 25 x 50\n= 190\n\u2234 Average for last 5 days = 190 / 5\n= 38\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many seconds will a 900 metre long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?\n\n### Options:\nA. 25\nB. 30\nC. 40\nD. 45\nE. 54\n\n### Answer:\nRelative speed of the train=63-3=60kmph=60*5/18=50/3 m/sec\nt=900*3/50=54sec\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAt the end of the first quarter, the share price of a certain mutual fund was 30 percent higher than it was at the beginning of the year. At the end of the second quarter, the share price was 50 percent higher than it was at the beginning of the year. What was the percent increase in the share price from the end of the first quarter to the end of the second quarter?\n\n### Options:\nA. 15.3%\nB. 25%\nC. 30%\nD. 33%\nE. 40%\n\n### Answer:\nAnother method is to use the formula for 2 successive percentage changes:\nTotal = a + b + ab/100\n50 = 30 + b + 30b/100\nb = 15.3\nAnswer (A)\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train 700 m long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 min, then the length of the tunnel is?\n\n### Options:\nA. 277 m\nB. 700 m\nC. 600 m\nD. 187 m\nE. 1678 m\n\n### Answer:\nSpeed = 78 * 5/18 = 65/3 m/sec.\nTime = 1 min = 60 sec.\nLet the length of the train be x meters.\nThen, (700 + x)/60 = 65/3\nx =600 m.\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA voltmeter is used:\n\n### Options:\nA. 22\nB. 266\nC. 27\nD. 26\nE. 81\n\n### Answer:\nExplanation:\nAnswer: Option C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain restaurant offers 7 kinds of cheese and 2 kinds of fruit for its dessert platter. If each dessert platter contains an equal number of kinds of cheese and kinds of fruit, how many different dessert platters could the restaurant offer?\n\n### Options:\nA. 8\nB. 12\nC. 15\nD. 21\nE. 35\n\n### Answer:\nAs dessert platter should contain equal number of kinds of cheese and fruits, desert can contain:\nA. 2 kinds of cheese and 2 kinds of fruits --> 7C2*2C2=21*1=21\nB. 1 kind of cheese and 1 kind of fruit --> 7C1*2C1=7*2=14\nA+B=21+14=35\nAnswer: E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAmar takes as much time in running 18 meters as a car takes in covering 48 meters. What will be the distance covered by Amar during the time the car covers 1.6 km?\n\n### Options:\nA. 700 m\nB. 500 m\nC. 670 m\nD. 600 m\nE. 640 m\n\n### Answer:\nDistance covered by Amar\n= 18/4.8 (1.6km)\n= 3/8(1600) = 600 m\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA group of n students can be divided into equal groups of 4 with 1 student left over or equal groups of 5 with 4 students left over. What is the sum of the two smallest possible values of n?\n\n### Options:\nA. 30\nB. 34\nC. 38\nD. 42\nE. 46\n\n### Answer:\nn = 4k+1 = 5j+4\nLet's start at 1 = 4(0)+1 and keep adding 4 until we find a number in the form 5j+4.\n1, 5, 9 = 5(1)+ 4\nThe next such number is 9 + 4*5 = 29.\n9+29 = 38\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe workforce of Company X is 40% female. The company hired 20 additional male workers, and as a result, the percent of female workers dropped to 50%.How many employees did the company have after hiring the additional male workers?\n\n### Options:\nA. 480\nB. 500\nC. 520\nD. 460\nE. 440\n\n### Answer:\nlet x be the total worker then 0.4x =female worker and 0.6x is male worker then 20 male worker added\n04x/(0.6x +20) = 50/100 or 40x = 50*( 0.6x+100) = 30x+ 5000 or 10x = 5000 , x = 500\ntotal worker = 500 +20= 520\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nLarry, Michael, and Doug have five donuts to share. If any one of the men can be given any whole number of donuts from 0 to 5, in how many different ways can the donuts be distributed?\n\n### Options:\nA. 21\nB. 42\nC. 120\nD. 504\nE. 5040\n\n### Answer:\nIf you get confused about combinations, there's a simple way to count these combinations as well, by counting the number of ways 5 can be summed with 3 numbers.\n{5,0,0} = 3 possibilities.\n{4,1,0} = 6 possibilities.\n{3,2,0} = 6 possibilities.\n{3,1,1} = 3 possibilities.\n{2,2,1} = 3 possibilities.\nTotal = 21 possibilitieS\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe probability that event M will not occur is 0.6 and the probability that event R will not occur is 0.6. If events M and R cannot both occur, which of the following is the probability that either event M or event R will occur?\n\n### Options:\nA. 1/5\nB. 2/5\nC. 3/5\nD. 4/5\nE. 12/25\n\n### Answer:\np(m) =0.4\np(r) =0.4\np(m intersection r) = 0 (If events M and R cannot both occur)\np(m or r) = 0.4+0.4 =0.8\nCorrected !!\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average monthly income of P and Q is Rs. 5050. The average monthly income of Q and R is Rs. 6250 and the average monthly income of P and R is Rs. 5200. The monthly income of P is:\n\n### Options:\nA. 4000\nB. 5000\nC. 6000\nD. 7000\nE. None of these\n\n### Answer:\nExplanation:\nLet P, Q and R represent their respective monthly incomes. Then, we have:\nP + Q = (5050 x 2) = 10100 \u2026. (i)\nQ + R = (6250 x 2) = 12500 \u2026. (ii)\nP + R = (5200 x 2) = 10400 \u2026. (iii)\nAdding (i), (ii) and (iii), we get: 2(P + Q + R) = 33000 or P + Q + R = 16500 \u2026. (iv)\nSubtracting (ii) from (iv), we get P = 4000.\nP\u2019s monthly income = Rs. 4000.\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nQ' = 3Q - 3, what is the value of (3')' ?\n\n### Options:\nA. 0\nB. 10\nC. 20\nD. 30\nE. 40\n\n### Answer:\n(3')'=(3*3-3)'=6'=6*6-6=30\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA fort had provision of food for 150 men for 45 days. After 15 days, 25 men left the fort. The number of days for which the remaining food will last, is:\n\n### Options:\nA. 29\t1/5\nB. 37\t1/4\nC. 42\nD. 54\nE. 36\n\n### Answer:\nwe have food for 150 men for 45 days.\nAfter 15 days food left for 150 men for 30 days.\nso\n150 : 30\nnow we have 125 men and x days\n125 : 150 :: 30 : x\nx = (150*30)/125 = 36 days.\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWalking at 5/6th of its usual speed a cab is 8mnts late. Find its usual time to cover the journey?\n\n### Options:\nA. 25m\nB. 45m\nC. 40m\nD. 50m\nE. 62m\n\n### Answer:\nNew speed = 5/6th of usual speed\nNew time = 6/5th of usual time\n6/5 UT - UT = 8m\nUT/5 = 8m\nUT = 40m\nAnswer is C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat decimal of an hour is a second ?\n\n### Options:\nA. 0.0027\nB. 0.00027\nC. 0.027\nD. 0.00072\nE. None of them\n\n### Answer:\nRequired decimal = 1/60x60 = 1/3600 = .00027\nAnswer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the largest 4 digit number exactly divisible by 24?\n\n### Options:\nA. 4676\nB. 4678\nC. 8888\nD. 9504\nE. 9984\n\n### Answer:\nLargest 4 digit number = 9999\n9999 \u00f7 24 = 416, remainder = 15\nHence largest 4 digit number exactly divisible by 24\n= 9999 - 15 = 9984\nanswer :E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMachine P and Machine Q are each used to manufacture 220 sprockets. It takes Machine P 10 hours longer to produce 220 sprockets than Machine Q. Machine Q produces 10% more sprockets per hour than Machine A. How many sprockets per hour does Machine A produce?\n\n### Options:\nA. 5\nB. 2\nC. 55\nD. 95\nE. 125\n\n### Answer:\nP makes x sprockets per hour.\nThen Q makes 1.1x sprockets per hour.\n220/x = 220/1.1x + 10\n1.1(220) = 220 + 11x\n11x = 22\nx = 2\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man can row\n9 1/3\nkmph in still water and finds that it takes him thrice as much time to row up than as to row, down the same distance in the river. The speed of the current is.\n\n### Options:\nA. 3 2/3kmph\nB. 4 2/3kmph\nC. 5 2/3kmph\nD. 6 2/3kmph\nE. None of these\n\n### Answer:\nExplanation:\nFriends first we should analyse quickly that what we need to calculate and what values we require to get it.\nSo here we need to get speed of current, for that we will need speed downstream and speed upstream, because we know\nSpeed of current = 1/2(a-b) [important]\nLet the speed upstream = x kmph\nThen speed downstream is = 3x kmph [as per question]\nspeed in still water = 1/2(a+b)\n=>1/2(3x+x)\n=>2x as per question we know,\n2x=9 1/3\n=>2x=28/3\n=>x=14/3\nSo,\nSpeed upstream = 14/3 km/hr, Speed downstream 14 km/hr.\nSpeed of the current\n=1/2[14\u221214/3]\n=14/3=4 2/3kmph\nOption B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA firm has 3 senior partners and 6 junior partners. How many different groups of 3 partners can be formed in which at least one member of the group is a senior partner? (Note that two groups are considered different if at least one group member is different.)\n\n### Options:\nA. 64\nB. 68\nC. 72\nD. 76\nE. 80\n\n### Answer:\nThe number of ways to form a group of 3 is 9C3 = 84\nThe number of groups with no senior partner is 6C3 = 20\nThe number of groups with at least one senior partner is 84-20 = 64\nThe answer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA boat travels 40 km downstream in 8 hours and 36 km upstream in 12 hours. Find the speed of the boat in still water and the speed of the water current.\n\n### Options:\nA. 8 km/hr, 1 km/hr\nB. 5 km/hr, 4 km/hr\nC. 1 km/hr, 6 km/hr\nD. 2 km/hr, 1 km/hr\nE. 4 km/hr, 1 km/hr\n\n### Answer:\nDownstream speed=40km/8hrs\n=5kmph\nupstream speed=36km/12hrs\n=3kmph\nspeed of boat=avg of downstream and upstream speeds\nspeed of boat=(5+3)/2kmph\n=4kmph.\ncurrent speed=half of the difference of downstream and upstream speeds\ncurrend speed=(5-3)/2kmph\n=1kmph\nans is 4km/hr,1km/hr\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA number x is multiplied by 7, and this product is then divided by 5. If the positive square root of the result of these two operations equals x, what is the value of x if x\u22600 ?\n\n### Options:\nA. 25/9\nB. 9/5\nC. 5/3\nD. 7/5\nE. 9/25\n\n### Answer:\nsqrt(7x/5) to be perfect square x has to 7/5\nAns: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIce-ColdIce-cream factory produces only tricolor ice-cream products, where each ice-cream has three stripes of different colors. The factory uses the colors pink, purple, orange, silver, blue and white. How many different ice-cream products have at least one stripe out of the following colors: pink, purple or orange (assume that the order of the stripes in a single ice-cream does not matter)?\n\n### Options:\nA. 12\nB. 14\nC. 18\nD. 19\nE. 20\n\n### Answer:\nIMO: D - 19\nThere are 6C3 = 20 ways to create different colored ice cream products. Out of these 20, only 1 (Silver, Blue, white) will not contain at least one of the colors pink, purple, or orange. 20 - 1 = 19.\nThe other way would be to calculate the number of ice cream products that contain at least one of the colors pink, purple, or orange (PPO).\n#1: Pick one out of PPO and two out of SBP: 3C1 * 3C2 = 3 * 3 = 9\n#2: Pick two out of PPO and one out of SBP: 3C2 * 3C1 = 3 * 3 = 9\n#3: Pick three out of PPO: 3C3 = 1\n9 + 9 + 1 = 19\nanswer is D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a is an even integer and b is an odd integer which of the following must be an odd integer :\n\n### Options:\nA. a/b\nB. ab\nC. 2a+b\nD. 2(a+b)\nE. 3a/b\n\n### Answer:\nWe can always look for low hanging fruits first to solve such questions under 30secs.\nExpression in C, is basically 2*Even+Odd or simply Even+Odd which is always going to be odd.\nHence C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain club has 10 members, including Harry. One of the 10 members is to be chosen at random to be the president, one of the remaining 9 members is to be chosen at random to be the secretary, and one of the remaining 8 members is to be chosen at random to be the treasurer. What is the probability that Harry will be the member chosen to be the secretary ?\n\n### Options:\nA. 1/720\nB. 1/80\nC. 1/10\nD. 1/9\nE. 1/5\n\n### Answer:\nThis question is much easier than it appears.\nEach member out of 10, including Harry, has equal chances to be selected for any of the positions (the sequence of the selection is given just to confuse us). The probability that Harry will be selected to be the secretary is 1/10 .\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA type of mixture is prepared by mixing brand at Rs.9 a kg with brand B at Rs.4 a kg.If a mixtue is worth rupees 7 a kg,how many kgs of brand A are needed to make 40 kgs of the mixture?\n\n### Options:\nA. 21\nB. 22\nC. 23\nD. 24\nE. 25\n\n### Answer:\n9 4\n7\n(7-4) 3 2 (9-7)\nthus ratio would be 3:2\nand thus 3x+2x=40\nso x=8 and 3x=24.\nthus A type of mixture would be of 24 kg.\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n8 men can do a piece of work in 12 days. 4 women can do it in 48 days and 10 children can do it in 24 days. In how many days can 18 men, 4 women and 10 children together complete the piece of work?\n\n### Options:\nA. 5 days\nB. 15 days\nC. 28 days\nD. 4 days\nE. 7 days\n\n### Answer:\nExplanation:\n1 man\u2019s 1 day\u2019s work = 1/8 \u00d7 12 = 1/96\n18 men\u2019s 1 day\u2019s work = 1 \u00d7 18/96 = 3/16\n1 woman\u2019s 1 day\u2019s work = 1/192\n4 women\u2019s 1 day\u2019s work = 1/192 \u00d7 4 = 1/48\n1 child\u2019s 1 day\u2019s work = 1/240\n10 children\u2019s 1 day\u2019s work = 1/24\nTherefore, (18 men + 4 women + 10 children)\u2019s 1 day\u2019s work = 3/16 + 1/48 + 1/24\n= 1/4\nThe required No. of days = 4 days\nAnswer: Option D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA mixture of 70 litres of milk and water contains 10% water. How many litres of water should be added to the mixture so that the mixture contains 12 1/2% water?\n\n### Options:\nA. 2\nB. 8\nC. 4\nD. 5\nE. None of these\n\n### Answer:\nQuantity of milk in the mixture = 90/100 (70) = 63 litres.\nAfter adding water, milk would form 87 1/2% of the mixture.\nHence, if quantity of mixture after adding x liters of water, (87 1/2) / 100 x = 63 => x = 72\nHence 72 - 70 = 2 litres of water must be added.\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhen working alone, painter W can paint a room in 2 hours, and working alone, painter X can paint the same room in e hours. When the two painters work together and independently, they can paint the room in 3/4 of an hour. What is the value of e?\n\n### Options:\nA. 3/4\nB. 1[1/5]\nC. 1[2/5]\nD. 1[3/4]\nE. 2\n\n### Answer:\nRate*Time=Work\nLet Painter W's rate be W and Painter X's rate be X\nR*T = Work\nW * 2 = 1 (If the work done is same throughout the question then the work done can be taken as 1) => W = 1/2\nX * e = 1 => X = 1/e\nWhen they both work together then their rates get added up\nCombined Rate = (W+X)\nR*T = Work\n(W+X) * 3/4 = 1\n=> W+X = 4/3\n=> 1/2 + 1/e = 4/3\n=> 1/e = (8-3)/6 = 5/6\n=> e = 6/5 = 1[1/5]\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf n is the greatest positive integer for which 2^n is a factor of 6!, then n =?\n\n### Options:\nA. 2\nB. 4\nC. 6\nD. 8\nE. 10\n\n### Answer:\n6! = 720\nE. 2^10 = 512 (720/512) - this is not a factor of 6!\nD. 2^8 = 256 (720/256) - this is not a factor of 6!\nC. 2^6 = 64 (720/64) - this is not a factor of 6!\nB. 2^4 = 16 (720/16) - this is a factor of 6!\nB is answer\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a certain city, 40% of the registered voters are democrats and the rest are republicans.In a mayoral race, if 75% of the registered voters who are democrats and 20% of the registered voters who are republicans are expected to vote for candidate A,What % of the registered voters are expected to vote for candidate A?\n\n### Options:\nA. a) 50%\nB. b) 53%\nC. c) 54%\nD. d) 55%\nE. e) 57%\n\n### Answer:\nLet total voters = 100\nso D= 60, vote for the mayor 60*75%=45 (60*3/4)\nR= 40, vote for the mayor 40*20%= (40*1/5)\n45+8=53\n53/100*100=55%\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nEvaluate combination\n16C2\n\n### Options:\nA. 120\nB. 1000\nC. 10\nD. 1\nE. 0\n\n### Answer:\nExplanation:\nnCn=1\nnCr=n!/r!(n-r)!\n16C2=16!/2!(16-2)!=120\nOption A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA scuba diver descends at a rate of 30 feet per minute. a diver dive from a ship to search for a lost ship at the depth of 2400feet below the sea level..how long will he take to reach the ship?\n\n### Options:\nA. 70 minutes\nB. 72 minutes\nC. 80 minutes\nD. 76 minutes\nE. 77 minutes\n\n### Answer:\nTime taken to reach = 2400/30= 80 minutes\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nDany bought a total of 26 game cards some of which cost $0.25 each and some of which cost $0.15 each. If Dany spent $4.2 to buy these cards, how many cards of each type did he buy?\n\n### Options:\nA. 4\nB. 10\nC. 7\nD. 23\nE. 12\n\n### Answer:\nLet X be the number of cards that cost $0.25 each and Y the number of cards that cost $0.15 each. The total number of cards is 26. Hence\nX + Y = 26\nIf X is the number of cards at $0.25, then the X cards cost\n0.25 X\nIf Y is the number of cards at $0.15, then the Y cards cost\n0.15 Y\nThe total cost of the X cards and the the Y cards is known to be $4.2 and also given by\n0.25 X + 0.15 Y = 4.2\nWe now need to solve the system of equations\nX + Y = 26\n0.25 X + 0.15 Y = 4.2\nThe first equation gives Y = 26 - X. Substitute y by 26 - x in the second equation and solve\n0.25 X + 0.15 (26 - X) = 4.2\nX(0.25 - 0.15) + 3.9 = 4.2\n0.1 X = 0.3\nX = 3 and Y = 26 - 3 = 23\ncorrect answer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nVijay sells a cupboard at 10% below cost price. Had he got Rs.1500 more, he would have made a profit of 10%. What is the cost price of the cupboard?\n\n### Options:\nA. 7450\nB. 7500\nC. 7400\nD. 7500\nE. None of these\n\n### Answer:\nExplanation:\nCost price = 1500/(0.10 + 0.10) = 1500/0.20\n= Rs.7500\nANSWER B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf (t-8) is a factor of t^2-kt-46, then k=\n\n### Options:\nA. 16\nB. 12\nC. 2\nD. 6\nE. 14\n\n### Answer:\nt^2-kt-48 = (t-8)(t+m) where m is any positive integer.\nif 48/8 = 6, then we know as a matter of fact that:\nm = +6\nand thus k = 8-6 = 14\nt^2-kt-m = (t-a)(t+m) where a>m\nt^2+kt-m = (t-a)(t+m) where a", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSound is said to travel in air at about 1100 feet per second. A man hears the axe striking the tree, 11/5 seconds after he sees it strike the tree. How far is the man from the wood chopper ?\n\n### Options:\nA. 2420 ft\nB. 2524 ft\nC. 2600 ft\nD. 2740 ft\nE. None of these\n\n### Answer:\nExplanation :\nDistance = [1100 * 11/5] feet\n= 2420 feet.\nAnswer : A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe market value of a 10.5% stock, in which an income of Rs. 756 is derived by investing Rs. 7000, brokerage being 1/4%, is:\n\n### Options:\nA. 96.97\nB. 114\nC. 114.75\nD. 124\nE. 124.75\n\n### Answer:\nFace Value = Rs. 7000.\nDividend = 10.5%.\nAnnual Income = Rs. 756.\nBrokerage per Rs. 100 = Rs. 0.25.\nDividend is always paid on the face value of a share.\nFace Value * Dividend / (Market Value + Brokerage per Rs. 100) = Annual income.\n= 7000 * 10.5 / 756 = Market Value of Rs. 100 stock + Brokerage per Rs. 100.\n= Market Value of Rs. 100 stock + Brokerage per Rs. 100 = Rs. 97.22.\n= Market Value of Rs. 100 stock = Rs. 97.22 - Re. 0.25.\n= Market Value of Rs. 100 stock = Rs. 96.97\nanswer : A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA can do a piece of work in 10 days. He works at it for 4 days and then B finishes it in 9 days. In how many days can A and B together finish the work?\n\n### Options:\nA. 6\nB. 8\nC. 12\nD. 15\nE. 20\n\n### Answer:\n4/10+9/X = 1/x = 15\n1/10+1/15 = 1/6 = 6 days\nANSWER A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a party attended by 10 persons, each clinch their glass with every other. How many glass clinches?\n\n### Options:\nA. 45\nB. 52\nC. 53\nD. 54\nE. 55\n\n### Answer:\nTotal no. of person = 11\nTotal no. of glass clinches = n(n-1)/2\n=10*9/2\n= 45\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf A speaks the truth 40% of the times, B speaks the truth 20% of the times. What is the probability that at least one will tell the truth\n\n### Options:\nA. 1.8\nB. 2.0\nC. 1.52\nD. 0.52\nE. 1.3\n\n### Answer:\nprobability of A speaks truth p(A)=4/10;false=6/10\nprobability of B speaks truth p(B)=2/10;false=8/10.For given qtn\nAns=1-(neither of them tell truth).Because A & B are independent events\n=1-[(6/10)*(8/10)]=1-48/100=1-0.48=0.52\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n40 is subtracted from 70% of a number, the result is 30. Find the number?\n\n### Options:\nA. 150\nB. 997\nC. 266\nD. 288\nE. 100\n\n### Answer:\n(70/100) * X \u2013 40 = 30\n7X = 700\nX = 100\nAnswer:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHowmany words (with or without meaning) of three distinct letters of the English alphabets are there?\n\n### Options:\nA. 15500\nB. 15800\nC. 15700\nD. 15400\nE. 15600\n\n### Answer:\nHere we have to fill up three places by distinct letters of the English alphabets. This can be done in 26 ways. The second place can be filled in by 25 ways. The third place can be filled in 24 ways. Hence the required number of words is 26x25x24=15600. Ans : E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA can give B 200 meters start and C 400 meters start in a kilometer race. How much start can B give C in a kilometer race?\n\n### Options:\nA. 111.12\nB. 250\nC. 111.64\nD. 111.11\nE. 101.12\n\n### Answer:\nA runs 1000 m while B runs 800 m and C runs 600 m.\nThe number of meters that C runs when B runs 1000 m,\n= (1000 * 600)/800 = 750 m.\nB can give C = 1000 - 750= 250 m.\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average of four positive integers is 69. The highest integer is 93 and the least integer is 39. The difference between the remaining two integers is 28. Which of the following integers is the higher of the remaining two integers?\n\n### Options:\nA. 32\nB. 86\nC. 44\nD. 22\nE. 55\n\n### Answer:\nLet the four integers be A, B, C and D where A > B > C > D.\n(A + B + C + D)/4 = 69 => A + B + C + D = 276 ---> (1)\nA = 93, D = 39 and B - C = 28\n(1) => B + C = 276 - (A + D) = 276 - 132 = 144.\nB + B -28 = 144\nB = (144 + 28)/2 = 86\nAnswer:Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many 3 digit numbers can be formed which are divisible by 3 using the numerals 0, 1, 2, 3, 4, 5 (WITH REPETITION)\n\n### Options:\nA. 216\nB. 133\nC. 240\nD. 600\nE. 305\n\n### Answer:\nDivisibilty rule for 3: Sum of all digits is a multiple of 3\nSelections for the above to be valid\n1,2,3,4,5\nNo of possible ways = 5*5*5 = 125\n0,1,2\nNo of possible ways = 2*2*1 = 4\n0,4,5\nNo of possible ways = 2*2*1 = 4\nTotal = 8+125 = 133\nOption\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train 200m long passes a standing man in 10 seconds. What is the speed of the train?\n\n### Options:\nA. 30km/hr\nB. 36km/hr\nC. 42km/hr\nD. 50km/hr\nE. 72km/hr\n\n### Answer:\nSpeed of the train = 200/10* 18/5 = 72km/hr\nAnswer is E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA patient was given a bottle of tablets by the doctor and he was asked to take five tablets in a gap of 15 minutes.\nIn how much time will he be able to take all the five tablets?\n\n### Options:\nA. 1 Hour.\nB. 2 Hour.\nC. 3 Hour.\nD. None\nE. Cannot be determined\n\n### Answer:\nSolution:\n1 Hour.\nSuppose he takes the first tablet at 12:00 pm. Then the second will be consumed by him at 12:15, third at 12:30, fourth at 12:45 and fifth at 1:00.\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSteve gets on the elevator at the 11th floor of a building and rides up at a rate of 57 floors per minute. At the same time Joyce gets on an elevator on the 51st floor of the same building and rides down at a rate of 63 floors per minute. If they continue traveling at these rates, at which floor will their paths cross?\n\n### Options:\nA. 19\nB. 28\nC. 30\nD. 32\nE. 44\n\n### Answer:\nUsing Speed Formula: Speed = Distance / Time\nDistance to be covered = 51-11 = 40\nSpeed of approach = 57 + 63 floors/min\nTime = 40/120 = 1/3\nSo Steve will cover 57x 1/3 floors in that time = 19\nSo he will be in 19 + 11 floor = 30th Floor\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA policeman spotted a criminal from a distance of 200 metres. When the policeman starts the chase, the criminal also starts running. If the criminal was running at 10 km/hr and the policeman was chasing at the speed of 12 km/hr, find the distance the criminal will run before he is catched by the policeman ?\n\n### Options:\nA. 1.5 km\nB. 700 m\nC. 900 m\nD. 1 km\nE. None of these\n\n### Answer:\nExplanation :\nSolution: Relative speed = (12 - 10) = 2 km/hr.\nTime taken by policeman to cover 200 m = (200/1000 * 1/2) hr\n= 1/10 hr.\nIn 1/10 hrs, the criminal covers a distance of (10*1/10) km = 1 km.\nAnswer : D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a group of cows and hens, the number of legs are 16 more than twice the number of heads. The number of cows is\n\n### Options:\nA. 5\nB. 8\nC. 10\nD. 12\nE. 14\n\n### Answer:\nExplanation:\nLet the number of cows be x and the number of hens be y.\nThen, 4x + 2y = 2 (x + y) + 16\n4x + 2y = 2x + 2y + 16\n2x = 16\nx = 8.\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe ratio of two natural numbers is 5:6. If a certain number is added to both the numbers, the ratio becomes 7:8. If the larger number exceeds the smaller number by 10, find the number added?\n\n### Options:\nA. 17\nB. 12\nC. 20\nD. 27\nE. 18\n\n### Answer:\nLet the two numbers be 5x and 6x.\nLet the number added to both so that their ratio becomes 7:8 be k.\n(5x + k)/(6x + k) = 7/8\n42x = 7k => k = 2x.\n6x - 5x = 10 => x = 10\nk = 2x = 20.\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA basket has 5 apples and 4 oranges. Three fruits are picked at random. The probability that at least 2 apples are picked is\n\n### Options:\nA. 25/42\nB. 25/40\nC. 25/49\nD. 25/47\nE. 25/44\n\n### Answer:\nExplanation:\nTotal fruits = 9\nSince there must be at least two apples,\n= 25/42.\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA family has two children. find the probability that both the children are girls given that at least\none of them is a girl?\n\n### Options:\nA. 1/2\nB. 1/3\nC. 1/7\nD. 2/5\nE. 2/7\n\n### Answer:\nLet b stand for boy and g for girl. The sample space of the experiment is\nS = {(g, g), (g, b), (b, g), (b, b)}\nLet E and F denote the following events :\nE : \u2018both the children are girls\u2019\nF : \u2018at least one of the child is a girl\u2019\nThen E = {(g,g)} and F = {(g,g), (g,b), (b,g)}\nNow E n F = {(g,g)}\nThus P(F) = 3/4\nand P (E n F )= 1/4\nTherefore P(E|F) = P(E \u2229 F)/P(F) = (1/4)/(3/4) = 1/3\nB)\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf neha is 10\nBoth Sonali and priyanka is 15\nBoth sadaf and tanu is 10.\nhow much is prinka by the same system ?\n\n### Options:\nA. 8\nB. 9\nC. 10\nD. 11\nE. 12\n\n### Answer:\nSolution:\nprinka is 10, in a system that awards five for each vowel.\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average of six numbers is 3.95. The average of two of them is 3.4, while the average of the other two is 3.85. What is the average of the remaining two numbers?\n\n### Options:\nA. 4.5\nB. 4.6\nC. 4.7\nD. 4.8\nE. 4.9\n\n### Answer:\nSum of the remaining two numbers\n= (3.95 \u00d7 6) \u2013 [(3.4 \u00d7 2) + (3.85 \u00d7 2)]\n= 23.70 \u2013 (6.8 + 7.7)\n= 23.70 \u2013 14.5 = 9.20\n\u2234 Required average = (9.2\u20442) = 4.6\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRavi purchased a refrigerator and a mobile phone for Rs. 10000 and Rs. 8000 respectively. He sold the refrigerator at a loss of 4 percent and the mobile phone at a profit of 10 percent. Overall he make a.\n\n### Options:\nA. loss of Rs. 200\nB. loss of Rs. 100\nC. profit of Rs. 100\nD. profit of Rs. 400\nE. None of these\n\n### Answer:\nTotal C.P. = 10000+8000 = 18000\nS.P. of fridge = 10000/100*96= 9600\nS.P. of Mobile = 8000/100*110 = 8800\nTotal S.P. = 9600 + 8800 = 18400\nTota. S.P. - Total C.P. = 18400 - 18000 = 400\nAnswer : D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe output of a factory was increased by 15% to keep up with rising demand. To handle the holiday rush, this new output was increased by 20%. By approximately what percent would the output now have to be decreased in order to restore the original output?\n\n### Options:\nA. 20%\nB. 27%\nC. 30%\nD. 32%\nE. 79%\n\n### Answer:\nThe original output increases by 15% and then 20%.\nTotal % change = a + b + ab/100\nTotal % change = 15 + 20 + 15*20/100 = 38%\nNow, you want to change it to 0, so,\n0 = 38 + x + 38x/100\nx = -38(100)/138 = 27% approximately\nAnswer is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSoniya deposited Rs.8000 which amounted to Rs.9200 after 3 years at simple interest. Had the interest been 2% more. She would get how much?\n\n### Options:\nA. 9680\nB. 9850\nC. 9745\nD. 9623\nE. 9324\n\n### Answer:\n(8000*3*2)/100 = 480\n9200\n--------\n9680\nANSWER A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA seven-digit phone number is divisible by 8. After adding the two digits of the area code the number is not divisible by 8, which of the following cannot be the area code?\n\n### Options:\nA. 07.\nB. 05.\nC. 08.\nD. 04.\nE. 02.\n\n### Answer:\nGiven that 7 digit number is divisible by 8\nwe know any number will not be divisible by 8 if the sum of all digits of the number is not the multiple of 8.\nHence looking at the option we can say that the number that should be added to the seven digit number must be 08 as adding it will make it divisible by 8... hence answer is C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA group of n students can be divided into equal groups of 4 with 2 student left over or equal groups of 5 with 2 students left over. What is the sum of the two smallest possible values of n?\n\n### Options:\nA. 33\nB. 46\nC. 49\nD. 64\nE. 86\n\n### Answer:\n4x+2 = 5y+2...........ie: 4x-5y = 0\nx,y must be >1 and y is even ie ( 2,4,6,..etc)\nif y = 2 thus x is fraction\nif y = 4 thus x =5 n =22\nif y = 6 thus x = not possible fraction\nif y =8 thus x = 10 n =42\nn= 22+42= 64\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf we have 10 people in a meeting, in how many ways they can sit around a table?\n\n### Options:\nA. 10*9!\nB. 9*8!\nC. 8*7!\nD. 7*6!\nE. 6*5!\n\n### Answer:\nIf there arenpeople sitting around a table, there are(n-1)!possible arrangements:\nHere, n=10\n(n-1)!=9!=9*8!\nAns:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAt a small company, 58 percent of the employees are women, and 60 percent of the employees are married. If 2/3 of the men are single, what fraction of the women are married?\n\n### Options:\nA. 5/16\nB. 1/3\nC. 9/20\nD. 7/10\nE. 41/58\n\n### Answer:\nLets take total employees are 100.\nGiven that,Total Women= 58 and Total Married = 60.\nTotal Men = 100 - 58 = 42 and Single men = 2/3*42 = 28.\nMarried men = total men - single men = 47 - 28 = 19.\nMarried women= Total married - Married men = 60 - 19 = 41.\nFraction of women are married = Married women / Total Women = 41 / 58 = 5/7. ANS E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n5358 x 51 = ?\n\n### Options:\nA. 273255\nB. 273257\nC. 273258\nD. 273260\nE. 273262\n\n### Answer:\n5358 x 51\t= 5358 x (50 + 1)\n= 5358 x 50 + 5358 x 1\n= 267900 + 5358\n= 273258.\nC)\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe prices of tea and coffee per kg were the same in june. In july the price of coffee shot up by 20% and that of tea dropped by 10%. if in july , a mixture containing equal quantities of tea and coffee costs 50/kg. how much did a kg of coffee cost in june ?\n\n### Options:\nA. 45\nB. 40\nC. 35\nD. 47.61\nE. 30\n\n### Answer:\nLet the price of tea and coffee be x per kg in June.\nPrice of tea in July = 1.2x\nPrice of coffee in July = 0.9x .\nIn July the price of 1/2 kg (500gm) of tea and 1/2 kg (500gm) of coffee (equal quantities) = 50\n1.2x(1/2) + 0.9x(1/2) = 50\n=> x =47.61\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSarah's seafood restaurant gets a delivery of fresh seafood every day, 5 days per week, and her delivery company charges herddollars per delivery plusccents per item delivered. If lst week Sarah's seafood restaurant had an average ofxitems per day delivered, then which of the following is the total cost, in dollars, of last week's deliveries ?\n\n### Options:\nA. 5cdx/100\nB. d + 5cx/100\nC. 5d + xc/100\nD. 5d + 5xc/100\nE. 5cdx\n\n### Answer:\nAnswer is D. Straight forward question.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA and B together can do a piece of work in 8 days. If A alone can do the same work in 12 days, then B alone can do the same work in?\n\n### Options:\nA. 65\nB. 77\nC. 24\nD. 71\nE. 27\n\n### Answer:\nExplanation:\nB = 1/8 \u00e2\u20ac\u201c 1/2 = 1/24 => 24 days\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWINK,INC recently conducted a survey and found that 180,000 of its customers live in rural areas. if the number of it customers who live in urban areas is 200 percents grater than the numbers of customers who live in rural areas, how many of WINK,INC customers live in urban areas ?\n\n### Options:\nA. 200,000\nB. 216,000\nC. 360,000\nD. 480,000\nE. 540.0\n\n### Answer:\nLet's say that we have a starting value of X...\n100% of X = X\n100% MORE than X = X + X = 2X\n200% MORE than X = X + 2X = 3X\n300% MORE than X = X + 3X = 4X\nEtc.\nHere, we're told that 180,000 customers live in rural areas and the number who live in urban areas is 200% GREATER than the number who live in rural areas. That means that the number who are in urban areas is 3 times the number in rural areas...\n3(180,000) = 540,000\nFinal Answer:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo diesel trains of length 120 m and 280 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively. In what time will they be clear of each other from the moment they meet?\n\n### Options:\nA. 10 sec\nB. 30 sec\nC. 40 sec\nD. 20 s\nE. 50 sec\n\n### Answer:\nD\nRelative speed = (42 + 30) * 5/18 = 4 * 5 = 20 mps.\nDistance covered in passing each other = 120 + 280 = 400 m.\nThe time required = d/s = 400/20 = 20 sec.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow much time will take for an amount of Rs. 360 to yield Rs. 81 as interest at 4.5% per annum of simple interest?\n\n### Options:\nA. 5 years\nB. 6 years\nC. 7 years\nD. 12 years\nE. 15 years\n\n### Answer:\nTime = (100 * 81) / (360 * 4.5) = 5 years\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich of the following CANNOT be a value of 4/(x\u20134)?\n\n### Options:\nA. -1\nB. -1/2\nC. 0\nD. 2\nE. 6\n\n### Answer:\nThe question doesn't ask for the value of x here, but for the possible results of the equation.\nIf 4/(x-4) = 0, then the numerator must be 0. But since the numerator is 4, the fraction can not be equal to 0.\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nO(x) represents the least odd integer greater than x, whereas o(x) represents the greatest odd integer less than x. Likewise, E(x) represents the least even integer greater than x, whereas e(x) represents the greatest even integer less than x. According to these definitions, the value of O(3.2) + E(\u20131.7) + o(\u20133.3) + e(4.7) is:\n\n### Options:\nA. 3\nB. 4\nC. 5\nD. 6\nE. 7\n\n### Answer:\nO(3.2) + E(\u20131.7) + o(\u20133.3) + e(4.7) = 5 + 0 + (-5) + 4 = 4\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA watch was sold at a loss of 46%. If it was sold for Rs.140 more, there would have been a gain of 4%. What is the cost price?\n\n### Options:\nA. 280\nB. 288\nC. 279\nD. 277\nE. 290\n\n### Answer:\n54%\n104%\n--------\n50% ---- 140\n100% ---- ? => Rs.280\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf Josh, Doug, and Brad have a total of $80 between them, and Josh has five times as much money as Brad but only half as much as Doug, how much money does Doug have?\n\n### Options:\nA. $8\nB. $9\nC. $27\nD. $32\nE. $50\n\n### Answer:\nJosh+Doug+Brad = 72 ; Josh = 5 Brad, Josh =1/2 Doug\nJosh+1/5 Josh+ 2/1 Josh = 80 (substituted the given values)\nJosh = 25. 25= 1/2 Doug => Doug =50\nAnswer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAdam borrowed some money at the rate of 6% p.a. for the first two years, at the rate of 9% p.a. for the next three years, and at the rate of 14% p.a. for the period beyond four years. If he pays a total interest of 11,900 at the end of nine years, how much money did he borrow?\n\n### Options:\nA. 10,526\nB. 12,526\nC. 14,000\nD. 16,000\nE. 16,536\n\n### Answer:\nLet the sum borrowed be x. Then,\n(x\u00d76\u00d721/00)+(x\u00d79\u00d73/100)+(x\u00d714\u00d74/100)= 11900\n\u21d2 (3\u204425x + 27\u2044100x + 14\u204425x) = 11400 \u21d2 95\u2044100x = 11900\n\u21d2 x = (11900\u00d7100/95)= 12526\nHence, sum borrowed = 12,526\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n3889 + 12.998 - ? = 3854.002\n\n### Options:\nA. A)47.996\nB. B)47.752\nC. C)47.932\nD. D)47.95\nE. of the above\n\n### Answer:\nLet 3889 + 12.998 - x = 3854.002.\nThen x = (3889 + 12.998) - 3854.002\n= 3901.998 - 3854.002\n= 47.996.\nAnswer = A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe Hobo Music Orchestra is comprised of, 3/5 wind instrument musicians, 1/4 string instrument musicians, and the rest are percussion instrument musicians. If half of the string instrument musicians are violinists, and the conductor doubles the number of violinists, what proportion of the orchestra are now wind instrument musicians?\n\n### Options:\nA. 9/10\nB. 6/11\nC. 7/15\nD. 1/2\nE. 6/7\n\n### Answer:\nWind = 3/5 = 12/20\nString = 1/4 = 4/20\nPercussion = 1 - (12/20 + 4/20) = 1 - 16/20 = 4/20\nViolinists = (1/2)(4/20) = 2/20\nIf Violinists doubled => (2)(2) = 4; then, total = 12 + 6 + 4 = 22,\nand 12 are Wind => proportion = 12/22 = 6/11.\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAt what rate percent on simple interest will Rs.750 amount to Rs.900 in 5 years?\n\n### Options:\nA. 5%\nB. 3 1/2%\nC. 4%\nD. 5 1/2 %\nE. 6 1/2 %\n\n### Answer:\nExplanation:\n150 = (750*5*R)/100\nR = 4%\nANSWER IS C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many 3-digit numbers are completely divisible 6 ?\n\n### Options:\nA. 149\nB. 150\nC. 151\nD. 166\nE. 172\n\n### Answer:\nExplanation:\n3-digit number divisible by 6 are: 102, 108, 114,... , 996\nThis is an A.P. in which a = 102, d = 6 and l = 996\nLet the number of terms be n. Then tn = 996.\na + (n - 1)d = 996\n102 + (n - 1) x 6 = 996\n6 x (n - 1) = 894\n(n - 1) = 149\nn = 150\nNumber of terms = 150.\nANSWER IS B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA pipe X is 30 meters and 45% longer than another pipe Y. find the length of the pipe Y.\n\n### Options:\nA. 20.12\nB. 20.68\nC. 20\nD. 20.5\nE. None of these\n\n### Answer:\nExplanation :\nLength of pipe X = 30 meter\nGiven that pipe X is 45% longer than Y\nLet the length of pipe Y = y\nThen, Length of pipe X =y\u00d7(100+45)/100\n\u21d2 30 = y \u00d7 (145/100) => y = 30\u00d7100/145=6\u00d7100/29=600/29=20.68\nAnswer : Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe purchase price of an article is $48. In order to include 30% of cost for overhead and to provide $12 of net profit, the markup should be\n\n### Options:\nA. 15%\nB. 25%\nC. 35%\nD. 40%\nE. 55%\n\n### Answer:\nCost price of article = 48$\n% of overhead cost = 30\nNet profit = 12 $\nWe need to calculate % markup\nNet profit as % of cost price = (12/48)*100 = 25%\nTotal markup should be = 25 + 30 = 55%\nAnswer E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the smallest number which when increased by 7 is divisible by 25, 49, 15, and 21?\n\n### Options:\nA. 3,551\nB. 3,668\nC. 3,733\nD. 3,822\nE. 3,957\n\n### Answer:\nFirst factor each of 25, 49, 15, and 21 into primes:\n25=5*5; 49=7*7; 15=3*5; 21=3*7\nthe smallest number divisible by each of the numbers is 3*5*5*7*7 = 3,675\n3,675-7 = 3,668 thus 3,668 + 7 is the smallest number divisible by 25, 49, 15, and 21\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe cost of 2 chairs and 3 tables is Rs.1500. The cost of 3 chairs and 2 tables is Rs.1200. The cost of each table is more than that of each chair by?\n\n### Options:\nA. 228\nB. 287\nC. 277\nD. 188\nE. 300\n\n### Answer:\nExplanation:\n2C + 3T = 1500 --- (1)\n3C + 2T = 1200 --- (2)\nSubtracting 2nd from 1st, we get\n-C + T = 300 => T - C = 300\nAnswer:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA bus leaves Burbank at 9:00 a.m. traveling east at 50 miles per hour. At 1:00 p.m. a plane leaves Burbank traveling east at 300 miles per hour. At what time will the plane overtake the bus?\n\n### Options:\nA. 12:45 p.m.\nB. 1:10 p.m\nC. 1:40 p.m\nD. 1:48 p.m\nE. 1:55 p.m\n\n### Answer:\ndistance = speed * time\nfrom 9:00 am to 1:00 pm total is 4 hrs\nIn 4 hrs bus travels a distance of 50 * 4 = 200 miles\nplane starts travelling in same direction so relative speed = 300 - 50 = 250 miles/hr\ndistance the plane needs to cover so as to overtake the bus is 200 miles\ntime = 200 /250 = 4/5 hrs = 48 minutes\nso at 1:48 pm the plane overtakes the bus\nCorrect answer - D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a garden, there are 10 rows and 12 columns of mango trees. The distance between the two trees is 2 metres and a distance of four metre is left from all sides of the boundary of the garden. What is the length of the garden?\n\n### Options:\nA. 22\nB. 24\nC. 26\nD. 28\nE. 30\n\n### Answer:\nBetween the 12 mango trees, there are 11 gaps and each gap has 2 meter length\nAlso, 4 meter is left from all sides of the boundary of the garden.\nHence, length of the garden = (11 \u00c3\u2014 2) + 4 + 4 = 30 meter\nAnswer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFive persons are to be selected from a group of 7 males and 6 females to form party so that at least 3 male members are there on the committee. What are the possible number of ways to form the party ?\n\n### Options:\nA. 756\nB. 765\nC. 785\nD. 789\nE. None\n\n### Answer:\nFrom a group of 7 men and 6 women, five persons are to be selected with at least 3 men. So we can have (5 men) or (4 men and 1 woman) or (3 men and 2 woman) (7C5)+(7C4 * 6C1)+(7C3** 6C2)=[21+35*6+35*15]=756\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nGiven that 100.48 = x, 100.70 = y and xz = y\u00b2, then the value of z is close to\n\n### Options:\nA. 1.2\nB. 1.45\nC. 2.2\nD. 2.9\nE. NOne\n\n### Answer:\nSol.\nxz = y\u00b2 \u21d4 (10 0.48 )z(100.70)2 (10 0.48z) = 10(2\u00d70.70) = 101.40\n\u21d4 0.48z = 1.40 \u21d4 z= 140/48 = 35/12 = 2.9 (approx).\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average of ten numbers is 7. If each number is multiplied by 10, then what is the average of the new set of numbers?\n\n### Options:\nA. 7\nB. 17\nC. 70\nD. 100\nE. 107\n\n### Answer:\nThe sum of the ten numbers is 7*10 = 70\nIf each number is multiplied by 10, the new sum is 10*(70).\nThe average is then 10*7 = 70\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a and b are integers and (2^a)(3^b) is a factor of 900^40, what is the largest possible value of ab?\n\n### Options:\nA. 2a\nB. 5a\nC. 20a\nD. 40a\nE. 80a\n\n### Answer:\n(2^a)(3^b) is a factor of 900^40\nWe need to find the largest possible value of ab.\nWe know that 900 = 2^2*5^2*3^2\nTherefore 900^40 will have 2 powers of 3 in it.\nHence in (2^a)(3^b), b has to 2\nTherefore value of ab = 2a\nCorrect Option: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA 5-year investment note offers a 10% return on purchase, and a compounding 5% for each year after the first. If there is a $500 penalty for early redemption, and the note is redeemed for $6430 after the second year, what was the original purchase price?\n\n### Options:\nA. $ 6,000\nB. $ 6,048\nC. $ 6,100\nD. $ 6,150\nE. $ 6,200\n\n### Answer:\nSince the note was redeemed after 2 years, so a penalty of $500 has to be submitted. So the amount that is redeemed after 6430 is after the deduction of $500.\nHence the amount after being compounded is 6930.\nLet the initial amount be P.\nAfter the return, the amount becomes 1.1P.\nNow use this 1.1P as the principle in the compound interest formula to get the amount 6930.\nA=1.1P(1+5/100)A=1.1P(1+5/100)\nwhere A=6930.\nTherefore, use\n6930=1.1P(1+5/100)6930=1.1P(1+5/100) to get P as $6000.\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA company recently conducted a survey and found that 25,000 of its customers live in rural areas. If the number of customers who live in urban areas is 120 percent greater than the number of customers who live in rural areas, how many customers live in urban areas?\n\n### Options:\nA. 50,000\nB. 55,000\nC. 60,000\nD. 65,000\nE. 70,000\n\n### Answer:\nThe number of customers in urban areas is 25,000+1.2*25,000=55,000.\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train 120 m long passed a pole in 6 sec. How long will it take to pass a platform 360 m long?\n\n### Options:\nA. 20 sec\nB. 21\nC. 22\nD. 23\nE. 24\n\n### Answer:\nSpeed = 120/6\n= 20 m/sec.\nRequired time\n= (120 + 360)/20\n= 24 sec.\nAnswer:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe smallest number when increased by \" 1 \" is exactly divisible by 2, 8, 24, 36 is:\n\n### Options:\nA. 71\nB. 70\nC. 72\nD. 73\nE. 36\n\n### Answer:\nLCM = 72\n72 - 1 = 71\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe subsets of the set {w, x, y} are {w}, {x}, {y}, {w, x}, {w, y}, {x,y}, {w, x, y}, and { } (the empty subset).\nHow many subsets of the set {w, x, y, z} contain w?\n\n### Options:\nA. Four\nB. Five\nC. Seven\nD. Eight\nE. Sixteen\n\n### Answer:\nThe number of ways of selecting 0 or more from n elements is 2^n.\nHence here, once you select w , the number of ways of selecting 0 or more from x,y and z ( 3 elements) is 2^3 = 8.\nThe same applies for {w, x, y}. If you select w here, the number of ways of selecting 0 or more from x and y = 2^2 = 4\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA bowl contains equal numbers of red, orange, green, blue, and yellow candies. Kaz eats all of the green candies and half of the orange ones. Next, he eats half of the remaining pieces of each color. Finally, he eats red and yellow candies in equal proportions until the total number of remaining candies of all colors equals 20% of the original number. What percent of the red candies remain?\n\n### Options:\nA. 5%\nB. 7.5%\nC. 10%\nD. 12.5%\nE. 15%\n\n### Answer:\nLet x be the original number of each color.\nKaz eats all of the green candies and half of the orange ones.\nThere are 0 green candies and 0.5x orange candies remaining.\nHe eats half of the remaining pieces of each color.\nThere are 0.25x orange candies, and 0.5x each of red, yellow, and blue candies.\nHe eats red and yellow candies in equal proportions.\norange+blue+red+yellow = 0.75x + red + yellow = x\nred + yellow = 0.25x\nred = 0.125x, since red = yellow.\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n9 people decided to split the restaurant bill evenly. If the bill was $314.16 dollars, how much money did they 1 cent is the smallest unit?\n\n### Options:\nA. $314.16\nB. $314.17\nC. $314.18\nD. $314.19\nE. $314.20\n\n### Answer:\nThis is equivalent to finding the first number that is divisible by 9 that occurs after 31416.\nIn order to divide the sum in 9 parts, the amount must be divisible by 9\nDivisibility rule of 9: The sum of the digits must be divisible by 9\nSum of digits of 31416 = 15 and 18 is divisible by 9.\nHence, we need to add 3 to this number for it to be divisible by 9\nCorrect Option: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA batsman in his 17th innings makes a score of 85 and their by increasing his average by 3. What is his average after the 17thinnings?\n\n### Options:\nA. 11\nB. 7\nC. 76\nD. 37\nE. 9\n\n### Answer:\n16x + 85 = 17(x + 3)\nx = 34 + 3 = 37\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe volume of a rectangular swimming pool is 840 cubic meters and water is flowing into the swimming pool. If the surface level of the water is rising at the rate of 0.5 meters per minute, what is the rate R, in cubic meters per minutes, at which the water is flowing into the swimming pool?\n\n### Options:\nA. 0.125\nB. 0.25\nC. 0.5\nD. 0.75\nE. Not enough information to determine the rate\n\n### Answer:\nThe correct answer is E.\nThere are not enough info to answer the question.\nA 840 cubic meters rectangle is built from: height*length*width.\nFrom the question we know the volume of the pool and the filling rate.\nA pool can have a height of 10*width8.4*length10 and have a volume of 840 cubic meters, and it can have a height of 1 meter, width of 100 meters and length of 8.4. In both cases the pool will fill up in a different rate = E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA shopkeeper buys mangoes at the rate of 4 a rupee and sells them at 3.5 a rupee. Find his net profit or loss percent?\n\n### Options:\nA. 13.2 %\nB. 15.2 %\nC. 14.28 %\nD. 32 1/3 %\nE. 33 1/2 %\n\n### Answer:\nThe total number of mangoes bought by the shopkeeper be 12.\nIf he buys 4 a rupee, his CP = 3.5\nHe selling at 3.5 a rupee, his SP = 4\nProfit = SP - CP = 4 - 3.5 = 0.5\nProfit Percent = 0.5/3.5 * 100 = 14.28 %\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo number are in the ratio 3 : 5. If 9 is subtracted from each, the new numbers are in the ratio 12 : 23. The smaller number is:\n\n### Options:\nA. 22\nB. 11\nC. 44\nD. 33\nE. 55\n\n### Answer:\nLet the numbers be 3x and 5x.\nThen, 3x - 9/5x - 9 = 12/23\n= 23(3x - 9)\n= 12(5x - 9)\n= 9x = 99\nx = 11.\nTherefore, The smaller number = (3 x 11) = 33.\nAnswer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA and B undertake to do a piece of work for Rs. 600. A alone can do it in 6 days while B alone can do it in 8 days. With the help of C, they finish it in 3 days. Find the share of A\n\n### Options:\nA. 300\nB. 450\nC. 750\nD. 800\nE. None of them\n\n### Answer:\nC's 1 day's work = 1/3-(1/6+1/8)=24\nA : B : C = Ratio of their 1 day's work = 1/6:1/8:1/24= 4 : 3 : 1.\nA\u2019s share = Rs. (600 *4/8) = Rs.300, B's share = Rs. (600 *3/8) = Rs. 225.\nC's share = Rs. [600 - (300 + 225\u00bb) = Rs. 75.\nAnswer is A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 3 people can do 3 times of a particular work in 3 days, then how many days would it take 9 people to do 9 times of that particular work?\n\n### Options:\nA. 1\nB. 2\nC. 3\nD. 9\nE. 12\n\n### Answer:\n3 people can do the work one time in one day.\n1 person can do 1/3 of the work in one day.\n9 people can do 9/3 of the work in one day.\n9 people can do 9 times the work in 3 days.\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA number consists of two digits. The sum of the digits is 9. If 63 is subtracted from the number, its digits are interchanged. Find the number.\n\n### Options:\nA. 81\nB. 90\nC. 100\nD. 61\nE. 73\n\n### Answer:\nLet the ten's digit be x. Then, unit's digit = (9 - x).\nNumber = l0x + (9 - x) = 9x + 9.\nNumber obtained by reversing the digits = 10 (9 - x) + x = 90 - 9x.\ntherefore, (9x + 9) - 63 = 90 - 9x => 18x = 144 => x = 8.\nSo, ten's digit = 8 and unit's digit = 1.\nHence, the required number is 81.\nAnswer A)81.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA watch was sold at a loss of 10%. If it was sold for Rs.140 more, there would have been a gain of 4%. What is the cost price?\n\n### Options:\nA. 1000\nB. 2287\nC. 2677\nD. 2887\nE. 2688\n\n### Answer:\n90%\n104%\n--------\n14% ---- 140\n100% ---- ? => Rs.1000\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a soccer bet,we play 4 teams.first team odd 1.25,second 5.23,third 3.25,fourth 2.05.we place the bet with 5.00 euros.\nhow much money we expect to win?\n\n### Options:\nA. 217.78\nB. 225.5\nC. 235.01\nD. 266.74\nE. 669.0\n\n### Answer:\nin the case we won the bet,we have:\n1.25* 5.23* 3.25* 2.0*5.00=219.50\nwe will win 217.78\nso correct answer is A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the tens digit x and the units digit y of a positive integer n are reversed, the resulting integer is 36 more than n. What is y in terms of x ?\n\n### Options:\nA. 36 - x\nB. 10 - x\nC. x + 4\nD. x - 4\nE. x + 26\n\n### Answer:\nOriginal Digits=xy i.e. Number=10x+y\nAfter reversing the digits:\nDigits=yx i.e. Number=10y+x\n10y+x is 36 more than 10x+y\n10x+y+36=10y+x\n10x-x+36=10y-y\n9x+36=9y\nx+4=y\nOR\ny=x+4\nAns:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the sum of all the prime factors of 220 and 330?\n\n### Options:\nA. 15\nB. 21\nC. 35\nD. 41\nE. 64\n\n### Answer:\nPrime factorization of both the numbers is as follows\n220 = 2 * 2 * 5 * 11\nsum of the prime factors of 220 = 20\n330 = 2 *3 * 5 * 11\nsum of prime factors of 330 = 21\naddition of both = 20 + 21 = 41\nANSWER D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nEight friends go to watch a movie but only 5 tickets were available. In how many different ways can 5 people sit and watch the movie?\n\n### Options:\nA. 8C5\nB. 8*7*6*5*4\nC. 5!\nD. 8!/5!\nE. 8*5\n\n### Answer:\nChoosing 5 out of 8, when order matters P58, or choosing 5 out of 8, without order and then arranging: C58\u22175!\nAnswer: B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man walking at a rate of 15km/hr crosses a bridge in 35 minutes. The length of the bridge is?\n\n### Options:\nA. 1250m\nB. 1750m\nC. 950m\nD. 1000m\nE. 1300m\n\n### Answer:\nSpeed = 15*5/18 = 15/18 m/sec\nDistance covered in 35 minutes = 15/18 *35 *60 = 1750 m\nAnswer is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat should be the least number to be added to the 51234 number to make it divisible by 9?\n\n### Options:\nA. 12\nB. 17\nC. 18\nD. 77\nE. 26\n\n### Answer:\nExplanation:\nThe least number to be added to the numbers to make them divisible by 9 is equal to the difference of the least multiple of 9 greater than the sum of the digits and sum of the digits.\nSum of digits = 15.\nNearest multiple of 9 greater than sum of digits = 18.\nHence 3 has to be added.\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a = 105 and a^3= 21 * 25 * 35 * b, what is the value of b?\n\n### Options:\nA. 35\nB. 42\nC. 45\nD. 49\nE. 63\n\n### Answer:\nFirst step will be to break down all the numbers into their prime factors.\n105 = 3 * 5 * 7\n21 = 7 * 3\n25 = 5 * 5\n35 = 7 * 5\nso, (105)^3 = 3 * 7 * 5 * 5 * 7 *5 *b\nTherefore (3 * 5 * 7) ^ 3 = 3 * 5^3 * 7^2 *b\nTherefore, b = 3^3 * 5^3 * 7 ^3/3 * 5 ^3 * 7^2\nb = 3^2*7 = 9*7=63\nCorrect answer E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is 15 percent of 54?\n\n### Options:\nA. 7.3\nB. 8.1\nC. 9.5\nD. 10.2\nE. 11.6\n\n### Answer:\n(15/100) * 54 = 8.1\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe area of a rectangular plot is 360 square metres. If the length is 25% less than the breadth, what is the breadth of the plot?\n\n### Options:\nA. 32 m\nB. 12 m\nC. 20 m\nD. 22 m\nE. 25 m\n\n### Answer:\nlength =75% of breadth.\nlength\u00d7breadth =360 m2\n\u21d2 75% of breadth\u00d7breadth =360 m2\n\u21d2 75/100\u00d7 breadth\u00d7breadth =360 m2\n\u21d2 breadth\u00d7breadth =480 m2\n\u21d2 breadth =22 m\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere is 60% increase in an amount in 6 years at S.I. What will be the C.I. of Rs. 12,000 after 3 years at the same rate?\n\n### Options:\nA. Rs. 2160\nB. Rs. 3120\nC. Rs. 3972\nD. Rs. 6240\nE. Rs. 6000\n\n### Answer:\nExplanation:\nLet P = Rs. 100. Then, S.I. Rs. 60 and T = 6 years.\nR = (100 * 60)/(100 * 6) = 10% p.a.\nNow, P = Rs. 12000, T = 3 years and R = 10% p.a.\nC.I. = [12000 * {(1 + 10/100)3 - 1}]\n= 12000 * 331/1000 = Rs. 3972\nANSWER IS C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf m and n are positive integers of K such that m is a factor of n, how many positive multiples of m are less than or equal to 2n ?\n\n### Options:\nA. 2m/n + 1\nB. 2n/m + 1\nC. 2n/(m+1)\nD. 2m/n\nE. 2n/m\n\n### Answer:\nLets say N=10, M=5\n2N=20. so the answer should be 4 (20/5)\nlets try to plug in the answers:\nA-not an integer\nB-not an integer\nC-not an integer\nD-1 (not the answer)\nE-4 - the answer. (the only one).\nI would choose E.\nMethod 2\nN=M*A (A is an integer)\nSo - A=N/M\ntherefore in 2N A will be 2N/M\nAgain - Answer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSeven years ago the average age of a family of 2 members was 25 years. A child has been born. due to Which the average age of the family is 23 years today. What is the present age of the child?\n\n### Options:\nA. 7 years\nB. 5 years\nC. 3 years\nD. 8 years\nE. 10 years\n\n### Answer:\nExplanation:\nAverage of the family of two numbers\n7 years ago = 25\n= (25+ 7) * 2 = 64 years\nAverage age of the family of three members at present = 23 years\n= 23 * 3 = 69 YEARS\nAge of child = 69 - 64 = 5 years\nAnswer: Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf an object travels 400 feet in 4 seconds, what is the object's approximate speed in miles per hour? (Note: 1 mile = 5280 feet)\n\n### Options:\nA. 68\nB. 54\nC. 87\nD. 96\nE. 15\n\n### Answer:\n1 mile = 5280 feet\n=> 1 feet = 1/5280 miles\nIf the object travels 400 feet in 4 sec\nthen it travels 400/4 * 60 * 60 feet in 1 hour (1 hr = 60 min * 60 sec)\n= 3600 * 100 feet in 1 hour\n= 360000 feet in 1 hr\n= 360000/5280 miles in 1 hour\n= 36000/528 miles/hr ~ 68 miles/hr\nAnswer - A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nBrand A coffee costs twice as much as brand B coffee. If a certain blend is 3/4 brand A and 1/4 brand B. what fraction of the cost of the blend is Brand A?\n\n### Options:\nA. a. 1/3\nB. b. 2/5\nC. 3. 1/2\nD. 4. 2/3\nE. 5. 6/7\n\n### Answer:\nAssume Cost of A= Ca = 200 , Cost of B = Cb=100\nThe blend contains 0.75 A and 0.25 B ---> Cost of the blend = Cbl = 0.75*200+0.25*100= 175\nThus fraction of A in the blend = 0.75*200/175 = 6/7.\nAnswer : E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe length of rectangle is thrice its breadth and its perimeter is 88 m, find the area of the rectangle?\n\n### Options:\nA. 432 sq m\nB. 363 sq m\nC. 452 sq m\nD. 428 sq m\nE. 528 sq m\n\n### Answer:\n2(3x + x) = 88\nl = 33 b = 11\nlb = 33 * 11 = 363\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRiya and Priya set on a journey. Riya moves eastward at a speed of 20kmph and Priya moves westward at a speed of 30 kmph.How far will be priya from Riya after 30 minutes\n\n### Options:\nA. 25kms\nB. 10kms\nC. 50kms\nD. 30kms\nE. 40kms\n\n### Answer:\ntotal eastward distance= 20kmph*1/2hr=10 km\ntotal westward distance= 30kmph*1/2hr=15 km\ntotal distn betn them= 10+15=25km\nans 25km\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo tains of equal lengths take 10 seconds and 12 seconds respectively to cross a telegraph post. If the length of each train be 120 metres, in what time (in seconds) will they cross each other travelling in opposite direction?\n\n### Options:\nA. 12\nB. 14\nC. 10.9\nD. 20\nE. 18\n\n### Answer:\nSol.\nSpeed of the first train = [120 / 10] m/sec = 12 m/sec.\nSpeed of the second train = [120 / 12] m/sec = 10 m/sec.\nRelative speed = (12 + 10) = m/sec = 22 m/sec.\n\u2234 Required time = (120 + 120) / 22 secc = 10.9 sec.\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA dishonest dealer professes to sell goods at the cost price but uses a false weight and gains 25%. Find his false weight age?\n\n### Options:\nA. 176\nB. 289\nC. 887\nD. 278\nE. 179\n\n### Answer:\n25 = E/(1000 - E) * 100\n1000 - E = 4E\n1000 = 5E => E = 200\n1000 - 200 = 800\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA company has two types of machines, type R and type S. Operating at a constant rate, a machine of type R does a certain job in 10 hrs and a machine of type S does the same job in 5 hours. If the company used the same number of each type of machine to do the job in 2 hours, how many machines of type R were used?\n\n### Options:\nA. A)3\nB. B)4\nC. C)6\nD. D)9\nE. E)12\n\n### Answer:\nRate of machine R =1/10\nRate of machine S =1/5\nsince same no of machines used for R and S to do the same work in 2 hrs\nSo collective rate needed to finish the work in 2 hrs= 1/2\nLet the no of machine be x\nSo, x/10 +x/5 =1/2\n3x/10=1/2\nx=30/5=6\nSo no of machine R is 6\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRamesh, Kiran and Ram started a business with capitals of Rs. 2000, Rs. 8000 and Rs. 6000 respectively. At the end of the year, the profit share of Kiran is Rs. 400. The difference between the profit shares of Ramesh and Ram is?\n\n### Options:\nA. 694\nB. 369\nC. 200\nD. 2356\nE. 1547\n\n### Answer:\nRatio of investments of Ramesh, Kiran and Ram is 2000 : 8000 : 6000 = 1 : 4 : 3\nAnd also given that, profit share of Kiran is Rs. 400\n=> 4 parts out of 8 parts is Rs. 400\nNow, required difference is 3 - 1 = 2 parts\nRequired difference = 2/4 (400) = Rs. 200.Answer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average of first ten prime numbers which are odd is?\n\n### Options:\nA. 15.9\nB. 15.7\nC. 15.1\nD. 15.8\nE. 15.3\n\n### Answer:\nSum of first 10 prime no. which are odd = 158\nAverage\n= 158/10\n= 15.8\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe simple interest on Rs.12000 at a certain rate of interest in five years is Rs.7200. Find the compound interest on the same amount for five years at the same rate of interest.\n\n### Options:\nA. 3052.89\nB. 3052.86\nC. 3092.8\nD. 3052.8\nE. 3052.81\n\n### Answer:\nR = 100 I / PT\n=> R = (100 * 7200)/ (12000 * 5) = 12%\nCI = P{ [1 + R /100]n - 1}\n= 12000 { [ 1 + 12 / 100]2 - 1} = Rs.3052.80.Answer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA sales staff is composed of a sales manager and two sales people, all of whom earn commission as a percentage of sales. Each sales person earns 5% commission on sales. In a given week, the sales staff earned a total of $2,000 in commissions on $5,000 worth of sales. What commission rate did the sales manager earn during that week?\n\n### Options:\nA. 25%\nB. 30%\nC. 35%\nD. 40%\nE. 45%\n\n### Answer:\nB for me.\nLet managers comminsion rate be M.\nm*5000+ 2*0.05*5000=2,000\n5000*m=1500\nm=30/100=30%\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA 260 metres long train runs at a speed of 55 Kmph.How much time will it take to cross a Platform 290 meters long?\n\n### Options:\nA. 36 seconds\nB. 18 seconds\nC. 60 seconds\nD. 20 seconds\nE. None of these\n\n### Answer:\ntotal distance =260m+290m=550m\nspeed=55*5/18=275/18\ntherefore time taken=(550/275)*18=36 sec\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are 18 stations between Ernakulam and Chennai. How many second class tickets have to be printed, so that a passenger can travel from one station to any other station?\n\n### Options:\nA. 800\nB. 380\nC. 360\nD. 478\nE. 566\n\n### Answer:\nThe total number of stations= 20\nFrom 20 Stations we have to choose any two stations and the direction of travel (Ernakulam to Chennai is different from Chennai to Ernakulam) in 20P2 ways.\n20P2= 20*19= 380\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the simple interest on $1500 increase by $20,when the time increase by 2 years. Find the rate percent per annum.\n\n### Options:\nA. 0.6%\nB. 0.5%\nC. 0.1%\nD. 0.2%\nE. 0.7%\n\n### Answer:\nApplying the above formula, we have\n20=1500*r*2/100\nr=20*100/1500*2=0.7%.\nAnswer is E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRatio of two numbers x and y is 1:2. If x is increased by 20% and y is increased by 4 then the new ratio becomes 1:5. What is the ratio 2y:x\n\n### Options:\nA. 1:3\nB. 3:1\nC. 2:3\nD. 4:1\nE. 1:4\n\n### Answer:\nLet:\nx = 1n\ny = 2n\n1.2n/(2n+4) = 1/5\n6n = 2n+4\nn = 1\nSo, x =1; y=2\n2y/x = 4/1 = 4:1\nAnswer = D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe speed of a boat in still water is 15 km/hr and the rate of current is 3 km/hr the distance travelled downstream in 12 minutes is :\n\n### Options:\nA. 2 km\nB. 2.6 km\nC. 3.6 km\nD. 4 km\nE. None\n\n### Answer:\nSol.\nSpeed downstream = (15 + 3) kmph = 18 kmph.\nDistance travelled = [18 * 12/60] km = 3.6 km.\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn Solution P, the proportion of water to alcohol is 5:2. In Solution Q, the proportion of water to alcohol is 3:2. If the two solutions are combined, what is the concentration of alcohol in the new solution if the original solutions were mixed in equal amounts?\n\n### Options:\nA. 25%\nB. 28%\nC. 31%\nD. 34%\nE. 37%\n\n### Answer:\nLet V be the total volume of the new solution.\nThe amount of alcohol added from Solution P is (2/7)*V/2=(1/7)*V\nThe amount of alcohol added from Solution Q is (2/5)*V/2=(1/5)*V\nThe total amount of alcohol in the new solution is (1/7+1/5)*V=(12/35)*V\nThe alcohol concentration is 12/35=34% (approximately)\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSolve x2 \u00e2\u20ac\u201c 3x \u00e2\u20ac\u201c 4 = 0.\n\n### Options:\nA. 1,4\nB. -1,4\nC. 2,3\nD. 2,4\nE. 2,6\n\n### Answer:\nThis one factors easily:\nx2 \u00e2\u20ac\u201c 3x \u00e2\u20ac\u201c 4 = 0\n(x + 1)(x \u00e2\u20ac\u201c 4) = 0\nx + 1 = 0 or x \u00e2\u20ac\u201c 4 = 0\nx = \u00e2\u20ac\u201c1 or x = 4\nThe solution is x = \u00e2\u20ac\u201c1, 4\nANSWER B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOf the three-digit integers greater than 200, how many have two digits that are equal to each other and the remaining digit different from the other two?\n\n### Options:\nA. 90\nB. 82\nC. 80\nD. 45\nE. 36\n\n### Answer:\nLet the three digit number be represented as X Y Z.\nThere are 3 cases:\nCase I.[ X=Y ]Z is not equal to XY :XXZorYYZ\nX can be either 7, 8 or 9, so digit at X can be chosen in 3 ways\nAfter X is chosen, Y can be chosen in 1 way\nAfter XY are chosen, Z can be chosen in 9 ways\nThus, possible No of digits = (3 ways) * (1 way) * (9 ways) = 27 ....(1)\n[example numbers: 774,779,882,993 etc]\nCase II.[ X=Z ]Y is not equal to XZ:XYXorZYZ\nX can be either 7, 8 or 9, so digit at X can be chosen in 3 ways\nAfter X is chosen, Z can be chosen in 1 way\nAfter XZ are chosen, Z can be chosen in 9 ways\nThus, possible No of digits = (3 ways) * (9 ways) * (1 way) = 27 ....(2)\n[example numbers: 747,797,828,939 etc]\nCase III.[ Y =Z ]X is not equal to YZ :XYYorXZZ\nX can be either 7, 8 or 9, so digit at X can be chosen in 3 ways\nAfter X is chosen, Y can be chosen in 9 ways\nAfter Y is chosen, Z can have 1 way\nThus, possible No of digits = (3 ways) * (1 way) * (9 ways) = 27 ....(3)\n[example numbers: 744,799,822,933 etc]\nTherefore, total numbers of possible digits [sum of Case (1), (2)(3) above] = 27 + 27 + 27 - 1 = 80\nOne digit is subtracted from total number of possible digits to eliminate one possibility of XYZ = 700 to satisfy the condition that digit > 200.\nAnswer:(E)\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAverage age of students of an adult school is 42 years. 120 new students whose average age is 32 years joined the school. As a result the average age is decreased by 4 years. Find the number of students of the school after joining of the new students.\n\n### Options:\nA. 1200\nB. 120\nC. 360\nD. 200\nE. None of these\n\n### Answer:\nExplanation :\nLet the original no. of students be x.\nAccording to situation, 42x + 120*32 = (x + 120)36 \u21d2 x = 80\nSo, Required no. of students after joining the new students\n= x + 120 = 200.\nAnswer : D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAn engineer undertakes a project to build a road 15 km long in 300 days and employs 55 men for the purpose. After 100 days, he finds only 2.5 km of the road has been completed. Find the (approximate) number of extra men he must employ to finish the work in time.\n\n### Options:\nA. a. 43\nB. b. 45\nC. c. 55\nD. d. 68\nE. e. 83\n\n### Answer:\n55 workers working already\nLet x be the total men required to finish the task in next 200 days\n2.5 km done hence remaining is 12.5 km\nAlso, work has to be completed in next 200 days (300 - 100 = 200)\nWe know that, proportion of men to distance is direct proportion\nand, proportion of men to days is inverse proportion\nHence, X = (55 * 12.5 * 100) / (2.5 * 200)\nthus, X = 137.5 that is approximately 138\nThus, more men needed to finish the task = 138-55=83\nhence Answer is E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many five-digit numbers are there, if the two leftmost digits are even, the other digits are odd and the digit 4 cannot appear more than once in the number?\n\n### Options:\nA. 1875\nB. 2000\nC. 2375\nD. 2500\nE. 3875\n\n### Answer:\nthe five-digit number: abcde\na have 4 choice of even numbers: 2, 4, 6, 8\nb have 4 choice of even numbers: 0, 2, 6, 8 because 4 cannot appear more than once\nc, d and e each have 5 choice from 1, 3, 5, 7, 9\nSo total: 4*4*5*5*5=2000 ANS:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe cost price of an article is 64% of the marked price. Calculate the gain percent after allowing a discount of 20%?\n\n### Options:\nA. 37.5%\nB. 48%\nC. 50.5%\nD. 52%\nE. 25%\n\n### Answer:\nExplanation:\nLet marked price = Rs. 100.\nThen, C.P. = RS. 64, S.P. = Rs. 80\nGain % = 16/64 * 100 =25%.\nAnswer: Option E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many seconds does Puja take to cover a distance of 500 m, if she runs at a speed of 30 km/hr?\n\n### Options:\nA. 60 sec\nB. 82 sec\nC. 95 sec\nD. 100 sec\nE. 120 sec\n\n### Answer:\nHint:\nTime =\tDistance / Speed\nWe see that the distance is given in metres while the speed is given in km/hr and the answer is asked in seconds.\nSo, convert km/hr into m/s by multiplying\t5 /18\tm/s to the given value of speed.\n30\tkm / hr\t= 30 x\t5 /18\t=\t75 /9 m/sec\ni.e. Place these values in the formula:\nTime = 500 x\t9 / 75= 60 sec\nANSWER IS A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFor every X, the action [X] is defined: [X] is the greatest integer less than or equal to X. What is the value of [6.5] x [2/3] + [2] x 7.2 + [8.4] - 9.8?\n\n### Options:\nA. 12.6.\nB. 14.4.\nC. 15.8.\nD. 16.2.\nE. 16.4.\n\n### Answer:\n[6.5] x [2/3] + [2] x 7.2 + [8.4] - 9.8\n= 6*0 + 2*7.2 + 8 - 9.8\n= 0 +14.4 -1.8\n12.6\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man invests in a 16% stock at 128. The interest obtained by him is :\n\n### Options:\nA. 12.9%\nB. 92.5%\nC. 12.5%\nD. 12.6%\nE. 12.7%\n\n### Answer:\nExplanation:\nBy investing Rs 128, income derived = Rs. 16\nBy investing Rs. 100, income derived = = Rs.12.5\nInterest obtained = 12.5%\nAnswer: C) Rs. 12.5%\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA car covers a distance of 636 km in 6 \u00bd hours. Find its speed?\n\n### Options:\nA. 104 kmph\nB. 176 kmph\nC. 298 kmph\nD. 106 kmph\nE. 268 kmph\n\n### Answer:\n636/6\n= 106 kmph\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA small, experimental plane has three engines, one of which is redundant. That is, as long as two of the engines are working, the plane will stay in the air. Over the course of a typical flight, there is a 1/3 chance that engine one will fail. There is a 65% probability that engine two will work. The third engine works only half the time. What is the probability that the plane will crash in any given flight?\n\n### Options:\nA. 7/12\nB. 1/4\nC. 1/2\nD. 7/24\nE. 17/24\n\n### Answer:\nIn probability questions the trap answer is just the multiple of the numbers in the question.\ni.e. if you multiply 1/3 * 1/4 * 1/2 = 1/24 is trap answer\nThe other trap answer could be 2/3 * 3/4 * 1/2 = 6/24 is trap answer\nSo lets say you have30 secsand you want to guess the answer then B, C are ruled out because they can be traps. You best guess is A, D, E. So you have 33% chances of being correct.\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe letters of the word 'SARITI' are written in all possible orders and these words are written in alphabetical order. Then what is the rank of the word 'SURITI'\n\n### Options:\nA. - 235\nB. - 245\nC. - 307\nD. - 315\nE. - 275\n\n### Answer:\nTotal Number of Words = 6!/2! = 360 [(number of characters)/(repeating group )!]\nAfter S, we have T and A.\nNumber of words starting with T = 5!/2! = 60\nNumber of words starting with U = 5!/2! = 60\nSo any word starting with S will have rank < 360 - 60(for Us) - 60(for Ts) = 240\nOnly option A < 240, so Answer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOn Monday, Lou drives his vehicle with 25-inch tires, averaging x miles per hour. On Tuesday, Lou switches the tires on his vehicle to 32-inch tires yet drives to work at the same average speed as on Monday. What is the percent change from Monday to Tuesday in the average number of revolutions that Lou's tires make per second?\n\n### Options:\nA. Decrease by 14.3%\nB. Decrease by 22%\nC. Increase by 14.3%\nD. Increase by 12.5%\nE. Cannot be determined with the given information.\n\n### Answer:\n800 the LCM\nOn Tuesday 800/32 =25\nOn Monday 800/25 = 32\nTherefore, 25-32/32= -2/9=-22% decrease\nAnswer is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe marks obtained by Vijay and Amith are in the ratio 4:5 and those obtained by Amith and Abhishek in the ratio of 3:2. The marks obtained by Vijay and Abhishek are in the ratio of?\n\n### Options:\nA. 6:8\nB. 6:9\nC. 6:5\nD. 6:2\nE. 6:3\n\n### Answer:\n4:5\n3:2\n-------\n12:15:10\n12:10\n6:5\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf pq = p^5 + q^2 \u2013 2pq, for what value of q is pq equal to p^5 for all values of p?\n\n### Options:\nA. -2\nB. -1\nC. 0\nD. 1\nE. 2\n\n### Answer:\nC\np5 + q2 \u00e2\u20ac\u201c 2pq = p5\n=> q2 - 2pq = 0\n=> q (q - 2p) = 0\n=> q = 0 or q = 2p\nim not following the logic you used here.. how did you replace pq with 0 could someone help explain it in MORE DETAI\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nif xy+z=x(y+z) which of the following must be true?\n\n### Options:\nA. x=2 or z=0\nB. x=1 or z=0\nC. x=1 or z=1\nD. x=0 or z=0\nE. x=0 or z=0\n\n### Answer:\nxy+z=xy+xz\nz=xz\nxz-z=0\nz(x-1)=0\nMeans;\neither z=0\nOR\nx-1=0 i.e. x=1\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMaria's grandparents were celebrating their 50th anniversary. Each of the children contributed $100 and the grandchildren each contributed $80. Together, all 15 members the family collected a total of $1,300 dollars for the celebration. How many children did Maria's grandparents have.\n\n### Options:\nA. 3\nB. 5\nC. 8\nD. 9\nE. 10\n\n### Answer:\nLet x = the number of children. That means the number of grandchildren = 15 - x.\nThe amount contributed by the children = 100x. The amount contributed by the grandchildren = 80(15 - x).\nThis means: 100x + 80(15 - x) = 1300\n100x + 1200 - 80x = 1300\n100x - 80x = 1300 - 1200\n20x = 100\nx = 5\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain population of bacteria doubles every 10 minutes. If the number of bacteria in the population initially was 10^5, then what was the number in the population 40 minutes later?\n\n### Options:\nA. 2(10^5)\nB. 4(10^5)\nC. (2^4)(10^5)\nD. (10^4)(10^5)\nE. (10^5)^4\n\n### Answer:\nEvery 10 minutes, the population is double the previous population.\nIn 40 minutes, the population doubles 4 times.\nThe population then is 2^4*10^5.\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA committee has 5 men and 6 women. What are the number of ways of selecting 2 men and 3 women from the given committee?\n\n### Options:\nA. 188\nB. 200\nC. 277\nD. 266\nE. 121\n\n### Answer:\nThe number of ways to select two men and three women = \u2075C\u2082 * \u2076C\u2083\n= (5 *4 )/(2 * 1) * (6 * 5 * 4)/(3 * 2)\n= 200\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a game of billiards, A can give B 30 points in 80 and he can give C 40 points in 80. How many points can B give C in a game of 100?\n\n### Options:\nA. 23\nB. 24\nC. 25\nD. 20\nE. 28\n\n### Answer:\nA scores 80 while B score 50 and C scores 40.\nThe number of points that C scores when B scores 100 = (100 * 40)/50 = 80.\nIn a game of 100 points, B gives (100 - 80) = 20 points to C\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe edges of a cuboid are respectively 3cm, 4cm and 12 cm. Find the length of the diagonal of cuboid.\n\n### Options:\nA. 9: 8\nB. 9: 5\nC. 9: 1\nD. 9: 2\nE. 9: 4\n\n### Answer:\na1 : a2 = 3 : 1\n6 a12 : 6 a22 = 9: 1\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf I walk at 3 km/h, I miss the bus by 12 minutes. If I walk at 6 km/h, I reach 10 minutes before the arrival of the bus. How far I walk to reach the bus stand ?\n\n### Options:\nA. 2.19 km\nB. 2.22 km\nC. 2.00 km\nD. 1.19 km\nE. 1.99 km\n\n### Answer:\nd = product of speed difference of time /difference of speed\nd = 3x6/60[12\u00e2\u02c6\u2019(\u00e2\u02c6\u201910)/6-3]\n[Here, \u00e2\u20ac\u201cve sign indicates before the schedule time]\n\u00e2\u2021\u2019 d = 2.19 km\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nBefore being simplified, the instructions for computing income tax in Country R were to add 2 percent of one's annual income to the average (arithmetic mean) of 100 units of Country R's currency and 1 percent of one's annual income. Which of the following represents the simplified formula for computing the income tax, in Country R's currency, for a person in that country whose annual income is Z?\n\n### Options:\nA. 50+Z/200\nB. 50+3Z/100\nC. 50+Z/40\nD. 100+Z/50\nE. 100+3A/100\n\n### Answer:\n50+Z/40=C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAjith can do a work in 12 days while Anand can do the same work in 18days. Both of them finish the work together and get $500. What is the share of Ajith?\n\n### Options:\nA. $150\nB. $200\nC. $350\nD. $250\nE. $300\n\n### Answer:\nAjith's wages: Anand's wages = 1/12 : 1/18 = 18:12 = 3:2\nAjith's share = 500*3/5 = $300\nAnswer is E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe speed of a boat in upstream is 40 kmph and the speed of the boat downstream is 80 kmph. Find the speed of the boat in still water and the speed of the stream?\n\n### Options:\nA. 10 kmph\nB. 67 kmph\nC. 22 kmph\nD. 20 kmph\nE. 12 kmph\n\n### Answer:\nSpeed of the boat in still water\n= (40+80)/2\n= 60 kmph. Speed of the stream\n= (80-40)/2\n= 20 kmph.\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhen m is divided by 9, the remainder is 4. When m is divided by 13, the remainder is 10. If 1 < m < 200, what is the greatest possible value of m?\n\n### Options:\nA. 47\nB. 65\nC. 103\nD. 117\nE. 166\n\n### Answer:\nLooking at the choices, options BD can be eliminated as they are divisible by 13\nStarting from the highest number 164;\n166 = 162 + 4 (162 divisible by 9)\n166 = 156 + 10 (156 divisible by 13)\nit fits the result\nAnswer = E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe difference between the place values of 9 and 4 in the number 927435 is\n\n### Options:\nA. 899600\nB. 856200\nC. 875200\nD. 896200\nE. None\n\n### Answer:\nSol.\r= (Place value of 9) \u2013 (place Value of 4)\r= (900000 - 400)\r= 899600 Answer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n. Star question:\nIf f(1)=4 and f(x+y)=f(x)+f(y)+7xy+4,then f(2)+f(5)=?\n\n### Options:\nA. 125\nB. 977\nC. 289\nD. 1077\nE. 111\n\n### Answer:\nLet x =1 and y = 1\nf(1 + 1) = f(1) + f(1) + 7 x 1 x 1 + 4 \u21d2\u21d2 f(2) = 19\nLet x =2 and y = 2\nf(2 + 2) = 19 + 19 + 7 x 2 x 2 + 4 \u21d2\u21d2 f(4) = 70\nLet x = 1 and y = 4\nf( 1 + 4) = 4 + 70 + 28 + 4 = 106\nf(2) + f(5) = 125\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA Coach is filling out the starting lineup for his indoor soccer team. There are 10 boys on the team, and he must assign 6 starters to the following positions: 1 goalkeeper, 2 on defence, 2 in midfield, and 1 forward. Only 2 of the boys can play goalkeeper, and they cannot play any other positions. The other boys can each play any of the other positions. How many different groupings are possible?\n\n### Options:\nA. 60\nB. 210\nC. 2580\nD. 3360\nE. 151200\n\n### Answer:\n2C1 select 1 goalkeeper from 2 boys;\n8C2 select 2 defense from 8 boys (as 2 boys can only play goalkeeper 10-2=8);\n6C2 select 2 midfield from 6 boys (as 2 boys can only play goalkeeper and 2 we've already selected for defense 10-2-2=6);\n4C1 select 1 forward from 4 boys (again as 2 boys can play only goalkeeper, 4 we've already selected for defense and midfield 10-2-4=4)\nTotal # of selection=2C1*8C2*6C2*4C1=3360\nAnswer: D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nApple Infotech has 4 Senior Managing Directors and 5 Managing Directors. Each investment banking deal requires the guidance of two managing directors, at least one of which must be a Senior Managing Director. How many possible investment banking deals can Apple Infotech possibly provide guidance for?\n\n### Options:\nA. 16\nB. 20\nC. 26\nD. 54\nE. 64\n\n### Answer:\nP(at least 1 S D) = P(Total) - P(0 Senior Director)\n=9C2 - 5C2\n= 26\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSet D consists of 19 elements. The average of set D is L. If a new element is added to the set and the average grows by K, what is the value of the new element?\n\n### Options:\nA. a) L(1 + K / 5)\nB. b) L * (K/100) - 20L\nC. c) 20L(1+K/100)\nD. d) 20(1+K/100)-19L\nE. e) L*(K/5)-19\n\n### Answer:\nLet's assume the value of new element to bea. So converting the word problem into equation,\n(19*L + a) / (19 + 1) = L + k ==> after solving the equation we will get a (value of newly added element) = L + 20K\nBut according to the answer options, problem writer wanted to conveyk% percent rise in average value.\nIf we consider this case than resulting equation will be,\n(19*L + a) / ( 19+1 ) = L + (K/100)*L ==> 19L + a = 20 [ L + KL/100]\n==> a= 20L + KL/5 -19L\n==> a= L + KL/5 , which is equivalent to option [A]\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf c is a positive even integer, and n and m are consecutive integers, then (n - m)^c/(m - n)^c =\n\n### Options:\nA. -2\nB. -1\nC. 0\nD. 1\nE. 2\n\n### Answer:\nc= +ve even integer\nSince,n and m are consecutive integers , their difference will be 1\n((n-m)^c)/((m-n)^c)= ((n-m)/(m-n))^c = (-1)^c\nSince we are raising the difference of n and m to power c , which is even , the answer will be 1 .\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the probability that a number selected from numbers 1, 2, 3,..., 30 is a prime number, when each of the given numbers is equally likely to be selected?\n\n### Options:\nA. 10/30\nB. 1/30\nC. 8/30\nD. 3/30\nE. 7/30\n\n### Answer:\nLet X be the event of selecting a prime number.\nX = {2, 3, 5, 7, 11, 13, 17, 19, 23,29}\nn(X) = 10,\nn(S) = 30\nHence, the required probability is 10/30.\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe HCF and LCM of two numbers m and n are respectively 6 and 210. If m + n = 80, then 1/m + 1/n is equal to\n\n### Options:\nA. 1/35\nB. 3/35\nC. 5/37\nD. 4/63\nE. None\n\n### Answer:\nAnswer\nWe have, m x n = 6 x 210 = 1260\n\u00e2\u02c6\u00b4 1/m + 1/n = (m + n)/mn = 80/1260 = 4/63\nCorrect Option: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe ratio between the speeds of two trains is 7 : 10. If the second train runs 400 kms in 8 hours, then the speed of the first train is\n\n### Options:\nA. 35 km/h\nB. 60 km/h\nC. 45 km/h\nD. 50km/h\nE. 30 km/h\n\n### Answer:\nA\n35 km/h\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA driver covers a certain distance by car driving at 60 km/hr and returns back to the starting point riding on a scooter at 20 km/hr. What was the average speed for the whole journey?\n\n### Options:\nA. 24 km/h\nB. 26 km/h\nC. 28 km/h\nD. 30 km/h\nE. 32 km/h\n\n### Answer:\ntime 1 = d / 60\ntime 2 = d / 20\ntotal time = d/60 + d/20 = 4d/60 = d/15\naverage speed = total distance / total time = 2d / (d/15) = 30 km/h\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average monthly salary of 20 employees in an organisation is Rs. 1700. If the manager's salary is added, then the average salary increases by Rs. 100. What is the manager's monthly salary ?\n\n### Options:\nA. 3800\nB. 3890\nC. 88798\nD. 2789\nE. 2891\n\n### Answer:\nExplanation:\nManager's monthly salary Rs. (1800 * 21 - 1700 * 20) = Rs. 3800.\nAnswer: A) 3800\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe no. of gift pack bought by Dexter is 1 more than the price, in rupees, of each gift pack. The amount of Rs.380 which Dexter had, fell short of the required amount. What is theamount by which he might have fallen short.\n\n### Options:\nA. 30\nB. 40\nC. 50\nD. 60\nE. 80\n\n### Answer:\nLet the price of gift pack be 'aa'\nThen number of packs bought =a+1=a+1\nHence total cost is a(a+1)a(a+1)\nIt is given that 380", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe compound interest on Rs. 30,000 at 7% per annum is Rs. 4347. The period(in years) is?\n\n### Options:\nA. 2\nB. 3\nC. 4\nD. 1\nE. 5\n\n### Answer:\nAmount = (30000 + 4347) = Rs. 34347\nLet the time be n years. Then,\n30000(1 + 7/100)n = 34347\n= (107/100)n = 34347/30000 = (107/100)2\nn = 2 years.\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nEach of the integers from 0 to 9, inclusive, is written on a separate slip of blank paper and the ten slips are dropped into hat. If the slips are then drawn one at a time without replacement, how many must be drawn to ensure that the numbers on two of the slips drawn will have a sum of 11?\n\n### Options:\nA. 7\nB. 5\nC. 9\nD. 4\nE. 1\n\n### Answer:\nYou should consider the worst case scenario: if you pick numbers 0, 1, 2, 3, 4, and 5 then no two numbers out of these 6 add up to 10.\nNow, the next, 7th number whatever it'll be (6, 7, 8, or 9) will guarantee that two number WILL add up to 11. So, 7 slips must be drawn to ensure that the numbers on two of the slips drawn will have a sum of 11.\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA cistern has three pipes, A, B and C. The pipes A and B can fill it in 4 and 5 hours respectively and C can empty it in 2 hours. If the pipes are opened in order at 1, 2 and 3 A.M. When will the cistern be empty?\n\n### Options:\nA. 2\nB. 3\nC. 5\nD. 81\nE. 6\n\n### Answer:\n:\n1 to 2 = 1/4\n2 to 3 = 1/4 + 1/5 = 9/20\nAfter 3 AM = 1/4 + 1/5 - 1/2 = -1/20\n1/4 + 9/20 = 14/20\n1 h ---- 1/20\n? ----- 14/20\n14 hours ==> 5 PM.Answer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf k is a non-negative integer and 21^k is a divisor of 435,961 then 7^k - k^7 =\n\n### Options:\nA. 0\nB. 1\nC. 42\nD. 118\nE. 242\n\n### Answer:\n4+3+5+9+6+1 = 28, so this number is not divisible by 3 and thus not divisible by 21.\nTherefore, k=0\n7^k - k^7 =1-0=1\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA person has to cover a distance of 6 km in 45 minutes. If he covers one-half of the distance in two-thirds of the total time; to cover the remaining distance in the remaining time, his speed (in km/hr) must be :\n\n### Options:\nA. 7 km/hr\nB. 8 km/hr\nC. 11 km/hr\nD. 12 km/hr\nE. None of these\n\n### Answer:\nSol.\nRemaing distance = 3 km and\nRemaining time = [1/3 * 45] min = 15 min = 1/4 hour.\n\u2234 Required speed = (3*4) km/hr = 12 km/hr.\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOf 800 surveyed students, 20% of those who read book A also read book B and 25% of those who read book B also read book A. If each student read at least one of the books, what is the difference between the number of students who read only book A and the number of students who read only book B?\n\n### Options:\nA. 20\nB. 25\nC. 30\nD. 55\nE. 100\n\n### Answer:\nSay the number of students who read book A is A and the number of students who read book B is B.\nGiven that 20% of those who read book A also read book B and 25% of those who read book B also read book A, so the number of students who read both books is 0.2A=0.25B --> A=1.25B.\nSince each student read at least one of the books then {total}={A}+{B}-{Both} --> 800=1.25B+B-0.25B --> B=400, A=1.25B=500 and {Both}=0.25B=100.\nThe number of students who read only book A is {A}-{Both}=500-100=400;\nThe number of students who read only book B is {B}-{Both}=400-100=300;\nThe difference is 400-300 = 100.\nAnswer: E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe edges of a cuboid are 4 cm, 5 cm and 6 cm. Find the volume of the cuboid?\n\n### Options:\nA. 120\nB. 298\nC. 272\nD. 827\nE. 278\n\n### Answer:\n4*5*6\n= 120\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how many ways can 4 boys and 4 girls be arranged a ta table if 4 girls are never together?\n\n### Options:\nA. 3365\nB. 3256\nC. 4464\nD. 5648\nE. 2456\n\n### Answer:\nTotal ways of arranging 8 person in a circle = 7! = 5040 ways\nIf we consider four women as one, then we have 4+1=5 persons. Arranging these five persons in circle will take = 4! = 24 ways\nAnd four women can arrange themselves in 4! ways\nTotal ways in which four women sit together in circle = 4!*4! = 576 ways\nTotal ways in which four women doesn\u2019t sit together in circle = 7! - 4!*4! = 5040 - 576 = 4464 ways\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n3 men and 8 women complete a task in same time as 6 men and 2 women do. How much fraction of work will be finished in same time if 4 men and 5 women will do that task.\n\n### Options:\nA. 13/14\nB. 13/10\nC. 13/18\nD. 13/16\nE. 13/11\n\n### Answer:\n3 m + 8 w = 6 m + 2 w\n3 m = 6 w\n1 m = 2 w\nTherefore 3 m + 8 w = 14 w\n4 m + 5 w =13 w\nAnswer is 13/14\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe sum Q of the arithmetic sequence a, a+d, a+2d,..., a+(n-1)d is give by Qn = (n/2)*(2a + n-1)d. What is the sum of the integers 1 to 100 inclusive, with the even integers between 25 and 63 omitted.\n\n### Options:\nA. 4345\nB. 4302\nC. 4258\nD. 4214\nE. 4170\n\n### Answer:\na method to do it under one minutes is to take advantage of the choices given...\nlets work on the last digit as we have different units digit in each choice...\ntotal sum of 1 to 100 inclusive will have 0 as the last digit..\nthis is so because the resultant will be 10*(sum of all single digits)... and since we are multiplying by 10,units digit will be 0...\nnow for single digit in sum Q of even number from 25 to 63..\n25 to 65 will have 4 times sum of single digit even int, 4*(2+4+6+8+0)=4*20..\nhere too the units digit is 0, but 64 has to be excluded from the total..\ntwo ways from here on..\n1) we are subtracting 0 from 0\nso units digit should be 0, but we have to add 64..\nso last/units digit =4..\n2)we subtract 64 from sum of even int..\nso units digit=80-4=76..\nor units digit =6...\nso our answer should have units digit as 10-6=4..\nonly D has 4 as units digit..\nans D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average age of a husband, wife and their child 2 years ago was 27 years and that of wife and the child 5 years ago was 20 years. The present age of the husband is?\n\n### Options:\nA. 19.2 years\nB. 28.5 years\nC. 16.4 years\nD. 15.6 years\nE. 14.2 years\n\n### Answer:\nSum of the present ages of husband, wife and child\n= (23 * 2 + 5 * 2) = 57 years.\nRequired average\n= 57/2\n= 28.5 years.\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf c \u2260 1 and if dc/(d - c) = 1, what is the value of d in terms of c?\n\n### Options:\nA. (c-1)/c\nB. c/(1-c)\nC. c/(c + 1)\nD. (c + 1)/c\nE. (1 - c)/c\n\n### Answer:\nThis question comes with a particular 'quirk' (one that you probably won't see on Test Day). The GMAT won't test you on the concept of undefined numbers (re: numbers divided by 0), so any time that this concept is a possibility, the question writers have to add a restriction that removes the option that a 0 could occur in the denominator.\nHere, we're told that B CANNOT = 1, which is a bit strange because that restriction doesn't seem to impact the original equation much. In fact, it impacts JUST ONE of the answer choices - so you have to ask WHY that restriction is even there. It's actually because that one answer is the correct one.\nFinal Answer:\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n(112 x 54) = ?\n\n### Options:\nA. 67000\nB. 70000\nC. 76500\nD. 77200\nE. 85200\n\n### Answer:\nExplanation:\n(112 x 54) = 112 x(10/2)4=112 X10 4 /2 4 =1120000/16 =70000\nANSWER IS B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA farmer has an apple orchard consisting of Fuji and Gala apple trees. Due to high winds this year 10% of his trees cross pollinated. The number of his trees that are pure Fuji plus the cross-pollinated ones totals 204, while 3/4 of all his trees are pure Fuji. How many of his trees are pure Gala?\n\n### Options:\nA. 22\nB. 33\nC. 36\nD. 77\nE. 88\n\n### Answer:\nLet f = pure fuji , g = pure gala and c - cross pollinated.\nc = 10% of x where x is total trees.\nc = .1x\nalso 3x/4 = f and c+f = 204 => .1x + 3/4x = 204 => x = 240\n240 - 204 = pure gala = 36.\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the odd man out\n2, 5, 11, 23, 48, 95\n\n### Options:\nA. 5\nB. 11\nC. 23\nD. 48\nE. 28\n\n### Answer:\n2*2+1 = 5\n5*2+1 = 11\n11*2+1 = 23\n23*2+1 = 47\n47*2+1 = 95\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRebecca's annual income is $15 and Jimmy's annual income is $18. By how much must Rebecca's annual income increase so that it constitutes 55% of Rebecca and Jimmy's combined income?\n\n### Options:\nA. 8\nB. 7\nC. 9\nD. 10\nE. 11\n\n### Answer:\ntotal rebecca = x+15; total = x+15+18\nx+15/x+33 = 55/100 therefore x =7\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe avearge score of a cricketer for ten matches is 38.9 runs. If the average for the first six matches is 47. Then find the average for the last four matches?\n\n### Options:\nA. 33.25\nB. 33.5\nC. 34.25\nD. 35\nE. 26.75\n\n### Answer:\nSolution\nRequired average\t=(38.9 x 10)-(47 x 6)/ 4\n= 107 / 4.\n= 26.75\nAnswer E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOn a trip, a cyclist averaged 8 miles per hour for the first 16 miles and 10 miles per hour for the remaining 16 miles. If the cyclist returned immediately via the same route and took a total of 6.8 hours for the round trip, what was the average speed (in miles per hour) for the return trip?\n\n### Options:\nA. 9\nB. 10\nC. 11\nD. 12\nE. 13\n\n### Answer:\nThe time to go 32 miles was 16/8+16/10=2+1.6=3.6 hours.\nThe average speed for the return trip was 32 miles/3.2 hours= 10 mph.\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nShannon and Maxine work in the same building and leave work at the same time. Shannon lives due north of work and Maxine lives due south. The distance between Maxine's house and Shannon's house is 60 miles. If they both drive home at the rate 2R miles per hour, Maxine arrives home 60 minutes after Shannon. If Maxine rider her bike home at the rate of R per hour and Shannon still drives at a rate of 2R miles per hour, Shannon arrives home 2 hours before Maxine. How far does maxine live from work?\n\n### Options:\nA. 20\nB. 34\nC. 38\nD. 40\nE. 48\n\n### Answer:\nNice question +1\nWe have that X/24 - (60-X)/2R = 40\nAlso X/R - (60-X)/2R = 120\nSo we get that 2x - 60 = 80R\n3x - 60 = 240R\nGet rid of R\n120 = 3x\nx = 48\nHence answer is E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThurston wrote an important seven-digit phone number on a napkin, but the last three numbers got smudged. Thurston remembers only that the last three digits contained at least one zero and at least one non-zero integer. If Thurston dials 20 phone numbers by using the readable digits followed by 20 different random combinations of three digits, each with at least one zero and at least one non-zero integer, what is the probability that he will dial the original number correctly?\n\n### Options:\nA. 1/9\nB. 10/243\nC. 2/27\nD. 10/271\nE. 1/1000000\n\n### Answer:\nIf the last three digits have 1 zero (XX0), the total # of numbers possible is 9*9*3 (multiply by 3 since XX0 can be arranged in 3 ways: XX0, X0X, or 0XX).\nIf the last three digits have 2 zeros (X00), the total # of numbers possible is 9*3 (multiply by 3 since X00 can be arranged in 3 ways: X00, 00X, or X0X).\nP = 20/(9*9*3+9*3) = 2/27.\nAnswer: C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAfter 6 games, team B had an average of 70 points per game. If it got only 47 points in game 7, how many more points does it need to score to get its total above 500?\n\n### Options:\nA. 85\nB. 74\nC. 67\nD. 33\nE. 28\n\n### Answer:\n(6*70) + 47 +x >500\n420+47+x > 500\n467+x >500\n=> x>33\nOption D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nCompound interest earned on a sum for the second and the third years are Rs.1200 and Rs.1440 respectively. Find the rate of interest?\n\n### Options:\nA. 70% p.a\nB. 50% p.a\nC. 20% p.a\nD. 10% p.a\nE. 90% p.a\n\n### Answer:\nExplanation:\nRs.1440 - 1200 = Rs.240 is the interest on Rs.1200 for one year.\nRate of interest = (100 * 240) / (100 * 1) = 20% p.a\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n4 apple and 3 mangoes costs rs.34, 2 mangoes and 5 oranges costs 49, 3 oranges and 6 apples costs 54. What is the price of 1 apple?\n\n### Options:\nA. 151/19\nB. 151/17\nC. 151/18\nD. 151/16\nE. 153/15\n\n### Answer:\n4A+3M = 34 -----(1)\n2M+5O = 49 -----(2)\n3O+6A = 54 -----(3)\nfrom (2) and (3)\n30A-6M = 123 -----(4)\nfrom (1) and (4)\nA = 191/38\nsubstituting in (1) and (3)\nM= 88/19\nO = 151/19\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn the faculty of Reverse-Engineering, 100 second year students study numeric methods, 300 second year students study automatic control of airborne vehicles and 200 second year students study them both. How many students are there in the faculty if the second year students are approximately 40% of the total?\n\n### Options:\nA. 550\nB. 500\nC. 600\nD. 650\nE. 700\n\n### Answer:\nTotal number of students studying both are 100 + 300 - 200 = 200 (Subtracting the 200 since they were included in the both the other numbers already).\nSo 40% of total is 200, so 100% is 500\nAnswer is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf n=5p where p is a prime number greater than 1, how many different positive even divisors does n have, including n?\n\n### Options:\nA. 1\nB. 2\nC. 32\nD. 4\nE. 3\n\n### Answer:\nN = 5P and that P is a prime number greater than 1. Let's TEST P = 2; so N = 10\nThe question now asks how many DIFFERENT positive EVEN divisors does 10 have, including 10?\n10:\n1,10\n5,2\nHow many of these divisors are EVEN? 2, 10\u2026..2 even divisors.\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe length of a rectangular plot is thrice its breadth. If the area of the rectangular plot is 867 sq m, then what is the breadth of the rectangular plot?\n\n### Options:\nA. 11\nB. 17\nC. 88\nD. 66\nE. 12\n\n### Answer:\nLet the breadth of the plot be b m.\nLength of the plot = 3 b m\n(3b)(b) = 867\n3b2 = 867\nb2 = 289 = 172 (b > 0)\nb = 17 m.Answer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRs. 800 becomes Rs. 956 in 3 years at a certain rate of simple interest.If the rate of interest is increased by 4% ,What amount will Rs. 800 become in 3 years ?\n\n### Options:\nA. Rs. 1020.80\nB. Rs. 1025\nC. Rs. 1052\nD. Data inadequate\nE. None of these\n\n### Answer:\nSolution\nS.I. = Rs.(956-800 )=Rs.156\nRate = (100x156/800x3) = 6 1/2%\nNew rate = (6 1/2 +4)% = 10 1/2%\nNew S.I. = Rs.(800 x21/2x3/100) Rs. 252.\n\u2234 New amount = Rs.(800+252)= Rs. 1052.\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n((-1.9)(0.6) \u2013 (2.6)(1.2))/4.0 = ?\n\n### Options:\nA. 1.07\nB. 1.0\nC. -1.065\nD. 1.71\nE. 2.71\n\n### Answer:\nDove straight into calculation but quickly realized that the sum of two negatives is a negative so there is only one option.\n-1.065\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo whole numbers whose sum is 36 cannot be in the ratio\n\n### Options:\nA. 2:4\nB. 3:4\nC. 3:6\nD. 1:3\nE. 3:36\n\n### Answer:\nB) 3:4\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many of the positive factors of 16 are not factors of 20\n\n### Options:\nA. 2\nB. 3\nC. 4\nD. 1\nE. 5\n\n### Answer:\nfactors of 16 - 1, 2, 4, 8, 16\nfactors of 20 -1, 2, 4, 5, 10, 20.\nComparing both, we have 2 factors of 16 which are not factors of 20- 8,16\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAnne bought a computer for $2,000 and then paid a 5 percent sales tax, and Henry bought a computer for $1,800 and then paid a 12 percent sales tax. The total amount that Henry paid, including sales tax, was what percent less than the total amount that Anne paid, including sales tax?\n\n### Options:\nA. 3%\nB. 4%\nC. 7%\nD. 10%\nE. 12%\n\n### Answer:\nCost of Computer = $2000\nSales tax = (5/100)*2000 = $100\nTotal Cost of Computer = 2000 + 100 = 2100\nFor Henry\nCost of Computer = $1800\nSales tax = (12/100)*1800 = $216\nTotal Cost of Computer = 1800 + 216 = 2016\n% that Henry paid less than Anne = (2100 - 2016)*100/2100 = 4%\nAnswer: Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe surface area of a sphere is 4\u03c0R2, where R is the radius of the sphere. If the area of the base of a hemisphere is 3, what is the surface area R of that hemisphere?\n\n### Options:\nA. 6/\u03c0\nB. 9/\u03c0\nC. 6\nD. 9\nE. 12\n\n### Answer:\nGiven Area of the base of a hemisphere is 3 = PI * R^2\nThus R = Sqrt ( 3 / PI ) .\nSurface area of whole sphere = 4 *PI*R^2 .\n= 4 * PI * 3 / PI\n= 12 .\nSince the hemisphere is half of a sphere the Surface area of the hemisphere = 12 / 2\n= 6 ( curved part , not including the flat rounded base ) .\nBut the total surface area = 6 + Area of the base of a hemisphere .\n= 6 + 3\n= 9.\nAnswer is D !!\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a farmer sells 5 of his goats, his stock of feed will last for 4 more days than planned, but if he buys 10 more goats, he will run out of feed 3 days earlier than planned. If no goats are sold or bought, the farmer will be exactly on schedule. How many goats does the farmer have?\n\n### Options:\nA. 12\nB. 20\nC. 48\nD. 55\nE. 60\n\n### Answer:\nSay farmer has n goat and he is good for d days.:-\nWe have 3 equations given in question:-\n(n-5) * d+4 =(n+10) *(d-3) = n * d\nSolving these: (You can solve 1st and 3rd and 2nd and 3rd together)\nWe get:\n10d-3n=30\n4n-5d =20\n=> n=20\nAns B it is!\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich of the following Equation is NOT equivalent to 25x^2 = y^2 - 16?Which of the following Equation is NOT equivalent to 25x^2 = y^2 - 16?\n\n### Options:\nA. 25x^2 + 4 = y^2\nB. 75x^2 = 3y^2 - 12\nC. 25x^2 = (y + 2)(y - 2)\nD. 5x = y - 4\nE. x^2 = (y^2 - 4)/25\n\n### Answer:\n1) Take the original equation and try to manipulate it so that it becomes 4 of the 5 answers\n2) Take each answer choice and see if you can manipulate it to make it into the original equation.\nWith Answer D, we have...\n5X = Y - 2\nIf we square both sides, we end up with....\n(5X)^2 = (Y-4)^2\n(5X)(5X) = (Y-4)(Y-4)\n25X^2 = Y^2 - 8Y + 16\nThis is NOT a match for the original equation, so it's the answer that is NOT equivalent. D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOne-sixth of the attendees at a certain convention are female students, two-thirds of the attendees are female, and one-third of the attendees are students. If 250 of the attendees are neither female nor students, what is the total number of attendees at the convention?\n\n### Options:\nA. 600\nB. 300\nC. 1200\nD. 1500\nE. 1600\n\n### Answer:\nLet no. of Attendee are A.\nNow As per the condition of the problem stated above .\nWe have following population in the convention as Attendee.\nTotal no. of females = [2/3]*A\nTotal no. of females as student : [1/6]*A\nTotal no. of students = [1/3]*A\nTotal no. of male as student = [1/6]*A\nTotal no. of males = A - [2/3]*A = [1/3]A\nNo. of males which are not student = [1/3]A - [1/6]*A = 250\nHence A = 1500\nTotal no of males who are not student will be the answer as it states it should be neither female nor student\nSo Answer is D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAn express A starts at 2.30 pm from nampali station and travels towards vizag station at speed of 80 kmph. Another expressstarts at 4.30 pmfrom nampali station to vizag station at speed of 100 kmph. How far awayfrom station Nampali will the two trains meet??\n\n### Options:\nA. 600 km\nB. 700 km\nC. 750 km\nD. 800 km\nE. 900 km\n\n### Answer:\nLet train A take x hours to reach the point of meeting(let it be P)\nThen train B will reach the same point in x-2 hours.\nDistance covered to reach P by train A in x hours=Distance covered by B to reach P in x-2 hrs.\n80*x=100(x-2)\n80x=100x-200\nx=10 hrs.\nDistance from Nampali=x*speed of train A\n=10*80\n=800 km\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo trains, each 100 m long, moving in opposite directions, cross other in 12 sec. If one is moving twice as fast the other, then the speed of the faster train is?\n\n### Options:\nA. 76 km/hr\nB. 66 km/hr\nC. 40 km/hr\nD. 67 km/hr\nE. 22 km/hr\n\n### Answer:\nLet the speed of the slower train be x m/sec.\nThen, speed of the train = 2x m/sec.\nRelative speed = ( x + 2x) = 3x m/sec.\n(100 + 100)/12 = 3x => x = 50/9\nSo, speed of the faster train = 100/9 = 100/9 * 18/5 = 40 km/hr.\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 4a = 16b and 9b = 11c, Find a:b:c?\n\n### Options:\nA. 52:13:7\nB. 44:11:9\nC. 7:13:52\nD. 7:13:54\nE. None of these\n\n### Answer:\nExplanation:\n(4a = 16b ==> a/b = 16/4)\nand (9b = 11c ==> b/c = 11/9)\n==> a:b = 16:4 and b:c = 11:9\na:b:c = 44:11:9\nAnswer: Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe C.P of 10 pens is equal to the S.P of 16 pens. Find his gain % or loss%?\n\n### Options:\nA. loss 16 2/8%\nB. loss 16 6/3%\nC. loss 16 2/3%\nD. loss 18 2/3%\nE. loss 37.5%\n\n### Answer:\n10 CP = 16 SP\n16 --- 6 CP loss\n100 --- ? => 37.5% loss\nAnswer:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA table is bought for Rs.800/- and sold at a loss of 10% find its selling price\n\n### Options:\nA. s.500/-\nB. s.530/-\nC. s.540/-\nD. s.600/-\nE. s.720/-\n\n### Answer:\n100 % ------> 800 (100 * 8 = 800)\n90 % ------> 720 (90 * 8 = 720)\nSelling price = Rs.720/-\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf there are 200 questions in a 3 hr examination. Among these questions are 100 type A problems, which requires twice as much as time be spent than the rest of the type B problems. How many minutes should be spent on type A problems?\n\n### Options:\nA. 72 min\nB. 62 min\nC. 70 min\nD. 74 min\nE. 120 min\n\n### Answer:\nx=time for type B prolems\n2x=time for type A problem\ntotal time=3hrs=180min\n100x+100*2x=180\nx=180/300\nx=0.6\ntime taken for type A problem=100*2*0.6=120min\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train 800 m long is running at a speed of 78 km/hr. If it crosses a tunnel in 2 min, then the length of the tunnel is?\n\n### Options:\nA. 2898\nB. 1800\nC. 500\nD. 297\nE. 435\n\n### Answer:\nSpeed = 78 * 5/18 = 65/3 m/sec.\nTime = 2 min = 120 sec.\nLet the length of the train be x meters.\nThen, (800 + x)/120 = 65/3\nx = 1800 m.\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJack has two dice, one has six equally probable sides, labeled 1, 2, 3, 4, 5, 6, and the other has seven equally probable sides, labeled 1, 2, 3, 4, 5, 6, 7. If Jack rolls both dice what is the probability that both of the numbers will be 7?\n\n### Options:\nA. 3/14\nB. 1/7\nC. 0\nD. 1/2\nE. 12/21\n\n### Answer:\nMETHOD-1\nProbability that the number on first die is 7 = 0\nProbability that the number on Second die is 7 = 1/7 [Because 1 out of 7 faces is 7]\nProbability that Both Dice result in odd numbers = (0)*(1/7) = 0\nAnswer: Option C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n10 men and 15 women together can complete a work in 6 days. It takes 100 days for one man alone to complete the same work. How many days will be required for one woman alone to complete the same work?\n\n### Options:\nA. 127 days\nB. 667 days\nC. 177 days\nD. 187 days\nE. 225 days\n\n### Answer:\n1 man's 1 day work = 1/100\n(10 men + 15 women)'s 1 day work = 1/6\n15 women's 1 day work = (1/6 - 10/100) = 1/15\n1 woman's 1 day work = 1/225\n1 woman alone can complete the work in 225 days.\nAnswer:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n3 pumps, working 8 hours a day, can empty a tank in 2 days. How many hours a day must 10 pumps work to empty the tank in 1 day?\n\n### Options:\nA. 4.8\nB. 3.6\nC. 1.1\nD. 1.2\nE. 1.3\n\n### Answer:\n3 pumps take 16 hrs total (8 Hrs a day)\nIf 1 pump will be working then, it will need 16*3=48 hrs\n1 pump need 48 Hrs\nIf I contribute 10 pumps then\n48/10=4.8 hrs.\nanswer :A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe length of rectangle is thrice its breadth and its perimeter is 88 m, find the area of the rectangle?\n\n### Options:\nA. 432 sq m\nB. 363 sq m\nC. 452 sq m\nD. 428 sq m\nE. 525 sq m\n\n### Answer:\n2(3x + x) = 88\nl = 33 b = 11\nlb = 33 * 11 = 363\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nShekhar started a business investing Rs.25,000 in 1999.In 2000,he invested an additional amount of Rs.10,000 and Rajeev joined him with an amount of Rs.35,000.In 2001,Shekhar invested another additional amount of Rs.10,000 and Jatin joined them with an amount of Rs.35,000.What will be Rajeev\u2019s share in the profit of Rs.1,80,000 earned at the end of 3 years from the start of the business in 1999 ?\n\n### Options:\nA. Rs.45,000\nB. Rs.60,000\nC. Rs.70,000\nD. Rs.75,000\nE. None of these\n\n### Answer:\nSolution\nShekhar : Rajeev : Jatin\n= (25000x12+35000x12+45000x12) :(35000x24) : (35000x12)\n= 1260000 : 840000 : 420000 = 3 : 2 : 1.\n\u2234 Rajeev\u2019s share = Rs.(18000x2/6) = Rs. 60,000. Answer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n1,5,6 ,25, 26,30,31, 125,126,130,131,150,151,155,156,\u2026\u2026\u2026 What is the value of 33rd term in the\ngiven series\n\n### Options:\nA. 3124\nB. 3125\nC. 3126\nD. 3127\nE. 3128\n\n### Answer:\n1st terms gives 2nd and 3rd terms\n1st term is 1\n2nd term 1*5=5 3rd term= 5+1=6\nsimilarly,\n4th term =5*5=25 5th term=25+1=26\n1st term gives 2nd and 3rd values\n2nd term gives 4th and 5th values\nlke wise\n16th term gives 32nd and 33rd values\n16 th term is 125*5=625\n32nd term is 625*5=3125 and 33rd value is 3126\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the number of square tiles to cover the floor of a room measuring 6.5 m * 8.5 m leaving 0.25 m space around the room. A side of square tile is given to be 25 cms?\n\n### Options:\nA. 768\nB. 476\nC. 429\nD. 428\nE. 413\n\n### Answer:\nFloor area to be covered by tiles = 6 * 8 = 48\ntiles area = 0.25 * 0.25 =0.0625\nNo. of tiles = 48/0.0625 = 768\nAnswer : A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train moves fast a telegraph post and a bridge 264 m long in 8 sec and 20 sec respectively. What is the speed of the train?\n\n### Options:\nA. 79.7\nB. 79.8\nC. 76.2\nD. 79.2\nE. 29.2\n\n### Answer:\nLet the length of the train be x m and its speed be y m/sec.\nThen, x/y = 8 => x = 8y\n(x + 264)/20 = y\ny = 22\nSpeed = 22 m/sec = 22 * 18/5\n= 79.2 km/hr.\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 213 \u00d7 16 = 3408, then 1.6 \u00d7 21.3 is equal to :\n\n### Options:\nA. 0.3408\nB. 3.408\nC. 34.08\nD. 340.8\nE. None of these\n\n### Answer:\nSolution\n1.6 \u00d7 21.3 = (16/10x 213/10)= (16x 213/100) = 3408/100 = 34.08. Answer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the sum The difference between the compound and S.I. on a certain sum of money for 2 years at 10% per annum is Rs. 100 of money?\n\n### Options:\nA. 1500\nB. 6000\nC. 2500\nD. 1400\nE. 2000\n\n### Answer:\nP = 100(100/10)2 => P = 2000\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\ny = 248 - 198x\nWhich of the following values of x gives the greatest value of y in the equation above?\n\n### Options:\nA. 200\nB. 100\nC. 0.5\nD. -5\nE. 4\n\n### Answer:\nClearly, the negative value of x will result in maximum value of y.\nDon't even look at the rest of the answer choices as only one negative value is being present.\nAnswer is D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAt 1:00, Annie starts to bicycle along a 84 mile road at a constant speed of 14 miles per hour. Thirty minutes earlier, Scott started bicycling towards Annie on the same road at a constant speed of 12 miles per hour. At what time will they meet?\n\n### Options:\nA. 2:30\nB. 3:00\nC. 4:00\nD. 5:00\nE. 6:00\n\n### Answer:\nIn the first 30 minutes, Scott can travel 6 miles, so there are 78 miles left.\nTogether Annie and Scott can complete 26 miles.\n78/26 = 3, so they will meet 3 hours after 1:00.\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA and B go around a circular track of length 600 m on a cycle at speeds of 24 kmph and 60 kmph. After how much time will they meet for the first time at the starting point?\n\n### Options:\nA. 120 sec\nB. 176 sec\nC. 178 sec\nD. 180 sec\nE. 189 sec\n\n### Answer:\nTime taken to meet for the first time at the starting point\n= LCM { length of the track / speed of A , length of the track / speed of B}\n= LCM { 600/ (24 * 5/18) , 600/ (60 * 5 /18) }\n=180 sec.\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train 350 m long, running with a speed of 63 km/hr will pass a tree in?\n\n### Options:\nA. 22 sec\nB. 16 sec\nC. 17 sec\nD. 88 sec\nE. 20 sec\n\n### Answer:\nSpeed = 63 * 5/18 = 35/2 m/sec\nTime taken = 350 * 2/35 = 20 sec\nAnswer:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA freight elevator can carry a maximum load of 1100 pounds. Sean, who weighs 200 pounds, is in the elevator with two packages weighing 150 pounds and 280 pounds. If he needs to fit three more packages in the elevator that weigh as much as possible without exceeding the elevator limit, what is the difference between their average and the average of the two packages already in the elevator?\n\n### Options:\nA. 59\nB. 85\nC. 190\nD. 215\nE. 210\n\n### Answer:\nThe average of existing 2 package is150 + 280/2 = 430/2 = 215\nRemaining allowed weight = 1100 - 200 - 430 = 470.\nallowed per package = 470 / 3 = 156\nSo difference in average of existing and allowable = 215 - 156 = 59\nHence A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFive bells begin to toll together at 12:00 noon and toll respectively at intervals of 4, 5, 6, 8, and 9. seconds. Not including the toll at 12:00 noon, how many more times will all five bells toll together before 3:01 pm (i.e. three hours and one minute later)?\n\n### Options:\nA. 25\nB. 30\nC. 35\nD. 40\nE. 45\n\n### Answer:\nThe least common multiple is 2*2*2*3*3*5=360.\n10860 seconds / 120 = 30 + remainder.\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf b < 3 and 3x - 3b = 0, which of the following must be true?\n\n### Options:\nA. x > -3\nB. x < 2\nC. x = 3\nD. x < 3\nE. D. x > 3\n\n### Answer:\n3x - 3b = 0\nTherefore, 3x = 3b\nAs, b<3\n3x < 3(3)\ni.e x < 3\nAnswer : D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA husband and wife can complete a certain task in 1 and 2 hours respectively. Their children, Rae and Herman, can complete the same task in 4 and 5 hours, respectively. What is the ratio of the couple's time working together to complete the task to the children's time working together to complete the task?\n\n### Options:\nA. a)15:46\nB. b)3:10\nC. c)12:23\nD. d)5:18\nE. e)10:3\n\n### Answer:\ncouples one hour work=1/1+1/2=3/2\nso total time=2/3..\nnow, kids one hour work=1/4+1/5=9/20\nso total time=20/9..\nratio=2/3:20/9=3/10\nans B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n-20 , -16 , -12 , -8 ....\nIn the sequence above, each term after the first is 4 greater than the preceding term. Which of the following could not be a term in the sequence?\n\n### Options:\nA. 0\nB. 200\nC. 440\nD. 668\nE. 762\n\n### Answer:\nSimplifying the question into easier words we just need to find which of the numbers is not divisible by 4\nclearly the answer is 762 because if we divide 762 by 4 we get a remainder of 2\nCorrect answer - E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn 1990 a total of 100 earthquakes occurred worldwide, some but not all of which occurred in Asia. If 20 of these earthquakes occurred in Asia, which of the following represents the ratio of the number of earthquakes that occurred in Asia to the number that did NOT occur in Asia?\n\n### Options:\nA. 1/7\nB. 1/6\nC. 1/2\nD. 1/4\nE. 1/3\n\n### Answer:\nWe're given a couple of facts to work with:\n1) There were a total of 100 earthquakes\n2) Of those earthquakes, 20 of them occurred in Asia\nWe're asked for the ratio of the number of earthquakes that occurred IN ASIA to the number of earthquakes that DID NOT occur in Asia.\nThus, there were 80 earthquakes that DID NOT occur in Asia....\nThe answer to the question is 20/80 ie. 1/4\nAnswer : D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA person buys an article at Rs.500. At what price should he sell the article so as to make a profit of 20%?\n\n### Options:\nA. 600\nB. 729\nC. 278\nD. 268\nE. 308\n\n### Answer:\nCost price = Rs.500\nprofit = 20% of 500 = Rs.100\nSelling price = Cost price + Profit\n= 500 + 100 = 600\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFour angles of a quadrilateral are in G.P. Whose common ratio is an intiger. Two of the angles are acute while the other two are obtuse. The measure of the smallest angle of the quadrilateral is\n\n### Options:\nA. 12\nB. 24\nC. 36\nD. 46\nE. 52\n\n### Answer:\nLet the angles be a, ar, ar 2, ar 3.\nSum of the angles = a ( r 4- 1 ) /r -1 = a ( r 2 + 1 ) ( r + 1 ) = 360\na< 90 , and ar< 90, Therefore, a ( 1 + r ) < 180, or ( r 2 + 1 ) > 2\nTherefore, r is not equal to 1. Trying for r = 2 we get a = 24\nTherefore, The angles are 24, 48, 96 and 192.\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a colony of 70 residents, the ratio of the number of men and women is 5: 2. Among the women, the ratio of the educated to the uneducated is 1 : 4. If the ratio of the number of educated to uneducated persons is 8 : 27, then find the ratio of the number of educated to uneducated men in the colony?\n\n### Options:\nA. A)1:5\nB. B)1:1\nC. C)1:8\nD. D)1:9\nE. E)1:3\n\n### Answer:\nNumber of men in the colony = 5/7 * 70 = 50.\nNumber of women in the colony = 2/7 * 70 = 20.\nNumber educated women in the colony = 1/5 * 30 = 6.\nNumber of uneducated women in the colony = 4/5 * 50 = 24.\nNumber of educated persons in the colony = 8 /35 * 70 = 16.\nAs 6 females are educated, remaining 10 educated persons must be men.\nNumber of uneducated men in the colony = 50 - 10 = 40.\nNumber of educated men and uneducated men are in the ratio 10 : 40 i.e., 1:4.\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf y exceeds x by 20%, then x is less than y by?\n\n### Options:\nA. 16%\nB. 16 1/3 %\nC. 16 2/3 %\nD. 16 3/5 %\nE. None of these\n\n### Answer:\nExplanation:\nX=100\ty=120\n120------20\n100-------? => 16 2/3%\nANSWER IS C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man can row downstream at 18 kmph and upstream at 12 kmph. Find the speed of the man in still water and the speed of stream respectively?\n\n### Options:\nA. 3\nB. 5\nC. 6\nD. 4\nE. 9\n\n### Answer:\nLet the speed of the man in still water and speed of stream be x kmph and y kmph respectively.\nGiven x + y = 18 --- (1)\nand x - y = 12 --- (2)\nFrom (1) & (2) 2x = 30 => x = 15, y = 3. Answer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average salary of a person for the months of January, February, March and April is Rs.8000 and that for the months February, March, April and May is Rs.8800. If his salary for the month of May is Rs.6500, find his salary for the month of January?\n\n### Options:\nA. s.3300\nB. s.4570\nC. s.4500\nD. s.4550\nE. s.2500\n\n### Answer:\nSum of the salaries of the person for the months of January, February, March and April\n= 4 * 8000 = 32000 ----(1)\nSum of the salaries of the person for the months of February, March, April and May\n= 4 * 8800\n= 35200 ----(2)\n(2)-(1) i.e. May - Jan = 3200\nSalary of May is Rs.6500\nSalary of January = Rs.3300\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe jogging track in a sports complex is 627 m in circumference. Deepak and his wife start from the same point and walk in opposite directions at 4.5 km/hr and 3.75 km/hr respectively. They will meet for the first time in?\n\n### Options:\nA. 4.56 min\nB. 5.28 min\nC. 5.08 min\nD. 9.28 min\nE. 5.988 min\n\n### Answer:\nClearly, the two will meet when they are 627 m apart.\nTo be (4.5 + 3.75) = 8.25 km apart, they take 1 hour.\nTo be 627 m apart, they take (100/825 * 627/1000) hrs = (627/8250 * 60) min = 4.56 min.\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA 260 m long train running at the speed of 120 km/hr crosses another train running in opposite direction at the speed of 80 km/hr in 9 sec. What is the length of the other train ?\n\n### Options:\nA. 240 mts\nB. 270 mts\nC. 260 mts\nD. 250 mts\nE. 280 mts\n\n### Answer:\nExplanation:\nRelative speed = 120 + 80 = 200 km/hr.\n= 200 x 5/18 = 500/9 m/sec.\nLet the length of the other train be L mts.\nThen, (L + 260)/9 = 500/9 => L = 240 mts.\nANSWER IS A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSix students are equally divided into 3 groups, then, the three groups were assigned to three different topics. How many different arrangements X are possible?\n\n### Options:\nA. 30\nB. 60\nC. 90\nD. 180\nE. 540\n\n### Answer:\n90 is the number of ways you can assign 3 teams formed out of 12 people to 3 different tasks.\nBut now you can order the 3 tasks in 3! ways. T1 T2 T3 or T2 T1 T3.... etc etc.\nI was confused between 90 and 540 but since question used the wordarrangementsdecided to go with complete arrangements X including the order of tasks.\ncould you explain the highlighted step... i'm getting 90 = 15 * 3!\nsuppose the students are numbered 1,2,3,4,5,6 and tasks are X,Y and Z\none of the 15 possible ways of forming teams is 12, 34, 56. these teams can be assigned to 3 tasks in 3! = 6 ways\nX--\tY--\tZ\n12--\t34--\t56\n12--\t56--\t34\n34--\t12--\t56\n34--\t56--\t12\n56--\t12--\t34\n56--\t34--\t12\nso the answer should be 15*6 = 90\nBut now you can fruther decide which task you want to perform first X Y or Z..C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRohit and Rohan can complete a work in 12 days and 6 days respectively. How much time will they take when working together?\n\n### Options:\nA. 4\nB. 3\nC. 5\nD. 2\nE. 1\n\n### Answer:\nTime taken by Rohit and Rohan = xy/ x+y\n=12*6/(12+6)\n= 4 days\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the money was put in for the same duration of time by A,B and C, three business partners and four times A\u2019s capital is equal to 6 times B\u2019s capital is equal to 10 times C\u2019s capital. Determine that out of a total profit of Rs 4650 what is C\u2019s share?\n\n### Options:\nA. Rs 9008\nB. Rs 906\nC. Rs 900\nD. Rs 905\nE. Rs 901\n\n### Answer:\nExplanation:\nIt is given that business partnership is independent of time in this case as all the investors have invested their money for same amount of time.\nLet A\u2019s capital be x, B\u2019s capital be y and C\u2019s capital be z.\n=>x+y+z = 4650\n=> 4x = 6y = 10z\n=>C\u2019s share is z so let us solve the question w.r.t. z\n=>x = 5z/2\n=>y = 5z/3\n=>(5z/2)+(5z/3)+(z) = 4650\n=>31z = 4650*6\n=>z = 900\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich of the following is not the square of an integer?\n\n### Options:\nA. 275625\nB. 385641\nC. 426437\nD. 532900\nE. 318096\n\n### Answer:\nThe square of an integer (n^2) can have only the following units digit:\n0, if the units digit of n is 0;\n1, if the units digit of n is 1 or 9;\n4, if the units digit of n is 2 or 8.\n5, if the units digit of n is 5;\n6, if the units digit of n is 6 or 4;\n9, if the units digit of n is 3 or 7.\nThe square of an integer cannot have the units digit of 2, 3, 7, or 8.\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAt what time between 5 and 6 o' clock are the hands of a 3 minutes apart ?\n\n### Options:\nA. 24\nB. 55\nC. 66\nD. 88\nE. 21\n\n### Answer:\nIn this type of problems the formuae is\n(5*x+ or - t)*12/11\nHere x is replaced by the first interval of given time. Here x is 5.\nt is spaces apart\nCase 1 : (5*x + t) * 12/11\n(5*5 + 3) * 12/11\n28 * 12/11 = 336/11= min\ntherefore the hands will be 3 min apart at 31 5/11 min past 5.\nCase 2 : (5*x - t) * 12/11\n(5*5 -3 ) * 12/11\n22 *12/11 = 24 min\ntherefore the hands will be 3 min apart at 24 min past 5\nAnswer: A) 24min\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRight triangle PQR is to be constructed in the xy-plane so that the right angle is at P and PR is parallel to the x-axis. The x and Y coordinates of P,Q and R are to be integers that satisfy the inequalitites -4\u2264 X\u2264 5 and 6\u2264 y\u2264 16. How many different triangles with these properties could be constructed?\n\n### Options:\nA. 110\nB. 1100\nC. 9900\nD. 10000\nE. 12100\n\n### Answer:\ntotal values for x=10;y=11\nx1,y1=10*11.......................coordinates of 1st pnt\nx2,y2=9*1(y2=y1)............... coordinates of 2nd pnt y coordinates will be same as that of 1st pnt bcoz it is parallel to x axis\nx3,y3=1*10(x2=x3)..........coordinates of 3rd pt. x coordinates will be same as that of 2nd point bcoz to make a right angle it has to be parallel to y axis\ntot ways=10*11*9*1*1*10=9900\nANS:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how many ways can 11 books on English and 9 books on French be placed in a row on a shelf so that two books on French may not be together?\n\n### Options:\nA. 220.\nB. 240\nC. 260\nD. 280\nE. 300\n\n### Answer:\nWe have 11 English and 9 French books, no French books should be adjacent.\nImagine 11 English books in a row and empty slots like below:\n*E*E*E*E*E*E*E*E*E*E*E*\nNow if 9 French books would be placed in 12 empty slots, all French books will be separated by English books.\nSo we can \"choose\" 9 empty slots from 12 available for French books, which is 12C9=220.\tANS:A\n_________________\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a bag there are a certain number of red balls and blue balls. The probability of picking up exactly 1 blue ball when 2 balls are randomly drawn, is 1/2. Which of the following is the ratio of the number of red balls to blue balls in the bag\n\n### Options:\nA. 5:1\nB. 1:6\nC. 1:4\nD. 1:46\nE. 1:1\n\n### Answer:\nsince the probability of drawing a blue ball out of two picks is 1/2.\nthe ratio of the blue ball to red balls should be 1:1\nAnswer : E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are some pigeons and hares in a zoo. If heads are counted, there are 100. If legs are counted, there are 580. The number of hares in the zoo is?\n\n### Options:\nA. 210\nB. 182\nC. 190\nD. 137\nE. 371\n\n### Answer:\n100*2 = 200\n580\n-----\n380\n1----2\n?----380 = 190\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a, b, and c are integer and ab + c is odd, which of the must be true?\nI. a + c is odd\nII. b + c is odd\nIII. abc is even\n\n### Options:\nA. I only\nB. II only\nC. III only\nD. I and III only\nE. II and III only\n\n### Answer:\nPersonally I'd approach this question in another way.\nab+c=odd, means:\n1. ab=even (which means that at least one of them is even) and c=odd\nOR:\n2. ab=odd (which means that both are odd) and c=even\nWe can see that in both cases at least one is even thus option III (abc=even) is always true.\nNow, for I: if c=odd(case 1) and a=odd(so b=even) then a+c=even\u2260odd, so this option is not always true.\nExactly the same for option II: if c=odd (case 1) and b=odd (so a=even) then b+c=even\u2260odd, so this option is not always true.\nAnswer: C (III only).\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHeinz produces tomato puree by boiling tomato juice. The tomato puree has only 20% water while the tomato juice has 90% water. How many liters of tomato puree will be obtained from 40 litres of tomato juice?\n\n### Options:\nA. 2.8 liters.\nB. 2.5 liters.\nC. 5 liters.\nD. 2.6 liters.\nE. 2.1 liters.\n\n### Answer:\nAnswer:\nExplanation:\nIn each of the solutions, there is a pure tomato component and some water. So while boiling, water evaporates but tomato not. So we equate tomato part in the both equations.\n\u00e2\u2021\u2019\u00e2\u2021\u2019 10%(40) = 80%(x)\n\u00e2\u2021\u2019\u00e2\u2021\u2019 x = 5 liters.\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nif 50% of (x-y) = 20% of (x+y) then what percent of x is y?\n\n### Options:\nA. 2.5%\nB. 10%\nC. 5%\nD. 15%\nE. 43%\n\n### Answer:\n50% of (x-y)=20% of(x+y)\n(50/100)(x-y)=(20/100)(x+y)\n5(x-y)=2(x+y)\n3x=7y\nx=7/3y\ntherefore required percentage\n=((y/x) X 100)% = ((y/(7/3)y) X 100) =43%\nAnswer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJane can make a handcrafted drum in 4 weeks. Zane can make a similar handcrafted drum in 6 weeks. If they both work together, how many weeks will it take for them to produce 15 handcrafted drums?\n\n### Options:\nA. 30\nB. 36\nC. 70\nD. 80\nE. 150\n\n### Answer:\nJane can make a handcrafted drum in 4 weeks. Zane can make a similar handcrafted drum in 6 weeks.\u201d Jane\u2019s rate is (1 drum)/(4 weeks) = 1/4. Zane\u2019s rate is (1 drum)/(6 weeks) = 1/6. The combined rate of Jane + Zane is\nR = 1/4 + 1/6 = 3/12 + 2/12 = 5/12\nThat\u2019s the combined rate. We need to make 15 drums \u2014 we have a rate and we have an amount, so use the \u201cart\u201d equation to solve for time:\nT = A/R = 15/(5/12) = 15*(12/5) = (15/5)*12 = 3*12 = 36\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTough and Tricky questions: Word Problems.\nIt takes Sarah 44 minutes to do one oil change, and it takes Alice 20 minutes. If Sarah and Alice both begin doing oil changes at exactly 9:00 a.m. without pausing, when is the first time at which they will finish changing the oil of a car simultaneously?\n\n### Options:\nA. 10:00 a.m.\nB. 10:42 a.m.\nC. 12:00 a.m.\nD. 12:40 p.m.\nE. 2:00 p.m.\n\n### Answer:\nLCM of 2044\n20 = 2 * 2 * 5\n44 = 2 * 2 * 11\nLCM = 2 * 2 * 5 * 11 = 220 = 3 hour 40 minutes\n1240PM\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA straight pipe 1 yard in length was marked off in halves and also in thirds. If the pipe was then cut into separate pieces at each of these markings, which of the following gives all the different lengths of the pieces, in fractions of a yard?\n\n### Options:\nA. 1/6 and 1/4 only\nB. 1/6 and 1/3 only\nC. 1/6, 1/4, and 1/3\nD. 1/12, 1/6 and 1/4\nE. 1/12, 1/6, and 1/3\n\n### Answer:\nGenerally fast way to solve such problem is writing the different marks in ascending/descending order with same denominator:\nHere 2th : 0/2, 1/2, 2/2\nand 3rd : 0/3, 1/3, 2/3, 3/3\nNow with understood common denominator 6 write the numbers : for 2th : 0,3,6 and for 3rd : 0,2,4,6\nNow comine : 0,2,3,4,6\nNow find the cut with denominator 6 (Substracrt adjacent terms : 1/3, 1/6, 1/6, 1/3 i.e. 1/3 and 1/6 after removing duplicates.\nanswer : B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAnthony and Cindy were each given x dollars in advance to perform at a community festival. Anthony eventually performed on all 14 days of the festival, while Cindy performed on 5 fewer days than Anthony performed. If Cindy gives Anthony y dollars of her advance payment so that they would have each received the same daily rate, what was Anthony paid in advance, in terms of y?\n\n### Options:\nA. 2y\nB. 4y\nC. 23/5y\nD. 6y\nE. 10y\n\n### Answer:\nAnthony performed for 14 days meansw Cindy performed for(14-5)=9 days.\nIf Cindy gives y dollars to Anthony their Daily rate will be equal.It means\n(x+y)/14=(x-y)/9\nSolving we get, x=23/5y\nNow Anthony's Advance is x=23.5y .So answer should be C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA rectangular floor measures 2 by 3 meters. There are 5 white, 5 black, and 5 red parquet blocks available. Each block measures 1 by 1 meter. In how many different f colors patterns can be floor be parqueted?\n\n### Options:\nA. 104\nB. 213\nC. 3^5\nD. 705\nE. 726\n\n### Answer:\nTotal number of squares we need to fill = 6\nNumber of colors we have f= 3\nTherefore, total number of patterns = 3*3*3*3*3*3 = 729\nHowever, this is considering that we can have a case in which all tiles are the same color. Since we are given that the quantity of each tile is 5 and the number of tiles required is 6, we know that this case cannot be possible. Therefore we must subtract the cases in which all tiles will be of the same color (3 cases since there are 3 colors).\nThus our answer should be :729 - 3 = 726\nAnswer : E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA, B and C can do a piece of work in 24 days, 30 days and 40 days respectively. They began the work together but C left 10 days before the completion of the work. In how many days was the work completed?\n\n### Options:\nA. 12.5 days\nB. 16 days\nC. 18 days\nD. 11 days\nE. 38 days\n\n### Answer:\nOne day work of A, B and C = 1/24 + 1/30 + 1/40 = 1/10 Work done by A and B together in the last 10 days = 10*(1/24 + 1/30) = 3/4\nRemaining work = 1/4\nThe number of days required for this initial work = 2.5 days.\nThe total number of days required = 10 + 2.5 = 12.5 days.\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nwhat is the unit digit in [(6273)^1793x(625)^317x(341)^491]?\n\n### Options:\nA. 0\nB. 2\nC. 3\nD. 5\nE. None of them\n\n### Answer:\nUnit digit in (6374)^1793=Unit digit in (4)^1793\n=Unit digit in [(4^2)^896 x 4]\n=Unit digit in (6x4)=4\nUnit digit in (625)^317=Unit digit in (5)^317=5\nUnit digit in (341)^491=Unit digit in (1)^491=1\nRequired digit = Unit digit in (4x5x1)=0\nAnswer is 0\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 2^z is a factor of 24!, which of the following could be the value of z?\nI. 22\nII. 23\nIII. 24\n\n### Options:\nA. I \u200bonly\nB. II only\nC. I\u200b and II\nD. I, II, and III\nE. None\n\n### Answer:\n24! contains all numbers from 1 to 24. To find the factor with the highest power of 2, we count the number of multiples of 2, 4, 8 and 16.\nMultiples of 2 = 12\nMultiples of 4 = 6\nMultiples of 8 = 3\nMultiples of 16 = 1\nTotal count = 22\nThe answer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nCalculate the value of u: 16u^2-7u+2 = 125\n\n### Options:\nA. 5\nB. 2\nC. 4\nD. 1\nE. 3\n\n### Answer:\nUsing the elimination method substitute options for x and find the correct option.\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFor an upcoming charity event, a male vocalist has agreed to sing 5 out of 8 \u201cold songs\u201d and 3 out of 7 \u201cnew songs.\u201d How many ways can the singer make his selection?\n\n### Options:\nA. 25\nB. 50\nC. 150\nD. 217.78\nE. 600\n\n### Answer:\n=8C5*7C3\n=8*7/3*7*5/3\n=217.78\nAns = D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn what ratio must a grocer mix two varieties of pulses costing Rs. 15 and Rs. 20 per kg respectively so as to get a mixture worth Rs. 16.50 kg?\n\n### Options:\nA. 7:3\nB. 3:7\nC. 4:6\nD. 5:7\nE. 8:9\n\n### Answer:\nRequired rate = 3.50 : 1.50 = 7 : 3.\nANSWER A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAll factors of a positive integer X are multiplied and the product obtained is X^3. If X is greater than 1, how many factors does X have?\n\n### Options:\nA. 2\nB. 3\nC. 4\nD. 5\nE. 6\n\n### Answer:\nThe question can be done in seconds if you understand the properties of factors of a number. Note that every distinct factor of a number which is not a perfect square has a complementary factor.\nFor example,\nFactors of 6: 1, 2, 3, 6\n1 has a complementary factor 6 such that 1*6 = 6 (the original number)\n2 has a complementary factor 3 such that 2*3 = 6 (the original number)\nSo if you have a number, n, which is not a perfect square, and start multiplying its factors, you will get n to a certain power. the power will half of the number of factors. For example, 6 has 4 factors and when you multiply all 4 factors, you get 6^2 (2 is half of 4).\nSo if you know that the product of all factors is X^3, it means there must have been twice the number of factors i.e. 3*2 = 6 factors.\nE)\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 0 < x < 1 < y, which of the following must be true?\n\n### Options:\nA. 1 < 1/x < 1/y\nB. 1/x < 1 < 1/y\nC. 1/x < 1/y < 1\nD. 1/y < 1 < 1/x\nE. 1/y < 1/x < 1\n\n### Answer:\nSoln:\n0", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nX starts a business with Rs.45000. Y joins in the business after 3 months with Rs.30000. What will be the ratio in which they should share the profit at the end of the year?\n\n### Options:\nA. 1:2\nB. 2:1\nC. 1:3\nD. 3:1\nE. 4:2\n\n### Answer:\nExplanation:\nRatio in which they should share the profit\n= Ratio of the investments multiplied by the time period\n=45000\u00c3\u201412:30000\u00c3\u20149=45\u00c3\u201412:30\u00c3\u20149=3\u00c3\u201412:2\u00c3\u20149=2:1\nANSWER IS B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nif the annual rate of simple interest increases from 10% to 12.5% .Then a man\u2019s yearly income from an investment increases by Rs.1250. His principle amount is:\n\n### Options:\nA. Rs,45000\nB. Rs.50,000\nC. Rs. 60,000\nD. Rs.65,000\nE. Rs.75,000\n\n### Answer:\nLet the sum be Rs.x Then, (x*25/2*1/100) \u2013 (x*10*1/100)= 1250\n25x-20x = 250000 ;\nx=50000\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nCP of 2 buffaloes are $30,000. By selling 1 at a loss of 15% and other at a profit of 19%, he foundthat SP of both buffaloes is the same. Find the CP of each?\n\n### Options:\nA. $9,500\nB. $10,500\nC. $11,500\nD. $12,000\nE. $12,500\n\n### Answer:\nLet the C.P of 1st buffalo = x\n\u2234C.P of 2nd buffalo = 30,000 - x\nS.P of 1st buffalo = ( 100 - loss% )\n------------------- x C.P\n100\nS.P = 100 - 15x\n-----------= 85x/ 100\n100\nS.P of 2nd buffalo = ( 100 - Profit%)\n--------------------- x C.P\n100\nS.P = (100 + 19)(30,000- x) 119(30,000 -x)\n-------------------- = ----------------\n100 100\nS.P of 1st buffalo = S.P of 2nd buffalo\n85x/ 100 = 119 ( 30,000 - x)/ 100\n\u21d2 85x = 119(30,000 - x)\n\u21d2 85x = 3,570,000 - 119x\n\u21d2 85x + 119 x = 3,570,000\n\u21d2 204x = 3,570,000\n\u21d2 x = 3,570,000 / 204\n\u21d2 x = $17,500\nC.P of 1st buffalo = $17,500\nC.P of 2nd buffalo = 30,000 - 17,500 = $12,500\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf you flip a coin three times, what is the probability that you will get three heads?\n\n### Options:\nA. 1/4\nB. 1/5\nC. 1/6\nD. 1/7\nE. 1/8\n\n### Answer:\nThe probability of getting heads on a single flip is 1/2,\nThe probability of getting heads on each flip is P_1st * P_2nd * P_3rd,\nThus, P = (1/2)^3 = 1/8.\nAnswer = E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA shipment of 8 TV sets contains 6 black and white sets and 2 color sets. If 2 TV sets are to be chosen at random from this shipment, what is the probability that at least 1 of the 2 sets chosen will be a black and white set?\n\n### Options:\nA. 1/7\nB. 1/4\nC. 5/14\nD. 11/28\nE. 27/28\n\n### Answer:\n2/8 * 1/7 = 2/56\n1-(2/56) = 54/56 = 27/28\nAnswer E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA young girl counted in the following way on the fingers of her left hand. She started collang the thumb 1, the index finger 2, the middle finger 3, the ring finger 4, the little finger 5, then reversed direction calling the ring finger 6, the the middle finger 7, the index finger 8, the thumb 9 then back to the index finger for 10, the middel finger for 11, and so on. She counted up to 1995. She ended on her\n\n### Options:\nA. a) thumb\nB. b) the index finger\nC. c) the middle finger\nD. d) the ring finger\nE. e) the little finger\n\n### Answer:\nNotice the pattern. The thumb lansd up at numbers 1,9,17,25,33,... so every 8th number\nBy this patter the thumb is also at number 1993 (multiple of 8 + 1)\nHence 1995 has to be the middle finger\nAnswer is (C)\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain automobile company\u2019s best-selling model is the Speedster. The Speedster, like all of their other models, comes in coupe and convertible styles. 2/3 of the current inventory is Speedsters, of which 4/5 are convertibles. If there are 40 vehicles that are not Speedsters, how many Speedster convertibles are there?\n\n### Options:\nA. 30\nB. 64\nC. 60\nD. 70\nE. 90\n\n### Answer:\nTotal Vehicle = 2/3 of speedster + 1/3 of others.\nSpeedster convertibles = 2/3 total vehicle * 4 /5\nGiven : 1/3 constitutes 40 Vehicles. hence 2/3 constitutes 80\nSpeedster convertibls = 80 * 4/5 = 64\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA container contains a dry mixture of sand and stones. Mass of sand and stones in the container is in the ratio 1:3. If 12 kg sand is added to the container, the ratio of masses of sand and stones becomes 5:3. Originally, how much more was the mass of stones than sand in the container?\n\n### Options:\nA. 12\nB. 9\nC. 6\nD. 3\nE. 1\n\n### Answer:\nSuppose originally the mass of sand in the container was x. So the mass of stones, originally, would be 3x because mass of sand and stones in the container is in the ratio 1:3.\nIf 12 kg sand is added, mass of sand becomes x + 12, and the mass of stones remains unchanged. But now the ratio of the mass of sand and stones is 5:3.\nThis means,\n(x + 12)/3x = 5/3, which gives x = 3.\nSo originally, there was 3 kg sand and 9 kg stones.\nSo, the mass of stones was 6 kg more than the mass of sand.\nAns C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the CP of Rs 100 stock at 8 discount, with 1/5% brokerage?\n\n### Options:\nA. 92.9\nB. 96.3\nC. 92.2\nD. 96.7\nE. 92.8\n\n### Answer:\nExplanation:\nUse the formula,\nCP= 100 \u00e2\u20ac\u201c discount + brokerage%\nCP= 100-8+1/5\n92.2\nThus the CP is Rs 92.2.\nANSWER: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe least common multiple of positive integer w and 3-digit integer n is 690. If n is not divisible by 3 and w is not divisible by 2, what is the value of n?\n\n### Options:\nA. 115\nB. 230\nC. 460\nD. 575\nE. 690\n\n### Answer:\nThe LCM of n and w is 690 = 2*3*5*23.\nw is not divisible by 2, thus 2 goes to n\nn is not divisible by 3, thus 3 goes to w.\nFrom above:\nn must be divisible by 2 and not divisible by 3: n = 2*... In order n to be a 3-digit number it must take all other primes too: n = 2*5*23 = 230.\nAnswer: B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf xerox paper costs 5 cents a sheet and a buyer gets 10% discount on all xerox paper one buys after the first 200 papers and 20% discount after first 1000 papers, how much will it cost to buy 2500 sheets of xerox paper?\n\n### Options:\nA. $125\nB. $106\nC. $135\nD. $90\nE. $100\n\n### Answer:\n30 sec approach - solve it using approximation\n2500 sheet at full price, 5 cent = 125\n2500 sheet at max discount price, 4 cent = 100\nYour ans got to be between these two.\nAns B it is.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich of the following numbers is two more than the square of an odd integer?\n\n### Options:\nA. 14,173\nB. 14,361\nC. 15,253\nD. 15,737\nE. 16,131\n\n### Answer:\nIf a square has an odd unit's digit, then its ten's digit must be even.\nOnly 16,131-2 = 16,129 satisfies this condition.\nThe answer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train 385 meters long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going?\n\n### Options:\nA. 15\nB. 61\nC. 21\nD. 14\nE. 12\n\n### Answer:\nSpeed of train relative to man = (60 + 6) km/hr = 66 km/hr\n[66 * 5/18] m/sec = [55/3] m/sec.\nTime taken to pass the man = [385 * 3/55] sec = 21 sec\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe wheel of a motorcycle, 70 cm in diameter makes 40 revolutions in every 10 seconds. What is the speed of the motorcycle in km/hr\n\n### Options:\nA. 30.68 km/hr\nB. 31.68 km/hr\nC. 32.68 km/hr\nD. 33.68 km/hr\nE. None of these\n\n### Answer:\nExplanation:\nIn this type of question, we will first calculate the distance covered in given time.\nDistance covered will be, Number of revolutions * Circumference\nSo we will be having distance and time, from which we can calculate the speed. So let solve.\nRadius of wheel = 70/2 = 35 cm\nDistance covered in 40 revolutions will be\n40 * Circumference =40 * 2*\\pi*r =40\u22172\u221722/7\u221735=8800cm\n=8800/100m=88m\nDistance covered in 1 sec =88/10=8.8m\nSpeed=8.8m/s=8.8\u221718/5=31.68km/hr\nOption B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a span of 24 hours, how many times would the two hands of a clock point exactly in opposite directions ?\n\n### Options:\nA. 10\nB. 11\nC. 23\nD. 22\nE. 24\n\n### Answer:\nExplanation:\nIn every hour, the two hands (minute and hour) of the clock would be exactly opposite to each other once. But, from 5 o'clock to 6 o'clock and from 6 o'clock to 7 o'clock (a span of hours), they would be exactly opposite only once (at exact 6 o'clock).\nThus, during the span of 12 hours, the two hands would be exactly opposite 11 times. Hence, in the span of 24 hours they would be exactly opposite 22 times.\nANSWER D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf six persons sit in a row, then the probability that three particular persons are always together is\n\n### Options:\nA. 1/5\nB. 1/8\nC. 1/5\nD. 1/3\nE. 1/1\n\n### Answer:\nSix persons can be arranged in a row in 6! ways. Treat the three persons to sit together as one unit then there four persons and they can be arranged in 4! ways. Again three persons can be arranged among them selves in 3! ways. Favourable outcomes = 3!4! Required probability = 3!4!/6! = 1/5.Answer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nI. a3 - 305 = 207,\nII. b2 - 72 = -8 to solve both the equations to find the values of a and b?\n\n### Options:\nA. a > b\nB. a \u2265 b\nC. a < b\nD. a \u2264 b\nE. a = b or the relationship between a and b cannot be established.\n\n### Answer:\na3 = 512 => a = 8\nb2 = 64 => b = \u00b1 8\na \u2265 b\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average of first 14 even numbers is?\n\n### Options:\nA. 10\nB. 11\nC. 12\nD. 13\nE. 15\n\n### Answer:\nSum of 14 even numbers = 14 * 15 = 210\nAverage =210/14= 15\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA shopkeeper sold an article for Rs 2552.36. Approximately what was his profit percent if the cost price of the article was Rs 2400\n\n### Options:\nA. 4%\nB. 5%\nC. 6%\nD. 7%\nE. 8%\n\n### Answer:\nExplanation:\nGain % = (152.36*100/2400) = 6.34 % = 6% approx\nOption C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf TEAR is coded as 4657 and BOX is coded as 125. How is BETA coded?\n\n### Options:\nA. 1465\nB. 1645\nC. 1654\nD. 1456\nE. 1546\n\n### Answer:\ne=6 t-4 a-5 from the code TEAR, b-1 from the code BOX, ANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a train, travelling at a speed of 90 kmph, crosses a pole in 4 sec, then the length of train is?\n\n### Options:\nA. 281\nB. 125\nC. 288\nD. 100\nE. 121\n\n### Answer:\nD = 90 * 5/18 * 4\n= 100 m\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe distance between Delhi and Mathura is 155 kms. A starts from Delhi with a speed of 20 kmph at 7 a.m. for Mathura and B starts from Mathura with a speed of 25 kmph at 8 p.m. from Delhi. When will they meet?\n\n### Options:\nA. 10.50 a.m.\nB. 11.00 a.m.\nC. 10.30 a.m.\nD. 11.40 a.m.\nE. 1.40 a.m.\n\n### Answer:\nD = 155 \u00e2\u20ac\u201c 20 = 135\nRS = 20 + 25 = 45\nT = 135/45 = 3 hours\n8 a.m. + 3 hrs = 11.00 a.m.\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a light flashes every 10 seconds, how many times will it flash in 2/3 of an hour?\n\n### Options:\nA. 152\nB. 241\nC. 345\nD. 451\nE. 542\n\n### Answer:\nThere are 60 minutes in an hour.\nIn 2/3 of an hour there are (60 * 2/3) minutes = 40minutes.\nIn 2/3 of an hour there are (60 * 40) seconds = 2400 seconds.\nLight flashed for every 10 seconds.\nIn 2400 seconds 2400/10 = 240 times.\nThe count start after the first flash, the light will flashes 241 times in 2/3 of an hour.\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThree positive integers a, b, and c are such that their average is 18 and a \u2264 b \u2264 c. If the median is (a + 11), what is the least possible value of c?\n\n### Options:\nA. 21\nB. 23\nC. 25\nD. 27\nE. 29\n\n### Answer:\nSolution:\nWe know that the average value is 18 therefore (a+b+c)/3 = 18\nso a+b+c = 54\nand b = a + 11\ntherefore a + (a + 11) + c = 54\nThe least value of c is when c = b\nso take c = a + 11\nhence, a + (a + 11) + (a + 11) = 54\ni.e., a = 32/3 a non integer therefore c is not equal to b\nso take c = b+1 therefore c = a+12\na + (a + 11) + (a + 12) = 54\ni.e., a= 31/3 again a non integer therefore c is not equal to b+1\nnext take c= b+2 therefore c = a+13\na + (a + 11) + (a + 13) = 54\ni.e., a=30/3 = 10\nhence, a = 10, b = 21, and c = 23\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA 40 gallon solution of salt and water is 10% salt. How many gallons of water must be added to the solution in order to decrease the salt to 8% of the volume?\n\n### Options:\nA. 810\nB. 12\nC. 13\nD. 14\nE. 16\n\n### Answer:\nAmount of salt = 4.0\nAssume x gallons of water are added.\n4.0 / 40 + x = 8/100\n400 = 8x + 320\n8x = 80\nx = 10\nCorrect Option: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nInsert the missing number\n100,91,....,76,70\n\n### Options:\nA. 82\nB. 83\nC. 84\nD. 81\nE. 80\n\n### Answer:\nMissing number: 83\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf Rs. 762 be divided into three parts, proportional to 1/2:2/3:3/4, then the first part is?\n\n### Options:\nA. A)426\nB. B)526\nC. C)207\nD. D)199\nE. E)297\n\n### Answer:\nGiven ratio\n= 1/2:2/3:3/4 = 6:8:9\n1st part = 762 * 6/23\n= Rs. 199.\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn what time will a train 100 meters long cross an electric pole, if its speed is 126 km/hr\n\n### Options:\nA. 8.5 seconds\nB. 2.86 seconds\nC. 3.5 seconds\nD. 2.5 seconds\nE. 2.6 seconds\n\n### Answer:\nFirst convert speed into m/sec\nSpeed = 126*(5/18) = 35 m/sec\nTime = Distance/speed\n= 100/35 = 2.86 seconds\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average of 7 numbers is 15. If each number be multiplied by 5. Find the average of new set of numbers?\n\n### Options:\nA. A)110\nB. B)122\nC. C)90\nD. D)85\nE. E)75\n\n### Answer:\nExplanation:\nAverage of new numbers = 15 * 5 = 75\nAnswer: Option E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe radius of a cylinder is 12 m, height 21 m. the lateral surface area of the cylinder is:\n\n### Options:\nA. 1584\nB. 1854\nC. 1458\nD. 1485\nE. None of them\n\n### Answer:\nLateral surface area = 2\u03c0rh\n= 2 \u00d7 22/7 \u00d7 12 \u00d7 21\n= 44 \u00d7 36\n= 1584 m(power2)\nAnswer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are n members in a certain department, including Michael. Two representatives are to be selected to attend a company conference. If there are 28 possible combinations in which Michael is not selected, what is the value of n?\n\n### Options:\nA. 7\nB. 8\nC. 9\nD. 10\nE. 11\n\n### Answer:\nThe combinations of two people, in which Michael was not selected = 28\nThe number of ways two people can be selected from m people = m*(m-1)/2\nLet m be the number of people excluding Michael.\nThen m*(m-1) = 56 = 8*7\nThus, n = m + 1(Michael) = 9\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA tradesman fixed his selling price of goods at 30% above the cost price. He sells half the stock at this price, one-quarter of his stock at a discount of 15% on the original selling price and rest at a discount of 30% on the original selling price. Find the gain percentage altogether?\n\n### Options:\nA. 14.875%\nB. 15.375%\nC. 15.575%\nD. 16.375%\nE. 16.5%\n\n### Answer:\nSolution: Let CP = 100; then, marked price=130;\nNow,\nrevenue = [(1/2)*130+(1/4)*0.85*130+(1/4)*0.7*130]\n= 65+27.65+22.5 = 115.4;\n% profit = 15.4*100/100 = 15.4%.\nAnswer: Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nDuring a special promotion, a certain filling station is offering a 10 percent discount on gas purchased after the first 5 gallons. If Kim purchased 20 gallons of gas, and Isabella purchased 25 gallons of gas, then Isabella\u201fs total per-gallon discount is what percent of Kim\u201fs total per-gallon discount?\n\n### Options:\nA. 80%\nB. 107%\nC. 116.7%\nD. 120%\nE. 140%\n\n### Answer:\nKim purchased 20 gallons of gas. She paid for 5 + 0.9*15 = 18.5 gallons, so the overall discount she got was 1.5/20 = 7.5%.\nIsabella purchased 25 gallons of gas. She paid for 5 + 0.9*20 = 23 gallons, so the overall discount she got was .5/25 = 8%.\n8 is 8/7.5*100 = 107% of 7.5.\nAnswer: B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average age 8 members of a committee are the same as it was 2 years ago, because an old number has been replaced by a younger number. Find how much younger is the new member than the old number?\n\n### Options:\nA. 12 years\nB. 14 years\nC. 18 years\nD. 16 years\nE. 26 years\n\n### Answer:\n8 * 2 = 16 years\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nBy travelling at 50 kmph, a person reaches his destination on time. He covered two-third the total distance in one-third of the total time. What speed should he maintain for the remaining distance to reach his destination on time?\n\n### Options:\nA. 23 kmph\nB. 24 kmph\nC. 25 kmph\nD. 26 kmph\nE. 27 kmph\n\n### Answer:\nLet the time taken to reach the destination be 3x hours. Total distance = 50 * 3x = 150x km\nHe covered 2/3 * 150x = 100x km in 1/3 * 3x = x hours So, the remaining 50x km, he has to cover in 2x hours. Required speed = 50x/2x\n=25 kmph.\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how many different number of ways 4 man and 3 woman can sit on a bench such that girls always sit together.\n\n### Options:\nA. 700\nB. 720\nC. 730\nD. 750\nE. 770\n\n### Answer:\nOption 'B'\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the length of a bridge (in meters), which a train 140 meters long and travelling at 45 km/h can cross in 30 seconds?\n\n### Options:\nA. 205\nB. 220\nC. 235\nD. 250\nE. 265\n\n### Answer:\nspeed = 45 km/h = 45000 m / 3600 s = 25/2 m/s\nIn 30 seconds, the train can travel 25/2 * 30 = 375 meters\n375 = length of train + length of bridge\nlength of bridge = 375 - 140 = 235 meters\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nM = {-6, -5, -4, -3, -2}\nT = {-3, -2, -1, 0, 1, 2, 3, 4, 5}\nIf an integer is to be randomly selected from set M above and an integer is to be randomly selected from set T above, what is the probability that the product of the two integers will be negative?\n\n### Options:\nA. 0\nB. 3/7\nC. 2/5\nD. 1/2\nE. 5/9\n\n### Answer:\nWe will have a negative product only if 1, 2, 3, 4, or 5 are selected from set T.\nP(negative product) = 5/9\nThe answer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf [Y] denotes the least integer greater than or equal to Y and [Y] = 0, which of the following statements must be true?\n\n### Options:\nA. Y = 0\nB. 0 <= Y < 1\nC. 0 < Y <= 1\nD. -1 < Y <= 0\nE. -1 <= Y < 0\n\n### Answer:\nThe answer for this is 0 < = Y< = 1\nHowever it is not available in the options. The match to the above is-1 < Y <= 0\nAnswer = D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the least number of squares tiles required to pave the floor of a room 2 m 25 cm long and 1 m 35 cm broad?\n\n### Options:\nA. 15\nB. 20\nC. 40\nD. 44\nE. 48\n\n### Answer:\nLength of largest tile = H.C.F. of 225 cm and 135 cm = 45 cm.\nArea of each tile = (45 x 45) cm2.\nRequired number of tiles =225 x 135/(45^2)= 15.\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe length of a rectangle is two - fifths of the radius of a circle. The radius of the circle is equal to the side of the square, whose area is 2025 sq.units. What is the area (in sq.units) of the rectangle if the rectangle if the breadth is 10 units?\n\n### Options:\nA. 140\nB. 150\nC. 160\nD. 170\nE. 180\n\n### Answer:\nGiven that the area of the square = 2025 sq.units\n=> Side of square = \u221a2025 = 45 units\nThe radius of the circle = side of the square = 45 units\nLength of the rectangle = 2/5 * 45 = 18 units\nGiven that breadth = 10 units\nArea of the rectangle = lb = 18 * 10 = 180 sq.units\nAnswer: Option E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMr. Kramer, the losing candidate in a two-candidate election, received 942,568 votes, which was exactly 45 percent of all votes cast. Approximately what percent of the remaining votes would he need to have received in order to have won at least 50 percent of all the votes cast?\n\n### Options:\nA. 9%\nB. 12%\nC. 15%\nD. 17%\nE. 20%\n\n### Answer:\nLet me try a simpler one.\nLets assume that candidate got 45% votes and total votes is 100.\nCandidate won = 45\nRemaining = 55\nTo get 50%, candidate requires 5 votes from 100 which is 5% and 5 votes from 55.\n5/55= 1/11 = .09 = 9%\nWhich is approx 9%. Hence the answer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo vessels P and Q contain 62.5% and 87.5% of alcohol respectively. If 2 litres from vessel P is mixed with 4 litres from vessel Q, the ratio of alcohol and water in the resulting mixture is?\n\n### Options:\nA. 19 : 7\nB. 17 : 5\nC. 19 : 8\nD. 19 : 5\nE. 29 : 5\n\n### Answer:\nQuantity of alcohol in vessel P = 62.5/100 * 2 = 5/4 litres\nQuantity of alcohol in vessel Q = 87.5/100 * 4 = 7/2 litres\nQuantity of alcohol in the mixture formed = 5/4 + 7/2 = 19/4 = 4.75 litres\nAs 6 litres of mixture is formed, ratio of alcohol and water in the mixture formed\n= 4.75 : 1.25 = 19 : 5.\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThree friends Ravi, Baskar and Chandran divide $1200 amongs them in such a way that if $10, $20 and $15 are removed from the sums that Ravi, Baskar and Chandran received respectively, then the share of the sums that they got will be in the ratio of 10 : 12 : 13. How much did Chandran receive?\n\n### Options:\nA. $444\nB. $445\nC. $446\nD. $447\nE. $448\n\n### Answer:\nA+B+C = 1200\nGiven ratio 10:12:13\nLet us say the shares of A,B,C deducting 10,20,15 be a,b,c\na+b+c = 1200-45= 1155 = 35K\nc share = (1155X13)/35 = 429\nC = chandran share = 429+15 = 444\nOption A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf P represents the product of the first 14 positive integers, then P is not a\nmultiple of:\n\n### Options:\nA. a) 99\nB. b) 84\nC. c) 72\nD. d) 65\nE. e) 57\n\n### Answer:\na) 99 = 9*11\nb) 84 = 4*7*3\nc) 72 =9*11\nd) 65 = 5*13\ne) 57 =19*3\nsince 19 is not there in first 15 positive numbers it is the only possibility\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the missing number in the given sequence : 1,2,3,5,?,13,21,?\n\n### Options:\nA. 8 & 34\nB. 7 & 34\nC. 9 & 34\nD. 7 & 35\nE. 7 & 36\n\n### Answer:\n1+2=3\n2+3=5\n3+5=8\n5+8=13\n8+13=21\n13+21=34\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow long does a train 165 meters long running at the rate of 54 kmph take to cross a bridge 660 meters in length?\n\n### Options:\nA. 55 sec\nB. 40 sec\nC. 45 sec\nD. 30 sec\nE. 35 sec\n\n### Answer:\nT = (660 + 165)/54 * 18/5\nT = 55\nANSWER A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA and B can finish a work in 16 days while A alone can do the same work in 24 days. In how many days B alone will complete the work?\n\n### Options:\nA. 38\nB. 48\nC. 27\nD. 21\nE. 20\n\n### Answer:\nB = 1/16 \u2013 1/24 = 1/48 => 48 days . Answer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf p and q are positive integers and q \u2260 1, then pq(q \u22122) is\n\n### Options:\nA. pq^2\nB. pq^2+2pq\nC. pq^2-2pq\nD. pq^2+pq\nE. pq^2-6pq\n\n### Answer:\npq(q-2) = pq^2-2pq\nAnswer : C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA can do a piece of work in 4 days. B can do it in 15 days. With the assistance of C they completed the work in 24 days. Find in how many days can C alone do it?\n\n### Options:\nA. 0.391 days\nB. 0.491 days\nC. 0.331 days\nD. 1.391 days\nE. 0.301 days\n\n### Answer:\nC = 1/2 - 1/24 - 1/15 = 0.391 days\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n(0.8)(power 3) - (0.5)(power 3)/ (0.8)(power 2) + 0.40 + (0.5)(power 2) is:\n\n### Options:\nA. 0.6\nB. 0.5\nC. 0.35\nD. 0.3\nE. None of them\n\n### Answer:\nGiven expression\n= (0.8) (power 3) - (0.5)(power 3) / (0.8)(power 2) + (0.8 x 0.5) + (0.5)(power 2)\n= a (power 3) - b(power 3) / a(power 2) + ab + b(power 2)\n= (a - b)\n= (0.8- 0.5)\n= 0.30\nAnswer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA company pays 12.5% dividend to its investors. If an investor buys Rs.50 shares and gets 25% on investment, at what price did the investor buy the shares?\n\n### Options:\nA. 25\nB. 66\nC. 18\nD. 19\nE. 01\n\n### Answer:\nExplanation:\nDividend on 1 share = (12.5 * 50)/100 = Rs.6.25\nRs.25 is income on an investment of Rs.100\nRs.6.25 is income on an investment of Rs. (6.25 * 100)/25 = Rs.25\nANSWER: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf |5x-15| = 100, then find the sum of the values of x?\n\n### Options:\nA. 1\nB. -2\nC. 6\nD. -3\nE. 4\n\n### Answer:\n|5x-15| = 100\n5x-15 = 100 or 5x-15 = -100\n5x = 115 or 5x = -85\nx = 23 or x = -17\nsum = 23-17 = 6\nAnswer is C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSobha's father was 38 years of age when she was born while her mother was 36 years old when her brother four years younger to her was born. What is the difference between the ages of her parents?\n\n### Options:\nA. 4\nB. 6\nC. 8\nD. 10\nE. 2\n\n### Answer:\nAge of Sobha's father when Sobha was born =38\nAge of Sobha's mother when Sobha was born =36\u22124=32\nRequired difference of age =38\u221232=6\nAnswer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe area of a square garden is A square feet and the perimeter is p feet. If a=2p+15, what is the perimeter of the garden, in feet?\n\n### Options:\nA. 28\nB. 36\nC. 40\nD. 56\nE. 64\n\n### Answer:\nPerimeter of square = P\nSide of square = P/4\nArea of Square = (P^2)/16 =A\nGiven that A = 2P + 15\n(P^2)/16 = 2P + 15\nP^2 = 32P +240\nP^2 -32P -240 = 0\nP^2 -40P + 6P -240 = 0\nP(P-40)+6(P+40) = 0\n(P-40)(P+6) = 0\nP = 40 or- 6\nDiscarding negative value , P = 40\nAnswer is C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTickets numbered from 1 to 20 are mixed and then a ticket is selected randomly. What is the probability that the selected ticket bearsa number which is a multiple of 3?\n\n### Options:\nA. 1/7\nB. 2/9\nC. 3/10\nD. 3/11\nE. 3/14\n\n### Answer:\nHere, S = [1, 2, 3, 4, \u2026., 19, 20]\nLet E = event of getting a multiple of 3 = [3, 6, 9, 12, 15, 18]\nP (E) = n (E) / n (S) = 6 / 20 = 3/10\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOne water pump can fill half of a certain empty tank in 5 hours. Another pump can fill half of the same tank in 5.5 hours. Working together, how long will it take these two pumps to fill the entire tank?\n\n### Options:\nA. 1 7/13\nB. 5 5/8\nC. 3 1/4\nD. 5 5/21\nE. 3 1/2\n\n### Answer:\nOne pump can fill a tank in 5 hours and another in 5.5 hours\nso the rate at which both can half fill the tank is (1/5+1/5.5) => 21/55\nThus half of the tank can be filled in 55/21\nso for filling the complete tank => 55/21*2 = 110/21 =5 5/21\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFor how many different positive integers n is a divisor of n^3 + 8?\n.\n\n### Options:\nA. None\nB. One\nC. Two\nD. Three\nE. Four\n\n### Answer:\nn^3 + 8 = (n+2)(n^2-2n+4)\n--> 2 divisors possible, plus 1 and n\nwe have 4 divisors. ANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat should be added to 4440 so that it may become a perfect square?\n\n### Options:\nA. 44\nB. 45\nC. 46\nD. 47\nE. 49\n\n### Answer:\n67x67=4489\n4489-4440 = 49\nIf added to 49 get perfect square\nanswer =E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nEntry fee is Re.1.there are 3 rides each is of Re.1. total boys entering are 3000.total income is Rs.7200. 800 students do all 3 rides. 1400 go for atleast 2 rides.none go the same ride twice. then no of students who do not go any ride is?\n\n### Options:\nA. 1328\nB. 1000\nC. 2378\nD. 8287\nE. 1872\n\n### Answer:\nTotal entries are 3000 So fee collected through entry fee = 3000 x 1 = Rs.3000\nIncome generated through rides = 7200 - 3000 = 4200\nNow 800 went for 3 rides so total fee paid by these 800 = 800 x 3 = 2400\n(1400 - 800) went for 2 rides so fee paid by these 600 = 600 x 2 = 1200\nAssume K went for exactly 1 ride\nThen K x 1 + 1200 + 2400 = 4200 \u21d2\u21d2 K = 600\nSo number of boys who did not go for any ride = 3000 - (600 + 600 + 800 ) = 1000\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOf the employees in a company, 20 % are female who have a master degree. If 10 % of the female employees do not have a master degree, what percent of the employees in the company are female?\n\n### Options:\nA. 27.24%\nB. 26.22%\nC. 25.22%\nD. 22.25%\nE. 22.22%\n\n### Answer:\nLet E be total no. of employees and F be total no of female employees.\nQuestion asked what is F/E X 100%?\nNo. of female employees with Masters = 0.2 x E (From the question)\nNo. of female employees without masters = 0.1 x F (From the question)\nTherefore No. of female employees with masters = F - 0.1 F = 0.9 F\nThe 2 expressions equal each other therefore 0.9F = 0.2E; F/E = 0.2/0.9 = 22.22%\nAns: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n4 couples are seating at a round tables how many ways can the 4 women sit together\n\n### Options:\nA. 4!*4!\nB. 3!*4!\nC. 4!*3!\nD. 5!*4!\nE. 6!*4!\n\n### Answer:\n4 men can be arranged around a table in (4-1)!=3! ways;\nNow, we can place 4 women in 4 slots between any two men and arrange these women in this slot in 4! ways.\nSo, total # of ways is 3!*4*4!=4!*4!\nANS:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe mean of a data set is equal to 10 and its standard deviation is equal to 1. If we add 5 to each data value, then the mean and standard deviation become\n\n### Options:\nA. mean = 15 , standard deviation = 6\nB. mean = 10 , standard deviation = 6\nC. mean = 15 , standard deviation = 1\nD. mean = 10 , standard deviation = 1\nE. None\n\n### Answer:\nSolution\nSince 5 is added to all data values, the mean will also increase by 5 and becomes 15. But the standard deviation which measure the \"distance\" between the mean and the data values does not change.\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nBy selling an article at Rs.800, a shopkeeper makes a profit of 25%. At what price should he sell the article so as to make a loss of 35%?\n\n### Options:\nA. 228\nB. 480\nC. 267\nD. 416\nE. 276\n\n### Answer:\nSP = 800\nProfit = 25%\nCP = (SP)*[100/(100+P)]\n= 800 * [100/125]\n= 640\nLoss = 25% = 25% of 640 = Rs.224\nSP = CP - Loss = 640 - 224 = Rs.416\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nn is a whole number which when divided by 4 gives 3 as remainder. What will be the remainder when 2n is divided by 4 ?\n\n### Options:\nA. 2\nB. 4\nC. 7\nD. 9\nE. 11\n\n### Answer:\nLet n = 4q + 3. Then 2n = 8q + 6 = 4(2q + 1 ) + 2.\nThus, when 2n is divided by 4, the remainder is 2.\nOption A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the area of circle whose radius is 7m?\n\n### Options:\nA. 298\nB. 154\nC. 267\nD. 268\nE. 298\n\n### Answer:\n22/7 * 7 * 7 = 154\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a renowned city, the average birth rate is 6 people every two seconds and the death rate is 2 people every two seconds. Estimate the size of the population net increase that occurs in one day.\n\n### Options:\nA. 32,300\nB. 172,800\nC. 468,830\nD. 338,200\nE. 259,200\n\n### Answer:\nEvery 2 seconds, 4 persons are added (6-2). Every second 2 persons are added.\nIn a day 24hrs = 24 * 60 Minutes = 24 * 60 * 60 = 86400 seconds.\n86400 * 2 = 172800\nOption B is the answer.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average of 11 numbers is 10.9. If the average of the first six numbers is 10.5 and that of the last six numbers is 11.4, then the middle number is\n\n### Options:\nA. 21.5\nB. 11.5\nC. 61.5\nD. 41.5\nE. 31.5\n\n### Answer:\nMiddle numbers = [(10.5 x 6 + 11.4 x 6) - 10.9 x 11]\n= (131.4 - 119-9) = 11.5.\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe number of sailors on a ship is 78% more than the number of officers. The ratio of sailors to officers would be\n\n### Options:\nA. 33:25\nB. 47:20\nC. 47:25\nD. 89:50\nE. 97:50\n\n### Answer:\nSailor = 1.78 * Officer\nSailor/Officer = 1.78/1 = 178/100 = 89/50\nAnswer will be D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a rectangular coordinate system, what is the area of a quadrilateral whose vertices have the coordinates (4,-3), (4, 7), (10, 4), (10,-7)?\n\n### Options:\nA. 51\nB. 54\nC. 57\nD. 60\nE. 63\n\n### Answer:\nBy graphing the points, we can see that this figure is a trapezoid. A trapezoid is any quadrilateral that has one set of parallel sides, and the formula for the area of a trapezoid is:\nArea = (1/2) \u00d7 (Base 1 + Base 2) \u00d7 (Height), where the bases are the parallel sides.\nWe can now determine the area of the quadrilateral:\nArea = 1/2 \u00d7 (10 + 11) \u00d7 6 = 63.\nThe answer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain league has two divisions. The respective divisions had 11 and 13 teams qualify for the playoffs. Each division held its own double-elimination tournament -- where a team is eliminated from the tournament upon losing two games -- in order to determine its champion. The four division champions then played in a single-elimination tournament -- where a team is eliminated upon losing one game -- in order to determine the overall league champion. Assuming that there were no ties and no forfeits, what is the maximum number of games that could have been played in order to determine the overall league champion?\n\n### Options:\nA. 41\nB. 42\nC. 45\nD. 47\nE. 49\n\n### Answer:\nOverall, there can be 47 minuses. Tus, it is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe floor of a rectangular room is 17 m long and 12 m wide. The room is surrounded by a veranda of width 2 m on all its sides. The area of the veranda is :\n\n### Options:\nA. 124 m2\nB. 132 m2\nC. 148 m2\nD. 152 m2\nE. None of these\n\n### Answer:\nArea of the outer rectangle = 21 \u00c3\u2014 16 = 336 m2\nArea of the inner rectangle = 17 \u00c3\u2014 12 = 204 m2\nRequired area = (336 \u00e2\u20ac\u201c 204) = 132 m2\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a coin is tossed twice, what is the probability that on the first toss the coin lands tails and on the second toss the coin lands tails?\n\n### Options:\nA. 1/6\nB. 1/3\nC. 1/2\nD. 1/4\nE. 1\n\n### Answer:\nSince there are two options for how a coin can land (heads or tails), that means there is a 1/2 chance to land on tails and a 1/2 chance to land heads. To solve this problem you multiply each probability for each flip together. (1/2) chance to land tails the first time * (1/2) chance to land tails the second time = (1/4) chance to land tails both times.\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAt a conference table, 6 employees gather around a table. One of the employees is the manager and he sits at the head of the table. Two of the employees sit on either side of the table. How many different seating arrangements can be made with these six employees?\n\n### Options:\nA. 60\nB. 80\nC. 100\nD. 120\nE. 140\n\n### Answer:\nHead's sit is fixed. Now 5 people is left with 5 seats.\n5 people can sit on 5 seats in 5! ways or 120 ways.\nAns is D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA charity collected $1,299 from donors during the last month. If each donor gave at least $20, what is the greatest possible number of donors the charity could have?\n\n### Options:\nA. 60\nB. 64\nC. 66\nD. 68\nE. 69\n\n### Answer:\nMin fund = 20\nTotal = 1299\nThe closest multiple of 20 to 1299 is : 63\nWhich implies 63 people gave 20 and 1 person gave 39\nAns. B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the area of the square with the following coordinates: (x, y), (20, 20), (20, 11), (x, 11)?\n\n### Options:\nA. 49\nB. 64\nC. 75\nD. 81\nE. 96\n\n### Answer:\nTo find the area of a square, knowing the length of one side is sufficient.\nFrom the coordinates given, we can see that one side equals 9.\nThe area is 9*9 = 81.\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n3 boys and 7 girls can complete John work in 10 days. 4 boys and 6 girls need 8 days to complete the same work . In how many days will 10 girls complete the same work?\n\n### Options:\nA. 20 days\nB. 30 days\nC. 40 days\nD. 60 days\nE. 70 days\n\n### Answer:\nWork done by 4 boys and 6 girls in 1 day = 1/8\nWork done by 3 boys and 7 girls in 1 day = 1/10\nLet 1 man does m work in 1 day and 1 woman does w work in 1 day. The above equations can be written as\n4m + 6w = 1/8 ---(1)\n3m + 7w = 1/10 ---(2)\nSolving equation (1) and (2) , we get m=11/400 and w=1/400\nAmount of work 10 girls can do in John day = 10 \u00d7 (1/400) = 1/40\nIe, 10 girls can complete the work in 40 days\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA group consists of 4 men, 6 women and 5 children. In how many ways can 3 men, 2 women and 3 children selected from the given group?\n\n### Options:\nA. 987 ways\nB. 346 ways\nC. 600 ways\nD. 157 ways\nE. 134 ways\n\n### Answer:\nThe number of ways of selecting three men, two women and three children is:\n= \u2074C\u2083 * \u2076C\u2082 * \u2075C\u2083\n= (4 * 3 * 2)/(3 * 2 * 1) * (6 * 5)/(2 * 1) * (5 * 4 * 3)/(3 * 2 * 1)\n= 4 * 15 * 10\n= 600 ways.\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nI have a few sweets to be distributed. If I keep 2, 3 or 4 in a pack, I am left with one sweet. If I keep 5 in a pack, I am left with none. What is the minimum number of sweets I have to pack and distribute ?\n\n### Options:\nA. 5\nB. 7\nC. 23\nD. 4\nE. 2\n\n### Answer:\nClearly, the required number would be such that it leaves a remainder of 1 when divided by 2, 3 or 4 and no remainder when divided by 5.\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the average (arithmetic mean) of 2a+16, 3a-8 is 94, what is the value of a?\n\n### Options:\nA. 25\nB. 30\nC. 28\nD. 36\nE. 42\n\n### Answer:\nAM of 2a+16, 3a-8=2a+16+ 3a-8 /2= 5a+8/2\nGiven that 5a+8 /2 = 94\na= 36\nAnswer is D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA straight pipe 1 meter in length was marked off in fourths and also in thirds. If the pipe was then cut into separate pieces at each of these markings, which of the following gives all the different lengths of the pieces, in fractions of a meter?\n\n### Options:\nA. 1/6 and 1/4 only\nB. 1/4 and 1/3 only\nC. 1/12, 1/6 and 1/4\nD. 1/6, 1/4, and 1/3\nE. 1/12, 1/6, and 1/3\n\n### Answer:\nGenerally fast way to solve such problem is writing the different marks in ascending/descending order with same denominator:\nHere 4th : 0/4, 1/4, 2/4, 3/4, 4/4\nand 3rd : 0/3, 1/3, 2/3, 3/3\nNow with understood common denominator 12 write the numbers : for 4th : 0,3,6,9,12 and for 3rd : 0,4,8,12\nNow comine : 0,3,4,6,8,9,12\nNow find the cut with denominator 12 (Substracrt adjacent terms : 3/12, 1/12, 2/12, 1/12,3/12 i.e. 1/4, 1/12 and 1/6 after removing duplicates.\nAnswer - C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nUsing all the letters of the word \"THURSDAY\", how many different words can be formed?\n\n### Options:\nA. 7\nB. 8!\nC. 7\nD. 5\nE. 2\n\n### Answer:\nTotal number of letters\n= 8\nUsing these letters the number of 8 letters words formed is \u2078P\u2088\n= 8!.\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf m and n are nonzero integers and 390m = 150n, then mn must be divisible by\n\n### Options:\nA. 10\nB. 45\nC. 50\nD. 65\nE. 75\n\n### Answer:\n390m = 150n;\nm/n = 5/13.\nm is a multiple of 5 and n is a multiple of 13, therefore mn must be a multiple of 5*13 = 65.\nAnswer: D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain hall contains two cuckoo clocks. If the first clock chirps 20 times per hour and the second clock chirps 8 times per hour, and both clocks chirp for the first time at 2:03 pm, at what time will the first clock have chirped three times as many times as the second clock can chirp per hour?\n\n### Options:\nA. 2:40 pm\nB. 2:55 pm\nC. 3:12 pm\nD. 3:24 pm\nE. 3:45 pm\n\n### Answer:\nThe question is asking when the first clock will have chirped 24 times (3*8 chirps).\nThe first clock chirps once every 3 minutes.\nIf the first chirp is at 2:03, then the 24th chirp is at 72 minutes after 2:00.\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA boat having a length 5 m and breadth 2 m is floating on a lake. The boat sinks by 1cm when a man gets on it. The mass of the man is:\n\n### Options:\nA. 100 kg\nB. 60 kg\nC. 72 kg\nD. 96 kg\nE. None of these\n\n### Answer:\nExplanation:\nVolume of water displaced = (5 x 2 x 0.01) m3\n= 0.10 m3.\n\u2234 Mass of man = Volume of Water displaced x Density of water\n= (0.10 x 1000)kg\n= 100 kg.\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo trains of equal are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. The faster train passes the slower train in 36 sec. The length of each train is?\n\n### Options:\nA. 50\nB. 88\nC. 77\nD. 66\nE. 45\n\n### Answer:\nLet the length of each train be x m.\nThen, distance covered = 2x m.\nRelative speed = 46 - 36 = 10 km/hr.\n= 10 * 5/18 = 25/9 m/sec.\n2x/36 = 25/9 => x = 50.\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nCan you please walk me through how to best approach this problem? Thanks\nIf #p# = ap^3+ bp \u2013 1 where a and b are constants, and #-2# = 2, what is the value of #2#?\n\n### Options:\nA. 5\nB. 0\nC. -4\nD. -3\nE. -5\n\n### Answer:\n#p# = ap^3 + bp - 1\n#-2# = 2\nputting p = -2 in above equation\n-8a -(2b +1) = 2 or\n#-2# = (8a+2b+1) = -2\ntherefore 8a+2b = -3 .....(1\nnow putting p =2\n#2# = 8 a+2b - 1\nusing equation 1(8a+2b = -3)\n#5# = -3-1 = -4\nhence C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA merchant marks his goods up by 30% and then offers a discount of 20% on the marked price. What % profit does the merchant make after the discount?\n\n### Options:\nA. 8%\nB. 10%\nC. 21%\nD. 15%\nE. 4%\n\n### Answer:\nLet the price be 100.\nThe price becomes 130 after a 30% markup.\nNow a discount of 20% on 130.\nProfit=104-100\n4%\nanswer E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nf (x + y)/(2x + y) = 4/5, then find (2x + y)/(3x + y) ?\n\n### Options:\nA. 5/9\nB. 5/6\nC. 5/7\nD. 5/4\nE. 5/1\n\n### Answer:\n(x + y)/(2x + y) = 4/5\n=> 5x + 5y = 8x + 4y => y = 3x\nNow, (2x + y)/(3x + y) = 5x/6x = 5/6.\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJane biked 21 2/3 miles in 3 hours and 20 minutes. What was her average rate of speed in miles per hour?\n\n### Options:\nA. 6 1/2\nB. 7\nC. 7 1/2\nD. 7 3/4\nE. 8\n\n### Answer:\nD = 21(2/3) = 65/3\nT = 3(1/3) = 10/3\nS = D/T = 6 1/2\nAnswer = A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA researcher computed the mean, the median, and the standard deviation for a set of performance scores. If7 were to be added to each score, which of these three statistics would change?\n\n### Options:\nA. The mean only\nB. The median only\nC. The standard deviation only\nD. The mean and the standard deviation\nE. The mean and the median\n\n### Answer:\nThe correct answer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man swims downstream 72 km and upstream 45 km taking 9 hours each time; what is the speed of the current?\n\n### Options:\nA. 1.9\nB. 1.5\nC. 2.8\nD. 3.0\nE. 3.9\n\n### Answer:\n72 --- 9 DS = 8\n? ---- 1\n45 ---- 9 US = 5\n? ---- 1 S = ?\nS = (8 - 5)/2 = 1.5\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nCompare the rates of two trains, one travelling at 45 km/hr and other is at 10m/s?\n\n### Options:\nA. 5:4\nB. 3:2\nC. 1:5\nD. 2:7\nE. 3:5\n\n### Answer:\nspeed of the 1st train = 45km/hr\nspeed of the 2nd train = 10m/s = 10*18/5 = 36km/hr\nratio of the speeds of the train = 45:36 = 5:4\nAnswer is A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA vendor bought toffees at 6 for a rupee. How many for a rupee must he sell to gain 20%?\n\n### Options:\nA. 3\nB. 4\nC. 5\nD. 6\nE. 7\n\n### Answer:\nC.P. of 6 toffees = Rs. 1\nS.P. of 6 toffees = 120% of Rs. 1 = Rs 6/5\nFor Rs. 6/5 Toffees Sold 6\nFor Rs. 1, toffees sold = 6x (5/6)= 5\nanswer :C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThree numbers which are co-prime to each other are such that the product of the first two is 551 and that of the last two is 1073. The sum of the three numbers is?\n\n### Options:\nA. 33\nB. 76\nC. 85\nD. 22\nE. 99\n\n### Answer:\nSince the numbers are co-prime, they contain only 1 as the common factor.\nAlso, the given two products have the middle number in common.\nSo, middle number = H.C.F of 551 and 1073 = 29;\nFirst number = 551/29 = 19\nThird number = 1073/29 = 37.\nRequired sum = 19 + 29 + 37 = 85.\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nLast year Manfred received 26 paychecks. Each of his first 6 paychecks was $750; each of his remaining paychecks was $40 more than each of his first 6 paychecks. To the nearest dollar, what was the average (arithmetic mean) amount of his pay checks for the year?\n\n### Options:\nA. $781\nB. $755\nC. $765\nD. $773\nE. $775\n\n### Answer:\n= (750*6+ 790 *20)/26\n= 781\nAnswer is A.\nPosted from my mobile device\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat will be the day of the week 15th August, 2010?\n\n### Options:\nA. Sunday\nB. Monday\nC. Tuesday\nD. Thursday\nE. Friday\n\n### Answer:\n15th August, 2010 = (2009 years + Period 1.1.2010 to 15.8.2010)\nOdd days in 1600 years = 0\nOdd days in 400 years = 0\n9 years = (2 leap years + 7 ordinary years) = (2 x 2 + 7 x 1) = 11 odd days 4 odd days.\nJan. Feb. March April May June July Aug.\n(31 + 28 + 31 + 30 + 31 + 30 + 31 + 15) = 227 days\n227 days = (32 weeks + 3 days) 3 odd days.\nTotal number of odd days = (0 + 0 + 4 + 3) = 7 0 odd days.\nGiven day is Sunday.\nAnswer: Option A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n40% of Ram's marks is equal to 20% of Rahim's marks which percent is equal to 30% of Robert's marks. If Robert's marks is 80, then find the average marks of Ram and Rahim?\n\n### Options:\nA. 76\nB. 56\nC. 56\nD. 90\nE. 15\n\n### Answer:\nGiven, 40% of Ram's marks = 20% of Rahim's marks = 30% of Robert's marks.\nGiven, marks of Robert = 80\n30% of 80 = 30/100 * 8 = 24\nGiven, 40% of Ram's marks = 24.\n=> Ram's marks = (24 * 100)/40 = 60\nAlso, 20% of Rahim's marks\n= 24\n=> Rahim's marks\n= (24 * 100)/20 = 120\nAverage marks of Ram and Rahim\n= (60 + 120)/2 = 90.\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA bag contains 23 purple jellybeans, 12 green jellybeans, and 15 yellow jellybeans; these jellybeans are the only items in the bag. If a person picks a jellybean at random out of the bag, what is the probability that the jellybean will be purple?\n\n### Options:\nA. 15%\nB. 20%\nC. 25%\nD. 30%\nE. 46%\n\n### Answer:\np = 23 , g=12 , y=15\ntotal = 50\np(purple)=(23/50)*100 = 46% . Ans = E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA larger hose connected to a swimming pool can fill the pool in 6 hours. A smaller hose can fill the pool in 12 hours. How many hours will it take for both of them to fill the pool?\n\n### Options:\nA. 3\nB. 7 1/2\nC. 5 3/5\nD. 8\nE. 4\n\n### Answer:\nWork hrs=AB/(A+B)= 72/18 =4\nAnswer is E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA can do a piece of work in 20 days and B can do it in 30 days and C can do it 10 days. They started the work together and A leaves after 2 days and C leaves after 4 days from the beginning. How long will work lost?\n\n### Options:\nA. 13\nB. 16\nC. 25\nD. 14\nE. 15\n\n### Answer:\n2/20 + x/30 + 4/10 = 1\nx = 300/20= 15\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA strain of bacteria reproduces @ 25% every 12 min. In how much time will it triple itself ??\n\n### Options:\nA. 96 min\nB. 72 min\nC. 60 min\nD. 48 min\nE. 40 min\n\n### Answer:\nThe original question is:\nA strain of bacteria reproduces at the rate of 25% every 12 min. In how much time will it triple itself ?\n1.25^x = 3 --> x = ~5 --> five 12 minute periods = 60 minutes.\nAnswer: C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe sum of three consecutive odd numbers is always divisible by:\nI. 2 II. 3 III. 5 IV. 6\n\n### Options:\nA. Only I\nB. Only II\nC. Only I and II\nD. Only II and IV\nE. None of these\n\n### Answer:\nLet the three consecutive odd numbers be (2x+1), (2x+3) and (2x+5). Their sum = (6x=9)= 3 (2x+3), which is always divisible by 3.\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the prime factors\u2019 number of 12?\n\n### Options:\nA. 2\nB. 3\nC. 4\nD. 5\nE. 6\n\n### Answer:\nprime factors\u2019 number, as I assume, for a number X=a^n*b^m*c^o*d^p... is = n+m+o+p...\nSo, 24 = 2^2*3^1\nprime factors\u2019 number will be 2+1 = 3.\nHence, answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a and n are integers, and a^2 = 24n, then n must be divisible by which of the following?\n\n### Options:\nA. 2\nB. 4\nC. 12\nD. 18\nE. 24\n\n### Answer:\na^2=24n\na^2=2^2\u22176n\nLeast value of n to make \"a\" a perfect square is 6\nAnswer = A = 2\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nLast year Jackie saved 5% of her annual salary. This year, she made 10% more money than last year, and she saved 8% of her salary. The amount saved this year was what percent of the amount she saved last year?\n\n### Options:\nA. 56%\nB. 76%\nC. 158%\nD. 176%\nE. 188%\n\n### Answer:\nAssuming Annual salary of last year = 100\n5 % Salary Saving (last year) would give = (5/100) * 100 = 5\nshe made 10% more money than last year = 110 (This year Salary)\n8 % Salary saving this year = (8/100) * 110 = 88/10 = 8.8\n(Amount saved this year/Amount saved last year) * 100= (8.8/5) * 100 = 8.8 * 20 = 176 %\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat approximate value should come in place of the question mark (?) in the following equation?\n159% of 6531.8 + 5.5 \u00d7 1015.2 = ? + 5964.9\n\n### Options:\nA. 10,000\nB. 10,900\nC. 11,000\nD. 10,600\nE. 12,000\n\n### Answer:\n? \u2248 160% of 6530 + 5.5 \u00d7 1010 \u2013 5965\n\u2248 10448 + 5555 \u2013 5965 \u2248 10,000\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the sum of prime numbers lying between 58 and 75?\n\n### Options:\nA. 198\nB. 331\nC. 252\nD. 272\nE. None\n\n### Answer:\nSolution\nRequired sum\t=59 + 61 + 67 + 71 + 73)\n= 331.\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA and B invested Rs.15000 and Rs.20,000 respectively in a business. How should a loss of Rs.2800 be divided between them at the end of year? (in rupees)\n\n### Options:\nA. 1500,1300\nB. 1200,1600\nC. 1300,1500\nD. 1600,1200\nE. 1700,1200\n\n### Answer:\nRatio btwn invest is == 3:4\nloss==2800\nso 2800/7==400\nA==3*400==1200\nB==4*400==1600\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many minutes does it take John to type z words if he types at the rate of x words per minute?\n\n### Options:\nA. x/y\nB. z/x\nC. xy\nD. 60x/y\nE. y/(60x)\n\n### Answer:\ntime*rate=job --> time*x=z --> time=z/x.\nAnswer: B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man purchased a fan and a tv for Rs. 5000 &Rs. 10000 respectively. He sold the fan at a loss of 6% and the tv at a profit of 12%. Overall how much he make a profit.\n\n### Options:\nA. 100\nB. 300\nC. 900\nD. 600\nE. 400\n\n### Answer:\nLet the SP of the fan and the tv be Rs. r and Rs. m respectively.\nr = 5000(1 - 6/100) = 5000 - 300\nm = 10000(1 + 12/100) = 10000 + 1200\nTotal SP - Total CP = r + m - (15000 + 8000) = -300 + 1200 = Rs. 900\nAs this is positive, an overall profit of Rs. 900 was made.\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a bag containing 3balls, a white ball was placed & then 1ball was taken out atrandom. What is the probability that the extracted ball would turn on to be white, if all possible hypothesis concerning the color of theballs that initiallyin the bag were equally possible ?\n\n### Options:\nA. 3\nB. 5/8\nC. 27\nD. 54\nE. 81\n\n### Answer:\nSince, all possible hypothesis regarding the colour of the balls are equally likely, therefore these could be 3 white balls, initially in the bag.\n\u2234 Required probability = 1/4 [1 + 3/4 + 1/2 + 1/4]\n= 1/4 [(4 + 3 + 2 + 1)/4] = 5/8\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average age of seven persons sitting in a row facing east is 28 years. If the average age of the first three persons is 25 years and the average age of the last three persons is 32 years, then find the age of the person sitting in the middle of the row?\n\n### Options:\nA. 9 years\nB. 29 years\nC. 25 years\nD. 19 years\nE. 17 years\n\n### Answer:\nTotal age seven persons = (28 * 7)years\nTotal age of the first three persons and the last three persons are (25 * 3) years and (32 * 3) years respectively.\nAge of the person sitting in the middle of the row = 28 * 7 - 25 * 3 - 32 * 3 = 196 - 75 - 96 = 25 years.\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA windmill is taking advantage of strong air currents in order to produce electrical energy. On a typical day the wind speed is around 20 mph and in that speed the windmill produces 900 kw/h (kilowatts per hour). On a stormy day a windmill produces 20% more energy. How much kw/h can three windmills produce in two hours on a stormy day?\n\n### Options:\nA. 2880.\nB. 4860.\nC. 5780.\nD. 5760.\nE. 6480.\n\n### Answer:\nEfficiency per machine = 900 watt/hr\nEfficiency due to increase in wind speed = 900*120% => 1080 watt/hr\nProduction by each machine in 2 hours is 1080*2 => 2160 watt\nProduction by 3 machines => 2160 watt * 3 = 6480 watt\nAnswer will be (E)\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a and b are different positive integers and a + b+1 = a(a + b), then which of the following must be true?\nI. a = 1\nII. b = 1\nIII. a < b\n\n### Options:\nA. I only\nB. II only\nC. III only\nD. I and II\nE. I and III\n\n### Answer:\nNumber picking might not be the best way to solve MUST BE TRUE questions.\nThe question asks which of the followingMUSTbe true, or which of the following isALWAYStrue no matter what set of numbers you choose. For such kind of questionsif you can prove that a statement is NOT truefor one particular set of numbers, it will mean that this statement is not always true and hence not a correct answer.\nSo the set you chose just proves that II is not always true and hence it's not a part of a correct choice. As for I and III: they might be true for this particular set of numbers but not true for another set, so you can not say that I and III are always true just based on one set of numbers (it just happens to be that I and III are always true).\nAs forCOULD BE TRUEquestions:\nThe questions asking which of the followingCOULDbe true are different:if you can prove that a statement is truefor one particular set of numbers, it will mean that this statement could be true and hence is a correct answer.\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe length of the rectangular field is double its width. Inside the field there is square shaped pond 4m long. If the area of the pond is 1/8 of the area of the field. What is the length of the field?\n\n### Options:\nA. 54\nB. 32\nC. 75\nD. 28\nE. 16\n\n### Answer:\nA/8 = 4 * 4 => A = 4 * 4 * 8\nx * 2x = 4 * 4 * 8\nx = 8 => 2x = 16\nAnswer:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe overall age of X and Y is 18 year greater than the overall age of Y and Z. Z is how many decades younger that X?\n\n### Options:\nA. 11\nB. 15\nC. 12\nD. 17\nE. 18\n\n### Answer:\nE\n18\n(X + Y) \u00e2\u20ac\u201c (Y + Z) = 18\nX \u00e2\u20ac\u201c Z = 18\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how many different number of ways 4 boys and 3 girls can sit on a bench such that girls always sit together.\n\n### Options:\nA. 720\nB. 740\nC. 760\nD. 790\nE. 800\n\n### Answer:\n720\nOption 'A'\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSam purchased 20 dozens of toys at the rate of Rs. 375 per dozen. He sold each one of them at the rate of Rs. 33. What was his percentage profit?\n\n### Options:\nA. 3.5\nB. 4.5\nC. 5.6\nD. 6.5\nE. None\n\n### Answer:\nSolution\nC.P of 1 toy\t= Rs.(375/12)\n= Rs.31.25\nS.P of 1 toy\t= Rs.33.\nTherefore,Profit\t= (1.75/31.25\u00d7100)%\n=(28/5)%\n=5.6%.\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nQ' = 3Q - 3, what is the value of (7')' ?\n\n### Options:\nA. 6\nB. 106\nC. 206\nD. 306\nE. 406\n\n### Answer:\n(7')'=(3*7-3)'=18'=18*18-18=306\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA, B and C started a shop by investing Rs. 10,000, Rs. 10,000 and Rs. 20,000 respectively. At the end of the year, the profits were distributed among them. If C\u00e2\u20ac\u2122s share of profit be Rs. 4,000, then the total profit was :\n\n### Options:\nA. 30,000\nB. 60,000\nC. 8,000\nD. 120,000\nE. None\n\n### Answer:\nSol.\nA : B : C = 10000 : 10000 : 20000 = 1: 1 : 2. so, C\u00e2\u20ac\u2122s share : Total Profit = 2 : 4\nLet the total profit be Rs. x. Then, 2/4 = 36000/x or x\n= 4000 * 4 / 2 = 8000.\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n10 men and 10 women are there, they dance with each other, is there possibility that 2 men are dancing with same women and vice versa?\n\n### Options:\nA. 22\nB. 20\nC. 10\nD. 15\nE. none\n\n### Answer:\nit is written that 10 men and 10 women dance with each other. so there is no chance of matching more than 2 partners at a time. so 2 men & 1 women is not possible.\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is 35% of 4/13 of 585?\n\n### Options:\nA. 52\nB. 63\nC. 74\nD. 85\nE. 96\n\n### Answer:\nThis problem can be solved easily if we just use approximation: 35% is a little over 1/3, while 4/13 is a little less than 4/12, which is 1/3. Thus, the answer is about 1/3 of 1/3 of 585, or 1/9 of 585. Since the first 1/3 is a slight underestimate and the second 1/3 is a slight overestimate, the errors will partially cancel each other out. Our estimate will be relatively accurate.\nThe number 585 is between 540 and 630, so (1/9)*585 will be about 65.\nKeeping track not only of your current estimate, but also of the degree to which you have overestimated or underestimated , can help you pinpoint the correct answer more confidently.\nThe closest answer is 63, so this is the answer to choose.\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many ways are there to award a gold, silver and bronze medal to 6 contending teams?\n\n### Options:\nA. 10 \u00d7 9 \u00d7 8\nB. 10!/(3!7!)\nC. 6!/3!\nD. 564\nE. 6 * 5 * 4\n\n### Answer:\nwe clearly know that there can be only one winning team which deserves the gold medal. we can do the selection in 10 ways\nif gold medal is given to 1 of the teams then only possible 5 teams can be considered for silver medal. we can do selection in 5 ways\nsimilarly if gold and silver medals are awarded then only remaining 4 teams can be considered for a bronze medal. we can do the selection in 4 ways\nTotal number of ways to select the 3 possible medal winners = 6 * 5 * 4\nCorrect answer - E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n20/25 = 4/5 . which method did you use to determine whether this proportion is true or false?\n\n### Options:\nA. true\nB. neutral\nC. false\nD. not sure\nE. none\n\n### Answer:\n20/25= 4/5 cross multiplication: 20 * 5= 100, 4 * 25 =100,\nwe see that 100 are not equal to 100. so there is proportion. corrcet answer: (A)\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA car gets 40 kilometers per gallon of gasoline. How many gallons of gasoline would the car need to travel 120 kilometers?\n\n### Options:\nA. 4.5\nB. 5.5\nC. 6.5\nD. 3\nE. 8.5\n\n### Answer:\nEach 40 kilometers, 1 gallon is needed. We need to know how many 40 kilometers are there in 120 kilometers?\n120 \u00f7 40 = 3 \u00d7 1 gallon = 3 gallons\ncorrect answer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf (x - 1)^2 = 324, which of the following could be the value of x - 4?\n\n### Options:\nA. 16\nB. 14\nC. -19\nD. -21\nE. -23\n\n### Answer:\n(x - 1)^2 = 324\n(x - 1) = 18 or -18\nx = 19 or -17\nx - 4 = 15 or -21\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe two lines y=x and x=-8 intersect on the coordinate plane. What is the value of the area of the figure formed by the intersecting lines and the x-axis?\n\n### Options:\nA. 28\nB. 32\nC. 36\nD. 40\nE. 44\n\n### Answer:\nThe point of intersection is (-8,-8).\nThe triangle has a base of length 8 and a height of 8.\narea = (1/2)*base*height = (1/2)*8*8 = 32\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 9 men and 2 boys working together, can do eight times as much work per hour as a man and a boy together. Find the ratio of the work done by a man and that of a boy for a given time?\n\n### Options:\nA. 2:5\nB. 1:3\nC. 5:8\nD. 6:1\nE. 7:2\n\n### Answer:\n9M + 2B =8(1M + 1B)\n9M + 2B = 8M + 8B\n1M = 6B\nThe required ratio of work done by a man and a boy =6:1\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWorking simultaneously at their respective constant rates, Machines A and B produce 800 nails in x hours. Working alone at its constant rate, Machine A produces 800 nails in t hours. In terms of x and t, how many hours does it take Machine B, working alone at its constant rate, to produce 800 nails?\n\n### Options:\nA. x/(x+y)\nB. y/(x+y)\nC. xy/(x+y)\nD. xy/(x-y)\nE. xt/(t-x)\n\n### Answer:\nPick some smart numbers for x and t.\nSay x=1 hour and t=2 hours (notice that t must be greater than x, since the time for machine A to do the job, which is t hours, must be more than the time for machines A and B working together to do the same job, which is x hours).\nIn this case, the time needed for machine B to do the job must also be 2 hours: 1/2+1/2=1.\nNow, plug x=1 and t=2 in the options to see which one yields 2. Only option E fits.\nAnswer: E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWeights of two friends Ram and Shyam are in the ratio 1:5. If Ram's weight is increased by 10% and total weight of Ram and Shyam become 82.8 kg, with an increases of 15%. By what percent did the weight of Shyam has to be increased?\n\n### Options:\nA. 19%\nB. 10%\nC. 21%\nD. 16%\nE. None\n\n### Answer:\nSolution:\ngiven ratio of Ram and Shayam's weight = 1:5\nHence, (x-15)/(15-10) = 1/5\nOr, x = 16%.\nAnswer: Option D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nnine children \u2014 A, B, C, D, E, F, and G \u2014 are going to sit in seven chairs in a row. Children AB must sit next to each other, and child C must be somewhere to the right of AB. How many possible configurations are there for the children?\n\n### Options:\nA. 600\nB. 720\nC. 1440\nD. 1650\nE. 4800\n\n### Answer:\nA, B, C, D, E, F, G- seven children, of which AB must sit next to each other. Considering them as one X (A, B), we have X, C, D, E, F, G. These can be arranged in 6! ways. But A,B can arrange themselves in 2! ways. So a total of 6!*2! ways = 1440. Since in exactly half of them, C will be to the right of AB, and exactly half, C will be to the left of AB, therefore 1440/2 = 1650\nD is the right answer.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the least number which should be added to 2782 so that the sum is exactly divisible by 5, 6, 4, and 3?\n\n### Options:\nA. 26\nB. 32\nC. 38\nD. 46\nE. 52\n\n### Answer:\nL.C.M. of 5, 6, 4 and 3 = 60.\nWhen dividing 2782 by 60, the remainder is 22.\nThe number to be added = 60 - 22 = 38.\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf Jan spent 40% of her monthly income on housing and 20% less than she spent on housing on a car payment, what percent of her monthly income did she have left after making both her housing payment and her car payment?\n\n### Options:\nA. 20%\nB. 28%\nC. 42%\nD. 50%\nE. 60%\n\n### Answer:\nLets say the total income of Jan is 100\nThen\nShe spends 40 on Housing\n20% less than she spent on Housing = 40\u221220/100\u221740=3240\u221220/100\u221740=32\nTotal expenditure = 40 + 32 = 72\nRemaining = 100 - 72 = 28\nHence the answer is B 28 %\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a colony of 70 residents, the ratio of the number of men and women is 4 : 3. Among the women, the ratio of the educated to the uneducated is 1 : 4. If the ratio of the number of educated to uneducated persons is 8 : 27, then find the ratio of the number of educated to uneducated men in the colony?\n\n### Options:\nA. 1:6\nB. 1:1\nC. 1:8\nD. 1:9\nE. 1:3\n\n### Answer:\nNumber of men in the colony = 4/7 * 70 = 40.\nNumber of women in the colony = 3/7 * 70 = 40.\nNumber educated women in the colony = 1/5 * 30 = 6.\nNumber of uneducated women in the colony = 4/5 * 50 = 24.\nNumber of educated persons in the colony = 8 /35 * 70 = 16.\nAs 6 females are educated, remaining 10 educated persons must be men.\nNumber of uneducated men in the colony = 40 - 10 = 30.\nNumber of educated men and uneducated men are in the ratio 10 : 30 i.e., 1:3.\nAnswer:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how many different ways can the letters of the word 'SENDING' be arranged in such a way that the vowels always come together?\n\n### Options:\nA. A)360\nB. B)480\nC. C)720\nD. D)5040\nE. of these\n\n### Answer:\nThe word 'SENDING' has 7 different letters.\nWhen the vowels EI are always together, they can be supposed to form one letter.\nThen, we have to arrange the letters SNDNG (EI).\nNow, 6 (5 + 1 = 6) letters can be arranged in 6! = 720 ways.\nThe vowels (EI) can be arranged among themselves in 2! = 2 ways.\nRequired number of ways = (720 x 2) = 1440.\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWater boils at 212\u00b0F or 100\u00b0C and melts at 32\u00b0F or 0\u00b0C . If the temparature of the particular day is 35\u00b0C , it is equal to :\n\n### Options:\nA. 85\u00c2\u00b0F\nB. 95\u00c2\u00b0F\nC. 96\u00c2\u00b0F\nD. 97\u00c2\u00b0F\nE. None of these\n\n### Answer:\nExplanation:\nLet F and C denotes the temparature in Fahrenheit anid Celcsius respectively.\nThen, (F - 32) /(212 - 32) = (C - 0)/(100 - 0), if c = 35, then F = 95.\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain school implemented a reading program for its students, with the goal of getting each student to read 7 books per month year-round. If the school has c classes made up of s students in each class, how many books will the entire student body read in one year?\n\n### Options:\nA. 20cs\nB. cs/2\nC. 84cs\nD. (2cs)/12\nE. (24c)/s\n\n### Answer:\nAns: C\nSolution: simple multiplication s students , c classes , 7 books/ month= 84 books a year\ntotal number of books = 84cs\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a garden, there are three blue flowers, three red flowers, three green flowers, and three pink flowers. What is the probability that a florist will choose three flowers of the same color when randomly picking three flowers?\n\n### Options:\nA. 11/10\nB. 1/55\nC. 31/10\nD. 3/55\nE. 1/16\n\n### Answer:\nTotal number of ways to pick 3 flowers out of 12 = 12c3\n12c3=12!/9!\u22173!=220\nTotal number of favorable outcomes = 4\n(Only 3 flowers per colour, so there is only one way all three flowers of any particular colour can be chosen. 4 colours mean 4 favorable outcomes)\nProbability = 4/220=1/55\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAn uneducated retailer marks all his goods at 65% above the cost price and thinking that he will still make 25% profit, offers a discount of 25% on the marked price. What is his actual profit on the sales?\n\n### Options:\nA. 12.50 %\nB. 13.50 %\nC. 14 %\nD. 23.75%\nE. None\n\n### Answer:\nSol.\nLet C.P. = Rs. 100. Then, marked price = Rs. 165.\nS.P. = 75% of Rs. 165 = Rs. 123.75.\n\u2234 Gain% = 23.75%.\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn store A there are 50 pairs of pants for every 40 store B has. The price ratio between the pants in store B and the pants in store A is 3:4. If all the pants were sold in both places until the stock ran out, what is the ratio between the total amount stores A earned to the total amount store B earned?\n\n### Options:\nA. 3:16.\nB. 2:3.\nC. 5:3.\nD. 3:4.\nE. 2:5.\n\n### Answer:\n1st statement : ratio of pants\nStore A : Store B\n50x : 40x\n5X:4X\nPrice :\n4y:3y\nTotal revenue\n20xy : 12xy\n5:3\nAnswer is C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat will be the difference between simple and compound interest at 10% per annum on a sum of Rs. 1000 after 4 years?\n\n### Options:\nA. 64.19\nB. 64.12\nC. 62.1\nD. 64.1\nE. 64.11\n\n### Answer:\nS.I. = (1000 * 10 * 4)/100 = Rs. 400\nC.I. = [1000 * (1 + 10/100)4 - 1000] = Rs. 464.10 Difference = (464.10 - 400) = Rs. 64.10\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n220% of a number X is 44. What is 44% of X.\n\n### Options:\nA. 8.8\nB. 8.9\nC. 6.6\nD. 7.7\nE. None\n\n### Answer:\nSolution: Given,\n220% of X = 44\nOr, X = 20.\nThus,\n44% of 20\n= (44 *20) /100\n= 8.8\nAnswer: Option A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf y is the smallest positive integer such that 7350 multiplied by y is the square of an integer, then y must be\n\n### Options:\nA. 2\nB. 5\nC. 6\nD. 7\nE. 14\n\n### Answer:\ni just tried plugging in the numbers and found out that\n6*7350 = 44, 100, which is a square of 210\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA bookseller has two display windows. She plans to display 3 new fiction books in the left window, and 3 new non-fiction books in the right window. Assuming she can put the four fiction books in any order, and separately, the three non-fiction books in any order, how many total configurations will there be for the two display windows?\n\n### Options:\nA. 24\nB. 72\nC. 144\nD. 36\nE. 420\n\n### Answer:\nThe left window will have permutations of the 3 fiction books, so the number of possibilities for that window is\npermutations = 3! = (3)(2)(1) = 6\nThe right window will have permutations of the 3 non-fiction books, so the number of possibilities for that window is\npermutations = 3! = (3)(2)(1) = 6\nAny of the 24 displays of the left window could be combined with any of the 6 displays of the right window, so the total number of configurations is 6*6 = 36\nAnswer: D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train left station X at A hour B minutes. It reached station Y at B hour C minutes on the same day, after travelling C hours A minutes (clock shows time from 0 hours to 24 hours). Number of possible value(s) of A is:\n\n### Options:\nA. 0\nB. 1\nC. 2\nD. 3\nE. 4\n\n### Answer:\nLet's try to get hours and minutes values separately..\nStarting time + time taken = Reaching time..\nA hours + C hours = B hours -------- (i)\nA, C and B cannot have values greater than or equal to 24\nB minutes + A minutes = C minutes -------- (ii)\nLooking at the two equations, we get that no value of A satisfies both the equations.\nHence, option A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe pilot of a small aircraft uses 60 gallons of fuel to fly 300 miles. At this rate, how many gallons of fuel are needed for a 700 mile flight?\n\n### Options:\nA. 140\nB. 155\nC. 160\nD. 170\nE. 175\n\n### Answer:\nNumber of gallons of fuel per mile = 300 /60 = 5 gallons per mile\nNumber of gallons of fuel for a 700 mile flight = 700/5 = 140\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train running at the speed of 72 km/hr crosses a pole in 9 sec. What is the length of the train?\n\n### Options:\nA. 288\nB. 279\nC. 277\nD. 272\nE. 180\n\n### Answer:\nSpeed = 72 * 5/18 = 20 m/sec\nLength of the train = speed * time = 20 * 9\n= 180 m\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf c persons take y days to complete z similar jobs, how long does it take y persons to complete 1 such job?\n\n### Options:\nA. z\nB. x\nC. x/y\nD. z/x\nE. y/z\n\n### Answer:\nthe Q doesn't seem to be having the any correct answer as a choice..\nsince we are looking for days, lets keep days in end and work out a solution..\nc person can do z jobs in y days..\nso c person can do 1 job in y/z days..\nand 1 person can do 1 job in y^2/z days..\nso y person can complete 1 job in y^2/zy=y/z..\nso the answer should be y/z=E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nToday is Monday. After 61 days, it will be :\n\n### Options:\nA. Thursday\nB. Saturday\nC. Monday\nD. Sunday\nE. Wednesday\n\n### Answer:\nEach day of the week is repeated after 7 days.\nSo, after 63 days, it will be Monday.\nAfter 61 days, it will be Saturday.\nAnswer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA shopkeeper sold an book offering a discount of 5% and earned a profit of 33%. What would have been the percentage of profit earned if no discount was offered?\n\n### Options:\nA. 140\nB. 120\nC. 130\nD. 110\nE. 150\n\n### Answer:\nLet C.P. be $100.\nThen, S.P. = $133\nLet marked price be $x. Then, 95/100 x = 133\nx = 13300/95 = $140\nNow, S.P. = $140, C.P. = $100\nProfit % = 40%.\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTomy's age 14 years hence will be thrice his age four years ago. Find Tomy's present age?\n\n### Options:\nA. 12 years\nB. 13 years\nC. 15 years\nD. 17 years\nE. 18 years\n\n### Answer:\nLet MTomy's present age be 'x' years.\nx+ 14 = 3(x- 4)\n=> 2x = 26 => x = 13 years.\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 7 persons meet at a reunion and each person shakes hands exactly once with each of the others, what is the total number of handshakes?\n\n### Options:\nA. 7 \u00d7 6 \u00d7 5 \u00d7 4 \u00d7 3 \u00d7 2 \u00d7 1\nB. 7 \u00d7 6 \u00d7 5 \u00d7 4 \u00d7 3 \u00d7 2 \u00d7 1\nC. 7 x 8\nD. 21\nE. 45\n\n### Answer:\n1st person will have 6 handshakes, 2nd will have 5, ....6th will have 1 and 7th will have 0\n= 6+5+4+3+2+1 = 21\nif we generalize this: if there are n people then there will be n(n-1)/2 handshakes.\nAns.D)\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA pump can fill a tank with water in 3 hours. Because of a leak, it took 3 1/3 hours to fill the tank. The leak can drain all the water of the tank in?\n\n### Options:\nA. 17 hr\nB. 19 hr\nC. 30 hr\nD. 14 hr\nE. 16 hr\n\n### Answer:\nWork done by the tank in 1 hour\n= (1/3 - 3 1/3)\n= 1/30 Leak will empty the tank in 30 hrs.\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn the xy-plane, a line has slope 4 and x-intercept 3. What is the y-intercept of the line?\n\n### Options:\nA. -12\nB. -3\nC. 0\nD. 3\nE. 9\n\n### Answer:\nLet the line be represented by a general equation y=mx+b, where m = slope (4) and b=y intercept. We are also given the value of x-intercept 3.\nTheory : y intercept represents the point on the line where the x=0, and x intercept represents the point on the line where the y=0.\nPutting these values in the equation : 0 = 4*3 + b => b = -12. Hence A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n2 trains starting at the same \u019fme from 2 stations 200 km apart and going in opposite direction cross\neach other at a distance of 110 km from one of the stations. What is the ratio of their speeds ?\n\n### Options:\nA. 11:9\nB. 13:9\nC. 17:9\nD. 21:9\nE. None of these\n\n### Answer:\nExplanation:\nWe know total distance is 200 Km\nIf both trains crossed each other at a distance of 110 km then one train covered 110 km and other 90 km\n[110+90=200km]\nSo ra\u019fo of their speed = 110:90 = 11:9\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRoy was suffering from severe headaches. He went to see his doctor and the doctor gave him five tablets asking him to take one tablet every 15 minutes.\nHow much time will it take Roy to consume all the five tablets?\n\n### Options:\nA. 60 min\nB. 50 min\nC. 70 min\nD. 65 min\nE. 80 min\n\n### Answer:\nA\n60 min\nRoy will be able to consume all the five tablets in an hour.\nTablet 1 will be taken in 0 min.\nTablet 2 will be taken in 15 min.\nTablet 3 will be taken in 30 min.\nTablet 4 will be taken in 45 min.\nTablet 5 will be taken in 60 min.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the average (arithmetic mean) of the four numbers K, 2K + 3, 3K \u2013 5 and 5K + 1 is 96, what is the value of K?\n\n### Options:\nA. 11\nB. 15 3/4\nC. 22\nD. 35\nE. 25 3/10\n\n### Answer:\nK + 2K +3 + 3K - 5 + 5K +1 = 11K -1\n(11K -1)/4 = 96\n11K = 96 * 4 +1 = 384 +1 = 385\nK = 385 / 11 = 35.\nAnswer D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 5 gallons of gasoline are added to a tank that is already filled to 3/4 of its capacity, the tank is then filled to 9/10 of its capacity. How many gallons does the tank hold?\n\n### Options:\nA. 20\nB. 30\nC. 36\nD. 40\nE. 60\n\n### Answer:\nLet the Capacity of the tank=C\n(3/4)C + 5 = (9/10)C\n=>(9/10)C - (3/4)C = 5\n=>(3/20)C = 5\n=>C = (5*20)/3 = 33.33\nNumber of gallons of gasoline that the tank currently holds = 3/4*C +5 = 24.99+5 = 29.99=30\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average salary per head of the entire staff of an office including the officers and clerks is Rs.90. The average salary of officers is Rs.600 and that of the clerks is Rs.84. If the number of officers is 2, find the number of officers in the office?\n\n### Options:\nA. 3\nB. 1\nC. 8\nD. 9\nE. 5\n\n### Answer:\n6 * 22 = 132\n7 * 19 = 133\n--------------\n1\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA 25 cm wide path is to be made around a circular garden having a diameter of 4 meters. Approximate area of the path is square meters is?\n\n### Options:\nA. 3.34\nB. 3.349\nC. 3.348\nD. 3.37\nE. 3.248\n\n### Answer:\nArea of the path = Area of the outer circle - Area of the inner circle = \u220f{4/2 + 25/100}2 - \u220f[4/2]2\n= \u220f[2.252 - 22] = \u220f(0.25)(4.25) { (a2 - b2 = (a - b)(a + b) }\n= (3.14)(1/4)(17/4) = 53.38/16 = 3.34 sq m\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRunning at the same constant rate, 6 identical machines can produce a total of 390 bottles per minute. At this rate, how many bottles could 10 such machines produce in 4 minutes?\n\n### Options:\nA. 648\nB. 1800\nC. 2600\nD. 10800\nE. 10900\n\n### Answer:\nLet the required number of bottles be x.\nMore machines, More bottles (Direct Proportion)\nMore minutes, More bottles (Direct Proportion)\nMachines\t6\t:\t10\t:: 390 : x\nTime (in minutes)\t1\t:\t4\n6 x 1 x x = 10 x 4 x 390\nx =\t(10 x 4 x 390)/(6)\nx = 2600.\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average age of 8 men is increased by 2 years. When two of them, whose ages are 20 years and 24 years respectively are replaced by two women. What is the average age of these women?\n\n### Options:\nA. 36 years\nB. 30 years\nC. 40 years\nD. 42 years\nE. None of these\n\n### Answer:\nLet the average age of 8 men be X years\nThus, Sum of the ages of 8 men = 8X years\nNow, according to the condition of the question, average age of (6 men + 2 women) = (x + 2) years\nThus, Sum of the ages of (6 men + 2 women)\n= 8(X + 2) = 8X x 16 years\nHence, it is clear that on replacing two men by two women, sum of their ages increased by 16 years.\nTherefore, sum of the ages of two women\n= (20 + 24) + 16 = 60 years\nThus, average age of the women = 60/2 = 30 years\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA sum fetched a total simple interest of 4034.25 at the rate of 9 %.p.a. in 5 years. What is the sum?\n\n### Options:\nA. 5768\nB. 8925\nC. 8965\nD. 6474\nE. 8723\n\n### Answer:\nPrincipal = (100 x 4034.25)/(9 x 5)\n= 403425/45\n= 8965.\nANSWER C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA and B enter into partnership with capital as 7:9. At the end of 8 months, A withdraws. If they receive the profits in the ratio of 8:9 find how long B's capital was used?\n\n### Options:\nA. 4\nB. 5\nC. 34\nD. 7\nE. 9\n\n### Answer:\n7 * 8 : 9 * x = 8:9 => x= 7\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA table is bought for Rs.600/- and sold at a loss of 10% find its selling price\n\n### Options:\nA. Rs.500/-\nB. Rs.530/-\nC. Rs.540/-\nD. Rs.600/-\nE. Rs.700/-\n\n### Answer:\n100 % ------> 600 (100 * 6 = 600)\n90 % ------> 540 (90 * 6 = 540)\nSelling price = Rs.540/-\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train travels 325 km in 3.5 hours and 470 km in 4 hours. Find the average speed of train ?\n\n### Options:\nA. 116 kmph\nB. 106 kmph\nC. 186 kmph\nD. 126 kmph\nE. 176 kmph\n\n### Answer:\nExplanation:\nAs we know that Speed = Distance / Time\nfor average speed = Total Distance / Total Time Taken\nThus, Total Distance = 325 + 470 = 795 km\nThus, Total Speed = 7.5 hrs\nAverage Speed = 795/7.5 => 106 kmph.\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many paying stones, each measuring 2 1/2 m * 2 m are required to pave a rectangular court yard 20 m long and 16 1/2 m board?\n\n### Options:\nA. 66\nB. 18\nC. 16\nD. 10\nE. 15\n\n### Answer:\n20 * 33/2 = 5/2 * 2 * x => x\n= 66\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA committee of 5 is to be selected from among 5 boys and 4 girls. I how many ways can this be done if the committee is to consist of at-least one Girl?\nwhat is the answer choice and how?\n\n### Options:\nA. 105\nB. 225\nC. 209\nD. 350\nE. 455\n\n### Answer:\nI'm sure there is some problem with the question.\nR U sure its atleast one boy and not atleast 1 boy and 1 girl?\nif its 1 boy and 1 girl\n6C1*4C1 + 6C2*4C2 + 6C3*4C3 + 6C4*4C4\n6*4 + 15*6 + 20*4 + 15*1\n24 + 90 + 80 + 15\n209\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA goods train leaves a station at a certain time and at a fixed speed. After ^hours, an express train leaves the same station and moves in the same direction at a uniform speed of 90 kmph. This train catches up the goods train in 4 hours. Find the speed of the goods train.\n\n### Options:\nA. 15 kmph\nB. 36 kmph\nC. 21 kmph\nD. 17 kmph\nE. 19 kmph\n\n### Answer:\nLet the speed of the goods train be x kmph.\nDistance covered by goods train in 10 hours= Distance covered by express train in 4 hours\n10x = 4 x 90 or x =36.\nSo, speed of goods train = 36kmph.\nAns: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo stations A and B are 65 km apart on a straight line. One train starts from A at 7 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet?\n\n### Options:\nA. 9\nB. 10\nC. 11\nD. 12\nE. 8\n\n### Answer:\nSuppose they meet x hours after 7 a.m.\nDistance covered by A in x hours = 20x km.\nDistance covered by B in (x - 1) hours = 25(x - 1) km.\nTherefore 20x + 25(x - 1) = 65\n45x = 90\nx = 2.\nSo, they meet at 9 a.m.\nAnswer: Option A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many words can be formed by using all letters of the word 'BIHAR' ?\n\n### Options:\nA. 112\nB. 120\nC. 157\nD. 136\nE. 142\n\n### Answer:\nThe word BIHAR contains 5 different letters\nRequired number of words = 5P5 = 5! = 5*4*3*2*1 = 120\nAnswer is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n270 candidates appeared for an examination, of which 252 passed. The pass percentage is :\n\n### Options:\nA. (93 + 1/9 )%\nB. (93 + 1/3 )%\nC. (93 + 9/3 )%\nD. (94 + 9/3 )%\nE. (43 + 1/3 )%\n\n### Answer:\nAnswer: B) (93 + 1/3 )%\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind out the C.I on Rs.7000 at 4% p.a. compound half-yearly for 1 1/2 years.\n\n### Options:\nA. A)Rs.426.45\nB. B)Rs.427.45\nC. C)Rs.428.45\nD. D)Rs.429.45\nE. E)Rs.430.45\n\n### Answer:\nA = 7000(51/50)3\n= 7428.45\n7000\n-----------\n428.45\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the greatest possible (straight line) distance, between any two points on a hemisphere of radius 4?\n\n### Options:\nA. n/8\nB. 0.8\nC. 8\nD. 18\nE. \u03c0\n\n### Answer:\nMaximum distance straight line is diameter\nd = 2r = 8..\nANS option C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA retailer set the tag price of an item at $200. On a certain public holiday, the retailer set a 20% discount on the tag price, thinking that he will still make a profit equal to 25% of the price he had originally paid for the item. How much did the retailer originally pay for the item?\n\n### Options:\nA. $96\nB. $120\nC. $128\nD. $144\nE. $160\n\n### Answer:\nPrice Tagged : $200\nPrice after discount = $160 = Original Price + 25% Extra\nOriginal Price = x\nSo, 1.25 x = 160\nor x = 128. Hence, C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMachine\u2013X produces 50% of the total output and Machine-Y produces 75% of the total output. An average of nine units out of a thousand goods manufactured by Machine-X and two unit of 500 units produced by Machine-X prove to be defective. What is the probability that a unit chosen at random from the total daily output of the factory is defective?\n\n### Options:\nA. 0.008\nB. 0.1\nC. 0.12\nD. 0.006\nE. 0.007\n\n### Answer:\nSuppose machine X produce 1000 units\ntotal defective = 9\nMachine Y then produces=1500 units\ntotal defective=6\nprobability=15/2500\n=0.006\nAnswer : D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAll the stocks on the over-the-counter market are designated by either a 2 letter or 3 letter codes that is created by using the 26 letters of the alphabet. Which of the following gives the maximum number of different stocks that can be designated with these codes?\n\n### Options:\nA. 2(26^5)\nB. 26(26^4)\nC. 27(26^2)\nD. 26(26^5)\nE. 27(26^5)\n\n### Answer:\nwith 2 letters: 26^2\nwith 3 letters: 26^3\n26^2 + 26^3 = 27*(26^2)\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n300 meter long train crosses a platform in 39 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform?\n\n### Options:\nA. 388\nB. 266\nC. 350\nD. 112\nE. 134\n\n### Answer:\nSpeed = [300 / 18] m/sec = 50/3 m/sec.\nLet the length of the platform be x meters.\nThen, x + 300 / 39 = 50/3\n3(x + 300) = 1950 \u00e8 x\n= 350m.\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n3A = 4B = 5C, A : B : C = ?\n\n### Options:\nA. 12:15:22\nB. 20:15:12\nC. 15:20:12\nD. 12:20:15\nE. None of these\n\n### Answer:\nExplanation :\nSolution: 3A = 4B = 5C,\nA : B : C = 1/3 : 1/4 : 1/5\n=> 20/60 : 15/60 : 12/60 = 20 : 15 : 12\nAnswer : B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train 510 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?\n\n### Options:\nA. 52\nB. 56\nC. 41\nD. 42\nE. 34\n\n### Answer:\nSpeed = 45 * 5/18 = 25/2 m/sec\nTotal distance covered = 360 + 140 = 500 m\nRequired time = 550 * 2/25 = 52 sec\nAnswer: Option A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn 30 years, A will be twice as old as B was 30 years ago. If A is now 5 years older than B, the present age of B is?\n\n### Options:\nA. 85yrs\nB. 95yrs\nC. 93yrs\nD. 82yrs\nE. 90yrs\n\n### Answer:\nLet B's present age = x years\nThen A's present age = x+5 years\nx+5+30 = 2(x-30)\nx + 35 = 2x - 60\nx = 95years\nAnswer is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n60% of Ram's marks is equal to 20% of Rahim's marks which percent is equal to 30% of Robert's marks. If Robert's marks is 80, then find the average marks of Ram and Rahim?\n\n### Options:\nA. 70\nB. 97\nC. 80\nD. 90\nE. 76\n\n### Answer:\nGiven, 60% of Ram's marks = 20% of Rahim's marks = 30% of Robert's marks.\nGiven, marks of Robert = 80\n30% of 80 = 30/100 * 8 = 24\nGiven, 60% of Ram's marks = 24.\n=> Ram's marks = (24 * 100)/60 = 40\nAlso, 20% of Rahim's marks = 24\n=> Rahim's marks = (24 * 100)/20 = 120\nAverage marks of Ram and Rahim = (40 + 120)/2 = 80.\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA company D has 30 percent of the employees are secretaries and 45 percent are salespeople. If there are 50 other employees of Company D, how many employees does Company D have?\n\n### Options:\nA. 200\nB. 162\nC. 180\nD. 152\nE. 250\n\n### Answer:\nLet the total number of employees in the company be x\n% of secretaries = 30%\n% of salespeople = 45%\n% of of employees other than secretaries and salespeople = 100 - 75 = 25%\nBut this number is given as 50\nso 25% of x = 50\nx = 200\nTherefore there a total of 200 employees in the company D\nCorrect answer - A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe dimensions of a room are 25 feet * 15 feet * 12 feet. What is the cost of white washing the four walls of the room at Rs. 5 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each?\n\n### Options:\nA. Rs. 4800\nB. Rs. 3600\nC. Rs. 3560\nD. Rs. 4530\nE. None of these\n\n### Answer:\nArea of the four walls = 2h(l + b)\nSince there are doors and windows, area of the walls = 2 * 12 (15 + 25) - (6 * 3) - 3(4 * 3) = 906 sq.ft.\nTotal cost = 906 * 5 = Rs. 4530\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThis year, MBB Consulting fired 9% of its employees and left remaining employee salaries unchanged. Sally, a first-year post-MBA consultant, noticed that that the average (arithmetic mean) of employee salaries at MBB was 10% more after the employee headcount reduction than before. The total salary pool allocated to employees after headcount reduction is what percent of that before the headcount reduction?\n\n### Options:\nA. 98.5%\nB. 100.1%\nC. 102.8%\nD. 104.5%\nE. 105.0%\n\n### Answer:\n100 employees getting 1000$ avg, so total salary for 100 ppl = 100000\n9% reduction in employees lead to 91 employees and a salary increase of 10% of previous avg salary\nThus the new avg salary is = 10%(1000)+1000 = 1100\nso total salary of 91 employees is 91*1100 = 100100\nNow the new salary is more than previous salary by x%. x = (100100/100000)*100 = 100.1%\nSo the Answer is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe probability that a number selected at random from the first 50 natural numbers is a composite number is?\n\n### Options:\nA. 17/29\nB. 17/21\nC. 17/22\nD. 17/29\nE. 17/25\n\n### Answer:\nThe number of exhaustive events = 50C1 = 50.\nWe have 15 primes from 1 to 50.\nNumber of favourable cases are 34.\nRequired probability = 34/50\n= 17/25.\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train crosses a platform of 150 m in 15 sec, same train crosses another platform of length 250 m in 20 sec. then find the length of the train?\n\n### Options:\nA. 150\nB. 878\nC. 277\nD. 992\nE. 187\n\n### Answer:\nLength of the train be \u2018X\u2019\nX + 150/15 = X + 250/20\n4X + 600 = 3X + 750\nX = 150m\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAn investment R gained an interest payment of $250 each month when the annual interest rate was 8%, how much more should we invest annually if we want to gain 12% more per month with a new annual interest rate of 7.5% ?\n\n### Options:\nA. $9,360\nB. $9,100\nC. $8,250\nD. $7,300\nE. $7,150\n\n### Answer:\nAnswer is D : 7,300\nAn investment R gained an interest payment of $250 each month when the annual interest rate was 8%,Interest per annum with 8% interest rate is = 250* 12 = Principal * Interest Rate(8/100)\nThis gives Principal as 37,500$\nFor an revised interest of 12% more and new interest rate of 7.5% , ie. 250* 12 * 1.12 = Principal * Interest Rate (7.5/100)\nThis gives the new Principal as 44,800.\nThe question is how much more should we invest, so 44,800 - 37,500 = 7,300.D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFrom the word 'HEARTLESS', how many independent words can be made with-out changing the order of the letters and using each letter only once ?\n\n### Options:\nA. 5\nB. 8\nC. 3\nD. 2\nE. 9\n\n### Answer:\nExplanation:\nThe words formed are\nHE, ART, LESS, HEART and EAR\nAnswer: A) 5\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many numbers between 1 and 100 are divisible by 7 ?\n\n### Options:\nA. 9\nB. 11\nC. 17\nD. 14\nE. 12\n\n### Answer:\nNo. of divisible by 7 7, 14 --------- 98, n = a + (N - 1)d\n98 = 7 + (N - 1) 7, 98 = 7 + 7N - 7\n98/7= N = 14\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain set of numbers has an average (arithmetic mean) of 50 and a standard deviation of 50.5. If k and n, two numbers in the set, are both within 2 standard deviations from the average, then which of the following could be the sum of k and n?\n\n### Options:\nA. -200\nB. -130\nC. -104\nD. 51\nE. 305\n\n### Answer:\n2 standard deviations from the average is from mean - 2*SDtomean + 2*SD, thus from 50-2*50.5=51 to 50+2*50.5=151:\n-51 < k < 151\n-51 < n < 151\n-102 < k+n < 302.\nOnly option D is in this range.\nAnswer: D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat will be the fraction of 10%\n\n### Options:\nA. 1/4\nB. 1/5\nC. 1/10\nD. 1/8\nE. None of above\n\n### Answer:\nExplanation:\nIt will 10*1/100 = 1/10\nAnswer: Option C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe sequence x1, x2, x3,..., is such that Xn = 1/n - (1/(n+1)). What is the sum of the first 200 terms of the sequence?\n\n### Options:\nA. 201/100\nB. 99/100\nC. 100/101\nD. 1/10000\nE. 200/201\n\n### Answer:\nEasy task and accomplish\nX1=1-1/2\nx2=1/2-1/3\nx3=1/3-1/4\n.....\nx199=1/199-1/200\nx200=1/200-1/201\nsum=X1+X2+X3+....X200=1-1/2+1/2-1/3+.......1/199-1/200+1/200-1/201=1-1/201=200/201\nE is the answer\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n140 is what percent of 40?\n\n### Options:\nA. 5%\nB. 20%\nC. 50%\nD. 350%\nE. 500%\n\n### Answer:\n40*x=140 --> x=3.5 --> 3.5 expressed as percent is 350%.\nAnswer: D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAn amount of Rs. 100000 is invested in two types of shares. The first yields an interest of 9% p.a and the second, 11% p.a. If the total interest at the end of one year is 9 1/2 %, then the amount invested at 11% was?\n\n### Options:\nA. 23777\nB. 25000\nC. 29977\nD. 26777\nE. 19871\n\n### Answer:\nLet the sum invested at 9% be Rs. x and that invested at 11% be Rs. (100000 - x). Then,\n(x * 9 * 1)/100 + [(100000 - x) * 11 * 1]/100 = (100000 * 19/2 * 1/100)\n(9x + 1100000 - 11x) = 950000\nx =75000\nSum invested at 9% = Rs. 75000\nSum invested at 11% = Rs. (100000 - 75000) = Rs. 25000.\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA product when sold with 10% rebate on the listed price gave a profit of Rs.70. What was its cost price?\n\n### Options:\nA. Rs. 200\nB. Rs. 250\nC. Rs. 300\nD. Cannot be determined\nE. None\n\n### Answer:\nSolution\nSince the marked price is not given, so the cost price cannot be determined.\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo whole numbers whose sum is 24 is the ratio\n\n### Options:\nA. 1:3\nB. 2:8\nC. 1:6\nD. 2:3\nE. 2:5\n\n### Answer:\nA) 1:3\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe length of a rectangular plot is 20 metres more than its breadth. If the cost of fencing the plot @ 26.50 per metre is Rs. 5300, what is the length of the plot in metres?\n\n### Options:\nA. 40\nB. 45\nC. 125\nD. Data inadequate\nE. None of these\n\n### Answer:\nExplanation:\nLet breadth = x metres.\nThen, length = (x + 20) metres.\nPerimeter = 5300/26.50m = 200 m\n2[(x + 20) + x] = 200\n2x + 20 = 100\n2x = 80\nx = 40.\nHence, length = x + 20 = 60 m.\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFour car rental agencies A, B, C and D rented a plot for parking their cars during the night. A parked 15 cars for 12 days, B parked 12 cars for 20 days, C parked 18 cars for 18 days and D parked 16 cars for 15 days. If A paid Rs. 1215 as rent for parking his cars, what is the total rent paid by all the four agencies?\n\n### Options:\nA. 6642\nB. 2778\nC. 1279\nD. 6150\nE. 2771\n\n### Answer:\nThe ratio in which the four agencies will be paying the rents = 15 * 12 : 12 * 20 : 18 * 18 : 16 * 15\n= 180 : 240 : 324 : 240 = 45 : 60 : 81 : 60\nLet us consider the four amounts to be 45k, 60k, 81k and 60k respectively.\nThe total rent paid by the four agencies = 45k + 60k + 81k + 60k= 246k\nIt is given that A paid Rs. 1215\n45k = 1215 => k = 27\n246k = 246(27) = Rs. 6642\nThus the total rent paid by all the four agencies is Rs. 6642.\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how many different ways can the letters of the word \u2018CAN\u2019 be arranged?\n\n### Options:\nA. 6\nB. 12\nC. 8\nD. 2\nE. 4\n\n### Answer:\nA\n6\nThe word SMART has 3 distinct letters.\nNumber of arrangements = 3!\n= 3 \u00d7 2 \u00d7 1 = 6\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many bricks, each measuring 25 cm x 11.25 cm x 6 cm, will be needed to build a wall of 8 m x 6 m x 22.5 cm?\n\n### Options:\nA. 3488\nB. 37799\nC. 6400\nD. 2777\nE. 2911\n\n### Answer:\nExplanation:\nNumber of bricks \\frac{800\\times 600\\times 22.5}{25\\times 11.25\\times 6} = 6400\nAnswer: C) 6400\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many numbers between 200 and 500 begin or end with 3?\n\n### Options:\nA. 20\nB. 60\nC. 100\nD. 110\nE. 120\n\n### Answer:\nHow many numbers between 200 and 500 begin or end with 3?\nJust think that those numbers are:\ni) The ones ending in 3: 203, 213, 223, ... , 493 --> 30 numbers\nii) The ones beginning in 3: 300, 301, 302, 303, ... , 393, ... , 399 --> 100 numbers\nBUT 10 out of the first 30 numbers are repeated in the second set.\nTHEREFORE, the solution is 120 numbers.\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA and B start walking towards each other at 5am at speed of 4kmph and 8kmph. They were initially 36km apart. At what time do they meet?\n\n### Options:\nA. 8am\nB. 6am\nC. 7am\nD. 10am\nE. 8pm\n\n### Answer:\nTime of meeting = distance / relative speed = 36/8 + 4 = 36/12 = 3 hrs after 5am = 8am\nAnswer is A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the remainder when 81+82+83\u2026\u2026+815 is divided by 6\n\n### Options:\nA. 0\nB. 1\nC. 2\nD. 4\nE. 5\n\n### Answer:\nThus odd powers will have remainder 2 ; and even powers will have remainder 4\nNow, 81+82+83\u2026\u2026+81581+82+83\u2026\u2026+815 will have the following powers -\nOdd = 1 , 3 , 5 , 7 , 9 , 11 , 13 , 15 ( 8 odd powers ) ; Sum of remainder = 16\nEven Powers = 2, 4 , 6 , 8 , 10 , 12 , 14 ( 7 even Powers ) ; Sum of remainder = 28\nTotal sum of remainder = 44\n44/6 = Remainder 2\nHence correct answer will be (C) 2....\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nLook at this series: 15, 15, 27, 27, 39, 39, 51, 51, ... What number should fill the blank?\n\n### Options:\nA. 51\nB. 39\nC. 63\nD. 15\nE. None\n\n### Answer:\nExplanation: In this simple addition with repetition series, each number in the series repeats itself, and then increases by 12 to arrive at the next number.\nAnswer: Option C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich of the following could be the value of x, if |14x \u2013 56| = 196?\n\n### Options:\nA. -14\nB. -18\nC. -10\nD. 10\nE. 1/4\n\n### Answer:\n|14x \u2013 56| = 196\n=> 14x - 56 = 196\nor 14x - 56 = -196\n=> 14x = 252 or 14x = -140\n=> x = 18 or x = -10\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA glass was filled with 15 ounces of water, and 0.05 ounce of the water evaporated each day during a 15-day period. What percent of the original amount of water evaporated during this period?\n\n### Options:\nA. 0.005%\nB. 0.05%\nC. 0.5%\nD. 5%\nE. 25%\n\n### Answer:\nIn 15 days 15*0.05=0.75 ounces of water evaporated, which is 0.75/15\u00e2\u02c6\u2014100=5 of the original amount of water.\nAnswer: D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\npow(1000,9) \u00f7 pow(10,24) = ?\n\n### Options:\nA. 10000\nB. 1000\nC. 100\nD. 10\nE. None of these\n\n### Answer:\nGiven Exp. = pow(1000,9) = pow(pow(10,3),9) = pow(10,27) = pow(10, (27-24)) = pow(10,3) = 1000\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a three digit number, the hundred digit is 2 more than the tens digit and the units digit is 2 less than the tens digit. If the sum of the digits is 18, find the number?\n\n### Options:\nA. 975\nB. 753\nC. 642\nD. 684\nE. None of these\n\n### Answer:\nLet the three digit numbers be 100a + 10b + c\na = b + 2\nc = b - 2\na + b + c = 3b = 18 => b = 6\nSo a = 8 and b = 4\nHence the three digit number is: 864\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n3 men or 9 women can do a piece of work in 20 days. In how many days will 12 men and 8 women do the same work?\n\n### Options:\nA. 2 days\nB. 3 days\nC. 4 days\nD. 5 days\nE. 6 days\n\n### Answer:\n3M = 9W ---- 20 days\n12M + 8W -----?\n36W + 8 W = 44W ---?\n9W ---- 20 44W -----?\n9 * 20 = 44 * x => x = 4 days\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n4/6 of the population of the country of Venezia lives in Montague Province, while the rest lives in Capulet Province. In the upcoming election, 80% of Montague residents support Romeo, while 70% of Capulet residents support Juliet; each resident of Venezia supports exactly one of these two candidates. Rounded if necessary to the nearest percent, the probability that a Juliet supporter chosen at random resides in Capulet is\n\n### Options:\nA. 28%\nB. 41%\nC. 45%\nD. 64%\nE. 78%\n\n### Answer:\nTotal population = 60 (assume).\n4/6*60=40 people from Montague.\n2/6*60=20 people from Capulet.\n0.2*40=8 people from Montague support Juliet.\n0.7*20=14 people from Capulet support Juliet.\nThe probability that a Juliet supporter chosen at random resides in Capulet is 14/(8+14)=~64.\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAyesha's father was 38 years of age when she was born while her mother was 36 years old when her brother four years younger to her was born. What is the difference between the ages of her parents?\n\n### Options:\nA. 4 years\nB. 8 years\nC. 2 years\nD. 4 years\nE. 6 years\n\n### Answer:\nMother's age when Ayesha's brother was born = 36 years.\nFather's age when Ayesha's brother was born = (38 + 4) years = 42 years.\nRequired difference = (42 - 36) years = 6 years.\nANSWER E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train passes a station platform in 27 seconds and a man standing on the platform in 16 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?\n\n### Options:\nA. 299\nB. 165\nC. 170\nD. 185\nE. 112\n\n### Answer:\nSpeed = [54 * 5/18] m/sec = 15 m/sec.\nLength of the train = (15 * 16) m = 240 m.\nLet the length of the platform be x meters.\nThen, x + 240 / 27 = 15\nx + 240 = 405\nx = 165 m.\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA sum is divided among W, X and Y in such a way that for each rupee W gets, X gets 30 paisa and Y gets 20 paisa. If the share of W is RS. 10, what is the total amount?\n\n### Options:\nA. 12\nB. 13\nC. 14\nD. 15\nE. 16\n\n### Answer:\nw:x:y = 100:30:20\n20:6:4\n20 --- 10\n30 --- ? => 15\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe ratio of a to b is 4 to 5, where a and b are positive. If x equals a increased by 25 percent of a, and m equals b decreased by 80 percent of b, what is the value of m/x?\n\n### Options:\nA. 1/5\nB. 3/4\nC. 4/5\nD. 5/4\nE. 3/2\n\n### Answer:\na/b = 4/5\nm/x = (1/5)*5 / (5/4)*4 = 1/5\nThe answer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a function they are distributing noble prize. In how many ways can 3 prizes be distributed among 5 boys when a boy gets any no. of prizes?\n\n### Options:\nA. 55\nB. 58\nC. 25\nD. 65\nE. 70\n\n### Answer:\nAns.(C)\nSol. In this case, repetitions are allowed, so all the three prizes can be given in 4 ways, i.e. (5x5) ways = 52 ways = 25 ways Or nr ways = 52 ways = 25 ways\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a caravan, in addition to 60 hens, there are 35 goats and 6 camels with some keepers. If the total number of feet be 193 more than the number of heads in the caravan, the number of keepers is\n\n### Options:\nA. 5\nB. 10\nC. 15\nD. 20\nE. 25\n\n### Answer:\nExplanation: Let number of keepers be x. Then, Total number of feet = 2 x 60 + 4 x 35 + 4 x 6 + 2x = 2x + 284. Total number of heads = 60 + 35 + 6 + x= 101 + x. Therefore (2x + 284) = (101 + x) + 193 or x = 10. Answer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train 100 m long crosses a platform 125 m long in 15 sec; find the speed of the train?\n\n### Options:\nA. 767 kmph\nB. 55 kmph\nC. 54 kmph\nD. 33 kmph\nE. 37 kmph\n\n### Answer:\nD = 100 + 125 = 225\nT = 15\nS = 225/15 * 18/5 = 54 kmph\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man traveled a total distance of 1800 km. He traveled one-third of the whole trip by plane and the distance traveled by train is one-half of the distance traveled by bus. If he traveled by train, plane and bus, how many kilometers did he travel by bus?\n\n### Options:\nA. 700\nB. 800\nC. 900\nD. 1000\nE. 1100\n\n### Answer:\ntotal distance traveled = 1800 km.\ndistance traveled by plane = 600 km.\ndistance traveled by bus = x\ndistance traveled by train = x/2\nx + x/2 + 600 = 1800\n3x/2 = 1200\nx = 800 km\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nCoins are to be put into 12 pockets so that each pocket contains at least one coin. At most 8 of the pockets are to contain the same number of coins, and no two of the remaining pockets are to contain an equal number of coins. What is the least possible number of coins needed for the pockets?\n\n### Options:\nA. 7\nB. 13\nC. 17\nD. 22\nE. 28\n\n### Answer:\nSince at most 3 of the pockets are to contain the same number of coins then minimize # of coins in each, so let each contain just 1 coin;\nNext, we are told that no two of the remaining 4 pockets should contain an equal number of coins, so they should contain 2, 3, 4, and 5 coins each (also minimum possible);\nTotal: 1+1+1+1+1+1+1+1+2+3+4+5=22\nAnswer: D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFresh grapes contain 65% by weight while dried grapes contain 10% water by weight. What is the weight of dry grapes available from 400 kg of fresh grapes?\n\n### Options:\nA. 105.00 kg\nB. 115.60 kg\nC. 125.00 kg\nD. 130.50 kg\nE. 155.55 kg\n\n### Answer:\nFrom the question we know: 400kg * 65% = 260kg of water in the fresh grapes\n400kg - 260kg of water = 140kg of non-water mass\nWe are looking for the weight of the dry grapes (X).\nSince the question tells us that 10% of the weight of the dry graps is water and we know that 140kg is non-water mass we can set up the following equation:\nX = 1/10(X) + 140kg\n9/10(X) = 140kg\nX = 155.55 kg\nAnswer- E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo pipes A and B can separately fill a cistern in 10 and 15 minutes respectively. A person opens both the pipes together when the cistern should have been was full he finds the waste pipe open. He then closes the waste pipe and in another 4 minutes the cistern was full. In what time can the waste pipe empty the cistern when fill?\n\n### Options:\nA. A)1/8\nB. B)1/3\nC. C)1/9\nD. D)1/2\nE. E)1/4\n\n### Answer:\n1/10 + 1/15 = 1/6 * 4 = 2/3\n1 - 2/3 = 1/3\n1/10 + 1/15 - 1/x = 1/3\nx = 8\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man can row upstream at 25 kmph and downstream at 45 kmph, and then find the speed of the man in still water?\n\n### Options:\nA. 86\nB. 67\nC. 35\nD. 15\nE. 17\n\n### Answer:\nUS = 25\nDS = 45\nM = (45 + 25)/2\n= 35\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich of the following can be expressed as a terminating decimal?\n\n### Options:\nA. 1/25 + 1/35\nB. 1/225 + 1/1,250\nC. 1/11,000 + 1/13,000\nD. 1/75 + 1/35\nE. 1/125 + 1/8\n\n### Answer:\nIn such questions, it is always easier to find an answer instead of eliminating choices. Let us start with the simplest ones first.\nA. 1/25 + 1/35 = 12/175 = 12/25*1/7\n1/7 does is not a terminating decimal.\nE. 1/125 + 1/8 = 8 + 125/ 1000 = 133/1000\nThis is a terminating decimal and our answer.\nCorrect Option: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many 5 digit number contain number 3 ?\n\n### Options:\nA. 31512\nB. 32512\nC. 33512\nD. 34512\nE. 37512\n\n### Answer:\ntotal 5 digit no. = 9*10*10*10* 10 = 90000\nnot containing 3 = 8*9*9*9*9 = 52488\ntotal 5 digit number contain 3 = 90000 - 52488 = 37512\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nUsing all the letters of the word \"NOKIAS\", how many words can be formed, which begin with N and end with A?\n\n### Options:\nA. 8\nB. 24\nC. 9\nD. 3\nE. 1\n\n### Answer:\nThere are five letters in the given word.\nConsider 6 blanks ....\nThe first blank and last blank must be filled with N and A all the remaining three blanks can be filled with the remaining 3 letters in 4! ways.\nThe number of words = 4! = 24.\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJoe drives 180 miles at 60 miles per hour, and then he drives the next 120 miles at 40 miles per hour. What is his average speed for the entire trip in miles per hour?\n\n### Options:\nA. 42\nB. 50\nC. 50\nD. 54\nE. 56\n\n### Answer:\nt1= 180/60=3 hours\nt2=120/40=3 hours\nT=t1+t2=6 hours\nAvg speed = Total Distance/T\n= 300/6 = 50mph=B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the average of all the numbers between 6 and 38 which are divisible by 4.\n\n### Options:\nA. 18\nB. 22\nC. 20\nD. 30\nE. 28\n\n### Answer:\nSolution\nAverage\t= ((8+12+16+20+24+28+32+36)/8)\n= 186 / 7\n= 22\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA batsman in his 12th innings makes a score of 48 and thereby increases his average by 2 runs. What is his average after the 12th innings if he had never been \u2018not out\u2019?\n\n### Options:\nA. 26\nB. 43\nC. 44\nD. 45\nE. 46\n\n### Answer:\nLet \u2018x\u2019 be the average score after 12 th innings\n\u21d2 12x = 11 \u00d7 (x \u2013 2) + 48\n\u2234 x = 26\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA committee of 5 people is to be selected from 7 people. How many different committees are possible?\n\n### Options:\nA. 21\nB. 40\nC. 56\nD. D.168\nE. 336\n\n### Answer:\nBecause the order does not matter in selecting 5 people for the committee, this is a combination question.\nThe number of ways to select 5 people from 7 = 7C5 = 7!/5!*2! = 21. Hence A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA courtyard is 25 meter long and 18 meter board is to be paved with bricks of dimensions 20 cm by 10 cm. The total number of bricks required is?\n\n### Options:\nA. 22877\nB. 27778\nC. 20000\nD. 22500\nE. 17799\n\n### Answer:\nNumber of bricks =Courtyard area/1 brick area\n=(2500\u00d71800/20\u00d710)=22500\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain car uses 12 gallons of gasoline in traveling 180 miles. In order for the car to travel the same distance using 10 gallons of gasoline, by how many miles per gallon must the car\u2019s gas mileage be increased?\n\n### Options:\nA. 2\nB. 3\nC. 6\nD. 8\nE. 10\n\n### Answer:\n180/10 = 18. The difference is 18 - 15 = 3.\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA student needs 30% of the marks on a test to pass the test. If the student gets 80 marks and fails the test by 40 marks, find the maximum marks set for the test.\n\n### Options:\nA. 400\nB. 500\nC. 600\nD. 700\nE. 800\n\n### Answer:\n30% = 120 marks\n1% = 4 marks\n100% = 400 marks\nThe answer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA juice drink contains 6% of the recommended daily amount of vitamin A. If the juice drink contains 3 units of vitamin A, how many units of vitamin A are recommended daily?\n\n### Options:\nA. 70\nB. 50\nC. 60\nD. 56\nE. 66\n\n### Answer:\n6% of the recommended amount of vitamin A is 3 units.\nIf the total number of units recommended is X then\n6/100 = 3/X\n100/6 * 3 = X\n300/6 = X\n50 = X\nB)\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nhe average weight of 6 persons increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person ?\n\n### Options:\nA. 75 kg\nB. 55 kg\nC. 45 kg\nD. 80 kg\nE. 25 kg\n\n### Answer:\nExplanation:\nTotal weight increased = (6 x 2.5) kg = 15 kg.\nWeight of new person = (65 + 15) kg = 80 kg.\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn the new budget the price of rise rose by 5%. By how much percent must a person reduce his consumption so that his expenditure on it does not increase?\n\n### Options:\nA. 7.5%\nB. 9.1%\nC. 4.76%\nD. 12.6%\nE. 15%\n\n### Answer:\nReduce in consumption = R/(100+R) *100% = 5/105 *100 =4.76%\nAnswer is C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man rows his boat 85 km downstream and 45 km upstream, taking 2 1/2 hours each time. Find the speed of the stream?\n\n### Options:\nA. 7 kmph\nB. 9 kmph\nC. 1 kmph\nD. 8 kmph\nE. 2 kmph\n\n### Answer:\nSpeed downstream = d/t = 85/(2 1/2) = 34 kmph\nSpeed upstream = d/t = 45/(2 1/2) = 18 kmph\nThe speed of the stream\n= (34 - 18)/2\n= 8 kmph\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA started a business with Rs. 18000. After 4 months B joins with Rs. 24000. After 2 more months C joins with Rs. 30000. At the end of 10 months C received Rs. 1850 as his share. Find the total profit.\n\n### Options:\nA. Rs. 7955\nB. Rs. 7030\nC. Rs. 8510\nD. Rs. 6845\nE. None of these\n\n### Answer:\nExplanation:\nRatio of capitals of A, B and C\n= (18000 \u00d7 10) : (24000 \u00d7 6) : (30000 \u00d7 4)\n= 15 : 12 : 10\nLet the total profit be Rs. x.\nC's share = Rs. 10x/37\n=> 10x/37 = 1850\n=> x (1850 \u00d7 37)/10 = 6845\nHence, the total profit = Rs. 6845\nAnswer: Option D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich of the following expressions CANNOT have a negative value\n\n### Options:\nA. |a + b| \u2013 |a \u2013 b|\nB. |a + b| \u2013 |a|\nC. a^2 + b^2\nD. |2a + b| \u2013 |a + b|\nE. |a^3 + b^3| \u2013 a \u2013 b\n\n### Answer:\nWhenever you are required to find if the equation is a perfect square or not, try to bring everything in the form of a perfect square as they are always positive.\nOf the given options, only option D can be written in from of a perfect square.\na^2+b^2\nThis will always be positive.\nCorrect Option: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man buys an article for $100. and sells it for $115. Find the gain percent?\n\n### Options:\nA. 10%\nB. 15%\nC. 25%\nD. 20%\nE. 30%\n\n### Answer:\nC.P. = $100\nS.P. = $115\nGain = $15\nGain% = 15/100 *100 = 25%\nAnswer is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a school of 700 boys, 44% of Muslims, 28% Hindus, 10% Sikhs and the remaining of other communities. How many belonged to the other communities?\n\n### Options:\nA. 173\nB. 126\nC. 153\nD. 143\nE. 133\n\n### Answer:\n44 + 28 + 10 = 82%\n100 \u2013 82 = 18%\n700 * 18/100 = 126\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n20% of the students in a class failed in an examination. Out of the students who failed, 75% were males. Male students who failed constitute 90% of the economically poor students in the class. What is the ratio of the number of economically poor students to the number of students in the class?\n\n### Options:\nA. 1:4\nB. 1:5\nC. 5:6\nD. 1:6\nE. None of these\n\n### Answer:\nExplanation :\nLet, the total number of students in the class be 't' and the total number of students in the class who are economically poor be 'p'.\nSo,Total number of students who failed = t/5.\nTotal number of male students who failed are:-\n=>(3/4)\u00d7(t/5)=9p/10.\n=>p/t=1/6.\nHence,Number of economically poor students/Number of Students=1/6=1:6.\nAnswer : D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n5 years ago Kate was 5 times as old as her Son. 5 years hence her age will be 8 less than three times the corresponding age of her Son. Find the age of son?\n\n### Options:\nA. 7\nB. 8\nC. 9\nD. 10\nE. 11\n\n### Answer:\nlet x be the mother's age and y be the son's age\nx-5=5(y-5)\nx+5=3(y+5)-8\nby solving this we get x=35 and y=11\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf you write down all the numbers from 1 to 50, then how many times do you write 3 ?\n\n### Options:\nA. A)11\nB. B)15\nC. C)20\nD. D)21\nE. E)22\n\n### Answer:\nExplanation:\nExplanation:\nClearly, from 1 to 50, there are ten numbers with 3 as the unit's digit- 3, 13, 23, 33, 43, and ten numbers with 3 as the ten's digit - 30, 31, 32, 33, 34, 35, 36, 37, 38, 39.\nSo, required number = 5 + 10 = 15.\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf x is an integer, then x(x - 1)(x - v) must be evenly divisible by three when v is any of the following values EXCEPT\n\n### Options:\nA. -4\nB. -2\nC. -1\nD. 2\nE. 5\n\n### Answer:\nhere's another approach\nx(x - 1)(x - v)\nall three are consecutive, so the product MUST be a multiple of 3\nwe don't know the value of v just yet ... so let's extend the series ... the extension itself reveals the answers\n..(x-5)..(x-2)(x-1)x(x+1)..(x+4)..\nwe can see the possible values of v too from the series\nv = 2 OR 2+3n [25]\nv = -1 OR -1+3n [-1-4]\nB i.e. -2 does not fit in any value of v\nso B it is\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA student writes a computer program that generates a sequence of numbers a1, a2, a3, ... such that a1=a2=1 and ak=a(k-1)*4+1 for 2", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOf 55 players on a cricket team, 37 are throwers. The rest of the team is divided so one third are left- handed and the rest are right handed. Assuming that all throwers are right handed, how many right- handed players are there total?\n\n### Options:\nA. 49\nB. 55\nC. 59\nD. 71\nE. 92\n\n### Answer:\nTotal = 55\nThrower = 37\nRest = 55 - 37 = 18\nLeft Handed = 18/3 = 6\nRight handed = 12\nIf all Thrower are right handed then total right handed is 37 + 12 = 49\nso A. 49 is the right answer\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo pipes can fill a tank in 18 minutes and 15 minutes. An outlet pipe can empty the tank in 45 minutes. If all the pipes are opened when the tank is empty, then how many minutes will it take to fill the tank?\n\n### Options:\nA. 1/15\nB. 1/16\nC. 1/11\nD. 1/10\nE. 1/12\n\n### Answer:\nPart of the filled by all the three pipes in one minute\n= 1/18 + 1/15 - 1/45 = (5 + 6 - 2)/90 = 9/90 = 1/10\nSo, the tank becomes full in 10 minutes.\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe sum of two numbers is 30 and their difference is 10. Find their product.\n\n### Options:\nA. 104\nB. 114\nC. 315\nD. 200\nE. 335\n\n### Answer:\nLet the numbers be x and y.\nThen x + y = 30 and x - y = 10\nx = 20; y = 10\nxy = 20 * 10 = 200\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\ni row from a to b against the current in 8 hrs and from b to a in 2 hrs if speed of river is 9 m/sec.what is the speed of boat in still water.\n\n### Options:\nA. 10 m/sec\nB. 15 m/sec\nC. 25 m/sec\nD. 18 m/sec\nE. 20 m/sec\n\n### Answer:\nIf x m/sec is my speed in still water , then\n(x+9)*2*3600= (x-9)*8*3600\n6x=90\nx= 15 m/sec\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA Cistern is filled by pipe A in 8 hrs and the full Cistern can be leaked out by an exhaust pipe B in 12 hrs. If both the pipes are opened in what time the Cistern is full?\n\n### Options:\nA. 12 hrs\nB. 24 hrs\nC. 16 hrs\nD. 32 hrs\nE. None of these\n\n### Answer:\nExplanation :\nPipe A can fill 1\u20448 of the cistern in 1 hour.\nPipe B can empty 1\u204412 of the cistern in 1 hour\nBoth Pipe A and B together can effectively fill 1\u20448-1\u204412= 1\u204424 of the cistern in 1 hour\ni.e, the cistern will be full in 24 hrs. Answer : Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo cars, Car1 and Car2 move towards each other from W and Y respectively with respective speeds of 20 m/s and 15 m/s. After meeting each other Car1 reaches Y in 10 seconds. In how many seconds does Car 2 reach W starting from Y?\n\n### Options:\nA. 15.5 sec\nB. 8.4 sec\nC. 33.6 sec\nD. 31.11 sec\nE. 16.8 sec\n\n### Answer:\nW--------------------------------------|----------------------------Y\nCar A(20mps)------------------------->P<---------------Car B(15mps)\nLet 2 cars meet each other at point P in t seconds.\nCar1 covers distance= 20t. Car2 covers distance=15t. So, total distance WY= 35t.\nFrom P, Car 1 reaches onto Y in 10 secs. So it covers 15t further.\nso, 15t/20 = 10\nSo t=40/3 sec and total distance = (35*40)/3\nHence Car2 will cover total distance in (35*40)/(3*15) = 31.11 sec approx.\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 3 cards are selected at random from the deck of 52 cards then What is the probability of one of the selected cards will be King, one of them will be Queen and one of them will be Jack?\nA deck of cards has a total of 52 cards, consisting of 4 suits; (spades(Black), hearts(Red), diamond(Red)s, and clubs(Black)); and 13 cards including 1 king, 1 queen and 1 jack in each suit\n\n### Options:\nA. 96/5525\nB. 48/5525\nC. 16/5525\nD. 8/16575\nE. 1/2197\n\n### Answer:\nLet K,Q and J represent King, Queen and Jack respectively.\nOne possible combination is KQJ and this can be arranged in 3! ways.\nProbability of KQJ = (4/52)*(4/51)*(4/50)\nTotal probability = 3! * (4/52)*(4/51)*(4/50) . No need for final calculation. Reduce this to simpler form and you only have 1 option with 16 in the numerator. C is the correct answer.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many terms are there in 2, 4, 8, 16,..., 16384?\n\n### Options:\nA. 14\nB. 11\nC. 12\nD. 10\nE. 8\n\n### Answer:\n2, 4, 8, 16, ..., 16384 is a G.P with a =2\nand r =4/2 =2\nLet the number of terms be n. Then\n2 x 2 ^n-1 = 16384\nor 2^n-1 = 8192 = 2^13\nThus n - 1 =13\nn= 14\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA bus can hold 40 passengers. If there are 10 rows of seats on the bus, how many seats are in each row?\n\n### Options:\nA. 0\nB. 2\nC. 4\nD. 6\nE. 5\n\n### Answer:\nNo. of seats = 40/10 = 4\nThere are 4 seats in each row\nAnswer : C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSolve the given two equations and find the inequality of X and Y. (a) x^2-1=0 and (b) y^2+4y+3=0\n\n### Options:\nA. If x>y\nB. If x>=y\nC. If x=Y\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nLength of a rectangular plot is 20 mtr more than its breadth. If the cost of fencin gthe plot at 26.50 per meter is Rs. 5300, what is the length of the plot in mtr?\n\n### Options:\nA. 30 m\nB. 60 m\nC. 65 m\nD. 70 m\nE. 90 m\n\n### Answer:\nLet breadth = x metres.\nThen, length = (x + 20) metres.\nPerimeter = 5300 m = 200 m.\n26.50\n2[(x + 20) + x] = 200\n2x + 20 = 100\n2x = 80\nx = 40.\nHence, length = x + 20 = 60 m\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe area of the square formed on the diagonal of a rectangle as its side is 108 1/3 % more than the area of the rectangle. If the perimeter of the rectangle is 28 units, find the difference between the sides of the rectangle?\n\n### Options:\nA. 7m\nB. 6m\nC. 5m\nD. 2m\nE. 4m\n\n### Answer:\nLet the sides of the rectangle be l and b respectively.\nFrom the given data,\n(\u221al2 + b2) = (1 + 108 1/3 %)lb\n=> l2 + b2 = (1 + 325/3 * 1/100)lb\n= (1 + 13/12)lb\n= 25/12 lb\n=> (l2 + b2)/lb = 25/12\n12(l2 + b2) = 25lb\nAdding 24lb on both sides\n12l2 + 12b2 + 24lb = 49lb\n12(l2 + b2 + 2lb) = 49lb\nbut 2(l + b) = 28 => l + b = 14\n12(l + b)2 = 49lb\n=> 12(14)2 = 49lb\n=> lb = 48\nSince l + b = 14, l = 8 and b = 6\nl - b = 8 - 6 = 2m.\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMary's income is 60% more Than Tim's income and Tim's income is 60% less than Juan's income.What % of Juan's income is Mary's income.\n\n### Options:\nA. 124%\nB. B.120%\nC. 64%\nD. 80%\nE. 64%\n\n### Answer:\nEven I got 96%\nJ = 100\nT = 100*0.4 = 40\nM = 40*1.6 = 64\nIf Mary's income is x percent of J\nM = J*x/100\nx = M*100/J = 64*100/100 = 64\nAns:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAn accurate clock shows 8 o'clock in the morning. Through how many degrees will the hour hand rotate when the clock shows 10 o'clock in the morning?\n\n### Options:\nA. 80\u00b0\nB. 60\u00b0\nC. 30\u00b0\nD. 10\u00b0\nE. 120\u00b0\n\n### Answer:\nThe angle traced by the hour hand in 12 hours is 360\u00b0, which is 30\u00b0 per hour.\nIn 2 hours, the angle traced by the hour hand is 2\u00d730\u00b0 = 60\u00b0\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJohn spent a total of $135 on baseball tickets. The price of a ticket is either $12 for the field seats or $5 for the balcony. What is the minimum amount W of dollars he could have spent for the $12 tickets?\n\n### Options:\nA. $48\nB. $60\nC. $84\nD. $96\nE. $120\n\n### Answer:\n60 ..... 12 *5 W= 60. (min). Thus answer .B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe ratio of the length and the breadth of a rectangle is 4 : 3 and the area of the rectangle is 6912 sq cm. Find the ratio of the breadth and the area of the rectangle?\n\n### Options:\nA. 1: 96\nB. 1: 99\nC. 1: 94\nD. 1: 92\nE. 1: 91\n\n### Answer:\nLet the length and the breadth of the rectangle be 4x cm and 3x respectively.\n(4x)(3x) = 6912\n12x2 = 6912\nx2 = 576 = 4 * 144 = 22 * 122 (x > 0)\n=> x = 2 * 12 = 24\nRatio of the breadth and the areas = 3x : 12x2 = 1 : 4x = 1: 96.\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf |x^2 \u2212 30| = x, which of the following could be the value of x?\n\n### Options:\nA. -6\nB. -5\nC. 1\nD. 5\nE. 15\n\n### Answer:\nThe LHS is not negative, so the RHS is also not negative. Thus x >= 0.\nFirst, let's assume that x^2-30 is negative.\n-(x^2 -30) = x\nx^2 + x - 30 = 0\n(x+6)(x-5) = 0\nx = 5 or x = -6 (However, x can not be negative.)\nThen x = 5 is a possible value for x.\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHowmany three digits odd numbers can be formed using the digits 4,5,6,7,8,9 (repetition of digits not allowed)\n\n### Options:\nA. 60\nB. 75\nC. 65\nD. 55\nE. 45\n\n### Answer:\nThere are 3 ways of filling the unit place of the number. The remaining ten's and 100's place canbe filled in 5ways and\n4 ways respectively. Required number of numbers =3x5x4=60. Ans: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe diagonals of a rhombus are 14 cm and 18 cm. Find its area?\n\n### Options:\nA. 176\nB. 190\nC. 150\nD. 126\nE. 292\n\n### Answer:\n1/2 * 14 * 18\n= 126\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA shopkeeper sold two radio sets for 792 each, gaining 10% on one, and losing 10% on the other. Then he\n\n### Options:\nA. neither gains nor loses\nB. gains 1%\nC. loses 1%\nD. gains 5%\nE. None of these\n\n### Answer:\nSol.(c) When selling price of two articles is same and\n% gain = % loss\nthen there will be always loss.\nand overall % loss = (10)2\u2044100% = 1%. Answer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf six boys sit in a row, then what is the probability that three particular boys are always together is?\n\n### Options:\nA. 1/5\nB. 1/4\nC. 1/3\nD. 1/7\nE. 2/5\n\n### Answer:\nSix boys can be arranged in a row in 6! ways.\nTreat the three boys to sit together as one unit then there 4 boys and they can be arranged in 4! ways.\nAgain 3 boys can be arranged among them selves in 3! ways.\nFavorable outcomes = 3!4!\nRequired probability = 3!4!/6! = 1/5\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe five sides of a pentagon have lengths of 2, 3, 4, 5 and 6 inches. one pentagons are considered different only when the positions of the side lengths are different relative to each others. What is the total number of different possible pentagons that could be drawn using these five side lengths ?\n\n### Options:\nA. 5\nB. 12\nC. 24\nD. 32\nE. 120\n\n### Answer:\nCONCEPT: The number of ways to arrange n elements around a circular Manner is (n-1)!.\nBut the number of ways to arrange n elements in circular manner where the arrangement can be flipped around (e.g. Necklace, Garland, Bracelet) = (n-1)!/2.\nThe pentagon in the problem above can be flipped over (Clockwise Arrangement of Sides = Counter-clockwise arrangement), the number of distinct ways to arrange the 5 sides = (5-1)!/2 = 5.\nAnswer: option A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the value of 3/11 \u00d7 [(1 + 1/3) (1 + 1/4) \u2026\u2026\u2026\u2026. (1 + 1/120)] is\n\n### Options:\nA. 11\nB. 12\nC. 13\nD. 14\nE. 15\n\n### Answer:\n3/11 \u00d7 [(1 + 1/3) (1 + 1/4) ....... (1 + 1/120)]\n3/11 \u00d7 [4/3 + 5/4 \u00d7 ........ 121/120]\n3/11 \u00d7 4/3 \u00d7 5/4 \u00d7 .... 121/120\n121/11 = 11.\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFor every integer n \u2265 3, the function g(n) is defined as the product of all the odd integers from 1 to n, inclusive. What is the value of g(106) \u2013 g(103)?\n\n### Options:\nA. 100\nB. 99\nC. 98\nD. 102\nE. 104\n\n### Answer:\ng(106) = 1*3*5*7*9*...*99*101*103*105\ng(103) = 1*3*5*7*9*...*99*101*103\ng(106) - g(103) = 1*3*5*7*9*...*99*101*103*105 - 1*3*5*7*9*...*99*101*103 = 1*3*5*7*9*...*103*(105 - 1) = 1*3*5*7*9*...*99*101*103*104\nhence:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf f(x) = 2*(x^4 - 1)/(x^2), what is f(1/x) in terms of f(x)?\n\n### Options:\nA. f(x)\nB. -2f(x)\nC. 1/f(x)\nD. -1/f(x)\nE. 2*f(x)\n\n### Answer:\nf(1/x) = ((1/x)^4 - 1) / ((1/x)^2)\n= ((1/x^4) - 1) / (1/x^2)\n= ((1-x^4)/(x^4)) / (1/x^2)\n= (1-x^4)/(x^2)\n= - 2( (x^4) -1) / (x^2)\n= -2*f(x)\nAnswer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the area of a cuboid of length 15cm , breadth 10 cm . and height 16cm.\n\n### Options:\nA. 2400 cm cube\nB. 2410 cm cube\nC. 2420 cm cube\nD. 2430 cm cube\nE. 2480 cm cube\n\n### Answer:\nArea of a cuboid = lxbxh =15cm x 10cm x 16cm = 2400 cm cube\nanswer :A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThree unbiased coins are tossed. What is the probability of getting at most two heads?\n\n### Options:\nA. 9/7\nB. 7/8\nC. 1/2\nD. 5/4\nE. 3/8\n\n### Answer:\nExplanation:\nHere S = {TTT, TTH, THT, HTT, THH, HTH, HHT, HHH}\nLet E = event of getting at most two heads.\nThen E = {TTT, TTH, THT, HTT, THH, HTH, HHT}.\nP(E)=n(E)/n(S)=7/8\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe duplicate ratio of 2:3 is?\n\n### Options:\nA. 4:9\nB. 1:4\nC. 1:8\nD. 1:18\nE. 1:13\n\n### Answer:\n2^2: 3^2 = 4:9\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFive friends go to see a movie at the local movie theater and sit in a row together. If there are two friends who refuse to sit next to each other, how many 5-person seating arrangements are possible?\n\n### Options:\nA. 72\nB. 90\nC. 120\nD. 140\nE. 180\n\n### Answer:\nThe number of ways to arrange 5 people in a row is 5! = 120\nFrom this we want to subtract all the arrangements where the two friends are next to each other. If we consider them as one unit, then the number of arrangements of this 2-person unit and the 3 other friends is 4! And the number of arrangements of the two friends within this unit are 2 because the two friends can switch places. So the total number of arrangements of the 5 friends with the 2-person unit together is 4!*2\nThe total number of permutations where these two friends are not seated next to each other is 5! - 4!*2 = 120 - 48 = 72\nThe answer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a certain company, the ratio of male to female employees is 7:8. If 3 more men were hired, this ratio would increase to 8:9. How many male employees are there in the company?\n\n### Options:\nA. 6\nB. 21\nC. 27\nD. 189\nE. 192\n\n### Answer:\nAnother approach is to use TWO variables.\nLet M = present number of males\nLet F = present number of females\nThe ratio of male to female employees is 7:8\nSo, M/F = 7/8\nCross multiply to get 7F = 8M\nIf 3 more men were hired, this ratio would increase to 8:9\nSo, (M+3)/F = 8/9\nCross multiply to get 9(M+3) = 8F\nExpand: 9M + 27 = 8F\nWe now have a system of two equations and two variables:\n7F = 8M\n9M + 27 = 8F\nSolve to get: M = 189 and F = 216\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe ratio of two numbers is 3 : 4 and their H.C.F. is 4. Their L.C.M. is\n\n### Options:\nA. 12\nB. 16\nC. 24\nD. 48\nE. 50\n\n### Answer:\nSolution\nLet the numbers be 3x and 4x. Then, their H.C.F. = x. So, x = 4.\nSo, the numbers are 12 and 16.\nL.C.M. of 12 and 16 = 48.\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a apartment, 30% of the people speak English, 20% speak Hindi and 14% speak both. If a people is selected at random, what is the probability that he has speak English or Hindi?\n\n### Options:\nA. 1/35\nB. 2/35\nC. 9/25\nD. 12/19\nE. 3/17\n\n### Answer:\nP (E) = 30 / 100 , P (H) = 20 / 100 and P (E \u00e2\u02c6\u00a9 H) = 14 / 100 =\nP (E or H) = P (E U H)\n= P (E) + P (H) - P (E \u00e2\u02c6\u00a9 H)\n= (30 / 100) + (20/100 - (14 / 100) = 36/100 = 9/25\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a class of 140 students, 60% of them passed. By what percent is the number of students who passed more than the number of failed students?\n\n### Options:\nA. 90%\nB. 58%\nC. 59%\nD. 50%\nE. 53%\n\n### Answer:\nNumber of students passed\n= 60% of 140 = 60/100 * 140 = 84\nNumber of students failed\n= 140 - 84 = 56.\nRequired percentage\n= 28/56 * 100 = 50%.\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n26 buckets of water fill a tank when the capacity of each bucket is 13.5 litres. How many buckets will be required to fill the same tank if the capacity of each bucket is 9 litres?\n\n### Options:\nA. 30\nB. 39\nC. 60\nD. Data inadequate\nE. None of these\n\n### Answer:\nCapacity of the tank = 26 \u00c3\u2014 13.5= 351 litres\nWhen the capacity of each bucket = 9 litres, then the required no. of buckets\n= 351\u00e2\u0081\u201e9 = 39\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the reciprocals of two consecutive positive integers are added together, what is the sum in terms of the greater integer m?\n\n### Options:\nA. (2m-2)/(m^2- m)\nB. (2m-1)/(m^2- m)\nC. (2m-1)/(m^4- m)\nD. (3m-1)/(m^2- m)\nE. (2m-1)\n\n### Answer:\nLet two consecutive positive integers be m and m-1 (Greater integer is m)\nSo,\n(1/m) + [1/(m-1)]\n= (2m-1)/m(m-1)\n=(2m-1)/(m^2- m)\nAnswer : B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOf the 4 numbers, whose average is 60, the first is one-fourth of the sum of the last three. The first number is?\n\n### Options:\nA. 36\nB. 40\nC. 48\nD. 52\nE. 56\n\n### Answer:\nLet the first number be x\nsum of the 4 numbers = x+4x = 5x\n5x/4 = 60\nx = 60*4/5 = 48\nAnswer is C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMary and Mike enter into a partnership by investing $700 and $300 respectively. At the end of one year, they divided their profits such that a third of the profit is divided equally for the efforts they have put into the business and the remaining amount of profit is divided in the ratio of the investments they made in the business. If Mary received $800 more than Mike did, what was the profit made by their business in that year?\n\n### Options:\nA. $2000\nB. $6000\nC. $4000\nD. $1333\nE. $3000\n\n### Answer:\nExplanatory Answer\nLet the profit made during the year be $3x\nTherefore, $x would have been shared equally and the remaining $2x would have been shared in the ratio 7 : 3.\ni.e., 70% of 2x would go to Mary and 30% of 2x would go to Mike.\nHence, Mary would get (70 - 30)% of 2x more than Mike\nOr 40% of 2x = $800\ni.e.,(40/100)*2x = 800\nor 2x = 2000.\nHence, the profit made by the company during the year $3x = $3000.\nThe correct choice is (E)\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the probability that the Detroit Lions win the Super Bowl is 1/20 and the probability that the Detroit Tigers win the World Series is 1/6, what is the probability that either the Bears win the Super Bowl or the Cub win the World Series (but not both)?\n\n### Options:\nA. 1/2\nB. 2/7\nC. 1/3\nD. 1/4\nE. 1/5\n\n### Answer:\n19/20*1/6 + 1/20*5/6 = 24/120 = 1/5\nThe answer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man in a train travelling at 24km/hr notices that a train going in the opposite direction passes him in 10 sec.If the length of this train is 220m find its speed .\n\n### Options:\nA. 30 km/hr\nB. 40 km/hr\nC. 55 km/hr\nD. 60 km/hr\nE. 70 km/hr\n\n### Answer:\nrelative speed of trains = 220/10 mtrs/sec = 220*18/(10*5)= 79 km/hr\nspeed of 2nd train = 79-24=55 km/hr\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how many ways the letters of the word RAIXBON be arranged?\n\n### Options:\nA. 4367\nB. 5657\nC. 8756\nD. 5040\nE. 4345\n\n### Answer:\nTotal ways of arranging the letters = 7! = 5040 ways.\nD)\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA palindrome is a number that reads the same forward and backward, such as 121. How many odd, 4-digit numbers are palindromes?\n\n### Options:\nA. 40\nB. 45\nC. 50\nD. 90\nE. 2500\n\n### Answer:\nFirst recognize you only need to consider the first two digits (because the second two are just the first two flipped)\nThere are 90 possibilities for the first two digits of a 4 digit number, 10-99 inclusive. Everything starting with a 1,3,5,7,9 will be odd, which is 5/9ths of the combinations.\n5/9*90 = 50\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA dishonest dealer professes to sell goods at the cost price but uses a weight of 850 grams per kg, what is his percent?\n\n### Options:\nA. 2%\nB. 25%\nC. 22%\nD. 17.65%\nE. 45%\n\n### Answer:\n850 --- 150\n100 --- ? => 17.65%\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA sum of money invested at C.I. amounts to Rs. 800 in 3 years to Rs. 840 in 4 years. The rate of interest per annum is?\n\n### Options:\nA. 2 1/2 %\nB. 4%\nC. 5%\nD. 6 2/3 %\nE. 6%\n\n### Answer:\nS.I. on Rs. 800 for 1 year = (840 - 800) = Rs. 40 Rate = (100 * 40)/(800 * 1) = 5%\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average monthly salary of laborers and supervisors in a factory is Rs.1250 per month; where as the average monthly salary of 6 supervisors is Rs.2450. If the average monthly salary of the laborers is Rs.950 find the number of laborers?\n\n### Options:\nA. 87\nB. 42\nC. 78\nD. 76\nE. 26\n\n### Answer:\n5x 6x 2x\n50 25 100\n250x + 150x + 200x = 4200\n600x = 4200\nx = 7 => 6x =42\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo cards are selected at random from 10 cards numbered 1 to 10. Find the probability that the sum is odd if two cards are drawn together.\n\n### Options:\nA. 11\nB. 88\nC. 77\nD. 19\nE. 17\n\n### Answer:\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe edge of a cube is 2a cm. Find its surface?\n\n### Options:\nA. 23a2 cm2\nB. 84a2 cm2\nC. 64a2 cm2\nD. 24a2 cm2\nE. 14a2 cm2\n\n### Answer:\n6a2 = 6 * 2a * 2a = 24a2\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe value of a \"Tin-Rin\" stock in the stock market decreased by 15% in the last two years. The economic experts believe that the value of the stock will increase by 7% during the following year, which will make the value $440. What was the approximate price of the stock two years ago?\n\n### Options:\nA. $473.\nB. $464.\nC. $455.\nD. $445\nE. $430.\n\n### Answer:\nLet the stock value was x.\nx* 0.85 * 1.07= 440\nx= 440/0.85*1.07= 490 (approximately)\nA is the answer\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a class of 20 students in an examination in Mathematics 2 students scored 100 Marks each, 3 get\nzero each and the average of the rest was 40. What is the average Of the whole class?\n\n### Options:\nA. 46\nB. 49\nC. 40\nD. 38\nE. 35\n\n### Answer:\nTotal marks obtained by a class of 20 students\n= 2 * 100 + 3 * 0 + 15 * 40\n= 200 + 600 = 800\n: Average marks of whole class = 800/20 = 40\nAnswer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a race of length L metres, Johnson beats Lewis by M metres and Greene by N metres, By how many metres does Lewis beat Greene in the same race ? (M", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train is moving at a speed of 132 km/hr. If the length of the train is 200 meters, how long will it take to cross a railway platform 295 meters long\n\n### Options:\nA. 6 \u00bd sec\nB. 7 \u00bd sec\nC. 8 sec\nD. 13 \u00bd sec\nE. 9 sec\n\n### Answer:\nExplanation:\nSpeed of train = 132 \u00d7(5/18) m/sec = 110/3 m/sec.\nDistance covered in passing the platform = (200 + 295) m = 495 m.\nTime taken =495 \u00d7(3/110) sec =27/2 sec = 13 \u00bd sec\nAnswer: Option D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe total marks obtained by a student in Physics, Chemistry and Mathematics is 150 more than the marks obtained by him in Physics. What is the average mark obtained by him in Chemistry and Mathematics?\n\n### Options:\nA. 75\nB. 28\nC. 279\nD. 271\nE. 27\n\n### Answer:\nLet the marks obtained by the student in Physics, Chemistry and Mathematics be P, C and M respectively.\nP + C + M = 150 + P\nC + M = 150\nAverage mark obtained by the student in Chemistry and Mathematics\n= (C + M)/2 = 150/2 = 75.\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhen 10 per cent of a number is added to another number the second number increases to its 140 per cent. What is the ratio between the first and the second number?\n\n### Options:\nA. 3 : 4\nB. 4 : 1\nC. 3 : 2\nD. Data inadequate\nE. None of these\n\n### Answer:\nLet the first and the second numbers be x and y respect then\ny + 10% of x = 140% of y\nor, y + 0.1x = 1.4y\nor, 0.1x = 0.4y\n\u2234 x : y = 0.4 : 0.1 = 4 : 1\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA tourist purchased a total of $1,300 worth of traveler\u2019s checks in $10 and $50 denominations, During the trip the tourist cashed 7 checks and then lost all of the rest. If the number of $10 checks cashed was one more or one less than the number of $50 checks cashed, what is the minimum possible value of the checks that were lost?\n\n### Options:\nA. $1,430\nB. $1,310\nC. $1,290\nD. $1,070\nE. $1,150\n\n### Answer:\nsince total cashed checks = 7 ans $10 check cashed = one less or more than $50 checks\nTherefore either $10 checks = 3 and $50 checks = 4 OR $10 checks = 4 and $50 checks = 3\nusing this information 1st option gives us the maximum cashed value therefore if we negate this value from total value we will get minimum value of which checks have lost\nTherfore 1300 - 230 = 1070 hence answer is D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn X game of billiards, X can give Y 20 points in 60 and he can give Z 30 points in 60. How many points can Y give Z in X game of 120?\n\n### Options:\nA. 30\nB. 20\nC. 25\nD. 40\nE. 50\n\n### Answer:\nX scores 60 while Y score 40 and Z scores 30.\nThe number of points that Z scores when Y scores 120 = (120 * 30)/40 = 90.\nIn X game of 100 points, Y gives (120 - 90) =30 points to C.\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA nickel is placed flat on a table. What is the maximum number of nickels that can be placed\naround it, flat on the table, with each one tangent to it?\n\n### Options:\nA. 4\nB. 5\nC. 6\nD. 7\nE. 8\n\n### Answer:\nConnect the midpoints of the given nickel and two others placed around it so that\nall three touch. This creates an equilateral triangle with 60 degree angles. Since 360=60 = 6,\nsix nickels can be placed around the given nickel.\ncorrect answer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAn entrepreneurship competition requires registering teams to have 3 team members, at least one of which must be a technology co-founder. If all team members must come from the auditorium during the meet and greet event which has 4 technologists and 6 businessmen, how many possible team submissions are possible?\n\n### Options:\nA. 76\nB. 100\nC. 162\nD. 198\nE. 202\n\n### Answer:\nWe have 3 scenarios here:\n1) 1 tech2 businessmen: 4C1 x 6C2 = 60\n2) 2 tech1 businessman: 4C2 x 6C1 = 36\n3) 3 tech0 businessmen: 4C3 = 4\nTotal: 60+36+4 = 100\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many divisions are there on the face of a clock?\n\n### Options:\nA. 1\nB. 5\nC. 6\nD. 22\nE. 25\n\n### Answer:\nB\n5\nAny clock or watch except a digital watch, has a dial. On the circular border of the dial of a watch or clock there are the hour numbers from 1 to 12 at equal intervals. Between the two numbers there are 5 divisions.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOf the teams competing in the world archery championships, Forty percent are from Europe. Half as many are from the United States and one twentieth are from Africa. What fraction of teams are from neither Europe, the US or Africa.\n\n### Options:\nA. 13/20\nB. 15/20\nC. 13/15\nD. 7/20\nE. 13/17\n\n### Answer:\nHalf as manymeans half of EU, then\nEU 40%\nUS 20%\nAF 5%\nthe rest is 35%, answer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is cost price of an article sold by a trader at 15% loss, given that the trader would have made a profit of 6% if he had sold it for $30 more?\n\n### Options:\nA. $576.19\nB. $436.19\nC. $476.19\nD. $470.19\nE. $276.19\n\n### Answer:\nLet C.P. be $x\nThen 106% of x - 85% of x = 100\n21% of x = 100\n21/100 *X = 100\n21x = 10000\nx = 476.19\nAnswer is C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the day before yesterday was Thursday, when will Sunday be?\n\n### Options:\nA. Day after tomorrow\nB. Tomorow\nC. Two days after today\nD. Today\nE. None of these\n\n### Answer:\nExplanation :\nDay before yesterday was Thursday\n=>Yesterday was a Friday\n=> Today is a Saturday\n=> Tomorrow is a Sunday. Answer : Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain fruit stand sold apples for $0.70 each and bananas for $0.60 each. If a customer purchased both apples and bananas from the stand for a total of $6.30, what total number of apples and bananas did the customer purchase?\n\n### Options:\nA. 8\nB. 9\nC. 10\nD. 11\nE. 12\n\n### Answer:\nLet's start with 1 apple for $0.70.\nLet's subtract $0.70 from $6.30 until we get a multiple of $0.60.\n$6.30, $5.60, $4.90, $4.20 = 7*$0.60\nThe customer purchased 7 bananas and 3 apples.\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe sale price sarees listed for Rs.298 after successive discount is 12% and 15% is?\n\n### Options:\nA. 321\nB. 223\nC. 245\nD. 265\nE. 162\n\n### Answer:\nExplanation:\n298*(88/100)*(85/100) = 223\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n7 people average age is 30. youngest person age is 5. find average of the people when youngest was born.\n\n### Options:\nA. 23\nB. 24\nC. 25\nD. 26\nE. 27\n\n### Answer:\naverage age of people =30\nso have total age =210\nbefore 7 years we have to deduct each person age by seven years 210-35=161\nso average age would be 175/7=25\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA and B rent a pasture for 10 months. A put in 80 cows for 7 months. How many can B put in for the remaining 3 months, if he pays half as much again as A?\n\n### Options:\nA. 388\nB. 277\nC. 266\nD. 280\nE. 191\n\n### Answer:\n80* 7: x* 3 = 1:1 1/2\n560: 3x = 2: 3\nx = 280\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain no. when divided by 80 leaves a remainder 25, what is the remainder if the same no.be divided by 15?\n\n### Options:\nA. 3\nB. 4\nC. 6\nD. 7\nE. 9\n\n### Answer:\nExplanation:\n80 + 25 = 105/15 = 7 (Remainder)\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJohn started driving on a highway at a constant speed of R miles per hour at 13:00. Then, 2 hours later, Tom started driving on the same highway at a constant speed of 2R miles per hour at 15:00. If both drivers maintained their speed, how many miles had John driven on the highway when Tom caught up with John?\n\n### Options:\nA. 2R\nB. 3R\nC. 4R\nD. 5R\nE. 6R\n\n### Answer:\nIn 2 hours, John drove 2R miles.\nTom can catch John at a rate of 2R - R = R miles per hour.\nThe time it takes Tom to catch John is 2R / R = 2 hours.\nIn 2 hours, John can drive another 2R miles for a total of 4R miles.\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSid began driving from home on a trip averaging 30 miles per hour. How many miles per hour must Carla drive on average to catch up to him in exactly 3 hours if she leaves 30 minutes after Sid?\n\n### Options:\nA. 35\nB. 55\nC. 39\nD. 40\nE. 60\n\n### Answer:\nCarla starts 30 minutes later and it takes 3 hr for carla to meet Sid\nSo Sid total time travelled = 3hr + 30 minutes\nSid distance = 30 * (3 1/2) = 105\nso carla need to travle 105 to meet Sid in 3 hrs\nspeed of carla = 105/3 = 35 miles per hour\nAnswer is A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAt a certain zoo, the ratio of sea lions to penguins is 4 to 11. If there are 84 more penguins than sea lions at the zoo, how many sea lions are there?\n\n### Options:\nA. 24\nB. 36\nC. 48\nD. 72\nE. 132\n\n### Answer:\nThe ratio as mentioned = 4/11\nalso\nsea lion + 84 = penguins\nor,\n4x+84=11x\nx=84/7=12\nnumber of sea lions= 12*4=48\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average of the marks of 12 students in a class is 36. If the marks of each student are doubled, find the new average?\n\n### Options:\nA. 72\nB. 23\nC. 29\nD. 26\nE. 13\n\n### Answer:\nSum of the marks for the 12 students\n= 12 * 36 = 432.\nThe marks of each student are doubled, the sum also will be doubled.\nThe new sum = 432 * 2 = 864. So, the new average\n= 864/12 = 72.\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nLaura took out a charge account at the General Store and agreed to pay 9% simple annual interest. If she charges $35 on her account in January, how much will she owe a year later, assuming she does not make any additional charges or payments?\n\n### Options:\nA. $2.10\nB. $37.10\nC. $37.16\nD. $38.10\nE. $38.15\n\n### Answer:\nPrincipal that is amount taken by Laura at year beginning = 35$\nRate of interest = 9%\nInterest = (9/100)*35 = 3.15$\nTotal amount that Laura owes a year later = 35+3.15 = 38.15 $\nAnswer E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMarla starts running around a circular track at the same time Nick starts walking around the same circular track. Marla completes 10 laps around the track per hour and Nick completes 5 laps around the track per hour. How many minutes after Marla and Nick begin moving will Marla have completed 4 more laps around the track than Nick?\n\n### Options:\nA. 5\nB. 48\nC. 12\nD. 15\nE. 20\n\n### Answer:\nMaria's rate - 10 laps per hour --> 10/60 laps/min\nNick's rate - 5 laps per hour --> 5/60 laps/min\nlets set equations:\n10/60*t=4 (since Maria had to run 4 laps before Nick would start)\n5/60*t=0 (Hick has just started and hasn't run any lap yet)\n(10/60-5/60)*t=4-0 (since Nick was chasing Maria)\nt=48 min needed Maria to run 4 laps\nAnswer : B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThree interviewers, A, B, and C are interviewing 30 applicants. Only with three interviewers' admission can an applicant be admitted. If interviewer A admitted 10 applicants, B admitted 12 applicants, and C admitted 15 applicants, at least how many applicants get the admission?\n\n### Options:\nA. 6\nB. 2\nC. 0\nD. 8\nE. 12\n\n### Answer:\nIf A admitted 10 are overlapping with B admission of 12 But C does not overlap with anybody.\nThen no student will get nod from all the 3.\nHence 0 student will get admission.\nAnswer : C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train passes a station platform in 38 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?\n\n### Options:\nA. 248 m\nB. 240 m\nC. 270 m\nD. 765 m\nE. 176 m\n\n### Answer:\nSpeed = (54 * 5/18) m/sec = 15 m/sec. Length of the train = (15 x 20)m = 300 m. Let the length of the platform be x meters. Then, (x + 300)/38 = 15 ==> x + 300 = 570 ==> x\n= 270 m.\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a mixture of 60 litres the ratio of milk to water is 5:1. Additional 20 litres of water is added to the mixture. Find the ratio of milk to water in the resulting mixture.\n\n### Options:\nA. 2:3\nB. 5:3\nC. 1:4\nD. 3:2\nE. 3:1\n\n### Answer:\nGiven that Milk/Water=5x/x and 5x+x=60 --> x=10.\nThus Milk=5x=50 liters and Water=x=10 liters.\nNew ratio = 50/(20+10) = 50/30 = 5/3.\nAnswer is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThis topic is locked. If you want to discuss this question please re-post it in the respective forum.\nIf y \u2260 3 and 3q/y is a prime integer greater than 2, which of the following must be true?\nI. q = y\nII. y = 1\nIII. q and y are prime integers.\n\n### Options:\nA. None\nB. I only\nC. II only\nD. III only\nE. I and III\n\n### Answer:\n3q/y and if q=y then ans is 3 and 3 is prime number, which is greater than 2. so ans must be B. Please post OA.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a is an odd integer and b is an even integer which of the following must be an integer :\n\n### Options:\nA. a/b\nB. ab\nC. 2a+b\nD. 2(a+b)\nE. option B C and D\n\n### Answer:\na= odd = e.g 3\nb=even = e.g 6\nA. odd/even for example 3/6 = 0.5 no even no odd\nB. odd * even = 3 * 6 = 18 even\nC. 2*odd + even = even + even even\nD. 2(even + odd) = 2(odd) even\nHence E it is.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the product of the greatest 2 digit multiple of 13 and the greatest 2 digit prime number?\n\n### Options:\nA. 9,312\nB. 9,408\nC. 9,506\nD. 8,827\nE. 9,702\n\n### Answer:\nthe greatest 2 digit multiple of 13: 91\nthe greatest 2 digit prime numebr: 97\n97*91.\n8827\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe rate of failure in an examination is 39.25%. Find the least number of total candidates appeared in the examination.\n\n### Options:\nA. 100\nB. 200\nC. 300\nD. 400\nE. 500\n\n### Answer:\nif 100 student appear then failure=39.25 ......... which is not possible because number of student can not be fraction,like wise in 200 student,failure=78.5, so we have to make the failure percentage into a unit digit failure not fraction...so min no of student =400 so that no of failure=157..........so least no of student appeared in the exam= 400.\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the charge of staying in a student youth hostel $18.00/day for the first week, and $15.00/day for each additional week, How much does it cost to stay for 23 days?\n\n### Options:\nA. $336\nB. $289\nC. $282\nD. $274\nE. $286\n\n### Answer:\nTotal number of days of stay = 23\nCharge of staying in first week = 18*7 = 126 $\nCharge of staying for additional days =(23-7)*15 = 16*15 = 240 $\nTotal charge =126 +240 = 366$\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich of the following is closest to (5!-4!)/(5!+4!)?\n\n### Options:\nA. 0.01\nB. 0.1\nC. 0.2\nD. 0.7\nE. 10\n\n### Answer:\n(5!-4!)/(5!+4!)\n4! (5-1)/4! (5+1)\n4/6 = 2/3 =0.7 (approximately)\nD is the answer\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe S.I. on a certain sum of money for 6 years at 14% per annum is half the C.I. on Rs. 7000 for 2 years at 7% per annum. The sum placed on S.I. is?\n\n### Options:\nA. 603.75\nB. 555.75\nC. 569.55\nD. 256.25\nE. 563.23\n\n### Answer:\nC.I. = [7000 * (1 + 7/100)2 - 7000]\r= (7000 * 11/10 * 11/10 - 7000) = Rs. 1014.3.\rSum = (507.15 * 100)/(6 * 14)\r= Rs.603.75\rAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat do you get if you add 7 to 290 three times?\n\n### Options:\nA. 305\nB. 296\nC. 289\nD. 297\nE. 309\n\n### Answer:\nD\n297 , 297 , 297\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe moon revolves around the earth at a speed of approximately 0.9 kilometers per second. This approximate speed is how many kilometers per hour?\n\n### Options:\nA. 60\nB. 61.2\nC. 3240\nD. 3,600\nE. 3,672\n\n### Answer:\nmoon revolves around the earth at a speed of 1.02kilometers per second.\none hour equal to 60 minutes.\none minute equals to 60 seconds. so one hour equals to 3600seconds.\nso one hour, speed= 0.9*3600=3240kilometers per hour.\nOption C is correct\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the missing number in the given sequence : 1,4,7,?,13,16,?\n\n### Options:\nA. 10 & 19\nB. 8 & 17\nC. 9 & 18\nD. 11 & 20\nE. 12 & 21\n\n### Answer:\n1+3=4\n4+3=7\n7+3=10\n10+3=13\n13+3=16\n16+3=19\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how many ways can the letters of the word RAVES be arranged in a row so that the vowels appear in alphabetic order?\n\n### Options:\nA. 60\nB. 30\nC. 120\nD. 240\nE. 90\n\n### Answer:\nTwo letters can be arranged in 2! ways.\nonly one combination EIU is required.\n5 letters can be arranged in 5! ways.\nthus 5!/ 2! * 1 = 60.\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFor a drama, Jack need to select 5 dramatist from a team of 8 members. What is the possible way to select dramatist?\n\n### Options:\nA. 60\nB. 56\nC. 48\nD. 25\nE. 10\n\n### Answer:\nThe question is out of 8 members, john needs 5 members.\nSo the combination is 8C5.\n8C5=8!/3!*5!\n=8*7*6*5!/5!*3*2*1\n=56 ways to select.\nOption B is answer\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how many ways can 6 boys and 3 girls sit around a table in such a way that no two girls sit together?\n\n### Options:\nA. 10000\nB. 14000\nC. 14400\nD. 18000\nE. 19000\n\n### Answer:\nThe 6 boys can be seated around a table in 5! Ways. In between them there are 6 places.\nThe 3 girls can be placed in the 6 places in 6P3 ways.\nTherefore, Required number of ways= 5!* 6P3\n=120*120\n=14400\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nthe price of a maruti car rises by 30% while the sales of the car came down by 20%. what is the percent change in the total revenue?\n\n### Options:\nA. -4\nB. 4\nC. -2\nD. 0\nE. none of these\n\n### Answer:\nAssume that price is 100 and sales are also 100. Total revenue is 100*100=10000(100%). Now price increased by 30%. So new price is 130. Similarly new sales are 80. Now revenue is 130*80=10400(104%)= So total change is 4%\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAt the opening of a trading day at a certain stock exchange, the price per share of stock K was $28. If the price per share of stock K was $29 at the closing of the day, what was the percent increase in the price per share of stock K for that day?\n\n### Options:\nA. 3.57%\nB. 5.9%\nC. 11.1%\nD. 12.5%\nE. 23.6%\n\n### Answer:\nOpening = 28\nClosing = 29\nRise in price = 1\nSo, percent increase = 1/28*100 = 3.57\nAnswer : A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo pipes A and B can separately fill a tank in 2 minutes and 15 minutes respectively. Both the pipes are opened together but 4 minutes after the start the pipe A is turned off. How much time will it take to fill the tank?\n\n### Options:\nA. 11\nB. 10\nC. 17\nD. 16\nE. 18\n\n### Answer:\n4/12 + x/15 = 1\nx = 10\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the charge of staying in a student youth hostel $18.00/day for the first week, and $14.00/day for each additional week, How much does it cost to stay for 23 days?\n\n### Options:\nA. $160\nB. $350\nC. $282\nD. $274\nE. $286\n\n### Answer:\nTotal number of days of stay = 23\nCharge of staying in first week = 18*7 = 126 $\nCharge of staying for additional days =(23-7)*14 = 16*14 = 224 $\nTotal charge =126 +224 = 350$\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA big beautiful cube is formed by rearranging the 160 coloured and 56 non-coloured similar cubes in such a way that the exposure of the coloured cubes to the outside is minimum. The percentage of exposed area to the coloured is :\n\n### Options:\nA. 25.9%\nB. 44.44%\nC. 35%\nD. 61%\nE. None of these\n\n### Answer:\nWell the big cube which has the side built with 6 little cubes (6^3) will haveinsidethe cube which has the side built with 4 little cubes (6-2 edges), so 4^3. .. Similarly, the cube which has the side built with 4 little cubes (4^3) will haveinsidethe cube which has the side built with 2 little cubes, (4-2 edges), so 2^3... answer is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAt a loading dock, each worker on the night crew loaded 3/4 as many boxes as each worker on the day crew. If the night crew has 5/6 as many workers as the day crew, what fraction of all the boxes loaded by the two crews did the day crew load?\n\n### Options:\nA. 4/7\nB. 5/9\nC. 6/11\nD. 7/12\nE. 8/13\n\n### Answer:\nLet x be the number of workers on the day crew.\nLet y be the number of boxes loaded by each member of the day crew.\nThen the number of boxes loaded by the day crew is xy.\nThe number of boxes loaded by the night crew is (5x/6)(3y/4) = 5xy/8\nThe total number of boxes is xy + 5xy/8 = 13xy/8\nThe fraction loaded by the day crew is xy / (13xy/8) = 8/13\nThe answer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nArrange the following in descending order :\nA) 111(4),\nB) 110 x 109 x 108 x 107,\nC)109 x 110 x 112 x 113\n\n### Options:\nA. all are equal\nB. B,A.C\nC. A,B,C\nD. A,C,B\nE. None\n\n### Answer:\nExplanation :\nif you see option B...you can easily say it is the lowest value. Now about A and C you can see the sum of the values on both side is equal on this type of cases the side which as more number of values closer than other side and to the maximum value among given numbers will be the biggest value..If you couldn't understand the explanation take two sample and compare\nAnswer : D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRahul is 30 years older than his daughter Mary. In 20 years Rahul will be twice as old as Mary. What is Mary current age.\n\n### Options:\nA. 12\nB. 14\nC. 10\nD. 16\nE. 18\n\n### Answer:\nNow: Mary = x, Rahul =x+30\nIn 20 years Mary = x+20, Rahul= x+30+20 or 2(x+20)\nx+30+20= 2(x+20)\nx+50=2x+40\n50-40=2x-x\nx= 10\nMary is 10 years old\nAnswer : C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 2^4, 3^3, and 10^3 are factors of the product of 1,452 and w, where w is a positive integer, what is the smallest possible value of w?\n\n### Options:\nA. 198\nB. 288\nC. 360\nD. 396\nE. 484\n\n### Answer:\nI will go with C (pending elements to match is 2^2*3^2*10^1 = 360\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe speeds of three asteroids were compared. Asteroids X-13 and Y-14 were observed for identical durations, while asteroid Z-15 was observed for 2 seconds longer. During its period of observation, asteroid Y-14 traveled three times the distance X-13 traveled, and therefore Y-14 was found to be faster than X-13 by 2500 kilometers per second. Asteroid Z-15 had an identical speed as that of X-13, but because Z-15 was observed for a longer period, it traveled five times the distance X-13 traveled during X-13's inspection. Asteroid X-13 traveled how many kilometers during its observation?\n\n### Options:\nA. 500\nB. 625\nC. 1,000\nD. 1,500\nE. 2,500\n\n### Answer:\nX13: (t, d, s)\nY14: (t, 3d, s+2500mi/hour)\nZ15: (t+2 seconds, s, 5d)\nd=?\nDistance = Speed*Time\nx13: d = s*t\nx14: 3d = (s+2500)*t ===> 3d = ts+2500t\nz15: 5d = s*(t+2t) ===> 5d = st+2st ===> 5d - 2st = st\n3d = 5d - 2st + 2500t\n-2d = -2st + 2500t\n2d = 2st - 2500t\nd = st - 1250t\nx13: d = s*t\nst - 1250t = s*t\ns - 1250 = s\n-625 = s\nI got to this point and couldn't go any further. This seems like a problem where I can set up individual d=r*t formulas and solve but it appears that's not the case. For future reference how would I know not to waste my time setting up this problem in the aforementioned way? Thanks!!!\nThe distance of Z15 is equal to five times the distance of X13 (we established that x13 is the baseline and thus, it's measurements are d, s, t)\nS(T+2) = 5(S*T)What clues would I have to know to set up the equation in this fashion? Is it because I am better off setting two identical distances together?\nST+2S = 5ST\nT+2 = 5T\n2=4T\nt= 1/2\nWe are looking for distance (d=s*t) so we need to solve for speed now that we have time.\nSpeed y14 - speed x13\nSpeed = d/t\n3d/t - d/t = 2500 (remember, t is the same because both asteroids were observed for the same amount of time)\n2d = 2500\n2 = 1250\nd=s*t\nd=1250*(1/2)\nd=625\nANSWER: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA sum of money amounts to 9800 after 5 years and 12005 after 8 years at the same rate of simple interest. The rate of interest per annum is:\n\n### Options:\nA. 10\nB. 18\nC. 11\nD. 12\nE. 15\n\n### Answer:\nD\n12\nS.I. for 3 years = (12005 - 9800) = 2205.\nS.I. for 5 years = (2205/3)x 5 = 3675\nPrincipal = (9800 - 3675) = 6125.\nHence, rate = (100 x 3675)/(6125x5)% = 12%\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA person travels equal distances with speeds of 50km/hr,100km/hr and 120km/hr and takes a total time of 23 minutes. The total distance is?\n\n### Options:\nA. 15km\nB. 30km\nC. 45km\nD. 50km\nE. 60km\n\n### Answer:\nLet the total distance be 3x km\nx/50 + x/100 + x/120 = 23/60\n23x/600 = 23/60\n23x = 230\nx = 10km\nTotal distance = 3x = 30km\nAnswer is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many integers are between 9 and 67/5, inclusive?\n\n### Options:\nA. 5\nB. 7\nC. 9\nD. 10\nE. 11\n\n### Answer:\n67/5 = 13.xx\nWe are not concerned about the exact value of 67/5 as we just need the integers.\nSince the values are small, we can write down the integers.\nThe different integers between 9 and 67/5 would be 9, 10, 11, 12,13\nTotal number of integers = 5\nOption A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe sum of 4 hours 45 minutes and 5 hours 55 minutes is approximately what percent of a day?\n\n### Options:\nA. 32%\nB. 36%\nC. 40%\nD. 44%\nE. 48%\n\n### Answer:\nSince the question is asking for an approximate percentage\n4:45+5:55 ~ 11 hours\n% of day = 11*100/24 ~ 11*100/25= 44%\nAnswer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe different of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and 15 as remainder.What is the smaller number ?\n\n### Options:\nA. 360\nB. 320\nC. 290\nD. 240\nE. 270\n\n### Answer:\nLet the smaller number be x.Then larger number =(x+1365).\nx+1365=6x+15\n5x=1350\nx=270\nsmaller number =270.\nAnswer is E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRiya and Priya set on a journey. Riya moves eastward at a speed of 21kmph and Priya moves westward at a speed of 22 kmph.How far will be priya from Riya after 60 minutes\n\n### Options:\nA. 43kms\nB. 45kms\nC. 50kms\nD. 30kms\nE. 40kms\n\n### Answer:\ntotal eastward distance= 21kmph*1hr=21 km\ntotal westward distance= 22kmph*1hr=22 km\ntotal distn betn them= 21+22=43km\nans 43km\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain artist is selling five paintings for the following prices: $7,000, $8,000, $9,000, $23,000, and $25,000. If the price of the most expensive painting is increased $3,000, which of the following statements best describes the change in the mean and the median of the paintings?\n\n### Options:\nA. The mean and the median will remain unchanged.\nB. The mean will remain unchanged but the median will increase.\nC. The mean will increase but the median will remain unchanged.\nD. The mean and the median will increase by the same amount.\nE. The mean and the median will increase by different amounts.\n\n### Answer:\nOld set = {7000, 8000, 9000, 23000, 25000}.\nNew set = {7000, 8000, 9000, 23000, 28000} --> the median (middle term) will remain the same and the mean will increase.\nAnswer: C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the % change in the area of a rectangle when its length increases by 20% and its width decreases by 20%?\n\n### Options:\nA. 0%\nB. 20% increase\nC. 20% decrease\nD. 4% decrease\nE. Insufficient data\n\n### Answer:\n(12/10)*(8/10) = 96/100 of original area\n96/100 is a 4% decrease from 100/100 ->D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nQ' = 3Q - 3, what is the value of (4')' ?\n\n### Options:\nA. 48\nB. 57\nC. 66\nD. 72\nE. 81\n\n### Answer:\n(4')'=(3*4-3)'=9'=9*9-9=72\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThree friends are buying a gift for a friend. Declan contributes 3 dollars more than 1/4 the cost of the gift, Ed contributes 1 dollar less than 1/3 the cost of the gift, and Frank contributes the remaining 22 dollars. What is the cost of the gift?\n\n### Options:\nA. 48\nB. 57.6\nC. 60\nD. 66\nE. 72\n\n### Answer:\nDeclan = D, Ed = E, Frank = F\nt = total\nD + E + F = t\n(t/4 + 3) + (t/3 - 1) + 22 = t\nt = 24 + (7t/12)\n12t = 24(12) + 7t\n5t = 24(12)\nt = 57.6\nThe correct answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA can do a job in 10 days and B can do it in 30 days. A and B working together will finish twice the amount of work in ------- days?\n\n### Options:\nA. 14 days\nB. 15 days\nC. 22 days\nD. 11 days\nE. 19 days\n\n### Answer:\nB\n1/10 + 1/30 = 2/15\n15/2 *2 = 15 days\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSolution for 2.01+.3+.34\n\n### Options:\nA. 2.91\nB. 2.65\nC. 2.938\nD. 2.986\nE. 2.999\n\n### Answer:\n2.01+.3+.34=0\n0=0-2.01-0.3-0.34\n0=-2.65\nanswer :B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe operation T is defined by x T y=1/x+1/y for all nonzero numbers x and y. If z is a number greater than 1, which of the following must be true.\nI. x T (-z)=0\nII. 2/z T 2/z=z\nIII. z T z/z-1=1\n\n### Options:\nA. a.) I\nB. b.) I and II only\nC. c) I and III only\nD. d) II and III only\nE. e) I, II and III only\n\n### Answer:\nStatement I is TRUE\nStatement II is TRUE\nStatement III is not TRUE\nAnswer : B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA dog takes 4 leaps for every 5 leaps of a hare but 3 leaps of a dog are equal to 4 leaps of the hare. Compare their speeds?\n\n### Options:\nA. 4:5\nB. 16:15\nC. 9:13\nD. 5:15\nE. 9:17\n\n### Answer:\nLet the distance covered in 1 leap of the dog be x and that covered in 1 leap of the hare be y\nThen 3x = 4y\nx = 4/3 y\n4x = 16/3 y\nRatio of speeds of dog and hare = Ratio of distances covered by them in the same time\n= 4x:5y = 16/3 y : 5 = 16:15\nAnswer is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf all the 6 are replaced by 9, then the algebraic sum of all the numbers from 1 to 100(both inclusive) varies by\n\n### Options:\nA. 330\nB. 340\nC. 350\nD. 360\nE. 370\n\n### Answer:\n1 11 21 .......91\n2 12 22........92\n3 13 23........93\n. . . .. . .. . .\n. . .. .. . .. .\n. . .. . . .. . ...\nthere are total 20 occurrence of 6. once place at 6 th row in every column and tens place in 6 th column\nand diff of 6 and 9 is 3 so\n3*1*10+3*10*10 = 330\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA,B and C started a business by investing Rs.2000/- , Rs.3000/- and Rs.4000/- respectively. Total profit is Rs.4500/-. Find the A\u2019s share?\n\n### Options:\nA. Rs.1000/-\nB. Rs.1500/-\nC. Rs.2000/-\nD. Rs.3000/-\nE. Rs.3400/-\n\n### Answer:\nA = Rs.2000/- , that is 2 parts\nB = Rs.3000/- , that is 3 parts\nC = Rs.4000/- , that is 4 parts\nTotal 9 parts -------> profit (4500/-)\n----->1 part -------->Rs.500/-\nthen A's share 2 parts -----> Rs.1000/-\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSeats for Maths, Physics and Biology are in the ratio of 7 : 7 : 8 respectively. There is a proposal to increase these seats by 40%, 50% and 75% respectively. What will be the respective ratio of increased seats?\n\n### Options:\nA. 14 : 15 : 20\nB. 6 : 7 : 8\nC. 6 : 8 : 9\nD. Cannot be determined\nE. None of these\n\n### Answer:\nReqd ratio 7 \u00c3\u2014 140\u00e2\u0081\u201e100 : 7 \u00c3\u2014 150\u00e2\u0081\u201e100 : 8 \u00c3\u2014 175\u00e2\u0081\u201e100\n= 7 \u00c3\u2014 140 : 7 \u00c3\u2014 150 : 8 \u00c3\u2014 175 = 14 : 15 : 20\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe rate of a certain chemical reaction is directly proportional to the square of the concentration of chemical A present and inversely proportional to the concentration of chemical B present. If the concentration of chemical B is increased by 100%, which of the following is closest to the percent change in the concentration of chemical A required to keep the reaction rate unchanged?\n\n### Options:\nA. 100% decrease\nB. 50% decrease\nC. 40% decrease\nD. 40% increase\nE. 50% increase\n\n### Answer:\nCA: Concentration A\nCB: Concentration B\nR: Reaction rate\nFormula for reaction rate:\nR = (CA^2) / CB\nThus if CB is increased by 100% >> means concentration doubles >> 2xCB\nThus, for R to remain the same (CA^2) also has to double.\n>> 2 x (CA^2) >> to see what happens to CA, take the 2 into the bracket by taking its root\n>> (SQRT 2 CA)^2\nSQRT 2 is roughly 40% >> answer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf you divide 7^115 by 5, which remainder do you get?\n\n### Options:\nA. 0\nB. 1\nC. 2\nD. 3\nE. 4\n\n### Answer:\nThe units digit of 7^1 is 7.\nThe units digit of 7^2 is 9.\nThe units digit of 7^3 is 3.\nThe units digit of 7^4 is 1.\nThe units digit of 7^5 is 7.\netc...\nThe units digit of 7^n repeats in blocks of 4: {7, 9, 3, 1}\nThe remainder of 115/4 is 3.\nSo the units digit of 7^115 is 3.\nThe remainder of 7^115 / 5 is 3.\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average weight of a class is x pounds. When a new student weighing 90 pounds joins the class, the average decreases by 1 pound. In a few months the student\u2019s weight increases to 110 pounds and the average weight of the class becomes x + 4 pounds. None of the other students\u2019 weights changed. What is the value of x?\n\n### Options:\nA. 85\nB. 86\nC. 88\nD. 90\nE. 99\n\n### Answer:\nWhen the student weighs 90 pounds the average weight is x - 1 pounds;\nWhen the student weighs 110 pounds the average weight is x + 4 pounds.\nSo, the increase in total weight of 110 - 90 = 20 pounds corresponds to the increase in average weight of (x + 4) - (x - 1) =5 pounds, which means that there are 20/5 = 4 students (including the new one). So, initially there were 5 student.\nTotal weight = 5x + 90 = 6(x-1) --> x = 96 pounds.\nAnswer: E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhen a merchant imported a certain item, she paid a 7 percent import tax on the portion of the total value of the item in excess of $1,000. If the amount of the import tax that the merchant paid was $111.30, what was the total value of the item?\n\n### Options:\nA. $2380\nB. $2590\nC. $2760\nD. $2940\nE. $3150\n\n### Answer:\nLet x be the value of the item.\n0.07*(x-1000) = 111.30\nx = 2590\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOne quantity of wheat at Rs 9.30 per Kg is mixed with another quality at a certain rate in the ratio 8:7. If the mixture so formed be worth Rs 10 per Kg, what is the rate per Kg of the second quality of wheat?\n\n### Options:\nA. Rs 12.47\nB. Rs 10.80\nC. Rs 10.80\nD. Rs 47.66\nE. None of these\n\n### Answer:\nExplanation :\nLet the rate of second quality be Rs x per Kg.\nC.P of 1Kg wheat of 1st kind = Rs 9.30\nC.P of 1 Kg wheat of 2nd kind = Rs. x.\nMean price = Rs 10.\nThe given ratio is 8 : 7.\nRs 9.30 Rs x\n\\ /\n(Mean Price)\nRs 10\n/ \\\nx-10 : 0.7\n8 : 7\nThen, the ratio is :-\n=>(x-10) : 0.7 = 8 : 7.\n=>7x -70=5.6.\n=>x=75.6/7.\nHence, the required amount is 10.80 per Kg.\nAnswer : B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA and B starts a business with Rs.8000 each, and after 4 months, B withdraws half of his capital . How should they share the profits at the end of the 16 months?\n\n### Options:\nA. 18:11\nB. 16:11\nC. 18:19\nD. 18:121\nE. 18:112\n\n### Answer:\nA invests Rs.8000 for 16 months, but B invests Rs.8000 for the first 4 months and then withdraws Rs.4000. So, the investment of B for remaining 14 months is Rs.4000 only.\nA : B\n8000*16 : (8000*4) + (4000*14)\n128000 : 88000\nA:B = 16:11.Answer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWalking at 75% of his usual speed a man takes 24 minutes more to cover a distance. What is his usual time to cover this distance?\n\n### Options:\nA. 30\nB. 36\nC. 42\nD. 48\nE. 72\n\n### Answer:\nspeed is inversly proprtional to time\nwalking at 75% of speed meand 3/4s takes 4/3t.\nIt takes 24 minutes extra to cover the distance. then\n4/3t=t+24\n4t=3t+72\nt=72\nOption E is correct\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo musicians, Maria and Perry, work at independent constant rates to tune a warehouse full of instruments. If both musicians start at the same time and work at their normal rates, they will complete the job in 45 minutes. However, if Perry were to work at thrice Maria\u2019s rate, they would take only 20 minutes. How long would it take Perry, working alone at his normal rate, to tune the warehouse full of instruments?\n\n### Options:\nA. 1 hr 20 min\nB. 1 hr 7 min\nC. 2 hr\nD. 2 hr 20 min\nE. 3 hr\n\n### Answer:\nSol:\nLets Perry Rate be P and Rate of Maria be M\n(rate)*(time)= Work or rate = work/time\nfirst equation=> P+M = 1/45\nconverting it to hrs P+M= 1/(45/60) => 1/(3/4) =>4/3\nsecond equation => M+3M =>1/20\nconverting it to hrs 4M=1/(20/60) =>1/(1/3) =>3\ntherefore M= 3/4 and P=7/12\nRate of Perry = 7/12\ntime= work/rate (work = 1 job)\nTime= 1 hrs 7 mins\nAnswer : B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe simple interest on Rs.12000 at a certain rate of interest in five years is Rs.7200. Find the compound interest on the same amount for five years at the same rate of interest?\n\n### Options:\nA. 3052.83\nB. 3052.22\nC. 3052.08\nD. 3052.8\nE. 3052.13\n\n### Answer:\nR = 100 I / PT\n=> R = (100 * 7200)/ (12000 * 5) = 12%\nCI = P{ [1 + R /100]n - 1}\n= 12000 { [ 1 + 12 / 100]2 - 1}\n= Rs.3052.80\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA circular rim 28 inches in diameter rotates the same number of inches per second as a circular rim 42 inches in diameter. If the smaller rim makes x revolutions per second, how many revolutions per minute does the larger rim makes in terms of x ?\n\n### Options:\nA. 40x\nB. 75x\nC. 48x\nD. 24x\nE. x/75\n\n### Answer:\nThe larger rim must circulate for the same number of inches the smaller rim does.\nC = (pi)d\nC(small): (pi)*28\nC(large): (pi)*42\nLets say the time horizon is 60 seconds, so during that time the smaller rim covers a distance of (pi)*28*60 = (pi)*(1680) inches\n(pi)*(1680) = (pi)*(42)(x)\npi*(40) = pi*(x)\n40=x\nAnswer: A. 40x\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn 1982 and 1983, Company B\u2019s operating expenses were $12.0 million and $14.0 million, respectively, and its revenues were $15.6 million and $18.8 million, respectively. What was the percent increase in Company B\u2019s profit (revenues minus operating expenses) from 1982 to 1983 ?\n\n### Options:\nA. 3%\nB. 16 2/3%\nC. 25%\nD. 33 1/3%\nE. 60%\n\n### Answer:\nProfit in 1982=15.6-12.0=3.6\nprofit in 1983=18.8-14.0=4.8\nincrease in profit=4.8-3.6=1.2\npercentage increase\n12*100/36 =33.33 ; ANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo pipes can fill the cistern in 10hr and 12 hr respectively, while the third empty it in 20hr.\nIf all pipes are opened simultaneously, then the cistern will be filled in\n\n### Options:\nA. 10.5\nB. 8\nC. 6\nD. 7.5\nE. 8.5\n\n### Answer:\nFirst pipe fills cistern in 10 hours.\nSo, in 1 hour, pipe fills 1/10 of the cistern capacity\n2nd pipe fills cistern in 12 hours.\nSo, in 1 hour, 2nd pipe fills 1/12 of the cistern capacity\n3rd pipe empties cistern in 20 hours\nSo, in 1 hour, 3rd pipe empties 1/20 of the cistern capacity\nNet volume added to cistern per hour = Volume filled by 1st pipe per hour + Volume filled by 2nd pipe per hour - Volume emptied by 3rd pipe per hour\n= 1/10 + 1/12 - 1/20\n=(6 + 5 - 3) / 60 = 8/60\n=> Net volume added to cistern per hour = 2/15\nSo, Cistern will be fill in 15/2 hours = 7.5 hours\nSo, answer is D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA ship sails out to a mark at the rate of 22 kmph. and sails back at the rate of 12 kmph. The average rate of sailing is ?\n\n### Options:\nA. 5 km/hr\nB. 12 km/hr\nC. 16 km/hr\nD. 25 km/hr\nE. None\n\n### Answer:\nAnswer\nAverage = ( 2uv / u +v ) km/hr\n= ( 2 x 22 x 12 ) / (22 +12 ) km/hr.\n= 16 km/hr.\nCorrect Option: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat distance will be covered by a bus moving at 126 kmph in 10 seconds?\n\n### Options:\nA. 287\nB. 600\nC. 350\nD. 276\nE. 207\n\n### Answer:\n126 kmph = 126 * 5/18\n= 35 mps\nD = Speed * time = 35 * 10\n= 350 m.\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA cistern can be filled by a tap in 3 hours while it can be emptied by another tap in 6 hours. If both the taps are opened simultaneously, then after how much time will the cistern get filled?\n\n### Options:\nA. 5.2 hrs\nB. 2.9 hrs\nC. 1.9 hrs\nD. 6 hrs\nE. 5 hrs\n\n### Answer:\nNet part filled in 1 hour = (1/3 - 1/6) = 1/6\nThe cistern will be filled in 6/1 hrs i.e., 6 hrs.\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf x is 12 percent greater than 80, then x =\n\n### Options:\nA. 89.6\nB. 91.0\nC. 88.0\nD. 70.9\nE. 71.2\n\n### Answer:\n12% of 80 = (80*0.12) = 9.6\n12% greater than 80 = 80 + 9.6 = 89.6\nAnswer is clearly A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf CRY is coded as MRYC then how will GET be coded?\n\n### Options:\nA. MTEG\nB. MGET\nC. MEGT\nD. METG\nE. METC\n\n### Answer:\nCRY=M+RYC\nGET=M+ETG\nMETG\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJoe invested a certain sum of money in a simple interest bond whose value grew to $260 at the end of 3 years and to $360 at the end of another 5 years. What was the rate of interest in which he invested his sum?\n\n### Options:\nA. 6%\nB. 8%\nC. 10%\nD. 12%\nE. 15%\n\n### Answer:\nIn 5 years, the value grew $100, so the simple interest was $20 per year.\nIn 3 years, the total interest was 3*$20 = $60\nThe principal is $260 - $60 = 200.\nThe interest rate is $20/$200 = 10%\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a - b = 3 and a(power 2) + b(power 2) = 27, find the value of ab.\n\n### Options:\nA. 5\nB. 9\nC. 4\nD. 10\nE. 3\n\n### Answer:\n2ab = (a(power 2) + b(power 2) - (a - b)(power 2)\n= 27 - 9 = 18\nab = 9.\nAnswer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man whose speed is 8 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 3 kmph, find his average speed for the total journey ?\n\n### Options:\nA. 1 kmph\nB. 5 kmph\nC. 6 kmph\nD. 4 kmph\nE. 6.8 kmph\n\n### Answer:\nExplanation:\nSpeed of Man = 8 kmph\nSpeed of stream = 3 kmph\nSpeed in DownStream = 11 kmph\nSpeed in UpStream = 5 kmph\nAverage Speed = (2 x 11 x 5)/16 = 6.8 kmph.\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 7 boys meet at a reunion and each boy shakes hands exactly once with each of the others, then what is the total number of handshakes\n\n### Options:\nA. 21\nB. 42\nC. 43\nD. 44\nE. 45\n\n### Answer:\nn(n-1)/2 =7*6/2\n=21\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nEvery letter in the alphabet has a number value that is equal to its place in the alphabet. Thus, the letter A has a value of 1, the letter B has a value of 2, the letter C has a value of 3, etc... The number value of a word is obtained by adding up the value of the letters in the word and then multiplying that sum by the length of the word. What is the number value of the word \"HEN\"?\n\n### Options:\nA. 69\nB. 72\nC. 75\nD. 78\nE. 81\n\n### Answer:\n\"HEN\" = (8+5+14)*3=81.\nThe answer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe radius of a semi circle is 35 cm then its perimeter is?\n\n### Options:\nA. 32.8\nB. 180\nC. 32.1\nD. 32.2\nE. 32.9\n\n### Answer:\nDiameter 70 cm\n1/2 * 22/7 * 70 +70 = 180\nAnswer : B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nNumber of ways in which the letters of word PARDENS can be arranged with vowels in alphabetical order, is\n\n### Options:\nA. 360\nB. 240\nC. 2520\nD. 480\nE. None of these\n\n### Answer:\nSolution\nOrder of vowels of fixed\n\u00e2\u02c6\u00b4 required number of ways are 7!/2!.\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSolving a linear equation with several occurrences of the variable, solve for w. Simplify answer as much as possible.\n(7w + 6)/6 + (9w +8)/2 = 22\n\n### Options:\nA. 1\nB. 2\nC. 3\nD. 4\nE. 5\n\n### Answer:\n(7w + 6)/6 + (9w +8)/2 = 22\nor, [7w + 6 + 3(9w + 8)]/6 = 22\nor, 7w + 6 + 27w + 24 = 132\nor, 34w + 30 = 132\nor, 34w = 132 - 30\nor, 34w = 102\nor, w = 102/34\nTherefore, w = 3\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind \u221a? /13 = 4 ?\n\n### Options:\nA. 76\nB. 5776\nC. 304\nD. 2704\nE. None\n\n### Answer:\nAnswer\nLet \u221aN/13= 4\nThen \u221aN = 13 x 4 = 52\n\u2234 N = 52 x 52 = 2704.\nCorrect Option: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA box contains eight bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that exactly three bulbs are good?\n\n### Options:\nA. 10/35\nB. 11/35\nC. 9/35\nD. 8/35\nE. 6/35\n\n### Answer:\nRequired probability = (4C3 . 4C1)/8C4 = (4 * 4)/70\n= 8/35\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe length of a rectangle is increased by 25% and its breadth is decreased by 20%. What is the effect on its area?\n\n### Options:\nA. Remains same\nB. 5% decrease\nC. 7% decrease\nD. 2% decrease\nE. 3% decrease\n\n### Answer:\n100 * 100 = 10000\n125 * 80 = 10000\nNo change\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOne pipe can fill a tank three times as fast as another pipe. If together the two pipes can fill tank in 36 min, then the slower pipe alone will be able to fill the tank in?\n\n### Options:\nA. 81 min\nB. 108 min\nC. 144 min\nD. 192 min\nE. 120 min\n\n### Answer:\nLet the slower pipe alone fill the tank in x min.\nThen, faster pipe will fill it in x/3 min.\n1/x + 3/x = 1/36\n4/x = 1/36 => x = 144 min.\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nCecilia, Robbie, and Briony all bought stamps. The number of stamps Cecilia purchased was equal to a single digit. The number of stamps only one of them purchased was divisible by 7. The number of stamps one of them bought was an even number. Which of the following could represent the numbers of stamps each purchased?\n\n### Options:\nA. 3, 8, 24\nB. 7, 9, 17\nC. 6, 9, 12\nD. 5, 15, 18\nE. 9, 10, 13\n\n### Answer:\nI didnt get your point on eliminating D.\nThe number of stamps only one purchased was divisible by 7.Could that not be Cecilia with 9 stamps.\nI choose this and marked D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSuganya and Suriya are partners in a business. Suganya invests Rs. 35,000 for 8 months and Suriya invests Rs.42,000 for 10 months. Out of a profit of Rs.30,570. Suganya's share is\n\n### Options:\nA. Rs.9471\nB. Rs.12,628\nC. Rs.262.8\nD. Rs.241.7\nE. None\n\n### Answer:\nSolution\nRatio of their shares\t=(35000\u00c3\u20148):(42000\u00c3\u201410)\n= 128 : 125\nSuganya's share\t= Rs.(30570 \u00c3\u20142/253)\n= Rs.241.7.\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the number of different 4-letter words with or without meaning that can be formed from the letters of the word \" NUMBER\"\n\n### Options:\nA. 340\nB. 360\nC. 320\nD. 420\nE. 440\n\n### Answer:\nThere are 6 letters in the word \"NUMBER\". So the number of 4-letter words 6P4 =360 Answer : B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a certain pond, 40 fish were caught, tagged, and returned to the pond. A few days later, 40 fish were caught again, of which 2 were found to have been tagged. If the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond, what`s the approximate number of fish in the pond?\n\n### Options:\nA. 400\nB. 625\nC. 1250\nD. 2500\nE. 1000\n\n### Answer:\nIf x is total number of fish in the pond :\n4 = 40/x * 100\n=> x = 1000\nSo answer is E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a certain game of dice, the player\u2019s score is determined as a sum of three throws of a single die. The player with the highest score wins the round. If more than one player has the highest score, the winnings of the round are divided equally among these players. If Jim plays this game against 24 other players, what is the probability of the minimum score that will guarantee Jim some monetary payoff?\n\n### Options:\nA. 1/216\nB. 1/221\nC. 1/212\nD. 1/84\nE. 1/42\n\n### Answer:\nToguaranteethat Jim will get some monetary payoff he must score the maximum score of 6+6+6=18, because if he gets even one less than that so 17, someone can get 18 and Jim will get nothing.\nP(18)=1/6^3=1/216.\nAnswer: A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf (2^13)(25^S) = 5(10^m) what is the value of m ?\n\n### Options:\nA. 7\nB. 13\nC. 15\nD. 16\nE. 23\n\n### Answer:\ngiven\n2^13 * 25^s = 5 * 10^2\n=> 2^13 * 5^(2s) = 2^m * 5^(m+1)\nAns B\non comparing the power of 2 => m=13\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWorking alone at its constant rate, pump F pumped out \u00bc of the water in a tank in 2 hours. Then pumps G and H started working and the three pumps, working simultaneously at their respective constant rates, pumped out the rest of the water in 3 hours. If pump G, working alone at its constant rate, would have taken 18 hours to pump out the rest of the water, how many hours would it have taken pump H, working alone at its constant rate, to pump out all of the water that was pumped out of the tank?\n\n### Options:\nA. 6\nB. 12\nC. 15\nD. 18\nE. 24\n\n### Answer:\nRate of pump F = 1/8\n3 hours are required to pump out the remaining (3/4)ths of tank --> 1 hr to pump out 1/4\nRate of F + Rate of G + Rate of H = 1/4\nRate of G + Rate of H = 1/4 - 1/8 = 1/8\nG takes 18 hours to pump out the remaining (3/4)ths of tank --> 6 hrs per (1/4)ths --> 24 hrs to pump out fully.\nRate of G = 1/24\n1/24 + Rate of H = 1/8\nRate of H = 1/8 - 1/24 = 1/12\nTime required to pump out all the water by H = 12 hrs\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n3 people are sitting in a 4 seat row watching a football game. At halftime they all get up. When they return, they each randomly sit down on one of the 4 chairs. What is the likelihood that none of the 4 end up sitting in the same chair that they sat in during the first half?\n\n### Options:\nA. 1/2\nB. 9/24\nC. 15/24\nD. 18/24\nE. 21/24\n\n### Answer:\nOriginally seated A B C D\nnow when after they get up and when they sit back again .\n1st- A has option to sit on 3 seats ( apart from his previous seat . thus he now sits on B's seat.)\n2nd- Similarly B has option to sit on 3 seats ( because A has already occupied B's previous seat, thus B sits on a's seat.)\n3rd- Now C has only 1 option to sit on D's seat . and similarly D also has one option to sit on C's seat.)\nhence total favourable outcomes 3*1*1=3\nand total possible outcomes =3!=6\nprobability of the favourable outcome=1/2. A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the average of first 20 natural numbers.\n\n### Options:\nA. A)11.5\nB. B)20.5\nC. C)10.5\nD. D)15.5\nE. E)21.9\n\n### Answer:\nSum of first n natural numbers = n(n+1)/2\nsum of first 20 natural numbers = 20*21/2 =210\naverage = 210/20 = 10.5\nAnswer is C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nBefore being simplified, the instructions for computing income tax in Country R were to add 2 percent of one's annual income to the average (arithmetic mean) of 100 units of Country R's currency and 1 percent of one's annual income. Which of the following represents the simplified formula for computing the income tax, in Country R's currency, for a person in that country whose annual income is X?\n\n### Options:\nA. 50X/200\nB. 50+3X/100\nC. 50+X/40\nD. 100+X/50\nE. 100+3X/100\n\n### Answer:\n50+X/40=C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA shipment of 1500 heads of cabbage, each of which was approximately the same size was purchased for $600.The day the shipment arrived 2/3 of the heads were sold, each at 25% above the cost per head.The following day the rest were sold at a price per head equal to 14% less than the price each head sold for the day before.what was the gross profit on this shipment?\n\n### Options:\nA. $100\nB. $115\nC. $125\nD. $130\nE. $135\n\n### Answer:\nSol:\n1500 heads -> $600\n1 head -> $600/1500\n1 head -> $(2/5)\n25% more of (2/5) -> 125/100 * 2/5 = $(1/2)\nHe sold 2/3*1500 = 1000 heads for $(1/2) per head\nTotal revenue by selling 1000 heads = 1000 * 1/2 = $500\nHeads left: 500\nCost per head: 86% of the previous price: 86/100 * 1/2 = $(3/7)\nTotal revenue by selling 500 heads = 3/7 * 500 = 215\nTotal revenue after selling 1500 cabbage heads - 215+500 = $715\nMoney spent on the purchase: $600\nProfit = 715-600 = $115\nAns: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a T.V. factory, an average of 60 TVs are produced per day for the fist 25 days of the months. A few workers fell ill for the next five days reducing the daily average for the month to 58 sets per day . The average production per day for day last 5 days is ?\n\n### Options:\nA. 45\nB. 48\nC. 52\nD. 58\nE. None\n\n### Answer:\nProduction during these 5 days = Total production in a month - production in first 25 days.\n= 30 x 58 - 25 x 60\n= 240\n\u2234 Average for last 5 days = 240 / 5\n= 48\nCorrect Option: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTimothy leaves home for school, riding his bicycle at a rate of 9 miles per hour. Fifteen minutes after he leaves, his mother sees Timothy\u2019s math homework lying on his bed and immediately leaves home to bring it to him. If his mother drives at 27 miles per hour, how far (in terms of miles) must she drive before she reaches Timothy?\nI think is a 700 level problem but I tag it as 600/700, let me know. Either way I hope in an explanationThanks\n\n### Options:\nA. 27/8\nB. 3\nC. 4\nD. 9\nE. 12\n\n### Answer:\nIn 15 mins, Timothy travels=9/4 miles.\nNow, let his mother takes x hours to reach him, traveling at 27mph.\nSo, 27x=9x+9/4\nx=1/8 hrs.\nThus, the distance traveled by his mother to reach= 27*1/8=27/8miles. Ans A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMandrake has to choose from 4 from 18 people. There are 3 girls, 5 boys , 10 children. What is total probability that he will choose 1G , 2B , 1C?\n\n### Options:\nA. 1/7\nB. 2/7\nC. 3/7\nD. 4/7\nE. 5/51\n\n### Answer:\n(3C1 * 5C2 * 10C1)/ 18C4 = 3*10*10/1820= 300/1820=5/51\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA number is 101102103104...150. As 101 102 103 103.... 150. What is reminder when divided by 3?\n\n### Options:\nA. 2\nB. 5\nC. 6\nD. 7\nE. 8\n\n### Answer:\nDivisibility rule for 3 also same as 9. so from the above discussion sum of the digits = 380 and remainder = 380/3 = 2.\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many positive integers between 5 and 5000(both are inclusive) are there such that they are multiples of 5?\n\n### Options:\nA. 1500\nB. 1000\nC. 999\nD. 1001\nE. 1005\n\n### Answer:\nMultiples of 5 = 5,10,15-----,5000\nNumber of multiples of 5 => 5000-5/5+1= 1000\nAnswer is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many positive integers less than 254 are multiple of 4 but NOT multiples of 6?\n\n### Options:\nA. 20\nB. 31\nC. 42\nD. 43\nE. 64\n\n### Answer:\n252/4=63\nMultiples of 4 which are a multiple of 6 will be of the form 2*2*3=12n where n>0\n240/12=20\n63-20=43\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe difference between C.I. and S.I. on an amount of Rs. 15,000 for 2 years is Rs. 96. What is the rate of interest per annum?\n\n### Options:\nA. 8\nB. 10\nC. 12\nD. 14\nE. 16\n\n### Answer:\n[15000 * (1 + R/100)2 - 15000] - (15000 * R * 2)/100 = 96\n15000[(1 + R/100)2 - 1 - 2R/100] = 96\n15000[(100 + R)2 - 10000 - 200R]/10000 = 96\nR2 = (96 * 2)/3 = 64 => R = 8\nRate = 8%\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA factory produces 4340 toys per week. If the workers at this factory work 2 days a week and if these workers make the same number of toys everyday, how many toys are produced each day?\n\n### Options:\nA. 1375 toys\nB. 2170 toys\nC. 2375 toys\nD. 2175 toys\nE. 5375 toys\n\n### Answer:\nTo find the number of toys produced every day, we divide the total number of toys produced in one week (of 2 days) by 2.\n4340 / 2 = 2170 toys\ncorrect answer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJosh and Dan have a 12 apples each. Together they flip a coin 6 times. For every heads, Josh receives an apple from Dan, and for every tails Dan receives an apple from Josh. After the coin has been flipped 6 times, what is the probability that Josh has more than 12 apples but fewer than 18?\n\n### Options:\nA. 1/64\nB. 15/64\nC. 21/64\nD. 21/32\nE. 5/6\n\n### Answer:\nminimum number of times to win is 4 to have more than 12 apples .\ncoz: if he wins 3 times => he gets 3 apples and give 3 apples ; no change\nso he needs to win 4 times OR 5 times\nNot 6 times because ,\nif he wins 6 times => he gets 6 apples and he will have 18 apples\nNow number of ways to win 4 times out of 6 times 6C4\nNow number of ways to win 5 times out of 6 times 6C5\nTotal number of ways 2626 ways\nProbability =(6C4) + (6C5)/2^6\n=21/64\nAnswer :C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRound trip time of 110 meters in a river is 16 min. the velocity of stream is 3m/min. what is the velocity of the person in the still water?\n\n### Options:\nA. 6\nB. 7\nC. 8\nD. 9\nE. 10\n\n### Answer:\nlet speed of boat be x.hence upstream=x-3 and downstream=x+3..so we have\n55/x+3 + 55/x-3 = 16...solving we get x=8\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many digits are in (8\u00d710^12)(10\u00d710^9)?\n\n### Options:\nA. 20\nB. 23\nC. 26\nD. 27\nE. 28\n\n### Answer:\nThe question simplfies to (8\u00d710^12)(10^10)\n=> 8*10^22\n=> Will contain 22 zeros +1 digit 8\n=>23\nAns B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere is a group of persons each of whom can completea piece of work in 16 days, when they are working individually. On the 1st day 1 person works, on the second day another person joins him, on the third day one more person joins them & this process continues till the work is completed. How many days are needed to complete the work?\n\n### Options:\nA. 5 1\u20442 days\nB. 5 1\u20443 days\nC. 5 1\u20446 days\nD. 6 1\u20446 days\nE. 7 1\u20446 days\n\n### Answer:\nWork completed in 1st day = 1/16\nWork completed in 2nd day = (1/16) + (1/16) = 2/16\nWork completed in 3rd day = (1/16) + (1/16) + (1/16) = 3/16\n\u2026\nAn easy way to attack such problems is from the choices. You can see the choices are\nvery close to each other. So just see one by one.\nFor instance, The first choice given in 3 1\u20444\nThe work done in 3 days = 1/16 + 2/16 + 3/16 = (1+2+3)/16 = 6/16\nThe work done in 4 days = (1+2+3+4)/16 = 10/16\nThe work done in 5 days = (1+2+3+4+5)/16 = 15/16, almost close, isn't it?\nThe work done in 6 days = (1+2+3+4+5+6)/16 > 1\nHence the answer is less than 6, but greater than 5. Hence the answer is 5 1\u20446 days.\n(Just for your reference, work done in 5 days = 15/16.\nPending work in 6th day = 1 \u2013 15/16 = 1/16.\nIn 6th day, 6 people are working and work done = 6/16.\nTo complete the work 1/16, time required = (1/16) / (6/16) = 1/6 days.\nHence total time required = 5 + 1/6 = 5 1\u20446 days\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn the quadrilateral PQRS d=7 cm, h1=4.2 cm and\nh2=2.1 cm. Find the area\n\n### Options:\nA. 21\nB. 22\nC. 23\nD. 24\nE. 25\n\n### Answer:\narea of quad.=1/2*any diagonal*(sum of 2 perpendiculars which is drawn on that diagona)\nso 1/2*7*(4.2+2.1)=22.05\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo trains 140m and 160m long run at the speed of 60kmph and 40kmph in opposite directions in parallel tracks. The time which they take to cross each other is?\n\n### Options:\nA. 5.6sec\nB. 8.9sec\nC. 10.8sec\nD. 12.6sec\nE. 15sec\n\n### Answer:\nRelative speed = 60+40 = 100kmph * 5/18 = 250/9 m/s\nDistance covered in crossing each other = 140+160 = 300m\nRequired time = 300*9/250 = 54/5 = 10.8sec\nAnswer is C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA envelop weight 8.5 gm,if 880 of these envelop are sent with an advertisement mail. How much wieght?\n\n### Options:\nA. 6.6kg\nB. 6.8kg\nC. 7.48kg\nD. 6.9kg\nE. 7.8kg\n\n### Answer:\n880*8.5\n7480.0gm\n7.48kg\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a city the doors of buildings where numbered from 1 to 100. How many 3\u2019s are there as the door number?\n\n### Options:\nA. 10\nB. 20\nC. 30\nD. 40\nE. 50\n\n### Answer:\nWe will have the 3\u2019s as follows 3,13,23,30,31,32,33,34,35,36,37,38,39,43,53,63,73,83,93.\nIn 33 we have 2 3\u2019s. So we get 20 3\u2019s from 1 to 100.\nNote: for any numbers from 1 to 9 we\u2019ll get 20 as answer.\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man can row upstream at 4km/hr and down stream at 10km/hr find mans rate in still water ?\n\n### Options:\nA. 4km/hr\nB. 5km/hr\nC. 5.5km/hr\nD. 6km/hr\nE. 7km/hr\n\n### Answer:\ngiven upstream(u) =4km/hr\ndown stream (v)= 10km/hr rate in still water =1/2(u+v)=1/2(4+10)=7km/hr Answer is (E):7\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSalaries of Ravi and Sumit are in the ratio 2:3. If the salary of each is increased by Rs. 4000, the new ratio becomes 40:57. What is Sumit's salary?\n\n### Options:\nA. 38000\nB. 46800\nC. 36700\nD. 50000\nE. 60000\n\n### Answer:\nExplanation:\nLet the original salaries of Ravi and Sumit be Rs. 2x and Rs. 3x respectively.\nThen,\n(2x+4000) / (3x+4000) = 40 / 57\n\u21d2 57 \u00d7 (2x + 4000) = 40 \u00d7 (3x+4000)\n\u21d2 6x = 68,000\n\u21d2 3x = 34,000\nSumit's present salary = (3x + 4000) = Rs.(34000 + 4000) = Rs. 38,000\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average weight of 16 boys in a class is 50.25 kg and that of the remaining 8 boys is 45.15 kg. Find the average weights of all the boys in the class.\n\n### Options:\nA. 48.0\nB. 48.55\nC. 49.05\nD. 49.0\nE. 45.0\n\n### Answer:\nAverage weight of 16 boys = 50.25\nTotal weight of 16 boys = 50.25 \u00d7 16\nAverage weight of remaining 8 boys = 45.15\nTotal weight of remaining 8 boys = 45.15 \u00d7 8\nTotal weight of all boys in the class = (50.25 \u00d7 16)+ (45.15 \u00d7 8)\nTotal boys = 16 + 8 = 24\nAverage weight of all the boys = ((50.25\u00d716)+(45.15\u00d78))/24\n=(50.25\u00d72)+(45.15\u00d71)/3\n=(16.75\u00d72)+15.05\n=33.5+15.05=48.55\nAnswer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain debt will be paid in 52 installments from January 1 to December 31 of a certain year. Each of the first 8 payments is to be $410; each of the remaining payments is to be $65 more than each of the first 8 payments. What is the average (arithmetic mean) payment that will be made on the debt for the year?\n\n### Options:\nA. 443\nB. 450\nC. 465\nD. 468\nE. 475\n\n### Answer:\nTotal number of installments = 52\nPayment per installment for the first 8 installments = 410\nPayment per installment for the remaining 32 installments = 410+65=475\nAverage = (8*410 + 44*475)/52 = 465\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nQuestion:\tA sporting good store sells one type of baseball bat and one type of baseball. The cost for 2 bats and 4 balls is $180. The cost for 1 bat and 6 balls is $170, as well. If someone were to buy an equal number of bats and balls, at most how many bats can he purchase if he has a budget of $210 for the purchase?\nOptions:\n\n### Options:\nA. 1\nB. 2\nC. 3\nD. 4\nE. 5\n\n### Answer:\nIMO it should be C that is C\nreason:\nformed an equation... bat = b ball = c\n2b+4c=180\n1b+6c=170\nsolving both we get b that is bat = 50 and c that is ball = 20\nnew equation 210 to be divided in equal\n3b+3c=210\n3*50 + 3*20 = 210\n150+60= 210\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA policeman noticed a criminal from a distance of 265 km. The criminal starts running and the policeman chases him. The criminal and the policeman run at the rate of 8 km and 9 km per hour respectively. What is the distance between them after 3 minutes ?\n\n### Options:\nA. 100 m\nB. 120 m\nC. 130 m\nD. 150 m\nE. None of these\n\n### Answer:\nExplanation :\nSolution: Relative speed = (9 - 8) = 1 km/hr.\nDistance covered in 3 minutes = (1 * 3/60) km = 1/20 km = 50 m.\n.'. Distance between the criminal and policeman = (265 - 50) m = 215 m.\nAnswer : E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 4a = 16b and 8b = 13c, Find a:b:c?\n\n### Options:\nA. 52:13:8\nB. 13:7:52\nC. 7:13:52\nD. 7:13:54\nE. None of these\n\n### Answer:\nExplanation:\n(4a = 16b ==> a/b = 16/4)\nand (8b = 13c ==> b/c = 13/8)\n==> a:b = 16:4 and b:c = 13:8\na:b:c = 52:13:8\nAnswer: Option A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the remainder when 1273 * 1275 * 1277 *1285 is divided by 12?\n\n### Options:\nA. 9\nB. 1\nC. 11\nD. 0\nE. 7\n\n### Answer:\n1271*1275*1277*1285 = (1272 + 1)(1272 + 3)(1284 - 7)(1284 + 1) = (multiple of 12 - 1)(multiple of 12 + 3)(multiple of 12 - 7)(multiple of 12 + 1)\nNow, if we expand this expression all terms but the last one will have a multiple of 12 in them, thus will leave no remainder upon division by 12, the last term will be (1)(3)(-7)(1) = 21. Thus the question becomes: what is the remainder upon division of 21 by 12? The answer to this question is 9.\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 50 honey bees make 50 grams of honey in 50 days, then 1 honey bee will make 1 gram of honey in how many days?\n\n### Options:\nA. 1\nB. 3.5\nC. 20\nD. 49\nE. 50\n\n### Answer:\nExplanation :\nLet the required number days be x.\nLess honey bees, More days (Indirect Proportion)\nLess honey, Less days (Direct Proportion)\nHoney bees 1 : 50 :: 50 : x\nHoney 50 : 1\n=> 1 x 50 x x = 50 x 1 x 50\n=> x = 50.\nAnswer : E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nEach of the integers from 1 to 9, inclusive, is written on a separate slip of blank paper and the ten slips are dropped into hat. If the slips are then drawn one at a time without replacement, how many must be drawn to ensure that the numbers on two of the slips drawn will have a sum of 10?\n\n### Options:\nA. 3\nB. 4\nC. 5\nD. 6\nE. 7\n\n### Answer:\nAnswer is 6. In the worst case, you could end up drawing 1,2,3,4,5. 7th draw will result in either of 6,7,8,9 which would result in the numbers adding to 10.\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo ants, Arthur and Lily, have discovered a picnic and are bringing crumbs back to the anthill. Lily makes twice as many trips and carries one and a half times as many crumbs per trip as Arthur. If Arthur carries a total of a crumbs to the anthill, how many crumbs will Lily bring to the anthill, in terms of a?\n\n### Options:\nA. a/2\nB. a\nC. 3a/2\nD. 2a\nE. 3a\n\n### Answer:\nLets do it by picking up numbers. Let Arthur carry 2 crumbs per trip, this means Lily carries 3 crumbs per trip. Also let Arthur make 2 trips and so Lily makes 4 trips.\nThus total crumbs carried by Arthur (a) = 2 x 2 = 4, total crumbs carried by Lily = 3 x 4 = 12. 12 is 3 times 4, so E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFour of the following five are alike in a certain way and hence form a group. Which one does not belong to the group?\n\n### Options:\nA. 70\nB. 80\nC. 52\nD. 48\nE. 68\n\n### Answer:\nA\nAll the numbers are multiple of 4, except 70.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA class is 6 meters 24 centimeters in length and 4 meters 32 centimeters in width. Find the least number of square tiles of equal size required to cover the entire floor of the class room ?\n\n### Options:\nA. 115\nB. 117\nC. 116\nD. 114\nE. 113\n\n### Answer:\nExplanation:\nLength = 6 m 24 cm = 624 cm\nWidth = 4 m 32 cm = 432 cm\nHCF of 624 and 432 = 48\nNumber of square tiles required = (624 x 432)/(48 x 48) = 13 x 9 = 117.\nANSWER IS B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many words of 11letters could be Formed with all the vowels present only in the even places ,and the consonants only in the odd places,using letters of english alphabet each letter may appear only once.\n\n### Options:\nA. 21!\nB. 26!/5!\nC. 21! /(5! * 5! )\nD. 21!* 5!/15!\nE. 21!* 6!/5!\n\n### Answer:\n(21*20*19*18*17*16)*5! = 21! * 5! / 15!\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe ratio of the volumes of two cubes is 729 : 1331. What is the ratio of their total surface areas?\n\n### Options:\nA. 81 : 121\nB. 81 : 128\nC. 81 : 120\nD. 81 : 125\nE. 81 : 122\n\n### Answer:\nRatio of the sides = 3\u221a729 : 3\u221a1331 = 9 : 11\nRatio of surface areas = 92 : 112 = 81 : 121\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe ratio of buses to cars on River Road is 1 to 17. If there are 80 fewer buses than cars on River Road, how many cars are on River Road?\n\n### Options:\nA. 40\nB. 85\nC. 60\nD. 30\nE. 20\n\n### Answer:\nB/C=1/17\nC-B=80.........> B=C-80\n(C-80)/C=1/17\nTesting answers. Clearly Eliminate ACDE\nPut C=85.........> (85-80)/85=5/85=1/17\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average age of a class of 22 students is 21 years. The average increased by 1 when the teacher's age also included. What is the age of the teacher?\n\n### Options:\nA. 44\nB. 48\nC. 45\nD. 43\nE. 50\n\n### Answer:\nTotal age = 22 * 21\ntot age of all stu + age of the teacher = 23*22\nage of the teacher = 23*22-22*21 = 44\nANSWER A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJohn makes $60 a week from his job. He earns a raise and now makes $80 a week. What is the % increase?\n\n### Options:\nA. 16%\nB. 16.66%\nC. 18%\nD. 21%\nE. 33.33%\n\n### Answer:\nIncrease = (20/60)*100 = 33.33%.\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSelling an kite for Rs. 30, a shop keeper gains 30%. During a clearance sale, the shopkeeper allows a discount of 10% on the marked price. His gain percent during the sale is?\n\n### Options:\nA. 8%\nB. 10%\nC. 11%\nD. 17%\nE. 20%\n\n### Answer:\nExplanation:\nMarked price = Rs. 30\nC.P. = 100/130 * 30 = Rs. 23.07\nSale price = 90% of Rs. 30 = Rs. 27\nRequired gain % = 3.92/23.07 * 100 = 17%.\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA person buys an article at Rs.500. At what price should he sell the article so as to make a profit of 20%?\n\n### Options:\nA. 600\nB. 882\nC. 772\nD. 652\nE. 271\n\n### Answer:\nCost price = Rs.500\nprofit = 20% of 500 = Rs.100\nSelling price = Cost price + Profit\n= 500 + 100 = 600\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo coins are tossed, find the probability that two Tails are obtained\n\n### Options:\nA. 1/3\nB. 1/4\nC. 1/5\nD. 1/7\nE. 2/3\n\n### Answer:\nThe sample space S is given by.\nS = {(H,T),(H,H),(T,H),(T,T)}\nLet E be the event \"two heads are obtained\".\nE = {(T,T)}\nP(E) = n(E) / n(S) = 1/4\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average of numbers 0.34204, 0.34203, 0.34202 and 0.34201 is ?\n\n### Options:\nA. 0.34202\nB. 0.34204\nC. 0.342022\nD. 0.342025\nE. None\n\n### Answer:\nAnswer\nAverage = (0.34204 + 0.34203 + 0.34202 + 0.34201)/ 4\n=1.3681/ 4\n=0.342025\nCorrect Option: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n12 points lie on a circle. How many cyclic quadrilaterals can be drawn by using these points?\n\n### Options:\nA. 990\nB. 495\nC. 1980\nD. none\nE. Cannot be determined\n\n### Answer:\nExplanation :\nFor any set of 4 points we get a cyclic quadrilateral. Number of ways of choosing 4 points out of 12 points is 12C4=495Therefore, we can draw 495 quadrilaterals.\nAnswer : B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the area of trapezium whose parallel sides are 10 cm and 18 cm long, and the distance between them is 15 cm.\n\n### Options:\nA. 287 cm2\nB. 785 cm2\nC. 285 cm2\nD. 785 cm2\nE. 210 cm2\n\n### Answer:\nExplanation:\nArea of a trapezium = 1/2 (sum of parallel sides) * (perpendicular distance between them) = 1/2 (10 + 18) * (15) = 210 cm2\nAnswer: Option E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWorking together, Wayne and his son can shovel the entire driveway in three hours. If Wayne can shovel five times as fast as his son can, how many hours would it take for his son to shovel the entire driveway on his own?\n\n### Options:\nA. 4\nB. 6\nC. 8\nD. 9\nE. 12\n\n### Answer:\nW: the time for Wyane to do the job\nS: the time for his son to do the job\nWe have 1/W + 1/S = 1/5 and W = 5S\nThen we have 1/(5*S) + 1/S = 1/5<=> 6/(5*S) = 1/5 <=> S = 6\nANS: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA book club rented the party room of a local restaurant to meet and discuss its current novel over dinner. The total charge, including food and service, was $ 900. If each member of the club paid at least $ 40, then what is the greatest possible number of members in the club?\n\n### Options:\nA. 19\nB. 20\nC. 21\nD. 23\nE. 25\n\n### Answer:\nGiven: Each person spends $40\nBy looking at the options, we see that if there were 20 members, each person will spend atleast $40\nHence the greatest number of members = 22.5 Option D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe decimal d is formed by writing in succession all the positive integers in descending order after the decimal point; that is d = 0.15141312111098765\nWhat is the 19th and 20th digits of d to the right of decimal point?\n\n### Options:\nA. 32\nB. 43\nC. 54\nD. 12\nE. 21\n\n### Answer:\nThe descending order of numbers begins with 15.\n0.15141312111098765\nSo, 15, 14, 13, 12, 11, 10, ...,(first 12 digits are 2 digit numbers).\nThen, 9, 8, 7, 6, 5, ...,(next 5 digits are single digit numbers).\nIt follows that 4, 3, and 2 are the next digits, thus 3 and 2 are the 19th and 20th digits, respectively.\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA number is four less than two times the other number. If their difference is 21, what is the greater number?\n\n### Options:\nA. 50\nB. 46\nC. 31\nD. 21\nE. 15\n\n### Answer:\nA = one number\nB = other number\nA = -4 + 2B\nA - B = 21\nsolve for A by adding B to each side\nA = B + 21\nSubstitute (B + 21) for A in A = -4 + 2B\n(B + 21) = -4 + 2B\nadd -B to each side\n21 = -4 + B\nadd 4 to each side\n25 = B\nSince A = B + 21 , A = 25 + 21 , A = 46\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA garrison of 2000 men has provisions for 54 days. At the end of 15 days, a reinforcement arrives, and it is now found that the provisions will last only for 20 days more. What is the reinforcement?\n\n### Options:\nA. 1778\nB. 1682\nC. 9178\nD. 1900\nE. 1782\n\n### Answer:\n2000 ---- 54\n2000 ---- 39\nx ----- 20\nx*20 = 2000*39\nx = 3900\n2000\n-------\n1900\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nI purchases perfume from a store and gave him a thousand rupee note.\nThe perfume cost Rs.300.\nSince the store person have no change, he gets the change from next shop and return me 800 rupees.\nAfter a while, the next shopkeeper comes and told the 1st shopkeeper that the note is a fraud and takes his money back.\nHow much loss does the 1st shopkeeper have to bear ?\n\n### Options:\nA. 2004\nB. 2011\nC. 5000\nD. 5400\nE. 1000\n\n### Answer:\nE\nRupees 1000\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA cistern can be filled by a tap in 3 hours while it can be emptied by another tap in 5 hours. If both the taps are opened simultaneously, then after how much time will the cistern get filled?\n\n### Options:\nA. 5.2 hrs\nB. 2.9 hrs\nC. 1.9 hrs\nD. 7.5 hrs\nE. 1.4 hrs\n\n### Answer:\nNet part filled in 1 hour = (1/3 - 1/5) = 2/15\nThe cistern will be filled in 15/2 hrs i.e., 7.5 hrs.\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n2400\u00f720\u00f710=?\n\n### Options:\nA. 43\nB. 12\nC. 15\nD. 20\nE. 24\n\n### Answer:\n2400 \u00f7 20 = 120\n120 \u00f7 10 = 12\nAnswer is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average earning of a mechanic for the first 4days of a week is Rs.18 and for the last four days is Rs.22. If he earns Rs.20 on the fourth day, his average earning forthe whole week is?\n\n### Options:\nA. Rs. 10\nB. Rs. 20\nC. Rs. 30\nD. Rs. 40\nE. Rs. 50\n\n### Answer:\nTotal earning for the week = Sum of earning of first four days + Sum of earning of last four days - Earning of 4th day\n= 4 x18 + 4 x 22 -20\n= Rs. 140\n\u2234 Average earning = 140 / 7\n= Rs. 20\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAt what price must an article costing Rs.150 be marked in order that after deducting 10% from the list price. It may be sold at a profit of 30% on the cost price?\n\n### Options:\nA. 62.5\nB. 62.0\nC. 62.6\nD. 216.67\nE. 62.2\n\n### Answer:\nCP = 150\nSP = 150*(130/100) = 195\nMP*(90/100) = 195\nMP = 216.67\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf x, y, and z are consecutive odd integers, with x < y < z, then which of the following must be true?\nI. x + y + z is odd\nII. (x+z)/y is not an integer\nIII. xy/2 is not an integer\n\n### Options:\nA. I only\nB. II only\nC. III only\nD. I and II only\nE. I, II, and III\n\n### Answer:\nconsecutive odds are:\n2x+1, 2x+3, 2x+5\nI. 2x+1+2x+3+2x+5=6x+9=3(2x+3), 2x+3 is not divisible by 2 hence odd, odd * odd = odd Hence I is odd - TRUE\nII. 2x+1+2x+5=4x+6/2x+3=2(2x+3)/2x+3=2, so integer - TRUE\nIII. (2x+1)*(2x+3)=4x^2+6x+2x+3=4x^2+8x+3=(4x(x+2)+3)/2 is not integer, so TRUE\nANSWER: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich of the following values is the greatest\n\n### Options:\nA. a) 11% of 89\nB. b) 22% of 78\nC. c) 33% of 67\nD. d) 55% of 56\nE. e) 55% of 45\n\n### Answer:\nAre you sure that you checked the answer key correctly? I just signed up forVeritas(haven't started yet, not until March) but I have access to the materials and the answer key I'm looking at says D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the odd man out\n36, 315, 612, 810, 966, 1362\n\n### Options:\nA. 966\nB. 612\nC. 315\nD. 36\nE. 1362\n\n### Answer:\n315is divisible by 3 which is odd number where as all others are even numbers divisible by 3.\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a camp, there is a meal for 120 men or 200 children. If 170 children have taken the meal, how many men will be catered to with remaining meal?\n\n### Options:\nA. 30\nB. 20\nC. 18\nD. 57\nE. 63\n\n### Answer:\nThere is a meal for 200 children.\n170 children have taken the meal.\nRemaining meal is to be catered to 30 children.\nNow, 200 children 120 men.\n30 children = (120/200)x 30 = 18 men.\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a city 100% votes are registered, in which 60% vote for congress and 40% vote for BJP. There is a person A, who gets 75% of congress votes and 8% of BJP votes. How many votes got by A?\n\n### Options:\nA. 48.9 %\nB. 78.2 %\nC. 48.2 %\nD. 48.7 %\nE. 48.6 %\n\n### Answer:\nAssume total votes are 100. So A got\n75% of 60 = 45\n8% of 40 = 3.2\nA total of 48.2 %\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOn Saturday morning, John will begin a camping vacation and he will return home at the end of the first day on which it rains. If on the first three days of the vacation the probability of rain on each day is 0.2, what is the probability that Malachi will return home at the end of the day on the following Monday?\n\n### Options:\nA. 0.008\nB. 0.125\nC. 0.128\nD. 0.512\nE. 0.64\n\n### Answer:\nRe-phrasing the question:\nWhat is the probability of: Saturday: No rain, Sunday: No rain, Monday: Rain\nProbability of rain = 0.2\nTherefore, probability of no rain = 0.8\n0.8*0.8*0.2 = 0.128\nHence C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn the sequence 1, 2, 4, 8, 16, 32, \u2026, each term after the first is twice the previous term. What is the sum of the 16th, 17th terms in the sequence?\n\n### Options:\nA. 2^18\nB. 3(2^17)\nC. 7(2^16)\nD. 3(2^15)\nE. 7(2^15)\n\n### Answer:\nthe sequence comes out to be 2^0,2^1,2^2,2^3 and so on...\nso 16th term will be 2^15\n17th term 2^16\nadding all three\nwe get\n2^15+(2^15)*2\nso answer is 2^15(1+2)=>3(2^15)\nanswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSimplify\n16\u2212[5\u2212(6+2(7\u22128\u22125\u00af\u00af\u00af\u00af\u00af\u00af\u00af\u00af\u00af\u00af\u00af))]\n\n### Options:\nA. 23\nB. 25\nC. 28\nD. 30\nE. 32\n\n### Answer:\nExplanation:\n=16\u2212[5\u2212(6+2(7\u22128+5))]\n(Please check due to overline, sign has been changed)\n=16\u2212[5\u2212(6+2\u00d74))]\n=16\u2212[\u22129]=16+9=25\nOption B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the cost price of 12 pens is equal to the selling price of 8 pens, the gain percent is:\n\n### Options:\nA. 80%\nB. 90%\nC. 50%\nD. 40%\nE. 10%\n\n### Answer:\nExplanation:\nLet C.P. of each pen be Re. 1.\nThen, C.P. of 8 pens = Rs. 8; S.P. of 8 pens = Rs. 12.\nGain % = 4/8 * 100 = 50%\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA factory produces x widgets per day. The factory's fixed costs are $7000 per day. The price per widget is $80 and the variable costs are $20 per widget. How many widgets need to be produced for profits of $6200 a day?\n\n### Options:\nA. 42.33\nB. 90.33\nC. 168\nD. 220\nE. 400\n\n### Answer:\nprofits=6200=60x-8000 --> x=220\nAnswer D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a man buys 1 liter of milk for 12 rs. and mixes it with 20% water and sells it for 15 rs then what is the %age of gain...\n\n### Options:\nA. 30\nB. 40\nC. 50\nD. 60\nE. 70\n\n### Answer:\nQuantity after adding 20% water=1.2 liter\nSP of 1.2 lit.@15 Rs./liter=15*1.2=18 Rs\nCP=12 Rs/lit.\n% profit=100*(18-12)/12=50\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSimplify 3/4 of 6 0 \u2013 8/5 of 60 + ? = 12\n\n### Options:\nA. 48\nB. 24\nC. 56\nD. 63\nE. 14\n\n### Answer:\n60 \u00d7 3/4 = 45, 60 \u00d7 8/5 = 96\n45 \u2013 96 + ? = 12 => 96 + 12 = 108 \u2013 45 = 63\n[63 + 45 = 108 \u2013 96 = 12]\nOption D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf in a certain sequence of consecutive multiples of 50, the median is 825, and the greatest term is 1050, how many terms that are smaller than 825 are there in the sequence?\n\n### Options:\nA. 6\nB. 5\nC. 8\nD. 12\nE. 13\n\n### Answer:\nSince the median is 825 we know there must be a even number of integers because 50 is not a multiple of 825.\nSo the list around 625 must go. 750 800 (825) 850 900 950 1000 1050\nSince we know there are 5 numbers greater than 825 then there must be 5 numbers less then 825.\nanswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n50 is what percent of 125?\n\n### Options:\nA. 35%\nB. 40%\nC. 45%\nD. 50%\nE. 55%\n\n### Answer:\n50/125\u00d7100=50% ANSWER : B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nEach of the 50 members in a high school class is required to sign up for a minimum of one and a maximum of three academic clubs. The three clubs to choose from are the poetry club, the history club, and the writing club. A total of 17 students sign up for the poetry club, 24 students for the history club, and 22 students for the writing club. If 3 students sign up for exactly two clubs, how many students sign up for all three clubs?\n\n### Options:\nA. 5\nB. 6\nC. 7\nD. 8\nE. 9\n\n### Answer:\nThe total number in the three clubs is 17+24+22=63.\nAll 50 students signed up for at least one club.\n3 of those students signed up for exactly one more club.\n63 - 53 = 10 so 5 students must have signed up for exactly three clubs.\nThe answer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 7", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf log303 = a, log305 = b, then log308 =?\n\n### Options:\nA. 3(1 - a - b)\nB. (a - b + 1)\nC. (1 - a - b)\nD. (a - b + 1)\nE. none of these\n\n### Answer:\na + b = log3015 = log30(30/2) = 1- log302\n=> log302 = (1 - a - b)\nTherefore, log308 = 3(1 - a - b).\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA Man can row upstream at 85kmph and downward stream at 47 kmph. Find Man's rate of the current\n\n### Options:\nA. 19km/hr\nB. 20km/hr\nC. 65km/hr\nD. 2.8km/hr\nE. 4.4km/hr\n\n### Answer:\nRate of the current=1/2(85-47)km/hr\n=19km/hr\ncorrect option is :A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA company seeks to hire a sales manager, a shipping clerk, and a receptionist. The company has narrowed its candidate search and plans to interview all remaining candidates including 7 persons for the position of sales manager, 4 persons for the position of shipping clerk, and 10 persons for the position of receptionist. How many different hirings of these three people are possible?\n\n### Options:\nA. 7 + 4 + 10\nB. 7 \u00d7 4 \u00d7 10\nC. 21 \u00d7 20 \u00d7 19\nD. 7! + 4! + 10!\nE. 7! \u00d7 4! \u00d7 10!\n\n### Answer:\nNumber of ways one person can be hired for the position of Sales Manager= C71C17=7\nNumber of ways one person can be hired for the position of Shipping Clerk= C41=4\nNumber of ways one person can be hired for the position of Receptionist= C101=10\nTherefore total number of different hiring possible for the three positions = 7 * 4 * 10\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many 2's are there between the terms 112 to 375?\n\n### Options:\nA. A)156\nB. B)157\nC. C)158\nD. D)159\nE. E)160\n\n### Answer:\nLet us calculate total 2's in the units place. (122, 132, 142 ... 192), (201, 212, 222, ... 292), (302, 312, ... 372) = 8 + 10 + 8 = 26\nTotal 2's in tenth's place, (120, 121, 122, ..., 129) + (220, 221, ..., 229) + (320, 321, ..., 329) = 30\nTotal 2's in hundred's place = (200, 201, ... 299) = 100.\nTotal 2's between 112 and 375 = 26 + 30 + 100 = 156\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA solution contains 8 parts of water for every 7 parts of Lemonade syrup. How many parts of the solution should be removed and replaced with water so that the solution will now contain 10% lemonade syrup?\n\n### Options:\nA. 1.5\nB. 1.75\nC. 2.14\nD. 2.34\nE. 2.64\n\n### Answer:\nLet the total solution is 150 L with 80 L water70 L syrup.\nTo make 10% syrup solution, the result solution must have 135 L syrup and 15 L syrup.\nTherefore we are taking 55 L of syrup from initial solution and replacing with water.\nusing urinary method:\n70 L syrup in 150 L solution\n55 L syrup in 117.9 L solution\nWe started by multiplying 10\nNow to get to the result we need to divide by 55 => amount of solution to be replaced with water = (117.9/55) = 2.14.\nCorrect option : C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n10% people of a village in Sri Lanka died by bombardment, 20% of the remainder left the village on account of fear. If now the population is reduced to 4554, how much was it in the beginning?\n\n### Options:\nA. 7349\nB. 6300\nC. 6325\nD. 6939\nE. 2989\n\n### Answer:\nX * (90/100) * (80/100) = 4554\nX = 6325\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many different ways can you select a pilot and a co pilot if you have 70 people to choose from?\n\n### Options:\nA. 199\nB. 200\nC. 398\nD. 4950\nE. 4830\n\n### Answer:\n1) PERMUTATION:-\nsince it is selection, we have to find permutation..\n70P2= 70!/(70-2)!=4830\nANS:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA sum of money at simple interest amounts to Rs. 1072 in 2 years and to Rs. 1144 in 4 years. The sum is:\n\n### Options:\nA. Rs. 1000\nB. Rs. 850\nC. Rs. 500\nD. Rs. 1200\nE. Rs. 900\n\n### Answer:\nS.I. for 2 years = Rs. (1144 - 1072) = Rs. 72.\nS.I. for 1 year = Rs. 72/2 = Rs. 36.\nPrincipal = Rs. (1072 - 72) = Rs. 1000.\nAnswer: Option A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMeera purchased two three items from a shop. Shop keeper says for one wallet : Rs.250/- and Shoe : 1250/- Meera give Rs. 2000/- to shop keeper. He paid balance Rs. 750/- to meera. How much she got?\n\n### Options:\nA. 250\nB. 500\nC. 600\nD. 350\nE. 400\n\n### Answer:\nCost of Wallet =250/-\nCost of Shoe = 1250/-\nTotal cost = 1500/-\namount paid to shop keeper = 2000/-\nBalance is : 2000 - 1500 = 500 (250 Balance + 250 additional)\nAnswer is A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe salary of all officers is increased twice successively by 20%. What is the net percentage increase in their salaries?\n\n### Options:\nA. 20%\nB. 40%\nC. 21%\nD. 44%\nE. 48%\n\n### Answer:\nM . F = 120/100*120/100 = 36/25\nNet % increase = ( M . F -1 ) *100 =( 36/25-1) * 100\n11/25 *100 = 44 %\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 'Pink' is called 'Orange', 'Orange' is called 'Blue', 'Blue' is called 'Red', 'Red' is called 'Green', 'Green' is called 'Black' and 'Black' is called 'white', what would be the color of charcoal ?\n\n### Options:\nA. White\nB. BLUE\nC. PINK\nD. ORANCE\nE. BLACK\n\n### Answer:\nExplanation:\nPink \u2192 Orange\nOrange \u2192 Blue\nBlue \u2192 Red\nRed \u2192 Green\nGreen \u2192 Black\nBlack \u2192 White\nThe color of charcoal is 'Black' but in coding language, 'Black' is called 'White'.\nANSWER: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA and B together can do a piece of work in 6 days and A alone can do it in 10 days. In how many days can B alone can do it?\n\n### Options:\nA. 12 days\nB. 18 days\nC. 15 days\nD. 21 days\nE. 22 days\n\n### Answer:\nExplanation:\nA and B can do work 1/6 in 1 day\nA alone can do 1/10 work in 1 day\nB alone can do (1/6 -1/10) =1/15 work in 1 day\n=> complete work can be done in 15 days by B\nAnswer: Option C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain collage has total of 600 seniors each majoring in exactly one of six subjects. A minimum of 20 seniors major in each six subjects. If three quarter of the seniors major in one of four subjects, what is the greatest possible number of seniors majoring in one of the other two subjects?\n\n### Options:\nA. 100\nB. 130\nC. 75\nD. 60\nE. 50\n\n### Answer:\nAnswer B\n600 = 450 + 20 + x => x = 130\n= 3/4 * 600 in 4 subjects + 20 min for 5th subject + x = 600\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nf1(x)f1(x) = 2x - 1 and fn(x)=f1(fn\u22121(x))fn(x)=f1(fn\u22121(x)) for n \u2265\u2265 2. Find f5(2)\n\n### Options:\nA. 7\nB. 6\nC. 78\nD. 9\nE. 1\n\n### Answer:\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich fraction will come next, 1/2,3/4,5/8,7/16,?\n\n### Options:\nA. 9/30\nB. 11/32\nC. 9/28\nD. 9/32\nE. 9/28\n\n### Answer:\nNumerators are getting increased by 2. i.e., numerators goes like 1,3,5,7,...\nHence, next numerator = 7+2 = 9\nDenominators are getting multiplied by 2. i.e., denominators goes like 2,4,8,16,...\nHence, next denominator = 16\u00d72 = 32\nSo, the next fraction is 9/32\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA candy company sells premium chocolate at $5 per pound and regular chocolate at $2 per pound in increment of whole pound only.If Barrett buys a pack of candies which costs him $31, how many pounds of premium chocolates are in the box?\n\n### Options:\nA. [A] 1\nB. [B] 2\nC. [C] 3\nD. [D] 4\nE. [E] 5\n\n### Answer:\nThis question is a bit of Special equations with a single set of unique values.\nthe Equation stands : 5X + 2Y = 31\nSubtract multiple of 5 from 31 and check whether the remaining total is divisible by 4\n31 - 5 = 26 -> Not divisible by 4\n31 - 10 = 21 -> Not divisible by 4\n31 - 15 =16 -> Divisible by 4\n31 - 20 =11 -> Not divisible by 4\n31 - 25 =6 -> Not divisible by 4\n31 - 30 =1 -> Not divisible by 4\nAny multiple of 5 hereon will give a negative value for regular chocolates bought and hence, inadmissible\nThus Amount spent on regular chocolate= $16\nAmount spent on Premium chocolate= $15\nPrice per premium chocolate = $5\nNo. Of boxes of premium chocolate bought = 10 / 5 = 2\nCorrect Option : B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe salary of a person was reduced by 10%. By what percent should his reduced salary be raised so as to bring it at par with his original salary?\n\n### Options:\nA. 10%\nB. 11 1/9%\nC. 13 2/7%\nD. 15 3/11%\nE. 12 1/3%\n\n### Answer:\nLet the original salary be $100\nNew salary = $90\nIncrease on 90 =10\nIncrease on 100 = 10/90 * 100 = 11 1/9%\nAnswer is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a sample of 800 high school students in which all students are either freshmen, sophomores, juniors, or seniors, 23 percent are juniors and 75 percent are not sophomores. If there are 160 seniors, how many more freshmen than sophomores are there among the sample of students?\n\n### Options:\nA. 42\nB. 48\nC. 56\nD. 64\nE. 72\n\n### Answer:\n200 are sophomores.\nThe number of freshmen is 600 - 160 - 0.23(800) = 256\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMonth\tAverage Price\nper Dozen\nApril $1.26\nMay $1.20\nJune $1.08\nThe table above shows the average (arithmetic mean) price per dozen of the large grade A eggs sold in a General store during three successive months. If 2/3 as many dozen were sold in April as in May, and twice as many were sold in June as in April, what was the average price per dozen of the eggs sold over the three-month period?\n\n### Options:\nA. 1.4\nB. 1.3\nC. 1.2\nD. 1.1\nE. 1.16\n\n### Answer:\nSay x dozen eggs were sold in May.\nThen 2x/3 dozen eggs were sold in April and 2*2x/3=4x/3 dozen eggs were sold in May.\nTotal x+2x/3+4x/3=3x dozen eggs were sold in three months.\nTotal sales: 2x/3*1.26+x*1.2+4x/3*1.08=$3.48x. The average price per dozen 3.48x/3x=$1.16.\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nDuring a certain two-week period, 72 percent of the movies rented from a video store were comedies, and of the remaining movies rented, there were 6 times as many dramas as action movies. If no other movies were rented during that two-week period and there were A action movies rented, then how many comedies, in terms of A, were rented during that two-week period?\n\n### Options:\nA. 1/20 A\nB. 10 A\nC. 15 A\nD. 18 A\nE. 23 A\n\n### Answer:\nMovies: 72 % comedies. 28 % remaining genre.\nNow in this 28 %, there are only 2 categories. Action movies and Drama Movies.\nIf Action = x; Drama movies = 6x. Total 7x.\n7x = 28; x = 4\nAction movies: 4 %\nDrama movies: 24 %\nwe can say that out of 100z,:\ncomedies: 72z\naction: 4z\ndrama: 24 z\nNow action movies were A\nThis means:\nA = 4z.\nz = (A/4)\nComedies: 72z = 72 * (A/4)\n18 A\nD is the answer.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWorking alone at its constant rate, machine A produces x boxes in 5 minutes and working alone at its constant rate, machine B produces 2x boxes in 10 minutes. How many minutes does it take machines A and B, working simultaneously at their respective constant rates, to produce 3x boxes?\n\n### Options:\nA. 3 minutes\nB. 7.5 minutes\nC. 5 minutes\nD. 6 minutes\nE. 12 minutes\n\n### Answer:\nRate = Work / Time\nGiven Rate of Machine A = 2X / 10 min\nMachine B Produces 2x boxes in 10 min hence , Machine B produces 2x boxes in 10 min .\nRate of Machine B = 2x / 10\nwe need tofind the combined time that machines A and B, working simultaneouslytakeat their respective constant rates\nlet's first find the combined Rate of Machine A and B\nRate of Machine A = 2X / 10 min + Rate of Machine B = 2x / 10 = 4X/10\nNow combine Time = combine work needs to be done / Combine Rate = 3x/4x * 10 = 7.5 Min\nAns: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a fuel station the service costs $1.75 per car, every liter of fuel costs 0.65$. Assuming that a company owns 12 cars and that every fuel tank contains 60 liters and they are all empty, how much money total will it cost to fuel all cars?\n\n### Options:\nA. 320$\nB. 389$\nC. 420$\nD. 450$\nE. 489$\n\n### Answer:\nTotal Cost = ( 1.75*12 ) + ( 0.65 * 12 * 60 ) =489\nHence answer will be (E)\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA coin is tossed live times. What is the probability that there is at the least one tail?\n\n### Options:\nA. 31/32\nB. 31/17\nC. 31/19\nD. 31/12\nE. 31/13\n\n### Answer:\nLet P(T) be the probability of getting least one tail when the coin is tossed five times.\n= There is not even a single tail.\ni.e. all the outcomes are heads.\n= 1/32 ; P(T) = 1 - 1/32\n=31/32\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSharron bakes 6 cookies for 6 friends. 2 of the friend arrive early and eat 3 cookies each. How many cookies are left over if the other friends all have the same number of cookies?\n\n### Options:\nA. 1\nB. 2\nC. 3\nD. 4\nE. 5\n\n### Answer:\nSharron made 6*6 cookies = 36 cookies. 2 friends eat 3 cookies, leaving 30 remaining for 4 friends.\n30=2*3*5. 30 is not divisible by 4. The 4 friends ate a cumulative number of cookies less than 30 that must be divisible by 4, because the number is the same.\nA 30 -1=29. 29=1*29, cannot be divided by four\nB 30-2=28. 28=2*2*7, can be divided by four\nC 30-3 = 27. 27=3*3*3, cannot be divided by four\nD. Because there are 4 people, 4 cannot be a remainder (remainder = 0)\nE. Because there are 4, people, 5 cannot be a remainder (remainder = 1)\nB is the correct answer\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nBy selling 9 pencils for a rupee a man loses 20%. How many for a rupee should he sell in order to gain 20%?\n\n### Options:\nA. 8\nB. 9\nC. 7\nD. 4\nE. 6\n\n### Answer:\n80% --- 9\n120% --- ?\n80/120 * 9 = 6\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn given series 582, 605, 588, 611, 634, 617, 600 only one number is incorrect. Find out that wrong number\n\n### Options:\nA. 615\nB. 634\nC. 600\nD. 620\nE. 617\n\n### Answer:\n582+23=605\n605-17=588\n588+23=611\n611-17=594....so 634 is wrong.\n594+23=617\n617-17=600\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFresh grapes contain 90% by weight while dried grapes contain 20% water by weight. What is the weight of dry grapes available from 40 kg of fresh grapes?\n\n### Options:\nA. 5 kg\nB. 2.4 kg\nC. 2.5 kg\nD. 10 kg\nE. none of these\n\n### Answer:\nThe weight of non-water in 20 kg of fresh grapes (which is 100-90=10% of whole weight) will be the same as the weight of non-water in x kg of dried grapes (which is 100-20=80% of whole weight), so 40\u00e2\u02c6\u20140.1=x\u00e2\u02c6\u20140.8--> x=5\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the compound ratio of (1:2), (1:3) and (3:5) is\n\n### Options:\nA. 1:10\nB. 2:3\nC. 3:4\nD. 4:5\nE. 3:2\n\n### Answer:\nRequired ratio = 1/2 * 1/3 * 3/5 = 1/10 = 1:10\nAnswer is A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJohn spent a total of $135 on baseball tickets. The price of a ticket is either $12 for the field seats or $5 for the balcony. What is the minimum amount Q of dollars he could have spent for the $12 tickets?\n\n### Options:\nA. $48\nB. $60\nC. $84\nD. $96\nE. $120\n\n### Answer:\n60 ..... 12 *5 Q= 60. (min). Thus answer .B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA composer\u2019s guild is planning its spring concert, and eleven pieces have been submitted for consideration. The director of the guild knows that they will only have time to present three of them. If the pieces can be played in any order, how many combinations of pieces are possible?\n\n### Options:\nA. 402\nB. 165\nC. 154\nD. 512\nE. 126\n\n### Answer:\nCombination question..\n11C3 = 165..\nIMO option B is correct..\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo trains running in opposite directions cross a man standing on the platform in 47 seconds and 38 seconds respectively and they cross each other in 40 seconds. The ratio of their speeds is:\n\n### Options:\nA. 3 : 1\nB. 3 : 2\nC. 2 : 7\nD. 3 : 25\nE. 3 : 4\n\n### Answer:\nLet the speeds of the two trains be x m/sec and y m/sec respectively. Then, length of the first train = 47 x meters, and length of the second train = 38 y meters. (47 x + 37 y) / (x + y) = 40 ==>\n47 x + 38 y = 40x + 40 y ==> 7x = 2 y ==> x/y = 2/7\nAnswer: Option C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the average (arithmetic mean) of x, x + 2, and x + 4 is 33, what is the value of x?\n\n### Options:\nA. 30\nB. 31\nC. 32\nD. 32\nE. 37\n\n### Answer:\nAM of x, x + 2, and x + 4 = x + (x + 2) + (x + 4) / 3 = 3x + 6 /3 = x + 2\nGiven that x + 2 = 33\nx = 31\nCorrect Option: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a is a positive integer, which of the following could NOT be the square of a?\n\n### Options:\nA. 2432\nB. 7426\nC. 5966\nD. 3415\nE. 2155\n\n### Answer:\nA number ending in 2 cannot be a perfect square.\n2432 ends in a number 2, making that the correct answer\n(A) 2432\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf (2^32 + 1) is completely divisible by a whole number, which of the following numbers is completely divisible by this number?\n\n### Options:\nA. (2^96+1)\nB. (7 \u00d7 223 )\nC. (2^16 - 1)\nD. (2^15 + 1)\nE. (2^17 + 1)\n\n### Answer:\nExplanation:\nLet\n2\n32\n=\nx\n232=x.\nThen\n(\n2\n32\n+\n1\n)\n=\n(\nx\n+\n1\n)\n(232+1)=(x+1)\nAssume that\n(\nx\n+\n1\n)\n(x+1) is completely divisible by a whole number, N\n(\n2\n96\n+\n1\n)\n=\n(\n2\n32\n)\n3\n+\n1\n=\n(\nx\n3\n+\n1\n)\n=\n(\nx\n+\n1\n)\n(\nx\n2\n\u2212\nx\n+\n1\n)\n(296+1)=(232)3+1=(x3+1)=(x+1)(x2\u2212x+1)\nif\n(\nx\n+\n1\n)\n(x+1) is completely divisible by N,\n(\nx\n+\n1\n)\n(\nx\n2\n\u2212\nx\n+\n1\n)\n(x+1)(x2\u2212x+1) will also be divisible by N\nHence\n(\n2\n96\n+\n1\n)\n(2^96+1) is completely divisible N\nA)\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the sum of two numbers is 12 and the sum of their squares is 124, then the product of the numbers is\n\n### Options:\nA. 10\nB. 44\nC. 80\nD. 88\nE. 90\n\n### Answer:\nSol.\nLet the numbers be x and y.\nThen, (x+y) = 12 and x2 + y2 = 124.\nNow, 2xy = (x+y)2 - (x2 + y2)\n= (12)2 - 124 = 144 - 124 = 20\nxy = 10.\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many days will there be from 28th January,1996 to 15th May,1996(both days included)?\n\n### Options:\nA. 102\nB. 103\nC. 111\nD. 109\nE. 121\n\n### Answer:\nExplanation:\nNumber of days from 28-Jan-1996 to 15-May-1996 (both days included)\n= 4(Jan) + 29(Feb) + 31 (Mar) + 30(Apr)+ 15(May) = 109\nAnswer: Option D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average of marks obtained by 120 boys was 38. If the average of marks of passed boys was 39 and that of failed boys was 15, the number of boys who passed the examination is?\n\n### Options:\nA. 100\nB. 110\nC. 115\nD. 125\nE. 140\n\n### Answer:\nLet the number of boys who passed = X.\nThen, 39 x X + 15 x (120 - X) = 120 x 38\n24X = 4560 - 1800\n=> X = 2760/24\nX = 115.\nHence, the number of boys passed = 115.\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the least number of complete years in which a sum of money put out at 25% compound interest will be more than double of itself?\n\n### Options:\nA. 6 years\nB. 7 years\nC. 9 years\nD. 4 years\nE. 1 years\n\n### Answer:\n4 years\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA part of certain sum of money is invested at 8% per annum and the rest at 12% per annum, if the interest earned in each case for the same period is equal, then ratio of the sums invested is?\n\n### Options:\nA. 3:2\nB. 4:8\nC. 4:3\nD. 4:0\nE. 4:9\n\n### Answer:\n12:8\n= 3:2\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJohn and Jacob set out together on bicycle traveling at 15 and 9 miles per hour, respectively. After 40 minutes, John stops to fix a flat tire. If it takes John one hour to fix the flat tire and Jacob continues to ride during this time, how many hours will it take John to catch up to Jacob assuming he resumes his ride at 15 miles per hour? (consider John's deceleration/acceleration before/after the flat to be negligible)\n\n### Options:\nA. 3\nB. 3 1/3\nC. 3 1/2\nD. 4\nE. 1 1/4\n\n### Answer:\nJohn's speed - 15 miles/hr\nJacob's speed - 9 miles/hr\nAfter 40min (i.e 2/3hr), distance covered by John = 15x2/3 = 10 miles.\nJacob continues to ride for a total of 1hour and 40min (until John's bike is repaired). Distance covered in 1 hour 40min (i.e 5/3hr) = 9x5/3 = 15 miles.\nNow, when John starts riding back, the distance between them is 7.5 miles. Jacob and John are moving in the same direction.For John to catch Jacob, the effective relative speed will be 15-9 = 6 miles/hr.\nThus, to cover 7.5 miles at 6 miles/hr, John will take 7.5/6 = 1.25 hours\nAnswer E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo pipes P and Q can fill a cistern in 12 and 19 minutes respectively. Both are opened together, but at the end of 3 minutes the first is turned off. How much longer will the cistern take to fill?\n\n### Options:\nA. 11 1/2 min\nB. 14 1/4 min\nC. 11 2/4 min\nD. 11 1/5 min\nE. 11 7/4 min\n\n### Answer:\n3/12 + x/19 = 1\nx= 14 1/4\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA student's mark was wrongly entered as 83 instead of 63. Due to that the average marks for the class got increased by 1/2. What is the number of students in the class?\n\n### Options:\nA. 20\nB. 30\nC. 10\nD. 40\nE. 50\n\n### Answer:\nLet the total number of students = x\nThe average marks increased by 1/2 due to an increase of 83 - 63 = 20 marks.\nBut total increase in the marks = (1/2)x=x/2\nHence we can write as\nx/2=20\n\u21d2x=20\u00d72=40\nAnswer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThree friends James, David and Charlie divide $1230 amongs them in such a way that if $5, $10 and $15 are removed from the sums that James, David and Charlie received respectively, then the share of the sums that they got will be in the ratio of 9: 10 : 11. How much did Charlie receive?\n\n### Options:\nA. $600\nB. $575\nC. $550\nD. $580\nE. $615\n\n### Answer:\nA+B+C = 1230\nGiven ratio 9:10:11\nLet us say the shares of A,B,C deducting 5,10,15 be a,b,c\na+b+c = 1230-30= 1200 = 30K\nc share = (1200X30)/60 = 600\nC = charlie share = 600+15= 615\nOption E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf A's height is 40% less than that of B, how much percent B's height is more than that of A?\n\n### Options:\nA. 66.66%\nB. 66.68%\nC. 66.766%\nD. 86.66%\nE. 66.65%\n\n### Answer:\nExcess of B's height over A's = [(40/(100 - 40)] x 100%\n= 66.66%\nAnswer: A) 66.66%\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe ratio of men to women in a class is 6 to 5. If 6 men and 6 woman drop out of the class and the ratio of men to women after the drop out is 4 to 3, then how many men are currently in the class?\n\n### Options:\nA. 10\nB. 11\nC. 14\nD. 15\nE. 12\n\n### Answer:\nEquation on the basis of question\n6x-6/5x-6=4/3\nx=3\nOriginal number of men = 6*3=18\nOriginal Number of Women = 5*3=15\nCurrent number of men = 18-6=12 (Answer)\nCurrent number of women = 15-6=9\nRatio = 12/9= 4/3 ( Just to verify)\nAns E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a certain game, a large bag is filled with blue, green, purple and red chips worth 1, 5, x and 11 points each, respectively. The purple chips are worth more than the green chips, but less than the red chips. A certain number of chips are then selected from the bag. If the product of the point values of the selected chips is 28160, how many purple chips were selected?\n\n### Options:\nA. 1\nB. 2\nC. 3\nD. 4\nE. 5\n\n### Answer:\n28160 = 1*5*8^3*11\nThe factors of 8 must come from the purple point value, so there are 3 purple chips.\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo persons start running simultaneously around a circular track of length 700 m from the same point at speeds of 15 km/hr and 25 km/hr. When will they meet for the first time any where on the track if they are moving in opposite directions?\n\n### Options:\nA. 63\nB. 10\nC. 28\nD. 27\nE. 12\n\n### Answer:\nTime taken to meet for the first time anywhere on the track\n= length of the track / relative speed\n= 700 / (15 + 25)5/18 = 700* 18 / 40 * 5 = 63 seconds.\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA can do a piece of work in 21 days and B in 28 days. Together they started the work and B left after 4 days. In how many days can A alone do the remaining work?\n\n### Options:\nA. 33\nB. 276\nC. 27\nD. 14\nE. 66\n\n### Answer:\nLet A worked for x days.\nx/21 + 4/28 = 1 => x/21 = 6/7 => x = 18\nA worked for 18 days. So, A can complete the remaining work in 18 - 4 = 14 days.\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA clock shows the time as 3:30 P.m. If the minute hand gains 2 minutes every hour, how many minutes will the clock gain by 5 a.m.?\n\n### Options:\nA. 23 Minutes\nB. 24 Minutes\nC. 25 Minutes\nD. 27 Minutes\nE. None of these\n\n### Answer:\nif the minute hand gains 2 minutes in 1 hour the from 3:30 p.m-4:00 p.m it gains 1 min\nthen from 4:00p.m-4:00 a.m =13*2=26 total=27\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a copier makes 5 copies every 5 seconds, then continues at this rate, how many minutes will it take to make 6,000 copies?\n\n### Options:\nA. 100\nB. 200\nC. 150\nD. 125\nE. 130\n\n### Answer:\n5 copies 5 seconds\n6000 copies = (6000*5)/5seconds\n= 6000/60 minutes\n= 100 minutes\nAnswer : B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJohn deposited $10,000 to open a new savings account that earned 4 percent annual interest, compounded quarterly. If there were no other transactions in the account, what was the amount of money in John\u2019s account 6 months after the account was opened?\n\n### Options:\nA. $10,100\nB. $10,101\nC. $10,200\nD. $10,201\nE. $10,400\n\n### Answer:\nApproach #1:\n4 percent annual interest compounded quarterly --> 1% in 3 moths.\nFor the first 3 moths interest was 1% of $10,000, so $100;\nFor the next 3 moths interest was 1% of $10,000, plus 1% earned on previous interest of $100, so $100+$1=$101;\nTotal interest for 6 months was $100+$101=$201, hence balance after 6 months was $10,000+ $201=$10,201.\nAnswer: D.\nApproach #2:\nIf the interest were compounded every 6 moths instead of every 3 months (quarterly) then in 6 months the interest would be 4%/2=2% of $10,000, so $200. Now, since the interest is compounded quarterly then there would be interest earned on interest (very small amount) thus the actual interest should be a little bit more than $200, only answer choice D fits.\nAnswer: D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nEight friends met for lunch at an expensive restaurant, and everyone decided to contribute equally to the total bill of $680. If one of the friends had a coupon for 12% off the total bill, and if each friend still contributed equally after the coupon was applied to the bill, how much did each friend pay?\n\n### Options:\nA. $90\nB. $74\nC. $45\nD. $37\nE. $35\n\n### Answer:\n680 * 0,12 = 81\n680 - 81 = 599\n599 / 8 = 74\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man can row 30 km downstream and 20 km upstream in 4 hours. He can row 45 km downstream and 40 km upstream in 7 hours. Find the speed of man in still water?\n\n### Options:\nA. 12.6\nB. 82.5\nC. 12.4\nD. 12.5\nE. 12.0\n\n### Answer:\nLet the speed of the man in still water be a kmph and let the speed of the stream be b kmph.\nNow 30/(a + b) + 20/(a - b) = 4 and 45/(a + b) + 40/(a - b) = 7\nSolving the equation, the speed of man in still water is 12.5 kmph.\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nS = { 1,2,3,5,6,9}\nT = { 4,5,6,7,1,3}\nwhat is the probability that x chosen from S and y chosen from T will result x*y = even\n\n### Options:\nA. 5/9\nB. 3/2\nC. 1/2\nD. 5/6\nE. 6/5\n\n### Answer:\np: the probability that x*y is even, then p=1-p(x*y is odd)\np(x*y odd)=p(x odd)*p(y odd)=4/6*4/6=16/36=4/9\nAnd p=1-4/9=5/9\nOption: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA sum of money is divided among A, B, C & D in the ratio 3:5:8:9 respectively. If the share of D Rs.1872 more than the share of A, then what is the total amount of money of B & C together?\n\n### Options:\nA. Rs. 4000\nB. Rs. 4056\nC. Rs. 5000\nD. Rs. 5050\nE. Rs. 6500\n\n### Answer:\nSol. Share of B + C = -3 x (5 + 8) = Rs. 4056\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA bag is filled with pennies and nickels in the ratio of 2 to 1. There are 10 nickles in the bag, how many coins are there in that bag?\n\n### Options:\nA. 30\nB. 50\nC. 65\nD. 70\nE. 80\n\n### Answer:\nA ratio of pennies to nickels of 2 to 1 means that we can write the number of pennies and nickels in the form\nnumber of pennies = 2x and number of nickels = x\nBut we know the number of nickels, 10. Hence\nx = 10\nThe total number of coins is given by\n2x + x = 3x = 3 \u00d7 10 = 30\nAnswer : A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo trains 140 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is?\n\n### Options:\nA. 7\nB. 8.2\nC. 2\nD. 10.8\nE. 11.2\n\n### Answer:\nAnswer: Option D\nRelative speed = 60 + 40 = 100 km/hr.\n= 100 * 5/18 = 250/9 m/sec.\nDistance covered in crossing each other = 140 + 160 = 300 m.\nRequired time = 300 * 9/250 = 54/5 = 10.8 sec\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf X = the product of eight distinct prime numbers, how many factors does X have besides 1 and itself?\n\n### Options:\nA. 166\nB. 188\nC. 210\nD. 232\nE. 254\n\n### Answer:\nSince X has 8 distinct prime factors, X has a total of 2^8 = 256 factors.\nBesides 1 and itself, X has 254 factors.\nThe answer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA watch which gains 5 seconds in 3 minutes was set right at 7 a.m. In the afternoon of the same day, when the watch indicated quarter past 4 o'clock, the true time is:\n\n### Options:\nA. 4 am\nB. 4 pm\nC. 5 am\nD. 6 am\nE. 6 pm\n\n### Answer:\ntime 7 am to 4.15 pm = 37/4\n37/720 hrs 1/20==>37/4\nclock(1/20*720/37*37/4)= 9 hrs after 7 am\n==> 4 pm\nANSWER B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA student has to obtain 35% of the total marks to pass. He got 100 marks and failed by 40 marks. The maximum marks are?\n\n### Options:\nA. 280\nB. 400\nC. 420\nD. 480\nE. 520\n\n### Answer:\nLet the maximum marks be x\nThen, 35% of x = 100+40\n35x/100 = 140\n35x= 140*100= 14000\nx = 400\nAnswer is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMr. Kramer, the losing candidate in a two-candidate election, received 942,568 votes, which was exactly 42 percent of all votes cast. Approximately what percent of the remaining votes would he need to have received in order to have won at least 50 percent of all the votes cast?\n\n### Options:\nA. 10%\nB. 12%\nC. 14%\nD. 17%\nE. 20%\n\n### Answer:\nLet me try a simpler one.\nLets assume that candidate got 42% votes and total votes is 100.\nCandidate won = 42\nRemaining = 58\nTo get 50%, candidate requires 8 votes from 100 which is 8% and 8 votes from 58.\n8/58 = .137 = 13.7%\nWhich is approx 14%. Hence the answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAyush was born two years after his father's marriage. His mother is five years younger than his father but 20 years older than Ayush who is 10 years old. At what age did the father get married ?\n\n### Options:\nA. 23 years\nB. 25 years\nC. 33 years\nD. 35 years\nE. 37 years\n\n### Answer:\nExplanation:\nAyush's present age = 10 years.\nHis mother's present age = (10 + 20) years = 30 years.\nAyush's father's present age = (30 + 5) years = 35 years.\nAyush's father's age at the time of Ayush's birth = (35 - 10) years = 25 years.\nTherefore Ayush's father's age at the time of marriage = (25 - 2) years = 23 years.\nAnswer: A) 23 year\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAnand and Deepak started a business investing Rs. 500 and Rs. 600 respectively. Out of a total profit of Rs. 420. Deepak's share is?\n\n### Options:\nA. s. 220.01\nB. s. 450.20\nC. s. 845.01\nD. s. 320.01\nE. s. 229.09\n\n### Answer:\nRatio of their shares = 500 : 600 = 5 : 6\nDeepak's share = Rs. (420* 6/11) = Rs. 229.09 ANSWER \"E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how many ways can 6 apples (identical) be distributed among 3 children? (Some children may get no apples.)\n\n### Options:\nA. 32\nB. 34\nC. 36\nD. 28\nE. 30\n\n### Answer:\nGeneralised form for n = number of identical objects, and r = number of children is n+r-1Cr-1.\nn=6 r= 3\n8C2 =28\nAnswer : D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n350 is increased by 50%. Find the final number.\n\n### Options:\nA. 725\nB. 625\nC. 225\nD. 525\nE. 425\n\n### Answer:\nExplanation\rFinal number = Initial number + 50%(original number) = 350 + 50%(350) = 350 + 175 = 525.\rAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA 110 cm long wire is to be cut into two pieces so that one piece will be 2/5th of the other, how many centimeters will the shorter piece be?\n\n### Options:\nA. 35\nB. 20\nC. 47\nD. 36\nE. 31\n\n### Answer:\n1: 2/5 = 5: 2\n2/7 * 110 =31\nAnswer:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nLine m lies in the xy-plane. The y-intercept of line m is -2, and line m passes through the midpoint of the line segment whose endpoints are (2, 4) and (6, -10). What is the slope of line m ?\n\n### Options:\nA. -3\nB. 1\nC. -1/3\nD. 0\nE. Undefined\n\n### Answer:\nAns: B\nSolution: line m goes through midpoint of (2, 4) and (6, -10). midpoint is (4,-3)\nas we can see that the y axis of intercept point is (0,-2) means line m is parallel to x axis\nslope M= 1\nAns: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are a lot of houses such that the numbers of their doorplates are odd numbers and the first number of the doorplates is 445, the last number of the doorplates is 705. How many houses are there?\n\n### Options:\nA. 141\nB. 111\nC. 121\nD. 131\nE. 101\n\n### Answer:\nSo it starts from 445 and goes like 447, 449,...... 705. and both first and last number are inclusive. Since every other number is odd, it's just 1/2 of the numbers and since it starts with an odd and ends with an odd inclusive add one to the result.\ni.e., ([705-445][/2]+1 = 131\nAns D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are 50 girls in a dance group in a private school. 30% of them dance hip hop and 80% dance ballet. How many of them dance both hip hop or ballet?\n\n### Options:\nA. 5\nB. 10\nC. 15\nD. 20\nE. 25\n\n### Answer:\nThe total number of girls in the class is n = 50.\nThe number of girls dancing hop hop is 30% of it, thus\nn (A)=30/100\u00d750=30/2=15.\nThe number of girls dancing ballet is 80%, thus\nn (B)=80/100\u00d750=80/2=40.\nIn order to calculate the number of girls dancing both hip hop and ballet we can use the following equation:\nn (AnB)=n (A)+n (B) -n =15+40-50=5.\nSo, 5 girls in this dance class dance both hip hop and ballet.\nANSWER: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe contents of two vessels containing copper and tin in the ratio 2:3 and 5:7 are mixed in the ratio 3:5. The resulting mixture will have copper and tin in the ratio?\n\n### Options:\nA. 210:283\nB. 312:433\nC. 178:213\nD. 197:283\nE. 145:256\n\n### Answer:\nThe ratio of copper and tin the new vessel= (2/5*3/8 + 5/12*5/8) : (3/5*3/8 + 7/12*5/8)\n= 197/480 : 283/480 = 197:283\nAnswer is D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a code word is defined to be a sequence of different letters chosen from the 10 letters A, B, C, D, E, F, G, H, I, and J, what is the ratio of the number of 5-letter code words to the number of 6-letter code words?\n\n### Options:\nA. 1\nB. 1/4\nC. 1/5\nD. 1/3\nE. 1/2\n\n### Answer:\nMethod #1: Using the permutation formula\n# of 5 letter code words:\nnPr = n! / (n \u2013 r)! = 10! / (10 \u2013 5)! = 10*9*8*7*6\n# of 6 letter code words:\nnPr = 10! / (10 \u2013 6)! = 10*9*8*7*6*5\n# of 5 words / # of 4 words = (10*9*8*7*6)/(10*9*8*7*6*5) = 1/5\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe sum of two numbers is 16. The difference is 10. What are the two numbers?\n\n### Options:\nA. 10-6\nB. 8-8\nC. 9-7\nD. 11-5\nE. 13-3\n\n### Answer:\n13+3 = 16\n13 - 3 = 10\nThe Answer is E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n9 men or 6 women can do a piece of work in 20 days. In how many days will 12 men and 8 women do the same work?\n\n### Options:\nA. 12/9 days\nB. 15/2 days\nC. 82/8 days\nD. 22/76 days\nE. 22/2 days\n\n### Answer:\n9M = 6W ---- 20 days\n12M + 8W -----?\n8W + 8 W = 16W ---?\n6W ---- 20 16 -----?\n6 * 20 = 16 * x => x = 15/2 days\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOne side of a rectangle is 3 cm shorter than the other side. If we increase the length of each side by 1 cm, then the area of the rectangle will increase by 16 cm2. Find the lengths of all sides.\n\n### Options:\nA. 10 and 3\nB. 9 and 6\nC. 10 and 7\nD. 3 and 10\nE. 10 and 10\n\n### Answer:\nLet x be the length of the longer side x>3, then the other side's length is x\u22123 cm. Then the area is S1 = x(x - 3) cm2. After we increase the lengths of the sides they will become (x+1) and (x\u22123+1)=(x\u22122) cm long. Hence the area of the new rectangle will be A2=(x+1)\u22c5(x\u22122) cm2, which is 16 cm2 more than the first area. Therefore\nA1+16=A2\nx(x\u22123)+16=(x+1)(x\u22122)\nx2\u22123x+16=x2+x\u22122x\u22122\n2x=18\nx=9. So, the sides of the rectangle are 9 cm and (9\u22123)=6 cm long.\nSo answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nLast year a worker saved 5% of her annual salary. This year, she made 20% more money than last year and she saved 6% of her salary. The amount she saved this year was what percent of the amount she saved last year?\n\n### Options:\nA. 136%\nB. 140%\nC. 144%\nD. 148%\nE. 152%\n\n### Answer:\nLet x be the worker's salary last year.\nLast year, she saved 0.05x.\nThis year, she saved 0.06(1.2x)=0.072x\n0.072x/0.05x=144%\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe length of a train and that of a platform are equal. If with a speed of 90 k/hr, the train crosses the platform in one minute, then the length of the train (in meters) is:\n\n### Options:\nA. 700\nB. 780\nC. 760\nD. 750\nE. 459\n\n### Answer:\nSpeed = [90 * 5/18] m/sec = 25 m/sec; Time = 1 min. = 60 sec.\nLet the length of the train and that of the platform be x meters.\nThen, 2x/60 = 25 \u00e8 x = 25 * 60 / 2 = 750\nAnswer: Option D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA fruit seller sells mangoes at the rate of Rs.12 per kg and thereby loses 15%. At what price per kg, he should have sold them to make a profit of 5%\n\n### Options:\nA. Rs 8.82\nB. Rs 9.82\nC. Rs 10.82\nD. Rs 14.82\nE. None of these\n\n### Answer:\nExplanation:\n85 : 12 = 105 : x\nx= (12\u00d7105/85)\n= Rs 14.82\nOption D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA straight pipe 1 meter in length was marked off in halves and also in thirds. If the pipe was then cut into separate pieces at each of these markings, which of the following gives all the different lengths of the pieces, in fractions of a meter?\n\n### Options:\nA. 1/6 and 1/3 only\nB. 1/4 and 1/3 only\nC. 1/6, 1/4, and 1/3\nD. 1/12, 1/6 and 1/4\nE. 1/12, 1/6, and 1/3\n\n### Answer:\nGenerally fast way to solve such problem is writing the different marks in ascending/descending order with same denominator:\nHere 4th : 0/4, 1/4, 2/4, 3/4, 4/4\nand 3rd : 0/3, 1/3, 2/3, 3/3\nGenerally fast way to solve such problem is writing the different marks in ascending/descending order with same denominator:\nHere 2th : 0/2, 1/2, 2/2\nand 3rd : 0/3, 1/3, 2/3, 3/3\nNow with understood common denominator 6 write the numbers : for 2th : 0,3,6 and for 3rd : 0,2,4,6\nNow comine : 0,2,3,4,6\nNow find the cut with denominator 6 (Substracrt adjacent terms : 1/3, 1/6, 1/6, 1/3 i.e. 1/3 and 1/6 after removing duplicates.\nanswer : A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn one hour, a boat goes 11 km along the stream and 5 km against the stream. The speed of the boat in still water in ( km/hr) is\n\n### Options:\nA. 3\nB. 5\nC. 8\nD. 9\nE. 7\n\n### Answer:\nSolution\nSpeed in still water\t= 1/2(11+5) km/hr\n= 8 km/hr.\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich of these must the factor W of the product of four consecutive even integers:-\n1) 48\n2) 64\n3) 96\n4) 192\n5) 80\n\n### Options:\nA. W=1,2 only\nB. W=2,3 only\nC. W=1,2,3 only\nD. W=1,2,3,4 only\nE. All of them\n\n### Answer:\nLet the four variables be a< b< c< d.\nAssume a worst case scenario where the a equal to a prime number (hence odd).\ntherefore\na = divisible by 1\nb = a + 1 (divisible by 2)\nc = a + 3 (divisible by 3)\nd = a + 4 (divisible by 4)\ntherefore\neach answer choice must be divisible by 2 x 3 x 4 = 24\nonly 80 is not divisible. Therefore answer = D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA rectangular park 60 m long and 40 m wide has two concrete crossroads running in the middle of the park and rest of the park has been used as a lawn. If the area of the lawn is 2109 sq. m, then what is the width of the road?\n\n### Options:\nA. 3\nB. 4\nC. 5\nD. 7\nE. 8\n\n### Answer:\nArea of the park = (60 x 40) m2 = 2400 m2.\nArea of the lawn = 2109 m2.\nArea of the crossroads = (2400 - 2109) m2 = 291 m2.\nLet the width of the road be x metres. Then,\n60x + 40x - x2 = 291\nx2 - 100x + 291 = 0\n(x - 97)(x - 3) = 0\nx = 3.\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJohn invested part of his savings into a investment X that earned a profit of 10% and the rest of the savings into an investment E that lost 15%. If John neither made a profit nor a loss, then what fraction of his savings was invested in investment X?\n\n### Options:\nA. a. 3/5\nB. b.2/3\nC. c.7/10\nD. d.3/4\nE. e.4/5\n\n### Answer:\nX(10) --- Net(0) --- E(-15) = -15/-10 = 3/2.\nSo, John invested 3/3+2 = 3/5 of his savings in investment X. Ans (A).\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe distance between Delhi and Mathura is 120 kms. A starts from Delhi with a speed of 20 kmph at 7 a.m. for Mathura and B starts from Mathura with a speed of 25 kmph at 8 p.m. from Delhi. When will they meet?\n\n### Options:\nA. 40.00 a.m.\nB. 10.13 a.m.\nC. 12.00 a.m.\nD. 18.00 a.m.\nE. 19.00 a.m.\n\n### Answer:\nExplanation:\nD = 120 \u00e2\u20ac\u201c 20 = 100\nRS = 20 + 25 = 45\nT = 100/45 = 2 hours 13 minutes\n8 a.m. + 2 hours 13 minutes = 10:13 a.m.\nAnswer: Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the probability that the sum of two dice will yield a 5, and then when both are thrown again, their sum will again yield a 5? assume that each die has 4 sides with faces numbered 1 to 4.\n\n### Options:\nA. 1/144\nB. 1/36\nC. 1/12\nD. 1/16\nE. 1/3\n\n### Answer:\nSolution -\nRolling dices is an independent event.\nThe combinations to get 5 are (1,4), (4,1), (2,3), (3,2), and total combinations of both dices is 16.\nThe probability of getting 5 in first attempt is 4/16=1/4.\nProbability of getting 5 again in second attempt = (1/4)*(1/4) = 1/16. ANS D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA can do half the work in one day where as B can do it full. B can also do half the work of C in one day. Ratio in their efficiency will be?\n\n### Options:\nA. 1:2:8\nB. 1:2:0\nC. 1:2:5\nD. 1:2:4\nE. 1:2:1\n\n### Answer:\nWC of A: B = 1:2\nB: C = 1:2\n---------------------\nA: B: C = 1:2:4\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe sum of number of boys and girls in a school is 300. If the number of boys is x, then the number of girls becomes x% of the total number of students. The number of boys is?\n\n### Options:\nA. 50\nB. 40\nC. 60\nD. 100\nE. 75\n\n### Answer:\nWe have x+x% of 300 = 300\nx + x/100 * 300 = 300\n4 * x = 300\nx = 75\nAnswer is E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf taxi fares were $1.00 for the first 1/5 mile and $0.40 for each 1/5 mile there after, then the taxi fare for a 3-mile ride was\n\n### Options:\nA. $1.56\nB. $2.40\nC. $3.80\nD. $4.20\nE. $6.60\n\n### Answer:\nIn 3 miles , initial 1/5 mile charge is $1\nrest of the distance = 3 - (1/5) = 14/5\nrest of the distance charge = 14(0.4) = $5.6 (as the charge is 0.4 for every 1/5 mile)\n=> total charge for 3 miles = 1+5.6 = 6.6\nAnswer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nCricket match is conducted in US. The run rate of a cricket game was only 3.2 in first 10 over. What should be the run rate in the remaining 40 overs to reach the target of 262 runs?\n\n### Options:\nA. 6\nB. 6.25\nC. 5.75\nD. 7.5\nE. 8\n\n### Answer:\nRequired run rate = 262 - (3.2 x 10) =\t230 = 5.75\n40\t40\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe perimeter of an equilateral triangle is 60. If one of the sides of the equilateral triangle is the side of an isosceles triangle of perimeter 70, then how long is the base of isosceles triangle?\n\n### Options:\nA. 15\nB. 20\nC. 25\nD. 30\nE. 35\n\n### Answer:\nThe base of the isosceles triangle is 70-20-20= 30 units\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a rare coin collection, all coins are either pure gold or pure silver, and there is initially one gold coin for every three silver coins. With the addition of 12 more gold coins to the collection, the ratio of gold coins to silver coins is 1 to 2. Based on this information, how many total coins are there now in this collection (after the acquisition)?\n\n### Options:\nA. 72\nB. 84\nC. 96\nD. 108\nE. 120\n\n### Answer:\nInitially the number of gold coins and silver coins is 2k and 6k.\nAfter adding gold coins, the number of coins is 3k and 6k.\nThus k = 12 and the total number of coins is 9k = 108.\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the odd man out. 1, 27, 216, 512, 1024, 1331\n\n### Options:\nA. 1024\nB. 512\nC. 27\nD. 1\nE. 2\n\n### Answer:\nExplanation :\nAll given numbers except 1024 are perfect cubes. Answer : Option A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe price of 5 kilograms of premium fertilizer is the same as the price of 10 kilograms of regular fertilizer. If the price of premium fertilizer is y cents per kilogram more than the price of regular fertilizer, what is the price, in cents, per kilogram of premium fertilizer?\n\n### Options:\nA. y/30\nB. 5/6*y\nC. 6/5*y\nD. 2y\nE. 6y\n\n### Answer:\nUsingpfor premium andrfor regular, I got two equations from the question stem:\n5p = 10r and p = r+y\nSubstitute for p: 5(r+y) = 10r\nDistribute: 5r + 5y = 10r\nSubtract 5r from both sides: 5y = 5r\nPlug back into the first equation: 5p = 10(y)\nDistribute: 5p = 10y\nDivide both sides by 5: p = 2y\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf books bought at prices ranging from Rs. 90 to Rs. 190 are sold at prices ranging from Rs. 120 to Rs 260, what is the greatest possible profit that might be made in selling 21 books ?\n\n### Options:\nA. Rs. 2500\nB. Rs. 3000\nC. Rs. 3570\nD. Rs. 3200\nE. Rs. 3600\n\n### Answer:\nThe greatest profit is possible only if the cost price of the books are minimum and selling prices are maximum.\nLet lowest cost price of the 21 books = 90*21 = Rs. 1,890\nMaximum selling price of 21 books = 260 *21 = Rs. 5,460\nSo, maximum profit = 5460 - 1890 = Rs. 3,570\nANSWER : OPTION C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf Janice was 21 years old z years ago and Lisa will be 19 years old in p years, what was the average (arithmetic mean) of their ages 8 years ago?\n\n### Options:\nA. (z + p)/2\nB. (z - p + 24)/4\nC. (z - p + 14)/4\nD. (z + p + 34)/2\nE. (z - p + 24)/2\n\n### Answer:\nToday, J = z+21 and L = 19-p\n8 years ago, J = z+13 and L = 11-p\nThe average of their ages was (z-p+24) / 2\nThe answer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the tens digit of 7^1213?\n\n### Options:\nA. 0\nB. 1\nC. 2\nD. 3\nE. 4\n\n### Answer:\n7^1 = 7\n7^2 = 49\n7^3 = 343\n7^4 = 2401\n7^5 = 16807\n7^6 = 117649\nWe should see this as pattern recognition . We have a cycle of 4 . (We can multiply the last 2 digits only as we care about ten's digit )\n0 , 4 , 4 , 0 .\n1213= 4*304 + 1\nThe ten's digit will be 0 .\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a certain store, the profit is 320% of the cost. If the cost increases by 25% but the selling price remains constant, approximately what percentage of the selling price is the profit?\n\n### Options:\nA. 20\nB. 70\nC. 77\nD. 26\nE. 12\n\n### Answer:\nLet C.P. = Rs. 100. Then, profit = Rs. 320, S.P. = Rs. 420\nNew C.P. = 125% of Rs. 100 = Rs. 125.\nNew S.P. = Rs. 420\nProfit = 420 - 125 = Rs. 295\nRequired percentage = 295/420 * 100 = 1475/21 = 70%\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average age of 39 students in a group is 10 years. When teacher\u2019s age is included to it, the average increases by one. What is the teacher\u2019s age in years?\n\n### Options:\nA. 50\nB. 55\nC. 60\nD. cannot be determined\nE. None of these\n\n### Answer:\nAge of the teacher = (40 \u00d7 11 \u2013 39 \u00d7 10) years\n= 50 years.\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the true discount on a certain sum due 6 months hence at 15% is Rs. 120, what is the banker\u2019s discount on the same sum for the same time and at the same rate?\n\n### Options:\nA. 100\nB. 115\nC. 120\nD. 129\nE. None\n\n### Answer:\nSol.\nB.G. = S.I. on T.D. = Rs. [120 * 15 * 1/2 * 1/100] = Rs. 9.\n\u2234 (B.D.) - (T.D.) = Rs.9.\n\u2234 B.D. = Rs. (120 + 9) = Rs. 129\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nLamp A flashes every 6 seconds, Lamp B flashes every 8 seconds, Lamp C flashes every 10 seconds. At a certain instant of time all three lamps flash simultaneously. During the period of 10 minutes after that how many times will exactly two lamps flash? (Please include any flash of exactly two lights which occurs at the 10 minute mark.)\n\n### Options:\nA. 41\nB. 42\nC. 43\nD. 44\nE. 45\n\n### Answer:\n10 minutes is 600 seconds.\nLamp A and Lamp B will flash together every 24 seconds.\n600/24=25.\nIn the time period, Lamp A and Lamp B will flash together 25 times.\nLamp A and Lamp C will flash together every 30 seconds.\n600/30=20.\nIn the time period, Lamp A and Lamp C will flash together 20 times.\nLamp B and Lamp C will flash together every 40 seconds.\n600/40=15.\nIn the time period, Lamp B and Lamp C will flash together 15 times.\nAll three lights will flash together every 2*2*2*3*5=120 seconds.\n600/120=5.\nWe have counted these triple flashes three times, so we need to subtract three times the number of times that all three lights flash together.\nThe number of times that exactly two lights flash together is 25+20+15-15=45 times.\nThe answer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a large pizza has a radius that is 60% larger that that of a medium pizza, what is the percent increase in area between a medium and a large pizza?\n\n### Options:\nA. 30%\nB. 60%\nC. 98%\nD. 120%\nE. 156%\n\n### Answer:\nLet the radius of medium pizza be r. Then the radius of large pizza is 1.6r.\nThe area of the medium pizza is pi*r^2\nThe area of the large pizza is pi*(1.6*r)^2 = 2.56*pi*r^2, an increase of 156%.\nThe answer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a book is sold at 9% profit instead of 9% loss, it would have brought Rs 9 more. Find out the cost price of the book\n\n### Options:\nA. 75\nB. 72\nC. 50\nD. 70\nE. 80\n\n### Answer:\nLet C.P. of the book be Rs. \u2019X\u2019\nGiven, 1.09 X - 0.91X = 9\n=> 0.18 X = 9 = 9/0.18 = Rs 50\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHOW MANY KGS OF TEA WORTH RS.25/KG MUST BE BLENDED WITH 30 KGS OF TEA WORTH RS.30/KG SO THAT BY SELLING THE BLENDED VARIETY AT RS.30/KG THERE SHOULD BE A GAIN OF 3%\n\n### Options:\nA. 36\nB. 8\nC. 7\nD. 6\nE. 6.3\n\n### Answer:\n(x+30)*30=(103/100)(25x+30*30)\nSolving we get 6.3.\nAnswer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nStacy and Heather are 15 miles apart and walk towards each other along the same route. Stacy walks at constant rate that is 1 mile per hour fast than heather's constant rate of 5 miles/hour. If Heather starts her journey 24 minutes after Stacy, how far from the original destination has Heather walked when the two meet?.\n\n### Options:\nA. 6.5mile\nB. 5.7mile\nC. 7.0mile\nD. 8.0mile\nE. 12 mile\n\n### Answer:\nSs - Stacy's speed = 6m/hr\nSh - Heather's speed = 5m/hr\nIn 24 minutes Stacy will cover = (24/60)*6 = 2.4miles\nNow since both are walking in opposite directions, add their speeds - 6+5 =11m/hr and distance to cover is 15 -2.4 = 12.6\nTime taken = Distance/ Speed = 12.6/11 = 1.145 hrs\nHeather will cover = 5*1.145 = 5.72miles.\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf an integer n is to be chosen at random from the integers 1 to 96, inclusive, what is the probability that n(n + 1)(n + 2) will be divisible by 4?\n\n### Options:\nA. 1/4\nB. 3/8\nC. 1/2\nD. 5/8\nE. 3/4\n\n### Answer:\nI get 5/8 as well\n1 to 96 inclusive means we have 48 odd and 48 even integers\nE O E / 4 = Integer, therefore we have 48 / 96 numbers divisible by 8\nO E O / 4 = Not Integer\nWe cannot forget multiples of 8 from 1 to 96\nWe have 24 numbers that are multiple of 4\nTherefore, 48/96 + 24/96 = 72/96 = 3/4\nanswer : E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n42573y is exactly divisible by 72, then what is the minimum value of y?\n\n### Options:\nA. 3\nB. 4\nC. 6\nD. 8\nE. 9\n\n### Answer:\n72 = 9 x8, where 9 and 8 are co-prime.\nThe minimum value of x for which 73x for which 73x is divisible by 8 is, x = 6.\nSum of digits in 425736 = (4 + 2 + 5 + 7 + 3 + 6) = 27, which is divisible by 9.\nRequired value of y is 6\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe ratio of the ages of a man and his wife is 4:3. After 4 years,the ratio will be 9:7.If at the time of marriage the ratio was 5:3,then how many years ago were they married ?\n\n### Options:\nA. 8\nB. 10\nC. 12\nD. 14\nE. 15\n\n### Answer:\nlet the present ages of the man and his wife be 4x and 3x\nthen (4x+4)/(3x+4)= 9/7\n[since given that after four years their ages will be 9/7]\nby solving it we have x=8\nso their present ages are 32 and 24 respectively\nnow suppose if they were married X years ago,\nthen (32-X)/(24-X)=5/3\nby solving it we have 2X=24\nso X=12\nso they were married 12 years ago\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n60 percent of movie theatres in Town X have 3 screens or less. 20% of those theatres sell an average of more than $300 worth of popcorn per showing. 56 percent of all the movie theatres in Town X sell $300 or less of popcorn per showing. What percent of all the stores on the street have 4 or more screens and sell an average of more than $300 worth of popcorn per day?\n\n### Options:\nA. 12\nB. 18\nC. 32\nD. 40\nE. 44\n\n### Answer:\nlet's take numbers here.\nAssume that the total number of movie theaters in the town = 100\nThen number of movie theaters with 3 screens or less = 60\n=> Number of movie theaters with 4 screens or more = 40\nMovie theaters with 3 screens or less selling popcorn at more than $300 = 20% of 60 = 12\nNumber of movie theaters selling popcorn at $300 or less = 56\n=> Number of movie theaters selling popcorn at more than $300 = 100-56 = 44\nOf these 44 theaters, 12 are those with 3 screens or less\nTherefore 32 (44-12) must be those with four screens or more\nC is the answer\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the units digit of n^43 is 7, which of the following could be the value of n?\nI. n = 41\nII. n = 43\nIII. n = 47\n\n### Options:\nA. Only I\nB. Only II\nC. Only III\nD. I and II\nE. II and III\n\n### Answer:\nI tried in this way.\nGiven n^43 units digit is 7.\nIf at all we have to get 7 as units digits only 3 and 7 series has 7\n3^! = 3 , 3^2 = 9 , 3^3 = 27 , 3^4 = 81\n7^1 = 7, 7^2 = 49 , 7^3 = 3 (units ) , 7^4 = 1 (units)\nWe have n^43 - then divide 43 by 4 = reminder 3.\nThen we have for only 7^3 - we have units digit as 7.\nHence 47^43 = 7 (units).\nOption A is correct answer , and with 41^43 we always get 1 as units digit and 43^43 - we get units as 3.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n40 men shake hands with each other. Maximum no of handshakes without cyclic handshakes.\n\n### Options:\nA. 780\nB. 200\nC. 210\nD. 220\nE. 230\n\n### Answer:\nor, if there are n persons then no. of shakehands = nC2 = 40C2 = 780\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average price of three items of furniture is Rs. 30000. If their prices are in the ratio 3:5:7, the price of the cheapest item is?\n\n### Options:\nA. 2379\nB. 2889\nC. 9288\nD. 9000\nE. 6000\n\n### Answer:\nLet their prices be 3x, 5x and 7x.\nThen, 3x + 5x + 7x = (15000 * 3) or x = 2000.\nCost of cheapest item = 3x = Rs. 6000.\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA wheel that has 6 cogs is meshed with a larger wheel of 7 cogs. When the smaller wheel has made 21 revolutions, then the number of revolutions made by the larger wheel is:\n\n### Options:\nA. 9\nB. 10\nC. 6\nD. 18\nE. 7\n\n### Answer:\nExplanation :\nLet the required number of revolutions made by larger wheel be x.\nThen, More cogs, Less revolutions (Indirect Proportion)\n7:6::21:x => 7 * x = 21 * 6\n=> x = (21 * 6)/7\n=> x = 18\nAnswer : D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n4, 6, 12, 14, 28, 30, ?\n\n### Options:\nA. 32\nB. 64\nC. 62\nD. 60\nE. 52\n\n### Answer:\nThe given sequence is a combination of two series 4, 12, 28, .... and 6, 14, 30, .... The pattern is +8, +16, +32. So, the missing number = (28 + 32) = 60\nAnswer : D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMurali travelled from city A to city B at a speed of 40 kmph and from city B to city C at 60 kmph. What is the average speed of Murali from A to C given that the ratio of distances between A to B and B to C is 2 : 3?\n\n### Options:\nA. 17 kmph\nB. 50 kmph\nC. 18 kmph\nD. 17 kmph\nE. 11 kmph\n\n### Answer:\nLet the distances between city A to B and B to C be 2x km and 3x km respectively.\nTotal time taken to cover from A to C\n= (2x)/40 + (3x)/60 = (6x + 6x)/120 = 12x/120 = x/10 Average speed = (2x + 3x)/(x/10)\n= 50 kmph.\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe total monthly income of four men and two women is 46,000. If every woman earns 500 more than a man then what is the monthly income of a woman?\n\n### Options:\nA. 7,500\nB. 8,000\nC. 9,000\nD. 6,500\nE. None of these\n\n### Answer:\n4M + 2W = 46000;\nAgain, W = M + 500\nor, M = W \u2013 500\n\u2234 (W \u2013 500) + 2W = 46000\nor, 6W = 46000 + 2000 = 48000\n\u2234 W = 8000\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nArun got 30% of the maximum marks in an examination and failed by 10 marks. However, Sujith who took the same examination got 40% of the total marks and got 15 marks more than the passing marks. What were the passing marks in the examination?\n\n### Options:\nA. 90\nB. 250\nC. 75\nD. 85\nE. 95\n\n### Answer:\nExplanation :\nLet x is the maximum marks of the examination\nMarks that Arun got = 30 % of x = 30x/100\nGiven that Arun failed by 10 marks\n\u21d2Minimum Pass Mark = (30x/100) + 10......(Equation 1)=85\nANSWER IS D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe ratio between the length and the breadth of a rectangular plot is 7 : 5. If the perimeter of the plot is 216 metres, what is its area?\n\n### Options:\nA. 1325 sq.metres\nB. 1260 sq.metres\nC. 2835 sq.metres\nD. 3380 sq.metres\nE. None of these\n\n### Answer:\nLet the length and breadth be 7x and 5x respectively.\nThen, P = 2(7x + 5x) = 216 \u00e2\u2021\u2019 x = 9\nArea = 7 \u00c3\u2014 9 \u00c3\u2014 5 \u00c3\u2014 9 = 2835 sq.m.\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe sides of a triangle are in the ratio 5: 12: 13 and its perimeter is 300 m, its area is?\n\n### Options:\nA. 150\nB. 377\nC. 297\nD. 266\nE. 971\n\n### Answer:\n5x + 12x + 13x = 300 => x = 10\na = 50, b = 120, c = 130\nS = (50 + 120 + 130)/2 = 150\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA group of 10 representatives is to be selected out of 12 seniors and 10 juniors. In how many different ways can the group be selected if it should have at least one senior?\n\n### Options:\nA. \u00b2\u00b2C\u2089\nB. \u00b2\u00b2C\u2081\u2080\nC. \u00b2\u00b2C\u2089 + \u00b9\u2070C\u2081\nD. \u00b2\u00b2C\u2081\u2080 - 1\nE. \u00b9\u2070C\u2081\n\n### Answer:\nThe total number of ways of forming the group of ten representatives is \u00b2\u00b2C\u2081\u2080.\nThe total number of ways of forming the group that consists of no seniors is \u00b9\u2070C\u2081\u2080 = 1 way\nThe required number of ways\n= \u00b2\u00b2C\u2081\u2080 - 1\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow much water must be added to 60 litres of milk at 1.5 litres for Rs. 20 So as to have a mixture worth Rs.32/3 a litre?\n\n### Options:\nA. 10 litres\nB. 12 litres\nC. 15 litres\nD. 18 litres\nE. 21 litres\n\n### Answer:\nC.P. of 1 litre of milk = Rs. 20\u00d72/3 = Rs. 40/3.\nC.P. of 1 litre of water =Rs 0.\nMean price = Rs. 32/3.\nBy the rule of alligation, we have :\nC.P of 1 litre C.P of 1 litre\nof water of milk\n(0) (Rs. 40/3)\n\\ /\nMean Price\n(Rs. 32/3)\n/ \\\n40/3\u221232/3 32/(3\u22120)\n8/3 32/3\nThe ratio of water and milk =8/3:32/3.\n=8:32=1:4.\nThus, Quantity of water to be added to 60 litres of milk:\n=(1/4)\u00d760 litres.\n=15 litres. ANSWER : C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf x^2 = 231, which of the following is closest to a potential value of x?\n\n### Options:\nA. -127\nB. -11\nC. 12\nD. 13\nE. 15\n\n### Answer:\nHere the thing we must not forget is that X^even has two potential solutions\n=> x =+- \u221a231 => +- 15 (approx)\nthis value is closer to 15\nHence E is correct.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWalking 7/6 of his usual rate, a boy reaches his school 2 min early. Find his usual time to reach the school?\n\n### Options:\nA. 14\nB. 28\nC. 99\nD. 77\nE. 66\n\n### Answer:\nSpeed Ratio = 1:7/6 = 6:7\nTime Ratio = 7:6\n1 -------- 7\n2 --------- ? 14 m\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 10 bulls can plough 20 identical fields in 3 days working 10 hours a day, then in how many days can 30 bulls plough 32 same identical fields working 8 hours a day?\n\n### Options:\nA. 8\nB. 7\nC. 5\nD. 2.0\nE. 1\n\n### Answer:\nExplanation:\nM1*D1*W2 = M2*D2*W1\n10*3*10*32 = 30*d*8*20\nd = 2 days\nANSWER: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a nationwide poll, N people were interviewed. If 1/6 of them answered yes to question 1, and of those, 1/2 answered yes to question 2, which of the following expressions represents the number of people interviewed who did NOT answer yes to both questions?\n\n### Options:\nA. N/8\nB. 7N/8\nC. 11N/12\nD. 17N/24\nE. 41N/48\n\n### Answer:\nThe number of people who answered yes to both questions is (1/2)(1/6)N = N/12\nThe number of people who did not answer yes to both is 1 - N/12 = 11N/12\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat approximate value should come in place of the question mark (?) in the following equation?47.05 \u00c3\u2014 8.65 \u00e2\u20ac\u201c 25.22 \u00c3\u2014 6.4 = (28 + ?) \u00c3\u2014 5\n\n### Options:\nA. 28.1149\nB. 24.1149\nC. 21.1149\nD. 22.1149\nE. 31.1149\n\n### Answer:\nSolve using approximation\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo pipes A and B can separately fill a cistern in 10 and 15 minutes respectively. A person opens both the pipes together when the cistern should have been was full he finds the waste pipe open. He then closes the waste pipe and in another 4 minutes the cistern was full. In what time can the waste pipe empty the cistern when fill?\n\n### Options:\nA. 7\nB. 9\nC. 5\nD. 4\nE. 8\n\n### Answer:\n1/10 + 1/15 = 1/6 * 4 = 2/3\n1 - 2/3 = 1/3\n1/10 + 1/15 - 1/x = 1/3\nx = 8\nANSWER E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWith out any halt a train travels a certain distance with an average speed of 75 km ph , and with halts it covers the same distance at an average speed of 60 kmph. When it is traveling with halts, how many minutes/per hour does the train halt on an average ?\n\n### Options:\nA. 48 min.\nB. 12min.\nC. 15min.\nD. 18min.\nE. 19min.\n\n### Answer:\nWith halt in 1 hour the train travels 60km\nWith out halt for traveling same distance it take 60/75 = 4/5 = 48 minutes\n:. 12 minutes is the halting time per hour\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe price of a certain product increased by the same percent from 1960 to 1970 as from 1970 to 1980. If its price of $1.10 in 1970 was 150 percent of its price in 1960, what was its price in 1980?\n\n### Options:\nA. a) $ 1.65\nB. b) $ 2.00\nC. c) $ 2.40\nD. d) $ 2.70\nE. e) $ 3.00\n\n### Answer:\nThe price in 1970 was 150 percent of its price in 1960, means that the percent increase was 50% from 1960 to 1970 (and from 1970 to 1980).\nTherefore the price in 1980 = $1.1*1.5 = $1.65.\nAnswer: A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe value of a machine depreciates at 20% per annum. If its present value is Rs. 1,50,000, at what price should it be sold after two years such that a profit of Rs. 24,000 is made?\n\n### Options:\nA. 328897\nB. 120000\nC. 877888\nD. 277768\nE. 188871\n\n### Answer:\nThe value of the machine after two years = 0.8 * 0.8 * 1,50,000 = Rs. 96,000\nSP such that a profit of Rs. 24,000 is made = 96,000 + 24,000 = Rs. 1,20,000\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAn escalator moves towards the top level at the rate of 8 ft.sec and its length is 160 feet. If a person walks on the moving escalator at the rate of 2 feet per second towards the top level, how much time does he take to cover the entire length.\n\n### Options:\nA. 14 sec\nB. 10 sec\nC. 16 sec\nD. 8 sec\nE. 9 sec\n\n### Answer:\nTime taken to cover the entire length = tot.dist/resultant speed\n= 160/ (8+2)\n= 16sec\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nPresent ages of Sameer and Anand are in the ratio of 5 : 4 respectively. Seven years hence, the ratio of their ages will become 11 : 9 respectively. What is Anand's present age in years?\n\n### Options:\nA. A)84\nB. B)89\nC. C)67\nD. D)56\nE. E)45\n\n### Answer:\nLet the present ages of Sameer and Anand be 5x years and 4x years respectively.\nThen,\t(5x + 7/4x + 7)=11/9\n9(5x + 7) = 11(4x + 7)\n45x + 63 = 44x + 77\n45x - 44x = 77 - 63\nx = 14.\nAnand's present age = 4x = 84 years.\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA boat with still water speed of a is traveling upstream where the streams speed is b. After covering certain distance s, the boat turns back and tries to come to the starting place. But the boat stops at 3/4th of the intended distance due to a technical fault. What is the ratio of the time taken for the return journey to that of the upstream journey.\n\n### Options:\nA. 3(a - b)/4(a + b)\nB. 4(a - b)/3(a + b)\nC. 3(a + b)/4(a - b)\nD. 4/3\nE. 4/8\n\n### Answer:\nspeed of boat upstream = a - b\nspeed of boat downstream = a + b\nFor upstream journey, time taken = distance / speed = s / (a - b)\nDuring return journey, the boat had covered on 3/4th of s :\nTherefore for return journey, time taken = distance / speed = (3s/4)/(a+b)\nRatio of time taken for return journey to the upstream journey = (3s/4)/(a+b)/ (s/(a - b)) = 3(a - b)/4(a + b)\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHDFC bank offers an interest of 5% per annum compounded annually on all its deposits. If $10,000 is deposited, what will be the ratio of the interest earned in the 4th year to the interest earned in the 5th year?\n\n### Options:\nA. 1:5\nB. 625:3125\nC. 100:105\nD. 100^4:105^4\nE. 725:3225\n\n### Answer:\nHi Bunuel,\nHere is my approach: is this correct?\nHDFC bank offers an interest of 5% per annum compounded annually on all its deposits.\nInterest earned in 4 year= 10000(1+0.05)^4\nInterest earned in 5 year= 10000(1+0.05)^5\nRatio= {10000(1.05)^4}/{10000(1.05^5)} =>1.05^4/1.05^5 =>1/1.05 Multiplied by 100 in both numerator and denominator gives 100:105\nHence Ans:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nEach book on a certain shelf is labeled by a single category. For every 2 history books, there are 7 fantasy books and for every 3 fantasy books, there are 8 reference books. If the proportion of history to reference books is doubled, while the proportion of fantasy to reference books is maintained, which of the following could be the number of history books if there are fewer than 60 fantasy books on the shelf after the changes?\n\n### Options:\nA. 12\nB. 21\nC. 27\nD. 35\nE. 36\n\n### Answer:\nFor every 2 history books, there are 7 fantasy books:\nOriginally H:F = 2:7 = 6:21.\nFor every 3 fantasy books, there are 8 reference books:\nF:R = 3:8 = 21:56\nH:F:R = 6:21:56\nAfter the changes, H:F:R = 12:21:56\nThere are fewer than 60 fantasy books, so there are 21 or 42 fantasy books.\nThe number of history books could be 12 or 24.\nThe answer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSeven children \u2014 A, B, C, D, E, F, G and H\u2014 are going to sit in seven chairs in a row. The children CF have to sit next to each other, and the others can sit in any order in any remaining chairs. How many possible configurations are there for the children?\n\n### Options:\nA. 600\nB. 720\nC. 1440\nD. 10080\nE. 4800\n\n### Answer:\nfor such questions , we can treat both as one then total person=7..\nthese 7 can be arranged in 7! ways.. but within these 7, one consists of two people who can be arranged in 2 ways CF or FC.. so ans =7!*2=10080\nans D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn the xy-plane, the points (c, d), (c, -d), and (-c, -d) are three vertices of a certain square. If c < 0 and d > 0, which of the following points N is in the same quadrant as the fourth vertex of the square?\n\n### Options:\nA. (-5, -3)\nB. (-5, 3)\nC. (5, -3)\nD. (3, -5)\nE. (3, 5)\n\n### Answer:\nThe question:In the xy-plane, the points N=(c, d), (c, -d), and (-c, -d) are three vertices of a certain square.If c < 0 and d > 0,which of the following points is in the same quadrant as the fourth vertex of the square?\nI marked the tricky part in red. It seems c is anegativenumber and d is a positive number. This means\nVertex #1 = (c, d) is in QII (that is, negative x and positive y)\nVertex #2 = (c, -d) is in QIII (that is, both xy negative)\nVertex #3 = (-c, -d) is in QIV (that is y is negative, but x is positive)\nThat means the last vertex should be in the first quadrant --- the only first quadrant point is (5, 3), answer =E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn the equation a = 36.12b, b and a are integers. If a/b leaves a remainder of r, which of the following must divide into r?\n\n### Options:\nA. 2\nB. 3\nC. 4\nD. 6\nE. 12\n\n### Answer:\n1) It says it is a equation, so a=36.12b should be 36.12 * b..\n2) It says b is an integer, again it means 36.12 * b..\nOtherwise b would be just a digit and it would be mentioned..\nAlthough not clearly mentioned that 36.12b is actually 36.12 * b, BUT entire info points towards that..\nand that is why I have taken a/b = 36.12\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA merchant marks his goods up in such a way that the profit made on selling 30 articles is equal to the cost price of 20 articles. What is the W % profit made by the merchant?\n\n### Options:\nA. 66.67 %\nB. 50 %\nC. 200 %\nD. 100 %\nE. 33.33 %\n\n### Answer:\nC.P of 1 article= $30(say)\nC.P of 20 articles=30*20=$600\nNow, C.P of 20 articles=Profit on 30 articles\nTherefore, profit on 1 article=$600/30=$20\nProfit W%=(20/30)*100=66.67%\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhen the positive integer x is divided by 9,the remainder is 5.What is the remainder when 8x is divided by 9?\n\n### Options:\nA. 0\nB. 1\nC. 3\nD. 4\nE. 6\n\n### Answer:\ni tried plugging in numbers\nx = 9q+5\nx = 14\n8x = 112\n8x/9= 9*12+4\nremainder is 4.\nAnswer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a college, 1 percent of students hate math, 2 percent of students hate English, 1 percent hate French and 4 percent hate German.\nCan you find out the percentage of students who hate all 4 subjects ?\n\n### Options:\nA. 8%\nB. 5%\nC. 7%\nD. 12%\nE. 19%\n\n### Answer:\nA\n8% of student hate all four subjects.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nChoose the missing terms out of the given alternatives.\nQPO, SRQ, UTS, WVU, ?\n\n### Options:\nA. XVZ\nB. ESD\nC. ZYA\nD. VWX\nE. YXW\n\n### Answer:\nE\nYXW\nEach term consists of three consecutive letters in reverse order. The first letter and the last letter of the next term are the same.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe sum of two consecutive integers is 15. Find the numbers.\n\n### Options:\nA. 17, 18\nB. 7, 8\nC. 5, 6\nD. 1, 2\nE. 8, 9\n\n### Answer:\nn + (n + 1) = 15\n2n + 1 = 15\n2n = 14\nn = 7\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA and B\u2019s salaries together amount to Rs. 3,000. A spends 95% of his salary and B spends 85% of his. If now their savings are the same, what is B\u2019s salary?\n\n### Options:\nA. 777\nB. 750\nC. 789\nD. 776\nE. 881\n\n### Answer:\n(5/100) A = (15/100) B\nA = 3B\nA + B =3000\n4B = 3000 => B = 750\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a\u00b7b\u00b7c\u00b7d=360, where a, b, c and d are positive integers, and a", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the speed of a man is 45 km per hour, then what is the distance traveled by him in 30 seconds ?\n\n### Options:\nA. 275m\nB. 360m\nC. 375 m\nD. 420 m\nE. 480 m\n\n### Answer:\nThe distance traveled in 30 sec = 45*(5/18) *30 =375m\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nLilly has 10 fish and Rosy has 9 fish. In total, how many fish do they have in all?\n\n### Options:\nA. 16\nB. 17\nC. 18\nD. 19\nE. 20\n\n### Answer:\n10+9=19\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n9548 + 7314 = 7362 + (?)\n\n### Options:\nA. 8300\nB. 8400\nC. 8500\nD. 8700\nE. 9500\n\n### Answer:\n9548 16862 = 7362 + x\n+ 7314 x = 16862 - 7362\n----- = 9500\n16862\n-----\nE)\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nPipe A can fill a tank in 8 hours, pipe B in 10 hours and pipe C in 40 hours. If all the pipes are open, in how many hours will the tank be filled?\n\n### Options:\nA. 2\nB. 2.5\nC. 3\nD. 4\nE. None\n\n### Answer:\nSol.\nPart filled by (A + B + C) in 1 hour = (1/8 + 1/10 + 1/40) = 1/4.\n\u00e2\u02c6\u00b4 All the three pipes together will fill the tank in 4 hours.\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe ages of Rahul and Madhan differ by 16 years. Six years ago, Madhan\u2019s age was thrice as that of Rahul\u2019s,find their present ages\n\n### Options:\nA. 14 years, 30 years\nB. 12 years, 28 years\nC. 16 years, 34 years\nD. 18 years, 38 years\nE. none of these\n\n### Answer:\nLet Rahul\u2019s age = x years\nSo, Madhan\u2019s age = ( x + 16 )years\nAlso, 3(x - 6) = x + 16 - 6 or, x = 14\nRahul\u2019s age = 14 years\nAnd, Madhan\u2019s age 14 + 16 = 30 years\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere is a 10% chance that Tigers will not win at all during the whole season. There is a 20% chance that Federer will not play at all in the whole season. What is the greatest possible probability that the Tigers will win and Federer will play during the season?\n\n### Options:\nA. 55%\nB. 60%\nC. 70%\nD. 72%\nE. 80%\n\n### Answer:\nThere is a 10% chance that Tigers will not win at all during the whole season\nWe can infer that there is 90% chance Tigers will win .\nSimilarly There is a 20% chance that Federer will not play at all in the whole season\nWe can also infer that there is 80% chance that Federer will play.\nAnswer E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf Tim had lunch at $50.50 and he gave 20% tip, how much did he spend?\n\n### Options:\nA. $57.45\nB. $35.42\nC. $60.60\nD. $21.56\nE. $78.45\n\n### Answer:\nThe tip is 20% of what he paid for lunch.\ntip = 20% of 50.50 = (20/100)*50.50 = 101/100 = $10.10\nTotal spent\n50.50 + 10.10 = $60.60\ncorrect answer is C)$60.60\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich one of the given numbers is divisible by 11?\n\n### Options:\nA. 4823718\nB. 8423718\nC. 8432718\nD. 4238718\nE. 4852718\n\n### Answer:\nExplanation:\n4238718 = (4+3+7+8) \u2013 (2+8+1) = 11\nSo, the given number is divisible by 11\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 2^z is a factor of 30!, which of the following could be the value of z?\nI. 23\nII. 26\nIII. 24\n\n### Options:\nA. I ONLY\nB. II ONLY\nC. BOTH I AND II\nD. III ONLY\nE. NONE OF THE ABOVE\n\n### Answer:\n2^z is a factor of 30!, what values can z take.\nPowers of 2 in 30! = [30/2] + [30/4] +[30/8] + [30/16] , where [x] is the integral part of x\nPowers of 2 in 30! = 15 + 7 + 3 + 1 = 26\nHence the maximum value of 2^z in 30! = 2^26\nOnly Statement II satisfies\nCorrect Option: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe difference between 3/5 of 2/3 of a number and 2/5 of 1/4 of the same number is 288. What is the number?\n\n### Options:\nA. 960\nB. 850\nC. 895\nD. 955\nE. 975\n\n### Answer:\naccording to the given condition\nx*(2/3)*(3/5) - x*(2/5)*(1/4) = 288\nso 2x/5 - x/10 = 288\nor 3x/10 = 288\nor x = 2880/3 = 960\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFour people are to be seated on a bench. How many different sitting arrangements are possible if Erik must sit next to Joe?\n\n### Options:\nA. 4\nB. 6\nC. 8\nD. 12\nE. 16\n\n### Answer:\nConsider E and J one. But, in this arrangement they can sit in two different combinations.\nE first and J second or J first and E second.\nTotal we have (E and J) and the two other persons= 4 arrangements to do.\nTotal arrangements= 4*2= 8\nC is the answer\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the value of 1.5 x [(3.6 x 0.48 x 2.50) / (0.12 x 0.09 x 0.5)]\n\n### Options:\nA. 800\nB. 500\nC. 900\nD. 1200\nE. None\n\n### Answer:\nAnswer\n1.5 x [(3.6 x 0.48 x 2.50) / (0.12 x 0.09 x 0.5)]\n= 1.5 x [(36 x 48 x 250) / (12 x 9 x 5)]\n= 1.5 x 4 x 4 x 50 = 1200\nCorrect Option: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn store A there are 10 pairs of pants for every 30 store B has. The price ratio between the pants in store B and the pants in store A is 3:4. If all the pants were sold in both places until the stock ran out, what is the ratio between the total amount stores A earned to the total amount store B earned?\n\n### Options:\nA. 3:16.\nB. 2:3.\nC. 4:9\nD. 3:4.\nE. 2:5.\n\n### Answer:\n1st statement : ratio of pants\nStore A : Store B\n10x : 30x\nX:3X\nPrice :\n4y:3y\nTotal revenue\n4xy : 9xy\n4:9\nAnswer : C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA glass was filled with 12 ounces of water, and 0.03 ounce of the water evaporated each day during a 22-day period. What percent of the original amount of water evaporated during this period?\n\n### Options:\nA. 5.002%\nB. 5.5%\nC. 0.5%\nD. 5%\nE. 20%\n\n### Answer:\nIn 22 days 22*0.03=0.66 ounces of water evaporated, which is 0.66/12\u00e2\u02c6\u2014100=5.5 of the original amount of water.\nAnswer: B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA, B and C rents a pasture for Rs.435. A put in 12 horses for 8 months, B 16 horses for 9 months and 18 horses for 6 months. How much should B pay?\n\n### Options:\nA. 180\nB. 227\nC. 268\nD. 198\nE. 176\n\n### Answer:\n12*8 :16*9 = 18*6\n8: 12: 9\n12/29 * 435 = 180\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf x=2, which of the following is(are) true? I. x^2=2x II x/-4 = 1 III |x|=-x\n\n### Options:\nA. II only\nB. III only\nC. II,III only\nD. I only\nE. I,III only\n\n### Answer:\n2^2 = 2 * 2\nAnswer : D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a box, there are 8 red, 7 blue and 6 green balls. One ball is picked up randomly. What is the probability that it is neither red nor green?\n\n### Options:\nA. 3/4\nB. 1/3\nC. 7/19\nD. 8/21\nE. 9/21\n\n### Answer:\n7C1/21C1=7/21=1/3\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRonald and Elan are working on an assignment. Ronald takes 6 hrs to type 32 pages on a computer, while Elan takes 5 hrs to type 40 pages. How much time will they take, working together on two different computers to type an assignment of 110 pages?\n\n### Options:\nA. 8 hrs 19 min\nB. 8 hrs 18 min\nC. 8 hrs 15 min\nD. 8 hrs 65 min\nE. 8 hrs 18 min\n\n### Answer:\nNumber of pages typed by Ronald in 1 hour\n= 32/6 = 16/3\nNumber of pages typed by Elan in 1 hour\n= 40/5 = 8\nNumber of pages typed by both in 1 hour\n= (16/3 + 8) = 40/3\nTime taken by both to type 110 pages\n= (110 * 3/40) = 8 1/4 = 8 hrs 15 min\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the difference between the compound interest & simple interest of a certain sum of money is\nRs.72 at 12% p.a. per two year. Find the sum(in Rs.)?\n\n### Options:\nA. 200/15\nB. 200/17\nC. 220/17\nD. 240/17\nE. 260/17\n\n### Answer:\n200/17\nC.I=A-P\nA=p(1+12/100)^2\nS.I=p*2*12/100\nC.I-S.I=72 given\nsubstitute and solve\np=200/17\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average age of the mother and her 6 children is 12 years which is reduced by 5 years if the age of the mother is excluded. How old is the mother?\n\n### Options:\nA. 42 years\nB. 40 years\nC. 48 years\nD. 50 years\nE. None of these\n\n### Answer:\nTotal age of the mother and six children = 12 \u00d7 7 = 84 years.\nTotal age of six children = 7 \u00d7 6 = 42 years. (since average is reduced by 5)\nMother is 42 years old.\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRaj and Roshan has some money with them in the ratio 5:4 respectively. If Raj has Rs. 45. How much money Raj has more than Roshan?\n\n### Options:\nA. 5\nB. 9\nC. 16\nD. 12\nE. 18\n\n### Answer:\nLet the money Roshan has be x then (45/x)=5/4\nUpon cross multiplication and solving for x we get x=36\nSo Raj has Rs. 9 more than Roshan\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the one which does not belong to that group ?\n\n### Options:\nA. 30\nB. 82\nC. 27\nD. 62\nE. 11\n\n### Answer:\nExplanation:\n27, 36, 72 and 45 are divisible by 9, but not 30.\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA wholesaler wishes to sell 100 pounds of mixed nuts at $2.00 a pound. She mixes peanuts worth $1.50 a pound with cashews worth $4.00 a pound. How many pounds of cashews must she use?\n\n### Options:\nA. 40\nB. 45\nC. 50\nD. 55\nE. 60\n\n### Answer:\nFrom the question stem we know that we need a mixture of 100 pounds of peanuts and cashews. If we represent peanuts as x and cashews as y, we get x + y = 100. Since the wholesaler wants to sell the mixture of 100 pounds @ $2.50, we can write this as: $2.5 * (x + y) = $1.5x + $4y\nFrom the equation x + y = 100, we can rewrite y as y = 100 - x and substitute this into our equation to get:\n$2.5 * (x + 100 - x) = $1.5x + $4(100 - x)\nIf you solve for x, you will get x = 60, and therefore y = 40. So the wholesaler must use 40 pounds of cashews.\nYou can substitute into the original equation to see that: $250 = $1.5(60) + $4(40)\nAnswer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA part-time employee\u2019s hourly wage was increased by 25%. She decided to decrease the number of hours worked per week so that her total income did not change. By approximately what percent should the number of hours worked be decreased?\n\n### Options:\nA. 9%\nB. 15%\nC. 20%\nD. 50%\nE. 100%\n\n### Answer:\nLet's plug in somenicenumbers and see what's needed.\nLet's say the employee used to make $1/hour and worked 100 hours/week\nSo, the TOTAL weekly income was $100/week\nAfter the 25% wage increase, the employee makes $1.25/hour\nWe want the employee's income to remain at $100/week.\nSo, we want ($1.25/hour)(new # of hours) = $100\nDivide both sides by 1.25 to get:\nnew # of hours = 100/1.25\n\u2248 80 hours\nSo, the number of hours decreases from 100 hours to (approximately) 80 hours.\nThis represents a 20% decrease (approximately) .\nAnswer : C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a, f, and c are consecutive even integers and a < f < c, all of the following must be divisible by 4 EXCEPT\n\n### Options:\nA. a + c\nB. f + c\nC. ac\nD. (bc)/2\nE. (abc)/4\n\n### Answer:\nI did get the correct answer within 80 seconds and it was not by luck either. I did not pick numbers but just used the concept stated by Ian.\nThe 3 numbers can be written as\na, (a + 2)(a + 4).\nIf 'a' is divisible by 4, then even 'c' or 'a + 4' is divisible by 4. However, is 'b' is divisible by 4, then both 'a' and 'a + 4' are still divisible by 2.\nA - (a + c) = a + (a + 4) = 2a + 4 = 2(a + 2) = 2b. 2b will always be divisible by 4 even if 'b' is not divisible by 4. Reason: 'b' already has a prime factorization of at least a '2'. Hence '2b' has two 2s.\nC - ac = a(a+4). If, as stated above, one of them is divisible by 4, then the product is divisible. If both of them are not divisible by 4, then the product is still divisible by 4 because of the presence of two 2s again in the prime factorization.\nD - bc/2 = (a + 2)(a + 4)/2. Either b or c is divisible by 2. Hence, if we assume that b is divisible by 2 and not divisible by 4, then it leaves us just one possibility. Is c divisible by 4? It has to be because c is the next consecutive even integer.\nE - abc/4 = a(a + 2)(a + 4)/4. One of these integers is divisible by 4 already. If we again assume 'b' to be that integer divisible by 4, then we are left with the question - Is a(a + 4) divisible by 4? This is the same as option C.\nB - f + c = (a + 2) + (a + 4) = 2a + 6 = 2(a + 3). (a + 3) will never be divisible by 2 because it is an odd integer. Hence, 2(a + 3), although divisible by 2, will not be divisible by 4 because it has just one 2 in its prime factorization.\nAs a whole, whether you choose numbers (2, 46 being the easiest) or solve conceptually, the answer is still easily obtainable within 2 minutes.B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 40% of a certain number is 160, then what is 20% of that number?\n\n### Options:\nA. 75\nB. 100\nC. 120\nD. 30\nE. 80\n\n### Answer:\nExplanation:\n40% = 40*4 = 160\n20% = 20*4 = 80\nAnswer: Option E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a garden, there are five blue flowers, five red flowers,five green flowers, and five pink flowers. What is the probability that a florist will choose three flowers of the same color when randomly picking three flowers?\n\n### Options:\nA. 11/10\nB. 3/95\nC. 31/10\nD. 3/55\nE. 1/16\n\n### Answer:\nP(all the same color) = P(1st flower is ANY colorAND2nd flower is same as firstAND3rd flower is also the same color)\n= P(1st flower is ANY color)xP(2nd flower is same as 1st)ANDP(3rd flower is the same color)\n= 1x4/20x3/19\n= 3/95\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf k is the greatest positive integer such that 3^k is a divisor of 15! then k =\n\n### Options:\nA. 3\nB. 4\nC. 5\nD. 6\nE. 7\n\n### Answer:\nFor solving this type of tasks we can use such approach\n15 / 3 = 5\n15 / 3^2 = 1 and remainder\nand 3^3 is more than 15 so we stop on second exponent\n5 + 1 = 6\nso maximum value of k = 6\nAnd answer is D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the number of square tiles to cover the floor of a room measuring 4 m * 9 m leaving 0.25 m space around the room. A side of square tile is given to be 25 cms?\n\n### Options:\nA. 388\nB. 476\nC. 557\nD. 2885\nE. 271\n\n### Answer:\n3 1/2 * 8 1/2 = 1/4 * 1/4 * x => x = 476\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a certain business school class, p students are accounting majors, q students are finance majors, r students are marketing majors, and s students are strategy majors. If pqrs = 1365, and if 1< p < q < r < s, how many students in the class are marketing majors?\n\n### Options:\nA. 3\nB. 5\nC. 7\nD. 11\nE. 17\n\n### Answer:\npqrs = 1365 = 3 * 5 * 7 * 13\nSince 1< p < q < r < s, the number of students who are marketing majors is r = 7.\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds. Its length is?\n\n### Options:\nA. 187 m\nB. 768 m\nC. 237 m\nD. 150 m\nE. 287 m\n\n### Answer:\nLet the length of the train be x meters and its speed be y m/sec.\nThey, x / y = 15 => y = x/15\nx + 100 / 25 = x / 15\nx = 150 m.\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe positive difference between Sam and Lucy\u2019s ages is b, and the sum of their ages is x. If Lucy is older than Sam, then which of the following represents Lucy\u2019s age?\n\n### Options:\nA. (x-b)/2\nB. b - x/2\nC. 2b+ x\nD. (x + b)/2\nE. (b - x)/2\n\n### Answer:\nlet Lucy's age be L and sam's age be S\nas given,\nL-S=b-- 1\nL+S=x --2\nadding both the equations 2L=a+z\nL= (b+x)/2 answer is D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nGiven that there are 4 basketball players per team, how many ways can you select 2 basketball players from 3 teams if no more than one player can be selected from each team?\n\n### Options:\nA. 15\nB. 30\nC. 48\nD. 75\nE. 90\n\n### Answer:\n2 teams can be selected from 3 teams in 3C2 ways = 3 ways\nas the condition is that the 2 players should be from different teams\none player can be chosen from 1st team in 5 ways\nsimilarly another player can be chosen from 2nd team in 5 ways\nTotal number of ways to choose the player = 4 * 4 * 3 = 48 ways\nCorrect Answer - C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIt takes a boat 3 hours to travel down a river from point A to point B, and 5 hours to travel up the river from B to A. How long would it take the same boat to go from A to B in still water?\n\n### Options:\nA. 9 hours and 45 minutes\nB. 3 hours and 45 minutes\nC. 1 hours and 45 minutes\nD. 6 hours and 45 minutes\nE. 8 hours and 45 minutes\n\n### Answer:\nLet: S be the speed of the boat in still water, r be the rate of the water current and d the distance between A and B.\nd = 3(S + r) : boat traveling down river\nd = 5(S - r) : boat traveling up river\n3(S + r) = 5(S - r)\nr = S / 4 : solve above equation for r\nd = 3(S + S/4) : substitute r by S/4 in equation B\nd / S = 3.75 hours = Let: S be the speed of the boat in still water, r be the rate of the water current and d the distance between A and B.\nd = 3(S + r) : boat traveling down river\nd = 5(S - r) : boat traveling up river\n3(S + r) = 5(S - r)\nr = S / 4 : solve above equation for r\nd = 3(S + S/4) : substitute r by S/4 in equation B\nd / S = 3.75 hours = 3 hours and 45 minutes.\ncorrect answer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA can do a certain work in 12 days. B is 60% more efficient than A. How many days does B alone take to do the same job?\n\n### Options:\nA. 15/2\nB. 14/2\nC. 15/4\nD. 14/4\nE. 13/4\n\n### Answer:\nLet the total units of work done be 60.\nUnits of work done by A in one day = 5.\nGiven, B is 60% more efficient than A.\nThus, B will be able to finish 8 units of work in a day.\nTherefore, time taken by B alone to complete the total work = 60/8 =15/2 days.\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nGraph G has a line of symmetry of x = \u20135. Graph G passes through the point (3, 3). What is the x-coordinate of another point that must have a y-coordinate of 3?\n\n### Options:\nA. \u20138\nB. \u20137\nC. \u20135\nD. \u20134\nE. -13\n\n### Answer:\nLine of symmetry is X=-5; one point is (3,3)\nRight side distance =5+3(distance from origin) = 8; therefore Left side distance should be same from line of symmetry =8;\ntherefore left side co-ordinate=8+5(distance from origin) = 13; as the X coordinate is in 2nd quadrant hence -13\nTherefore answer is E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train of 45 carriages, each of 60 meters length, when an engine also of 60 meters length is running at a speed of 60 kmph. In what time will the train cross a bridge 1.5 km long?\n\n### Options:\nA. 6\nB. 3\nC. 4.2\nD. 9\nE. 4\n\n### Answer:\nD = 45 * 60 + 1500 = 4200 m\nT = 4200/60 * 18/5 = 252 sec = 4.2 mins\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train crosses a platform of 150 m in 15 sec, same train crosses another platform of length 250 m in 20 sec. then find the length of the train?\n\n### Options:\nA. 150m\nB. 278m\nC. 286m\nD. 121m\nE. 112m\n\n### Answer:\nLength of the train be \u2018X\u2019\nX + 150/15 = X + 250/20\n4X + 600 = 3X + 750\nX = 150m\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf John invested $ 1 at 5 percent interest compounded annually, the total value of the investment, in dollars, at the end of 6 years would be\n\n### Options:\nA. (1.5)^4\nB. 4(1.5)\nC. (1.05)^6\nD. 1 + (0.05)^4\nE. 1 + 4(0.05)\n\n### Answer:\nf John invested $ 1 at 5 percent interest compounded annually, the total value of the investment, in dollars, at the end of 6 years would be\n1(1.05)^6\n1.05^6\nC. (1.05)^6\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a class,9 students like to play Basketball and 8 like to play Cricket. 6 students like to play on both Basketball and Cricket. How many students like to play Basketball or Cricket or both?\n\n### Options:\nA. 12\nB. 11\nC. 16\nD. 18\nE. 22\n\n### Answer:\nDraw a Venn Diagram yourself !\nB + C - BC = Number of students that play either Basketball or Cricket\n9 +8 - 6 = 11\nB)\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat will be the day of the week 15th August, 2010?\n\n### Options:\nA. Tuesday\nB. Saturday\nC. Monday\nD. Sunday\nE. Friday\n\n### Answer:\n15th August, 2010 = (2009 years + Period 1.1.2010 to 15.8.2010)\nOdd days in 1600 years = 0\nOdd days in 400 years = 0\n9 years = (2 leap years + 7 ordinary years) = (2 x 2 + 7 x 1) = 11 = 4 odd days.\nJan. Feb. Mar. Apr. May. Jun. Jul. Aug.\n(31 + 28 + 31 + 30 + 31 + 30 + 31 + 15) = 227 days\n227 days = (32 weeks + 3 days) 3 odd days.\nTotal number of odd days = (0 + 0 + 4 + 3) = 7 = 0 odd days.\nGiven day is Sunday\nAnswer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average of 11 numbers is 12.9. If the average of first six is 12.5 and that of the last six is 11.4 the sixth number is?\n\n### Options:\nA. 10.5\nB. 11.5\nC. 12.5\nD. 13.5\nE. 14.5\n\n### Answer:\n1 to 11 = 11 * 12.9 = 141.9\n1 to 6 = 6 * 15.5 = 93\n6 to 11 = 6 * 11.4 = 68.4\n93 + 68.4 = 161.4 \u2013 149.9 = 11.5\n6th number = 11.5\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the sum of all 3 digit positive integers that can be formed using the digits 1, 4, and 7, if the digits are allowed to repeat within a number?\n\n### Options:\nA. 10,655\nB. 11,988\nC. 12,433\nD. 13,766\nE. 14,322\n\n### Answer:\nThe number of these 3-digit numbers is 3*3*3 = 27\nEach digit 1, 4, and 7 will appear in the ones, tens, and hundreds place 9 times each.\nThe sum equals 9(111) + 9(444) + 9(777) = 11,988\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how many ways can the letters of the word AGENDA be rearranged such that the vowels always appear together?\n\n### Options:\nA. 6!/2!\nB. 3!*3!\nC. 4!/2!\nD. (4! *3!)/2!\nE. 3!*3!/2\n\n### Answer:\nIn the word ABACUS , there are 3 vowels - 2 A's and E\nNumber of ways the letters of word AGENDA be rearranged such that the vowels always appear together\n= (4! * 3! )/2!\nWe can consider the the 3 vowels as a single unit and there are 3 ways to arrange them . But since 2 elements of vowel group are identical we divide by 2! .\nThe entire vowel group is considered as a single group .\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are 3 numbers A, B and C. If A:B = 3/4, B:C = 4/5, C:D = 5/6, then A:D will be?\n\n### Options:\nA. 1 : 2\nB. 3 : 5\nC. 5 : 7\nD. 6 : 11\nE. 5 : 3\n\n### Answer:\nSol. A : B = 3 : 4, B : C = 4 : 5, C : D = 5 : 6\n\u2234A\u2236B\u2236C\u2236D= 3 : 4 : 5 : 6.\nThus, A : D = 3 : 6 or, 1 : 2\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA fruits marks his fruit baskets 40% more than the real price and allows 15% discount. His profit is:\n\n### Options:\nA. 16%\nB. 17%\nC. 18%\nD. 19%\nE. 20%\n\n### Answer:\nLet the CP = 100 Rs.\nMark Price = 140\nDiscount = 15%\nSelling price 85/100 \u00c3\u2014 140\nHence profit = 19%\nAnswer: D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA 15% stock yielding 12% is quoted at:\n\n### Options:\nA. s. 83.33\nB. s. 110\nC. s. 112\nD. s. 125\nE. s. 140\n\n### Answer:\nIncome of Rs 12 on investment of Rs 100\nIncome of Rs 15 on investment of ?\n= (15*100)/12=125\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train 50m long takes 6 sec to cross a man walking at 5kmph in a direction opposite to that of the train. Find the speed of the train?\n\n### Options:\nA. 15kmph\nB. 25kmph\nC. 35kmph\nD. 45kmph\nE. 55kmph\n\n### Answer:\nLet the speed of the train be x kmph\nSpeed of the train relative to man = x+5 = (x+5)*5/18 m/sec\n50/[(x+5)*5/18] = 6\n30(x+5) = 900\nx = 25kmph\nAnswer is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many liters of a 40% iodine solution need to be mixed with 35 liters of a 20% iodine solution to create a 32% iodine solution?\n\n### Options:\nA. 35\nB. 49\nC. 100\nD. 102\nE. 140\n\n### Answer:\nSolution 1:\nAssume the iodine solution to be mixed = x lts.\nIodine = 0.4x lts, Water = 0.6x lts.\nSolution 2: 35 liters of a 20% iodine solution\nIodine = 7 lts, Water = 28 lts.\nTotal iodine = 0.4x + 7\nTotal water = 0.6x + 28\nThe resultant is a 35% idoine solution.\nHence (0.4x + 7) / (x + 35) = 32/100\n40x + 700 = 32x + 1120\n8x = 820\nx = 102 lts\nCorrect Option: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn an election between two candidates, 70% of the voters cast their votes, out of which 4% of the votes were declared invalid. A candidate got 6552000 votes which were 75% of the total valid votes. Find the total number of votes enrolled in that election.\n\n### Options:\nA. 13000000\nB. 12500\nC. 14000\nD. 12000\nE. None of these\n\n### Answer:\nExplanation :\nSolution: let the total number of votes enrolled be x. then, number of votes cast = 70% of x. valid votes = 96% of(70% of x). .'. 75% of(96% of (70% of of x)) = 6552000.\n(75/100 * 96/100 * 70/100 * x) = 6552000.\n=> x = (6552000*100*100*100)/(75*96*70) = 13000000\nAnswer : A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nCost of 16 mirror and 8 comb is Rs.336 and the cost of 4 mirror and 4 comb is Rs.96. Find the cost of each mirror?\n\n### Options:\nA. 10\nB. 18\nC. 20\nD. 21\nE. 22\n\n### Answer:\nLet the cost of each pen and pencil be 'p' and 'q' respectively.\n16m + 8c = 336 --- (1)\n4m + 4c = 96\n8m + 8c = 192 --- (2)\n(1) - (2) => 8p = 144\n=> m = 18\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average speed of a car decreased by 3 miles per hour every successive 8-minutes interval. If the car traveled 4.4 miles in the fifth 8-minute interval, what was the average speed of the car, in miles per hour, in the first 8 minute interval?\n\n### Options:\nA. 45\nB. 48\nC. 51\nD. 54\nE. 57\n\n### Answer:\n(4.4 miles / 8 minutes)*60 minutes/hour = 33 mph\nLet x be the original speed.\nx - 4(3) = 33\nx = 45 mph\nThe answer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRamesh can complete a work in 12 days, working 7 hours a day. Suresh can complete the same work in 8 days, working 9 hours a day. If Ramesh and Suresh work together working 7 hours a day, in how many days can they complete the work?\n\n### Options:\nA. 5 * 7 / 13\nB. 5 * 7 / 19\nC. 5 * 7 / 11\nD. 5 * 7 / 19\nE. 5 * 6 / 11\n\n### Answer:\nExplanation:\nRamesh can finish the work in 12 * 7 = 84 hours\nAmount of work he can complete in 1 hour = 1/84\nSuresh can finish the same work in 8 * 9 = 72 hours\nAmount of work he can complete in 1 hour = 1/72 hours\nWork done by both of them in 1 hour =\n= 1/84 + 1/72 = 13/504\nRamesh and Suresh together can complete the work in 504/13 hours.\ni.e. 504/13 * 1/7 = 72/13 days\ni.e. 5 * 7 / 13 days\nANSWER: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe number of bacteria in a petri dish increased by 50 percent every 2 hours. If there were 108 million bacteria in the dish at 1: 00 p.m., at what time were there 32 million bacteria in the dish?\n\n### Options:\nA. 7: 00 p.m.\nB. 8: 00 p.m.\nC. 6: 00 a.m.\nD. 8: 00 a.m.\nE. 10: 00 a.m.\n\n### Answer:\nGiven:\nThe number of bacteria in a petri dish increased by 50 percent every 2 hours\nThere were 108 million bacteria in the dish at 2: 00 p.m\nSince the bacteria is increasing by 50% every 2 hours, this means that the number is multiplied by 1.5 every 2 hours.\nRequired: At what time were there 32 million bacteria in the dish?\nAssume that there were n intervals of 2 hours between 32 million and 108 million.\n32 * (1.5)^n = 108\n(3/2)^n = 108/32 = 27/8 = (3/2)^3\nHence n = 3 intervals.\nEach interval was of 2 hours. Therefore, the number of hours = 6\nSubtracting 6 hours from 1 PM, we get 7 AM as the answer.\nOption A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average of 8 numbers is 21. If each of the number is multiplied by 8, the average of the new set of numbers is :\n\n### Options:\nA. 168\nB. 667\nC. 288\nD. 1991\nE. 111\n\n### Answer:\nAverage of new numbers = (21\u00d78)=168\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe sum of ages of 5 children born 4 years different each is 70 yrs. What is the age of the Elder child?\n\n### Options:\nA. 8\nB. 9\nC. 22\nD. 17\nE. 18\n\n### Answer:\nLet the ages of children be x, (x + 4), (x + 8), (x + 12) and (x + 16) years.\nThen, x + (x + 4) + (x + 8) + (x + 12) + (x + 16) = 70\n5x = 30\nx = 6\nx+16= 6+16= 22\nAnswer : C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nEight people are planning to share equally the cost of a rental car. If one person withdraws from the arrangement and the others share equally the entire cost of the car, then the share of each of the remaining persons increased by:\n\n### Options:\nA. 1by7\nB. 1/8\nC. 1/9\nD. 7/8\nE. 1/5\n\n### Answer:\nOriginal share of 1 person = 1/8\nNew share of 1 person = 1/7\nIncrease =(1/7-1/8) = 1/56\nRequired fraction = (1/56)/(1/8)\n= (1/56)*8\n= 1/7\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf Rs.420 amount to Rs.540 in 4 years, what will it amount to in 6 years at the same rate % per annum?\n\n### Options:\nA. s.575\nB. s.595\nC. s.590\nD. s.600\nE. s.585\n\n### Answer:\n80 = (420*4*R)/100\nR = 7.14%\nI = (420*6*7.14)/100 = 180\n420 + 180 = 600\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nEntry fee in an exhibition was Rs. 1. Later, this was reduced by 25% which increased the sale by 20%. The percentage increase in the number of visitors is :\n\n### Options:\nA. 33\nB. 37\nC. 60\nD. 28\nE. 27\n\n### Answer:\nExplanation:\nLet the total original sale be Rs. 100. Then, original number of visitors = 100.\nNew number of visitors = 120/0.75 = 160.\nIncrease % = 60 %.\nAnswer: C) 60 %\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhen positive integer x is divided by positive integer y, the remainder is 9. If x/y = 96.45, what is the value of y?\n\n### Options:\nA. 96\nB. 75\nC. 48\nD. 20\nE. 12\n\n### Answer:\nGuys, one more simple funda.\n5/2= 2.5\nnow .5 x2 =1 is the remainder\n25/4 = 6.25\nnow .25x4=1 is the remainder\n32/5=6.4\nnow.4x5 = 2 is the remainder\ngiven x/y = 96.45 and remainder is 9\nSo .45 X y = 9\nhence y= 20\nAns D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA shoe store sells Adidas shoes for $60 each and Puma shoes for $50 each. On every Adidas shoe the restaurant makes a profit of $10 while on every Puma shoe it makes a profit of $8. If on a given day the storest's sales amounted to $1600, which of the following cannot be the profit made on that day?\n\n### Options:\nA. 262\nB. 260\nC. 258\nD. 256\nE. 254\n\n### Answer:\n$254 is the only option that does not fit into a combination of Adidas and Puma sales profits, given the total sales of the day. Answer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the remainder is 10 when positive integer n is divided by 14, what is the remainder when n is divided by 7?\n\n### Options:\nA. 0\nB. 1\nC. 2\nD. 3\nE. 4\n\n### Answer:\nAssume x is quotient here,\nn=14x+7 ----------(1)\nand n=7x+ ?\nWe can also write equation (1) as:\nn=(14x+7)+3.\nie 7(2x+1)+3 ie the first term is perfectly divisible by 7.\nSo,the remainder left is 3.\nSo,answer (D) is right choice.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHarkamal purchased 10 kg of grapes at the rate of 70 per kg and 9 kg of mangoes at the rate of 55 per kg. How much amount did he pay to the shopkeeper?\n\n### Options:\nA. A)1190\nB. B)1065\nC. C)1070\nD. D)1075\nE. E)1080\n\n### Answer:\nCost of 10 kg grapes = 70 \u00d7 10 = 700.\nCost of 9 kg of mangoes = 55 \u00d7 9 = 490.\nTotal cost he has to pay = 700 + 490 = 1190\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 2/3rd of the contents of a container evaporated on the 1st day. And 1/4th of the remaining evaporated on the second day. What part of the contents of the container is left at the end of the second day?\n\n### Options:\nA. 1/4\nB. 1/12\nC. 1/18\nD. 1/6\nE. 1/2\n\n### Answer:\nAfter first day, 1/3 of the contents remain.\nAfter second day,\n(1/3) - (1/4(2/3)) = (1/3) - (1/6) = 1/6 of the contents remain\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA batsman makes a score of 87 runs in the 17th inning and thus increases his averages by 3. What is his average after 17th inning?\n\n### Options:\nA. 25\nB. 31\nC. 27\nD. 29\nE. 39\n\n### Answer:\nLet the average after 17 innings = x\nTotal runs scored in 17 innings = 17x\nAverage after 16 innings = (x-3)\nTotal runs scored in 16 innings = 16(x-3)\nTotal runs scored in 16 innings + 87 = Total runs scored in 17 innings\n=> 16(x-3) + 87 = 17x\n=> 16x - 48 + 87 = 17x\n=> x = 39\nAnswer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn an objective test, a correct answer scores 4 marks, and a wrong answer scores 2 marks. A student scores 480 marks from 150 questions. how many answers are correct?\n\n### Options:\nA. 90\nB. 80\nC. 70\nD. 60\nE. 50\n\n### Answer:\nif all ans. right the marks=4*150=600\nbut score=480\nwrong attempt marks=600-480=120\nwrong ans.=120/2=60\nright ans.=150-60=90.\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf x is 12 percent greater than 70, then x =\n\n### Options:\nA. 78.4\nB. 91.0\nC. 88.0\nD. 70.4\nE. 71.2\n\n### Answer:\n12% of 70 = (70*0.11) = 8.4\n12% greater than 70 = 70 + 8.4 = 78.4\nAnswer is clearly A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf x^2 \u2013 x = 2, then one possible value of x \u2013 4 =\n\n### Options:\nA. -9\nB. -5\nC. -3\nD. -1\nE. 5\n\n### Answer:\nx^2 \u2013x = 2\ni.e. x^2 \u2013 x - 2 = 0\ni.e. x^2 +x -2x -2 = 0\ni.e. (x-2)(x+1) = 0\ni.e. x = 2 or -1\ni.e. x-4 = 2-4 or -1-4\ni.e. x-4 = -2 or -5\nAnswer: Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 60! is written out as an integer, with how many consecutive 0\u2019s will that integer end?\n\n### Options:\nA. 6\nB. 12\nC. 14\nD. 42\nE. 56\n\n### Answer:\nSoln:-\n60/5+60/52=12+2=14\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA room of 6m 44cm long and 3m 00cm broad is to be paved with square tiles. Find the least number of square tiles required to cover the floor.\n\n### Options:\nA. 12076\nB. 12070\nC. 12077\nD. 12075\nE. 12074\n\n### Answer:\nExplanation:\narea of the room = 644 * 300sq cm\nsize of largest square tile = H.C.F of 644cm and 300cm= 4cm\narea of 1 tile = 4*4 sq cm\nno. of tiles required = (644*300) / (4 * 4) = 12075\nAnswer: D) 12075\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the equation of a circle of radius 5 units centered at (3, 2)?\n\n### Options:\nA. x^2 + y^2 + 6x \u2013 4y = 23\nB. x^2 + y^2 - 6x + 4y = 23\nC. x^2 + y^2 + 6x + 4y = 23\nD. x^2 + y^2 - 6x \u2013 4y = - 12\nE. x^2 + y^2 - 6x \u2013 4y = 12\n\n### Answer:\nthe equation of a circle with center at (a,b) and radius R is (X-a)^2+(Y-b)^2=R^2\n=> answer = (X-3)^2+(Y-2)^2=5^2\nsolving,,we get the equation in answer choice E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a certain game, each player scores either 2 points or 5 points. If n players score 2 points and m players score 5 points, and the total number of points scored is 50, what is the least possible positive R difference between n and m?\n\n### Options:\nA. 1\nB. 3\nC. 5\nD. 7\nE. 9\n\n### Answer:\nWe have equation 2n + 5m = 50\nWe have factor 2 in first number and we have factor 5 in second number.\nLCM(2, 5) = 10\nSo we can try some numbers and we should start from 5 because it will be less list than for 2\n2 * 5 = 10 and n should be equal 20\n4 * 5 = 20 and n should be equal 15\n6 * 5 = 30 and n should be equal 10\n8 * 5 = 40 and n should be equal 5\n10 * 5 = 50 and n should be equal 0\nthird variant give us the mininal difference\nn - m = 10 - 6 = 4\nAnd there is some mistake in my way of thinking because we don't have such answer )\nIf we change the task and will seek for difference between m and n\nthan minimal result R will be 8 - 5 = 3\nAnd answer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA can finish a work in 12days, B in 9days and C in 2days, B and C start the work but are forced to leave after 3 days. The remaining work was done by A in?\n\n### Options:\nA. 10days\nB. 12days\nC. 6days\nD. 7days\nE. 5days\n\n### Answer:\nB+C 1day work = 1/9 + 1/12 = 7/36\nwork done by B and C in 3days = 7/36 * 3 = 7/12\nRemaining work = 1 - 7/12 = 5/12\n1/24 work is done by A in 1day\n5/12 work is done by A in 12*5/12 = 5days\nAnswer is E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n7^1+7^2+7^3+...........+7^2015 find out how many numbers present which unit place contain 3 ?\n\n### Options:\nA. 504\nB. 505\nC. 506\nD. 507\nE. 508\n\n### Answer:\n7^3,7^7,7^11,7^15,7^19.........7^2015 contains last digit=3.\nNow,we see\n3,7,11,15....2015 are in AP\ntn=a+(n-1)d\n2015=3+(n-1)4\n2015=3+4n-4\n4n=2016\nn=504\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\na;b = 8: 10, b:c = 7: 9, a:b:c = ?\n\n### Options:\nA. 56 : 70: 80\nB. 56 : 70: 70\nC. 56 : 70: 60\nD. 56 : 70: 95\nE. 56 : 70: 90\n\n### Answer:\na;b = 8: 10\nb:c = 7: 9\na:b:c =56 : 70: 90\nAnswer : E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n2,3,5,8,13,21,34,?\n\n### Options:\nA. 57\nB. 58\nC. 55\nD. 54\nE. 56\n\n### Answer:\nEach number is the sum of the previous two numbers, ie 18 + 29 = 55.\nAnswer : C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA geometric shape is obtained by combining a square of side 8 cm and a semicircle of diameter 8cm. What is the perimeter of the shape obtained?\n\n### Options:\nA. 28.32\nB. 36.57\nC. 44.57\nD. 48.93\nE. 54.24\n\n### Answer:\nCircumference of the semicircle= \u00cf\u20acxD/2 = (22/7)x4 = 12.57\nPerimeter of the square plot = 3x8 = 24\nPerimeter of the shape=36.57cm\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many distinct integer values of n satisfy the inequality||n-3| + 4| \u2264 11?\n\n### Options:\nA. 15\nB. 16\nC. 17\nD. 8\nE. 19\n\n### Answer:\nso i can write this as In-3I+4<=11\nor In-3I<=7\nso n can have -4 to 10 = 8 true values....\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many multiples of 3 are there between 81 and 358?\n\n### Options:\nA. 94\nB. 95\nC. 93\nD. 97\nE. 98\n\n### Answer:\n3 * 27 = 81\n3 * 119 = 357\nTotal multiples of 3 = (119 - 27) + 1\n= 93\nAnswer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich of the following CANNOT be the least common multiple of two positive integers x and y\n\n### Options:\nA. xy\nB. x\nC. y\nD. x + y\nE. x - y^2\n\n### Answer:\nThe least common multiple of two positive integers cannot be less than either of them. Therefore, since x - y^2 is less than x, it cannot be the LCM of a x and y.\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA pipe can fill a cistern in 20 minutes whereas the cistern when fill can be emptied by a leak in 30 minutes. When both pipes are opened, find when the cistern will be full?\n\n### Options:\nA. 17 minutes\nB. 87 minutes\nC. 60 minutes\nD. 27 minutes\nE. 11 minutes\n\n### Answer:\n1/20 - 1/30 = 1/60\n60 minutes\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA number is doubled and 5 is added. If the resultant is trebled, it becomes 135. What is that number?\n\n### Options:\nA. 12\nB. 29\nC. 20\nD. 15\nE. 99\n\n### Answer:\nExplanation:\nLet the number be x.\nTherefore,\n3(2x + 5) = 135\n6x + 15 = 135\n6x = 120\nx = 20\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSides of a rectangular park are in the ratio 3: 2 and its area is 3750 sq m, the cost of fencing it at 20 ps per meter is?\n\n### Options:\nA. s.122\nB. s.129\nC. s.125\nD. s.95\nE. s.121\n\n### Answer:\n3x * 2x = 3750 => x = 25\n2(75 + 20) = 190 m\n190 * 1/2 = Rs.95\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA cistern is normally filled in 4 hrs,but takes 2 hrs longer to fill because of a leak on its bottom,if Cistern is full ,how much time citern would empty?\n\n### Options:\nA. 10 hours\nB. 20 hours\nC. 30 hours\nD. 40 hours\nE. 12 hours\n\n### Answer:\nIf leakage/hour=1/x, then 1/4 -1/x= 1/6, solving 1/x=1/12\nSo in 12 hours full cistern will be empty.\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOne pipe can fill a tank three times as fast as another pipe. If together the two pipes can fill tank in 38 min, then the slower pipe alone will be able to fill the tank in?\n\n### Options:\nA. 229\nB. 787\nC. 152\nD. 128\nE. 121\n\n### Answer:\nLet the slower pipe alone fill the tank in x min.\nThen, faster pipe will fill it in x/3 min.\n1/x + 3/x = 1/38\n4/x = 1/38 => x = 152 min.\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFive children, Anaxagoras, Beatrice, Childeric, Desdemona, and Ethelred, sit randomly in five chairs in a row. What is the probability that Childeric and Ethelred sit next to each other?\n\n### Options:\nA. 1/30\nB. 1/15\nC. 1/5\nD. 2/5\nE. 7/20\n\n### Answer:\nTotal no of empty space is 5 so total no of ways A B C D and E can sit is 5 !\nSolution 1:\nNow condition is C&E will sit together\nIf they sit at 1st and 2nd place . # of ways will be 1*3! but C&E can be either at 1 or at 2 so # of ways will be 1*3!*2!\nSimilarly they can sit together at position 2 and 3 or 3 and 4 or 4 and 5\nSo total # ways will be 1*3!*2! + 1*3!*2! + 1*3!*2! + 1*3!*2! = 4 *1*3! *2 !\nSo probability is (4! * 2! ) / 5! = 2/5\nSolution 2:\nConsider C*E as 1 person . So we have 4 ppl and 4 places . # of ways they can sit is 4!\nC&E can sit as C&E or E&C so total # of ways is 4! * 2!\nSo probability will be 2/5\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA dress on sale in a shop is marked at $D. During the discount sale its price is reduced by 15%. Staff are allowed a further 10% reduction on the discounted price. If a staff member buys the dress what will she have to pay in terms of D ?\n\n### Options:\nA. 0.965D\nB. 0.760D\nC. 0.765D\nD. 0.865D\nE. 4.765D\n\n### Answer:\nExplanation:\nIf the price is reduced by 15 %, then the new price will be 0.85D\nIf this new price is further reduced by 10%, the discounted price will be 0.9 x 0.85D = 0.765D\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train passes a man standing on a platform in 8 seconds and also crosses the platform which is 276 metres long in 20 seconds. The length of the train (in metres) is:\n\n### Options:\nA. 184\nB. 176\nC. 175\nD. 96\nE. None of these\n\n### Answer:\nExplanation:\nLet the length of train be L m.\nAcc. to question\n(276+L)/20 = L/8\n2208+8L=20L\nL= 2208/12 = 184 m\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nrahul played weel in this season.his current batting averagge is 53.if he score 78 runs in today match.his batting average will become 58.how many matches had he played in this season.\n\n### Options:\nA. 4\nB. 10\nC. 9\nD. 6\nE. 5\n\n### Answer:\n53x+78=58(x+1)\n=>5x=20\n=>x=4\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTom invested Rs. 15000 @ 8% per annum for two years. If the interest is compounded half-yearly, then the amount received by Tom at the end of the year will be?\n\n### Options:\nA. 17,546.75\nB. 17,547.40\nC. 17,547.88\nD. 17,548.32\nE. 17,548.80\n\n### Answer:\nP = Rs. 15000; R = 8% p.a. = 4% per half-year; T = 2 years = 4 half-year\nAmount = [15000 * (1 + 4/100)4]\n= (15000 * (1.04)4) = Rs. 17547.88\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nManie spent 2\u20445 of her money on new clothes and then deposited 1\u20442 of what remained into her savings account. If she then had $21 left, how much did she have at the start?\n\n### Options:\nA. $30\nB. $35\nC. $70\nD. $105\nE. $210\n\n### Answer:\nManie spent 2\u20445 of her money on new clothes but if you see 21 is half of 3/5 money so 210 is too huge to be correct..\nsolution..\nlet the money be x..\n2/5 is used...\n1/2 of remaining 3/5 is put in savings account and remaining half is 21..\nso 1/2 * 3/5 *x=21..\nx=21*2*5/3=70..\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nCar A runs at the speed of 65km/hr & reaches its destination in 8hr. Car B runs at the speed of 70 km/h & reaches its destination in 5h. What is the respective ratio of distances covered by Car A & Car B?\n\n### Options:\nA. 11 : 6\nB. 52 : 35\nC. 13 : 7\nD. 15 : 6\nE. 13 : 6\n\n### Answer:\nSol. Distance travelled by Car A = 65 \u00c3\u2014 8 = 520 km\nDistance travelled by Car B = 70 \u00c3\u2014 5 = 350 km\nRatio = 520/350 = 52 : 35\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the sum E of all 3 digit numbers that leave a remainder of '2' when divided by 3?\n\n### Options:\nA. 897\nB. 164,850\nC. 164,749\nD. 149,700\nE. 156,720\n\n### Answer:\nThe series is => 101+...998\nNumber of terms => 300\nsum => 300/2 * [101+998]\nhence sum E=> 164850 i.e. option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n150 is what percent of 60 ?\n\n### Options:\nA. 250%\nB. 20%\nC. 50%\nD. 200%\nE. 500%\n\n### Answer:\n60*x=150 --> x=2.5 -->2.5 expressed as percent is 250%.\nAnswer: A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn an examination, the percentage of students qualified to the students appeared from school 'P' is 70%. In school 'Q', the number of students appeared is 30% more than the students appeared from school 'P' and the number of students qualified from school 'Q' is 50% more than the students qualified from school 'P'. What is the % of students qualified to the number of students appeared from school 'Q' ?\n\n### Options:\nA. 80.76%\nB. 75.5%\nC. 60.50%\nD. 43 %\nE. None of these\n\n### Answer:\nExplanation:\nNumber of students appeared from school 'P' = 100, say\nNumber of students qualified from school 'P' = 70\nand Number of students appeared from school 'Q' = 130\nNumber of students qualified from school 'Q' = 50% more than those qualified from school 'P'.\n= 70 + 35 = 105 % of students qualified to the number of students appeared from school B = 105 / 130 * 100\n= 80.76%\nANSWER A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf two letters are chosen at random (without replacement) from the word JUPITER, what is the probability that none of the letters are vowels?\n\n### Options:\nA. 1/7\nB. 2/7\nC. 3/14\nD. 5/14\nE. 11/21\n\n### Answer:\nThe number of ways to choose two letters is 7C2 = 21\nThe number of ways to choose two consonants is 4C2 = 6.\nP(no vowels) = 6/21 = 2/7\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 6 (A's capital) = 8 (B's capital) = 10 (C's capital). Then the ratio of their capitals is:\n\n### Options:\nA. 20:15:33\nB. 20:25:33\nC. 20:15:12\nD. 20:15:09\nE. 20:15:11\n\n### Answer:\nExplanation:\n6A = 8B = 10 C\nA:B:C = 1/6:1/8:1/10\n= 20:15:12\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe least number of five digits which is exactly divisible by 12,15 and 18 is :\n\n### Options:\nA. 10010\nB. 10015\nC. 10020\nD. 10080\nE. None of these\n\n### Answer:\nSolution\nLeast number of 5 digits is 10000. L.C.M. of 12, 15 and 18 is 180.\nOn dividing 1000 by 180, the remainder is 100.\n\u2234 Required number = 10000 + (180 - 100) = 10080. Answer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTrain W leaves New York at 7:00 am traveling to Boston at 80mph. Train B leaves Boston at 7:45 am traveling to New York at 70 mph on a parallel track. If the distance between New York and Boston is 210 miles, at what time will the two trains pass each other?\n\n### Options:\nA. 8:15 am\nB. 8:45 am\nC. 9:00 am\nD. 9:30 am\nE. Cannot be determined from the information given\n\n### Answer:\ntrain W will cover 60 kms in 45 min at 7:45, the time when train B starts...\ndistance left to cover is 210-60=150..\ncombined speed=80+70=150..\nso the trains meet in 1 hour i.e. 7:45 + 1 hr=8:45\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nEighty percent of the lights at Hotel California are on at 8 p.m. a certain evening. However, forty percent of the lights that are supposed to be off are actually on and ten percent of the lights that are supposed to be on are actually off. What percent Z of the lights that are on are supposed to be off?\n\n### Options:\nA. 22(2/9)%\nB. 16(2/3)%\nC. 11(1/9)%\nD. 10%\nE. 5%\n\n### Answer:\nIs the Answer D.\nlet me try..\nLet the light which are supposed to be OFF = SO\nLet the light which are supposed to be ON = SN\nLet the light which are ACTUALLY OFF = AO\nLet the light which are ACTUALLY ON = AN\nLet the total no. of lights be 100,\nSo ACTUALLY ON lights = 80\nAnd ACTUALLY OFF lights = 20\nAlso given >> forty percent of the lights that are supposed to off are actually on >>> (40/100)*SO are ACTUALLY ON\nit means >>> (60/100)*SO are ACTUALLY OFF\nAlso given >> ten percent of the lights that are supposed to be on are actually off >>> (10/100)*SN are ACTUALLY OFF\nit means >>> (90/100)*SN are ACTUALLY ON\nSo, Total ACTUALLY ON lights = (40/100)*SO + (90/100)*SN = 80\nand Total ACTUALLY OFF lights = (60/100)*SO + (10/100)*SN = 80\nFrom here we get SO = 20\nwe need to find: What percent of the lights that are on are supposed to be off >>> So light ACTUALLY ON are 80 and light which are ACTUALLY ON, which are supposed to be OFF = (40/100)*SO = 8.\nSo (8/80)*100 Z= 10%.D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA cistern is filled by a tap in 8 1/2 hours. Due to leak in the bottom of the cistern, it takes half an hour longer to fill the cistern. If the cistern is full how many hours will it take the leak to empty it?\n\n### Options:\nA. 133\nB. 143\nC. 153\nD. 163\nE. 173\n\n### Answer:\nfilling rate - leak rate = net rate\n1/8.5 - leak rate = 1/9\nleak rate = 2/17 - 1/9 = 1/153\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nCan you find the missing number in the sequence given below?\n11 15 19 12 16 ? 13 17 21 14 18 22\n\n### Options:\nA. 20\nB. 21\nC. 22\nD. 23\nE. 24\n\n### Answer:\nSolution:\n20\nExplanation :\nThe sequence is given in the puzzle is :\n11 15 19 12 16 ? 13 17 21 14 18 22\nLet's break the given series as below:\n11 15 19\n12 16 ?\n13 17 21\n14 18 22\nNow read the number from left hand side from top to bottom as :\nSo the number that will replace '?' is 20.\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSeries F(n) is such that i*F(i) = j*F(j) for any pair of positive integers (i, j). If F(1) is a positive integer, which of the following is possible?\nI. 2*F(100) = F(99) + F(98)\nII. F(1) is the only integer in the series\nIII. The series does not contain negative numbers\n\n### Options:\nA. I only\nB. II only\nC. IIII only\nD. IIIII only\nE. I, IIIII\n\n### Answer:\nFirst thing I want to understand is this relation: i*F(i) = j*F(j) for any pair of positive integers. I will take examples to understand it.\nWhen i = 1 and j = 2, F(1) = 2*F(2)\nSo F(2) = F(1)/2\nWhen i = 1 and j = 3, F(1) = 3*F(3)\nSo F(3) = F(1)/3\nI see it now. The series is: F(1), F(1)/2, F(1)/3, F(1)/4 and so on...\nII and III are easily possible. We can see that without any calculations.\nII. F(1) is the only integer in the series\nIf F(1) = 1, then series becomes 1, 1/2, 1/3, 1/4 ... all fractions except F(1)\nIII. The series does not contain negative numbers\nAgain, same series as above applies. In fact, since F(1) is a positive integer, this must be true.\nI. 2*F(100) = F(99) + F(98)\n2*F(1)/100 = F(1)/99 + F(1)/98 (cancel F(1) from both sides)\n2/100 = 1/99 + 1/98\nNot true hence this is not possible\nAnswer (D)\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe CI on Rs. 30,000 at 7% per year is Rs. 4347. The period is?\n\n### Options:\nA. 1 years\nB. 2 years\nC. 3 years\nD. 4 years\nE. 5 years\n\n### Answer:\nAmount = Rs. (30000 + 4347) = Rs. 34347.\nLet the time be n years.\nThen, 30000 1 + 7 n = 34347\n100\n107 n = 34347 = 11449 = 107 2\n100 30000 10000 100\nn = 2 years\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA person travels from K to L a speed of 50 km/hr and returns by increasing his speed by 50%. What is his average speed for both the trips ?\n\n### Options:\nA. 55 kmph\nB. 58 kmph\nC. 60 kmph\nD. 66 kmph\nE. 70 kmph\n\n### Answer:\nExplanation:\nSpeed on return trip = 150% of 50 = 75 km/hr.\nAverage speed = (2 x 50 x 75)/(50 + 75) = 60 km/hr.\nANSWER IS C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf Rs.1000 be invested at interest rate of 5% & the interest be added to the principal every 10 yrs, then the no. of yrs in which it will amount to Rs.2000 is:\n\n### Options:\nA. 15\nB. 17 1/3\nC. 16 2/3\nD. 19 2/5\nE. 21 1/5\n\n### Answer:\nTotal time= (10+6 2/3) = 16 2/3 years\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nCindy wants to buy dolls for her playhouse. Each doll costs $10. Cindy's mother gives her $30 to spend. How many dolls can Cindy buy with the money her mother gave her?\n\n### Options:\nA. 5\nB. 10\nC. 2\nD. 1\nE. 3\n\n### Answer:\nE. 3\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nLook at this series: 201, 202, 204, 207, ... What number should come next?\n\n### Options:\nA. 211\nB. 205\nC. 209\nD. 210\nE. 212\n\n### Answer:\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many even number in the range between 15 to 100 inclusive are not divisible by 3\n\n### Options:\nA. 29\nB. 30\nC. 31\nD. 33\nE. 46\n\n### Answer:\nWe have to find the number of terms that are divisible by 2 but not by 6( as the question asks for the even numbers only which are not divisible by 3)\nFor 2,\n16,18...100\nusing AP formula, we can say 100 = 16 + (n-1) *2\nor n=43.\nFor 6,\n18,...96\nusing AP formula, we can say 96 = 18 + (n-1) *6\nor n=14.\nHence, only divisible by 2 but not 3 = 43-14 = 29. hence, Answer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf x is the interest on y and y is the interest on z, the rate and time is the same on both the cases. What is the relation between x, y and z?\n\n### Options:\nA. Y2=XY\nB. X2=YZ\nC. Y2=XZ\nD. Z2=XZ\nE. Y2=XZ\n\n### Answer:\nX = (Y*NR)/100 Y = (Z*NR)/100\nX/Y = NR/100 Y/Z = NR/100\nX/Y = Y/Z\nY2 = XZ\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 2x +3y = 30 and (x+y)/y = 11/8, then find the value of 5y + 6x\n\n### Options:\nA. 72\nB. 58\nC. 64\nD. 29\nE. 28\n\n### Answer:\nExplanation:\nThe given equations are :\n2x + 3y = 30 --------- (i)\nand, (x+y)/y = 11/8\n8x + 8y = 11y\n8x \u2013 3y =0 ----(ii)\nAdding (i) & (ii), we get : 10 x = 30 or x = 3.\nPut x = 3 in (i), we get : y = 8\nTherefore, 5y + 6x = (5 * 8 + 6 * 3) = 40 + 18 = 58.\nANSWER: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a recent head-to-head run-off election, 15,000 absentee ballets were cast. 1/5 of the absentee ballets were thrown out and 1/4 of the remaining absentee ballets were cast for Candidate A. How many absentee votes did Candidate B receive?\n\n### Options:\nA. 2,000\nB. 3,000\nC. 6,000\nD. 8,000\nE. 9,000\n\n### Answer:\n4/5 * 3/4 (total absentee votes) = 3/5 (total votes)=3/5*15000=9000\nAnswer is E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo pipes P and Q can fill a cistern in 12 and 15 minutes respectively. Both are opened together, but at the end of 3 minutes the first is turned off. How much longer will the cistern take to fill?\n\n### Options:\nA. 11 1/5\nB. 11 1/4\nC. 11 1/5\nD. 11 1/3\nE. 11 2/3\n\n### Answer:\n3/12 + x/15 = 1\nx= 11 1/4\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nCurrently guavas cost 30 cents/pound. Due to a disease affecting the guava trees it is expected that next month guavas will cost 50% more than they do currently. How much are guavas expected to cost next month?\n\n### Options:\nA. 50 cents /pound\nB. 45 cents /pound\nC. 55 cents /pound\nD. 60 cents /pound\nE. 65 cents /pound\n\n### Answer:\nIf a new cost is p percent greater than the old cost, then (new cost) = (old cost) + (p/100)(old cost).\nIn this case, (new cost) = 30 cents/pound + (50/100)(30 cents/pound)\n= 30 cents/pound + 15 cents/pound\n= 45 cents /pound\nAnswer : B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train 100 m long can cross an electric pole in 20 sec and then find the speed of the train?\n\n### Options:\nA. 19 Kmph\nB. 18 Kmph\nC. 72 Kmph\nD. 17 Kmph\nE. 91 Kmph\n\n### Answer:\nLength = Speed * time\nSpeed = L/T\nS = 100/20\nS = 5 M/Sec\nSpeed= 5*18/5 (To convert M/Sec in to Kmph multiply by 18/5)\nSpeed = 18 Kmph\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a stream running at 2 Kmph, a motor boat goes 10 Km upstream and back again to the starting point in 55 minutes. Find the speed of motor boat in still water?\n\n### Options:\nA. 11\nB. 15\nC. 22\nD. 18\nE. 25\n\n### Answer:\nLet the speed of motor boat instill water be X kmph\nThen, speed in downstream = (X + 2) km\nand. speed in upstream = (X - 2) kmph\nTime taken to row 10km & back = (10/X+2,10/X-2)\n10/X+2 + 10/X-2 = 55/60\n11X2 - 240X - 44 = 0\n(X - 22)(11x + 2) = 0\nX = 22 or X = -2/11\nThen X = 22 kmph\nAnswer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nX, Y, and Z are consecutive numbers and X > Y > Z. Also, X + 3Y + 3Z = 5Y + 6. What is the value of Z?\n\n### Options:\nA. 2\nB. 3\nC. 4\nD. 5\nE. 6\n\n### Answer:\nIf X, Y, and Z are consecutive numbers and X > Y > Z, then Y = Z+1 and X = Z+2.\nX + 3Y + 3Z = 5Y + 6\nZ+2+3Z+3+3Z = 5Z+5+6\n2Z = 6\nZ = 3\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain company reported that the revenue on sales increased 60 % from 2000 to 2003, and increased 80 % from 2000 to 2005. What was the approximate percent increase in revenue for this store from 2003 to 2005?\n\n### Options:\nA. 50 %\nB. 40 %\nC. 35 %\nD. 32 %\nE. 13 %\n\n### Answer:\nAssume the revenue in 2000 to be 100. Then in 2003 it would be 160 and and in 2005 180, so from 2003 to 2005 it increased by (180-160)/160=20/160=13%\nAnswer: E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf x inches are cut from the length, l, of a rectangle and y inches are cut from the width, w, of the same rectangle, then which of the following correctly expresses the amount of the area of the original rectangle that was removed in terms of l, w, x, and y?\n\n### Options:\nA. xy\nB. lw \u2013 yx\nC. ly + wx \u2013 xy\nD. lx + wy \u2013 xy\nE. xy \u2013 lw \u2013 wy\n\n### Answer:\nInitial Area = l*w\nArea after cutting rectangle = (l-x)*(w-y)\nArea removed = Initial Area - Final Area = l*w - (l-x)*(w-y) = l*w - [l*w-x*w-l*y+x*y) = x*w+l*y-x*y\nAnswer: Option C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man spends 1/5 of his salary on food, 1/10 of his salary on house rent and 3/5 of his salary on clothes. He still has $18000 left with him. Find his salary.\n\n### Options:\nA. $100000\nB. $200000\nC. $140000\nD. $180000\nE. $250000\n\n### Answer:\nThe expenditure incurred on each item is expressed as part of the total amount (salary), so it is an independent activity.\nIn general for independent activities\n[1 \u2013 (x1/y1 + x2/y2 + x3/y3)] \u00d7 Total amount = Balance amount\n[1 \u2013 (1/5 + 1/10 + 3/5)] \u00d7 Total salary = $18000\n[1 \u2013 9/10] \u00d7 Total salary = $18000\nTherefore total salary = $18000 \u00d7 10 = $180000\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the greatest value of x such that 4^x is a factor of 21! ?\n\n### Options:\nA. 5\nB. 6\nC. 3\nD. 2\nE. 4\n\n### Answer:\nPretty simple, really.\nIf m = 6, then 4m = 24, which is 12x2, both of which are included in 21!\nSince 6 is the largest number here, its the answer.\nAnswer is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the amount on Rs.5000 in 2 years, the rate of interest being 4% per first year and 5% for the second year?\n\n### Options:\nA. 2328\nB. 2798\nC. 5460\nD. 2799\nE. 2771\n\n### Answer:\n5000 * 104/100 * 105/100 => 5460.Answer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf n and k are integers whose product is 2500, which of the following statements must be true?\n\n### Options:\nA. n+k>0\nB. n does not equal k\nC. Either n or k is a multiple of 10\nD. If n is even, then k is odd\nE. If n is odd, then k is even\n\n### Answer:\nIf n is odd and k is odd, then the product is odd.\nThe answer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA rectangular-shaped carpet that measures x feet by y feet is priced at $24. What is the cost of the carpet, in dollars per square yard? (1 square yard = 9 square feet)\n\n### Options:\nA. 180xy\nB. 216/(xy)\nC. 20xy\nD. 20xy/9\nE. xy/180\n\n### Answer:\nThe area of the carpet in feet is xy.\nThe area in square yards is xy / 9.\nThe price per square yard is 24 / (xy/9) = 216/(xy).\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nI am an odd number; take away an alphabet and I become even. What number am I?\n\n### Options:\nA. 6\nB. 8\nC. 9\nD. 3\nE. 7\n\n### Answer:\nE\n7 (SEVEN-S=EVEN)\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a number p is prime, and 2p+1 = q, where q is also prime, then the decimal expansion of 1/q will produce a decimal with q-1 digits. If this method produces a decimal with 166 digits, what is the units digit of the product of p and q\n\n### Options:\nA. 1\nB. 3\nC. 5\nD. 7\nE. 9\n\n### Answer:\n3/7 = 0.428571... (a repeating pattern one digit long)\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain list consists of 21 different numbers. If n is in the list and n is 4 times the average(arithmetic mean) of the other 20 numbers in the list, then n is what fraction U of the sum of the 21 numbers in the list?\n\n### Options:\nA. 1/20\nB. 1/6\nC. 1/5\nD. 4/21\nE. 5/21\n\n### Answer:\nThis is how I used to calculate which I think works pretty well:\nif you let the average of the 20 other numbers equal a, can you write this equation for sum of the list (S)\nn + 20a = S\nthe question tells us that\nn = 4a\nplug this back into the first equation and you get that the sum is 24a\n4a + 20a = 24a\ntherefore fraction U of n to the total would be\n4a/24a or 1/6\nanswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a trader sold two cars each at Rs. 325475 and gains 15% on the first and loses 15% on the second, then his profit or loss percent on the whole is?\n\n### Options:\nA. 1.44%\nB. 1.74%\nC. 1.84%\nD. 1.97%\nE. 2.25%\n\n### Answer:\nSP of each car is Rs. 325475, he gains 15% on first car and losses 15% on second car.\nIn this case, there will be loss and percentage of loss is given by\n= [(profit%)(loss%)]/100\n= (15)(15)/100 % = 1.44%\nAnswer:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAverage of all prime numbers between 35 to 50\n\n### Options:\nA. 42\nB. 37.8\nC. 39\nD. 39.8\nE. 40\n\n### Answer:\nExplanation:\nPrime numbers between 35 and 50 are:\n37, 41, 43, 47\nAverage of prime numbers between 35 to 50 will be\n(37+41+43+47 / 4)=168 / 4=42\nOption A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA tap can fill a tank in 12 hours. After half the tank is filled three more similar taps are opened. What is the total time taken to fill the tank completely?\n\n### Options:\nA. 13 hrs 30 mins\nB. 14 hrs 30 mins\nC. 15 hrs 30 mins\nD. 16 hrs 30 mins\nE. 17 hrs 30 mins\n\n### Answer:\nTime taken by one tap to fill the tank = 6 hrs.\nPart filled by the taps in 1 hour = 4 * 1/12 = 1/3\nRemaining part = 1 - 1/2 = 1/2\n1/3 : 1/2 :: 1 : x\nx = 1/2 * 1 * 3 = 1.5 hrs = 1 hrs 30 min\nSo, total time taken = 13 hrs 30 mins\nANSWER: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the least value of k. So that 123k578 is divisible by 11.\n\n### Options:\nA. 8\nB. 7\nC. 5\nD. 6\nE. 4\n\n### Answer:\nExplanation:\nThe Difference of the sum of the digits at odd place and the sum of the digits at even place of the number, is either 0 or a number divisible by 11.\n(1 + 3 + 5 + 8) - (2 + k + 7) = 17 - 9 - k = 8 - k\nTherefore if k = 8, then the value become zero.\nk = 8 is the least value\nso that 123k578 is divisible by 11.\nAnswer: Option A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a group of 6 boys and 4 girls, four children are to be selected. In how many different ways can they be selected?\n\n### Options:\nA. 159\nB. 194\nC. 210\nD. 209\nE. 166\n\n### Answer:\nOut of 10 students 4 children should to be selected.\nSo the combination will be 10C4.\n10C4=10!/6!*4!=10*9*8*7*6!/6!*(4*3*2*1)\n10C4=210\nThere are 210 differect possible ways to select 4 children out of 10 students.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA box contains 5 red, 4 blue, and 3 white balls. In how many ways can we select 4 balls such that at least 2 are red?\n\n### Options:\nA. 235\nB. 270\nC. 280\nD. 285\nE. 240\n\n### Answer:\nExplanation:\nYou decline to mention whether balls of the same color are identical. If they are, then you have only 99 ways to do so. Why? Two positions are dedicated to red. For the remaining two, you can have red, blue or white (all are sufficiently numerous to allow that) and so that's 3\u00d73=93\u00d73=9 ways.\nIf, on the other hand balls of the same color are non-identical, then you can select four balls of any color is (5+4+3/4)=495(5+4+34)=495 ways. No red ball is selected in (4+3/4)=35 ways. Exactly one red ball is selected in 5\u00d7(4+3/3)175 ways. Thus, you select at least two red balls in 495\u2212(35+175)=285 ways\nAnswer is D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA, B and C shared profits in ratio of 5 : 3 : 8. Theypartnered for 14months, 8months and 7months respectively. What was he ratio of their investments ?\n\n### Options:\nA. 10 : 49 : 45\nB. 20 : 49 : 64\nC. 12 : 21 : 64\nD. 20 : 29 : 64\nE. 30 : 29 : 63\n\n### Answer:\nSimply multiply profit sharing ratio with investment ratio to get investment amount ratio.\nLet X is the total investment\n\u00e2\u2021\u201914 x = 5\n\u00e2\u2021\u2019 8 x = 3\n\u00e2\u2021\u2019 7x = 8\n\u00e2\u2021\u2019 Final investment ratio = 12 : 21 : 64\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA polygon has 230 diagonals. How many sides does it have?\nSelf made\n\n### Options:\nA. 22\nB. 23\nC. 24\nD. 25\nE. 26\n\n### Answer:\nThe best way to solve this problem is to use the formula: An n sided polygon can have n*(n - 3)/2 diagonals\nn*(n - 3)/2 = 230\nn*(n - 3) = 460\nSubstitute n from the answer choices. n = 23\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTriangle STV has sides ST = TV = 26, and SV = 20. What is the area?\n\n### Options:\nA. 160\nB. 180\nC. 200\nD. 220\nE. 240\n\n### Answer:\nLet the base B of the triangle be SV = 20. Then we need to find the height H.\nH^2 = 26^2 - 10^2 = 576 and then H = 24.\nThe area is (1/2)*B*H = 10*24 = 240\nThe answer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the probability of rolling four six-sided dice, and getting a different number on each die?\n\n### Options:\nA. 1/12\nB. 1/3\nC. 4/9\nD. 5/9\nE. 5/13\n\n### Answer:\nMAGOOSHOFFICIAL SOLUTION\nFor the first die, we can roll any one of six numbers. For the second die, we can roll any number save for the number we rolled on the first die, giving us 5 possibilities. For the third die, we can roll four different numbers (we can\u2019t roll the number we rolled on the first or second die.\n6 x 5 x 4 x 3 = 360 possibilities out of 216 total possibilities. (For total possibilities we get 6 x 6 x 6x6 = 1296).\n360/1296 = 5/13\nAnswer: E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWorldwide production of motor vehicles was 3.9 million vehicles in 1946 and 65.4 million in 1987. Of the following, which is closest to the average (arithmetic mean) annual increase, in millions, in worldwide production of motor vehicles during this period?\n\n### Options:\nA. 0.08\nB. 1.0\nC. 1.1\nD. 1.5\nE. 41.8\n\n### Answer:\nChange in production of motor vehicles = 65.4 - 3.9 = 61.5 million in 41 years (1987 - 1946)\naverage increase per year = 61.5/41 = 1.5 million (apporx.)\nAnswer (D)\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the average (arithmetic mean) of a and b is 45 and the average of b and c is 80, what is the value of c \u00e2\u02c6\u2019 a?\n\n### Options:\nA. 25\nB. 70\nC. 90\nD. 140\nE. It cannot be determined from the information given\n\n### Answer:\nthe arithmetic mean of a and b =(a+b)/2=45 -- a+b=90 --1\nsimilarly for b+c=160 --2\nsubtracting 1 from 2 we have\nc-a=70;\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAt what time between 4 and 5 o\u2019clock the hands are in opposite direction?\n\n### Options:\nA. 3 2/11 minutes past 4 o\u2019clock\nB. 3 5/11 minutes past 4 o\u2019clock\nC. 10 10/11 minutes past 4 o\u2019clock\nD. 10 2/11 minutes past 4 o\u2019clock\nE. 54 6/11 mintues past 4'0 clock\n\n### Answer:\nTo be in opposite directions, they must be 30 min. spaces apart.\nMinute hand will have to gain 50 min. spaces.\n55 min. spaces are gained in 60 min.\n50 min. spaces are gained in 60/55 x 50 min. or 54 6/11 min. Required time = 54 6/11 min. past 4 o\u2019clock\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn 19 years time the combined ages of my three brothers will be 94. What will it be in nine years time?\n\n### Options:\nA. 45\nB. 62\nC. 82\nD. 97\nE. 56\n\n### Answer:\nC\n82\nCombined age in 9 years time will 94 \u2013 (3 x (13 \u2013 9))\n94 \u2013 12 = 82.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 213 \u00d7 16 = 3408, then 1.6 \u00d7 213.0 is equal to :\n\n### Options:\nA. 0.3408\nB. 3.408\nC. 34.08\nD. 340.8\nE. None of these\n\n### Answer:\nSolution\n1.6 \u00d7 21.3 = (16/10x 213)= (16x 213/10) = 3408/10 = 340.8. Answer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 21520 books need to be placed in boxes and each box can contain at most 9 books. How many books will be in the last unfilled box?\n\n### Options:\nA. 9 books\nB. 8 books\nC. 1 book\nD. 4 books\nE. 5 books\n\n### Answer:\nThe number of books that can be placed in boxes of 9 books is the first number that is divisible by 9 that occurs before 21520.\nIn order to divide the sum in 9 parts, the amount must be divisible by 9\nDivisibility rule of 9: The sum of the digits must be divisible by 9\nSum of digits of 21520 = 10 and 9 is divisible by 9.\nHence, we need to remove 1 to this number for it to be divisible by 9\nCorrect Option: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf x 2 \u2013 y 2 = 101, find the value of x 2 + y 2 ,\ngiven that x and y are natural numbers.\n\n### Options:\nA. 5100\nB. 5101\nC. 5102\nD. 5103\nE. 5104\n\n### Answer:\nx^2 \u2013 y^2 = 101\n=> (x+y)*(x-y) = 101*1\nx+y = 101\nx-y = 1\nso, x = 51, y = 50\n(x^2 + y^2) = 51^2 + 50^2 = 5101\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man buys oranges at Rs 5 a dozen and an equal number at Rs 4 a dozen. He sells them at Rs 5.50 a dozen and makes a profit of Rs 50. How many oranges does he buy?\n\n### Options:\nA. 30 dozens\nB. 40 dozens\nC. 50 dozens\nD. 60 dozens\nE. 70 dozens\n\n### Answer:\nExplanation:\nCost Price of 2 dozen oranges Rs. (5 + 4) = Rs. 9.\nSell price of 2 dozen oranges = Rs. 11.\nIf profit is Rs 2, oranges bought = 2 dozen.\nIf profit is Rs. 50, oranges bought = (2/2) * 50 dozens = 50 dozens. Answer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the CP of Rs 100 stock at 7 discount, with 1/5% brokerage?\n\n### Options:\nA. 93.9\nB. 96.3\nC. 93.2\nD. 96.7\nE. 96.21\n\n### Answer:\nExplanation:\nUse the formula,\nCP= 100 \u00e2\u20ac\u201c discount + brokerage%\nCP= 100-7+1/5\n93.2\nThus the CP is Rs 93.2.\nANSWER: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA factory produces x widgets per day. The factory's fixed costs are $8000 per day. The price per widget is $80 and the variable costs are $20 per widget. How many widgets need to be produced for profits of $5000 a day?\n\n### Options:\nA. 42.33\nB. 90.33\nC. 168\nD. 216.67\nE. 400\n\n### Answer:\nprofits=5000=60x-8000 --> x=216.67\nAnswer D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe length and breadth of a rectangle is increased by 11% and 22% respectively. What is the increase in the area?\n\n### Options:\nA. 35.22\nB. 33.52\nC. 35.42\nD. 36.22\nE. 38.42\n\n### Answer:\n100*100=10000\n111*122=13542\n------------\n3542\n10000-------3542\n100----------35.42\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe present population of a town is 4320. Population increase rate is 20% p.a. Find the population of town before 2 years?\n\n### Options:\nA. 2500\nB. 2100\nC. 3500\nD. 3000\nE. 2050\n\n### Answer:\nP = 4320\nR = 20%\nRequired population of town = P/(1 + R/100)^T\n= 4320/(1 + 20/100)^2\n= 4320/(6/5)^2\n= 3000(approximately)\nAnswer is D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA wheel that has 6 cogs is meshed with a larger wheel of 14 cogs. When the smaller wheel has made 21 revolutions, then the number of revolutions mad by the larger wheel is:\n\n### Options:\nA. 4\nB. 9\nC. 12\nD. 21\nE. 35\n\n### Answer:\nMore cogs less revolution,..\nso\n6:14::x:21\n(21*6)/14=9\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf $20,000 interest is invested in x percent simple annual interest for n years, which of the following represents the total amount of interest, in dollars, that will be earned by this investment in the n years?\n\n### Options:\nA. 10,000(x^n)\nB. 20,000n(x/100)\nC. 20,000(x/100)^n\nD. 10,000(1 + x/100)^n\nE. 10,000n(1 + x/100)\n\n### Answer:\nPrincipal * no.of years * percentage of interest\nAnswer : B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\ntwo friends deepak and rajeev have agreed to meet at a definite spot on a particular day between 9pm and 10pm. the first person to come waits for some time and leaves.If the other one does not turn up by that time.If Deepak comes first,he waits for 45minutes and if Rajeev comes first,he waits for 15minutes.What is the probability of meeting between Deepak and rajeev if their arrival times are independent of eachother and each person arrives during the indicated period at random?\n\n### Options:\nA. 3/4\nB. 11/16\nC. 7/8\nD. 3/16\nE. 3/15\n\n### Answer:\ndeepak : 45/60 = 3/4\nrajeev : 15/60= 1/4\nas these are independent events\ntotal probability = (3/4)*(1/4)\n= 3/16\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the area, diameter = 10m.\n\n### Options:\nA. 78.24 square meter\nB. 78.57 square meter\nC. 78.26 square meter\nD. 24.24 square meter\nE. 24.43 square meter\n\n### Answer:\nDiameter = 10 meter.\nRadius = diameter/2.\n= 10/2.\n= 5 meter.\nArea of a circle = \u00cf\u20acr2.\nHere, pi (\u00cf\u20ac) = 3.14 meter, radius (r) = 5.\nArea of a circle = 3.14 \u00c3\u2014 5 \u00c3\u2014 5..\n= 3.14 \u00c3\u2014 25.\n= 78.57 square meter ANSWER : B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe smallest number when increased by \" 1 \" is exactly divisible by 6,18,36,48, 60 is:\n\n### Options:\nA. 724\nB. 721\nC. 720\nD. 719\nE. 700\n\n### Answer:\nLCM = 720\n720 - 1 = 719\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 3g + 1 < 2g < 9 - g, which of the following must be true?\nI. -1 < g < 3\nII. g < -1\nIII. g < 3\n\n### Options:\nA. II only\nB. III only\nC. I and II only\nD. II and III only\nE. I, II and III\n\n### Answer:\nJust try plugging g in a number like 0 or 1, and you'll quickly find that the inequality doesn't hold.\nSo you can immediately cross out any answers with I or III, leaving just (A) II only.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nBy investing Rs. 1620 in 8% stock, Michael earns Rs. 135. The stock is then quoted at:\n\n### Options:\nA. Rs 96\nB. Rs 100\nC. Rs 150\nD. Rs 160\nE. Rs 200\n\n### Answer:\nto earn Rs 135 investment = Rs 1620\nto earn Rs 8 investment =>1620/135*8=96\nANSWER A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf integers w and b are distinct factors of 30, which of the following CANNOT be a factor of 30?\nI. wb + b^2\nII. (w+ b)^2\nIII. w + b\n\n### Options:\nA. I only\nB. II only\nC. III only\nD. I and II only\nE. I, II, and III\n\n### Answer:\nFactors of 30 are: 1, 2, 3, 5, 6, 10, 15, and 30.\nI. wb + b^2 --> if w=1 and b=2 then wb + b^2=6, which is a factor of 30. OK;\nII. (w + b)^2 --> (w + b)^2 is a perfect square, no perfect square (but 1) is a factor of 30. DISCARD;\nIII. w + b --> if w=1 and b=2 then w + b=3, which is a factor of 30. OK.\nAnswer: B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA sum of Rs. 1360 has been divided among A, B and C such that A gets of what B gets and B gets of what C gets. B\u2019s share is:\n\n### Options:\nA. Rs. 120\nB. Rs. 160\nC. Rs. 240\nD. Rs. 300\nE. None\n\n### Answer:\nEXPLANATION\nLet C\u2019s share = Rs. x\nThen, B\u2019s share = Rs. x/4 , A\u2019s share = Rs. (2/3 x x/4 ) = Rs. x/6\n=x/6 + x/4 + x = 13660\n=> 17x/12 = 13660\n=> 13660 x 12/ 17 = Rs.960\nHence, B\u2019s share = Rs. (960/4) = Rs. 240.\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAt Jefferson Elementary School, the number of teachers and students (kindergarten through sixth grade) totals 510. The ratio of students to teachers is 16 to 1. Kindergarten students make up 1/10 of the student population and fifth and sixth graders account for 1/3 of the remainder. Students in first and second grades account for 1/4 of all the students. If there are an equal number of students in the third and fourth grades, then the number of students in third grade is how many greater or fewer than the number of students in kindergarten?\n\n### Options:\nA. 20 greater\nB. 17 fewer\nC. 28 fewer\nD. 36 fewer\nE. 44 fewer\n\n### Answer:\nSoln>> from the given ratio of 16:1 u can derive that ter are 480 students\nKG= 1/10 * 480 =48\n5th and 6th graders = 1/3 * 384= 128 (1/3 of remainder)\n1st and 2nd grade = 1/4 * 480 =120 ( 1/4 of all students)\nequal number of students in 3rd and 4th => 480 - 344= 136 and 136/2=68 each since equal number\n(344 is the sum of remaining students)\nthus 48-68 =20>>> therfore answer is 20 greater\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are 81 people in a certain community who belong to the local golf club, tennis club or both clubs. If twice as many people belong to the tennis club as belong to the golf club, what could be the number of people who belong to both clubs?\n\n### Options:\nA. 4\nB. 7\nC. 27\nD. 21\nE. 37\n\n### Answer:\nlet's find the range of Both and hence the range of x. Minimum value of Both: Say there is no overlap in the two sets. 81 = x + 2x\rx = 27\rIn this case Both = 0 Maximum value of Both: Say there is maximum overlap between the two sets. One set has x so it could be a subset of the set 2x.\r81 = 2x\rBut x cannot be a decimal so (x-1) could be the overlap (= Both) and there could be 1 in only the Golf club.\r81 = 2 x + x - (x - 1)\rx = 40\rIn this case Both = 40 - 1 = 39 So Both lies between 0 and 39 Only option (E) satisfies this condition. ANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe present worth of a sum due sometime hence is Rs. 576 and the banker\u2019s gain is Rs. 16. The true discount is :\n\n### Options:\nA. 36\nB. 52\nC. 66\nD. 96\nE. None\n\n### Answer:\nSol.\nT.D. = \u221aP.W. * B.G. = \u221a576 * 16 = 96.\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe Royals softball team played 75 games and won 55 of them. What percent of the games did they lose? (round to the nearest tenth)\n\n### Options:\nA. 26.7% games lost\nB. 27.7% games lost\nC. 25.7% games lost\nD. 20.7% games lost\nE. 22.7% games lost\n\n### Answer:\nTotal 100%=75\nWon=55\nLost=20\n75-55\n=20\nx/100=20/75\nMultiply the opposites:\n100 x 20 = 2000\nDivide by the remaining number:\n26.667/2000.000\n75\n26.7% games lost (rounded to tenth)\ncorrect answer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn Company B, the total monthly payroll for the 20 factory workers is $36,000 and the total monthly payroll for the 50 office workers is $110,000. By how much does the average (arithmetic mean) monthly salary of an office worker exceed that of a factory worker in this company?\n\n### Options:\nA. $400\nB. $450\nC. $500\nD. $550\nE. $600\n\n### Answer:\nThe average monthly salary of a factory worker is: $36,000 / 20 = $1800.\nThe average monthly salary of an office worker is: $110,000 / 50 = $2200.\nThe difference in average salary is: $2200 - $1800 = $400.\nThe answer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA seller of used cars has 12 cars to sell and each of his clients selected 4 cars that he liked most. If each car was selected exactly thrice, how many clients visited the garage?\n\n### Options:\nA. 9\nB. 10\nC. 12\nD. 14\nE. 16\n\n### Answer:\nIfNo caris selected more than once then the number of clients = 12/4 = 3\nBut since every car is being selected three times so No. of Clients must be thrice as well =3*3 = 9\nAnswer: option A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is:\n\n### Options:\nA. 200 m\nB. 225 m\nC. 245 m\nD. 250 m\nE. 350 m\n\n### Answer:\nExplanation:\nSpeed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (130 + x)/30 = 25/2 => 2(130 + x) = 750 => x = 245 m.\nANSWER IS C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nPeter invests $100,000 in an account that pays 10% annual interest: the interest is paid once, at the end of the year. Martha invests $100,000 in an account that pays 10% annual interest, compounding monthly at the end of each month. At the end of one full year, compared to Peter's account, approximately how much more does Martha\u2019s account have?\n\n### Options:\nA. $471.31\nB. $4713.10\nC. $47.13\nD. $4.71\nE. Zero\n\n### Answer:\nPeters interest= $100,000*0.10 = $10,000 or $833.33 each month.\nMartha\u2019s interest, 10%/12 = 0.833% each month:\nFor the 1st month = $100,000*0.00833 = $833.33;\nFor the 2nd month = $833.33 + 0.833% of 833.33 = ~$840, so we would have interest earned on interest (very small amount);\nFor the 3rd month = $840 + 0.833% of 840 = ~$847;\nFor the 4th month = $847 + 0.833% of 847 = ~$854;\n...\nFor the 12th month = $905 + 0.833% of 905 = ~$912.\nThe difference between Peters interest and Martha\u2019s interest = ~(7 + 14 + ... + 77) = $462.\nAnswer: A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOf the 800 employees of Company X, 90 percent have been with the company for at least ten years. If y of theselong-termmembers were to retire and no other employee changes were to occur, what value of y would reduce the percent oflong-termemployees in the company to 60 percent ?\n\n### Options:\nA. 200\nB. 160\nC. 112\nD. 80\nE. 600\n\n### Answer:\nThe # oflong-termemployees is 90%*800=720.\nAfter y of them retire new # oflong-termemployees would become 720-y.\nTotal # of employees would become 800-y.\nWe want 720-y to be 60% of 800-y --> 720-y=(800 -y)*60% --> y = 600.\nAnswer: E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA, B and C started a business A's investment is 2 times of B's investment is 5 times of C's investment. Find the profit of B in the total profit of Rs. 1600.\n\n### Options:\nA. Rs. 25600\nB. Rs. 8500\nC. Rs. 7200\nD. Rs. 500\nE. None of these\n\n### Answer:\nExplanation:\nA = 2B and B = 5C\n=> A : B = 2:1 and B : C = 5 : 1\n=> A : B : C = 10 : 5 : 1\nRatio of capitals of A, B and C = 10 : 5 : 1\nB's share = Rs.[(5/16) \u00d7 1600] = Rs. 500\nAnswer: Option D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA starts business with Rs.3500 and after 9 months, B joins with A as his partner. After a year, the profit is divided in the ratio 2 : 3. What is B\u00e2\u20ac\u2122s contribution in the Capital ?\n\n### Options:\nA. 24887\nB. 20778\nC. 23788\nD. 21000\nE. 2811\n\n### Answer:\nExplanation:\nA invested Rs.3500 for 12 months.\nLet B joined with investment x. And he invested for 12 - 9 = 3 months.\nSo there profit ratio = (3500 \u00c3\u2014 12) : (3x) = 2 : 3\n\u00e2\u2021\u2019 x = 21000\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFor what range of values of 'x' will the inequality 15x - 2/x > 1?\n\n### Options:\nA. x > 0.4\nB. x < 1/3\nC. -1/3 < x < 0.4, x > 15/2\nD. -1/3 < x and x< 0, x > 2/5\nE. x < -1/3 and x > 2/5\n\n### Answer:\nIn Case 1 where x > 0, I agree. I calculated x > (-1/3) and x > 2/5, and because x > 0, it must be x > 2/5.\nIn Case 2 where x < 0, I don't understand why you say that the range must be x > -1/3 and x < 0, since the values that satisfy the inequality 15x^2 - x - 2 < 0show that x < -1/3 and x < 2/5.\nI have the same doubt. Shouldn't the answer be D?\n____________\nThe answer IS D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train 300 m long can cross an electric pole in 30 sec and then find the speed of the train?\n\n### Options:\nA. 76 Kmph\nB. 54 Kmph\nC. 72 Kmph\nD. 36 Kmph\nE. 91 Kmph\n\n### Answer:\nLength = Speed * time\nSpeed = L/T\nS = 300/30\nS = 10 M/Sec\nSpeed= 10*18/5 (To convert M/Sec in to Kmph multiply by 18/5)\nSpeed = 36 Kmph\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe sum of all the integers a such that -26 < a < 24 is\n\n### Options:\nA. 0\nB. -2\nC. -25\nD. -49\nE. -51\n\n### Answer:\nEasy one -\n-25, -24, -23,-22,...... -1,0, 1, 2...., 22, 23\nCancel everyhitng and we're left with - -25 and -24 a = -49.\nD is the answer.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA polling company surveyed a certain country, and it found that 35% of that country\u2019s registered voters had an unfavorable impression of both of that state\u2019s major political parties and that 20% had a favorable impression only of Party R. If one registered voter has a favorable impression of both parties for every two registered voters who have a favorable impression only of Party B, then what percentage of the country\u2019s registered voters have a favorable impression of both parties (assuming that respondents to the poll were given a choice between favorable and unfavorable impressions only)?\n\n### Options:\nA. 15\nB. 20\nC. 30\nD. 35\nE. 45\n\n### Answer:\nS=100\nnot( R and B ) =35\nonly R=20\n(R and B)/B=1/2\nlet ( R and B ) =x\nonly B =2x\nso now, 20+35+x+2x=100\nx= 15\nA ans\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nI chose a number and divide it by 9. Then I subtracted 100 from the result and got 10. What was the number I chose?\n\n### Options:\nA. 600\nB. 700\nC. 990\nD. 900\nE. None\n\n### Answer:\nSolution:\nLet x be the number I chose, then\nx/9\u00e2\u02c6\u2019100=10\nx/9=110\nx=990\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf grapes are 92% water and raisins are 20% water, then how much did a quantity of raisins, which currently weighs 13 pounds, weigh when all the raisins were grapes? (Assume that the only difference between their raisin-weight and their grape-weight is water that evaporated during their transformation.)\n\n### Options:\nA. 25 pounds\nB. 46 pounds\nC. 92 pounds\nD. 130 pounds\nE. 146 pounds\n\n### Answer:\nSince only water evaporates, then the weight of pulp (non-water) in grapes and raisins is the same. Thus 0.08*{weight of grapes}=0.8*{weight of raisins} --> 0.08x = 0.8*13 --> x = 130.\nAnswer: D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man can row his boat with the stream at 26 km/h and against the stream in 4 km/h. The man's rate is?\n\n### Options:\nA. 1 kmph\nB. 7 kmph\nC. 98 kmph\nD. 11 kmph\nE. 4 kmph\n\n### Answer:\nDS = 26\nUS = 4\nS = ?\nS = (26 - 4)/2 = 11 kmph\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSheila works 8 hours per day on Monday, Wednesday and Friday, and 6 hours per day on Tuesday and Thursday. She does not work on Saturday and Sunday. She earns $360 per week. How much does she earn in dollars per hour?\n\n### Options:\nA. 11\nB. 10\nC. 9\nD. 8\nE. 7\n\n### Answer:\nLet Sheila earn x dollars per hour\nSo, on Monday, Wednesday and Friday , she earns 8x each\nAnd, on Tuesday and Thursday, she earns 6x each\nIn total , over the week she should earn, 3(8x) + 2(6x) = 36x\nShe earns $360 per week\n36x =360\nx =10\nCorrect Option : B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n4, 12, 48, (...)\n\n### Options:\nA. 7620\nB. 10080\nC. 6200\nD. 10020\nE. 240\n\n### Answer:\nExplanation :\nGo on multiplying the given numbers by 3, 4, 5, 6, 7\nAnswer : Option E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat will come in place of the x in the following Number series? 73205, 6655, 605, 55, x\n\n### Options:\nA. 32564\nB. 73205\nC. 62343\nD. 54756\nE. 78564\n\n### Answer:\n(B)\n5 x 11 = 55, 55 x 11 = 605, 605 x 11 = 6655, 6655 x 11 = 73205\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n1 blue dice and 2 red Dice are thrown....what is the probability that the no. appeared on blue dice is always greater than both the no. appeared on the 2 red dice..\n\n### Options:\nA. 55/216\nB. 56/216\nC. 57/216\nD. 54/216\nE. 53/216\n\n### Answer:\nif the no. on blue dice is 2 then 2 red dice can take (1,1) value = 1^2\nif the no. on blue dice is 3 then 2 red dice can take (1,1)(1,2)(2,1)(2,2) = 2^2\nif the no. on blue dice is 4 then 2 red dice can take (1,1)(1,2)(2,1)(2,2)(1,3)(2,3)(3,2)(3,1)(3,3) = 3^2\nSimilarly, if the no. on blue dice is 5 then 2 red dice can take = 4^2\nand if the no. on blue dice is 6 then 2 red dice can take = 5^2\ntherefor, probability = total no. of favourable outcome/total no. of possible outcome\n= 1^2+2^2+3^2+4^2+5^2 / 216\n= 55/216\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nBenny goes to the market for buying some apples to be distributed between her nine kids equally.She takes 420 dollars with her .The cost of each apple is 4 dollars .How many apples does she buy to share them equally between her five kids?\n\n### Options:\nA. 8\nB. 9\nC. 3\nD. 21\nE. 10\n\n### Answer:\ncost of each apple = 4 dollars\nApples that Benny can buy with the amount she has=420/4 = 90.\nApples that each kid gets evenly = 105/5 =21 Apples.\nSo the answer is D=21\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA money lender lent a total of $1700 to two of his customers. He charged at the rate of 5%p.a. to one of them and 6% p.a. to the other. If he earned an average of 5.67% on $1700, how much did he lend to each of the two customers?\n\n### Options:\nA. 700; 1100\nB. 1139; 561\nC. 1000; 800\nD. 1200; 800\nE. None of the above\n\n### Answer:\nThe method given above is the one given in the book.\nHowever the method I used was\n(1*x*5)/100 + (1700-x)*6/100 = 1700*5.67/100\nSimplifying we get x=561\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOn a certain transatlantic crossing, 25 percent of a ship's passengers held round-trip tickets and also took their cars aboard the ship. If 60 percent of the passengers with round-trip tickets did not take their cars aboard the ship, what percent of the ship's passengers held round-trip tickets?\n\n### Options:\nA. 33 1/3%\nB. 40%\nC. 50%\nD. 62.5%\nE. 66 2/3%\n\n### Answer:\nOn a certain transatlantic crossing, 20 percent of a ship\u2019s passengers held round-trip tickets and also took their cars abroad the ship. If 60 percent of the passengers with round-trip tickets did not take their cars abroad the ship, what percent of the ship\u2019s passengers held round-trip tickets?\nSolution: Let total number of passengers be 100\nAccording to Q stem 40% of passengers who had round-trip tics have taken cars - let number of passengers with round trip be X then\n40% of X = 25 => X= 62.5.\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the units' digit of the following expression (11)^5*(1)^3*(21)^5?\n\n### Options:\nA. 0\nB. 1\nC. 3\nD. 5\nE. 9\n\n### Answer:\nWe do not have to do any calculations or find units digit of remaining numbers...\nall three terms - 11,1,21 - are ODD and since the PRODUCT contains 1, the units digit of the product will remain 1\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are 5 bags three of which each contains 5 white and 2 black balls, and remaining 2 bags each contains 1 white and 4 black ball; a white ball has been drawn, find the chance that it came from second group.\n\n### Options:\nA. 2/7\nB. 6/35\nC. 8/25\nD. 14/89\nE. 3/5\n\n### Answer:\nChances of selecting a white ball from group 1: 2/7----------------------Chances of selecting a white ball from group 2: 4/5\nThus combined probability of section of white ball from group 1:\n3/5 x 5/7 = 3/7\nThus combined probability of section of white ball from group 2:\n2/5 x 1/5 = 2/25\nOut of these chances, chance of occurrence of first case : (2/25) / (3/7 + 2/25) = 14/89\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a, b and c are even integers, which of the following could be the value of a^2 + b^2 + c^2?\n\n### Options:\nA. a)36\nB. b)38\nC. c)42\nD. d)46\nE. e)50\n\n### Answer:\na, b and c are even integers which means that, supposing that x, y and z are integers, then a=2x, b=2y and c=2z\nTherefore we have: a^2+b^2+c^2=2^2*x^2+2^2*y+2^2*z=4x^2+4y^2+4z^2=4(x^2+y^2+z^2).\nWhich means that the total a^2+b^2+c^2 must be divisible by 4.\nThe only choice which is divisible by 4 is: A)\n36=4^2+4^2+2^2\nAnswer: A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn honor of the year 2012, a donor has purchased 2016 books to be distributed evenly among the elementary schools in a certain school district. If each school must receive the same number of books, and there are to be no books remaining, which of the following is NOT a number of books that each school could receive?\n\n### Options:\nA. 18\nB. 36\nC. 42\nD. 51\nE. 56\n\n### Answer:\nAll options other than 'D' are factors of 2012. Hence, 'D' is the answer\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe side of a cube is 8 m, Find the voiume?\n\n### Options:\nA. 515\nB. 509\nC. 502\nD. 508\nE. 512\n\n### Answer:\nCube Volume = a(power)3\na(power)3 = 8(power)3\n= 512 m(power)3.\nAnswer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOf the 200 employees in a certain company, 30 percent will be relocated to City X and the remaining 70 percent will be relocated to City Y. However, 40 percent of the employees prefer City Y and 60 percent prefer City X. What is the highest possible number of employees who will be relocated to the city they prefer?\n\n### Options:\nA. 115\nB. 120\nC. 140\nD. 152\nE. 165\n\n### Answer:\n120 prefer X (Group 1);\n80 prefer Y (Group 2).\nCity Y needs 140 people: letall 80 who prefer Y (entire Group 2) be relocated there, the rest 60 will be those who prefer X from Group 1;\nCity X needs 60 people: 120-60=60 from Group 1 will be relocated to X, which they prefer.\nSo, the highest possible number of employees who will be relocated to the city they prefer is 80+60=140.\nAnswer: C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nStatement: Put thechild in school at the age of 5. Assumptions: At that age the child reaches appropriate level of development and is ready to learn. The schools do not admit children after 6years of age.\n\n### Options:\nA. Only assumption I is implicit\nB. Only assumption II is implicit\nC. Either I or II is implicit\nD. Neither I nor II is implicit\nE. Both I and II are implicit\n\n### Answer:\nSince the statement talks of putting the child in school at the age of 5, it means that the child is mentally prepared for the same at this age. So, I is implicit. But nothing about admission after 6 years of age is mentioned in the statement. So, II is not implicit.\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe dimensions of a room are 25 feet * 15 feet * 12 feet. What is the cost of white washing the four walls of the room at Rs. 4 per square feet if there is one door of dimensions 6 feet * 3 feet and three WINDOWS of dimensions 4 feet * 3 feet each?\n\n### Options:\nA. 4000\nB. 3624\nC. 5673\nD. 4530\nE. 4566\n\n### Answer:\nArea of the four walls = 2h(l + b)\nSince there are doors and WINDOWS, area of the walls = 2 * 12 (15 + 25) - (6 * 3) - 3(4 * 3) = 906 sq.ft.\nTotal cost = 906 * 4 = Rs. 3624\nAnswer: Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOn the number line, if x is halfway between -6 and 4, and if y is halfway between -2 and 6, what number is halfway between x and y?\n\n### Options:\nA. -2.5\nB. -1.5\nC. -0.5\nD. 0.5\nE. 1.5\n\n### Answer:\nx= -1 and y = 2.\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain number when divided by 80 leaves a remainder 25, what is the remainder if the same no.be divided by 15?\n\n### Options:\nA. 4\nB. 5\nC. 6\nD. 7\nE. 9\n\n### Answer:\nExplanation:\n80 + 25 = 105/15 = 7 (Remainder)\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJohn works at a science lab that conducts experiments on bacteria. The population of the bacteria multiplies at a constant rate, and his job is to notate the population of a certain group of bacteria each hour. At 1 p.m. on a certain day, he noted that the population was 1,000 and then he left the lab. He returned in time to take a reading at 4 p.m., by which point the population had grown to 216,000. Now he has to fill in the missing data for 2 p.m. and 3 p.m. What was the population at 3 p.m.?\n\n### Options:\nA. 72,000\nB. 48,000\nC. 50,000\nD. 36,000\nE. 40,000\n\n### Answer:\nlet the rate be x, then population of the bacteria after each hour can be given as 1000, 1000x, 1000(x^2), 1000(x^3)\nnow population at 4pm =216,000\nthus we have 1000(x^3) = 216,000 =216\nthus x=6\ntherefore population at 3pm = 1000(36) = 36,000\nAnswer : D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAn amount of money is to be divided between P, Q and R in the ratio of 3:7:12. If the difference between the shares of P and Q is Rs.2800, what will be the difference between Q and R's share?\n\n### Options:\nA. 2788\nB. 3500\nC. 7282\nD. 2782\nE. 2729\n\n### Answer:\n4 --- 2800\n5 --- ? => 3500\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFor a party 240 guests were invited.Contracted have gained 12.5% profit but 30 guest were absent.He charged same cost , lost 100 rs. what is the meal cost?\n\n### Options:\nA. 20/3\nB. 80/3\nC. 10/3\nD. 40/3\nE. 50/3\n\n### Answer:\nLet Cost of one meal be x.\nHence, C.P. of 240 meals = 240 x.\nSince contractor gains 12.5 % profit therefore\ntotal selling price = 240x + 240*12.5/100 x\n= 270x.\nNow 30 guest were absent.\nTherefore C.P will remain same = 240x\nAnd new S.P for 210 guest = (270/240 ) *\n210 x\nIn this case he incurrs a loss of Rs 100.\n240x - (9/8) x * 210 = 100\nx=80/3.\nSo, cost of one meal is Rs. 80/3.\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf log 27 = 1.437, then the value of log 9 is:\n\n### Options:\nA. 0.934\nB. 0.945\nC. 0.954\nD. 0.958\nE. 0.998\n\n### Answer:\nlog 27 = 1.437\nlog (3cube ) = 1.437\n3 log 3 = 1.437\nlog 3 = 0.479\nlog 9 = log(3square ) = 2 log 3 = (2 x 0.479) = 0.958.\nAnswer: Option D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many numbers between 0 and 1670 have a prime tens digit and a prime units digit?\n\n### Options:\nA. 268\nB. 272\nC. 202\nD. 112\nE. 262\n\n### Answer:\nThere are 4 single digit prime numbers: 2, 3, 5 and 7. Hence, last two digits (tens and units) can take 4*4=16 different values: 22, 23, ..., 77.\nSo, in each hundred there are 16 such numbers. In 17 hundreds there will be 17*16=272 such numbers, but 4 out of them will be more than 1670, namely: 1672, 1673, 1675 and 1677. Which means that there are 272-4=268 numbers between 0 and 1670 which have a prime tens digit and a prime units digit.\nAnswer: A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRam and Shakil run a race of 2000m. First Ram gives Shakil a start of 200m and beats him by 1 minute.Next Ram gives shakil a start of 6 min and is beaten by 1000 meters . Find the time in minutes in which Ram and Shakil can run the race seperately.\n\n### Options:\nA. 12 , 18\nB. 8 , 10\nC. 18 , 20\nD. 20 , 25\nE. None of these\n\n### Answer:\nExplanation :\nLet speed of ram and shakil be x and y resp.\nCase 1 : Ram gives a start of 200m and beats Shakil by 1 minute.\n2000/x - 1800/y= -60\n2000/x= 1800/y -60---------------------(1)\nCase2: Ram gives Shakil a start of 6 min and is beaten by 1000 meters\ndistance travelled by shakil in 6 minutes= (6*60*y) meters = 360y meters\n1000/x = (2000- 360y)/y------------------(2)\nSolve equation 1 and 2 to obtain x and y\nAnswer is x = 8 minutes, y = 10 minutes\nHence (B) is the corret answer.\nAnswer : B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a*b denotes the greatest common divisor of a and b, then ((16*20)*(18*24)) = ?\n\n### Options:\nA. 24\nB. 12\nC. 6\nD. 4\nE. 2\n\n### Answer:\nThe greatest common divisor of 16 and 20 is 4. Hence 16*20 = 4 (note that * here denotes the function not multiplication).\nThe greatest common divisor of 18 and 24 is 6. Hence 18*24 = 6.\nHence ((16*20)*(18*24)) = 4*6.\nThe greatest common divisor of 4 and 6 is 2.\nAnswer; E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe number of sequences in which 7 players can throw a ball, so that the youngest player may not be the last is -.\n\n### Options:\nA. 1879\nB. 7899\nC. 4320\nD. 1680\nE. 1692\n\n### Answer:\nx Not younger_______ \u2191\nThe last ball can be thrown by any of the remaining 6 players. The first 6 players can throw the ball in \u2076P\u2086 ways.\nThe required number of ways = 6(6!)\n= 4320\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nE is the set of the first n positive odd numbers, where n is a positive integer. Given that n > k, where k is also a positive integer, x is the maximum value of the sum of k distinct members of E, and y is the minimum value of the sum of k distinct members of E, what is x + y?\n\n### Options:\nA. kn\nB. kn + k^2\nC. kn + 2k^2\nD. 2kn \u2013 k^2\nE. 2kn\n\n### Answer:\nProbably the easiest way to solve this question would be to assume some values for n and k.\nSay n=3, so E, the set of the first n positive odd numbers would be: E={1, 3, 5};\nSay k=1, so E, the maximum value of the sum of K distinct members of Z would simply be 5. Similarly, Y, the minimum value of the sum of K distinct members of E would simply be 1.\nX+Y=5+1=6.\nNow, substitute n=3 and k=1 in the options provided to see which one yields 6. Only asnwer choice E fits: 2kn=2*3*1=6.\nAnswer: E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nDawson got a weekly raise of $160. If he gets paid every other week, write an integer describing how the raise will affect his paycheck.\n\n### Options:\nA. 150\nB. 160\nC. 170\nD. 180\nE. 190\n\n### Answer:\nLet the 1st paycheck be x (integer).\nDawson got a weekly raise of $ 160.\nSo after completing the 1st week she will get $ (x+160).\nSimilarly after completing the 2nd week she will get $ (x + 160) + $ 160.\n= $ (x + 160 + 160)\n= $ (x + 320)\nSo in this way end of every week her salary will increase by (B)$ 160.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nLet x be a positive integer, what is the remainder when 2^(3x+3)+3 is divided by 3?\n\n### Options:\nA. 0\nB. 1\nC. 2\nD. 3\nE. 4\n\n### Answer:\nFor: (2^(3x+3)+3)/3\nLet n = 3x + 3\n2^n\n2^1 = 2\n2^2 = 4\n2^3 = 8\n2^4 = 16\n2^5 = 32, last digit pattern repeats 2, 4, 8, 6, 2, ....\nRule: x^(m+n) = (x^m)(x^n)\n(2^(3x))(2^3)\nRule: x^(mn) = (x^m)^n\n((2^3)^x)(8) => Now, (8)(8) + 3 = (64) + 3 => and, 4 + 2 + 1 => Finally, (6 + 1)/3, and remainder is 1.\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA straight fence is to be constructed from posts 6 inches wide and separated by lengths of chain 7 feet long. If a certain fence begins and ends with a post, which of the following could not be the length of the fence in feet? (12 inches = 1 foot)\n\n### Options:\nA. 18\nB. 23\nC. 38\nD. 53\nE. 68\n\n### Answer:\nThere is one post for each length of chain, plus one final post at the end.\nThe length of the fence in feet is 7.5x + 0.5, where each is the number of chain lengths.\nThe length of the fence is an integer when x = 1,3,5,7,...\nThe length of the fence could be 8, 23, 38, 53, 68,...\nThe answer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn the xy-plane the point (-2 -3) is the centre of a circle, the point (-2, 1) lies inside the circle and the point (4, -3) lies outside the circle. If the radius r of the circle r is an integer then diameter ?\n\n### Options:\nA. 6\nB. 10\nC. 4\nD. 3\nE. 2\n\n### Answer:\nCan be solved without much calculations.\nYou are given that (-2,-3) is the center of the circle. Point (4,-3) lies inside the circle ---> the radius is lesser than distance of (-2,-3) from (4,-3) ---> lesser than 6 units but the radius will also be greater than the distance of (-2,-3) from (-2,1) ----> greater than 4 units.\nThus the radius is >4 but <6 and as it is an integer, the only possible value of radius = 5 units.\nDiameter =2r= 10\nB is the correct answer.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a: b = 3:4, b:c = 7:9, c:d = 5:7, find a:d?\n\n### Options:\nA. 5:12\nB. 7:12\nC. 3:11\nD. 5:11\nE. 7:11\n\n### Answer:\nExplanation:\na/d = (3/4)*(7/9)*(5/7) => 5/12\nANSWER IS A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe amount of an investment will double in approximately 70/ p years, where p is the percent interest, compounded annually. If Thelma invests $ 40,000 in a long-term CD that pays 5 percent interest, compounded annually, what will be the approximate total value of the investment when Thelma is ready to retire 56 years later?\n\n### Options:\nA. $ 280,000\nB. $ 320,000\nC. $ 360,000\nD. $ 450,000\nE. $ 640,000\n\n### Answer:\nThe amount of an investment will double in approximately 70/ p years, where p is the percent interest, compounded annually. If Thelma invests $ 40,000 in a long-term CD that pays 5 percent interest, compounded annually, what will be the approximate total value of the investment when Thelma is ready to retire 42 years later?\nThe investment gets doubled in 70/p years. Therefore, the investment gets doubled in 70/5= every 14 years. After 56 years, the investment will get doubled 56/14= 4 times.\nSo the amount invested will get doubled thrice.\nSo, 40000 *2^4 = 640000\nHence, the answer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n12 men take 18 days to complete a job whereas 12 women in 18 days can complete 5/6 of the same job. How many days will 10 men and 8 women together take to complete the same job?\n\n### Options:\nA. 6\nB. 13 1\u00e2\u0081\u201e2\nC. 13\nD. Data inadequate\nE. None of these\n\n### Answer:\n12 M \u00c3\u2014 18 = 12 W \u00c3\u2014 18 \u00c3\u2014 6/5\n\\ w = 5/6 M\n10M + 8W = 10M + 8 \u00c3\u2014 5/6M = 16 2/3 M\n\\16 2/3men can complete the same work\nin 12\u00c3\u201418/16 2/3=13 days\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train running at the speed of 6 km/hr crosses a pole in 2 seconds. Find the length of the train?\n\n### Options:\nA. 150\nB. 872\nC. 3.33\nD. 3.21\nE. 30.1\n\n### Answer:\nSpeed = 6*(5/18) m/sec = 5/3 m/sec\nLength of Train (Distance) = Speed * Time\n5/3) * 2 = 3.33 meter\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA credit card company has a cash back option for their customers which is based on the annual amount that they charge on their credit cards. The customer receives 1.5% cash on their first $5000 of purchase, 2.5% on the next $5000 of purchase and a 3% on cash back on portion that exceeds $10,000. If a customer receives a cash back of 2.5% on their total annual charges made on the credit card, then what was the customer's annual charge?\n\n### Options:\nA. $17,500\nB. $20,000\nC. $22,500\nD. $25,000\nE. $27,500\n\n### Answer:\nThe customer receives $75 for the first $5000.\nThe customer receives $125 for the next $5000.\nLet x be the total amount of the customer's annual charge.\n$200 + 0.03(x-10,000)=0.025x\n0.005x=100\nx=20,000\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA bowl contains equal numbers of red, orange, green, blue, and yellow candies. Kaz eats all of the green candies and half of the orange ones. Next, he eats half of the remaining pieces of each color. Finally, he eats red and yellow candies in equal proportions until the total number of remaining candies of all colors equals 30% of the original number. What percent of the red candies remain?\n\n### Options:\nA. 22.5%\nB. 31.5%\nC. 37.5%\nD. 42.5%\nE. 46.5%\n\n### Answer:\nLet x be the original number of each color so there are a total of 5x candies.\nKaz eats all of the green candies and half of the orange ones.\nThere are 0 green candies and 0.5x orange candies remaining.\nHe eats half of the remaining pieces of each color.\nThere are 0.25x orange candies, and 0.5x each of red, yellow, and blue candies.\nHe eats red and yellow candies in equal proportions.\norange+blue+red+yellow = 0.75x + red + yellow = 1.5x\nred + yellow = 0.75x\nred = 0.375x, since red = yellow.\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOn the xy-coordinate plane, point A lies on the y-axis and point B lies on the x-axis. Points A, B, and C form a right triangle with a 90-degree angle at point C and the triangle has an area of 20. If AC is parallel to the x-axis, and BC is parallel to the y-axis, which of the following could be the coordinates of point C?\n\n### Options:\nA. (3, 7)\nB. (-8, 4)\nC. (5, -8)\nD. (-2, 10)\nE. (-5, -5)\n\n### Answer:\nThe area of the triangle formed will be:\n1/2 * base * height =\n1/2 * |(X-coordinate of point C)| * |(Y-coordinate of point C)| = 20\nThus |product of coordinates of point C| = 40\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe red triangle is equilateral with a side of 23 centimetres. Its perimeter is\n\n### Options:\nA. 68 cm\nB. 69 cm\nC. 70 cm\nD. 71 cm\nE. None\n\n### Answer:\nSolution:\nAll three sides of an equilateral triangle are equal. Thus, its perimeter will be 23 \u00d7 3 = 69 cm\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo persons , Ram & Lakshman , who are at a distance of 100 km from each other, move towards each other from two places P and Q at speeds of 20 kmph and 25 kmph respectively. Lakshman reaches P, returns immediately and meets Ram at R, who started on the return journey to P immediately after reaching Q. What is the distance between Q and R?\n\n### Options:\nA. 33 1/3 km\nB. 25 km\nC. 30km\nD. 27 1/3 km\nE. None of these\n\n### Answer:\nRam takes 100/20 = 5 hours to cover the distance from P to Q. By that time Lakshman covers\ncovers 5 *25 = 125 km\nLakshman covers 25 km more than the distance PQ . Now the distance between them = 75 km\nTime taken by them to meet = Distance/ Relative speed = 75/(20+25) = 75/45 = 5/3 hrs.\nDistance between Q and R is nothing but the distance covered by Ram in 5/3 hours = 20 *5/3 = 100/3 km or 33 1/3 km\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe can empty 3 gallons per minute. All the three pipes working together can fill the tank in 15 minutes. The capacity of the tank is?\n\n### Options:\nA. 60 gallons\nB. 100 gallons\nC. 120 gallons\nD. 180 gallons\nE. 130 gallons\n\n### Answer:\nWork done by the waste pipe in 1 minute = 1/15 - (1/20 + 1/24) = - 1/40\nVolume of 1/40 part = 3 gallons\\\nVolume of whole = 3 * 40 = 120 gallons.\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain company consists of 7 managers and 8 non-managers. How many different teams of 3 employees can be formed in which at least one member of the team is a manager and at least one member of the team is not a manager? (Two groups are considered different if at least one group member is different)\n\n### Options:\nA. 84\nB. 108\nC. 135\nD. 270\nE. 364\n\n### Answer:\nTotal # of teams of 3 possible is 15C3=455\n# of teams with only managers or only non-managers is: 7C3+8C3=35+56=91;\n# of teams of 3 with at least one manager or at least one non-manager is: 455-91=364.\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe owner of a furniture shop charges his customer 20% more than the cost price. If a customer paid Rs. 3000 for a computer table, then what was the cost price of the computer table?\n\n### Options:\nA. 2500\nB. 2772\nC. 1991\nD. 6725\nE. 2099\n\n### Answer:\nCP = SP * (100/(100 + profit%))\n= 3000(100/120) = Rs. 2500.\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA six-sided die is rolled once. What is the probability that the number rolled is an even number greater than 2?\n\n### Options:\nA. 1/4\nB. 2/4\nC. 1/2\nD. 1/3\nE. 2/3\n\n### Answer:\nOut of the 6 possible numbers that may rolled, 3 are even: 2, 4 and 6 BUT only 4 and 6 are greater than 2. Hence the probability that the number rolled is an even number greater than 2 is given by\n(number of even numbers greater than 2) / 6 = 2 / 6 = 1 / 3\ncorrect answer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe owner of a furniture shop charges his customer 32% more than the cost price. If a customer paid Rs. 5400 for a computer table, then what was the cost price of the computer table?\n\n### Options:\nA. Rs.4090\nB. Rs.4067\nC. Rs.6290\nD. Rs.6725\nE. Rs.6708\n\n### Answer:\nCP = SP * (100/(100 + profit%))\n= 5400(100/132) = Rs.4090.\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA bullet train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the bullet train is 54 km/hr, what is the length of the platform?\n\n### Options:\nA. 210 cm\nB. 120 cm\nC. 340 cm\nD. 240 cm\nE. 330 cm\n\n### Answer:\nD\n240 cm\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo stations P and Q are 155 km apart on a straight track. One train starts from P at 7 a.m. and travels towards Q at 20 kmph. Another train starts from Q at 8 a.m. and travels towards P at a speed of 25 kmph. At what time will they meet?\n\n### Options:\nA. 10 am\nB. 12 am\nC. 10.30 am\nD. 12.30 am\nE. 11 am\n\n### Answer:\nAssume both trains meet after x hours after 7 am\nDistance covered by train starting from P in x hours = 20x km\nDistance covered by train starting from Q in (x-1) hours = 25(x-1)\nTotal distance = 155\n=> 20x + 25(x-1) = 155\n=> 45x = 180\n=> x= 4\nMeans, they meet after 3 hours after 7 am, ie, they meet at 11 am\nAnswer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe cross-section of a cannel is a trapezium in shape. If the cannel is 8 m wide at the top and 6 m wide at the bottom and the area of cross-section is 700 sq m, the depth of cannel is?\n\n### Options:\nA. 76\nB. 100\nC. 27\nD. 80\nE. 25\n\n### Answer:\n1/2 * d (8+ 6) = 700\nd = 100\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nLet Q represent a set of three distinct prime numbers. If the sum of the numbers in Q is even and x is a member of Q, then what is the least possible value that x can be?\n\n### Options:\nA. 1\nB. 2\nC. 3\nD. 5\nE. 7\n\n### Answer:\nQ = p1+p2+p3= even (and all primes are distinct)\nif the least prime is 2 then we have sum of Q = even.\nAns. B. 2\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA corporation triples its annual bonus to 50 of its employees. What percent W of the employees\u2019 new bonus is the increase?\n\n### Options:\nA. 50%\nB. 662\u20443%\nC. 100%\nD. 200%\nE. 300%\n\n### Answer:\nW of the employees\u2019 new bonus is the increase Hence B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nCara leaves her home and walks toward Don's house. Two hours later, Don leaves his home and walks toward Cara's house. The distance between their homes is 45 kilometers, Cara's walking speed is 6 km/h, and Don's walking speed is 5 km/h. How many kilometers will Cara walk before she meets Don?\n\n### Options:\nA. 26\nB. 27\nC. 28\nD. 29\nE. 30\n\n### Answer:\nCara walks 12 km in the first two hours so there are 33 km remaining.\nWhen Don starts walking, they complete a total of 11 km per hour.\nThey will meet three hours after Don starts walking.\nSince Cara walks for 5 hours, she walks 30 km.\nThe answer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nGiven a two-digit number, the unit's digit exceeds its ten's digit by 5 and the product of the given number and the sum of its digits is equal to 90, which of the options is the number?\n\n### Options:\nA. 27\nB. 16\nC. 38\nD. 61\nE. 83\n\n### Answer:\nUsing the elimination method the option that fits this description is 27\n7-2 = 5 (unit's digit that exceeds its ten's digit by 3)\n27*9 = 243 (the product of the given number and the sum of its digits is equal to 175)\nanswer :A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAn employer pays Rs. 30 for each day a worker works, and forfeits Rs. 5 for each day he is idle. At the end of 60 days, a worker gets Rs. 500. For how many days did the worker remain idle?\n\n### Options:\nA. 52\nB. 27\nC. 99\nD. 61\nE. 11\n\n### Answer:\nExplanation:\nSuppose the worker remained idle for m days. Then, he worked for (60 - m) days.\n30 (60 - m) \u2013 5m = 500\n1800 \u2013 25m = 500\n25m = 1300\nm = 52\nSo, the worker remained idle for 52 days.\nANSWER: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind out the C.I on Rs.5000 at 4% p.a. compound half-yearly for 1 1/2 years.\n\n### Options:\nA. 306.03\nB. 306.01\nC. 306.04\nD. 306.0\nE. 306.06\n\n### Answer:\nA = 5000(51/50)3\n= 5306.04\n5000\n-----------\n306.04\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA clock is started at noon. By 10 minutes past 3, the hour hand has turned through how many degrees?\n\n### Options:\nA. 95\u00c2\u00b0\nB. 100\u00c2\u00b0\nC. 105\u00c2\u00b0\nD. 110\u00c2\u00b0\nE. 115\u00c2\u00b0\n\n### Answer:\nThe angle traced by the hour hand in 12 hrs is 360\u00c2\u00b0\nThe angle traced by the hour hand in 1 hour is 30\u00c2\u00b0\nThe angle traced by the hour hand in 10 minutes is 5\u00c2\u00b0\nThe angle traced by the hour hand in 3 hours and 10 minutes is 3*30\u00c2\u00b0 + 5\u00c2\u00b0 = 95\u00c2\u00b0\nThe answer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA, B and C invests Rs.2000, Rs.3000 and Rs.4000 in a business. After one year A removed his money; B and C continued the business for one more year. If the net profit after 2 years be Rs.3200, then A's share in the profit is?\n\n### Options:\nA. 222\nB. 287\nC. 277\nD. 400\nE. 281\n\n### Answer:\n2*12 : 3*12 : 4*24\n1: 3: 4\n1/8 * 3200 = 400\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n60% of a number is added to 150, the result is the same number. Find the number?\n\n### Options:\nA. 375\nB. 277\nC. 266\nD. 99\nE. 121\n\n### Answer:\n:\n(60/100) * X + 150 = X\n2X = 750\nX = 375\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe perimeter of an equilateral triangle is 60. If one of the sides of the equilateral triangle is the side of an isosceles triangle of perimeter 45, then how long is the base of isosceles triangle?\n\n### Options:\nA. 5 units\nB. 10 units\nC. 15 units\nD. 20 units\nE. 25 units\n\n### Answer:\nThe base of the isosceles triangle is 45-20-20= 5 units\nThe answer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA basket contains 5 apples, of which 1 is spoiled and the rest are good. If Henry is to select 2 apples from the basket simultaneously and at random, what is the probability R that the 2 apples selected will include the spoiled one?\n\n### Options:\nA. a. 1/5\nB. b. 3/10\nC. c. 2/5\nD. d. 1/2\nE. e. 3/5\n\n### Answer:\nthere can be two ways in which one can select a spoiled apple and a good apple.\n1. you pick the spoiled one first and the good one later..\nProb of picking bad one = 1/5 (one bad apple)\nProb of picking a good one from the remaining 4 good apples (4/4 =1)\ntherefore the total prob for case 1 = i/5 * 1 = 1/5\nTotal prob R= porb1 + prob2 = 1/5+1/5 = 2/5.C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nDanny is sitting on a rectangular box. The area of the front face of the box is half the area of the top face, and the area of the top face is 1.5 times the area of the side face. If the volume of the box is 5184, what is the area of the side face of the box?\n\n### Options:\nA. 123\nB. 167\nC. 178\nD. 199\nE. 288\n\n### Answer:\nLets suppose length= l, breadth= b, depth= d\nFront face area= l*w = 1/2 w*d (l=1/2 d or d=2l)\ntop face area= w*d\nside face area= w*d = 1.5 d*l (w=1.5l)\nVolume = l*w*d= 5184\nl*1.5l*2l= 5184\nl=12\nSide face area= l*d= l*2l= 12*2*12=288\nE is the answer\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf y = x^2 + px + q, y is minimum when x is:\n\n### Options:\nA. p /q\nB. -p/q\nC. -p/2\nD. -q/2\nE. q/p\n\n### Answer:\nWe're given the equation Y = X^2 + pX + q.\nIF.. we use a simple Classic Quadratic....\np = 2\nq = 1\nY = X^2 + 2X + 1\nWe can then go about finding the answer that yields the MINIMUM result when X = ...\nAnswer A: p/q = 2/1 = 2 --> 4+4+1 = +9\nAnswer B: -p/q = -2/1 = -2 --> 4-4+1 = +1\nAnswer C: -p/2 = -2/2 = -1 --> 1-2+1 = 0\nAnswer D: -q/2 = -1/2 -->(1/4)-1+1 = +1/4\nAnswer E: q/p = 1/2 --> (1/4)+1+1 = +2 1/4\nFrom these results, we can see the minimum result:\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAn alloy weighing 20 ounces is 70 percent gold. How many ounces of pure gold must be added to create an alloy that is 90 percent gold?\n\n### Options:\nA. 6\nB. 9\nC. 12\nD. 76\nE. 48\n\n### Answer:\nIn 24 ounces, gold is 20 * (70/100) = 14 ounces. Now we add x ounces of pure gold to make it 90% gold.\nSo 14 + x = (24 + x)* 90/100 => x =76.\nAnswer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the probability that a number selected from numbers 1, 2, 3,..., 20 is a prime number, when each of the given numbers is equally likely to be selected?\n\n### Options:\nA. 10/20\nB. 1/20\nC. 8/20\nD. 3/20\nE. 7/20\n\n### Answer:\nLet X be the event of selecting a prime number.\nX = {2, 3, 5, 7, 11, 13, 17, 19}\nn(X) = 8,\nn(S) = 20\nHence, the required probability is 8/20.\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWalking 5/4 of his usual rate, a boy reaches his school 4 min early. Find his usual time to reach the school?\n\n### Options:\nA. 22\nB. 99\nC. 27\nD. 28\nE. 20\n\n### Answer:\nSpeed Ratio = 1:5/4 = 4:5\nTime Ratio = 5:4\n1 -------- 5\n4 --------- ?20 m.Answer:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThree friends were having a party and they ordered garlic bread sticks from a nearby restaurant. Upon arrival, they divided the number of sticks among them equally. After each one of them have had four breadsticks, the total number of breadsticks that remained were equal to the breadsticks that each one of them had upon equal division.\nWith the data given, can you calculate the original number of garlic bread sticks ?\n\n### Options:\nA. 13\nB. 26\nC. 22\nD. 19\nE. 18\n\n### Answer:\nE\n18\nLet us suppose that there were (3 * G) garlic bread sticks originally.\nOn dividing equally, the number of bread sticks with each of the friend = G\nEach one of them ate four. The remaining sticks with each one of them = (G - 4)\nNow, the total number of breadsticks left = 3 * (G - 4)\nThis number is equal to the breadsticks each one of them had after division.\n=> 3 * (G - 4) = G\n(3 * G) - 12 = G\n2 * G = 12\nG = 6.\nTherefore, the number of breadsticks originally = 3 * G = 3 * 6 = 18.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich is the least number that must be subtracted from 1256 so that the remainder when divided by 7, 12, 16 is 4?\n\n### Options:\nA. 242\nB. 232\nC. 236\nD. 240\nE. 244\n\n### Answer:\nFirst we need to figure out what numbers are exactly divisible by 7,12,16. This will be the set {LCM,LCMx2,LCMx3,...}\nLCM(7,12,16) = 48*7 = 336\nThe numbers which will leave remainder 4 will be {336+4, 336x2 +4, 336x3 +4,...}\nThe largest such number less than or equal to 1256 is 336x3+4 or 1012\nTo obtain this you need to subtract 244.\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAt a restaurant, glasses are stored in two different-sized boxes. One box contains 12 glasses, and the other contains 16 glasses. If the average number of glasses per box is 15, and there are 16 more of the larger boxes, what is the total number of glasses T at the restaurant? (Assume that all boxes are filled to capacity.)\n\n### Options:\nA. 96\nB. 240\nC. T=256\nD. T=384\nE. T=480\n\n### Answer:\nMost Test Takers would recognize the system of equations in this prompt and just do algebra to get to the solution (and that's fine). The wording of the prompt and the 'spread' of the answer choices actually provide an interesting 'brute force' shortcut that you can take advantage of to eliminate the 4 wrong answers....\nWe're told that there are 2 types of boxes: those that hold 12 glasses and those that hold 16 glasses. Since the AVERAGE number of boxes is 15, we know that there MUST be at least some of each. We're also told that that there are 16 MORE of the larger boxes.\nThis means, at the minimum, we have...\n1 small box and 17 large boxes = 1(12) + 17(16) = 12 + 272 = 284 glasses at the MINIMUM\nSince the question asks for the total number of glasses, we can now eliminate Answers A, B and C....\nThe difference in the number of boxes MUST be 16 though, so we could have....\n2 small boxes and 18 large boxes\n3 small boxes and 19 large boxes\netc.\nWith every additional small box + large box that we add, we add 12+16= 28 MORE glasses. Thus, we can justadd 28suntil we hit the correct answer....\n284+28 = 312\n312+28 = 340\n340+28 = 368\n368+28 = 396\nAt this point, we've 'gone past' Answer D, so the correct answer MUST be Answer E.....But here's the proof....\n396+28 = 424\n424+28 = 452\n452+28 = 480\nFinal Answer:\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSimplify: 5358 x 51\n\n### Options:\nA. 523258\nB. 254692\nC. 253582\nD. 263258\nE. 273258\n\n### Answer:\n5358 x 51\t= 5358 x (50 + 1)\n= 5358 x 50 + 5358 x 1\n= 267900 + 5358\n= 273258.\nAnswer is E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA transport company\u2019s 120 buses running 20 hrs a day consume 360 of fuel in a day. In the next 3 days, the company will invest in 30 more green buses that use 30% less fuel. How many lts of fuel will be consumed in a five day week after the new buses are added to the fleet?\n\n### Options:\nA. 3,060\nB. 1, 512\nC. 1,800\nD. 1,260\nE. 3,312\n\n### Answer:\nold buses use 360* 5 days = 1,800 lts\nNew buses use (0.70* 360)/120* 5 days * 30 buses = 1,512 lts\nTotal fuel is 3,312 lts\nAnswer is E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA water tank is three-fifths full. Pipe A can fill a tank in 10 minutes and pipe B can empty it in 6 minutes. If both the pipes are open, how long will it take to empty or fill the tank completely?\n\n### Options:\nA. 6 min\nB. 8 min\nC. 7 min\nD. 9 min\nE. 1 min\n\n### Answer:\nThe combined rate of filling/emptying the tank = 1/10 - 1/6 = -1/15\nSince the rate is negative, the tank will be emptied.\nA full tank would take 15 minutes to empty.\nSince the tank is only three-fifths full, the time is (3/5) * 15 = 9 minutes\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA car covers a distance of 526 km in 9 hours. Find its speed?\n\n### Options:\nA. 104 kmph\nB. 289 kmph\nC. 58 kmph\nD. 277 kmph\nE. 177 kmph\n\n### Answer:\n526/9\n= 58 kmph\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA tin of oil was 4/5 full. when 6 bottles of oil were taken out and four bottles of oil were poured into it, it was \u00be full. how many bottles of oil can the tin contain?\n\n### Options:\nA. 20\nB. 10\nC. 40\nD. 50\nE. 20\n\n### Answer:\nSuppose x bottles can fill the tin completely\nThen 4/5x-3/4x=6-4\nX/20=2\nX=40\nTherefore required no of bottles =40\nAnswer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo kinds of Vodka are mixed in the ratio 1:2 and 2:1 and they are sold fetching the profit 10% and 25% respectively. If the vodkas are mixed in equal ratio and the individual profit percent on them are increased by 4/3 and 5/3 times respectively, then the mixture will fetch the profit of\n\n### Options:\nA. 18%\nB. 20%\nC. 25%\nD. 23%\nE. Cannot be determined\n\n### Answer:\nAnswer: C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nCity A to city B, Andrew drove for 1 hour at 50 mph and for 3 hours at 60 mph. What was the average speed for the whole trip?\n\n### Options:\nA. 56\nB. 57.5\nC. 58.9\nD. 61.3\nE. 67.23\n\n### Answer:\nThe total distance is 1\u00d750+3\u00d760=2301\u00d750+3\u00d760=230. And the total time is 4 hours. Hence,\nAverage Speed=(Total DistanceTotal Time)=2304=57.5\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are 19 teams in the hockey league, and each team faces all the other teams 10 times each. How many games are played in the season?\n\n### Options:\nA. 1710\nB. 1920\nC. 2440\nD. 2860\nE. 3260\n\n### Answer:\nThe number of ways to choose two teams is 19C2 = 19*18/2 = 171\nThe total number of games in the season is 10*171 = 1710.\nThe answer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn an examination, a student scores 4 marks for every correct answer and loses 1 mark for every wrong answer. If he attempts all 50 questions and secures 130 marks, the no of questions he attempts correctly is :\n\n### Options:\nA. A)36\nB. B)38\nC. C)90\nD. D)88\nE. E)37\n\n### Answer:\nLet the number of correct answers be X.\nNumber of incorrect answers = (60 \u2013 X).\n4x \u2013 (50 \u2013 x) = 130\n=> 5x = 180\n=> x = 36\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA basket has 6 apples and 4 oranges. FOUR fruits are picked at random. The probability that at least 3 apples are picked is\n\n### Options:\nA. 25/42\nB. 25/48\nC. 19/42\nD. 25/47\nE. 25/43\n\n### Answer:\nTotal fruits = 10\rSince there must be at least two apples,\r(6C3 * 4C1)/10C4 + 6C4/10C4 = 19/42.\rAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf n = 14p, where p is a prime number greater than 2, how many different positive even divisors does n have, including n ?\n\n### Options:\nA. Two\nB. Three\nC. Four\nD. Six\nE. Eight\n\n### Answer:\nIf n = 14p, where p is a prime number greater than 2, how many different positive even divisors does n have, including n ?\n(A) Two\n(B) Three\n(C) Four\n(D) Six\n(E) Eight\nSince we cannot have two correct answers just pick a prime greater than 2, and see how many different positiveevendivisors will 14p have.\np = 3 --> 14p = 42--> 42 has 4 even divisors: 2, 6, 14, 42 .\nAnswer: C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA circular box kept around a circular place. If the difference between the circumference of the outer circle and the inner circle is 44m, find the width of the box?\n\n### Options:\nA. 2 m\nB. 3 m\nC. 4 m\nD. 7 m\nE. 8 m\n\n### Answer:\nLet radius of the outer circle be R and radius of the inner circle be r.\nCircumference of the outer circle =\nCircumference of the inner circle =\nBut,\nor, R - r =\nThus, width of the road = 7 m\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAn escalator moves towards the top level at the rate of 11 ft.sec and its length is 140 feet. If a person walks on the moving escalator at the rate of 3 feet per second towards the top level, how much time does he take to cover the entire length.\n\n### Options:\nA. 14 sec\nB. 10 sec\nC. 12 sec\nD. 8 sec\nE. 9 sec\n\n### Answer:\nTime taken to cover the entire length = tot.dist/resultant speed\n= 140/ (11+3)\n= 10sec\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average weight of a class of 24 students is 35 kg. If the weight of the teacher be included, the average rises by 400 g. The weight of the teacher is\n\n### Options:\nA. 45 kg\nB. 75kg\nC. 25kg\nD. 35 kg\nE. 55 kg\n\n### Answer:\nExplanation:\nWeight of the teacher = (35.4 x 25 - 35 x 24) kg = 45 kg.\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo trains 140 m and 210 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is?\n\n### Options:\nA. 12.6 sec\nB. 11.8 sec\nC. 27.7 sec\nD. 10.8 sec\nE. 17.8 sec\n\n### Answer:\nRelative speed = 60 + 40 = 100 km/hr.\n= 100 * 5/18 = 250/9 m/sec.\nDistance covered in crossing each other = 140 + 210 = 350 m.\nRequired time = 350 * 9/250 =12.6 sec.\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA bulldog received 1,600 votes in a bulldog competition, giving him 20 percent of the votes. What percent of the remaining votes would he have needed to receive in order to win 36 percent of the total votes?\n\n### Options:\nA. 10%\nB. 12.5%\nC. 15%\nD. 17.5%\nE. 20%\n\n### Answer:\nThere were 80% of the votes remaining and he needed 16%/80% = 2/10 = 20%\nThe answer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe cost per pound of milk powder and coffee were the same in June. In July, the price of coffee shot up by 200% and that of milk powder dropped by 60%. If in July, a mixture containing equal quantities of milk powder and coffee costs $5.10 for 3lbs, how much did a pound of milk powder cost in July?\n\n### Options:\nA. $4\nB. $0.4\nC. $1\nD. $3\nE. $1.65\n\n### Answer:\nLets assume price of Coffee in June =100x\nPrice of Tea in June =100x\nPrice of Coffee in July = 300x (because of 200% increase in price)\nPrice of Tea in July = 40x (because of 60% Decrease in price)\nPrice of 1.5 pound of Coffee1.5 pound of Tea in July will be = 450x + 60x = 510x\nAs per question\n510x= 5.10$\nx = 0.01S\nSo the Price of Tea in July = 40x = 40 x 0.01 = 0.4$/pound\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how many ways can 5 boysand 2 girls be arranged at a table if 2 girls are never together?\n\n### Options:\nA. 200\nB. 240\nC. 250\nD. 260\nE. 480\n\n### Answer:\nTotal ways of arranging 7 person in a circle = 6! = 720 ways\nIf we consider two women as one, then we have 5+1=6 persons. Arranging these six persons in circle will take = 5! = 120 ways\nAnd two women can arrange themselves in 2! ways\nTotal ways in which two women sit together in circle = 5!*2! = 240 ways\nTotal ways in which two women doesn\u2019t sit together in circle = 6! - 5!*2! = 720 - 240 = 480 ways\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n220, 218, 214, 208, 200, 190, ?\n\n### Options:\nA. 176\nB. 174\nC. 178\nD. 180\nE. 172\n\n### Answer:\n220\n220 - 2 = 218\n218 - 4 = 214\n214 - 6 = 208\n208 - 8 = 200\n200 - 10 = 190\n190 - 12 = 178\nAnswer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwelve men and six women together can complete a piece of work in four days. The work done by a women in one day is half the work done by a man in one day. If 12 men and six women started working and after two days, six men left and six women joined, then in hoe many more days will the work be completed?\n\n### Options:\nA. 2 (1/9)\nB. 2 (4/2)\nC. 5 (1/2)\nD. 2 (1/2)\nE. 2 (1/6)\n\n### Answer:\nWork done by a women in one day = 1/2 (work done by a man/day)\nOne women's capacity = 1/2(one man's capacity)\nOne man = 2 women.\n12 men = 24 women.\n12 men + 6 women = 30 women\n30 women can complete the work in four days. In the first 2 days they can complete 1/2 of the work. Remaining part of the work = 1/2. If 6 men leave and 6 new women join, then new work force = 30 women - 12 women + 6 women = 24 women.\nTime taken by them to complete the remaining work = 1/2 (Time taken by 24 women to complete the work) = 1/2 * (30 * 4)/24 = 2 (1/2) days.\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA piece of cloth cost Rs 35. if the length of the piece would have been 4m longer and each meter cost Re 1 less , the cost would have remained unchanged. how long is the piece?\n\n### Options:\nA. 5 mtrs\nB. 10 mtrs\nC. 12 mtrs\nD. 15 mtrs\nE. 18 mtrs\n\n### Answer:\nIf length of piece is x and cost per mtr is C, then\nx*C = 35 or C =35/x\n(x+4)*(C-1) = 35 or x*C +4C-x -4 =35 or 35+4C-x -4 = 35\n4C-x =4\n4*(35/x)-x =4\nx= 10 mtrs\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n100 is increased by 50%. Find the final number.\n\n### Options:\nA. 100\nB. 110\nC. 150\nD. 155\nE. 160\n\n### Answer:\nFinal number = Initial number + 50%(original number) = 100 + 50%(100) = 100 + 50 = 150.\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nEach side of a given polygon is parallel to either the X or the Y axis. A corner of such a polygon is said to be convex if the internal angle is 90\u00b0 or concave if the internal angle is 270\u00b0.\nIf the number of convex corners in such a polygon is 25, the number of concave corners must be\n\n### Options:\nA. 20\nB. 10\nC. 21\nD. 22\nE. 23\n\n### Answer:\n90(25) + 270(n-25) = (n-2)*180.\n=25 + 3(n-25) = (n-2)*2.\n= 3n - 50 = 2n-4\n= n = 46.\nHence, the required number of corners must be 46 - 25 = 21. ANSWER : C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a certain lottery, the probability that a number between 12 and 20, inclusive, is drawn is 1/6 . If the probability that a number 12 or larger is drawn is 1/3 , what is the probability that a number less than or equal to 20 is drawn?\n\n### Options:\nA. 1/18\nB. 1/6\nC. 1/3\nD. 1/2\nE. 5/6\n\n### Answer:\nYou can simply use sets concept in this question. The formula\nTotal = n(A) + n(B) - n(A and B) is applicable here too.\nSet 1: Number 12 or larger\nSet 2: Number 20 or smaller\n1 = P(Set 1) + P(Set 2) - P(Set 1 and Set 2) (combined probability is 1 because every number will be either12 or moreOR20 or lessOR both)\n1/3 + P(Set 2) - 1/6 = 1\nP(Set 2) = 5/6\nAnswer (E)\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJulie put half of her savings in a savings account that pays an annual simple interest and half in a savings account that pays an annual compound interest. After two years she earned $120 and $126 from the simple interest account and the compound interest account respectively. If the interest rates for both accounts were the same, what was the amount of Julie's initial savings?\n\n### Options:\nA. 600\nB. 720\nC. 1080\nD. 1200\nE. 1440\n\n### Answer:\nWe need to find the amount off Julie's Initial savings...Let that be 2x\nSo x goes in simple interest and x goes in compund interest for a period of 2 years...\nIn case of Simple interest, The interest paid out is same for each year..Hence if $120 was interest for 2 years that means interest per year will be 60 $\nSo we have S.I,120 = x\u22172\u2217R100x\u22172\u2217R100\nor 6000 =x*R\nFor CI, in 126 $, 6$ represents nothing but interest earned on interest of 1st year.\nIn the First year, Interest amount is same for S.I and C.I\nSo we have\nx(1+R100)2\u2212x=126x(1+R100)2\u2212x=126\nor x(1 + R^2/10000+ 2R/100)-x=126\nx+xR^2/10000+2xR/100)-x=126\nx+R*6000/10000+12000/100-x=126\n0.6R+120=126\n0.6R=6 or R=10\nSo x=600...2x=1200 is the Initial savings. Answer is D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the two-digit number? I. The difference between the two-digit number and the number formed by interchanging the digits is 27. II. The difference between the two digits is 3. III. The digit at unit's place is less than that at ten's place by 3.\n\n### Options:\nA. I and II\nB. II and III only\nC. all\nD. Even with all I, II and III, answer cannot be give.\nE. I and either II or III\n\n### Answer:\nLet the tens and units digit be x and y respectively.\nI. (10x + y) - (10y + x) x - y = 3.\nII. x - y = 3.\nIII. x - y = 3.\nThus, even all the given three statements together do not give the answer.\nCorrect answer is (D).\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the probability of flipping a fair coin eight times and the coin landing on heads on at least two flips?\n\n### Options:\nA. 61/64\nB. 117/128\nC. 123/128\nD. 247/256\nE. 253/256\n\n### Answer:\nThe number of possible outcomes is 2^8=256.\n0 heads: There is 1 way to have all tails.\n1 head: There are 8 ways to have one head.\nP(0 or 1 head)=9/256\nP(at least 2 heads)=1 - 9/256 = 247/256\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat will come in place of the question mark (?) in the following question?\n112.36 + 225.05 + ? = 815.30\n\n### Options:\nA. 474.46\nB. 477.89\nC. 524.41\nD. 564.40\nE. None of these\n\n### Answer:\nExplanation:\n815.30 - ( 112.36 + 225.05) = ?\n= 477.89\nANSWER: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf k is the sum of the digits of integer m, and m=10n, where n is an integer, which of the following must be true?\n\n### Options:\nA. k is not divisible by 9\nB. The sum of the digits of k is divisible by 3\nC. m is a multiple of 10k\nD. k is a multiple of 9\nE. k is a multiple of 6\n\n### Answer:\nm= 10n i.e n =1,2,3 ,4 etc or -1,-2.-3 ,-4 then m =10,20,30,40 or -10 ,-20 ,-30 ,-40 then k 1,2, 3,4 or -(1+0) , -(2+0) , -(3+0) ,-(4+0) .\nans(C)\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average weight of 8 person's increases by 6 kg when a new person comes in place of one of them weighing 40 kg. What might be the weight of the new person?\n\n### Options:\nA. 80 kg\nB. 85 kg\nC. 90 kg\nD. 88 kg\nE. 110 kg\n\n### Answer:\nTotal weight increased = (8 x 6) kg = 48 kg.\nWeight of new person = (40 + 48) kg = 88 kg.\nAnswer : D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn what ratio should water and wine be mixed so that after selling the mixture at the cost price a profit of 33.33% is made?\n\n### Options:\nA. 1:4\nB. 1:3\nC. 2:3\nD. 3:4\nE. None of these\n\n### Answer:\nExplanation:\n33.33% profit means there is one part water and 3 part is pure wine. so the required ratio of water and wine in the mixture is 1:3. Answer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf (4.2)x = (0.42)y = 100, then (1/x) - (1/y) =\n\n### Options:\nA. 1\nB. 2\nC. 1/2\nD. 1/4\nE. 2\n\n### Answer:\n(4.2)x = 100\n=> (42)x = 102+x\n=> 42 = 10(2/x+1) ---------- (i)\n[42/100]y = 100 => 42y = 102+2y\n=> 42 = 102/y+2-------- (ii)\nFrom (i) and (ii), 2/x - 2/y = 1\n=>1/x - 1/y = 1/2.\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA person can swim in still water at 4 km/h. If the speed of water 2 km/h, how many hours will the man take to swim back against the current for 10km?\n\n### Options:\nA. 3\nB. 5\nC. 8\nD. 9\nE. 6\n\n### Answer:\nM = 4\nS = 2\nUS = 4 - 2 = 2\nD = 10\nT = 10/2 = 5\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA type of extra-large SUV averages 12.2 miles per gallon (mpg) on the highway, but only 7.6 mpg in the city. What is the maximum distance, in miles, that this SUV could be driven on 23 gallons of gasoline?\n\n### Options:\nA. 190\nB. 284.6\nC. 300\nD. 280\nE. 312\n\n### Answer:\nso 12.2 * 23 = 280..\nIMO option D is correct answer..\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSix bells commence tolling together and toll at intervals of 2,4,6,8,10 and 12 seconds respectively. in 30 m9nutes,how many times do they toll together ?\n\n### Options:\nA. 4\nB. 10\nC. 15\nD. 16\nE. 17\n\n### Answer:\nSolution\nL.C.M. of 2,4,6,8,10,12 is 120.\nSo, the bells will toll together after every 120 seconds, i.e., 2 minutes\nIn 30 minutes, they will toll together left [ ( 30/2 )+ 1 ] = 16 times. Answer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSimplify: 32 \u00f7 8 \u00d7 24 + 16 =\n\n### Options:\nA. 130\nB. 124\nC. 120\nD. 115\nE. 112\n\n### Answer:\n32 \u00f7 8\n\u00d7\n\u00d7 24 + 16 => 4\n\u00d7\n\u00d7 24 + 16 = 96 + 16 = 112\nOption E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the largest 3 digit number which is exactly divisible by 88?\n\n### Options:\nA. 765\nB. 907\nC. 944\nD. 954\nE. 968\n\n### Answer:\nLargest 3 digit number is 999\nAfter doing 999 \u00f7 88 we get remainder 31\nHence largest 3 digit number exactly divisible by 88 = 999 - 31 = 968\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJohn deposited $10,000 to open a new savings account that earned 6 percent annual interest, compounded quarterly. If there were no other transactions in the account, what was the amount of money in John\u2019s account 6 months after the account was opened?\n\n### Options:\nA. $10,100.30\nB. $10,101.50\nC. $10,200.75\nD. $10,302.25\nE. $10,400.25\n\n### Answer:\n6 percent annual interest compounded quarterly --> 1.5% in 3 moths.\nFor the first 3 moths interest was 1.5% of $10,000, so $150;\nFor the next 3 moths interest was 1.5% of $10,000,plus2.25 earned on previous interest of $150, so $150+$2.25=$152.25;\nTotal interest for 6 months was $150+$152.25=$302.25, hence balance after 6 months was $10,000+ $302.25=$10,302.25.\nAnswer: D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMary purchased Brand X pens for $2 apiece and brand Y for $1 apiece. If Elena purchased a total of 12 of these pens for $20.00, how many brand X pens did she purchase?\n\n### Options:\nA. 8\nB. 9\nC. 5\nD. 4\nE. 6\n\n### Answer:\n2x+y=20 -only one positive integers solutions x=8 and y=4\nAnswer is A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the area of circle whose radius is 10m?\n\n### Options:\nA. 138\nB. 154\nC. 288\nD. 280\nE. 314.3\n\n### Answer:\n22/7 * 10 * 10\n= 314.3\nAnswer:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA large research project was scheduled over the course of a 30-month period, and a budget of $90,000 was allotted for the course of the entire project. After seven months, the project had spent $20,000. Was the project at this point over budget or under budget, and by how much?\n\n### Options:\nA. under, $4200\nB. under, $1200\nC. under, $1000\nD. over $1800\nE. over $5800\n\n### Answer:\ncost per month = 90,000/30 = 3,000.\nNow, multiply by seven months: 7*($3000) = $21,000. That would be the budgeted amount, the amount theoretically supplied to the project. The real amount spent is less than this, so it is under budget.\n$21,000 \u00e2\u20ac\u201c #20,000 = $1000\nAnswer = (C)\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf w,x,y,z are consecutive positive integers ; then which of the following is always odd?\n[1] w*x+(y+2)^2*z\n[2] w^x + z^y\n[3] 13x^2\n\n### Options:\nA. 1\nB. 2\nC. 3\nD. 1 and 2\nE. 2 and 3\n\n### Answer:\nPlug in some numbers\nw = 1\nx = 2\ny = 3\nz = 4\nCheck the options -\n[1] w*x+(y+2)^2*z = 1*2 + (3+2)^2 * 4 => 2 + 25*4 = 102{ Not an odd Number }\n[2] w^x + z^y = 1^2 + 4^3 => 1 + 64 = 65{ Odd number }\n[3] 13x^2 = 13*4 =52 even\n[2]\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe perimeter of a triangle is 28 cm and the inradius of the triangle is 2.5 cm. What is the area of the triangle\n\n### Options:\nA. 72\nB. 828\nC. 729\nD. 34\nE. 35\n\n### Answer:\nExplanation:\nArea of a triangle = r * s\nWhere r is the inradius and s is the semi perimeter of the triangle.\nArea of triangle = 2.5 * 28/2 = 35 cm2\nAnswer: Option E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf x is an integer such that 0 < x < 7, 0 < x < 15, 5 > x > \u20131, 3 > x > 0, and x + 2 < 4, then x is\n\n### Options:\nA. 1\nB. 2\nC. 3\nD. 4\nE. 5\n\n### Answer:\n0 < x < 7,\n0 < x < 15,\n5 > x > \u20131\n3 > x > 0\nx<2\nFrom above: 0 < x < 2 --> x = 1.\nAnswer: A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf x and y are positive integers such that x/y = 2.18, which of the following numbers could be y?\n\n### Options:\nA. 50\nB. 5\nC. 150\nD. 2\nE. 100\n\n### Answer:\nWith the given information, we are trying to find the value of y.\nTo achieve this we must convert the given decimal to a fraction and reduce it to it's lowest integer form.\nTake the decimal x/y = 2.18 and because it's in the hundreds decimal place, put the given value (x/y = 2.18/1) and multiply it by 100.\nTake the resulting fraction (x/y = 218/100) and reduce it to it's lowest form.\nBoth of the numbers are divisible by 2.\nThe result is x/y = 109/50.\nThus y = 50.\nThe correct answer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRs. 6000 is lent out in two parts. IN that One part is lent at 7% p.a simple interest and the second one is lent at 10% p.a simple interest. The total interest at the end of one year was Rs. 450. Find the ratio of the amounts lent at the lower rate and higher rate of interest?\n\n### Options:\nA. 5 : 7\nB. 5 : 1\nC. 6: 1\nD. 7 : 1\nE. 5 : 3\n\n### Answer:\nLet the amount lent at 7% be Rs. x\nAmount lent at 10% is Rs. (6000 - x)\nTotal interest for one year on the two sums lent\n= 7/100 x + 10/100 (6000 - x) = 600 - 3x/100\n=> 600 - 3/100 x = 450 => x = 5000\nAmount lent at 10% = 1000\nRequired ratio = 5000 : 1000 = 5 : 1\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFree notebooks were distributed in a class among all the students. Each student got notebooks which were one-eighth of the number of student. If number of student been half, then each child would have received 16 notebooks in total. Find the total number of books distributed among students?\n\n### Options:\nA. 435\nB. 456\nC. 467\nD. 489\nE. 512\n\n### Answer:\nLet suppose total number of students in class are X.\nThen from the question we can conclude it that,\nX\u221718X=X2\u221716=>X=64Total notebooks,=18X2=(18\u221764\u221764)=512\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA college has classes from 10:00 AM until 1:55 PM. In this duration, there are five periods. If 5 minutes are provided between each period to leave one class and enter the next class, how many minutes long is each period?\n\n### Options:\nA. 38 min\nB. 41 min\nC. 40 min\nD. 42 min\nE. 43 min\n\n### Answer:\nThe total time is 235 minutes.\nThere are four breaks of five minutes between the classes for a total of 20 minutes.\nThe total class time is 215 minutes.\n215 / 5 classes = 43 minutes per class\nThe answer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nObserve the dots on a dice (one to six dots) in the following figures. How many dots are contained on the face opposite to that containing four dots?\n\n### Options:\nA. 2\nB. 6\nC. 7\nD. 8\nE. 9\n\n### Answer:\nExplanation:\nWe shall assume the dice in fig. (ii) to be rotated so that the 5 dots appear at the same position as in fig. (i) i.e. on RHS face (i.e. on face II as per activity 1) and 1 dot appears at the same position as in fig; (i) i.e. on Front face (i.e. on face I). Then, from the, two figures, 2 dots appear on the top face (i.e. on face V) and 4 dots appear on the Bottom face (i.e. on face VI).\nSince, these two faces are opposite to each other, therefore, two dots are contained on the face opposite to that containing four dots.\nAnswer: A) 2\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSix students are equally divided into 3 groups, then, the three groups were assigned to three different topics. How many different arrangements W are possible?\n\n### Options:\nA. 30\nB. 60\nC. 90\nD. 180\nE. 540\n\n### Answer:\n90 is the number of ways you can assign 3 teams formed out of 12 people to 3 different tasks.\nBut now you can order the 3 tasks in 3! ways. T1 T2 T3 or T2 T1 T3.... etc etc.\nI was confused between 90 and 540 but since question used the wordarrangementsdecided to go with complete arrangements W including the order of tasks.\ncould you explain the highlighted step... i'm getting 90 = 15 * 3!\nsuppose the students are numbered 1,2,3,4,5,6 and tasks are X,Y and Z\none of the 15 possible ways of forming teams is 12, 34, 56. these teams can be assigned to 3 tasks in 3! = 6 ways\nX--\tY--\tZ\n12--\t34--\t56\n12--\t56--\t34\n34--\t12--\t56\n34--\t56--\t12\n56--\t12--\t34\n56--\t34--\t12\nso the answer should be 15*6 = 90\nBut now you can fruther decide which task you want to perform first X Y or Z..=C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many integers are there between 42 and 97, inclusive?\n\n### Options:\nA. 51\nB. 55\nC. 56\nD. 57\nE. 58\n\n### Answer:\nI guess the easiest way to answer this is -\nSay you have two positive integers, x and y where y > x\nThen the number of integers between x and y is given by - (y - x) + 1\nIn this case, it's (97 - 42) + 1 =56\nOption C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nP , Q and R started a business by investing Rs 120000 , Rs 135000 & Rs 150000 respectively. Find the share of each, out of the annual profit of Rs 56700\n\n### Options:\nA. 16800 , 18900 , 21000\nB. 17850 , 18900 , 21000\nC. 16800 , 18900 , 22000\nD. 17850, 18500 , 22000\nE. None of these\n\n### Answer:\nExplanation :\nP : Q : R = 120000 : 135000 : 150000 = 120:135:150\n= 24:27:30\n= 8:9:10\nShare of P= 56700*8/27 = 2100*8 = 16800\nShare of Q = 56700*9/27 = 2100*9 = 18900\nShare of R = 56700*10/27 = 2100*10 = 21000. Answer : Option A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAmar takes as much time in running 18 meters as a car takes in covering 48 meters. What will be the distance covered by Amar during the time the car covers 1.8 km?\n\n### Options:\nA. 660 m\nB. 650 m\nC. 570 m\nD. 670 m\nE. 680 m\n\n### Answer:\nDistance covered by Amar = (18/48)*1800 = 670 m\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a mixture of milk and water, the proportion of milk by weight was 80%. If, in a 210-gram mixture, 40 grams of pure milk is added, what would be the percentage of milk in the resulting mixture?\n\n### Options:\nA. 82.2%\nB. 83.2%\nC. 84.2%\nD. 85.2%\nE. 86.2%\n\n### Answer:\nThe amount of milk is 0.8(210) + 40 = 208 grams.\nThe proportion is 208/250 = 0.832 which is 83.2%\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the third day of the month is Monday, Which of the following will be the fifth day from 21st of that month?\n\n### Options:\nA. Tuesday\nB. Monday\nC. Wednesday\nD. Thursday\nE. None of these\n\n### Answer:\n3rd dy is monday----so----1st day must be saturdy\n1-8-15-22 are all saturdy..ok\nso 21 will be friday so,\nfrom firdy 5th day will be wednesday\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nP and Q started a business investing Rs. 85,000 and Rs. 15,000 respectively. In what ratio the profit earned after 2 years be divided between P and Q respectively?\n\n### Options:\nA. 17:6\nB. 17:0\nC. 17:4\nD. 17:2\nE. 17:3\n\n### Answer:\nP:Q = 85000 : 15000\n= 17:3.\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA box contains eight apples out of which 4 are rotten. If four apples are chosen at random, find the probability that all the four apples are rotten?\n\n### Options:\nA. 1/113\nB. 1/90\nC. 1/80\nD. 1/70\nE. None of these\n\n### Answer:\nOut of nine apples , five are good and four are rotten.\nRequired probability = 4C4/8C4 = 1/70\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nPablo plays 3 rounds of a game, in which his chances of winning each round are 1/2, 1/4, and 1/n, respectively. If n \u2260 0, what is the probability that Pablo wins the first two rounds, but loses the third?\n\n### Options:\nA. 1/16n\nB. (n-1)/8n\nC. 1/2n\nD. (n+2)/2n\nE. (3n-2)/2n\n\n### Answer:\n1/2 * 1/4 * (1-1/n)\n= 1/8 * (n-1)/n\n= (n-1)/8n\nAnswer - B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJessica can text 125 words per minute, while Maurice can text 10 words per minute. An abridged English translation of Tolstoy\u2019s War and Peace contains 410,400 words. Working together, how many days will it take Jessica and Maurice to text the entire abridged translation of War and Peace?\n\n### Options:\nA. 0.3\nB. 2.1\nC. 3\nD. 9\nE. 11.3\n\n### Answer:\nSince the answer choices are reasonably spaced out, we can approximate and save time\nCombined words per day = 135*60*24 which should be 194400\n410400/194400 will be 2.1,\nSo, Answer should be B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nEvaluate 75 / .05\n\n### Options:\nA. 1400\nB. 1500\nC. 1505\nD. None of these\nE. 1506\n\n### Answer:\nExplanation:\n75/.05 = 7500/5 = 1500\nOption B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nList I: 4, 8, 12, 16 List II: x,4, 8, 12, 16\n\n### Options:\nA. 5\nB. 4\nC. 3\nD. 10\nE. 2\n\n### Answer:\nList I has even number of terms, thus its median is the average of two middle terms (when arranged in ascending/descending order), so median=(8+12)/2=10\nList II has odd number of terms, thus its median is the middle term (when arranged in ascending/descending order). As no other number in the list equal to 10, then x=10.\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA pet store holds cats and dogs. If the difference between the number of cats and the number of dogs is 5. What could be the ratio of Cats to dogs in the pet store?\n\n### Options:\nA. 1:3\nB. 20:25\nC. 1:5\nD. 2:5\nE. 4:6\n\n### Answer:\nSay theratioof cats to dogs is a/b. Then thenumberof cats would be ax and thenumberof dogs bx, for some positive integer x.\nWe are told that ax - bx = 5 --> x(a - b) = 5. Since 5 is a prime number it could be broken into the product of two positive multiples only in one way: x(a - b) = 1*5.\nThe above implies that either x = 1 and a - b = 5 or x = 5 and a - b = 1.\nTherefore the correct answer should have the difference between numerator and denominator equal to 1 or 13.\nFor the original question only option which fits is E, 4:5. Cats = 5*4 = 20 and dogs = 5*5 = 25.\nAnswer: B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 36 men can do a piece of work in 25 hours, in how mwny hours will15 men do it?\n\n### Options:\nA. 22\nB. 38\nC. 60\nD. 88\nE. 72\n\n### Answer:\nExplanation:\nLet the required no of hours be x. Then\nLess men , More hours (Indirct Proportion)\n\\inline \\fn_jvn \\therefore 15:36 ::25:x \\inline \\fn_jvn \\Leftrightarrow (15 x X)=(36 x 25) \\inline \\fn_jvn \\Leftrightarrow \\inline \\fn_jvn x=\\frac{36\\times 25}{15}=60\nHence, 15 men can do it in 60 hours.\nAnswer: C) 60\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average wages of a worker during a fortnight comprising 15 consecutive working days was $90 per day. During the first 7 days, his average wages was $87 per day and the average wages during the last 7 days was $91 per day. What was his wage on the 8th day?\n\n### Options:\nA. $83\nB. $90\nC. $92\nD. $97\nE. $104\n\n### Answer:\nAverage daily wage of a worker for 15 consecutive working days = 90$\nDuring the first 7 days , the daily average daily wage = 87$\nDuring the last 7 days , the daily average daily wage = 91$\nWage on 8th day = 90*15 -( 87*7 + 91 *7)\n= 1350 - (609 + 637)\n=1350 - 1246\n= 104\nAnswer E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average of runs of a cricket player of 10 innings was 18. How many runs must he make in his next innings so as to increase his average of runs by 4?\n\n### Options:\nA. 87\nB. 16\nC. 62\nD. 76\nE. 17\n\n### Answer:\nAverage after 11 innings = 22\nRequired number of runs\n= (33* 11) - (18* 10) = 242 - 180\n= 62.\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nStudents are asked to create a record of the recital of a poem for English class in groups of three. The tape length should be 1,200 seconds. The students assigned different stanzas of the poem to each member, and the individual records were compiled. If member three took 3 times longer than member two, and member two took equal time as member one, how many seconds did member three record for his/her reading?\n\n### Options:\nA. 720\nB. 240\nC. 1200\nD. 40\nE. 500\n\n### Answer:\nmember one, two and three as m1, m2 and m3 respectively.\nm2=m1 as eq.a\nm3=m2*3 as eq.b\nm3+m2+m1=1,200 as eq.c\nSubstitute eq.b into eq. c, making (m2*3) + m2+ m2=1,200\n(m2*5)/5=1,200/5 reduces to m2=240 seconds.\nm3 is then m2*3, which is 720 seconds.\nAnswer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n1,2,2,4,8,32,?(mult)\n\n### Options:\nA. 2816\nB. 1816\nC. 2812\nD. 2817\nE. 6816\n\n### Answer:\nEach number is the product of the previous two numbers, ie 8*32 = 2816.\nAnswer :A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhen running a mile during a recent track meet, Nuria was initially credited with a final time of 7 minutes, 44 seconds. Shortly after her run, officials realized that the timing mechanism malfunctioned. The stopwatch did not begin timing her until 11/25 of a minute after she began to run. If the time was otherwise correct, how long did it actually take Nuria to run the mile?\n\n### Options:\nA. 8 minutes, 10.4 seconds\nB. 5 minutes, 21.8 seconds\nC. 5 minutes, 43.56 seconds\nD. 5 minutes, 44.44 seconds\nE. 5 minutes, 17.6 seconds\n\n### Answer:\nOne approach:\nThe watch starts to work after Nuria began his running. It means the time should be greater than credited 7 minutes, 44 seconds. The only number is 8 minutes, 10.4 seconds.\nAnother approach:\n11/25 close to 30 second when added to the 7 minutes, 44 seconds, it means it passes 8 minute.\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA snail, climbing a 24 feet high wall, climbs up 4 feet on the first day but slides down 2 feet on the second. It climbs 4 feet on the third day and slides down again 2 feet on the fourth day. If this pattern continues, how many days will it take the snail to reach the top of the wall?\n\n### Options:\nA. 12\nB. 16\nC. 17\nD. 20\nE. 21\n\n### Answer:\ntotal transaction in two days = 4-2 = 2 feet\nin 20 days it will climb 20 feet\non the 21st day , the snail will climb 4 feet , thus reaching the top\ntherefore , total no of days required =21\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAn advertising agency finds that, of its 200 clients, 115 use Television, 110 use Radio and 130 use Magazines. Also, 85 use Television and Magazines, 75 use Television and Radio, 95 use Radio and Magazines. How many use all the three?\n\n### Options:\nA. 100\nB. 70\nC. 90\nD. 98\nE. 95\n\n### Answer:\nTotal=200\nTelevision=115\nRadio=110\nMagazine=130\nAll the three =200-115-110-130+85+75+95=100\nANSWER A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nCompany A has 13 employees, 8 of whom belong to the union. If 5 people work any one shift, and the union contract specifies that at least 5 union members work each shift, then how many different combinations of employees might work any given shift?\n\n### Options:\nA. 56\nB. 231\nC. 336\nD. 350\nE. 406\n\n### Answer:\nLooks easy: -- 8C5*5C1 + 8C5 -- 336 (C).\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA, B and C shared the profit in a business in the ratio 5 : 7 : 8. They had partnered for 14 months, 8 months and 7 months respectively. What was the ratio of their investments?\n\n### Options:\nA. 20:64:49\nB. 49:20:64\nC. 64:20:49\nD. 64:49:20\nE. 20:49:64\n\n### Answer:\nRatio in which A,B and C shared the profit =5:7:8\nAssume that the ratio of their investments =a:b:c\n\u21d214a:8b:7c=5:7:8\u22ef(A)\nFrom (A),\n14a:8b=5:7\n\u21d214a\u00d77=8b\u00d75\n\u21d27a\u00d77=4b\u00d75\n\u21d2b=49a/20\u22ef(1)\nFrom (A),\n14a:7c=5:8\n\u21d2(14a)\u00d78=(7c)\u00d75\n\u21d2(2a)\u00d78=c\u00d75\n\u21d2c=16a/5\u22ef(2)\na:b:c=a:49a/20:16a/5\n=1:49/20:16/5\n=20:49:64\nAnswer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nPoint X is located on line segment AB and point Y is located on line segment CD. If AB = CD and AX < CY, then\n\n### Options:\nA. XB > AB\nB. XB < YD\nC. AX > XB\nD. AX < CD\nE. AX > AB\n\n### Answer:\nA--X------B\nC-----Y---D\nAX < CD.\nAnswer: D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the area of circle is 616 sq cm then its circumference?\n\n### Options:\nA. 88\nB. 99\nC. 62\nD. 27\nE. 12\n\n### Answer:\n22/7 r2 = 616 => r = 14\n2 * 22/7 * 14 = 88\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA wall photo 2 inches wide is placed around a rectangular paper with dimensions 8 inches by 12 inches. What is the area of the wall photo, in square inches?\n\n### Options:\nA. 96\nB. 86\nC. 108\nD. 144\nE. 118\n\n### Answer:\nThis question is an example of a 'punch out' question - we have to find the area of EVERYTHING, then 'punch out' the part that we don't want.\nWe're told that a wall photo 2 inches wide is placed around a rectangular paper with dimensions 8 inches by 12 inches. We're asked for the area of the wall photo, in square inches.\nArea of a rectangle = (length)(width)\nSo the area of the wall photo is... (8)(12) = 96\nThe wall photo 'adds' 2 inches to the top, bottom, left and right 'sides' of the picture, so the area of EVERYTHING is...\n(8+2+2)(12+2+2) = (12)(16) = 196\nWhen we 'punch out' the area of the paper, we'll be left with the area of the wall photo:\n192 - 96 = 96\nFinal Answer:\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe total of 342 of 20 paise and 25 paise make a sum of Rs. 71. The no of 20 paise coins is\n\n### Options:\nA. 238\nB. 290\nC. 278\nD. 200\nE. 288\n\n### Answer:\nExplanation:\nLet the number of 20 paise coins be x. Then the no of 25 paise coins = (342 - x).\n0.20 * (x) + 0.25 (342 - x) = 71 => x = 290..\nAnswer: B) 290\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo trains are running in opposite directions with the same speed. If the length of each train is 180 m and they cross each other in 12 sec, then the speed of each train is?\n\n### Options:\nA. 54\nB. 31\nC. 36\nD. 25\nE. 24\n\n### Answer:\nLet the speed of each train be x m/sec.\nThen, relative speed of the two trains = 2x m/sec.\nSo, 2x = (180 + 180)/12 => x = 15\nSpeed of each train = 15 m/sec.\n= 15 * 18/5 =54 km/hr.\nAnswer: Option A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a tire rotates at 400 revolutions per minute when the car is traveling 48km/h, what is the circumference of the tire?\n\n### Options:\nA. 2 meters\nB. 6 meters\nC. 5 meters\nD. 3 meters\nE. 7 meters\n\n### Answer:\n400 rev / minute = 400 * 60 rev / 60 minutes\n= 24,000 rev / hour\n24,000 * C = 48,000 m : C is the circumference\nC = 2 meters\ncorrect answer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn Kaya's teacher's desk there are 9 pink highlighters, 8 yellow highlighters, and 5 blue highlighters. How many highlighters are there in all?\n\n### Options:\nA. 11\nB. 22\nC. 77\nD. 33\nE. 88\n\n### Answer:\nAdd the numbers of highlighters.\n9 + 8 + 5 =22.\nAnswer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA real estate agent received a 6% commission on the selling price of a house. If his commission was $8,880, what was the selling price of the house?\n\n### Options:\nA. $234,000\nB. $227,000\nC. $148,000\nD. $479,000\nE. $337,000\n\n### Answer:\n6% x = 8,880 : x = selling price of house.\nx = $148,000 : solve for x\ncorrect answer C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe value of x + x(xx) when x = 7\n\n### Options:\nA. A) 350\nB. B) 346\nC. C) 358\nD. D) 336\nE. E) 364\n\n### Answer:\nx + x(xx)\nPut the value of x = 7 in the above expression we get,\n7 + 7(77)\n= 7 + 7(7 \u00c3\u2014 7)\n= 7 + 7(49)\n= 7 + 343\n= 350 The answer is (A)\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe three sides of an acute angled triangle (all in cms) are 12, 19 and k. How many integer values can k take?\n\n### Options:\nA. 23\nB. 22\nC. 15\nD. 8\nE. 7\n\n### Answer:\nIn acute angle triangles all angles in the triangle should be less than 90.\nThe maximum length of k can be when it is the hypotenuse of the triangle.\nSo, k= sqrt(12^2 + 19^2) = 22.5 (approx)\nThe maximum length of k can be when side of length 12 is the hypotenuse of the triangle.\nSo, k = sqrt (19^2 - 12^2) = 14.7 (approx)\nSo, k>14.7 and k<22.5.\nHence, possible values for k can be 15,16,17,18,19,20,21 and 22. Total 8 values.\nAnswer D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe length of a rectangle is twice the breadth. If the area is 128 cm2, determine the length and the breadth.\n\n### Options:\nA. b=2,l=9\nB. b=8,l=16\nC. b=9,l=9\nD. b=4,l=14\nE. b=3,l=9\n\n### Answer:\nWe are given length l=2b and l\u00d7b=128\n\u22342b\u00d7b=128\n2b^2=128\nb^2=64\nb=\u00b18\nBut breadth must be positive, therefore b=8 cm, and l=2b=16 cm.\nAnswer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf (x-10)(x-3) < 0, which of the following must be true?\n\n### Options:\nA. x^2 + 5x + 6 < 0\nB. x^2 + 5x + 6 > 0\nC. 5 - x < 0\nD. x - 5 < 0\nE. 10 - x > 0\n\n### Answer:\n(x-10)(x-3)<0 can be written as (10-x)(x-3)>0\nSo,to inequality hold true multiple of (10-x) and (x-3) must be positive and if I let both elements positive/negative then the range becomes 30 or x<10,which must be true (I started to look from E to A for making easy decision first)\nCorrect Answer E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe ratio of spinsters to cats is 2 to 7. If there are 35 more cats than spinsters, how many spinsters are there?\n\n### Options:\nA. 14\nB. 21\nC. 28\nD. 35\nE. 42\n\n### Answer:\nLet 2x be the number of spinsters. Then 7x is the number of cats.\n7x-2x=35\nx=7 and the number of spinsters is 2(7)=14.\nThe answer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe cost of an article (which is composed of raw materials and wages) was 3 times the value of raw materials used. The cost of raw materials increased in the ratio 3 : 7 and wages increased in the ratio 4 : 9. Find the present cost of the article if its original cost was Rs. 18.\n\n### Options:\nA. Rs. 41\nB. Rs. 30\nC. Rs. 40\nD. Rs. 46\nE. Rs. 56\n\n### Answer:\nAssume the raw materials\u2019 cost as Rs.150, then the total cost will be Rs. 450, (Thus, wages cost is Rs. 300)\nSince, the cost of raw materials goes up in the ratio of 3 : 7, the new raw material cost would become Rs. 350\nThe new wages cost would be in the ratio 4 : 9 as Rs. 675.\nThe new total cost would become, Rs. 1025.\nSince Rs 450 become Rs. 1025 (change in total cost),\nUnitary method calculation would give us that Rs. 18 would become Rs. 41.\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the solution of the equations x - y = 5 and 5(x + y)-1 = 2 ?\n\n### Options:\nA. x = 3.75, y = 1.25\nB. x = 1, y = 0.1\nC. x = 2, y = 1.1\nD. x = 1.2, y = 0.3\nE. None\n\n### Answer:\nAnswer\nx - y = 5 ...(i)\nand 11(x + y)-1=2\n\u21d2 5/ (x + y) = 2\n\u21d2 2(x + y) =5\n\u21d2 x + y = 5/2 ...(ii)\nOn solving Eqs.(i) and (ii),we get\nx = 3.75\nand y = 1.25\nCorrect Option: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe speed at which a man can row a boat in still water is 15 kmph. If he rows downstream, where the speed of current is 3 kmph, what time will he take to cover 100 metres?\n\n### Options:\nA. 16 seconds\nB. 20 seconds\nC. 14 seconds\nD. 12 seconds\nE. 15 seconds\n\n### Answer:\nSpeed of the boat downstream = 15 + 3 = 18 kmph\n= 18 * 5/18 = 5 m/s\nHence time taken to cover 100 m = 100/5\n= 20 seconds.\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA tap can fill a tank in 16 minutes and another can empty it in 8 minutes. If the tank is already 1/2 full and both the taps are opened together, will the tank be filled or emptied? How long will it take before the tank is either filled completely or emptied completely as the case may be? .\n\n### Options:\nA. Emptied; 16 mins\nB. Filled; 8 mins\nC. Emptied; 12 mins\nD. Filled; 12 mins\nE. None of These\n\n### Answer:\nif A and B open together\nsince B can empty faster than A so tank will empty not fill.\nthe whole tank will empty in 16*8/(16-8)\n=16 min\nsince tank is half so it will take only 8 min to empty.\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA car traveling at a certain constant speed takes 10 seconds longer to travel 1 kilometer than it would take to travel 1 kilometer at 40 kilometers per hour. At what speed, in kilometers per hour, is the car traveling?\n\n### Options:\nA. 35\nB. 35.5\nC. 36\nD. 36.5\nE. 37\n\n### Answer:\n40 * T = 1 km => T = 1/40 km/h\nV*(T+10/3600) = 1\nV (1/40 + 10/3600) = 1\nV (100/3600) = 1\nV = 36 km/h\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAt a loading dock, each worker on the night crew loaded 3/4 as many boxes as each worker on the day crew. If the night crew has 4/9 as many workers as the day crew, what fraction of all the boxes loaded by the two crews did the day crew load?\n\n### Options:\nA. 1/2\nB. 2/5\nC. 3/4\nD. 4/5\nE. 5/8\n\n### Answer:\nMethod: X = No. of boxes loaded by day crew.\nBoxes by night crew = 3/4 * 4/9 X = 1/3 X\n% loaded by day crew = X/(X + 1/3X) = 3/4\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich one of the following numbers is exactly divisible by 11?\n\n### Options:\nA. 235641\nB. 245642\nC. 315624\nD. 415624\nE. Done\n\n### Answer:\n(4 + 5 + 2) - (1 + 6 + 3) = 1, not divisible by 11.\n(2 + 6 + 4) - (4 + 5 + 2) = 1, not divisible by 11.\n(4 + 6 + 1) - (2 + 5 + 3) = 1, not divisible by 11.\n(4 + 6 + 1) - (2 + 5 + 4) = 0, So, 415624 is divisible by 11.\nD)\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe sum of two numbers is 35. Their difference is 5. The bigger number is\n\n### Options:\nA. 20\nB. 25\nC. 30\nD. 35\nE. 45\n\n### Answer:\nX + Y = 35\nX - Y = 5\nAdding 2X = 40 ==> X = 20 and Y = 35 - 20 = 15\nBigger number is X = 20\nAnswer A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how many ways can 4 black and 4 white chess pieces be arranged in a row such that they occupy alternate places? Assume that the pieces are distinct.\n\n### Options:\nA. 144\nB. 24\nC. 576\nD. 48\nE. 16\n\n### Answer:\n4 black chess pieces can be arranged in 4! ways and 4 white pieces can be arranged in 4! ways.\nW_W_W_W\nNumber of ways = 4!*4! = 24 * 24 = 576\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA perfect square is defined as the square of an integer and a perfect cube is defined as the cube of an integer. How many positive integers n are there such that n is less than 30,000 and at the same time n is a perfect square and a perfect cube?\n\n### Options:\nA. 4\nB. 5\nC. 6\nD. 7\nE. 8\n\n### Answer:\nIf n is a perfect square and a perfect cube, then n = a^6 for some integer a.\nThe numbers are 1^6=1, 2^6=64, 3^6= 729, 4^6=4096, 5^6=15,625.\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA boat running downstream covers a distance of 22 km in 4 hours while for covering the same distance upstream, it takes 5 hours. What is the speed of the boat in still water?\n\n### Options:\nA. 2.75\nB. 5.95\nC. 7.95\nD. 3.25\nE. 4.95\n\n### Answer:\nSpeed downstream =22/4 = 5.5 kmph\nSpeed upstream =22/5 = 4.4 kmph\nSpeed of the boat in still water=(5.5+4.4)/2= 4.95 kmph\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\na,b and c are positive integers less than or equal to 9. If a,b and c are assembled into the six-digit number aabbcc, which of the following must be a factor of aabbcc?\n\n### Options:\nA. 9\nB. 3\nC. 7\nD. 11\nE. None of these\n\n### Answer:\nThe sum of the digits in place 1,3 and 5 is a+b+c is equal to the sum of the digits in place 2,4 and 6 which is a+b+c. thus the number abcabc is divisible by 11. thus 11 must be a factor of abcabc.\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train 400 m long can cross an electric pole in 40 sec and then find the speed of the train?\n\n### Options:\nA. 36 Kmph\nB. 40 Kmph\nC. 42 Kmph\nD. 45 Kmph\nE. 38 Kmph\n\n### Answer:\nLength = Speed * time\nSpeed = L/T\nS = 400/40\nS = 10 M/Sec\nSpeed= 10*18/5 (To convert M/Sec in to Kmph multiply by 18/5)\nSpeed = 36 Kmph\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMike weighs twice as much as Mary. Mike's weight is 150% of Michelle's weight. Alan weighs 140% of Charlie's weight. Charlie weighs 180% of Mary's weight. Which of these 5 people weighs the highest?\n\n### Options:\nA. Mary\nB. Mike\nC. Michelle\nD. Alan\nE. Charlie\n\n### Answer:\nMary < Michelle < Mike\nCharlie < Alan\nLet x be Mary's weight.\nMike's weight is 2x and Alan's weight is 1.4*1.8x = 2.52x.\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nEach of three investments has a 20% of becoming worthless within a year of purchase, independently of what happens to the other two investments. If Simone invests an equal sum in each of these three investments on January 1, the approximate chance that by the end of the year, she loses no more than 1/3 of her original investment is\n\n### Options:\nA. 90%\nB. 80%\nC. 70%\nD. 60%\nE. 40%\n\n### Answer:\nSince amount invested is same for all 3 , and probability of investment turning worthless is 20%, the required probability is\n80%\u00d780%\u00d780% + 20%\u00d780%\u00d780\u00d7\\frac{3!}{2!}\n=89.6%\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the total number of prime factors in the expression (4)11 x (7)5 x (11)2.\n\n### Options:\nA. 22\nB. 29\nC. 19\nD. 5\nE. 2\n\n### Answer:\n(4)11x (7)5 x (11)2 = (2 x 2)11 x (7)5 x (11)2 = 211 x 211 x75x 112\n= 222 x 75 x112\nTotal number of prime factors = (22 + 5 + 2)\n= 29.\nANSWER B 29\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n(((13!)^16)-((13!)^8))/(((13!)^8)+((13!)^4))=a\nthen what is the units digit for a/((13!)^4)=\n\n### Options:\nA. 7\nB. 8\nC. 9\nD. 6\nE. 5\n\n### Answer:\n(((13!)^16)-((13!)^8))/(((13!)^8)+((13!)^4))=a\nsolving it , we get\na/((13!)^4)= ((13!)^4-1)\nlast digit of (13!)^4 will be 0.\nso last digit of ((13!)^4-1) will be 9.\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHaving received his weekly allowance, John spent 3/5 of his allowance at the arcade. The next day he spent one third of his remaining allowance at the toy store, and then spent his last $0.88 at the candy store. What is John\u2019s weekly allowance?\n\n### Options:\nA. $2.70\nB. $3.00\nC. $3.30\nD. $3.60\nE. $3.90\n\n### Answer:\nx = 3x/5 + 1/3*2x/5 + 88\n4x/15 = 88\nx = 330 = $3.30\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn covering a distance of 30 km, Abhay takes 2 hours more than Sameer. If Abhay doubles his speed, then he would take 1 hour less than Sameer. Abhay's speed is:\n\n### Options:\nA. 5 kmph\nB. 6 kmph\nC. 6.25 kmph\nD. 7.5 kmph\nE. 7 kmph\n\n### Answer:\nLet Abhay's speed be x km/hr.\nThen,30/x\t-30/2x = 3\n6x = 30\nx = 5 km/hr\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAman started a business investing Rs. 70,000. Rakhi joined him after six months with an amount of Rs. 1,05,000 and Sagar joined them with Rs. 1.4 lakhs after another six months. The amount of profit earned should be distributed in what ratio among Aman, Rakhi and Sagar respectively, 3 years after Aman started the business?\n\n### Options:\nA. 12:15:17\nB. 12:15:16\nC. 12:15:10\nD. 12:15:155\nE. 12:15:11\n\n### Answer:\nAman : Rakhi : Sagar = (70000 * 36) : (105000 * 30) : (140000 * 24)\n= 12:15:16\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA is faster than B. A and B each walk 24 km. The sum of their speeds is 7 km/hr and the sum of times taken by them is 14 hours. Then, A's speed is equal to?\n\n### Options:\nA. 6 km/hr\nB. 3 km/hr\nC. 1 km/hr\nD. 9 km/hr\nE. 4 km/hr\n\n### Answer:\nLet A's speed = x km/hr. Then, B's speed = (7 - x) km/ hr.\nSo, 24/x + 24/(7 - x) = 14\nx2 - 98x + 168 = 0\n(x - 3)(x - 4) = 0 => x = 3 or 4.\nSince, A is faster than B, so A's speed = 4 km/hr and B's speed = 3 km/hr.\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo men and 7 children complete a certain piece of work in 4 days while 4 men and 4 children complete the same work in only 3 days. The number of days required by 1 man to complete the work is\n\n### Options:\nA. 60 days\nB. 15 days\nC. 6 days\nD. 51 days\nE. 50 days\n\n### Answer:\nTwo men and 7 children complete a certain piece of work in 4 days\nor 8 men and 28 children complete a certain piece of work in 1 days\n4 men and 4 children complete the same work in only 3 days.\nor 12 men and 12 children complete the same work in only 3 days.\nso 8 men +28 children = 12 men +12 children\n1Man = 4 children\n4 men and 4 children complete the same work in only 3 days\nor 4 men and 1 man ( in place of 4 children ) complete the same work in only 3 days\nor 5 men complete the same work in 3 days\nor 1 man will complete the same work in 5* 3 =15 days\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average of six numbers is 3.85. The average of two of them is 3.4, while the average of the other two is 3.85. What is the average of the remaining two numbers ?\n\n### Options:\nA. 4.3\nB. 4.6\nC. 4.2\nD. 4.1\nE. 4.9\n\n### Answer:\nExplanation:\nSum of the remaining two numbers = (3.85 * 6) - [(3.4 * 2) + (3.85 * 2)]\n= 23.10 - (6.8 + 7.7) = 23.10 - 14.5 = 8.60.\nRequired average = (8.6 / 2) = 4.3.\nAnswer: A) 4.3\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA salesman sold twice as much pears in the afternoon than in the morning. If he sold 360 kilograms of pears that day, how many kilograms did he sell in the morning and how many in the afternoon?\n\n### Options:\nA. 150\nB. 190\nC. 100\nD. 240\nE. 280\n\n### Answer:\nLet x be the number of kilograms he sold in the morning.Then in the afternoon he sold 2x kilograms. So, the total is x+2x=3x This must be equal to 360.\n3x=360\nx=360/3\nx=120\nTherefore, the salesman sold 120 kg in the morning and 2\u22c5120=240 kg in the afternoon.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA single discount equivalent to the discount series of 20%, 10% and 5% is?\n\n### Options:\nA. 31.6\nB. 31.9\nC. 31.6\nD. 31.4\nE. 31.1\n\n### Answer:\n100*(80/100)*(90/100)*(95/100) = 68.4\n100 - 68.4 = 31.6\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nConnie paid a sales tax of 8 percent on her purchase. If the sales tax had been only 5 percent, she would have paid $12 less in sales tax on her purchase. What was the total amount that Connie paid for her purchase including sales tax?\n\n### Options:\nA. $368\nB. $380\nC. $400\nD. $420\nE. $432\n\n### Answer:\nConnie paid x dollar before sales tax\nso,\n1.08x - 1.05x = 12\n0.03x = 12\nx = 400\nsales tax 400*8% = 32\nConnie paid = 400+32= $432\nAns. E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe no. of girls in a class are seven times the no. of boys, which value can neverbe the of total students?\n\n### Options:\nA. 4\nB. 5\nC. 8\nD. 10\nE. 12\n\n### Answer:\nLet the boys are X, then girls are 7X, total = X+7X = 8X\nSo it should be multiple of 8, 30 is not a multiple of 8.\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJohn traveled 80% of the way from Yellow-town to Green-fields by train at an average speed of 80 miles per hour. The rest of the way John traveled by car at an average speed of v miles per hour. If the average speed for the entire trip was 60 miles per hour, what is v in miles per hour?\n\n### Options:\nA. 30\nB. 40\nC. 50\nD. 55\nE. 70\n\n### Answer:\nLet distance be D.\nWe can find the total time & equate it, which comes as:\n0.8D / 80 + 0.2D / v = D / 60\n=> v = 30\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train 130 m long passes a man,running at 6 kmph in the direction opposite to that of the train,in 6 seconds.The speed of the train is\n\n### Options:\nA. 54 kmph\nB. 60 kmph\nC. 66 kmph\nD. 72 kmph\nE. 82 kmph\n\n### Answer:\nspeed of train relative to man: 130/6 * 18/5 km/hr\n= 78 km/hr\nlet speed of train= x\ntherefore x+6 = 78\nx= 78-6\nx=72 km/hr\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe total marks obtained by a student in Mathematics and Physics is 32 and his score in Chemistry is 20 marks more than that in Physics. Find the average marks scored in Mathamatics and Chemistry together.\n\n### Options:\nA. 40\nB. 26\nC. 27\nD. 28\nE. 22\n\n### Answer:\nLet the marks obtained by the student in Mathematics, Physics and Chemistry be M, P and C respectively.\nGiven , M + C = 32 and C - P = 20 M + C / 2 = [(M + P) + (C - P)] / 2 = (32 + 20) / 2 = 26.Answer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n24 oz of juice P and 25 oz of juice V are mixed to make smothies R and Y . The ratio of p to V in smothie R is 4 is to 1 and that in Y is 1is to 5.How many ounces of juice P are contained in the smothie R?\n\n### Options:\nA. 5\nB. 10\nC. 15\nD. 20\nE. 25\n\n### Answer:\nThe ratio of p to V in smothie R is 4 is to 1 and that in Y is 1is to 5. p1 + p2 = 24\nv1 + v2 = 25\np1 = 4v1\np2 = v2/5\n4v1 + v2/5 = 24\nv1 + v2 = 25\n4v2 - v2/5 = 76\n19v2/5 = 76 => v2 = 20\n=> v1 = 5\n=> p1 = 20\nAnswer - D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man can row 5 kmph in still water. When the river is running at 2 kmph, it takes him 1 hour to row to a place and black. What is the total distance traveled by the man?\n\n### Options:\nA. 5.75\nB. 5.7\nC. 5.76\nD. 4.2\nE. 5.71\n\n### Answer:\nM = 5\nS = 2\nDS = 7\nUS = 3\nx/7 + x/3 = 1\nx = 2.1\nD = 2.1 * 2 = 4.2 Answer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe amount of time that three people worked on a special project was in the ratio of 1 to 2 to 3. If the project took 120 hours, how many more hours did the hardest working person work than the person who worked the least?\n\n### Options:\nA. 35 hours\nB. 40 hours\nC. 36 hours\nD. 38 hours\nE. 42 hours\n\n### Answer:\nLet the persons be A, B, C.\nHours worked:\nA = 1*120/6 = 20 hours\nB = 2*120/6 = 40 hours\nC = 3*120/6 = 60 hours\nC is the hardest worker and A worked for the least number of hours. So the difference is 60-20 = 40 hours.\nAnswer : B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA and B can do a piece of work in 8 days. B and C can do it in 12 days and A and C in 16 days. Working together they will complete the work in how many days?\n\n### Options:\nA. 7.78 days\nB. 7.88 days\nC. 7.38 days\nD. 7.38 days\nE. 7.36 days\n\n### Answer:\nA + B = 1/8\nB + C = 1/12\nC + A = 1/16\n-------------------------------\n2(A + B +C) = 1/8 + 1/12 + 1/16 = 13/48\nA + B +C = 13/96\n96/13 = 7.38 days\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSandy bought 65 books for $1380 from one shop and 55 books for $900 from another shop. What is the average price that Sandy paid per book?\n\n### Options:\nA. $13\nB. $15\nC. $17\nD. $19\nE. $21\n\n### Answer:\naverage price per book = (1380 + 900) / (65 + 55) = 2280 / 120 = $19\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA gets 3 times as much money as B gets, B gets only Rs.25 more then what C gets. The three gets Rs.675 in all. Find the share of B?\n\n### Options:\nA. 287\nB. 219\nC. 168\nD. 140\nE. 779\n\n### Answer:\nA+B+C = 675\nA = 3B\n3B+B+B-25 = 675\n5B = 700\nB = 140\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n575.104 x 15.98 \u00c3\u00b7 9.001 + 21.25 = ?\n\n### Options:\nA. 983.578\nB. 1043.65\nC. 1033.65\nD. 656.112\nE. 456.512\n\n### Answer:\nExplanation:\n? = 575.104 x 15.98 \u00c3\u00b7 9.001 + 21.25\n\u00e2\u2030\u02c6 (575.104 x 16/9) + 21.25 \u00e2\u2030\u02c6 1022.40 + 21.25 \u00e2\u2030\u02c6 1043.65\nAnswer: Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nP is a set of four numbers 1, 2, 3 and 1. In every step, one is added to any two numbers in the set P. In how many such steps is it possible to make all the four numbers in the set P equal?\n\n### Options:\nA. 4\nB. 5\nC. 6\nD. 1\nE. 2\n\n### Answer:\nIf all the four numbers are equal, then their sum in the end of the process must be multiple of 4.\nNow the sum of the given numbers is equal to 7. Each time we are adding 1 to two of any two numbers, so the sum increases by 2 each time. So the sum never becomes a multiple of 4 as odd + even = always odd.\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf N = 2^0.15 and N^b = 1, b must equal\n\n### Options:\nA. 3/80\nB. 20/3\nC. 4\nD. 5/3\nE. 80/3\n\n### Answer:\n15/100 = 3/20\nN = 2 ^ 3/20\nN^b = 2^1\n(2^3/20)^b = 2^1\nb = 20/3\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA began business with 10000 and is joined afterwards by B with 20000. When did B join, if the profits at the end of the year are divided equally?\n\n### Options:\nA. 8 months\nB. 9 months\nC. 6 months\nD. 7 months\nE. None of these\n\n### Answer:\nLet B join after x months of the start of the business so that B\u2019s money is invested for (12 \u2013 x) months.\n\u2234 Profit ratio is 12 \u00d7 10000 : (12 \u2013 x) \u00d7 20000\nor 12 : 2(12 \u2013 x)\nSince profit is equally divided so\n12 = 2(12 \u2013 x) or x = 6. Thus B joined after 8 months.\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat should be added to 4872 so that it may become a perfect square?\n\n### Options:\nA. 24\nB. 25\nC. 26\nD. 27\nE. 28\n\n### Answer:\n70x70=4900\n4900-4872 = 28\nIf added to 28 get perfect square\nanswer =E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nEach person who attended a company meeting was either a stockholder in the company, an employee of the company or both. If 62 percent of these who attended the meeting were stockholders and 51 percent were employees. What percent were stockholders, who were not employees?\n\n### Options:\nA. 52\nB. 49\nC. 54\nD. 55\nE. 56\n\n### Answer:\nI came up with the same answer choice B, but my approach was slightly different!\n51% were employees which shall cover those who were only employees and those who were both shareholders and employees.\nThus, the number of attendants who were only shareholders is 100% - 51% = 49%.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMary invested a certain sum of money in a bank that paid simple interest. The amount grew to $260 at the end of 2 years. She waited for another 3 years and got a final amount of $350. What was the principal amount that she invested at the beginning?\n\n### Options:\nA. $220\nB. $230\nC. $240\nD. $200\nE. $250\n\n### Answer:\nWhat shall be the rate of interest.? Does that is not required for the calculation?\nNot really!\nKeep in mind that the interest earned each year will be the same in Simple Interest.\nAt the end of 2 years, Amount = $260\nAt the end of 5 years, Amount = $350\nThis means she earned an interest of $90 in 3 years. Or $30 in each year.\nWe know that the interest earned each year will be the same.\nTherefore she must have earned $60 in 2 years.\nHence Principal Amount = $260 - $60 = $200 Option D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThree workers have a productivity ratio of 2 to 4 to 8. All three workers are working on a job for 4 hours. At the beginning of the 5th hour, the slowest worker takes a break. The slowest worker comes back to work at the beginning of the 9th hour and begins working again. The job is done in ten hours. What was the ratio of the work performed by the fastest worker as compared to the slowest?\n\n### Options:\nA. 20 to 3\nB. 6 to 1\nC. 5 to 1\nD. 1 to 6\nE. 1 to 5\n\n### Answer:\nThe fastest worker who does 8 units of job worked for all 10 hours, so he did 8*10=80 units of job;\nThe slowest worker who does 2 unit of job worked for only 4+2=6 hours (first 4 hours and last 2 hours), so he did 2*6=12 units of job;\nThe ratio thus is 80 to 12, or 20 to 3.\nAnswer: A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf $500 was invested at an annual interest rate of 5.6% compounded annually, which of the following represents the amount the investment was worth after 3 years?\n\n### Options:\nA. 500 (1.056)(3)\nB. 500 (3+1.056)\nC. 500 (1+3(0.056))\nD. 500 (1.056)^3\nE. 500 (1+(0.056)^3)\n\n### Answer:\nthe formula is CI=P(1+r/100)^t\nin this case i think D is the ans\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nW and X start a business with Rs.5000 and Rs.20000 respectively. Hoe should they share their profits at the end of one year?\n\n### Options:\nA. 4:1\nB. 1:3\nC. 1:4\nD. 1:5\nE. 2:1\n\n### Answer:\nThey should share the profits in the ratio of their investments.\nThe ratio of the investments made by W and X =\n5000 : 20000 => 1:4 .\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe operation # is defined for all nonzero d and y by d#y = d + d/y. If a>0, then 1#(1#a) =\n\n### Options:\nA. a\nB. a+1\nC. a/(a+1)\nD. (a+2)/(a+1)\nE. (2a+1)/(a+1)\n\n### Answer:\nd#y = d + d/y. If a>0, then 1#(1#a) =\nYou can see that a stands for y and 1 stands for d. I like to work with numbers so I did d=1 a=2 and a=y so y=2\n1#a= 1+(1/2)=1.5 so now a is 1.5 --> 1+(1/1.5)=1 2/3 = 5/3\nSo now you can check by filling in a, which is 2:\nA. a --> 2\nB. a+1 --> 2+1=3\nC. a/(a+1)-->2/(2+1)=2/3\nD. (a+2)/(a+1)-->(2+2)/(2+1)=4/3\nE. (2a+1)/(a+1)-->(2*2+1)/(2+1)=5/3\nSo E is the answer.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA type W machine can complete a job in 5 hours and a type B machine can complete the job in 7 hours. How many hours will it take 2 type W machines and 3 type B machines working together and independently to complete the job?\n\n### Options:\nA. 1/5\nB. 29/35\nC. 5/6\nD. 35/29\nE. 35/12\n\n### Answer:\nnow D should be the answer.\nW need 5 hours to complete\nand B needs 7 hours to compete\nso 2W + 3B will complete 2/5 + 3/7 or 29/35 portion of the job in 1 hour\nso the whole job will take 35/29 hours....=D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a village of 100 households, 85 have at least one DVD player, 90 have at least one cell phone, and 55 have at least one MP3 player. If x and y are respectively the greatest and lowest possible number of households that have all three of these devices, x \u2013 y is:\n\n### Options:\nA. 65\nB. 55\nC. 45\nD. 35\nE. 25\n\n### Answer:\nAm I missing something here??? it seems straightforward......\nThe obvious maximum that have all 3 is 55, because you are limited by the SMALLEST number.\nThe minimum is simply the sum of the max of each people who DONT have the product, so:\n100-90 = 10 don't have Cell\n100-85 = 15 don't have DVD\nand 100-55 = 45 don't have MP3\nSO a total of 10+15+45 = 70 combined who might NOT have SOME combination of the 3 products. So subtract that from 100, to give you the minimum of the people who COULD have all 3 and you get 100-70 = 30.\n55-30 = 25\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the greatest prime factor of (11!10!) + (11!12!)?\n\n### Options:\nA. 11\nB. 17\nC. 19\nD. 23\nE. 29\n\n### Answer:\n11!10! + 11!12!\n= 11!10! (1+11*12)\n= 12!11!(133)\n= 12!11!(7*19)\nThe greatest prime factor is 19.\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average weight of 8 person's increases by 4.2 kg when a new person comes in place of one of them weighing 65 kg. What is the weight of the new person?\n\n### Options:\nA. 75 Kg\nB. 50 Kg\nC. 85 Kg\nD. 80 Kg\nE. 98.6 KG\n\n### Answer:\nExplanation:\nTotal increase in weight = 8 \u00c3\u2014 4.2 = 33.6\nIf x is the weight of the new person, total increase in weight = x\u00e2\u02c6\u201965\n=> 33.6 = x - 65\n=> x = 33.6 + 65 = 98.6\nAnswer: Option E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nDivide Rs. 5500 among A, B and C so that A receives 1/3 as much as B and C together and B receives 1/5 as A and C together. A's share is?\n\n### Options:\nA. 1227\nB. 1268\nC. 1375\nD. 1200\nE. 1210\n\n### Answer:\nA+B+C = 5500\nA = 1/3(B+C); B = 1/5(A+C)\nA/(B+C) = 1/3\nA = 1/4 * 5500 => 1375\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA flight takes off at 2.00 a.m. from a place at 18N 10E and landed 10 hours later at a place with co-ordinates 36N 70W. What is the local time when the plane landed?\n\n### Options:\nA. 6.00 a.m.\nB. 6.40 a.m.\nC. 7.00 a.m.\nD. 7.40 a.m.\nE. 8.00 a.m.\n\n### Answer:\nTime difference between places will be 4*(70+10) minutes = 320 min =\n5 hrs 20 min\nas change of 1 degree in longitude cause change of 4 minutes in time.\nand that change is 80 degrees here.\nso when plane land. time will be = 2.00 + 10.00 -5.20 = 6.40 a.m.\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA motor boat takes 12 hours to go downstream and it takes 24 hours to return the same distance. what is the time taken by boat in still water?\n\n### Options:\nA. 26 h\nB. 16 h\nC. 86 h\nD. 96 h\nE. 66 h\n\n### Answer:\nExplanation:\nIf t1 and t2 are the upstream and down stream times. Then time taken in still water is given by\n\\inline \\frac{2\\times t1\\times t2}{t1+t2}=\\frac{2\\times 12\\times 24}{36}=16h\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA cyclist rides a bicycle over a route which is 1/3 uphill, 1/3 level, and 1/3 downhill. If the cyclist covers the uphill part of the route at the rate of 8 km per hour and the level part at the rate of 12 km per hour, what rate in km per hour would the cyclist have to travel the downhill part of the route in order to average 12 km per hour for the entire route?\n\n### Options:\nA. 16\nB. 20\nC. 24\nD. 28\nE. 32\n\n### Answer:\nLet V be the speed on the downhill section.\nLet D be the distance of each of the three equal sections.\nTotal time T = T1+T2+T3 and 3D/T = 12 km/hour\n3D / (D/8 + D/12 + D/V) = 12\n1/4 = 1/8 + 1/12 + 1/V\n1/V = 1/24 and so V = 24 km/h\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nif x+y+z=9 and both y and z are positive integers greater than zero, then the maximum value x can take is?\n\n### Options:\nA. 7\nB. 3\nC. 8\nD. 6\nE. data insufficient\n\n### Answer:\nif y=z=1, then x will be equal to 7.\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA grocer has a sale of Rs. 2500, Rs. 4000, Rs. 3540 for 3 consecutive months. How much sale must he have in the fourth month so that he gets an average sale of Rs. 2890?\n\n### Options:\nA. Rs.3500\nB. Rs. 1520\nC. Rs. 4996\nD. Rs. 4000\nE. Rs. 900\n\n### Answer:\nTotal sale for 5 months = Rs. ( 2500 + 4000 + 3540) = Rs. 10040.\nRequired sale = Rs. [ (2890 x 4) -10040 ]\n= Rs. (11560 - 10040)\n= Rs. 1520.\nB)\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf b is the sum of consecutive even integers w, x, y, and z, where w < x < y < z, all of the following must be true EXCEPT\n\n### Options:\nA. z - w = 3(y - x)\nB. b is divisible by 8\nC. The average of w, x, y, and z is odd\nD. b is divisible by 4\nE. w + x + 8 = y + z\n\n### Answer:\nJust assume that the numbers are 2a, 2a+2, 2a+4 and 2a+6.\nb = 2a + 2a+2 + 2a+4 + 2a+6 = 8a + 12\nFocus on the easiest options first. You see that b is not divisible by 8. Answer (B)\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the ratio whose terms differ by 40 and the measure of which is 2\u20447\n\n### Options:\nA. 16 : 56\nB. 14 : 56\nC. 15 : 56\nD. 16 : 72\nE. None of these\n\n### Answer:\nLet the ratio be x: (x + 40).Then,\nx/(x+40)=2/7 \u21d2 2x + 80 \u21d2 x = 16.\n\u2234 Required ratio = 16 : 56.\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 2805 / 2.55 = 1100, then 280.5 / 25.5 is equal to ?\n\n### Options:\nA. 1.01\nB. 1.1\nC. 0.11\nD. 11\nE. None\n\n### Answer:\nAnswer\nGiven expression 280.5 / 25.5 = 2805 / 255\n= 2805 / (2.55 x 100)\n= 1100 / 100\n=11\nCorrect Option: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf three machines working at the same rate can do 3/4 of a job in 30 minutes, how many minutes would it take two machines working at the same rate to do 3/5 of the job?\n\n### Options:\nA. 36\nB. 60\nC. 75\nD. 80\nE. 100\n\n### Answer:\nusing the std formula\nm1d1h1/w1=m2d2h2/w2\nsubstituting the values we have\n3*1/2*4/3=2*5/3*x (converted 30 min into hours =1/2)\n2=10/3*x\nx=3/5 hour\nso 36 minutes\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAt present, the ratio between the ages of Amit and Dhiraj is 5 : 4. After 6 years, Amit\u2019s age will be 26 years. What is the age of Dhiraj at present?\n\n### Options:\nA. 16\nB. 77\nC. 566\nD. 197\nE. 161\n\n### Answer:\nExplanation:\nLet the present ages of Amit and Dhiraj be 5x years and 4x years respectively. Then,\n5x + 6 = 26\n5x = 20\nx = 4\nDhiraj\u2019s age = 4x = 16 years\nANSWER: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nCindy has her eye on a sundress but thinks it is too expensive. It goes on sale for 15% less than the original price. Before Cindy can buy the dress, however, the store raises the new price by 25%. If the dress cost $85 after it went on sale for 15% off, what is the difference between the original price and the final price?\n\n### Options:\nA. $0.00\nB. $1.00\nC. $3.40\nD. $5.00\nE. $6.25\n\n### Answer:\n0.85*{Original Price} = $85 --> {Original Price} = $100.\n{Final Price} = $85*1.25 = $106.25.\nThe difference = $106.25 - $100 = $6.25.\nAnswer: E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 8 spiders make 4 webs in 9 days, then how many days are needed for 1 spider to make 1 web?\n\n### Options:\nA. 10\nB. 20\nC. 12\nD. 16\nE. 18\n\n### Answer:\nExplanation:\nLet, 1 spider make 1 web in x days.\nMore spiders, Less days (Indirect proportion)\nMore webs, more days (Direct proportion)\nHence we can write as\n(spiders)8:1\n(webs) 1:9}::x:4\n\u00e2\u2021\u20198\u00c3\u20141\u00c3\u20149=1\u00c3\u20144 \u00c3\u2014 x\n\u00e2\u2021\u2019x=18\nAnswer: Option E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively . If they cross each other in 23 seconds, what is the ratio of their speeds?\n\n### Options:\nA. 3/2\nB. 1/2\nC. 4/3\nD. 3/4\nE. 1/5\n\n### Answer:\nLet the speed of the trains be x and y respectively\nlength of train1 = 27x\nlength of train2 = 17y\nRelative speed= x+ y\nTime taken to cross each other = 23 s\n=> (27x + 17 y)/(x+y) = 23\n=> (27x + 17 y)/ = 23(x+y)\n=> 4x = 6y\n=> x/y = 6/4 = 3/2\nAnswer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAt a certain organisation, the number of male members went up by 15% in the year 2001 from year 2000, and the number of females members went down by 6% in the same time period. If the total membership at the organisation went up by 1.2% from the year 2000 to 2001, what was the ratio of male members to female members in the year 2000?\n\n### Options:\nA. 1:2\nB. 1:3\nC. 2:3\nD. 3:2\nE. 2:1\n\n### Answer:\nmen increase by 15% ==> 1.15M = males in 2001\nwomen decrease by 6% ==> 0.94F = women in 2001\ntotal employees increase by 1.2% ==> 1.012*(M + F) = total number of employees in 2001\nObviously\n(males in 2001) + (females in 2001) = total number of employees in 2001\n1.15M + 0.94F = 1.012*(M + F)\n1.15M + 0.94F = 1.012M + 1.012F\n1.15M - 1.012M = 1.012F - 0.94F\n0.138M = 0.072F\nM/F = (0.072)/(0.138) = 72/138 = 1/2\nAnswer =(A)\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat Is The Next Number\n12 13 15 17 111 113 ?\n\n### Options:\nA. 154\nB. 220\nC. 129\nD. 428\nE. 117\n\n### Answer:\n117\nThese are the first 10 prime numbers (2, 3, 5...) prefixed with a 1\nAnswer : E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe third proportional to 1 and 3 is?\n\n### Options:\nA. 9\nB. 10\nC. 11\nD. 12\nE. 13\n\n### Answer:\n(3*3)/1 = 9\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe H.C.F. and L.C.M. of two numbers are 10 and 5040 respectively If one of the numbers is 144, find the other number\n\n### Options:\nA. 400\nB. 256\nC. 350\nD. 420\nE. None of these\n\n### Answer:\nExplanation:\nSolve this question by using below formula.\nProduct of 2 numbers = product of their HCF and LCM\n144 * x = 10 * 5040\nx = (10*5040)/144 = 350\nOption C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA sum of Rs. 4000 amounts to Rs. 4600 in 5 years at a certain rate of simple interest. What would be the amount, if the rate of interest is increased by 3 %.\n\n### Options:\nA. Rs. 5202\nB. Rs. 5200\nC. Rs. 5228\nD. Rs. 5212\nE. Rs. 5182\n\n### Answer:\nExplanation:\nPrincipal = Rs. 4000, Amount = Principal + SI = Rs. 4600\nSI = Amount \u2013 Principal = 4600 \u2013 4000 = Rs. 600\nGiven : Principal = Rs. 4000, Time = T = 5 years and SI = Rs. 600\nSI =PRT/100\n600 = 4000 *R * 5/100\n600 = 200R\nR = 3 % p.a.\nNow the new interest rate is = 3% + 3% = 6 % p.a.\nSI = PRT/ 100 = 4000 * 6 * 5/ 100 = Rs. 1200\nAmount = Principal + SI\n= 4000 + 1200\n= 5200\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man has Rs. 480 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has?\n\n### Options:\nA. 90\nB. 70\nC. 50\nD. 80\nE. 60\n\n### Answer:\nLet number of notes of each denomination be x.\nThen x + 5x + 10x = 480\n16x = 480\nx = 30.\nHence, total number of notes = 3x = 90.\nAnswer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the probability that a two digit number selected at random will be a multiple of '3' and not a multiple of '5'?\n\n### Options:\nA. 2/15\nB. 4/15\nC. 1/15\nD. 4/90\nE. 5/60\n\n### Answer:\nSolution:\nThere are a total of 90 two digit numbers. Every third number will be divisible by '3'. Therefore, there are 30 of those numbers that are divisible by '3'.\nOf these 30 numbers, the numbers that are divisible by '5' are those that are multiples of '15'. i.e. numbers that are divisible by both '3' and '5'.\nThere are 6 such numbers -- 15,30,45,60,75 and 90.\nWe need to find out numbers that are divisible by '3' and not by '5', which will be:\n30\u00e2\u02c6\u20196=24\n24 out of the 90 numbers are divisible by '3' and not by '5'.\nThe required probability is therefore,\n=24/90\n=4/15\nANSWER IS B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe overall ages of Kumar, Hathim and Rahul is 93 years. 1 decade ago, the ratio of their ages was 2 : 3 : 4. What is the current age of Rahul?\n\n### Options:\nA. 38\nB. 37\nC. 34\nD. 35\nE. 33\n\n### Answer:\nA\n38\nIf the ages of Kumar, Hathim and Rahul 1 decade ago be 2A, 3A and 4A years correspondingly\nThen, (2A + 10) + (3A + 10) + (4A + 10) = 93\n9A = 93-30\n9A = 63\nA = 7\nRahul\u2019s current age = (4A + 10)\n= 38 years.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA person crosses a 1080 m long street in 12 minutes. What is his speed in km per hour?\n\n### Options:\nA. 4.1\nB. 4.5\nC. 4.8\nD. 5.4\nE. 5.5\n\n### Answer:\nSpeed = 1080/(12x60) m/sec\n= 1.5 m/sec.\nConverting m/sec to km/hr =1.5 x(18/5) km/hr\n= 5.4 km/hr.\nANSWER :D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA garrison of 2000 men has provisions for 65 days. At the end of 15 days, a reinforcement arrives, and it is now found that the provisions will last only for 20 days more. What is the reinforcement?\n\n### Options:\nA. 1977\nB. 1893\nC. 1979\nD. 3000\nE. 1278\n\n### Answer:\n2000 ---- 65\n2000 ---- 50\nx ----- 20\nx*20 = 2000*50\nx = 5000\n2000\n-------\n3000\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a class, the average age of 25 boys is 10 years and the average of 18 girls is 10 years. what is the average age of the whole class?\n\n### Options:\nA. 10 Years\nB. 12.6 Years\nC. 13 Years\nD. 13.5 Years\nE. 14 Years\n\n### Answer:\nTotal age of 43 students\n(25X 10+18 X 10) = 430\nAverage = 430/43 = 10 Years\nA)\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA parallelogram has a base that is four time the size of it's height. The total area of this parallelogram is 2,304 Sq ft. What is the height of the parallelogram?\n\n### Options:\nA. 19\nB. 23\nC. 24\nD. 16\nE. 17\n\n### Answer:\n4x * x = 2304 => x\n= 24\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich of the following is equal to 3^k*5^(k-1)?\n\n### Options:\nA. 3*15^(k-1)\nB. 5*10^(k-1)\nC. 15^k\nD. 3*15^k\nE. 15^(2k-1)\n\n### Answer:\n3^k*5^(k-1) = 3*3^(k-1)*5^(k-1) = 3*15^(k-1)\nThe answer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere is 60% increase in an amount in 6 years at S.I. What will be the C.I. of Rs. 12,000 after 3 years at the same rate?\n\n### Options:\nA. 2387\nB. 2978\nC. 3972\nD. 2671\nE. 1871\n\n### Answer:\nExplanation:\nLet P = Rs. 100. Then, S.I. Rs. 60 and T = 6 years.\nR = (100 * 60)/(100 * 6) = 10% p.a.\nNow, P = Rs. 12000, T = 3 years and R = 10% p.a.\nC.I. = [12000 * {(1 + 10/100)3 - 1}]\n= 12000 * 331/1000 = Rs. 3972\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSam\u2019s car was fined when he gave Joe and Peter a ride, so they decided to help Sam pay the fine. Joe paid $7 more than 1/4 of the fine and Peter paid $7 less than 1/3 of the fine, leaving pay $12 less than 1/2 the fine to complete the payment. What fraction of the fine did Sam pay?\n\n### Options:\nA. $65\nB. $55\nC. $50\nD. $60\nE. $45\n\n### Answer:\nCall the fine F. Joe paid (1/4)F + 4 and Peter paid (1/3)F \u2013 4, leaving (1/2)F \u2013 5 left. If we add those three up, they should add up to F.\nF = [(1/4)F + 7] + [(1/3)F \u2013 7] + [(1/2)F \u2013 12]\nF = (1/4)F + (1/3)F + (1/2)F \u2013 12\nMultiply all terms by 12 to clear the fractions.\n12F = 3F + 4F + 6F \u2013 144\n12F = 13 F \u2013 144\n\u2013F = \u2013 144\nF = 144\nWell, if the fine cost $144, then Sam paid the part not covered by Joe or Peter. Half the fine is $72, and Sam paid $12 less than this: $60.\nAnswer = D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat will be the ratio of simple interest earned by certain amount at the same rate of interest for 3 years and that for 9 years?\n\n### Options:\nA. 1 : 3\nB. 2 : 3\nC. 1 : 2\nD. 3 : 2\nE. 1 : 4\n\n### Answer:\nLet the principal be P and rate of interest be R%.\nRequired ratio =\n(P x R x 3)/100 DIVIDED BY\t(P x R x 9)/100\n=\t3PR/9PR\t=\t3/9\t= 1 : 3.\nANSWER : A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThree partners A, B, C in a business invested money such that 3(A\u00e2\u20ac\u2122s capital) = 6(B\u00e2\u20ac\u2122s capital) = 9(C\u00e2\u20ac\u2122s capital) then, The ratio of their capitals is\n\n### Options:\nA. 63 : 45 : 34\nB. 6 : 3 : 2\nC. 36 : 54 : 28\nD. 63 : 45 : 35\nE. None of these\n\n### Answer:\nExplanation:\nLet3(A\u00e2\u20ac\u2122s capital) = 6(B\u00e2\u20ac\u2122s capital) = 9(C\u00e2\u20ac\u2122s capital) = Rs.x\nThen, A\u00e2\u20ac\u2122s capital = Rs x/3, B\u00e2\u20ac\u2122s capital = Rs. x/6 and C\u00e2\u20ac\u2122s capital = Rs. x/9.\nA : B : C = x/3 : x/6 : x/9\n6 : 3 : 2\nAnswer: Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf xy is an integer, which of the following must also be an integer?\nI. x/y\nII. y/x\nIII. y\n\n### Options:\nA. I alone\nB. II alone\nC. III alone\nD. None of the above\nE. I and II\n\n### Answer:\nLets take X = 8/3 and Y = 3/2\nThen XY = 4 which is an integer.\nBut X/Y = 8/3 divided by 3/2 = 16/9 --> Not an integer.\nY/X = 3/2 divided by 8/3 = 9/16 --> Not an integer.\nY alone is 3/2. Not an integer.\nHence D. None of the above.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA fair price shopkeeper takes 10% profit on his goods. He lost 60% goods during theft. His loss percent is:\n\n### Options:\nA. 72%\nB. 42%\nC. 56%\nD. 12%\nE. 22%\n\n### Answer:\nExplanation:\nSuppose he has 100 items. Let C.P. of each item be Re. 1.\nTotal cost = Rs. 100. Number of items left after theft = 40.\nS.P. of each item = Rs. 1.10\nTotal sale = 1.10 * 40 = Rs. 44\nHence, loss % = 56/100 * 100 = 56%\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 8 minutes, then the area of the park (in sq. m) is:\n\n### Options:\nA. 153600 m^2\nB. 153660 m^2\nC. 153700 m^2\nD. 153800 m^2\nE. 153900 m^2\n\n### Answer:\nPerimeter = Distance covered in 8 min. = 12000\tx 8\tm = 1600 m.\n60\nLet length = 3x metres and breadth = 2x metres.\nThen, 2(3x + 2x) = 1600 or x = 160.\nLength = 480 m and Breadth = 320 m.\nArea = (480 x 320) m2 = 153600 m^2.\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe perimeter of one square is 48 cm and that of another is 20 cm. Find the perimeter and the diagonal of a square which is equal in area to these two combined?\n\n### Options:\nA. 13\u221a6\nB. 13\u221a2\nC. 13\u221a9\nD. 13\u221a1\nE. 13\u221a5\n\n### Answer:\n4a = 48 4a = 20\na = 12 a = 5\na2 = 144 a2 = 25\nCombined area = a2 = 169 => a = 13\nd = 13\u221a2\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n10^25 - 360 is divisible by all of the following except:\n\n### Options:\nA. A.7\nB. B.8\nC. C.5\nD. D.4\nE. E.2\n\n### Answer:\nThe last three digits ( 1000 - 360 ) 640\n640 is divisible by 2,4,8,5\n640 is not evenly divisible by 7 so the answer is A) 7\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average of 25 result is 18.The average of 1st 12 of them is 14 & that of last 12 is 17.Find the 13th result.\n\n### Options:\nA. 57\nB. 48\nC. 36\nD. 78\nE. 52\n\n### Answer:\nClearly 13th result=(sum of 25 results)-(sum of 24 results)\n=(18*25)-(14*12)+(17*12)\n=450-(168+204)\n=450-372\n=78.\nAns: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe perimeter of one square is 48 cm and that of another is 20 cm. Find the perimeter and the diagonal of a square which is equal in area to these two combined?\n\n### Options:\nA. 13\u221a2\nB. 15\nC. 48\nD. 75\nE. 23\n\n### Answer:\nxplanation:\n4a = 48 4a = 20\na = 12 a = 5\na2 = 144 a2 = 25\nCombined area = a2 = 169 => a = 13\nd = 13\u221a2\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat annual payment will discharge a debt of Rs. 1050 due in 2 years at the rate of 5% compound interest?\n\n### Options:\nA. 993.2\nB. 551.25\nC. 534.33\nD. 543.33\nE. 564.69\n\n### Answer:\nExplanation:\nLet each installment be Rs. x. Then,\nx/(1 + 5/100) + x/(1 + 5/100)2 = 1050\n820x + 1050 * 441\nx = 564.69\nSo, value of each installment = Rs. 564.69\nAnswer: Option E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe number of degrees that the hour hand of a clock moves through between noon and 2.30 in the afternoon of the same day is?\n\n### Options:\nA. 38\nB. 27\nC. 75\nD. 28\nE. 21\n\n### Answer:\nExplanation:\nThe hour hand moves from pointing to 12 to pointing to half way between 2 and 3. The angle covered between each hour marking on the clock is 360/12 = 30. Since the hand has covered 2.5 of these divisions the angle moved through is 75.\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf k^2 = t^2, which of the following must be true?\n\n### Options:\nA. |k| = |t|\nB. k = -m\nC. k = |m|\nD. k = -|m|\nE. k = m\n\n### Answer:\nSolution:\nWe are given that k^2 = t^2, and we can start by simplifying the equation by taking the square root of both sides.\n\u221ak^2 = \u221at^2\nWhen we take the square root of a variable squared, the result is the absolute value of that variable. Thus:\n\u221ak^2 = \u221at^2 is |k| = |t|\nNote that answer choices A through D could all be true, but each of them would be true only under specific circumstances. Answer choice E is the only one that is universally true.\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIt is dark in my bedroom and I want to get two socks of the same color from my drawer, which contains 24 red and 24 blue socks. How many socks do I have to take from the drawer to gate at least two socks of the same color?\n\n### Options:\nA. 2\nB. 3\nC. 48\nD. 25\nE. 26\n\n### Answer:\nlet\nif first is red\nand by luck if 2nd is not red then we u hav to take 3rd one.\nwhich will be either red or blue.\nbut u will get 2 socks of same color,either red or blue.\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf it is 7:19 in the evening on a certain day, what time in the morning was it exactly 2,880,705 minutes earlier? (Assume standard time in one location.)\n\n### Options:\nA. 7:25\nB. 7:34\nC. 7:43\nD. 7:47\nE. 7:52\n\n### Answer:\n7:19 minus 2,880,705 must end with 4, the only answer choice which ends with 4 is B.\nAnswer : B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the sides of a square are multiplied by sqrt(20), the area of the original square is how many times as large as the area of the resultant square?\n\n### Options:\nA. 2%\nB. 5%\nC. 20%\nD. 50%\nE. 150%\n\n### Answer:\nLet x be the original length of one side.\nThen the original area is x^2.\nThe new square has sides of length sqrt(20)*x, so the area is 20x^2.\nThe area of the original square is 1/20 = 5% times the area of the new square.\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe owner of a furniture shop charges his customer 24% more than the cost price. If a customer paid Rs. 7967 for a computer table, then what was the cost price of the computer table?\n\n### Options:\nA. 6425\nB. 6887\nC. 6728\nD. 6725\nE. 2871\n\n### Answer:\n:\nCP = SP * (100/(100 + profit%))\n= 7967(100/124) = Rs. 6425.\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n6 points are marked on a straight line and another 7 points are marked on a second straight line with no points in common. How many triangles can be constructed with vertices from among the above points?\n\n### Options:\nA. 9\nB. 105\nC. 196\nD. 21\nE. 14\n\n### Answer:\nassuming that the top line can have either 2 points or 1 point...\n6! / 1!5! - 6! / 2! 4! yields 9.\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe number of even factors of 21600 is\n\n### Options:\nA. 32\nB. 42\nC. 60\nD. 25\nE. 52\n\n### Answer:\nMake a prime factorization of the number: 21,600=25\u221733\u221752\nAccording to the above the number of factors is (5+1)(3+1)(2+1)=72\nNow, get rid of powers of 2 as they give even factors --> you'll have 33\u221752 which has (3+1)(2+1)=12 factors. All the remaining factors will be odd, therefore 21,600 has 72-12=60 even factors.\nAnswer: C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe rate of Interest on a sum of money is 11% p.a. for the first 3 years, 4% p.a. for the next 4 years, and 5% for the period beyond 7 years. If the S.I, Occured on the sum for the total period of 8 years is Rs. 540/-, the sum is\n\n### Options:\nA. 1,000\nB. 2,000\nC. 2,100\nD. 2,250\nE. 2,540\n\n### Answer:\nExplanation:\nI1 = (P x 3 x 11)/100 = P/3\nI2 = (P x 4 x 4)/100 = 4P/25\nI3 = (P x 1 x 5)/100 = P/20\nP/3 + 4P/25 + P/20 = 540\n27P/50 = 540\nP = 1000\nAnswer: Option A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA trader marks his product 40% above its cost. He sells the product on credit and allows 10% trade discount. In order to ensure prompt payment, he further gives 10% discount on the reduced price. If he makes a profit of Rs. 67 from the transaction, then the cost price of the product is\n\n### Options:\nA. Rs. 300\nB. Rs. 400\nC. Rs. 325\nD. Rs. 500\nE. Rs. 600\n\n### Answer:\nM.P = C.P *1.4\nProfit = S.P - C.P = C.P ( 1.4 ) ( 0.9 ) ( 0.9 ) \u2013 C.P = 67\nC.P ( 1.134 \u2013 1 ) = 67,\nC.P = 500\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nLast year, sales at Company Dopler were 10% greater in February than in January, 5% less in March than in Feb, 5% greater in April than in March, 10% less in May than in April, and 10% greater in June than in May. In which month were sales closest to Jan?\n\n### Options:\nA. Feb\nB. April\nC. Mar\nD. May\nE. June\n\n### Answer:\nJan = $100\n10% greater in February than in January ---> Feb = $110\n10% less in March than in Feb ---> Mar = $99\n5% greater in April than in March ---> Apr = $103.95\n10% less in May than in April ---> May $93.55\n10% greater in June than in May --->Jun = $102.90\nAnswer : C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA parking garage rents parking spaces for $10 per week or $35 per month. How much does a person save in a year by renting by the month rather than by the week?\n\n### Options:\nA. $100\nB. $160\nC. $220\nD. $240\nE. $260\n\n### Answer:\n10$ per week!\nAn year has 52 weeks.\nAnnual charges per year = 52* 10 = 520$\n35$ per month!\nAn year has 12 months.\nAnnual charges per year = 12 * 35 = 420$\n520 - 420 = 100\nAns A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nVenkat purchased twenty dozens of toys at the rate of 375 per dozen. He sold each one of them at the rate of 33. What was his percentage profit?\n\n### Options:\nA. 6.5\nB. 5.6\nC. 3.5\nD. 4.5\nE. None of these\n\n### Answer:\nCost price of 20 dozen toys = 20 \u00d7 375 = 7,500\nSelling price of 20 dozen toys = 20 \u00d7 33 \u00d7 12 = 7,920\nProfit percentage = 7920\u22127500/7500\u00d7100=5.6%\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA is twice as good workman as B, and together they complete a work in 15 days. In how many days can the work be complete by B alone?\n\n### Options:\nA. 35 days\nB. 65 days\nC. 45 days\nD. 75 days\nE. 95 days\n\n### Answer:\nC\n45 days\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA parking space have 8 different slots. 8 cars has to arrange in 8 slots. But there are exactly 4 cars between 1 specified cars. In how many ways cars can be arranged?\n\n### Options:\nA. 1210\nB. 120\nC. 1500\nD. 1640\nE. 1440\n\n### Answer:\nwe arranged 1 specified cars in 1 slots = 1!\nremaining 5 cars in 5 slots = 5!\nnumber of ways = 1!*5! = 120\ncorrect option is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA, B and C can do a work in 6, 8 and 12 days respectively doing the work together and get a payment of Rs.1800. What is B\u2019s share?\n\n### Options:\nA. 600\nB. 278\nC. 298\nD. 267\nE. 127\n\n### Answer:\nWC = 1/6:1/8:1/12 => 4:3:2\n3/9 * 1800 = 600\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the slope of the line perpendicular to the line y = x - 7\n\n### Options:\nA. 1\nB. 2\nC. -1\nD. 4\nE. 5\n\n### Answer:\nTwo lines are perpendicular if the product of their slopes is equal to -1. The slope of the given line is equal to 1. If m is the slope of the line perpendicular to the given line, then\nm \u00d7 1 = -1\nSolve for m\nm = - 1\ncorrect answer C) -1\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how much time will a train of length 100 m, moving at 36 kmph cross an electric pole?\n\n### Options:\nA. 15 sec\nB. 12 sec\nC. 10 sec\nD. 14 sec\nE. 11 sec\n\n### Answer:\nC\n10 sec\nConvert kmph to mps. 36 kmph = 36 * 5/18 = 10 mps.\nThe distance to be covered is equal to the length of the train.\nRequired time t = d/s = 100/10 = 10 sec.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe value of 1/(1-x) + 1/ (1+x) + 2/(1+x^2) + 4/(1+x^4)\n\n### Options:\nA. 8/(1-x^8)\nB. 4x/(1+x^2)\nC. 4/(1-x^6)\nD. 4/(1+x^4)\nE. 4x/(1-x^4)\n\n### Answer:\nHighlighted part has mistake as the exponent of x must be 4 in last term\nCORRECT QUESTION ISThe value of 1/(1-x) + 1/(1+x) + 2/(1+x^2) + 4/(1+x^4) = ?\nSolution is as mentioned below...\none more way that could get the answer in the type of eqn and choices given is to substitute some value for x...\n0 would be better as the eq has constant term free of term 'x'..\nthe Eq gives us 8 as the ans , as also only choice A..\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe number of girls in a class are 7 times the number of boys, which value can never be the of total students\n\n### Options:\nA. 40\nB. 48\nC. 24\nD. 30\nE. 34\n\n### Answer:\nExplanation:\nLet the boys are X, then girls are 7X, total = X+7X = 8X\nSo it should be multiple of 8, 30 is not a multiple of 8.\nOption D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAndrew travelling to 7 cities. Gasoline prices varied from city to city. What is the median gasoline price?\n\n### Options:\nA. $1\nB. $1.84\nC. $2.54\nD. $2.65\nE. $3\n\n### Answer:\nOrdering the data from least to greatest, we get:\n$1.61, $1.75, $1.79, $1.84, $1.96, $2.09, $2.11\nThe median gasoline price is $1.84. (There were 3 states with higher gasoline prices and 3 with lower prices.)\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how many ways can 10 Frenchmen, 10 Spanish be seated along a circle so that they are alternate?\n\n### Options:\nA. 8!*7!\nB. 10!*9!\nC. 5!*9!\nD. 10!*5!\nE. 11!9!\n\n### Answer:\nRequired number is = 10!*9!\nAnswer is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA set of data consists of the following 6 numbers: 0, 2, 4, 6,10 and 8. Which two numbers, if added to create a set of 7 numbers, will result in a new standard deviation that is close to the standard deviation for the original 5 numbers?\n\n### Options:\nA. -1 and 9\nB. 4 and 4\nC. 3 and 5\nD. 2 and 6\nE. 0 and 8\n\n### Answer:\nIf you are in for some calculations , this is how I got to it\nmean = 4\nsd = \\sqrt{8} = 2.8\nExpected values for the SD to not change are - One value below SD from mean is (4 - 2.8) = 1.2 , and one value above SD is (4 + 2.8) = 6.8\nThis would mean , adding 1.2 ans 6.8 would have no impact on the SD . SD remains the same when these two numbers are added. Now for SD to change the least , we need to add two values that are closest to these two values.\nHence any two values that are closest to 1.2 and 6.8 would change the SD , the least.\n1. -1 , 9\ndistance between (1,9) and (1.2 and 6.8) is 2.2 and 2.2\n2. 4 , 4\ndistance etween (4,4) and (1.2 , 6.8) is 2.8 and 2.8\n3. 3 , 5\nDistance is - 1.8 and 1.8\n4. 2 , 6\nDistance is - 0.8 and 0.8\n5. 0 , 8\nDistnace is - 1.2 and 1.2\nHence from above , we see that adding 0 and 8 , results in a value that would change the SD to the least. Hence E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train leaves Delhi at 9 a.m. at a speed of 30 kmph. Another train leaves at 2 p.m. at a speed of 40 kmph on the same day and in the same direction. How far from Delhi, will the two trains meet?\n\n### Options:\nA. 900 km\nB. 800 km\nC. 600 km\nD. 690 km\nE. 609 km\n\n### Answer:\nExplanation:\nD = 30 * 5 = 150\nRS = 40 \u2013 30 = 10\nT = 150/10 = 15\nD = 40 * 15 = 600 km\nAnswer: Option C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nDuring a Thanksgiving weekend, a car rental company rented six-tenths of their vehicles, including two-fifths of the 4WDs that it had. If 60% of the vehicles are 4WDs, then what percent of the vehicles that were not rented were not 4WDs?\n\n### Options:\nA. 10%\nB. 15%\nC. 20%\nD. 25%\nE. 30%\n\n### Answer:\n4/10 of all the vehicles were not rented.\n(3/5)(3/5) = 9/25 of all the vehicles are 4WDs that were not rented.\n(9/25) / (4/10) = 9/10 is the fraction of non-rented vehicles that were 4WDs\n1 - 9/10 = 10% of non-rented vehicles were not 4WDs.\nThe answer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the fourth proportion to 6,12,18\n\n### Options:\nA. 24\nB. 12\nC. 36\nD. 8\nE. 15\n\n### Answer:\nExplanation:\n6:12 :: 18:x\n=> 6/12= 18/x\n=> x = 18*12/6\n=> x = 24\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat will be the compound interest on a sum of Rs.25,000 after 3 years at the rate of 12 p.c.p.a?\n\n### Options:\nA. Rs.9000.30\nB. Rs. 9720\nC. Rs. 10123.20\nD. Rs. 10483.20\nE. None\n\n### Answer:\nSolution\nAmount\t= Rs.(25000x(1+12/100)\u00b3\n=Rs.(25000x28/25x28/25x28/25)\n= Rs. 35123.20.\nC.I\t=Rs(35123.20-25000)\n=Rs.10123.20.\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwelve people are planning to share equally the cost of a rental van. If one person withdraws from the arrangement and the others share equally the cost of the rental van, then the share of each of the remaining people will increase by...?\n\n### Options:\nA. 1/12\nB. 1/8\nC. 1/11\nD. 12/11\nE. 10/11\n\n### Answer:\nLet P = total cost of the rental van.\nThe original share per person is P/12.\nThe new share per person is P/11.\nP/11 = P/12 * 12/11 = (1 + 1/11)*original share\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA sum of money at simple interest amounts to Rs. 1717 in 1 year and to Rs. 1734 in 2 years. The sum is:\n\n### Options:\nA. Rs. 1200\nB. Rs. 1690\nC. Rs. 1600\nD. Rs. 1700\nE. Rs. 1500\n\n### Answer:\nS.I. for 1 year = Rs. (1734 - 1717) = Rs. 17.\nPrincipal = Rs. (1717 - 17) = Rs. 1700.\nAnswer: Option D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a school there are 4 sections in LKG. Average students of the section is 30. A, B, C sections have 28, 30, 34 students respectively. Therefore how much students in section D?\n\n### Options:\nA. 30\nB. 29\nC. 35\nD. 32\nE. 28\n\n### Answer:\nEXPLANATION\nTotal students of 3 sections = (28 + 30 + 34) = 92\nStudents of section D = [ (30 x 4) \u2013 92 ]\n= (120 \u2013 92)\n= 28\nAnswer E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn May, the groundskeeper at Spring Lake Golf Club built a circular green with an area of 70\u03c0 square feet. In August, the groundskeeper doubled the distance from the center of the green to the edge of the green. What is the total area of the renovated green?\n\n### Options:\nA. 1000\u03c0\nB. 400\u03c0\nC. 280\u03c0\nD. 200\u03c0\nE. 20\u03c0\n\n### Answer:\nArea = \u03c0R^2, so doubling the radius results in an area that is 4 times the original area.\n4(70\u03c0) = 280\u03c0\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a100m race A beats B by 25m B beats C by 4 then A beats C by\n\n### Options:\nA. 24 m\nB. 25m\nC. 26m\nD. 27m\nE. 28m\n\n### Answer:\nA : B = 100 : 75\nB : C = 100 : 96.\nA : C =\t(A/B\tx\tB/C)\t=\t(100/75\tx\t100/96)\t=\t100/72\t= 100 : 72.\nA beats C by (100 - 72) m = 28 m.\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the probability of randomly selecting one of the shortest diagonals from all the diagonals of a regular 9-sided polygon)?\n\n### Options:\nA. 1/2\nB. 1/3\nC. 1/4\nD. 1/6\nE. 1/9\n\n### Answer:\nFrom any vertex, there are two vertices on sides, which do not make a diagonal but a side.\nSo the remaining n-3 vertices make diagonals.\nThere are 2 of these diagonals which are the shortest.\nThe probability of choosing one of the shortest diagonals is 2/6 = 1/3.\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a group of 25, 13 can speak Latin, 15 can speak French, and 6 don't speak either. How many of these speak both Latin and French?\n\n### Options:\nA. 9\nB. 10\nC. 11\nD. 12\nE. 8\n\n### Answer:\nlet no.of persons who speeks booth latin and french = x\nso, no.of persons who speeks only latin = 13-x\nno.of persons who speeks only french= 15-x\nno.of persons who speeks dont speek any lag = 6\ntherefore (13-x)+(15-x)+x+6=25\n34-x=25\nx=9\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA collector collects stamps from foreign countries. In June, she gave 20 percent of her stamps to her friend. In July, she gave 35 percent of her remaining stamps to another friend. If these were the only changes in the number of stamps in the stamp collection during those two months, what percent of her collection at the beginning of June did she give to away in June and July?\n\n### Options:\nA. 32%\nB. 36%\nC. 40%\nD. 44%\nE. 48%\n\n### Answer:\nLet x be the number of stamps in the original collection.\nThe percentage of the collection given away is:\n0.2x + 0.35(0.8x) = 0.2x + 0.28x = 0.48x = 48%\nThe answer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhen positive integer N is divided by positive integer J, the remainder is 16. If N/J = 134.08, what is value of J?\n\n### Options:\nA. 22\nB. 56\nC. 78\nD. 112\nE. 200\n\n### Answer:\nWhen a number is divided by another number, we can represent it as : Dividend = Quotient * Divisor + Remainder\nSo, Dividend/Divisor = Quotient + Remainder/Divisor\nGiven that N/J = 134.08\nHere 134 is the quotient.\nGiven that Remainder = 16\nSo, 134.08 = 134 + 16/J\nSo, J = 200 ANS E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe product of a and b is equal to 10 more than twice the sum of a and b. If b = 9, what is the value of b - a?\n\n### Options:\nA. 2\nB. 5\nC. 7\nD. 24\nE. 35\n\n### Answer:\nab= 10 + 2(a+b)\n9a= 10+2a +18\n7a= 28\na=4\nb-a= 9-4=5\nB is the answer\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nDiana is painting statues. She has 1/2 of a gallon of paint remaining. Each statue requires 1/4 gallon of paint. How many statues can she paint?\n\n### Options:\nA. 2\nB. 20\nC. 28\nD. 14\nE. 19\n\n### Answer:\nnumber of statues=all the paint\u00f7amount used per statue\n=1/2 \u00f7 1/4\n=1/2*4/1\n=2\nAnswer is A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe fourth proportional to 12, 14 and 12 is?\n\n### Options:\nA. 14\nB. 66\nC. 77\nD. 88\nE. 99\n\n### Answer:\n(14*12)/12 = 14\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA rower can row upstream at 7 km/hr and downstream at 14 km/hr. What is the rower's rate in still water?\n\n### Options:\nA. 9.5 km/hr\nB. 10.0 km/hr\nC. 10.5 km/hr\nD. 11.0 km/hr\nE. 11.5 km/hr\n\n### Answer:\nThe rate in still water is 1/2 * (14 + 7) = 10.5 km/hr\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe ratio of incomes of two person P1 and P2 is 5 : 4 and the ratio of their expenditures is 3 : 2. If at the end of the year, each saves Rs.1600, then what is the income of P1?\n\n### Options:\nA. Rs.800\nB. Rs.2400\nC. Rs.4000\nD. Rs.3200\nE. Rs.4200\n\n### Answer:\nLet the income of P1 and P2 be Rs. 5x and Rs.4x respectively and let their\nexpenditures be Rs.3y and 2y respectively.\nThen, 5x \u2013 3y = 1600 \u2026(i) and 4x \u2013 2y = 1600 \u2026\u2026..(ii)\nOn multiplying (i) by 2, (ii) by 3 and subtracting, we get : 2x = 1600 -> x = 800\nP1\u2019s income = Rs 5*800 = Rs.4000\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average of 11 results is 50, if the average of first six results is 49 and that of the last six is 52. Find the sixth result?\n\n### Options:\nA. 21\nB. 56\nC. 18\nD. 25\nE. 23\n\n### Answer:\n1 to 11 = 11 * 50 = 550\n1 to 6 = 6 * 49 = 294\n6 to 11 = 6 * 52 = 312\n6th = 294 + 312 \u2013 550 = 56\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf Jack walked 9 miles in 1 hour and 15 minutes, what was his rate of walking in miles per hour?\n\n### Options:\nA. 4\nB. 4.5\nC. 6\nD. 6.25\nE. 7.2\n\n### Answer:\nDistance walked in 1 hour and 15 mins = 9 miles\nSpeed per hour = Distance/Time = 9/(5/4) = 7.2 miles per hour\nAnswer E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average salary of Raj and Roshan is Rs. 4000 but the average salary of Raj, Roshan and Thomas is Rs. 5000. What is the salary of Thomas?\n\n### Options:\nA. 4000\nB. 5000\nC. 6000\nD. 7000\nE. 8000\n\n### Answer:\nTotal salary of Raj and Roshan= 2x4000=8000\nTotal salary of Raj Roshan and Thomas= 3x5000=15000\nSalary of Thomas= 15000-8000= Rs. 7000\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat will be the fraction of 75%\n\n### Options:\nA. 3/4\nB. 1/5\nC. 1/10\nD. 1/11\nE. None of above\n\n### Answer:\nExplanation:\nIt will 75*1/100 = 3/4\nOption A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA glucose solution contains 15 grams of glucose per 100 cubic centimeters of solution. If 45 cubic centimeters of the solution were poured into an empty container, how many grams of glucose would be in the container?\n\n### Options:\nA. 3.0\nB. 5.0\nC. 5.5\nD. 6.5\nE. 6.75\n\n### Answer:\nConstruct an equation: 15/100=x/45-> x=6.75\nAnswer: E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAt Pat's Pet Shop, 25 cups of bird seed are used every 5 days to feed 20 parakeets. How many cups of bird seed would be required to feed 15 parakeets for 7 days?\n\n### Options:\nA. 35.25\nB. 15\nC. 64\nD. 104\nE. 26 1/4\n\n### Answer:\nLet's go step-by-step.\n25 cups are used over a 5 day period, which means 5 cups a day. This feeds 20 parakeets, which means each parakeet needs 1/4 of a cup every day.\nFor 15 parakeets, we need 15*1/4 cups = 3 3/4 cups a day. Over 7 days, we need 26 1/4 cups. Choice E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train passes a platform in 44 seconds. The same train passes a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, The length of the platform is\n\n### Options:\nA. 240\nB. 250\nC. 360\nD. 230\nE. 220\n\n### Answer:\nSpeed of the train = 54 km/hr = (54\u00d710)/36 m/s = 15 m/s\nLength of the train = speed \u00d7 time taken to cross the man = 15\u00d720 = 300 m\nLet the length of the platform = L\nTime taken to cross the platform = (300+L)/15\n=> (300+L)/15 = 36\n=> 300+L = 15\u00d744 = 660\n=> L = 660-300 = 360 meter\nAnswer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIt takes John 25 minutes to walk to the car park and 45 to drive to work. At what time should he get out of the house in order to get to work at 9:00 a.m.?\n\n### Options:\nA. 5:40 a.m\nB. 7:50 a.m\nC. 6:55 a.m\nD. 8:00 a.m\nE. 4:25 a.m\n\n### Answer:\nThe time it takes John to get to work: time to walk to car park + time to drive\n25 + 45 = 70 minutes = 1 hour and 10 minutes\nJohn needs to get out of the house 1 hour and 10 minutes before 9:00 am at\n9:00 - 1:10 = 7:50 a.m\ncorrect answer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA rectangular tiled patio is composed of 30 square tiles. The rectangular patio will be rearranged so that there will be 2 fewer columns of tiles and 4 more rows of tiles. After the change in layout, the patio will still have 30 tiles, and it will still be rectangular. How many rows are in the tile patio before the change in layout?\n\n### Options:\nA. 5\nB. 6\nC. 10\nD. 13\nE. 28\n\n### Answer:\nSuppose there are c columns and there are r rows\nOriginal Situation\nSo, Number of tiles = c*r = 30\nAlso. Reach column has r tiles and each row has c tiles\nNew Situation\nNumber of tiles in each column is r-2 and number of tiles in each row is c+4\nSo, number of rows = r-2 and number of columns is c+4\nSo, Number of tiles = (r-2)*(c+4) = 30\nComparing both of them we get\nc*r = (r-2)*(c+4)\n=> 4r -2c = 8\nc = 2r - 4\nPutting it in c*r=30\n(2r-4)*r = 30\n2r^2 - 4r - 30=0\nr cannot be negative so r =5\nand c = 6\nSo, Answer will be A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the cost price is 96% of the selling price, then what is the profit percent?\n\n### Options:\nA. 4.17%\nB. 5%\nC. 6.12%\nD. 3.25%\nE. 5.75%\n\n### Answer:\nLet S.P. = $100\nC.P. = $96\nProfit = $4\nProfit% = 4/96 * 100 = 25/6 = 4.17%\nAnswer is A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train covers a distance of 100km in 1 hour. If its speed is decreased by 30km/hr, the time taken by the car to cover the same distance will be?\n\n### Options:\nA. 1hr\nB. 1hr 25min\nC. 50min\nD. 1hr 30min\nE. 1hr 45min\n\n### Answer:\nSpeed = 100/1 = 100km/hr\nNew speed = 100-30 = 70 km/hr\nTime taken = 100/70 = 1hr 25min\nAnswer is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA fruit seller had some oranges. He sells 40% oranges and still has 480 oranges. How many oranges he had originally?\n\n### Options:\nA. 800\nB. 710\nC. 720\nD. 730\nE. 740\n\n### Answer:\n60% of oranges = 480\n100% of oranges =(480\u00d7100)/6=800\ntotal oranges = 700\nANSWER : A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAt the opening of a trading day at a certain stock exchange, the price per share of stock M was $25. If the price per share of stock M was $28 at the closing of the day, what was the percent increase in the price per share of stock M for that day?\n\n### Options:\nA. 1.4%\nB. 5.9%\nC. 12%\nD. 12.5%\nE. 23.6%\n\n### Answer:\nOpening = 25\nClosing = 28\nRise in price = 3\nSo, percent increase = 3/25*100 = 12\nAnswer : C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe L.C.M. of two numbers is 36. The numbers are in the ratio 2 : 3. Then sum of the number is:\n\n### Options:\nA. 28\nB. 30\nC. 40\nD. 53\nE. 54\n\n### Answer:\nLet the numbers be 2x and 3x.\nThen, their L.C.M. = 6x.\nSo, 6x = 36 or x = 6.\nThe numbers are 12 and 18.\nHence, required sum = (12 + 18) = 30.\nAnswer: Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are six cards in which it has two king cards. all cards are turned down and two cards are opened what is the possibility to get two kings.\n\n### Options:\nA. 1/15\nB. 2/15\nC. 3/15\nD. 4/15\nE. 6/15\n\n### Answer:\nP0SSIBLITY TO GET TWO KINGS IS 2C2/6C2=1/15\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJohn makes $30 a week from his job. He earns a raise and now makes $40 a week. What is the % increase?\n\n### Options:\nA. 16%\nB. 16.66%\nC. 18%\nD. 21%\nE. 33.33%\n\n### Answer:\nIncrease = (10/30)*100 = 33.33%.\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nn^(n/2)=4 is true when n=4 in the same way what is the value of n if n^(n/2) =8?\n\n### Options:\nA. 4\nB. 8\nC. 2\nD. 6\nE. 10\n\n### Answer:\nn^(n/2)=8\rApply log\rN/2logn=log8\rnlogn=2log8=log8^2=log64\rLogn=log64\rNow apply antilog\rn=64/n\rNow n=8.\rANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA can have a piece of work done in 5 days, B can work three times faster than the A, C can work four times faster than A. How many days will they take to do the work together ?\n\n### Options:\nA. 3 days\nB. 8/9 days\nC. 3/2 days\nD. can't say\nE. none\n\n### Answer:\nA's 1 day work is 1/12\nB's 1 day work is 3/12\nC's 1 day work is 4/12\n(A+B+C)'s 1 day work(1/12+3/12+4/12) is 2/3\nso, they can finish the work in 3/2 days\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA three digit number divisible by 7 becomes divisible by 3 when 16 is subtracted from it. The largest such number is :\n\n### Options:\nA. 994\nB. 981\nC. 963\nD. 951\nE. 942\n\n### Answer:\nOut of all the 5 options, only 994 is NOT divisible by 3. All others are divisible\nSo Answer = A (No further calculation required)\nAddition of any two non-divisible numbers by 3 gives the resultant divisible by 3\n16 is non-divisible by 3; we are subtracting a number from that so that the resultant becomes divisible by 3\nApplying the above rule,It means that the number which we are going to add should be non-divisible by 3\nSo comes the answer = 994\nAnswer : A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat will be in unit's place digit of 3 to the power 34.\n\n### Options:\nA. 1\nB. 6\nC. 3\nD. 0\nE. 9\n\n### Answer:\nas the unit place digit of 3 to the power of 1 is 3, to the power of 2 is 9.to the power of 3 is 7 ,to the power of 4 is 1 and it'll be repeated again in the same order.... so the unit place digit of 3 to the power of 34 is 9..\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA sum fetched total simple interest of 4016.25 at the rate of 10 p.c.p.a. in 5 years. What is the sum?\n\n### Options:\nA. 8925\nB. 8032.5\nC. 4462.5\nD. 8900\nE. None of these\n\n### Answer:\nLet the sums be P.\nNow, 50% of P = 4016.25\nor, P = 8032.5\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRobert is travelling on his cycle andhas calculated to reach point A at 2 PM. if he travels at 10 kmph, he will reach there at 12Pm if he travels at 15 kmph. At what speed musthe travel to reach A at 1 PM?\n\n### Options:\nA. 8 kmph\nB. 10 kmph\nC. 12 kmph\nD. 16 kmph\nE. 18 kmph\n\n### Answer:\nLet the distance travelled by x km.\nThen, x - x = 2\n10 15\n3x - 2x = 60\nx = 60 km.\nTime taken to travel 60 km at 10 km/hr = 60 hrs = 6 hrs.\n10\nSo, Robert started 6 hours before 2 P.M. i.e., at 8 A.M.\nRequired speed = 60 kmph. = 12 kmph.\n5\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA batsman makes a score of 83 runs in the 17th inning and thus increases his averages by 3.Find his average after 17th inning?\n\n### Options:\nA. 19\nB. 29\nC. 35\nD. 49\nE. 59\n\n### Answer:\nlet the average after 17th inning =x\nThen average after 16th inning=(x-3)\nTherefore 16(x-3)+83=17x\nTherefore x=35\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a bag there are 3 Snicker's bars and 2 Milky Way bars. What is the probability of choosing at least one Snickers when choosing two consecutive candy bars randomly?\n\n### Options:\nA. 9/10\nB. 16/20\nC. 2/5\nD. 3/5\nE. \u00bd\n\n### Answer:\nP(at least one Snicker's Bar) = 1 - P(no Snicker's Bar, so 2 Milky Way Bars) = 1- 2/5*1/4 = 9/10.\nAnswer: A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the sides of a triangle are 65 cm, 60 cm and 25 cm, what is its area?\n\n### Options:\nA. 120 cm2\nB. 750 cm2\nC. 216 cm2\nD. 197 cm2\nE. 275 cm2\n\n### Answer:\nThe triangle with sides 65 cm, 60 cm and 25 cm is right angled, where the hypotenuse is 65 cm.\nArea of the triangle\n= 1/2 * 60 * 25\n= 750 cm2\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA chemical lab is scheduled to go through two air ventilation systems, a basic system and a more advanced system that takes half an hour and 1.5 hours respectively to fully ventilate the room. If both ventilation systems were to operate at the same time with their respective constant rates, how many hours would it take to fully ventilate the chemical lab?\n\n### Options:\nA. 1/4\nB. 1/3\nC. 2/5\nD. 5/4\nE. 3/8\n\n### Answer:\nThe rate of the basic system is 1 room/half hour = 2 rooms per hour\nThe rate of the advanced system is 1 room/1.5 hours = 2/3 of a room per hour\nThe combined rate is 8/3 rooms per hour.\nThe time to ventilate one room is 3/8 of an hour.\nThe answer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn what time will a railway train 50 m long moving at the rate of 36 kmph pass a telegraph post on its way?\n\n### Options:\nA. 5 sec\nB. 4 sec\nC. 3 sec\nD. 6 sec\nE. 1 sec\n\n### Answer:\nT = 50/36 * 18/5 = 5 sec\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOf the total amount that Jill spent on a shopping trip, excluding taxes, she spent 50 percent on clothing, 25 percent on food, and 25 percent on other items. If Jill paid a 10 percent tax on the clothing, no tax on the food, and an 20 percent tax on all other items, then the total tax that she paid was what percent of the total amount that she spent, excluding taxes?\n\n### Options:\nA. 5\nB. 10\nC. 15\nD. 20\nE. 25\n\n### Answer:\nAssume she has $200 to spend.\nTAX\nClothing = 50% = $100= $10.00\nFood = 25% = $ 50 = $0.00\nItems = 25% = $ 50 = $ 10.00\nTotal tax = $20.00\n% of total amount = 20/200 * 100 = 10%\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo cyclists are running on a circular track of 500m.They start from the same point A at the same time.If they meet for the first time at a point 300 m from A, which of the following could be the possible ratio of their speeds?\n\n### Options:\nA. 1:3\nB. 2:3\nC. 3:2\nD. 5:7\nE. 7:11\n\n### Answer:\nwell, the key aspect of this question is the distance mentioned, when they met for the first time, which is 300m away from the starting point. This distance between their first meeting can be less than 500 in only two circumstance.\n1) if both are travelling in the same direction and one of them has been given a head start say by few meters.\n2) or if both are travelling in the opposite direction.\nnow since they start their journey at the same time. hence option 1 is ruled out. hence they must be running in the opposite direction. hence answer should be 3:2\nWhy?? here is a solution\nAs here time is constant, therefore, distance traveled will be directly proportional to the the respective velocities/speed of the two runners.(d1/d2=v1/v2)\nnow one of them has covered 300m, therefore other must have covered 200m, therefore ratio of their speeds/velocities will be 3:2\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf n = 9^11 \u2013 9, what is the units digit of n?\n\n### Options:\nA. 0\nB. 1\nC. 4\nD. 6\nE. 8\n\n### Answer:\nAlways divide the power (incase 11) by 4 and use the remainder as the new power. The question now becomes 9^3 - 9. Now 9^3 has last digit 9. , we subtract 9 from 9 , thus 9 -9 = 0 is the answer. Option A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe \u2018moving walkway\u2019 is a 300-foot long walkway consisting of a conveyor belt that moves continuously at 3 feet per second. When Bill steps on the walkway, a group of people that are also on the walkway stands 120 feet in front of him. He walks toward the group at a rate of 3 feet per second. Once Bill reaches the group of people, he stops walking and stands with them until the walkway ends. What is Bill\u2019s average rate Q of movement for his trip along the moving walkway?\n\n### Options:\nA. 2 feet per second\nB. 2.5 feet per second\nC. 3 feet per second\nD. 4 feet per second\nE. 5 feet per second\n\n### Answer:\nA, B, and C don't make ANY sense! we know for some time...(a majority of the 300ft) Bill will walk at a pace of 6ft per second...and then at some later time he will stop and move at 3 ft per second... The average MUST bebetween3-6 ft per second or the Earth is FLAT!!!.\nSo we are down to DE, D doesn't make sense on a weighted averages level because we know when Bill gets on the walkway the patrons are already 40% of the way down the 300ft walkway AND they are still moving at half the rate of Bill!! So for Bill to average 4 ft per second he would have had to spend a majority of the 300 ft at 3ft per second because 4 is much closer (when you factor in the size of the values we're dealing with 2 is double 1) to 3 than to 6. We know from the information that isn't possible. Billmust havespent the majority of his time at 6 ft Q per second before he stopped walking. That leaves only answer E as plausible.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf Rs. 782 be divided into three parts, proportional to 1/2:2/3:3/4, then the first part is:\n\n### Options:\nA. Rs. 182\nB. Rs. 190\nC. Rs. 196\nD. Rs. 204\nE. Rs. 210\n\n### Answer:\nExplanation:\nGiven ratio =1/2:2/3:3/4=6:8:9\n1st part = Rs. 782*6/23=Rs. 204\nAnswer is D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nLast year Manfred received 26 paychecks. Each of his first 6 paychecks was $760; each of his remaining paychecks was $30 more than each of his first 6 paychecks. To the nearest dollar, what was the average (arithmetic mean) amount of his pay checks for the year?\n\n### Options:\nA. $752\nB. $755\nC. $765\nD. $783\nE. $775\n\n### Answer:\n= (760*6+ 790 *20)/26\n= 783\nAnswer is D.\nPosted from my mobile device\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTen cards numbered 1 to 10 are placed in a box, mixed up thoroughly and then one card is drawn\nrandomly. If it is known that the number on the drawn card is more than 3, what is the probability\nthat it is an even number?\n\n### Options:\nA. 3/7\nB. 4/7\nC. 5/7\nD. 5/9\nE. 5/11\n\n### Answer:\nLet A be the event \u2018the number on the card drawn is even\u2019 and B be the\nevent \u2018the number on the card drawn is greater than 3\u2019. We have to find P(A|B).\nNow, the sample space of the experiment is S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}\nThen A = {2, 4, 6, 8, 10}, B = {4, 5, 6, 7, 8, 9, 10}\nand A n B = {4, 6, 8, 10}\nAlso P(A) = 5/2, P(B) = 7/10 and P(A n B) = 4/10\nThen P(A|B) = P(A n B)/P(B) = (4/10)/(7/10) = 4/7\nB)\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA and B started a partnership business investing some amount in the ratio of 3 : 5. C joined then after six months with an amount equal to that of B. In what proportion should the profit at the end of one year be distributed among A, B and C?\n\n### Options:\nA. 3 : 5 : 2\nB. 3 : 5 : 5\nC. 6 : 10 : 5\nD. 8 : 12 : 4\nE. Data inadequate\n\n### Answer:\nExplanation:\nLet the initial investments of A and B be 3x and 5x.\nA : B : C = (3x x 12) : (5x x 12) : (5x x 6) = 36 : 60 : 30 = 6 : 10 : 5.\nAnswer is C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA worker's take-home pay last year was the same each month, and she saved the same fraction of her take-home pay each month. The total amount of money that she had saved at the end of the year was 8 times the amount of that portion of her monthly take-home pay that she did NOT save. If all the money that she saved last year was from her take-home pay, what fraction of her take-home pay did she save each month?\n\n### Options:\nA. 6/25\nB. 5/16\nC. 4/9\nD. 3/7\nE. 2/5\n\n### Answer:\nLet x be the fraction of her take-home pay that the worker saved.\nLet P be the monthly pay.\n12xP = 8(1-x)P\n12xP = 8P - 8xP\n20xP = 8P\nx = 2/5\nThe answer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA car mechanic purchased four old cars for Rs. 1 lakh. He spent total 2 lakh in the maintenance and repairing of these four cars. what is the average sale price of the rest three cars to get 90% total profit if he has already sold one of the four cars at Rs. 1.2 lakh?\n\n### Options:\nA. 1.8 lakh\nB. 1.5 lakh\nC. 1.9 lakh\nD. 8.1 lakh\nE. 6.1 lakh\n\n### Answer:\nExplanation:\nTotal cost of 4 cars = 1+2 = 3 lakh\nTotal SP of 4 cars = 3 x 1.9 = 5.7 lakh\nSP of 1 car = 1.2 lakh\nSP of rest 3 cars = 5.7 - 1.2 = 4.5 lakh\nAverage SP of all the 3 cars = 1.5 lakh\nAnswer: B)\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA meeting has to be conducted with 4 managers. Find the number of ways in which the managers be selected from among 7 managers, if 2 managers will not attend the meeting together?\n\n### Options:\nA. 25\nB. 20\nC. 35\nD. 36\nE. 38\n\n### Answer:\nwe can either choose all 4 people from 5 manager who have no problems or choose 3 from the 5 and 1 from the 2 managers who have a problem sitting together\nso 5C4 + (5C3 * 2C1)\nthis is 5 + 20=25\nAnswer : A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man can row upstream at 25 kmph and downstream at 31 kmph, and then find the speed of the man in still water?\n\n### Options:\nA. 22\nB. 28\nC. 30\nD. 27\nE. 18\n\n### Answer:\nUS = 25\nDS = 31\nM = (31 + 25)/2 = 28\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n117 + 1.017 + 0.117 + 1.0017 = ?\n\n### Options:\nA. 109.3657\nB. 119.7563\nC. 119.1357\nD. 119.5637\nE. 119.6753\n\n### Answer:\n117\n1.017\n0.117\n+ 1.0017\n--------\n119.1357\n---------\nAnswer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA, B and C start a business each investing 10,000. After 6 months A withdrew 5000, B withdrew 4000 and C invests 6000 more. At the end of the year, a total profit of 34,200 was recorded. Find the share of B.\n\n### Options:\nA. 9,600\nB. 21,200\nC. 28,200\nD. 20,500\nE. None of these\n\n### Answer:\nRatio of the capitals of A, B and C\n= 10000 \u00c3\u2014 6 + 5000 \u00c3\u2014 6 : 10000 \u00c3\u2014 6 + 6000 \u00c3\u2014 6 : 10000 \u00c3\u2014 6 + 16000 \u00c3\u2014 6\n=90000 : 96000 : 156000 = 90 : 96 : 156\nB\u00e2\u20ac\u2122s share = (34200 \u00c3\u2014 96\u00e2\u0081\u201e342) = 9600\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many 1's are there preceded by 2 but not followed by 0?\n5 9 3 2 1 7 4 2 6 9 7 4 2 1 3 2 8 7 0 1 3 8 3 2 5 6 7 4 3 9 5 8 2 2 1 0 7 4 6 3\n\n### Options:\nA. 4\nB. 2\nC. 6\nD. 8\nE. 9\n\n### Answer:\n2 1 7\n2 1 3\nOnly at these places 2 is preceded by 2 but not followed by 0\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo trains 140 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is?\n\n### Options:\nA. 10.9 sec\nB. 14.8 sec\nC. 10.6 sec\nD. 10.8 sec\nE. 20.8 sec\n\n### Answer:\nRelative speed = 60 + 40 = 100 km/hr.\n= 100 * 5/18 = 250/9 m/sec.\nDistance covered in crossing each other = 140 + 160 = 300 m.\nRequired time = 300 * 9/250 = 54/5\n= 10.8 sec.\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many odd numbers between 10 and 1500 are the squares of integers?\n\n### Options:\nA. 11\nB. 14\nC. 17\nD. 20\nE. 23\n\n### Answer:\nThe numbers are the squares of 5, 7, 9,...,37 which includes 17 numbers.\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRam sold two bicycles, each for Rs.990. If he made 10% profit on the first and 10% loss on the second, what is the total cost of both bicycles?\n\n### Options:\nA. Rs.2000\nB. Rs.2028\nC. Rs.2020\nD. Rs.2720\nE. Rs.2026\n\n### Answer:\n(10*10)/100 = 1%loss\n100 --- 99\n? --- 1980 => Rs.2000\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n2,7,14,32,58,?\n\n### Options:\nA. 112\nB. 154\nC. 123\nD. 132\nE. 144\n\n### Answer:\n1^2+1=2\n2^2+3=7\n3^2+5=14\n5^2+7=32\n7^2+9=58\n11^2+11=132\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the area of the square field if a train 800 metres long passes the field with a speed of 120 kmph in one minute.\n\n### Options:\nA. 1.44 sq. km\nB. 4 sq. km\nC. 2 sq. km\nD. 2.64 sq. km\nE. None of these\n\n### Answer:\nExplanation:\n120 km/hr = 120 * 5/18 = 33.33 m/s\nv = d/t ; 33.33 = d/60\nd = 2000 m\nHence, in one minute the train travels 2000 m. But, as the train is 800 m long and it passes the field, the length of the field is 2000 \u2013 800 = 1200 m.\nArea = 1200 * 1200 = 1.44 sq. km\nANSWER: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n33 1/3% of 36 ?\n\n### Options:\nA. 16\nB. 21\nC. 18\nD. 12 number\nE. 18\n\n### Answer:\nExplanation:\n33 1/3 % = 1/3\n1/3 * 36 = 12\nAnswer: Option D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the minimum number of years upon which SI on Rs 2600 at 6.67% interest rate will be in whole number?\n\n### Options:\nA. 2\nB. 6\nC. 3\nD. 4\nE. 5\n\n### Answer:\nExplanation:\nSimple Interest =Principal * Rate * Time\nPrincipal = 2600 Rs\nInterest Rate = 6.67%\n=> SI = 2600 * (20/3)*Time\nSI of the number will be a whole number for the first time when time is three as denominator of rate is 3.\nHence time should be set to 3 years.\nANSWER C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA, B and C play a cricket match. The ratio of the runs scored by them in the match is A:B = 2:3 and B:C = 2:5. If the total runs scored by all of them are 150, the runs scored by B are?\nA. 15 B. 18\n\n### Options:\nA. 22\nB. 18\nC. 99\nD. 36\nE. 24\n\n### Answer:\nA:B = 2:3\nB:C = 2:5\nA:B:C = 4:6:15\n6/25 * 150 = 36\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA car engine is half filled and holds 15 litres of petrol.what fraction of the engine is full if it contains 18 litres of petrol?\n\n### Options:\nA. 1/4\nB. 2/3\nC. 2/5\nD. 3/5\nE. 4/5\n\n### Answer:\nhalf of the car engine filed with 15 ltrs means full engine filed with 30 ltrs so the fraction will be=18/30=6/10=3/5\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train with 120 wagons crosses John who is going in the same direction, in 36 seconds. It travels for half an hour from the time it starts overtaking the John ( he is riding on the horse) before it starts overtaking the Mike(who is also riding on his horse) coming from the opposite direction in 24 seconds. In how much time (in secs) after the train has crossed the Mike do the John meets to Mike?\n\n### Options:\nA. 2534 s\nB. 5435 s\nC. 7645 s\nD. 7456 s\nE. 3576 s\n\n### Answer:\nLet the length of the train be L metres and speeds of the train Arun and Sriram be R, A and S respectively, then\n---------- (i)\nand ---------(ii)\nFrom eq.(i) and (ii)\n3(R - A ) = 2 (R + K)\nR = 3A + 2K\nIn 30 minutes (i.e 1800 seconds), the train covers 1800R (distance) but the Arun also covers 1800 A (distance) in the same time. Therefore distance between Arun and Sriram, when the train has just crossed Sriram\n= 1800 ( R - A) - 24 ( A + K)\nTime required =\n= (3600 - 24) = 3576 s\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nKelly and Jody packed boxes with books. If Jody packed 30% of the total number of boxes, what was the ratio of the number of boxes Kelly packed to the number that Jody packed?\n\n### Options:\nA. 1 to 6\nB. 1 to 4\nC. 3 to 7\nD. 3 to 5\nE. 2 to 3\n\n### Answer:\nExplanation:\nIf Jody packed 30% of the boxes then Kelly packed 70%. The ratio of the number of boxes Kelly packed to the number Jody packed is thus 30%/70%=3/7\nAnswer: Option C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nI flew my tiny seaplane to visit my mother. On the flight up, I flew at 140 mph. On the way home, I flew 88 mph. What was my average speed for the trip?\n\n### Options:\nA. 114 mph\nB. 110 mph\nC. 88 mph\nD. 100 mph\nE. 99 mph\n\n### Answer:\n(140 mph +88 mph)/2= 114 mph\nCorrect answer is: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train leaves Mumabai at 9 am at a speed of 40 kmph. After one hour, another train leaves Mumbai in the same direction as that of the first train at a speed of 50 kmph. When and at what distance from Mumbai do the two trains meet?\n\n### Options:\nA. 111\nB. 771\nC. 200\nD. 873\nE. 811\n\n### Answer:\nWhen the second train leaves Mumbai the first train covers 40 * 1 = 40 km\nSo, the distance between first train and second train is 40 km at 10.00am\nTime taken by the trains to meet\n= Distance / relative speed = 40 / (50 -40) = 4 hours\nSo, the two trains meet at 2 p.m. The two trains meet 4 * 50 = 200 km away from Mumbai.\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRobin's average (arithmetic mean) test score on 9 tests is 82. What must be Robin's score on a 10th test for his average score on the 10 tests to be 83?\n\n### Options:\nA. 92\nB. 82\nC. 72\nD. 62\nE. 52\n\n### Answer:\n(9*82+x)/10=83\nx=(10*83)-(9*82)\nx= 830 - 738\ntotal score required 830 - 738=92\nCorrect answer is A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf n > 2, then the sum, S, of the integers from 1 through n can be calculated by the following formula: S = n(n + 1)/2. Which one of the following statements about S must be true?\n\n### Options:\nA. S is always odd.\nB. S is always even.\nC. S must be a prime number\nD. S must not be a prime number\nE. S must be a perfect square\n\n### Answer:\nIf n > 2, then the sum, S, of the integers from 1 through n can be calculated by the following formula: S = n(n + 1)/2. Which one of the following statements about S must be true?\nA. S is always odd.\nB. S is always even.\nC. S must be a prime number\nD. S must not be a prime number\nE. S must be a perfect square\nNotice that we are askedwhich of the following MUST be true, not COULD be true. For such kind of questionsif you can prove that a statement is NOT truefor one particular set of numbers, it will mean that this statement is not always true and hence not a correct answer.\nA. S is always odd --> not necessarily true if n=3 then 1+2+3=6=even.\nB. S is always even --> not necessarily true if n=5 then 1+2+3+4+5=15=odd.\nC. S must be a prime number --> not true if n=3 then 1+2+3=6=not prime.\nE. S must be a perfect square --> not necessarily true if n=3 then 1+2+3=6=not a perfect square.\nOnly choice D is left.\nAnswer: D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe triplicate ratio of 1:2 is?\n\n### Options:\nA. 1:7\nB. 1:8\nC. 1:3\nD. 1:1\nE. 1:2\n\n### Answer:\n13: 23 = 1:8\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSome of 50%-intensity red paint is replaced with 25% solution of red paint such that the new paint intensity is 30%. What fraction of the original paint was replaced?\n\n### Options:\nA. 1/30\nB. 1/5\nC. 2/3\nD. 3/4\nE. 4/5\n\n### Answer:\nLet total paint = 1\nLet amount replaced = x\n50 (1-x) + 25x = 30\nx = 4/5\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe mean daily profit made by a shopkeeper in a month of 30 days was Rs. 350. If the mean profit for the first fifteen days was Rs. 225, then the mean profit for the last 15 days would be\n\n### Options:\nA. Rs. 200\nB. Rs. 350\nC. Rs. 475\nD. Rs. 425\nE. None of these\n\n### Answer:\nAverage would be : 350 = (225 + x)/2\nOn solving, x = 475.\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the consumer price index for a sample of goods and services purchased in Dallas rose from 100 at the end of 1967 to x at the end of 1985, what was the average R (arithmetic mean) annual increase in the index over this period?\n\n### Options:\nA. (x + 100)/18\nB. x/18\nC. (100 \u2212 x)/18\nD. (x \u2212 100)/18\nE. 100x/18\n\n### Answer:\nCPI in end of 1967 = 100\nCPI in end of 1985 = x\nNumber of years = 18\nAverage annual increase in CPI R= (x-100)/18\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA coin is weighted so that the probability of heads on any flip is 0.2, while the probability of tails is 0.8. If the coin is flipped 5 times independently, which of the following represents the probability that tails will appear no more than twice?\n\n### Options:\nA. (0.2)^5 + 5(0.2)^4(0.8) + 10(0.2)^3(0.8)^2\nB. (0.3)^5 + 4(0.3)^4(0.8) + 6(0.3)^3(0.8)^2\nC. (0.3)^5 + 3(0.3)^4(0.8) + 2(0.3)^3(0.8)^2\nD. (0.3)^5 + 2(0.3)^4(0.8) + (0.3)^3(0.8)^2\nE. (0.6)^5 + (0.6)^4(0.4) + (0.6)^3(0.4)^2\n\n### Answer:\nProbability of Head, P(H) = 0.2\nProbability of Tail, P(T) = 0.8\nTail will appear NO more than twice\ni.e. favourable cases\n2 Tails and 3 Heads, Probability = 5C2*(0.2)^3*(0.8)^2\n1 Tail and 4 Heads, Probability = 5C1*(0.2)^4*(0.8)^2\n0 Tail and 5 Heads, Probability = (0.2)^5\nRequired Probability = Sum of all Favourable cases = (0.2)^5 + 5(0.2)^4(0.8) + 10(0.2)^3(0.8)^2\nAnswer: option A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe sum of 9 hours 25 minutes and 4 hours 35 minutes is approximately what percent of a day?\n\n### Options:\nA. 64%\nB. 56%\nC. 58%\nD. 48%\nE. 72%\n\n### Answer:\nSince the question is asking for an approximate percentage\n9:25+4:35 = 14 hours\n% of day = 14*100/24 = 7*100/25 ~ 58%\nAnswer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 10 ounces of a strong vinegar solution are diluted with 50 ounces of water to form a four-percent vinegar solution, what was the concentration of the original solution?\n\n### Options:\nA. 20%\nB. 24%\nC. 25%\nD. 28%\nE. 30%\n\n### Answer:\nLet x be the concentration of the original solution.\n10x = 0.04(60)\nx = 0.24\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how many ways Chief Minister and Minister be elected from a team of 12 members?\n\n### Options:\nA. 128\nB. 134\nC. 132\nD. 167\nE. 169\n\n### Answer:\nTo do this, if captain is elected first, then we have 12 ways of doing this.\nFor election of vice-captain, we have only 11 ways left, coz 1 way is already consumed. (Situations like this is called dependent situation. One selection depends upon other selection.)\nSo, the ans is 12*11 = 132 ways.\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nLight glows for every 13 seconds . How many max. times did it glow between 1:57:58 and 3:20:47 am.\n\n### Options:\nA. 380 times\nB. 381 times\nC. 382 times\nD. 392 times\nE. 482 times\n\n### Answer:\nTime difference is 1hr,22min,49sec=4969sec. So, light glows floor(4969/13)=382 times.\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAn exam consists of 200 questions to be solved in 3 hours, out of which 50 are maths questions. It is suggested that twice as much time be spent on each math question as for each other question. How many minutes should be spent on maths problems?\n\n### Options:\nA. 36/25 minutes\nB. 36/24 minutes\nC. 36/26 minutes\nD. 35/25 minutes\nE. 34/25 minutes\n\n### Answer:\nx=time for each math problem\ny= time for every other problem\n50x+150y=180 minutes\nx=2y because spent twic as much time on the math problems as the other\n50(2y)+150y=180\n100y+150y=180\n250y=180\ny= 180/250=18/25 of a minute per problem on the other questions\nx=2(18/25)\nx=36/25 minutes\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nEach of the integers from 1 to 14 is written on the a seperate index card and placed in a box. If the cards are drawn from the box at random without replecement, how many cards must be drawn to ENSURE that the product of all the integers drawn is even?\n\n### Options:\nA. 19\nB. 12\nC. 11\nD. 10\nE. 8\n\n### Answer:\nOut of the 14 integers: 7 are odd and 7 are even.\nIf we need to make sure that the product of all the integers withdrawn is even then we need to make sure that we have at least one even number. In the worst case:\n1. we will end up picking odd numbers one by one, so we will pick all 7 odd numbers first\n2. 8th number will be the first even number\nSo we need to withdraw at least 8 numbers to make sure that we get one even number and the product of all the integers picked is even.\nSo, answer will be 8. (E)\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA horse and cow were sold for Rs.12000 each. The horse was sold at a loss of 20% and the cow at a gain of 20%. The entire transaction resulted in :\n\n### Options:\nA. No loss or gain\nB. Loss of Rs.1000\nC. Gain of Rs.1000\nD. Gain of Rs.2000\nE. None of these\n\n### Answer:\nExplanation:\nIn the special case of profit and loss percentages are equal and Selling price is same, then the transaction always results in Loss. This loss percentage is given by a simple formula \u2212(x/10)2\nSo in this case, Profit% = Loss% = 20. So x = 20\nLoss percentage = \u2212(20/10)2=\u22124\nTotal S.P = Rs.24000\nCost price = 24000\u00d7100/96 = 25000\nLoss = Rs.1000\nCorrect Option : B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAn aeroplane covers a certain distance at a speed of 320 kmph in 4 hours. To cover the same distance in 1 2/3 hours, it must travel at a speed of:\n\n### Options:\nA. 520\nB. 620\nC. 820\nD. 768\nE. 720\n\n### Answer:\nDistance = (240 x 5) = 1280 km.\nSpeed = Distance/Time\nSpeed = 1280/(5/3) km/hr. [We can write 1 2/3 hours as 5/3 hours]\nRequired speed = (1280 x\t3/5) km/hr = 768 km/hr\nAnswer D) 768 Km/hr\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nInsert the missing number\n3, 4, 7, 16, 43, 124, ...\n\n### Options:\nA. 367\nB. 356\nC. 125\nD. 1222\nE. 1322\n\n### Answer:\nSeries is having difference between susequest next number and the nuber with multiplication by 3\n3, 4, 7, 16, 43, 124, ...\nDiffernce between 4 and 3 is 1, multiply with three and add 4 to it. 7 will come\nDiffernce between 7 and 4 is 3, multiply with three and add 7 to it. 16 will come\ndiffernce between 16 and 7 is 9, multiply with three and add 16 to it. 43 will come\ndiffernce between 43 and 16 is 27, multiply with three and add 43 to it. 124 will come\ndiffernce between 124 and 43 is 81, multiply with three and add 124 to it. 367 will come\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA sum of money at simple interest amounts to Rs. 2240 in 2 years and to Rs. 2600 in 5 years. What is\nthe principal amount\n\n### Options:\nA. 1000\nB. 1500\nC. 2000\nD. 2500\nE. None of these\n\n### Answer:\nExplanation:\nSI for 3 year = 2600-2240 = 360\nSI for 2 year 360/3 * 2 = 240\nprincipal = 2240 - 240 = 2000\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA, B and C invested Rs.6300, Rs.4200 and Rs.10500 respectively, in a partnership business. Find the total share of A & B in profit of Rs.12100 after a year?\n\n### Options:\nA. Rs.6030\nB. Rs.4050\nC. Rs.6050\nD. Rs.7050\nE. Rs.6080\n\n### Answer:\n6300:4200:10500\n3:2:5\nA'share =3/10 * 12100 = 3630\nB's share =2/10*12100 = 2420\nRequired total share = 3630 + 2420 = 6050\nAnswer : C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a business, A and C invested amounts in the ratio 2 : 1 , whereas the ratio between amounts invested by A and B was 3 : 2 . If Rs 157300 was their profit, how much amount did B receive?\n\n### Options:\nA. Rs. 48000\nB. Rs. 48200\nC. Rs. 48400\nD. Rs. 48600\nE. None\n\n### Answer:\nSolution: Assume that investment of C = x\nThen, investment of A =2x\nInvestment of B = 4x/3\nA:B:C = 2x : 4x/3 : x = 2 : 4/3 : 1 =6 : 4 : 3\nB's share = 157300 * 4/(6+4+3) = 157300*4/13\n= 12100*4 = Rs. 48400.\nAnswer: Option C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe effective annual rate of interest corresponding to a nominal rate of 12% per annum payable half-yearly is?\n\n### Options:\nA. 16.06%\nB. 16.07%\nC. 12.36%\nD. 6.09%\nE. 6.19%\n\n### Answer:\nAmount of Rs. 100 for 1 year when compounded half-yearly = [100 * (1 + 6/100)2] = Rs. 112.36 Effective rate = (112.36 - 100) = 12.36%\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nPumping alone at their respective constant rates, one inlet pipe fills an empty tank to 1/2 of capacity in 6 hours and a second inlet pipe fills the same empty tank to 2/3 of capacity in 6 hours. How many hours will it take both pipes, pumping simultaneously at their respective constant rates, to fill the empty tank to capacity?\n\n### Options:\nA. 3.25\nB. 3.6\nC. 4.2\nD. 4.4\nE. 5.14\n\n### Answer:\nTime taken by First tank Fill 1/2 the tank = 6 hours\ni.e. Time taken by First tank to Fill 1 complete the tank =12 hours\nTime taken by Second tank Fill 2/3 the tank = 6 hours\ni.e. Time taken by First tank to Fill 1 complete the tank = (3/2)*6 = 9 hours\nin 1 Hour, Both tanks together Fill the tank = (1/12)+(1/9) = 7/36 tank\ni.e. Time taken by Both tank to Fill 1 complete the tank = 36/7 hours = 5.14 hours\nAnswer: option E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThree numbers are in the ratio 3 : 4 : 8. The sum of its longest and smallest numbers equals the sum of the third number and 42. Find the third number?\n\n### Options:\nA. A)54\nB. B)75\nC. C)24\nD. D)46\nE. E)63\n\n### Answer:\nLet the numbers be 3x, 4x, 8x.\nLargest number = 8x.\nSmallest number = 3x.\nThird number = 4x.\n8x + 3x = 4x + 42\n7x = 42 =>x=6\n4x=24 =>third number is 24.\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow long does a train 105 m long running at the speed of 68 km/hr takes to cross a bridge 90 m length?\n\n### Options:\nA. 13.9 sec\nB. 10.7 sec\nC. 17.9 sec\nD. 61.9 sec\nE. 47.98 sec\n\n### Answer:\nSpeed = 68 * 5/18 = 19m/sec\nTotal distance covered = 105 + 90 = 205 m.\nRequired time = 205/19 = 10.7 sec.\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA boat can travel with a speed of 13 km/hr in still water. If the speed of the stream is 4 km/hr, find the time taken by the boat to go 68 km downstream.\n\n### Options:\nA. 2 hours\nB. 1 hours\nC. 7 hours\nD. 4 hours\nE. 3 hours\n\n### Answer:\nSpeed downstream = (13 + 4) km/hr = 17 km/hr.\nTime taken to travel 68 km downstream = 68/17 hrs = 4 hrs.\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average number of shirts with Salman, Ambani and Dalmiya is 60, if all of them reached a shopping mall in Delhi and purchased 1 shirts each of them then average number of shirt each of them now has\n\n### Options:\nA. 66\nB. 63\nC. 62\nD. 64\nE. 61\n\n### Answer:\nRequired average\n= Old average + New average\n= 60 + 1 = 61\nanswer :E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere is a soccer tournament that is single elimination meaning that after one loss the team is out. There are 15 teams in this tournament. How many games are played?\n\n### Options:\nA. 15\nB. 7\nC. 8\nD. 14\nE. 10\n\n### Answer:\nD\nThe number of games always adds up to one less than the number of teams in a single elimination tournament. You may calculate it any way. Therefore, 14 games were played.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 15% of 40 is greater than 25% of a number by 2, then the number is?\n\n### Options:\nA. 12\nB. 8\nC. 15\nD. 20\nE. 16\n\n### Answer:\nLet the number be x\n50% of 40 - 25% of x = 2\n25/100 x = (15/100 * 40)-2\nx/4 = 4\nx = 16\nAnswer is E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nCompany ABC imported 10,000 widgets made of either brass or aluminum. The widgets are painted blue, red or green. If 10 percent of the widgets are made of brass and of those 20 percent are painted green and 40 percent are painted red how many brass widgets painted blue were imported?\n\n### Options:\nA. 420\nB. 400\nC. 1050\nD. 1680\nE. 2100\n\n### Answer:\nAnswer A.\nWe are told that 10% of all imported widgets are made of brass and of those, 20% are green and 40% are red. Since we know that there are only three colors, the remaining 40% must be blue. 40% blue of 10% brass widgets leads to 4% blue brass widgets out of the total 10,550 widgets.\n10,000 /100 * 4 = 400.\nAnswer B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average of the first five multiples of 9 is:\n\n### Options:\nA. 20\nB. 27\nC. 28\nD. 30\nE. None of these\n\n### Answer:\nSolution: Required average = (total sum of multiple of 9)/5\n= (9+18+27+36+45)/5\n= 27\nNote that, average of 9 and 45 is also 27.\nAnd average of 18 and 36 is also 27.\nAnswer: Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn what time will Rs.4000 lent at 3% per annum on simple interest earn as much interest as Rs.5000 will earn in 5 years at 4% per annum on simple interest?\n\n### Options:\nA. 8 1/3\nB. 8 1/5\nC. 8 1/6\nD. 8 1/2\nE. 8 1/7\n\n### Answer:\n(4000*3*R)/100 = (5000*5*4)/100\nR = 8 1/3.Answer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA person bought 129 glass bowls at a rate of Rs. 11 per bowl. He sold 118 of them at Rs. 15 and the remaining broke. What is the percentage gain for A?\n\n### Options:\nA. 40\nB. 2900/129\nC. 2430/70\nD. 2791/11\nE. 2719/8\n\n### Answer:\nCP=129*11=1419 and SP=118*15=1770\nGain %= 100*(1770-1419)/1419= 2900/129\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo trains are moving at 50 kmph and 70 kmph in opposite directions. Their lengths are 150 m and 100 m respectively. The time they will take to pass each other completely is?\n\n### Options:\nA. 7 1/2 sec\nB. 7 1/7 sec\nC. 7 2/2 sec\nD. 8 1/2 sec\nE. 7 1/9 sec\n\n### Answer:\n70 + 50 = 120 * 5/18 = 100/3 mps\nD = 150 + 100 = 250 m\nT = 250 * 3/100 = 15/2 = 7 1/2 sec\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSum of the squares of 3 no. is 149 and the sum of their products taken two at a time is 70. Find the sum?\n\n### Options:\nA. 17\nB. 19\nC. 21\nD. 13\nE. 18\n\n### Answer:\n(a + b + c)2 = a2 + b2 + c2 + 2(ab +bc + ca) = 149 + 2* 70\na + b + c = \u00e2\u02c6\u0161289 = 17\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAfter allowing a discount of 15% on the marked price, the selling price is Rs. 6800 for an article. If it was sold at marked price, there would have been a profit of 60%. The cost price of the article is?\n\n### Options:\nA. 3347\nB. 2788\nC. 5000\nD. 2787\nE. 2811\n\n### Answer:\nGiven SP = Rs. 6800\nMarked price = [SP(100)]/(100 - d%) = (6800 * 100)/(100 - 15) = Rs. 8000\nIf SP = Rs. 8000, profit = 60%\nCP = [SP(100)]/(100 + 60) = (8000 * 100)/160 = Rs. 5000\nAnswer: C:\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the remainder when 14,451 \u00d7 15,651 \u00d7 16,788 is divided by 5?\n\n### Options:\nA. 1\nB. 2\nC. 4\nD. 3\nE. 5\n\n### Answer:\nOnly the unit's digit of the product will decide the remainder when divided by 5.\nHence, 1*1*8= will give units digit as 8\nSo, whatever be the number, if it ends in 8, the remainder after dividing with 5 will be 3.\nOptionD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA, B, C subscribe Rs. 50,000 for a business. If A subscribes Rs. 4000 more than B and B Rs. 5000 more than C, out of a total profit of Rs. 35,000, what will be the amount A receives?\n\n### Options:\nA. 14700\nB. 14500\nC. 14000\nD. 15000\nE. 15200\n\n### Answer:\nTotal amount invested = 50000\nAssume that investment of C =x.\nThen investment of B =5000+x,\nInvestment of A =4000+5000+x=9000+x\nx+5000+x+9000+x=50000\n\u21d23x+14000=50000\n\u21d23x=50000\u201314000=36000\n\u21d2x=36000/3=12000\nInvestment of C =x=12000\nInvestment of B =5000+x=17000\nInvestment of A =9000+x=21000\nRatio of the investment of A, B and C\n=21000:17000:12000=21:17:12\nShare of A = Total profit \u00d721/50\n=35000\u00d72150=700\u00d721=14700\nAnswer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are 5 bags three of which each contains 5 white and 2 black balls, and remaining 2 bags each contains 1 white and 4 black ball; a white ball has been drawn, find the chance that it came from first group.\n\n### Options:\nA. 2/7\nB. 6/35\nC. 8/25\nD. 75/89\nE. 3/175\n\n### Answer:\nPlease go through my solution and suggest any mistake.\nChances of selecting a white ball from group 1: 5/7----------------------Chances of selecting a white ball from group 2: 1/5\nThus combined probability of section of white ball from group 1:\n3/5 x 5/7 = 3/7\nThus combined probability of section of white ball from group 2:\n2/5 x 1/5 = 2/25\nOut of these chances, chance of occurrence of first case : (3/7) / (3/7 + 2/25) = 75/89\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe price of a certain house this year is $140,000, which is 25 percent greater than the cost of the house last year. What was the price of the house last year?\n\n### Options:\nA. $112,000\nB. $114,000\nC. $116,000\nD. $118,000\nE. $120,000\n\n### Answer:\nThe price of the house last year was $140,000/1.25=$112,000\nThe answer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nZoey won the lottery and got $7,348,340. she wants to split it among herself and 5 friends evenly. how much money must she add if she wants to split it evenly?\n\n### Options:\nA. $3\nB. $2\nC. $9\nD. $1\nE. $4\n\n### Answer:\nZoey and her 5 friends is 6 people in all. $7,348,340 must be divisible by 6 if she wants to split it evenly. The money is divisible by 6 if it's divisible by 2 and 3. 7+3+4+8+3+4+0=29. 2 and 3 cant go into 29. Adding 1 dollar makes it 30. 2 and 3 can go into 30 so 6 can also. The answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA book store bought copies of a new book by a popular author, in anticipation of robust sales. The store bought 400 copies from their supplier, each copy at wholesale price x. The store sold the first 150 copies in the first week at 80% more than x, and then over the next month, sold a 100 more at 20% more than x. Finally, to clear shelf space, the store sold the remaining copies to a bargain retailer at 40% less than x. What was the bookstore\u2019s net percent profit or loss on the entire lot of 400 books?\n\n### Options:\nA. 30% loss\nB. 10% loss\nC. 10% profit\nD. 20% profit\nE. 60% profit\n\n### Answer:\n[[x(150)(1.8)+x(100)(1.2)+x(150)(0.6)]/400x] - 1\n[50[(3)(1.8) + (2)(1.2) + (3)(0.6)] / (50)(8)] - 1\n[(5.4 + 2.4 + 1.8)/8] - [8/8]\n+1.6/8\n+20%\nanswer is D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe ratio of the ages of Anil and his son at present is 7:3. Six years hence, the ratio of the ages of the Anil's wife and the son will be 2:1. Find the ratio of the present ages of Anil and his wife?\n\n### Options:\nA. 2:2\nB. 2:9\nC. 2:4\nD. Cannot be determined\nE. None of these\n\n### Answer:\nLet the present ages of Anil and his son be 7x and 3x years respectively.\nLet the present age of the son's mother be m years.\n(m + 6)/(3x + 6) = 2/1\nm = 6x + 6\nRatio of the present ages of Anil and his son's mother = 7x/(6x + 6).\nThis cannot be found uniquely.\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSophia finished 2323 of a book. She calculated that she finished 90 more pages than she has yet to read. How long is her book?\n\n### Options:\nA. 140\nB. 320\nC. 745\nD. 270\nE. 350\n\n### Answer:\nLet x be the total number of pages in the book, then she finished 23\u22c5x pages.\nThen she has x\u221223\u22c5x=13\u22c5xpages left.\n23\u22c5x\u221213\u22c5x=90\n13\u22c5x=90\nx=270\nSo the book is 270 pages long.\ncorrect answer is D)270\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe sum of five numbers is 655. The average of the first two numbers is 85 and the third number is 125. Find the average of the two numbers?\n\n### Options:\nA. 180\nB. 88\nC. 278\nD. 268\nE. 267\n\n### Answer:\nLet the five numbers be P, Q, R, S and T.\n=> P + Q + R + S + T = 655.\n(P + Q)/2 = 85 and R = 125\nP + Q = 170 and R = 125\nP + Q + R = 295\nS + T = 655 - (P + Q + R) = 360\nAverage of the last two numbers = (S + T)/2 = 180.\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSCORE INTERVAL----------------NUMBER OF SCORES\n50-59-------------------------- 8\n60-69--------------------------10\n70-79--------------------------16\n80-89--------------------------27\n90-99--------------------------18\nThe table above shows the distribution of test scores for a group of management trainees. Which score interval contains the median of the 79 scores?\n\n### Options:\nA. 39th (80-89)\nB. 40th\nC. 34th\nD. 37th\nE. 35th\n\n### Answer:\nTotal scores= 8+10+16+27+18 = 79, which is odd, therefore the median is the Floor(79/2)+1 = 39th score. And the 39th score is in the 80-89 range, because 50-79 only reference 34 scores.\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the sum of all the numbers between 300 and 1000 which are divisible by 179?\n\n### Options:\nA. 1267\nB. 2876\nC. 1865\nD. 2506\nE. 1812\n\n### Answer:\nExplanation:\n358/179 \u00e2\u20ac\u00a6.. 895/179\n179(2 + 3 + 4 + 5) => 2506\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe ages of two persons differ by 16 years. If 6 years agao, the elder one be 3 times as old as the younger one, find their present ages.\n\n### Options:\nA. 20 years.\nB. 30 years.\nC. 40 years.\nD. 50 years.\nE. 60 years.\n\n### Answer:\nSol.\nLet the age of the younger person be x years.\nThen, age of the elder perosn = (x + 16) years.\n\u2234 3(x - 6) = (x + 16 - 6) \u21d4 3x - 18 = x + 10\n\u21d4 2x = 28 \u21d4 x = 14\nHence, their present ages are 14 years and 30 years.\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat will be the ratio of simple interest earned by certain amount at the same rate of interest for 4 years and that for 9 years?\n\n### Options:\nA. 1 : 3\nB. 2 : 3\nC. 1 : 2\nD. 4 : 9\nE. 1 : 4\n\n### Answer:\nLet the principal be P and rate of interest be R%.\nRequired ratio =\n(P x R x 4)/100 DIVIDED BY\t(P x R x 9)/100\n=\t4PR/9PR\t=\t4/9\t= 4 : 9.\nANSWER : D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe angles of a triangle are in the ratio 1 : 3 : 8. Find the measurement of the 3angles of triangle.\n\n### Options:\nA. 100\u00b0\nB. 110\u00b0\nC. 120\u00b0\nD. 180\u00b0\nE. 190\u00b0\n\n### Answer:\nIf the ratio of the three angles is 1:3:8, then the measures of these angles can be written as x, 3x and 8x. Also the sum of the three interior angles of a triangle is equal to 180\u00b0. Hence\nx + 3x + 8x = 180\nSolve for x\n12x = 180\nx = 15\nThe measures of the three angles are\nx = 15\u00b0\n3x = 3 \u00d7 15 = 45\u00b0\n8x = 8 \u00d7 15 = 120\u00b0\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhen x is divided by 6, the quotient is y and the remainder is 1. When x is divided by 6, the quotient is z and the remainder is 6. Which of the following is the value of y in terms of z?\n\n### Options:\nA. 4z/7 + 5\nB. (7z + 5) / 6\nC. (6z + 5) / 6\nD. (7z + 5) / 4\nE. (4z + 6) / 7\n\n### Answer:\nWhen x is divided by 6, the quotient is y and the remainder is 1: x = 6y + 1.\nWhen x is divided by 6, the quotient is z and the remainder is 6: x = 6z + 6.\nEquate those two:\n6y + 1 = 6z + 6;\ny = (6z + 5)/6.\nAnswer: C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTourist purchased a total of 30 travelers checks in $50 and $100 denominations. The total worth of the travelers checks is $1800. How many checks of $50 denominations can he spend so that average amount (arithmetic mean) of the remaining travelers checks is $100?\n\n### Options:\nA. 4\nB. 12\nC. 15\nD. 22\nE. 24\n\n### Answer:\nyou could set-up a quick table and brute force the answer.\nA\t4\t*\t50\t200 1800\t-200 1600\t26 61.54\nB\t12\t*\t50\t600 1800\t-600 1200\t18 66.67\nC\t15\t*\t50\t750 1800\t-750 1050\t15 70.00\nD\t22\t*\t50\t1000 1800\t-1000\t800\t8 100.00\nE\t24\t*\t50\t1200 1800\t-1200\t600\t6 100.00\nAnswer is D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain board game has a row of squares numbered 1 to 100. If a game piece is placed on a random square and then moved 7 consecutive spaces in a random direction, what is the probability R the piece ends no more than 7 spaces from the square numbered 49?\n\n### Options:\nA. 7%\nB. 8%\nC. 14%\nD. 15%\nE. 28%\n\n### Answer:\nOA is E\nrequired prob is 7 spaces any side of 49.\nso total 14 spaces are required in 7 moves which can be achieved by max 7 move on any side\nso total spaces = 28\nprobability R= 28%.E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA 340-liter solution of Kola is made from 80% water, 6% concentrated Kola and the rest is made from sugar. If 3.2 liters of sugar, 10 liter of water and 6.8 liters of concentrated Kola were added to the solution, what percent of the solution is made from sugar?\n\n### Options:\nA. 6%.\nB. 7.5%.\nC. 9.2%.\nD. 10.5%.\nE. 14%.\n\n### Answer:\nDenominator:\n340+10+3.2+6.8=360\nNumerator:\n340(1-.80-.06)+3.2\n340(0.14)+3.2\n47.6+3.2\n50.8\nRatio:\n50.8/360=0.14\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe radius of a cylindrical vessel is 7cm and height is 5cm. Find the whole surface of the cylinder?\n\n### Options:\nA. 281\nB. 528\nC. 440\nD. 767\nE. 1981\n\n### Answer:\nr = 7 h = 5\n2\u03c0r(h + r) = 2 * 22/7 * 7(12) = 528\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA right triangle has sides of a, b, and 9, respectively, where a and b are both integers. What is the value of (a + b)?\n\n### Options:\nA. 64\nB. 49\nC. 96\nD. 81\nE. 72\n\n### Answer:\nLET a= hypotenuse , b =base ,9 = perpendicular . therefore a^2 -b^2 =9^2 or (a+b)(a-b) = 81\na+b =81/a-b ' a-b cannot be zero ..therefore a+ b =81 where a-b is equal to 1\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe \u201ca-number\u201d of a number x is defined as the ones digit of 2^x. Antony rolls a die with 6 sides labeled with the integers from 1 to 6, each of which has an equal probability of landing face-up. He then takes 3^a, where a is the a-number of the result of his die roll, and plots 3^a on a number line as the point A. Finally, he repeats this entire process, this time plotting the result as the point B. What is the probability that the distance between A and B is greater than the value of B?\n\n### Options:\nA. 3/8\nB. 13/36\nC. 17/36\nD. 19/36\nE. 23/36\n\n### Answer:\nIf you calculate 3^a for 1st roll, all 6 results will be 9, 81, 6561, 729, 9, 81. This result is the same for 2nd roll. 9, 81, 6561, 729, 9, 81.\nAbout distance: If the first result is 9 and the second is also 9, the distance is 9-9=0 which is smaller than 9. If the first result is 9 and the second is 81, the distance is 81-9=72 which is also smaller than B which has the value of 81. If the first result is 81 and the second is 9, the distance will be greater than B. Distance 81-9=72>9.\nOn the first roll, the probability of getting result 9 is 2/6. In this case no other alternative values for second roll which would make the distance greater than B. So probability is 0. So next estimations are:\nprobability of getting 81 on the first roll (2/6) * probability of getting 9 on the second roll (2/6) = 1/9\nprobability of getting 729 on the first roll (1/6) * probability of getting 9, 81 on the second roll (4/6) = 1/9\nprobability of getting 6561 on the first roll (1/6) * probability of getting 9, 81, 729 on the first roll (5/6) = 5/36\nAll together: 1/9 + 1/9 + 5/36 = 13/36=B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA and B began business with Rs.6000 and Rs.4000 after 8 months, A withdraws Rs.1000 and B advances Rs.1000 more. At the end of the year, their profits amounted to Rs.630 find the share of A.\n\n### Options:\nA. 240\nB. 288\nC. 277\nD. 357\nE. 361\n\n### Answer:\n(6*8 + 5*4):(4*8 + 5*4)\n17:13\n17/30 * 630 = 357\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nCalculate the effect changes in dimension of a rectangle will have on its area, if length is increased by 35% and its breadth is decreased by 21%?\n\n### Options:\nA. 4.65% increase\nB. 5.65% increase\nC. 6.65% increase\nD. 6.65% decrease\nE. 7.65% increase\n\n### Answer:\nlet L and B be 100 each\n100 * 100 = 10000\nL increase by 35% = 135\nB decrease by 21% = 79\n135 * 79 = 10665\n6.65% increase\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the remainder is 12 when the integer n is divided by 22, what is the remainder when 2n is divided by 11?\n\n### Options:\nA. 0\nB. 2\nC. 3\nD. 6\nE. 7\n\n### Answer:\nn = 22k+12\n2n = 2(22k+12) = 4*11k + 24 = 4*11k + 2*11 + 2 = 11j+2.\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA and B can do a piece of work in 4 days, B and C in 6 days, C and A in 3 days. How long will C take to do it?\n\n### Options:\nA. 8 days\nB. 10 days\nC. 12 days\nD. 4 days\nE. 12 days\n\n### Answer:\n2c = 1/6 + 1/3 \u2013 1/4 = 1/4\nc = 1/8 => 8 days\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a man buys 20 lollipops for $90 and sold them for $2 dollars determine his loss\n\n### Options:\nA. $25\nB. $30\nC. $50\nD. $40\nE. $42\n\n### Answer:\n20 lollipops = $90, sold each for $2, so he sold 20 lollipops for 20 * $2= $40, Loss = $(90-40), loss = $50. correct answer : (C)\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average (arithmetic mean) monthly income of four workers is $1,000. After one worker\u2019s income increases by 50 percent the new average income is $1,200. What was the original income of the worker whose monthly income increased?\n\n### Options:\nA. $1,800\nB. $1,500\nC. $1,300\nD. $1,600\nE. $1,100\n\n### Answer:\nIncrease in total income was 200*4=$800, we know that this increase was 50% (1/2) of the workers original income, thus his/her original income was 800*2=$1,600.\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a dairy farm, 40 cows eat 40 bags of husk in 40 days. In how many days one cow will eat one bag of husk ?\n\n### Options:\nA. 34 days\nB. 40 days\nC. 46 days\nD. 50 days\nE. None of these\n\n### Answer:\nExplanation:\nLess Cows, More days (Indirect Proportion)\nLess bags, Less days (Direct Proportion)\n[Cows1 40\nBags 40 1]::40:x\n=>x\u221740\u22171=40\u22171\u221740\n=>x=40\nOption B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAt a certain supplier, a machine of type A costs $20,000 and a machine of type B costs $50,000. Each machine can be purchased by making a 20 percent down payment and repaying the remainder of the cost and the finance charges over a period of time.If the finance charges= 40 percent of the remainder the cost, how much less would 2 machines of type A cost than 1 machine of type B?\n\n### Options:\nA. $10,000\nB. $11,200\nC. $12,000\nD. $12,800\nE. $13,200\n\n### Answer:\n1 machine of type B will cost: 20% down payment of 50,000 = 10,000 plus remaining sum (50,000-10,000=40,000) with 40% of finance charges 40,000*1.4=56,000 --> 10,000+56,000=66,000;\n2 machine of type A will cost: 20% down payment of 2*20,000 = 8,000 plus remaining sum (40,000-8,000=32,000) with 40% of finance charges 32,000*1.4=44,800 --> 8,000+44,800=52,800;\nDifference = 66,000 - 52,800 = 13,200.\nAnswer: E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA theater charges $12 for seats in the orchestra and $8 for seats in the balcony. On a certain night, a total of 340 tickets were sold for a total cost of $3,320. How many more tickets were sold that night for seats in the balcony than for seats in the orchestra?\n\n### Options:\nA. 40\nB. 110\nC. 120\nD. 130\nE. 220\n\n### Answer:\nOrchestra Seats - a\nBalcony Seats - b\na+b = 340\nand 12a + 8b = 3320\nSolving equations simultaneously (Multiply Equation 1 with 8 and subtract from second equation)\n4a = 3320 - 8*340 = 3320 - 2720 = 600\ni.e. a = 150\nand b = 340-150 = 190\nMore seats in balcony than orchestra = b-a = 190 - 150 = 40\nAnswer: option A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA 25 cm wide path is to be made around a circular garden having a diameter of 4 meters. Approximate area of the path is square meters is?\n\n### Options:\nA. 3.34\nB. 3.37\nC. 3.35\nD. 3.76\nE. 3.31\n\n### Answer:\nArea of the path = Area of the outer circle - Area of the inner circle\n= \u220f{4/2 + 25/100}2 - \u220f[4/2]2\n= \u220f[2.252 - 22] = \u220f(0.25)(4.25) { (a2 - b2 = (a - b)(a + b) }\n= (3.14)(1/4)(17/4) = 53.38/16 = 3.34 sq m\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThree positive integers a, b, and c are such that their average is 80 and a \u2264 b \u2264 c. If the median is (a + 20), what is the least possible value of c?\n\n### Options:\nA. 88\nB. 89\nC. 90\nD. 92\nE. 94\n\n### Answer:\nSolution\nGiven Data\n3 positive integers\nAverage of a, b, and c = 80\nSo, a+b+c3a+b+c3 = 240 or a + b + c = 240\na \u2264 b \u2264 c\nMedian = (a + 20)\nMedian of these 3 numbers a, b, and c is \u2018b\u2019 because a \u2264 b \u2264 c\nTherefore, b = a + 20\nObjective To find the least value of 'c'\nTheoretically, the least value of c is when c = b.\nTherefore, a + (a + 20) + (a + 20) = 240 (b and c are equal and b, the median, is a + 20)\nOr 3a = 200 or a = 66.66\nSo, b = c = 66.66+ 20 = 86.66\nHowever, we know that these numbers are all integers.\nTherefore, a, b, and c cannot take these values.\nSo, the least value for c with this constraint is NOT likely to be when c = b\nLet us increment c by 1. Let c = (b + 1)\nIn this scenario, a + (a + 20) + (a + 21) = 240\nOr 3a = 199. The value of the numbers is not an integer in this scenario as well.\nLet us increment c again by 1. i.e., c = b + 2\nNow, a + (a + 20) + (a + 22) = 240\nOr 3a = 198 or a = 66\nIf a = 66, b = 86 and c = 88.\nThe least value for c that satisfies all these conditions is 88.\nCorrect answer is choice A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nNitin's age was equal to square of some number last year and the following year it would be cube of a number. If again Nitin's age has to be equal to the cube of some number, then for how long he will have to wait?\n\n### Options:\nA. 10 years\nB. 38 years\nC. 39 years\nD. 64 years\nE. 44 years\n\n### Answer:\ncurrent age = 26 years because Nitin's age was equal to square of some number ( 25= 5^2) last year and the following year it would be cube of a number (27= 3^3).\nNext cube age will be 64 =4^3 which will come after 64-26 = 38 years.\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA case contains C cartons. Each carton contains B boxes, and each box contains 200 paper clips. How many paper clips are contained in 2 cases?\n\n### Options:\nA. 200BC\nB. 200B/C\nC. 400BC\nD. 400B/C\nE. 400/BC\n\n### Answer:\n2 cases * C cartons/case * B boxes/carton * 200 clips/box = 400BC paper clips\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA baker filled with a measuring cup with 3/4 cup water. He poured 1/2 of the water into the batter, and then spilled 1/8 of the water on the floor. How much water will the baker needed to add what is left in the cup to have 50% more than what he started with?\n\n### Options:\nA. 1/8 cup\nB. 3/8 cup\nC. 1/4 cup\nD. 1/2 cup\nE. 7/8 cup\n\n### Answer:\n3/4 is the original water in cup .half in batter.So left is 3/8 out which 1/8 is spilled out.So again left with 2/8.\nso 50% more than what he started was = 3/4+1/2*(3/4)=9/8\nAmount of water needed to add = 9/8 - 2/8=7/8\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average age 9 members of a committee are the same as it was 4 years ago, because an old number has been replaced by a younger number. Find how much younger is the new member than the old number?\n\n### Options:\nA. 20 years\nB. 21 years\nC. 18 years\nD. 29 years\nE. 36 years\n\n### Answer:\n9 * 4 = 36 years\nAnswer:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA password of a computer used four digits where they are from 0 and 9. What is the probability that the password only consists of even numbers?\n\n### Options:\nA. 1/4\nB. 1/16\nC. 1/32\nD. 1/400\nE. 1/800\n\n### Answer:\nThere are five possibilities out of ten that the each digit is even, so the overall probability is 1/2 * 1/2 * 1/2 * 1/2 (answer B)\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhen w is divided by 5, the remainder is 3. When y is divided by 5, the remainder is 4. What is the remainder when w + y is divided by 5?\n\n### Options:\nA. 0\nB. 1\nC. 2\nD. 3\nE. 4\n\n### Answer:\nIn my view the answer should be C\nw/5 has Remainder=3 -> w = 5 x Q + 3\nY/5 has a Remainder=4 -> Y = 5 x Q + 3\nCombining both\n((5 x Q1 + 3) + (5 x Q2 + 3))/5 =\n5(Q1+Q2)/5 + 7/5 =\nQ1+Q2 + 7/5\n7/5 = 1+ 2/5 => Remainder 2\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nP and Q started a business investing Rs.85,000 and Rs.15,000 respectively. In what ratio the profit earned after 2 years be divided between P and Q respectively?\n\n### Options:\nA. 3 : 4\nB. 3 : 5\nC. 15 : 23\nD. 17 : 3\nE. None\n\n### Answer:\nSolution\nP : Q\t= 85000 : 15000\n=85 : 15\n=17 : 3\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a rectangular coordinate system, what is the area of a rectangle whose vertices have the coordinates (-7, 1), (1, 1), (1, -6) and (-7, -6)?\n\n### Options:\nA. 112\nB. 64\nC. 42\nD. 24\nE. 56\n\n### Answer:\nLength of side 1= 7+1=8\nLength of side 2= 6+1= 7\nArea of rectangle= 7*8= 56\nE is the answer\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the principle on a certain sum of money at 5% per annum for 3 1/5 years if the amount being Rs.580?\n\n### Options:\nA. Rs.500\nB. Rs.5100\nC. Rs.530\nD. Rs.540\nE. None of these\n\n### Answer:\nExplanation:\n580 = P [1 + (5*16/5)/100]\nP= 500\nAnswer: Option A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a shop, the cost of 4 shirts, 4 pairs of trousers and 2 hats is $560. The cost of 9 shirts, 9 pairs of trousers and 6 hats is $1,290. What is the total cost of 1 shirt, 1 pair of trousers and 1 hat?\n\n### Options:\nA. $50\nB. $320\nC. $150\nD. $100\nE. $400\n\n### Answer:\nLet x be the price of one shirt, y be the price of one pair of trousers and z be the price of one hat.\n4x + 4y + 2z = 560 :\n9x + 9y + 6z = 1,290\n3x + 3y + 2z = 430 : divide all terms of equation C by 3\nx + y = 130 : subtract equation D from equation B\n3(x + y) + 2z = 430 : equation D with factored terms.\n3*130 + 2z = 430\nz = 20 : solve for z\nx + y + z = 130 + 20 = $150\ncorrect answer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nCamel and carriage for Rs. 5000. He SP the camel at a gain of 20% and the carriage at a loss of 10%. If he gains 3% on the whole, then find the CP of the camel?\n\n### Options:\nA. Rs.2166.67\nB. Rs.2234\nC. Rs.2345.13\nD. Rs.2456.34\nE. Rs.2550.34\n\n### Answer:\nNow, in this numerical, there is no common loss and gain %.\nHence, solve it making equations.\nLet cost price of camel be x.\nAs cost of camel and carriage = Rs 5000\nCost of carriage = Rs. (5000 \u2013 x)\nAfter selling camel he gains 20% and on carriage a loss of 10%. But on the whole he gains 3%.\nTherefore,\n20% of x \u2013 10 % of (5000 \u2013 x) = 3 % of 5000\n20 \u00d7 x \u2013 10 \u00d7 (5000 \u2013 x) = 3 \u00d7 5000\n100 100 100\nx \u2013 (5000 \u2013 x) = 150\n5 10\n10x \u2013 (5000 \u2013 x) \u00d7 10 = 150 \u00d7 10\n5 10\n2x-5000+x=1500\n3x=1500+5000\nx=2166.67\nThe cost of camel = Rs.2166.67\nOption (A) is the correct answer\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nI. j; k; m; n; p\nII. j - 10; m; m; m; p + 15\nIII. j + 2; k + 1; m; n - 1; p - 2\nIf j, k, m, n, and p are consecutive positive integers such that j < k < m < n < p, the data sets I, II, and III above are ordered from greatest standard deviation D to least standard deviation in which of the following?\n\n### Options:\nA. I, III, II\nB. II, I, III\nC. II, III, I\nD. III, I, II\nE. III, II, I\n\n### Answer:\nRange of 1st Set = (p-j)\nRange of 2nd Set = P+15 - j +10 = (p-j) +25\nRange of 3rd Set = P -2 - j - 2 = (p-j) - 4\nR2 > R1 > R3 ==> SD2 > SD1 > SD3\nSince,D= Higher the Range -> More Dispersion in the Set -> More Standard Deviation.B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nKelly and Jody packed boxes with books. If Jody packed 60% of the total number of boxes, what was the ratio of the number of boxes Kelly packed to the number that Jody packed?\n\n### Options:\nA. 1 to 6\nB. 1 to 4\nC. 2 to 5\nD. 3 to 5\nE. 2 to 3\n\n### Answer:\nExplanation:\nIf Jody packed 60% of the boxes then Kelly packed 40%. The ratio of the number of boxes Kelly packed to the number Jody packed is thus 40%/60%=2/3\nAnswer: Option E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man performs 1/2 of the total journey by rail, 1/3 by bus and the remaining 3km on foot. His total journey is\n\n### Options:\nA. 18km\nB. 10km\nC. 12km\nD. 24km\nE. 25km\n\n### Answer:\nExplanation:\nLet the journey be x km\nThen, 1x/2 + 1x/3 +3 =x\n5x +18 =6x\nX = 18km\nAnswer: Option A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a bag there are coins of 50 paisa, 25 paisa and one rupee in the proportion 4:3:2. If there are in all Rs.42, the number of one rupee coins is?\n\n### Options:\nA. 22\nB. 26\nC. 18\nD. 16\nE. 24\n\n### Answer:\n4x 3x 2x\n50 25 100\n200x + 75x + 200x = 3800\n475x = 3800\nx = 8 => 2x = 16\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe elevator in an eleven-story office building travels at the rate of one floor per 1/4 minute, which allows time for picking up and discharging passengers. At the main floor and at the top floor, the operator stops for 1 minute. How many complete trips will an operator make during a 6-hour period?\n\n### Options:\nA. 88\nB. 56\nC. 42\nD. 51\nE. 64\n\n### Answer:\nComplete trip = 10 floors up and 10 floors down = 20 floors = 20*1/4 = 5 minutes plus 2 minutes = 7 minutes.\n6 hour = 360 minutes.\nIn 360 minutes operator can make 360/7=51 trips.\nAnswer: D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFor a certain exam,a score of 58 was 2 standard deviations below mean and a score of 98 was 3 standard deviations above mean.What was the mean score W for the exam?\n\n### Options:\nA. 74\nB. 76\nC. 78\nD. 80\nE. 82\n\n### Answer:\nA score of 58 was 2 standard deviations below the mean --> 58 = Mean - 2d\nA score of 98 was 3 standard deviations above the mean --> 98 = Mean + 3d\nSolving above for Mean W= 74.\nAnswer: A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf N = 23\u00d734 , M = 22\u00d73\u00d75, then find the number of factors of N that are common with the factors of M.\n\n### Options:\nA. 3\nB. 9\nC. 8\nD. 6\nE. 2\n\n### Answer:\nAnswer: c\nExplanation:\nN = 23\u00d734\nM = 22\u00d73\u00d75\nBy taking common powers we get 22\u00d73\nSo common factors = (2 + 1)(1 + 1) = 6.\n(formula for number of factors of a number)\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA and B can do a piece of work in 6 2/3 days and 5 days respectively. They work together for 2 days and then A leaves. In how many days after that B will complete the work alone.\n\n### Options:\nA. 1 1/8 days\nB. 1 1/2 days\nC. 3 1/2 days\nD. 1 1/5 days\nE. 1 5/2 days\n\n### Answer:\n3/20 * 2 + (2 + x)/5 = 1\nx = 1 1/2 days\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that all the four bulbs are defective.\n\n### Options:\nA. 1/187\nB. 1/127\nC. 1/178\nD. 1/129\nE. 1/126\n\n### Answer:\nOut of nine, five are good and four are defective. Required probability\n= \u2074C\u2084/\u2079C\u2084\n= 1/126\nAnswer:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nDue to construction, the speed limit along an 9-mile section of highway is reduced from 55 miles per hour to 20 miles per hour. Approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ?\n\n### Options:\nA. A) 5.61\nB. B) 8\nC. C) 10\nD. D) 17.19\nE. E) 24\n\n### Answer:\nOld time in minutes to cross 9 miles stretch = 9*60/55 = 9*12/11 = 9.81\nNew time in minutes to cross 9 miles stretch = 9*60/20 = 9*3/1 = 27\nTime difference = 17.19\nAns:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHaris can wash all the windows of his house in 10 hours. His wife Maggie can wash all the windows in 5 hours. How many hours will it take for both of them working together to wash all the windows?\n\n### Options:\nA. 2\nB. 3 1/3\nC. 4 1/4\nD. 5\nE. 6\n\n### Answer:\nWork hrs=AB/(A+B)= 50/15 =3 1/3\nAnswer is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA family made a down payment of $25\nand borrowed the balance on a set of\nencyclopedias that cost $400. The\nbalance with interest was paid in 28\nmonthly payments of $16 each and a\nfinal payment of $19. The amount of\ninterest paid was what percent of the\namount borrowed?\n\n### Options:\nA. 6.75%\nB. 12.25%\nC. 14.23%\nD. 16.66%\nE. 24.53%\n\n### Answer:\ninterest paid = 16*28+19 - 375 = 92\n% off the balance = (92/375) * 100 = 24.53%\nAnswer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJohn bought a shirt on sale for 25% off the original price and another 25 % off the discounted price. If the final price was $19, what was the price before the first discount?\n\n### Options:\nA. $45.10\nB. $34.31\nC. $28.44\nD. $67.54\nE. $33.77\n\n### Answer:\nlet x be the price before the first discount. The price after the first discount is\nx - 25%x (price after first discount)\nA second discount of 25% of the discounted price after which the final price is 19\n(x - 25%x) - 25%(x - 25%x) = 19\nSolve for x\nx = $33.77\ncorrect answer E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFive years ago, the average age of A, B, C and D was 45 yr. with E joining them now, the average of all the five is 42 yr. How old is E?\n\n### Options:\nA. 10 yr\nB. 40 yr\nC. 45yr\nD. 64 yr\nE. NOne\n\n### Answer:\nSolution:\nTotal present age of A, B, C and D,\n= (45*4)+(4*5) = 200 yr;\nTotal age present age of A, B, C, D and E,\n= 42*5 = 210 yr.\nSo, age of E = 10 yr.\nAnswer: Option A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA group of students was interviewed for that if it was asked whether or not they speak French and / or English. Among those who speak French, 20 speak English well, while 60 of them do not speak English. If 60% of students do not speak French, how many students were surveyed?\n\n### Options:\nA. 250\nB. 225\nC. 175\nD. 195\nE. 200\n\n### Answer:\nNumber of students who speak French are 60 + 20 = 80\nOf total students, the percentage of students who do not speak French was 60% --> percentage of who do is 40%\n80-------40%\nx ------- 100%\nx = 80*100/40 = 200 = number of all students\nAnswer is E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWithout stoppages a train travels a certain distance with an average speed of 80 km/h and with stoppages with an average speed speed of 60 km/h. How many minutes per hour does the train stops ?\n\n### Options:\nA. 25 min\nB. 10 min\nC. 18 min\nD. 15 min\nE. 20 min\n\n### Answer:\nlet us assume the distance is x km.\nif the train travels 80km/h without stopages then it takes (x/80) hour to rech.\nand with stopage it takes (x/60) hour.\nlet the train stops t min per hour.\nthen according to the question\n(x/80)=(x/60)+(t/60)*(x/60)\nthen t=15 min.\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train 280 m long, running with a speed of 63 km/hr will pass a tree in?\n\n### Options:\nA. 28 sec\nB. 16 sec\nC. 21 sec\nD. 11 sec\nE. 18 sec\n\n### Answer:\nSpeed = 63 * 5/18 = 35/2 m/sec\nTime taken = 280 * 2/35\n= 16 sec\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA woman invested $1,000, part at 5% and the rest at 6%. Her total investment with interest at the end of the year was $1,055. How much did she invest at 5%?\n\n### Options:\nA. $500\nB. $600\nC. $700\nD. $900\nE. $950\n\n### Answer:\net x be the portion invested at 5% and\nLet (1-x) be the rest which is invested at 6%\nThe question states that the return after 1 year is (1055/1000)-1 = 0.055 = 5.5%\nWe want to find the dollar amount invested in X\nUsing our defined variables, put together the equation and solve for x (the percentage of 1000 invested at 5%)\n0.05x+0.06(1-x)= 0.055\n(0.05)x +0.06 - (0.06)x = 0.055\n-0.01x = -0.005\nx= -0.005/-0.01 = 5/10 = 50%\nSo X = 50% of the 1000 which is 500\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOne pump drains one-half of a pond in 4 hours, and then a second pump starts draining the pond. The two pumps working together finish emptying the pond in one-half hour. How long would it take the second pump to drain the pond if it had to do the job alone?\n\n### Options:\nA. 1 hour\nB. 1.1 hour\nC. 3 hours\nD. 5 hours\nE. 6 hours\n\n### Answer:\nFirst pump drains 1/2 of the tank in 4 hours\nso 8 hours it will take to drain the full tank.\nLet, 2nd pump drains the full tank in a hours\nso both together can drain (1/8+1/a) part in 1 hour\nson in 1/2 hour they drain 1/2*(1/8+1/a) part of the tank\ngiven that in 1/2 hour they drain 1/2 of the tank\nhence we can say\n1/2*(1/8+1/a) = 1/2\nsolving u get a = 8/7=1.1\nHence answer is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n8 men can do a piece of work in 12 days. 4 women can do it in 48 days and 10 children can do it in 24 days. In how many days can 6 men, 4 women and 10 children together complete the piece of work?\n\n### Options:\nA. 5 days\nB. 15 days\nC. 28 days\nD. 8 days\nE. 7 days\n\n### Answer:\nExplanation:\n1 man\u2019s 1 day\u2019s work = 1/8 \u00d7 12 = 1/96\n6 men\u2019s 1 day\u2019s work = 1 \u00d7 6/96 =1/16\n1 woman\u2019s 1 day\u2019s work = 1/192\n4 women\u2019s 1 day\u2019s work = 1/192 \u00d7 4 = 1/48\n1 child\u2019s 1 day\u2019s work = 1/240\n10 children\u2019s 1 day\u2019s work = 1/24\nTherefore, (6 men + 4 women + 10 children)\u2019s 1 day\u2019s work = 1/16 + 1/48 + 1/24\n= 1/8\nThe required No. of days = 8 days\nAnswer: Option D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIt takes Jim two hours to wash the car and it takes Julia one hour to wash the car. Working together, how many minutes will it take them to wash the car?\n\n### Options:\nA. 36\nB. 38\nC. 40\nD. 42\nE. 44\n\n### Answer:\nJim can wash (1/2) of the car per hour.\nJulia can wash 1 car per hour.\nTogether they can wash 1/2+1=3/2 cars per hour.\n1 car / (3/2) cars per hour = 2/3 hours = 40 minutes.\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA furniture dealer purchased a desk for $180 and then set the selling price equal to the purchase price plus a markup that was 40% of the selling price. If the dealer sold the desk at the selling price, what was the amount of the dealer's gross profit from the purchase and the sale of the desk?\n\n### Options:\nA. $40\nB. $60\nC. $80\nD. $120\nE. $100\n\n### Answer:\nPurchase price = 180\nSelling price = x\n180 + 0.4*x = x\n0.6*x = 180\nx = 300\nProfit = 300 - 180 = 120\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA reduction of 5% in the price of oil enables a house wife to obtain 10kgs more for Rs.5000, what is the reduced price for kg?\n\n### Options:\nA. 23\nB. 27\nC. 25\nD. 35\nE. 15\n\n### Answer:\n5000*(5/100) = 250 ---- 10\n? ---- 1 => Rs.25\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a student handwrites her homework it takes her 5 hours to complete it, instead if she types it takes her 8 hours to compete. Since her teacher does not mind, she starts handwriting and after 1 hour, she switches to the computer and continues by typing for 2 hours. Then asking her brother to help, he types another 11 hours and homework is completed. How long would it take to complete the homework, if she had asked her brother for help in the first place.\n\n### Options:\nA. 5 hours\nB. 10 hours\nC. 15 hours\nD. 20 hours\nE. 25 hours\n\n### Answer:\n1/5+2/8 + 3/x = 1\rx =20 hours. ANSWER =D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 6", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJim is able to sell a hand-carved statue for $660 which was a 20% profit over his cost. How much did the statue originally cost him?\n\n### Options:\nA. $496.30\nB. $512.40\nC. $550\nD. $574.90\nE. $588.20\n\n### Answer:\nCost Price = 660/120 * 100 = 550\nAnswer : C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMarty's Pizza Shop guarantees that their pizzas all have at least 75% of the surface area covered with toppings, with a crust of uniform width surrounding them. If you order their best seller \u2013 a circular pizza with a diameter of 16 inches \u2013 what is the maximum width you can expect to see for the crust?\n\n### Options:\nA. 0.8 inches\nB. 1.1 inches\nC. 1.6 inches\nD. 2.0 inches\nE. 2.5 inches\n\n### Answer:\nTotal Area = 8 * 8 * pi\nRadius = 64 pi\nSurface = .75 * 64 * pi = 48 pi\nRadius of surface = 4 sqrt (3) ~ 6.8\nRadius width = 8 - 6.8 = 1.2\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAt a meeting of 10 Chiefs of Staff, the Chief of Naval Operations does not want to sit next to the Chief of the National Guard Bureau. How many ways can the Chiefs of Staff be seated around a circular table?\n\n### Options:\nA. 263,320\nB. 271,180\nC. 282,240\nD. 291,470\nE. 308,560\n\n### Answer:\n10 people can be arranged around a table in 9! ways.\nConsider the two chiefs who will not sit together as a single unit.\nThe number of ways to arrange 9 units around a table is 8!\nWe need to multiply this by 2 as the two people can be switched in each arrangement.\nThe total number of ways to arrange the chiefs is 9! - 2*8! = 7*8! = 282,240\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe ages of Krish and Vaibhav are in the proportion of 3 : 5. After 9 years, the proportion of their ages will be 3 : 4. Then the current age of Vaibhav is:\n\n### Options:\nA. 10\nB. 13\nC. 15\nD. 18\nE. 19\n\n### Answer:\nExplanation:\nKrish\u2019s age = 3A and Vaibhav\u2019s age = 5A =(3A + 9)/(5A + 9)=3/4\n=> 4 (3A + 9) = 3 (5A + 9)\n=> A = 3\nTherefore, Vaibhav\u2019s age = 15 years. Answer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe area of square ABCD above is 12. The shaded region is the intersection of the square and a circular region centered at C. What is the area of the shaded region?\n\n### Options:\nA. 18\u22129\u2217\u03c0\nB. 12\u22123\u2217\u03c0\nC. 9+9/4\u2217\u03c0\nD. 9+9/2\u2217\u03c0\nE. 9/2\u22129/4\u2217\u03c0\n\n### Answer:\n=Square - Quarter circle\n=12- pi*12/4\n=12- pi*3\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how many ways letters of the word RSCUPERATE be arranged?\n\n### Options:\nA. 275788\nB. 287578\nC. 4357809\nD. 437479\nE. 302400\n\n### Answer:\nRESUPERATE has 10 letters, out of which E repeated 3 times, R repeated 2 times. Hence total ways = 10! / (3!*2!) = 302400 ways\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA women walking at 5 Kmph reaches her office 8 minutes late. If she walks at 6 Kmph, she reaches there 8 minutes earlier. How far is the office from her house?\n\n### Options:\nA. 2 1/5 Km\nB. 3 1/5 Km\nC. 4 1/3 Km\nD. 8 Km\nE. 8 1/3 Km\n\n### Answer:\nFormula = S1*S2/S2-S1 * T1+T2/60\n= 5*6/1 * 16/60\n= 30/1 * 16/60\n= 30 * 4/15\n= 8 Km\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf x=3, which of the following is(are) true? I. x^2=2x II x/3 = 1 III |x|=-x\n\n### Options:\nA. I only\nB. III only\nC. II only\nD. I,II only\nE. I,III only\n\n### Answer:\n3/3 =1\nAnswer : C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nP is three times as fast as Q and working together, they can complete a work in 10 days. In how many days can Q alone complete the work?\n\n### Options:\nA. 11 days\nB. 16 days\nC. 40 days\nD. 15 days\nE. 19 days\n\n### Answer:\nB\n16 days\nP = 3Q\nP + Q = 3Q + Q = 4Q\nThese 4Q people can do the work in 10 days, which means Q can do the work in 4*10 =40 days.\nAnswer : C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n144, 121, 100, 81, 64, ?\n\n### Options:\nA. 9\nB. 16\nC. 25\nD. 36\nE. 49\n\n### Answer:\nExplanation :\nThe pattern is 12^2, 11^2, 10^2, 9^2, 8^2, ...\nSo next number is 7^2 = 49\nAnswer : Option E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich of the following equations has a root in common with x^2\u22123x+2=0 ?\n\n### Options:\nA. x^2-2x+1=0\nB. x^2-2x-1=0\nC. x^2-x+1=0\nD. x^2-3x+3=0\nE. x^2-7x=0\n\n### Answer:\nIf we carefully look at the given equation we can arrange it in the following manner:\n(x-1)(x-2)= 0\nso the two roots are 1 and 2.\nNow put 1 and 2 in given equations. The equation in which one of them gives value 0, that will be our answer.\n(A) putting 1: we get 0. This is the equation.\nWe are lucky. No need to check other options.\nA is the answer.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOf the 120 passengers on Flight 750, 30% are female. 10% of the passengers sit in first class, and the rest of the passengers sit in coach class. If 1/3 of the passengers in first class are male, how many females are there in coach class?\n\n### Options:\nA. 44\nB. 28\nC. 50\nD. 52\nE. 56\n\n### Answer:\nNumber of passengers on flight = 120\nNumber of female passengers= .3*120 = 36\nNumber of passengers in first class = (10/100)* 120 = 12\nNumber of passengers in coach class = (90/100)* 120 = 108\nNumber of male passengers in first class = 1/3 * 12 = 4\nNumber of female passengers in first class = 12-4 = 8\nNumber of female passengers in coach class = 36 - 8 = 28\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average monthly income of A and B is Rs. 5050. The average monthly income of B and C is Rs. 6250 and the average monthly income of A and C is Rs. 5200. What is the monthly income of A?\n\n### Options:\nA. 2000\nB. 3000\nC. 4000\nD. 5000\nE. 6200\n\n### Answer:\nExplanation:\nLet monthly income of A = a\nmonthly income of B = b\nmonthly income of C = c\na + b = 2 \u00d7 5050 .... (Equation 1)\nb + c = 2 \u00d7 6250 .... (Equation 2)\na + c = 2 \u00d7 5200 .... (Equation 3)\n(Equation 1) + (Equation 3) - (Equation 2)\n=> a + b + a + c - (b + c) = (2 \u00d7 5050) + (2 \u00d7 5200) - (2 \u00d7 6250)\n=> 2a = 2(5050 + 5200 - 6250)\n=> a = 4000\ni.e., Monthly income of A = 4000\nANSWER IS C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAt a small company, 64 percent of the employees are women, and 60 percent of the employees are married. If 2/3 of the men are single, what fraction of the women are married?\n\n### Options:\nA. 5/16\nB. 3/4\nC. 9/20\nD. 7/10\nE. 5/7\n\n### Answer:\nLets take total employees are 100.\nGiven that,Total Women= 64 and Total Married = 60.\nTotal Men = 100 - 64 = 36 and Single men = 2/3*36 = 24.\nMarried men = total men - single men = 36 - 24 = 12.\nMarried women= Total married - Married men = 60 - 12 = 48.\nFraction of women are married = Married women / Total Women = 48 / 64 = 3/4. ANS B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA sum of money amounts to Rs. 9800 after 5 years and Rs. 12005 after 8 years at the same rate of simple interest. The rate of interest per annum is:\n\n### Options:\nA. 5%\nB. 8%\nC. 12%\nD. 15%\nE. 10%\n\n### Answer:\nS.I. for 3 years = Rs. (12005 - 9800) = Rs. 2205.\nS.I. for 5 years = Rs.\t((2205/3)x 5)\t= Rs. 3675\nPrincipal = Rs. (9800 - 3675) = Rs. 6125.\nHence, rate =((100 x 3675)/(6125 x 5))%\t= 12%\nAnswer :C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA and B began business with Rs.6000 and Rs.4000 after 8 months, A withdraws Rs.1000 and B advances Rs.1000 more. At the end of the year, their profits amounted to Rs.630 find the share of B.\n\n### Options:\nA. 240\nB. 288\nC. 273\nD. 877\nE. 361\n\n### Answer:\n(6*8 + 5*4):(4*8 + 5*4)\n17:13\n13/30 * 630 = 273\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA and b make a business together, and make a profit of Rs 84000. If A get Rs 48000, what was the ratio of investment between them?\n\n### Options:\nA. 4 : 3\nB. 3 : 2\nC. 5 : 2\nD. 4 : 5\nE. 6 : 5\n\n### Answer:\nA get 48000\nThen B get = (84000-48000) = 36000\nRatio between A and B is = 48000 : 36000 = 4 : 3\nAnswer : Option A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a randomly selected positive single digit multiple of 3 is multiplied by a randomly selected prime number less than 20, what is the probability W that this product will be a multiple of 45?\n\n### Options:\nA. 1/32\nB. 1/28\nC. 1/24\nD. 1/16\nE. 1/14\n\n### Answer:\nThere are 3 single digit multiple of 3, that is, 3,6,9.\nThere are 8 prime nos less than 20 - 2,3,5,7,11,13,17,19\nTotal outcome - 8*3 = 24\nFavourable outcome = 1 (9*5)\nHence required probability W= 1/24. Answer C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n5^100 is divided by 18. Then what is the remainder?\n\n### Options:\nA. 10\nB. 11\nC. 13\nD. 15\nE. 19\n\n### Answer:\nHere N = 18=2\u00d732\n\u03d5(18)=18(1\u221212)(1\u221213) = 6\nSo 56 when divided by 18, remainder is 1.\nSo we can write the given expression 5100=(56)16\u00d754 = (1)16\u00d754 = 52\u00d752=7\u00d77=49\nNow 49 when divided by 18, remainder is 13.\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average age of a husband and his wife was 17 years at the time of their marriage. After five years they have a one-year old child. The average age of the family now is :\n\n### Options:\nA. 55/3\nB. 15\nC. 19\nD. 287\nE. 27\n\n### Answer:\nExplanation:\nSum of the present ages of husband, wife and child = (17 * 2 + 5 * 2) + 1 = 45 years.\nRequired average = (45/3)= 15years.\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf x dollars is invested at 12.5 percent for one year and y dollars is invested at 9.5 percent for one year, the annual income from the 12.5 percent investment will exceed the annual income from the 8 percent investment by $60. If $2500 is the total amount invested, how much is invested at 9.5 percent?\n\n### Options:\nA. a. $1097.83\nB. b. $1231.57\nC. c. $1101.52\nD. d. $1147.72\nE. e. $1352.27\n\n### Answer:\n2 equations with 2 unknowns\n12.5x / 100 - 9.5y / 100 = 60\nand\nx + y = 2500\nSolving these 2 equations, x =1352.27 and y = 1147.72\nAnswer D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMani paid a sum of money for purchasing 40 pens, which he recovered in full when he sold 25 of them. What was his percentage of profit or loss per pen?\n\n### Options:\nA. 50%\nB. 60%\nC. 70%\nD. 65%\nE. 55%\n\n### Answer:\nB\n33.33%\nIf the sum he paid whilst purchasing 40 pens = A,\nThen the Cost Price of each pen = A/40.\nSince the amount he got whilst selling 25 pens is also = A\nThen the Selling Price of each pen = A/25.\nSince Selling Price > Cost Price, he made a profit.\nProfit per pen = Selling Price - Cost Price = A/25 - A/40 = 3A/200.\nProfit percentage per pen = Profit per pen / Cost per pen x 100 = (3A/200) / (A/40) x 100 = 60%. Answer : B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man walking at the speed of 4 kmph crosses a square field diagonally in 3 minutes. The area of the field is:\n\n### Options:\nA. 18000m2\nB. 20000m2\nC. 19000m2\nD. 25000m2\nE. 15000m2\n\n### Answer:\nLength of the diagonal= Distance covered in 3 min. at 4 km/hr.\n= (4000/ 60 *3)= 200m.\nTherefore, Area of the field= 1/2 * diagonal2\n= \u00bd * 200*200 = 20000 m2\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man can row with a speed of 15 kmph in still water. If the stream flows at 15 kmph, then the speed in downstream is?\n\n### Options:\nA. 27\nB. 30\nC. 20\nD. 99\nE. 2\n\n### Answer:\nM = 15\nS = 15\nDS = 15 + 15 = 30\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA bag contains a certain number of 50 paise coins, 20 paise coins and 10 paise coins inthe ratio 2:3:4. If the total value of all the coins in the bag is Rs.400, find the number of coins of each kind?\n\n### Options:\nA. 800\nB. 277\nC. 266\nD. 288\nE. 1221\n\n### Answer:\n50*2k + 20*3k + 10*4k = 40000\n200k = 40000 => k = 200\n50p coins = 2k = 2*200 = 400\n20p coins = 3k = 3*200 = 600\n10p coins = 4k = 4*200 = 800\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe C.P of 15 books is equal to the S.P of 18 books. Find his gain% or loss%?\n\n### Options:\nA. 16 2/3% loss\nB. 100/3% loss\nC. 50/3% profit\nD. 100/3% loss\nE. 200/3% loss\n\n### Answer:\nExplanation:\n15 CP = 18 SP\n18 --- 3 CP loss\n100 --- ? => 16 2/3% loss\nANSWER IS A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 500 resolutions.\n\n### Options:\nA. 287 m\nB. 704 m\nC. 176 m\nD. 186 m\nE. 197 m\n\n### Answer:\nIn one resolution, the distance covered by the wheel is its own circumference. Distance covered in 500 resolutions.\n= 500 * 2 * 22/7 * 22.4\n= 70400 cm\n= 704 m\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nEvaluate: 50 - 12\u00f72\u00d72 =\n\n### Options:\nA. A)36\nB. B)38\nC. C)40\nD. D)42\nE. E)44\n\n### Answer:\nAccording to order of operations, 12\u00f72\u00d72 (division and multiplication) is done first from left to right\n12\u00f72\u00d72 = 6 \u00d7 2 = 12\nHence\n50 - 12\u00f76\u00d72 = 50 - 12 = 38\ncorrect answer is B) 38\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nBrowny owns b video game cartridges. If Browny\u2019s total is one-third the total owned by James and two times the total owned by Charlie, how many video game cartridges do the three of them own altogether, in terms of b?\n\n### Options:\nA. (16/3)b\nB. (17/4)b\nC. (13/4)b\nD. (9/2)b\nE. (7/12)b\n\n### Answer:\nb = Browny\u2019s total\n3b = James\u2019s total\n(1/2)b = Charlie\u2019s total\nAdd each total\nb + 3b+ (1/2)b = 4b + (1/2)b = = (9/2)b\nAnswer : D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nEvaluate permutation\n3P3\n\n### Options:\nA. 6\nB. 7\nC. 8\nD. 9\nE. 10\n\n### Answer:\nExplanation:\nnPn=n!\n3P3=3\u22172\u22171=6\nOption A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nCarmen made a sculpture from small pieces of wood. The sculpture is 2 feet 6 inches tall.Carmen places her sculpture on a base that is 12 inches tall. How tall are the sculpture andbase together?\n\n### Options:\nA. 3.1 feet\nB. 3.2 feet\nC. 3.3 feet\nD. 3.4 feet\nE. 3.83 feet\n\n### Answer:\nwe know 1 feet =12 inch then\n2 feet =24 inch\n24+10=34 then\n34+12=44\n46/12=3.83 feet\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich of the following is closest to the difference between sum R of all proper fractions (fractions less than 1) in the form 1/x , where x is a positive digit, and the product of all proper fractions in the form y/(y+1), where y is a positive digit?\n\n### Options:\nA. 2.82\nB. 2.72\nC. 1.82\nD. 1.72\nE. 0.82\n\n### Answer:\nSum R of all proper fractions (fractions less than 1) in the form 1/x, where x is a positive digit:\n1/1 + 1/2 + 1/3 +.....+ 1/9\nThis is a harmonic progression. Harmonic progression is inverse of arithmetic progression.\nApproximate sum of a harmonic progression with even number of terms = number of terms * (average of middle 2 terms)\nApproximate sum of a harmonic progression with odd number of terms = number of terms * (middle term)\nThe actual sum will be slightly more than the approximation.\nHere we have 9 terms (odd).\nSum = 9 * 1/5\n= 9/5\nProduct of all proper fractions in the form y/(y+1), where y is a positive digit:\n1/2 * 2/3 * 3/4 *.....*9/10\nWe will be left with 1/10.\nRequired = 9/5 - 1/10\n= 1.8 - 0.1\n= 1.7\nClosest is 1.72\nAnswer (D).\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man swims downstream 35 km and upstream 20 km taking 5 hours each time, what is the speed of the man in still water?\n\n### Options:\nA. 6.5\nB. 5.5\nC. 5.2\nD. 4.6\nE. 9.7\n\n### Answer:\n35 --- 5 DS = 7\n? ---- 1\n20 ---- 5 US = 4\n? ---- 1 M = ?\nM = (7+ 4)/2 = 5.5\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nKiran travels from A to B by car and returns from B to A by cycle in 7 hours. If he travels both ways by car he saves 3 hours. What is the time taken to cover both ways by cycle?\n\n### Options:\nA. 10\nB. 28\nC. 277\nD. 299\nE. 22\n\n### Answer:\nLet the time taken to cover from A to B in car and cycle be x hours and y hours respectively.\nx + y = 7 --- (1) ; 2x = 4 --- (2)\nsolving both the equations, we get y = 5\nSo, time taken to cover both ways by cycle = 2y hours = 10 hours.\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf (a-7)(b-2) =0, which of the following must be true ?\nI. a=7 and b=2\nII. if a is not 7, then b=2\nIII. if a=7, then b is not=2\n\n### Options:\nA. I only\nB. II only\nC. III only\nD. I and II\nE. II and III\n\n### Answer:\n(a-7)(b-2)=0\nSo either a=7 or b=2 or both. It is 'or' not 'and', so it could be any of the three possibilities. Thus I and III are not necessarily true.\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how many ways 3 boys and 3 girls can be seated in a row so that boys and girls are alternate?\n\n### Options:\nA. 69\nB. 70\nC. 71\nD. 72\nE. 73\n\n### Answer:\nnumber of ways = 2*3!*3! = 72\nAnswer is D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nGirl and Boy together can complete a piece of work in 35 days while Girl alone can complete the same work in 60 days. Boy alone will be able to complete the same working in:\n\n### Options:\nA. 72\nB. 75\nC. 84\nD. 88\nE. 90\n\n### Answer:\nSubtraction of fraction\nab\u2212cd=ad\u2212cbbd\nGirl\nand Boy finish one work with company = 35\ndays\n(Girl+Boy)\u2032\ns one day\u2019s work = 135\nGirl alone finish the same work = 60\ndays\nGirl\u2032\ns one day\u2019s work = 160\nB\u2032\ns one day\u2019s work = (A+B)\u2032s one day\u2019s work - A\u2032\ns one day\u2019s work\n135\u2212160=184\nHence B alone can complete the work in 84 days\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe distance between two villages P and Q is 330 Km. A train starts from P at 8 a.m. and travel towards Q at 60 km/hr. Another train starts from Q at 9 a.m and travels towards P at 75 Km/hr. At what time do they meet?\n\n### Options:\nA. 11 am\nB. 10 am\nC. 9 am\nD. 12 pm\nE. 11.30 am\n\n### Answer:\nmeet x hrs after 8 a.m.\n(Distance moved by first in x hrs) + [Distance moved by second in (x-1) hrs]\n= 330\n==>60x+75(x-1) = 330\nx=3.\nSo,they meet at (8+3). i.e 11a.m.\nANSWER A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich one of the following numbers is exactly divisible by 11?\n\n### Options:\nA. 417269\nB. 315624\nC. 615624\nD. 715624\nE. 415624\n\n### Answer:\nE\n415624 is exactly divisible by 11.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA 300 m long train crosses a platform in 39 sec while it crosses a signal pole in 16 sec. What is the length of the platform?\n\n### Options:\nA. 287 m\nB. 431.25 m\nC. 267 m\nD. 287.25 m\nE. 656 m\n\n### Answer:\nSpeed = 300/16 = 75/4 m/sec.\nLet the length of the platform be x meters.\nThen, (x + 300)/39 = 75/4\n=> x = 731.25 m\nAnswer:B (431.25)\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train 55 meters long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going?\n\n### Options:\nA. 5\nB. 6\nC. 7\nD. 3\nE. 5\n\n### Answer:\nSpeed of train relative to man = (60 + 6) km/hr = 66 km/hr\n[66 * 5/18] m/sec = [55/3] m/sec.\nTime taken to pass the man = [55 * 3/55] sec = 3 sec\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA motorcycle importer is planning on increasing the price of a certain model by $1000. At this new price 8 fewer motorcycles will be sold per month, but the total revenues will increase by $26,000 to $594,000. What is the number of motorcycles the manufacturer will sell at this new price?\n\n### Options:\nA. 61\nB. 62\nC. 65\nD. 63\nE. 64\n\n### Answer:\nResponding to a pm: To solve this question, I will make an equation in x and then make educated guesses. Here's how:\nAssuming x motorcycles were sold every month initially.\n(568000/x + 1000)(x-8) = 594000\n(568/x + 1)(x-8) = 594\nNow 568 = 8*71\nAssuming x = 71 (We have all integers so it is obvious that 568/x should be an integer.\nWe get 9*66 = 594 (matches)\nSo he will sell 71 - 8 = 63 bikes this month\nAnswer (D)\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nConsider the word ROTOR. Whichever way you read it, from left to right or from right to left, you get the same word. Such a word is known as palindrome. Find the maximum possible number of 5-letter palindromes?\n\n### Options:\nA. 56678\nB. 16789\nC. 17576\nD. 35142\nE. None of these\n\n### Answer:\nExplanation :\nThe first letter from the right can be chosen in 26 ways because there are 26 alphabets.Having chosen this, the second letter can be chosen in 26 ways.=> The first two letters can be chosen in 26*26=676 waysHaving chosen the first two letters, the third letter can be chosen in 26 ways.=> All the three letters can be chosen in 676*26=17576 ways.It implies that the maximum possible number of five letter palindromes is 17576 because the fourth letter is the same as the second letter and the fifth letter is the same as the first letter.\nAnswer : C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhen a=4+(3/4) and b=4-(3/4), (2^a^2)/(2^b^2)=?\n\n### Options:\nA. 496\nB. 486\nC. 4096\nD. 456\nE. 426\n\n### Answer:\n--> (2^a^2)/(2^b^2) ={(2)^(a^2-b^2)}=2^(a-b)(a+b). Since a-b=6/4 and a+b=8, 2^(a-b)(a+b)=2^(6/4)(8)=2^12=4096\nTherefore, the answer is C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRoy is now 6 years older than Julia and half of that amount older than Kelly. If in 2 years, Roy will be twice as old as Julia, then in 2 years what would be Roy\u2019s age multiplied by Kelly\u2019s age?\n\n### Options:\nA. 84\nB. 96\nC. 100\nD. 108\nE. 120\n\n### Answer:\nR = J+6 = K+3\nR+2 = 2(J+2)\n(J+6)+2 = 2J+4\nJ = 4\nR = 10\nK = 7\nIn 2 years (R+2)(K+2) = 12*9 = 108\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe difference in compound interest earned on a deposit (compounded annually) in year 1 and year 2 is $ 40. Had the interest rate been three times its present value, the difference q would have been how much?\n\n### Options:\nA. 40/3\nB. 40\nC. 120\nD. 360\nE. 420\n\n### Answer:\nCASE 1:\nDeposit = $x;\nRate of increase = r.\nInterest yearned in 1 year = xr. Deposit in 1 year = x + xr.\nInterest yearned in 2 year = (x + xr)r.\nThe difference q= (x + xr)r - xr = xr^2 = 40.\nCASE 2:\nDeposit = $x;\nRate of increase = 3r.\nInterest yearned in 1 year = x(3r). Deposit in 1 year = x + 3xr.\nInterest yearned in 2 year = (x + 3xr)3r.\nThe difference = (x + 3xr)3r - 3xr = 9xr^2. Since from CASE 1 we know that xr^2 = 40, then 9xr^2 = 9*40 = 360.\nAnswer: D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe cost of a car was $3,000 in 1960. In 2010, the price had increased to $5,000. What was the percent increase in the cost of the car?\n\n### Options:\nA. 33.3%\nB. 45%\nC. 60%\nD. 66.6%\nE. 55.8%\n\n### Answer:\nIncrease = 5000-3000 = 2000\n% increase = 2000*100/3000 = 66.6%\nAnswer: option D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nBy selling 99 pencil, a trader gains the cost of 33 Pencil. Find his gain percentage?\n\n### Options:\nA. 26 1/3%\nB. 51 1/3%\nC. 33 1/3%\nD. 53 1/3%\nE. 34 1/3%\n\n### Answer:\nC\n33 1/3%\nLet the CP of each pencil be Rs. 1.\nCP of 99 pens = Rs. 99\nProfit = Cost of 33 pencil = Rs. 33\nProfit% = 33/99 * 100 = 33 1/3%\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average weight of 40 girls sitting in a bus had some value. A new girl added to them whose weight was 60 kg only. Due to her arrival, the average weight of all the girls decreased by 20 kg. Find the average weight of first 40 boys?\n\n### Options:\nA. 850\nB. 80\nC. 176\nD. 500\nE. 880\n\n### Answer:\n40x + 60 = 41(x \u00e2\u20ac\u201c 20)\nx = 880\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf money is invested at r percent interest, compounded annually, the amount of the investment will double in approximately 48/r years. If Pat's parents invested $5,000 in a long-term bond that pays 8 percent interest, compounded annually, what will be the approximate total amount of the investment 18 years later, when Pat is ready for college?\n\n### Options:\nA. $20000\nB. $15000\nC. $12000\nD. $10000\nE. $9000\n\n### Answer:\nSince investment doubles in 48/r years, then for r=8 it'll double in 48/8=~6 years (we are not asked about the exact amount so such an approximation will do). Thus after 18 years investment will become $5,000*3=$15,000 .\nAnswer: B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo fair die with sides numbered 1 to 6 are tossed. What is the probability that the sum of the exposed faces on the die is a prime number?\n\n### Options:\nA. 5/11!\nB. 7/8!\nC. 5/9!\nD. 15/21!\nE. 4/9!\n\n### Answer:\nTwo dices are thrown ! So we may get 1+1 or 1+2 ... or 1+6.. or 2+6 or 3+6 etc\nTherefore the total different sum values we can get are :2,3,4,5,6,7,8,9,10,11,12[Sample space] ----------------(1)\nOut of these values, 5 numbers are primes i.e.2,3,5,7,11[Favorable events] --------------------(2)\nFrom (1)(2)\nThe answer is5/11!!\nAns: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the rate percent when the simple interest on Rs.800 amount to Rs.200 in 4 Years?\n\n### Options:\nA. 5%\nB. 7%\nC. 6.25%\nD. 2%\nE. 4%\n\n### Answer:\n200 = (800*4*R)/100\nR = 6.25%\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTough and Tricky questions: Combinations.\nThe product of the digits of the four-digit number h is 30. No two digits of h are identical. How many different numbers are possible values of h?\n\n### Options:\nA. 24\nB. 30\nC. 36\nD. 42\nE. 54\n\n### Answer:\nAnswer = A= 24\nLet number =abcd\nGiven that a*b*c*d = 30\na,b,c,d can be 1,2,3,5\nNumber of ways = 4*3*2 = 24\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe effective annual rate of interest corresponding to a nominal rate of 6% per annum payable half yearly is\n\n### Options:\nA. 6.06%\nB. 6.07%\nC. 6.08%\nD. 6.09%\nE. None\n\n### Answer:\nSolution\nAmount of Rs.100 for 1 year when compounded half yearly\n= Rs.[100 x (1+3/100)2]\n= Rs. 106.09%.\nEffective rate\t= (106.09 - 100)%\n= Rs. 6.09%.\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average age of a husband and a wife is 23 years when they were married five years ago but now the average age of the husband, wife and child is 22 years(the child was born during the interval). What is the present age of the child?\n\n### Options:\nA. 6\nB. 5\nC. 10\nD. 4\nE. 2\n\n### Answer:\n28 * 2 = 56\n22 * 3 = 66\n-----------\n10 years.Answer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA can complete a project in 20 days while B can complete same project in 30 days. If A and B start working together and A leaves the work 10 days before completion of project, then in how many days the project will be completed?\n\n### Options:\nA. 15\nB. 16\nC. 17\nD. 18\nE. 19\n\n### Answer:\nA's 1day work=1/20;\nB's 1day work=1/30;\n(A+B) 1day work=(1/20+1/30)=1/12;\nIt is given that A leaves the work 10 days before completion of the project..\nThus,B alone does the remaining job in 10 days.\nSo,In 10 days ,B can do 1/3 w ..\nThus,(A+B) have worked (1-1/3)=2/3 w..\n(A+B)can do 1/12 work in 1 day...\nThey did 2/3 w in 8 days.\nTotal days=(8+10) = 18\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe side of a square is increased by 25% then how much % does its area increases?\n\n### Options:\nA. 56.28 %\nB. 56.25 %\nC. 56.75 %\nD. 52.25 %\nE. 56.25 %\n\n### Answer:\na = 100 a2 = 10000\na = 125 a2 = 15625\n----------------\n10000 --------- 5625\n100 -------? => 56.25 %\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the price of 100 toys is 2500, then what will the price of 50 toys ?\n\n### Options:\nA. 144\nB. 1250\nC. 117\nD. 287\nE. 112\n\n### Answer:\nOne toy price = 2500/100 = 25\n50 toy price = 50 * 25 = 1250\nAnswer : B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA chemical tank of capacity 2000m3 which is 65% full is found to be leaking. The chemical in the tank needs to be transported to a new destination using tanker trucks. If the capacity of a truck is 16m3 which can be filled upto 93% full. How many truck loads would be needed to transport the chemical?\n\n### Options:\nA. 64\nB. 71\nC. 85\nD. 92\nE. 97\n\n### Answer:\nVolume of chemical in the tank=2000x0.65=1300\nVolume of the truck=16x.93=15.36\nNumber of truck loads needed= 1300/15.36=84.63\u00e2\u2030\u02c685\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA letter lock consists of three rings each marked with EIGHT different letters. The number of distinct unsuccessful attempts to open the lock is at the most?\n\n### Options:\nA. 4002\nB. 4090\nC. 4095\nD. 177\nE. 123\n\n### Answer:\nSince each ring consists of eight different letters, the total number of attempts possible with the three rings is\n= 8 * 8 * 8 = 4096. Of these attempts, one of them is a successful attempt.\nMaximum number of unsuccessful attempts = 4096 - 1\n= 4095\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many three letter words are formed using the letters of the word TIME?\n\n### Options:\nA. 20\nB. 24\nC. 26\nD. 28\nE. 32\n\n### Answer:\nExplanation:\nThe number of letters in the given word is four.\nThe number of three letter words that can be formed using these four letters is \u2074P\u2083 = 4 * 3 * 2 = 24.\nAnswer: Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nEach child has 2 pencils and 13 Skittles. If there are 9 children, how many pencils are there in total?\n\n### Options:\nA. 16\nB. 12\nC. 18\nD. 22\nE. 08\n\n### Answer:\n2*9=18.Answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA cube is divided into 64 identical cubelets. Each cut is made parallel to some surface of the cube. But before doing that, the cube is painted with green on one set of opposite faces, red on another set of opposite faces, and blue on the third set of opposite faces. How many cubelets are painted with exactly one colour?\n\n### Options:\nA. 12\nB. 16\nC. 20\nD. 24\nE. 30\n\n### Answer:\nEach side of the cube has 4 x 4 = 16 cubelets.\nOnly the interior cubelets are painted one colour.\nOn each side, 2 x 2 = 4 cubelets are painted one colour.\nSince the cube has six sides, the number of cubes with one colour is 6*4 = 24\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMary, Peter, and Lucy were picking chestnuts. Mary picked twice as much chestnuts than Peter. Lucy picked 3 kg more than Peter. Together the three of them picked 27 kg of chestnuts. How many kilograms of chestnuts did Mary, Peter, and Lucy pick respectively?\n\n### Options:\nA. 6, 9 and 12\nB. 12, 9 and 6\nC. 9, 6 and 12\nD. 12, 6 and 9\nE. 6, 12 and 9\n\n### Answer:\nM = 2P\nL = P+3\nM + P + L = 27\n2P + P + (P+3) = 27\nP = 6, M = 12, L = 9\nTherefore, Mary, Peter, and Lucy picked 12, 6, and 9 kg, respectively.\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a no. when divided by 44, gives 432 as quotient and 0 as remainder. What will be the remainder when dividing thesame no. by 31\n\n### Options:\nA. 1\nB. 3\nC. 5\nD. 7\nE. 9\n\n### Answer:\nP \u00f7 44 = 432\n=> P = 432 * 44 = 19008\nP / 31 = 19008 / 31 = 613, remainder = 5\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA bus starts from city X. The number of women in the bus is half of the number of men. In city Y, 10 men leave the bus and five women enter. Now, number of men and women is equal. In the beginning, how many passengers entered the bus ?\n\n### Options:\nA. 15\nB. 30\nC. 36\nD. 45\nE. 54\n\n### Answer:\nno of women be A\nno of men be B\nin city X -> A=B/2-----(1)\nin city Y -> A+5=B-10\nB-A=15\nfrom 1 B=2A sub in above equation\n2A-A=15\nA=15 means B=30\nin the beginning no of passengers entered the bus is A+B=30+15=45\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe manager at a health foods store mixes a unique superfruit juice cocktail that costs $1399.45 per litre to make. The cocktail includes mixed fruit juice and a\u00e7ai berry juice, which cost $262.85 per litre and $3104.35 per litre, respectively. The manager has already opened 34 litres of the mixed fruit juice. How many litres of the a\u00e7ai berry juice does he need to add?\n\n### Options:\nA. 17 litres\nB. 22.67 litres\nC. 11 litres\nD. 07 litres\nE. 38.67 litres\n\n### Answer:\n262.85(34)+3,104.35x = 1,399.45(34 + x)\nSolve the equation.\n262.85(34)+3,104.35x = 1,399.45(34 + x)\n8936.9+ 3,104.35x = 47,581.3 + 1,399.45x\n8936.9 + 1,704.9x = 47,581.3\n1,704.9x = 38,644.40\nx \u2248 22.67\nAnswer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe majority owner of a business received 25% of the profit, with each of 4 partners receiving 25% of the remaining profit. If the majority owner and two of the owners combined to receive $76,875, how much profit did the business make?\n\n### Options:\nA. $98,000\nB. $106,000\nC. $112,000\nD. $118,000\nE. $123,000\n\n### Answer:\nLet P be the total profit.\nP/4 + 1/2*(3P/4) = P/4 + 3P/8 = 5P/8 = $76,875\nP = $123,000\nThe answer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nExpress 25 mps in kmph?\n\n### Options:\nA. 299\nB. 29\nC. 90\nD. 77\nE. 11\n\n### Answer:\n25 * 18/5 = 90 kmph Answer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA wooden box of dimensions 8m\u00d77m\u00d76m is to carrry rectangular boxes of dimensions 8cm\u00d77cm\u00d76cm . The maximum number of boxes that can be carried in 1 wooden box is :\n\n### Options:\nA. 1200000\nB. 1000000\nC. 9800000\nD. 7500000\nE. none\n\n### Answer:\nExplanation:\nNumber of boxes = Volume of wooden box in cm3/Volume of 1 small ball = 800\u00d7700\u00d7600/8\u00d77\u00d76=1000000\nCorrect Option: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo friends P & Q started a business investing amounts in the ratio of 5 : 6. R joined them after six months investing an amount equal to that of Q\u2019s amount. At the end of the year 20% profit was earned which was equal to 98,000. What was the amount invested by R?\n\n### Options:\nA. 2,10,000\nB. 1,05,000\nC. 1,75,000\nD. Data inadequate\nE. None of these\n\n### Answer:\nRatio for amount invested by P, Q & R\n= 5x \u00d7 12 : 6x \u00d7 12 : 6x \u00d7 6\n= 60x : 72x : 36x\n= 5x : 6x : 3x\nProfit = 98000 = 20% of T\nwhere, T = Total amount\nT = 490000\nAmount received by\nR = 3x /3x+6x+5x(490000)\n= 105000\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe total marks obtained by a student in Mathematics and Physics is 40 and his score in Chemistry is 20 marks more than that in Physics. Find the average marks scored in Mathamatics and Chemistry together.\n\n### Options:\nA. 40\nB. 30\nC. 25\nD. Data inadequate\nE. None of these.\n\n### Answer:\nLet the marks obtained by the student in Mathematics, Physics and Chemistry be M, P and C respectively.\nGiven , M + C = 40 and C - P = 20 M + C / 2 = [(M + P) + (C - P)] / 2 = (40 + 20) / 2 = 30.\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train passes a station platform in 36 seconds and a man standing on the platform in 25 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?\n\n### Options:\nA. 37\nB. 240\nC. 288\nD. 267\nE. 165\n\n### Answer:\nSpeed = (54 * 5/18) m/sec = 15 m/sec. Length of the train = (15 x 25)m = 375 m. Let the length of the platform be x meters. Then, (x + 375)/36 = 15 ==> x + 375 = 540 ==> x = 165 m.Answer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nExcluding stoppages, the speed of the bus is 54 kms /hr and with stoppages, it is 45 kmph. For how many minutes does the bus stop per hour?\n\n### Options:\nA. 9\nB. 10\nC. 11\nD. 12\nE. 20\n\n### Answer:\nBy including stoppages, bus will cover 9km less..(54km -45km = 9km)\nExcluding stoppages, x = 54 kmph\nIncluding stoppages, y = 45 kmph\nDifference, z = 9km\nTime taken to cover that 9km(bus stops per hour(60minutes))= z/x(60minutes)\n= 9/54(60)\n= 1/6(60)\n= 10minutes.\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSolve the equation for x : 19(x + y) + 17 = 19(-x + y) - 21\n\n### Options:\nA. -1\nB. -9\nC. -7\nD. -2\nE. -4\n\n### Answer:\nExplanation:\n19x + 19y + 17 = -19x + 19y - 21\n38x = -38 => x = -1\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf k is a non-negative integer and 18^k is a divisor of 624,938 then 6^k - k^6 =\n\n### Options:\nA. 0\nB. 1\nC. 36\nD. 118\nE. 420\n\n### Answer:\n6+2+4+9+3+8 = 32, so this number is not divisible by 3 and thus not divisible by 18.\nTherefore, k=0\n6^k - k^6 =1-0=1\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe first three terms of a proportion are 5, 15 and 20. The fourth term is?\n\n### Options:\nA. 60\nB. 65\nC. 89\nD. 78\nE. 88\n\n### Answer:\n(15*20)/5= 60\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a certain number when divided by the numbers 5,3,2 one after other successively, leaves a remainder 0,2,1 Then what will be the remainders if it is divided by the numbers 2,3,5\n\n### Options:\nA. 1,2,0\nB. 1,2,1\nC. 1,2,2\nD. 1,2,3\nE. 1,2,4\n\n### Answer:\nThe Number is 35 ,When divided by 5,3,2 leaves remainder 0,2,1 respectively.\nSo if 35 is divided by 2,3,5 leaves remainder 1,2,0 respectively.\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJane makes toy bears. When she works with an assistant, she makes 62 percent more bears per week and works 10 percent fewer hours each week. Having an assistant increases Jane\u2019s output of toy bears per hour by what percent?\n\n### Options:\nA. 20%\nB. 80%\nC. 100%\nD. 180%\nE. 200%\n\n### Answer:\nLet's assume just Jane 40 bears per 40/hrs a week, so that is 1 bear/hr. With an assistant she makes 64.8 bears per 36 hours a week or 1.8 bears/hr ([40 bears * 1.62] / [40 hrs * .90]).\n[(1.8 - 1)/1] * 100% = 80%\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a = 105 and a^3= 21 * 25 * 15 * b, what is the value of b?\n\n### Options:\nA. 35\nB. 42\nC. 45\nD. 147\nE. 54\n\n### Answer:\nFirst step will be to break down all the numbers into their prime factors.\n105 = 3 * 5 * 7\n21 = 7 * 3\n25 = 5 * 5\n15 = 3 * 5\nso, (105)^3 = 3 * 7 * 5 * 5 *3 *5 *b\nTherefore (3 * 5 * 7) ^ 3 = 3^2 * 5^3 * 7 *b\nTherefore, b = 3^3 * 5^3 * 7 ^3/3 ^2 * 5 ^3 * 7\nb = 3*7^2 =3* 49=147\nCorrect answer D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich is better investment 11% stock at 143 or 9 \u00c2\u00be% stock at 117\n\n### Options:\nA. 11 % stock at 143\nB. 9 3/4 stock at 117\nC. both\nD. cannot be compared\nE. none of these\n\n### Answer:\nLet the investment in each (143*117)\nIncome in first case = (11/143*143*117)=1287\nIncome in second case=((39/117*4)*143*117)=1394.25\nClearly, 9 \u00c2\u00be% stock at 117\nANSWER B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nPeter takes a loan of $100,000 with 12% annual interest: the interest is paid once, at the end of the year. Martha takes a loan of $100,000 with 12% annual interest, compounding monthly at the end of each month. At the end of one full year, compared to Peter's loan interest, approximately how much more does Martha have to repay?\n\n### Options:\nA. $68.25\nB. Zero\nC. $6825.00\nD. $6.82\nE. $682.50\n\n### Answer:\nPeters interest= $100,000*0.12 = $12,000 or $1,000 each month.\nMartha\u2019s interest, 12%/12 = 1% each month:\nFor the 1st month = $100,000*0.01 = $1,000;\nFor the 2nd month = $1,000 + 1% of 1,000 = $1,010, so we would have interest earned on interest (very small amount);\nFor the 3rd month = $1,010 + 1% of 1,010 = ~$1,020;\nFor the 4th month = $1,020 + 1% of 1,020 = ~$1,030;\n...\nFor the 12th month = $1,100 + 1% of 1,100 = ~$1,110.\nThe difference between Peters interest and Martha\u2019s interest = ~(10 + 20 + ... + 110) = $660.\nAnswer: E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain car averages 35 miles per gallon when driving in the city and 40 miles per gallon when driving on the highway. According to these rates, which of the following is closest to the number of miles per gallon that the car averages when it is driven 10 miles in the city and then 50 miles on the highway?\n\n### Options:\nA. 28\nB. 30\nC. 33\nD. 39\nE. 38\n\n### Answer:\nAnswer D\nNo of Miles per Gallon = Total no of miles/Total no of Gallons\n=10+50/(10/35+50/40) ~ 39.06\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe length of a rectangle is two - fifths of the radius of a circle. The radius of the circle is equal to the side of the square, whose area is 1225 sq.units. What is the area (in sq.units) of the rectangle if the rectangle if the breadth is 10 units?\n\n### Options:\nA. 140 sq.units\nB. 149\nC. 148\nD. 17\nE. 143\n\n### Answer:\nGiven that the area of the square = 1225 sq.units\n=> Side of square = \u221a1225 = 35 units\nThe radius of the circle = side of the square = 35 units Length of the rectangle = 2/5 * 35 = 14 units\nGiven that breadth = 10 units\nArea of the rectangle = lb = 14 * 10 = 140 sq.units\nAnswer: Option A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nX is the largest prime number less than positive integer N. P is an integer such that P = X \u2013 16. Also, Z = 1*2*\u2026*P\u221aP. If N is the first non-zero perfect square whose tens digit and units digit are same, How many different prime factors does Z have?\n\n### Options:\nA. 4\nB. 5\nC. 6\nD. 160\nE. 320\n\n### Answer:\nIf N is the first perfect square whose tens digit and units digit are same, then N=100.\nX is the largest prime number less than positive integer N , then X is\n97.\nP is an integer such that P = X \u2013 16.\nSo P=81\nZ=(P^1/2)! = 9!\nHow many different prime factors does Z have?\nAnswer 4 (2,3,5,7)\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many bricks, each measuring 25 cm x 11.25 cm x 6 cm, will be needed to build a wall of 7.5 m x 6 m x 22.5 cm?\n\n### Options:\nA. 6000\nB. 6410\nC. 6440\nD. 6500\nE. 6800\n\n### Answer:\nNumber of bricks = Volume of Wall/Volume of Bricks\n=750x600x22.5/25x11.25x6= = 6000\nanswer :A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich of the following will give a non-integer on taking cube root?\n\n### Options:\nA. \u201364\nB. \u20131\nC. 8\nD. 9\nE. 27\n\n### Answer:\nall except 9, square root of 9 is 3 which is an integer but cube root is not an integer\nso answer is D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich of the following is a prime number ??\n\n### Options:\nA. 33\nB. 81\nC. 89\nD. 93\nE. 10\n\n### Answer:\nC\n89\nClearly, 89 is a prime number.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA jogger running at 9 km/hr along side a railway track is 240 m ahead of the engine of a 120 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger?\n\n### Options:\nA. 3.6 sec\nB. 18 sec\nC. 36 sec\nD. 72 sec\nE. None\n\n### Answer:\nSpeed of train relative to jogger = 45 - 9 = 36 km/hr.\n= 36 * 5/18 = 10 m/sec.\nDistance to be covered = 240 + 120 = 360 m.\nTime taken = 360/10 = 36 sec\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWater is leaking out from a cylinder container at the rate of 0.31 m^3 per minute. After 10 minutes, the water level decreases 9 meters. What is value of the radius in meters?\n\n### Options:\nA. 1/2\nB. 1/3\nC. 1.5\nD. 3\nE. 6\n\n### Answer:\n10*0.31 = 3.1 = pi*R^2*h\nR^2 = 3.1 / (pi*9) which is about 1/9\nR = 1/3\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA cyclist rides a bicycle 7 km at an average speed of 10 km/hr and again travels 10 km at an average speed of 7 km/hr. What is the average speed for the entire trip?\n\n### Options:\nA. 7.59\nB. 7.79\nC. 7.99\nD. 8.19\nE. 8.39\n\n### Answer:\ndistance = 17 km\ntime = 7/10 + 10/7 = (49 + 100) / 70 = 149 / 70 hours\naverage speed = (17 * 70) / 149 = 7.99 km/h\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA group of men decided to do a work in 15days, but 8 of them became absent. If the rest of the group did the work in 18days, Find the original number of men?\n\n### Options:\nA. 15\nB. 48\nC. 54\nD. 33\nE. 45\n\n### Answer:\nOriginal number of men = 8*18 / (18-15) = 48\nAnswer is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n4 dice are thrown simultaneously on the board. Find the probability show the same face.\n\n### Options:\nA. 1/121\nB. 1/213\nC. 1/216\nD. 2/211\nE. 3/213\n\n### Answer:\nThe total number of elementary events associated to the random experiments of throwing four dice simultaneously is:\n=6\u00d76\u00d76\u00d76=64=6\u00d76\u00d76\u00d76=64\nn(S)=64n(S)=64\nLet XX be the event that all dice show the same face.\nX={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)}X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)}\nn(X)=6n(X)=6\nHence required probability,\n=n(X)n(S)=664=n(X)n(S)=664\n=1/216\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a bag, there are coins of 25 p, 10 p and 5 p in the ratio of 1 : 2 : 3. If there is Rs. 30 in all, how many 5 p coins are there?\n\n### Options:\nA. 100\nB. 150\nC. 50\nD. 250\nE. 75\n\n### Answer:\nLet the number of 25 p, 10 p and 5 p coins be x, 2x, 3x respectively.\nThen, sum of their values = Rs. ((25x/100) + (10 x 2x/100)+(5 x 3x)/100= Rs. 60x/100\nTherefore, 60x/100 = 30\nx = 30 x 100/60 = 50.\nHence, the number of 5 p coins = (3 x 50) = 150.\nAnswer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe sum of money at compound interest amounts to thrice itself in 3 years. In how many years will it be 9 times itself?\n\n### Options:\nA. 7 years\nB. 5 years\nC. 4 years\nD. 6 years\nE. 3 years\n\n### Answer:\n100 ---- 300 --- 3\n900 --- 3\n----\n6 years\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSubmarine P and Submarine Q are equipped with sonar devices that can operate within a 2,000 yard range. Submarine P remains in place while Submarine Q moves 1,700 yards south from Submarine P. Submarine Q then changes course and moves due east, stopping at the maximum range of the sonar devices. In which of the following directions can Submarine Q continue to move and still be within the sonar range of Submarine P? I. North II. South III. West\n\n### Options:\nA. III only\nB. I,II only\nC. II only\nD. I only\nE. I and III only\n\n### Answer:\nIt's evident if we make a diagram for the Movement of Q respect to P.\nFrom its South position to the east position, it has covered the maximum radius for the south direction. Similarly, it's east movement further will also make it out of range.\nThus it can only move north or west or anything in that curve.\nAnswer : E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe profit earned by selling an article for Rs. 832 is equal to the loss incurred when the same article is sold for Rs. 448. What should be the sale price for making 40% profit?\n\n### Options:\nA. 277\nB. 960\nC. 896\nD. 266\nE. 121\n\n### Answer:\nLet C.P. = Rs. x.\nThen, 832 - x = x - 448\n2x = 1280 => x = 640\nRequired S.P. = 14% of Rs. 640 = 140/100 * 640 = Rs. 896.\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many integers between 1000 and 10000 have\nno digits other than 4, 5 or 6?\n\n### Options:\nA. 91\nB. 51\nC. 81\nD. 71\nE. 61\n\n### Answer:\nAny number between 1,000 and 10,000 is of 4 digits. The unit\u2019s place can be filled up by 4,5 or 6, that is, in 3 ways.\nSimilarly, the ten\u2019s place can be filled up by 4 or 5 or 6, that is in 3 ways. The hundred\u2019s place can be filled up by 4, 5 or 6, that is in 3 ways and the thousand\u2019s place can.be filled up by 4 or 5 or 6, that is, in 3 ways.\nHence the required numbers = 3 x 3 x 3 x 3 = 81\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nDefine q* by the equation q* = \u03c0-q. Then ((\u2212\u03c0)*)* =\n\n### Options:\nA. \u22122\u03c0\nB. -1\nC. \u2212\u03c0\nD. 2\u03c0\nE. 4\u03c0\n\n### Answer:\nfor q* f(f(\u2212\u03c0)) = f(\u03c0 \u2212 (\u2212\u03c0)) = f(\u03c0 + \u03c0) = f(2\u03c0) = \u03c0 \u2212 2\u03c0 = \u2212\u03c0=C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man can row his boat with the stream at 6 km/h and against the stream in 4 km/h. The man's rate is?\n\n### Options:\nA. 1 kmph\nB. 6 kmph\nC. 8 kmph\nD. 9 kmph\nE. 3 kmph\n\n### Answer:\nDS = 6\nUS = 4\nS = ?\nS = (6 - 4)/2 = 1 kmph\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA committee is reviewing a total of 20x black-and-white films and 6y color films for a festival. If the committee selects y/x% of the black-and-white films and all of the color films, what fraction R of the selected films are in color?\n\n### Options:\nA. 1/130\nB. 1/5\nC. 3/13\nD. 10/13\nE. 30/31\n\n### Answer:\nIt's y/xpercentnot y/x.\nIf x=20 and y=10. Then:\n20x=400 black-and-white films;\n6y=60 color films.\ny/x%=10/20%=0.5% of the black-and-white films, so 2 black-and-white films and all 60 color films, thus total of 62 films were selected.\nColor films thus compose R=60/62=30/31 of the selected films.\nAnswer: E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJohn makes $30 a week from his job. He earns a raise andnow makes $40 a week. What is the % increase?\n\n### Options:\nA. 16%\nB. 33.33%\nC. 33.69%\nD. 33.98%\nE. 37%\n\n### Answer:\nIncrease = (10/30)*100 = (1/3)*100 = 33.33%.\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 21,394 + x is a multiple of 3, which of the following could be the value of x?\n\n### Options:\nA. 1\nB. 2\nC. 3\nD. 4\nE. 6\n\n### Answer:\nSum of the digits of 21,394 is 2+1+3+9+4 = 19\nNow 19 is not a multiple of 3, the next multiple of 3 close to 19 is 21, which is 2 added to 19.\nSo the least number to be added to 21,394 is 2\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf Rs. 782 be divided into three parts, proportional to 1/2:2/3 :3/4, then the first part is:\n\n### Options:\nA. 402\nB. 408\nC. 48\nD. 24\nE. 204\n\n### Answer:\nGiven ratio = 1/2: 2/3:3/4\n= 6 : 8 : 9.\nTherefore, 1st part = Rs. (782 x 6/23)= Rs. 204.\nAnswer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a school where there are more than 100 students when they are grouped into 12 and 16, always 6 students remain ungrouped. What would be the minimum number of new students to be registered to this school such that when they are grouped into 20 then none of the stundents remains ungrouped ?\n\n### Options:\nA. 6\nB. 8\nC. 9\nD. 10\nE. 12\n\n### Answer:\nS=12a+6=16b+6\n6a = 8b --> for S>100 min(a,b) = (12,9)\nthen number of stundent in school --> 12*12 +6 = 150\n20k = 150 + x so that none will be ungrouped --> min( k) = 8 then\n20*8 =150 + x\nx = 10 new students to be registered\nANSWER: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSix animals of a circus has to be placed inside in six cages one in each cage. If 4 of the cage are too small for 6 of the animal then find the number of ways of caging the animal.\n\n### Options:\nA. A.240\nB. B.808250\nC. C.502450\nD. D.784200\nE. E.302400\n\n### Answer:\nways for cages that are too small = 5*4*3*2=120\nsince we have 2 cages and 2 animal left therefore ways for 2 cages =2!\ntotal ways =120*2!=604800\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many positive even integers less than 100 contain digits 3 or 7?\n\n### Options:\nA. 16\nB. 17\nC. 18\nD. 10\nE. 20\n\n### Answer:\nTwo digit numbers:\n3 at tens place: 30,32,34,36,38\n7 at tens place: 70,72,74,76,78\nIf 3 and 7 is at units place, the number cant be even\nTotal:5+5= 10\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSeven consecutive traffic signals each show either red or green. How many different arrangements of the seven signals are possible?\n\n### Options:\nA. 40\nB. 69\nC. 88\nD. 128\nE. 156\n\n### Answer:\nSince the answer choices to the question are so small (relatively speaking), you can get to the correct answer without having to do any fancy calculations. With a drawing and a bit of 'brute force', you can answer this question relatively quickly.\nWe're told that 7 consecutive traffic signals each show either red or green. We're asked how many different arrangements of the 7 signals are possible.\nTotal Options: 128\nFinal Answer:\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the area of a circle is 81pi square feet, find its circumference.\n\n### Options:\nA. 8\nB. 28\nC. 18\nD. 48\nE. 38\n\n### Answer:\nThe area is given by pi \u00d7 r \u00d7 r. Hence\npi \u00d7 r \u00d7 r = 81 pi\nr \u00d7 r = 81 ; hence r = 81 feet\nThe circumference is given by\n2 \u00d7 pi \u00d7 r = 2 \u00d7 pi \u00d7 9 = 18 pi feet\ncorrect answer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich of the following is a possible length for side AB of triangle ABC if AC = 3 and BC = 10?\nI. 7\nII. 9 \u221a3\nIII. 11.5\n\n### Options:\nA. I only\nB. II only\nC. III only\nD. II and III\nE. I, II, and III\n\n### Answer:\n(10-3) < AB < (10+3)\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe perimeter of a rectangle is 60 mete(132)7 \u00d7 (132)? = (132)11.5.\n\n### Options:\nA. 3\nB. 3.5\nC. 4\nD. 4.5\nE. 5\n\n### Answer:\n7+x=11.5\nx=11.5-7\nx=4.5\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA, B and C play a cricket match. The ratio of the runs scored by them in the match is A:B = 2:3 and B:C = 2:5. If the total runs scored by all of them are 75, the runs scored by B are?\n\n### Options:\nA. 16\nB. 18\nC. 98\nD. 27\nE. 17\n\n### Answer:\nA:B = 2:3\nB:C = 2:5\nA:B:C = 4:6:15\n6/25 * 75 = 18\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA can do a piece of work in 4 days. B can do it in 5 days. With the assistance of C they completed the work in 2 days. Find in how many days can C alone do it?\n\n### Options:\nA. 87 days\nB. 20 days\nC. 66 days\nD. 77 days\nE. 44 days\n\n### Answer:\nC = 1/2 - 1/4 - 1/5 = 1/20\n=> 20 days\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow much 70% of 100 is greater than 60% of 80?\n\n### Options:\nA. 18\nB. 99\nC. 22\nD. 26\nE. 71\n\n### Answer:\n(70/100) * 100 \u2013 (60/100) * 80\n70- 48 = 22\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the fourth proportion to 2,3,6\n\n### Options:\nA. 18\nB. 12\nC. 9\nD. 3\nE. 4\n\n### Answer:\nExplanation:\n2:3 :: 6:x\n=> 2/3 = 6/x\n=> x = 18/2\n=> x = 9\nOption C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMolly and Max are driving at a rate of 100 kilometers per hour. What is their driving speed in miles per hour? [1km = 0.6 miles]\n\n### Options:\nA. 600\nB. 60\nC. 6\nD. 0.6\nE. None of the above\n\n### Answer:\nTo calculate the equivalent of miles in a kilometer\n0.6 kilometers= 1 mile\n100 kilometers = (0.6)*100 = 60 miles\nSpeed in kilometers/hour = 60\nCorrect answer - B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nfour children \u2014 A, B, C, D, E, F, and G \u2014 are going to sit in seven chairs in a row. Children AB must sit next to each other, and child C must be somewhere to the right of AB. How many possible configurations are there for the children?\n\n### Options:\nA. 560\nB. 720\nC. 1440\nD. 4320\nE. 4800\n\n### Answer:\nA, B, C, D, E, F, G- seven children, of which AB must sit next to each other. Considering them as one X (A, B), we have X, C, D, E, F, G. These can be arranged in 6! ways. But A,B can arrange themselves in 2! ways. So a total of 6!*2! ways = 1440. Since in exactly half of them, C will be to the right of AB, and exactly half, C will be to the left of AB, therefore 1440/2 = 560.\nA is the right answer.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA shopkeeper buys mangoes at the rate of 4 a rupee and sells them at 2 a rupee. Find his net profit or loss percent?\n\n### Options:\nA. 33 1/8 %\nB. 100 %\nC. 33 1/3 %\nD. 33 5/8 %\nE. 34 1/3 %\n\n### Answer:\nThe total number of mangoes bought by the shopkeeper be 8.\nIf he buys 4 a rupee, his CP = 2\nHe selling at 2 a rupee, his SP = 4\nProfit = SP - CP = 4 - 2 = 2\nProfit Percent = 2/2 * 100 = 100 %\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe product of two numbers is 266 and their difference is 5. What is the bigger number ?\n\n### Options:\nA. 13\nB. 15\nC. 19\nD. 24\nE. None of these\n\n### Answer:\nExplanation:\nLet the two numbers be A and B, here A > B\nAB = 266\nB = 266/A -----------------(I)\nGiven,\nA \u2013 B = 5 ----------- (II)\nSubstitute from (I) in (II), we get\nA \u2013 266/A = 5\nA2 \u2013 5A + 266 = 0\n(A \u2013 19)(A \u2013 14) = 0\nTherefore , A = 19 or A = 14\nHence, bigger number = A = 19\nANSWER: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe contents of a certain box consist of 24 carrots and 30 kiwis. How many kiwis must be added to the box so that exactly 30% of the pieces of fruit in the box will be carrrots?\n\n### Options:\nA. 24\nB. 26\nC. 30\nD. 46\nE. 50\n\n### Answer:\ncarrrots = (carrrots + kiwi + x)*0.3\n24 = (30 + 24 + x)*0.3\nx = 26.\nAnswer: B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nLast year a certain bond yielded 8 percent of its face value in interest. If that interest was approximately 4 percent of the bonds selling price of $7,500, what is the bonds face value?\n\n### Options:\nA. $6,000\nB. $3,750\nC. $7,425\nD. $7,500\nE. $9,375\n\n### Answer:\nInterest = 0.08*face value = 0.04*7,500 --> face value = 0.04*7,500/0.08 = 3,750.\nAnswer: B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a tree, 2/5 of the birds are robins while the rest are bluejays. If 1/3 of the robins are female and 2/3 of the bluejays are female, what fraction of the birds in the tree are male?\n\n### Options:\nA. 3/5\nB. 4/15\nC. 7/15\nD. 8/15\nE. 17/30\n\n### Answer:\nThe fraction of birds that are male robins is (2/3)(2/5)=4/15.\nThe fraction of birds that are male bluejays is (1/3)(3/5)=1/5.\nThe total fraction of male birds is 4/15 + 1/5 = 7/15.\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWorking alone, Jerry finishes cleaning half the house in a third of the time it takes Nick to clean the entire house alone. Jerry alone cleans the entire house in 6 hours. How many hours will it take Nick and Jerry to clean the entire house if they work together?\n\n### Options:\nA. 1.5\nB. 2\nC. 2.4\nD. 3\nE. 3.6\n\n### Answer:\nAnswer is 3.6 hours.\nJerry does the complete house in 6 hours while Nick does it in 9 hours. 1/ (1/6+1/9)= 3.6\nanswer is E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train of 24 carriages, each of 60 meters length, when an engine also of 60 meters length is running at a speed of 60 kmph. In what time will the train cross a bridge 1.3 km long?\n\n### Options:\nA. 2 mins 14 sec\nB. 2 mins 34 sec\nC. 168 sec\nD. 344 sec\nE. 2 mins 44 sec\n\n### Answer:\nD = 25 * 60 + 1300 = 2800 m\nT = 2800/60 * 18/5 = 168 sec\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA salesperson receives a base salary of $1000 per month and a commission of 7.5% of the selling price of each item sold above the first 50 item. If this month she sold 530 items for $150 each, what will her monthly salary be?\n\n### Options:\nA. $1,500\nB. $1,800\nC. $6,400\nD. $2,500\nE. $2,800\n\n### Answer:\nAns : 1000+ 7.5 % * 150 * (530-50) = $ 6400\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJuan is a gold medalist in athletics. In the month of May, if Juan takes 13 seconds to run y yards, how many seconds will it take him to run x yards at the same rate?\n\n### Options:\nA. 10x/y\nB. 11x/y\nC. 9x/y\nD. 12x/y\nE. 13x/y\n\n### Answer:\nvelocity=distance/time;\nsince he ran at same rate both d tyms,\ny/13=x/t\nso t=13x/y\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAt a certain supplier, a machine of type A costs $20,000 and a machine of type B costs $55,000. Each machine can be purchased by making a 20 percent down payment and repaying the remainder of the cost and the finance charges over a period of time. If the finance charges are equal to 40 percent of the remainder of the cost, how much less would 2 machines of type A cost than 1 machine of type B under this arrangement?\n\n### Options:\nA. $10,000\nB. $11,200\nC. $12,000\nD. $12,800\nE. $19,800\n\n### Answer:\nTotal Cost of 2 Machines of Type A\n= 20% of (Cost of 2 machine A) + remainder + 40 % remainder\n= 20% of 40000 + (40000 - 20% of 40000) + 40% of (40000 - 20% of 40000)\n= 52800\nTotal Cost of 1 Machine of Type B\n= 20% of (Cost of 1 machine B) + remainder + 40 % remainder\n= 20% of 55000 + (55000 - 20% of 55000) + 40% of (50000 - 20% of 55000)\n= 72600\nDiff = 72600 - 52800 = 19800\nHence, E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nDue to construction, the speed limit along an 4-mile section of highway is reduced from 55 miles per hour to 35 miles per hour. Approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ?\n\n### Options:\nA. 5\nB. 8\nC. 10\nD. 15\nE. 2\n\n### Answer:\n4/35 - 4/55 = 4/5 * ( 11 - 7)/77\n= 4/5 * 4/77 * 60 min\n= 4 * 12 * 4/77\n= 192/77 ~ 2.4\nAnswer - E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nLook at this series: 5.2, 4.8, 4.4, 4, ... What number should come next?\n\n### Options:\nA. 4.1\nB. 3.6\nC. 2.6\nD. 5.0\nE. 5.5\n\n### Answer:\nB\n3.6\nIn this simple subtraction series, each number decreases by 0.4.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAn object thrown directly upward is at a height of h feet after t seconds, where h = -12 (t-3)^2 + 120. At what height, in feet, is the object 2 seconds after it reaches its maximum height?\n\n### Options:\nA. 48\nB. 54\nC. 60\nD. 66\nE. 72\n\n### Answer:\nWe see that h will be a maximum h=120 when t-3=0, that is when t=3.\nAt t=5, h = -12*(5-3)^2 + 120 = -12(4) + 120 = 72\nThe answer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA and B together can do a work in 6 days. If A alone can do it in 15 days. In how many days can B alone do it?\n\n### Options:\nA. 7\nB. 13\nC. 19\nD. 10\nE. None\n\n### Answer:\n1/6 \u00e2\u20ac\u201c 1/15 = 1/10\nB can do the work in 10 days\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the odd man out. 3, 8, 18, 38, 78, 158, 316\n\n### Options:\nA. 38\nB. 158\nC. 316\nD. 8\nE. None of these\n\n### Answer:\nExplanation :\n3\n3 \u00d7 2 + 2 = 8\n8 \u00d7 2 + 2 = 18\n18 \u00d7 2 + 2 = 38\n38 \u00d7 2 + 2 = 78\n78 \u00d7 2 + 2 = 158\n158 \u00d7 2 + 2 = 318\nHence, 316 is wrong and 318 should have come in place of that. Answer : Option C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nExpress a speed of 36 kmph in meters per second?\n\n### Options:\nA. 10\nB. 22\nC. 88\nD. 299\nE. 22\n\n### Answer:\n36 * 5/18 = 10 mps\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA cistern can be filled by a tap in 4 hours while it can be emptied by another tap in 8 hours. If both the taps are opened simultaneously, then after how much time will the cistern get filled?\n\n### Options:\nA. 2.9 hrs\nB. 8.9 hrs\nC. 2.9 hrs\nD. 7.2 hrs\nE. 8 hrs\n\n### Answer:\nNet part filled in 1 hour = (1/4 - 1/8)\n= 1/8\nThe cistern will be filled in 8 hrs i.e., 8 hrs.\nAnswer:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the middle one when The sum of three consecutive even numbers is 36?\n\n### Options:\nA. 10\nB. 12\nC. 14\nD. 15\nE. 16\n\n### Answer:\n3 consecutive numbers can be a - 1, a, a + 1\nSo sum of numbers = 3a = 36.\nHence a = 12.\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a and b are negative and positive integers respectively,which of the following options must be positive?\n\n### Options:\nA. ab\nB. a/b\nC. 2a/b\nD. 4a/b\nE. (a + b)^2\n\n### Answer:\nA. np\n-ve*+ve=-ve\nwill be negative\nB. n/p\n-ve/+ve=-ve\nC.2a/b\n-ve/+ve=-ve\nD.4a/b\n-ve/+ve=-ve\nE.(a + b)^2\nwill be positive irrespective of the absolute values of x and y\nwill be positive always\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nBy selling 14 pencils for a rupee a man loses 20%. How many for a rupee should he sell in order to gain 20%?\n\n### Options:\nA. 28\nB. 26\nC. 25\nD. 23\nE. 21\n\n### Answer:\n80% --- 14\n120% --- ?\n80/120 * 14 = 21\nAnswer:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFor any function Fn(x)=Fn\u22121(F(x))Fn(x)=Fn\u22121(F(x)) if for n > 1 also g(x) = 1/x, h(x) = x\u2212\u2212\u221ax and k(x) = x2x2 then what is the value of g(h3(k2(x)))?\n\n### Options:\nA. 1\nB. 8\nC. 7\nD. 6\nE. 12\n\n### Answer:\nGiven Fn(x)=Fn\u22121(F(x));Fn(x)=Fn\u22121(F(x)); g(x) = 1/x; h(x) = x\u2212\u2212\u221ax; k(x) = x\u2212\u2212\u221ax\nThen, k(k(x)) = (x2)2=x4(x2)2=x4\nAnd, h3(k2(x))=h(h(h(k2(x))))=h(h(x2))=h(x)=x\u2212\u2212\u221a.h3(k2(x))=h(h(h(k2(x))))=h(h(x2))=h(x)=x.\nAnd, g(h3(k2(x)))=g(x\u2212\u2212\u221a)=1/x\u2212\u2212\u221a.g(h3(k2(x)))=g(x)=1/x.\nHence answer is option (A).\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo trains 121 meters and 165 meters in length respectively are running in opposite directions, one at the rate of 80 km and the other at the rate of 65 kmph. In what time will they be completely clear of each other from the moment they meet?\n\n### Options:\nA. 7.16\nB. 7.12\nC. 7.11\nD. 7.15\nE. 7.13\n\n### Answer:\nT = (121 + 165)/ (80 + 65) * 18/5\nT = 7.15\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe length of a train and that of a platform are equal. If with a speed of 90 k/hr, the train crosses the platform in one minute, then the length of the train (in meters) is?\n\n### Options:\nA. 828\nB. 788\nC. 378\nD. 750\nE. 288\n\n### Answer:\nSpeed = [90 * 5/18] m/sec = 25 m/sec; Time = 1 min.\n= 60 sec.\nLet the length of the train and that of the platform be x meters.\nThen, 2x/60\n= 25 \u00e8 x = 25 * 60 / 2\n= 750\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich of the following values is the greatest?\n\n### Options:\nA. 11% of 89\nB. 22% of 78\nC. 33% of 67\nD. 44% of 56\nE. 55% of 45\n\n### Answer:\nNow, 89 < 78*2 < 67*3 < 56*4 < 45*5;as we can see option E, has the highest value for 11% , hence the answer must be E.\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhen the positive integer e is divided by 5 and 7, the remainder is 3 and 4, respectively. When the positive integer f is divided by 5 and 7, the remainder is 3 and 4, respectively. Which of the following is a factor of e-f?\n\n### Options:\nA. 12\nB. 24\nC. 35\nD. 16\nE. 30\n\n### Answer:\nIf I have a number n which when divided by 5 gives a remainder 3 and when divided by 7 gives a remainder 4, the number is of the form:\nn = 5e + 3\nn = 7f + 4\nI will need to check for the smallest such number.\nI put f= 1. n = 11. Is it of the form 5e + 3? No.\nPut f= 2. n = 18. Is it of the form 5e + 3? Yes.\nWhen 18 is divided by 5, it gives a remainder of 3. When it is divided by 7, it gives a remainder if 4.\nNext such number will be 35 + 18 because 35 will be divisible by 5 as well as 7 and whatever is the remainder from 18, will still be the remainder\nNext will be 35*2 + 18\nand so on...\nDifference between such numbers will be a multiple of 35 so your answer is 35.\nyour answer is C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFor a,f,d are the positive integers, and d|a means that \u201ca is divisible by d\u201d, if d|af, which of the following must be true?\n\n### Options:\nA. d|a\nB. d|f\nC. d|2af\nD. d|(a+f)\nE. d|(a-f)\n\n### Answer:\nd/a means a is divisible by d\nd/af means af divisible by d.\nall are integers so ,\nif af is divisible by d,\n1 a can be divisible by d\nor\n2 f can be divisble by d.\nso the question stem asks must true.\nso option a and b are could but not must.\noption c is 2af divisible by d. if ab is divisible by d then 2af is divisible by d.\noption d and e we can't predict.\nso option C is correct.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA woman begins bicycling with a pace of 10 kmph and she increases her pace every two hours by 2 kmph. She rests from bicycling 2 hours after her pace reaches her maximum speed of 14 kmph. She does a cool-down for the final 8 km at a pace of 2 kmph. How far in km did she bicycle?\n\n### Options:\nA. 96 km\nB. 100 km\nC. 106 km\nD. 116 km\nE. 126 km\n\n### Answer:\nDistance covered in first two hours = 10 \u00c3\u2014 2 = 20 km\nDistance covered in next two hours = 12 \u00c3\u2014 2 = 24 km\nDistance covered in next two hours = 14 \u00c3\u2014 2 = 48 km\nDistance covered in first six hours\n20 + 24 + 48 = 92 km\nRemaining distance = 8 km\n92 + 8 = 100 km\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nLook at this series: 36, 34, 30, 28, 24, ... What number should come next?\n\n### Options:\nA. 20\nB. 22\nC. 23\nD. 26\nE. 28\n\n### Answer:\nExplanation: This is an alternating number subtraction series. First, 2 is subtracted, then 4, then 2, and so on.\nAnswer: Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the 2532nd position of the number in the sequence\n1,2,2,3,3,3,4,4,4,4,1,1,2,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,\u2026..\n\n### Options:\nA. 1\nB. 2\nC. 3\nD. 4\nE. 5\n\n### Answer:\n10,20,30,40...\n10(1+2+3----+22)=2530\nThat mean upto 22 th pos total numbers are 2530\n2532 th numner must be 1..\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 4x + y = 8 and \u22122x + y = 13, then what is the value of 2x + 2y?\n\n### Options:\nA. 1/7\nB. 3\nC. 15\nD. 21\nE. 60/7\n\n### Answer:\n4x + y = 8\n\u22122x + y = 13\nAdding both the equations --> 2x + 2y = 21\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe ratio between the school ages of Neelam and Shaan is 5:6 respectively. If the ratio between the one-third age of Neelam and half of Shaan's age of 5:9, then what is the school age of Shaan?\n\n### Options:\nA. 25 years\nB. 30 years\nC. 36 years\nD. Cannot be determined\nE. None of these\n\n### Answer:\nLet the school ages of Neelam and Shaan be 5x and 6x years respectively.\nThen, (1/3 * 5x)/(1/2 * 6x) = 5/9\n15 = 15\nThus, Shaan's age cannot be determined.\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe cost price of a radio is Rs.1500 and it was sold for Rs.1230, find the loss %?\n\n### Options:\nA. 18%\nB. 19%\nC. 68%\nD. 19%\nE. 38%\n\n### Answer:\n1500 ---- 270\n100 ---- ? => 18%\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhen positive integer m is divided by positive integer x, the reminder is 7 and when positive integer n is divided by positive integer y, the reminder is 11. Which of the following W is a possible value for x + y?\nI. 18\nII. 19\nIII. 20\n\n### Options:\nA. I only\nB. II only\nC. W=III only\nD. II and III only\nE. None\n\n### Answer:\nTIP FOR SUCH QUESTIONS:Make Algebraic Equation in the beginning to understand how to proceed further. Then Start thinking the possible values of variables asked about\ni.e.When positive integer m is divided by positive integer x, the reminder is 7can be understood as\nm = ax +7which means thevalue of x must be greater than 7as the remainder 7 is possible only when the Divisor is bigger than the Remainder 7\ni.e. Min Value of x = 8\nAND\ni.e.When positive integer n is divided by positive integer y, the reminder is 11can be understood as\nn = by +11which means thevalue of y must be greater than 11as the remainder 11 is possible only when the Divisor is bigger than the Remainder 11\ni.e. Min Value of y = 12\ni.e. Minimum Value of x+y = 8+12 = 20\nHence III only can be True\nAnswer: Option\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThree guests check into a hotel room. The clerk says the bill is $30, so each guest pays $10. Later the clerk realizes the bill should only be $25. To rectify this, he gives the bellhop $5 to return to the guests. On the way to the room, the bellhop realizes that he cannot divide the money equally. As the guests didn\u2019t know the total of the revised bill, the bellhop decides to just give each guest $1 and keep $2 for himself.\nNow that each of the guests has been given $1 back, each has paid $9, bringing the total paid to $27. The bellhop has $2. If the guests originally handed over $30, what happened to the remaining $1?\n\n### Options:\nA. $30\nB. $20\nC. $10\nD. $40\nE. $50\n\n### Answer:\nThere is no missing dollar. A dollar only goes \"missing\" because the statement \"each man paid $9 for the room\" is wrong - each of three men paid out a total of $9, but that $9 included both the room charge and the bellboy's tip. All in all, each man paid out a total of $9 and had $1 left over, completely accounting for the $30 they started with.. Hotel - $25 Bellhop - $2 Customers - $1 each $25 + $2 + $3 = $30\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA clock shows the time as 9 a.m. If the minute hand gains 5 minutes every hour, how many minutes will the clock gain by 6 p.m.?\n\n### Options:\nA. 30 min\nB. 35 min\nC. 45 min\nD. 50 min\nE. 55 min\n\n### Answer:\nthere are 9 hours in between 9 a.m. to 6 p.m.\n9*5=45 minutes.\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSeries Problem like 4 12 x 44 46 132 134 begin of the Skype highlighting 44 46 132 134 end of the Skype highlighting. Find x?\n\n### Options:\nA. 13\nB. 14\nC. 15\nD. 16\nE. 17\n\n### Answer:\n134-132=2\n46-44=2\nx-12=2\nx=14\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhen tossed, a certain coin has equal probability of landing on either side. If the coin is tossed 3 times, what is the probability that it will land once on heads and twice tails?\n\n### Options:\nA. 1/3\nB. 1/6\nC. 1/4\nD. 1/8\nE. 1/5\n\n### Answer:\nMust be once on heads and twice on tails\n1/2*1/2*1/2 = 1/8\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the diagonals of a rhombus are 24 cm and 10 cm, what will be its perimeter\n\n### Options:\nA. 42 cm\nB. 64 cm\nC. 56 cm\nD. 52 cm\nE. None of these\n\n### Answer:\nExplanation : Let the diagonals be PR and SQ such that PR = 24 cm and SQ = 10 cm PO = OR = 24/2=12 cm\nSO = OQ = 10/2=5 cm\nPQ = QR = RS = SP = \u221a(122 + 52) = \u221a(144+25) = \u221a169 = \u221a13 cm\nperimeter = 4 \u00d7 13 = 52 cm Answer : Option D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf x dollars is invested at 9 percent for one year and y dollars is invested at 8 percent for one year, the annual income from the 9 percent investment will exceed the annual income from the 8 percent investment by $48. If $2,000 is the total amount invested, how much is invested at 8 percent?\n\n### Options:\nA. a. $280\nB. b. $776.47\nC. c. $892\nD. d. $1108\nE. e. $1200\n\n### Answer:\n2 equations with 2 unknowns\n9x / 100 - 8y / 100 = 48\nand\nx + y = 2000\nSolving these 2 equations, x = 1223.53 and y = 776.47\nAnswer B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA rectangular lawn of length 200m by 120m has two roads running along its center, one along the length and the other along the width. If the width of the roads is 5m what is the area R covered by the two roads?\n\n### Options:\nA. 400\nB. 1550\nC. 1575\nD. 1600\nE. 1625\n\n### Answer:\nArea Covered by Road Along the Length = 5*200 = 1000 Square Meter\nArea Covered by Road Along the Width = 5*120 = 600 Square Meter\nCommon Area in both Roads (where the roads intersect) = Square with Side 5 meter = 5*5 = 25\nTotal Area of the Roads R = 1000+600-25 = 1575\nAnswer: option C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA and B entered into a partnership investing Rs. 13,000 and Rs. 12,000 respectively.After 3 months, A withdrew Rs. 5000 while B invested Rs. 5000 more, After 3 more months, C joins the business with a capital of Rs. 21,000, The share of B exceeds that of C, out of a total profit of Rs. 26,400 after one year by?\n\n### Options:\nA. 8340\nB. 3600\nC. 2787\nD. 1287\nE. 3627\n\n### Answer:\nA : B : C = (16000 * 3 + 11000 * 9) : (12000 * 3 + 17000 * 9) : (21000 * 6)\n= 147 : 189 : 126\n= 7 : 9 ; 6.\nDifference of B and C's shares = Rs. ( 26400 * 9/22 - 26400 * 6/22 )\n= Rs. 3600.\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA sum of Rs. 2743 is lent into two parts so that the interest on the first part for 8 years at 3% per annum may be equal to the interest on the second part for 3 years at 5% per annum. Find the second sum?\n\n### Options:\nA. 1642\nB. 1640\nC. 1632\nD. 1688\nE. 6386\n\n### Answer:\n(x*8*3)/100 = ((2743 - x)*3*5)/100\n24x/100 = 41145/100 - 15x/100\n39x = 41145 => x = 1055\nSecond sum = 2743 \u2013 1055\n=1688\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA lemonade stand sold only small and large cups of lemonade on Tuesday. 3/5 of the cups sold were small and the rest were large. If the large cups were sold for 7/3 as much as the small cups, what fraction of Tuesday's total revenue was from the sale of large cups?\n\n### Options:\nA. (a) 14/23\nB. (b) 7/15\nC. (c) 10/21\nD. (d) 17/35\nE. (e) 1/2\n\n### Answer:\nThis problem is very good example how easy and quick plug-in method might be.\nLet the total # of cups be 10.\n# of small cups sold 3/5*10=6;\n# of large cups sold 10-6=4;\nLet the price of small cup be $6, then the price of larges cup would be 7/3*6=$14;\nRevenue from small cups: 6*$6=$36;\nRevenue from large cups cups: 4*$14=$56;\nFraction of total revenue from large cups: 56/(36+56)=14/23.\nAnswer: A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nPipe A can fill a tank in 10 hours, pipe B in 8 hours, and pipe C in 40 hours. If all the pipes are open, in how many hours will the tank be filled?\n\n### Options:\nA. 2\nB. 3\nC. 4\nD. 5\nE. 6\n\n### Answer:\nThe part filled by A + B + C in 1 hour\n= 1/10 + 1/8 + 1/40\n= 10/40 = 1/4\nAll the three pipes together will fill the tank in 4 hours.\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe sum of the squares of the fifth and the eleventh term of an AP is 3 and the product of the second and fourteenth term is equal to P.Find the product of the first and the fifteenth term of the AP.\n\n### Options:\nA. (58P-39)/45\nB. (98P+39)/72\nC. (116P-39)/90\nD. (98P+39)/90\nE. None of these\n\n### Answer:\n(T5)^2+(T11)^2=3\nT2*T14=P\nT1*T15=?\n(a+4d)^2+(a+10d)^2=3\n2a^2+28ad+116d^2=3.....(1)\n(a+d)(a+13d)=P\na^2+14ad+13d^2=P\na^2+14ad = P- 13d^2\n1.5-45d^2=P\n2P=3-90d^2...........(2)\na^2+14ad=?\n=P-13d^2\n=P-13(3-2P)/90\n=(116P-39)/90\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFrom given equation find the value of x: 2x\u00b2 + 9x \u2212 5\n\n### Options:\nA. 1\nB. 1/2\nC. 1/3\nD. 2/3\nE. 2/5\n\n### Answer:\nThat quadratic is factored as follows:\n2x\u00b2 + 9x \u2212 5 = (2x \u2212 1)(x + 5).\nLesson 17.\nNow, it is easy to see that the second factor will be 0 when x = \u22125.\nAs for the value of x that will make\n2x \u2212 1 = 0,\nwe must solve that little equation. (Lesson 9.)\nWe have:\n2x = 1\nx = 1\n2\nThe solutions are:\nx = 1/2 or \u22125\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the units digit of 17^83 \u00d7 13^82 \u00d7 11^67?\n\n### Options:\nA. 4\nB. 5\nC. 6\nD. 7\nE. 8\n\n### Answer:\nTo find : the units digit of 17^83 \u00d7 13^82 \u00d7 11^87\nLet's reduce the clutter and simplify the product\n(7^83) (3^82) (1^87)\n7 has a cyclicity of 4 : the last digit of any positive power of 7 repeats itself after every 4th power\nso 7^5 has the same last digit as 7^1, 7^9, 7^13\nThus , 7^83 has the same last digit as 7^3, 7^7, 7^11 i.e.3\n3 has a cyclicity of 4 : exactly the same routine as above\nThus , 3^82 has the same last digit as 3^2, 3^6, 3^10 i.e.9\nAny power of 1 will result in1as the last digit\nSo, product of our last digits = 3 x 9 x 1 = 27....last digit is 4\nCorrect Option : A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n3,5,8,13,22,__\n\n### Options:\nA. 37\nB. 38\nC. 39\nD. 40\nE. 41\n\n### Answer:\n5=3*2-1\n8=5*2-2\n13=8*2-3\n22=13*2-4\n39=22*2-5\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf w = 20! + 17, then w is divisible by which of the following?\nI. 15\nII. 17\nIII. 19\n\n### Options:\nA. None\nB. I only\nC. II only\nD. I and II\nE. II and II\n\n### Answer:\nAnother crude way to answer this, if you did not know the properties above would be to consider that that 20! will have the number ending in 00 due to 10 and 20 being included.\nSo w!+17 = xxxx00 +17 = xxxx17 which is only possibly divisible by 17. Hence Option C is the answer.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nCar Dealership X, the total profit from sales increased by 10 percent over the previous years, while the number of cars sold decreased by 10 percent over the previous years. Approximately what was the average percent increase in profit per car over the previous year.\n\n### Options:\nA. 18%\nB. 20%\nC. 22%\nD. 23%\nE. 25%\n\n### Answer:\nLet Profit be x and cars sold be y\nOriginally Profit/Car = x/y\nNow it is 1.1x / 0.9 y = 11/9 (x/y)\nIncrease in profit per car = ((2/9) (x/y)) / (x/y) * 100 = 22.22%\nAnswer = C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a division sum, the divisor is ten times the quotient and five times the remainder. If the remainder is 38, the dividend is:\n\n### Options:\nA. 3648\nB. 3642\nC. 3636\nD. 3644\nE. 3864\n\n### Answer:\nDivisor = (5 * 38) = 190\n= 10 * Quotient = Divisor\n=> Quotient = 190/10 = 19\nDividend = (Divisor * Quotient) + Remainder\nDividend = (190 * 19) + 38 = 3648.\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nPooja is selling her books at puzzles land at a strange price as\n* she sells her book \"Vanity\" at $30\n* she sells her book \"Sybil\" at $25\n* she sells her book \"xmen\" at $20\nAt what price does she sell her book \"twilight\" ?\n\n### Options:\nA. 54\nB. 23\nC. 40\nD. 87\nE. 20\n\n### Answer:\nC\n40\nCost of each alphabet is 5\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThree 6 faced dice are thrown together. The probability that no two dice show the same number on them is\n\n### Options:\nA. 7/12\nB. 5/9\nC. 1/36\nD. 5/12\nE. 8/9\n\n### Answer:\nNo two dice show same number would mean all the three faces should show different numbers. The first can fall in any one of the six ways. The second die can show a different number in five ways. The third should show a number that is different from the first and second. This can happen in four ways.\nThus 6 * 5 * 4 = 120 favourable cases.\nThe total cases are 6 * 6 * 6 = 216.\nThe probability = 120/216 = 5/9.\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRamu bought an old car for Rs. 42000. He spent Rs. 13000 on repairs and sold it for Rs. 64900. What is his profit percent?\n\n### Options:\nA. 19%\nB. 11%\nC. 18%\nD. 218%\nE. 14%\n\n### Answer:\nTotal CP = Rs. 42000 + Rs. 13000\n= Rs. 55000 and SP = Rs. 64900\nProfit(%) = (64900 - 55000)/55000 * 100\n= 18%\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOne fourth of one third of two fifth of a number is 35. What will be40% of that number\n\n### Options:\nA. A)140\nB. B)420\nC. C)180\nD. D)200\nE. E)220\n\n### Answer:\nExplanation:\n(1/4) * (1/3) * (2/5) * x = 35\nthen x = 35 * 30 = 1050\n40% of 1050 = 420\nAnswer: Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nBrenda and Sally run in opposite direction on a circular track, starting at diametrically opposite points. They first meet after Brenda has run 300 meters. They next meet after Sally has run 150 meters past their first meeting point. Each girl runs at a constant speed. What is the length of the track in meters?\n\n### Options:\nA. 250\nB. 300\nC. 350\nD. 700\nE. 500\n\n### Answer:\nNice problem. +1.\nFirst timetogetherthey run half of the circumference.\nSecond timetogetherthey run full circumference.\nFirst time Brenda runs 300 meters, thus second time she runs 2*300 = 600 meters.\nSince second time (when they run full circumference) Brenda runs 600 meters and Sally runs 150 meters, thus the circumference is 600 + 150 = 750 meters.\nAnswer: D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA room is 7 meters 20 centimeters in length and 4 meters 32 centimeters in Width. Find the least number of square tiles of equal size required to cover the entire floor of the room.\n\n### Options:\nA. 10\nB. 15\nC. 17\nD. 19\nE. 21\n\n### Answer:\nLet us calculate both the length and width of the room in centimeters.\nLength = 7 meters and 20 centimeters = 720 cm\nwidth = 4 meters and 32 centimeters = 432 cm\nAs we want the least number of square tiles required, it means the length of each square tile should be as large as possible.Further,the length of each square tile should be a factor of both the length and width of the room.\nHence, the length of each square tile will be equal to the HCF of the length and width of the room = HCF of 720 and 432 = 144\nThus, the number of square tiles required = (720 x 432 ) / (144 x 144) = 5 x 3 = 15\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo numbers are in the ratio of 5:9. If 25 be subtracted from each, they are in the ratio of 35:59. Find the numbers?\n\n### Options:\nA. 150,170\nB. 150,270\nC. 50,270\nD. 180,270\nE. 150,290\n\n### Answer:\n(5x-25):(9x-25) = 35:59\nx = 30 => 150,270\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nLindsay can paint a room in 8 hours at a constant rate. If Lindsay paints the room for 4 hours and Joseph paints the rest of the room, who works at 1/2 constant rate of Lindsay. How long will it take for Joseph alone to paint the rest of the room?\n\n### Options:\nA. 4hrs\nB. 8hrs\nC. 10hrs\nD. 12hrs\nE. 16hrs\n\n### Answer:\nLindsay will do 4/8 in 4 hrs, so Lindsay does 1/2 of the work ..\nTherefore, Joseph will do the remaining 1/2 work alone..\nAs the speed of Joseph is 1/2 rate of Lindsay, Joseph will do the 1/2 work in same time that Lindsay takes to complete full job...\nans 8\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the odd man out\n4, 9, 16, 25, 36, 50, 64, 81\n\n### Options:\nA. 4\nB. 9\nC. 25\nD. 36\nE. 50\n\n### Answer:\nas 50 is only odd number.\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train speeds past a pole in 10seconds and a platform 50 m long in 20 seconds. Its length is:\n\n### Options:\nA. 30 m.\nB. 40 m.\nC. 60 m.\nD. 50 m.\nE. 70 m.\n\n### Answer:\nLet the length of the train be x meters and its speed be y m/sec.\nThey, x / y = 10 => y = x/10\nx + 50 / 20 = x / 10\nx = 50 m.\nAnswer: Option D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich of the following points is symmetric with y=x at (-2,-3)?\n\n### Options:\nA. (-3,-2)\nB. (-2,1)\nC. (2,1)\nD. (-1,-2)\nE. (-1,2)\n\n### Answer:\nWe can think of line y = x as a mirror. Any point (x,y) becomes (y,x) when it isreflectedover the mirror. Reverse the coordinate and keep the same sign. These two points will be symmetric to the line y = x.\n(-2,-3) would become (-3,-2).\nAnswer (A).\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSimplify: 0.4*0.5+0.3*0.2\n\n### Options:\nA. 0.52\nB. 0.26\nC. 0.48\nD. 0.64\nE. 0.46\n\n### Answer:\nGiven exp. = 0.4*0.5+(0.3*0.2) = 0.2+0.06 = 0.26\nAnswer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nBy using the numbers 0, 2, 3, 5 and 4 only once, how many five digit numbers can be made that are divisible by 8?\n\n### Options:\nA. 18\nB. 24\nC. 48\nD. 16\nE. 52\n\n### Answer:\nA number to be divisible by 8 must end with 8, 16, 24,32,40...\nSo, there are the following cases possible:\n035-24 --> the first three digits can be arranged in 3=6 ways.\n054-32--> the first three digits can be arranged in 3=6 ways.\n235-40--> the first three digits can be arranged in 3=6 ways.\nTotal = 6+6+6 = 18.\nAnswer: A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA driving school claims an average test pass rate of 76.8 percent. What is the least number of pupils required to achieve this result?\n\n### Options:\nA. 125\nB. 113\nC. 189\nD. 153\nE. 142\n\n### Answer:\nA\n125\n96 passes out of 125 give an average of 76.8% .\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe simple interest on a sum of money will be Rs.600 after 10 years. If the principal is trebled after 5 years what will be the total interest at the end of the tenth year?\n\n### Options:\nA. 1277\nB. 2977\nC. 1200\nD. 2769\nE. 1971\n\n### Answer:\nP --- 10 ---- 600\nP --- 5 ----- 300\n3P --- 5 ----- 900\n------\n=> 1200\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nKrishan and Nandan jointly started a business. Krishan invested three times as Nandan did and invested his money for fourtime as compared to Nandan. Nandan earned Rs. 4000. If the gain is proportional to the money invested and the time for which the money is invested and the total gain was\n\n### Options:\nA. Rs.32000\nB. Rs.62000\nC. Rs.42000\nD. Rs.52000\nE. Rs.22000\n\n### Answer:\n3:1\n4:1\n------\n12:1\n1 ----- 4000\n13 ----- ? => Rs.52,000\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOn Monday morning, Chris receives tickets to a baseball game that will be played at 7pm on the next evening that it does not rain. However, Chris is only in town until Wednesday morning, at which point he must fly to another city. If there is a 60% chance of rain each of the next two evenings, what is the probability that Chris will be able to attend the game?\n\n### Options:\nA. 64%\nB. 60%\nC. 66%\nD. 80%\nE. 84%\n\n### Answer:\nChris won't be able to attend the game if it be raining on Monday eveningandTuesday evening. The probability of that is 0.6*0.6 = 0.36. So, the probability that he will be able to attend is 1 - 0.36 = 0.64.\nAnswer: A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf each edge of cube increased by 10%, the percentage increase in surface area is:\n\n### Options:\nA. 33.1\nB. 33.5\nC. 33.7\nD. 33.2\nE. 33.9\n\n### Answer:\n100 \u00d7 (110)/100 \u00d7 (110)/100 \u00d7 (110)/100 => 1331/100 = 33.1%\nAnswer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe music class consists of 4 girls and 6 boys. How many ways can a group of 3 be formed if it has to include at least one boy?\n\n### Options:\nA. 116\nB. 158\nC. 161\nD. 165\nE. 172\n\n### Answer:\nReverse combinatorics approach is preferred method on this one\nNote that at least 1 boy gives clue to using this method\nAll combinations - four girls = answer\nAll combinations is 10C3 = 120\nAll girls 4C3 = 4\nSo our answer is 120-4 = 116\nHence, answer is (A)\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOn a certain transatlantic crossing, 35 percent of a ship's passengers held round-trip tickets and also took their cars aboard the ship. If 60 percent of the passengers with round-trip tickets did not take their cars aboard the ship, what percent of the ship's passengers held round-trip tickets?\n\n### Options:\nA. 33 1/3%\nB. 87.5%\nC. 50%\nD. 60%\nE. 66 2/3%\n\n### Answer:\nOn a certain transatlantic crossing, 20 percent of a ship\u2019s passengers held round-trip tickets and also took their cars abroad the ship. If 60 percent of the passengers with round-trip tickets did not take their cars abroad the ship, what percent of the ship\u2019s passengers held round-trip tickets?\nSolution: Let total number of passengers be 100\nAccording to Q stem 40% of passengers who had round-trip tics have taken cars - let number of passengers with round trip be X then\n40% of X = 35 => X= 87.5.\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe \u201cs-number\u201d of a number x is defined as the ones digit of 2^x. Antony rolls a die with 6 sides labeled with the integers from 1 to 6, each of which has an equal probability of landing face-up. He then takes 3^s, where s is the s-number of the result of his die roll, and plots 3^s on a number line as the point A. Finally, he repeats this entire process, this time plotting the result as the point B. What is the probability that the distance between A and B is greater than the value of B?\n\n### Options:\nA. 3/8\nB. 13/36\nC. 17/36\nD. 19/36\nE. 23/36\n\n### Answer:\nIf you calculate 3^s for 1st roll, all 6 results will be 9, 81, 6561, 729, 9, 81. This result is the same for 2nd roll. 9, 81, 6561, 729, 9, 81.\nAbout distance: If the first result is 9 and the second is also 9, the distance is 9-9=0 which is smaller than 9. If the first result is 9 and the second is 81, the distance is 81-9=72 which is also smaller than B which has the value of 81. If the first result is 81 and the second is 9, the distance will be greater than B. Distance 81-9=72>9.\nOn the first roll, the probability of getting result 9 is 2/6. In this case no other alternative values for second roll which would make the distance greater than B. So probability is 0. So next estimations are:\nprobability of getting 81 on the first roll (2/6) * probability of getting 9 on the second roll (2/6) = 1/9\nprobability of getting 729 on the first roll (1/6) * probability of getting 9, 81 on the second roll (4/6) = 1/9\nprobability of getting 6561 on the first roll (1/6) * probability of getting 9, 81, 729 on the first roll (5/6) = 5/36\nAll together: 1/9 + 1/9 + 5/36 = 13/36=B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA box contains 2 white balls, 3 black balls and 4 red balls. In how many ways can 3 balls be drawn from the box, if atleast one black ball is to be included in the draw?\n\n### Options:\nA. 64\nB. 36\nC. 52\nD. 86\nE. 24\n\n### Answer:\nWe may have (1 black and 2 non black) or (2 black and 1 non black) or (3 black)\nRequired number of ways = 3C1*6C2+3C2*6C1+3C3 = 64\nAnswer is A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average age of a class of 39 students is 15 years. If the age of the teacher be included, then the average increased by 3months. Find the age of the teacher?\n\n### Options:\nA. 25\nB. 28\nC. 30\nD. 35\nE. 39\n\n### Answer:\nTotal age of 39 persons = 39*15 = 585 years\nAverage age of 40 persons = 15yrs 3months = 61/4 years\nTotal age of 40 persons = 61/4 * 40 = 610 years\nAge of the teacher = 610-585 = 25 years\nAnswer is A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe current birth rate per thousand is 32, whereas corresponding death rate is 11 per thousand. The net growth rate in terms of population increase in percent is given by\n\n### Options:\nA. 0.0021%\nB. 0.021%\nC. 2.1%\nD. 21%\nE. None\n\n### Answer:\nSol.\nNet growth on 1000 = (32 - 11) = 21.\nNet growth on 100 = (21/1000 \u00d7 100)% = 2.1 %.\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe LCM of three numbers is four times their GCF. Which of the following must be true of the numbers?\nI. At least o ne of the numbers is odd.\nII. Two of the three numbers must be same.\nIII. At least one number is the same as GCF.\n\n### Options:\nA. only\nB. option II only\nC. and III only\nD. and II only\nE. I and III only\n\n### Answer:\nConsider the following set: {2, 4, 8}.\nGCF = 2.\nLCM = 8 = 4*2.\nThe set discards options I and II. Only B fits.\nAnswer: B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA number when divided by 221 gives a remainder 43, what remainder will be obtained by dividing the same number 17?\n\n### Options:\nA. 9\nB. 11\nC. 15\nD. 5\nE. 20\n\n### Answer:\n221 + 43 = 264/17 = 9\nANSWER A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf q > a and L < a, which of the following cannot be true?\n\n### Options:\nA. d + L = 14\nB. d - L = 7\nC. d - L = 1\nD. a - q = 9\nE. a + d = 9\n\n### Answer:\nIs the answer D?\nIf q>a, then q-a>0 (always positive). The converse would be a-q<0 (always negative). Option D states that a-q=9, which can never be true.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 20 men can build a wall 66 metres long in 6 days, what length of a similar can be built by 86 men in 8 days?\n\n### Options:\nA. 278.4 mtrs\nB. 378.4 mtrs\nC. 478.4 mtrs\nD. 488.4 mtrs\nE. 578.4 mtrs\n\n### Answer:\nIf 20 men can build a wall 66 metres long in 6 days,\nlength of a similar wall that can be built by 86 men in 8 days = (66*86*8)/(6*20) = 11*172/5 = 1892/5 mtrs = 378.4 mtrs\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhen a number is divided by 3 &then multiply by 12 the answer is 9 what is the no.?\n\n### Options:\nA. 4.5\nB. 5\nC. 2.25\nD. 5.7\nE. 6.5\n\n### Answer:\nif $x$ is the number, x/3 * 12 = 9\n=> 4x = 9\n=> x = 2.25\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe sum of two consecutive number is 87. Which is the larger number?\n\n### Options:\nA. 42\nB. 43\nC. 44\nD. 45\nE. 46\n\n### Answer:\nLet consecutive number be x, x+1\nTherefore sum of the consecutive number is x + x+1=87\n2x+1=87\n2x=86\nx=43\nTherefore larger number is x+1=44\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA total of 22 men and 28 women were at a party, and the average (arithmetic mean) age of all of the adults at the party was exactly 35 years. If the average age of the men was exactly 38 years, which of the following was closest to the average age, in years, of the women?\n\n### Options:\nA. 31\nB. 31.5\nC. 32.6\nD. 32.5\nE. 33\n\n### Answer:\nLet Aw = average age of women\nAverage = (Number of men X average age of men + Number of women X average age of women)/total number of people\n35 * 50 = 22 * 38 + 28 * Aw\n=>1750 = 836 + 28 Aw\n=> 28 Aw = 914\n=>Aw = 32.6\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many diagonals does a 62-sided convex polygon have?\n\n### Options:\nA. 1829\nB. 2356\nC. 3458\nD. 3843\nE. 4820\n\n### Answer:\nA 62-sided convex polygon has 62 vertices.\nIf we examine a single vertex, we can see that we can connect it with 59 other vertices to create a diagonal. Note that we can't connect the vertex to itself and we can't connect it to its adjacent vertices, since this would not create a diagonal.\nIf each of the 62 vertices can be connected with 59 vertices to create a diagonal then the total number of diagonals would be (62)(59) = 3658\nHowever, we must recognize that we have counted every diagonal twice.\nTo account for counting each diagonal twice, we must divide 3658 by 2 to get 1829.\nThe answer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJim has arrived late for his golf tee time with his friends. When he arrives at the course, he discovers that his friends have already walked 180 yards ahead on the course and that they are continuing to walk forward at a rate of 1.5 yards per second. A bystander with a golf cart takes pity on Jim and drives him to meet his friends at the rate of 4 yards per second. Once Jim meets his friends, he exits the cart and walks with them at their rate for the next 120 yards. What is Jim\u2019s approximate average speed for his total trip?\n\n### Options:\nA. 1.8 yards per second\nB. 2.0 yards per second\nC. 2.4 yards per second\nD. 2.7 yards per second\nE. 3.0 yards per second\n\n### Answer:\nGiven Jim's friends has a lead of 180 yards and moving at 1.5 yards/sec speed\nJim on golf cart with speed 4 yards/sec has to meet this friends, assuming he meets them after \"t\" secs\nSo the total distance traveled by Jim and his friends should be same so as to meet them=> 180+1.5t=4t\n=> 180=2.5t\n=>72 secs, so Jim meets his friends after traveling 72 secs at 4 yards/sec speed---First part of his journey (288 yards in 72 secs)\nNow, Jim travels 120 yards with speed 1.5 yards/sec in 120/1.5=80 secs---second part of his journey (120 yards in 80 secs)\nSo avg speed of Jim= total distance traveled/ total time\n=> (288+120)/(72+80)=408/152\n=>2.7 yards/sec approx\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSuresh can complete a job in 15 hours. Ashutosh alone can complete the same job in 15 hours. Suresh works for 9 hours and then the remaining job is completed by Ashutosh. How many hours will it take Ashutosh to complete the remaining job alone?\n\n### Options:\nA. 4\nB. 5\nC. 6\nD. 12\nE. None of these\n\n### Answer:\nThe part of job that Suresh completes in 9 hours\n= 9\u00e2\u0081\u201e15 = 3\u00e2\u0081\u201e5\nRemaining job = 1 - 3\u00e2\u0081\u201e5 = 2\u00e2\u0081\u201e5\nRemaining job can be done by Ashutosh in 2\u00e2\u0081\u201e5 \u00c3\u2014 15 = 6 hours\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFor a certain art exhibit, a museum sold admission tickets to a group of 30 people every 6 minutes from 9:00 in the morning to 6:00 in the afternoon, inclusive. The price of a regular admission ticket was $10 and the price of a student ticket was $6. If on one day 2 times as many regular admission tickets were sold as student tickets, what was the total revenue from ticket sales that day?\n\n### Options:\nA. $23400\nB. $25920\nC. $28080\nD. $28500\nE. $29160\n\n### Answer:\nFrom 9:00 in the morning to 6:00 in the afternoon, inclusive there are 9*10=90 five-minute intervals, thus total of 54*30 tickets were sold.\nSay x student and 2x regular tickets were sold, then x+2x=90*30 --> x=30*30 and 2x=2*(30*30)=30*60.\nTherefore, the total revenue from ticket sales that day was 30*30*6+30*60*10=$23,400.\nAnswer: A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf x = y+3+4.5x and y = x+18, what is the value of x/y ?\n\n### Options:\nA. -6/5\nB. -7/20.\nC. 1/4.\nD. 5/6.\nE. 1.5\n\n### Answer:\nGiven x = y+3+4.5x --> Eq 1\nand y = x+18 --> Eq 2\nHere we are asked to find the value of X/Y ?\nIf you observe eq 1 , then we can understand that if we take Y as X then we get X value very quickly\nLet's take X/Y = 1/4 => 4X = Y - eq 3.\nSub this value in eq 1 => we get X = 4X + 3 + 4.5 X\n=> - 7.5X = 3\n=> X = -2/5 --> Sub X in eq 3 to get Y, we get Y as -8/5.\nX/Y = -2/5 / -8/5 => 1/4. we get the same value again.\nAnswer:option C is correct answer\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the value of (P + Q)/(P - Q) if P/Q is 5?\n\n### Options:\nA. 4/3\nB. 3/2\nC. 2/6\nD. 7/8\nE. 8/7\n\n### Answer:\n(P + Q)/(P - Q) = [(P/Q) + 1]/[(P/Q) - 1]\n= (5 + 1)/(5 - 1)\n= 6/4\n= 3/2\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nk = 2^n + 8, where n is an integer greater than 1. If k is divisible by 9, which of the following MUST be divisible by 9?\n\n### Options:\nA. 2^n - 8\nB. 2^n - 2\nC. 2^n\nD. 2^n + 4\nE. 2^n + 5\n\n### Answer:\nGiven: k, M and N are integers\nIf k is a divisor of both N and M, then k is a divisor of N+M (and N\u2013M and M\u2013N)\nWe're told that 9 is a divisor of 2^n + 8\nWe also know that 9 is a divisor of9.\nSo, applying the above rule, 9 is a divisor of 2^n + 8 +9, and 9 is a divisor of 2^n + 8 -9=2^n -1\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf Q is the least common multiple of 90,196, and 300, which of the following is NOT a factor of Q?\n\n### Options:\nA. 600\nB. 700\nC. 900\nD. 2,100\nE. 4,900\n\n### Answer:\nIF Q is the least common multiple of 90,196 and 300, which of the following is NOT a factor of Q?\nA- 600\nB- 700\nC- 900\nD- 2100\nE- 4900\n90 = 2 * 3 * 3 * 5\n196 = 2 * 2 * 7 * 7\n300 = 2 * 2 * 3 * 5 * 5\nLCM = 2 * 2 * 3 * 3 * 5 * 5 * 7 * 7\n(TWO 2, TWO 3, TWO 5, TWO 7)\n600 = 2 * 2 * 2 * 3 * 5 * 5\n700 = 2 * 2 * 5 * 5 * 7\n900 = 2 * 2 * 3 * 3 * 5 * 5\n2100 = 2 * 2 * 3 * 5 * 5 * 7\n4900 = 2 * 2 * 5 * 5 * 7 * 7=A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA watch passes through three hands and each gains 25%. If the 3rd sells it for Rs250, what did the 1st pay for it?\n\n### Options:\nA. 110\nB. 120\nC. 128\nD. 143\nE. 145\n\n### Answer:\nFirst Purchased = 250 Wes= 128\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAn ice cream store received shipments of ingredients on Tuesday and Wednesday. Tuesday's shipment had 6 different packages, with an average (arithmetic mean) of 11 and 2/3 pounds. Wednesday's shipment included 7 packages, weighing an average of 9 and 3/7 pounds. What was the average package weight, in pounds, of the shipments received on both days?\n\n### Options:\nA. 9 and 6/7 pounds\nB. 10 and 1/10 pounds\nC. 10 and 2/5 pounds\nD. 136/13 pounds\nE. 11 and 1/7 pounds\n\n### Answer:\nSolution: Average weight = Total weight/number of packages. The total weight on Tuesday was 6 * (11 and 2/3 pounds), or 70 pounds. The total weight on Wednesday was 7 * (9 and 3/7 pounds), or 66 pounds. The sum of the weights for both days is 66 + 70, or 136 pounds. The average is 136 pounds/13 packages.\nanswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the odd man out. 2, 5, 10, 17, 26, 38, 50, 65\n\n### Options:\nA. 50\nB. 38\nC. 26\nD. 65\nE. 50\n\n### Answer:\nExplanation :\nThe pattern is (1\u00d71)+1 , (2\u00d72)+1 , (3\u00d73)+1 , (4\u00d74)+1 , (5\u00d75)+1 , (6\u00d76)+1 , (7\u00d77)+1 , (8\u00d78)+1\nHence, in place of 38, the right number was (6\u00d76)+1 = 37\nAnswer : Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nPositive integers indicated by x and y satisfy 3 1/x * y 2/5 = 13 3/4, the fractions being in their lowest terms, then x = ? and y = ?\n\n### Options:\nA. x = 4, y = 8\nB. x = 4, y = 4\nC. x = 2, y = 4\nD. x = 8, y = 4\nE. None of these\n\n### Answer:\n3 1/x * y 2/5 = 13\u00be\n=> (3x + 1) / x + (5y + 1) / 2 += 55 / 4\nonly choice (4) i.e x = 8 and y = 4 satisfies the given equation.\n3 (1/8) * 4 (2/5) = (25 / 8 ) * (22 / 5) = 55/4 = 13\u00be\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMike weighs twice as much as Mary. Mike's weight is 150% of Michelle's weight. Alan weighs 20% more than Charlie. Charlie weighs 160% of Mary's weight. Which of these 5 people weighs the highest?\n\n### Options:\nA. Mary\nB. Mike\nC. Michelle\nD. Alan\nE. Charlie\n\n### Answer:\nMary < Michelle < Mike\nCharlie < Alan\nLet x be Mary's weight.\nMike's weight is 2x and Alan's weight is 1.2*1.6x = 1.92x.\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe value of (8x10^7)(8x10^8) is closest to which of the following?\n\n### Options:\nA. 10^17\nB. 10^14\nC. 10^18\nD. 10^19\nE. 10^20\n\n### Answer:\nmultiplying these we get,\n64 x 10^7 x 10^8\n= 6.4 x 10^16\nwhich is closer to 10^17\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIts festive time and all big companies are offering the big discount especially on iPhone whose price is staggering Rs. 65,000.\nFollowing is the offer from the three major companies in India.\n: Amazon offers Flat 65% discount\n: Flipkart offers 10% discount over and over again.\n: Snapdeal offers RS 42,000 off.\nWhich is the best offer for you ?\n\n### Options:\nA. Flipkart\nB. Amazon\nC. Snapdeal\nD. All\nE. None of Above\n\n### Answer:\nA\nExplanation:\nFlipkart : 22664, Amazon: 22750 and Snapdeal: 23000\nSnapDeal discount :\n65000 - 42000 = 23000\nAmazon 65% discount :\n35/100 * 65000 = 22750\nFlipkart 10% recursive discount:\nAfter 1st 10% discount, Amount is 58500\nAfter 2nd 10% discount, Amount is 52650\nAfter 3rd 10% discount, Amount is 47385\nAfter 4th 10% discount, Amount is 42646.5\nAfter 5th 10% discount, Amount is 38381.85\nAfter 6th 10% discount, Amount is 34543.665\nAfter 7th 10% discount, Amount is 31089.2985\nAfter 8th 10% discount, Amount is 27980.36865\nAfter 9th 10% discount, Amount is 25182.331785\nAfter 10th 10% discount, Amount is 22664.0986065\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a, b, and c are consecutive odd positive integers and a < b < c, which of the following could be equal to c - b - a+4 ?\n\n### Options:\nA. -2\nB. 5\nC. -3\nD. -4\nE. -5\n\n### Answer:\nlet we put values. a=1, b=3, c=5\n5-3-1=1\n1+4 =5\nAnswer :B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the value of sin 75\u00b0 + sin 15\u00b0 = ?\n\n### Options:\nA. 0\nB. 1/2\nC. 1\nD. 3/2\nE. 2\n\n### Answer:\nsin A + sin B = 2 sin [ (A + B) / 2 ] cos [ (A - B) / 2 ]\n=2 sin [ (75 +15) / 2 ] cos [ (75 - 15) / 2 ]\n=2 sin90cos60=2*1*(1/2)=1\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how many ways can the letters of the word REPEATED be arranged?\n\n### Options:\nA. 1206\nB. 1348\nC. 6720\nD. 3000\nE. 3478\n\n### Answer:\nREPEATED has 8 words, but E is repeated three times. Thus ways = 8! / 3! = 6720 ways\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn the manufacture of a certain product, 7 percent of the units produced are defective and 4 percent of the defective units are shipped for sale. What percent of the units produced are defective units that are shipped for sale?\n\n### Options:\nA. 0.125%\nB. 0.28%\nC. 0.8%\nD. 1.25%\nE. 2.0%\n\n### Answer:\nPercent of defective produced = 7%\nPercent of the defective units that are shipped for sale = 4%\nPercent of units produced are defective units that are shipped for sale = (4/100)*(7/100)*100%\n= (28/10000)*100%\n= (28/100)%\n= .28 %\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nDavid and Rachel are getting married. The extended family wants to have its picture taken, but David's father is unwilling to stand next to Rachel's mother. How many options does the photographer have to arrange the 6 family members in a row for the picture?\n\n### Options:\nA. 9!\nB. 9\u00d78!\nC. 4x5!\nD. 10!/2!\nE. 10!\n\n### Answer:\nIn how many ways David's father and Rachel's mother can stand together? Consider them as one unit: {F, M}. So, we'd have 9 units {F, M}, 1, 2, 3, 4, which can be arranged in 9! ways. David's father and Rachel's mother within their unit can be arranged in 2! ways. Therefore, David's father and Rachel's mother can stand together in 5!*2! ways.\nTotal - Restriction =\n= 6! - 5!*2! =\n= 5!(6- 2!) =\n= 4*5!.\nAnswer: C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nDifference between the length &breadth of a rectangle is 23 m. If its perimeter is 206 m, then its area is?? We have: (l - b) = 23 and 2(l + b) = 206 or (l + b) = 103?\n\n### Options:\nA. 2400 m^2\nB. 2420 m^2\nC. 2520 m^2\nD. 2600 m^2\nE. 2630 m^2\n\n### Answer:\nSolving the two equations, we get: l = 63 and b = 40.\nArea = (l x b) = (63 x 40) m2 = 2520 m^2\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIt is required to fix a pipe such that water flowing through it at a speed of 7 metres per minute fills a tank of capacity 1760 cubic metres in 10 minutes. The inner radius of the pipe should be :\n\n### Options:\nA. \u221a2 m\nB. 2 m\nC. 1\u20442 m\nD. 2\u221a2 m\nE. None of these\n\n### Answer:\nLet inner radius of the pipe be r.\nThen, 1760 = 22\u20447 \u00d7 r2 \u00d7 7 \u00d7 10\nor r2=1760/22\u00d710=8\nor r = 2\u221a2 m\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain restaurant offers 6 different salads, 4 different main courses, and 7 different desserts. If customers choose one salad, one main course, and two different desserts for their meal, how many different meals are possible?\n\n### Options:\nA. 260\nB. 388\nC. 436\nD. 504\nE. 520\n\n### Answer:\nThe number of possible choices for desserts is 7C2 = 21\nThe number of possible meals is 6*4*21 = 504\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nGeorge has 8 candies in a bag, 3 of which are sweet while the other 5 are sour. He pulls out 2 of the candies simultaneously, and at random. What is the probability that exactly one of the candies he picked is sour?\n\n### Options:\nA. 2/8\nB. 3/15\nC. 2/28\nD. 3/5\nE. 15/28\n\n### Answer:\nThe probability is equal to the number of desired choices divided by the total number of possibilities.\nProbability = Favorable/Total\nTotal = 8C2 = 8*7/2 = 28\nFavorable:\nPick 1 sour out of 3 sour\nAND\npick 1 sweet out of 5 sweet.\n3C1*5C1=3*5=15\nP=15/28\nWhen you use combination method, it is picking all possible cases and the order doesn't matter. Whereas, upon choosing probability method to solve, order matters.\nThus,\nTotal Probability:\nProbability of choosing sour candy first AND Probability of choosing sweet candy\nOR\nProbability of choosing sweet candy first AND Probability of choosing sour candy\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 6th March, 2005 is Monday, what was the day of the week on 6th March, 2004?\n\n### Options:\nA. Sunday\nB. Saturday\nC. Tuesday\nD. Wednesday\nE. Monday\n\n### Answer:\nThe year 2004 is a leap year. So, it has 2 odd days.\nBut, Feb 2004 not included because we are calculating from March 2004 to March 2005. So it has 1 odd day only.\nThe day on 6th March, 2005 will be 1 day beyond the day on 6th March, 2004.\nGiven that, 6th March, 2005 is Monday.\n6th March, 2004 is Sunday (1 day before to 6th March, 2005).\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many odd 4-digit positive integers Q that are multiples of 5 can be formed without using the digit 3?\n\n### Options:\nA. 648\nB. 729\nC. 900\nD. 1296\nE. 3240\n\n### Answer:\nI choose A.\nPossible n\u00b0 of 1st digit: 8 (0 can't be the first number, or else it wouldn't have 4 digits. 3 is exlcuded)\nPossible n\u00b0 of 2nd digit: 9 (3 is excluded)\nPossible n\u00b0 of 3rd digit: 9 (3 is excluded)\nPossible n\u00b0 of 4th digit: 1 (a number is a multiple of 5 if it ends in 5 or 0, here we are asked for the odd numbers, hence the last digit can't be 0)\nSo, Q=8*9*9*1=648 (A)\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA father said to his son, \"I was as old as you are at the present at the time of your birth\". If the father's age is 44 years now, the son's age five years back was?\n\n### Options:\nA. 17years\nB. 18years\nC. 19years\nD. 20years\nE. 21years\n\n### Answer:\nLet the son's present age be x years. Then, (44 - x) = x\n2x = 44.\nx = 22.\nSon's age 5 years back (22 - 5) = 17 years.\nA)\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSet S consists of integers {2,3,4,5}. If two numbers are chosen from set S at random, what is the probability that the sum of 2 numbers is more than 5?\n\n### Options:\nA. 5/6\nB. 1/2\nC. 2/3\nD. 1/4\nE. 2/7\n\n### Answer:\nNumber of ways you can choose 2 from 4 = 4C2 = 6\nE = event of getting the 2 numbers is more than 5 = (2,4),(2,5),(3,4)(3,5),(4,5) = 5\nprobability = 5/6\nAnswer is A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nLast month, John rejected 0.7% of the products that he inspected and Jane rejected 0.8 percent of the products that she inspected. If total of 0.75 percent of the products produced last month were rejected, what fraction of the products did Jane inspect?\n\n### Options:\nA. 1/6\nB. 1/2\nC. 5/8\nD. 5/6\nE. 15/16\n\n### Answer:\nX - fraction of products Jane inspected\n(1 - X) - fraction of products John inspected\n0.8(X) + 0.7(1-X) = 0.75\n0.1X = 0.75 - 0.7\nX = 0.05/0.1\nX = 1/2\nTherefore the answer is B: 1/2.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA building is to be completed in 48 days. To meet the deadline 54 men were employed and were made to work for 10 hours a day. After 30 days 5/9th of the work was completed. How many more workers should be employed to meet the deadline if each workers are now made to work 8 hours a day?\n\n### Options:\nA. 36\nB. 55\nC. 40\nD. 45\nE. None of these\n\n### Answer:\nExplanation :\n54 men work 10 hours a day for 30 days and 5/9th of the work is completed.\nNow, let x workers be employed to work 8 hours a day for the rest 18 days to complete 4/9th of the work.\nM1D1T1W2 = M2D2T2W1\n54*30*10*4/9 = x*18*8*5/9\nx = 90\nHence, 36 more workers should be employed.\nAnswer : A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n12 members were present at a board meeting. Each member shake hands with all of the other members before and after the meeting .How many hand shakes were there?\n\n### Options:\nA. 237\nB. 268\nC. 132\nD. 827\nE. 261\n\n### Answer:\nExplanation:\nIn order to have a hand shake there must be two members. Therefore to select 2 out of 12 we have 12C2.\nThis happens twice that is before and after the meeting\nAnswer = 12C2 \u00d72 = 132\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nwhat is the units digit of the expression 17^7-2?\n\n### Options:\nA. 1\nB. 2\nC. 3\nD. 7\nE. 9\n\n### Answer:\n7^1=7\n7^2=49\n7^3=343\n7^4=1(last digit)\n7^5=7(last digit) and the cycle repeats after every 4 powers\nTherefore, last digit of 17^7=3\n3-2=1\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain sum is invested at simple interest at 18% p.a. for two years instead of investing at 12% p.a. for the same time period. Therefore the interest received is more by Rs. 840. Find the sum?\n\n### Options:\nA. 7000\nB. 7029\nC. 2778\nD. 2800\nE. 2791\n\n### Answer:\nLet the sum be Rs. x.\n(x * 18 * 2)/100 - (x * 12 * 2)/100 = 840 => 36x/100 - 24x/100 =840\n=> 12x/100 = 840 => x = 7000.Answer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe value of ((x \u2013 y)\u00b3 + (y - z)\u00b3 + (z \u2013 x)\u00b3)/(12 (x \u2013 y) (y \u2013 z) (z \u2013 x))\nis equal to :\n\n### Options:\nA. 0\nB. 1/12\nC. 1\nD. 1/4\nE. 1/3\n\n### Answer:\nSince (x \u2013 y) + (y \u2013 z) + (z \u2013 x) = 0,\nso (x \u2013 y)\u00b3 + (y \u2013 z)\u00b3 + (z \u2013 x)\u00b3= 3 (x \u2013 y) (y \u2013 z) (z \u2013 x).\n(3 (x \u2013 y) (y \u2013 z) (z \u2013 x))/(12(x \u2013 y) (y \u2013 z) (z \u2013 x)) = 1/4.\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf P is a prime number greater than 100, what is the remainder when P^2 is divided by 4.\n\n### Options:\nA. 4\nB. Cannot be determined\nC. 2\nD. 3\nE. 1\n\n### Answer:\ntake square of any prime number\nremainder will be 1\nAns E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThree numbers are in the ratio of 2 : 3 : 4 and their L.C.M. is 300. What is their H.C.F.?\n\n### Options:\nA. 20\nB. 25\nC. 30\nD. 60\nE. 75\n\n### Answer:\nLet the numbers be 2x, 3x, and 4x.\nLCM of 2x, 3x and 4x is 12x.\n12x = 300\nx = 25\nHCF of 2x, 3x and 4x = x = 25\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA can do a piece of work in 30 days. He works at it for 5 days and then B finishes it in 20 days. In what time can A and B together it?\n\n### Options:\nA. 13 1/7 days\nB. 13 1/3 days\nC. 13 1/8 days\nD. 13 8/3 days\nE. 12 1/3 days\n\n### Answer:\n5/30 + 20/x = 1\nx = 24\n1/30 + 1/24 = 3/40\n40/3 = 13 1/3 days\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe mall charges 40 cents for the first hour of parking and $3 for each additional hour until the customer reaches 4 hours, after that the parking fee is $2 per hour. If Mr.Park parked his car in the mall for 7 hours and 30 minutes, how much is he going to pay?\n\n### Options:\nA. $6.8\nB. $12.\nC. $13.\nD. $14.5.\nE. $15.\n\n### Answer:\n0.40+2*2+1*2+0.40= $6.8\nAnswer : $6.8\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a and b are each greater than x and y, which of the following must be true?\nI. ab > xy\nII. |a| + |b| > |x| + |y|\nIII.a + b > x + y\n\n### Options:\nA. I only\nB. II only\nC. I and II\nD. I and III\nE. I, II and III\n\n### Answer:\nI. a + b > x + y. Since a and b are each greater than x and y, then the sum of a and b will also be greater than the sum of x and y.\nII. ab > xy. Not necessarily true, consider a = b = 0 and x = y = -1 --> ab = 0 < 1 = xy.\nIII. |a| + |b| > |x| + |y|. Not necessarily true, consider a = b = 0 and x = y = -1 --> |a| + |b| = 0 < 2 = |x| + |y|.\nAnswer: B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf each participant of a chess tournament plays exactly one game with each of the remaining participants, then 171 games will be played during the tournament. Find the number of participants.\n\n### Options:\nA. 15\nB. 16\nC. 17\nD. 18\nE. 19\n\n### Answer:\nLet P be the number of participants.\nPC2 = 171\n(P)(P-1) = 342 = 19*18\nP = 19\nThe answer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 5^29 * 4^15 = 2 * 10^n, what is the value of n?\n\n### Options:\nA. 11\nB. 21\nC. 22\nD. 29\nE. 32\n\n### Answer:\nMy attempt:\n5^(29) * 4^(15) = 2*10^p\n5^(29) * 2 ^ (30) = 2 * (2*5)^p\n5^(29) * 2 ^ (30) = 2 * 2^(p) * 5^(p)\n5^(29) * 2 ^ (30) = 2^(p+1) * 5^(p)\n=> (p+1) = 30\n=> p = 29\nAnswer: 29 (D)\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJohn must arrange 2 different physics books and 3 different mathematics books on one shelf. If the first book on the leftmost side is a mathematics book and no physics book is next to another physics book. How many different arrangements exist?\n\n### Options:\nA. 6\nB. 12\nC. 36\nD. 120\nE. 720\n\n### Answer:\nFirst Place, is reserved for Math book. There are 3 Math books which can be arranged in3 ways\nRestriction comes into playhysics book cannot be together. Hence, the maththe physics books take alternate places\nSecond Place, Physics Book - in 3 ways\nThird Place, Math Book - in 2 ways (only 2 books left)\nFourth Place, Physics - in 2 ways (only 2 Physics book left)\nRest two places can be arranged in one way only.\nTotal no of ways = 3*2*2*1*1 = 12 ways\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the sides of a triangle are 30 cm, 28 cm and 12 cm, what is its area?\n\n### Options:\nA. 120 cm2\nB. 112 cm2\nC. 776 cm2\nD. 666 cm2\nE. 168 cm2\n\n### Answer:\nThe triangle with sides 30 cm, 28 cm and 12 cm is right angled, where the hypotenuse is 30 cm.\nArea of the triangle = 1/2 * 28 * 12 = 168 cm2\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a^5 \u2264 a, which of the following must be true?\nI. \u20131 \u2264 a \u2264 0\nII. a=0\nIII. 0 \u2264 a \u2264 1\n\n### Options:\nA. None of the above\nB. I only\nC. II only\nD. III only\nE. I and III only\n\n### Answer:\nThe trick here is more on the answer choices.\nLook at I II and III. all are right (pick out some numbers).\nTherefore I was totally confused because non of the answers had the right answer (I II and III)\nI finally chose D, but hesitate between A and D quite a long time...\nThis is a tricky tricky question, since it takes into consideration that the answers are correct but they do not cover all the POSSIBLE answers.\nTherefore it is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA can do a piece of work in 20 days. B in 15 days A and C in 12 days. In how many days can A finish the work if he is assisted by B on one day and C on the next, alternately?\n\n### Options:\nA. 2 days\nB. 5 days\nC. 8 days\nD. 7 days\nE. 9 days\n\n### Answer:\nC\n8 days\nA + B = 1/20 + 1/15 = 7/60\nA + C = 1/20 + 1/12 = 8/60\n7/60 + 8/60 = 15/60 = 1/4\n4 days * 2 = 8 days\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA shopkeeper loses 15%,if an article is sold for Rs. 102. What should be the selling price of the article to gain 20%?\n\n### Options:\nA. 128\nB. 144\nC. 176\nD. 186\nE. 111\n\n### Answer:\nExplanation:\nGiven that SP = Rs. 102 and loss = 15%\nCP = [100(SP)]/(100 - l%) = (100 * 102)/85 = 20 * 6 = Rs. 120.\nTo get 20% profit, New SP = [(100 + p%)CP]/100 = (120 * 120)/100 = Rs. 144\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe letters of the word 'SURITE' are written in all possible orders and these words are written in alphabetical order. Then what is the rank of the word 'SURITI'\n\n### Options:\nA. - 236\nB. - 245\nC. - 307\nD. - 315\nE. - 475\n\n### Answer:\nTotal Number of Words = 6! = 720 [(number of characters)/(repeating group )!]\nAfter S, we have T and U.\nNumber of words starting with T = 5! = 120\nNumber of words starting with U = 5! = 120\nSo any word starting with S will have rank < 720 - 120(for Us) - 120(for Ts) = 480\nOnly option A < 480, so Answer is E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMachine A and machine B are each used to manufacture 880 sprockets. It takes machine A 10 hours longer to produce 880 sprockets than machine B. Machine B produces 10% more sprockets per hour than machine A. How many sprockets per hour does machineAproduce?\n\n### Options:\nA. 6\nB. 6.6\nC. 8.8\nD. 100\nE. 110\n\n### Answer:\ntime taken by B = t\ntime taken by A = t+10\nqty produced by A = q\nqty produced by B = 1.1 q\nfor B: t(1.1q) =880\nqt=800\nfor A: (t+10)(q) = 880\nqt+10q=880\n800+10q=880\nq=8\nso A can produce 8/hour.\nthen B can produce = 8(1.1)=8.8/hour.\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf P(A) = 2/15, P(B) = 4/15, and P(A \u00e2\u02c6\u00aa B) = 12/15 Find P(B|A)\n\n### Options:\nA. 1/2\nB. 2/3\nC. 3/2\nD. 4/5\nE. 6\n\n### Answer:\nP(B|A) = P(A \u00e2\u02c6\u00aa B)/P(A)\nP(B|A) = (12/15)/(2/15) = 6.\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA cashier mentally reversed the digits of one customer's correct amount of change and thus gave the customer an incorrect amount of change. If the cash register contained 27 cents more than it should have as a result of this error, which of the following could have been the correct amount of change in cents?\n\n### Options:\nA. 14\nB. 45\nC. 54\nD. 65\nE. 52\n\n### Answer:\nJust check the answers and reverse the numbers until you get 27.\n52 - 25 = 27\nAnswer E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAn amount of Rs. 100000 is invested in two types of shares. The first yields an interest of 9% p.a and the second, 11% p.a. If the total interest at the end of one year is 9 2/3 %, then the amount invested in each share was?\n\n### Options:\nA. 23777\nB. 35000\nC. 29977\nD. 26777\nE. 19871\n\n### Answer:\nLet the sum invested at 9% be Rs. x and that invested at 11% be Rs. (100000 - x). Then,\n(x * 9 * 1)/100 + [(100000 - x) * 11 * 1]/100 = (100000 * 29/3 * 1/100)\n(9x + 1100000 - 11x)/100 = 29000/3 = 9700\n(9x + 1100000 - 11x) = 970000\nx = 65000\nSum invested at 9% = Rs. 65000\nSum invested at 11% = Rs. (100000 - 65000) = Rs. 35000.\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHal bought walnuts at 5 for $1 and apples at 4 for $1.He spent a total of $19.50 . He sells both at 20 for $5 and as a result gains $3 .How many walnuts did Hal buy ?\n\n### Options:\nA. 50\nB. 45\nC. 60\nD. 80\nE. 55\n\n### Answer:\nLet's start with the concrete information:\nHe buys everything for $19.50 and earns $3 after selling so he sells everything for $22.50 (= 2250 cents).\nHe sells each item for 5/20 = 25 cents so in all he sells 2250/25 = 90 items\nCost of each walnut = 1/5 = $.2 = 20 cents\nCost of each apple = 1/4 = $.25 = 25 cents\nNow we have one equation to solve:\n20*w + 25*(90 - w) = 1950 (w is the number of walnuts he buys)\n4w + 5(90 - w) = 390\nw = 60\nAnswer (C)\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA survey was sent to 80 customers, 9 of whom responded. Then the survey was redesigned and sent to another 63 customers, 12 of whom responded. By approximately what percent did the response rate increase from the original survey to the redesigned survey?\n\n### Options:\nA. 2%\nB. 5%\nC. 14%\nD. 28%\nE. 69%\n\n### Answer:\nRate of first survey = 9/80\nRate of second survey = 12/63\n% Response rate increase (12/63-9/80)/(9/80) = 69%\nAnswer is E = 69%\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the average marks of three batches of 55, 60 and 45 students respectively is 50, 55, 60, then the\naverage marks of all the students is\n\n### Options:\nA. 54.48\nB. 54.68\nC. 54.6\nD. 54.58\nE. None of these\n\n### Answer:\nExplanation:\n(55\u00d750)+(60\u00d755)+(45\u00d760)55+60+45\n8750160=54.68\nAnswer: Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFrom a pack of cards two cards are drawn one after the other, with replacement. The probability that the first is a red card and the second is a king is ?\n\n### Options:\nA. 1/26\nB. 1/07\nC. 1/22\nD. 1/29\nE. 1/21\n\n### Answer:\nLet E1 be the event of drawing a red card.\nLet E2 be the event of drawing a king .\nP(E1 \u2229 E2) = P(E1) . P(E2)\n(As E1 and E2 are independent)\n= 1/2 * 1/13 = 1/26\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAn bus covers a certain distance at a speed of 140 kmph in 5 hours. To cover the samedistance in 1hr, it must travel at a speed of?\n\n### Options:\nA. 520 km/hr\nB. 640 km/hr\nC. 656 km/hr\nD. 731 km/hr\nE. 700 km/hr\n\n### Answer:\nDistance = (140 x 5) = 700 km.\nRequired speed = 700 km/hr.\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe current of a stream at 1 kmph. A motor boat goes 35 km upstream and back to the starting point in 12 hours. The speed of the motor boat in still water is?\n\n### Options:\nA. 6\nB. 9\nC. 8\nD. 3\nE. 1\n\n### Answer:\nS = 1\nM = x\nDS = x + 1\nUS = x - 1\n35/(x + 1) + 35/(x - 1) = 12\nx = 6\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf two numbers are in the ratio 2:3. If 10 is added to both of the numbers then the ratio becomes 3:4 then find the smallest number?\n\n### Options:\nA. 10\nB. 20\nC. 24\nD. 26\nE. 29\n\n### Answer:\n2:3\n2x + 10 : 3x + 10 = 3 : 4\n4[2x + 10] = 3[3x + 10]\n8x + 40 = 9x + 30\n9x - 8x = 40 - 30\nx = 10\nThen smallest number is = 2\n2x = 20\nShort cut method:\na:b = 2:3\nc:d = 3:4\n1.Cross multiplication with both ratios\na * d ~ b * c = 2 * 4 ~ 3 * 3 = 8 ~ 9 = 1\n2. If 10 is added both the number means 10 * 3 = 30 and 10 * 4 = 40,\nThen 30 ~ 40 = 10\n===> 1 -----> 10\n===> 2 -----> 20\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train overtakes 2 girls who are walking inthe opposite direction in which the train is going at the rate of 3 km/hour & 6km/hour and passes them completely in 36sec & 30 sec respectively. Find the length of the train is?\n\n### Options:\nA. 120 m\nB. 130 m\nC. 150 m\nD. 200 m\nE. 250 m\n\n### Answer:\nLet the length of the train e x meter, and let the speed of train be y km/h, then\n\\inline x=\\left ( y+3 \\right )\\frac{5}{18}\\times 36 ........(1)\nand \\inline x=\\left ( y+6\\right )\\frac{5}{18}\\times 30 ........(2)\nFrom eq (1) and (2), we get\n\\inline (y+3)\\times 36 = ( y+6)\\times 30\ny = 12 km/h\n\\inline \\therefore \\inline x=(y+3)\\times \\frac{5}{18}\\times 36\nx= 150 m\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a man reduces the selling price of a fan from Rs. 420 to Rs. 402, his loss increases by 3%. The cost price of the fan is :\n\n### Options:\nA. Rs.600\nB. Rs.650\nC. Rs.475\nD. Rs.525\nE. None of these\n\n### Answer:\nExplanation :\nSolution: let C.P. be Rs. X. then, 3% of x = (420-402) =18 => 3x/100 = 18 => x =Rs.600.\nAnswer : A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA pump can fill a tank with a water in 2 hours. Because of a leak, it took 3 hours to fill the tank. The leak can drain all the water of the full tank in how many hours?\n\n### Options:\nA. 2\nB. 3\nC. 4\nD. 5\nE. 6\n\n### Answer:\nThe rate of the pump + leak = 1/3\n1/2 - leak's rate = 1/3\nleak's rate = 1/2 - 1/3 = 1/6\nThe leak will empty the tank in 6 hours.\nThe answer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA and B started a partnership business investing some amount in the ratio of 4 : 5. C joined then after six months with an amount equal to that of B. In what proportion should the profit at the end of one year be distributed among A, B and C?\n\n### Options:\nA. 4 : 9 : 8\nB. 5 : 7 : 4\nC. 6 : 10 : 5\nD. 7 : 9: 4\nE. 8 : 10 : 5\n\n### Answer:\nLet the initial investments of A and B be 4x and 5x.\nA : B : C = (4x x 12) : (5x x 12) : (5x x 6) = 48 : 60 : 30\n= 8 : 10 : 5.\nANSWER :E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nToday John, who is 38 years old, and his daughter, who is 13 years old, celebrate their birthdays. How many years will pass before John\u2019s age is twice his daughter\u2019s age?\n\n### Options:\nA. 13\nB. 14\nC. 15\nD. 16\nE. 12\n\n### Answer:\nForget conventional ways of solving math questions. In PS, IVY approach is the easiest and quickest way to find the answer.\nAfter x years passes John\u2019s age will be (38+x) years old, and his daughter\u2019s age will be (13+x) years old. Since the John\u2019s age is twice his daughter\u2019s age (38+x)= 2 * (13+x) --->\n38+x=26+2x ---> x= 12\nThe answer is (E).\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOn my sister's birthday, she was 132 cm in height, having grown 10% since the year before. How tall was she the previous year?\n\n### Options:\nA. 130 cm\nB. 126 cm\nC. 120 cm\nD. 116 cm\nE. 112 cm\n\n### Answer:\nLet the previous year's height be x.\n1.1x = 132\nx = 120\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA seller has 1000kg of rice part of which he sells at 8% profit and the rest at 18% profit. He gains 14%. The quantity sold at 18% profit is?\n\n### Options:\nA. 200 kg\nB. 300 kg\nC. 400 kg\nD. 600 kg\nE. 800 kg\n\n### Answer:\nBy rule of alligation,\nProfit% by selling 1st part Profit% by selling 2nd part\n8 18\nNet % profit\n14\n18-14=4 14-8=6\n=> Quantity of part1 : Quantity of part2 = 4 : 6 = 2 : 3\nTotal quantity is given as 1000 kg. So quantity of part2 (quantity sold at 18% profit)\n=1000\u00d735\n= 600 kg\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe number 0.5 is how much greater than 1/3 ?\n\n### Options:\nA. 1/6\nB. 2/10\nC. 1/50\nD. 1/500\nE. 2/500\n\n### Answer:\nlet x be the difference\nthen\n.5-1/3=x\n5/10-1/3=x\nx=1/6\nans A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?\n\n### Options:\nA. 277\nB. 266\nC. 288\nD. 150\nE. 332\n\n### Answer:\nSpeed=(60 * 5/18) m/sec = (50/3) m/sec Length of the train = (Speed x Time) = (50/3 * 9) m\n= 150 m\n.\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSuresh started a business with Rs.20,000. Kiran joined him after 4 months with Rs.30,000. After 2 more months, Suresh withdrew Rs.5,000 of his capital and 2 more months later, Kiran brought in Rs.20,000 more. What should be the ratio in which they should share their profits at the end of the year?\n\n### Options:\nA. 17:12\nB. 12:17\nC. 21:32\nD. 32:21\nE. 17:32\n\n### Answer:\nHere capital is not the same.\nSuresh invested 20000 for initial 6 months and 15000 for the next 6 months. Hence his term of ratio\n=(20000\u00d76+15000\u00d76)\nKiran invested Rs.30000 for 4 months and Rs.50000 for next 4 months. Hence his term of ratio\n=(30000\u00d74+50000\u00d74)\nSuresh : Kiran\n=(20000\u00d76+15000\u00d76) :(30000\u00d74+50000\u00d74)\n=(20\u00d76+15\u00d76):(30\u00d74+50\u00d74)=(20\u00d73+15\u00d73):(30\u00d72:50\u00d72)\n=105:160=21:32\nAnswer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA wire in the form of a circle of radius 3.5 m is bent in the form of a rectangule, whose length and breadth are in the ratio of 6 : 5. What is the area of the rectangle?\n\n### Options:\nA. 19 cm2\nB. 30 cm2\nC. 17 cm2\nD. 18 cm2\nE. 12 cm2\n\n### Answer:\nThe circumference of the circle is equal to the permeter of the rectangle.\nLet l = 6x and b = 5x 2(6x + 5x) = 2 * 22/7 * 3.5\n=> x = 1\nTherefore l = 6 cm and b = 5 cm Area of the rectangle = 6 * 5\n= 30 cm2\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe length of a rectangular plot is thrice its breadth. If the area of the rectangular plot is 867 sq m, then what is the breadth of the rectangular plot?\n\n### Options:\nA. 12\nB. 17\nC. 10\nD. 12\nE. 19\n\n### Answer:\nLet the breadth of the plot be b m.\nLength of the plot = 3 b m\n(3b)(b) = 867\n3b2 = 867\nb2 = 289 = 172 (b > 0)\nb = 17 m.\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are 4 more women than there are men on a local co-ed softball team. If there are a total of 20 players on the team, what is the ratio of men to women?\n\n### Options:\nA. 10/16\nB. 6/16\nC. 4/16\nD. 6/10\nE. 8/12\n\n### Answer:\nw = m+4\nw+m = 20\nm+4+m = 20\n2m = 16\nm = 8\nw = 12\nratio:8:12\nAns: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nEfficiency with which Adam and Mike work is in the ratio 2:1. How much time will they, working together, take to complete a job which Adam alone could have done in 10 days?\n\n### Options:\nA. 15 days\nB. 20 days\nC. 6 days\nD. 6 1\u00e2\u0081\u201e3 days\nE. None of these\n\n### Answer:\nRatio of times taken by Adam and Mike = 100 : 200 = 1 : 2.\nSuppose Mike takes x days to do the work.\nThen, 1 : 2 : : 10 : x \u00e2\u2021\u2019 x = (10\u00c3\u20142)/1 \u00e2\u2021\u2019 x = 20\nAdam\u00e2\u20ac\u2122s 1 day\u00e2\u20ac\u2122s work = 1\u00e2\u0081\u201e10; Mike\u00e2\u20ac\u2122s 1 days work = 1\u00e2\u0081\u201e20\n(Adam + Mike)\u00e2\u20ac\u2122s 1 day\u00e2\u20ac\u2122s work = (1\u00e2\u0081\u201e10 + 1\u00e2\u0081\u201e20) = 3\u00e2\u0081\u201e20\n\u00e2\u02c6\u00b4 Adam and Mike together can complete the job in 20\u00e2\u0081\u201e3 days or 6 2\u00e2\u0081\u201e3 days.\nAnswer E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo trains of equal length are running on parallel lines in the same directions at 46km/hr. and 36km/hr. The faster trains pass the slower train in 72 seconds. The length of each train is:\n\n### Options:\nA. 82m\nB. 50m\nC. 72m\nD. 100m\nE. None of these\n\n### Answer:\nExplanation:\nThe relative speed of train is 46-36 = 10 Km/hr = (10 X 5) / 18 = 25/9 m/s10\u00d7518=259m/s\nIn 72 secs the total distance traveled is 72x25/9 = 200 m.\nTherefore the length of each train is = 200/2 = 100 m.\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train running at a speed of 60 kmph crosses a pole in 6 seconds.What is the length of the train?\n\n### Options:\nA. 120 m\nB. 180 m\nC. 100 m\nD. 150 m\nE. 160 m\n\n### Answer:\n60 kmph=50/3 m/sec\n50/3*6=100 m\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe ratio of ducks and frogs in a pond is 37 : 39 respectively. The average number of ducks and frogs in the pond is 132. What is the number of frogs in the pond ?\n\n### Options:\nA. 148\nB. 134\nC. 156\nD. 144\nE. None\n\n### Answer:\nSolution:\nRatio of Ducks and Frogs in Pond,\n= 37 : 39.\nAverage of Ducks and Frogs in Pond,\n= 132.\nSo, total number of Ducks and Frogs in the Pond,\n= 2* 132 = 262.\nTherefore,\nNumber of Frogs, = (262*39)/76 = 134.\nAnswer: Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nExcluding stoppages, the speed of a bus is 80 km/hr and including stoppages, it is 70 km/hr. For how many minutes does the bus stop per hour?\n\n### Options:\nA. 11 min\nB. 10 min\nC. 8 min\nD. 6 min\nE. 5 min\n\n### Answer:\nDue to stoppages, it covers 10 km less.\nTime taken to cover 10 km = 10/80 * 60\n= 8 min.\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n1,3,5,7,9,..50 find term of sequnce\n\n### Options:\nA. 1234\nB. 1456\nC. 1456\nD. 1678\nE. 2500\n\n### Answer:\nThis is an arithmetic progression, and we can write down\na=1a=1 ,d=2d=2 , n=50n=50 .\nWe now use the formula, so that\nSn=12n(2a+(n\u22121)l)Sn=12n(2a+(n\u22121)l)\nS50=12\u00d750\u00d7(2\u00d71+(50\u22121)\u00d72)S50=12\u00d750\u00d7(2\u00d71+(50\u22121)\u00d72)\n=25\u00d7(2+49\u00d72)=25\u00d7(2+49\u00d72)\n=25\u00d7(2+98)=25\u00d7(2+98)\n=2500=2500 .\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nInteger X represents the product of all integers between 1 to 24 (inclusive). The smallest prime factor of (x+1) must be\n\n### Options:\nA. Between 1 to 10\nB. Between 11 to 15\nC. Between 15 to 20\nD. Between 20 to 25\nE. Greater than 24\n\n### Answer:\nAnswer = E = Greater than 24\nThis problem is asking smallest prime factor of (24!+1)\n25! already have there prime factors 2,3,5,7,11,13.......... so on upto 23 (1 cannot be considered prime factor)\nJust adding 1 to 24! will remove all the factors stated above;\nso the smallest possible prime factor has to be greater than 24\nAnswer = E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nYou have been given a physical balance and 7 weights of 52, 50, 48, 44, 45, 46 and 78 kgs. Keeping weights on one pan and object on the other, what is the maximum you can weigh less than 183 kgs.\n\n### Options:\nA. 180\nB. 181\nC. 182\nD. 178\nE. 168\n\n### Answer:\nadd the max weights\n52+50+78=180\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThree competing juice makers conducted a blind taste test with mall shoppers. The shoppers could choose to taste any number of the three brands of juices but had to select at least one juice that they liked. If 100 shoppers liked brand J, 200 shoppers liked brand K, 700 shoppers liked brand L, 250 shoppers liked exactly 2 juices, and 50 shoppers liked all three juices, how many shoppers took the taste test?\n\n### Options:\nA. 1,300\nB. 1,000\nC. 900\nD. 700\nE. 650\n\n### Answer:\nGiven: Atleast 1 juice was liked by the participants. --> Neither = 0\nAssume, I -->No overlap between the sets\nII --> Overlap between 2 sets\nIII --> Overlap between 3 sets\nI + 2*(II) + 3*(III) = 100 + 200 + 700\nI + 2*(250) + 3*(50) = 1000\nI = 350\nTotal number of shoppers who took the taste test = I + II + III = 350 + 250 + 50 = 650\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAn gun can take a maximum of four shotsat an enemyplane moving away from it. The probability of hitting the plane at the 1st, 2nd, third and 4th shots are 1.4, 1.3, 1.2 & 1.1 respectively. What is the probability that the plane is hit when all the four shots are fired?\n\n### Options:\nA. 0.6976\nB. 0.7893\nC. 0.8212\nD. 0.7541\nE. 0.9847\n\n### Answer:\nRequired probability:\n=(0.4\u00d70.7\u00d70.8\u00d70.9)+(0.6\u00d70.3\u00d70.8\u00d70.9)+(0.6\u00d70.7\u00d70.2\u00d70.9)+(0.6\u00d70.7\u00d70.8\u00d70.1)+(0.4\u00d70.3\u00d70.8\u00d70.9)+(0.4\u00d70.7\u00d70.2\u00d70.9)+(0.4\u00d70.7\u00d70.8\u00d70.1)+(0.6\u00d70.3\u00d70.2\u00d70.9)+(0.6\u00d70.3\u00d70.8\u00d70.1)+(0.6\u00d70.7\u00d70.2\u00d70.1)+(0.4\u00d70.3\u00d70.2\u00d70.9)+(0.6\u00d70.3\u00d70.2\u00d70.1)+(0.4\u00d70.3\u00d70.8\u00d70.1)+(0.4\u00d70.7\u00d70.2\u00d70.1)+(0.4\u00d70.3\u00d70.2\u00d70.1)=(0.4\u00d70.7\u00d70.8\u00d70.9)+(0.6\u00d70.3\u00d70.8\u00d70.9)+(0.6\u00d70.7\u00d70.2\u00d70.9)+(0.6\u00d70.7\u00d70.8\u00d70.1)+(0.4\u00d70.3\u00d70.8\u00d70.9)+(0.4\u00d70.7\u00d70.2\u00d70.9)+(0.4\u00d70.7\u00d70.8\u00d70.1)+(0.6\u00d70.3\u00d70.2\u00d70.9)+(0.6\u00d70.3\u00d70.8\u00d70.1)+(0.6\u00d70.7\u00d70.2\u00d70.1)+(0.4\u00d70.3\u00d70.2\u00d70.9)+(0.6\u00d70.3\u00d70.2\u00d70.1)+(0.4\u00d70.3\u00d70.8\u00d70.1)+(0.4\u00d70.7\u00d70.2\u00d70.1)+(0.4\u00d70.3\u00d70.2\u00d70.1)\n=0.2016+0.1296+0.756+0.336+0.864+0.504+0.224+0.324+0.144+0.0084+0.0216+0.0036+0.0096+0.0056+0.002=0.2016+0.1296+0.756+0.336+0.864+0.504+0.224+0.324+0.144+0.0084+0.0216+0.0036+0.0096+0.0056+0.002\n=0.6976=0.6976\nEdit: Thank you Vaibhav for providing an alternative method.\nAlternate Method:\nprobability that the plane is hit when all the four shots are fired,\nP=1\u2212probability of not hitting the targetP=1\u2212probability of not hitting the target\n=1\u2212(0.6\u00d70.7\u00d70.8\u00d70.9)=1\u2212(0.6\u00d70.7\u00d70.8\u00d70.9)\n=1\u22120.3024=1\u22120.3024\n=0.6976\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the remainder when 6990990900032 is divided by 32 ?\n\n### Options:\nA. 5\nB. 0\nC. 4\nD. 2\nE. 3\n\n### Answer:\nThough i was unaware of the divisibility test for 32 but i guessed the pattern!!\ndivisibility rule for 4- last two digits must be divisible by 4\ndivisibility rule for 8- last three digits must be divisible by 8\nsimilarly, divisibility rule for 32 - last five digits must be divisible by 32\nHence, Ans B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf x and y are positive integers and 12x=21y what is the least possible value of xy?\n\n### Options:\nA. 9\nB. 28\nC. 63\nD. 84\nE. 252\n\n### Answer:\n12x=21y\n=> x/y = 7/4\n=> 4x=7y\n4(3)=7(3) => x*y=9\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train running at the speed of 60 km/hr crosses a pole in 12 seconds. What is the length of the train?\n\n### Options:\nA. 186 m\nB. 176 m\nC. 300 m\nD. 150 m\nE. 200 m\n\n### Answer:\nSpeed=(60 * 5/18) m/sec = (50/3) m/sec Length of the train\n= (Speed x Time) = (50/3 * 12) m\n= 200 m.\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAt a restaurant, glasses are stored in two different-sized boxes. One box contains 12 glasses, and the other contains 16 glasses. If the average number of glasses per box is 15, and there are 16 more of the larger boxes, what is the total number of glasses E at the restaurant? (Assume that all boxes are filled to capacity.)\n\n### Options:\nA. 96\nB. 240\nC. E=256\nD. E=384\nE. E=480\n\n### Answer:\nMost Test Takers would recognize thesystemof equations in this prompt and just do algebra to get to the solution (and that's fine). The wording of the prompt and the 'spread' of the answer choices actually provide an interesting 'brute force' shortcut that you can take advantage of to eliminate the 4 wrong answers....\nWe're told that there are 2 types of boxes: those that hold 12 glasses and those that hold 16 glasses. Since the AVERAGE number of boxes is 15, we know that there MUST be at least some of each. We're also told that that there are 16 MORE of the larger boxes.\nThis means, at the minimum, we have...\n1 small box and 17 large boxes = 1(12) + 17(16) = 12 + 272 = 284 glasses at the MINIMUM\nSince the question asks for the total number of glasses, we can now eliminate Answers A, B and C....\nThe difference in the number of boxes MUST be 16 though, so we could have....\n2 small boxes and 18 large boxes\n3 small boxes and 19 large boxes\netc.\nWith every additional small box + large box that we add, we add 12+16= 28 MORE glasses. Thus, we can justadd 28suntil we hit the correct answer....\n284+28 = 312\n312+28 = 340\n340+28 = 368\n368+28 = 396\nAt this point, we've 'gone past' Answer D, so the correct answer MUST be Answer E.....But here's the proof....\n396+28 = 424\n424+28 = 452\n452+28 = 480\nFinal Answer:\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA local bank that has 12 branches uses a two-digit code to represent each of its branches. The same integer can be used for both digits of a code, and a pair of two-digit numbers that are the reverse of each other (such as 17 and 71) are considered as two separate codes. What is the fewest number of different integers required for the 12 codes?\n\n### Options:\nA. 3\nB. 4\nC. 12 ( 2 integers 4 codes)\nD. 6\nE. 7\n\n### Answer:\nPick any two integer.\nIntegers: 12\nCode: 11, 12, 21, 22 = 4 Codes\nAdd one more integer: 3\n13, 31, 33, 23, 32 = 5 Codes\nAdd one more integer: 4\n44, 14, 41, 24, 42, 34, 43 = 7 Codes\nTotal = 16 Codes. Enough. Answer: C\n4 integers create 12 codes.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nCars emerging from a motorway arrive at a junction that splits the road into two separate lanes. The number of cars per hour that continue in either lane is constant. If 7 cars per hour were diverted from the left lane to the right lane, the number of cars entering the right lane per hour would be twice as big as the number of cars entering the left lane per hour. Alternatively, if 7 cars per hour were diverted from the right lane to the left lane, the number of cars entering the left lane per hour would be four times as great as the number of cars entering the right lane per hour. How many cars enter the left lane per hour?\n\n### Options:\nA. 21\nB. 18\nC. 17\nD. 19\nE. 28\n\n### Answer:\nas per question 7 cars diverted from left lane to right lane. Thus we get equation R+7=2(L-7)\nas per question 7 cars diverted from right lane to left lane .thus we get equation L+7=4(R-7)\nby solving two equation i.e R +7 =2L-14 OR. R =2L -21 AND L+7= 4R -28 OR L= 4R -35\nBY SOLVING WE GET L= 4( 2L -21) -35 OR L= 8L -84-35 OR 119 =7L THUS L =17\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the fraction which has the same ratio to 2/6 that 3/4 has to 1/2\n\n### Options:\nA. 1/2\nB. 2/5\nC. 6/8\nD. 9/4\nE. 7/5\n\n### Answer:\nP : 2/6 = 3/4 : 1/2\nAs the product of the means is equal to the product of the extremes.\nP*1/2 = 2/6 * 3/4\nP*1/2 = 6/24\nP = 1/2 => P = 1/2\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWorkers at a campaign office have 2000 fliers to send out. If they send out 1/10 of them in the morning and 1/4 of the remaining ones out during the afternoon, how many are left for the next day?\n\n### Options:\nA. 300\nB. 1350\nC. 1100\nD. 1200\nE. 1900\n\n### Answer:\n(1/10)*2000 = 200\nRemaining = 2000-200 = 1800\n(1/4) of remaining = (1/4)*1800 = 450\nRemaining now = 1800-450 = 1350\nAnswer: Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\na batmans runs just before the last match of the season adds up750 in his last two innings his scores only 6 scores and his avg drop by 2 fond his final avg of the season?\n\n### Options:\nA. 21\nB. 22\nC. 23\nD. 24\nE. 25\n\n### Answer:\nFormula for this question is\n6 = 2*avg-2(N+2)\n6 = 2*(750/n) - 2(n+2)\nn*n+5n-750 = 0\nn= 25\nso final ans 23\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe speed of a train is 70 kmph excluding stoppages and including stoppages it is 63 kmph. Of how many minutes does the train stop per hour?\n\n### Options:\nA. 3\nB. 6\nC. 7\nD. 9\nE. 14\n\n### Answer:\nExplanation:\nT = 7/70 * 60 = 6\nAnswer: Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAn bus covers a certain distance at a speed of 240 kmph in 5 hours. To cover the samedistance in 1hr, it must travel at a speed of?\n\n### Options:\nA. 520 km/hr\nB. 640 km/hr\nC. 656 km/hr\nD. 731 km/hr\nE. 720 km/hr\n\n### Answer:\nDistance = (240 x 5) = 1200 km.\nSpeed = Distance/Time\nSpeed = 1200/(5/3) km/hr. [We can write 1 hours as 5/3 hours]\nRequired speed = 1200 x\t3\tkm/hr\t= 720 km/hr.\n5\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe cash realised on selling a 14% stock is Rs.106.25, brokerage being 1/4% is\n\n### Options:\nA. 123\nB. 106\nC. 100\nD. 156\nE. 240\n\n### Answer:\nExplanation:\nCash realised= Rs. (106.25 - 0.25)\n= Rs. 106.\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo numbers are in the ratio 3:5. If 9 be subtracted from each, they are in the ratio of 9:17. The first number is?\n\n### Options:\nA. 36\nB. 67\nC. 87\nD. 56\nE. 51\n\n### Answer:\n(3x-9):(5x-9)\n= 9:17\nx = 12 => 3x\n= 36\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat will come in place of the x in the following Number series? 46080, 3840, 384, 48, 8, 2, x\n\n### Options:\nA. 1\nB. 3\nC. 5\nD. 6\nE. 7\n\n### Answer:\n46080 /12 = 3840\n3840 /10 = 384\n384 /8 = 48\n48 /6 = 8\n8/4 = 2\n2 /2 = 1\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many bricks, each measuring 25 cm x 11.25 cm x 6 cm, will be needed to build a wall of 8.5 m x 6 m x 22.5 cm?\n\n### Options:\nA. 6400\nB. 6410\nC. 6440\nD. 6500\nE. 6800\n\n### Answer:\nNumber of bricks = Volume of Wall/Volume of Bricks\n=850x600x22.5/25x11.25x6= = 6800\nanswer :E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n2 chairs and 1 table cost $110. 4 chairs and 1 table cost $166. How much does one chair cost?\n\n### Options:\nA. 26\nB. 56\nC. 110\nD. 28\nE. 54\n\n### Answer:\nLet the cost of 1 chair = x, let the cost of 1 table = y\n2x + y = 110\ny = 110 - 2x\nAgain,\n4x + y = 166\n4x + (110 - 2x) = 166\n4x + 110 - 2x = 166\n2x + 110 = 166\n2x = 56\nx = 28\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSekar started a business investing Rs.25,000 in 1999. In 2000, he invested an additional amount of Rs.10,000 and Rajeev joined him with an amount of Rs.35,000. In 2001, Sekar invested another additional amount of Rs.10,000 and Jatin joined them with an amount of Rs.35,000. What will be Rajeev's share in the profit of Rs.2,40,000 earned at the end of 3 years from the start of the business in 1999?\n\n### Options:\nA. Rs.45,000\nB. Rs.80,000\nC. Rs.70,000\nD. Rs.75,000\nE. none\n\n### Answer:\nSolution\nSekar:Rajeev:Jatin=\t(25000\u00d712+35000\u00d712+45000\u00d712):(35000\u00d724) : (35000\u00d712)\n= 1260000 : 840000 : 420000\n= 3 : 2 : 1.\nRajeev's share\t=Rs.(240000\u00d72/6)\n= Rs.80000.\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe list price of an article is Rs.65. A customer pays Rs.56.16 for it. He was given two successive discounts, one of them being 10%. The other discount is?\n\n### Options:\nA. 8%\nB. 4%\nC. 6%\nD. 3%\nE. 1%\n\n### Answer:\n65*(90/100)*((100-x)/100) = 56.16\nx = 4%\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a group of 24 students, each student is registered for at least one of three classes \u2013 History, Math and English. 15 students are registered for History, 15 students are registered for Math, and 20 students are registered for English. If only three students are registered for all three classes, how many students are registered for exactly two classes?\n\n### Options:\nA. 13\nB. 10\nC. 9\nD. 20\nE. 7\n\n### Answer:\nEach student is registered forat least one of three classesmeans thatthere are no students who are registered for none of the classes.\nTotal = {people in group A} + {people in group B} + {people in group C} - {people in exactly 2 groups} - 2*{people in exactly 3 groups} + {people in none of the groups}:\n24 = 15 + 15 + 20 - {people in exactly 2 groups} - 2*3 + 0-->{people in exactly 2 groups}=20\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTough and Tricky questions: Combinations.\nFive contestants representing four different countries advance to the finals of a fencing championship. Assuming all competitors have an equal chance of winning, how many possibilities are there with respect to how a first-place and second-place medal can be awarded?\n\n### Options:\nA. 6\nB. 7\nC. 12\nD. 15\nE. 24\n\n### Answer:\nFour contestants representing four different countries advance to the finals of a fencing championship. Assuming all competitors have an equal chance of winning, how many possibilities are there with respect to how a first-place and second-place medal can be awarded?\nWe have 2 slots to be filled using 5 contestants:5 options for slot1*3 option for slot2\n= 5* 3\n= 15\nAns. D) 15\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the average (arithmetic mean) of a list of numbers is 12 and the standard deviation of that list of numbers is 1.3, then which of the following numbers is more than two standard deviations from the mean?\nI. 13.7\nII. 12.3\nIII. 9.3\n\n### Options:\nA. I only\nB. I and II only\nC. II only\nD. III only\nE. I and III only\n\n### Answer:\nMean = 12\nSD = 1.3\n2 SD above mean = 12+2*1.3 = 14.6\n2 SD below mean = 12-2*1.3 = 9.4\n12.3 and 13.7 lies in the range of 2SD from mean\nAnswer: Option D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the length of an edge of cube P is twice the length of an edge of cube Q, what is the ratio of the volume of cube Q to the volume of cube P?\n\n### Options:\nA. 1/8\nB. 1/4\nC. 1/3\nD. 1/7\nE. 1/9\n\n### Answer:\nThe length of cube Q = 1;\nThe length of cube P = 2;\nThe ratio of the volume of cube Q to the volume of cube P = 1^3/2^3 = 1/8.\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA rectangular-shaped carpet that measures x feet by y feet is priced at $12. What is the cost of the carpet, in dollars per square yard? (1 square yard = 9 square feet)\n\n### Options:\nA. 108/(xy)\nB. 90xy\nC. xy/90\nD. xy/10\nE. 10/(xy)\n\n### Answer:\nThe area of the carpet in feet is xy.\nThe area in square yards is xy / 9.\nThe price per square yard is 12 / (xy/9) = 108/(xy).\nThe answer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn what time will a train 180 meters long cross an electric pole, if its speed is 154 km/hr\n\n### Options:\nA. 5 seconds\nB. 4.3 seconds\nC. 3 seconds\nD. 2.5 seconds\nE. None of these\n\n### Answer:\nExplanation:\nFirst convert speed into m/sec\nSpeed = 154*(5/18) = 42 m/sec\nTime = Distance/speed\n= 180/42 = 4.3 seconds\nOption B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOne out of every 300 light bulbs are defected. If 2 out of every 10 defected light bulbs have a broken glass and there are 20 broken glass light bulbs in the shipment, how many light bulbs total are there in the shipment?\n\n### Options:\nA. 2,000\nB. 30000\nC. 10,000\nD. 50,000\nE. 52,000\n\n### Answer:\n20 broken glasses indicates that 10*10= 100 defected bulbs are present.\n100 defected bulbs indicates that 100*300= 30,000 light bulbs are present.\nB is the answer\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n40 onions on a scale weigh 7.68 kg. When 5 onions are removed from the scale, the average weight of the 35 onions is 190 grams. What is the average weight (in grams) of the 5 onions which were removed?\n\n### Options:\nA. 200\nB. 202\nC. 204\nD. 206\nE. 208\n\n### Answer:\n35*190=6650.\nThe other 5 onions weigh a total of 1030 grams.\nThe average weight is 1030/5 = 206 grams.\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOf 70 players on a football team, 43 are throwers. The rest of the team is divided so one third are left- handed and the rest are right handed. Assuming that all throwers are right handed, how many right- handed players are there total?\n\n### Options:\nA. 54\nB. 59\nC. 63\nD. 61\nE. 92\n\n### Answer:\nTotal = 70\nThrower = 43\nRest = 70 - 43 = 27\nLeft Handed = 27/3 = 9\nRight handed = 18\nIf all Thrower are right handed then total right handed is 43 + 18 = 61\nso D. 61 is the right answer\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is:\n\n### Options:\nA. 10 km/hr\nB. 50 km/hr\nC. 14 km/hr\nD. 17 km/hr\nE. 77 km/hr\n\n### Answer:\nSpeed of the train relative to man = (125/10) m/sec = (25/2) m/sec. [(25/2) * (18/5)] km/hr = 45 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 45 ==> x = 50 km/hr.\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the odd man out. 187, 264, 316, 473, 682, 781\n\n### Options:\nA. 187\nB. 316\nC. 781\nD. 682\nE. 473\n\n### Answer:\nIn all numbers except 316, the middle digit is the sum of other two digits.\rAnswer is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAt a meeting, 3 people are to be seated around a circular table. Two seating arrangements are considered different only when the positions of the people are different relative to each other. What is the total number of different possible seating arrangements for the group?\n\n### Options:\nA. 2\nB. 7\nC. C)120\nD. D)144\nE. E)720\n\n### Answer:\nThe number of arrangements of n distinct objects in a row is given by n!\nThe number of arrangements of n distinct objects in a circle is given by (n\u22121)!\n\"The difference between placement in a row and that in a circle is following: if we shift all object by one position, we will get different arrangement in a row but the same relative arrangement in a circle. So, for the number of circular arrangements of n objects we have:\nR=n!-n=(n\u22121)!\n(n\u22121)!=(7\u22121)!=720\nAnswer: E\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA tank is filled in eight hours by three pipes A, B and C. Pipe A is twice as fast as pipe B, and B is twice as fast as C. How much time will pipe B alone take to fill the tank?\n\n### Options:\nA. 17 hours\nB. 28 hours\nC. 19 hours\nD. 14 hours\nE. 14 hours\n\n### Answer:\n1/A + 1/B + 1/C = 1/8 (Given)\nAlso given that A = 2B and B = 2C\n=> 1/2B + 1/B + 2/B = 1/8\n=> (1 + 2 + 4)/2B = 1/8\n=> 2B/7 = 8\n=> B = 28 hours.\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA bakery opened yesterday with its daily supply of 60 dozen rolls. Half of the rolls were sold by noon, and 80 percent of the remaining rolls were sold between noon and closing time. How many dozen rolls had not been sold when the bakery closed yesterday?\n\n### Options:\nA. 1\nB. 2\nC. 3\nD. 4\nE. 6\n\n### Answer:\nanswer is E ...6 dozens ....\nhalf sold by noon --> 30 dozens (30 *12 =360)\nremaining --> 30 dozens i.e 360 eggs...\n80% sold --> 80*360/100 =288 eggs\nremaining 20 % --> 72 eggs (6 dozens ) --> answer\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man can row his boat with the stream at 6 km/h and against the stream in 4 km/h. The man's rate is?\n\n### Options:\nA. 1\nB. 2\nC. 3\nD. 4\nE. 5\n\n### Answer:\nDS = 6\nUS = 4\nS = ?\nS = (6 - 4)/2 = 1 kmph\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA carpenter worked alone for 1 day on a job that would take him 6 more days to finish. He and another carpenter completed the job in 8 more days. How many days would it have taken the second carpenter to do the complete job working alone?\n\n### Options:\nA. 4 2/3\nB. 7\nC. 9\nD. 14\nE. 28\n\n### Answer:\nA carpenter worked only 1 day on something that takes him 6 MORE days.\nMeans;\nCarpenter finishes his work in 7 days.\nLet his buddy finish the same task in x days.\nRespective rates per day:\n1/7 AND 1/x\nTo complete 1 work:\nFirst guy worked for 5 days @ rate=1/7 per day.\nSecond one worked for 8 days @ rate=1/x per day\nExpression:\nDays*Rate=Work\n5*1/7+8*1/x=1\n5x+56=7x\n2x=56\nx=28 days.\nAns:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how many years Rs 100 will produce the same interest at 5% as Rs. 600 produce in 4 years at 10%\n\n### Options:\nA. 44\nB. 52\nC. 50\nD. 46\nE. 48\n\n### Answer:\nExplanation:\nClue:\nFirstly we need to calculate the SI with prinical 600,Time 4 years and Rate 10%, it will be Rs. 240\nThen we can get the Time as\nTime = (100*240)/(100*5) = 48\nOption E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the sum of 5 consecutive integers is 125, what is sum of the 5 consecutive integers preceding the former sequence?\n\n### Options:\nA. 35\nB. 25\nC. 100\nD. 105\nE. 103\n\n### Answer:\n1) least of each will have a difference of 5 and next least too will have a difference of 5 and so on...\nTherefore all 5 terms will have a term LESS by 5..\nSum = 125-(5*5) = 100\n2.) if sum is 125, the average = median = 125/5 = 25. The median of previous 5 will be 25-5 = 20.\nAnd sum would be 20*5 = 100\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many 3 digit numbers can be formed from the digits 2,3,5,6,7 and 9 which are divisible by 5 and none of the digits is repeated?\n\n### Options:\nA. 30\nB. 20\nC. 10\nD. 45\nE. 50\n\n### Answer:\nSince each desired number is divisible by 5,\nso we much have 5 at the unit place.\nThe hundreds place\ncan now be filled by any of the remaining 4 digits .\nso, there4 ways of filling it.\nRequired number of numbers = (1 * 5 * 4)\n= 20\nAns: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe profit obtained by selling an article for Rs. 86 is the same as the loss obtained by selling it for Rs. 42. What is the cost price of the article?\n\n### Options:\nA. Rs. 40\nB. Rs. 50\nC. Rs. 49\nD. Rs. 59\nE. Rs.64\n\n### Answer:\nS.P 1- C.P = C.P \u2013 S.P 2\n86 - C.P = C.P - 42\n2 C.P = 86 + 42;\nC.P = 128/2 = 64\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe salary of a typist was at first raised by 10% and then the same was reduced by 5%. If he presently draws Rs.1045.What was his original salary?\n\n### Options:\nA. 2277\nB. 2999\nC. 1000\nD. 2651\nE. 1971\n\n### Answer:\nX * (110/100) * (95/100) = 1045\nX * (11/10) * (1/100) = 11\nX = 1000\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA can finish a work in 18 days and B can do same work in half the time taken by A. then working\ntogether, what part of same work they can finish in a day\n\n### Options:\nA. 1\\5\nB. 1\\6\nC. 1\\7\nD. 1\\8\nE. None of these\n\n### Answer:\nExplanation:\nPlease note in this ques\u019fon, we need to answer part of work for a day rather than complete work. It was\nworth mentioning here because many do mistake at this point in hurry to solve the question\nSo lets solve now,\nA's 1 day work = 1/18\nB's 1 day work = 1/9 [because B take half \u019fme than A]\n(A+B)'s one day work =\n(118+19)=(1+218)=16\nSo in one day 1/6 work will be done\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average weight of 10 persons increases by 7.2 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person?\n\n### Options:\nA. 120 kg\nB. 130 kg\nC. 137 kg\nD. 190 kg\nE. None\n\n### Answer:\nSolution\nTotal weight increased\t= (10 x 7.2)kg\n= 72 kg.\nWeight of new person\t= (65 + 72)kg\n= 137 kg.\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man jumps into a river from a overbridge ,at the same time a hat drops in the river which flows with the stream of the water. That man travels 10 minute upstream and returns back where he was asked to catch the hat. He catches hat at a distance of 1000 yard down at a second bridge . Find the speed of the river.\n\n### Options:\nA. 50\nB. 60\nC. 55\nD. 70\nE. 75\n\n### Answer:\nExplanation :\nSuppose x is the distance travelled by the man in 10 min upstream.\nThen\n=> x/(v-u) = 10 where v is man's speed and u is river speed)\nTotal time taken to swim by the man upstream and down stream is equal to the time taken by the\nhat to travel 1000 yards with the speed of river :\n=> 1000/u = 10 + (x+1000) / (u+v)\n=> now substitute x = 10(v-u) and simplify\nwe will get,\n=> 100v = 2uv\n=> 2u = 100\n=> u = 50 yards per minute\nHence (A) is the correct answer.\nAnswer : A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the ratio of the roots of the equation x2+3px-6=0 is equal to that of the roots x2+6rx-12=0, then:\n\n### Options:\nA. 5r=3p\nB. 2p=r\nC. r=p\nD. 2r=p\nE. None\n\n### Answer:\nx2+3px-6=0 for this eqn... roots are R1=-3p R2=6\nx2+6rx-12=0 for this eqn... roots are R3=-6r R4=12\nAs per Question, -3p/6=-6r/12\n=> r=p\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOn a certain road 10% of the motorists exceed the posted speed limit and receive speeding tickets, but 22% of the motorists who exceed the posted speed limit do not receive speeding tickets. What percent of the motorists on the road exceed the posted speed limit?\n\n### Options:\nA. 10.5%\nB. 12.8%\nC. 15%\nD. 22%\nE. 30%\n\n### Answer:\nAnswer is B.\nThis question is in the OG and thus well explained by ets.\nthose who exceed : X\nso X = 10%+0,22X\nid est X = 12,8%\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe owner of a furniture shop charges his customer 24% more than the cost price. If a customer paid Rs. 8463 for a computer table, then what was the cost price of the computer table?\n\n### Options:\nA. 6825\nB. 2977\nC. 2871\nD. 6725\nE. 2981\n\n### Answer:\nExplanation:\nCP = SP * (100/(100 + profit%))\n= 8463(100/124) = Rs. 6825.\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n18! is equal to which of the following?\n\n### Options:\nA. 6,402,373,705,728,125\nB. 6,402,373,705,728,216\nC. 6,402,373,705,728,624\nD. 6,402,373,705,728,000\nE. 6,402,373,705,728,989\n\n### Answer:\nAfter 4!, the units digit of every factorial is 0.\n5!=120\n6!=720\netc...\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAn empty bottle weighs 1/6th of the full bottle. When a certain percent of water was removed and the bottle was weighed, the weight of the bottle turned out to be 1/3rd of the bottle when it was full. What is the percent of water removed?\n\n### Options:\nA. 70%\nB. 85%\nC. 80%\nD. 75%\nE. 65%\n\n### Answer:\nExplanation:\nLet the weight of full bottle be 6kg.\nTherefore, weight of empty bottle is 1kg and that of water is 5kg.\nIf x% of water is removed, the weight of the bottle becomes 2kg.\nTherefore, the amount of water removed is 4kg.\n% of water removed = 4/5 *100 = 80%\nANSWER C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThree seventh of a number is 12 more than 40% of that number. What will be the 10% of that number?\n\n### Options:\nA. A)148\nB. B)210\nC. C)21\nD. D)248\nE. E)258\n\n### Answer:\n3/7 x \u2013 40/100 x = 12\nx = 35 * 12\n35 * 12 * 10/100 = 42/2 = 21\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the sum of the first 15 terms of an A.P whose 11 th and 7 th terms are 5.25 and 3.25 respectively\n\n### Options:\nA. 56.25\nB. 60\nC. 52.5\nD. 5.25\nE. None of these\n\n### Answer:\na +10d = 5.25, a+6d = 3.25, 4d = 2, d = \u00bd\na +5 = 5.25, a = 0.25 = \u00bc, s 15 = 15/2 ( 2 * \u00bc + 14 * \u00bd )\n= 15/2 (1/2 +14/2 ) = 15/2 *15/2 =225/ 4 = 56.25\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich is the smallest fraction:\n\n### Options:\nA. 11/13\nB. 9/11\nC. 5/4\nD. 5/7\nE. 6/7\n\n### Answer:\n11/13=.846\n9/11=.818\n5/4=1.25\n5/7=.714\nSo smallest is 5/7\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nReena took a loan of Rs. 1200 with simple interest for as many years as the rate of interest. If she paid Rs. 768 as interest at the end of the loan period, what was the rate of interest?\n\n### Options:\nA. 3.6\nB. 6\nC. 8\nD. 24\nE. None of these\n\n### Answer:\nLet rate = R% and time = R years.\nThen, (1200 x R x R)/100 = 768\n12R2 = 768\nR2 = 64\nR = 8.\nAnswer: Option C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA rectangular table seats 6 people on each of two sides, with every person directly facing another person across the table. If 12 people choose their seats at random, what is probability that person P directly faces person Q?\n\n### Options:\nA. 1/13\nB. 1/12\nC. 1/11\nD. 1/10\nE. 1/9\n\n### Answer:\nPerson P will be seated somewhere at the table.\nEach of the other 11 people has an equal chance of sitting opposite person P.\nThe probability that person Q sits across is 1/11.\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn the city of San Durango, 60 people own cats, dogs, or rabbits. If 32 people owned cats, 40 owned dogs, 10 owned rabbits, and 12 owned exactly two of the three types of pet, how many people owned all three?\n\n### Options:\nA. 5\nB. 4\nC. 8\nD. 12\nE. 32\n\n### Answer:\nTotal = C + D + R - (CD + DR + CR) - 2CDR\n60 = 32 + 40 + 10 - (12) - 2x\nx = 5\nSo, answer will be A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIF 2+7=57 ; 3+6=63 ; 5+9=206 Then 5+8=?\n\n### Options:\nA. 185\nB. 186\nC. 177\nD. 168\nE. 189\n\n### Answer:\n2^3 + 7^2= 57\n3^3 + 6^2=63\n5^3 + 9^2=206\nand\n5^3 + 8^2=189\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAn empty bucket being filled with paint at a constant rate takes 6 minutes to be filled to 7/10 of its capacity. How much more time D will it take to fill the bucket to full capacity?\n\n### Options:\nA. 7/18\nB. 9/18\nC. 2\nD. 18/7\nE. 18/5\n\n### Answer:\nSolution -\nWork and Time are directly proportional. W1/W2=T1/T2\n7/10 work in 6 mins\n1 work in T mins\n(7/10)/1 = 6/T -> T = 60/7 mins.\nRemaining minutes to fill the tank D= 60/7 - 6 = 18/7 mins. ANS D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe H.C.F. of two numbers is 20 and the other two factors of their L.C.M. are 13 and 14. The larger of the two numbers is:\n\n### Options:\nA. 276\nB. 280\nC. 322\nD. 345\nE. 354\n\n### Answer:\nClearly, the numbers are (20 x 13) and (20 x 14).\nLarger number = (20 x 14) = 280.\nAnswer: Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nDhoni weighs twice as much as Nameetha. Nameetha's weight is 55% of Bima's weight. Dravid weighs 35% of Leela's weight. Leela weighs 30% of Dhoni's weight. Who among these 5 persons weighs the least?\n\n### Options:\nA. Dravid\nB. Dhoni\nC. Bima\nD. Nameetha\nE. Leela\n\n### Answer:\nif\nBima weight = x\nwe get\nNameetha's weight = 0.55x\nDhoni's weight = 1.1x\nLeela's weight = 0.33x\nand Dravid's weight = 0.1155x\nAnswer : A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA shopkeeper loses 15%,if an article is sold for Rs. 102. What should be the selling price of the article to gain 20%?\n\n### Options:\nA. Rs. 150\nB. Rs. 144\nC. Rs. 138\nD. Rs. 132\nE. None of these\n\n### Answer:\nGiven that SP = Rs. 102 and loss = 15%\nCP = [100(SP)]/(100 - l%) = (100 * 102)/85 = 20 * 6 = Rs. 120.\nTo get 20% profit, New SP = [(100 + p%)CP]/100 = (120 * 120)/100 = Rs. 144\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many numbers are divisible by 4 between 1 and 100?\n\n### Options:\nA. 25\nB. 24\nC. 23\nD. 22\nE. 20\n\n### Answer:\nNumbers divisible by 4 till 100=(100/4)=25\nBut we should not consider 100 as we are asked to find the numbers between 1 and 100 which are divisible by 4.\nso answer is 24 numbers.\nAnswer is option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf y is the smallest positive integer such that 3,150 multiplied by y is the square of an integer, then y must be\n\n### Options:\nA. 2\nB. 5\nC. 6\nD. 7\nE. 14\n\n### Answer:\n3150*y = A^2\n3 * 1050 * y = A^2\n3*5*210*y = A^2\n3*5*7*3*2*5*y = A^2\n2*3^2*5^2*7*y = A^2\nConcept: The factors of squared integer should occur in pair. So, the only numbers left are 2*7\nHence 14\t;\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe cost to rent a small bus for a trip is x dollars, which is to be shared equally among the people taking the trip. If 10 people take the trip rather than 12, how many more dollars, in terms of x, will it cost per person?\n\n### Options:\nA. x/6\nB. x/16\nC. x/40\nD. 3x/40\nE. 3x/80\n\n### Answer:\nChoose x as a multiple of 16, I chose 64:\nSo for 10 people, that's 6.4 each and for 12 people it's 4 USD each... Pick one of the options that gives you 6.4 - 4 = 2.4... The answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOf the families in City X in 1992, 60 percent owned a personal computer. The number of families in City X owning a computer in 1993 was 50 percent greater than it was in 1992, and the total number of families in City X was 3 percent greater in 1993 than it was in 1992. what percent of the families in City X owned a personal computer in 1993?\n\n### Options:\nA. 68.99%\nB. 66.55%\nC. 91.23%\nD. 77.77%\nE. 87.37%\n\n### Answer:\nSay a 100 families existed in 1994 then the number of families owning a computer in 1994 - 60\nNumber of families owning computer in 1998 = 60 * 150/100 = 90\nNumber of families in 1998 = 103\nThe percentage = 90/103 * 100 = 87.37%.\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the average marks of 3classes of 55, 60 and 45 students respectively is 50, 55, 60, then find the average marksof all the students is\n\n### Options:\nA. 53\nB. 53.5\nC. 54.68\nD. 55.6\nE. 67.2\n\n### Answer:\nRequired average\n= 55 x 50 + 60 x 55 + 45 x 60\n55 + 60 + 45\n= 2750 + 3300 + 2700\n160\n=\t8750\n160\n= 54.68\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo trains of length 100 m and 200 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 54 kmph and 72 kmph. After how much time will the trains meet?\n\n### Options:\nA. 20/8 sec\nB. 22/7 sec\nC. 20/7 sec\nD. 20/2 sec\nE. 30/7 sec\n\n### Answer:\nThey are moving in opposite directions, relative speed is equal to the sum of their speeds.\nRelative speed = (54 + 72)*5/18 = 7*5\n=35 mps.\nThe time required = d/s\n= 100/35\n=20/7 sec.\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA, B, C subscribe Rs. 50,000 for a business. If A subscribes Rs. 4000 more than B and B Rs. 5000 more than C, out of a total profit of Rs. 36,000, what will be the amount A receives?\n\n### Options:\nA. 15120\nB. 14500\nC. 14900\nD. 14300\nE. 14000\n\n### Answer:\nTotal amount invested = 50000\nAssume that investment of C =x.\nThen investment of B =5000+x,\nInvestment of A =4000+5000+x=9000+x\nx+5000+x+9000+x=50000\n\u21d23x+14000=50000\n\u21d23x=50000\u201314000=36000\n\u21d2x=36000/3=12000\nInvestment of C =x=12000\nInvestment of B =5000+x=17000\nInvestment of A =9000+x=21000\nRatio of the investment of A, B and C\n=21000:17000:12000\n=21:17:12\nShare of A = Total profit \u00d721/50\n=36000\u00d721/50=15,120\nAnswer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFor every integer n \u2265 3, the function h(n) is defined as the product of all the odd integers from 1 to n, inclusive. What is the value of h(102) \u2013 h(101)?\n\n### Options:\nA. 102\nB. 0\nC. 101\nD. 98\nE. 100\n\n### Answer:\nh(101) = 1*3*5*7*9*...*99*101\nh(102) = 1*3*5*7*9*...*99*101\nThey are going to be the same. Hence their difference will be 0\nhence:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich of the following is the lowest positive integer that is divisible by 6, 7, 8, 9, and 10?\n\n### Options:\nA. 2140\nB. 2520\nC. 2980\nD. 3260\nE. 3680\n\n### Answer:\nThe number needs to be divisible by 2*3, 7, 2^3, 3^2, and 2*5.\nThe lowest positive integer is 7 * 2^3 * 3^2 * 5 = 2520\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf xy not equal 0 and x^2*y^2 -xy = 12, which of the following could be y in terms of x?\nI. 1/2x\nII. -4/x\nIII. 3/x\n\n### Options:\nA. II and III\nB. II\nC. III\nD. IV\nE. I &II\n\n### Answer:\nx2y2 - xy = 12\nx2y2-xy-12 = 0\n(xy-3)(xy+4)=0\nxy = 3 or xy=-4\ny = 3/x or y = -4/x\nII and III only\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAn author received $0.80 in royalties for each of the first 100,000 copies of her book sold, and $0.30 in royalties for each additional copy sold. If she received a total of $260,000 in royalties, how many copies of her book were sold?\n\n### Options:\nA. 700,000\nB. 300,000\nC. 380,000\nD. 400,000\nE. 420,000\n\n### Answer:\nTotal royalties for first 100.000 books = .8*100,000= 80,000\nTotal royalties for the rest of the books = 260,000-80,000 = 180,000\nRemaining books = 180,000/0.3 = 600,000\nTotal books = 600,000+100,000 = 700,000 Answer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the value of x from the below equation? : x^2+5x+25 = 0\n\n### Options:\nA. No answer\nB. 25\nC. 1\nD. 0\nE. -2\n\n### Answer:\na = 1, b = 5, c = 25\nx1,2 = (-5 \u00c2\u00b1 \u00e2\u02c6\u0161(5^2 - 4\u00c3\u20141\u00c3\u201425)) / (2\u00c3\u20141) = (-5 \u00c2\u00b1 \u00e2\u02c6\u0161(25-100)) / 2 = (-5 \u00c2\u00b1 \u00e2\u02c6\u0161 -75) / 2\nNo real roots\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA box contains 2 red, 3 black and 4 blue balls. 3 balls are randomly drawn from the box. If two balls are found to be different, what is the probability that the third ball is blue?\n\n### Options:\nA. 8/3\nB. 9/3\nC. 5/3\nD. 2/3\nE. 1/3\n\n### Answer:\nthere are 6 ways to draw a blue ball at third attempt if first two balls are different. they are\n1)RED BLACK BLUE\n2)RED BLUE BLUE\n3)BLACK RED BLUE\n4)BLACK BLUE BLUE\n5)BLUE RED BLUE\n6)BLUE BLACK BLUE\nProbability of 1st way is (2/9)*(3/8)*(4/7)\nas at first attempt we got red which are two in number out of 9 and in second we got black which are 3 in number out of 8 (as first ball is removed)and in 3rd attempt we got blue which are 4 in number out of 7 balls left.\nsimilarly probability of other ways is as follows\n(2/9)*(4/8)*(3/7)\n(3/9)*(2/8)*(4/7)\n(3/9) *(4/8)*(3/7)\n(4/9)*(2/8)*(3/7)\n(4/9)*(3/8)*(3/7)\ntotal probability of getting a blue ball is sum of all above ways so p=(2/9)*(3/8)*(4/7)+(2/9)*(4/8)*(3/7)+(3/9)*(2/8)*(4/7)+(3/9) *(4/8)*(3/7)+(4/9)*(2/8)*(3/7)+(4/9)*(3/8)*(3/7)=1/3\nso probability of ball to be blue is 1/3\nAnswer E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe arithmetic mean of 5 negative integers is -100. If the average of 3 of these integers is -90, what is the least possible value that one of the other 2 integers can have?\n\n### Options:\nA. 229\nB. -1\nC. -229\nD. 90\nE. -90\n\n### Answer:\nThe Arithmetic Mean of 5 negative integers is (a+b+c+d+e)/5=-100\nSo, The sum of 5 negative integers would be a+b+c+d+e=-100*5 = -500\nSimilarly, The sum of 3 negative integers would be a+b+c= -90*3 = -270\nThus, the sum of the other 2 integers is -500 + 270= -230. Since we know that the integers are negative then the least one from these two can be -229, the other one being -1.\nHence, the correct ans is C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTom planted vegetables in a rectangular garden that was 23 feet long and 15 feet wide. He used\n1/3 of the area for corn and 1/5 of it for peas. How many square feet are left for other vegetables?\n\n### Options:\nA. 155 sq. ft.\nB. 156 sq. ft.\nC. 161 sq. ft.\nD. 168 sq. ft.\nE. 179 sq. ft.\n\n### Answer:\narea of garden is 23 x 15 = 345 sq. ft.\n1/3 x 345 = 115 sq. ft. for corn\n1/5 x 345 = 69 sq. ft. for peas\n115 + 69 = 184 sq. ft. used\n345 - 184 = 161 sq. ft. left over\ncorrect answer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf you are given $4, and the amount doubles every day, how much money will you have after 8 days?\n\n### Options:\nA. $256\nB. $512\nC. $1024\nD. $65536\nE. $4096\n\n### Answer:\n4^8=65536\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA motorist knows six different routes from Bristol to Birmingham. From Birmingham to Sheffield he knows three different routes and from Sheffield to Carlisle he knows two different routes. How many routes does he know from Bristol to Carlisle ?\n\n### Options:\nA. 4\nB. 8\nC. 12\nD. 24\nE. 36\n\n### Answer:\nExplanation:\nTotal number of routes from Bristol to Carlisle = (6 x 3 x 2) = 36.\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain league has four divisions. The respective divisions had 9, 10, 11, and 12 teams qualify for the playoffs. Each division held its own double-elimination tournament -- where a team is eliminated from the tournament upon losing two games -- in order to determine its champion. The four division champions then played in a single-elimination tournament -- where a team is eliminated upon losing one game -- in order to determine the overall league champion. Assuming that there were no ties and no forfeits, what is the maximum number of games that could have been played in order to determine the overall league champion?\n\n### Options:\nA. 79\nB. 83\nC. 85\nD. 87\nE. 88\n\n### Answer:\nConsider 4 teams.\nMax possible games if a team is eliminated after 2 loses = 3 + 2 = 5\nSimilarly, if 5 teams are there,\nMax possible games = 4 + 3 = 7.\nSo going forth we can play 15,17,19,21 max possible games for 9,10,11,12 teams respectively.\nAdding them up gives 72. Now there are two teams left in each group still. So four more games to give a winner in each team.\nSo 72+ 4 = 76.\nNow of the four teams we can have max 3 games if its a knock out round.\nSo 76 + 3 = 79.\nAnswer A = 79.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA and B can do a piece of work in 10 days. With the help of C they finish the work in 5 days. C alone can do that piece of work in?\n\n### Options:\nA. 33\nB. 878\nC. 30\nD. 10\nE. 11\n\n### Answer:\nC = 1/5 \u00e2\u20ac\u201c 1/10 = 1/10 => 10 days\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the 28th digit to the right of the decimal point in the decimal form of 5/11?\n\n### Options:\nA. 3\nB. 4\nC. 5\nD. 6\nE. 7\n\n### Answer:\n5/11 = 0.45454545...\nThe even numbered positions in the decimal expansion are all 5.\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man sells two articles for Rs.3250 each and he gains 40% on the first and loses 40% on the next. Find his total gain or loss?\n\n### Options:\nA. 19%loss\nB. 12%loss\nC. 16%loss\nD. 18%loss\nE. 11%loss\n\n### Answer:\nExplanation:\n(40*40)/100\n= 16%loss\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n60 percent of movie theatres in Town X have 3 screens or less. 20% of those theatres sell an average of more than $200 worth of popcorn per showing. 56 percent of all the movie theatres in Town X sell $300 or less of popcorn per showing. What percent of all the stores on the street have 4 or more screens and sell an average of more than $300 worth of popcorn per day?\n\n### Options:\nA. 12\nB. 18\nC. 32\nD. 40\nE. 44\n\n### Answer:\nLets take numbers here.\nAssume that the total number of movie theaters in the town = 100\nThen number of movie theaters with 3 screens or less = 60\n=> Number of movie theaters with 4 screens or more = 40\nMovie theaters with 3 screens or less selling popcorn at more than $200 = 20% of 60 = 12\nNumber of movie theaters selling popcorn at $300 or less = 56\n=> Number of movie theaters selling popcorn at more than $300 = 100-56 = 44\nOf these 44 theaters, 12 are those with 3 screens or less\nTherefore 18 (44-12) must be those with four screens or more\nB is the answer\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n0.35 represents what percent of 0.7?\n\n### Options:\nA. 0.05%\nB. 0.5%\nC. 50%\nD. 500%\nE. 5000%\n\n### Answer:\nOne more method\n0.35 represents what percent of 0.7?\nAdjusting the decimal\n3.5 represents what percent of 7?\nDivide by 7\n0.5 represents what percent of 1?\nAnswer = 0.5*100 = 50% = C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe captain of a cricket team of 11 members is 26 years old and the wicket keeper is 2 years older. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. What is the average age of the team?\n\n### Options:\nA. 23 years\nB. 22 years\nC. 25 years\nD. 26 years\nE. 27 years\n\n### Answer:\nEXPLANATION\nLet the average age of the whole team by x years.\n11x \u00e2\u20ac\u201c (26 + 28) = 9(x -1)\n11x \u00e2\u20ac\u201c 9x = 45\n2x = 45\nx = 22.\nSo, average age of the team is 22 years.\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain high school has 500 students. Of these students, 20 are taking music, 20 are taking art, and 10 are taking both music and art. How many students are taking neither music nor art?\n\n### Options:\nA. 430\nB. 440\nC. 450\nD. 460\nE. 470\n\n### Answer:\nWe're given a series of facts to work with:\n1) A certain high school has 500 students.\n2) Of these students:\nX are taking music,\nY are taking art, and\nZ are taking BOTH music and art.\nWe're asked how many students are taking NEITHER music nor art?\nLet's TEST\nX = 20\nY = 20\nZ = 10\nSo, we have 20 students taking music, 20 taking art and 10 taking BOTH music and art. That 10 person has been counted TWICE though (once in the music 'group' and once in the art 'group'), so what we really have is...\n10 student taking JUST music\n10 student taking JUST art\n10 student taking BOTH music and art\nTotal = 30 students\nWe're asked for the total number of students who are taking NEITHER Course. That is 5000 - 30 = 470.\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the radius of a circle that centers at the origin is 5, how many M points on the circle have integer coordinates?\n\n### Options:\nA. 4\nB. 8\nC. 12\nD. 15\nE. 20\n\n### Answer:\nI understand this might not be required but I used the equation of a circle.\nSince the origin is at 0, x^2+y^2=5^2.\nX,Y could be +/- (0,5 or 5,0) - 4 possibilities.\nX,Y could be +/- (3,4 or 4,3) - 8 possibilities.\nAns: M=C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n[1+(1/5)]^n=2?\nWhat is the value of n?\n\n### Options:\nA. 1.999\nB. 2.999\nC. 3.88\nD. 4.88\nE. 5.88\n\n### Answer:\n1+1/5 = 6/5 = 1.2\n1.2*1.2 = 1.44 *1.2 = 1.728 *1.2 = 2.0736\nso if N is integer, N=4. if not, N = 3.8\n(1.2)^3.8 = 1.999\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf x and y are non-zero integers, and 64x^4 \u2013 4y^4 = 8x^2 + 2y^2, which of the following could be the value of x2 in terms of y?\n\n### Options:\nA. 2y^2\nB. 2y\nC. 2y^2/8\nD. 2y^2-1/8\nE. 2y^2+1/8\n\n### Answer:\n64x^4 \u2013 4y^4 = 8x^2 + 2y^2\n(8x^2 + 2y^2) (8x^2 - 2y^2) = 8x^2 + 2y^2\n8x^2 - 2y^2 = 1\n8x^2 = 2y^2+1\nx^2 = 2y^2+1/8\nAnswer : E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nYou have a pair of unbiased dices. You throw them together till you get a sum of 4 or 7.\nWhat is the probability that you get a sum of 4 before the sum of 7?\n\n### Options:\nA. 5/6\nB. 4/5\nC. 2/5\nD. 1/8\nE. 4/4\n\n### Answer:\nC\n2/5\nThis problem can be solved with different approaches. Let us not go into the complicated generic stuff to avoid confusion and try to solve it with simpler means.\nLet us find the results separately. There can be 4 different results that give the sum of 5 and there can be 6 different results that give the sum of 7.\nThus, the probability that we get the sum of 4 before the sum of 7 will be:\n4/(4+6) = 4/10 = 2/5.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are 720 male and female participants in a meeting. Half the female participants and one-quarterof the male participants are Democrats. One-third of all the participants are Democrats. How many of the Democrats are female?\n\n### Options:\nA. 75\nB. 100\nC. 120\nD. 175\nE. 225\n\n### Answer:\nLet m be the number of male participants and f be the number of female articipants in the meeting. Thetotal number of participants is given as 720.\nHence, we have m+f= 720\nNow, we have that half the female participants and one-quarter of the male participants are Democrats.\nLet d equal the number of the Democrats.\nThen we have the equation f/2 + m/4 =d\nNow, we have that one-third of the total participants are Democrats. Hence, we have the equation\nd = 720/3 = 240\nSolving the three equations yields the solution\nf = 240,m= 480, and d= 240.\nThe number of female democratic participants equals half the female participants equals\n240/2 = 120.\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average height in a group of 4 people is 175 cm. If the average height increased when 2 more people were added to the group, which of the following cannot be the heights of the two new people?\n\n### Options:\nA. 179 cm and 172 cm\nB. 181 cm and 169 cm\nC. 173 cm and 178 cm\nD. 176 cm and 176 cm\nE. 174 cm and 177 cm\n\n### Answer:\nDenote X as the sum of the heights of the two new people. From the stem it follows that (700+X)6>175. This reduces to X>350. Only the heights from B add up to 350 cm. All other pairs add up to more than 350 cm.\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n96 is divided into two parts in such a way that seventh part of first and ninth part of second are equal. Find the smallest part?\n\n### Options:\nA. 66\nB. 77\nC. 42\nD. 88\nE. 12\n\n### Answer:\nx/7 = y/9 => x:y = 7:9\n7/16 * 96 = 42.Answer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA, B and C started a shop by investing Rs. 4,000, Rs. 12,000 and Rs. 8,000 respectively. At the end of the year, the profits were distributed among them. If C\u00e2\u20ac\u2122s share of profit be Rs. 1,000, then the total profit was :\n\n### Options:\nA. 3,000\nB. 60,000\nC. 80,000\nD. 120,000\nE. None\n\n### Answer:\nSol.\nA : B : C = 4000 : 12000 : 8000 = 1: 3 : 2. so, C\u00e2\u20ac\u2122s share : Total Profit = 2 : 6\nLet the total profit be Rs. x. Then, 2/6 = 1000/x or x\n= 1000 * 6/ 2 = 3000.\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf ab - 2c = a(b - c), which of the following must be true?\n\n### Options:\nA. a=2 and c=0\nB. a=1/2 and b=2\nC. b=1 and c=0\nD. a=1 or b=0\nE. a=1/2 or c=0\n\n### Answer:\nab-2c = a (b-c)\nab - 2c = ab - ac\n2c= ac\nac-2c = 0\nc(a-2) = 0\nEither c = 0; or a = 2\nA is the answer\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf there are 80 red and blue marbles in a jar, and the ratio of red to blue marbles is 2:3, what is the probability that, drawing twice, you will select two red marbles if you return the marbles after each draw?\n\n### Options:\nA. 1/25\nB. 2/25\nC. 3/25\nD. 4/25\nE. 21/25\n\n### Answer:\n30 red and blue marbles in a jar, and the ratio of red to blue marbles is 2:3\nSo, 5x=80 ---> x=16\nRed marbles = 2*x = 2*16 = 32\nBlue marbles = 3*x = 3*16 = 48\nProb to select a red marble = 32/80 = 2/5\nProb to select 2 red marbles with replacement = 2/5*2*5 = 4/25\nHence, answer will be D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOn Saturday morning, Malachi will begin a camping vacation and he will return home at the end of the first day on which it rains. If on the first three days of the vacation the probability of rain on each day is 0.6, what is the probability that Malachi will return home at the end of the day on the following Monday?\n\n### Options:\nA. 0.096\nB. 0.128\nC. 0.488\nD. 0.512\nE. 0.64\n\n### Answer:\nRe-phrasing the question:\nWhat is the probability of: Saturday: No rain, Sunday: No rain, Monday: Rain\nProbablity of rain = 0.6\nTherefore, probability of no rain = 0.4\n0.4*0.4*0.6 = 0.096\nHence A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA shopkeeper expects a gain of 22.5% on his cost price. If in a week, his sale was of Rs. 588, what was his profit?\n\n### Options:\nA. s. 64\nB. s. 69\nC. s.108\nD. s.75\nE. s.90\n\n### Answer:\nC.P. = Rs. (100/122.5)x588\n= Rs. (1000/1225)x588\n= Rs. 480\nProfit = Rs. (588 - 480) = Rs. 108.\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA truck covers a distance of 392 km at a certain speed in 8 hours. How much time would a car take at an average speed which is 18 kmph more than that of the speed of the truck to cover a distance which is 70 km more than that travelled by the truck ?\n\n### Options:\nA. 6 hours\nB. 5 hours\nC. 7 hours\nD. 8 hours\nE. None\n\n### Answer:\nExplanation :\nSpeed of the truck = Distance/time = 392/8 = 49 kmph\nNow, speed of car = (speed of truck + 18) kmph = (48 + 18) = 66 kmph\nDistance travelled by car = 392 + 70 = 462 km\nTime taken by car = Distance/Speed = 462/66 = 7 hours.\nAnswer \u2013 C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n2 men catch 2 fish in 2 minutes. At this rate, how many men could catch 500 fish in 500 minutes?\n\n### Options:\nA. 2\nB. 4\nC. 6\nD. 500\nE. 0\n\n### Answer:\n2 men.....there are no other!!!!\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAt Veridux Corporation, there are 215 employees. Of these, 90 are female, and the rest are males. There are a total of 40 managers, and the rest of the employees are associates. If there are a total of 135 male associates, how many female managers are there?\n\n### Options:\nA. 50\nB. 20\nC. 25\nD. 30\nE. 35\n\n### Answer:\nWell, first let\u00e2\u20ac\u2122s take care of the \u00e2\u20ac\u0153totals\u00e2\u20ac\u009d. The numbers in the \u00e2\u20ac\u0153totals\u00e2\u20ac\u009d row must add up. If 90 are females, the other 215 \u00e2\u20ac\u201c 90 = 125 must be males. Similarly, the numbers in the \u00e2\u20ac\u0153totals\u00e2\u20ac\u009d column must add up. If 40 are managers, then the other 215 \u00e2\u20ac\u201c 40 = 175 must be associates.\nNow, in the \u00e2\u20ac\u0153associate\u00e2\u20ac\u009d row, 135 + E = 175, which means E = 40\u00e2\u20ac\u201d the other 40 associates must be female.\nNow, to find B, which is what the question is asking, we need only look at the sum in the \u00e2\u20ac\u0153female\u00e2\u20ac\u009d column: B + 40 = 90, which means B = 50. There are fifteen female managers in this company. Thus, the answer = 50(A).\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHuey's Hip Pizza sells two sizes of square pizzas: a small pizza that measures 14 inches on a side and costs $10, and a large pizza that measures 21 inches on a side and costs $20. If two friends go to Huey's with $30 apiece, how many more square inches of pizza can they buy if they pool their money than if they each purchase pizza alone?\n\n### Options:\nA. 5 square inches\nB. 10 square inches\nC. 49 square inches\nD. 25 square inches\nE. 350 square inches\n\n### Answer:\nIn the first case each can buy one pizza of $10 and one pizza of $20.\nIn square inches that would be (14*14=196) for the small pizza and (21*21=441) for the large pizza. In total sq inches that would be (196+441)*2= 1274 sq inches.\nIn the second case if they pool their money together they can buy 3 large pizzas. In terms of square inches that would be 3*441= 1323 sq inches.\nHence, the difference is 49 square inches more (1323-1274).\nThe correct answer is C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man whose speed is 5.5 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 1.5 kmph, find his average speed for the total journey?\n\n### Options:\nA. 5\nB. 4\nC. 7\nD. 3\nE. 5.1\n\n### Answer:\nM = 5.5\nS = 1.5\nDS = 7\nUS = 4\nAS = (2 * 7 * 4) /11 = 5.1\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIt was calculated that 75 men could complete a piece of work in 10 days. When work was scheduled to commence, it was found necessary to send 25 men to another project. How much longer will it take to complete the work?\n\n### Options:\nA. 10 days.\nB. 20 days.\nC. 25 days.\nD. 12.5 days.\nE. 15 days.\n\n### Answer:\nOne day work = 1 / 10\nOne man\u2019s one day work = 1 / ( 10 * 75)\nNow:\nNo. Of workers = 50\nOne day work = 50 * 1 / ( 10 * 75)\nThe total no. of days required to complete the work = (75 * 10) / 50 = 15\nAnswer:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the number 653 xy is divisible by 90, then (x + y) = ?\n\n### Options:\nA. 2\nB. 3\nC. 4\nD. 6\nE. 5\n\n### Answer:\n90 = 10 x 9\nClearly, 653xy is divisible by 10, so y = 0\nNow, 653x0 is divisible by 9.\nSo, (6 + 5 + 3 + x + 0) = (14 + x) is divisible by 9. So, x = 4.\nHence, (x + y) = (4 + 0) = 4.\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf sy + z = s(y + z), which of the following must be true?\n\n### Options:\nA. x = 0 and z = 0\nB. s= 1 and y = 1\nC. s = 1 and z = 0\nD. s = 1 or y = 0\nE. s = 1 or z = 0\n\n### Answer:\nsy + z = sy + sz\nz = sz\ncase 1: z not= 0, s = z/z = 1\ncase 2: z = 0, 0 = s0 = 0\nCombining 2 cases: s = 1 or z =0\nE. is the answer.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAnnie and Sam set out together on bicycles traveling at 15 and 12 km per hour respectively. After 40 minutes, Annie stops to fix a flat tire. If it takes Annie 15 minutes to fix the flat tire and Sam continues to ride during this time, how many minutes will it take Annie to catch up with Sam assuming that Annie resumes riding at 15 km per hour?\n\n### Options:\nA. 20\nB. 40\nC. 60\nD. 80\nE. 100\n\n### Answer:\nAnnie gains 3 km per hour (or 1 km every 20 minutes) on Sam.\nAfter 40 minutes Annie is 2 km ahead.\nIn the next 15 minutes, Sam rides 3 km so Sam will be 1 km ahead.\nIt will take Annie 20 minutes to catch Sam.\nThe answer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average weight of 6 students decreases by 3 kg when one of them weighing 80 kg is replaced by a new student. The weight of the student is\n\n### Options:\nA. 62 kg\nB. 60 kg\nC. 70 kg\nD. 72 kg\nE. None of these\n\n### Answer:\nExplanation :\nLet the weight of student be x kg.\nGiven, Difference in average weight = 3 kg\n=> (80-x)/6 = 3\n=> x = 62\nAnswer : A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRane can make a handcrafted drum in 4 weeks. Zane can make a similar handcrafted drum in 6 weeks. If they both work together, how many weeks will it take for them to produce 15 handcrafted drums?\n\n### Options:\nA. 30\nB. 36\nC. 70\nD. 80\nE. 150\n\n### Answer:\nMethod I: the rates solution\n\u201cRane can make a handcrafted drum in 4 weeks. Zane can make a similar handcrafted drum in 6 weeks.\u201d Rane\u2019s rate is (1 drum)/(4 weeks) = 1/4. Zane\u2019s rate is (1 drum)/(6 weeks) = 1/6. The combined rate of Rane + Zane is\nR = 1/4 + 1/6 = 3/12 + 2/12 = 5/12\nThat\u2019s the combined rate. We need to make 15 drums \u2014 we have a rate and we have an amount, so use the \u201cart\u201d equation to solve for time:\nT = A/R = 15/(5/12) = 15*(12/5) = (15/5)*12 = 3*12 = 36\nBTW, notice in the penultimate step, the universal fraction strategy: cancelbeforeyou multiply (Tip #3:http://magoosh.com/gmat/2012/can-i-use- ... -the-gmat/. Rane and Zane need 36 weeks to make 15 drums.\nAnswer = B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRoy opened a shop investing Rs.20000. Alex joined him 8 months later, investing Rs.34000. They earned a profit of Rs.32000 after completion of two years. What will be Roy's share of profit?\n\n### Options:\nA. 18000\nB. 19000\nC. 20000\nD. 15000\nE. 17000\n\n### Answer:\nSoL = ~s- So Roy's share = [15/32] x 32000 = 15000\nAnswer : D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain boxer has agreed to pay his opponent a fee of 3% of his total purse for every pound over the specified weight limit he weighs in. If the boxer pays his opponent a fee of $26,250 after weighing in seven pounds over the specified limit, what was the boxer's purse?\n\n### Options:\nA. $65,625\nB. $105,000\nC. $125,000\nD. $183,750\nE. $1,050,000\n\n### Answer:\n.03*7 = .21\n26250/.21 = $125,000\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train 110 meters long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going?\n\n### Options:\nA. 7 sec\nB. 6 sec\nC. 4 sec\nD. 2 sec\nE. 1 sec\n\n### Answer:\nSpeed of train relative to man = (60 + 6) km/hr\n= 66 km/hr\n[66 * 5/18] m/sec = [55/3] m/sec.\nTime taken to pass the man = [110 * 3/55] sec\n= 6 sec\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAn accurate clock shows 8 o\u2019clock in the morning. Through how many degrees will the hour hand rotate when the clock shows 12 o\u2019clock in the afternoon?\n\n### Options:\nA. 120\u00b0\nB. 90\u00b0\nC. 180\u00b0\nD. 320\u00b0\nE. None of these\n\n### Answer:\nSol.\nAngle traced by the hour hand in 4 hours = [360/12 * 4]\u00b0 = 120\u00b0\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA boy traveled from the village to the post-office at the rate of 12.5 kmph and walked back at the rate of 2 kmph. If the whole journey took 5 hours 48 minutes, find the distance of the post-office from the village.\n\n### Options:\nA. 5 km\nB. 7 km\nC. 9 km\nD. 10 km\nE. 12 km\n\n### Answer:\nExplanation :\nSolution: Average speed = 2xy/(x+y) km/hr\n= (2*12.5*2)/(12.5+2) km/hr\n= 50/14.5 km/hr.\nTotal distance = (50/14.5 * 29/5) km.\n= 20 km.\nRequired distance = 20/2 = 10 km.\nAnswer : D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered. If the area of the field is 80 sq. feet, how many feet of fencing will be required?\n\n### Options:\nA. 28\nB. 40\nC. 68\nD. 88\nE. 78\n\n### Answer:\nWe have: l = 20 ft and lb = 80 sq. ft.\nSo, b = 4 ft.\nLength of fencing = (l + 2b) = (20 + 8) ft = 28 ft.\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man spent 1/5 of his loan amount on house construction and 1/4 of the remaining on his office renovation. How much fraction of the loan amount is he left with after spending on house and office renovation?\n\n### Options:\nA. 3/5\nB. 2/6\nC. 5/4\nD. 1/5\nE. 4/3\n\n### Answer:\nThe man spent 1/5 his loan amount on house construction, remaining amount is 4/5\nHe spent 1/4 of the remaining amount for office renovation, 1/4*4/5=4/20\nTotal loan amount spent on house and office renovation =1/5+4/20\nTo get a common denominator we use 20, so 1/5 is 4/20\n4/20+4/20=8/20 is the total amount spent on house construction and office renovation.\nremaining 12/20 is left with the man, 3/5\nAnswer is A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a college students can play cricket or basketball. 500 play cricket.220 played both and 600 played basketball. What is the total strength of college?\n\n### Options:\nA. 800\nB. 880\nC. 920\nD. 950\nE. 980\n\n### Answer:\nP(C)= 500\nP(B)=600\nP(C n B) =220\nP(C U B)= P(C)+ P(B) - P(C n B)\n= 500+600-220= 880\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA milk man has 20 liters of milk. If he mixes 5 liters of water, which is freely available, in 20 liters of pure milk.If the cost of pure milk is Rs.18 per liter,then the profit of the milkman, when he sells all the mixture at cost price is:\n\n### Options:\nA. 20%\nB. 25%\nC. 33.33%\nD. 18%\nE. None of these\n\n### Answer:\nExplanation:\nwhen the water is freely available and all the water is sold at the price of the milk, then the water gives the profit on the cost of 20 liters of milk.\nTherefore, profit percentage = 25 %. Answer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMrs. Rodger got a weekly raise of $135. If she gets paid every other week, write an integer describing how the raise will affect her paycheck.\n\n### Options:\nA. $ 145.\nB. $ 146\nC. $ 135\nD. $ 148\nE. None\n\n### Answer:\nSolution:\nLet the 1st paycheck be x (integer).\nMrs. Rodger got a weekly raise of $ 135.\nSo after completing the 1st week she will get $ (x+135).\nSimilarly after completing the 2nd week she will get $ (x + 135) + $ 135.\n= $ (x + 135 + 135)\n= $ (x + 270)\nSo in this way end of every week her salary will increase by $ 135.\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe probability that a visitor at the mall buys a pack of candy is 30%. If three visitors come to the mall today, what is the probability T that exactly two visitors will buy a pack of candy?\n\n### Options:\nA. 0.343\nB. 0.147\nC. 0.189\nD. 0.063\nE. 0.027\n\n### Answer:\n3C2 * (3/10)^2 * 7/10\n= 3 * 9/100 * 7/10\n= 189/1000\n= 0.189=T\nAnswer - C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe apartment on King-Williams street is an asset that its value is tramping about. From the year 1973 to 1983 it's value decreased by 16% and from 1983 to 1993 it's value increased by 16%. What is the value of the asset in 1993 if in 1973 it was worth $55,000?\n\n### Options:\nA. $38,796.\nB. $40,000.\nC. $38,976.\nD. $39,679.\nE. $53,592.\n\n### Answer:\n55,000 *1.16*.84= 53,592\nAnswer E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?\n\n### Options:\nA. 150 m\nB. 350 m\nC. 300 m\nD. 240 m\nE. none\n\n### Answer:\nSpeed =(54 x5/18m/sec) = 15 m/sec.\nLength of the train = (15 x 20)m =300 m.\nLet the length of the platform be x metres.\nThen,x + 300/36= 15\nx + 300 = 540\nx = 240 m\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 1 + 9 + 11 = 1, Then what is the value of\n12 + 11 + 9 = ?\n\n### Options:\nA. 12\nB. 7\nC. 11\nD. 9\nE. 10\n\n### Answer:\nE\nExplanation:\nEquation 1 + 9 + 11 = 1 can be derived from\nOne (o) + nine (n) + eleven (e) = one => 1\nSimilarly for equation,\n12 + 11 + 9\nTwelve (t) + eleven (e) + nine (n) => ten (10)\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo trains of equal are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. The faster train passes the slower train in 72 sec. The length of each train is?\n\n### Options:\nA. 50\nB. 26\nC. 27\nD. 28\nE. 100\n\n### Answer:\nLet the length of each train be x m.\nThen, distance covered = 2x m.\nRelative speed = 46 - 36 = 10 km/hr.\n= 10 * 5/18 = 25/9 m/sec.\n2x/72 = 25/9 => x = 100.\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain Maroon paint contains 70 percent blue pigment and 30 percent red pigment by weight. A certain green paint contains 10 percent blue pigment and 90 percent yellow pigment. When these paints are mixed to produce a brown paint, the brown paint contains 40 percent blue pigment. If the brown paint weighs 10 grams, then the red pigment contributes how many grams of that weight?\n\n### Options:\nA. 1.5\nB. 2\nC. 2.5\nD. 3\nE. 3.5\n\n### Answer:\n10 Grams of combined mixture and 40% blue pigment means that the mixtures were mixed 50% each. Thus 5 grams a piece. Out of the 5 grams of the Dark Blue paint, 60% is red. Therefore, 5*.3 =1.5 Grams of red pigment\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRaman mixed 48 kg of butter at Rs. 150 per kg with 36 kg butter at the rate of Rs. 125 per kg. At what price per kg should he sell the mixture to make a profit of 40% in the transaction?\n\n### Options:\nA. 129\nB. 287\nC. 195\nD. 188\nE. 112\n\n### Answer:\nExplanation:\nCP per kg of mixture = [48(150) + 36(125)]/(48 + 36) = Rs. 139.28\nSP = CP[(100 + profit%)/100]\n= 139.28 * [(100 + 40)/100] = Rs. 195\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA wire can be bent in the form of a circle of radius 56cm. If it is bent in the form of a square, then its area will be\n\n### Options:\nA. 7744\nB. 2388\nC. 3778\nD. 2992\nE. 2888\n\n### Answer:\nExplanation:\nlength of wire = {\\color{Blue}2 \\Pi r}= 2 *(22/7 )*56 = 352 cm\nside of the square = 352/4 = 88cm\narea of the square = 88*88 = 7744sq cm\nAnswer: A) 7744\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA store raised the price of an item by exactly 20 percent. Which of the following could NOT be the resulting price of the item?\n\n### Options:\nA. 6\nB. 12\nC. 18\nD. 24\nE. 58\n\n### Answer:\nIf it raised the value by 20% then the resulting price is 1.2 times the original price. So the final answer has to be a multiple of 1.2. Check the answers.\n6 - Yes\n12 - Yes\n18 - Yes\n24 - Yes\n58 - No\nAnswer : E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo pipes A and B can fill a cistern in 20 and 30 minutes respectively, and a third pipe C can empty it in 60 minutes. How long will it take to fill the cistern if all the three are opened at the same time?\n\n### Options:\nA. 17 1/4 min\nB. 28 1/7 min\nC. 15 min\nD. 17 1/8 min\nE. 17 5/7 min\n\n### Answer:\n1/20 + 1/30 - 1/60 = 4/60 = 1/15\n15/1 = 15\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average age of 15 students of a class is 15 years. Out of these, the average age of 5 students is 14 years and that of the other 9 students is 16 years, The age of the 15th student is\n\n### Options:\nA. 11 years\nB. 12 years\nC. 13 years\nD. 18 years\nE. 10 years\n\n### Answer:\nAge of the 15th student = [15 * 15 - (14 * 5 + 16 * 9)] = (225-214)\n= 11 years.\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf both a and b belongs to the set {1,2,3,4 }, then the number of equations of the form ax2 + bx + 1 = 0 having real roots is\n\n### Options:\nA. 10\nB. 7\nC. 6\nD. 12\nE. 15\n\n### Answer:\nExplanation :\nax2 + bx + 1 = 0 .\nFor real roots\n=> b2 -4ac \u2265 0 .\ni.e b2 - 4a(1) \u2265 0 .\ni.e b2 \u2265 4a.\nFor a = 1, 4a = 4, \u2234 b = 2, 3, 4\na = 2, 4a = 8, \u2234 b = 3, 4\na = 3, 4a = 12, \u2234 b = 4\na = 4, 4a = 16, \u2234 b = 4\n\u2234 Number of equations possible = 7.\nHarsh Mishra a year ago\n0 upvotes\nAnswer : B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average weight of 10 oarsmen in a boat is increased by 1.8 kg when one of the crew, who weighs 53 kg is replaced by a new man. Find the weight of the new man.\n\n### Options:\nA. 69\nB. 72\nC. 75\nD. 71\nE. None of them\n\n### Answer:\nTotal weight increased =(1.8 x 10) kg =18 kg.\n:. Weight of the new man =(53 + 18) kg =71 kg.\nAnswer is D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSamantha is driving from City A to City B. The distance between the two cities is 88 miles. She is driving at a constant speed of 22 miles per hour, and has been travelling for half an hour after starting from City A. What percent of the total distance she is yet to cover?\n\n### Options:\nA. 87\nB. 87.5\nC. 88\nD. 90\nE. 97.5\n\n### Answer:\nShe is driving at the rate of 22 miles per hour for half an hour.\nMeans the distance she has covered so far is = speed x time = 22 miles per hour x 0.5 hour = 11 miles.\nTherefore, the distance she is yet to cover is 88 - 11 = 77 miles.\nWe want to know 77 miles is what percent of the total distance (88 miles). Let it be x % of the total distance.\nThis means x % of 88 = 77\nSolving we get, x = 87.5\nAns B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train covers a distance at a speed of 240kmph in 5 hours. To cover the same distance in 5/3 hours, it must travel at a speed of?\n\n### Options:\nA. 516\nB. 840\nC. 560\nD. 720\nE. 920\n\n### Answer:\nDistance = 240*5 = 1200km\nRequired speed = 1200*3/5 = 720 km/hr\nAnswer is D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average age of 30 students of a class is 20 years. Out of these, the average age of 10 students is 16 years and that of the other 19 students is 22 years. The age of the 30th student is:\n\n### Options:\nA. 22 years\nB. 24 years\nC. 15 years\nD. 16 years\nE. None of these\n\n### Answer:\nExplanation :\nAge of the 30th student = [30 x 20 - (10 x 16 + 19 x 22)] = (600 - 278) = 22 years.\nAnswer : A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the complement of a certain angle is six times the measure of that certain angle, then what is the measure of that certain angle?\n\n### Options:\nA. 45\u00b0\nB. 30\u00b0\nC. 12.9\u00b0\nD. 18\u00b0\nE. 15\u00b0\n\n### Answer:\nThecomplementof angle A is the angle which, when added to angle A, gives 90 degrees. The two acute angles of a right triangle are complements, for example.\nThe original angle is x, so the complement is 6x, and together, these add up to 90 degrees.\nx + 6x = 90\n7x = 90\nx = 12.9\u00b0\nAnswer = (C)\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe difference of the squares of two consecutive even integers is divisible by which of the following integers ?\n\n### Options:\nA. 5\nB. 18\nC. 7\nD. 45\nE. 4\n\n### Answer:\nExplanation:\nLet the two consecutive even integers be 2n and (2n + 2). Then,\n(2n+2)^2 = (2n+2 2n)(2n 2-2n)\n= 2(4n + 2)\n=4(2n + 1), which is divisible by 4.\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 8 men or 12 women can do a piece of work in 40 days, in how many days can the same work be done by 6 men and 11 women?\n\n### Options:\nA. 10 days\nB. 11 days\nC. 13 days\nD. 15 days\nE. 24 days\n\n### Answer:\n8men = 12women (i.e 2men = 3women)\n12women 1 day work= 1/40\nsoln:\n6men(9women)+ 11women=20women=?\n1 women 1 day work =12*40= 1/480\nso, 20 women work= 20/480=1/24\nans: 24 days\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a two-digit positive integer has its digits reversed, the resulting integer differs from the original by 54. By how much do the two digits differ?\n\n### Options:\nA. 3\nB. 4\nC. 5\nD. 6\nE. 7\n\n### Answer:\nGiven that (10a + b) - (10b + a) = 54 --> 9a - 9b =54 --> a - b = 6.\nAnswer: D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat number is that, to which if 1, 5, and 13, be severally added, the first sum shall be to the second, as the second to the third?\n\n### Options:\nA. 1\nB. 2\nC. 3\nD. 4\nE. 5\n\n### Answer:\nSolution\nLet x= the number required.\nBy the conditions, x+1:x+5 = a+5:x+13\nSubtracting terms, (Art. 385,2.) x+1:4 = x+5:8\nTherefore 8x+8 = 4x+20. And x = 3.\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe area of a square is 144 m\u00b2. Find its perimeter.\n\n### Options:\nA. 18 m\nB. 28 m\nC. 38 m\nD. 42 m\nE. 48 m\n\n### Answer:\nArea of square = side \u00d7 side\nGiven; area of square = 144 m\u00b2\nTherefore, side\u00b2 = 144 m\u00b2\nTherefore, side = \u221a(144 m\u00b2) = \u221a(2 \u00d7 2 \u00d7 2 \u00d7 2 \u00d7 3 \u00d7 3) m\u00b2 = 2 \u00d7 2 \u00d7 3 m = 12 m\nNow, the perimeter of the square = 4 x side = 4 \u00d7 12 m = 48 m\nANSWER : E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn the expression 51840/x^4, for which of the following values of x will the expression NOT be an integer?\n\n### Options:\nA. 1/2\nB. 1\nC. 2\nD. 3\nE. 5\n\n### Answer:\nWe can straightaway eliminate A & B, since the expression will always yields an integer for those values\nOut of C, D, and E. Let us consider option E. 51840 has only one trailing zero and tens digit is not 5, so It has just one 5 in it. But for the expression to be an integer numerator should have 5^4.\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA jogger running at 9 kmph alongside a railway track is 240 metres ahead of the engine of a 120 metre long train running at 45 kmph in the direction opposite to that in which the train is going ?\n\n### Options:\nA. 3.6sec\nB. 18sec\nC. 36sec\nD. 72sec\nE. None\n\n### Answer:\nSolution\nSpeed of train relative to jogger =(45-9)km/hr =36km/hr\n(36*5/18)m/sec = 10 m/sec\nDistance to be covered = (240 +120)m= 360m\n\u2234 Time taken =(360/10)sec= 36 sec\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n1600 men have provisions for 28 days in the temple. If after 4 days, 400 men leave the temple, how long will the food last now?\n\n### Options:\nA. 22\nB. 77\nC. 32\nD. 27\nE. 29\n\n### Answer:\n1600 ---- 28 days\n1600 ---- 24\n1200 ---- ?\n1600*24 = 1200*x\nx = 32 days\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a+b=\u22129, and a=30/b, what is the value of a^2+b^2?\n\n### Options:\nA. 31\nB. 21\nC. 41\nD. 61\nE. 51\n\n### Answer:\na^2 + b^2 should make you think of these formulas:\n(a+b)(a+b) = a^2+b^2+2ab\nWe already know (a+b) = -9 and a*b = 30\n(a+b)(a+b) = (-9)(-9) = a^2+b^2+2*(30)\na^2+b^2 = 81 - 60 = 21\nAnswer : B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA thief steals at a car at 2.30 p.m. and drives it at 40 km/hr. The theft is discovered at 3 p.m. and the owner sets off in another car at 75 km/hr. When will he overtake the thief?\n\n### Options:\nA. 6:34 p.m\nB. 9:34 p.m\nC. 3:34 p.m\nD. 2:34 p.m\nE. 3:41 p.m\n\n### Answer:\n:\nSuppose the thief is overtaken x hrs after 2.30 p.m.\nThen, distance covered by the owner in (x - 1/2) hrs.\n40x = 75(x - 1/2) => x = 15/14hrs.\nSo, the thief is overtaken at 3:34 p.m.'\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many times are the hands of a clock at right angle in a day?\n\n### Options:\nA. 44\nB. 21\nC. 22\nD. 41\nE. 40\n\n### Answer:\nA\n44\nIn 12 hours, they are at right angles 22 times.\nIn 24 hours, they are at right angles 44 times.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n2 students appeared at an examination. 1 of them secured 9 marks more than the other one and hismarks was 56% of the sum of their marks. Find the marks obtained by them are?\n\n### Options:\nA. 39 and 31\nB. 40 and 33\nC. 42 and 33\nD. 37 and 31\nE. 35 and 32\n\n### Answer:\nLet their marks be (x+9) and x.\nThen, x+9 = 56/100(x + 9 +x)\n=> 25(x+9)\n=> 14 (2x + 9)\n=> 3x = 99\n=> x = 33.\nSo, their marks are 42 and 33\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many figures are required to number the pages the pages of a book containing 2200 pages?\n\n### Options:\nA. 7593\nB. 6693\nC. 7693\nD. 7793\nE. 7893\n\n### Answer:\n1 to 9 = 9 * 1 = 9\n10 to 99 = 90 * 2 = 180\n100 to 999 = 900 * 3 = 2700\n1000 to 2200 = 1201 * 4 = 4804\n-----------\n7693\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn the biology lab of \"Jefferson\" High School there are 4.32*10^6 germs, equally divided among 10,800 Petri dishes. How many germs live happily in a single dish?\n\n### Options:\nA. 100\nB. 200\nC. 400\nD. 1000\nE. 5000\n\n### Answer:\n4.32*10^6/ 10800==> 43.2*10^3/108==> 43200/108= 400\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOn a game show, a contestant spins two different wheels; each wheel is numbered 1 to 15. What is the probability that the contestant will spin all tens?\n\n### Options:\nA. 25\nB. 64\nC. 8/7\nD. 4/6\nE. 1/225\n\n### Answer:\nAll 15s:\n1st wheel = 15 = 1/15\n2nd wheel = 15 = 1/15\n(1/15)(1/15)= 1/225\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n200 hundred multiples of seven are chosen at random, and 500 multiples of eight are chosen at random. Approximately what percentage of the 700 selected numbers are odd?\n\n### Options:\nA. 14.29%\nB. 15.29%\nC. 16.29%\nD. 17.29%\nE. 18.29%\n\n### Answer:\n--> Multiples of 7 are 7, 14, 21, 28, 35, 42....\nOut of first 4 multiples, 2 are odd; out of first 6 multiples, 3 are odd.\nSo approx. 50 % of the 200 multiples are odd i.e 100 multiples.\n--> Similalrly, for 8 multiples are:8,16,24...\nAll are even so 0 % are odd.\nTotal odd= (100+0)/(200+500)= 100/700=1/7 = 14.29%\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the first day of a year (other than leap year) was Sunday, then which was the last day of that year?\n\n### Options:\nA. Saturday\nB. Sunday\nC. Tuesday\nD. Monday\nE. None of these\n\n### Answer:\nExplanation :\nGiven that first day of a normal year was Sunday\nOdd days of the mentioned year = 1 (Since it is an ordinary year)\nHence First day of the next year = (Sunday+ 1 Odd day) = Monday\nTherefore, last day of the mentioned year = Sunday. Answer : Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf log 2 = 0.3010 and log 3 = 0.4771, the value of log5 512 is:\n\n### Options:\nA. 2.87\nB. 2.965\nC. 3.876\nD. 3.9\nE. 4.526\n\n### Answer:\nlog5 512 = log 512/ log 5\n= log 2^9/log(10/2)\n=9 log 2 /log 10 - log 2\n=(9*0.3010)/1-0.3010\n=2.709/0.699 = 2709/699\n= 3.876\nANSWER C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOut of first 20 natural numbers, one number is selected at random. The probability that it is either an even number or a prime number is?\n\n### Options:\nA. 17/25\nB. 17/24\nC. 17/29\nD. 17/20\nE. 17/21\n\n### Answer:\nn(S) = 20\nn(Even no) = 10 = n(E)\nn(Prime no) = 8 = n(P)\nP(E\u1d1cP) = 10/20 + 8/20 - 1/20 = 17/20\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo men and three women working 7 hours a day finish a work in 5 days. Four men and four women working 3 hours a day complete the work in 7 days. The number of days in which only 7 men working 4 hours a day will finish the work is?\n\n### Options:\nA. 6 days\nB. 2 days\nC. 7 days\nD. 5 days\nE. 1 days\n\n### Answer:\nD\n2M + 3W ----- 35 h\n4M + 4W ------- 21 h\n7M -------? d\n70M + 105W = 84M +84M\n21W = 14M => 2M = 3W\n4 * 35 = 7 * x => x = 20 hours\n20/4 = 5 days\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFor any number s, s* is defined as the greatest positive even integer less than or equal to s. What is the value of 5.2 \u2013 5.2*?\n\n### Options:\nA. 0.2\nB. 1.2\nC. 1.8\nD. 2.2\nE. 4.0\n\n### Answer:\nSince s* is defined as the greatest positive even integer less than or equal to s, then 5.2* = 4 (the greatest positive even integer less than or equal to 5.2 is 4).\nHence, 5.2 \u2013 5.2* = 5.2 - 4 = 1.2\nAnswer: B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo trains are running in opposite directions with the same speed. If the length of each train is 120 m and they cross each other in 8 sec, then the speed of each train is?\n\n### Options:\nA. 54\nB. 77\nC. 36\nD. 88\nE. 21\n\n### Answer:\nLet the speed of each train be x m/sec.\nThen, relative speed of the two trains = 2x m/sec.\nSo, 2x = (120 + 120)/8 => x = 15\nSpeed of each train = 15 m/sec.\n= 15 * 18/5 =- 54 km/hr.Answer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn the first 10 overs of a cricket game, the run rate was only 3.2. What should be the rate in the remaining 40 overs to reach the target of 282 runs?\n\n### Options:\nA. 6.25\nB. 6.22\nC. 6.29\nD. 6.39\nE. 6.13\n\n### Answer:\nRequired run rate\n= [282 - (3.2 * 10)]/40\n= 250/40\n= 6.25\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many of the following numbers are divisible by 132 ?\n264, 396, 462, 792, 968, 2178, 5184, 6336\n\n### Options:\nA. 1\nB. 4\nC. 5\nD. 7\nE. 3\n\n### Answer:\nB\nBy using your calculator you can calculate that the following numbers are divisible by 132 : 264, 396, 792 and 6336.\nRequired number of number = 4.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 2x = 3y = 10, then 6xy = ?\n\n### Options:\nA. 100\nB. 200\nC. 120\nD. 40\nE. 20\n\n### Answer:\n2x = 10;x=5\n3y = 10;y=10/3\nMultiply: 6xy=6*5*10/3=100\nAnswer: A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a committee of 3 people is to be selected from among 5 married couples so that the committee does not include two people who are married to each other, how many B such committees are possible?\n\n### Options:\nA. B=20\nB. 40\nC. 50\nD. B=80\nE. 120\n\n### Answer:\nEach couple can send only onerepresentativeto the committee. Let's see in how many ways we can choose 3 couples (as there should be 3 members) each to send onerepresentativeto the committee: 5C3=10.\nBut these 3 chosen couples can send two persons (either husband or wife): 2*2*2=2^3=8.\nTotal # of ways: 5C3*2^3=80.\nAnswer: D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nExpress 25 mps in kmph?\n\n### Options:\nA. 22\nB. 87\nC. 90\nD. 77\nE. 22\n\n### Answer:\n25 * 18/5 = 90 kmph\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJohn and Peter are among the eight players a volleyball coach can choose from to field a six-player team. If all six players are chosen at random, what is the probability of choosing a team that includes John and Peter?\n\n### Options:\nA. 7/15\nB. 11/20\nC. 14/25\nD. 15/28\nE. 16/35\n\n### Answer:\nThe total possible ways of selecting a 6-member team is 8C6 = 28\nThe possible ways which include John and Peter is 6C4 = 15\nThe probability of choosing both John and Peter is 15/28\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe difference between simple and compound interests compounded annually on a certain sum of money for 2 years at 4% per annum is Re. 1. The sum (in Rs. ) is?\n\n### Options:\nA. 625\nB. 286\nC. 266\nD. 191\nE. 811\n\n### Answer:\nExplanation:\nLet the sum be Rs. x. Then,\n[x (1 + 4/100)2 - x] = (676/625 x - x) = 51/625 x\nS.I. = (x * 4 * 2)/100 = 2x/25\n51x/625 - 2x/25 = 1 or x = 625.\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nBy selling an article at Rs.120, a profit of 25% is made. Find its cost price?\n\n### Options:\nA. s.96\nB. s.45\nC. s.120\nD. s.180\nE. s.189\n\n### Answer:\nSP = 120\nCP = (SP)*[100/(100+P)]\n= 120* [100/(100+25)]\n= 120* [100/125]\n= Rs.96\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a, t, and c are consecutive even integers and a < t < c, all of the following must be divisible by 4 EXCEPT\n\n### Options:\nA. a + c\nB. t + c\nC. ac\nD. (bc)/2\nE. (abc)/4\n\n### Answer:\nI did get the correct answer within 80 seconds and it was not by luck either. I did not pick numbers but just used the concept stated by Ian.\nThe 3 numbers can be written as\na, (a + 2)(a + 4).\nIf 'a' is divisible by 4, then even 'c' or 'a + 4' is divisible by 4. However, is 'b' is divisible by 4, then both 'a' and 'a + 4' are still divisible by 2.\nA - (a + c) = a + (a + 4) = 2a + 4 = 2(a + 2) = 2b. 2b will always be divisible by 4 even if 'b' is not divisible by 4. Reason: 'b' already has a prime factorization of at least a '2'. Hence '2b' has two 2s.\nC - ac = a(a+4). If, as stated above, one of them is divisible by 4, then the product is divisible. If both of them are not divisible by 4, then the product is still divisible by 4 because of the presence of two 2s again in the prime factorization.\nD - bc/2 = (a + 2)(a + 4)/2. Either b or c is divisible by 2. Hence, if we assume that b is divisible by 2 and not divisible by 4, then it leaves us just one possibility. Is c divisible by 4? It has to be because c is the next consecutive even integer.\nE - atc/4 = a(a + 2)(a + 4)/4. One of these integers is divisible by 4 already. If we again assume 'b' to be that integer divisible by 4, then we are left with the question - Is a(a + 4) divisible by 4? This is the same as option C.\nB - b + c = (a + 2) + (a + 4) = 2a + 6 = 2(a + 3). (a + 3) will never be divisible by 2 because it is an odd integer. Hence, 2(a + 3), although divisible by 2, will not be divisible by 4 because it has just one 2 in its prime factorization.\nAs a whole, whether you choose numbers (2, 46 being the easiest) or solve conceptually, the answer is still easily obtainable within 2 minutes.B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the side of a square is increased by 55%, its area is increased by?\n\n### Options:\nA. 140%\nB. 145%\nC. 150%\nD. 160%\nE. none of these\n\n### Answer:\nSince Side x Side = Area\nTherefore, net% change in area\n= ( x + y + xy/100) %\n= [55 + 55 + (55 x 55)/100]% or 140.25%\nTherefore, area is increased by 140.25%\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRectangle A has sides a and b, and rectangle B has sides c and d. If a/c=b/d=3/5, what is the ratio of rectangle A\u2019s area to rectangle B\u2019s area?\n\n### Options:\nA. 5/3\nB. 9/5\nC. 9/25\nD. 3/5\nE. 25/9\n\n### Answer:\nThe area of rectangle A is ab.\nc=5a/3 and d=5b/3.\nThe area of rectangle B is cd=25ab/9.\nThe ratio of rectangle A's area to rectangle B's area is ab / (25ab/9) = 9/25.\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nLet p and q be the root of the quadratic equation x2 - (\u221d - 2)x - \u221d -1 =0. what is the minimum possible value of p2 + q2 ?\n\n### Options:\nA. 0\nB. 3\nC. 4\nD. 5\nE. 6\n\n### Answer:\nExplanation :\np + q = \u03b1 \u20132 and pq = \u2013\u03b1 \u2013 1\n(p + q)2 = p2 + q2 + 2pq,\nThus (\u03b1 \u20132)2 = p2 + q2 + 2(\u2013\u03b1 \u2013 1)\np2 + q2 = \u03b12 \u2013 4\u03b1 + 4 + 2\u03b1 + 2\np2 + q2 = \u03b12 \u2013 2\u03b1 + 6\np2 + q2 = \u03b12 \u2013 2\u03b1 + 1 + 5\np2 + q2 = (\u03b1 \u2013 1)2 + 5\nThus, minimum value of p2 + q2 is 5.\nAnswer : D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nI chose a number and divide it by 5. Then I subtracted 154 from the result and got 6. What was the number I chose?\n\n### Options:\nA. 200\nB. 600\nC. 300\nD. 800\nE. 1000\n\n### Answer:\nLet x be the number I chose, then\nx/5\u2212154=6\nx/5=160\nx=800\ncorrect answer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n12 chairs are arranged in a row and are numbered 1 to 12. 4 men have to be seated in these chairs so that the chairs numbered 1 to 8 should be occupied and no two men occupy adjacent chairs. Find the number of ways the task can be done.\n\n### Options:\nA. 360\nB. 384\nC. 432\nD. 470\nE. None\n\n### Answer:\nSolution:\nGiven there are 12 numbered chairs, such that chairs numbered 1 to 8 should be occupied.\n1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12.\nThe various combinations of chairs that ensure that no two men are sitting together are listed.\n(1, 3, 5,__), The fourth chair can be 5,6,10,11 or 12, hence 5 ways.\n(1, 4, 8, __), The fourth chair can be 6,10,11 or 12 hence 4 ways.\n(1, 5, 8, __), the fourth chair can be 10,11 or 12 hence 3 ways.\n(1, 6, 8,__), the fourth chair can be 10,11 or 12 hence 3 ways.\n(1,8,10,12) is also one of the combinations.\nHence, 16 such combinations exist.\nIn case of each these combinations we can make the four men inter arrange in 4! ways.\nHence, the required result =16*4!= 384.\nAnswer: Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJake bought oranges at the supermarket for Y dollars an orange and sugar for M dollars per kilogram.\nThen, he made lemonade using P oranges and Q kgs of sugar per liter and he sold Z liters of lemonade for X dollars per liter.\nHow much money has he made after selling all the lemonade?\n\n### Options:\nA. ZX(PY+QM)\nB. ZPM-ZQY\nC. XZ-PYZ-QMZ\nD. XZ-(MQ-YP)\nE. XQ-PY+ZM\n\n### Answer:\nFirst, the cost of the lemonade per liter= PY+QM dollars\nSince Jake sold Z liters of lemonade, the cost price= Z(PY+QM) dollars\nThe selling price=ZX dollars\nProfit=ZX-Z(PY+QM)\n=(X-PY-QM)Z\nThe answer is C!!\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf S is the product of all positive integers less than 31, than what is the greatest integer k for which S/18^k is an integer?\n\n### Options:\nA. 3\nB. 6\nC. 7\nD. 14\nE. 26\n\n### Answer:\n30! S must be divisible by (3*3*2)^k.\nAs I will find a lot of 2's among 30!'s factors I will focus on the 3's (that also occurs twice instead of only once as a factor in 18).\nEvery multiple of 3 will provide me with atleast one factor of 3. There aren't that many so I list them quickly.\n3 6 9*\n12 15 18*\n21 24 27**\n30\nThe stars are marked as they are multiples of 9* or 27** and thus provides two or three 3's respectively.\n3=3 (occurs 10 times) +10\n3*3=9 (occurs 3 times) +3(adding just one additional three each as they were not counted for in the multiples of 3)\n3*3*3=27 (occurs 1 time) +1 (again, adding just one as they were previously not counted)\nTotal: 14.\nFor every k we add two 3's. So we must divide 14 by 2 to get the highest integer K before we receive a non-integer result.\nAnswer: 7 -> Answer choice: C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n6x \u2212 12 = 6y\n4y + 4x = 12\nWhich of the following is the number of solutions to the system of equations shown above?\n\n### Options:\nA. More than three\nB. Exactly one\nC. Exactly two\nD. Exactly three\nE. None\n\n### Answer:\n6x \u2212 12 = 6y\n=> 6x - 6y = 12\n=> x- y =2 -- 1\n4y + 4x = 12\n=>x + y = 3 -- 2\nFrom equation 1 and 2 , we get\n2x = 5\n=> x=2.5\ny=.5\nTherefore , the given system will have Exactly one solution\nAnswer : B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average weight of A, B and C is 45 kg. If the average weight of A and B be 40 kg and that of B and C be 41 kg, then the weight of B is:\n\n### Options:\nA. 27 kg\nB. 20 kg\nC. 26 kg\nD. 31 kg\nE. 35 kg\n\n### Answer:\nlet d sum of a, b, c is 3*45=135\nand sum of a and b s 2*40=80\nsum of b and c is 2*41=82\nhence 80+82-135=27\nans=27\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf x > 1, which of the following decreases as x decreases?\nI. x + x^3\nII. 2x^2 \u2212 x\nIII. 1/(x + 1)\n\n### Options:\nA. I only\nB. II only\nC. III only\nD. I and III\nE. II and II\n\n### Answer:\nlet x= 4 and 3 b old and new values\nST1: x= 4 -> 4+64 = 68\nx=3-> 3+27= 30 ...decreased\nST2:x= 4-> 2*16-4 = 28\nx=3->2*9-3 = 15\ndecreased\nSt3: x=4-> 1/4 = .25\nx=3->1/3 = .33\nAns: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJohn have a 630ml mixture of milk and water in the ratio 7:2. How much water must be added to make the ratio 7:3?\n\n### Options:\nA. 50 ml\nB. 60 ml\nC. 70 ml\nD. 80 ml\nE. 90 ml\n\n### Answer:\nconcentration of water in mixture1 =29 (since the ratio of milk and water = 7:2) ...(1)\nconcentration of water in pure water= 1 ...(2)\nNow the above mentioned items are mixed to form mixture2 where milk and water ratio = 7 : 3\n=> concentration of water in mixture2 =310\nBy rule of alligation,\nconcentration of water in mixture1 (29)\nconcentration of water in pure water (1)\nMean concentration\n(310)\n1\u2212310=710\n310\u221229=790\n=> Quantity of mixture1 : Quantity of water\n=710:790=110:190=1:19\nGiven that Quantity of mixture1 = 630 ml\n=> 630 : Quantity of water =1:19\n=> Quantity of water =630\u00d719=70 ml\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA warehouse is labeling computer inventory with 3-digit codes. Each code is to consist of four digits between the numbers 0 and 8. The manager is debating whether to allow any 3-digit codes to have leading zero's before a non-zero number is used. If not allowed, then numbers like0025cannot be used.\nThe manager wants to measure the magnitude of the number of 3-digit code possibilities that are lost if he disallows the use of leading zero's. How many such codes would be lost?\n\n### Options:\nA. 981\nB. 1000\nC. 1011\nD. 1101\nE. 200\n\n### Answer:\nThe number of codes possible if leading zero is allowed = 10*10*10=10^3\nThe number of codes possible if leading zero is NOT allowed = 8*10*10=9*10^2\nThe difference = 10^3 - 8*10^2 = 10^2(10-8) = 2*10^2.\nAnswer: E.\nSimilar questions to practice:\nHope it helps.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the cost of A metres of wire is C rupees, then what is the cost of E metres of wire at the same rate?\n\n### Options:\nA. Rs. (EC/A)\nB. Rs. (EC)\nC. Rs. (C/A)\nD. Rs. (E/A)\nE. Rs. (AC/E)\n\n### Answer:\ncost of A metres of wire = Rs.C\ncost of 1 metre of wire = Rs.(C/A)\ncost of E metre of wire = Rs.(E\u00d7C/A)=Rs. (EC/A)\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a copier makes 20 copies every 6 seconds, then continues at this rate, how many minutes will it take to make 2,000 copies?\n\n### Options:\nA. 13\nB. 15\nC. 12\nD. 11\nE. 10\n\n### Answer:\n20 copies 6 seconds\n2000 copies = (2000*6)/20 seconds\n= 600/60 minutes\n= 10 minutes\nAnswer : E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn an increasing sequence of 8 consecutive even integers, the sum of the first 4 integers is 284. What is the sum of all the integers in the sequence?\n\n### Options:\nA. 552\nB. 568\nC. 574\nD. 586\nE. 600\n\n### Answer:\nlet the first term of the sequence be x\nsince it is consecutive even integers the terms be we x, x+2,x+4...x+14 (up to 8 terms)\nnow,\nsum of first 4 terms =284\nor,\n4x+12=284\nx=272/4=68\nThus the answer can now be calculated by either summing up 68+70+72+... 8th term\nor\ns=n/2(2a+(n-1)d\n=8/2(2*68+(7*2))\n=4(136+14)=600\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA sales staff is composed of a sales manager and two sales people, all of whom earn commission as a percentage of sales. Each sales person earns 5% commission on sales. In a given week, the sales staff earned a total of $2,500 in commissions on $5,000 worth of sales. What commission rate did the sales manager earn during that week?\n\n### Options:\nA. 25%\nB. 30%\nC. 35%\nD. 40%\nE. 45%\n\n### Answer:\nD for me.\nLet managers comminsion rate be M.\nm*5000+ 2*0.05*5000=2500\n5000*m=2000\nm=40/100=40%\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe banker's gain of a certain sum due 2 years hence at 10% per annum is Rs.24. The present worth is\n\n### Options:\nA. Rs. 480\nB. Rs. 520\nC. Rs. 600\nD. Rs. 960\nE. None\n\n### Answer:\nSolution\nT.D\t= (B.G x 100/Rate x Time)\n= Rs.(24x100 / 10x 2)\n= Rs.120.\nP.W\t= (100 x T.D/Rate x Time)\n= Rs.(100x120 / 10x 2)\n= Rs.600.\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA person lent a certain sum of money at 4% per annum at simple interest and in 8 years the interest amounted to Rs.238 less than the sum lent. What was the sum lent?\n\n### Options:\nA. 228\nB. 350\nC. 289\nD. 500\nE. 821\n\n### Answer:\nP - 238 = (P*4*8)/100\nP = 350\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the greatest number of three digits which is divisible by 8, 16, 32 ?\n\n### Options:\nA. 997\nB. 992\nC. 999\nD. 998\nE. 990\n\n### Answer:\nGreatest number of 3 digits = 999\nLCM of 8, 16, 32 = 32\n999 \u00f7 32 = 31, remainder = 7\nHence, greatest number of four digits which is divisible by 8,16,32\n= 999 - 7 = 992\nanswer : B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAlice can bake a pie in 5 minutes. Bob can bake a pie in 6 minutes. Compute how many more\npies Alice can bake than Bob in 60 minutes.\n\n### Options:\nA. 1\nB. 2\nC. 3\nD. 4\nE. 5\n\n### Answer:\nAlice can bake 60/5 = 12 pies in 60 minutes. Bob can bake 60/6 = 10 pies in 60 minutes.\nAlice can therefore bake 12 - 10 = 2 more pies than Bob.\ncorrect answer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA, B and C started a business with capitals of Rs. 8000, Rs. 10000 and Rs. 12000 respectively. At the end of the year, the profit share of B is Rs. 1500. The difference between the profit shares of A and C is?\n\n### Options:\nA. 8867\nB. 299\nC. 279\nD. 600\nE. 2612\n\n### Answer:\nRatio of investments of A, B and C is 8000 : 10000 : 12000 = 4 : 5 : 6\nAnd also given that, profit share of B is Rs. 1500\n=> 5 parts out of 15 parts is Rs. 1500\nNow, required difference is 6 - 4 = 2 parts\nRequired difference = 2/5 (1500) = Rs. 600.Answer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIt has been raining at the rate of 5 centimeters per hour. If the rain filled a cylindrical drum with a depth of 15 centimeters, and area 300 square centimeters, how long did it take to fill the drum completely?\n\n### Options:\nA. 3 hours\nB. 4 hours 15 minutes\nC. 6 hours\nD. 2 hours 5 minutes\nE. 8 hours\n\n### Answer:\nAnswer is : A, 3 hours\nThe volume of the drum is irrelevant and only height matters since rain fell all over the city.\nThus, it takes only 15 / 5 = 3 hours of rain to fill the drum\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRs.4500 amounts to Rs.5544 in two years at compound interest, compounded annually. If the rate of the interest for the first year is 12%, find the rate of interest for the second year?\n\n### Options:\nA. 10%\nB. 18%\nC. 19%\nD. 12%\nE. 13%\n\n### Answer:\nLet the rate of interest during the second year be R%. Given,\n4500 * {(100 + 12)/100} * {(100 + R)/100} = 5544\nR = 10%\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n12 times a positive integer is more than its square by 36, then the positive integer is\n\n### Options:\nA. 6\nB. 10\nC. 11\nD. 12\nE. 14\n\n### Answer:\nExplanation:\nLet the number be x. Then,\n12x = x2 + 36\n=> x2 - 12x + 36 = 0\n=>(x - 6)(x - 6) = 0\n=> x = 6\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA and B walk around a circular track. They start at 8 a.m. from the same point in the opposite directions. A and B walk at a speed of 1 rounds per hour and 1 rounds per hour respectively. How many times shall they cross each other before 9.30 a.m. ?\n\n### Options:\nA. A)5\nB. B)6\nC. C)8\nD. D)3\nE. E)9\n\n### Answer:\nRelative speed = 1 + 1 = 2 rounds per hour.\nSo, they cross each other 2 times in an hour and 1 times in half an hour.\nHence, they cross each other 3 times before 9.30 a.m.\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIt is being given that (2^32 + 1) is completely divisible by a whole number. Which of the following numbers is completely divisible by this number?\n\n### Options:\nA. (2^90 - 1)\nB. (2^90 + 1)\nC. (2^96 - 1)\nD. (2^96 + 1)\nE. (2^95 + 1)\n\n### Answer:\nLet 232 = x. Then, (232 + 1) = (x + 1).\nLet (x + 1) be completely divisible by the natural number N. Then,\n(296 + 1) = [(232)3 + 1] = (x3 + 1) = (x + 1)(x2 - x + 1), which is completely divisible by N, since (x + 1) is divisible by N.\nD)\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man on tour travels first 160 km at 64 km/hr and the next 160 km at 80 km/hr. The average speed for the first 320 km of the tour is?\n\n### Options:\nA. 11.11 km/hr\nB. 21.11 km/hr\nC. 71.11 km/hr\nD. 81.11 km/hr\nE. 41.11 km/hr\n\n### Answer:\nExplanation:\nTotal time taken = (160/64 + 160/8)hrs\n= 9/2 hrs.\nAverage speed = (320 x 2/9) km.hr\n= 71.11 km/hr.\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThree partners A, B, C in a business invested money such that 2(A\u00e2\u20ac\u2122s capital) = 5(B\u00e2\u20ac\u2122s capital) = 10(C\u00e2\u20ac\u2122s capital) then, The ratio of their capitals is\n\n### Options:\nA. 63 : 45 : 34\nB. 63 : 54 : 34\nC. 5 : 2 : 1\nD. 63 : 45 : 35\nE. None of these\n\n### Answer:\nExplanation:\nLet 2(A\u00e2\u20ac\u2122s capital) = 5(B\u00e2\u20ac\u2122s capital) = 10(C\u00e2\u20ac\u2122s capital) = Rs.x\nThen, A\u00e2\u20ac\u2122s capital = Rs x/2, B\u00e2\u20ac\u2122s capital = Rs. x/5 and C\u00e2\u20ac\u2122s capital = Rs. x/10\nA : B : C = x/2 : x/5 : x/10\n5 : 2 : 1\nAnswer: Option C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf X and Y are both positive two-digit integers and share no digits, and X > Y, what is the smallest possible value of X - Y?\n\n### Options:\nA. 0\nB. 1\nC. 2\nD. 3\nE. 9\n\n### Answer:\nAnswer = B = 1\n20 - 19 = 30-29 = 40-39 = 50-49 = 1\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf -5 < x < 7 and -6 < y < 3, which of the following specifies all the possible values of xy?\n\n### Options:\nA. -42 < xy < 30\nB. -42 < xy < 24\nC. -28 < xy < 18\nD. -24 < xy < 21\nE. -24 < xy < 24\n\n### Answer:\nThe least value of xy is a bit more than 7*(-6)=-42 and the largest value of xy is a bit less than (-5)*(-6)=30.\nTherefore -42 < xy < 30.\nAnswer: A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA completes a work in 12 days and B complete the same work in 24 days. If both of them work together, then the number of days required to complete the work will be\n\n### Options:\nA. 8 days\nB. 9 days\nC. 10 days\nD. 12 days\nE. 13 days\n\n### Answer:\nIf A can complete a work in x days and B can complete the same work in y days, then, both\nof them together can complete the work in x y/ x+ y days\nTherefore, here, the required number of days = 12 \u00d7 24/ 36 = 8 days.\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nBunny's brother Sunny is 562 days older to him while his sister Jenny is 75 weeks older to Sunny. If Jenny was born on Tuesday, on which day was Bunny born?\n\n### Options:\nA. Monday\nB. Tuesday\nC. Friday\nD. Saturday\nE. Thursday\n\n### Answer:\n562-(75*7)=37\n37--------7*5=35\nremaing 2+tuesday\nans:thursday\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSravan travelled for 15 hours. He covered the first half of the distance at 45 kmph and remaining half of the distance at 30 kmph. Find the distance travelled by Sravan?\n\n### Options:\nA. 520\nB. 540\nC. 550\nD. 560\nE. 440\n\n### Answer:\nLet the distance travelled be x km.\nTotal time = (x/2)/45 + (x/2)/30 = 15 => x/90+ x/60 = 15 => (2x + 3x)/180 = 15\n=> x = 540 km\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how many different number of ways 4 boys and 2 girls can sit on a bench?\n\n### Options:\nA. 600\nB. 640\nC. 720\nD. 740\nE. 760\n\n### Answer:\nnpn = n!\n6p6 = 6 \u00d7 5 \u00d7 4 \u00d7 3 \u00d7 2 \u00d7 1 = 720\nC)\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhen positive integer k is divided by 5, the remainder is 2. When k is divided by 6, the remainder is 5. If k is less than 38, what is the remainder when k is divided by 7?\n\n### Options:\nA. 2\nB. 4\nC. 3\nD. 5\nE. 6\n\n### Answer:\nCant think of a straight approach but here is how I solved it:\nK is divided by 5 and remainder is 2. This means k = 5n + 2 (n is an integer)\nso the possible values of K = {2, 7, 12, 17, 22, 27, 32, 37} (less than 38)\nSecondly, if K is divided by 6, the remainder is 5 => k= 6m + 5\nso the possible value set for k = {5, 11, 17, 23, 29,35} (less than 38)\n17 is the only common number in both the sets. Hence k = 17\nAnswer : C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAs a treat for her two crying children, a mother runs to the freezer in which she has two cherry ice pops, four orange ice pops, and four lemon-lime ice pops. If she chooses two at random to bring outside to the children, but realizes as she runs out the door that she cannot bring them different flavors without one invariably being jealous of the other and getting even more upset, what is the probability that she has to return to the freezer to make sure that they each receive the same flavor?\n\n### Options:\nA. 1/9\nB. 1/6\nC. 5/18\nD. 4/45\nE. 5/6\n\n### Answer:\nProbability of not getting the same flavor ->\nFavorable -> Cherry - orange [ 2C1 * 4C1 [or simply 2*4 ] or Cherry - lemon [ 2*4] or orange - lemon [4*4]\nProb = (2*4 + 2*4 + 4*4 ) / 9C2 = 32/360 = 4/45\nAnswer -> D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf log 27 = 1.431, then the value of log 9 is :\n\n### Options:\nA. 0.934\nB. 0.945\nC. 0.954\nD. 0.958\nE. None of these\n\n### Answer:\nSolution\nLog 27 = 1.431 \u21d2 log (33) = 1.431 \u21d2 3 log 3 = 1.431\n\u21d2 log 3 = 0.477\n\u2234 log 9 = log (32) = 2 log 3 = (2 \u00d7 0.477) = 0.954. Answer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nDavidson has a corporate proposal. The probability that vice-president Adams will approve the proposal is 0.7. The probability that vice-president Baker will approve the proposal is 0.5. The probability that vice-president Corfu will approve the proposal is 0.4. The approvals of the three VPs are entirely independent of one another.\nSuppose the Johnson must get VP Adam\u2019s approval, as well as the approval of at least one of the other VPs, Baker or Corfu, to win funding. What is the probability that Johnson\u2019s proposal is funded?\n\n### Options:\nA. 0.8\nB. 0.7\nC. 0.6\nD. 0.5\nE. 0.49\n\n### Answer:\nprobability of adams approval = 0.7\nbaker approval =0.5\ncorfu approval=0.4\nproabability of approval is must adam approval and atleast one approval\n= adam approval*baker approval*corfu approval(approval of both remaining)+adam approval*baker approval*corfu not approval(atleast one remaining approval)+\nadam approval*baker not approval*coffu approval( atleast one remaining approval\n= 0.7*0.5*0.4+0.7*0.5*0.6+0.7*0.5*0.4\n=0.14+0.21+0.14\n=0.49\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 50 percent of X is 25 percent of Y, then what is the relation between X and Y?\n\n### Options:\nA. X=Y\nB. 2X=Y\nC. X=2Y\nD. 1\nE. NONE OF ABOVE\n\n### Answer:\n50/100(X) = 25/100(Y)\n2X=Y..\nOption B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA mixture of 125 gallons of wine and water contains 20% of water. How much water must be added to the mixture in order to increase the percentage of water to 25% of the new mixture?\n\n### Options:\nA. 10 gallons\nB. 8.5gallons\nC. 8gallons\nD. 8.33gallons\nE. 9.33gallons\n\n### Answer:\nIn 125 gallons of the solution there are 0.2\u2217125=25 gallons of water. We want to add w gallons of water to 125 gallons of solution so that 25+w gallons of water to be 25% of new solution: 25+w=0.25(125+w) --> w=253\u22488.33.\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRobert walks from point A to point B at an average speed of 10 kilometers per hour. At what speed, in kilometers per hour, must Robert walk from point B to point A so that her average speed for the entire trip is 12 kilometers per hour?\n\n### Options:\nA. 15km/hr\nB. 21km/hr\nC. 16km/hr\nD. 20km/hr\nE. 17km/hr\n\n### Answer:\nLet's suppose that speed while returning was x km/h\nSince the distance is same, we can apply the formula of avg speed\nAvg speed= 2S1S2/S1+S2\n12= 2*10*x/10+x\nx= 15 km/hr\nanswer is A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf books bought at prices ranging from Rs. 250 to Rs. 350 are sold at prices ranging from Rs. 300 to Rs. 425, what is the greatest possible profit that might be made in selling eight books ?\n\n### Options:\nA. 23267\nB. 1400\nC. 1800\nD. 2778\nE. 76611\n\n### Answer:\nExplanation:\nLeast Cost Price = Rs. (250 * 8) = Rs. 2000.\nGreatest Selling Price = Rs. (425 * 8) = Rs. 3400.\nRequired profit = Rs. (3400 - 2000) = Rs. 1400.\nAnswer: B) 1400\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a 3 cm cube is cut into 1 cm cubes, then what is the percentage increase in the surface area of the resulting cubes?\n\n### Options:\nA. 40%\nB. 100%\nC. 150%\nD. 200%\nE. 300%\n\n### Answer:\nThe area A of the large cube is 3*3*6 = 54 square cm.\nThe area of the 27 small cubes is 27*6 = 54*3 = 3A, an increase of 200%.\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nCost of 16 mirror and 8 comb is Rs.352 and the cost of 4 mirror and 4 comb is Rs.96. Find the cost of each mirror?\n\n### Options:\nA. 10\nB. 12\nC. 20\nD. 21\nE. 22\n\n### Answer:\nLet the cost of each pen and pencil be 'p' and 'q' respectively.\n16m + 8c = 352 --- (1)\n4m + 4c = 96\n8m + 8c = 192 --- (2)\n(1) - (2) => 8p = 160\n=> m = 20\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many integers between 1 and 1,800 are divisible by 20,30,40?\n\n### Options:\nA. 14\nB. 15\nC. 16\nD. 17\nE. 18\n\n### Answer:\nLCM of the given numbers=120\nTherefore , number of integers = 1800/120\n=15\nOption B is answer\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nToday is Varun's birthday. One year, from today he will be twice as old as he was 12 years ago. How old is Varun today ?\n\n### Options:\nA. 33\nB. 98\nC. 25\nD. 29\nE. 27\n\n### Answer:\nExplanation:\nLet Varun's age today = x years.\nThen, Varun's age after 1 year = (x + 1) years.\nTherefore x + 1 = 2 (x - 12) x + 1 = 2x - 24 x = 25\nAnswer: C) 25 years\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nDifference between the length &breadth of a rectangle is 23 m. If its perimeter is 206 m, then its area is?? We have: (l - b) = 23 and 2(l + b) = 206 or (l + b) = 103?\n\n### Options:\nA. 1245 m^2\nB. 1345 m^2\nC. 2520 m^2\nD. 2560 m^2\nE. 2678 m^2\n\n### Answer:\nSolving the two equations, we get: l = 63 and b = 40.\nArea = (l x b) = (63 x 40) m2 = 2520 m^2\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a certain sample of data has a mean of 25.0 and a standard deviation of 2.0, which of the following pairs contain two values that are each at least 2.5 standard deviations from the mean?\n\n### Options:\nA. (19.0; 26.5)\nB. (14.5; 28.0)\nC. (23.0; 28.5)\nD. (22.5; 26.0)\nE. (19.0; 30.5)\n\n### Answer:\nThe standard deviation is 2, so 2.5 standard deviations would be (2.5)(2) = 5.\nThe values between 20 and 30 are within 2.5 standard deviations from the mean.\nThe answer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA bag contains 7 red, 2 green balls. 3 balls are drawn randomly. What is the probability that balls drawn contain exactly two green balls?\n\n### Options:\nA. 1/7\nB. 2/9\nC. 1/12\nD. 4/17\nE. 2/3\n\n### Answer:\nTotal number of balls = 7+2 = 9\nn(S) = 9C3 = 9*8*7 / 3*2 = 84\nn(E) = 2C2* 7C1 = 7\nProbability = 7/84 = 1/12\nAnswer is C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat approximate value should come in place of question mark (?) in the following equation\n287.532 + 1894.029 \u2013 657.48 = 543.095 + ?\n\n### Options:\nA. 870\nB. 790\nC. 980\nD. 770\nE. 890\n\n### Answer:\n? = 285 + 1895 \u2013 655 \u2013 545 or, ? = 980\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSmitha bought 8 Kg of kiwi fruit at an average rate of 360.If she returned 3.5kg to the retailer,at an average rate of remaining fruit was 202.5, Then what is the average price, of the returned 3.5 Kgs ?\n\n### Options:\nA. 41.5\nB. 43\nC. 42\nD. 45\nE. 47.3\n\n### Answer:\nTotal price of 8Kg kiwi fruit=8*45=360\nTotal price of 4.5Kg kiwi fruit=4.5*45=202.5\nTotal price of 3.5Kg kiwi fruit=360-202.5=157.5\nAverage price of 3.5 Kgs kiwi fruit= 157.5/3=45\nCorrect option Answer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAman started a business investing Rs. 60,000. Rakhi joined him after six months with an amount of Rs. 1,05,000 and Sagar joined them with Rs. 1.4 lakhs after another six months. The amount of profit earned should be distributed in what ratio among Aman, Rakhi and Sagar respectively, 3 years after Aman started the business?\n\n### Options:\nA. 12:15:18\nB. 72:105:112\nC. 52:105:112\nD. 62:105:112\nE. 12:105:112\n\n### Answer:\nExplanation:\nAman : Rakhi : Sagar = (60000 * 36) : (105000 * 30) : (140000 * 24)\n= 72:105:112\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSixty men can stitch 200 shirts in 30 days working 8 hours a day. In how many days can 45 men stitch 300 shirts working 6 hours a day?\n\n### Options:\nA. 70\nB. 90\nC. 60\nD. 80\nE. 10\n\n### Answer:\nD\n80\nWe have M1 D1 H1 / W1 = M2 D2 H2 / W2 (Variation rule)\n(60 * 30 * 8)/ 200 = (45 * D2 * 6) / 300\nD2 = (60 * 30 * 8 * 300) / (200 * 45 * 6) => D2 = 80.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo men A and B start from place X walking at 4 \u00bd kmph and 5 \u00be kmph respectively. How many km apart they are at the end of 3 \u00bd hours if they are walking in the same direction?\n\n### Options:\nA. 7 3/8 km\nB. 5 7/8 km\nC. 17 7/8 km\nD. 7 7/8 km\nE. 2 7/8 km\n\n### Answer:\nRS = 6 \u00be - 4 \u00bd = 2 \u00bc\nT = 3 \u00bd h.\nD = 9/4 * 7/2 = 63/8 = 7 7/8 km\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFor any positive number x, the function [x] denotes the greatest integer less than or equal to x. For example, [1] = 1, [1.267] = 1 and [1.999] = 1. If k is a positive integer such that k^2 is divisible by 45 and 80, what is the units digit of k^3/4000 ?\n\n### Options:\nA. 0\nB. 0\nC. 27\nD. 54\nE. Cannot be determined\n\n### Answer:\nK=[lCM of 80 and 45] * (any integer)\nhowever minimum value of k is sq.rt of 3^2*4^2*5^2 = 60 * any integer\nfor value of k(60) * any integer unit value will be always zero .\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo men A and B start from place X walking at 4 \u00bd kmph and 5 \u00be kmph respectively. How many km apart they are at the end of 3 \u00bd hours if they are walking in the same direction?\n\n### Options:\nA. 5 km\nB. 10 4/3 km\nC. 4 3/8 km\nD. 18 km\nE. 6 km\n\n### Answer:\nExplanation:\nRS = 5 \u00be - 4 \u00bd = 1 \u00bc\nT = 3 \u00bd h.\nD = 5/4 * 7/2 = 35/8 = 4 3/8 km\nC)\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how many different ways can the letters of the word \"CORPORATION\" be arranged in such a way that no two vowels are together?\n\n### Options:\nA. 6!/2!\u2217C57\u22175!3!\nB. 4!/2!\u2217C57\u22175!3!\nC. 6!/2!\u2217C57\u22176!3!\nD. 3!/2!\u2217C57\u22175!3!\nE. 12!/2!\u2217C57\u22175!3!\n\n### Answer:\nStep 1: Separate consonants with 7 empty slots *C*R*P*R*T*N*.\nStep 2: 6 consonants CRPRTN can be arranged in 6!/2! ways (6 letters with two R's);\nStep 3: we have 5 vowels OOAIO. Choose 5 slots out of 7 for them (this way no two vowels will be together): C57\nStep 4: 5 vowels in their slots can be arranged in 5!/3! ways (5 letters with three O's).\nTotal = 6!/2!\u2217C57\u22175!3!\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA and B entered into a partnership investing Rs.25000 and Rs.30000 respectively. After 4 months C also joined the business with an investment of Rs.35000. What is the share of C in an annual profit of Rs.47000?\n\n### Options:\nA. Rs.14000\nB. Rs.1000\nC. Rs.10500\nD. Rs.2050\nE. Rs.5500\n\n### Answer:\nExplanation:\n25*12: 30*12: 35*8\n15:18:14\n14/47 * 47000 = Rs.14000\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf in k+1 years from now John will be m years old, then how old was John t-1 years ago?\n\n### Options:\nA. m-k-t\nB. m+k-t+2\nC. m+k-t+1\nD. k-m-t+2\nE. k+t-m\n\n### Answer:\nAge t-1 years ago is m - k - 1 - ( t - 1 )\nOr, Age t-1 years ago is m - k - 1 - t + 1\nOr, Age t-1 years ago is m - k - t\nHence, Answer will definitely be (A) m - k - t\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average earning of amechanic for the first 4days of a week is Rs.25 and for the last four days is Rs.22. If heearns Rs.20 on the fourth day, his average earning forthe whole week is?\n\n### Options:\nA. s. 10\nB. s. 24\nC. s. 30\nD. s. 40\nE. s. 50\n\n### Answer:\nTotal earning for the week = Sum of earning of first four days + Sum of earning of last four days - Earning of 4th day\n= 4 x 25+ 4 x 22 -20\n= Rs. 168\n\u00e2\u02c6\u00b4 Average earning = 168/ 7\n= Rs. 24\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nx, y and z are consecutive positive integers such that x < y < z; which of the following must be true?\n1. xyz is divisible by 6\n2. (z-x)(y-x+1) = 4\n3. xy is even\n\n### Options:\nA. I only\nB. II only\nC. III only\nD. I and II only\nE. I, II, and III\n\n### Answer:\nSince x, y and z are consecutive integers such that x < y < z, we can say x = y-1 and Z = y+1\nStatement 1 would be true as at least one of the three numbers is divisible by 2 and one by 3 so xyz would be divisible by 6.\nStatement 2 can be simplified if we write everything in terms of y as ((y+1)-(y-1))*(y-(y-1)+1) = 2*2 = 4 So, always true\nStatement 3 talks about xy Since x and y are consecutive integers one of them is odd and other is even so product would always be even and hence true.\nSo, I II and III are always true and hence answer is\nE.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nif 5x*x+14*x+k=0 having two reciprocal roots find the value of k.\n\n### Options:\nA. 1\nB. 2\nC. 3\nD. 4\nE. 5\n\n### Answer:\nProduct of reciprocal roots =1\nProduct of roots of quadratic eqn ax^2+bx+c = 0 is c/a.\nHence k/5 =1\nk=5\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 34 men completed 2/5th of a work in 8 days working 9 hours a day. How many more man should be engaged to finish the rest of the work in 6 days working 9 hours a day?\n\n### Options:\nA. 100 men\nB. 101 men\nC. 102 men\nD. 103 men\nE. 104 men\n\n### Answer:\nC\n102 men\nFrom the above formula i.e (m1*t1/w1) = (m2*t2/w2)\nso, (34*8*9/(2/5)) = (x*6*9/(3/5))\nso, x = 136 men\nnumber of men to be added to finish the work = 136-34 = 102 men\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 3a = 4b and ab \u22600, what is the ratio of a/4 to b/3?\n\n### Options:\nA. 64/27\nB. 9/16\nC. 1\nD. 6/8\nE. 8/6\n\n### Answer:\nA nice fast approach is the first find a pair of numbers that satisfy the given equation: 3a = 4b\nHere's one pair: a =4 and b =3\nWhat is the ratio of a/9 to b/8?\nIn other words, what is the value of (a/4)/(b/3)?\nPlug in values to get: (a/4)/(b/3) = (4/4)/(3/3)\n= 1/1\n= 1\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA is B's sister. C is B's mother. D is C's father. E is D's mother. Then, how is A related to D?\n\n### Options:\nA. Grandfather\nB. Daughter\nC. Grandmother\nD. Granddaughter\nE. SISTER\n\n### Answer:\nA is the sister of B and B is the daughter of C.\nSo, A is the daughter of C. Also, D is the father of C.\nSo, A is the granddaughter of D.\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe tax on a commodity is diminished by 20% but its consumption is increased by 10%. Find the decrease percent in the revenue derived from it?\n\n### Options:\nA. 11%\nB. 82%\nC. 14%\nD. 12%\nE. 17%\n\n### Answer:\n100 * 100 = 10000\n80 * 110 = 8800\n10000------- 1200\n100 ------- ? = 12%\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n17200 x 223 + 17200 x 77 = ?\n\n### Options:\nA. 2736900\nB. 2738800\nC. 2658560\nD. 5160000\nE. None of them\n\n### Answer:\n=17200 x (223+77) (by distributive law)\n=17200 x 300\n=5160000\nAnswer is D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf P represents the product of the first 16 positive integers, then P is NOT a multiple of\n\n### Options:\nA. 99\nB. 84\nC. 72\nD. 65\nE. 51\n\n### Answer:\nAnswer is E.\nSince prime factor of 51 is 3x17. 17 is a prime number and not part of the first 15 positive integers.\nA) 9 x 11\nB) 12 x 7\nC) 12 x 6\nD) 13 x 5\nE) 3 x 17\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe sum of two numbers is 25 and their difference is 13. Find their product.\n\n### Options:\nA. 104\nB. 108\nC. 114\nD. 325\nE. None\n\n### Answer:\nSol.\nLet the numbers be x and y.\nThen, x + y = 25 and x - y = 13.\n4xy = (x+y)2 - (x-y)2\n= (25)2 - (13)2 = 625 - 169 = 456\n\u21d2 xy = 114.\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe present worth of Rs.169 due in 2 years at 4% per annum compound interest is\n\n### Options:\nA. Rs 155.25\nB. Rs 156.25\nC. Rs 157.25\nD. Rs 158.25\nE. None of these\n\n### Answer:\nExplanation:\nIn this type of question we apply formula\nAmount=P /(1+R/100)n\nAmount=169 /(1+4/100)2\nAmount=169\u221725\u221725/26\u221726\nAmount=156.25\nOption B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA bag contains 10 red and 6 white balls. One ball is drawn at random. What is the probability that the ball drawn is white?\n\n### Options:\nA. 4/7\nB. 2/3\nC. 5/8\nD. 1/4\nE. 5/7\n\n### Answer:\nTotal number of balls = 10+6 = 16\nnumber of white balls = 10\nProbability = 10/16 = 5/8\nAnswer is C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the speed of X meters per hour is equivalent to the speed of Y kilometers per hour, what is Y in terms of X? (1 kilometer=1000 meters)\n\n### Options:\nA. 0.1X\nB. 0.01X\nC. 0.001X\nD. 0.0001X\nE. 0.005X\n\n### Answer:\nX meters per hour -->\n--> 1X meters per hour(as there are 3,600 seconds in one hour);\n--> X/1,000=0.001X kilometers per hour (as there are 1,000 meters in one kilometer).\nAnswer: C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA's speed is 20/13 times that of B. If A and B run a race, what part of the length of the race should A give B as a head start, so that B beats A by 80% of the length of the race?\n\n### Options:\nA. 44%\nB. 48%\nC. 52%\nD. 42%\nE. 87%\n\n### Answer:\nFirst calculate the distance, B has covered with his speed in the time, in which A reached 20% of the race.\nThen Add the remaining distance as head start for B to win the race.\nIts best to apply Ratios concept here.\nSince A's speed is 20/13 of B, therefore, B's speed is 13/20 of A\nDistance covered by B = speed x time = (13/20) x (0.2) = 0.13%\n(Which means B would have covered 0.13 of the race length during the time in which A has covered 0.2 of the race length.\nTherefore to win, B needs a headstart of (1 - 0.13 = ) 0.87 of the race length.\nSo the answer is E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nExpress of the following as a fraction:\n44%\n\n### Options:\nA. 11/25\nB. 13/25\nC. 11/25\nD. 17/25\nE. None of them\n\n### Answer:\n44% = 44/100= 11/25.\nAnswer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA theater box office sold an average (arithmetic mean) of 64 tickets per staff member to a particular movie. Among the daytime staff, the average number sold per member was 80, and among the evening staff, the average number sold was 60. If there are no other employees, what was the ratio of the number of daytime staff members to the number of evening staff members?\n\n### Options:\nA. 1:2\nB. 1:4\nC. 3:7\nD. 7:12\nE. 4:5\n\n### Answer:\nDeviation from the mean for the daytime staff = 80 - 64 = 16.\nDeviation from the mean for the evening staff = 64 - 60 = 4.\nThus, the ratio of the number of daytime staff members to the number of evening staff members is 4:16 = 1:4.\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTaylor is making a bracelet. He Starts with 3 blue knots, 6 red knots, and 2 yellow knots, in that order, and repeats the pattern until there is no more string. If the last Knot is yellow which of the following could be the total number of knots on the bracelet.\n\n### Options:\nA. 89\nB. 90\nC. 95\nD. 97\nE. 87\n\n### Answer:\nRepeating sequence = 3 + 6 + 2 = 11.\nAs the pattern ends in Y this could be the 10th thread or 11 thread (both are yellow)\nOut of the answer choices, correct on should be a multiple of 11(since 11 threads are repeating) and if not, multiple of 11 + 10 (since 11 threads are repeating and last sequence end at first yellow)\nnone of the options is a direct multiple of 11 and only option that is multiple of 11; + 10 is 87 (11*7) + 10\nHence, answer is E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are 6 boxes numbered 1, 2,3,4,5 and 6. Each box is to be filled up either with a red or a green ball in such a way that at least 1 box contains a green ball & the boxes containing green balls are consecutively numbered. The total no. of ways in which this can be done is?\n\n### Options:\nA. 18\nB. 19\nC. 21\nD. 23\nE. 25\n\n### Answer:\nIf only one of the boxes has a green ball, it can be any of the 6 boxes. So, this can be achieved in 6 ways.\nIf two of the boxes have green balls and then there are 5 consecutive sets of 2 boxes. 12, 23, 34, 45, 56.\nSimilarly, if 3 of the boxes have green balls, there will be 4 options.\nIf 4 boxes have green balls, there will be 3 options.\nIf 5 boxes have green balls, then there will be 2 options.\nIf all 6 boxes have green balls, then there will be just 1 options.\nTotal number of options = 6 + 5 + 4 + 3 + 2 + 1 = 21\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nList R contains five numbers that have an average value of 40. If the median of the numbers in the list is equal to the mean and the largest number is equal to 20 more than two times the smallest number, what is the smallest possible value in the list?\n\n### Options:\nA. 12\nB. 16\nC. 20\nD. 24\nE. 28\n\n### Answer:\nThe middle number is 40.\nLet the smallest number be x. Then the largest number is 2x+20.\nTo make x as small as possible, let's make the remaining numbers as large as possible.\nSo the second largest = the largest = 2x+20.\nThe second smallest should be equal to the median.\nThe numbers are x, 40, 40, 2x+20, 2x+20.\nx + 40 + 40 + 2x + 20 + 2x + 20 = 5*40 = 200\n5x = 80\nx = 16\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe length of the bridge, which a train 120 meters long and travelling at 45 km/hr can cross in 30 seconds, is:\n\n### Options:\nA. 239\nB. 277\nC. 255\nD. 88\nE. 232\n\n### Answer:\nSpeed = (45 * 5/18) m/sec = (25/2) m/sec. Time = 30 sec. Let the length of bridge be x meters. Then, (120 + X)/30\n= 25/2 ==> 2(120 + X) = 750 ==> X = 255 m.\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If four marbles are picked at random, what is the probability that none is blue?\n\n### Options:\nA. 33/96\nB. 33/91\nC. 33/67\nD. 33/28\nE. 33/19\n\n### Answer:\nGiven that there are three blue marbles, four red marbles, six green marbles and two yellow marbles. When four marbles are picked at random, then the probability that none is blue is\n= \u00b9\u00b2C\u2084/\u00b9\u2075C\u2084\n= (12 * 11 * 10 * 9)/(15 * 14 * 13 * 12)\n= 33/91\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA can do half the work in one day where as B can do it full. B can also do half the work of C in one day. Ratio in their efficiency will be?\n\n### Options:\nA. 3:2:4\nB. 2:2:4\nC. 1:2:4\nD. 4:2:4\nE. 5:2:4\n\n### Answer:\nc\n1:2:4\nWC of A: B = 1:2\nB: C = 1:2\n---------------------\nA: B: C = 1:2:4\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAish started a business investing Rs. 25,000 in 2010, In 2011, he invested an additional amount of Rs. 10,000 and Roshan joined him with an amount of Rs. 35,000. In 2012, Aish invested another additional amount of Rs. 10,000 and Atul joined them with an amount of Rs. 35,000. What will be Roshan\u2019s share in the profit of Rs. 2,40,000 earned at the end of 3 years from the start of the business in 2010?\n\n### Options:\nA. Rs.45000\nB. Rs.50000\nC. Rs.60000\nD. Rs.80000\nE. None of these\n\n### Answer:\nExplanation :\nAish : Roshan : Atul\n= (25000 x 12 + 35000 x 12 + 45000 x 12) : (35000 x 24) : (35000 x 12)\n= 1260000 : 840000 : 420000 = 3 : 2 : 1\nRoshan's share = Rs. 240000 x 2/6\n= Rs. 80000.\nAnswer : D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nsome digits were given like 0 2 2 3 3 4 4 then how many no will be there which is greater than 1 lac ,all numbers are distinct\n\n### Options:\nA. 530\nB. 540\nC. 550\nD. 560\nE. 570\n\n### Answer:\n( 6*6*5*4*3*2)/(2! *2!*2!)= 540 ways\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhen (6767 +67) is divided by 68, the remainder is?\n\n### Options:\nA. 58\nB. 59\nC. 62\nD. 66\nE. 67\n\n### Answer:\n=> (67^67 + 1) is divisible by (67 + 1)\n=> (67^67 + 1) is divisible by 68\n=> (67^67+1) \u00f7 68 gives a remainder of 0\n=> [(67^67+1) + 66] \u00f7 68 gives a remainder of 66\n=> (67^67 + 67) \u00f7 68 gives a remainder of 66\nOption D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n50^51^52 /11\n\n### Options:\nA. 6\nB. 4\nC. 7\nD. 3\nE. 5\n\n### Answer:\nWe know that 6^1=6 or 6^2=36 so for all power of 6 unit digit is 6 now que is 50^51^52 now if we divide 50/11 then rem is 6 means 6^51=6 at unit place same for 6^52 salso give 6 at unit place now finally 50^51^52 gives 6 at unit place now 6/11=6\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe greatest possible length which can be used to measure exactly the length 7m, 3m 85cm, 12 m 95 cm is\n\n### Options:\nA. 15 cm\nB. 25 cm\nC. 35 cm\nD. 42 cm\nE. None of these\n\n### Answer:\nSolution\nRequired length\t= H.C.F of 700 cm, 385 cm and 1295 cm\n\u2039=\u203a 35 cm.\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJoe is painting a rectangular room whose dimensions are given by a, b and c meters. Joe takes 8 hours to paint a wall with dimensions a and c. He takes 4 hours to paint a wall with dimensions b and c and 12 hours to paint the ceiling with dimensions a and b. If Joe works at a constant rate and a = 7, then what is the volume of the room?\n\n### Options:\nA. 18 cubic meters\nB. 24 cubic meters\nC. 30 cubic meters\nD. 36 cubic meters\nE. 57.1 cubic meters\n\n### Answer:\nTime to paint each wall as given in problem:\nAC = 8 hours\nBC = 4 hours\nAB = 12 hours\nSince he works at constant rate and it takes him twice as long to paint AC compared to BC\nAC=2BC\nPlug in 6 for A and you find that B=3.5\nSince painting AB takes 3 times as long compared to BC,\nAB=3BC\nPlug in 6 for A and 3 for B and you find that C=2.33\nA*B*C=7*3.5*2.3=57.1 cubic meters\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA boat can travel with a speed of 25km/hr in still water. If the speed of the stream is 5km/hr, find the time taken by the boat to go 90km downstream.\n\n### Options:\nA. 1 hr\nB. 2 hrs\nC. 3 hrs\nD. 4 hrs\nE. 5 hrs\n\n### Answer:\nSpeed downstream = (25 + 5) km/hr = 30 km/hr.\nTime taken to travel 90 km downstream = 90/30 hrs = 3 hrs.\nAnswer : C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe ratio of the present age of Viju to that of Aju is 7:2. Four years from now, the ratio of the ages of Viju to Aju will be 5:2. What was Viju age 6 years ago ?\n\n### Options:\nA. 10 years\nB. 15 years\nC. 20 years\nD. 25 years\nE. 30 years\n\n### Answer:\nLet the present age of Viju be 7x years and that of Aju be 2x years.\nThen, 4 years from now\n7x + 4 / 2x + 4 = 5 / 2\nor 4x = 12\nor x = 3\nViju present age = 7 * 3 = 21 years\nViju age 6 years ago = 21 - 6 = 15 years\nanswer :B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a particular is never chosen, in how many ways can a cricketbe chosen out of 15 players?\n\n### Options:\nA. 245\nB. 256\nC. 364\nD. 370\nE. 390\n\n### Answer:\nA particular players is never chosen, it means that 11 players are selected out of 14 players.\n=> Required number of ways = 14C11\n= 14!/11!x3! = 364\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe area of a square field is 900 km2. How long will it take for a horse to run around at the speed of 12 km/h ?\n\n### Options:\nA. 12 h\nB. 10 h\nC. 8 h\nD. 6 h\nE. None of these\n\n### Answer:\nExplanation Area of field = 900 km2. Then, each side of field = \u221a900=30km Distance covered by the horse = Perimeter of square field = 30 \u00d7 4 = 120 km \u2234 Time taken by horse = distances/peed=120/12=10h Answer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe area of a rectangle is 460 square metres. If the length is 15% more than the breadth, what is the breadth of the rectangular field?\n\n### Options:\nA. 20\nB. 27\nC. 26\nD. 188\nE. 11\n\n### Answer:\nExplanation:\nLet breadth=x meters.\nThen,Length = meters\nGiven that,\n=> x = 20\nBreadth = 20\nAnswer: A) 20 m\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average of 11 results is 50, if the average of first six results is 49 and that of the last six is 52. Find the sixth result?\n\n### Options:\nA. 26\nB. 56\nC. 22\nD. 29\nE. 21\n\n### Answer:\n1 to 11 = 11 * 50 = 550\n1 to 6 = 6 * 49 = 294\n6 to 11 = 6 * 52 = 312\n6th = 294 + 312 \u2013 550\n= 56\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a theater, the first row has 14 seats and each row has 2 more seats than previous row. If the last row has 56 seats, what is the total number of seats in the theater?\n\n### Options:\nA. 770\nB. 780\nC. 790\nD. 800\nE. 810\n\n### Answer:\nThe number of seats in the theater is\n14 + (14+2) + ...+ (14+42)=\n22(14) + 2(1+2+...+21)=\n22(14) + 2(21)(22)/2=\n22(14+21) = 22(35) = 770\nThe answer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat will be the reminder when (31^31+31) is divided by 32?\n\n### Options:\nA. 72\nB. 43\nC. 91\nD. 40\nE. 30\n\n### Answer:\n(x^n+1) will be divisible by (x+1) only when n is odd;\n(31^31+1) will be divisible by (31+1);\n(31^31+1)+30 when divided by will give 30 as remainder.\nCorrect Option : E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA shipment of 9 television sets contains 2 black-and-white sets and 6 color sets. If 2 television sets are to be chosen at random from this shipment, what is the probability that at least 1 of the 2 sets chosen will be a black-and-white set?\n\n### Options:\nA. 1/7\nB. 1/4\nC. 5/14\nD. 11/28\nE. 7/12\n\n### Answer:\nI get 7/12, which is not in the answer choices.\nthe probability of getting at least one b/w TV is 1-(the probability of getting 2 color TVs)\n1-C(6,2)/C(9/2)=21/36=7/12\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n55 word in the arrangement of letter PERFECT?\n\n### Options:\nA. CEPFERT\nB. CEPFERS\nC. CEPFERT\nD. CEPFERJ\nE. CEPFERG\n\n### Answer:\narrange in ascending order CEEFPRT\nCEE4*3*2*1=24\nCEF4*3*2*1=24\nCEPE3*2*1=6\n24+24+6=54\nnext word will be CEPFERT\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf n is a positive integer and n^3 is a multiple of 550, what is the least possible value of n?\n\n### Options:\nA. 8\nB. 27\nC. 81\nD. 110\nE. 125\n\n### Answer:\ncube of a number entails having 3 copies of the original prime factors. Since 550 is a factor of n^3 the least possible value of n is 5(11)2 = 110\nthe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the average (arithmetic mean) of a and b is 45 and the average of b and c is 70, what is the value of c \u2212 a?\n\n### Options:\nA. 25\nB. 50\nC. 90\nD. 140\nE. It cannot be determined from the information given.\n\n### Answer:\nthe arithmetic mean of a and b =(a+b)/2=45 -- a+b=90 --1\nsimilarly for b+c=140 --2\nsubtracting 1 from 2 we have\nc-a=50 ANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf an object travels at seven feet per second, how many feet does it travel in one hour?\n\n### Options:\nA. 30\nB. 300\nC. 720\nD. 25200\nE. 18000\n\n### Answer:\nSpeed = 7 feet per second.\n1 Hour= 60X60 Seconds = 3600 Seconds.\nTotal no of feet traveled in 1 hour = 3600X7= 25200\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat percent of a day is four hours?\n\n### Options:\nA. 16.67%\nB. 16x1/2%\nC. 18x2/3%\nD. 22x1/2%\nE. None of these\n\n### Answer:\nExplanation :\nRequired percentage = (4/24100)%.\n= 16.67%.\nAnswer : A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe largest 5 digit number exactly divisible by 91 is?\n\n### Options:\nA. 99918\nB. 99919\nC. 99921\nD. 99923\nE. 99929\n\n### Answer:\nLargest 5-digit number = 99999\n91) 99999 (1098\n91\n---\n899\n819\n----\n809\n728\n---\n81\n---\nRequired number = (99999 - 81)\n= 99918.\nOption A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nPhotography changed drastically _________ introduced in the market.\n\n### Options:\nA. when polariod\nB. when polariod\nC. when polariod\nD. as polaroid\nE. 1312\n\n### Answer:\nExplanation:\nThere is no adequation information is given about details of subsequent changes. So \"when\" is the right word. Option a. \"As\" inditates reason.\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a certain sample of data has a mean of 24.0 and a standard deviation of 3.0, which of the following values is more than 2.5 standard deviations from the mean?\n\n### Options:\nA. 12.0\nB. 13.5\nC. 17.0\nD. 23.5\nE. 26.5\n\n### Answer:\nValue ismore than 2.5SDfrom the mean means that the distance between the mean and the value must be more than 2.5*SD=7.5. So the value must be either less than 24-7.5=16.5or more than 24+7.5=31.5.\nAnswer: C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe marks obtained by Vijay and Amith are in the ratio 8:5 and those obtained by Amith and Abhishek in the ratio of 3:2. The marks obtained by Vijay and Abhishek are in the ratio of?\n\n### Options:\nA. 12:5\nB. 12:1\nC. 6:5\nD. 12:2\nE. 6:3\n\n### Answer:\n8:5\n3:2\n-------\n24:15:10\n24:10\n12:5\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many paying stones, each measuring 2 m * 1 m are required to pave a rectangular court yard 30 m long and 16 m board?\n\n### Options:\nA. 240\nB. 18\nC. 26\nD. 17\nE. 12\n\n### Answer:\n30 * 16 = 2 * 1 * x => x\n= 240\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nVeena ranks 44rd from the top in a class of 182. What is her rank from the bottom if 22 students have failed the examination?\n\n### Options:\nA. 88\nB. 108\nC. 110\nD. 90\nE. 117\n\n### Answer:\ntotal student=182\nfailed=22\npaasd student=182-22=160\nfrom bottom her rank is=160-44+1=117\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf five persons sit in a row, then the probability that three particular persons are always together is?\n\n### Options:\nA. 3/5\nB. 3/4\nC. 1/9\nD. 1/6\nE. 3/10\n\n### Answer:\nFive persons can be arranged in a row in 5! ways.\nTreat the three persons to sit together as one unit then there three persons and they can be arranged in 3! ways.\nAgain three persons can be arranged among them selves in 3! ways.\nFavourable outcomes = 3!3!\nRequired probability = 3!3!/5! = 3/10\nAnswer:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA single discount equivalent to the discount series of 16%, 10% and 5% is?\n\n### Options:\nA. 28.18\nB. 38.9\nC. 41.6\nD. 31.4\nE. 31.1\n\n### Answer:\n100*(84/100)*(90/100)*(95/100) = 71.82\n100 - 71.82 = 28.18\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA rectangular field has to be fenced on three sides leaving a side of 20 feet uncovered. If the area of the field is 680 sq. feet, how many feet of fencing will be required?\n\n### Options:\nA. 80 feet\nB. 85 feet\nC. 83 feet\nD. 88 feet\nE. 90 feet\n\n### Answer:\nGiven that area of the field = 680 sq. feet\n=> lb = 680 sq. feet\nLength(l) = 20 feet\n=> 20 \u00d7 b = 680\n=> b = 680/20 = 34 feet\nRequired length of the fencing = l + 2b = 20 + (2 \u00d7 34) = 88 feet\nAnswer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a hostel there were 100 students. To accommodate 25 more students the average is decreased by some rupees. But total expenditure increased by Rs.500. If the total expenditure of the hostel now 8500, find decrease of average budget?\n\n### Options:\nA. 20\nB. 15\nC. 12\nD. 18\nE. 24\n\n### Answer:\nLet average is x\n100x + 500=8500\nx = 80\nlet decrease = y\n125(80\u2013 y)= 8500\ny = 12\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe mean of 50 observations was 36. It was found later that an observation 60 was wrongly taken as 23. The corrected new mean is?\n\n### Options:\nA. 36.7\nB. 36.1\nC. 36.5\nD. 36.9\nE. 36.3\n\n### Answer:\nCorrect sum\n= (36 * 50 + 60 - 23)\n= 1837.\nCorrect mean = 1837/50\n= 36.7\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJim is mixing up a salad dressing. Regardless of the number of servings, the recipe requires that 5/8 of the finished dressing mix be Canola oil, 1/4 vinegar, and the remainder an even mixture of salt, pepper and sugar. If Jim accidentally doubles the vinegar and forgets the sugar altogether, what proportion of the botched dressing will be Canola oil?\n\n### Options:\nA. 15/29\nB. 5/8\nC. 5/16\nD. 1/2\nE. 13/27\n\n### Answer:\nCanola oil = 5/8 = 15/24 --> 15 parts out of 24;\nVinegar = 1/4 = 6/24 --> 6 parts out of 24;\nSalt + pepper + sugar = 1-(15/24+6/24)= 3/24, so each = 1/24 --> 1 part out of 24 each;\nIf vinegar = 12 (instead of 6) and sugar = 0 (instead of 1) then total = 15+12+1+1+0 = 29 parts out of which 15 parts are Canola oil --> proportion = 15/29.\nAnswer: A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAssume that f(1)=0 and f(m+n)=f(m)+f(n)+4(9mn-1). For all natural numbers (Integers>0)m and n. What is the value of f(17)?\n\n### Options:\nA. 4832\nB. 4855\nC. 4825\nD. 4895\nE. 4862\n\n### Answer:\nExplanation:\nf(1) = 0\nf(2) = f(1+1) = f(1)+f(1)+4(9\u00d71\u00d71 \u2013 1) = 0+0+4\u00d78 = 32\nf(4) = f(2+2) = f(2)+f(2)+4(9\u00d72\u00d72 \u2013 1) = 32+32+4\u00d735 = 204\nf(8) = f(4+4) = f(4)+f(4)+4(9\u00d74\u00d74 \u2013 1) = 204+204+4\u00d7143 = 980\nf(16) = f(8+8) = f(8)+f(8)+4(9\u00d78\u00d78 \u2013 1) = 980+980+4\u00d7575 = 4260\nf(17) = f(1+16) = f(16)+f(1)+4(9\u00d716\u00d71 \u20131) = 4260+0+ 4\u00d7143 = 4832\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a bouquet of flowers, all but two are roses, all but two are tulips, and all but two are daisies. How many flowers are in the bouquet?\n\n### Options:\nA. 1\nB. 2\nC. 3\nD. 4\nE. 5\n\n### Answer:\nC\n3\nThere are 3 flowers (1 rose, 1 tulip, and 1 daisy).\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nDawson is going with 14 friends on a trip to Washington D.C for spring break. Airfare and hotel costs a total of $13500.00 for the group of 15 friends. How much does each person have to pay for their hotel and airfare?\n\n### Options:\nA. $900\nB. $800\nC. $850\nD. $950\nE. $920\n\n### Answer:\nAnswer= A\nThe total cost of the trip ($13500.00) divided by 15 equals $900.00.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many gallons of milk that is 10 percent butter-fat must be added to 8 gallons of milk that is 25 percent butterfat to obtain milk that is 20 percent butterfat?\n\n### Options:\nA. 4\nB. 12\nC. 14\nD. 16\nE. 28\n\n### Answer:\nEquate the fat:\n0.1x + 0.25*8 = 0.2(x + 8) --> x = 4.\nAnswer: A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA person incurs loss for by selling a watch for Rs1140.at what price should the watch be sold to earn a 5% profit ?\n\n### Options:\nA. 1205\nB. 1260\nC. 1300\nD. 1340\nE. 1450\n\n### Answer:\nlet the new sp be Rsx.then\n(100-loss%) : (1st sp)=(100+gain%) (2nd sp)\n{(100-5)/1400}={(100+5)/x}=> x={(105*1140)/95} =1260.\nANSWER B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRahim bought 65 books for Rs.6500 from one shop and 35 books for Rs.2000 from another. What is the average price he paid per book ?\n\n### Options:\nA. 80\nB. 138\nC. 100\nD. 129\nE. 85\n\n### Answer:\nAverage price per book\n= (6500+ 2000) / (65 + 35)\n= 8500 / 100\n= Rs.85\nAnswer:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe ratio of the earnings of P and Q is 9 : 10. If the earnings of P increases by one-fourth and the earnings of Q decreases by one-fourth, then find the new ratio of their earnings?\n\n### Options:\nA. 3/9\nB. 3/2\nC. 3/5\nD. 3/6\nE. 3/1\n\n### Answer:\nLet the earnings of P and Q be Rs. 9x and Rs. 10x respectively.\nNew ration = [9x + 1/4(9x)]/[10x - 1/4(10x)]\n=> [9x(1 + 1/4)]/[10x(1 - 1/4)]\n= 9/10 * (5/4)/(3/4) => 3/2.\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a kilo meter race, if A gives B a 40 m start, A wins by 19 s. But if A gives B a 30 s start, B wins by 40 m. Find the time taken by B to run 5,000 m?\n\n### Options:\nA. 150 s\nB. 450 s\nC. 750 s\nD. 825 s\nE. 925 s\n\n### Answer:\nWhen B is given a 40 m start then B runs 960m in T secs and A runs 1000m in T-19 secs.\nWhen B is given a 30 second start then B runs 1000m in t secs and A runs 960m in t - 30 secs.\nAssume that the speed of A (Va) and B (Vb) is constant in both situations.\nThen Vb = 960 \u00f7 T = 1000 \u00f7 t, and Va = 1000 \u00f7 (T - 19) = 960 \u00f7 (t - 30)\nSo 960t = 1000T, and 1000t - 30000 = 960T - 18240. Then 40t = -40T + 11760, t = -T + 294.\nSubstituting for t in 960t = 1000T\ngives : -960T + 282240 = 1000T\n1960T = 282240\nT = 144\nB 's speed is 960 / T = 960 / 144 = 6.67 metres per second.\nAssuming the same constant speed to run 5000 metres then the time taken is\n5000 / 6.67 = 750 seconds\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFox jeans regularly sell for $15 a pair and Pony jeans regularly sell for $18 a pair. During a sale these regular unit prices are discounted at different rates so that a total of $9 is saved by purchasing 5 pairs of jeans: 3 pairs of Fox jeans and 2 pairs of Pony jeans. If the sum of the two discounts rates is 33 percent, what is the discount rate on Pony jeans?\n\n### Options:\nA. 9%\nB. 10%\nC. 11%\nD. 12%\nE. 65%\n\n### Answer:\nx discount on Pony jeans, (0.33-x) discount on Fox jeans.\nSet the equation: 3*15(0.33-x)+2*18x=9 --> x=0.65=65%\nAnswer: E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich of the following numbers is between 1\u20442 and 1\u20443?\n\n### Options:\nA. .55\nB. .38\nC. .29\nD. .22\nE. .20\n\n### Answer:\n1/3 = .333...\n1/2 = .5\nThe only number between these two is 0.38.\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many seconds does a train 120 meters long, traveling at 54 km/h, take to completely cross a bridge of 180 meters in length?\n\n### Options:\nA. 18\nB. 20\nC. 22\nD. 24\nE. 26\n\n### Answer:\n54 km/h = 54000/3600 = 15 m/s\nTime = 300 / 15 = 20 seconds\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAs part of her MBA program, Karen applied for three different Spring Break outreach projects, each of which selects its students by a random lottery of its applicants. If the probability of her being accepted to each individual project is 30%, what is the probability that Karen will be accepted to at least one project?\n\n### Options:\nA. 729/1000\nB. 657/1000\nC. 343/500\nD. 123/250\nE. 17/100\n\n### Answer:\nSince the probability of Karen's being accepted to each individual project is 30%, the probability of her not being accepted to each project is 70%. The probability that she will be accepted to none is, therefore, (7/10)*(7/10)*(7/10)=343/1000.\nP(Karen will be accepted to at least one project) = 1 - (343/1000) = 657/1000.\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nColin has an app on his phone that generates a random integer betwen 1 and 10. He generates\n10 random numbers and computes the sum. Compute the number of distinct possible sums\nColin can end up with.\n\n### Options:\nA. 41\nB. 32\nC. 75\nD. 91\nE. 82\n\n### Answer:\nThe maximum possible sum is 10 * 10 = 100. The minimum possible sum is 10.\nHence, there are 100 - 10 + 1 = 91 possible sums\ncorrect answer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA shopkeeper sells 200 metres of cloth for Rs. 12000 at a loss of Rs.12 per metre. Find his cost price for one metre of cloth?\n\n### Options:\nA. s.59\nB. s.72\nC. s.62\nD. s.50\nE. s.13\n\n### Answer:\nSP per metre = 12000/200\n= Rs. 60 Loss per metre\n= Rs. 12 CP per metre = 60 + 12\n= Rs.72\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many prime numbers between 50 to 100?\n\n### Options:\nA. 11\nB. 10\nC. 15\nD. 14\nE. 12\n\n### Answer:\nprimes are of the form 6n+1 or 6n-1\nPut n=9\n6n+1=6*9+1=55 where 55 is not prime\nfor n=9\n6n-1=6*9-1=53\nfor n=10 , 6n-1= 59 and 61\nfor n=11 , ==> 67\nfor n =12 ==> 73 and 71\nfor n =13 ==> 79\nfor n =14 ==> 83\nfor n=15 ==> 89\nfor n =16 ==> 97\ntherefore total number of prime numbers = 10\nAns - B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n6 friends go out to dinner at Outback Steakhouse. The total of their meal comes to 118.60 without a tip. They decide to leave a 20% tip to the waitress. They want to split the costs if the bill including the tip evenly among them. How much does each person have to pay if the bill is split evenly?\n\n### Options:\nA. 19.77\nB. 71.16\nC. 18.6\nD. 23.72\nE. 42.32\n\n### Answer:\nThe amount of the tip= 118.60*.20=23.72\n118.60+23.62= 142.32 = amount of bill after the tip\n142.32/6=23.72= amount each person must pay\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAt present the age of the father is 3 times that of the age of the son. Three years hence the father's age would be 2 times that of his son. Find the present age of the father?\n\n### Options:\nA. 18years\nB. 12years\nC. 20years\nD. 16years\nE. 25years\n\n### Answer:\nAge of the son = (3-1)*3 / (3-2) = 6 years\nAge of the father = 6*3 = 18 years\nAnswer is A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the sum of the different positive prime factors of 550?\n\n### Options:\nA. 10\nB. 11\nC. 15\nD. 16\nE. 18\n\n### Answer:\nI think answer is E: 27\n550 = 55 * 10 = (5 * 11) * (2 * 5)\nSum of theDIFFERENTpositive prime factors = 2 + 5 + 11 = 18\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a certain quiz that consists of 10 questions, each question after the first is worth 4 points more than the preceding question. If the 10 questions on the quiz are worth a total of 340 points, how many points is the third question worth?\n\n### Options:\nA. 39\nB. 24\nC. 28\nD. 26\nE. 30\n\n### Answer:\nx\nx+4\nx+8\nx+12\nx+16\nx+20\nx+24\nx+28\nx+32\nx+36\n10x+180=340\n10x=160\nx=16\n3rd question = x+8 = 16+8 = 24\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 5x + y = 6 and 2y \u2212 4x = 7, then what is the value of x + 3y?\n\n### Options:\nA. 1/7\nB. 13\nC. 15\nD. 52/7\nE. 60/7\n\n### Answer:\n5x + y = 6\n\u22124x + 2y = 7\nAdding both the equations --> x + 3y = 13\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe base of a right triangle is 8 and hypotenuse is 10. Its area is?\n\n### Options:\nA. 12\nB. 80\nC. 59\nD. 24\nE. 25\n\n### Answer:\nExplanation:\nh2=(10)2-(8)2-(6)2->h=6\n1/2*8*6=24\nANSWER IS D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that exactly three bulbs are good.\n\n### Options:\nA. 20/69\nB. 20/63\nC. 20/61\nD. 20/66\nE. 20/63\n\n### Answer:\nExplanation:\nRequired probability =\n= (10 * 4)/126 = 20/63\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain bag contains 100 balls \u00e2\u20ac\u201d 10 white, 30 green, 10 yellow, 47 red, and 3 purple. If a ball is to be chosen at random, what is the probability that the ball will be neither red nor purple?\n\n### Options:\nA. 0.9\nB. 0.75\nC. 0.6\nD. 0.8\nE. 0.5\n\n### Answer:\nAccording to the stem the ball can be white, green or yellow, so the probability is (white + green + yellow)/(total) = (10 + 30 + 10)/100 = 50/100 = 0.5.\nAnswer is E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA individuals pledged to pay equal contributions so that a charity\u2019s goal of $x could be reached. If d of the contributors failed to pay their share, which of the following represents the additional number of dollars that each of the remaining individuals would have to pay in order to allow the charity to reach its goal?\n\n### Options:\nA. dx/A(A - d)\nB. dx\nC. a\nD. A-d\nE. nA-d\n\n### Answer:\nNumber of individuals = A\nAmount paid by each individual = n\nTotal expected amount = Charity's goal = nA = x\nn = x/A\nNumber of individuals who fail to pay = d\nContribution from individuals who would fail to pay = dx/A --> Additional amount\nNumber of individuals who are paying = A - d\nAdditional amount has to be divided among the (A - d) individuals --> dx/A(A - d)\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe denominator of a fraction is 1 less than twice the numerator. If the numerator and denominator are both increased by 1, the fraction becomes 4/5. Find the fraction?\n\n### Options:\nA. A)2/3\nB. B)5/7\nC. C)4/7\nD. D)5/9\nE. E)None of these\n\n### Answer:\nLet the numerator and denominator of the fraction be 'n' and 'd' respectively.\nd = 2n - 1\n(n + 1)/(d + 1) = 4/5\n5n + 5 = 4d + 4\n5n + 5 = 4(2n - 1) + 4 => n = 5/3\nd = 2n - 1 => d = 3/7\nHence the fraction is : 5/7\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe ages of X and Y are in the proportion of 6:5 and total of their ages is 44 years. The proportion of their ages after 8 years will be\n\n### Options:\nA. 8:7\nB. 6:9\nC. 4:9\nD. 3:6\nE. 1:9\n\n### Answer:\nA\n8:7\nLet current ages of X and Y correspondingly, is 6A & 5A\nGiven: 6A + 5A = 44\n=> A = 4\nProportion of ages after 0.8 decades will be\n6A + 8 : 5A + 8\nor, 32:28 or, 8:7\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man gets a simple interest of Rs.400 on a certain principal at the rate of 5% p.a in two years. Find the compound interest the man will get on twice the principal in two years at the same rate?\n\n### Options:\nA. s.550\nB. s.556\nC. s.656\nD. s.750\nE. s.820\n\n### Answer:\nLet the principal be Rs.P\nS.I at 5% p.a in 8 years on Rs.P = Rs.400\n(P)(8)(5)/100 = 400\nP = 4000\nC.I on Rs.2P i.e., Rs.8000 at 5% p.a in two years\n=8000{ [1 + 5/100]^2 - 1}\n= 8000(41/400)\n= Rs. 820\nAnswer:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nLet us say that a table tennis tournament was going on with knock out terms which means the one who loses the match is out of the tournament. 91 players took part in that tournament. How many matches were played?\n\n### Options:\nA. 90 matches\nB. 95 matches\nC. 99 matches\nD. 85 matches\nE. 87 matches\n\n### Answer:\nA 90 matches. The number of matches will always sum up to one less than the number of players in a knock out tournament. You may calculate it in any manner. Thus 90 matches were played.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAn inspector rejects 0.08% of the meters as defective. How many will he examine to reject 2?\n\n### Options:\nA. 1200\nB. 1240\nC. 1852\nD. 3200\nE. 2500\n\n### Answer:\nThen, 0.08% of x = 2\n(8/100)*(1/100)x = 2\nx = (2*100*100)/8 = 2500\nAnswer is E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA warehouse is labeling computer inventory with 4-digit codes. Each code is to consist of four digits between the numbers 0 and 7. The manager is debating whether to allow any 4-digit codes to have leading zero's before a non-zero number is used. If not allowed, then numbers like0025cannot be used.\nThe manager wants to measure the magnitude of the number of 4-digit code possibilities that are lost if he disallows the use of leading zero's. How many such codes would be lost?\n\n### Options:\nA. 7000\nB. 1000\nC. 1011\nD. 1101\nE. 1110\n\n### Answer:\nThe number of codes possible if leading zero is allowed = 10*10*10*10=10^4\nThe number of codes possible if leading zero is NOT allowed = 7*10*10*10=9*10^3\nThe difference = 10^4 - 7*10^3 = 10^3(10-7) = 7*10^3.\nAnswer: A.\nSimilar questions to practice:\nHope it helps.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJohn deposited $10,000 to open a new savings account that earned 12 percent annual interest, compounded quarterly. If there were no other transactions in the account, what was the amount of money in John\u2019s account 6 months after the account was opened?\n\n### Options:\nA. $10,101\nB. $10,609\nC. $10,209\nD. $10,601\nE. $10,404\n\n### Answer:\n12 percent annual interest compounded quarterly --> 3% in 3 moths.\nFor the first 3 moths interest was 3% of $10,000, so $300;\nFor the next 3 moths interest was 3% of $10,000,plus9 earned on previous interest of $100, so $300+$9=$309;\nTotal interest for 6 months was $300+$309=$609, hence balance after 6 months was $10,000+ $609=$10,609.\nAnswer: B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\na car runs 10,000 miles using 5 tyres interchangably. to have equal wornout by all tyres, how many miles each tyre should have run?\n\n### Options:\nA. 7000 miles\nB. 8000 miles\nC. 9000 miles\nD. 6000 miles\nE. 5000 miles\n\n### Answer:\nsimply 10000*4/5=8000\nor\ntake a,b,c,d,e are tyres then each tyre travells 8000 miles first car runs with\na,b,c,d for 2000 miles\nb,c,d,e for 2000 miles\na,c,d,e for 2000 miles\na,b,d,e for 2000 miles\na,b,c,e for 2000 miles\nso total distance travelled is 10000 miles and each tyre travells 8000 miles\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA person lent a certain sum of money at 4% per annum at simple interest and in 8 years the interest amounted to Rs.340 less than the sum lent. What was the sum lent?\n\n### Options:\nA. 228\nB. 278\nC. 289\nD. 500\nE. 821\n\n### Answer:\nP - 340 = (P*4*8)/100\nP = 500\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTough and Tricky questions: Number Properties.\nIf (z + 3)/6 is an integer, what is remainder when z is divided by 6?\n\n### Options:\nA. 2\nB. 3\nC. 4\nD. 5\nE. 6\n\n### Answer:\n6/6=1\nAns B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAfter decreasing 80% in the price of an article costs Rs.320. Find the actual cost of an article?\n\n### Options:\nA. 2777\nB. 2987\nC. 1200\nD. 9977\nE. 1600\n\n### Answer:\nCP* (20/100) = 320\nCP= 16* 100 => CP = 1600\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n6th March, 2005 is Monday, what was the day of the week on 6th March, 2004\n\n### Options:\nA. wednessday\nB. Thursday\nC. Friday\nD. Saturday\nE. Sunday\n\n### Answer:\nNumber of days from 6th March, 2004 to 5th March 2005 = 365 days\nFeb 2004 has 29 days ( leap year),\n365 days = 1 odd day\nGiven that 6th March, 2005 is Monday\nHence 6th March, 2004 = (Monday - 1 odd day) = Sunday\nAnswer : E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA speaks truth in 75% of cases and B in 80% of cases. In what percentage of cases are they likely to contradict each other, narrating the same incident?\n\n### Options:\nA. 30/100\nB. 32/100\nC. 35/100\nD. 41/100\nE. None of these\n\n### Answer:\nExplanation :\nLet A = Event that A speaks the truthB = Event that B speaks the truthThen P(A) = 75/100 = 3/4P(B) = 80/100 = 4/5P(A-lie) = 1-3/4 = 1/4P(B-lie) = 1-4/5 = 1/5Now ,A and B contradict each other =[A lies and B true] or [B true and B lies]= P(A).P(B-lie) + P(A-lie).P(B)= (3/5*1/5) + (1/4*4/5) = 7/20= (7/20 * 100) % = 35%\nAnswer : C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nsale of Rs 6835, Rs. 9927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs, 6900 ?\n\n### Options:\nA. 4966\nB. 6477\nC. 7391\nD. 2676\nE. 1881\n\n### Answer:\nTotal sale for 5 months = Rs. (6435 + 6927 + 6855 + 7230 + 6562) = Rs. 34009.\nRequired sale = Rs.[(6900 x 6) - 34009]\n= Rs. (41400 - 34009)\n= Rs. 7391\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIt takes ten minutes to fry a steak (five minutes for each side). You are frying the steaks in a pan that can accommodate only two steaks at one time. What is the least amount of time by which you can fry all the three steaks you have?\n\n### Options:\nA. 13 minutes\nB. 14 minutes\nC. 15 minutes\nD. 16 minutes\nE. 17 minutes\n\n### Answer:\nSolution:\nFifteen Minutes.\nAfter frying for five minutes, you can take out one steak and put the third one inside while turning the other one inside. After five more minutes, one steak is fried from both sides and you can take it out. Now put in the steak that we removed and turn the other one inside. After five more minutes, they both will also be fried from both sides.\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain business produced x rakes each month form November through February and shipped x/2 rakes at the beginning of each month from March through October. The business paid no storage costs for the rakes from November through February, but it paid storage costs of $0.30 per rake each month from March through October for the rakes that had not been shipped. In terms of x, what was the total storage cost, in dollars, that the business paid for the rakes for the 12 months form November through October?\n\n### Options:\nA. 0.40x\nB. 4.20x\nC. 1.40x\nD. 1.60x\nE. 3.20x\n\n### Answer:\nbecause we have a total of 4X\nAlso from Mar- Oct the rakes will be deducted by 1/8 X\nso\nIn Apr they pay for the storage 0.3 * 4X * 7/8\nIn May they pay for the storage 0.3 * 4X * 6/8\nIn Jun they pay for the storage 0.3 * 4X * 5/8\nIn Jul they pay for the storage 0.3 * 4X * 4/8\nIn Aug they pay for the storage 0.3 * 4X * 3/8\nIn Sep they pay for the storage 03 * 4X * 2/8\nIn Oct they pay for the storage 0.3 * 4X * 1/8\ntotal = 0.3 * 4X * 1/8 * [ 1+2+3+4+5+6+7]\n= 0.3 * X/2 * (28)\n= 4.2X\n(B)\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSeven different books (A, B, C, D,E,F,G and H) are to be arranged on a shelf. Books A and B are to be arranged first and second starting from the right of the shelf. The number of different orders in which books C, D,E,F and G may be arranged is\n\n### Options:\nA. 9!\nB. 12!\nC. 5!\nD. 25!\nE. 18!\n\n### Answer:\nSolution\nSince books A and B are arranged first and second, only books C,D,E,F and G will change order. Therefore it an arrangement problem involving 5 items and the number of different order is given by\n5!\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThree numbers are in the ratio 1:4:8 and their H.C.F is 3. The numbers are?\n\n### Options:\nA. 3, 15, 24\nB. 3, 12, 27\nC. 3, 12, 22\nD. 3, 12, 24\nE. 3, 12, 21\n\n### Answer:\nLet the required numbers be x, 4x and 8x. Then, their H.C.F = x. So, x = 3.\nThe numbers are 3, 12, 24.\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA, B and C enter into partnership. A invests some money at the beginning, B invests double the amount after 6 months, and C invests thrice the amount after 8 months. If the annual gain be Rs.18000. A's share is?\n\n### Options:\nA. Rs.7500\nB. Rs.7200\nC. Rs.6000\nD. Rs.5750\nE. Rs.6750\n\n### Answer:\nx* 12 : 2x* 6: 3x* 4\n1:1:1\n1/3 * 18000 = 6000\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf x^2+4x+3 is odd, then which one of the following could be the value of x.\n\n### Options:\nA. 3\nB. 4\nC. 5\nD. 6\nE. 9\n\n### Answer:\nfor any x, 4x+3->odd\nso x^2 should be even, means x should be even;\nonly ans we have 4 as even.\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn what ratio must rice of Rs.32per kg be mixed with rice of Rs.42 per kg so that cost of mixture is Rs.20 per kg?\n\n### Options:\nA. 13:6\nB. 13:5\nC. 11:6\nD. 11:5\nE. 12:5\n\n### Answer:\n(20-42)/(32-20)=22/12=11:6\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA can do a piece of work in 8 days which B can do in 12 days. B worked at it for 9 days. A can finish the remaining work in ?\n\n### Options:\nA. 2 days\nB. 5 days\nC. 6 days\nD. 7 days\nE. 11 days\n\n### Answer:\nB's 9 day's work = 9 x (1/12) = 3/4\nRemaining work = (1 - 3/4) = 1/4\n1/4 work is done by A in = 8 x (1/4) = 2 days.\nanswer : A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSeven children \u2014 A, B, C, D, E, F, and G \u2014 are going to sit in seven chairs in a row. Child A has to sit next to both BG, with these two children immediately adjacent to here on either side. The other four children can sit in any order in any of the remaining seats. How many possible configurations W are there for the children?\n\n### Options:\nA. 240\nB. 480\nC. 720\nD. 1440\nE. 3600\n\n### Answer:\nMAGOOSHOFFICIAL SOLUTION:\nFirst, we will consider the restricted elements \u2014 children ABG have to be in three seats in a row. How many \u201cthree in a row\u201d seats are there in a row of seven seats?\nX X X _ _ _ _\n_ X X X _ _ _\n_ _ X X X _ _\n_ _ _ X X X _\n_ _ _ _ X X X\nThere are five different \u201cthree in a row\u201d locations for these three children. Now, for any given triplet of seats, we know A has to be in the middle, so the children could be seated B-A-G or G-A-B \u2014 just those two orders. This means the total number of configurations for these three children is 5*2 = 10.\nNow, consider the non-restricted elements, the other four. Once ABG are seated, the remaining four children can be seated in any order among the remaining four seats \u2014 that\u2019s a permutation of the 4 items \u2014- 4P4 = 4! = 24. For any single configuration of ABG, there are 24 ways that the other children could be seated in the remaining seats.\nFinally, we\u2019ll combine with the Fundamental Counting Principle. We have 10 ways for the first three, and 24 ways for the remaining four. That\u2019s a total number of configurations W of 24*10 = 240.\nAnswer = A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe sum of the non-prime numbers between 60 and 70, non-inclusive, is\n\n### Options:\nA. 387\nB. 429\nC. 457\nD. 499\nE. 536\n\n### Answer:\nsum of consecutive integers from 61 to 69, inclusive ====> (A1 + An)/2 * # of terms = (61 + 69)/2 * 9 = 65 *9 = 585\nsum of non-prime numbers b/w 60 and 70, non inclusive ===> 585 - 128 (i.e., 61 + 67, being the prime #s in the range) =457\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are two circles of different radii. The are of a square is 784 sq cm and its side is twice the radius of the larger circle. The radius of the larger circle is seven - third that of the smaller circle. Find the circumference of the smaller circle.\n\n### Options:\nA. 6\u220f cm\nB. 8\u220f cm\nC. 12\u220f cm\nD. 16\u220f cm\nE. None of these.\n\n### Answer:\nLet the radii of the larger and the smaller circles be l cm and s cm respectively. Let the side of the square be a cm.\na2 = 784 = (4)(196) = (22).(142)\na = (2)(14) = 28\na = 2l, l = a/2 = 14\nl = (7/3)s\nTherefore s = (3/7)(l) = 6 Circumference of the smaller circle = 2\u220fs = 12\u220f cm.\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf q and t are positive integers, qt + q + t cannot be\n\n### Options:\nA. 5\nB. 6\nC. 7\nD. 8\nE. 9\n\n### Answer:\nLet qt + t +q = x\nAdd 1 on both sides:\nqt + t + q + 1 = x + 1\ntq + 1) + q + 1 = x + 1\n(q + 1)(t + 1) = x + 1\nMinimum value of (q + 1) = 2\nMinimum value of (t + 1) = 2\nHence x + 1 cannot be prime\nSubstitute x from the given options: 6 + 1 = 7 --> prime --> qt + t + s cannot be 6\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA meeting has to be conducted with 6 managers. Find the number of ways in which the managers may be selected from among 9 managers, if there are 2 managers who refuse to attend the meeting together.\n\n### Options:\nA. 36\nB. 40\nC. 42\nD. 45\nE. 49\n\n### Answer:\nThe total number of ways to choose 6 managers is 9C6 = 84\nWe need to subtract the number of groups which include the two managers, which is 7C4 = 35.\n84 - 35 = 49\nThe answer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man buys an item at Rs. 1300 and sells it at the loss of 20 percent. Then what is the selling price of that item\n\n### Options:\nA. Rs. 660\nB. Rs. 760\nC. Rs. 860\nD. Rs. 1040\nE. None of these\n\n### Answer:\nExplanation:\nHere always remember, when ever x% loss,\nit means S.P. = (100 - x)% of C.P\nwhen ever x% profit,\nit means S.P. = (100 + x)% of C.P\nSo here will be (100 - x)% of C.P.\n= 80% of 1300\n= 80/100 * 1300\n= 1040\nOption D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nDavid biked 16 1/3 miles in 2 hours and 20 minutes. What was his average rate of speed in miles per hour?\n\n### Options:\nA. 7\nB. 7 2/3\nC. 8 1/3\nD. 9\nE. 9 1/3\n\n### Answer:\nD = 16(1/3) = 49/3\nT = 2(1/3) = 7/3\nS = D/T = 7\nAnswer = A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA sum was put at SI at certain rate for 2 years.Had it been put at 3% higher rate, it would have fetched Rs.300 more.Find the Sum\n\n### Options:\nA. RS 4000\nB. RS 5000\nC. RS 6000\nD. RS 7000\nE. RS 8000\n\n### Answer:\nlet P be the sum.and X be the interest rate.\n(2*(X+3)*P/100) - (2*X*P/100)=300\nTHEREFORE 6P/100=300\nP=RS 5000\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the ratio in which rice at Rs. 7.20 a kg be mixed with rice at Rs. 5.60 a kg to produce a mixture worth Rs. 6.30 a kg\n\n### Options:\nA. 2:0\nB. 2:3\nC. 2:1\nD. 2:2\nE. 7:9\n\n### Answer:\nBy the rule of alligation:\nCost of 1 kg rice of 1st kind Cost of 1 kg rice of 2nd kind\nRequired ratio = 70 : 90 = 7 : 9\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train A leaves Mysore at 6 a.m. and reaches Bangalore at 10 a.m. Another train leaves B Bangalore at 8 a.m. and reaches Mysore at 11.30 a.m. At what time do the two trains cross each other ?\n\n### Options:\nA. 8.30 a.m.\nB. 8.45 a.m.\nC. 8.56 a.m.\nD. 9 a.m.\nE. None of these\n\n### Answer:\nExplanation :\nSolution: Let the distance between mysore and bangalore be x km and let the trains meet y hours after 8 a.m.\nClearly, A covers x km in 4 hours and B covers x km in 4.5 hrs = (7/2) hrs\n.'. Speed of A = x/4 kmph, speed of B = 2x/7 kmph.\nDistance covered by A in (y+2) hrs + distance covered by B in y hrs = x.\n.'. x/4(y+2) + 2x/7 * y = x\n=> (y+2)/4 + 2y/7 = 1\n=> y = 14/15 hrs =14*60/15 = 56 min.\nHence, the trains meet at 8.56 a.m.\nAnswer : C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nCONVERT 2.5 hectares in ares\n\n### Options:\nA. 130 ares.\nB. 160 ares.\nC. 180 ares.\nD. 230 ares.\nE. 250 ares.\n\n### Answer:\n2.5 hectares in ares\n1 hectare = 100 ares\nTherefore, 2.5 hectares = 2.5 \u00d7 100 ares\n= 250 ares.\nANSWER- E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRs. 6000 is lent out in two parts. One part is lent at 4% p.a simple interest and the other is lent at 10% p.a simple interest. The total interest at the end of one year was Rs. 450. Find the ratio of the amounts lent at the lower rate and higher rate of interest?\n\n### Options:\nA. 5:1\nB. 5:7\nC. 5:2\nD. 5:8\nE. 5:2\n\n### Answer:\nLet the amount lent at 4% be Rs. x\nAmount lent at 10% is Rs. (6000 - x)\nTotal interest for one year on the two sums lent\n= 4/100 x + 10/100 (6000 - x) = 600 - 3x/100\n=> 600 - 3/100 x = 450 => x = 2500\nAmount lent at 10% = 3500\nRequired ratio = 5:7\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average of first 35 prime numbers is?\n\n### Options:\nA. 14.54\nB. 15.6\nC. 15.8\nD. 14.7\nE. 14.8\n\n### Answer:\nExplanation:\nAverage = (2+3+5+7+11+13+17+19+23+29+31)/11= 160/11= 14.54(Approx)\nAnswer is A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe number of arrangements that can be made with the letters of the word JOHNNIE so that the vowels occupy the even places?\n\n### Options:\nA. A)122\nB. B)134\nC. C)144\nD. D)156\nE. E)176\n\n### Answer:\nExplanation:\nThe word JOHNNIE has 7 letters of which 3 are vowels.\n-V-V-V-\nAs the vowels have to occupy even places, they can be arranged in the 3 even places in 3! i.e., 6 ways. While the consonants can be arranged among themselves in the remaining 4 places in 4! i.e., 24 ways.\nHence the total ways are 24 * 6 = 144.\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nToday is Sunday. The day after 59 days will be\n\n### Options:\nA. Monday\nB. Wednesday\nC. Saturday\nD. Sunday\nE. None of these\n\n### Answer:\nExplanation :\n59 days = 8 weeks 3 days = 3 odd days\nHence if today is Sunday, After 59 days, it will be = (Sunday + 3 odd days)\n= Wednesday. Answer : Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA squirrel can climb 5 metres of a pole in one minute but slips 2 metres in the next minute. How much time will the squirrel take to climb 26 metres?\n\n### Options:\nA. 15 minutes\nB. 18 minutes\nC. 12 minutes\nD. 58 minutes\nE. 10 minutes\n\n### Answer:\nExplanation:\nAs the squirrel climbs 5 m in one minute and slips 2 metres in the next minute, it climbs 3 metres in 2 minute\nTo climb 26 metres, the time required is:\nThe squirrel will climb (26 \u2013 5) = 21 metres = 7 * 3 metres in 7 * 2 = 14 minutes\nAlso, the last 5 metres it climbs in another 1 minute\nHence, total time required = 14 + 1 = 15 minutes\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA taxi charges v dollars for the first two miles and c cents per quarter mile for every mile after the first two. Which equation describes cost of a taxi ride of n miles in dollars.\n\n### Options:\nA. vn \u2013 c/8(100)\nB. cv + 4n-8/200\nC. v + (4cn-8c)/100\nD. v + 100cn/4\nE. 4cv(n-2) \u2013 100\n\n### Answer:\nThis is about as complicated as these types of problems come, but it is essentially the same as any problem which has an initial cost which is added to a dependent additional cost. Looking at the problem, we notice that the cost v is added to the mile dependent cost, which is some combination of the other terms listed in the problem. With just that knowledge we can eliminate all but two of the answer choices! Choices (A), (B), and (E) either do some strange calculation with the initial cost v, or subtract the additional cost from v. Both of these circumstances would be next to impossible if there is an initial cost being added to another cost. Thus, we only have to choose between choice (C) and choice (D). We can easily find the right answer by plugging in real numbers and checking which choice yields a correct answer. We can also see that answer choice (D) seems to be multiplying the cost in cents by 100, which, if the trip was 6 miles and the charge per mile was 25 cents, would make the taxi cost an additional $3750! This seems impossible, and leaves only the correct answer choice, (C).\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nEighty percent of the lights at Hotel California are on at 8 p.m. a certain evening. However, forty percent of the lights that are supposed to be off are actually on and ten percent of the lights that are supposed to be on are actually off. What percent L of the lights that are on are supposed to be off?\n\n### Options:\nA. 22(2/9)%\nB. 16(2/3)%\nC. 11(1/9)%\nD. 10%\nE. 5%\n\n### Answer:\nIs the Answer D.\nlet me try..\nLet the light which are supposed to be OFF = SO\nLet the light which are supposed to be ON = SN\nLet the light which are ACTUALLY OFF = AO\nLet the light which are ACTUALLY ON = AN\nLet the total no. of lights be 100,\nSo ACTUALLY ON lights = 80\nAnd ACTUALLY OFF lights = 20\nAlso given >> forty percent of the lights that are supposed to off are actually on >>> (40/100)*SO are ACTUALLY ON\nit means >>> (60/100)*SO are ACTUALLY OFF\nAlso given >> ten percent of the lights that are supposed to be on are actually off >>> (10/100)*SN are ACTUALLY OFF\nit means >>> (90/100)*SN are ACTUALLY ON\nSo, Total ACTUALLY ON lights = (40/100)*SO + (90/100)*SN = 80\nand Total ACTUALLY OFF lights = (60/100)*SO + (10/100)*SN = 80\nFrom here we get SO = 20\nwe need to find: What percent of the lights that are on are supposed to be off >>> So light ACTUALLY ON are 80 and light which are ACTUALLY ON, which are supposed to be OFF = (40/100)*SO = 8.\nSo (8/80)*100 L= 10%.D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average of four consecutive odd numbers is 12. Which is the lowest odd number?\n\n### Options:\nA. 9\nB. 3\nC. 5\nD. Cannot be determined\nE. None of these\n\n### Answer:\nLet the four consecutive odd nos. be\n2x \u2013 3, 2x \u2013 1, 2x + 1 and 2x + 3.\nNow, 2x = 12 or, x = 6\nLowest odd no. = 2 \u00d7 6 \u2013 3 = 9\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA batsman scored 140 runs which included 3 boundaries and 8 sixes. What percent of his total score did he make by running between the wickets?\n\n### Options:\nA. 50%\nB. 40%\nC. 60%\nD. 57%\nE. 80%\n\n### Answer:\nNumber of runs made by running = 140 - (3 x 4 + 8 x 6)\n= 140 - (60)\n= 80\nNow, we need to calculate 80 is what percent of 140.\n=> 80/140 x 100 = 57 %\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn the equation 2x \u2013 cy = 18, c is a constant. If the value of y is 2 when x is 6, what is the value of x when y is 3 ?\n\n### Options:\nA. \u22129/2\nB. -4\nC. -3\nD. 4\nE. 9/2\n\n### Answer:\n2x - cy = 18\nx=6, y=2;\n12-2c=18\nc=-3\n2x-cy=18\nwhen y=3, c=-3, x=\nx=9/2\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIt takes Beth 9 minutes to do one oil change, and it takes Logan 12 minutes. At 4:56 pm, they both finish an oil change simultaneously. If Beth and Logan both began doing oil changes at exactly the same time and worked without pausing, when did they both start doing oil changes?\n\n### Options:\nA. 4:11 pm\nB. 4:20 pm\nC. 4:29 pm\nD. 4:38 pm\nE. 4:47 pm\n\n### Answer:\nSince Beth finishes s oil changes after s \u00d7 9 minutes and Logan finishes c oil changes after c \u00d7 12 minutes, they both finished doing an oil change at the same time when s \u00d7 9 = c \u00d7 12. Since s and c must be integers (they represent the number of oil changes finished) this question is asking you to find a common multiple of 9 and 12. The question asks for the first time they began a car simultaneously, so you must find the least common multiple and subtract. The least common multiple of 9 and 12 is 36, so in the context of the question, this would be 36 minutes. Therefore, they began changing the oil of a car at the same time at 4:56 - 36 minutes, or 4:20 p.m. The answer is (B).\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSuresh started a business with Rs.20,000. Kiran joined him after 4 months with Rs.30,000. After 2 months, Suresh withdrew Rs.5,000 of his capital and 2 more months later, Kiran brought in Rs.20,000 more. What should be the ratio in which they should share their profits at the end of the year?\n\n### Options:\nA. 32:21\nB. 22:21\nC. 21:32\nD. 31:21\nE. 32:28\n\n### Answer:\nHere capital is not the same.\nSuresh invest 20000 for initial 6 months and 15000 for the next 6 months.\nHence his term of ratio\n=( 20000*6 + 15000*6)\nKiran invest Rs.30000 for 4 months and Rs.50000 for next 4 months.\nHence his term of ration\n= (30000*4 : 50000*4)\nSuresh : Kiran = ( 20000*6 + 15000*6) : (30000*4 : 50000*4)\n= (20*6 + 15*6) : (30*4 + 50*4)\n= (20*3 + 15*3) : (30*2 : 50*2)\n= 105:160\n= 21:32\nAnswer is C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the roots of the quadratic equation: x2 + 2x - 15 = 0?\n\n### Options:\nA. -5, 3\nB. 3, 5\nC. -3, 5\nD. -3, -5\nE. 5, 2\n\n### Answer:\nExplanation:\nx2 + 5x - 3x - 15 = 0\nx(x + 5) - 3(x + 5) = 0\n(x - 3)(x + 5) = 0\n=> x = 3 or x = -5.\nANSWER IS A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain bridge is 4,024 feet long. Approximately how many minutes does it take to cross this bridge at a constant speed of 40 miles per hour? (1 mile = 5,280 feet)\n\n### Options:\nA. 1\nB. 2\nC. 4\nD. 6\nE. 7\n\n### Answer:\nDistance: 4024 feet. This is (4024/5280) miles = 0.76 miles\nSpeed: 40 miles per hour\nTime: (Distance / Speed) (0.76/40) {This will come in Hours}. Multiply by 60 to get answer in minutes. It is 1.14 minutes.\nAnswer to be 1 minutes.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat are the next two letters in the following series and why?\nW A T N T L I T F S _ _\n*Hint : Look into the title of the Riddle\n\n### Options:\nA. A and W\nB. A and E\nC. B and W\nD. A and C\nE. S and W\n\n### Answer:\nA\nA and W.\nThe letters are the first letters of the words in the question. Thus, the next two letters are A and W.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 20 men take 15 days to to complete a job, in how many days can 20 men finish that work?\n\n### Options:\nA. 15\nB. 16\nC. 17\nD. 18\nE. 19\n\n### Answer:\nAns. 15 days\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are 8 red, 7 blue and 6 green balls, 1 ball is picked up randomly thenwhat is the probability that neither blue nor green?\n\n### Options:\nA. 7/22\nB. 7/25\nC. 8/21\nD. 8/23\nE. 8/25\n\n### Answer:\nTotal number of balls = (8 + 7 + 6) = 21\nLet E = event that the ball drawn is neither blue nor green =e vent that the ball drawn is red.\nTherefore, n(E) = 8.\nP(E) = 8/21.\nC)\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the principle on a certain sum of money at 8% per annum for 2 2/5 years if the amount being Rs.1120?\n\n### Options:\nA. 939.6\nB. 928.8\nC. 927.78\nD. 926.82\nE. 902.1\n\n### Answer:\n1120 = P [1 + (8*12/5)/100]\nP=939.60\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n5358 x 52 = ?\n\n### Options:\nA. 273762\nB. 278616\nC. 273298\nD. 273258\nE. 277382\n\n### Answer:\nB\n5358 x 52 = 5358 x (50 + 2)\n= 5358 x 50 + 5358 x 2\n= 267900 + 10716\n= 278616.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the perimeter of square region Z and the perimeter of rectangular region R are equal and the sides of R are in the ratio 2:3 then the ratio of the area of R to the area of Z\n\n### Options:\nA. 25:16\nB. 24:25\nC. 5:6\nD. 4:5\nE. 4:9\n\n### Answer:\nWe know Perimeter of a square (Pz) = 4*side\nPerimeter of a rectangle (Pr) = 2(length+breath)\nLet us assume 40 to be the perimeter of the square (since we know each side of a square is equal and the perimeter is divisible by 4, also take in to account the length and breadth of the rectangle is in the ration 2k:3k = 5k; we can assume such a number)\nTherefore,\nPz = Pr = 40\nArea of the square = 100 sq. units\nWe know 2(length+breadth) = 40\ni.e. length + breadth = 20 (or 5k = 20 given that l:b (or b:l) = 2:3)\nTherefore length = 8, breath = 12\nArea of the rectangle = 8*12 = 96 sq. units\nQuestion asked = Area of the rectangle : Area of the square = 96:100 ==> 24:25=B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the average (arithmetic mean) of all the multiples of ten from 10 to 210 inclusive?\n\n### Options:\nA. 90\nB. 95\nC. 100\nD. 105\nE. 110\n\n### Answer:\nThe multiples of ten from 10 to 190 inclusive would be an evenly spaced set with 21 terms - 10, 20, 30,.......210\nSo average = (First term + Last Term)/2 = (10 + 210)/2 = 220/2 = 110\nHence, the correct answer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a and b are both negative and ab < b^2, which of the following must be true?\n\n### Options:\nA. a < b < a^2 < b^2\nB. a < b < b^2 < a^2\nC. b < a < a^2 < b^2\nD. a^2 < b^2 < b < a\nE. b^2 < a^2 < b < a\n\n### Answer:\nBecause ab < b^2 and both are negative, I thought a < b. So I crossed off answers c), d), and e).\nAnd because a < b , a^2 < b^2\nans C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat day of the week was 1 January 1901\n\n### Options:\nA. Monday\nB. Tuesday\nC. Saturday\nD. Friday\nE. Sunday\n\n### Answer:\nExplanation:\n1 Jan 1901 = (1900 years + 1st Jan 1901)\nWe know that number of odd days in 400 years = 0\nHence the number of odd days in 1600 years = 0 (Since 1600 is a perfect multiple of 400)\nNumber of odd days in the period 1601-1900\n= Number of odd days in 300 years\n= 5 x 3 = 15 = 1\n(As we can reduce perfect multiples of 7 from odd days without affecting anything)\n1st Jan 1901 = 1 odd day\nTotal number of odd days = (0 + 1 + 1) = 2\n2 odd days = Tuesday\nHence 1 January 1901 is Tuesday.\nAnswer: Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo pipes A and B can separately fill a tank in 2 minutes and 15 minutes respectively. Both the pipes are opened together but 4 minutes after the start the pipe A is turned off. How much time will it take to fill the tank?\n\n### Options:\nA. 15\nB. 10\nC. 12\nD. 17\nE. 14\n\n### Answer:\n4/12 + x/15 = 1\nx = 10\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nPeter has 9 candies, rina has 5 candies. Totally how many candies they have in all?\n\n### Options:\nA. 14\nB. 4\nC. 23\nD. 12\nE. 9\n\n### Answer:\n9+5=14. Answer is A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo trains are moving at 50 kmph and 70 kmph in opposite directions. Their lengths are 150 m and 100 m respectively. The time they will take to pass each other completely is?\n\n### Options:\nA. 3 sec\nB. 5 sec\nC. 6 \u00bd sec\nD. 7 \u00bd sec\nE. 5 \u00bd sec\n\n### Answer:\nD\n7 \u00bd sec\n70 + 50 = 120 * 5/18 = 100/3 mps\nD = 150 + 100 = 250 m\nT = 250 * 3/100 = 15/2 = 7 \u00bd sec\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n15.06 * 0.000001 = ?\n\n### Options:\nA. 15060000\nB. 0.001506\nC. 0.01506\nD. 1.506e-05\nE. None of these\n\n### Answer:\nExplanation:\nClearly after decimal 8 digits should be there.\nOption D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA photography dealer ordered 60 Model X cameras to be sold for $250 each, which represents a 10 percent markup over the dealer\u2019s initial cost for each camera. Of the cameras ordered, 6 were never sold and were returned to the manufacturer for a refund of 50 percent of the dealer's initial cost. What was the dealer's approximate profit or loss as a percent of the dealer\u2019s initial cost for the 60 cameras?\n\n### Options:\nA. 7% loss\nB. 13% loss\nC. 4% profit\nD. 13% profit\nE. 15% profit\n\n### Answer:\nTotal cost 60*($250/1.1)=54.54*250;\n# of cameras sold is 60-6=54 total revenue is 54*250;\n# of cameras returned is 6 total refund 6*(250/1.1)*0.5;\nSo, total income 54*250+ 6*(250/1.1)*0.5\nThe dealer's approximate profit is (54*250+ 6*(250/1.1)*0.5-54.54*250)/(54.54*250)*100=4%\nAnswer: C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a rectangular coordinate system, what is the area of a rectangle whose vertices have the coordinates (-3, 1), (1, 1), (1, -2) and (-3, -2)?\n\n### Options:\nA. 12\nB. 24\nC. 20\nD. 30\nE. 36\n\n### Answer:\nLength of side 1= 3+1=4\nLength of side 2= 2+1= 3\nArea of rectangle= 4*3= 12\nA is the answer\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIncomes of two companies A and B are in the ratio of 5 : 8. Had the income of company A been more by 40 lakh, the ratio of their incomes would have been 5 : 4. What is the income of company B?\n\n### Options:\nA. 80 lakh\nB. 50 lakh\nC. 40 lakh\nD. 64 lakh\nE. None of these\n\n### Answer:\nLet the incomes of two companies A and B be 5x and 8x respectively.\nFrom the question,\n5x+40/8x=5/4 \u21d2 20x + 160 = 40x\n\u2234 x = 8\n\u2234 Income of company B = 8x = 64 lakh\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nEach day a man meets his wife at the train station after work, and then she drives him home. She always arrives exactly on time to pick him up. One day he catches an earlier train and arrives at the station an hour early. He immediately begins walking home along the same route the wife drives. Eventually his wife sees him on her way to the station and drives him the rest of the way home. When they arrive home the man notices that they arrived 12 minutes earlier than usual. How much time did the man spend walking?\n\n### Options:\nA. 45 minutes\nB. 50 minutes\nC. 40 minutes\nD. 54 minutes\nE. 35 minutes\n\n### Answer:\nAs they arrived 12 minutes earlier than usual, they saved 12 minutes on round trip from home to station (home-station-home) --> 6 minutes in each direction (home-station) --> wife meets husband 6 minutes earlier the usual meeting time --> husband arrived an hour earlier the usual meeting time, so he must have spent waking the rest of the time before their meeting, which is hour-6 minutes=54 minutes.\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n1/3th of the passengers got down at first stop and 30 people got into the bus, 1/4th of the passengers got down at second stop and 12 people got into the bus.In last stop 84 people got down from the bus. What is the initial capacity of the bus?\n\n### Options:\nA. 98\nB. 99\nC. 97\nD. 96\nE. 95\n\n### Answer:\nLet x be the no of initial passenger\nno of passengr left in 1st stop (2x/3)+30\nno of passenger in the 2nd stop 3/4((2x/3)+30) + 12\nwhich is equal to 84 (passngr on last stop)\nso final eqn....3/4((2x/3)+30) + 12 = 84\nAns x = 99\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many kg of sugar costing Rs. 9/kg must be mixed with 27kg of sugar costing Rs. 7/ kg so that there may be a gain of 10% the mixture at Rs. 9.24 per kg?\n\n### Options:\nA. 52\nB. 55\nC. 57\nD. 60\nE. 63\n\n### Answer:\nSelling Price(SP) of 1 kg mixture= Rs. 9.24\nProfit = 10%\nCost Price(CP) of 1 kg mixture =100(100+Profit%)\u00d7SP\n=100(100+10)\u00d79.24=100110\u00d79.24=92.411= Rs.8.4\nBy rule of alligation,\nCP of 1 kg sugar of 1st kind CP of 1 kg sugar of 2nd kind\nRs. 9 Rs. 7\nMean Price\nRs.8.4\n8.4 - 7 = 1.4 9 - 8.4 = 0.6\ni.e., to get a cost price of 8.4, the sugars of kind1 and kind2 should be mixed in the ratio 1.4 : 0.6 = 14 : 6 = 7 : 3\nSuppose x\nkg of kind1 sugar is mixed with 27 kg of kind2 sugar.\nthen x : 27 = 7 : 3\n\u21d23x=27\u00d77\u21d2x=9\u00d77=63\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the odd man out. 3, 5, 15, 75, 1120, 84375\n\n### Options:\nA. 84375\nB. 1120\nC. 15\nD. 3\nE. 75\n\n### Answer:\nExplanation :\nPattern : 1st * 2nd = 3rd, 2nd * 3rd = 4th, etc.\n3\n5\n3 \u00d7 5 = 15\n5 \u00d7 15 = 75\n15 \u00d7 75 = 1125\n75 \u00d7 1125 = 84375\nHence, 1120 is wrong. 1125 should have come in place of 1120\nAnswer : Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nNine people are planning to share equally the cost of a rental car. If one person withdraws from the arrangement and the others share equally the entire cost of the car, then the share of each of the remaining persons increased by:\n\n### Options:\nA. 7/8\nB. 1/8\nC. 1/3\nD. 1/7\nE. 1/9\n\n### Answer:\nOriginal share of 1 person =1/9\nNew share of 1 person =1/8\nIncrease =1/8 -\t1/9\t=1/72\nRequired fraction =\t(1/72)/(1/9)=1/8\nAnswer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n49 \u00c3\u2014 49 \u00c3\u2014 49 \u00c3\u2014 49 x 49 \u00c3\u2014 49 \u00c3\u2014 49 \u00c3\u2014 49= 7?\n\n### Options:\nA. 4\nB. 7\nC. 8\nD. 16\nE. None of these\n\n### Answer:\n49 \u00c3\u2014 49 \u00c3\u2014 49 \u00c3\u2014 49 x 49 \u00c3\u2014 49 \u00c3\u2014 49 \u00c3\u2014 49 = 7?\nor, 7(2) \u00c3\u2014 7(2) \u00c3\u2014 7(2) \u00c3\u2014 7(2) x 7(2) \u00c3\u2014 7(2) \u00c3\u2014 7(2) \u00c3\u2014 7(2)= 7^?\nor 7(16) = 7? or, ? =16\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nS1 = 3 S2 = 6 ... Sn = 3n + 4 For the sequence above, in which any term n is defined as 3n + 4, what is the value of n for the first term in the sequence to exceed 50?\n\n### Options:\nA. 13\nB. 16\nC. 12\nD. 9\nE. 8\n\n### Answer:\nterm 16 = 3*16+4 = 52\nAnswer : B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA two digit number is 18 less than the square of the sum of its digits. How many such numbers are there?\n\n### Options:\nA. 22,33\nB. 22,22\nC. 221,1\nD. 63,82\nE. 23,17\n\n### Answer:\nOption 2\nTake N = 10a+b.\nGiven that, (10a+b)+18 = K2 = (a+b)2\nGiven number = K2 - 18 = (10a+b)\nThat means, when we add 18 to the given number it should be a perfect square. So K2 takes the following values. 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, ....\n1 to 16 are ruled out as if we subtract 18 from them, the resulting number is a single digit number.\nNow 25 - 18 = 7\n36 - 18 = 18\n49 - 18 = 31\n64 - 18 = 46\n81 - 18 = 63\n100 - 18 = 82\n121 - 18 = 103\nNow 63, 82 satisfies.\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA trader sells 85 meters of cloth for Rs. 8925 at the profit of Rs. 15 per metre of cloth. What is the cost price of one metre of cloth?\n\n### Options:\nA. Rs.90\nB. Rs.76\nC. Rs.98\nD. Rs.18\nE. Rs.02\n\n### Answer:\nSP of 1m of cloth = 8925/85 = Rs. 105\nCP of 1m of cloth = SP of 1m of cloth - profit on 1m of cloth\n= Rs. 105 - Rs. 15 = Rs.90.\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many different ways can you select a pilot and a co pilot if you have 30 people to choose from?\n\n### Options:\nA. 870\nB. 920\nC. 1398\nD. 4950\nE. 9900\n\n### Answer:\nYou are not just choosing two from 30. Each of the two people chosen fills a particular slot. The first filling the pilot slot and the second filling the copilot slot is different from the first filling the copilot slot and the second filling the pilot slot.\nSo the answer is in a sense (30C2) x 2 = 870.\nAns A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a City, 35% of the population is composed of migrants, 20% of whom are from rural areas. Of the local population, 48% is female while this figure for rural and urban migrants is 30% and 40% respectively. If the total population of the city is 728400, what is its female population ?\n\n### Options:\nA. 324138\nB. 248888\nC. 378908\nD. 277880\nE. 379010\n\n### Answer:\nExplanation:\nTotal Population = 728400\nMigrants = 35 % of 728400 = 254940\nlocal population = (728400 - 254940) = 473460.\nRural migrants = 20% of 254940 = 50988\nUrban migrants = (254940 - 50988) = 203952\nFemale population = 48% of 473460 + 30% of 50988 + 40% of 203952 = 324138\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe sum of the present ages of two persons A and B is 90. If the age of A is twice that of B, find the sum of their ages 5 years hence?\n\n### Options:\nA. 50\nB. 60\nC. 70\nD. 80\nE. 100\n\n### Answer:\nA + B = 90, A = 2B\n2B + B = 90 => B = 30 then A = 60.\n5 years, their ages will be 65 and 35.\nSum of their ages = 65 + 35 = 100.\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTough and Tricky questions: Word Problems.\nIn a rare coin collection, one in six coins is gold, and all coins are either gold or silver. If 10 silver coins were to be subsequently traded for an additional 10 gold coins, the ratio of gold coins to silver coins would be 1 to 7. Based on this information, how many gold coins would there be in this collection after the proposed trade?\n\n### Options:\nA. 50\nB. 60\nC. 180\nD. 200\nE. 350\n\n### Answer:\nThe correct answer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many times the keys of a writter haveto be pressedin order to write first 400 counting no.'s?\n\n### Options:\nA. 998\nB. 1000\nC. 1092\nD. 1100\nE. 1200\n\n### Answer:\n1 to 9 = 9 * 1 = 9\n10 to 99 = 90 * 2 = 180\n100 to 400 = 301 * 3 = 903\n-----------\n1092\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf in a race of 100m, A covers the distance in 20 seconds and B in 25 seconds, then A beats B by:\n\n### Options:\nA. 20m\nB. 16m\nC. 11m\nD. 10m\nE. 15m\n\n### Answer:\nExplanation:\nThe difference in the timing of A and B is 5 seconds. Hence, A beats B by 5 seconds.\nThe distance covered by B in 5 seconds = (100 * 5) / 25 = 20m\nHence, A beats B by 20m.\nANSWER A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow much time does a train 150 metres long running at 90 km/hr take to pass a pole?\n\n### Options:\nA. 7.9s\nB. 6s\nC. 7.5s\nD. 7.6s\nE. 7.4s\n\n### Answer:\nExplanation:\n90 km/hr = 90 * 5/18 = 25 m/s\nSpeed = distance/time; v = d/t\n25 = 150/t\nt = 6s\nANSWER: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFor what value(s) of n is the following equation satisfied: 2n-6-5n = 5n+7-4n\n\n### Options:\nA. a. -5/4\nB. b. -13/4\nC. c. 5/4 only\nD. d. No value\nE. e. Any value\n\n### Answer:\n2n-6-5n = 5n+7-4n\n-3n - 6 = n + 7\n-13 = 4n,\nn=13/4\nAnswer: B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf (m-8) is a factor of m^2-pm-24, then p=\n\n### Options:\nA. 3\nB. 5\nC. 6\nD. 11\nE. 16\n\n### Answer:\n(m-8)(m-a)=m^2-pm-24\nA=-3\np=8+a=5=B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA shopkeeper labels the price of articles 20% above the cost price. If he allows 31.20 off on a bill of 312, find his profit per cent on the article?\n\n### Options:\nA. 8\nB. 12 1\u20443\nC. 11 2\u20443\nD. 8 1\u20443\nE. None of these\n\n### Answer:\nLet the CP = 100 Marked price = 120\nDiscount = 312\u204431.2 \u00d7 1\u2044100 = 10% = 12\nSP = 120 \u2013 12 = 108 Profit% = 108 \u2013 100 = 8%\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nInsert the missing number. 12, 25, 49, 99, 197, 395, (...)\n\n### Options:\nA. 789\nB. 1579\nC. 12\nD. 23\nE. 28\n\n### Answer:\nEach number is twice the previous one with 1 added or subtracted alternatively. Missing Number is 789\nAnswer is A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA sum fetched a total simple interest of Rs. 4016.25 at the rate of 1% p.a. in 3 years. What is the sum?\n\n### Options:\nA. 122762\nB. 132877\nC. 122882\nD. 133875\nE. 132887\n\n### Answer:\nPrincipal = (100 * 4016.25) / (1 * 3)\n= Rs.133875.\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA merchant purchased a jacket for $210 and then determined a selling price that equaled the purchase price of the jacket plus a markup that was 25 percent of the selling price. During a sale, the merchant discounted the selling price by 20 percent and sold the jacket. What was the merchant\u2019s gross profit on this sale?\n\n### Options:\nA. $0\nB. $3\nC. $4\nD. $12\nE. $14\n\n### Answer:\nLet selling price = x\nSo, x = 210 + 25x/100\nCalculating above, x = 280\nSelling price = 280\n20% Discount on Selling price = 224\nSo, profit = 224-210 = 14 Answer = E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAlbert invested amount of 20000 in a fixed deposit for 2 years at compound interest rate of 5 % per annum. How much Albert will get on the maturity of the fixed deposit\n\n### Options:\nA. Rs. 8510\nB. Rs. 22050\nC. Rs. 8730\nD. Rs. 8820\nE. None of these\n\n### Answer:\nExplanation:\n=>(20000\u00d7(1+5/100)2)\n=>20000\u00d721/20\u00d721/20\n=>22050\nOption B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMarcella has 25 pairs of shoes. If she loses 9 individual shoes, what is the greatest number of matching pairs she could have left?\n\n### Options:\nA. 21\nB. 20\nC. 19\nD. 16\nE. 15\n\n### Answer:\ngreatest number of paired shoes means greatest number of lost pairs\n9 shoes have 4 pairs and 1 extra shoes of a pair .so a otal of 5 pairs she loses\nleftover pair=20\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nDuring the last four years, a large truck company purchased diesel at rates of $1.2, $1.4, $1.7 and $2.1 per gallon. What was the mean cost of diesel over the four-year period if the company spends the same amount of dollars on diesel each year?\n\n### Options:\nA. $2.5\nB. $2.55\nC. $1.53\nD. $3.25\nE. $3.0\n\n### Answer:\nfinding the Harmonic mean here.\nHM = 4/(1/12 + 1/14 + 1/17 + 1/21) = 15.31\nThe calculation is the same either way.\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA boy has nine trousers and 14 shirts. In how many different ways can he select a trouser and a shirt?\n\n### Options:\nA. 88\nB. 98\nC. 126\nD. 108\nE. 111\n\n### Answer:\nExplanation:\nThe boy can select one trouser in nine ways.\nThe boy can select one shirt in 14 ways.\nThe number of ways in which he can select one trouser and one shirt is 9 * 14 = 126 ways\nC)\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf x and y are integers such that (x+1)^2 is less than or equal to 64 and (y-1)^2 is less than 64, what is the sum of the maximum possible value of xy and the minimum possible value of xy?\n\n### Options:\nA. -16\nB. -18\nC. 0\nD. 14\nE. 16\n\n### Answer:\n(x+1)^2 <= 64\nx <= 7\nx >= -9\n(y-1)^2 < 64\ny < 9\ny > -7\nMax possible value of xy is -9 \u00d7 -6 = 54\nminimum possible value of xy is -9 \u00d7 8 = -72\n-72 + 54 = -18\nAnswer : B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe ratio of the present age of Viju to that of Aju is 7:2. Four years from now, the ratio of the ages of Viju to Aju will be 5:2. What was Viju age 7 years ago ? (RBI Assistant 2015)\n\n### Options:\nA. 24\nB. 18\nC. 14\nD. 15\nE. 13\n\n### Answer:\nLet the present age of Viju be 7x years and that of Aju be 2x years.\nThen, 4 years from now\n7x + 4 / 2x + 4 = 5 / 2\nor 4x = 12\nor x = 3\nViju present age = 7 * 3 = 21 years\nViju age 7 years ago = 21 - 7 = 14 years\nanswer :C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA person purchased a TV set for Rs. 16000 and a DVD player for Rs. 6250. He sold both the items together for Rs. 31150. What percentage of profit did he make?\n\n### Options:\nA. 33\nB. 277\nC. 40\nD. 88\nE. 11\n\n### Answer:\nThe total CP = Rs. 16000 + Rs. 6250 = Rs. 22250 and SP = Rs. 31150\nProfit(%) = (31150 - 22250)/22250 * 100 = 40%\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many multiples of 2 are less than 2400, and also multiples of 8?\n\n### Options:\nA. 104\nB. 208\nC. 300\nD. 832\nE. 833\n\n### Answer:\nThe LCM of 2 and 8 is 8. Divide 2400/8 = 300.xxx. So C is your answer.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many ways are there to select a subcommittee of 7 members from among a committee of 17?\n\n### Options:\nA. 22888\nB. 19448\nC. 28791\nD. 27711\nE. 12111\n\n### Answer:\nExplanation:\nSince it does not matter what order the committee members are chosen in, the combination formula is used.\nCommittees are always a combination unless the problem states that someone like a president has higher hierarchy over another person. If the committee is ordered, then it is a permutation.\nC(17,7)= 19,448\nAnswer: B) 19448\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA bag contains 7 green and 8 white balls. If two balls are drawn simultaneously, the probability that both are of the same colour is\n\n### Options:\nA. 7/16\nB. 7/12\nC. 7/19\nD. 7/12\nE. 7/15\n\n### Answer:\nDrawing two balls of same color from seven green balls can be done in \u2077C\u2082 ways.\nSimilarly from eight white balls two can be drawn in \u2078C\u2082 ways.\nP = \u2077C\u2082/\u00b9\u2075C\u2082 + \u2078C\u2082/\u00b9\u2075C\u2082\n= 7/15\nAnswer:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a person walks at 14 km/hr instead of 10 km/hr, he would have walked 20 km more. The actual distance traveled by him is?\n\n### Options:\nA. 50\nB. 267\nC. 26\nD. 87\nE. 62\n\n### Answer:\nLet the actual distance traveled be x km. Then,\nx/10 = (x + 20)/14\n4x - 200 =>x = 50 km.\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe toll for crossing a certain bridge is $0.75 each crossing. Drivers who frequently use the bridge may instead purchase a sticker each month for $13.00 and then pay only $0.10 each crossing during that month. If a particular driver will cross the bridge twice on each of x days next month and will not cross the bridge on any other day, what is the least value of x for which this driver can save money by using the sticker?\n\n### Options:\nA. 12\nB. 15\nC. 16\nD. 28\nE. 29\n\n### Answer:\nOption #1: $0.75/crossing....Cross twice a day = $1.5/day\nOption #2: $0.30/crossing....Cross twice a day = $0.6/day + $13 one time charge.\nIf we go down the list of possible answers, you can quickly see that 14 days will not be worth purchasing the sticker. 1.5x14 (21) is cheaper than 0.6x14 +13 (21.4)...it's pretty close so let's see if one more day will make it worth it... If we raise the number of days to 15, the sticker option looks like a better deal...1.5x15 (22.5) vs 0.6x15 + 13 (22). Answer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a company of 160 employees, 90 are females. A total of 80 employees have advanced degrees and the rest have a college degree only. If 40 employees are males with college degree only, how many employees are females with advanced degrees?\n\n### Options:\nA. 40\nB. 45\nC. 50\nD. 55\nE. 60\n\n### Answer:\nThe number of males is 160-90=70.\nThe number of males with advanced degrees is 70-40=30.\nThe number of females with advanced degrees is 80-30=50.\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train 120 m long passed a pole in 12 sec. How long will it take to pass a platform 380 m long?\n\n### Options:\nA. 25 sec\nB. 50 sec\nC. 75 sec\nD. 100 sec\nE. 125 sec\n\n### Answer:\nSpeed = 120/12 = 10 m/sec.\nRequired time = (120 + 380)/10 = 50 sec\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nApproximately how many revolutions will be made by a car tire with a 10-inch diameter if the car travels 1\u20442 mile?\n\n### Options:\nA. 120\nB. 180\nC. 1003\nD. 1000\nE. 1,440\n\n### Answer:\nDiameter of car tire = 10 inches\nRadius of car tire = 5 inches = 5*2.54 cm = 12.7 cm\nCircumference of the car tire = 2*pi * 12.7 = 2 *3.14 *12.7= 79.76 cm\nDistance traveled by car = .5 mile = .5 *1.6 km = .8 km = 800 m = 8 * 10^4 cm\nNumber of revolutions =Distance traveled / Circumference of tire = 8 * 10^4 / 79.76 = 1003\nSince the answer choices are far apart we should use estimation in this question .\nIdeally ,in the GMAT the conversion between units would be provided .\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n4 women can complete a work in 7 days and 10 children take 14 days to complete the work. How many days will 5 women and 10 children take to complete the work?\n\n### Options:\nA. 4 days\nB. 6 days\nC. 7 days\nD. 9 days\nE. 1 days\n\n### Answer:\n1 women's 1 day work = 1/28\n1 child's 1 day work = 1/140\n(5 women + 10 children)'s 1 day work\n= (5/28 + 10/140) = 1/4\n5 women and 10 children will complete the work in 4 days.\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA watch passes through three hands and each gains 25%. If the 3rd sells it for Rs250, what did the 1st pay for it?\n\n### Options:\nA. 100\nB. 110\nC. 128\nD. 134\nE. 156\n\n### Answer:\nFirst Purchased = 250 Wes= 128\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n. A car covers a distance of 1028 km in 4 hours. Find its speed?\n\n### Options:\nA. 104\nB. 255\nC. 266\nD. 257\nE. 276\n\n### Answer:\n1028/4= 257 kmph\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf f and g are distinct prime numbers less than 10, which of the following cannot be the product of f and g?\n\n### Options:\nA. 6\nB. 9\nC. 10\nD. 14\nE. 15\n\n### Answer:\nprime numbers less than 10 are 2, 3, 5, 7\nall except 9 is product of any two numbers picked from above set.\nAns: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSpeed of boat in water is 12km/hr. and the speed of the stream is 3km/hr. Find the time taken by the boat to go upstream a distance of 45km.\n\n### Options:\nA. 3\nB. 4\nC. 5 hrs.\nD. 6\nE. 2\n\n### Answer:\nUS =speed of the boat - speed of the stream 12-3 =9km/hr. Time taken to cover 45km =45/9 = 5hrs. Answer : C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train leaves Mumabai at 9 am at a speed of 40 kmph. After one hour, another train leaves Mumbai in the same direction as that of the first train at a speed of 50 kmph. When and at what distance from Mumbai do the two trains meet?\n\n### Options:\nA. 287\nB. 279\nC. 200\nD. 278\nE. 379\n\n### Answer:\nWhen the second train leaves Mumbai the first train covers 40 * 1 = 40 km\nSo, the distance between first train and second train is 40 km at 10.00am\nTime taken by the trains to meet\n= Distance / relative speed = 40 / (50 -40) = 4 hours\nSo, the two trains meet at 2 p.m. The two trains meet 4 * 50 = 200 km away from Mumbai.\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJohn makes $60 a week from his job. He earns a raise andnow makes $70 a week. What is the % increase?\n\n### Options:\nA. 16%\nB. 16.66%\nC. 17.9%\nD. 18.12%\nE. 18%\n\n### Answer:\nIncrease = (10/60)*100 = (1/6)*100 = 16.66%.\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n5301 x 13 =?\n\n### Options:\nA. 89136\nB. 31986\nC. 68910\nD. 53113\nE. 68913\n\n### Answer:\nAppend 0 before and after: 053010\nCalculation:\n1 x 3 + 0 = 3 (take 3 as ones digit of the product)\n0 x 3 + 1 = 1 (take 1 tens digit of the product)\n3 x 3 + 0 = 9 (take 9 hundreds digit of the product)\n5 x 3 + 3 = 18 (take 8 as thousands digit of the product, carry over 1)\n0 x 3 + 5 = 5; 5 + 1 = 6 (take 6 as ten thousands digits of the product)\nSo, 5301 x 13 = 68913\nAnswer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe cost of a one-family home was $ 120,000 in 1980. In 1988, the price had increased to $ 174,000. What was the percent increase in the cost of the home?\n\n### Options:\nA. 60%\nB. 50%\nC. 55%\nD. 40%\nE. 45%\n\n### Answer:\nIncrease = 174000-120000 = 54000\n% increase = 54000*100/120000 = 45%\nAnswer: option E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo goods trains each 500 m long are running in opposite directions on parallel tracks. Their speeds are 90 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one?\n\n### Options:\nA. 12 sec\nB. 24 sec\nC. 30 sec\nD. 60 sec\nE. 62 sec\n\n### Answer:\nRelative speed = 90 + 30 = 120 km/hr.\n120 * 5/18 = 100/3 m/sec.\nDistance covered = 500 + 500 = 1000 m.\nRequired time = 1000 * 3/100 = 30 sec.\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA committee of 5 is to be selected from among 5 boys and 5 girls. I how many ways can this be done if the committee is to consist of at-least one Girl?\nwhat is the answer choice and how?\n\n### Options:\nA. 105\nB. 250\nC. 230\nD. 350\nE. 455\n\n### Answer:\nI'm sure there is some problem with the question.\nR U sure its atleast one boy and not atleast 1 boy and 1 girl?\nif its 1 boy and 1 girl\n5C1*5C4 + 5C2*5C3 + 5C3*5C2 + 5C4*5C1\n5*5 + 10*10 + 10*10 + 5*5\n25 + 100 + 100 + 25\n250\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain number when divided by 65 leaves a remainder 25, what is the remainder if the same no.be divided by 15?\n\n### Options:\nA. 4\nB. 5\nC. 6\nD. 8\nE. 9\n\n### Answer:\nExplanation:\n65 + 25 =90/15 =6 (Remainder)\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA boat M leaves shore A and at the same time boat B leaves shore B. They move across the river.\nThey met at 500 yards away from A and after that they met 300 yards away from shore B without\nhalting at shores. Find the distance between the shore A & B\n\n### Options:\nA. 1100 yards\nB. 1200 yards\nC. 1300 yards\nD. 1400 yards\nE. None of these\n\n### Answer:\nExplanation :\nThe boats first met after 500yards from A.\nLet the total distance between A and B be x.\nThen,\n500/a = x - 500 / b, ------------(1)\nwhere, a = speed of A,\nb = speed of B.\nAssuming both boats are coming back to their original start place without halting at the shores,\nDistance coverred by A = x + 300\nDistance covered by B = 2x - 300\nx+300/a = 2x-300/b -----------------------(2)\nFrom above,\n500/x-500 = x+300/2x-300\nSolve, for x = 1200\nAnswer : B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA telephone number contains 10 digit, including a 3-digit area code. Bob remembers the area code and the next 5 digits of the number. He also remembers that the remaining digits are not 0, 1, 2, 7, or 9. If Bob tries to find the number by guessing the remaining digits at random, the probability that he will be able to find the correct number in at most 2 attempts is closest to which of the following ?\n\n### Options:\nA. 51/625\nB. 50/625\nC. 4/625\nD. 25/625\nE. 53/625\n\n### Answer:\nI think most of the answers are missing a point. Let me try to put it across:\nTotal number of possible numbers are : 5x5 = 25\nCorrect number =1\nCase 1: When he gets it right in first attempt: P(E1) = 1/25\nCase 2: He gets 1st attempt wrong and second right:\nWhen he gets it wrong then the probability of getting wrong is 24/25.\nNow there are 24 cases with him and he chooses the right one this time.\nProbability of right case is 1/24\nThus, P(E2) = 24/25 x 1/24\n=1/25\nProbability of getting it right in at most two cases = P(E1) + P(E2)\n= 1/25 + 1/25\n= 2/25\n= 50/625\nOption (B) is therefore right as most of you mentioned but the method employed was wrong.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe relationship between quantities m and n is expressed by the equation 11m = 5(n - 52). If the difference between the two chosen values of n is 40, what is the difference in the corresponding values of m?\n\n### Options:\nA. 200/11\nB. 42/11\nC. 60/11\nD. 150/11\nE. 14\n\n### Answer:\nAnother Simple way\n11m=5(n-52)\nAssume n = 52 to make one side equal to 0\nthen 11m=0\nand m = 0\nRepeat it by assuming n as 52+40 i.e 92\n11m= 5(92-52)\n11m=200\nm=200/11\ndiff = 200/11 - 0 = 200/11\nAnswer : A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the distance covered by a man walking for 10min at a speed of 6km/hr?\n\n### Options:\nA. 1km\nB. 2km\nC. 3km\nD. 1.5km\nE. 4km\n\n### Answer:\nDistance = 6*10/60 = 1km\nAnswer is A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf x is 11 percent greater than 70, then x =\n\n### Options:\nA. 77.7\nB. 91.0\nC. 88.0\nD. 70.9\nE. 71.2\n\n### Answer:\n11% of 70 = (70*0.11) = 7.7\n11% greater than 70 = 70 + 7.7 = 77.7\nAnswer is clearly A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a colony the municipality decided to number the houses and the shops. They want to number the shops with the numbers containing 3 between 1-100. The houses are 10-20 floored and at the back of the houses 8 feet is left for fire exit. How many shops can be numbered?\n\n### Options:\nA. 19\nB. 20\nC. 21\nD. 22\nE. 23\n\n### Answer:\n3numbers containing 3\n--->3,13,23,... = 10 numbers\n---->30,31,32... = 10 numbers\ntotal = 20 -1 = 19\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOil cans x and y are right circular cylinders and the height and radius of y are each twice those of x. If the oil in can x filled to capacity sells for $3, how much does the oil in y sell for if y is only half filled?\n\n### Options:\nA. $11\nB. $12\nC. $13\nD. $14\nE. $18\n\n### Answer:\nformula for vol of a cyl is PI*r^2*h\nso Vy = 8*Vy\ny when half filled will cost 4 times x so ans is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOut of 400 students of a school, 325 play football, 175 play cricket and 50 neither play football nor cricket. How many students play both football and cricket ?\n\n### Options:\nA. 120\nB. 150\nC. 100\nD. 180\nE. 220\n\n### Answer:\nn(A)=325,n(B)=175,n(AuB)=400-50=350.\nRequired number = n(AnB)=n (A)+n (B)-n(AuB)=325+175-350=150.\nAnswer is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat will be the difference in simple and compound interest on 3000 after three years at the rate of 10 percent per annum?\n\n### Options:\nA. 93\nB. 42\nC. 62\nD. 20\nE. None of these\n\n### Answer:\nFor 3 years:\nDiff.=Sum\u00d7(rate)2(300+rate)/(100)3\n= 3000\u00d710\u00d710\u00d7310/100\u00d7100\u00d7100 = 93\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n20 % of 2 is equal to\n\n### Options:\nA. 0.2\nB. 0.4\nC. 0.6\nD. 0.7\nE. 0.9\n\n### Answer:\n20 % of 2 = (20 / 100) * 2 = 0.4\nAnswer: Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRichard has to paint a mural with seven horizontal stripes. He only has enough paint for four brown stripes, four green stripes, four pink stripes, four red stripes, four blue stripes, four white stripes, four black stripes, and four yellow stripes. If his patron wants at most two different colors in the mural, how many different ways can he paint the wall?\n\n### Options:\nA. 120\nB. 350\nC. 700\nD. 1,960\nE. 5,040\n\n### Answer:\nNumber of ways to choose 2 colors among 8 - 8c2\nNumber of ways that the chosen colors can be painted for 7 horizontal stripes - 2 (either (4,3) or (3,4))\nNow the order,\nthe number of ways in which a particular color among the 2 chosen colors can be painted for 4 stripes is - 7c4\n[Note: We don't need to calculate the ways for the remaining 3 stripes as they are obvious and already counted under this]\nTotal number of combinations -8c2 * 2* 7c4 = 1960\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nx^2 + rx + 72 = 0 has two distinct integer roots; how many values are possible for r?\n\n### Options:\nA. 3\nB. 6\nC. 8\nD. 12\nE. 24\n\n### Answer:\nFor a quadratic equation ax^2+rx+c=0, we know that -r/a is sum of roots and c/a is product of roots.\nThe quadratic equation here is x^2 + rx + 72 = 0, where product of roots is 72.\nIf we find all the factors of 72, we have the answer.\nBy prime factorization, we get 72= 2^3*3^2.\nWe know that total factors are (3+1)*(2+1) = 12 (Reason: with 2^n, we have n+1 possibilities. n^0 to n^n. so n+1)=D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the perimeter and area of the rectangle of length 15 cm and breadth 13 cm.\n\n### Options:\nA. 71 cm2\nB. 121 cm2\nC. 141 cm2\nD. 195 cm2\nE. 221 cm2\n\n### Answer:\nlength = 15 cm, breadth = 13 cm\nPerimeter of rectangle = 2 (length + breadth)\n= 2 (15 + 13) cm\n= 2 \u00d7 28 cm\n= 56 cm\nWe know that the area of rectangle = length \u00d7 breadth\n= (15 \u00d7 13) cm22\n= 195 cm2\nANSWER : D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSet #1 = {A, B, O, D, E}\nSet #2 = {K, L, M, N, U, P}\nThere are these two sets of letters, and you are going to pick exactly one letter from each set. What is the probability of picking at least one vowel?\n\n### Options:\nA. 1/6\nB. 1/4\nC. 1/2\nD. 1/3\nE. 2/3\n\n### Answer:\nAt least questions are best solved by taking the opposite scenario and subtracting it from 1. Probability of choosing no vowel from set 1 is 2/5 and set 2 is 5/6. Multiply these to get 1/3. Therefore, probability of picking at least one vowel = 1-1/3=2/3.\nANSWER =E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man whose speed is 4.5 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 1.5 kmph, find his average speed for the total journey?\n\n### Options:\nA. 2 kmph\nB. 4 kmph\nC. 5 kmph\nD. 7 kmph\nE. 6 kmph\n\n### Answer:\nM = 45\nS = 1.5\nDS = 6\nUS = 3\nAS = (2 * 6 * 3) /9 = 4\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train travelled from station P to Q in 8 hours and came back from station Q to P is 6 hours. What would be the ratio of the speed of the train while traveling from station P to Q to that from station Q to P?\n\n### Options:\nA. 3 : 6\nB. 3 : 9\nC. 3 : 3\nD. 3 : 4\nE. 3 : 1\n\n### Answer:\nSince S # 1/t\nS1 : S2 = 1/t1 : 1/t2 = 1/8 : 1/6 = 3 : 4\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train 200 m long can cross an electric pole in 20 sec and then find the speed of the train?\n\n### Options:\nA. 17 Kmph\nB. 78 Kmph\nC. 72 Kmph\nD. 36 Kmph\nE. 19 Kmph\n\n### Answer:\nLength = Speed * time\nSpeed = L/T\nS = 200/20\nS = 10 M/Sec\nSpeed= 10*18/5 (To convert M/Sec in to Kmph multiply by 18/5)\nSpeed = 36 Kmph\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average of the two-digit numbers, which remain the same when the digits interchange their positions, is?\n\n### Options:\nA. 56\nB. 86\nC. 55\nD. 87\nE. 88\n\n### Answer:\nAverage = (11 + 22 + 33 + 44 + 55 + 66 + 77 + 88 + 99)/9\n= [(11 + 99) + (22 + 88) + (33 + 77) + (44 + 66) + 55]/9\n= [(4 * 110) + 55]/9 = 495/9 =55.\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 13 lions can kill 13 deers in 13 minutes how long will it take 100 lions to kill 100 deers?\n\n### Options:\nA. 1 minutes\nB. 13 minute\nC. 100 minutes\nD. 10000 minutes\nE. 1000 minutes\n\n### Answer:\nwe can try the logic of time and work,our work is to kill the deers so 13(lions)*13(min)/13(deers)=100(lions)*x(min)/100(deers)hence answer is x=13\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe dimensions of a certain machine are 48*32*52,if the size of the machine is increased proportionally until sum of dimensions equals 156.\n\n### Options:\nA. 56*40*50\nB. 56*40*40\nC. 56*40*30\nD. 56*40*20\nE. 56*40*60\n\n### Answer:\nGiven dimensions of a machine are 48*32*52\nif the size is raised proportionally untill the sum of dimensions\nsum of given dimensions is 48+32+52=132\ndifference of actual and increased=156-132=24\n24/3=8\nthis means each dimension has to raise for 8 units\nthus the new dimensions are 56*40*60\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn the exam the average was found to be p mark. After deducting typographical error the average marks of 120 student reduced from 90 to 70 . Due to this the average came down by 12 marks. What was the number of students who took the exam?\n\n### Options:\nA. 100\nB. 120\nC. 200\nD. 130\nE. 160\n\n### Answer:\nExplanation :\nNumber of student = (90-70) * 120/12 = 200\nAnswer : C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n144 choclates are distributed to children with the same number. What can\u2019t be the range including the number of children?\n\n### Options:\nA. 1~10\nB. 50~60\nC. 20~30\nD. 10~20\nE. 70~80\n\n### Answer:\n-> In 144=1*144=2*72=4*36=6*24=8*18=9*16, you can come up with 4 cases.\nAmongst these cases, what is not included is B. 50~60. Therefore, the answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe smallest number which when diminished by 6, is divisible 12, 14, 16, 18 and 22 is:\n\n### Options:\nA. 11099\nB. 11094\nC. 11091\nD. 10323\nE. 10483\n\n### Answer:\nRequired number = (L.C.M. of 12, 14, 16, 18, 22 ) + 6\n= 11088 + 6\n= 11094\nAnswer: Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe price of 2 saris and 4 shirts is Rs. 1600. With the same money one can buy 1 saree and 6 shirts. If one wants to buy 12 shirts, how much shall he have to pay ?\n\n### Options:\nA. Rs. 2400\nB. Rs. 2490\nC. Rs. 2500\nD. Rs. 2550\nE. Rs. 2600\n\n### Answer:\nLet the price of a saree and a shirt be Rs. x and Rs. y respectively.\nThen, 2x + 4y = 1600 .... (i)\nand x + 6y = 1600 .... (ii)\nDivide equation (i) by 2, we get the below equation.\n=> x + 2y = 800. --- (iii)\nNow subtract (iii) from (ii)\nx + 6y = 1600 (-)\nx + 2y = 800\n----------------\n4y = 800\n----------------\nTherefore, y = 200.\nNow apply value of y in (iii)\n=> x + 2 x 200 = 800\n=> x + 400 = 800\nTherefore x = 400\nSolving (i) and (ii) we get x = 400, y = 200.\nCost of 12 shirts = Rs. (12 x 200) = Rs. 2400.\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf B and C are digits and 8BC is a 3-digit number that is divisible by 5, which of the following is a possible product of B and C?\n\n### Options:\nA. 1\nB. 2\nC. 5\nD. 7\nE. 14\n\n### Answer:\nTry with the options -\nA. If BC = 1 , both B and C must be 1\nB. If BC = 2 , either B or C must be 1 or 2 ; In that case sum of the digits will be 8 + 1 + 2 = 11 which is not divisible by 3\nC. If BC = 5 , either B or C must be 1 or 5 ; In that case sum of the digits will be 8 + 1 + 5 = 14 which is not divisible by 3\nD. If BC = 6 , then we can have the following possibilities\ni. Either B or C must be 2 or 3 ; In that case sum of the digits will be 8 + 2 + 3 = 13 which is not divisible by 3\nii. Either B or C must be 1 or 6 ; In that case sum of the digits will be 8 + 1 + 6 = 15 which is divisible by 3\nE. If BC = 14 , then either B or C must be 2 or 7 ; In that case sum of the digits will be 8 + 2 + 7 = 17 which is not divisible by 5\nThus answer is (D)\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a person throw 2 dice simultaneously then find the probability of the sum of dots is a prime number?\n\n### Options:\nA. 5/12\nB. 6/13\nC. 8/17\nD. 9/11\nE. 3/5\n\n### Answer:\nIf 2 dies are thrown E = event of getting a prime number = 15\ntotal number of possible out comes = 36\nprobability = 15/36 = 5/12\nAnswer is A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf x/y = 3 and (2a - x)/(3b - y) = 3, then the value of a/b is?\n\n### Options:\nA. \u20133\nB. 9/2\nC. 1\nD. 2\nE. 3\n\n### Answer:\nx = 3y\n2a - 3y = 3(3b - y)\n2a - 3y = 9b - 3y\n2a = 9b\na/b = 9/2\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn each series, look for the degree and direction of change between the numbers. In other words, do the numbers increase or decrease, and by how much?\rLook at this series: 1, 5, 7, 3, __, 1 ...Which number is missing?\n\n### Options:\nA. 2\nB. 4\nC. 12\nD. 0\nE. 13\n\n### Answer:\nE\r13\rThis is an alternating addition and subtraction series. In the first pattern, 6 is added to each number to arrive at the next. In the second, 2 is subtracted from each number to arrive at the next.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA boy has nine trousers and 10 shirts. In how many different ways can he select a trouser and a shirt?\n\n### Options:\nA. 50ways\nB. 90ways\nC. 100ways\nD. 108ways\nE. 56ways\n\n### Answer:\nThe boy can select one trouser in nine ways.\nThe boy can select one shirt in 10 ways.\nThe number of ways in which he can select one trouser and one shirt is 9 * 10\n= 90 ways.\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA Jar contains a mixture of AB in the ratio 4:1. When 40 L of Mixture is replaced with liquid B, ratio becomes 2:3. How many liters of liquid A was present in mixture initially.\n\n### Options:\nA. 12\nB. 15\nC. 16\nD. 64\nE. 25\n\n### Answer:\n40 litres of mixture that is replaced will contain 32 litres of A and 8 litres of B (as A:B = 4:1)\nLet the initial volume of the mixture be 4K + 1K = 5K\nSo by condition ,\n[ 4K-32 ]/ [ K-8+40 ] = 2/3 => 12K -96= 2K-16+80 => 10K = 160\nSolve for K which is K = 16\nSo initial volume of liquid A = 4K = 64 litres\nAnswer : D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average age of a class of 39 students is 15 years. If the age of the teacher be included, then the average increases by3 months. Find the age of the teacher.\n\n### Options:\nA. 22 Yrs\nB. 25 Yrs\nC. 26 Yrs\nD. 32 Yrs\nE. 34 Yrs\n\n### Answer:\nSol. Total age of 39 persons = (39 x 15) years\n= 585 years.\nAverage age of 40 persons= 15 yrs 3 months\n= 61/4 years.\nTotal age of 40 persons = (_(61/4 )x 40) years= 610 years.\n:. Age of the teacher = (610 - 585) years=25 yANSWER B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA person crosses a 600 m long street in 5 minutes. What is his speed in km per hour?\n\n### Options:\nA. 7.2\nB. 4.2\nC. 6.1\nD. 7.2\nE. 8.2\n\n### Answer:\nExplanation:\ndistance = 600 meter\ntime = 5 minutes = 5 x 60 seconds = 300 seconds\nSpeed = distance/time = 600/300 = 2m/s\n= 2\u00d7185 km/hr = 365 km/hr = 7.2 km/hr\nAnswer: Option A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are 20 poles with a constant distance between each pole. A car takes 21 second to reach the 12th pole. How much will it take to reach the last pole.\n\n### Options:\nA. 36.4543\nB. 36.2727\nC. 31.45128\nD. 36.41288\nE. 31.41222\n\n### Answer:\nAssuming the car starts at the first pole.\nTo reach the 12th pole, the car need to travel 11 poles (the first pole doesn't count, as the car is already there).\n11 poles 21 seconds\n1 pole (21/11) seconds\nTo reach the last (20th) pole, the car needs to travel 19 poles.\n19 pole 19 x (21/11) seconds\n= 36.2727 seconds\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich of the following could be the sides of an obtuse angled triangle? all values are in degree only\nI. 51, 29, 100\nII. 10,110, 60\nIII.30 ,30 ,120\n\n### Options:\nA. I and III only\nB. II only\nC. III only\nD. I and II only\nE. I, II and III\n\n### Answer:\nobtuse angled triangle means one angle more than 90 deg and total 180 deg. I,II and III only\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo years ago, Arthur gave each of his five children 20 percent of his fortune to invest in any way they saw Fit. In the first year, three of the children, Alice, Bob, and Carol, each earned a profit of 50 percent on their Investments, while two of the children, Dave and Errol, lost 40 percent on their investments. In the second Year, Alice and Bob each earned a 10 percent profit, Carol lost 60 percent, Dave earned 25 percent in profit, And Errol lost all the money he had remaining. What percentage of Arthur's fortune currently remains?\n\n### Options:\nA. 93%\nB. 97%\nC. 100%\nD. 107%\nE. 120%\n\n### Answer:\nSay Arthur's fortune was $100. Then:\nA = 20*1.5*1.1 = 33\nB = 20*1.5*1.1 = 33\nC = 20*1.5*0.4 = 12\nD = 20*0.6*1.25 = 15\nE = 0\nTotal 33 + 33 + 12 + 15 = 93.\nAnswer: A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA Guava costs Rs 8 each and a apple costs Rs. 21 each. If I spend Rs 101 on total what is the number of guava I purchased?\n\n### Options:\nA. 5\nB. 4\nC. 3\nD. 6\nE. 10\n\n### Answer:\n10 * 8+21 = 101\nAnswer : 10\nOption : E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn 1 hour, a boat goes 9 km along the stream and 3 km against the stream. The speed of the boat in still water (in km/hr) is :\n\n### Options:\nA. 3 km/hr.\nB. 2 km/hr.\nC. 6 km/hr.\nD. 8 km/hr.\nE. 5 km/hr.\n\n### Answer:\nSpeed in still water = 1/2(9 + 3) km/hr\n= 6 km/hr. ANSWER :C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA batsman makes a score of 64 runs in the 16th innings and thus increased his average by 3. Find his average after the 16th inning?\n\n### Options:\nA. 17\nB. 12\nC. 15\nD. 19\nE. 65\n\n### Answer:\nLet the average after the 16th inning be P.\nSo, the average after the 15th inning will be (P-3) Hence, 15(P-30) + 64\n= 16P => P = 19.\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn an examination, there were 2,000 candidates, out of which 900 candidates were girls and rest were Boys. If 34% of the boys and 32% of the girls passed, then the total percentage of failed candidates is?\n\n### Options:\nA. 35.67%\nB. 66.90%\nC. 68.57%\nD. 69.57%\nE. none of these\n\n### Answer:\nGirls = 900, Boys = 1100\nPassed = ( 34% of 1100 ) + ( 32% of 900)\n= 374 + 288 = 662\nFailed = 2000 - 662 = 1338\nFailed % = [(1338/2000) x 100]%\n= 66.9%.\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nExactly 3/7 of the people in the room are under the age of 21, and exactly 5/11 of the people in the room are over the age of 65. If the total number of the people in the room is greater than 50 and less than 100, how many people in the room are under the age of 21?\n\n### Options:\nA. 21\nB. 35\nC. 33\nD. 60\nE. 65\n\n### Answer:\nThe total number of the people in the room must be a multiple of both 7 and 11 (in order 3/7 and 5/11 of the number to be an integer), thus the total number of the people must be a multiple of LCM of 7 and 11, which is 77.\nSince, the total number of the people in the room is greater than 50 and less than 100, then there are 77 people in the room.\nTherefore there are 3/7*77=33 people in the room under the age of 21.\nAnswer: C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA woman can row upstream 14 kmph and downstream 26 kmph. Find the rate of the stream and woman rate in still water.\n\n### Options:\nA. 4,20\nB. 20,20\nC. 8,20\nD. 20,5\nE. 6,20\n\n### Answer:\nExplanation:\nPlease remember,\nIf a is rate downstream and b is rate upstream\nRate of current = 1/2(a-b)\nRate in still water = 1/2(a+b)\n=> Rate of current = 1/2(26-14) = 6 kmph\n=> Rate in still water = 1/2(26+14) = 20 kmph\nOption E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n2/5 of the fish in an aquarium is red and 1/4 of the fish is brown. 1/4of the red fish and 1/5 of the brown fish is male. If the rest of the fish in the aquarium is female, what is the probability that a fish randomly picked from the aquarium is male?\n\n### Options:\nA. 3/20\nB. 7/30\nC. 5/16\nD. 1/3\nE. 2/5\n\n### Answer:\nStraight method....\n1/4 of 2/5 + 1/5 of 1/4 = 2/20 +1/20 =3/20\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA type T machine can complete a job in 5 hours and a type B machine can complete the job in 7 hours. How many hours will it take 2 type T machines and 3 type B machines working together and independently to complete the job?\n\n### Options:\nA. 1/5\nB. 29/35\nC. 5/6\nD. 35/29\nE. 35/12\n\n### Answer:\nnow D should be the answer.\nT need 5 hours to complete\nand B needs 7 hours to compete\nso 2T + 3B will complete 2/5 + 3/7 or 29/35 portion of the job in 1 hour\nso the whole job will take 35/29 hours....=D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average of 11 results is 44, if the average of first six results is 49 and that of the last six is 52. Find the sixth result?\n\n### Options:\nA. 122\nB. 156\nC. 118\nD. 125\nE. 123\n\n### Answer:\n1 to 11 = 11 * 44 = 484\n1 to 6 = 6 * 49 = 294\n6 to 11 = 6 * 52 = 312\n6th = 294 + 312 \u00e2\u20ac\u201c 484 = 122\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a hockey championship, there are 153 matches played. Every two team played one match with each other. The number of teams participating in the championship is:\n\n### Options:\nA. 16\nB. 17\nC. 18\nD. 19\nE. 14\n\n### Answer:\nLet there were x teams participating in the games, then total number of matches,\nnC2 = 153.\nOn solving we get,\n=> n =\u221217 and n =18.\nIt cannot be negative so,\nn = 18 is the answer.\nOPTION:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAt a certain restaurant, the average (arithmetic mean) number of customers served for the past x days was 80. If the restaurant serves 120 customers today, raising the average to 90 customers per day, what is the value of x?\n\n### Options:\nA. 2\nB. 3\nC. 9\nD. 15\nE. 30\n\n### Answer:\nWITHOUTusing the formula, we can see that today the restaurant served 30 customers above the average. The total amount ABOVE the average must equal total amount BELOW the average. This additional 30 customers must offset the \u201cdeficit\u201d below the average of 90 created on the x days the restaurant served only 80 customers per day.\n30/10 = 3 days.Choice (A).\nWITHthe formula, we can set up the following:\n90 = (80x + 120)/(x + 1)\n90x + 90 = 80x + 120\n10x = 30\nx = 3Answer Choice (B)\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAn engineer undertakes a project to build a road 15 km long in 300 days and employs 50 men for the purpose. After 100 days, he finds only 2.5 km of the road has been completed. Find the (approximate) number of extra men he must employ to finish the work in time.\n\n### Options:\nA. a. 43\nB. b. 45\nC. c. 75\nD. d. 68\nE. e. 60\n\n### Answer:\n50 workers working already\nLet x be the total men required to finish the task in next 200 days\n2.5 km done hence remaining is 12.5 km\nAlso, work has to be completed in next 200 days (300 - 100 = 200)\nWe know that, proportion of men to distance is direct proportion\nand, proportion of men to days is inverse proportion\nHence, X = (50 * 12.5 * 100) / (2.5 * 200)\nthus, X = 125\nThus, more men needed to finish the task = 125-50=75\nhence Answer is C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nBradley owns b video game cartridges. If Bradley\u2019s total is one-seventh the total owned by Andrew and four times the total owned by Charlie, how many video game cartridges do the three of them own altogether, in terms of b?\n\n### Options:\nA. 27b / 4\nB. 29b / 4\nC. 31b / 4\nD. 33b / 4\nE. 35b / 4\n\n### Answer:\nb = Bradley\u2019s total\n7b = Andrew\u2019s total\nb/4 = Charlie\u2019s total\nThe total number of cartridges is:\nb + 7b+ b/4 = (4b + 28b + b) / 4 = 33b / 4\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAB\n+BA\n___\n202\nIn the addition problem above, A and B represent digits in two different two-digit numbers. What is the sum of A and B?\n\n### Options:\nA. 6\nB. 8\nC. 9\nD. 20\nE. 14\n\n### Answer:\ntwo ways to do it..\n1) straight logic..\nonly 20 fits in..\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a particular is never chosen, in how many ways can a cricketbe chosen out of 15 players?\n\n### Options:\nA. 250\nB. 320\nC. 364\nD. 390\nE. 430\n\n### Answer:\nA particular players is never chosen, it means that 11 players are selected out of 14 players.\n=> Required number of ways = 14C11\n= 14!/11!x3! = 364\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA tap can fill a tank in 6 hours. After half the tank is filled three more similar taps are opened. What is the total time taken to fill the tank completely?\n\n### Options:\nA. 3 hrs 45 min\nB. 3 hrs 45 min\nC. 3 hrs 42 min\nD. 3 hrs 65 min\nE. 3 hrs 35 min\n\n### Answer:\nTime taken by one tap to fill the tank = 3 hrs.\nPart filled by the taps in 1 hour = 4 * 1/6 = 2/3\nRemaining part = 1 - 1/2 = 1/2\n2/3 : 1/2 :: 1 : x\nx = 1/2 * 1 * 3/2 = 3/4 hrs. i.e., 45 min\nSo, total time taken = 3 hrs 45 min.\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf two sides of a triangle are 10 and 8, which of the following could be the area of triangle?\n1. 35\n2. 48\n3. 56\n\n### Options:\nA. a) 1 only\nB. b) 1 and 2 only\nC. c) 1 and 3 only\nD. d) 2 and 3 only\nE. e) 1, 2 and 3 only\n\n### Answer:\nwhen two sides of a triangle are known , the maximum area occurs when the angle between those two sides is 90.\nlets say base = 12 , height =8 (angle = 90)\nmaximum area = (1/2)*12*8 = 48 ( this is the same maximum area even when base is 8 and height is 12).\nif we fix the base and keep lowering the angle, it will result in a lower height . hence the resulting area will always be < 48.\nC,D and E are ruled out.\n1 and 3 are possible areas as their areas are less than 48.\nHence the answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the L.C.M of 40,60,800\n\n### Options:\nA. 2600\nB. 1200\nC. 800\nD. 2400\nE. 4800\n\n### Answer:\n40=2^3*5 60=2^2*3*5 800=2^5*5^2\nL.C.M=2^5*3*5^2=2400\nAnswer=(D)\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a group of 86 students, each student is registered for at least one of three classes \u2013 History, Math and English. Twenty-eight students are registered for History, twenty-three students are registered for Math, and forty-four students are registered for English. If only three students are registered for all three classes, how many students are registered for exactly two classes?\n\n### Options:\nA. 3\nB. 10\nC. 9\nD. 8\nE. 7\n\n### Answer:\nA U B U C = A + B + C - AB-BC-AC + ABC\n86 = 28 + 23+ 44 -AB-BC-AC +3 => AB+BC+AC = 12\nExactly Two classes = AB+BC+AC - 3ABC = 12 -3*3 = 3\nHence A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHaving received his weekly allowance, John spent 3/5 of his allowance at the arcade. The next day he spent one third of his remaining allowance at the toy store, and then spent his last $0.96 at the candy store. What is John\u2019s weekly allowance?\n\n### Options:\nA. $3.00\nB. $3.20\nC. $3.40\nD. $3.60\nE. $3.80\n\n### Answer:\nx = 3x/5 + 1/3*2x/5 + 96\n4x/15 = 96\nx = $3.60 = $3.60\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a stack of boards at a lumber yard, the 20th board counting from the top of the stack is immediately below the 18th board counting from the bottom of the stack. How many boards are in the stack?\n\n### Options:\nA. 38\nB. 36\nC. 35\nD. 34\nE. 32\n\n### Answer:\nCounting from the top, after the 20th board, there are 16 boards left to count.\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man buys a field of agricultural land for Rs. 3,60,000. He sells one-third at a loss of 20% and two-fifths at a gain of 25%. At what price must he sell the remaining field so as to make an overall profit of 10%?\n\n### Options:\nA. Rs.1,00,000\nB. Rs. 1,15,000\nC. Rs. 1,20,000\nD. Rs. 1,25,000\nE. None of these\n\n### Answer:\nSolution: First Method\nCP = 3600000.\nTo gain 10% on whole land, SP = 360000 + 10% of 360000 = Rs. 396000.\n1/3 of the land sold on 20% loss.\nSP of 1/3 land = (360000/3) - 20% of (360000/3) = Rs. 96000.\nSP of 2/5 of the land = (360000 * 2)/5 + 25% of (360000*2)/5 = Rs. 180000.\nThus, SP of the remaining land = 396000 - 96000 - 180000 = Rs. 120000.\nAnswer: Option C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man had a stock of 500 books in his bookshop. He sold 25 on Monday, 50 on Tuesday 30 on Wednesday, 100 on Thursday and 150 on Friday. What percentage of the books were not sold?\n\n### Options:\nA. 8%\nB. 10%\nC. 29%\nD. 44%\nE. 16%\n\n### Answer:\nLet N be the total number of books sold. Hence\nN = 25 + 50 + 30 + 100 + 150= 355\nLet M be the books NOT sold\nM = 500 - N = 500- 355 = 145\nPercentage\nBooks not sold / total number of books = 145/500 = 0.29= 29%\ncorrect answer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA military commander has to choose 2 soldiers out of a company of 9 for guarding the headquarters. How many different group combinations of 2 does he have to choose from?\n\n### Options:\nA. 4\nB. 15\nC. 36\nD. 27\nE. 35\n\n### Answer:\nA military commander has to choose 2 soldiers out of a company of 9.\ndifferent group combinations of 2\nHe can do this in 9C2 ways\n9*8/2*1= 36 ways\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA invested some money in 10% stock at 96.If B wants to invest in an equally good 12% stock ,he must purchase a stock worth of :\n\n### Options:\nA. Rs. 80\nB. Rs. 115.20\nC. Rs. 120\nD. Rs. 125.40\nE. None of these\n\n### Answer:\nSolution\nFor an income of Rs. 10, investment = Rs. 96.\nFor an income of Rs. 12, investment = Rs.(96/12x12) = Rs. 115.20.\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA motorcyclist goes from Bombay to Pune, a distance of 192 kms at an average of 32 kmph speed. Another man starts from Bombay by car 2 \u00bd hours after the first, and reaches Pune \u00bd hour earlier. What is the ratio of the speed of the motorcycle and the car?\n\n### Options:\nA. 1:2\nB. 1:5\nC. 1:4\nD. 1:1\nE. 1:8\n\n### Answer:\nT = 192/32 = 6 h\nT = 6 - 3 = 3\nTime Ratio = 6:3 = 2:1\nSpeed Ratio = 1:2\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMolly can do a task in 15 days while Sandy can do the task in 30 days. How many days will it take to complete the task if both work together?\n\n### Options:\nA. 8\nB. 10\nC. 11\nD. 12\nE. 14\n\n### Answer:\nEach day, Molly can do 1/15 of the task.\nEach day, Sandy can do 1/30 of the task.\nEach day, they can do 1/15 + 1/30 = 1/10 of the task.\nThe task will be completed in 10 days.\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA, B, C subscribe Rs. 50,000 for a business. A subscribes Rs. 4000 more than B and B Rs. 5000 more than C. Out of a total profit of Rs. 30,000, C receives:\n\n### Options:\nA. s. 7,000\nB. s. 7,200\nC. s. 7,400\nD. s. 7,700\nE. s. 7,800\n\n### Answer:\nLet C = x.\nThen, B = x + 5000 and A = x + 5000 + 4000 = x + 9000.\nSo, x + x + 5000 + x + 9000 = 50000\n3x = 36000\nx = 12000\nA : B : C = 21000 : 17000 : 12000 = 21 : 17 : 12.\nC's share = Rs. (30000 x 12/50) = Rs. 7,200.\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nhe distance light travels in one year is approximately 5,870,000,000,000 miles. The distance light travels in 100 years is:\n\n### Options:\nA. 587 \u00d7 108 miles\nB. 587 \u00d7 1010 miles\nC. 587 \u00d7 10-10 miles\nD. 587 \u00d7 1012 miles\nE. 587 \u00d7 10-12 miles\n\n### Answer:\nThe distance of the light travels in 100 years is:\n5,870,000,000,000 \u00d7 100 miles.\n= 587,000,000,000,000 miles.\n= 587 \u00d7 1012 miles.\nCORRECT ANSWER :D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn the following list of numerals, how many 3s are followed by 3, but NOT preceded by 3?\n2 4 6 3 3 1 5 7 8 3 3 3 4 6 2 3 3 3 3 9 7 2 3\n\n### Options:\nA. 1\nB. 2\nC. 3\nD. 4\nE. 5\n\n### Answer:\n633\n833\n233\nAns:3\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n__2A\nx__B\n____\nCC\nIn the multiplication problem above, A, B, and C represent distinct digits. If the sum of A and B is equal to 3, what is the value of C?\n\n### Options:\nA. 6\nB. 5\nC. 4\nD. 3\nE. 2\n\n### Answer:\nIf A+B=3\nassuming A and B are positive then A*B<10 (they could be either 1,2,)\ntherefore\nA*B=C\n2*B=C\nA+B=3\nThree simple equations - divide the 1st/2nd --> A=2 plug it the 3rd --> B=1 --> C=2 (ANSWER E)\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo numbers are respectively 20% and 50% more than a third number. The ratio of the two numbers is:\n\n### Options:\nA. 2:5\nB. 3:5\nC. 4:5\nD. 7:5\nE. 2:4\n\n### Answer:\nLet the third number be x.\nThen, first number = 120% of x =\t120x\t=\t6x\n100\t5\nSecond number = 150% of x =\t150x\t=\t3x\n100\t2\nRatio of first two numbers = 6x\t:\t3x = 12x : 15x = 4 : 5.\n5\t2\nso the correct answer is option C)\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nwhat will be the next number in the following series??\n2, 1, (1/2), (1/4),...\n\n### Options:\nA. 1/3\nB. 1/8\nC. 2/8\nD. 1/16\nE. 3/8\n\n### Answer:\n4/2=2\n2/2=1\n1/2=1/2\n(1/2)/2=1/4\n(1/4)/2=1/8\nso answer is 1/8\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA salesman\u2019s terms were changed from a flat commission of 5% on all his sales to a fixed salary of Rs.1000 plus 2.5% commission on all sales exceeding Rs. 4,000. If his remuneration as per new scheme was Rs. 600 more than that by the previous schema, his sales were worth?\n\n### Options:\nA. 18997\nB. 12000\nC. 28992\nD. 13009\nE. 28811\n\n### Answer:\n[1000 + (X-4000) * (2.5/100)] - X * (5/100)\n= 600\nX = 12000\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe ratio 6 : 3 expressed as a percent equals\n\n### Options:\nA. 12.5%\nB. 40%\nC. 80%\nD. 200%\nE. None\n\n### Answer:\nSolution\n6 : 3\t= 6/3\n= (6/3 x 100)%.\n= 200 %.\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA bag marked at Rs. 80 is sold for Rs. 68. The rate of discount is\n\n### Options:\nA. 10%\nB. 15%\nC. 20%\nD. 22%\nE. None\n\n### Answer:\nSolution\nRate of discount\t= (12 / 80 x 100)%\n= 15%.\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA shopkeeper sold an article offering a discount of 5% and earned a profit of 38.7%. What would have been the percentage of profit earned if no discount had been offered?\n\n### Options:\nA. 28.5\nB. 46\nC. 30\nD. Data inadequate\nE. None of these\n\n### Answer:\nGiving no discount to customer implies selling the product on printed price. Suppose the cost price of the article is 100.\nThen printed price = 100\u00c3\u2014(100+38.7)/(100\u00e2\u02c6\u20195) =146\nHence, required % Profit = 146 \u00e2\u20ac\u201c 100 = 46%\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA school has received 60% of the amount it needs for a new building by receiving a donation of $400 each from people already solicited. People already solicited represent 40% of the people from whom the school will solicit donations. How much average contribution is requited from the remaining targeted people to complete the fund raising exercise?\n\n### Options:\nA. $200\nB. $177.78\nC. $100\nD. $277.78\nE. $377.78\n\n### Answer:\nLet us suppose there are 100 people. 40% of them donated $16000 ( 400 * 40 )\n$16000 is 60% of total amount.\nSo total amount = 16000 * 100/60\nRemaining amount is 40% of total amount.\n40% of total amount = 16000 * (100/60) * (40/100) = 32000/3\nThis amount has to be divided by 60 ( remaining people are 60 )\nSo per head amount is 32000/3 / 60 = 32000/180 = 1600/9 = $177.78;\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMr X, a businessman, had income in the year 1995 such that he earned a profit of 20% on his investment in the business. In the year 1996 his investment was less by 7000 but still had the same income (Income = Investment + Profit) as that in 1995. Thus the per cent profit earned in 1996 increased by 6%. What was his investment in 1995?\n\n### Options:\nA. 100000\nB. 100500\nC. 147000\nD. Data inadequate\nE. None of these\n\n### Answer:\nLet the investment of X in 1995 be x.\n\u2234 Profit = x\u20445\n\u2234 Income = (x + x\u20445) = 6\u20445x\nInvestment of company X in 1996 would be (x \u2013 7000) From the question,\n(x - 7000) \u00d7 126\u2044100 = 6\u20445x \u21d2 x = 147000\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf two integers x, y (x>y) are selected from -10 to 1 (inclusive), how many possible cases are there?\n\n### Options:\nA. 150\nB. 66\nC. 190\nD. 210\nE. 240\n\n### Answer:\nIf two integers x, y (x>y) are selected from -10 to 9 (inclusive), how many possible cases are there?\nA. 150\nB. 180\nC. 190\nD. 210\nE. 240\n--> 12C2=12*11/2=66. Therefore, the answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nConsider four digit numbers for which the first two digits are equal and the last two digits are also equal. How many such numbers are perfect squares ?\n\n### Options:\nA. 3\nB. 2\nC. 4\nD. 0\nE. 1\n\n### Answer:\nExplanation :\nIf we let the four-digit number be XXYY, then this number can be expressed as:\n1000X + 100X + 10Y + Y = 1100X + 11Y = 11(100X + Y) = k^2 (since it's a perfect square)\nIn order for this to be true, 100X + Y must be the product of 11 and a perfect square, and looks like X0Y. So now our question is \"which product of 11 and a perfect square looks like X0Y?\" We can test them:\n11 x 16 = 176; 11 x 25 = 275; 11 x 36 = 396; 11 x 49 = 593; 11 x 64 = 704; 11 x 81 = 891\nThe only one that fits the bill is 704.\nThis means there is only one four-digit number that works, and it's 7744.\nAnswer : E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn what time a sum of money double itself at 7% per annum simple interest?\n\n### Options:\nA. 33 1/8%\nB. 33 1/3%\nC. 14 2/7%\nD. 32 1/3%\nE. 23 1/3%\n\n### Answer:\nP = (P*7*R)/100\nR = 14 2/7%\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man takes 5 hours 45 min in walking to a certain place and riding back. He would have gained 2 hours by riding both ways. The time he would take to walk both ways is\n\n### Options:\nA. 11 hrs\nB. 8 hrs 45 min\nC. 7 hrs 45 min\nD. 9 hrs 20 min\nE. 10 hrs 25 min\n\n### Answer:\nExplanation:\nSolution 1Given that time taken for riding both ways will be 2 hours lesser than the time needed for waking one way and riding back.\nTherefore,\ntime needed for riding one way = time needed for waking one way - 2 hours\nGiven that time taken in walking one way and riding back =5 hours 45 min\nHence, the time he would take to walk both ways\n=5 hours 45 min + 2 hours\n=7 hours 45 min\nANSWER IS C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJohn takes 10 hours to complete a certain job, while Bill takes only 6 hours to complete the same job. If Steve is faster than John but slower than Bill at completing the same job, then which of the following could be the time it takes the three men together, working at their constant, individual rates, to complete the job?\n\n### Options:\nA. 2 hours, 10 minutes\nB. 2 hours, 30 minutes\nC. 3 hours, 20 minutes\nD. 3 hours, 45 minutes\nE. 4 hours, 10 minutes\n\n### Answer:\nThe rate of John plus Bill is 1/10 + 1/6 = 4/15 of the job completed per hour.\nIf Steve worked at the same rate as John, the rate would be 4/15 + 1/10 = 11/30\nThe slowest possible time would be 30/11 hours = 2 hours + 8/11 hours.\nIf Steve worked at the same rate as Bill, the rate would be 4/15 + 1/6 = 13/30\nThe fastest possible time would be 30/13 hours = 2 hours + 4/13 hours.\nThe actual time is somewhere between these two extreme points.\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA cement mixture is composed of 3 elements. By weight, 1/4 of the mixture is sand, 2/5 of the mixture is water, and the remaining 14 pounds of the mixture is gravel. What is the weight of the entire mixture in pounds?\n\n### Options:\nA. 9\nB. 14\nC. 28\nD. 40\nE. 60\n\n### Answer:\nLet the total weight be x.\nSand content= (1/4)x\nWater content= (2/5)x\nGravel=x-(1/4)x-(2/5)x=(7/20)x=14\nx=40\nThen answer will be D=40\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a + b > 0 and a * b < 0, which of the following must be true?\nI. a > 0 or b > 0\nII. a < 0 or b < 0\nIII. a and b have the same sign\n\n### Options:\nA. I only\nB. II only\nC. III only\nD. I and II only\nE. I, II, and III\n\n### Answer:\nI. True, for the sum to be greater than 0, at least one of a or b has to be positive\nII. True, for the product to be less than 0, one of a or b has to be negative\nIII. Not true, by the previous two, one of a or b has to be positive and the other has to be negative\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFor any number y, y* is defined as the greatest positive even integer less than or equal to y. What is the value of 6.2 \u2013 6.2*?\n\n### Options:\nA. 0.2\nB. 1.2\nC. 1.8\nD. 2.2\nE. 4.0\n\n### Answer:\nSince y* is defined as the greatest positive even integer less than or equal to y, then 6.2* = 4 (the greatest positive even integer less than or equal to 6.2 is 4).\nHence, 6.2 \u2013 6.2* = 6.2 - 4 = 2.2\nAnswer: D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train crosses a platform of 120 m in 15 sec, same train crosses another platform of length 180 m in 18 sec. then find the length of the train?\n\n### Options:\nA. 877m\nB. 180m\nC. 786m\nD. 165m\nE. 456m\n\n### Answer:\nLength of the train be \u2018X\u2019\nX + 120/15 = X + 180/18\n6X + 720 = 5X + 900\nX = 180m\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how many ways can the letters of the word ED456 be rearranged such that the numbers always appear together?\n\n### Options:\nA. 25\nB. 16\nC. 36\nD. 9\nE. 29\n\n### Answer:\nED456\n456 will come together as a group which can be arranged in 3!=6ways.\n456,E,D can be arranged in 3!=6 ways.\ntotal possible arrangements = 6*6=36 ways\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA contest will consist of n questions, each of which is to be answered eithertrueorfalse. anyone who answers all n questions correctly will be a winner. what is the least value of n for which the probability is less than 1/100000 that a person who randomly guesses the answer to each question will be a winner?\n\n### Options:\nA. 5\nB. 10\nC. 50\nD. 100\nE. 1000\n\n### Answer:\nA contest will consist of n questions, each of which is to be answered eithertrueorfalse. anyone who answers all n questions correctly will be a winner. what is the least value of n for which the probability is less than 1/1000 that a person who randomly guesses the answer to each question will be a winner?\nA.5\nB.10\nC.50\nD.100\nE.1000\nSoln: ans is B\nProbability that one question is answered right is 1/2.\nNow for minimum number of questions needed to take probability less than 1/1000 is\n=> (1/2)^n < 1/100000\nn = 1000 satisfies this.\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain car traveled twice as many miles from Town A to Town B as it did from Town B to Town C. From Town A to Town B, the car averaged 20 miles per gallon, and from Town B to Town C, the car averaged 25 miles per gallon. What is the average miles per gallon that the car achieved on its trip from Town A through Town B to Town C?\n\n### Options:\nA. 20\nB. 18\nC. 21.4\nD. 16\nE. 10\n\n### Answer:\nstep 1) took LCM of 20 and 25.. came as 100.\nstep 2) 100 distance between B to C... do 100/25 hence 4 gallons used\nstep 3) twice distance.. hence 100*2= 200... do as above.. 200/20= 10 gallons used\nstep 4) total gallons.. 4+10= 14 gallons\nstep ) total miles= 100+200= 300 miles\nhence.. average of whole journey = 300/14 which comes to 21.4\nAnswer : C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nExcluding stoppages, the average speed of a bus is 60 km/hr and including stoppages, the average speed of the bus is 40 km/hr. For how many minutes does the bus stop per hour?\n\n### Options:\nA. 22\nB. 88\nC. 77\nD. 20\nE. 99\n\n### Answer:\nIn 1hr, the bus covers 60 km without stoppages and 40 km with stoppages.\nStoppage time = time take to travel (60 - 40) km i.e 20 km at 60 km/hr.\nstoppage time = 20/60 hrs = 20 min.\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many terms are in the G.P. 3, 6, 12, 24, ......., 384 ,768,1536\n\n### Options:\nA. 8\nB. 9\nC. 67\nD. 5\nE. 10\n\n### Answer:\nExplanation:\nHere a = 3 and r = 6/3 = 2. Let the number of terms be n.\nThen, t = 384 => a * r^(n-1) = 1536\n=> 3 * 2^(n-1) = 1536 => 2^(n-1) = 512 = 2^(9)\n=> n-1 = 9 => n = 10\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA machine fills 150 bottles of water every 8 minutes. How many minutes it takes this machine to fill 675 bottles?\n\n### Options:\nA. 32 minutes\nB. 28 minutes\nC. 29 minutes\nD. 30 minutes\nE. 31 minutes\n\n### Answer:\n8 minutes are needed to fill 150 bottles. How many groups of 150 bottles are there in 675 bottles?\n675 /150 = 4.5 = 4 and 1/2\nFor each of these groups 8 minutes are needed. For 4 groups and 1/2\n8 * 4 + 4 = 32 + 4 = 36 minutes. (4 is for 1/2 a group that needs half time)\nWe can also find the final answer as follows\n4.5 x 8 = 32 minutes\ncorrect answer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how many ways can 6 arts and 4 science students be arranged in a row so that the arts and the science students are placed alternately?\n\n### Options:\nA. 12880\nB. 11850\nC. 13260\nD. 15200\nE. 17280\n\n### Answer:\nThe six art students can be arranged in those 6 A-slots in 6! = 720 ways.\nThe four science students can be arranged in those 4 S-slots in 4! = 24 ways.\nTotal arrangements = 720*24 = 17280\nAnswer =(E)\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn State X, all vehicle license plates have 2 letters from the 26 letters of the alphabet followed by 4 one digit numbers. How many different license plates can State X have if repetition of letters and numbers is allowed?\n\n### Options:\nA. 23,400\nB. 60,840\nC. 67,600\nD. 45,697,600\nE. 676,000\n\n### Answer:\nThe choices give us the answer without any calculations--\n4 one digits places can take 10*10*10*10 ways..\n2 letters places can be filled up in 26*26 ways\nans= 26*26*10*10*10*10=45,697,600\nans D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the numerator of a fraction be increased by 12% and its denominator decreased by 2% the value of the fraction becomes 6/7. Thus, the original fraction is:\n\n### Options:\nA. 1/4\nB. 2/4\nC. 3/4\nD. 2/3\nE. 1/3\n\n### Answer:\nIf original fraction is x/y , then\n1.12x/0.98y = 6/7\n(8/7)*(x/y)=6/7\nx/y =6/8=3/4\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAnand and Deepak started a business investing Rs. 22,500 and Rs. 35,000 respectively. Out of a total profit of Rs. 13,800, Deepak's share is?\n\n### Options:\nA. Rs. 9400\nB. Rs. 8900\nC. Rs. 8400\nD. Rs. 3400\nE. Rs. 8440\n\n### Answer:\nRatio of their shares = 22500 : 35000 = 9:14\nDeepak's share = 13800 * 14/23 = Rs. 8400.\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n1+2+2^2+2^3+2^4+2^5+2^6+2^7=\uff1f\n\n### Options:\nA. (2^4-1)(2^4+1)\nB. 2^6+1\nC. 2^5-1\nD. 2^5+1\nE. 2^5-2\n\n### Answer:\nFrom 1+2+2^2+2^3+2^4+2^5+2^6+2^7=1(2^8-1)/(2-1)=2^8-1=(2^4-1)(2^4+1), the correct answer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n0,1,2.9,5.61,9.05,?\n\n### Options:\nA. 11.15\nB. 12.15\nC. 13.15\nD. 14.15\nE. 15.15\n\n### Answer:\nThe series is 0, 1, 2.9, 5.61, 9.05, ...\nFisrt oder differences are 1, 1.9, 2.71, 3.44, ...\nSecond order differences are 0.9, 0.81, 0.73, ...\nNote that the second order differences are powers of 0.9 (0.9, 0.81, 0.729, ...), rounded off to two decimal digits. So next term in second order difference is 0.9^4 = 0.6561 = 0.66. Then, the next term in first order difference is 3.44+0.66 = 4.1. So, the term in the series is 9.05+4.1 = 13.15\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJasmine has a toaster with two slots that toasts one side of each piece of bread at a time, and it takes one minute to do so.\nIf she wants to make 3 pieces of toast, what is the least amount of time she needs to toast them on both sides?\n\n### Options:\nA. 1\nB. 2\nC. 3 min\nD. 4\nE. 5\n\n### Answer:\n3 minutes. She puts two pieces in the toaster, toasting one side of each. Then she flips one of them, takes one out, and puts the completely untoasted piece into the toaster. Finally, she takes out the toasted piece and puts the two half-toasted pieces of bread into the toaster for a minute and she's done. C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe annual birth and death rate in a country per 1000 are 39.4 and 19.4 respectively . the number of years B in which the population would be doubled assuming there is no emigration or immigration is\n\n### Options:\nA. 20\nB. 25\nC. B=30\nD. B=35\nE. B=40\n\n### Answer:\nSuppose the population of the country in current year is 1000.\nSo annual increase is 1000 + 39.4 - 19.4=1020\nHence every year there is an increase of 2%.\n2000=1000(1+(2/100))^n\nn=35 Answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe present age of a father is 4 years more than three times the age of his son. Three years hence, father's age will be 10 years more than twice the age of the son. Find the present age of the father.\n\n### Options:\nA. 30\nB. 38\nC. 29\nD. 40\nE. 48\n\n### Answer:\nif the present age be x years.\nfather's will be (3x+4)years..\nso, (3x+4+3)=2(x+3)+10\nor, x=9\nso the fathers present age =(3x+3)=(3*9+3)years =30years..\nANSWER : OPTION A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA circular rim 30 inches in diameter rotates the same number of inches per second as a circular rim 15 inches in diameter. If the smaller rim makes x revolutions per second, how many revolutions per minute does the larger rim makes in terms of x ?\n\n### Options:\nA. 48pi/x\nB. 75x\nC. 48x\nD. 24x\nE. 120x\n\n### Answer:\nRevolutions - circumference of the rim.\n=> 30pi*X*60 = 15pi*Revolutions\n=> 2/1 *X *60 = Revolutions => 120X - Option E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe value of 0.1 x 0.1 x 0.1 + 0.02 x 0.02 x 0.02/ 0.2 x 0.2 x 0.2 + 0.04 x 0.04 x 0.04\tis:\n\n### Options:\nA. 0.125\nB. 0.135\nC. 0.145\nD. 0.155\nE. 0.165\n\n### Answer:\nGiven expression\n=(0.1)(power 3) + (0.02)(power 3) /2(power 3) [(0.1)(power 3) + (0.02)(power 3)]\n=1/8\n= 0.125\nAnswer is A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA person crosses a 500m long street in 5 minnutes. What is his speed in km per hour?\n\n### Options:\nA. 6.01km/hr\nB. 7.2km/hr\nC. 9km/hr\nD. 2.5km/hr\nE. 3km/hr\n\n### Answer:\nSpeed = 500/5*60 = 1.67m/sec\n=1.67*18/5\n=6.01km/hr\nAnswer is A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe Smiley Pie Eating team won 30% of the first contests they entered. An amazingly winning streak increased their average to 50%. How many consecutive contests must they have won to have achieved this average?\n\n### Options:\nA. 30\nB. 20\nC. 10\nD. 25\nE. 35\n\n### Answer:\nExplanation: Let's set up an equation to find the solution. Total number of contest won to start was 30% of 75 = 22.5. Then, an amazing winning streak increases the percentage to 50%. Let x represent the unknown number of consecutive winning contests. Therefore, the total number of contests entered is (75+x). The total contests won is (22.5+x). With a 50% increase in the total contests won, we end up with a solution equation of 50% * (75+x)+22.5+x. Next, let's get rid of the percent sign and rewrite, then solve the equation. 50/100 * (75+x)=22.5+x\n1/2 * (75+x)=22.5+x\n2[ 1/2 * (75+x)]=2(22.5+x)\n1 * (75+x)=45+2x\n75+x=45+2x\n(75-45)+x=(45-45)+2x\n30+x=2x\n(30+x =2x)/x\n30=x\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a recent survey at a local deli, it was observed that 3 out of 5 customers bought a bagel and 5 out of 7 customers bought a coffee. Some customers bought both. If 7 customers are selected, what are the chances that at least 1 customer bought a coffee and a bagel?\n\n### Options:\nA. 27/343\nB. 3/7\nC. 27/125\nD. 341/422\nE. 9/125\n\n### Answer:\nLet us take 7*5=35 as the total number of customers. So 7*3=21 customers bought a bagel and 5*5=25 customers bought a coffee.\nchances that at least 1 customer bought a coffee and a bagel = 1 - chances that no customer bought a coffee and a bagel\nchances that no customer bought a coffee and a bagel= 24/35*23/34*22/33*21/32*20/31*19/30*18/29=81/422\nchances that at least 1 customer bought a coffee and a bagel= 1 - 81/422 = 341/422\nAnswer D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTough and Tricky questions: Combinations.\nEight contestants representing four different countries advance to the finals of a fencing championship. Assuming all competitors have an equal chance of winning, how many possibilities are there with respect to how a first-place and second-place medal can be awarded?\n\n### Options:\nA. 6\nB. 7\nC. 12\nD. 16\nE. 24\n\n### Answer:\nNumber of ways First-place medal can be awarded to four contestants = 8\nNumber of ways Second-place medal can be awarded to contestants after awarding First-place medal =3\nTherefore number of possibilities = 8 *3 =24\nAnswer:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the median from the below series\n5, 8, 11, 6, 10, 4, 18, 16, 13, 12 and 14\n\n### Options:\nA. 11\nB. 5\nC. 12\nD. 13\nE. 10\n\n### Answer:\nOrdering the data from least to greatest, we get:\n4, 5, 6, 8, 10, 11, 12, 13, 14, 16, 18\nThe median number was 11. (Five numbers were higher than 11 and five were lower.)\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nEach night before he goes to bed, Jordan likes to pick out an outfit to wear the next day. He has 12 different shirts, 10 different pairs of jeans, and 7 pairs of sneakers. If an outfit consists of 1 shirt, 1 pair of jeans, and 1 pair of sneakers, how many different outfits does Jordan have?\n\n### Options:\nA. 30\nB. 840\nC. 240\nD. 480\nE. 960\n\n### Answer:\nTotal # of outfits = 12 * 10 * 7 = 840\nAnswer - B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo trains are running at 40 km/hr and 20 km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 4 seconds. What is the length of the fast train?\n\n### Options:\nA. 23 m\nB. 22 (2/9)m\nC. 27 (7/9)m\nD. 29 m\nE. 28 m\n\n### Answer:\nRelative speed = (40 - 20) km/hr =\t(20 x(5/18))m/sec =\t(50/9)m/sec.\nTherefore Length of faster train =\t((50/9)\tx 4) m =\t(200/9)m = 22\t(2/9)\tm.\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the wheel is 15 cm then the number of revolutions to cover a distance of 1056 cm is?\n\n### Options:\nA. 18\nB. 11.2\nC. 14\nD. 12\nE. 91\n\n### Answer:\n2 * 22/7 * 15 * x = 1056 => x\n= 11.2\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo vessels P and Q contain 62.5% and 87.5% of alcohol respectively. If 2 litres from vessel P is mixed with 4 litres from vessel Q, the ratio of alcohol and water in the resulting mixture is?\n\n### Options:\nA. 19:1\nB. 19:4\nC. 19:8\nD. 19:5\nE. 19:2\n\n### Answer:\nQuantity of alcohol in vessel P = 62.5/100 * 2 = 5/4 litres\nQuantity of alcohol in vessel Q = 87.5/100 * 4 = 7/2 litres\nQuantity of alcohol in the mixture formed = 5/4 + 7/2 = 19/4 = 4.75 litres\nAs 6 litres of mixture is formed, ratio of alcohol and water in the mixture formed\n= 4.75 : 1.25 = 19:5.\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many alphabets need to be there in a language if one were to make 1 million distinct 3 digit initials using the alphabets of the language?\n\n### Options:\nA. 26\nB. 50\nC. 1000\nD. 100\nE. 90\n\n### Answer:\n1 million distinct 3 digit initials are needed.\nLet the number of required alphabets in the language be \u2018n\u2019.\nTherefore, using \u2018n\u2019 alphabets we can form n * n * n = n3 distinct 3 digit initials.\nNote distinct initials is different from initials where the digits are different.\nFor instance, AAA and BBB are acceptable combinations in the case of distinct initials while they are not permitted when the digits of the initials need to be different.\nThis n3 different initials = 1 million\ni.e. n3 = 106 (1 million = 106)\n=> n3 = (102)3 => n = 102 = 100\nHence, the language needs to have a minimum of 100 alphabets to achieve the objective.\nANSWER D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nCaleb and Kyle built completed the construction of a shed in 10 and half days. If they were to work separately, how long will it take each for each of them to build the shed, if it will take Caleb 2 day earlier than Kyle?\n\n### Options:\nA. 10 and 12\nB. 9 and 11\nC. 20 and 22\nD. 8 and 10\nE. 19 and 21\n\n### Answer:\nWork = (A)(B)/(A+B) where A and B are the individual times of each entity.\nHere, we're told that (working together) the two workers would complete a job in 12 days. This means that (individually) each of them would take MORE than 10 days to do the job.\nAnswers E, A and C are illogical, since the individual times must both be greater than 10 days.\nso we can TEST the values for Answers B and D.\nUsing the values for Answers B and D...\nAnswer B: (20)(22)/(20+22) = 440/42 = 10.5 This is a match\nFinal Answer:\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a and b are positive numbers, and a^3 + b^3 = 30, then the greatest possible value of a is between:\n\n### Options:\nA. 0 and 3\nB. 3 and 4\nC. 4 and 5\nD. 5 and 7\nE. 7 and 9\n\n### Answer:\nIf a = 3.1 and b is very small, then a^3 + b^3 can equal 30.\nIf a > 4, then a^3 + b^3 > 30.\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 3x+4y=60 and 6x-4y=12, what is the product of x and y?\n\n### Options:\nA. 80\nB. 54\nC. 54\nD. 72\nE. 12\n\n### Answer:\nGiven 3x+4y=60 ---Eq 1\n6x -4y =12 -- Eq 2\nSum both eqns we get 9X = 72 => X = 8\nsum 6X in eq 2 => 48 - 4y = 12.\n=> Y = 9\nNow XY = 8 * 9 = 72\nOption D is correct answer.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhen x is divided by y, the quotient is z with remainder s. Which of the following is equal to s?\n\n### Options:\nA. yz \u2013 x\nB. y/x\u2212z\nC. x \u2013 y \u2013 z\nD. x \u2013 yz\nE. zx \u2013 y\n\n### Answer:\n(x/y)=z(+s)\n(18/8)=2(+2)\nx-yz\nwhich is 18-(8*2)=2\nAnswer is D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo trains of length 100 m and 200 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 54 kmph and 72 kmph. After how much time will the trains meet?\n\n### Options:\nA. 27/7 sec\nB. 20/7 sec\nC. 33/7 sec\nD. 21/7 sec\nE. 32/7 sec\n\n### Answer:\nB\n20/7 sec\nThey are moving in opposite directions, relative speed is equal to the sum of their speeds.\nRelative speed = (54 + 72)*5/18 = 7*5 = 35 mps.\nThe time required = d/s = 100/35 = 20/7 sec.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAn article was sold after a discount of 20% and therewas a gain of 20%. If the profit madeon it was Rs.6 less thanthe discount offered on it, find its SP?\n\n### Options:\nA. Rs. 60\nB. Rs. 69\nC. Rs. 72\nD. Rs. 89\nE. Rs. 92\n\n### Answer:\nLet CP = Rs. 100x\nSP = Rs. 120x\nMP = 120x/80 * 100 = Rs. 150x\nD = Rs. 150x - Rs. 120x = Rs. 30x\nD - P = 30x - 20x = Rs. 6, 10x = Rs. 6\n120x = 120/10 * 6 = Rs. 72\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat sum of money put at C.I amounts in 2 years to Rs.8820 and in 3 years to Rs.9261?\n\n### Options:\nA. 8000\nB. 8877\nC. 2877\nD. 2678\nE. 1011\n\n### Answer:\n8820 ---- 441\n100 ---- ? => 5%\nx *105/100 * 105/100 = 8820\nx*1.1025=8820\nx=8820/1.1025 => 8000\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTough and Tricky questions: Distance/Rate.\nOn a reconnaissance mission, a state-of-the-art nuclear powered submarine traveled 600 miles to reposition itself in the proximity of an aircraft carrier. This journey would have taken 2 hour less if the submarine had traveled 10 miles per hour faster. What was the average speed, in miles per hour, for the actual journey?\n\n### Options:\nA. 20\nB. 40\nC. 60\nD. 50\nE. 100\n\n### Answer:\nSay, if speed is 50, 600/50 = 12 hrs and 600/60 = 10 hrs (a reduction of 2 hr -> Correct answer)\nAnswer (D)\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA bike owner buys petrol at Rs 75, Rs. 80 and Rs. 85 per litre for three successive years. What approximately is the average cost per litre of petrol if he spends Rs. 40000 each year?\n\n### Options:\nA. Rs 79.8\nB. Rs 80.4\nC. Rs 85.5\nD. Rs 90\nE. Rs 60\n\n### Answer:\nExplanation :\nTotal quantity of petrol consumed in 3 years = 40000/75 + 40000/80 + 40000/85 litres\n= 40000 (1/75 + 1/80 + 1/85 ) = 40000(767/20,400) = 76700/51 litres\nTotal amount spent = Rs. (3 x 40000) = Rs. 120000.\nAverage cost = Rs. 120000 x 51/76700\n= Rs. 61200/767\n= Rs. 79.8\nAnswer : A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA sum was put at simple interest at a certain rate for 10 years . Had it been put at 5% higher rate , it would have fetched Rs.300 more. What was the Sum?\n\n### Options:\nA. s.1200\nB. s.1300\nC. s.600\nD. s.800\nE. s.1200\n\n### Answer:\nAt 5% more rate, the increase in S.I for 10 years = Rs.300 (given)\nSo, at 5% more rate, the increase in SI for 1 year = 300/10 = Rs.30/-\ni.e. Rs.30 is 5% of the invested sum\nSo, 1% of the invested sum = 30/5\nTherefore, the invested sum = 30 \u00d7 100/5 = Rs.600 Answer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA car ferry can hold up to 70 tons of cargo. What is the greatest number of vehicles that the ferry can carry if half the vehicles are cars with an average (arithmetic mean) weight of 0.75 tons and half of the vehicles are trucks with an average (arithmetic mean) weight of 6 tons?\n\n### Options:\nA. 20\nB. 24\nC. 28\nD. 32\nE. 36\n\n### Answer:\nThe weight of one car and one truck is 6.75 tons.\n70/6.75 = 10 plus a remainder\nThe ferry could carry 10 cars and 10 trucks for a total of 20 vehicles.\nThe answer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe length of a rectangular plot is 20 mtr more than its breadth. If the cost of fencingthe plot at 26.50 per meter is Rs. 5300, what is the length of the plot in mtr?\n\n### Options:\nA. 50 m\nB. 60 m\nC. 65 m\nD. 75 m\nE. 80 m\n\n### Answer:\nLet breadth = x metres.\nThen, length = (x + 20) metres.\nPerimeter = 5300 m = 200 m.\n26.50\n2[(x + 20) + x] = 200\n2x + 20 = 100\n2x = 80\nx = 40.\nHence, length = x + 20 = 60 m\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man has Rs. 480 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?\n\n### Options:\nA. 90\nB. 10\nC. 20\nD. 50\nE. 80\n\n### Answer:\nExplanation:\nLet number of notes of each denomination be x.\nThen x + 5x + 10x = 480\n16x = 480\nx = 30.\nHence, total number of notes = 3x = 90.\nAnswer is A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA jar contains 5 black and 2 white balls. If you pick two balls at the same time, what's the probability that one ball is black and one is white?\n\n### Options:\nA. 2/7\nB. 5/21\nC. 4/21\nD. 3/7\nE. 1/2\n\n### Answer:\nP(1st black, 2nd white) = 5/7*2/6 = 10/42;\nP(1st white, 2nd black) = 2/7*5/6 = 10/42.\nP = 10/42 + 10/42 = 20/84= 10/42 = 5/21\nAnswer: B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average of 13 numbers is 60. Average of the first 6 of them is 57 and that of the last 8 is 61. Find the 8th number?\n\n### Options:\nA. 46\nB. 48\nC. 50\nD. 52\nE. 54\n\n### Answer:\nSum of all the 13 numbers = 13 * 60 = 780\nSum of the first 6 of them = 6 * 57 = 342\nSum of the last 8 of them = 8 * 61 = 488\nSo, the 8th number = 342 + 488 - 780 = 50.\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIndu gave Bindu Rs.1250 on compound interest for 2 years at 4% per annum. How much loss would Indu has suffered had she given it to Bindu for 2 years at 4% per annum simple interest?\n\n### Options:\nA. 1\nB. 2\nC. 3\nD. 4\nE. 5\n\n### Answer:\n1250 = D(100/4)2\nD = 2\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the average of first 5 multiples of 5?\n\n### Options:\nA. 10\nB. 15\nC. 12.5\nD. 13\nE. 21\n\n### Answer:\naverage = (5+10+15+20+25)/5 = 15\nAnswer is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the next number in the sequence : 15,21,24,30,33,39,51,57__?\n\n### Options:\nA. 69\nB. 71\nC. 67\nD. 65\nE. 79\n\n### Answer:\nnext no. = previous + (sum of digits)\n15 + (1+5) = 21\n21 + (2+1) = 24\n24 + (2+4) = 30\n30 + (3+0) = 33\n33 + (3+3) = 39\n39 + (3+9) = 51\n51 +(5+1) = 57\n57 + (5+7) = 69\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the compound interest on a certain sum of money for 2 years at 10% per annum be Rs. 993, what would be the simple interest?\n\n### Options:\nA. Rs. 600\nB. Rs. 890\nC. Rs. 895\nD. Rs. 900\nE. None\n\n### Answer:\nLet P = Principal\nA - Amount\nWe have a = P(1 + R/100)3 and CI = A - P\nATQ 993 = P(1 + R/100)3 - P\n? P = 3000/-\nNow SI @ 10% on 3000/- for 2 yrs = (3000 x 10 x 2)/100\n= 600/-\nAnswer: A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn what time will a train 40 m long cross an electric pole, it its speed be 144 km/hr?\n\n### Options:\nA. 2.5 sec\nB. 1.0 sec\nC. 7.5 sec\nD. 2.3 sec\nE. 1.5 sec\n\n### Answer:\nSpeed = 144 * 5/18\n= 40 m/sec\nTime taken = 40/40\n= 1.0 sec.\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average age of husband, wife and their child 3 years ago was 27 years and that of wife and the child 5 years ago was 20 years. The present age of the husband is\n\n### Options:\nA. 33\nB. 40\nC. 38\nD. 27\nE. 211\n\n### Answer:\nExplanation:\nSum of the present ages of husband, wife and child = (27 x 3 + 3 x 3) years = 90 years.\nSum of the present ages of wife and child (20 x 2 + 5 x 2) years = 50 years.\nHusband's present age = (90 - 50) years = 40 years.\nAnswer: B) 40\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA and B runs around a circular track. A beats B by one round or 10 minutes. In this race, they had completed 4 rounds. If the race was only of one round, find the A's time over the course:\n\n### Options:\nA. 8.5 min\nB. 7.5 min\nC. 1.5 min\nD. 9.5 min\nE. 4.5 min\n\n### Answer:\nExplanation:\nB runs around the track in 10 min.\ni.e , Speed of B = 10 min per round\nA beats B by 1 round\nTime taken by A to complete 4 rounds\n= Time taken by B to complete 3 rounds\n= 30 min\nA's speed = 30/4 min per round\n= 7.5 min per round\nHence, if the race is only of one round A's time over the course = 7 min 30 sec\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the average (arithmetic mean) of x^2, 2x^2, and 3x^2 is 200, what is the value of x?\n\n### Options:\nA. 10\nB. 12\nC. 15\nD. 20\nE. 25\n\n### Answer:\nAM of x^2, 2x^2 and 3x^2 = x^2 + 2x^2 + 3x^2 / 3 = 6x^2/3\nGiven that 2x^2 = 200\nx^2 = 100\nx = 10\nAnswer is A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow long does a train 120 meters long running at the rate of 54 kmph take to cross a bridge 660 meters in length?\n\n### Options:\nA. 33\nB. 72\nC. 52\nD. 82\nE. 62\n\n### Answer:\nExplanation:\nT = (660 + 120)/54 * 18/5\nT = 52\nAnswer: Option C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe ratio of two quantities is 1 to 2. If each of the quantities is increased by 15, what is the ratio of these 2 new quantities?\n\n### Options:\nA. 5:6\nB. 25:27\nC. 15:16\nD. 20:21\nE. It cannot be determined from the information given\n\n### Answer:\nThe ratio cannot be straight way added any quantity...\n1:2means 1X:2X...\nSo when you add a quantity, it becomes 1x + 15 : 2x +15..\nSo value of x is must..\nAns E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFill in the missing number:\n18 ? 12 11 10.5 10.25\n\n### Options:\nA. 10.1\nB. 10.4\nC. 10.2\nD. 14\nE. 10.3\n\n### Answer:\n14\nDivide each number by 2 and then add 5 to it.\nANSWER D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain toy store's revenue in November was 1/5 of its revenue in December and its revenue in January was 3/4 of its revenue in November, then the store's revenue in December was how many times the average (arithmetic mean) of its revenues in November and January?\n\n### Options:\nA. 1/4\nB. 1/2\nC. 2/3\nD. 2\nE. 6\n\n### Answer:\nLet Dec rev =100\nThen Nov rev is 1/5 (100) => 20\nTherefore Jan rev = 3/4(Nov rev) = 3/4(20) => 15\nHence Dec rev = x*( Nov rev+Jan rev)/2\n100 = x* (20+15)/2\nx = 100/17.5 => 5.71=6\nAns) E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA merchant gets a 5% discount on each meter of fabric he buys after the first 2,000 meters and a 7% discount on every meter after the next 1,500 meters. The price, before discount, of one meter of fabric is $2, what is the total amount of money the merchant spends on 7,000 meters of fabric?\n\n### Options:\nA. $13,360\nB. $14,450\nC. $15,720\nD. $16,780\nE. $17,240\n\n### Answer:\nFor first 2000 meters he does not get any discount.\nThe price is 2*2000 = $4000\nFor next 1500 meters, he gets a 5% discount.\nThe price is 1.9*1500 = $2850\nFor the next 1500 meters, he gets a 7% discount.\nThe price is 1.86*3500 = $6510\nThe total price is $4000 + $2850 + $6510 = $13,360\nThe answer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf y exceeds x by 25%, then x is less than y by?\n\n### Options:\nA. 28%\nB. 21%\nC. 20%\nD. 30%\nE. 29%\n\n### Answer:\nX=100\ty=125\n125--------25\n100--------? => 20%\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAman started a business investing Rs. 70,000. Rakhi joined him after six months with an amount of Rs. 1,05,000 and Sagar joined them with Rs. 1.4 lakhs after another six months. The amount of profit earned should be distributed in what ratio among Aman, Rakhi and Sagar respectively, 3 years after Aman started the business?\n\n### Options:\nA. 12:15:15\nB. 12:15:16\nC. 12:15:19\nD. 12:45:15\nE. 12:15:11\n\n### Answer:\nAman : Rakhi : Sagar = (70000 * 36) : (105000 * 30) : (140000 * 24)\n= 12:15:16\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that all the four bulbs are defective.\n\n### Options:\nA. 1/128\nB. 1/127\nC. 1/125\nD. 1/121\nE. 1/126\n\n### Answer:\nExplanation:\nOut of nine, five are good and four are defective. Required probability\n= 4C4/9C4 = 1/126\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWater consists of hydrogen and oxygen, and the approximate ratio, by mass, of hydrogen to oxygen is 2:16. Approximately how many grams of oxygen are there in 108 grams of water?\n\n### Options:\nA. 16\nB. 96\nC. 112\nD. 128\nE. 142\n\n### Answer:\nSolution:\nWe are given that the ratio of hydrogen to oxygen in water, by mass, is 2 : 16. Using our ratio multiplier we can re-write this as 2x : 16x. We can now use these expressions to determine how much oxygen is in 108 grams of water.\n2x + 16x = 108\n18x = 108\nx = 6\nSince x is 6, we know that there are 16 x 6 = 96 grams of oxygen in 108 grams of water.\nAnswer B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nEach of the positive integers a, b, and c is a three-digit integer. If each of the digits 0 through 8 appears in one of these three integers, what is the minimum possible value of the sum of a, b, and c?\n\n### Options:\nA. 45\nB. 666\nC. 711\nD. 801\nE. 1368\n\n### Answer:\nAccording to the stem we should use the digits 0 through 7 to construct 3 three-digit integers, so that their sum is as small as possible.\nTo minimize the sum, minimize the hundreds digits of a, b, and c, so make them 1, 2, and 3.\nNext, minimize tens digits. Make them 0, 4, and 5.\nUse the remaining digits (6, 7, and 8) for units digits.\nSo, a would be 106, b would be 247 and c would be 358.\n106 + 247 + 358 = 711.\nAnswer: C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the least number of squares tiles required to pave the floor of a room 15 m 17 cm long and 9 m 2 cm broad?\n\n### Options:\nA. 617\nB. 746\nC. 808\nD. 812\nE. 814\n\n### Answer:\nLength of largest tile = H.C.F. of 1517 cm and 902 cm = 41 cm.\nArea of each tile = (41 x 41) cm2.\nRequired number of tiles = (1517 x 902)/(41X41) = 814.\nAnswer: Option E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nBill made a profit of 10% by selling a product. If he had purchased that product for 10% less and sold it at a profit of 30%, he would have received $ 56 more. What was his original selling price?\n\n### Options:\nA. $770\nB. $660\nC. $700\nD. $1100\nE. $880\n\n### Answer:\nLet the original purchase price be X\nSo original selling price at 10% profit = 1.1X\nIf product is purchased at 10% less of original = 0.9X\nProfit of 30% on this price = 1.3(0.9X)\nHe would have received $56 more in second scenario => 1.3(0.9X) - 1.1X = 56\n=> 0.07X = 56\n=> X = $800\nOriginal purchase price = $800\nHence, original selling price (at 10% of profit) = 1.1(800) = $880\nOption E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a division sum, the remainder is 0. As student mistook the divisor by 12 instead of 21 and obtained 42 as quotient. What is the correct quotient ?\n\n### Options:\nA. 0\nB. 12\nC. 13\nD. 20\nE. 24\n\n### Answer:\n12*42=504\n504%21=24\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAmong the members of the Malmo family, there are three times as many members who do not wear glasses as members who do. Half of the Malmo family members have blue eyes, and 4/5 of the family members who have blue eyes do not wear glasses. What percent of the Malmo family members wear glasses and do not have blue eyes?\n\n### Options:\nA. 10\nB. 15\nC. 20\nD. 25\nE. 35\n\n### Answer:\nNumber in black are given and in red are calculated.\nNow, since x+3x=100, then x=25 and therefore =25\u221210=15\nAnswer: B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\na, b, c and d are four consecutive numbers. If the sum of a and dis 109, what is the product of b and c?\n\n### Options:\nA. 2652\nB. 2578\nC. 2970\nD. 3354\nE. 4234\n\n### Answer:\nC\n2970\nHere d = a + 3\na + a + 3 = 109\n2a = 106\na = 53\nSo, numbers are 53, 54, 55 and 56\n\u2234 b \u00d7 c= 54 \u00d7 55 = 2970\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nCan you replace the question mark with the number to complete the series, provided the pair of numbers exhibits a similar relationship ?\n? : 4623 :: 9 : 647\n\n### Options:\nA. ?= 17\nB. 18\nC. 13\nD. 10\nE. 20\n\n### Answer:\nA\n17\nThe relationship holds for below formula :\npow(x,3) - pow(x,2) - 1\n=> 9*9*9 - 9*9 - 1\n=> 729 - 81 - 1\n=> 647\nSimilarly,\n17*17*17 - 17*17 - 1\n=> 4913 - 289 - 1\n=> 4623\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many different values of positive integer x, for which |x+5|", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man swims downstream 36 km and upstream 48 km taking 6 hours each time, what is the speed of the man in still water?\n\n### Options:\nA. 5\nB. 24\nC. 7\nD. 42\nE. 6\n\n### Answer:\n36--- 6 DS = 6\n? ---- 1\n48 ---- 6 US = 8\n? ---- 1 M = ?\nM = (6 + 8)/2 = 7\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the operation \u20ac is defined for all x and y by the equation x \u20ac y = 3*x*y, then 3 \u20ac (4 \u20ac 5) =\n\n### Options:\nA. 80\nB. 120\nC. 160\nD. 540\nE. 660\n\n### Answer:\nworking inside out,\n(4 \u20ac 5) = 3*4*5 = 60\n3 \u20ac 60 = 3*3*60 = 540\nHence, answer is D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA number consists of two digits whose sum is 11. If 27 is added to the number, then the digits change their places. What is the number ?\n\n### Options:\nA. 47\nB. 65\nC. 83\nD. 92\nE. 98\n\n### Answer:\nExplanation:\nLet the ten's digit be x. Then, unit's digit = (11 - x).\nSo, number = 10x + (11 - x) = 9x + 11.\nTherefore (9x + 11) + 27 = 10 (11 - x) + x 9x + 38 = 110 - 9x 18x = 72 x = 4.\nThus, ten's digit = 4 and unit's digit = 7.\nHence, required number = 47.\nAnswer: Option A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf n is an odd integer less than 10, which of the following must also be an odd integer?\n\n### Options:\nA. 2n + n^2 + 2\nB. n^3 + 2n\nC. 3n + 2^n\nD. n^3 + 1\nE. 3n\n\n### Answer:\nAnswer: D\nA: 2n = even\nB: 3n = even\nC: 3n + n^2 + 2 = even\nD: n^2 + 1 = odd\nE: 2n + n^2 = even\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n28 buckets of water fill a tank when the capacity of each bucket is 13.5 litres. How many buckets will be required to fill the same tank if the capacity of each bucket is 9 litres?\n\n### Options:\nA. 30\nB. 42\nC. 60\nD. Data inadequate\nE. None of these\n\n### Answer:\nCapacity of the tank = 28 \u00c3\u2014 13.5= 378 litres\nWhen the capacity of each bucket = 9 litres, then the required no. of buckets\n= 378\u00e2\u0081\u201e9 = 42\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nC individuals pledged to pay equal contributions so that a charity\u2019s goal of $x could be reached. If d of the contributors failed to pay their share, which of the following represents the additional number of dollars that each of the remaining individuals would have to pay in order to allow the charity to reach its goal?\n\n### Options:\nA. dx / C\nB. x / (C-d)\nC. d / (C-dx)\nD. x / (C(C-d))\nE. dx / (C(C-d))\n\n### Answer:\nNumber of individuals = C\nAmount paid by each individual = n\nTotal expected amount = Charity's goal = nC = x\nn = x/C\nNumber of individuals who fail to pay = d\nContribution from individuals who would fail to pay = dx/C --> Additional amount\nNumber of individuals who are paying = C - d\nAdditional amount has to be divided among the (C - d) individuals --> dx/C(C - d)\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA vertical tower OP stands at the centre O of a square ABCD. Let h and b denote the lengths OP and AB respectively. Suppose \u2220APB = 60\u00b0, then the relationship between h and b can be expressed as :\n\n### Options:\nA. 2b^2 = h^2\nB. 2h^2 = b^2\nC. 3b^2 = 2h^2\nD. 3h^2 = 2b^2\nE. None of these\n\n### Answer:\nExplanation :\nAs OP is at centre of square so clearly PA = PB.\nso, angle \u2220PAB = \u2220 PBA.\nand as \u2220APB = 60,so we can see that in \u2206 APB, \u2220 PAB = \u2220 PBA = 60.\nHence, its an equilateral triangle thus making AP = PB = AB = b.\nNow lets see \u2206 AOB ,\nO is centre of square so angle AOB=900\u200b.\ngiving us AO = OB = AB/\u221a2.\nso AO= b/\u221a2\nNow in triangle AOP right angled at O,\n=> AO2 + OP2 = PA2 .\n=> b2/2 + h2 = b2 .\n=> h2 = b2/2\nAnswer : B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA thief goes away with a SANTRO car at a speed of 40 kmph. The theft has been discovered after half an hour and the owner sets off in a bike at 50 kmph when will the owner over take the thief from the start?\n\n### Options:\nA. 2 hours\nB. 6 hours\nC. 8 hours\nD. 9 hours\nE. 3 hours\n\n### Answer:\n|-----------20--------------------|\n50 40\nD = 20\nRS = 50 \u2013 40 = 10\nT = 20/10 = 2 hours\n14. If I walk at 3 kmph, I miss\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nEvaluate 75% of 450 + 45% of 750\n\n### Options:\nA. 632\nB. 642\nC. 652\nD. 675\nE. 572\n\n### Answer:\nExplanation:\n= (75/100) * 450 + (45/100) * 750\n= 675\nOption E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many seconds will a 500 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?\n\n### Options:\nA. 25\nB. 30\nC. 35\nD. 40\nE. 45\n\n### Answer:\nSpeed of train relative to man = 63 - 3 = 60 km/hr.\n= 60 * 5/18 = 50/3 m/sec.\nTime taken to pass the man = 500 * 3/50 = 30 sec.\nAnswer: Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe simple interest on Rs. 20 for 6 months at the rate of 5 paise per rupeeper month is\n\n### Options:\nA. 1.2\nB. 1.4\nC. 6\nD. 7\nE. None\n\n### Answer:\nSol.\nS.I. = Rs. [20 * 5/100 * 6] = Rs. 6\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTrains A and B start simultaneously from stations 450 miles apart, and travel the same route toward each other on adjacent parallel tracks. If Train A and Train B travel at a constant rate of 50 miles per hour and 50 miles per hour, respectively, how many miles will Train A have traveled when the trains pass each other, to the nearest mile?\n\n### Options:\nA. 112\nB. 133\nC. 150\nD. 167\nE. 225\n\n### Answer:\nSince we know the distance (450) and the combined rate (100), we plug it into the formula:\nDistance = Rate * Time\n450 = 100 * Time\nWe can solve for the time they will meet cause we added the rate of Train A and Train B together.\nSo the time will be 450/100 from dividing 100 on both sides to isolate Time in the equation above.\nTime will be 4.5 hours so now you can plug that in for Train A\u2019s distance.\nDistance = Rate * Time\nDistance = 50 * 4.5\nDistance = 225 according to answer choice E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe price of a mobile was increased by 40 percent. The new price was then decreased by 15 percent. A single increase of what percent is equivalent to these two successive changes?\n\n### Options:\nA. 25%\nB. 19%\nC. 30%\nD. 22.5%\nE. 15%\n\n### Answer:\nconsider base price - $100\n25% increase = 1.40*100 = $140\nThen a 15% decrease on new price = 0.85* 140 = $119\nso final price of radio - $119\ntherefore a 19% increase\ncorrect option - B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA solution of X pounds of water and sugar is boiled until 20% of the water content evaporates. Originally p% of sugar was present in the solution. After evaporation, what percentage of the solution is sugar?\n\n### Options:\nA. 100p/(1-p)\nB. 80p/(1-p)\nC. 75p/(1-p)\nD. 100p/(80-0.2p)\nE. 100p/(80+0.2p)\n\n### Answer:\nWe'll go for the ALTERNATIVE approach since there are variables in all the answers (which means that any number could work). Since the question deals with percents, the easiest number to use is X = 100. Now let's say that p = 10. Before the evaporation we had 10 pound of sugar and 90 pounds of water. Since only water evaporated, after the evaporation the 10 pounds of sugar remained the same, but the water reduced by 20% of 90 (18 pounds), so we have only 72 pounds of water. 10 out of 82 is the fraction of sugar, so if we multiply it by 100 we get the percents. The correct answer is E: 100p/(80+0.2p) >>> 100x10 / 82\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo airplanes take off from one airfield at noon. One flies due east at 204 miles per hour while the other flies directly northeast at 283 miles per hour. Approximately how many miles apart are the airplanes at 2 p.m.?\n\n### Options:\nA. 166\nB. 408\nC. 400\nD. 483\nE. 566\n\n### Answer:\nB\nIn two hours:\nthe plane flying East will be 408 miles away from airport.\nthe other plane will be 566 miles away from airport.\n566/408 = ~1.4 = ~sqrt(2)\nThis means that planes formed a right isocheles triangle => sides of such triangles relate as 1:1:sqrt(2) => the planes are 408 miles apart.B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a, b and c are the sides of a triangle, and a2 + b2 + c2 = bc + ca + ab, then the triangle is\n\n### Options:\nA. equilateral\nB. isosceles\nC. right-angled\nD. obtuse-angled\nE. None of these\n\n### Answer:\nExplanation :\nWe know that (a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ac = 3ab + 3bc + 3ac\nNow assume values of a, b, c and substitute in this equation to check the options.\nShortcut:\n(a \u2013 b)2 + (b \u2013 c)2 + (c \u2013 a)2 = 0.\nHence, a = b = c.\nAnswer : A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRobin mixes two liquids, one blue in coloUr and other red in colour in the ratio 2:3 and sells the mixture at the rate of $20 per liter, thereby making a 25% profit on his outlay. The blue liquid costs Robin $5 per litre lesser than the red liquid. How much does a liter of red liquid cost?\n\n### Options:\nA. 12\nB. 13\nC. 14\nD. 15\nE. 16\n\n### Answer:\nLet x be the required cost per litre of red paint.\nTake 5 litres of this mixture.\nSold at 100 with a profit of 1/4th of total cost. So, total cost will be 1/5th less than 100; total cost = 80.\n2(x-5) + 3(x) = 80\nx = 14\nAnswer is C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA, B, C started a business with their investments in the ratio 1:3 :5. After 4 months, A invested the same amount as before and B as well as C withdrew half of their investments. The ratio of their profits at the end of the year is :\n\n### Options:\nA. 5 : 6 : 18\nB. 5 : 6 : 12\nC. 5 : 6 : 11\nD. 5 : 6 : 10\nE. 5 : 6 : 128\n\n### Answer:\nLet their initial investments be x, 3x and 5x respectively. Then,\n20x : 24x : 40x = 5 : 6 : 10\nAnswer: D) 5 : 6 : 10\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMachine A takes 100 hours to complete a certain job and starts that job at 7AM. After two hour of working alone, machine A is joined by machine B and together they complete the job at 6PM. How long would it have taken machine B to complete the jobif it had worked alone for the entire job?\n\n### Options:\nA. 10.11\nB. 9.99\nC. 11.1\nD. 44.11\nE. 1.01\n\n### Answer:\nLet us assume total job = 100 units\nA finishes 100 units in 100 hrs(given)\nHence A (working rate)= 1 units /hr\nNow Given that A works for 2 hr( so 2 units done) then A and B finish total work in 15 hours. Hence A and B finish 98 units in 9 hours. Of these 1x9=9 units were done by A. Hence B did 89units in 9 hours.\nHence B(working rate)= 89/9 units /hr\nHence B takes 100x9/89 = 10.11 hours to complete the job.\nAnswer A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nLook at this series: VI, 10, V, 11, __, 12, III, ... What number should fill the blank?\n\n### Options:\nA. II\nB. IV\nC. IX\nD. 14\nE. 12\n\n### Answer:\nThere will be two series.\n1st : VI, V , ?? , III (decreasing by 1 in roman letters of numbers)i.e,6,5,4\n2nd : 10, 11, 12 , 13 (Increasing by 1 number)\nFinal sequence : VI, 10, V, 11, 1V, 12, III\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a and b are the roots of the equation x2 - 6x + 6 = 0, then the value of a2 + b2 is:\n\n### Options:\nA. 36\nB. 24\nC. 17\nD. 6\nE. 5\n\n### Answer:\nSol.(b) The sum of roots = a+ b = 6\nProduct of roots = ab = 6\nNow, a2 + b2 = (a + b)2 - 2ab = 36 - 12 = 24\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA grocer has 400 pounds of coffee in stock, 25 percent of which is decaffeinated. If the grocer buys another 100 pounds of coffee of which 60 percent is decaffeinated, what percent, by weight, of the grocer\u2019s stock of coffee is decaffeinated?\n\n### Options:\nA. 28%\nB. 30%\nC. 32%\nD. 34%\nE. 40%\n\n### Answer:\n1. 25% of 400=100 pounds of decaffeinated coffee\n2. 60% of 100=60 pounds of decaffeinated coffee\n3. Wt have 160 pounds of decaffeinated out of 500 pounds, that means 160/500*100%=32%. The correct answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA company recently conducted a survey and found that 35,000 of its customers live in rural areas. If the number of customers who live in urban areas is 140 percent greater than the number of customers who live in rural areas, how many customers live in urban areas?\n\n### Options:\nA. 78,000\nB. 80,000\nC. 82,000\nD. 84,000\nE. 86,000\n\n### Answer:\nThe number of customers in urban areas is 35,000+1.4*35,000=84,000.\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the smallest four-digit number which is a multiple of 112.\n\n### Options:\nA. 896\nB. 1008\nC. 1120\nD. 1024\nE. None of these\n\n### Answer:\nThe smallest four digit number is 1000. If 1000 is divided by 112, the remainder is 104.\n112 - 104 = 8, if 8 is added to 1000, it will become the smallest four digit number and a multiple of 112.\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFor one toss of a certain coin, the probability that the outcome is heads is 0.8. If this coin is tossed 5 times, which of the following is the probability that the outcome will be heads at least 4 times?\n\n### Options:\nA. (0.8)^5\nB. 2(0.8)^4\nC. 3(0.8)^4\nD. 4(0.8)^4(0.2) + (0.8)^5\nE. 5(0.8)^4(0.2) + (0.8)^5\n\n### Answer:\nP(5 heads) = (0.8)^5\nThere are 5 ways to get 4 heads: HHHHT, HHHTH, HHTHH, HTHHH, THHHH\nP(4 heads) = 5*(0.8)^4(0.2)\nThe answer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 4a = 16b and 9b = 14c, Find a:b:c?\n\n### Options:\nA. 52:13:7\nB. 13:7:52\nC. 7:13:52\nD. 64:14:9\nE. None of these\n\n### Answer:\nExplanation:\n(4a = 16b ==> a/b = 16/4)\nand (9b = 14c ==> b/c = 14/9)\n==> a:b = 16:4 and b:c = 14:9\na:b:c = 64:14:9\nAnswer: Option D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJohn invested part of his savings into a investment X that earned a profit of 10% and the rest of the savings into an investment Y that lost 15%. If John neither made a profit nor a loss, then what fraction of his savings was invested in investment X?\n\n### Options:\nA. 3/5\nB. 2/3\nC. 7/10\nD. 3/4\nE. 4/5\n\n### Answer:\nX(1+10/100) + Y(1-15/100) = X+Y\nthis gives 2X = 3Y\nor X/Y = 3/2\nSo, fraction invested in X = 3/5\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the difference of two numbers is 3 and the difference of their square is 39, then the larger number is:\n\n### Options:\nA. 9\nB. 2\nC. 12\nD. 14\nE. 8\n\n### Answer:\nLet the numbers be x and y\nThen x2-y2=39\nAnd x-y=3\nWe get x+y=13\nSolving x-y=3, x+y=13\nX=8, y=5\nLarger number 8\nANSWER E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA = {2,0, 1, -3, 6, -8}\nB = {-1, 2, -4, 7,-6,20}\nIf a is a number that is randomly selected from Set A, and b is a number that is randomly selected from Set B, what is the probability that ab > 0?\n\n### Options:\nA. 1/4\nB. 1/3\nC. 5/12\nD. 4/9\nE. 1/2\n\n### Answer:\nFor the product of 2 numbers to be positive either both of them must be positive or both of them must be negative:\nP(positive, positive) = 3/6*3/6 = 9/36;\nP(negative, negative) = 2/6*3/6 = 6/36.\nP = 9/36 + 6/36\n= 15/36\n= 5/12.\nAnswer: C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA and B Started a business with Rs.15000 and 12000 respectively. After 6 months B puts Rs.1000 more in his capital while after 8 months A puts Rs.5000 more in his capital. If there is a profit of Rs.35,000 after one year then B will get\n\n### Options:\nA. Rs.15,000\nB. Rs.18,000\nC. Rs.16,000\nD. Rs.20,000\nE. Rs.22,000\n\n### Answer:\nRatio of A and B\n=15000*8+20,000*4 : 12000*6+1300*6\n= 4 :3\nThen B will get\n= 3/7*35,000\n=15,000\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA gets 3 times as much money as B gets, B gets only Rs.25 more then what C gets. The three gets Rs.675 in all. Find the share of B?\n\n### Options:\nA. 130\nB. 120\nC. 218\nD. 140\nE. 145\n\n### Answer:\nA+B+C = 675\nA = 3B\n3B+B+B-25 = 675\n5B = 700\nB = 140\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA person says that their speed while going to a city was 10mph however while\nreturning as there is no much traffic they came with a speed of 15mph. what is their\naverage speed?\n\n### Options:\nA. 12\nB. 13\nC. 14\nD. 15\nE. 16\n\n### Answer:\nAvg speed= 2xy/x+y\nHence Ans: 12\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nKim purchased n items from a catalog for $8 each. Postage and handling charges consisted of $5 for the first item and $1 for each additional item. Which of the following gives the total dollar amount for Kim\u2019s purchase, including postage and handling, in terms of n ?\n\n### Options:\nA. 8n + 2\nB. 8n + 4\nC. 9n + 2\nD. 9n + 3\nE. 9n + 4\n\n### Answer:\nits C\nn items for $8 each\ntotal price $8n\npostage and handling of $3 for 1st item and $1 for the rest\ntotal postage and handling = $ [5+ (n-1)]\n= $ n+4\ntotal cost\n8n+n+4 = 9n+4\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOn retirement, a person gets 1.53 lakhs of his provident fund which he invests in a scheme at 20% p.a. His monthly income from this scheme will be\n\n### Options:\nA. 2,450\nB. 2,500\nC. 2,550\nD. 2,600\nE. None of these\n\n### Answer:\nLet S.I. = x\n= 1.53\u00d710(5)\u00d720/100\n= 2,500\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a coconut grove, (x + 3) trees yield 60 nuts per year, x trees yield 120 nuts per year and (x \u2013 3) trees yield 180 nuts per year. If the average yield per year per tree be 100, find x.\n\n### Options:\nA. 3\nB. 4\nC. 5\nD. 6\nE. None of the above\n\n### Answer:\n(x+3)\u00d760+x\u00d7120+(x\u22123)\u00d7180/(x+3)+x+(x\u22123)=100\n\u21d2 360x\u2212360/3x = 100\n\u21d2 60x = 360 \u21d2 x = 6\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAlok ordered 16 chapatis, 5 plates of rice, 7 plates of mixed vegetable and 6 ice-cream cups. The cost of each chapati is Rs.6, that of each plate of rice is Rs.45 and that of mixed vegetable is Rs.70. The amount that Alok paid the cashier was Rs.931. Find the cost of each ice-cream cup?\n\n### Options:\nA. 25\nB. 76\nC. 29\nD. 12\nE. 20\n\n### Answer:\nExplanation:\nLet the cost of each ice-cream cup be Rs.x\n16(6) + 5(45) + 7(70) + 6(x) = 931\n96 + 225 + 490 + 6x = 931\n6x = 120 => x = 20.\nAnswer:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the smallest positive integer x, such that 1,152x is a perfect cube?\n\n### Options:\nA. 4\nB. 6\nC. 8\nD. 12\nE. 18\n\n### Answer:\nWe need to make 1152x a perfect cube, hence we need to have the powers a multiple of 3\n1152 = 2^7*3^2\nThe minimum value of x for which 1152x is a perfect cube = 2^2*3 = 12\nCorrect Option: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are 100 students in a certain geometry class. If one half of the students are boys and one fifth of the boys are under six feet tall, how many boys in the class are under six feet tall?\n\n### Options:\nA. 6\nB. 10\nC. 18\nD. 24\nE. 27\n\n### Answer:\nTotal Students = 100\nOne half of the students are boys = 1/2*100 = 50\nOne fifth of the boys are under six feet tall = 1/5*50 = 10 ...\nTherefore Number of boys in the class under six feet tall = 10 ... Answer B....\nAlternatively... Number of boys in the class under six feet tall = 1/5 of 1/2 of Total Students = 1/5*1/2*100 = 10...\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how many ways the letters of the word MOUSE be arranged?\n\n### Options:\nA. 140\nB. 150\nC. 160\nD. 120\nE. 170\n\n### Answer:\nTotal ways of arranging the letters = 5! = 120 ways.\nD)\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA 300 m long train crosses a platform in 39 sec while it crosses a signal pole in 18 sec. What is the length of the platform?\n\n### Options:\nA. 100 m\nB. 350 m\nC. 25 m\nD. 30 m\nE. 35 m\n\n### Answer:\nExplanation:\nSpeed = 300/18 = 50/3 m/sec.\nLet the length of the platform be x meters.\nThen, (x + 300)/39 = 50/3\n3x + 900 = 1950 => x = 350 m.\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf each year the population of the country grows by 50%, how many years will elapse before the population of the country doubles?\n\n### Options:\nA. 3\nB. 4\nC. 2\nD. 6\nE. 7\n\n### Answer:\nTill Year 2000, population is 100 .\nYear 2001: Population becomes 150 ............. 1 Year elapsed\nYear 2002: Population > 200 ............. 2 Year elapsed\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn one year, the population, of a village increased by 12% and in the next year, it decreased by 12%. If at the end of 2nd year, the population was 14784, what was it in the beginning?\n\n### Options:\nA. 7787\nB. 8000\nC. 15000\nD. 1277\nE. 2081\n\n### Answer:\nx*112/100 * 88/100 = 14784\nX*0.9856=14784\nX=14784/0.9856\n=> 15000\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA fair silver coin with sides marked heads and tails is to be tossed eight times. What is the probability that the coin will land tails side up more than five times?\n\n### Options:\nA. A)37/256\nB. B)56/256\nC. C)65/256\nD. D)70/256\nE. E)81/256\n\n### Answer:\nLanding on tails more than 5 times means tails has to hit 6, 7 or 8 times.\n8!/6!2! = 7*4 = 28\n8!/7!1! = 8\n8!/8! = 1\n28 + 8 + 1 = 37/256\nans:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nBy selling a book for 300, 20% profit was earned. What is the cost price of the book?\n\n### Options:\nA. A)215\nB. B)250\nC. C)230\nD. D)235\nE. E)240\n\n### Answer:\nSP = 120% of CP; :. CP = 300 \u00d7 100/120 = 250\nOption 'B'\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOf the two square fields, the area of the one is 1 hectare, while anothe one is broader by 1%. There differences in area is:\n\n### Options:\nA. 201 m(power)2\nB. 220 m(power)2\nC. 211 m(power)2\nD. 219 m(power)2\nE. 205 m(power)2\n\n### Answer:\nArea of one square field = 10000 m(power)2\n10000 \u00d7 1 = 10000\nSide of this field = \u221a10000 m = 100 m\nSide of another square = 101 m\nDifference of areas = [ 101(power)2 - 100(power)2 ] m(power)2\n[101+100][101-100] m(power)2\n(201)(1) m2 = 201 m(power)2\nAnswer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the greatest number which on dividing 1661 and 2045, leaves a reminder of 10 and 13 respectively\n\n### Options:\nA. 125\nB. 127\nC. 129\nD. 131\nE. 150\n\n### Answer:\nExplanation:\nIn this type of question, its obvious we need to calculate the HCF, trick is\nHCF of (1661 - 10) and (2045 -13)\n= HCF (1651, 2032) = 127\nOption B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRavi's 4days average income is 1025.68. But in a form he should write his average income as the greatest positive even integer less than or equal to his 4days average income. what is the difference between his real average and form filling average?\n\n### Options:\nA. 2\nB. 4.3\nC. 1.68\nD. 1.5\nE. 3.2\n\n### Answer:\nSince Ravi's 4days average income for form filling is defined as the greatest positive even integer less than or equal to his avg income, then avg income for form filling =1024 (the greatest positive even integer less than or equal to 1025.68 is 1024).\nHence the difference = 1025.68 - 1024 = 1.68\nAnswer: C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average age of A and B is 13 years. If C were to replace A, the average would be 24 and if C were to replace B, the average would be 36. What are the age of A, B and C?\n\n### Options:\nA. 22, 18, 20\nB. 20, 20, 18\nC. 24, 0, 48\nD. 25, 01, 47\nE. None of the above\n\n### Answer:\nGiven A + B = 26\u00e2\u20ac\u00a6(i)\nC + B = 48 \u00e2\u20ac\u00a6 (ii)\nA + C = 72\u00e2\u20ac\u00a6(iii)\n(i) + (ii) + (iii) \u00e2\u2021\u2019 A + B + C = 73\u00e2\u20ac\u00a6(iv)\nfrom (i) and (iv), we get\nC = 47 years\n\u00e2\u02c6\u00b4 B = 1 years and A = 25years\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the least possible product of 4 different integers, each of which has a value between \u20136 and 10, inclusive?\n\n### Options:\nA. \u20134320\nB. \u20133600\nC. \u2013720\nD. \u2013600\nE. \u2013120\n\n### Answer:\nMaximize the total product with a -ve sign\nso -6 * 10 * 9 * 8 = 720 * -6 = -4320\nAnswer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain lab experiments with white and brown mice only. In one experiment, 3/7 of the mice are white. If therare24 brown mice in the experiment, how many mice in total are in the experiment?\n\n### Options:\nA. 14\nB. 16\nC. 18\nD. 12\nE. 20\n\n### Answer:\nLet total number of mice = M\nNumber of white mice = 3/7 M\nNumber of brown mice = 4/3 M = 18\n=> M = 18\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the sum The difference between the compound and S.I. on a certain sum of money for 2 years at 10% per annum is Rs.12 of money?\n\n### Options:\nA. 1200\nB. 1992\nC. 9921\nD. 2798\nE. 2789\n\n### Answer:\nP = 12(100/10)2\n=> P = 1200\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a certain state, the ratio of registered Republicans to registered Democrats is 3 to 2, and every registered voter is either a Republican or a Democrat. If 80 percent of the Republicans and 25 percent of the Democrats are expected to vote for Candidate X, and everyone else is expected to vote for Candidate Y, by what percent is Candidate X expected to win the election?\n\n### Options:\nA. 2%\nB. 5%\nC. 16%\nD. 20%\nE. 25%\n\n### Answer:\nSince we were expected to find a percentage figure - It thought that it might be easier to pick a 'smart number' to represent the total number of voters (republicans and democrats). Therefore, I picked 100 (as the total number of voters) and thus 30:20 represents the number ratio of Republicans:Democrats. If 80% of Republicans (which is (60*0.8) = 48) and 25% of Democrats (40*0.25 = 10) voted for candidate X, means that out of total of 100 voters; 58 (48 + 10) voters voted for candidate X and 42 voted for candidate Y. Thus we can infer that candidate X is expected to win the election by 16 (58-42) votes. Therefore candidate X is expected to win the election by (16/100) votes which is equivalent to 16%.\nI think the answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA person starting with Rs.64 and making 6 bets, wins three times and loses 3times, the wins and loses occurring in random order. The chance for a win is equal to the chance for a loss. If each wager is for half the money remaining at the time of the bet, then the final result is?\n\n### Options:\nA. Rs.37\nB. Rs.56\nC. Rs.65\nD. Rs.76\nE. Rs.81\n\n### Answer:\nAs the win leads to multiplying the amount by 1.5 and loss leads to multiplying the amount by 0.5, we will multiply initial amount by 1.5 thrice and by 0.5 thrice (in any order).\nThe overall resultant will remain same.\nSo final amount with the person will be (in all cases):\n=64(1.5)(1.5)(1.5)(0.5)(0.5)(0.5)==64(1.5)(1.5)(1.5)(0.5)(0.5)(0.5)= Rs 2727\nHence the final result is:\n64\u221227=3764\u221227=37:\nA loss of Rs.37\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf xy is an integer, which of the following must also be an integer?\nI. x/y\nII. x\nIII. y/x\n\n### Options:\nA. I alone\nB. II alone\nC. I and II\nD. I and III\nE. None of the above\n\n### Answer:\nLets take X = 3 and Y = 7\nThen XY = 21 which is an integer.\nBut X/Y = 3/7 --> Not an integer.\nY/X = 7/3 --> Not an integer.\nX alone is 3. which is an integer.\nHence B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf x/y=4 and y is not '0' what % of x is 2x-y\n\n### Options:\nA. 150%\nB. 175percent\nC. 200%\nD. 250%\nE. 350%\n\n### Answer:\nlet z be the percent\nx*z/100= 2x-y\nzx=7y* 100\nz=700y/4y\nz=350/2\nz=175%\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf A^4 + B^4 = 100, then the greatest possible value of B is between\n\n### Options:\nA. 0 and 1\nB. 1 and 2\nC. 2 and 3\nD. 3 and 4\nE. 4 and 5\n\n### Answer:\nfor the greatest possible value of B^4, we must minimize the value of B^4 i.e. lets say A^4 = 0\nthen we need to find a number B such that B^4 < 100. 3^4 = 81 and 4^4 = 256 so we can say that the maximum possible value of B can be a little more than 3 hence answer = between 3 and 4\nhence D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf positive integers x is even and y is odd, which of the following must be odd?\n\n### Options:\nA. 2xy\nB. 3x+y-1\nC. x+y\nD. x + y -1\nE. 3(x + y) - 3\n\n### Answer:\nLet x = 2 and y = 1\n2xy = 2*2*1 = 4\n3x+y-1 = 3*2 + 1 -1 = 6\nx+y = 2+1 = 3\nx+y-1 = 2+1-1 = 2\n3(x+y) - 3 = 6+3-3 = 6\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n#p is defined as 2p-20 for any number p. What is p, if #(#(#p))=12?\n\n### Options:\nA. \u2013108\nB. 19\nC. 10\nD. 16\nE. 18\n\n### Answer:\n#p = 2p-20 --->#(#p) = 2(2p-20)-20 = 4p-60 and thus #(4p-60) = 2(4p-60)-20 = 8p-140 = 12 ---> 8p= 152 ---> p = 19, B is the correct answer.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTough and Tricky questions: Percents.\nOver the course of a year, a certain microbrewery increased its beer output by 50 percent. At the same time, it decreased its total working hours by 0 percent. By what percent did this factory increase its output per hour?\n\n### Options:\nA. 125\nB. 130\nC. 150\nD. 155\nE. 160\n\n### Answer:\nLets assume the initial production was 100 litres of beer for 100 hr.\nWith the 50% increase the total amount of beer production will be 150 litres\n100hr ----> 100 lts\n1hr -----> 1 lts\n100hr -----> 150 lts\n1hr -----> 1.5 lts\nTotal Increase in production for 1 hr = 150%\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many positive integers less than 100 have a reminder 5 when divided by 7?\n\n### Options:\nA. 11\nB. 12\nC. 13\nD. 14\nE. 15\n\n### Answer:\ntake the multiples of 7 and add 5\n0X7+5=5 ....13X7+5=96\nthere are 14 numbers\nanswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a 3-member subcommittee is to be formed from a certain 8-member committee, how many different such subcommittee are possible?\n\n### Options:\nA. 6\nB. 18\nC. 40\nD. 108\nE. 216\n\n### Answer:\nAnother way:\n1st member can be selected in 8 ways\n2nd can be selected in 6 ways\n3rd can be selected in 5 ways\nSo total ways : 240\nBut to avoid the similar scenarios 240/3!=40\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAnand and Deepak started a business investing Rs. 22,500 and Rs. 35,000 respectively. Out of a total profit of Rs. 13,800, Deepak's share is?\n\n### Options:\nA. 8428\nB. 8199\nC. 8400\nD. 8419\nE. 8412\n\n### Answer:\nRatio of their shares = 22500 : 35000 = 9:14\nDeepak's share = 13800 * 14/23\n= Rs. 8400.\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAt 6\u2032o a clock ticks 6 times. The time between first and last ticks is 40 seconds. How long does it tick at 12\u2032o clock\n\n### Options:\nA. 47\nB. 88\nC. 28\nD. 66\nE. 11\n\n### Answer:\nExplanation:\nFor ticking 6 times, there are 5 intervals.\nEach interval has time duration of 40/5 = 8 secs\nAt 12 o'clock, there are 11 intervals,\nSo total time for 11 intervals = 11 \u00d7 8 = 88 secs.\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many seconds will a 600 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?\n\n### Options:\nA. 22\nB. 36\nC. 99\nD. 77\nE. 12\n\n### Answer:\nSpeed of train relative to man = 63 - 3 = 60 km/hr.\n= 60 * 5/18 = 50/3 m/sec.\nTime taken to pass the man = 600 * 3/50 = 36 sec.\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nConvert the following into a fraction:1.0%\n\n### Options:\nA. 1/1\nB. 10/1\nC. 1/10\nD. 1/100\nE. None of the Above\n\n### Answer:\n1.0% =1/1\nAnswer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a group of hats consisting of only blue hats, green hats, and purple hats, the ratio of blue hats to green hats to purple hats is 7:4:12. If there are a total of 161 hats in this group, how many of these hats are not blue?\n\n### Options:\nA. 28\nB. 112\nC. 48\nD. 64\nE. 76\n\n### Answer:\nB:G:P = 7:4:12 --> total of 23 parts.\nNot blue = (G + P)/(total)*92 = 16/23*161 = 112.\nAnswer: B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA luxury liner, Queen Marry II, is transporting several cats as well as the crew (sailors, a cook, and captain) to a nearby port. Altogether, these passengers have 15 heads and 42 legs. How many cats does the ship host?\n\n### Options:\nA. 5\nB. 6\nC. 7\nD. 8\nE. 9\n\n### Answer:\nsa's +co +ca +cats = 15. sa's + 1 +1 +cats =15 or sa's +cats =13.\nsa's(2) +2 +2 +cats*4 =42 sa's*2 +cats*4 = 38 or sa's +cats*2 =19 or 13-cats +cat*2 =19\nthen cats =6\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a tire rotates at 400 revolutions per minute when the car is traveling 72km/h, what is the circumference of the tire?\n\n### Options:\nA. 7 meters\nB. 9 meters\nC. 8 meters\nD. 5 meters\nE. 3 meters\n\n### Answer:\n400 rev / minute = 400 * 60 rev / 60 minutes\n= 24,000 rev / hour\n24,000 * C = 72,000 m : C is the circumference\nC = 3 meters\ncorrect answer E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe true discount on Rs. 2562 due 4 months hence is Rs. 122. The rate percent is?\n\n### Options:\nA. 12%\nB. 13%\nC. 15%\nD. 14%\nE. 18%\n\n### Answer:\nExplanation:\nP.W = 2562 - 122 = Rs.2440\nRate=100\u00d7122/2440\u00d713Rate=100\u00d71222440\u00d713\n=15%\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many alphabets need to be there in a language if one were to make 1 million distinct 3 digit initials using the alphabets of the language?\n\n### Options:\nA. 254\nB. 100\nC. 132\nD. 503\nE. 50\n\n### Answer:\n1 million distinct 3 digit initials are needed.\nLet the number of required alphabets in the language be \u2018n\u2019.\nTherefore, using \u2018n\u2019 alphabets we can form n * n * n = n^3 distinct 3 digit initials.\nNote distinct initials is different from initials where the digits are different.\nFor instance, AAA and BBB are acceptable combinations in the case of distinct initials while they are not permitted when the digits of the initials need to be different.\nThis n^3 different initials = 1 million\ni.e. n^3 = 106 (1 million = 106)\n=> n^3 = (102)^3 => n = 102 = 100\nHence, the language needs to have a minimum of 100 alphabets to achieve the objective.\nAns:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf two dice are thrown together, the probability of getting an even number on both dice is\n\n### Options:\nA. 1/4\nB. 1/5\nC. 1/6\nD. 1/3\nE. 1/2\n\n### Answer:\nThe number of exhaustive outcomes is 36.\nLet E be the event of getting an even number on both dies is 9/36 = 1/4\nP(E) = 1/4.\nA)\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a = -0.4, which of the following is true?\n\n### Options:\nA. a < a^2 < a^3\nB. a^2 < a^3 < a\nC. a^2 < a < a^3\nD. a < a^3 < a^2\nE. a^3 < a < a^2\n\n### Answer:\na=-0.4;\na^2=0.16;\na^3=-0.064;\nAnswer : D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA single discount equivalent to the discount series of 20%, 10% and 5% is?\n\n### Options:\nA. 20\nB. 99\nC. 7878\nD. 656\nE. 27\n\n### Answer:\nSP2 = 2/3 SP1\nCP = 100\nSP2 = 80\n2/3 SP1 = 80\nSP1 = 120\n100 --- 20 => 20% Answer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich of the following is closest to the difference between sum E of all proper fractions (fractions less than 1) in the form 1/x , where x is a positive digit, and the product of all proper fractions in the form y/(y+1), where y is a positive digit?\n\n### Options:\nA. 2.82\nB. 2.72\nC. 1.82\nD. 1.72\nE. 0.82\n\n### Answer:\nSum E of all proper fractions (fractions less than 1) in the form 1/x, where x is a positive digit:\n1/1 + 1/2 + 1/3 +.....+ 1/9\nThis is a harmonic progression. Harmonic progression is inverse of arithmetic progression.\nApproximate sum of a harmonic progression with even number of terms = number of terms * (average of middle 2 terms)\nApproximate sum of a harmonic progression with odd number of terms = number of terms * (middle term)\nThe actual sum will be slightly more than the approximation.\nHere we have 9 terms (odd).\nSum = 9 * 1/5\n= 9/5\nProduct of all proper fractions in the form y/(y+1), where y is a positive digit:\n1/2 * 2/3 * 3/4 *.....*9/10\nWe will be left with 1/10.\nRequired = 9/5 - 1/10\n= 1.8 - 0.1\n= 1.7\nClosest is 1.72\nAnswer (D).\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe cost price of a radio is Rs.1500 and it was sold for Rs.1230, find the loss %?\n\n### Options:\nA. 18%\nB. 19%\nC. 28%\nD. 38%\nE. 16%\n\n### Answer:\n1500 ---- 270\n100 ---- ? => 18%\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA and B start a business with Rs.6000 and Rs.8000 respectively. Hoe should they share their profits at the end of one year?\n\n### Options:\nA. 3:3\nB. 3:4\nC. 3:8\nD. 3:1\nE. 3:2\n\n### Answer:\nThey should share the profits in the ratio of their investments.\nThe ratio of the investments made by A and B =\n6000 : 8000 => 3:4.Answer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nShekhar started a business investing Rs.25,000 in 1999.In 2000,he invested an additional amount of Rs.10,000 and Rajeev joined him with an amount of Rs.35,000.In 2001,Shekhar invested another additional amount of Rs.10,000 and Jatin joined them with an amount of Rs.35,000.What will be Rajeev\u2019s share in the profit of Rs.1,50,000 earned at the end of 3 years from the start of the business in 1999 ?\n\n### Options:\nA. Rs.45,000\nB. Rs.50,000\nC. Rs.70,000\nD. Rs.75,000\nE. None of these\n\n### Answer:\nSolution\nShekhar : Rajeev : Jatin\n= (25000x12+35000x12+45000x12) :(35000x24) : (35000x12)\n= 1260000 : 840000 : 420000 = 3 : 2 : 1.\n\u2234 Rajeev\u2019s share = Rs.(15000x2/6) = Rs. 50,000. Answer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nLloyd normally works 7.5 hours per day and earns $4.00 per hour. For each hour he works in excess of 7.5 hours on a given day, he is paid 1.5 times his regular rate. If Lloyd works 10.5 hours on a given day, how much does he earn for that day?\n\n### Options:\nA. $33.75\nB. $48.00\nC. $51.75\nD. $54.00\nE. $70.00\n\n### Answer:\nDaily working hour*Regular Rate + Overtime*Increased Rate\n7.5*4.0+ 3*4.0*1.5=48\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA pipe can fill a cistern in 20 minutes whereas the cistern when fill can be emptied by a leak in 70 minutes. When both pipes are opened, find when the cistern will be full?\n\n### Options:\nA. 17 minutes\nB. 87 minutes\nC. 70 minutes\nD. 28 minutes\nE. 11 minutes\n\n### Answer:\n1/20 - 1/70 = 1/28\n28 minutes\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA sum fetched a total simple interest of Rs. 4016.25 at the rate of 9 p.c.p.a. in 5 years.What is the sum ?\n\n### Options:\nA. Rs. 4462.50\nB. Rs. 8032.50\nC. Rs. 8900\nD. Rs. 8925\nE. None of these\n\n### Answer:\nSolution\nPrincipal = Rs. (100x4016.25/9x5)= Rs.401625/25= Rs. 8925.\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA fair price shopkeeper takes 10% profit on his goods. He lost 20% goods during theft. His loss percent is:\n\n### Options:\nA. 8\nB. 10\nC. 11\nD. 12\nE. 13\n\n### Answer:\nExplanation:\nSuppose he has 100 items. Let C.P. of each item be Re. 1.\nTotal cost = Rs. 100. Number of items left after theft = 80.\nS.P. of each item = Rs. 1.10\nTotal sale = 1.10 * 80 = Rs. 88\nHence, loss % = 12/100 * 100 = 12%\nAnswer is D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe harmonic mean of two numbers xx and yy, symbolized as h(x,y)h(x,y), is defined as 2 divided by the sum of the reciprocals of xx and yy, whereas the geometric mean g(x,y)g(x,y) is defined as the square root of the product of xx and yy (when this square root exists), and the arithmetic mean m(x,y)m(x,y) is defined as x+y2x+y2. For which of the following pairs of values for xx and yy is g(x,y)g(x,y) equal to the arithmetic mean of h(x,y)h(x,y) and m(x,y)m(x,y)?\n\n### Options:\nA. x=\u22122 y=\u22121\nB. x=\u22121, y=2\nC. x=2, y=8\nD. x=8, y=8\nE. x=8, y=64\n\n### Answer:\nA. x=\u22122 , y=\u22121\nB. x=\u22121 , y=2\nC. x=2 , y=8\nD. x=8 , y=8\nE. x=8 , y=64\nThe arithmetic mean, the geometric mean and the harmonic mean of two equal numbers are equal((x+x)/2=x, sqrt(x*x)=x, (2x*x)/(x+x)=x).\nSo without tedious calculation, (D) should be answer.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nEnrollment in City College in 1980 was 85/3 percent of enrollment in 1990. What was the percent increase in the college\u2019s enrollment from 1980 to 1990?\n\n### Options:\nA. 100%\nB. 16 2/3 %\nC. 200%\nD. 253%\nE. 183 1/3%\n\n### Answer:\nAssume 100 enrollments present in 1990\n85/3 % of 1990 = enrollments on 1980\nenrollments on 1980 = 28.33\n% change = (enrollment in 1990 - enrollment in 1980)*100/(enrollment in 1980)\n=(100 - 28.33) *100 / 28.333\n= 7166.67 / 28.333\n= 253 %\nAns - D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf Rs. 782 is divided into three parts, proportional to\n1/2:2/3:3/4\n\n### Options:\nA. 190\nB. 204\nC. 220\nD. 230\nE. 250\n\n### Answer:\nExplanation:\n1/2:2/3:3/4\n=6:8:9\nFirst part =782\u22176/23\n=204\nANSWER IS B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n5% people of a village in Sri Lanka died by bombardment, 15% of the remainder left the village on account of fear. If now the population is reduced to 3553, how much was it in the beginning?\n\n### Options:\nA. 4400\nB. 3000\nC. 4200\nD. 5000\nE. 5500\n\n### Answer:\nX * (95/100) * (85/100) = 3553\nX = 4400\nANSWER A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 85 percent of the test takers taking an old paper and pencil GMAT exam answered the first question on a given math section correctly, and 70 percent of the test takers answered the second question correctly, and 5 percent of the test takers answered neither question correctly, what percent answered both correctly?\n\n### Options:\nA. 60 %\nB. 65 %\nC. 70%\nD. 75%\nE. 80%\n\n### Answer:\n{Total} = {First correctly} + {Second correctly} - {Both correctly} + {Neither correctly}\n100 = 85 + 70 - {Both correctly} + 5\n{Both correctly} = 60.\nAnswer: A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain industrial loom weaves 0.128 meters of cloth every second. Approximately how many seconds will it take for the loom to weave 25 meters of cloth?\n\n### Options:\nA. 205\nB. 200\nC. 180\nD. 195\nE. None of these\n\n### Answer:\nExplanation :\nLet the required number of seconds be x\nMore cloth, More time, (direct proportion)\nHence we can write as\nCloth0.128:25}::1:x\n\u21d20.128x=25\n\u21d2x = 25/128 = 25000/128 = 3125/16 \u2248 195. Answer : Option D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nin base 7, a number is written only using digits 0,1,2,3,4,5,6. the number 135 in base 7 is 1*72+3*7+5=75 in base 10. what is the sum of the base 7 numbers 1234 & 6543 in base 7?\n\n### Options:\nA. 11101\nB. 11110\nC. 10111\nD. 11011\nE. 11010\n\n### Answer:\n4+3=7 since base is 7 so it will become 0 giving 1 carry to next digits(so 4+7=0)\n3+4 + 1 carry from above step= 1 and 1 carry to next digit\n2+5 + 1 carry to next digit= 1 and 1 carry\n1+6= 11\nso ans=11110\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe rate of increase of the price of sugar is observed to be two percent more than the inflation rate expressed in percentage. The price of sugar, on January 1, 1994, is Rs. 18 per kg. The inflation rate for the years 1994 and 1995 are expected to be 6% each. The expected price of sugar on January 1, 1996 would be\n\n### Options:\nA. 20.99\nB. 21.9\nC. 25.4\nD. 20.19\nE. None of these\n\n### Answer:\nExplanation :\nIncrease in the price of sugar = (6+2)= 8%\nHence, price of the sugar on Jan 1, 1996\n=> (18 * 108 * 108)/( 100 * 100 ) = Rs 20.99.\nAnswer : A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA small beaker is 1/2 filled with salt water. Another beaker, which has five times the capacity of the small beaker, is 2/5 filled with fresh water. After dumping all of the salt water from the small beaker into the large beaker, to what fraction of its capacity will the large beaker be filled?\n\n### Options:\nA. 5/6\nB. 4/5\nC. 3/4\nD. 2/3\nE. 1/2\n\n### Answer:\n1/2 of the small beaker is 1/10 of the large beaker.\n1/10 + 2/5 = 1/2\nThe answer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA 150 meter long train crosses a man standing on the platform in 3 sec. What is the speed of the train?\n\n### Options:\nA. 176 kmph\nB. 108 kmph\nC. 176 kmph\nD. 134 kmph\nE. 180 kmph\n\n### Answer:\nS = 150/3 * 18/5\n= 180 kmph\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a die has 3,4 and 1,6 and 2,5 opposite each other, then how many such dies can be made.\n\n### Options:\nA. 13\nB. 3\nC. 5\nD. 12\nE. 11\n\n### Answer:\nthere are 3 pairs . consider it A,B,C\nA-(1,6)\nB-(3,4)\nC-(2,5)\nNow the possible combinations to place A B C is 6.\nbecause for A - 3 possible place\nB- 2 POSSIBLE PLACE\nC-1 POSSIBLE PLACE\n3*2*1=6\nNOW A HAS TWO PAIR SO POSSIBLE COMBO FOR 1 AND 6 IS 2 ..SAME FOR B AND C\n2+2+2=6\nSO 6+6=12\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf A is thrice as fast as B and together can do a work in 18 days. In how many days A alone can do the work?\n\n### Options:\nA. 36\nB. 42\nC. 24\nD. 54\nE. 45\n\n### Answer:\nA\u2019s one day\u2019s work= 1/X\nB\u2019s one day\u2019s work= 1/3x\nA + B\u2019s one day\u2019s work= 1/x + 1/3x = 1/18\n= 3+1/3x = 4/3x = 1/18\nx = 18*4/3 = 24\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJones covered a distance of 50 miles on his first trip. On a later trip he traveled 300 miles while going three times as fast. His new time compared with the old time was\n\n### Options:\nA. three times as much\nB. twice as much\nC. the same\nD. half as much\nE. a third as much\n\n### Answer:\nLet speed of the 1st trip x miles / hr. and speed of the 2nd trip 3x / hr.\nWe know that\nSpeed = Distance/Time.\nOr, Time = Distance/Speed.\nSo, times taken to covered a distance of 50 miles on his first trip = 50/x hr.\nAnd times taken to covered a distance of 300 miles on his later trip = 300/3x hr.\n= 100/x hr.\nSo we can clearly see that his new time compared with the old time was: twice as much.\nAnswer: (B)\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMachines X and Y produce bottles at their respective constant rates. Machine X produces k bottles in 4 hours and machine Y produces k bottles in 5 hours. How many hours does it take machines X and Y , working simultaneously , to produce 10k bottles?\n\n### Options:\nA. 8 2/3\nB. 12 5/3\nC. 15\nD. 18\nE. 22 2/9\n\n### Answer:\nx rate = k/4\ny rate = k/5\nk/4 + k/5 = 10k / T\nsolving T = 200/9 = 22 (2/9)\nAnswer E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe present population of a town is 300. Population increase rate is 10% p.a. Find the population of town after 1 years?\n\n### Options:\nA. 100\nB. 120\nC. 200\nD. 220\nE. 330\n\n### Answer:\nP = 300\nR = 10%\nRequired population of town = P*(1 + R/100)^T\n= 300*(1 + 10/100)\n= 300*(11/10)\n= 330\nAnswer is E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe HCF of two numbers is 52 and the other two factors of their LCM are 11 and 12. What is the largest number.\n\n### Options:\nA. 624\nB. 450\nC. 480\nD. 504\nE. 555\n\n### Answer:\nExplanation:\nHCF of the two numbers = 52\nHCF will be always a factor of LCM\n52 is factor of LCM\nother two factors are 11 & 12\nThen the numbers are (52 *11) and (52 x 12)\n= 572 and 624\nAnswer: Option A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA mixture of 150 liters of wine and water contains 20% water. How much more water should be added so that water becomes 25% of the new mixture?\n\n### Options:\nA. 65 liters\nB. 88 liters\nC. 10 liters water\nD. 45 liters\nE. 8 liters\n\n### Answer:\nNumber of liters of water in150 liters of the mixture = 20% of 150 = 20/100 * 150 = 30 liters.\nP liters of water added to the mixture to make water 25% of the new mixture.\nTotal amount of water becomes (30 + P) and total volume of mixture is (150 + P).\n(30 + P) = 25/100 * (150 + P)\n120 + 4P = 150 + P => P = 10 liters. Answer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA, B and C invested Rs.6300, Rs.4200 and Rs.10500 respectively, in a partnership business. Find the share of A in profit of Rs.14200 after a year?\n\n### Options:\nA. 3630\nB. 9232\nC. 4260\nD. 2387\nE. 2813\n\n### Answer:\n6300:4200:10500\n3:2:5\n3/10 * 14200 = 4260\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average (arithmetic mean) of the even integers from 0 to 40 inclusive is how much greater than the average (arithmetic mean) of the even integers from 0 to 20 inclusive?\n\n### Options:\nA. 10\nB. 20\nC. 5\nD. 30\nE. 15\n\n### Answer:\nSo, according to A mean of a set of even numbers from 0 to 40 =(0+40)/2=20 and mean of a set of even numbers from 0 to 20 =(0+20)/2=10\nDifference=20-10=10\nAnswer: A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man buy a book in Rs50 & sale it Rs80. What is the rate of profit ???\n\n### Options:\nA. 10%\nB. 60%\nC. 30%\nD. 25%\nE. 28%\n\n### Answer:\ncp=50\nsp=80\nprofit=80-50=30\n%=30/50*100=60%\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOne day, Connie plays a game with a fair 6-sided die. Connie rolls the die until she rolls a 6, at\nwhich point the game ends. If she rolls a 6 on her first turn, Connie wins 6 dollars. For each\nsubsequent turn, Connie wins 1\n6 of the amount she would have won the previous turn. What is\nConnie's expected earnings from the game?\n\n### Options:\nA. 32/31\nB. 33/31\nC. 34/31\nD. 36/31\nE. 0/31\n\n### Answer:\nConnie has a 1\n6 chance of winning 6 dollars her first turn. She has a 5/6\n1/6 chance of\nwinning 1 dollar her second turn. Next, she has a 25\n36\n1/6 chance of winning 1/6 dollars her third turn.\nGeneralizing, Connie's expected earnings form a geometric series with initial term 1/6 *6 = 1 and\ncommon ratio 5/6* 1/6 = 5/36 . Hence, Connie's expected earnings are\n1/1- 5/36\n=\n36/31\ncorrect answer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a man can cover 14 metres in one second, how many kilometres can he cover in 3 hours 30 minutes?\n\n### Options:\nA. 165km\nB. 170km\nC. 176.4km\nD. 180km\nE. 190km\n\n### Answer:\n14 m/s = 14 * 18/5 kmph\n3 hours 30 minutes = 3 1/2 hours = 7/2 hours\nDistance = speed * time = 14 * 18/5 * 7/2 km = 176.4 km.\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many such 3's are there in the following number sequence which are immediately Preceded by an odd number and immediately f ollowed by an even number? 5 3 8 9 4 3 7 2 3 8 1 3 8 4 2 3 5 7 3 4 2 3 6\n\n### Options:\nA. 1\nB. 2\nC. 3 three\nD. 4\nE. More than four\n\n### Answer:\nA is followed by B means : A comes first,B comes next\nA preceded by B means : B comes first, A comes next\nThe sets which satisfy the condition is: 5 3 8\n1 3 8\n7 3 4\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n597**6 is divisible by both 3 and 11. The non-zero digits in the Hundred\u2019s and ten\u2019s places are respectively:\n\n### Options:\nA. 3 and 6\nB. 7 and 9\nC. 2 and 6\nD. 4 and 7\nE. None\n\n### Answer:\nSolution : Let the given number be 597xy6.\nThen (5+9+7+x+y+6)=(27+x+y) must be divisible by 3\nAnd, (6+x+9)-(y+7+5)=(x-y+3) must be either 0 or divisible by 11. x-y+3=0\n=> y=x+3 27+x+y)\n=>(27+x+x+3)\n=>(30+2x)\n=> x = 3 and y = 6.\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFor what values of k will the pair of equations 6x + 8y = 24 and kx + 12y = 30 does not have a unique solution?\n\n### Options:\nA. 12\nB. 9\nC. 3\nD. 7.5\nE. 2.5\n\n### Answer:\nwe have 2 equations\n1. 6x + 8y = 24 --> 3x + 4y = 12 -- > 9x + 12y = 36\n2. kx + 12y = 30\nsubstract 1-2, we get (9-K)x = 6\ni.e. x = 6/(9-k)\nthen, by looking at options, we get some value of x except for B. When we put k=9, x becomes 6/0 and hence answer is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average age of students of a class is 15.8 years. The average age of boys in the class is 16.4 years and that of the girls is 15.7 years. The ration of the number of boys to the number of girls in the class is?\n\n### Options:\nA. 1:6\nB. 2:3\nC. 2:5\nD. 2:1\nE. 2:4\n\n### Answer:\nLet the ratio be k : 1. Then,\nk * 16.4 + 1 * 15.7 = (k + 1) * 15.8\n= (16.4 - 15.8)k = (15.8 - 15.7)\n= k = 0.1/0.6 = 1/6\nRequired ratio = 1/6 : 1 = 1:6.\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA boat crossed a lake from East to West at the speed of 5 km/h, entered a river and covered twice as much distance going upstream at 4 km/h. It then turned around and stopped at the south shore of the lake. If it averaged 3.6 km/h that day, what was its approximate downstream speed?\n\n### Options:\nA. 4\nB. 5\nC. 6\nD. 7\nE. 8\n\n### Answer:\nOne way of solving this is:\nSpeed of boat on still water (lake)=5kmph\nSpeed upstream = 4kmph = speed in still water - speed of river => speed of river = 1kmph\n=>Speed downstream = speed in still water + speed of river = 5+1 =6kmph\nAns is C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe total of the ages of Amar, Akbar and Anthony is 66 years. What was the total of their ages four years ago ?\n\n### Options:\nA. 71\nB. 44\nC. 54\nD. 16\nE. 18\n\n### Answer:\nExplanation:\nRequired sum = (66 - 3 x 4) years = (66 - 12) years = 54 years.\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?\n\n### Options:\nA. 29\nB. 77\nC. 28\nD. 10\nE. 12\n\n### Answer:\nlb = 150\n2(l + b) = 50 => l + b = 25\nl \u2013 b = 5\nl = 15 b = 10\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf (2 to the x) - (2 to the (x-2)) = 3 (2 to the 12), what is the value of x?\n\n### Options:\nA. 9\nB. 11\nC. 13\nD. 15\nE. 14\n\n### Answer:\nI am guessing the question is:\n(2 to the power x) - (2 to the power (x-2)) = 3 (2 to the power 12)\n2^x - 2^(x-2) = 3. 2^12\nHence x = 14.\nAnswer is E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n50% of a number is added to 120, the result is the same number. Find the number?\n\n### Options:\nA. 300\nB. 277\nC. 240\nD. 99\nE. 121\n\n### Answer:\n:\n(50/100) * X + 120 = X\n2X = 480\nX = 240\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJoshua and Jose work at an auto repair center with 2 other workers. For a survey on health care insurance, 2 of the 6 workers will be randomly chosen to be interviewed. What is the probability that Joshua and Jose will both be chosen?\n\n### Options:\nA. 1/15\nB. 1/12\nC. 1/9\nD. 1/6\nE. 1/3\n\n### Answer:\nTwo Methods\n1) Probability of chosing Josh first = 1/4\nProbability of chosing Jose second = 1/3\ntotal = 1/12\nProbability of chosing Jose first = 1/4\nProbability of chosing Josh second = 1/3\nTotal = 1/12\nFinal = 1/12 + 1/12 = 1/6\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n10 men and 15 women together can complete a work in 7 days. It takes 100 days for one man alone to complete the same work. How many days will be required for one woman alone to complete the same work?\n\n### Options:\nA. 127 days\nB. 667 days\nC. 177 days\nD. 187 days\nE. 350 days\n\n### Answer:\n1 man's 1 day work = 1/100\n(10 men + 15 women)'s 1 day work = 1/7\n15 women's 1 day work = (1/7 - 10/100) = 3/70\n1 woman's 1 day work = 1/350\n1 woman alone can complete the work in 350 days.\nAnswer:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain car can travel 40 minutes on a gallon of gasoline at 60 miles per hour. If the car had started with a full tank and had 8 gallons of gasoline left in its tank at the end, then what percent of the tank was used to travel 120 miles at 60 mph?\n\n### Options:\nA. 15%\nB. 20%\nC. 25%\nD. 27%\nE. 40%\n\n### Answer:\nTotal time for travelling 120 miles @ 60 mph = 120/60 = 2 hour = 120 minutes.\nGiven, the car uses 1 gallon for every 40 minutes of driving @ 60 mph. Thus in 120 minutes it will use = 3 gallons. Thus, full tank = 3+8 = 11 gallons --->3/11= 27% of the fuel used. D is the correct answer.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the average (arithmetic mean) of (2a+16) and (3a-8) is 74, what is the value of a?\n\n### Options:\nA. 25\nB. 30\nC. 28\nD. 36\nE. 42\n\n### Answer:\n((2a+16) + (3a-8)) / 2 = (5a+8)/2 = 74\na= 28\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nShawn and Raquel want to have gardens that are the same size. Shawn plants a garden 25 feet by 24 feet. Raquel wants one side of his garden to be 30 feet. How long should the other side be?\n\n### Options:\nA. 22\nB. 29\nC. 20\nD. 15\nE. 18\n\n### Answer:\nS1 S2 = R1 R2\nSo 25*24 = 30*R2=> R2 = 20\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf X is invested in a bank at a rate of simple interest of y% p.a. for two years, then the interest earned is 400. if X is invested at y% p.a., for two years when the interest is compounded annually, the interest is 410. What is the value of X?\n\n### Options:\nA. 8000\nB. 6000\nC. 5000\nD. 4000\nE. 3000\n\n### Answer:\nSimple way to solve this question is to use options.\nFrom SI, we know that X*y=20,000.\nNow, put the value of X = 4000, we will have y = 5%\nTo calculate CI,\nNow, we know 1st year Amount= 4000+5% of 4000= 4200.\n2nd year, Amount = 4200 + 5% of 4200 = 4410.\nWe can see after 2 years Interest = 4410-4000= 410. hence, it satisfies the question. Hence D is the correct answer\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many integers from 101 to 900, inclusive, remains the value unchanged when the digits were reversed?\n\n### Options:\nA. 50\nB. 60\nC. 70\nD. 80\nE. 90\n\n### Answer:\nquestion is asking for palindrome\nfirst digit possibilities - 1 through 8 = 8\n9 is not possible here because it would result in a number greater than 9 (i.e 909 , 919..)\nsecond digit possibilities - 0 though 9 = 10\nthird digit is same as first digit\n=>total possible number meeting the given conditions = 8 *10 = 80\nAnswer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA and B complete a work in 10 days. A alone can do it in 40 days. If both together can do the work in how many days?\n\n### Options:\nA. 1.0875 days\nB. 0.125 days\nC. 0.0675 days\nD. 0.0875 days\nE. 0.0775 days\n\n### Answer:\n1/10 + 1/40 = 0.125 days\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n50, 47, 45, 42, 40, 37, 35, 32, ?\n\n### Options:\nA. 31\nB. 30\nC. 29\nD. 28\nE. 27\n\n### Answer:\nThis is an alternating number subtraction series. The pattern is -3, -2, -3, -2, ....\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nat a special sale 5 ticket can be purchased as a price of 3 ticket, if 5 ticket are purchased at the sale, the amount saved will be what % of the original price of the 5 ticket.\n\n### Options:\nA. 10%\nB. 20%\nC. 30%\nD. 40%\nE. 50%\n\n### Answer:\nlet the price of 1 ticket be Rs.10\nOriginal C.P. of 5 tickets = Rs.50\nAfter sale 5 Tickets were bought for Rs. 30\n%amount saved = ((50-30)/50)*100 = 40%\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe ratio between the sale price and the cost price of an article is 4:3. What is the ratio between the profit and the cost price of that article?\n\n### Options:\nA. 2:9\nB. 2:5\nC. 3:6\nD. 2:0\nE. 1:3\n\n### Answer:\nLet C.P. = Rs. 3x and S.P. = Rs. 4x.\nThen, Gain = Rs. x\nRequired ratio = x : 3x = 1:3\nAnswer:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRs. 6000 is lent out in two parts. One part is lent at 5% p.a simple interest and the other is lent at 10% p.a simple interest. The total interest at the end of one year was Rs. 450. Find the ratio of the amounts lent at the lower rate and higher rate of interest?\n\n### Options:\nA. 5:1\nB. 5:5\nC. 5:8\nD. 5:4\nE. 5:2\n\n### Answer:\nLet the amount lent at 5% be Rs. x\nAmount lent at 10% is Rs. (6000 - x)\nTotal interest for one year on the two sums lent\n= 5/100 x + 10/100 (6000 - x) = 600 - 1x/20\n=> 600 - 1/20 x = 450 => x = 3000\nAmount lent at 10% = 3000\nRequired ratio = 3000 : 3000 = 5:5\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA type Q machine can complete a job in 5 hours and a type B machine can complete the job in 7 hours. How many hours will it take 2 type Q machines and 3 type B machines working together and independently to complete the job?\n\n### Options:\nA. 1/5\nB. 29/35\nC. 5/6\nD. 35/29\nE. 35/12\n\n### Answer:\nnow D should be the answer.\nQ need 5 hours to complete\nand B needs 7 hours to compete\nso 2Q + 3B will complete 2/5 + 3/7 or 29/35 portion of the job in 1 hour\nso the whole job will take 35/29 hours....=D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAnne and Katherine are both saving money\nfrom their summer jobs to buy bicycles. If\nAnne had $150 less, she would have exactly 1/3\nas much as Katherine. And if Katherine\nhad twice as much, she would have exactly\n3 times as much as Anne. How much\nmoney have they saved together?\n(\n\n### Options:\nA. $300\nB. $400\nC. $450\nD. $625\nE. $750\n\n### Answer:\nIf Anne had $150 less, Katherine would have three times more than Anne. Make this\nstatement into an equation and simplify:\n3(a \u2013 150) = k\n3a \u2013 450 = k\nAnd if Katherine had twice as much, she would have three times more than Anne:\n2k = 3a\nSubstitute 3a \u2013 450 for k into the last equation and solve for a\n2(3a \u2013 450) = 3a\n6a \u2013 900 = 3a\n\u2013900 = \u20133a\n300 = a\nNow substitute 300 for a into the same equation and solve for k:\n2k = 3(300)\n2k = 900\nk = 450\nThus, together Anne and Katherine have 300 + 450 = 750\ncorrect answer E)$750\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nP is four times as fast as Q and working together, they can complete a work in 20 days. In how many days can Q alone complete the work?\n\n### Options:\nA. 35 days\nB. 15 days\nC. 16 days\nD. 25 days\nE. 18 days\n\n### Answer:\nP = 4Q\nP + Q = 4Q + Q = 5Q\nThese 5Q people can do the work in 20 days, which means Q can do the work in 100 days.\nHence, P can do the work in 25 days.\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 85 percent of the test takers taking an old paper and pencil GMAT exam answered the first question on a given math section correctly, and 80 percent of the test takers answered the second question correctly, and 5 percent of the test takers answered neither question correctly, what percent answered both correctly?\n\n### Options:\nA. 60 %\nB. 65 %\nC. 70%\nD. 75%\nE. 80%\n\n### Answer:\n{Total} = {First correctly} + {Second correctly} - {Both correctly} + {Neither correctly}\n100 = 85 + 80 - {Both correctly} + 5\n{Both correctly} = 70.\nAnswer: C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSreenivas sells a table to Shiva at 10% profit and Shiva sells it to Mahesh at 10% loss. At what price did Sreenivas purchase the table if Mahesh paid Rs. 2772?\n\n### Options:\nA. 2277\nB. 2669\nC. 2200\nD. 2800\nE. 2998\n\n### Answer:\nLet the cost price of table for Sreenivas be Rs. x and given that, cost price of table for Mahesh = Rs. 2772.\n=> (90%) of (110%) of x = Rs. 2772.\n=> (90/100)(110/100)x = 2772\n=> x = (2772 * 100)/(9 * 11)\n=> x = Rs. 2800\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA cistern is filled by a tap in 6 1/2 hours. Due to leak in the bottom of the cistern, it takes half an hour longer to fill the cistern. If the cistern is full how many hours will it take the leak to empty it?\n\n### Options:\nA. 81\nB. 85\nC. 88\nD. 91\nE. 95\n\n### Answer:\nfilling rate - leak rate = net rate\n1/6.5 - leak rate = 1/7\nleak rate = 2/13 - 1/7 = 1/91\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nit is a small town railway station and there are 25 stations on that line.at each of the 25 stations the passengers can get tickets for any other 24 stations.how many different kind of tickets do you think the booking clerk has to keep?\n\n### Options:\nA. 24\nB. 25\nC. 26\nD. 27\nE. 28\n\n### Answer:\n600 different kind of tickets booking clerk has to keep.\n24 type of tickets are to be issued from each originating station.\nTherefore, 25*24 = 600 tickets\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSolve the inequality\n{(x^2)-7|x|+10}/{(x^2)-6x+9}\n\n### Options:\nA. -3\nB. -5\nC. 3\nD. 5\nE. 0\n\n### Answer:\ntaking one time |x| as +ve we get x=5 while\ntaking |x| as -ve we get x= -5\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nGopi gives Rs. 90 plus one turban as salary to his servant for one year. The servant leaves after 9 months and receives Rs. 60 and the turban. Find the price of the turban.\n\n### Options:\nA. 27\nB. 30\nC. 29\nD. 10\nE. 11\n\n### Answer:\nLet the price of turban be x.\nThus, for one year the salary = (90 + x)\nFor 9 months he should earn 3434 (90 + x).\nNow he gets one turban and Rs. 60.\nThus, 3434 (90 + x) = 60 + x or 270 + 3x = 240 + 4x or x = 30\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMr. Wayne bungee jumps from the top of a building straight to the ground at a constant speed. 3 seconds after he starts plummeting he passes the 20th floor. 15 seconds after he starts plummeting he passes the 5th floor. Each floor is 3.6 meters high. What is Mr. Wayne's speed in meters per second?\n\n### Options:\nA. 3\nB. 3.75\nC. 4.5\nD. 4.25\nE. 5\n\n### Answer:\nIMO: C\n15 Floors * 3.6 Meter/Floor = 54 Meters\nTime= 12 sec\nRate * 12 = 54\nRate= 54/12\n=4.5\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAfter allowing a discount of 15% on the marked price, the selling price is Rs. 6800 for an article. If it was sold at marked price, there would have been a profit of 60%. The cost price of the article is?\n\n### Options:\nA. 2338\nB. 2298\nC. 5000\nD. 2871\nE. 1171\n\n### Answer:\nExplanation:\nGiven SP = Rs. 6800\nMarked price = [SP(100)]/(100 - d%) = (6800 * 100)/(100 - 15) = Rs. 8000\nIf SP = Rs. 8000, profit = 60%\nCP = [SP(100)]/(100 + 60) = (8000 * 100)/160 = Rs. 5000\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA polling company surveyed a certain country, and it found that 35% of that country\u2019s registered voters had an unfavorable impression of both of that state\u2019s major political parties and that 20% had a favorable impression only of Party Q. If one registered voter has a favorable impression of both parties for every two registered voters who have a favorable impression only of Party B, then what percentage of the country\u2019s registered voters have a favorable impression of both parties (assuming that respondents to the poll were given a choice between favorable and unfavorable impressions only)?\n\n### Options:\nA. 15\nB. 20\nC. 30\nD. 35\nE. 45\n\n### Answer:\nS=100\nnot( Q and B ) =35\nonly Q=20\n(Q and B)/B=1/2\nlet ( Q and B ) =x\nonly B =2x\nso now, 20+35+x+2x=100\nx= 15\nA ans\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe product of x and y is a constant. If the value of x is increased by 50%, by what percentage must the value of y be decreased?\n\n### Options:\nA. 50%\nB. 40%\nC. 33 1\u20443%\nD. 25%\nE. 12 1\u20442%\n\n### Answer:\nProduct of x and y = xy\nIf the value of x is increased by 50% , value of y needs to be = xy/(1.5 x ) = 2/3 y\nDecrease in value of y = y - 2/3 y = 1/3 y\n% decrease in value of y = (1/3 y)/y * 100%\n=33 1\u20443%\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAjay spends 25 per cent of his salary on house rent, 5 percent on food, 15 percent travel, 10 percent on clothes and the remaining amount of Rs.27000 is saved. What is Ajay\u2019s income?\n\n### Options:\nA. Rs.60000\nB. Rs.80500\nC. Rs.60700\nD. Rs.70500\nE. None of these\n\n### Answer:\nExplanation:\nSavings = Income \u2013 expenditure\n100 \u2013 (25+5+15+10) = 45%\n45% of income = Rs.27000\n:. Income = 27000 x 100/45 = Rs. 60000.\nAnswer: Option A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich is better investment: 11% stock at 143 or 9% stock at 117?\n\n### Options:\nA. 9 3/4% stock at 119\nB. 9 3/4% stock at 117\nC. 9 3/4% stock at 112\nD. 9 3/4% stock at 118\nE. 9 3/4% stock at 111\n\n### Answer:\nLet investment in each case be Rs. (143 x 117).\nIncome in 1st case = Rs. 11\tx 143 x 117 = Rs. 1287.\n143\nIncome in 2nd case = Rs. 39\tx 143 x 117 = Rs. 1394.25\n4 x 117\nClearly, 9\t3\t% stock at 117 is better.\n4\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average age 10 members of a committee are the same as it was 2 years ago, because an old number has been replaced by a younger number. Find how much younger is the new member than the old number?\n\n### Options:\nA. 14 years\nB. 17 years\nC. 20 years\nD. 12 years\nE. 11 years\n\n### Answer:\n10 * 2\n= 20\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf n = 8^9 \u2013 8, what is the units digit of n?\n\n### Options:\nA. 4\nB. 0\nC. 1\nD. 2\nE. 3\n\n### Answer:\n8 ^ 9 - 8 = 8 (8 ^ 8 - 1)\n==> 8 (2 ^ 24 - 1)\nLast digit of 2 ^ 24 is 6 based on what explanation LiveStronger is saying. 2 ^ 24 - 1 yields 6 - 1 = 5 as the unit digit. Now on multiply this with 8, we get unit digit as 0\nAnswer : B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a group of cows and hens, the number of legs are 20 more than twice the number of heads. The number of cows is :\n\n### Options:\nA. 5\nB. 6\nC. 7\nD. 10\nE. 12\n\n### Answer:\nLet no of cows be x, no of hens be y.\nSo heads=x+y\nLegs=4x+2y\nNow, 4x+2y = 2(x+y)+ 20\n2x = 20\nx = 10.\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA pipe can fill a cistern in 20 minutes whereas the cistern when fill can be emptied by a leak in 60 minutes. When both pipes are opened, find when the cistern will be full?\n\n### Options:\nA. 17 minutes\nB. 87 minutes\nC. 30 minutes\nD. 27 minutes\nE. 11 minutes\n\n### Answer:\n1/20 - 1/60 = 1/30\n30 minutes\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA fence consists of m lengths of fence that are each n feet long. A fence post separates each length of fence by its width of x feet. What is the total length Q of the fence including the fence posts on each end?\n\n### Options:\nA. mn\nB. m(n + x)\nC. Q=m(n + x) + x\nD. m(n + x) + 2x\nE. 2mn\n\n### Answer:\nNotice that since a fence post separates each length of fence, then there will be m+1 posts, for example if there are m=2 fences, then there will be 3 posts: PFPFP. Thus the total length of the posts is (m+1)x.\nThe total length Q of the fence is mn, therefore the total length of the fence including the fence posts on each end is (m+1)x+mn=mx+x+mn=m(n+x)+x.\nAnswer: C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nx/(y/z)\nIn the expression above, x, y, and z are different numbers and each is one of the numbers 1, 5, or 6. What is the least possible value of the expression?\n\n### Options:\nA. 6/5\nB. 2/15\nC. 5/6\nD. 3/10\nE. 6/6\n\n### Answer:\nx/(y/z)\n= (x*z)/y\nThe expression will have the least value when numerator (x*z) is the smallest.\n= (1*5)/6\n=5/6\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nM = {-6, -5, -4, -3, -2, -1}\nT = {-4, -3, -2, -1, 0, 1, 2, 3, 4, 5}\nIf an integer is to be randomly selected from set M above and an integer is to be randomly selected from set T above, what is the probability that the product of the two integers will be negative?\n\n### Options:\nA. 0\nB. 1/3\nC. 2/5\nD. 1/2\nE. 3/5\n\n### Answer:\nWe will have a negative product only if 1, 2, 3, 4, or 5 are selected from set T.\nP(negative product) = 5/10 = 1/2\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n5 goats\u2019s and 10 hens are brought for Rs.2500. If the average price of a hen be Rs.50. What is the average price of a goat.\n\n### Options:\nA. 425\nB. 375\nC. 350\nD. 400\nE. 500\n\n### Answer:\nExplanation:\nAverage price of a hen = Rs.50\ntotal price of 10 hens = 10*50 = Rs.500\nBut total price of 5 goats and 10 hens = Rs. 2500\nTotal price of 5 goats is = 2500 - 500\n= 2000\nAverage price of a goat = 2000/5\n= Rs. 400\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many different arrangements are possible to place seven different books on a shelf if all three math books must be placed next to each other?\n\n### Options:\nA. 120\nB. 148\nC. 360\nD. 540\nE. 720\n\n### Answer:\nLet the 3 math books be M1,M2,M3 while the rest be A,B,C,D for a total of 7 different books.\nConsider 3 math books to be 1 collective item (=M1M2M3 = M , as they need to be together). Thus, number of arrangements of 3 different books (M1M2M3)= 3P3 = 3!\nTotal number of arrangements of M,A,B,C,D = 5P5= 5!\nThus, The total possible arrangements will be : M1M2M3 ABCD = 5!*3! = 720, E is the correct answer\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf radius of a circle is diminished by 10% then its area is diminished by\n\n### Options:\nA. 22\nB. 19\nC. 877\nD. 26\nE. 271\n\n### Answer:\nExplanation:\nLet old radius = 10 units.\nNew radius is diminshed by 10%. So new radius = 90% (10) = 9 units.\nOld area = \u03c0 \u00d7 r2 = 100\u03c0\nNew area = \u03c0 \u00d7 92 = 81\u03c0\nChange = 19\u03c0/100\u03c0 \u00d7100 = 19%\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWorking alone at its constant rate, machine A produces x boxes in 10 minutes and working alone at its constant rate, machine B produces x boxes in 5 minutes. How many minutes does it take machines A and B, working simultaneously at their respective constant rates, to produce 3x boxes?\n\n### Options:\nA. 3 minutes\nB. 4 minutes\nC. 10 minutes\nD. 6 minutes\nE. 12 minutes\n\n### Answer:\nRate = Work / Time\nGiven Rate of Machine A = X / 10 min\nMachine B Produces 2x boxes in 5 min hence , Machine B produces 4x boxes in 10 min .\nRate of Machine B = 2x / 10\nwe need tofind the combined time that machines A and B, working simultaneouslytakeat their respective constant rates\nlet's first find the combined Rate of Machine A and B\nRate of Machine A = X / 10 min + Rate of Machine B = 2x / 10 = 3X/10\nNow combine Time = combine work needs to be done / Combine Rate = 3x/3x * 10 = 10 Min\nAns: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train running at the speed of 60 km/hr crosses a pole in 18 seconds. Find the length of the train?\n\n### Options:\nA. 150 meter\nB. 876 meter\nC. 300 meter\nD. 719 meter\nE. 169 meter\n\n### Answer:\nSpeed = 60*(5/18) m/sec = 50/3 m/sec\nLength of Train (Distance) = Speed * Time\n(50/3) * 18\n= 300 meter\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA fraction bears the same ratio to 1/27 as 3/7 does to 5/9. The fraction is?\n\n### Options:\nA. 1/35\nB. 2/35\nC. 3/45\nD. 4/25\nE. 4/27\n\n### Answer:\nLet the fraction be x. Then,\nx:1/27 = 3/7 : 5/9\nx \u00d7 5/9 = 1/27 \u00d7 3/7\nx \u00d7 5/9 = 1/9 \u00d7 1/7\nx \u00d7 5/9 = 1/63\nx \u00d7 5 = 9/63\n5x = 1/7 = 1/35\nA)\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nEvaluate the expression\n[x : (y - 3)] \u22c5 (-4) - [xy + (-3)] : -1 = ?\nwhen x = -5 and y = -2\n\n### Options:\nA. 3\nB. 4\nC. 5\nD. 6\nE. None\n\n### Answer:\nSolution:\nEvaluate the expression\n[x : (y - 3)] \u22c5 (-4) - [xy + (-3)] : -1 =\n[(-5) : (-2 - 3)] \u22c5 (-4) - [(-5) \u22c5 (-2) + (-3)] : -1 =\n[(-5) : (-5)] \u22c5 (-4) - [10 + (-3)] : -1 =\n(+1) \u22c5 (-4) - (+7) : -1 = -4 - (-7) = -4 + 7 = 3\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a certain mathematical activity, we have five cards with five different prime numbers on them. We will distribute these five cards among three envelope: all could go in any envelope, or they could be broken up in any way among the envelopes. Then in each envelop, we find the product of all the cards in that envelope: that is the \u201cnumber\u201d of the envelope. An envelope containing no cards has the number 1. We then put the three envelope numbers in order, from lowest to highest, and that is our set. How many different W sets can be produced by this process?\n\n### Options:\nA. 41\nB. 89\nC. 125\nD. 243\nE. 512\n\n### Answer:\nCase 1: 1 used envelope => 1 way\nCase 2: 2 used envelopes\n- 4-1-0: Choose 4 from 5 cards: 5 ways\n- 3-2-0: Choose 3 from 5 cards: 10 ways\nCase 3: All envelopes used\n- 3-1-1: Choose 3 from 5 andno need to choose 1 from 2: 10 ways\n- 2-2-1: Choose 2 from 5 and choose 2 from 3, but two groups are the same => (10X3):2 = 15\nTotal W: 1+5+10+10+15=41 => Answer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nCan anyhow help me with an easy solution for this\n2, 3, 9, 5, 6, 81, 6, 7, ?\n\n### Options:\nA. 256\nB. 221\nC. 121\nD. 144\nE. 169\n\n### Answer:\n2, 3, 9, 5, 6, 81, 6, 7, ?\n2+73=5 and 5-2=3 and 3^2=9\n5+6=11 and 11-2=9 and 9^2=81\n6+7=13 and 13-2=11 and 11^2=121\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA cistern which could be filled in 8 hours takes one hour more to be filled owing to a leak in its bottom. If the cistern is full in what time will the leak empty it?\n\n### Options:\nA. 76 hrs\nB. 99 hrs\nC. 55 hrs\nD. 90 hrs\nE. 40 hrs\n\n### Answer:\n1/8 - 1/x = 1/10\n=> 40 hrs\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSudesh was standing in the garden early in the morning after sunrise. His sister Gauri, who was coming from the opposite directions, saw that Sudesh's shadow had fallen to his right. Which directions was Gauri facing?\n\n### Options:\nA. North\nB. South\nC. South-West\nD. North-East\nE. None of these\n\n### Answer:\nas sun rises from east so the boy's shadow must be fall behind him that means toward west ......if the boy is facing towards north then and only then his sister is able to see a shadow had fallen to his right side\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf A,B,C,D,E,F,G,H,I,J are in an decreasing Arithmetic Progression as such. Then Which of the following operations will result in either mean or the median being modified.\nA) A is replaced by J\nB) A and H are removed\nC) B and I are removed\nD) A,B,C,H,I,J are removed\nE) A and D are removed\n\n### Options:\nA. 1) A and B\nB. 2) A and E\nC. 3) A,B,E\nD. 4) All of them\nE. 5) None of them\n\n### Answer:\nHere answer will be (C).\nThere are 10 equidistant numbers on the number line.\nMean and median will be the average of middle two numbers.\nIf you remove two numbers which is equidistant from either extreme (e.g. B and I), the total deviation on either side of the mean stays the same so mean stays the same. Also, the median is still the average of middle two numbers. Other changes will affect the mean and median.\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFrom a vessel on the first day, 1/3rd of the liquid evaporates. On the second day 3/4th of the remaining liquid evaporates. what fraction of the volume is present at the end of the 2 day\n\n### Options:\nA. 1/3\nB. 1/4\nC. 1/5\nD. 1/6\nE. 1/7\n\n### Answer:\nlet x be the volume...\nafter 1st day volume remaining=(x-x/3)=2x/3\nafter 2st day volume remaining=(2x/3)-((2x/3)*(3/4))\n=(2x/3)(1-3/4)=(2x/3)*(1/4)=x/6\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average weight of 5 person's increases by 5.5 kg when a new person comes in place of one of them weighing 68 kg. What might be the weight of the new person?\n\n### Options:\nA. 60 kg\nB. 95.5 kg\nC. 80 kg\nD. 85 kg\nE. 90 kg\n\n### Answer:\nTotal weight increased = (5 x 5.5) kg = 27.5 kg.\nWeight of new person = (68 + 27.5) kg = 95.5 kg\nOption B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA student was asked to find 4/5 of a number. But the student divided the number by 4/5, thus the student got 9 more than the correct answer. Find the number.\n\n### Options:\nA. 16\nB. 18\nC. 20\nD. 22\nE. 24\n\n### Answer:\nLet the number be x.\n(5/4) * x = (4/5)*x + 9\n25x = 16x + 180\n9x = 180\nx = 20\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich of the following correctly lists the data sets in order of greatest to least standard deviation?\nI. 8, 9, 10, 11, 12, 13\nII. 12, 12, 12, 12, 12, 12\nIII. 47, 56, 58, 60, 64, 69\n\n### Options:\nA. I, II, III\nB. I, III, II\nC. III, I, II\nD. II, III, I\nE. II, I, III\n\n### Answer:\nout of three given sets,\nII has all numbers same, so it has zero standard deviation hence it is Least\nI has consecutive numbers , hence all are closedly spaced hence std deviation will be less\nwhile in III,numbers are spread widely hence std deviation should be more than II\nhence order should be II, I,III\nIMO E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA woman has $133,982 in her savings account. What is the least amount of money (in whole number of dollars) that she must add to her account if she wants to split this money evenly among her Three children?\n\n### Options:\nA. $1\nB. $11\nC. $3\nD. $2\nE. none\n\n### Answer:\nTo find the least amount the woman should add to her saving account to split the money evenly among her 3 children,\nshe needs to make the total divisible by 3\nSimply add the individual digits of the total = 1+3+3+9+8+2=26\nIf you add 1 , the number is divisible by 3 (26+ 1)\nCorrect Option : A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe GDP of a country is $13.8 billion, and the total production of one of its industries is $3.3 billion. If the GDP were to grow by 5% per year in the future, which of the following would be the MINIMUM required annual growth in this industry that would it represent more than half of the GDP in ten years?\n\n### Options:\nA. 10%\nB. 15%\nC. 20%\nD. 25%\nE. 35%\n\n### Answer:\nGDP in 10 years with this rate would be - 13.8 (1+0.05)^10\nHalf of the above value - 6.9 (1.05)^10\nIndustry's annual growth (say x is the rate of growth of the industry annually) = 3.3 (1+(x/100))^10\nNow, the minimum of above value has to be greater than the half of the value of GDP.\n3.3 (1+(x/100))^10 > 6.9 (1.05)^10\n((1+(x/100))/1.05)^10 > 2 (approx)\nMinimum value of x to satisfy this equation is 15\nHence B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf A and B get profits of Rs.5,000 and Rs.2,000 respectively at the end of year then ratio of their investments are\n\n### Options:\nA. 4:1\nB. 1:4\nC. 5:2\nD. 2:3\nE. 2:5\n\n### Answer:\nRatio = 5000/2000 = 5 : 2\nAnswer : C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf -4 < x < 8 and -6 < y < 3, which of the following specifies all the possible values of xy?\n\n### Options:\nA. -42 < xy < 21\nB. -42 < xy < 24\nC. -48 < xy < 24\nD. -24 < xy < 21\nE. -24 < xy < 24\n\n### Answer:\nThe least value of xy is a bit more than 8*(-6)=-48 and the largest value of xy is a bit less than (-4)*(-6)=24.\nTherefore -48 < xy < 24.\nAnswer: C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat least number must be added to 1056, so that the sum is completely divisible by 23 ?\n\n### Options:\nA. 1\nB. 2\nC. 3\nD. 4\nE. 5\n\n### Answer:\nB\n2\nIf the number 1056 is completely divisible by 23 means, remainder should come zero.\nBut if we divide 1056 by 23, the remainder is 2.\nSo if 2 is added to the 1056, we get remainder 0.\nTherefore solution is 2\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the sum of the odd integers from 35 to 65, inclusive?\n\n### Options:\nA. 800\nB. 550\nC. 555\nD. 600\nE. 605\n\n### Answer:\nThe mean is 50.\nSum=Mean(# of elements)\nThere are 16 odd numbers between 35-65 inclusive. 16*50=800\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMartha has the unique talent of being able to guess other people\u2019s height and weight. For every six people that Martha meets, she consistently guesses the people\u2019s correct height five times, and for every eight people that she meets, she consistently guesses the people\u2019s correct weight six times. If Martha meets three people and her success rate remains constant, what is the probability that Martha correctly guesses a person\u2019s weight and height at least once?\n\n### Options:\nA. 8/27\nB. 2/5\nC. 485/512\nD. 98/125\nE. 625/952\n\n### Answer:\nProbability that she guesses the height correctly P(h)=5/6\nProbability that she guesses the weight correctlyP(w)=6/8\nProbability that she guesses both weight and height correctly(P(h)*P(w))=5/6 * 6/8= 30/48\nNow the Q asks about the probability of this happening atleast once.\nWe calculate it by finding the probability of not being able to guess in any of the three occasions.\nProbability of not being able to guess any no. of times =1-30/48=18/48=3/8\nFor all three occasions P(A)=3/8 * 3/8 * 3/8=27/512\nProbability of the event happening atleast once=1- P(A)=1-27/512=485/512\nAns should be C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAn agent, gets a commission of 2.5% on the sales of cloth. If on a certain day, he gets Rs. 21 as commission, the cloth sold through him on that day is worth\n\n### Options:\nA. 333\nB. 500\nC. 840\nD. 299\nE. 132\n\n### Answer:\nExplanation:\nLet the total sale be Rs. x.\nThen, 2.5%. of x = 21 <=> (25/10 * 1/100 * x) = 21 <=> x = 840.\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJulie decided to save a certain amount of her monthly salary each month and her salary was unchanged from month to month. If Julie 's savings by the end of the year from these monthly savings were four times the amount she spent per month, what should be the fraction of her salary that she spent each month?\n\n### Options:\nA. 5/3\nB. 3/9\nC. 3/2\nD. 3/5\nE. 3/4\n\n### Answer:\nLet Julie 's monthly savings = S\nJulie 's monthly pay = P\nJulie 's monthly expenditure = P-S\nJulie 's savings by the end of the year from these monthly savings were Four times the amount she spent per month\n12S = 4*(P-S)\n=>3S = P-S\n=> P = 4S\nJulie's monthly expenditure = P-S = 4S-S = 3S\nfraction of her salary that Julie spent each month = 3S / 4S=P-S/P = 3/4. Answer is E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMr. Johnson was to earn \u00a3 300 and a free holiday for seven weeks' work. He worked for only 4 weeks and earned \u00a3 30 and a free holiday. What was the value of the holiday?\n\n### Options:\nA. \u00a3 300\nB. \u00a3 330\nC. \u00a3 360\nD. \u00a3 420\nE. \u00a3 460\n\n### Answer:\n7week=300+holiday\n1 week= (300+ holiday)/7\n4 week =(300+ hliday)*4/7-- eqn1\nbt 4 week = 30 + holiday(given)--eqn2\nequate eqn 1 and eqn 2 to get th ecost of holiday=330\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA person buys an article at Rs.480. At what price should he sell the article so as to make a profit of 24%?\n\n### Options:\nA. 595\nB. 882\nC. 772\nD. 662\nE. 521\n\n### Answer:\nCost price = Rs.480\nprofit = 24% of 480 = Rs.115\nSelling price = Cost price + Profit\n= 480 + 115 = 595\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n4 mat-weavers can weave 4 mats in 4 days. At the same rate, how many mats would be woven by 8 mat-weavers in 8 days?\n\n### Options:\nA. 4\nB. 16\nC. 8\nD. 1\nE. 2\n\n### Answer:\nExplanation:\nLet the required number of mats be x\nMore mat-weavers, more mats (direct proportion)\nMore days, more mats (direct proportion)\nHence we can write as\n(mat-weavers) 4:8\n(days) 4:8}::4:x\n\u21d24\u00d74\u00d7x=8\u00d78\u00d74\n\u21d2x=2\u00d72\u00d74=16\nAnswer: Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how many ways can the letters of the word ABROAD be rearranged such that the vowels always appear together?\n\n### Options:\nA. 6!/2!\nB. 3!*3!\nC. 4!/2!\nD. 4! *(3!/2!)\nE. 3!*3!/2\n\n### Answer:\nIn the word ABROAD , there are 3 vowels - 2 A's and O\nNumber of ways the letters of word ABACUS be rearranged such that the vowels always appear together\n= (4! * 3! )/2!\nWe can consider the the 3 vowels as a single unit and there are 3 ways to arrange them . But since 2 elements of vowel group are identical we divide by 2! .\nThe entire vowel group is considered as a single group .\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe ratio of the number of ladies to gents at a party was 1:2 but when 2 ladies and 2 gents left, the ratio became 1:3. How many people were at the party originally?\n\n### Options:\nA. 43\nB. 52\nC. 12\nD. 65\nE. 13\n\n### Answer:\nExplanation:\nx, 2x\n(x-2):(2x-2) = 1:3\n3x-6 = 2x-2\nx = 4\nx+2x = 3x\n=> 3*4 = 12\nAnswer: Option C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSuppose you flip a fair coin 8 times. What is the probability that, in 8 flips, you get at least one head?\n\n### Options:\nA. 55/256\nB. 255/256\nC. 155/256\nD. 5/256\nE. 201/256\n\n### Answer:\nBest way of solving an at least 1 type of question is to compute 1 - probability of flipping 0 heads\nprobability of flipping either a head or a tail = 1/2\nprobability of flipping 3 tails in a row (1/2)^5\nprobability of flipping at least 1 head = 1 - (1/2)^8 = 255/256\nAnswer : B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA merchant can place 8 large boxes or 10 small boxes into a carton for shipping. In one shipment, he sent a total of 96 boxes. If there are more large boxes than small boxes, how many cartons did he ship?\n\n### Options:\nA. 13\nB. 25\nC. 17\nD. 12\nE. 11\n\n### Answer:\n11 cartons total\n7 large boxes (7 * 8 = 56 boxes)\n4 small boxes (4 *10 = 40 boxes\n11 total cartons and 96 boxes\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe total price of a basic computer and printer are $2,500. If the same printer had been purchased with an enhanced computer whose price was $500 more than the price of the basic computer, then the price of the printer would have been 1/4 of that total. What was the price of the basic computer?\n\n### Options:\nA. 1500\nB. 1600\nC. 1750\nD. 1900\nE. 2000\n\n### Answer:\nLet the price of basic computer be C and the price of the printer be P: C+P=$2,500.\nThe price of the enhanced computer will be C+500 and total price for that computer and the printer will be 2,500+500=$3,000. Now, we are told that the price of the printer is 1/4 of that new total price: P=1/4*$3,000=$750.\nPlug this value in the first equation: C+750=$2,500 --> C=$1,750\nAnswer: C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man can swim in still water at 4 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is?\n\n### Options:\nA. 1.3\nB. 7.5\nC. 2.25\nD. 1.5\nE. 4\n\n### Answer:\nM = 4\nS = x\nDS = 4 + x\nUS = 4 - x\n4 + x = (4 - x)2\n4 + x = 8 -2x\n3x = 4\nx = 1.3\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo cards are drawn at random from a pack of 52 cards.what is the probability that either both are black or both are queen\n\n### Options:\nA. 44/221\nB. 55/221\nC. 76/221\nD. 45/221\nE. 63/221\n\n### Answer:\nWE HAVE N(S)=52C2=(52*51)/(2*1)=1326.\nLET A=EVENT OF GETTING BOTH BLACK CARDS\nB=EVENT OF GETTING BOTH QUEENS\nA\uf0c7B=EVENT OF GETTING QUEEN OF BLACK CARDS\nN(A)=26C2=(26*25)/(2*1)=325,\nN(B)=4C2=(4*3)/(2*1)=6 AND\nN(A\uf0c7B)=2C2=1\nP(A)=N(A)/N(S)=325/1326;\nP(B)=N(B)/N(S)=6/1326 AND\nP(A\uf0c7B)=N(A\uf0c7B)/N(S)=1/1326\nP(A\uf0c8B)=P(A)+P(B)-P(A\uf0c7B)=(325+6-1/1326)=330/1326=55/221\nOption: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf q, r, and s are consecutive even integers and q < r < s, which of the following CANNOT be the value of s^2 \u2013 r^2 \u2013 q^2?\n\n### Options:\nA. -20\nB. 0\nC. 8\nD. 12\nE. 16\n\n### Answer:\ns > r > q are consecutive even integers\nTesting for s2\u2212r2\u2212q2\nI: For s = 0, r = -2, q = -4,\ns2\u2212r2\u2212q2=\u221220\nII: For s = 2, r = 0, q = -2\ns2\u2212r2\u2212q2=0\nIII: For s = 4, r = 2, q = 0\ns2\u2212r2\u2212q2=12\nStep II & Step III have consecutive representation of values of s, r, q. No other combination is possible.\n8 cannot be the answer as for value of s = 6 & above, the resultant would be greater than 12\nAnswer = C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nBradley owns b video game cartridges. If Bradley\u2019s total is one-fourth the total owned by James and six times the total owned by Charlie, how many video game cartridges do the three of them own altogether, in terms of b?\n\n### Options:\nA. (16/3)b\nB. (31/6)b\nC. (13/6)b\nD. (19/12)b\nE. (7/12)b\n\n### Answer:\nb = Bradley\u2019s total\n4b = James\u2019s total\n(1/6)b = Charlie\u2019s total\nAdd each total\nb + 4b+ (1/6)b = 5b + (1/6)b = = (31/6)b\nAnswer : B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for Rs. 3200. With the help of C, they completed the work in 3 days. How much is to be paid to C?\n\n### Options:\nA. 375\nB. 400\nC. 600\nD. 800\nE. 550\n\n### Answer:\nC's 1 day's work =1/3-1/6\t+1/7\t=1/3\t-7/24=1/24\t.\nA's wages : B's wages : C's wages =\t1/6 : 1/8 : 1/24= 4 : 3 : 1.\nC's share (for 3 days) = Rs. 3 x\t1/24\tx 3200 = Rs. 400.\nOption B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man sells a book at 5% profit. If he had bought it at 5% less and sold it for Re 1 less, he would have gained 10%. The cost price of the book is\n\n### Options:\nA. Rs 200\nB. Rs 150\nC. Rs 250\nD. Rs 240\nE. None of these\n\n### Answer:\nLet the C.P of the article be Rs X\nProfit = 5%\nTherefore, S.P. = X + 5 % of X = 21X / 20\nIf C.P would have been (X - 5% of X), i.e.,\nRs 19 X / 20 and S.P would have been Rs [ (21 X / 20) - 1 ],\nThen, gain % = 10 %\nTherefore, [ { ( 21 X / 20) - 1 } - 19 X / 20 ] / (19 X /20 ) x 100 = 10\n(2 X - 20 / 19 X) x 100 = 10\n=> X = 200\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMrs. Rodger got a weekly raise of $165. If she gets paid every other week, write an integer describing how the raise will affect her paycheck.\n\n### Options:\nA. $204\nB. $231\nC. $156\nD. $165\nE. $200\n\n### Answer:\nLet the 1st paycheck be x (integer).\nMrs. Rodger got a weekly raise of $ 165.\nSo after completing the 1st week she will get $ (x+165).\nSimilarly after completing the 2nd week she will get $ (x + 165) + $ 165.\n= $ (x + 165 + 165)\n= $ (x + 330)\nSo in this way end of every week her salary will increase by $ 165.\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe number 70 can be written as the sum of the squares of 3 different positive integers. What is the sum of these 3 integers?\n\n### Options:\nA. 17\nB. 16\nC. 15\nD. 14\nE. 13\n\n### Answer:\nI think brute force with some common sense should be used to solve this problem.\nWrite down all perfect squares less than 70: 1, 4, 9, 16, 25, 36, 49, 64.\nNow, 70 should be the sum of 3 of those 8 numbers. Also to simplify a little bit trial and error, we can notice that as 70 is an odd numbers then either all three numbers must be odd (odd+odd+odd=odd) OR two must be even and one odd (even+even+odd=odd).\nWe can find that 60 equals to 9+25+36=3^2+5^2+6^2=70 --> 3+5+6=14.\nAnswer: D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA car traveled 75% of the way from town A to town B at an average speed of 90 miles per hour. The car travels at an average speed of S miles per hour for the remaining part of the trip. The average speed for the entire trip was 40 miles per hour. What is S ?\n\n### Options:\nA. 15\nB. 20\nC. 25\nD. 30\nE. 37.5\n\n### Answer:\nTotal distance = 100 miles (easier to work with %)\n75% of the distance = 75 miles\n25% of the distance = 25 miles\n1st part of the trip \u2192 75/90 = 0.833\n2nd part of the trip \u2192 25/S = t\nTotal trip \u2192 (75+25)/40 = 0.833+ t \u00bb 100/40 = 0.833 + t \u00bb 2.5 = 0.833+ t \u00bb t = 1.667\nBack to 2nd part of the trip formula: 25/S = 1.667 \u00bb S = 15\nAns A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe sector of a circle has radius of 21 cm and central angle 135o. Find its perimeter?\n\n### Options:\nA. 91.5\nB. 91.4\nC. 91.7\nD. 91.3\nE. 91.1\n\n### Answer:\nPerimeter of the sector = length of the arc + 2(radius)\n= (135/360 * 2 * 22/7 * 21) + 2(21)\n= 49.5 + 42 = 91.5 cm\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA, B and C are partners. A receives 2/3 of profits, B and C dividing the remainder equally. A's income is increased by Rs.200 when the rate to profit rises from 5 to 7 percent. Find the Capital of B?\n\n### Options:\nA. 3377\nB. 2899\nC. 2500\nD. 2778\nE. 1991\n\n### Answer:\nA:B:C = 2/3:1/6:1/6 = 4:1:1\nx * 2/100 * 2/3 = 200\nB capital = 15000*1/6 = 2500\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf we know that a positive integer is a multiple of 4, how many (distinct) possibilities are there for the last digit of the integer?\n\n### Options:\nA. 3\nB. 4\nC. 5\nD. 6\nE. 7\n\n### Answer:\nthe last digit of the integer may be any of (0,2,4,6,8)\nso, 1/5\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn Orange County one tenth of the people are gathering mushrooms and one seventh of the people are collecting apples. What can be the number of people in Orange County?\n\n### Options:\nA. 60.\nB. 42.\nC. 85.\nD. 70.\nE. 252.\n\n### Answer:\nThe number must be an integer and multiple of both 10 and 7.\nOnly option D fulfill this condition and hence is the answer.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhen the integer x is divided by the integer y, the remainder is 60. Which of the following is a possible value of the quotient x/y?\nI. 15.19\nII.18.16\nIII. 17.17\n\n### Options:\nA. I only\nB. II only\nC. III only\nD. I and II only\nE. I and III only\n\n### Answer:\nProblem statement was difficult to parse. but some how I managed to understand what we can do.\n1) x/y = 15 + 0.19\n2) x/y = 18 + 0.16\n3) x/y = 17 + 0.17\nw.k.t x = yn (i.e Q) + yk=60 (i.e remainder)\ntherefore :\n1) y*0.19=60 -- we can't get y an integer.\n2) y*0.16=60 -- we can get y an integer.\n3) y*0.17=60 -- we can't get y an integer.\nTherefore 2 are possible answers.\nAns B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nLook at this series: 53, 53, 40, 40, 27, 27, ... What number should come next?\n\n### Options:\nA. 12\nB. 14\nC. 27\nD. 53\nE. None of these\n\n### Answer:\nExplanation:\nIn this series, each number is repeated, then 13 is subtracted to arrive at the next number.\nAnswer: Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA town in California fines residents who do not pay their property taxes on time. All residents must pay their taxes before July 1st for that calendar year or face the following fine structure: For the first month the taxes are overdue (that would be any payment made on July 1st through July 31st), the total fine is 1% of the original tax bill; for each additional month that the taxes are overdue, the total fine is increased by $600 or tripled, whichever results in the lesser amount. What is the total fine for a resident of that town who originally owed $45,000 in property taxes, but did not pay until October 15th?\n\n### Options:\nA. $1,400\nB. $1,800\nC. $2,400\nD. $21,400\nE. $12,150\n\n### Answer:\nOriginal amount = 20,000\nFine for July = 20,000 * 1% = 450\nFine for August = lesser of the 2 , 450+600= 1050 or 450*3=1350 . Pick 1350\nFine for September = 1350+600=1950 or 1350*3 = 4050. Pick 4050\nFine for October = 4050+600=4650 or 4050*3 = 12150. Pick 12150.\nThe wording of the question should be have been clearer as total fines should be = 12150+4050+1350+450 = 18000 and NOT 12150.\n12150 is the fine ONLY for the month of October!\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n10(150) \u00f7 10(146) = ?\n\n### Options:\nA. 10(6)\nB. 100000\nC. 1000\nD. 10000\nE. None of these\n\n### Answer:\n10(150) \u00f7 10(146) = ?\nor ? = 10(150)/10(146)=10(150\u2212146)\ni.e, [m(x)/m(y)=m(x\u2212y)]\n= 10(4) = 10000\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nUSC invited each South Carolina high school to send up to 39 students\nto watch a football game. A section which has 199 seats in each row is\nreserved for those students. What is the least number of rows needed to\nguarantee that if 2006 students show up, then all students from the same\nhigh school can be seated in the same row?\n\n### Options:\nA. 11\nB. 12\nC. 13\nD. 14\nE. 15\n\n### Answer:\nThe answer is 12 rows. If 59 schools send 34 students each, then we can sit at\nmost 5 groups of students in the same row, so we will need 12 rows. Next, 12 rows are\nsufficient. Assume that this is not the case. Suppose the groups of students are seated\nlike this: first the largest group, then the second largest group, then the third largest\ngroup, etc. Suppose we run out of space - there are not enough seats in any row to\nseat together the next group. Suppose the first group that can not be seated together\nis the kth group and it consists of N students. Then k 61 since any row fits at least\n5 groups. Also, N 2006/k 2006/61 < 33 (all groups already seated are no smaller\nthan the kth group). So, N 32. Since there is not enough space in any of the 12 rows\nto seat the kth group, then there must be at least 168 students seated in each of the 12\nrows. Now, 12 \u00d7 168 = 2016 > 2006 a contradiction. So, 12 rows are sufficient.\ncorrect answer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the circumference and area of radius 13 cm.\n\n### Options:\nA. 124 cm\u00b2\nB. 531 cm\u00b2\nC. 354 cm\u00b2\nD. 584 cm\u00b2\nE. 594 cm\u00b2\n\n### Answer:\nArea of circle = \u03c0r\u00b2\n= 22/7 \u00d7 13 \u00d7 13 cm\u00b2\n= 531 cm\u00b2\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAnna worked for h hours each day for d consecutive days. If she earns $3.50 per hour, what is the total amount she earned?\n\n### Options:\nA. 3.50/d + h\nB. 3.50 + d + h\nC. 3.50 + dh\nD. 3.50h + d\nE. 3.50dh\n\n### Answer:\nH hours for d days.\nIncome each day = 3.5*h\nTotal income = 3.5*h*d\nCorrect option: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA new tower has just been built at the Verbico military hospital; the number of beds available for patients at the hospital is now 7 times the number available before the new tower was built. Currently, 1/3 of the hospital's original beds, as well as 1/5 of the beds in the new tower, are occupied. For the purposes of renovating the hospital's original wing, all of the patients in the hospital's original beds must be transferred to beds in the new tower. If patients are neither admitted nor discharged during the transfer, what fraction of the beds in the new tower will be unoccupied once the transfer is complete?\n\n### Options:\nA. 67/90\nB. 29/60\nC. 17/30\nD. 19/30\nE. 11/15\n\n### Answer:\nI think A - 67/90 is the correct answer.\nHere goes:\nLets assume originally the number of beds = x\nAfter the new tower, the total combined no of beds = 7x\nSo old = x, New = 6x\nNow 1/3 of x are occupied and 1/5 of 6x are occupied which simplifies to (6/5)x\nWe are shifting 1/3 of x to the new ward so there will now be:\n1/3 of x plus 6/5 of x occupied in the new ward. Add them up to get 23/15 of x\nThere are 6x beds in New Tower so ratio is:\n(23/15)x / 6x = 23/90 of x\nSubtract that from 90/90 of x and you get the number of un-occupied beds to total capacity of New Tower = 67/90.\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe C.P of 15 books is equal to the S.P of 20 books. Find his gain% or loss%?\n\n### Options:\nA. 28%\nB. 25%\nC. 24%\nD. 23%\nE. 27%\n\n### Answer:\nexplanation:\n15 CP = 20 SP\n20 --- 5 CP loss\n100 --- ? => 25% loss\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf r \u2260 1 and if sr/(s - r) = 1, what is the value of s in terms of r?\n\n### Options:\nA. (r+1)/r\nB. (r - 1)/r\nC. r/(r + 1)\nD. r/(1-r)\nE. (1 - r)/r\n\n### Answer:\nThis question comes with a particular 'quirk' (one that you probably won't see on Test Day). The GMAT won't test you on the concept of undefined numbers (re: numbers divided by 0), so any time that this concept is a possibility, the question writers have to add a restriction that removes the option that a 0 could occur in the denominator.\nHere, we're told that B CANNOT = 1, which is a bit strange because that restriction doesn't seem to impact the original equation much. In fact, it impacts JUST ONE of the answer choices - so you have to ask WHY that restriction is even there. It's actually because that one answer is the correct one.\nFinal Answer:\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nif x/4-x-3/6=1,then find the value of x.\n\n### Options:\nA. 2\nB. 4\nC. 6\nD. 8\nE. 5\n\n### Answer:\n(x /4)-((x-3)/6)=1= (3x-2(x-3) )/12 = 1 = 3x-2x+6=12 = x=6\nAnswer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich of the following fractions is greater than 3 /4 and less than 5 / 6 ?\n\n### Options:\nA. 4/8\nB. 4/5\nC. 4/6\nD. 4/1\nE. 4/4\n\n### Answer:\nExplanation:\n3 /4 = 0.75, 5/6 = 0.833, 1/2 = .5, 2/3 = 0.66, 4/5 = 0.8, 9/10 = 0.9.\nclearly 0.8 lies between 0.75 and .833.\n4/5 lies between 3/4 and 5/6..\nAnswer: B) 4 / 5\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nwhat is the distance between two parallel chords of length 32 cm and 24 cm in a circle of radius 20 cm ?\n\n### Options:\nA. 1 or 7\nB. 3 or 21\nC. 4 or 28\nD. 2 or 14\nE. 5 or 14\n\n### Answer:\nsince the chord length=2sqrrt(r^2-d^2)\nchord length=32,r=20 then we get d=12\nchord length=24,r=20 then we get d=16\nthen we add/subtract we get option c) 4 or 28\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe jogging track in a sports complex is 1000 meters in circumference. Deepak and his wife start from the same point and walk in opposite directions at 20 km/hr and 13 km/hr respectively. They will meet for the first time in?\n\n### Options:\nA. 50min\nB. 33min\nC. 35min\nD. 25min\nE. 20min\n\n### Answer:\nClearly, the two will meet when they are 1000 m apart\nTo be 20+13 = 33 km apart, they take 1 hour\nTo be 1000 m apart, they take 33 * 1000/1000 = 33 min.\nAnswer is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAn empty wooden vessel weighs 14% of its total weight when filled with paint. If the weight of a partially filled vessel is one half that of a completely filled vessel, what fraction of the vessel is filled.\n\n### Options:\nA. 6/13\nB. 5/9\nC. 1/24\nD. 4/9\nE. 2/5\n\n### Answer:\nAn empty wooden vessel weighs 14% of its total weight when filled with paint:\nVessel = 0.14(Vessel + Paint);\n14V = V + P (so the weight of completely filled vessel is 14V)\nP = 13V (so the weight of the paint when the vessels is completely filled is 13V).\nThe weight of a partially filled vessel is one half that of a completely filled vessel:\nV + P' = 1/2*14V;\nP' = 6V (so the weight of the paint when the vessels is partially filled is 6V).\nWhat fraction of the vessel is filled?\nSo, we need to find the ratio of the weight of the paint when the vessel iscompletely filledto the weight of the paint when the vessel ispartially filled:\nP'/P = 6V/13V = 6/13.\nAnswer: A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe ratio of the present age of Viju to that of Aju is 7:2. Four years from now, the ratio of the ages of Viju to Aju will be 5:2. What was Viju age 5 years ago ? (RBI Assistant 2015)\n\n### Options:\nA. 24\nB. 18\nC. 12\nD. 16\nE. 13\n\n### Answer:\nLet the present age of Viju be 7x years and that of Aju be 2x years.\nThen, 4 years from now\n7x + 4 / 2x + 4 = 5 / 2\nor 4x = 12\nor x = 3\nViju present age = 7 * 3 = 21 years\nViju age 5 years ago = 21 - 5 = 16 years\nanswer :D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe daily wage is increased by 50% and a person now gets Rs 25 per day. What was his daily wage before the increase ?\n\n### Options:\nA. Rs 20\nB. Rs 16.6\nC. Rs 18\nD. Rs 19\nE. none of these\n\n### Answer:\nLet A be the daily wages before the increase,\nA ( 1 + x/100) = 25 (Given)\nHere, x = 50\nTherefore, A( 1 + 50/100) = 25\nA = (25 x 100) / (150) = Rs 16.6.\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the remainder when the number R=14^2 * 15^8 is divided by 5?\n\n### Options:\nA. 0\nB. 1\nC. 2\nD. 4\nE. 5\n\n### Answer:\n14^2 has units digit 6\n15^8 has units digit 5\nThus R=14^2*15^8 has units digit 0 and will be divisible by 5. The remainder will be zero\nAnswer: (A)\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA car crosses a 600 m long bridge in 5 minutes. What is the speed of car in km per hr?\n\n### Options:\nA. 7 km/hr\nB. 7.2 km/hr\nC. 7.5 km/hr\nD. 8 km/hr\nE. 8.9 km/hr\n\n### Answer:\nSpeed = 600 m/sec.\n5 x 60\n= 2 m/sec.\nConverting m/sec to km/hr (see important formulas section)\n= 2 x 18 km/hr\n5\n= 7.2 km/hr\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man goes from A to B at a speed of 20 kmph and comes back to A at a speed of 30 kmph. Find his average speed for the entire journey?\n\n### Options:\nA. 20 kmph\nB. 24 kmph\nC. 50 kmph\nD. 35 kmph\nE. 30 kmph\n\n### Answer:\nExplanation:\nDistance from A and B be 'd'\nAverage Speed = total distance/total time\nAverage Speed = (2d)/[(d/20) + (d/30)]\n= (2d)/[5d/60) => 24 kmph.\nANSWER IS B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n0.1+0.1^2+0.1^3 =\n\n### Options:\nA. 0.1\nB. 0.111\nC. 0.1221\nD. 0.2341\nE. 0.3\n\n### Answer:\nYou have a mistake in your question. Choice B should be (.111) and not (.11).\nThe equation in the solution can be simplified to (.1 + .01 + .001).\nAdding those together you get:\n.100\n.010\n.001\n------\n.111 - Which is answer choice (B)\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA bowl contains 3 parts of which are milk and 5 parts water. How much of the mixture must be drawn off and replaced with milk sothat the mixture may be half milk and half water?\n\n### Options:\nA. 2/5\nB. 3/5\nC. 1/5\nD. 1/7\nE. 2/7\n\n### Answer:\nSuppose the vessel initially contains 8 litres of liquid.\nLet x litres of this liquid be replaced with water.\nQuantity of water in new mixture = 3 -\t3x\t+ x litres\n8\nQuantity of syrup in new mixture = 5 -\t5x litres\n8\n3 -\t3x\t+ x = 5 -\t5x\n8\t8\n5x + 24 = 40 - 5x\n10x = 16\nx =\t8\t.\n5\nSo, part of the mixture replaced = 8\tx\t1 =\t1/5\n5\t8\t5\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA 290 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train?\n\n### Options:\nA. 230 m\nB. 210 m\nC. 260 m\nD. 320 m\nE. 330 m\n\n### Answer:\nRelative speed = (120 + 80) km/hr\n=\t(200 x(5/18))m/sec\n=\t(500/9)m/sec.\nLet the length of the other train be x metres.\nThen,\t(x + 290)/9 = 500/9\nx + 290 = 500\nx = 210.\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are 8 stations between Vijayawada and Chennai. How many second class tickets have to be printed, so that a passenger can travel from any station to any other station?\n\n### Options:\nA. 100\nB. 90\nC. 190\nD. 110\nE. 105\n\n### Answer:\nThe total number of stations = 10\nFrom 10 stations we have to choose any two stations and the direction of travel (i.e.,Vijayawada to Chennai is different from Chennai to Vijayawada) in 10P2 ways.\n10P2= 10 * 9 = 90\nANSWER: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe sum of four consecutive odd numbers is equal to the sum of 3 consecutive even numbers. Given that the middle term of the even numbers is greater than 101 and lesser than 208, how many such sequences can be formed?\n\n### Options:\nA. 26\nB. 17\nC. 25\nD. 33\nE. 50\n\n### Answer:\nFour consecutive odd numbers: k-2, k, k+2, k+4\nThree consecutive even numbers: n-2, n, n+2\nk-2+k+k+2+k+4=n-2+n+n+2\n4k+4=3n\n4(k+1)=3n\nk+1=(3/4)n\nk=(3/4)n-1\nAll n's that's divisible by 4 will have an integral k. So, we need to find out how many such n's are available within given range:\nWe know,\n101", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA can do a piece of work in 4 hours; B and C together can do it in 3 hours, while A and C together can do it in 2 hours. How long will B alone take to do it?\n\n### Options:\nA. 12\nB. 9\nC. 8\nD. 6\nE. 5\n\n### Answer:\nA's 1 hour's work = 1 ;\n4\n(B + C)'s 1 hour's work = 1 ;\n3\n(A + C)'s 1 hour's work = 1 .\n2\n(A + B + C)'s 1 hour's work = ( 1 + 1 ) = 7 .\n4 3 12\nB's 1 hour's work = ( 7 - 1 ) = 1 .\n12 2 12\nTherefore A alone will take 12 hours to do the work.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA tree on first day grows 1/2 of its size second day 1/3 of its size on the previous day similarly than 1/4 and so on..U have calculate after how many days the tree will be 100 times of original size.\n\n### Options:\nA. 188 days\nB. 198 days\nC. 178 days\nD. 168 days\nE. 158 days\n\n### Answer:\nsuppose 'x' is initial size and 'n' is no. of days.\n1st day increment in size of tree = (1/2)x\nAfter 1st day , size of tree = x+(1/2)x= (3/2)x\n2nd day increment in size of tree = (1/3)*(3/2)x=(1/2)x\nAfter 2nd day , size of tree = (3/2)x+(1/2)x=2x\n3rd day increment in size of tree =(1/4)*2x=(1/2)x\nAfter 3rd day , size of tree = 2x+(1/2)=(5/2)x\nIt is clear that every day tree grows (1/2)x in size.\ntherefore , according to given condition\nx+ (1/2)x*n=100x\nn=198 days.\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThree numbers are in the ratio 1:4:6 and their H.C.F is 9. The numbers are:\n\n### Options:\nA. 1,4,6\nB. 12,24,36\nC. 10, 20, 30\nD. 12, 24, 36\nE. 9,36,54.\n\n### Answer:\nLet the required numbers be x, 4x and 6x. Then, their H.C.F = x. So, x = 9.\nThe numbers are 9,36,54.\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJohn and Jacob set out together on bicycle traveling at 18 and 15 miles per hour, respectively. After 40 minutes, John stops to fix a flat tire. If it takes John one hour to fix the flat tire and Jacob continues to ride during this time, how many hours will it take John to catch up to Jacob assuming he resumes his ride at 18 miles per hour? (consider John's deceleration/acceleration before/after the flat to be negligible)\n\n### Options:\nA. 3\nB. 3 1/3\nC. 3 1/2\nD. 4\nE. 4 1/3\n\n### Answer:\nJohn's speed - 18 miles/hr\nJacob's speed - 15 miles/hr\nAfter 40min (i.e 2/3hr), distance covered by John = 18x2/3 = 12 miles.\nJacob continues to ride for a total of 1hour and 40min (until John's bike is repaired). Distance covered in 1 hour 40min (i.e 5/3hr) = 15x5/3 = 25 miles.\nNow, when John starts riding back, the distance between them is 13 miles. Jacob and John are moving in the same direction.For John to catch Jacob, the effective relative speed will be 18-15 = 3 miles/hr.\nThus, to cover 13 miles at 3 miles/hr, John will take 13/3 = 4 1/3 hours\nAnswer E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average of five integers is 63, and none of these integers is greater than 100. If the average of three of the integers is 69, what is the least possible value of one of the other two integers?\n\n### Options:\nA. 5\nB. 8\nC. 20\nD. 21\nE. 30\n\n### Answer:\nWhen it comes to averages, we know thataverage value = (sum of n values)/n\nWe can rewrite this into a useful formula:sum of n values = (average value)(n)\nThe average of five integers is 63\nSo, the sum of ALL 5 integers = (63)(5) =315\nThe average of three of the integers is 65\nSo, the sum of the 3 integers = (69)(3) =207\nSo, the sum of the 2 REMAINING integers =315-207=108\nIf the sum of the 2 REMAINING integers =108, and we want to minimize one value, we must MAXIMIZE the other value.\n100 is the maximum value so let 1 integer = 100, which means the other must equal 8\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOne pipe can fill a tank three times as fast as another pipe. If together the two pipes can fill the tank in 35 minutes, then the slower pipe alone will be able to fill the tank in\n\n### Options:\nA. 144 mins\nB. 140 mins\nC. 136 mins\nD. 132 minw\nE. None of these\n\n### Answer:\nExplanation:\nLet the slower pipe alone fill the tank in x minutes\nthen faster will fill in x/3 minutes.\nPart filled by slower pipe in 1 minute = 1/x\nPart filled by faster pipe in 1 minute = 3/x\nPart filled by both in 1 minute =\n1/x+3/x=1/35\n=>4/x=1/35\nx=35\u22174=140 mins\nOption B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat will come in place of the x in the following Number series? 5,28,57,88,125\n\n### Options:\nA. 123\nB. 143\nC. 166\nD. 190\nE. 210\n\n### Answer:\n28=23+5\n57=29+28\n88=31+57\n125=37+88\n166=41+125\n=166\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA company has two types of machines, type R and type S. Operating at a constant rate, a machine of type R does a certain job in 49 hrs and a machine of type S does the same job in 14 hours. If the company used the same number of each type of machine to do the job in 2 hours, how many machines of type R were used?\n\n### Options:\nA. 49/9\nB. 44/9\nC. 46/9\nD. 41/9\nE. 43/9\n\n### Answer:\nRate of machine R =1/49\nRate of machine S =1/14\nsince same no of machines used for R and S to do the same work in 2 hrs\nSo collective rate needed to finish the work in 2 hrs= 1/2\nLet the no of machine be x\nSo, x/49 +x/14 =1/2\n9x=49\nx=49/9\nSo no of machine R is 49/9\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThree liquids were mixed in 5:4:1 ratios. If cost per kg for ach of them is 4.50,\n3.75& 5.10. Then in what price mixture should be sold to get 25% profit?\n\n### Options:\nA. 52.25\nB. 53.25\nC. 54.25\nD. 55.25\nE. 56.25\n\n### Answer:\ncp of the liquid=5*4.50+4*3.75+1*5.10=42.6\nIn order to gain 25%profit\nSp=1.25*42.6=53.25\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA number is doubled and 5 is added. If the resultant is trebled, it becomes 105. What is that number?\n\n### Options:\nA. 9\nB. 15\nC. 18\nD. None of these\nE. Cannot be determined\n\n### Answer:\nExplanation:\nLet the number be x.\nTherefore,\n3(2x + 5) = 105\n6x + 15 = 105\n6x = 90\nx = 15\nANSWER: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSreenivas sells a table to Shiva at 10% profit and Shiva sells it to Mahesh at 10% loss. At what price did Sreenivas purchase the table if Mahesh paid Rs. 2376?\n\n### Options:\nA. 2277\nB. 2400\nC. 2200\nD. 2766\nE. 2998\n\n### Answer:\nLet the cost price of table for Sreenivas be Rs. x and given that, cost price of table for Mahesh = Rs. 2376.\n=> (90%) of (110%) of x = Rs. 2376.\n=> (90/100)(110/100)x = 2376\n=> x = (2376 * 100)/(9 * 11)\n=> x = Rs. 2400\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAt what rate percent on simple interest will Rs.750 amount to Rs.900 in 5 years?\n\n### Options:\nA. 6\nB. 5\nC. 4\nD. 78\nE. 2\n\n### Answer:\n150 = (750*5*R)/100\nR = 4%.Answer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf Teena is driving at 55 miles per hour and is currently 7.5 miles behind Joe, who is driving at 40 miles per hour in the same direction then in how many minutes will Teena be 37.5 miles ahead of Joe?\n\n### Options:\nA. 15\nB. 60\nC. 180\nD. 90\nE. 105\n\n### Answer:\nThis type of questions should be solved without any complex calculations as these questions become imperative in gaining that extra 30-40 seconds for a difficult one.\nTeena covers 55 miles in 60 mins.\nJoe covers 40 miles in 60 mins\nSo teena gains 15 miles every 60 mins\nTeena need to cover 7.5 +37.5 miles.\nTeena can cover 7.5 miles in 30 mins\nTeena will cover 37.5 miles in 150 mins\nSo answer 30+150= 180 mins. (ANSWER C)\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf f is a function defined for all k by f(k) = k^(2/3)/16, what is f(64 k) in terms of f(k)?\n\n### Options:\nA. 1/8 f(k)\nB. 5/8 f(k)\nC. 2 f(k)\nD. 16 f(k)\nE. 32 f(k)\n\n### Answer:\nf(k) = k^(2/3)/16\nf(64 k) = (64k)^(2/3)/16 = 16 * k^(2/3)/16 = 16 * (k^(2/3)/16) = 16 f(k).\nSo answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe length of the bridge, which a train 180 meters long and travelling at 45 km/hr can cross in 30 seconds, is?\n\n### Options:\nA. 388\nB. 167\nC. 195\nD. 288\nE. 261\n\n### Answer:\nSpeed = (45 * 5/18) m/sec = (25/2) m/sec. Time = 30 sec. Let the length of bridge be x meters. Then, (180 + X)/30 = 25/2 ==> 2(180 + X) = 750 ==> X = 195 m.\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man buys a cycle for Rs. 1200 and sells it at a loss of 15%. What is the selling price of the cycle?\n\n### Options:\nA. s. 1020\nB. s. 1160\nC. s. 1190\nD. s. 1202\nE. s. 1256\n\n### Answer:\nS.P. = 85% of Rs. 1200 = Rs.85/100x 1200\t= Rs. 1020\nANSWER :A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average weight of 10 men is increased by 2 \u00bd kg when one of the men who weighs 68 kg is replaced by a new man. What is the weight of the new man?\n\n### Options:\nA. 80 kg\nB. 93 kg\nC. 70 kg\nD. 75 kg\nE. 85 kg\n\n### Answer:\nSince the average has increased by 1.5 kg, the weight of the man who stepped in must be equal to 68+10x2.5\n68+25=93 Kg\nAns: 'B'\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?\n\n### Options:\nA. 40\nB. 99\nC. 88\nD. 66\nE. 21\n\n### Answer:\nSpeed = 45 * 5/18 = 25/2 m/sec\nTotal distance covered = 360 + 140 = 500 m\nRequired time = 500 * 2/25 = 40 sec.Answer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average (arithmetic mean) of y numbers is x. If 25 is added to the set of numbers, then the average will be x - 5. What is the value of y in terms of x ?\n\n### Options:\nA. x/6 - 6\nB. x/6 - 5\nC. x/7 - 5\nD. x/5 - 7\nE. x/5 - 6\n\n### Answer:\n(A1 + A2 + .. + Ay)/y = x\n(A1 + A2 + .. + Ay + 25)/(y+1) = x - 5\n=> (xy + 25)/(y+1) = x - 5\n=> xy + 25 = yx -5y + x - 5\n=> 30 = x - 5y\n=> 5y = x - 30\n=> y = x/5 - 6\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the remainder when 2^31 is divided by 5.\n\n### Options:\nA. 3\nB. 7\nC. 1\nD. 9\nE. None of them\n\n### Answer:\n2^10 = 1024. Unit digit of 2^10 x 2^10 x 2^10 is 4 [as 4 x 4 x 4 gives unit digit 4].\nUnit digit of 231 is 8.\nNow, 8 when divided by 5, gives 3 as remainder.\nHence, 231 when divided by 5, gives 3 as remainder.\nAnswer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nGiven that a \u201c16-inch pizza\u201d means circular pizza with a diameter of 12 inches, changing from an 8-inch pizza to a 16-inch pizza gives you approximately what percent increase in the total amount of pizza?\n\n### Options:\nA. 33\nB. 50\nC. 67\nD. 180\nE. 300\n\n### Answer:\narea of 8 inch pizza= 4*4*pi=16 pi\narea of 16 inch pizza =8*8*pi=64 pi\n48/16*100=300% increase\nhence answer is E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 64 hours respectively. The ratio of their speeds is?\n\n### Options:\nA. 4:5\nB. 8:3\nC. 8:4\nD. 4:8\nE. 4:1\n\n### Answer:\nLet us name the trains A and B.\nThen, (A's speed) : (B's speed)\n= \u221ab : \u221aa = \u221a64 : \u221a9\n= 8:3\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a tire rotates at 400 revolutions per minute when the car is traveling 168km/h, what is the circumference of the tire?\n\n### Options:\nA. 7 meters\nB. 9 meters\nC. 8 meters\nD. 5 meters\nE. 3 meters\n\n### Answer:\n400 rev / minute = 400 * 60 rev / 60 minutes\n= 24,000 rev / hour\n24,000 * C = 168,000 m : C is the circumference\nC = 3 meters\ncorrect answer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAnthony and Michael sit on the six member board of directors for company X. If the board is to be split up into 2 three-person subcommittees, what percent E of all the possible subcommittees that include Michael also include Anthony?\n\n### Options:\nA. 20%\nB. 30%\nC. 40%\nD. 50%\nE. 60%\n\n### Answer:\nThe answer is C. Let's look at a committee where Mike belongs (he's person # 1) on that committee. When we choose person #2, there is a 1/5 probability that it's going to be Anthony (then it doesn't matter who the third person is), and 4/5 probability that it's going to be someone else (then person #3 is going to be Anthony with probability 1/4). Total probability E= 1/5+4/5*1/4 = 2/5.C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the original mass of an element, in grams, is a whole number and the element has decayed by exactly 93 percent in some time period, which of the following could be the final mass of that element?\n\n### Options:\nA. 27 grams\nB. 30 grams\nC. 29 grams\nD. 31 grams\nE. 35 grams\n\n### Answer:\nLet original mass be 100\nThe final mass of that element will be 7\nSo whatever option we have it will be divisible by 7\nCheck for the options the one that doesn't produce non terminating decimal is our answer\nA. 27 grams\n27/7 = 3.857...\nB. 30 grams\n28/7 = 4.285...\nC. 29 grams\n29/7 = 4.142.......\nD. 31 grams\n31/7 = 4.428.....\nE. 35 grams\n35/7 = 5\nHence our answer will be (E)\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nLet us say that a table tennis tournament was going on with knock out terms which means the one who loses the match is out of the tournament. 120 players took part in that tournament.\nHow many matches were played?\n\n### Options:\nA. 99 matches.\nB. 88 matches.\nC. 77 matches.\nD. 66 matches.\nE. 119 matches.\n\n### Answer:\nSolution:\n119 matches.\nThe number of matches will always sum up to one less than the number of players in a knock out tournament. You may calculate it in any manner. Thus 119 matches were played.\nAnswer E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA milk vendor has 2 cans of milk. The first contains 25% water and the rest milk. The second contains 50% water. How much milk should he mix from each of the containers so as to get 12 litres of milk such that the ratio of water to milk is 3 : 5?\n\n### Options:\nA. 5litres, 7 litres\nB. 7litres, 4 litres\nC. 6litres, 6 litres\nD. 4litres, 8 litres\nE. 8litres, 10 litres\n\n### Answer:\nExplanation:\nSolution 1\nLet x and (12\u00e2\u02c6\u2019x) litres of milk be mixed from the first and second container respectively.\nAmount of milk in x litres of the the first container =.75x\nAmount of water in x litres of the the first container =.25x\nAmount of milk in (12\u00e2\u02c6\u2019xlitres of the the second container =5(12\u00e2\u02c6\u2019x)\nAmount of water in (12\u00e2\u02c6\u2019x)litres of the the second container =.5(12\u00e2\u02c6\u2019x)\nRatio of water to milk\nSince x=6,12\u00e2\u02c6\u2019x=12\u00e2\u02c6\u20196=6\nHence 6 and 6 litres of milk should mixed from the first and second container respectively.\nAnswer IS C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n7^6n -1^ 6n When n is an integer > 0 is divisible by\n\n### Options:\nA. 119\nB. 127\nC. 134\nD. 145\nE. 154\n\n### Answer:\n127\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 1/(m \u2013 2) = 1/(m + 2) + 1/(m \u2013 1), which of the following is a possible value of m?\n\n### Options:\nA. 0\nB. -1\nC. -2\nD. 1\nE. 2\n\n### Answer:\nMultiply by (m-2)*(m+2)*(m-1) throughout to get:\n(m+2)*(m-1) = (m-2)*(m-1) + (m+2)(m-2)\nOf the given options, only m=0 satisfies this.\nAnswer : A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average of four positive integers is 69. The highest integer is 93 and the least integer is 39. The difference between the remaining two integers is 28. Which of the following integers is the higher of the remaining two integers?\n\n### Options:\nA. 65\nB. 48\nC. 37\nD. 23\nE. 12\n\n### Answer:\nLet the four integers be A, B, C and D where A > B > C > D.\n(A + B + C + D)/4 = 69 => A + B + C + D = 276 ---> (1)\nA = 93, D = 39 and B - C = 28\n(1) => B + C = 276 - (A + D) = 276 - 132 = 144.\nB + B -28 = 144\nB = (144 + 28)/2 = 86\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train 300 m long is running at a speed of 68 kmph. How long does it take to pass a man who is running at 8 kmph in the same direction as the train?\n\n### Options:\nA. 5 sec\nB. 9 sec\nC. 12 sec\nD. 15 sec\nE. 18 sec\n\n### Answer:\nSpeed of the train relative to man = (68 - 8) kmph\n= (60* 5/18) m/sec = (50/3)m/sec\nTime taken by the train to cross the man\n= Time taken by It to cover 300 m at 50/3 m / sec\n= 300 *3/ 50 sec = 18sec\nAnswer : E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how many ways can 21 books on English and 19 books on Hindi be placed in a row on a shelf so that two books on Hindi may not be together?\n\n### Options:\nA. 3990\nB. 1540\nC. 1995\nD. 3672\nE. 2314\n\n### Answer:\nWe must place all these books as under:\nXEXEX\u2026.XEX\nThere are 21 books on English, 19 books on Hindi\n19 places out of 22 can be chosen 22C19=22C3=1540 ways\nANSWER B 1540\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich of the following CANNOT be a product of two distinct positive integers p and q?\n\n### Options:\nA. p\nB. q\nC. 3q + 2p\nD. q - p\nE. qp\n\n### Answer:\nIn these questions it is best to take an example as if something is true for all positive integers than it as to be true for the smallest and the easiest integers to work with\ntake p = 1 and q = 2 and work with the options\npq = 2\nA) p take p =2, q = 1\nB) q take p = 1 q = 2\nC) 3q + 2p Seems tricky, lets see other options and then come back to it.\nD) q - p take q = 1 and p = 2 --> q - p = -1 .. How the hell can product of two positive integers be negative ?? or less than each of them?\nE)qp Always true\nYou don't even have to worry what C is !\nans D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf P(A) = 6/17, P(B) = 5/17, and P(A \u222a B) = 4/17 Find P(B|A)?\n\n### Options:\nA. 2/3\nB. 3/5\nC. 2/7\nD. 3/7\nE. 4/9\n\n### Answer:\nP(B|A) = P(A \u222a B)/P(A)\nP(B|A) = (4/17)/(6/17) = 4/6 = 2/3.\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 3 persons can do 3 times of a particular work in 3 days, then, 7 persons can do 7 times of that work in?\n\n### Options:\nA. 2 days\nB. 3 days\nC. 4 days\nD. 5 days\nE. 6 days\n\n### Answer:\nThat is, 1 person can do one time of the work in 3 days.\nTherefore, 7 persons can do 7 times work in the same 3 days itself.\nB)\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream. If the speed of the boat in still water is 45 kmph, find the speed of the stream?\n\n### Options:\nA. 12 kmph\nB. 13 kmph\nC. 14 kmph\nD. 15 kmph\nE. 16 kmph\n\n### Answer:\nThe ratio of the times taken is 2:1.\nThe ratio of the speed of the boat in still water to the speed of the stream = (2+1)/(2-1) = 3/1 = 3:1\nSpeed of the stream = 45/3 = 15 kmph\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the average (arithmetic mean) of 5 positive temperatures is x degrees Fahrenheit, then the sum Q of the 3 greatest of these temperatures, in degrees Fahrenheit, could be\n\n### Options:\nA. 6x\nB. Q=4x\nC. Q=5x/3\nD. Q=3x/2\nE. 3x/5\n\n### Answer:\nOA please. Yeah so 5x is the sum of the 5, then I guess 4x could be the answer (B)\nBut what about C,D,E? Any ideas why these could be wrong?\nNote that we have 5 positive temperatures.\nNext, as the average is x then the sum of the temperatures is 5x and as all the temperatures are positive then the sum of the 3 greatest must be more than (or equal to) 3x (as the average of the 3 greatest must be at least x) and less than 5x: 3x only option B fits.\nAnswer: B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a group of 800 people, 1/5 play at least one instrument, 128 play two or more. What is the probability that one student play exactly one instrument?\n\n### Options:\nA. 2/125\nB. 3/125\nC. C)2/25\nD. 3/25\nE. 1/25\n\n### Answer:\nP(playing 2 or more instruments) = 128/800 = 4/25.\nThen, the probability of playing exactly one instrument is given by:\nP(playing 1 or more instruments) - P(playing 2 or more instruments) = 1/5 - 4/25 = 1/25.\nAnswer E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn three annual examinations, of which the aggregate marks of each was 500, a student secured\naverage marks 45% and 55% in the first and the second yearly examinations respectively. To secure 65% average total marks, it is necessary for him in third yearly examination to secure marks :\n\n### Options:\nA. 300\nB. 350\nC. 400\nD. 475\nE. 500\n\n### Answer:\ntotal marks:1500 for three exams\n65% of 1500=975\nfirst exam marks=45% of 500=225\nsecond exam marks=55% of 500=275\nlet X be the third exam marks\n225 + 275 + X =975\nX=475\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n275, 132, 462, 396, 327, 891, 121\n\n### Options:\nA. 327\nB. 228\nC. 2768\nD. 028\nE. 272\n\n### Answer:\nExplanation:\nIn each number except 327, the middle digit is the sum of the other two.\nANSWER: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nBag A contains red, white and blue marbles such that the red to white marble ratio is 1:3 and the white to blue marble ratio is 2:3. Bag B contains red and white marbles in the ratio of 1:4. Together, the two bags contain 60 white marbles. How many red marbles could be in bag A?\n\n### Options:\nA. 1\nB. 3\nC. 4\nD. 12\nE. 8\n\n### Answer:\n6 is the answer.\nBag A-\nR:W:B = 2:6:9\nLet W in bag A be 6K\nBab B -\nR:W = 1:4\nLet W in bag B be 4k\nW = 60 = 6K+4k\n=> k =6\nTotal Red's in bag A will be 2K = 12\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nShannon and Maxine work in the same building and leave work at the same time. Shannon lives due north of work and Maxine lives due south. The distance between Maxine's house and Shannon's house is 60 miles. If they both drive home at the rate 2R miles per hour, Maxine arrives home 40 minutes after Shannon. If Maxine rider her bike home at the rate of R per hour and Shannon still drives at a rate of 2R miles per hour, Shannon arrives home 2 hours before Maxine. How far does maxine live from work?\n\n### Options:\nA. 20\nB. 34\nC. 38\nD. 40\nE. 46\n\n### Answer:\nWe have that X/24 - (60-X)/2R = 40\nAlso X/R - (60-X)/2R = 120\nSo we get that 2x - 60 = 80R\n3x - 60 = 240R\nGet rid of R\n120 = 3x\nx = 40\nHence answer is D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAn company has 6 employees; there are 5 female employees and 1 male employee. In how many ways can a 3-person committee be created if the committee must include the male employee?\n\n### Options:\nA. 10\nB. 12\nC. 15\nD. 24\nE. 30\n\n### Answer:\nAn company has 6 employees;for male 1C1 = 1 ........ A\nfoe female = 5C2 = 10.........B\ntotal = 10*1\n= 10 - answer=A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the units digit of 2222^(333)*3333^(222)?\n\n### Options:\nA. 0\nB. 2\nC. 4\nD. 6\nE. 8\n\n### Answer:\n(2222^333)*(3333^222)=2222^111*(2222^222*3333^222)\nhere please pay attention to the fact that the unit digit of multiplication of 2222 and 3333 is 6 (2222^222*3333^222). since 6 powered in any number more than 0 results in 6 as a units digit, as a result we have-\n6*2222^111\n2 has a cycle of 4 . 111=27*4+3 . 2^3=8\n6*8=48\nso the units digit is 8, and the answer is E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nX = 101102103104105106107......146147148149150 (From numbers 101-150). Find out the remainder when this number is divided by 9.\n\n### Options:\nA. 2\nB. 4\nC. 5\nD. 6\nE. 7\n\n### Answer:\nSol:\nThe divisibility rule for 9 is sum of the digits is to be divisible by 9. So\nWe calculate separately, sum of the digits in hundreds place, tenths place, and units place.\nSum of the digits in hundreds place: 1 x 50 = 50\nSum of the digits in tenths place : 0 x 9 + 1 x 10 + 2 x 10 + 3 x 10 + 4 x 10 + 5 x 1 = 105\nSum of the digits in units place : (1 + 2 + 3 + ...+ 9) x 5 = 225\nSo total = 380\nSo remainder = 380 / 9 = 2\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA cistern 7 m long and 5 m wide contains water up to a breadth of 1 m 40 cm. Find the total area of the wet surface.\n\n### Options:\nA. 69 m sqaure\nB. 49 m sqaure\nC. 52 m sqaure\nD. 64 m sqaure\nE. None of these\n\n### Answer:\nExplanation:\nArea of the wet surface =\n2[lb+bh+hl] - lb = 2 [bh+hl] + lb\n= 2[(5*1.40+7*1.40)]+7*5 = 69 m square\nOption A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n[( 3.241 x 14 ) / 100] = ?\n\n### Options:\nA. 0.045374\nB. 4.5388\nC. 453.88\nD. 473.88\nE. None of these\n\n### Answer:\nAnswer\nMultiplying 3.241 x 14=4.5374\nNow divide 4.5374 by 100\nSo, 4.5374 \u00f7 100= 0.045374\n\u2234 Shift the decimal two places to the left as 100\nCorrect Option: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo taps A and B can fill a tank in 5 hours and 20hours respectively. If both the taps are open then due to a leakage, it took 30 minutes more to fill the tank. If the tank is full, how long will it take for the leakage alone to empty the tank?\n\n### Options:\nA. 24 hr\nB. 36 hr\nC. 18 hr\nD. 42 hr\nE. 30 hr\n\n### Answer:\nPart filled by A+B in 1 hour = 1/5 + 1/20 = 1/4\nA and B together can fill the tank in 4 hour\nWork done by the leak in 1 hour = 1/4 - 2/9 = 1/36\nleak will empty the tank in 36 hours.\nAnswer is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder. What is the smaller number ?\n\n### Options:\nA. 270\nB. 280\nC. 290\nD. 300\nE. 310\n\n### Answer:\nLet the smaller number be x. Then larger number = (x + 1365).\nx + 1365 = 6x + 15\n5x = 1350\nx = 270\nSmaller number = 270.\nA)\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 5x^2 has two different prime factors, at most how many different prime factors does x have?\n\n### Options:\nA. 1\nB. 2\nC. 3\nD. 4\nE. 5\n\n### Answer:\nx cannot have more than 2 prime factors, because in this case 5x^2 would also have more than 2 prime factors.\nCan x have 2 prime factors? Yes, consider x=2*5=10 (in this case 5x^2 still has 2 prime factors).\nAnswer: B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the perimeter of a square with area 9p^2/25 ?\n\n### Options:\nA. 3p/4\nB. 3p^2/4\nC. 12p/5\nD. 3p^2\nE. 4p/3\n\n### Answer:\nArea of square, (side)^2 = (3p/5)^2\nTherefore side of the square = 3p/5\nPerimeter of square = 4*side = 4* (3p/5) = 12p/5\nAnswer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhen a=4+(2/4) and b=4-(2/4), (2^a^2)/(2^b^2)=?\n\n### Options:\nA. 260\nB. 256\nC. 240\nD. 210\nE. 225\n\n### Answer:\n--> (2^a^2)/(2^b^2) ={(2)^(a^2-b^2)}=2^(a-b)(a+b). Since a-b=4/4 and a+b=8, 2^(a-b)(a+b)=2^(4/4)(8)=2^8=256\nTherefore, the answer is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are two box,one containing 39 red balls and the other containing 26 green balls. You are allowed to move the balls between the boxes so that when you choose a box at random and a ball at random from the chosen box, the probability of getting a red ball is maximized. This maximum probability is\n\n### Options:\nA. .60\nB. .50\nC. .70\nD. .80\nE. .90\n\n### Answer:\nHere we are allowed to transfer the balls between the two boxes, so we keep only one red ball in first box and move all the remaining balls to the second box, so that we get maximum probability of drawing red ball from first box\nSo first box--- only one red ball\nsecond box--- 38 red and 26 green\nProbability of choosing any box is 1/ 2.\nprobability of choosing the red ball from first box is 1\nprobability of choosing the red ball from second box is 38/64\nSo probability of taking one red ball = [(1/2)\u00d7(1)]+[(1/2)*(38/64)]\u22430.8\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a + b - c = 2d, and if a - b + c =-2e, then a =\n\n### Options:\nA. 2(d + e)\nB. d \u2013 e\nC. (d + e)/2\nD. d-2e\nE. e-d\n\n### Answer:\nAdd both equations:\na + b - c = 2d\na - b + c =-2e\na+b-c+a-b+c=2d-2e\n2a=2d-2e\na=(d-e)\nAns:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average weight of 8 persons increases by 3.5 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person ?\n\n### Options:\nA. 75 kg\nB. 65 kg\nC. 55 kg\nD. 85 kg\nE. 93 kg\n\n### Answer:\nTotal weight increased = (8 x 3.5) kg = 28 kg.\nWeight of new person = (65 + 28) kg = 93 kg.\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOne half of a two digit number exceeds its one third by 7. What is the sum of the digits of the number?\n\n### Options:\nA. A)3\nB. B)5\nC. C)7\nD. D)9\nE. E)10\n\n### Answer:\nx/2 \u2013 x/3 = 7 => x =46\n4 + 6 = 10\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFor all positive integers m and v, the expression m \u0398 v represents the remainder when m is divided by v. What is the value of (( 94 \u0398 33 ) \u0398 17 ) - ( 96 \u0398 (33 \u0398 17)) ?\n\n### Options:\nA. -10\nB. -2\nC. 8\nD. 13\nE. 17\n\n### Answer:\n(( 94 \u0398 33 ) \u0398 17 )\nThe remainder of 98 divided by 33 is 28;\nThe remainder of 28 divided by 17 is 11;\n( 96 \u0398 (33 \u0398 17))\nThe remainder of 33 divided by 17 is 16;\nThe remainder of 96 divided by 16 is 0.\n11 - 0 = 11.\nAnswer: D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJ is 25% less than P and 20% less than T. T is r% less than P. What is the value of r?\n\n### Options:\nA. 93.5\nB. 90\nC. 6.75\nD. 6.25\nE. 2\n\n### Answer:\nUsually We can solve every question of this type by choosing appropriate value of the Variable and deriving the value of other related variables.\nLet, P = 400\nthen J = (75/100)*400 = 300\nalso J = (80/100)*T\ni.e. T = 300*100/80 = 375\nand T = [1-(r/100)]*P\ni.e. 100-r = 100*T/P = 100*375/400 = 93.75\ni.e. r = 6.25\nAnswer: Option D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain sum of money at simple interest amounted Rs.840 in 10 years at 3% per annum, find the sum?\n\n### Options:\nA. 971\nB. 973\nC. 268\nD. 646\nE. 365\n\n### Answer:\n840 = P [1 + (10*3)/100]\nP = 646\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOn a two-dimensional coordinate plane, the line A = x^2 - x^3 touches the x-axis in how many places?\n\n### Options:\nA. 0\nB. 1\nC. 2\nD. 3\nE. 4\n\n### Answer:\nApparently it's A = x^2 - x^3 instead of A = x^2 - A^3.\nIn this case: the x-intercept is the value(s) of x for A = 0.\n0 = x^2 - x^3;\n0 = x^2(1 - x);\nx = 0 or x = 1.\nAnswer: C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMary's income is 40 percent more than Tim's income, and Tim's income is 40 percent less than Juan's income. What percent of Juan's income is Mary's income?\n\n### Options:\nA. 124%\nB. 120%\nC. 96%\nD. 80%\nE. 84%\n\n### Answer:\nJuan's income = 100 (assume);\nTim's income = 60 (40 percent less than Juan's income);\nMary's income = 84 (40 percent more than Tim's income).\nThus, Mary's income (84) is 84% of Juan's income (100).\nAnswer: E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA box contains 5 pairs of shoes (10 shoes in total). If two shoes are selected at random, what it is the probability that they are matching shoes?\n\n### Options:\nA. 1/190\nB. 1/20\nC. 1/9\nD. 1/10\nE. 1/92\n\n### Answer:\nThe problem with your solution is that we don't choose 1 shoe from 20, but rather choose the needed one AFTER we just took one and need the second to be the pair of it. So, the probability would simply be: 1/1*1/9(as after taking one at random there are 9 shoes left and only one is the pair of the first one)=1/9\nAnswer: C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 9 is added to twice a number and this sum is multiplied by 3, the result is the same as if the number is multiplied by 4 and 13 is added to the product. What is the number?\n\n### Options:\nA. -7\nB. -8\nC. -9\nD. -10\nE. -11\n\n### Answer:\nlet the number be x;\n3(9+2x)=4x+13;\nx=-7\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nLook at this series: 2, 1, (1/2), (1/4), (1/8), ... What number should come next?\n\n### Options:\nA. (1/3)\nB. (1/5)\nC. (1/6)\nD. (1/10)\nE. (1/16)\n\n### Answer:\nThis is a simple division series; each number is one-half of the previous number.\nIn other terms to say, the number is divided by 2 successively to get the next result.\n4/2 = 2\n2/2 = 1\n1/2 = 1/2\n(1/2)/2 = 1/4\n(1/4)/2 = 1/8\n(1/8)/2= 1/16 and so on.\nAnswer is E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a division sum, the remainder is 5 and the divisor is 3 times the quotient and is obtained by adding 3 to the thrice of the remainder. The dividend is:\n\n### Options:\nA. 72\nB. 76\nC. 100\nD. 113\nE. 112\n\n### Answer:\nDiver = (5*3)+3 = 18\n3* Quotient = 18\nQuotient = 6\nDividend = (Divisor * Quotient) + Remainder\nDividend = (18* 6) + 5 = 113\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe principal that amounts to Rs. 3913 in 3 years at 6 1/4 % per annum C.I. compounded annually, is?\n\n### Options:\nA. s. 3096\nB. s. 4076\nC. s. 4085\nD. s. 4096\nE. s. 5096\n\n### Answer:\nPrincipal = [4913 / (1 + 25/(4 * 100))3]\n= 3913 * 16/17 * 16/17 * 16/17 = Rs. 3096.\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn what time will a train 100 m long cross an electric pole, it its speed be 144 km/hr?\n\n### Options:\nA. 2.5 sec\nB. 3.9 sec\nC. 2.9 sec\nD. 2.7 sec\nE. 2.3 sec\n\n### Answer:\nSpeed = 144 * 5/18 = 40 m/sec\nTime taken = 100/40\n= 2.5 sec.\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf each permutation of the digits 1,2,3,4,5,6 are listed in the increasing order of magnitude, then 289thterm will be\n\n### Options:\nA. 361452\nB. 321546\nC. 321456\nD. 341256\nE. None of these\n\n### Answer:\nExplanation :\nLet's see how many numbers can be formed with the left most digit as 1\nThe digit '1' is placed at the 1st position (only 1 way of doing this)\nSince one digit is placed at the 1st position,\nany of the remaining 5 digits can be placed at 2nd position.\nSince one digit is placed at the 1st position and another digit is placed\nat the 2nd position, any of the remaining 4 digits can be placed at the\n3rd position.\nSo on ...\n1\t5\t4\t3\t2\t1\ni.e., total number of ways = (1)( 5)( 4)( 3)( 2)( 1) = 120\ni.e., total count of numbers which can be formed\nwith the left most digit as 1 = 120\nSimilarly, total count of numbers which can be formed\nwith the left most digit as 2 = 120\nSimilarly, total count of numbers which can be formed\nwith the left most digit as 3 = 120\ni.e., 240 numbers (=120 + 120) can be formed\n(with left most digit as 1) or (with left most digit as 2)\nSimilarly, 360 numbers (=120 + 120 + 120) can be formed\n(with left most digit as 1) or (with left most digit as 2)\nor (with left most digit as 3)\nHence, the left most digit of the 249th number = 3\nNow, let's find out how many numbers can be formed\nwith the left most digit as 3 and next digit as 1\nThe digit '3' is placed at the 1st position (only 1 way of doing this)\nThe digit '1' is placed at the 2nd position (only 1 way of doing this)\nAny of the remaining 4 digits can be placed at 3rd position.\nSince 3 digits are placed in the first three positions, any of the remaining 3 digits\ncan be placed at the 4th position.\nSince 4 digits are placed in the first four positions, any of the remaining 2 digits\ncan be placed at the 5th position.\nSince 5 digits are placed in the first five positions, the remaining 1 digit\ncan be placed at the 6th position.\n1\t1\t4\t3\t2\t1\ni.e., total number of ways = (1)(1)(4)(3)(2)(1) = 24\ni.e., Total count of numbers which can be formed\n(with the left most digit as 3) and (next digit as 1) = 24\nSimilarly, total count of numbers which can be formed\n(with the left most digit as 3) and (next digit as 2) = 24\nHence, 120 + 120 + 24 + 24 = 288 numbers can be formed\n(with left most digit as 1) or (with left most digit as 2)\nor (with left most digit as 3 and next digit as 1)\nor (with left most digit as 3 and next digit as 2)\nHence, the 289th number is the minimum value number which is formed\nwith the left most digit as 3 and next digit as 4.\ni.e., the number is 341256\nAnswer : D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn the first 20 overs of a cricket game, the run rate was only 4.2. What should be the run rate in the remaining 30 Overs to reach the target of 324 runs?\n\n### Options:\nA. 7.25\nB. 8.5\nC. 8\nD. 9.15\nE. 10\n\n### Answer:\nExplanation :\nRequired run rate = (324 - 4.2 20 ) = 240/ 30 = 8.\nAnswer : C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe effective annual rate of interest corresponding to a nominal rate of 6% per annum payable half-yearly is?\n\n### Options:\nA. 6.99%\nB. 6.89%\nC. 6.08%\nD. 6.09%\nE. 6.19%\n\n### Answer:\nAmount of Rs. 100 for 1 year when compounded half-yearly\n= [100 * (1 + 3/100)2]\n= Rs. 106.09 Effective rate\n= (106.09 - 100) = 6.09%\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe vertex of a rectangle are (1, 0), (5, 0), (1, 1) and (5, 1) respectively. If line L passes through the origin and divided the rectangle into two identical quadrilaterals, what is the slope of line L?\n\n### Options:\nA. 1/2\nB. 2\nC. 1/6\nD. 3\nE. 1/4\n\n### Answer:\nIf line L divides the rectangle into two identical quadrilaterals, then it must pass through the center (3, 0.5). The slope of a line passing through (0,0) and (3, 0.5) is 0.5/3 = 1/6.\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe remainder when dividing the expression (X + Y) by 5 is 4. The remainder of X divided by 10 is 2. What is the remainder T of Y divided by 5?\n\n### Options:\nA. T=1.\nB. T=2.\nC. 3.\nD. 4.\nE. 5.\n\n### Answer:\nX divided by 10 gives reminder of 2. X can be 2/12/22....\nX+Y divided by 5 is 4. X + Y can be 4/ 9/ 19....\nIf X+Y= 4 and X is 2 then Y = 2 and Y/5 will give a reminder of 2\nSimilarly, if X+Y= 9 and X = 2, then y/5 will give a reminder of 2\nHence the answer must be 2 (B)\nAlso....\nx+y=5m+4 and x=10K+2\nhence 10k+2+y=5m+4 or y=5(m-2k)+2, m-2k being a constant remainder is 2 hence answer is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nGiven that 268 * 74 = 19832, find the values of 2.68 * 0.74.\n\n### Options:\nA. 1.9328\nB. 1.9832\nC. 1.9823\nD. 1.9382\nE. None of them\n\n### Answer:\nSum of decimal places = (2 + 2) = 4\n2.68 * 0.74 = 1.9832.\nAnswer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOn a windy day, out of every 3 sand dunes formed, only 1 remains. Out of 5 blown-out\nsand-dunes, 1 has treasure and only 2 out of 7 sand dunes formed have lucky coupons. Find\nthe probability that the blown-out sand dune will contain both the things.\n\n### Options:\nA. 2/25\nB. 4/75\nC. 7/75\nD. 3/79\nE. 4/5\n\n### Answer:\nProbability of sand dune blown out = 2/3\nProbability that it has treasure = 1/5\nProbability that it has lucky coupon = 2/7\ntotal probability = 2/3 * 1/5 * 2/7 = 3/79\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA team P of 20 engineers can complete work or task in 32 days. Another team Q of 16 engineers can complete same task in 30 days.Then the ratio of working capacity of 1 member of P to the 1 member of Q is\na. 3 : 2\n\n### Options:\nA. 22\nB. 34\nC. 77\nD. 29\nE. 21\n\n### Answer:\nExplanation:\nLet the capacity of an engineer in P = x units, and in Q = y units.\nWorking capacity of P = x \u00d7 32 \u00d7 20\nWorking capacity of Q = y \u00d7 16 \u00d7 30\nAs the total work is same, we equate the above equations.\n\u21d2 x \u00d7 32 \u00d7 20 = y \u00d7 16 \u00d7 30\n\u21d2 xy=16\u00d73032\u00d720=34\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo trains of equal lengths take 10 sec and 15 sec respectively to cross a telegraph post. If the length of each train be 120 m, in what time will they cross other travelling in opposite direction?\n\n### Options:\nA. 16 sec\nB. 12 sec\nC. 41 sec\nD. 09 sec\nE. 15 sec\n\n### Answer:\nSpeed of the first train = 120/10 = 12 m/sec.\nSpeed of the second train = 120/5 = 8 m/sec.\nRelative speed = 12 + 8 = 20 m/sec.\nRequired time = (120 + 120)/20\n=12 sec.\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf two-third of a bucket is filled in 100 seconds then the time taken to fill the bucket completely will be .\n\n### Options:\nA. 90 seconds\nB. 150 seconds\nC. 60 seconds\nD. 100 seconds\nE. 120 seconds\n\n### Answer:\n2/3 filled in 100 seconds\n1/3 filled in 50 secs\nthen 2/3+1/3=100 + 50 seconds = 150 seconds\nANSWER: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA metal company's old machine makes bolts at a constant rate of 100 bolts per hour. The company's new machine makes bolts at a constant rate of 150 bolts per hour. If both machines start at the same time and continue making bolts simultaneously, how many minutes will it take the two machines to make a total of 350 bolts?\n\n### Options:\nA. 84\nB. 72\nC. 120\nD. 144\nE. 180\n\n### Answer:\nOld Machine\n100 bolts in 60 mins\nso,\n5/3 bolts in 1 min\nNew Machine\n150 bolts in 60 mins\nso,\n5/2 bolts in 1 min\ntogether,\n5/3 + 5/2 =\n25/6 bolts in 1 min\nso, for 350 bolts\n350 * 6 / 25 = 84 mins\nAns A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOne robot builds a robot in 1 hour, another one builds a robot in 2 hours. The 2 robots work together and when a new robot is complete, it joins the others, working at a constant rate of one robot in 2 hours. How much time will it take until there are 7 robots altogether, if the robots build only one robot at a time?\n\n### Options:\nA. 70 1/7 min\nB. 94 1/7 min\nC. 110 1/7 min\nD. 112 1/7 min\nE. 131 1/7 min\n\n### Answer:\nFirst the 2 robots work at the rate of\n1 + 1/2 = 3/2\nso they complete one robot in 2/3 rd of an hour = 40 minutes - (1)\nNow the 3 robots work together at the rate of\n1 + 1/2 + 1/2 = 4/2 = 2/1\nso they complete one robot in 1/2 an hour,i.e 30 minutes - (2)\nNow the 4 robots work together at the rate of\n1 + 1/2 + 1/2 + 1/2 = 5/2\nso they complete one robot in 2/5th of an hour - (3)\nNow the 5 robots work together at the rate of\n1 + 1/2 + 1/2 + 1/2+1/2 = 3\nso they complete one robot in 1/3th of an hour - (4)\nNow the 6 robots work together at the rate of\n1 + 1/2 + 1/2 + 1/2 + 1/2 + 1/2=7/2\nso they complete one robot in 2/5th of an hour - (5)\nAnd now we have 7 robots\nSo Total = (1) + (2) + (3)+(4)+(5) = 131 1/7minutes\nAnswer - E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nPipe A can fill a tank in 16 hrs and pipe B can fill it in 24 hrs. If both the pipes are opened in the empty tank. In how many hours will it be fill 5/4th of that tank?\n\n### Options:\nA. 10\nB. 12\nC. 14\nD. 16\nE. 18\n\n### Answer:\nPart filled A in 1 hr= (1/16)\nPart filled B in 1 hr= (1/24)\nPart filled by (A+B) together in 1 hr=(1/16)+(1/24)=5/48\nSo, The tank will be full in 48/5 hrs\nTime taken to fill Exact quarter tank = (48/5) * (5/4) = 12 hrs\nAnswer : B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average (arithmetic mean) of eight numbers is 43.2. If the sum of half of these numbers is 154.4, what is the average of the other half?\n\n### Options:\nA. 44.2\nB. 47.8\nC. 50.5\nD. 53.6\nE. 56.9\n\n### Answer:\nThe average of this half is 154.4/4 = 38.6\nThis is 4.6 below the overall average, thus the average of the other half of the numbers must be 4.6 above the overall age, that is 43.2+4.6 = 47.8\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 1,000 microns = 1 decimeter, and 1,000,000,000 angstroms = 1 decimeter, how many angstroms equal 1 micron?\n\n### Options:\nA. 1,000\nB. 100\nC. 1,000,000\nD. 10\nE. 10,000\n\n### Answer:\nGiven that 1,000 microns = 1 decimeter =1,000,000,000 angstroms\nSo, 1 micron = 1,000,000,000/1,000\n=1,000,000\nAnswer : C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich of the following does NOT have a divisor greater than 1 that is the square of an integer?\n\n### Options:\nA. 28\nB. 32\nC. 49\nD. 62\nE. 25\n\n### Answer:\nPrime Factorization\n28=2*2*7=2^2*7. Includes a perfect square of 4.\n32=2*2*2*2*2=4^2*2. Includes the perfect square of 16.\n49=7*7. Is a perfect square.\n62=2*31. No perfect square here, so a possibility.\n25= 5*5. Is a perfect square.\nAll but 62 have perfect squares as a factor so D is the correct answer.\n28=2*2*7=2^2*7. Perfect square of 4.\n32=2*2*2*2*2=4^2*2. Perfect square of 16.\n49=7*7. Perfect square.\n62=2*31. No perfect square.\n25= 5*5. Perfect square.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA shop owner professes to sell his articles at certain cost price but he uses false weights with which he cheats by 20% while buying and by 10% while selling. What is his percentage profit?\n\n### Options:\nA. 10.22%\nB. 20.22%\nC. 21.22%\nD. 20%\nE. Can't be calculated\n\n### Answer:\nThe owner buys 100kg but actually gets 120kg;\nThe owner sells 100kg but actually gives 90kg;\nProfit: (120-90)/90*100=20%\nAnswer: D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the value of x. (47% of 1442 - 36% of 1412) + 61 = x?\n\n### Options:\nA. 1\nB. 2\nC. 3\nD. 4\nE. 5\n\n### Answer:\nB) 2\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSet A of 8 positive integers may have the same element and have 36. And set B of 8 positive integers must have different elements and have 36. When m and n are the greatest possible differences between 36 and other elements\u2019 sums in set A and set B, respectively, m-n=?\n\n### Options:\nA. 20\nB. 21\nC. 23\nD. 25\nE. 26\n\n### Answer:\nThis is maximum-minimum. Hence, 36-(1+1+1+1+1+1+1)=29 and 36-(1+2+3+4+5+6+7)=8. So, 29-8=21. The correct answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf A lends Rs.2000 to B at 10% per annum and B lends the same sum to C at 11.5% per annum then the gain of B in a period of 3 years is?\n\n### Options:\nA. 90\nB. 122.5\nC. 132.5\nD. 114.5\nE. 212.5\n\n### Answer:\n(2000*1.5*3)/100 => 90\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n75% of the guestrooms at the Stagecoach Inn have a queen-sized bed, and each of the remaining rooms has a king-sized bed. Of the non-smoking rooms, 60% have a queen-sized bed. If 28% of the rooms at the Stagecoach Inn are non-smoking rooms with king-sized beds, what percentage of the rooms permit smoking?\n\n### Options:\nA. 25%\nB. 30%\nC. 50%\nD. 55%\nE. 75%\n\n### Answer:\nLet x be the number of non-smoking rooms.\nLet N be the total number of rooms at the inn.\n40% of non-smoking rooms have a king-sized bed.\n0.4x = 0.28N\nx = 0.7N\nThe percentage of rooms which permit smoking is 1 - 0.7 = 30%\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe difference between the two numbers is 1/3 of the larger number. If the smaller one is 48 the larger one is\n\n### Options:\nA. 72\nB. 60\nC. 32\nD. 96\nE. 65\n\n### Answer:\nExplanation:\nLet the larger number be x. Then,\nx - 48 = 1/3 x\nx - x/3 = 48\n=> 2x/3 = 48 => x = 72\nAnswer: Option A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo pipes A and B can separately fill a cistern in 24 minutes and 48 minutes respectively. There is a third pipe in the bottom of the cistern to empty it. If all the three pipes are simultaneously opened, then the cistern is full in 12 minutes. In how much time, the third pipe alone can empty the cistern?\n\n### Options:\nA. 90 min\nB. 48 min\nC. 54 min\nD. 120 min\nE. 130 min\n\n### Answer:\n1/12-(1/24+1/48)=-1/48\nthird pipe can empty in 48 minutes\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train running at the speed of 60 km/hr crosses a pole in 15 seconds. Find the length of the train?\n\n### Options:\nA. 150\nB. 872\nC. 250\nD. 288\nE. 212\n\n### Answer:\nSpeed = 60*(5/18) m/sec = 50/3 m/sec\nLength of Train (Distance) = Speed * Time\n(50/3) * 15 = 250 meter\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA trader sells 80 meters of cloth for Rs. 10000 at the profit of Rs. 7 per metre of cloth. What is the cost price of one metre of cloth?\n\n### Options:\nA. 118\nB. 88\nC. 90\nD. 42\nE. 22\n\n### Answer:\nSP of 1m of cloth = 8925/85 = Rs. 125\nCP of 1m of cloth = SP of 1m of cloth - profit on 1m of cloth\n= Rs. 125 - Rs. 7 = Rs. 118\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA gardener grows cabbages in her garden that is in the shape of a square. Each cabbage takes 1 square feet of area in her garden. This year, she has increased her output by 197 cabbages as compared to last year. The shape of the area used for growing the cabbages has remained a square in both these years. How many cabbages did she produce this year?\n\n### Options:\nA. 9801\nB. 10,000\nC. 14,400\nD. 12,696\nE. can not be determined\n\n### Answer:\nLet the side for growing cabbages this year be X ft. Thus the area is X^2.\nLet the side for growing cabbages last year be Y ft. Thus, the area was Y^2.\nThe area would have increased by 197 sq ft as each cabbage takes 1 sq ft space.\nX^2 - Y^2 = 197\n(X + Y)(X - Y) = 197\n197 is a prime number and thus it will be (99+98)*(99-98).\nThus X = 99 and Y = 98\nX^2 = 99^2 = 9801\nThe answer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf an integer n is to be chosen at random from the integers 1 to 96, inclusive, what is the probability that n(n + 1)(n + 2) will be divisible by 8?\n\n### Options:\nA. 1/4\nB. 3/8\nC. 1/2\nD. 5/8\nE. 3/4\n\n### Answer:\ntotal nos of ways in which we can choose n = 96\nn(n + 1)(n + 2) will be divisible by 8?\ncase 1: n = odd then n+2 =odd & n+1 will be even i.e this needs get divided by 8, hence is a multiple of 8 so we have 8..96 = 12 multiples to fill the n+1 pos hence 12 ways\ncase 2: n is even then n+2 will be even & the product will be divisible by 24 & thus 8\nso nos of values that can be used for n= 2....96 (all even nos) i.e 48 nos\ntotal = 48+12 =60 ways\nso reqd P =60/96 =5/8;\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe length of a rectangular floor is more than its breadth by 100%. If Rs. 600 is required to paint the floor at the rate of Rs. 3 per sq m, then what would be the length of the floor?\n\n### Options:\nA. 15.0m.\nB. 14.4m.\nC. 12.0m.\nD. 16.2m.\nE. 16.5m.\n\n### Answer:\nLet the length and the breadth of the floor be l m and b m respectively.\nl = b + 100% of b = l + 1b = 2b\nArea of the floor = 600/3 = 200 sq m\nl b = 200i.e., l * l/2 = 108\nl2 = 216 => l = 14.4m.\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nVarma can read a book in k minutes. What part of the book can he read in 8 minutes?(k>8)\n\n### Options:\nA. 6/k\nB. 8/k\nC. 83k\nD. 2/k\nE. 1/k\n\n### Answer:\nPart of the book he can read in 1 minute = 1/k\nPart of the book he can read in 8 minutes =8/k.\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many positive integers less than 20 can be expressed as the sum of a positive multiple of 2 and a positive multiple of 3?\n\n### Options:\nA. 14\nB. 13\nC. 12\nD. 11\nE. 10\n\n### Answer:\nThe numbers must be of the form 2a+3b,2a+3b, where aa and bb are positive integers.\nThe smallest number is 5=2\u22171+3\u22171.5=2\u22171+3\u22171. Starting with 55, we can get all the other numbers by adding either 22 or 33 to the already existing numbers on our list. Adding either 22 or 33 to 2a+3b2a+3b will give another number of the same form.\nSo, after 55, we get 5+2=7,5+3=8,7+2=9,8+2=10,...5+2=7,5+3=8,7+2=9,8+2=10,... We will get all the numbers up to 1919 inclusive, except 1,2,3,4,1,2,3,4,and 6,6, because once we have 77 and 8,8, by adding 22 all the time we can get any odd or even number.\nWe get a total of 19\u22125=1419\u22125=14 numbers.\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the invalid no.from the following series 13, 18, 25, 30, 37, 40\n\n### Options:\nA. 30\nB. 35\nC. 40\nD. 47\nE. 50\n\n### Answer:\nThe differences between two successive terms from the beginning are 7, 5, 7, 5, 7, 5. So, 40 is wrong.\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich answer is closest to the \u221a17?\n\n### Options:\nA. a 4.1\nB. b 4.2\nC. c 4.4\nD. d 4.5\nE. e 4.6\n\n### Answer:\nTry filling the numbers into the y's. y x y =\n4.1 x 4.1= 16.81\n4.2 x 4.2 = 17.64\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the number 517*324 is completely divisible by 9, then the smallest whole number in the place of * will be:\n\n### Options:\nA. 3\nB. 1\nC. 5\nD. 4\nE. 2\n\n### Answer:\nSum of digits = (5 + 1 + 7 + x + 3 + 2 + 4) = (22 + x), which must be divisible by 9.\nx = 5.\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nLast year, sales at Company Zora were 10% greater in February than in January, 10% less in March than in Feb, 20% greater in April than in March, 10% less in May than in April, and 10% greater in June than in May. In which month were sales closest to Jan?\n\n### Options:\nA. March\nB. April\nC. May\nD. June\nE. February\n\n### Answer:\nJan = $100\n10% greater in February than in January ---> Feb = $110\n10% less in March than in Feb ---> Mar = $99\n20% greater in April than in March ---> Apr = $118.80\n10% less in May than in April ---> May $106.92\n10% greater in June than in May --->Jun = $117.61\nAnswer : A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA and B go around a circular track of length 600 m on a cycle at speeds of 36 kmph and 54 kmph. After how much time will they meet for the first time at the starting point?\n\n### Options:\nA. 120 sec\nB. 198 sec\nC. 178 sec\nD. 665 sec\nE. 276 sec\n\n### Answer:\nTime taken to meet for the first time at the starting point\n= LCM { length of the track / speed of A , length of the track / speed of B}\n= LCM { 600/ (36 * 5/18) , 600/ (54 * 5 /18) }\n= LCM (60, 40) = 120 sec.\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe equation of line q is y = 4/3*x - 100. What is the smallest possible distance in the xy-plane from the point with coordinates (0, 0) to any point on line q?\n\n### Options:\nA. 48\nB. 50\nC. 60\nD. 75\nE. 100\n\n### Answer:\nThis can be solve in two steps and without any complex calculation.\nGiven : equation of line q as y=(4/3)x -100. So the line intercept the axes at (0,-100) and (75,0).\nThis can be considered a right angle triangle with right angle at (0,0) . So Base=100 , Height=75 and Hypotenuse =125 (By Pythagoras triplet)\nSo a perpendicular from the (0,0) to hypotenuse will be the answer.\nArea of triangle= 0.5*100*75=0.5*125* x\n=> x=60;\nSO answer is 60=C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how many years will a sum of money doubles itself at 5% per annum on simple interest?\n\n### Options:\nA. 29%\nB. 20%\nC. 07%\nD. 50%\nE. 23%\n\n### Answer:\nP = (P*5*R)/100\nR = 20%\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 30% of a number is equal to one-third of another number, what is the ratio of first number to the second number ?\n\n### Options:\nA. 2:5\nB. 3:7\nC. 10:9\nD. 7:3\nE. None of these\n\n### Answer:\nExplanation :\nLet 30% of A=1/3B\nThen, 30A/100=1B/3\n=> 3A/10=B/3\n=> A:B= 10 : 9\nAnswer : C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf X is the set of prime single-digit numbers and Y is a set containing each of the numbers in set X raised to the power of 2, how much greater is the median of set Y than the median of set X?\n\n### Options:\nA. 2\nB. 4\nC. 9\nD. 13\nE. 17\n\n### Answer:\nset X={2,3,5,7} set of prime single digit numbers\nset Y={4,9.25.49} each of the numbers in set X raised to the power of 2\nMedian set X= (3+5)/2= 4\nMedian set Y= (9+25)/2= 17\nRequired set Y - set X= 13\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average weight of 10 persons increases by 4.2 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person?\n\n### Options:\nA. 107 kg\nB. 80 kg\nC. 120 kg\nD. 90 kg\nE. 100\n\n### Answer:\nSolution\nTotal weight increased\t= (10 x 4.2)kg\n= 42 kg.\nWeight of new person\t= (65 + 42)kg\n= 107kg.\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe cost price of an book is 64% of the marked price. Calculate the gain percent after allowing a discount of 12%?\n\n### Options:\nA. 33%\nB. 28.02%\nC. 37.5%\nD. 30.5%\nE. 22%\n\n### Answer:\nC\n37.5%\nLet marked price = $100.\nThen, C.P. = $64, S.P. = $88\nGain % = 24/64 * 100 = 37.5%.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 13 = 13w/(1-w) ,then (w)2 =\n\n### Options:\nA. 1/4\nB. 1/2\nC. 1\nD. 2\nE. 3\n\n### Answer:\n13-13w=13w\n26w=13\nw=1/2\n2w*2=1/2*2=1\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA box contains 15 mangoes out of which 8 are spoilt. If eight mangoes are chosen at random, find the probability that A number is selected at random from first twenty natural numbers. What is the chance that it is a multiple of either 4 or 15?\n\n### Options:\nA. 17/10\nB. 1/10\nC. 7/10\nD. 1/5\nE. 3/10\n\n### Answer:\nThe probability that the number is a multiple of 4 is 5/20. (Since 4*5 = 20).\nSimilarly the probability that the number is a multiple of 15 is 1/20. {Since 15*1 =\n15).\nNeither 4 nor 15 has common multiple from 1 to 20. Hence these events are mutually exclusive events. Therefore chance that the selected number is a multiple of 4 or 15 is (5+1)/20 = 3/10.\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling alongthe oundary of the park at the speed of 12 km/hr completes one round in 8 minutes, then the area of the park (in sq. m) is\n\n### Options:\nA. 124345 m\nB. 233234 m\nC. 153600 m\nD. 123567 m\nE. 168999 m\n\n### Answer:\nPerimeter = Distance covered in 8 min. = 12000\tx 8\tm = 1600 m.\n60\nLet length = 3x metres and breadth = 2x metres.\nThen, 2(3x + 2x) = 1600 or x = 160.\nLength = 480 m and Breadth = 320 m.\nArea = (480 x 320) m2 = 153600 m\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf an article is sold at 20% profit instead of 14% profit, then the profit would be Rs. 180 more. What is the cost price?\n\n### Options:\nA. Rs.1000\nB. Rs. 2000\nC. Rs. 3000\nD. Rs. 4000\nE. Rs.5200\n\n### Answer:\nExplanation:\nLet the cost price of an article be Rs. x.\n(20% of x) - (14% of x) = 180\n20x/100 - 14x/100 = 105 => 6x = 180 * 100\n=> x = 3000\nCost price = Rs. 3000\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA metallic sheet is of rectangular shape with dimensions 48 m x 36 m. From each of its corners, a square is cut off so as to make an open box. If the length of the square is 6 m, the volume of the box (in m3) is:\n\n### Options:\nA. 4830\nB. 5184\nC. 6420\nD. 8960\nE. 7960\n\n### Answer:\nClearly, l = (48 - 12)m = 36 m,\nb = (36 -12)m = 24 m,\nh = 8 m.\nVolume of the box = (36 x 24 x 12) m3 = 5184 m3. Answer: Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA bowl was filled with 10 ounces of water, and 0.010 ounce of the water evaporated each day during a 50-day period. What percent of the original amount of water evaporated during this period?\n\n### Options:\nA. 0.004%\nB. 0.04%\nC. 0.40%\nD. 5%\nE. 40%\n\n### Answer:\nTotal amount of water evaporated each day during a 50-day period = .008 * 50\n=.010 * 100/2\n= 1.0/2\n= .5\npercent of the original amount of water evaporated during this period = (.5/10) * 100%\n= 5 %\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA farmer used 1,034 acres of land for beans, wheat, and corn in the ratio of 5 : 2 : 4, respectively. How many R acres were used for corn?\n\n### Options:\nA. 188\nB. 258\nC. 376\nD. 470\nE. 517\n\n### Answer:\nconsider 5x acres of land used for bean\nconsider 2x acres of land used for wheat\nconsider 4x acres of land used for corn\nTotal given is 1034 acres\n11x =1034\nx = 94\nland used for corn R= 4 * 94 = 376\ncorrect option - C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average age of seven persons sitting in a row facing east is 28 years. If the average age of the first three persons is 25 years and the average age of the last three persons is 36 years, then find the age of the person sitting in the middle of the row?\n\n### Options:\nA. 9 years\nB. 29 years\nC. 18 years\nD. 13 years\nE. 17 years\n\n### Answer:\nTotal age seven persons = (28 * 7)years\nTotal age of the first three persons and the last three persons are (25 * 3) years and (36 * 3) years respectively.\nAge of the person sitting in the middle of the row = 28 * 7 - 25 * 3 - 36 * 3 = 196 - 75 - 108 = 13 years.\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe largest four digit number which is a multiple of 8, 10,12 and 15 is:\n\n### Options:\nA. 9960\nB. 9950\nC. 9940\nD. 9930\nE. 9920\n\n### Answer:\nlcm=120\n9999/120=83\n83*120=9960\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe sum of the first n positive perfect squares, where n is a positive integer, is given by the formula n^3/3 + c*n^2 + n/6, where c is a constant. What is the sum of the first 18 positive perfect squares?\n\n### Options:\nA. 1,010\nB. 1,164\nC. 1,240\nD. 1,316\nE. 2,109\n\n### Answer:\nFirst we need to find the constant 'c'. The easiest way to find this is for the sum of the first two perfect squares for 1 and 2 = 1 and 4 respectively.\nHence LHS = 1+4 and plug n=2 for RHS and simplify to get c = 1/2.\nPlug values of n = 18 and c = 1/2 into the equation and simplify to get the answer 2109.\nOption E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf it takes a tub 6 minutes to drain 5/7 of its content, how much more time will it take for the tub to be empty?\n\n### Options:\nA. 48 seconds\nB. 1 minute, 12 seconds\nC. 1 minute, 50 seconds\nD. 2 minutes, 24 seconds\nE. 4 minutes, 12 seconds\n\n### Answer:\nIf 5/7 of tub's content is drained 2/7 th of tub still needs to be drained.\nIf it takes 6 minutes to drain 5/7 th of tub it takes 6*(7/5) minutes to drain the entire tub and 6*(7/5)*(2/7) min to drain 2/7 th of the tub which is 2.4 minutes or 12/5 minutes or 2 minute 24 seconds\nSo answer is D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThree workers have a productivity ratio of 1 to 2 to 4. All three workers are working on a job for 4 hours. At the beginning of the 5th hour, the slowest worker takes a break. The slowest worker comes back to work at the beginning of the 9th hour and begins working again. The job is done in ten hours. What was the ratio of the work performed by the fastest worker as compared to the slowest?\n\n### Options:\nA. 12 to 1\nB. 6 to 1\nC. 5 to 1\nD. 20 to 3\nE. 1 to 5\n\n### Answer:\nThe fastest worker who does 4 units of job worked for all 10 hours, so he did 4*10=40 units of job;\nThe slowest worker who does 1 unit of job worked for only 4+2=6 hours (first 4 hours and last 2 hours), so he did 1*6=6 units of job;\nThe ratio thus is 40 to 6, or 20 to 3.\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSeries B(n) is such that i*B(i) = j*B(j) for any pair of positive integers (i, j). If B(1) is a positive integer, which of the following is possible?\nI. 2*B(100) = B(99) + B(98)\nII. B(1) is the only integer in the series\nIII. The series does not contain negative numbers\n\n### Options:\nA. I only\nB. II only\nC. IIII only\nD. IIIII only\nE. I, IIIII\n\n### Answer:\nFirst thing I want to understand is this relation: i*B(i) = j*B(j) for any pair of positive integers. I will take examples to understand it.\nWhen i = 1 and j = 2, B(1) = 2*B(2)\nSo B(2) = B(1)/2\nWhen i = 1 and j = 3, B(1) = 3*B(3)\nSo B(3) = B(1)/3\nI see it now. The series is: B(1), B(1)/2, B(1)/3, B(1)/4 and so on...\nII and III are easily possible. We can see that without any calculations.\nII. B(1) is the only integer in the series\nIf B(1) = 1, then series becomes 1, 1/2, 1/3, 1/4 ... all fractions except B(1)\nIII. The series does not contain negative numbers\nAgain, same series as above applies. In fact, since B(1) is a positive integer, this must be true.\nI. 2*B(100) = B(99) + B(98)\n2*B(1)/100 = B(1)/99 + B(1)/98 (cancel B(1) from both sides)\n2/100 = 1/99 + 1/98\nNot true hence this is not possible\nAnswer (D)\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train passes a platform in 32 seconds. The same train passes a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, The length of the platform is\n\n### Options:\nA. 180 meter\nB. 240 meter\nC. 200 meter\nD. 260 meter\nE. None of these\n\n### Answer:\nExplanation:\nSpeed of the train = 54 km/hr = (54\u00d710)/32 m/s = 15 m/s\nLength of the train = speed \u00d7 time taken to cross the man = 15\u00d720 = 300 m\nLet the length of the platform = L\nTime taken to cross the platform = (300+L)/15\n=> (300+L)/15 = 32\n=> 300+L = 15\u00d732 =480\n=> L = 480-300 = 180 meter\nAnswer: Option A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe no. of gift pack bought by Dexter is 1 more than the price, in rupees, of each gift pack. The amount of Rs.380 which Dexter had, fell short of the required amount. What is theamount by which he might have fallen short.\n\n### Options:\nA. 38\nB. 40\nC. 45\nD. 48\nE. 49\n\n### Answer:\nLet the price of gift pack be 'aa'\nThen number of packs bought =a+1=a+1\nHence total cost is a(a+1)a(a+1)\nIt is given that 380", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf x and y are different integers and x^2 = xy, which of the following must be true ?\nI. x = 0\nII. y = 0\nIII. x = -y\n\n### Options:\nA. I only\nB. II only\nC. III only\nD. I and III only\nE. I, II, and III\n\n### Answer:\nRe-arrange equation: x^2 - xy = 0 => x*(x-y) = 0\nTherefore, either x=0 or x=y. We know that x and y are different, so x must be equal to 0.\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich of the following inequalities has (have) a finite range of values of \"x\" satisfying it (them)?\n\n### Options:\nA. x^2 + 5x + 6 > 0\nB. |x + 2| > 4\nC. 9x - 7 < 3x + 14\nD. x^2 - 4x + 3 < 0\nE. (B) and (D)\n\n### Answer:\nFactorizing x^2 - 4x + 3 < 0 we get, (x - 3)(x - 1) < 0.\nThis inequality will hold good when one of the terms (x - 3) or (x - 1) is positive and the other is negative.\nEvaluating both the options, we get 1 < x < 3. i.e., a finite range of values for \"x\".\nANSWER : D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe speed of a car increases by 2 kms after every one hour. If the distance travelling in the first one hour was 35 kms. what was the total distance travelled in 12 hours?\n\n### Options:\nA. 252 kms\nB. 152 kms\nC. 552 kms\nD. 752 kms\nE. 152 kms\n\n### Answer:\nExplanation:\nTotal distance travelled in 12 hours =(35+37+39+.....upto 12 terms)\nThis is an A.P with first term, a=35, number of terms,\nn= 12,d=2.\nRequired distance = 12/2[2 x 35+{12-1) x 2]\n=6(70+23)\n= 552 kms.\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSales price is $54, gross profit is 125% of cost, what is the value of gross profit?\n\n### Options:\nA. 32\nB. 30\nC. 39\nD. 40\nE. 42\n\n### Answer:\nCost + Profit = Sales\nCost + (125/100)Cost = 54\nCost = 24\nProfit = 54 - 24 = 30\nAnswer (B)\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMr X, a businessman, had income in the year 1995 such that he earned a profit of 20% on his investment in the business. In the year 1996 his investment was less by 5000 but still had the same income (Income = Investment + Profit) as that in 1995. Thus the per cent profit earned in 1996 increased by 6%. What was his investment in 1995?\n\n### Options:\nA. 100000\nB. 100500\nC. 105000\nD. Data inadequate\nE. None of these\n\n### Answer:\nLet the investment of X in 1995 be x.\n\u2234 Profit = x\u20445\n\u2234 Income = (x + x\u20445) = 6\u20445x\nInvestment of company X in 1996 would be (x \u2013 5000) From the question,\n(x - 500) \u00d7 126\u2044100 = 6\u20445x \u21d2 x = 105000\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA sales representative receives a salary of $100 per week and earns a commission of 20% on all sales she makes. How many dollars\u2019 worth of sales does she need to make in order to bring her total weekly income to $600?\n\n### Options:\nA. $3,000\nB. $3,150\nC. $4,000\nD. $2,500\nE. $5,000\n\n### Answer:\nWe're told that a sales representative receives a salary of $100 per week and earns a commission of 20% on all sales she makes. We're asked how many dollars\u2019 worth of sales will bring her total weekly income to $600.\nSince the salesperson receives a $100 salary, the remaining $500 has to be accounted for by the 20% commission. Since those numbers are rather specific, we're likely dealing with a 'round number' for total sales.\nLet's TEST Answer C: $4,000\nSince 20% of $1,000 = $200\n20% of $4,000 = 4($200) = $800\nThis is TOO HIGH (it's supposed to be $500), so we need a LOWER total sales figure.\nLet's TEST Answer D: $2,500\nSince 20% of $1,000 = $200\n20% of $2,500 = 2.5($200) = $500\nThis is an exact MATCH for what we were told, so this MUST be the answer.\nFinal Answer:\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA and B together invested Rs. 15,000 in a business. At the end of the year, out of total profit is Rs. 3,000 B's share was Rs. 1000. A's investment was\n\n### Options:\nA. s. 4,500\nB. s. 8,250\nC. s. 9,500\nD. s. 10,000\nE. s. 12,250\n\n### Answer:\nA+B=15000\ntotal profit=3000\n3000-1000=2000\n2000;1000=2:1\nthen 2*15000/3=10000\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the circumference of a circle increases from 4pi to 8 pi, what change occurs in the area ?\n\n### Options:\nA. Area is quadrupled\nB. Area is tripled\nC. Area is doubles\nD. Area become half\nE. None of these\n\n### Answer:\nExplanation:\n2\u03c0R1=4\u03c0\n=>R1=22\u03c0R2=8\u03c0\n>R2=4Original Area =4\u03c0\u221722=16\u03c0New Area =4\u03c0\u221742=64\u03c0\nSo the area quadruples.\nOption A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAmong 700people, 56% like strawberry jam, 44% like apple jam, and 40% like raspberry jam. If 30% of the people like both strawberry and apple jam, what is the largest possible number of people who like raspberry jam but do not like either strawberry or apple jam?\n\n### Options:\nA. 20\nB. 60\nC. 80\nD. 186\nE. 210\n\n### Answer:\n56%+44%-30%=70% who like either Strawberry, Apple, or both.\nThat means 100%-70% = 30% do not like either Apple of Strawberry jam.\n30% is the most possible that like raspberry jam but do not like either strawberry or apple (assuming nobody in the group does not like any)\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nShane is playing a board game. For his first turn he moved ahead 3 spaces, for the second, 5\nspaces and for the third, 1 space. For his next turn he had to go back 6 spaces. After that he got\na card that said he could move two times the biggest forward move he had done so far. Now how\nmany spaces from the beginning is Shane\u2019s game piece?\n\n### Options:\nA. 3\nB. 13\nC. 23\nD. 33\nE. 43\n\n### Answer:\nYou may want to draw this one.\nbiggest move is 5, so two times\nbiggest move is 10.\n3 + 5 + 1 = 9\n9 - 6 = 3\n3 + 10 = 13, so he is 13 spaces\nfrom the beginning.\ncorrect answer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe ratio of three numbers is 6:7:5 and their sum is 108. The second number of the three numbers is?\n\n### Options:\nA. 12\nB. 42\nC. 30\nD. 36\nE. None of these\n\n### Answer:\nExplanation:\n6:7:5\nTotal parts = 18\n18 parts --> 108\n1 part ---->6\nThe second number of the three numbers is = 7\n7 parts ----> 42\nAnswer: Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn covering a distance of 24 km, Abhay takes 2 hours more than Sameer. If Abhay doubles his speed, then he would take 1 hour less than Sameer. Abhay's speed is:\n\n### Options:\nA. 4 kmph\nB. 6 kmph\nC. 6.25 kmph\nD. 7.5 kmph\nE. 7.8 kmph\n\n### Answer:\nLet Abhay's speed be x km/hr.\nThen,\t24/X\t-\t24/2X\t= 3\n6x = 24\nx = 4 km/hr. Answer: Option A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOn a certain transatlantic crossing, 40 percent of a ship\u2019s passengers held round-trip tickets and also took their cars abroad the ship. If 50 percent of the passengers with round-trip tickets did not take their cars abroad the ship, what percent of the ship\u2019s passengers held round-trip tickets?\n\n### Options:\nA. 40%\nB. 50%\nC. 60%\nD. 80%\nE. 90%\n\n### Answer:\nLet T be the total number of passengers.\nLet x be the number of people with round trip tickets.\n0.4T had round trip tickets and took their cars.\n0.5x had round trip tickets and took their cars.\n0.5x = 0.4T\nx = 0.8T\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe division of a whole number N by 14 gives a quotient of 18 and a remainder of 2. Find N.\n\n### Options:\nA. 797\nB. 254\nC. 597\nD. 997\nE. 297\n\n### Answer:\nAccording to the division process of whole numbers, N can be written, using multiplication, as follows\nN = quotient *divisor + remainder = 18* 14 + 2 = 254 correc answer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nfor which value of n, 4^85+2^3373+4^n will be the perfect square ??\n\n### Options:\nA. 1878\nB. 1978\nC. 1578\nD. 2578\nE. 3287\n\n### Answer:\ngiven expression is in the form of a^2+2ab+b^2\n4^85=2^2(85)\n4^n=2^2n\n2^3373=2*2^85*2^n\n3373=85+1+n\nn=3373-86=3287\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe president of a country and 4 other dignitaries are scheduled to sit in a row on the 5 chairs represented above. If the president must sit in the center chair, how many different seating arrangements are possible for the 5 people?\n\n### Options:\nA. 4\nB. 5\nC. 20\nD. 24\nE. 120\n\n### Answer:\nIf the president is sitting in the center, you only have 4 chairs left. There are 4 possibilities for 1st chair, 3 possibilities for 2nd chair, 2 possibilities for 3rd chair, and 1 for last chair. Multiply all those and you get 24.\nANS:D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA and B started business in partnership investing Rs. 20,000 and Rs. 15,000 respectively. After six months, C joined them with Rs. 20,000. What will be B's share in the total profit of Rs. 24,000 earned at the end of 2 years from the starting of the business?\n\n### Options:\nA. A)7500\nB. B)7389\nC. C)7200\nD. D)7453\nE. E)7637\n\n### Answer:\nA:B:C = (20000 * 24) : (15000 * 24) : (20000 * 18) = 4:3:3\nB's share = 24000 * 3/10 = Rs.7200.\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe sum of the first 50 positive even integers is 2550. What is the sum W of even integers from 102 to 200 inclusive?\n\n### Options:\nA. 5100\nB. 7550\nC. 10100\nD. 15500\nE. 20100\n\n### Answer:\nMy solution is:\nFirst 50 even integers:\n2\n4\n6\n8\n<...>\nIntegers from 102 to 200\n102\n104\n106\n108\n<...>\nWe notice that each integer from the second set is 100 more than the respective integer in the first set. Since we have 50 even integers from 102 to 200, then:\nW=2550+(100*50)=7550.B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA sum of money deposited at C.I. amounts to Rs.6000 in 6 years and to Rs.7500 in 7 years. Find the rate percent?\n\n### Options:\nA. 25%\nB. 20%\nC. 15%\nD. 10%\nE. 5%\n\n### Answer:\n6000 --- 1500\n100 --- ? => 25%\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTrain A left Centerville Station, heading toward Dale City Station, at 3: 00 p.m. Train B left Dale City Station, heading toward Centerville Station, at 0: 20 p.m. on the same day. The trains rode on straight tracks that were parallel to each other. If Train A traveled at a constant speed of 30 miles per hour and Train B traveled at a constant speed of 10 miles per hour, and the distance between the Centerville Station and Dale City Station is 90 miles, when did the trains pass each other?\n\n### Options:\nA. 4: 45 p.m.\nB. 2: 20 p.m.\nC. 5: 20 p.m.\nD. 5: 35 p.m.\nE. 6: 00 p.m.\n\n### Answer:\nthe distance travelled by the train A in first 20 minutes will be 10.\nThe distance which will be remaining is 80.\nNow both trains are running in opposite direction.Their speed will be added so 40.\nTime at which they will meet =80/40=2\ntime of train B will be 0:20 +2=2:20\nHence answer is B.Hope i am correct\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man's speed with the current is 15 km/hr and the speed of the current is 2.5 km/hr. The man's speed against the current is:\n\n### Options:\nA. 8.5 km/hr\nB. 9 km/hr\nC. 10 km/hr\nD. 12.5 km/hr\nE. 25km/hr\n\n### Answer:\nExplanation:\nMan's rate in still water = (15 - 2.5) km/hr = 12.5 km/hr.\nMan's rate against the current = (12.5 - 2.5) km/hr = 10 km/hr.\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 3 tic equals 6 tacs and 2 tacs equal 7 tocs, what is the ratio of one tic to one toc?\n\n### Options:\nA. 7/1\nB. 6/5\nC. 5/6\nD. 3/10\nE. 1/15\n\n### Answer:\n3Tic=6*Tac and 2*Tac=7*Toc;\n6*Tic=12*Tac and 12*Tac=42*Toc --> 6*Tic=42*Toc --> Tic/Toc=42/6=7/1.\nAnswer: A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJohn invests $x at the semi-annual constant compounded rate of 2 percent and also does $8,000 at the quarterly constant compounded rate of 4 percent. If the interests are the same after 1 year, what is the value of x??\n\n### Options:\nA. 10000\nB. 12000\nC. 16160.8\nD. 14000\nE. 15000\n\n### Answer:\nA = P(1+r/n)^nt\nA= total amount accrued\nP = principal deposited\nr = rate of interest in decimal form\nn = number of times per year, interest compounded\nt = time in number of years.\n.\nx(1+0.02/2)^2 - x = 8,000(1+0.04/4)^4 - 8,000 [ when the principal is subtracted from the total amount accrued , the resulting difference is the interest portion and question states interests are equal)\n=> x[(1.01)^2 - 1] = 8,000[(1.01)^4 - 1]\n=> x[(1.01)^2 - 1] = 8,000[(1.01)^2+1][(1.01)^2-1] --> Using a^2-b^2 = a+b X a-b formula and cancel common expression on both sides\n=> x = 8,000(1.0201+1) =16160.8\nHence answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the simple interest on Rs. 70,400 at 16 2/3% per annum for 9 months.\n\n### Options:\nA. s.8500\nB. s.8000\nC. s.7500\nD. s.8800\nE. s.6500\n\n### Answer:\nP = Rs.70400,R = 50/3% p.a and T = 9/12 years = 3/4years.\nS.I. = (P*R*T)/100 = Rs.(70,400*(50/3)*(3/4)*(1/100))\n= Rs.8800\nAnswer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe sum of four consecutive even numbers is 36. Find the sum of the squares of these numbers?\n\n### Options:\nA. 323\nB. 377\nC. 344\nD. 239\nE. 112\n\n### Answer:\nExplanation:\nLet the four numbers be x, x + 2, x + 4 and x + 6.\n=> x + x + 2 + x + 4 + x + 6 = 36\n=> 4x + 12 = 36 => x = 6\nThe numbers are 6, 8, 10 and 12.\nSum of their squares = 62 + 82 + 102 + 122 = 36 + 64 + 100 + 144 = 344.\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n80% of 5/8 =\n\n### Options:\nA. 0.2\nB. 0.5\nC. 0.6\nD. 0.75\nE. 1.0\n\n### Answer:\nShould be simple.\n0.8*5/8 = 4/8 = 1/2 = 0.5\nCorrect Option : B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the unit digit in 8^100?\n\n### Options:\nA. 0\nB. 1\nC. 6\nD. 3\nE. 5\n\n### Answer:\nUnit digit in 8^100 = unit digit in [(8^4)^25 ]\rBut unit digit in 8^4=6\runit digit 8^100= 6\rAnswer is C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMark bought a set of 6 flower pots of different sizes at a total cost of $8.25. Each pot cost 0.1 more than the next one below it in size. What was the cost, in dollars, of the largest pot?\n\n### Options:\nA. $1.62\nB. $1.85\nC. $2.00\nD. $2.15\nE. $2.30\n\n### Answer:\nThis question can be solved with a handful of different Algebra approaches (as has been shown in the various posts). Since the question asks for the price of the largest pot, and the answers are prices, we can TEST THE ANSWERS.\nWe're told that there are 6 pots and that each pot costs 25 cents MORE than the next. The total price of the pots is $8.25. We're asked for the price of the largest (most expensive) pot.\nSince the total price is $8.25 (a 10-cent increment) and the the difference in sequential prices of the pots is 10 cents, the largest pot PROBABLY has a price that is a 10-cent increment. From the answer choices, I would then TEST Answer A first\nIF....\nThe largest pot = $1.625\n1.125\n1.225\n1.325\n1.425\n1.525\n1.625\nTotal = $8.25\nSo this MUST be the answer.\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMohit sold an article for Rs. 18000. Had he offered a discount of 10% on the selling price, he would have earned a profit of 8%. What is the cost price of the article?\n\n### Options:\nA. 15000\nB. 15002\nC. 15029\nD. 15329\nE. 15012\n\n### Answer:\nLet the CP be Rs. x.\nHad he offered 10% discount, profit = 8%\nProfit = 8/100 x and hence his SP = x + 8/100 x = Rs. 1.08x = 18000 - 10/100(18000) = 18000 - 1800 = Rs. 16200\n=> 1.08x = 16200\n=> x = 15000\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\na man prpare the technical document it takes 2 hours for half an hour presentation and technical preparation. its screening takes 30 more minuts to prepare with the other guy.for to present a 7 half an hours how much time it will take\n\n### Options:\nA. 37 hours\nB. 35 hours\nC. 37 1/2 hours\nD. 33 hours\nE. 34 hours\n\n### Answer:\nhere first 2 hours to prepare a technical document and half-an-hour to screen it ..so total 2 1/2 hour work is need to 1/2 hour presentation....\nFor 7 1/2 hours presentation...\n1/2 hour presentation-------------->>2 1/2 hour work done\n7 1/2 hr presentation --------------> x hours work done\njust do cross multiplication u will get x value i.e. required amount of time\nsince 7 1/2 hours contains 15 half-an-hours ...15* 2 1/2===== 30+7.5===total 37 1/2 hours\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOn Sunday, Bill ran 4 more miles than he ran on Saturday. Julia did not run on Saturday, but she ran twice the number of miles on Sunday that Bill ran on Sunday. If Bill and Julia ran a total of 20 miles on Saturday and Sunday, how many miles did Bill run on Sunday?\n\n### Options:\nA. 5\nB. 6\nC. 7\nD. 8\nE. 9\n\n### Answer:\nLet Bill run x on saturday, so he will run x+4 on sunday..\nJulia will run 2*(x+4) on sunday..\ntotai= x+x+4+2x+8=20..\n4x+12=20..\nx=2..\nans =x+4=2+4=6\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTough and Tricky questions: Arithmetic.\n(8^2 + 8^2)/4^2 =\n\n### Options:\nA. 4\nB. 29\nC. 8\nD. 58\nE. 116\n\n### Answer:\nAns is 8\nmy approach was:\n(8^2 + 8^2)/4^2 =8(8+8)/4*4\n=8*16/4*4=2*4=8\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf n is a 27-digit positive integer, all of whose digits are the same, which of the following must be true?\nI. n is divisible by 3\nII. n is divisible by 9\nIII. n is divisible by 27\n\n### Options:\nA. I only\nB. I and II only\nC. I and III only\nD. II and III only\nE. I, II and III\n\n### Answer:\nRule for divisibility by 3: The sum of the digits of the number should be multiple of 3\nRule for divisibility by 9: The sum of the nos digits of the number should be divisible by 9 or the number should be divisible by 3 two times.\nRules for divisibility by 27: The sum of the digits should a multiple of 27\nConsider no 11111111...27 times = The sum 27*1=27----> divisbible by 3,9 and 27\nconsider number to be 222....27 times, then sum of the no. 27*2=54 divisible by 3,9 and 27\nSo why so because when you sum the numbers either you can add the digits 27 times or multiply the digit *27..\nNote that since 27 is divisible by 27,9 and 3 and thus the sum of the nos will be divisible by all the nos.\nAnswer is E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the odd man out. 742, 743, 633, 853, 871, 990, 532\n\n### Options:\nA. 532\nB. 990\nC. 633\nD. 742\nE. 871\n\n### Answer:\nExplanation :\nIn all numbers except 742, the difference of third and first digit is the middle digit.\nAnswer : Option D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe C.P of 10 pens is equal to the S.P of 12 pens. Find his gain % or loss%?\n\n### Options:\nA. 16 2/6%\nB. 16 9/3%\nC. 16 2/3%\nD. 16 3/3%\nE. 12 2/3%\n\n### Answer:\n10 CP = 12 SP\n12 --- 2 CP loss\n100 --- ? => 16 2/3%\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRobert ate 10 chocolates, Nickel ate 5 chocolates. How many more chocolates did Robert ate than nickel?\n\n### Options:\nA. A)4\nB. B)7\nC. C)9\nD. D)5\nE. E)2\n\n### Answer:\n10-5=5. Answer is D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the minimum value of z for which z^2 + z - 3/8> 0 is not true?\n\n### Options:\nA. -5/2\nB. -3/2\nC. -1/2\nD. -3/4\nE. 1/2\n\n### Answer:\nI think D -3/4 is the best ans...\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nBenny goes to the market for buying some apples to be distributed between her nine kids equally.She takes 360 dollars with her .The cost of each apple is 4 dollars .How many apples does she buy to share them equally between her eighteen kids?\n\n### Options:\nA. 8\nB. 9\nC. 5\nD. 7\nE. 10\n\n### Answer:\ncost of each apple = 4 dollars\nApples that Benny can buy with the amount she has=360/4 = 90.\nApples that each kid gets evenly = 90/18 = 5 Apples.\nSo the answer is C=5\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nLine m lies in the xy-plane. The y-intercept of line m is -1, and line m passes through the midpoint of the line segment whose endpoints are (2, 4) and (6, -8). What is the slope of line m ?\n\n### Options:\nA. -3\nB. -1\nC. -1/3\nD. 0\nE. Undefined\n\n### Answer:\nAns: E\nSolution: line m goes through midpoint of (2, 4) and (6, -8). midpoint is (4,-2)\nas we can see that the y axis of intercept point is (0,-1) means line m is parallel to x axis\nslope M= 0\nAns: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich of the following is a prime number\n\n### Options:\nA. 13\nB. 14\nC. 15\nD. 16\nE. 18\n\n### Answer:\nClearly, 13 is a prime number.\nOption A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the next number in the series below ?\n298 209 129 58 ?\n\n### Options:\nA. 5\nB. 10\nC. -4\nD. -10\nE. 0\n\n### Answer:\nC\n-4\n298 less 209 is 89\n209 less 129 is 80\n129 less 58 is 71\n58 less -4 is 62\nThe result of each subsequent equation is 9 less than the previous one.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man sells an article at a gain 15%. If he had bought it at 10% less and sold it for 6 less, he would have gained 25%. Find the cost price of the article.\n\n### Options:\nA. 150\nB. 160\nC. 170\nD. 180\nE. 240\n\n### Answer:\nLet the C.P. be 100\nFirst S.P. = 115\nSecond C.P. = 90\nSecond S.P = 125% of 90 = 112.50\nDifference of two selling prices is 115 \u2013 112.50 = 2.50 and C.P. of the article is 100\nBut actual difference is 6.\n\u2234 C.P. = 100\u20442.50 \u00d7 6 = 240.\nAnswer E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train 210 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?\n\n### Options:\nA. 40 sec\nB. 50 sec\nC. 44 sec\nD. 49 sec\nE. 28 sec\n\n### Answer:\nSpeed = 45 * 5/18 = 25/2 m/sec\nTotal distance covered = 210 + 140 = 350 m\nRequired time = 350 * 2/25 = 28 sec\nAnswer:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many ways are there to split a group of 4 girls into two groups of 2 girls each? (The order of the groups does not matter)\n\n### Options:\nA. 7\nB. 6\nC. 5\nD. 4\nE. 3\n\n### Answer:\nthe combination is 4C2 /2\n= 4!/2!*2! *2 = 3\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the least value of x, So that 2x5478 is divisible by 9\n\n### Options:\nA. 7\nB. 8\nC. 9\nD. 1\nE. 2\n\n### Answer:\nExplanation:\nThe sum of the digits of the number is divisible by 9.\nThen the number is divisible by 9.\n2 + x + 5 + 4 + 7 + 8 = 26 + x\nLeast value of x may be '1',\nSo that the total 26 + 1 = 27\nis divisible by 9.\nAnswer: Option D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf Rs. 782 be divided into three parts, proportional to 1/2: 2/3: 3/4, then the first part is:\n\n### Options:\nA. 202\nB. 203\nC. 204\nD. 205\nE. 206\n\n### Answer:\n(1/2+2/3+3/4)x=782\nx=782*12/23=408\nfist part is: (1/2)x=408/2=204\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 13 and 19. The larger of the two numbers is:\n\n### Options:\nA. 437\nB. 299\nC. 322\nD. 345\nE. 355\n\n### Answer:\nClearly, the numbers are (23 x 13) and (23 x 19).\nLarger number = (23 x 19) = 437. Answer: Option A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nthere is park of length 100 m and width 80m.there is path in middle of park across the length and breadth crossing each other.the breadth of path 3m.what % of park used for path?\n\n### Options:\nA. 5.53\nB. 6.63\nC. 4.43\nD. 8.61\nE. 5.81\n\n### Answer:\narea of park=100*80=8000m2.\narea of path=100*3+80*3-3*3=300+240-9=540-9=531m2.\n%of path=531/8000*100=6.6375%\nanswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a fuel station the service costs $2.05 per car, every liter of fuel costs 0.6$. Assuming that you fill up 3 mini-vans and 2 trucks, how much money will the fuel cost to all the cars owners total, if a mini- van's tank is 70 liters and a truck's tank is 120% bigger and they are all empty-?\n\n### Options:\nA. 312.6$\nB. 321.05$\nC. 343.7$\nD. 398.85$\nE. 412.12$\n\n### Answer:\nService cost of 3 van and 2 truck = 2.05*(3+2)=10.5\nFuel in 3 Van = 3*70=210 litre\nFuel in 2 Trucks =2 * 70(1+120/100)= 308\nTotal fuel(Van+Truck) = 518 Litre\nTotal Fuel cost = 518*0.6 =310.8\nTOTAL COST =FUEL+SERVICE=310.8+10.25=321.05\nANSWER IS B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA can do a piece of work in 4 hours . A and C together can do it in just 2 hours, while B and C together need 3 hours to finish the same work. B alone can complete the work in --- hours.\n\n### Options:\nA. 12 hours\nB. 6 hours\nC. 8 hours\nD. 10 hours\nE. 4 hours\n\n### Answer:\nExplanation :\nWork done by A in 1 hour = 1/4\nWork done by B and C in 1 hour = 1/3\nWork done by A and C in 1 hour = 1/2\nWork done by A,B and C in 1 hour = 1/4+1/3 = 7/12\nWork done by B in 1 hour = 7/12 \u2013 1/2 = 1/12 => B alone can complete the work in 12 hours\nAnswer : Option A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich of the following functions f(x) satisfies the condition f(y-z) = f(y)-f(z) for all possible values of y and z?\n\n### Options:\nA. f(x) = x2\nB. f(x) = x + (x\u22121)^2\nC. f(x) = x-1\nD. f(x) = 5/x\nE. f(x) = x/5\n\n### Answer:\nE. f(x) = x/5\nNow for LHS x=y-z\nso F(x) = F(y-z)\nput x as Y-Z in X/5\nf(y-z)=y-z/5= y/5-z/5---------1\nsimilarly RHS\nF(Y) = y/5---\nF(Z)=Z/5 ---\nF(Y)-F(Z)=Y/5 - Z/5------------2\nwe can see LHS =RHS ..so E remains.\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe sum of money at compound interest amounts to thrice itself in 5 years. In how many years will it be 21 times itself?\n\n### Options:\nA. 18 years\nB. 9 years\nC. 12 years\nD. 16 years\nE. 30 years\n\n### Answer:\n100 ---- 300 --- 5\n900 --- 5\n1200---5\n1500----5\n1800---5\n2100---5\n6 years\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nEach month a retailer sells 100 identical items. On each item he makes a profit of $30 that constitutes 10% of the item's price to the retailer. If the retailer contemplates giving a 5% discount on the items he sells, what is the least number of items he will have to sell each month to justify the policy of the discount?\n\n### Options:\nA. 191\nB. 213\nC. 221\nD. 223\nE. 226\n\n### Answer:\nFor this question, we'll need the following formula:\nSell Price = Cost + Profit\nWe're told that the profit on 1 item is $20 and that this represents 10% of the cost:\nSell Price = Cost + $30\nSell Price = $300 + $30\nThus, the Sell Price is $330 for each item. Selling all 100 items gives the retailer...\n100($30) = $2,000 of profit\nIf the retailer offers a 5% discount on the sell price, then the equation changes...\n5%(330) = $16.5 discount\n$313.5 = $300 + $13.5\nNow, the retailer makes a profit of just $13.5 per item sold.\nTo earn $2,000 in profit, the retailer must sell....\n$13.5(X) = $2,000\nX = 2,000/13.5\nX = 222.222222 items\nYou'll notice that this is not among the answer choices.... 221 and 223 are.\nSelling 221 items would get us 9(221) = $1989 which is NOT enough money. To get back to AT LEAST $2,000, we need to sell 223 items.\nFinal Answer:\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf n is a positive integer, then n*(n+1)*(n+2) is\n\n### Options:\nA. even only when n is even\nB. even only when n is odd\nC. odd whenever n is odd\nD. divisible by 3 only when n is odd\nE. divisible by 4 whenever n is even\n\n### Answer:\nn*(n+1)*(n+2)= +ve even integer divisible by 4 ( e.g 6,7&8)\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n10^(60) \u00c3\u00b7 10^(58) = ?\n\n### Options:\nA. 10(6)\nB. 100000\nC. 100\nD. 10000\nE. None of these\n\n### Answer:\n10^(60) \u00c3\u00b7 10^(58) = 10^ (60-58) = 10^2\n= 10*10 = 100\nAnswer : C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how many ways can 5 letters be posted in 3 post boxes, if any number of letters can be posted in all of the three post boxes?\n\n### Options:\nA. 3\nB. 9\nC. 3^5\nD. 5^3\nE. 2^4\n\n### Answer:\nThe first letter can be posted in any of the 3 post boxes. Therefore, we have 3 possibilities.\nSimilarly, the second, the third, the fourth and the fifth letter can each be posted in any of the 3 post boxes.\nEach of the 5 letters has 3 possibilities because we can post any number of letters in all of the boxes.\nTherefore, the total number of ways the 5 letters can be posted in 3 boxes is\n3 * 3 * 3 * 3 * 3 = 3^5\nAns:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA and B\u2019s salaries together amount to Rs. 2,000. A spends 95% of his salary and B spends 85% of his. If now their savings are the same, what is A\u2019s salary?\n\n### Options:\nA. 7189\nB. 7282\nC. 7298\nD. 1500\nE. 1576\n\n### Answer:\n(5/100) A = (15/100) B\nA = 3B\nA + B = 2000\n4B = 2000 => B = 500\nA = 1500\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nP says to Q \"I am thrice as old as you were when i was as old as you are\". If the sum of their present age is 100 years, then the present age of Q?\n\n### Options:\nA. 35.5\nB. 36.5\nC. 37.5\nD. 38.5\nE. 39.5\n\n### Answer:\nlet the present age of q be x\nthe age of q years back(to be defined) is x/3\nas the age of p will be x by then .\nYears passed= x-x/3=2x/3(subtracting age of q)\nso p acurrent age is x+2x/3\nand q current age is x\nadding them to 100\nwe get x =37.5\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA, B and C started a business with a total investment of Rs. 72000. A invests Rs. 6000 more than B and B invests Rs. 3000 less than C. If the total profit at the end of a year is Rs. 8640, Find B's share.\n\n### Options:\nA. Rs. 3240\nB. Rs. 2520\nC. Rs. 2880\nD. Rs. 3360\nE. None of these\n\n### Answer:\nExplanation:\nLet C's investment = Rs. x\nB's investment = Rs. (x - 3000)\nA's investment = Rs. (x - 3000 + 6000) = Rs. (x + 3000)\nNow, (A + B + C)'s investment = Rs. 72000\n=> x + (x - 3000) + (x + 3000) = 72000\n=> 3x = 72000\n=> x = 24000\nHence, A's investment = Rs. 27000\nB's investment = Rs. 21000\nC's investment = Rs. 24000\nRatio of the capitals of A, B and C\n= 27000 : 21000 : 24000\n= 9 : 7 : 8\nA's share = Rs. [(7/24) \u00c3\u2014 8640] = Rs. 2520\nAnswer: Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a shop 80% of the articles are sold at a profit of 10% and the remaining at a loss of 40%.what is the overall profit/loss?\n\n### Options:\nA. 10% profit\nB. 10% loss\nC. 15% profit\nD. no profit, no loss\nE. none\n\n### Answer:\n80*1.1+20*0.6/100=1\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a, b are the two roots of a quadratic equation such that a + b = 24 and a \u2013 b = 8, then the quadratic equation having a and b as its roots is :\n\n### Options:\nA. x2 + 2x + 8 = 0\nB. x2 - 4x + 8 = 0\nC. x2 - 24x + 128 = 0\nD. 2x2 + 8x + 9 = 0\nE. None of these\n\n### Answer:\nSol.(c) a + b = 24 and a \u2013 b = 8\n=> a = 16 and b = 8 => ab = 16 \u00d7 8 = 128\nA quadratic equation with roots a and b is\nx2 - (a + b)x + ab = 0 or x2 - 24x + 128 = 0\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe bankers gain of a certain sum due 2 years hence at 10% per annum is Rs 24 .The percent worth is\n\n### Options:\nA. 387\nB. 238\nC. 278\nD. 600\nE. 281\n\n### Answer:\nExplanation:\nT.D = (B.G * 100) / (Rate * Time)\n(24*100) / (10 * 2)\n= 120.\nP.W = (100 *T.D) / (Rate * Time)\n= (100 * 120) /(10 * 2)\n= 600\nAnswer: D) 600\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOn a certain Monday, Carlos drove to work at an average speed of 50 miles per hour and home from work along exactly the same route at an average speed of 40 miles per hour. Which of the following is closest to his average speed for both trips combined?\n\n### Options:\nA. 40\nB. 44.44\nC. 42\nD. 46\nE. 48\n\n### Answer:\nTo solve the average speed questions, we need to know the total distance and the total time.\nLet us assume that the distance from work = D\nThis will also be the distance from work to home\nHence total distance travelled = 2D\nTime in going to work = D/50,\nTime in coming back from work = D/40\nHence average speed of both the trips = 2D/ (D/50 + D/40)\n= 2*200/12 = 44.44\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSolve 7x \u2013 5 = 4x + 11\n\n### Options:\nA. 5(1/3)\nB. 6(1/3)\nC. 7(1/3)\nD. 8(1/3)\nE. 9(1/3)\n\n### Answer:\nSol.\n7x \u2013 5 = 4x + 11\n=> 7x \u2013 4x = 11 + 5\n=> 3x = 16 => x = 16/3 = 5(1/3).\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSimplify: (4 \u2013 6) \u2013 (12+17+3)-(3+5)\n\n### Options:\nA. -10\nB. -42\nC. -44\nD. -41\nE. 50\n\n### Answer:\nSolution:\n(4-6)-(12+17+3)-(3+5)\n=(-1)-32-8\n=-1-32-8\n=-33-8\n-41\nAnswer: (D)\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many steel rods, each of length 14 m and diameter 4 cm can be made out of 1.76 cm3 of steel?\n\n### Options:\nA. 80\nB. 90\nC. 100\nD. 110\nE. 120\n\n### Answer:\nVolume of 1 rod = (22/7)x(2/100) x (2/100) x 14 ) m3 =11/625 m3\nVolume of steel = 1.76 m3\nNumber of rods =(1.76 x 625/11) =100\nanswer :C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nhow many square are there between 2001....2300 I don't remember the exact series.\n\n### Options:\nA. 1\nB. 4\nC. 2\nD. 3\nE. 5\n\n### Answer:\nseries was from 2001 to 2300\n45^2=2025\n46^2=2116\n47^2=2209\n48^2=2304 (so exclude 48)\nso ans is 3 (45,46 and 47)\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe ratio of two numbers is 2 : 5 and their H.C.F. is 5. Their L.C.M. is\n\n### Options:\nA. 50\nB. 22\nC. 56\nD. 27\nE. 67\n\n### Answer:\nExplanation:\nLet the numbers be 2x and 5x. Then, their H.C.F. = x. So, x = 5.\nSo, the numbers 10 and 25.\nL.C.M. of 10 and 25 = 50.\nOption A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf an item that originally sold for c dollars was marked up by a percent and then discounted by b percent, which of the following expressions represents the final price of the item?\n\n### Options:\nA. (10,000c + 100c(a \u2013 b) \u2013 abc)/10,000\nB. (10,000c + 100c(b \u2013 a) \u2013 abc)/10,000\nC. (100c(a \u2013 b) \u2013 abc)/10000\nD. (100c(b \u2013 a) \u2013 abc)/10000\nE. 10000 /(a \u2013 b)\n\n### Answer:\nAssume c=100, a=10, b=10. So final price is 99. Now put these value each option. Only option A will give right answer.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSneha went to the stationers and bought things worth Rs. 50, out of which 50 paise went on sales tax on taxable purchases. If the tax rate was 5%. then what was the cost of the tax free items?\n\n### Options:\nA. Rs. 39.60\nB. Rs. 39.50\nC. Rs. 39.80\nD. Rs. 49.50\nE. Rs. 49.75\n\n### Answer:\nSolution\nLet the amount of taxable purchases be Rs.x.\nThen, 5% of x\t= 50/100\nx \u2039=\u203a (50/100\u00d7100/5)\n= 10\nCost of tax free items\t= Rs.[50 - (10 + 0.50)]\n= Rs. 39.50\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA person covered one-fourth of the total distance at 15 kmph and remaining distance at 24 kmph. What is the average speed for the total distance?\n\n### Options:\nA. 20 (1/8)kmph\nB. 20 (20/23)kmph\nC. 20 (17/23)kmph\nD. 27 (1/23)kmph\nE. 21 (1/8)kmph\n\n### Answer:\nLet the total distance be x km\ntotal time taken = (x/4)/15 + (3x/4)/24 = x/60 + x/32 = 23x/480\nAverage speed = x/(23x/480) = 480/23kmph\n= 20 (20/23)kmph.\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average of 2,7,6 and x is 5. Find the value of x?\n\n### Options:\nA. 10\nB. 8\nC. 12\nD. 15\nE. 5\n\n### Answer:\naverage = (2+7+6+x)/4 = 5\nx = 5\nAnswer is E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA diagonal is a line segment that connects non-adjacent vertices in a polygon. How many diagonals does an octagon have?\n\n### Options:\nA. 20\nB. 40\nC. 60\nD. 90\nE. 80\n\n### Answer:\nSelect one vertex and you can draw 5 diagonals.\nIf you draw 5 such diagonals for each of the 8 vertices, you will draw a total of 5 \u00d7 8 = 40 diagonals. But you actually draw each diagonal twice, once from each of its ends. Therefore, there are a total of 40 \u00f7 2 = 20 different diagonals\ncorrect answer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how many years Rs 160 will produce the same interest at 8% as Rs. 500 produce in 4 years at 8%\n\n### Options:\nA. 13\nB. 13.5\nC. 11.5\nD. 12.5\nE. 12\n\n### Answer:\nExplanation:\nClue:\nFirstly we need to calculate the SI with prinical 500,Time 4 years and Rate 8%, it will be Rs. 160\nThen we can get the Time as\nTime = (100*160)/(160*8) = 12.5\nOption D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nf a card is drawn from a well shuffled pack of cards, the probability of drawing a spade or a king is -.\n\n### Options:\nA. 4/15\nB. 4/10\nC. 4/18\nD. 4/13\nE. 4/11\n\n### Answer:\nP(S\u1d1cK) = P(S) + P(K) - P(S\u2229K), where S denotes spade and K denotes king.\nP(S\u1d1cK) = 13/52 + 4/52 - 1/52 = 4/13\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe two lines y=x and x=-5 intersect on the coordinate plane. What is the value of the area of the figure formed by the intersecting lines and the x-axis?\n\n### Options:\nA. 7.5\nB. 10\nC. 12.5\nD. 15\nE. 17.5\n\n### Answer:\nThe point of intersection is (-5,-5).\nThe triangle has a base of length 5 and a height of 5.\narea = (1/2)*base*height = (1/2)*5*5 = 12.5\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how many ways can you seat 5 people on a bench if one of them, Rohit, does not want to sit on the middle seat or at either end?\n\n### Options:\nA. 720\nB. 1720\nC. 48\nD. 5040\nE. 10080\n\n### Answer:\nSince Rohit does not want to sit on the middle seat or at either end (3 chairs), then he can choose 2 chairs to sit. The remaining 4 people can sit in 4! ways. Thus the # of arrangements is 2*4! = 48.\nAnswer: C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf xyz represents a positive three-digit number, where x, y and z are one-digit integers, which of the following CANNOT be true?\n\n### Options:\nA. y \u2013 x - z = 9\nB. x \u2013 y - z = 9\nC. x + y + z = 9\nD. xyz = 9\nE. x/y/z = 9\n\n### Answer:\nThe (hundreds place digit, x) cannot be zero, but (tens and ones place digits; y and z) can be zero.\nA is NOT possible\nB is possible\nC is possible\nD is possible\nE is possible\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe C.P of 17 books is equal to the S.P of 20 books. Find his gain% or loss%?\n\n### Options:\nA. 16 2/3% loss\nB. 16 2/8% loss\nC. 16 3/3% loss\nD. 36 2/3% loss\nE. 15% loss\n\n### Answer:\n17 CP = 20 SP\n20 --- 3 CP loss\n100 --- ? => 15% loss\nAnswer:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train 110 meters long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going?\n\n### Options:\nA. 7 sec\nB. 6 sec\nC. 8 sec\nD. 5 sec\nE. 4 sec\n\n### Answer:\nSpeed of train relative to man = (60 + 6) km/hr = 66 km/hr\n[66 * 5/18] m/sec = [55/3] m/sec.\nTime taken to pass the man = [110 * 3/55] sec = 6 sec\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA coin is tossed live times. What is the probability that there is at the least one tail?\n\n### Options:\nA. 31/32\nB. 31/39\nC. 37/32\nD. 11/32\nE. 31/82\n\n### Answer:\nLet P(T) be the probability of getting least one tail when the coin is tossed five times.\n= There is not even a single tail.\ni.e. all the outcomes are heads.\n= 1/32 ; P(T) = 1 - 1/32\n= 31/32\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe area of one square is x^2 + 10x + 25 and the area of another square is 4x^2 \u2212 20x + 25. If the sum of the perimeters of both squares is 36, what is the value of x?\n\n### Options:\nA. 3\nB. 5\nC. 7\nD. 9\nE. 11\n\n### Answer:\nThe areas are (x+5)^2 and (2x-5)^2.\nThe lengths of the sides are x+5 and 2x-5.\nIf we add the two perimeters:\n4(x+5) + 4(2x-5) = 36\n12x = 36\nx = 3\nThe answer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo musicians, Maria and Perry, work at independent constant rates to tune a warehouse full of instruments. If both musicians start at the same time and work at their normal rates, they will complete the job in 45 minutes. However, if Perry were to work at four Maria\u2019s rate, they would take only 30 minutes. How long would it take Perry, working alone at his normal rate, to tune the warehouse full of instruments?\n\n### Options:\nA. 1 hr 20 min\nB. 1 hr 45 min\nC. 1 hr\nD. 2 hr 20 min\nE. 3 hr\n\n### Answer:\nSol:\nLets Perry Rate be P and Rate of Maria be M\n(rate)*(time)= Work or rate = work/time\nfirst equation=> P+M = 1/45\nconverting it to hrs P+M= 1/(45/60) => 1/(3/4) =>4/3\nsecond equation => M+4M =>1/30\nconverting it to hrs 5M=1/(30/60) =>1/(1/2) =>2\ntherefore M= 2/5 and P=14/15\nRate of Perry = 14/15\ntime= work/rate (work = 1 job)\nTime ~ 1 hrs\nAnswer : C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nLast year, for every 100 million vehicles that travelled on a certain highway, 94 vehicles were involved in accidents. If 3 billion vehicles travelled on the highway last year, how many of those vehicles were involved in accidents? (1 billion = 1,000,000,000)\n\n### Options:\nA. 288\nB. 320\nC. 2,820\nD. 3,200\nE. 28,800\n\n### Answer:\nTo solve we will set up a proportion. We know that \u201c100 million vehicles is to 94 accidents as 3 billion vehicles is to x accidents\u201d. To express everything in terms of \u201cmillions\u201d, we can use 3,000 million rather than 3 billion. Creating a proportion we have:\n100/94= 3,000/x\nCross multiplying gives us:\n100x = 3,000 * 94\nx = 30 * 94 = 2,820\nCorrect answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nLength of a rectangular plot is 20 mtr more than its breadth. If the cost of fencingthe plot at 26.50 per meter is Rs. 5300, what is the length of the plot in meterr?\n\n### Options:\nA. 40 m\nB. 60 m\nC. 65 m\nD. 70 m\nE. 80 m\n\n### Answer:\nLet breadth = x metres.\nThen, length = (x + 20) metres.\nPerimeter = 5300 m = 200 m.\n26.50\n2[(x + 20) + x] = 200\n2x + 20 = 100\n2x = 80\nx = 40.\nHence, length = x + 20 = 60 m\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHendrix works 20 days a month at d dollars per day for m months out of the year. Which of the following represents his 5 year pay?\n\n### Options:\nA. m/(20d*5)\nB. 100md\nC. 50md/6\nD. 20d/5m\nE. 20d/5\n\n### Answer:\nTotal income of Amber in a year = d*20*m dollars. Now 5 year income = Total*5= d*20*m *5 = 100md Answer is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn an IT company, there are a total of 90 employees including 50 programmers. The number of male employees is 80, including 35 male programmers. How many employees must be selected to guaranty that we have 3 programmers of the same sex?\n\n### Options:\nA. 10\nB. 45\nC. 55\nD. 35\nE. 65\n\n### Answer:\nYou could pick 40 non-programmers, 2 male programmers, and 2 female programmers, and still not have 3 programmers of the same sex. But if you pick one more person, you must either pick a male or a female programmer, so the answer is 45.\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA pipe can fill a cistern in 18 minutes whereas the cistern when fill can be emptied by a leak in 36 minutes. When both pipes are opened, find when the cistern will be full?\n\n### Options:\nA. 17\nB. 36\nC. 70\nD. 13\nE. 12\n\n### Answer:\n1/18 - 1/36 = 1/36\n36 minutes\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are 12 stamps from which two stamps will be selected. We have five stamps which are the same as five of the stamps which could be selected. What is the probability that the two stamps selected will be different from the stamps that we have?\n\n### Options:\nA. 3/14\nB. 5/19\nC. 7/22\nD. 9/23\nE. 11/28\n\n### Answer:\nP(first stamp is different) = 7/12\nP(second stamp is different) = 6/11\nP(both stamps are different) = 7/12*6/11 = 7/22\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat sum of money will produce Rs.70 as simple interest in 5 years at 3 1/2 percent?\n\n### Options:\nA. 337\nB. 500\nC. 266\nD. 400\nE. 211\n\n### Answer:\n70 = (P*5*7/2)/100\nP = 400\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a pack of playing cards a card is drawn at random. What is the probability that the card selected is a red king card?\n\n### Options:\nA. 1/26\nB. 1/13\nC. 3/26\nD. 2/13\nE. 5/26\n\n### Answer:\nTotal cards=52. Number of red king cards=2. Probability of selecting a red king card=2/52=1/26.\nCorrect Answer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn an election, candidate Smith won 52% of the total vote in Counties A and E. He won 61% of the vote in County A. If the ratio of people who voted in County A to County E is 3:1, what percent of the vote did candidate Smith win in County E ?\n\n### Options:\nA. A.25%\nB. B.27%\nC. C.34%\nD. D.43%\nE. E.49%\n\n### Answer:\n(61%)*3x + (y%)*x = (52%)*4x\ny = 25% of County E\nhence answer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA caterer ordered 125 ice-cream bars and 125 sundaes. If the total price was $250.00 and the price of each ice-cream bar was $0.60, what was the price of each sundae?\n\n### Options:\nA. $0.60\nB. $0.80\nC. $1.00\nD. $1.20\nE. $1.40\n\n### Answer:\nLet price of a sundae = S\nPrice of ice cream bar = .6 $\n125 * .6 + 125*S = 250\n=> 125*S = 175\n=> S = 1.4\nAnswer E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\ntotal 63 matches are conducted in Knockout match type. How many players will be participated in that tournament?\n\n### Options:\nA. 60\nB. 61\nC. 62\nD. 63\nE. 64\n\n### Answer:\n64 players\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA number when divided by the sum of 555 and 445 gives two times their difference as quotient and 30 as remainder. The number is\n\n### Options:\nA. 22030\nB. 220030\nC. 23030\nD. 24030\nE. 20303\n\n### Answer:\nExplanation:\n(555 + 445) * 2 * 110 + 30 = 220000 + 30 = 220030\nOption B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are 193 items that are members of set U. Of these items, 49 are members of set B, 59 are not members of either of set A or set B, and 25 are members of both sets A and B. How many of the members of set U are members of set A ?\n\n### Options:\nA. 72\nB. 85\nC. 110\nD. 98\nE. 108\n\n### Answer:\nYou had the answer almost right. The x = 85 refers to ONLY set A.\nHowever what's being asked is how many members are part of set A. This will include:\n1. Only Set A\n2. Set A and Set B\nSo the answer is Set A = 85 + Set AB = 85+25= 110\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe triplicate ratio of 1:9 is?\n\n### Options:\nA. 1:0\nB. 1:8\nC. 1:7\nD. 1:2\nE. 1:729\n\n### Answer:\n13: 93 = 1:729\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA, B and C invested Rs.6300, Rs.4200 and Rs.10500 respectively, in a partnership business. Find the share of A in profit of Rs.12100 after a year?\n\n### Options:\nA. Rs.3630\nB. Rs.2840\nC. Rs.3200\nD. Rs.5600\nE. Rs.3000\n\n### Answer:\nExplanation:\n6300:4200:10500\n3:2:5\n3/10 * 12100 = 3630\nANSWER IS A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWalking 6/7th of his usual speed, a man is 12 minutes too late. What is the usual time taken by him to cover that distance?\n\n### Options:\nA. 1 hour 10 minutes\nB. 1 hour 82 minutes\nC. 2 hour 12 minutes\nD. 1 hour 12 minutes\nE. 1 hour 62 minutes\n\n### Answer:\nNew speed = 6/7 of usual speed\nSpeed and time are inversely proportional.\nHence new time = 7/6 of usual time\nHence, 7/6 of usual time - usual time = 12 minutes\n=> 1/6 of usual time = 12 minutes\n=> usual time = 12 x 6 = 72 minutes = 1 hour 12 minutes\nAnswer :D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a certain sample of data has a mean of 11.0 and the value 20.0 is more than 2.5 standard deviations from the mean, which of the following could be the standard deviation of the sample\n\n### Options:\nA. 14.75\nB. 3.55\nC. 4.25\nD. 4.0\nE. 2.75\n\n### Answer:\n20.0 is more than 2.5 standard deviations from 11 --> 20 > 11 + 2.5*{SD} --> 2.5*{SD} < 9 --> {SD} < 3.6. Only option B offers the standard deviation less than 3.6.\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the President and Vice President must sit next to each other in a row with 4 other members of the Board, how many different seating arrangements are possible?\n\n### Options:\nA. 120\nB. 240\nC. 300\nD. 360\nE. 720\n\n### Answer:\nWe need to take President and VP as one unit. Therefore we have 5 people to arrange=5! ways\nAlso, we both President and VP can be arranged in 2 ! ways.\nReqd no of ways=5!*2!=240 ways\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOut of 9 fruits in a basket, 2 are rotten. If two fruits are drawn at random from the basket, the probability of both being rotten is\n\n### Options:\nA. 1/36\nB. 10/36\nC. 20/36\nD. 11/36\nE. 2/36\n\n### Answer:\nThe number of exhaustive events = 9C2 = 36.\nLet E be event of the 2 fruits being rotten. The number of favourable cases are\n2C2 = 1 way.\nRequired probability = 1/36.\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA bowl of nuts is prepared for a party. Brand P mixed nuts are 20% almonds and Brand Q's Deluxe nuts are 25% almonds. If a bowl contains a total of 64 ounces of nuts, representing a mixture of both brands, and 14 ounces of the mixture are almonds, how many ounces of Brand Q's Deluxe mixed nuts are used?\n\n### Options:\nA. 14\nB. 20\nC. 32\nD. 44\nE. 48\n\n### Answer:\nlets say x ounces of P is mixed with Q.\n=> 64-x ounces of Q is present in the mixture (as the total = 64 ounces)\ngiven total almond weight = 14 ounces\n(20x/100)+(25/100)(64-x) = 14\n=> x = 40\n=> 64-40 = 14 ounces of Q is present in the mixture.\nAnswer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe speed at which a man can row a boat in still water is 15 kmph. If he rows downstream, where the speed of current is 3 kmph, what time will he take to cover 60 metres?\n\n### Options:\nA. 22 seconds\nB. 65 seconds\nC. 78 seconds\nD. 12 seconds\nE. 21 seconds\n\n### Answer:\nSpeed of the boat downstream\n= 15 + 3 = 18 kmph\n= 18 * 5/18 = 5 m/s\nHence time taken to cover 60 m\n= 60/5 = 12 seconds.\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 144/x is an integer and 180/x is an integer, which of the following must be true?\nI. 9/x is an integer.\nII. 12/x is an integer.\nIII. 36/x is an integer.\n\n### Options:\nA. I, II, and III\nB. I and II only\nC. II and III only\nD. III only\nE. I only\n\n### Answer:\nThe largest possible value of x is 36 (the greatest common factor of 108 and 180), and if x=36 then\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOn a certain Monday, Carlos drove to work at an average speed of 20 miles per hour and home from work along exactly the same route at an average speed of 40 miles per hour. Which of the following is closest to his average speed for both trips combined?\n\n### Options:\nA. 24\nB. 26\nC. 27\nD. 26.66\nE. 28\n\n### Answer:\nTo solve the average speed questions, we need to know the total distance and the total time.\nLet us assume that the distance from work = D\nThis will also be the distance from work to home\nHence total distance travelled = 2D\nTime in going to work = D/20,\nTime in coming back from work = D/40\nHence average speed of both the trips = 2D/ (D/20 + D/40)\n= 2*40/3 = 26.66\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nEight people are planning to share equally the cost of a rental car. If one person withdraws from the arrangement and the others share equally the entire cost of the car, then the share of each of the remaining persons increased by:\n\n### Options:\nA. 1/7\nB. 1/8\nC. 1/9\nD. 7/8\nE. 1/5\n\n### Answer:\nOriginal share of 1 person = 1/8\nNew share of 1 person = 1/7\nIncrease =(1/7-1/8) = 1/56\nRequired fraction = (1/56)/(1/8)\n= (1/56)*8\n= 1/7\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOf the 75 house in a development, 50 have a two-car garage, 40 have an in-the-ground swimming pool, and 35 have both a two-car garage and an in-the-ground swimming pool. How many houses in the development have neither a two-car garage nor an in-the-ground swimming pool?\n\n### Options:\nA. 10\nB. 15\nC. 20\nD. 25\nE. 30\n\n### Answer:\nNeither Car nor Garage\n= Total - Garage - (Swim - Common)\n= 75 - 50 - (40-35) = 75-55 = 20\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain ski shop sells pairs of gloves in 13 different colors. If one pair of each color is dropped in a bag and a store clerk reaches in to draw two individual gloves simultaneously and at random, what is the probability that she draws two gloves of the same color?\n\n### Options:\nA. 1/144\nB. 1/143\nC. 1/25\nD. 1/23\nE. 1/12\n\n### Answer:\nthere are 13 different colours sothere are 13 pairs of gloves dropped..\nfirst can be any of 26..so 26/26..\nsecond has to be its pair, which will be just one out of remaining 25.. 1/25..\noverall prob=26/26*1/25= 1/25..\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a regular week, there are 5 working days and for each day, the working hours are 8. A man gets Rs. 2.40 per hour for regular work and Rs. 3.20 per hours for overtime. If he earns Rs. 432 in 4 weeks, then how many hours does he work for ?\n\n### Options:\nA. 160\nB. 175\nC. 180\nD. 195\nE. 172\n\n### Answer:\nExplanation:\nSuppose the man works overtime for x hours.\nNow, working hours in 4 weeks = (5 x 8 x 4) = 160.\nTherefore, 160 x 2.40 + x x 3.20 = 432\n=> 3.20x = 432 - 384 = 48\n=> x = 15.\nHence, total hours of work = (160 + 15) = 175.\nANSWER IS B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many possible ways are there to select 2 stocks at random from 7 stocks?\n\n### Options:\nA. 17\nB. 19\nC. 21\nD. 23\nE. 25\n\n### Answer:\n7C2 = 21\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nP is 6 times greater than Q then by what per cent is Q smaller than P?\n\n### Options:\nA. 84%\nB. 85.5%\nC. 80%\nD. 83.33%\nE. None\n\n### Answer:\nSolution: Let Q = 10.\nThen, P = 60.\nQ is 50 less than P.\nQ, % less than P = (50 /60)*100 = 83.33%.\nAlternative Method\n10 (Q)==(6 times greater)==> 60(P)==x%\u2193(Less than Q)==>10 (Q).\nNow, x = 50*100/60 = 83.33%.\nAnswer: Option D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA speed of 11 metres per second is the same as :\n\n### Options:\nA. 50.4 km/hr\nB. 55 km/hr\nC. 60 km/hr\nD. 68.5 km/hr\nE. 39.6 km/hr\n\n### Answer:\nSol.\n11 m/sec = [11 * 18/5] km/hr = 39.6 km/hr.\nAnswer E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a decade, a town\u2019s population increases from 175000 to 262500. What is the average % increase of population each year?\n\n### Options:\nA. 9%\nB. 2%\nC. 5%\nD. 7%\nE. 1%\n\n### Answer:\nExplanation:\nIncrease in population in 10 years= 262500-175000= 87500\nNow, % increase will be increase in (population /original population) * 100\n=> 87500/175000*100= 50% increase in population over 10 years\nTherefore, Average % increase each year= 50/10= 5%\nANSWER: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nEvaluate combination\n11C3\n\n### Options:\nA. 10000\nB. 1000\nC. 165\nD. 1\nE. 0\n\n### Answer:\nExplanation:\nnCn=1\nnCr=n!/r!(n-r)!\n11C3=11!/3!(11-3)!=165\nOption C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA candidate appearing for an examination has to secure 42% marks to pass paper I. But he secured only 42 marks and failed by 22 marks. What is the maximum mark for paper I?\n\n### Options:\nA. 110\nB. 120\nC. 130\nD. 152\nE. 150\n\n### Answer:\nhe secured 42 marks nd fail by 22 marks so\ntotal marks for pass the examinatn=64\nlet toal marks x\nx*42/100=64\nx=152\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 13 and 15. The larger of the two numbers is:\n\n### Options:\nA. 276\nB. 299\nC. 322\nD. 345\nE. 355\n\n### Answer:\nClearly, the numbers are (23 x 13) and (23 x 15).\nLarger number = (23 x 15) = 345. Answer: Option D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the value of 72519 x 9999 = m?\n\n### Options:\nA. 345466221\nB. 345455672\nC. 353456678\nD. 725117481\nE. 789545233\n\n### Answer:\n72519 x 9999 = 72519 x (10000 - 1)\n= 72519 x 10000 - 72519 x 1\n= 725190000 - 72519\n= 725117481\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA number consists of 3 digits whose sum is 10. The middle digit is equal to the sum of the other two and the number will be increased by 99 if its digits are reversed. The number is:\n\n### Options:\nA. 251\nB. 253\nC. 255\nD. 257\nE. 260\n\n### Answer:\nLet the middle digit be x.\nThen, 2x = 10 or x = 5. So, the number is either 253 or 352.\nSince the number increases on reversing the digits, so the hundred's digits is smaller than the unit's digit.\nHence, required number = 253.\nOption B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are 97 lights which are functional and each is controlled by a separate On/Off switch. Two children A and B start playing with the switches. A starts by pressing every third switch till he reaches the end. B, thereafter, presses every fifth switch till he too reaches the end. If all switches were in Off position at the beggining, How many lights are switched On by the end of this operation?\n\n### Options:\nA. 29\nB. 49\nC. 39\nD. 59\nE. 69\n\n### Answer:\nEditing my solution:\nNumber of switches = 97\nNumber of switches turned on by A: 3, 6, ... 96 = 32\nNumber of switches turned on by B: 5, 10, ....95 = 19\nFew switches are turned on by A and later turned off by B: LCM(3,5) = 15x = 15, 30,....90 = 6.\nSubtract the above 6 switches from both A and B as they are turned off.\nNumber of switches that are turned on = (32 - 6) + (19 - 6) = 39\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAjay can ride 50km in 1 hour. In how many hours he can ride 750km?\n\n### Options:\nA. 10hrs\nB. 15hrs\nC. 20hrs\nD. 25hrs\nE. 18hrs\n\n### Answer:\n1 hour he ride 50km\nhe ride 750km in = 750/50 * 1 = 15hours\nAnswer is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the annual income derived by investing $ 6800 in 20% stock at 136.\n\n### Options:\nA. 550\nB. 1000\nC. 2500\nD. 300\nE. 4000\n\n### Answer:\nBy investing $ 136, income obtained = $ 20.\nBy investing $ 6800, income obtained = $ [(20/136)*6800] = $ 1000.\nAnswer B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nBaseball's World Series matches 2 teams against each other in a best-of-seven series. The first team to win four games wins the series and no subsequent games are played. If you have no special information about either of the teams, what is the probability u that the World Series will consist of fewer than 7 games?\n\n### Options:\nA. 12.5%\nB. 25%\nC. 31.25%\nD. 68.75%\nE. 75%\n\n### Answer:\nIn order to determine the probability u that the World Series will last less than 7 games, we can first determine the probability that the World Series WILL last exactly 7 games and then subtract this value from 1.\nIn order for the World Series to last exactly 7 games, the first 6 games of the series must results in 3 wins and 3 losses for each team.\nLet's analyze one way this could happen for Team 1:\nGame 1 Game 2 Game 3 Game 4 Game 5 Game 6\nT1 Wins T1 Wins T1 Wins T1 Loses T1 Loses T1 Loses\nThere are many other ways this could happen for Team 1. Using the permutation formula, there are 6!/(3!)(3!) = 20 ways for Team 1 to win 3 games and lose 3 games in the first 6 games.\nLogically, there are also 20 ways for Team 2 to win 3 games and lose 3 games in the first 6 games.\nThus, there are a total of 40 ways for the World Series to last the full 7 games.\nThe probability that any one of these 40 ways occurs can be calculated from the fact that the probability of a team winning a game equals the probability of a team losing a game = 1/2.\nGiven that 7 distinct events must happen in any 7 game series, and that each of these events has a probability of 1/2, the probability that any one particular 7 game series occurs is.\nSince there are 40 possible different 7 game series, the probability that the World Series will last exactly 7 games is:\nThus the probability that the World Series will last less than 7 games is 100% - 31.25% = 68.75%.\nThe correct answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n9548+7314=8362=?\n\n### Options:\nA. 8230\nB. 8410\nC. 8500\nD. 8600\nE. None of them\n\n### Answer:\n=(9548+7314)=8362+x\n16862=8362+x\nx=16862-8362\n=8500\nAnswer is C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf A and B get profits of Rs. 6000 and Rs. 4000 respectively at the end of year the ratio of their investments are ?\n\n### Options:\nA. 1:4\nB. 3:2\nC. 2:3\nD. 2:5\nE. None of these\n\n### Answer:\nprofit=Investment * Time\nso,\n6000=i1 *1=6000\n4000=i2 * 1= 4000\ni1/i2=6000/4000=3/2\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf .08216 and 68.01 are multiplied to give x as product , how many digit to the right of the decimal point does x have?\n\n### Options:\nA. 8\nB. 7\nC. 6\nD. 8\nE. 9\n\n### Answer:\nProduct of .08216 and 68.01 is 5.5877016.\nTherefore number of digits to right of decimal point is 7\nAnswer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how many ways can a cricket eleven be chosen out of a batch of 15 players.\n\n### Options:\nA. 1365\nB. 1500\nC. 1406\nD. 1879\nE. 2000\n\n### Answer:\nRequired number of ways\n= 15C 11 = 15C (15-11)\n= 15 C 4\n15C4 = 15 * 14 * 13 * 12 / 4 * 3 * 2 *1\n= 1365\nANSWER A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA is two years older than B who is twice as old as C.If the total of the ages of A,B nd C be 27,then how old is B ?\n\n### Options:\nA. 7\nB. 8\nC. 9\nD. 10\nE. 11\n\n### Answer:\nSolution\nLet C's age be x years .Then,B's age =2x years.A's age =(2x +2) years.\n\u2234 (2x +2) +2x + x =27 \u21d4 5x =25 \u21d4 x =5.\nHence,B's age =2x = 10 years. Answer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many of the integers between 10 and 40 are even ?\n\n### Options:\nA. 21\nB. 20\nC. 15\nD. 10\nE. 9\n\n### Answer:\nNumber start between 10 to 40 is 30 numbers\nhalf of them is even..which is 15\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn the xy-coordinate system, if (m, n) and (m + 4, n + k) are two points on the line with the equation x = 2y + 5, then k =\n\n### Options:\nA. 1/2\nB. 1\nC. 2\nD. 5/2\nE. 4\n\n### Answer:\nSince (m, n) and (m + 2, n + k) are two points on the line with the equation x = 2y + 5 they should satisfy m=2n +5 and m+4 =2 *(n+k)+5.\nBy 1st equation we have m-2n=5 and by 2nd equation m-2n = 2k+1 ---> 5=2k+1 --->k=2.\nThe answer is, therefore, (C).\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA trail mix company keeps costs down by employing the peanuts:cashews:almonds ratio of 10:4:1 in each bag of up to 75 total nuts. What is the maximum percentage by which the company could decrease its number of peanuts per bag and still have peanuts constitute more than half the total amount of nuts?\n\n### Options:\nA. 40%\nB. 48%\nC. 49%\nD. 50%\nE. 58%\n\n### Answer:\nPeanuts = 50\nCashews = 20\nAlmonds = 5\nWe want to remove as many peanuts as possible while still having peanuts represent MORE than half of the mixture...\nThe number of cashews and almonds will stay the same though, so we have 20 + 5 = 25 of those non-peanuts in total.\nIf we had 25 peanuts and 25 non-peanuts, then that would be 50% EXACTLY. We want MORE than 50% though, so we need to add in 1 more peanut. This gives us...\nPeanuts = 26\nCashews = 20\nAlmonds = 5\nThe question asked for the decrease in the number of peanuts as a percentage. We started with 50 peanuts and removed 24 = 24/50 = 48% ;ANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSam deposited $12,000 to open a new savings account that earned eight percent annual interest, compounded semi-annually. If there were no other transactions in the account, what the amount of money in Sam account one year after the account was opened?\n\n### Options:\nA. $13,128\nB. $12,763\nC. $12,968\nD. $12,942\nE. $12,865\n\n### Answer:\nApproach #1:\n8 percent annual interest compounded semi-annually --> 2.5% in 6 moths.\nFor the first 6 moths interest was 4% of $12,000, so $480;\nFor the next 6 moths interest was 4% of $12,000,plus8% earned on previous interest of $480, so $480+$8=$488;\nTotal interest for one year was $480+$488=$968, hence balance after one year was $12,000+ $968=$12,968.\nAnswer: C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a school 50% of the students are younger than 10, 1/20 are 10 years old and 1/10 are older than 10 but younger than 12, the remaining 70 students are 12 years or older. How many students are 10 years old?\n\n### Options:\nA. 10 students\nB. 20 students\nC. 30 students\nD. 40 students\nE. 50 students\n\n### Answer:\nLet us write the fraction for each group of students\nGroup A: younger than 10: 50% = 50/100 = 1/2\nGroup B: 10 years old: 1/20\nGroup C: older that 10 but younger than 12: 1/10\nGroup D: 12 years or older: 70 students\nThe fraction for group A, B and C together is given by\n1 / 2 + 1 / 20 + 1 / 10 = 10 / 20 + 1 / 20 + 2 / 20 , common denominator\n= 13 / 20 , add numerators\nThe fraction for group D is given by\n20 / 20 - 13 / 20 = 7 / 20 and corresponds to 70 students\nIf X is the total number of students, then\n7 / 20 of X = 70\nor (7 / 20) ? X = 70\nSolve for X\nX = 70 ? (20 / 7) = 200\nStudents who are 10 years old have a fraction of 1 / 20 of the total X and their number is equal to\n(1 / 20) of 200 = 10 students\ncorrect answer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn climbing a round pole of 80 meters height, a monkey climbs 5 meters in a minute and slips 2\nmeters in the alternate minute. To get to the top of the pole, the monkey would take :\n\n### Options:\nA. 51 minutes\nB. 54 minutes\nC. 58 minutes\nD. 61 minutes\nE. 63 minutes\n\n### Answer:\na monkey climbs 5 meters in one min & slips 2m in other min.\ntherefore the monkey reach 3meters in 2min\n3m=2min\n25*3m=25*2min - >75m=50min\nhence the remaining 5m jumps the monkey in 1min to reach original height\nso 51 min\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a rod is sold for Rs.34.80, there is a loss of 25%. Find out the CP of the rod?\n\n### Options:\nA. 45\nB. 46\nC. 46.4\nD. 47.23\nE. 47.34\n\n### Answer:\nSP=34.80Loss=25%CP=100(100\u2212Loss%)\u00d7SP=100(100\u221225)\u00d734.80=10075\u00d734.80=4\u00d734.803=4\u00d711.60=46.40\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA father said to his son, \"I was as old as you are at the present at the time of your birth\". If the father's age is 42 years now, the son's age 4 years back was:\n\n### Options:\nA. 12 years.\nB. 14 years.\nC. 17 years.\nD. 16 years.\nE. 19 years.\n\n### Answer:\nLet the son's present age be x years. Then, (42 - x) = x\n2x = 42.\nx = 21\nSon's age 5 years back (21- 4) = 17 years.\nANSWER :C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe water from one outlet, flowing at a constant rate, can fill a swimming pool in 16 hours. The water from a second outlet, flowing at a constant rate, can fill the same pool in 12 hours. If both outlets are used at the same time, approximately what is the number of hours required to fill the pool?\n\n### Options:\nA. 0.22\nB. 0.31\nC. 2.50\nD. 3.21\nE. 6.85\n\n### Answer:\nAlways remember RT=W i.e Rate*Time = Work\nAlso remember that rate can be added or subtracted. For e.g if A do a work in 2 day and B do a work in 2 day.\nThey both of them together will do a work in 1 day.\nSo now your question first determine both outlets rate.\n1st outlet rate = 1/16 (R=W/T here W=1 work, T = 16hrs)\n2nd outlet rate = 1/12 (R=W/T here W=1 work, T = 12hrs)\nBoth of them working together rate = 1st outlet rate + 2nd outlet rate = 1/16+1/12 = 7/48\nagain apply the formula RT=W\nT = W/R = 1/7/48 = 48/7 =6.85\nAnswer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe largest one digit number which is a perfect cube, is:\n\n### Options:\nA. 7\nB. 8\nC. 9\nD. 1\nE. 0\n\n### Answer:\nExplanation:\n2*2*2 = 8\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nS is a set of 100 consecutive multiples of 8. If the smallest number in S is 108, then the greatest number in S is\n\n### Options:\nA. 998\nB. 297\nC. 999\nD. 902\nE. 900\n\n### Answer:\nlast term =first term +(total no. of terms-1)consecutive difference\nS is a set of 100 consecutive multiples of 8. If the smallest number in S is 108, then the greatest number in S is\nfirst term = 102 ; total terms =100 ; difference = 3\n108+(99)8 = 900\nAns E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhile purchasing one item costing Rs. 400, I had to pay the sales tax at 7% and on another costing Rs. 6400, the sales tax was 9%. What percent of the sales tax I had to pay, taking the two items together on an average ?\n\n### Options:\nA. 8 + 15/17\nB. 8 + 15/18\nC. 8 + 15/12\nD. 8 + 15/11\nE. 8 + 15/110\n\n### Answer:\nExplanation:\nTotal sales tax paid = 7% of Rs, 400 + 9% of Rs. 6400\n== Rs. (28 + 576) = Rs. 604.\nTotal cost of the items = Rs. (400 + 6400) = Rs. 6800.\nRequired percentage =% =%.\nAnswer: A) 8 + 15/17\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many seconds will a 600 meter long train moving with a speed of 63 km/hr take to cross a man walking with a speed of 3 km/hr in the direction of the train ?\n\n### Options:\nA. 48\nB. 36\nC. 26\nD. 11\nE. 18\n\n### Answer:\nExplanation:\nHere distance d = 600 mts\nspeed s = 63 - 3 = 60 kmph = 60 x 5/18 m/s\ntime t = = 36 sec.\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHealth insurance Plan P requires the insured person to pay $600 but then the insurance pays 70% of the cost over $600. Plan Q requires the insured to pay the initial $400, but then pays 60% of the cost over $400. Which of the following is a cost level for which both insurance plans pay out the same amount?\n\n### Options:\nA. $1200\nB. $1400\nC. $1600\nD. $1800\nE. $2000\n\n### Answer:\n0.7(x-600)=0.6(x-400)\n0.1x=420-240\nx=1800\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA bus started its journey from Chennai and reached Mumbai in 50 min with its average speed of 60 km/hr. If the average speed of the bus is increased by 6 km/hr, how much time will it take to cover the same distance?\n\n### Options:\nA. 45 min.\nB. 55 min.\nC. 65 min.\nD. 60 min.\nE. 50 min.\n\n### Answer:\nSol. Distance between Mumbai and Pune=(60*50)/60=50\nAverage speed of the bus is increased by 6 km/hr then the\nspeed of the bus = 66 km/hr\nRequired time = 50*66/60 = 55min.\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are 12 students in a class. On the day the test was given, Ella was absent. The other 11 students took the test and their average was 74. The next day, Ella took the test, and with this grade included, the new average was 75. What was Ella's grade on the test?\n\n### Options:\nA. 82\nB. 83\nC. 84\nD. 85\nE. 86\n\n### Answer:\n11*74+Ella's grade=12*75\nElla's grade is 12*75-11*74=86.\nThe answer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe ratio of the adjacent angles of a parallelogram is 4 : 11. Also, the ratio of the angles of quadrilateral is 5 : 6 : 7 : 12. What is the sum of the smaller angle of the parallelogram and the second largest angle of the quadrilateral?\n\n### Options:\nA. 132\u00b0\nB. 228\u00b0\nC. 156\u00b0\nD. 224\u00b0\nE. None of these\n\n### Answer:\nThe measures of the adjacent angles of a parallelogram add up to be 180\u00b0\nGiven\nSo, 4x + 11x = 180\u00b0\nOr, 15x = 180\u00b0\nOr, x = 12\u00b0\nHence the angles of the parallelogram are 48\u00b0 and 132\u00b0\nFurther it is given\nWe know sum of all the four angles of a quadrilateral is 360\u00b0\nSo, 5y + 6y + 7y + 12 y = 360\u00b0\nOr, 5y + 6y + 7y + 12 y = 360\u00b0\nOr, 30y = 360\u00b0\nOr, y = 12\u00b0\nHence the angles of the quadrilateral are 60\u00b0 , 72, 84\u00b0 and 144\u00b0\nWill be 48\u00b0 + 84\u00b0 = 132\u00b0\nAnswer : A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOut of 9 persons, 8 persons spent Rs. 30 each for their meals. The ninth one spent Rs. 20 more than the average expenditure of all the nine. The total money spent by all of them was\n\n### Options:\nA. Rs. 292.50\nB. Rs. 292.77\nC. Rs. 292.21\nD. Rs. 292.19\nE. Rs. 292.11\n\n### Answer:\nExplanation:\nLet the average expenditure be Rs. x Then,\nTotal money spent = 9x = Rs. (9 x 32.5O) = Rs 292. 50\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a group of ducks and cows, the total no.of legs are 24 more than twice the no.of heads. Find the total no.of buffaloes.\n\n### Options:\nA. 10\nB. 12\nC. 14\nD. 16\nE. 19\n\n### Answer:\nLet the number of buffaloes be x and the number of ducks be y\n=> 4x + 2y = 2 (x + y) + 24\n=> 2x = 24 => x = 12\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow much time will take for an amount of Rs. 360 to yield Rs. 81 as interest at 4.5% per annum of simple interest?\n\n### Options:\nA. 8 years\nB. 4 years\nC. 3 years\nD. 9 years\nE. 5 years\n\n### Answer:\nTime = (100 * 81) / (360 * 4.5)\n= 5 years\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich fraction should be added to:\n1/(2 \u00c3\u2014 3) + 1/(3 \u00c3\u2014 4) + 1/(4 \u00c3\u2014 5) + ....... + 1/(23 \u00c3\u2014 24)\nso that the result is equal to 1?\n\n### Options:\nA. 7/24\nB. 11/24\nC. 13/24\nD. 17/24\nE. 19/24\n\n### Answer:\nThe given expression\n= 1/(2 \u00c3\u2014 3) + 1/(3 \u00c3\u2014 4) + 1/(4 \u00c3\u2014 5) + ...... + 1/(23 \u00c3\u2014 24)\n= (1/2 - 1/3) + (1/3 - 1/4) + (1/4 - 1/5) + .......... + (1/23 - 1/24)\n= 1/2 - 1/24 = 11/24\nThus, the fraction we should add = 1 - 11/24 = 13/24\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man can row downstream at 28 kmph and upstream at 16 kmph. Find the speed of stream ?\n\n### Options:\nA. 8\nB. 5\nC. 4\nD. 6\nE. 3\n\n### Answer:\nLet the speed of the man in still water and speed of stream be x kmph and y kmph respectively.\nGiven x + y = 28 --- (1)\nand x - y = 16 --- (2)\nFrom (1) & (2) 2x = 44 => x = 22, y = 6.\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA crate measures 2 feet by 8 feet by 12 feet on the inside. A stone pillar in the shape of a right circular cylinder must fit into the crate for shipping so that it rests upright when the crate sits on at least one of its six sides. What is the radius, in feet, of the pillar with the largest volume that could still fit in the crate?\n\n### Options:\nA. 2\nB. 4\nC. 6\nD. 8\nE. 12\n\n### Answer:\nWe can find the radius of all the three cases of cylinders.\nThe only crux to find the answer faster is that:\nVoulme is pi*r^2*h. The volume is a function of r^2. so r has to be the highest to find the largest volume.\nSo r=2 for the surface 8*12 face.\nVolume = 8pi\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA car traveled from San Diego to San Francisco at an average speed of 45 miles per hour. If the journey back took twice as long, what was the average speed of the trip?\n\n### Options:\nA. 30.\nB. 32.\nC. 36.\nD. 42.\nE. 44.\n\n### Answer:\nLet the time taken be = x\nOne way distance = 45x\nTotal distance traveled = 2 * 45x = 90x\nTotal time taken = x + 2x = 3x\nAverage speed = 90x/3x = 30\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA container holding 12 ounces of a solution that is 1 part alcohol to 2 parts water is added to a container holding 8 ounces of a solution that is 1 part alcohol to 3 parts water. What is the ratio of alcohol to water in the resulting solution?\n\n### Options:\nA. 2:5\nB. 3:7\nC. 3: 5\nD. 4:7\nE. 7:3\n\n### Answer:\nContainer 1 has 12 ounces in the ratio 1:2\nor,\nx+2x=12 gives x(alcohol)=4 and remaining water =8\ncontainer 2 has 8 ounces in the ratio 1:3\nor,\nx+3x=8 gives x(alcohol)=2 and remaining water =6\nmixing both we have alcohol=4+2 and water =8+6\nratio thus alcohol/water =6/14=3/7\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA dishonest dealer professes to sell his goods at Cost Price but still gets 35% profit by using a false weight. What weight does he substitute for a kilogram?\n\n### Options:\nA. 740 1/7 grams\nB. 740 20/27 grams\nC. 740 8/3 grams\nD. 740 1/3 grams\nE. 740 1/27 grams\n\n### Answer:\nIf the cost price is Rs.100, then to get a profit of 35%, the selling price should be Rs.135.\nIf 135kg are to be sold, and the dealer gives only 100kg, to get a profit of 35%.\nHow many grams he has to give instead of one kilogram(1000 gm).\n135 gm ------ 100 gm\n1000 gm ------ ?\n(1000 * 100)/135 = 740 20/27 grams.\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA and B together can complete a work in 12 days. A alone can complete it in 20 days. If B does the work only for half a day daily, then in how many days A and B together will complete the work?\n\n### Options:\nA. 11 days\nB. 77 days\nC. 15 days\nD. 18 days\nE. 19 days\n\n### Answer:\nB's 1 day work = (1/12 - 1/20) = 1/30\nNow, (A + B)'s 1 day work = (1/20 + 1/60) = 1/15\nSo, A and B together will complete the work in 15 days.\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n96 is divided into two parts in such a way that seventh part of first and ninth part of second are equal. Find the smallest part?\n\n### Options:\nA. 66\nB. 26\nC. 42\nD. 27\nE. 11\n\n### Answer:\nx/7 = y/9 => x:y = 7:9\n7/16 * 96 = 42\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA speaks truth in 75% case and B in 80% of the cases. In what percentage of cases are they likely to contradict each other, narrating the same incident?\n\n### Options:\nA. 40\nB. 23\nC. 35\nD. 60\nE. 21\n\n### Answer:\nP( A)=75/100, P(B)=80/100\nP( A\u2019)=1/4\nP(B\u2019)=1/5\nP( A and B contradict each other)=P(A).P(B\u2019)+P(A\u2019).P(B)\n=35%\nANSWER C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf in a certain sequence of consecutive multiples of 100, the median is 750, and the greatest term is 1200, how many terms that are smaller than 650 are there in the sequence?\n\n### Options:\nA. 6\nB. 7\nC. 8\nD. 12\nE. 13\n\n### Answer:\nSince the median is 750 we know there must be a even number of integers\nSo the list around 750 must go. 700 (750) 800 900 1000 1100 ,1200\nSince we know there are 5 numbers greater than 750 then there must be 5 numbers less then 750\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA, B, K start from the same place and travel in the same direction at speeds of 30 km/hr, 40 km/hr, 100 km/hr respectively. B starts two hours after A. If B and K overtake A at the same instant, how many hours after A did K start?\n\n### Options:\nA. 4.2\nB. 4.8\nC. 5.6\nD. 6.4\nE. 7.2\n\n### Answer:\nIn 2 hours, A travels 60 km.\nB can catch A at a rate of 10 km/hr, so B catches A 6 hours after B starts.\nSo A and B both travel a distance of 240 km.\nC needs 2.4 hours to travel 240 km, so C leaves 5.6 hours after A.\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a(a - 4) = 12 and b(b -4) = 12, where a \u2260 b, then a + b =\n\n### Options:\nA. \u221248\nB. \u22125\nC. 4\nD. 46\nE. 48\n\n### Answer:\ni.e. if a = 6 then b = -2\nor if a = -2 then b = 6\nBut in each case a+b = -2+6 = 4\nAnswer: option C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nDavid covered a distance of 50 miles on his first trip. On a later trip he travelled 300 miles while going three times as fast. His new time compared with the old time was:\n\n### Options:\nA. twice as much\nB. three times as much\nC. the same\nD. half as much\nE. a third as much\n\n### Answer:\nB\nLet speed of the 1st trip x miles / hr. and speed of the 2nd trip 3x / hr.\nWe know that\nSpeed = Distance/Time.\nOr, Time = Distance/Speed.\nSo, times taken to covered a distance of 50 miles on his first trip = 50/x hr.\nAnd times taken to covered a distance of 300 miles on his later trip = 300/3x hr.\n= 100/x hr.\nSo we can clearly see that his new time compared with the old time was: twice as much.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 8 workers can build 8 cars in 8 days, then how many days would it take 6 workers to build 6 cars?\n\n### Options:\nA. 2\nB. 4\nC. 6\nD. 8\nE. 12\n\n### Answer:\n8 workers can build 1 car per day on average.\n1 worker can build 1/8 of a car per day.\n6 workers can build 6/8 car per day.\nThe time required to build 6 cars is 6 / (6/8) = 8 days\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 10 percent of national ice cream sales are for strawberry flavored ice cream, 20 percent are chocolate, and 60 percent vanilla, what fraction of of total ice cream sales are for other flavors?\n\n### Options:\nA. 4/5\nB. 3/5\nC. 3/10\nD. 1/5\nE. 1/10\n\n### Answer:\n100%-(10%+20%+60%)=10% of sales are for other flavors --> 10% = 10/100 = 1/10.\nAnswer: E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train crosses a platform of 170 m in 15 sec, same train crosses another platform of length 250 m in 20 sec. then find the length of the train?\n\n### Options:\nA. 70\nB. 88\nC. 167\nD. 197\nE. 161\n\n### Answer:\nLength of the train be \u2018X\u2019\nX + 170/15 = X + 250/20\n20X + 3400 = 15X + 3750\n5x=350\nX = 70m\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nBruce purchased 8kg of grapes at the rate of 70 per kg and 8 kg of mangoes at the rate of 55 per kg. How much amount did he pay to the shopkeeper?\n\n### Options:\nA. A)1040\nB. B)1050\nC. C)1000\nD. D)1065\nE. E)1075\n\n### Answer:\nCost of 8 kg grapes = 70 \u00d7 8 = 560.\nCost of 8 kg of mangoes = 55 \u00d7 8 = 440.\nTotal cost he has to pay = 560 + 440 = 1000\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMrs. Napier has 67 stickers to give to 9 students for a reward. How many\nstickers will each student get? Will there be any stickers left over?\n\n### Options:\nA. 2-5\nB. 7-4\nC. 2-6\nD. 2-3\nE. 2-8\n\n### Answer:\n67/9 = 7 R 4 Mrs. Napier will give each student 7 stickers and there\nwill be 4 left over.\ncorrect answer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average of 11 numbers is 10.9. If the average of first six is 10.5 and that of the last six is 11.4 the sixth number is?\n\n### Options:\nA. 11.4\nB. 11.3\nC. 11.8\nD. 11.5\nE. 11.1\n\n### Answer:\n1 to 11 = 11 * 10.9 = 119.9\n1 to 6 = 6 * 10.5 = 63\n6 to 11 = 6 * 11.4 = 68.4\n63 + 68.4 = 131.4 \u2013 119.9 = 11.5\n6th number = 11.5\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf (20)\u00b2 is subtracted from the square of a number, the answer so obtained is 4321. What is the number?\n\n### Options:\nA. 68\nB. 69\nC. 70\nD. 71\nE. 72\n\n### Answer:\nx^2=4321+400=4721\n4761=69*69\nx=69\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe captain of a cricket team of 11 members is 27 years old and the wicket keeper is 3 years older. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. What is the average age of the team?\n\n### Options:\nA. 21\nB. 22\nC. 23\nD. 24\nE. 25\n\n### Answer:\nLet the average age of the whole team be x years.\n11x - (27 + 30) = 9 (x - 1)\n11x - 9x = 48\n2x = 48\nx = 24.\nThe average age of the team is 24 years.\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nCheese, bologna, and peanut butter sandwiches were made for a picnic in a ratio of 5 to 7 to 8. If a total of 120 sandwiches were made, how many bologna sandwiches\nwere made?\n\n### Options:\nA. 15\nB. 30\nC. 38\nD. 42\nE. 48\n\n### Answer:\nFor deciding such task we should calculate all parts 5 + 7 + 8 = 20 parts\nand we should calculate how many sandwiches holds 1 part:\n120 / 20 = 6 sandwiches in one part\nFor bologna we have 7 parts so:\n7 * 6 = 42\nAnswer is D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a certain Parallelogram the degree measure of one angle exceeds that of the other by 40 what is the degree measure of the smaller angle?\n\n### Options:\nA. 70\nB. 80\nC. 85\nD. 90\nE. 95\n\n### Answer:\nIn a parallelogram opposite angles are equal and the angles at each side are supplementary to each other (supplementary angles are two angles that add up to 180\u00b0).\nGiven: x+(x+40)=180 --> x=70.\nAnswer: A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n4, 5, 7, 11, 19, (...)\n\n### Options:\nA. 32\nB. 22\nC. 35\nD. 27\nE. 28\n\n### Answer:\n4\n4 \u00d7 2 - 3 = 5\n5 \u00d7 2 - 3 = 7\n7 \u00d7 2 - 3 = 11\n11 \u00d7 2 - 3 = 19\n19 \u00d7 2 - 3 = 35\nAnswer is C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n6 men and 12 boys finish a job in 12 days, 12 men and 12 boys finish it in 10 days. 10 men and 10 boys shall finish it in how many days?\n\n### Options:\nA. 12 days\nB. 11 days\nC. 14 days\nD. 16 days\nE. 18 days\n\n### Answer:\n6M + 12B ----- 12 days\n12M + 12B ------- 10 days\n10M + 10B -------?\n72M + 144B = 120M +120B\n24B = 48M => 2M = B\n3B + 12B = 15B ---- 12 days\n5B + 10B = 15B -----? => 12 days\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 9x-3y=12 and 3x-5y=7 then 6x-2y = ?\n\n### Options:\nA. -5\nB. 4\nC. 2\nD. 8\nE. 6\n\n### Answer:\n9x-3y=12-----eq(1)\n3x-5y=7------eq(2)\nsolving we get x=13/12 and y=-3/4\nso, 6x-2y=6*(13/11)-2(-3/4)=8\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe cash difference between the selling prices of an article at a profit of 6% and 8% is Rs 3. The ratio of two selling prices is\n\n### Options:\nA. 51:52\nB. 52:53\nC. 53:54\nD. 54:55\nE. None of these\n\n### Answer:\nExplanation:\nLet the Cost price of article is Rs. x\nRequired ratio = (106% of x) / (108% of x)\n=106/108\n=53/54 = 53:54.\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA trader sells 85 meters of cloth for Rs. 8500 at the profit of Rs. 15 per metre of cloth. What is the cost price of one metre of cloth?\n\n### Options:\nA. Rs. 80\nB. Rs. 85\nC. Rs. 90\nD. Rs. 95\nE. None of these\n\n### Answer:\nSP of 1m of cloth = 8500/85 = Rs. 105\nCP of 1m of cloth = SP of 1m of cloth - profit on 1m of cloth\n= Rs. 100 - Rs. 15 = Rs. 85.\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA walks around a circular field at the rate of one round per hour while B runs around it at the rate of four rounds per hour. They start in the same direction from the same point at 7.30 a.m. They shall first cross each other after___ minutes?\n\n### Options:\nA. 11 min\nB. 12 min\nC. 10 min\nD. 15 min\nE. 20 min\n\n### Answer:\nSince A and B move in the same direction along the circle, so they will first meet each other when there is a difference of one round between the two.\nRelative speed of A and B = 4 - 1 = 3 rounds per hour.\nTime taken to complete one round at this speed = 1/3 hr = 20 min.\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA car after travelling 100 km from point A meets with an accident and then proceeds at 3/4 of its original speed and arrives at the point B 90 minutes late. If the car meets the accident 60 km further on, it would have reached 15 minutes sooner. Find the original speed of the train?\n\n### Options:\nA. 60km/hr\nB. 80km/hr\nC. 100km/hr\nD. 120km/hr\nE. None of these\n\n### Answer:\nExplanation :\nlet distance between A and B be D km and real speed of the car be S km/hr\nFirst time car takes 90 minutes more and second time car takes 75 minutes more than scheduled time.\nSo, T1 \u2013 T2 = 15/60 = 100\n15/60 = [100/s + (D -100)/(3s/4)] \u2013 [160/s + (D \u2013 160)/(3s/4)] Solve this D will be cancelled and S comes out to be 80km/hr\nAnswer \u2013B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a man walks to his office at \u00be of his usual rate, he reaches office 1/3 of an hour late than usual. What is his usual time to reach office?\n\n### Options:\nA. 1\nB. 5\nC. 6\nD. 7\nE. 3\n\n### Answer:\nSpeed Ratio = 1:3/4 = 4:3\nTime Ratio = 3:4\n1 -------- 1/3\n3 --------- ? \u00e8 1 hour\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a graduating class, the difference between the highest and lowest salaries is $100,000. The median salary is $50,000 higher than the lowest salary and the average salary is $20,000 higher than the median. What is the minimum number of students W in the class?\n\n### Options:\nA. A)10\nB. B)12\nC. C)15\nD. D)20\nE. E)25\n\n### Answer:\nthe difference between the highest and lowest salaries is $100,000.\nSo there are at least 2 people - say one with salary 0 and the other with 100k. No salary will be outside this range.\nMedian = 50k more than lowest. So median is right in the center of lowest and highest since lowest and highest differ by 100k. In our example, median = 50k. Since there are more than 2 people, there would probably be a person at 50k.\nMean = 20k more than median so in our example, mean salary = 70k\nOn the number line,\n0........50k (median)........100k\nMean = 70k\nSo there must be people more toward 100k to bring the mean up to 70k. Since we want to add minimum people, we will add people at 100k to quickly make up the right side deficit. 0 and 50k are (70k + 20k) = 90k away from 70k. 100k is 30k away from 70k. To bring the mean to 70k, we will add two people at 100k each to get:\n0....50k.....100k, 100k, 100k\nBut when we add more people to the right of 70k, the median will shift to the right. We need to keep the median at 50k. So every time we add people to the right of 70k, we need to add people at 50k too to balance the median. 50k is 20k less than 70k while 100k is 30k more than 70k. To keep the mean same, we need to add 2 people at 100k for every 3 people we add at 50k. So if we add 3 people at 50k and 2 people at 100k, we get:\n0, ... 50k, 50k, 50k, 50k, ... 100k, 100k, 100k, 100k, 100k\nthe median is not at 50k yet.\nAdd another 3 people at 50k and another 2 at 100k to get\n0, 50k, 50k, 50k, 50k, 50k, 50k, 50k, 100k, 100k, 100k, 100k, 100k, 100k, 100k\nNow the median is 50k and mean is 70k.\nTotal number of people is 15.\nAnswer (C)\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 6 men and 8 boys can do a piece of work in 10 days while 26 men and 48 boys can do the same in 2 days, the time taken by 15 men and 20 boys in doing the same type of work will be:\n\n### Options:\nA. 4 days\nB. 5 days\nC. 6 days\nD. 8 days\nE. 2 days\n\n### Answer:\nLet 1 man's 1 day's work = x and 1 boy's 1 day's work = y.\nThen, 6x + 8y =1/10\tand 26x + 48y =1/2\nSolving these two equations, we get : x =1/100 and y =1/200\n(15 men + 20 boy)'s 1 day's work =(15/100+20/200)\t=1/4\t.\n15 men and 20 boys can do the work in 4 days.\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 5400 mn = k^4, where m, n, and k are positive integers, what is the least possible value of m + n?\n\n### Options:\nA. 11\nB. 18\nC. 20\nD. 25\nE. 33\n\n### Answer:\nk^4=5400\u2217mn\nk^4=3^3.2^3.5^2.mn\nIn order to make RHS a perfect power of 4, we require it to be multiplied by 3, 2 & 5^2\nmn=3.2.5^2\nmn = 150 = 10 * 15 (Least possible)\nAnswer = 10 + 15 = 25\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many real solutions does the equation x5 + 2x3 + 8x2 + 16 = 0 have?\n\n### Options:\nA. 0\nB. 1\nC. 2\nD. 3\nE. 5\n\n### Answer:\nNote that x5+2x3+8x2+16 = (x3+8)(x2+2) = (x+2)(x2-2x+4)(x2+2).\nSince the quadratic equations x2 - 2x + 4 = 0 and x2 + 2 = 0 have no real solutions, the\noriginal equation has just one real solution, x = -2.\ncorrect answer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA baseball card decreased in value 20% in its first year and 20% in its second year. What was the total percent decrease of the card's value over the two years?\n\n### Options:\nA. 28%\nB. 30%\nC. 32%\nD. 36%\nE. 72%\n\n### Answer:\nconsider the initial value of the baseball card as $100\nAfter first year price = 100*0.8 = 80\nAfter second year price = 80 *0.8 = 64\nfinal decrease = [(100 - 64)/100] * 100 = 36%\ncorrect answer - D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the sides of a triangle are 9 cm, 16 cm and 19 cm, what is its area?\n\n### Options:\nA. 69\nB. 72\nC. 75\nD. 89\nE. 93\n\n### Answer:\nThe triangle with sides 9 cm, 16 cm and 19 cm is right angled, where the hypotenuse is 19 cm.\nArea of the triangle = 1/2 * 9 * 16 = 72 cm2\nAnswer: Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train 390 metres long is moving at a speed of 25 kmph. It will cross a man coming from the opposite direction at a speed of 2 km per hour in :\n\n### Options:\nA. 30 sec\nB. 32 sec\nC. 36 sec\nD. 38 sec\nE. 52 sec\n\n### Answer:\nRelative speed = (25+2) km/hr = 27 km/hr\n= (27\u00d75/18) m/sec = 15/2 m/sec.\nTime taken by the train to pass the man =(390\u00d72/15) sec=52 sec\nANSWER :E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSandy can do a job in 15 days and Molly can do the same job in 30 days. If they work together, in how many days will they complete the job?\n\n### Options:\nA. 8\nB. 9\nC. 10\nD. 11\nE. 12\n\n### Answer:\nSandy can do 1/15 of the job each day.\nMolly can do 1/30 of the job each day.\nThe combined rate is 1/15 + 1/30 = 1/10 of the job each day.\nThe job will take 10 days.\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many different section of 4 books can be made from 10 different books if two particular books are never selected?\n\n### Options:\nA. 90\nB. 50\nC. 60\nD. 80\nE. 70\n\n### Answer:\nThis means four books are seclected out of the remaining 8 books. Required number of ways = 8C4= 8!/4!x4!=70. Ans: E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe diagonals of a rhombus are 16 cm and 20 cm. Find its area?\n\n### Options:\nA. 160\nB. 288\nC. 150\nD. 238\nE. 31\n\n### Answer:\n1/2 * 16 * 20 = 160\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train covers a distance of 12 km in 10 min. If it takes 16 sec to pass a telegraph post, then the length of the train is?\n\n### Options:\nA. 320 m\nB. 188 m\nC. 120 m\nD. 178 m\nE. 189 m\n\n### Answer:\nSpeed = (12/10 * 60) km/hr = (72 * 5/18) m/sec\n= 20 m/sec.\nLength of the train = 20 * 16\n= 320 m.\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe banker's discount on Rs.1250 due a certain time hence is Rs.125. Find the true discount and the banker's gain.\n\n### Options:\nA. 11\nB. 15\nC. 18\nD. 21\nE. None\n\n### Answer:\nSolution\nSum\t=B.D x T.D/ B.D - T.D\n= B.D x T.D/ B.G\nT.D / B. G\t=Sum / B.D\n= 1250 / 125\n= 10 / 1\nIf B.D is Rs. 11,T.D= Rs.10.\nIf B.D is Rs.125,\nT.D\t= Rs.(10 / 11 x 125)\n= Rs.114.\nAnd, B.G\t= Rs(125 - 114)\n= Rs.11.\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a 5-digit numerical with local value of digits 3 is 300, 4 is 40000, 5 is 50, 6 is 6 and 7 is 7000, is multiplied by 7 then the difference between local value of 4 in the new numerical and the face value of 3 is\n\n### Options:\nA. 397\nB. 2997\nC. 49997\nD. 697\nE. 497\n\n### Answer:\nAccording to the given local values of the 5-digit number the number is 47356\nMultiplying it with 7,\n47356 x 7 = 331492\n(Local value of 4 in 331492) - (Face value of 3) = 400 - 3 = 397\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a division sum, the quotient is 36, the divisor 85 and the remainder 26, find the dividend?\n\n### Options:\nA. 3066\nB. 3586\nC. 3086\nD. 3968\nE. 3286\n\n### Answer:\nExplanation:\n36 * 85 + 26 = 3086\nAnswer : C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n3889 + 16.952 - ? = 3854.002\n\n### Options:\nA. 51.95\nB. 49.75\nC. 45.97\nD. 47.59\nE. 45.79\n\n### Answer:\nLet 3889 + 16.952 - x = 3854.002.\nThen x = (3889 + 16.952) - 3854.002\n= 3905.952 - 3854.002\n= 51.95.\nAnswer is A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are 9 books on a shelf that consist of 4 paperback books and 5 hardback books. If 4 books are selected at random without replacement, how many different combinations are there which include at least one paperback book?\n\n### Options:\nA. 88\nB. 99\nC. 110\nD. 121\nE. 132\n\n### Answer:\nThe total number of ways to select 4 books is 9C4 = 126\nThe number of ways which do not include any paperbacks is 5C4 = 5\nThe number of combinations with at least one paperback is 126-5 = 121\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn the equation s = 36.12t, t and s are integers. If s/t leaves a remainder of r, which of the following must divide into r?\n\n### Options:\nA. 2\nB. 3\nC. 4\nD. 6\nE. 12\n\n### Answer:\n1) It says it is a equation, so s=36.12t should be 36.12 * t..\n2) It says t is an integer, again it means 36.12 * t..\nOtherwise t would be just a digit and it would be mentioned..\nAlthough not clearly mentioned that 36.12t is actually 36.12 * t, BUT entire info points towards that..\nand that is why I have taken s/t = 36.12\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n21 friends went to a hotel and decided to pay the bill amount equally. But 20 of them could pay Rs. 30 each as a result 21st has to pay Rs. 200 extra than his share. Find the amount paid by him.\n\n### Options:\nA. 120\nB. 250\nC. 110\nD. 220\nE. None\n\n### Answer:\nExplanation:\nAverage amount paid by 20 persons = Rs. 30\nIncrease in average due to Rs. 200 paid extra by the 21st men = Rs. 200/20= Rs. 10\nTherefore, Average expenditure of 21 friends = Rs. 30 + Rs. 10 = Rs. 40\nTherefore, Amount paid by the 21st men = Rs. 40 + Rs. 200 = Rs. 240\nCorrect Option: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn an examination, a student scores 4 marks for every correct answer and loses 1 mark for every wrong answer. If he attempts all 80 questions and secures 120 marks, How many questions does he answer correctly?\n\n### Options:\nA. 20\nB. 10\nC. 30\nD. 50\nE. 40\n\n### Answer:\nLet the number of correct answers be x\nThen, number of wrong answers = (80 - x)\n4x \u2013 (80 - x) = 120\n=> 4x \u2013 80 + x = 120\n=> 5x = 200\n=> x = 200/5 = 40\ni.e., he does 40 questions correctly\nAnswer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn an election, candidate A got 75% of the total valid votes. If 15% of the total votes were declared invalid and the total numbers of votes is 560000, find the number of valid vote polled in favor of candidate.\n\n### Options:\nA. 330000\nB. 340000\nC. 347000\nD. 356000\nE. 357000\n\n### Answer:\nTotal number of invalid votes = 15 % of 560000\n= 15/100 \u00d7 560000\n= 8400000/100\n= 84000\nTotal number of valid votes 560000 \u2013 84000 = 476000\nPercentage of votes polled in favour of candidate A = 75 %\nTherefore, the number of valid votes polled in favour of candidate A = 75 % of 476000\n= 75/100 \u00d7 476000\n= 35700000/100\n= 357000\nE)\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAt a certain supplier, a machine of type A costs $30,000 and a machine of type B costs $65,000. Each machine can be purchased by making a 20 percent down payment and repaying the remainder of the cost and the finance charges over a period of time. If the finance charges are equal to 40 percent of the remainder of the cost, how much less would 2 machines of type A cost than 1 machine of type B under this arrangement?\n\n### Options:\nA. $6,600\nB. $11,200\nC. $12,000\nD. $12,800\nE. $13,200\n\n### Answer:\nTotal Cost of 2 Machines of Type A\n= 20% of (Cost of 2 machine A) + remainder + 40 % remainder\n= 20% of 30000 + (30000 - 20% of 30000) + 40% of (30000 - 20% of 30000)\n= 79200\nTotal Cost of 1 Machine of Type B\n= 20% of (Cost of 1 machine B) + remainder + 40 % remainder\n= 20% of 65000 + (65000 - 20% of 65000) + 40% of (65000 - 20% of 65000)\n= 85800\nDiff = 85800 - 79200 = 6600\nHence, A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJames can eat 25 marshmallows is 20 minutes. Dylan can eat 25 in one hour. In how much time will the two eat 150 marshmallows?\n\n### Options:\nA. 40 minutes.\nB. 1 hour and 30 minutes.\nC. 1 hour\nD. 1 hour and 40 minutes.\nE. 2 hours and 15 minutes\n\n### Answer:\nRate =Output/Time\nJames Rate=25/20=5/4\nDylan Rate=25/60=5/12\nCombined rate = 5/4+5/12= 20/12\nCombined Rate*Combined Time= Combined Output\n20/12*t=150\nt=90 mins => 1 hr 30 min\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFor a group of n people, k of whom are of the same sex, the (n-k)/n expression yields an index for a certain phenomenon in group dynamics for members of that sex. For a group that consists of 20 people, 7 of whom are females, by how much does the index for the females exceed the index for the males in the group?\n\n### Options:\nA. 0.05\nB. 0.0625\nC. 0.2\nD. 0.3\nE. 0.6\n\n### Answer:\nIndex for females = (20-7)/20 = 13/20 = 0.65\nIndex for males = (20-13/20 = 7/20 = 0.35\nIndex for females exceeds males by 0.65 - 0.35 = 0.3\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA waitress's income consists of her salary and tips.During one week ,her tips were 11/4 of her salary.What fraction of her income for the week came from tips?\n\n### Options:\nA. 1/9\nB. 1/6\nC. 1/3\nD. 4/9\nE. 11/15\n\n### Answer:\nHer tips were 11/4 of her salary.\nLet's say her salary =$4\nThis mean her tips = (11/4)($4) =$11\nSo, her TOTAL INCOME =$4+$11=$15\nWhat fraction of her income for the week came from tips\n$11/$15 =11/15\n= E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOn dividing 15968 by a certain number, the quotient is 89 and the remainder is 37. Find the divisor.\n\n### Options:\nA. 170\nB. 179\nC. 37\nD. 67\nE. 32\n\n### Answer:\nDivisor = (Dividend \u2013 Remainder/Quotient)\n=(15968-37)/89 =179\nANSWER B 179\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf x*y = xy \u2013 2(x + y) for all integers x and y, then 1* (\u20133) =\n\n### Options:\nA. \u201316\nB. \u201311\nC. \u20134\nD. 4\nE. 1\n\n### Answer:\n1*(-3) = 1*(-3) - 2 (1 + (-3) ) = -3 +4 = 1\nOption (E)\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn the infinite sequence 10, 15, 20, 25, 30, . . . , where each term is 5 greater than the previous term, the 32th term is\n\n### Options:\nA. 183\nB. 178\nC. 165\nD. 139\nE. 179\n\n### Answer:\nT(n) = a + (n-1) d\nHere d =5, a=10, n=32\nSolving we get T(n) = 165.\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMax invested Rs. 15000 @ 10% per annum for one year. If the interest is compounded quarterly, then the amount received by Max at the end of the year will be?\n\n### Options:\nA. 16557.1\nB. 16557.19\nC. 16557.25\nD. 16557.3\nE. 16557.38\n\n### Answer:\nP = Rs. 15000; R = 10% p.a. = 2.5% per quarter; T = 1 year = 4 quarters\nAmount = [15000 * (1 + 2.5/100)4]\n= (15000 * (1.025)4) = Rs. 16557.19\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf xy+4z = x(y+z), which of the following must be true?\n\n### Options:\nA. 1. x=0 and z=0\nB. 2. x=1 and y=1\nC. 3. y=1 and z=0\nD. 4. x=1 or y=0\nE. 5. x=4 or z=0\n\n### Answer:\nxy+4z=x(y+z)\nxy+4z=xy+xz\n4z=xz\nit means x=4 or z=0\nAnswer E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n40 is subtracted from 60% of a number, the result is 50. Find the number?\n\n### Options:\nA. 150\nB. 189\nC. 177\nD. 167\nE. 190\n\n### Answer:\n(60/100) * X \u2013 40 = 50\n6X = 900\nX = 150\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a clothing store, there are six different colored neckties (red, orange, yellow, green, blue, and indigo) and three different colored shirts (red, orange, yellow, green, blue, and indigo) that must be packed into boxes for gifts. If each box can only fit one necktie and one shirt, what is the probability that all of the boxes will contain a necktie and a shirt of the same color?\n\n### Options:\nA. 719/720\nB. 1/120\nC. 2/233\nD. 1/6\nE. 1/720\n\n### Answer:\n6 ties and 6 shirts...\nred tie can take any of 6 shirts..\norange can take any of the remaining 5 shirts\nyellow any of remaining 4..\nand so on till last indigo chooses the 1 remaining..\nTotal ways= 3*2*1= 6\nout of this 6, ONLY 1 way will have same colour tie and shirt..\nprob = 1/6\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many possible integer values are there for x if |7x - 3| < 6 ?\n\n### Options:\nA. One\nB. Two\nC. Three\nD. Four\nE. Five\n\n### Answer:\nSolution: |7x-3| < 6\nlet 7x=a therefore we have |a-3| < 6 ==> read this as origin is at +3 and we have to move +6 to the right and -6 to the left\n(the less than sign represents that the a must be within boundaries )\n(3-6)----------3----------(3+6)\nnow, we have -3 -3<7x<9\ndividing all values by +4 we have -0.46 ", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nif you invested $25000 and received $35251 after 10 years. what was the interest rate?\n\n### Options:\nA. 0.15%\nB. 0.25%\nC. 0.04%\nD. 0.50%\nE. 0.40%\n\n### Answer:\nP=25000\nI= 35251-25000=10251\nt=10 years\n10251=(25000)(r)(10)\n10251=250000r\n10251/250000\n=.04\nANSWER:0.40%\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nArrange the given words in the sequence in which they occur in the dictionary and choose the correct sequence.\n\n### Options:\nA. 3, 5, 2, 1, 4\nB. 3, 5, 2, 1, 8\nC. 3, 5, 2, 1, 2\nD. 3, 5, 2, 1, 5\nE. 3, 5, 2, 5, 5\n\n### Answer:\nExplanation:\nThe correct alphabetical order is\nEach, Eager, Earlier, Economic, Edition\nANSWER: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the least number of complete years in which a sum of money put out at 13% compound interest will be more than double of itself?\n\n### Options:\nA. 5\nB. 6\nC. 7\nD. 8\nE. 9\n\n### Answer:\n6 years\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo cars, Car1 and Car2 move towards each other from R and Y respectively with respective speeds of 20 m/s and 15 m/s. After meeting each other Car1 reaches Y in 10 seconds. In how many seconds does Car 2 reach R starting from Y?\n\n### Options:\nA. 15.5 sec\nB. 8.4 sec\nC. 33.6 sec\nD. 31.11 sec\nE. 16.8 sec\n\n### Answer:\nR--------------------------------------|----------------------------Y\nCar A(20mps)------------------------->P<---------------Car B(15mps)\nLet 2 cars meet each other at point P in t seconds.\nCar1 covers distance= 20t. Car2 covers distance=15t. So, total distance RY= 35t.\nFrom P, Car 1 reaches onto Y in 10 secs. So it covers 15t further.\nso, 15t/20 = 10\nSo t=40/3 sec and total distance = (35*40)/3\nHence Car2 will cover total distance in (35*40)/(3*15) = 31.11 sec approx.\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow much water should be added to 15 liters of a 20%-solution of alcohol to reduce the concentration of alcohol in the solution by 75% ?\n\n### Options:\nA. 25 liters\nB. 27 liters\nC. 30 liters\nD. 32 liters\nE. 35 liters\n\n### Answer:\nLet x ltr water to be added\n2ltr alcohol to be represented as (20(1-3/4(new soln.=15+x)))\n2=5%*(15+x)-------->x=25\nAns A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds. Its length is:\n\n### Options:\nA. 227\nB. 277\nC. 266\nD. 150\nE. 881\n\n### Answer:\nLet the length of the train be x meters and its speed be y m/sec.\nThey, x / y = 15 => y = x/15\nx + 100 / 25 = x / 15\nx = 150 m.\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIndu gave Bindu Rs.1250 on compound interest for 2 years at 4% per annum. How much loss would Indu has suffered had she given it to Bindu for 2 years at 4% per annum simple interest?\n\n### Options:\nA. 5\nB. 2\nC. 9\nD. 5\nE. 1\n\n### Answer:\n1250\n= D(100/4)2\nD = 2\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMr. Smith calculated the average of 10three digit numbers. But due to a mistake he reversed the digits of a number and thus his average increased by 59.4. The difference between the unit digit and hundreds digit of that number is :\n\n### Options:\nA. a) 6\nB. b) 3\nC. c) 2\nD. d) 1\nE. e) 0\n\n### Answer:\nSince the average increased by 59.4 and there were a total of 10 numbers, it means the incorrect number was 594 greater than the correct number.\nSay, the correct number was abc (where a, b and c are the digits of the 3 digit number)\nThen the incorrect number was cba.\n100c + 10b + a - (100a + 10b + c) = 594\n99c - 99a = 99(c - a) = 594\n594 = 99*6 = 99(c - a)\nSo c - a = 6\nAnswer (A)\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe area of the floor of a room is 20 m2 that of a longer wall 15 m2 and of the shorter wall 12 m2, find the edge of the new cube?\n\n### Options:\nA. 33 m3\nB. 77 m3\nC. 60 m3\nD. 27 m3\nE. 29 m3\n\n### Answer:\nlb = 20 ; lh = 15 ; fh = 12\n(lbh)2 = 20 * 15 * 12 => lbh = 60 m3\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe perimeter of a semi circle is 122 cm then the radius is?\n\n### Options:\nA. 17\nB. 28\nC. 24\nD. 11\nE. 12\n\n### Answer:\n36/7 r = 122 => r\n= 24\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf c= (a-1)(a+2), then what is the least possible value of c?\n\n### Options:\nA. 1/2\nB. 2\nC. -9/4\nD. 1\nE. -2\n\n### Answer:\nAnswer : C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain quantity of 45% concentration solution is replaced with 15% concentration solution such that the concentration of the combined amount is 35%.\nWhat's the ratio of the amount of solution that was replaced to the amount of solution that was not replaced?\n\n### Options:\nA. 1:3\nB. 1:2\nC. 2:3\nD. 2:1\nE. 3:1\n\n### Answer:\n15% - - - - - - - - - 35% - - - - - - 45%\nFrom 15 to 35 =20\nFrom 35 to 45 = 10\nSo the ratio is 20/10 = 2 to 1\nB it is\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA student travels from his house to school at 10 km/hr and reaches school 2 hours late. The next day he travels 18 km/hr and reaches school 1 hour early. What is the distance between his house and the school?\n\n### Options:\nA. 65.0\nB. 67.5\nC. 70.0\nD. 72.5\nE. 75.0\n\n### Answer:\nLet x be the distance from his house to the school.\nx/10 = x/18 + 3\n9x = 5x + 270\n4x = 270\nx = 67.5 km\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n16384, 8192, 2048, 256, 16, ?\n\n### Options:\nA. 0.3\nB. 9.0\nC. 0.5\nD. 1.0\nE. 2.0\n\n### Answer:\n16384\n16384 \u00f7 2 = 8192\n8192 \u00f7 4 = 2048\n2048 \u00f7 8 = 256\n256 \u00f7 16 = 16\n16 \u00f7 32 = 0.5\nAnswer is C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a simultaneous throw of 2 dice, what is the probability of not getting a doublet?\n\n### Options:\nA. 2/3\nB. 1/6\nC. 4/7\nD. 5/6\nE. 4/9\n\n### Answer:\nn(S) = 6*6 = 36\nE = event of not getting a doublet = 36- event of getting a doublet= 36-6 =30\n{(1,1),(2,2),(3,3),(4,4),(5,5),(6,6)}\nProbability = 30/36 = 5/6\nAnswer is D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are 15 balls in a box: 8 balls are green, 4 are blue and 3 are white. Then 1 green and 1 blue balls are taken from the box and put away. What is the probability that a blue ball is selected at random from the box?\n\n### Options:\nA. 1/13\nB. 4/13\nC. 3/13\nD. 5/13\nE. 6/13\n\n### Answer:\nIf 1 green and 1 blue ball are taken from the box, then there are 7 green, 3 blue and 3 white balls, a total of 13 balls. If one ball is selected at random, the probability that it is blue is given by 3 / 13\ncorrect answer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMr. Karan borrowed a certain amount at 6% per annum simple interest for 9 years. After 9 years, he returned Rs. 8310/-. Find out the amount that he borrowed.\n\n### Options:\nA. s. 5266\nB. s. 5396\nC. s. 5228\nD. s. 5218\nE. s. 52192\n\n### Answer:\nExplanation:\nLet us assume Mr. Karan borrowed amount is Rs. A. (the principal)\nBy formula of simple interest, S.I. = PRT / 100\nWhere P = The principal, R = Rate of interest as a %, T = Time in years\nS.I. = (P * 6 * 9)/100 = 54 P/100\nAmount = Principal + S.I.\n8310 = P + (54P/100)\n8310 = (100P + 54P)/100\n8310 = 154P/100\nP = (8310 * 100)/154 = Rs. 5396.104\nANSWER: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how many ways can 16 different gifts be divided among four children such that each child receives exactly three gifts?\n\n### Options:\nA. 16^4\nB. (4!)^4\nC. 16!/(3!)^4\nD. 16!/4!\nE. 4^16\n\n### Answer:\nTotal 16 different Gifts, and 4 children.\nThus any one child gets 16C3 gifts,\nthen the other child gets 13C3 gifts(16 total - 3 already given),\nthen the third one gets 10C3 gifts,\nand the last child gets 7C3 gifts.\nSince order in which each child gets the gift is not imp, thus, ans :\n16C3 * 13C3 * 10C3 * 7C3 = 16! / (3!)^4\nAns : C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat will come in place of the x in the following Number series? 11, 14, 19, 22, 27, 30, 35, 38, x\n\n### Options:\nA. 29\nB. 31\nC. 23\nD. 43\nE. 53\n\n### Answer:\n(D)\nThe pattern is + 3, + 5, + 3, + 5, \u2026\u2026\u2026\u2026\nSo the missing term is = 38 + 5 = 43.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf |b| \u2265 1 and x= -| a| b, then which one of the following is necessarily true?\n\n### Options:\nA. a -xb < 0\nB. a -xb \u2265 0\nC. a -xb > 0\nD. a -xb \u2264 0\nE. None of these\n\n### Answer:\nExplanation :\nx = \u2013|a| b\nNow a \u2013 xb = a \u2013 (\u2013 |a| b) b\n= a + |a| b2\n\u2234 a \u2013 xb = a + ab2 \u2026 a 0 \u2265 OR a \u2013 xb\n= a - ab2 \u2026a < 0\n= a(1 + b2) = a(1 \u2013 b2).\nConsider first case:\nAs a \u2265 0 and |b| \u2265 1, therefore (1 + b2) is positive.\n\u2234 a (1 + b2) \u2265 0\n\u2234 a \u2013 xb \u2265 0\nConsider second case.\nAs a < 0 and |b| \u2265 1, therefore (1 \u2013 b2) \u2264 0\n\u2234 a (1 \u2013 b2) \u2265 0 (Since \u2013ve \u00d7 -ve = +ve and 1 \u2013 b2 can be zero also), i.e. a \u2013 xb \u2265 0\nTherefore, in both cases a \u2013 xb \u2265 0.\nAnswer : B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe cost of 6 pens is 10 more than 5 marker's cost. The 12 pens is Rs.240.\n\n### Options:\nA. Rs.11\nB. Rs.42\nC. Rs.24\nD. Rs.110\nE. Rs.22\n\n### Answer:\nLet the cost of each pen and marker be 'p' and 'q' respectively.\n6p - 5q = 10 --- (1)\n12p= 240 . P=20\n6p - 5q = 10 --- (2)\n120-5q =10\n=>5q = 110\n=> q=22\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the sum of the number of combinations possible by using 1,2,3,4 such that no number is repeated(ex:- 1223,4322 are invalid 1234,4321 are valid)more than once.\n\n### Options:\nA. 66660\nB. 66760\nC. 66860\nD. 66960\nE. 67660\n\n### Answer:\ntotal no. formed = 4!=4*3*2*1=24\neach digit will be used at each positions, 6 times\nsum of digits at unit place = 6*1+6*2+6*3+6*4 = 6*(1+2+3+4)= 60\nthis sum will be same for hundred, tens & unit places\nsum of all 4 digit numbers formed using digits 1,2,3,4\n= 1000*60+100*60+10*60+60\n=60*(1000+100+10+1)\n=60*1111\n=66660\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nClub X has more than 30 but fewer than 60 members. Sometimes the members sit at tables with 3 members at one table and 4 members at each of the other tables, and sometimes they sit at tables with 3 members at one table and 5 members at each of the other tables. If they sit at tables with 6 members at each table except one and fewer than 6 members at that one table, how many members will be at the table that has fewer than 6 members?\n\n### Options:\nA. 1\nB. 2\nC. 3\nD. 4\nE. 5\n\n### Answer:\nThe number of members is 4j+3 = 5k+3.\nLet's start at 4(7)+3 = 31 and keep adding 4 until we find a number in the form 5k+3.\n31, 35, 39, 43 = 5(8) + 3\nThe club has 43 members.\n43/6 = 6(7) + 1\nThe answer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a/x = 1/3 and a/y =1/ 6, then (x + y) =\n\n### Options:\nA. A)2a\nB. B)a/2\nC. C)6a\nD. D)7a\nE. E)9a\n\n### Answer:\nRatio 1:\n3a = x\nRatio 2:\n6a = y\nx+y = 9a\nAnswer is E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nCompound interest earned on a sum for the second and the third years are Rs.2400 and Rs.2640 respectively. Find the rate of interest?\n\n### Options:\nA. 10% p.a.\nB. 20% p.a.\nC. 15% p.a.\nD. 12% p.a.\nE. None of these.\n\n### Answer:\nRs.2640 - 2400 = Rs.240 is the interest on Rs.2400 for one year.\nRate of interest = (240/2400) * 100 = 10% p.a\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nDuring a certain two-week period, 60 percent of the movies rented from a video store were comedies, and of the remaining movies rented, there were 3 times as many dramas as action movies. If no other movies were rented during that two-week period and there were A action movies rented, then how many comedies, in terms of A, were rented during that two-week period?\n\n### Options:\nA. 5 A\nB. 6 A\nC. 8 A\nD. 14 A\nE. 20 A\n\n### Answer:\nMovies: 60 % comedies. 40 % remaining genre.\nNow in this 40 %, there are only 2 categories. Action movies and Drama Movies.\nIf Action = x; Drama movies = 3x. Total 4x.\n4x = 40; x = 10\nAction movies: 10 %\nDrama movies: 30 %\nwe can say that out of 100z,:\ncomedies: 60z\naction: 10z\ndrama: 30 z\nNow action movies wereA\nThis means:\nA = 10z.\nz = (A/10)\nComedies: 60z = 60 * (A/10)\n6 A\nB is the answer.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average age of husband, wife and their child 3 years ago was 27 years and that of wife and the child 5 years ago was 20 years. The present age of the husband is\n\n### Options:\nA. 35 years\nB. 40 years\nC. 50 years\nD. 55 years\nE. None\n\n### Answer:\nSolution\nSum of the present ages of husband, wife and child\t= (27x3+3x3) years\n= 90 years.\nSum of the present ages of wife and child\t= (20x2+5x2) years\n= 50 years.\n\u2234 Husband's present age\t= (90 - 50) years\n= 40 years.\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man saves 20% of his monthly salary. If an account of dearness of things he is to increase his monthly expenses by 20%, he is only able to save Rs. 200 per month. What is his monthly salary?\n\n### Options:\nA. 5000\nB. 2889\nC. 2779\nD. 6257\nE. 5362\n\n### Answer:\nIncome = Rs. 100\nExpenditure = Rs. 80\nSavings = Rs. 20\nPresent Expenditure 80*(20/100) = Rs. 96\nPresent Savings = 100 \u2013 96 =Rs. 4\n100 ------ 4\n? --------- 200 => 5000\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe length of the bridge, which a train 140 metres long and travelling at 45 km/hr can cross in 30 seconds, is?\n\n### Options:\nA. 876 m\nB. 157 m\nC. 235 m\nD. 156 m\nE. 167 m\n\n### Answer:\nSpeed = [45 X 5/18] m/sec\n= [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (140 + x)/30 = 25/2\n=> 2(140 + x) = 750 => x\n= 235 m.\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA salesman's income consists of a commission and a base salary of $400 per week. Over the past 5 weeks, his weekly income totals have been $406, $413, $420, $436 and $395. What must his average (arithmetic mean) commission be per week over the next two weeks so that his average weekly income is $500 over the 7-week period?\n\n### Options:\nA. $150\nB. $245\nC. $365\nD. $315\nE. $730\n\n### Answer:\nTotal weekly income over 5 weeks=$406+$413+$420+$436+$395=$2070\nFor avg weekly income to be $500 over 7 weeks, we need total weekly income over 7 weeks=$3500\nNow, $3500-$2070=$1430\nFrom this, we subtract base salary for 2 weeks i.e $350*2=$700\nTherefore, commission=$1430-$800=$630 for 2 weeks\nAvg weekly commission=$315\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nExpress a speed of 56 kmph in meters per second?\n\n### Options:\nA. 10.2 mps\nB. 05 mps\nC. 09.1 mps\nD. 12 mps\nE. 15.5 mps\n\n### Answer:\nE\n15.5 mps\n56 * 5/18 = 15.5 mps\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe greatest common factor of two numbers is 5!. Which of the following can be the second number, if one of the numbers is 9!?\n\n### Options:\nA. 3(5!)\nB. 4(5!)\nC. 6(5!)\nD. 5(5!)\nE. 7(5!)\n\n### Answer:\nGCF is the product of common factors of the numbers involved.\nGCF = 5!\na = 9! = 9*8*7*6*5!\nb will certainly have 5! and cannot have any more common factors with a (as this will increase the GCF)\nLooking at the answers only 5 (5!) and 9! will have GCF as 5!\nAns D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n(17)4.25 x (17)? = 178\n\n### Options:\nA. 2.29\nB. 2.75\nC. 4.25\nD. 3.75\nE. None of these\n\n### Answer:\nSolution\nlet (17)4.25 * (17)x = 178. then, (17)4.25 + x = (17)8.\n\u2234 4.25 + x = 8 \u21d4 x = (8 - 4.25) \u21d4 x = 3.75\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nDifference of two numbers is 1660. If 7.5% of the number is 12.5% of the other number, find the number ?\n\n### Options:\nA. 1660\nB. 2500\nC. 3250\nD. 4150\nE. 5250\n\n### Answer:\nLet the numbers be x and y. Then , 7.5 % of x =12.5% of y\nX = 125*y/75 = 5*y/3.\nNow, x-y =1660\n5*y/3 \u2013y =1660\n2*y/3= 1660\ny =[ (1660*3)/2] =2490.\nOne number = 2490, Second number =5*y/3 =4150.\nAnswer Option D) 4150.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average of 25 results is 8. The average of first 12 of them is 14 and that of last 12 is 17. Find the 13 result?\n\n### Options:\nA. 52\nB. 68\nC. 78\nD. 92\nE. 65\n\n### Answer:\n13th result = sum of 25results - sum of 24 results\n18*25-14*12+17*12 = 78\nAnswer is D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 4/(a + 5) = 7/(a - 4), then a = ?\n\n### Options:\nA. -15\nB. -19\nC. -17\nD. -18\nE. -13\n\n### Answer:\nMultiply all terms of the given equation by (a + 5)(a - 4), simplify and solve\n(a + 5)(a - 4)[ 4/(a + 5) ] = (a + 5)(a - 4) [ 7/(a - 4) ]\n4 (a - 4) =7 (a + 5)\na = -17\ncorrect answer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSeats for Maths, Physics and Biology are in the ratio of 6 : 7 : 8 respectively. There is a proposal to increase these seats by 40%, 50% and 75% respectively. What will be the respective ratio of increased seats?\n\n### Options:\nA. 12 : 15 : 20\nB. 6 : 7 : 8\nC. 6 : 8 : 9\nD. Cannot be determined\nE. None of these\n\n### Answer:\nReqd ratio 6 \u00c3\u2014 140\u00e2\u0081\u201e100 : 7 \u00c3\u2014 150\u00e2\u0081\u201e100 : 8 \u00c3\u2014 175\u00e2\u0081\u201e100\n= 6 \u00c3\u2014 140 : 7 \u00c3\u2014 150 : 8 \u00c3\u2014 175 = 12 : 15 : 20\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn Town X, 64 percent of the population are employed, and 44 percent of the population are employed males. What percent of the employed people in Town X are females?\n\n### Options:\nA. 16%\nB. 55%\nC. 29%\nD. 40%\nE. 52%\n\n### Answer:\nanswer b\nmale-employed - 64%\nfemale-employed-20%\nTotal employed 64%\nmeans total unemployed = 36%\ntherefore d and e are not correct because female unemployed has to be less than 36%\nfemale-unemployed = 32% male unemployed = 4%\n48% + 4% = 52%\n16% + 32% = 48%\nplug in a and b in place of 32% and the sum is not 100%\n20/64 =29 C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAbbey's income is 30 percent more than Abigail's income, and Abigail's income is 35 percent less than Jenny's income. What percent of Jenny's income is Abbey's income?\n\n### Options:\nA. 84.5%\nB. 81.5%\nC. 82.5%\nD. 83.5%\nE. 86.5%\n\n### Answer:\nJenny's income = 100 (assume);\nAbigail's income = 65 (40 percent less than Jenny's income);\nAbbey's income = 84.5 (30 percent more than Abigail's income).\nThus, Abbey's income (84.5) is 84.5% of Juan's income (100).\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a division, divident is 690, divisior is 36 and quotient is 19. Find the remainder.\n\n### Options:\nA. A)4\nB. B)3\nC. C)2\nD. D)5\nE. E)6\n\n### Answer:\nExplanation:\n690 = 36 x 19 + r\n690 = 684 + r\nr = 690 - 684 = 6\nAnswer: Option E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf x is an integer, which of the following is a possible value of Q=(x^2 +2x \u2013 7)/9?\n\n### Options:\nA. -2.4\nB. 0.268\nC. 1.166 repeating\nD. 4.555 repeating\nE. 8.125\n\n### Answer:\nx is an integer, which of the following is a possible value of Q=(x^2 +2x \u2013 7)/9?\nUsed process of elimination\nA. -2.4\nwhen this is multiplied by 9, x is not an integer\nB. 0.268\nwhen this is multiplied by 9, x is not an integer\nC. 1.166 repeating\nwhen this is multiplied by 9, x is not an integer\nD. 4.555 repeating\nE. 8.125\nwhen this is multiplied by 9, x is not an integer\nAnswer choice D seems to fit.D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOf the teams competing in the world archery championships, Forty percent are from Europe. Half as many are from the United States and one twentieth are from Africa. What fraction of teams are from neither Europe, the US or Africa.\n\n### Options:\nA. 13/20\nB. 15/20\nC. 13/15\nD. 17/20\nE. 7/17\n\n### Answer:\nAssume 100 total people.\n40% of 100 = 40 --->Europeans\n1/2 of 40 ---> 20 Americans\n1/20 of 100 ---> 5 Africans\nNow you would add them all up, and minus it by the total (100). 100 - 65= 35. So, 35 people out of 100 are not EU, US or Africans. 35/100 is also equal to 7/20.\nSo therefore, the answer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn the formula A = 22/7*b^2, if b is halved, then A is multiplied by\n\n### Options:\nA. 4\nB. 1/8\nC. 1/4\nD. 8\nE. 1/2\n\n### Answer:\nSay b=2 => A1 = 88/7\nwhen r=1; A2 = 22/7\nA2 = 1/4*A1.\nAnswer : C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nLast month, John rejected 0.5% of the products that he inspected and Jane rejected 0.6 percent of the products that she inspected. If total of 0.75 percent of the products produced last month were rejected, what fraction of the products did Jane inspect?\n\n### Options:\nA. 1/4\nB. 1/2\nC. 5/8\nD. 5/6\nE. 15/16\n\n### Answer:\nX - fraction of products Jane inspected\n(1 - X) - fraction of products John inspected\n0.6(X) + 0.5(1-X) = 0.75\n0.1X = 0.75 - 0.5\nX = 0.25/0.1\nX = 1/4\nTherefore the answer is A: 1/4.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nComplete the sequence:\nD F J P ?\n\n### Options:\nA. M\nB. D\nC. S\nD. F\nE. X\n\n### Answer:\nD+2=F\nF+4=J\nJ+6=P\nP+8=X\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nin a soccer bet,we play 4 teams.first team odd 1.26,second 5.23,third 3.25,fourth 2.05.we place the bet with 5.00 euros.\nhow much money we expect to win?\n\n### Options:\nA. 219.5\nB. 225.5\nC. 235.01\nD. 266.74\nE. 669.0\n\n### Answer:\nin the case we won the bet,we have:\n1.26* 5.23* 3.25* 2.0*5.00=219.50\nwe will win 219.50\nso correct answer is A)219.50\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe organizers of a week-long fair have hired exactly seven security guards to patrol the fairgrounds at night for the duration of the event. Exactly two guards are assigned to patrol the grounds every night, with no guard assigned consecutive nights. If the fair begins on a Monday, how many different pairs of guards will be available to patrol the fairgrounds on the following Saturday night?\n\n### Options:\nA. 6\nB. 8\nC. 10\nD. 12\nE. 14\n\n### Answer:\nFor any given day, only the guards patrolling on the previous day won't be available. So, 2 guards who patrolled on Friday won't be available. We are thus left with 5 guards.\nTo choose 2 out of 5, we will have 5C2 = 10 different pairs.\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are 12 cans in the refrigerator. 8 of them are red and 4 of them are blue. In how many ways we can remove 8 cans so that at least one red and at least one blue cans to remain the refrigerator.\n\n### Options:\nA. 460\nB. 490\nC. 493\nD. 455\nE. 424\n\n### Answer:\nWays to pick 4 cans so that at least one red and at least one blue cans to remain the refrigerator =\ntotal ways to pick 4 can out of 12 - ways to pick 4 red out of 8 red - ways to pick 4 blue out of 4 blue\n12C4\u00e2\u02c6\u20198C4\u00e2\u02c6\u20194C4=495\u00e2\u02c6\u201970\u00e2\u02c6\u20191=424\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nChandigarh express of 100 m runs at a speed of 60 km/hr. What will be the time taken to cross a platform of 150 meters long?\n\n### Options:\nA. 11.00 sec\nB. 12.50 sec\nC. 15.00 sec\nD. 15.23 sec\nE. 5.23 sec\n\n### Answer:\nEXPLANATION:\nGiven: Length of train = 100 m, speed of train = 60 km/hr, length of platform = 150 m\n1) Always remember first step is the conversion of units.\nConvert 60 km/hr into m/s by multiplying it with (5/18)\nSpeed of the train = 60 x\t5/18=16.66 m/s\n2) Distance covered by the train in passing the platform = (Length of train + Length of platform) = (100 + 150) = 250 m\nTherefore,\nThe time taken =\tDistance/Speed\n= 250/16.66\n= 15 sec\nANSWER IS C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a can, there is a mixture of milk and water in the ratio 4 : 5. If it is filled with an additional 8 litres of milk the can would be full and ratio of milk and water would become 6 : 5. Find the capacity of the can?\n\n### Options:\nA. 18\nB. 74\nC. 15\nD. 44\nE. 63\n\n### Answer:\nExplanation:\nLet the capacity of the can be T litres.\nQuantity of milk in the mixture before adding milk = 4/9 (T - 8)\nAfter adding milk, quantity of milk in the mixture = 6/11 T.\n6T/11 - 8 = 4/9(T - 8)\n10T = 792 - 352 => T = 44.\nCorrect Option : D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nYou collect pens. Suppose you start out with 5. Mike gives you another 20 pens. Since her father makes pens, Cindy decides to double your pens. Since you're nice, you give Sharon 10 pens. How many pens do you have at the end?\n\n### Options:\nA. 39\nB. 40\nC. 41\nD. 42\nE. 43\n\n### Answer:\nSolution\nStart with 5 pens.\nMike gives you 20 pens: 5 + 20 = 25 pens.\nCindy doubles the number of pens you have: 25 \u00c3\u2014 2 = 50 pens.\nSharon takes 10 pens from you: 50 - 10 = 40 pens.\nSo you have 40 at the end.\nCorrect answer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nGold is 19 times as heavy as water and copper is 9 times heavy. In what ratio must these metals be mixed so that the mixture may be 15 times as heavy as water?\n\n### Options:\nA. 2 : 3\nB. 3 : 2\nC. 1 : 3\nD. 2 : 1\nE. None of these\n\n### Answer:\n? Required ratio = 6?4 = 3 : 2\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain galaxy is known to comprise approximately 4 x 10^10 stars. Of every 50 million of these stars, one is larger in mass than our sun. Approximately how many stars in this galaxy are larger than the sun?\n\n### Options:\nA. 800\nB. 1,250\nC. 8,000\nD. 12,000\nE. 80,000\n\n### Answer:\nTotal no. of stars on galaxy = 4 * 10^10\nOf every 50 million stars, 1 is larger than sun.\n1 million = 10^6 therofore, 50 million = 50 * 10^6\ntotal no. of stars larger than sun = 4 * 10^10 / 50 * 10^6\n=40 * 10^2 /5\n= 800\ntherefore answer is A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJack and Christina are standing 150 feet apart on a level surface. Their dog, Lindy, is standing next to Christina. At the same time, they all begin moving toward each other. Jack walks in a straight line toward Christina at a constant speed of 7 feet per second and Christina walks in a straight line toward Jack at a constant speed of 8 feet per second. Lindy runs at a constant speed of 10 feet per second from Christina to Jack, back to Christina, back to Jack, and so forth. What is the total distance, in feet, that Lindy has traveled when the three meet at one place?\n\n### Options:\nA. 40\nB. 60\nC. 80\nD. 100\nE. 120\n\n### Answer:\nThe relative speed of Jack and Christina is 7 + 8 = 15 feet per second.\nThe distance between them is 210 feet, hence they will meet in (time) = (distance)/(relative speed) = 150/15 = 10 seconds.\nFor all this time Lindy was running back and forth, so it covered (distance) = (speed)*(time) = 10*10 = 100 feet.\nAnswer: D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nCan you deduce the pattern and find the next number in the series?\n7, 15, 27, 99, __?\n\n### Options:\nA. 276\nB. 277\nC. 278\nD. 279\nE. None of these\n\n### Answer:\nSolution:\n277\nExplanation:\n7 = (1^1 + 2^1 + 3^1) +1\n15 = (1^2 + 2^2 + 3^2) +1\n37 = (1^3 + 2^3 + 3^3) +1\n99 = (1^4 + 2^4 + 3^4) +1\nThus the next number will be\n(1^5 + 2^5 + 3^5) +1 = 277\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRAJA complete a journey in 10 hours. He travels first half of the journey at the rate of 21 km/hr and second half at the rate of 24 km/hr. Find the total journey in km.\n\n### Options:\nA. 200 km\nB. 250 km\nC. 224 km\nD. 255 km\nE. 260 km\n\n### Answer:\nconsider x -- > (1/2)x/21 + (1/2)x/24 = 10\n==> x/21+x/24 = 20\n15x = 168 * 20\n==> 224km\nANSWER C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIt takes eight hours for a 600 km journey, if 120 km is done by train and the rest by car. It takes 20 minutes more, if 200 km is done by train and the rest by car. The ratio of the speed of the train to that of the cars is:\n\n### Options:\nA. 2 : 3\nB. 3 : 2\nC. 3 : 4\nD. 4 : 3\nE. 4:6\n\n### Answer:\nLet the speed of the train be x km/hr and that of the car be y km/hr.\nThen, 120/x + 480/y = 8 --> 1/x + 4/y = 1/15 ------ (i)\nAlso, 200/x + 400/y = 25/3 --> 1/x + 2/y = 1/24 ----(ii)\nSolving (i) and (ii), we get: x = 60 and y = 80.\nRatio of speeds = 60 : 80 = 3 : 4.\nAnswer : C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n7 members have to be selected from 12 men and 3 women ,Such that no two women can come together .In how many ways we can select them ?\n\n### Options:\nA. 12c6*3c1 + 12c7\nB. 12c6*3c1 + 2c7\nC. 1c6*3c1 + 12c7\nD. 11c6*3c1 + 12c7\nE. 12c6*3c1 + 11c7\n\n### Answer:\nsince no two women can come together,therfore women can be selected in 3c1 ways ...and men will be chosen in 12c6 so to complete the 7 group members...\n=12c6*3c1\nand only selection of men also possible = 12c7\nso final ans : 12c6*3c1 + 12c7\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man is trying to climb over a frozen mountain that is sixty feet high. Every minute, he can climb 3 feet, but due to the slippery ice, he slips back 2 feet.\nHow long will it take him to reach the top of the mountain?\n\n### Options:\nA. 57 minutes\nB. 58 minutes\nC. 59 minutes\nD. 53 minutes\nE. 54 minutes\n\n### Answer:\nSolution:\nIt will take the man 58 minutes to reach the top.\nSince he is climbing 3 feet and falling 2 feet back every passing minute, he is actually climbing 1 feet every minute.\nTherefore, he would have climbed 57 feet in 57 minutes. The remaining distance is 3 feet. He will take one more minute to climb it and reach the surface. Since he has reached the top surface, he won't slip back.\n58 minutes\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA card is drawn from a pack of 52 cards. The probability of ge\u01abng a queen of club or a king of heart is\n\n### Options:\nA. 1/13\nB. 2/13\nC. 1/26\nD. 1/52\nE. None of these\n\n### Answer:\nExplanation:\nTotal number of cases = 52\nFavourable cases = 2\nProbability = 2/56 = 1/26\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo sides of a triangle have length 6 and 8. Which of the following are possible areas of the triangle?\nI. 4\nII. 12\nIII. 24\n\n### Options:\nA. I, II, and III\nB. I and II only\nC. II and III only\nD. I and III only\nE. II only\n\n### Answer:\nAnswer = A. I, II, and III\nWith dimensions of only 2 sides given (for a triangle), this becomes an open ended question\nAny area is possible out of the three\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA thief is noticed by a policeman from a distance of 450 m. The thief starts running and the policeman chases him. The thief and the policeman run at the rate of 10 km and 11 km per hour respectively. What is the distance between them after 6 minutes?\n\n### Options:\nA. 150 m\nB. 200 m\nC. 170 m\nD. 100 m\nE. 350 m\n\n### Answer:\nRelative speed of the thief and policeman = 11 - 10 = 1 km/hr.\nDistance covered in 6 minutes = 1/60 * 6 = 1/10 km = 100 m.\nDistance between the thief and policeman = 450 - 100 = 350 m\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSuresh borrowed some money at the rate of 4% p.a. for the first three years, 9% p.a. for the next five years and 13% p.a. for the period beyond eight years. If the total interest paid by him at the end of 11 years is Rs.8160, how much money did he borrow?\n\n### Options:\nA. s.8500\nB. s.6000\nC. s.8500\nD. s.9000\nE. s.7000\n\n### Answer:\nusing the formula S.I=P*T*R/100\n(x*4*3/100)+(x*9*5/100)+(x*13*3/100)=8160\nx=8500\ni.e money borrowed is Rs.8500\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA school having four classes only have student strength of 10, 40, 30 and 20 respectively. The pass percentages of these classes are 20%, 30%, 60% and 100% respectively. What is the pass percentage for the entire school?\n\n### Options:\nA. 56%\nB. 76%\nC. 52%\nD. 66%\nE. 46%\n\n### Answer:\n20% of 10+30% of 40+60% of 30+100% of 20\n=2+12+18+20 =\nnow 52 of 100\n= 52%\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe value of x + x(x^x) when x = 10 is\n\n### Options:\nA. 100000000010\nB. 10000000010\nC. 10000000000\nD. 1200000000\nE. 12000000010\n\n### Answer:\nSolution:\nx + x(x^x)\nPut the value of x = 10 in the above expression we get,\n10 + 10(10^10)\n= 10 + 10(10 \u00c3\u2014 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10)\n= 10 + 10(10000000000)\n= 10 + 100000000000\n= 100000000010\nAnswer: (a)\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThree number are in the ratio 5:6:7. The sum of its largest and smallest numbers equals the sum of the third number and 48. Find the third number?\n\n### Options:\nA. 87\nB. 57\nC. 48\nD. 26\nE. 28\n\n### Answer:\nLet the numbers be 5x, 6x and 7x.\nLargest number = 7x\nSmallest number = 5x\nThird number = 6x\n7x + 5x = 6x + 48\n6x = 48\nThird number is: 48.\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA, B and C can do a work in 90, 30 and 45 days respectively. If they work together, in how many days will they complete the work?\n\n### Options:\nA. 15\nB. 66\nC. 77\nD. 88\nE. 11\n\n### Answer:\nOne days's work of A, B and C = 1/90 + 1/30 + 1/45\n= (1 + 3 + 2)/90 = 1/15\nA, B and C together can do the work in 15 days.\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA dishonest dealer professes to sell goods at the cost price but uses a weight of 850 grams per kg, what is his percent?\n\n### Options:\nA. 28%\nB. 25%\nC. 55%\nD. 17.6%\nE. 55%\n\n### Answer:\n850 --- 150\n100 --- ? => 17.6%\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nExcluding stoppages, the average speed of a bus is 60 km/hr and including stoppages, the average speed of the bus is 15 km/hr. For how many minutes does the bus stop per hour?\n\n### Options:\nA. 22\nB. 88\nC. 77\nD. 20\nE. 45\n\n### Answer:\nIn 1hr, the bus covers 60 km without stoppages and 15 km with stoppages.\nStoppage time = time take to travel (60 - 15) km i.e 45 km at 60 km/hr.\nstoppage time = 45/60 hrs = 45 min.\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the value for m?\n21(m + n) + 21 = 21(-m + n) + 21\n\n### Options:\nA. 0\nB. -1\nC. 1\nD. 2\nE. 3\n\n### Answer:\n21m + 21n - 21 = -21m + 21n + 21\n42m= 42 => m = 1\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a group of cows and hens, the number of legs are 14 more than twice the number of heads. The number of cows is :\n\n### Options:\nA. 5\nB. 6\nC. 7\nD. 10\nE. 12\n\n### Answer:\nLet no of cows be x, no of hens be y.\nSo heads=x+y\nLegs=4x+2y\nNow, 4x+2y = 2(x+y)+ 14\n2x = 14\nx = 7.\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA cubical tank is filled with water to a level of 1 foot. If the water in the tank occupies 16 cubic feet, to what fraction of its capacity is the tank filled with water?\n\n### Options:\nA. 1/2\nB. 1/3\nC. 1/4\nD. 1/5\nE. 1/6\n\n### Answer:\nThe volume of water in the tank is H*L*B = 16 cubic feet.\nSince H = 1, then L*B = 16 and L = B = 4.\nSince the tank is cubical, the capacity of the tank is 4*4*4 = 64.\nThe ratio of the water in the tank to the capacity is 16/64 = 1/4\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train 800 m long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 min, then the length of the tunnel is?\n\n### Options:\nA. 288 m\nB. 256 m\nC. 500 m\nD. 278 m\nE. 287 m\n\n### Answer:\nSpeed = 78 * 5/18 = 65/3 m/sec.\nTime = 1 min = 60 sec.\nLet the length of the train be x meters.\nThen, (800 + x)/60\n= 65/3\nx = 500 m.\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow long does a train 110 m long running at the speed of 90 km/hr takes to cross a bridge 132 m length?\n\n### Options:\nA. 82.1 sec\nB. 9.68 sec\nC. 16.1 sec\nD. 13.1 sec\nE. 12.15sec\n\n### Answer:\nSpeed = 90 * 5/18 = 25 m/sec\nTotal distance covered = 110 + 132 = 242 m.\nRequired time = 242/25 = 9.68 sec.\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nExpress the following as a fraction 56%\n\n### Options:\nA. 13/50\nB. 17/30\nC. 11/25\nD. 14/25\nE. 14/19\n\n### Answer:\n56% = 56/100\n= 14/25\nAnswer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA disease has infected an ant colony that consists ofworkersandsoldiers: 30% of the soldiers and 14% of theworkerswere infected. If that colony is inhabited by 7000 ants, out of which 1660 are infected, how manyworkersinhabit the colony?\n\n### Options:\nA. 1500\nB. 2500\nC. 2750\nD. 3000\nE. 3250\n\n### Answer:\nFrom two question we get wo equations:\n(1) 0,3s + 0,14w = 1660\n(2) s + w = 7000\nFrom (2) we get w=7000-s\nIn (1) 0,3s + 980-0,14s= 1660\n0,16s=680\n68000:16= 4250 =s\nIn (2) 4250 + w = 7000\nw= 2750 C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe scoring system in a certain football competition goes as follows: 3 points for victory, 1 point for a draw, and 0 points for defeat. Each team plays 20 matches. If a team scored 10 points after 5 games, what is the least number of the remaining matches it has to win to reach the 45-point mark by the end of the tournament?\n\n### Options:\nA. 6\nB. 7\nC. 8\nD. 9\nE. 10\n\n### Answer:\nTo get 45 points as end of season we need another 35 points or more from remaining 15 matches:\nOption A= 6*3+9*1=27\nOption B=7*3 + 8*1=29\nOption C=8*3+7*1=31\nOption D=9*3+6*1=33\nOption E=10*3+5*1=35\nhence option E-10\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nLorna invests $8000, with some at 6% annual interest and some at 11% annual interest. If she receives a total of $580 from these investments at the end of a year, how much was invested at the 6% interest rate?\n\n### Options:\nA. $160\nB. $1,700\nC. $2,200\nD. $4,400\nE. $5,840\n\n### Answer:\nWe have that 'x' invested at 6%\nWe also have that '8000-x' invested at 11%\nNow then 580/8000 is approx 10%\nTherefore, -4x+8000-x=0\n5x=8000\nx=1600 approximately. Probably higher\nOnly B matches\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe amount of principal Rs.8000 at compound interest at the ratio of 5% p.a. for 1 year is\n\n### Options:\nA. s.9621\nB. s.6921\nC. s.8400\nD. s.6261\nE. s.6361\n\n### Answer:\nc.i=p(1+r/100)^n\n=8000(1+5/100)\n=Rs8400\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the value for m?\n19(m + n) + 17 = 19(-m + n) - 173\n\n### Options:\nA. 0\nB. -1\nC. -5\nD. 2\nE. 3\n\n### Answer:\n19m + 19n + 17 = -19m + 19n - 173\n38m= -190 => m = -5\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThree friends A, B and C decided to share a lot of apples. Each of them had half of the total plus half an apple in order. After each of them took their share thrice, no apples were left.How many apples were there?\n\n### Options:\nA. 500\nB. 510\nC. 511\nD. 501\nE. 504\n\n### Answer:\nWhenever the rate of reduction is 'half of the total and half of it', the answer is always (2^n)-1, where 'n' is the number of times the process is repeated. Here, the process is repeated 9 times. So answer is (2^9)-1=511.\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man goes into a barbershop and gets a $15 haircut. He pays the barber with a $20 bill, but the barber doesn't have change because it is an especially slow day. The barber goes to the flower shop next to his own and trades the $20 bill for a $10 dollar bill and two $5 bills. Then he gives the man his $5 in change.\nLater the lady from the flower shop confronts the barber and tells him that the $20 bill he gave her was counterfeit. The barber agrees and he gives the lady a different $20 bill.\nLater that day he tries to figure out how much money he lost. What did he lose?\n\n### Options:\nA. $5\nB. $10\nC. $12\nD. $15\nE. $20\n\n### Answer:\nHe lost $5. The lady from the flower shop gave him $20 in change, but eventually got $20 back. She broke even. The man who got the haircut gave the barber nothing (except counterfeit money) but got $5 back from the barber. So the barber lost only $5, and gave a free haircut.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA car crosses a 600 m long bridge in 5 minutes. Whatis the speed of car in km per hour?\n\n### Options:\nA. 7 km/hr\nB. 7.2 km/hr\nC. 8 km/hr\nD. 8.2 km/hr\nE. 8.3 km/hr\n\n### Answer:\nSpeed = 600 m/sec.\n5 x 60\n= 2 m/sec.\nConverting m/sec to km/hr (see important formulas section)\n= 2 x 18 km/hr\n5\n= 7.2 km/hr\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf (A-B-C+D = 18) and (A+B-C-D = 4), what is the value of (B-D)^2?\n\n### Options:\nA. 49.\nB. 8.\nC. 12.\nD. 16.\nE. 64.\n\n### Answer:\nEQ1: A - B - C + D = 18\nEQ2: A + B - C - D = 4\n(1) Subtract EQ1 from EQ2\nA - B - C + D = 18\n- A +B - C - D = 4\n------------------------\n-2B + 2D = 14\n(2) Simplify\n-B + D = 7\nB - D = -7\n(B-D)^2 = (-7)^2 = 49\nMy answer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf X gets 25% more than Y and Y gets 20% more than Z, the share of Z out of Rs. 1480 will be:\n\n### Options:\nA. Rs. 300\nB. Rs. 200\nC. Rs. 240\nD. Rs. 400\nE. None of these\n\n### Answer:\nZ share = Z,\nY = 1.2Z\nX = 1.25\u00c3\u20141.2Z,\nX+Y+Z =1480\n(1.25\u00c3\u2014 1.2+1.2+1)Z=1480\n3.7Z=1480, Z=400\nAnswer: . D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo horses begin running on an oval course at the same time. One runs each lap in 4 minutes; the other takes 16 minutes to run each lap. How Many minutes after the start will the faster horse have a one lap lead?\n\n### Options:\nA. 36\nB. 12\nC. 16/3\nD. 4\nE. 3\n\n### Answer:\nThe rate of the faster horse is 1/4 lap/minute;\nThe rate of the slower horse is 1/16 lap/minute;\nTheir relative rate is 1/4-1/16=3/16 lap/minute;\nThe faster horse to gain one full lap will need time=distance/rate=1/(3/16)=16/3 minutes.\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a certain diving competition, 5 judges score each dive on a scale from 1 to 10. The point value of the dive is obtained by dropping the highest score and the lowest score and multiplying the sum of the remaining scores by the degree of difficulty. If a dive with a degree of difficulty of 3.2 received scores of 7.5, 8.1, 9.0, 6.0, and 8.5, what was the point value of the dive?\n\n### Options:\nA. 68.8\nB. 73.6\nC. 75.2\nD. 77.12\nE. 81.6\n\n### Answer:\nDegree of difficulty of dive = 3.2\nScores are 6.0 , 7.5 , 8.1 , 8.5 and 9.0\nWe can drop 6.0 and 9.0\nSum of the remaining scores = (7.5+8.1+8.5)= 24\nPoint of value of the dive = 24.1*3.2 =77.12\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat least number mustbe subtracted from 427398 so that remaining no.is divisible by 15\n\n### Options:\nA. 354665677\nB. 436557678\nC. 457676788\nD. 725117481\nE. 567768788\n\n### Answer:\nExplanation:\nOn dividing 427398 by 15 we get the remainder 3, so 3 should be subtracted\nAnswer: Option D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average (arithmetic mean) of 20, 40, and 60 is 8 more than the average of 10, 70, and what number?\n\n### Options:\nA. 16\nB. 25\nC. 35\nD. 45\nE. 55\n\n### Answer:\na1 = 120/3 = 40\na2 = a1 -8 = 32\nsum of second list = 32*3 = 96\ntherefore the number = 96 -80 = 16\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWorking simultaneously and independently at an identical constant rate, 5 machines of a certain type can produce a total of x units of product P in 8 days. How many of these machines, working simultaneously and independently at this constant rate, can produce a total of 3x units of product P in 4 days?\n\n### Options:\nA. 30\nB. 18\nC. 16\nD. 12\nE. 8\n\n### Answer:\n5 machines do x units in 8 days\nwe have x/8 => rate of the 5 machines\nwe know that we need to have 3x units in 4 days\ntherefore, we need to get to 3x/4 rate of the machines.\nrate of one machine is x/8*1/5 = x/40.\nnow, we need to know how many machines need to work simultaneously, to get 3x done in 4 days.\n3x/4 work needs to be done by machines that work at x/40 rate.\nlet's assign a constant Y for the number of machines:\n(x/40)*y = 3x/4\ny = 3x/4 * 40/x\ncancel 4 with 40, and x with x and get -> 30. Answer choice A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe difference between a two-digit number and the number obtained by interchanging the positions of its digits is 36. What is the difference between the two digits of that number?\n\n### Options:\nA. 3\nB. 4\nC. 9\nD. 11\nE. None of these\n\n### Answer:\nAnswer: Option B\nLet the ten's digit be x and unit's digit be y.\nThen, (10x + y) - (10y + x) = 36\n9(x - y) = 36\nx - y = 4.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a,b, and c are consecutive positive integers and a>b>c, what can be the value of (a^2-b^2)(b^2-c^2)?\n\n### Options:\nA. 54\nB. 63\nC. 75\nD. 86\nE. 98\n\n### Answer:\n(a^2-b^2)(b^2-c^2) = (a+b)*(a-b)*(b+c)*(b-c) = (a+b)*(-1)*(b+c)*(-1) = (a+b)*(b+c)\nTherefore, the product should have factors with a difference of 2.\n63 = 7*9, so this is a possible value for the original expression.\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how many ways, a committee of 5 members can be selected from 6 men and 5 ladies, consisting of 3 men and 2 ladies?\n\n### Options:\nA. 200\nB. 120\nC. 245\nD. 320\nE. 147\n\n### Answer:\n(3 men out 6) and (2 ladies out of 5) are to be chosen.\nRequired number of ways = (6c3x5c2)\n= [6x5x4/3x2x1] x [5x4/2x1] = 200.\nAns: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the greatest number which on dividing 1255 and 1490, leaves a reminder of 8 and 11 respectively\n\n### Options:\nA. 27\nB. 29\nC. 33\nD. 39\nE. 41\n\n### Answer:\nExplanation:\nIn this type of question, its obvious we need to calculate the HCF, trick is\nHCF of (1255 - 8) and (1490 -11)\n= HCF (1247, 1479) = 29\nOption B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo trains of equal lengths take 10 sec and 15 sec respectively to cross a telegraph post. If the length of each train be 120 m, in what time will they cross other travelling in opposite direction?\n\n### Options:\nA. 8\nB. 10\nC. 12\nD. 11\nE. 15\n\n### Answer:\nSpeed = 120/10 = 12 m/sec\nspeed of the second train = 120/5 = 8 m/sec\nrelative speed = 12+8 = 20 m/sec\nReq time = 120+120/20 = 12 sec\nANSWER C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA and B started a business investing Rs. 92,000 and Rs 20,000 respectively. In what ratio the profit earned after 2 years be divided between A and B respectively?\n\n### Options:\nA. 9:2\nB. 3:2\nC. 23:5\nD. 18:4\nE. 17:4\n\n### Answer:\nA: B = 92000 : 20000\n= 92 : 20\n= 46 : 10\n= 23 : 5\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhen 1/20% of 6,000 is subtracted from 1/10 of 6,000, the difference is\n\n### Options:\nA. 50\nB. 200\nC. 380\nD. 598\nE. 400\n\n### Answer:\n1/20 % of 6000 = 3\n1/10 of 6000 = 600\n600-3 = 598\nAns:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train passes a station platform in 36 sec and a man standing on the platform in 20 sec. If the speed of the train is 54 km/hr. What is the length of the platform?\n\n### Options:\nA. 120 m\nB. 240 m\nC. 300 m\nD. 400 m\nE. None of these\n\n### Answer:\nSpeed = 54 * 5/18 = 15 m/sec.\nLength of the train = 15 * 20 = 300 m.\nLet the length of the platform be x m . Then,\n(x + 300)/36 = 15 => x = 240 m.\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe ratio of the two natural numbers is 6 : 5. If a certain number is subtracted to both the numbers, the ratio becomes 5 : 4. If the larger number exceeds the smaller number by 5, find the number subtracted?\n\n### Options:\nA. 8\nB. 5\nC. 15\nD. 22\nE. 6\n\n### Answer:\nLet the two numbers be 6x and 5x.\nLet the numbers subtracted to both so that their ratio becomes 5 : 4 be k.\n(6x - k) / (5x - k) = 5/4\n=> 24x - 4k = 25x - 5k => k = x.\n6x - 5x = 5 => x = 5\nk = x = 5.\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average of first five prime numbers greater than 20 is?\n\n### Options:\nA. 32.2\nB. 32.98\nC. 32.3\nD. 32.8\nE. 32.4\n\n### Answer:\n23 + 29 + 31 + 37 + 41\n= 161/5\n= 32.2\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n|x+3| \u2013 |4-x| = |9+x| How many solutions will this equation have?\n\n### Options:\nA. 0\nB. 1\nC. 2\nD. 3\nE. 4\n\n### Answer:\nYou have |x+3| - |4-x| = |8+x|\nFirst, look at the three values independently of their absolute value sign, in other words:\n|x+3| - |4-x| = |8+x|\n(x+3) - (4-x) = (8+x)\nNow, you're looking at x < - 8, so x is a number less than -8. Let's pretend x = -10 here to make things a bit easier to understand.\nwhen x=-10\nI.) (x+3)\n(-10+3)\n(-7)\nII.) (4-x)\n(4-[-10]) (double negative, so it becomes positive)\n(4+10)\n(14)\nIII.) (8+x)\n(8+-10)\n(-2)\nIn other words, when x < -8, (x+3) and (8+x) are NEGATIVE. To solve problems like this, we need to check for the sign change.\nHere is how I do it step by step.\nI.) |x+3| - |4-x| = |8+x|\nII.) IGNORE absolute value signs (for now) and find the values of x which make (x+3), (4-x) and (8+x) = to zero as follows:\n(x+3)\nx=-3\n(-3+3) = 0\n(4-x)\nx=4\n(4-4) = 0\n(8+x)\nx=-8\n(8+-8) = 1\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo negative numbers are multiplied to give a product of 48. If the lesser number is 10 less than thrice the greater number, what is the greater number?\n\n### Options:\nA. -6\nB. -8\nC. -5\nD. -9\nE. -10\n\n### Answer:\nTest the options. The options give you the greater number.\n(A) - 6\nTriple of -6 is -18 and 10 less is -8.\n-8 * -6 =48 (Correct)\nCorrect\nAnswer (A)\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA store sells a certain product at a fixed price per unit. At the product's current price, w units cost a total of exactly $300. If the price were lowered by $5 from its current value, then w + 2n units would cost exactly $300; if the price were raised by $5, then w \u2013 n units would cost exactly $300. What is the value of w?\n\n### Options:\nA. 10\nB. 15\nC. 20\nD. 25\nE. 30\n\n### Answer:\nIt got too complicated when I used algebra. Using plugging in, it was quite fast.\nPrice Quantity total value\np w pw = 300\np-5 w+2n (p-5)(w+2n) = 300\np+5 w-n (p+5)(w-n) = 300\nSolving three equations for three unknowns. Tough!!\nPlugging in, I always start with C. C was the answer here, so saved calculation!\nPutting values in above equations:\nPrice Quantity total value\n15 20 300\n10 20+2n 300 -> 10(20 + 2n)=300 -> 200 +20n = 300 -> 20n = 100 -> n =5\n20 15 300\nSo w = 20 satisfies all equations!!\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe 44 parents participating in the Smithville PTA have been assigned to at least 1 of 3 committees: festival planning, classroom aid, and teacher relations. 21 parents are assigned to the festival planning committee, 18 parents are assigned to the classroom aid committee, and 19 parents are assigned to the teacher relations committee. If 5 parents are assigned to all 3 committees, how many parents are assigned to exactly 2 committees?\n\n### Options:\nA. 4\nB. 6\nC. 8\nD. 9\nE. 10\n\n### Answer:\nThe formula is Total = A+B+C - sum of exactly two + 2*all three + neither\n21+18+19-x-2*5=44\nsolving for x you get 4\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA can do a piece of work in 40 days; B can do the same in 30 days. A started alone but left the work after 10 days, then B worked at it for 10 days. C finished the remaining work in 10 days. C alone can do the whole work in?\n\n### Options:\nA. 24 days\nB. 65 days\nC. 86 days\nD. 45 days\nE. 17 days\n\n### Answer:\n10/40 + 10/30 + 10/x = 1\nx = 24 days\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA and B started business in partnership investing Rs. 20,000 and Rs. 15,000 respectively. After six months, C joined them with Rs. 20,000. What will be B's share in the total profit of Rs. 25,000 earned at the end of 2 years from the starting of the business?\n\n### Options:\nA. 7500\nB. 4366\nC. 2877\nD. 2768\nE. 26871\n\n### Answer:\nA:B:C = (20000 * 24) : (15000 * 24) : (20000 * 18) = 4:3:3\nB's share = 25000 * 3/10\n= Rs. 7500.\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nCalculate the ratio between x and y if 25% of x equal to 40% of y?\n\n### Options:\nA. 5 : 8\nB. 5 : 9\nC. 5 : 7\nD. 5 : 6\nE. 5 : 4\n\n### Answer:\nExplanation:\n25 x = 40 y\nx: y = 25 : 40 = 5 : 8\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA cube of edge 6 cm is cut into cubes each of edge 1 cm. The ratio of the total surface area of one of the small cubes to that of the large cube is equal to:\n\n### Options:\nA. 1:25\nB. 1:36\nC. 1:52\nD. 1:522\nE. None\n\n### Answer:\nSol.\nRequired ratio = 6 * 1 * 1 / 6 * 6 * 6 = 1/36 = 1:36.\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n85% of a number is added to 24, the result is the same number. Find the number?\n\n### Options:\nA. 257\nB. 267\nC. 187\nD. one hundred sixty (160)\nE. 122\n\n### Answer:\n(85/100) * X + 24 = X\n3X = 480\nX = 160\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nCountry X imported approximately $1.44 billion of goods in 1996. If Country X imported $388 million of goods in the first two months of 1997 and continued to import goods at the same rate for the rest of the year, by how much would Country Xs 1997 imports exceed those of 1996?\n\n### Options:\nA. $24 million\nB. $120 million\nC. $144 million\nD. $240 million\nE. $888 million\n\n### Answer:\nConvert units to millions as answer is in millions\n1996 Imports = $1.44 bill = $1440 mill\ni.e. 1440/12 = $120 mill/month\n1997 Imports = $388 mill/2 month\ni.e. $194 mill/month\nDifference/month = 194-120 = 74\nDifference/year = $74 mill * 12 = $988 mill\nANSWER: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA 270 m long train running at the speed of 120 km/hr crosses another train running in opposite direction at the speed of 80 km/hr in 9 sec. What is the length of the other train?\n\n### Options:\nA. 230\nB. 9927\nC. 267\nD. 1268\nE. 181\n\n### Answer:\nRelative speed = 120 + 80 = 200 km/hr.\n= 200 * 5/18 = 500/9 m/sec.\nLet the length of the other train be x m.\nThen, (x + 270)/9 = 500/9 => x = 230.\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA credit card number has 6 digits (between 1 to 9 inclusive). The first two digits are 12 in that order, the third digit is bigger than 6, the fourth digit is divisible by 2, and the fifth digit is 4 times the sixth. How many different credit card numbers are possible?\n\n### Options:\nA. 12\nB. 18\nC. 24\nD. 36\nE. 48\n\n### Answer:\nThe first two digits are fixed.\nThe third digit can be 7, 8, or 9 so there are 3 choices.\nThe fourth digit can be 2, 4, 6, or 8 so there are 4 choices.\nThe fifth digit depends entirely on the sixth digit.\nThe sixth digit can be 1 or 2 so there are 2 choices.\nThe number of possibilities is 3*4*2 = 24\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe amount of an investment will double in approximately 70/ p years, where p is the percent interest, compounded annually. If Thelma invests $ 60,000 in a long-term CD that pays 5 percent interest, compounded annually, what will be the approximate total value of the investment when Thelma is ready to retire 42 years later?\n\n### Options:\nA. $ 280,000\nB. $ 320,000\nC. $ 360,000\nD. $ 480,000\nE. $ 540,000\n\n### Answer:\nThe amount of an investment will double in approximately 70/ p years, where p is the percent interest, compounded annually. If Thelma invests $ 60,000 in a long-term CD that pays 5 percent interest, compounded annually, what will be the approximate total value of the investment when Thelma is ready to retire 42 years later?\nThe investment gets doubled in 70/p years. Therefore, the investment gets doubled in 70/5= every 14 years. After 42 years, the investment will get doubled 42/14= 3 times.\nSo the amount invested will get doubled thrice.\nSo, 60000 *2^3 = 480000\nHence, the answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nEle, the circus Elephant, is currently three times older than Lyn, the circus Lion. In 15 years from now, Lyn the circus Lion will be exactly half as old as Ele, the circus Elephant. How old is Ele today?\n\n### Options:\nA. 40\nB. 48\nC. 43\nD. 45\nE. 41\n\n### Answer:\nEle, the circus Elephant, is currently three times older than Lyn, the circus Lion.\nEle = 3*Lyn\nUsually, ages are integers so there is a good possibility that the age of Ele is 45 (the only option that is a multiple of 3).\nThen age of Lyn would be 15. In 15 yrs, Ele would be 60 and Lyn would be 30 - so Lyn would be half as old as Ele.\nAnswer (D)\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA lady bought five books namely A,B,C,D,E to distribute her 6 children. How many ways she can distribute books?\n\n### Options:\nA. 6^3\nB. 5^6\nC. 6^5\nD. 6^6\nE. 3^6\n\n### Answer:\n6*6*6*6*6\n6^5\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMike drives his new Corvette from San Francisco to Las Vegas, a journey of 640 miles. He drives the first half of the trip at an average rate of 80 miles per hour, but has to slow down for the second half of his journey. If the second half of the trip takes him 200 percent longer than the first half, what is his average rate P in miles per hour for the entire trip?\n\n### Options:\nA. P=26.7\nB. P=30.0\nC. P=40.0\nD. P=53.3\nE. P=60.0\n\n### Answer:\nVERITAS PREPOFFICIAL SOLUTION\nCorrect Answer : C\nUsing the formula: Time = Distance/Rate, we find that Mike takes 4 hours to cover the first 320 miles of his trip. Since the 2nd 320 miles take 200% longer than the first, it takes Mike 8 hours longer, or 12 hours. (Note: 200% longer than the first half is not 200% of the first half.) The overall time is 4 hours + 12 hours or 16 hours. Since the definition of Average Rate = Total Distance Traveled/Total Time of Travel, Mike's average rate = 640/16 or 40 miles per hour.\nAnswer choice C is correct.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train 140 m long is running with a speed of 50 km/hr. In what time will it pass a man who is running at 4 km/hr in the direction opposite to that in which the train is going?\n\n### Options:\nA. 8.1\nB. 7.0\nC. 9.33\nD. 8\nE. 9\n\n### Answer:\nSpeed of train relative to man = 50 +4 = 54 km/hr.\n= 54 * 5/18 = 15 m/sec.\nTime taken to pass the men = 140 * 1/15 = 9.33 sec.\nAnswer: Option C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a race, A beats B by 15 metres and C by 29 metres. If B and C run over the course together, B wins by 15 metres. What is the length of the course?\n\n### Options:\nA. 225m\nB. 120m\nC. 220m\nD. 160m\nE. 180m\n\n### Answer:\nExplanation:\nLet X be the length of the course\naccording to the question,\nA beats B by 15 metres and C by 29 metres\nApplying this,\nIf A runs X metres, B runs (X-15) and C runs ( X-29) metres.\nB and C together run, B runs X metres and C runs (X-15)\n=> If B runs 1 metre, C runs X-15/X\n=> B runs X-15 m, C runs (X-15/x) * (X-15)\nAPPLYING THIS,\nX-29 = (X-15)(X-15) / X\nSolving,\nX2 -29X= X2 \u2013 30 X + 225\nX = 225\nThus, length of the course is 225 metres.\nANSWER A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA contractor agreeing to finish a work in 150 days, employed 75 men each working 8 hours daily. After 90 days, only 2/7 of the work was completed. Increasing the number of men by ________ each working now for 10 hours daily, the work can be completed in time.\n\n### Options:\nA. 322 men\nB. 232 men\nC. 838 men\nD. 539 men\nE. 150 men\n\n### Answer:\nOne day\u2019s work = 2 / (7 * 90)\nOne hour\u2019s work = 2 / (7 * 90 * 8)\nOne man\u2019s work = 2 / (7 * 90 * 8 * 75)\nThe remaining work (5/7) has to be completed within 60 days, because the total\nnumber of days allotted for the project is 150 days.\nSo we get the equation\n(2 * 10 * x * 60) / (7 * 90 * 8 * 75) = 5/7 where x is the number of men\nworking after the 90th day.\nWe get x = 225\nSince we have 75 men already, it is enough to add only 150 men.\nAnswer:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn what time will a train 100 m long cross an electric pole, it its speed be 90 km/hr?\n\n### Options:\nA. 2.5 sec\nB. 2.8 sec\nC. 8.5 sec\nD. 2.2 sec\nE. 4 sec\n\n### Answer:\nSpeed = 90 * 5/18\n= 25 m/sec\nTime taken = 100/25\n= 4 sec.\nAnswer:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJill invests $10000 in an account that pays an annual rate of 3.96%, compounding semi-annually. Approximately how much does she have in her account after two years?\n\n### Options:\nA. $10079.44\nB. $10815.83\nC. $12652.61\nD. $14232.14\nE. $20598.11\n\n### Answer:\nSolution: first of all, notice the magic word \u201capproximately\u201d \u2014 the test-writer is letting us know estimation is perfectly fine. Furthermore, the answer choices are nicely spread out, which will facilitate estimating.\nOK, get ready for some fast & furious estimation. The interest rate 3.96% is an ugly number, so I\u2019m going to approximate that as 4%. It compounds semiannually, so that means that there\u2019s 2% every six months, and that happens four times in two years. Well, 2% of $10000 is $200. If you get $200, or a little more, on four occasions, that\u2019s a little more than $800 in interest. We expect an answer slightly higher than $10800, so of course (B) is just right.\nNotice, I estimated so that everything up until the last sum was single-digit math. Single-digit calculations are a good standard for which to strive when you are practicing estimation.\nBy the way, if you find the bank that will do answer (E), double your money in only two years, that\u2019s terrific, but it probably is something wildly illegal, a Ponzi scheme or worse! In the real world, that just doesn\u2019t happen. On word problems, especially in financial situations, you should always have your antenna up for what\u2019s realistic or unrealistic.\nanswer (B)\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA and B go around a circular track of length 300 m on a cycle at speeds of 18 kmph and 54 kmph. After how much time will they meet for the first time at the starting point?\n\n### Options:\nA. 120 sec\nB. 198 sec\nC. 60 sec\nD. 665 sec\nE. 276 sec\n\n### Answer:\nTime taken to meet for the first time at the starting point\n= LCM { length of the track / speed of A , length of the track / speed of B}\n= LCM { 300/ (90 * 5/18) , 300/ (54 * 5 /18) }\n= LCM (12, 20) = 60 sec.\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA company selected 250 zip codes in Northeastern, Florida, Arizona and California in order to mail a product catalog. The number of Northeastern zip codes was twice Florida's, and four times Arizona's, and 4/3 California's. 450,000 catalogues were mailed to California and 25% resulted in product orders. What is the ratio of the number of orders to the number of California's zip codes?\n\n### Options:\nA. a) 500\nB. b) 750\nC. c) 1,000\nD. d) 1,250\nE. e) 1,500\n\n### Answer:\nSince N = 2F, no of Florida zip codes (F) will be N/2.\nSince N = 4A, no of Arizona zip codes (A) will be N/4\nSince N = (4/3)C, no of California zip codes (C) will be 3N/4\nN + N/2 + N/4 + 3N/4 = 5N/2 = 250\nN = 100\nC = 3N/4 = 75\nNo of orders is 25% of 450,000 = 112,500\nSo required ratio = 112,500/75 = 1500\nAnswerr E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA driver took a trip consisting of three segments at three different speeds. The driver drove a distance of (3D) at a speed of (2V), then a distance of (7D) at a speed of (3V), then a distance of D at a speed of (6V). In terms of D and V, what was the total time of the trip?\n\n### Options:\nA. 3D/V\nB. 4D/V\nC. 5D/V\nD. 6D/V\nE. 7D/V\n\n### Answer:\nThe total time of the trip was:\n3D/2V + 7D/3V + D/6V =\n18D/12V + 28D/12V + 2D/12V =\n48D/12V = 4D/V\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the area of square field whose side of length 5 m?\n\n### Options:\nA. 80 sq m\nB. 26 sq m\nC. 25 sq m\nD. 45 sq m\nE. 96 sq m\n\n### Answer:\n5 * 5\n= 25 sq m\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA football player scores 5 goals in his fifth match thus increasing his average goals score by 0.2. The total number of goals in his 5 matches would be\n\n### Options:\nA. 14\nB. 16\nC. 18\nD. 10\nE. 21\n\n### Answer:\nWhile this question can be solved with a rather straight-forward algebra approach (as the other posters have noted), it can also be solved by TESTing THE ANSWERS. One of those numbers MUST be the total number of goals...\nFrom a tactical standpoint, it's best to TEST either Answer B or Answer D, so if the answer is not correct, then you would have a gauge for whether you should gohigherorlowerwith your next TEST.\nHere, I'll start with Answer E =21 goals\nIf....\nTotal goals = 21 goals\n5th game = 5 goals\n1st 4 games = 16 goals\nAvg. for 1st 4 games = 16/4 = 4 goal/game\nAvg. for all 5 games = 21/5 = 4.2 goals/game\nThis is an EXACT MATCH for what we're told in the prompt, so Answer E MUST be the answer.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the diffference between the place value and face value of 7 in the numeral 9751?\n\n### Options:\nA. 691\nB. 692\nC. 693\nD. 694\nE. 695\n\n### Answer:\nplace value of 7 = 7 * 100 = 700\nface value of 7 = 7\n700 - 7 = 693\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFor what value of x, is |x \u2013 3| + |x + 1| + |x| = 11?\n\n### Options:\nA. 0\nB. 3\nC. -3\nD. 4\nE. -2\n\n### Answer:\nFor what value of x, is |x \u2013 3| + |x + 1| + |x| = 11?\nIt's easiest just to plug in answer choices:\n(C): -3\n|x \u2013 3| + |x + 1| + |x| = 11?\n|-3 - 3| + |-3 + 1| + |-3| = 11?\n|6| + |2| + |3| = 11\n(C)\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe probability that event A occurs is 0.4, and the probability that events A and B both occur is 0.25. If the probability that either event A or event B occurs is 0.6, what is the probability that event B will occur?\n\n### Options:\nA. 0.05\nB. 0.15\nC. 0.45\nD. 0.5\nE. 0.55\n\n### Answer:\nP(A or B) = P (A) + P(B) - p(a n b)\n0.6= 0.4 + P(B) - 0.25\nP(B) = 0.45\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf p and q are two different odd prime numbers, such that p < q, then which of the following must be true?\n\n### Options:\nA. (2p + q) is a prime number\nB. p + q is divisible by 4\nC. q - p is divisible by 4\nD. (p + q + 1) is the difference between two perfect squares of integers\nE. p2+q2 is the difference between two perfect squares of integers\n\n### Answer:\n1. (2p + q) for sure is an odd number , but may or may not be a prime number .\nEg - if we take 3 and 5 as p and q resp, we get 11, which is a prime number.\nBut if we take 7 and 11, we get 25, which is not a prime number.\n2. p + q for sure gives us an even number. It may or may not be divisible by 4.\nEg - (7 + 5) = 12 , which is divisible by 4. But (11 + 7) = 18 , not divisible by 4\n3. Same way as 2nd.\n4. (p + q + 1) gives us an odd number.\nLets see the trend of difference between squares of consecutive integers.\n2^2 - 1^2 = 3\n3^2 - 2^2 = 5\n4^2 - 3^2 = 7\n5^2 - 4^2 = 9\n6^2 - 5^2 = 11 and so on.\nThe trend is : The difference between squares of consc. integers is always odd number. And it covers all the odd numbers.\nHowever , when we don't take consecutive integers, this trend is not followed.\nEg : 5^2 - 3^2 = 16 , which is an even number\n3^2 - 1^2 = 8 , again not an odd number\nHence : Any odd number can be expressed as the difference of the squares of integers.\n5. (p^2 + q^2) gives an even number.\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSum of the squares of three numbers is 116 and the sum of their products taken two at a time is 70. Find the sum?\n\n### Options:\nA. 14\nB. 15\nC. 16\nD. 17\nE. 18\n\n### Answer:\n(a + b + c)2 = a2 + b2 + c2 + 2(ab +bc + ca) = 116 + 2* 70\na + b + c = \u221a256 = 16\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a rectangular coordinate system, what is the area of a quadrilateral whose vertices have the coordinates (3,-1), (3, 8), (12, 2), (12,-7)?\n\n### Options:\nA. 69\nB. 75\nC. 81\nD. 87\nE. 93\n\n### Answer:\nBy graphing the points, we can see that this figure is a trapezoid. A trapezoid is any quadrilateral that has one set of parallel sides, and the formula for the area of a trapezoid is:\nArea = (1/2) \u00d7 (Base 1 + Base 2) \u00d7 (Height), where the bases are the parallel sides.\nWe can now determine the area of the quadrilateral:\nArea = 1/2 \u00d7 (9 + 9) \u00d7 9 = 81.\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA boy has Rs. 720 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?\n\n### Options:\nA. 90\nB. 110\nC. 140\nD. 135\nE. 120\n\n### Answer:\nLet number of notes of each denomination be x.\nThen x + 5x + 10x = 720\n16x = 720\nx = 45\nHence, total number of notes = 3x = 135\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nx varies inversely as square of y. Given that y=3 for x=1. The value of x for y = 2 will be equal to:\n\n### Options:\nA. 3\nB. 6\nC. 1/9\nD. 1/3\nE. 9/4\n\n### Answer:\nExplanation :\nSolution: Given x = k/y^2, where k is constant. Now, y=3 and x =1 gives k = 9.\n.'. x = 9/y^2\n=> x =9 /2^2 = 9/4\nAnswer : E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA student chose a number, multiplied it by 2, then subtracted 138 from the result and got 102. What was the number he chose?\n\n### Options:\nA. 120\nB. 335\nC. 784\nD. 217\nE. 210\n\n### Answer:\nLet x be the number he chose, then\n2*x*138=102\n2x=240\nx=120\ncorrect answer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nInsert the missing number\n4, -8, 16, -32, 64, (....)\n\n### Options:\nA. 128\nB. -128\nC. 192\nD. -132\nE. 0\n\n### Answer:\n4*-2=-8\n-8*-2=16\n16*-2=-32\n-32*-2=64\n64*-2=-128\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo trains, each 100 m long, moving in opposite directions, cross other in 8 sec. If one is moving twice as fast the other, then the speed of the faster train is?\n\n### Options:\nA. 29\nB. 29\nC. 60\nD. 19\nE. 12\n\n### Answer:\nLet the speed of the slower train be x m/sec.\nThen, speed of the train = 2x m/sec.\nRelative speed = ( x + 2x) = 3x m/sec.\n(100 + 100)/8 = 3x => x = 25/3.\nSo, speed of the faster train = 50/3 = 50/3 * 18/5\n= 60 km/hr.\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf x = y+3+4.5x and y = x+33, what is the value of x/y ?\n\n### Options:\nA. -6/5.\nB. -8/25\nC. 1/4.\nD. 5/6.\nE. 1.5.\n\n### Answer:\n(1) x = y + 3 + 4.5x\nSubstitute y for y = x + 33 (Eq. we are given)\nx = x + 33 + 3 + 4.5x\nCombine like terms\nx = 5.5x +36 --> -4.5x = 36 --> x = -8\n(2) y = x + 18\nSubstitute x for x = -8\ny = (-8) + 33 = 25\n(3) x/y = ?\nSubstitute x and y we found above\nx/y = (-8) / (25) =-8/25\nMy answer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA credit card number has 6 digits (between 1 to 9). The first two digits are 12 in that order, the third digit is bigger than 4, the forth is divisible by 3 and the fifth digit is 3 times the sixth. How many different credit card numbers exist?\n\n### Options:\nA. 27\nB. 36\nC. 72\nD. 112\nE. 45\n\n### Answer:\n{1}{2}{greater than 6}{divisible by 3}{3x}{x}:\nThe third digit can take 5 values: 5,6,7, 8, or 9.\nThe fourth digit can take 3 values: 3, 6, or 9.\nThe fifth and sixth digits can take 3 values: 31, 62, or 93.\nTotal = 5*3*3 = 45.\nAnswer: E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA and B go around a circular track of length 600 m on a cycle at speeds of 36 kmph and 54 kmph. After how much time will they meet for the first time at the starting point?\n\n### Options:\nA. 120 sec\nB. 176 sec\nC. 178 sec\nD. 187 sec\nE. 189 sec\n\n### Answer:\nTime taken to meet for the first time at the starting point\n= LCM { length of the track / speed of A , length of the track / speed of B}\n= LCM { 600/ (36 * 5/18) , 600/ (54 * 5 /18) }\n= LCM (60, 40) = 120 sec.\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn the graduating class of a certain college, 48 percent of the students are male and 52 percent are female. In this class 50 percent of the male and 20 percent of the female students are 25 years old or older. If one student in the class is randomly selected, approximately what is the probability that he or she will be less than 25 years old?\n\n### Options:\nA. A)0.9\nB. B)0.6\nC. C)0.45\nD. D)0.3\nE. E)0.25\n\n### Answer:\nPercent of students who are 25 years old or older is 0.5*48+0.2*52=~34, so percent of people who are less than 25 years old is 100-3=66.\nAnswer: B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the compound ratio of (2:3), (6:11) and (11:4) is\n\n### Options:\nA. 3:2\nB. 2:1\nC. 1:1\nD. 4:5\nE. 2:3\n\n### Answer:\nRequired ratio = 2/3 * 6/11 * 11/4 = 2/1 = 1:1\nAnswer is C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOn his first 3 tests, Rajeev received an average score of X points. If on his fourth test, he exceeds his previous average score by 24 points, what is his average score for his first 4 tests?\n\n### Options:\nA. X\nB. X+6\nC. X+4\nD. X+3\nE. X+2\n\n### Answer:\nTotal of 1st 3 tests= 3X\n4th test score = X + 24\nTotal of all 4 tests = 4X + 24\nAverage = X + 6\nAnswer : B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the tens digit of 6^21?\n\n### Options:\nA. 1\nB. 3\nC. 5\nD. 7\nE. 9\n\n### Answer:\nThe tens digit of 6 in integer power starting from 2 (6^1 has no tens digit) repeats in a pattern of 5: {3, 1, 9, 7, 5}:\nThe tens digit of 6^2=36 is 3.\nThe tens digit of 6^3=216 is 1.\nThe tens digit of 6^4=...96 is 9.\nThe tens digit of 6^5=...76 is 7.\nThe tens digit of 6^6=...56 is 5.\nThe tens digit of 6^7=...36 is 3 again.\netc...\n21 has the form 5n+1, so the tens digit of 6^21 is 5.\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAt The KHOOL Company, high quality and low quality solar reflecting sunglasses are made, where 70 percent of the sunglasses made are high quality and 25 percent are low quality (defective sunglasses are tossed away into the recycle bin, but must be counted as product produced). If there are 50 sunglasses made per day that are defective and can't be sold as low or high quality sunglasses, how many sunglasses does The KHOOL Company make total per day?\n\n### Options:\nA. 100\nB. 1,800\nC. 1,090\nD. 200\nE. 1,000\n\n### Answer:\nLet the total number of sunlasses produced be x\n% of high quality sunglasses = 70%\n% of low quality sunglasses = 25%\n% of sunglasses defective = 100% - 95% = 5%\nBut this number is given as 50\nso 5% of x = 50 and x = (50)(100/5))\nx = 180\nTherefore there a total of 1,000 sunglasses made per day.\nCorrect answer - E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf x^2 = 111, which of the following is closest to a potential value of x?\n\n### Options:\nA. -127\nB. -11\nC. 12\nD. 13\nE. 131\n\n### Answer:\nHere the thing we must not forget is that X^even has two potential solutions\n=> x =+- \u221a111 => +- 11\nthis value is closer to -11\nHence B is correct.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThree hundred students at College Q study a foreign language. Of these, 160 of those students study French, and 190 study Spanish. If at least 90 students who study a foreign language at College Q study neither French nor Spanish, then the number of students who study Spanish but not French could be any number from\n\n### Options:\nA. 30 to 50\nB. 40 to 100\nC. 60 to 100\nD. 60 to 110\nE. 70 to 110\n\n### Answer:\n160 students study French\n140 students do not study French\n190 students study Spanish\n110 students do not study Spanish\n90 students study neither French nor Spanish\n140-110=30\n140-90=50\nA. 30 to 50\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain company had a total annual expenditure of 2.55\u221710^7 on employee salaries last year. If the company employed 425 people, what was the average employee salary?\n\n### Options:\nA. $60,000\nB. $25,000\nC. $35,000\nD. $40,000\nE. $45,000\n\n### Answer:\nGiven: Total annual expenditure of 2.55\u221710^7 on employee salaries\nTotal employees = 425\nObserve that 425*6 = 2550\nTherefore try to bring the numerator in terms of 2550\nAverage salary = (2550*10^4) /425 = 6*10^4 = 60,000\nOption A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nLouie takes out a three-month loan of $4000. The lender charges him 10% interest per month compounded monthly. The terms of the loan state that Louie must repay the loan in three equal monthly payments. To the nearest dollar, how much does Louie have to pay each month?\n\n### Options:\nA. A)333\nB. B)383\nC. C)1608\nD. D)433\nE. E)483\n\n### Answer:\nHere's the calculation for that case, assume monthly payment is X.\nAfter 1st month: (4000)(1.1)-X = 4400-X\nAfter 2nd month: (4400-X)(1.1)-X = 4840-2.21X\nAfter 3rd month: (4840-2.21X)(1.1)-X = 5324-3.31X\nNow, the amount after the last payment in 3rd month must bring the total to 0. Hence:\n5324-3.31X = 0\nX = 5324/3.31 = 1608.45\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nKiran had 85 currency notes in all , some of which were of Rs.100 denaomination and the remaining of Rs.50 denomination the total amount of all these currency note was Rs.5000.how much amount did she have in the denomination of Rs.50?\n\n### Options:\nA. rs.2500\nB. rs.3500\nC. rs.1500\nD. rs.4500\nE. rs.5500\n\n### Answer:\n100X +50 (85-X) =5000\non solving:\nx=15\n100-x=no. of 50 notes = 70\namount =70*50= rs.3500\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA corporation triples its annual bonus to 50 of its employees. What percent R of the employees\u2019 new bonus is the increase?\n\n### Options:\nA. 50%\nB. 662\u20443%\nC. 100%\nD. 200%\nE. 300%\n\n### Answer:\nR of the employees\u2019 new bonus is the increase Hence B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA bowl was filled with 10 ounces of water, and 0.008 ounce of the water evaporated each day during a 50-day period. What percent of the original amount of water evaporated during this period?\n\n### Options:\nA. 0.004%\nB. 0.04%\nC. 0.40%\nD. 4%\nE. 40%\n\n### Answer:\nTotal amount of water evaporated each day during a 50-day period = .008 * 50\n=.008 * 100/2\n= .8/2\n= .4\npercent of the original amount of water evaporated during this period = (.4/10) * 100%\n= 4 %\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nNine children \u2014 A, B, C, D, E, F, G, H, and I \u2014 are going to sit in nine chairs in a row. Child C must be somewhere to the left of child D. How many possible configurations are there for the children?\n\n### Options:\nA. 155,880\nB. 164,770\nC. 173,660\nD. 181,440\nE. 192,550\n\n### Answer:\nThe number of ways to seat 9 people is 9! = 362,880.\nChild C will sit to the left of Child D in exactly half of these arrangements.\nThe total number of possible arrangements is 362,880/2 = 181,440\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the no.of ways of arranging the boy and 8 guests at a circular table so that the boy always sits in a particular seat?\n\n### Options:\nA. 4!\nB. 8!\nC. 9!\nD. 10!\nE. 12!\n\n### Answer:\nAns.(B)\nSol. Total number of persons = 9 Host can sit in a particular seat in one way. Now, remaining positions are defined relative to the host. Hence, the remaining can sit in 8 places in 8P8 = 8! Ways ... The number of required arrangements = 8! x 1= 8! = 8! ways\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA dishonest dealer claims to sell a product at its cost price. He uses a counterfeit weight which is 20% less than the real weight. Further greed overtook him and he added 30% impurities to the product. Find the net profit percentage of the dealer?\n\n### Options:\nA. 44%\nB. 40%\nC. 50%\nD. 56.25%\nE. 37.5%\n\n### Answer:\nThe dealer uses weight which is 20% less than the real weight. or (1- 1/5) or 4/5 of real weight.\nIt means that he is selling $4 worth of product for $5.\nThe dealer then further added 30% impurities to the product.\nIt means that he is selling $5 worth of product for $5.5.\nSo his profit is $5.5-$4 = $1.5\nand his profit percent is\n(1.5/4)*100 = 37.5%\nAnswer:- E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAnand and Deepak started a business investing Rs. 22,500 and Rs. 35,000 respectively. Out of a total profit of Rs. 13,800, Deepak's share is:\n\n### Options:\nA. 3776\nB. 2687\nC. 8400\nD. 2688\nE. 2671\n\n### Answer:\nRatio of their shares = 22500 : 35000 = 9:14\nDeepak's share = 13800 * 14/23 = Rs. 8400.\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many integer values Q are there for x such that 1 < 3x + 5 < 17?\n\n### Options:\nA. Two\nB. Three\nC. Four\nD. Five\nE. Six\n\n### Answer:\n1 < 3x + 5 < 17\n=> -4 < 3x < 12\n=> -4/3 < x < 4\nx can take integer values Q=-1,0 , 1 , 2 , 3\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train 210 metres long is moving at a speed of 25 kmph. It will cross a man coming from the opposite direction at a speed of 2 km per hour in :\n\n### Options:\nA. 28 sec\nB. 32 sec\nC. 36 sec\nD. 38 sec\nE. 40 sec\n\n### Answer:\nRelative speed = (25+2) km/hr = 27 km/hr\n= (27\u00d75/18) m/sec = 15/2 m/sec.\nTime taken by the train to pass the man =(210\u00d72/15) sec=28 sec\nANSWER :A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAbigail has $460 in 5-and 10-dollar bills only. If she has fewer 10-than 5-dollar bills, what is the least possible number of 5-dollar bills she could have?\n\n### Options:\nA. 32\nB. 30\nC. 29\nD. 28\nE. 27\n\n### Answer:\n5g + 10h = 460\ng > h\nPick an easy number to work with.\nsuppose g=30.\nThen you have 150.\nYou need another 310 and that means you need h=31 which is greater than g.\nTherefore, g > 30.\nThe only answer choice where g > 30 is if g = 32.\nA is the answer.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a graduating class of 232 students, 144 took geometry and 119 took biology. What is the difference between the greatest possible number R and the smallest possible number of students that could have taken both geometry and biology?\n\n### Options:\nA. 144\nB. 119\nC. 113\nD. 88\nE. 31\n\n### Answer:\nOFFICIAL SOLUTION:\nFirst of all, notice that since 144 took geometry and 119 took biology, then the number of students who took both geometry and biology cannot be greater than 119.\n{Total} = {geometry} + {biology} - {both} + {neither};\n232 = 144 + 119 - {both} + {neither};\n{both} = 31 + {neither}.\n{both} is minimized when {neither} is 0. In this case {both} = 31.\nThe greatest possible number R of students that could have taken both geometry and biology, is 119.\nThus, the answer is 119 - 31 = 88.\nAnswer: D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nDana borrows 7500 pounds annually for her college education. If Dana gives her parents 5% of that amount back each month, how much will she still owe her parents after four years of college?\n\n### Options:\nA. 8000\nB. 9000\nC. 10000\nD. 11000\nE. 12000\n\n### Answer:\ndana borrows 7500 and returns 5% per month.\nso returns 375 per month. and 4500 per year.\nso dana owes 7500-4500=3000 per year.\nafter 4 years she will owe 12000.\nAns (E)\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA number x is 5 times another number y. The percentage that y is less than x is\n\n### Options:\nA. 12.5%\nB. 87.5%\nC. 80%\nD. 11%\nE. 1%\n\n### Answer:\nSay y=1 and x=5.\nThen y=1 is less than x=5 by (5-1)/5*100=4/5*100=80%.\nAnswer: C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAt a certain resort, each of the 39 food service employees is trained to work in a minimum of 1 restaurant and a maximum of 3 restaurants. The 3 restaurants are the family buffet, the dining room, and the snack bar. Exactly 15 employees are trained to work in the family buffet, 18 are trained to work in the dining room, and 12 are trained to work in the snack bar. If 4 employees are trained to work in exactly 2 restaurants, how many employees are trained to work in all 3 restaurants?\n\n### Options:\nA. 2\nB. 3\nC. 4\nD. 5\nE. 1\n\n### Answer:\n39 = 15+ 18 + 12 - 4 - 2x\n2x = 15 + 18 + 12 - 4 - 39\n= 41 - 39\n= 2\nx =1\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA car during its journey travels 30 minutes at a speed of 40 kmph, another 45 minutes at a speed of 80 kmph, and 2 hours at a speed of 50 kmph.The average speed of the car is\n\n### Options:\nA. 60.07 kmph\nB. 55.38 kmph\nC. 50.02 kmph\nD. 44.02 kmph\nE. None of these\n\n### Answer:\nFirst car travels 30 min at speed of 40 kmph\ndistance = 40 x 1/2 = 20 m\nThen car travels 45 min at a speed of 80 kmph\ndistance = 45 min at speed of 80 kmph\ndistance = 80 x 3/4 = 60 m\nat last it travels 2 hours at speed of 50 kmph\ndistance = 50 x 2 = 100 m\nTotal distance = 20 + 60 + 100 = 180\nTotal time= 1/2 + 3/4 + 2 = 3.25\nAverage speed of the car = 180/3.25 = 55.38\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train 70 m long, running with a speed of 63 km/hr will pass a tree in?\n\n### Options:\nA. 140 sec\nB. 160 sec\nC. 176 sec\nD. 150 sec\nE. 170 sec\n\n### Answer:\nSpeed = 63 * 5/18 = 35/2 m/sec\nTime taken = 70 * 2/35 = 140 sec\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA football coach must choose 4 freshers from a team of 12players. How many different ways can the coach choose the freshers?\n\n### Options:\nA. 495\nB. 650\nC. 729\nD. 800\nE. 890\n\n### Answer:\nChoose 4 starters from a team of 12 players. Order is not important.\n\\inline {\\color{Black} 12C_{4}}= 495\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf x = -2 and y = -4, what is the value of 5(x-y)^2 - xy ?\n\n### Options:\nA. 12\nB. 13\nC. 15\nD. 18\nE. 22\n\n### Answer:\nx = -2 and y = -4\nx-y = -2 - (-4) = -2+4 = 2\nx*y = -2 * -4 = 8\nNow we apply it in the equation 5(x-y)^2 - xy =5 (2)^2-8\n==>5*4 -8 = 20-8 =12\nAnswer : A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nElena purchased Brand X pens for $4.00 apiece and brand Y for $2.20 apiece. If Elena purchased a total of 12 of these pens for $42.00, how many brand X pens did she purchase?\n\n### Options:\nA. 4\nB. 5\nC. 6\nD. 7\nE. 8\n\n### Answer:\n4x+2.8y=42 --> multiply by 2.5 (to get the integers) --> 10x+7y=105 --> only one positive integers solutions x=6 and y=5 (how to solve: 7y must have the last digit of 5 in order the last digit of the sum to be 5).\nAnswer: C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo trains having equal lengths, take 10 seconds and 15 seconds respectively to cross a post. If the length of each train is 120 meters, in what time (in seconds) will they cross each other when traveling in opposite direction?\n\n### Options:\nA. 10\nB. 25\nC. 12\nD. 20\nE. 30\n\n### Answer:\nExplanation:\nSpeed of train 1 = 12 m/sec\nSpeed of train 2 = 8 m/sec\nif they travel in opposite direction, relative speed = 12 + 8 = 20 m/sec\ndistance covered = 120 + 120 = 240 m\ntime = distance/speed = 240/20 = 12 sec\nANSWER IS C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average age of a husband and a wife is 23 years when they were married FOUR years ago but now the average age of the husband, wife and child is 20 years(the child was born during the interval). What is the present age of the child?\n\n### Options:\nA. 7 years\nB. 9 years\nC. 6 years\nD. 4 years\nE. 5 years\n\n### Answer:\n27 * 2 = 54\n20 * 3 = 60\n-----------\n6 years\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMother,her daughter and her grand child weighs 140 kg. daughter and her daughter(child) weighs 60 kg. child is 1/5th of her grand mother. What is the age of the daughter?\n\n### Options:\nA. 44\nB. 47\nC. 48\nD. 49\nE. 50\n\n### Answer:\nmother + daughter + child = 140kg\ndaughter + child = 60kg\nmother = 140 - 60 = 80kg\nchild = 1/5th of mother = (1/5)*80 = 16kg\nSo now daughter = 140 -(mother + child) = 140 - (80+16) = 44kg\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nReema took a loan of Rs 1200 with simple interest for as many years as the rate of interest. If she paid Rs. 432 as interest at the end of the loan period, what was the rate of interest.\n\n### Options:\nA. 5%\nB. 6%\nC. 7%\nD. 8%\nE. 9%\n\n### Answer:\nExplanation:\nLet rate = R% then Time = R years.\n=>1200\u2217R\u2217R /100=432\n=>R2=36\n=>R=6%\nOption B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn 1995, there are 28 days in February and there are 365 days in the year. In 1996, there are 29 days in February and there are 366 days in the year. If the date February 12, 1995 is a Wednesday, then which one of the following would the date February 12, 1996 be?\n\n### Options:\nA. Thursday\nB. Friday\nC. Saturday\nD. Sunday\nE. Monday\n\n### Answer:\nFrom the information given, Feb 12, 1996 is 366 days after Feb 12, 1995.\n366 days = 52 weeks and 2 more days. Therefore if Feb 12, 1995 is a Wednesday, then Feb 12, 1996 is Wednesday + 2 days = Friday\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many multiples of 100 are there between 100 and 1000 (both are inclusive)?\n\n### Options:\nA. 2\nB. 8\nC. 4\nD. 5\nE. 10\n\n### Answer:\nthe answer is (1000-100)/100+1=10\nAnswer is E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the average (arithmetic mean) of the four numbers 3, 25, 52, and (N + 1) is 50, then N =\n\n### Options:\nA. 119\nB. 120\nC. 121\nD. 122\nE. 129\n\n### Answer:\n3+25+52+N+1= 50 x 4 = 200\n=>N +81 = 200\n=>N=119\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many seconds will a 500 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?\n\n### Options:\nA. 30\nB. 88\nC. 66\nD. 44\nE. 31\n\n### Answer:\nSpeed of train relative to man = 63 - 3 = 60 km/hr.\n= 60 * 5/18 = 50/3 m/sec.\nTime taken to pass the man = 500 * 3/50 = 30 sec.\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe ratio of two quantities is 2 to 5. If each of the quantities is increased by 6, what is the ratio of these two new quantities?\n\n### Options:\nA. 2/5\nB. 5/8\nC. 7/13\nD. 22/25\nE. It cannot be determined from the information given.\n\n### Answer:\nCorrect Answer: E\nLet x and y be the two quantities such that x/y = 2/5. There is no algebraic operation that can be used to increase x and y each by 3 and determine what happens to the ratio 2/5.\nFor example, if x = 2 and y = 5, then (x+6)/(y+6) = (2+6)/(5+6) = 8/11. However, if x = 4 and y = 10 (which would still set x/y = 2/5), then (x+6)/(y+6) = (4+6)/(10+6) = 10/16. The ratio of the two new quantities cannot be uniquely determined from the information given, and the correct answer is (E).\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAt a certain college, 80 percent of the total number of students are freshmen. If 60 percent of the fresh-men are enrolled in the school of liberal arts and, of these, 50 percent are psychology majors, what percent of the students at the college are freshmen psychology majors enrolled in the school of liberal arts?\n\n### Options:\nA. 25%\nB. 30%\nC. 24%\nD. 28%\nE. 20%\n\n### Answer:\nLet's say there is a TOTAL of 100students at this college.\n80 percent of the total number of students are freshmen.\n# of freshmen = 80% of 100 =80\n60 percent of the fresh-men are enrolled in the school of liberal arts...\nNumber of liberal arts freshmen = 60% of 80 = 48\n...and, of these, 50 percent are psychology majors...\nNumber of liberal arts freshmen who are psychology majors = 50% of 48=24\nWhat percent of the students at the college are freshmen psychology majors enrolled in the school of liberal arts?\n24/100= 24%\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 4f^4 \u2212 41f^2 + 100 = 0, then what is the sum of the two greatest possible values of f ?\n\n### Options:\nA. 4\nB. 9/2\nC. 7\nD. 41/4\nE. 25\n\n### Answer:\njust forget about the value of f^4 for the moment and let f^2= X. (its better to work with power of 2 than 4)\nnow we have equation as 4x^2 -41x +100 =0, factoring them gives us 4X^2 -16x -25x +100 =0. which can be solved as (4x-25)(x-4) , so x= 4 and 25/4.\nso f^2 = 4 and 25/4\nso f= +2 and minus 2 and +5/2 and minus 5/2\nThe two greatest values are +2 and +5/2. so their sum 2+5/2 =9/2 = B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nDiane find 3 and a half cans of paint are just enough to paint one third of her room. How many more cans of paint will she need to finish her room and paint a second room of the same size?\n\n### Options:\nA. 5\nB. 17 and a half\nC. 10\nD. 12 and a half\nE. 15\n\n### Answer:\nShe will need 7 cans to paint the rest of this room and 10 1/2 for the next room for a total of 17 1/2 cans.\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe county-mandated guidelines at a certain community college specify that for the introductory English class, the professor may choose one of three specified novels, and choose two from a list of 5 specified plays. Thus, the reading list for this introductory class is guaranteed to have one novel and two plays. How many different reading lists could a professor create within these parameters?\n\n### Options:\nA. 15\nB. 30\nC. 90\nD. 150\nE. 360\n\n### Answer:\nThere are three possibilities for the novel. With the plays, we are taken a combination of 2 from a set of 5 right n = 5, r = 2, n \u2013 r = 3\n# of combinations = 5!/2!3! = (5)(4)(3)(2)(1)/(2)(1)(3)(2)(1) = (5)(4)/2 = 10\nIf the plays are P, Q, R, S, and T, then the 10 sets of two are PQ, PR, PS, PT, QR, QS, QT, RS, RT, & ST.\nAny of the three novels can be grouped with any of the 10 possible pairs of plays, for a total of 30 possible reading lists.\nAnswer: B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a games hour 4 different types of players came to the ground? cricket 11, hockey 15, football 21, softball 15. In these 4 people play both cricket and hockey, 3people play both softball and football. 6 people play both cricket and football. How many people play only cricket?\n\n### Options:\nA. 11\nB. 1\nC. 5\nD. 3\nE. 9\n\n### Answer:\npeople play only cricket = total players in cricket- both cricket and football- both cricket and hockey.\npeople play only cricket = 11-4-6 = 1\nAnswer is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe perimeter of a triangle is 20 cm and the inradius of the triangle is 3 cm. What is the area of the triangle?\n\n### Options:\nA. 22\nB. 30\nC. 77\nD. 54\nE. 23\n\n### Answer:\nArea of a triangle = r * s\nWhere r is the inradius and s is the semi perimeter of the triangle.\nArea of triangle = 3 * 20/2\n= 30 cm2\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the number 98348*0 is exactly divisible by 72, then the minimum value of * is?\n\n### Options:\nA. 1\nB. 2\nC. 3\nD. 4\nE. 5\n\n### Answer:\n72=8*9\ndivisibility 0f 8 last 3place should be divisible by 8\nlly divisibility of 9 sum of digit should be divisible by 9\n840 divisible by 8 nd 36 divisible by 9\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOf the science books in a certain supply room, 50 are on botany, 65 are on zoology, 90 are on physics. 50 are on geology, and 110 are on chemistry. If science books are removed randomly from the supply room, how many must be removed to ensure that 80 of the books removed are on the same science?\n\n### Options:\nA. 81\nB. 159\nC. 166\nD. 285\nE. 324\n\n### Answer:\nWe can remove 80 books only from physics or from chemistry. Worst case scenario would be if we remove all books on botany, zoology, geology, 79 books on physics and 79 books on chemistry.\nWe would have 50(botany)+65(zoology)+50(geology)+79(physics)+79(chemistry)=323 books and still won't have 80 books from the same science. As after this, only books on physics and chemistry will be left then any next book would become the 80th book either on physics or on chemistry.\nAnswer: E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAll of the students of Music High School are in the band, the orchestra, or both. 40 percent of the students are in only one group. There are 100 students in the band. If 20 percent of the students are in the band only, how many students are in the orchestra only?\n\n### Options:\nA. 30\nB. 25\nC. 40\nD. 55\nE. 35\n\n### Answer:\n% of students in one group only = 40%\n% of students in both groups = 100 - 40 = 60%\n% of students in the band only = 20%\nNumber of students who are in band = 100\n60% + 20% = 80% = 100 Students\nFinding total students:\nx = (100 x 100)/80\nx = 125\nStudents in orchestra only = 125 - 100 = 25\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n#p is defined as 2p+20 for any number p. What is p, if #(#(#p))=-4?\n\n### Options:\nA. \u2013108\nB. \u201344\nC. 10\nD. -18\nE. 18\n\n### Answer:\n#p = 2p+20 --->#(#p) = 2(2p+20)+20 = 4p+60 and thus #(4p+60) = 2(4p+60)+20 = 8p+140 = -4 ---> 8p= -144 ---> p = -18, D is the correct answer.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nCompany S produces two kinds of stereos: basic and deluxe. Of the stereos produced by Company S last month, 3/4 were basic and the rest were deluxe. If it takes 7/5 as many hours to produce a deluxe stereo as it does to produce a basic stereo, then the number of hours it took to produce the deluxe stereos last month was what fraction of the total number of hours it took to produce all the stereos?\n\n### Options:\nA. 6/22\nB. 5/22\nC. 7/22\nD. 4/22\nE. 3/22\n\n### Answer:\n# of basic stereos was 3/4 of total and # of deluxe stereos was 1/4 of total, let's assume total=16, then Basic=12 and Deluxe=4.\nNow, if time needed to produce one Deluxe stereo is 1 unit than time needed to produce one Basic stereo would be 7/5 units. Total time for Basic would be 12*1=12 and total time for Deluxe would be 4*7/5=28/5 --> total time for both of them would be 12+28/5=88/5 --> deluxe/total=28/5 / 88/5= 28/88 =7/22\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n-69*39+450=?\n\n### Options:\nA. 2736\nB. 2309\nC. -2801\nD. -2241\nE. None of these\n\n### Answer:\n=> -69*(40-1)+450;\n=> -(69*40)+69+450;\n=> -2760+519=-2241.\nCorrect Option: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe speed of a boat in still water is 60kmph and the speed of the current is 20kmph. Find the speed downstream and upstream?\n\n### Options:\nA. 20 kmph\nB. 40 kmph\nC. 27 kmph\nD. 28 kmph\nE. 22 kmph\n\n### Answer:\nSpeed downstream = 60 + 20\n= 80 kmph\nSpeed upstream = 60 - 20\n= 40 kmph\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA tank is filled in 5 hours by three pipes A, B and C. The pipe C is twice as fast as B and B is twice as fast as A. How much time will pipe A alone take to fill the tank?\n\n### Options:\nA. 15 hours\nB. 18 hours\nC. 20 hours\nD. 25 hours\nE. 35 hours\n\n### Answer:\nLet A fill tank in x hrs.\nTherefore tank filled in one hrs is 1/x.\nAnd B pipe is twice than A means 2 (1/x).\nC pipe is twice than B means 2 (2 (1/x) ) i.e 4/x.\n1/x+2/x+4/x = 1/5.\n7/x = 1/5.\nx = 35 hrs.\nANSWER :e\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe captain of a cricket team of 11 members is 26 years old and the wicket keeper is 5 years older. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. What is the average age of the team?\n\n### Options:\nA. 23 years\nB. 24 years\nC. 25 years\nD. 26 years\nE. 27 years\n\n### Answer:\nEXPLANATION\nLet the average age of the whole team by x years.\n11x \u00e2\u20ac\u201c (26 + 21) = 9(x -1)\n11x \u00e2\u20ac\u201c 9x = 48\n2x = 48\nx = 24.\nSo, average age of the team is 24 years.\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe ratio of 2 numbers is 2:8 and their H.C.F. is 40. Their L.C.M. is ?\n\n### Options:\nA. 400\nB. 120\nC. 80\nD. 320\nE. 40\n\n### Answer:\nLet the numbers be 2x and 8x\nTheir H.C.F. = 40\nso the numbers are 2*40 , 8*40 = 80, 320\nL.C.M. = 320\nAnswer is D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nCalculate the least possible number of vans needed to transport 280 students, given that each van can only take 12 students each?\n\n### Options:\nA. 23\nB. 22\nC. 21\nD. 20\nE. 24\n\n### Answer:\nTo find the number of vans, we divide 280 by 12.\n280/12 = 23 and remainder = 4\nSo 23 vans are needed to transport 276 students, and 1 van is needed to transport the 4 remaining students. A total of 24 vans are needed.\ncorrect answer E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many different ways can a group of 8 people be divided into 4 teams of 2 people each?\n\n### Options:\nA. 56\nB. 105\nC. 75\nD. 120\nE. 112\n\n### Answer:\nThe required answer is = 8!/(4!*2!*2!*2!*2!) = 105\nAnswer is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nBy selling an article at Rs.800, a shopkeeper makes a profit of 25%. At what price should he sell the article so as to make a loss of 25%?\n\n### Options:\nA. Rs.429\nB. Rs.480\nC. Rs.429\nD. Rs.427\nE. Rs.482\n\n### Answer:\nSP = 800\nProfit = 25%\nCP = (SP)*[100/(100+P)]\n= 800 * [100/125]\n= 640\nLoss = 25% = 25% of 640 = Rs.160\nSP = CP - Loss = 640 - 160 = Rs.480\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe price of a VCR is marked at Rs. 12,000. If successive discounts of 15%, 10% and 5% be allowed, then at what price does a customer buy it?\n\n### Options:\nA. Rs. 8400\nB. Rs. 8721\nC. Rs. 8856\nD. Rs. 8956\nE. None of these\n\n### Answer:\nActual price = 95% of 90% of 85% of Rs. 12000\n= 95/100 * 90/100 * 85/100 * 12000 = Rs. 8721.\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf log102 = 0.3010, log10 3 = 0.4771, then the number of zeros between the decimal point and the first\nsignificant figure in (0.0432)10 is?\n\n### Options:\nA. 10\nB. 13\nC. 14\nD. 15\nE. 16\n\n### Answer:\nX = (0.0432)10 = (432/10000)10 = (33.24/104)10\nTherefore, log10X = 10 (log103 + 4log102-4)\n= 10(1.4313 + 1.2040 - 4)\n= 10(-1.3647)\n= -13.647\n= -14.353\nTherefore, X = antilog(-14.053)\nThus, number of zeros between the decimal and the first significant figure = 13\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a group of buffaloes and ducks, the number of legs are 24 more than twice the number of heads. What is the number of buffaloes in the group?\n\n### Options:\nA. 12\nB. 3\nC. 5\nD. 8\nE. 10\n\n### Answer:\nLet the number of buffaloes be x and the number of ducks be y.\nThen 4x+2y=2(x+y)+24\n=>x=12\nANSWER A 12\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the remainder when the number Y=14^2 * 15^8 is divided by 5?\n\n### Options:\nA. 0\nB. 1\nC. 2\nD. 4\nE. 5\n\n### Answer:\n14^2 has units digit 6\n15^8 has units digit 5\nThus Y=14^2*15^8 has units digit 0 and will be divisible by 5. The remainder will be zero\nAnswer: (A)\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n(166)^2 - (167)^2 =\n\n### Options:\nA. 1\nB. 100\nC. 229\nD. 329\nE. 335\n\n### Answer:\nUsing the formula:\n(a+1)^2 - a^2 = 2a+1\nSo, Answer = 167*2 + 1\n= 334+1 = 335 = Answer = E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a certain animal population, for each of the first 3 months of life, the probability that an animal will die during that month is 1/10. For a group of 500 newborn members of the population, approximately how many would be expected to survive the first 3 months of life?\n\n### Options:\nA. 340\nB. 346\nC. 352\nD. 365\nE. 370\n\n### Answer:\nNumber of newborns that can die in first month = 1/10 * 500 = 50\nSurvived = 450\nNumber of newborns that can die in second month = 1/10 * 450 = 45\nSurvived = 405\nNumber of newborns that can die in third month = 1/10 * 405 = 40\nSurvived = 365\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA and B entered into a partnership investing Rs.25000 and Rs.30000 respectively. After 4 months C also joined the business with an investment of Rs.35000. What is the share of C in an annual profit of Rs.47000?\n\n### Options:\nA. 22277\nB. 29977\nC. 267676\nD. 14000\nE. 18811\n\n### Answer:\n25*12: 30*12: 35*8\n15:18:14\n14/47 * 47000 = 14000\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA person purchased a TV set for Rs. 2000 and a DVD player for Rs. 2000 . He sold both the items together for Rs. 5000. What percentage of profit did he make?\n\n### Options:\nA. 80%\nB. 80%\nC. 40%\nD. 48%\nE. 25%\n\n### Answer:\nThe total CP = Rs. 2000 + Rs. 2000\n= Rs. 4000 and SP = Rs. 5000\nProfit(%) = (5000 - 4000)/4000 * 100\n= 25%\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf Greg buys 5 shirts, 4 trousers and 2 ties, the total cost is $80. If Greg buys 7 shirts, 4 trousers and 2 ties, the total cost is $70. How much will it cost him to buy 2 trousers, 3 shirts and 1 ties?\n\n### Options:\nA. $37.5\nB. $64\nC. $75\nD. $96\nE. Cannot be determined\n\n### Answer:\nSolution: 5x+4y+2z=80 7x+4y+2z=70\nadding both the equations= 12x+8y+4z=150\n3x+2y+1z=37.5\nans A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe sum of the digits of a two-digit number is 15 and the difference between the digits is 3. What is the two-digit number ?\n\n### Options:\nA. 69\nB. 78\nC. 96\nD. Cannot be determined\nE. None of these\n\n### Answer:\nSolution\nLet the ten's digit be x and unit's digit be y.\nThen, x + y = 15 and x = y =3 or y = x = 3.\nSolving x + y = 15 and x - y = 3, we get : x = 9, y = 6.\nSolving x + y = 15 and y - x = 3, we get : x = 6, y = 9.\nSo, the number is either 96 or 69. Hence, the number cannot be determined\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the leastvalue of x. So that 45x09 is divisible by 3?\n\n### Options:\nA. 0\nB. 5\nC. 2\nD. 6\nE. 7\n\n### Answer:\nThe sum of the digits of the number is divisible by 3, then the number is divisible by3.\n4 + 5 + x + 0+ 9 = 18 + x\nLeast value of x may be 0\nTherefore 18 + 0= 18 is divisible by 3.\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA batsman makes a score of 74 runs in the 17th inning and thus increases his averages by 3. What is his average after 17th inning?\n\n### Options:\nA. 25\nB. 31\nC. 26\nD. 29\nE. 39\n\n### Answer:\nLet the average after 17 innings = x\nTotal runs scored in 17 innings = 17x\nAverage after 16 innings = (x-3)\nTotal runs scored in 16 innings = 16(x-3)\nTotal runs scored in 16 innings + 74 = Total runs scored in 17 innings\n=> 16(x-3) + 74 = 17x\n=> 16x - 48 + 74 = 17x\n=> x = 26\nAnswer is C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 12 men and 16 boys can do a piece of work in 5 days and 13 men together will 24 boys can do it in 4 days. Compare the daily work done by a man with that of a boy.\n\n### Options:\nA. 1:1\nB. 2:1\nC. 3:1\nD. 5:1\nE. 4:1\n\n### Answer:\nB\n2:1\n12M + 16B ----- 5 days\n13M + 24B ------- 4 days\n60M + 80B = 52M + 96B\n8M = 16B => 1M = 2B\nM: B = 2:1\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n45% of major airline companies equip their planes with wireless internet access. 70% of major airlines offer passengers free on-board snacks. What is the greatest possible percentage of major airline companies that offer both wireless internet and free on-board snacks?\n\n### Options:\nA. 25%\nB. 35%\nC. 45%\nD. 55%\nE. 65%\n\n### Answer:\nTo maximize the percentage of companies offering both, let's assume that all 45% of companies which offer wireless internet also offer snacks.\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe remainder obtained when a prime number greater than 3 is divided by 3 is\n\n### Options:\nA. a) 1 or 3\nB. b) 2 or 4\nC. c) 3 or 5\nD. d) 4 or 5\nE. e) 5\n\n### Answer:\nThe easiest way to answer this question is probably to pick numbers. Use the next two prime numbers greater than 3, i.e. 7 and 5:\n7/3 = 1 + remainder of 4\n5/3 = 1 + remainder of 2\nThis is already sufficient to see that answer choice b) is correct.\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a certain province in France there are 9 cities. If a single road segment connects only two cities, how many road segments are required in order to connect the cities so that each city is connected to all other cities with a single road segment?\n\n### Options:\nA. 36\nB. 105\nC. 330\nD. 14\nE. 15\n\n### Answer:\n1 city needs 8 roads to connect directly to the rest => 9 city needs 9*8 roads.\nOne road is counted twice => the number of road needed is 9*8/2 = 36\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a coin is tossed twice, what is the probability that one of the flips was heads and one of the flips was tails?\n\n### Options:\nA. 1/2\nB. 1/8\nC. 1/4\nD. 1/6\nE. 3/4\n\n### Answer:\nThe possible cases are =>{Head,Head} {Head,Tail} {Tail,Head} {Tail,Tail}\nPossible Cases=4\nFavourable cases = 2\nP(E) = 2/4 = 1/2\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf it takes a machine 2\u20443 minute to produce one item, how many items will it produce in 1 hours?\n\n### Options:\nA. 1\u20443\nB. 4\u20443\nC. 90\nD. 120\nE. 180\n\n### Answer:\n1 item takes 2/3 min so it takes 60 min to produce x\n2x/3=60 the x=90\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf q and r are both odd numbers N, which of the following must also be odd?\n\n### Options:\nA. q \u2013 r\nB. (q + r)^2\nC. q(q + r)\nD. (qr)^2\nE. q/r\n\n### Answer:\nWe're told that q and r are both ODD numbers N. We're asked which of the following must also be odd.\nIF...\nq = 1\nr = 3\nAnswer A) q \u2013 r = 1-3 = -2 NOT odd\nAnswer B) (q + r)^2 = (1+3)^2 = 16 NOT odd\nAnswer C) q(q + r) = (1)(4) = 4 NOT odd\nAnswer D) (qr)^2 = (3)^2 = 9 This IS ODD\nAnswer E) q/r = 1/3 NOT odd\nFinal Answer:\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many four digit numbers have no repeat digits, do not contain zero, and have a sum of digits H equal to 28?\n\n### Options:\nA. 14\nB. 24\nC. 28\nD. 48\nE. 96\n\n### Answer:\nFirst, look for all 4 digits without repeat that add up to 28. To avoid repetition, start with the highest numbers first.\nStart from the largest number possible 9874.\nThen the next largest number possible is 9865.\nAfter this, you'll realize no other solution. Clearly the solution needs to start with a 9 (cuz otherwise 8765 is the largest possible, but only equals 26). With a 9, you also need an 8 (cuz otherwise 9765 is the largest possible, but only equals 27). With 98__ only 74 and 65 work.\nSo you have two solutions. Each can be rearranged in 4!=24 ways. So H=24+24=48.D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain drive-in movie theater has total of 12 rows of parking spaces. There are 10 parking spaces in the first row and 11 parking spaces each in the next two rows. In each subsequent row there are 2 more parking spaces than in the previous row. What is the total number of parking spaces in the movie theater?\n\n### Options:\nA. 219\nB. 221\nC. 321\nD. 192\nE. 202\n\n### Answer:\nFirst row 10, Second row 11 and then other 10 rows form an Arithmetic Progression with first term 11 and last term 29 and Avg is 20.\nso 20*10+10+11=221\nAnswer is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMars travels around the Sun at an approximate speed of 14.4 miles per second. This speed is how many kilometers per hour? (1 km = 0.6 miles)\n\n### Options:\nA. 64,200\nB. 75,300\nC. 86,400\nD. 97,500\nE. 108,600\n\n### Answer:\nThe speed is 14.4 miles/s. Then 14.4/0.6 = 24 km/s\n24*3600 = 86,400 kph\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n100 oranges are bought at the rate of Rs. 350 and sold at the rate of 48 per dozen. The percentage of profit is\n\n### Options:\nA. 12 2/7%\nB. 13 2/7%\nC. 14 2/7%\nD. 15 2/7%\nE. 16 2/7%\n\n### Answer:\nExplanation:\nSo before solving this question we will get the C.P. and S.P. of 1 article to get the gain percent.\nC.P. of 1 orange = 350/100 = Rs 3.50\nS.P. of one orange = 48/12 = Rs 4 [note: divided by 12 as 1 dozen contains 12 items]\nGain = 4 - 3.50 = Rs 0.50\nGain%=0.50/ 3.50\u2217100=100 /7%=14 2/7%\nOption C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAfter running a series of television advertisements, a leading beverage producer saw its sales increase by 25% to $6 million dollars per month. Prior to the advertising campaign, about how many dollars in sales did the company average per day?\n\n### Options:\nA. $1.25 million\nB. $800,000\nC. $750,000\nD. $27,000\nE. $160,000\n\n### Answer:\nLet sales in previous month = X\n1.25 X=6,000,000\n5/4 X= 6,000,000 ..........> X=4,800,000\nsales per day= 4,800,000/30= less than 160,000\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe value of 489.1375 x 0.0483 x 1.956/0.0873 x 92.581 x 99.749 is closest to:\n\n### Options:\nA. 0.04\nB. 0.08\nC. 0.07\nD. 0.06\nE. 0.05\n\n### Answer:\n= 489.1375 x 0.0483 x 1.956/0.0873 x 92.581 x 99.749\n= 489 x 0.05 x 2/0.09 x 93 x 100\n= 489/9 x 93 x 10\n= 163/279 x 1/10\n= 0.58/10\n= 0.058 (or) 0.06.\nAnswer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nfind the odd man out in the following series\n3, 6, 9, 12, 14\n\n### Options:\nA. 3\nB. 6\nC. 9\nD. 12\nE. 14\n\n### Answer:\nIn the series except 14 all others are the multiples of 3\nso the answer is option E) 14\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many keystrokes are needed to type numbers from 56 to 200?\n\n### Options:\nA. 310\nB. 391\nC. 270\nD. 289\nE. None of these\n\n### Answer:\nExplanatory Answer\nWhile typing numbers from 56 to 200, there are 44 two-digit numbers: from 56 to 99.\nEach of these numbers requires 2 keystrokes.\nTherefore, 88 keystrokes to type the 2-digit numbers.\nThere are 101 three-digit numbers: from 100 to 200.\nEach of these numbers requires 3 keystrokes.\nTherefore, 303 keystrokes to type the 3-digit numbers.\nTotally, therefore, one requires 88 + 303 = 391 keystrokes.\nChoice B is the correct answer.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe C.I. on a certain sum for 2 years at 10% per annum is Rs. 525. The S.I. on the same sum for double the time at half the rate percent per annum is?\n\n### Options:\nA. 238\nB. 500\nC. 287\nD. 197\nE. 172\n\n### Answer:\nExplanation:\nLet the sum be Rs. P. Then,\n[P(1 + 10/100)2 - p] = 525\nP[(11/10)2 - 1] = 525\nP = (525 * 100) / 21 = 2500\nSum = Rs. 2500\nSo, S.I. = (2500 * 5 * 4)/100 = Rs. 500\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n(935421 x 625) = ?\n\n### Options:\nA. 584638125\nB. 584638150\nC. 584638180\nD. 584638220\nE. 584638225\n\n### Answer:\n935421 x 625 = 935421 x 54 = 935421 x 10 4\n2\n=\t935421 x 104\t=\t9354210000\n24\t16\n= 584638125\nA)\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nBaseball's World Series matches 2 teams against each other in a best-of-seven series. The first team to win four games wins the series and no subsequent games are played. If you have no special information about either of the teams, what is the probability W that the World Series will consist of fewer than 7 games?\n\n### Options:\nA. 12.5%\nB. 25%\nC. 31.25%\nD. 68.75%\nE. 75%\n\n### Answer:\nYour explanation is very close toManhattan GMAT's official answer - it's quite uncanny:\n\"There are many other ways this could happen. Using the permutation formula, there are 6!/(3!)(3!) = 20 ways for the two teams to split the first 6 games (3 wins for each).\nThere are then 2 possible outcomes to break the tie in Game 7. Thus, there are a total of 202 = 40 ways for the World Series to last the full 7 games.\nThe probability that any one of these 40 ways occurs can be calculated from the fact that the probability of a team winning a game equals the probability of a team losing a game = 1/2.\nGiven that 7 distinct events must happen in any 7 game series, and that each of these events has a probability of 1/2, the probability that any one particular 7 game series occurs is.\nSince there are 40 possible different 7 game series, the probability that the World Series will last exactly 7 games is: (1/2)^7 = 1/128\n40*1/128 = 40/128 = 31.25%\nThus the probability W that the World Series will last less than 7 games is 100% - 31.25% = 68.75%.\nThe correct answer is D.\"\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man can row with a speed of 15 kmph in still water. If the stream flows at 5 kmph, then the speed in downstream is?\n\n### Options:\nA. 278\nB. 276\nC. 20\nD. 288\nE. 21\n\n### Answer:\nM = 15\nS = 5\nDS = 15 + 5 = 20\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRohith,who works in a parcel service, has a certain number of small plastic boxes to pack into parcels. If he packs 3,4,5 or 6 in a parcel, he is left with one over; if he packs 7 in a parcel, none is left over. What is the number of boxes, he may have to pack?\n\n### Options:\nA. 223\nB. 301\nC. 377\nD. 1368\nE. 222\n\n### Answer:\nThe required number of boxes is such that it leaves a remainder of 1 when divided by 3, 4, 5 or 6 and no remainder of 1 when divided by 3, 4, 5 or 6 and no remainder when divided by 7. Such a number is 301.\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered. If the area of the field is 50 sq. feet, how many feet of fencing will be required?\n\n### Options:\nA. 34\nB. 40\nC. 25\nD. 88\nE. 78\n\n### Answer:\nWe have: l = 20 ft and lb = 50 sq. ft.\nSo, b = 2.5 ft.\nLength of fencing = (l + 2b) = (20 + 5) ft = 25 ft.\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nGary\u2019s Gas Station serves an average of 14 cars per hour on Saturdays, 10 cars per hour on Sundays, and 9 cars per hour on all other days of the week. If the station is open from 6 a.m. to 10 p.m. every day, how many cars does Gary\u2019s station serve over the course of a typical week?\n\n### Options:\nA. 1,104\nB. 1,200\nC. 1,240\nD. 1,280\nE. 1,320\n\n### Answer:\n6 a.m. to 10 p.m. = 16 hours\nNumber of cars serviced on weekdays = (16 * 9 * 5)\nNumber of cars serviced on Saturday = (16 * 14)\nNumber of cars serviced on Sunday = (16 * 10)\nNumber of cars served in a week = 16(45 + 14 + 10) = 16 * 69 = 1104\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA plant manager must assign 6 new workers to one of five shifts. She needs a first, second, and third shift, and two alternate shifts. Each of the shifts will receive 2 new workers. How many different ways can she assign the new workers?\n\n### Options:\nA. 24\nB. 27\nC. 33\nD. 45\nE. 54\n\n### Answer:\nwhatever : my take selecting team of 2 out of 10 to assign to the shifts =6C2 = 15 ways.\nnow 2 out of 10 means total of 3 group possible.\nso putting them in shifts = counting methode: first, second, third, alt , alt\n= 3*2*1 = 6\nhere alt and alt are the same: so 6/2 = 3 ways.\ntotal ways of selecting = (selecting 2 out of 6)*arranging those teams in shifts\n= 15*3 = 45\nAns: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf x \u00a4 y = (x + y)^2 - (x - y)^2. Then \u221a6 \u00a4 \u221a6 =\n\n### Options:\nA. 0\nB. 5\nC. 10\nD. 24\nE. 20\n\n### Answer:\nX = \u221a6 and Y also =\u221a6\nApplying the function (\u221a6+\u221a6)^2 - (\u221a6-\u221a6)^2 = (2\u221a6)^2 - 0 = 4 x 6 = 24.\nNote: Alternative Approach is the entire function is represented as X^2 - Y^2 = (X+Y)(X-Y) which can be simplified as (x+y+x-y)(x+y-(x-y)) = (2x)(2y)=4xy. Substituting x=\u221a6 and y = \u221a6 you get the answer 24.\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are a total of 100 jars on the shelf. Small jars hold 3 liters and large jars hold 5 liters. The jars can hold a total of 376 liters. How many small jars are on the shelf?\n\n### Options:\nA. 49\nB. 53\nC. 56\nD. 59\nE. 62\n\n### Answer:\nLet S be the number of small jars and let L be the number of large jars.\nS + L = 100.\nL = 100 - S.\n3S + 5L = 376.\n3S + 5(100-S)= 376.\n-2S+500=376.\n2S = 124.\nS = 62.\nThe answer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo cards are drawn together from a pack of 52 cards. The probability that one is a spade and one is a heart, is:\n\n### Options:\nA. 13/109\nB. 13/162\nC. 13/111\nD. 13/102\nE. 13/112\n\n### Answer:\nLet S be the sample space.\nThen, n(S) = \\inline {\\color{Black}52C_{2} }=(52 x 51)/(2 x 1) = 1326.\nLet E = event of getting 1 spade and 1 heart.\nn(E)= number of ways of choosing 1 spade out of 13 and 1 heart out of 13 = \\inline {\\color{Black}13C_{1}\\times 13C_{1} } = 169.\nP(E) = n(E)/n(S) = 169/1326 = 13/102.\nAnswer: D) 13/102\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAt Company K, 15 percent of the employees are secretaries and 60 percent are salespeople. If there are 65 other employees of Company K, how many employees does Company K have?\n\n### Options:\nA. 260\nB. 180\nC. 190\nD. 200\nE. 400\n\n### Answer:\nLet the total number of employees in the company be x\n% of secretaries = 15%\n% of salespeople = 60%\n% of of employees other than secretaries and salespeople = 100 - 75 = 25%\nBut this number is given as 65\nso 25% of x = 65\nx = 260\nTherefore there a total of 260 employees in the company K\nCorrect answer - A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe radius of a cylindrical vessel is 9cm and height is 3cm. Find the whole surface of the cylinder?\n\n### Options:\nA. 308 sq cm\nB. 220 sq cm\nC. 440 sq cm\nD. 132 sq cm\nE. 678.8 sq cm\n\n### Answer:\nr = 9 h = 3\n2\u03c0r(h + r) = 2 * 22/7 * 9(12) = 678.8\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many three letter words are formed using the letters of the word TIME?\n\n### Options:\nA. 12\nB. 65\nC. 26\nD. 24\nE. 71\n\n### Answer:\nThe number of letters in the given word is four.\nThe number of three letter words that can be formed using these four letters is 4P3\n= 4 * 3 * 2 = 24.\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n(18)7 x (5832)-2 \u00f7 (324)-1 = (18)7\n\n### Options:\nA. 5\nB. 4\nC. 3\nD. 2\nE. 1\n\n### Answer:\nExplanation :\n(18)7 x (183)-2 \u00f7 (182)-1\n(18)7 x (18)-6 \u00f7 (18)-2\n(18)7-6+2 = (18)3\nAnswer : Option C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nadd 11% of 36 and 12% of 64.\n\n### Options:\nA. 9.5\nB. 10.5\nC. 11.5\nD. 12\nE. 15\n\n### Answer:\n11% of 36 + 12% of 64\n36*11/100+64*12/100\n3.9+7.6=11.5\nanswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe radii of two cones are in ratio 2:1, their volumes are equal. Find the ratio of their heights.\n\n### Options:\nA. 1:4\nB. 1:3\nC. 1:2\nD. 1:5\nE. None of these\n\n### Answer:\nExplanation:\nLet their radii be 2x, x and their heights be h and H resp.\nThen,\nVolume of cone =1/3\u03c0r2h\n1/3\u2217\u03c0\u2217(2x)2\u2217h /1/3\u2217\u03c0\u2217x2\u2217H\n=>hH=14\n=>h:H=1:4\nOption A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn the recent, education conference in US, out of 500 men, 800 women, 1000 children present inside the building premises, 30% of the men, 25% of the women and 35% of the children were Russian. Find the percentage of people who were not Russian?\n\n### Options:\nA. 63.50%\nB. 65.23%\nC. 62.30%\nD. 69.57%\nE. 67.23%\n\n### Answer:\nSolution: Number of Russian men present there = 500*30/100 = 150\nRussian women = 800*25/100 = 200\nRussian children = 1000*35/100 = 350.\nTotal member present in education conference = 500+800+1000 = 2300\nTotal Russian = 150+200+350 = 700\nHence, % of Russian present there = 700*100/2300 = 30.43%\n% of people who were not Russian = 100-30.43 = 69.57%.\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf Rs.10 be allowed as true discount on a bill of Rs.110 at the end of a certain time , then the discount allowed on the same sum due at the end of double the time is?\n\n### Options:\nA. 68.33\nB. 18.33\nC. 28.33\nD. 48.33\nE. 98.33\n\n### Answer:\nExplanation:\nPresent worth = Amount - TrueDiscount\n= 110 -10 = Rs.100\nSI on Rs.100 for a certain time = Rs.10\nSI on Rs.100 for doube the time = Rs.20\nTrueDiscount on Rs.120 = 120 - 100 = Rs.20\nTrueDiscount on Rs.110 = = Rs.18.33\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a quarter kg of onions costs 80 paise, how many paise will 100 gm cost?\n\n### Options:\nA. 32 paise\nB. 65 paise\nC. 56 paise\nD. 87 paise\nE. 15 paise\n\n### Answer:\nExplanation:\nLet the required cost be x paise.\nLess weight, Less cost (Direct proportion)\n250 : 100 : : 80 : x\n250 * x = (100 * 80)\nx = (100 * 80) / 250\nx = 32\nANSWER: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich of these lines in the xy-plane does not contain any point with two negative coordinates?\n\n### Options:\nA. y = 5x\nB. y = x + 6\nC. y = x^2 - 7\nD. y = x^3 + 2x\nE. y = 3x^6\n\n### Answer:\n3x^6 is 0 when x is 0 and positive for all other values of x.\nThe answer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat will be the difference between simple and compound interest at 10% per annum on a sum of Rs. 1000 after 4 years?\n\n### Options:\nA. Rs. 64.12\nB. Rs. 64.19\nC. Rs. 14.19\nD. Rs. 64.10\nE. Rs. 64.99\n\n### Answer:\nExplanation:\nS.I. = (1000 * 10 * 4)/100 = Rs. 400\nC.I. = [1000 * (1 + 10/100)4 - 1000] = Rs. 464.10 Difference = (464.10 - 400) = Rs. 64.10\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA dealer offers a cash discount of 20%. Further, a customer bargains and receives 20 articles for the price of 15 articles. The dealer still makes a profit of 20%. How much percent Q above the cost price were his articles marked?\n\n### Options:\nA. 100%\nB. 80%\nC. 75%\nD. 66+2/3%\nE. 50%\n\n### Answer:\nGood question...2:11 min\nMarked Price (M) = Cost Price (C) + Mark up...(EQN. A)\nSelling price = 20% Discount over M = 0.8*M\nGiven that, a customer bargains and receives 20 articles for the price of 15 articles-->*afurther loss of 25%to the dealer--> BUT aNET PROFIT of 20%over cost price (C)\n0.75* 0.8 * M =1.2 * C\nHence, M/C = 2/1 Q= 200%\nFrom Eqn. A , (C + Mark up)/C = 200% -->Mark up / C = 100%\nAns. A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA can lay railway track between two given stations in 16 days and B can do the same job in 12 days. With help of C, they did the job in 4 days only. Then, C alone can do the job in:\n\n### Options:\nA. 7 4/5\nB. 9 3/5\nC. 4 1/6\nD. 7 7/12\nE. 8 6/7\n\n### Answer:\nA + B + C's 1 day's work = 1/4\nA's 1 day's work = 1/16\nB's 1 day's work = 1/12\nTherefore C's 1 day's work = 1/4\t- ( A's 1 day's work + B's 1 day's work )\n=> C's 1 day's work = 1/4 - ( 1/16 + 1/12 )\n=> C's 1 day's work = (12-3-4)/48 = 5/48\nSo, C alone can do the work in 48/5 = 9 3/5 days.\nSo correct answer is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA tap can fill a tank in 10 hours. After half the tank is filled, two more similar taps are opened. What is the total time taken to fill the tank completely?\n\n### Options:\nA. 1 hr 20 min\nB. 4 hr\nC. 3 hr\nD. 6 hr 40 min\nE. 2 hr 50 min\n\n### Answer:\nExplanation:\n1 tap can fill the tank in 10 hours.\nTherefore\n1 tap can fill half tank in 5 hours.\n3 taps can fill the tank in 10/3 hour.\nTherefore\n3 taps can fill half tank in 10/6 hour =1 hour 40 minutes.\nTotal time taken=6 hour 40 minutes\nAnswer: Option D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA 300 meter long train crosses a platform in 39 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform?\n\n### Options:\nA. 399\nB. 267\nC. 350\nD. 788\nE. 277\n\n### Answer:\nSpeed = [300 / 18] m/sec = 50/3 m/sec.\nLet the length of the platform be x meters.\nThen, x + 300 / 39 = 50/3\n3(x + 300) = 1950 \u00e8 x = 350m.\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMaxwell leaves his home and walks toward Brad's house at the same time that Brad leaves his home and runs toward Maxwell's house. If the distance between their homes is 40 kilometers, Maxwell's walking speed is 3 km/h, and Brad's running speed is 5 km/h. What is the distance traveled by Maxwell when they meet in the middle?\n\n### Options:\nA. 16\nB. 17\nC. 18\nD. 15\nE. 14\n\n### Answer:\nConsider Max starts from Point A and Brad Starts from Point B and move towards each other.\nAssume they shall meet at point O after Time 'T'. The question asks us to find OA.\nFrom the question stem we can make out :- Distance OA = 50km - Distance OB\n=> 3xT = 40 - 5xT (i.e distance =Speed x Time)\n=> 8T = 40\nHence T = 5\nOA = 3 x 5 = 15 Km\nAnswer : D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf f(x) = ax^5 \u2013 3x^2 + ax^2 \u2013 x, then f(b) \u2013 f(-b) will equal:\n\n### Options:\nA. 0\nB. 2ab\nC. 2ab^4 \u2013 6\nD. 2ab^5-2b\nE. ab^5\n\n### Answer:\nf(x)=ax^5 \u2013 3x^2 + ax^2 \u2013 x\nf(b) = ab^5 \u2013 3b^2 + ab^2 \u2013 b\nf(-b) = -ab^5 \u2013 3b^2 + ab^2 + b\nf(b) - f(-b) = ab^5 \u2013 3b^2 + ab^2 \u2013 b + ab^5 + 3b^2 - ab^2 \u2013 b\n=2ab^5-2b\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich of the following equations has a solution in common with x^2 + 14x + 33 = 0?\n\n### Options:\nA. 3x^2 - 5x - 2 = 0\nB. -x^2 - 3x + 28 = 0\nC. -x^2 - 2x + 99 = 0\nD. 3x^2 + 30x + 27 = 0\nE. none of the above\n\n### Answer:\nGiven : x^2 + 14x + 33 = 0 => (x+3) (x+11) = 0 => -3 and -11 are the roots..\nA. 3x^2 - 5x - 2 = 0 => (x-2) (3x+1)\nB. -x^2 - 3x + 28 = 0 => (-x+7) (x+4)\nC. -x^2 - 2x + 99 = 0 => (x+11) (-x+9)\nD. 3x^2 + 30x + 27 = 0 => (x+9) (3x+3)\nNone of the answer equations have exactly both the same roots as the question equation, but at least one of them does share one of the two roots.\nSo IMO \"C\" is correct answer... because it shares the one root (part of the solution), (-11), from the (x+11) portion of its simplification.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 12 persons meet at a reunion and each person shakes hands exactly once with each of the others, what is the total number of handshakes?\n\n### Options:\nA. 10\u20229\u20228\u20227\u20226\u20225\u20224\u20223\u20222\u20221\nB. 10\u202210\nC. 10\u20229\nD. 66\nE. 36\n\n### Answer:\nWe got #12 people who shake each other's hands once ==> a pair of 2\n12!/10!2! = 12*11 / 2*1 = 66.\nHence answer D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nCalculate how many men are needed to finish a specific task in 35 days if it will take 20 men to complete the same task in 70 days. ?\n\n### Options:\nA. 40\nB. 20\nC. 10\nD. 30\nE. 60\n\n### Answer:\nmen required to finish the work in 35 days = 20*70/35 = 40\nAnswer is A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the diffference between the place value and face value of 4 in the numeral 2694?\n\n### Options:\nA. 10\nB. 0\nC. 5\nD. 3\nE. 1\n\n### Answer:\nplace value of 4 = 4 * 1 = 4\nface value of 4 = 4\n4 - 4 = 0\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered. If the area of the field is 390 sq. feet, how many feet of fencing will be required?\n\n### Options:\nA. 34\nB. 59\nC. 68\nD. 88\nE. 92\n\n### Answer:\nGiven that length and area, so we can find the breadth.\nLength x Breadth = Area\n20 x Breadth = 390\nBreadth = 19.5 feet\nArea to be fenced = 2B + L = 2 (19.5) + 20 = 59 feet answer : B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf Dale works at full efficiency he needs a break of 1 day after every 2 days of work and he completes a job in a total of 14 days. If he works at reduced efficiency, he can work without break and finish that same job in 14 days. Dale's output at reduced efficiency is what fraction of his output at full efficiency?\n\n### Options:\nA. 3/9\nB. 4/5\nC. 3/2\nD. 4/6\nE. 5/2\n\n### Answer:\nWe're told that there are 2 ways for Dale to complete a job:\n1) Full Efficiency: 2 days of work followed by 1 dayofffor a total of 14 days.\n2) Reduced Efficiency: 14 straight days with no days off.\nWorking at Full Efficiency creates the following pattern:\n2 days on, 1 day OFF, 2 days on, 1 day OFF, 2 days on, 1 day OFF, 2 days on = 2+1+2+1+2+1+2+1+2= 14 days\nTotals: 10 days on, 4 days off\nReduced Efficiency means that Dale will do 10 days of work in 14 days, thus those Reduceddaysare 10/4=5/2 of Full Efficiency.\nAnswer : E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat amount does Kiran get if he invests Rs.8000 at 10% p.a. compound interest for two years, compounding done annually?\n\n### Options:\nA. Rs.19828.89\nB. Rs.19828.80\nC. Rs.19878.80\nD. Rs.19825.80\nE. Rs.19828.90\n\n### Answer:\nLet the sum be Rs.P\nP{ [ 1 + 8/100]2 - 1 } = 2828.80\nP(8/100)(2 + 8/100) = 2828.80 [a2 - b2 = (a - b) ( a + b)] P\n= 2828.80 / (0.08)(2.08) = 1360/0.08 = 17000 Principal + Interest\n= Rs.19828.80\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf set A={2,2,2,....,n times} , set B={3,3,3,3....m times} and set C={12,12,12...k time} , then in terms of m,n and k , how many possible subsets from sets A,B, and C can be created ?\n\n### Options:\nA. a) k(n+m+mn)+ k\nB. b) (1+n+m+mn)(k+1)\nC. c) k^2(mn+n/m)\nD. d) kmn(k+m+n)\nE. e) None of the above.\n\n### Answer:\na) how many 2's are included?\nb) how many 3's are included?\nand\nc) how many 11's are included?\nFor the number of 2, we could have zero 2's, or one 2, or two 2's, all the way up to n 2's. That's (n + 1) possibilities for the 2's. Similarly, (m + 1) possibilities for the 3's and (k + 1) possibilities for the 11's. We simply multiply these three numbers.\nNOTICE that one set, the set that includes no 2's, no 3's, and no 11's, is included. This is known in mathematics as thenull set, sometimes called the empty set, a set with no members. Technically, this is a subset of every possible set, but that's a technical detail of set theory that goes well beyond what the GMAT would expect students to know. Even the the calculation is not that difficult, some of the technical aspects of this question are not in line with the GMAT's expectations.\nThe number of subsets is (m + 1)(n + 1)(k + 1). The answer is not given in that form. Instead, the first two factors have been FOILed together:\n(mn + m + n + 1)(k + 1).\nMike\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMedals are to be awarded to three teams in a 10-team competition. If one medal is gold, one medal is silver, and one medal is bronze, how many different ways are there to award the three medals to teams in the competition?\n\n### Options:\nA. 10!/7!\nB. 10!/(3!7!)\nC. 10!/3!\nD. 7!/3!\nE. 7!/94!3!)\n\n### Answer:\nChoosing 3 teams out of 10 when order of the teams matters - P310=10!7!\nOr: choosing which 3 teams out of 10 will get the medals - C310C103 and arranging them - 3!3!, so total - C310\u22173!=10!7!\nOr:\n1-2-3-4-5-6-7-8-9-10 (teams);\nG-S-B-N-N-N-N-N-N-N (GSB - medals, N - no medal);\nPermutation of 10 letters out of which 7 N's are identical is 10!7!10!7! (so you'll get 10!7!10!7! different ways of assigning the medals to the teams).\nAnswer: A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n10 men working 12 hours daily finish a work in 24 days. In how many days will they finish 1/4th of the work working 8 hours daily?\n\n### Options:\nA. 9 days\nB. 10 days\nC. 11 days\nD. 12 days\nE. 18 days\n\n### Answer:\nThe number of days needed to finish 1/4 of the work =1/4*12/8*24 =9 days. Answer : A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man can row his boat with the stream at 6 km/h and against the stream in 4 km/h. The man's rate is?\n\n### Options:\nA. 1 kmph.\nB. 2 kmph.\nC. 3 kmph.\nD. 4 kmph.\nE. 5 kmph.\n\n### Answer:\nDS = 6\nUS = 4\nS = ?\nS = (6 - 4)/2 = 1 kmph\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSpeed of a boat in standing water is 10kmph and speed of the stream is 1.5kmph. A man can rows to a place at a distance of 105km and comes back to the starting point. The total time taken by him is?\n\n### Options:\nA. 20.48hours\nB. 21.48hours\nC. 22.48hours\nD. 23.48hours\nE. 24.48hours\n\n### Answer:\nSpeed upstream = 8.5kmph\nSpeed downstream = 11.5kmph\nTotal time taken = 105/8.5 + 105/11.5 = 21.48 hours\nAnswer is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAt Joes Steakhouse the hourly wage for a chef is 22% greater than that of a dishwasher, and the hourly wage of a dishwasher is half as much as the hourly wage of a manager. If a managers wage is $8.50 per hour, how much less than a manager does a chef earn each hour?\n\n### Options:\nA. $1.40\nB. $2.40\nC. $3.315\nD. $4.40\nE. $5.40\n\n### Answer:\nManager wages per hour = $8.50\nDishwasher wages per hour = half of manager's wages. = 1/2($8.50) ==> $4.25\nChef wages per hour = 22% greater than Dishwasher wages\n--> 22% of $4.25 = (22*($4.25)) /100\n--> ($93.5)/100\n--> $0.935\nTherefore,\nChef wages per hour = $4.25 + $0.935 ==> $5.185\nDifference of wages between manager and chef = $8.50 - $5.185 ==> $3.315\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA magician has five animals in his magic hat: 3 doves and 2 rabbits. If he pulls two animals out of the hat at random, what is the chance W that he will have a matched pair?\n\n### Options:\nA. W=2/5\nB. W=3/5\nC. W=1/5\nD. 1/2\nE. 7/5\n\n### Answer:\nP(both doves) + P(both rabbits) = p(matched pair)\n(3/5)*(2/4) + (2/5)*(1/4) = 2/5\nHi How did you get the probability 2/4 and 1/4???\nYou have 3 doves and 2 rabbits i.e. a total of 5 animals.\nThe probability that you pick a dove on your first pick is 3/5 (since there are 3 doves)\nThe probability that you pick a dove on your second pick too is 2/4 (because now only 2 doves are left after we picked a dove in the first pick. ALso only 4 animals are left to choose from)\nSimilarly,\nThe probability that you pick a rabbit on your first pick is 2/5 (since there are 2 rabbits)\nThe probability that you pick a rabbit on your second pick too is 1/4 (because now only 1 rabbit is left after we picked a rabbit in the first pick. Also only 4 animals are left to choose from)\nProbability of picking a matched pair = 3/5 * 2/4 + 2/5 * 1/4 = 2/5\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?\n\n### Options:\nA. 288\nB. 240\nC. 277\nD. 127\nE. 922\n\n### Answer:\nSpeed = (54 * 5/18) m/sec = 15 m/sec. Length of the train = (15 x 20)m = 300 m. Let the length of the platform be x meters. Then, (x + 300)/36 = 15 ==> x + 300 = 540 ==> x = 240 m.Answer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA mixture of sand and cement contains, 3 parts of sand and 5 parts of cement. How much of the mixture must be substituted with sand to make the mixture half sand and half cement?\n\n### Options:\nA. 1/3\nB. 1/4\nC. 1/5\nD. 1/7\nE. 1/8\n\n### Answer:\nWe have total of 8 parts: 3 parts of sand and 5 parts of cement.\nIn order there to be half sand and half cement (4 parts of sand and 4 parts of cement), we should remove 1 part of cement. With 1 part of cement comes 3/5 parts of sand, so we should remove 1 + 3/5 = 8/5 part of the mixture, which is (8/5)/8 = 1/5 of the mixture.\nAnswer: C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMs. Feldman invested $10,000 for 1 year, part at 7% and part at 6.25%.\nIf she earned a total interest of $656.50, how much was invested at each rate?\n\n### Options:\nA. 4200 & 5800\nB. 4600 & 5400\nC. 9000 & 1000\nD. 7000 & 3000\nE. 6000 & 4000\n\n### Answer:\nInterest rate of 4200/- =294\nInterest rate of 5800/- =362.50\nAnswer is A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are 7 red cups and 5 blue cups on a shelf. If 4 cups are selected at random from the shelf, what is the probability that all 4 cups selected are blue cups?\n\n### Options:\nA. 1/80\nB. 1/88\nC. 1/90\nD. 1/95\nE. 1/99\n\n### Answer:\nThe number of ways of choosing 4 cups from the shelf is 12C4 = 495.\nThe number of ways of choosing 4 blue cups is 5C4 = 5.\nP(4 blue cups) = 5/495=1/99.\nThe answer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA group of 13 people plan to rent a van and agree to share equally the total cost of the rental, which is E dollars. If n of the people decide not to participate at the last minute, by how many dollars will each remaining person's share of the total cost increase?\n\n### Options:\nA. E/(12 - n)\nB. (12 - n)/E\nC. E/[12(12-n)]\nD. (12-n)E/(12n)\nE. nE / [13(13-n)]\n\n### Answer:\ntotal cost =E\nno of people willing to participate initially =13\ninitial cost for each =E/13\nwhen n people decided not to participate\nCost for each =E/13-n\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the area of the quadrilateral of one of its diagonals is 28 cm and its off sets 9 cm and 6 cm?\n\n### Options:\nA. 210 cm2\nB. 150 cm2\nC. 168 cm2\nD. 198 cm2\nE. 987 cm2\n\n### Answer:\n1/2 * 28(9 + 6)\n= 210 cm2\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf population of certain city increases at the rate of 5%. If population in 1981 was 138915, then population in 1978 was?\n\n### Options:\nA. 120000\nB. 27778\nC. 27779\nD. 27767\nE. 29087\n\n### Answer:\nX * (105/100) * (105/100) * (105/100) = 138915\nX = 138915/1.157625\nX = 120000\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo brothers took the GMAT exam, the higher score is M and the lower one is N. If the difference between the two scores is equal to their average, what is the value of N/M ?\n\n### Options:\nA. 3\nB. 2\nC. 1/2\nD. 1/3\nE. There isn't enough data to answer the question.\n\n### Answer:\nM - N = (M + N)/2\nSolving for N/M = 1/3\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf an object travels at three feet per second, how many feet does it travel in one hour?\n\n### Options:\nA. 3488\nB. 10800\nC. 12788\nD. 1800\nE. 2881\n\n### Answer:\nExplanation:\nIf an object travels at 2 feet per second it covers 3x60 feet in one minute, and 3x60x60 feet in one hour.\nAnswer = 10800\nAnswer: B) 10800\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWe bought a total of 80 books at the store. Math books cost $4 and history books cost $5. The total price was $368. How many math books did we buy?\n\n### Options:\nA. 28\nB. 32\nC. 36\nD. 40\nE. 44\n\n### Answer:\nM + H = 80\nH = 80 - M\n4M + 5H = 368\n4M + 5*(80 - M) = 368\nM = 32\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOn decreasing the price of a cooler by 25 %, its sale is increased by 50%. The effect on the revenue is?\n\n### Options:\nA. 4 % decrease\nB. 12.5 % increase\nC. 16% decrease\nD. 16% increase\nE. none of these\n\n### Answer:\nNet% change in revenue\n= ( x + y + xy/100) %\n= [-25 + 50+ ( -25 x 50)/100]% or 12.5%\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA square and an equilateral triangle have the same perimeter. What is the ratio of the area of the circle circumscribing the square to the area of the circle inscribed in the triangle?\n\n### Options:\nA. 9:8\nB. 15:8\nC. 27:8\nD. 8:9\nE. 8:15\n\n### Answer:\nlet x be side of square\nperimeter of square=4x=perimeter of triangle=3*side of triangle\nso side of eq. triangle=(4/3)*x\ndiameter of circle circumscribing the square=sqrt(2)*x\narea of circle circumscribing the square=pi*(sqrt(2)*x)^2/4=(pi/2)*x^2 ----(1)\nto find radius of the circle inscribed in the triangle\narea of triangle=r*s=sqrt(3)/4 * (4x/3)^2\nnow s=(4/3)*x+(4/3)*x+(4/3)*x/2=2x\nso sqrt(3)/4 * (4x/3)^2=r*2x gives\nr={2/3*(3^1/2)}*x\narea of the circle inscribed in the triangle=pi*[{2/3*(3^1/2)}*x]^2\n=pi*(4/27)*x^2 -------(2)\nso reqd ratio= eqn(1)/eqn(2)\n=[(pi/2)*x^2]/[pi*(4/27)*x^2]=27/8\nso reqd ratio=27:8\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo trains of equal length are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. The faster train catches and completely passes the slower train in 54 seconds. What is the length of each train (in meters)?\n\n### Options:\nA. 45\nB. 55\nC. 65\nD. 75\nE. 85\n\n### Answer:\nThe relative speed = 46 - 36 = 10 km/hr = 10 * 5/18 = 25/9 m/s\nIn 54 seconds, the relative difference in distance traveled is 54 * 25/9 = 150 meters\nThis distance is twice the length of each train.\nThe length of each train is 150/2 = 75 meters\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nClaire can paint the living room in 7 hours and Barry can paint the living room in 5 hours. How many hours will it take for both of them working together to paint the living room?\n\n### Options:\nA. 2\nB. 2 11/12\nC. 3 5/11\nD. 4 1/2\nE. 5\n\n### Answer:\nWork hrs=AB/(A+B)= 35/12 =2 11/12\nAnswer is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe length of the bridge, which a train 155 metres long and travelling at 45 km/hr can cross in 30 seconds, is?\n\n### Options:\nA. 76 m\nB. 178 m\nC. 220 m\nD. 187 m\nE. 176 m\n\n### Answer:\nSpeed = [45 X 5/18] m/sec\n= [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (155 + x)/30 = 25/2\n=> 2(155+ x)= 750 => x = 220 m.\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf A can do 1/4 of a work in 3 days and B can do 1/6 of the same work in 4 days, how much will A get if both work together and are paid Rs. 180 in all?\n\n### Options:\nA. Rs. 36\nB. Rs. 60\nC. Rs. 108\nD. Rs. 120\nE. None of these\n\n### Answer:\nWhole work is done by A in (3*4) = 12days.\nWhole work is done by B in (4*6)=24days.\nA's wages: B's wages = A's 1 day's work:\nB's 1 day's work =1/12:1/24=2:1\nA's share = Rs. (2/3*180)=Rs. 120.\nCorrect Option: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf s, t, and p are positive numbers such that (s/(s+t))(10) + (t/(s+t))(20)=p and if s p is > 15 -> 18 is the answer.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average height of 50 pupils in a class is 160 cm. Five of them whose height is 146 cm, leave the class and five others whose average height is 156 cm, join. The new average height of the pupils of the class (in cm) is ?\n\n### Options:\nA. 287 cm\nB. 151 cm\nC. 276 cm\nD. 287 cm\nE. 161 cm\n\n### Answer:\nTotal height = 160 * 50 = 8000 cm.\nNew average = [8000 - 5 * 146 + 5 * 156 ] / 50\n= 161 cm.\nAnswer:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man can row a boat three quarters of a kilometre in 11.25 minutes. What is the speed of the boat in still water?\n\n### Options:\nA. 4 kmph\nB. 8 kmph\nC. 6 kmph\nD. 5 kmph\nE. 12 kmph\n\n### Answer:\nExplanation:\nSimple Division.\nNo stream current mentioned.\nTrick question.\nSpeed= Distance/Time.\nSpeed= 3/4 km / (11.25/60) hr\nTherefore, Speed = 4 km/hr\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf x<0, y<0, and |x| > |y|, which of the following must be true?\n\n### Options:\nA. x > y\nB. y^2 > x^2\nC. x^3 > y^2\nD. x < y\nE. x < \u2013y\n\n### Answer:\nCorrect Answer: (E)\nLet\u2019s go through each answer choice: (A) can never be true, since no negative is greater than a positive. (B) doesn\u2019t have to be true \u2013 consider what would happen if x = -2 and y = 1. (C) can never be true, as x^3 must be negative, and y^2 must be positive. (D) can never be true, since if x < 0, -x is the same thing as |x|, and |x| > y. (E) can be manipulated by multiplying both sides by -1, which gives us \u2013x > y. Remember that x < 0, so \u2013x = |x|, and y is positive, so |y| = y. Thus x < y is the same statement as |x| > |y|, and (D) must be true.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the product of two positive integers is 144, which of the following could be the LCM and HCF of the two numbers?\nI. LCM : 24; HCF : 6\nII. LCM : 18; HCF : 8\nIII. LCM : 16; HCF : 9\n\n### Options:\nA. I only\nB. II and III only\nC. I and II only\nD. I and III only\nE. I, II and III\n\n### Answer:\nWe need to keep two things in mind here:\n1. Product of two numbers = LCM*HCF\n2. LCM should be a multiple of HCF\nOnly Statement I follows these two rules.\nCorrect Option A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain ski shop sells pairs of gloves in 10 different colors. If one pair of each color is dropped in a bag and a store clerk reaches in to draw two individual gloves simultaneously and at random, what is the probability that she draws two gloves of the same color?\n\n### Options:\nA. 1/144\nB. 1/143\nC. 1/24\nD. 1/23\nE. 1/19\n\n### Answer:\nthere are 10 different colours sothere are 10 pairs of gloves dropped..\nfirst can be any of 20..so 20/20..\nsecond has to be its pair, which will be just one out of remaining 19.. 1/19..\noverall prob=20/20*1/19= 1/19..\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are different 6 circles. What is the number of the greatest possible points with which the circles intersect?\n\n### Options:\nA. 90\nB. 100\nC. 110\nD. 180\nE. 30\n\n### Answer:\nMaximum points of intersection between n different circles = n*(n - 1) = 6*5 = 30\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTom drives from town W to town B, driving at a constant speed of 60 miles per hour. From town B Tom immediately continues to town C. The distance between W and B is twice the distance between B and C. If the average speed of the whole journey was 36 mph, then what is Tom's speed driving from B to C in miles per hour?\n\n### Options:\nA. 12\nB. 20\nC. 24\nD. 30\nE. 36\n\n### Answer:\nLet's assume that it takes 4 hours to go from point W to B. Then the distance between them becomes 240 which makes distance between B and C 120. (240+120)/(4+x) gives us the average speed which is 36. You find x=6. So the question simplifies itself to 120/6=20\nHence the answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA circular rim 28 inches in diameter rotates the same number of inches per second as a circular rim 35 inches in diameter. If the smaller rim makes x revolutions per second, how many revolutions per second does the larger rim makes in terms of x ?\n\n### Options:\nA. 4x/5\nB. 75x\nC. 48x\nD. 24x\nE. x/75\n\n### Answer:\nLet's try the explanation. We have two wheels. One with 28pi and the other one with 35pi. They have the same speed. In the smaller wheel it's 28pi*x, which must be equal to the speed of the bigger one (35pi*a number of revolutions).They are asking that number of revolutions (but in minutes, which makes the question even harder).\nAnyway, we have 28pi*x=35pi*a.\n(28pi*x)/(35pi). = 4x/5.\nAns :A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe sum of the first k positive integers is equal to k(k+1)/2. What is the sum of the integers from c to d, inclusive, where 0 then d+c=7. Let see which option yields 7.\nA. d(d+1)/2 - (c+1)(c+2)/2 = 10-10=0;\nB. d(d+1)/2 - c(c+1)/2 = 10-6=4;\nC. d(d+1)/2 - (c-1)c/2 = 10-3=7 --> OK;\nD. (d-1)d/2 - (c+1)(c+2)/2 = 6-10=-4;\nE. (d-1)d/2 - c(c+1)/2 = 6-6=0.\nAnswer: C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 5 men can dig a field in 20 days, how much time it will take 4 men to dig the same field?\n\n### Options:\nA. 21\nB. 22\nC. 23\nD. 24\nE. 25\n\n### Answer:\nE\nLess the number of men, more time it will take to dig the field (inversely proportion)\n5 : 4 :: N : 20\nN = 20 X 5 / 4 = 25\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n33 1/3% OF 210?\n\n### Options:\nA. 70\nB. 90\nC. 110\nD. 120\nE. 130\n\n### Answer:\n33 1/3 % = 1/3\n1/3 \u00d7 210 = 70\nA)\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe positive integers y and z leave remainders of 2 and 3, respectively, when divided by 6. y > z. What is the remainder when y\u2013 z is divided by 6?\n\n### Options:\nA. 1\nB. 2\nC. 5\nD. 3\nE. 4\n\n### Answer:\nLet's test out some values of p and q that satisfy the given information.\ny leaves are remainder of 2 when divided by 6\nSo, y COULD equal 8\nz leaves are remainder of 3 when divided by 6\nSo, z COULD equal 3\nWhat is the remainder when y \u2013 z is divided by 6?\nSo, y - z = 8 - 3 = 5, and when we divide 5 by 6, we get 0 with remainder 5\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n3+3.3+333+33.33=?\n\n### Options:\nA. 362.33\nB. 372.63\nC. 702.33\nD. 702\nE. None of them\n\n### Answer:\n3\n3.3\n333\n33.33\n----------\n372.63\n----------\nAnswer is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nZYXW\u2019 as coded as \u2018ABCD\u2019 then \u2018STUV\u2019 is coded as\n\n### Options:\nA. YU\nB. YY\nC. U\nD. H\nE. W\n\n### Answer:\nHere each letter is coded with its opposite letter. i.e. Z \u2013 A, Y \u2013 B, X \u2013 C, W \u2013 D. Similarly, S \u2013 H, T \u2013 G, U \u2013 F, V \u2013 E.\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the area of a right angle triangle with base = 12 and height = 14 ?\n\n### Options:\nA. 80\nB. 81\nC. 82\nD. 83\nE. 84\n\n### Answer:\nSince the area of a right angle triangle is 1/2 * base * height\nArea = 1/2 * 12 * 14\n= 84\nAns: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average of 1st 3 of 4 numbers is 16 and of the last 3 are 15. If the sum of the first and the last number is 13. What is the last numbers?\n\n### Options:\nA. 2\nB. 4\nC. 6\nD. 5\nE. 7\n\n### Answer:\nA + B + C = 48\nB + C + D = 45\nA + D = 13\nA \u2013 D = 3\nA + D = 13\n2D = 10\nD = 5\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA and B go around a circular track of length 1800 m on a cycle at speeds of 36 kmph and 54 kmph. After how much time will they meet for the first time at the starting point?\n\n### Options:\nA. 120 sec\nB. 165 sec\nC. 186 sec\nD. 167 sec\nE. 360 sec\n\n### Answer:\nTime taken to meet for the first time at the starting point\n= LCM { length of the track / speed of A , length of the track / speed of B}\n= LCM {1800/ (36 * 5/18) , 1800/ (54 * 5 /18) }\n= LCM (180, 120)\n=360 sec.\nAnswer:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nBarbara has 8 shirts and 9 pants. How many clothing combinations does Barbara have, if she doesn\u2019t wear 2 specific shirts with 3 specific pants?\n\n### Options:\nA. 41\nB. 66\nC. 36\nD. 70\nE. 56\n\n### Answer:\n8 shirts\n9 pants\nwe can combine 2 shirts with (9-3) pants\n2*6=12\nwe can combine the other shirts (6) with any pants (9)\n6*9=54\nThus total :12+54=66\tANS:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA number consists of two digits. If 3/5 of 1/5 of the number is 9. Find the sum of its two digits?\n\n### Options:\nA. 60\nB. 8\nC. 7\nD. 12\nE. 13\n\n### Answer:\nx * 3/5 * 1/5 = 9\nx = 75 => 7 + 5 = 12\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA researcher computed the mean, the median, and the standard deviation R for a set of performance scores. If 5 were to be added to each score, which of these three statistics would change?\n\n### Options:\nA. The mean only\nB. The median only\nC. The standard deviation only\nD. The mean and the median\nE. The mean and the standard deviation\n\n### Answer:\nIf we add or subtract a constant to each term in a set the standard deviation R will not change..\nIf we add (or subtract) a constant to each term in a set the mean and the median will increase (decrease) by the value of that constant.\nAnswer: D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nLakshmi has $100 in her piggy bank. How much will she have in her bank 15 weeks from now if she puts $1 in the bank next week, $2 two weeks from now, $3 three weeks from now, and continues to increase the amount that she puts in by $1 each week?\n\n### Options:\nA. 210\nB. 220\nC. 230\nD. 240\nE. 250\n\n### Answer:\nThe dollar deposits are in an A.P.\n1,2,3,4...15with common difference 1\nSum of the terms is n(n+1) / 2\ni.e 15* (15+1) /2\n= 15* 16/2 = 120\nTotal deposit therefore with Chiu-Lihas is 100 + 120= 220$\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a simultaneous throw of pair of dice .find the probability of getting the total more than 7\n\n### Options:\nA. 5/2\nB. 4/7\nC. 4/3\nD. 5/12\nE. 2/7\n\n### Answer:\nHere n(S)=(6*6)=36\nlet E=event of getting a total more than 7\n={(2,6),(3,5),(3,6),(4,4),(4,5),(4,6),(5,3),(5,4),(5,5),(5,6),(6,2),(6,3),(6,4),(6,5),(6,6)}\nP(E)=n(E)/n(S)=15/36=5/12.\nAns: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a bag containing only blue, red and green marbles, all but 15 are blue, all but\n13 are red and all but 12 are green. How many are red?\n\n### Options:\nA. 13\nB. 7\nC. 25\nD. 20\nE. 10\n\n### Answer:\nAll but blue means number of marbles except blue..hence, let x be the red marble,y\nbe the green marble,z be the blue marble...\nx+y=15\ny+z=13\nx+z=12\nsolving this eqns, we get x=7 y=8 z=5 hence number of red marbles are 7\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSpeed of boat in still water is 9km/hr . if boat moves upstream A to B in 2 hrs. &\nB to A in 1 hrs. Then find distance between A&B\n\n### Options:\nA. 10km\nB. 11km\nC. 12km\nD. 13km\nE. 14km\n\n### Answer:\nLet speed of stream = s kmph\ndistance be x\nfor upstream\n(9-s)*2=x (speed*time=distance)\nfor downstream\n(9+s)*1=x\nOn solving we get x=12km\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA bag contains $510 in the form of 50 p, 25 p and 20 p coins in the ratio 2 : 3 : 4. Find the number of coins of each type.\n\n### Options:\nA. 200, 400, 500\nB. 300, 200, 600\nC. 800, 400, 600\nD. 400, 600, 800\nE. 600, 700, 900\n\n### Answer:\nLet the number of 50 p, 25 p and 20 p coins be 2x, 3x and 4x.\nThen 2x \u00d7 50/100 + 3x \u00d7 25/100 + 4x \u00d7 20/100 = 510\nx/1 + 3x/4 + 4x/5 = 510\n(20x + 15x + 16x)/20 = 510\n\u21d2 51x/20 = 510\nx = (510 \u00d7 20)/51\nx = 200\n2x = 2 \u00d7 200 = 400\n3x = 3 \u00d7 200 = 600\n4x = 4 \u00d7 200 = 800.\nTherefore, number of 50 p coins, 25 p coins and 20 p coins are 400, 600, 800 respectively.\nAnswer is D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf x/6 and x/15 are integers, then x must be divisible by -\n\n### Options:\nA. 12\nB. 18\nC. 30\nD. 45\nE. 60\n\n### Answer:\nFactors of 6 2 and 3\nfactors of 15 are 3 and 5\nSo number is 2*3*5 = 30\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average of numbers 0.44204, 0.44203, 0.44202 and 0.44201 is ?\n\n### Options:\nA. 0.44202\nB. 0.44204\nC. 0.442022\nD. 0.442025\nE. None\n\n### Answer:\nAnswer\nAverage = (0.44204 + 0.44203 + 0.44202 + 0.44201)/ 4\n=1.7681/ 4\n=0.442025\nCorrect Option: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhen two coins are tossed,Find the probability of getting all tails?\n\n### Options:\nA. 1/3\nB. 3/4\nC. 1/8\nD. 3/8\nE. 1/4\n\n### Answer:\nWhen two coins are tossed,\nS = {HH, HT, TH, TT} where H = Head and T = Tail\nLet E = event of getting all tails\nThen E = {TT}\nso, P(E) = n(E)/n(S) =1/4\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA 25 cm wide path is to be made around a circular garden having a diameter of 4 meters. Approximate area of the path is square meters is\n\n### Options:\nA. 3.34\nB. 3.36\nC. 3.34\nD. 6.32\nE. 3.31\n\n### Answer:\nArea of the path = Area of the outer circle - Area of the inner circle = \u220f{4/2 + 25/100}2 - \u220f[4/2]2\n= \u220f[2.252 - 22] = \u220f(0.25)(4.25) { (a2 - b2 = (a - b)(a + b) }\n= (3.14)(1/4)(17/4) = 53.38/16 = 3.34 sq m.Answer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe difference between simple interest and compound interest of a certain sum of money at 20% per annum for 2 years is $48. Then the sum is\n\n### Options:\nA. $600\nB. $1000\nC. $1200\nD. $1500\nE. $2000\n\n### Answer:\n20% of (Year 1 Interest) = 20% of (20% of Principal) = 48\nPrincipal = $1200\nAnswer (C)\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAishwarya Rai walks into a bank to cash out her check.\nBy mistake the bank teller gives her dollar amount in change, and her cent amount in dollars.\nOn the way home she spends 5 cent, and then suddenly she notices that she has twice the amount of her check.\nHow much was her check amount ?\n\n### Options:\nA. 21.55\nB. 25.89\nC. 30.56\nD. 31.55\nE. 31.63\n\n### Answer:\nE\nThe check was for dollars 31.63.\nThe bank teller gave her dollars 63.31\nShe spent .05, and then she had dollars 63.26, which is twice the check.\nLet x be the dollars of the check, and y be the cent.\nThe check was for 100x + y cent\nHe was given 100y + x cent\nAlso\n100y + x - 5 = 2(100x + y)\nExpanding this out and rearranging, we find:\n98y = 199x + 5\nor 199x \u2261 -5 (mod 98)\nor 98*2*x + 3x \u2261 -5 (mod 98)\n3x \u2261 -5 \u2261 93 (mod 98)\nthis quickly leads to x = 31\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA sum of money place at compound interest doubles itself in 7 years. In how many years will it amount to eight times itself?\n\n### Options:\nA. 15 years\nB. 11 years\nC. 12 years\nD. 18 years\nE. 21 years\n\n### Answer:\n100 ---- 200 ---- 7\n400 ---- 7\n800 ---- 7\n------\n21 years\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the number of white balls in a box are 6 times the black balls, which of the below is the total number of balls, if there are 8 black balls in the box?\n\n### Options:\nA. A - 56\nB. B - 57\nC. C - 58\nD. D - 59\nE. E - 60\n\n### Answer:\nLet the number of black balls = x and the number of white balls = 6x Then, total number of balls in the box = x + 6x = 7x i.e., the total number of balls must be a multiple of 7 From the given choices, only 56 is the multiple of 7. Hence, 56 are the number of balls in the box. Answer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the number that should come in the place of question mark?\n1050\t420\t168\t67.2\t?\n\n### Options:\nA. 29.88\nB. 10.752\nC. 4.3008\nD. 26.88\nE. 27.88\n\n### Answer:\n1050/2.5 = 420\n420/2.5 = 168\n168/2.5 = 67.2\nso 67.2/2.5 = 26.88\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSimplify\n80\u00e2\u02c6\u2019[5\u00e2\u02c6\u2019(6+2(7\u00e2\u02c6\u20198\u00e2\u02c6\u20195\u00c2\u00af\u00c2\u00af\u00c2\u00af\u00c2\u00af\u00c2\u00af\u00c2\u00af\u00c2\u00af\u00c2\u00af\u00c2\u00af\u00c2\u00af\u00c2\u00af))]\n\n### Options:\nA. 23\nB. 25\nC. 89\nD. 30\nE. 32\n\n### Answer:\nExplanation:\n=80\u00e2\u02c6\u2019[5\u00e2\u02c6\u2019(6+2(7\u00e2\u02c6\u20198+5))]\n(Please check due to overline, sign has been changed)\n=80\u00e2\u02c6\u2019[5\u00e2\u02c6\u2019(6+2\u00c3\u20144))]\n=80\u00e2\u02c6\u2019[\u00e2\u02c6\u20199]=80+9=89\nOption C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA university needs to select a nine-member committee on extracurricular life, whose members must belong either to the student government or to the student advisory board. If the student government consists of 9 members, the student advisory board consists of 8 members, and 6 students hold membership in both organizations, how many different committee are possible?\n\n### Options:\nA. 44\nB. 55\nC. 66\nD. 77\nE. 88\n\n### Answer:\nstudent government + the student advisory board consists of 9 + 8 = 17 members.\n6 students hold membership in both, so they were counted twice.\nThe total number of people to choose from is 17 - 6 = 11\nThe number of ways to choose 9 members from 11 is 11C9 = 55\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nwhen W is divided by 13, the reminder is 0. if W is one lesser than it value and when divided by 5 its remainder is 0. what is the value of W ?\n\n### Options:\nA. 13\nB. 25\nC. 26\nD. 52\nE. 65\n\n### Answer:\nW is divided by 13 so that is multiple of 14 as 13,26,39...\nW-1 is divided by 5 the remainder is 0 so it is divisible by 5. Consider from option let us take the number is 13 it is divisible by 13 but 13-1 is not divisible by 5 so it is not answers so let us take 2nd option 25 which is not divisible by 13 in 3rd option 26 is divisible by 13 and 26-1 is divisible by 5 so ans is C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA shop owner sells 60mtr of cloth and gains SP of 10 mtrs. Find the gain %?\n\n### Options:\nA. 20%\nB. 40%\nC. 50%\nD. 60%\nE. 70%\n\n### Answer:\nHere, selling price of 10 m cloth is obtained as profit.\nProfit of 10 m cloth = (S.P. of 60 m cloth) \u2013 (C.P. of 60 m cloth)\nSelling price of 50 m cloth = Selling Price of 60 m of cloth\nLet cost of each metre be Rs. 100.\nTherefore, cost price of 50 m cloth = Rs. 5000 and S.P. of 50 m cloth = Rs. Rs. 6000\nProfit% = 10/50 \u00d7 100 = 20%\n20\nProfit of 20% was made by the merchant.\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAn Olympic diver received the following scores: 4, 3, 7, 6, and 5. The standard deviation of her scores is in which of the following ranges?\n\n### Options:\nA. 2.4 to 2.8\nB. 1.4 to 1.8\nC. 3.4 to 3.8\nD. 4.4 to 4.8\nE. 5.4 to 5.8\n\n### Answer:\n4+3+7+6+5/5 = 5\n|4-5| = 1 1^2 = 0\n|3-5| = 2 2^2 = 4\n|7-5| = 2 2^2 = 4\n|6-5| = 1 1^2 = 1\n|5-5| = 0 0^2 = 0\nSD = sqrt 10/5 =1.41\nAnswer : B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is:\n\n### Options:\nA. 49\nB. 50\nC. 12\nD. 13\nE. 67\n\n### Answer:\nSpeed of the train relative to man = (125/10) m/sec = (25/2) m/sec. [(25/2) * (18/5)] km/hr = 45 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 45 ==> x = 50 km/hr.\nAnswer: Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA fort of 2000 soldiers has provisions for 50 days. After 10 days some of them left and the food was now enough for the same period of 50 days as before. How many of them left?\n\n### Options:\nA. 400\nB. 288\nC. 266\nD. 121\nE. 158\n\n### Answer:\n2000 ---- 50\n2000 ---- 40\nx ----- 50\nx*50 = 2000*40\nx=1600\n2000\n-------\n400\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA person covers a distance in 12 minutes. If runs at a speed of 12 km per hour on an average. Find the speed at which he must run to reduce the time of journey to 5 minutes.\n\n### Options:\nA. 8 m/s\nB. 4 m/s\nC. 15 m/s\nD. 10 m/s\nE. 5 m/s\n\n### Answer:\nExplanation:\nT = 12 m\nSpees = 12 kmph\n= 12 x 5/18 = 10/3 m/s\nLet new speed be \"x\"\n12 x (10/3) = 5x\nx = 8 m/s\nAnswer: Option A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA plane moves from a place 9N 40E to a place 9N 40W taking 8 hours to travel. If the plane had left at 10.00 a.m. then what is the local time of arrival at the destination?\n\n### Options:\nA. 11.40 p.m.\nB. 12.40 p.m.\nC. 1.40 p.m.\nD. 2.40 p.m.\nE. 4.40 p.m.\n\n### Answer:\nTime difference between places will be 4*(40+40) minutes = 320 min =\n5 hrs 20 min\nas change of 1 degree in longitude cause change of 4 minutes in time.\nand that change is 80 degrees here.\nso when plane land. time will be = 10.00 + 8.00 -5.20 = 12.40 p.m.\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a set of numbers from 100 to 1000 inclusive, how many integers are odd and do not contain the digit 3?\n\n### Options:\nA. 180\nB. 288\nC. 286\nD. 284\nE. 324\n\n### Answer:\nWe have to find the total number of 3-digit odd numbers not having 3 as a digit.\nUnits digits will be among 1,5,7,9\nTenth digits will be among 0,1,2,5,4,6,7,8,9\nHundredth digits will be among 1,2,5,4,6,7,8,9\nSo total numbers = 4*9*8 =288\nAnswer : B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA can do a job in 20 days and B can do it in 30 days. A and B working together will finish thrice the amount of work in ------- days?\n\n### Options:\nA. 22 days\nB. 22 days\nC. 36 days\nD. 72 days\nE. 24 days\n\n### Answer:\n1/20 + 1/30 =5/60 = 1/12\n12/1 = 12 *3= 36 days\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf selling price is doubled, the profit triples. Find the profit percent.\n\n### Options:\nA. 20%\nB. 25%\nC. 30%\nD. 60%\nE. 100%\n\n### Answer:\nLet C.P. be Rs. x and S.P. be Rs. y.\nThen, 3(y - x) = (2y - x) y = 2x.\nProfit = Rs. (y - x) = Rs. (2x - x) = Rs. x.\nProfit % = x\tx 100\t% = 100%\nx\nE)\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA jar contains 9 marbles consisting of an equal number of red, green, and blue marbles. Three marbles are removed from the jar and discarded. What is the probability that only two colors will remain in the jar after the Three marbles have been removed?\n\n### Options:\nA. 1/49\nB. 1/16\nC. 1/28\nD. 1/3\nE. 1/2\n\n### Answer:\nJar contains {3-red, 3-green, 3-blue} marbles. We are asked to find the probability that after removing 3 marbles only 2 colours remain in the jar, i.e., the probability of removing EITHER red, OR green, OR blue.\nSample space = 9C3 = 84.\nProbability of choosing 3 red = 3C3/9C3 = 1/84.\nProbability of choosing 3 green = 3C3/9C3 = 1/84.\nProbability of choosing 3 blue = 3C3/9C3 = 1/84.\nRequired probability = 1+1+1/84 = 3/84 = 1/28. Ans (C).\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe S.I. on a certain sum of money for 3 years at 8% per annum is half the C.I. on Rs. 4000 for 2 years at 10% per annum. The sum placed on S.I. is?\n\n### Options:\nA. Rs.1718\nB. Rs.1729\nC. Rs.1750\nD. Rs.1724\nE. Rs.1723\n\n### Answer:\nC.I. = [4000 * (1 + 10/100)2 - 4000]\n= (4000 * 11/10 * 11/10 - 4000) = Rs. 840.\nSum = (420 * 100)/(3 * 8) = Rs.1750\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA box contains 11 apples, 10 of which are red. An apple is drawn from the box and its color is noted before it is eaten. This is done a total of n times, and the probability that a red apple is drawn each time is less than 0.5. What is the smallest possible value of n?\n\n### Options:\nA. 3\nB. 4\nC. 5\nD. 6\nE. 7\n\n### Answer:\nP(choosing a red apple 6 times in a row) = 10/11*9/10*8/9*7/8*6/7*5/6 = 5/11 < 0.5\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe Average of 11 results is 16, if the average of the 1st 6 results is 58 & that of the last 63. Find the 6th result.\n\n### Options:\nA. 60\nB. 59\nC. 62\nD. 66\nE. 58\n\n### Answer:\n6th result = (58*6+63*6-60*11)=66\nAnswer is D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n15.03 \u00c3\u2014 0.01 = ?\n\n### Options:\nA. 0.1503\nB. 0.001503\nC. 1.503\nD. 0.001503\nE. None of these\n\n### Answer:\n15.03 \u00c3\u2014 0.01 = ?\nor,? = 0.1503\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFOG + FOG + FOG + FOG = 1460.\nIf F,O and G are digits in a three-digit number in the preceding equation the F + O + G = ?\n\n### Options:\nA. 11\nB. 12\nC. 13\nD. 14\nE. 15\n\n### Answer:\ngiven,FOG + FOG + FOG + FOG = 1460\n4(FOG)=1460\n=>FOG=365\nFace value of F is:3\nFace value of O is:6\nFace value of G is:5\nso F+O+G=3+6+5=14\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSandy gets 3 marks for each correct sum and loses 2 marks for each incorrect sum. Sandy attempts 30 sums and obtains 45 marks. How many sums did Sandy get correct?\n\n### Options:\nA. 18\nB. 21\nC. 24\nD. 27\nE. 28\n\n### Answer:\nLet x be the correct sums and (30-x) be the incorrect sums.\n3x - 2(30-x) = 45\n5x = 105\nx = 21\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf two positive numbers are in the ratio 1/8 : 1/5, then by what percent is the second number more than the first?\n\n### Options:\nA. 67%.\nB. 70%.\nC. 60%.\nD. 68%.\nE. 80%.\n\n### Answer:\nGiven ratio = 1/8 : 1/5 = 5 : 8\nLet first number be 5x and the second number be 8x.\nThe second number is more than first number by 3x.\nRequired percentage = 3x/5x * 100 = 60%.\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train 250 m long passed a pole in 25 sec. How long will it take to pass a platform 700 m long?\n\n### Options:\nA. 28 sec\nB. 89 sec\nC. 95 sec\nD. 16 sec\nE. 15 sec\n\n### Answer:\nSpeed = 250/25 = 10 m/sec.\nRequired time = (250 + 700)/10\n= 95 sec.\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich one of the following is the sum of the numbers 1, 3, 5, 7, 9\u00e2\u20ac\u00a6. up to nth number?\n\n### Options:\nA. N2 + 1\nB. N2 - 1\nC. N(N + 1)/2\nD. N2\nE. N(N + 1)\n\n### Answer:\nExplanation:\nN2\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nI have a few sweets to be distributed. If I keep 2, 3 or 4 in a pack, I am left with one sweet. If I keep 5 in a pack, I am left with none. What is the minimum number of sweets I have to pack and distribute ?\n\n### Options:\nA. 25\nB. 37\nC. 54\nD. 65\nE. 75\n\n### Answer:\nwhen divided 2,3,4 leaves remainder 1 and leaves remainder 0 while dividing 5\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a certain store, the profit is 320% of the cost. If the cost increases by 35% but the selling price\nremains constant, approximately what percentage of the selling price is the profit\n\n### Options:\nA. 68%\nB. 80%\nC. 90%\nD. 100%\nE. None of above\n\n### Answer:\nExplanation:\nLet C.P.= Rs. 100.\nThen, Profit = Rs. 320,\nS.P. = Rs. 420.\nNew C.P. = 135% of Rs. 100 = Rs. 135\nNew S.P. = Rs. 420.\nProfit = Rs. (420 - 135) = Rs. 285\nRequired percentage = (285/420) * 100\n= 68%(approx)\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA car traveled 281 miles in 4 hours 41 minutes. What was the average speed of the car in miles per hour?\n\n### Options:\nA. 60 miles / hour\nB. 50 miles / hour\nC. 80 miles / hour\nD. 90 miles / hour\nE. 40 miles / hour\n\n### Answer:\nWe first convert the time of 4 hours 41 minutes in minutes\n4 hours 41 minutes = 4 ? 60 + 41 = 281 minutes\nAverage speed S is given by distance / time. Hence\nS = 281 miles / 281 minutes = 1 mile / minute\n= 60 miles / hour\ncorrect answer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA feed shop sells two varieties of birdseed: Product A, which is 40% millet and 60% sunflower, and Product B, which is 65% millet and 35% safflower. If a customer purchases a mix of the both types of birdseed that is 50% millet, what percent of the mix is Product A?\n\n### Options:\nA. 50%\nB. 55%\nC. 60%\nD. 40%\nE. 45 %\n\n### Answer:\nYes there is a simple method :\nConsider the following method\nProduct A : 40% millet and 60% sunflower\nProduct B : 65% millet and 35% safflower\nMix : 50% millet\nHere the weighted average is 50%,\nNow Product A has 40% millet, which is 10% less than the weighted average of mix = - 0.10 A --------------- I\nSimilarly, Product B has 65 % millet, which is 15 % more than the weighted average of mix = + 0.15 B ------------ II\nNow, both Product A and Product B are combined to give a 50% mix containing millet, so equate I and II\nimplies, 0.10 A = 0.15 B\nTherefore A/B = 0.15/0.10 = 3/2\nA : B : (A + B) = 3 : 2 : (3+2) = 3 : 2 : 5\nWe have to find, percent of the mix is Product A i.e. A : (A + B) = 3 : 5 = (3 / 5) * 100 = 60 %\nHere is a pictorial representation :\nProduct A= 40%------------------------10% or 0.10 below average, A times-----------------Total below = - 0.10 A\n----------------------------------------------------------------------------------------Average = 50% or 0.50\nProduct B = 65 %--------------------------15% or 0.15 above average, B times-----------------Total above = + 0.15 B\nSince the amount below the average has to equal the average above the average; therefore,\n0.10 A = 0.15 B\nA/B = 3/2\nA:B: Total = 3:2:5\nA/Total = 3:5 = 60 %\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwelve machines, each working at the same constant rate, together can complete a certain job in 12 days. How many additional machines, each working at the same constant rate, will be needed to complete the Job in 8 days?\n\n### Options:\nA. 2\nB. 3\nC. 4\nD. 6\nE. 8\n\n### Answer:\nAnother solution which is faster is Since each machine works at a constant rate. The time needs to bought down from 12 to 8. So the new time is 2/3 of the original time. Thus to achieve this we need the rate to be 3/2 of original.\nSo 3/2*12 =18\nSo we need 18-12 = 6 more machines.\nAnswer : D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 5 machines can produce 20 units in 10 hours, how long would it take 20 machines to produce 200 units?\n\n### Options:\nA. 50 hours\nB. 40 hours\nC. 25 hours\nD. 12 hours\nE. 8 hours\n\n### Answer:\nHere, we're told that 5 machines can produce 20 units in 10 hours....\nThat means that EACH machine WORKS for 10 hours apiece. Since there are 5 machines (and we're meant to assume that each machine does the same amount of work), then the 5 machines equally created the 20 units.\n20 units/5 machines = 4 units are made by each machine every 10 hours\nNow that we know how long it takes each machine to make 4 units, we can break THIS down further if we choose to...\n10 hours/4 units = 2.5 hours per unit when 1 machine is working.\nThe prompt asks us how long would it take 20 machines to produce 200 units.\nIf 20 machines each work for 2.5 hours, then we'll have 20 units. Since 200 units is '10 times' 20, we need '10 times' more TIME.\n(2.5 hours)(10 times) = 25 hours\nFinal Answer:\n[Reveal]Spoiler:\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nCamel and carriage for Rs. 5000. He SP the camel at a gain of 20% and the carriage at a loss of 10%. If he gains 3% on the whole, then find the CP of the camel?\n\n### Options:\nA. Rs.2166.67\nB. Rs.2187.67\nC. Rs.2188\nD. Rs.2200\nE. Rs.2234.7\n\n### Answer:\nNow, in this numerical, there is no common loss and gain %.\nHence, solve it making equations.\nLet cost price of camel be x.\nAs cost of camel and carriage = Rs 5000\nCost of carriage = Rs. (5000 \u2013 x)\nAfter selling camel he gains 20% and on carriage a loss of 10%. But on the whole he gains 3%.\nTherefore,\n20% of x \u2013 10 % of (5000 \u2013 x) = 3 % of 5000\n20 \u00d7 x \u2013 10 \u00d7 (5000 \u2013 x) = 3 \u00d7 5000\n100 100 100\nx \u2013 (5000 \u2013 x) = 150\n5 10\n10x \u2013 (5000 \u2013 x) \u00d7 10 = 150 \u00d7 10\n5 10\n2x-5000+x=1500\n3x=1500+5000\nx=2166.67\nThe cost of camel = Rs.2166.67\nOption (A) is the correct answer\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA can do a piece of work in 8 days. B can do it in 12 days. With the assistance of C they completed the work in 4 days. Find in how many days can C alone do it?\n\n### Options:\nA. 87 days\nB. 20 days\nC. 16 days\nD. 24 days\nE. 36 days\n\n### Answer:\nC = 1/4 - 1/8 - 1/12 = 1/24\n=> 24 days\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nVisitors to show were charged Rs.15 each on the first day. Rs.7.50 on the second day, Rs.2.50 on the third day and total attendance on the three days were in ratio 2:5:13 respectively. The average charge per person for the whole show is?\n\n### Options:\nA. 1\nB. 4\nC. 5\nD. 6\nE. 8\n\n### Answer:\n2: 5: 13\n2x 5x 13x\n15 7.5 2.5\n30x + 37.5x + 32.5x = 100x/20x\nAverage = 5\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nCar A runs at the speed of 50km/hr & reaches its destination in 8hr. Car B runs at the speed of 25 km/h & reaches its destination in 4h. What is the respective ratio of distances covered by Car A & Car B?\n\n### Options:\nA. 4 : 1\nB. 11 : 8\nC. 13 : 7\nD. 15 : 7\nE. 16 : 9\n\n### Answer:\nSol. Distance travelled by Car A = 50 \u00d7 8 = 400 km\nDistance travelled by Car B = 25 \u00d7 4 =100 km\nRatio = 400/100 = 4 : 1\nAnswer : A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe cost of producing x tools by a company is given by\nC(x) = 1200 x + 5500 (in $)\na) What is the cost of 100 tools?\n\n### Options:\nA. 125500 $\nB. 125800 $\nC. 125900 $\nD. 126500 $\nE. 122500 $\n\n### Answer:\nSolution\nC(100) = 1200*100 + 5500 = 125500 $\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train traveled the first d miles of its journey it an average speed of 60 miles per hour, the next d miles of its journey at an average speed of y miles per hour, and the final d miles of its journey at an average speed of 160 miles per hour. If the train\u2019s average speed over the total distance was 90 miles per hour, what is the value of y?\n\n### Options:\nA. 68\nB. 84\nC. 90\nD. 110\nE. 135\n\n### Answer:\nAverage speed=Total distance traveled /Total time taken\n3d/d/60+d/y+d/160=90\nSolving for d and y,\n15y=11y+480\n4y=440\ny=110\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA furniture store owner decided to drop the price of her recliners by 20% to spur business. By the end of the week she had sold 50% more recliners. What is the percentage increase of the gross?\n\n### Options:\nA. 10%\nB. 15%\nC. 20%\nD. 25%\nE. 50%\n\n### Answer:\nSay a recliner is actually worth $100\nIf she sells 100 recliners then she earns $10000\nAfter the discount of 20%, she will earn $80 per recliner and she sells 50% more ie.,150 recliners\nHence her sales yields 150*80=$12000\nIncrease in sales=12000-10000=$2000\nSo% increase = 2000*100/10000 =20%\nC is the answer\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA began business with Rs.45000 and was joined afterwards by B with Rs.5400. When did B join if the profits at the end of the year were divided in the ratio of 2:1?\n\n### Options:\nA. 8\nB. 2\nC. 7\nD. 5\nE. 3\n\n### Answer:\n45*12 : 54*x = 2: 1\nx = 5\n12 -5 = 7\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain factory produces buttons and buckles at a uniform weight. If the total weight of 2 buttons and 2 buckles is one third of 11 buckles and 3 buttons, then the weight of 3 buttons and 3 buckles is how many times that of 5 buckles and 6 buttons?\n\n### Options:\nA. 7/15.\nB. 4/9.\nC. 6/11.\nD. 5/9.\nE. 8/15.\n\n### Answer:\n2buttons + 2buckles = 1/3(11buckles + 3buttons)\n6buttons + 6buckles = 11buckles + 3buttons\n3buttons = 5buckles\nWeight of 3buttons and 3buckles = 5buckles + 3buckles = 8buckles\nWeight of 6buttons and 5buckles = 10buckles + 5buckles = 15buckles\n(3buttons and 2buckles) = x * (6buttons and 5buckles)\n8 = x*15\nx = 8/15\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA large tank can filled by A and B in 30 minutes and 45 minutes respectively. How many minutes will it take to fill the tanker from empty state if B is used for half the time and A and B fill it together for the other half?\n\n### Options:\nA. 30min\nB. 20min\nC. 25min\nD. 40min\nE. 45min\n\n### Answer:\nPart filled by A+B in 1 minute = 1/30 + 1/45 = 1/45\nSuppose the tank is filled in x minutes\nThen, x/2(1/45 + 1/45) = 1\nx/2 * 2/45 = 1\nx = 45 min\nAnswer is E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many two-element subsets of {2,4,6,8} are there that do not contain the element 4?\n\n### Options:\nA. 1\nB. 2\nC. 3\nD. 4\nE. 5\n\n### Answer:\nRequired subsets are = {2,6}, {2,8}, {6,8}= 3\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe below sequence is a bit tricky. Can you solve it to find the next number?\n8, 28, 328, 4328, ?\n\n### Options:\nA. 29816\nB. 38291\nC. 54325\nD. 38290\nE. 54328\n\n### Answer:\nSee the pattern. With every digit, the previous numbers are added after that digit\nSo the next number in the series is 54328\nAnswer : E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn the first 10 overs of a cricket game, the run rate was only 3.2. What should be the rate in the remaining 40 overs to reach the target of 282 runs?\n\n### Options:\nA. 6.25\nB. 6.28\nC. 6.11\nD. 6.19\nE. 6.21\n\n### Answer:\nRequired run rate\n= [282 - (3.2 * 10)]/40\n= 250/40\n= 6.25\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many times will the hands of a clock coincide in a day?\n\n### Options:\nA. 24\nB. 22\nC. 23\nD. 44\nE. 42\n\n### Answer:\nsolution\nThe hands of a clock coincide 11 times in every 12 hours (Since between 11 and 1, they coincide only once, i.e., at 12 o'clock). The hands overlap about every 65 minutes, not every 60 minutes. Thus the minute hand and the hour hand coincide 22 times in a day\nso Answer is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a 10 percent deposit that has been paid toward the purchase of a certain product is $120, how much more remains to be paid?\n\n### Options:\nA. $880\nB. $990\nC. $1,000\nD. $1,100\nE. $1,080\n\n### Answer:\n10/100P = 120 >> p= 120*100/10 = 1200\n1200 - 120 = 1080\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe arithmetic mean of the scores of a group of students in a test was 42. The brightest 20% of them secured a mean score of 80 and the dullest 25% a mean score of 31. The mean score of remaining 55% is?\n\n### Options:\nA. A)61.4.\nB. B)51.7\nC. C)33.18\nD. D)51.1\nE. E)51.2\n\n### Answer:\nLet the required mean score be x. Then,\n20 * 80 + 25 * 31 + 55 * x = 42 * 100\n= 1600 + 775 + 55x = 4200\n= 55x = 1825\n= x = 33.18\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe cost of registration at a professional association meeting was $50 per person; a lunch for registrants only was available for an additional $22 per person. If the number of registrants who paid for lunch was 40 more than the number who did not, and if receipts for registration and lunch totaled $39,480, how many people paid just for registration at the meeting?\n\n### Options:\nA. 700\nB. 800\nC. 300\nD. 1,500\nE. 1,800\n\n### Answer:\nHope this might be useful to you.\nLet the number of people who have opted only to register = x\nNow since the registration cost is 50$ per person, the total amount sums to = 50x $\nAs per the information given in the question, the number of registrants who paid for lunch was 40 more than the number who did not. That means, total number of people who registered and paid for lunch = 40 + x.\nFor the people who registered for lunch the cost is 50 $ (for the event registration) + 22 $ (for lunch) = 72 $.\nTotal amount in this case sums to = 72(40 + x) = 2880 + 72x\nNow, total amount received was 39480\nThus, from the above data,\n50x + 2880 + 72x = 39480\n122x = 39480 - 2880\n122x = 36600\nx = 300.\nHence the correct Ans is C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe food in a camp lasts for 20 men for 50 days. If twenty more men join, how many days will the food last?\n\n### Options:\nA. 22 days\nB. 25 days\nC. 28 days\nD. 16 days\nE. 27 days\n\n### Answer:\none man can consume the same food in 20*50 = 1000 days.\n20 more men join, the total number of men = 40\nThe number of days the food will last = 1000/40 = 25 days.\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA rectangular floor is covered by a rug except fo a strip p meters along each of the four edges. If the floor is m meters by e meteres, What is the area of the rug in square meters?\n\n### Options:\nA. mn - p(m+n)\nB. mn \u2013 2p(m+n)\nC. mn \u2013 p^2\nD. (m - p)(n - p)\nE. (m - 2p)(e - 2p)\n\n### Answer:\nThe answer must be E.\nPlug in M 100\nN 50\ne 10.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how many different ways can pennies (1 cent), nickels (5 cents), dimes (10 cents), and quarters (25 cents) be combined for a total of $1.05 (105 cents), if at least one of each type of coin must be included?\n\n### Options:\nA. 49\nB. 69\nC. 73\nD. 91\nE. 99\n\n### Answer:\nI. Case I = Four Quarters = this is impossible, because if we already have a dollar in quarters, then we cannot have any dimes. We can't have all four coins represented if we have four quarters.\nII. Case II = Three Quarters (75 cents)\nThis allows for two or one dime. Three dimes would bring us up to $1.05, and we wouldn't have room for any pennies or nickels.\nSubcase 1 = 3 Q, 2 D (95 cents)\n1) one nickel (N) and 5 pennies (P) (2 nickels would not allow for any pennies)\nSubcase 2 = 3 Q, 1 D (85 cents)\n2) 3 N and 5 P\n3) 2 N and 10 P\n4) 1 N and 15 P\nCase II allows for a total of four ways.\nIII. Case III = Two Quarters (50 cents)\nThis allows for 1-4 dimes.\nSubcase 1 = 2 Q, 4 D (90 cents)\n(2 ways) we could have 1-2 nickels\nSubcase 2 = 2 Q, 3 D (80 cents)\n(4 ways) we could have 1-4 nickels\nSubcase 3 = 2 Q, 2 D (70 cents)\n(6 ways) we could have 1-6 nickels\nSubcase 4 = 2 Q, 1 D (60 cents)\n(8 ways) we could have 1-8 nickels\nCase III allows for a total of 20 ways\nIV. Case IV = One Quarter (25 cents)\nThis allows for 1-7 dimes\nSubcase 1 = 1 Q, 7 D (95 cents)\n(1 way) we could have 1 nickel\nSubcase 2 = 1 Q, 6 D (85 cents)\n(3 ways) we could have 1-3 nickels\nSubcase 3 = 1 Q, 5 D (75 cents)\n(5 ways) we could have 1-5 nickels\nSubcase 4 = 1 Q, 4 D (65 cents)\n(7 ways) we could have 1-7 nickels\nSubcase 5 = 1 Q, 3 (55 cents)\n(9 ways) we could have 1-9 nickels\nSubcase 6 = 1 Q, 2 D (45 cents)\n(11 ways) we could have 1-11 nickels\nSubcase 7 = 1 Q, 1 D (35 cents)\n(13 ways) we could have 1-13 nickels\nCase IV allows for a total of 49 ways.\nThere's no other case, because we have to have at least one quarter and one dime. The total over the cases equals\nTotal = 4 + 20 + 49 =73 ways.\nOA =(C)\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nKiran had 85 currency notes in all , some of which were of Rs.100 denomination and the remaining of Rs.50 denomination the total amount of all these currency note was Rs.5000.how much amount did she have in the denomination of Rs.50?\n\n### Options:\nA. 3500\nB. 1500\nC. 2500\nD. 4500\nE. None of them\n\n### Answer:\nLet the no of fifty rupee notes be x\nThen,no of 100 rupee notes =(85-x)\n50x+100(85-x)=5000\nx+2(85-x)=100\nx=70\nso, required amount=Rs.(50*70)= Rs.3500\nAnswer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nBy selling 50 meters of cloth. I gain the selling price of 15 meters. Find the gain percent?\n\n### Options:\nA. 42 6/8%\nB. 42 8/7%\nC. 482 6/7%\nD. 42 6/7%\nE. 42 1/7%\n\n### Answer:\nSP = CP + g\n50 SP = 50 CP + 15 SP\n35 SP = 50 CP\n35 --- 15 CP gain\n100 --- ? => 42 6/7%\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man buys an article and sells it at a profit of 20%. If he had bought it at 20% less and sold it for Rs.75 less, he could have gained 25%. What is the cost price?\n\n### Options:\nA. 337\nB. 375\nC. 297\nD. 266\nE. 291\n\n### Answer:\nCP1 = 100 SP1 = 120\nCP2 = 80 SP2 = 80 * (125/100) = 100\n20 ----- 100\n75 ----- ? => 375\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the greatest prime factor of 8^11 - 2^30?\n\n### Options:\nA. 2\nB. 3\nC. 5\nD. 7\nE. 11\n\n### Answer:\n8^11 - 2^30\n=(2^3)^11 - 2^30\n= 2^33 - 2^30\n= 2^30 (2^3 -1)\n= 2^30 * (8-1)\n= 2^30 * 7\nThe greatest prime factor is 7.\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 6 (A's capital) = 8 (B's capital) = 12 (C's capital). Then the ratio of their capitals is?\n\n### Options:\nA. 20:15:16\nB. 4:3:1\nC. 4:3:2\nD. 20:15:11\nE. 20:15:19\n\n### Answer:\n6A = 8B = 12 C\nA:B:C = 1/6:1/8:1/12\n= 4:3:2\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMohan purchased 15 kgs of rice at the rate of Rs.20 per kg and 8 kgs of pulses at the rate of Rs.20 per kg. Whaat is the total amount that he paid to the shopkeeper?\n\n### Options:\nA. A)Rs.598\nB. B)Rs.594\nC. C)Rs.460\nD. D)Rs.595\nE. None of these\n\n### Answer:\nExplanation:\nPrice of 15 kgs of rice at Rs.20/kg = 15x20 = Rs.300\nPrice of 8 kgs of pulses at Rs.20/kg = 8x20 = Rs.160\nTherefore, Total amount = Rs.300+Rs.160 = Rs.460\nAnswer: Option C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA clock is set at 5 a.m. The clock loses 16 minutes in 24 hours. What will be the true time when the clock indicates 10 p.m. on 4th day?\n\n### Options:\nA. 38\nB. 11\nC. 237\nD. 29\nE. 112\n\n### Answer:\nTime from 5 a.m. on a day to 10 p.m. on 4th day = 89 hours.\nThe faulty clock shows only 1424 min for 24 hours in correct clock.\nSo 1 minute of the faulty clock = 24/1424 hours\n1 hour of the faulty clock = 24/1424 \u00d7 60 hours\n89 hours of the faulty clock = 24/1424 \u00d7 60 \u00d7 89 = 90 hours.\nSo true time is 1 hour more than 10 pm. i.e., 11 pm.AnswerB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf Rs.7500 are borrowed at C.I at the rate of 4% per annum, then after 2 years the amount to be paid is?\n\n### Options:\nA. 2288\nB. 2778\nC. 8297\nD. 8112\nE. 3241\n\n### Answer:\nA = 7500(26/25)2 = 8112.Answer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA student took 6 courses last year and received an average (arithmetic mean) grade of 100 points. The year before, the student took 5 courses and received an average grade of 50 points. To the nearest tenth of a point, what was the student\u2019s average grade for the entire two-year period?\n\n### Options:\nA. 79\nB. 89\nC. 95\nD. 77.27\nE. 97.2\n\n### Answer:\nLet the 6 courses that were taken last year be A1 , A2, A3 , A4 , A5 , A6\nA1+A2+A3+A4+A5+A6 = 100*6 = 600\nThe year before , the 5 courses be B1, B2 , B3 , B4 , B5\nB1+B2+B3+B4+B5 = 50*5 = 250\nStudent's average = (600+250)/11 = 77.27\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf The GCD of two numbers (not equal, both integers, greater than 1) is 2, then which of the following can be true?\nA. They are prime.\nB. They are even.\nC. They do not have a common prime factor.\nD. They do not have a common factor other than 2.\n\n### Options:\nA. Only A\nB. Only B\nC. Only C\nD. Only D\nE. Only B and D\n\n### Answer:\nThe GCD of two numbers (not equal, both integers, greater than 1) is 2 means that they don't share factors other than 1 and 2.\nThis also means that both numbers are even ( divisible by 2.)\nA. They are not prime. 2 is the only even number that is prime, so one number can be prime but the other number cannot be.\nB. They are even. Since they are divisible by 2, they are even..\nC. They have a common prime factor. The question defines the numbers as having a GCD of 2, which is prime.\nD. They have a common factor other than 2. Both numbers have common factors of 2 and 1. For example:\nThe factors of 4 are 1 and 2, the factors of 6 are 1, 2, and 3.\nTherefore, (B) is the only correct answer.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n21 ball numbered 1 to 21. A ballis drawn and then another ball is drawn without replacement.\n\n### Options:\nA. 5/34\nB. 3/37\nC. 9/42\nD. 5/41\nE. 7/43\n\n### Answer:\nThe probability that first toy shows the even number,\n=1021=1021\nSince, the toy is not replaced there are now 9 even numbered toys and total 20 toys left.\nHence, probability that second toy shows the even number,\n=920=920\nRequired probability,\n=(1021)\u00d7(920)=(1021)\u00d7(920)\n=9/42\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are three secretaries who work for four departments. If each of the four departments have one report to be typed out, and the reports are randomly assigned to a secretary, what is the probability W that all three secretary are assigned at least one report?\n\n### Options:\nA. 8/9\nB. 64/81\nC. 4/9\nD. 16/81\nE. 5/9\n\n### Answer:\nI got the same answer: Here's my reasoning\nFirst Report you have 3 choices\nSecond Report you have 2 choices\nThird Report you have 1 choice\nFourth report 3 choices again\nThen total number of ways is: 3*2*1*3=3^2*2\nThis is not correct. You have assumed that the 4th report must go to someone who already has a report. There is no such constraint. You can easily give the 1st and 2nd reports to secretary 1, 3rd report to secretary 2 and 4th report to secretary 3. But you have ignored all such cases.\nThe number of ways of ensuring at least one report goes to each secretary is 4C2 (select 2 reports out of 4 which go to the same person)*3C1 (select the person who must type 2 reports)*2! (since you have 2 reports left which you must distribute to the 2 remaining people such that each person gets one) = 36\nRequired probability W= 36/81.C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe labeled price of a table is Rs. 6,000. The shopkeeper sold it by giving 5% discount on the labeled price and earned a profit of 15%. What approximately is the cost price of the table?\n\n### Options:\nA. Rs. 4956\nB. Rs. 6195\nC. Rs. 6425\nD. Rs. 7200\nE. None of these\n\n### Answer:\nExplanation:\nLabeled price = Rs. 6,000\nBy giving 5% discount on labeled price, the selling price is\n= 95 / 100 * 6,000 = Rs. 5700\nBy earning 15% profit on the selling of price Rs. 5700 the cost price is\n= 100 / 115 * 5700 = Rs. 4956\nTherefore, approximate cost is 4956\nANSWER A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJoshua and Jose work at an auto repair center with 1 other workers. For a survey on health care insurance, 2 of the 6 workers will be randomly chosen to be interviewed. What is the probability that Joshua and Jose will both be chosen?\n\n### Options:\nA. 1/15\nB. 1/12\nC. 1/9\nD. 1/6\nE. 1/3\n\n### Answer:\nTwo Methods\n1) Probability of chosing Josh first = 1/3\nProbability of chosing Jose second = 1/2\ntotal = 1/6\nProbability of chosing Jose first = 1/3\nProbability of chosing Josh second = 1/2\nTotal = 1/6\nFinal = 1/6 + 1/6 = 1/3\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nLocal kennel has cats and dogs in the ratio of 6:12. If there are 24 fewer cats than dogs, how many dogs are in the kennel?\n\n### Options:\nA. 50\nB. 48\nC. 52\nD. 54\nE. 56\n\n### Answer:\nLets work with the data given to us. We know that there ratio of cats to dogs is 6:12 or\ncats 6\ndogs 12\nwe can write number of cats as 6x and number of dogs as 12x and we know that 12x-6x= 24(therefore 6x = 24 => x=4)\nThen # of dogs = 12x4= 48\nAnswer is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf\n1 = 6\n2 = 12\n3 = 18\n4 = 24\n5 = 30\n6 = 36\nThen 12 = ?\nHint: Its a logic Riddle not a mathematical riddle\n\n### Options:\nA. 1\nB. 2\nC. 3\nD. 4\nE. 5\n\n### Answer:\nB\n2\nAs stated\n2=12 => 12=2\nAnswer is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAt what rate percent on simple interest will a sum of money double itself in 60 years?\n\n### Options:\nA. 3 1/3%\nB. 3 1/9%\nC. 1 2/3%\nD. 3 2/3%\nE. 3 6/3%\n\n### Answer:\nP = (P*60*R)/100\nR = 1 2/3%\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMother is aged 3times more than her daughter Rose. After 8 years, she would be two and a 1/2times of Rose's age. After further 8 years, how many times would he be of Rose's age?\n\n### Options:\nA. 1\nB. 2\nC. 4\nD. 5\nE. 6\n\n### Answer:\nLet Ronit's present age be x years. Then, father's present age =(x + 3x) years = 4x years.\n(4x + 8) = 5 (x + 8)\n2\n8x + 16 = 5x + 40\n3x = 24\nx = 8.\nHence, required ratio = (4x + 16)/(x + 16) = 48/24= 2.\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man is standing on a railway bridge which is 180 m long. He finds that a train crosses the bridge in 20 seconds but himself in 5 seconds. Find the length of the train and its speed.\n\n### Options:\nA. 5.6 m/sec\nB. 15 m/sec\nC. 18 m/sec\nD. 9 m/sec\nE. 25 m/sec\n\n### Answer:\nIf length of train is l and speed of train is s, then\nl/s = 5\n(l+180)/s = 20\n(l+180)/l = 20/5 =4\nl+180 =5*l\n4*l=180\nl=45 mtrs\ns= l/5 = 45/5 = 9 m/sec\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe sum of the present ages of two persons A and B is 60. If the age of A is twice that of B, find the sum of their ages 5 years hence?\n\n### Options:\nA. 40\nB. 45\nC. 70\nD. 12\nE. 25\n\n### Answer:\nAnswer: Option C\na + b = 60, a = 2b\n2b + b = 60 => b = 20 then a = 40.\n5 years, their ages will be 45 and 25.\nSum of their ages = 45 + 25 = 70.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA Cuban cigar would cost 1 dollar less than 1.5 times a French cigar, had the French cigar cost 0.7 dollar less than it does now. An Arabian cigar costs 50 cents more than 1.5 times the Cuban cigar. The three cigars together cost 74.7 dollars. What is the price of the French cigar?\n\n### Options:\nA. 16.7$.\nB. 23$.\nC. 25.5$.\nD. 35$.\nE. 37.4$.\n\n### Answer:\nThe three cigars together cost 74.7 dollars. If each cost the same , they would have cost a little less than 25 dollars each.\nFrom the given data we know French cigar < Cuban cigar < Arabic cigar\nand each is more expensive 1.5 times. Therefore eliminate options C,D,E straightaway . Since French cigar is at least 1.5 times cheaper we know B cannot be the answer.\nTherefore A is the answer\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 70 percent of 600 is 40 percent of x, then x=?\n\n### Options:\nA. 105\nB. 168\nC. 342\nD. 660\nE. 1050\n\n### Answer:\nGiven: 0.7*600=0.4x --> 420=4/10*x --> x=1,050.\nAnswer: E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMary has 1803 dollars with her. What is the amount that she should keep with her inorder to distribute the same among nine kids equally?\n\n### Options:\nA. 3\nB. 0\nC. 10\nD. 2\nE. 6\n\n### Answer:\nThe answer is 3. (1803-3=1800). 1800 is divisible by nine which gives an answer of 20.So,she will be distributing 20 each for the nine kids and the remaining 3 will be left with her. So the answer is A=3\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many different 4-digit numbers can be written using the digits 1 to 8 without repetition such that the number always contains the digit 2?\n\n### Options:\nA. 360\nB. 560\nC. 760\nD. 840\nE. 1260\n\n### Answer:\nThe most restrictive case. We should have a two.\nNo repetition. Numbers range from 1 to 8.\n= 1*7*6*5 = 210 ways we can write if '2' is in the first position.\n= 4*(210)\n=840 ways.\nAnother method.\nWithout restriction for 8 digits- 8*7*6*5 = 1680 Ways we can write.\nWithout restriction for 7 digits- 7*6*5*4 = 840 Ways.\nWith restriction = 1680 - 840 = 840 Ways.\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA is a set containing 8 different positive odd numbers. B is a set containing 7 different numbers, all of which are members of A. Which of the following statements CANNOT be true?\n\n### Options:\nA. The range of B is even.\nB. The mean of A is even.\nC. The mean of B is even.\nD. The range of A is equal to the range of B.\nE. The median of B is equal to the mean of B.\n\n### Answer:\nGiven: A is a set containing 8 different positive odd numbers\nEasily inferred: B is a set containing 7 differentoddnumbers\n(A) The range of B is even. - Always even, since it is a difference of two odd numbers\n(B) The mean of A is even. - can be. suppose 8 numbers consist of 4 pairs of (16n-1,16n+1) for different values of n. Adding these will give a multiple of 16, which when divided by 8 (to arrive at mean), will give an even number\n(C) The mean of B is even. - Cannot be. Mean = (sum of 7 odd numbers)/7 = Odd number/odd number thus cannot be even.\n(D) The range of A is equal to the range of B.\n(E) The median of B is equal to the mean of B\nOption C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo men are going along a track rail in the opposite direction. One goods train crossed the first person in 20 sec. After 10 min the train crossed the other person who is coming in opposite direction in 18 sec .After the train has passed, when the two persons will meet?\n\n### Options:\nA. 95 minutes\nB. 90 minutes\nC. 88 minutes\nD. 95 minutes\nE. None of these\n\n### Answer:\nExplanation :\nLet us consider that speed of train , first man and second man are respectively t, f and s.\nAccording to first given condition goods train crossed the first person moving in same direction in 20 sec.\nSo length of the will be 20(t-f)\nSimilarly train crossed the second man in 18 sec.\nSo length of the train will be 18(t+s) on comparing these two equations, we get 20(t-f) = 18(t+s)\n=> 2t = 20f + 18s\n=> t = 10f + 9s\nNow it is given that After 10 min the train crossed the other person who is coming in opposite direction.\nSo,If we consider this way of train as L then the next equation will be\nL = 600t (here 600 is used for 10 minutes)\nFinally as asked in the question the time required to meet the two man after the train has passed will\nbe given by\nTime = (L-600 f)/(f+s) {here 600f is used for the distance traveled by first man in 10 minutes}\n=> = (600t-600f) / (f+s)\n=> = [600(10f+9s)-600f] / (f+s)\n=> = 600(10f+9s-f) / (f+s) = 600 * 9(f+s) / (f+s)\n=> =600*9 seconds\n=> = 600*9/60min\n=> = 90 minutes\nHence (B) is the correct answer.\nAnswer : B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe total age of A and B is 11 years more than the total age of B and C. C is how many year younger than\n\n### Options:\nA. 14 years\nB. 12 years\nC. 56 years\nD. 66 years\nE. 11 years\n\n### Answer:\nGiven that A+B = 11 + B + C\n=> A \u00e2\u20ac\u201c C = 11 + B \u00e2\u20ac\u201c B = 11\n=> C is younger than A by 11 years\nAnswer:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how many different number of ways 4 boys and 2 girls can sit on a bench such that girls always sit together.\n\n### Options:\nA. A)720\nB. B)240\nC. C)740\nD. D)780\nE. E)790\n\n### Answer:\n240\nOption 'B'\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA 270 m long train running at the speed of 120 km/hr crosses another train running in opposite direction at the speed of 80 km/hr in 9 sec. What is the length of the other train?\n\n### Options:\nA. 230\nB. 997\nC. 266\nD. 289\nE. 179\n\n### Answer:\nRelative speed = 120 + 80 = 200 km/hr.\n= 200 * 5/18 = 500/9 m/sec.\nLet the length of the other train be x m.\nThen, (x + 270)/9 = 500/9 => x = 230.\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a > 1, which of the following is equal to (2a + 4)/(a^2 + 2a - 3)?\n\n### Options:\nA. 2(a+2)/(a+3)(a-1)\nB. a + 3\nC. 2/(a - 1)\nD. 2a/(a - 3)\nE. (a - 1)/2\n\n### Answer:\nHere's the algebraic approach:\n(2A + 4)/(A^2 + 2A - 3) can be rewritten as...\n2(A + 2)/(A+3)(A-1)\nWe can simplify the fraction, which leaves us with...\nAns : A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSam purchased 20 dozens of toys at t he rate of Rs. 375 per dozen. He sold each one of them at the rate of Rs. 33. What was his percentage profit?\n\n### Options:\nA. 3.5\nB. 4.5\nC. 5.6 percent\nD. 6.5\nE. None\n\n### Answer:\nSolution\nC.P of 1 toy\t= Rs.(375/12)\n= Rs.31.25\nS.P of 1 toy\t= Rs.33.\nTherefore,Profit\t= (1.75/31.25\u00d7100)%\n=(28/5)%\n=5.6%.\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average of seven numbers is 18. The average of first three numbers is 14 and the average of last three numbers is 19. What is the middle number?\n\n### Options:\nA. 27\nB. 29\nC. 30\nD. 34\nE. 35\n\n### Answer:\nThe total of seven numbers = 7X18 = 126\nThe total of first 3 and last 3 numbers is = 3 X 14+3 X 19 = 99\nSo, the middle number is (126 - 99 ) = 27\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain car uses 12 gallons of gasoline in traveling 120 miles. In order for the car to travel the same distance using 10 gallons of gasoline, by how many miles per gallon must the car\u2019s gas mileage be increased?\n\n### Options:\nA. 2\nB. 4\nC. 6\nD. 8\nE. 10\n\n### Answer:\n120/10 = 12. The difference is 12- 10 = 2.\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n9. On level farmland, two runners leave at the same time from the intersection of two country roads. One runner jogs due north at a constant rate of 8 miles per hour while the second runner jogs due east at a constant rate that is 42 miles per hour faster than the first runner's rate. How far apart, to the nearest mile, will they be after 1/2 hour ?\n\n### Options:\nA. 6\nB. 7\nC. 8\nD. 12\nE. 14\n\n### Answer:\nIf runner 1 is going north and runner 2 is going east they are like two sides of a 90 degree triangle.\nSide 1 = 8 m/h --> 4 m in 1/2 hr\nSide 2 = 10 m/h --> 5 m in 1/2 hr\nto complete this right angle triangle\nd^2 = 4^2 + 5^2\nd^2 = 41\n= ~ 6\nAnswer option A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAyesha's father was 58 years of age when she was born while her mother was 42 years old when her brother four years younger to her was born. What is the difference between the ages of her parents?\n\n### Options:\nA. 6\nB. 40\nC. 50\nD. 10\nE. 20\n\n### Answer:\nMother's age when Ayesha's brother was born = 42 years.\nFather's age when Ayesha's brother was born = (58 + 4) years = 62 years.\nRequired difference = (62 - 42) years = 20 years.\nAnswer:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA boat can move upstream at 25 kmph and downstream at 35 kmph, then the speed of the current is?\n\n### Options:\nA. 5\nB. 6\nC. 7\nD. 4\nE. 32\n\n### Answer:\nUS = 25\nDS = 35\nM = (35 - 25)/2 = 5\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOn a map, 1 inch represents 28 miles. How many Z inches would be necessary to represent a distance of 383.6 miles?\n\n### Options:\nA. 5.2\nB. 7.4\nC. 13.7\nD. 21.2\nE. 28.7\n\n### Answer:\nZ inches necessary to represent a distance of 383.6 miles = 383.6/28\n= 13.7\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nhat should come in place of question mark (?) in the following equation ?\n197 \u00d7 ? + 16(2) = 2620\n\n### Options:\nA. 22\nB. 12\nC. 14\nD. 16\nE. None of these\n\n### Answer:\n? = 2620\u2212256 /197=12\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average score in an examination of 10 students of a class is 60. If the scores of the top five students are not considered, the average score of the remaining students falls by 5. The pass mark was 50 and the maximum mark was 100. It is also known that none of the students failed. If each of the top five scorers had distinct integral scores, the maximum possible score of the topper is\n\n### Options:\nA. 90\nB. 99\nC. 92\nD. 94\nE. 97\n\n### Answer:\nThe average score in an examination of 10 students of a class is 60 --> the total score = 10*60 = 600;\nThe 5 smallest scores have an average of 55 --> the total score of the 5 smallest scores = 275.\nFrom above, the total score of the 5 largest scores = 600 - 275 = 325.\nSay the 5 largest scores are a, b, c, d, and e (where a", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nToday is Thursday. A person wants to meet a lawyer and as that lawyer is busy he asks him to come three days after the before day of the day after tomorrow? On which day the lawyer asks the person to come?\n\n### Options:\nA. SUNDAY\nB. MONDAY\nC. TUESDAY\nD. WEDNESDAY\nE. FRIDAY\n\n### Answer:\nToday is Thursday\nafter three days--->Sunday\nnow, (sunday)after before day--->saturday\nthen, (saturday)day after tomorrow--->monday\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a square mirror has a 20-inch diagonal, what is the approximate perimeter T of the mirror, in inches?\n\n### Options:\nA. 40\nB. 60\nC. 80\nD. 100\nE. 120\n\n### Answer:\nif you draw the square and diagonal inside the square. u can see square becomes part of two triangles opposite to each other.\nAnd We know the property of the triangle, addition of two sides of triangle must be greater than its diagonal in order to complete the triangle. And each side must be less than 20 and perimeter T must be less than 80, so we can eliminate answer choice C, D and E.\nso Side 1 + side 2 > 20, that means Side 1 or Side 2 must be > 10. so we can eliminate the answer choice A.\nNow we are left with is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf in a certain code, If NEPOLEAN is written as OBFMPQFO, how can IMPOSING be written?\n\n### Options:\nA. HOJTPQNI\nB. HOJTPQNK\nC. HOJTPQNL\nD. HOJTPQNJ\nE. HOJTPQND\n\n### Answer:\nNEPOLEAN - OBFMPQFO\nN+1 = O\nE+1 = F\nP+1 = Q\nO+1 = P\nL+1 = M\nE+1 = F\nA+1 = B\nN+1 = O\nNow write in reverse order... You ll get OBFMPQFO\nSimilarly for IMPOSING\nI+1 = J\nM+1 = N\nP+1 = Q\nO+1 = P\nS+1 = T\nI+1 = J\nN+1 = O\nG+1 = H\nNow write in reverse order... HOJTPQNJ\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train 280 m long, running with a speed of 63 km/hr will pass a tree in\n\n### Options:\nA. 15 sec.\nB. 16 sec.\nC. 18 sec.\nD. 20 sec.\nE. None\n\n### Answer:\nSolution\nSpeed\t= (63 x 5/18) m/sec\n= 35/2 msec\nTime taken\t= (280 x 2 /35)m/sec\n= 16 sec.\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe parameter of a square is double the perimeter of a rectangle. The area of the rectangle is 480 sq cm. Find the area of the square.\n\n### Options:\nA. 378\nB. 277\nC. 389\nD. 480\nE. 881\n\n### Answer:\nLet the side of the square be a cm. Let the length and the breadth of the rectangle be l cm and b cm respectively.\n4a = 2(l + b)\n2a = l + b\nl . b = 480\nWe cannot find ( l + b) only with the help of l . b. Therefore a cannot be found .\nArea of the square cannot be found.\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA fence consists of m lengths of fence that are each n feet long. A fence post separates each length of fence by its width of x feet. What is the total length W of the fence including the fence posts on each end?\n\n### Options:\nA. mn\nB. m(n + x)\nC. W=m(n + x) + x\nD. m(n + x) + 2x\nE. 2mn\n\n### Answer:\nNotice that since a fence post separates each length of fence, then there will be m+1 posts, for example if there are m=2 fences, then there will be 3 posts: PFPFP. Thus the total length of the posts is (m+1)x.\nThe total length of the fence is mn, therefore the total length of the fence including the fence posts on each end is (m+1)x+mn=mx+x+mn=m(n+x)+x.\nAnswer: C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf |3x+20|=|5x-5|, which of the following could be a value of x?\n\n### Options:\nA. 15/8\nB. 12\nC. -25/8\nD. 15/2\nE. 25/2\n\n### Answer:\n3x + 20 = 5x - 5 or 3x + 20 = -5x + 5\n-2x = -25 or 8x = -15\nx = 25/2 or x = -15/8\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA boat whose speed is 15 k/hr in still water goes 30 k/he downwards and come back in total 4 hr 30 min what is the speed of stream in k/hr ?\n\n### Options:\nA. 1km/hr\nB. 2km/hr\nC. 3km/hr\nD. 4km/hr\nE. 5km/hr\n\n### Answer:\nIf the speed of stream=x\nSpeed in downstream=15+x , Speed in Upstream=15-x,\nTotal time=4 hr 30 min=9/2 hr\n[30/(15+x) + 30/(15-x)]=9/2,Solving x=5\nx=5km/hr\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf (10^4 * 3.456789)^14 is written as a single term, how many digits would be to the right of the decimal place?\n\n### Options:\nA. 9\nB. 14\nC. 21\nD. 28\nE. 42\n\n### Answer:\n3.456789^14 has 6*14 = 84 decimal places.\n10^56 moves the decimal place to the right 56 places.\n(10^4 * 3.456789)^14 has 84-56 = 28 digits after the decimal point.\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere is a 4 digit no. in which 3rd digit is twice of first one. Second digit is the sum of first and third. Fourth digit is twice of third. What is the no?\n\n### Options:\nA. 1224\nB. 1324\nC. 1444\nD. 1524\nE. 1354\n\n### Answer:\nLet the 4-digit no. be \"abcd\"\nc = 2*a\nb=a+c\nd = 2*c => d=4a\nabcd => (a)(a+c)(2a)(4a)\nPossible values of a ll be 1 nd 2... Bcozzz a>2 implies d>10....Digits should ranges between 0 nd 9...\nIf a=1, then c=2,d=4, b=3... The no. is 1324\nIf a=2, then c=4,d=8, b=6... The no. is 2648\nAns : 1324 (or) 2648\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA can complete the job in 4 hours and B can complete the same job in 3 hours. A works for 1 hour and then B joins and both complete the job. What fraction of the job did B complete\n\n### Options:\nA. 1/7\nB. 3/10\nC. 1/2\nD. 5/6\nE. 8/9\n\n### Answer:\nA=1/7\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train 110 m long is running with a speed of 60 km/hr. In what time will it pass a man who is running at 6 km/hr in the direction opposite to that in which the train is going?\n\n### Options:\nA. 7\nB. 6\nC. 8\nD. 2\nE. 4\n\n### Answer:\nSpeed of train relative to man = 60 + 6 = 66 km/hr.\n= 66 * 5/18 = 55/3 m/sec.\nTime taken to pass the men = 110 * 3/55\n= 6 sec.\nAnswerB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAt a certain committee meeting only associate professors and assistant professors are present. Each associate professor has brought 2 pencils and 1 chart to the meeting, while each assistant professor has brought 1 pencil and 2 charts. If a total of 10 pencils and 5 charts have been brought to the meeting, how many people are present?\n\n### Options:\nA. 5\nB. 7\nC. 8\nD. 9\nE. 10\n\n### Answer:\nSay there are 'A' associate professors. So we have 2A pencils and A charts.\nSay there are 'B' assistant professors. So we have B pencils and 2B charts.\nTotal pencils are 10 so 2A + B = 10\nTotal charts are 11 so A + 2B = 5\nAdd both: 3A + 3B = 15 so A + B = 5\nTotal number of people = 5\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMark has a rectangular driveway with a line painted diagonally across. The length of the driveway is 6 feet longer than its width. If the total area of the driveway is 40 square feet, what is the length of the painted line (in feet)?\n\n### Options:\nA. Between 9 and 10\nB. Between 10 and 11\nC. Between 11 and 12\nD. Between 12 and 13\nE. Between 13 and 14\n\n### Answer:\nTo solve this, we first need to set up an equation for the area of the room. If x is the width, then we have\nx(x + 6) = 40. By putting the equation in standard form, we get x^2+6x-40=0. By using the quadratic formula, we get roots of 4 and -10. We know that x is the width, and x+6 is the length, so by using the roots, we get 4 as the width (x), and 10 as the length (x+5).\nOnce we have this, we can use the Pythagorean Theorem to solve for the diagonal. Plugging in the length and width, we will get d^2=4^2+10^2\n=16+100\n=116\nThe square root of 97 is more than 10, since 10^2 = 100. Going up a number, we can compute 11^2 = 121 >116. Therefore, the length of the diagonal must be between 10 and 11.\nThe correct answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train runs across a post in 15 seconds and across a platform of length 100m in 25 seconds. Determine the length of this train:\n\n### Options:\nA. 137\nB. 150\nC. 287\nD. 167\nE. 172\n\n### Answer:\nExplanation:\nLet us assume for this question that the length of train is x metres and it is assumed to be running at the speed of y m/sec.\nA pole is assumed as a point object.\n=>Time taken by the train to pass the pole= x/y\n=>15=x/y\n=>y=x/15\nNow, the train passes the platform which is 100 m in length in 25 seconds.\n=>x+100/y=25\n=>x+100/25=y\nEquating speed generated from both cases:\nx+100/25=x/15\nTherefore x = 150 metres.\nANSWER: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind compound interest on $ 16000 at 15% per annum for 2 years 4 months, compounded annually.\n\n### Options:\nA. 6109\nB. 6209\nC. 6218\nD. 6107\nE. 6100\n\n### Answer:\nTime = 2 years 4 months = 2(4/12) years = 2(1/3) years.\nAmount = $ [16000 X (1+\u00ad(15/100))2 X (1+((1/3)*15)/100)]\n=$ [16000 * (23/20) * (23/20) * (21/20)]\n= $ 22218\t.\n:. C.I. = Rs. (22218 - 16000) = $ 6218\nAnswer C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe end of a blade on an airplane propeller is 20 feet from the center. If the propeller spins at the rate of 1,320 revolutions per second, how many miles will the tip of the blade travel in one minute? (1 mile = 5,280 feet)\n\n### Options:\nA. 200\u03c0\nB. 240\u03c0\nC. 600\u03c0\nD. 480\u03c0\nE. 1,200\u03c0\n\n### Answer:\nDistance traveled in 1 revolution = 2\u03c0r= 2\u03c020/5280\nRevolutions in one second= 1320\nRevolutions in 60 seconds (one minute)= 1320*60\nTotal distance traveled= total revolutions *distance traveled in one revolution\n1320*60 *2\u03c020/5280= 600\u03c0\nC is the answer\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf it is true that x > -3 and x < 7, which of the following must be true?\n\n### Options:\nA. x > 3\nB. x < -7\nC. x < 3\nD. -3 < x < 7\nE. none of the above.\n\n### Answer:\nthe range is -3 < x < 7\nA. x > 3 - no because x can be between -3 < x < 3\nB. x < -7 - no because the values of x are always >-7\nC. x < 3 - no because x can be between 3 < x < 7\nD. -3 < x < 7 - true because x can be between -3 < x < 7\nE. none of the above.\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe largest three digit number which is a perfect cube, is:\n\n### Options:\nA. 125\nB. 999\nC. 343\nD. 512\nE. 729\n\n### Answer:\nExplanation:\n9*9*9 = 729\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA is thrice as efficient as B and is, therefore, able to finish a piece of work 10 days earlier than B. In how many days A and B will finish it together?\n\n### Options:\nA. 7 days\nB. 6 days\nC. 9 days\nD. 5 days\nE. 4 days\n\n### Answer:\nWC = 3:1\nWT = 1:3\nx 3x\n1/x \u2013 1/3x = 1/10\nx = 20/3\n3/20 + 1/20 = 1/5 => 5 days\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf watches bought at prices ranging from Rs 200 to Rs 350 are sold at prices ranging from Rs 300 to Rs 425. What is the greatest possible profit that might be made in selling eight watches?\n\n### Options:\nA. Rs 900\nB. Rs 800\nC. Rs 1,800\nD. Rs 2,800\nE. None of these\n\n### Answer:\nProfit would be maximum if watches are brought for Rs 200 and sold for Rs 425\nProfit = Rs (425 - 200) = Rs 225\nProfit of 8 watches = Rs 225 x 8 = Rs 1,800\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many digits are in the number 50^8 \u00d7 8^3 \u00d7 11^2?\n\n### Options:\nA. 22\nB. 20\nC. 19\nD. 18\nE. 17\n\n### Answer:\ncalculate the Number of 0's through the powers of 10\n50^8 \u00d7 8^3 \u00d7 11^2 = (5^2*2)^8*2^9*11^2 = 5^16*2^17*11^2 = 2*11^2*10^16 = 242*10^16\nHence we would have 16 trailing 0's and the three digits from 242\nTotal digits = 3 + 16 = 19\nCorrect Option: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf air is called green , green is called blue, blue is called purple, sky is called yellow, yellow is called water and water is called pink, then what is the color of clear sky ?\n\n### Options:\nA. Blue\nB. Sky\nC. Water\nD. Yellow\nE. Purple\n\n### Answer:\nExplanation:\rThe colour of clear sky is 'blue' and as given, 'purple' is called 'sky'.\rSo, the colour of clear sky is 'purple'.\rAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n10% of the inhabitants of village having died of cholera.,a panic set in , during which 25% of the remaining inhabitants left the village. The population is then reduced to 4050. Find the number of original inhabitants.\n\n### Options:\nA. 600\nB. 6500\nC. 6000\nD. 6500\nE. 7000\n\n### Answer:\nLet the total number of orginal inhabitants be x.\n((75/100))*(90/100)*x)=4050 \uf0f3 (27/40)*x=4050\nx=((4050*40)/27)=6000.\nANSWER C 6000\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man can row with a speed of 15 kmph in still water. If the stream flows at 5 kmph, then the speed in downstream is?\n\n### Options:\nA. 22 kmph\nB. 24 kmph\nC. 20 kmph\nD. 27 kmph\nE. 83 kmph\n\n### Answer:\nM = 15\nS = 5\nDS = 15 + 5 = 20\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMercury travels around the sun at a speed of approximately 30 miles per second. The approximate speed is how many miles per hour?\n\n### Options:\nA. 108,000\nB. 96,000\nC. 84,000\nD. 72,000\nE. 60,000\n\n### Answer:\n30 * 3600 = 108,000\nThe answer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe product X of two prime numbers is between 15 and 90. If one of the prime numbers is greater than 2 but less than 6 and the other is greater than 13 but less than 25, then X =\n\n### Options:\nA. 18\nB. 29\nC. 37\nD. 44\nE. 85\n\n### Answer:\nOption BC can be ruled out as they themselves are prime numbers\n18 = 2*9 = 3*6 >> Ignore\n44 = 2 * 22 = 4 * 11 >> Ignore\n85 = 5*17 >> Answer\nAnswer = E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a group of 70 children and 10 youngsters, each child got sweets that are 15% of the total number of children and each youngster got sweets that are 25% of the total number of children. How many sweets were there?\n\n### Options:\nA. 1140\nB. 1160\nC. 1180\nD. 1200\nE. 1040\n\n### Answer:\nNumber of sweets each child got = 15% of 80 = 15/100 * 80 = 12.\nNumber of sweets 80 children got = 70 * 12 = 840.\nNumber of sweets each youngster got = 25% of 80 = 25/100 * 80 = 20.\nNumber of sweets 10 youngsters got = 10 * 20 = 200.\nTotal number of sweets = 840 + 200 = 1040.\nE)\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA circular logo is enlarged to fit the lid of a jar. The new diameter is 10 per cent larger than the original. By what percentage has the area of the logo increased?\n\n### Options:\nA. 50\nB. 80\nC. 100\nD. 125\nE. 21\n\n### Answer:\nLet old diameter be 4 , so radius is 2\nOld area = 4\u03c0\nNew diameter is 4.4 , so radius is 2.2\nNew area = 4.84\u03c0\nIncrease in area is 0.84\u03c0\n% increase in area = 0.84/4*100\nSo, % increase is 21%\nAnswer will be (E)\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA 1200 m long train crosses a tree in 120 sec, how much time will I take to pass a platform 700 m long?\n\n### Options:\nA. 288\nB. 190\nC. 188\nD. 188\nE. 12\n\n### Answer:\nL = S*T\nS= 1200/120\nS= 10 m/Sec.\nTotal length (D)= 1900 m\nT = D/S\nT = 1900/10\nT = 190 Sec\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 0 < a < b and k = (5a + 5b)/b , which of the following must be true?\n\n### Options:\nA. k < 2\nB. k < 7\nC. k < 9\nD. k > 9\nE. k > 11\n\n### Answer:\nPlease follow posting guidelines (link in my signature) especially writing the correct topic title. Also do mention the source of the question if you select the tag:Source-Other Please Specify.\nAs for your question, it is very simple and straightforward with number plug in.\nAssume a=1 and b=2 as a < b, you get k = (5+10)/2 = 7.5. This eliminates all but option C , making it the correct answer.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA rectangle having length 105 cm and width 40 cm. If the length of the rectangle is increased by twenty five percent then how much percent the breadth should be decreased so as to maintain the same area.\n\n### Options:\nA. 25%\nB. 19.23%\nC. 40%\nD. 75%\nE. None of these\n\n### Answer:\nExplanation :\nSolution: (25/(105+25) * 100)% = 19.23%\nAnswer : B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA boat having a length 3 m and breadth 2 m is floating on a lake. The boat sinks by 1 cm when a man gets on it. The mass of man is :\n\n### Options:\nA. 12 kg\nB. 60 kg\nC. 72 kg\nD. 96 kg\nE. None of these\n\n### Answer:\nSolution\nVolume of water displaced = (3 \u00d7 2 \u00d7 0.01) m3 = 0.06 m3.\n\u2234 Mass of man = Volume of water displaced \u00d7 Density of water\n= (0.06 \u00d7 100)kg = 60 kg.\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nD and E are two points respectively on sides AB and AC of triangle ABC such that DE is parallel to BC. If the ratio of area of triangle ADE to that of the trapezium DECB is 144:25 and BC=13 cm, then find the length of DE.\n\n### Options:\nA. 12\nB. 13\nC. 14\nD. 11\nE. 15\n\n### Answer:\nABC and ADE are similar triangles.\nSo (side of ABC/side of ADE)^2=25/169\nside of ABC/side of ADE = 5/13\nSo the length of DE = 5\nAnswer - C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA bag contains nine white and four red balls. Two balls are picked at random from the bag. What is the probability that they both are different color?\n\n### Options:\nA. 5/8\nB. 6/13\nC. 5/16\nD. 5/13\nE. 5/11\n\n### Answer:\nTwo balls can be picked from thirteen balls in 13C\u00e2\u201a\u201a ways.\nWe select one white ball and one red ball from five white balls and four red balls. This can be done \u00e2\u0081\u00b5 ways.\nThe required probability = (9 * 4) = 36/78 = 6/13\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man can row with a speed of 24 kmph in still water. If the stream flows at 6 kmph, then the speed in downstream is?\n\n### Options:\nA. 27\nB. 23\nC. 30\nD. 28\nE. 12\n\n### Answer:\nM = 24\nS = 6\nDS = 24 + 6 = 30\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nGordon is twice as old as Tony was when Gordon was as old as Tony is now. The combined age of Gordon and Tony is 112 years. How old are Gordon and Tony now?\n\n### Options:\nA. Gordon 64 and Tony 48\nB. Gordon 74 and Tony 38\nC. Gordon 84 and Tony 48\nD. Gordon 64 and Tony 58\nE. None of the above\n\n### Answer:\nWhen Gordon was 48, Tony was 32(ie half the age Gordon is now).\nAnswer : A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe line Z represented by which of the following equation does not intersect with the line represented by y = 3x^2+5x+1\n\n### Options:\nA. y = 2x^2+5x+1\nB. y = x^2+5x+2\nC. y = 3x^2+5x+2\nD. y = 3x^2+7x+2\nE. y = x^2+7x+1\n\n### Answer:\nconcept of slope for linesparabolas are different. Bunuel, please correct if I am wrong. Also please help to solve this problem if its a GMAT type question.\nThe general form of parabolic equ. is y^2= 4ax which implies the axis is x or x^2 = 4ay where axis is y.\nWe have a similar form as x^2 = 4ay.\nhere the vertex is origin.\nSo if we have same values of x and y but constant term changes then we will have parallel parabolas.\nThis is same as for straight line Z which are parallel for different values of constant term c\nax + by +c1 = 0 and ax +by+ c2 =0\nWe have quadratic equations. These equations when drawn give parabolas, not lines. The question is: which of the following parabolas does not intersect with the parabola represented by y=3x^2+5x+1.C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOf the 5 numbers, whose average is 200, the first is one-fourth of the sum of the last 4. The first number is?\n\n### Options:\nA. 200\nB. 80\nC. 78.63\nD. 56.98\nE. 67.85\n\n### Answer:\nTotal of 5 numbers = 5 * 200 = 1000\nLet total of last 4 numbers = x\n1st number = x/4\nx+ x/4 = 1000\n5x = 4000 => x = 800\n1st number = 800/ 4 = 200\nAnswer : A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn what time will a train 100 meters long cross an electric pole, if its speed is 72 km/hr\n\n### Options:\nA. 5 seconds\nB. 2.8 seconds\nC. 3.5 seconds\nD. 2.5 seconds\nE. 2.6 seconds\n\n### Answer:\nFirst convert speed into m/sec\nSpeed = 72*(5/18) = 20 m/sec\nTime = Distance/speed\n= 100/20 = 5 seconds\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind large number from below question The difference of two numbers is 1345. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder\n\n### Options:\nA. 1234\nB. 1596\nC. 1350\nD. 1467\nE. 1635\n\n### Answer:\nLet the smaller number be x. Then larger number = (x + 1345).\nx + 1345 = 6x + 15\n5x = 1330\nx = 266\nLarge number = 266+1330 = 1596\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how many ways Chief Minister and Minister be elected from a team of 12 members?\n\n### Options:\nA. 125\nB. 131\nC. 132\nD. 145\nE. 147\n\n### Answer:\nTo do this, if captain is elected first, then we have 12 ways of doing this.\nFor election of vice-captain, we have only 11 ways left, coz 1 way is already consumed. (Situations like this is called dependent situation. One selection depends upon other selection.)\nSo, the ans is 12*11 = 132 ways.\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA palindrome is a number that reads the same forward and backward, such as 120. How many odd, 4-digit numbers are palindromes?\n\n### Options:\nA. 40\nB. 55\nC. 50\nD. 90\nE. 2500\n\n### Answer:\nA palindrome is a number that reads the same forward and backward. Examples of four digit palindromes are 1221, 4334, 2222 etc\nYou basically get to choose the first two digits and you repeat them in opposite order. Say, you choose 45 as your first two digits. The next two digits are 54 and the number is 4554.\nAlso, you need only odd palindromes. This means that you need an odd digit at the end i.e. 1/3/5/7/9. This means that you need to start the number with an odd digit. Only then will it end with an odd digit.\nIn how many ways can you pick two digits such that the first one is an odd digit?\nThe first digit can be selected in 5 ways.(1/3/5/7/9)\nThe second digit can be selected in 10 ways.(0/1/2/3...8/9)\nTotal = 5*11 = 55 ways\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA watch passes through three hands and each person gains 25%. If the third person sells it for $62.50, what did the first person pay for it?\n\n### Options:\nA. $24\nB. $28\nC. $32\nD. $36\nE. $40\n\n### Answer:\n1.25*1.25*1.25 * original price = 62.5\n(5/4)^3 * original price = 62.5\noriginal price = 64*62.5 / 125 = $32\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAn engineer designed a ball so that when it was dropped, it rose with each bounce exactly one-half as high as it had fallen. The engineer dropped the ball from a 16-meter platform and caught it after it had traveled 40 meters. How many times did the ball bounce?\n\n### Options:\nA. 2\nB. 6\nC. 7\nD. 8\nE. 9\n\n### Answer:\nDivision of total distance travelled will be 16+16+8\nAns:2\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf f and t are integers and f^2 \u2013 t^2 is an odd integer, which of the following must be an even integer?\nI. f + t + 2\nII. f^2 + 2ft + t^2\nIII. f^2 + t^2\n\n### Options:\nA. None\nB. I only\nC. II only\nD. III only\nE. I, II, and III\n\n### Answer:\nf^2\u2013t^2 is an odd integer means that either f is even and t is odd or f is odd and t is even.\nCheck all options:\nI. f + t + 2 --> even+odd+even=odd or odd+even+even=odd. Discard;\nII. f^2 + 2ft + t^2 --> even+even+odd=odd or odd+even+even=odd. Discard;\nIII. f^2 + t^2 --> even+odd=odd or odd+even=odd. Discard.\nAnswer: A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nPositive integer y is 50 percent of 25 percent of positive integer x, and y percent of x equals 100. What is the value of y?\n\n### Options:\nA. 50\nB. 125\nC. 200\nD. 1,000\nE. 2,000\n\n### Answer:\ny = 50% of 25 % 0f x\n= x/8\nand\ny/100 of x = 100\ny /100 *8y =100\ny = 125\nAnswer - B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf n is a natural number, then (6n2 + 6n) is always divisible by?\n\n### Options:\nA. 6 and 12 both\nB. 6 only\nC. 12 only\nD. 6 or 12\nE. None\n\n### Answer:\n(6n2 + 6n) = 6n(n + 1), which is always divisible by 6 and 12 both, since n(n + 1) is always even.\nA)\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a group of hats consisting of only blue hats, green hats, and purple hats, the ratio of blue hats to green hats to purple hats is 7:4:12. If there are a total of 138 hats in this group, how many of these hats are not blue?\n\n### Options:\nA. 96\nB. 42\nC. 48\nD. 64\nE. 76\n\n### Answer:\nB:G:P = 7:4:12 --> total of 23 parts.\nNot blue = (G + P)/(total)*92 = 16/23*138 = 96.\nAnswer: A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe Racing magic takes 40 seconds to circle the racing track once. The Charging bull makes 40 rounds of the track in an hour. If they left the starting point together, how many minutes will it take for them to meet at the starting point for the second time?\n\n### Options:\nA. 3\nB. 6\nC. 9\nD. 12\nE. 15\n\n### Answer:\nTime taken by Racing magic to make one circle = 40 seconds\nTime taken byCharging bullto make one circle = 60 mins / 40 = 1.5 mins = 90 seconds\nLCM of 90 and 40 seconds = 360 seconds = 6 mins\nTime taken for them to meet at the starting point for the second time = 6 mins *2 = 12 mins\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n90 percent of your marbles are a solid color. 5 percent of your marbles are solid yellow. What percentage of your marbles are a solid color other than yellow?\n\n### Options:\nA. 5\nB. 15\nC. 85\nD. 90\nE. 95\n\n### Answer:\n90 percent are solid colors including solid yellow. 5 percent are solid yellow. 90% - 5% = 85%, so 85 percent are a solid color other than yellow => (C)\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nCity A's population is 68000, decreasing at a rate of 80 people per year. City B having population 42000 is increasing at a rate of 120 people per year. In how many years both the cities will have same population?\n\n### Options:\nA. 130years\nB. 140years\nC. 150years\nD. 160years\nE. 170years\n\n### Answer:\ncity A population = 68000\ncity B population = 42000\n68000 decreasing at a rate 0f 80p = 42000 increasing at a rate of 120p\n68000-80p=42000+120p\n200p=26000\np=130years\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a cube of dimension 4 by 4 by 4 is cut into 1 by 1 by 1 after painting it by red color then which of the following is/are true.\nI) Ratio of number of painted surfaces of resultant cubes to total number of surfaces is 1/4\nII) Number of cubes having no faces pointed is equal to number of cubes having three faces painted.\nIII) Number of cubes having 2 faces painted is same as number of cubes having one face painted\n\n### Options:\nA. None\nB. II and III\nC. II only\nD. I, II & III\nE. I & III only\n\n### Answer:\nLong explanation, probably too detailed\nHypercube facts (n=3 for a cube):\n2^n vertices 2n\u22121n edges 2+E\u2212V faces\nFor a cube: 8 vertices, 12 edges and 6 faces\nLet G=4be the size of the original cube.\nI) Ratio of number of painted surfaces of resultant cubes to total number of surfaces is 1/4\nThere is 1 large cube with 6 sides of G2 painted faces.\nThere is G3x1 cubes with 6 sides of surface area 1.\n1\u00d76\u00d7G^2/G3\u00d76\u00d71=G^2/G^3=G\u22121=1/4\nTrue\nII) Number of cubes having no faces pointed is equal to number of cubes having three faces painted.\nThere are always 8 vertices on a cube, each vertex is the only 1x1 block which has 3 coloured faces.\nInside the cube, there is a secondary unpainted cube. Each side of this unpainted cube is equal to the size of the original cube minus two (on each axis, there will be two 1x1 cubes on the exterior of the larger cube). The size of this cube is (G\u22122)3\nThere are (G\u22122)3( cubes with 0 sides painted. =23=8\nThere are V=23 cubes with 3 sides painted =8\nTrue\nIII) Number of cubes having 2 faces painted is same as number of cubes having one face painted\nThere are 12 edges on a cube. Each edge consists of G cubes, two of which are the vertices of the cube (and have 3 colours), the rest have two colours.\nOn each exterior face, there is a square of (G\u22122) cubes, surrounded by 4 vertex cubes and (G\u22122)\u00d74 edge cubes.\nEach square consists of (G\u22122)^2 coloured faces. There is 1 square per face.\nThere are (G\u22122)\u00d7E cubes with 2 sides painted. =2\u00d712=24\nThere are (G\u22122)2\u00d7F cubes with 1 side painted. =22\u00d76=24\nTrue\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain truck uses 18 gallons of diesel fuel in traveling 260 miles. In order for the truck to travel the same distance using 10 gallons of diesel fuel, by how many miles per gallon must the truck\u2019s fuel mileage be increased?\n\n### Options:\nA. 8\nB. 9\nC. 12\nD. 11\nE. 27\n\n### Answer:\nThere are two sets 18G1 gallons and 10G2 gallons details given.\n18 gallons covering 260 miles\nThen 1 G1 is used to cover 15 miles.\nNow for 10 G2 covering 260 miles.\nthen 1 G2 is used to cover 26 miles.\nThere must 26- 15 = 11 miles per gallon increment is needed for 10 gallons to improve the mileage to cover 270 miles.\nIMO D is correct answer.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAn employer has 5 applicants for a programming position and 4 applicants for a manager position. If the employer must hire 3 programmers and 2 managers, what is the total number of ways the employer can make the selection?\n\n### Options:\nA. a) 1,490\nB. b) 132\nC. c) 60\nD. d) 68\nE. e) 23\n\n### Answer:\n5C3 * 4C2 = 60. Answer C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the area of a parallelogram with base 24 cm and height 12 cm?\n\n### Options:\nA. 297 cm2\nB. 384 cm2\nC. 672 cm2\nD. 267 cm2\nE. 288 cm2\n\n### Answer:\nArea of a parallelogram\n= base * height\n= 24 * 12\n= 288 cm2\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nEdward invested five-ninths of his money at an annual rate of 2r% compounded semi-annually, and the remaining money at an annual rate of r% compounded annually. If after one year, Edward\u2019s money had grown by one-thirds, the value of r is equal to which of the following?\n\n### Options:\nA. 10%\nB. 15%\nC. 20%\nD. 25%\nE. 33%\n\n### Answer:\nX=Amount invested\n5/9*X*(1+2r/2)^2+4/9*X*(1+r)=4/3X\nSet X = 9 because we can pick any value\n5*(1+r)^2+4(1+r)=12\n5r^2+14r-3=0\nHere you can use the formula for roots of a quadratic, but it is faster to guess and check using the answers\n5*(1/5)^2+14(1/5)-3=5*(1/25)+14/5-3=1/5+14/5-3=0\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich of the following values is the greatest\n\n### Options:\nA. a) 11% of 89\nB. b) 22% of 78\nC. c) 33% of 67\nD. d) 65% of 45\nE. e) 44% of 56\n\n### Answer:\nAre you sure that you checked the answer key correctly? I just signed up forVeritas(haven't started yet, not until March) but I have access to the materials and the answer key I'm looking at says D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA cicketer Has a certain average for 10 innings, In the eleventh inning, he scorod 88 runs, thereby increasing his average by 6 runs. His new average is\n\n### Options:\nA. 18 runs\nB. 28 runs\nC. 48 runs\nD. 42 runs\nE. 46 runs\n\n### Answer:\nExplanation:\nLet average for 10 innings be x. Then,\n(10x + 88)/11 = x + 6 => 11x + 66 = 10x + 88 => x = 22.\nNew average = (x + 6) = 28 runs.\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man can row upstream at 25 kmph and downstream at 37 kmph, and then find the speed of the man in still water?\n\n### Options:\nA. 86\nB. 67\nC. 31\nD. 15\nE. 17\n\n### Answer:\nUS = 25\nDS = 37\nM = (37 + 25)/2\n= 31\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the simple interest on $1200 for 5 years at 20% per annum?\n\n### Options:\nA. $1200\nB. $1000\nC. $500\nD. $1100\nE. $1500\n\n### Answer:\nSI = PTR/100\n= 1200*5*20/100 = $1200\nAnswer is A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTap 'A' can fill the tank completely in 4 hrs while tap 'B' can empty it by 8 hrs. By mistake, the person forgot to close the tap 'B', As a result, both the tapes, remained open. After 4 hrs, the person realized the mistake and immediately closed the tap 'B'. In how much time now onward, would the tank be full?\n\n### Options:\nA. 2\nB. 3\nC. 1/2\nD. 1/4\nE. 5\n\n### Answer:\nExplanation :\nRate of filling tap A = 1/4 per hr\nRate of emptying of tap B = 1/8 per hr\nWhen both the taps remain open, the effective rate of filling\n= 1/4 - 1/8 = 1/8 of the tank\nHence in 4 hr, the tank must have been full to the\nExtent of 4 x 1/8 = 1/2 Capacity\nRemaining volume = 1/2 capacity\nNow emptying tap is closed rate of filling would be 1/4 per hr\nTime reqd. to fill = Empty volume/Filling rate\n= (1/2)/(1/4) = 2 hrs\nAnswer : A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA jogger running at 9 km/hr along side a railway track is 280 m ahead of the engine of a 120 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger?\n\n### Options:\nA. 67 sec\nB. 89 sec\nC. 36 sec\nD. 87 sec\nE. 40 sec\n\n### Answer:\nSpeed of train relative to jogger = 45 - 9 = 36 km/hr.\n= 36 * 5/18 = 10 m/sec.\nDistance to be covered = 280 + 120 = 400 m.\nTime taken = 400/10\n=40 sec.\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRohit paid $4,000 for 100 shares of stock X and $2,000 for 100 shares of stock Y. He later sold the same shares of both stocks, gaining 3/5 the amount he paid for stock Y. If the prices he had paid for the stocks had been reversed and everything else remained the same, then the net result would have been:\n\n### Options:\nA. A Gain of 1.4 times as much\nB. A Gain of 3 times as much\nC. A Gain of 2 times as much\nD. A Gain of 1.5 times as much\nE. A Loss of 2 times as much\n\n### Answer:\nA = 4000; B = 2000; Profit = (3/5)*2000 = 1200\nAfter prices are reversed:\nA = 2000; B =4000; Profit = (3/5)*4000 = 2400\n2400 --> Gain of 2 times 1200\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf y > 0, (2y)/20 + (3y)/10 is what percent of y?\n\n### Options:\nA. 40%\nB. 50%\nC. 60%\nD. 70%\nE. 80%\n\n### Answer:\nsoln:-\ncan be reduced to y/10+3y/10 =2y/5=40%\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAn inspector rejects 0.04% of the meters as defective. How many will he examine to reject 2?\n\n### Options:\nA. A)1500\nB. B)2000\nC. C)2500\nD. D)5000\nE. E)3100\n\n### Answer:\nLet the number of meters to be examined be x\nThen, 0.04% of x = 2\n(4/100)*((1/100)*x = 2\nx = 5000\nAnswer is D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAn express traveled at an average speed of 100 km/hr, stopping for 4 min after every 75 km. How long did it take to reach its destination 450 km from the starting point ?\n\n### Options:\nA. 8 hrs 29 min\nB. 4 hrs 50 min\nC. 2 hrs 28 min\nD. 6 hrs 28 min\nE. 1 hrs 28 min\n\n### Answer:\nExplanation:\nTime taken to cover 450 km = 450/100 = 4 hrs 30 mins\nNumber of stoppages = 450/75 - 1 = 5\nTotal time of stoppages = 4 x 5 = 20 min\nHence, total time taken = 4 hrs 50 min.\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the sum of first 10000 numbers in the series -1,+1,-1,+1,-1.......??\n\n### Options:\nA. 0\nB. 1\nC. 2\nD. 3\nE. 4\n\n### Answer:\n-1+1=0\nand for 10000 numbers it will form 5000 pairs\nso 5000*0 = 0\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe product X of two prime numbers is between 17 and 60. If one of the prime numbers is greater than 2 but less than 6 and the other is greater than 13 but less than 25, then X =\n\n### Options:\nA. 18\nB. 29\nC. 37\nD. 44\nE. 57\n\n### Answer:\nOption BC can be ruled out as they themselves are prime numbers\n18 = 2*9 = 3*6 >> Ignore\n44 = 2 * 22 = 4 * 11 >> Ignore\n57 = 3*19 >> Answer\nAnswer = E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nPat will walk from intersection X to intersection Y along a route that is confined to the square grid of four streets and three avenues shown in the map above. How many routes from X to Y can Pat take that have the minimum possible length?\n\n### Options:\nA. 6\nB. 8\nC. 10\nD. 14\nE. 16\n\n### Answer:\nIn order the length to be minimum Pat should only go UP and RIGHT: namely thrice UP and twice RIGHT.\nSo combination of UUURR: # of permutations of 5 letters out of which there are 3 identical U's and 2 identical R's is 5!/3!2!=10.\nAnswer: C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the area of a square field whose diagonal of length 22 m?\n\n### Options:\nA. 287\nB. 269\nC. 270\nD. 242\nE. 230\n\n### Answer:\nd2/2 = (22 * 22)/2\n= 242\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA car owner buys petrol at Rs.7.50, Rs. 8 and Rs. 8.50 per litre for three successive years. What approximately is the average cost per litre of petrol if he spends Rs. 4000 each year?\n\n### Options:\nA. Rs. 7.98\nB. Rs. 8\nC. Rs. 8.50\nD. Rs. 9\nE. Rs. 9.50\n\n### Answer:\npetrol used in 1st yr = 4000/7.5 = 533.33 ltr\npetrol used in 2nd yr = 4000/8 = 500 ltr\npetrol used in 3 rd year = 4000/8.5= 470.59 ltr\nTotal petrol used for Rs.12000(4000/- for each yaer) in 3rd yrs = 1503.92 ltr\nAverage cost per litre = 12000/1503.92 = Rs 7.98\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFrom a number of mangoes, a man sells half the number of existing mangoes plus 1 to the first customer, then sells 1/3rd of the remaining number of mangoes plus 1 to the second customer, then 1/4th of the remaining number of mangoes plus 1 to the third customer and 1/5th of the remaining number of mangoes plus 1 to the fourth customer. He then finds that he does not have any mangoes left. How many mangoes did he have originally?\n\n### Options:\nA. 12\nB. 14\nC. 15\nD. 13\nE. 16\n\n### Answer:\nLet the No. of mangoes that the man had originally = X\nNo. of mangoes sold balance\n1st customer = (X/2) + 1 (X - 2)/2\n2nd customer = (X - 2)/6 + 1 (X - 5)/3\n3rd customer = (X - 5)/12 + 1 (X - 9)/4\n4th customer = (X - 9)/20 + 1 0\n(X - 9)/20 + 1= (X - 9)/4 => X = 14\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 854 in 4 years. The sum is?\n\n### Options:\nA. 688\nB. 798\nC. 698\nD. 699\nE. 998\n\n### Answer:\nS.I. for 1 year = Rs. (854 - 815) = Rs. 39.\nS.I. for 3 years = Rs.(39 x 3) = Rs. 117.\nPrincipal = Rs. (815 - 117) = Rs. 698.\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe total number of even prime number is\n\n### Options:\nA. 0\nB. 1\nC. 2\nD. 3\nE. None of these\n\n### Answer:\nSolution\nThere is only one prime number, namely 2.\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind large number from below question The difference of two numbers is 1515. On dividing the larger number by the smaller, we get 16 as quotient and the 15 as remainder\n\n### Options:\nA. 1209\nB. 1615\nC. 1245\nD. 1300\nE. 1635\n\n### Answer:\nLet the smaller number be x. Then larger number = (x + 1515).\nx + 1515 = 16x + 15\n15x = 1500\nx = 100\nLarge number = 100+1515 = 1615\nAnswer : B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nohn invested part of his savings into a investment X that earned a profit of 10% and the rest of the savings into an investment Y that lost 15%. If John neither made a profit nor a loss, then what fraction of his savings was invested in investment X?\n\n### Options:\nA. 3/5\nB. 2/3\nC. 7/10\nD. 3/4\nE. 4/5\n\n### Answer:\nX(1+10/100) + Y(1-15/100) = X+Y\nthis gives 2X = 3Y\nor X/Y = 3/2\nSo, fraction invested in X = 3/5\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA vendor sells 30 percent of the apples he had and throws away 20 percent of the remainder. The next day, the vendor sells 50 percent of the remaining apples and throws away the rest. In total, what percent of his apples does the vendor throw away?\n\n### Options:\nA. 40\nB. 42\nC. 44\nD. 46\nE. 48\n\n### Answer:\nLet x be the original number of apples.\nOn day one, the vendor throws away (0.2)(0.7)x=0.14x.\nThe remaining apples are (0.8)(0.7)x = 0.56x.\nOn day two, the vendor throws away (0.5)(0.56)x=0.28x.\nThe vendor throws away a total of 0.14x + 0.28x = 0.42x.\nThe vendor throws away 42 percent of the apples.\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 7/10 of a pencil is green, 4/5 of the remaining is gold and the remaining 1/2 is white, what is the total length of the pencil?\n\n### Options:\nA. 5\nB. 3\nC. 1\nD. 4\nE. 2\n\n### Answer:\nGreen is 7/10 Gold is 4/5 which can also be written as 8/10\rWhite is 1/2 which can also be written as 5/10\r7/10 + 8/10 + 5/10= 2\rAnswer is E) 2\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAn eight-digit telephone number consists of exactly two zeroes. One of the digits is repeated thrice. Remaining three digits are all distinct. If the first three digits (from left to right) are 987, then find the probability of having only one 9, one 8 and one 7 in the telephone number.\n\n### Options:\nA. 1/18\nB. 1/20\nC. 1/10\nD. 5/47\nE. 5/45\n\n### Answer:\nExplanation :\nCase A: There is only one 9, one 8 and one 7 in the number.\nHence there has to be one digit from {1,2,3,4,5,6} repeated thrice.\nTotal number of ways in which such a number can exist is :\n=>6C1\u00d75!/(3!\u00d72!).\n=60.\nCase B: One of the three digit {9,8,7} is repeated thrice.\nHence, there will be one digit from {1,2,3,4,5,6}.\nTotal number of ways in which such a number can exist:\n=>3C1\u00d76C1\u00d75!/(3!\u00d72!).\n=>540\nTotal possible telephone numbers:\n=60+540=600.\nHence the required Probability is 60/600 = 1/10.\nAnswer : C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA committee is reviewing a total of 20x black-and-white films and 6y color films for a festival. If the committee selects y/x% of the black-and-white films and all of the color films, what fraction X of the selected films are in color?\n\n### Options:\nA. 1/130\nB. 1/5\nC. 3/13\nD. 10/13\nE. 30/31\n\n### Answer:\nIt's y/xpercentnot y/x.\nIf x=20 and y=10. Then:\n20x=400 black-and-white films;\n6y=60 color films.\ny/x%=10/20%=0.5% of the black-and-white films, so 2 black-and-white films and all 60 color films, thus total of 62 films were selected.\nColor films thus compose X= 60/62=30/31 of the selected films.\nAnswer: E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA sells his goods 50% cheaper than B but 50% dearer than C. The cheapest is?\n\n### Options:\nA. 33.9\nB. 33.6\nC. 33.3\nD. 33.1\nE. 33.2\n\n### Answer:\nLet B = 100\nA = 50\nC * (150/100) = 50\n3C = 100\nC = 33.3 then 'C' Cheapest\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain city with a population of 120,000 is to be divided into 11 voting districts , and no district is to have a population that is more than 10 percent greater than the population of any other district What is the minimum possible population that the least populated district could have ?\n\n### Options:\nA. a) 10,700\nB. b) 10,000\nC. c) 10,900\nD. d) 11,000\nE. e) 11,100\n\n### Answer:\nLet x = number of people in smallest district\nx*1.1 = number of people in largest district\nx will be minimised when the number of people in largest district is maximised\n10*x*1.1 = 11x = total number of people in other districts\nSo we have 11x + x = 120k\nx = 10,000\nAnswer : B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe ratio between the speeds of two trains is 8 : 9. If the second train runs 405 kms in 5 hours, then the speed of the first train is\n\n### Options:\nA. 87.5 km/h\nB. 72 km/h\nC. 70 km/h\nD. 80 km/h\nE. 81 km/h\n\n### Answer:\nB\n72 km/h\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA customer went to a shop and paid a total of $30, out of which $1.28 was for sales tax on taxable purchases. If the tax rate was 8%, then what was the cost of the tax free items?\n\n### Options:\nA. $9.84\nB. $10.68\nC. $11.26\nD. $12.72\nE. $13.54\n\n### Answer:\nThe total cost was $30.\nThe tax was $1.28\nLet the original price of the taxable items = x\nGiven that tax rate = 8%\n0.08x = 1.28\nx = $16\nThe cost of the tax free items was $30 - $16 - $1.28 = $12.72\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nArabica coffee costs $0.3 per ounce while Robusta coffee costs $0.2 per ounce. If the blend of Arabica and Robusta costs $0.22per ounce, what is the share of Arabica in this blend?\n\n### Options:\nA. 20%\nB. 24%\nC. 30%\nD. 33%\nE. 40%\n\n### Answer:\na= amount of arabica coffee\n1-a = amount of robusta coffee. because if you subtract a from the 1 ounce, the remaining amount is robusta\ntherefore:\n.3a + .2(1-a) = .22\n.3a + .2 - .2a = .22\na= .2\ntherefore: .2/1 ounce = 20%. Therefore, the answer should be A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe dimensions of a room are 25 feet * 15 feet * 12 feet. What is the cost of white washing the four walls of the room at Rs. 8 per square feet if there is one door of dimensions 6 feet * 3 feet and three WINDOWS of dimensions 4 feet * 3 feet each?\n\n### Options:\nA. 4000\nB. 345\nC. 5673\nD. 7248\nE. 8566\n\n### Answer:\nArea of the four walls = 2h(l + b)\nSince there are doors and WINDOWS, area of the walls = 2 * 12 (15 + 25) - (6 * 3) - 3(4 * 3) = 906 sq.ft.\nTotal cost = 906 * 8 = Rs. 7248\nAnswer: Option D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the unknown term X,8,6,2,-4, -12\n\n### Options:\nA. 2\nB. 4\nC. 6\nD. 8\nE. 9\n\n### Answer:\nX,8,6,2,-4, -12\ni guess each differ in d range of 2\n8 - 8 = 0\n8 - 6 = 2\n6 - 2 = 4\n2 - 6 = -4\n-4 - 8 = -12\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf P is a prime number greater than 3, find the remainder when P^2 + 13 is divided by 12.\n\n### Options:\nA. 6\nB. 1\nC. 0\nD. 2\nE. 7\n\n### Answer:\nEvery prime number greater than 3 can be written 6N+1 or 6N-1.\nIf P = 6N+1, then P^2 + 13 = 36N^2 + 12N + 1 + 13 = 36N^2 + 12N + 12 + 2\nIf P = 6N-1, then P^2 + 13 = 36N^2 - 12N + 1 + 13 = 36N^2 - 12N + 12 + 2\nWhen divided by 12, it must leave a remainder of 2.\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the perimeter of \u0394ACD is 9+3\u221a3, what is the perimeter of equilateral triangle \u0394ABC?\n\n### Options:\nA. 9\nB. 18\u22123\u221a3\nC. 18\nD. 18+3\u221a3\nE. 27\n\n### Answer:\nThe altitude of an equilateral triangle is side*\u221a3/2.\nAs perimeter of triangle ACD is 9+3\u221a3, AC + CD + AD =\n(side+side/2+side*\u221a3/2) = 9 + 3\u221a3 or side =6.\nPerimeter of equilateral triangle, ABC is 3(side) or 18.\nAnswer:(OptionC)\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA customer bought a product at the shop. However, the shopkeeper increased the price of the product by 20% so that the customer could not buy the required amount of the product. The customer managed to buy only 80% of the required amount. What is the difference in the amount of money that the customer paid for the second purchase compared to the first purchase?\n\n### Options:\nA. 10%\nB. 8%\nC. 6%\nD. 4%\nE. 2%\n\n### Answer:\nLet x be the amount of money paid for the first purchase.\nThe second time, the customer paid 0.8(1.2x)=0.96x.\nThe difference is 4%.\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA and B can do a piece of work in 12 days and 16 days respectively. Both work for 3 days and then A goes away. Find how long will B take to complete the remaining work?\n\n### Options:\nA. 6\nB. 7\nC. 5\nD. 9\nE. 3\n\n### Answer:\n3/12 + (3 + x)/16 = 1\nx = 9 days\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow much time will take for an amount of Rs. 450 to yield Rs. 81 as interest at 4.5% per annum of simple interest?\n\n### Options:\nA. 7\nB. 4\nC. 5\nD. 3\nE. 2\n\n### Answer:\nTime = (100 * 81) / (450 * 4.5) = 4 years'\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA grocer has a sale of Rs. 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 6500?\n\n### Options:\nA. 4991\nB. 5991\nC. 5491\nD. 6991\nE. 6491\n\n### Answer:\nTotal sale for 5 months = Rs. (6435 + 6927 + 6855 + 7230 + 6562) = Rs. 34009.\nRequired sale = Rs. [ (6500 x 6) - 34009 ]\n= Rs. (39000 - 34009)\n= Rs. 4991\nAnswer: Option A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOut of four numbers ,the average of first three is 16 and that of the last three is 15. If the last number is 20,the first number is :\n\n### Options:\nA. 22\nB. 23\nC. 77\nD. 99\nE. 27\n\n### Answer:\nExplanation:\nLet the numbers be a,b,c,d\nGiven, a + b + c = 48, b + c + d = 45\nNow, d = 20\nthus, b + c + 20 = 45 \u21d2 b + c = 25\nPutting the value of b + c in a + b + c = 48\na + 25 = 48 \u21d2 a = 23\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many positive 5-digit integers have the odd sum R of their digits?\n\n### Options:\nA. 9*10^2\nB. 9*10^3\nC. 10^4\nD. 45*10^3\nE. 9*10^4\n\n### Answer:\nWe are looking at numbers between 10000 and 99999 both inclusive.\nThere are 90000 numbers.\nNow for\n10000 : sum of digits is odd;\n10001 :sum of digits is even;\n10002 : sum of digits is odd ; so on and so forth. So every alternate number is such that the sum of digit is odd.\n(Exception for the above statement :\nWhen it is 10009 the sum is even and for 10010 again the sum is even; But if you look at 10019 :sum is odd; 10020 : sum is odd\nand this pattern continues so basically the number of odd sum of digits and even sum of digits are equal)\nThis means exactly half of the numbers will have odd sum of their digits. i.e 45000\nAnswer :D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMonika purchased a pressure cooker at 9/10th of its selling price and sold it at 8% more than its Selling Price. Find her gain percent.\n\n### Options:\nA. 10\nB. 20\nC. 25\nD. 15\nE. 18\n\n### Answer:\nLet the Selling Price be $X. then Cost Price = $9x/10, Receipt=108% of $x= $27x/25 Gain=$(27x/25*9x/10)=$(108x-90x/100)=$18x/100\nGain%=(18x/100*10/9x*100)%=20%\nAnswer B) 20.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nExpress a speed of 70 kmph in meters per second?\n\n### Options:\nA. 10 mps\nB. 19.44 mps\nC. 97.44 mps\nD. 17.44 mps\nE. 18.44 mps\n\n### Answer:\n70* 5/18\n= 19.44 mps\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nLloyd normally works 7.5 hours per day and earns $5.50 per hour. For each hour he works in excess of 7.5 hours on a given day, he is paid 1.5 times his regular rate. If Lloyd works 10.5 hours on a given day, how much does he earn for that day?\n\n### Options:\nA. $33.75\nB. $47.25\nC. $51.75\nD. $54.00\nE. $66.00\n\n### Answer:\nDaily working hour*Regular Rate + Overtime*Increased Rate\n7.5*5.5+ 3*5.5*1.5=66.00\nAnswer E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFour car rental agencies A, B, C and D rented a plot for parking their cars during the night. A parked 15 cars for 12 days, B parked 12 cars for 20 days, C parked 18 cars for 18 days and D parked 16 cars for 15 days. If A paid Rs. 1305 as rent for parking his cars, what is the total rent paid by all the four agencies?\n\n### Options:\nA. Rs. 4500\nB. Rs. 4800\nC. Rs. 5250\nD. Rs. 7134\nE. None of these\n\n### Answer:\nThe ratio in which the four agencies will be paying the rents = 15 * 12 : 12 * 20 : 18 * 18 : 16 * 15\n= 180 : 240 : 324 : 240 = 45 : 60 : 81 : 60\nLet us consider the four amounts to be 45k, 60k, 81k and 60k respectively.\nThe total rent paid by the four agencies = 45k + 60k + 81k + 60k= 246k\nIt is given that A paid Rs. 1305\n45k = 1305 => k = 29\n246k = 246(29) = Rs. 7134\nThus the total rent paid by all the four agencies is Rs. 7134.\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf after 700 grams of water were added to the 24%-solution of alcohol, the strength of the solution decreased by one-third, how much of the 24%-solution was used?\n\n### Options:\nA. 180 grams\nB. 220 grams\nC. 250 grams\nD. 350 grams\nE. 1400 grams\n\n### Answer:\nI too think 1400 grams should be the answer.\nMy reasoning is\nThe h20 content in 700 gms of water is 1\nh20 content in 24% solution is 0.76\nResulting new solution's concentration decreases by one third means. Now it becomes 16% solution which means h20 content is 0.84\nLet amount of solution be X\nThen the equation can be set up\n700*1 + 0.76X = 0.84 (X+700)\n0.08X = 112\n8X = 11200\nX = 1400 (ANS E)\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA person buys an article at Rs.500. At what price should he sell the article so as to make a profit of 50%?\n\n### Options:\nA. 750\nB. 882\nC. 772\nD. 652\nE. 271\n\n### Answer:\nCost price = Rs.500\nprofit = 50% of 500 = Rs.250\nSelling price = Cost price + Profit\n= 500 + 250 = 750\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOf the d students at a certain college, x are studying French and y are studying German. If w are studying both French and German, which of the following expresses the number of students at the college not studying either French or German ?\n\n### Options:\nA. d + w- x- y\nB. d - w- x- y\nC. d- w - x + y\nD. w + x + y- z\nE. w - x - y - z\n\n### Answer:\n{Total} = {French} + {German} - {Both} + {Neither}\nd = x + y - w + {Neither}\n{Neither} = d + w - x - y.\nAnswer: A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n96% of the population of a village is 23040. The total population of the village is?\n\n### Options:\nA. 16800\nB. 1689\nC. 6795\nD. 24000\nE. 12654\n\n### Answer:\nExplanation:\nX * (96/100) = 23040\nX = 240 * 100\nX = 24000\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn 10 years, A will be twice as old as B was 10 years ago. If A is now 9 years older than B, the present age of B is\n\n### Options:\nA. 27\nB. 66\nC. 39\nD. 28\nE. 21\n\n### Answer:\nLet B's present age = x years. Then, A's present age = (x + 9) years.\n(x + 9) + 10 = 2(x - 10)\n=> x + 19 = 2x - 20\n=> x =39.\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average monthly salary of 10 employees in an organisation is Rs. 1600. If the manager's salary is added, then the average salary increases by Rs. 100. What is the manager's monthly salary?\n\n### Options:\nA. Rs.3601\nB. Rs.3618\nC. Rs.2700\nD. Rs.3619\nE. Rs.3610\n\n### Answer:\nManager's monthly salary\n= Rs. (1700 * 11 - 1600 * 10)\n= Rs. 2700 Answer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are three secretaries who work for four departments. If each of the four departments have one report to be typed out, and the reports are randomly assigned to a secretary, what is the probability that all three secretary are assigned at least one report?\n\n### Options:\nA. 8/9\nB. 64/81\nC. 12/27\nD. 16/81\nE. 5/9\n\n### Answer:\n\"We hav\u00e9 total possibilities N =3^4\"\nWhat are these total possibilities? They are the ways in which the 4 reports can be distributed among 3 secretaries so that all reports may go to one secretary, the reports may be distributed among 2 secretaries or they may be distributed among all 3. So such cases are included (4, 0, 0), (0, 4, 0), (2, 2, 0), (1, 3, 0), (1, 1, 2), etc\nIn how many ways can you give 4 reports to only 1 secretary? You choose the secretary who will get the reports in 3C1 = 3 ways\nIn how many ways can you give 4 reports to only 2 secretaries? Choose the 2 secretaries in 3C2 ways. Each secretary must get at least one report so you can distribute them in 2 ways:\n'1 and 3' - Choose one report in 4C1 ways and give it to one secretary in 2C1 ways. The other secretary gets the other 3 reports.\nor\n'2 and 2' - Choose 2 reports in 4C2 ways and give to the first secretary. The other secretary gets the other two reports.\nTotal number of ways is 3C2 * (4C1*2C1 + 4C2) = 42 ways\nNote that in your method 2^4 is incorrect. It includes the ways in which all 4 reports go to one secretary.\nSo this means that in 3 + 42 = 45 ways, at least one secretary gets no report. In the rest of 81 - 45 = 36 ways, each secretary gets at least one report.\nRequired Probability = 36/81 = 12/27\nANS:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn 1995 a certain store had 1,800 tools in stock that had been purchased for $30 each. If 1,000 of these tools were sold in 1995 for $50 each and the remaining 800 were sold in 1996 for $60 each, how many greater was the gross profit on the tools sold in 1996 than the gross profit on those sold in 1995?\n\n### Options:\nA. $0\nB. $4,000\nC. $8,000\nD. $32,000\nE. $40,000\n\n### Answer:\nThe keyword here isGross Profit:\nGross Profit = (Selling Price - Original Price)*(# of Items Sold)\nSo lets figure out what the Gross Profit for 1995:\nGP1995 = (50-30)*(1000) = 20000\nAnd the Gross Profit for 1996:\nGP1996 = (60-30)*(800) = 24000\nSo the difference would be:\n24000-20000 = 4000\nANSWER: B. 4000\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n62467 \u00d7 9998 = ?\n\n### Options:\nA. 624545037\nB. 627745452\nC. 624545077\nD. 624545066\nE. 625454211\n\n### Answer:\nD\n624545066\n62467 \u00d7 9998 = 62467 \u00d7 (10000 - 2)\n= 62467 \u00d7 10000 - 62467 \u00d7 2\n= 624670000 - 124934\n= 624545066\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe edges of a cuboid are 4 cm, 5 cm and 6 cm. Find the volume of the cuboid?\n\n### Options:\nA. 120\nB. 388\nC. 278\nD. 298\nE. 271\n\n### Answer:\n4*5*6 = 120\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe price of a Maruti car rises by 30% while the sales of the car come down by 20%. What is the percentage change in the total revenue?\n\n### Options:\nA. -4%\nB. -2%\nC. +4%\nD. +2%\nE. None of these\n\n### Answer:\nExplanation :\nLet initial price of Maruti car be Rs. 100.\nAs price increases 30%, the price of car become 100 + 30% of 100 = Rs. 130.\nDue to increase in price, sales is down by 20 %.\nIt means, it is going to make 20% less revenue as expected after increment of price.\nSo, new revenue = 130 - 20 % of 130 = Rs 104.\nThe initial revenue was Rs 100 which becomess Rs 104 at the end.\nIt means there is 4% increment in the total revenue.\nAnswer : C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are 10 seats around a circular table. If 8 men and 2 women have to seated around a circular table, such that no two women have to be separated by at least one man. If P and Q denote the respective number of ways of seating these people around a table when seats are numbered and unnumbered, then P : Q equals?\n\n### Options:\nA. 10:1\nB. 9:1\nC. 72:1\nD. 8:1\nE. None of these\n\n### Answer:\nExplanation :\nInitially we look at the general case of the seats not numbered.The total number of cases of arranging 8 men and 2 women, so that women are together:\u21d2 8\u00d7!2!The number of cases where in the women are not together:\u21d29!\u2212(8!\u00d72!)=QNow, when the seats are numbered, it can be considered to a linear arrangement and the number of ways of arranging the group such that no two women are together is:\u21d2 10!\u2212(9!\u00d72!)But the arrangements where in the women occupy the first and the tenth chairs are not favourable as when the chairs which are assumed to be arranged in a row are arranged in a circle, the two women would be sitting next to each other.The number of ways the women can occupy the first and the tenth position:=8!\u00d72!The value of P =10!\u2212(9!\u00d72!)\u2212(8!\u00d72!)Thus P : Q = 10 : 1\nAnswer : A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average age of father and his two sons is 18 Years. Five years ago, the average age of the two sons was 11 Years. If the difference between the ages of the two sons is four years, what is the present age of the father?\n\n### Options:\nA. 22\nB. 24\nC. 25\nD. 28\nE. 49\n\n### Answer:\nThe total present age of father and two sons is 3x18 = 54 yrs\nThe total present age of sons is (11+5) X 2 = 32Years\nso, present age of father is 54 \u00e2\u20ac\u201c 32 = 22 yrs\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 25th of August in a year is Thursday, the number of Mondays in that month is\n\n### Options:\nA. 4\nB. 5\nC. 2\nD. 3\nE. 1\n\n### Answer:\nExplanation:\nGiven that 25th August = Thursday\nHence 29th August = Monday\nSo 22nd,15th and 8th and 1st of August also will be Mondays\nNumber of Mondays in August = 5\nAnswer: Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe price of a T.V. set worth Rs. 20000 is to be paid in 20 installments of Rs. 1000 each. If the rate of interest be 6% per annum, and the first installment be paid at the time of purchase, then the value of the last installment covering the interest as well will be?\n\n### Options:\nA. 22678\nB. 26699\nC. 26788\nD. 19000\nE. 26711\n\n### Answer:\nMoney paid in cash = Rs. 1000\nBalance payment = (20000 - 1000) = Rs. 19000\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a renowned city, the average birth rate is 7 people every two seconds and the death rate is 1 people every two seconds. Estimate the size of the population net increase that occurs in one day.\n\n### Options:\nA. 32,300\nB. 172,800\nC. 468,830\nD. 338,200\nE. 259,200\n\n### Answer:\nEvery 2 seconds, 6 persons are added (7-1). Every second 3 persons are added.\nIn a day 24hrs = 24 * 60 Minutes = 24 * 60 * 60 = 86400 seconds.\n86400 * 3 = 259200\nOption E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA ladies hostel had provision of food for 300 women for 45 days. After 10 days, 275 women left the hostel. The number of days for which the remaining food will last is:\n\n### Options:\nA. 420\nB. 430\nC. 450\nD. 480\nE. 425\n\n### Answer:\nExplanation :\nAfter 10 days : 300 women had food for 35 days.\nSuppose 25 women had food for x days.\nNow, Less women, More days (Indirect Proportion)\n25 : 300 :: 35 : x\n=> 25 x x = 300 x 35\n=> x = 300 x 35 / 25\n=> x = 420\nAnswer : A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe cost price of 13 articles is equal to the selling price of 11 articles. Find the profit percent?\n\n### Options:\nA. 18 2/19%\nB. 18 2/11%\nC. 18 2/91%\nD. 18 2/81%\nE. 18 2/121%\n\n### Answer:\n13 CP = 11 SP\n11 --- 2 CP\n100 --- ? =>18 2/11%\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA \u201cSophie Germain\u201d prime is any positive prime number p for which 2p + 1 is also prime. The product of all the possible units digits of Sophie Germain primes greater than 6 is\n\n### Options:\nA. 3\nB. 7\nC. 21\nD. 189\nE. 198\n\n### Answer:\nIn that case, the Sophie prime numbers greater than 6 are 7,11,23,47,59, .. which yields units digit as 1,3,7 and 9\nProduct would be 1 x 3 x 7x9 =189 Answer should be D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average weight of 8 person's increases by 3.5 kg when a new person comes in place of one of them weighing 65 kg. What is the weight of the new person?\n\n### Options:\nA. 93 Kg\nB. 50 Kg\nC. 85 Kg\nD. 80 Kg\nE. 60 KG\n\n### Answer:\nExplanation:\nTotal increase in weight = 8 \u00c3\u2014 3.5 = 28\nIf x is the weight of the new person, total increase in weight = x\u00e2\u02c6\u201965\n=> 28 = x - 65\n=> x = 28 + 65 = 93\nAnswer: Option A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are m cities. What is the number of airlines that connected 2 different cities (airline from city A to city B is different with airline from city B to city A)?\n\n### Options:\nA. n(n-1)\nB. m(m-1)\nC. n(n-1)/2\nD. n(n+1)/2\nE. n2\n\n### Answer:\nFirst of all, the possible number of airlines is m. Then, the possible number of airlines departing from one city to another becomes (m-1). Hence, the answer is m(m-1), which makes A an answer choice.\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf x^2=3x+1, then x^3 = ?\n\n### Options:\nA. 8x+2\nB. 10x+3\nC. 6x+1\nD. 2x+3\nE. 6x+4\n\n### Answer:\nx^2 = 3x+1\nx^3 = x*x^2 = x*(3x+1) = 3x^2 + x = 3(3x+1)+x = 10x+3\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSet A = {1, 2, 3, 4, 5, 6, y}\nWhich of the following possible values for y would cause Set A to have the smallest standard deviation?\n\n### Options:\nA. 1\nB. 2.5\nC. 3\nD. 3.5\nE. 7\n\n### Answer:\nSD is minimum or least when the number is closest to the mean of the existing numbers\nCalculating mean of the rest of the numbers gives mean = (approx)3.6\nSo the new number should be near to the mean and only number closest to the mean is 3.5\nAnswer: Option D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nPam and Stanley packed several boxes with reams of paper. While both packed, Pam packed 40% of the boxes. After Pam stopped, Stanley packed the same number of boxes that he had packed while working with Pam. What is the ratio of the number of boxes Pam packed to the number of boxes Stanley packed?\n\n### Options:\nA. 2 to 6\nB. 1 to 3\nC. 3 to 5\nD. 3 to 4\nE. 3 to 2\n\n### Answer:\nCorrect Answer: A\nSolution: A. We know that when Pam and Stanley were both working, the ratio was 2 boxes by Pam to 3 boxes by Stanley. We also know that Stanley continued working after Pam stopped. He packed as many boxes alone as he had packed whlie working with Pam, effectively doubling his number of boxes. Thus, the ratio of Pam's boxes to Stanley's boxes is 2 to 6. Answer A is correct.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA person covered one-fourth of the total distance at 26 kmph and remaining distance at 24 kmph. What is the average speed for the total distance?\n\n### Options:\nA. 21 (1/36)kmph\nB. 21 (1/3)kmph\nC. 21 (8/3)kmph\nD. 27 (1/3)kmph\nE. 25 (1/3)kmph\n\n### Answer:\nLet the total distance be x km\ntotal time taken = (x/4)/16 + (3x/4)/24\n= x/64 + x/32 = 3x/64\nAverage speed = x/(3x/64)\n= 64/3kmph\n= 21 (1/3)kmph.\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSteel company has four empty trucks that will head out in the morning, all four to the same destination. The clerk has four different boxes to ship to that same destination. All four boxes could go on any one of the trucks, or the boxes could be split up into any groupings and given to the trucks in any combinations (ie. two to one truck, one to another, and one to another). In how many different ways could the boxes be put on the four trucks?\n\n### Options:\nA. 16\nB. 64\nC. 256\nD. 576\nE. 4096\n\n### Answer:\nMAGOOSHOFFICIAL SOLUTION:\nSteel company has four empty trucks that will head out in the morning, all four to the same destination.Where we put one box has absolutely no bearing on where we put any of the other boxes. The placement of the four boxes is completely independent of one another. For each box, we have four choices.\nN = 4*4*4*4 = 16*16 = 256\nAnswer = (C)\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRoger can read a book in k minutes. What part of the book can he read in 7 minutes? (k>8)\n\n### Options:\nA. 8+k\nB. k/8\nC. 7/k\nD. (k+ 8)/k\nE. (k-8) / k\n\n### Answer:\nLet's sayk = 24\nThat is, it takes 24 minutes to read the entire book.\nSo, in 8 minutes, Roger can read1/3of the book\nSo, we're looking for the answer choice that yields an OUTPUT of1/3whenk = 24\nA) 8+24=32ELIMINATE\nB) 8/24=1/3KEEP\nC)24/8 =3ELIMINATE\nD) (24+ 8)/24=32/24 = 4/3ELIMINATE\nE) (24-8) /24=16/24 = 2/3ELIMINATE\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn the formula V = 1/(2r)^4, if r is halved, then V is multiplied by?\n\n### Options:\nA. 16\nB. 8\nC. 1\nD. 1/8\nE. 1/64\n\n### Answer:\nSay r=2 => V1 = 1/256\nwhen r=1; V2 = 1/16\nV2 = 16*V1.\nAnswer : A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the units digit of 23^2 * 17^2 * 39^2?\n\n### Options:\nA. 1\nB. 3\nC. 5\nD. 7\nE. 9\n\n### Answer:\nThe units digit of 23^2 is the units digit of 3*3 = 9 which is 9.\nThe units digit of 17^2 is the units digit of 7*7 = 49 which is 9.\nThe units digit of 39^2 is the units digit of 9*9 = 81 which is 1.\nThe units digit of 9*9*1 = 81 is 1.\nThe answer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a contest, a bowl contains 5 keys, one of which will open a treasure chest and Four of which will not. If a contestant selects the key that opens the treasure chest, she wins the contents of that chest. If priya is allowed to draw two keys, simultaneously and at random, from the bowl as the first contestant, what is the probability that she wins the prize?\n\n### Options:\nA. 2/7\nB. 2/5\nC. 2/9\nD. 2/11\nE. 2/13\n\n### Answer:\nThe total possibilities existing while withdrawing two keys are: 5C2 = 10\nFor priya to win, 4 combinations exist assuming Key 1 to unlock the treasure E.g(1,2), (1,3)....(1,4)\nP = 4/10= 2/5\nOption B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSome part of a 50% solution of acid was replaced with an equal amount of 30% solution of acid. If, as a result, 40% solution of acid was obtained, what part of the original solution was replaced?\n\n### Options:\nA. 1/5\nB. 1/4\nC. 1/2\nD. 3/4\nE. 4/5\n\n### Answer:\nOriginal Acid : Total ratio = 50:100 . let us say you replaced x part of this. So you are left with (1-x) of the original. So volume of acid left is (1-x)50.\nin the new solution.. you added x of 30% solution. i.e 30x acid\n(1-x)50 + 30x is the volume of acid. The total volume is still 100. And this concentration is 40%\n[(1-x)50 + 30x] / 100 = 40/100\nsolve to get x=1/2\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe purchase price of an article is $48. In order to include 25% of cost for overhead and to provide $12 of net profit, the markup should be\n\n### Options:\nA. 50%\nB. 25%\nC. 35%\nD. 40%\nE. 45%\n\n### Answer:\nCost price of article = 48$\n% of overhead cost = 25\nNet profit = 12 $\nWe need to calculate % markup\nNet profit as % of cost price = (12/48)*100 = 25%\nTotal markup should be = 25 + 25 = 50%\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nExcluding stoppages, the speed of a bus is 54 km/hr and including stoppages, it is 45 km/hr. For how many minutes does the bus stop per hour?\n\n### Options:\nA. 11 min\nB. 10 min\nC. 37 min\nD. 17 min\nE. 16 min\n\n### Answer:\nDue to stoppages, it covers 9 km less.\nTime taken to cover 9 km\n= 9/54 * 60 = 10 min.\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nthree men invested sum. and their ratio is 5:7:6. profit is 900.then b's share\n\n### Options:\nA. 2000\nB. 2100\nC. 2200\nD. 350\nE. 2400\n\n### Answer:\nb's share =7/18*900=350\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nShekar scored 76, 65, 82, 62 and 85 marks in Mathematics, Science, Social studies, English and Biology respectively. What are his average marks?\n\n### Options:\nA. 74\nB. 69\nC. 75\nD. 85\nE. 90\n\n### Answer:\nExplanation :\nAverage= (76+65+82+62+85)/5 = 370/5 =74\nHence average=74\nAnswer : A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhen the integer k is divided by 7, the remainder is 6. Which of the following expressions below when divided by 7, will have a remainder of 5?\nI. 4k + 2\nII. 6k + 4\nIII. 8k + 3\n\n### Options:\nA. I only\nB. II only\nC. III only\nD. I and II only\nE. I, II and III\n\n### Answer:\nk = 7j + 6\n4k + 2 = 28j + 24 + 2 = 28j + 21 + 5\n6k + 4 = 42j + 36 + 4 = 42j + 35 + 5\n8k + 3 = 56j + 48 + 3 = 56j + 49 + 2\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA reduction of 25% in the price of oil enables a house wife to obtain 5kgs more for Rs.800, what is the reduced price for kg?\n\n### Options:\nA. 55\nB. 66\nC. 40\nD. 88\nE. 12\n\n### Answer:\n800*(25/100) = 200 ---- 5\n? ---- 1 => Rs.40\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many digits are in (8\u00d710^14)(10\u00d710^10)?\n\n### Options:\nA. 24\nB. 25\nC. 26\nD. 27\nE. 28\n\n### Answer:\nhe question simplifies to (8\u00d710^14)(10^11)\n=> 8*10^25\n=> Will contain 25 zeros +1 digit 8\n=>26\nAns C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n180,131,95,70,?\n\n### Options:\nA. 42\nB. 43\nC. 54\nD. 40\nE. 39\n\n### Answer:\n180 - 131 = 49 = 7^2\n131 - 95 = 36 = 6^2\n95 - 70 = 25 = 5^2\nso we can write\n70 - x = 16 = 4^2 , where x is the next number\nx = 70 - 16 = 54\nso the next number will be 54\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n50% of the apartments in a certain building have windows and hardwood floors. 25% of the apartments without windows have hardwood floors. If 40% of the apartments do not have hardwood floors, what V percent of the apartments with windows have hardwood floors?\n\n### Options:\nA. 10\nB. 16 2/3\nC. 40\nD. 50\nE. 83 1/3\n\n### Answer:\nyup you need to construct a matrix\nX********| Windows'|No Windows'''| total\nhardFl****'|50*****''|10*********'|60\nNot hardFl*|10******|30*********'|40\nTotal*****|60******'|40*********'|100\nso V percent of the apartments with windows have hardwood floors = 50/60 *100\n= 83 1/3\nso E is the answer.[/u]\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAbby and Bobby type at constant rates of 70 words per minute and 60 words per minute, respectively. Bobby begins typing before Abby and has typed 600 words when Abby begins typing at 1:30 pm. If they continue typing at their respective rates, at what time will Abby have typed exactly 200 more words than Bobby?\n\n### Options:\nA. 1:40 PM\nB. 2:50 PM\nC. 2:00 PM\nD. 2:10 PM\nE. 2:20 PM\n\n### Answer:\nSay time needed for Abby to type 200 more words than Bobby is t. In that time she would type 70t words and Bobby would type 60t words.\nNow, total words typed by Bobby would be 600+60t and we want that number to be 200 less than 70t: 600+60t=70t-200 --> t=80.\n1:30 PM + 80 minutes = 2:50 PM.\nAnswer: B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAn equilateral triangle T2 is formed by joining the mid points of the sides of another equilateral triangle T1. A third equilateral triangle T3 is formed by joining the mid-points of T2 and this process is continued indefinitely. If each side of T1 is 30 cm, find the sum of the perimeters of all the triangles.\n\n### Options:\nA. 180 cm\nB. 220 cm\nC. 240 cm\nD. 270 cm\nE. 300 cm\n\n### Answer:\nWe have 30 for first triangle, when we join mid-points of first triangle we get the second equilateral triangle then the length of second one is 15 and continues.\nSo we have 30,15,7.5,...\nWe have ratio = 1/2, and it is GP type.\nSum of infinite triangle is a/1-r = 30/1-(1/2) = 60\nEquilateral triangle perimeter is 3a = 3*60 = 180.\nSo option A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA number is selected at random from the first 40 natural numbers. What is the probability that the number is a multiple of either 2 or 21?\n\n### Options:\nA. 21/40\nB. 2/5\nC. 7/15\nD. 4/15\nE. 11/30\n\n### Answer:\nNumber of Multiples of 2 from 1 through 40 = 40/2 = 20\nNumber of Multiples of 21 from 1 through 40 = 40/21 = 1\nNumber of Multiples of 2 and 21 both from 1 through 40 = Number of Multiples of 21*2(=42) = 0\nTotal favourable cases = 20 + 1 - 0 = 21\nProbability = 21 / 40\nAnswer: option A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA palindrome is a number that reads the same front-to-back as it does back-to-front (e.g. 202, 575, 1991, etc.) p is the smallest integer greater than 100 that is both a prime and a palindrome. What is the sum of the digits of p?\n\n### Options:\nA. 3\nB. 4\nC. 5\nD. 6\nE. 7\n\n### Answer:\nGiven that p is smallest integer greater than 200 - assume there is a 3-digit that satisfies the above conditions. Let the number be xyx ; question asks us the values of 2x+y\nWe can straight away cross out options A) and D) - sum of digits 3 or 6 implies it is divisible by 3 ---> we know that p is a prime number\nComing to option B) 2x + y = 4 --> only x = 2 and y = 0 satisfy this equation ( x> 2 will never give sum of digits = 4) ; but 202 is divisible by 2 ; we know that p is a prime number\nSimilarly option C) 2x+y = 5 --> only x = 2 and y = 1 satisfy this equation ( x> 2 will never give sum of digits = 5) ; but 212 is divisible by 2 ; we know that p is a prime number\nTherefore answer option should be E ---> can be verified by taking 2x+y = 7 ---> x = 3 and y = 1 ; gives 313\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThink of a number, divide it by 6 and add 5 to it. The result is 17. What is the number thought of?\n\n### Options:\nA. 24\nB. 72\nC. 297\nD. 267\nE. 29\n\n### Answer:\nExplanation :\n17-5 = 12\n12 x 6 = 72\nAnswer : B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nYou have a bag of 9 letters: 3 Xs, 3 Ys and 3 Zs. You are given a box divided into 3 rows and 3 columns for a total of 9 areas. How many Q different ways can you place one letter into each area such that there are no rows or columns with 2 or more of the same letter?\n\n### Options:\nA. 5\nB. 6\nC. 9\nD. 12\nE. 18\n\n### Answer:\nConsider one particular arrangement of the first row: XYZ, then we can construct only two boxes with so that no rows or columns have 2 or more of the same letter:\nXYZ\nYZX\nZXY\nAnd:\nXYZ\nZXY\nYZX\nNow, the first row itself can be arranged in 3!=6 ways (since there are three distinct letter), hence the total number of boxes possible Q is 2*6=12.\nAnswer: D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo unbiased coins are tossed.What is the probability of getting at most one head?\n\n### Options:\nA. 2/3\nB. 1\nC. 3/4\nD. 2\nE. 1/2\n\n### Answer:\ns={hh,tt,ht,th}\ne=event of getting at most one head.\ne={tt,ht,th}.\np(e)=n(e)/n(s)=3/4\nAnswer is option C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe total marks obtained by a student in Mathematics and Physics is 60 and his score in Chemistry is 20 marks more than that in Physics. Find the average marks scored in Mathamatics and Chemistry together.\n\n### Options:\nA. 40\nB. 30\nC. 25\nD. Data inadequate\nE. None of these.\n\n### Answer:\nLet the marks obtained by the student in Mathematics, Physics and Chemistry be M, P and C respectively.\nGiven , M + C = 60 and C - P = 20 M + C / 2 = [(M + P) + (C - P)] / 2 = (60 + 20) / 2 = 40.\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA tradesman by means of his false balance defrauds to the extent of 28%? in buying goods as well as by selling the goods. What percent does he gain on his outlay?\n\n### Options:\nA. 44%\nB. 48%\nC. 94%\nD. 45%\nE. 64%\n\n### Answer:\ng% = 28 + 28 + (28*28)/100\n= 64%\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo pens and three pencils cost 86. Four pens and a pencil cost 112. What is the difference between the cost of a pen and that of a pencil?\n\n### Options:\nA. 25\nB. 13\nC. 19\nD. Cannot be determined\nE. None of these\n\n### Answer:\nLet the cost of a pen and a pencil be \u2018x\u2019 and \u2018y\u2019 respectively. We have to find (x \u2013 y).\nFrom the question,\n2x + 3y = 86 ..... (i)\n4x + y = 112 ......(ii)\nSubtracting (i) from (ii), we get\n2x \u2013 2y = 26 or, x \u2013 y = 13\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf p and q are positive integers, how many integers are larger than pq and smaller than p(q + 3)?\n\n### Options:\nA. 3\nB. P + 2\nC. p \u2013 2\nD. 3p \u2013 1\nE. 2p + 1\n\n### Answer:\nThe number of integers between x and y, where x>y is (x-y)-1. For example, the number of integers between 1 and 5 is (5-1)-1=3: 2, 3, and 4.\nThus, the number of integers between pq and p(q+3)=pq+3p is (pq+3p-pq)-1=3p-1.\nAnswer: D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf each side of a square is increased by 25%, find the percentage change in its area?\n\n### Options:\nA. 54%\nB. 56%\nC. 56.25%\nD. 58.25%\nE. 59%\n\n### Answer:\nlet each side of the square be a , then area = a x a\nNew side = 125a / 100 = 5a / 4\nNew area =(5a x 5a) / (4 x 4) = (25a\u00b2/16)\nincreased area== (25a\u00b2/16) - a\u00b2\nIncrease %= [(9a\u00b2/16 ) x (1/a\u00b2 ) x 100]% = 56.25%\nanswer :C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat least number must be subtracted from 12702 to get number exactly 99 ?\n\n### Options:\nA. 49\nB. 30\nC. 29\nD. 31\nE. 32\n\n### Answer:\nExplanation:\nDivide the given number by 99 and find the remainder. If you subtract the remainder from the given number then it is exactly divisible by 99.\n99) 12702 (128\n99\n280\n198\n822\n792\n30\nRequired number is 30.\nANSWER IS B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA bowl contains pecans, cashews, and almonds in a ratio of 3 : 4 : 6, respectively. If some of the nuts of one of the three types are removed, which of the following could be the ratio of pecans to cashews to almonds remaining in the bowl? i. 1 : 2 : 3 ii. 2 : 3 : 4 iii. 4 : 7 : 10\n\n### Options:\nA. II only\nB. I,II only\nC. III only\nD. I,III only\nE. I only\n\n### Answer:\ni. The ratio 2 : 3 is the same as the given ratio 4 : 6. If one pecan were removed, the new ratio would be 2 : 4 : 6, or 1 : 2 : 3.\nii. None of the nuts currently have a ratio of 3 : 4. The cashews and almonds do have a ratio of 2 : 3, but there are not enough pecans in the bowl to complete the ratio.\niii. The ratio 4 : 10 is the same as the given ratio 6 : 15. To see this, multiply the ratio by 3/2 . The new ratio is 6 : 10.5 : 15. Unfortunately, this means that there are fewer cashews that this ratio would require. Removing cashews won\u2019t create the desired ratio.\nAnswer : E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo trains of equal are running on parallel lines in the same direction at 48km/hr and 36 km/hr. The faster train passes the slower train in 36 sec. The length of each train is?\n\n### Options:\nA. 50\nB. 88\nC. 60\nD. 55\nE. 22\n\n### Answer:\nLet the length of each train be x m.\nThen, distance covered = 2x m.\nRelative speed = 48 - 36 = 12 km/hr.\n= 12 * 5/18 = 10/3 m/sec.\n2x/36 = 10/3 => x = 60.\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTanya prepared 4 different letters to be sent to 4 different addresses. For each letter she prepared an envelope with its correct address. If the 4 letters are to be put in 4 envelopes at random, what is the probability that only 1 letter will be put into the envelope with its correct address?\n\n### Options:\nA. 1/24\nB. 1/8\nC. 1/4\nD. 1/3\nE. 3/8\n\n### Answer:\nPossible sequences are CIII, ICII, and so on...C=correct, I=incorrect\nTotal possible sequences are 4P1=4 ways.\nLets take the probability of having one particular sequence CIII.\nP = 1/4*2/3*1/2*1 = 1/12.\nSo the probability of having any of the sequence is 4*1/12 =1/3\nANS:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThirty percent of the women in a college class are science majors, and the non-science majors make up 80% of the class. What percentage of the women are science majors if 40% of the class are men?\n\n### Options:\nA. 2%\nB. 5%\nC. 28%\nD. 30%\nE. 45%\n\n### Answer:\n3/k + 2/m = 6/t\nAssuming total # is 100 :\n[Science - Women] will have - 0.3 * 60 = 18\n[Non-Science-Women] will have - 42\n[Science-Men] will have = 20-18 = 2\nS0 18/60 * 100 = 30%\nAnswer - D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a kilometer race, A beats B by 40 meters or 10 seconds. What time does A take to complete the race?\n\n### Options:\nA. 167 sec\nB. 190 sec\nC. 176 sec\nD. 240 sec\nE. 123 sec\n\n### Answer:\nTime taken by B run 1000 meters\n= (1000 * 10)/40 = 250 sec.\nTime taken by A = 250 - 10\n= 240 sec.\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA coin is tossed 4 times. What is the probability a that the number of Heads is equal to the number of Tails?\n\n### Options:\nA. 1/8\nB. 1/4\nC. 3/8\nD. 1/2\nE. 9/16\n\n### Answer:\nWe have to find the probability that we get 2 heads and 2 tails in 4 tosses of the coin.\nUsing the binary formula and defining a head as a success,\nP(2 heads in 4 tosses) = 4C2* (1/2)^2 * (1/2)^2\n= 6/16\na= 3/8\nThe answer is therefore (C)\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn the xy-plane, the points (c, d), (c, -d), and (-c, -d) are three vertices of a certain square. If c < 0 and d > 0, which of the following points R is in the same quadrant as the fourth vertex of the square?\n\n### Options:\nA. (-5, -3)\nB. (-5, 3)\nC. (5, -3)\nD. (3, -5)\nE. (3, 5)\n\n### Answer:\nThe question:In the xy-plane, the points (c, d), (c, -d), and (-c, -d) are three vertices of a certain square.If c < 0 and d > 0,which of the following points R is in the same quadrant as the fourth vertex of the square?\nI marked the tricky part in red. It seems c is anegativenumber and d is a positive number. This means\nVertex #1 = (c, d) is in QII (that is, negative x and positive y)\nVertex #2 = (c, -d) is in QIII (that is, both xy negative)\nVertex #3 = (-c, -d) is in QIV (that is y is negative, but x is positive)\nThat means the last vertex should be in the first quadrant --- the only first quadrant point is (5, 3), answer =E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the greatest number that will divide 150, 230 and 175 leaving 50, 5 and 25 as remainders respectively\n\n### Options:\nA. 19\nB. 17\nC. 32\nD. 9\nE. 8\n\n### Answer:\nExplanation:\nAnswer will be HCF of (150-50, 230-5, 175-25)\nHCF of (100, 225, 150) = 32\nOption C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average age of husband, wife and their child 3 years ago was 27 years and that of wife and the child 5 years ago was 20 years. The present age of the husband is:\n\n### Options:\nA. 35 years\nB. 40 years\nC. 50 years\nD. 45 years\nE. None of these\n\n### Answer:\nSum of the present ages of husband, wife and child = (27 x 3 + 3 x 3) years = 90 years.\nSum of the present ages of wife and child = (20 x 2 + 5 x 2) years = 50 years.\nHusband's present age = (90 - 50) years = 40 years.\nAnswer: Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe integer x is divisible by both 9 and 36. Which of the following must be an integer?\n\n### Options:\nA. x/16\nB. x/36\nC. x/25\nD. x/46\nE. x/24\n\n### Answer:\nPrime factorization of 9 = 3^2\nPrime factorization of 36= 3^2*2^2\nLCM of 9 and 36 = 3^2 * 2^2 = 36\nTherefore x/36 must be an integer\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf t>0.9, which of the following options can be the value of t?\n\n### Options:\nA. 0.9^2\nB. \u221a(0.9)\nC. 0.09\nD. 0.9\nE. 0.9^3\n\n### Answer:\nLets take a few examples\nWhen .2 is squared it gives .04\nwhen .5 is squared it gives .25\nWhen .9 is squared it gives .81\nSo raising a fraction to its power of 2 or 3 only reduces the value of the fraction\nThis is because\n.2 = 2/10\n.2^2= 4/100\n.2^3=8/1000\nSince the denominator gets an extra 0 each time u increase the power , it is going to drag the value down\nBut if you just think about the opposite case :\nThen we can see , if squaring a fraction diminish its value, then taking the square root of it will again increase its value\nthat is \u221a(0.04) will give you back 0.2\nso \u221a(0.04) > 0.04\nso obviously diminishing the power will appreciate the value\nSo t \u221a(0.9) > 0.9\nHence Correct Answer is (B)\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA trader mixes 80 kg of tea at 15 per kg with 20 kg of tea at cost price of 20 per kg. In order to earn a profit of 35%, what should be the sale price of the mixed tea?\n\n### Options:\nA. 23.75\nB. 21.6\nC. 20\nD. 19.2\nE. None of these\n\n### Answer:\nC.P. of mixture = 80\u00d715+20\u00d720 /80+20=16\n\u2234 S.P. = (100+35)/100\u00d716=21.6\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRs.20 is the true discount on Rs. 260 due after a certain time. What will be the true discount on the same sum due after half of the former time, the rate of interest being the same?\n\n### Options:\nA. 10.4\nB. 11\nC. 14.8\nD. 15.4\nE. none\n\n### Answer:\nSol.\nS.I. on Rs. (260 - 20) for a given time = Rs. 20.\nS.I. on Rs. 240 for half the time = Rs. 10.\nT.D. on Rs. 250 = Rs. 10.\n\u2234 T.D. on Rs. 260 = Rs. [10/250 * 260] = Rs. 10.40\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA retailer sells 10 shirts. The first 3 he sells for $20,$22 and $25. If the retailer wishes to sell the 10 shirts for an overall average price of over $20, what must be the minimum average price of the remaining 7 shirts?\n\n### Options:\nA. $14.00\nB. $16.00\nC. $17.00\nD. $19.00\nE. $23.00\n\n### Answer:\nFirst 3 shirts are sold for $20,$22 and $25=$67.\nTo get average price of $20,total sale should be 10*$20=$200\nSo remaining 7 shirts to be sold for $200-$67=$133\nAnswer should be 133/7=$19.00 that is D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA number is increased by 70 % and then decreased by 70 %. Find the net increase or decrease per cent.\n\n### Options:\nA. 49%\nB. 18%\nC. 17%\nD. 13%\nE. 16%\n\n### Answer:\nLet the number be 100.\nIncrease in the number = 70 % = 70 % of 100\n= (70/100 \u00c3\u2014 100)\n= 70\nTherefore, increased number = 100 + 70 = 170\nThis number is decreased by 70 %\nTherefore, decrease in number = 70 % of 170\n= (70/100 \u00c3\u2014 170)\n= 11900/100\n= 119\nTherefore, new number = 170 - 119 = 51\nThus, net decreases = 100 - 51 = 49\nHence, net percentage decrease = (49/100 \u00c3\u2014 100) %\n= (4900/100) %\n= 49 %\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average weight of 8 people increases by 2.5 kg when a new person comes in place of one of them weighing 35 kg. What is the weight of the new person?\n\n### Options:\nA. 75 kg\nB. 85 kg\nC. 95 kg\nD. 65 kg\nE. 55 kg\n\n### Answer:\nThe total weight increase = (8 x 2.5) kg = 20 kg\nweight of new person = (35 + 20) kg = 55 kg\nThe answer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If three marbles are picked at random, what is the probability that they are all blue?\n\n### Options:\nA. 1/455\nB. 1/429\nC. 1/408\nD. 1/421\nE. 1/420\n\n### Answer:\nGiven that there are three blue marbles, four red marbles, six green marbles and two yellow marbles.\nProbability that all the three marbles picked at random are blue\n= \u00b3C\u2083/\u00b9\u2075C\u2083 = (1 * 3 * 2 * 1)/(15 * 14 * 13)\n= 1/455\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe L.C.M of two numbers is 48. The numbers are in the ratio 2:3. The sum of numbers is?\n\n### Options:\nA. 22\nB. 67\nC. 40\nD. 88\nE. 11\n\n### Answer:\nLet the numbers be 2x and 3x.\nThen, their L.C.M = 6x. So, 6x = 48 or x = 8.\nThe numbers are 16 and 24.\nHence, required sum = (16 + 24) = 40.\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the sum of four consecutive positive integers is A, then the sum of the next four consecutive integers in terms of A is:\n\n### Options:\nA. A+4\nB. A+16\nC. 2A\nD. 2A + 4\nE. 4A\n\n### Answer:\nIn Case of Consecutive Integers or Integers in Arithmetic Progression Mean = Median\nI.e. Median = A/4 = Mean = Average of Second and Third Integer\nFirst Integer = A/4 - 1.5\nSecond Integer = A/4 - .5\nThird Integer = A/4 + .5\nFourth Integer = A/4 + 1.5\ni.e.\nFifth Integer = A/4 + 2.5\nSixth Integer = A/4 + 3.5\nSeventh Integer = A/4 + 4.5\nEighth Integer = A/4 + 5.5\nNow Mean of next 4 Integers = Median = A/4 + 4\ni.e. Sum of Next 4 integers = (A/4 + 4)*4 = A+16\nAnswer: option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMary received a 20% raise each month for three consecutive months. What was her salary after the three raises if her starting salary was $1,000 per month?\n\n### Options:\nA. $1,348\nB. $1,500\nC. $1,631\nD. $1,728\nE. $1,863\n\n### Answer:\n1000 * 1.2 * 1.2 * 1.2 = 1000 * 1.728 = 1728\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA father was as old as his son's present at the time of your birth. If the father's age is 42 years now, the son's age 5years back was?\n\n### Options:\nA. 10 years\nB. 12 years\nC. 14 years\nD. 16 years\nE. 20 years\n\n### Answer:\nLet the son's present age be x years. Then, (42 - x) = x\n2x = 42.\nx = 21.\nSon's age 5 years back (21 - 5) = 16 years.\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many different pairs of numbers (s, t) such that s = 3t can be obtained if s and t are selected from the set of number {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}\n\n### Options:\nA. 1\nB. 2\nC. 3\nD. 4\nE. 5\n\n### Answer:\ns = 3t.\nSo, s/3 = t\nThat means s is divisible by 3.\nOnly 0, 3, 6, 9 are divisible by 3.\nHence option (D).\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf two letters are taken at random from the word HOME, what is the probability that none of the letters would be vowels?\n\n### Options:\nA. 1/6\nB. 1/9\nC. 8\nD. 2/2\nE. 1/1\n\n### Answer:\nAnswer: A) 1/6\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is?\n\n### Options:\nA. 767 m\nB. 467 m\nC. 245 m\nD. 567 m\nE. 544 m\n\n### Answer:\nSpeed = [45 X 5/18] m/sec = [25/2] m/sec Time\n= 30 sec Let the length of bridge be x metres. Then, (130 + x)/30 = 25/2\n=> 2(130 + x) = 750 => x = 245 m.\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n5358 x 71 = ?\n\n### Options:\nA. 273762\nB. 283758\nC. 383298\nD. 273258\nE. 380418\n\n### Answer:\nE\n5358 x 71 = 5358 x (70 + 1)\n= 5358 x 50 + 5358 x 1\n= 375060 + 5358\n= 380418\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA person can swim in still water at 10 km/h. If the speed of water 4 km/h, how many hours will the man take to swim back against the current for 12 km?\n\n### Options:\nA. 2\nB. 7\nC. 5\nD. 9\nE. 6\n\n### Answer:\nM = 10\nS = 4\nUS =10 - 4 = 6\nD = 12\nT = 12/6 = 2\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nReplace the ? mark with an appropriate approximate value in the following equation\u2019?\n2 4/3 of 165.83+25% of 1847= ? - 554.7\n\n### Options:\nA. 1563.22\nB. 1568.22\nC. 179.22\nD. 15659.22\nE. 1569.22\n\n### Answer:\n2 4/3 of 165.83+25% of 1847= ? - 554.7\n10/3 of 165.83+25/100 of 1847= ? - 554.7\n552.77+461.75= ? - 554.7\n552.77+461.75 + 554.7= ?\n\u2248 1569.22\nAnswer E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nBy selling a house for Rs.45000, it was found that 1/8 of the outlay was gained, what ought the selling to price to have been in order to have lost 5 p.c?\n\n### Options:\nA. 38008\nB. 38000\nC. 38005\nD. 38001\nE. 38002\n\n### Answer:\nCP + CP/8 = 45000\nCP = 40000\nSP = 40000*(95/100) = 38000\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTaylor is making a bracelet. He Starts with 2 blue knots, 6 red knots, and 2 yellow knots, in that order, and repeats the pattern until there is no more string. If the last Knot is yellow which of the following could be the total number of knots on the bracelet.\n\n### Options:\nA. 89\nB. 79\nC. 95\nD. 97\nE. 102\n\n### Answer:\nRepeating sequence = 2 + 6 + 2 = 10.\nAs the pattern ends in Y this could be the 9th thread or 10 thread (both are yellow)\nOut of the answer choices, correct on should be a multiple of 10(since 10 threads are repeating) and if not, multiple of 10 + 9 (since 10 threads are repeating and last sequence end at first yellow)\nnone of the options is a direct multiple of 10 and only option that is multiple of 10; + 9 is 79 (10*7) + 9\nHence, answer is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many of the following numbers are divisible by 132 ?\n264, 396, 462, 792, 968, 2178, 5184, 6336\n\n### Options:\nA. 3\nB. 4\nC. 6\nD. 7\nE. 8\n\n### Answer:\n132 = 4 x 3 x 11\nSo, if the number divisible by all the three number 4, 3 and 11, then the number is divisible by 132 also.\n264 11,3,4 (/)\n396 11,3,4 (/)\n462 11,3 (X)\n792 11,3,4 (/)\n968 11,4 (X)\n2178 11,3 (X)\n5184 3,4 (X)\n6336 11,3,4 (/)\nTherefore the following numbers are divisible by 132 : 264, 396, 792 and 6336.\nRequired number of number = 4.\nB)\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMayank Bothra purchased 20 dozens of toys at the rate of 375 Rs per dozen .He sold each one of them at the rate of Rs 33.What was his percentage profit?\n\n### Options:\nA. 5.6 %\nB. 6.5 %\nC. 7.5 %\nD. 7.6 %\nE. None\n\n### Answer:\nSol.\nCost = 375 * 20 = 7500\nsale price 33 * 20 * 12\n= 7920 profit = 420 profit in % = 420/7500 * 100 =5.6 %\nAns: A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how many different number of ways 3 boys and 2 girls can sit on a bench?\n\n### Options:\nA. 700\nB. 710\nC. 120\nD. 720\nE. 740\n\n### Answer:\nnpn = n!\n5p5 = 5 \u00c3\u2014 4 \u00c3\u2014 3 \u00c3\u2014 2 \u00c3\u2014 1 = 120\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a village there are 150 men and 90 women in present time.if in next year population will be P=(a^2 +b^2)^1/2 , and in every year men are reduces 6%.what is population of after 2 year.\n\n### Options:\nA. 140\nB. 141\nC. 142\nD. 143\nE. 145\n\n### Answer:\nnext year total population=[150^2+90^2]^.5=174.92=175\nman decreased by 6% so total man =150*.94=141\nwomen will be= 175-141=34\nso population after two years= [135^2+34^2]^.5=145.04=145\nso population after two year= 145\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMike took a taxi to the airport and paid $2.50 to start plus $0.25 per mile. Annie took a different route to the airport and paid $2.50 plus $5.00 in bridge toll fees plus $0.25 per mile. If each was charged exactly the same amount, and Annie's ride was 22 miles, how many miles was Mike's ride?\n\n### Options:\nA. 30\nB. 36\nC. 42\nD. 48\nE. 54\n\n### Answer:\nThe cost of Annie's ride was 2.5+5+(0.25*22) = $13\nLet x be the distance of Mike's ride.\nThe cost of Mike's ride is 2.5+(0.25*x) = 13\n0.25*x = 10.5\nx = 42 miles\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMary and Joe are to throw three dice each. The score is the sum of points on all three dice. If Mary scores 10 in her attempt what is the probability that Joe will outscore Mary in his?\n\n### Options:\nA. 24/64\nB. 32/64\nC. 36/64\nD. 40/64\nE. 42/64\n\n### Answer:\nExpected value of one die is 1/6*(1+2+3+4+5+6)=3.5.\nExpected value of three dice is 3*3.5=10.5.\nMary scored 10 so the probability to get the sum more then 10 (11, 12, 13, ..., 18), or more then the average, is the same as to get the sum less than average (10, 9, 8, ..., 3) = 1/2 = 32/64.\nThat's because the probability distribution is symmetrical for this case:\nThe probability of getting the sum of 3 (min possible sum) = the probability of getting the sum of 18 (max possible sum);\nThe probability of getting the sum of 4 = the probability of getting the sum of 17;\nThe probability of getting the sum of 5 = the probability of getting the sum of 16;\n...\nThe probability of getting the sum of 10 = the probability of getting the sum of 11;\nThus the probability of getting the sum from 3 to 10 = the probability of getting the sum from 11 to 18 = 1/2.\nAnswer: B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average height of 30 girls out of a class of 40 is 160 cm. and that of the remaining girls is 156 cm. The average height of the whole class is :\n\n### Options:\nA. 158 cms\nB. 158.5 cms\nC. 159 cms\nD. 159.5 cms\nE. none\n\n### Answer:\nExplanation:\nAverage height of the whole class =(36\u00d7160+10\u00d7156/40)=159 cms\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nVinoth can complete a painting work in 20 days. Prakash can do the same work in 25 days. They start the work together but Vinoth quit after 3 days of work. How many days are required to complete the remaining painting work by Prakash.\n\n### Options:\nA. 15.25 days\nB. 16.25 days\nC. 17.25 days\nD. 18.25 days\nE. 19.25 days\n\n### Answer:\nVinoth can complete the painting work in one day is 1/20\nPrakash can complete the same work in one day is 1/25\nBoth of them can complete the work in 1/20+ days=9/100( 1/20+1/25)\nthey must have completed in three days=9/100*3=27/100\nRemaining work to be done is by Prakash =1-27/100=73/100\nFor one work, Prakash can do in 25 days\nFor 73/100 work, he can do in 73/100*25=73/4days or 18.25 days\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a parallelogram, the length of one diagonal and the perpendicular dropped on that diagonal are 30 and 20 metres respectively. Find its area\n\n### Options:\nA. 600 m2\nB. 540 m2\nC. 680 m2\nD. 574 m2\nE. None of these\n\n### Answer:\nIn a parallelogram.\nArea = Diagonal \u00d7 length of perpendicular on it.\n= 30 \u00d7 20 = 600 m2\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat are the last two digits of (301*402*503*604*646*547*449*349)^2\n\n### Options:\nA. 96\nB. 76\nC. 56\nD. 36\nE. 24\n\n### Answer:\n((301*402*503*604*646)*(547*449*349))^2\nIf you observe above digits, last digit are: 1,2,3,4,6,7,9,9; 5&9 are missing; so I have rearranged them so that multiplication will be easy for me as initial 4 digits have last two digits as 01,02,03,04,46 and final three as 47*49*49.\nSolving for only last two digits and multiplying them we get:( (06*04*46)(47*01))^2 = (44*47)^2=68^2=24\nHence answer is E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf x is an integer, then x(x \u2013 1)(x \u2013 k) must be evenly divisible by three when k is any of the following values EXCEPT\n\n### Options:\nA. -4\nB. -2\nC. -1\nD. 2\nE. 5\n\n### Answer:\nThere is probably an easier way, but I just used the picking numbers option for this.\nI chose x=2\n2(1)(2-k) then just plugged in the answer choices for K until one wasn't evenly divisible by 3.\nB gives you 8. 8/3 is not an integer.\nB is the answer\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSet M contains numbers that satisfy the condition that, if integer x is in the set then x-3 will also be in the set M. If -4 is one of the value in the set, which of the following numbers must also be present in the set M.\nI.-7\nII. -1\nIII. 2\n\n### Options:\nA. I only\nB. II only\nC. I and II only\nD. II and III only\nE. I, II and III\n\n### Answer:\nNotice that we are askedwhich of the following numbers MUST also be present in the set MnotCOULD be in the set.\nNow, if -4 is in the set, then -4-3=-7mustbe in the set. Could -1 or 2 be in the set? Certainly, but we don't know that for sure.\nAnswer: A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRay writes a two digit number. He sees that the number exceeds 4 times the sum of its digits by 3. If the number is increased by 18, the result is the same as the number formed by reversing the digits. Find the number.\n\n### Options:\nA. 2\nB. 5\nC. 6\nD. 7\nE. 8\n\n### Answer:\nSolution: Let the two digit number be xy.\n4(x + y) +3 = 10x + y .......(1)\n10x + y + 18 = 10 y + x ....(2)\nSolving 1st equation we get 2x - y = 1 .....(3)\nSolving 2nd equation we get y - x = 2 .....(4)\nSolving 3 and 4, we get x = 3 and y = 5\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe cost price of an article is 64% of the marked price. Calculate the gain percent after allowing a discount of 12%.\n\n### Options:\nA. 37.5 %\nB. 38.5 %\nC. 42 %\nD. 27.5 %\nE. none\n\n### Answer:\nSol.\nLet marked price = Rs. 100. Then, C.P. = Rs. 64. S.P = Rs. 88.\n\u2234 Gain % = [24/64 * 100]% = 37.5%.\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMy grandson is about as many days as my son in weeks, and my grandson is as many months as I am in years. My grandson, my son and I together are 120 years. Can you tell me my age in years ?\n\n### Options:\nA. 70\nB. 69\nC. 82\nD. 89\nE. 72\n\n### Answer:\nLet m be my age in years. If s is my son's age in years, then my son is 52s weeks old. If g is my grandson's age in years, then my grandson is 365g days old. Thus,\n365g = 52s.\nSince my grandson is 12g months old,\n12g = m.\nSince my grandson, my son and I together are 120 years,\ng + s + m = 120.\nThe above system of 3 equations in 3 unknowns (g, s and m) can be solved as follows.\nm / 12 + 365 m / (52 x 12) + m = 120 or\n52 m + 365 m + 624 m = 624 x 120 or\nm = 624 x 120 / 1041 = 72.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nPump A can fill a tank of water in 5 hours. Pump B can fill the same tank in 8 hours. How long does it take the two pumps working together to fill the tank?(round your answer to the nearest minute).\n\n### Options:\nA. 2 hours 2 minutes\nB. 3 hours 5 minutes\nC. 4 hours 6minutes\nD. 5 hours 7 minutes\nE. 7 hours 9 minutes\n\n### Answer:\nIn 1 hour pump A can fill 1/5 of a tank and pump B can fill 1/8 of the same tank. So in 1 hour the two pumps working together can fill\n1/5 + 1/8 = 13 / 40 of a tank\nSince the rate of the two pumps working together is 13/40, the time t needed to fill the tank by the two pumps is found by solving\n(13/40) t = 1\nt = 40 / 13 = 39/13 + 1/13 hours\n= 3 hours and (1/13)*60 minutes\n= 3 hours 5 minutes (rounded to the nearest minute)\ncorrect answer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA student was asked to find the arithmetic mean of the numbers 3, 11, 7, 9, 15, 13, 8, 19, 17, 21, 14 and x. He found the mean to be 12. What should be the number in place of x ?\n\n### Options:\nA. 8\nB. 7\nC. 6\nD. 5\nE. 4\n\n### Answer:\nClearly, we have (3 + 11 + 7 + 9 + 15 + 13 + 8 + 19 + 17 + 21 + 14 + x) / 12 = 12.\nor 137 + x = 144 o144 - 137 = 7.\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nBy selling 150 mangoes, a fruit-seller gains the selling price of 15 mangoes. Find the gain percent?\n\n### Options:\nA. 27%\nB. 25%\nC. 11%\nD. 85%\nE. 24%\n\n### Answer:\nSP = CP + g\n150 SP = 150 CP + 15 SP\n135 SP = 150 CP\n135 --- 15 CP\n100 --- ? => 11%\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo bus tickets from city A to B and three tickets from city A to C cost Rs. 77 but three tickets from city A to B and two tickets from city A to C cost Rs. 73. What are the fares for cities B and C from A ?\n\n### Options:\nA. 11\nB. 13\nC. 44\nD. 55\nE. 61\n\n### Answer:\nExplanation:\nLet Rs. x be the fare of city B from city A and Rs. y be the fare of city C from city A. Then, 2x + 3y = 77 ...(i) and 3x + 2y = 73 ...(ii) Multiplying (i) by 3 and (ii) by 2 and subtracting, we get: 5y = 85 or y = 17. Putting y = 17 in (i), we get: x = 13.\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man, a woman and a boy can complete a job in 3, 4 and 12 days respectively. How many boys must assist 1 man and 1 woman to complete the job in 1/4 of a day?\n\n### Options:\nA. 22\nB. 66\nC. 28\nD. 41\nE. 61\n\n### Answer:\n(1 man + 1 woman)'s 1 day work = (1/3 + 1/4) = 7/12 Work done by 1 man and 1 woman in 1/4 day = (7/12 * 1/4) = 7/48\nRemaining work = (1 - 7/48) = 41/48\nWork done by 1 boy in 1/4 day = ( 1/12 * 1/4) = 1/48\nNumber of boys required = 41/48 * 41 = 41.\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf two dice are thrown together, the probability of getting an even number on one die and an odd number on the other is?\n\n### Options:\nA. 1/8\nB. 1/2\nC. 4/2\nD. 1/9\nE. 7/2\n\n### Answer:\nThe number of exhaustive outcomes is 36.\nLet E be the event of getting an even number on one die and an odd number on the other. Let the event of getting either both even or both odd then\n= 18/36 = 1/2\nP(E) = 1 - 1/2 = 1/2.\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWe have 36kg flour and 60kg sugar in stock and we would like to use the minimum number of packs that would have the same weight for both flour and sugar. How much more sugar is required if we would like to full 10 packs either of flour or sugar?\n\n### Options:\nA. 12\nB. 18\nC. 20\nD. 24\nE. 30\n\n### Answer:\nk is the integer that represents kg of pack\nak = 36 --> k = 36/a\nbk = 60 --> k = 60/b\n36/a = 60/b --> 5a = 3b and then k=12 for min(a+b)\na=36/12=3 , b=60/12=5\nTotal number of packs = 3+5 = 8\n10-8=2 packs more required\n2 *12 = 24 kg more sugar required to have 10 packs.\nANSWER: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 85% of 3/5 of a number is 36, then the number is?\n\n### Options:\nA. 80\nB. 100\nC. 70.5\nD. 90\nE. None of these\n\n### Answer:\nLet the number be x. Then 85% of 3/5 of x=36\n85/100*3/5*x=36\nx=(36*100/51)=70.5\nRequired number=70.5.\nCorrect Option: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf books bought at prices ranging from Rs. 200 to Rs. 350 are sold at prices ranging from Rs. 300 to Rs. 425, what is the greatest possible profit that might be made in selling eight books ?\n\n### Options:\nA. 23267\nB. 2677\nC. 1800\nD. 2778\nE. 76611\n\n### Answer:\nExplanation:\nLeast Cost Price = Rs. (200 * 8) = Rs. 1600.\nGreatest Selling Price = Rs. (425 * 8) = Rs. 3400.\nRequired profit = Rs. (3400 - 1600) = Rs. 1800.\nAnswer: C) 1800\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\na spider web consists of 3 concurrent lines forming radial support for 20 concentric regular hexagon .the hexagon vertices are 5mm from their immidiate neighbour. if the innermost hexagon has a side length 3mm how many meters is the length of the entire web including the 3 diagonals ?\n\n### Options:\nA. 7.354 m\nB. 8.354 m\nC. 6.354 m\nD. 9.354 m\nE. 5.354 m\n\n### Answer:\nfor perimeter of all hexagon =6*(3+8+13+...........20th term.)\nsum will be 6060 mm\nand for length of one diagonal find 20th term=98\nso total length =6060+294=6354 mm=6.354 m\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nConsider below info to be a table:\nAMOUNT OF BACTERIA\nTIME - AMOUNT\n1PM - 10gms\n4PM - x gms\n7PM - 22.5 gms\nData for a certain biology experiment are given in the table above. If the amount of bacteria present increased by the same factor during each of the two 3-hour periods shown, how many grams of bacteria were present at 4PM ?\n\n### Options:\nA. 15.0\nB. 12.1\nC. 12.2\nD. 12.3\nE. 12.4\n\n### Answer:\nlet say the factor is x, the at 7PM quantity = 10 (i.e. quantity @1PM)* x^2 =22.5 => x^2 =2.25 or x = 1.5 => @4PM quantity = 10x =10*1.5 =15.\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA bus travels k miles in n hours. How many miles will it travel in x hours at the same rate?\n\n### Options:\nA. knx\nB. k\u2044n\nC. x\nD. kx\u2044n\nE. kn\u2044x\n\n### Answer:\nGiven Speed = k/n\nTo Find distance in x hours with same speed\nDistance = speed * time\nDistance = k/n*x = kx/n\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain list consists of 21 different numbers. If n is in the list and n is 4 times the average(arithmetic mean) of the other 20 numbers in the list, then n is what fraction W of the sum of the 21 numbers in the list?\n\n### Options:\nA. 1/20\nB. 1/6\nC. 1/5\nD. 4/21\nE. 5/21\n\n### Answer:\nThis is how I used to calculate which I think works pretty well:\nif you let the average of the 20 other numbers equal a, can you write this equation for sum of the list (S)\nn + 20a = S\nthe question tells us that\nn = 4a\nplug this back into the first equation and you get that the sum is 24a\n4a + 20a = 24a\ntherefore fraction W of n to the total would be\n4a/24a or 1/6\nanswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe cost price of a radio is Rs.4800 and it was sold for Rs.4400, find the loss %?\n\n### Options:\nA. 8\nB. 9\nC. 7\nD. 6\nE. 4\n\n### Answer:\n4800 ---- 400\n100 ---- ? => 8%\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how many different ways can 3 identical green boots and 3 identical red boots be distributed among 6 people such that each person receives a pair of boots?\n\n### Options:\nA. 7209\nB. 4059659\nC. 2169\nD. 20\nE. 7291\n\n### Answer:\nHow to solve:\n1st Person: 6 has options\n2nd Person: 5 has options\u2026\nTherefore, for all people: 6 x 5 x 4 x 3 x 2 = 720 arrangements.\nSince the reds are identical, we divide by 3! Since the greens are identical, we divide by another 3!\nSo: in all, 720/[ 3! X 3! ] = 20 ways.\n(e.g. Answer: D)\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a radio is purchased for Rs 490 and sold for Rs 465.50 Find the loss%?\n\n### Options:\nA. 3%\nB. 4%\nC. 5 percent\nD. 6%\nE. None of these\n\n### Answer:\nExplanation :\nLoss = 490 \u2013 465.5 = 24.5 loss in % = 24.5/ 490 x 100 = 5%.\nAnswer : C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a supermarket shows $49 of sales for apples, and on that same day there are sales of $64 in oranges. What is the ratio of sales for apples to oranges?\n\n### Options:\nA. 1 : 2\nB. 2 : 3\nC. 4 : 7\nD. 1 : 5\nE. None\n\n### Answer:\nSolution\nLet us name the apples\nas A and the oranges as B.\t= (A'S sales) : (B's sales)\n=\u00e2\u02c6\u0161b : \u00e2\u02c6\u0161a\n= \u00e2\u02c6\u016149 : \u00e2\u02c6\u016164\n= 7 : 8\nAnswer E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRs.8000 become Rs.10210 in a certain interval of time at the rate of 5% per annum of C.I. Find the time?\n\n### Options:\nA. 6 YEARS\nB. 7\nC. 5\nD. 3\nE. 4\n\n### Answer:\nExplanation:\n10210 = 8000(21/20)N\n(21/20)5 = (21/20)N => N = 5\nAnswer: Option C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the sum of the multiples of 4 between 34 and 135 inclusive?\n\n### Options:\nA. 2000\nB. 2100\nC. 2150\nD. 2200\nE. 2500\n\n### Answer:\nthe fastest way in an AP is to find the average and multiply with total integers..\nbetween 34 and 135, the smallest multiple of 4 is 36 and largest =132..\naverage=(36+132)/2=84..\ntotal numbers = (132-36)/4 + 1= 24+1=25..\nsum=25*84=2100\nans B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a garden, 26 trees are planted at equal distances along a yard 600 metres long, one tree being at each end of the yard. What is the distance between two consecutive trees?\n\n### Options:\nA. 10\nB. 8\nC. 12\nD. 24\nE. 16\n\n### Answer:\n26 trees have 25 gaps between them.\nLength of each gap = 600/25 = 24\ni.e., distance between two consecutive trees = 24\nAnswer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the ratio of the sum of the first 6 terms of a G.P. to the sum of the first 3 terms of the G.P. is 126, what is the common ratio of the G.P?\n\n### Options:\nA. 3\nB. 1/3\nC. 2\nD. 5\nE. 1/5\n\n### Answer:\n126=(a1+a2+a3+a4+a5+a6)/(a1+a2+a3)\nFactorize the same terms\n126=1+(a4+a5+a6)/(a1+a2+a3)\nWrite every term with respect to r\na1=a1\na2=a1*r^1\na3=a1*r^2\n.........\n126=1+(a1(r^3+r^4+r^5))/(a1(1+r^1+r^2))\n125=(r^3 (1+r^1+r^2))/((1+r^1+r^2))\n125=r^3\nr=5\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA sun is divided among X, Y and Z in such a way that for each rupee X gets, Y gets 45 paisa and Z gets 30 paisa. If the share of Y is RS. 27, what is the total amount?\n\n### Options:\nA. 166\nB. 105\nC. 178\nD. 177\nE. 169\n\n### Answer:\nx:y:z = 100:45:30\n20:9:6\n9 --- 27\n35 --- ? => 105\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo goods trains each 500 m long are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one?\n\n### Options:\nA. 12 sec\nB. 24 sec\nC. 48 sec\nD. 60 sec\nE. 65 sec\n\n### Answer:\nExplanation:\nRelative speed = 45 + 30 = 75 km/hr.\n75 * 5/18 = 125/6 m/sec.\nDistance covered = 500 + 500 = 1000 m.\nRequired time = 1000 * 6/125 = 48 sec.\nANSWER IS C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA, B and C jointly thought of engaging themselves in a business venture. It was agreed that A would invest Rs. 6500 for 6 months, B, Rs. 8400 for 5 months and C, Rs. 10,000 for 3 months. A wants to be the working member for which, he was to receive 5% of the profits. The profit earned was Rs. 7400. What is the share of B in the profit.\n\n### Options:\nA. 2670\nB. 2560\nC. 2440\nD. 2550\nE. 2660\n\n### Answer:\nA is a working member and for that, he receives 5% of the profit\n= 5% of 7400 =(5\u00d77400)/100=370\nRemaining amount =7400\u2212370=7030\nRatio of their investments\n=6500\u00d76:8400\u00d75:10000\u00d73=65\u00d76:84\u00d75:100\u00d73=13\u00d76:84:20\u00d73=13\u00d72:28:20=13:14:10\nShare of B in the profit\n=7030\u00d714/37=190\u00d714=2660\nAnswer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThree houses of the same type were advertised to be let in a locality. Two men made separate applications for a house. What is the probability that each of them applied for the same house.\n\n### Options:\nA. 1/3\nB. 2/3\nC. 1/6\nD. 1/9\nE. 1/27\n\n### Answer:\nSince each of the house has same probability of getting selected so for each men proability of selecting a house out of 3 houses 1/3\nLet us consider case where all 2 men choose House no 1\nSo for First men it will be 1/3,second men 1/3\nSo probability of selecting house no 1 is 1/3*1/3= 1/9\nAnd since there are 3 such house so probability that each men select the same house is 3*1/9 or 1/3\nAns is A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAfter increasing 20% in the price of a Book costs Rs.240. Find the actual cost of an article?\n\n### Options:\nA. 100\nB. 150\nC. 200\nD. 220\nE. 250\n\n### Answer:\nCP* (120/100) = 240\nCP= 2* 100 => CP = 200\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA bag contains 6 white marbles and 6 black marbles. If each of 6 girls and 6 boys randomly selects and keeps a marble, what is the probability that all of the girls select the same colored marble?\n\n### Options:\nA. 1/35\nB. 1/10\nC. 1/3\nD. 1/462\nE. 1/252\n\n### Answer:\nfirst, total ways to select for all boys and girls, i.e 12!/(6!*6!) = 12*11*10*9*8*7/6*5*4*3*2 =924\nthen there are one two way girls can have all same colors, either white or black.\nThe number of ways in which 6 girls can select 6 white balls = 6C6 = 1\nThe number of ways in which 6 girls can select 6 black balls = 6C6 = 1\nTherefore, total favorable outcomes/total outcomes = 2/924 = 1/462\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 6 men and 8 boys can do a piece of work in 10 days while 26 men and 48 boys can do the same in 2 days, the time taken by 15 men and 20 boys in doing the same type of work will be?\n\n### Options:\nA. 4\nB. 5\nC. 6\nD. 7\nE. 8\n\n### Answer:\nLet 1 men's 1 day work = x and 1 boy's 1 day work = y.\nThen, 6x + 8y = 1/10 and 26x + 48y = 1/2\nSolving these two equations, we get:\nx = 1/100 and y = 1/200\n(15 men + 20 boys)'s 1 day work = (15/100 + 20/200) = 1/4\n15 men and 20 boys can do the work in 4 days.\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA new tower has just been built at the Verbico military hospital; the number of beds available for patients at the hospital is now 4 times the number available before the new tower was built. Currently, 1/3 of the hospital's original beds, as well as 1/5 of the beds in the new tower, are occupied. For the purposes of renovating the hospital's original wing, all of the patients in the hospital's original beds must be transferred to beds in the new tower. If patients are neither admitted nor discharged during the transfer, what fraction of the beds in the new tower will be unoccupied once the transfer is complete?\n\n### Options:\nA. 11/30\nB. 29/60\nC. 17/30\nD. 31/45\nE. 11/15\n\n### Answer:\nI think D - 31/45 is the correct answer.\nHere goes:\nLets assume originally the number of beds = x\nAfter the new tower, the total combined no of beds = 4x\nSo old = x, New = 3x\nNow 1/3 of x are occupied and 1/5 of 3x are occupied which simplifies to (3/5)x\nWe are shifting 1/3 of x to the new ward so there will now be:\n1/3 of x plus 3/5 of x occupied in the new ward. Add them up to get 14/15 of x\nThere are 3x beds in New Tower so ratio is:\n(14/15)x / 3x = 14/45 of x\nSubtract that from 45/45 of x and you get the number of un-occupied beds to total capacity of New Tower =31/45\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOn a game show, a contestant is given three keys, each of which opens exactly one of three identical boxes. The contestant assigns each key to one of the boxes and wins the amount of money contained in any box that is opened by the key assigned to it. The first box contains $1.5, the second $150, and the third $1500. What is the probability that a contestant will win more than $1500?\n\n### Options:\nA. 1/9\nB. 2/3\nC. 1/6\nD. 1/3\nE. 1/2\n\n### Answer:\nLet's call the boxes that contain $1.5, $150, and $1500, respectively, Box A, Box B, Box C. These are opened, respectively, by Key A, Key B, and Key C.\nWe want to know the probability of winning more than $1500. Notice that if the distribution of keys is:\nBox A = Key B\nBox B = Key A\nBox C = Key C\nthen the contestant wins exactly $1500, not more than $1500. The only configuration that leads to winning more than $1000 is:\nBox A = Key A\nBox B = Key B\nBox C = Key C\ni.e., getting all three keys correct. That's the only way to be more than $1500. So, really, the question can be rephrased: what is the probability of guessing the order of keys so that each key matches the correct box?\nWell, for a set of three items, the number of possible permutations is 3! = 3*2*1 = 6.\nOf those 6 possible permutations, only one of them leads to all three keys being paired with the right box. So, the answer is\nProbability = 1/6\nAnswer = C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe ratio between the number of sheep and the number of horses at the Stewar farm is 2 to 7. If each of horse is fed 230 ounces of horse food per day and the farm needs a total 12880 ounces of horse food per day. what is number sheep in the form??\n\n### Options:\nA. 18\nB. 16\nC. 32\nD. 56\nE. 58\n\n### Answer:\net no of sheep and horses are 2k and 7k\nno of horses= 12880/230=56\nnow 7K=56 and k=8\nno of sheep=(2*8) =16\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJason's team scored 60 points in a game basketball and he accounted for 60 percent of their points. How much did he score?\n\n### Options:\nA. 42\nB. 38\nC. 36\nD. 44\nE. 40\n\n### Answer:\n600/10 x (6/10) = 3600/100 or 36\nAnswer is C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo cyclist start from the same places in opposite directions. One is going towards north at 18kmph and the other is going towards south 20kmph. What time will they take to be 190km apart?\n\n### Options:\nA. 1 1/4 hours\nB. 5 hours\nC. 4hours\nD. 3 3/4 hours\nE. 6hours\n\n### Answer:\nTo be (18+20) km apart, they take 1 hour\nTo be 190 km apart, they take 1/38 * 190 = 5 hrs\nAnswer is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nDistance between two stations A and B is 778 km. A train covers the journey from A to B at 84 km per hour and returns back to A with a uniform speed of 56km per hour. Find the average speed of the train during the whole journey?\n\n### Options:\nA. 67.0 km /hr\nB. 67.2 km /hr\nC. 69.0 km /hr\nD. 69.2 km /hr\nE. None\n\n### Answer:\nSolution\nRequired average speed\t=(2xy / x+y)km/hr\n= 2 x 84 x 56 /(84 + 56)\n= (2 x 84 x 85 /140)\n= 67.2 km/hr.\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe angle of elevation of the sun, when the length of the shadow of a tree is \u221a3 times the height of the tree is\n\n### Options:\nA. 30\u00b0\nB. 45\u00b0\nC. 60\u00b0\nD. 90\u00b0\nE. None\n\n### Answer:\nSolution\nLet AB be the tree and AC be its shadow.\nThen, < ABC\t= \u03b8.\nThen, AC/AB\t= \u221a3\ncot\u03b8= \u221a3\n\u03b8=30\u00b0\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 8 minutes, then the area of the park (in sq. m) is:\n\n### Options:\nA. 153601\nB. 153600\nC. 153602\nD. 153603\nE. 153604\n\n### Answer:\nPerimeter = Distance covered in 8 min. =(12000/60) x 8m = 1600 m.\nLet length = 3x metres and breadth = 2x metres.\nThen, 2(3x + 2x) = 1600 or x = 160.\nLength = 480 m and Breadth = 320 m.\nArea = (480 x 320) m2 = 153600 m2.\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe tax on a commodity is diminished by 15% and its consumption increased by 10%. The effect on revenue is?\n\n### Options:\nA. 8.5\nB. 6.5\nC. 5.5\nD. 5.6\nE. 4.4\n\n### Answer:\n100 * 100 = 10000\n85 * 110 = 9350\n-----------\n10000-----------650\n100-----------? => 6.5% decrease\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA tap can fill a tank in 8 hours. After half the tank is filled three more similar taps are opened. What is the total time taken to fill the tank completely?\n\n### Options:\nA. 5 hrs\nB. 6 hrs\nC. 8 hrs\nD. 7.5 hrs\nE. 4 hrs\n\n### Answer:\nTime taken by one tap to fill the tank = 4 hrs.\nPart filled by the taps in 1 hour = 4 * 1/8 = 1/2\nRemaining part = 1 - 1/2 = 1/2\n1/2 : 1/2 :: 1 : x\nx = 1/2 * 1 * 2 = 1 hrs. i.e., 60 min\nSo, total time taken = 3 hrs 60 min = 4 hrs\nANSWER: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMr. Smith calculated the average of 10three digit numbers. But due to a mistake he reversed the digits of a number and thus his average increased by 49.5. The difference between the unit digit and hundreds digit of that number is :\n\n### Options:\nA. a) 4\nB. b) 3\nC. c) 2\nD. d) 1\nE. e) 5\n\n### Answer:\nSince the average increased by 49.5 and there were a total of 10 numbers, it means the incorrect number was 495 greater than the correct number.\nSay, the correct number was abc (where a, b and c are the digits of the 3 digit number)\nThen the incorrect number was cba.\n100c + 10b + a - (100a + 10b + c) = 495\n99c - 99a = 99(c - a) = 495\n495 = 99*5 = 99(c - a)\nSo c - a = 5\nAnswer (E)\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA welder received an order to make a 1 million liter cube-shaped tank. If he has only 4x2 meter sheets of metal that can be cut, how many metal sheets will be required for this orderT? (1 cubic meter = 1,000 liters)\n\n### Options:\nA. 92\nB. 90\nC. 82\nD. 78\nE. 75\n\n### Answer:\nI get 75. A cube with 1 million liters cube would be a cube with the dimensions of 100*100*100. 4*2 covers 8 sq liters so 100/8 = 12.5.\nT=12.5*6 = 75.E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 638521 is to be divisible by 5, what is the least whole number that should be added to?\n\n### Options:\nA. 8\nB. 7\nC. 5\nD. 4\nE. 3\n\n### Answer:\nA number is divisible by 5 if the last digit is either 0 or 5.\nHere, 638521=1(last digit is neither 0 or 5).\nthe next multiple of 5 i.e to make the last digit 0 or 5 add 4\n4 must be added to 638521 to make it divisible by 5\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n0.999999+0.111111=?\n\n### Options:\nA. 1\nB. 1.0001\nC. 1.0021\nD. 1.111\nE. 1.11111\n\n### Answer:\n0.999999 + 0.111111\n= 0.999999 + 0.11111 + 0.000001\n= (0.999999 + 0.000001) + 0.11111\n= 1 + 0.11111\n= 1.11111\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA furniture manufacturer has two machines, but only one can be used at a time. Machine K is utilized during the first shift and Machine B during the second shift, while both work half of the third shift. If Machine K can do the job in 12 days working two shifts and Machine B can do the job in 15 days working two shifts, how many days will it take to do the job with the current work schedule?\n\n### Options:\nA. 14\nB. 13\nC. 11\nD. 9\nE. 7\n\n### Answer:\n'Approximately' could actually make such a question ambiguous. Not this one though but a similar question with the answer as 9.2 days. You round off 8.89 days as 9 days and everything is fine in this question. What do you do when you get 9.2 days? Do you need 9 days or 10 days? Can you round off 9.2 as 9 even though that is what you do with numbers? No, because in 9 days your work is not over. You do need 10 days.\nTo finish a work say Machine K you need to work full 9 days and a part of the 10th day. If I ask you how many days do you need to complete the work, will you say 9 or 10? You will say 10 even if you don't use the 10th day fully=D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are 300 seniors at Morse High School, and 50% of them have cars. Of the remaining grades (freshmen, sophomores, and juniors), only 10% of them have cars. If 25% of all the students at Morse have cars, how many students are in the three lower grades?\n\n### Options:\nA. 500\nB. 900\nC. 1200\nD. 1350\nE. 1500\n\n### Answer:\nLet x be the number of students in the lower three grades.\n0.1x + 150 = 0.25(x+300)\n0.15x = 75\nx = 500\nThe answer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe total age of A and B is 16 years more than the total age of B and C. C is how many year younger than\n\n### Options:\nA. 14 years\nB. 12 years\nC. 56 years\nD. 16 years\nE. 55 years\n\n### Answer:\nGiven that A+B = 16 + B + C\n=> A \u00e2\u20ac\u201c C = 16 + B \u00e2\u20ac\u201c B = 16\n=> C is younger than A by 16 years\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf by selling an article for Rs.60, a person loses 1/7 of money, what would he have gained or lost % by selling it for Rs.77?\n\n### Options:\nA. 5%\nB. 10%\nC. 15%\nD. 20%\nE. 25%\n\n### Answer:\nSol. CP - = EC7 = 70 1-7 6 77-70 % Profit = 100 = 10%\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA cycle is bought for Rs.900 and sold for Rs.1080, find the gain percent?\n\n### Options:\nA. 20%\nB. 30%\nC. 15%\nD. 10%\nE. 35%\n\n### Answer:\n900---- 180\n100---- 20%\nANSWER A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a > 1, which of the following is equal to (2a + 6)/(a^2 + 2a - 3)?\n\n### Options:\nA. a\nB. a + 3\nC. 2/(a - 1)\nD. 2a/(a - 3)\nE. (a - 1)/2\n\n### Answer:\n(2a + 6)/(a^2 + 2a - 3) = 2(a + 3) / (a + 3)(a - 1)\n= 2/(a - 1)\nOption C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe speed of a boat in upstream is 30 kmph and the speed of the boat downstream is 70 kmph. Find the speed of the boat in still water and the speed of the stream?\n\n### Options:\nA. 22 kmph\nB. 20 kmph\nC. 21 kmph\nD. 26 kmph\nE. 28 kmph\n\n### Answer:\nSpeed of the boat in still water = (30+70)/2 = 50 kmph. Speed of the stream\n= (70-30)/2\n= 20 kmph.\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n325 metres long yard, 26 trees are palnted at equal distances, one tree being at each end of the yard. What is the distance between 2consecutive trees\n\n### Options:\nA. 13\nB. 12\nC. 14\nD. 16\nE. 18\n\n### Answer:\n26 trees have 25 gaps between them,\nRequired distance (325/25) = 13\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFor each color copy, Print Shop X charges $1.25 and Print Shop Y charges $2.75. How much greater is the charge for 80 color copies at Print Shop Y than at Print Shop X?\n\n### Options:\nA. $120\nB. $125\nC. $130\nD. $135\nE. $140\n\n### Answer:\nThe difference in the two prices is $2.75 - $1.25 = $1.50 for each color copy.\nEach color copy will cost an extra $1.50 at Print Shop Y.\n80*$1.50 = $120\nThe answer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA dog takes 10 leaps for every 2 leaps of a hare. If one leap of the dog is equal to 2 leaps of the hare, the ratio of the speed of the dog to that of the hare is :\n\n### Options:\nA. 5:1\nB. 10:1\nC. 15:1\nD. 20:1\nE. 25:1\n\n### Answer:\nExplanation:\nDog : Hare = (10*2) leaps of hare : 2 leaps of hare = 20 : 2.\nAnswer: B) 10:1\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n2y - x = 2xy . If x and y are integers, which of the following could equal y?\n\n### Options:\nA. 2\nB. 1\nC. 0\nD. 3\nE. 4\n\n### Answer:\nPlug in the answer choices in the equation from the question stem.\nA) y = 2 >>> 4-x = 4x >>> No value of x will satisfy this, not even 0. POE\nB) y = 1 >>> 2 - x = 2x >>> Same, POE\nC) y = 0 >>> -x = 0 >>> x This is the answer\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThree investors, A, B, and C, divide the profits from a business enterprise in the ratio of 5 : 7 : 8, respectively. If investor A earned $ 5,000, how much money did investors B and C earn in total?\n\n### Options:\nA. $15,000\nB. $4,900\nC. $5,600\nD. $9,500\nE. $10,500\n\n### Answer:\nLet profit for A = 5x\nprofit for B = 7x\nprofit for C = 8x\nInvestor A earned = 5000\n5x = 5000=>x=1000\nTotal profit for B and C = 7x+ 8x = 15x\nTherefore , 15x =15*1000= 15,000\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat annual instalment will discharge a debt of Rs 1092 due in 3 years at 12% simple interest?\n\n### Options:\nA. Rs.325\nB. Rs.545\nC. Rs.560\nD. Rs.550\nE. Rs.450\n\n### Answer:\nLet each instalment be Rs.x .\n1st year = [x + (x * 12 * 2)/100]\n2nd year = [ x + (x *12 * 1)/100]\n3rd year = x\nThen, [x + (x * 12 * 2)/100] + [ x + (x *12 * 1)/100] + x =1092\n3x + ( 24x/100 ) + ( 12x/100 ) = 1092\n336x =109200\nx = 325\nEach instalment = Rs. 325 Answer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nI sold a book at a profit of 10%. Had I sold it for $100 more, 15% would have been gained. Find the cost price?\n\n### Options:\nA. $2000\nB. $2500\nC. $3000\nD. $3120\nE. $1540\n\n### Answer:\n115% of cost - 110% of cost = $100\n5% of cost = $100\ncost = 100*100/5 = $2000\nAnswer is A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe difference of the squares of two consecutive even integers is divisible by which of the following integers ?\n\n### Options:\nA. 6\nB. 4\nC. 2\nD. 5\nE. 1\n\n### Answer:\nLet the two consecutive even integers be 2n and (2n + 2). Then,\n(2n + 2)^2 = (2n + 2 + 2n)(2n + 2 - 2n)\n= 2(4n + 2)\n= 4(2n + 1), which is divisible by 4.\nANSWER B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA tradesman by means of his false balance defrauds to the extent of 20%? in buying goods as well as by selling the goods. What percent does he gain on his outlay?\n\n### Options:\nA. 74%\nB. 94%\nC. 44%\nD. 24%\nE. 74%\n\n### Answer:\ng% = 20 + 20 + (20*20)/100\n= 44%\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man can swim in still water at 12 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is?\n\n### Options:\nA. 4\nB. 4.2\nC. 5.3\nD. 1.5\nE. 5.2\n\n### Answer:\nM = 12\nS = x\nDS = 12 + x\nUS = 12 - x\n12 + x = (12 - x)2\n12 + x = 24 -2x\n3x = 12\nx = 4\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the greatest possible value of integer n if 100! is divisible by 15^n\n\n### Options:\nA. 20\nB. 21\nC. 22\nD. 23\nE. 24\n\n### Answer:\n15^n = 5^n * 3^n\nHighest prime factor will be the limiting factor.\n100/5 +100/25 =20+4 = 24\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAn uneducated retailer marks all his goods at 55% above the cost price and thinking that he will still make 25% profit, offers a discount of 25% on the marked price. What is his actual profit on the sales?\n\n### Options:\nA. 12.50 %\nB. 13.50 %\nC. 14 %\nD. 14.50 %\nE. None\n\n### Answer:\nSol.\nLet C.P. = Rs. 100. Then, marked price = Rs. 155.\nS.P. = 75% of Rs. 155 = Rs. 116.25.\n\u2234 Gain% = 16.25%.\nAnswer E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are three rooms in a motel: one single, one double and one for four persons. How many ways are there to house seven persons in these rooms ?\n\n### Options:\nA. 7! / 1! 2! 3!\nB. 7!\nC. 7! / 3\nD. 7! / 3!\nE. 7! / 4\n\n### Answer:\nChoose 1 person for the single room & from the remaining choose 2 for the double room & from the remaining choose 4 people for the four person room,\nThen, 7C1 x 6C2 x 4C4 = 7! / 1! 2! 3!\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe probability of a team winning a match given Matt is playing the match is 0.7. The probability of the team winning a match given Matt is not playing the match is 0.5. The probability of Matt playing any match is 0.8.\nIf it is known that the team has won the last match, what is the probability that Matt played the match?\n\n### Options:\nA. A)0.848\nB. B)0.7\nC. C)0.8571\nD. D)0.7531\nE. E)0.8213\n\n### Answer:\nOut of 100 matches:\nMatt is plays in 80 and not plays in 20.\nOut of 80 matches Matt plays in, team wins 0.70*80 = 56.\nOut of 20 matches Matt does not play in, team wins 0.5*20 = 10.\nSo, out of 100 matches 56 + 10 = 66 are won.\nIt is known that the team has won the last match. Out of 66 matches won, Matt is in 56: 56/66 = 0.848...\nAnswer: A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe sum of the ages of a father and son is 45 years. Five years ago, the product of their ages was four times the fathers age at that time. The present age of father and son\n\n### Options:\nA. 6\nB. 7\nC. 9\nD. 2\nE. 5\n\n### Answer:\nLet sons age = x years. Then fathers age = (45 - x)years.\n(x\u20145)(45\u2014x\u20145) = 4(45- x - 5) hence (x\u20145) = 4 so x = 9\nTheir ages are 36 years and 9 years.\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n100 people are standing in a circle. The person standing at number 1 is having a sword. He kills the person next to him with the sword and then gives the sword to the third person. This process is carried out till there is just one person left.\nCan you find out who survives?\n\n### Options:\nA. 93\nB. 73\nC. 90\nD. 75\nE. 87\n\n### Answer:\nB\nThe person on 73rd number will survive.\nTill the number is the power of 2, the last person to survive will be the one who started it. But since the number here is not the power of 2, we will take the greatest power of 2 that is less than the number which is 64.\n100 - 64 = 36\n36 people are killed as 2, 4, 6, ..., 72. Thus the sword will now be given to the 73rd person. Now he is the first person to start in the remaining 64 people. Thus he will be the one to survive.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf A, B and C together can finish a piece of work in 4 days. A alone in 12 days and B in 18 days, then C alone can do it in?\n\n### Options:\nA. 1\nB. 7\nC. 8\nD. 9\nE. 6\n\n### Answer:\nC = 1/4 - 1/12 \u2013 1/18 = 1/9 => 9 days'\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n5 friends visited a fruit stall, and everyone decided to contribute equally to the total bill of $100. If one of the friends had a coupon for 6% off the total bill, and if each friend still contributed equally after the coupon was applied to the bill, how much did each friend pay?\n\n### Options:\nA. 18\nB. 18.8\nC. 19\nD. 17.8\nE. 17.9\n\n### Answer:\nAt the non-discounted price, each friend would pay $20, as $100 divided by 5 friends is $20 per friend. But if the bill is 6% off, then each friend would pay 6% less. 6% of $20 is $1.2, so each friend saves $1.2 and pays the remaining 18.8\nCORRECT OPTION:OPTION B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are 35 students in a hostel. If the no. of students increases by 7, the expenses of the mess increase by Rs.42/day while the average expenditure per head diminishes by Rs1. Find the original expenditure of the mess?\n\n### Options:\nA. Rs. 34\nB. Rs. 39\nC. Rs. 42\nD. Rs. 49\nE. Rs. 51\n\n### Answer:\nSuppose the average join the mess , total expenditure = 35x + 42\nNow, the average expenditure = (35x + 42)/ (35 + 7) = x \u2013 1\nor, 35x + 42 = 42x \u2013 42\nor, x = 12\nThus the original expenditure of the mess = 35 x 12 = Rs. 42\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a shop, 40% socks are white and rest are black. 60% socks are made of cotton and rest are made of wool. 25% white socks are made of cotton and 20 of the black socks are made of wool. How many black socks D are made of cotton?\n\n### Options:\nA. 100\nB. 80\nC. 60\nD. 50\nE. 25\n\n### Answer:\nI'll prefer to solve this with plug n play method.\nAs we know, White Cotton socks are only 25% and Total Cotton socks is 60% - Hence Black Cotton socks D has to be [highlight]HIGH[/highlight]number. Thats why we've to pick high number... say 100 or 80.\n100 fits perfectly after relevant calculations. Hence answer A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe median of a triangle is the line from any vertex to the midpoint of the opposite side. Triangle ABC has vertices A = (0, 5), B = (\u20131, \u20131), and C = (5, 2). What is the slope of the median from A to the midpoint of BC?\n\n### Options:\nA. \u20133/4\nB. >\u20134/3\nC. \u20135\nD. \u20135/2\nE. \u20139/4\n\n### Answer:\nFirst to find the midpoint of B & C \u2014 average the x-coordinates: (\u20131+ 5)/2 = 2; and average the y-coordinates: (\u20131 + 2)/2 = 1/2. Thus, the midpoint has coordinates (2, 1/2). We want the slope from A = (0, 5) to (2, 1/2). The rise is the change in the y-coordinates: 1/2 \u2013 5 = -9/2. The run is the change in the x-coordinates: 2 \u2013 0 = 2. Slope = rise/run = [\u20139/2]/2 = \u20139/4. Answer = (E)\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe inner circumference of a circular race track, 14 m wide, is 440 m. Find radius of the outer circle?\n\n### Options:\nA. 22\nB. 37\nC. 87\nD. 84\nE. 82\n\n### Answer:\nLet inner radius be r metres. Then, 2\nr = 440 ; r = = 70 m.\nRadius of outer circle = (70 + 14) m = 84 m.\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nConvert 100 inches into centimeter?\n\n### Options:\nA. 112cm\nB. 120cm\nC. 150cm\nD. 210cm\nE. 254cm\n\n### Answer:\n1 inch = 2.54cm\n100 inches = 100*2.54 = 254cm\nAnswer is E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf A : B = 4 : 7 and B : C = 5 : 9 then A : B : C is :\n\n### Options:\nA. ratio 20 : 35 : 63\nB. 35 : 36 : 63\nC. 30 : 35 : 65\nD. 25 :34: 68\nE. None of these\n\n### Answer:\nA : B = 4 : 7\nB : C = 5 :9 = 5*7/5 : 9 *7/5 = 7 : 63/5\nA : B : C = 4 : 7 : 63/5 = 20 : 35 : 63\nANSWER: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n40% of a number is more than 20% of 650 by 190. Find the number?\n\n### Options:\nA. 299\nB. 277\nC. 800\nD. 289\nE. 271\n\n### Answer:\n(40/100) * X \u2013 (20/100) * 650 = 190\n2/5 X = 320\nX = 800\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo trains of length 140 m and 280 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively. In what time will they be clear of each other from the moment they meet?\n\n### Options:\nA. 28\nB. 266\nC. 990\nD. 20\nE. 21\n\n### Answer:\nRelative speed = (42 + 30) * 5/18 = 4 * 5 = 20 mps.\nDistance covered in passing each other = 140 + 280 = 420 m.\nThe time required = d/s = 420/20 = 21 sec.\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn what time will a railway train 20 m long moving at the rate of 36 kmph pass a telegraph post on its way?\n\n### Options:\nA. 8 sec\nB. 1 sec\nC. 9 sec\nD. 6 sec\nE. 2 sec\n\n### Answer:\nT = 20/36 * 18/5\n= 2 sec\nAnswer:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a certain random experiment, exactly one of the outcomes A, B, and C will occur. In each random experiment, the probability that outcome A will occur is 1/3 , and the probability that outcome B will occur is 1/3. What is the probability that when the random experiment is conducted 6 independent times, each of outcomes A, B, and C will occur twice?\n\n### Options:\nA. 5/243\nB. 1/12\nC. 10/81\nD. 1/6\nE. 16/81\n\n### Answer:\nGiven that P(A) = P(B) = P(C) = 1/3.\nP(AABBCC) = (13)^6\u22176!2!2!2!=1081 we multiply by 6!/(2!2!2!) because AABBCC scenario can occur in several ways: AABBCC, AABCBC, AACBBC, ... (the number of permutations of 6 letters AABBCC is 6!(2!2!2!)).\nAnswer: C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 2x-1 + 2x+1 = 1280, then find the value of x.\n\n### Options:\nA. 0\nB. 2\nC. 4\nD. 9\nE. 6\n\n### Answer:\nSol.\n2x-1 + 2x+1 = 1280 \u21d4 2x-1 (1+22) = 1280\n\u21d4 2x-1 = 1280 / 5 = 256 = 28\n\u21d4 x - 1 = 8 \u21d4 x = 9.\nHence, x = 9.\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the compound interest on $800 for 1year at 10% p.a. if CI is component yearly?\n\n### Options:\nA. $40\nB. $400\nC. $840\nD. $800\nE. $80\n\n### Answer:\nA = P(1 + R/100)^T\n= 800(1 + 10/100)^1\n= 800*21/20\n=$840\nCI = A-P = 840-800 = $40\nAnswer is A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the average of ten numbers is 30, then which of the following could be the standard deviation of the ten numbers?\nI. 0\nII. 30\nIII. 20\n\n### Options:\nA. I\nB. all three options\nC. II\nD. III\nE. I&II\n\n### Answer:\nWe know that we have 10 numbers (and they could be ANY values - including negatives and non-integers) and we know that the average of those numbers is 10. This is meant to say that there are an INFINITE number of possible sets of 10 numbers that fit this prompt.\nIF all ten numbers were the same (meaning that we had ten 10s), then the SD would be 0. The more 'spread out' those ten numbers get, the higher the SD becomes. Since there's no limit to the 'spread', then there's no limit to what the SD could be either. Thus, it could be 10 or 20 or any other number.\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n7 baseball players each stand at different corners of a baseball diamond. The sides of the diamond are all of equal length. Two arrangements of baseball players are considered different only when the relative positions of the players differ. How many different ways can the baseball players arrange themselves around the diamond?\n\n### Options:\nA. 4\nB. 6\nC. 16\nD. 24\nE. 720\n\n### Answer:\nit is like a circular arrangement.\ntotal ways for n people to arrange in a circle is = factorial (n-1)\nin this case n= 7\nhence ans = 6 factorial = 720\nhence E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man said to his son, \"I was two-third of your present age when you were born\". If the present age of the man is 48 years, find the present age of the son?\n\n### Options:\nA. 25.7 years\nB. 28 years\nC. 29.3 years\nD. 28.8 years\nE. 28.9 years\n\n### Answer:\nPresent age of the son be P, he was born P years ago.\nThe age of the man was: (48 - P).\nHis age when the son was born should be equal to 2/3 of P.\n(48 - P) = 2/3 P\n5P = 144 => P = 28.8\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn the city of San Durango, 60 people own cats, dogs, or rabbits. If 34 people owned cats, 40 owned dogs, 10 owned rabbits, and 12 owned exactly two of the three types of pet, how many people owned all three?\n\n### Options:\nA. 2\nB. 6\nC. 8\nD. 12\nE. 32\n\n### Answer:\nTotal = C + D + R - (CD + DR + CR) - 2CDR\n60 = 34 + 40 + 10 - (12) - 2x\nx = 6\nSo, answer will be B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhen processing flower-nectar into honey bees' extract, a considerable amount of water gets reduced. How much flower-nectar must be processed to yield 1kg of honey, if nectar contains 50% water, and the honey obtained from this nectar contains 25% water?\n\n### Options:\nA. 1.2 kg\nB. 1.5 kg\nC. 1.7 kg\nD. 1.9 kg\nE. None of these\n\n### Answer:\nExplanation :\nFlower-nectar contains 50% of non-water part.\nIn honey this non-water part constitutes 75% (100-25).\nTherefore 0.5 X Amount of flower-nectar = 0.75 X Amount of honey = 0.75 X 1 kg\nTherefore amount of flower-nectar needed =\n(0.75/0.51)kg=1.5 kgs\nAnswer : B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how many ways 8 different tickets Q can be distributed between Jane and Bill if each is to receive any even number of tickets and all 8 tickets to be distributed.\n\n### Options:\nA. From 2 to 6 inclusive.\nB. From 98 to 102 inclusive.\nC. From 122 to 126 inclusive.\nD. From 128 to 132 inclusive.\nE. From 196 to 200 inclusive.\n\n### Answer:\nPossibilities\nJ 8 6 4 2 0\nB 0 2 4 6 8\n# of ways 8C8 8C6 8C4 8C2 8C0\nQ=1+28+70+28+1 = 128 Answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA and B walk around a circular track. A and B walk at a speed of 2 rounds per hour and 3 rounds per hour respectively. If they start at 8 a.m. from the same point in opposite directions, how many times shall they cross each other before 9.30 a.m.?\n\n### Options:\nA. 9.39 am\nB. 9.80 am\nC. 9.30 am\nD. 9.32 am\nE. 5.30 am\n\n### Answer:\nRelative speed = Speed of A + Speed of B (\u2234 they walk in opposite directions)\n= 2 + 3 = 5 rounds per hour\n=> They cross each other 5 times in 1 hour and 2 times in 1/2 hour\nTime duration from 8 am to 9.30 am = 1.5 hour\nHence they cross each other 7 times before 9.30 am\nAnswer : C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRs.8000 become Rs.8652.8 in a certain interval of time at the rate of 4% per annum of C.I. Find the time?\n\n### Options:\nA. 6 years\nB. 8 years\nC. 9 years\nD. 3 years\nE. 2 years\n\n### Answer:\n8652.8 = 8000(26/25)N\n(26/25)^2 = (26/25)N => N = 2\nAt the end of two years what will be the comp.Answer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n5358 x 53 = ?\n\n### Options:\nA. 283974\nB. 283758\nC. 273298\nD. 273258\nE. 277382\n\n### Answer:\nA\n5358 x 53 = 5358 x (50 + 3)\n= 5358 x 50 + 5358 x 3\n= 267900 + 16074\n= 283974.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA student chose a number, multiplied it by 2, then subtracted 138 from the result and got 112. What was the number he chose?\n\n### Options:\nA. 123\nB. 267\nC. 125\nD. 267\nE. 120\n\n### Answer:\nLet xx be the number he chose, then\n2\u00e2\u2039\u2026x\u00e2\u02c6\u2019138=112\nx=125\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA can finish a work in 10 days and B can do same work in half the time taken by A. then working together, what part of same work they can finish in a day?\n\n### Options:\nA. 1/5\nB. 1/6\nC. 1/7\nD. 3/10\nE. None of these\n\n### Answer:\nExplanation:\nPlease note in this question, we need to answer part of work for a day rather than complete work. It was worth mentioning here because many do mistake at this point in hurry to solve the question\nSo lets solve now,\nA's 1 day work = 1/10\nB's 1 day work = 1/5 [because B take half the time than A]\n(A+B)'s one day work =\n(1/10+1/5)=3/10\nSo in one day 3/10 work will be done\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe number of bacteria in a petri dish increased by 50 percent every 2 hours. If there were 108 million bacteria in the dish at 2: 30 p.m., at what time were there 32 million bacteria in the dish?\n\n### Options:\nA. 6: 00 p.m.\nB. 8: 00 p.m.\nC. 6: 00 a.m.\nD. 8: 30 a.m.\nE. 10: 00 a.m.\n\n### Answer:\nGiven:\nThe number of bacteria in a petri dish increased by 50 percent every 2 hours\nThere were 108 million bacteria in the dish at 2: 00 p.m\nSince the bacteria is increasing by 50% every 2 hours, this means that the number is multiplied by 1.5 every 2 hours.\nRequired: At what time were there 32 million bacteria in the dish?\nAssume that there were n intervals of 2 hours between 32 million and 108 million.\n32 * (1.5)^n = 108\n(3/2)^n = 108/32 = 27/8 = (3/2)^3\nHence n = 3 intervals.\nEach interval was of 2 hours. Therefore, the number of hours = 6\nSubtracting 6 hours from 2H30 PM, we get 8H30 AM as the answer.\nOption D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a(a + 7) = 18 and b(b + 7) = 18, where a \u2260 b, then a + b =\n\n### Options:\nA. \u221248\nB. \u22125\nC. 2\nD. -7\nE. 48\n\n### Answer:\ni.e. if a = 2 then b = -9\nor if a = -9 then b = 2\nBut in each case a+b = -9+2 = -7\nAnswer: option D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA chair is bought for Rs.600/- and sold at a loss of 10% find its selling price\n\n### Options:\nA. Rs.540/-\nB. Rs.550/-\nC. Rs.560/-\nD. Rs.590/-\nE. Rs.580/-\n\n### Answer:\n100 % ------> 600 (100 * 6 = 600)\n90 % ------> 540 (90 * 6 = 540)\nSelling price = Rs.540/-\nA)\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA tank is 25 m long, 12 m wide and 6 m deep. The cost of plastering its walls and bottom at 75 paise per sq. m, is:\n\n### Options:\nA. Rs. 456\nB. Rs. 458\nC. Rs. 558\nD. Rs. 568\nE. None of these\n\n### Answer:\nExplanation:\nArea to be plastered = [2(l + b) x h] + (l x b)\n= {[2(25 + 12) x 6] + (25 x 12)} m2\n= (444 + 300) m2\n= 744 m2.\nCost of plastering = Rs. 744 x 75 / 100 = Rs. 558\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThree friends Dhoni, Rahul and Aswin divide $1540 amongs them in such a way that if $10, $12 and $18 are removed from the sums that Dhoni, Rahul and Aswin received respectively, then the share of the sums that they got will be in the ratio of 15: 17: 18. How much did Aswin receive?\n\n### Options:\nA. $560\nB. $562\nC. $564\nD. $558\nE. $570\n\n### Answer:\nA+B+C = 1540\nGiven ratio 15:17:18\nLet us say the shares of A,B,C deducting 10,12,18 be a,b,c\na+b+c = 1540-40= 1500 = 50K\nc share = (1500X18)/50 = 540\nC = Aswin share = 540+18= 558\nOption D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are 600 boys in a hostel. Each plays either hockey or football or both. If 75% play hockey and 55% play football, how many play both?\n\n### Options:\nA. 120\nB. 150\nC. 200\nD. 180\nE. 160\n\n### Answer:\nn(A) = 75*600/100 = 450\nn(B) = 55*600/100 = 330\nn(AUB) = 600\nn(AnB) = 450+330-600 = 180\nAnswer is D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the are of an equilateral triangle of side 16 cm?\n\n### Options:\nA. 64\u221a6 cm2\nB. 84\u221a3 cm2\nC. 64\u221a9 cm2\nD. 64\u221a3 cm2\nE. 66\u221a3 cm2\n\n### Answer:\nArea of an equilateral triangle = \u221a3/4 S2\nIf S = 16, Area of triangle = \u221a3/4 * 16 * 16\n= 64\u221a3 cm2;\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe pages of a report are numbered consecutively from 1 to 13. If the sum of the page numbers up to and including page number x of the report is equal to one less than the sum of the page numbers following page number x, then x =\n\n### Options:\nA. 5\nB. 6\nC. 7\nD. 8\nE. 9\n\n### Answer:\nsum of the first few numbers =1+2+3+4+5+6+7+8+9 =45\nsum of the last few = 10 +11+12+13 =46 page no.9 answer .E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOf the 20 members of a kitchen crew, 17 can use the meat-cutting machine, 18 can use the bread-slicing machine, and 15 can use both machines. If one member is chosen at random, what is the probability that the member chosen will be someone who cannot use either machine?\n\n### Options:\nA. 0\nB. 1/10\nC. 1/7\nD. 1/4\nE. 1/3\n\n### Answer:\nYou know how to solve for Total number of people who can use at least one machine:\nTotal = n(A) + n(B) - n(A and B)\nTotal people who can use at least one machine = 17 + 18 - 15 = 20\nSo all 20 people know how to use at least one machine. Hence, if you pick anyone, the probability is 0 that he wouldn't know how to use any machine.\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf q = 20! + 17, then q is divisible by which of the following?\nI. 15\nII. 17\nIII. 19\n\n### Options:\nA. None\nB. I only\nC. II only\nD. I and II\nE. II and II\n\n### Answer:\nAnother crude way to answer this, if you did not know the properties above would be to consider that that 20! will have the number ending in 00 due to 10 and 20 being included.\nSo q!+17 = xxxx00 +17 = xxxx17 which is only possibly divisible by 17. Hence Option C is the answer.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn the number 11,0AB, A and B represent the tens and units digits, respectively. If 11,0AB is divisible by 52, what is the greatest possible value of B \u00d7 A?\n\n### Options:\nA. 0\nB. 5\nC. 10\nD. 15\nE. 22\n\n### Answer:\nYou should notice that 52*2=110 so 11,000 is divisible by 55: 55*200=11,000 (or you can notice that 11,000 is obviously divisible by both 5 and 11 so by 55) --> B*A=0*0=0. Next number divisible by 55 is 11,000+55=11,055: B*A=5*5=22 (next number won't have 110 as the first 3 digits so we have only two options 0 and 25).\nAnswer: E.\n!\nPlease post PS questions in the PS subforum:gmat-problem-solving-ps-140/\nPlease post DS questions in the DS subforum:gmat-data-sufficiency-ds-141/\nNo posting of PS/DS questions is allowed in the mainMath forum.\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe speed of a boat in still water is 60kmph and the speed of the current is 25kmph. Find the speed downstream and upstream?\n\n### Options:\nA. 80,47 kmph\nB. 80,80 kmph\nC. 85,35 kmph\nD. 80,40 kmph\nE. 83,40 kmph\n\n### Answer:\nSpeed downstream = 60 + 25 = 85 kmph\nSpeed upstream = 60 - 25 = 35 kmph.Answer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the domain of function f given by f(x) = -x 2 + 6x is given by the interval [0 , 6], then the range of f is given by the interval\n\n### Options:\nA. [0 , 9]\nB. [0 , 6]\nC. [0 , 3]\nD. [3 , 6]\nE. None\n\n### Answer:\nIf the domain of function f given by f(x) = -x 2 + 6x is given by the interval [0 , 6], then the range of f is given by the interval\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf Y > X and XM < YM, what must be true?\n\n### Options:\nA. M >0.\nB. M < Y.\nC. X < 0.\nD. M < 0.\nE. Y < 0.\n\n### Answer:\nX>Y, bus as soon as M is multiplied to both sides inequality sign changes.\nThis is only possible when -ve is multiplied on both sides. That means M is -ve\nA is the answer\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRight triangle ABC is to be drawn in the xy-plane so that the right angle is at A and AB is parallel to the y-axis. If the x- and y-coordinates of A, B, and C are to be integers that are consistent with the inequalities -4 \u2264 x \u2264 2 and 4 \u2264 y \u2264 9 , then how many different triangles can be drawn that will meet these conditions?\n\n### Options:\nA. 54\nB. 432\nC. 864\nD. 2,916\nE. 148,824\n\n### Answer:\nWe have the rectangle with dimensions 9*4 (9 horizontal dots and 4 vertical). AB is parallel to y-axis and AC is parallel to x-axis.\nChoose the (x,y) coordinates for vertex A: 9C1*4C1;\nChoose the x coordinate for vertex C (as y coordinate is fixed by A): 8C1, (9-1=8 as 1 horizontal dot is already occupied by A);\nChoose the y coordinate for vertex B (as x coordinate is fixed by A): 3C1, (4-1=3 as 1 vertical dot is already occupied by A).\n9C1*4C1*8C1*3C1=864.\nAnswer: C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain sum amounts to Rs.1550 in 2 years and Rs.1700 in 3 years. Find the rate % per annum?\n\n### Options:\nA. 5.67%\nB. 7.67%\nC. 6.67%\nD. 4.67%\nE. 8.67%\n\n### Answer:\n2 --- 1550\n3 --- 1700\n--------------\n1 --- 150\nN = 1 I = 150 R = ?\nP = 1550 - 300= 1250\n150 = (1250*1*R)/100\nR = 6.67%\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many terms are there in 2, 4, 8, 16,..., 2048?\n\n### Options:\nA. 14\nB. 11\nC. 12\nD. 10\nE. 8\n\n### Answer:\n2, 4, 8, 16, ...,2048 is a G.P with a =2\nand r =4/2 =2\nLet the number of terms be n. Then\n2 x 2 ^n-1 = 2048\nor 2^n-1 = 1024= 2^10\nThus n - 1 =10\nn= 11\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn the following sequence: [x, y, z, 6, 8, 16, 28] each number is equal to the sum of the three numbers preceding it. What is x+y?\n\n### Options:\nA. 2\nB. 3\nC. 4\nD. 5\nE. -2\n\n### Answer:\nlets start from z, as per the question stem\nz + 6 + 8 = 16\n-->> z= 2\nsimilarly, y +2 + 6 = 8\n--> y = 0\nsimilarly,, x + 0 + 2 = 6\n--> x = 4\nhence , x+y = 4-0 = 4 --> x+y=4\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a 1000 m race Usha beats Shiny by 50 m. In the same race, by what time margin Shiny beat Mercy.\nwho runs at 4 m/s ?\n\n### Options:\nA. 100 sec.\nB. 50 sec\nC. 25 sec\nD. Data not sufficient\nE. None of these\n\n### Answer:\nExplanation:\nSpeed of Shiny = 50/ 10 = 5m/s\nTime taken by shiny to complete the race is B = 1000/5 = 200 sec.\nTime taken by Baley to complete the race is D = 1000/4 = 250 sec.\nHence, D-B = 50 sec\nAnswer : B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOf 30 applicants for a job, 12 had at least 4 years' experience, 18 had degrees, and 3 had less than 4 years' experience and did not have a degree.How many of the applicants had at least 4 years' experience and a degree?\n\n### Options:\nA. 14\nB. 13\nC. 9\nD. 7\nE. 5\n\n### Answer:\nD. 7\n30 - 3 = 27\n27 - 12 - 18 = -7\nThen 7 are in the intersection between 4 years experience and degree.\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFor any integer k greater than 1, the symbol k* denotes the product of all integers between 1 and k, inclusive. If k* is a multiple of 2835 what is the least possible value of k?\n\n### Options:\nA. 5\nB. 7\nC. 9\nD. 11\nE. 13\n\n### Answer:\n2835 = 3*3*3*3*5*7\nThus k must include numbers at least up to the number 9 so that there are at least four appearances of 3 (that is: 3, 6, and 9=3*3).\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nEddy and Freddy start simultaneously from city A and they travel to City B and City C respectively. Eddy takes 3 hours and Freddy takes 4 hours to complete the journey. If the distance between City A and City B is 480 kms and City A and City C is 300 kms. What is the ratio of their average speed of travel? (Eddy: Freddy)\n\n### Options:\nA. 32/15\nB. 3/8\nC. 8/5\nD. 5/8\nE. 5/3\n\n### Answer:\nDistance traveled by Eddy = 480 km\nTime taken by Eddy = 3 hours\nAverage speed of Eddy = 480/3 = 160 km/hour\nDistance traveled by Freddy = 300 km\nTime taken by Freddy = 4 hours\nAverage speed of Freddy = 300/4 = 75 km/hour\nRatio of average speed of Eddy to Freddy = 160/75 = 32/15\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAngelina walked 100 meters from her home to the grocery at a constant speed. She then walked 180 meters to the gym at double the speed. She spent 40 seconds less on her way from the grocery to the gym than on her way from home to the grocery. What was Angelina's speed, in meters per second, from the grocery to the gym?\n\n### Options:\nA. 2\nB. 3\nC. 0.5\nD. 6\nE. 12\n\n### Answer:\nlet the speed be X...\nso time taken from home to grocery= 100/x..\nthe speed to gym = 2x..\nso time taken = 180/2x=90/x..\nits given 100/x-90/x=40..\n10/x=40..\nx=0.25m/secs..\nso grocery to gym=2*0.25=0.5m/s...\nAnswer : C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA started a business with an investment of Rs. 70000 and after 6 months B joined him investing Rs. 120000. If the profit at the end of a year is Rs. 91000, then the share of B is?\n\n### Options:\nA. A)44500\nB. B)42000\nC. C)44098\nD. D)43007\nE. E)44098\n\n### Answer:\nRatio of investments of A and B is (70000 * 12) : (120000 * 6) = 7 : 6\nTotal profit = Rs. 91000\nShare of B = 6/13 (91000)\n= Rs. 42000\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA copy machine, working at a constant rate, makes 30 copies per minute. A second copy machine, working at a constant rate, makes 55 copies per minute. Working together at their respective rates, how many copies do the two machines make in half an hour ?\n\n### Options:\nA. 90\nB. 2,700\nC. 4,500\nD. 2,550\nE. 324,000\n\n### Answer:\nTogether the two machines make 30+55=85 copies per minute. So, in half an hour they will make 85*30=2,550 copies.\nAnswer: D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo trains of equal lengths take 10 sec and 18 sec respectively to cross a telegraph post. If the length of each train be 120 m, in what time will they cross other travelling in opposite direction?\n\n### Options:\nA. 11\nB. 9\nC. 13\nD. 14\nE. 12.8\n\n### Answer:\nSpeed of the first train = 120/10 = 12 m/sec.\nSpeed of the second train = 120/18 = 6.7 m/sec.\nRelative speed = 12 + 6.7 = 18.7 m/sec.\nRequired time = (120 + 120)/18.7 = 12.8 sec.\nAnswer: Option E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the maximum value of vx - yz. If the value of v,x,y,z have to be chosen from the set A where A(-3,-2,-1,0,1,2,3)\n\n### Options:\nA. 15\nB. 66\nC. 25\nD. 88\nE. 17\n\n### Answer:\nExplanation:\nTo maximize the value of vx - yz, we make yz negative and vx as maximum as possible using given value.\nvx\u2212yz=(\u22123)2\u2212(\u22123\u00d72)vx\u2212yz=(\u22123)2\u2212(\u22123\u00d72) = 15\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nDan's age after 18 years will be 8 times his age 3 years ago. What is the present age of Dan?\n\n### Options:\nA. 4\nB. 6\nC. 8\nD. 10\nE. 12\n\n### Answer:\nLet Dan's present age be x.\nx+18 = 8(x-3)\n7x = 42\nx = 6\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train can travel 50% faster than a car. Both start from point A at the same time and reach point B 75 kms away from A at the same time. On the way, however, the train lost about 12.5 minutes while stopping at the stations. What is the speed of the car?\n\n### Options:\nA. 22\nB. 28\nC. 120\nD. 287\nE. 278\n\n### Answer:\nLet speed of the car = x kmphThen speed of the train = (100+50)100x=150100x=32x kmphTime taken by the car to travel from A to B=75x hoursTime taken by the train to travel from A to B=75(32x)+12.560 hoursSince Both start from A at the same time and reach point B at the same time75x=75(32x)+12.56025x=12.560x=25\u00d76012.5=2\u00d760=120\nAnswer : C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a hockey team of 11 members, the captain's age is 26 years old and the goalkeeper is 3 years older If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. What is the average age of the team?\n\n### Options:\nA. 23 years\nB. 24 years\nC. 25 years\nD. 27 years\nE. 29 years\n\n### Answer:\nExplanation :\nLet the average age of the whole team be x years.\n11x - (26 + 29) = 9(x - 1)\n11x - 9x = 46\n2x = 46\nx = 23\nSo, average age of the team is 23 years.\nAnswer : A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA shopkeeper sold an article at $100 with 20% profit. Then find its cost price?\n\n### Options:\nA. $120\nB. $100\nC. $91\nD. $83\nE. $69\n\n### Answer:\ncost price = selling price *100/(100+profit)\nC.P. = 100*100/120 = $83(approximately)\nAnswer is D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the sum lend at C.I. at 5 p.c per annum will amount to Rs.441 in 2 years?\n\n### Options:\nA. 200\nB. 400\nC. 378\nD. 883\nE. 732\n\n### Answer:\n441 = P(21/20)2\nP = 400\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOf the 500 employees in a certain company, 25 percent will be relocated to City X and the remaining 75 percent will be relocated to City Y. However, 40 percent of the employees prefer City Y and 60 percent prefer City X. What is the highest possible number of employees who will be relocated to the city they prefer?\n\n### Options:\nA. 65\nB. 100\nC. 115\nD. 130\nE. 325\n\n### Answer:\n300 prefer X (Group 1);\n200 prefer Y (Group 2).\nCity Y needs 375 people: letall 200 who prefer Y (entire Group 2) be relocated there, the rest 175 will be those who prefer X from Group 1;\nCity X needs 125 people: 300-175=125 from Group 1 will be relocated to X, which they prefer.\nSo, the highest possible number of employees who will be relocated to the city they prefer is 200+125=325.\nAnswer: E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA part of certain sum of money is invested at 10% per annum and the rest at 12% per annum, if the interest earned in each case for the same period is equal, then ratio of the sums invested is?\n\n### Options:\nA. 4:2\nB. 4:8\nC. 4:3\nD. 4:0\nE. 6:5\n\n### Answer:\n12:10\n= 6:5\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA numberais squared and then multiplied by negative 3. The result of this operation Q is equal to three times the sum of three timesaand two. What is one possible value ofa?\n\n### Options:\nA. -3\nB. -2\nC. 1\nD. 2\nE. 3\n\n### Answer:\nQ=-3*a^2=3(3a+2)\na= -2 or -1\na=-2=B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n(X)+4671+6514-7687=19190. Calculate the value of X\n\n### Options:\nA. 15615\nB. 15692\nC. 15687\nD. 15112\nE. 15690\n\n### Answer:\nx+4671+6514-7687=19190\n=x+4671+6514=19190+7687\n=x+11185=26877\n=x=26877-11185\n=15692\nAnswer is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA horse chases a pony 3 hours after the pony runs. Horse takes 4 hours to reach the pony. If the average speed of the horse is 35 kmph, what s the average speed of the pony?\n\n### Options:\nA. 20kmph\nB. 22kmph\nC. 24kmph\nD. 26kmph\nE. 28kmph\n\n### Answer:\npony take 7 hours and horse take 4 hours...then Distance chased by them is 35*4.so speed of pony is (35*4)/7=20kmph.\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the average of 55, 48, 507, 2, 684 and y is 223, then what is y?\n\n### Options:\nA. 701\nB. 120\nC. 42\nD. 868\nE. 1\n\n### Answer:\ny=42, because:\n(55+48+507+2+684+y)/6 = 223\n(55+48+507+2+684+y)/6 *6 = 223*6\n(55+48+507+2+684+y)-1296= 1338-1296\ny=42\nSo the correct answer is C, 42.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the simple interest on Rs.580 for 11 months at 9 paisa per month?\n\n### Options:\nA. 574\nB. 270\nC. 566\nD. 266\nE. 121\n\n### Answer:\nI = (580*11*9)/100 = 574\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the invalid no.from the following series 15, 16, 34, 105, 424, 2123, 12756\n\n### Options:\nA. 16\nB. 34\nC. 105\nD. 424\nE. 2123\n\n### Answer:\n2nd term = (1st term) * 1 + 1 = 15 *1 + 1 = 16.\n3rd term = (2nd term) * 2 + 2 = 16 * 2 + 2 = 34\n4th term = (3th term) *3 + 3 = 34 * 3 + 3 = 105\n5th term = (4th term) * 4 + 4 = 105 * 4 + 4 = 424\n6th term = (5th term) * 5 + 5 = 424 * 5 + 5 = 2125\n6th term should 2125 instead of 2123.\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf Rs.3250 be divided among Ram, Shyam and Mohan in the ratio of 1/2:1/3:1/4 then the share of each are?\n\n### Options:\nA. Ram = Rs.1500, Shyam = Rs.1000, Mohan = Rs.750\nB. Ram = Rs.2500, Shyam = Rs.500, Mohan = Rs.250\nC. Ram = Rs.1200, Shyam = Rs.1300, Mohan = Rs.750\nD. Ram = Rs.3500, Shyam = Rs.500, Mohan = Rs.250\nE. None\n\n### Answer:\n1/2:1/3:1/4 = 6:4:3\nRam = 6/13 * 3250 = 1500\nShyam = 4/13 * 3250 = 1000\nMohan = 3/13 * 3250 = 750\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA departmental store has 4 managers and 16 associates. The 4 managers have an average salary of $900. The 16 associates have an average salary of $10,000. What is the average salary for the departmental store?\n\n### Options:\nA. $8180\nB. $9190\nC. $4140\nD. $5150\nE. $6160\n\n### Answer:\nNumber of managers is 4\nTheir average salary is $900\nNumber of associates is 16\nTheir average salary is $10,000\nTotal salary of managers is 4*900=$3600\nTotal salary of associates is 16*10,000=$160,000\nTotal salary for the departmental store is 160,000+3600=163600\nAverage salary for the departmental store is 163600/20=8180\nAnswer is A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a certain match all the teams were to play with each other. If there are 5 teams, how many matches will have to be played?\n\n### Options:\nA. 40\nB. 45\nC. 60\nD. 10\nE. None of the above\n\n### Answer:\n5c2\n=10\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA and B started a partnership business investing Rs. 20,000 and Rs. 15,000 respectively. C joined them with Rs. 20,000 after six months. Calculate B's share in total profit of Rs. 25,000 earned at the end of 2 years from the starting of the business?\n\n### Options:\nA. 6500\nB. 2500\nC. 5000\nD. 10000\nE. 7500\n\n### Answer:\nA : B : C\n=20000\u00d724:15000\u00d724:20000\u00d718\n=20\u00d74:15\u00d74:20\u00d73\n=4\u00d74:3\u00d74:4\u00d73\n=4:3:3\nB's share = 25000\u00d7(3/10)=7500\nAnswer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a group of 2 boys and 8 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be selected?\n\n### Options:\nA. 120\nB. 140\nC. 160\nD. 180\nE. 200\n\n### Answer:\nNumber of ways to select four children is 10C4 = 210\nNumber of ways to choose only girls is 8C4 = 70\nNumber of ways that at least one boy is selected is 210 - 70 = 140\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA barrel full of beer has 2 taps one midway,,which draw a litre in 6 minutes and the other at the bottom,which draws a litre in 4 minutes. The lower tap is lower normally used after the level of beer in the barrel is lower than midway.The capacity of the barrel is 36 litres. A new assistant opens the lower tap when the barrel is full and draws out some beer. As a result the lower tap has been used 24 minutes before the usual time. For how long was the beer drawn out by the new assistant ?\n\n### Options:\nA. 15 minutes\nB. 16 minutes\nC. 17 minutes\nD. 18 minutes\nE. None of these\n\n### Answer:\nSol. The top tab is operational till 18 litres is drawn out.\n\u2234 Time after which the lower tap is usually open\n= 18 \u00d7 6 = 108 minutes\n\u2234 Time after which it is open now = 108 \u2013 24 = 84 minutes\n\u2234 Litres drawn = 84/6 = 14 litres\n\u2234 18 \u2013 14 = 4 litres were drawn by the new assistant.\n\u2234 Time = 4 \u00d7 4 = 16 minutes Answer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA grocer has a sale of Rs. 435, Rs. 927, Rs. 855, Rs. 230 and Rs. 562 for 5 consecutive days. How much sale must he have in the sixth day so that he gets an average sale of Rs. 625?\n\n### Options:\nA. Rs 741\nB. Rs 5991\nC. Rs 6001\nD. Rs 6991\nE. None of these\n\n### Answer:\nExplanation :\nTotal sale for 5 days = Rs. (435 + 927 + 855 + 230 + 562)\n= Rs. 3009.\nRequired sale = Rs. [ (625 x 6) - 3009 ]\n= Rs. (3750 - 3009)\n= Rs. 741.\nAnswer : A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSolution P is 20 percent lemonade and 80 percent carbonated water by volume; solution Q is 45 percent lemonade and 55 percent carbonated water by volume. If a mixture of PQ contains 67.5% percent carbonated water, what percent of the volume of the mixture is P?\n\n### Options:\nA. 25%\nB. 40%\nC. 50%\nD. 60%\nE. 75%\n\n### Answer:\n67.5% is 12.5%-points below 80% and 12.5%-points above 55%.\nSo the ratio of solution P to solution Q is 1:1.\nMixture P is 1/2 = 50% of the volume of mixture PQ.\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf grapes are 93% water and raisins are 16% water, then how many kilograms did a quantity of raisins, which currently weighs 8 kilograms, weigh when all the raisins were grapes? (Assume that the only difference between their raisin-weight and their grape-weight is water that evaporated during their transformation.)\n\n### Options:\nA. 92\nB. 96\nC. 100\nD. 104\nE. 108\n\n### Answer:\nLet x be the original weight.\nThe weight of the grape pulp was 0.07x.\nSince the grape pulp is 84% of the raisins, 0.07x = 0.84(8).\nThen x = 12*8 = 96 kg.\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many words can be formed by using all letters of the word \u2018PENCIL\u2019 ?\n\n### Options:\nA. 480\nB. 600\nC. 720\nD. 900\nE. 1060\n\n### Answer:\nThe word contains 6 different letters.\nThe number of permutations is 6! = 720\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the President and Vice President must sit next to each other in a row with 1 other members of the Board, how many different seating arrangements are possible?\n\n### Options:\nA. 4\nB. 16\nC. 8\nD. 10\nE. 2\n\n### Answer:\nWe need to take President and VP as one unit. Therefore we have 2 people to arrange=2! ways\nAlso, we both President and VP can be arranged in 2 ! ways.\nReqd no of ways=2!*2!=4 ways\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the day before yesterday was Wednesday, when will Sunday be?\n\n### Options:\nA. Day after tomorrow\nB. Tomorow\nC. Two days after today\nD. Today\nE. none\n\n### Answer:\nExplanation:\nDay before yesterday was Wednesday\n=>Yesterday was a Thursday\n=> Today is a Friday\n=> Tomorrow is a Saturday\n=> The day after tomorrow will be a Sunday\nAnswer: Option A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFrom the beginning to the end of 2007, the price of a stock rose 20 percent. In 2008, it dropped 25 percent. In 2009, it rose 30 percent. What percent of the stock\u00e2\u20ac\u2122s 2007 starting price was the price of the stock at the end of 2009?\n\n### Options:\nA. 80\nB. 117\nC. 95\nD. 100\nE. 108\n\n### Answer:\nAssume a value at the beginning of 2007. As this is a % question, assume P=100.\nAt the end of 2007 it becmae = 1.2*100=120\nAt the end of 2008 it decreased by 25% = 120*.75 = 90\nAt the end of 2009 it increased by 30% = 90*1.3 = 117\nThus ratio = 117/100 = 1.17 (in % terms = 117%). Thus B is the correct answer.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. How far is the place?\n\n### Options:\nA. 2.98\nB. 2.88\nC. 2.82\nD. 2.86\nE. 2.81\n\n### Answer:\nM = 6\nS = 1.2\nDS = 6 + 1.2 = 7.2\nUS = 6 - 1.2 = 4.8\nx/7.2 + x/4.8 = 1\nx = 2.88\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a simultaneous throw of two coins the probability of getting at least one head is ?\n\n### Options:\nA. 3/4\nB. 1/2\nC. 1/4\nD. 2/3\nE. 1/5\n\n### Answer:\nS={HH,HT,TH,TT}\nE be the event of getting at least one head is {HT,TH,HH}\nP(E)=n(E)/n(S)=3/4\nAnswer(A)\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe radius of a cone is 10 m, height 21 m. The volume of the cone is:\n\n### Options:\nA. 2200\nB. 1100\nC. 5500\nD. 3300\nE. 1050\n\n### Answer:\n1/3 \u03c0rh = 1/3 \u00d7 22/7 \u00d7 100 \u00d7 21\n= 2200 m(power3)\nAnswer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf P represents the product of the first 13 positive integers, which of the following must be true?\nI. P is an odd number\nII. P is a multiple of 18\nIII. P is a multiple of 29\n\n### Options:\nA. I only\nB. II only\nC. III only\nD. None of the above\nE. All of the above\n\n### Answer:\nAnswer = B) II only\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe lenght of a room is 5.5 m and width is 4 m. Find the cost of paving the floor by slabs at the rate of Rs. 950 per sq. metre.\n\n### Options:\nA. s. 20,550\nB. s. 15,600\nC. s. 20,900\nD. s. 17,600\nE. s. 17,900\n\n### Answer:\nArea of the floor = (5.5 \u00c3\u2014 4) m2 = 22 m2.\nCost of paving = Rs. (950 \u00c3\u2014 22) = Rs. 20900\nAnswer: Option C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJohn bought an old Vehicle for $42000. He spent $13000 on repairs and sold it for $64900. What is his profit percent?\n\n### Options:\nA. 11%\nB. 15%\nC. 18%\nD. 17%\nE. 13%\n\n### Answer:\nC\n18%\nTotal CP = Rs. 42000 + Rs. 13000 = Rs. 55000 and SP = Rs. 64900\nProfit(%) = (64900 - 55000)/55000 * 100 = 18%\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA \u201cpalindromic integer\u201d is an integer that remains the same when its digits are reversed. So, for example, 43334 and 516615 are both examples of palindromic integers. How many 6-digit palindromic integers are both even and greater than 300,000?\n\n### Options:\nA. 200\nB. 216\nC. 300\nD. 400\nE. 2,500\n\n### Answer:\nThe first digit and last digit are the same so the 3 possibilities are 4, 6, or 8.\nThe second and third digits can be any digit from 0 to 9.\nThe total number of palindromic integers is 3*10*10 = 300\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a certain number is divisible by 12 and 10, it is NOT necessarily divisible by which of the following?\n\n### Options:\nA. 4\nB. 6\nC. 15\nD. 20\nE. 24\n\n### Answer:\nIf a certain number is divisible by 12 and 10, it is NOT necessarily divisible by which of the following?\nlet the certain number be 60, which is both divisible by 12 and 10.\n60/24 = 5/2\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?\n\n### Options:\nA. 186 m\nB. 176 m\nC. 872 m\nD. 150 m\nE. 765 m\n\n### Answer:\nSpeed=(60 * 5/18) m/sec = (50/3) m/sec Length of the train\n= (Speed x Time) = (50/3 * 9) m\n= 150 m.\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAn engagement team consists of a project manager, two team leaders, and four consultants. There are 2 candidates for the position of project manager, 3 candidates for the position of team leader, and 7 candidates for the 4 consultant slots. If 2 out of 7 consultants refuse to be on the same team, how many different teams are possible?\n\n### Options:\nA. 25\nB. 35\nC. 150\nD. 210\nE. 300\n\n### Answer:\nAnswer= Total number combinations - Total number of combinations with constraints\nTotal number of combinations = 2C1*3C2*7C4= 210\nTotal number of combinations with constraints = 2C1*3C2*5C2=60\nAnswer=210-60=150\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 18 is 15 percent of 25 percent of a certain number, what is the number?\n\n### Options:\nA. 9\nB. 36\nC. 480\nD. 81\nE. 400\n\n### Answer:\nLet the certain number be x.\n=> (15/100)*(25/100)*x = 18;\n=> x=480;\nAns is (C).\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n4 persons a, b, c, d are to be lined up in a row. If a, b, and c adhere always together, how many possible cases are there?\n\n### Options:\nA. 12\nB. 36\nC. 48\nD. 72\nE. 144\n\n### Answer:\nfirstly it is not GEOMETRY but COMBINATIONS, so changing the TAG accordingly..\ntotal 4 are there..\ntake a,b, and c as one,so total =2..\nthese 2 can be arranged in 2! ways..\na,b, and c can be arranged within themselves in 3! ways ..\nTOTAL = 2!*3!=12\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf apples cost x dollars per m dozen, how many dollars will it cost to buy n apples?\n\n### Options:\nA. xn/(12m) dollars\nB. xn/m\nC. m/(xn)\nD. 12m/(xn)\nE. 12mn/x\n\n### Answer:\nlet it 2 dollars for 2 dozens(24) and we are asked to find the value n apples...let n be 4...\nIn order to buy 24 apples it took 2 dollars...then for 4 apples it'll take 4*2/12*2 = 1/3.. i.e. n*x/12*m.\nAnswer: option A is correct answer...\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA company produces 65000 bottles of water everyday. If a case can hold 13 bottles of water .How many cases are required by the company to hold its one day production\n\n### Options:\nA. 2000\nB. 4500\nC. 5000\nD. 8000\nE. 9000\n\n### Answer:\nNumber of bottles that can be held in a case = 13\nNumber of cases required to hold 65000 bottles = 65000/13=5000 cases.\nSo the answer is C =5000\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average of first 12 natural numbers is?\n\n### Options:\nA. 7.6\nB. 6.5\nC. 6.1\nD. 6.8\nE. 7.2\n\n### Answer:\nSum of 12 natural no.\n= 156/2 = 78\nAverage = 78/12\n= 6.5\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nCubes with each side one inch long are glued together to form a larger cube. The larger cube's face is painted with red color and the entire assembly is taken apart. 24 small cubes are found with no paints on them . How many of unit cubes have at least one face that is painted red?\n\n### Options:\nA. 64\nB. 72\nC. 86\nD. 98\nE. 101\n\n### Answer:\nUse the options.\nThe options which after getting added to 24 shows a cube of a number could be right.\nHere\n64+24 = 88\n72+24 = 96\n86+24 = 110\n98+24 = 122\n101+24=125 ---(5*5*5)\nSo we have 101 as the answer!\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average weight of a group of boys is 30 kg. After a boy of weight 38 kg joins the group, the average weight of the group goes up by 1 kg. Find the number of boys in the group originally ?\n\n### Options:\nA. A)4\nB. B)8\nC. C)6\nD. D)2\nE. E)7\n\n### Answer:\nLet the number off boys in the group originally be x.\nTotal weight of the boys = 30x\nAfter the boy weighing 38 kg joins the group, total weight of boys = 30x + 38\nSo 30x + 38 = 31(x + 1) = > x = 7.\nAnswer:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 6 men and 8 boys can do a piece of work in 10 days while 26 men and 48 boys can do the same in 2 days, the time taken by 15 men and 20 boys in doing the same type of work will be?\n\n### Options:\nA. 4 days\nB. 8 days\nC. 6 days\nD. 5 days\nE. 3 days\n\n### Answer:\nLet 1 men's 1 day work = x and 1 boy's 1 day work = y.\nThen, 6x + 8y = 1/10 and 26x + 48y = 1/2\nSolving these two equations, we get:\nx = 1/100 and y = 1/200\n(15 men + 20 boys)'s 1 day work = (15/100 + 20/200) = 1/4\n15 men and 20 boys can do the work in 4 days.\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAt what price must an article costing Rs.47.50 be marked in order that after deducting 6% from the list price. It may be sold at a profit of 25% on the cost price?\n\n### Options:\nA. 63.16\nB. 62.6\nC. 62.1\nD. 62.7\nE. 62.2\n\n### Answer:\nCP = 47.50\nSP = 47.50*(125/100) = 59.375\nMP*(94/100) = 59.375\nMP = 63.16\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n15 men take 20 days of 8 hours each to do a piece of work. How many days of 6 hours each would 21 women take to do the same. If 3 women do as much work as 2 men?\n\n### Options:\nA. 27.57\nB. 28.57\nC. 29.57\nD. 30.57\nE. 32\n\n### Answer:\n3W = 2M\n15M ------ 20 * 8 hours\n21 W ------ x * 6 hours\n14 M ------ x * 6\n15 * 20 * 8 = 14 * x * 6\nx = 28.57\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the remainder of G=3^19 when divided by 10?\n\n### Options:\nA. 0\nB. 1\nC. 5\nD. 7\nE. 9\n\n### Answer:\nI looked for patterns:\n^2 - units digit 9\n^3 - units digit 7\n^4 - units digit 1\n^5 - units digit 3\nhence, we can see that when raised to a power which is multiple of 4, the units digit is 1, and when to an even power not multiple of 4, the units digit is 9\nand we can then see:\n^16 - units digit 1, or\n^18 - units digit 9\nand ^19 - units digit 7\ntherefore, G=when divided by 10, the remainder must be 7.D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJohn bought 9.25m of cloth for $416.25. Find the cost price per metre.\n\n### Options:\nA. 46\nB. 47\nC. 45\nD. 56\nE. 54\n\n### Answer:\nCloth bought by John = 9.25 m\nCost of 9.25 m = $416.25\nCost per metre = 416.25 \u00f7 9.25\nThe cost of the cloth per metre = $ 45\nAnswers: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhen 3 fair coins are tossed together, what is the probability of getting 2 tails?\n\n### Options:\nA. 1/2\nB. 1/3\nC. 1/4\nD. 3/4\nE. 2/3\n\n### Answer:\nWe can get 2 tails in 3C2 ways.\nWe can get 3 tails in exactly one way.\nAlso, there are a total out 8 possible outcomes.\nThus, the required probability = (3 + 1)/8 = 1/2\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTownville has 100 residents, and 60 of them are females. If half of Townville\u2019s male residents are smokers, and 1/2 of the female residents are smokers, which of the following represents the total number of Townville\u2019s residents who are NOT smokers?\n\n### Options:\nA. 48\nB. 50\nC. 52\nD. 54\nE. 56\n\n### Answer:\nNumber of people =100\nFemales = 60\nmen = 100-60=40\nHalf of the men are smoker40/2=20, that means the remaining men 40-20=20 are non smokers.\n1/2 females are smoker. i.e 1/2*60 = 30\n60-30=30 females are non smokers\nSo, total number of non smokers in the town are 20+30 =50\nAnswer : B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nStock / Number of shares\nV ------------ 68\nW ---------- 112\nX ------------ 56\nY ------------ 94\nZ ------------ 45\nThe table shows the number of shares of each of the 5 stocks owned by Mr Sami. If Mr. Sami was to sell 20 shares of Stock X and buy 23 shares of stock Y, what would be the increase in the range of the numbers of shares of the 5 stocks owned by Mr. Sami?\n\n### Options:\nA. 4\nB. 6\nC. 9\nD. 14\nE. 20\n\n### Answer:\nBased on the original number of shares, the range would be: 112 - 45 = 67\nHowever, the prompt tells us that two of the values in the table are going to change. After the changes, the values will be:\nV 68\nW 112\nX 36\nY 117\nZ 45\nNow the range is 117 - 36 = 81\nThe INCREASE in the range requires us to compare thenewrange to theoldrange: 81 - 67 = 14\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHalf the people on a bus get off at each stop after the first, and no one gets on after the first stop. If only one person gets off at stop number 5, how many people got on at the first stop?\n\n### Options:\nA. 128\nB. 64\nC. 32\nD. 16\nE. 8\n\n### Answer:\n7 - > 1\n6 - > 2\n5 - > 4\n4 - > 8\n3 - > 16\n2 - > 32\n1 - > 64\nbecause people get off after the first stop\n=> the formula will be : 2^(n-1) where n is the stop number\nin this case n = 5\n=> 2^(5-1) = 2^4 = 16\n=> answer is D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the value of: -9^7 + 9^9 ?\n\n### Options:\nA. 9^2\nB. -18^16\nC. 63(9^7)\nD. -80(9^7)\nE. 80(9^7)\n\n### Answer:\n-9^7 + 9^9 = 9^7 (-1 + 9^2) = 9^7 (-1 + 81) = 80 (9^7), Answer E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nP is able to do a piece of work in 20 days and Q can do the same work in 10 days. If they can work together for 2 days, what is the fraction of work left?\n\n### Options:\nA. 5/10\nB. 9/10\nC. 7/10\nD. 6/10\nE. 4/10\n\n### Answer:\nExplanation :\nAmount of work P can do in 1 day = 1/20\nAmount of work Q can do in 1 day = 1/10\nAmount of work P and Q can do in 1 day = 1/20+ 1/10 = 3/20\nAmount of work P and Q can together do in 2 days = 2 \u00d7 (3/20) =3/10\nFraction of work left = 1 \u2013 3/10= 7/10\nAnswer : Option C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nStacy has a 63 page history paper due in 7 days. How many pages per day would she have to write to finish on time?\n\n### Options:\nA. 9\nB. 8\nC. 10\nD. 8.5\nE. 6\n\n### Answer:\n63/7=9\nA.9\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many multiples of 3 are there between 100 and 300 (both are inclusive)?\n\n### Options:\nA. 67.6\nB. 1.58\nC. 2.47\nD. 3.54\nE. 6.51\n\n### Answer:\nthe answer is (300-100)/3+1=67.6\nAnswer is A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA sum of Rs. 395 was divided among A, B, and C in such a way that B gets 25% more than A and 20% more than C. What is the share of A?\n\n### Options:\nA. Rs.195\nB. Rs.180\nC. Rs. 98\nD. Rs. 120\nE. Rs. 130\n\n### Answer:\nLet each one\u2019s share is A,B and C respectively, then\nB =125A/100 = 120C/100\nA =100B/125 =4/5B, C = 100B/120 = 5/6B\n4/5B +B +5/6B =395, 79B/30 =395, B =395*30/79 =150\nA = 4*150/5 = 120\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the least number which when divided by 26, 36 and 46 leaves the remainders 12, 22 and 32 respectively.\n\n### Options:\nA. 10570\nB. 10750\nC. 17050\nD. 10075\nE. 10085\n\n### Answer:\nExplanation:\nThe difference between any divisor and the corresponding remainder is 14,\nL.C.M of 26,36,46 -14\n= 10764-14\n= 10750\nAnswer: Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man cycles round the boundary of a rectangular park at the rate of 12 kmph and completes one full round in 8 minutes. If the ratio between the length and breadth of the park be 3:2, then its area is:\n\n### Options:\nA. 1536m2\nB. 15360m2\nC. 153600m2\nD. 163600m2\nE. None of these\n\n### Answer:\nPerimeter= Distance covered in 8 min\n= (12000/60 *8)m= 1600m\nLet, length= 3x meters and breadth= 2x meters\nThen, 2(3x+2x)= 1600 or x= 160\nTherefore, length= 480 m and breadth= 320m\nTherefore, area= (480*320)m2 = 153600 m2\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe cost to park a car in a certain parking garage is $15.00 for up to 2 hours of parking and $1.75 for each hour in excess of 2 hours. What is the average (arithmetic mean) cost per hour to park a car in the parking garage for 9 hours?\n\n### Options:\nA. $1.09\nB. $1.67\nC. $2.25\nD. $2.37\nE. $3.03\n\n### Answer:\nTotal cost of parking for 9 hours = 15$ for the first 2 hours and then 1.75 for (9-2) hours = 15+7*1.75 = 27.25\nThus the AVERAGE parking price = 27.25/9 = 3.03 $\nE is the correct answer.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWorking together, Wayne and his son can shovel the entire driveway in three hours. If Wayne can shovel six times as fast as his son can, how many hours would it take for his son to shovel the entire driveway on his own?\n\n### Options:\nA. 4\nB. 6\nC. 8\nD. 7\nE. 12\n\n### Answer:\nW: the time for Wyane to do the job\nS: the time for his son to do the job\nWe have 1/W + 1/S = 1/6 and W = 6S\nThen we have 1/(6*S) + 1/S = 1/6 <=> 7/(6*S) = 1/6 <=> S = 7\nANS: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe smallest number when increased by \" 1 \" is exactly divisible by 12, 18, 24, 32 and 40 is:\n\n### Options:\nA. 1439\nB. 1440\nC. 1459\nD. 1449\nE. 1500\n\n### Answer:\nLCM = 1440\n1440 - 1 = 1439\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA tradesman by means of his false balance defrauds to the extent of 32%? in buying goods as well as by selling the goods. What percent does he gain on his outlay?\n\n### Options:\nA. 74.5%\nB. 74.24%\nC. 84.6%\nD. 24.89%\nE. 45%\n\n### Answer:\ng% = 32 + 32 + (32*32)/100\n= 74.24%\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA can do a piece of work in 12 days. When he had worked for 2 days B joins him. If the complete work was finished in 8 days. In how many days B alone can finish the work?\n\n### Options:\nA. 15 days\nB. 25 days\nC. 18 days\nD. 20 days\nE. 21 days\n\n### Answer:\nExplanation:\n8/12 + 6/x = 1\nX = Explanation:\n8/12 + 6/x = 1\nX = 18 days\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average of six numbers is 3.95. The average of two of them is 3.2, while the average of the other two is 3.85. What is the average of the remaining two numbers?\n\n### Options:\nA. 4.5\nB. 4.6\nC. 4.7\nD. 4.8\nE. 4.9\n\n### Answer:\nSum of the remaining two numbers\n= (3.95 \u00d7 6) \u2013 [(3.2 \u00d7 2) + (3.85 \u00d7 2)]\n= 23.70 \u2013 (6.4 + 7.7)\n= 23.70 \u2013 14.1 = 9.60\n\u2234 Required average = (9.6\u20442) = 4.8\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 2 men or 3 women can reap a field in 5 days how long will 5 men and 6 women take to reap it?\n\n### Options:\nA. 2/24\nB. 6/18\nC. 2/22\nD. 5/12\nE. 9/10\n\n### Answer:\nExplanation:\n2 men reap 2/5 field in 1 day\n1 man reap 1/(2 x 5)\n3 women reap 1/43 field in 1 day\n1 woman reap 1/(5 x 3)\n5 men and 6 women reap (5/(2 x 5)+ 6/(3 x 5)) =9/10 in 1 day\n5 men and 6 women will reap the field in 9/10 days\nAnswer: Option E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA bus starts from city X. The number of women in the bus is half of the number of men. In city Y, 20 men leave the bus and ten women enter. Now, number of men and women is equal. In the beginning, how many passengers entered the bus ?\n\n### Options:\nA. 15\nB. 90\nC. 36\nD. 45\nE. 46\n\n### Answer:\nExplanation:\nOriginally, let number of women = x. Then, number of men = 2x.\nSo, in city Y, we have : (2x - 20) = (x + 10) or x = 30.\nTherefore Total number of passengers in the beginning = (x + 2x) = 3x = 90.\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many times in a day, the hands of a clock are straight?\n\n### Options:\nA. 22\nB. 44\nC. 48\nD. 24\nE. 36\n\n### Answer:\nThe hands of a clock point in opposite directions (in the same straight line, making an angle 180\u00b0 between them) 11 times in every 12 hours because between 5 and 7 they point in opposite directions at 6 'o clock only. Hence the hands point in the opposite directions 22 times in a day.\nThe hands of a clock coincide(0\u00b0 between them) 11 times in every 12 hours (between 11 and 1, they coincide only once, at 12 o'clock). Hence the hands coincide 22 times in a day.\nSo In 24 hours, the hands come in opposite direction or coincide 44 times.\nThis is already given as a formula and it's is better to learn the answer by heart as 44\nwhich can save time in competitive exams.(However you should know the theory behind). Answer: Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the difference between the C.I. on Rs. 8000 for 1 1/2 years at 4% per annum compounded yearly and half-yearly?\n\n### Options:\nA. s.3.26\nB. s.2.08\nC. s.2.02\nD. s.2.83\nE. s.2.42\n\n### Answer:\nC.I. when interest is compounded yearly\n= [8000 * (1 + 4/100) * (1 + (1/2 * 4)/100]\n= 8000 * 26/25 * 51/50 = Rs. 8486.4\nC.I. when interest is compounded half-yearly\n= [8000 * (1 + 2/100)2]\n= (8000 * 51/50 * 51/50 * 51/50)\n= Rs. 8489.66 Difference\n= (8489.66 - 8486.4\n= Rs.3.26.\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe area of one square is x^2 + 10x + 25 and the area of another square is x^2 \u2212 6x + 9. If the sum of the perimeters of both squares is 32, what is the value of x?\n\n### Options:\nA. 3\nB. 2\nC. 2.5\nD. 4.67\nE. 10\n\n### Answer:\nspotting the pattern of equations both are in form of (X+C)^2 so\nA1= (x+5)^2A2= (x-3)^2\nL1= x+5L2= -3\nP1 = 4( x+5)P2=4(x-3)\nP1+P2=32\n4( x+5) +4(x-3)=32.....3\nAns :A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA merchant purchased a jacket for $54 and then determined a selling price that equalled the purchase price of the jacket plus a markup that was 40 percent of the selling price. During a sale, the merchant discounted the selling price by 20 percent and sold the jacket. What was the merchant\u2019s gross profit on this sale?\n\n### Options:\nA. $0\nB. $3\nC. $4\nD. $12\nE. $18\n\n### Answer:\nActual Cost = $54\nSP = Actual Cost + Mark up\n= Actual Cost + 40% SP\n= 54*100/60\non sale SP = 80/100(54*100/60) = 72\nGross profit = $18\nAnswer is E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain sum of money at simple interest amounted Rs.840 in 10 years at 3% per annum, find the sum?\n\n### Options:\nA. 378\nB. 288\nC. 287\nD. 646\nE. 217\n\n### Answer:\n840 = P [1 + (10*3)/100]\nP = 646\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nif 36% of a number is 72, what is the number?\n\n### Options:\nA. 100\nB. 200\nC. 250\nD. 300\nE. 350\n\n### Answer:\nAssume number as x then\n0.36*x = 72\nx = 200\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAverage of 5 numbers is -10, and the sum of three of the numbers is 16, wat is the average of the other 2 numbers?\n\n### Options:\nA. -33\nB. -35\nC. -39\nD. -42\nE. 32\n\n### Answer:\nLet the five numbers be a, b, c, d, e. Then their average is (a+b+c+d+e5)=10.(a+b+c+d+e5)=10.\nNow three of the numbers have a sum of 16, say, a+b+c=16a+b+c=16.\nSo substitute 16 for a+b+ca+b+c in the average above: (16+d+e5)=10.(16+d+e5)=10.\nSolving this equation for d+ed+e gives d+e=\u221266d+e=\u221266.\nFinally, dividing by 2 (to form the average) gives (d+e2)=\u221233.(d+e2)=\u221233.\nHence, the answer is A: -33\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe can empty 6 gallons per minute. All the three pipes working together can fill the tank in 15 minutes. The capacity of the tank is?\n\n### Options:\nA. 60 gallons\nB. 100 gallons\nC. 240 gallons\nD. 180 gallons\nE. 130 gallons\n\n### Answer:\nWork done by the waste pipe in 1 minute = 1/15 - (1/20 + 1/24) = - 1/40\nVolume of 1/40 part = 6 gallons\\\nVolume of whole = 6 * 40 = 240 gallons.\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a certain game, a large bag is filled with blue, green, purple and red chips worth 1, 5, x and 11 points each, respectively. The purple chips are worth more than the green chips, but less than the red chips. A certain number of chips are then selected from the bag. If the product of the point values of the selected chips is 11,000, how many purple chips were selected?\n\n### Options:\nA. 1\nB. 2\nC. 3\nD. 4\nE. 5\n\n### Answer:\n11,000 = 1*5^3*8*11\nThe factor of 8 must come from the purple point value, so there is 1 purple chip.\nThe answer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf n is a natural number, then(6n^2+6n) is always divisible by?\n\n### Options:\nA. 6 only\nB. 6 and 12 both\nC. 12 only\nD. by 18 only\nE. None of these\n\n### Answer:\n(6n^2+6n)=6n(n+1), which is always divisible by 6 and 12 both, since n(n+1) is always even.\nCorrect Option: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhen running a mile during a recent track meet, Nuria was initially credited with a final time of 6 minutes, 44 seconds. Shortly after her run, officials realized that the timing mechanism malfunctioned. The stopwatch did not begin timing her until 11/25 of a minute after she began to run. If the time was otherwise correct, how long did it actually take Nuria to run the mile?\n\n### Options:\nA. 5 minutes, 17.6 seconds\nB. 5 minutes, 21.8 seconds\nC. 5 minutes, 43.56 seconds\nD. 5 minutes, 44.44 seconds\nE. 7 minutes, 10.4 seconds\n\n### Answer:\nOne approach:\nThe watch starts to work after Nuria began his running. It means the time should be greater than credited 6 minutes, 44 seconds. The only number is 7 minutes, 10.4 seconds.\nAnother approach:\n11/25 close to 30 second when added to the 6 minutes, 44 seconds, it means it passes 7 minute.\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nLook at this series: 72, 76, 73, 77, 74, __, 75, ... What number should fill the blank?\n\n### Options:\nA. 44\nB. 78\nC. 15\nD. 92\nE. 29\n\n### Answer:\nD\n78\nThis series alternates the addition of 4 with the subtraction of 3.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe value of log2(log5625) is\n\n### Options:\nA. 2\nB. 5\nC. 10\nD. 15\nE. 20\n\n### Answer:\nSolution\nLet log5625\t= x.\nThen, 5x\t= 625\n= 54\n\u2039=\u203a x=4.\nLet log2( log5625)\t= y.\nThen, log 24= y\n\u2039=\u203a 2y= 4\ny;2.\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA sum of Rs. 1360 has been divided among A, B and C such that A gets of what B gets and B gets of what C gets. B's share is:\n\n### Options:\nA. 240\nB. 120\nC. 190\nD. 200\nE. 250\n\n### Answer:\nLet C's share = Rs. x\nThen, B's share = Rs. x/4, A's share = Rs. (2/3 x (x/4))= Rs. x/6\nTherefore, x/6 + x/4 + x = 1360\n=17x/12 = 1360\nx = 1360 x 12/17= Rs. 960\nHence, B's share = Rs. (960/4)= Rs. 240.\nAnswer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain junior class has 100 students and a certain senior class has 80 students. Among these students, there are 6 siblings pairs each consisting of 1 junior and 1 senior. If 1 student is to be selected at random from each class, what is the probability that the 2 students selected will be a sibling pair?\n\n### Options:\nA. 3/40000\nB. 1/3600\nC. 9/2000\nD. 3/4000\nE. 1/15\n\n### Answer:\nLet's see\nPick 6/100 first\nThen we can only pick 1 other pair from the 800\nSo total will be 6 / 80 *100\nSimplify and you get 3/4000\nAnswer is D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf Re.1 amounts to Rs.9 over a period of 20 years. What is the rate of simple interest?\n\n### Options:\nA. 70%\nB. 47%\nC. 49%\nD. 40%\nE. 20%\n\n### Answer:\n8 = (1*20*R)/100\nR = 40%\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAn electric pump can fill a tank in 10 hours. Because of a leak in the tank, it took 20 hours to fill the tank. If the tank is full, how much time will the leak take to empty it?\n\n### Options:\nA. 10hours\nB. 12hours\nC. 20hours\nD. 5hours\nE. 15hours\n\n### Answer:\nWork done by the leak in 1 hour = 1/10 - 1/20 = 1/20\nThe leak will empty the tank in 20hours\nAnswer is C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average of 5 consecutive integers starting with m as the first integer is n. What is the average of 13 consecutive integers that start with (m + 2)?\n\n### Options:\nA. m + 6\nB. n + 6\nC. n + 3\nD. m + 5\nE. n + 4\n\n### Answer:\nThe average of consecutive numbers is the middle number.\nThen n = m+2.\nThe average of 13 consecutive numbers starting from n is n+6.\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nwhen n divided by 3, the remainder is 2.\nwhen n divided by 4, the remainder is 1\nwhat is the the remainder when divided by 11\n\n### Options:\nA. 1\nB. 3\nC. 4\nD. 5\nE. 6\n\n### Answer:\ncase1\nN=5,8,11,14,17,20\ncase 2\nM=5,9,13,17,21\nTherefore n=17\nRemainder of 17/11 will be 6\nE 6 correct\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nEach light bulb at a hotel is either incandescent or fluorescent. At a certain moment, thirty percent of the incandescent bulbs are switched on, and eighty percent of the fluorescent bulbs are switched on. If 70 percent of all the bulbs are switched on at this moment, what percent of the bulbs that are switched on are incandescent?\n\n### Options:\nA. 4.5%\nB. 8.6%\nC. 12.3%\nD. 16.7%\nE. 20%\n\n### Answer:\nLet I be the number of incandescent bulbs.\nLet F be the number of fluorescent bulbs.\n0.3I + 0.8F = 0.7(I+F)\n0.1F = 0.4I\nF = 4I\nThis means that for every 1 incandescent bulb, there are 4 fluorescent bulbs.\nThe percent of bulbs that are switched on which are incandescent is:\n0.3I / (0.3I + 0.8F) = 0.3I / (0.3I + 0.8*4I) = 0.3I / 3.5I = 3/35 which is about 8.6%.\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf log3(2), log3(2x - 5), log3(2x - 7/2) are in arithmetic progression, then the value of x is equal to\n\n### Options:\nA. 5\nB. 4\nC. 2\nD. 3\nE. 1\n\n### Answer:\nExplanation :\nUsing log a \u2013 log b = log(a/b) ,\n=> 2/(y-5) = (y-5) / (y-3.5), where y = 2x.\nSolving we get, y= 4 or 8 i.e x = 2 or 3.\nIt can't be 2 as log of negative number is not deifned.\nAnswer : D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThree cubes of metal whose edges are 9, 12 and 15 cm respectively, are melted and one new cube is made. Find the edge of the new cube?\n\n### Options:\nA. 99\nB. 88\nC. 71\nD. 18\nE. 77\n\n### Answer:\n93 + 123 + 153 = a3 => a = 18\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n10^185 - 10^30 =\nWhich of the following best approximates the value of the expression above?\n\n### Options:\nA. 10^180\nB. 10^179\nC. 10^170\nD. 10^160\nE. 10^185\n\n### Answer:\n10^185 - 10^30 =\nWhich of the following best approximates the value of the expression above?\nYes, answer 10^185 is correct. Note that we need approximate value of the given expression and as 10^(185) is much larger number than 10^(30) then 10^(30) is pretty much negligible in this case: 10^(185)-10^(30)=~10^(185).\nAnswer : E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn what time will a train 200 m long cross an electric pole, it its speed be 144 km/hr?\n\n### Options:\nA. 2.5 sec\nB. 2.8 sec\nC. 5 sec\nD. 2.2 sec\nE. 4.5 sec\n\n### Answer:\nSpeed = 144 * 5/18\n= 40 m/sec\nTime taken = 200/40\n= 5 sec.\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA bottle contains a certain solution. In the bottled solution, the ratio of water to soap is 3:2, and the ratio of soap to salt is three times this ratio. The solution is poured into an open container, and after some time, the ratio of water to soap in the open container is halved by water evaporation. At that time, what is the ratio of water to salt in the solution?\n\n### Options:\nA. 1:1\nB. 2:3\nC. 3:2\nD. 9:4\nE. 27:8\n\n### Answer:\nWater:soap = 3:2\nSoap:Salt=9:2\n=> For 9 soap, salt = 2\n=> For 2 Soap, salt = (2/9)*2 = 4/9\nSo, water:soap:salt = 3:2:4/9 = 27:18:4\nAfter open container, water:soap:salt = 13.5:18:4\nSo, water:salt = 13.5:4 = 27:8\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe probability of pulling a black ball out of a glass jar is 1/C. The probability of pulling a black ball out of a glass jar and breaking the jar is 1/Y. What is the probability of breaking the jar?\n\n### Options:\nA. 1/(XY)\nB. C/Y\nC. Y/X\nD. 1/(X+Y)\nE. 1/(X-Y)\n\n### Answer:\nP of pulling a black ball out of a glass jar AND breaking the jar = 1/Y\nP of pulling a black ball out of a glass jar is 1/C\nLets say P of breaking the jar = n\nThat means 1/C*n=1/Y\nn= C/Y\nB is the answer\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMartin bought 10 concert tickets, some at the full price of $2.00 per ticket, and some at a discounted price of $1.60 per ticket. If he spent a total of $18.00, how many discounted tickets did he buy?\n\n### Options:\nA. 3\nB. 4\nC. 5\nD. 6\nE. 7\n\n### Answer:\nLet x be the number of tickets he bought at $2 per ticket.\nthen 2 x + (10-x)1.6 = 18\n0.4x = 2 => x = 5\ndiscounted tickets = 10 -x = 5\nAns : C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOf the three numbers, the first is twice as second and three times the third. The average of the three numbers is 55, and the three numbers in order are?\n\n### Options:\nA. 116,58,36\nB. 90,45,30\nC. 126,63,36\nD. 108,54,36\nE. None of these\n\n### Answer:\nExplanation :\nSolution: Let A =x,\nB =x/2, C = x/3.\n=x + x/2 + x/3 / 3 = 55\nBy solving we will get x = 90.\nHence A= 90\nB= 90/2= 45\nC= 90/3 = 30\nAnswer : B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJoseph\u2019s grade was in the 80th percentile out of 100 grades in his class. In another class of 60 students there were 15 grades higher than Joseph\u2019s. If nobody had Joseph\u2019s grade, then Joseph\u2019s was what percentile of the two classes combined?\n\n### Options:\nA. 80\nB. 78\nC. 75\nD. 60\nE. 90\n\n### Answer:\nBeing in 80% percentile out of 100 grades means Joseph was 81st (from the least grade) in the class (as long as nobody had Joseph\u2019s grades), he outscored 80.\nIn another class his grade would rank him 46 (from the least grade out of 61, 60+Joseph), 45 had the grades lower than Amy.\nSo in combined classes he outscored 80+45=125. There are 160 students 125/160=0.78\nAnswer: B (78%)\nGenerally being in x% means that x% has the grades less than you.\nJoseph in 80% --> he outscored 80% of of 100=80 (Joseph is 81st).\nOf the 60 grades from another class, 15 were higher than Joseph 's, and the rest were lower --> rest is 45, hence Amy outscored 45.\nSo out of total 100+60=160, Joseph outscored 80+45=125. Hence he is in 125/160=78%.\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA brick measures 20 cm * 10 cm * 7.5 cm how many bricks will be required for a wall 29 m * 2 m * 0.75 m?\n\n### Options:\nA. 29000\nB. 27908\nC. 78902\nD. 25000\nE. 27991\n\n### Answer:\n29 * 2 * 0.75 = 20/100 * 10/100 * 7.5/100 * x\n29 = 1/100 * x => x\n= 29000\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nExpress 45 mps in kmph?\n\n### Options:\nA. 170\nB. 160\nC. 162\nD. 130\nE. 122\n\n### Answer:\n45 * 18/5 = 162 kmph\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn Town X, 64 percent of the population are employed, and 50 percent of the population are employed males. What percent of the employed people in Town X are females?\n\n### Options:\nA. 16%\nB. 22%\nC. 32%\nD. 40%\nE. 52%\n\n### Answer:\nWe are asked to find the percentage of females in employed people.\nTotal employed people 64%, out of which 50 are employed males, hence 14% are employed females.\n(employed females)/(total employed people)=14/64=22%\nAnswer: B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo persons start running simultaneously around a circular track of length 400 m from the same point at speeds of 20 km/hr and 30 km/hr. When will they meet for the first time any where on the track if they are moving in opposite directions?\n\n### Options:\nA. 28 sec\nB. 37 sec\nC. 21.6 sec\nD. 23 sec\nE. 27 sec\n\n### Answer:\nTime taken to meet for the first time anywhere on the track\n= length of the track / relative speed\n= 400 / (20 + 30)5/18 = 300* 18 / 50 * 5 = 21.6 seconds.\nAnswer : C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo men can complete a piece of work in four days. Two women can complete the same work in eight days. Four boys can complete the same work in five days. If four men, eight women and 20 boys work together in how many days can the work be completed?\n\n### Options:\nA. 1/2 day\nB. 1/8 day\nC. 1/3 day\nD. 8/2 day\nE. 1/7 day\n\n### Answer:\nTwo men take four days to complete the work four men would take (2 * 4)/4 = 2 days to complete it.\nSimilarly four women would take two days to complete it and 20 children would take one day to complete it.\nAll the three groups working togerther will complete 1/2 + 1/2 + 1/1 work in a day\n= 2 times the unit work in a day.\nThey will take 1/2 a day to complete it working together.\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the units digit of 18! + 2 ?\n\n### Options:\nA. 1\nB. 2\nC. 3\nD. 4\nE. 5\n\n### Answer:\nAny number above 4!, such as 5!, 6!, etc... are always multiples of 10, so their units digit is 0.\nThe units digit of 18! + 2 is 2.\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the odd man out\n2, 7, 32, 157, 782, 3907, 17251\n\n### Options:\nA. 7\nB. 32\nC. 157\nD. 3907\nE. 17251\n\n### Answer:\n1*5-3 = 2\n2*5-3 = 7\n7*5-3 = 32\n32*5-3 = 157\n157*5-3 = 782\n782*5-3 = 3907\n3907*5-3= 19532\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf A : B = 4 : 7 and B : C = 5 : 8 then A : B : C is :\n\n### Options:\nA. 20 : 35 : 56\nB. 35 : 36 : 63\nC. 30 : 35 : 65\nD. 25 :34: 68\nE. None of these\n\n### Answer:\nExpl : A : B = 4 : 7\nB : C = 5 :8 = 5*7/5 : 8 *7/5 = 7 : 56/5\nA : B : C = 4 : 7 : 56/5 = 20 : 35 : 56\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA, B and C work on a task. To complete the task alone, B takes twice the time that A would take to complete the task alone and 1/4rd the time that C would take to complete the task alone. If B actually worked for half the number of days that A worked and 3/2 times the number of days that C worked, what proportion of the total work was completed by B?\n\n### Options:\nA. 1/3\nB. 2/9\nC. 9/49\nD. 16/81\nE. 1/6\n\n### Answer:\nThe first thing to notice is that A is faster than B and B is faster than C.\nSince work is proportional to time, in 1 day lets say if A does 2 works, B does 1 work and C does 2/3rd of a work.\nIf A works for 2 days, B works for 1 day and C works for only 2/3 of the day.\nTherefore total work done = (2*2) + (1*1) + (1/4*1/4) = 81/16\nProportion of work done by B = (1*1) / (81/16) = 16/81\nHence Answer D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMurphy and Cooper are having the same amount of petrol in the petrol tanks of their respective cars. Murphy can drive for four hours with that amount whole Cooper can drive for five hours.\nThey both starts together and keep driving for a few hours. After some time, they find that the amount of petrol remaining in one car is four times that of the other car.\nUsing all these facts, can you find out how long they drove their cars?\n\n### Options:\nA. 2 3/4 hours.\nB. 3 3/4 hours.\nC. 4 3/4 hours.\nD. 5 3/4 hours.\nE. 6 3/4 hours.\n\n### Answer:\nSolution:\n3 3/4 hours\nExplanation:\nSuppose that the amount of petrol in each of the cars in the beginning was M.\nNow, suppose that they drove for X hours.\nIn that case, the amount of petrol used by one car in X hours will be = M*X /4\nThe amount of petrol used by the other car will be = M*X/5\nTherefore, the petrol left in one car = M - M*X / 4\nPetrol left in the other car = M - M*X / 5\nNow, according to the question,\nM - M*X / 5 = 4 (M - M*X / 4)\n=> X = 15 / 4 = 3 3/4 hours.\nTherefore Murphy and Cooper drove for 3 3/4 hours.\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train 100 meters long completely crosses a 300 meters long bridge in 45 seconds. What is the speed of the train is?\n\n### Options:\nA. 32\nB. 55\nC. 6\nD. 78\nE. 81\n\n### Answer:\nS = (100 + 300)/45 = 400/45 * 18/5\n= 32\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how many different number of ways 7 boys and 4 girls can sit on a shopa which can accommodate 3 persons?\n\n### Options:\nA. 800\nB. 900\nC. 200\nD. 990\nE. None\n\n### Answer:\nOption 'D'\n11p3 = 11x10x9 = 990\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 11 and 13 are prime numbers, which of the following CANNOT be the sum of a and b?\n\n### Options:\nA. 24\nB. 48\nC. 72\nD. 47\nE. 96\n\n### Answer:\nans =D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA person buys an article at $200. At what price should he sell the article so as to make a profit of 10%?\n\n### Options:\nA. 240\nB. 260\nC. 220\nD. 300\nE. 360\n\n### Answer:\nC\n220\nCost price = $200\nprofit = 10% of 200 = $20\nSelling price = Cost price + Profit\n= 200 + 20 = 220\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe length of a rectangular plot is 10mtr more than its width. The cost of fencing the plot along its perimeter at the rate of Rs. 6.5mtr is Rs.1170. The perimeter of the plot is?\n\n### Options:\nA. 126\nB. 156\nC. 180\nD. 321\nE. 260\n\n### Answer:\nSol. Let width = x, Length = (10+x)\nPerimeter = 2(x+(10+x))\n= 2(2x=10)\n& 2(2x+10)*6.5 = 1170\nX = 40\nRequired perimeter = 2(40+50) = 180\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJohn must arrange 3 different physics books and 3 different mathematics books on one shelf. If the first book on the leftmost side is a mathematics book and no physics book is next to another physics book. How many different arrangements exist?\n\n### Options:\nA. 6\nB. 9\nC. 36\nD. 120\nE. 720\n\n### Answer:\nFirst place the maths book -\nsince all are different books, they can be arranged in 3! ways - 6 ways...\nnext we have 4 places for physics book, but leftmost is not a valid place as left is always maths..\n_M_M_M_, but valid ways are M_M_M_\nso 3 places for 3 books - again 3! ways...\nTotal = 3!\u22173!=36\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the tens digit of 6^22?\n\n### Options:\nA. 1\nB. 3\nC. 5\nD. 7\nE. 9\n\n### Answer:\nThe tens digit of 6 in integer power starting from 2 (6^1 has no tens digit) repeats in a pattern of 5: {3, 1, 9, 7, 5}:\nThe tens digit of 6^2=36 is 3.\nThe tens digit of 6^3=216 is 1.\nThe tens digit of 6^4=...96 is 9.\nThe tens digit of 6^5=...76 is 7.\nThe tens digit of 6^6=...56 is 5.\nThe tens digit of 6^7=...36 is 3 again.\netc...\n22 has the form 5n+2, so the tens digit of 6^22 is 3.\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA part of Rs. 38800 is lent out at 6% per 6 months. The rest of the amount is lent out at 5% per annum after 1 year. The ratio of interest after 3 years from the time when first amount was lent out is 5:4. Find the second part that was lent out at 5%.\n\n### Options:\nA. 28800\nB. 27800\nC. 29800\nD. 26500\nE. 55055\n\n### Answer:\nLet the 1st part that is lent out be x at 6%. then 2nd part will be (38800-x) at 5%.then the S.I1 of 1st part is (p*r*t)/100 = (x*6*6)/100 [t=6 becoz we r calculating till 3yrs & der is six 6months in 3yrs]\nsimilarly S.I2 of 2nd part = {(38800-x)*5*2}/100 [t=2 since the 5% rate is to be calculated after the 1st year & per annum, so no. of years left is 2]therefore, S.I1/S.I2=5/4, by calculating it we get x=10000So, 2nd part is 38800-10000=28800\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf X = the product of six distinct prime numbers, how many factors does X have besides 1 and itself?\n\n### Options:\nA. 50\nB. 56\nC. 62\nD. 68\nE. 74\n\n### Answer:\nSince X has 6 distinct prime factors, X has a total of 2^6 = 64 factors.\nBesides 1 and itself, X has 62 factors.\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhile playing a certain dice game, Chris wins if the sum of the two dice is 7, at which point the game is over. If the game allows Chris three rolls in an attempt to win, what is the probability that Chris will win?\n\n### Options:\nA. 1/2\nB. 17/36\nC. 91/216\nD. 11/36\nE. 25/216\n\n### Answer:\nTotal outcomes possible: 36\nTotal outcomes possible with sum 7: 6\nProbability to win when rolled once = 6/36\nProbability not to win when rolled once = 30/36 = 5/6\nProbability to win in three attempts= 1- Probability will not to win in all three attempts\n= 1- (5/6* 5/6*5/6)\n= 91/216\nAnswer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nComplete the series 20, 19, 17, ...., 10, 5\n\n### Options:\nA. 15\nB. 16\nC. 13\nD. 14\nE. 12\n\n### Answer:\nExplanation :\n20 - 1 = 19\n19 - 2 = 17\n17 - 3 = 14\n14 - 4 = 10\n10 - 5 = 5\nAnswer : Option D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe probability of having a girl is identical to the probability of having a boy. In a family with seven children, what is the probability that all the children are of the same gender?\n\n### Options:\nA. 1/64\nB. 1/9\nC. 1/16\nD. 1/25\nE. 1/2\n\n### Answer:\nThere are two cases. All boys and all girls\ncase 1. all boys.\n1/2*1/2*1/2*1/2*1/2*1/2*1/2= 1/128\ncase 2 .all girls.\n1/2*1/2*1/2*1/2*1/2*1/2*1/2=1/128\nWe will add the cases to get 1/64\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are three foam generators in the factory, each of the first two can generate 12 liters of foam in one hour and the third can generate 18 liters in an hour. The three generators start working together at the same time and after one hour and a half one of the first generators stops working and two hours after that the third generator stops working and only one generator is left. If 5 hours after they all started to work the last generator stops working, how many liters of foam were generated?\n\n### Options:\nA. 120.\nB. 132.\nC. 141\nD. 154.\nE. 166.\n\n### Answer:\nLet the foam generators capacity be -\nA = 12 lit/hr\nB = 12 lit/hr\nC = 18 lit/hr\nTotal foam generation in 1 hour will be 42 lit ( 12 + 12 + 18 ) ; since in 1 and 1/2 hr they will generate 42 + 21 => 63 litres...\nNow one of the first generators stops working ( Say A stops working ) , so we have -\nB = 12 lit/hr\nC = 18 lit/hr\nTotal foam generation in 2 hour will be 60 litres {2 (12+18)}\nThe third generator stops working and now only B works for the remaining time 1 and 1/2 ( 5 - 1 and 1/2 - 2 )...\nFoam generated by B will be 3/2 * 12 => 18 litres\nSo, total foam generated will be 141 Litres ( 63 + 60 + 18 ) ; hence answer will be (C)\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain sum becomes three times itself at simple interest in five years. the sum become 1200 after 9 year.calculate the principal amount.\n\n### Options:\nA. 250\nB. 260.86\nC. 288.6\nD. 265.66\nE. 280\n\n### Answer:\nLet the sum be Rs. x, then it becomes Rs. 3x in five years Rs. 2x is the interest on x for five years.\nR = (100 * 2x)/(x * 5) = 40 %\ns.i=p*r*t/100=x*40*9/100=3.6x\nx+3.6x=1200=4.6x=1200,x=1200/4.6=260.86\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe list price of an article is Rs.69. A customer pays Rs.56.16 for it. He was given two successive discounts, one of them being 10%. The other discount is?\n\n### Options:\nA. 9.33%\nB. 9.44%\nC. 9.45%\nD. 9.56%\nE. 9.67%\n\n### Answer:\n69*(90/100)*((100-x)/100) = 56.16\nx = 9.56%\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n1397 x 1397 = ?\n\n### Options:\nA. 1951609\nB. 1951601\nC. 1951602\nD. 1951603\nE. 1951604\n\n### Answer:\n1397 x 1397\t= (1397)2\n= (1400 - 3)2\n= (1400)2 + (3)2 - (2 x 1400 x 3)\n= 1960000 + 9 - 8400\n= 1960009 - 8400\n= 1951609.\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSeven unbiased coin are tossed. What is the probability of getting almost\none head?\n\n### Options:\nA. 1/2\nB. 1/4\nC. 127/128\nD. 127/5\nE. 127/6\n\n### Answer:\nHere n(S)= 2^7\nLet E=event of getting atmost one head =\nn(E)= 127\nP(E)=n(E)/n(S)=127/128\nAnswer option C)\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n30 pens and 75 pencils were purchased for 630. If the average price of a pencil was 2.00, find the average price of a pen.\n\n### Options:\nA. 10\nB. 11\nC. 12\nD. 13\nE. 16\n\n### Answer:\nSince average price of a pencil = 2\n\u2234 Price of 75 pencils = 150\n\u2234 Price of 30 pens = (630 \u2013 150) = 480\n\u2234 Average price of a pen = 480\u204460 = 16\nAnswer E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a meeting of 3 representatives from each of 5 different companies, each person shook hands with every person not from his or her own company. If the representatives did not shake hands with people from their own company, how many handshakes took place?\n\n### Options:\nA. 125\nB. 120\nC. 110\nD. 90\nE. 100\n\n### Answer:\nIn fact, all 15 people will shake hands with 12 others.\nSo, it SEEMS like the TOTAL number of handshakes = (15)(12)\nHOWEVER, we need to keep in mind that we have counted each handshake TWICE.\nTo account for this DUPLICATION, we must divide (15)(12) by 2.\nSo, the TOTAL # of handshakes = (15)(12)/2 = 90\nAnswer : D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe price of commodity X increases by 40 paise every year, while the price of commodity Y increases by 15 paise every year. If in 2001, the price of commodity X was Rs. 4.20 and that of Y was Rs. 6.30, in which year commodity X will cost 40 paise more than the commodity Y ?\n\n### Options:\nA. 2010\nB. 2011\nC. 2012\nD. 2013\nE. 2014\n\n### Answer:\nSuppose commodity X will cost 40 paise more than Y after z years.\nThen, (4.20 + 0.40z) - (6.30 + 0.15z) = 0.40\n0.25z = 0.40 + 2.10\nz = 2.50/0.25\nz = 250/25\nz =10\nX will cost 40 paise more than Y 10 years after 2001 i.e., 2011.\nAnswer = B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nwhat is the minimum value of f(x) where\nf(x)=(logax+logbx+logcx) and a>b>c>1..\n\n### Options:\nA. 3\nB. 2\nC. 1\nD. 4\nE. 5\n\n### Answer:\nhere a,b,c are base for log..they aren't multiplied with x.\nso logax=logex/logea;\nf(x)= (logx/loga + logx/logb+ logx/logc);\n= logx * (1/loga + 1/logb + 1/logc);\nfor minimum value of f(x) log values must me max 1\n=1*3\n= 3\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nCindy has her eye on a sundress but thinks it is too expensive. It goes on sale for 15% less than the original price. Before Cindy can buy the dress, however, the store raises the new price by 25%. If the dress cost $78.2 after it went on sale for 15% off, what is the difference between the original price and the final price?\n\n### Options:\nA. $0.00\nB. $5.75\nC. $3.40\nD. $5.00\nE. $6.80\n\n### Answer:\n0.85*{Original Price} = $78.2 --> {Original Price} = $92.\n{Final Price} = $78.2*1.25 = $97.75.\nThe difference = $97.75 - $92 = $5.75\nAnswer: B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA retailer buys 60 pens at the market price of 36 pens from a wholesaler, if he sells these pens giving a discount of 1%, what is the profit % ?\n\n### Options:\nA. 40\nB. 65\nC. 72\nD. 78\nE. 20\n\n### Answer:\nlet the market price of each pen be $1\nthen, Cost Price of 60 pens = $ 36 Selling Price of 60 pens =99% of $60=$ 59.40\nprofit %=((23.40*100)/36) %=65%\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a sample of data has mean of 23 and SD of 3, which of the following values is more than 2.5 SDs from the mean?\n\n### Options:\nA. a. 16\nB. b. 13.5\nC. c. 17\nD. d. 23.5\nE. e. 26.5\n\n### Answer:\nValue ismore than 2.5SDfrom the mean means that the distance between the mean and the value must be more than 2.5SD=7.5. So the value either <23-7.5=15.5 or >23+7.5=30.5.\nAnswer: B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf v, w, x, y, and z are positive integers, which of the following could not become a terminating decimal?\n\n### Options:\nA. 33/2^(4x)\nB. 34/5^(2y)\nC. 35/100^z\nD. 36/4^w\nE. 37/3^(5v)\n\n### Answer:\nKnowledge of Decimal equivalent Fractions will work wonders here , no need to consider the Numerator part\n1/ 2 = 0.50 ( Terminating )\n1/5 = 0.20 ( Terminating )\n1/100 = 0.01 ( Terminating )\n1/4 = 0.25 ( Terminating )\n1/3 = 0.33 ( Non Terminating )\nCheck the above rule with any higher powers the result will be same.....\nAmong the given options only (E) has a non terminating denominator , so this will be our answer..\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the odd man out\n2880, 480, 90, 24, 8, 4, 4\n\n### Options:\nA. 480\nB. 90\nC. 24\nD. 8\nE. 4\n\n### Answer:\nfrom the right side\n4*1=4,\n4*2=8\n8*3=24\n24*4=96 but here given 90 so it's not.\n96*5=480\n480*6=2880\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOne hour after Adrienne started walking the 60 miles from X to Y, John started walking from X to Y as well. Adrienne walks 3 miles per hour and John walks 1 mile per hour faster than Adrienne. How far from X will John be when he catches up to Adrienne?\n\n### Options:\nA. 12 miles\nB. 9 miles\nC. 10 miles\nD. 11 miles\nE. 18 miles\n\n### Answer:\nFirst, determine how far Adrienne has walked in the one hour. She has walked three miles which means she is three miles ahead of John when he sets off. John walks at four miles/hour which means that every hour, John will get one mile closer to Adrienne. If he gets one mile closer every hour, it will take him three hours to catch up to her which means he travels 3hours * 4 miles/hour = 12 miles and she travels 4 hours * 3 miles/hour = 12 miles. He will be 12 miles from X when he catches up to her.\nA slightly different way to solve...\nWe don't know how long they will walk before they catch up to one another but we do know that A walks for one hour more than J. J = T and A = T+1. We are looking for the distance at which they meet up which means the distance will be the same. D=r*t so,\nr*t (John ) = r*t (adrienne)\nr*(t) = r*(t+1)\n4t = 3t+3\nt=3\nd=r*t\nd=4*3\nd=12\nA) 12 miles\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe H.C.F of two numbers is 15 and their L.C.M is 3300. If one of the numbers is 225, then the other is?\n\n### Options:\nA. 200\nB. 210\nC. 220\nD. 230\nE. 240\n\n### Answer:\nOther number = (15 * 3300)/225\n= 220.\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many two-digit numbers are there whose remainder when divided by 15 is 1, and whose remainder when divided by 6 is 5?\n\n### Options:\nA. 3\nB. 4\nC. 5\nD. 6\nE. 7\n\n### Answer:\n2 digit numbers whose remainder when divided by 10 is 1 are\n11 , 21 , 31 , 41 , 51 , 61 , 71 , 81 , 91\nOut of above , numbers whose remainder when divided by 6 is 5 are\n11 , 41 and 71\nAnswer E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf (1 \u2013 1.5)N = 1, then N =\n\n### Options:\nA. \u2212400\nB. \u2212140\nC. \u22122\nD. 4\nE. 400\n\n### Answer:\n(1 \u2013 1.5)N = 1\nSimplify to get: -0.5N = 1\nRewrite as (-1/2)N = 1\nMultiply both sides by -2 to get: N = -2\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf y is 80% greater than x, than x is what % less than y?\n\n### Options:\nA. 20\nB. 25\nC. 33 1/3\nD. 44 4/9\nE. 80\n\n### Answer:\nLet x = 100\nSo y = 180\nWe want percentage change.\nSo, (100-180)/180\n= -44.44%\n= 44 4/9% lesser than y.\nHence option (D).\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a cinema hall for the matinee show which started at 2.30 pm and ended at 5.30 pm the vehicle parking lot had only three wheelers (auto rickshaws) and four wheelers. Today the wheels of the vehicles parked was counted and found to be 240. What could be the number of three wheelers parked therein ?\n\n### Options:\nA. 48\nB. 37\nC. 26\nD. 98\nE. 27\n\n### Answer:\nExplanation:\n3X + 4y = 240\nby substitute through options 48 is correct\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nemblem is coded as 216;\ncrude is coded as 125\nCrickets will be ?\n\n### Options:\nA. 243\nB. 644\nC. 512\nD. 380\nE. 464\n\n### Answer:\ncoding follows (no. of letters)^3\nemblem = 216 = 6^3\ncrude = 125 = 5^3\nCrickets = 8^3 =512\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nCharlie, a painter, has 9 jars of paint: 4 are Red, 2 are yellow, and the rest are brown. Charlie will combine 3 jars of paint into a new container to make a new colour, which he will name according to the following conditions: 1) C1, if the paint contains 2 jars of brown paint and no red paint 2) C2, if the paint contains 3 jars of brown paint. 3) J1, if the paint contains at least 2 jars of red paint 4) J2, if the paint contains exactly 1 jar of red paint What is the probability that the new colour will be a shade of J (J1 or J2)?\n\n### Options:\nA. 21/37\nB. 37/21\nC. 37/42\nD. 42/37\nE. 74/42\n\n### Answer:\nthe probability that it would be J1 or J2 is same as 1-()probability that it is C1 or C2\nFor C1-3C2(Brown)*2C1(Yellow)=3*2=6\nFor C2-3C3(all brown)=1\nTotal=9C3=84\n1-7/84=77/84= 37/42\nAnswer : C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nLet S be the set of all positive integers that, when divided by 8, have a remainder of 5. What is the 72th number in this set?\n\n### Options:\nA. 573\nB. 608\nC. 613\nD. 616\nE. 621\n\n### Answer:\nThe set S = {5, 13, 21, 29, ..................... }\n1st Number = 8 * 0 + 5 = 5\n2nd Number = 8 * 1 + 5 = 13\n3rd Number = 8 * 2 + 5 = 21\n72th Number = 8 * (72-1) + 5 = 573\nAnswer = A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man divides Rs. Among 5 sons,4daughters and 2 nephews .If each daughter receives four times as much as each nephews and each son receives five times as much as each nephews ,how much does each daughter receive?\n\n### Options:\nA. 200\nB. 300\nC. 400\nD. 500\nE. None of them\n\n### Answer:\nLet the share of each nephews be Rs.x.\nThen,share of each daughter=rs4x;share of each son=Rs.5x;\nSo,5*5x+4*4x+2*x=8600\n25x+16x+2x=8600\n=43x=8600\nx=200;\nAnswer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the ratio of boys to girls in a class is B and the ratio of girls to boys is G; then 5 (B + G) is ?\n\n### Options:\nA. Equal to 3\nB. Less than 3\nC. More than 3\nD. Less than 1/3\nE. none of these\n\n### Answer:\nLet number of boys = x\nLet number of girls = y\nTherefore x/y = B and y/x = G\n5(B + G) = 5[(x/y) + (y/x)] = 5[(x2 + y2)/xy] > 5\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the least number of complete years in which a sum of money put out at 50% compound interest will be more than double of itself?\n\n### Options:\nA. 2\nB. 3\nC. 4\nD. 5\nE. 6\n\n### Answer:\n2 years\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf x \u2260 0 and x - (2+ x^2)/x = y/x, then y =\n\n### Options:\nA. -5\nB. -2\nC. -4\nD. -3\nE. -1\n\n### Answer:\nx - (2+ x^2)/x = y/x\nx^2 -2 - x^2/x = y/x\ny= -2\nAnswer : B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA student worked for 20 days. For each of the amounts shown in the first row of the table, the second row gives the number of days that the student earned that amount. What is the total amount of money that the student earned for the 20 days?\nAmounts earned per day : $96 $84 $80 $70 $48\nNumber of days : 4 7 4 3 2\n\n### Options:\nA. (1) $120\nB. (2) $320\nC. (3) $378\nD. (4) $240\nE. (5) $296\n\n### Answer:\n4+7+4+3+2 = 20\nThe series is as follows. Arrange the terms in increasing order of amounts earned and cumulatively add up the number of days of each amount.\n1st to 2nd term = 48 (2 days)\n3rd to 5th term = 70 (3 days)\n6th to 9th term = 80 (4 days)\n10th to 16th term = 84 (7 days)\n17th to 20th term = 96 (4 days)\ntotal amount earned = 48+70+80+84+96\n= 378\nPick C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the remainder when 43^91 is divided by 5?\n\n### Options:\nA. 0\nB. 1\nC. 2\nD. 3\nE. 4\n\n### Answer:\nThe units digit of the exponents of 3 cycle in a group of 4: {3, 9, 7, 1}\n91 has the form 4k+3 so the units digit of 43^91 is 7.\nThe remainder when dividing by 5 is 2.\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf x-y=8, which of the following must be true?\nI. If x is negative, y must be negative\nII. Both x and y are positive\nIII. If x is positive, y must be positive\n\n### Options:\nA. I only\nB. II only\nC. III only\nD. I and II\nE. II and III\n\n### Answer:\nIf x-y=8, which of the following must be true?\nI. Both x and y are positive\nII. If x is positive, y must be positive\nIII. If x is negative, y must be negative\n1. x and y can be negative, for instance, -2 - (-10) = 8 =>Eliminate A and D\n2. x can be positive and y can be negative, for instance, 2 - (-6) = 8 => Eliminate B and E\nA) I only\nB) II only\nC) III only\nD) I and II\nE) II and III\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n587 x 999 = ?\n\n### Options:\nA. 586413\nB. 587523\nC. 614823\nD. 615173\nE. None of them\n\n### Answer:\n=587 x 999 = 587 x (1000-1)\n=587 x 1000 - 587 - 1\n=587000 - 587\n=586413\nAnswer is A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the President and Vice President must sit next to each other in a row with 8 other members of the Board, how many different seating arrangements are possible?\n\n### Options:\nA. 120510\nB. 632010\nC. 725760\nD. 705262\nE. 851032\n\n### Answer:\nWe need to take President and VP as one unit. Therefore we have 9 people to arrange=5! ways\nAlso, we both President and VP can be arranged in 2 ! ways.\nReqd no of ways=9!*2!= 725760 ways\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man buys 58 pens at marked price of 46 pens from a whole seller. If he sells these pens giving a discount of 1% , what is the profit percent?\n\n### Options:\nA. 7.6 %\nB. 7.7 %\nC. 24.82 %\nD. 13.6 %\nE. 27.82 %\n\n### Answer:\nExplanation:\nLet Marked price be Re. 1 each\nC.P. of 58 pens = Rs. 46\nS.P. of 58 pens = 99% of Rs. 58 = Rs. 57.42\nProfit % = (Profit /C.P.) x 100\nProfit% = (11.42/46) x 100 = 24.82 %\nANSWER: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA collector collects stamps from foreign countries. In June, she gave 20 percent of her stamps to her friend. In July, she gave 20 percent of her remaining stamps to another friend. If these were the only changes in the number of stamps in the stamp collection during those two months, what percent of her collection at the beginning of June did she give to away in June and July?\n\n### Options:\nA. 36%\nB. 40%\nC. 44%\nD. 48%\nE. 52%\n\n### Answer:\nLet x be the number of stamps in the original collection.\nThe percentage of the collection given away is:\n0.2x + 0.2(0.8x) = 0.2x + 0.16x = 0.36x = 36%\nThe answer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich one of the following is not a prime number?\n\n### Options:\nA. 2\nB. 3\nC. 5\nD. 9\nE. 7\n\n### Answer:\n9 is divisible by 3. So, it is not a prime number.\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a club with 310 peopl, 138 play tennis, 255 play baseball, and 94 people play both sports. How many people do not pla a sport?\n\n### Options:\nA. 9\nB. 8\nC. 4\nD. 10\nE. 11\n\n### Answer:\nTake 94 off the baseball players-->161\nthen 161 + 138 = 299 play either baseball or tennis\n310 - 299 = 11\nAnswer is E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWith an average speed of 40 km/hr a car reaches its destination on time. If it goes with an average speed of 35 km/h, it is late by 15 minutes. The total journey is?\n\n### Options:\nA. 30 km\nB. 40 km\nC. 70 km\nD. 80 km\nE. 90 km\n\n### Answer:\nLet the total journey be X km.\nX/35 - X/40 = 15/60\nSolving for X, we get X = 70\nTherefore, total journey = 70 km.\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA box contains 4 black, 3 red and 6 green marbles. 3 marbles are drawn from the box at random. What is the probability that both the marbles are of the same color?\n\n### Options:\nA. 24/286\nB. 25/709\nC. 25/286\nD. 24/268\nE. 24/226\n\n### Answer:\nExplanation:\nTotal marbles in a box = 4 black + 3 red + 6 green marbles = 13 marbles\n3 marbles are drawn from 13 marbles at random. Therefore,\nn(S) = 13C3= 286 ways\nLet A be the event that 2 marbles drawn at random are of the same color. Number of cases favorable to the event A is\nn(A) = 4C3 + 3C3+ 6C3 = 4 +1 + 20 = 25\nTherefore, by definition of probability of event A,\nP(A) = n(A)/n(S) = 25/286\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA boy was asked to find the arithmetic mean of the numbers 23, 17, 19, 25, 23, 18, 29, 27, 31 and P. He found the mean to be 24. What should be the number in place of P?\n\n### Options:\nA. 3\nB. 7\nC. 33\nD. 28\nE. 38\n\n### Answer:\nExplanation :\nClearly, we have (23+17+19+25+23+18+29+27+31+P/10) =24\nNumber in place of P is\n=> 212+P = 240\n=> P= 240 -212\n=> P = 28.\nAnswer : D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSix children \u2014 A, B, C, D, E and F \u2014 are going to sit in six chairs in a row. The children C & F have to sit next to each other, and the others can sit in any order in any remaining chairs. How many possible configurations are there for the children?\n\n### Options:\nA. 240\nB. 720\nC. 1440\nD. 4320\nE. 4800\n\n### Answer:\nfor such questions , we can treat both as one then total person=5..\nthese 5 can be arranged in 5! ways.. but within these 5 , one consists of two people who can be arranged in 2 ways CF or FC.. so ans =5!*2=240\nans A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe area of a square is equal to five times the area of a rectangle of dimensions 36 cm * 20 cm. What is the perimeter of the square?\n\n### Options:\nA. 289 cm\nB. 800 cm\nC. 829 cm\nD. 240 cm\nE. 289 cm\n\n### Answer:\nArea of the square = s * s\n= 5(36 * 20)\n=> s = 60\n= 60 cm\nPerimeter of the square\n= 4 * 60\n= 240 cm.\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf W is a negative integer and K is a positive integer, which of the following could be the standard deviation of a set {-7, -5, -3, W, 0, 1, 3, K, 7}?\nI. -1.5\nII. -2\nIII. 0\n\n### Options:\nA. I only\nB. II only\nC. III only\nD. I and III only\nE. None\n\n### Answer:\nIf W is a negative integer and K is a positive integer, The answer should be (E) as S.D cannot be negative. It is only 0 if all numbers in the set are equal, which is not the case either.E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA woman traveled 20 kilometer in 14 meter per second and another 20 kilometer in 18 miles per second. what is the average speed of the entire trip?\n\n### Options:\nA. 12.25\nB. 13.75\nC. 15.75\nD. 18.25\nE. 19.75\n\n### Answer:\nSince the distance traveled is same, we can apply direct formula= 2XS1XS2/(S1+S2)\n2X14X18/32= 15.75. 'C' is the answer.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many times the keys of a writer have to be pressed in order to write first 500 counting no's?\n\n### Options:\nA. 1372\nB. 1382\nC. 1392\nD. 1362\nE. 1352\n\n### Answer:\n1 to 9 = 9 * 1 = 9\n10 to 99 = 90 * 2 = 180\n100 to 500 = 401 * 3 = 1203\n-----------\n1392\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe length of a rectangle is twice its breadth. If its length is decreased by 5 cm and breadth is increased by 5 cm, the area of the rectangle is increased by 75 sq.cm. What is the length of the rectangle\n\n### Options:\nA. 18 cm\nB. 16 cm\nC. 40 cm\nD. 20cm\nE. 28 cm\n\n### Answer:\nExplanation:\nLet breadth =x cm\nThen, length =2x cm\nArea =x\u00d72x=2x^2 sq.cm.\nNew length =(2x\u22125) cm\nNew breadth =(x+5) cm\nNew area =(2x\u22125)(x+5) sq.cm.\nGiven that, new area = initial area +75 sq.cm.\n\u21d2(2x\u22125)(x+5)=2x^2+75\n\u21d22x^2+10x\u22125x\u221225=2x^2+75\n\u21d25x\u221225=75\n\u21d25x=75+25=100\n\u21d2x=1005=20 cm\nLength =2x=2\u00d720=40 cm\nAnswer: Option C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nManish, Rahul and Bharti have some stones with each of them. Five times the number of stones with Rahul equals seven times the number of stones with Manish while five times the number of stones with Manish equals seven times the number of stones with Bharti. What is the minimum number of stones that can be there with all three of them put together?\n\n### Options:\nA. 113\nB. 109\nC. 93\nD. 97\nE. 66\n\n### Answer:\nExplanation :\nLet the stones with Manish, rahul and Bharti be m,r and b respectively.\nGiven,\n=>5r=7m and 5m=7b.\n=>25r=35m and 35m=49b.\n=>25r=35m=49b=k.\n=>r/49=m/35=b/25.\nThe least possible integral values for r,m,b will be r=49, m=35 and b=25.\n=>Total=49+35+25=109.\nAnswer : B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRs.1690 is divided so that 4 times the first share, thrice the 2nd share and twice the third share amount to the same. What is the value of the third share?\n\n### Options:\nA. s.528\nB. s.542\nC. s.780\nD. s.540\nE. s.549\n\n### Answer:\nA+B+C = 1690\n4A = 3B = 2C = x\nA:B:C = 1/4:1/3:1/2 = 3:4:6\n6/13 * 1690 = Rs.780\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the dividend. divisor 14, the quotient is 9 and the remainder is 5?\n\n### Options:\nA. A)130\nB. B)131\nC. C)148\nD. D)158\nE. E)160\n\n### Answer:\nD = d * Q + R\nD = 14 * 9 + 5\nD = 126 + 5\nD = 131\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf n=4p where p is a prime number greater than 2, how many different positive even divisors does n have, WITHOUT N VALUE?\n\n### Options:\nA. 1\nB. 2\nC. 3\nD. 4\nE. 5\n\n### Answer:\nWe're told that N = 4P and that P is a prime number greater than 2. Let's TEST P = 3; so N = 12\nThe question now asks how many DIFFERENT positive EVEN divisors does 12 have, including 12?\n12:\n1,12\n2,6\n3,4\nHow many of these divisors are EVEN? 2, 4, 6, \u2026..3 even divisors.\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSandy leaves her home and walks toward Ed's house. Two hours later, Ed leaves his home and walks toward Sandy's house. The distance between their homes is 52 kilometers, Sandy's walking speed is 6 km/h, and Ed's walking speed is 4 km/h. How many kilometers will Sandy walk before she meets Ed?\n\n### Options:\nA. 33\nB. 34\nC. 35\nD. 36\nE. 37\n\n### Answer:\nSandy walks 12 km in the first two hours so there are 40 km remaining.\nWhen Ed starts walking, they complete a total of 10 km per hour.\nThey will meet four hours after Ed starts walking.\nSince Sandy walks for 6 hours, she walks 36 km.\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRon walks to a viewpoint and returns to the starting point by his car and thus takes a total time of 6 hours 45 minutes. He would have gained 2 hours by driving both ways. How long K would it have taken for him to walk both ways.\n\n### Options:\nA. 8 h 45 min\nB. 7 h 45 min\nC. 6 h 45 min\nD. 5 h 30 min\nE. None of these\n\n### Answer:\n1.Walking to to a viewpoint+Driving back=6 hours 45 minutes\n2.Driving to a viewpoint+Driving back=6 hours 45 minutes - 2 hours=4 hours 45 minutes, thereforeone way driving=4 hours 45 minutes/2 =2 hours 22.5 minutes.\n3. From 1.one way driving=6 hours 45 minutes-2 hours 22.5 minutes=4 hours 22.5 minutes.\n4.Walking to to a viewpoint+Walking back K=4 hours 22.5 minutes+4 hours 22.5 minutes=8 hours 45 minutes.\nAnswer: A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a class everyone will play at least one sport viz table tennis, cricket and badminton. 73\nstudents play table tennis, 79 play badminton, 75 play cricket and 25 students play both table\ntennis and badminton, 24 play both table tennis and cricket 30 play. Badminton and cricket and\n16 students play all the sports. How many students are there in the class ?\n\n### Options:\nA. 84\nB. 164\nC. 97\nD. 94\nE. 74\n\n### Answer:\ntotal no. of students\n= n(B U T U C)= n(B)+n(T)+n(C)-n(B\u2229T)-n(B\u2229C)-n(C\u2229T)+n(B\u2229T\u2229C)\n= n(B U T U C)= 73+79+75-25-24-30+16\n= n(B U T U C)= 164\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow much more would Rs.20000 fetch, after two years, if it is put at 20% p.a. compound interest payable half yearly than if is put at 20% p.a. compound interest payable yearly?\n\n### Options:\nA. 482\nB. 725\nC. 992\nD. 837\nE. 923\n\n### Answer:\n20000(11/10)4 - 20000(6/5)2 = 482\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA group of medical interns at Bohemus Medical School want to go on dates. There are 6 girls and 6 guys. Assuming girls go on dates with guys, how many possible ways can these 12 medical interns date each other?\n\n### Options:\nA. A)320\nB. B)420\nC. C)520\nD. D)620\nE. E)720\n\n### Answer:\n1st girl can go with 6 guys\n2nd girl can go with remaining 5\n3rd girl can go with remaining 4 and so on\nso the total ways are 6!= 720\nE should be the answer\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOn the coordinate plane , points M and Q are defined by the coordinates (-1,0) and (3,3), respectively, and are connected to form a chord of a circle which also lies on the plane. If the area of the circle is (25/4) \u03c0 , what are the coordinates of the center of the circle ?\n\n### Options:\nA. (1.5,1)\nB. (2,-5)\nC. (0,0)\nD. (1,1.5)\nE. (2,2)\n\n### Answer:\nAlthough it took me 3 mins to solve this question using all those equations, later I thought this question can be solved easily using options.\nOne property to keep in mind - A line passing through the centre of the circle bisects the chord (or passes from the mid point of the chord).\nNow mid point of chord here is (-1+3)/2, (3+0)/2 i.e. (1,1.5) now luckily we have this in our Ans. choice. so definitely this is the ans. It also indictaes that MQ is the diameter of the circle.\nThere can be a case when MQ is not a diameter but in that case also the y-coordinate will remain same as it is the midpoint of the chord and we are moving up in the st. line to locate the centre of the circle.\nIf ans choices are all distinct (y cordinates) ONLY CHECK FOR Y CORDINATE and mark the ans=D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTabby is training for a triathlon. She swims at a speed of 1 mile per hour. She runs at a speed of 11 miles per hour. She wants to figure out her average speed for these two events. What is the correct answer for her?\n\n### Options:\nA. 6 mph\nB. 5.25 mph\nC. 3.5 mph\nD. 4 mph\nE. 0.5 mph\n\n### Answer:\n(1 mph +11 mph)/2 = 6 mph\nCorrect option is: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe speed of a car is 90 km in the first hour and 60 km in the second hour. What is the average speed of the car?\n\n### Options:\nA. 79 kmph\nB. 85 kmph\nC. 34 kmph\nD. 23 kmph\nE. 14 kmph\n\n### Answer:\nS = (90 + 60)/2\n= 75 kmph\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMachine A and machine B process the same work at different rates. Machine C processes work as fast as Machines A and B combined. Machine D processes work three times as fast as Machine C; Machine D\u2019s work rate is also exactly four times Machine B\u2019s rate. Assume all four machines work at fixed unchanging rates. If Machine A works alone on a job, it takes 7 hours. If all four machines work together on the same job simultaneously, how many minutes will it take all of them to complete it?\n\n### Options:\nA. 8\nB. 21\nC. 24\nD. 27\nE. 30\n\n### Answer:\nC = A + B\nD = 3C = 3(A+B) = 4B\nThen B = 3A and C = 4A\nThe combined rate of the four machines is A + 3A + 4A + 12A = 20A\nMachine A can complete the work in 420 minutes, so its rate is 1/420 of the work per minute.\nThe combined rate is 20/420 = 1/21 so the work will be completed in 21 minutes.\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a number between 0 and 1/2 is selected at random, which of the following will the number most likely be between\n\n### Options:\nA. 0 and 3/20\nB. 3/9 and 1/2\nC. 1/5 and 1/4\nD. 1/4 and 3/10\nE. 3/10 and 1/2\n\n### Answer:\nE. 3/9 and 1/2\nDefinitely not. I am always happy to explain a given question or issue if I can. However, I sometime donot put my explanation if I am answering first because I want to put others first for their explanation.\nNow you have excellent explanantion byscthakur. In fact the question is asking the likelyness of or high chances/probability of having a given number. Hope you already got it. B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf you divide 7^84 by 5, which remainder do you get?\n\n### Options:\nA. 0\nB. 1\nC. 2\nD. 3\nE. 4\n\n### Answer:\nThe units digit of 7^1 is 7.\nThe units digit of 7^2 is 9.\nThe units digit of 7^3 is 3.\nThe units digit of 7^4 is 1.\nThe units digit of 7^5 is 7.\netc...\nThe units digit of 7^n repeats in blocks of 4: {7, 9, 3, 1}\nThe remainder of 84/4 is 0.\nSo the units digit of 7^84 is 1.\nThe remainder of 7^84 / 5 is 1.\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average of 6 observations is 15. A new observation is included and the new average is decreased by 1. The seventh observation is?\n\n### Options:\nA. 1\nB. 8\nC. 5\nD. 6\nE. 7\n\n### Answer:\nLet seventh observation = X.\nThen, according to the question we have\n=> (90 + X) / 7 = 14\n=> X = 8\nHence, the seventh observation is 8\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n(2^2+4^2+6^2+.....+20^2)=?\n\n### Options:\nA. 770\nB. 1155\nC. 1540\nD. 385x385\nE. None of them\n\n### Answer:\n=(1x2)^2+(2x2)^2,+(2x3)^3+......(2x10)^2\n=2^2 x (1^2+2^2+3^2+.......+10^2)\nformula is =1/6 n(n+1)(2n+1)\n=(4x1/6x10x11x21)\n=(4x5x77)=1540\nAnswer is C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA person travels equal distances with speed of 3 km/hr, 4 km/hr and 5 km/hr and takes a total of 47 minutes. Find the total distane\n\n### Options:\nA. 3 km\nB. 4 km\nC. 6 km\nD. 9 km\nE. 5 km\n\n### Answer:\nExplanation:\nLet the distance be 3x km,\nthen,\nx/3+x/4+x/5=47/60\n47x /60= 47 /60\nx=1\nSo total distance = 3*1 = 3 Km\nOption A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat percent is 20% of 25%?\n\n### Options:\nA. 20%\nB. 30%\nC. 50%\nD. 60%\nE. 80%\n\n### Answer:\nRequired percentage = 20%/25% * 100 = 20/25 * 100 = 80%\nAnswer is E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the SI on Rs 8000 for 4 yrs at 10% per annum rate of interest?\n\n### Options:\nA. Rs 3000\nB. Rs 3500\nC. Rs 4000\nD. Rs 4400\nE. Rs 4800\n\n### Answer:\nSimple Interest =\nPTR\n100\n= 8000 X 5 X\n10\n100\n= Rs 4000\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA class consists of 100 students, 20 of them are girls and 80 boys; 20 of them are rich and remaining poor; 40 of them are fair complexioned. The probability of selecting a fair complexioned rich girl is\n\n### Options:\nA. 2/125\nB. 1/59\nC. 1/56\nD. 1/54\nE. 1/53\n\n### Answer:\nThe probability of selecting girl is: 20/100 = 1/5\nThe probability of selecting rich is: 20/100 = 1/5\nThe probability of selecting fair complexioned is: 40/100 = 2/5\nThree are independent;probability of rich and fair complexioned girl is:\n(1/5) \u00c3\u2014(1/5) \u00c3\u2014 (2/5) = 2/125\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSimplify: 839478 x 625\n\n### Options:\nA. 524673750\nB. 546273750\nC. 562473750\nD. 564273750\nE. None of them\n\n### Answer:\n839478 x 625 = 839478 x 5^4 = 8394780000/16 = 524673750.\nAnswer is A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo pipes A and B can fill a tank in 2 and 6 minutes respectively. If both the pipes are used together, then how long will it take to fill the tank?\n\n### Options:\nA. 2.5 min\nB. 1.8 min\nC. 1.5 min\nD. 3.5 min\nE. 2 min\n\n### Answer:\nPart filled by the first pipe in 1 minute = 1/2\nPart filled by the second pipe in 1 minute = 1/6\nNet part filled by pipe A and pipe B in 1 minute = (1/2)+(1/6)=2/3\ni.e, pipe A and B together can fill the tank in 3/2 minutes = 1.5 minutes\nAnswer is C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nInitially, the men and women in a room were in the ratio of 4 : 5. Then, 2 men entered the room and 3 women left the room. Then, the number of women doubled. Now there are 14 men in the room. How many R women are currently in the room?\n\n### Options:\nA. 12\nB. 14\nC. 15\nD. 24\nE. 36\n\n### Answer:\nthe number of women doubled means that they have become 24 from 12..\nand we have to tell the current strength so 24 is the answer..\nlet the number be 4x and 5x..\ngiven 4x+2=14.. so x=3..\nwomen number=5*3-3=12, then doubled=24..\nans D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich of the following is satisfied with |x-4|+|x-3|<6?\n\n### Options:\nA. 1 If there is addition when there are 2 absolute values, you can just ignore the middle. That is, |x-4|+|x-3|<6 -> |x-4+x-3|<6 -> |2x-7|<6, -6<2x-7<6, 1<2x<13, 1/20.5", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA lighting store is stocked with 410 fixtures. Some of the fixtures are floor lamps and the rest are table lamps. If 5% of the floor lamps and 30% of the table lamps are imported, what is the smallest possible number T of imported lamps stocked at the store?\n\n### Options:\nA. 3\nB. 10\nC. 13\nD. 20\nE. 23\n\n### Answer:\nWe want to minimize not maximize the expression,.\nT=x/20+(410-x)*3/10=123+x/20-3x/10=123-5x/20 --> maximize x to minimize the expression --> x must be the greatest multiple of 20 less than 410, so 400 --> 123-5*400/20=23.\nBut i'm guessing 123-5x/20 can be written as 123- x/4\nif x has to be the greatest multiple of 4 less then 410, then it would be 408.\nHence 123-408/4 --> 123-102 -->21\nYes, you cannot reduce in this case. If x=408, then 5/100*x and (410-x)*3/10 won't be integers.E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSuppose 6 monkeys take 6 minutes to eat 6 bananas. How many monkeys would it take to eat 18 bananas in 18 minutes?\n\n### Options:\nA. 9\nB. 10\nC. 11\nD. 6\nE. 13\n\n### Answer:\nOne monkey takes 6 min to eat 1 banana , so in 18 mins 1 monkey will eat 3 bananas , so for 18 bananas in 18 min we need 18/3 =6 monkeys\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a man walks at a rate of 10kmph, he misses a train by 14minutes. However, if he walks at the rate of 12kmph, he reaches the station 10minutes before the arrival of the train. Find the distance covered by him to reach the station.\n\n### Options:\nA. 6\nB. 15\nC. 12\nD. 4\nE. 8\n\n### Answer:\nLet the required distance x km\ndifference in the times taken at two speeds = 12min = 1/5 hr\n(x/10)-(x/12) = 1/10\nx = 6\nthe required distance is 6 km\nAnswer is A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train running at the speed of 60 km/hr crosses a pole in 3 seconds. Find the length of the train?\n\n### Options:\nA. 150 meter\nB. 170 meter\nC. 156 meter\nD. 168 meter\nE. 50 meter\n\n### Answer:\nSpeed = 60*(5/18) m/sec\n= 50/3 m/sec\nLength of Train (Distance)\n= Speed * Time\n(50/3) * 3\n= 50 meter\nAnswer:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf p and q are integers and p divided by q is 16.15, then which of the following integers is a possible value for the remainder when p is divided by q?\nI. 15\nII. 5\nIII. 3\n\n### Options:\nA. I only\nB. II only\nC. III only\nD. I,III only\nE. II,III only\n\n### Answer:\np=16.15q from which p = 16q + 15q/100 or p = 16q + 3q/20.\nSince p and q are integers, 3q/20 must also be an integer. 3 is not divisible by 20, then q must be divisible by 20, and therefore, q/20 is an integer and 3q/20 is an integer which is a multiple of 3. From the given answers, only 15 and 3 are divisible by 3.\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 18 hours and 8 hours respectively. The ratio of their speeds is\n\n### Options:\nA. 4 : 9\nB. 4 : 3\nC. 4 : 12\nD. 4 : 8\nE. 4 : 5\n\n### Answer:\nLet us name the trains as A and B. Then, (A's speed) : (B's speed) = b : a = 8 : 18 = 4 : 9.\rAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n3 singers will pick a song among a list of 3 songs. What is the probability that exactly one singer will pick a different song?\n\n### Options:\nA. 3!/3^3\nB. 1/3^3\nC. 3/3!\nD. 3/3^3\nE. 1/3!\n\n### Answer:\nEach singer out of 3 has 3 options, hence total # of outcomes is 3^3;\nFavorable outcomes will be 3!, which is # of ways to assign 3 different song to 3 singers.\nP=favorable/total=3!/3^3\nAnswer: A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf we have 12 people in a meeting, in how many ways they can sit around a table?\n\n### Options:\nA. 11*10!\nB. 9*8!\nC. 8*7!\nD. 7*6!\nE. 6*5!\n\n### Answer:\nIf there arenpeople sitting around a table, there are(n-1)!possible arrangements:\nHere, n=12\n(n-1)!=11!=11*10!\nAns:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the product of the prime numbers between 10 and 20\n\n### Options:\nA. 10^1\nB. 10^2\nC. 10^3\nD. 10^4\nE. 10^5\n\n### Answer:\nE)\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train covers a distance of 90 km in 20 min. If it takes 9 sec to pass a telegraph post, then the length of the train is?\n\n### Options:\nA. 675\nB. 680\nC. 685\nD. 690\nE. 695\n\n### Answer:\nSpeed = (90/20 * 60) km/hr = (270 * 5/18) m/sec = 75 m/sec.\nLength of the train = 75 * 9 = 675 m.\nAnswer: Option A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 15% of 40 is greater than 25% of a number by 2,then find the number is?\n\n### Options:\nA. 20\nB. 15\nC. 16\nD. 25\nE. 30\n\n### Answer:\n15/100 * 40 - 25/100 * x = 2 or x/4 = 4 so x = 16\nANSWER C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRamu bought an old car for Rs. 48000. He spent Rs. 14000 on repairs and sold it for Rs. 72900. What is his profit percent?\n\n### Options:\nA. 16%\nB. 17.5%\nC. 18.2%\nD. 58.5%\nE. 13%\n\n### Answer:\nTotal CP = Rs. 48000 + Rs. 14000\n= Rs. 62000 and SP = Rs. 72900\nProfit(%)\n= (72900 - 62000)/62000 * 100\n= 17.5%\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhen a certain shoe store reduces the price of its best-selling style of shoe by 20 percent, the weekly sales of this style increase by 10 percent. Which of the following best describes the resulting change in the store's weekly revenue from sales of this style of shoe?\n\n### Options:\nA. Revenue decreases by 10%\nB. Revenue decreases by 12%\nC. There is no change in revenue\nD. Revenue increases by 12%\nE. Revenue increases by 10%\n\n### Answer:\nOld price = 10, old sales = 10 --> old revenue = 100;\nNew price = 8, new sales = 11 --> new revenue = 88.\nRevenue decreased by 12%.\nAnswer: B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA rectangular cube has a volume of 6 cubic feet. If a similar cube is twice as long, twice as wide, and twice as high, then the volume, in cubic feet of such cube is?\nChoices\n\n### Options:\nA. 24\nB. 48\nC. 64\nD. 80\nE. 100\n\n### Answer:\nLets say the sides of the rectangular cube are x, y and z. Problem states volume is 6.\ni.e,\nx*y*z = 6 .\nIf every side is increased twice as before. then new volume is\n2x*2y*2z = 8*(x*y*z) = 8*6 = 48.\nAnswer is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf two 2-digit positive integers have their respective tens digits exchanged, the difference between the pair of integers changes by 4. What is the greatest possible difference between the original pair of integers?\n\n### Options:\nA. 76\nB. 80\nC. 82\nD. 90\nE. 94\n\n### Answer:\nFor maximizing most of 2 digit integer questions, you will have numbers closes to 90s and 10s.\nStart with 10 and 99 you see that the differences are 89 (=99-10) and 71 (=90-19) giving you a change of 89-71=18, a lot more than 4.\nNext check with 15 and 99, you get 84 (=99-15) and 76 (=95-19), you get 84-76=8. Thus the difference has been decreasing.\nFinally check with 99 and 17, you get 82 (=99-17) and 78 (=97-19), giving you 82-78 = 4 . This is the answer.\nThus, the maximum difference is 99-17=82. C is the correct answer.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf x^2 + 9/x^2 = 7, what is the value of x - 3/x\n\n### Options:\nA. 1\nB. 25\nC. 9\nD. 5\nE. 3\n\n### Answer:\nTo find : x-3/x. Let it be t.\n=> x-3/x = t\n=> (x^2 + 9/x^2) - 2*x*3/x = t^2 (Squaring both sides).\n=> (7) - 2*3 = 1\n=> t^2 = 1. Thus t=1 or t=-1.\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe rate of spin of a certain gyroscope doubled every 10 seconds from the moment a particular stopwatch started. If after a minute and a half the gyroscope reached a speed of 1600 meters per second, what was the speed, in meters per second, when the stopwatch was started?\n\n### Options:\nA. 25/3\nB. 25/4\nC. 25/8\nD. 25/16\nE. 25/32\n\n### Answer:\nLet x be the original speed when the stopwatch was started.\nIn 90 seconds, the speed doubled 9 times.\n2^9 * x = 1600\nx = (2^6 * 25) / 2^9 = 25/8\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA, B and C started a business with capitals of Rs. 8000, Rs. 10000 and Rs. 12000 respectively. At the end of the year, the profit share of B is Rs. 1500. The difference between the profit shares of A and C is?\n\n### Options:\nA. 621\nB. 276\nC. 236\nD. 600\nE. 211\n\n### Answer:\nExplanation:\nRatio of investments of A, B and C is 8000 : 10000 : 12000 = 4 : 5 : 6\nAnd also given that, profit share of B is Rs. 1500\n=> 5 parts out of 15 parts is Rs. 1500\nNow, required difference is 6 - 4 = 2 parts\nRequired difference = 2/5 (1500) = Rs. 600\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo same glasses are respectively 1/4th 1/5th full of milk. They are then filled with water and the contents mixed in a tumbler. The ratio of milk and water in the tumbler is?\n\n### Options:\nA. 9:37\nB. 9:31\nC. 9:27\nD. 9:19\nE. 9:17\n\n### Answer:\n1/4 : 3/4 = (1:3)5 = 5:15\n1/5 : 4/5 = (1:4)4 = 4:16\n------\n9:31\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA committee of 3 has to be formed randomly from a group of 6 people. If Tom and Mary are in this group of 6, what is the probability that Tom will be selected into the committee but Mary will not?\n\n### Options:\nA. .1\nB. .2\nC. 3/10\nD. .4\nE. .5\n\n### Answer:\nC (3,6) - all the possible arrangements\nC(2,4) is the number of ways the committe with Tom and without Mary.\nP = C(2,4)/(C 3,6) = 3/10 C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFor which of the following functions f is f(b) = f(1-b) for all b?\n\n### Options:\nA. f (x) = 1 - x\nB. f (b) = 1 - b^2\nC. f (b) = b^2 - (1 - b)^2\nD. f (b) = b^2*(1 - b)^2\nE. f (x) = x/(1 - x)\n\n### Answer:\nI remember seeing this problem in a GMATprep test. I think choice D should be F(b)=(b^2) (1-b)^2. If that is true then substituting (1-b) for will give us the same function back and the answer choice is D, where the function is multiplicative\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the greatest value of n such that 18^n is a factor of 18! ?\n\n### Options:\nA. 1\nB. 2\nC. 3\nD. 4\nE. 5\n\n### Answer:\nWe know that 18 = 2 *3^2.\nHence, we need to find total number of 3s in 18! ( As out of 3 and 2 , we will have count of 3 least)\nNo. of 3s = 18/3 = 6/3 = 2.\nAdd the numbers in Bold, you will get total number of 3s = 8.\nHence, total number of 3^2 = 8/2 = 4.\nHence, answer is 4.\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAn error 5% in excess is made while measuring the side of a square. The percentage of error in the calculated area of the square is\n\n### Options:\nA. 10.4%\nB. 10.25%\nC. 10.23%\nD. 10.26%\nE. 10.5%\n\n### Answer:\n100 cm is read as 102 cm.\nA1 = (100 x 100) cm2 and A2 (105 x 105) cm2.\n(A2 - A1) = [(105)2 - (100)2]\n= (105 + 100) x (105 - 100)\n= 1025 cm2.\nPercentage error = 10.25\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nParameshwaran invested an amount of 12,000 at the simple interest rate of 10 pcpa and another amount at the simple interest rate of 20 pcpa. The total interest earned at the end of one year on the total amount invested became 14 pcpa. Find the total amount invested\n\n### Options:\nA. 22,000\nB. 25,000\nC. 20,000\nD. 24,000\nE. None of these\n\n### Answer:\nLet the amount invested at 20% rate be x. According to the question,\n12000 \u00d7 10\u2044100 + x \u00d7 20\u2044100 = (12000 + x) \u00d7 14\u2044100\nor, 1200 + x\u20445 = 1680 + 7\u204450x\nor, x\u20445 - 7\u204450x = 480\nor, 3\u204450x = 480\n\\ x = 8000\n\\ Total amount invested = (12000 + 8000)= 20000\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA car covers a distance of 624 km in 6 \u00bd hours. Find its speed?\n\n### Options:\nA. 104\nB. 376\nC. 1267\nD. 198\nE. 621\n\n### Answer:\n624/6 = 104 kmph\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf x=2y=4z, what is y-z, in terms of x?\n\n### Options:\nA. 2x\nB. x/2\nC. x/4\nD. 3x/5\nE. 3x/7\n\n### Answer:\nx=2y=4z\nx/4 = z\nand y = x/2\ny-z = x/2 - x/4 = x/4\nAnswer is C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMario and Nina each have a bag of marbles, each of which contains 5 blue marbles, 10 red marbles, and 5 white marbles. If Mario and Nina each select one marble from their respective bags, what is the probability that either Mario or Nina select a red marble?\n\n### Options:\nA. 3/4\nB. 1/4\nC. 2/4\nD. 1/8\nE. 1/16\n\n### Answer:\nMario and Nina each select one marble from their respective bags.\nProbability that either Mario or Nina select a red marble = Probability that Mario selects a red marble + Probability that Nina selects a red marble\nProbability that either Mario or Nina select a red marble = (10/20)*(10/20) + (10/20)*(10/20) = 2*(1/4)\nProbability that either Mario or Nina select a red marble = 1/2\nAnswer would be C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA car covers a distance of 624 km in 4 hours. Find its speed?\n\n### Options:\nA. 104 kmph\nB. 126 kmph\nC. 156 kmph\nD. 174 kmph\nE. 101 kmph\n\n### Answer:\n624/4\n=156 kmph\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain sum of money at simple interest amounted Rs.840 in 10 years at 3% per annum, find the sum?\n\n### Options:\nA. 337\nB. 299\nC. 277\nD. 646\nE. 271\n\n### Answer:\n840 = P [1 + (10*3)/100]\nP = 646\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe current of a stream runs at the rate of 4 kmph. A boat goes 6 km and back to the starting point in 2 hours, then find the speed of the boat in still water?\n\n### Options:\nA. 3\nB. 7\nC. 8\nD. 5\nE. 1\n\n### Answer:\nS = 4\nM = x\nDS = x + 4\nUS = x - 4\n6/(x + 4) + 6/(x - 4) = 2\nx = 8\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n5358 x 81 = ?\n\n### Options:\nA. 423762\nB. 433758\nC. 433298\nD. 433998\nE. 437382\n\n### Answer:\nD\n273258\n5358 x 81 = 5358 x (80 + 1)\n= 5358 x 80 + 5358 x 1\n= 428640 + 5358\n= 433998\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the simple interest on a sum of money for 5 years at 18% per annum is Rs. 900, what is the compound interest on the same sum at the rate and for the same time?\n\n### Options:\nA. Rs. 1287.76\nB. Rs. 1284.76\nC. Rs. 1587.76\nD. Rs. 1266.76\nE. Rs. 1283.76\n\n### Answer:\nSum = (900 * 100) / (5 * 18) = Rs. 1,000.00\nC.I. on Rs. Rs. 1,000.00 for 5 years at 18% = Rs. 2,287.76.\n= Rs. 2,287.76 - 1,000.00 = Rs. 1287.76\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n75% of x is greater than 1/3rd of x by 110.what is x?\n\n### Options:\nA. 160\nB. 264\nC. 360\nD. 354\nE. 400\n\n### Answer:\n75x/100-x/3=110\n5x/12=110\nx=264\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA number whose fifth part increased by 2 is equal to its fourth part diminished by 2 is ?\n\n### Options:\nA. 160\nB. 80\nC. 200\nD. 220\nE. None\n\n### Answer:\nAnswer\nLet the number be N.\nThen, (N/5) + 2 = (N/4) - 2\n\u00e2\u2021\u2019 (N/4) - (N/5) = 4\n\u00e2\u2021\u2019 (5N - 4N)/20 = 4\n\u00e2\u02c6\u00b4 N = 80\nOption: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSolve the following quadratic equation by factoring.\n\n### Options:\nA. -2,7\nB. 2,-7\nC. 1,8\nD. 1,-8\nE. 2,6\n\n### Answer:\nWe already have zero on one side of the equation, which we need to proceed with this problem. Therefore, all we need to do is actually factor the quadratic.\nTherefore the two solutions are : (u+2)(u-7)=0 -> (u+2)(u-7)=0 therefore u=-2, u=7\nANSWER A -2,7\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?\n\n### Options:\nA. 40 sec\nB. 32 sec\nC. 12 sec\nD. 85 sec\nE. 56 sec\n\n### Answer:\nAnswer: Option A\nSpeed = 45 * 5/18 = 25/2 m/sec\nTotal distance covered = 360 + 140 = 500 m\nRequired time = 500 * 2/25 = 40 sec\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf YWVSQ is 25 - 21 - 21 - 19 - 17, Then MKIGS\n\n### Options:\nA. 13 - 11 - 9 - 7 - 9\nB. 13 - 11 - 6 - 7 - 6\nC. 13 - 11 - 9 - 7 - 7\nD. 13 - 11 - 9 - 7 - 3\nE. 13 - 11 - 9 - 7 - 1\n\n### Answer:\nMKIGS = 13 - 11 - 6 - 7 - 6\nNote: this is a dummy question. Dont answer these questions\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOf the 600 residents of Clermontville, 35% watch the television show Island Survival, 40% watch Lovelost Lawyers and 50% watch Medical Emergency. If all residents watch at least one of these three shows and 18% watch exactly 2 of these shows, then how many Clermontville residents V watch all of the shows?\n\n### Options:\nA. 150\nB. 108\nC. 42\nD. 21\nE. -21\n\n### Answer:\nOA is D.\n100= A+B+C-AB-AC-BC+ABC, which is the same as the following formula\n100= A+B+C+(-AB-AC-BC+ABC+ABC+ABC)-2ABC.\nThe term between parantheses value 18% so the equation to resolve is\n100=35+40+50-18-2ABC\ntherefore the value of ABC is 3.5% of 600,V is 21. D is the correct answer\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 5 workers collect 48 kg of cotton in 4 days, how many kg of cotton will 9 workers collect in 2 days?\n\n### Options:\nA. 47.6 kg\nB. 52.6 kg\nC. 59.6 kg\nD. 56.6 kg\nE. 57.6 kilogram\n\n### Answer:\n(3 * 5)/48 = (9 * 2)/ x\nx = 57.6 kg\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf f(x) = x - 4, then (f o f)(3) = ?\n\n### Options:\nA. -5\nB. -4\nC. -6\nD. -3\nE. -7\n\n### Answer:\n(f o f)(3) = f(f(3)) = f(3 - 4) = f(-1) = - 5\ncorrect answer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA jogger running at 9 km/hr along side a railway track is 290 m ahead of the engine of a 120 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger?\n\n### Options:\nA. 67 sec\nB. 89 sec\nC. 36 sec\nD. 87 sec\nE. 41 sec\n\n### Answer:\nSpeed of train relative to jogger = 45 - 9 = 36 km/hr.\n= 36 * 5/18 = 10 m/sec.\nDistance to be covered = 290 + 120 =410 m.\nTime taken = 410/10\n=41 sec.\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe avg weight of A,B & C is 84 kg. If D joins the group, the avg weight of the group becomes 80 kg.If another man E who weights is 4 kg more than D Replaces A, Then the avgof B,C,D&E becomes 79 kg. What is the weight of A?\n\n### Options:\nA. 76\nB. 65\nC. 75\nD. 89\nE. 90\n\n### Answer:\nA + B + C = 3 *84 = 252\nA + B + C + D = 4 * 80 = 320 ---- (i)\nSo, D = 68& E = 68 + 4 = 72\nB + C + D +E = 79 * 4 = 316 --- (ii)\nFrom Eq. (i) & (ii)\nA-E = 320 \u2013 316 = 4\nA = E +4 = 72 + 4 = 76\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train , having a length of 330 meter is running at a speed of 60 kmph. In what time, it will pass a man who is running at 6 kmph in the direction opposite to that of the train\n\n### Options:\nA. 10 sec\nB. 18 sec\nC. 6 sec\nD. 4 sec\nE. 2 sec\n\n### Answer:\nExplanation:\nDistance = 330 m\nRelative speed = 60+6 = 66 kmph (Since both the train and the man are in moving in opposite direction)\n= 66\u00d710/36 mps = 110/6 mps\nTime = distance/speed =330/(110/6) = 18 s\nAnswer: Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are 40 balls which are red, blue or green. If 15 balls are green and the sum of red balls and green balls is less than 25, at most how many red balls are there?\n\n### Options:\nA. 4\nB. 5\nC. 6\nD. 7\nE. 9\n\n### Answer:\nr+g+b=40\ng=15\nr + g < 25\n=> r + 15 < 25\n=> r < 10\n=> at most 6 red balls\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is x if x + 2y = 10 and y = 4?\n\n### Options:\nA. A)10\nB. B)8\nC. C)6\nD. D)4\nE. E)2\n\n### Answer:\nx = 10 - 2y\nx = 10 - 8.\nx = 2\nAnswer : E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nR campers fished for 7 hours. If m of the campers caught 2 fish apiece and the rest caught a combined total of n fish, how many fish did the R campers catch per hour?\n\n### Options:\nA. 2m + n(R-m)\nB. (2m + n(R-m))/3\nC. (2m + n(m-R))/3\nD. (2m + n)/7\nE. (2m + n)/R\n\n### Answer:\nm of the campers caught 2 fish apiece in 7 hours --> total fish caught by m campers = 2m;\nThe rest caught a combined total of n fish.\nTotal fish caught in 7 hours = 2m+n --> per hour (2m+n)/7.\nAnswer: D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA housewife has 11 litre of solution that contains sodium carbonate solution and benzene solution in the ratio 3 : 1. She adds 250 ml of 3 : 2 solution of sodium carbonate and benzene solution to it and then uses 250 ml of the combined mixture to make strong organic solution How much of pure sodium carbonate solution is she left with?\n\n### Options:\nA. 1000 ml\nB. 912.5 ml\nC. 750 ml\nD. 720 ml\nE. 630 ml\n\n### Answer:\nln a mixture of 1,000 ml sodium carbonate : benzene solution = 3 : 1.\nHence, sodium carbonate: 750 ml benzene solution 250 ml\nA 250 ml of 3 : 2 solution contains 150 ml sodium carbonate solution and l00ml benzene solution.\nTotal sodium carbonate solution = 900 ml, total benzene solution = 350 ml\nAfter using 250 ml to make strong organic solution , sodium carbonate solution used\n= 250/1250 x 900 = 180 ml\npure sodium carbonate solution left = 900 -180 =720ml\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the number of square tiles to cover the floor of a room measuring 6 m * 10 m leaving 0.50 m space around the room. A side of square tile is given to be 50 cms?\n\n### Options:\nA. 100\nB. 180\nC. 277\nD. 18\nE. 150\n\n### Answer:\n5*9= 1/2 * 1/2 * x => x =180\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTickets for all but 100 seats in a 10,000-seat stadium were sold. Of the tickets sold, 10% were sold at half price and the remaining tickets were sold at the full price of $2. What was the total revenue from ticket sales?\n\n### Options:\nA. $15,840\nB. $17,820\nC. $18,000\nD. $19,800\nE. $18,810\n\n### Answer:\n10000 seats --> Full Price : Half Price = 9000 : 1000\nPrice when all seats are filled = 18000 + 1000 = 19000\n100 seats are unsold --> Loss due to unfilled seats = 10 + 2*90 = 190\nRevenue = 19000 - 190 = 18810\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the absolute value of twice the difference of the roots of the equation J= 5y^2 \u2212 20y + 15 = 0 ?\n\n### Options:\nA. 0\nB. 1\nC. 2\nD. 3\nE. 4\n\n### Answer:\nJ=5y^2 \u2212 20y + 15 = 0 --> y^2 \u2212 4y + 3 = 0 --> y=1 or y=3. The difference is 2, twice the difference is 4.\nAnswer: E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHarish can paint a wall in just 3 hours. However it takes 6 hours for Ganpat to complete the same job of painting the wall.\nHow long would it take for both of them to paint the wall , if both work together ?\n\n### Options:\nA. 3 Hours\nB. 1 Hours\nC. 3.20 Hours\nD. 2 Hours\nE. 1.35 Hours\n\n### Answer:\nD\nTwo hours.\nHarish who could paint the wall in 3 hours could paint 2/3 of the wall in just two hours. Ganpat who paint the wall in 6 hours could paint 1/3 of the wall in two hours.\n2/3 + 1/3 = 1.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat approximate value should come in place of the question mark (?) in the following equation?\n8.539 + 16.84 \u00d7 6.5 \u00f7 4.2 = ?\n\n### Options:\nA. 25\nB. 42\nC. 44\nD. 35\nE. None of these\n\n### Answer:\n? 8.6 + 4 \u00d7 6.5 = 35\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSimplify\n25+[5\u00e2\u02c6\u2019(6+2(7\u00e2\u02c6\u20198\u00e2\u02c6\u20195\u00c2\u00af\u00c2\u00af\u00c2\u00af\u00c2\u00af\u00c2\u00af\u00c2\u00af\u00c2\u00af\u00c2\u00af\u00c2\u00af\u00c2\u00af\u00c2\u00af))]\n\n### Options:\nA. 23\nB. 25\nC. 28\nD. 30\nE. 16\n\n### Answer:\nExplanation:\n=25+[5\u00e2\u02c6\u2019(6+2(7\u00e2\u02c6\u20198+5))]\n(Please check due to overline, sign has been changed)\n=25+[5\u00e2\u02c6\u2019(6+2\u00c3\u20144))]\n=25+[\u00e2\u02c6\u20199]=25-9=16\nOption E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe age of father 10 years ago was thrice the age of his son. Ten years hence, father's age was five times the age of the son. After 6 years, son's age will be?\n\n### Options:\nA. 7:9\nB. 7:3\nC. 7:2\nD. 7:9\nE. 7:1\n\n### Answer:\nLet the age of father and son 10 years ago be 3x and x years respectively.\nThen, (3x + 10) + 10 = 2[(x + 10) + 10]\n3x + 20 = 2x + 40 => x = 20.\nRequired ratio = (3x + 10):(x + 10) = 70:30 = 7:3\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nNitin borrowed some money at the rate of 6% p.a. for the first three years, 9% p.a. for the next five years and 13% p.a. for the period beyond eight years. If the total interest paid by him at the end of eleven years is Rs. 10200, how much money did he borrow?\n\n### Options:\nA. 10000\nB. 80288\nC. 2668\nD. 2600\nE. 2781\n\n### Answer:\nLet the sum be Rs. x. Then,\n[(x * 6 * 3)/100] + [(x * 9 * 5)/100] + [(x * 13 * 3)/100] = 10200\n18x + 45x + 39x = (10200 * 100)\n102x = 1020000 => x = 10000.\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA perfect square is defined as the square of an integer and a perfect cube is defined as the cube of an integer. How many positive integers n are there such that n is less than 1,000 and at the same time n is a perfect square and a perfect cube?\n\n### Options:\nA. 2\nB. 3\nC. 4\nD. 5\nE. 6\n\n### Answer:\nGiven: positive integer n is a perfect square and a perfect cube --> n is of a form of n=x6 for some positive integer x --> 0 0 x can be 1, 2 or 3 hence nn can be 1^6, 2^6 or 3^6.\nAnswer: B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe area of sector of a circle whose radius is 12 metro and whose angle at the center is 39\u00b0 is?\n\n### Options:\nA. 40m2\nB. 45m2\nC. 49m2\nD. 51m2\nE. 55m2\n\n### Answer:\n39/360 * 22/7 * 12 * 12\n= 49m2\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a certain alphabet, 11 letters contain a dot and a straight line. 24 letters contain a straight line but do not contain a dot. If that alphabet has 40 letters, all of which contain either a dot or a straight line or both, how many letters contain a dot but do not contain a straight line?\n\n### Options:\nA. 5\nB. 8\nC. 14\nD. 20\nE. 28\n\n### Answer:\nWe are told that all of the letters contain either a dot or a straight line or both, which implies that there are no letters without a dot and a line (no line/no dot box = 0).\nFirst we find the total # of letters with lines: 11 +24 = 35;\nNext, we find the total # of letters without line: 40 - 35 = 5;\nFinally, we find the # of letters that contain a dot but do not contain a straight line: 5 - 0 = 5.\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man is 24 years older than his son.In two years,his age will be twice the age of his son.The present age of the son is:\n\n### Options:\nA. 14 years\nB. 18 years\nC. 20 years\nD. 22 years\nE. None of these\n\n### Answer:\nSolution\nLet the son's present age be x years.Then,man's present age =(x + 24)years.\n\u2234 (x + 24)+ 2 =2(x + 2) \u21d4 x + 26 =2x + 4 \u21d4 x =22. Answer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA sum of money deposited at compound interest (compounded yearly) amounts to $6200 in 2 years and to $6324 in 3 years. What is the interest rate?\n\n### Options:\nA. 2%\nB. 3%\nC. 4%\nD. 5%\nE. 6%\n\n### Answer:\n6324 - 6200 = 124\n124 / 6200 = 0.02 = 2%\nThe answer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf n is a positive integer and the greatest common divisor of n and 16 is 4, and the greatest common divisor of n and 15 is 3, which of the following is the greatest common divisor of n and 48?\n\n### Options:\nA. 12\nB. 18\nC. 24\nD. 30\nE. 36\n\n### Answer:\nThe greatest common divisor of n and 16 is 4 --> n is a multiple of 4 but not a multiple of 8.\nThe greatest common divisor of n and 15 is 3 --> n is a multiple of 3 but not a multiple of 5.\n48=2*3*8 is divisible by 12. therefore the greatest common divisor is 12\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo trains are moving in opposite directions at 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.4 km respectively. The time taken by the slower train to cross the faster train in seconds is?\n\n### Options:\nA. 12\nB. 77\nC. 48\nD. 99\nE. 36\n\n### Answer:\nRelative speed = 60 + 90 = 150 km/hr.\n= 150 * 5/18 = 125/3 m/sec.\nDistance covered = 1.10 + 0.4 = 1.5 km = 1500 m.\nRequired time = 1500 * 3/125 = 36 sec.\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how many ways can a group of 7 men and 5 women be made out of a total of 10 men and 7 women?\n\n### Options:\nA. 2200\nB. 2520\nC. 2689\nD. 2540\nE. 2680\n\n### Answer:\nWe need to select 7 men from 10 men and 5 women from 7 women. Number of ways to do this\r= 10C7 \u00d7 7C5\r=2520\rB)\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the mean of numbers 28, x, 42, 78 and 104 is 90, then what is the mean of 128, 255, 511, 1023 and x?\n\n### Options:\nA. 395\nB. 275\nC. 355\nD. 415\nE. 423\n\n### Answer:\nThe mean of numbers 28, x, 42, 78 and 104 is 62: 28+x+42+78+104=90*5 --> x=198;\nSo, the mean of 128, 255, 511, 1023 and x is (128+255+511+1023+198)/5=423.\nAnswer: E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the sum of two numbers is 16 and the sum of their squares is 200, then the product of the numbers is\n\n### Options:\nA. 40\nB. 44\nC. 80\nD. 88\nE. 28\n\n### Answer:\naccording to the given conditions x+y = 16\nand x^2+y^2 = 200\nnow (x+y)^2 = x^2+y^2+2xy\nso 16^2 = 200+ 2xy\nso xy = 56/2 =28\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a triangle, one side is 6 Cm and another side is 12 Cm. which of the following can be the perimeter of the triangle?\n\n### Options:\nA. 18.\nB. 25.\nC. 30.\nD. 32.\nE. 34.\n\n### Answer:\nGiven : one side is 6 Cm and another side is 9 Cm. So the 3rd side will be > 3 and < 15. Thus the perimeter will be : 18 < perimeter < 30. Only option satisfying this condition is 32. Hence D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOn Monday morning, Chris receives tickets to a baseball game that will be played at 7pm on the next evening that it does not rain. However, Chris is only in town until Wednesday morning, at which point he must fly to another city. If there is a 10% chance of rain each of the next two evenings, what is the probability that Chris will be able to attend the game?\n\n### Options:\nA. 36%\nB. 60%\nC. 66%\nD. 80%\nE. 99%\n\n### Answer:\nChris won't be able to attend the game if it be raining on Monday eveningandTuesday evening. The probability of that is 0.1*0.1 = 0.01. So, the probability that he will be able to attend is 1 - 0.01 = 0.99.\nAnswer: E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow much time will it take for an amount of Rs. 450 to yield Rs. 81 as interest at 4.5% per annum of simple interest?\n\n### Options:\nA. 8 years\nB. 4 years\nC. 7 years\nD. 6 years\nE. 2 years\n\n### Answer:\nExplanation:\nTime = (100 x 81)/(450 x 4.5) years\n= 4 years.\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHalf a number plus 5 is 15.What is the number?\n\n### Options:\nA. 8\nB. 20\nC. 10\nD. 11\nE. 12\n\n### Answer:\nLet x be the number. Always replace \"is\" with an equal sign\n(1/2)x + 5 = 15\n(1/2)x = 15 - 5\n(1/2)x = 10\nx = 20\ncorrect answer is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n25.25/3000 is equal to:\n\n### Options:\nA. 0.008416667\nB. 0.110773333\nC. 0.12526234\nD. 0.01072333\nE. 0.12725002\n\n### Answer:\n25.25/3000 = 2525/300000\n= 0.008416667\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average number of shirts with Salman, Ambani and Dalmiya is 60, if all of them reached a shopping mall in Delhi and purchased 2 shirts each of them then average number of shirt each of them now has\n\n### Options:\nA. 66\nB. 63\nC. 62\nD. 64\nE. 61\n\n### Answer:\nRequired average\n= Old average + New average\n= 60 + 2 = 62\nanswer :C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nQuestion: What is the remainder when I= (1!)!^3 + (2!)^3 + (3!)^3 + \u2026 + (432!)^3 is divided by 144?\n\n### Options:\nA. 0\nB. 25\nC. 49\nD. 81\nE. 100\n\n### Answer:\n144 =12 *12\n(1!)^3=1\n2!=2, therefore (2!)^3=2*2*2=8\n3!=6, therefore (3!)^3=6*6*6=216\n4!=24 therefore (4!)^3= 24*24*24 which is completely divisible by 144\nthus from 4! onwards each term will be divisible by 144 and will leave the remainder of 0\nnow the remainder when I=(1!)^3 + (2!)^3 + (3!)^3 + \u2026 + (432!)^3 is divided by 144 is same as, when 1+8+216 =225 is divided by 144\nnow remainder when 225 is divided by 144 is 81. hence answer should be D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many positive integers N less than 20 are either a multiple of 2, an odd multiple of 9, or the sum of a positive multiple of 2 and a positive multiple of 9 ?\n\n### Options:\nA. 19\nB. 18\nC. 17\nD. 16\nE. 15\n\n### Answer:\nWe're asked to deal with the positive integers LESS than 20. There are only 19 numbers in that group (1 to 19, inclusive). We're asked to find all of the numbers that fit one (or more) of the given descriptions. Looking at the answer choices, we have every value form 15 to 19, inclusive, so most (if not all) of the numbers from 1 to 19 fit one (or more) of the descriptions. How long would it take you to find the ones that DON'T fit.....?\nThe first several should be pretty easy to find - the prompt wants us to focus on multiples of 2 and 9 (and sums of those multiples). So what ODD numbers are less than 9?\n1, 3, 5, 7\nNone of these values fit the given descriptions. That's 4 out of 19 that we know for sure do NOT fit. 19 - 4 = 15 = E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how many ways can be 7 boys and 7 girls sit around circular table so that no two boys sit next to each other?\n\n### Options:\nA. (5!)^2\nB. (6!)^2\nC. 6!7!\nD. 11!\nE. (5!)^2*6!\n\n### Answer:\nfirst fix one boy and place other 6 in alt seats so total ways is 6!\nnow place each girl between a pair of boys... total ways of seating arrangement of girls 7!\ntotal is 6!*7!\nANS C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA rectangular box measures internally 1.6m long, 1m broad and 60cm deep. The number of cubical box each of edge 20cm that can be packed inside the box is:\n\n### Options:\nA. 30\nB. 60\nC. 90\nD. 120\nE. 140\n\n### Answer:\nExplanation:\nNumber of blocks =(160x100x60/20x20x20)=120\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSeventy five percent of a number is 21 less than four fifth of that number. What is the number ?\n\n### Options:\nA. 240\nB. 340\nC. 420\nD. 130\nE. 125\n\n### Answer:\nLet the number be x.\nThen, 4*x/5 \u00e2\u20ac\u201c(75% of x) = 21\n4x/5 \u00e2\u20ac\u201c 75x/100 = 21\nx = 420.\nAnswer C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA 270 m long train running at the speed of 120 km/hr crosses another train running in opposite direction at the speed of 80 km/hr in 9 sec. What is the length of the other train?\n\n### Options:\nA. 230\nB. 200\nC. 250\nD. 300\nE. 500\n\n### Answer:\nAnswer: Option A\nExplanation:\nRelative speed = 120 + 80 = 200 km/hr.\n= 200 * 5/18 = 500/9 m/sec.\nLet the length of the other train be x m.\nThen, (x + 270)/9 = 500/9 => x = 230.\nANSWER A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSolution A is 20% barium and Solution B is 80% barium. If you have 30 ounces of solution A and 60 ounces of solution B, in what ratio could you mix Solution A with Solution B to produce 50 ounces of a 50% barium solution?\n\n### Options:\nA. 6:4\nB. 6:14\nC. 4:4\nD. 4:6\nE. 3:7\n\n### Answer:\nForget the volumes for the time being.\nYou have to mix 20% and 80% solutions to get 50%. This is very straight forward since 50 is int he middle of 20 and 80 so we need both solutions in equal quantities. If this doesn't strike, use\nw1/w2 = (A2 - Aavg)/(Aavg - A1)\nw1/w2 = (80 - 50)/(50 - 20) = 1/1\nSo the volume of the two solutions will be equal. Answer has to be 4:4=C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRob has 8 toy trucks. He gives 3 trucks to his best friend as a gift. How many trucks does Rob have left?\n\n### Options:\nA. 5\nB. 20\nC. 2\nD. 5\nE. 8\n\n### Answer:\nA. 5\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo pipes A and B can fill a cistern in 20 and 30 minutes respectively, and a third pipe C can empty it in 40 minutes. How long will it take to fill the cistern if all the three are opened at the same time?\n\n### Options:\nA. 17 1/4 min\nB. 28 1/7 min\nC. 17 1/7 min\nD. 17 1/8 min\nE. 17 5/7 min\n\n### Answer:\n1/20 + 1/30 - 1/40 = 7/120\n120/7 = 17 1/7\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA trader sells 40 metres of cloth for Rs.8200 at a profit of Rs.20 per metre of cloth. How much profit will the trder earn on 40 metres of cloth?\n\n### Options:\nA. Rs.800\nB. Rs.1500\nC. Rs.1000\nD. Rs.1200\nE. None of these\n\n### Answer:\nExplanation:\nSP of 1 metre cloth = 8200/40 = Rs.205.\nCP of 1 metre cloth = Rs.205 \u2013 20 = Rs.185\nCP on 40 metres = 185 x 40 = Rs.7400\nProfit earned on 40 metres cloth = Rs.8200 \u2013 Rs.7400 = Rs.800.\nAnswer: Option A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf in a certain sequence of consecutive multiples of 100, the median is 650, and the greatest term is 1000, how many terms that are smaller than 650 are there in the sequence?\n\n### Options:\nA. 6\nB. 4\nC. 8\nD. 12\nE. 13\n\n### Answer:\nSince the median is 650 we know there must be a even number of integers\nSo the list around 625 must go. 600 ( 650) 700 800 900 1000\nSince we know there are 4 numbers greater than 650 then there must be 4 numbers less then 650.\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJohn started driving on a highway at a constant speed of R miles per hour at 13:00. Then, 2 hours later, Tom started driving on the same highway at a constant speed of 6R/5 miles per hour at 15:00. If both drivers maintained their speed, how many miles had John driven on the highway when Tom caught up with John?\n\n### Options:\nA. 6R\nB. 8R\nC. 9R\nD. 10R\nE. 12R\n\n### Answer:\nIn 2 hours, John drove 2R miles.\nTom can catch John at a rate of 6R/5 - R = R/5 miles per hour.\nThe time it takes Tom to catch John is 2R / (R/5) = 10 hours.\nIn 10 hours, John can drive another 10R miles for a total of 12R miles.\nThe answer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe current in a river is 3 mph. A boat can travel 21 mph in still water. How far up the river can the boat travel if the round trip is to take 10 hours?\n\n### Options:\nA. 69 miles\nB. 88 miles\nC. 96 miles\nD. 102.8 miles\nE. 112 miles\n\n### Answer:\nUpstream Speed = 21-3=18mph\nDownstream Speed = 21+3 = 24 mph\nD/18 + D/24 = 10 hours\nSolving for D we get D=102.8\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe sale price sarees listed for Rs.400 after successive discount is 10% and 5% is?\n\n### Options:\nA. 297\nB. 879\nC. 342\nD. 762\nE. 269\n\n### Answer:\n400*(90/100)*(95/100)\n= 342\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe 5 th term and 21 st term of a series in A.P are 10 and 42 respectively. Find the 31 st term.\n\n### Options:\nA. 50\nB. 55\nC. 65\nD. 62\nE. 52\n\n### Answer:\na + 4d = 10 \u2026\u2026\u2026\u2026.. (1)\na + 20d = 42 \u2026\u2026\u2026\u2026.. (2)\nEqn (2) \u2013 Eqn (1) gives 16d = 32 , d = 2\nSubstituting d =2 in either (1) or (2), a = 2.\n31 st term = a + 30d = 2 + 30*2 = 62\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe cross-section of a cannel is a trapezium in shape. If the cannel is 14 m wide at the top and 8 m wide at the bottom and the area of cross-section is 550 sq m, the depth of cannel is?\n\n### Options:\nA. 76\nB. 28\nC. 50\nD. 80\nE. 25\n\n### Answer:\n1/2 * d (14 + 8) = 550\nd = 50\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA, B, and C contest an election from a particular constituency. A and B together got 50% more votes than C. The vote share of A and C together is 30 percentage points more than the vote share of B. Who won the election?\n\n### Options:\nA. A\nB. B\nC. C\nD. Cannot be determined\nE. none\n\n### Answer:\nLet a,b,c be the vote share of A, B, C respectively\na + b = 1.5 c\na + c = b + 30\na + b + c = 100, 2b + 30 = 100,\nb = 35\na = 25, c = 40, So, C won the election.\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf q is an integer greater than 6, which of the following must be divisible by 3?\n\n### Options:\nA. Q(Q+1)(Q-4)\nB. N(N+2)(N-1)\nC. N(N+3)(N-5)\nD. N(N+4)(N-2)\nE. N(N+5)(N-6)\n\n### Answer:\nNow take Q = 3k , Q = 3k+1 Q = 3k+2..put in all the choices. If by putting all the values of Q we get it is divisible by 3, then it is correct answer choice.\nA is correct. It will hardy take 10 sec per choice as we have to consider only 3k+1 and 3k+2.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many terms are in the G.P. 3, 6, 12, 24, ......., 384,768\n\n### Options:\nA. 8\nB. 9\nC. 67\nD. 5\nE. 2\n\n### Answer:\nExplanation:\nHere a = 3 and r = 6/3 = 2. Let the number of terms be n.\nThen, t = 768 => a * r^(n-1) = 768\n=> 3 * 2^(n-1) = 768 => 2^(n-1) = 256 = 2^(8)\n=> n-1 = 8 => n = 9.\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSuresh can complete a job in 15 hours. Ashutosh alone can complete the same job in 30 hours. Suresh works for 9 hours and then the remaining job is completed by Ashutosh. How many hours will it take Ashutosh to complete the remaining job alone?\n\n### Options:\nA. 4\nB. 5\nC. 6\nD. 12\nE. None of these\n\n### Answer:\nThe part of job that Suresh completes in 9 hours\n= 9\u00e2\u0081\u201e15 = 3\u00e2\u0081\u201e5\nRemaining job = 1 - 3\u00e2\u0081\u201e5 = 2\u00e2\u0081\u201e5\nRemaining job can be done by Ashutosh in 2\u00e2\u0081\u201e5 \u00c3\u2014 30 = 12 hours\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average monthly income of P and Q is Rs. 5050. The average monthly income of Q and R is Rs. 6250 and the average monthly income of P and R is Rs. 5200. The monthly income of P is:\n\n### Options:\nA. 3500\nB. 4000\nC. 4050\nD. 5000\nE. 5500\n\n### Answer:\nExplanation:\nLet P, Q and R represent their respective monthly incomes. Then, we have:\nP + Q = (5050 x 2) = 10100 .... (i)\nQ + R = (6250 x 2) = 12500 .... (ii)\nP + R = (5200 x 2) = 10400 .... (iii)\nAdding (i), (ii) and (iii), we get: 2(P + Q + R) = 33000 or P + Q + R = 16500 .... (iv)\nSubtracting (ii) from (iv), we get P = 4000.\nP's monthly income = Rs. 4000.\nANSWER IS B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf X> 0 and X is divisible by the product of the first nine positive integers, all of the following must be factors of X except\n\n### Options:\nA. 35\nB. 40\nC. 63\nD. 315\nE. 704\n\n### Answer:\nThe question states taht X is divisible by 9!,which is 1*2*3*4*5*6*7*8*9\nX=(9!) * some number\nA. 35 = 5*7 so will divide X\nB. 40 =5*8 so will divide X\nC. 63 =9*7 so will divide X\nD. 315 =5*7*9 so will divide X\nE. 704 =8*8*11 This will not divide X\nAns E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA garrison of 400 men had a provision for 31 days. After 28 days 280 persons re-enforcement leave the garrison. Find the number of days for which the remaining ration will be sufficient?\n\n### Options:\nA. 16 days\nB. 34 days\nC. 10 days\nD. 16 days\nE. 15 days\n\n### Answer:\n400 --- 31\n400 --- 3\n120 --- ?\n400*3 = 120*x => x\n=10 days\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn year Y imported machine tools accounted for 25 percent of total machine - tool sales in the United States, and Japanese imports accounted for 50 percent of the sales of imported machine tools. If the total sales of machine tools imported Japan that year was x billion dollars, then the total sales of all machine tools in the United States was how many billion dollars?\n\n### Options:\nA. 8X/1\nB. 13X/20\nC. 80/9X\nD. 20X/13\nE. 80X/9\n\n### Answer:\nIMT = 0.25T\nJI = 0.50 IMT\n0.50 IMT = $x b\nIMT = $x/(0.50) b\nT = 4*IMT = 4x/0.50 = 4x*100/50 = 8x/1\nAns: \"A\"\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe compound interest earned by Sunil on a certain amount at the end of two years at the rate of 8% p.a. was Rs.2828.80. Find the total amount that Sunil got back at the end of two years in the form of principal plus interest earned.\n\n### Options:\nA. 19828.77\nB. 19828.8\nC. 19828.82\nD. 19888.82\nE. 19828.22\n\n### Answer:\nLet the sum be Rs.P\nP{ [ 1 + 8/100]2 - 1 } = 2828.80\nP(8/100)(2 + 8/100) = 2828.80 [a2 - b2 = (a - b) ( a + b)] P = 2828.80 / (0.08)(2.08) = 1360/0.08 = 17000 Principal + Interest = Rs. 19828.80\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nat a time A,do 20% less work than B.if A do any work in 15/2 hour,then in how many hour B will finish work?\n\n### Options:\nA. 5 hour\nB. 11/2 hour\nC. 6 hour\nD. 13/2 hour\nE. 8 hour\n\n### Answer:\nlet B will finish a work in x hour.then,in x hour A,80/100=4/5 work do\nratio of work done by A and B=inverse ratio of time taken\n4/5:1=2/15:1/x\n4/5*1/x=1*2/15=4/5x=2/15;x=6.\ntime= 6 hour\nanswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn May, the grounds keeper at Spring Lake Golf Club built a circular green with an area of 49\u03c0 square feet. In August, he doubled the distance from the center of the green to the edge of the green. What is the total area of the renovated green?\n\n### Options:\nA. 100PI\nB. 144PI\nC. 196 PI\nD. 80\nE. 90\n\n### Answer:\nAREA OF CIRCLE 49PI SQ FEET =PI R^2 THEREFORE R =7\nNOW GREEN RADI DOUBLED I.E R =14 AREA =196 PI\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSumitra has an average of 56% on her first 7 examinations. How much should she make on her eighth examination to obtain an average of 60% on 8 examinations?\n\n### Options:\nA. 88%\nB. 78%\nC. 98%\nD. Cannot be determined\nE. None of these\n\n### Answer:\nSince the weight age of eighth examination is not known, hence can not be determined.\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 10 and 15 are the lengths of two sides of a triangular region, which of the following can be the length of the third side?\nI. 5\nII. 15\nIII. 20\n\n### Options:\nA. I only\nB. II only\nC. I and II only\nD. II and III only\nE. I, II, and III\n\n### Answer:\nThe length of any side of a triangle must be larger than the positive difference of the other two sides, but smaller than the sum of the other two sides.\nLet x be the length of the third side.\n15-10 < x < 15+10\n5 < x < 25\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAt a conference table, 8 employees gather around a table. One of the employees is the manager and he sits at the head of the table. Two of the employees sit on either side of the table. How many different seating arrangements can be made with these 8 employees?\n\n### Options:\nA. 5060\nB. 5050\nC. 5060\nD. 5040\nE. 5030\n\n### Answer:\nHead's sit is fixed. Now 7 people is left with 7 seats.\n7 people can sit on 7 seats in 7! ways or 5040 ways.\nAns is D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAn aeroplane covers a certain distance at a speed of 150 kmph in 2 hours. To cover the same distance in 1 2/3 hours, it must travel at a speed of:\n\n### Options:\nA. 1300 kmph\nB. 160 kmph\nC. 180 kmph\nD. 1080 kmph\nE. none\n\n### Answer:\nExplanation: Distance = (150 x 2) = 300 km.\nSpeed = Distance/Time\nSpeed = 300/(5/3) km/hr. [We can write 1 2/3 hours as 5/3 hours]\nRequired speed = 300 x 3/5 km/hr = 180 km/hr.\nAnswer: Option C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average marks of a class of 30 students is 40 and that of another class of 50 students is 60. Find the average marks of all the students?\n\n### Options:\nA. 52.5\nB. 52.9\nC. 52.1\nD. 52.3\nE. 42.5\n\n### Answer:\nSum of the marks for the class of 30 students = 30 * 40 = 1200\nSum of the marks for the class of 50 students = 50 * 60 = 3000\nSum of the marks for the class of 80 students =\n1200 + 3000 = 4200\nAverage marks of all the students = 4200/80\n= 52.5\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a and b are nonzero integers such that 6a = 15b, then each of the following must be true EXCEPT\n\n### Options:\nA. 0 < b/a < 1\nB. ab is positive.\nC. On the number line, b lies between 0 and a.\nD. The ratio of a to b is equivalent to 10/4.\nE. a \u2013 b is positive.\n\n### Answer:\nThis question can be solved by TESTing VALUES. Based on its wording, you would likely need to do 2 TESTs to get to the correct answer though.\nWe're told that a and b are NONZERO INTEGERS and that 6a=15b or 2a = 5b. We're told that each of the answer is always true EXCEPT for one of them...\nBefore we get to the actual work, it's important to note a few details:\n1) We are NOT told that a and b are positive - we're just told that they're NONZERO - that's interesting - it means that we have to consider the possibility that they're both NEGATIVE...\n2) 4 of the answers will always be true, while one of them will EITHER be sometimes true OR never true. We'll have to keep working until we find 1 answer that is not true (for whatever reason) - that will be the solution to this question.\nSince 2A = 5B, I'm going to run 2 pairs of TESTs at the same time...\nA = 5\nB = 2\nAND\nA = -5\nB = -2\nAnswer A: 0 < B/A < 1\n2/5 and -2/-5 both = 2/5. Answer A appears true.\nAnswer B: AB is positive\n(2)(5) and (-2)(-5) both = +10. Answer B appears true.\nAnswer C: B is between 0 and A on the number line\n0....2....5\n-5....-2....0\nAnswer C appears true.\nAnswer D: A/B = 10/4\n5/2 = -5/-2\n10/4 = 5/2\nAnswer D appears true.\nAnswer E: A - B is positive\n5 - 2 = 3\n-5 - (-2) = -3 *****This is NOT always true.\nFinal Answer:\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how many different ways can the letters of the word 'OPTICAL' be arranged so that the vowels always come together?\n\n### Options:\nA. 120\nB. 720\nC. 4320\nD. 2160\nE. 3570\n\n### Answer:\nThe word 'OPTICAL' contains 7 different letters.\nwhen the vowels OIA are always together, they can be supposed to form one letter.\nThen, we have to arrange the letters PTCL (OIA)\nNow, 5 letters can be arranged among themselves in 3!=6 ways.\nRequired number of ways =(120*6)=720.\nAnswer is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA tank is filled by three pipes with uniform flow. The first two pipes operating simultaneously fill the tank in the same during which the tank is filled by the third pipe alone. The second pipe fills the tank 5 hours faster than the first pipe and 4 hours slower than the third pipe. The time required by the first pipe is?\n\n### Options:\nA. 12\nB. 14\nC. 15\nD. 19\nE. 10\n\n### Answer:\nSuppose, first pipe alone takes x hours to fill the tank. Then, second and third pipes will take (x - 5) and (x - 9) hours respectively to fill the tank.\n1/x + 1/(x - 5) = 1/(x - 9)\n(2x - 5)(x - 9) = x(x - 5)\nx2 - 18x + 45 = 0\n(x- 15)(x - 3) = 0 => x = 15. Answer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA car was initially traveling at an average speed of 36 miles per hour. During each of ten successive 5-minute intervals, the car decreased its average speed by 2 miles per hour. How many miles did the car travel in the fourth 5-minute interval?\n\n### Options:\nA. 1.32\nB. 5.32\nC. 4.56\nD. 2.33\nE. 1.44\n\n### Answer:\nThe question does not specifically mentioned whether 36miles/h is the speed in first interval or before that... So I got confused.\nIf former is the case, then average speed of the car in 4th interval will be 28. This gives 28 * (5/60) = m = 2.33 miles\ncorrect option is D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many ways are there for 3 males and 3 females to sit (around a circular table) if no male should sit next to a male (and no female next to female) and Mary wants to sit with her back on the wall?\n\n### Options:\nA. 6\nB. 12\nC. 72\nD. 100\nE. 720\n\n### Answer:\nLets first sit the 3 man, 2! ways.\nNow since one position is fixed for women, there are 2 women left and they have 2! ways\n2! X 2! = 4 answer is diff this way.\nor shall we give possibility of 3 ways for women to be fixed with back facing so 3! ways, ANS:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA team scored a total of 98 points. If each player on the team scored at least 14 points, then what is the greatest possible number of players on the team?\n\n### Options:\nA. A)6\nB. B)7\nC. C)8\nD. D)9\nE. E)10\n\n### Answer:\n98/14=7 plus remainder.\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn the kitchen of a busy restaurant, it takes M minutes to wash P pots. At this rate, how many hours does it take to wash 15P pots?\n\n### Options:\nA. 4/M\nB. 4M\nC. 900M\nD. M/900\nE. M/4\n\n### Answer:\nThe time it takes to wash 15P pots is 15M minutes which is 15M / 60 = M/4 hours.\nThe answer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n3/5 of all married couples have more than one child. 2/5 of all married couples have more than 3 children. What fraction of all married couples have 2 or 3 children?\n\n### Options:\nA. 1/5\nB. 1/4\nC. 7/20\nD. 3/5\nE. It cannot be determined from the given information.\n\n### Answer:\nPlug in simple numbers. Take 100 couples for example.\n3/5 of 100 couples have more than one child = 60 couples.\n2/5 of 100 couples have more than 3 kids = 40 couples.\nThis implies that 40 couples are a subset of 60 couples and the complement of 60 couples within those 100 couples, which equals 20 couples have either one or no kids at all.\nWe need to find couples that have 2 or 3 kids, so essentially, it is 60 - 40 = 20. Fraction will be 20/100 = 1/5.\nOption A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the one which does not belong to that group?\n\n### Options:\nA. 16\nB. 36\nC. 77\nD. 64\nE. 4\n\n### Answer:\nExplanation:\n16, 36, 64 and 4 are perfect squares but not 77.\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo employees X and Y are paid a total of Rs. 650 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week?\n\n### Options:\nA. s.200.45\nB. s.250.45\nC. s.295.45\nD. s.300.45\nE. s.310.45\n\n### Answer:\nLet the amount paid to X per week = x\nand the amount paid to Y per week = y\nThen x + y = 650\nBut x = 120% of y = 120y/100 = 12y/10\n\u223412y/10 + y = 650\n\u21d2 y[12/10 + 1] = 650\n\u21d2 22y/10 = 650\n\u21d2 22y = 6500\n\u21d2 y = 6500/22 = Rs.295.45\nC)\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nUsing all the letters of the word \"THURSDAY\", how many different words can be formed?\n\n### Options:\nA. 8!\nB. 1\nC. 7\nD. 6\nE. 5\n\n### Answer:\nTotal number of letters = 8\nUsing these letters the number of 8 letters words formed is 8P8 = 4.\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA shopkeeper sells his goods at cost price but uses a faulty meter that weighs 960 grams. Find the profit percent.\n\n### Options:\nA. 4.166\nB. 3.1\nC. 2.1\nD. 1.256\nE. 3.759\n\n### Answer:\nExplanation:\n(100 + g) / (100 + x) = True measure / Faulty measure\nx = 0\ntrue measure = 1000\nfaulty measure = 960\n100 + g / 100 + 0 = 1000 / 960\n100+g = 100/96*100\ng = 4.166\nANSWER: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFour staff members at a certain company worked on a project. The amounts of time that the four staff members worked on the project were in the ratio 2 to 3 to 5 to 6. If one of the four staff members worked on the project for 15 hours, which of the following CANNOT be the total number of hours that the four staff members worked on the project?\n\n### Options:\nA. 120\nB. 80\nC. 48\nD. 192\nE. 40\n\n### Answer:\nFour members worked in ration 2:3:5:6, hence as everyone mentioned, individual work could be taken as 2x, 3x,5x, and 6x. Also this gives us total work as 16x.\nBut we are told that one of these individual works is 15hrs. hence, possible scenarios, if\n(1)2x =15 => 16x = 120 (2) 3x =15 => 16x = 80 (3) 5x =15 => 16x = 48 (4) 6x =15 => 16x = 40\nHence Answer is D 192 which can not be any of these.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train leaves Mumabai at 9 am at a speed of 40 kmph. After one hour, another train leaves Mumbai in the same direction as that of the first train at a speed of 50 kmph. When and at what distance from Mumbai do the two trains meet?\n\n### Options:\nA. 2:00pm, 206 km\nB. 2:00pm, 220 km\nC. 2:00pm, 200 km\nD. 2:00pm, 208 km\nE. 2:00pm, 230 km\n\n### Answer:\nWhen the second train leaves Mumbai the first train covers 40 * 1 = 40 km\nSo, the distance between first train and second train is 40 km at 10.00am\nTime taken by the trains to meet\n= Distance / relative speed\n= 40 / (50 -40) = 4 hours\nSo, the two trains meet at 2 p.m. The two trains meet 4 * 50\n= 200 km away from Mumbai.\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf X = 2 + 1/(1+1/(1-1/2))then the value of 4x+7/3?\n\n### Options:\nA. 9 2/3\nB. 10 1/3\nC. 11\nD. 11 2/3\nE. 12\n\n### Answer:\nX = 2 + 1/(1+1/(1-1/2))\n= 2 + 1/(1+2)\n= 2 + 1/3\nX = 7/3 ==> 4X + 7/3 => 4(7/3) + 7/3\n==> 28/3 + 7/3\n==> 35/3\n==> 11 2/3.\nD)\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe original price of a car was $25,200. Because the car owner thought he could get more money for the car, he increased the price of the car to 110% of its original price. After a week, the car had not sold, so the owner then discount ed the price by 10%, and the car was finally sold. What price was the car sold for?\n\n### Options:\nA. $25,200\nB. $25,000\nC. $24,948\nD. $24,542\nE. $23,658\n\n### Answer:\nThe car is sold for 1.1*0.9*25200\n=0.99 * 25200\n=(1 - 0.01) * 25200\n=25200 - 252\n=24948\nC is the answer\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nLook at this series: 2, 1, (1/2), (1/4), ... What number should come next?\n\n### Options:\nA. (1/3)\nB. (1/8)\nC. (2/8)\nD. (1/16)\nE. None\n\n### Answer:\nExplanation: This is a simple division series; each number is one-half of the previous number. In other terms to say, the number is divided by 2 successively to get the next result.\n4/2 = 2\n2/2 = 1\n1/2 = 1/2\n(1/2)/2 = 1/4\n(1/4)/2 = 1/8 and so on.\nAnswer: Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a certain accounting class of 100 students, 70% of the students took the final exam on the assigned day while the rest of the students took the exam on a make-up date. If the students on the assigned day had an average score of 65%, and the students on the make-up date had an average score of 95%, what was the average score for the entire class?\n\n### Options:\nA. 68%\nB. 70%\nC. 72%\nD. 74%\nE. 77%\n\n### Answer:\n70% of the class scored 65% and 30% of the class scored 95%.\nThe difference between 65% and 95% is 30%.\nThe average will be 65% + 0.3(30%) = 74%.\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nthere is one designed bedsheets having length 6m and breadth 4m.in the middle there is square shape design with 3m side.calculate the % of bedsheet which do not have any design.\n\n### Options:\nA. 62\nB. 60\nC. 75\nD. 62.5\nE. 65\n\n### Answer:\narea of bedsheet=24m2.\narea of square shape design=9m2.\nundesigned area=24-9=15m2.\n%of undesigned area=15/24*100=62.5%\nanswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe length of a rectangle is halved, while its breadth is tripled. Wat isthe % change in area?\n\n### Options:\nA. 20%\nB. 40%\nC. 50%\nD. 60%\nE. 70%\n\n### Answer:\nLet original length = x and original breadth = y.\nOriginal area = xy.\nNew length = x .\n2\nNew breadth = 3y.\nNew area = x x 3y = 3 xy.\n2 2\nIncrease % = 1 xy x 1 x 100 % = 50%.\n2 xy\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA professional janitor can clean a certain high school in 8 hours, working at a constant rate. A student sentenced to detention can clean that same high school in (10+10) hours, also working at a constant rate. If the student is paid $7 total per hour and the janitor is paid $21 per hour, how much more would it cost the school to pay the janitor to do the job himself than it would to pay the student and the janitor to do the job together?\n\n### Options:\nA. -$56\nB. -$6\nC. $0\nD. $6\nE. $8\n\n### Answer:\nA professional janitor can clean a certain high school in 8 hours\nSo (applying rule #1), the janitor can clean 1/8 of the school in ONE HOUR\nA student sentenced to detention can clean that same high school in 20 hours\nSo (applying rule #1), the student can clean 1/(10+10) or 1/20 of the school in ONE HOUR\nSo, COMBINED, the student and janitor can clean (1/8 + 1/20) of the school in ONE HOUR\n1/8 + 1/20 = 5/40 + 2/40 = 7/40\nSo, in ONE HOUR they can clean 7/40 of the school.\nApplying rule #2, it will takethem40/7 hoursto clean the ENTIRE school.\nThe janitor earns $21/hour and the student earns $7/hour, so their combined rate is$28/hour.\nTheircombined wages= (pay rate)(time) = ($28/hour)(40/7 hours) =$160\nWorking ALONE, the janitor takes 8 hours and earns $21/hour\nSo, working alone, the janitor's earnings = (pay rate)(time) = ($21/hour)(8 hours) =$168\n$168-$160= $8, so the answer is E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJohn invests $x at the semi-annual constant compounded rate of 2 percent and also does $15,000 at the quarterly constant compounded rate of 4 percent. If the interests are the same after 1 year, what is the value of x??\n\n### Options:\nA. 20000\nB. 30000\nC. 40000\nD. 30301.5\nE. 50000\n\n### Answer:\nA = P(1+r/n)^nt\nA= total amount accrued\nP = principal deposited\nr = rate of interest in decimal form\nn = number of times per year, interest compounded\nt = time in number of years.\n.\nx(1+0.02/2)^2 - x = 15,000(1+0.04/4)^4 - 15,000 [ when the principal is subtracted from the total amount accrued , the resulting difference is the interest portion and question states interests are equal)\n=> x[(1.01)^2 - 1] = 15,000[(1.01)^4 - 1]\n=> x[(1.01)^2 - 1] = 15,000[(1.01)^2+1][(1.01)^2-1] --> Using a^2-b^2 = a+b X a-b formula and cancel common expression on both sides\n=> x = 15,000(1.0201+1) =30301.5\nHence answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf x and y are integers such that |y + 3| \u2264 3 and 2y \u2013 3x + 6 = 0, what is the least possible value T of the product xy?\n\n### Options:\nA. -12\nB. -3\nC. 0\nD. 2\nE. None of the above\n\n### Answer:\nHow to deal with inequalities involving absolute values? First example shows us the so callednumber case\nIn this case we have |y + 3| \u2264 3 which is generalized |something| \u2264 some number. First we solve as if there were no absolute value brackets:\ny + 3 \u2264 3\ny \u2264 0\nSo y is 0 or negative\nSecond scenario - remove the absolute value brackets. Put a negative sign around the other side of the inequality,ANDflip the sign:\ny + 3 >= -3\ny >= -6\nTherefore we have a possible range for y: -6=", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the cost of fencing around a circular field of diameter 14 m at the rate of Rs.2.50 a meter?\n\n### Options:\nA. 288\nB. 110\nC. 772\nD. 592\nE. 261\n\n### Answer:\n2 * 22/7 * 7 = 44\n44 * 2.5 = Rs.110\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nEmployees at a company will vote for an executive team of five people from eight qualified candidates. The executive team consists of a president, a treasurer, and three warrant officers. If an executive team is considered different if any of the same people hold different offices, then how many possible executive teams S could be selected from the eight candidates?\n\n### Options:\nA. 56\nB. 120\nC. 210\nD. 1120\nE. 6720\n\n### Answer:\nIf an executive team is considered different if any of the same people hold different offices,....\nso you will not have answer as 6720..\npresident could be by any of 8 person..\ntreasurer could be any out of remaining 7 person..\nremaining three order does not matter, so we have to choose 3 out of 6=6c3=20..\ntotal ways S= 8*7*20=1120..\nans D...\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSet S is given as S = {1,3,5,7,9,11,13,15,17}. In how many ways can three numbers be chosen from Set S such that the sum of those three numbers is 18?\n\n### Options:\nA. zero\nB. one\nC. two\nD. three\nE. four\n\n### Answer:\n1,3,5,7,9,11,13,15,17 are all odd numbers and as such we can not get an even number from three odd number...\nSum of Odd Number of Odd Numbers = Odd Number..\nSo, Answer will be (A) Zero...\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are 780 male and female participants in a meeting. Half the female participants and one-quarterof the male participants are Democrats. One-third of all the participants are Democrats. How many of the Democrats are female?\n\n### Options:\nA. 130\nB. 100\nC. 125\nD. 175\nE. 225\n\n### Answer:\nLet m be the number of male participants and f be the number of female articipants in the meeting. Thetotal number of participants is given as 780.\nHence, we have m+f= 780\nNow, we have that half the female participants and one-quarter of the male participants are Democrats.\nLet d equal the number of the Democrats.\nThen we have the equation f/2 + m/4 =d\nNow, we have that one-third of the total participants are Democrats. Hence, we have the equation\nd = 780/3 = 260\nSolving the three equations yields the solution\nf = 260,m= 520, and d= 260.\nThe number of female democratic participants equals half the female participants equals\n260/2 = 130.\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n3-3*8+2=\n\n### Options:\nA. A)2\nB. B)-13\nC. C)-19\nD. D)-17\nE. of the above\n\n### Answer:\n3-3*6+2 = 5-24 = -19...\nso the answer is -19... C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo stations A and B are 110 km apart on a straight line. One train starts from A at 2 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet?\n\n### Options:\nA. 15 a.m\nB. 10 a.m\nC. 12 a.m\nD. 02 a.m\nE. 05 a.m\n\n### Answer:\nSuppose they meet x hours after 2 a.m.\nDistance covered by A in x hours = 20x km.\nDistance covered by B in (x - 1) hours = 25(x - 1) km.\nTherefore 20x + 25(x - 1) = 110\n45x = 135\nx = 3.\nSo, they meet at 5 a.m.\nAnswer:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe cost price of 18 articles is equal to the selling price of 11 articles. Find the profit percent?\n\n### Options:\nA. 18 2/15\nB. 36 2/11\nC. 45 2/14\nD. 54 2/16\nE. 63 7/11\n\n### Answer:\n18 CP = 11 SP\n11 --- 2 CP\n100 --- ? =>63 7/11%.Answer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA began business with Rs.36000 and was joined afterwards by B with Rs.54000. When did B join if the profits at the end of the year were divided in the ratio of 2:1?\n\n### Options:\nA. 1\nB. 6\nC. 7\nD. 8\nE. 2\n\n### Answer:\n36*12 : 54*x = 2: 1\nx = 4\n12 -4 = 8\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn 1990 a total of s earthquakes occurred worldwide, some but not all of which occurred in Asia. If t o f these earthquakes occurred in Asia, which of the following represents the ratio of the number of earthquakes that occurred in Asia to the number that did NOT occur in Asia?\n\n### Options:\nA. s/t\nB. t/s\nC. t/(s-t)\nD. s/(s-t)\nE. 1- (t/s)\n\n### Answer:\nWe're given a couple of facts to work with:\n1) There were a total of s earthquakes\n2) Of those earthquakes, t of them occurred in Asia\nWe're asked for the ratio of the number of earthquakes that occurred IN ASIA to the number of earthquakes that DID NOT occur in Asia.\nLet's TEST VALUES\ns = 5 total earthquakes\nt = 2 occurred in Asia\nThus, there were 3 earthquakes that DID NOT occur in Asia....\nThe answer to the question is 2:3\nWe just need to plug in the values for s and t and find the match...\nAnswer A: s/t = 5/2 NOT a match\nAnswer B: t/s = 2/5 NOT a match\nAnswer C: t/(s-t) = 2/(5-2) = 2/3 This IS a match\nAnswer D: s/(s-t) = 5/(5-2) = 5/3 NOT a match\nAnswer E: 1 - (t/s) = 1-2/5 = 3/5 NOT a match\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the cube root of 185193.\n\n### Options:\nA. 33\nB. 57\nC. 99\nD. 17\nE. 01\n\n### Answer:\nObserve unit digit here is 3 so unit digit of the answer is 7. Now omit 193. Now find after which perfect cube 193 lies. It is 125. So our tenth place is 5. So answer is 57.\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a = (1/5)b and c = 9a, then which of the following represents the average (arithmetic mean) of a, b, and c, in terms of a ?\n\n### Options:\nA. a + 4\nB. (11/3)a\nC. 4a\nD. 5a\nE. (7 1/4)a\n\n### Answer:\nOfficial Answer: D\nThe average of the three variables isa + b + c/3. However, we need to solve in terms of a, which means we must convert b and c into something in terms of a.\nWere told that a =1/5b, which is equivalent to b = 5a. We can plug that in and simplify the average to:a + 5a + c/3\nWe also know that c = 9a, which we can plug directly into the average expression:\na + 5a + 9a/3\n= 15a/3 = 5a, choiceD.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWater is leaking out from a cylinder container at the rate of 0.31 m^3 per minute. After 10 minutes, the water level decreases 1/9 meters. What is value of the radius in meters?\n\n### Options:\nA. 2\nB. 3\nC. 4\nD. 6\nE. 9\n\n### Answer:\n10*0.31 = 3.1 = pi*R^2*h\nR^2 = 3.1 / (pi*1/9) which is about 9\nR = 3\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo trains of equal length, running with the speeds of 60 and 16 kmph, take 50 seconds to cross each other while they are running in the same direction. What time will they take to cross each other if they are running in opposite directions?\n\n### Options:\nA. 10.11\nB. 8.11\nC. 77.2\nD. 13.15\nE. 22.22\n\n### Answer:\nRS = 60 -40 = 20 * 5/18 = 100/18\nT = 50\nD = 50 * 100/18 = 2500/9\nRS = 60 + 16 = 76 * 5/18\nT = 2500/9 * 18/380= 13.15 sec.Answer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nPipe A can fill a tank in 16 minutes and pipe B cam empty it in 24 minutes. If both the pipes are opened together after how many minutes should pipe B be closed, so that the tank is filled in 30 minutes?\n\n### Options:\nA. 11\nB. 21\nC. 33\nD. 51\nE. 61\n\n### Answer:\nExplanation:\nLet the pipe B be closed after x minutes.\n30/16 - x/24 = 1 => x/24 = 30/16 - 1 = 14/16\n=> x = 14/16 * 24 = 21.\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nCompound interest earned on a sum for the second and the third years are Rs.1200 and Rs.1440 respectively. Find the rate of interest?\n\n### Options:\nA. 27%\nB. 28%\nC. 20%\nD. 16%\nE. 25%\n\n### Answer:\nRs.1440 - 1200\n= Rs.240 is the interest on Rs.1200 for one year.\nRate of interest\n= (100 * 240) / (100 * 1)\n= 20% p.a\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe maitre 'd at an expensive Manhattan restaurant has noticed that 60% of the couples order dessert and coffee. However, 20% of the couples who order dessert don't order coffee. What is the probability Y that the next couple the maitre 'd seats will not order dessert?\n\n### Options:\nA. 20%\nB. 25%\nC. 40%\nD. 60%\nE. 75%\n\n### Answer:\ncould you use a venn diagram and just go with the number 100.\n60 people order dessert and coffee... which is the union of D and C.\nY=2/10 of D aren't in D U C = so 8/10 of D are in DUC which means =60 =8/10D. So D in total=75, and 15 D's aren't in D union C. which means 25 people are in C only + Neither.\nB 25%\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many seconds will a 500 meter long train moving with a speed of 63 km/hr, take to cross a man walking with a speed of 3 km/hr in the direction of the train ?\n\n### Options:\nA. 15s\nB. 20s\nC. 25s\nD. 30s\nE. 35s\n\n### Answer:\nDistance = 500m\nSpeed = 63 -3 km/hr = 60 km/hr = 600/36 m/s = 50/3 m/s\nTime taken = distance/speed = 500/(50/3) = 30 s\nAnswer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how many different ways can the letters of the word 'LEADING' be arranged such that the vowels should always come together?\n\n### Options:\nA. 120\nB. 190\nC. 250\nD. 370\nE. 720\n\n### Answer:\nThe word 'LEADING' has 7 letters. It has the vowels 'E','A','I' in it and these 3 vowels should always come together. Hence these 3 vowels can be grouped and considered as a single letter. that is, LDNG(EAI).\nHence we can assume total letters as 5 and all these letters are different. Number of ways to arrange these letters\n=5!=5\u00d74\u00d73\u00d72\u00d71=120\nIn the 3 vowels (EAI), all the vowels are different. Number of ways to arrange these vowels among themselves\n=3!=3\u00d72\u00d71=6=3!=3\u00d72\u00d71=6\nHence, required number of ways=120\u00d76=720\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the odd man out. 1, 3, 9, 12, 19, 29\n\n### Options:\nA. 12\nB. 9\nC. 1\nD. 3\nE. 4\n\n### Answer:\nExplanation :\n12 is an even number. All other given numbers are odd.. Answer : Option A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA shop sells floor tiles at Rs 48 per square meter. A building contractor employs a machine that polishes the tiles that damages 10% of the total number of tiles which cannot be used any more. Calculate the amount that needs to be paid by contractor to tile shop owner, if the hall is of a square shape and has a perimeter of 400 meters?\n\n### Options:\nA. Rs 4,00,000\nB. Rs 5,00,000\nC. Rs 5,28,000\nD. Rs 3,65,000\nE. Rs 3,75,000\n\n### Answer:\n4 sides of a square then 400/4=100\narea of the hall 100*100=10000\n10% damaged so 10000*110/100=11000\n48 per square meter then 48*11000=528000\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 3 persons can do 3 times of a particular work in 3 days, then, 7 persons can do 7 times of that work in?\n\n### Options:\nA. 3 days\nB. 4 days\nC. 6 days\nD. 7 days\nE. 8 days\n\n### Answer:\nThat is, 1 person can do one time of the work in 3 days.\nTherefore, 7 persons can do 7 times work in the same 3 days itself\nA)\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf there are 4 peanuts in a box and Mary puts 12 more peanuts inside, how many peanuts are in the box?\n\n### Options:\nA. 8\nB. 16\nC. 10\nD. 11\nE. 12\n\n### Answer:\n12+4=16\ncorrect answer is B)16\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n10, 25, 45, 54, 60, 75, 80\n\n### Options:\nA. 10\nB. 45\nC. 49\nD. 54\nE. 75\n\n### Answer:\nEach of the numbers except 54 is multiple of 5.\nanswer : C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nLength and Breadth of a rectangle is 7 m and 3.5 m respectively. Find the area of circle of maximum radius\n\n### Options:\nA. 9.625\nB. 9.74\nC. 9.8\nD. 9.725\nE. 9.547\n\n### Answer:\nExplanation:\narea of circle = \u03c0b2/4\n= 22/7 \u00d7 3.52/4\n= 9.625sq.m\nAnswer: Option A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAlbert father was 48 years of age when she was born while her mother was 46 years old when her brother 2 years younger to her was born. What is the difference between the ages of her parents?\n\n### Options:\nA. 2\nB. 4\nC. 6\nD. 8\nE. 10\n\n### Answer:\nMother's age when Albert's brother was born = 46years\nFather's age when Albert's brother was born = 48+2 = 50years\nRequired difference = 50-46 = 4 years\nAnswer is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nEvaluate: 37 - 18\u00f73\u00d72 =\n\n### Options:\nA. 20\nB. 25\nC. 27\nD. 22\nE. 17\n\n### Answer:\nAccording to order of operations, 18\u00f73\u00d72(division and multiplication) is done first from left to right\n18\u00f73\u00d72 = 6 \u00d7 2 = 12\nHence\n37 - 18\u00f73\u00d72 = 37 - 12 = 25\ncorrect answer B)25\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the cost of fencing around a circular field of diameter 28 m at the rate of Rs.1.50 a meter?\n\n### Options:\nA. 288\nB. 132\nC. 772\nD. 592\nE. 261\n\n### Answer:\n2 * 22/7 * 14 = 88\n88 * 1 1/2 = Rs.132\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA shopkeeper sells two articles at Rs.1000 each, making a profit of 20% on the first article and a loss of 20% on the second article. Find the net profit or loss that he makes?\n\n### Options:\nA. 3%\nB. 8%\nC. 9%\nD. 4%\nE. 24%\n\n### Answer:\nSP of first article = 1000\nProfit = 20%\nCP = (SP)*[100/(100+P)] = 5000/6 = 2500/3\nSP of second article = 1000\nLoss = 20%\nCP = (SP)*[100/(100-L)] = 5000/4 = 1250\nTotal SP = 2000\nTotal CP = 2500/3 + 1250 = 6250/3\nCP is more than SP, he makes a loss.\nLoss = CP-SP = (6250/3)- 2000 = 250/3\nLoss Percent = [(250/3)/(6250/3)]*100\n=0.04 * 100\n= 4%\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOn his drive to work, Leo listens to one of three radio stations A, B or C. He first turns to A. If A is playing a song he likes, he listens to it; if not, he turns it to B. If B is playing a song he likes, he listens to it; if not, he turns it to C. If C is playing a song he likes, he listens to it; if not, he turns off the radio. For each station, the probability is 0.10 that at any given moment the station is playing a song Leo likes. On his drive to work, what is the probability that Leo will hear a song he likes?\n\n### Options:\nA. 0.027\nB. 0.271\nC. 0.417\nD. 0.657\nE. 0.9\n\n### Answer:\nProbability he hears a song is like:\nTune to A and likes what he is hearing = 0.1\nTune to A, don't find he like what they are airing, then tune to B and likes what he finds there = 0.9 * 0.1 = 0.09\nTune to A, finds crap there, Tune to B, hears a similar crap, Tune to C and finally falls in love with the program = 0.9^2 * 0.1 = 0.081\nTotal = 0.271\nAns B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nGold is 19 times as heavy as water and copper is 9 times as heavy as water. In what ratio should these be mixed to get an alloy 13 times as heavy as water?\n\n### Options:\nA. 1:2\nB. 2:3\nC. 4:1\nD. 5:2\nE. 6:5\n\n### Answer:\nG = 19W\nC = 9W\nLet 1gm of gold mixed with x gm of copper to get 1+x gm of the alloy\n1gm gold + x gm copper = x+1 gm of alloy\n19W+9Wx = x+1 * 13W\n19+9x = 13(x+1)\nx = 3/2\nRatio of gold with copper = 1:3/2 = 2:3\nAnswer is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average of first five prime numbers greater than 20 is?\n\n### Options:\nA. 32.5\nB. 32.9\nC. 32.3\nD. 32.2\nE. 32.1\n\n### Answer:\n23 + 29 + 31 + 37 + 41\n= 161/5\n= 32.2\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAt the start of the fall shopping season, a pair of boots cost $700. By the end of the season, the price was reduced to $420. If you waited to purchase the boots at the lower price, what percentage of the original price will you have paid?\n\n### Options:\nA. 25%\nB. 33%\nC. 50%\nD. 60%\nE. 75%\n\n### Answer:\nA certain percentage of questions in the Quant section of the GMAT are just 'math questions' - you'll use a formula, do some calculations and you'll have the answer. This is one of those types of questions. You still have to write everything down and stay organized, but the work involved is relatively straight-forward.\nHere, we're told that the original price of the boots is $700 but that the purchase price is $420. We're asked what PERCENTAGE OF the original price is the purchase price.\nOriginal Price = $700\nPurchase Price = $420\nThe percentage of the original price of the boots:\n$420/$700 = 3/5 = 60%\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA bank pays interest to its customers on the last day of the year. The interest paid to a customer\nis calculated as 10% of the average monthly balance maintained by the customer. John is a\ncustomer at the bank. On the last day, when the interest was accumulated into his account, his\nbank balance doubled to $1710. What is the average monthly balance maintained by John in his\naccount during the year?\n\n### Options:\nA. 2840\nB. 5680\nC. 6840\nD. 8550\nE. 28400\n\n### Answer:\nSoln:-\nBank balance is doubled with accumulation of interest to 1710..\nthis means INTEREST is 1710/2=855 for entire year..\nalthough since interest is 10% of avg MONthly balance, it becomes 8550..\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many ways are there for 6 males and 3 females to sit (around a circular table) if no male should sit next to a male (and no female next to female) and Mary wants to sit with her back on the wall?\n\n### Options:\nA. 6\nB. 12\nC. 72\nD. 100\nE. 1440\n\n### Answer:\nSo Mary has her own chair, fixed position. Other two females around the table can sit in 2 ways: the first to the left of Mary and the second to the right or vise-versa. Now, if 6 males will sit between them then no two female or two male will sit next to each other (female-male-female-male-female-male). But these males on their spots can also sit in different ways, namely in 6! different ways, so total 2*6!=1440\nAnswer E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhen four dice are thrown, what is the probability that the same number appears on each of them ?\n\n### Options:\nA. 1/36\nB. 1/18\nC. 1/216\nD. 1/5\nE. 1/8\n\n### Answer:\nExplanation :\nWhen four dice are rolled the total no of outcomes are : 64\nAll dice show up same number in the following cases: (1,1,1,1), (2,2,2,2), (3,3,3,3), (4,4,4,4), (5,5,5,5), (6,6,6,6)\nSo in above six cases, all dice will show up the same number.\nRequired probability: 6/64 = 1/216\nAnswer : C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA set has exactly five consecutive positive integers starting with 1. What is the percentage decrease in the average of the numbers when the greatest one of the numbers is removed from the set?\n\n### Options:\nA. 8.54\nB. 12.56\nC. 15.25\nD. 16.66\nE. None of these\n\n### Answer:\nExplanation :\nThe average of the five consecutive positive integers 1,2,3,4 and 5 is:\n(1+2+3+4+5)/5=15/5=3.\nAfter removing the the greatest number i.e 5, the new average becomes:\n(1+2+3+4)/4=104=2.5.\nNow, % drop in the average =(Old average \u2013 New average)\u00d7100/Old average.\n=>(3\u22122.5)\u00d7100/3.\n=>100/6=16.66.\nAnswer : D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn the sequence S, each term after the first is twice the previous term. If the first term of sequence S is 3, what is the sum of the 14th and 15th terms in sequence S?\n\n### Options:\nA. 3(2^16)\nB. 9(2^15)\nC. 21(2^14)\nD. 9(2^14)\nE. 9(2^13)\n\n### Answer:\nThe terms in the sequence can be shown as\na(n) = 2* a(n-1)\nSo, the sequence will look like: 3, 2*3, (2^2) *3,...\nAnd the nth term will be given as 2^(n-1) *3\nTherefore, a(14) = (2^13)*3, a(15) = (2^14) *3,\nSo, a(14) + a(15) = (2^13) *3 + (2^14) *3\n= 3* (2^13) *(1+2) = 3* (2^13) *3\n= 9 * (2^13)\nAnswer : E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSusan is traveling from one end of a forest to the other. In order to find her way back, she is leaving morsels of bread in the following pattern: 2 morsels of wheat, 3 morsels of white, and 1 morsel of bap. The pattern repeats after she leaves the morsel of rye. If Susan drops 2,000 morsels of bread, what are the last 3 morsels of bread that she drops?\n\n### Options:\nA. wheat \u2212 wheat \u2212 white\nB. bap \u2212 wheat \u2212 wheat\nC. white \u2212 bap \u2212 wheat\nD. white \u2212 white \u2212 white\nE. white \u2212 white \u2212 bap\n\n### Answer:\nIn a single round Susan drops 6 morsels.\nRemainder (2000/6) = 2\nFinal action = 2 drops of Wheat --> Options A, C, D and E can be eliminated\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train running at the speed of 60 km/hr crosses a pole in 9 sec. What is the length of the train?\n\n### Options:\nA. 356\nB. 278\nC. 127\nD. 279\nE. 150\n\n### Answer:\nSpeed = 60 * 5/18 = 50/3 m/sec\nLength of the train = speed * time = 50/3 * 9 = 150 m\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA taxi leaves Point A 5 hours after a bus left the same spot. The bus is traveling 20 mph slower than the taxi. Find the speed of the taxi, if it overtakes the bus in three hours.\n\n### Options:\nA. 34\nB. 32\nC. 36\nD. 38\nE. 40\n\n### Answer:\nLet the speed of bus be v - 20, speed of taxi be v\nThe bus travelled a total of 8 hrs and taxi a total of 3 hrs.\nHence 8 * (v-20) = 3v\n8v - 160 = 3v\n5v = 160\nv = 32 mph\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe length of a cold storage is double its breadth. Its height is 3 metres. The area of its four walls(including doors) is 108 m2. Find its volume.\n\n### Options:\nA. 206\nB. 216\nC. 226\nD. 246\nE. 288\n\n### Answer:\nlet xbe breadth ,then 2x is the length\nthen 2x*3*2+x*3*2=108\n12x+6x=108\nx=108/18=6\nlength 12,breadth 6 ,height 3\nvolume=12*6*3=216m^3\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the difference between the compound interest on Rs.12000 at 20% p.a. for one year when compounded yearly and half yearly?\n\n### Options:\nA. 399\nB. 383\nC. 120\nD. 288\nE. 133\n\n### Answer:\nWhen compounded annually, interest\n= 12000[1 + 20/100]1 - 12000 = Rs.2400\nWhen compounded semi-annually, interest\n= 12000[1 + 10/100]2 - 12000 = Rs.2520\nRequired difference = 2520 - 2400 = Rs.120\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMr. Yutaro\u2019s class contains 6 boys and 10 girls. If two students are chosen, one at a time, from the class, what is the probability that a boy and a girl are chosen?\n\n### Options:\nA. 9/48\nB. 9/20\nC. 1/2\nD. 27/48\nE. 13/16\n\n### Answer:\nProbability of a boy being chosen first, then a girl:\n6/16 * 10/15\nProbability of a girl being chosen first, then a boy:\n10/16 * 6/15\nProbability of a boy and a girl being chosen:\n(6*10+6*10) / (15*16)\n=1/2\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe least number, which when divided by 12, 15, 20 and 63 leaves in each case a remainder of 8 is:\n\n### Options:\nA. 448\nB. 488\nC. 542\nD. 1268\nE. 560\n\n### Answer:\nRequired number = (L.C.M. of 12, 15, 20, 63) + 8\n= 1260+ 8\n= 1268.\nanswer :D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAn article when sold for 200 fetches 25 per cent profit. What would be the percentage profit/loss if 6 such articles are sold for 1,056?\n\n### Options:\nA. 10 per cent loss\nB. 10 per cent profit\nC. 5 per cent loss\nD. 5 per cent profit\nE. None of these\n\n### Answer:\nCP = 200\u2044125 \u00d7 100 = 160\n\u2234 CP of 6 articles = 6 \u00d7 160 = 960\n\u2234 profit = 1056 \u2013 960 = 96\nPercentage profit = 96\u2044960 \u00d7 100 = 10%\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 9975 kg of wheat is packed in 95 bags, how much wheat will each bag contain?\n\n### Options:\nA. 105\nB. 109\nC. 119\nD. 218\nE. 288\n\n### Answer:\nSolution:\nSince 95 bags contain wheat 9975 kg\nTherefore, 1 bag contains wheat (9975 \u00f7 95) kg\n= 105 kg\nANSWER IS A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA bus takes 3 hours to cover a distance of 500 Km. how much should the speed in Kmph be maintained to cover the same direction in 5/3th of the previous time?\n\n### Options:\nA. 75 Kmph\nB. 100 Kmph\nC. 90 Kmph\nD. 65 Kmph\nE. 70 Kmph\n\n### Answer:\nTime = 3\nDistance = 500\n5/3 of 3 hours = 3 * 5/3 = 5 Hours\nRequired speed = 500/5 = 100 Kmph\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo painters 'P1' & 'P2' paint the bungalow in 3 days. If P1 alone can paint the bungalow in 12 days, in how many days can 'P2'' alone complete the same paint work?\n\n### Options:\nA. 4 days\nB. 6 days\nC. 9 days\nD. 12 days\nE. 15 days\n\n### Answer:\nEXPLANATION:\nHint:\nIf a person can do a part of work in 'n' days, then person's work in 1 day =\t1/n\nAs painters P1 & P2 paint the bungalows in 3 days, then work done by both painters =\t1/3\nAs P1 paint it alone in 12 days, then work done by painter P1 =\t1/12\nWork done by painter P2 =\t1/3\t\u2013\t1/12\t=\t4 \u2013 1/12\t=\t3/12\t=\t1/4\nTherefore, same work will be completed by painter P2 in 4 days.\nANSWER IS A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo trains are moving at 85 kmph and 70 kmph in opposite directions. Their lengths are 150 m and 100 m respectively. The time they will take to pass each other completely is?\n\n### Options:\nA. 5 25/31 sec\nB. 7 1/17 sec\nC. 7 2/2 sec\nD. 8 1/2 sec\nE. 7 1/9 sec\n\n### Answer:\n70 + 85 = 155 * 5/18 = 775/18 mps\nD = 150 + 100 = 250 m\nT = 250 * 18/775 = 180/31 = 5 25/31 sec\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat sum of money will produce Rs.70 as simple interest in 3 years at 3 1/2 percent?\n\n### Options:\nA. 667\nB. 500\nC. 266\nD. 288\nE. 211\n\n### Answer:\n70 = (P*3*7/2)/100\nP = 667\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRavi can do a piece of work in 25 days while Prakash can do it in 35 days. In how many days will they finish it together?\n\n### Options:\nA. 15 7/9 days\nB. 16 17/9 days\nC. 15 1/19 days\nD. 14 7/12 days\nE. 14 7/9 days\n\n### Answer:\n1/25 + 1/35 = 12/175\n175/12 = 14 7/12 days\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the tens digit x and the units digit y of a positive integer n are reversed, the resulting integer is 27 less than n. What is y in terms of x ?\n\n### Options:\nA. 10 - x\nB. 9 - x\nC. x + 3\nD. x - 3\nE. x - 9\n\n### Answer:\nOriginal Digits=xy i.e. Number=10x+y\nAfter reversing the digits:\nDigits=yx i.e. Number=10y+x\n10y+x is 27 less than 10x+y\n10x+y-27=10y+x\n10x-x-27=10y-y\n9x-27=9y\nx-3=y\nOR\ny=x-3\nAns:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many odd, positive divisors does 440 have?\n\n### Options:\nA. 3\nB. 8\nC. 12\nD. 15\nE. 24\n\n### Answer:\nMake a prime factorization of a number: 540=2^2*3^3*5 --> get rid of powers of 2 as they give even factors --> you'll have 3^3*5 which has (3+1)(1+1)=3 factors.\nAnother example: 60=2^2*3*5 it has (2+1)(1+1)(1+1)=12 factors out of which (1+1)(1+1)=4 are odd: 1, 3, 5 and 15 the same # of odd factors as 60/2^2=15 has.\nAnswer: A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a survey of political preferences, 78% of those asked were in favour of at least one of the proposals: I, II and III. 50% of those asked favoured proposal I, 30% favoured proposal II, and 20% favoured proposal III. If 5% of those asked favoured all three of the proposals, what X percentage of those asked favoured more than one of the 3 proposals.\n\n### Options:\nA. 10\nB. 12\nC. 17\nD. 22\nE. 30\n\n### Answer:\nBunuel, my answer for exactly 2 people was 17 and this was my approach:\n100%=(A+B+C)-(AnB+AnC+BnC)-5%+22% which leads me to\nX=100%=(50+30+20)-(at least 2 people)-5%+22%.C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRobert is travelling on his cycle andhas calculated to reach point A at 2 PM. if he travels at 10 kmph, he will reach there at 12Pm if he travels at 15 kmph. At what speed must he travel to reach A at 1 PM?\n\n### Options:\nA. 8 kmph\nB. 10 kmph\nC. 12 kmph\nD. 14 kmph\nE. 16 kmph\n\n### Answer:\nLet the distance travelled by x km.\nThen,\tx\t-\tx\t= 2\n10\t15\n3x - 2x = 60\nx = 60 km.\nTime taken to travel 60 km at 10 km/hr = 60\thrs\t= 6 hrs.\n10\nSo, Robert started 6 hours before 2 P.M. i.e., at 8 A.M.\nRequired speed = 60\tkmph.\t= 12 kmph.\n5\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAn empty fuel tank with a capacity of 200 gallons was filled partially with fuel A and then to capacity with fuel B. Fuel A contains 12% ethanol by volume and fuel B contains 16% ethanol by volume. If the full fuel tank contains 28 gallons of ethanol, how many gallons of fuel A were added?\n\n### Options:\nA. 160\nB. 150\nC. 100\nD. 80\nE. 50\n\n### Answer:\nSay there are A gallons of fuel A in the tank, then there would be 200-A gallons of fuel B.\nThe amount of ethanol in A gallons of fuel A is 0.12A;\nThe amount of ethanol in 200-A gallons of fuel B is 0.16(200-A);\nSince the total amount of ethanol is 28 gallons then 0.12A+0.16(200-A)=28 --> A=100.\nAnswer: C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA person can row at 9 kmph and still water. He takes 4 1/2 hours to row from A to B and back. What is the distance between A and B if the speed of the stream is 1 kmph?\n\n### Options:\nA. 28\nB. 26\nC. 25\nD. 21\nE. 20\n\n### Answer:\nLet the distance between A and B be x km.\nTotal time = x/(9 + 1) + x/(9 - 1) = 4.5\n=> x/10 + x/8 = 9/2 => (4x + 5x)/40 = 9/2 => x = 20 km.\nAnswer:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 9 boys meet at a reunion and each boy shakes hands exactly once with each of the others, then what is the total number of handshakes\n\n### Options:\nA. 41\nB. 42\nC. 36\nD. 44\nE. 45\n\n### Answer:\nn(n-1)/2 =9*8/2\n=36\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf P's height is 40% less than that of Q, how much percent Q's height is more than that of P?\n\n### Options:\nA. 66.66\nB. 86.88\nC. 70.05\nD. 76.66\nE. 89.99\n\n### Answer:\nQ'S height over P's = ((40/(100-40)) * 100\n= 66.66%\nANSWER A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a function they are distributing noble prize. In how many ways can 3 prizes be distributed among 7 boys when a boy gets any no. of prizes?\n\n### Options:\nA. 55\nB. 58\nC. 343\nD. 354\nE. 200\n\n### Answer:\nAns.(C)\nSol. In this case, repetitions are allowed, so all the three prizes can be given in 4 ways, i.e. (7 x 7 x 7) ways = 73 ways = 343 ways Or nr ways = 73 ways = 343 ways\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf f(x) =6* (x^4 - 1)/(x^2), what is f(1/x) in terms of f(x)?\n\n### Options:\nA. f(x)\nB. -f(x)\nC. 1/f(x)\nD. -1/f(x)\nE. -6*f(x)\n\n### Answer:\nf(1/x) =6* ((1/x)^4 - 1) / ((1/x)^2)\n= 6*((1/x^4) - 1) / (1/x^2)\n= 6*((1-x^4)/(x^4)) / (1/x^2)\n= 6*(1-x^4)/(x^2)\n= - 6*( (x^4) -1) / (x^2)\n= -6f(x)\nAnswer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich of the following has 15^80 as a factor?\n\n### Options:\nA. 15^60\nB. 30^40\nC. 40^80\nD. 60^60\nE. 90^80\n\n### Answer:\nHere 15^80 = 3^80 * 5^80 Only Option E has both .\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe area of the largest circle that can be drawn inside a square of side 112 Cm in length is:\n\n### Options:\nA. 9856\nB. 8646\nC. 2616\nD. 1636\nE. 3606\n\n### Answer:\nRadius of required circle = 56 Cm\nits area = 22/7 \u00d7 56 \u00d7 56\n176 \u00d7 56 = 9856 Cm(power)2\nAnswer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA team of 8 persons joins in a shooting competition. The best marksman scored 85 points. If he had scored 92 points, the average score for the team would have been 84. The number of points, the team scored was\n\n### Options:\nA. 665\nB. 287\nC. 297\nD. 255\nE. 191\n\n### Answer:\nExplanation:\nLet the total score be x.\n(x + 92 - 85) / 8 = 84.\nSo, x + 7 = 672 => x = 665.\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe area of the square formed on the diagonal of a rectangle as its side is 108 1/3 % more than the area of the rectangle. If the perimeter of the rectangle is 28 units, find the difference between the sides of the rectangle?\n\n### Options:\nA. 8m\nB. 7m\nC. 5m\nD. 2m\nE. 1m\n\n### Answer:\nLet the sides of the rectangle be l and b respectively.\nFrom the given data,\n(\u221al2 + b2) = (1 + 108 1/3 %)lb\n=> l2 + b2 = (1 + 325/3 * 1/100)lb\n= (1 + 13/12)lb\n= 25/12 lb\n=> (l2 + b2)/lb = 25/12\n12(l2 + b2) = 25lb\nAdding 24lb on both sides\n12l2 + 12b2 + 24lb = 49lb\n12(l2 + b2 + 2lb) = 49lb\nbut 2(l + b) = 28 => l + b = 14\n12(l + b)2 = 49lb\n=> 12(14)2 = 49lb\n=> lb = 48\nSince l + b = 14, l = 8 and b = 6\nl - b = 8 - 6 =2m.\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the remainder when 7^74 - 5^74 is divided by 12?\n\n### Options:\nA. 1\nB. 0\nC. 2\nD. 3\nE. None of these\n\n### Answer:\neasiest way for me: 7^74 - 5^74 = (49)^37-25^37 = (12*4+1)^37 - (12*2+1)^37 -> remainder is 1^37 - 1^37 = 0\nAns : B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train 550 m long is running with a speed of 60 km/hr. In what time will it pass a man who is running at 6 km/hr in the direction opposite to that in which the train is going?\n\n### Options:\nA. 8\nB. 6\nC. 5\nD. 54\nE. 30\n\n### Answer:\nSpeed of train relative to man = 60 + 6 = 66 km/hr.\n= 66 * 5/18 = 55/3 m/sec.\nTime taken to pass the men = 550 * 3/55 = 30 sec.\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nEvaluate : (2.39)(power 2) - (1.61) (power 2) / 2.39 - 1.61\n\n### Options:\nA. 4\nB. 5\nC. 6\nD. 7\nE. 8\n\n### Answer:\nGiven Expression = a(power 2) - b(power 2) / a-b\n= (a + b)(a - b) / (a-b)\n= (a + b) = (2.39 + 1.61) = 4.\nAnswer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n(23341379 \u00d7 72) = ?\n\n### Options:\nA. 1223441288\nB. 2142579288\nC. 2142339288\nD. 2142339277\nE. 1680579288\n\n### Answer:\n23341379 \u00d7 72\n= 23341379(70 + 2)\n= (23341379 \u00d7 70) + (23341379 \u00d7 2)\n= 1633896530 + 46682758\n= 1680579288\nAnswer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a urban village of india named \"owlna\" , 75% people have refrigerator , 90% people have television , 85% people got computers and 75% got Air-conditionor. how many people(minimum) got all these luxury.\n\n### Options:\nA. 23%\nB. 17%\nC. 11%\nD. 10%\nE. 25%\n\n### Answer:\nE\n10%\n100 - [ (100-75)+(100-90)+(100-85) +(100-75)]\n=100-(25+10+15+25)\n=100-75\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf (1 \u2013 1.25)N = 4, then N =\n\n### Options:\nA. \u2212400\nB. \u221216\nC. \u22124\nD. 4\nE. 400\n\n### Answer:\n(1 \u2013 1.25)N = 4\nSimplify to get: -0.25N = 4\nRewrite as (-1/4)N = 4\nMultiply both sides by -4 to get: N = -16\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 400 resolutions?\n\n### Options:\nA. 708 m\nB. 704 m\nC. 774 m\nD. 714 m\nE. 563.2 m\n\n### Answer:\nIn one resolution, the distance covered by the wheel is its own circumference. Distance covered in 500 resolutions.\n= 400 * 2 * 22/7 * 22.4 = 56320 cm\n= 563.2 m\nAnswer:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA fruit seller had some oranges. He sells 20% oranges and still has 400 oranges. How many oranges he had originally?\n\n### Options:\nA. 420\nB. 700\nC. 220\nD. 500\nE. None of these\n\n### Answer:\nExplanation :\nHe sells 20% of oranges and still there are 400 oranges remaining\n=> 80% of oranges = 400\n\u21d2 (80 \u00d7 Total Oranges)/100 = 400\n\u21d2 Total Oranges/100 = 5\n\u21d2 Total Oranges = 5 \u00d7 100 = 500\nAnswer : Option D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA bottle of coke contains 200gm in place of 1kg of fluid. Find the actual % difference, given a 10% gain on initial fluid?\n\n### Options:\nA. 32.5%\nB. 112.5%\nC. 35%\nD. 40%\nE. 50%\n\n### Answer:\nfluid price of 200gm = 100+10 = 110\nDifference = 110-20 = 90\n% of difference = 90*100/80 =112.5 %\nAnswer is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich of the following describes all values of x for which 4\u2013x^2 >= 0?\n\n### Options:\nA. x >= 1\nB. x <= \u20131\nC. 0 <= x <= 1\nD. x <= \u20131 or x >= 1\nE. \u20132 <= x <= 2\n\n### Answer:\n4 - x^2 >=0\nmeans x^2 - 4 <=0\n=> (x-2)(x+2) <= 0\n=> -2 <= x <= 2\nAnswer - E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are 84 supermarkets in the FGH chain. All of them are either in the US or Canada. If there are 10 more FGH supermarkets in the US than in Canada, how many FGH supermarkets are there in the US?\n\n### Options:\nA. 20\nB. 31\nC. 42\nD. 47\nE. 64\n\n### Answer:\nx + (x - 10) = 84 --> x = 47.\nAnswer: D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how many different number of ways 4 boys and 3 girls can sit on a bench such that girls always sit together?\n\n### Options:\nA. 700\nB. 720\nC. 800\nD. 820\nE. 830\n\n### Answer:\nOption 'B'\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the simple interest on a certain sum of money for 5 years is one\u2013fifth of the sum, then the rate of interest per annum is\n\n### Options:\nA. 4%\nB. 7%\nC. 6%\nD. 4%\nE. 3%\n\n### Answer:\nExplanation:\nLet the Principal(P) be x\nThen, Simple Interest(SI) = x/5\nTime(T) = 5 years\nRate of interest per annum(R) = (100\u00d7SI)/PT\n= (100 \u00d7 (x/5)/(x \u00d7 5) = 20/5 = 4%\nAnswer: Option D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA worker earns $20 on the first day and spends $15 on the second day. The worker earns $20 on the third day and spends $15 on the fourth day. If this pattern continues, on which day will the worker first reach a net total of $80?\n\n### Options:\nA. 24\nB. 25\nC. 27\nD. 30\nE. 32\n\n### Answer:\nEvery two days, the net total is $5.\nAfter 24 days, the worker will have $60.\nOn day 25, the worker will receive $20 for a net total of $80.\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nEveryone shakes hands with everyone else in a room. Total number of handshakes is 55. Number of persons=?\n\n### Options:\nA. 14\nB. 12\nC. 11\nD. 15\nE. 16\n\n### Answer:\nIn a room of n people, the number of possible handshakes is C(n,2) or n(n-1)/2\nSo n(n-1)/2 = 55 OR n(n-1)=110 OR n=11\nAnswer is (C)\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nKramer can pack X boxes of cigarettes per minute. If there are Y boxes of cigarettes in one case, how many cases can Kramer pack in 1 hours?\n\n### Options:\nA. 60X/Y.\nB. 120X/Y.\nC. 60Y/X.\nD. 120Y/X.\nE. (X + Y)/60.\n\n### Answer:\nKramer can pack X boxes per min.\nTherefore in 1 hrs(60mins)he can pack 60X boxes.\nIf there are Y boxes in one case then then the total number of cases packed by Kramer = 60X/Y\n(ANSWER A)\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nVictor's job requires him to complete a series of identical jobs. If Victor is supervised at work, he finishes each job three days faster than if he is unsupervised. If Victor works for 144 days and is supervised for half the time, he will finish a total of 36 jobs. How long Q would it take Victor to complete 10 jobs without any supervision?\n\n### Options:\nA. 34\nB. 52\nC. 60\nD. 70\nE. 92\n\n### Answer:\nRate when supervised = (job)/(time) = 1/t.\nRate when unsupervised = (job)/(time) = 1/(t+3).\nFor 144/2=72 days he is supervised and for 144/2=72 days he is unsupervised and does 36 jobs:\n72/t + 72/(t+3) = 36 --> t=3 days --> t+3 = 6 days.\nVictor to complete 10 jobs without any supervision will need Q 10(t + 3) = 60 days.\nAnswer: C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nReduce\n803/876\nto the lowest terms.\n\n### Options:\nA. 11/12\nB. 23/24\nC. 26/27\nD. 4/7\nE. 6/9\n\n### Answer:\nExplanation:\nHCF of 803 and 876 is 73, Divide both by 73, We get the answer 11/12\nOption A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIts a very poor village so sahara group organized a beneficiary cricket match for these people.\nThe event raised Rs300000.\nTickets were priced as follows:\nRs 748 for males\nRs 712 for ladies\nRs 45 for kids\nHow many males,ladies and kids were there ?\n\n### Options:\nA. 100 males , 209 ladies & 52 kids\nB. 120 males , 359 ladies & 72 kids\nC. 149 males , 259 ladies & 92 kids\nD. 150 males , 256 ladies & 92 kids\nE. 135 males , 259 ladies & 50 kids\n\n### Answer:\nC\n149 males , 259 ladies & 92 kids\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nDavid obtained 76, 65, 82, 67 and 85 marks (out of 100) in English, Mathematics,Physics, Chemistry and Biology What are his average marks ?\n\n### Options:\nA. 75\nB. 37\nC. 26\nD. 97\nE. 27\n\n### Answer:\nAverage = (76 + 65 + 82 + 67 + 85 )/ 5 = 375/5\n= 75.\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRs. 9800 are invested partly in 9% stock at 75 and 10% stock at 80 to have equal amount of incomes. The investment in 9% stock is:\n\n### Options:\nA. 5000\nB. 4500\nC. 5400\nD. 5600\nE. 6000\n\n### Answer:\nLet the investment 9% stock rs x\nthen investment in 10% stock = rs(9800-x)\n9/75 xx = 10/80 *(9800-x)\n3x/25 = 9800 - x\nx=5000\nANSWER A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA boy runs 200 metres in 72 seconds. What is his speed ?\n\n### Options:\nA. 10 km/hr\nB. 14 km/hr\nC. 20 km/hr\nD. 12 km/hr\nE. 24 km/hr\n\n### Answer:\n200/72 * 18/5 = 10 km/hr\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe area of a square is 4096 sq cm. Find the ratio of the breadth and the length of a rectangle whose length is twice the side of the square and breadth is 24 cm less than the side of the square.\n\n### Options:\nA. 5 : 12\nB. 5 : 13\nC. 5 : 167\nD. 5 : 19\nE. 5 : 16\n\n### Answer:\nLet the length and the breadth of the rectangle be l cm and b cm respectively. Let the side of the square be a cm.\na2 = 4096 = 212\na = (212)1/2 = 26 = 64\nL = 2a and b = a - 24\nb : l = a - 24 : 2a = 40 : 128 = 5 : 16\nAnswer: Option E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train with a length of 100 meters, is traveling at a speed of 72 km/hr. The train enters a tunnel 2.3 km long. How many minutes does it take the train to pass through the tunnel from the moment the front enters to the moment the rear emerges?\n\n### Options:\nA. 2.0\nB. 2.5\nC. 3.0\nD. 3.5\nE. 4.0\n\n### Answer:\n72 km/hr = 1.2 km/min\nThe total distance is 2.4 km.\n2.4 / 1.2 = 2 minutes\nThe answer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA candidate who gets 30% of the marks fails by 50 marks. But another candidate who gets 45% marks gets 25 marks more than necessary for passing. Find the number of marks for passing?\n\n### Options:\nA. 200\nB. 150\nC. 275\nD. 300\nE. 350\n\n### Answer:\n30% ------------ 50\n45% ------------ 25\n----------------------\n15% ------------- 75\n30% -------------- ?\n150 + 50 = 200 Marks\nANSWER A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many liters of water must be evaporated from 50 liters of a 3 percent sugar solution to get a 4 percent sugar solution?\n\n### Options:\nA. 12.5\nB. 15.5\nC. 17.5\nD. 21.5\nE. 24.5\n\n### Answer:\nLet x be the amount that needs to be evaporated.\n0.03(50) = 0.04(50-x)\n0.04x = 2 - 1.5\nx = 0.5/0.04 = 12.5 liters\nThe answer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nBefore leaving home for the town of Madison, Pete checks a map which shows that Madison is 5 inches from his current location, Gardensquare. Pete arrives in Madison 1.5 hours later and drove at an average speed of 60 miles per hour. At what scale, in inches per mile, is the map drawn?\n\n### Options:\nA. 1/3\nB. 1/18\nC. 1/10\nD. 2\nE. 30\n\n### Answer:\nPete covered 1.5*60=90 miles which correspond to 5 inches on the map --> scale in inches per mile is 5/90=1/18.\nAnswer: B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind odd one among 2,3, 4, 4, 6, 8, 9,12, 16 ?\n\n### Options:\nA. 9\nB. 8\nC. 77\nD. 65\nE. 212\n\n### Answer:\nANSWER: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nEmployees of a certain company are each to receive a unique 9-digit identification code consisting of the digits 0, 1, 2, 3, 4, 5, 6, 7, and 8 such that no digit is used more than once in any given code. In valid codes, the second digit in the code is exactly twice the first digit. How many valid codes are there?\n\n### Options:\nA. 14,720\nB. 16,240\nC. 18,320\nD. 20,160\nE. 22,480\n\n### Answer:\nThere are 7! ways to make codes starting with 12.\nThere are 7! ways to make codes starting with 24.\nThere are 7! ways to make codes starting with 36.\nThere are 7! ways to make codes starting with 48.\nThe number of codes is 4*7! = 20,160.\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe ratio of the age of a man and his women is 4:3. At the time of first meet theratio was 5:3 and After 4 years this ratio will become 9:7. How many yrs ago were they met?\n\n### Options:\nA. 10\nB. 12\nC. 15\nD. 16\nE. 20\n\n### Answer:\nLet the present age of the man and his wife be 4x and 3x respectively.\nAfter 4 years this ratio will become 9:7\n\u21d2(4x+4):(3x+4)=9:7\u21d27(4x+4)=9(3x+4)\u21d228x+28=27x+36\u21d2x=8\nPresent age of the man =4x=4\u00d78=32\nPresent age of his wife =3x=3\u00d78=24\nAssume that they got married before t years. Then,\n(32\u2212t):(24\u2212t)=5:3\u21d23(32\u2212t)=5(24\u2212t)\u21d296\u22123t=120\u22125t\u21d22t=24\u21d2t=242=12\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a fuel station the service costs $1.75 per car, every liter of fuel costs 0.65$. Assuming that a company owns 12 cars and that every fuel tank contains 57 liters and they are all empty, how much money total will it cost to fuel all cars?\n\n### Options:\nA. 320.50$\nB. 380.50$\nC. 425.50$\nD. 450.50$\nE. 465.60$\n\n### Answer:\nTotal Cost = ( 1.75*12 ) + ( 0.65 * 12 * 57 ) = 465.60\nHence answer will be (E)\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n8 couples (husband and wife) attend a dance show \"Nach Baliye' in a popular TV channel ; A lucky draw in which 4 persons picked up for a prize is held, then the probability that there is atleast one couple will be selected is ?\n\n### Options:\nA. 8/39\nB. 15/39\nC. 12/13\nD. 11/13\nE. None of these\n\n### Answer:\nP( selecting atleast one couple) = 1 - P(selecting none of the couples for the prize)\n= 1 - [16C1x14C1x12C1x10C1/16C4] = 15/39\nAnswer is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA Man can row upstream at 95kmph and downward stream at 47 kmph. Find Man's rate of the current\n\n### Options:\nA. 87km/hr\nB. 20km/hr\nC. 24km/hr\nD. 2.8km/hr\nE. 4.4km/hr\n\n### Answer:\nRate of the current=1/2(95-47)km/hr\n=24km/hr\ncorrect option is :C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many integers between 362,855 and 852,755have tens digit 1 and units digit 3?\n\n### Options:\nA. 4,888\nB. 4,898\nC. 4,889\nD. 4,869\nE. 4,896\n\n### Answer:\nThere is one number in hundred with 1 in the tens digit and 3 in the units digit: 13, 113, 213, 313, ...\nThe difference between 362,855 and 852,755 is 852,755-362,855=489,900 - one number per each hundred gives 133,900/100=4,889 numbers.\nAnswer: C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe simple interest accrued on an amount Rs.10,000 at the end of two years is same as the compound interest on Rs.8,000 at the end of two years. The rate of interest is same in both the cases. What is the rate of interest?\n\n### Options:\nA. 80% p.a\nB. 100% p.a.\nC. 40% p.a\nD. 44% p.a\nE. 50% p.a\n\n### Answer:\nGiven that Rs.10,000 is invested in S.I for two years and Rs.8,000 in C.I for two years\n=> C.I - S.I\n=>9,000 { [1 + r/100]2 - 1} = (10,000)2r /100\n=> 9{ 1 + 2r/100 + r2 / (100)2 - 1} = r/5\n=> r = 0% of 40%\nSince r!= 0%, r =40%\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the simplified result of following the steps below in order?\n(1)\tadd 5y to 2q\n(2)\tmultiply the sum by 3\n(3)\tsubtract q + y from the product\n\n### Options:\nA. 5q + 14y\nB. 5x + 16y\nC. 5x + 5y\nD. 6x + 4y\nE. 3x + 12y\n\n### Answer:\n3(5Y+2Q) -Q-Y= 14Y+5Q\n'A' is the answer\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nCalculate the number of urns of water needed to fill a tank of dimensions of 10x10x5m to 90% full, if the volume of the urn is 0.8m3 and can only be filled to 80%.\n\n### Options:\nA. 520\nB. 650.2\nC. 685.5\nD. 703.1\nE. 712.2\n\n### Answer:\nVolume of the tank that needed to be filled=10x10x5x0.9=450\nVolume of the urn that can be filled=0.8x0.8=0.64\nNo. of urns of water needed to fill the tank=450/0.64= 703.1\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAn empty pool being filled with water at a constant rate takes 8hours to fill to 2/5 of its capacity.how much more time will it take to finish filling the pool?\n\n### Options:\nA. 5hr 30min\nB. 5hr 20min\nC. 4hr 48min\nD. 3 hr 12min\nE. 2hr 40 min\n\n### Answer:\nAs pool is filled to 2/5 of its capacity then 2/5 of its capacity is left to fill.\nTo fill 3/5 of the pool took 8 hours --> to fill 2/5 of the pool will take 8/(3/5)*2/5=16/3 hours = 5 hours 20 minutes (because if t is the time needed to fill the pool then t*3/5=8 --> t=8*5/3 hours --> to fill 2/5 of the pool 8*5/3*2/5=16/3 hours will be needed).\nOr plug values: take the capacity of the pool to be 5 liters --> 3/5 of the pool or 3 liters is filled in 8 hours, which gives the rate of 3/8 liters per hour --> remaining 2 liters will require: time = job/rate = 2/(3/8) = 16/3 hours = 5 hours 30 minutes.\nAnswer: A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA rectangular-shaped carpet that measures x feet by y feet is priced at $9. What is the cost of the carpet, in dollars per square yard? (1 square yard = 9 square feet)\n\n### Options:\nA. 90/(xy)\nB. 90xy\nC. xy/90\nD. xy/10\nE. 81/(xy)\n\n### Answer:\nThe area of the carpet in feet is xy.\nThe area in square yards is xy / 9.\nThe price per square yard is 9 / (xy/9) = 81/(xy).\nThe answer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJohn and Jane went out for a dinner and they ordered the same dish. Both used a 10% discount coupon. John paid a 15% tip over the original price of the dish, while Jane paid the tip over the discounted price for the coupon. If John paid $0.54 more than Jane, what was the original price of the dish?\n\n### Options:\nA. 24\nB. 34.8\nC. 36\nD. 42\nE. 84\n\n### Answer:\nThe difference between the amounts John paid and Jane paid is the deference between 15% of p and 15% of 0.9p:\n0.15p - 0.15*0.9p = 0.54 --> 15p - 13.5p = 54 --> p = 36.\nAnswer: C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average marks of a class of 30 students is 40 and that of another class of 50 students is 60. Find the average marks of all the students?\n\n### Options:\nA. 52.3\nB. 52.2\nC. 52.1\nD. 52.5\nE. 52.4\n\n### Answer:\nSum of the marks for the class of 30 students = 30 * 40 = 1200\nSum of the marks for the class of 50 students = 50 * 60 = 3000\nSum of the marks for the class of 80 students =\n1200 + 3000 = 4200\nAverage marks of all the students = 4200/80\n= 52.5\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo vessels having volumes in the ratio 3:5 are filled with water and milk solutions. The ratio of milk and water in the two vessels are 1:2 and 6:4 respectively. If the contents of both the vessel are empties into a larger vessel, find the ratio of milk and water in the larger vessel.\n\n### Options:\nA. 1:1\nB. 2:1\nC. 3:1\nD. 5:1\nE. 6:1\n\n### Answer:\nVessel A = 300 gallons --> milk = 100, water = 200;\nVessel B = 500 gallons --> milk = 300, water = 200;\nVessel A + B = 800 gallons --> milk = 400, water 400\nThe ratio =400/400 --> 1:1\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many four digit numbers have no repeat digits, do not contain zero, and have a sum of digits A equal to 28?\n\n### Options:\nA. 14\nB. 24\nC. 28\nD. 48\nE. 96\n\n### Answer:\nFirst, look for all 4 digits without repeat that add up to 28. To avoid repetition, start with the highest numbers first.\nStart from the largest number possible 9874.\nThen the next largest number possible is 9865.\nAfter this, you'll realize no other solution. Clearly the solution needs to start with a 9 (cuz otherwise 8765 is the largest possible, but only equals 26). With a 9, you also need an 8 (cuz otherwise 9765 is the largest possible, but only equals 27). With 98__ only 74 and 65 work.\nSo you have two solutions. Each can be rearranged in 4!=24 ways. So A=24+24=48.D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 5 (A's capital) = 10 (B's capital) = 15 (C's capital). Then the ratio of their capitals is?\n\n### Options:\nA. 5:3:2\nB. 7:3:2\nC. 6:3:3\nD. 6:3:2\nE. 5:3:2\n\n### Answer:\n5A = 10B = 15 C\nA:B:C = 1/5:1/10:1/15\n= 6:3:2\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf x is an integer and y = 3x + 5, which of the following CANNOT be a divisor of y?\n\n### Options:\nA. 4\nB. 12\nC. 2\nD. 7\nE. 6\n\n### Answer:\nFor any value of x, the expression 3x + 5 would never be divisible by 3,6,9...... onwards\nSo answer = 6 = E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA, B, C together started a business. A invested Rs.6000 for 5 months B invested Rs.3600 for 6 months and C Rs.7500 for 3 months. If they get a total profit of Rs.7410. Find the share of A?\n\n### Options:\nA. 3999\nB. 3000\nC. 3882\nD. 2661\nE. 1234\n\n### Answer:\n60*5:36*6:75*3\n100: 72: 75\n100/247 * 7410\n= 3000\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOn a trip, a cyclist averaged 11 miles per hour for the first 22 miles and 10 miles per hour for the remaining 20 miles. If the cyclist returned immediately via the same route and took a total of 9 hours for the round trip, what was the average speed (in miles per hour) for the return trip?\n\n### Options:\nA. 7.6\nB. 7.8\nC. 8\nD. 8.2\nE. 8.4\n\n### Answer:\nThe time to go 42 miles was 22/11+20/10=2+2=4 hours.\nThe average speed for the return trip was 42 miles/5 hours= 8.4 mph.\nThe answer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA large delicatessen purchased p pounds of cheese for K dollars per pound. If d pounds of the cheese had to be discarded due to spoilage and the delicatessen sold the rest for s dollars per pound, which of the following represents the gross profit on the sale of the purchase? (gross profitequalssales revenueminusproduct cost)\n\n### Options:\nA. (p \u2212 d)(s \u2212 c)\nB. s(p-d) - Kp\nC. c(p \u2212 d) \u2212 ds\nD. d(s \u2212 c) \u2212 pc\nE. pc \u2212 ds\n\n### Answer:\nTotal cost price = K*p ............... (1)\nWastage = d pounds\nQuantity sold = p-d\nSelling price per pound = s\nTotal selling price = s(p-d) ........... (2)\nProfit = (2) - (1)\n= s(p-d) - Kp\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind large number from below question The difference of two numbers is 1000. On dividing the larger number by the smaller, we get 10 as quotient and the 10 as remainder\n\n### Options:\nA. 1234\nB. 1110\nC. 1456\nD. 1200\nE. 1600\n\n### Answer:\nLet the smaller number be x. Then larger number = (x + 1365).\nx + 1000 = 10x + 10\n9x = 990\nx = 110\nLarge number = 110+1000=1110\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average weight of a group of boys is 30 kg. After a boy of weight 37 kg joins the group, the average weight of the group goes up by 1 kg. Find the number of boys in the group originally ?\n\n### Options:\nA. A)4\nB. B)8\nC. C)6\nD. D)2\nE. E)1\n\n### Answer:\nLet the number off boys in the group originally be x.\nTotal weight of the boys = 30x\nAfter the boy weighing 37 kg joins the group, total weight of boys = 30x + 37\nSo 30x + 37 = 31(x + 1) = > x = 6.\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA jogger running at 9 kmph alongside a railway track in 240 metres ahead of the engine of a 120 metres long train running at 45 kmph in the same direction. In how much time will the train pass the jogger?\n\n### Options:\nA. 3.6 sec\nB. 18 sec\nC. 36 sec\nD. 72 sec\nE. 84 sec\n\n### Answer:\nSpeed of train relative to jogger = (45 - 9) km/hr = 36 km/hr.\n= 36 x\t5/18\tm/sec\n= 10 m/sec.\nDistance to be covered = (240 + 120) m = 360 m. Answer: Option C\nTime taken = 360/10\tsec\t= 36 sec.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSubtracting 10% from X is the same as multiplying X by what number?\n\n### Options:\nA. 97%\nB. 90%\nC. 80%\nD. 98%\nE. 20%\n\n### Answer:\nX - (10/100) X = X * ?\n? = 90%\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average of 9 observations was 9, that of the 1st of 5 being 10 and that of the last 5 being 8. What was the 5th observation?\n\n### Options:\nA. 9\nB. 8\nC. 7\nD. 6\nE. 3\n\n### Answer:\n1 to 9 = 9 * 9 = 81\n1 to 5 = 5 * 10 = 50\n5 to 9 = 5 * 8 = 40\n5th = 50 + 40 = 90 \u2013 81 = 9\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe ratio of investments of two partners P and Q is 7:5 and the ratio of their profits is 7:9. If P invested the money for 5 months, find for how much time did Q invest the money?\n\n### Options:\nA. 9\nB. 17\nC. 13\nD. 10\nE. 12\n\n### Answer:\n7*5: 5*x = 7:9\nx = 9\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRice weighing 33/4 pounds was divided equally and placed in 4 containers. How many ounces of rice were in each?\n\n### Options:\nA. 18 ounces\nB. 15 ounces\nC. 19 ounces\nD. 17 ounces\nE. 14 ounces\n\n### Answer:\n33/4 \u00f7 4 pounds.\n= (4 \u00d7 3 + 3)/4 \u00f7 4 pounds.\n= 15/4 \u00f7 4 pounds.\n= 15/4 \u00d7 1/4 pounds.\n= 15/16 pounds.\nNow we know that, 1 pound = 16 ounces.\nTherefore, 15/16 pounds = 15/16 \u00d7 16 ounces.\n= 15 ounces.\nAnswer: (B)15 ounces.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIF x is an integer greater than 6, then all the following must be divisible by 3 EXCEPT\n\n### Options:\nA. 9x/3\nB. 9x^2\nC. x(x+1)(x+2)\nD. x+1\nE. 3x^3\n\n### Answer:\n*any number multiplied by 3, will be divided by 3\nfor option D if we put value x=7, 7+1=8 is not divisible by 3\nAnswer : E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain city with population of 132,000 is to be divided into 11 voting districts, and no district is to have a population that is more than 10 percent greater than the population of any other district. What is the minimum possible population that the least populated district could have?\n\n### Options:\nA. 10,700\nB. 10,800\nC. 10,900\nD. 11,000\nE. 11,100\n\n### Answer:\npopulation that is 10% greater than the population of any other district..\n11000.. 10% of 11000 = 1100.. so the next population will be 12100..\n10*12,100 + 11000 = 132000. D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA boat travels 72 km downstream in 8 hours and 84 km upstream in 12 hours. Find the speed of the boat in still water and the speed of the water current ?\n\n### Options:\nA. 6 and 1 kmph\nB. 8 and 2 kmph\nC. 8 and 1 kmph\nD. 9 and 1 kmph\nE. 2 and 1 kmph\n\n### Answer:\nExplanation:\nDownstream speed = 72km/8hrs = 9 kmph\nupstream speed = 84km/12hrs = 7 kmph\nspeed of boat = avg of downstream and upstream speeds\nspeed of boat = (9+7)/2kmph = 8 kmph.\ncurrent speed = half of the difference of downstream and upstream speeds\ncurrend speed = (9-7)/2kmph = 1 kmph\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSonika deposited Rs.8000 which amounted to Rs.9200 after 3 years at simple interest. Had the interest been 1% more. She would get how much?\n\n### Options:\nA. 9440\nB. 96288\nC. 26667\nD. 1662\nE. 2882\n\n### Answer:\n(8000*3*1)/100 = 240\n9200\n--------\n9440\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat will come in place of the x in the following Number series? 279936, 46656, 7776, 1296, 216, x\n\n### Options:\nA. 124\nB. 165\nC. 36\nD. 178\nE. 215\n\n### Answer:\nGo on dividing by 6 to the next number\nC)\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train 100 meters long completely crosses a 300 meters long bridge in 36 seconds. What is the speed of the train is?\n\n### Options:\nA. 32 kmph\nB. 76 kmph\nC. 34 kmph\nD. 43 kmph\nE. 40 kmph\n\n### Answer:\nS = (100 + 300)/36\n= 400/36 * 18/5\n= 40\nAnswer:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man buys Rs. 52 shares paying 9% dividend. The man wants to have an interest of 12% on his money. The market value of each share is:\n\n### Options:\nA. s. 12\nB. s. 15\nC. s. 18\nD. s. 21\nE. s. 39\n\n### Answer:\nDividend on Rs. 52 = Rs.\t9/100\tx 52 =Rs.\t4.68\t.\nRs. 12 is an income on Rs. 100.\nRs.\t4.68\tis an income on Rs.100/12 x 4.68\t= Rs. 39.\nAnswer: Option E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA thief is spotted by a policeman from a distance of 100metres. When the policeman starts the chase, the thief also starts running. If the speed of the thief be 15km/hr and that of the policeman 20km/hr, how far the thief will have run before he is overtaken ?\n\n### Options:\nA. A)1km\nB. B)300m\nC. C)650m\nD. D)750m\nE. E)800m\n\n### Answer:\nRelative speed of the policeman = 20-15 = 5 km/hr\ntime taken by policeman to cover 100m = (100/1000)*(1/5) = 1/50 hr\nIn 1/50 hr the thief covers a distance of 15/50 km = 3/10 km = 300m\nAnswer is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a group of 6 boys and 4 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be there?\n\n### Options:\nA. 80\nB. 90\nC. 15\nD. 209\nE. 105\n\n### Answer:\nWe may have (1 boy and 3 girls) or (2 boys and 2 girls) or (3 boys and 1 girl) or (4 boys).\nRequired number\nof ways\t= (6C1 x 4C3) + (6C2 x 4C2) + (6C3 x 4C1) + (6C4)\n= (6C1 x 4C1) + (6C2 x 4C2) + (6C3 x 4C1) + (6C2)\n= (24 + 90 + 80 + 15)\n= 209.\nANSWER D 209\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTom can hit a target 3 times in 6 shots, Karan can hit the target 2 times in 6 shots & Ashwini can hit 4 times in 4shots. What is the probability that at least 2 shots hit the target ?\n\n### Options:\nA. 1/2\nB. 2/5\nC. 2/3\nD. 3/7\nE. 3/11\n\n### Answer:\nAshwini hits the target definitely, hence required probability that atleast 2 shots hit the target is given by\nKaran hits tha target and Raja not hit the target.\nor\nKaran does not hit the target and Raja hits the target.\nor.\nKaran hits the target and Raja hits the target\n= 2/6 x 3/6 + 4/6 x 3/6 + 2/6 x 3/6\n= 24/36 = 2/3\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA group of 4 students bought movie tickets in one row next to each other. If Bob and Lia are in this group, what is the probability that Bob and Lia will each sit next to only one of the three other students from the group?\n\n### Options:\nA. 5.67%\nB. 16.67%\nC. 15.57%\nD. 20.25%\nE. 25.75%\n\n### Answer:\nThe question basically asks about the probability that Bob and Lisa sit at the ends.\nThe total # of sitting arrangements is 4!.\nDesired arrangement is either BYZL or LYZB. Now, YZ can be arranged in 2! ways, therefore total # of favorable arrangements is 2*2!.\nP=(favorable)/(total)=(2*2!)/4!=1/6.\nAnswer: B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA basket has 5 apples and 4 oranges. Three fruits are picked at random. The probability that at least 2 apples are picked is\n\n### Options:\nA. 25/42\nB. 25/44\nC. 25/409\nD. 25/45\nE. 25/41\n\n### Answer:\nTotal fruits = 9\nSince there must be at least two apples,\n(5C2 * 4C1)/8C1 +2C2/2C2 = 25/42.\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA table is bought for Rs.400/- and sold at Rs.550/- find gain or loss percentage\n\n### Options:\nA. l10%oss\nB. 30%gain\nC. 37.5%gain\nD. 10%loss\nE. 25% loss\n\n### Answer:\nFormula = (Selling price ~ Cost price)/Cost price * 100\n= (550 - 400)/400 = 37.5% gain\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a stockpile of products produced by three machines M1, M2 and M3, 40% and 30% were manufactured by M1 and M2 respectively. 3% of the products of M1 are defective, 1% of products of M2 defective, while 91% of the products of M3 III are not defective. What is the percentage of defective in the stockpile?\n\n### Options:\nA. 3%\nB. 5%\nC. 2.5%\nD. 4.2%\nE. 6%\n\n### Answer:\nExplanation :\nLet there be 100 products in the stockpile. 40% and 30% were manufactured by M1 and M2 respectively. So, 30% are manufactured by M3.\nProducts from M1 = 40, from M2 = 30 and from M3 = 30.\nNumber of defective products from M1 = 0.03 x 40 = 1.2, from M2 = 0.01 x 30 = 0.3 and from M3 = 0.09 x 30 = 2.7\nTherefore, total number of defective products = 4.2.\nAnswer : D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow long does a train 150 m long running at the speed of 72 km/hr takes to cross a bridge 132 m length?\n\n### Options:\nA. 14.1 sec\nB. 12.1 sec\nC. 16.1 sec\nD. 13.1 sec\nE. 12.15sec\n\n### Answer:\nSpeed = 72 * 5/18 = 20 m/sec\nTotal distance covered = 150 + 132 = 282 m.\nRequired time = 282/20 = 14.1 sec.\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man walked diagonally across a square lot. Approximately, what was the percent saved by not walking along the edges?\n\n### Options:\nA. 20%\nB. 30%\nC. 35%\nD. 40%\nE. 50%\n\n### Answer:\nLet the side of the square(ABCD) be x metres.\nThen, AB + BC = 2x metres.\nAC = 2x = (1.41x) m.\nSaving on 2x metres = (0.59x) m.\nSaving % = 0.59x x 100 % = 30% (approx.)\n2x\nB)\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAt what price must an article costing Rs.47.50 be marked in order that after deducting 5% from the list price. It may be sold at a profit of 25% on the cost price?\n\n### Options:\nA. 62.5\nB. 62.3\nC. 62.7\nD. 62.2\nE. 62.9\n\n### Answer:\nCP = 47.50\nSP = 47.50*(125/100)\n= 59.375\nMP*(95/100)\n= 59.375\nMP = 62.5\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA container holding 12 ounces of a solution that is 1 part alcohol to 2 parts water is added to a container holding 9 ounces of a solution that is 1 part alcohol to 2 parts water. What is the ratio of alcohol to water in the resulting solution?\n\n### Options:\nA. 1:2\nB. 3:7\nC. 3: 5\nD. 4:7\nE. 7:3\n\n### Answer:\nContainer 1 has 12 ounces in the ratio 1:2\nor,\nx+2x=12 gives x(alcohol)=4 and remaining water =8\ncontainer 2 has 9 ounces in the ratio 1:2\nor,\nx+2x=9 gives x(alcohol)=3 and remaining water =6\nmixing both we have alcohol=4+3 and water =8+6\nratio thus alcohol/water =7/14=1/2\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nwhich one is odd?\n4377\n3954\n9865\n8454\n9831\n\n### Options:\nA. 4377\nB. 3954\nC. 9865\nD. 8454\nE. None\n\n### Answer:\nCorrect Answer : C\nsum of digit of all other number is 21, but sum of digit of 9865 is 28\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n54671 - 14456 - 33466 = ?\n\n### Options:\nA. 2449\nB. 5449\nC. 6749\nD. 6449\nE. 6468\n\n### Answer:\nC\nIf we calculate we will get 6749\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA car traveled 340 miles per tankful of gasoline on the highway and 336 miles per tankful of gasoline in the city. If the car traveled 6 fewer miles per gallon in the city than on the highway, how many miles per gallon did the car travel in the city?\n\n### Options:\nA. 504\nB. 416\nC. 321\nD. 220\nE. 170\n\n### Answer:\nLet the speed in highway be h mpg and in city be c mpg.\nh = c+6\nh miles are covered in 1 gallon\n340 miles will be covered in 340/h.\nSimilarly c miles are covered in 1 gallon\n336 miles will be covered in 336/c.\nBoth should be same (as car's fuel capacity does not change with speed)\n=> 336/c = 340/h\n=> 336/c = 340/(c+6)\n=> 336c+336*6=340c\n=>c=336*6/4=504\nAnswer A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo boats are heading towards each other at constant speeds of 4 miles/hr and 20 miles/hr respectively. They begin at a distance 20 miles from each other. How far are they (in miles) one minute before they collide ?\n\n### Options:\nA. 1/12\nB. 6/15\nC. 1/6\nD. 1/3\nE. 1/5\n\n### Answer:\nThe question asks: how far apart will they be 1 minute=1/60 hours before they collide?\nSince the combined rate of the boats is 4+20=25 mph then 1/60 hours before they collide they'll be rate*time=distance --> 24*1/60=6/15miles apart.\nAnswer: B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nEach shelf of a bookcase contained 12 books. If the librarian took out 21 books and rearranged the remaining books so that all shelves but the last one contained 8 books and that last shelf contained 7 books, how many shelves does the bookcase have?\n\n### Options:\nA. 5\nB. 6\nC. 7\nD. 8\nE. 9\n\n### Answer:\nLet x be the number of shelves.\n12x - 21 = 8(x-1) + 7\n4x = 20\nx= 5\nThe answer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n15 different biology books and 8 different chemistry books lie on a shelf. In how many ways can a student pick 2 books of each type?\n\n### Options:\nA. 80\nB. 160\nC. 720\nD. 2100\nE. 2940\n\n### Answer:\nNo. of ways of picking 2 biology books(from 15 books) = 15c2 = (15*14)/2 = 105\nNo. of ways of picking 2 chemistry books(from 8 books) = 8c2 = (8*7)/2 = 28\nTotal ways of picking 2 books of each type = 105*28 =2940\n(Option E)\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If two marbles are drawn at random, what is the probability that at least one is green?\n\n### Options:\nA. 23/35\nB. 23/32\nC. 23/31\nD. 23/30\nE. 63/35\n\n### Answer:\nExplanation:\nGiven that there are three blue marbles, four red marbles, six green marbles and two yellow marbles.\nProbability that at least one green marble can be picked in the random draw of two marbles = Probability that one is green + Probability that both are green\n= (\u00e2\u0081\u00b6C\u00e2\u201a\u0081 * \u00e2\u0081\u00b9C\u00e2\u201a\u0081)/\u00c2\u00b9\u00e2\u0081\u00b5C\u00e2\u201a\u201a + \u00e2\u0081\u00b6C\u00e2\u201a\u201a/\u00c2\u00b9\u00e2\u0081\u00b5C\u00e2\u201a\u201a\n= (6 * 9 * 2)/(15 * 14) + (6 * 5)/(15 * 14) = 36/70 + 1/7\n= 46/70 = 23/35\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nKim bought a total of $2.65 worth of postage stamps in four denominations. If she bought an equal number of 5-cent and 25-cent stamps and twice as many 10-cent stamps as 5-cent stamps, what is the least number of 2-cent stamps she could have bought ?\n\n### Options:\nA. 5\nB. 10\nC. 7.5\nD. 20\nE. 25\n\n### Answer:\n2.65 = 0.05x + 0.25x + 2 * 0.10x + 0.02y\n=> 2.65 = 0.30x + 0.20x + 0.02y\n=> 265 = 50x + 2y\nSo Max value of 50x < 265 = 250\nHence y = 7.5\nAnswer - C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSome times small town drivers can be very rude. One taxi driver I had the occasion to travel with was particularly lacking in courtesy, and so I asked for his number.\nThe driver gave me a sardonical smile and said. 'Well, if you divide my number by 2, 3, 4, 5 or 6 you will find there is always 1 remaining. But if you divide it by 11 there is no remainder. Do you want to know something more? There is no other cabby in this town with a lower number than---who can say the same.,' and he drove off, while I stood there completely baffled.\nWhat was the man's number?\n\n### Options:\nA. 121\nB. 143\nC. 165\nD. 133\nE. 117\n\n### Answer:\nA\nThe driver's number was 121.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThree numbers are in the ratio 5 : 6 : 7. The sum of its longest and smallest numbers equals the sum of the third number and 84. Find the third number?\n\n### Options:\nA. A)37\nB. B)85\nC. C)48\nD. D)43\nE. E)84\n\n### Answer:\nLet the numbers be 5x, 6x, 7x.\nLargest number = 7x.\nSmallest number = 5x.\nThird number = 6x.\n7x + 5x = 6x + 84\n6x = 84 => third number is 84.\nAnswer: Option E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA boat goes 8 km upstream in 24 minutes. The speed of stream is 4 km/hr. The speed of boat in still water is:\n\n### Options:\nA. 24 km/hr\nB. 25 km/hr\nC. 26 km/hr\nD. 23 km/hr\nE. 22 km/hr\n\n### Answer:\nSpeed upstream =8/(24/60) = 20 km/hr\nSpeed of the stream = 4 km/hr\nspeed of boat in still water = (20+4) = 24 km/hr\nAnswer : Option A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is?\n\n### Options:\nA. 28\nB. 50\nC. 88\nD. 22\nE. 12\n\n### Answer:\nSpeed of the train relative to man = (125/10) m/sec = (25/2) m/sec. [(25/2) * (18/5)] km/hr = 45 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 45 ==> x\n= 50 km/hr.Answer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA 240 m long train running at the speed of 120 km/hr crosses another train running in opposite direction at the speed of 80 km/hr in 9 sec. What is the length of the other train?\n\n### Options:\nA. 260\nB. 250\nC. 240\nD. 230\nE. 220\n\n### Answer:\nRelative speed = 120 + 80 = 200 km/hr.\n= 200 * 5/18 = 500/9 m/sec.\nLet the length of the other train be x m.\nThen, (x + 240)/9 = 500/9 => x = 260.\nAnswer: Option A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSandy bought 65 books for $1080 from one shop and 55 books for $840 from another shop. What is the average price that Sandy paid per book?\n\n### Options:\nA. $14\nB. $16\nC. $18\nD. $20\nE. $22\n\n### Answer:\naverage price per book = (1080 + 840) / (65 + 55) = 1920 / 120 = $16\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFrances can complete a job in 10 hours, and Joan can complete the same job in 10 hours. Frances starts the job at 9 a.m., and stops working at 3 p.m. If Joan starts working at 6 p.m. to complete the job, at what time is the job finished?\n\n### Options:\nA. 6 p.m.\nB. 7 p.m.\nC. 8 p.m.\nD. 10 p.m.\nE. 12 p.m.\n\n### Answer:\nLet the total work be 24 units.\nFrances can complete 2.4 units/hr\nJoan can complete 2.4 units/hr\nWork done by Frances in 6 hours is 14.4 units ; work left for Joan is 9.6 units ( 24 - 14.4)\nTime required by Jones to complete the remaining work will be 14.4/2.4 => 4 hours\nGiven Jones starts at 6 PM , so she would complete the work at 10 PM\nAnswer will be (D)\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nKamal started a business with Rs.25000 and after 4 months, Kiran joined him with Rs.60000. Kamal received Rs.58000 including 10% of profit as commission for managing the business. What amount did Kiran receive?\n\n### Options:\nA. 75000\nB. 70000\nC. 72000\nD. 78000\nE. None of these\n\n### Answer:\nExplanation :\nRatio of the profits = 25000*12 : 60000*8\n= 25*12 : 60*8 = 5*3 : 12:2 = 5 : 4*2\n= 5:8\nLet the total profit = x.\nThen Kamal received 10x/100 = x/10 as commission for managing the business\nRemaining profit = x- x/10 = 9x/10 which is shared in the ration 5:8\nKamal's share = x/10 + (9x/10) * (5/13) = 58000\n=> x + 9x(5/13) = 580000\n=> x(1 + 45/13) = 580000\n=> x ( 58/13) = 580000\n=> x ( 1/13) = 10000\n=> x = 130000\nKiran's share = 130000 - 58000 = 72000. Answer : Option C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA starts business with a capital of Rs.1200 B and C join with some investments after 3 and 6 months respectively. If the end of a year, the profit is divided in the ratio 2:3:5 respectively. What is B's investment in the business?\n\n### Options:\nA. 2400\nB. 2882\nC. 2277\nD. 2656\nE. 2778\n\n### Answer:\n1200 * 12: x * 9 = 2:3\nx = 2400\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA and B started a business with initial investments in the ratio 14 : 15 and their annual profits were in the ratio 7 : 6. If A invested the money for 10 months, for how many months did B invest his money?\n\n### Options:\nA. 2\nB. 4\nC. 6\nD. 8\nE. 9\n\n### Answer:\nSol.\nSuppose A invested Rs. 14x for 10 months and B invested Rs. 15x for y months. Then,\n14x * 10 / 15x * y = 7/6 \u21d2 y = 840 / 105 = 8\nHence, B invested the money for 8 months.\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe circumference of the front wheel of a cart is 30 ft long and that of the back wheel is 40 ft long. What is the distance traveled by the cart, when the front wheel has done five more revolutions than the rear wheel?\n\n### Options:\nA. 20 ft\nB. 25 ft\nC. 600ft\nD. 900 ft\nE. 1000 ft\n\n### Answer:\nPoint to note: Both the wheels would have traveled the same distance.\nNow consider, no. of revolutions made by back wheel as x, which implies that the number of revolutions made by the front wheel is (x+5).\nEquating the distance traveled by front wheel to back wheel: (x+5)*30 = x * 40. (Formula for calculating the distance traveled by each wheel is: # of revolutions * circumference.)\nSolving this eqn. gives x=15.\nSub x=15 either in (x+5)*30 or in x * 40 to get the distance, which is 600. So the correct choice is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nX and Y are two towns. Ganesh covers the distance from X to Y at an average speed of 43 Km/hr. However, he covers the distance from Y to X at an average speed of 34 Km/hr. His average speed during the whole journey in km/hr. is :\n\n### Options:\nA. 34\nB. 43\nC. 40\nD. 38\nE. 29\n\n### Answer:\nSolution: Average speed = 2XY / X+Y\n= 2*43*34 / 43+34\n= 2924 / 77\n= 37.974... = 38\nAnswer : D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n2 oranges, 3 bananas and 4 apples cost Rs.15. 3 oranges 2 bananas 1 apple costs Rs.10. what is the cost of 3 oranges, 3 bananas and 3 apples?\n\n### Options:\nA. 30\nB. 15\nC. 10\nD. 20\nE. 40\n\n### Answer:\n2or+3ba+4ap=15--->(1)\n3or+2ba+1ap=10---->(2)\n(1)+(2)\n5or+5ba+5ap=15+10\n5(or+ba+ap)=25\nor+ba+ap=25/5\nor+ba+ap=5\ntherefore 3or+3ba+3ap===>3(or+ba+ap);\n3(5)=15;\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a regular week, there are 5 working days and for each day, the working hours are 8. A man gets Rs. 2.60 per hour for regular work and Rs. 3.20 per hours for overtime. If he earns Rs. 432 in 4 weeks, then how many hours does he work for ?\n\n### Options:\nA. 165\nB. 175\nC. 190\nD. 200\nE. 210\n\n### Answer:\nSuppose the man works overtime for x hours.\nNow, working hours in 4 weeks = (5 x 8 x 4) = 160.\n160 x 2.60 + X x 3.20 = 432\nX = 5.\nHence, total hours of work = (160 + 5) = 165.\nanswer :A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat will come in place of the x in the following Number series? 49920, 4160, 416, 52, x\n\n### Options:\nA. 8.67\nB. 7.67\nC. 6.67\nD. 5.67\nE. 4.67\n\n### Answer:\n49920 /12 = 4160\n3840 /10 = 416\n416 /8 = 52\n52/6 = 8.67\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwenty percent of Country Y's yearly exports come from fruit exports. One-sixth of all fruit exports from Country Y are orange exports. If country Y generates $5 million from its orange exports, how much money does it generate from its yearly total of exports?\n\n### Options:\nA. $21.25m\nB. $25.5m\nC. $106.25m\nD. $127.5m\nE. $150m\n\n### Answer:\n2/10*1/6*(total) = 5\n1/30*(total) = 5\n(total) = 5*30 = 150\nAnswer: E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a hostel there were 100 students. To accommodate 25 more students the average is decreased by rupees 5. But total expenditure increased by Rs.400. Find the total expenditure of the hostel now?\n\n### Options:\nA. A)Rs.5800\nB. B)Rs.5480\nC. C)Rs.5400\nD. D)Rs.4500\nE. E)Rs.5430\n\n### Answer:\n100x + 400\n= 125(x \u2013 5)\nx = 41\n100 * 41 + 400\n= 4500\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow to additions fast. For example we have to do a simple addition like 234 + 563+ 985 + 349.\n\n### Options:\nA. 2131\nB. 7399\nC. 2997\nD. 2769\nE. 2771\n\n### Answer:\nInstead of doing like this we first add all the digits in the hundred's place. 2 + 5 + 9 + 3 = 19. Put 2 zero's to the right hand side so we get 1900.\nNow add the digits in the tenth's place. 3 + 6 + 8 + 4 = 21. Put 1 zero to the right hand side so we get 210.\nNow add the digits in the units place 4 + 3 + 5 + 9 = 21.\nNow 1900 + 210 + 21 = 2131\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 4 boys can color 60 m long cloth in 3 days, then 6 boys can color 36 m long cloth in\n\n### Options:\nA. day\nB. days\nC. days\nD. days\nE. days\n\n### Answer:\nThe length of cloth painted by one boy in one day = 60 / 4 \u00d7 3 =5 m\nNo. of days required to paint 36 m cloth by 6 boys = 36/ 5 \u00d7 6 = 6/5 day.\nA)\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOf the 24 participants in a certain competition, half are male, and half of the males are younger than 18 years of age. If half of the female competitors are also younger than 18 years of age, into how many distinct groups of 4 competitors could the participants be divided if each group must contain two males under 18 years of age and 2 females over 18 years of age?\n\n### Options:\nA. 225\nB. 45\nC. 65\nD. 95\nE. 200\n\n### Answer:\nM under 18 - 6\nF above 18 - 6\nHow many distinct groups can be formed now: 6c2 * 6c2 = 225\nAnswer : A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the area of a square with sides of length 3 centimeters is equal to the area of a rectangle with a width of 4 centimeters, what is the length of the rectangle, in centimeters?\n\n### Options:\nA. 4\nB. 8\nC. 12\nD. 3\nE. 18\n\n### Answer:\nLet length of rectangle = L\n3^2 = L*4\n=> L = 9/4 = 3\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n10 men, working 7 hours a day can complete a work in 18 days. How many hours a day must 15 men work to complete the work in 12 days ?\n\n### Options:\nA. 4 hours a day\nB. 5 hours a day\nC. 6 hours a day\nD. 7 hours a day\nE. 8 hours a day\n\n### Answer:\nExplanation:\nMore Men, Less Hours {Indirect Proportion}\nLess Days, More Hours {Indirect Proportion}\n[men 15 10\ndays 12 18] ::7:x\n=>x\u00e2\u02c6\u201415\u00e2\u02c6\u201412=10\u00e2\u02c6\u201418\u00e2\u02c6\u20147\n=>x=10\u00e2\u02c6\u201418\u00e2\u02c6\u20147/ 15\u00e2\u02c6\u201412\n=>x=7\nOption D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the units digit of 16^83 \u00d7 13^82 \u00d7 11^87?\n\n### Options:\nA. 4\nB. 5\nC. 6\nD. 7\nE. 8\n\n### Answer:\nTo find : the units digit of 17^83 \u00d7 13^82 \u00d7 11^87\nLet's reduce the clutter and simplify the product\n(7^83) (3^82) (1^87)\n7 has a cyclicity of 4 : the last digit of any positive power of 7 repeats itself after every 4th power\nso 7^5 has the same last digit as 7^1, 7^9, 7^13\nThus , 7^83 has the same last digit as 7^3, 7^7, 7^11 i.e.3\n3 has a cyclicity of 4 : exactly the same routine as above\nThus , 3^82 has the same last digit as 3^2, 3^6, 3^10 i.e.9\nAny power of 1 will result in1as the last digit\nSo, product of our last digits = 3 x 9 x 1 = 27....last digit is 6\nCorrect Option : C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA, B, C together started a business. A invested Rs.6000 for 5 months B invested Rs.3600 for 6 months and C Rs.7500 for 3 months. If they get a total profit of Rs.7410. Find the share of A?\n\n### Options:\nA. 9179\nB. 3000\nC. 2997\nD. 2678\nE. 2682\n\n### Answer:\n60*5:36*6:75*3\n100: 72: 75\n100/247 * 7410 = 3000\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSari and Ken climb up a mountain. At night, they camp together. On the day they are supposed to reach the summit, Sari wakes up at 08:00 and starts climbing at a constant pace. Ken starts climbing only at 10:00, when Sari is already 700 meters ahead of him. Nevertheless, Ken climbs at a constant pace of 500 meters per hour, and reaches the summit before Sari. If Sari is 50 meters behind Ken when he reaches the summit, at what time did Ken reach the summit?\n\n### Options:\nA. 13:00\nB. 13:30\nC. 14:00\nD. 15:00\nE. 15:30\n\n### Answer:\nBoth Sari and Ken climb in the same direction.\nSpeed of Sari = 700/2 = 350 meters/hr (since she covers 700 meters in 2 hrs)\nSpeed of Ken = 500 meters/hr\nAt 8:00, distance between Ken and Sari is 700 meters. Ken needs to cover this and another 50 meters.\nTime he will take = Total distance to be covered/Relative Speed = (700 + 50)/(500 - 350) = 5 hrs\nStarting from 10:00, in 5 hrs, the time will be 15:00\nAnswer (D)\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich of the following is closest to the difference between sum Z of all proper fractions (fractions less than 1) in the form 1/x , where x is a positive digit, and the product of all proper fractions in the form y/(y+1), where y is a positive digit?\n\n### Options:\nA. 2.82\nB. 2.72\nC. 1.82\nD. 1.72\nE. 0.82\n\n### Answer:\nSum Z of all proper fractions (fractions less than 1) in the form 1/x, where x is a positive digit:\n1/1 + 1/2 + 1/3 +.....+ 1/9\nThis is a harmonic progression. Harmonic progression is inverse of arithmetic progression.\nApproximate sum of a harmonic progression with even number of terms = number of terms * (average of middle 2 terms)\nApproximate sum of a harmonic progression with odd number of terms = number of terms * (middle term)\nThe actual sum will be slightly more than the approximation.\nHere we have 9 terms (odd).\nSum = 9 * 1/5\n= 9/5\nProduct of all proper fractions in the form y/(y+1), where y is a positive digit:\n1/2 * 2/3 * 3/4 *.....*9/10\nWe will be left with 1/10.\nRequired = 9/5 - 1/10\n= 1.8 - 0.1\n= 1.7\nClosest is 1.72\nAnswer (D).\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA and B together can do a work in 6 days. If A alone can do it in 15 days. In how many days can B alone do it?\n\n### Options:\nA. 15\nB. 10\nC. 20\nD. 18\nE. 12\n\n### Answer:\n1/6 \u00e2\u20ac\u201c 1/15 = 1/10 => 10\nANSWER B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA circular mat with diameter 12 inches is placed on a square tabletop, each of whose sides is 24 inches long. Which of the following is closest to the fraction of the tabletop covered by the mat?\n\n### Options:\nA. 5/12\nB. 2/5\nC. 1/5\nD. 3/4\nE. 5/6\n\n### Answer:\nSO we are looking for the area of the cloth over the area of the table\nArea of the Cloth = (pi)(r)^2 which is about (3)(6)(6)\nArea of the Table = (24)(24)\nSo the quick way to estimate is looking at the fraction like this: (3/24)(36/24)\nI hope this is easy to follow, so with some simplification i get (1/8)(3/2) =3/16= (1/5) Answer is C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the sum of the greatest common factor and the lowest common multiple of 45 and 125?\n\n### Options:\nA. 1920\nB. 2201\nC. 3240\nD. 1130\nE. 3840\n\n### Answer:\nPrime factorization of the given numbers\n45= 3^2\n125= 5^3\nGreatest common factor =5\nLowest common multiple = 3^2*5^2 *5 =1125\nSum = 5+ 1125 = 1130\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFive kids were walking down the street. At a shop, they saw three brands of chocolates viz. Cadbury, Nestle and Ferrero being displayed. The shopkeeper has three chocolates which are of three different flavors of each brand. The kids bought all the chocolates available and decided to play a game. The chocolates will be distributed only to the winners of that game. Also they have decided that any winner cannot have all three brands of chocolates as his prize. Find the number of ways in which the chocolates can be distributed when there are four winners of the game and the best of them gets at least 4 chocolates?\n\n### Options:\nA. 12312\nB. 22536\nC. 4320\nD. 11268\nE. 45072\n\n### Answer:\nSince, one child cannot have more than two brands of chocolates, therefore, one child can get a maximum of six chocolates.\nWhen there are four winners, the winners can have the chocolates in the following possible way\nCase I\nOne of them gets six chocolates and the other three get one each.\nThe one who gets six chocolates can be selected in 4C1 ways and he will get any two brands out of three in 3C2 ways.\nThe three chocolates of the same brand will be distributed among the other three in 3! ways.\nHence, the total number of ways = 4 \u00d7 3 \u00d7 6 = 72\nCase II\nOne of them gets 5 chocolates, one of them gets 2 chocolates and the other two get 1 each.\nKid with 5 chocolates:\nThe one who gets five chocolates can be selected in 4C1 ways and he will get any two brands out of three in 3C2 ways.\nAfter choosing the two brands (say AB), he can get all three chocolates of one brand in 2 ways (i.e. either A or B). The other two chocolates can be chosen from the second brand in 3 ways. Thus, there are 4 \u00d7 3 \u00d7 2 \u00d7 3 = 36 ways\nKid with 2 chocolates:\nThis person can be chosen in 3 ways. Now, he can either get two chocolates from the same brand or from two different brands.\nThus, there are 6 \u00d7 3 = 18 ways\nKids with 1 chocolate each\nThe remaining chocolates can be distributed between the two remaining winners in 2 ways.\nTherefore, total number of ways = 36 \u00d7 18 \u00d7 2 = 1296 ways.\nCase III\nSimilarly for four chocolates the following combinations are possible:\na) 4 3 1 1\nThe number of ways = 4 \u00d7 3 \u00d7 [{6 \u00d7 3(1 + ( 6 + 3))} + {1 \u00d7 9 \u00d7 3 (1 + 6)}] \u00d7 2 = 8856\nb) 4 2 2 1\nThe number of ways = 4 \u00d7 3 \u00d7 [{6 \u00d7 3(2 \u00d7 6 \u00d7 3 + (3 + 9))} + {9 \u00d7 (9 + 9)}] = 12312\nSince, the best of them can\u2019t have less than 4 chocolates the above are the only cases applicable.\nHence, the total number of ways = 72 + 1296 + (8856 + 12312) = 22536.\nOption B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJill is dividing her 12-person class into two teams of equal size for a basketball game. If no one will sit out, how many different match-ups between the two teams are possible?\n\n### Options:\nA. 10\nB. 25\nC. 462\nD. 252\nE. 630\n\n### Answer:\nWith 12 players, the process of figuring out how many groups of 6 can be formed is pretty straight-forward....\n12C6 = 12!/(6!6!) = 924 possible groups of 6\nOnce forming that first group of 6, the remaining 6 players would all be placed on the second team by default.\nThe 'twist' is that the two teams of 6 canshow upin either order:\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nLet N be the greatest number that will divide 1305, 4665 and 6905, leaving the same remainder in each case. Then sum of the digits in N is:\n\n### Options:\nA. 4\nB. 5\nC. 6\nD. 7\nE. 8\n\n### Answer:\nN = H.C.F. of (4665 - 1305), (6905 - 4665) and (6905 - 1305)\n= H.C.F. of 3360, 2240 and 5600 = 1120.\nSum of digits in N = ( 1 + 1 + 2 + 0 ) = 4\nAnswer: Option A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe C.P of 15 books is equal to the S.P of 18 books. Find his gain% or loss%?\n\n### Options:\nA. 16 2/3% loss\nB. 16 8/3% loss\nC. 19 2/3% loss\nD. 13 2/3% loss\nE. 26 2/3% loss\n\n### Answer:\n15 CP = 18 SP\n18 --- 3 CP loss\n100 --- ? => 16 2/3% loss\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n3^b + 3^b + 3^b =\n\n### Options:\nA. 7^b\nB. 7^(b + 1)\nC. 7^(7b)\nD. 3^(b + 1)\nE. 49^B\n\n### Answer:\nEasy one.\n3*3^b = 3^(b+1)\nAns. D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a \u00c3\u2014 b = 2a - 3b + ab, then 2 \u00c3\u2014 5 + 5 \u00c3\u2014 2 is equal to :\n\n### Options:\nA. 18\nB. 23\nC. 24\nD. 25\nE. 26\n\n### Answer:\nExplanation:\n2 \u00c3\u2014 5 + 5 \u00c3\u2014 2 = (2 \u00c3\u2014 2 - 3 \u00c3\u2014 5 + 2 \u00c3\u2014 5) + ( 2 \u00c3\u2014 5 - 3 \u00c3\u2014 2 + 5 \u00c3\u2014 3)\n= (4 -15 + 10 + 10 - 6 + 15) = 18.\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA car is running at a speed of 80kmph. What distance will it cover in 20sec?\n\n### Options:\nA. 100m\nB. 440m\nC. 180m\nD. 200m\nE. 250m\n\n### Answer:\nSpeed = 80kmph = 80*5/18 = 22 m/s\nDistance covered in 20sec = 22*10 = 440m\nAnswer is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe sector of a circle has radius of 21 cm and central angle 135o. Find its perimeter?\n\n### Options:\nA. 91.5 cm\nB. 23.9 cm\nC. 62.9 cm\nD. 27.8 cm\nE. 21.2 cm\n\n### Answer:\nPerimeter of the sector = length of the arc + 2(radius)\n= (135/360 * 2 * 22/7 * 21) + 2(21)\n= 49.5 + 42\n= 91.5 cm\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTrain R leaves New York at 7:00 am traveling to Boston at 80mph. Train B leaves Boston at 7:45 am traveling to New York at 70 mph on a parallel track. If the distance between New York and Boston is 210 miles, at what time will the two trains pass each other?\n\n### Options:\nA. 8:15 am\nB. 8:45 am\nC. 9:00 am\nD. 9:30 am\nE. Cannot be determined from the information given\n\n### Answer:\ntrain R will cover 60 kms in 45 min at 7:45, the time when train B starts...\ndistance left to cover is 210-60=150..\ncombined speed=80+70=150..\nso the trains meet in 1 hour i.e. 7:45 + 1 hr=8:45\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the selling price of 100 articles is equal to the cost price of 63 articles, then the loss or gain percent is:\n\n### Options:\nA. 39%\nB. 36%\nC. 35%\nD. 40%\nE. 37%\n\n### Answer:\nLet C.P. of each article be Re. 1.\nThen, C.P. of 100 articles = Rs. 100;\nS.P. of 100 articles = Rs. 63.\nLoss % = 37/100 * 100 = 37%\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the area of the quadrilateral of one of its diagonals is 20 cm and its off sets 5 cm and 4 cm?\n\n### Options:\nA. 189 cm2\nB. 150 cm2\nC. 127 cm2\nD. 177 cm2\nE. 90 cm2\n\n### Answer:\n1/2 * 20(5 + 4)\n= 90 cm2\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average amount with a group of seven numbers is Rs. 20. If the newly joined member has Rs. 56 with him, what was the average amount with the group before his joining the group?\n\n### Options:\nA. s.13\nB. s.12\nC. s.15\nD. s.22\nE. s.14\n\n### Answer:\nTotal members in the group = 7\nAverage amount = Rs. 20\nTotal amount with them = 7 * 20 = Rs. 140\nOne number has Rs. 56. So, the amount with remaining 6 people = 140 - 56 = Rs. 84\nThe average amount with them = 84/6 = Rs.14.\nAnswer:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nGeorge baked a total of 150 pizzas for 7 straight days, beginning on Saturday. He baked 3/5 of the pizzas the first day, and 3/5 of the remaining pizzas the second day. If each successive day he baked fewer pizzas than the previous day, what is the maximum number of pizzas he could have baked on Wednesday?\n\n### Options:\nA. 5\nB. 6\nC. 4\nD. 3\nE. 2\n\n### Answer:\n3/5 of the 150 pizzas cooked on Saturday = 90 pizzas\n3/5 of the remaining pizzas on Sunday = 36 pizzas\nWe're left with (150-90-36) =24 pizzas for the remaining 5 days. The prompt tells us that each day has FEWER pizzas than the day before it, so we can't have duplicate numbers.\nM T W TH F\n8 7 6 2 1 =24\nW =6\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA vendor bought toffees at 6 for a rupee. How many for a rupee must he sell to gain 30%?\n\n### Options:\nA. 1/2\nB. 2/6\nC. 3/6\nD. 9/6\nE. 15/2\n\n### Answer:\nC.P. of 6 toffees = Re. 1\nS.P. of 6 toffees = 180% of Re. 1 = Rs. 9/5\nFor Rs. 9/5 , toffees sold = 6.\nFor Re. 1, toffees sold = 9 x 5 /6 =15/2.\nAnswer E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train 540 meters long is running with a speed of 54 kmph. The time taken by it to cross a tunnel 180 meters long is?\n\n### Options:\nA. 66 sec\nB. 46 sec\nC. 48 sec\nD. 65 sec\nE. 64 sec\n\n### Answer:\nD = 540 + 180 = 720\nS = 54 * 5/18 = 15 mps\nT = 720/15 = 48 sec\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man can row upstream at 5km/hr and down stream at 13km/hr find mans rate in still water ?\n\n### Options:\nA. 7.5km/hr\nB. 3.5km/hr\nC. 9km/hr\nD. 4km/hr\nE. 5km/hr\n\n### Answer:\ngiven upstream(u) =5km/hr\ndown stream (v)= 13km/hr rate in still water =1/2(u+v)=1/2(5+13)=9km/hr Answer is (C)\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe area of a square field 3136 sq m, if the length of cost of drawing barbed wire 3 m around the field at the rate of Rs.1.50 per meter. Two gates of 1 m width each are to be left for entrance. What is the total cost?\n\n### Options:\nA. 299\nB. 277\nC. 999\nD. 255\nE. 245\n\n### Answer:\na2 = 3136 => a = 56\n56 * 4 * 3 = 672 \u2013 6 = 666 * 1.5\n= 999\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nExactly 3/7 of the people in the room are under the age of 21, and exactly 5/14 of the people in the room are over the age of 65. If the total number of the people in the room is greater than 50 and less than 100, how many people in the room are under the age of 21?\n\n### Options:\nA. 21\nB. 35\nC. 39\nD. 42\nE. 65\n\n### Answer:\nThe total number of the people in the room must be a multiple of both 7 and 14 (in order 3/7 and 5/14 of the number to be an integer), thus the total number of the people must be a multiple of LCM of 7 and 14, which is 98.\nSince, the total number of the people in the room is greater than 50 and less than 100, then there are 98 people in the room.\nTherefore there are 3/7*98=42 people in the room under the age of 21.\nAnswer: D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAt a certain conference, 62% of the attendees registered at least two weeks in advance and paid their conference fee in full. If 20% of the attendees who paid their conference fee in full did not register at least two weeks in advance, what percent of conference attendees registered at least two weeks in advance?\n\n### Options:\nA. 18.0%\nB. 62.0%\nC. 79.2%\nD. 77.5%\nE. 82.0%\n\n### Answer:\nRefer to the table in the attachment:\nLet y= No. of members who have paid in Full\n20 % members paid in full and did not register in advance = 0.2y\n62 % registerd in advance and paid in full.\nSo if total No. of members = 100, then 62 members paid Full and registered in advance.\nHence total members who paid full amount = 0.2y + 62 =y\n0.8y =62\nHence y = 77.5\ni.e. 77.5 out of 100 or 77.5 %\nAns. D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA person purchases 90 clocks and sells 40 clocks at a gain of 10% and 50 clocks at a gain of 20%. If he sold all of them at a uniform profit of 15%, then he would have got Rs. 40 less. The cost price of each clock is:?\n\n### Options:\nA. 40\nB. 60\nC. 80\nD. 67\nE. 30\n\n### Answer:\nLet C.P. of clock be Rs. x.\nThen, C.P. of 90 clocks = Rs. 90x.\n[(110% of 40x) + (120% of 50x)] - (115% of 90x) = 40\n44x + 60x - 103.5x = 40\n0.5x = 40 => x = 80\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe size of a flat-screen television is given as the length of the screen\u2019s diagonal. How many square inches greater is the screen of a square 28-inch flat-screen television than a square 25 -inch flat-screen television?\n\n### Options:\nA. 79.5\nB. 89.3\nC. 85.5\nD. 75.4\nE. 72.5\n\n### Answer:\nIf we take a square with side length x and draw a diagonal, we get two isosceles right triangles.\nIf we focus on one such right triangle, we see that the legs have length x.\nsquare 28-inch flat-screen television\nThe diagonal (hypotenuse) = 28\nSo, we can apply the Pythagorean Theorem to get x\u00b2 + x\u00b2 = 28\u00b2\nSimplify: 2x\u00b2 = 28\u00b2\nDivide both sides by 2 to get: x\u00b2 = 28\u00b2/2\nSince the area of the square = x\u00b2, we can see that the area of this square is 28\u00b2/2\nsquare 25-inch flat-screen television\nThe diagonal (hypotenuse) = 25\nSo, we can apply the Pythagorean Theorem to get x\u00b2 + x\u00b2 = 25\u00b2\nSimplify: 2x\u00b2 = 25\u00b2\nDivide both sides by 2 to get: x\u00b2 = 25\u00b2/2\nSince the area of the square = x\u00b2, we can see that the area of this square is 25\u00b2/2\nDIFFERENCE IN AREAS =28\u00b2/2-25\u00b2/2\n= (28\u00b2- 25\u00b2)/2 = (784-625)/2 =159/2=79.5\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe bankers discount of a certain sum of money is Rs. 18 and the true discount on the same sum for the same time is Rs. 15. The sum due is:\n\n### Options:\nA. 89\nB. 90\nC. 91\nD. 92\nE. 93\n\n### Answer:\nSum = (B.D*T.D)/(B.D-T.D)\n(18*15)/18-15;\n90\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the value of k for which there are infinite solutions for the given set of equations.\n5x + 2y = k and 10x + 4y = 3\n\n### Options:\nA. 3/0\nB. 3/2\nC. 3/1\nD. 3/8\nE. 3/4\n\n### Answer:\nFor the two sets of equation to have infinite solutions, we have 510=24=k3510=24=k3. Hence, k = 3/2\nAnswer:\tB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA 80 gallon solution of salt and water is 10% salt. How many gallons of water must be added to the solution in order to decrease the salt to 8% of the volume?\n\n### Options:\nA. 20\nB. 12\nC. 13\nD. 14\nE. 16\n\n### Answer:\nAmount of salt = 8.0\nAssume x gallons of water are added.\n8.0 / 80 + x = 8/100\n800 = 8x + 640\n8x = 160\nx = 20\nCorrect Option: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJohn and Tony began business with Rs.12000 and Rs.14000 after 8 months, John withdraws Rs.2000 and Tony withdraws Rs.4000. At the end of the year, their profits amounted to Rs.4500 find the share of Tony.\n\n### Options:\nA. 2375\nB. 2325\nC. 2300\nD. 3375\nE. 3300\n\n### Answer:\n(12*8 + 10*4):(14*8 + 10*4)\n17:19\n19/36 * 4500 = 2375. Answer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf $800 is deposited into a savings account at an annual interest rate of 3% that compounds monthly, what is the value of the investment after 5 years?\n\n### Options:\nA. $950.00\nB. $929.29\nC. $973.25\nD. $100.25\nE. $110.00\n\n### Answer:\nUsing CI Formula:\nA=P(1+r/n)^n*t\nA=800(1+3/5)^3*5\nA=929.29\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAt a certain high school, a student\u2019s popularity is determined by his or her locker number. Whoever has the locker number with the greatest number of distinct prime factors is the most popular student in the school. If Johanna, Jamal, Brianna, and Dyson get lockers with the numbers 300, 400, 150, and 420, respectively, who is the most popular student?\n\n### Options:\nA. Johanna\nB. Jamal\nC. Brianna\nD. Dyson\nE. They have equal popularity\n\n### Answer:\nDistinct prime factors of 300 (Johanna) : 3, 2 5\nDistinct prime factors of 400 (Jamal): 2 and 5.\nDistinct prime factors of 150 (Brianna): 2,3, and 5\nDistinct prime factors of 420 (Dyson): 2,3,5 and 7.\nSo most popular student - Dyson\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf x>0, y>0, and |x| > |y|, which of the following must be true?\n\n### Options:\nA. x > y\nB. y^2 > x^2\nC. x^3 > y^2\nD. \u2013x < y\nE. x < \u2013y\n\n### Answer:\nCorrect Answer: (E)\nLet\u2019s go through each answer choice: (A) can never be true, since no negative is greater than a positive. (B) doesn\u2019t have to be true \u2013 consider what would happen if x = -2 and y = 1. (C) can never be true, as x^3 must be negative, and y^2 must be positive. (D) can never be true, since if x < 0, -x is the same thing as |x|, and |x| > y. (E) can be manipulated by multiplying both sides by -1, which gives us \u2013x > y. Remember that x < 0, so \u2013x = |x|, and y is positive, so |y| = y. Thus x > y is the same statement as |x| > |y|, and (A) must be true.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA and B start a business, with A investing the total capital of Rs.500000, on the condition that B pays A interest @ 10% per annum on his half of the capital. A is a working partner and receives Rs.15000 per month from the total profit and any profit remaining is equally shared by both of them. At the end of the year, it was found that the income of A is twice that of B. Find the total profit for the year?\n\n### Options:\nA. A)590280\nB. B)590100\nC. C)591900\nD. D)590000\nE. E)927000\n\n### Answer:\nInterest received by A from B = 10% of half of Rs.500000 = 10% * 250000 = 25000.\nAmount received by A per annum for being a working partner = 15000 * 12 = Rs.180000.\nLet 'P' be the part of the remaining profit that A receives as his share. Total income of A = (25000 + 180000 + P)\nTotal income of B = only his share from the remaining profit = 'P', as A and B share the remaining profit equally.\nIncome of A = Twice the income of B\n(25000 + 180000 + P) = 2(P)\nP = 205000\nTotal profit = 2P + 180000\n= 2*205000 + 180000 = 590000\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the missing figures :\n?% of 30 = 2.125\n\n### Options:\nA. 8.5\nB. 6.5\nC. 8.07\nD. 7.08\nE. 4.05\n\n### Answer:\n(i)\tLet x% of 30 = 2.125. Then , (x/100)*30 = 2.125\nX = (2.125 * 100/30) = 7.08\nAnswer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA bag holds 4 red marbles and 3 green marbles. If you removed two randomly selected marbles from the bag, without replacement, what is the probability that both would be red?\n\n### Options:\nA. 1/10\nB. 1/5\nC. 3/10\nD. 2/7\nE. 1/2\n\n### Answer:\nprobability of selecting first red marble = 4/7\nprobability of selecting second red marble without replacement = 3/6\nfinal probability = 4/7 * 3/6 = 2/7\nThe correct answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe C.P of 10 pens is equal to the S.P of 12 pens. Find his gain % or loss%?\n\n### Options:\nA. 6 2/5%\nB. 6 2/7%\nC. 6 2/3%\nD. 6 5/3%\nE. 6 7/3%\n\n### Answer:\n10 CP = 12 SP\n12 --- 2 CP loss\n100 --- ?\n=> 16 2/3%\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA coin is tossed 3 times. Find out the number of possible outcomes.\n\n### Options:\nA. None of these\nB. 8\nC. 2\nD. 1\nE. 3\n\n### Answer:\nExplanation :\nWhen a coin is tossed once, there are two possible outcomes - Head(H) and Tale(T)\nHence, when a coin is tossed 3 times, the number of possible outcomes\n= 2 x 2 x 2 = 8\n(The possible outcomes are HHH, HHT, HTH, HTT, THH, THT, TTH, TTT ) Answer : Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain elevator has a safe weight limit of 2,500 pounds. What is the greatest possible number of people who can safely ride on the elevator at one time with the average (arithmetic mean) weight of half the riders being 180 pounds and the average weight of the others being 230 pounds?\n\n### Options:\nA. 7\nB. 8\nC. 9\nD. 10\nE. 12\n\n### Answer:\nLets assume there are 2X people.\nHalf of them have average weight of 180 and other half has 230.\nMaximum Weight is = 2500\nSo 180*X + 230*X = 2500\n=> 410X = 2500\n=> X is approximately equal to 6.\nSo total people is 2*6 = 12\nAnswer E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA bus takes 4 hours to cover a distance of 480 Km. how much should the speed in Kmph be maintained to cover the same direction in 4/3th of the previous time?\n\n### Options:\nA. 50 Kmph\nB. 90 Kmph\nC. 95.9 Kmph\nD. 95.4 Kmph\nE. 90.5 Kmph\n\n### Answer:\nTime = 4\nDistance = 480\n4/3 of 4 hours = 4 * 4/3 = 5.3 Hours\nRequired speed = 480/5.3 = 90.5 Kmph\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nArnold and Danny are two twin brothers that are celebrating their birthday. The product of their ages today is smaller by 13 from the product of their ages a year from today. What is their age today?\n\n### Options:\nA. 2.\nB. 6.\nC. 5.\nD. 7.\nE. 9.\n\n### Answer:\nad = (a+1) (d+1) -13\n0= a+d-12\na+d = 12\na=d (as they are twin brothers)\na=d=6\nB is the answer\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA cubical block of metal weighs 4 pounds. How much will another cube of the same metal weigh if its sides are twice as long?\n\n### Options:\nA. 48\nB. 32\nC. 24\nD. 18\nE. 12\n\n### Answer:\nFor example our cube have a side 1 meter, so we have 1 cubical meter in this cube\nand this cubical meter weigth 4 pounds\nIf we take cube with side 2 meters we will have 8 cubical meters in this cube\n8 meters * 4 pounds = 32 pounds\nSo answer is B\nAnd similar but more theoretical approach:\nif we have sides a and b than they have equal ration with their areas:\na/b = a^2/b^2\nand they have equal ration with their volumes:\na/b = a^3/b^3\nwe have two sides 1/2 so their volume will be in ratio 1/8\nweight of one cube * volume of another cube\n4 * 8 = 32\nSo answer is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf x and d are integers and 2x\u2013d= 11, then 4x+ d CANNOT be\n\n### Options:\nA. \u20135\nB. 1\nC. 13\nD. 17\nE. 551\n\n### Answer:\n2x-d=11....d=2x-11\n4x+d=4x+2x-11=6x-11\n6x-11=-5...x=1\n6x-11=1... x=2\n6x-11=13...x=4\n6x-11=17..X is not integer\n6x-11=551..X is not integer\nI think the choice E is 55 not 551. Otherwise both DE CANNOT be solution=D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nx<3y<0 which of the following is the greatest?\n\n### Options:\nA. x+2y\nB. -2x+y\nC. 3x-y\nD. -(2x+2y)\nE. x-y\n\n### Answer:\nPlugging in -1 for both x and y we get\nA. x+2y =-3\nB. -2x+y =1\nC. 3x-y =-2\nD. -(2x+2y) =4\nE. x-y =0\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the units digit of (493) (915) (381) (756) (22)\n\n### Options:\nA. 0\nB. 1\nC. 4\nD. 5\nE. 6\n\n### Answer:\nJust multiply the digits in the units place for each term and you will get the answer. It should be 0. you got a 5 as a unit digit and an even number term. so the multiplication of this will definitely yield a 0. Answer has to be 0.\nI also tried it using the calculator and the answer is 1.\nIMO B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nEach month a retailer sells 100 identical items. On each item he makes a profit of $30 that constitutes 16% of the item's price to the retailer. If the retailer contemplates giving a 5% discount on the items he sells, what is the least number of items he will have to sell each month to justify the policy of the discount?\n\n### Options:\nA. 157\nB. 213\nC. 221\nD. 223\nE. 226\n\n### Answer:\nFor this question, we'll need the following formula:\nSell Price = Cost + Profit\nWe're told that the profit on 1 item is $20 and that this represents 16% of the cost:\nSell Price = Cost + $20\nSell Price = $125 + $20\nThus, the Sell Price is $145 for each item. Selling all 100 items gives the retailer...\n100($20) = $2,000 of profit\nIf the retailer offers a 5% discount on the sell price, then the equation changes...\n5%(145) = $7.25 discount\n$137.75 = $125 + $12.75\nNow, the retailer makes a profit of just $12.75 per item sold.\nTo earn $2,000 in profit, the retailer must sell....\n$12.75(X) = $2,000\nX = 2,000/12.75\nX = 156.8627 =157 items\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many words can be formed by using all letters of the word \u201cPACKHORSE\u201d\n\n### Options:\nA. 40320\nB. 44000\nC. 42340\nD. 56000\nE. 14000\n\n### Answer:\nThe word PACKHORSE contains 8 different letters.\nRequired number of words = 8p8 = 8! = (8x7x6x5x4x3x2x1) = 40320.\nAnswer A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA car covers a certain distance at aspeed of 60 kmph in 4 hours. To cover the same distance in 2hr, it must travel at a speed of?\n\n### Options:\nA. 567 km/hr\nB. 678 km/hr\nC. 782 km/hr\nD. 120 km/hr\nE. 720 km/hr\n\n### Answer:\nDistance = (60 x 4) = 240 km.\nSpeed = Distance/Time\nSpeed = 240/2 = 120 kmph\nAnswer : D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is:\n\n### Options:\nA. 200 meters\nB. 225 meters\nC. 245 meters\nD. 250 meters\nE. 300 meters\n\n### Answer:\nGiven, Length of the train = 130 meters\nSpeed of the train = 45 km/hr = 45 * 518 m/sec = 252 m/sec\nTime = 30 secs\nLet the length of the bridge be x meters .\nThe distance travelled by the train while crossing the bridge will be sum of the length of train and Length of the bridge = (x+130) meters\nso , 252 = x+13030\n= 30*25 = 2x + 260\n= 750 - 260 = 2x\n= 490 = 2x\n=x = 245 meters. ANSWER C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe value of land increases by x% during June and decreases by y% during July. If the value of the land is the same at the end of July as at the beginning of June, what is y in terms of x?\n\n### Options:\nA. 200x/(100+2x)\nB. 100x/(100+x)\nC. x(2+x)/(1+x)2\nD. x(200+x)/10000\nE. 2x/x+2x\n\n### Answer:\nThe simplest pairing is a 25% increase will be offset by a 20% decrease.\nHere's the proof:\nStarting value = 100\n25% increase = 100 + (.25)(100) = 125\n20% decrease = 125 - (.2)(125) = 100\nEnding value = 100\nSo we would be looking for an answer that equals 20 when A=25. While the answers might appear 'complex', you can actually avoid much of the 'math' if you just fill in the parts and take a good look at what you have...\nAnswer A: (200)(25)/(150) ... since 200>150, this answer will be greater than 25. ELIMINATE A.\nAnswer B: (100)(25)/125) = (100)(1/5) = 20 This is a MATCH.\nAnswer C: (25)(27)/(26)2 ... nothing 'cancels out', so this cannot = 20. ELIMINATE C.\nAnswer D: (25)(225)/10000... the 'units' digit of the numerator is a 5; when dividing by 10,000, this won't end in a 0. ELIMINATE D.\nAnswer E: (50/25) + 50 = 52. ELIMINATE E.\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA batsman makes a score of 87 runs in the 17th match and thus increases his average by 3. Find his average after 17th match\n\n### Options:\nA. 36\nB. 37\nC. 38\nD. 39\nE. 40\n\n### Answer:\nExplanation:\nLet the average after 17th match is x\nthen the average before 17th match is x-3\nso 16(x-3) + 87 = 17x\n=> x = 87 - 48 = 39\nAnswer: Option D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the price of a TV is first decreased by 20% and then increased by 40%, then the net change in the price will be :\n\n### Options:\nA. 4% increase\nB. 12% increase\nC. 10% decrease\nD. 6% increase\nE. None of these\n\n### Answer:\nExplanation :\nSolution: let the original price be Rs. 100.\nNew final price = 140% of(80% of 100) =Rs. 140/100 * 80/100 * 100 = Rs. 112.\n.'. Increase = 12%\nAnswer : B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 4x + y = 12 and \u2212x + y = 44, then what is the value of 3x + 2y?\n\n### Options:\nA. 1/7\nB. 3\nC. 15\nD. 52/7\nE. 56\n\n### Answer:\n4x + y = 12\n\u2212x + y = 44\nAdding both the equations --> 3x + 2y = 56\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA shopkeeper sells 300 metres of cloth for Rs. 18000 at a loss of Rs.5 per metre. Find his cost price for one metre of cloth?\n\n### Options:\nA. 12\nB. 27\nC. 29\nD. 50\nE. 65\n\n### Answer:\nSP per metre = 18000/300 = Rs. 60 Loss per metre = Rs. 5 CP per metre = 60 + 5 = Rs. 65.Answer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nExactly 3/5 of the people in the room are under the age of 21, and exactly 5/13 of the people in the room are over the age of 65. If the total number of the people in the room is greater than 50 and less than 100, how many people in the room are under the age of 21?\n\n### Options:\nA. 21\nB. 35\nC. 39\nD. 60\nE. 42\n\n### Answer:\nThe total number of the people in the room must be a multiple of both 5 and 14 (in order 3/5 and 5/14 of the number to be an integer), thus the total number of the people must be a multiple of LCM of 5 and 14, which is 70.\nSince, the total number of the people in the room is greater than 50 and less than 100, then there are 70 people in the room.\nTherefore there are 3/5*70=42 people in the room under the age of 21.\nAnswer: E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe measurements obtained for the interior dimensions of a rectangular box are 100 cm by 100 cm by 150cm. If each of the three measurements has an error of at most 1 centimeter, which of the following is the closes maximum possible difference, in cubic centimeters, between the actual capacity of the box and the capacity computed using these measurements?\n\n### Options:\nA. 50,000\nB. 40,000\nC. 45,000\nD. 50,000\nE. 60,000\n\n### Answer:\nThe options are well spread so we can approximate.\nChanging the length by 1 cm results in change of the volume by 1*100*150 = 15,000 cubic centimeters;\nChanging the width by 1 cm results in change of the volume by 100*1*150 = 15,000 cubic centimeters;\nChanging the height by 1 cm results in change of the volume by 100*100*1 = 10,000 cubic centimeters.\nSo, approximate maximum possible difference is 15,000 + 15,000 + 10,000 = 40,000 cubic centimeters.\nAnswer: B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nBy investing in 16 2/3% stock at 64, one earns Rs. 1500. The investment made is:\n\n### Options:\nA. Rs. 5640\nB. Rs. 5760\nC. Rs. 7500\nD. Rs. 8600\nE. Rs. 9600\n\n### Answer:\nTo earn Rs.\t50/3\t, investment = Rs. 64.\nTo earn Rs. 1500, investment = Rs.64 x\t3/50x 1500\t= Rs. 5760.\nANSWER :B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhen Rajeev was born, his father was 32 years older than his brother and his mother was 25 years older than his sister. If Rajeev's brother is 6 years older than Rajeev and his mother is 3 years younger than his father, how old was Rajeev's sister when Rajeev was born?\n\n### Options:\nA. 10 years\nB. 11 years\nC. 12 years\nD. 13 years\nE. 14 years\n\n### Answer:\nhis brother is x years old\nthn his father is 6+32=38 when rajeev was born\nand his mother is 3 years yonger thn hi father so his mother was 35 years old whn rajeev was born\nand his sister is 25 year younger thn his mother\nso rajeev's sister was 10 years old when rajeev was born.\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe sector of a circle has radius of 21 cm and central angle 270o. Find its perimeter?\n\n### Options:\nA. 145 cm\nB. 135 cm\nC. 121 cm\nD. 141 cm\nE. 151 cm\n\n### Answer:\nPerimeter of the sector = length of the arc + 2(radius)\n= (270/360 * 2 * 22/7 * 21) + 2(21)\n= 99 + 42 = 141 cm\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOf the 150 employees at company X, 80 are full-time, and 100 have worked at company X for at least a year. There are 10 employees at company X who aren\u2019t full-time and haven\u2019t worked at company X for at least a year. How many full-time employees of company X have worked at the company for at least a year?\n\n### Options:\nA. 10\nB. 30\nC. 50\nD. 80\nE. 100\n\n### Answer:\nFull time employee who have NOT worked for at least one year = a\nFull time employee who have worked for at least one year = b\nNON Full time employee who have worked for at least one year = c\nNON Full time employee who have NOT worked for at least one year = d\na+b+c+d = 150\na+b = 80\ni.e. c+d = 70\nb+c = 100\ni.e. a+d = 50\nd = 20\ni.e. c = 70-20 = 50\ni.e. b = 100-50 = 50\ni.e. a = 80-50 = 30\nb = 10\nAnswer: Option A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf $5,000 is invested in an account at a simple annual rate of r percent, the interest is $250. When $19,000 is invested at the same interest rate, what is the interest from the investment?\n\n### Options:\nA. $700\nB. $750\nC. $800\nD. $950\nE. $900\n\n### Answer:\n-> 250/5,000=5% and 19,000*5%=950.\nThus, D is the answer.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain sum amounts to Rs.640 in 4 years and Rs.760 in 6 years. Find the rate % per annum?\n\n### Options:\nA. 9%\nB. 5%\nC. 3%\nD. 1%\nE. 8%\n\n### Answer:\n4 --- 640\n6 --- 760\n--------------\n2 --- 120\nN = 1 I = 60 R = ?\nP = 640 - 240 = 400\n60 = (400*1*R)/100\nR = 15%\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man buys an article and sells it at a profit of 20%. If he had bought it at 20% less and sold it for Rs.75 less, he could have gained 25%. What is the cost price?\n\n### Options:\nA. 256\nB. 375\nC. 287\nD. 255\nE. 123\n\n### Answer:\nCP1 = 100 SP1 = 120\nCP2 = 80 SP2 = 80 * (125/100) = 100\n20 ----- 100\n75 ----- ? => 375\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the value of a/b + b/a, if a and b are the roots of the quadratic equation x2 + 9x +3 = 0?\n\n### Options:\nA. 28.3\nB. 1.45\nC. 2.78\nD. 6.84\nE. 7.23\n\n### Answer:\na/b + b/a = (a2 + b2)/ab = (a2 + b2 + a + b)/ab\n= [(a + b)2 - 2ab]/ab\na + b = -9/1 = -9\nab = 3/1 = 3\nHence a/b + b/a = [(-9)2 - 2(3)]/3 = 56/4 = 28.3.\nA)\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average of runs of a cricket player of 10 innings was 35. How many runs must he make in his next innings so as to increase his average of runs by 4 ?\n\n### Options:\nA. 76\nB. 79\nC. 85\nD. 87\nE. 89\n\n### Answer:\nExplanation:\nAverage = total runs / no.of innings = 35\nSo, total = Average x no.of innings = 35 x 10 = 350.\nNow increase in avg = 4runs. So, new avg = 35+4 = 39runs\nTotal runs = new avg x new no. of innings = 39 x 11 = 429\nRuns made in the 11th inning = 429 - 350 = 79 Answer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain quantity is measured on two different scales, the P-scale and the S-scale, that are related linearly. Measurements on the P-scale of 6 and 24 correspond to measurements on the S-scale of 30 and 60, respectively. What measurement on the P-scale corresponds to a measurement of 100 on the S-scale?\n\n### Options:\nA. 20\nB. 36\nC. 48\nD. 60\nE. 84\n\n### Answer:\nFirst, we have to understand what linearly means. It's not a straight ratio (since 6:30 does NOT equal 24:60). We need to look at the increases in each measurement to see what the scalar actually is.\nFrom 6 to 24 we have an increase of 18. From 30 to 60 we have an increase of 30. Therefore, the increase ratio is 18:30 or 3:5. In other words, for every 3 that P increases, S increases by 5.\nWe know that S is 100. To get from 60 to 100, we went up by 40, or 8 jumps of 5; therefore, P will go up by 8 jumps of 3.\n24 + 8(3) = 24 + 24 = 48=C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA completes 80% of a work in 20 days. Then B also joins and A and B together finish the remaining work in 3 days. How long does it need for B if he alone completes the work?\n\n### Options:\nA. 35 Days\nB. 36.5 Days\nC. 37 Days\nD. 37.5 Days\nE. 38 Days\n\n### Answer:\nWork done by A in 20 days = 80/100 = 8/10 = 4/5\nWork done by A in 1 day = (4/5) / 20 = 4/100 = 1/25 --- (1)\nWork done by A and B in 3 days = 20/100 = 1/5 (Because remaining 20% is done in 3 days by A and B)\nWork done by A and B in 1 day = 1/15 ---(2)\nWork done by B in 1 day = 1/15 \u2013 1/25 = 2/75\n=> B can complete the work in 75/2 days = 37 \u00bd days\nAnswer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo trains are running in opposite directions with the same speed. If the length of each train is 130 m and they cross each other in 12 sec, then the speed of each train is?\n\n### Options:\nA. 30\nB. 35\nC. 36\nD. 37\nE. 39\n\n### Answer:\nLet the speed of each train be x m/sec.\nThen, relative speed of the two trains = 2x m/sec.\nSo, 2x = (130 + 130)/12 => x = 10.83\nSpeed of each train = 10 m/sec.\n= 10.83 * 18/5 =- 39 km/hr.\nAnswer: Option E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain car traveled twice as many miles from Town A to Town B as it did from Town B to Town C. From Town A to Town B, the car averaged 25 miles per gallon, and from Town B to Town C, the car averaged 30 miles per gallon. What is the average miles per gallon that the car achieved on its trip from Town A through Town B to Town C?\n\n### Options:\nA. 24\nB. 25\nC. 23\nD. 22\nE. 26.5\n\n### Answer:\nstep 1) took LCM of 25 and 30.. came as 150.\nstep 2) 150 distance between B to C... do 150/30 hence 5 gallons used\nstep 3) twice distance.. hence 150*2= 300... do as above.. 300/25= 12 gallons used\nstep 4) total gallons.. 5+12= 17 gallons\nstep ) total miles= 150+300= 450 miles\nhence.. average of whole journey = 450/17 which comes to 26.5\nAnswer : E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA mixture of 70 liters of wine and water contains 10% water. How much water must be added to make water 12 \u00bd% of the total mixture?\n\n### Options:\nA. 8\nB. 7\nC. 5\nD. 2\nE. 1\n\n### Answer:\n70 * (10/100) = 7\nWine Water\n87 1/2% 12 1/2%\n87 1/2% ------- 63\n12 1/2% -------? => 9-7=2\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nDifference between two numbers is 5, six times of the smaller lacks by 6 from the four times of the greater. Find the numbers?\n\n### Options:\nA. 12,7\nB. 12,9\nC. 10,5\nD. 11,6\nE. 15,4\n\n### Answer:\nx \u00e2\u20ac\u201c y = 5\n4x \u00e2\u20ac\u201c 6y = 6\nx = 12 y = 7\nANSWER A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nPointing to a girl in the photograph, Amar said, \"Her mother's brother is the only son of my mother's father.\" How is the girl's mother related to Amar ?\n\n### Options:\nA. Mother\nB. Sister\nC. Aunt\nD. Grandmother\nE. Brother\n\n### Answer:\nExplanation:\nOnly son of Amar's mother's father \u2014 Amar's maternal uncle.\nSo, the girl's maternal uncle is Arnar's maternal uncle. Thus, the girl's mother is Amar's aunt.\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n5358 x 51 = ?\n\n### Options:\nA. 273762\nB. 283758\nC. 273298\nD. 273258\nE. 277382\n\n### Answer:\nD\n273258\n5358 x 51 = 5358 x (50 + 1)\n= 5358 x 50 + 5358 x 1\n= 267900 + 5358\n= 273258.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJohn found that the average of 15 numbers is 40. If 10 is added to each number then the mean of number is?\n\n### Options:\nA. 50\nB. 58\nC. 60\nD. 65\nE. 70\n\n### Answer:\n(x+x1+...x14)/15 = 40\n50\nOption A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAjay can complete a piece of work in 4 days. Balu takes double the time taken by Ajay, Charan takes double that of Balu, and Danush takes double that of Charan to complete the same task. They are paired in groups of two each. One pair takes two thirds the time needed by the second pair-to complete the work. Which is the first pair?\n\n### Options:\nA. A, B\nB. A, C\nC. B, C\nD. A, D\nE. None of these\n\n### Answer:\nTime taken by Ajay, Balu, Charan, Dhanush is 4 days, 8 days, 16 days and 32 days respectively.\nTherefore, grouping Ajay and Dhanush work will be two third of the work that will be completed by grouping Balu and Charan.\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSix bells commence tolling together and toll at intervals of 2, 4, 6, 8 10 and 12 seconds respectively.\nIn 30 minutes, how many times do they toll together?\n\n### Options:\nA. 12\nB. 14\nC. 15\nD. 16\nE. 17\n\n### Answer:\nExplanation :\nHere's the simple solution :\nTake lcm of 2,4,6,8,10,12 seconds\nThe outcome is 120seconds.\nConvert it into minutes = 120 / 60\n= 2 minutes\nIn 30mins it will rings 15times together\nBut ,In 0th second all bells rings together\nHence Total number of bell rings is = 15 + 1\n= 16\nHence (D) is the correct answer.\nAnswer : D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nL = {3, 4, 5, 5, 6, 7}\nM = {2, 2, 2, 8, 8, 8}\nN = {15, 15, 15, 15, 15, 15}\nRank those three sets from least standard D eviation to greatest standard deviation.\n\n### Options:\nA. L, M, N\nB. M, L, N\nC. M, N, L\nD. RANKING=N, L, M\nE. N, M,\n\n### Answer:\nSquare of Standard deviation is sum of squares of deviation from the mean divided by the number of terms.\nIf deviation from the mean is higher for the same number of elements, standard deviation will be higher.\nL = {3, 4, 5, 5, 6, 7}\nMean is 5 and deviation of 2 elements from mean is 0, of 2 elements is 1 and of 2 elements is 2.\nM = {2, 2, 2, 8, 8, 8}\nMean is 5 and deviation of all elements from the mean is 3. So SD here will be higher than SD of L.\nN = {15, 15, 15, 15, 15, 15}\nMean is 15 here and all elements have 0 deviation from mean so SD = 0 here. This is the minimum possible SD.\nAnswer N, L, M\nAnswer (D)\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nPositive integer y is 50 percent of 50 percent of positive integer x, and y percent of x equals 100. What is the value of x?\n\n### Options:\nA. 50\nB. 100\nC. 200\nD. 1,000\nE. 2,000\n\n### Answer:\ny = 50% of 50% 0f x\n= x/4\nand\ny/100 of x = 100\ny /100 *4y =100\ny = 50\nand x= 200\nAnswer - C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA quadilateral pqrs is inscribes in a circle of center o. PQ is parallel to RS and pq= 3rs,\nalso QR=PS. perimeter(pqrs)= perimeter of square whose area is 36sqm,then find the approx area of pqrs\n\n### Options:\nA. 6root(3)\nB. 12root(3)\nC. 9root(3)\nD. 18root(3)\nE. 12root(3)\n\n### Answer:\nLets take, QR=PS= a m and RS=b m, So, PQ=3b m\nnow if are of a square is 36 sqm, then perimeter is 24\nnow perimeter of the inscribed quadrilateral is 4b+2a= 24\nso, 2b+a=12\nfrom this we can get set of solutions like (a,b)= (6,3), (8,2), (10,2)\nNow, formula for area of inscribed quadrilater is root{(s-a)(s-b)(s-c)(s-d)}\nHere s= 12\nnow by trial and error method we can get the solution\nappprox area is 18root(3)\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe sum of three consecutive even numbers is 63. Find the middle number of the three?\n\n### Options:\nA. 14\nB. 23\nC. 25\nD. 29\nE. 21\n\n### Answer:\nMiddle no=63/3\n=21\nAns E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man can row downstream at the rate of 32 Kmph and upstream at 8 Kmph. Find the man\u2019s rate in still water and rate of current?\n\n### Options:\nA. 20 Kmph, 10 Kmph\nB. 12 Kmph, 22 Kmph\nC. 22 Kmph, 12 Kmph\nD. 20 Kmph, 12 Kmph\nE. None of these\n\n### Answer:\nExplanation:\nRate of still water = 1/2 (down stream + upstream)\n= 1/2 (32 + 8) = 20 Kmph\nRate of current = 1/2 (down stream - upstream)\n= 1/2 (32 - 8)\n= 1/2 (24)\n= 12 kmph\nAnswer: Option D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are, in a certain league, 8 teams, and each team face another team for a total of 12 times. How many games are played in the season?\n\n### Options:\nA. 150\nB. 121\nC. 144\nD. 180\nE. 1200\n\n### Answer:\nBy using the formula, t[n(n - 1) / 2], where t = no. of games between two teams and n = total no. of teams, we get: 144\nOption C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMonica planned her birthday party. She prepared 5 muffins for each of her guests and kept aside two additional muffins in case someone will want extra. After the party, it turned out that one of the guests didn't come but every one of the guests that did come ate six muffins and 1 muffins remained. How many guests did Monica plan on?\n\n### Options:\nA. 3.\nB. 4.\nC. 5.\nD. 6.\nE. 7.\n\n### Answer:\nLet x be the number of guests.\nNumber of muffins prepared = 5x + 2\nNumber of muffins eaten + Number of muffins remaining = Number of muffins prepared\n6(x - 1) + 1 = 5x + 2\n6x - 5 = 5x + 2\nx = 7\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how many ways can five boys, three girls and a teacher sit in a row such that all boys sit together?\n\n### Options:\nA. A)10000\nB. B)12100\nC. C)14400\nD. D)1097\nE. E)2781\n\n### Answer:\nTreat all boys as one unit. Now there are four students and a teacher and they can be arranged in 5! ways. Again five boys can be arranged among themselves in 5! ways.\nRequired number of arrangements\n= 5! * 5! = 120 * 120\n= 14400.\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average mark of the students of a class in a particular exam is 80. If 5 students whose average mark in that exam is 40 are excluded, the average mark of the remaining will be 90. Find the number of students who wrote the exam.\n\n### Options:\nA. 11\nB. 23\nC. 25\nD. 77\nE. 81\n\n### Answer:\nLet the number of students who wrote the exam be x.\nTotal marks of students = 80 x.\nTotal marks of (x - 5) students = 90(x - 5)\n80x - (5 * 40) = 90(x - 5)\n250 = 10x => x = 25\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nPZQW : NXOU :: FISK :?\n\n### Options:\nA. EFPJ\nB. FERI\nC. DGQI\nD. HKUM\nE. HKUN\n\n### Answer:\nDifference of one alphabet on each side of proportion term. Answer is thus DGQI\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA, B and C have Rs.900 between them, A and C together have Rs.400 and B and C Rs.750. How much does C have?\n\n### Options:\nA. 100\nB. 150\nC. 200\nD. 250\nE. 350\n\n### Answer:\nA+B+C = 900\nA+C = 400\nB+C = 750\n--------------\nA+B+2C = 1150\nA+B+C = 900\n----------------\nC = 250\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo sides of a triangle have length 5 and 8. Which of the following are possible areas of the triangle?\nI. 2\nII. 12\nIII. 24\n\n### Options:\nA. I, II, and III\nB. I and II only\nC. II and III only\nD. I and III only\nE. I only\n\n### Answer:\nAnswer = A. I, II, and III\nWith dimensions of only 2 sides given (for a triangle), this becomes an open ended question\nAny area is possible out of the three\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA car going at 40 miles per hour set out on an 90-mile trip at 9:00 A.M. Exactly 10 minutes later, a second car left from the same place and followed the same route. How fast, in miles per hour, was the second car going if it caught up with the first car at 10:30 A.M.?\n\n### Options:\nA. 45\nB. 50\nC. 53\nD. 55\nE. 90\n\n### Answer:\nLet Car A = car that starts at 9 AM\nCar B = car that starts at 9:10 AM\nTime for which car A travels at speed of 40 m per hour = 1.5 hours\nDistance travelled by Car A = 40 *1.5 = 60 miles\nSince Car B catches up Car A at 10:30 , time = 90 mins = 3/2 hour\nSpeed of Car B = 60/(3/2) = 90 miles per hour\nAnswer E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOf the three-digit positive integers that have no digits equal to zero, how many have two digits that are equal to each other and the remaining digit different from the other two?\n\n### Options:\nA. 24\nB. 36\nC. 72\nD. 1\nE. 216\n\n### Answer:\nAssume: a,b,c is the digit and a,b,c not= 0\nThus a,b,c could be 1, 2, 3, 4, 5, 6, 7, 8, and 9\nCount the possible way to get three digit number abc.\na = b, and c must be different from a, b\nThus, there are 3 possible ways of digit arrangement: aac, aca, caa\nCase I: aac\n=> (digit 1st) x (digit 2nd) x (digit 3rd)\n=> 9 x 1 x 8 {pick any number from group = 9 possible ways} x {pick number the same as the first pick = 1 way} x {pick any number from the rest = 8 possible ways}\n= 9 x 1 x 8 = 72 possible ways\nCase II: aca\n=> same as case I you have 72 possible ways\nCase III: caa\n=> same as case I you have 72 possible ways\ntotal of this set of number = 72 + 72 + 72 = 216\nE) is the answer\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nEach of the cucumbers in 100 pounds of cucumbers is composed of 99% water, by weight. After some of the water evaporates, the cucumbers are now 95% water by weight. What is the new weight of the cucumbers, in pounds?\n\n### Options:\nA. 2\nB. 20\nC. 92\nD. 96\nE. 98\n\n### Answer:\nOut of 100 pounds 99% or 99 pounds is water and 1 pound is non-water. After somewaterevaporates the cucumbers become 95% water and 5% of non-water, so now 1 pound of non-water composes 5% of cucucmbers, which means that the new weight of cucumbers is 1/0.05=20 pounds.\nAnswer: B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn an examination it is required to get 30% of minimum marks to pass. A student got 170 marks and was declared failed by 10 marks difference. Then what is total marks:?\n\n### Options:\nA. 550\nB. 500\nC. 600\nD. 700\nE. None of these\n\n### Answer:\nExplanation:\n30 % -------> 180 ( 30 * 6 = 180)\n100% -------> 600 (100 * 6 = 600)\nAnswer: Option C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the length of the altitude of an equilateral triangle of side 3\u221a3 cm.\n\n### Options:\nA. 4.5cm\nB. 7.2cm\nC. 4.3cm\nD. 5.6cm\nE. 5.7cm\n\n### Answer:\nArea of the triangle = (\u221a3/4) x (3\u221a3)2 = 27\u221a3. Let the height be h.\nThen, (1/2) x 3\u221a3 x h = (27\u221a3/4) X(2/\u221a3) = 4.5 cm.\nAns: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAverage expenditure of a person for the first 3 days of a week is Rs. 330 and for the next 4 days is Rs. 420. Average expenditure of the man for the whole week is:\n\n### Options:\nA. 350\nB. 370\nC. 390\nD. 430\nE. None\n\n### Answer:\nExplanation:\nAssumed mean = Rs. 330\nTotal excess than assumed mean = 4 \u00d7 (Rs. 420 - Rs. 350) = Rs. 280\nTherefore, Increase in average expenditure = Rs. 280/7 = Rs. 40\nTherefore, Average expenditure for 7 days = Rs. 330 + Rs. 40 = Rs. 370\nCorrect Option: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the principle on a certain sum of money at 5% per annum for 3 1/5 years if the amount being Rs.1740?\n\n### Options:\nA. Rs.1000\nB. Rs.1550\nC. Rs.1510\nD. Rs.1500\nE. None of these\n\n### Answer:\nExplanation:\n1740 = P [1 + (5*16/5)/100]\nP= 1500\nAnswer: Option D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how many different number of ways 1 boys and 3 girls can sit on a bench?\n\n### Options:\nA. 720\nB. 730\nC. 740\nD. 24\nE. 800\n\n### Answer:\nnpn = n!\n4p4 = 4 \u00d7 3 \u00d7 2 \u00d7 1 = 24\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFour friends decided to go on a vacation to a hill station. During their vacation, they experienced 13 days of heavy snowfall. When it used to snow in the morning, the afternoon was clear and when it used to snow in the afternoon, the day was followed by a clear morning.\nIn total, they had eleven clear mornings and twelve clear afternoons. Is there a way you can calculate the number of days they spent in their vacation?\n\n### Options:\nA. 16\nB. 21\nC. 18\nD. 19\nE. 25\n\n### Answer:\nC\n18\nNumber of days with snow in morning and clear afternoon = A\nNumber of days with clear morning and snow in afternoon = B\nNumber of days with no snowfall in morning or afternoon = C\nNow, number of days with snowfall = A + B = 13\nNumber of days with clear mornings = B + C = 11\nNumber of days with clear afternoons = A + C = 12\nAdding these three equations, we get\n2 * (A + B + C) = 36\nOr, A + B + C = 18\nTherefore, they spent eighteen days in total at their vacation.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA person can row at 10 kmph in still water. If the velocity of the current is 2 kmph and it takes him 25 hour to row to a place and come back, how far is the place?\n\n### Options:\nA. 24km\nB. 30km\nC. 48km\nD. 120km\nE. 15km\n\n### Answer:\nSpeed of down stream = 10+2 = 12kmph\nspeed of upstream = 10-2 = 8kmph\nLet the required distance be xkm\nx/12 + x/8 = 25\n2x+3x = 600\nx = 120 km\nAnswer is D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich of the following equations describes a line that is perpendicular to y = x/2 + 5?\n\n### Options:\nA. y = x \u2212 5\nB. y = \u22123 \u2212 2x\nC. y = 5x\nD. y = 5x - 1\nE. y = 1/x + 5\n\n### Answer:\nTwo perpendicular lines have slopes that are inverse reciprocals of each other.\nThe slope of y = x/2 + 5 is 1/2 so the slope of a perpendicular line will be -2.\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n5 men are equal to as many women as are equal to 8 boys. All of them earn Rs.180 only. Men\u00e2\u20ac\u2122s wages are?\n\n### Options:\nA. 6Rs\nB. 2Rs\nC. 4Rs\nD. 9Rs\nE. 12Rs\n\n### Answer:\n5M = xW = 8B\n5M + xW + 8B ----- 180 Rs.\n5M + 5M + 5M ----- 180 Rs.\n15M ------ 180 Rs. => 1M = 12Rs.\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the least number of five digits which is exactly divisible by 12, 15 and 18?\n\n### Options:\nA. 10080\nB. 1080\nC. 10025\nD. 10050\nE. 10024\n\n### Answer:\nLCM = 180\n180) 10000 (55\n9900\n---------\n100\n10000 + 180 - 100 = 10080\nANSWER A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the circumference of radius 7 cm.\n\n### Options:\nA. 44\nB. 55\nC. 66\nD. 77\nE. 88\n\n### Answer:\nCircumference of circle = 2\u03c0r\n= 2 \u00d7 22/7 \u00d7 7\n= 44 cm\nANSWER : A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the number of integers from 1 to 900 (inclusive) that are divisible by neither 11 nor by 35?\n\n### Options:\nA. 884\nB. 890\nC. 892\nD. 910\nE. 945\n\n### Answer:\nNormally, I would use the method used by Bunuel. It's the most accurate. But if you are looking for a speedy solution, you can use another method which will sometimes give you an estimate. Looking at the options (most of them are spread out), I wont mind trying it. (Mind you, the method is accurate here since the numbers start from 1.)\nIn 1000 consecutive numbers, number of multiples of 11 = 1000/11 = 90 (Ignore decimals)\nIn 1000 consecutive numbers, number of multiples of 35 = 1000/35 = 28\nNumber of multiples of 11*35 i.e. 385 = 1000/385 = 2\nNumber of integers from 1 to 1000 that are divisible by neither 11 nor by 35 = 1000 - (90 + 28 - 2) {Using the concept of sets here) = 892\nThink: Why did I say the method is approximate in some cases?\nThink what happens if the given range is 11 to 1010 both inclusive (again 1000 numbers)\nWhat is the number of multiples in this case?\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA and B walk around a circular track. A and B walk at a speed of 2 rounds per hour and 3 rounds per hour respectively. If they start at 8 a.m. from the same point in opposite directions, how many times shall they cross each other before 10 a.m.?\n\n### Options:\nA. 5\nB. 6\nC. 7\nD. 8\nE. 10\n\n### Answer:\nRelative speed = Speed of A + Speed of B (? they walk in opposite directions)\n= 2 + 3 = 5 rounds per hour\n=> They cross each other 5 times in 1 hour\nTime duration from 8 am to 10 am = 2 hour\nHence they cross each other 10 times before 10 am\nAnswer is E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA, Band C enter into a partnership by investing in the ratio of 3 : 2: 4. After 1 year, B invests another Rs. 2,70,000 and C, at the end of 2 years, also invests Rs.2,70,000. At the end of three years, profits are shared in the ratio of 3 : 4 : 5. Find initial investment of each.\n\n### Options:\nA. 360000;180000;270000\nB. 270000;180000;360000\nC. 180000;360000;270000\nD. 270000;360000;270000\nE. None of them\n\n### Answer:\nLet the initial investments of A, Band C be Rs. 3x, Rs. 2x and Rs. 4x respectively. Then,\n(3x x 36) : [(2x x 12) + (2x + 270000) x 24] : [(4x x 24) + (4x +270000) x 12]=3:4:5\n1O8x : (72x + 6480000) : (144x + 3240000) = 3 : 4 : 5\n108x /(72x+6480000)=3/4 \uf0f3 432x = 216x + 19440000\n=216x = 19440000\n=x=90000\nHence, A\u2019s initial investment = 3x = Rs. 2,70,000;\nB's initial investment = 2x = Rs. 1,80,000;\nC's initial investment = 4x = Rs. 3,60,000.\nAnswer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 14 kmph and 21 kmph respectively. When they meet, it is found that one train has traveled 60 km more than the other one. The distance between the two stations is?\n\n### Options:\nA. 11\nB. 444\nC. 420\nD. 287\nE. 221\n\n### Answer:\n1h ----- 5\n? ------ 60\n12 h\nRS = 14 + 21 = 35\nT = 12\nD = 35 * 12 = 420\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nBob wants to run a mile in the same time as his sister. If Bob\u2019s time for a mile is currently 10 minutes and his sister\u2019s time is currently 8 minutes 48 seconds, by what percent does Bob need to improve his time in order run a mile in the same time as his sister?\n\n### Options:\nA. 3%\nB. 5%\nC. 8%x\nD. 10%\nE. 12%\n\n### Answer:\nBob's time = 600 secs.\nHis sis' time = 528 secs.\nPercent increase needed = (600-528/600) * 100 = 72/600 * 100 = 12%. Ans (E).\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA woman bought a pack of 36 eggs, but the seller told her that there were 3 rotten eggs in the pack. She forgot it and begun to prepare a recipe that needs 2 eggs. What is the probability that both choosen eggs will be rotten?\n\n### Options:\nA. 1/210\nB. 2/210\nC. 3/210\nD. 1/119\nE. 2/119\n\n### Answer:\nThere are 3 rotten eggs in a pack of 36. Thus the probability of picking 2 rotten eggs is: (3/36)(2/35) = 1/210. The correct answer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe parameter of a square is equal to the perimeter of a rectangle of length 16 cm and breadth 14 cm. Find the circumference of a semicircle whose diameter is equal to the side of the square. (Round off your answer to two decimal places)\n\n### Options:\nA. 77.14 cm\nB. 47.14 cm\nC. 84.92 cm\nD. 94.94 cm\nE. 23.57 cm\n\n### Answer:\nLet the side of the square be a cm.\nParameter of the rectangle = 2(16 + 14) = 60 cm Parameter of the square = 60 cm\ni.e. 4a = 60\nA = 15\nDiameter of the semicircle = 15 cm\nCircimference of the semicircle\n= 1/2(\u220f)(15)\n= 1/2(22/7)(15) = 330/14 = 23.57 cm to two decimal places\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe president of a country and 6 other dignitaries are scheduled to sit in a row on the 7 chairs represented above. If the president must sit in the center chair, how many different seating arrangements are possible for the 5 people?\n\n### Options:\nA. 720\nB. 5\nC. 20\nD. 24\nE. 120\n\n### Answer:\nIMO A\nGiven that one chair is taken, i think the remaining 6 dignitaries can be arranged 6!. That is 6*5*4*3*2*1=720.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOf the science books in a certain supply room, 50 are on botany, 65 are on zoology, 90 are on physics. 30 are on geology, and 100 are on chemistry. If science books are removed randomly from the supply room, how many must be removed to ensure that 80 of the books removed are on the same science?\n\n### Options:\nA. 81\nB. 159\nC. 166\nD. 285\nE. 304\n\n### Answer:\nI solve it using the tough luck technique:\nAccording to question: What is the least number of books you should pick so as to get at least 80 books of the same science subject.\n80 books of the same science subjects is possible only for two subjects: Physics=90>80 OR Chemistry=100>80\nNow, we need to be certain that out of the books we picked, there are either at least 80 physics books or 80 chemistry books\nWhat if we pick the first 80 books and none of them is either Physics or Chemistry. Possible. Thus, we first count all our negatives.\nWe picked:\n50 Botany Books\n65 Zoology Books\n30 Geology Books\nNow, any book we pick will be either Chemistry or Physics. But unfortunately, we can't be lucky enough to pick 80 books and all of them will be Physics, right!!\nThus, in order to make sure that we have 80 books of either of these 2 subjects, we must pick\n79*2+1 books\nBecause, we could have picked the books in following order;\n1st book picked: Physics\n2nd book picked: Chemistry\n3rd book picked: Physics\nThus, Total= 50+65+30+79*2+1=145+1+158=304\nAns:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nX and Y started a business by investing Rs.36000 and Rs.42000 respectively after 4 months Z joined in the business with an investment of Rs.48000, then find share of Z in the profit of Rs.13970 ?\n\n### Options:\nA. 3200\nB. 4064\nC. 3250\nD. 3825\nE. 3985\n\n### Answer:\nRatio of investment, as investments is for different time.\nInvestment x Number of units of time.\nRatio of investments X : Y : Z = 36000 : 42000 : 48000 => 6 : 7 : 8.\nX = 6 x 12 Months = 72, Y = 7 x 12 = 84, Z = 8 X 8 = 64 => 18 : 21 : 16.\nRatio of investments => X : Y : Z = 18 : 21 : 16.\nInvestment Ratio = Profit sharing Ratio.\nZ = 13970 \u00c3\u2014 16/55 = Rs.4064.\nShare of Z in the profit is Rs.4064.\nOption B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the remainder when 1201 \u00d7 1202 \u00d71203 \u00d7 1207 is divided by 6?\n\n### Options:\nA. 0\nB. 1\nC. 2\nD. 3\nE. 4\n\n### Answer:\nThe remainders when dividing each number by six are: 1, 2, 3, and 1.\nThe product is 1*2*3*1 = 6\nThe remainder when dividing 6 by 6 is 0.\nThe answer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThree cards are drawn successively, without replacement from a pack of 52 well shuffled cards.\nWhat is the probability that first two cards are queens and the third card drawn is an ace?\n\n### Options:\nA. 2\nB. 2/5525\nC. 2/5527\nD. 3\nE. None\n\n### Answer:\nLet Q denote the event that the card drawn is queen and A be the event that\nthe card drawn is an ace. Clearly, we have to find P (QQA)\nNow P(Q) = 4/52\nAlso, P (Q|Q) is the probability of second queen with the condition that one queen has\nalready been drawn. Now there are three queen in (52 - 1) = 51 cards.\nTherefore P(Q|Q) = 3/51\nP(A|QQ) is the probability of third drawn card to be an ace, with the condition\nthat two queens have already been drawn. Now there are four aces in left 50 cards.\nTherefore P(A|QQ) = 4/50\nBy multiplication law of probability, we have\nP(QQA) = P(Q) P(Q|Q) P(A|QQ)\n= 4/52 \u00d7 3/51 \u00d7 4/50\n= 2/5525.\nAnswer: Option 'B'\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf x/5 - 6/x = 1/5, what are the values of 3x - 7?\n\n### Options:\nA. -22 and 11\nB. 8 and 24\nC. 17 and 21\nD. 12 and 29\nE. 17 and 29\n\n### Answer:\nI got the same thing A is the answer -22 or 11\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe value of x + x(x*x*(in x)) when x = 2 is:\n\n### Options:\nA. 10\nB. 16\nC. 18\nD. 36\nE. 64\n\n### Answer:\nx + x(xx)\nPut the value of x = 2 in the above expression we get,\n2 + 2(22)\n= 2 + 2(2 \u00d7 2)\n= 2 + 2(4)\n= 2 + 8\n= 10\nCorrect Answer:A)10\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA clothing store originally bought 100 jackets at a total cost of j dollars. If each jacket was sold for 70 percent more than its original cost, what was the individual price, in terms of j, of each jacket sold?\n\n### Options:\nA. j/59\nB. 7j/500\nC. 140j\nD. j/100+40\nE. 140j/100\n\n### Answer:\nlets take j=1000, as decided by you..\nnow 70% increase makes it 1700..\nthis is the price for 100 jackets, so selling price for each jacket=1700/100=$17..\nso ans is correct as A..\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the maximum number of pieces of birthday cake of size 10\u201d by 10\u201d that can be cut from a cake 20\u201d by 20\u201d?\n\n### Options:\nA. 4\nB. 10\nC. 16\nD. 20\nE. 25\n\n### Answer:\nThe prompt is essentially asking for the maximum number of 10 x 10 squares that can be cut from a larger 20 by 20square. Since each 'row' and each 'column' of the larger square can be sub-divided into 2 'pieces' each, we have (2)(2) = 4 total smaller squares (at maximum).\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nx is the product of each integer from 1 to 100, inclusive and y=100^k, where k is an integer . What is the greatest value of k for which y is a factor of x?\n\n### Options:\nA. 5\nB. 6\nC. 8\nD. 10\nE. 12\n\n### Answer:\nThe number of trailing zeros in the decimal representation of n!, the factorial of a non-negative integer n, can be determined with this formula:\nn5+n52+n53+...+n5k, where k must be chosen such that 5k\u2264n\nx = 1*2*3....*100 = 100!\nNo. of trailing zeros in 100! = 100/5 + 100/5^2 = 20+4 = 24\n100^k = 10^2k \u2192 k = 24/2 = 12\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe area of sector of a circle whose radius is 12 metro and whose angle at the center is 41\u00b0 is?\n\n### Options:\nA. 49m2\nB. 50m2\nC. 51.5m2\nD. 53m2\nE. 59m2\n\n### Answer:\n41/360 * 22/7 * 12 * 12\n= 51.5 m2\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n10 speakers gathered to deliver speeches on two topics. Even though 10 speeches were initially planned to be delivered, due to lack of time only 2 speeches were finally decided to be delivered. Topics are to be spoken in a specific order and the speeches differ with respect to speaker or topic. How many such two speeches are possible?\n\n### Options:\nA. 2\nB. 20\nC. 50\nD. 100\nE. 1024\n\n### Answer:\n1)there are 10 speeches in ONE topic and 10 in OTHER..\n2)there is a specific order for topics, so\na) both the topics are to be spoken on- so ONE from each\nb) the order does not matter since there is ONLY one specific order..\nso 10C1\u221710C1=10\u221710=100\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe G.C.D. of 1.08, 0.36 and 0.15 is?\n\n### Options:\nA. 0.03\nB. 0.9\nC. 0.03\nD. 0.108\nE. none of these\n\n### Answer:\nGiven numbers are 1.08,0.36 and 0.15.\nH.C.F of 108, 36 and 15 is 3\nH.C.F of given numbers=0.03.\nCorrect Options:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man buys an article and sells it at a profit of 20%. If he had bought it at 20% less and sold it for Rs.55 less, he could have gained 25%. What is the cost price?\n\n### Options:\nA. 197\nB. 375\nC. 275\nD. 278\nE. 268\n\n### Answer:\nCP1 = 100 SP1 = 120\nCP2 = 80 SP2 = 80 * (125/100) = 100\n20 ----- 100\n55 ----- ? => 275\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n1/2 is what percent of 1/3\n\n### Options:\nA. 150%\nB. 200%\nC. 250%\nD. 300%\nE. None of these\n\n### Answer:\nExplanation:\n1/2/1/3 * 100 = 1/2 * 3/1 * 100 = 150 %\nOption A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n?% of 360 = 180\n\n### Options:\nA. 277\nB. 36\nC. 50\nD. 72\nE. None of these\n\n### Answer:\n?% of 360 = 180\nor, ? = 180\u00d7100/360=50\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf Q is a positive integer, and Q/15 = 8.2, what is the remainder when Q is divided by 15?\n\n### Options:\nA. A.1\nB. B.2\nC. C.3\nD. D.4\nE. E.8\n\n### Answer:\nIf Q were a multiple of 15, the quotient Q/15 would be an integer. The fact that it's a decimal tells us that 15 goes into Q eight whole times and some decimal part of a time. This decimal part, 0.2 is the remainder divided by the divisor. Let R be the remainder.\nR/15 = 0.2 = 1/5\nR = (15)*(1/5) = 3\nAnswer =(C)\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf TIER is written as 7163 and BRAIN is written as 23415, how is RENT coded ?\n\n### Options:\nA. 7536\nB. 7653\nC. 3657\nD. 3765\nE. None of these\n\n### Answer:\nExplanation:\nGiven :\nLetter : T I E R B A N\nCode : 7 1 6 3 2 4 5\nThus, the code for RENT is 3657.\nANSWER C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFor any positive number x, the function [x] denotes the greatest integer less than or equal to x. For example, [1] = 1, [1.367] = 1 and [1.996] = 1. If k is a positive integer such that k^2 is divisible by 45 and 80, what is the units digit of k^3/4000 ?\n\n### Options:\nA. 0\nB. 1\nC. 0\nD. 54\nE. Cannot be determined\n\n### Answer:\nK=[lCM of 80 and 45] * (any integer)\nhowever minimum value of k is sq.rt of 3^2*4^2*5^2 = 60 * any integer\nfor value of k(60) * any integer unit value will be always zero .\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRahul's Mathematics test had 75 problems, 10 arithmetic, 30 algebra, 35 geometry problems.\nAlthough he answered 74% of arithmetic, 40% of arithmetic and 60% of geometry problems correctly,\nstill he got less than 58% problems right. How many more questions he would have to answer more to get\npassed\n\n### Options:\nA. 3\nB. 6\nC. 7\nD. 8\nE. 9\n\n### Answer:\nExplanation:\nNumber of questions attempted correctly = (70% of 10 + 40% of 30 + 60% of 35)\n= 7 + 12 + 21 = 40.\nQuestions to be answered correctly for 58% = 58% of total quations\n= 58 % of 74 = 43.\nHe would have to answer 43 - 40 = 3\nAnswer: Option A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe ratio, by volume, of soap to alcohol to water in a certain solution is 4:40:90. The solution will be altered so that the ratio of soap to alcohol is doubled while the ratio of soap to water is halved. If the altered solution will contain 200 cubic centimeters of alcohol, how many cubic centimeters of water will it contain?\n\n### Options:\nA. 1300\nB. 1500\nC. 1600\nD. 1700\nE. 1800\n\n### Answer:\nsoap:alcohol\nInitial ratio soap:alcohol: water --> 4:40:90\nInitial soap:alcohol = 4/40 =4:40\nafter doubled soap:alcohol =2* 4/40 = 8:40\nInitial soap:water = 4/90=4:90\nafter halved soap:water: 1/2 * 4/90 = 2/90 = 2:90\nAfter soap: alcohol:water --> 8:40:360-->1:5:45\ngiven alcohol 200 cubic centimeter.\nratio is 40:200:1800(1:5:45)\nFor 200 cubic centimeter of Alcohol --- 1800cubic cm water is required.\nAnswer-E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train 150 m long is running with a speed of 68 kmph. In what time will it pass a man who is running at 8 kmph in the same direction in which the train is going ?\n\n### Options:\nA. 5 seconds\nB. 6 seconds\nC. 9 seconds\nD. 8 seconds\nE. 7 seconds\n\n### Answer:\nRelative speed of train and man=60kmph or 300/18m/s\nTime taken by the train to pass the man:\nLength of the train/relative speed\n150/300/18=9 seconds.\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe area of the floor of a room is 20 m2 that of a longer wall 15 m2 and of the shorter wall 12 m2, find the edge of the new cube?\n\n### Options:\nA. 50 m^3\nB. 60 m^3\nC. 70 m^3\nD. 80 m^3\nE. 100 m^3\n\n### Answer:\nExplanation:\nlb = 20 ; lh = 15 ; fh = 12\n(lbh)2 = 20 * 15 * 12 => lbh = 60 m^3\nB)\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n300 metres long yard, 26 trees are palnted at equal distances, one tree being at each end of the yard. What is the distance between 2consecutive trees\n\n### Options:\nA. 10\nB. 12\nC. 14\nD. 16\nE. 17\n\n### Answer:\n26 trees have 25 gaps between them,\nRequired distance (300/25) = 12\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSimplify (212 * 212 + 312 * 312 )\n\n### Options:\nA. 132288\nB. 142088\nC. 142188\nD. 142288\nE. None of these\n\n### Answer:\nExplanation:\nTrick: Above equation can be solved by using following formula\n(a2+b2)=1/2((a+b)2+(a\u2212b)2)\nOption D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAlok ordered 16 chapatis, 5 plates of rice, 7 plates of mixed vegetable and 5 ice-cream cups. The cost of each chapati is Rs.6, that of each plate of rice is Rs.45 and that of mixed vegetable is Rs.70. The amount that Alok paid the cashier was Rs.961. Find the cost of each ice-cream cup?\n\n### Options:\nA. 25\nB. 30\nC. 29\nD. 12\nE. 20\n\n### Answer:\nExplanation:\nLet the cost of each ice-cream cup be Rs.x\n16(6) + 5(45) + 7(70) + 6(x) = 961\n96 + 225 + 490 + 5x = 961\n5x = 150 => x = 30.\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are 5,290 feet in 1 mile and 12 inches in one foot. How many inches are in a mile?\n\n### Options:\nA. 5,280 - 12\nB. 5,280/12\nC. 12(5,280)\nD. 12^2(5,280)\nE. 12*5,290\n\n### Answer:\n1 feet = 12 inches\n1 mile = 5290 feet\n1 mile = 5290*12 inches\nAns: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a soccer bet,we play 4 teams.first team odd 1.30,second 5.23,third 3.25,fourth 2.05.we place the bet with 5.00 euros.\nhow much money we expect to win?\n\n### Options:\nA. 219.5\nB. 226.49\nC. 235.01\nD. 266.74\nE. 669.0\n\n### Answer:\nin the case we won the bet,we have:\n1.30* 5.23* 3.25* 2.0*5.00=219.50\nwe will win 226.49\nso correct answer is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA shopkeeper sells 400 metres of cloth for Rs. 18000 at a loss of Rs.5 per metre. Find his cost price for one metre of cloth?\n\n### Options:\nA. 35\nB. 77\nC. 28\nD. 50\nE. 22\n\n### Answer:\nExplanation:\nSP per metre = 18000/400 = Rs. 45 Loss per metre = Rs. 5 CP per metre\n= 45 + 5\n= Rs. 50\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA is twice as good a workman as B and they took 7 days together to do the work B alone can do it in.\n\n### Options:\nA. 11 days\nB. 13 days\nC. 21 days\nD. 16 days\nE. 18 days\n\n### Answer:\nWC = 2:1\n2x + x = 1/7\nx = 1/21 => 21 days\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a game of 80 points; A can give B 5points and C 15 points. Then how many points Bcan give C in a game of 60 ?\n\n### Options:\nA. 8\nB. 9\nC. 10\nD. 11\nE. 12\n\n### Answer:\nA: B = 80 : 75, A : C = 80 : 65.\nB/C = ( B/ A * A/C) = (75 / 80 * 80 / 65) = 15/13 = 60 /52 = 60: 5\nTherfore ,In a game of 60, B can give C 8 points\nOption A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA family consists of two grandparents, two parents and three grandchildren. The average age of the grandparents is 67 years, that of the parents is 35 years and that of the grandchildren is 6 years. What is the average age of the family?\n\n### Options:\nA. 28 4/7 years\nB. 31 5/7 years\nC. 32 1/7 years\nD. None of these\nE. 31\n\n### Answer:\nRequired average\n=((67 x 2 + 35 x 2 + 6 x 3)/(2 + 2 + 3))\n=(134 + 70 + 18)/7\n=222/7\n= 31 5/7\tyears.\nAnswer : B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOf 25 applicants for a job, 14 had at least 4 years' experience, 18 had degrees, and 3 had less than 4 years' experience and did not have a degree. How many of the applicants had at least 4 years' experience and a degree?\n\n### Options:\nA. 14\nB. 10\nC. 9\nD. 7\nE. 5\n\n### Answer:\nset A : people with more than 4 years exp\nset B : people with degree\nAUB = total - (less than 4 exp and no degree)\nAUB = 25-3=22\nAUB = A + B - AiB\nAiB = 18+14-22\n=10\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the difference between the largest and the smallest number written with 7, 7, 0, 7?\n\n### Options:\nA. 6893\nB. 6993\nC. 6093\nD. 693\nE. None\n\n### Answer:\n7770\n7077\n-------------\n693\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the twenty-fourth decimal to the right in the fraction 47/48?\n\n### Options:\nA. 1\nB. 2\nC. 4\nD. 6\nE. 8\n\n### Answer:\n47/48 = 0.979166666666666....\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA trader bought a car at 20% discount on its original price. He sold it at a 55% increase on the price he bought it. What percent of profit did he make on the original price?\n\n### Options:\nA. 17%\nB. 24%\nC. 12%\nD. 82%\nE. 16%\n\n### Answer:\nOriginal price = 100\nCP = 80\nS = 80*(155/100) = 124\n100 - 124 = 24%\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain college party is attended by both male and female students. The ratio of male to female students is 4 to 5. If 9 of the male students were to leave the party, the ratio would change to 1 to 2. How many total students are at the party?\n\n### Options:\nA. 46\nB. 50\nC. 54\nD. 58\nE. 62\n\n### Answer:\nThe ratio is 4:5 = 8:10, so there are 8k males and 10k females.\nIf 9 males left, the ratio would be 1:2 = 5:10, so there would be 5k males and 10k females.\n8k-5k = 9\nk = 3\n8k + 10k = 24 + 30 = 54\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe present population of a town is 1000. Population increase rate is 25% p.a. Find the population of town after 2 years?\n\n### Options:\nA. 1000\nB. 2000\nC. 1563\nD. 2153\nE. 1245\n\n### Answer:\nP = 1000\nR = 25%\nRequired population of town = P(1 + R/100)^T\n= 1000(1 + 25/100)^2\n= 1000(5/4)^2\n= 1563(approximately)\nAnswer is C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nKevin plants corn and cotton. Once he harvests the crops, he has 30 pounds of corn and x\npounds of cotton. Corn sells for $5 per pound and cotton sells for $10 per pound. If Kevin sells\nall his corn and cotton for a total of $640, then compute x.\n\n### Options:\nA. 39\nB. 49\nC. 59\nD. 69\nE. 79\n\n### Answer:\nKevin sells his corn for 305 dollars and his cotton for x10 dollars. Thus 30-5+x*10 =\n640, so x = 640-30*5/10 = 490/10 = 49 .\ncorrect answer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n1(1!)+2(2!)+3(3!)....2012(2012!) = ?\n\n### Options:\nA. 1\nB. 5\nC. 6\nD. 7\nE. 8\n\n### Answer:\n1(1!)=1 \u21d2\u21d2 2!-1\n1(1!)+2(2!)=1+4=5 \u21d2\u21d2 3!-1\n1(1!)+2(2!)+3(3!)=1+4+18=23 \u21d2\u21d2 4!-1\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA starts business with a capital of Rs.1200 B and C join with some investments after 3 and 6 months respectively. If the end of a year, the profit is divided in the ratio 2:3:5 respectively. What is B's investment in the business?\n\n### Options:\nA. 2400\nB. 2880\nC. 2787\nD. 3087\nE. 0728\n\n### Answer:\n1200 * 12: x * 9 = 2:3\nx = 2400\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n17 chess players take part in a tournament. Every player plays twice with each of his opponents. How many games are to be played?\n\n### Options:\nA. 154\nB. 184\nC. 240\nD. 272\nE. 306\n\n### Answer:\n2*17C2 = 2*136 = 272\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAn article is bought for Rs.600 and sold for Rs.500, find the loss percent?\n\n### Options:\nA. 16 2/3%\nB. 16 7/3%\nC. 19 2/3%\nD. 16 2/3%\nE. 16 4/3%\n\n### Answer:\n600 ---- 100\n100 ---- ? => 16 2/3%\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 5^k + 5^k = (5^9)^(5^9) - 5^k, then k = ?\n\n### Options:\nA. 5^11 - 1\nB. 11/2\nC. 242\nD. 3^10\nE. 3^11 - 1\n\n### Answer:\n5^k + 5^k = (5^9)^5^9 - 5^k\n5*(5^k) = 5 ^ (25 * 5^9 ) = 5^(5^2 * 5^9) = 5^(5^11)\n5^k+1 = 5^(5^11)\nSo k+1 = 5^11\nSo k = 5^11 -1\nAnswer is A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWithout stoppages, a train travels certain distance with an average speed of 200 km/h, and with stoppages, it covers the same distance with an average speed of 160 km/h. How many minutes per hour the train stops ?\n\n### Options:\nA. 8\nB. 9\nC. 10\nD. 11\nE. 12\n\n### Answer:\nDue to stoppages, it covers 40 km less .\nTime taken to cover 40 km = 40\u00e2\u0081\u201e200h = 1\u00e2\u0081\u201e5h\n= 1\u00e2\u0081\u201e5 \u00c3\u2014 60 min = 12 min\nAnswer E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain bacteria colony doubles in size every day for 22 days, at which point it reaches the limit of its habitat and can no longer grow. If two bacteria colonies start growing simultaneously, how many days will it take them to reach the habitat\u2019s limit?\n\n### Options:\nA. 6.33\nB. 7.5\nC. 21\nD. 15\nE. 19\n\n### Answer:\nIf there is one bacteria colony, then it will reach the limit of its habitat in 20 days.\nIf there are two bacteria colonies, then in order to reach the limit of habitat they would need to double one time less than in case with one colony. Thus colonies need to double 21 times.\nAnswer: C.\nSimilar questions to practice:\nHope it helps.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA 50 ml after-shave lotion at 30% alcohol is mixed with 30 ml of pure water. What is the percentage of alcohol in the new solution?\n\n### Options:\nA. 16.75%\nB. 17.75%\nC. 18.75%\nD. 19.75%\nE. None of these\n\n### Answer:\nThe amount of the final mixture is given by\n50 ml + 30 ml = 80 ml\nThe amount of alcohol is equal to the amount of alcohol in pure water ( which is 0) plus the amount of alcohol in the 30% solution. Let x be the percentage of alcohol in the final solution. Hence\n0 + 30% 50 ml = x (80)\nSolve for x\nx = 0.1817 = 18.75%\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf x = 1 + \u221a2, then what is the value of x4 - 4x3 + 4x2 + 1?\n\n### Options:\nA. -1\nB. 0\nC. 1\nD. 2\nE. 3\n\n### Answer:\nAnswer\nx = 1 + \u221a2\n\u2234 x4 - 4x3 + 4x2 + 5 = x2(x2 - 4x + 4) + 1\n= x2(x - 2)2 + 1\n= (1 + \u221a2)2(1 + \u221a2 - 2)2 + 1\n=(\u221a2 + 1)2 (\u221a2 - 1)2 + 1\n=[(\u221a2)2 - (1)2]2 + 1\n=(2 - 1)2 =1 + 1=2\nCorrect Option: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many positive integers less than 160 are there such that they are multiples of 13 or multiples of 12 but not both?\n\n### Options:\nA. 18\nB. 19\nC. 20\nD. 23\nE. 25\n\n### Answer:\nfor 13: 13...160=13*12\nfor 12: 12...156=12*13\nbut there is one integer 13*12. so\nN=(12-1)+(13-1)=23\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA password of a computer consists of nine digits 1 through 7. What is the probability that the first digit is a 2 and the second digit is divisible by 3 ?\n\n### Options:\nA. 1/9\nB. 1/21\nC. 1/24.5\nD. 1/49\nE. 1/98\n\n### Answer:\nThere is one possibility out of seven that the first digit is correct, and two possibilities that the second digit is correct (3 and 6). We don't care about the remaining digits, so the overall probability is 1/7 * 2/7 or 1/24.5 (answer C)\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are two examinations rooms A and B. If 10 students are sent from A to B, then the number of students in each room is the same. If 20 candidates are sent from B to A, then the number of students in A is double the number of students in B. The number of students in room A is:\n\n### Options:\nA. 20\nB. 80\nC. 100\nD. 200\nE. 220\n\n### Answer:\nLet the number of students in rooms A and B be x and y respectively.\nThen, x - 10 = y + 10 x - y = 20 .... (i)\nand x + 20 = 2(y - 20) x - 2y = -60 .... (ii)\nSolving (i) and (ii) we get: x = 100 , y = 80.\nThe required answer A = 100.\nAnswer: Option C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe Malibu Country Club needs to drain its pool for refinishing. The hose they use to drain it can remove 60 cubic feet of water per minute. If the pool is 60 feet wide by 100 feet long by 10 feet deep and is currently at 80% capacity, how long will it take to drain the pool?\n\n### Options:\nA. 1000\nB. 1400\nC. 1200\nD. 800\nE. 1000\n\n### Answer:\nvolume of pool = 60*100*10 cu.ft , 80% full = 60*100*10*0.8 cu.ft water is available to drain.\ndraining capacity =60 cu.ft /min therefore time taken = 60*100*10*0.8/ 60 min= 800 min\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf N = 2^0.3 and N^b = 16, b must equal\n\n### Options:\nA. 3/80\nB. 3/5\nC. 4\nD. 5/3\nE. 40/3\n\n### Answer:\n30/100 = 3/10\nN = 2 ^ 3/10\nN^b = 2^4\n(2^3/10)^b = 2^4\nb = 40/3\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\na man owns 2/3 of market reserch beauro buzness,and sells 3/4 of his shares for 45000rs,what is the value of buzness?\n\n### Options:\nA. 150000\nB. 90000\nC. 85000\nD. 190000\nE. 250000\n\n### Answer:\nIf value of business=x\nTotal sell (2x/3)(3/4)=45000\n->x=150000\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nDeby normally drives to work in 45 minutes at an average speed of 40 miles per hour. This week, however, she plans to bike to work along a route that decreases the total distance she usually travels when driving by 20% . If Deby averages between 12 and 16 miles per hour when biking, how many minutes earlier will she need to leave in the morning in order to ensure she arrives at work at the same time as when she drives?\n\n### Options:\nA. 135\nB. 105\nC. 95\nD. 75\nE. 45\n\n### Answer:\nDeby normally drives to work in 45 minutes at an average speed of 40 miles per hour.Use formula D = RT\nCar:\nT1: 45 min\nR1: 40 mph\nD1: [(40*45)/60] = 30 miles\nBike:\nT1:?\nR2: 12 - 16 mph\nD2: 08*D1 = 24 miles\nT1: [(24*60)/12] = 120 min (Only 12 mph speed yields an answer given in the choices)\nTherefore, Deb has to leave 120 min - 45 min = 75 min early\nANSWER: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe ratio of red boxes to blue boxes in a certain warehouse is 12 to 20. If the number of the red boxes were doubled and the number of blue boxes were increased by 150 the ratio would be halved. How many total boxes are in the warehouse?\n\n### Options:\nA. 80\nB. 74\nC. 111\nD. 148\nE. 244\n\n### Answer:\nRatio = R/B = 12/20 or R = 12/20 B -----------(1)\n2R/B+150 = 12/20*1/2 = 6/20 or we can say that 20R=3B+450 -------------(2)\nsolving (1) and (2) we get\nB=50 and R = 30\nso total boxes is B + R = 50+30=80\nHence A. 80 is the correct answer\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn an election between two candidates first candidate got 60% of votes polled and second Candidate got 290 votes. The total number of votes polled was?\n\n### Options:\nA. votes\nB. votes\nC. votes\nD. votes\nE. votes\n\n### Answer:\nTotal = 100 %,\nFirst person got 60%\nsecond person got remaining 40 % of votes.\nthan 40 % = 290\n40% = 40\u00d77 = 290\n100% =100\u00d77 =700 votes\nA)\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\na, b, c, d, and e are positive consecutive odd integers and a < b < c < d < e.\nIf the sum of a+c+e is four less than the square of b, what is the product of de?\n\n### Options:\nA. 25\nB. 35\nC. 53\nD. 99\nE. 143\n\n### Answer:\na+c+e = bb - 4\nBecause we know the numbers are consecutive odd integers, we can rewrite the list as versions of the first number:\nb = a+2\nc = a+4\nd = a+6\ne = a+8\nTherefore we can rewrite the original problem: a+(a+4)+(a+8) = (a+2)(a+2) - 4\nSimplify: 3a + 4 + 8 = (aa + 4a + 4) - 4\nSimplify: 3a + 12 = aa + 4a\nSwap (just switch the sides in their entirety): aa + 4a = 3a + 12\nSeparate the number from the variables: aa + 4a - 3a = 12\nSimplify: aa + a = 12\nSo the square of a, plus another a, equals 12. We can try out a few numbers quickly:\n1x1 = 1, +1 = not 12\n5x5 = 25, +5 = not 12\n3x3 = 9, +3 = there we go!\nSo a = 3, and the sequence of consecutive odd numbers is 3, 5, 7, 9, 11.\nThe answer is the product of the last two numbers: 9x11 = 99 (option D).\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a 500 m race, the ratio of speeds of two runners P and Q is 3:5. P has a start of 200 m then the distance between P and Q at the finish of the race is:\n\n### Options:\nA. Both reach at the same time\nB. P wins by 100 m\nC. Q wins by 50 m\nD. Q wins by 100 m\nE. None of these\n\n### Answer:\nExplanation :\nWhen P starts running for 300 m and Q for 500 m then, the ratio of speeds of P and Q is 3 : 5.\nAccording to question P has already covered 200 m when Q is starting at starting point and Q needs to cove 300 m more mean while P covers this 300 m when Q can cover 500 m. So, both P and Q will reach the finishing point at the same time.\nThus, Both reach at the same time.\nAnswer : A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 125% of j is equal to 25% of k, 150% of k is equal to 50% of l, and 175% of l is equal to 75% of m, then 20% of m is equal to what percent of 100% of j ?\n\n### Options:\nA. 0.35\nB. 3.5\nC. 35\nD. 350\nE. 700\n\n### Answer:\nIMO answer should be 350...\nconsider j=10, then k=50, l=150 and m=350....\n20% of 350, comes out to be 70....\n100% of 10 is 10....\n(70*100)/10=700....\nAns : E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how many ways can a four-letter password be chosen, using the letters A, B, C, D, E, F, and/or G such that at least one letter is repeated within the password?\n\n### Options:\nA. 720\nB. 864\nC. 900\nD. 936\nE. 1561\n\n### Answer:\nTotal number of four letter passwords = 7*7*7*7= 2401 ------(1)\nTotal number of passwords in which no letter repeats = 7C4*4!= 35*24=840------(2)\ntherefore required value = (1)-(2)= 2401-840=1561\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\njudith is practicing her dance steps along with her friends. In a particular sequence, all of them form a row. At that point, judithis standing on the 4th position from either end of the row.\nCan you find out how many girls are practicing together?\n\n### Options:\nA. 4\nB. 9\nC. 7\nD. 6\nE. 8\n\n### Answer:\nAs judith is 4th from either end of the row, it means that 3 girls are on one of her sides and 3 are present on the other.\n3 + 3 + 1(judith herself) = 7.\nHence, 7 girls are practicing the dance together.\ncorrect answer is C)7\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA person can swim in still water at 12 km/h. If the speed of water 2 km/h, how many hours will the man take to swim back against the current for 10km?\n\n### Options:\nA. 1\nB. 4\nC. 5\nD. 6\nE. 7\n\n### Answer:\nM = 12\nS = 2\nUS = 12 - 2 = 10\nD = 10\nT = 10/10 = 1 Answer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nArun spent six lucky days in Las Vegas. On his first day he won a net amount of only $20, but on each of the following days, the daily net amount he won grew by d dollars. If Arun won a total net amount of $1620 during his stay in Las Vegas, how much did he win on the last day?\n\n### Options:\nA. 330\nB. 500\nC. 520\nD. 540\nE. 620\n\n### Answer:\nI drew a diagram:\n1 - $20\n2 -\n3 -\n4 - $320\n5 -\n6 -\nTotal: $1,620\nBetween 1 and 6 are 5 days where he won $1,600. This means he averaged $320 per day (1600/5). You can put $320 by 4 because it's the middle number. Now you just find the two points betwenn $20 and $320 (320-20 = 300 / 3 = 100). So each day, he earned $100 more. This means on day 6, Arun earned$520. Answer choice C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe population of a town increases 25% and 15% respectively in two consecutive years. After the growth the present population of the town is 1150. Then what is the population of the town 2 years ago?\n\n### Options:\nA. A)400\nB. B)500\nC. C)600\nD. D)700\nE. E)800\n\n### Answer:\nExplanation:\nFormula: (After =100 denominator\nAgo = 100 numerator)\n1150 * 100/125 * 100/115 = 800\nAnswer: Option E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMr Katial buys a house for Rs 1,00,000 and rents it. He puts 12.5% of each month\u2019s rent aside for upkeep and repairs, pays Rs 325 per year as taxes and realizes 5.5% annually on his investment . Find the monthly rent?\n\n### Options:\nA. Rs 634.76\nB. Rs 554.76\nC. Rs 654.76\nD. Rs 664.76\nE. none of these\n\n### Answer:\nLet the monthly rent be Rs X.\nWe have,\n5.5% of 100000 = 12 (X - 12.5% of X) - 325\n5500/12 = X - (X/8) - 325/12\n5500/12 + 325/12 = 7/8 x X\nX = 5825/12 x 8/7\nRs 554.76 per month\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe side of a square is increased by 25% then how much % does its area increases?\n\n### Options:\nA. 56.28 %\nB. 56.25 %\nC. 56.28 %\nD. 46.25 %\nE. 56.21 %\n\n### Answer:\na = 100 a2 = 10000\na = 125 a2 = 15625\n----------------\n10000 --------- 5625\n100 -------? => 56.25 %\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many 4-letter words with or without meaning, can be formed out of the letters of the word, 'LOGARITHMS', if repetition of letters is not allowed?\n\n### Options:\nA. 40\nB. 400\nC. 5040\nD. 5400\nE. 5800\n\n### Answer:\n'LOGARITHMS' contains 10 different letters.\nRequired number of words\t= Number of arrangements of 10 letters, taking 4 at a time.\n= 10P4\n= (10 x 9 x 8 x 7)\n= 5040.\nAnswer: Option C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA cylindrical bucket of height 36 cm and radius 21 cm is filled with sand. The bucket is emptied on the ground and a conical heap of sand is formed, the height of the heap being 12 cm. The radius of the heap at the base is :\n\n### Options:\nA. 63 cm\nB. 53 cm\nC. 56 cm\nD. 66 cm\nE. None of these\n\n### Answer:\nVolume of the bucket = volume of the sand emptied\nVolume of sand = \u03c0(21)2 \u00d7 36\nLet r be the radius of the conical heap.\nThen, 1\u20443\u03c0r2 \u00d7 12 = \u03c0(21)2 \u00d7 36\nor r2 = (21)2 \u00d7 9 or r = 21 \u00d7 3 = 63\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe cash realised on selling a 14% stock is Rs.101.25, brokerage being 1/4% is\n\n### Options:\nA. 123\nB. 106\nC. 100\nD. 101\nE. 240\n\n### Answer:\nExplanation:\nCash realised= Rs. (101.25 - 0.25)\n= Rs. 101.\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA can do a piece of work in 20days, and B can do it in 15days. How long will they take if both work together?\n\n### Options:\nA. 7days\nB. 8.6days\nC. 13days\nD. 5.6days\nE. 10days\n\n### Answer:\nA+B can do the work in 20*15 / 20+15 = 20*15/35 = 8.6days\nAnswer is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are two numbers. If 40% of the first number is added to the second number, then the second number increases to its five-fourth. Find the ratio of the first number to the second number?\n\n### Options:\nA. 5/9\nB. 5/7\nC. 5/3\nD. 5/8\nE. 5/1\n\n### Answer:\nLet the two numbers be x and y.\n40/100 * x + y = 5/4y\n=> 2/5 x = 1/4 y => x/y\n= 5/8\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the fourth proportional to 0.2,0.12 and 0.3?\n\n### Options:\nA. 0.18\nB. 0.21\nC. 0.22\nD. 0.34\nE. 0.45\n\n### Answer:\nFormula = Fourth propotional = (b \u00d7 c)/a\nA = 0.2 , B = 0.12 and C = 0.3\n(0.12 \u00d7 0.3)/0.2\n0.036/0.2 = 0.18\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf x and y are positive integers and 25x=10y what is the least possible value of xy?\n\n### Options:\nA. 14\nB. 25\nC. 63\nD. 84\nE. 252\n\n### Answer:\n25x=10y\n=> x/y = 2/5\n=> 5x=2y\n5(3)=2(3) => x*y=9 But it is not given\n5(5)=2(5) => x*y=25\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how many different ways can the letters of the word 'DETAIL' be arranged such that the consonants must occupy only the even positions?\n\n### Options:\nA. None of these\nB. 64\nC. 120\nD. 36\nE. 360\n\n### Answer:\nD\n3 consonants DTL can be arranged in 3!=6 ways. Similarly 3 vowels can be arranged on odd places in 3!=6 ways.\nTotal = 6*6 = 36.\nAnswer: D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFrom January 1, 1991, to January 1, 1993, the number of people enrolled in health maintenance organizations increased by 15 percent. The enrollment on January 1, 1993, was 45 million. How many million people, to the nearest million, were enrolled in health maintenance organizations on January 1, 1991 ?\n\n### Options:\nA. 38\nB. 39\nC. 40\nD. 41\nE. 42\n\n### Answer:\nSoln:-\n15x=45 --> 23/20*x=45 --> x=45*20/23=900/23=~39.\nAnswer: B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the function f(x) is defined for all real numbers x as the maximum value of 2x + 4 and 12 + 4x, then for which one of the following values of x will f(x) actually equal 2x + 4 ?\n\n### Options:\nA. \u20133\nB. \u20135\nC. \u20136\nD. \u20137\nE. \u20139\n\n### Answer:\nSince f(x) defines maximum of 2x + 4 and 12 + 4x,\nto find those x when 2x+4 has greater value,\n2x + 4 > 12 + 4x\nor x < -4\nOnly value that satisfy this is -5.\nAnswer is (B),\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA family consists of two grandparents, two parents and four grandchildren. The average age of the grandparents is 70 years, that of the parents is 40 years and that of the grandchildren is 6 years. What is the average age of family?\n\n### Options:\nA. 8/4years\nB. B)31\nC. C)30\nD. D)33\nE. E)35\n\n### Answer:\nRequired average\n= (70 x 2 + 40 x 2 + 6 x 4 )/(2 + 2 + 4)\n= (140 + 80 + 24)/8\n= 244/8\n= 30 8/4years.\nAnswer is A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many zeroes are there at the end of the number N, if N = 150! + 300! ?\n\n### Options:\nA. 28\nB. 31\nC. 34\nD. 37\nE. 40\n\n### Answer:\nThe number of zeroes at the end of 150! will be less than the number of zeroes at the end of 300!\nHence it is sufficient to calculate the number of zeroes at the end of 150!\nThe number of zeroes = [150/5] + [150/25] + [150/125] = 30 + 6 + 1 = 37\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA metallic sphere of radius 12 cm is melted and drawn into a wire, whose radius of cross section is 16 cm. What is the length of the wire?\n\n### Options:\nA. 7 cm\nB. 5 cm\nC. 2 cm\nD. 1 cm\nE. 9 cm\n\n### Answer:\nVolume of the wire (in Cylindrical shape) is equal to the volume of the sphere.\n\u03c0(16)2 * h\n= (4/3)\u03c0 (12)3\n=> h = 9 cm\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the present worth of Rs. 132 due in 2 years at 5% simple interest per annum\n\n### Options:\nA. 110\nB. 120\nC. 130\nD. 140\nE. 150\n\n### Answer:\nExplanation:\nLet the present worth be Rs.x\nThen,S.I.= Rs.(132 - x)\n=\u203a (x*5*2/100) = 132 - x\n=\u203a 10x = 13200 - 100x\n=\u203a 110x = 13200\nx= 120\nOption B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain truck uses 18 gallons of diesel fuel in traveling 230 miles. In order for the truck to travel the same distance using 10 gallons of diesel fuel, by how many miles per gallon must the truck\u2019s fuel mileage be increased?\n\n### Options:\nA. 8\nB. 9\nC. 12\nD. 15\nE. 27\n\n### Answer:\nThere are two sets 18G1 gallons and 10G2 gallons details given.\n18 gallons covering 230 miles\nThen 1 G1 is used to cover 15 miles.\nNow for 10 G2 covering 230 miles.\nthen 1 G2 is used to cover 23 miles.\nThere must 23 - 15 = 8 miles per gallon increment is needed for 10 gallons to improve the mileage to cover 230 miles.\nIMO A is correct answer.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn an election between two candidates, 70% of the voters cast their votes, out of which 4% of the votes were declared invalid. A candidate got 655200000 votes which were 75% of the total valid votes. Find the total number of votes enrolled in that election.\n\n### Options:\nA. 1300000000\nB. 12500\nC. 14000\nD. 12000\nE. None of these\n\n### Answer:\nExplanation :\nSolution: let the total number of votes enrolled be x. then, number of votes cast = 70% of x. valid votes = 96% of(70% of x). .'. 75% of(96% of (70% of of x)) = 655200000.\n(75/100 * 96/100 * 70/100 * x) = 655200000.\n=> x = (655200000*100*100*100)/(75*96*70) = 1300000000\nAnswer : A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSix mobsters have arrived at the theater for the premiere of the film \u201cGoodbuddies.\u201d One of the mobsters, Frankie, is an informer, and he's afraid that another member of his crew, Joey, is on to him. Frankie, wanting to keep Joey in his sights, insists upon standing behind Joey in line at the concession stand, though not necessarily right behind him. How many ways can the six arrange themselves in line such that Frankie\u2019s requirement is satisfied?\n\n### Options:\nA. 6\nB. 24\nC. 120\nD. 360\nE. 720\n\n### Answer:\nTotal arrangement of 6 = 6!. In half of the cases Frankie will be behind Joey and in half of the cases Joey will be behind Frankie (as probability doesn't favor any of them). So, the needed arrangement is 6!/2=360.\nAnswer: D (360)\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the odd man out\n1, 2, 5, 14, 41, 123\n\n### Options:\nA. 2\nB. 14\nC. 124\nD. 123\nE. 21\n\n### Answer:\n1*3-1 =2\n2*3-1 = 5\n5*3-1 = 14\n14*3-1 = 41\n41*3 -1 = 122\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the smallest number H which when increased by 5 is completely divisible by 8, 11 and 24?\n\n### Options:\nA. 264\nB. 259\nC. 269\nD. 270\nE. 282\n\n### Answer:\nThis question includes a number of great Number Property shortcuts that you can take advantage of:\n1) The question asks for the SMALLEST number that, when increased by 5 is divisible by 8, 11 and 24. Since the answers are numbers, we can TEST THE ANSWERS.\n2) Any number that is divisible by 24 is ALSO divisible by 8, so we really just need to consider the 11 and the 24.\n3) To be divisible by 24, the end number MUST be EVEN. Since we're adding 5 to get to that end number, the starting number MUST be ODD.\nThe last shortcut allows us to eliminate Answers A, D and E. Between Answers B and C, TESTING B first will prove that, when increased by 5, the end sum is divisible by both 11 and 24.\nFinal Answer:\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA question paper consists of five problems, each problem having three internal choices. In how many ways can a candidate attempt one or more problems?\n\n### Options:\nA. 1546\nB. 1054\nC. 1023\nD. 1608\nE. 1065\n\n### Answer:\nGiven that, the question paper consists of five problems. For each problem, one or two or three or none of the choices can be attempted.\nHence, the required number of ways = 45 - 1.\n= 210 - 1 = 1024 - 1 = 1023\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe length of the rectangular field is double its width. Inside the field there is square shaped pond 8m long. If the area of the pond is 1/8 of the area of the field. What is the length of the field?\n\n### Options:\nA. 54\nB. 32\nC. 75\nD. 28\nE. 11\n\n### Answer:\nA/8 = 8 * 8 => A = 8 * 8 * 8\nx * 2x = 8 * 8 * 8\nx = 16 => 2x = 32\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAt a garage sale, all of the items were sold at different prices. If the price of a radio sold at the garage sale was both the 15th highest price and the 22nd lowest price among the prices of the items sold, how many items were sold at the garage sale?\n\n### Options:\nA. 34\nB. 35\nC. 36\nD. 37\nE. 38\n\n### Answer:\nThere were 14 items sold at a higher price than the radio and 21 items sold at a lower price than the radio. Including the radio, there were 14 + 21 + 1 = 36 items sold.\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo trains are running in opposite directions with the same speed. If the length of each train is 360 m and they cross each other in 12 sec, then the speed of each train is?\n\n### Options:\nA. 22\nB. 77\nC. 36\nD. 108\nE. 21\n\n### Answer:\nLet the speed of each train be x m/sec.\nThen, relative speed of the two trains = 2x m/sec.\nSo, 2x = (360 + 360)/12 => x = 30\nSpeed of each train = 30 m/sec.\n= 30 * 18/5 =- 108 km/hr.\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the area of a parallelogram with base 12 cm and height 10 cm?\n\n### Options:\nA. 297 cm2\nB. 384 cm2\nC. 120 cm2\nD. 267 cm2\nE. 186 cm2\n\n### Answer:\nArea of a parallelogram\n= base * height\n= 12 * 10\n= 120 cm2\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf n is a prime number, which of the following could be true\n\n### Options:\nA. n^n=n\nB. n^2/4= is even\nC. (n)(n^n) = is negative\nD. n^n/4 = 1^(n-1)\nE. n^2+n^3= n^5\n\n### Answer:\nD should be the answer.\n2^2/4 = 1^(2-1)\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain office supply store stocks 2 sizes of self-stick notepads, each in 6 colors. The store packs the notepads in packages that contain either 3 notepads of the same size and the same color or 3 notepads of the same size and of 3 different colors. If the order in which the colors are packed is not considered, how many different packages of the types described above are possible?\n\n### Options:\nA. 6\nB. 8\nC. 16\nD. 24\nE. 52\n\n### Answer:\nNotepads of the same color = 6 (we have 6 colors). As we have two sizes then total for the same color=6*2=12\nNotepads of the different colors = 6C3=20 (we should choose 3 different colors out of 6). As we have two sizes then total for the different color=20*2=40\nTotal=40+12=52\nAnswer: E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nLiz drove from point A to point B at 40 Km/h. On her way back she drove at 50 Km/h and therefore her way back lasted one hour less. What is the distance (in Km) between A and B?\n\n### Options:\nA. 150\nB. 200\nC. 450\nD. 500\nE. 600\n\n### Answer:\nDistance is same\nS1t1=s2t2\n40t= 50 (t-1)\nt=5\ndistance= speed *time\n40*5= 200\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOver a three-week period, the price of an ounce of gold increased by 25% in the first week, decreased by 20% in the following week, and increased by 5% in the third week. If the price of gold was G dollars per ounce at the beginning of the three weeks, what was the price, in terms of G, at the end of the three weeks?\n\n### Options:\nA. 0.95G\nB. 1G\nC. 1.05G\nD. 1.1G\nE. 1.15G\n\n### Answer:\nInitial price =G\nBy end of first week increased by 25% => Price =1.25G\nBy end of second week decreased by 20% => Price= 1.25*0.8G\nBy end of third week increased by 5% => Price=1.25*0.8*1.05G\n=> Price= 1.05G\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 854 in 4 years. The sum is?\n\n### Options:\nA. 650\nB. 690\nC. 698\nD. 700\nE. 710\n\n### Answer:\nS.I. for 1 year = Rs. (854 - 815) = Rs. 39.\nS.I. for 3 years = Rs.(39 x 3) = Rs. 117.\nPrincipal = Rs. (815 - 117) = Rs. 698.\nAnswer: Option C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich of the following inequalities is always true for any real number 'x' and 'y'?\n\n### Options:\nA. |x-y| < |x| +|y|\nB. |x + y| > |y| + |x|\nC. |x + y| <= |x| + |y|\nD. |x - y| <= |x| - |y|\nE. |x - y| > |x| - |y|\n\n### Answer:\nThe answer is (C). One of the fundamental properties of absolute value, which is subadditivity, essentially means that evaluating the function for the sum of two elements (numbers) always returns something less than or equal to the sum of the function's values at each element; therefore, |x + y| <= |x| + |y|\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich of the following cannot be the sum of 2 different prime numbers?\n\n### Options:\nA. 10\nB. 13\nC. 14\nD. 15\nE. 19\n\n### Answer:\nOption A: 10 = 7 + 3. Sum of 2 different prime numbers.\nOption B: 13 = 11 + 2. sum of 2 different prime numbers\nOption C: 4 = This is not a sum of 2 different prime numbers.\nOption D: 15 = 13 + 2. Sum of 2 different prime numbers\nOption E: 19 = 17 + 2. Sum of 2 different prime numbers\nCorrect Option: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man's speed with the current is 22 km/hr and the speed of the current is 5 km/hr. The man's speed against the current is\n\n### Options:\nA. 9\nB. 10\nC. 11\nD. 12\nE. 13\n\n### Answer:\nMan's rate in still water = (22 - 5) km/hr = 17 km/hr.\nMan's rate against the current = (17 - 5) km/hr = 12 km/hr.\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the money was put in for the same duration of time by A,B and C, three business partners and four times A\u2019s capital is equal to 6 times B\u2019s capital is equal to 10 times C\u2019s capital. Determine that out of a total profit of Rs 4650 what is C\u2019s share?\n\n### Options:\nA. Rs 2250\nB. Rs 1550\nC. Rs 450\nD. Rs 900\nE. None of these\n\n### Answer:\nExplanation:\nIt is given that business partnership is independent of time in this case as all the investors have invested their money for same amount of time.\nLet A\u2019s capital be x, B\u2019s capital be y and C\u2019s capital be z.\n=>x+y+z = 4650\n=> 4x = 6y = 10z\n=>C\u2019s share is z so let us solve the question w.r.t. z\n=>x = 5z/2\n=>y = 5z/3\n=>(5z/2)+(5z/3)+(z) = 4650\n=>31z = 4650*6\n=>z = 900\nANSWER D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich of the following is the Highest Common Factor of 25, 40 and 20?\n\n### Options:\nA. 8\nB. 5\nC. 6\nD. 14\nE. 12\n\n### Answer:\nCOMMON FACTOR IS 5\rAns is :B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n12500 shares, of par value Rs. 20 each, are purchased from Ram by Mohan at a price of Rs. 25 each. If Mohan further sells the shares at a premium of Rs. 11 each, find his gain in the transaction.\n\n### Options:\nA. 75000\nB. 76000\nC. 77000\nD. 74000\nE. 70000\n\n### Answer:\nFace value of each share = Rs.20\nMarket value of each share = Rs.25\nNumber of shares = 12500\nAmount required to purchase the shares = 12500 \u00d7 25 = 312500\nMohan further sells the shares at a premium of Rs. 11 each\nie, Mohan further sells the shares at Rs.(20+11) = Rs.31 per share\ntotal amount he gets by selling all the shares = 12500 \u00d7 31 = 387500\nHis gain = 387500 - 312500 = Rs.75000\nAnswer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nX starts a business with Rs.45000. Y joins in the business after 6 months with Rs.30000. What will be the ratio in which they should share the profit at the end of the year?\n\n### Options:\nA. 1:2\nB. 2:1\nC. 3:1\nD. 2:3\nE. 5:3\n\n### Answer:\nRatio in which they should share the profit\n= Ratio of the investments multiplied by the time period\n=45000\u00d712:30000\u00d76\n=45\u00d712:30\u00d76\n=3\u00d712:2\u00d76\n=3:1\nAnswer is C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are 5 men and 11 women. In how many ways one can select a group of 6 with at-least 3 men?\n\n### Options:\nA. 1935\nB. 1936\nC. 1937\nD. 1938\nE. 1939\n\n### Answer:\n5c3*11c3+5c4*11c2+5c5*11c1=1936\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe number 94 can be written as the sum of the squares of 4 different positive integers in two ways. Of the following, which can be the sum of these 4 integers?\n\n### Options:\nA. 9\nB. 14\nC. 15\nD. 18\nE. 20\n\n### Answer:\nThe only possible sum for 4 different squares of an integer with total sum number is 95 are :\n48 + 36 + 9 + 1 = 95 which are the square from numbers :8, 6, 3, 1 (total sum number is 16)\nor\n80 + 9 + 4 + 1 = 95 which are the square from numbers : 9, 3, 2, 1 (total sum number is 14)\nhence the answer is (B)\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFor any integer n greater than 1, n* denotes the product of all the integers from 1 to n, inclusive. How many prime numbers T are there between 6* + 2 and 6* + 6, inclusive?\n\n### Options:\nA. None\nB. One\nC. Two\nD. Three\nE. Four\n\n### Answer:\nGiven that n* denotes the product of all the integers from 1 to n, inclusive so, 6*+2=6!+2 and 6*+6=6!+6.\nNow, notice that we can factor out 2 our of 6!+2 so it cannot be a prime number, we can factor out 3 our of 6!+3 so it cannot be a prime number, we can factor out 4 our of 6!+4 so it cannot be a prime number, ... The same way for all numbers between 6*+2=6!+2 and 6*+6=6!+6, inclusive. Which means that there are no primes T in this range.\nAnswer: A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAt what rate of interest (compounded yearly)will Rs.10,000 amount to Rs.12100 in 2 years?\n\n### Options:\nA. 11%\nB. 8%\nC. 10%\nD. 9%\nE. 7%\n\n### Answer:\nC.I=P(1+R/100)^N\n12100=10000(1+R/100)^2\n121/100=(1+R/100)^2\n(11/10)^2=(1+R/100)\nR=10%\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the greatest number of identical bouquets that can be made out of 21 white and 91 red tulips if no flowers are to be left out? (Two bouquets are identical whenever the number of red tulips in the two bouquets is equal and the number of white tulips in the two bouquets is equal)\n\n### Options:\nA. 3\nB. 4\nC. 5\nD. 6\nE. 7\n\n### Answer:\nSince no flowers are to be left out, then the number of bouquets must be a factor of both 21 and 91. For example, we cannot have 2 bouquets since we cannot divide 91 red tulips into 2 bouquets without one tulip left over.\nOnly answer choice which is a factor of 91 is E (7).\nAnswer: E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA number consists of 3 digits whose sum is 10. The middle digit is equal to the sum of the other two and the number will be increased by 99 if its digits are reversed. The number is\n\n### Options:\nA. 145\nB. 185\nC. 253\nD. 370\nE. None\n\n### Answer:\nSolution\nLet the number be x.\nThen 2x = 10 or x = 5. So, the number is either 253 or 352. Since the number increases on reversing the digits, so the hundred's digit is smaller than the units digit.\nHence, required number = 253.\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If two marbles are drawn at random, what is the probability that at least one is green?\n\n### Options:\nA. 23/35\nB. 23/36\nC. 23/18\nD. 23/17\nE. 23/12\n\n### Answer:\nGiven that there are three blue marbles, four red marbles, six green marbles and two yellow marbles.\nProbability that at least one green marble can be picked in the random draw of two marbles = Probability that one is green + Probability that both are green\n= (\u2076C\u2081 * \u2079C\u2081)/\u00b9\u2075C\u2082 + \u2076C\u2082/\u00b9\u2075C\u2082\n= (6 * 9 * 2)/(15 * 14) + (6 * 5)/(15 * 14) = 36/70 + 1/7\n= 46/70 = 23/35\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA salt manufacturing company produced a total of 2500 tonnes of salt in January of a particular year. Starting from February its production increased by 100 tonnes every month over the previous months until the end of the year. Find its average monthly production for that year?\n\n### Options:\nA. 2060\nB. 3050\nC. 5550\nD. 2889\nE. 2506\n\n### Answer:\nTotal production of salt by the company in that year = 2500 + 2600 + 2700 + .... + 3600 = 36600.\nAverage monthly production of salt for that year = 36600/12 = 3050.\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a Company, there are certain number of team members and certain number of team leaders. If five team members are assigned to each team leader, then one member is left out without team leader. If six members are assigned to each team leader, then one team leader has no member at all. Find the number of team leaders in that company?\n\n### Options:\nA. 7\nB. 36\nC. 5\nD. 8\nE. 9\n\n### Answer:\non the basis of question\nx = 5y+1\nx = 6(y-1)\non solving these 2 equations x = 36\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain company has records stored with a record storage firm in 15-inch by 12-inch by 10-inch boxes. The boxes occupy 1.08 million cubic inches of space. If the company pays $0.6 per box per month for the record storage, what is the total amount that the company pays each month for record storage?\n\n### Options:\nA. a. 150\nB. b. 300\nC. c. 600\nD. d. 1,200\nE. e. 360\n\n### Answer:\nVolume Per Box: 15x12x10 = 1,800\nTotal Volume: 1,080,000\nNumber of Boxes: Total Volume / Volume Per Box = 1,080,000 / 1,800 = 600\nPrice Per Month: Number of Boxes * Price Per Box = 600 * 0.6 = 360\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n30 is to be divided into two parts such that the sum of 10 times the first and 22 times the second is 780. The bigger part is :\n\n### Options:\nA. 33\nB. 34\nC. 26\nD. 10\nE. 19\n\n### Answer:\nExplanation:\nLet the two parts be (30- x) and x.\nThen, 10 (30 - x) + 22x = 780\n=> 12x = 480\n=> x = 40.\nBigger part = (30- x) = 10.\nAnswer: D) 10\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA factory produces 3400 toys per week. If the workers at this factory work 5 days a week and if these workers make the same number of toys everyday, how many toys are produced each day?\n\n### Options:\nA. 575 toys\nB. 375 toys\nC. 680 toys\nD. 475 toys\nE. 675 toys\n\n### Answer:\nTo find the number of toys produced every day, we divide the total number of toys produced in one week (of 5 days) by 5.\n3400 / 5 = 680 toys\ncorrect answer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the fraction which has the same ratio to 2/13 that 5/34 has to 7/48.\n\n### Options:\nA. 240/1577\nB. 240/1527\nC. 240/1547\nD. 240/1518\nE. 240/1273\n\n### Answer:\nP : 2/13 = 5/34 : 7/48\nAs the product of the means is equal to the product of the extremes.\nP*7/48 = 2/13 * 5/34\nP*7/48 = 10/442\nP = 480/3094 => P = 240/1547\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe probability that a number selected at random from the first 50 natural numbers is a composite number is?\n\n### Options:\nA. 17/22\nB. 17/25\nC. 17/21\nD. 17/91\nE. 17/12\n\n### Answer:\nThe number of exhaustive events = \u2075\u2070C\u2081 = 50.\nWe have 15 primes from 1 to 50.\nNumber of favourable cases are 34.\nRequired probability = 34/50 = 17/25.\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA departmental store charges the commission of 15 percent on the first sale of items worth $50,000 and then an additional 10 percent on any sale price that exceeds the initial $50,000. If the department store earned $20,000 in commissions for the sale of a series of diamonds, what was the sale price of the diamond set?\n\n### Options:\nA. $215,000\nB. $365,000\nC. $115,000\nD. $175,000\nE. $160,000\n\n### Answer:\n20,000 = 0.15 *(50000) + 0.10 (x - 50000)\n20000 - 7500 = 0.10 (x-50000)\n125000 = x - 50000\nx = 1,75,000\nAnswer : D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a company allocates 10 percent of its budget to advertising, 10 percent to capital improvements, and 5 percent to salaries, what fraction of its budget remains for other allocations?\n\n### Options:\nA. 1/4\nB. 2/4\nC. 3/4\nD. 1/5\nE. 2/5\n\n### Answer:\n100%-(10%+10%+5%)=75% remains for other allocations --> 75% = 75/100 = 3/4.\nAnswer: C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe total of company C's assets in 1994 was 600% greater than the total in 1993, which in turn was 400% greater than the total in 1992. If the total of company C's assets in in 1992 was N dollars, which one of the following represents company C's assets in 1994:\n\n### Options:\nA. 7N\nB. 8N\nC. 9N\nD. 12N\nE. 35N\n\n### Answer:\nLet's use actual numbers. Starting in 1992, let's say company C had $100 in assets.\nIn 1993, the total assets were 400% GREATER, which means 1992 PLUS 400% of 1992:\n$100 + 4x$100 = $100 + $400 = $500\nIn 1994, the total assets were 600% GREATER than they were in 1993, which means 1993 PLUS 600% of 1993:\n$500 + 6x$500 = $500 + $3000 = $3500\nThis is 35 times the 1992 number, so the correct answer is 35N.\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?\n\n### Options:\nA. 40\nB. 41\nC. 45\nD. 49\nE. 46\n\n### Answer:\nSpeed = 45 * 5/18 = 25/2 m/sec\nTotal distance covered = 360 + 140 = 500 m\nRequired time = 500 * 2/25 = 40 sec\nAnswer: Option A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf y is 90% greater than x, than x is what % less than y?\n\n### Options:\nA. 35.7%\nB. 39.8%\nC. 43.2%\nD. 47.4%\nE. 51.2%\n\n### Answer:\ny = 1.9x\nx = y/1.9 = 10y/19\nx is 9/19 less which is 47.4% less than y.\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n18 men working 8 hours per day dig 30 m deep. How many extra men should be put to dig to a depth of 50 m working 6 hours per day?\n\n### Options:\nA. 22\nB. 66\nC. 88\nD. 100\nE. 281\n\n### Answer:\n(18 * 8)/30 = (x * 6)/50 => x =40\n40 \u2013 18 = 22\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRoberto has three children: two girls and a boy. All were born on the same date in different years. The sum of the ages of the two girls today is smaller than the age of the boy today, but a year from now the sum of the ages of the girls will equal the age of the boy. four years from today, the difference between the age of the boy and the combined ages of the girls will be\n\n### Options:\nA. 1\nB. 2\nC. -3\nD. \u20132\nE. \u20131\n\n### Answer:\nApproach I (Plugin's)\nGirl I ............... Girl II ................ Boy\n1 ....................... 1 ........................ 3 (Assume the current ages)\n1 + 1 < 3 .......... (Satisfies the given condition)\n1 Year later there ages are\n2 ....................... 2 ......................... 4\n2 + 2 = 4 ............ (Satisfies the given condition)\nAfter 4 years there ages are\n5 ....................... 5 ............................ 7\nDifference = 7 - (5+5) = 7 - 10 = -3\nAnswer = C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 8 minutes, then the area of the park (in sq. m) is:\n\n### Options:\nA. 30720\nB. 153600\nC. 15360\nD. 307200\nE. 153700\n\n### Answer:\nPerimeter = Distance covered in 8 min. =12000/60x 8\tm = 1600 m.\nLet length = 3x metres and breadth = 2x metres\nThen, 2(3x + 2x) = 1600 or x = 160.\nLength = 480 m and Breadth = 320 m.\nArea = (480 x 320) m2 = 153600 m2\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOf the 200 stamps in a collection, 90 are foreign and 80 are more than 10 years old. If 20 stamps are both foreign and more than 10 years old, how many stamps are neither foreign nor more than 10 years old?\n\n### Options:\nA. 50\nB. 80\nC. 100\nD. 130\nE. 150\n\n### Answer:\n20 stamps are both foreign and more than 10 years old.\n70 stamps are foreign only.\n60 stamps are 10 years old only.\nThe number of remaining stamps is 200 - (20+70+60) = 50\nThe answer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf it is 6:27 in the evening on a certain day, what time in the morning was it exactly 2,880,715 minutes earlier? (Assume standard time in one location.)\n\n### Options:\nA. 6:22\nB. 6:24\nC. 6:27\nD. 6:30\nE. 6:33\n\n### Answer:\n6:27minus 2,880,715in any way must end with 2, the only answer choice which ends with 2 is A.\nAnswer: A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a * b = a + b/ab , find the value of 5 * (5 * -2) :\n\n### Options:\nA. -3\nB. -10\nC. -1.66\nD. 3/5\nE. -12\n\n### Answer:\n(5 * -2) = (5 x (-2))/(5 + (-2)) = -10/3\nSo, 5 * (5 * -2) = 5 * (-10/3) = (5 * (-10/3))/(5 + (-10/3))\n= (-50/3) * (3/5)\n= -10.\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThree independent strategies A, B and C have been initiated for cost cutting in a company producing respectively 30%, 40% and 10% savings. Assuming that they operate independently, what is the net saving achieved?\n\n### Options:\nA. 56%\nB. 64%\nC. 62.2%\nD. 68%\nE. 61%\n\n### Answer:\nIf initial cost is Rs 100, then\nFinal cost will be 100*0.7*0.6*0.9 = Rs. 37.8\nsavings = 100-37.8=62.2\nso 62.2%\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 0.764 B = 1.236 A, then what is the value of (B - A)/(B + A) ?\n\n### Options:\nA. 0.764\nB. 0.236\nC. 2\nD. 0.472\nE. None\n\n### Answer:\nAnswer\nGiven, 0.764 B = 1.236 A\n\u21d2 B/A = 1.236 / 0.764\nNow, (B - A)/(B + A) = (B/A - 1) / (B/A + 1)\n= (1.236/0.764 - 1) / (1.236/0.764 + 1)\n= (1.236 - 0.764)/(1.236 + 0.764)\n= 0.472/2.000\n= 0.236\nCorrect Option: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRitesh and Co. generated revenue of Rs. 1,700 in 2006. This was 12.5% of its gross revenue. In 2007, the gross revenue grew by Rs. 2,500. What is the percentage increase in the revenue in 2007?\n\n### Options:\nA. 18.38%\nB. 20%\nC. 25%\nD. 50%\nE. None of these\n\n### Answer:\nExplanation :\nGiven, Ritesh and Co. generated revenue of Rs. 1,700 in 2006 and that this was 12.5% of the gross revenue.\nHence, if 1700 is 12.5% of the revenue, then 100% (gross revenue) is:\n=>(100/12.5)\u00d71700.\n=>13,600.\nHence, the total revenue by end of 2007 is Rs. 13,600. In 2006, revenue grew by Rs. 2500. This is a growth of:\n=>(2500/13600)\u00d7100.\n=>18.38%.\nAnswer : A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf you multiply all the numbers on your mobile phone , what is the answer?\n\n### Options:\nA. 2\nB. 6\nC. 1\nD. 0\nE. 7\n\n### Answer:\nD\n0\nTheir is a zero in your phone.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many numbers from 39 to 79 are exactly divisible by 11?\n\n### Options:\nA. 5\nB. 7\nC. 4\nD. 11\nE. 12\n\n### Answer:\n39/11 = 1 and 79/11 = 7 ==> 7 - 3 = 4 Numbers\nAnswer : C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat will be the reminder when (67^67+67) is divided by 68?\n\n### Options:\nA. 1\nB. 63\nC. 66\nD. 67\nE. None of these\n\n### Answer:\n(x^n+1) will be divisible by (x+1) only when n is odd;\n(67^67+1) will be divisible by (67+1);\n(67^67+1)+66 when divided by 68 will give 66 as remainder.\nCorrect Option : C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA fruit seller had some oranges. He sells 40% oranges and still has 420 oranges. How many oranges he had originally?\n\n### Options:\nA. 500\nB. 700\nC. 750\nD. 900\nE. 950\n\n### Answer:\nHe sells 40% of oranges and still there are 420 oranges remaining.\n=> 60% of oranges = 420\n=> Total oranges\n\u00d7\n60\n100\n=\n420\n\u00d760100=420\n=> Total oranges\n=\n420\n\u00d7\n100\n60\n=\n700\nOption B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many cubes will remain if the cubes having black and green coloured are removed ?\n\n### Options:\nA. 16\nB. 15\nC. 8\nD. 12\nE. 10\n\n### Answer:\nNumber of small cubes which are Black and Green is 8 in all.\nHence, the number of remaining cubes are = 24 - 8 = 16\nANSWER A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n30% people of a village in Sri Lanka died by bombardment, 25% of the remainder left the village on account of fear. If now the population is reduced to 6695, how much was it in the beginning?\n\n### Options:\nA. 7000\nB. 6700\nC. 6695\nD. 7645\nE. 6575\n\n### Answer:\nX * (70/100) * (75/100) = 3515\nX = 6695\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the odd man out\n864, 420, 200, 85, 40, 16, 6\n\n### Options:\nA. 420\nB. 85\nC. 16\nD. 40\nE. 6\n\n### Answer:\n6x2+4=16\n16x2+8=40\n40x2+12=92\n92x2+16=200.. and so on. 85\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA no. when divided by the sum of 555 and 445 gives 2times their difference as quotient & 40 as remainder. Find the no. is?\n\n### Options:\nA. 220044\nB. 145778\nC. 220400\nD. 220014\nE. 220040\n\n### Answer:\n(555 + 445) * 2 * 110 + 30 = 220000 + 30 = 220040\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAarti can do a piece of work in 6 days. In how many days will she complete three time of work of same type?\n\n### Options:\nA. 6 days\nB. 18 days\nC. 21 days\nD. 3 days\nE. 13 days\n\n### Answer:\nWe have the important relation, More work, More time (days)\nA piece of work can be done in 6 days.\nThree times of work of same type can be done in 6 x 3\n= 18 days\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man has Rs. 480 in the denominations of one-rupee notes, five-rupee notes and ten rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has?\n\n### Options:\nA. 45\nB. 60\nC. 75\nD. 90\nE. 95\n\n### Answer:\nLet number of notes of each denomination be x.\nThen x + 5x + 10x = 480\n16x = 480\nx = 30.\nHence, total number of notes = 3x = 90\nAnswer: Option D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nVishal invested 10% more than Trishul. Trishul invested 10% less than Raghu. If the total sum of their investments is Rs. 6647, how much amount did Raghu invest ?\n\n### Options:\nA. 2300\nB. 2887\nC. 2000\nD. 1129\nE. 1192\n\n### Answer:\nLet money invested by Raghu = Rs. x\nMoney invested by Trishul = 9/10 x = 0.9x\nMoney invested by Vishal = 9/10x * 110/100 = 0.99x\nAlso, x+0.9x+0.99x = 6647\n= x= 6647/2.89 = 2300\nTherefore, amount invested by Raghu is Rs. 2300.\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe price of a cycle is reduced by 25 % The new price is reduced by a further 20 %. The 2reductions together are equalto a single reduction of\n\n### Options:\nA. 39\nB. 45\nC. 60\nD. 56\nE. 70\n\n### Answer:\nLet the original price of the cycle be 100. After the first reduction the price will be 75.\nThis new price is then reduced by 20% = 0.8 x 75 = 60\n60 represents a reduction of 40 percent on the original.\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average of 20 numbers is zero. Of them, How many of them may be greater than zero, at the most?\n\n### Options:\nA. 3\nB. 1\nC. 0\nD. 19\nE. 20\n\n### Answer:\nAverage of 20 numbers = 0\nSum of 20 numbers / 20=0\n=> Sum of 20 numbers = 0\nHence at the most, there can be 19 positive numbers.\n(Such that if the sum of these 19 positive numbers is x, 20th number will be -X)\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n12 persons can complete the work in 18 days. after working for 6 days, 4 more persons added to complete the work fast. in how many more days they will complete the work?\n\n### Options:\nA. 10 days\nB. 9 days\nC. 8 days\nD. 7 days\nE. 6 days\n\n### Answer:\ntotal work 12*18=216 units\nafter 6 days work finished 6*12=72 units\nremaining work 216-72=144 units\nremaing days =144(12+4)=9 days\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAn analyst will recommend a combination of 3 industrial stocks, 2 transportation stocks, and 2 utility stocks. If the analyst can choose from 7 industrial stocks, 4 transportation stocks, and 3 utility stocks, how many different combinations of 7 stocks are possible?\n--\n\n### Options:\nA. 12\nB. 19\nC. 60\nD. 180\nE. 630\n\n### Answer:\n7C3 * 4C2 * 3C2 = 35*6*3 = 630.\nAnswer: E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n4 dice are thrown simultaneously on the board. Find the probability which show the same face?\n\n### Options:\nA. 2/113\nB. 3/117\nC. 1/216\nD. 3/111\nE. 4/121\n\n### Answer:\nThe total number of elementary events associated to the random experiments of throwing four dice simultaneously is:\n=6\u00d76\u00d76\u00d76=64=6\u00d76\u00d76\u00d76=64\nn(S)=64n(S)=64\nLet XX be the event that all dice show the same face.\nX={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)}X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)}\nn(X)=6n(X)=6\nHence required probability,\n=n(X)n(S)=664=n(X)n(S)=664\n=1/216\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe age of father 10 years ago was thrice the age of his son. Ten years hence, father's age will be twice that of his son. The ratio of their present ages is:\n\n### Options:\nA. 5 : 2\nB. 7 : 3\nC. 9 : 2\nD. 13 : 4\nE. 13 : 6\n\n### Answer:\nLet the present ages of father and son be x and y years respectively.\nThen (x-10) = 3 (y-10) or\n3y-x = 20 ------ (1)\nand (x+10) = 2 (y+10) or\nx-2y = 10 ----- (2)\n(1) + (2) -> y = 30\nSubstituting y = 30 in equation (1) we get x = 70\nRatio of their ages = 70 : 30 or 7:3\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA group of men decided to do a work in 20 days, but 10 of them became absent. If the rest of the group did the work in 40 days, Find the original number of men?\n\n### Options:\nA. 20\nB. 50\nC. 40\nD. 100\nE. 25\n\n### Answer:\nOriginal number of men = 10*40 / (40-20) =20\nAnswer is A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAt what time between 9 and 10 o\u2019clock will the hands of a watch be together?\n\n### Options:\nA. 49 1/11 min. past 9\nB. 40 min. past 9\nC. 45 min. past 9\nD. 50 min. past 9\nE. None\n\n### Answer:\nSol.\nTo be together between 9 and 10 o\u2019clock, the minute hand has to gain 45 min. spaces. 55 min. spaces gined in 60 min.\n45 min. spaces are gained in [60 / 55 * 45] min. or 49 1/11 min.\n\u2234 The hands are together at 49 1/11 min. past 9.\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo trains of length 100 m and 200 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 54 kmph and 72 kmph. After how much time will the trains meet?\n\n### Options:\nA. 21/9 sec\nB. 32/3 sec\nC. 20/7 sec\nD. 32/3 sec\nE. 53/2 sec\n\n### Answer:\nThey are moving in opposite directions, relative speed is equal to the sum of their speeds.\nRelative speed = (54 + 72)*5/18 = 7*5 = 35 mps.\nThe time required = d/s = 100/35 = 20/7 sec.\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMr. Evans will states that each of his children will receive an equal share of his estate and that his grandchildren will split a portion of the estate that is equal to the share received by each of his children. If Mr. Evans has 2 children and 6 grandchildren, then approximately what percentage of Mr. Evans estate will each grandchild receive?\n\n### Options:\nA. 20%\nB. 17%\nC. 5.5%\nD. 3.3%\nE. 2.8%\n\n### Answer:\n33.33/6=5.5\nAnswer : C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many 3-digit numerals begin with a digit that represents a prime and end with a digit that represents a odd prime number?\n\n### Options:\nA. 16\nB. 120\nC. 160\nD. 180\nE. 240\n\n### Answer:\nprime digits 2,3,5 and 7.\nthree digit numbers _ _ _\n1st place can be filled in 4 ways\n2nd place can be filled in 10 ways\n3rd place can be filled in 3 ways\nTotal=4*10*3=120\nAns : B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA bank issued credit card numbers and the corresponding PIN (Personal Identification Number). Both are 3-digit numbers up to 996. Pinaki was the last to get the credit card and so he had the last possible credit card number.\nHe was afraid of forgetting his PIN. He wrote down the number 126 in his diary to remember his PIN. He also wrote out the way to calculate 126 : \"Multiply the card number by PIN. Divide the product by 997. The remainder is 126\".\nOnce, Prafull saw his diary in which Pinaki wrote this number 126. Prafull did a lot of purchasing, as he now knows Pinaki's PIN. What is Pinaki's PIN?\n\n### Options:\nA. 871\nB. 873\nC. 875\nD. 877\nE. 879\n\n### Answer:\nExplanation :\nLet, the PIN is x.\nAccording to the question,\nThe card number =996 and Remainder =126.\nThus, (996 \u00d7 x)/997=126.\n=>x= 871.\nAnswer : A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the arithmetic mean of p and q is 10 and the arithmetic mean of q and r is 20, what is the value of r-p?\n\n### Options:\nA. 20\nB. 10\nC. 30\nD. 40\nE. 5\n\n### Answer:\nArithmetic mean expression for p and q:\n(p+q)/2=10 ; p+q=20 ----eq1\nArithmetic mean expression for q and r:\n(q+r)/2=20 ; q+r=40 ----eq2\nSubtracting eq1 from eq2 we get: r-p=20\nHence, the correct answer is A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf T = 5/9 * (K - 32), and if T = 50, then what is the value of K?\n\n### Options:\nA. 116\nB. 119\nC. 122\nD. 125\nE. 128\n\n### Answer:\nK-32=9T/5\nK=9T/5 + 32\nK=9(50)/5 + 32 = 122\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain rectangular window is (1/3) times as long as it is wide. If its perimeter is 28 feet, what are its dimensions in terms of length by width?\n\n### Options:\nA. 12 by 2\nB. 11 by 3\nC. 10.5 by 3.5\nD. 10 by 4\nE. 9 by 3\n\n### Answer:\n2x+2y=28\nx+y=14\nx+(1/3)x=14\n4x=14*3\nx=10.5\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA and B together can do a piece of work in 1 days. If A alone can do the same work in 20days, then B alone can do the same work in?\n\n### Options:\nA. 0.35 days\nB. 0.45 days\nC. 0.55 days\nD. 0.25 days\nE. 0.95 days\n\n### Answer:\nB = 1/1 \u2013 1/20 =0.95 days\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the next number in this sequence:\n1, 11, 21, 1211, 111221, 312211, 13112221, _________?\n\n### Options:\nA. 1113213211\nB. 1113213244\nC. 1113213233\nD. 1113213222\nE. 1113213255\n\n### Answer:\nA\n1113213211\nThe next number in sequence is 1113213211.\nEXPLANATION-\nThe sequence goes like\nYou need to spell the no of digits.\ne.g. take the no 1,11,21\nTake 1. it spells as one 1 so we get the no 11,\ntake 11 we spell it as two ones\u2018 and we get 21\n.so take the last given no in the sequence 13112221 so we spell it as one 1 one 3 two 1 three 2\u2019s one 1.\nSo\nthe next no in sequence is 1113213211.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nif 8^25 divided by 7 then what is reminder\n\n### Options:\nA. 25\nB. 1\nC. 0\nD. 2\nE. 3\n\n### Answer:\n8^25/7\n8 can be written as 7*1+1\n(7*1+1)^25/7\n(ax+1)^n/a always gives the remainder 1\nhere a=7,x=1,n=25\nHence remainder is 1\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nP, Q and R have $6000 among themselves. R has two-thirds of the total amount with P and Q. Find the amount with R?\n\n### Options:\nA. 2400\nB. 2403\nC. 3998\nD. 2539\nE. 1930\n\n### Answer:\nA\n2400\nLet the amount with R be $ r\nr = 2/3 (total amount with P and Q)\nr = 2/3(6000 - r) => 3r = 12000 - 2r\n=> 5r = 12000 => r = 2400.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nworkers decided to raise Rs.3 lacs by equal contribution from each. Had they contributed Rs.50 eachextra, the contribution would have been Rs.3.25 lacs. How many workers were they?\n\n### Options:\nA. 250\nB. 400\nC. 500\nD. 560\nE. 650\n\n### Answer:\nN * 50 = (325000 - 300000) = 25000\nN = 25000 / 50\n= 500\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the sides of a triangle are 17.2 cm, 14 cm and 10 cm, what is its area?\n\n### Options:\nA. 60 cm^2\nB. 70 cm^2\nC. 80 cm^2\nD. 85 cm^2\nE. 90 cm^2\n\n### Answer:\nThe triangle with sides 17.2 cm, 14 cm and 10 cm is right angled, where the hypotenuse is 17.2 cm.\nArea of the triangle\n= 1/2 * 14 * 10\n= 70 cm^2\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA person travels equal distances with speeds of 3 km/hr, 4 km/hr and 5 km/hr and takes a total time of 47 minutes. The total distance (in km) is :\n\n### Options:\nA. 1\nB. 2\nC. 3\nD. 4\nE. 5\n\n### Answer:\nSol.\nLet the total distance be 3x km.\nThen, x/3 + x/4 + x/5 = 47/60 \u21d4 47x/60 = 47/60 \u21d4 x = 1.\n\u2234 total distance = (3*1) km = 3km.\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf x/y =2/4, then (x-y)/x?\n\n### Options:\nA. -1/2\nB. -1\nC. 1/3\nD. 1\nE. 5\n\n### Answer:\nwe have this law of fraction:\na/b=c/d= (a-c)/(b-d)\nx/y=2/4 ---> x/2=y/4= (x-y)/(2-4)=(x-y)/(-1\n2) ---> (x-y)/x= -2/2 = -1\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average (arithmetic mean) of eight numbers is 49.1. If the sum of half of these numbers is 158.4, what is the average of the other half?\n\n### Options:\nA. 12.8\nB. 24.2\nC. 58.6\nD. 72.1\nE. 96.8\n\n### Answer:\narithmetic mean = sum / total numbers\nsum = 49.1 * 8 = 392.8\nsum of half of these numbers is 158.4. So, 4 numbers sum is 158.4. Rest 4 numbers sum = 392.8-158.4 = 234.4\nArithmetic mean of the 4 nos = 234.4/4 = 58.6\nHence, C is the answer.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the sum of three consecutive even numbers is 30 more than the average of these numbers, then the largest of these numbers is?\n\n### Options:\nA. 20\nB. 19\nC. 18\nD. 17\nE. 16\n\n### Answer:\nExplanation:\nLet the smallest of these number be x. The other two numbers are (x + 2) and (x + 4).\nx + (x + 2) + (x + 4) = (X + (X+2) + (x+4)) / 3 + 30\n3x + 3*(x + 2) + 3*(x + 4) = x + (x + 2) + (x + 4) + 90\n9x + 18 = 3x + 96\n6x = 78\nx = 13\nTherefore, the largest number is 17.\nANSWER D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the sides of a triangle are 26 cm, 24 cm and 10 cm, what is its area?\n\n### Options:\nA. 120\nB. 110\nC. 130\nD. 140\nE. 150\n\n### Answer:\nThe triangle with sides 26 cm, 24 cm and 10 cm is right angled, where the hypotenuse is 26 cm.\nArea of the triangle = 1/2 * 24 * 10 = 120 cm2\nAnswer: Option A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how many different ways can the letters of the word \u2018LOVE\u2019 be arranged ?\n\n### Options:\nA. 24\nB. 120\nC. 720\nD. 40320\nE. 6\n\n### Answer:\nA\n24\nRequired number of arrangements = 4! = 24\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFor the past n days, the average (arithmetic mean) daily production at a company was 50 units. If today's production of 60 units raises the average to 55 units per day, what is the value of n ?\n\n### Options:\nA. 30\nB. 18\nC. 10\nD. 9\nE. 1\n\n### Answer:\n(average production for n days) * n = (total production for n days) --> 50n=(total production for n days);\n(total production for n days) + 60 = (average production for n+1 days) * (n+1) --> 50n + 60 = 55 * (n+1) --> n=1.\nAnswer: E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how many W ways can a four-letter password be chosen, using the letters A, B, C, D, E, and/or F, such that at least one letter is repeated within the password?\n\n### Options:\nA. 720\nB. 864\nC. 900\nD. 936\nE. 1,296\n\n### Answer:\nTotal number of four letter passwords = 6*6*6*6= 1296 ------(1)\nTotal number of passwords in which no letter repeats = 6C4*4!= 15*24=360------(2)\ntherefore required value W= (1)-(2)= 1296-360=936.D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA bullet train 140 m long is running at 60 kmph. In how much time will it pass a platform 260 m long?\n\n### Options:\nA. 34 Seconds\nB. 22 Seconds\nC. 41 Seconds\nD. 24 Seconds\nE. 29 Seconds\n\n### Answer:\nD\n24 Seconds\nDistance travelled = 140 + 260m = 400m\nSpeed = 60 * 5/8 = 50/3m\nTime = 400 * 3/50 = 24 Seconds\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the operation @ is defined for all a and b by the equation a@b =(a^b)/2,then (3@2)=?\n\n### Options:\nA. 4\nB. 2\nC. 9/2\nD. -9/2\nE. -8/2\n\n### Answer:\nwork within the parenthesis first so solve (3@2) first\n(3@2)=(3^2)/2=9/2\nso 9/2 is the answer....this question is merely testing order of operations\nremember PEMDAS\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train 800 m long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 min, then the length of the tunnel is?\n\n### Options:\nA. 300\nB. 400\nC. 500\nD. 600\nE. 700\n\n### Answer:\nSpeed = 78 * 5/18 = 65/3 m/sec.\nTime = 1 min = 60 sec.\nLet the length of the train be x meters.\nThen, (800 + x)/60 = 65/3\nx = 500 m.\nAnswer: Option C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nin a bus left side are 15 seats available,3 few seats in right side because in rear exit door .Each seat hold 3 people.In addition ,there is a seat back can sit 7 people all together .how many people can sit in a bus?\n\n### Options:\nA. 52\nB. 49\nC. 95\nD. 88\nE. 66\n\n### Answer:\nRight Side =15 seat\nLeft Side =15-3 (3 few seat in right side)= 12 seat\nTotal= 15+12= 27\nPeople can seat in 27 seat= 27*3=81\nPeople can seat in Last Seat = 7\nTotal People can seat= 81+7=88\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain car's price decreased by 2.5% (from the original price) each year from 1996 to 2002, during that time the owner of the car invested in a new carburetor and a new audio system for the car, which increased car's price by $3,500. If the price of the car in 1996 was $22,000, what is the car's price in 2002?\n\n### Options:\nA. $18,400\nB. $19,500\nC. $22,200\nD. $20,400\nE. $21,100\n\n### Answer:\nPrice in 96 = 22000\nPrice decrease each year = 2.5/100*22000 = 550\nPrice in 97 = 22000 - 550\nPrice in 98 = 22000 - 2*550\nPrice in 99 = 22000 - 3*550\nPrice in 00 = 22000 - 4*550\nPrice in 01 = 22000 - 5*550\nPrice in 02 = 22000 - 6*550 = 18700\nInvestment in the car = 3500\nNet price of the car in 02 = 18700 + 3500 = $22200\nCorrect Option: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train passes a station platform in 38 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?\n\n### Options:\nA. 180 m\nB. 270 m\nC. 260 m\nD. 280 m\nE. 380 m\n\n### Answer:\nSpeed = 54 x 5/18 = 15 m/s\nLength of the train = (15 x 20)m = 300 m.\nLet the length of the platform be x metres.\nThen, (x + 300)/38 = 15\n--> x + 300 = 570\nx = 270m.\nAnswer : B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 16 kmph and 21 kmph respectively. When they meet, it is found that one train has traveled 60 km more than the other one. The distance between the two stations is?\n\n### Options:\nA. 277\nB. 444\nC. 128\nD. 127\nE. 109\n\n### Answer:\n1h ----- 5\n? ------ 60\n12 h\nRS = 16 + 21 = 37\nT = 12\nD = 37 * 12 = 444\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the next number: 2, 10, 82, __\n\n### Options:\nA. 630\nB. 730\nC. 830\nD. 848\nE. 900\n\n### Answer:\n3^0 + 1 = 2\n3^2 + 1 = 10\n3^4 + 1 = 82\n3^6 + 1 = 730\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA ladies hostel had provision of food for 200 women for 35 days. After 10 days, 25 women left the hostel. The number of days for which the remaining food will last is:\n\n### Options:\nA. 28.97\nB. 28.0\nC. 28.47\nD. 27.47\nE. 29.47\n\n### Answer:\nExplanation :\nAfter 10 days : 200 women had food for 25 days.\nSuppose 175 women had food for x days.\nNow, Less women, More days (Indirect Proportion)\n175 : 200 :: 25 : x\n=> 175 x x = 200 x 25\n=> x = 200 x 25 / 175\n=> x =28.47\nAnswer : C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many D ways are there of placing 6 marbles in 4 bowls, if any number of them can be placed in each bowl?\n\n### Options:\nA. 6C4\nB. 6P4\nC. 4^6\nD. 6^4\nE. 6!\n\n### Answer:\nEach marble has 4 options, so there are total of D=4*4*4*4*4*4=4^6 ways.\nAnswer: C.\nThe total number of ways of dividing n identical items among r persons, each one of whom, can receive 0,1,2 or more items is (n+r -1)C(r-1).\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the angle between the hour and the minute hand of a clock when the time is 3.25.\n\n### Options:\nA. 47 \u00bd\nB. 49 \u00bd\nC. 55 \u00bd\nD. 57 \u00bd\nE. None\n\n### Answer:\nSolution\nAngle traced by the hour hand in 12 hours\t= 360\u00b0.\nAngle traced by it in 3 hrs 25 min\t= 41 / 12 hrs\n= (360 / 12 x 41 / 12)\u00b0\n= 102 \u00bd\u00b0.\nAngle traced by minute hand in 60 min\t= 360\u00b0.\nAngle traced by it in 25 min.\t= (360/ 60 x 25)\u00b0\n= 150\u00b0\nRequired angle\t= (150- 102 \u00bd\u00b0)\n= 47 \u00bd\u00b0.\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe concentration of spirit in three different vessels A, B and C are 45%, 30% and 10% respectively. If 4 litres from vessel A, 5 litres from vessel B and 6 litres from vessel C are mixed, find the concentration of spirit in the resultant solution.\n\n### Options:\nA. 26%\nB. 33%\nC. 34%\nD. 35%\nE. 24%\n\n### Answer:\nQuantity of spirit in new solution=(4*45/100)+(5*30/100)+(6*10/100)=1.8+1.5+0.6=3.9 liters\nSo % concentration of spirit=100*3.9/(4+5+6)=26%\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn the xy-coordinate plane, the graph of y = -x^2 + 9 intersects line L at (p,5) and (t,-8). What is the least possible value of the slope of line L?\n\n### Options:\nA. -6.5\nB. 2\nC. -2\nD. -6\nE. -10\n\n### Answer:\nWe need to find out the value of p and L to get to the slope.\nLine L and Graph y intersect at point (p,5). hence, x= p and Y=5 should sactisfy the graph. soliving\n5 = -p2 +9\np2 = 4\np = + or - 2\nsimillarly point (t,-8) should satisfy the equation. hence x=t and Y=-8.\n-7 = -t2+9\nt = +or - 4\nconsidering p = -2 and t =4, the least slope is (-8-5)/(4-2) = -6.5\nIMO option A is correct answer.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo trains of length 150 m and 200 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 54 kmph and 72 kmph. In how much time will the trains cross each other?\n\n### Options:\nA. 100/7 sec\nB. 80/7 sec\nC. 57/7 sec\nD. 110/7 sec\nE. 50/7 sec\n\n### Answer:\nRelative speed = (54 + 72)* 5/18 = 7 * 5 = 35 mps.\nThe time required = d/s = (150 + 100 + 300)/35\n= 550/35 = 110/7 sec.\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nBy approximately what percent is x greater than 4/7 if (1/7)(x) = 1?\n\n### Options:\nA. 1125%\nB. 956%\nC. 417%\nD. 3788%\nE. 219%\n\n### Answer:\nwhat percent is x greater than 4/7 if (1/7)(x) = 1?\n=> x = 7\n% change =[(7 -4/7) /(4/7) ] * 100\n= (49/4 - 1) *100\n= 45 * 25\n=1125%\nAns ,A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere is 60% increase in an amount in 6years at SI. What will be the CI of Rs. 14,000 after 3 years at the same rate?\n\n### Options:\nA. 2372\nB. 4634\nC. 4542\nD. 2343\nE. 3972\n\n### Answer:\nLet P = Rs. 100. Then, S.I. Rs. 60 and T = 6 years.\nR = 100 x 60 = 10% p.a.\n100 x 6\nNow, P = Rs. 14000. T = 3 years and R = 10% p.a.\nC.I.\n= Rs. 14000 x 1 +\t10 3\t- 1\n100\n= Rs. 14000 x\t331\n1000\n= 4634.\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe largest four digit number which is a perfect cube, is:\n\n### Options:\nA. 7000\nB. 8000\nC. 9261\nD. 9999\nE. None of these\n\n### Answer:\nExplanation:\n21*21*21 = 9261\nOption C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain sum of money doubles itself in 20 years in how much many years will it trible itself at the same rate?\n\n### Options:\nA. 20 years\nB. 76 years\nC. 88 years\nD. 40 years\nE. 11 years\n\n### Answer:\n100 ---- 100 --- 20\n100 --- 20\n--------------------\n300 ---- 40 years\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe radius of a wheel is 22.6 cm. What is the distance covered by the wheel in making 750 resolutions?\n\n### Options:\nA. 754 m\nB. 704 m\nC. 1055.04 m\nD. 1058.04 m\nE. 204 m\n\n### Answer:\nIn one resolution, the distance covered by the wheel is its own circumference. Distance covered in 750 resolutions.\n= 750 * 2 * 22/7 * 22.6 = 105504 cm\n= 1055.04 m\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOne red flower, three white flowers and two blue flowers are arranged in a line such that\nI. No two adjacent flowers are of the same colour.\nII. The flowers at the two ends of the line are of different colours.\nIn how many different ways can the flowers be arranged?\n\n### Options:\nA. 6\nB. 4\nC. 10\nD. 12\nE. 14\n\n### Answer:\nThe total possibilities are W@W@W@ (or) @W@W@W, where 2 blue and 1 red flowers occupy the space marked as @. Hence, the Total number of permutations is 2 x (3! / 2!) = 6.\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA father said to his son, \"I was as old as you are at the present at the time of your birth\". If the father's age is 68 years now, the son's age five years back was:\n\n### Options:\nA. 14\nB. 17\nC. 19\nD. 29\nE. 24\n\n### Answer:\nLet the son's present age be x years. Then, (68 - x) = x\n2x = 68.\nx = 34.\nSon's age 5 years back (34 - 5) = 29 years.\nanswer :D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMona and Donald fly to Rome for the weekend. They take cash only in notes of $10 and notes of \u20ac10. Mona carries three times the amount of euros Donald carries. She also carries as many dollars as Donald carries. The number of \u20ac10 notes they take is double the number of $10 notes they take. If Donald carries a total of 33 notes (of either $10 or \u20ac10,) then what is the total number of notes (of either $10 or \u20ac10,) they take?\n\n### Options:\nA. 70\nB. 110\nC. 100\nD. 120\nE. 150\n\n### Answer:\nlet e10 =x no. d10 =y no. donald is having x+y notes mona carries 3x+y again x =2y or donald x+y =33\nor 3y =33 y =11 ;x =22 , total notes they carry = 4x+2y = 88+22 =110\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf one of the followings is the product of the two 3-digit integers 8L7 and 6K9 (K and L denote the tens digit of the respective integers), then that product must be\n\n### Options:\nA. 511,913\nB. 478,823\nC. 531,875\nD. 538,424\nE. 569,114\n\n### Answer:\nTo know the unit digit you can multiply both digit number: 7 x 9 = 63\nThis eliminates C, D, and E, because the number must end with a 3\nTo know the answer you can multiply both the thousand digit giving 8 x 6 = 48 so the number must be bigger than 480.000.\nSo the answer is A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe area of a triangle is with base 2m and height 5m?\n\n### Options:\nA. 11\nB. 10\nC. 787\nD. 122\nE. 5\n\n### Answer:\n1/2 * 2 * 5 = 5 m2\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train is moving at a speed of 75km/hr and its length is 500m. Find the time taken by it to pass a man standing near the railway line?\n\n### Options:\nA. 30sec\nB. 45sec\nC. 36sec\nD. 24sec\nE. 52sec\n\n### Answer:\nSpeed of the train = 75*5/18 = 125/6 m/sec\nDistance moved in passing the standing man = 500m\nRequired time taken = 500/(125/6) = 24sec\nAnswer is D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man buys a cycle for Rs. 1400 and sells it at a loss of 20%. What is the selling price of the cycle?\n\n### Options:\nA. s. 1090\nB. s. 1120\nC. s. 1190\nD. s. 1202\nE. s. 1204\n\n### Answer:\nsince,c.p=1400\nloss%=(c.p-s.p)/c.p*100\n20=(1400-s.p)/1400*100\nso,after solving answer=1120.\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe perimeter of a rectangular yard is completely surrounded by a fence that measures 14 meters. What is the length of the yard if the area of the yard is 6 meters squared?\n\n### Options:\nA. 8\nB. 6\nC. 2\nD. 4\nE. 3\n\n### Answer:\nPerimeter of rectangular yard = 2(l + b) = 14 --> l + b = 7\nArea = l * b = 6\nb = 7 - l\nl(7 - l) = 6\n7l - l^2 = 6\nl^2 - 7l + 6 = 0\nUpon simplifying we get l = 1 or 6. Only 6 is there in the answer choice.\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many three digit numbers contain the digit 5 at least once?\n\n### Options:\nA. 52\nB. 128\nC. 252\nD. 648\nE. 900\n\n### Answer:\nThe question is basically asking how many numbers between 100-999 contain at least one digit as 5.\nLet ABC be a 3 digit number A can be filled with 9 digits, B can be filled with 10 digits and C can be filled with 10 digits. (because hundredth digit can only be between 1-9= 9 digits)\nTherefore total number of ways we can form 3 digit number=9*10*10=900 ways (100-999)\nNumber of ways we can form a 3 digit number without the digit 5= 8*9*9= 648 ways\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo trains 121 meters and 165 meters in length respectively are running in opposite directions, one at the rate of 80 km and the other at the rate of 65 kmph. In what time will they be completely clear of each other from the moment they meet?\n\n### Options:\nA. 7.19\nB. 7.18\nC. 7.16\nD. 7.15\nE. 7.12\n\n### Answer:\nT = (121 + 165)/ (80 + 65) * 18/5\nT = 7.15\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 1 > 1 - ab > 0, which of the following must be true?\nI. a/b < 1\nII. a/b > 0\nIII. ab < 1\n\n### Options:\nA. I only\nB. II only\nC. III only\nD. II and III only\nE. I and III only\n\n### Answer:\nMANHATTAN GMATOFFICIAL SOLUTION:\nYou can manipulate the original compound inequality as follows, making sure to perform each manipulation on every term:\n1 > 1 - ab > 0\n0 > -a b > -1 Subtract 1 from all three terms.\n0 < ab < 1 Multiply all three terms by -1 and flip the inequality signs.\nTherefore you know that 0 < ab < 1. This tells you that ab is positive, so a/b must be positive (a and b have the same sign). Therefore, I must be true. However, you do not know whether a/b < 1, so II is not necessarily true. But you do know that ab must be less than 1, so III must be true.\nTherefore, the correct answer is (D).\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the next number of the following sequence\n1,3,4,5,6,7,1,9,16,25,36,...\n\n### Options:\nA. 14\nB. 15\nC. 16\nD. 17\nE. 49\n\n### Answer:\n(1, 3 ,4, 5, 6, 7) (1, 9, 16, 25, 36, x)\nsquare of 1st group gives 2nd group\n1^2 = 1\n3^2 = 9\n4^2 = 16\n5^2 =25\n6^2 =36\n7^2 = 49\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe compound ratio of 5:6, 3:2 and 4:5?\n\n### Options:\nA. 1:5\nB. 1:8\nC. 1:2\nD. 1:1\nE. 1:9\n\n### Answer:\n5/6 * 3/2 * 4/5\n= 1/1\n1:1\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA bowl contains many kinds of fruit. In the bowl there are twice as many apples then there are bananas, and three times as many oranges as bananas. If the total number of pieces of fruit is X, then how many apples are in the bowl as a fraction of X\n\n### Options:\nA. X/2\nB. X/3\nC. 2*X\nD. X/6\nE. X/4\n\n### Answer:\nSince X is the total number of fruit: X = apples + bananas + oranges.\nSince there are three times as many oranges as bananas then 1*orange = 3*bananas\nThus X = apples + bananas + (3*bananas); which simplifies to X = apples + 4*bananas\nSince there are twice as many apples as bananas then 1*apple = 2*bananas; which converts to bananas=apple/2\nThus X = apples + 4*(apples/2); which simplifies to X = 2*apples.\nThus apples = X/2\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA motor starts with the speed of 70 kmph with its speed increasing every two hours by 10 kmph. In how many hours will it cover 345 kms?\n\n### Options:\nA. 2 1\u20444 hours\nB. 4 1\u20442 hours\nC. 4 hours 5 minutes\nD. Cannot be determined\nE. None of these\n\n### Answer:\nDistance covered in first two hours = 70 \u00d7 2 = 140 km\nDistance covered in next two hours = 80 \u00d7 2 = 160 km\nDistance covered in first four hours\n140 + 160 = 300 km\nRemaining distance = 345 \u2013 300 = 45 km.\nNow, this distance will be covered at the speed of 90 km/hr.\n\u2234 Time taken = 45\u204490 = 1\u20442 hour.\nTotal time= 4 + 1\u20442 = 41\u20442 hour\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA can do a work in 60days and B in 12 days.Then A and B together do the work in,how many days?\n\n### Options:\nA. 5 days\nB. 4 days\nC. 10 days\nD. 2 days\nE. 6 days\n\n### Answer:\nExplanation:\nA's 1day's work = 1/60\nB's 1day's work = 1/12\nThey work together = 1/60 + 1/12 = 10 days\nAnswer: Option C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a kilometer race, A beats B by 40 meters or 10 seconds. What time does A take to complete the race?\n\n### Options:\nA. 180 sec\nB. 190 sec\nC. 290 sec\nD. 490 sec\nE. 240 sec\n\n### Answer:\nTime taken by B run 1000 meters = (1000 * 10)/40\n= 250 sec.\nTime taken by A = 250 - 10\n= 240 sec.\nAnswer:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat amount does Kiran get if he invests Rs.8000 at 10% p.a. compound interest for two years, compounding done annually?\n\n### Options:\nA. 3388\nB. 2177\nC. 2877\nD. 1678\nE. 9680\n\n### Answer:\nA= P{1 + R/100}n\n=> 8000{1 + 10/100}2 = Rs.9680\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA and B invest money in the ratio 8:9 and they has loss of Rs.6900 at the end of year. what is the share of loss of B?\n\n### Options:\nA. Rs.1600\nB. Rs.1500\nC. Rs.1400\nD. Rs.1300\nE. None of the above\n\n### Answer:\net ratio of A and B be 8x & 9x\nso net loss = 8x+9x= 6800\nx=400\nA=3x=3(400)=1200\nB= 4x=4(400)=1600\nso, B= 1600\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo cars start from the opposite places of a main road, 140 km apart. First car runs for 25 km and takes a right turn and then runs 15 km. It then turns left and then runs for another 25 km and then takes the direction back to reach the main road. In the mean time, due to minor break down the other car has run only 35 km along the main road. What would be the distance between two cars at this point?\n\n### Options:\nA. 65\nB. 38\nC. 20\nD. 55\nE. 21\n\n### Answer:\nAnswer: D) 55 km\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe number of positive integers valued pairs (x, y) satisfying 4x -17y = 1 and x <= 1000 (x is less than or equal to 1000) is\n\n### Options:\nA. fifty nine\nB. 57\nC. 55\nD. 58\nE. 60\n\n### Answer:\n4x-17y=1\ny=(4x-1)/17\nx has to be a positive integer such that 1 <=x<=1000(4x-1) is a factor of 17 so that y is also a positive integer\nSo we need to know how many numbers in the set {3,7,11,15,....,3999} are divisible by 17\nLets try to observe the pattern\n1. 3 mod 17 = 3\n2. 7 mod 17 = 7\n3. 11 mod 17 = 11\n4. 15 mod 17 = 15\n5. 19 mod 17 = 2\n6. 23 mod 17 = 6\n7. 27 mod 17 = 10\n8. 31 mod 17 = 14\n9. 35 mod 17 = 1\n10. 39 mod 17 = 5\n11. 43 mod 17 = 9\n12. 47 mod 17 = 13\n13.51 mod 17 = 0\n14. 55 mod 17 = 4\n15. 59 mod 17 = 8\n16. 63 mod 17 = 12\n17. 67 mod 17 = 16\n... and after this the remainders will repeat (this is no co-incidence that the cyclicity is also 17)\nSo the right choices are x=13,13+17,13+17+17,.....\nThe number of such numbers is 59 (highest one being 999) A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo pipes can fill a tank in 15 minutes and 12 minutes. The outlet pipe can empty the tank in 20 minutes. If all the pipes are opened when, the tank is empty, then in how many minutes will it take to fill the tank?\n\n### Options:\nA. 12\nB. 13\nC. 11\nD. 10\nE. 9\n\n### Answer:\nPart of tank filled by all three pipes in one minute =\n1/15 + 1/12 \u2013 1/20 = (8+10-6) / 120\n= 18-6 / 120\n= 1/10\nSo, the tank becomes full in 10 minutes.\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a division sum, the remainder is 6 and the divisor is 5 times the quotient and is obtained by adding 17 to the thrice of the remainder. The dividend is\n\n### Options:\nA. 74\nB. 146\nC. 86\nD. 92\nE. 98\n\n### Answer:\nDivisor = (6 * 3) + 17 = 35\n5 * Quotient = 35\nQuotient = 7.\nDividend = (Divisor * Quotient) + Remainder\nDividend = (20 * 7) + 6 = 146.\nB)\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf it takes a tub 2 minutes to drain 5/7 of its content, how much more time will it take for the tub to be empty?\n\n### Options:\nA. 48 seconds\nB. 1 minute, 12 seconds\nC. 1 minute, 50 seconds\nD. 2 minutes, 14 seconds\nE. 4 minutes, 12 seconds\n\n### Answer:\nIf 5/7 of tub's content is drained 2/7 th of tub still needs to be drained.\nIf it takes 2 minutes to drain 5/7 th of tub it takes 2*(7/5) minutes to drain the entire tub and 2*(7/5)*(2/7) min to drain 2/7 th of the tub which is 4/5 minutes or 48 minutes\nSo answer is A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJohn weighs twice as much as Susan. Susan's weight is 60% of Sam's weight. Mark weighs 50% of Lynn's weight. Lynn weighs 140% of John's weight. Which of these 5 people weighs the least?\n\n### Options:\nA. John\nB. Susan\nC. Sam\nD. Mark\nE. Lynn\n\n### Answer:\nJohn weighs twice as much as Susan --> J=2S --> John cannot weigh the least;\nSusan's weight is 60% of Sam's weight --> S=0.6*Sam --> Sam cannot weigh the least;\nMark weighs 50% of Lynn's weight --> M=0.5*L --> Lynn cannot weigh the least;\nLynn weighs 140% of John's weight --> L=1.9*J --> John cannot weigh the least (we already know that);\nAs you can see the answer is either Susan (S) or Mark (M). To compare their weights we should express their weights in regards of the same person: M=0.5*L=0.5*(1.4*J)=0.7*J and from J=2S, S=0.5*J --> Susan weights the least: Susan's weight is 50% of that of John and Mark's weight is more than 50%of that of John.\nAnswer: B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA rectangular circuit board is designed to have width w inches, perimeter p inches, and area r square inches. Which of the following equations must be true?\n\n### Options:\nA. w^2 + pw + r = 0\nB. w^2 - pw + 2r = 0\nC. 2w^2 + pw + 2r = 0\nD. 2w^2 - pw - 2r = 0\nE. 2w^2 - pw + 2r = 0\n\n### Answer:\nNotice that we can discard options A, and C right away. The sum of 3 positive values Cannot be 0.\nNow, assume:\nWidth =w = 1 inchand length = 1 inch;\nPerimeter =p = 4 inches;\nArea =r = 1 square inches.\nPlug the values of w, p, and r into the answer choices: only for E 2w^2 - pw + 2r = 2 - 4 + 2 = 0.\nAnswer: E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn the number 11,0AB, A and B represent the tens and units digits, respectively. If 11,0AB is divisible by 65, what is the greatest possible value of B \u00d7 A?\n\n### Options:\nA. 0\nB. 5\nC. 10\nD. 15\nE. 25\n\n### Answer:\nYou should notice that 65*2=110 so 11,000 is divisible by 55: 55*200=11,000 (or you can notice that 11,000 is obviously divisible by both 5 and 11 so by 55) --> B*A=0*0=0. Next number divisible by 55 is 11,000+55=11,055: B*A=5*2=10 (next number won't have 110 as the first 3 digits so we have only two options 0 and 25).\nAnswer: C\n!\nPlease post PS questions in the PS subforum:gmat-problem-solving-ps-140/\nPlease post DS questions in the DS subforum:gmat-data-sufficiency-ds-141/\nNo posting of PS/DS questions is allowed in the mainMath forum.\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf four coins are tossed, the probability of getting two heads and two tails is\n\n### Options:\nA. 3/8\nB. 6/11\nC. 2/5\nD. 4/5\nE. 5/11\n\n### Answer:\nSince four coins are tossed, sample space = 24\nGetting two heads and two tails can happen in six ways.\nn(E) = six ways\np(E) = 6/24 = 3/8\nAnswer : A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMary's income is 70 percent more than Tim's income, and Tim's income is 40 percent less than Juan's income. What percent of Juan's income is Mary's income?\n\n### Options:\nA. 124%\nB. 102%\nC. 96%\nD. 80%\nE. 64%\n\n### Answer:\nJuan's income = 100 (assume);\nTim's income = 60 (40 percent less than Juan's income);\nMary's income = 102 (70 percent more than Tim's income).\nThus, Mary's income (102) is 102% of Juan's income (100).\nAnswer: B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a certain appliance store, each model of television is uniquely designated by a code made up of a particular ordered pair of letters. If the store has 60 different models of televisions, what is the minimum number of letters that must be used to make the codes?\n\n### Options:\nA. 6\nB. 7\nC. 8\nD. 9\nE. 10\n\n### Answer:\nIf n is the number of distinct letters used to create the two lettered codes, then a total of n\u2217n=n^2 different codes can be created. We need n2\u226560. The smallest n which fulfills this condition is n = 8.\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average (arithmetic mean) of four distinct positive integers is 5. If the average of the smaller two of these four integers is 6, which of the following represents the maximum possible value of the largest integer?\n\n### Options:\nA. 2\nB. 4\nC. 3\nD. 8\nE. 1\n\n### Answer:\nLet the distinct number be A,B,C, and D\nIts given A > B > C > D\nalso A + B + C + D =20 and A + B = 6 means C + D = 14\nSince the question ask for the largest possible number we should choose the least value for A and B,C. So D should be 8\nAnswer : D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average (arithmetic mean) of eight numbers is 44.1. If the sum of half of these numbers is 158.4, what is the average of the other half?\n\n### Options:\nA. 12.8\nB. 24.2\nC. 48.6\nD. 72.1\nE. 96.8\n\n### Answer:\narithmetic mean = sum / total numbers\nsum = 44.1 * 8 = 352.8\nsum of half of these numbers is 158.4. So, 4 numbers sum is 158.4. Rest 4 numbers sum = 352.8-158.4 = 194.4\nArithmetic mean of the 4 nos = 194.4/4 = 48.6\nHence, C is the answer.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average of four consecutive odd numbers is 24. Find the largest number?\n\n### Options:\nA. 25\nB. 29\nC. 27\nD. 31\nE. None\n\n### Answer:\nLet the numbers are x, x+2, x+4, x+6, then\nx+(x+2)+(x+4)+(x+6)/4=24\n4x+12/4=24\nx+3=24\nx=21\nSo largest number is 21 + 6 = 27\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn Township K, 1/5 of the housing units are equiped with cable Tv. If 1/15 of the housing units, including 1/3 of those that are equiped with cable tv, are equipped with videocassette recorders, what fraction of the housing units have neither cable tv nor videocassette recorders?\n\n### Options:\nA. 23/30\nB. 11/15\nC. 7/10\nD. 4/5\nE. 2/15\n\n### Answer:\n1/5 -- cable TV (This includes some data from video cassette recorder)\n1/15 -- video cassette recorder including 1/3(equiped with cable tv) i.e. 1/3(1/5) = 1/15\ntherefore only video cassette recorder = 1/15 - 1/15 = 0\nTotal = 1/5+0+neither cable tv nor videocassette recorders\n1 = 1/5 + neither cable tv nor videocassette recorders\ntherefore neither cable tv nor videocassette recorders = 1-1/5 = 4/5\nHence D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA money lender lent Rs. 1000 at 3% per year and Rs. 1400 at 5% per year. The amount should be returned to him when the total interest comes to Rs. 350. Find the number of years.\n\n### Options:\nA. 3.5\nB. 3.75\nC. 4\nD. 4.25\nE. 4.5\n\n### Answer:\n(1000xtx3/100) + (1400xtx5/100) = 350 \u2192 t =3.5 answer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a certain business school class, p students are accounting majors, q students are finance majors, r students are marketing majors, and s students are strategy majors. If pqrs = 1,155, and if 1< p < q < r < s, how many students in the class are accounting majors?\n\n### Options:\nA. 3\nB. 5\nC. 8\nD. 11\nE. 17\n\n### Answer:\nPrime factorization of the product\npqrs = 1155\n= 3* 5 *7 * 11\nSince 1< p < q < r < s\nNumber of students who are accounting majors , p = 3\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJohnny makes $6.75 per hour at his work. If he works 10 hours, how much money will he earn?\n\n### Options:\nA. $67.50\nB. $54\nC. $28.50\nD. $12.50\nE. $9.60\n\n### Answer:\n6.75*10=67.50. Answer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n10 women can complete a work in 7 days and 10 children take 14 days to complete the work. How many days will 5 women and 10 children take to complete the work?\n\n### Options:\nA. 6\nB. 5\nC. 7\nD. 8\nE. 2\n\n### Answer:\n1 women's 1 day work = 1/70\n1 child's 1 day work = 1/140\n(5 women + 10 children)'s 1 day work\n= (5/10 + 10/140) = (1/14 + 1/14) = 1/7\n5 women and 10 children will complete the work in 7 days.\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a car travels a distance of 300 km in 8 hours, partly at a speed of 40 kmh-1 and partly at 30 kmh-1, what is the distance it travelled at the speed of 40 kmh-1?\n\n### Options:\nA. 200 km\nB. 210 km\nC. 220 km\nD. 240 km\nE. 250 km\n\n### Answer:\nlet the distance travelled at 40 kmph=x km\ndistance travelled at 30 kmph =300-x km\nx/40 + (300-x)/30 = 8\nx = 240\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAn employer pays Rs.20 for each day a worker works and for fests Rs.3 for each day is ideal at the end of sixty days a worker gets Rs.280 . for how many days did the worker remain ideal?\n\n### Options:\nA. 40\nB. 30\nC. 70\nD. 20\nE. 10\n\n### Answer:\nSuppose a worker remained ideal for x days then he worked for 60-x days\n20*(60-x)-3x=280\n1200-23x=280\n23x=920\nx=40\nAnswer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA squirrel runs up a cylindrical post , in a perfect spiral path making one circuit for each rise of 4 feet . How many feet does the squirrel travels if the post is 16 feet tall and 3 feet in circumference?\n\n### Options:\nA. 10 feet\nB. 12 feet\nC. 13 feet\nD. 15 feet\nE. 18 feet\n\n### Answer:\ntotal circuit=16/4=4\ntotal feet squirrel travels=4*3=12 feet\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFresh grapes contain 70% water by weight and raisins obtained by drying fresh grapes contain 25% water by weight. How many kgs of fresh grapes are needed to get 30kgs of raisins?\n\n### Options:\nA. 75 kgs\nB. 64kgs\nC. 72 kgs\nD. 65 kgs\nE. 70 kgs\n\n### Answer:\nThe weight of non-water in 30 kg of dried grapes (which is 100-25=75% of whole weight) will be the same as the weight of non-water in x kg of fresh grapes (which is 100-70=30% of whole weight),\nso 30*0.75 = x*0.3\n--> x = 75.\nAnswer: A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the invalid no.from the following series 15 46 63 71 75 77 78\n\n### Options:\nA. 15\nB. 46\nC. 75\nD. 77\nE. 78\n\n### Answer:\nIn this question, if you start from the beginning, firstly the difference is 31, then the difference is 17, then the difference is 8. So there is no logic. If you start backwards,you can see that firstly, 1 is added, then 2 is added, then 4 is added, then 8,16 and 32 should have been added. So you have got the right clue. So 15 + 32 the first number should be 47 and afterwards, the series becomes + 16, + 8, + 4and so on.\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nLast September the sales total for a certain car dealership was 400% greater than the average monthly sales total for the other 11 months. The sales total for September was approximately what percent of the year\u00b4s sales?\n\n### Options:\nA. 15 %\nB. 27%\nC. 31%\nD. 42%\nE. 75%\n\n### Answer:\n11 moth avg = x\n11 month total = 11x\nsept = 400% of x + x = 5x\nsept/total = =5x/(11x+5x) = =31%\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a certain kindergarten, every child has got either a dog or a cat or both. 18 children have got dogs only and 6 children have got both dogs and cats. If there are 30 children in the kindergarten, how many of them have cats?\n\n### Options:\nA. 6\nB. 12\nC. 14\nD. 16\nE. 20\n\n### Answer:\nA : Only Cats\nB : Both Cats and Dogs\nC : Only Dogs\nAs per question, A + B + C =30\nC = 18\nB = 6, so A = 6. Hence, A + b = 12. Answer is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf A:B is 7:5, B:C is 3:4 and C is 30 then what is the value of A?\n\n### Options:\nA. 31.5\nB. 25.5\nC. 32.5\nD. 33.8\nE. 35.7\n\n### Answer:\nA/B=7/5,\nB/C=3/4,C=30\nB=90/4\n4A/90=7/5\nA=630/20\nA=31.5\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhen a is divided by b, the quotient is c with remainder 5. What is a in terms of 5, b, and c?\n\n### Options:\nA. bc-5\nB. 5bc\nC. 5b/c\nD. b/c\nE. bc+5\n\n### Answer:\na/b =c with remainder 5\ni.e, a-5 = bc\na= bc+5\nAnswer : E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nprofessor absentminded has a very peculiar problem that he cannot remember number larger than 15. however he tells his wife, i can remember any number up to 100 by remembering the three numbers obtained as remainder when the numbers is divided by 3,7 and 11 respectively. for example (2,3,6)is 17. professor remembers that he had(2,4,8)rupees in the purse, and he paid(2,5,4) rupees to the servant. how much money is left in the purse?\n\n### Options:\nA. 45\nB. 46\nC. 47\nD. 48\nE. 49\n\n### Answer:\nfind out the common term in those 3 series for (2,4,8)\n3N+2=2,5,8,11,14......71,74\n7N+4=4,11,18...67,74\n11N+8=8,19,30......63,74\nfind out the common term in those 3 series for (2,5,4)\n3N+2=2,5.....23,26\n7N+5=5,12,19,26\n11N+4=4,15,26\nnow 74-26=48\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n1, 8, 27, 64, 125, 216, (....)\n\n### Options:\nA. 354\nB. 343\nC. 245\nD. 392\nE. 400\n\n### Answer:\nThe pattern is 1^3, 2^3, 3^3, 4^3, 5^3, 6^3, etc\nHence, next number is 7^3 = 343\nAnswer is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nX and Y together can completes a work in 12 days and Y complete the same work in 24 days. Then the number of days X required to complete the work will be?\n\n### Options:\nA. 15 days.\nB. 12 days.\nC. 24 days.\nD. 13 days.\nE. 16 days.\n\n### Answer:\nX and y complete in one day =1/12 part, y completes in one day=1/24 parts. Therefore X alone can do in one day =1/24part. Therefore the work can be finished by X = 24 days. Ans: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich of the following best approximates the value of q if 5^25+5^15=5^q ?\n\n### Options:\nA. 40\nB. 26\nC. 25\nD. 24\nE. 20\n\n### Answer:\nWe have: 5^25+5^15=5^q\n==> because 5^15 > 0 --> 5^q MUST be equal or greater than 5^25 ==>q MUST be equal or greater than 25\n==> Option D and E are out immediately.\nDivide both sides by 5^q and q >= 25\nWe have:\n5^(25-q) + 5^15/5^q = 1\nBecause q >= 25 ==>5^15/5^q = 0.0000xyz, that is very small,we can ignore it.\nThus, 5^(25-q) must be approximately 1\n==> 25-q = 0 ==> q is approximately 25\nC is the answer.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAverage temperature of first 4 days of a week is 6\u00b0C and that of the last 4 days is 40.3\u00b0C. If the average temperature of the week be 39.1\u00b0C, the temperature on 4th day is?\n\n### Options:\nA. 36.7\u00b0C\nB. 38.6\u00b0C\nC. 39.8\u00b0C\nD. 41.9\u00b0C\nE. 51.9\u00b0C\n\n### Answer:\nLet temperature on 4th day be X\u00b0C\nTherefore, 4 x 38.6 + 4 x 40.3 - X = 7 x 39.1\n=> X = 41.9\nTherefore, temperature on 4th day = 41.9\u00b0C.\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf A and B are positive integers, and the remainder obtained when A is divided by B is the same as the remainder obtained when B is divided by A, which of the following is a possible value of AB?\n\n### Options:\nA. 62\nB. 55\nC. 49\nD. 34\nE. 24\n\n### Answer:\nI am not too sure on this. I guess it is possible only when A and B are both same. If they are both same, AB must be a perfect square.\n49 is a perfect square.\nAns:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind out the C.I on Rs.6000 at 4% p.a. compound half-yearly for 1 1/2 years\n\n### Options:\nA. 367.25\nB. 306.07\nC. 306.04\nD. 306.03\nE. 306.01\n\n### Answer:\nA = 6000(51/50)3\n= 6367.248\n6000\n-----------\n367.25\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA and B start a business, with A investing the total capital of Rs.50000, on the condition that B pays A interest @ 10% per annum on his half of the capital. A is a working partner and receives Rs.1500 per month from the total profit and any profit remaining is equally shared by both of them. At the end of the year, it was found that the income of A is twice that of B. Find the total profit for the year?\n\n### Options:\nA. 59028\nB. 59010\nC. 59190\nD. 59000\nE. 92700\n\n### Answer:\nInterest received by A from B = 10% of half of Rs.50000 = 10% * 25000 = 2500.\nAmount received by A per annum for being a working partner = 1500 * 12 = Rs.18000.\nLet 'P' be the part of the remaining profit that A receives as his share. Total income of A = (2500 + 18000 + P)\nTotal income of B = only his share from the remaining profit = 'P', as A and B share the remaining profit equally.\nIncome of A = Twice the income of B\n(2500 + 18000 + P) = 2(P)\nP = 20500\nTotal profit = 2P + 18000\n= 2*20500 + 18000 = 59000\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSam invested Rs. 12000 @ 10% per annum for one year. If the interest is compounded half-yearly, then the amount received by Sam at the end of the year will be?\n\n### Options:\nA. 13230.0\nB. 12300.02\nC. 16537.5\nD. 15000.0\nE. 16537.11\n\n### Answer:\nP = Rs. 12000 ; R = 10% p.a. = 5% per half-year; T = 1 year\n= 2 half-year\nAmount = [12000 * (1 + 5/100)2]\n= (12000 * 21/20 * 21/20)\n= Rs.13230.00\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the sum of the integers from -150 to 155, inclusive?\n\n### Options:\nA. 865\nB. 955\nC. 1050\nD. 765\nE. 750\n\n### Answer:\nIn an arithmetic progression,\nthe nth term is given by tn=a+(n-1)d\nhere tn=155, a=-150, d=1\nhence, 155=-150+(n-1)\nor n=306\nSum of n terms can be calculated by sn=n/2(a+l)\na=first term, l=last term, n=no. of terms\nsn=306*(-150+155)/2\nsn=306*5/2 = 765\nAnswer : D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA is thrice as good a workman as B and takes 10 days less to do a piece of work than B takes. B alone\ncan do the whole work in\n\n### Options:\nA. 15 days\nB. 10 days\nC. 9 days\nD. 8 days\nE. None of these\n\n### Answer:\nExplanation:\nRatio of times taken by A and B = 1:3\nMeans B will take 3 times which A will do in 1 \u019fme\nIf difference of time is 2 days, B takes 3 days\nIf difference of time is 10 days, B takes (3/2) * 10 =15 days\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe sum of three consecutive even numbers multiples of 3 is 72. what is the largest number ?\n\n### Options:\nA. 21\nB. 24\nC. 27\nD. 36\nE. None\n\n### Answer:\nSolution\nlet the number be x and x + 2.\nThen, (x + 2)2 - x2 = 84 \u21d4 4 x + 4 = 84 \u21d4 4 x = 80 \u21d4 x = 20.\n\u2234 Required sum = x + (x + 2) = 2 x + 2 = 42.\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the price has fallen by 15% what percent of its consumption be: increased so that the expenditure may be the same as before?\n\n### Options:\nA. 11 1/8%\nB. 11 1/5%\nC. 17 11/17%\nD. 18 7/9%\nE. 21 1/9%\n\n### Answer:\n100 \u00e2\u20ac\u201c 15 = 85\n85------15\n100------? => 17 11/17%\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a young child was 15 months old one year ago, how old was the child, in months, x months ago?\n\n### Options:\nA. x \u2212 27\nB. x \u2212 12\nC. 15 \u2212 x\nD. 24 \u2212 x\nE. 27 \u2212 x\n\n### Answer:\nThe child's age today is 15 months + 12 months = 27 months\nx months ago, the child's age was (27 - x) months old.\nThe answer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFrom January 1, 2015, to January 1, 2017, the number of people enrolled in health maintenance organizations increased by 12 percent. The enrollment on January 1, 2017, was 45 million. How many million people, to the nearest million, were enrolled in health maintenance organizations on January 1, 2015 ?\n\n### Options:\nA. 38\nB. 39\nC. 40\nD. 41\nE. 42\n\n### Answer:\nSoln:-\n12x=45 --> 28/25*x=45 --> x=45*25/28=1125/28=~40\nAnswer: C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nShopkeeper rise price by 34% and gives successive discount of 10% and 15%. What is overall % gain or loss?\n\n### Options:\nA. 2.51%\nB. 4.51%\nC. 3.51%\nD. 6.51%\nE. 7.51%\n\n### Answer:\nLet d initial price be 100\n34 % rise\nnow price = 134/100*100 = 134\n10% discount\nThen price = 134 * 90/100 = 120.6\n15 % discount\nThen price = 120.6 * 85/100 = 102.51\nSo Gain = 102.51 - 100 = 2.51\nGain % = Gain * 100 /CP\n==> 2.51 * 100 /100 = 2.51%\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe present worth of a sum due sometimes hence is Rs.5760 and the banker's gain is Rs.10. What is the true discount?\n\n### Options:\nA. Rs. 480\nB. Rs. 420\nC. Rs. 120\nD. Rs. 240\nE. None of these\n\n### Answer:\nTD = \u221aPW \u00d7 BG\n=\u221a5760\u00d710\n=\u221a57600\n= Rs. 240\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nApple Street begins at Peach Street and runs directly east for 3.2 kilometers until it ends when it meets Cherry Street. Apple Street is intersected every 200 meters by a perpendicular street, and each of those streets other than Peach Street and Cherry Street is given a number beginning at 1st Street (one block east of Peach Street) and continuing consecutively (2nd Street, 3rd Street, etc...) until the highest-numbered street one block west of Cherry Street. What is the highest-numbered street that intersects Apple Street?\n\n### Options:\nA. 14th\nB. 15th\nC. 16th\nD. 17th\nE. 18th\n\n### Answer:\n3.2 km / 200 m = 16.\nHowever, the street at the 3.2-km mark is not 16th Street; it is Cherry Street.\nTherefore, the highest numbered street is 15th Street.\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a coin is tossed twice what is the probability that it will land either heads both times or tails both times?\n\n### Options:\nA. 1/8\nB. 1/6\nC. 1/4\nD. 1/2\nE. 1\n\n### Answer:\nProb to get 2 heads = 1/2*1/2 = 1/4\nProb to get 2 tails = 1/2*1/2 = 1/4\nSo, Prob to get either 2 heads or 2 tails = 1/4+1/4 = 1/2\nAnswer will be D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 625(5^x) = 1 then x=\n\n### Options:\nA. \u20132\nB. -4\nC. 0\nD. -1\nE. 2\n\n### Answer:\n5^x = 1/625\n5^x = 1/5^4\n5^x= 5^-4\nx = -4\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA can do a piece of work in 8 hours; B and C together can do it in 12 hours, while A and C together can do it in 16 hours. How long will B alone take to do it?\n\n### Options:\nA. 7 8/5 hours\nB. 5 9/8 hours\nC. 5 6/8 hours\nD. 6 6/7 hours\nE. none of the above\n\n### Answer:\nA's 1 hour's work = 1/8 ;\n(B + C)'s 1 hour's work = 1/12 ;\n(B + C)'s 1 hour's work = 1/16\n(A + B + C)'s 1 hour's work = (1/8 + 1/12) = 5/24\nB's 1 hour's work = (5/24 - 1/16) = 7/48\nB alone will take 48/7 hours to do the work.\n=6 6/7\nAnswer = D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nGiven two fair dice, what is the probability Q that the sum of their numbers is 4 if exactly one die shows a 3?\n\n### Options:\nA. a) 2/11\nB. b) 1/18\nC. c) 3/11\nD. d) 2/39\nE. e) 1/5\n\n### Answer:\nIf exactly one die shows 3, there are 10 such combinations (given that we have 2 fair dice).\n1:3, 2:3, 4:3, 5:3, 6:3,\n3:1, 3:2, 3:4, 3:5, 3:6\nThe sum of numbers would be 4 for two events: 1:3, 3:1.the probability Q that the sum of their numbers is 4 if exactly one die shows a 3\n2/11 would be the answer if 'at least one of the die shows a 3'.A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf x, 3, 5, 7 are there and the range and median of them are the same, what is the value of x?\n\n### Options:\nA. 0\nB. 1\nC. 2\nD. 5\nE. 4\n\n### Answer:\nTry taking the values of x as you suggested and then see if the median and the range are equal.\nOnce you do that, you will get the answer yourself.\nTried substituting values starting with 3, 5, 7...\nonly x = 5 satisfies the condition.\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average expenditure of a man for the first five months is Rs.180 and for the next seven months it is Rs.130. If he saves Rs.290 in that year, his monthly average income is :\n\n### Options:\nA. Rs.140\nB. Rs.150\nC. Rs.160\nD. Rs.175\nE. none\n\n### Answer:\nExplanation:\nTotal income = Rs.(180\u00c3\u20145+130\u00c3\u20147+290)=Rs.2100\nAverage monthly income\n= Rs. (2100/12)=Rs.175\nCorrect Option: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf two dice are thrown together, the probability of getting an even number on one die and an odd number on the other is -.\n\n### Options:\nA. 1/4\nB. 1/2\nC. 3/4\nD. 3/5\nE. None of these\n\n### Answer:\nThe number of exhaustive outcomes is 36.\nLet E be the event of getting an even number on one die and an odd number on the other. Let the event of getting either both even or both odd then = 18/36 = 1/2\nP(E) = 1 - 1/2 = 1/2.\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nDuring a car trip, Maria stopped to rest after she traveled 1/2 of the total distance to her destination. she stopped again after she traveled 1/4 of the distance remaining between her first stop and her destination, and then she drove the remaining 150 miles to her detination. What was the total distance, in miles from Maria's starting point to her destination?\n\n### Options:\nA. 280\nB. 320\nC. 360\nD. 400\nE. 480\n\n### Answer:\nEasy 400 is the answer.\n3/4 ( x/2) = 150\nx = 150 * 8 /3 = 400.\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOn a certain day, Tim invested $1,000 at 10 percent annual interest, compounded annually, and Lana invested 2,000 at 5 percent annual interest, compounded annually.The total amount of interest earned by Tim\u2019s investment in the first 2 years was how much greater than the total amount of interest earned by Lana\u2019s investment in the first 2 years?\n\n### Options:\nA. $5\nB. $15\nC. $50\nD. $100\nE. $105\n\n### Answer:\nCompounded annually means that the interest is applied once per year. One can have 10% annual interest compounded monthly - in this case 10%/12 would be applied each month, or 10% annual interest compounded daily etc.\nWith respect to the problem at hand, at the end of two years, Tim would have\n1,000(1.10)^2 = 1,000(1.21) = 1,210\nand Lana would have\n2,000(1.05)^2 = 2,000(1.1025) = 2,205\nThus, Tim earned 210 dollars, while Lana earned 205 dollars\nThe difference is $5 and the answer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf it takes 6 identical printing presses exactly 4 hours T to print 5,000 newspapers, how long would it take 3 of these presses to print 3,000 newspapers?\n\n### Options:\nA. 3 hours, 20 minutes\nB. 4 hours, 20 minutes\nC. 4 hours, 48 minutes\nD. 5 hours, 48 minutes\nE. 6 hours, 50 minutes\n\n### Answer:\n6 presses - 5,000 newspapers - 4 hours ;\n3 presses - 2,500 newspapers - 4 hours ;\n3 presses - 3,000 newspapers - 4 hours + 1/5*4 hours = 4 hours, 48 minutes (since 2,500+1/5*2,500=3,000) = T.\nAnswer: C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind LCM of fraction series 4/5, 8/35, 2/15, 6/25 ?\n\n### Options:\nA. 36/5\nB. 24/5\nC. 16/5\nD. 36/7\nE. 25/2\n\n### Answer:\nWe know that the LCM for fraction can be calculated as:\nLCM = (LCM of numerators) / (HCF of denominators)\n= (LCM of 4, 8, 2, 6) / (HCF of 5, 35, 15, 25)\n= (2 x 2 x 2 x 3) / (5)\n= 24 / 5\nAns - B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA can do a work in 3 days. B can do the same work in 6 days. If both A & B are working together in how many days they will finish the work?\n\n### Options:\nA. 3\nB. 5\nC. 4\nD. 2\nE. 6\n\n### Answer:\nA rate = 1/3\nB rate = 1/6\n(A+B) rate = (1/3)+(1/6) = 1/2\nA & B finish the work in 2days\ncorrect option is D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA cricket player whose bowling average was 20.5 runs per wicket, takes 5 wicket for 52 runs in a match. Due to this his average decreases by 0.5. What will be the number of wickets taken by him till the last match?\n\n### Options:\nA. 64\nB. 72\nC. 101\nD. 111\nE. 128\n\n### Answer:\nAverage = Total Runs / Total wickets\nTotal runs after last match = 20.5w + 52\nTotal wickets after last match = w + 5\n(20.5w + 52) / (w + 5) = 20.5 - 0.5 = 20\nw = 96\nso total wickets aftr last match = w+5 = 101\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat distance will be covered by a bus moving at 72 kmph in 30 seconds?\n\n### Options:\nA. 700 m\nB. 500 m\nC. 800 m\nD. 600 m\nE. 400 m\n\n### Answer:\nD\n600 m\n72 kmph = 72 * 5/18 = 20 mps\nD = Speed * time = 20 * 30 = 600 m.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are 10 magazines lying on a table; 5 are fashion magazines and the other 5 are sports magzines. If 4 magazines are to be selected at random from the 8 magazines, what is the probability that at least one of the fashion magazine will be selected?\n\n### Options:\nA. 60/61\nB. 40/42\nC. 41/42\nD. 45/46\nE. 54/55\n\n### Answer:\n1- (5c4/10c4) = 1-1/42 = 41/42\nAnswer : C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n20 men do a work in 20days. How many men are needed to finish the work in 5days?\n\n### Options:\nA. 50\nB. 20\nC. 80\nD. 10\nE. 15\n\n### Answer:\nmen required to finish the work in 5days = 20*20/5 = 80\nAnswer is C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAverage monthly income of a family of 4 earning members was Rs. 735. One of the earning members died and therefore, the average income came down to Rs 590. The income of the deceased was?\n\n### Options:\nA. Rs. 692.80\nB. Rs. 820\nC. Rs. 1170\nD. Rs. 1385\nE. None\n\n### Answer:\nAnswer\nIncome of the deceased = Total income of 4 members - total income of remaining 3 members.\n= 735 x 4 - 590 x 3 Rs.\n= 1170 Rs.\nCorrect Option: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA room 14 m 21 cm long and 7m 77 cm broad is to be paved with square tiles. Find the least number of square tiles required to cover the floor.\n\n### Options:\nA. 22636\nB. 22640\nC. 22647\nD. 22533\nE. 22675\n\n### Answer:\nExplanation:\nArea of the room = (1421 x 777) cm2.\nSize of largest square tile = H.C.F. of 1421 cm and 777 cm = 7 cm.\nArea of 1 tile = (7 x 7) cm2.\nNumber of tiles required =(1147\u00d7777)/(7\u00d77)=22533\nAnswer: Option D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average age of a group of persons going for picnic is years. Sixteen new persons with an average age of 15 years join the group on the spot due to which their average age becomes 15.5 years. The number of persons initially going for picnic is\n\n### Options:\nA. 5\nB. 10\nC. 16\nD. 45\nE. 52\n\n### Answer:\nSolution\nLet the initial number of persons be x. Then\n16x + 16 x 15 = 15.5(x+20)\n= 0.5x = 8\nx = 16\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many two digit numbers are there such that the product of their digits after reducing it to the smallest form is a prime number? for example if we take 98 then 9*8=72, 72=7*2=14, 14=1*4=4. Consider only 4 prime numbers (2,3,5,7)\n\n### Options:\nA. 27\nB. 28\nC. 18\nD. 99\nE. 01\n\n### Answer:\nExplanation:\n2 = 12 or 21 So 1\u00d72, 2\u00d71, 3\u00d74, 4\u00d73, 2\u00d76, 6\u00d72, 3\u00d77, 7\u00d73\n3 = 13 or 31 So 1\u00d73, 3\u00d71\n5 = 15, 51 So 1\u00d75, 5\u00d71, 3\u00d75, 5\u00d73, 7\u00d75, 5\u00d77\n7 = 17 or 71 So 1\u00d77, 7\u00d71\n15 = 3\u00d75 = 5\u00d73\nSo total 18 numbers = 12,13,15,17,21,26,31,34,35,37,43,51,53,57,62,71,73,75\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA can give B 100 meters start and C 200 meters start in a kilometer race. How much start can B give C in a kilometer race?\n\n### Options:\nA. 111.12\nB. 111.13\nC. 111.22\nD. 111.0\nE. 111.12\n\n### Answer:\nA runs 1000 m while B runs 900 m and C runs 800 m.\nThe number of meters that C runs when B runs 1000 m,\n= (1000 * 800)/900 = 8000/9\n= 888.88 m.\nB can give C = 1000 - 888.88\n=111.12m.\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe curved surface of a sphere is 64 \u03c0 cm2. Find its radius?\n\n### Options:\nA. 8\nB. 6\nC. 4\nD. 2\nE. 5\n\n### Answer:\n4 \u03c0r2\n= 64\n=> r = 4\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA deer is standing 50 meters in from the west end of a tunnel. The deer sees a train approaching from the west at a constant speed ten times the speed the deer can run. The deer reacts by running toward the train and clears the exit when the train is 80 meters from the tunnel. If the deer ran in the opposite direction it would barely escape out the eastern entrance just as the train came out of the eastern entrance. How long is the tunnel in meters?\n\n### Options:\nA. 90\nB. 100\nC. 110\nD. 120\nE. 130\n\n### Answer:\nLet x be the length of the tunnel.\nWhen the deer runs 50 meters west, the train goes 500 meters to a point 80 meters from west entrance of the tunnel.\nWhen the deer runs east, the deer runs x-50 meters while the train goes x + 500 + 80 meters.\nx + 500 + 80 = 10(x-50)\n9x = 1080\nx = 120 meters\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA, B and C are partners. A receives 2/3 of profits, B and C dividing the remainder equally. A's income is increased by Rs.200 when the rate to profit rises from 5 to 7 percent. Find the Capital of B?\n\n### Options:\nA. 3989\nB. 2772\nC. 2500\nD. 2888\nE. 1551\n\n### Answer:\nA:B:C = 2/3:1/6:1/6 = 4:1:1\nx * 2/100 * 2/3 = 200\nB capital = 15000*1/6 = 2500\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA began a business with Rs. 85,000. He was joined afterwards by B with Ks. 42,500. For how much period does B join, if the profits at the end of the year are divided in the ratio of 3 : 1 ?\n\n### Options:\nA. 4 months\nB. 5 months\nC. 6 months\nD. 8 months\nE. 9 months\n\n### Answer:\nSuppose B joined for x months . Then, ( 85000 * 12 )/(42500 * x) = 3. or x = (85000 * 12) / (42500 * 3) = 8.\nSo, B joined for 8 months.ANSWER D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\na number divided by 44 leaves remainder 12 what is the remainder when same number divided by 12\n\n### Options:\nA. 7\nB. 8\nC. 9\nD. 10\nE. 11\n\n### Answer:\nadd 44+12=56\nnow 56divided by 12 so we get 8 as reaminder\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFrom a group of 5 managers (Joon, Kendra, Lee, Marnie and Noomi), 2 people are randomly selected to attend a conference in Las Vegas. What is the probability that Marnie and Noomi are both selected?\n\n### Options:\nA. 0.1\nB. 0.2\nC. 0.25\nD. 0.4\nE. 0.6\n\n### Answer:\n(1/6)*(1/5)+(1/6)*(1/5)=2/30=1/15\nANS:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a simultaneous throw of two coins, the probability of getting atleast one headis:\n\n### Options:\nA. 1/2\nB. 1/3\nC. 2/3\nD. 3/4\nE. 1/4\n\n### Answer:\nn(S)=4\nE = even getting at least one head\nN(E)=3\nP(E)=3/4\nANSWER D 3/4\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAce Transport has acquired two trucks to carry different types of cargo. One costs $70,000; the other costs $52,000. The company expects that the first will last 165,000 miles, after which it can be sold for salvage for about $4,000. The other will fetch the same salvage price, but will last 200,000 miles. The two trucks convoy together, so they always show the same mileage readings. If the value of each truck declines at different constant rates for every mile driven, at what mileage reading will the residual values of the two trucks be equal?\n\n### Options:\nA. 87,500 miles\nB. 100,000 miles\nC. 107,750 miles\nD. 112,500 miles\nE. The residual values will never be equal.\n\n### Answer:\nTruck 1 : 70,000 = m1 * 165,000 + 4,000 , where m1 is the depreciation $ per mile\nSolve for m1 = 0.4\nSo the depreciation line for Truck 1 is y = 0.4 x + 4,000 , where y is in dollars and x is in mileage.\nSimilarly for Truck 2 : 52,000 = m2 * 200,000 + 4,000\nand this gives m2 = 0.24\nand similar line for Truck 2 is y = 0.24 x + 4,000.\nThe question is where values are same, and in terms of the equation, it's where the two depreciation lines meet.\nso solve for x, 0.4 x + 4,000 = 72,000\n0.24x + 4,000 = 52,000\ngives x = 112,500,\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAlbert invested amount of 12000 in a fixed deposit for 2 years at compound interest rate of 5 % per annum. How much Albert will get on the maturity of the fixed deposit\n\n### Options:\nA. Rs. 8510\nB. Rs. 8620\nC. Rs. 8730\nD. Rs. 13230\nE. None of these\n\n### Answer:\nExplanation:\n=>(12000\u00d7(1+5/100)2)\n=>12000\u00d721/20\u00d721/20\n=>13230\nOption D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat will be the remainder of the following division:\n(1234567....141516...20212223....404142)/43?\n\n### Options:\nA. 0\nB. 1\nC. 2\nD. 3\nE. 4\n\n### Answer:\nfirst add the digits\n1+2+3+.........+42\n=>903\nthen 903 divided by 43\nbecause it is the rule of division by 43( a prime number)\nso 903%43=0\n% is modulo operator it returns the remainder part\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nPatanjali walked for 3 days. She walked 18 miles on the first day, walking 3 miles per hour. On the second day she walked for one less hour but she walked one mile per hour, faster than on the first day. On the third day she walked the same number of hours as on the first day, but at the same speed as on the second day. How many miles in total did she walk?\n\n### Options:\nA. 24\nB. 44\nC. 58\nD. 60\nE. 62\n\n### Answer:\nPatanjali walked 18 miles on the first day, walking 3 miles per hour i.e. total time of walk on Day-1 = 18/3 = 6 Hours\nSecond day time of walk = 6-1 = 5 hours and Speed = 3+1=4 miles per hour i.e. Distance walked on second day = 5*4 = 20 miles\nThird day time of walk = 6 hours and Speed = 4 miles per hour i.e. Distance walked on second day = 6*4 = 24 miles\nTotal Distance travelled on three days = 18+20+24 = 62\nAnswer: Option E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA can finish a piece of work in 5 days. B can do it in 25 days. They work together for four days and then A goes away. In how many days will B finish the work?\n\n### Options:\nA. 3 days\nB. 1 day\nC. 2 days\nD. 4 days\nE. 5 days\n\n### Answer:\n4/5 + (4 + x)/25 = 1 => x = 1 day\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFoodmart customers regularly buy at least one of the following products: milk, chicken, or apples. 60% of shoppers buy milk, 50% buy chicken, and 25% buy apples. If 10% of the customers buy all 3 products, what percentage of Foodmart customers purchase exactly 2 of the products listed above?\n\n### Options:\nA. 5%\nB. 10%\nC. 15%\nD. 25%\nE. 30%\n\n### Answer:\nThe formula is\nn(AUBUC) = n(A)+n(B)+n(C)-B+A-N\nwhere B is both (it will sum of (AB), (BC), (CA)).\nand A is All\nand N is neither\nso plugging in we get\n100 = 60+50+25+10-B-0\nB = 45.\nexactly two = 45 - 3(10) = 15\nsubtracting 10% three times as this value is including in all the (AB), (BC), (CA).\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA feed store sells two varieties of birdseed: Brand A, which is 65% millet and 35% sunflower, and Brand B, which is 40% millet and 60% safflower. If a customer purchases a mix of the two types of birdseed that is 50% millet, what percent of the mix is Brand A?\n\n### Options:\nA. 40%\nB. 45%\nC. 50 %\nD. 60 %\nE. 55 %\n\n### Answer:\nYes there is a simple method :\nConsider the following method\nBrand A : 65% millet and 35% sunflower\nBrand B : 40% millet and 60% safflower\nMix : 50% millet\nHere the weighted average is 50%,\nNow Brand A has 65% millet, which is 15% more than the weighted average of mix = + 0.15 A --------------- I\nSimilarly, Brand B has 40 % millet, which is 10 % less than the weighted average of mix = - 0.10B ------------ II\nNow, both Brand A and Brand B are combined to give a 50% mix containing millet, so equate I and II\nimplies, 0.15 A = 0.10 B\nTherefore A/B = 0.10/0.15 = 2/3\nA : B : (A + B) = 2 : 3 : (3+2) = 2 : 3 : 5\nWe have to find, percent of the mix is Brand A i.e. A : (A + B) = 2 : 5 = (2 / 5) * 100 = 40 %\nHere is a pictorial representation :\nBrand A= 65%------------------------15% or 0.15 above average, A times-----------------Total below = + 0.15 A\n----------------------------------------------------------------------------------------Average = 50% or 0.50\nBrand B = 40%--------------------------10% or 0.10 below average, B times-----------------Total above = - 0.10 B\nSince the amount below the average has to equal the average above the average; therefore,\n0.15 A = 0.10 B\nA/B = 2/3\nA:B: Total = 2:3:5\nTherefore\nA/Total = 2:5 = 40 %\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe output of a factory is increased by 10% to keep up with rising demand. To handle the holiday rush, this new output is increased by 50%. By approximately what percent would the output of the factory now have to be decreased in order to restore the original output?\n\n### Options:\nA. 20%\nB. 24%\nC. 30%\nD. 32%\nE. 39%\n\n### Answer:\ntake it as original output =100.\nto meet demand increase by 10%, then output=110.\nto meet holiday demand , new output increase by 50% then output equals 165\nTo restore new holidy demand output to original 100.\nfinal -initial/final*100\n=65/165*100=39% approxiamately.\noption E is correct.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nB completes a work in 6 days. A alone can do it in 10 days. If both work together, the work can be completed in how many days?\n\n### Options:\nA. 3.33 days\nB. 4.33 days\nC. 5.33 days\nD. 6.33 days\nE. 7.33 days\n\n### Answer:\n1/5 + 1/10 = 3/10\n10/3 = 3.33 days\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nCurrent ages of Rahim and Thomas are in the ratio of 5 : 4 correspondingly. 0.2 decades hence, the ratio of their ages will become 11 : 9 correspondingly, What is Thomas\u00e2\u20ac\u2122s current age in years?\n\n### Options:\nA. 24 years\nB. 44 years\nC. 34 years\nD. 64 years\nE. 16 years\n\n### Answer:\n16 years\nIf current ages of Rahim and Thomas be 5A years and 4A years correspondingly\nThen, 5A + 2 = 11\n4A + 2 = 9\n9(5A + 2)=11(4A + 2)\nA = 4\nThomas\u00e2\u20ac\u2122s current age = 4A\n= 16 years.\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA shipment of 1500 heads of cabbage, each of which was approximately the same size was purchased for $600.The day the shipment arrived 2/3 of the heads were sold, each at 25% above the cost per head.The following day the rest were sold at a price per head equal to 10% less than the price each head sold for the day before.what was the gross profit Q on this shipment?\n\n### Options:\nA. a) $100\nB. b) $115\nC. c) $125\nD. d) $130\nE. e) $135\n\n### Answer:\nI recommend one should use fractions to solve this one rather than converting it into decimals\nSol:\n1500 heads -> $600\n1 head -> $600/1500\n1 head -> $(2/5)\n25% more of (2/5) -> 125/100 * 2/5 = $(1/2)\nHe sold 2/3*1500 = 1000 heads for $(1/2) per head\nTotal revenue by selling 1000 heads = 1000 * 1/2 = $500\nHeads left: 500\nCost per head: 90% of the previous price: 90/100 * 1/2 = $(9/20)\nTotal revenue by selling 500 heads = 9/20 * 500 = 225\nTotal revenue after selling 1500 cabbage heads - 225+500 = $725\nMoney spent on the purchase: $600\nProfit Q= 725-600 = $125\nAns:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many numbers between 0 and 1770 have a prime tens digit and a prime units digit?\n\n### Options:\nA. 266\nB. 272\nC. 278\nD. 284\nE. 290\n\n### Answer:\nFrom 1-9 there are 4 prime numbers {2, 3, 5, 7}. The 10s and 1s of the number must be made with these numbers. The total number of combinations is 4*4 = 16. Thus every set of 100 consecutive positive integers has 16 such numbers.\nFrom 0 to 1700, there 16*17 = 272 such numbers.\nFrom 1701 to 1770, the 10s units can only use 3 numbers {2, 3, 5}. 3*4 =12.\nThe total number is then 272+12 = 284\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nLast week we got 3.5 inches of snow. Six-tenths of an inch melted before another storm added\n8.3 inches. Since then we have lost 4.2 inches to melting or evaporation. How may inches of snow\nare left on the ground?\n\n### Options:\nA. 7\" remaining\nB. 5\" remaining\nC. 8\" remaining\nD. 6\" remaining\nE. 10\" remaining\n\n### Answer:\n3.5 - .6 = 2.9\"\n2.9 + 8.3 = 11.2\"\n11.2 - 4.2 = 7\" remaining\ncorrect answer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA club wants to mix 10 pounds of candy worth $8.00 per pound with candy worth $5.00 per pound to reduce the cost of the mixture to $6.00 per pound. How many pounds of the $5.00 per pound candy should be used?\n\n### Options:\nA. 20\nB. 30\nC. 40\nD. 50\nE. 60\n\n### Answer:\nLet number of pounds of 5$ candy to be used be w\n6 = (10*8 + 5*w)/(10 +w)\n=> 60 + 6w = 80 + 5w\n=> w = 20\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMolly can do a task in 15 days while Sandy can do the task in 10 days. How many days will it take to complete the task if both work together?\n\n### Options:\nA. 6\nB. 7\nC. 7.5\nD. 8\nE. 9\n\n### Answer:\nEach day, Molly can do 1/15 of the task.\nEach day, Sandy can do 1/10 of the task.\nEach day, they can do 1/15 + 1/10 = 1/6 of the task.\nThe task will be completed in 6 days.\nThe answer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is 0.1 percent of 12,356?\n\n### Options:\nA. 0.12356\nB. 1.2356\nC. 12.356\nD. 0.012356\nE. 0.0012356\n\n### Answer:\nSince, Percent=1/100, what=something(s), and is:=. We can write the question as s=0.1(1/100)12,356. The answer is 12.356. Hence, the correct answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe speed of a boat in upstream is 60 kmph and the speed of the boat downstream is 80 kmph. Find the speed of the boat in still water and the speed of the stream?\n\n### Options:\nA. 10\nB. 99\nC. 77\nD. 55\nE. 22\n\n### Answer:\nSpeed of the boat in still water = (60+80)/2 = 70 kmph. Speed of the stream\n= (80-60)/2\n= 10 kmph.\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe ratio between the length and the breadth of a rectangular plot is 7 : 5. If the perimeter of the plot is 360 metres, what is its area?\n\n### Options:\nA. 1320 sq.metres\nB. 4260 sq.metres\nC. 6870 sq.metres\nD. 7875 sq.metres\nE. None of these\n\n### Answer:\nLet the length and breadth be 7x and 5x respectively.\nThen, P = 2(7x + 5x) = 360 \u00e2\u2021\u2019 x = 15\nArea = 7 \u00c3\u2014 15 \u00c3\u2014 5 \u00c3\u2014 15 = 7875 sq.m.\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAt a certain supplier, a machine of type A costs $24,000 and a machine of type B costs $50,000. Each machine can be purchased by making a 20 percent down payment and repaying the remainder of the cost and the finance charges over a period of time. If the finance charges are equal to 40 percent of the remainder of the cost, how much less would 2 machines of type A cost than 1 machine of type B under this arrangement?\n\n### Options:\nA. $2,640\nB. $11,200\nC. $12,000\nD. $12,800\nE. $13,200\n\n### Answer:\nTotal Cost of 2 Machines of Type A\n= 20% of (Cost of 2 machine A) + remainder + 40 % remainder\n= 20% of 48000 + (48000 - 20% of 48000) + 40% of (48000 - 20% of 48000)\n= 63360\nTotal Cost of 1 Machine of Type B\n= 20% of (Cost of 1 machine B) + remainder + 40 % remainder\n= 20% of 50000 + (50000 - 20% of 50000) + 40% of (50000 - 20% of 50000)\n= 66000\nDiff = 66000 - 63360 = 2640\nHence, A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich of the following functions does not intersect with E = 3x^2 + 2x + 1\n\n### Options:\nA. E = 3x^2 + 3x + 1\nB. E = 2x^2 + 3x + 1\nC. E = 3x^2 + 2x + 3\nD. E = 4x^2 + 2x - 3\nE. E = x^2 + 2x + 3\n\n### Answer:\nLet\u2019s find the actual intersecting point of given function and each choice E.\nA. 3x^2 + 2x + 1 = 3x^2 + 3x + 1 --> x=0\nB. 3x^2 + 2x + 1 = 2x^2 + 3x + 1 --> x^2 \u2013 x =0 --> x=0 or 1\nC. 3x^2 + 2x + 1 = 3x^2 + 2x + 3 --> 1=3(X) --> they don\u2019t have any intersect.\nD. 3x^2 + 2x + 1 = 4x^2 + 2x - 3 --> x^2 \u20134=0 --> x= 2 or -2\nE. 3x^2 + 2x + 1 = x^2 + 2x + 3 --> 2x^2 \u20132 =0 --> x= 1 or \u20131.\nSo only choice (C) has no intersecting point. The answer is (C).\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nKramer can pack 10 boxes of cigarettes per minute. If there are 5 boxes of cigarettes in one case, how many cases can Kramer pack in 2 hours?\n\n### Options:\nA. 100\nB. 120\nC. 240\nD. 150\nE. 200\n\n### Answer:\nKramer can pack 10 boxes per min.\nTherefore in 2 hrs(120mins)he can pack 120*10= 1200 boxes.\nIf there are 5 boxes in one case then then the total number of cases packed by Kramer = 1200/5 = 240\nAnswer is C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the median of the data 25, 37, 47, 18, 19, 26, 36.\n\n### Options:\nA. 22\nB. 23\nC. 24\nD. 25\nE. 26\n\n### Answer:\nArranging the data in ascending order, we get 18, 19, 25, 26, 36, 37, 47\nHere, the number of observations is odd, i.e., 7.\nTherefore, median = (n + 1/2)th observation.\n= (7 + 1/2)th observation.\n= (8/2)th observation\n= 4th observation.\n4th observation is 26.\nTherefore, median of the data is 26. ANSWER :E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWalking at 5/6 of her normal speed, a worker is 12 minutes later than usual in reaching her office. The usual time (in minutes) taken by her to cover the distance between her home and her office is\n\n### Options:\nA. 36\nB. 42\nC. 48\nD. 54\nE. 60\n\n### Answer:\nLet V be her normal speed and let T be her normal time.\nD = (5/6)V * (T+12)\nSince the distance is the same we can equate this to a regular day which is D = V*T\nV*T = (5/6)V * (T+12)\nT/6 = 10\nT=60\nThe answer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train running at the speed of 60 km/hr crosses a pole in 12 seconds. Find the length of the train.\n\n### Options:\nA. 150\nB. 278\nC. 179\nD. 200\nE. 191\n\n### Answer:\n:\nSpeed = 60*(5/18) m/sec = 50/3 m/sec\nLength of Train (Distance) = Speed * Time\n(50/3) * 12 = 200 meter\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTough and Tricky questions: Coordinate Geometry.\nLine L contains the points (2,3) and (e,q). If q = 2, which of the following could be the equation of line m, which is perpendicular to line L?\n\n### Options:\nA. 2x + y = ex + 7\nB. 2x + y = \u2013ex\nC. x + 2y = ex + 7\nD. y \u2013 7 = x \u00f7 (e \u2013 2)\nE. 2x + y = 7 \u2013 ex\n\n### Answer:\nwe need m=e-2, so we should gety=mx+bform in answer choices\n(A) 2x+y=ex+7 => y=ex-2x+7 => y=x(e-2)+7. It is what we need\n(B) 2x + y = \u2013ex => y=-ex-2x => y=x(-e-2). Wrong\n(C) x + 2y = ex + 7 => y=x(e-1/2)+7/2. Wrong\n(D) y \u2013 7 = x \u00f7 (e \u2013 2) => y=(1/e-2)x+7. Wrong\n(E) 2x + y = 7 \u2013 ex => y=-ex-2x+7 => y=x(-e-2)+7. Wrong\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf I walk at 3 kmph, I miss the train by 2 min, if however, I walk at 4 kmph. I reach the station 2 min before the arrival of the train. How far do I walk to reach the station?\n\n### Options:\nA. 4/5\nB. 4/9\nC. 4/6\nD. 4/2\nE. 4/1\n\n### Answer:\nx/3 \u2013 x/4 = 4/60\nx = 4/5 km\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA and B entered into a partnership with capitals in the ratio 4 : 5. After 3 months, A withdrew 1/4 of his capital and B withdrew 1/5 of his capital. At the end of 10 months, the gain was Rs.760. What is A's share in the profit?\n\n### Options:\nA. 310\nB. 320\nC. 330\nD. 340\nE. 350\n\n### Answer:\nRatio of the initial capital of A and B = 4 : 5\nHence we can take the initial capitals of A and B as 4x and 5x respectively\nRatio in which profit will be divided\n=((4x)3)+(3/4)\u00d7(4x)7 :((5x)3)+4/5\u00d7(5x)7\n=(12+21):(15+28)\n=33:43\nA's share =760\u00d733/76=330\nAnswer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn 10 years, P will be as old as Q is now. Ten years ago, Q was twice as old as P was then. How old is P now?\n\n### Options:\nA. 15\nB. 20\nC. 25\nD. 30\nE. 35\n\n### Answer:\nQ = P+10\nQ-10 = 2(P-10)\nP = 2P-20\nP = 20\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAt a restaurant, glasses are stored in two different-sized boxes. One box contains 12 glasses, and the other contains 16 glasses. If the average number of glasses per box is 15, and there are 16 more of the larger boxes, what is the total number of glasses R at the restaurant? (Assume that all boxes are filled to capacity.)\n\n### Options:\nA. 96\nB. 240\nC. R=256\nD. R=384\nE. R=480\n\n### Answer:\nMost Test Takers would recognize thesystemof equations in this prompt and just do algebra to get to the solution (and that's fine). The wording of the prompt and the 'spread' of the answer choices actually provide an interesting 'brute force' shortcut that you can take advantage of to eliminate the 4 wrong answers....\nWe're told that there are 2 types of boxes: those that hold 12 glasses and those that hold 16 glasses. Since the AVERAGE number of boxes is 15, we know that there MUST be at least some of each. We're also told that that there are 16 MORE of the larger boxes.\nThis means, at the minimum, we have...\n1 small box and 17 large boxes = 1(12) + 17(16) = 12 + 272 = 284 glasses at the MINIMUM\nSince the question asks for the total number of glasses, we can now eliminate Answers A, B and C....\nThe difference in the number of boxes MUST be 16 though, so we could have....\n2 small boxes and 18 large boxes\n3 small boxes and 19 large boxes\netc.\nWith every additional small box + large box that we add, we add 12+16= 28 MORE glasses. Thus, we can justadd 28suntil we hit the correct answer....\n284+28 = 312\n312+28 = 340\n340+28 = 368\n368+28 = 396\nAt this point, we've 'gone past' Answer D, so the correct answer MUST be Answer E.....But here's the proof....\n396+28 = 424\n424+28 = 452\n452+28 = 480\nFinal Answer:\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSix points lie on the circumference of a circle. What is the positive difference between the number of triangles and the number of quadrilaterals that can be created by connecting these points?\n\n### Options:\nA. 4\nB. 5\nC. 6\nD. 15\nE. 20\n\n### Answer:\nLet's start with the triangle: You have 6 points to choose from but only 3 points you will connect and 3 points you will not connect.\nHence number of possibilities for triangle: 6! / 3! * 3! = 20\nSame goes for the quadrilateral: 6 points to choose from, 4 points which you will connect and 2 points which you won't connect.\nNumber of possibilities for quadrilateral: 6! / 4! * 2! = 15\nDifference = 5\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA shopkeeper has 280 kg of apples. He sells 50% of these at 20% profit and remaining 60% at 30% profit. Find his % profit on total.\n\n### Options:\nA. 24%\nB. 25%\nC. 26%\nD. 28%\nE. 35%\n\n### Answer:\nIf the total quantity was 100\nThen 50X 20% + 60 X30%= 28\nThis profit will remain same for any total quantity unless the % of products remains the same. Hence 'D' is the answer\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man travels from A to B at a speed of 30 kmph and returns with a speed of 60 kmph. What is the average speed of the man?\n\n### Options:\nA. 87\nB. 29\nC. 40\nD. 77\nE. 101\n\n### Answer:\nExplanation:\nThe average speed \u2018v\u2019, when a man travels two same distance with different speeds \u2018v1\u2019 and \u2018v2\u2019 is:\nv = (2*v1*v2) / (v1 + v2)\nIn the above problem, v1 = 30 and v2 = 60\nTherefore, v = (2*30*60)/(30 + 60) = 3600/90\nv = 40\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe length of a rectangle is two - fifths of the radius of a circle. The radius of the circle is equal to the side of the square, whose area is 1225 sq.units. What is the area (in sq.units) of the rectangle if the rectangle if the breadth is 10 units?\n\n### Options:\nA. 140 sq.units\nB. 786sq.units\nC. 167sq.units\nD. 178sq.units\nE. 176sq.units\n\n### Answer:\nGiven that the area of the square = 1225 sq.units\n=> Side of square = \u221a1225 = 35 units\nThe radius of the circle = side of the square = 35 units Length of the rectangle = 2/5 * 35 = 14 units\nGiven that breadth = 10 units\nArea of the rectangle = lb = 14 * 10 = 140 sq.units\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe positive integers p and r have exactly three prime factors in common: two 2's and one 3. If p has exactly one additional prime factor x and r has exactly one additional prime factor y such that x \u2260 y , which of the following represents the least common multiple of p and r?\n\n### Options:\nA. 12xy\nB. 6xy\nC. xy\nD. 12\nE. 6\n\n### Answer:\nP and R have exactly 3 factors i.e. 2 , 2 and 3 which comes out to be 12 ;\nso p and r will have 12 for sure as a factor ; ok .\nnow considering that both p -> x as a prime factor and r-> y as prime factor and x is not equal to y ;\nLCM will be 12 * x * y\neg: -\nlet p and r be 12 and 12 each ; then 7 added to p and 11 added to r we get Least LCM as\n12 *7* 11 ; ANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the length of the wire required to go 14 times round a square field containing 5625 m2.\n\n### Options:\nA. 15840\nB. 3388\nC. 4200\nD. 8766\nE. 66711\n\n### Answer:\na2 = 5625 => a = 75\n4a = 300\n300 * 14 = 4200\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how many different ways can 3 identical gold shirts and 3 identical sliver shirts be distributed among 6 children such that each child receives a shirt?\n\n### Options:\nA. 100\nB. 400\nC. 20\nD. 96416\nE. 62\n\n### Answer:\nApproach 1:\n1st Child: 6 has options\n2nd Child: 5 has options\u2026\nTherefore, for all kids: 6 x 5 x 4 x 3 x 2 = 720 arrangements.\nSince the golds are identical, we divide by 3!; Since the silvers are identical, we divide by another 3!\nSo: in all, 720/[ 3! X 3! ] = 20 ways.\n(e.g. Answer: C)\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are 35 students in a hostel. If the no. of students increases by 7, the expenses of the mess increase by Rs.42/day while the average expenditure per head diminishes by Rs1. Find the original expenditure of the mess?\n\n### Options:\nA. Rs. 34\nB. Rs. 39\nC. Rs. 42\nD. Rs. 48\nE. Rs. 49\n\n### Answer:\nSuppose the average join the mess , total expenditure = 35x + 42\nNow, the average expenditure = (35x + 42)/ (35 + 7) = x \u2013 1\nor, 35x + 42 = 42x \u2013 42\nor, x = 12\nThus the original expenditure of the mess = 35 x 12 = Rs. 42\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAn office supply store stocks three sizes of notebooks, each in five colors: blue, green, yellow, red, or pink. The store packs the notebooks in packages that contain either 4 notebooks of the same size and the same color or 4 notebooks of the same size and of 4 different colors. If the order in which the colors are packed is not considered, how many different packages of the types described above are possible?\n\n### Options:\nA. 18\nB. 24\nC. 30\nD. 45\nE. 60\n\n### Answer:\nFirst let's consider the small notebooks.\nThere are 5 ways to choose notebooks of the same color.\nThe number of ways to choose four notebooks with different colors is 5C4=5.\nThere are 10 different packages we can make with the small notebooks.\nWe can use the same process to find 10 different packages with medium and large notebooks.\nThe total number of different packages is 30.\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe two lines y = x and x = -3 intersect on the coordinate plane. If z represents the area of the figure formed by the intersecting lines and the x-axis, what is the side length of a cube whose surface area is equal to 6z?\n\n### Options:\nA. 16\nB. 3/\u221a2\nC. 8\nD. 2\u221a2\nE. (\u221a2)/3\n\n### Answer:\n800score Official Solution:\nThe first step to solving this problem is to actually graph the two lines. The lines intersect at the point (-3, -3) and form a right triangle whose base length and height are both equal to 4. As you know, the area of a triangle is equal to one half the product of its base length and height: A = (1/2)bh = (1/2)(3 \u00d7 3) = 9/2; so z = 9/2.\nThe next step requires us to find the length of a side of a cube that has a face area equal to 9/2. As you know the 6 faces of a cube are squares. So, we can reduce the problem to finding the length of the side of a square that has an area of 9/2. Since the area of a square is equal to s\u00b2, where s is the length of one of its side, we can write and solve the equation s\u00b2 = 9/2. Clearly s = \u221a9/2 = 3/\u221a2 , oranswer choice (B).\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA five-digit number divisible by 3 is to be formed using numerical 0, 1, 2, 3, 4 and 5 without repetition. The total number of ways this can be done is:\n\n### Options:\nA. 122\nB. 210\nC. 216\nD. 217\nE. 225\n\n### Answer:\nFirst step:\nWe should determine which 5 digits from given 6, would form the 5 digit number divisible by 3.\nWe have six digits: 0, 1, 2, 3, 4, 5. Their sum=15.\nFor a number to be divisible by 3 the sum of the digits must be divisible by 3. As the sum of the six given numbers is 15 (divisible by 3) only 5 digits good to form our 5 digit number would be 15-0={1, 2, 3, 4, 5} and 15-3={0, 1, 2, 4, 5}. Meaning that no other 5 from given six will total the number divisible by 3.\nSecond step:\nWe have two set of numbers:\n1, 2, 3, 4, 5 and 0, 1, 2, 4, 5. How many 5 digit numbers can be formed using these two sets:\n1, 2, 3, 4, 5 --> 5! as any combination of these digits would give us 5 digit number divisible by 3. 5!=120.\n0, 1, 2, 4, 5 --> here we can not use 0 as the first digit, otherwise number won't be any more 5 digit and become 4 digit. So, desired # would be total combinations 5!, minus combinations with 0 as the first digit (combination of 4) 4! --> 5!-4!=4!(5-1)=4!*4=96\n120+96=216\nAnswer: C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA sum of Rs. 2795 is lent into two parts so that the interest on the first part for 8 years at 3% per annum may be equal to the interest on the second part for 3 years at 5% per annum. Find the second sum?\n\n### Options:\nA. 1642\nB. 1640\nC. 1720\nD. 2795\nE. 6386\n\n### Answer:\n(x*8*3)/100 = ((2795 - x)*3*5)/100\n24x/100 = 41925/100 - 15x/100\n39x = 41925 => x = 1075\nSecond sum = 2795 \u2013 1075\n=1720\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe difference of two numbers is 1385. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder. What is the smaller number ?\n\n### Options:\nA. 274\nB. 270\nC. 295\nD. 360\nE. 252\n\n### Answer:\nLet the smaller number be x. Then larger number = (x + 1385).\nx + 1385 = 6x + 15\n5x = 1370\nx = 274\nSmaller number = 274.\nANSWER A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a simultaneous throw of pair of dice .find the probability of getting the total more than 7\n\n### Options:\nA. 7/9\nB. 5/7\nC. 11/7\nD. 8/9\nE. 5/12\n\n### Answer:\nHere n(S)=(6*6)=36\nlet E=event of getting a total more than 7\n={(2,6),(3,5),(3,6),(4,4),(4,5),(4,6),(5,3),(5,4),(5,5),(5,6),(6,2),(6,3),(6,4),(6,5),(6,6)}\nP(E)=n(E)/n(S)=15/36=5/12\nAns: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nhow many 6 digit no. can be formed using digits 0 to 5,without repetition such that number is divisible by digit at its unit place?\n\n### Options:\nA. 420\nB. 426\nC. 432\nD. 456\nE. 485\n\n### Answer:\nwhen unit place is 1 then numbers which are divisible by 1 = 96 (4*4*3*2*1*1 ways)\nwhen unit place is 2 then numbers which are divisible by 2 = 96 (4*4*3*2*1*1 ways)\nwhen unit place is 3 then numbers which are divisible by 3 = 96 (4*4*3*2*1*1 ways)\nwhen unit place is 3 then numbers which are divisible by 4 = 42 (3*3*2*1*1*1 ways when last two digits are 24 and 4*3*2*1*1*1 ways when last two digits are 04)\nwhen unit place is 3 then numbers which are divisible by 5 = 96 (4*4*3*2*1*1 ways)\ntotal=426\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSusan can type 10 pages in 5 minutes. Mary can type 5 pages in 10 minutes. Working together, how many pages can\nthey type in 30 minutes?\n\n### Options:\nA. 15\nB. 20\nC. 25\nD. 65\nE. 75\n\n### Answer:\nsusan can type 2 pages in 1 min\nmary can type 0.5pages in 1 min\nso, both of them work together they type 2.5 pages in 1 min\nso,in 30 min they type (30*2.5)= 75 pages\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nExcluding stoppages, the speed of a bus is 90 km/hr and including stoppages, it is 84 km/hr. For how many minutes does the bus stop per hour?\n\n### Options:\nA. 18 min\nB. 4 min\nC. 8 min\nD. 6 min\nE. 5 min\n\n### Answer:\nDue to stoppages, it covers 6 km less.\nTime taken to cover 6 km = 6/90 * 60\n= 4 min.\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo sets of 3 consecutive positive odd integers have exactly one integer in common. The sum of the integers in the set with greater numbers is how much greater than the sum of the integers in the other set?\n\n### Options:\nA. 4\nB. 7\nC. 8\nD. 12\nE. it cannot be determined from the information given.\n\n### Answer:\nA=(1,3,5), sum of this=9\nB=(5,7,9), sum of this=21,\nThe differenct between 21-9=12\nHence,12 is the answer i.e.D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe integer K is positive, but less than 400. If 21K is a multiple of 180, how many unique prime factors does K have?\n\n### Options:\nA. 1\nB. 2\nC. 3\nD. 4\nE. 5\n\n### Answer:\nAlso note here the relevance of 'K must be less than 400'.\n21K is 180n (a multiple of 180).\n180n = 2^2 * 3^2 * 5 * n = 3*7*K\nn must have a 7 at least.\nK must have two 2s, a 3 and a 5 at least. This means it must be at least 2*2*3*5 = 60.\nSo K has the following prime factors: 2, 3 and 5. Can it have any other prime factors? The next smallest prime factor is 7. But 60*7 = 420 - a number greater than 400. This means that if K is greater than 60, the only other prime factors that K can have must be out of 2, 3 and 5 only. That is, K may be 60*2 or 60*3*2 or 60*5 etc. This tells us that K has exactly 3 prime factors. If we did not have this condition of K less than 400, we would not know exactly how many factors K has.\nAnswer (C)\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA pupil's marks were wrongly entered as 83 instead of 63. Due to that the average marks for the class got increased by half. The number of pupils in the class is\n\n### Options:\nA. 36\nB. 40\nC. 99\nD. 13\nE. 12\n\n### Answer:\nLet there be x pupils in the class.\nTotal increase in marks = (x * 1/2) = x/2.\nx/2 = (83 - 63) => x/2 = 20 => x = 40.\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA boat can travel with a speed of 12 km/hr in still water. If the speed of the stream is 4 km/hr, find the time taken by the boat to go 68 km downstream.\n\n### Options:\nA. 4.25 hr\nB. 5.25 hr\nC. 8.25 hr\nD. 2.25 hr\nE. 2.50 hr\n\n### Answer:\nspeed of boat in still water = 12 km/hr\nspeed of the stream = 4 km/hr\nSpeed downstream = (12+4) = 16 km/hr\nTime taken to travel 68 km downstream = 68\u204416 = 17\u20444 = 4.25 hours\nAnswer is A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere is a clock which shows false timing ie it shows 10 minutes less for each 1 hour....if the clock shows 12 noon now how many minutes will be lost when it shows 3 pm ?\n\n### Options:\nA. 16 minutes\nB. 26 minutes\nC. 36 minutes\nD. 46 minutes\nE. 56 minutes\n\n### Answer:\nFor 1 hour, 10minutes is slower, then for\n06 miuntes - 1 minutes is slower\n30 minutes - 5 minutes\nActual time false time\n12 12\n01 PM 12.50 PM (10 minutes slower)\n02 PM 01.40 PM (12.50 + 60 min - 10 minutes slower)\n03 PM 02.30 PM (01.40 + 60 min - 10 minutes slower)\n03.36 PM 03.00 PM (02.30 + 36 min - 6 minutes slower )\nSo, 36 minutes will be lost when it is showing 3.00 PM. and the actual time is 3.36 PM\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nH.C.F of 136, 144 and a third number is 8 and their L.C.M is 2^4 * 3^2 * 17 * 7. The third number is:\n\n### Options:\nA. 154\nB. 248\nC. 360\nD. 424\nE. 168\n\n### Answer:\n136 = 2^3 * 17;\n144 = 2^4 * 3^2\nH.C.F = 2^3 = 8\nSince H.C.F is the product of lowest powers of common factors, so the third number must have (2^3 ) as its factor.\nSince L.C.M is the product of highest powers of common prime factors, so the third number must have 3 and 7 as its factors.\nThird number = 2^3 * 3 * 7\n= 168\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe following sets each have a mean of 5 and the standard deviations are given in variable form.\nSet I = {5, 5, 5, 5, 5, 5}, standard deviation = H\nSet II = {1, 1, 1, 9, 9, 9}, standard deviation = J\nSet III = {2, 3, 4, 6, 7, 8}, standard deviation = K\nRank these three standard deviations from least to greatest.\n\n### Options:\nA. K, J, H\nB. K, H, J\nC. H, J, K\nD. H, K, J\nE. J, H, K\n\n### Answer:\nThe answer should be D as the mean is least deviated in Set I followed by Set III and then Set II.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man swims downstream 120 km and upstream 50 km taking 5 hours each time; what is the speed of the current?\n\n### Options:\nA. 3 kmph\nB. 7 kmph\nC. 13 kmph\nD. 6.5 kmph\nE. 7:3kmph\n\n### Answer:\nExplanation:\n120 --- 5 DS = 24\n? ---- 1\n50 ---- 5 US = 10\n? ---- 1 S = ?\nS = (24 - 10)/2 = 7\nAnswer: Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA factory has a fixed cost of $45,000 a month, and a cost of $2.5 for every item produced. If the selling price of a single item is $5.5, what is the number of items must be sold monthly for the factory to cover its cost exactly?\n\n### Options:\nA. 9,000\nB. 15,000\nC. 18,000\nD. 22,500\nE. 27,000\n\n### Answer:\nselling price - Cost price = 3 so per unit profit =3\ncost to recover =45000\nno of items required = 45000/3 = 15000\nAns B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?\n\n### Options:\nA. 120 m\nB. 240 m\nC. 300 m\nD. 120 m\nE. None of these\n\n### Answer:\nSpeed = 54 x\t5/18\tm/sec = 15 m/sec.\nLength of the train = (15 x 20)m = 300 m.Let the length of the platform be x metres.\nThen,\t9x + 3000/36\t= 15\nx + 300 = 540\nx = 240 m. Answer: Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf x : y = 1 : 2, find the value of (2x + 3y) : (x + 4y)\n\n### Options:\nA. 5 : 6\nB. 7 : 8\nC. 8 : 9\nD. 9 : 10\nE. 11 : 12\n\n### Answer:\nx : y = 1 : 2 means x/y = 1/2\nNow, (2x + 3y) : (x + 4y) = (2x + 3y)/(x + 4y) [Divide numerator and denominator by y.]\n= [(2x + 3y)/y]/[(x + 4y)/2] = [2(x/y) + 3]/[(x/y) + 4], put x/y = 1/2\nWe get = [2 (1/2) + 3)/(1/2 + 4) = (1 + 3)/[(1 + 8)/2] = 4/(9/2) = 4/1 \u00d7 2/9 = 8/9\nTherefore the value of (2x + 3y) : (x + 4y) = 8 : 9\nAnswer is C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the approx. value of W, if W=(1.5)11, Given log2 = 0.301, log3 = 0.477\n\n### Options:\nA. 85\nB. 84\nC. 86\nD. 87\nE. 99\n\n### Answer:\nExplanation :\nW = (1.5)11\nTake log both sides:\n=> logW = 11 x log(1.5) =11 x log(3/2)\n=> logW = 11 x (log3 - log2) = 11 x 0.176 = 1.936\n=> W = 101.936\n=> W = 86 (approx)\nAnswer : C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe positive number a is q percent greater than the positive number b, which is y percent less than a itself. If a is increased by y percent, and the result is then decreased by q percent to produce a positive number c, which of the following could be true?\nI. c > a\nII. c = a\nIII. c < a\n\n### Options:\nA. I only\nB. II only\nC. III only\nD. I and II only\nE. II and III only\n\n### Answer:\nLet q = 10% then y = 100/11 %\nlet b = 100 then a = 110\nafter increasing a by y and decreasing b yq we get c= 108\ntherefore c", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nClaire has a total of 90 pets consisting of gerbils and hamsters only. One-quarter of the gerbils are male, and one-third of the hamsters are male. If there are 25 males altogether, how many gerbils does Claire have?\n\n### Options:\nA. 39\nB. 50\nC. 66\nD. 57\nE. 60\n\n### Answer:\nG+H =90 ...1 ; G/4 +H/3 =25 ....2 OR 3G +4H =25*12 =300\nG =90-H OR 3(90-H) +4H =300 H = 300-270 =30 THEN G= 96-30 =66\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nhow much time does Suresh take to cover a distance of 280 m, if he runs at a speed of 7 km/hr ?\n\n### Options:\nA. 2 min. 24 sec.\nB. 3 min. 10 sec.\nC. 1 min. 56 sec.\nD. 4 min. 32 sec.\nE. None of these\n\n### Answer:\nExplanation :\nSolution: s= 7 km/hr = (7*5/18) m/sec = 35/18 m/sec.\nRequired time = (280*18/35)sec = 144 sec.\n= 1min. 24 sec.\nAnswer : A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTough and Tricky questions: Combinations.\nSeven contestants representing four different countries advance to the finals of a fencing championship. Assuming all competitors have an equal chance of winning, how many possibilities are there with respect to how a first-place and second-place medal can be awarded?\n\n### Options:\nA. 6\nB. 7\nC. 12\nD. 16\nE. 21\n\n### Answer:\nNumber of ways First-place medal can be awarded to four contestants = 7\nNumber of ways Second-place medal can be awarded to contestants after awarding First-place medal =3\nTherefore number of possibilities = 7*3 =21\nAnswer:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the value of y from (12)^3 x 6^3 \u00f7 432 = y?\n\n### Options:\nA. 2134\nB. 2234\nC. 2540\nD. 2560\nE. 864\n\n### Answer:\n5184\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA block of wood has dimensions 10cm x 10cm x 50cm. The block is painted red and then cut evenly at the 25 cm mark, parallel to the sides, to form two rectangular solids of equal volume. What percentage of the surface area of each of the new solids is not painted red?\n\n### Options:\nA. 5.5%\nB. 8.3%\nC. 11.6%\nD. 14.2%\nE. 17.5%\n\n### Answer:\nThe area of each half is 100+4(250)+100 = 1200\nThe area that is not painted is 100.\nThe fraction that is not painted is 100/1200 = 1/12 = 8.3%\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA garrison of 400 men had a provision for 31 days. After 26 days 275 persons re-enforcement leave the garrison. Find the number of days for which the remaining ration will be sufficient?\n\n### Options:\nA. 16 days\nB. 45 days\nC. 10 days\nD. 17 days\nE. 18 days\n\n### Answer:\n400 --- 31\n400 --- 5\n125 --- ?\n400*5 = 125*x => x =16 days.\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf x and y are integers and x + y = 5, which of the following must be true?\n\n### Options:\nA. x and y are consecutive integers.\nB. If x < 0, then y > 0.\nC. If x > 0, then y < 0.\nD. Both x and y are even.\nE. Both x and y are less than 5.\n\n### Answer:\nNotice that the question asks which of the following MUST be true, not COULD be true.\nGiven: x + y = 5\nA. x and y are consecutive integers: not necessarily true, for example x=1 and y=4;\nB. If x < 0, then y > 0: if x is negative then y must be positive in order x+y to be positive, so this statement must be true;\nC. If x > 0, then y < 0: not necessarily true, for example x=1 and y=4;\nD. Both x and y are even: never true, as the sum of two even numbers is even and can not equal to odd number 5;\nE. Both x and y are less than 5: not necessarily true, for example x=6 and y=-1;\nAnswer: B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA and B starts a business with Rs.8000 each, and after 9 months, B withdraws half of his capital . How should they share the profits at the end of the 18 months?\n\n### Options:\nA. 4:3\nB. 18:5\nC. 14:10\nD. 18:14\nE. 14:11\n\n### Answer:\nA invests Rs.8000 for 18 months, but B invests Rs.8000 for the first 9 months and then withdraws Rs.4000. So, the investment of B for remaining 9 months is Rs.4000 only.\nA : B\n8000*18 : (8000*9) + (4000*9)\n14400 : 108000\nA:B = 4:3\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 2 cards are selected at random from the deck of 52 cards then What is the probability of one of the selected cards will be King and other will be 10?\nA deck of cards has a total of 52 cards, consisting of 4 suits; (spades(Black), hearts(Red), diamond(Red)s, and clubs(Black)); and 13 cards including 1 king, 1 queen and 1 jack in each suit\n\n### Options:\nA. 8/2652\nB. 18/2652\nC. 1/2652\nD. 12/2652\nE. 16/2652\n\n### Answer:\n2 possible cases:\nKing - 10 or 10 -King (4 kings and 4 10).\nEither way,\nthe total probability = 2( King -10) = 2 (4/52 * 4/51) = 18/2652. B is the correct answer.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSpecial codes are designated by either a 7-letter or an 8-letter code that is created by using the 26 letters of the alphabet. Which of the following gives the maximum number of different codes that can be designated with this system?\n\n### Options:\nA. 2 (26)^8\nB. 26(26)^7\nC. 27(26)^7\nD. 26(26)^8\nE. 27(26)^8\n\n### Answer:\n26^7+26^8 = 26^7(1+26)=27*26^7\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRam's age and Shyam's age are in the ratio 3:4. Seven years ago the ratio of their ages was 2:3. Find the ratio of their ages five years hence?\n\n### Options:\nA. 26/73\nB. 26/39\nC. 26/93\nD. 26/33\nE. 26/13\n\n### Answer:\nLet ages of Ramu and Shyam be x and y respectively.\nx/y = 3/4 => x = 3/4 y\n(x- 7)/(y - 7) = 2/3\n=> 3x - 21 = 2y - 14 => 3x = 2y + 7\nBut x = 3/4 y\n3 * 3/4 y = 2y + 7\n9y = 8y + 28 => y = 28years\n=> x = 21 years\nRatio of their ages five years hence, (21 + 5)/(28 + 5) = 26/33.\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat least number must be added to 3000 to obtain a number exactly divisible by 19 ?\n\n### Options:\nA. 1\nB. 2\nC. 3\nD. 4\nE. 5\n\n### Answer:\nSol. On dividing 3000 by 19, we get 17 as remainder.\nNumber to be added = (19 - 17) = 2.\nOption B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf A lends Rs.3500 to B at 10% per annum and B lends the same sum to C at 11.5% per annum then the gain of B in a period of 3 years is?\n\n### Options:\nA. 157.55\nB. 157.76\nC. 157.5\nD. 157.57\nE. 157.87\n\n### Answer:\n(3500*1.5*3)/100\n=> 157.50\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRam professes to sell his goods at the cost price but he made use of 900 grms instead of a kg, what is the gain percent?\n\n### Options:\nA. 11 1/8%\nB. 31 1/9%\nC. 11 1/9%\nD. 11 8/9%\nE. 13 1/9%\n\n### Answer:\n900 --- 100\n100 --- ? => 11 1/9%\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf r = 2^3 * 5^2 * 7 and s = 2^3 * 3^2 * 5^3, which of the following is equal to the greatest common divisor of r and s?\n\n### Options:\nA. 2 * 5\nB. 2^2 * 5\nC. 2^3 * 5^2\nD. 2*3*5*7\nE. 2^3 * 3^2 *5^2 * 7\n\n### Answer:\nGCD = product of prime factors raised to the least power = 2^3 * 5^2\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTickets to a certain concert sell for $20 each. The first 10 people to show up at the ticket booth received a 40% discount, and the next 20 received a 15% discount. If 52 people bought tickets to the concert, what was the total revenue from ticket sales?\n\n### Options:\nA. $600\nB. $740\nC. $850\nD. $900\nE. $1,140\n\n### Answer:\nPrice of 1 ticket = 20$\nRevenue generated from sales of first 10 tickets = 10 * (60/100 * 20 )\n= 10 * 12 = 120\nRevenue generated from sales of next 20 tickets = 20 *(85/100 * 20 )\n=20*17 = 340\nRevenue generated from sales of last 22 tickets = 20 * 22\n= 440\nRevenue generated from sales of 52 tickets = 120 + 340 + 440\n= 900 $\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nDuring a Pizza buffet where A eats more times 5 than B, and B eats 7 times less than C.find the least number of times all the three has to eat\n\n### Options:\nA. 35\nB. 45\nC. 25\nD. 28\nE. 42\n\n### Answer:\nA eats more than B if B eats 1 times than the ratio of A and B is A:B is 5:1 and as B eat 7 times less the C the the ratio of B : C is 1:7 the the least number of times all three has eat is the LCM of A,B,C that is 35 ..\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a market, a dozen eggs cost as much as a pound of rice, and a half-liter of kerosene costs as much as 4 eggs. If the cost of each pound of rice is $0.33, then how many cents does a liter of kerosene cost? [One dollar has 100 cents.]\n\n### Options:\nA. 0.22\nB. 0.44\nC. 0.55\nD. 22\nE. 55\n\n### Answer:\nA dozen eggs cost as much as a pound of rice --> 12 eggs = 1 pound of rice = 33 cents;\nA half-liter of kerosene costs as much as 8 eggs --> 4 eggs = 1/2 liters of kerosene.\nHow many cents does a liter of kerosene cost --> 1 liter of kerosene = 8 eggs = 8/12*33 = 22 cents.\nAnswer: D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA dog has 15 bones, then he finds 8 more bones. Now how many bones does he have.\n\n### Options:\nA. A) 7\nB. B) 27\nC. C) 23\nD. D) 19\nE. E) 21\n\n### Answer:\n15 + 8 = 23. Answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nBy selling an article at Rs.600, a profit of 25% is made. Find its cost price?\n\n### Options:\nA. 228\nB. 267\nC. 287\nD. 480\nE. 811\n\n### Answer:\nSP = 600\nCP = (SP)*[100/(100+P)]\n= 600 * [100/(100+25)]\n= 600 * [100/125] = Rs.480\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJulie put half of her savings in a savings account that pays an annual simple interest and half in a savings account that pays an annual compound interest. After two years she earned $120 and $122 from the simple interest account and the compound interest account respectively. If the interest rates for both accounts were the same, what was the amount of Julie's initial savings?\n\n### Options:\nA. 600\nB. 720\nC. 1080\nD. 2200\nE. 3600\n\n### Answer:\n$120 for 2 years = $60 per year.\nExtra $2 yearned with the compound interest is the percent yearned on percent. So, $2 is yearned on $60, which means that the interest = 30%.\nThis on the other hand means that half of the savings = 60*30 = $1800. Twice of that = $3,600.\nAnswer: E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAt a particular graduation party with 220 guests, 70% of the guests brought gifts, and 40% of the female guests brought gifts. If 12 males did not bring gifts to the party, how many females did bring gifts?\n\n### Options:\nA. 18\nB. 36\nC. 42\nD. 68\nE. 70\n\n### Answer:\nthe correct method\ntotal = 220..\n70% of 220= 154 got gifts..\n66 did not get gift, out of which 12 are males, so remaining 60-12=54 are females..\nBut 40% females brought gift, so 60% did not get it..\nso 60% = 54, 100%= 54*100/60= 90..\nans 40% of 90 =36\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average of seven numbers is 18. The average of first three numbers is 14 and the average of last three numbers is 19. What is the middle number?\n\n### Options:\nA. 19\nB. 22\nC. 27\nD. 29\nE. 31\n\n### Answer:\nThe total of seven numbers = 7X18 = 126\nThe total of first 3 and last 3 numbers is = 3 X 14+3 X 19 = 99\nSo, the middle number is (126 - 99 ) = 27\nC)\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf n is an integer, then the least possible value of |31 - 4n| is?\n\n### Options:\nA. 0\nB. 1\nC. 2\nD. 3\nE. 4\n\n### Answer:\n|31 - 4n| represents the distance between 31 and 4n on the number line. Now, the distance will be minimized when 4n, which is multiple of 4, is closest to 31. Multiple of 4 which is closest to 31 is 32 (for n = 8),\nso the least distance is 1: |31 - 32| = 1.\nAnswer: B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nX and Y invest Rs.21000 and Rs.17500 respectively in a business. At the end of the year, they make a profit of Rs.26400. What is the share of X in the profit?\n\n### Options:\nA. 14400\nB. 26400\nC. 12000\nD. 12500\nE. 14500\n\n### Answer:\nExplanation:\nRatio of the investment\n=21000:17500=210:175\n=42:35=6:5\nShare of X in the profit\n=2400 x 6/11\n=2400\u00d76=14400\nAnswer: Option A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA was born when B was 1 year and 3 months old. C was born when A was 2 years 1 month old. What is the age of B when C is 4 years and 6 months old?\n\n### Options:\nA. 4 yr 10 month\nB. 6 yr 10 month\nC. 7 yr 11 month\nD. 7 yr 10 month\nE. 8 yr 10 month\n\n### Answer:\nWhen C is 4yr 6 month i.e. 54 months old\nA is 79 month old..\nB is 15 month older than A\nWhen A is 79 months old then,\nB is 94 months old i.e. 7yr 10 month\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTap 'A' can fill the tank completely in 6 hrs while tap 'B' can empty it by 12 hrs. By mistake, the person forgot to close the tap 'B', As a result, both the taps, remained open. After 4 hrs, the person realized the mistake and immediately closed the tap 'B'. In how much time now onwards, would the tank be full?\n\n### Options:\nA. 2 hours\nB. 4 hours\nC. 5 hours\nD. 1 hour\nE. None of these\n\n### Answer:\nExplanation :\nTap A can fill the tank completely in 6 hours\n=> In 1 hour, Tap A can fill 1\u20446 of the tank\nTap B can empty the tank completely in 12 hours\n=> In 1 hour, Tap B can empty 1\u204412 of the tank\ni.e., In one hour, Tank A and B together can effectively fill 1\u20446 - 1\u204412 = 1\u204412 of the tank\n=> In 4 hours, Tank A and B can effectively fill 1\u204412 \u00d7 4 = 1\u20443 of the tank.\nTime taken to fill the remaining 1\u2212(1/3) = 2/3 of the tank = (2/3)/(1/6) = 4 hours. Answer : Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf there are ten positive real numbers n1 < n2 < n3 \u2026 < n10, how many triplets of these numbers (n1, n2, n3), (n2, n3, n4) \u2026 can be generated such that in each triplet the first number is always less than the second number, and the second number is always less than the third number?\n\n### Options:\nA. 45\nB. 90\nC. 120\nD. 180\nE. 150\n\n### Answer:\nThree numbers can be selected and arranged out of ten numbers in 10P3 ways=10!/7!=10*9*8. Now this arrangement is restricted to a given condition that first number is always less than the second number, and the second number is always less than the third number. Hence three numbers can be arranged among themselves in 3! ways.\nRequired number of arrangements=(10*9*8)/(3*2)=120\nANS:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe perimeter of a semi circle is 180 cm then the radius is?\n\n### Options:\nA. 22\nB. 28\nC. 35\nD. 37\nE. 13\n\n### Answer:\n36/7 r = 180\n=> r\n= 35\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nLet y = 2g + x^2 and g = 5x + 1.\nIf g^2 = 121, then which of the following can be a value of 2y + 3g?\n\n### Options:\nA. 81\nB. 130\nC. 141\nD. 142\nE. 160\n\n### Answer:\n800score Official Solution:\nFirst note that g can either be 11 or -11. We are going to have to use both to find all solutions before we can choose a final answer. We begin by substituting g = 11 and then g = -11. If g = 11, then x = 2. If g = -11, then x = -12/5. Since all of our solutions are whole numbers, we can dismiss -12/5. We use g = 11 and x = 2 to determine the value of y: y = 2(11) + 4 = 24. Finally, we substitute the values for y and g into the last expression to determine its value : 2(24) + 3(11) = 48 + 33 = 81;the correct answer is (A).\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the compound interest on $1200 for 6 years at 20% p.a. if CI is component yearly?\n\n### Options:\nA. $120\nB. $150\nC. $2383\nD. $250\nE. $300\n\n### Answer:\nA = P(1 + R/100)^T\n= 1200(1 + 20/100)^6\n=$3583\nCI = $2383\nAnswer is C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe sum of two numbers is 216 and their H.C.F. is 27. The number are:\n\n### Options:\nA. 27, 189\nB. 81,189,\nC. 108, 108\nD. 154, 162\nE. none of these\n\n### Answer:\nLet the required numbers be 27a and 27b.Then, 27a+27b=216\na+b=8\nNow, co-primes with sum 8 are(1, 7)and(3,5).\nrequired numbers are (27*1*, 27*7) and (27*3,27*5)\ni.e., (27, 189)and (81,135)\nout of these, the given one in the answer is the pair(27,189).\ncorrect Option:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the smallest integer q greater than 1 that leaves a remainder of 1 when divided by any of the integers 6, 8, and 10?\n\n### Options:\nA. q=21\nB. q=41\nC. q=121\nD. q=241\nE. q=481\n\n### Answer:\nOr u can just use the answer choices here. Since the answers are already arranged in ascending order, the first number which gives remainder q as 1 for all three is the correct answer. In the given question, the first number which gives a remainder of 1 for 6,8 and 10 is 121.C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFill in the blank with the correct number in this number series: 3, 9, 8, 7, __, 5, 18, ?\n\n### Options:\nA. 6\nB. 7\nC. 9\nD. 10\nE. 13\n\n### Answer:\nThis is a simple alternating subtraction and addition series; The first series begins with 3 and adds 5; the second begins with 9 and subtracts 2, and so on.\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 4 people are selected from a group of 6 married couples, what is the probability that none of them would be married to each other?\n\n### Options:\nA. 1/33\nB. 2/33\nC. 1/3\nD. 16/33 probability\nE. 11/12\n\n### Answer:\nEach couple can send only one \"representative\" to the committee. We can choose 4 couples (as there should be 4 members) to send only one \"representatives\" to the committee in C46C64 # of ways.\nBut these 4 chosen couples can send two persons (either husband or wife): 2\u22172\u22172\u22172=242\u22172\u22172\u22172=24.\nSo # of ways to choose 4 people out 6 married couples so that none of them would be married to each other is: C46\u221724C64\u221724.\nTotal # of ways to choose 4 people out of 12 is C412C124.\nP=C46\u221724C412=1633P=C64\u221724C124=1633\nAnswer: D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the average marks of three batches of 55, 60 and 45 students respectively is 40, 55, 60, then the average marks of all the students is:\n\n### Options:\nA. 51.25\nB. 54.68\nC. 55\nD. 56\nE. None of these\n\n### Answer:\nExplanation:\nRequired average = (55 \u00d7 40 + 60 \u00d7 55 + 45 \u00d7 60/55 + 60 + 45)\n= (2200 + 3300 + 2700/160)\n= 8200/160\n= 51.25\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA box contains Six bulbs out of which five are defective. If five bulbs are chosen at random, find the probability that all the four bulbs are defective?\n\n### Options:\nA. 1/127\nB. 1/129\nC. 1/12\nD. 1/8\nE. 1/6\n\n### Answer:\nOut of six, one are good and five are defective. Required probability\n= 5C5/6C5\n= 1/6\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nwhich of the following statement is not correct?\n\n### Options:\nA. log10 10 = 1\nB. log(2+3)= log(2*3)\nC. log10 1= 0\nD. log(1+2+3)= log1 + log2 + log3\nE. none\n\n### Answer:\na) loga a=1, so log10 10 = 1\nb) log(2+3) = log 5 and log(2*3) = log 6 = log 2 + log 3\ntherefore log(2+3) # log (2*3)\nc) since loga 1=0, so log10 1 = 0\nd) log(1+2+3) = log 6= log(1*2*3)= log 1+log 2+log 3\ne)none\nCorrect Answer (B)\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the price has fallen by 16% what percent of its consumption be: increased so that the expenditure may be the same as before?\n\n### Options:\nA. 11 1/8%\nB. 11 1/5%\nC. 11 1/9%\nD. 19 1/21%\nE. 21 1/9%\n\n### Answer:\n100 \u00e2\u20ac\u201c 16 = 84\n84------16\n100------? => 19 1/21%\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain number X when divided by 243 leaves a remainder of 95. Which of the following can be subtracted from X to make X divisible by 79?\n\n### Options:\nA. 17\nB. 22\nC. 37\nD. 47\nE. 57\n\n### Answer:\nLeast possible value of the number is 243 + 95 = 338\nFurther it is given the number must be divisible by 79 .\n338/79 = Gives remainder as 22\nSo, 22 must be subtracted from the number , answer is (B)\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJake, Lena, and Inna need to drive home from a corporate reception in an SUV that can seat 5 people. If only Inna or Jake can drive, how many seat allocations are possible?\n\n### Options:\nA. 24\nB. 42\nC. 120\nD. 360\nE. 720\n\n### Answer:\n3 people ,5 seats, only 2 can drive\nif inna is in one seat remaining, 2 people can be arranged in 2p2 i.e 2! =2 ways\nsince any one can drive total ways = 2 *2= 4 ways\n4 seats can be chosen out of remaining 5 seats in 5c4 ways = 5!/(3!*2!)= 6 ways\n4*6=24\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a number is formed by writing integers 1 to 150 one after another, like 12345...150. How many T digits does this integer consists of?\n\n### Options:\nA. 150\nB. 339\nC. 342\nD. 359\nE. 362\n\n### Answer:\nNumber of single digit integers = 9\nNumber of 2 digit integers = 99 - 10 + 1 = 90\nNumber of 3 digit integers = 150 - 100 + 1 = 51\nNumber of digits in the integer T= 1*9 + 2*90 + 3*51 = 9 + 180 + 153 = 342\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe cost of 3 kg of sugar is $ 60. What will the cost of 8 kg of sugar be?\n\n### Options:\nA. 20\nB. 40\nC. 80\nD. 160\nE. 180\n\n### Answer:\nThis is a situation of direct variation, now we solve using unitary method.\nCost of 3 kg of sugar = $ 60\nCost of 1 kg of sugar = $ 60/3 = $ 20\nCost of 8 kg of sugar = $ 20 \u00d7 8\nTherefore, cost of 8 kg of sugar = $ 160\nANSWER -D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how many ways, a committee of 8 members can be selected from 10 men and 8 ladies, consisting of 5 men and 3 ladies?\n\n### Options:\nA. 15000\nB. 14567\nC. 14112\nD. 13445\nE. 14431\n\n### Answer:\n(5 men out 10) and (3 ladies out of 8) are to be chosen\nRequired number of ways = 10C5*8C3 = 14112\nAnswer is C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFor integers x and y if x^2+x/y is always an odd integer then which of the following must be true?\n\n### Options:\nA. x is even ; y is odd\nB. x is even ; y is even\nC. x is odd ; y is odd\nD. x is odd ; y is even\nE. cannot be determined\n\n### Answer:\nGiven x and y are integers...NOTE : While taking values, x/y must be properly divisible and the result has to integer itself..\nx^2+x/y = odd always...\nlets take x even (2) and y even (2)\n4 + 2/2 = odd...\nlets take x odd(3) and y odd(3)\n9+3/3 = even...\nSo only x even and y even satisfies the equation..\nIf we take one even and other odd then we get x/y as non integer..which shouldn't be the case as per our question stem.\nOption B is correct...\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn one hour, a boat goes 14 km/hr along the stream and 8 km/hr against the stream. The speed of the boat in still water (in km/hr) is:\n\n### Options:\nA. 12 km/hr\nB. 11 km/hr\nC. 18 km/hr\nD. 10 km/hr\nE. 13 km/hr\n\n### Answer:\nSpeed in still water =1/2(14+8) kmph = 11 kmph.\nAnswer : Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nLorna invests $7000, with some at 6% annual interest and some at 11% annual interest. If she receives a total of $580 from these investments at the end of a year, how much was invested at the 6% interest rate?\n\n### Options:\nA. $160\nB. $1,600\nC. $2,200\nD. $1,400\nE. $5,840\n\n### Answer:\nWe have that 'x' invested at 6%\nWe also have that '6000-x' invested at 11%\nNow then 580/7000 is approx 10%\nTherefore, -4x+7000-x=0\n5x=7000\nx=1400 approximately. Probably higher\nOnly D matches\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA sells his goods 50% cheaper than B but 50% dearer than C. The cheapest is?\n\n### Options:\nA. 33.8\nB. 33.7\nC. 33.3\nD. 33.2\nE. 33.1\n\n### Answer:\nLet B = 100\nA = 50\nC * (150/100) = 50\n3C = 100\nC = 33.3 then 'C' Cheapest\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train covers a distance in 50 min, if it runs at a speed of 48kmph on an average. The speed at which the train must run to reduce the time of journey to 40min will be\n\n### Options:\nA. 45 min\nB. 60 min\nC. 55 min\nD. 70 min\nE. 75 min\n\n### Answer:\nTime = 50/60 hr = 5/6hr\nSpeed = 48mph\ndistance = S*T = 48 * 5/6 = 40km\ntime = 40/60hr = 2/3hr\nNew speed = 40* 3/2 kmph = 60kmph\nAnswer : B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe salaries of A and B together amount to $2000. A spends 95% of his salary and B, 85% of his. If now, their savings are the same, what is A's salary?\n\n### Options:\nA. $1000\nB. $1250\nC. $2500\nD. $1500\nE. $1200\n\n### Answer:\nLet A's salary is x\nB's salary = 2000-x\n(100-95)% of x = (100-85)% of (2000-x)\nx = $1500\nAnswer is D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe distance from City A to City B is 30 miles. While driving from City A to City B, Bob drives at a constant speed of 40 miles per hour. Alice leaves City A 30 minutes after Bob. What is the minimum constant speed in miles per hour that Alice must exceed in order to arrive in City B before Bob?\n\n### Options:\nA. 45\nB. 88\nC. 120\nD. 152\nE. 154\n\n### Answer:\nThe time it takes Bob to drive to City B is 30 / 40 =0.75 hours.\nAlice needs to take less than 0.25 hours for the trip.\nAlice needs to exceed a constant speed of 30 /0.25 = 120 miles per hour.\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nEach digit in the two-digit number G is halved to form a new two-digit number H. Which of the following could be the sum of G and H\n\n### Options:\nA. 153\nB. 150\nC. 137\nD. 132\nE. 89\n\n### Answer:\nlet the number be x, now x is halved => x/2..the question asks what is x?\nx(number) + x/2 (half of that number) = something\n=> 3x/2 = something\n=> x = 2 (something) / 3\nso the answer choice must be divisible by 3\neliminate C, E right away\ncheck the rest\nD satisfies\n3x/ 2 = 132\n=> x = 88\nVerify. 88 + 44 = 132\nAnswer is D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA big container is 30% full with water. If 27 liters of water is added, the container becomes 3/4 full. What is the capacity of the big container?\n\n### Options:\nA. 36 liters\nB. 40 liters\nC. 45 liters\nD. 54 liters\nE. 60 liters\n\n### Answer:\nA big container is 30% full with water and after 27 liters of water is added, the container becomes 75% full. Hence these 27 liters account for 45% of the container, which means that the capacity of it is 27/0.45=60 liters.\nOR: if the capacity of the container is x liters then: 0.3x+27=0.75x --> x=60 liters.\nAnswer: E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich of the following numbers must be added to 5678 to give a remainder of 35 when divided by 460?\n\n### Options:\nA. 797\nB. 798\nC. 799\nD. 796\nE. 795\n\n### Answer:\n5678 - 35 + (one of the answer option) should be divisible by 460. Only option C satisfies.\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFive men and nine women can do a piece of work in 10 days. Six men and twelve women can do the same work in 8 days. In how many days can three men and three women do the work?\n\n### Options:\nA. 80 days\nB. 70 days\nC. 20 days\nD. 10 days\nE. 30 days\n\n### Answer:\nC\n20 days\n(5m + 9w)10 = (6m + 12w)8\n=> 50m + 90w = 48w + 96 w => 2m = 6w => 1m = 3w 5m + 9w = 5m + 3m = 8m\n8 men can do the work in 10 days.\n3m +3w = 3m + 1w = 4m\nSo, 4 men can do the work in (10 * 8)/4 = 20 days.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow much time will a train of length 250 m moving at a speed of 72 kmph take to cross another train of length 300 m, moving at 36 kmph in the same direction?\n\n### Options:\nA. 55\nB. 99\nC. 88\nD. 76\nE. 12\n\n### Answer:\nThe distance to be covered = Sum of their lengths = 250 + 300 = 550 m.\nRelative speed = 72 -36 = 36 kmph = 36 * 5/18 = 10 mps.\nTime required = d/s = 550/10 = 55 sec.\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA can do a piece of work in 8 days and B alone can do it in 12 days. How much time will both take to finish the work ?\n\n### Options:\nA. A)4.8\nB. B)6.333\nC. C)7.333\nD. D)8.5\nE. E)9\n\n### Answer:\nThis question can be solved by different methods. We need to conserve time in exams so solving this problem using equations is the good idea.\nTime taken to finish the job = XY / (X + Y)\n= 8 x 12 / (8 + 12)\n= 96 / 20\n= 4.8 days\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the number of ways in which 10 different beads can be arranged to form a necklace.\n\n### Options:\nA. 181440\nB. 245890\nC. 457890\nD. 124560\nE. 231560\n\n### Answer:\nSince in forming a necklace clockwise and anticlockwise arrangements are not different, therefore,10 beads can be arranged to form a necklace in(10-1)! /2 ways\n= 9!/2 = 181440ways\nAnswer is A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat are the total number of divisors of 600(including 1 and 600)?\n\n### Options:\nA. 4\nB. 24\nC. 40\nD. 16\nE. 20\n\n### Answer:\nWrite the prime factorization.\n600 = (2^3)(3^1)(5^2)\nThe number of divisors (including 1 and the number itself) is the product of one plus the exponents.\n(3+1)(1+1)(2+1) = 24\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the length of the longest pole which can be kept in a room 12 m long, 4 m broad and 3 m high ?\n\n### Options:\nA. 13 m\nB. 14 m\nC. 15 m\nD. 16 m\nE. 17 m\n\n### Answer:\nExplanation:\nthe length of the longest pole which can be kept in a room 12 m long, 4 m broad and 3 m high is=13mts.\nANSWER IS A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe proportion of water to alcohol in Solution A is 5:4 and the proportion of water to alcohol in Solution B is 6:5. If an equal amount of each solution is mixed together, what is the concentration of alcohol in the new solution?\n\n### Options:\nA. 40.9%\nB. 41.9%\nC. 42.9%\nD. 43.9%\nE. 44.9%\n\n### Answer:\nLet V be the total volume of the new solution.\nThen a volume of V/2 was added from each solution A and B.\nThe amount of alcohol added to the new solution was:\n(4/9)(V/2)+(5/11)(V/2)=2V/9+5V/22=89V/198.\nThe concentration of alcohol is 89/198=44.9%\nThe answer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average of 35 numbers is 25. If each number is multiplied by 5, find the new average?\n\n### Options:\nA. 125\nB. 298\nC. 267\nD. 260\nE. 182\n\n### Answer:\nSum of the 35 numbers = 35 * 25\n= 875\nIf each number is multiplied by 5, the sum also gets multiplied by 5 and the average also gets multiplied by 5.\nThus, the new average = 25 * 5\n= 125.\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA small pool filled only with water will require an additional 600 gallons of water in order to be filled to 80% of its capacity. If pumping in these additional 600 gallons of water will increase the amount of water in the pool by 30%, what is the total capacity of the pool in gallons?\n\n### Options:\nA. 1000\nB. 1250\nC. 1300\nD. 1600\nE. 2000\n\n### Answer:\nSince pumping in additional 600 gallons of water will increase the amount of water in the pool by 30%, then initially the pool is filled with 1,000 gallons of water.\nSo, we have that 1,000 + 600 = 0.8*{total} --> {total} = 2,000.\nAnswer: E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA can do a piece of work in 15 days and B alone can do it in 10 days. B works at it for 5 days and then leaves. A alone can finish the remaining work in\n\n### Options:\nA. 5days\nB. 6days\nC. 7.5days\nD. 8.5days\nE. 9days\n\n### Answer:\nExplanation:\nB's 5 days work =\n1/10\u22175=1/2\nRemaining work =1\u22121/2=1/2\nA can finish work =15\u22171/2=7.5days\nOption C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many words can be formed from the letters of the word \u2018EXTRA\u2019 so that the vowels are never together?\n\n### Options:\nA. 48\nB. 120\nC. 72\nD. 110\nE. 116\n\n### Answer:\nThe given word contains 5 different letters.\nTaking the vowels EA together, we treat them as one letter.\nThen, the letters to be arranged are XTR (EA).\nThese letters can be arranged in 4! = 24 ways.\nThe vowels EA may be arranged among themselves in 2! = 2 ways.\nNumber of words, each having vowels together = (24x2) = 48 ways.\nTotal number of words formed by using all the letters of the given words = 5! = (5x4x3x2x1) = 120.\nNumber of words, each having vowels never together = (120-48) = 72.\nAnswer C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe second of two numbers is two less than three times the first. Find the numbers if there sum is\n26.\n\n### Options:\nA. 7-19\nB. 8-20\nC. 10-16\nD. 15-9\nE. 20-6\n\n### Answer:\nWe are looking for two numbers.\n#1 - x\n#2 - 3x \u2013 2\nThe sum is 26. #1 + #2 = 26\nSubstituting x + 3x \u2013 2 = 26\n4x \u2013 2 = 26\n4x = 28\nx = 7\nThe first number is 7, the second number is two less than three times 7 or 19.\ncorrect answer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the largest 4 digit number exactly divisible by 88?\n\n### Options:\nA. 9944\nB. 9999\nC. 9988\nD. 9900\nE. None of these\n\n### Answer:\nExplanation :\nLargest 4 digit number = 9999\n9999 \u00f7 88 = 113, remainder = 55\nHence largest 4 digit number exactly divisible by 88 = 9999 - 55 = 9944. Answer : Option A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIt is currently 7:05 PM. What time was it in the morning exactly 51,132 minutes ago?\n\n### Options:\nA. 6:53\nB. 6:55\nC. 6:59\nD. 7:03\nE. 7:09\n\n### Answer:\nConvert 51,132 minutes to hours by dividing by 60: 51,132/60 = 852 R12. That is 852 hours, 12 minutes. Convert 852 hours to days by dividing by 24: 852/24 = 35 R12. That is 35 days, 12 hours. Thus 852 hours before 7:05 PM is 12 hours before 7:05 PM which is 7:05 AM. 12 minutes before that is 6:53 AM. A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how many ways can 4 arts and 5 science students be arranged in a row so that the arts and the science students are placed alternately?\n\n### Options:\nA. 2880\nB. 1850\nC. 3260\nD. 5200\nE. 360*120\n\n### Answer:\nThe four art students can be arranged in those 4 A-slots in 4! = 24 ways.\nThe five science students can be arranged in those 5 S-slots in 5! =120 ways.\nTotal arrangements = 24 *120 = 2880\nAnswer =(A)\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many prime numbers between 1 and 100 are factors of 67830?\n\n### Options:\nA. 4\nB. 5\nC. 6\nD. 3\nE. 2\n\n### Answer:\nfactor of 67830 = 2*3*5*7*17*19--- 6 prime numbers\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn the seaside summer camp there are 50 children. 90% of the children are boys and the rest are girls. The camp administrator decided to make the number of girls only 5% of the total number of children in the camp. How many more boys must she bring to make that happen?\n\n### Options:\nA. 50.\nB. 45.\nC. 40.\nD. 30.\nE. 25.\n\n### Answer:\nGiven there are 50 students In the seaside summer camp , 90% of 50 = 45 boys and remaining 5 girls.\nNow here 90% are Boys and 10% are Girls.\nNow question is asking about how many boys do we need to add, to make the girls percentage to 5 or 5%..\nIf we add 50 to existing 45 then the count will be 95 and the girls number will be 5 as it.\nNow boys are 95% and girls are 5%. ( out of 100 students = 95 boys + 5 girls ).\nIMO option A is correct.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe difference between a two-digit number and the number obtained by interchanging the two digits is 63. Which is the smaller of the two numbers?\n\n### Options:\nA. 2\nB. 3\nC. 9\nD. 7\nE. 1\n\n### Answer:\nExplanation:\nLet the ten's digit be x and units digit by y.\nThen,\n(10x + y) - (10y + x) = 63\n9(x - y) = 63\nx - y = 7\nThus, none of the numbers can be determined.\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the terms of a series are either2or24and the sum of all the terms S of the series is 124, then which of the following could be the number of2sin the series?\n\n### Options:\nA. 26\nB. 29\nC. 35\nD. 40\nE. 48\n\n### Answer:\nAns: A\nSolution: we are not certain how many 2 or 24 are there. but as given sum of all the terms is 124 means 24*5= 120 so number of 24 can't be more than 5\nso S=24x +2y = 124\n24*5 + 2y =124 then y=2\n24*4 + 2y = 124 then y=14\n24*3 +2y = 124 then y= 26\n24*2 +2y =124 then y = 38\n24 +2y = 124 then y= 50\n26 is the ans.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAravind had $ 2100 left after spending 30 % of the money he took for shopping. How much money did he\ntake along with him?\n\n### Options:\nA. 3000\nB. 3300\nC. 3400\nD. 3700\nE. 4000\n\n### Answer:\nLet the money he took for shopping be m.\nMoney he spent = 30 % of m\n= 30/100 \u00d7 m\n= 3/10 m\nMoney left with him = m \u2013 3/10 m = (10m \u2013 3m)/10 = 7m/10\nBut money left with him = $ 2100\nTherefore 7m/10 = $ 2100\nm = $ 2100\u00d7 10/7\nm = $ 21000/7\nm = $ 3000\nTherefore, the money he took for shopping is $ 3000.\nA)\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAfter decreasing 24% in the price of an article costs Rs.532. Find the actual cost of an article?\n\n### Options:\nA. 118\nB. 677\nC. 700\nD. 2688\nE. 1991\n\n### Answer:\nCP* (76/100) = 532\nCP= 7 * 100 => CP = 700\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe population of cities A and B is equal. The population of city A increases in two successive years by 20% and 15% respectively and that of city B increases successively by 20% and 10% respectively. If the difference in the population of two cities after 2 years is 768, then what was the total population of the two cities initially?\n\n### Options:\nA. 12,800\nB. 26,500\nC. 24,600\nD. 25,600\nE. 27,600\n\n### Answer:\nPopulation of city A = Population of city B = A\nM . F of A = 120/100*115/100 = 138/100\nM . F of B = 120/100*110/100 =132/100\nPopulation of A after 2 years = A*138/100\nPopulation of B after 2 years = A*132/100\nDifference = A/100( 138 \u2013132 ) = 768\nA = 768*100/6 = 12800\nTotal initial population = 12800+12800 = 25,600\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAn amount of Rs. 75000 is invested in two types of shares. The first yields an interest of 9% p.a and the second, 11% p.a. If the total interest at the end of one year is 9 3/4 %, then the amount invested in each share was?\n\n### Options:\nA. s. 46875; Rs. 28125\nB. s. 62500; Rs. 37500\nC. s. 72500; Rs. 27500\nD. s. 82500; Rs. 17500\nE. s. 72500; Rs. 17500\n\n### Answer:\nLet the sum invested at 9% be Rs. x and that invested at 11% be Rs. (75000 - x). Then,\n(x * 9 * 1)/100 + [(75000 - x) * 11 * 1]/100 = (75000 * 39/4 * 1/100)\n(9x + 825000 - 11x)/100 = 39000/4 = 14625/2\nx = 46875\nSum invested at 9% = Rs. 46875\nSum invested at 11% = Rs. (75000 - 46875) = Rs. 28125.\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man is 24 years older than his son.In two years, his age will be twice the age of his son.The present age of the son is :\n\n### Options:\nA. 22\nB. 25\nC. 45\nD. 32\nE. 15\n\n### Answer:\nLet the son's present age be x years. Then, man's present age =(x+24) years.\n(x+24)+2=2(x+2)\nx+26=2x+4\nx=22.\nAnswer is A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are 7 couples. If they will sit 14 chairs in a row such that each couple sits side by side, how many possible cases are there?\n\n### Options:\nA. 120\nB. 240\nC. 1,200\nD. 2,460\nE. 654120\n\n### Answer:\nTie the couples. Then we have 5 persons that have to be arranged in 4 places. 4! ways.\nNow the couples can change position with each other. 2! ways.\n7! * (2!)^7=5040 *128 = 645120\nAnswer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a box, there are 7 red, 3 blue and 5 green balls. One ball is picked up randomly. What is the probability that it is neither blue nor green?\n\n### Options:\nA. 2/3\nB. 8/21\nC. 3/7\nD. 7/15\nE. 10/21\n\n### Answer:\nExplanation:\nTotal number of balls = (7 + 3 + 5) = 15.\nLet E = event that the ball drawn is neither blue nor green =e vent that the ball drawn is red.\nTherefore, n(E) = 7.\nP(E) = 7/15.\nAnswer: Option D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAn aircraft is flying at a height of 3000m from the ground at an average speed of 400 km/hr while descending. It has to travel 5 kms before it can touch down the runway and start operating its break system. It will take less than 10 seconds to reach the touch down point. How far it is from the touch down point if it had been on they ground.\n\n### Options:\nA. 5 kms\nB. 4 kms\nC. 3 kms\nD. 6 kms\nE. none of these\n\n### Answer:\nanswer is 4\nsimple Pythagoras theorem\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA cube marked 1, 2, 3, 4, 5, and 6 on its six faces. Three colors, red, blue, and green are used to paint the six faces of the cube. If the adjacent faces are painted with the different colors, in how many ways can the cube be painted?\n\n### Options:\nA. 3\nB. 6\nC. 8\nD. 12\nE. 27\n\n### Answer:\nThere are 4 adjacent sides for every face of the cube.\nLet's say side 1 is painted red, then the 4 adjacent sides can be either green or blue alternating. This can be done in 2 ways.\nGBGB\nBGBG\nSixth side should be the same color as side 1.\nFor each color chosen for side 1(and side6) there are 2 ways of painting side 2,3,4 and 5.\nNo. of colors that can be chosen for side 1(and side6) is 3.\nSo 3*2 = 6..\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFor any numbers a and b, a#b = ab(5 \u2212 b). If a and a#b both represent positive numbers, which of the following could be a value of b?\n\n### Options:\nA. 3,2\nB. 3,2,1\nC. 4,3,2,1\nD. 4.4\nE. 5,4\n\n### Answer:\na#b positive then b may be positive or negative. if positive then b< 5 may be 4,3,2 or 1 and if negative then it is more than or equal to -1 negative . ab will be -ve which is not possible as a and a#b should be positive.\nans 4 ,3,2 and 1\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSachin can cover a distance in 1hr 24 min by covering 2/3 of the distance at 4 kmph and the rest at 5 kmph. The total distance is?\n\n### Options:\nA. 6 km\nB. 8 km\nC. 9 km\nD. 11 km\nE. 12 km\n\n### Answer:\nLet total distance =D=D\nDistance travelled at 4 kmph speed =(23)D=(23)D\nDistance travelled at 5 kmph speed =(1\u221223)D=(13)D=(1\u221223)D=(13)D\nTotal time =1 hr 24 min = (60+24) min =8460=8460 hr =2115=2115 hr\nWe know,\nTime=DistanceSpeedTime=DistanceSpeed\nTotal time\n2115=2/34D+1/35D2115=2/34D+1/35D\n2115=2D12+D152115=2D12+D15\n84=14D84=14D\nD=6 km\nOption A is correct\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a village there are 20 men and 25 women. In how many ways can a man and a woman be selected?\n\n### Options:\nA. 200\nB. 300\nC. 500\nD. 600\nE. 650\n\n### Answer:\nWe can select one men from 20 women in 20 ways.\nWe select one woman from 25 women in 25 ways\nWe select a Men and women in 20 * 25 ways i.e., = 500 ways.\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich of the following is/are terminating decimal(s)?\nI 299/(32^123)\nII 189/(49^99)\nIII 127/(25^37)\n\n### Options:\nA. I only\nB. I and III\nC. II and III\nD. II only\nE. I, II, III\n\n### Answer:\nThe fraction will have terminating decimal if and only if the denominator of the fraction is of the form (2^n)(5^m).\nIf you look at the denominators:\n1) (32^123) => (2^(5*123))(5^0) => Terminating Decimal\n2) (49^99) => Can't be expressed as (2^n)(5^m) => Non terminating Decimal\n3) (25^37) => (2^0)(5^(2*37)) => Terminating Decimal\nHence 1 and 3 are terminating decimals => Choice [B]\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a bag, there are 5 green, 6 black and 7 red pens. One pen is picked up randomly. What is the probability that it is neither red nor green?\n\n### Options:\nA. 5/18\nB. 7/18\nC. 1/3\nD. 1/2\nE. 1/5\n\n### Answer:\nExplanation :\nNeither red nor green means the pen drawn is black.\nTotal number of outcomes = (5+6+7) = 18.\nNumber of Favourable outcomes = 6 = Number of black pens.\nHence, Probability of the event = 6/18 = 1/3.\nAnswer : C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn an election between two candidates, the winner has a margin of 20% of the votes polled. If 3000 people change their mind and vote for the loser, the loser would have won by a margin of 20% of the votes polled. Find the total number of votes polled in the election?\n\n### Options:\nA. 15000\nB. 20000\nC. 30000\nD. 60000\nE. 45000\n\n### Answer:\nWinner - Looser\n60% - 40%\nIf 3000 people change their mind and vote for the loser:\nWinner - Looser\n40% - 60%\nThus 3,000 people compose 20% of all voters, which means that the total number of votes is 15,000.\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn the line xy plane line m has the equation y = 3x - 10, then the line m passes through which of the following points?\n\n### Options:\nA. (3, 1)\nB. (3, 4)\nC. (4, 2)\nD. (6, 9)\nE. (6, 15)\n\n### Answer:\nYes it is y=3x-8....extremely sorry for mistake....\nIF that's the case then answer is C\ny=3x-8\n2=3X4-10\n2=12-10\n2=2 (satisfied)\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man bought a horse and a carriage for Rs. 3000. He sold the horse at a gain of 20% and the carriage at a loss of 10%, thereby gaining 2% on the whole. Find the cost of the horse.\n\n### Options:\nA. 2200\nB. 1800\nC. 1200\nD. 1000\nE. 1500\n\n### Answer:\nLet the C.P of the horse be Rs. X, Then, C.P of the carriage = Rs.(3000- x).\n20% of x - 10% of ( 3000-x ) =2% of 3000 = 60,\nx/5 - ( 3000-x )/10 = 60, 3x - 3000 = 600, 3x =3600, x = 1200.\nHence, C.P of the horse = Rs. 1200\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSix years ago, the ratio of ages of Kunal and Sagar was 6:5. Four years hence, the ratio of their ages will be 11:10. What is Sagar's age at present?\n\n### Options:\nA. 16\nB. 17\nC. 8\nD. 12\nE. 10\n\n### Answer:\nLet the ages of Kunal and Sagar 6 years ago be 6x and 5x years respectively.\nThen, [(6x + 6) + 4] / [(5x + 6) + 4] = 11/10\n10(6x + 10) = 11(5x + 10) => x = 2\nSagar's present age = (5x + 6) = 16 years.Answer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRs.1170 is divided so that 4 times the first share, thrice the 2nd share and twice the third share amount to the same. What is the value of the third share?\n\n### Options:\nA. 177\nB. 169\nC. 199\nD. 540\nE. 123\n\n### Answer:\nA+B+C = 1170\n4A = 3B = 2C = x\nA:B:C = 1/4:1/3:1/2 = 3:4:6\n6/13 * 1170 = Rs.540\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe speed at which a girl can row a boat in still water is 30 kmph. If she rows downstream, where the speed of current is 6 kmph, what time will he take to cover 240 metres?\n\n### Options:\nA. 21\nB. 22\nC. 23\nD. 20\nE. 24\n\n### Answer:\nSpeed of the boat downstream = 30 + 6 = 36 kmph\n= 36 * 5/18 = 10 m/s\nHence time taken to cover 240 m = 240/10 = 24 seconds.\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf money is invested at r percent interest, compounded annually, the amount of investment will double in approximately 70/r years. If Pat's parents invested $ 5000 in a long term bond that pays 8 percent interest, compounded annually, what will be the approximate total amount of investment 18 years later, when Pat is ready for college?\n\n### Options:\nA. 20000 dollars\nB. $15000\nC. $12000\nD. $10000\nE. $9000\n\n### Answer:\nSince investment doubles in 70/r years then for r=8 it'll double in 70/8=~9 years (we are not asked about the exact amount so such an approximation will do). Thus in 18 years investment will double twice and become ($5,000*2)*2=$20,000 (after 9 years investment will become $5,000*2=$10,000 and in another 9 years it'll become $10,000*2=$20,000).\nAnswer: A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the price of a certain computer increased 30 percent from x dollars to 351 dollars, then 2x =\n\n### Options:\nA. 540\nB. 570\nC. 619\nD. 649\nE. 700\n\n### Answer:\nBefore Price increase Price = x\nAfter 30% Price increase Price = x+(30/100)*x= 1.3x = 351 (Given)\ni.e. x= 351/1.3 = $270\ni.e. 2x = 2*270 = 540\nAnswer: option A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere were two candidates in an election. Winner candidate received 62% of votes and won the election by 324 votes. Find the number of votes casted to the winning candidate?\n\n### Options:\nA. 456\nB. 837\nC. 912\nD. 1200\nE. 1400\n\n### Answer:\nW = 62% L = 38%\n62% - 38% = 24%\n24% -------- 324\n62% -------- ? => 837\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nBag A contains red, white and blue marbles such that the red to white marble ratio is 1:3 and the white to blue marble ratio is 2:3. Bag B contains red and white marbles in the ratio of 1:4. Together, the two bags contain 50 white marbles. How many red marbles could be in bag A?\n\n### Options:\nA. 1\nB. 5\nC. 4\nD. 6\nE. 8\n\n### Answer:\n6 is the answer.\nBag A-\nR:W:B = 2:6:9\nLet W in bag A be 6K\nBab B -\nR:W = 1:4\nLet W in bag B be 4k\nW =50 = 6K+4k\n=> k= 5\nTotal Red's in bag A will be 2K = 10\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn January of 2016, there were 100 cats and 125 dogs in a town. In January of 2017, there were 115 cats and 150 dogs. By approximately what percent did the ratio of cats to dog decrease from the 2016 to 2017.\n\n### Options:\nA. 12.9%\nB. 11.0%\nC. 15%\nD. 18%\nE. 5%\n\n### Answer:\n2016: cats/dogs = 100/125 =660/750\n2017: cats/dogs = 115/150 =575/750\nASIDE: It's useful to write both ratios with the same denominator. This allows us to IGNORE the denominator and focus solely on the numerators.\nSo, our ratio went from 660/750 to 575/750\nIgnoring the denominators, we went from 660 to 575\nThe percent change = 100(difference in values)/(original value)\n= (100)(660-575)/660\n= (100)(85)/660)\n\u2248 12.878...\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow much space, in cubic units, is left vacant when maximum number of 7x7x7 cubes are fitted in a rectangular box measuring 14x21x17 ?\n\n### Options:\nA. 878\nB. 879\nC. 880\nD. 881\nE. 882\n\n### Answer:\nNo of cubes that can be accommodated in box = (14*21*17)/(7*7*7)\n12*16 in numerator can be perfectly divided by 7*7 in denominator.\nside with length 17 can't be perfectly divided by 7 and hence is the limiting factor. Closet multiple of 7 less that 17 is 14. so vacant area in cube =\n=14*21*(17-14)\n=14*21*3\n=882\nAns - E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA and B entered into a partnership investing Rs.25000 and Rs.30000 respectively. After 4 months C also joined the business with an investment of Rs.35000. What is the share of C in an annual profit of Rs.47000?\n\n### Options:\nA. Rs.18000\nB. Rs.15000\nC. Rs.17000\nD. Rs.14000\nE. NONE\n\n### Answer:\n25*12: 30*12: 35*8\n15:18:14\n14/47 * 47000 = 14000\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe shopkeeper sale, all of the prices of the items sold were different. If the price of a radio sold at the shopkeeper sale was both the 9th highest price and the 14th lowest price among the prices of the items sold, how many items were sold at the shopkeeper sale?\n\n### Options:\nA. 23\nB. 22\nC. 32\nD. 26\nE. 17\n\n### Answer:\n8+13+1= 22\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA boat goes 100 km downstream in 10 hours, and 80 km upstream in 20 hours. The speed of the stream is?\n\n### Options:\nA. 4km/h\nB. 3km/h\nC. 2km/h\nD. (1/2) km/h\nE. E)None\n\n### Answer:\n100 --- 10 DS = 10\n? ---- 1\n80 ---- 20 US = 4\n? ----- 1 S = (10 - 4)/2\n= 3 kmph\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nLisa and Robert have taken the same number of photos on their school trip. Lisa has taken 3 times as many photos as Claire and Robert has taken 24 more photos than Claire. How many photos has Claire taken?\n\n### Options:\nA. 6\nB. 8\nC. 10\nD. 12\nE. 14\n\n### Answer:\nL = R\nL = 3C\nR = C + 24\n3C = C + 24\nC = 12\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the distance covered by a man walking for 30min at a speed of 10km/hr?\n\n### Options:\nA. 1km\nB. 3km\nC. 4km\nD. 5km\nE. 6km\n\n### Answer:\nDistance = 10*20/60 = 5km\nAnswer is D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many liters of water must be added to 20 liters of milk and water containing 10% water to make it 50% water?\n\n### Options:\nA. 10\nB. 12\nC. 14\nD. 16\nE. 18\n\n### Answer:\nBy rule of alligation:\n50% - 10% = 40%\n100% - 50% = 50%\nQuantity of pure water : Quantity of the mixture = 4 : 5\nThere are 20 liters of mixture, so we need to add 16 liters of pure water.\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA batsman makes a score of 87 runs in the 17th inning and thus increases his average by 3. Find his average after 17th inning?\n\n### Options:\nA. 33\nB. 44\nC. 39\nD. 66\nE. none of these\n\n### Answer:\nLet the average after 7th inning = x\nThen average after 16th inning = x - 3\ninline fn_jvn therefore 16(x-3)+87 = 17x\ninline fn_jvn therefore x = 87 - 48 = 39 Answer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn eight years, David will be four times as old as Aaron. Twenty years ago, David was twice as old as Ellen. If David is seven years older than Ellen, how old is Aaron?\n\n### Options:\nA. 1\u20135\nB. 1.5\u20135\nC. 11\u201315\nD. 16\u201320\nE. 21\u201325\n\n### Answer:\nLet David's present age be 'd', Aaron's present age be 'a' and Ellen's present age be 'e'\nIn ten years, David will be four times as old as Aaron --> d+8 = 4(a+8)\nTwenty years ago, David was twice as old as Ellen --> d-16 = 2(e-16)\nDavid is seven years older than Ellen --> d = e + 7\ne+7-16 = 2e-32\ne-9= 2e-32\ne = 23\nd = 30\n38 = 4a + 32\na = 1.5\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAt what rate percent on simple interest will Rs.600 amount to Rs.950 in 5 years?\n\n### Options:\nA. 3.33%\nB. 5.93%\nC. 4.33%\nD. 9.33%\nE. 11.67%\n\n### Answer:\n350 = (600*5*R)/100\nR = 11.67%\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA car is running at a speed of 96kmph. What distance will it cover in 14sec?\n\n### Options:\nA. 378m\nB. 350m\nC. 380m\nD. 200m\nE. 250m\n\n### Answer:\nSpeed = 96kmph = 96*5/18 = 27 m/s\nDistance covered in 14sec = 27*14 = 378m\nAnswer is A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAn error 12% in excess is made while measuring the side of a square. Now What is the percentage of error in the calculated area of the square?\n\n### Options:\nA. 6.64%\nB. 16.64%\nC. 15.64%\nD. 25.44%\nE. 10.64%\n\n### Answer:\nPercentage error in calculated area\n=(12+12+(12\u00c3\u201412)/100)%=25.44%\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRavi bought 5 pencil and 10 eraser for Rs 4 . Sheetal bought 3 pencil and 9 eraser for Rs 3 then what would be the cost of pencil and eraser.\n\n### Options:\nA. .15p, .30p\nB. .50p,.27p\nC. .40p,.20p\nD. .20p,.40p\nE. .50p,.40p\n\n### Answer:\nLet pencil be x and eraser be y so\n5x+10y=4\n3x+9y=3\nBy solving the above two equations we get x=.40p and y=.20p correct ans is C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a mixture of milk and water, the proportion of milk by weight was 80%. If, in a 180 gm mixture, 36 gms of pure milk is added, what would be the percentage of milk in the mixture formed?\n\n### Options:\nA. 83.43%\nB. 83.73%\nC. 83.23%\nD. 83.93%\nE. 83.33%\n\n### Answer:\nPercentage of milk in the mixture formed\n= [80/100 (180) + 36] / (180 + 36) * 100% = (144 + 36)/216 * 100%\n= 5/6 * 100% = 83.33%.\nAnswer:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many positive integers less than 9,000 are there in which the sum of the digits equals 5?\n\n### Options:\nA. 56\nB. 57\nC. 58\nD. 59\nE. 60\n\n### Answer:\nBasically, the question asks how many 4 digit numbers (including those in the form 0XXX, 00XX, and 000X) have digits which add up to 5. Think about the question this way: we know that there is a total of 5 to be spread among the 4 digits, we just have to determine the number of ways it can be spread.\nLet X represent a sum of 1, and | represent a seperator between two digits. As a result, we will have 5 X's (digits add up to the 5), and 3 |'s (3 digit seperators).\nSo, for example:\nXX|X|X|X = 2111\n||XXX|XX = 0032\netc.\nThere are 8C3 ways to determine where to place the separators. Hence, the answer is 8C3 = 56.\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo machines, Y and Z, work at constant rates producing identical items. Machine Y produces 30 items in the same time Machine Z produces 24 items. If machine Y takes 36 minutes to produce a batch of items, how many minutes does it take for machine Z to produce the same number of items?\n\n### Options:\nA. 60\nB. 90\nC. 9 1/2\nD. 45\nE. 13 1/2\n\n### Answer:\nrate z/rate y=24/30\ntime z/time y=30/24\n30/24*36=45 minutes\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo brothers took the GMAT exam, the higher score is X and the lower one is Y. If the difference between the two scores is 1/3, what is the value of X/Y ?\n\n### Options:\nA. 3.\nB. 2.\nC. 1/2.\nD. 4\nE. There isn't enough data to answer the question.\n\n### Answer:\nAnswer is D : 4\nX - Y = (X + Y)/2\nSolving for X/Y = 4\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat annual payment will discharge a debt of Rs. 1025 due in 2 years at the rate of 5% compound interest?\n\n### Options:\nA. 993.2\nB. 551.25\nC. 534.33\nD. 543.33\nE. 646.33\n\n### Answer:\nExplanation:\nLet each installment be Rs. x. Then,\nx/(1 + 5/100) + x/(1 + 5/100)2 = 1025\n820x + 1025 * 441\nx = 551.25\nSo, value of each installment = Rs. 551.25\nAnswer: Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nlets say that the average (arithmetic mean) of seven numbers is 12.2\nIf the sum of four of these numbers is 42.8, what is the average of the other 3 numbers?\n\n### Options:\nA. (a) 12.4\nB. (b) 14.2\nC. (c) 16.8\nD. (d) 18.6\nE. (e) 19.2\n\n### Answer:\nWe're told that the average of 7 numbers is 12.2\n(Sum of numbers)/7 = 12.2\nSum of numbers = (12.2)(7) = 85.4\nNext, we're told that the sum of 4 (of the 7) numbers is 42.8\nFrom this information, we can calculate the sum of the OTHER 3 numbers:\n85.4 - 42.8 = 42.6\nThe question asks for the AVERAGE of the OTHER 3 numbers....\n42.6/3 = 14.2\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe difference between the compound interest compounded annually and simple interest for 2 years at 20% per annum is Rs.288. Find the principal?\n\n### Options:\nA. 2277\nB. 2667\nC. 3600\nD. 7200\nE. 1811\n\n### Answer:\nP = 288(100/5)^2 => P = 7200\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nthere are 30 students in a classroom. The ratio of the # of girls to boys was 1:2, how many boys are there?\n\n### Options:\nA. 10\nB. 15\nC. 20\nD. 25\nE. 30\n\n### Answer:\n# OF GIRLS = X\n# OF BOYS =2X\nX + 2X = 30\n3X = 30\nX = 30/3 = 10\nBOYS = 2X = 2 * 10 =20\nANSWER: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many seconds will a 200 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?\n\n### Options:\nA. 11 sec\nB. 30 sec\nC. 77 sec\nD. 14 sec\nE. 12\n\n### Answer:\nSpeed of train relative to man = 63 - 3 = 60 km/hr.\n= 60 * 5/18 = 50/3 m/sec.\nTime taken to pass the man = 200 * 3/50\n= 12 sec.\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRaffle tickets numbered consecutively from 101 through 350 are placed in a box. What is the probability that a ticket selected at random will have a number with a hundreds digit of 3?\n\n### Options:\nA. 2/5\nB. 2/7\nC. 33/83\nD. 51/250\nE. 100/249\n\n### Answer:\nSOLUTION\nThe number of integers from 101 to 350, inclusive is 250, out of which 100 (from 200 to 299) will have a hundreds digit of 2. Thus the probability is 51/250.\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a division sum, the divisor is ten times the quotient and five times the remainder. If the remainder is 48, the dividend is:\n\n### Options:\nA. 5324\nB. 5334\nC. 5336\nD. 5356\nE. 5808\n\n### Answer:\nDivisor = (5 * 48) = 240\n= 10 * Quotient = Divisor\n=> Quotient = 240/10 = 24\nDividend = (Divisor * Quotient) + Remainder\nDividend = (240 * 24) + 48 = 5808.\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf |z|/w = 5,which of the following must be true?\n\n### Options:\nA. z = -5w\nB. z = 5w\nC. z^2 = 25w^2\nD. z^2 = 25w^3\nE. z^3 = 125w^3\n\n### Answer:\n|z|/w = 5.\n|z| = 5w.\nThen z = 5w or -5w and so z^2 = 25w^2.\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the total income of a state increases by 50% and the population of the state increases by 20%, What is the percent change in per capita income for the state?\n\n### Options:\nA. A net increase of 40%\nB. A net increase of 30%\nC. A net increase of 25%\nD. A net increase of 20%\nE. A net decrease of 20%\n\n### Answer:\nWe're told that the total income of a state increases by 50% and the total population increases by 20%\nTo start:\nTotal Income = $100\nTotal Population = 100 people\n$100/100 = $1 per person\nAfter the increase:\nNew Total Income = $150\nNew Total Population = $120\n$150/120 = $5/4 per person\nThe question asks for the percent increase in per capita income, which means that we need to use the Percentage Change Formula:\nPercent Change = (New - Old)/Old\nNew = 5/4\nOld = 1\n(5/4 - 1)/1 = (1/4)/1 = 1/4 = 25% increase\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nGroup A has 6 boys and 3 girls, group B has 2 boys and 2 girls and group C has 4 boys and 2 girls. One student is selected from each of the group. Find the probability that one girl and two boys are among the three selected?\n\n### Options:\nA. 3/45\nB. 1/18\nC. 29/10\nD. 7/18\nE. 7/27\n\n### Answer:\nGroup A has 6 boys and 3 girls; 9\nGroup B has 2 boys and 2 girls; 4\nGroup C has 4 boys and 2 girls. 6\nSelected group should have one girl and two boys.\nGirl from A, boy from B, boy from C: 3/9*2/4*4/6 = 1/9;\nBoy from A, girl from B, boy from C: 2/4*2/4*4/6 = 1/6;\nBoy from A, boy from B, girl from C: 6/9*2/4*2/6 = 1/9.\nSum = 1/9 + 1/6 + 1/9 = 7/18.\nAnswer: D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe speed of a boat in still water is 15 km/hr and the rate of current is 3 km/hourr. The distance travelled downstream in 24 mins is?\n\n### Options:\nA. 6 km\nB. 7 km\nC. 7.2 km\nD. 8 km\nE. 8.4 km\n\n### Answer:\nspeed of a boat in still water = 15 km/hr\nSpeed of the current = 3 km/hr\nSpeed downstream = (15+3) = 18 km/hr\nDistance travelled downstream in 24 minutes =2460\u00d718=2\u00d7185 = 7.2 km\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSeven 6 faced dice are thrown together. The probability that all the three show the same number on them is?\n\n### Options:\nA. 1/32\nB. 1/46656\nC. 1/33\nD. 1/38\nE. 1/34\n\n### Answer:\nThe three dice can fall in 6 * 6 * 6 * 6 * 6 * 6 * 6 = 279936 ways.\nHence the probability is 6/279936\n= 1/46656\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe sale price of a trolley bag including the sale tax is Rs. 1190. The rate of sale tax is 12% . If the shopkeeper has made a profit of 25%, the cost price of the trolley bag is:\n\n### Options:\nA. Rs 800\nB. Rs 820\nC. Rs 860\nD. Rs 850\nE. None of these\n\n### Answer:\nExplanation :\n112% of S.P. = 1190\nS.P. = Rs.(1190 x 100/112) = Rs.1062.50.\nC.P. = Rs (100/125x 1062.50) = Rs 850\nAnswer : D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nQ is the set of the first n positive odd numbers, where n is a positive integer. Given that n > k, where k is also a positive integer, x is the maximum value of the sum of k distinct members of Q, and y is the minimum value of the sum of k distinct members of Q, what is x + y?\n\n### Options:\nA. kn\nB. kn + k^2\nC. kn + 2k^2\nD. 2kn \u2013 k^2\nE. 2kn\n\n### Answer:\nProbably the easiest way to solve this question would be to assume some values for n and k.\nSay n=3, so Q, the set of the first n positive odd numbers would be: Q={1, 3, 5};\nSay k=1, so X, the maximum value of the sum of K distinct members of Q would simply be 5. Similarly, Y, the minimum value of the sum of K distinct members of Q would simply be 1.\nX+Y=5+1=6.\nNow, substitute n=3 and k=1 in the options provided to see which one yields 6. Only asnwer choice E fits: 2kn=2*3*1=6.\nAnswer: E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAn exam consists of 8 true/false questions. Brian forgets to study, so he must guess blindly on each question. If any score above 90% is a passing grade, what is the probability that Brian passes?\n\n### Options:\nA. 1/16\nB. 37/256\nC. 1/2\nD. 219/256\nE. 15/16\n\n### Answer:\nIf you have 8 T or F and Brian is going to guess then each question he has a 50% chance of getting correct.\nIf a passing score is 70% it means Brian needs to get 6/8=75%, 7/8=87.5%, or 8/8=100% to pass. Each is a possibility. If Brian gets a 5/8(=62.5%) or below he fails.\nSo first figure out the number of ways that Brian can get 6 out of 8, 7 out of 8, and 8 out of 8 questions correct.\nWhich is 8 choose 6, equals is 28, 8 choose 7, equals 8, and 8 choose 8, equals 1. This sums to 37.\nThe number of possible questions outcomes -the sum of 8 choose 8, 7 choose 8, 6 choose 8\u2026.2 choose 8, 1 choose 8, and 0 choose 8 is 256, so the chance of him passing is 15/16.\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA merchant marks goods up by 75% and then offers a discount on the marked price. The profit that the merchant makes after offering the discount is 5%. What % discount did the merchant offer?\n\n### Options:\nA. 20%\nB. 25%\nC. 35%\nD. 40%\nE. 45%\n\n### Answer:\nLet P be the original price of the goods and let x be the rate after the markup.\n(1.75P)*x = 1.05P\nx = 1.05/1.75 = 0.6 which is a discount of 40%.\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe ratio between the present ages of A and B is 5:3 respectively. The ratio between A's age 4 years ago and B's age 4 years hence is 1:1. What is the ratio between A's age 4 years hence and B's age 4 years ago?\n\n### Options:\nA. 3:4\nB. 3:0\nC. 3:1\nD. 3:2\nE. 3:7\n\n### Answer:\nLet the present ages of A and B be 5x and 3x years respectively.\nThen, (5x - 4)/(3x + 4) = 1/1\n2x = 8 => x = 4\nRequired ratio = (5x + 4):(3x - 4) = 24:8 = 3:1.Answer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average of first 20 natural numbers is?\n\n### Options:\nA. 5.6\nB. 10.5\nC. 10.1\nD. 5.8\nE. 5.2\n\n### Answer:\nSum of 20 natural no.\n= 420/2 = 210\nAverage = 210/20\n= 10.5\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe value of a stock is Y dollars. On Sunday the stock's value grew by half of its value, but on Monday its value dropped to a third of its new value. What is the stock's value at the end of Monday?\n\n### Options:\nA. Y.\nB. Y/2.\nC. 2Y/3.\nD. Y/3.\nE. Y/4.\n\n### Answer:\nStock value= Y\nAT sunday end= y+.5Y= 1.5 Y\nOn monday the value drop to 1/3rd of its value on sunday\n1.5y/3= .5y= Y/2\nB is the answer\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a function f is defined by f(x)= -1/x for all non zero numbers x. If f(a) = -1/3 and f(ab) = 1/6 then b= ?\n\n### Options:\nA. 2\nB. 1/2\nC. -1/2\nD. -2\nE. -12\n\n### Answer:\nf(a) = -1/3 = -1/a, and thus a = 3\nf(ab) = 1/6, and thus ab = -6\n3b = -6\nb = -2\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man sold 20 articles for $60 and gained 10%. How many articles should he sell for $90 to incur a loss 20%?\n\n### Options:\nA. 45\nB. 36\nC. 40\nD. 50\nE. 48\n\n### Answer:\nProduction cost per article: $60*(100%-10%) / 20 = $2.70\nRequired production costs for a loss of 20%: $90*(100% + 20%) = $108\nNumber of articles to be sold for $108 to incur a 20% loss: $108 / $2.70 = 40\nThus, solution C is correct.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n5 identical snow plows can clear an iced parking lot in 4 hours. How long would it take 6 such snow plows to clear the same parking lot?\n\n### Options:\nA. 3 hour, 10 minutes\nB. 2 hours, 30 minutes\nC. 3 hours\nD. 7 hours, 30 minutes\nE. 10 hourss\n\n### Answer:\n6/5 as many plows will take 5/6 as many hours --> 4*5/6=10/3 hours =3 hours, 10 minutes.\nAnswer: A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train travels from station A to station B. If it travels at a speed of 100 miles per hour, it ends up reaching the station 15 minutes late. If it travels at 120 miles per hour, it reaches the station 15 minutes early. What is the amount of time that the train is scheduled to take for the journey and what is the distance between the stations?\n\n### Options:\nA. 2 hours, 225 miles\nB. 3 hours, 350 miles\nC. 4 hours, 450 miles\nD. 2.75 hours, 325 miles\nE. 6 hours, 650 miles\n\n### Answer:\nLet t be the usual time and x be the distance between AB. So we need to find t and Distance x. The question gives us 2 combinations of speedtime, but the distance remains the same for both condition.\nEquation 1 - x= 100 (t+.25) (converted 30 mins into hr) added .5 hrs because it is late or took more time than usual.\nEquation 2 - x= 120 (t-.25) subtracted .25 hrs because it is early or took less time than usual.\nNow equating 12 we get 100(t+.25)=120(t-.25)\n=> 10t +2.5 = 12t - 3\n=> 2t=5.5 => t= 2.75 hrs.\nHence x= 100(2.75+.5) =>100 X 3.25 => 325 miles.\nHence correct answer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAn institute organised a fete and 1/5 of the girls and 1/8 of the boys participated in the same. What fraction of the total number of students took part in the fete ?\n\n### Options:\nA. 2/13\nB. 13/40\nC. Data inadequate\nD. 14/50\nE. None of these\n\n### Answer:\nExplanation:\nData insufficient to solve the question\nAnswer is C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe unit digit in the product (445 * 534 * 999 * 234) is:\n\n### Options:\nA. 2\nB. 0\nC. 6\nD. 5\nE. 1\n\n### Answer:\nExplanation:\nUnit digit in the given product = Unit Digit in (5*4*9*4) = 0\nANSWER: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAt a certain restaurant, the ratio of the number of cooks to the number of waiters is 3 to 10. When 12 more waiters are hired, the ratio of the number of cooks to the number of waiters changes to 3 to 14. How many cooks does the restaurant have?\n\n### Options:\nA. 4\nB. 6\nC. 9\nD. 12\nE. 15\n\n### Answer:\nOriginally there were 3k cooks and 10k waiters.\n14k = 10k+12\nk=3\nThere are 9 cooks.\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a: b = 14: 3, b: c = 11: 9, find a: b: c?\n\n### Options:\nA. 104: 23: 37\nB. 114: 43: 47\nC. 124: 53: 17\nD. 144: 13: 57\nE. 154: 33: 27\n\n### Answer:\na: b = 14: 3\nb: c = 11: 9\na: b: c = 154: 33: 27\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSujit incurred a loss of 45% on selling an article for Rs.3630/-. What was the cost price of the article?\n\n### Options:\nA. Rs.5725/-\nB. Rs.6600/-\nC. Rs.6250/-\nD. Rs.6750/-\nE. None of these\n\n### Answer:\nExplanation:\n45% loss means SP of Rs.3630/- is 55% of CP\n:. CP = 3630x100/55 = Rs.6600/-\nAnswer: Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain NYC taxi driver has decided to start charging a rate of 10 cents per person per mile. How much, in dollars, would it cost 3 people to travel x miles if he decides to give them a 50% discount?\n\n### Options:\nA. 15x/100\nB. 3x/100\nC. 3/200\nD. 3x/300\nE. x/200\n\n### Answer:\n1 person for x miles = 10 x cents\n3 person for x miles = 3x10 x = 30x cents\nAfter discount 50% = 30x/2 = 15x cents\nIn dollars = 15x/100\nAnswer : A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf two numbers are in the ratio 2:3. If 10 is added to both of the numbers then the ratio becomes 5:6then find the smallest number?\n\n### Options:\nA. 22/3\nB. 19/3\nC. 20/3\nD. 25/3\nE. 24/3\n\n### Answer:\n2:3\n2x + 10 : 3x + 10 = 5 : 6\n6[2x + 10] = 5[3x + 10]\n12x + 60 = 15x + 50\n15x -12x = 60 - 50\n3x = 10, then X=10/3\nThen the first number is = 2\n2x = 10\nOption C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nYou have been given a physical balance and 7 weights of 40, 42, 36, 33, 47, 52 and 67 kgs. Keeping weights on one pan and object on the other, what is the maximum you can weigh less than 169 kgs.\n\n### Options:\nA. 163\nB. 166\nC. 162\nD. 164\nE. 165\n\n### Answer:\n67 + 52 + 47 = 166\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA, B, and C were to be paid in proportion to the part of work they did while working on the same piece of work. A and B individually can finish the piece of work in 12 days and 15 days respectively. They worked together for five days and then C completed the remaining work all alone. If $1350 was the net sum to be paid for the entire work, what was the average daily wage of B?\n\n### Options:\nA. $144\nB. $90\nC. $60\nD. $54\nE. $48\n\n### Answer:\nThe correct answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMatt gets a $1,000 commission on a big sale. This commission alone raises his average commission by $150. If Matt's new average commission is $250, how many sales has Matt made?\n\n### Options:\nA. 3\nB. 4\nC. 5\nD. 6\nE. 7\n\n### Answer:\nLet, Average Commission = x\nNo. of items sold = y\nTotal Commission = xy\nNew Commission = xy+1000\nNew Average = (xy+1000) / (y+1) = 150+x\ni.e. (xy+1000) = (y+1)* (150+x)\ni.e. (xy+1000) = (xy+x+150y+150)\ni.e. (850) = (x+150y)\nNew Commission = 250 = 150+x\ni.e. x=100\ni.e. y = 5\nNew Sales = y+1 = 6\nAnswer: option D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA company plans to assign identification numbers to its employees. Each number is to consist of four different digits from 0 to 9, inclusive, except that the first digit cannot be 0. How many different identification numbers are possible?\n\n### Options:\nA. 3,024\nB. 4,536\nC. 5,040\nD. 9,000\nE. 10,000\n\n### Answer:\nNo. of ways select first digit (other than 0) * No of wasy select second digit (exclude first digit selected) * no of ways select 3rd digit (exclude first 2) * no of ways to select 4 th digit (excllude first 3 digits)\n= 9*9*8*6= 4536\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA person can swim in still water at 4 km/h. If the speed of water 2 km/h, how many hours will the man take to swim back against the current for 6km?\n\n### Options:\nA. 3\nB. 4\nC. 5\nD. 6\nE. 7\n\n### Answer:\nM = 4\nS = 2\nUS = 4 - 2 = 2\nD = 6\nT = 6/2 = 3 Answer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAt a certain automobile dealership that sells only Tajima's and Franks, the number of non hybrid Tajima's is 35 less than 3 times the number of hybrid Tajima's. 205 total Tajima's are currently owned by the dealership. If the ratio of hybrid Tajima's to non hybrid Franks is 5:4 and there are 280 total automobiles owned by the dealership, how many hybrid Franks are there?\n\n### Options:\nA. 20\nB. 27\nC. 48\nD. 60\nE. 87\n\n### Answer:\nFirst, I only focus on Tajima's. Let x be hybrid Tajima's and y be non hybrid Tajima's. We know that x + y = 205 and we know that y=3x-35, Therefore we can conclude that x= 60 and y= 145\nNext, let a be the number of non hybrid franks, we know the ratio, 60/a = 5/4, therefore a=48\nTotal number of franks is 75, so 75 - 48 = 27\nTook me 47 sec\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA candidate who gets 30% of the marks fails by 50 marks. But another candidate who gets 45% marks gets 25 marks more than necessary for passing. Find the number of marks for passing?\n\n### Options:\nA. 276 Marks\nB. 200 Marks\nC. 186 Marks\nD. 187 Marks\nE. 167 Marks\n\n### Answer:\n30% ------------ 50\n45% ------------ 25\n----------------------\n15% ------------- 75\n30% -------------- ?\n150 + 50 = 200 Marks\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a ratio which is equal to 3:4, if the antecedent is 12, then the consequent is?\n\n### Options:\nA. 12\nB. 16\nC. 20\nD. 22\nE. 25\n\n### Answer:\nWe have 3/4 = 12/x\n3x = 48\nx = 16\nconsequent = 16\nAnswer is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nYou are gifted a coin that is dated 378 B.C. How much worth the coin is as per your assumption?\n\n### Options:\nA. 1\nB. 0\nC. 2\nD. 5\nE. 6\n\n### Answer:\nSolution:\nThe worth of that coin is zero. This is because the B.C. and A.D. dating system was not empowered till the year 525. So the coin is probably fake.\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA goods train runs at the speed of 72 km/hr and crosses a 250 m long platform in 26 sec. What is the length of the goods train?\n\n### Options:\nA. 200\nB. 230\nC. 240\nD. 270\nE. 260\n\n### Answer:\nSpeed = 72 * 5/18 = 20 m/sec.\nTime = 26 sec.\nLet the length of the train be x meters.\nThen, (x + 250)/26 = 20\nx = 270 m.\nAnswer: Option D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA and B can do a work in 2 days, B and C in 6 days and C and A in 8 days. In how many days will the work be completed, if all three of them work together?\n\n### Options:\nA. 12/28\nB. 48/19\nC. 16/48\nD. 18/48\nE. 12/64\n\n### Answer:\nOne day work of A and B = 1/2\nOne day work of B and C = 1/6\nOne day work of C and A = 1/8\n2(A + B + C) = 1/2 + 1/6 + 1/8\n2(A + B + C) = 19/24\n(A + B + C) = 19/48\nNumber of days required = 48/19 days.\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat number fits best in the missing place?\n_\t4\t5\t3\t5\n9\t5\t7\t10\t3\n\n### Options:\nA. 3\nB. 8\nC. 4\nD. 5\nE. 6\n\n### Answer:\nC\n4\n5 = Five (four letters) => 4\n7 = Seven (five letters) => 5\n10 = Ten (three letters) => 3\n3 = Three (five letters) => 5\nTherefore, 9 = Nine (four letters) => 4.\nTherefore the missing number is 4.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the consumer price index for a sample of goods and services purchased in Dallas rose from 100 at the end of 1967 to x at the end of 1985, what was the average T(arithmetic mean) annual increase in the index over this period?\n\n### Options:\nA. (x + 100)/18\nB. x/18\nC. (100 \u2212 x)/18\nD. (x \u2212 100)/18\nE. 100x/18\n\n### Answer:\nCPI in end of 1967 = 100\nCPI in end of 1985 = x\nNumber of years = 18\nAverage annual increase in CPI T= (x-100)/18\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAt present, the ratio between the ages of Arun and Deepak is 4 : 3. After 6 years, Arun's age will be 26 years. What is the age of Deepak at present ?\n\n### Options:\nA. 12 years\nB. 15 years\nC. 17 years\nD. 19 years\nE. 21 years\n\n### Answer:\nLet the present ages of Arun and Deepak be 4x years and 3x years respectively.\n4x + 6 = 26 4x = 20\nx = 5.\nDeepak's age = 3x = 15 years.\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA bag contains equal number of Rs.5, Rs.2 and Re.1 coins. If the total amount in the bag is Rs.1152, find the number of coins of each kind?\n\n### Options:\nA. 432\nB. 288\nC. 144\nD. 72\nE. 152\n\n### Answer:\nLet the number of coins of each kind be x.\n=> 5x + 2x + 1x = 1152\n=> 8x = 1152 => x = 144\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJohn has purchased an item on sale for $25.00. A few days later John sees the price is now $32.00. By what percentage of the price John paid has the price risen?\n\n### Options:\nA. 5\nB. 7\nC. 15\nD. 20\nE. 28\n\n### Answer:\nC.P.=25.00\nN.P.=32.00\nmarkup%=(N.P.-C.P.)/C.P.*100=(32-25)/25*100=28%\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe consumption of diesel per hour of a bus varies directly as square of its speed. When the bus is travelling at 60 kmph its consumption is 1 litre per hour. if each litre costs $60 and other expenses per hous is $ 60, then what would be the minimum expenditure required to cover a distance of 600 Km?\n\n### Options:\nA. 120\nB. 1250\nC. 1200\nD. 1100\nE. 1150\n\n### Answer:\n60 kmph consumption is 1 lt/hr\nso 600 km will take 10 hrs and the consumption is 10 lt for entire distance.\n1 lt costs $60\nso 10 lt costs $600\nextra expenses for 1 hr - $60\n10 hrs - $600\ntotal expense - $600 + $600 = $1200\nAnswer : C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nKail purchased n items from a catalog for $10 each. Postage and handling charges consisted of $4 for the first item and $1 for each additional item. Which of the following gives the total dollar amount for Kim\u2019s purchase, including postage and handling, in terms of n ?\n\n### Options:\nA. 11n + 2\nB. 11n + 4\nC. 11n + 3\nD. 9n + 3\nE. 9n + 4\n\n### Answer:\nits C\nn items for $10 each\ntotal price $10n\npostage and handling of $4 for 1st item and $1 for the rest\ntotal postage and handling = $ [4+ (n-1)]\n= $ n+3\ntotal cost\n10n+n+3 = 11n+3\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat least number must be substracted from 427398 so that the remaining number is divisible by 15?\n\n### Options:\nA. 1\nB. 3\nC. 11\nD. 16\nE. 17\n\n### Answer:\nSolution\nOn dividing 427398 by 15, we get remainder\t= 3.\nRequired number be substracted\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA, B and C run around a circular track starting from the same point simultaneously and in the same direction at speeds of 4 kmph, 6 kmph and 8 kmph respectively. If the length of the track is 400 meters, when will A, B and C meet at the starting point for the first time after they started the race?\n\n### Options:\nA. 1 minute\nB. 5 minutes\nC. 12 minutes\nD. 20 minutes\nE. 24 minutes\n\n### Answer:\n4 kmph, 6 kmph and 8 kmph is equal to 4000/60 mtrs/min, 6000/60 mtrs/min and 8000/60 mtrs/min or 200/3, 100, 400/3 mtrs/min respectively.\nSeeing this we can infer that the answer should be at least divisible by 3. (minutes in options are integers. So if the answer is not divisible by 3, we will have 200/3*answer = distance traveled by A in fractions whereas 100*answer = distance traveled by A as integer)\nSo, A,B and D are out.\nAt 12 min A,B and C will travel 800, 1200 and 1600 mtrs respectively. Length of the circle is given as 400 mtrs.\nAs 800, 1200 and 1600 are divisible by 400, we can say that A,B and C will be at starting point after 12 min.\nHence, C will be the answer.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFor any integer k greater than 1, the symbol k* denotes the product of all integers between 1 and k, inclusive. If k* is a multiple of 1701 what is the least possible value of k?\n\n### Options:\nA. 8\nB. 10\nC. 12\nD. 14\nE. 16\n\n### Answer:\n1701 = 3*3*3*3*3*7\nThus k must include numbers at least up to the number 12 so that there are at least five appearances of 3 (that is: 3, 6, 9=3*3, and 12).\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many three letter words are formed using the letters of the word KEYBOARD?\n\n### Options:\nA. 220\nB. 289\nC. 27\nD. 336\nE. 346\n\n### Answer:\nExplanation:\nThe number of letters in the given word is EIGHT.\nThe number of three letter words that can be formed using these four letters is \u00c3\u00a2\u00c2\u00b4P\u00c3\u00a2\u00e2\u20ac\u0161\u00c6\u2019 = 8*7*6 =336.\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a 1000 m race, A beats B by 50 m and B beats C by 100 m. In the same race, by how many meters does A beat C?\n\n### Options:\nA. 156 m\nB. 140 m\nC. 145 m\nD. 169 m\nE. 172 m\n\n### Answer:\nC\n145 m\nBy the time A covers 1000 m, B covers (1000 - 50) = 950 m.\nBy the time B covers 1000 m, C covers (1000 - 100) = 900 m.\nSo, the ratio of speeds of A and C =\n1000/950 * 1000/900 = 1000/855 So, by the time A covers 1000 m, C covers 855 m.\nSo in 1000 m race A beats C by 1000 - 855 = 145 m.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA person travels from P to Q a speed of 40 km/hr and returns by increasing his speed by 50%. What is his average speed for both the trips?\n\n### Options:\nA. 27 km/hr\nB. 28 km/hr\nC. 48 km/hr\nD. 19 km/hr\nE. 10 km/hr\n\n### Answer:\nSpeed on return trip = 150% of 40\n= 60 km/hr.\nAverage speed = (2 * 40 * 60)/(40 + 60)\n= 48 km/hr.\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe length of a train and that of a platform are equal. If with a speed of 90 k/hr, the train crosses the platform in one minute, then the length of the train (in meters) is?\n\n### Options:\nA. 752\nB. 799\nC. 719\nD. 750\nE. 712\n\n### Answer:\nSpeed = [90 * 5/18] m/sec = 25 m/sec; Time = 1 min. = 60 sec.\nLet the length of the train and that of the platform be x meters.\nThen, 2x/60 = 25 \u00e8 x = 25 * 60 / 2 = 750\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nEvaluate 28% of 450 + 45% of 280\n\n### Options:\nA. 232\nB. 242\nC. 252\nD. 262\nE. 250\n\n### Answer:\nExplanation:\n= (28/100) * 450 + (45/100) * 280\n= 126 + 126 = 252\nAnswer IS C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFour people each roll a four die once. Find the probability that at least two people will roll the same number ?\n\n### Options:\nA. 3378\nB. 27778\nC. 2211\nD. 1318\nE. 2882\n\n### Answer:\nThe number of ways of rolling a dice where no two numbers probability that no one rolls the same number = 6 x 5 x 4 x 3\nNow total possibilities of rolling a dice = 64\nThe probability that a no one gets the same number = 6\u00d75\u00d74\u00d7364=518\nSo the probability that at least two people gets same number = 1\u2212518=1318\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhen positive integer N is divided by positive integer P, the quotient is 18, with a remainder of 7. When N is divided by (P + 2), the quotient is 15 and the remainder is 1. What is the value of N?\n\n### Options:\nA. 151\nB. 331\nC. 511\nD. 691\nE. 871\n\n### Answer:\nUse the rule dividend = (integer quotient)*(divisor) + remainder to translate each sentence.\nThe first sentence becomes N = 18P + 7. The second equation becomes N = (P + 2)*15 + 1, which simplifies to N = 15P + 31. These are ordinary simultaneous equations Since they both equal N already, let\u2019s set them equal and solve for P.\n18P + 7 = 15P + 31\n3P + 7 = 31\n3P = 24\nP = 8\nNow that we know P = 8, we can just plug in. The product 15*8 is particularly easy to do, without a calculator, by using the \u201cdoubling and halving\u201d trick. Double 15 to get 30, and take half of 8 to get 4 \u2014- 15*8 = 30*4 = 120. So\nN = 15(8) + 31 = 120 + 31 = 151\nN = 151, answer = A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA sum of 725 is lent in the beginning of a year at a certain rate of interest. After 8 months, a sum of 362.50 more is lent but at the rate twice the former. At the end of the year, 33.50 is earned as interest from both the loans. What was the original rate of interest?\n\n### Options:\nA. 3.6%\nB. 4.5%\nC. 5%\nD. 3.46%\nE. None of these\n\n### Answer:\nLet the original rate be R%. Then, new rate = (2R)%\n\u2234 (725\u00d7R\u00d71/100)+(362.50\u00d72R\u00d71/100\u00d73)=33.50\n\u21d2 (2175 + 725)R = 33.50 \u00d7 100 \u00d7 3 = 10050\n\u21d2 R = 10050\u20442900 = 3.46%\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRam will arrange 6 people of 6 different heights for photograph by placing them in two rows of three so that each person in the first row is standing is standing in front of someone in the second row. The heights of the people within each row must increase from left to right, and each person in the second row must be taller than the person standing in front of him or her. How many such arrangements of the 6 people are possible?\n\n### Options:\nA. 5\nB. 6\nC. 9\nD. 24\nE. 26\n\n### Answer:\nRam will arrange 6 people of 6 different heights for photograph by placing them in two rows of three so that each person in the first row is standing is standing in front of someone in the second row. person with max height is in the second row, person with min height is in the first row. We need to select 1 person in the middle of each row... In the middle of the first row we can put only 2, 3 or 4. In the middle of the second row we can put only 3, 4, 5. If we select {3 in the sec. row, 2 in the first}, {4,2}, {5,2}, {4,3}, {5,3}, {5,4}. So, there are 0*1 + 1*1 + 2*1 + 1*1 + 1*1 + 0*1 = 5 cases...A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe ratio between the radii of two spheres is 1:3. Find the ratio between their volumes?\n\n### Options:\nA. 1:28\nB. 1:27\nC. 1:29\nD. 1:39\nE. 1:22\n\n### Answer:\nExplanation:\nr1 : r2 = 1:3\nr13 : r23 = 1:27\nAnswer: Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n6 private companies bought a share of 2 million dollars. If the all companies have to pay the same amount and none of them have bills smaller than $1, how much money would they have to pay?\nOptions:\n\n### Options:\nA. $2,000,000\nB. $2,000,001\nC. $2,000,004\nD. $2,000,007\nE. $2,000,009\n\n### Answer:\nIn order to divide the sum in 6 shares, the amount must be divisible by 6\nDivisibility rule of 6: The sum of the digits must be divisible by 6\nSum of digits of 2,000,000 = 2 and 6 is divisible by 6.\nHence, we need to add 4 to this number for it to be divisible by 6\nCorrect Option: c\nCorrect Option:\t$2,000,004\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nCoins are to be put into 9 pockets so that each pocket contains at least one coin. At most 5 of the pockets are to contain the same number of coins, and no two of the remaining pockets are to contain an equal number of coins. What is the least possible number of coins needed for the pockets?\n\n### Options:\nA. 7\nB. 13\nC. 16\nD. 19\nE. 28\n\n### Answer:\nSince at most 5 of the pockets are to contain the same number of coins then minimize # of coins in each, so let each contain just 1 coin;\nNext, we are told that no two of the remaining 4 pockets should contain an equal number of coins, so they should contain 2, 3, 4, and 5 coins each (also minimum possible);\nTotal: 1+1+1+1+1+2+3+4+5=19\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nLook at this series: 97, 97, 97, 87, 87, 87, 67, 67, 67 ... What number should come next?\n\n### Options:\nA. 47\nB. 57\nC. 45\nD. 48\nE. 55\n\n### Answer:\nExplanation:\nIn this series, each number 20 is subtracted from previous number to arrive at the next number.\nAnswer: Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train 800 m long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 min, then the length of the tunnel is?\n\n### Options:\nA. 992\nB. 389\nC. 500\nD. 277\nE. 781\n\n### Answer:\nSpeed = 78 * 5/18 = 65/3 m/sec.\nTime = 1 min = 60 sec.\nLet the length of the train be x meters.\nThen, (800 + x)/60 = 65/3\nx = 500 m.\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAt what price must an article costing Rs.47.50 be marked in order that after deducting 5% from the list price. It may be sold at a profit of 25% on the cost price?\n\n### Options:\nA. Rs.62.50\nB. Rs.72.50\nC. Rs.75.00\nD. Rs.80.00\nE. Rs.85.00\n\n### Answer:\nCP = 47.50\nSP = 47.50*(125/100) = 59.375\nMP*(95/100) = 59.375\nMP = 62.5\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe total of a company's assets in 1994 was 100% greater than the total in 1993, which in turn was 300% greater than the total in 1992. If the total of the company's assets in 1992 was N dollars, what were the company's assets in 1994?\n\n### Options:\nA. 4N\nB. 6N\nC. 8N\nD. 10N\nE. 12N\n\n### Answer:\nIn 1992, the company's assets were N.\nIn 1993, the company's assets were N + 3N =4N.\nIn 1994, the company's assets were 4N + 4N = 8N.\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHarkamal purchased 8kg of grapes at the rate of 70 per kg and 9 kg of mangoes at the rate of 55 per kg. How much amount did he pay to the shopkeeper?\n\n### Options:\nA. 1000\nB. 1055\nC. 1065\nD. 1075\nE. 1080\n\n### Answer:\nCost of 8 kg grapes = 70 \u00d7 8 = 560.\nCost of 9 kg of mangoes = 55 \u00d7 9 = 490.\nTotal cost he has to pay = 560 + 490 = 1055.\nB)\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe cricket team of 11members is 26yrs old & the wicket keeper is 3 yrs older. If the ages ofthese 2are excluded, the average age of theremaining players is 1 year less than the average age of the whole team. What is the average age of the team ?\n\n### Options:\nA. 19\nB. 21\nC. 23\nD. 25\nE. 27\n\n### Answer:\nLet the average age of the whole team be x years.\n11x - (26 + 29) = 9 (x - 1)\n=> 11x - 9x = 46\n=> 2x = 46\n=> x = 23.\nSo, average age of the team is 23 years.\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAt a dinner party, 4 people are to be seated around a circular table. Two seating arrangements are considered different only when the positions of the people are different relative to each other. What is the total number of different possible seating arrangements for the group?\n\n### Options:\nA. 1) 6\nB. 2) 10\nC. 3) 24\nD. 4) 32\nE. 5) 120\n\n### Answer:\nfor number of distinct arrangements of 'n' items around a circular table, we get the arrangements by way of (n-1)!\nin this case, there are 4 guests, so number of distinct arrangements = 3! = 6\nhence A\nAnswer : A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nNathan took out a student loan for 1200$ at 10 percent annual interest, compounded annually. If he did not repay any of the loan or interest during the first 3 years, which of the following is the closest to the amount of interest he owed for the 3 years.\n\n### Options:\nA. 360\nB. 390\nC. 400 dollars\nD. 410\nE. 420\n\n### Answer:\nA straight Q requiring direct formulae..\nwhen compounded annually the final amount= P(1+ r/100)^n..\nhere P=1200, r=10 and n=3..\n1200(1+ 10/100)^3..\n1200*1.1^3=1597.2\ninterest =1597-1200=397, which is nearly 400 in the choices given\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIt takes Jim N minutes to prepare one omelet. It takes Cole N/2 minutes to prepare one omelet. It takes Mitch N/2 minutes to prepare 2 omelets. If Jim, Cole and Mitch together prepare a total of 30 omelets in 40 minutes, then how many minutes would it take Mitch alone to prepare 30 omelets?\n\n### Options:\nA. 70\nB. 120\nC. 140\nD. 160\nE. 280\n\n### Answer:\nCole is twice as fast as Jim and Mitch is 4 times as fast as Jim (it takes Mitch N/2 minutes to prepare 2 omelets, thus N/4 minutes to prepare one omelet).\nSay the rate of Jim is x omelet/minute, the rate of Cole 2x omelet/minute, and the rate of Mitch 4x omelet/minute.\nThen, from (time)(rate) = (job done):\n(40 minutes)(x + 2x + 4x) = (30 omelets);\n(40 minutes)(7x) = (30 omelets);\nSince it takes 40 minutes to prepare 30 omelets at the rate of 7x omelet/minute, then it would take 40*7/4 = 70 minutes to prepare the same 30 omelets at the rate of 7x*4/7 = 4x omelet/minute (the rate of Mitch).\nOr:\n(40 minutes)(7x) = (30 omelets);\n(40*7/4 minutes)(7x*4/7) = (30 omelets);\n(70 minutes)(4x) = (30 omelets);\nAnswer: A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe wages earned by Robin is 30% more than that earned by Erica. The wages earned by Charles is 60% more than that earned by Erica. How much % is the wages earned by Charles more than that earned by Robin?\n\n### Options:\nA. 23%\nB. 18.75%\nC. 30%\nD. 50%\nE. 100%\n\n### Answer:\nExplanatory Answer\nLet the wages earned by Erica be $100\nThen, wages earned by Robin and Charles will be $130 and $160 respectively.\nCharles earns $30 more than Robin who earns $130.\nTherefore, Charles' wage is 30/130*100 = 23.07%.\ncorrect choice is (A)\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA and B can do a piece of work in 12 days and 16 days respectively. Both work for 3 days and then A goes away. Find how long will B take to complete the remaining work?\n\n### Options:\nA. 9\nB. 8\nC. 7\nD. 5\nE. 2\n\n### Answer:\n3/12+(3+x)/16 = 1\nx = 9 days\nANSWER A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe ratio of the earnings of P and Q is 9:10. If the earnings of P increases by one-fourth and the earnings of Q decreases by one-fourth, then find the new ratio of their earnings?\n\n### Options:\nA. 2/3\nB. 3/2\nC. 4/5\nD. 5/8\nE. 4/2\n\n### Answer:\nLet the earnings of P and Q be 9x and 10x respectively.\nNew ratio = [9x + 1/4 (9x)]/[10x - 1/4 (10x)]\n=> 9*(1 + 1/4)/10*(1 - 1/4)\n=> 9/10 * (5/4)/(3/4) = 3/2\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nDepartments A, B, and C have 6 employees each, and department D has 20 employees. Departments A, B, C, and D have no employees in common. A task force is to be formed by selecting 1 employee from each of departments A, B, and C and 2 employees from department D. How many different task forces are possible?\n\n### Options:\nA. 19,000\nB. 41,040\nC. 100,000\nD. 190,000\nE. 400,000\n\n### Answer:\n6c1 * 6c1* 6c1*20c2 = 6*6*6*190=41,040. Hence B is the correct answer.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe labeled price of a table is Rs. 7,500. The shopkeeper sold it by giving 5% discount on the labeled price and earned a profit of 15%. What approximately is the cost price of the table?\n\n### Options:\nA. Rs. 6195\nB. Rs. 6199\nC. Rs. 6192\nD. Rs. 6191\nE. Rs. 6194\n\n### Answer:\nExplanation:\nLabeled price = Rs. 7,500\nBy giving 5% discount on labeled price, the selling price is\n= 95 / 100 * 7500 = Rs. 7125\nBy earning 15% profit on the selling of price Rs. 7125 the cost price is\n= 100 / 115 * 7125 = Rs. 6195.65\nTherefore, approximate cost is 6195.65\nANSWER: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSix 6 faced dice are thrown together. The probability that all the three show the same number on them is?\n\n### Options:\nA. 1/32\nB. 1/7776\nC. 1/33\nD. 1/38\nE. 1/34\n\n### Answer:\nThe three dice can fall in 6 * 6 * 6 * 6 * 6 * 6 = 46656 ways.\nHence the probability is 6/46656\n= 1/7776\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a group of cows and chickens, the number of legs was 14 more than twice the number of heads. The number of cows was:\n\n### Options:\nA. 8\nB. 7\nC. 6\nD. 5\nE. 4\n\n### Answer:\nLet the number of cows be x and their legs be 4x.\nLet the number of chicken be y and their legs be 2x.\nTotal number of legs = 4x + 2y.\nTotal number of heads = x + y.\nThe number of legs was 14 more than twice the number of heads.\nTherefore, 2 \u00d7 (x + y) + 14 = 4x + 2y.\nor, 2x + 2y + 14 = 4x + 2y.\nor, 2x + 14 = 4x [subtracting 2y from both sides].\nor, 14 = 4x \u2013 2x [subtracting 2x from both sides].\nor, 14 = 2x.\nor, x = 7 [dividing by 2 on both sides].\nTherefore, the number of cows = 7.\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe greatest common factor of two numbers is 5!. Which of the following can be the second number, if one of the numbers is 6!?\n\n### Options:\nA. 3(5!)\nB. 5(5!)\nC. 4(5!)\nD. 6(5!)\nE. 7(5!)\n\n### Answer:\nGCF is the product of common factors of the numbers involved.\nGCF = 5!\na = 6! = 6*5!\nb will certainly have 5! and cannot have any more common factors with a (as this will increase the GCF)\nLooking at the answers only 5 (5!) and 6! will have GCF as 5!\nAns B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nBy selling a house for Rs.45000, it was found that 1/8 of the outlay was gained, what ought the selling to price to have been in order to have lost 5 p.c?\n\n### Options:\nA. 28000\nB. 29000\nC. 38000\nD. 40000\nE. 42000\n\n### Answer:\nCP + CP/8 = 45000\nCP = 40000\nSP = 40000*(95/100) = 38000\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA trader sells 85 meters of cloth for Rs. 8925 at the profit of Rs. 5 per metre of cloth. What is the cost price of one metre of cloth?\n\n### Options:\nA. 21\nB. 28\nC. 90\nD. 100\nE. 11\n\n### Answer:\nExplanation:\nSP of 1m of cloth = 8925/85 = Rs. 105\nCP of 1m of cloth = SP of 1m of cloth - profit on 1m of cloth\n= Rs. 105 - Rs. 5 = Rs. 100.\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the probability of rolling three six-sided dice, and getting a different number on each die?\n\n### Options:\nA. 1/12\nB. 1/3\nC. 4/9\nD. 5/9\nE. 7/18\n\n### Answer:\nthree dices were rolled\ntotal outcome 6x6x6\ndifferent number should appear on each\nfavorable outcome= 6c1*5c1*4c1\nprobability= favorable/total\nans=(6*5*4)/(6*6*6)= 5/9\nans= D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a poll of 44,000 dentists, only 30 percent responded; of these, 20 percent claimed to prefer Toothpaste A. How many of the dentists who responded did not claim a preference for Toothpaste A?\n\n### Options:\nA. 2,200\nB. 2,640\nC. 6,160\nD. 8,800\nE. 10,560\n\n### Answer:\nFind those who responded to the poll-\n44000\u22173/10=4400\u22173=13200\nFind those who responded who do not prefer toothpaste A-\n13200\u22178/10=1320\u22178=10560\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 4 men can color 48 m long cloth in 2 days, then 6 men can color 36 m long cloth in\n\n### Options:\nA. 2 days\nB. 1 day\nC. 3 days\nD. 4 days\nE. 5 days\n\n### Answer:\nThe length of cloth painted by one man in one day = 48 / 4 \u00d7 2 = 6 m\nNo. of days required to paint 36 m cloth by 6 men = 36/ 6 \u00d7 6 = 1 day.\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability taht the ticket drawn has a number which is a multiple of 3 or 5?\n\n### Options:\nA. 1/2\nB. 2/5\nC. 8/15\nD. 9/20\nE. None\n\n### Answer:\nSolution\nHere S=(1,2,3,4,5,...,19,20).\nLet E=event of getting a multiple of 3 or 5\n= (3,6,9,12,15,18,5,10,20)\nP(E)= n(E) / n(S)\n= 9/20.\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA and B can do a work in 8days, B and C can do it in 12days; A,B and C together can finish it in 6days. A and C together will do it in?\n\n### Options:\nA. 8days\nB. 10days\nC. 12days\nD. 7days\nE. 5days\n\n### Answer:\nA+B+C 1day work = 1/6\nA+B 1day work = 1/8\nB+C 1day work = 1/12\nA+C 1day work = 2*1/6 - 1/8+1/12 = 1/3 - 5/24 = 3/24 = 1/8\nA and C together will do the work in 8 days.\nAnswer is A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain bus driver is paid a regular rate of $16 per hour for any number of hours that does not exceed 40 hours per week. For any overtime hours worked in excess of 40 hours per week, the bus driver is paid a rate that is 75% higher than his regular rate. If last week the bus driver earned $864 in total compensation, how many total hours did he work that week?\n\n### Options:\nA. 36\nB. 40\nC. 44\nD. 48\nE. 52\n\n### Answer:\nFor 40 hrs = 40*16=640\nExcess = 864-640=224\nFor extra hours =.75(16)=12+16=28\nNumber of extra hrs =224/28=56/7=8\nTotal hrs =40+8=48\nAnswer D 48\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nLarge number of people went to an party and they decided to make some fun at the bar.\nThe first person asks the barman for half a pint of beer.\nThe second person asks for a quarter pint of beer\nThe third person asks for one-eighth of beer and so on ...\nHow many pints of beer will the barman need to fulfill the people need of beer ?\n\n### Options:\nA. 1\nB. 3\nC. 6\nD. 2\nE. 8\n\n### Answer:\nA\nJust 1\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJohn purchased a house for Rs.45000 and a site for Rs.25000 respectively, if he sold the house for Rs.55000 and the site for Rs.16000, then find the resultant percentage of gain?\n\n### Options:\nA. 1.39%\nB. 1.40%\nC. 1.41%\nD. 1.42%\nE. 1.43%\n\n### Answer:\nSol.\nTotal CP = 70000 & total SP = 71000 \u21d2 gain = SP/CP = 71000/70000 = 1.0142 = 1.42%.\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhen the number 72y6139 is exactly divisible by 11, then the smallest whole number that can replace y is?\n\n### Options:\nA. 1\nB. 3\nC. 5\nD. 6\nE. 9\n\n### Answer:\nThe given number =72y6139\nSum of the odd places =9+1+y+7\nSum of the even places = 3+6+2=11\n(Sum of the odd places)- (Sum of even places) = Number (exactly divisible by 11)\n(16+y)-(11) = divisible by 11\ny \ufffd 5 = divisible by 11.\nY must be 6, to make given number divisible by 11.\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA rectangular block 6cm by 12cm by 15cm is cut into an exact number of equal cubes. Find the least possible number of cubes?\n\n### Options:\nA. 20\nB. 25\nC. 40\nD. 50\nE. 35\n\n### Answer:\nVolume of the block = 6*12*15 = 1080 cm^3\nSide of the largest cube = H.C.F of 6,12,15 = 3cm\nVolume of the cube = 3*3*3 = 27 cm^3\nNumber of cubes = 1080/27 = 40\nAnswer is C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf it takes 8 identical printing presses exactly 4 hours to print 6,000 newspapers, how long would it take 4 of these presses to print 4,000 newspapers?\n\n### Options:\nA. 4 hours, 45 minutes\nB. 4 hours, 30 minutes\nC. 4 hours, 50 minutes\nD. 5 hours, 20 minutes\nE. 4 hours, 36 minutes\n\n### Answer:\n8 presses - 6,000 newspapers - 4 hours ;\n4 presses - 3,000 newspapers - 4 hours ; (240 mins)\n4 presses - 4,000 newspapers - 240/3000*4000 = 320 mins = 5 hrs 20 mins\nAnswer : D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 3 women can color 180 m long cloth in 2 days, then 5 women can color 300 m long cloth in?\n\n### Options:\nA. 2 days\nB. 3 days\nC. 5 days\nD. 1 day\nE. 4 days\n\n### Answer:\nThe length of cloth painted by one woman in one day = 180/ 3\u00d7 2 = 30 m\nNo. of days required to paint 300 m cloth by 5 women = 300/ 5 \u00d7 30 = 2 days\nAnswer : A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTom reads at an average rate of 30 pages per hour, while Jan reads at an average rate of 38 pages per hour. If Tom starts reading a novel at 4:30, and Jan begins reading an identical copy of the same book at 5:18, at what time will they be reading the same page?\n\n### Options:\nA. 7:48\nB. 8:18\nC. 8:48\nD. 9:18\nE. 9:48\n\n### Answer:\nSince Tom reads an average of 1 page every 2 minutes, Tom will read 24 pages in the first 48 minutes. Jan can catch Tom at a rate of 8 pages per hour, so it will take 3 hours to catch Tom.\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFrom a nine-member dance group, five will be chosen at random to volunteer at a youth dance event. If Kori and Jason are two of the nine members, what is the probability that both will be chosen to volunteer?\n\n### Options:\nA. a) 1/21\nB. b) 35/2\nC. c) 4/21\nD. d) 2/7\nE. e) 3/7\n\n### Answer:\nTotal number of ways to choose 5 out of 9 = 9C5 = 144.\nNumber of ways to choose 2 (any but Kori and Jason) out of 7 (excluding Kori and Jason) = 7C2 = 2520.\nP = favorable/total = 2520/144 = 35/2.\nAnswer: B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average age of three boys is 20 years and their ages are in the proportion 2 : 3 : 5. The age of the youngest boy is:\n\n### Options:\nA. 21 years\nB. 18 years\nC. 15 years\nD. 9 years\nE. None of these\n\n### Answer:\nTotal age of 3 boys = (20 \u00c3\u2014 3) years = 60 years. Ratio of their ages = 2 : 3 : 3.\nAge of the youngest = (60 \u00c3\u2014 3\u00e2\u0081\u201e10) years = 18 years.\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA and B can finish a work in 16 days while A alone can do the same work in 24 days. In how many days B alone will complete the work?\n\n### Options:\nA. 56\nB. 48\nC. 30\nD. 40\nE. 50\n\n### Answer:\nB = 1/16 \u00e2\u20ac\u201c 1/24 = 1/48 => 48 days\nANSWER B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn shop contains 500 articles each of a cost of $10. He sold them at a price of $20. If the shop keeper has a order of 200 articles, how much profit he will get?\n\n### Options:\nA. A)200\nB. B)4000\nC. C)1500\nD. D)2000\nE. E)600\n\n### Answer:\nTotal money after selling articles = 200*20 = 4000\ncost price = 200*10 = 2000\nprofit = 2000\ncorrect option is D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nLet N be the greatest number that will divide 1305, 4665 and 6905, leaving the game remainder in each case. Then sum of the digits in N is :\n\n### Options:\nA. 4\nB. 5\nC. 6\nD. 8\nE. 9\n\n### Answer:\nSolution\nN = H.C.F. of (4665 - 1305), (6905 - 4665) and (6905 - 1305)\n= H.C.F. of 3360, 2240 and 5600 = 1120.\nSum of digits in N = (1 + 1 + 2 + 0) = 4. Answer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nLast year the price per share of Stock X increased by k percent and the earnings per share of Stock X increased by m percent, where k is greater than m. By what percent did the ratio of price per share to earnings per share increase, in terms of k and m?\n\n### Options:\nA. k/m %\nB. (k-m) %\nC. [100(k-m)]/(100+k) %\nD. [100(k-m)]/(100+m) %\nE. [100(k-m)]/(100+k+m) %\n\n### Answer:\nIf old price per share = X, old Earnings per share = Y\n=> Old ratio = X/Y\nNew price per share = X(100+k)/100, new Earnings per share = Y(100+m)/100\n=>New ratio = X(100+K)/[(100+m)(Y)]\nIncrease in the ratios after simplifying comes to [100(k-m)]/(100+m) %\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nDivide Rs. 1500 among A, B and C so that A receives 1/3 as much as B and C together and B receives 2/3 as A and C together. A's share is?\n\n### Options:\nA. s.360\nB. s.400\nC. s.375\nD. s.500\nE. s.900\n\n### Answer:\nA+B+C = 1500\nA = 1/3(B+C); B = 2/3(A+C)\nA/(B+C) = 1/3\nA = 1/4 * 1500 => 375\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n9548 + 7314 = 4362 + (?)\n\n### Options:\nA. 8300\nB. 8400\nC. 12500\nD. 8700\nE. 9000\n\n### Answer:\n9548 16862 = 4362 + x\n+ 7314 x = 16862 - 4362\n----- = 12500\n16862\n-----\nC)\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n31 of the scientists that attended a certain workshop were Wolf Prize laureates, and 16 of these 31 were also Nobel Prize laureates. Of the scientists that attended that workshop and had not received the Wolf prize, the number of scientists that had received the Nobel Prize was 3 greater than the number of scientists that had not received the Nobel Prize. If 50 of the scientists attended that workshop, how many of them were Nobel Prize laureates?\n\n### Options:\nA. A)11\nB. B)18\nC. C)24\nD. D)27\nE. D)36\n\n### Answer:\nlets solve by creating equation..\nW = 31..\nTotal = 50..\nNot W = 50 -31= 19..\nNow let people who were neither be x, so out of 19 who won Nobel = x+3..\nso x+x+3=19 or x=8..\nso who won Nobel but not Wolf = x+3 = 11..\nBut people who won BOTH W and N = 13..\nso total who won N = 11+16 = 27..\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf x and y are integers and 4^(x-4) = 4^(y+4), what is y in terms of x?\n\n### Options:\nA. x - 8\nB. x - 5\nC. x - 2\nD. x + 2\nE. x + 6\n\n### Answer:\nAnswer: A\n4^(x-4) = 4^(y+4)\nSince the base is the same, I isolated the equations and solved for y.\nx-4 = y+4\ny=x-8\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe length of a rectangular landscape is 4times its breadth. There is a playground in it whose area is 1200 square mtr & which is 1/3rd of the total landscape. What is the length of the landscape?\n\n### Options:\nA. 110\nB. 115\nC. 120\nD. 130\nE. 145\n\n### Answer:\nSol. x * 4x = 3 * 1200\nx = 30\nLength = 4 * 30 = 120\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOf the diplomats attending a summit conference, 30 speak French, 32 do not speak Russian, and 20% of the diplomats speak neither French nor Russian. If 10% of the diplomats speak both languages, then how many diplomats attended the conference?\n\n### Options:\nA. 20\nB. 96\nC. 108\nD. 120\nE. 150\n\n### Answer:\n{Total} = {French} + {Russian} - {Both} + {Neither}\n{Total} = 30 + ({Total} - 32) - (0.1*{Total}) + 0.2*{Total}\nSolving gives {Total} = 20.\nAnswer: A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average speed of a car is 1 3/5 times the avg speed of a bike. A tractor covers 575km in 23hrs. How much distance will the car cover in 4hrs if the speed of the bike is twice speed of the tractor?\n\n### Options:\nA. 400 km\nB. 320 km\nC. 360 km\nD. 550 km\nE. 600 km\n\n### Answer:\nSol. Average speed of a tractor = 25 km / h\nThe speed of a bike in an hour = 25 \u00d7 2 = 50 km\nThe speed of a car in an hour = 8/5 * 50 = 80 km\nSo, the distance covered by car in 4 h is\n80 \u00d7 4 = 320 km\nAns.(B)\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many 6-digits number are Palindromic numbers? A Palindromic number reads the same forward and backward, example\n\n### Options:\nA. 100\nB. 610\nC. 729\nD. 900\nE. 1000\n\n### Answer:\nThe hundred-thousand's digit won't be zero or else it's no longer a 6 digit integer (you could form a palindromic number with five digits though). The subesquent two digits, ten-thousand's and thousand's digit, can be 10 different numbers each, zero - nine. Thus,\n9\u221710\u221710\u22171\u22171\u22171=9009\u221710\u221710\u22171\u22171\u22171=900 Answer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA number is increased by 10% and then decreased by 10%, the final value of the number is ?\n\n### Options:\nA. decreases by 1%\nB. decreases by 2%\nC. decreases by 3%\nD. decreases by 4%\nE. none of the above\n\n### Answer:\nHere, x = 10 and y = - 10\nTherefore, the net % change in value\n= ( x + y + xy/100)%\n= [10 - 10 + (10 * -10)/100]% or - 1%\nSince the sign is negative, there is a decrease in value by 1%.\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA trade analyst announced 10% reduction in the unit price of bike. As a result, the sales volume went up by 10%. What was the net effect on the sales revenue?\n\n### Options:\nA. no change\nB. decreases by 1%\nC. increases by 1%\nD. increases by 10%\nE. None of these\n\n### Answer:\nExplanation :\nReduction of price = (100 -10)% = 90% = 0.9\nIncrease of sale = (100+10)% = 110% = 1.1\nTotal effect = 0.9 X 1.1 = 99%, Decreases by 1%\nAnswer : B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSet A: {1, 3, 4, 6, 9, 12, 16}\nIf three numbers are randomly selected from set A without replacement, what is the probability that the sum of the three numbers is divisible by 4?\n\n### Options:\nA. 3/14\nB. 2/7\nC. 9/14\nD. 5/7\nE. 1/35\n\n### Answer:\nusing probability you can solve: 3/7*2/6*1/5=1/35.\nAns E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA shopkeeper sells some articles at the profit of 25% on the original price. What is the exact amount of profit? To find the answer, which of the following information given in Statements I and II is/are necessary?\nI. Sale price of the article\nII. Number of articles sold\n\n### Options:\nA. Only I is necessary\nB. Only II is necessary\nC. Either I or II is necessary\nD. Both I and II are necessary\nE. None of these\n\n### Answer:\nEXPLANATION\nGain = 25% of C.P.\nIn order to find gain, we must know the sale price of each article and the number of articles sold.\nanswer is (D).\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nBookman purchased 30 copies of a new book released recently, 10 of which are hardback and sold for $20 each, and rest are paperback and sold for $10 each. If 14 copies were sold and the total value of the remaining books was 240, how many paperback copies were sold?\n\n### Options:\nA. 8\nB. 12\nC. 6\nD. 4\nE. 5\n\n### Answer:\nThe bookman had 10 hardback ad 30-10=20 paperback copies;\n14 copies were sold, hence 30-14=16 copies were left. Let # of paperback copies left be p then 10p+20(16-p)=240 --> 10 p=80 --> p=8\n# of paperback copies sold is 20-8=12\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo tracks are parallel. The first track has 6 checkpoints and the second one has 10 checkpoints. In how many ways can the 6 checkpoints of first track be joined with the 10 checkpoints of the second to form a triangle?\n\n### Options:\nA. 120\nB. 150\nC. 200\nD. 270\nE. 420\n\n### Answer:\nTo make a triangle, you need 2 checkpoints from one track and 1 from the other. You cannot have all 3 from the same track since then the points will be in a line (assuming straight line of track)\nYou select 2 checkpoints from the first track and one from the second or two from the second track and one from the first.\n6C2 * 10C1 + 10C2 * 6C1 = 150 + 270 = 420\nAnswer (E)\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA trader mixes 26 kg of rice at Rs. 20 per kg with 30 kg of rice of other variety at Rs. 36 per kg and sells the mixture at Rs. 30 per kg. His profit percent is:\n\n### Options:\nA. 5%\nB. 8%\nC. 10%\nD. 12%\nE. 6%\n\n### Answer:\nC.P. of 56 kg rice = Rs. (26 x 20 + 30 x 36)\n= Rs. (520 + 1080)\n= Rs. 1600.\nS.P. of 56 kg rice = Rs. (56 x 30) = Rs. 1680.\nGain =(80/1600x 100)% = 5%.\nAnswer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFor four days of work, a clerk had daily earnings of $120, $110, $120, and $120 respectively. In which of the following intervals does the standard deviation of the daily earnings lie?\n\n### Options:\nA. Between $50 and $100\nB. Between $20 and $40\nC. Between $20 and $60\nD. Between $0 and $10\nE. Between $70 and $100\n\n### Answer:\nThe standard deviation is between 0 and 10.\nThe reason is that none of the numbers in the set is further away from the mean than 10(or rather Abs(110-(120*3+110)/4)). I am not fully sure how to calculate the standard deviation(I simply remember that there were some formula for calculating the average of the squared distances from the mean for all items in the set from statistics classes - variation), but I believe this will suffice for any GMAT question related to standard deviation.\nAnswer : D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train crosses a platform of 150 m in 15 sec, same train crosses another platform of length 250 m in 20 sec. then find the length of the train?\n\n### Options:\nA. 150m\nB. 180m\nC. 159m\nD. 250m\nE. 152m\n\n### Answer:\nLength of the train be \u2018X\u2019\nX + 150/15 = X + 250/20\n4X + 600 = 3X + 750\nX = 150m\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow much time will a train of length 200 m moving at a speed of 72 kmph take to cross another train of length 300 m, moving at 36 kmph in the same direction?\n\n### Options:\nA. 50 sec\nB. 77\nC. 55\nD. 44\nE. 11\n\n### Answer:\nAnswer: Option A\nExplanation:\nThe distance to be covered = Sum of their lengths = 200 + 300 = 500 m.\nRelative speed = 72 -36 = 36 kmph = 36 * 5/18 = 10 mps.\nTime required = d/s = 500/10\n= 50 sec.\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo equally sized jugs full of water are each emptied into two separate unequally sized empty jugs, X and Y. Now, jug X is 1/3 full, while jug Y is 2/3 full. If water is poured from jug X into jug Y until jug Y is filled, what fraction of jug X then contains water?\n\n### Options:\nA. 0\nB. 1/15\nC. 2/15\nD. 1/6\nE. 2/10\n\n### Answer:\nSuppose the water in each jug is L liters\nCX x (1/3) = L\nCX = 3L liters\nCX is capacity of X\nCY x (2/3) = L\nCY = 3L/2 liters\nCY is capacity of Y\nNow, Y is 3L/2 - L empty = L/2 empty\nSo, we can put only L/2 water in jug Y from Jug X\nJug X's remaining water = L - L/2 = L/2\nFraction of X which contains water = water / CX\n= (L/2)/ 3L\n= 1/6\nAnswer will be D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf two numbers are in the ratio 2:3. If 10 is added to both of the numbers then the ratio becomes 3:4 then find the smallest number?\n\n### Options:\nA. 10\nB. 20\nC. 30\nD. 40\nE. 50\n\n### Answer:\nExplanation:\n2:3\n2x + 10 : 3x + 10 = 3 : 4\n4[2x + 10] = 3[3x + 10]\n8x + 40 = 9x + 30\n9x - 8x = 40 - 30\nx = 10\nThen smallest number is = 2\n2x = 20\nShort cut method:\na:b = 2:3\nc:d = 3:4\n1.Cross multiplication with both ratios\na * d ~ b * c = 2 * 4 ~ 3 * 3 = 8 ~ 9 = 1\n2. If 10 is added both the number means 10 * 3 = 30 and 10 * 4 = 40,\nThen 30 ~ 40 = 10\n===> 1 -----> 10\n===> 2 -----> 20\nAnswer: Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAn old priest fell on a bottom of the well of a church.\nThe well is 16 inches deep.\nAt day time, the old priest climbs 5-inches but when at dark he slip back 4 inches.\nIn how many days priest will come out of the well ?\n\n### Options:\nA. 12-days\nB. 14-days\nC. 11-days\nD. 19-days\nE. 10-days\n\n### Answer:\nA\n12-days\nIn 11-days, he will climb 11-inch and when he climbs 5 inch more, he will be out of the well :-)\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man can row 30 km downstream and 20 km upstream in 4 hours. He can row 45 km downstream and 40 km upstream in 7 hours. Find the speed of man in still water?\n\n### Options:\nA. 12.2\nB. 12.9\nC. 12.6\nD. 12.5\nE. 12.3\n\n### Answer:\nLet the speed of the man in still water be a kmph and let the speed of the stream be b kmph.\nNow 30/(a + b) + 20/(a - b) = 4 and 45/(a + b) + 40/(a - b) = 7\nSolving the equation, the speed of man in still water is 12.5 kmph.\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how many different ways can 5 girls and 4 boys form a circle such that the boys and the girls alternate?\n\n### Options:\nA. 576\nB. 425\nC. 215\nD. 321\nE. None of these\n\n### Answer:\nExplanation :\nIn a circle, 5 boys can be arranged in 4! ways\nGiven that the boys and the girls alternate.\nHence there are 4 places for girls which can be arranged in 4! ways\nTotal number of ways = 4! x 4! = 24 x 24 = 576. Answer : Option A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn Township K each property is taxed at 8 percent of its assessed value. If the assessed value of a property in Township K is increased from $18,000 to $28,000, by how much will the property tax increase?\n\n### Options:\nA. $320\nB. $800\nC. $320\nD. $600\nE. $850\n\n### Answer:\nIncrease in house value = $28,000 - $18,000 =$10000\nSo, tax increase = 8% of$10000=$800\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average marks of a class of 30 students is 40 and that of another class of 50 students is 60. Find the average marks of all the students?\n\n### Options:\nA. 50\nB. 52.5\nC. 60\nD. 62.5\nE. 65\n\n### Answer:\nSum of the marks for the class of 30 students = 30 * 40 = 1200\nSum of the marks for the class of 50 students = 50 * 60 = 3000\nSum of the marks for the class of 80 students =\n1200 + 3000 = 4200\nAverage marks of all the students = 4200/80 = 52.5\nANSWER B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain car averages 15 miles per gallon of gasoline when driven in the city and 40 miles per gallon when driving on the highway. According to these rates, which of the following is closest to the number of miles per gallon that the car averages when it is driven 10 miles in the city and then 50 miles on the highway?\n\n### Options:\nA. 28\nB. 30\nC. 32\nD. 36\nE. 38\n\n### Answer:\n10*1/15 gpm+50*1/40 gpm=1.85 total gallons\n60 total miles/1.85 total gallons=32.4 average mpg\nC. 32\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTim and Jim enter into a partnership by investing $700 and $300 respectively. At the end of one year, they divided their profits such that a third of the profit is divided equally for the efforts they have put into the business and the remaining amount of profit is divided in the ratio of the investments they made in the business. If Tim received $800 more than Jim did, what was the profit made by their business in that year?\n\n### Options:\nA. 4565\nB. 3000\nC. 4654\nD. 353464\nE. 3465463\n\n### Answer:\nSay the profit was $x.\nTim share = x/6 (half of the third) + (x-x/3)*0.7\nJim share = x/6 (half of the third) + (x-x/3)*0.3\nThus (x-x/3)*0.7-(x-x/3)*0.3=800 --> x=3000.\nanswer is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA water tank is two-fifth full. Pipe A can fill a tank in 10 minutes and pipe B can empty in 6 minutes. If both the pipes are open, how long will it take to empty or fill the tank completely ?\n\n### Options:\nA. 7 min to empty\nB. 5 min to full\nC. 4 min to full\nD. 2 min to empty\nE. 6 min to empty\n\n### Answer:\n1/6-1/10 == 1/15\n1/15:2/5::1 : x\n2/5*15 = 6 min\nANSWER E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nBy selling 16 pencils for a rupee a man loses 5%. How many for a rupee should he sell in order to gain 15%?\n\n### Options:\nA. 12.95\nB. 19\nC. 17.56\nD. 16.56\nE. 15\n\n### Answer:\n85% --- 16\n105% --- ?\n85/105 * 16 = 8\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMother is aged thrice than her daughter Silvia. After 8 years, he would be 2(1/2) times of Silvia\u2019s age. After 8 years, how many times would she be of Silvia\u2019s age?\n\n### Options:\nA. 2 years\nB. 4 years\nC. 3 years\nD. 5 years\nE. 6 years\n\n### Answer:\nA\n2 years\nLet Silvia\u2019s current age is A years.\nThen, mom\u2019s current age = (A + 3A) years = 4A years.\n(4A + 8) = (5/2) (A + 8)\n=> 8A + 16 = 5A + 40\n=> 3A = 24\nA = 8\nNeeded ratio = { (4A + 16)/(A+16) }\n= 48/24\n= 2\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAlex deposited x dollars into a new account that earned 6 percent annual interest, compounded annually. One year later Alex deposited an additional x dollars into the account. If there were no other transactions and if the account contained w dollars at the end of two years, which of the following expresses x in terms of w ?\n\n### Options:\nA. w/(1+1.08)\nB. w/(1.08+1.16)\nC. w/(1.16+1.24)\nD. w/(1.06+1.06^2)\nE. w/(1.08^2+1.08^2)\n\n### Answer:\nAccount at the end of the first year would be 1.06x dollars. At this time x dollars was deposited, hence the account at the beginning of the second year would be (1.06x+x) dollars. Account at the end of the second year would be (1.06x+x)*1.06=w --> x(1.06^2+1.06)=w --> x=w/(1.06+1.06^2).\nAnswer: D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAdam borrowed some money at the rate of 6% p.a. for the first two years , at the rate of 9% p.a. for the next three years , and at the rate of 14% p.a. for the period beyond five years. 1\u00a3 he pays a total interest of Rs. 11,400 at the end of nine years how much money did he borrow?\n\n### Options:\nA. Rs.8,000\nB. Rs.09,000\nC. Rs.11,000\nD. Rs.10,000\nE. Rs.12,000\n\n### Answer:\nLet the sum borrowed be x. Then,\n(x*2*6)/100 + (x*9*3)/100 + (x*14*4)/100 = 11400\n(3x/25 + 27x/100 + 14x / 25) = 11400\n95x/100 = 11400\nx = (11400*100)/95 = 12000.\nHence , sum borrowed = Rs.12,000\nAnswer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA rectangular grass field is 75 m * 55 m, it has a path of 2.5 m wide all round it on the outside. Find the area of the path and the cost of constructing it at Rs.3 per sq m?\n\n### Options:\nA. 1350\nB. 1357\nC. 2025\nD. 2052\nE. 2122\n\n### Answer:\nArea = (l + b +2d) 2d\n= (75 + 55 +2.5 * 2) 2*2.5 => 675\n675 * 3 = Rs.2025\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nBy selling a house for Rs.45000, it was found that 1/8 of the outlay was gained, what ought the selling to price to have been in order to have lost 5 p.c?\n\n### Options:\nA. 38008\nB. 38000\nC. 27888\nD. 27799\nE. 27761\n\n### Answer:\nCP + CP/8 = 45000\nCP = 40000\nSP = 40000*(95/100) = 38000\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 2464 / 1.12 = 2200, then 246.4 / 11.2 is equal to?\n\n### Options:\nA. 24\nB. 23\nC. 22\nD. 21\nE. 25\n\n### Answer:\nAnswer\nGiven expression 246.4 / 11.2 = 2464 / 112\n= 2464 / (1.12 x 100)\n= 2200 / 100\n=22\nCorrect Option: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nthe cost of manufacturing a popular model car is made up of three items:cost of raw material,labour and overheads- in a year the cost of three items were in the ration of 4:3:2.next year the cost of the raw material rose by 10% ,labour cost increased by 8% but overhead reduced by 5%.then %increase int the price of the car ?\n\n### Options:\nA. 7.67%\nB. 6%\nC. 0.54%\nD. 9.54%\nE. 8.54%\n\n### Answer:\nbefore increase total cost = 4+3+2=9,\nafter increasing the cost = 9.54\nso increase of .54 over 9 , equal to 6%\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWorking together, Wayne and his son can shovel the entire driveway in three hours. If Wayne can shovel eight times as fast as his son can, how many hours would it take for his son to shovel the entire driveway on his own?\n\n### Options:\nA. 4\nB. 6\nC. 8\nD. 9\nE. 12\n\n### Answer:\nW: the time for Wyane to do the job\nS: the time for his son to do the job\nWe have 1/W + 1/S = 1/8 and W = 8S\nThen we have 1/(8*S) + 1/S = 1/8 <=> 9/(8*S) = 1/8 <=> S = 9\nANS: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n2 men or 6 women can do a piece of work in 20 days. In how many days will 12 men and 8 women do the same work?\n\n### Options:\nA. 12/9 days\nB. 30/11 days\nC. 82/8 days\nD. 22/76 days\nE. 22/2 days\n\n### Answer:\n2M = 6W ---- 20 days\n12M + 8W -----?\n36W + 8 W = 44W ---?\n6W ---- 20 44 -----?\n6 * 20 = 44 * x => x = 30/11 days\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train travels 290 km in 4.5 hours and 400 km in 5.5 hours.find the average speed of train.\n\n### Options:\nA. 80 kmph\nB. 69 kmph\nC. 70 kmph\nD. 90 kmph\nE. None of these\n\n### Answer:\nAs we know that Speed = Distance / Time\nfor average speed = Total Distance / Total Time Taken\nThus, Total Distance = 290 + 400 = 690 km\nThus, Total Speed = 10 hrs\nor,Average Speed = 690/10\nor, 69 kmph.\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA shopkeeper fixes the marked price of an item 30% above its cost price. The percentage of discount allowed to gain 8% is\n\n### Options:\nA. 15.92%\nB. 16.92%\nC. 17.92%\nD. 18.92%\nE. None of these\n\n### Answer:\nExplanation:\nLet the cost price = Rs 100\nthen, Marked price = Rs 130\nRequired gain = 8%,\nSo Selling price = Rs 108\nDiscount = 130 - 108 = 22\nDiscount% = (22/130)*100 = 16.92%\nOption B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA car covers a distance of 1122 km in 6 \u00bd hours. Find its speed?\n\n### Options:\nA. 104 kmph\nB. 187 kmph\nC. 164 kmph\nD. 175 kmph\nE. 106 kmph\n\n### Answer:\n1122/6\n= 187 kmph\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf an integer n is to be chosen at random from the integers 1 to 96, inclusive, what is the probability that n(n + 1)(n + 2) will be divisible by 6?\n\n### Options:\nA. 2/3\nB. 3/8\nC. 1/2\nD. 5/8\nE. 3/4\n\n### Answer:\nI get 5/8 as well\n1 to 96 inclusive means we have 48 odd and 48 even integers\nE O E / 6 = Integer, therefore we have 48 / 96 numbers divisible by 6\nO E O / 6 = Not Integer\nWe cannot forget multiples of 6 from 1 to 96\nWe have 16 numbers that are multiple of 8\nTherefore, 48/96 + 16/96 = 64/96 = 2/3\nanswer : A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe perimeter of an equilateral triangle is 60. If one of the sides of the equilateral triangle is the side of an isosceles triangle of perimeter 65, then how long is the base of isosceles triangle?\n\n### Options:\nA. 10\nB. 15\nC. 20\nD. 25\nE. 30\n\n### Answer:\nThe base of the isosceles triangle is 65-20-20= 25 units\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOn Monday, a certain animal shelter housed 50 cats and dogs. By Friday, 1/5 of the cats and 1/4 of the dogs had been adopted; no new cats or dogs were brought to the shelter during this period. What is the greatest possible number of pets that could have been adopted from the animal shelter between Monday and Friday?\n\n### Options:\nA. 12\nB. 14\nC. 16\nD. 18\nE. 20\n\n### Answer:\nTo maximize the number of pets adopted, we should maximize the number of dogs adopted since 1/4 > 1/5.\nThe greatest multiple of 4 less than 50 is 40 (such that the remaining number is divisible by 5), so let's assume there were 40 dogs and 10 cats.\nThen the maximum number of adopted pets is 1/4*(40) + 1/5*(10) = 10 + 2 = 12.\nThe answer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat should come in place of question mark (?)?\n138.009 + 341.981 \u2013 146.305 = 123.6 + ?\n\n### Options:\nA. 210.85\nB. 120.85\nC. 220.085\nD. 120.085\nE. None of these\n\n### Answer:\n? = 138.009 + 341.981 \u2013 146.305 \u2013 123.60\n\u2234 ? = 210.085\nAnswer E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nS and T are two-digit positive integers that have the same digits but in reverse order. If the positive difference between S and T is less than 50, what is the greatest possible value of S minus T?\n\n### Options:\nA. 40\nB. 42\nC. 44\nD. 45\nE. 48\n\n### Answer:\nA two-digit integer \"ab\" can be expressed algebraically as 10a+b.\nS-T=(10a+b)-(10b+a)=9(a-b)<50.\nThe greatest multiple of 9 which is less than 50 is 45.\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe ratio of boarders to day students at a school was originally 5 to 12. However, after a number of new boarders join the initial 150 boarders, the ratio changed to 1 to 2. If no boarders became day students and vice versa, and no students left the school, how many new boarders joined the school?\n\n### Options:\nA. 30\nB. 50\nC. 70\nD. 80\nE. 90\n\n### Answer:\nLet x be the number of new boarders.\nThe ratio changed from 5:12 up to 1:2 = 6:12.\n150 / (150+x) = 5/6\nx = 30\nThe answer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nEleven men and eleven women have to sit around a circular table so that no 2 women are together. In how many ways can that be done?\n\n### Options:\nA. 5!*6!\nB. 7!*8!\nC. 10!*11!\nD. 10!*12!\nE. 11!*12!\n\n### Answer:\nThe number of arrangements of n distinct objects in a row is given by n!.\nThe number of arrangements of n distinct objects in a circle is given by (n-1)!.\nThe difference between placement in a row and that in a circle is following: if we shift all object by one position, we will get different arrangement in a row but the same relative arrangement in a circle. So, for the number of circular arrangements of n objects we have: n!/n=(n-1)!\nNow, 11 men in a circle can be arranged in (11-1)! ways and if we place 11 women in empty slots between them then no two women will be together. The # of arrangement of these 11 women will be 11! and not 10! because if we shift them by one position we'll get different arrangement because of the neighboring men.\nSo the answer is indeed 10!*11!.\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average age of a committee of 8 members is 40 years. A member aged 55 years\nretired and his place was taken by another member aged 32 years . The average age of\npresent committee is;\n\n### Options:\nA. 39 years\nB. 38 years\nC. 36 years\nD. 37.125 years\nE. 34 years\n\n### Answer:\nExp. Total age of the committee = 40*8 = 320,\nTotal age when a member is retired\nand a new one was joined = 320-55 +32, =297\nAverage age of present committee = 297/8 = 37.125.\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nDarren bought 5 packs of white T-shirts and 3 packs of blue T-shirts for his basketball team. The white T-shirts come in packs of 6, and the blue T-shirts come in packs of 9. How many T-shirts did Darren buy in all?\n\n### Options:\nA. 77\nB. 57\nC. 34\nD. 65\nE. 21\n\n### Answer:\nStep 1: Find the number of white T-shirts.\n5 \u00d7 6 = 30\nStep 2: Find the number of blue T-shirts.\n3 \u00d7 9 = 27\nStep 3: Find the total number of T-shirts.\n30 + 27 = 57\nDarren bought 57 T-shirts.\nAnswer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n14, 35, 56, 91, 126\nIn the sequence above, each term is related with the others. Which of the following could not be a term in the sequence?\n\n### Options:\nA. 407\nB. 259\nC. 322\nD. 686\nE. 847\n\n### Answer:\nSimplifying the question into easier words we just need to find which of the numbers is not divisible by 7\nclearly the answer is 407 because if we divide 407 by 4 we get a remainder of 1\nCorrect answer - A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many positive integers will divide evenly into 230?\n\n### Options:\nA. 4\nB. 6\nC. 8\nD. 12\nE. 16\n\n### Answer:\nThe question is asking how many factors 230 has.\n230 = 2*5*23\nThe number of factors is 2^3 = 8\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nExcluding stoppages, the speed of a train is 35 kmph and including stoppages it is 22 kmph. Of how many minutes does the train stop per hour?\n\n### Options:\nA. 82\nB. 17\nC. 22\nD. 82\nE. 18\n\n### Answer:\nExplanation:\nT = 13/35 * 60 = 22\nAnswer: Option C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train 280 m long, running with a speed of 63 km/hr will pass a tree in?\n\n### Options:\nA. 21\nB. 16\nC. 18\nD. 12\nE. 112\n\n### Answer:\nSpeed = 63 * 5/18 = 35/2 m/sec\nTime taken = 280 * 2/35 = 16 sec.Answer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nS is a set containing 8 different positive odd primes. T is a set containing 7 different numbers, all of which are members of S. Which of the following statements CANNOT be true?\n\n### Options:\nA. The median of S is prime.\nB. The median of T is prime\nC. The median of S is equal to the median of T.\nD. The sum of the terms in S is prime.\nE. The sum of the terms in T is prime.\n\n### Answer:\nHere is my explanation. The question states:S is a set containing 9 different positive odd primes. T is a set containing 8 different numbers, all of which are members of S. Which of the following statements CANNOT be true?\n(A) The median of S is prime.\nThismust be true. If there are an odd number of members of a set, then the median is a member of the set: it's the middle number, when all the numbers are ranked from smallest to biggest. Every number in S is a positive odd prime, so the median is one of them, and is prime.\n(B) The median of T is prime.\nThismay or may not be true. If a set has an even number of members, the median is average of the two numbers in the middle, when ranked from smallest to biggest. The average of two odd numberscould beeven (average of 71 and 73 is 72), and hence not prime, or itcould beodd (the average of 71 and 79 is 75). For particularly well chosen odd numbers, the average can be not only odd but also prime -- for example, the average of 89 and 113 is 101, another prime number. If the two middle numbers of T were 89 and 113, the median would be 101, a prime number.\n(C) The median of S is equal to the median of T.\nUnder most configurations for S and T, this wouldn't happen. If you weren't trying to make it happen, it would be unlikely to happen by chance. BUT, if the number dropped going from from S to T was the median of S (say, 101), and if the two middle numbers of T happen to have an average of that number that was dropped (for example, if the two numbers were 89 and 113), then the medians would be equal. In other words, the three middle numbers of S would have to be {. . ., 89, 101, 133, . . .}, and when 101 is dropped in going to T, the median of two would be the average of 89113, which happens to be 101. It's an exceptional case, but itcouldbe true.\n(D) The sum of the terms in S is prime.\nThismay or may not be true. The sum of 9 odd numbermustbe an odd number. That odd numbercould beprime. For example, the sum of the first nine odd prime numbers {3, 5, 11, 13, 17, 19, 23, 29} is 127, which is prime. If you drop 3 and include the next prime, 31, the set {5, 11, 13, 17, 19, 23, 29, 31} has a sum of 155, which is clearly not prime.\n(E) The sum of the terms in T is prime.\nThismust be false. The sum of eight odd numbers must be an even number. Only 2 is prime, and all other even numbers are not. Therefore, the sum of eight odd prime numbers will be an even number bigger than two, and absolutely cannot be prime.\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo trains 140 metre and 160 metre long run at the speed of 60 km/hr and 40 km/hr respectively in opposite direction on parallel tracks. What time these will take to cross each other ?\n\n### Options:\nA. 10.7 Seconds\nB. 10.8 Seconds\nC. 10.9 Seconds\nD. 11.8 Seconds\nE. None of these\n\n### Answer:\nExplanation:\nRelative Speed = 60+40 = 100 Kmph\n= 100*(5/18) = 250/9 m/sec\nDistance to be covered = 140 + 160 = 300 metres\nTime = Distance/Speed\nTime=300\u22179/250=54/5=10.8 seconds\nOption B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. How far is the place?\n\n### Options:\nA. 2.89\nB. 2.88\nC. 2.82\nD. 2.84\nE. 2.83\n\n### Answer:\nM = 6\nS = 1.2\nDS = 6 + 1.2 = 7.2\nUS = 6 - 1.2 = 4.8\nx/7.2 + x/4.8 = 1\nx = 2.88\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat will be the cost of building a fence around a square plot with area equal to 289 sq ft, if the price per foot of building the fence is Rs. 58?\n\n### Options:\nA. 17\nB. 18\nC. 19\nD. 14\nE. 16\n\n### Answer:\nLet the side of the square plot be a ft.\na2 = 289 => a = 17\nLength of the fence = Perimeter of the plot = 4a = 68 ft.\nCost of building the fence = 68 * 58 = Rs. 3944.\nAnswer: Option A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nExpress a speed of 90 kmph in meters per second?\n\n### Options:\nA. 10 mps\nB. 76 mps\nC. 26 mps\nD. 97 mps\nE. 25 mps\n\n### Answer:\n90 * 5/18\n= 25 mps\nAnswer:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA, B and C enter into a partnership by investing $7000, $11000 and $18000 respectively. At the end of 8 months, B receives $2200 as his share. Find the share of A.\n\n### Options:\nA. $1200\nB. $1300\nC. $1400\nD. $1500\nE. $1600\n\n### Answer:\nThe ratio of capital of A, B and C = 7000 : 11000 : 18000 = 7 : 11 : 18\nA's share = (7/11)*2200 = $1400\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe sum of a rational number and its reciprocal is 13/6. Find the number.\n\n### Options:\nA. 4/3 or 3/4\nB. 0\nC. 1/3 or 3\nD. 2/3 or 3/2\nE. 2\n\n### Answer:\nLet the number be x.\nThen, x + (1/x) = 13/6 => (x2 + 1)/x = 13/6 => 6x2 \u2013 13x + 6 = 0\n=> 6x2 \u2013 9x \u2013 4x + 6 = 0 => (3x \u2013 2) (2x \u2013 3) = 0\n\uf0f0\tx = 2/3 or x = 3/2\nHence the required number is 2/3 or 3/2.\nAnswer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSet M contains number that satisfy the condition that, if integer x is in the set then x + 4 will also be in the set M. If -4 is one value in the set, which of the following values must also be present in the set M? I) -8 II) 4 III) 8\n\n### Options:\nA. I only\nB. II only\nC. I and II only\nD. II and III only\nE. I, II and III\n\n### Answer:\nSince -4 is in the set, then the set must also include 0, 4, 8, 12, etc...\nDepending on whether -4 is the starting element in the set or not, we can have -8...or not.\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWeights of two friends Ram and Shyam are in the ratio of 4 : 5. Ram\u2019s weight increases by 10% and the total weight of Ram and Shyam together becomes 82.8 kg, with an increase of 15%. By what per cent did the weight of Shyam increase?\n\n### Options:\nA. 12.5%\nB. 17.5%\nC. 19%\nD. 21%\nE. None of these\n\n### Answer:\nLet the weights of Ram and Shyam be 4x and 5x. Now,according to question,\n4x\u00d7110/100+Shyam?snewwt4x\u00d7110100+Shyam?s new wt = 82.8........ (i)\nand 4x + 5x = 9x+115/100= 82.8........ (ii)\nFrom (ii), x = 8\nPutting in (i),\nwe get Shyam\u2019s new wt = (82.8 \u2013 35.2) = 47.6\n% increase in Shyam\u2019s wt = (47.6\u221240/40\u00d7100) = 19\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n7 dogs have got 7 puppies each. Each puppy has got 7 kitten as friend. They are all members of a club along with me. What is the strength of club ?\n\n### Options:\nA. 300\nB. 400\nC. 500\nD. 600\nE. 700\n\n### Answer:\ntotal strength = (7+7*7+7*7*7)+1=400\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the probability that the sum of two numbers that are selected randomly from a set of numbers will be greater than 6 if the given set is {2,4,6}\n\n### Options:\nA. 5/3\nB. 1/7\nC. 1/2\nD. 1/4\nE. 1/3\n\n### Answer:\nFirst problem is 3C2 = 6 .. Not 20..\nPoint 2, your sum should be greater than 6, so these are the following possibilities you have\n({2,6},{4,6}) which leads to 2 pairs\nSo the probability is 2 on 6 or 1/3..\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFifthty percent of the members of a swim club have passed the lifesaving test. Among the members who havenotpassed the test, 10 have taken the preparatory course and 30 have not taken the course. How many members are there in the swim club?\n\n### Options:\nA. 60\nB. 80\nC. 100\nD. 120\nE. 140\n\n### Answer:\n50% of the members have passed the test, thus 50% have not passed the test.\nWe also know that 30+10=40 members have not passed the test, thus 0.5*Total=40 --> Total=80.\nAnswer: B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHeinz produces tomato puree by boiling tomato juice. The tomato puree has only 20% water while the tomato juice has 90% water. How many liters of tomato puree will be obtained from 25 litres of tomato juice?\n\n### Options:\nA. 2.8 liters.\nB. 3.125 liters.\nC. 8.5 liters.\nD. 2.6 liters.\nE. 2.1 liters.\n\n### Answer:\nAnswer:\nExplanation:\nIn each of the solutions, there is a pure tomato component and some water. So while boiling, water evaporates but tomato not. So we equate tomato part in the both equations.\n\u00e2\u2021\u2019\u00e2\u2021\u2019 10%(25) = 80%(x)\n\u00e2\u2021\u2019\u00e2\u2021\u2019 x = 3.125 liters.\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA can do a work in 9 days and B can do the same work in 18 days. If they work together, in how many days will they complete the work?\n\n### Options:\nA. 6 days\nB. 7 days\nC. 5 days\nD. 3 days\nE. 2 days\n\n### Answer:\nOne day's work of A and B = 1/9 + 1/8 = (2+1)/18 = 1/6 So, the time taken to complete the work is 6 days.\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average of four positive integers is 69. The highest integer is 93 and the least integer is 39. The difference between the remaining two integers is 28. Which of the following integers is the higher of the remaining two integers?\n\n### Options:\nA. 11\nB. 86\nC. 66\nD. 55\nE. 44\n\n### Answer:\nLet the four integers be A, B, C and D where A > B > C > D.\n(A + B + C + D)/4 = 69 => A + B + C + D = 276 ---> (1)\nA = 93, D = 39 and B - C = 28\n(1) => B + C = 276 - (A + D) = 276 - 132 = 144.\nB + B -28 = 144\nB = (144 + 28)/2 = 86\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nKamal started a business investing Rs. 9000. After five months, Sameer joined with a capital of Rs. 8000. If at the end of the year, they earn a profit of Rs. 6970, then what will be the share of Sameer in the profit?\n\n### Options:\nA. 2388\nB. 2380\nC. 2888\nD. 2663\nE. 2922\n\n### Answer:\nKamal : Sameer = (9000 * 12) : (8000 * 7)\n= 108:56 = 27:14\nSameer's share = 6970 * 14/41 = Rs. 2380.\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a certain company 20% of the men and 40% of the women attended the annual company picnic.If 55% of all the employees are men .What % of all the employee went to the picnic?\n\n### Options:\nA. 29%\nB. 34%\nC. 35%\nD. 36%\nE. 37%\n\n### Answer:\ntotal men in company 55% means total women in company 45%(assume total people in company 100%)\nno of men employees attended picnic=55x(20/100)=11\nno of women employees attend picnic=45x(40/100)=18\ntotal percentage of employees attend the picnic=11+18=29%\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the price of sugar rises from Rs. 10 per kg to Rs. 11 per kg, a person, to have no increase in the expenditure on sugar, will have to reduce his consumption of sugar by\n\n### Options:\nA. 9%\nB. 20%\nC. 25%\nD. 30%\nE. none\n\n### Answer:\nSol.\nLet the original consumption = 100 kg and new consumption = x kg.\nSo, 100 x 10 = x \u00d7 11 = x = 91 kg.\n\u2234 Reduction in consumption = 9%.\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe speed of a boat in still water is 60kmph and the speed of the current is 20kmph. Find the speed downstream and upstream?\n\n### Options:\nA. 80, 49\nB. 80, 40\nC. 80, 48\nD. 80, 46\nE. 82, 41\n\n### Answer:\nSpeed downstream = 60 + 20 = 80 kmph\nSpeed upstream = 60 - 20 = 40 kmph Answer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If three marbles are drawn what is the probability that one is yellow and two are red?\n\n### Options:\nA. P(E)=12/455\nB. 12/458\nC. 12/487\nD. 12/456\nE. 12/4512\n\n### Answer:\nGiven that there are three blue marbles, four red marbles, six green marbles and two yellow marbles.\nWhen three marbles are drawn , the probability that one is yellow and two are red\n= (2 * 4 * 3 * 3 * 2)/(1 * 2 * 15 * 14 * 13)\n= 12/455\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA group consists of 4 men, 6 women and 2 children. In how many ways can 2 men , 3 women and 1 child selected from the given group?\n\n### Options:\nA. 400\nB. 240\nC. 287\nD. 278\nE. 281\n\n### Answer:\nExplanation:\nTwo men, three women and one child can be selected in \u00e2\u00b4C\u00e2\u201a\u201a * \u00e2\u00b6C\u00e2\u201a\u0192 * \u00e2\u00b5C\u00e2\u201a ways\n= (4 * 3)/(2 * 1) * (6 * 5 * 4)/(3 * 2) * 2\n= 240 ways.\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA 1200 m long train crosses a tree in 120 sec, how much time will I take to pass a platform 700 m long?\n\n### Options:\nA. 388\nB. 190\nC. 277\nD. 288\nE. 261\n\n### Answer:\nL = S*T\nS= 1200/120\nS= 10 m/Sec.\nTotal length (D)= 1900 m\nT = D/S\nT = 1900/10\nT = 190 Sec .Answer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many seconds does a train 130 meters long, traveling at 72 km/h, take to completely cross a bridge of 210 meters in length?\n\n### Options:\nA. 13\nB. 15\nC. 17\nD. 19\nE. 21\n\n### Answer:\n72 km/h = 72000/3600 = 20 m/s\nTime = 340 / 20 = 17 seconds\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSolve the quickfire maths brain teaser \u00e2\u02c6\u016116% = ?\n\n### Options:\nA. 30%\nB. 40%\nC. 85%\nD. 19%\nE. 29%\n\n### Answer:\n\u00e2\u02c6\u016116%\n=> \u00e2\u02c6\u016116/\u00e2\u02c6\u0161100\n=> 4/10\n=> 40/100\n=> 40%\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a - b = 6 and a2 + b2 = 50, find the value of ab.\n\n### Options:\nA. A)7\nB. B)12\nC. C)15\nD. D)18\nE. E)20\n\n### Answer:\nExplanation:\n2ab = (a2 + b2) - (a - b)2\n= 50 - 36 = 14\nab = 7.\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA contractor undertakes to do a piece of work in 40 days. He engages 100 men at the begining and 100 more after 35 days and completes the work in stipulated time. If he had not engaged the additional men, how many days behind schedule would it be finished?\n\n### Options:\nA. 1\nB. 5\nC. 7\nD. 8\nE. 2\n\n### Answer:\nExplanation:\n\\inline \\fn_jvn [(100\\times 35)+(200\\times 5)] men can finish the work in 1 day\n\\inline \\fn_jvn \\therefore 4500 men can finish the work in 1 day. 100 men can finish it in \\inline \\fn_jvn \\frac{4500}{100} = 45 days.\nThis is 5 days behind Schedule\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA money lender lends Rs.2000 for six months at 20% p.a. rate. It the interest is reckoned quarterly than find the amount given after time limit.\n\n### Options:\nA. 22075\nB. 2622\nC. 2677\nD. 2666\nE. 267\n\n### Answer:\nExplanation:\nA = 2000(21/20)2 = 2205\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf \u00e2\u20ac\u02dcMADURAI\u00e2\u20ac\u2122 is coded as \u00e2\u20ac\u02dcDADCIAI\u00e2\u20ac\u2122, then \u00e2\u20ac\u02dcDELHI\u00e2\u20ac\u2122 is coded as\n\n### Options:\nA. DEHIE\nB. DDEHI\nC. EDDIH\nD. DECHI\nE. CHIDE\n\n### Answer:\nM=13,1+3=4=D\nA=1=A\nSIMILARLY,\nM=13=1+3=4=D\nD=4=D\nE=5=E\nL=12=1+2=C\nH=8=H\nI=9=I\nSO ANS IS\nDECHI\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n15 binders can bind 1400 books in 21 days. How many binders will be required to bind 1600 books in 20 days?\n\n### Options:\nA. 87\nB. 18\nC. 17\nD. 16\nE. 10\n\n### Answer:\nBinders Books Days\n15 1400 21\nx 1600 20\nx/15 = (1600/1400) * (21/20) => x = 18\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n(565945 x 121) = ?\n\n### Options:\nA. 68463812\nB. 68463813\nC. 68479345\nD. 68463814\nE. 68463814\n\n### Answer:\n565945*121\r=68479345\rAns C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe compound interest earned on a sum for the second and the third years are $1400 and $1498 respectively. What is the rate of interest?\n\n### Options:\nA. 3%\nB. 5%\nC. 7%\nD. 9%\nE. 11%\n\n### Answer:\n1498 - 1400 = 98 is the rate of interest on $1400 for one year.\nThe rate of interest = (100 * 98) / (1400) = 7%\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhen running a mile during a recent track meet, Nuria was initially credited with a final time of 5 minutes, 30 seconds. Shortly after her run, officials realized that the timing mechanism malfunctioned. The stopwatch did not begin timing her until 2/7 of a minute after she began to run. If the time was otherwise correct, how long did it actually take Nuria to run the mile?\n\n### Options:\nA. 5 minutes, 17.6 seconds\nB. 5 minutes, 21.8 seconds\nC. 5 minutes, 23.6 seconds\nD. 5 minutes, 44.44 seconds\nE. 6 minutes, 10.4 seconds\n\n### Answer:\nOne approach:\nThe watch starts to work after Nuria began his running. It means the time should be greater than credited 5 minutes, 30 seconds. The only number is 5 minutes, 44.44 seconds.\nAnother approach:\n2/7 close to 20 second when added to the 5 minutes, 30 seconds, it means it passes 5 minute 44.44 seconds\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a garden, carrots are planted in rows. In each row there are as many carrots as the number of rows in the garden. If each plant attracts as many bunnies as the number of carrots in each row and if the total number of bunnies is n, then :\n\n### Options:\nA. n is a perfect square\nB. n is an odd number\nC. n is an even number\nD. n is a perfect cube\nE. none\n\n### Answer:\nFor example, if there were 4 carrot rows, the garden would have a 4x4 arrangement. If each carrot attracts 4 bunnies, the number of bunnies would be (4*4)*4 = 64 pieces, which is a cube of 4.\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n84/12/0.8 = ?\n\n### Options:\nA. 8.17\nB. 7.14\nC. 6.23\nD. 4.35\nE. 8.75\n\n### Answer:\nE\n8.75\n? = 84/(12*0.8) = 8.75\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train 250 m long running at 72 kmph crosses a platform in 40 sec. What is the length of the platform?\n\n### Options:\nA. 450m\nB. 200m\nC. 250m\nD. 270m\nE. 300 m\n\n### Answer:\nD = 72 * 5/18 = 40 = 800 \u00e2\u20ac\u201c 250 = 450m\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIF\n1= O\n2= T\n3= T\n4=F\n5= F\nTHEN 6=?\n\n### Options:\nA. S\nB. J\nC. K\nD. L\nE. M\n\n### Answer:\nIF\n1= O... First letter of ONE.\n2= T.... First letter of TWO.\n3= T\n4=F\n5= F\nTHEN 6=S ... First letter of SIX.\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the smallest integer that is the sum of 2 distinct prime integers, each greater than 70 ?\n\n### Options:\nA. 147\nB. 142\nC. 173\nD. 144\nE. 186\n\n### Answer:\nA prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself. Here are the first few prime numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, etc.\nImmediate two prime numbers after 70 are - 71 and 73\nSum = 71 + 73 = 144\nAnswer - D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nGiven that 2x + 17 > 5 and 5x - 13 < 7, all values of x must be between which of the following pairs of integers?\n\n### Options:\nA. -4 and -1\nB. -1 and 4\nC. -4 and 1\nD. -6 and 4\nE. 2 and 5\n\n### Answer:\n2x + 17 > 5\ni.e 2x >5-17\ni.e. 2x > -12\ni.e. x > -6\nAlso, 5x - 13 < 7\ni.e. 5x <7+13\ni.e 5x < 20\ni.e x < 4\ni.e. -6 < x < 4\nAnswer: Option D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOn an xy-graph, three corners of a\nparallelogram are located at (3, 3), (4, \u2013 4),\nand (\u20132, \u20131). Which of the following points\ncould be the remaining corner?\n\n### Options:\nA. (8, 0)\nB. (8, \u20131)\nC. (\u20131, 9)\nD. (\u20133, 6)\nE. (\u20135, 7)\n\n### Answer:\nA good way to begin is to draw a picture showing the three points given, including\npossible places where a fourth point would form a parallelogram. Here\u2019s what your\npicture may look like:\ny\nA\nB\nC\n(4, \u20134)\n(\u20132, \u20131)\n(3, 3)\nx\nThis figure shows three possible points for the remaining corner of the parallelogram: A, B,\nand C. To find the exact coordinates of these three additional points, choose any of the\ngiven points and count up and over (or down and over) to a second given point. Then,\nstarting from the third given point, count the same number of steps up and over (or down\nand over) and label the point where you end up.\nBy this method, you find that A = (\u20133, 6), B = (9, 0), and C = (\u20131, \u20138). Only point A is listed\nas an answer.\ncorrect answer A)(8, 0)\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA shop purchased a pair of shoes for $150 and was selling it at a price that equaled the purchase price of the shoes plus a markup that was 25 percent of the selling price. After some time a shop owner decided to decrease the selling price by 20 percent. What was the shop's gross profit on this sale?\n\n### Options:\nA. $0\nB. $2\nC. $10\nD. $6\nE. $8\n\n### Answer:\nSale Price(SP) = 150 + Markup(MP)\n--> Mp = SP-150\nand given MP=SP/4 ( 25% is 1/4th)\nso SP/4= SP-150\n3SP/4= 150\nSP=200\nNow a discount of 20% is given so NEW SP is .8 *200 =160\nProfit=160-150 =$10\nAnswer is C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe present worth of Rs. 242 due in 2 years at 10% per annum compound interest is:\n\n### Options:\nA. Rs. 180\nB. Rs. 240\nC. Rs. 220\nD. Rs. 200\nE. Rs. 300\n\n### Answer:\nExplanation:\nPresent worth of Rs. x due T years hence is given by\nPresent Worth (PW) = x/(1+R/100)^T\nPresent Worth (PW) = 242/(1+10/100)^2=242/(11/10)^2=Rs. 200\nAnswer : Option D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many integers between 100 and 1000 are there such that their unit digit is odd?\n\n### Options:\nA. 400\nB. 420\nC. 500\nD. 450\nE. 350\n\n### Answer:\n900 numbers between - 100 and 1000\nOut of which half would be even, half odd.\nNumber of odd unit digit number = 450.\ncorrect option is D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a coin is flipped, the probability that the coin will land tails is 1/2. If the coin is flipped 5 times, what is the probability that it will land tails up on the first 2 flips and not on the last 3 flips?\n\n### Options:\nA. 3/5\nB. 1/32\nC. 1/5\nD. 1/4\nE. 1/2\n\n### Answer:\n(1/2) * (1/2) * (1/2) * (1/2) * (1/2) = 1/32 Answer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe ratio of investments of two partners P and Q is 7:5 and the ratio of their profits is 7:14. If P invested the money for 5 months, find for how much time did Q invest the money?\n\n### Options:\nA. 19\nB. 14\nC. 13\nD. 10\nE. 12\n\n### Answer:\n7*5: 5*x = 7:14\nx = 14\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe population of a bacteria colony doubles every day. If it was started 11 days ago with 2 bacteria and each bacteria lives for 12 days, how large is the colony today?\n\n### Options:\nA. 512\nB. 768\nC. 1024\nD. 2048\nE. 4096\n\n### Answer:\n2^11(2) = 2^12 = 4096\nThe answer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA lighting store is stocked with 410 fixtures. Some of the fixtures are floor lamps and the rest are table lamps. If 5% of the floor lamps and 30% of the table lamps are imported, what is the smallest possible number J of imported lamps stocked at the store?\n\n### Options:\nA. 3\nB. 10\nC. 13\nD. 20\nE. 23\n\n### Answer:\nWe want to minimize not maximize the expression,.\nJ=x/20+(410-x)*3/10=123+x/20-3x/10=123-5x/20 --> maximize x to minimize the expression --> x must be the greatest multiple of 20 less than 410, so 400 --> 123-5*400/20=23.\nBut i'm guessing 123-5x/20 can be written as 123- x/4\nif x has to be the greatest multiple of 4 less then 410, then it would be 408.\nHence 123-408/4 --> 123-102 -->21\nYes, you cannot reduce in this case. If x=408, then 5/100*x and (410-x)*3/10 won't be integers.E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 2 cards are selected at random from the deck of 52 cards then What is the probability of one of the selected cards will be Jack and other will be Queen?\nA deck of cards has a total of 52 cards, consisting of 4 suits; (spades(Black), hearts(Red), diamond(Red)s, and clubs(Black)); and 13 cards including 1 king, 1 queen and 1 jack in each suit\n\n### Options:\nA. 8/2652\nB. 1/2652\nC. 28/2652\nD. 6/2652\nE. 18/2652\n\n### Answer:\n2 possible cases:\nJack - Queen or Queen - Jack (4 Jacks and 4 queens).\nEither way,\nthe total probability = 2( Jack -Queen) = 2 (4/52 * 4/51) = 18/2652. E is the correct answer.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA, B, C and D enter into partnership. A subscribes 1/3 of the capital B 1/4, C 1/5 and D the rest. How much share did A get in a profit of Rs.2490 ?\n\n### Options:\nA. Rs. 832\nB. Rs. 830\nC. Rs. 822\nD. Rs. 812\nE. Rs. 810\n\n### Answer:\nLet the total amount in the partnership be 'x'.\nThen A's share = x/3\nB's share = x/4\nC's share = x/5\nD's share = x - (x/3 + x/4 +x/5) = 13x/60\nA : B : C : D = x/3 : x/4 : x/5 : 13x/60 = 20 : 15 : 12 : 13\nA's share in the profit of Rs. 2490 = 20 (2490/60) = Rs. 830.\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA bus travel 5/7 of its speed covers 42 km in 1 hr 40 min48 sec. What is theactual speed of the bus ?\n\n### Options:\nA. 25 km/hr\nB. 35 km/hr\nC. 40 km/hr\nD. 42 km/hr\nE. 45 km/hr\n\n### Answer:\nTime = 1 hr 40 min 48 sec = 1hr +4060hr+483600hr=1+23+175=12675hrdistance = 42 kmspeed=distancetime=42(12675)=42\u00d775126\u21d257 of the actual speed = 42\u00d775126\u21d2actual speed = 42\u00d775126\u00d775=42\u00d71518=7\u00d7153=7\u00d75=35 km/hr\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAn article is bought for Rs.1200 and sold for Rs.800, find the loss percent?\n\n### Options:\nA. 16%\nB. 35%\nC. 33%\nD. 18%\nE. 12%\n\n### Answer:\n1200 ---- 400\n100 ---- ? => 33%\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJanuary 1, 2008 is Tuesday. What day of the week lies on Jan 1, 2009?\n\n### Options:\nA. Saturday\nB. Wednesday\nC. Thursday\nD. Tuesday\nE. Monday\n\n### Answer:\nExplanation:\nNumber of odd days in 2008 = 2 (since it is a leap year)\n(we have taken the complete year 2008 because we need to find out the odd days from 01-Jan-2008 to 31-Dec-2008, that is the whole year 2008)\nGiven that January 1, 2008 is Tuesday.\nHence January 1, 2009 = (Tuesday + 2 odd days) = Thursday\nAnswer: Option C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn an examination, a student scores 4 marks for every correct answer and loses 1 mark for every wrong answer. If he attempts all 80 questions and secures 120 marks, the number of questions he attempts correctly, is:\n\n### Options:\nA. 35\nB. 46\nC. 42\nD. 30\nE. 40\n\n### Answer:\nLet the number of correct answers be x.\nNumber of incorrect answers = (80 \u00e2\u20ac\u201c x).\n4x \u00e2\u20ac\u201c 1(80 \u00e2\u20ac\u201c x) = 120 or 5x = 200 or x = 40.\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA, B and C are partners. A receives 2/3 of profits, B and C dividing the remainder equally. A's income is increased by Rs.200 when the rate to profit rises from 5 to 7 percent. Find the Capital of B?\n\n### Options:\nA. 12227\nB. 2787\nC. 2500\nD. 2778\nE. 2789\n\n### Answer:\nA:B:C = 2/3:1/6:1/6 = 4:1:1\nx * 2/100 * 2/3 = 200\nB capital = 15000*1/6 = 2500\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nPositive integer p has n factors; 3p has 3 factors; Which of the following values can n take?\nI. 1\nII. 2\nIII. 3\n\n### Options:\nA. I or II\nB. II or III\nC. only I is true\nD. only II is true\nE. I or III\n\n### Answer:\nSquares have odd number of factors.The square which is a multiple of 3 is 9.\n3 has factors 1,3 .\nTherefore 2 factors\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a colony of 70 resident s, the ratio of the number of men and women is 4:3. Among the women, the ratio of the educated to the uneducated is 1:4. If the ratio of the number of education to uneducated persons is 8:27, then find the ratio of the number of educated and uneducated men in the colony?\n\n### Options:\nA. 1:9\nB. 1:6\nC. 1:3\nD. 1:1\nE. 1ratio 3\n\n### Answer:\nNumber of men in the colony = 4/7 (70) = 40\nNumber of women in the colony = 3/7 (70) = 30\nNumber of educated women in the colony = 1/5 (30) = 6\nNumber of uneducated women in the colony = 4/5 (30) = 24\nNumber of educated persons in the colony = 8/35 (70) = 16\nAs 6 females are educated, remaining 10 educated persons must be men.\nNumber of uneducated men in the colony = 40 - 10 = 30\nNumber of educated men and uneducated men are in the ratio 10:30 => 1:3\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind a sum for first 8 prime no's from number series?\n\n### Options:\nA. 77\nB. 79\nC. 89\nD. 34\nE. 36\n\n### Answer:\nRequired sum = (2+ 3+ 5+ 7+11+ 13+17+ 19) = 77\nNote: 1 is not a prime number\nOption A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA and B walk around a circular track. A and B walk at a speed of 2 rounds per hour and 3 rounds per hour respectively. If they start at 8 a.m. from the same point in opposite directions, how many times shall they cross each other before 10.30 a.m.?\n\n### Options:\nA. 5\nB. 6\nC. 7\nD. 8\nE. 12\n\n### Answer:\nRelative speed = Speed of A + Speed of B (? they walk in opposite directions)\n= 2 + 3 = 5 rounds per hour\n=> They cross each other 5 times in 1 hour and 2 times in 1/2 hour\nTime duration from 8 am to 10.30 am = 2.5 hour\nHence they cross each other 12 times before 10.30 am\nAnswer is E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n97 students take part in a test and the median score is 85. Which of the following descriptions must be correct?\nI.At least 49 students\u2019 score are less than 85.\nII. At least 49 students\u2019 score are equal to or more than 85\nIII. At most 49 students\u2019 score are equal to or more than 85.\n\n### Options:\nA. I\nB. II\nC. III\nD. III\nE. IIII\n\n### Answer:\nIf we order the scores increasingly, then on the 49th place we have the score of 85. There must be 48 scores (those on the right of the 85 score) greater or equal to 85. So, I is necessarily correct.\nThe scores on the left of the 49th place, all have to be equal or less than 85. Since we can have the extreme case of all the scores 85, neither II, nor III is correct. The question asks for descriptions thatmustbe correct.\nAnswer B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a, b, c and g are non-zero integers, 3 \u2265 c \u2265 \u2013 9 , 5 \u2265 a \u2265 \u20132 , 10 \u2265b \u2265 \u20131 , 4 \u2265 g \u2265 1, then which of the following expresses the smallest possible value of ag/(bc)?\n\n### Options:\nA. \u201390\nB. \u201320\nC. \u201310\nD. 1/90\nE. 15/4\n\n### Answer:\nag have to be greatest from its range && bc to be smallest with -ve sign to became ag/bc smallest\nA)-90 never possible case.(all nos. are integers and ag has max. 20 value)\nB)-20 a=5,b=4 and b=1,c=-1 then it is possible\nOption C,D,E are > -20....\nAns B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe market value of a 10.5% stock, in which an income of Rs. 756 is derived by investing Rs. 6000, brokerage being 1/4%, is:\n\n### Options:\nA. 83.08\nB. 114\nC. 114.75\nD. 124\nE. 124.75\n\n### Answer:\nFace Value = Rs. 6000.\nDividend = 10.5%.\nAnnual Income = Rs. 756.\nBrokerage per Rs. 100 = Rs. 0.25.\nDividend is always paid on the face value of a share.\nFace Value * Dividend / (Market Value + Brokerage per Rs. 100) = Annual income.\n= 6000 * 10.5 / 756 = Market Value of Rs. 100 stock + Brokerage per Rs. 100.\n= Market Value of Rs. 100 stock + Brokerage per Rs. 100 = Rs. 83.33.\n= Market Value of Rs. 100 stock = Rs. 83.33 - Re. 0.25.\n= Market Value of Rs. 100 stock = Rs. 83.08\nanswer : A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow much time will take for an amount of Rs. 200 to yield Rs. 81 as interest at 4.5% per annum of simple interest?\n\n### Options:\nA. 7\nB. 4\nC. 5\nD. 3\nE. 9\n\n### Answer:\nTime = (100 * 81) / (200 * 4.5) = 4 years'\nAnswer:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA watch which gains uniformly is 2 minutes low at noon on Monday and is 4 min. 48 sec fast at 2 p.m. on the following Monday. When was it correct\n\n### Options:\nA. 2 p.m. on Monday\nB. 2 p.m. on Tuesday\nC. 2 p.m. on Wednesday\nD. 3 p.m. on Thursday\nE. None\n\n### Answer:\nSol.\nTime from 12 p.m. on Monday to 2 p.m. on the following Monday = 7 days 2 hours = 170 hours.\n\u2234 The watch gains [2 + 4 4/5] min. or 34/5 min. in 170 hrs.\nNow, 34/5 min. are gained in 170 hrs.\n\u2234 2 min. are gained in [170 * 5/34 * 2] hrs = 50 hrs.\n\u2234 Watch is correct 2 days 2 hrs. after 12 p.m. on Monday i.e. it will be correct at 2 p.m. on Wednesday.\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf x is 30 percent more than y and y is 50 percent less than z, then x is what percent of z?\n\n### Options:\nA. 500%\nB. 250%\nC. 65%\nD. 125%\nE. 60%\n\n### Answer:\nZ = 100 ; Y = 50 so X = 65\nX as % of Z = 65/100 * 100 => 65%\nAnswer will be (C)\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf x and q are integers and 2x\u2013q= 11, then 4x+ q CANNOT be\n\n### Options:\nA. \u20135\nB. 1\nC. 13\nD. 17\nE. 551\n\n### Answer:\n2x-q=11....q=2x-11\n4x+q=4x+2x-11=6x-11\n6x-11=-5...x=1\n6x-11=1... x=2\n6x-11=13...x=4\n6x-11=17..X is not integer\n6x-11=551..X is not integer\nI think the choice E is 55 not 551. Otherwise both E CANNOT be solution=D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMarla is hanging a banner diagonally across a rectangular room. The length of the room is 2 feet shorter than its width. If the total area of the room is 120 square feet, what is the length of the banner (in feet)?\n\n### Options:\nA. Between 13 and 14\nB. Between 14 and 15\nC. Between 15 and 16\nD. Between 16 and 17\nE. Between 17 and 18\n\n### Answer:\nTo solve this, we first need to set up an equation for the area of the room. If x is the width, then we have\nx(x - 2) = 120. By putting the equation in standard form, we get x^2-2x-120=0. By using the quadratic formula, we get roots of -10 and 12. We know that x is the width, and x-2 is the length, so by using the roots, we get 12 as the width (x), and 10 as the length (x-2).\nOnce we have this, we can use the Pythagorean Theorem to solve for the diagonal. Plugging in the length and width, we will get d^2=12^2+10^2\n=144+100\n=244\nThe square root of 244 is less than 16, since 16^2 = 256. Going down a number, we can compute 15^2 = 225 < 224. Therefore, the length of the diagonal must be between 15 and 16.\nThe correct answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf x is 11 percent greater than 80, then x =\n\n### Options:\nA. 88.8\nB. 91.0\nC. 88.0\nD. 70.9\nE. 71.2\n\n### Answer:\n11% of 80 = (80*0.11) = 8.8\n11% greater than 80 = 80 + 8.8 = 88.8\nAnswer is clearly A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAt 1:00 pm, there were 10.0 grams of bacteria. The bacteria increased to x grams at 4:00 pm, and 28.9 grams at 7:00 pm. If the amount of bacteria present increased by the same fraction during each of the 3-hour periods, how many grams of bacteria were present at 4:00 pm?\n\n### Options:\nA. 16.2\nB. 16.4\nC. 16.6\nD. 16.8\nE. 17.0\n\n### Answer:\nLet x be the factor by which the bacteria increases every three hours.\nAt 4:00 pm, the amount of bacteria was 10x and at 7:00 pm it was 10x^2.\n10x^2 = 28.9\nx^2=2.89\nx=1.7\nAt 4:00 pm, the amount of bacteria was 10(1.7)=17 grams.\nThe answer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA student traveled 10 percent of the distance of the trip alone, continued another 30 miles with a friend, and then finished the last half of the trip alone. How many miles long was the trip?\n\n### Options:\nA. 75\nB. 100\nC. 125\nD. 150\nE. 175\n\n### Answer:\nLet x be the total length of the trip.\n0.1x + 30 miles + 0.5x = x\n30 miles = 0.4x\nx = 75 miles\nThe answer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRahul went to a shop and bought things worth Rs. 25, out of which 48 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?\n\n### Options:\nA. 19\nB. 19.7\nC. 19.9\nD. 16.7\nE. 22.8\n\n### Answer:\nTotal cost of the items he purchased = Rs.25\nGiven that out of this Rs.25, 48 Paise is given as tax\n=> Total tax incurred = 48 Paise = Rs.48/100\nLet the cost of the tax free items = x\nGiven that tax rate = 6%\n\u2234 (25\u221230/100\u2212x)6/100 = 48/100\n\u21d2 6(25 \u22120.3 \u2212x) = 48\n\u21d2 (25 \u2212 0.3 \u2212 x) = 8\n\u21d2 x = 25 \u2212 0.3 \u2212 8 = 16.7\nD)\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe sum of the fourth and twelfth term of an arithmetic progression is 20. What is the sum of the first 16 terms of the arithmetic progression?\n\n### Options:\nA. 300\nB. 120\nC. 150\nD. 160\nE. 270\n\n### Answer:\nn th term of A.P. is given by a+(n-1)d\n4 th term = a+3d\n12 th term = a+11d\nGiven a+3d+a+11d=20 --> 2a+14d=20 --> a+7d = 10\nSum of n term of A.P = n/2[2a+(n-1)d]\nsubsitiuing n = 16 ...we get 15/2[ 2a + 14d] = 16 [a+7d] = 16*10 = 160...\nAnswer is D...\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train 100 m long crosses a platform 125 m long in 40 sec; find the speed of the train?\n\n### Options:\nA. 36.21\nB. 77.11\nC. 54.12\nD. 33.0\nE. 20.25\n\n### Answer:\nD = 100 + 125 = 225\nT = 40\nS = 225/40 * 18/5 = 20.25 kmph\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA recipe requires 2 1/2 (mixed number) cups of flour 2 3/4 (mixed number) cups of sugar and 1 1/3 (mixed number) cups of milk to make one cake. Victor has 15 cups if flour, 16 cups of sugar and 8 cups of milk. What is the greatest number of cakes William can make using this recipe?\n\n### Options:\nA. 5\nB. 6\nC. 7\nD. 8\nE. 9\n\n### Answer:\nLess work up front: Go through each item and see what the greatest number of cakes you can make with each. The lowest of these will be the right answer.\nFlour: 15 cups, we need 2.5 cups each. Just keep going up the line to see how many cakes we can make: That means I can make 2 cakes with 5 cups, so 6 cakes overall with 15 cups. I've already got the answer narrowed to either A or B.\nSugar: 16 cups, we need 2.75 cups each. Same principle. I can make 2 cups with 5.5 cups, so to make 6 cakes I'd need 16.5 cups. I don't have that much sugar, so we're limited to 5 cakes. No need to even do milk because we're already at 5. Sugar will be the limiting factor.\nanswer is A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMachine A can process 6000 envelopes in 3 hours. Machines B and C working together but independently can process the same number of envelopes in 2.5 hours. If Machines A and C working together but independently process 3000 envelopes in 1 hour, then how many hours would it take Machine B to process 4200 envelopes.\n\n### Options:\nA. 2\nB. 3\nC. 4\nD. 6\nE. 60/7\n\n### Answer:\nYou can either take the amount of work done as the same as Karishma has done or take the work done by each in the same time. I will do the latter\n1. Work done in 1 hr by A is 2000 envelopes\n2. Work done in 1 hr by A and C is 3000 envelopes\n3. So work done in 1 hr by C is 1000 envelopes\n4. Work done in 1 hr by B and C is 2400 envelopes\n5. So work done in 1 hr by B is 1400 envelopes\n6. So to process 4200 envelopes B will take 4200/1400 hrs = 3 hrs\nSo the answer is choice B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n(1000)7\u00f7(10)18=?\n\n### Options:\nA. 10\nB. 100\nC. 1000\nD. 10000\nE. None of these\n\n### Answer:\nExplanation:\n=(103)7/(10)18\n=(10)21/(10)18=10(3)=1000\nOption C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAs x increases from 131 to 132, which of the following increases?\nI) x\u22121/x\nII) 17\u22121/x\nIII) (17+x)/x\n\n### Options:\nA. I only\nB. II only\nC. I,II only\nD. II,III only\nE. III only\n\n### Answer:\nOn Increasing the value of x from 131 to 132\nI) x\u22121/x will increase as 1/x will be very small and x will increase by 1 unit\nII) 17\u22121/x Will Increase as the value of 1/x will decrease thereby increasing the value of 17-(1/x)\nIII) (17+x)/x = (17/x)+1 will Decrease as 1/x will decrease thereby decreasing the value of (17/x)\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf an average hard drive had a capacity of 0.7 TB in 2000, and average hard drive capacities double every 5 years, what will be the average hard drive capacity in 2050?\n\n### Options:\nA. 256\nB. 512\nC. 768\nD. 1024\nE. 7168\n\n### Answer:\n0.7*2^10=0.7*1024=716.8\nThe answer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe compound interest earned by Sunil on a certain amount at the end of two years at the rate of 10% p.a. was Rs.420. Find the total amount that Sunil got back at the end of two years in the form of principal plus interest earned.\n\n### Options:\nA. Rs.2530\nB. Rs.2430\nC. Rs.2420\nD. Rs.2410\nE. Rs.2440\n\n### Answer:\nLet the sum be Rs.P\nP{ [ 1 + 10/100]2 - 1 } = 420\nP(10/100)(2 + 10/100) = 420 [a2 - b2 = (a - b) ( a + b)] P = 420 / (0.1)(2.1) = 2000. Amount =2000+420=Rs.2420 Answer : C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA rectangular photograph is surrounded by a border that is 1 inch wide on each side. The total area of the photograph and the border is M square inches. If the border had been 4 inches wide on each side, the total area would have been (M + 90) square inches. What is the perimeter of the photograph, in inches?\n\n### Options:\nA. 10\nB. 20\nC. 30\nD. 40\nE. 50\n\n### Answer:\nLet x and y be the width and length of the photograph.\n(x+2)(y+2)=M and so (1) xy + 2x + 2y + 4 = M\n(x+8)(y+8)=M and so (2) xy + 8x + 8y + 64 = M+90\nLet's subtract equation (1) from equation (2).\n6x + 6y + 60 = 90\n2x + 2y = 10, which is the perimeter of the photograph.\nThe answer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that all the four bulbs are defective?\n\n### Options:\nA. 1/126\nB. 1/122\nC. 1/129\nD. 1/136\nE. 1/126\n\n### Answer:\nOut of nine, five are good and four are defective. Required probability\n= \u2074C\u2084/\u2079C\u2084\n= 1/126\nAnswer:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA dealer purchased an article at 3/4 of its list price and sold 50% more than the list price. Find his gain percent?\n\n### Options:\nA. 227\nB. 188\nC. 100\nD. 988\nE. 271\n\n### Answer:\nMP = 100\nCP = 75\nSP = 150\n------\n75 ---- 75\n100 ---- ? => 100%\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the simple interest on $10000 at 8% per annum for 12 months?\n\n### Options:\nA. $410\nB. $500\nC. $650\nD. $800\nE. $1000\n\n### Answer:\nP = $10000\nR = 8%\nT = 12/12 YEARS = 1 YEAR\nS.I. = P*R*T/100 = 10000*8*1/100 = $800\nAnswer is D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA Train requires 10 seconds to pass a pole while it requires 30 seconds to cross a stationary train which is 600 mtrs long. Find the speed of the train.\n\n### Options:\nA. 110 kmph\nB. 120 kmph\nC. 108 kmph\nD. 100 kmph\nE. 98 kmph\n\n### Answer:\nIn 10s the train crosses the pole and in 30 sec the train crosses one more stationary train\nIn 20 sec the train travels a distance of 600 mtrs\nSpeed = 600/20 = 30 m/s = 30 (3600/1000) = 30 * 18/5 = 108 kmph\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nin a rectangle 8 vertical and 4 horizontal lines are drawn find the number of rectangle formed ?\n\n### Options:\nA. 654\nB. 664\nC. 674\nD. 684\nE. 694\n\n### Answer:\n8 vertical lines plus the 2 lines of the existing rectangle(as its mentioned in the question \"in a rectangle\") accordingly 4 plus 2 horizontal lines.\ntherefore\n10C2*6C2= 675 and if its asked for the new rectangle formed than\n675-1=674 (excluding the existing rectangle)\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average of first five multiples of 3 is?\n\n### Options:\nA. 6\nB. 8\nC. 9\nD. 5\nE. 7\n\n### Answer:\nAverage = 3(1 + 2 + 3 + 4 + 5)/5\n= 45/5\n= 9.\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA, B, C together started a business. A invested Rs.6000 for 5 months B invested Rs.3600 for 6 months and C Rs.7500 for 3 months. If they get a total profit of Rs.7410. Find the share of A?\n\n### Options:\nA. 3002\nB. 3000\nC. 3018\nD. 3019\nE. 3012\n\n### Answer:\n60*5:36*6:75*3\n100: 72: 75\n100/247 * 7410 = 3000\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRs. 700 is divided among A, B, C so that A receives half as much as B and B half as much as C. Then C's share is\n\n### Options:\nA. Rs 429\nB. Rs 412\nC. Rs 400\nD. Rs 129\nE. Rs 122\n\n### Answer:\nLet C = x.\nThen B = x/2\nand A = x/4\nA:B:C = 1:2:4.\nC's share Rs.[(4/7)*700) = 400\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n2 people meet for a business lunch. Each person shakes hands once with each other person present. How many handshakes take place?\n\n### Options:\nA. 1\nB. 2\nC. 5\nD. 0\nE. 4\n\n### Answer:\nthe formula to count handshakes is n(n\u22121)2n(n\u22121)2\nWhere n is the number of people\n=> 2(2-1)/2 = 2*1/2 = 2/2 = 1\n=> the answer is A(1)\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf log12 27 = a, then log6 16 is:\n\n### Options:\nA. (3-a)/4(3+a)\nB. (3+a)/4(3-a)\nC. 4(3+a)/(3-a)\nD. 4(3-a)/(3+a)\nE. 5(3-a)/(3+a)\n\n### Answer:\nlog12 27 = a => log 27/ log 12 = a\n=> log 33 / log (3 * 22) =a\n=> 3 log 3 / log 3 + 2 log 2 = a => (log 3 + 2 log 2)/ 3 log 3 = 1/a\n=> (log 3/ 3 log 3) + (2 log 2/ 3 log 3) = 1/3\n=> (2 log 2)/ (3 log 3) = 1/a \u2013 1/3 = (3-a)/ 3a\n=> log 2/ log 3= (3-a)/3a => log 3 = (2a/3-a)log2\nlog16 16 = log 16/ log 6 = log 24/ log (2*3) = 4 log 2/ (log 2 + log 3)\n= 4(3-a)/ (3+a)\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA woman can do a piece of work in 40 days. Man is 25% more efficient than Woman. In how many days a man can do the same piece of work?\n\n### Options:\nA. 32 days\nB. 36 days\nC. 38 days\nD. 40 days\nE. 53 days\n\n### Answer:\nThe ratio of the efficiencies of a woman and man = 100 : 125\n= 4 : 5\nThe ratio of the days taken by woman and man to finish the work = 5 :4\nWoman takes 32 days to finish the work.=> 5 parts = 40\nThe number of days taken by man to finish the work = 4 parts = 40/5x 4 = 32 days\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train passes a station platform in 39 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?\n\n### Options:\nA. 328\nB. 279\nC. 240\nD. 285\nE. 231\n\n### Answer:\nSpeed = [54 * 5/18] m/sec = 15 m/sec.\nLength of the train = (15 * 20) m = 300 m.\nLet the length of the platform be x meters.\nThen, x + 300 / 39 = 15\nx + 300 = 585\nx = 285 m. Answer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA person buys an article at Rs.500. At what price should he sell the article so as to make a profit of 45%?\n\n### Options:\nA. 600\nB. 887\nC. 256\nD. 654\nE. 725\n\n### Answer:\nCost price = Rs.500\nprofit = 45% of 500 = Rs.225\nSelling price = Cost price + Profit\n= 500 + 225 = 725\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAn alloy weighing 60 ounces is 20 percent copper. How many ounces of copper must be added to create an alloy that is 60 percent copper?\n\n### Options:\nA. 40\nB. 50\nC. 60\nD. 70\nE. 80\n\n### Answer:\nAn alloy of 60oz which is 20% copper means there is 12 oz of gold. To get to an alloy that is 60% copper, let's use this expression: (12 + x)/(60 + x) = 0.60 with x representing the amount of pure copper that must be added to get to 60%. The expression we are using represents the new total weight of pure copper over the new total weight of the alloy and this fraction should represent 60% or 0.6. you will see that 60 is the correct answer, as 72/120=0.6\nChoose C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAn article is bought for Rs.685 and sold for Rs.900, find the gain percent?\n\n### Options:\nA. 30 1/3%\nB. 33 1/3%\nC. 31 53/137%\nD. 35 1/3%\nE. 29 1/3%\n\n### Answer:\nC\n31 53/137%\n685 ---- 215\n100 ---- ? => 31 53/137%\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAt present, the ratio between the ages of Arun and Deepak is 4:3. After 6 years, Arun's age will be 26 years. What is the age of Deepak at present?\n\n### Options:\nA. 77 years\nB. 15 years\nC. 66 years\nD. 88 years\nE. 55 years\n\n### Answer:\nLet the present ages of Arun and Deepak be 4x and 3x years respectively.\nThen, 4x + 6 = 26 => x = 5\nDeepak's age = 3x = 15 years.\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many four digit numbers can be formed using the digits {1, 3, 4, 5, 7,9}(repetition of digits is not allowed)?\n\n### Options:\nA. 360\nB. 817\nC. 145\nD. 346\nE. 342\n\n### Answer:\nThe given digits are six.\nThe number of four digit numbers that can be formed using six digits is \u2076P\u2084\n= 6 * 5 * 4 * 3\n= 360.\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA, B and C can independently complete a piece of work in 8,12 and 6 days respectively. A and B work together for 4 days and leave. How long will C take to finish the remaining work?\n\n### Options:\nA. 1\nB. 2\nC. 3\nD. 4\nE. 5\n\n### Answer:\nA and B work together for 4 days and completed 4*(1/8 +1/12) =5/6 work.\nBalance 1/6 work will be completed by C in one day.\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf x and y are positive integers such that x < y and z=x/y, which of the following must be true?\nI. z>(x \u2212 1)/(y \u2212 2)\nII. z<(x \u2212 1)/(y \u2212 2)\nIII. z>(x + 1)/(y + 2)\n\n### Options:\nA. I only\nB. I and II\nC. II and III\nD. II only\nE. I and III\n\n### Answer:\nx < y --> Let x = 2 and y = 3 --> z = 2/3\nI. z>(x \u2212 1)/(y \u2212 2) --> 2/3 > 1/1 --> False\nII. z<(x \u2212 1)/(y \u2212 2) --> 2/3 < 1/1 --> True\nIII. z>(x + 1)/(y + 2) --> 2/3 > 3/5 --> True\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the greatest number of four digits which is divisible by 15, 25, 40 and 75 ?\n\n### Options:\nA. 9800\nB. 9600\nC. 9400\nD. 9500\nE. 9200\n\n### Answer:\nGreatest number of four digits = 9999\nLCM of 15, 25, 40 and 75 = 600\n9999 \u00f7 600 = 16, remainder = 399\nHence, greatest number of four digits which is divisible by 15, 25, 40 and 75\n= 9999 - 399 = 9600\nanswer :B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSteve gets on the elevator at the 11th floor of a building and rides up at a rate of 72 floors per minute. At the same time Joyce gets on an elevator on the 61st floor of the same building and rides down at a rate of 78 floors per minute. If they continue traveling at these rates, at which floor will their paths cross?\n\n### Options:\nA. 19\nB. 28\nC. 30\nD. 35\nE. 44\n\n### Answer:\nSteve gets on the elevator at the 11th floor of a building and rides up at a rate of 72 floors per minute. At the same time Joyce gets on an elevator on the 61st floor of the same building and rides down at a rate of 78 floors per minute. If they continue traveling at these rates, at which floor will their paths cross?\n50 floors/150 floors per minute=1/3 minutes\n11+72/3=35\n61-78/3=35\nAnswer : D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe length of a rectangular plot is thrice its breadth. If the area of the rectangular plot is 432 sq m, then what is the breadth of the rectangular plot?\n\n### Options:\nA. 12\nB. 17\nC. 18\nD. 19\nE. 14\n\n### Answer:\nLet the breadth of the plot be b m.\nLength of the plot = 3 b m\n(3b)(b) = 432\n3b2 = 432\nb2 = 144\nb = 12 m.\nAnswer: Option A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere 3 kinds of books in the library physics, chemistry and biology. Ratio of physics to chemistry is 3 to 2; ratio of chemistry to biology is 4 to 3, and the total of the books is more than 3000. Which one of following can be the total W of the book?\n\n### Options:\nA. 3003\nB. 3027\nC. 3024\nD. 3021\nE. 3018\n\n### Answer:\nFirst, you have to find the common ratio for all 3 books. You have:\nP:C:B\n3:2 --> multiply by 2 (gives you row 3)\n4:6\n6:4:3\nHence:\nP:C:B:T(Total)W\n6:4:3:13 ----> This means, the Total Number must be a multiple of 13.\nAnswer A is correct since 299 is divisible by 13, hence is 2990 and so is 3003 (2990+13).\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is?\n\n### Options:\nA. 1 : 3\nB. 3 : 2\nC. 3 : 4\nD. 4 : 3\nE. 3 : 5\n\n### Answer:\nExplanation:\nLet the speeds of the two trains be x m/sec and y m/sec respectively.\nThen, length of the first train = 27x metres,\nand length of the second train = 17y metres.\n( 27x + 17y ) / (x+ y )= 23\n=> 27x + 17y = 23x + 23y\n=> 4x = 6y\n=> ( x/y ) = ( 3/2 )\nAnswer: Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a group of ducks and cows, the total number of legs are 24 more than twice the no. of heads. Find the total no.of buffaloes.\n\n### Options:\nA. 10\nB. 12\nC. 13\nD. 15\nE. 16\n\n### Answer:\nLet the number of buffaloes be x and the number of ducks be y\n=> 4x + 2y = 2 (x + y) + 24\n=> 2x = 24 => x = 12\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the wrong number below mentioned series\n11,150,280,560,800\n\n### Options:\nA. 800\nB. 560\nC. 280\nD. 150\nE. 11\n\n### Answer:\n11 is the only prime number or odd number in the series.\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man can row at 5 kmph in still water .If the velocity of current is 1 kmph and it takes him 1 hour to row to a place and come back ,how far is the place ?\n\n### Options:\nA. 2.4 km\nB. 2.5 km\nC. 3 km\nD. 3.6 km\nE. None of these\n\n### Answer:\nAnswer A\nSolution\nSpeed downstream = kmph = 6 kmph,Speed upstream = (5 - 1)\nkmph = 4 kmph.\nLet the required distance be x km.\nThen,x/6 + x/4 = 1 => 2x + 3x = 12 5x = 12=> x = 2.4 km. Answer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf .005^4 is represented in its shortest possible decimal form, how many 0\u2019s to the right of the decimal point does it contain?\n\n### Options:\nA. 0\nB. 8\nC. 9\nD. 10\nE. 11\n\n### Answer:\n0.005^4= (5*10^-3)^4 = 625*10^-12 = 0.625*10^-9 which would have 9 zeros to the right of the decimal point. The answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a river flowing at 2 km/hr, a boat travels 40 km upstream and then returns downstream to the starting point. If its speed in still water be 6 km/hr, find the total journey time.\n\n### Options:\nA. 10 hours\nB. 12 hours\nC. 14 hours\nD. 15 hours\nE. None of these\n\n### Answer:\nExplanation :\nspeed of the boat = 6 km/hr\nSpeed downstream = (6+2) = 8 km/hr\nSpeed upstream = (6-2) = 4 km/hr\nDistance travelled downstream = Distance travelled upstream = 40 km\nTotal time taken = Time taken downstream + Time taken upstream\n= (40/8) + (40/4) = 15\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMy 5 sons are enrolled in an army's platoon of 80 men. The General is choosing randomly 2 men to a suicide mission. What is the probability of both of the selected men will be two of my sons?\n\n### Options:\nA. 1/80\nB. 2/80\nC. 5/80\nD. 1/316\nE. 2/316\n\n### Answer:\nMy sons are 5 in a group of 80 men. Thus the probability of choosing 2 of my sons is: (5/80)(4/79) = 1/316. The correct answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nP, Q and R have $4000 among themselves. R has two-thirds of the total amount with P and Q. Find the amount with R?\n\n### Options:\nA. 2400\nB. 2403\nC. 3998\nD. 2539\nE. 1600\n\n### Answer:\nE\n1600\nLet the amount with R be $ r\nr = 2/3 (total amount with P and Q)\nr = 2/3(4000 - r) => 3r = 8000 - 2r\n=> 5r = 8000 => r = 1600.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAnu can do a work in 6 days and Binu alone in 9 days. Anu and Binu undertook to do it for Rs.5400. With help of Minu, they completed the work in 3 days. How much is to be paid to Minu and Anu?\n\n### Options:\nA. s.750, Rs.2250\nB. s.2000, Rs.750\nC. s.750, Rs.2000\nD. s.800, Rs.1250\nE. s.900, Rs.2700\n\n### Answer:\nMinu\u00e2\u20ac\u2122s one day\u00e2\u20ac\u2122s work = 1/3 - 1/6 + 1/9= 1/3 - 5/18 = 1/18\nAnu\u00e2\u20ac\u2122s wages: Binu\u00e2\u20ac\u2122s wages: Minu\u00e2\u20ac\u2122s wages = 1/6 : 1/9 : 1/18 = 6: 4: 2\nMinu\u00e2\u20ac\u2122s share = Rs.5400* 2/12 = Rs.900\nAnu\u00e2\u20ac\u2122s share = Rs.5400* 6 /12 = Rs.2700\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n375 metres long yard, 26 trees are palnted at equal distances, one tree being at each end of the yard. What is the distance between 2consecutive trees\n\n### Options:\nA. 10\nB. 12\nC. 14\nD. 16\nE. 15\n\n### Answer:\n26 trees have 25 gaps between them,\nRequired distance (375/25) = 15\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average of 5 numbers is 6.8. If one of the numbers is multiplied by a factor of 4, the average of the numbers increases to 9.2. What number is multiplied by 4?\n\n### Options:\nA. 1.5\nB. 3.0\nC. 3.9\nD. 4.0\nE. 6.0\n\n### Answer:\nThe average of 5 numbers is 6.8\nThe sum of 5 numbers will be 6.8 x 5 = 34\nThe average of 5 number after one of the number is multiplied by 4 is 9.2\nThe sum of the numbers will now be 9.2 x 5 = 46\nSo the sum has increased by 46-34 = 12\nLet the number multiplied by 4 be n\nThen,\n4n = n+12\nor 3n = 12\nor n = 4\nAnswer:- D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA can do a piece of work in 20 days. When he had worked for 2 days B joins him. If the complete work was finished in 8 days. In how many days B alone can finish the work?\n\n### Options:\nA. 18\nB. 77\nC. 66\nD. 55\nE. 10\n\n### Answer:\n8/20 + 6/x = 1\nX = 10 days\nAnswer:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nLet R1 and R2 respectively denote the maximum and minimum possible remainders when (276)n is divided by 91 for any natural number n , n>= 144. Find R1+R2.\n\n### Options:\nA. 90\nB. 82\nC. 84\nD. 64\nE. None\n\n### Answer:\nExplanation :\nThe remainder when 276 divided by 91 is 3 hence\nremainder of (276)n/91 = remainder 3n/91\nTaking n = 1,2,3,4,5\nWe get the possible remainders as 3, 9, 27, 81, 61, 1 respectively.\nFor n>5, the pattern repeats\nHence R1 = 81 and R2 = 1\nR1+R2 = 81+1 = 82\nAnswer : B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n2 men and 4 boys can complete a work in 4 days. 5 men and 6 boys can complete the same work in 3 days. The work done by 2 boys is equal to the work of how many men?\n\n### Options:\nA. 4\nB. 5\nC. 6\nD. 7\nE. 8\n\n### Answer:\nExp: (2m + 4b)\u2019s one day\u2019s work = 1/4\n(5m + 6b)\u2019s one day\u2019s work = 1/3\n=> (8m + 16b)\u2019s one day\u2019s work = (15m + 18b) \u2019s one day\u2019s work\n=> 7 men\u2019s work = 2 boy\u2019s work\nSo, we should be employ 5 more men to be completed the work.\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a box of 8 pencils, a total of 2 are defective. If a customer buys 3 pencils selected at random from the box, what is the probability that neither pencils will be defective?\n\n### Options:\nA. 1/12\nB. 5/14\nC. 2/13\nD. 2/15\nE. 1/17\n\n### Answer:\nFirst, there are 6C3 ways you can select 3 good pencils from 4 good ones.\nSecond, there are 8C3 ways you select 3 pencils from 6 ones in the box.\nThen, the probability that neither pen will be defective is: 6C3/8C3=20/56 = 5/14\nAnswer is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA rich merchant had collected many gold coins. He did not want anybody to know about them. One day, his wife asked, \u201cHow many gold coins do we have?\u201d After pausing a moment, he replied, \u201cWell! If I divide the coins into two unequal numbers, then 37 times the difference between the two numbers equals the difference between the squares of the two numbers.\u201d The wife looked puzzled. Can you help the merchant\u2019s wife by finding out how many gold are\n\n### Options:\nA. 36\nB. 37\nC. 38\nD. 39\nE. 40\n\n### Answer:\n37(x-y)=x^2-y^2. u no tht x^2-y^2=(x-y)(x+y).so (x-y) cancels on both sides to give x+y=37.so sum of unequal halves=37 which is the required answer.\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nPeter age after 5 years will be 5 times his age 5 years back. what is the present age of Peter?\n\n### Options:\nA. A)20\nB. B)25\nC. C)15\nD. D)22\nE. E)10\n\n### Answer:\nPeter present age= x\nafter 5 years = x+5\n5 years back = x-5\nx+5= 5(x-5)\nx=20\nAnswer is A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhen the smallest of 3 consecutive odd integers is added to four times the largest, it produces a result 728 more than 4times the middle integer. Find the numbers?\n\n### Options:\nA. 650\nB. 678\nC. 698\nD. 728\nE. 729\n\n### Answer:\nx + 4 (x + 4) = 728 + 4 (x + 2)\nSolve for x and find all three numbers\nx + 4 x + 16 = 728 + 4 x + 8\nx = 720\nx + 2 = 722\nx + 4 = 724\nCheck: the smallest is added to four times the largest\n720 + 4 * 724 = 3616\nfour times the middle\n4 * 722 = 2888\n3616 is more than 2888 by\n3616 - 2888 = 728\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nBruce purchased 8kg of grapes at the rate of 70 per kg and 9 kg of mangoes at the rate of 55 per kg. How much amount did he pay to the shopkeeper?\n\n### Options:\nA. 1040\nB. 1050\nC. 1055\nD. 1065\nE. 1075\n\n### Answer:\nCost of 8 kg grapes = 70 \u00d7 8 = 560.\nCost of 9 kg of mangoes = 55 \u00d7 9 = 490.\nTotal cost he has to pay = 560 + 490 = 1055\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA no. when divided by the sum of 555 and 445 gives 2times their difference as quotient & 20 as remainder. Find the no. is?\n\n### Options:\nA. 122456\nB. 220020\nC. 220022\nD. 235467\nE. 220026\n\n### Answer:\n(555 + 445) * 2 * 110 + 20 = 220000 + 20 = 220020\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA person invested in all Rs. 2600 at 4%, 6% and 8% per annum simple interest. At the end of the year, he got the same interest in all the three cases. The money invested at 4% is?\n\n### Options:\nA. 3477\nB. 2688\nC. 2699\nD. 1200\nE. 2671\n\n### Answer:\nLet the parts be x, y and [2600 - (x + y)].\nThen,\n(x * 4 * 1)/100 = (y * 6 * 1)/100 = {[2600 - (x + y)] * 8 * 1}/100\ny/x = 4/6 = 2/3 or y = 2/3 x\nSo, (x * 4 * 1)/100 = [(2600 - 5/3 x) * 80/100\n52x = (7800 * 8) => x = 1200\nMoney invested at 4% = Rs. 1200.\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nEvery year Taylor goes to the same carnival, and he attempts to shoot a basketball into a small hoop, hoping that he will win a ten-foot tall teddy bear. If the probability that Taylor does not make a basket is 9/10, what is the probability that Taylor makes exactly one basket in three tries?\n\n### Options:\nA. 3^5/10^3\nB. 3^4/10^3\nC. 3^3/10^3\nD. 3^2/10^3\nE. 3^4/10^4\n\n### Answer:\nProbability of basket = 1/10\nProbability of no basket = 9/10\nRequired probability= 3* (1*9*9/1000)\n= 3^5/10^3\nA is the answer\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA and B start a business with Rs.6000 and Rs.8000 respectively. Hoe should they share their profits at the end of one year?\n\n### Options:\nA. 3:5\nB. 3:4\nC. 3:8\nD. 3:9\nE. 3:1\n\n### Answer:\nThey should share the profits in the ratio of their investments.\nThe ratio of the investments made by A and B\n=6000 : 8000 => 3:4\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the sum of all three digit integers formed using the digits 1, 2, and 3 (repetition is allowed)\n\n### Options:\nA. 4443\nB. 5980\nC. 5992\nD. 5990\nE. 5994\n\n### Answer:\nn = 3*3*3 = 27\n = (333 + 111) / 2 = 222\nSum = number of integers x average value\nn * = 27 * 222 = 5994\nanswer = E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA rectangular ground is to be filled with square tiles of unit area. The border of the ground should be of red coloured tiles and inside white. If the number of red and white tiles are the same, find the minimum dimensions of the ground.\n\n### Options:\nA. 44\nB. 45\nC. 46\nD. 47\nE. 48\n\n### Answer:\nLet us consider R for RED & W for WHITE\n[R01][R02][R03][R04][R05][R06][R07][R08]\n[R24][W01][W02][W03][W04][W05][W06][R09]\n[R23][W07][W08][W09][W10][W11][W12][R10]\n[R22][W13][W14][W15][W16][W17][W18][R11]\n[R21][W19][W20][W21][W22][W23][W24][R12]\n[R20][R19][R18][R17][R16][R15][R14][R13]\nIn this rectangle there are 24 RED & 24 WHITE.\nSo the dimension is (6*8) or (8*6).\nTotal number of tiles is 48.\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe compound interest on Rs. 30,000 at 7% per annum is Rs. 4347. The period(in years) is?\n\n### Options:\nA. 2 years\nB. 6 years\nC. 7 years\nD. 9 years\nE. 4 years\n\n### Answer:\nAmount = (30000 + 4347) = Rs. 34347\nLet the time be n years. Then,\n30000(1 + 7/100)n = 34347\n= (107/100)n = 34347/30000 = (107/100)2\nn = 2 years.\nAnswer: A:\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe ratio of the radius of two circles is 2: 5, and then the ratio of their areas is?\n\n### Options:\nA. 4:25\nB. 2:9\nC. 1:9\nD. 3:7\nE. 3:4\n\n### Answer:\nr1: r2 = 2: 5\n\u00ce r1^2: \u00ce r2^2\nr1^2: r2^2 = 4:25\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOne side of rectangular field is 15 meter and one of its diagonals is 17 meter. Then find the area of the field.\n\n### Options:\nA. 120m2\nB. 130m2\nC. 140m2\nD. 150m2\nE. 160m2\n\n### Answer:\nExplanation:\nWe know h2=b2+h2\n=>Other side\n=\u221a(17)2\u2212(15)2\n=\u221a289\u2212225\n=\u221a64\n=\u221a8meter\nArea=Length\u00d7Breadth\n=15\u00d78m2=120m2\nANSWER IS A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a drawer of shirts 8 are blue, 6 are green and 4 are magenta. If Mason draws 2 shirts at random, what is the probability W at least one of the shirts he draws will be blue?\n\n### Options:\nA. 25/153\nB. 28/153\nC. 5/17\nD. 4/9\nE. W=12/17\n\n### Answer:\nP(at least one blue) = 1- P(0 blue) = 1 - 10/18*9/17 =W= 12/17.\nAnswer: E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA vessel is filled with liquid, 3 parts of which are water and 5 parts of syrup. How much of the\nmixture must be drawn off and replaced with water so that the mixture may be half water and half\nsyrup?\n\n### Options:\nA. 13\nB. 14\nC. 15\nD. 16\nE. 17\n\n### Answer:\nExplanation :\nLet the quantity of the initial liquid in the vessel = 8 litre and quantity of water in the initial liquid = 3\nlitre andquantity of syrup in the initial liquid = 5 litreLet x litre of the mixture is drawn off and replaced\nwith waterQuantity of water in the new mixture = 3\u22123x8+xQuantity of syrup in the new mixture =\n5\u22125x8Given that in the new mixture, quantity of water = quantity of\nsyrup\u21d23\u22123x8+x=5\u22125x8\u21d210x8=2\u21d25x4=2\u21d2x=85\u21d285litre\nInitially we assumed that the quantity of the initial liquid in the vessel = 8 litre for\nthe ease of calculations. For that 8/5 litre of the mixture to be drawn off and replaced\nwith water so that the mixture may be half water and half syrup\nNow, if the initial liquid in the vessel = 1 litre, quantity of the mixture to be drawn off\nand replaced with water so that the mixture may be half water and half syrup\n=85\u00d718=15\nIt means 1/5 of the mixture has to be drawn off and replaced with water so that the mixture\nmay be half water and half syrup\nAnswer : Option C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAndy solves problems 74 to 135 inclusive in a Math exercise. How many problems does he solve?\n\n### Options:\nA. 53\nB. 62\nC. 51\nD. 50\nE. 49\n\n### Answer:\n135-74+1= 62\n'B' is the answer\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nConsider a right triangle WBC with length of sides being x,y and z where y represents the hypotenuse , Which of these represent the radius of the circle which is inscribed in triangle WBC\n\n### Options:\nA. [A] x+y+z/3\nB. [B] x-y+z/3\nC. [C] x-y+z/2\nD. [D] (x^2 + y^2 + z^2)/3\nE. [E] cannot be determined\n\n### Answer:\nRadius of a circle inscribed in the right triangle WBC r = (x + z - y)/2 where y is the hypotenuse and x and y are other two sides.\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTorry has submitted 2/5 of his homework assignments, and he received an average grade of 75 for those assignments. If he wishes to receive an average grade of 105 for all his homework assignments, the average grade for Torry's remaining homework assignments must be what percent greater than the average grade for the assignments he has already submitted?\n\n### Options:\nA. 15%\nB. 20%\nC. 25%\nD. 66 2/3%\nE. 40%\n\n### Answer:\n0.4*75 + 0.6x = 105\n30 + 0.6x=107\n0.6x = 75\nx= 125\n125/75= 1.66666...\nAns:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf difference between compound interest and simple interest on a sum at 10% P.a. for 2 years is Rs.65 then sum is\n\n### Options:\nA. s.5000\nB. s.6500\nC. s.5800\nD. s.6000\nE. s.6200\n\n### Answer:\np(r/100)^2=C.I-S.I\nP(10/100)^2=65\n6500\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe L.C.M of two numbers is 2310 and their H.C.F is 30. If one number is 330 the Other is\n\n### Options:\nA. 330\nB. 300\nC. 210\nD. 250\nE. 350\n\n### Answer:\nThe other number\n= L.C.M * H.C.F/given number\n= 2310*30/330 = 210\nAnswer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA sum of money at simple interest amounts to Rs.720 after 2 years and to Rs.1020 after a further period of 5 years. The sum is :\n\n### Options:\nA. 400\nB. 500\nC. 600\nD. 700\nE. 800\n\n### Answer:\nSI of 5 year = (1020-720)=300\nso, SI of 1 year=300/5=60\nso, SI of 2 year=60*2=120\nso, sum is =(720-120)=600\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich of the following is true about 0<|x|-2x<5?\n\n### Options:\nA. -1", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a trader sold two cars each at Rs. 325475 and gains 12% on the first and loses 12% on the second, then his profit or loss percent on the whole is?\n\n### Options:\nA. 1.44%\nB. 2.45%\nC. 7.44%\nD. 8.44%\nE. 2.44%\n\n### Answer:\nExplanation:\nSP of each car is Rs. 325475, he gains 12% on first car and losses 12% on second car.\nIn this case, there will be loss and percentage of loss is given by = [(profit%)(loss%)]/100 = (12)(12)/100 % = 1.44%\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAn insect leaps 72 centimeters in 1.5 seconds. What is its speed?\n\n### Options:\nA. 90 centimeters per second\nB. 10.8 centimeters per second\nC. 1.08 meters per second\nD. 4.8 centimeters per second\nE. 0.48 meters per second\n\n### Answer:\n72 / 1.5 = 48 cm/s = 0.48 m/s\nThe answer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are 10 books on a shelf, of which 4 are paperbacks and 6 are hardbacks. How many possible selections of 5 books from the shelf contain at least one paperback and at least one hardback?\n\n### Options:\nA. 75\nB. 120\nC. 210\nD. 246\nE. 252\n\n### Answer:\nPaperbacks - 4, hardbacks - 6\n5 books in total and at least 1 from each.\nTotal combinations for 5 books = (1pb, 4 hb) + (4pb, 1hb) + (3pb, 2hb) + (2pb, 3hb)\n1pb, 4hb = 4c1*6c4 = 60\n4pb,1hb = 4c4*6c1 = 6\n3pb,2hb = 4c3*6c2 = 60\n2pb,3hb = 4c2*6c3 = 120\nTotal combinations of 5 books = 60+6+60+120 = >246\nAns D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA cyclist covers a distance of 750 meter in 2 minutes 40 seconds. What is the speed in km/hr of cyclist\n\n### Options:\nA. 16 km/hr\nB. 16.85 km/hr\nC. 18 km/hr\nD. 19 km/hr\nE. 20 km/hr\n\n### Answer:\nExplanation:\nSpeed=Distance/Time\nDistance=750meter\nTime=2 min 40sec=160sec\nSpeed=750/160=4.68m/sec\n=>4.68\u00e2\u02c6\u201418/5km/hr=16.85km/hr\nOption B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are some 2 wheelers and 4 wheelers parked total number of wheels present is 240 then how many 4 wheelers were there\n\n### Options:\nA. 20\nB. 30\nC. 40\nD. 50\nE. 60\n\n### Answer:\n2x+4x=240;\nx=40;\nthen two whl=2*40=80\n4 whl =4*40=160;\nans: 160/4= i-e 40\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFoodmart customers regularly buy at least one of the following products: milk, chicken, or apples. 90% of shoppers buy milk, 50% buy chicken, and 35% buy apples. If 10% of the customers buy all 3 products, what percentage of Foodmart customers purchase exactly 2 of the products listed above?\n\n### Options:\nA. \uf0a7 5%\nB. \uf0a7 10%\nC. \uf0a7 15%\nD. \uf0a7 55%\nE. \uf0a7 30%\n\n### Answer:\nTotal = n(A) + n(B) - n(Exactly 2 products) -2 (AnBnC) + Neither.\nNeither is zero.\nHence 100 = 90 + 50 + 35 - n (Exactly 2 products) - 2*10\n100 = 155 - n (Exactly 2 products) => n (Exactly 2 products) = 55.\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA sum of money deposited at C.I. amounts to Rs.1980 in 3 years and to Rs.2492 in 4 years. Find the rate percent?\n\n### Options:\nA. 30%\nB. 10%\nC. 25%\nD. 19%\nE. 50%\n\n### Answer:\n1980--- 512\n100 --- ? => 25%\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA veterinarian surveys 26 of his patrons.He discovers that 14 have dogs, 10 have cats, and 5 have fish.Four have dogs and cats, 3 have dogs and fish, and one has a cat and fish.If no one has all three kinds of pets, how many patrons have none of these pets?\n\n### Options:\nA. 3\nB. 4\nC. 5\nD. 6\nE. 7\n\n### Answer:\nno. of patron have dogs = 14\nno. of patron have cats = 10\nno. of patron have fish = 5\nno. of patron have dogs and cats = 4\nno. of patron have dogs and fish = 3\nno. of patron have cats and fish = 1\nno. of patron have all three pets = 0\nno. of patron have only dogs = 7\nno. of patron have only cats = 5\nno. of patron have only dogs = 1\nSo total no. of patron have pets =7+5+1+4+3+1=21\nSo no. of patron don't have any pets =26-21=5\n5 patrons don't have any these pets\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are 192 items that are members of set U. Of these items, 49 are members of set B, 59 are not members of either of set A or set B, and 23 are members of both sets A and B. How many of the members of set U are members of set A ?\n\n### Options:\nA. 72\nB. 85\nC. 107\nD. 98\nE. 108\n\n### Answer:\nYou had the answer almost right. The x = 84 refers to ONLY set A.\nHowever what's being asked is how many members are part of set A. This will include:\n1. Only Set A\n2. Set A and Set B\nSo the answer is Set A = 84+ Set AB = 84+23 = 17\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average of 20 numbers is zero. Of them, at the most, how many may be greater than zero?\n\n### Options:\nA. 18\nB. 16\nC. 17\nD. 19\nE. 13\n\n### Answer:\nAverage of 20 numbers = 0\nSum of 20 numbers = (0 * 20) = 0\nIt is quite possible that 19 of these numbers may be positive and if their sum is a, then 20th number is (-a).\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAfter taking N tests, each containing 100 questions, John had an average of 70% of correct answers. How much does John need to score on the next test to make his average equal 75%?\nM13-03.\n\n### Options:\nA. N\u221235\nB. N+72\nC. 2N+78\nD. 2N+72\nE. 2N\u221235\n\n### Answer:\nSay N=1.\nSo, after 1 test John has 70 correct answers.\nIn 2 tests, so in 200 questions he needs to have 0.75*200=150 correct answers, so in the second test he must get 150-70=80 questions correctly.\nNow, plug N=1 into the answer choices to see which one yields 80. Only option D fits.\nAnswer: C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain smoothie A is three-fifths blueberries and 40% raspberries by weight. Another smoothie B is three-quarters banana and one-quarter raspberries by weight. If the mixed smoothie of A and B is 30% raspberries by weight, how much weight of this mixture belongs to smoothie A?\n\n### Options:\nA. 10%\nB. 33.33%\nC. 45%\nD. 50%\nE. 66.66%\n\n### Answer:\nA is 40% raspberries;\nB is 25% raspberries.\nA and B is 30% raspberries;\n30% raspberries in the mixed smoothie of A and B come from 40% raspberries in A and 25% raspberries in B, thus:\n0.3(A+B)=0.4A+0.25B --> 0.1A=0.05B --> A/B=1/2 --> A/(A+B)=1/3.\nAnswer: B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHalf the people on a bus get off at each stop after the first, and no one gets on after the first stop. If only one person gets off at stop number 8, how many people got on at the first stop?\n\n### Options:\nA. 128\nB. 64\nC. 32\nD. 16\nE. 8\n\n### Answer:\n7 - > 1\n6 - > 2\n5 - > 4\n4 - > 8\n3 - > 16\n2 - > 32\n1 - > 64\nbecause people get off after the first stop\n=> the formula will be : 2^(n-1) where n is the stop number\nin this case n = 5\n=> 2^(8-1) = 2^7 = 128\n=> answer is A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train 100 meters long completely crosses a 300 meters long bridge in 45 seconds. What is the speed of the train is?\n\n### Options:\nA. 32 kmph\nB. 33 kmph\nC. 34 kmph\nD. 35 kmph\nE. 36 kmph\n\n### Answer:\nA\n32 kmph\nS = (100 + 300)/45 = 400/45 * 18/5 = 32\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA squirrel runs up a cylindrical post , in a perfect spiral path making one circuit for each rise of 4 feet . How many feet does the squirrel travels if the post is 12 feet tall and 3 feet in circumference?\n\n### Options:\nA. 9 feet\nB. 12 feet\nC. 13 feet\nD. 15 feet\nE. 18 feet\n\n### Answer:\ntotal circuit=12/4=3\ntotal feet squirrel travels=3*3=9 feet\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n210 reputed university students were asked in a survey if they preferred Windows or Mac brand computers. 60 Students claimed that they preferred Mac to Windows brand computers. One third as many of the students who preferred Mac to Windows, equally preferred both brands. 90 of the students had no preference. How many of the students in the survey preferred Windows to Mac brand computers?\n\n### Options:\nA. 25\nB. 40\nC. 50\nD. 60\nE. 75\n\n### Answer:\nWe are told that60 Students claimed that they preferred Mac to Windows, which means that 60 preferred Mac but NOT Windows, so # of students who preferred Mac (P(A) as you wrote), does not equal to 60, it equals to 60+20 (20 is # of students who equally preferred both brands). Also we are asked to find # of the students who preferred Windows to Mac, so if you denote x as those who prefer Windows then you should calculate x-20.\nSo, if we use your formula it should be: 210={Mac}+{Windows}-{Both}+{Neither}=(60+20)+x-20+90 --> x=60 (# of student who prefer Windows) --> # of the students who preferred Windows to Mac is x-20=40.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJohn borrowed 3 soccer boots from Jake, and forgot them on the field, if peter came across a total of 15 boots on the field Jake's boots inclusive, and he took 4 boots at random, what is the probability that Jake's boots were not amongst the 4 taken?.\n\n### Options:\nA. 12/91\nB. 3/15\nC. 12/15\nD. 33/91\nE. 3/91\n\n### Answer:\nSince Jake owns 3 of the boots, the subset from which the 4 boots should be chosen are the 12 boots not owned by Jake from the universe of 15.\nThe first boot can be one of the 12 from the 15 with probability 12/15.\nThe second boot can be one of the 11 from the 14 remaining with probability 11/14.\nThe third boot can be one of the 10 from the 13 remaining with probability 10/13.\nThe fourth boot can be one of the 9 from the 12 remaining with probability 9/12.\nThe total probability will be 12/15 \u00d7 11/14 \u00d7 10/13 \u00d7 9/12 . On cancellation, this comes to 33/91.\nThus, the answer is D - 33/91\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMeera purchased two three items from a shop. Total price for three items is Rs.5200/- She have given Rs. 6000/- What is the balance amount meera got?\n\n### Options:\nA. 650\nB. 400\nC. 350\nD. 800\nE. 750\n\n### Answer:\nTotal cost of Items : 5200/-\namount Paid : 6000/-\nBalance receivable : 6000 - 5200 = 800/-\nAnswer is D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA, B, C subscribe Rs. 50,000 for a business, A Subscribes Rs. 4000 more than B and B Rs. 5000 more thanC. Out of a total profit of Rs. 35,000, A receives?\n\n### Options:\nA. 14700\nB. 14298\nC. 23877\nD. 27297\nE. 17281\n\n### Answer:\nLet C = x. Then, B = x + 5000 and A = x + 5000 + 4000 = x + 9000.\nSo, x + x + 5000 + x + 9000 = 50000 <=> 3x = 36000 <=>\nx = 12000.\nA : B : C = 21000 : 17000 : 12000 = 21 : 17 : 12.\nA's share = Rs. (35000 * 21/50 ) = Rs. 14,700.\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf I, J and K are digits and 9IJK is a 4-digit number that is divisible by 5, which of the following is a possible product of I, J and K?\n\n### Options:\nA. 23\nB. 48\nC. 72\nD. 25\nE. 94\n\n### Answer:\nKey to this question is to remember the fact that a number divisible by 5 must end with 5 OR 0 (i.e K).\nIf K had to be 0, product should also be 0 regardless of I and J.\nThe product is a multiple of 5. Only one answer choice meets the requirement.\nAns D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe number of meters in EB is equal to the square root of the number of centimeters in EB. What is the length of EB (1 meter=100 centimeters)?\n\n### Options:\nA. 100 meters\nB. 10 meters\nC. 100 centimeters\nD. 10 centimeter\nE. 1 centimeter\n\n### Answer:\nI'd plug in the options for this question.\nCheck option A: if the number of meters in EB is 100, then the number of centimeters is 100*100. The square root of 100*100 is 100: 100 = 100.\nAnswer: A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWorking alone at its constant rate, machine A produces x boxes in 10 minutes and working alone at its constant rate, machine B produces 3x boxes in 5 minutes. How many minutes does it take machines A and B, working simultaneously at their respective constant rates, to produce 3x boxes?\n\n### Options:\nA. 3 minutes\nB. 4 minutes\nC. 4.2 minutes\nD. 6 minutes\nE. 12 minutes\n\n### Answer:\nRate = Work / Time\nGiven Rate of Machine A = X / 10 min\nMachine B Produces 3x boxes in 5 min hence , Machine B produces 4x boxes in 10 min .\nRate of Machine B = 6x / 10\nwe need tofind the combined time that machines A and B, working simultaneouslytakeat their respective constant rates\nlet's first find the combined Rate of Machine A and B\nRate of Machine A = X / 10 min + Rate of Machine B = 6x / 10 = 7X/10\nNow combine Time = combine work needs to be done / Combine Rate = 3x/7x * 10 = 4.2 Min\nAns: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how many T ways can the letters of the word JUPITER be arranged in a row so that the vowels appear in alphabetic order?\n\n### Options:\nA. 736\nB. 768\nC. 792\nD. 840\nE. 876\n\n### Answer:\nthree letters can be arranged in 3! ways.\nonly one combination EIU is required.\n7 letters can be arranged in 7! ways.\nthus T=7!/ 3! * 1 = 840.\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFive years ago, the average age of A, B, C and D was 45 years. With E Joining them now, the average of all the five is 51 years. The age of E is?\n\n### Options:\nA. 45\nB. 47\nC. 55\nD. 49\nE. 46\n\n### Answer:\nSolution\n5 years ago average age of A,B,C,D = 45 years\n=> 5 years ago total age of A, B, C, D = 45 x 4 = 180 years\n=> Total present age of A, B, C, D = 180 + 5x4 = 200 years\nIf E's present age is x years = 200+x/5= 51\nx=55 years. Answer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf air is called green , green is called blue, blue is called orange, sky is called yellow, yellow is called water and water is called pink, then what is the color of clear sky ?\n\n### Options:\nA. Orange\nB. Sky\nC. Water\nD. Yellow\nE. Black\n\n### Answer:\nExplanation:\rThe colour of clear sky is 'blue' and as given, 'blue' is called 'orange'.\rSo, the colour of clear sky is 'orange'.\rAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe profits of QRS company rose 20% from March to April, then dropped 20% from April to May, then rose 50% from May to June. What was the percent increase for the whole quarter, from March to June?\n\n### Options:\nA. 15%\nB. 32%\nC. 44%\nD. 62%\nE. 80%\n\n### Answer:\nAssume 100 in march , then 120 in April as 20% increase , Then 96 in may as 20% decrease from April , and then 144 in june which is 150% of 96 .\nSo overall increase is from 100 to 144 is 44%\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA person travelled from his house to office at 30km/hr and office to house at 15km/hr. Then find the average speed?\n\n### Options:\nA. 15km/hr\nB. 20km/hr\nC. 32km/hr\nD. 24km/hr\nE. 25km/hr\n\n### Answer:\nAverage speed = (2*30*15)/(30+15)\n= 20km/hr\nAnswer is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSophika can buy watches at a price of P dollars per watch, which she marks up by a certain percentage before selling. If she makes a total profit of X by selling Y watches, then in terms of P and X and Y, what is the percent of the markup from her buy price to her sell price?\n\n### Options:\nA. (YP)/100X\nB. 100X/(YP)\nC. (YP)+100X\nD. (YP)-100X\nE. (YP)*100X\n\n### Answer:\nAlgebraic Solution:If she makes a total profit of X for Y watches, then that must be a profit of X/Y for each watch. That must be the markup above cost on each watch, the amount of the increase. Well, percent increase = (amount of increase)/(starting amount) x 100% = (X/Y)/P *100 = 100X/(YP)\nAnswer : B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMukesh borrowed a sum of Rs. 10000 at simple interest from a bank. After two years he takes Rs. 12000 more as loan and discharge all the debt at the end of next 3 years depositing Rs. 27160 to the bank. What is the rate of interest per annum?\n\n### Options:\nA. 5%\nB. 6%\nC. 8%\nD. 10%\nE. None of these\n\n### Answer:\nsi=27160-(principal amount)=27160-22000=5160.\nnow,(10000*5*R/100) + (12000*3*R/100)=5160.\n500R+360R=5160.....Rate=6%.\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn the accounting branch of a commercial institute, the percentage of male and female workers is 48% and 52% respectively. In this branch, 40% of males and 20% of females are age 25 or older. If one of the workers is selected at random, what is the probability Q that the worker is under 25 years old?\n\n### Options:\nA. 0.30\nB. 0.25\nC. 0.45\nD. 0.70\nE. 0.90\n\n### Answer:\nPercentage of male worker = 48\nPercentage of female worker = 52\nLet total number of workers = 1000\nnumber of male workers= 480\nnumber of female workers = 520\nNumber of male age 25 or older = (4/10)*480 = 192\nNumber of female age 25 or older =(2/10)*520 = 104\nTotal number of workers 25 or older = 192+104 = 296\nTotal number of workers under 25 = 1000 - 296 = 704\nProbability that a worker randomly selected is under 25 years old = 704/1000 = .704\nAlternatively , since the answer options are not close , we can use estimation here .\nPercentage of male worker 25 or older = (4/10)*48 = 20 % approx\nPercentage of female worker 25 or older = (2/10)*52 = 10 % approx\nPercentage of total worker 25 or older = 30 %\nPercentage of total worker under 25 = 70 %\nProbability that a worker randomly selected is under 25 years old Q= .7\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nCindy paddles her kayak upstream at b kilometers per hour, and then returns downstream the same distance at n kilometers per hour. How many kilometers upstream did she travel if she spent a total of p hours for the round trip?\n\n### Options:\nA. bnp\nB. bn/p\nC. (b + n)/p\nD. bnp/(b + n)\nE. pm/n- pn/m\n\n### Answer:\nlet t1 and t2 be the time taken to row upstream and downstream respectively\nnow,\nt1=distance/speed=d/b\nsimilarly,\nt2=d/n (as same distance has to be rowed)\nalso,\nt1+t2=p\ntherefore,\np=(d/b)+(d/n)\n=d(b+n)/bn\nd=pbn/(b+n)=D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRahul went to a shop and bought things worth Rs. 35, out of which 30 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?\n\n### Options:\nA. A)19.7\nB. B)19.9\nC. C)20.9\nD. D)21.9\nE. E)29.7\n\n### Answer:\nTotal cost of the items he purchased = Rs.35\nGiven that out of this Rs.35, 30 Paise is given as tax\n=> Total tax incurred = 30 Paise = Rs.30/100\nLet the cost of the tax free items = x\nGiven that tax rate = 6%\n\u2234 (35\u221230/100\u2212x)6/100 = 30/100\n\u21d2 6(35 \u22120.3 \u2212x) = 30\n\u21d2 (35 \u2212 0.3 \u2212 x) = 5\n\u21d2 x = 35 \u2212 0.3 \u2212 5 = 29.7\nE)\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA tourist purchased a total of $1,100 worth of traveler\u2019s checks in $10 and $50 denominations, During the trip the tourist cashed 7 checks and then lost all of the rest. If the number of $10 checks cashed was one more or one less than the number of $50 checks cashed, what is the minimum possible value of the checks that were lost?\n\n### Options:\nA. $1,430\nB. $1,310\nC. $1,290\nD. $1,270\nE. $870\n\n### Answer:\nsince total cashed checks = 7 ans $10 check cashed = one less or more than $50 checks\nTherefore either $10 checks = 3 and $50 checks = 4 OR $10 checks = 4 and $50 checks = 3\nusing this information 1st option gives us the maximum cashed value therefore if we negate this value from total value we will get minimum value of which checks have lost\nTherfore 1100 - 230 = 870 hence answer is E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe charge for a single room at Hotel P is 20 percent less than the charge for a single room at Hotel R and 10 percent less than the charge for a single room at Hotel G. The charge for a single room at Hotel R is what percent greater than the charge for a single room at Hotel G ?\n\n### Options:\nA. 15%\nB. 20%\nC. 12.5%\nD. 50%\nE. 150%\n\n### Answer:\nLet rate in R = 100x\nthen P = 80x\nG = 100y\nP = 90y\nThus\n80 x=90y\nor x = 1.125 y\nAns R = 112.5y\nso increase = 12.5%\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA bowl has only 7 apples and 7 bananas. If one piece of fruit is selected from the bowl at random, and a second piece is selected from the bowl without replacing the first, what is the probability that both pieces of fruit chosen are apples?\n\n### Options:\nA. 1/10\nB. 1/5\nC. 2/9\nD. 2/5\nE. 3/13\n\n### Answer:\n7/14 * 6/13\n=3/13\nE. 3/13\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWe have 10 people and 3 chairs. In how many ways chairs can be occupy?\n\n### Options:\nA. 650\nB. 720\nC. 810\nD. 790\nE. 915\n\n### Answer:\nno. of ways they can be occupy = 10*9*8 = 720\nAnswer is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow much interest will $10,000 earn in 9 months at an annual rate of 4%?\n\n### Options:\nA. $300\nB. $350\nC. $450\nD. $550\nE. $650\n\n### Answer:\nSoln:-\n9 months = 3/4 of year;\n4% = 4/100=1/25;\n$10,000(principal)*1/25(interest rate)*3/4(time)=$300.\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe number of bacteria in a petri dish increased by 50 percent every 2 hours. If there were 108 million bacteria in the dish at 5: 00 p.m., at what time were there 32 million bacteria in the dish?\n\n### Options:\nA. 11: 00 a.m.\nB. 8: 00 p.m.\nC. 6: 00 a.m.\nD. 8: 00 a.m.\nE. 10: 00 a.m.\n\n### Answer:\nGiven:\nThe number of bacteria in a petri dish increased by 50 percent every 2 hours\nThere were 108 million bacteria in the dish at 2: 00 p.m\nSince the bacteria is increasing by 50% every 2 hours, this means that the number is multiplied by 1.5 every 2 hours.\nRequired: At what time were there 32 million bacteria in the dish?\nAssume that there were n intervals of 2 hours between 32 million and 108 million.\n32 * (1.5)^n = 108\n(3/2)^n = 108/32 = 27/8 = (3/2)^3\nHence n = 3 intervals.\nEach interval was of 2 hours. Therefore, the number of hours = 6\nSubtracting 6 hours from 5 PM, we get 11 AM as the answer.\nOption A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe probability that A speaks truth is 3/5 and that of B speaking truth is 4/7. What is the probability that they agree in stating the same fact?\n\n### Options:\nA. 18/35\nB. 18/38\nC. 18/34\nD. 18/31\nE. 18/30\n\n### Answer:\nIf both agree stating the same fact, either both of them speak truth of both speak false.\nProbability = 3/5 * 4/7 + 2/5 * 3/7\n= 12/35 + 6/35 = 18/35.\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo trains 140 m and 190 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is?\n\n### Options:\nA. 17.9 sec\nB. 11.88 sec\nC. 27.7 sec\nD. 10.8 sec\nE. 17.8 sec\n\n### Answer:\nRelative speed = 60 + 40 = 100 km/hr.\n= 100 * 5/18 = 250/9 m/sec.\nDistance covered in crossing each other = 140 + 190 = 330 m.\nRequired time = 330 * 9/250 = 11.88 sec.\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat annual payment dischargea debit of Rs.12900, due in 4yrs.At 5% rate?\n\n### Options:\nA. 2000\nB. 2200\nC. 3000\nD. 3400\nE. 3500\n\n### Answer:\nA.P.=(200X12900)/[4(200+5X3)]=3000 Ans\nAlternative\n100+105+110+115=12900\n430=12900\n100=12900/(430)X100=3000\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n40% of a number is more than 20% of 650 by 190. Find the number?\n\n### Options:\nA. 227\nB. 266\nC. 800\nD. 277\nE. 261\n\n### Answer:\n(40/100) * X \u2013 (20/100) * 650 = 190\n2/5 X = 320\nX = 800\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAt a certain supplier, a machine of type A costs $20,000 and a machine of type B costs $55,000. Each machine can be purchased by making a 20 percent down payment and repaying the remainder of the cost and the finance charges over a period of time. If the finance charges are equal to 40 percent of the remainder of the cost, how much less would 2 machines of type A cost than 1 machine of type B under this arrangement?\n\n### Options:\nA. $10,000\nB. $11,200\nC. $12,000\nD. $19,800\nE. $13,200\n\n### Answer:\n1 machine of type B will cost: 20% down payment of 55,000 = 11,000plusremaining sum (55,000-11,000=44,000) with 40% of finance charges 44,000*1.4=61,600 --> 11,000+61,600=72,600;\n2 machine of type A will cost: 20% down payment of 2*20,000 = 8,000plusremaining sum (40,000-8,000=32,000) with 40% of finance charges 32,000*1.4=44,800 --> 8,000+44,800=52,800;\nDifference = 72,600 - 52,800 = 19,800.\nAnswer: D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nEvaluate :\n28% of 400 + 45 % of 250\n\n### Options:\nA. 224.8\nB. 224.9\nC. 224.5\nD. 224.6\nE. 224.1\n\n### Answer:\nExplanation:\n28% of 400 + 45 % of 250\n= (28/100 *400 + 45/100 * 250)\n= (112 + 112.5)\n= 224.5\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is?\n\n### Options:\nA. 10 m\nB. 16 m\nC. 245 m\nD. 19 m\nE. 27 m\n\n### Answer:\nSpeed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (130 + x)/30\n= 25/2 => 2(130 + x) = 750 => x\n= 245 m.\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nGwen drove an average speed of 15 miles per hour for the first 40 miles of a tripthen at a average speed of 30 miles/hr for the remaining 40 miles of the trip if she made no stops during the trip what was Gwen's avg speed in miles/hr for the entire trip\n\n### Options:\nA. 35\nB. 20\nC. 45\nD. 50\nE. 55\n\n### Answer:\nAvg. speed = total distance / total time\nTotal distance = 80 miles\nTotal time = 40 / 15 + 40/30 = 4\nAvg. speed = 20.\nAnswer - B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n40% of the employees in a factory are workers. All the remaining employees are executives. The annual income of each worker is Rs. 390. The annual income of each executive is Rs. 420. What is the average annual income of all the employees in the factory together?\n\n### Options:\nA. 390\nB. 405\nC. 408\nD. 415\nE. None\n\n### Answer:\nSolution:\nLet X be the number of employees.\nWe are given that 40% of the employees are workers. Now, 40% of X is (40/100)*X =0.4X.\nHence, the number of workers is 2X/5.\nAll the remaining employees are executives, so the number of executives equals,\n(The number of Employees)\u2013(The number of Workers),\n= X\u2013(2X/5)\n=(3X/5)\nThe annual income of each worker is Rs. 390.\nHence, the total annual income of all the workers together is,\n= (2X/5)*390 =156X.\nAlso, the annual income of each executive is Rs. 420. Hence, the total income of all the executives together is,\n(3X/5)\u00d7420 =252X\nHence, the total income of the employees is,\n= 156X +252X =408X.\nThe average income of all the employees together equals,\nAnswer: Option C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA student has to obtain 33% of the total marks to pass. He got 92 marks and failed by 40 marks. The maximum marks are?\n\n### Options:\nA. 400\nB. 300\nC. 500\nD. 610\nE. 175\n\n### Answer:\nLet the maximum marks be x\nThen, 33% of x = 92+40\n33x/100 = 132\nx = 400\nAnswer is A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA family made a down payment of $100\nand borrowed the balance on a set of\nencyclopedias that cost $400. The\nbalance with interest was paid in 20\nmonthly payments of $17.2 each and a\nfinal payment of $3. The amount of\ninterest paid was what percent of the\namount borrowed?\n\n### Options:\nA. 6%\nB. 12%\nC. 14%\nD. 15.6%\nE. 20%\n\n### Answer:\ninterest paid = 17.2*20+3 - 300=47\n% off the balance = (47/300) * 100 = 15.67%\nAnswer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nif in one hour, a canoe rows at 16 km/hr downstream and 9 km/hr upstream, Calculate the speed of a boat in still water (in km/hr).\n\n### Options:\nA. 18 kmph\nB. 15.5 kmph\nC. 12.5 kmph\nD. 13.5 kmph\nE. 22.5 kmph\n\n### Answer:\nSpeed in still water = (16 + 9)1/2 kmph = 12.5 kmph.\nanswer :C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 3x\u2212y=27 and 3x+y=243, then find the value of x\n\n### Options:\nA. 1\nB. 2\nC. 3\nD. 4\nE. 5\n\n### Answer:\nExplanation:\n3x\u2212y=27=33<=>x\u2212y=3... (i)3x+y=243=35<=>x+y=5... (ii) adding (i) and (ii)=>2x=8=>x=4\nOption D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn an election only two candidates contested. A candidate secured 70% of the valid votes and won by a majority of 172 votes. Find the total number of valid votes?\n\n### Options:\nA. 430\nB. 287\nC. 267\nD. 262\nE. 927\n\n### Answer:\nLet the total number of valid votes be x.\n70% of x = 70/100 * x = 7x/10\nNumber of votes secured by the other candidate\n= x - 7x/100 = 3x/10\nGiven, 7x/10 - 3x/10\n= 172 => 4x/10 = 172\n=> 4x = 1720 => x\n= 430.\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSixteen telegenic contestants with a variety of personality disorders are to be divided into two \u201ctribes\u201d of three members each, tribe A and tribe B, for a competition. How many distinct groupings of two tribes are possible?\n\n### Options:\nA. 120\nB. 126\nC. 252\nD. 560\nE. 1260\n\n### Answer:\nMy ans is 16C3 = 560\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo discounts of 40% and 20% equal to a single discount of?\n\n### Options:\nA. 52%\nB. 48%\nC. 60%\nD. 80%\nE. 70%\n\n### Answer:\n{[(100-40)/100]*[(100-20)/100]}%=(60*80)/(100*100)%\n=48%\nsingle discount is equal to (100-48)%=52%\nANSWER A 52%\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n9 students bought burgers for $143 dollars. If the bill has to be divided among these students, how much amount should be added to the amound to make it\ndivided amoung them equally in dollars(in whole number of dollars)\n\n### Options:\nA. $1\nB. $2\nC. $3\nD. $4\nE. $5\n\n### Answer:\nIn order to divide the sum in 9 parts, the amount must be divisible by 9\nDivisibility rule of 9: The sum of the digits must be divisible by 9\nSum of digits of 143 = 8 and 9 is divisible by 9.\nHence, we need to add 1 to this number for it to be divisible by 9\nCorrect Option: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a mixture of 45 litres the ratio of milk to water is 4:1. Additional 12 litres of water is added to the mixture. Find the ratio of milk to water in the resulting mixture.\n\n### Options:\nA. 12/7\nB. 4/1\nC. 2/3\nD. 3/4\nE. 3/2\n\n### Answer:\nGiven that Milk/Water=4x/x and 4x+x=45 --> x=9.\nThus Milk=4x=36 liters and Water=x=9 liters.\nNew ratio = 36/(9+12) = 36/21 = 12/7.\nAnswer: A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe radius of the wheel of a bus is 140 cms and the speed of the bus is 66 km/h, then the r.p.m. (revolutions per minutes)of the wheel is\n\n### Options:\nA. 125\nB. 250\nC. 300\nD. 330\nE. None of these\n\n### Answer:\nRadius of the wheel of bus = 140 cm. Then,\ncircumference of wheel = 2\u00cf\u20acr = 280\u00cf\u20ac = 880 cm\nDistance covered by bus in 1 minute\n= 66\u00e2\u0081\u201e60 \u00c3\u2014 1000 \u00c3\u2014 100 cms\nDistance covered by one revolution of wheel\n= circumference of wheel\n= 880 cm\n\u00e2\u02c6\u00b4 Revolutions per minute = 6600000/60\u00c3\u2014880 = 125\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA hiker walking at a constant rate of 4 miles per hour is passed by a cyclist travelling in the same direction along the same path at a constant rate of 28 miles per hour. the cyclist stopswaits for the hiker 5 min after passing her while the hiker continues to walk at her constant rate. how many minutes must the cyclist wait until the hiker catches up\n\n### Options:\nA. 6 2/3\nB. 15\nC. 20\nD. 25\nE. 30\n\n### Answer:\nHere is how I did it:\nThe cyclist travels 28 miles in 60 mins, so in 5 mins he will travel [(28*5)/60] miles, which equals 7/3 miles in 5 mins.\nNow the hiker travels 4 miles in 60 mins. To travel 7/3 miles, he will take [(60*7/3)/4] = 35 mins.\nhence 35-5 =30 mins\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the least number of 5 digits, which is exactly divisible by 89.\n\n### Options:\nA. 27\nB. 37\nC. 932\nD. 12\nE. 91\n\n### Answer:\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSolve the given two equations and find the inequality of X and Y. (a) x^2-1=0 and (b) y^2+4y+3=0\n\n### Options:\nA. If x>y\nB. If x>=y\nC. If x < y\nD. If x<=y\nE. x=y or relationship cannot be established\n\n### Answer:\nSolution:-\nX=+1,-1 and Y= -1,-3\nComparing we get X>=Y\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA university cafeteria offers 4 flavors of pizza - pepperoni, chicken, Hawaiian and vegetarian. If a customer has an option (but not the obligation) to add extra cheese, mushrooms or both to any kind of pizza, how many different pizza varieties are available ?\n\n### Options:\nA. 4\nB. 8\nC. 12\nD. 16\nE. 32\n\n### Answer:\nThere are 4 flavors of pizza and each can be:\n1. Without cheese and mushrooms;\n2. With cheese;\n3. With mushrooms;\n4. With cheese and mushrooms.\nSo, the total number of pizza varieties is 4*4 = 16.\nAnswer: D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are r red ball, b blue ball and w white ball in a bag. What is the ratio of the number of blue ball to the total no. of ball in terms of r, b and w.?\n\n### Options:\nA. r / (r + b + w)\nB. r / (r + b)\nC. (r + b + w)/r\nD. r / (b + w)\nE. r * (r + b + w)\n\n### Answer:\nThe total number of marbles is\nr + b + w\nThe total ratio of blue marbles to the total number of marbles is\nr / (r + b + w)\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 15,555 \u2013 n is divisible by 11, and 0 < n < 11, what is n?\n\n### Options:\nA. 1\nB. 3\nC. 5\nD. 7\nE. 9\n\n### Answer:\n15,555 / 11 = 1414 with a remainder of 1.\nWe need to subtract the remainder to get a multiple of 11.\nThe answer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMs. Lovely deposits $ 300 in an account that pays 20% interest, compounded semiannually. How much money will there be in the account at the end of one year?\n\n### Options:\nA. $118.00\nB. $120.00\nC. $121.00\nD. $122.00\nE. $140.00\n\n### Answer:\nUsing Formula - A = P(1+r/n)^nt\nGiven\nP=300\nn=2\nt=1\nr=0.2\nSubstituting value in formula\nA = 300(1+0.2/2)^2\nA= 363.00$=C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich of the following fractions T, if written as a decimal, would have a 2 in the thousandths place ?\n\n### Options:\nA. 3/11\nB. 7/9\nC. 1/8\nD. 4/7\nE. 1/6\n\n### Answer:\n(A) T=3/11 = 0.2727272727....\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA case contains c cartons. Each carton contains b boxes, and each box contains 500 paper clips. How many paper clips are contained in 2 cases?\n\n### Options:\nA. 500bc\nB. 500b/c\nC. 1000bc\nD. 1000b/c\nE. 1000/bc\n\n### Answer:\n2 cases * c cartons/case * b boxes/carton * 500 clips/box = 1000bc paper clips\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA can do a piece of work 40 days. B can do work in 60 days. In how many days they will complete the work together?\n\n### Options:\nA. 15 days\nB. 16 days\nC. 19 days\nD. 17 days\nE. 24 days\n\n### Answer:\nLCM = 120, Ratio= 40:60=2:3\nNo of days= 120/(2 + 3) = 90/5 = 24 days\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the 56743rd term in the series 1234567891011121314\u2026\u2026.?\n\n### Options:\nA. 1\nB. 3\nC. 7\nD. 5\nE. 6\n\n### Answer:\n1 to 9=9 no.s 1 digit each no.\n9 to 99=90no.s 2 digit each,total digit=90*2=180 terms\n99 to 999=900 no.s 3 digit each,total digit=900*3=2700\n999 to 9999=9000 no.s 4 digit each,total digit=9000*4=36,000\nnow till 999,we have=9+180+2700=2889 digits\ntill 9999 we hv=2889+36000=38889 digits\n56743-38889=17854\nafter 9999 each no. has 5 digit\nso 17584/5=3570 with remainder 4.\n3570th no after 9999 =9999+3570=13569\nnext term=13570...4th digit=7 ..so ans=7\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nDifference between two numbers is 5, six times of the smaller lacks by 6 from the four times of the greater. Find the numbers?\n\n### Options:\nA. 9\nB. 8\nC. 7\nD. 6\nE. 4\n\n### Answer:\nExplanation:\nx \u2013 y = 5\n4x \u2013 6y = 6\nx = 12 y = 7\nAnswer: Option C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nExcluding stoppages, the speed of a bus is 54 kmph and including stoppages, it is 45 kmph. For how many minutes does the bus stop per hour?\n\n### Options:\nA. 22\nB. 37\nC. 10\nD. 28\nE. 27\n\n### Answer:\nspeed of the bus excluding stoppages = 54 kmph\nspeed of the bus including stoppages = 45 kmph\nLoss in speed when including stoppages = 54 - 45 = 9kmph\n=> In 1 hour, bus covers 9 km less due to stoppages\nHence, time that the bus stop per hour = time taken to cover 9 km\n=distancespeed=954 hour=16 hour = 606 min=10 min\nAnswer :C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA bag contains 25 paise, 50 paise and 1 rupee coins in the ratio 7:4:3 . total no. of coins is 360. sum of total coins is Rs. 99 so how many 25 paise coins?\n\n### Options:\nA. 160\nB. 170\nC. 180\nD. 190\nE. 200\n\n### Answer:\ntotal coins=360\n25 p coins =(7/14)*360=180\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe length and breadth of a rectangle is increased by 10% and 30% respectively. What is the increase in the area?\n\n### Options:\nA. 43.0\nB. 44.0\nC. 43.5\nD. 45.0\nE. 42.0\n\n### Answer:\n100*100=10000\n110*130=14300\n----------\n4300\n10000-------4300\n100-------43.00\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat number would replace the question mark in this quite difficult number sequence ?\n21 32 54 87 131 ?\n\n### Options:\nA. 300\nB. 125\nC. 450\nD. 340\nE. 186\n\n### Answer:\nE\n186\nExplanation :\n21+11*1 => 32\n32+11*2 => 54\n54+11*3 => 87\n87+11*4 => 131\n131+11*5 => 186\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA professional stock trader just signed her new yearly contract with her employer. She will receive a 6% raise over last year's pay for her base pay, plus the chance to earn a performance bonus of up to $3,000. Last year, she earned no performance bonus. This year, assuming that she earns the full performance bonus, her new pay will be effectively an 8% raise. What will her new pay be assuming that she earns the full performance bonus.\n\n### Options:\nA. 162,000\nB. 173,000\nC. 180,000\nD. 213,000\nE. 284,000\n\n### Answer:\nlet x = last year's pay\nthis year's pay + 3,000 = this year's effective pay\n(1+.06)*x + 3,000 = (1+.08)*x\n1.06x + 3,000 = 1.08x\n3,000 = .02x\n150,000 = x\nthus the new pay effectively is (1+.08)*150,000 = 162,000\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe number 50 can be written as the sum of squares of 3 integers. Which of the following could be the difference between the largest and smallest integers of the 3?\n\n### Options:\nA. 2\nB. 5\nC. 7\nD. 8\nE. 9\n\n### Answer:\nNotice that the question asks which of the followingcouldbe the difference between the largest and smallest integers, not must be. The 3 integers could be: +/-3,+/-4and +/-5, so the difference could be 2,-2 or 1. Since only one of them is among the choices, then it must be the correct answer.\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\ncomplete the numerical series with the correct number\n5+3+1=15517\n9+2+2=181834\n5+6+4=302044\n5+4+2=201026\n9+3+5= ?\n\n### Options:\nA. 468645\nB. 454586\nC. 274569\nD. 454386\nE. 444586\n\n### Answer:\n9+3+5= 274569\nAnswer : C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA vendor bough toffees at 6 for a rupee. how many for a rupee must he sell to gain 20%?\n\n### Options:\nA. 3\nB. 8\nC. 5\nD. 9\nE. 1\n\n### Answer:\nC.P or toffees = Rs.1, S.P of 6 toffee = 120% of Rs.1 = Rs.6/5\nfor Rs. 6/5, toffees sold=6, for Rs.1, toffees sold= (6*5/6)= 5\nCorrect answer (C)\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat amount does Kiran get if he invests Rs.8000 at 10% p.a. compound interest for two years, compounding done annually?\n\n### Options:\nA. Rs.9688\nB. Rs.9687\nC. Rs.3338\nD. Rs.9632\nE. Rs.9680\n\n### Answer:\nExplanation:\nA= P{1 + R/100}n\n=> 8000{1 + 10/100}2 = Rs.9680\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n5358 x 51 = ?\n\n### Options:\nA. 272258\nB. 272358\nC. 273258\nD. 274258\nE. 274358\n\n### Answer:\n5358 x 51\t= 5358 x (50 + 1)\n= 5358 x 50 + 5358 x 1\n= 267900 + 5358\n= 273258.\nC)\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA life insurance company insured 25,000 young boys, 14,000 young girls and 16,000 young adults. The probability of death within 10 years of a young boy, young girl and a young adult are 0.02, 0.03 and 0.15 respectively. One insured person dies. What is the probability that the dead person is a young boy?\n\n### Options:\nA. 36/165\nB. 25/166\nC. 26/165\nD. 32/165\nE. 33/165\n\n### Answer:\nThe number of young boys that will die = 0.02 x 25,000 = 500\nThe number of young girls that will die = 0.03 x 14,000 = 420\nThe number of young adults that will die = 0.15 x 16,000 = 2400\nThe required probability = The number of young boys who will die / The total number of people who will die.\n= 500 / (500 + 420 + 2400) = 25/166\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average of first five multiples of 7 is:\n\n### Options:\nA. 9\nB. 16\nC. 15\nD. 8\nE. 21\n\n### Answer:\nExplanation :\n(7(1+2+3+4+5)/5\n= 7x15/5\n= 21\nAnswer : E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat will come in place of the x in the following Number series? 2, 7, 10, 22, 18, 37, 26, x\n\n### Options:\nA. 29\nB. 32\nC. 35\nD. 42\nE. 52\n\n### Answer:\nThere are two series here\n2, 10, 18, 26, ... (Increase by 8)\n7, 22, 37, ... (Increase by 15)\nHence, next term is 37+15 = 52\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe H.C.F of two numbers is 11 and their L.C.M is 7700. If one of the numbers is 275 , then the other is\n\n### Options:\nA. 344\nB. 387\nC. 308\nD. 299\nE. 882\n\n### Answer:\nExplanation:\nother number = \\inline \\fn_jvn \\left ( \\frac{11\\times 7700}{275} \\right ) = 308\nAnswer: C) 308\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n31 of the scientists that attended a certain workshop were Wolf Prize laureates, and 18 of these 31 were also Nobel Prize laureates. Of the scientists that attended that workshop and had not received the Wolf prize, the number of scientists that had received the Nobel Prize was 3 greater than the number of scientists that had not received the Nobel Prize. If 50 of the scientists attended that workshop, how many of them were Nobel Prize laureates?\n\n### Options:\nA. A)11\nB. B)18\nC. C)24\nD. D)29\nE. D)36\n\n### Answer:\nlets solve by creating equation..\nW = 31..\nTotal = 50..\nNot W = 50 -31= 19..\nNow let people who were neither be x, so out of 19 who won Nobel = x+3..\nso x+x+3=19 or x=8..\nso who won Nobel but not Wolf = x+3 = 11..\nBut people who won BOTH W and N = 13..\nso total who won N = 11+18 = 29..\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo varieties of wheat - A and B costing Rs. 9 per kg and Rs. 15 per kg were mixed in the ratio 3 : 7. If 5 kg of the mixture is sold at 25% profit, find the profit made?\n\n### Options:\nA. 16.5\nB. 12.5\nC. 14.5\nD. 12\nE. 13\n\n### Answer:\net the quantities of A and B mixed be 3x kg and 7x kg.\nCost of 3x kg of A = 9(3x) = Rs. 27x\nCost of 7x kg of B = 15(7x) = Rs. 105x\nCost of 10x kg of the mixture = 27x + 105x = Rs. 132x\nCost of 5 kg of the mixture = 132x/10x (5) = Rs. 66\nProfit made in selling 5 kg of the mixture = 25/100 (cost of 5 kg of the mixture) = 25/100 * 66 = Rs. 16.50\nANSWER A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a certain deck of cards, each card has a positive integer written on it, in a multiplication game a child draws a card and multiplies the integer on the card with the next large integer. If the each possible product is between 11 and 200, then the least and greatest integer on the card would be\n\n### Options:\nA. 3 and 15\nB. 3 and 20\nC. 4 and 13\nD. 4 and 14\nE. 5 and 14\n\n### Answer:\nGiven: 1111 --> so, the least value is 4. Test for the largest value: if x=15 then\nx(x+1)=15*16=240>200 --> discard B.\nAnswer: A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMrs. Rodger got a weekly raise of $145. If she gets paid every other week, write an integer describing how the raise will affect her paycheck.\n\n### Options:\nA. $204\nB. $231\nC. $156\nD. $145\nE. $200\n\n### Answer:\nLet the 1st paycheck be x (integer).\nMrs. Rodger got a weekly raise of $ 145.\nSo after completing the 1st week she will get $ (x+145).\nSimilarly after completing the 2nd week she will get $ (x + 145) + $ 145.\n= $ (x + 145 + 145)\n= $ (x + 290)\nSo in this way end of every week her salary will increase by $ 145.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWrite 890,000,000,000 in scientific notation.\n\n### Options:\nA. 8.9 * 10 11\nB. 800.900 * 10 11\nC. 8.900 * 10 11\nD. 80.9000* 10 11\nE. 08.900 * 10 11\n\n### Answer:\na * 10 n , where a is a real number such that 1 * |a| < 10 and n is an integer.\n890,000,000,000 = 8.9* 100,000,000,000 = 8.9 * 10 11**\ncorrect answer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMarcella has 27 pairs of shoes. If she loses 9 individual shoes, what is the greatest number of matching pairs she could have left?\n\n### Options:\nA. 22\nB. 20\nC. 19\nD. 16\nE. 15\n\n### Answer:\nMarcella has 27 pairs of shoes and loses 9 shoes.\nTo minimize the loss of identical pairs of shoes we want Marcella to lose as many identical pairs as possible. This would yield 4 identical pairs and 1 additional shoe (destroying 5 pairs of shoes).\nThe 27 pairs of shoes minus the 5 'destroyed' pairs yields 22 pairs that still fulfill the requirements.\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOn my sister's 15th birthday, she was 159 cm in height, having grown 6% since the year before. How tall was she the previous year?\n\n### Options:\nA. 150 cm\nB. 140 cm\nC. 142 cm\nD. 154 cm\nE. None of these\n\n### Answer:\nExplanation :\nGiven that height on 15th birthday = 159 cm and growth = 6%\nLet the previous year height = x\nThen height on 15th birthday = x \u00d7100+6/100=x\u00d7106/100\n\u21d2159 = x \u00d7 (106/100)\n\u21d2\ufffdx=159\u00d7100/106=1.5\u00d7100=150;cm\nAnswer : Option A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nEach shelf of a bookcase contained 11 books. If the librarian took out 31 books and rearranged the remaining books so that all shelves but the last one contained 7 books and that last shelf contained 4 books, how many shelves does the bookcase have?\n\n### Options:\nA. 5\nB. 6\nC. 7\nD. 8\nE. 9\n\n### Answer:\nLet x be the number of shelves.\n11x - 31 = 7(x-1) + 4\n4x = 28\nx = 7\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train 180 m long passed a pole in 3 sec. How long will it take to pass a platform 330 m long?\n\n### Options:\nA. 5\nB. 6\nC. 7\nD. 8\nE. 9\n\n### Answer:\nSpeed = 180/3\n= 60 m/sec.\nRequired time\n= (180 + 300)/60\n= 8 sec.\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nLength of a rectangular plot is 20 mtr more than its breadth. If the cost of fencin gthe plot at 26.50 per meter is Rs. 5300, what is the length of the plot in mtr?\n\n### Options:\nA. 20 m\nB. 60 m\nC. 50 m\nD. 45 m\nE. 65 m\n\n### Answer:\nLet breadth = x metres.\nThen, length = (x + 20) metres.\nPerimeter = 5300 m = 200 m.\n26.50\n2[(x + 20) + x] = 200\n2x + 20 = 100\n2x = 80\nx = 40.\nHence, length = x + 20 = 60 m\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n(4300231)-?=2535618\n\n### Options:\nA. 1865113\nB. 1775123\nC. 1764613\nD. 1675123\nE. None of them\n\n### Answer:\nLet 4300231-x=2535618\nthen x=4300231-2535618\n=1764613\nAnswer is C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA boat goes 100 km downstream in 10 hours, and 60 m upstream in 15 hours. The speed of the stream is?\n\n### Options:\nA. 3\nB. 22 1/4\nC. 22 1/2\nD. 22 1/1\nE. 22 1/3\n\n### Answer:\n100 --- 10 DS = 10\n? ---- 1\n60 ---- 15 US = 4\n? ----- 1 S = (10 - 4)/2\n= 3 kmp Answer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe first doughnut is priced at $1 and then if you purchase additional doughnuts as dozens then the price is $6/dozen. What is the total number of doughnuts purchased if you paid $21?\n\n### Options:\nA. 33\nB. 35\nC. 37\nD. 39\nE. 41\n\n### Answer:\n$21 = 3 * $6 + $3\nThe number of doughnuts is 3*12 + 3 = 39\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOn a sum of money, the simple interest for 2 years is Rs. 325, while the compound interest is Rs. 340, the rate of interest being the same in both the cases. The rate of interest is\n\n### Options:\nA. 15%\nB. 14.25%\nC. 9.23%\nD. 10.5%\nE. 11.5%\n\n### Answer:\nExplanation:\nThe difference between compound interest and simple interest on Rs. P for 2 years at R% per annum\n= (R \u00c3\u2014 SI)/(2 \u00c3\u2014 100)\nDifference between the compound interest and simple interest = 340 - 325 = 15\n(R \u00c3\u2014 SI)/(2 \u00c3\u2014 100) = 15\n(R \u00c3\u2014 325)/(2 \u00c3\u2014 100) = 15\nR = 9.23%\nAnswer: Option C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich of the following is the Highest Common Factor of 27, 81 and 54?\n\n### Options:\nA. 8\nB. 9\nC. 6\nD. 14\nE. 12\n\n### Answer:\nthe Highest Common Factor is 9\rAns is :B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe distance from Steve's house to work is 30 Km. On the way back Steve drives twice as fast as he did on the way to work. Altogether, Steve is spending 6 hours a day on the roads. What is Steve's speed on the way back from work?\n\n### Options:\nA. 5.\nB. 10.\nC. 14.\nD. 15\nE. 20.\n\n### Answer:\nTime is in the ratio 2:1 :: to: fro office\nTherefore, 2x+1x=6 hrs\nTime take to come back - 2 hrs, distance travelled - 30 km => Speed = 15 kmph\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat quadrants do the line y = 2x - 4 go through?\n\n### Options:\nA. 1 and 2\nB. 1 and 3\nC. 1 and 4\nD. 1,2 and 3\nE. 1,3 and 4\n\n### Answer:\nFind the x-intercept and the y-intercept of the line.\nTo find the x intercept, set y = 0 and solve for x.\n0 = 2x - 4\nx = 2\nTo find the y intercept, set x = 0 and solve for y.\ny = 0 - 4\ny = -4\nDraw the line using the two intercepts.\nThus, the line goes through the 1st, 3rd and 4th quadrants.\nAnswer is E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf x, y, and z are positive integers and x = 14y = 7z, then the least possible value of x + y + z is\n\n### Options:\nA. 33\nB. 40\nC. 49\nD. 61\nE. 17\n\n### Answer:\nx + y + z = x/14 + x + x/7\n= (1 + 14 + 2 )x/14 = 17x/14\n17 is not divisible by 14(it's a prime #), so for least value, x = 14\nAnswer -E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOperation#is defined as adding a randomly selected two digit multiple of 4 to a randomly selected two digit prime number and reducing the result by half. If operation#is repeated 10 times, what is the probability that it will yield at least two integers?\n\n### Options:\nA. 0%\nB. 10%\nC. 20%\nD. 30%\nE. 40%\n\n### Answer:\nAny multiple of 4 is even.\nAny two-digit prime number is odd.\n(even+odd)/2 is not an integer. Thus # does not yield an integer at all.\nTherefore P=0.\nAnswer: A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA sum of money at simple interest amounts to Rs. 1560 in 4 years and to Rs. 1590 in 6 years. The sum is:\n\n### Options:\nA. Rs. 1400\nB. Rs. 1450\nC. Rs. 1500\nD. Rs. 1550\nE. Rs. 1525\n\n### Answer:\nS.I. for 2 years = Rs. (1590 - 1560) = Rs. 30.\nS.I. for 4 years = Rs.(30 x 2) = Rs. 60.\nPrincipal = Rs. (1560 - 60) = Rs. 1500.\nAnswer: Option C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nLook at this series: 55, 55, 40, 40, 25, 25, ... What number should come next?\n\n### Options:\nA. 14\nB. 15\nC. 17\nD. 10\nE. 11\n\n### Answer:\nIn this series, each number is repeated, then 15 is subtracted to arrive at the next number.\nThe next number should be 10\nAnswer : D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nB @ K I 9 D \u00c2\u00a9 5 2 T $ M 4 E J # U R 1 A \u00ce\u00b4 K 5 W 6 % F Q 7 H P 8 Z\nHow many such numbers are there in the above arrangement each of which is immediately followed by a symbol but not immediately preceded by a consonant?\n\n### Options:\nA. None\nB. One\nC. Two\nD. Three\nE. More than three\n\n### Answer:\nExplanation:\nConsonant Number Symbol\nThere is no such combination.\nANSWER IS A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn an examination, a student scores 6 marks for every correct answer and loses 1 mark for every wrong answer. If he attempts all 60 questions and secures 280 marks, the no of questions he attempts correctly is :\n\n### Options:\nA. A)20\nB. B)38\nC. C)90\nD. D)88\nE. E)37\n\n### Answer:\nLet the number of correct answers be X.\nNumber of incorrect answers = (60 \u2013 X).\n6x \u2013 (60 \u2013 x) = 280\n=> 7x = 340\n=> x = 20\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo stations P and Q are 65 km apart on a straight track. One train starts from P at 7 a.m. and travels towards Q at 20 kmph. Another train starts from Q at 8 a.m. and travels towards P at a speed of 25 kmph. At what time will they meet?\n\n### Options:\nA. 9 am\nB. 12 am\nC. 10.30 am\nD. 12.30 am\nE. 11 am\n\n### Answer:\nAssume both trains meet after x hours after 7 am\nDistance covered by train starting from P in x hours = 20x km\nDistance covered by train starting from Q in (x-1) hours = 25(x-1)\nTotal distance = 65\n=> 20x + 25(x-1) = 65\n=> 45x = 90\n=> x= 2\nMeans, they meet after 2 hours after 7 am, ie, they meet at 9 am\nAnswer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich of the following is not a prime number ?\n\n### Options:\nA. 502\nB. 503\nC. 509\nD. 521\nE. 523\n\n### Answer:\nClearly, 502 is not a prime number.\nAnswer : A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nxy=1 then what is (3^(x+y)^2) / (3^(x-y)^2)\n\n### Options:\nA. 81\nB. 4\nC. 8\nD. 16\nE. 32\n\n### Answer:\n(x+y)^2 - (x-y)^2\n(x+y+x-y)(x+y-x+y)\n(2x)(2y)\n4xy\n4\n3^4 = 81\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe number N is 5,3H7, where H represents the ten's digit. If N is divisible by 9, what is the value of H?\n\n### Options:\nA. 4\nB. 3\nC. 5\nD. 8\nE. 2\n\n### Answer:\nIf the number is divisible by 9, it must also be divisible by 3. Only 3 yields such a number.\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWorker A takes 8 hours to do a job. Worker B takes 10 hours to do a job. How long should it take both A and B, working together to do same job.\n\n### Options:\nA. 4/9\nB. 2 4/9\nC. 3 4/9\nD. 4 4/9\nE. None of these\n\n### Answer:\nExplanation:\nIn this type of questions, first we need to calculate 1 hours work, then their collective work as,\nA's 1 hour work is 1/8\nB's 1 hour work is 1/10\n(A+B)'s 1 hour work = 1/8 + 1/10\n= 9/40\nSo both will finish the work in 40/9 hours\n=\n4 4/9\nOption D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOn Monday, Lou drives his vehicle with 26-inch tires, averaging x miles per hour. On Tuesday, Lou switches the tires on his vehicle to 32-inch tires yet drives to work at the same average speed as on Monday. What is the percent change from Monday to Tuesday in the average number of revolutions that Lou's tires make per second?\n\n### Options:\nA. Decrease by 14.3%\nB. Decrease by 19%\nC. Increase by 14.3%\nD. Increase by 12.5%\nE. Cannot be determined with the given information.\n\n### Answer:\n416 is the LCM\nOn Tuesday 416/32 =13\nOn Monday 416/26 = 16\nTherefore, 13-16/16 = -1/5=-19% decrease\nAnswer is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo pipes A and B can fill a cistern in 37 \u00bd min and 45 minutes respectively. Both the pipes are opened. The cistern will be filled in just half an hour, if the pipe B is turned off after\n\n### Options:\nA. 6 minutes\nB. 9 minutes\nC. 45 minutes\nD. 3 minutes\nE. 4 minutes\n\n### Answer:\nIf pipe B is turned off after x mins, then\n(2*30)/75 + x/45 =1\nx/45 = 1-60/75 = 1/5\nx= 45/5= 9 mins\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf \u00e2\u20ac\u02dcKARNATAKA\u00e2\u20ac\u2122 is coded as \u00e2\u20ac\u02dcBAIEABABA\u00e2\u20ac\u2122, then \u00e2\u20ac\u02dcBIHAR\u00e2\u20ac\u2122 is coded as\n\n### Options:\nA. BARHI\nB. BHARI\nC. BHIAR\nD. BIHAI\nE. BIHAR\n\n### Answer:\nM=13,1+3=4=D\nA=1=A\nSIMILARLY,\nB=2=B\nI=9=I\nH=8=H\nA=1=A\nR=18=1+8=9=I\nSO ANS IS\nBIHAI\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nLast year, the taxes for small enterprises, was a minimum of 28 dollars for every 5000 dollars of revenue. Tax rates were revised this year to a minimum tax of 2.5 dollars for every 1500 dollars of revenue. By approximately what percent did the ratio of tax to revenue decrease from the previous charge?\n\n### Options:\nA. 70\nB. 69\nC. 71\nD. 66\nE. 72\n\n### Answer:\nInitial tax/revenue ratio = 28/5000 = 84/15000\nRevised charge/transaction ratio = 2.5/1500 = 25/15000\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average weight of 8 persons increases by 1.5 kg. If a person weighing 65 kg is replaced by a new person, what could be the weight of the new person?\n\n### Options:\nA. 76 kg\nB. 77 kg\nC. 76.5 kg\nD. Data inadequate\nE. None of these\n\n### Answer:\ntotal weight increases = 8 \u00d7 1.5 = 12 kg\nso the weight of new person = 65 + 12 = 77 kg\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man invested Rs.1552 in a stock at 97 to obtain an income of Rs.128. What is the dividend from the stock?\n\n### Options:\nA. 4\nB. 8\nC. 6\nD. 10\nE. 12\n\n### Answer:\nBy investing Rs.1552, income = Rs.128\nBy investing Rs.97, income = 128\u00d797/1552=8\nie, dividend = 8%\nAnswer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFor what values of k will the pair of equations 3x + 4y = 12 and (kx + 12y)/2 = 15 does not have a unique solution?\n\n### Options:\nA. 12\nB. 9\nC. 3\nD. 7.5\nE. 2.5\n\n### Answer:\nwe have 2 equations\n1. 3x + 4y = 12 -- > 9x + 12y = 36\n2. (kx + 12y)/2 = 15 --> kx + 12y = 30\nsubstract 1-2, we get (9-K)x = 6\ni.e. x = 6/(9-k)\nthen, by looking at options, we get some value of x except for B. When we put k=9, x becomes 6/0 and hence answer is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA computer manufacturer produces a certain electronic component at a cost of $100 per component. Shipping costs for delivering the components are $2 per unit. Further, the manufacturer has costs of $10,000 a month related to the electronic component regardless of how many it produces. If the manufacturer produces and sells 1000 components a month, what is the lowest price it can sell them for such that the costs don't exceed the revenues?\n\n### Options:\nA. 122\nB. 112\nC. 134\nD. 108\nE. 101\n\n### Answer:\n$10000 is a fixed cost\nEach component is $102 ($100 to produce, $2 to ship)\nManufacturer will be producing and selling 1000 components\nso therefore the equation to find price would be\n1000*p = 10000+(1000*100)+(1000*2)\np = (10000+100000+2000)/1000\np = 112\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA tank is filled in 5 hours by three pipes A, B and C. The pipe C is twice as fast as B and B is twice as fast as A. How much time will pipe A alone take to fill the tank?\n\n### Options:\nA. 20 hours\nB. 25 hours\nC. 35 hours\nD. Cannot be determined\nE. None of these\n\n### Answer:\nIf c takes x hrs, B takes 2x hrs and A takes 4x hrs,\nthen\n1/x +1/2x = 1/4x = 1/5\n7/4x = 1/5\nx= 7*5/4 hrs = 35/4 hrs\nSo A alone will take 4*35/4 = 35 hrs\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich of the following values is the greatest\n\n### Options:\nA. a) 11% of 89\nB. b) 22% of 78\nC. c) 50% of 67\nD. d) 44% of 56\nE. e) 55% of 45\n\n### Answer:\nAre you sure that you checked the answer key correctly? I just signed up forVeritas(haven't started yet, not until March) but I have access to the materials and the answer key I'm looking at says C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe H.C.F. of two numbers is 25 and the other two factors of their L.C.M. are 14 and 16. The larger of the two numbers is\n\n### Options:\nA. 276\nB. 299\nC. 312\nD. 400\nE. None\n\n### Answer:\nSolution\nClearly, the numbers are (25 x 14) and (25 x 16).\nLarger number = (25 x 16)\t= 400.\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n80 x 100 + 80 x 11 = ?\n\n### Options:\nA. 7500\nB. 8880\nC. 6200\nD. 5200\nE. None of them\n\n### Answer:\n=80 x (100+11) (by distributive law)\n=80 x 111\n=8880\nAnswer is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAt the faculty of Aerospace Engineering, 312 students study Random-processing methods, 222 students study Scramjet rocket engines and 112 students study them both. If every student in the faculty has to study one of the two subjects, how many students are there in the faculty of Aerospace Engineering?\n\n### Options:\nA. 404\nB. 452\nC. 444\nD. 468\nE. 422\n\n### Answer:\n312 + 222 - 112 (since 112 is counted twice )= 422\nE is the answer\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n895.7 \u2013 573.07 \u2013 95.007 = ?\n\n### Options:\nA. 227.623\nB. 224.777\nC. 233.523\nD. 414.637\nE. None of these\n\n### Answer:\nSolution\nGiven expression = 895.7 - (573.07 + 95.007) = 895.7 - 668.077 = 227.623. Answer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf p^3 is divisible by 80, then the positive integer p must have at least how many distinct factors?\n\n### Options:\nA. 2\nB. 3\nC. 6\nD. 8\nE. 10\n\n### Answer:\nLet say p = 10, checking divisibility by 80\n10\u221710\u221710/80=25/2\nNumerator falling short of 2\nSo, lets say p = 20, again checking divisibility by 80\n20\u221720\u221720/80=100\n20 is the least value of p for which p3 can be completely divided by 80\nThere are 6 distinct factors of 20 >> 1, 2, 4, 5, 10, 20\nAnswer = C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\na, b, c, d, and e are five consecutive numbers in increasing order of size. Deleting one of the five\nnumbers from the set decreased the sum of the remaining numbers in the set by 20%. Which one of\nthe following numbers S was deleted?\n\n### Options:\nA. a\nB. b\nC. c\nD. d\nE. e\n\n### Answer:\na+b+c+d+e => 1+2+3+4+5=15\nS=20%*15= 3 =>C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man invests some money partly in 12% stock at 108 and partly in 10% stock at 60.To obtain equal dividends from both,he must invest the money in the ratio :\n\n### Options:\nA. 3 : 4\nB. 3 : 2\nC. 4 : 5\nD. 16 : 15\nE. None\n\n### Answer:\nSolution\nFor an income of Rs. 1 in 12% stock at 108, investment = Rs. (108/12)= Rs. 9 .\nFor an income of Rs. 1 in 10% stock at 60, investment = Rs.(60/10) = Rs. 6.\n\u2234 Ratio of investments = 9 :6 =3:2\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe price of 2 sarees and 4 shirts is Rs. 1600. With the same money one can buy 1 saree and 6 shirts. If one wants to buy 12 shirts, how much shall he have to pay ?\n\n### Options:\nA. Rs. 2400\nB. Rs. 2200\nC. Rs. 2300\nD. Rs. 2500\nE. Rs. 2600\n\n### Answer:\nLet the price of a saree and a shirt be Rs. x and Rs. y respectively.\nThen, 2x + 4y = 1600 .... (i)\nand x + 6y = 1600 .... (ii)\nDivide equation (i) by 2, we get the below equation.\n=> x + 2y = 800. --- (iii)\nNow subtract (iii) from (ii)\nx + 6y = 1600 (-)\nx + 2y = 800\n----------------\n4y = 800\n----------------\nTherefore, y = 200.\nNow apply value of y in (iii)\n=> x + 2 x 200 = 800\n=> x + 400 = 800\nTherefore x = 400\nSolving (i) and (ii) we get x = 400, y = 200.\nCost of 12 shirts = Rs. (12 x 200) = Rs. 2400.\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe compound interest on a certain sum for 2 years at 10% per annum is $525. The simple interest on the same sum for double the time at half the rate percent per annum is:\n\n### Options:\nA. $400\nB. $500\nC. $600\nD. $800\nE. $900\n\n### Answer:\nLet the sum be $. P.\nThen,[P(1+10/100)^2 - P] = 525\n->P[(11/10)^2 - 1] = 525\nP = (525*100/21) = 2500\nSUM = $2500\nSO SI = $(2500*5*4/100) = $ 500\nANSWER : B $500\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many two-element subsets of <1, 2,3,4,5,6,7,8> are there that do not contain the pair of elements 2 and 4?\n\n### Options:\nA. 11\nB. 22\nC. 24\nD. 25\nE. 27\n\n### Answer:\n8C2 - 1 = 27 Answer is E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf b is an even integer and b/18 is an odd integer, which of the following is NOT an even integer?\n\n### Options:\nA. (b^2)/54\nB. (b^2)/8\nC. (b^2)/9\nD. (b^2)/6\nE. (b^2)/2\n\n### Answer:\nsince b is an even integer and b/18 is an odd integer. thus maximum power of 2 in a is one. why ?? because if the power of 2 in the expression has been 2 or greater, then the b/18 must have been an even integer. (18=2*3^2. as 18 contain only one 2 in the expression)\nnow, any expression in which we have 4 at the denominator will be odd. out of the given options only 8 is a multiple of 4. hence answer should be B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat number is obtained by adding the units digits of 734^100 and 347^83?\n\n### Options:\nA. 7\nB. 8\nC. 9\nD. 10\nE. 11\n\n### Answer:\nThe units digit of 734^100 is 6 because 4 raised to the power of an even integer ends in 6.\nThe units digit of 347^83 is 3 because powers of 7 end in 7, 9, 3, or 1 cyclically. Since 83 is in the form 4n+3, the units digit is 3.\nThen 6+3 = 9.\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA student chose a number, multiplied it by 2, then subtracted 148 from the result and got 110. What was the number he chose?\n\n### Options:\nA. 90\nB. 129\nC. 120\nD. 160\nE. 200\n\n### Answer:\nSolution:\nLet x be the number he chose, then\n2*x*148=110\n2x=258\nx=129\ncorrect answer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf (64)2 - (36)2 = 20 x a, then a = ?\n\n### Options:\nA. 70\nB. 120\nC. 180\nD. 140\nE. 130\n\n### Answer:\n20 x a = (64 + 36)(64 - 36) = 100 x 28\na = (100 x 28)/20 = 140\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nLCM of 2/7,3/14 and 5/3is\n\n### Options:\nA. 45\nB. 35\nC. 30\nD. 25\nE. None\n\n### Answer:\nExplanation:\nLCM of numerators /HCF of denominators= LCM of 2, 3, 5/HCFof7,14,3 = 30/1=30\nCorrect Option: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a series of football matches, the probability that Team P wins a match against Team Q is 1/5 and the probability that the match ends in a draw is 2/3. If the two teams play five matches, what is the probability that all five matches end in a draw?\n\n### Options:\nA. 2/3\nB. 4/9\nC. 8/27\nD. 16/81\nE. 32/243\n\n### Answer:\nP(5 draws)=(2/3)^5=32/243\nThe answer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n9 basketball players are trying out to be on a newly formed basketball team. Of these players, 5 will be chosen for the team. If 6 of the players are guards and 3 of the players are forwards, how many different teams of 3 guards and 2 forwards can be chosen?\n\n### Options:\nA. 23\nB. 30\nC. 42\nD. 60\nE. 126\n\n### Answer:\nOut of 6 gaurds we have to select 3 -> selection means we use C -> so 6C3\nOut of 3 forwards we have to select 2 -> selection means we use C -> so 3C2\nTotal ways = 6C3 x 3C2 = 60\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\na train length 100 m going with speed 10m/sec another train 150m long going with speed 15m/sec.the distance between two train is 50m.then how much time second train will take to cross the first train?\n\n### Options:\nA. 60sec\nB. 40sec\nC. 30sec\nD. 45sec\nE. 1min10sec\n\n### Answer:\nnet speed=15-10=5m/sec\nnet distance=100+150+50=300\ntotal time =300/5=60sec\nanswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. How far is the place?\n\n### Options:\nA. 2.89\nB. 2.88\nC. 2.86\nD. 2.82\nE. 2.81\n\n### Answer:\nM = 6\nS = 1.2\nDS = 6 + 1.2 = 7.2\nUS = 6 - 1.2 = 4.8\nx/7.2 + x/4.8 = 1\nx = 2.88.Answer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRam borrowed some money at the rate of 6% p.a. for the first three years, 8% p.a.for the next six years and 10% p.a.for the period beyond nine years If the total interest paid by him at the end of 12 years is 19200, how much money did he borrow?\n\n### Options:\nA. 18,000\nB. 10,000\nC. 25,000\nD. 20,000\nE. None of these\n\n### Answer:\nLet the sum be x. Then,\n(x\u00d73\u00d76/100)+(x\u00d76\u00d78/100)+(x\u00d73\u00d710/100)=19200\n\u21d2 18x + 48x + 30x = (19200 \u00d7 100)\n\u21d2 96x = 1920000\n\u21d2 x = 20000.\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA group of two women and three men have tickets for seven adjacent seats in one row of a theatre. If the three men will not sit in three adjacent seats, how many possible different seating arrangements are there for these 7 theatre-goers?\n\n### Options:\nA. 7! \u2013 2!3!2!\nB. 7! \u2013 4!3!\nC. 5! \u2013 3!3!\nD. 7 \u00d7 2!3!2!\nE. 2!3!2!\n\n### Answer:\n5 people can sit in 5! different ways. But because 3 men cannot sit together, we take them as a unit.\nThis unit of men, among themselves can sit in 3! ways.\nHence, 5! - 3!.\nThis unit of men along with 2 women can sit in 3! different ways which also needs to be eliminated.\nHence 5! - 3!3!\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo taps can separately fill a cistern 5 minutes and 7.5 minutes respectively and when the waste pipe is open, they can together fill it in 18 minutes. The waste pipe can empty the full cistern in?\n\n### Options:\nA. 3.8\nB. 3.7\nC. 3.6\nD. 3.9\nE. 3.5\n\n### Answer:\n1/5 + 1/7.5 - 1/x = 1/18\nx = 3.6\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a garden, there are yellow and green flowers which are straight and curved. If the probability of picking a green flower is 1/5 and picking a straight flower is 1/2, then what is the probability of picking a flower which is yellow and straight\n\n### Options:\nA. 1/7\nB. 1/8\nC. 2/5\nD. 3/4\nE. 7/8\n\n### Answer:\nGood question.\nSo we have a garden where all the flowers have two properties: color (green or yellow) and shape (straight or curved).\nWe're told that 1/5 of the garden is green, so, since all the flowers must be either green or yellow, we know that 4/5 are yellow. We're also told there is an equal probability of straight or curved, 1/2.\nWe want to find out the probability of something being yellow and straight, Pr( Yellow and Straight ).\nSo if we recall, the probability of two unique events occurring simultaneously is the product of the two probabilities, Pr( A and B ) = P(A) * P(B). So we multiply the two probabilities, Pr(yellow)* Pr(straight) = 4/5 * 1/2 = 2/5, or C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nM and N started a business by investing Rs.4000/- and Rs.5000/- respectively. Find the M\u2019s share out of a total profit of Rs.1800:\n\n### Options:\nA. Rs.500/-\nB. Rs.550/-\nC. Rs.600/-\nD. Rs.650/-\nE. Rs.800/-\n\n### Answer:\nM = Rs.4000/-\nN = Rs.5000/-\nM share 4 parts & N share 5 parts\nTotal 9 parts -----> Rs.1800/-\n----> 1 part -------> Rs.200/-\nM share = 4 parts -----> Rs.800/-\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo trains are running in opposite directions with the same speed. If the length of each train is 180 m and they cross each other in 12 sec, then the speed of each train is?\n\n### Options:\nA. 54\nB. 77\nC. 36\nD. 88\nE. 21\n\n### Answer:\nLet the speed of each train be x m/sec.\nThen, relative speed of the two trains = 2x m/sec.\nSo, 2x = (180 + 180)/12 => x = 15\nSpeed of each train = 10 m/sec.\n= 15 * 18/5 =- 54 km/hr.\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how many ways can 5 men & 4 women can be made from a gang of 7 men & 8 women ?\n\n### Options:\nA. 91\nB. 98\nC. 97\nD. 86\nE. 90\n\n### Answer:\nExplanation:\n7C5 * 8C4 = 91\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf daily wages of a man is double to that of a woman, how many men should work for 20 days to earn Rs.14400? Given that wages for 40 women for 30 days are Rs.21600.\n\n### Options:\nA. 12\nB. 14\nC. 16\nD. 18\nE. 20\n\n### Answer:\nExplanation :\nWages of 1 woman for 1 day = 21600/40\u00c3\u201430\nWages of 1 man for 1 day = 21600\u00c3\u20142/40\u00c3\u201430\nWages of 1 man for 20 days = 21600\u00c3\u20142\u00c3\u201420/40\u00c3\u201430\nNumber of men = 14400/(21600\u00c3\u20142\u00c3\u201420/40\u00c3\u201430)=144/(216\u00c3\u201440/40\u00c3\u201430)= 20\nAnswer : Option E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the simple interest on Rs. 70,000 at 16 2/3% per year for 9 months.\n\n### Options:\nA. 7500\nB. 6500\nC. 8750\nD. 9500\nE. None of them\n\n### Answer:\nP = Rs.70000,R = 50/3% p.a and T = 9/12 years = 3/4years.\nSimple Interest = (P*R*T)/100 = Rs.(70,000*(50/3)*(3/4)*(1/100))= Rs.8750\nAnswer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a function f is defined by f(x)= 1/x for all non zero numbers x. If f(a) = -1/2 and f(ab) = 3/2 then b= ?\n\n### Options:\nA. -3\nB. 1/3\nC. -1/3\nD. 3\nE. -12\n\n### Answer:\nGiven that f(x) = 1/x and f(a) = -1/2, then f(a) =1/a=-1/2 ===> a=-2, then backsolve using the answer choices:\nf(ab) = f(-2b) = 1/6\nA) -3 ===> f(-2*-3) = f(6) = 1/6\nB) 1/3 ===> f((-2*1/3) = f(-2/3) = 1/(-2/3) = -3/2\nC) -1/3 ===> f(-2*-1/3) = f(2/3) = 1/(2/3) = 3/2 WINS\nD) 3 ===> f(-2*3) = f(-6) = -1/6\nE) -12 ===> f(-2*-12) = f(24) = 1/-24 = -1/24\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo brothers Ram and Ravi appeared for an exam. The probability of selection of Ram is 4/7 and that of Ravi is 1/5. Find the probability that both of them are selected.\n\n### Options:\nA. 4/35\nB. 2/3\nC. 7/35\nD. 5/7\nE. 7/5\n\n### Answer:\nLet A be the event that Ram is selected and B is the event that Ravi is selected.\nP(A) = 4/7\nP(B) = 1/5\nLet C be the event that both are selected.\nP(C) = P(A) x P(B) as A and B are independent events:\n= 4/7 x 1/5 = 4/35\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many 3 digit numbers can be formed from the digits 2,3,5,6,7 and 9 which are divisible by 5 and none of the digits is repeated?\n\n### Options:\nA. 16\nB. 12\nC. 20\nD. 25\nE. 30\n\n### Answer:\nSince each desired number is divisible by 5,\nso we much have 5 at the unit place.\nThe hundreds place\ncan now be filled by any of the remaining 4 digits .\nso, there4 ways of filling it.\nRequired number of numbers = (1 * 5 * 4)\n= 20\nAns: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n56 is to be divided into two parts such that the sum of 10 times the first and 22 times the second is 780. The bigger part is :\n\n### Options:\nA. 33.0\nB. 37.66\nC. 32.1\nD. 31.23\nE. 19\n\n### Answer:\nExplanation:\nLet the two parts be (56 - x) and x.\nThen, 10 (56 - x) + 22x = 780\n=> 12x = 220\n=> x = 20.\nBigger part = (56 - x) = 37.66.\nAnswer: B) 37.66\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA firm has 4 senior partners and 6 junior partners. How many different groups F of 3 partners can be formed in which at least one member of the group is a senior partner. (2 groups are considered different if at least one group member is different)\n\n### Options:\nA. 48\nB. 100\nC. 120\nD. 288\nE. 600\n\n### Answer:\nWhat seems to work as well, though its tougher to come up with this solution:\n(10*9*8) * 2/3 + (10*9*4)*1/3 = 600. Divided by all possible permutations (=3!) yields 100.\nExplanation: For the first spot you have 10 possible canditates, for the 2nd 9. For the 3rd spot you need to differentiate if a senior partner has been picked for one of the first 2 spots or not. If yes, then you can pick one of the 8 remaining guys, so 10*9*8. If no senior partner has been picked yet, you need 10*9*4.\nNow you need to weight the 2 cases with the corresponding probabilities: probability of no senior partner being picked in the first 2 draws = 6/10*5/9=1/3, so you weight 10*9*4 with 1/3. For the complementary case (senior partner was picked in the first 2 draws) you just take the complementary prob (1-1/3)= 2/3 and weight 10*9*8 with it.\nNow you just need to divide the answer (600) by the number of different positions (=3!) and get F=600/6=100.B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe value of (1/log3 60 + 1/log4 60 + 1/log5 60) is:\n\n### Options:\nA. 0\nB. 1\nC. 5\nD. 60\nE. 2\n\n### Answer:\nlog60 3 + log60 4 + log60 5 + log60 (3*4*5)\n= log60 60 = 1\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nDue to 10% decrease in the price of sugar and John can buy 4kg more sugar in Rs100 , then find the CP of sugar?\n\n### Options:\nA. s. 1(2/9)\nB. s. 2(7/9)\nC. s. 2(1/9)\nD. s. 3(2/7)\nE. s. 4(2/9)\n\n### Answer:\nHere r = 10 % ,x = 100 and A = 4 kg\nActual price of sugar = 10*100/((100-10 )*4) = Rs. 2(7/9)\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf y is a positive integer, which of the following could NOT be the square of y?\n\n### Options:\nA. 5,228,644\nB. 5,224,169\nC. 4,989,696\nD. 4,985,225\nE. 4,998,752\n\n### Answer:\nA number ending with 2 can never be a perfect square.\nUnits digit of a perfect square must be:\n1,4,9,6,5\nAnswer E)\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe sides of a cube are in the ratio 1:2 the ratio of their volume is?\n\n### Options:\nA. 1:9\nB. 1:7\nC. 1:8\nD. 1:6\nE. 1:4\n\n### Answer:\n1:8\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nP is four times as fast as Q and working together, they can complete a work in 5 days. In how many days can Q alone complete the work?\n\n### Options:\nA. 5 3/4 days\nB. 6 1/4 days\nC. 16 days\nD. 25 days\nE. 18 days\n\n### Answer:\nP = 4Q\nP + Q = 4Q + Q = 5Q\nThese 5Q people can do the work in 5 days, which means Q can do the work in 25 days.\nHence, P can do the work in 6 1/4 days.\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA sock drawer contains seven socks, each one a different solid color. The colors of the socks are orange, yellow, green, blue, indigo, and violet. A person reaches into the drawer, pulls out two socks, and puts a single sock on each foot. If each sock can fit either the left or the right foot, and if it matters whether a particular sock is on the left or the right foot, how many different sock fashion combinations could the person make from the six socks?\n\n### Options:\nA. 12\nB. 15\nC. 21\nD. 36\nE. 30\n\n### Answer:\nIt's a question of permutation since order matters here ....\nIt can be deduced to-\n6P2 = 6!/4! = 6*5 = 30 .........Answer is - E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a certain school, 20% of students are below 8 years of age. The number of students above 8 years of age is of the number of students of 8 years of age which is 48. What is the total number of students in the school?\n\n### Options:\nA. 72\nB. 80\nC. 120\nD. 150\nE. 100\n\n### Answer:\nAnswer: Option E\nLet the number of students be x. Then,\nNumber of students above 8 years of age = (100 - 20)% of x = 80% of x.\n80% OF X= 48+2/3 OF 48\n80/100 X=80\nX=100\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a mixture of milk and water, the proportion of milk by weight was 70%. If, in a 150-gram mixture, 50 grams of pure milk is added, what would be the percentage of milk in the resulting mixture?\n\n### Options:\nA. 75.5%\nB. 76.5%\nC. 77.5%\nD. 78.5%\nE. 79.5%\n\n### Answer:\nThe amount of milk is 0.7(150) + 50 = 155 grams.\nThe proportion is 155/200 = 0.775 which is 77.5%\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJohn has 4 friends who want to ride in his new car that can accommodate only 3 people at a time (John plus 2 passengers). How many different combinations of 2 passengers can be formed from John's 4 friends?\n\n### Options:\nA. 6\nB. 8\nC. 10\nD. 15\nE. 18\n\n### Answer:\n4C2 = 6\nThe answer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA coin is tossed live times. What is the probability that there is at the least one tail?\n\n### Options:\nA. 31/32\nB. 31/38\nC. 31/34\nD. 31/31\nE. 31/36\n\n### Answer:\nLet P(T) be the probability of getting least one tail when the coin is tossed five times.\n= There is not even a single tail.\ni.e. all the outcomes are heads.\n= 1/32 ; P(T) = 1 - 1/32 = 31/32\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a/b = 5/4, Then (4a + 3b) / (4a - 3b) = ?\n\n### Options:\nA. 7\nB. 6\nC. 3\nD. 5\nE. 4\n\n### Answer:\nAnswer\nDividing numerator as well as denominator by b, we get\nGiven Exp. = (4a + 3b) / (4a - 3b) = (4a/b + 3) / (4a/b - 3)\nSince a/b = 5/4\nthis implies that\n=[(4*5)/4 +3]/[(4*5)/4 -3)]\n= (5+ 3) / (5 - 3)\n= 4\nOption: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the area of trapezium whose parallel sides are 18 cm and 12 cm long, and the distance between them is 14 cm?\n\n### Options:\nA. 288 cm2\nB. 277 cm2\nC. 224 cm2\nD. 226 cm2\nE. 227 cm2\n\n### Answer:\nArea of a trapezium = 1/2 (sum of parallel sides) * (perpendicular distance between them)\n= 1/2 (18 + 12) * (14)\n= 224 cm2\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTabby is training for a triathlon. She swims at a speed of 1 mile per hour. She runs at a speed of 9 miles per hour. She wants to figure out her average speed for these two events. What is the correct answer for her?\n\n### Options:\nA. 8 mph\nB. 5.25 mph\nC. 3.5 mph\nD. 5 mph\nE. 0.5 mph\n\n### Answer:\n(1 mph +9 mph)/2 = 5 mph\nCorrect option is: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n3,6,9,12,15....\n\n### Options:\nA. 58\nB. 60\nC. 18\nD. 62\nE. 63\n\n### Answer:\n1*3=3\n2*3=6\n3*3=9\n4*3=12\n5*3=15\n6*3=18\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAamir saves 32% of his monthly salary. If he spends Rs. 27200, then find his savings?\n\n### Options:\nA. 15400\nB. 14300\nC. 13200\nD. 12800\nE. None of these\n\n### Answer:\nLet the monthly salary of Aamir be Rs. x.\n68% of x = 27200\n=> x = (27200 * 100)/68 = 40000\nHis savings = 32/100 * 40000 = 12800.\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many factors of 880 are odd numbers greater than 1?\n\n### Options:\nA. 3\nB. 4\nC. 5\nD. 6\nE. 7\n\n### Answer:\nWhen factorized, 880 has 6 prime factors. Of these prime factors 2 are odd and 4 are even. Hence total number of odd factors is 2*2(4), which includes 4. The total number of odd factors greater than 1 are 3.(option A)\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe length of a side of a hexagon is 5 inches. What is the perimeter?\n\n### Options:\nA. 116\nB. 25\nC. 30\nD. 24\nE. 15\n\n### Answer:\nHexagon. It means 6 equal sides.\np = 5 + 5 + 5 + 5 + 5 + 5 = 10+ 10 + 10 = 30 inches\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFor the past n days, the average (arithmetic mean) daily production at a company was 50 units. If today's production of 105 units raises the average to 55 units per day, what is the value of n?\n\n### Options:\nA. 8\nB. 10\nC. 12\nD. 14\nE. 16\n\n### Answer:\nThe daily production was raised by 5 units for n days, which has a weighting of 5n.\n5n = 105-55 = 50\nn = 10\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo employees X and Y are paid a total of Rs. 330 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week?\n\n### Options:\nA. s.150\nB. s.200\nC. s.250\nD. s.350\nE. s.400\n\n### Answer:\nLet the amount paid to X per week = x\nand the amount paid to Y per week = y\nThen x + y = 330\nBut x = 120% of y = 120y/100 = 12y/10\n\u00e2\u02c6\u00b412y/10 + y = 330\n\u00e2\u2021\u2019 y[12/10 + 1] = 330\n\u00e2\u2021\u2019 22y/10 = 330\n\u00e2\u2021\u2019 22y = 3300\n\u00e2\u2021\u2019 y = 3300/22 = 300/2 = Rs.150\nA)\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIt was Sunday on Jan 1, 2006. What was the day of the week Jan 1, 2010?\n\n### Options:\nA. Tuesday\nB. Saturday\nC. Monday\nD. Friday\nE. Sunday\n\n### Answer:\nOn 31st December, 2005 it was Saturday.\nNumber of odd days from 2006 to 2009 = (1 + 1 + 2 + 1) = 5 days.\nOn 31st December 2009, it was Thursday.\nThus, on 1st Jan, 2010 it is Friday\nAnswer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the sides of a triangle are 26 cm, 24 cm and 12 cm, what is its area?\n\n### Options:\nA. 144\nB. 772\nC. 288\nD. 266\nE. 2848\n\n### Answer:\nThe triangle with sides 26 cm, 24 cm and 12 cm is right angled, where the hypotenuse is 26 cm.\nArea of the triangle = 1/2 * 24 * 12 = 144 cm2\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAn bus covers a certain distance at a speed of 260 kmph in 5 hours. To cover the samedistance in 1hr, it must travel at a speed of?\n\n### Options:\nA. 600 km/hr\nB. 720 km/hr\nC. 730 km/hr\nD. 750 km/hr\nE. 780 km/hr\n\n### Answer:\nDistance = (260 x 5) = 1300 km.\nSpeed = Distance/Time\nSpeed = 1300/(5/3) km/hr. [We can write 1 hours as 5/3 hours]\nRequired speed = 1300 x 3 km/hr = 780 km/hr.\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA, B and C completed a piece of work, A worked for 6 days, B for 9 days and C for 4 days. Their daily wages were in the ratio of 3:4:5. Find the daily wages of C, if their total earning was Rs.1480?\n\n### Options:\nA. 170Rs\nB. 108Rs\nC. 100Rs\nD. 160Rs\nE. 103Rs\n\n### Answer:\n3x 4x 5x\n6 9 4\n18x + 36x + 20x = 1480\n74x = 1480 => x = 20\n5x =100Rs.\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe number of girls in a class is 5 times the number of boys. Which one of the following numbers cannot represent the total number of children in the class.\n\n### Options:\nA. 36\nB. 41\nC. 48\nD. 72\nE. 11\n\n### Answer:\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe combined age of husband and wife on their 20th wedding anniversary was twice than it was at the time of wedding. If the husband is 3 years older than his wife. How old was he at the time of his marriage?\n\n### Options:\nA. 21.5 years\nB. 21.9 years\nC. 31.5 years\nD. 21.7 years\nE. 61.5 years\n\n### Answer:\nExplanation:\nLet the ages of husband and wife at the time of their 20th wedding anniversary be X years and Y years respectively and X > Y.\nTheir combined age = (X + Y) years.\nThe ages of both husband and wife at the time of wedding will be (X \u2013 20) years and (Y \u2013 20) years respectively.\nTheir combined age = (X \u2013 20) + (Y \u2013 20)\n= (X + Y \u2013 40) Years\nBy first information, we have\n(X + Y) = 2( X + Y \u2013 40)\nX + Y = 2X + 2Y - 80\nTherefore, X + Y = 80-------A\nand by second information, we have\nX \u2013 Y =3 ----------------------B\nSolving A and B, we get X = 41.5 years\nTherefore, the age of husband at the time of their 20th wedding anniversary X = 41.5 years\nAge at the time of marriage = 41.5 years \u2013 20 years = 21.5 years.\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich of the following is a prime number ?\n\n### Options:\nA. 72\nB. 86\nC. 88\nD. 97\nE. 98\n\n### Answer:\nClearly, 97 is a prime number.\nOption D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the height of an equilateral triangle TBC is equal in length to the hypotenuse of an isosceles right triangle DEF, a side of \u0394TBC is how many times as long as a leg of the right triangle DEF?\n\n### Options:\nA. (\u221a2)/(\u221a3)\nB. (\u221a3)/(\u221a2)\nC. \u221a2\nD. (2\u221a2)/(\u221a3)\nE. 2/(\u221a3)\n\n### Answer:\nSide of the equilateral triangle TBC = 2m ----> height = m * sqtr(2)\nHipotenuse of the right triangle TBC = m * sqrt(3) ----> side = m * sqtr(3) / sqtr(2)\nQuestion is 2m/m * sqtr(3) / sqtr(2) = 2*sqrt(2)/sqrt(3)=D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJohn and David can finish a job together in 6 hours. If John can do the job by himself in 8 hours, what percent of the job does David do?\n\n### Options:\nA. 35%\nB. 45%\nC. 25%\nD. 30%\nE. 20%\n\n### Answer:\nYou can also plug in numbers. For example, Bob and Alice work at a donut factory and make 24 donuts which is the job ( I picked this as a SMART number).\nJohn on his own works 24/8 = 3 donuts per hour.\nJohn and David work 24/6 = 4 donuts per hour so David works 1 donuts/hour\nTo find out the percentage, David works 1 donuts/hr x 6 hours = 6 donuts per hour.\nTherefore 6 donuts/24donuts = 1/4 = 25%\nAnswer : C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the L.C.M of 32,84,126\n\n### Options:\nA. 2000\nB. 2018\nC. 5032\nD. 1008\nE. 2016\n\n### Answer:\n32=2^5 84=2^2*3*7 126=2*3^2*7\nL.C.M=2^5*3^2*7=2016\nAnswer=(E)\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWorldwide production of motor vehicles was 3.9 million vehicles in 1946 and 57.2 million in 1987. Of the following, which is closest to the average (arithmetic mean) annual increase, in millions, in worldwide production of motor vehicles during this period?\n\n### Options:\nA. 1.3\nB. 1.0\nC. 1.1\nD. 10.5\nE. 41.8\n\n### Answer:\nChange in production of motor vehicles = 57.2 - 3.9 = 53.3 million in 41 years (1987 - 1946)\naverage increase per year = 53.3/41 = 1.3 million (apporx.)\nAnswer (A)\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n10 2 = 0.3010, the value of log10 80 is:\n\n### Options:\nA. 1.602\nB. 1.903\nC. 2.903\nD. 3.903\nE. 4.903\n\n### Answer:\nlog10 80\t= log10 (8 x 10)\n= log10 8 + log10 10\n= log10 (23 ) + 1\n= 3 log10 2 + 1\n= (3 x 0.3010) + 1\n= 1.9030.\nAnswer: Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a, b, y are integers, 33 = aby, and a < b < y, what is the smallest possible value of a?\n\n### Options:\nA. -33\nB. -3\nC. 1\nD. 3\nE. 11\n\n### Answer:\nGiven : a * b * y = 33.\n33 is a Positive Odd number.Side Note:Thus, all 3 numbers will be odd.\nPrime factorization will also give you numbers. 1, 3, 11. The 3 numbers will be combination of these 3 numbers with possible variation in sign(+/-).\nWe could have any 2 digits as negative. --> negative * negative * positive. We have negative values in answer option, so eliminate C, D and E from answer choices.\n-33 * -1 * 1 = 33.\nCorrect answer is A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind out the square of a number which when doubled exceeds its quarter by 7 ?\n\n### Options:\nA. 16\nB. 25\nC. 19\nD. 26\nE. 17\n\n### Answer:\nA\nLet the number be p, then the square will be p^2\nAccording to question:\n2p = (p/4) + 7\n=> 8p = p + 28\n=> p = 4\np^2 = 4^2 = 16.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how many years does a sum of Rs. 5000 yield a simple interest of Rs. 16500 at 15% p.a.?\n\n### Options:\nA. 22 years\nB. 17 years\nC. 97 years\nD. 16 years\nE. 14 years\n\n### Answer:\nT = (100 * 16500)/(15 * 5000)\n= 22 years\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind out the wrong term in the series 2, 5, 10, 50, 500, 5000\n\n### Options:\nA. 5000\nB. 3877\nC. 6777\nD. 2892\nE. 2881\n\n### Answer:\nExplanation:\nEach term of the series is the product of the preceding two terms\nSo, 5000 is wrong and it must be replaced by (500*50) = 25000\nAnswer: A) 5000\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n2^(24) + 2^(25) + 2^(26) + ... + 2^(43) + 2^(44) =\n\n### Options:\nA. 2^24(2^(21)-1)\nB. 2^24(2^(20)-1)\nC. 2^24(2^(23)-1)\nD. 2^21(2^(20)-1)\nE. 2^21(2^(21)-1)\n\n### Answer:\n2^(24) + 2^(25) + 2^(26) + ... + 2^(43) + 2^(44) =\n2^(24)*(1+2+4+...+2^(20)) =\n2^(24)*(2^(21) - 1)\nThe answer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAn elementary school houses primarily kindergartners, first graders, second graders, and third graders. If an assembly included 30 kindergartners, 20 first graders, and 80 other children, and the ratio of first graders to third graders is tripled, what is the ratio of the first graders to the rest of the children?\n\n### Options:\nA. 40: 20\nB. 42: 21\nC. 50: 100\nD. 15: 25\nE. It cannot be determined by the information given.\n\n### Answer:\nWhile you can figure out most of this question, there is not enough information to completely tell. the answer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWith both valves open, the pool will be filled with water in 48 minutes. The first valve alone would fill the pool in 2 hours. If the second valve emits 50 cubic meters of water more than the first every minute, then what is the capacity W of the pool?\n\n### Options:\nA. 9000 cubic meters\nB. 10500 cubic meters\nC. 11750 cubic meters\nD. 12000 cubic meters\nE. 12500 cubic meters\n\n### Answer:\nD. 12000 cubic meters.\nIf both hte valves fill the pool in 48 minutes and valve 1 only fills in 120 minutes then valve 2 alone will fill the pool in (48*120)/(120-48) = 80 minutes.\nNow, if valve 1 admits x cubic meter of water per minute then the capacity of pool will be 120x and also 80 (x+50).\nor, 120x = 80 (x + 50).\nor x = 100.\nHence, the capacity of pool = 120x = 12000 cubic meters.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train speeds past a pole in 15 sec and a platform 100 m long in 25 sec, its length is?\n\n### Options:\nA. 288\nB. 150\nC. 277\nD. 269\nE. 261\n\n### Answer:\nLet the length of the train be x m and its speed be y m/sec.\nThen, x/y = 15 => y = x/15\n(x + 100)/25 = x/15 => x = 150 m.\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nP, Q, R, S and T are five speakers who have to speak on a particular day, not necessarily in the same order. R is neither the first nor the last speaker. There are three speakers after S and three speakers ahead of T. If P speaks after Q, then who is the last speaker to speak?\n\n### Options:\nA. S\nB. T\nC. P\nD. Q\nE. Cannot be determined.\n\n### Answer:\nExplanation:\nThere are three speakers after S. So, S is the 2nd speaker.\nThere are three speakers before T. So, T is the 4th speaker.\nR is neither the 1st nor the 5th. So, R is the 3rd speaker.\nP speaks after Q, So P is the 5th and Q is the 1st speaker. So, P is the last speaker.\nANSWER IS C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nM = {-6, -5, -4, -3, -2}\nT = {-2, -1, 1, 2, 3, 4}\nIf an integer is to be randomly selected from set M above and an integer is to be randomly selected from set T above, what is the probability that the product of the two integers will be negative?\n\n### Options:\nA. 0\nB. 1/3\nC. 2/5\nD. 1/2\nE. 4/5\n\n### Answer:\nAnswer E.\nTotal # of outcomes: 5*6= 30\n# of outcomes where Product is -ve : (-6,1) ,(-6,2), (-6,3)... Hence, total: 24\nProbability: 24/30 = 4/5\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nDylan is on a road trip. He planned on arriving at his destination, 2150 miles away, in 6 days. In the first day, he traveled 310 miles. In the next three days, he travels 1140 miles. How many miles, on average, does Dylan need to travel in the next two days to reach his destination?\n\n### Options:\nA. 330\nB. 340\nC. 350\nD. 360\nE. 370\n\n### Answer:\nHe still has to travel 2150 - 300 - 1130 = 720 miles\n720 miles / 2 days = 360 miles per day.\nCorrect answer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nif the price of a book is first decreased by 20% and then increased by 10%, then the net change in the price will be :\n\n### Options:\nA. 10\nB. 12\nC. 37\nD. 29\nE. 22\n\n### Answer:\nExplanation:\nLet the original price be Rs. 100.\nDecreased by 20% = 80\nThen increased 10% on Rs 80 = 80 + 8 = 88\nNet change in price = 100 - 88 = 12\nAnswer : B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSiva Reddy walked 2 km west of his house and then turned south covering 4 km. Finally, He moved 3 km towards east and then again 1 km west. How far is he from his initial position?\n\n### Options:\nA. 10 km\nB. 9 km\nC. 2 km\nD. 4 km\nE. 8 km\n\n### Answer:\n4 km\nANSWER D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n12.1212+17.0005 - 9.1104 = ?\n\n### Options:\nA. 20.0015\nB. 20.0105\nC. 20.0113\nD. 20.1015\nE. None\n\n### Answer:\nSolution\nGiven expression\n=(12.1212+17.0005)-9.1104\n= (29.1217 - 9.1104)\n=20.0113.\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo trains 100 meters and 120 meters long are running in the same direction with speeds of 100 km/hr, 82 km/hr. In how much time will the first train cross the second\n\n### Options:\nA. 37 sec\nB. 35 sec\nC. 48 sec\nD. 44 sec\nE. 36 sec\n\n### Answer:\nExplanation:\nRelative speed of the trains = (100 - 82) km/hr = 18 km/hr\n= (18\u00c3\u2014 5/18) m/sec = 5 m/sec.\nTime taken by the trains to cross each other\n= Time taken to cover (100 + 120) m at 5 m /sec = (220/5) sec = 44 sec.\nAnswer: Option D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are 14 players in a chess group, and each player plays each of the others once. Given that each game is played by two players, how many total games will be played?\n\n### Options:\nA. 91\nB. 30\nC. 45\nD. 60\nE. 90\n\n### Answer:\n10 players are there.\ntwo players play one game with one another.\nso 14C2=14*13/2\n=91\nSO OPTION A is correct\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man walked diagonally across a square lot. Approximately, what was the percent saved by not walking along the edges?\n\n### Options:\nA. 20%\nB. 30%\nC. 40%\nD. 50%\nE. 55%\n\n### Answer:\nLet the side of the square(ABCD) be x metres.\nThen, AB + BC = 2x metres.\nAC = 2x = (1.41x) m.\nSaving on 2x metres = (0.59x) m.\nSaving % = (0.59x)/2x\tx 100\t%\t= 30% (approx.)\nB)\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nEach child has 3 crayons and 12 apples. If there are 6 children, how many crayons are there in total?\n\n### Options:\nA. 22\nB. 65\nC. 18\nD. 36\nE. 10\n\n### Answer:\n3*6=18.Answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe Average of 11 results is 16, if the average of the 1st 6 results is 58 & that of the last 63. Find the 6th result.\n\n### Options:\nA. 66\nB. 55\nC. 44\nD. 77\nE. 88\n\n### Answer:\n6th result = (58*6+63*6-60*11)\n=66\nAnswer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nDacid obtained 86, 85, 92, 87 and 95 marks (out of 100) in English, Mathematics, Physics, Chemistry and Biology. What are his average marks?\n\n### Options:\nA. 67\nB. 26\nC. 89\nD. 26\nE. 75\n\n### Answer:\nAverage\n= (86+ 85+ 92+ 87+95)/5\n= 445/5 = 89.\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhen a number is added to another number the total becomes 33 1\u20443 per cent of the second number. What is the ratio between the first and the second number?\n\n### Options:\nA. 3 : 7\nB. 7 : 4\nC. 7 : 3\nD. Data inadequate\nE. None of these\n\n### Answer:\nLet the first and second numbers be x and y respectively.\nThen, x + y = 10\u20443y\nor, x = 7\u20443y\n\u2234 x : y = 7 : 3\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many combinations of three letters taken from letters (a, a, b, b, c, c, d) are possible?\n\n### Options:\nA. 12\nB. 13\nC. 35\nD. 36\nE. 56\n\n### Answer:\nCombinations only... total 13\nSo 4C3 for abcd - 4 choices\n3 more for aa(b,c or d)\n3 more for bb(a,c or d)\n3 more for cc(a,b or d)\ntotal 13\n(Answer B)\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the two-digit integers F and N are positive and have the same digits, but in reverse order, which of the following CANNOT be the sum of F and N?\n\n### Options:\nA. 181\nB. 165\nC. 121\nD. 99\nE. 44\n\n### Answer:\nSince the question asks for the answer that CANNOT be the sum of F and N, and the answers are numbers, we can use a combination of TESTing VALUES and TESTing THE ANSWERS to eliminate the possible values and find the answer to the question.\nWe're told that F and N are two-digit positive integers and have the SAME DIGITS but in REVERSE ORDER. We're asked which of the 5 answers CANNOT be the SUM of F and N.\nLet's start with the 'easiest' answer first:\n44. Can we get to 44 in the manner described?\nYes, if the numbers are 13 and 31.....13+31 = 44. Eliminate Answer E\nNow let's work through the rest of the list....\nCan we get to 99 in the manner described?\nYes, there are several ways to do it. For example, if the numbers are 18 and 81.....18+81 = 99. Eliminate Answer D\nCan we get to 121 in the manner described?\nYes, there are several ways to do it. For example, if the numbers are 38 and 83.....38+83 = 121. Eliminate Answer C\nCan we get to 165 in the manner described?\nYes, there are a couple of ways to do it. For example, if the numbers are 78 and 87.....78+87 = 165. Eliminate Answer B\nThere's only one answer left....\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man is 24 years older than his son. In three years, his age will be twice the age of his son. The present age of the son is\n\n### Options:\nA. 14 years\nB. 18 years\nC. 20 years\nD. 21 years\nE. None\n\n### Answer:\nSolution\nLet the son's present age be x years .Then, man's present age\t= (x+24)years.\nThen\t\u00e2\u20ac\u00b9=\u00e2\u20ac\u00ba(x+24)+3= 2(x+3)\n\u00e2\u20ac\u00b9=\u00e2\u20ac\u00bax+27=2x+6\nx= 21.\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nBrenda and Sally run in opposite direction on a circular track, starting at diametrically opposite points. They first meet after Brenda has run 100 meters. They next meet after Sally has run 200 meters past their first meeting point. Each girl runs at a constant speed. What is the length of the track in meters?\n\n### Options:\nA. 250\nB. 300\nC. 350\nD. 400\nE. 500\n\n### Answer:\nNice problem. +1.\nFirst timetogetherthey run half of the circumference.\nSecond timetogetherthey run full circumference.\nFirst time Brenda runs 100 meters, thus second time she runs 2*100 = 200 meters.\nSince second time (when they run full circumference) Brenda runs 200 meters and Sally runs 200 meters, thus the circumference is 200 + 200 = 400 meters.\nAnswer: D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe tax on a commodity is diminished by 14% and its consumption increased by 15%. The effect on revenue is?\n\n### Options:\nA. 2.1%\nB. 8.1%\nC. 5.1%\nD. 6.1%\nE. 1.1%\n\n### Answer:\n100 * 100 = 10000\n86 * 115 = 9890\n-----------\n10000-----------110\n100-----------? => 1.1% decrease\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n60, 67, 63, 15, 61, 10, 15\nWhich of the following numbers is lower than the median but greater than the mean of the set of the numbers in the list?\n\n### Options:\nA. 25\nB. 36\nC. 53\nD. 60\nE. 62\n\n### Answer:\nYes, it can be solved with observation even without approximation in 30 sec.\nJust observe given numbers: 10, 15 ,15, 60, 61, 63, 67\nMedian is very easy to tell - its 60. Now we want a number lower than 55 and greater than mean. How many numbers are lower than 60\nDE are already out.\nNow, we have 25, 36 and 53 and we want a number among these which is greater than mean. logically whatever be the mean, if one value out of these 5 has to be greater than mean it has to be 53. (Notice, if 25 is more than mean then 53 is also. If 36 is more than mean, 53 is also. )\nHence C it is!\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo sides of a triangle have lengths x and e and meet at a right angle. If the perimeter of the triangle is 4x, what is the ratio of x to e ?\n\n### Options:\nA. a) 2 : 3\nB. b) 3 : 4\nC. c) 4 : 3\nD. d) 3 : 2\nE. e) 2 : 1\n\n### Answer:\nAhhhh....my bad. Thank you, you're correct. 8x = 6e --> x/e = 3/4.\nActually B is the right answer.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich is a better investment 9% stock at 580 or 6 2/5 stock at 312?\n\n### Options:\nA. 9% stock at 580\nB. Both are equally good\nC. 6 2/5 stock at 312\nD. None\nE. Cannot be compared, as the total amount of investment is not given\n\n### Answer:\nLet investment in each case be Rs. (580 x 312).\nIncome in 1st case = Rs. 9 x 580 x 312/580= Rs. 2808.\nIncome in 2nd case = Rs.32 x 580 x 312/(5*312)= Rs. 3712\nClearly, 6 2/5 stock at 312 is better.\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n50 percent of Andrea's living room floor is covered by a carpet that is 4 feet by 9 feet. What is the area of her living room floor?\n\n### Options:\nA. 14.4\nB. 180/7\nC. 50.4\nD. 64.8\nE. 90\n\n### Answer:\n50% of Area of the floor = 4*9 square feet = 36 square feet\ni.e. 100% Area of Floor = (36/50)*100 = 64.8 square feet\nAnswer: Option D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThree Englishmen and three Frenchmen work for the same company. Each of them knows a secret not known to others. They need to exchange these secrets over person-to-person phone calls so that eventually each person knows all six secrets. None of the Frenchmen knows English, and only one Englishman knows French. What is the minimum number of phone calls needed for the above purpose?\n\n### Options:\nA. 5\nB. 8\nC. 11\nD. 15\nE. 17\n\n### Answer:\nExplanation :\nLet a, b, c be the Englishmen and d, e, f be the Frenchmen.\nLet a be the Englishman who knows French. 'a' calls 'b & c' and now knows the secret of both of them. So now 'a' knows 'abc' secrets. 'd' calls 'e & f' and now knows the secret of both of them. So now 'd' knows 'def' secrets. 'a' now calls 'd', and exchange all secrets in French, so now 'a' and 'd' know all the 6 secrets. Now 'a' calls 'b & c' again, and 'd' calls 'e & f' again and tell all the secrets. So, totally 9 calls.\nAnswer : B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 8^x = 2^9, what is x?\n\n### Options:\nA. 2\nB. 3\nC. 4\nD. 5\nE. 6\n\n### Answer:\n2^3x= 2^9\n3x=9, therefore x=3\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the value of x from the equation:\nx^2\u22127x+10=0\n\n### Options:\nA. 5 or 2\nB. 4 or 1\nC. 4 or 2\nD. 6 or 1\nE. 7 or 4\n\n### Answer:\nHere we need to find out a and b such that a + b = -7 and ab = +10\na = -5 and b = -2 satisfies the above condition.\nHence\nx\n2\n\u2212\n7\nx\n+\n10\n=\n(\nx\n\u2212\n5\n)\n(\nx\n\u2212\n2\n)\nx2\u22127x+10=(x\u22125)(x\u22122)\nx\n2\n\u2212\n7\nx\n+\n10\n=\n0\n\u21d2\n(\nx\n\u2212\n5\n)\n(\nx\n\u2212\n2\n)\n=\n0\nx2\u22127x+10=0\u21d2(x\u22125)(x\u22122)=0\nStep 3: Equate each factor to 0 and solve the equations\n(\nx\n\u2212\n5\n)\n(\nx\n\u2212\n2\n)\n=\n0\n\u21d2\n(\nx\n\u2212\n5\n)\n=\n0\nor\n(\nx\n\u2212\n2\n)\n=\n0\n\u21d2\nx\n= 5 or 2\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA pipe can empty 2/3rd of a cistern in 12 mins. In 8 mins, what part of the cistern will be empty?\n\n### Options:\nA. 2/3\nB. 2/5\nC. 4/9\nD. 5/7\nE. 4/11\n\n### Answer:\n2/3 ---- 12\n? ----- 8 ==> 4/9\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the tens digit of positive integers m, y are 6, how many values of the tens digit of 2(m+y) can be there?\n\n### Options:\nA. 2\nB. 3\nC. 4\nD. 5\nE. 6\n\n### Answer:\nIf the tens digit of positive integers m, y are 6, how many values of the tens digit of 2(m+y) can be there?\nA. 2\nB. 3\nC. 4\nD. 5\nE. 6\n-> If m=y=60, 2(m+y)=240 is derived. If m=y=69, 2(m+y)=276 is derived, which makes 4,5,6,7 possible for the tens digit. Therefore, the answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the difference between the C.I. on Rs. 6000 for 1 1/2 years at 4% per annum compounded yearly and half-yearly?\n\n### Options:\nA. s.2.04\nB. s.2.08\nC. s.2.02\nD. s.2.83\nE. s.2.45\n\n### Answer:\nC.I. when interest is compounded yearly\n= [6000 * (1 + 4/100) * (1 + (1/2 * 4)/100]\n= 6000 * 26/25 * 51/50 = Rs. 6364.8\nC.I. when interest is compounded half-yearly\n= [6000 * (1 + 2/100)2]\n= (6000 * 51/50 * 51/50 * 51/50)\n= Rs. 6367.25 Difference\n= (6367.25 - 6364.8)\n= Rs.2.45.\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAn order was placed for a carpet whose length and width were in the ratio of 3 : 2. Subsequently, the dimensions of the carpet were altered such that its length and width were in the ratio 1 : 1 but were was no change in its perimeter. What is the ratio of the areas of the carpets?\n\n### Options:\nA. 4:5\nB. 9:10\nC. 14:15\nD. 19:20\nE. 24:25\n\n### Answer:\nLet the length and width of one carpet be 3x and 2x.\nLet the length and width of the other carpet be y and y.\n2(3x + 2x) = 2(y + y)\n5x = 2y\n(5/2) * x = y\nThe ratio of the areas of the carpet in both cases:\n= 3x * 2x : y * y\n= 6x^2 : y^2\n= 6x^2 : (25/4) * x^2\n= 24 : 25\nThe answer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain manufacturer of cake, muffin, and bread mixes has 140 buyers, of whom 50 purchases cake mix, 40 purchase muffin mix, and 20 purchase both cake mix and muffin mix. If a buyer is to be selected at random from the 100 buyers, what is the probability that the buyer selected will be one who purchases neither cake mix nor muffin mix?\n\n### Options:\nA. a. 1/10\nB. b. 3/10\nC. c. 1/2\nD. d. 7/10\nE. e. 3/14\n\n### Answer:\nC+M+B-CM-MB-CB-2CMB = 140\nC - cake buyers, M - muffin an0d B - Bread buyers. CM,MB,CB and CMB are intersecting regions.\nthe question asks for people who have bought only bread mixes = B-CB-MB-2CMB has to be found out.\n50 + 40 + B-CB-MB-20-2CMB = 140\nB-CB-MB-2CMB = 30\nhence the probability = 30/140 = 3/14.\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA 2-year certificate of deposit is purchased for K dollars. If the certificate earns interest at a n annual rate of 6 percent compound quarterly, which of the following represents the value, in dollars, of the certificate at the end of 2 years?\n\n### Options:\nA. k(1.06)^2\nB. k(1.06)^8\nC. k(1.015)^2\nD. k(1.015)^8\nE. k(1.03)^4\n\n### Answer:\nterm (n) = 2\nvalue of k at the end of 2 yrs, if compounded annually=k(1+r)^n=k(1+0.06)^2\nquarterly int. rate (r) = 1.5%\nterm (n) = 2x4 = 8\nvalue of k at the end of 2 yrs, if compounded qtrly =k(1+r)^n=k(1+0.015)^8\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe smallest of three consecutive even integers is 40 less than three times the largest. What is the largest of these integers?\n\n### Options:\nA. 14\nB. 17\nC. 18\nD. 19\nE. 20\n\n### Answer:\nlet the three numbers be a,b and c..\nnow The smallest of three consecutive even integers is 40 less than three times the largest means 3c-40=a..\n3c-a=40..\n2c+c-a=40..\nc-a=4, as a,b,and c are consecutive even integers..\n2c+4=40..\n2c=36 or c=18\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf Rs.7500 are borrowed at C.I at the rate of 4% per annum, then after 3 years the amount to be paid is?\n\n### Options:\nA. 8118\nB. 8127\nC. 8618\nD. 8436\nE. 8128\n\n### Answer:\nA = 7500(26/25)3\n= 8436\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the set S is composed of the following numbers {99, 100, 100, 105, 106, 115, 124}, which of the following is largest?\n\n### Options:\nA. The average (arithmetic mean) of set S\nB. The median of set S\nC. The mode of set S\nD. The range of set S\nE. The standard deviation of set S\n\n### Answer:\nA) 99, 100, 100, 105, 106, 115, 124 = 749 and its mean is 749/7 = 107.\nB) The list is of 7 numbers and median is 105.\nC) Mode is number of repetition of a number in the list , here it is 100.\nD) Range = Max value - min value = 124 -99 = 25.\nE) SD = square root of (sum of ( mean of series - number)^2 ) / n => < 100\nIMO option A is correct answer..\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo letters from the word JARKHANT are selected at random. What is the probability that at least one of the selected letters is a consonant?\n\n### Options:\nA. 40/28\nB. 30/28\nC. 50/28\nD. 26/28\nE. 27/28\n\n### Answer:\nThere are 6 consonants and 2 vowels in JARKHANT .\nprobability that at least one of the selected letters is a consonant = 1 - (Probability of both vowels)\nProbability of both vowels = 2C2/8C2 = 1/28\nSo,Answer is 1 - 1/28 = 27/28\nAnswer : E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe cost of carpeting a room 18 m long with a carpet 75 cm wide at 4.50 per metre is 810. The breadth of the room is:\n\n### Options:\nA. 7 m\nB. 7.5 m\nC. 8 m\nD. 8.5 m\nE. None of these\n\n### Answer:\nLength of the carpet = TotalCost/Rate/m\n= (8100\u204445)m = 180 m.\nArea of the room = Area of the carpet\n= (180 \u00d7 75\u2044100) m2 = 135 m2\n\u2234 Breadth of the room = AreaLength=135/18m\n= 7.5 m\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many consonants are present between the first and third vowel in the sequence of English alphabet ?\n\n### Options:\nA. 12\nB. 13\nC. 6\nD. 10\nE. None of these\n\n### Answer:\nExplanation:\nRef : A B C D E F G H I J K L M N O P Q R S T U V W X Y Z\nThe first and third vowels are A and I respectively. There are 7 letters between A and I; out of which 'E' is a vowel. Thus, there are 6 consonants between A and I.\nANSWER C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA and B started a business in partnership investing Rs.20,000 and Rs.15,000 respectively. After 6months, C joined them with Rs.20,000. Whatwill be B's share in total profit of Rs.25,000 earned at the end of 2years from the startingof the business?\n\n### Options:\nA. Rs. 5,000\nB. Rs. 5,500\nC. Rs. 5,700\nD. Rs. 6,500\nE. Rs. 7,500\n\n### Answer:\nA : B : C = (20,000 x 24) : (15,000 x 24) : (20,000 x 18) = 4 : 3 : 3.\nB's share = Rs. 25000 x\t3/10\t= Rs. 7,500.\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOn a counter of a donuts store, there are only 16 identical donuts, 11 filled with chocolate and 5 filled with jelly, but the seller tells me that the donuts are randomly placed on the counter. If would want to buy two, what is the probability that I choose one donuts of each flavor?\n\n### Options:\nA. 2/16\nB. 1/32\nC. 11/12\nD. 11/48\nE. 11/24\n\n### Answer:\nWe are told that we have 16 donuts, 11 of chocolate and 5 of jelly. The donuts are picked simultaneous and randomly, D1 and D2, in different flavors. There are two acceptable outcomes: 1) D1 is chocolate and D2 is jelly; 2) D1 is jelly and D2 is chocolate. Let's go: 1) D1 = (11/16)(5/15)= 11/48 chance of this happening. 2) D2 = (5/16)(11/15) = 11/48 chance of this happening. Then: (11/48)+(11/48)= 11/24, chance of getting the result that you wanted. Answer E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nEach truck from Jones Removal Company can haul 500 pounds of trash at a time.\nOn Wednesday the company has jobs to remove 1,500 pounds of trash from one\nsite, 500 from another site, and 2,500 from a third site. How many total pounds of\ntrash will be moved by Jones Company that day? How many trips will it take for the\nJones Company to remove all of the trash?\n\n### Options:\nA. 5500 lbs.-2 Trips\nB. 4500 lbs.-9 Trips\nC. 2500 lbs.-3 Trips\nD. 3500 lbs.-7 Trips\nE. 6500 lbs.-8 Trips\n\n### Answer:\nAdd: 1500 4,500 \u00f7 500 = 9\n2500\n+ 500\n4500\nAnswer 1: 4500 lbs. (Total) Answer 2: 9 Trips\ncorrect answer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe distance from City A to City B is 60 miles. While driving from City A to City B, Bob drives at a constant speed of 40 miles per hour. Alice leaves City A 30 minutes after Bob. What is the minimum constant speed in miles per hour that Alice must exceed in order to arrive in City B before Bob?\n\n### Options:\nA. 45\nB. 48\nC. 50\nD. 52\nE. 60\n\n### Answer:\nThe time it takes Bob to drive to City B is 60 / 40 = 1.5 hours.\nAlice needs to take less than 1 hour for the trip.\nAlice needs to exceed a constant speed of 60 / 1 = 60 miles per hour.\nThe answer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRahul's Mathematics test had 75 problems, 10 arithmetic, 30 algebra, 35 geometry problems.\nAlthough he answered 70% of arithmetic, 40% of arithmetic and 60% of geometry problems correctly,\nstill he got less than 60% problems right. How many more questions he would have to answer more to get\npassed\n\n### Options:\nA. 5\nB. 6\nC. 7\nD. 8\nE. 9\n\n### Answer:\nExplanation:\nNumber of questions attempted correctly = (70% of 10 + 40% of 30 + 60% of 35)\n= 7 + 12 + 21 = 40.\nQuestions to be answered correctly for 60% = 60% of total quations\n= 60 % of 75 = 45.\nHe would have to answer 45 - 40 = 5\nAnswer: Option A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nZada has to distribute 15 choclates among 5 of her children Sana,ada,jaya,amir and farhan. She has to make sure that sana gets at least 3 and ada at most 6 choclates. In how many ways can this be done?\n\n### Options:\nA. 495\nB. 77\nC. 417\nD. 435\nE. 455\n\n### Answer:\n(3,1,11)=165\n(4,1,10)=120\n(5,1,9)=84\n(6,1,8)=56\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow much interest can a person get on Rs. 6280 at 15.5% p.a. simple interest for a period of five years and six months?\n\n### Options:\nA. 5353.72\nB. 5353.71\nC. 5353.7\nD. 5353.73\nE. 5353.74\n\n### Answer:\nI = (6280 * 5.5 * 15.5)/100\n= (6280 * 11 * 31)/(100 * 2 * 2)\n= Rs. 5353.7\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA crew can row a certain course up the stream in 84 minutes; they can row the same course down stream in 6 minutes less than they can row it in still water. How long would they take to row down with the stream\n\n### Options:\nA. 45 or 23 minutes\nB. 63 or 12 minutes\nC. 78 minutes\nD. 19 minutes\nE. 25 minutes\n\n### Answer:\nA method has been discussed here to nullify the calculations though.\nAll I can input here is,\nspeed of a crew in still water = 1/2 ( speed upstream + speed downstream)\napproximating this for time,\nt = 1/2(84+ (t-6))\ngiving t = 78\nC.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf n is a positive integer, which of the following is a possible value of |71 - 5n| ?\n\n### Options:\nA. 7\nB. 5\nC. 19\nD. 15\nE. 20\n\n### Answer:\nWhen 71>5n, then |71- 5n| = 71- 5n = (70-5n) + 1 = {multiple of 5} + 1\nWhen 71<=5n, then |71 - 5n| = -(71- 5n) = (5n-70) - 1 = {multiple of 5} - 1\nSo, the correct answer must be 1 greater or 1 less than a multiple of 5. Only C fits.\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train covers a distance of 12 km in 10 minutes. If it takes 6 seconds to pass a telegraph post, then the length of the train is :\n\n### Options:\nA. 120 m\nB. 140 m\nC. 240 m\nD. 300 m\nE. None\n\n### Answer:\nSol.\nSpeed = [12/10 * 60] km/hr = [72 * 5/18] m/sec = 20 m/sec.\nLength of the train = (speed * Time) = (20 * 6) m = 120 m.\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMachine A produces pencils at a constant rate of 9000 pencils per hour, and machine B produces pencils at a constant rate of 7000 pencils per hour. If the two machines to gather must produce 100,000 pencils and if each machine can operate for at most 8 hours, what is the least amount of time S, in hours, that machine B must operate?\n\n### Options:\nA. 4\nB. 4 2/3\nC. 5 1/3\nD. 6\nE. 6 1/4\n\n### Answer:\nMachine A produces pencils at a constant rate of 9,000 pencils per hour, and machine B produces pencils at a constant rate of 7,000 pencils per hour. If the two machines together must produce 100,000 pencils and if each machine can operate for at most 8 hours, what is the least amount of time S , in hours, that machine B must operate?\na) 4\nb) 4 and 2/3\nc) 5 and 1/3\nd) 6\ne) 6 and 1/4\nTo minimize the time that machine B must operate we must maximize the time machine A can operate, so make it operate 8 hours. In 8 hours machine A will produce 8*9,000=72,000 pencils, so 100,000-72,000=28,000 pencils are left to produce, which can be produced by machine B in 28,000/7,000=4 hours.\nAnswer: A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe ratio of investments of two partners P and Q is 7:5 and the ratio of their profits is 7:10. If P invested the money for 5 months, find for how much time did Q invest the money?\n\n### Options:\nA. 7 months\nB. 10 months\nC. 9 months\nD. 11 months\nE. 8 months\n\n### Answer:\n7*5: 5*x = 7:10\nx = 10\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nDavid gets on the elevator at the 11th floor of a building and rides up at the rate of 57 floors per minute. At the same time, Albert gets on an elevator at the 51st floor of the same building and rides down at the rate of 63 floors per minute. If they continue travelling at these rates, then at which floor will their paths cross ?\n\n### Options:\nA. 19\nB. 28\nC. 30\nD. 37\nE. None\n\n### Answer:\nEXPLANATION\nSuppose their paths cross after x minutes.\nThen, 11 + 57x = 51 \u2013 63x <=> 120x = 40\nx= 1/3\nNumber of floors covered by david in (1/3) min = (1/3 x 57) = 19\nSo, their paths cross at (11 +19) i.e., 30th floor.\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA bag contains 3 red, 4 black and 2 white balls. What is the probability of drawing a red and a white ball in two successive draws, each ball being put back after it is drawn?\n\n### Options:\nA. 2/27\nB. 1/9\nC. 1/3\nD. 4/27\nE. 2/9\n\n### Answer:\nP=2\u22173/9\u22172/9=4/27\nWe are multiplying by 2 as there are two possible wining scenarios RW and WR.\nAnswer: D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTotal number of people attending a party is 600. 70% of the men are wearing black shirt and rest are wearing red. If 60% of the total people are women then how many men are wearing red shirts?\n\n### Options:\nA. 168\nB. 72\nC. 56\nD. 170\nE. 60\n\n### Answer:\nNumber of woman in the party = 0.60*600 = 360\nnumber of men in the party = 600-360 = 240\n% of men wearing red shirts = 100-70 = 30%\nnumber of men wearing red shirt = 0.30*240 = 72. B is the correct answer\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAn insect leaps 48 centimeters in 1.2 seconds. What is its speed?\n\n### Options:\nA. 0.4 meters per second\nB. 4 meters per second\nC. 40 meters per second\nD. 4 centimeters per second\nE. 0.4 centimeters per second\n\n### Answer:\n48 / 1.2 = 40 cm/s = 0.4 m/s\nThe answer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train running at the speed of 180 km/hr crosses a pole in 8 seconds. Find the length of the train.\n\n### Options:\nA. 150\nB. 88\nC. 480\nD. 288\nE. 400\n\n### Answer:\nSpeed = 180*(5/18) m/sec = 50 m/sec\nLength of Train (Distance) = Speed * Time\n50 *8 = 400 meter\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRs.1560 is divided so that 4 times the first share, thrice the 2nd share and twice the third share amount to the same. What is the value of the third share?\n\n### Options:\nA. s.528\nB. s.542\nC. s.528\nD. s.720\nE. s.549\n\n### Answer:\nA+B+C = 1560\n4A = 3B = 2C = x\nA:B:C = 1/4:1/3:1/2 = 3:4:6\n6/13 * 1560 = Rs.720\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn the fifth grade at Parkway elementary school there are 420 students. 312 students are boys and 250 students are playing soccer. 82% of the students that play soccer are boys. How many girl student are in Parkway that is not playing soccer?\n\n### Options:\nA. 63.\nB. 73.\nC. 81\nD. 91\nE. 108\n\n### Answer:\nTotal students = 420\nBoys = 312, Girls = 108\nTotal playing soccer = 250\n82%of 250 = 205 are boys who play soccer.\nGirls who play soccer = 45.\nTotal girls who do not play soccer = 108 - 45 = 63.\nCorrect option: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA boat can move upstream at 20 kmph and downstream at 35 kmph, then the speed of the current is?\n\n### Options:\nA. 5\nB. 6\nC. 7.5\nD. 8\nE. 9\n\n### Answer:\nUS = 20\nDS = 35\nM = (35 - 20)/2 = 7.5\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat will be the difference between simple interest and compound interest @10% per annum on a sum of Rs. 1000 after 4 years?\n\n### Options:\nA. Rs. 31\nB. Rs. 32.10\nC. Rs. 40.40\nD. Rs. 64.10\nE. None\n\n### Answer:\nSolution\nS.I.\t=Rs(1000x10x4 / 100)\n= Rs.400.\nC.I.\t=Rs.[1000x(1x10/100)4-1000]\n= Rs. 464.10\n\u2234 Difference = Rs.(464.10 - 400)\n= Rs. 64.10\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nStella buys an advertising agency for rs.16,000,000 and sells it for rs.20,000,000. Find her gain %.\n\n### Options:\nA. 9%\nB. 20%\nC. 14%\nD. 87%\nE. 25%\n\n### Answer:\nsol. cp=rs16,000,000, sp=rs 20,000,000\ngain=rs(20,000,000 \u201316,000,000)=rs4,000,000\nso gain%={(4,000,000/16,000,000)*100}=25%\nAnswer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA welder received an order to make a 1 million liter cube-shaped tank. If he has only 4x2 meter sheets of metal that can be cut, how many metal sheets will be required for this order P? (1 cubic meter = 1,000 liters)\n\n### Options:\nA. 92\nB. 90\nC. 82\nD. 78\nE. 75\n\n### Answer:\nI get 75. A cube with 1 million liters cube would be a cube with the dimensions of 100*100*100. 4*2 covers 8 sq liters so 100/8 = 12.5.\nP=12.5*6 = 75.E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA salesman travels a distance of 100 km in 5hours. How much faster in kilometer per hour, on an average, must he travel to make such trip in 1 hour less time?\n\n### Options:\nA. 2km/hr\nB. 3km/hr\nC. 5km/hr\nD. 7km/hr\nE. 10km/hr\n\n### Answer:\nTime required = 5 hrs- 1hr = 4hr\nRequired speed = 100/4 = 25km/hr\nOriginal speed = 100/5 = 20 km/hr\nDifference = 25-20 = 5 km/hr\nAnswer is C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn Cliff\u2019s impressive rock collection, there are half as many igneous rocks as sedimentary rocks. Of the igneous rocks, 4/5 are shiny and the rest are matte, while 1/5 of the sedimentary rocks are shiny. If there are 40 shiny igneous rocks, how many total rocks does Cliff have?\n\n### Options:\nA. 30\nB. 150\nC. 60\nD. 90\nE. 135\n\n### Answer:\nWe can start with the known quantity and then go on to find the others.\nShiny igneous ricks are 40. These are (4/5) of total igneous rocks.\n(4/5)*Total igneous rocks = 40\nTotal igneous rocks = 40 * (5/4) = 50\nTotal sedimentary rocks = 2*Total igneous rocks = 2*50 = 100\nTotal number of rocks = 50 + 100 = 150\nAnswer (B)\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOut of a total of 1,000 employees at a certain corporation, 52 percent are female and 40 percent of these females work in research. If 65 percent of the total number of employees work in research, how many male employees do NOT work in research?\n\n### Options:\nA. 520\nB. 480\nC. 392\nD. 208\nE. 38\n\n### Answer:\ntotal number of female employees =52% =520\nfemale employees working in research =(2/5)*520=208\nTotal no of employees working in research =65% =650\nTotal male employees =48%=480\nmale employees working in research =650-208=442\nmale employees not working in research =480-442=38\nAnswer E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man purchased 3 blankets @ Rs.100 each, 5 blankets @ Rs.150 each and two blankets at a certain rate which is now slipped off from his memory. But he remembers that the average price of the blankets was Rs.150. Find the unknown rate of two blankets?\n\n### Options:\nA. 289\nB. 278\nC. 211\nD. 450\nE. 476\n\n### Answer:\n10 * 150 = 1500\n3 * 100 + 5 * 150 = 1050\n1500 \u2013 1050\n= 450\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn an examination 35% of the students passed and 481 failed. How many students appeared for the examination?\n\n### Options:\nA. A)540\nB. B)400\nC. C)700\nD. D)740\nE. E)840\n\n### Answer:\nLet the number of students appeared be x\nthen, 65% of x = 481\n65x/100 = 481\nx = 481*100/65 = 740\nAnswer is D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWalking across campus, a student interviewed a group of students. 25% of the students took a finance class last semester, 55% took a marketing class last semester, and 40% took neither a finance nor a marketing class last semester. What percent of the students in the group took both a finance and a marketing class?\n\n### Options:\nA. 60%\nB. 50%\nC. 25%\nD. 20%\nE. 10%\n\n### Answer:\n{Total} = {finance} + {marketing} - {both} + {neither}\n100 = 25 + 55 - {both} + 40\n{both} = 20%.\nAnswer: D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA building contractor employs 20 male, 15 female and 5 child workers. To a male worker he pays Rs.25 per day, to a female worker Rs.20 per day and a child worker Rs.8 per day. The average wage per day paid by the contractor is?\n\n### Options:\nA. 22\nB. 21\nC. 77\nD. 88\nE. 66\n\n### Answer:\n20 15 5\n25 20 8\n500 + 300 + 40 = 840/40 = 21\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\none men and three women working 7 hours a day finish a work in 5 days. Four men and four women working 3 hours a day complete the work in 7 days. The number of days in which only 7 men working 4 hours a day will finish the work is?\n\n### Options:\nA. 4 days\nB. 5 days\nC. 6 days\nD. 7 days\nE. 8 days\n\n### Answer:\n1M + 3W ----- 35 h\n4M + 4W ------- 21 h\n7M -------? d\n35M + 105W = 84M +84M\n21W = 49M\n4 * 35 = 7 * x => x = 20 hours\n20/4 = 5 days\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA hiker walked for 3 days. She walked 25 miles on the first day, walking 5 miles per hour. On the second day she walked for one less hour but she walked one mile per hour, faster than on the first day. On the third day she walked the same number of hours as on the first day, but at the same speed as on the second day. How many miles in total did she walk?\n\n### Options:\nA. 24\nB. 79\nC. 58\nD. 60\nE. 62\n\n### Answer:\nShe walked 25 miles on the first day, walking 5 miles per hour i.e. total time of walk on Day-1 = 25/5 = 5 Hours\nSecond day time of walk = 5-1 = 4 hours and Speed = 5+1=6 miles per hour i.e. Distance walked on second day = 4*6 = 24 miles\nThird day time of walk = 5 hours and Speed = 6 miles per hour i.e. Distance walked on second day = 5*6 = 30 miles\nTotal Distance travelled on three days = 25+24+30 = 79\nAnswer: Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA 300 meter long train crosses a platform in 39 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform?\n\n### Options:\nA. 227\nB. 266\nC. 230\nD. 288\nE. 271\n\n### Answer:\nSpeed = [300 / 18] m/sec = 50/3 m/sec.\nLet the length of the platform be x meters.\nThen, x + 300 / 39 = 50/3\n3(x + 300) = 1950 \u00e8 x = 350m.\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a 100 m race, A can beat B by 25 m and B can beat C by 4 m. In the same race, A can beat C by:\n\n### Options:\nA. 21\nB. 22\nC. 28\nD. 25\nE. 30\n\n### Answer:\nA:B = 100:75\nB:C=100:96\nA:C = 100/72 = 100:72\nA beats(100-72) = 28 m\nANSWER C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nExcluding stoppages, the speed of a train is 55 kmph and including stoppages it is 30 kmph. Of how many minutes does the train stop per hour?\n\n### Options:\nA. 82\nB. 27\nC. 12\nD. 82\nE. 18\n\n### Answer:\nExplanation:\nT = 25/55 * 60 = 27\nAnswer: Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA straight line in the xy- plane has a slope of 4 and a y-intercept of 4. On this line, what is the x-coordinate of the point whose y-coordinate is 800 ?\n\n### Options:\nA. 233\nB. 299\nC. 333\nD. 199\nE. 339\n\n### Answer:\nEq of line = Y = MX +C\nM = 4,\nC= 4\nY=4X + 4,\nSubstitute Y by 800 as given in question.\n800=4X+4 , X = 199.\ncorrect option is D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA school has 30% students from Maharashtra .Out of these 20% are Bombey students. Find the total percentage of Bombay?\n\n### Options:\nA. 3%\nB. 4%\nC. 5%\nD. 6%\nE. 7%\n\n### Answer:\nIf total no of students is 100.\nNo of students from Maharashtra = 30\nNo of students from Bombay = 30*20/100 = 6\nso 6% students are from Bombay\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train running at the speed of 60 km/hr crosses a pole in 15 seconds. Find the length of the train?\n\n### Options:\nA. 150 meter\nB. 170 meter\nC. 250 meter\nD. 168 meter\nE. 154 meter\n\n### Answer:\nSpeed = 60*(5/18) m/sec\n= 50/3 m/sec\nLength of Train (Distance)\n= Speed * Time\n(50/3) * 15\n= 250 meter\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHaving received his weekly allowance, John spent 3/5 of his allowance at the arcade. The next day he spent one third of his remaining allowance at the toy store, and then spent his last $0.60 at the candy store. What is John\u2019s weekly allowance?\n\n### Options:\nA. $2.25\nB. $3.00\nC. $3.25\nD. $3.65\nE. $4.80\n\n### Answer:\nx = 3x/5 + 1/3*2x/5 + 60\n4x/15 = 60\nx = 225 = $2.25\nThe answer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSimplify: 18800+470+20\n\n### Options:\nA. 4\nB. 1\nC. 5\nD. 2\nE. 3\n\n### Answer:\n18800+470+20=(18800/470)+20=40/20=2.\nAnswer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMurali travelled from city A to city B at a speed of 40 kmph and from city B to city C at 60 kmph. What is the average speed of Murali from A to C given that the ratio of distances between A to B and B to C is 2 : 3?\n\n### Options:\nA. 70 kmph\nB. 50 kmph\nC. 57 kmph\nD. 54 kmph\nE. 70 kmph\n\n### Answer:\nLet the distances between city A to B and B to C be 2x km and 3x km respectively.\nTotal time taken to cover from A to C\n= (2x)/40 + (3x)/60\n= (6x + 6x)/120 = 12x/120\n= x/10 Average speed\n= (2x + 3x)/(x/10) = 50 kmph.\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA wheel rotates 20 times every minute and moves 15 cm during each rotation. How many metres does the wheel move in one hour?\n\n### Options:\nA. 6 metre\nB. 18 metre\nC. 180 metre\nD. 1200 metre\nE. 130 metre\n\n### Answer:\nNumber of times wheel moves in 1 hour = 12 * 60 = 1200\n:. Distance moves = (1200*15) cms = 18000 cms\nIn metres = 180 metre\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo trains 140 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is?\n\n### Options:\nA. 12.9 sec\nB. 29.0 sec\nC. 28.9 sec\nD. 10.8 sec\nE. 12.3 sec\n\n### Answer:\nRelative speed = 60 + 40 = 100 km/hr.\n= 100 * 5/18 = 250/9 m/sec.\nDistance covered in crossing each other = 140 + 160 = 300 m.\nRequired time = 300 * 9/250 = 54/5 = 10.8 sec.\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a(a - 6) = 27 and b(b - 6) = 27, where a \u2260 b, then a + b =?\n\n### Options:\nA. \u221248\nB. \u22122\nC. 46\nD. 6\nE. 48\n\n### Answer:\ni.e. if a =-3 then b = 9\nor if a = 9 then b =-3\nBut in each case a+b = -3+9 = 6\nAnswer: option D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average marks of 25 students in a class is 100. But a student mark is wrongly noted as 60 instead of 10 then find the correct average marks?\n\n### Options:\nA. A)78\nB. B)82\nC. C)98\nD. D)91\nE. E)85\n\n### Answer:\ncorrect avg marks = 100+(10-60)/25\navg = 100-2 = 98\nAnswer is C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf f(x)=4x\u22121 and g(x)=2x+6 for all integers, which of the following is a possible value of g(f(x))?\n\n### Options:\nA. -23\nB. -17\nC. 0\nD. 8\nE. 20\n\n### Answer:\ng(f(x)) = 2*f(x)+6 = 2*(4x-1)+6 = 8x+4\nOf these five options, only 20 has the form 8x+4.\nThe answer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat amount does Kiran get if he invests Rs. 18000 at 15% p.a. simple interest for two years?\n\n### Options:\nA. 29893\nB. 27773\nC. 29989\nD. 28800\nE. 23400\n\n### Answer:\nSimple interest = (18000 * 2 * 15)/100 = Rs. 5400\nAmount = P + I = 18000 + 5400 = Rs. 23400\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA corporation paid $8 million in federal taxes on its first $50 million of gross profits and then $30 million in federal taxes on the next $150 million in gross profits. By approximately what percent did the ratio of federal taxes to gross profits increase from the first $50 million in profits to the next $150 million in profits?\n\n### Options:\nA. 6%\nB. 14%\nC. 20%\nD. 23%\nE. 86%\n\n### Answer:\nDifference in Ratios = (30/150) - (8/50) = (6/50)\n% Change = (Change (6/50) / Original ratio (7/50)) *100 = 86%\nAnswer - E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA 600 meter long train crosses a signal post in 40 seconds. How long will it take to cross a 1.8 kilometer long bridge, at the same speed?\n\n### Options:\nA. 4 min\nB. 2 min\nC. 8 min\nD. 9 min\nE. 3 min\n\n### Answer:\nS = 600/40 = 15 mps\nS = 1800/15 = 120 sec = 2 min.Answer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n3x^2-6x+3 = 0 Find the above equation find the value of x\n\n### Options:\nA. 0\nB. 1\nC. 2\nD. 4\nE. 6\n\n### Answer:\na = 3, b = -6, c = 3\nx1,2 = (6 \u00b1 \u221a( (-6)2 - 4\u00d73\u00d73)) / (2\u00d73) = (6 \u00b1 \u221a(36-36)) / 6 = (6 \u00b1 0) / 6\nx1 = x2 = 1\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA woman takes 5hr 45min in walking to certain place and riding back. She would have gained 2hrs by riding both ways. The time she would take to walk both ways is?\n\n### Options:\nA. 6 hr 45 min\nB. 3 hr 45 min\nC. 8 hr 55 min\nD. 7 hr 45 min\nE. 4 hr 60 min\n\n### Answer:\nD\n7 hr 45 min\nLet x be the speed of walked\nLet y be the speed of ride\nLet D be the distance\nThen D/x + D/y = 23/4 hr -------------------(1)\nD/y + D/y = 23/4 \u2013 2 hr\nD/y = 15/8 ----------------------------------(2)\nsubstitute 2 in 1\nD/x + 15/8 = 23/4\nD/x = 23/4 -15/8 =46-15/8 =31/8\nTime taken for walk one way is 31/8 hr\ntime taken to walk to and fro is 2*31/8 = 31/4 hr\n=7 hr 45 min\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA company issued 20000 shares of par value Rs. 10 each. If the total divided declared by the company is Rs.24000, find the rate of dividend paid by the company.\n\n### Options:\nA. 10\nB. 11\nC. 12\nD. 13\nE. 15\n\n### Answer:\nNumber of shares = 20000\nFace value of each share = Rs.10\ndivided per share = 10\u00d7R/100 where R is the rate of interest\nTotal divided = 20000\u00d710\u00d7R/100\n20000\u00d710\u00d7R/100=24000\n\u21d2R=24000/2000=12\nie, divided = 12%\nAnswer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a hostel, the number of students decreased by 12% and the price of food increased by 20% over the previous year. If each student consumes the same amount of food then By how much should the consumption of food be cut short by every student, so that the total cost of the food remains the same as that of the previous year?\n\n### Options:\nA. 19%\nB. 15%\nC. 25%\nD. 40%\nE. 5.3%\n\n### Answer:\nCost of food (C) = Food consumed per student (F) * Number of students (N) * Price of food (P)\nOriginally,\nC = FNP\nWhen number of students decrease by 12%, and the price of food increases by 20%,\nC = F(new) * (0.88N) * (1.2P)\n=> F(new) = F/(0.88*1.2)\n=> F(new) = 0.9469F\nTherefore the new cost of food must be 94.69% of the old cost, or the cost of food must decrease by 5.3% (option E)\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nif integer N has p factors ; how many factors will 5N have ?\n\n### Options:\nA. p\nB. 2p\nC. P+1\nD. 2p+1\nE. Cannot be determined\n\n### Answer:\nCase 1:\nLet N = 6 => 2 x 3 (prime factorization) => p = 4;\n5N =30 => no. of factors = 8; (p+2)\nCase 2:\nLet N = 7 => p = 2;\n5N = 35 => no of factors = 4; (p+2)\nFor different N different results are observed. So, shouldn't E be the right answer?\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA and B began business with Rs.3000 and Rs.4000 after 8 months, A withdraws Rs.1000 and B advances Rs.1000 more. At the end of the year, their profits amounted to Rs.630 find the share of A ?\n\n### Options:\nA. 240\nB. 388\nC. 208\nD. 112\nE. 102\n\n### Answer:\nThe ratio of A & B investments = (3x8 + 2x4):(4x8 + 5x4)\n=> 8:13\n=> 8/21 x 630 = 240.\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a panel of 10 light bulbs, the odds of any light bulb to burn out are 0.02 at any given 10 minutes. Should a light bulb burn out, the whole panel would instantly turn off. What are the odds that the panel would be turned off within the first 10 minutes after it was switched on?\n\n### Options:\nA. 1-0.02^10\nB. 1-0.98^10\nC. (1-0.98)^10\nD. 0.06\nE. 1-10*0.06\n\n### Answer:\nans B.\nProb that light will not turned off = 0.98^10. Hence prob (turn off) = 1 - prob (not turn off).\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a particular year, the month of january had exactly 4 thursdays, and 4 sundays. On which day of the week did january 1st occur in the year.\n\n### Options:\nA. 33\nB. Monday\nC. 299\nD. 299\nE. 277\n\n### Answer:\nAns: If a month has 31 days, and it starts with sunday, Then Sundays, Mondays, tuesdays are 5 for that month. If this month starts with monday, then mondays, tuesdays, and wednesdays are 5 and remaining days are 4 each. so this month start with Monday.\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA metallic hemisphere is melted and recat in the shape of a cone with the same base radius (R) as that of the hemisphere. If H is the height of the cone, then :\n\n### Options:\nA. H = 2R\nB. H = 4R\nC. H = \u221a4R\nD. H = 2/3 R\nE. None\n\n### Answer:\nSol.\n2/3 \u220fR\u00b3 = 1/3 \u220fR\u00b2H \u21d2 H = 2R.\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe diagonals of a rhombus are 12 cm and 20 cm. Find its area?\n\n### Options:\nA. 176\nB. 186\nC. 120\nD. 179\nE. 172\n\n### Answer:\n1/2 * 12 * 20\n= 120\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain clock marks every hour by striking a number of times equal to the hour,and the time required for a stroke is exactly equal to the time interval between strokes. At 6:00 the time lapse between the beginning of the first stroke and the end of the last stroke is 11 seconds. at 12:00 ,how many seconds elapse between the beginning of the first stroke and the end of the last stroke?\n\n### Options:\nA. A.72\nB. B.50\nC. C.48\nD. D.46\nE. E.23\n\n### Answer:\nAt 6:00 it'll chime 6 times. If we assume that the time taken to chime is x, then time between chimes is also x. So you have 6 chimes, which is 6x and 5 time intervals between chimes. This means that 11x = 11 seconds. Thus x = 1 seconds.\nBy a similar logic, at 12:00, there are 12 chimes and 11 intervals so the total time is (12+11)x = 23x = 23 seconds.\nAnswer E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nCity A to city B, Andrew drove for 1 hour at 50 mph and for 3 hours at 60 mph. What was the average speed for the whole trip?\n\n### Options:\nA. 57\nB. 57.5\nC. 58.2\nD. 59\nE. 62\n\n### Answer:\nThe total distance is 1\u00d750+3\u00d760=2301\u00d750+3\u00d760=230. And the total time is 4 hours. Hence,\nAverage Speed=(Total DistanceTotal Time)=2304=57.5\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nDavid and Rachel are getting married. The extended family wants to have its picture taken, but David's father is unwilling to stand next to Rachel's mother. How many options does the photographer have to arrange the 13 family members in a row for the picture?\n\n### Options:\nA. 14!\nB. 12\u00d711!\nC. 11\u00d712!\nD. 13!/2!\nE. 13!\n\n### Answer:\nThe number of ways to arrange 13 people is 13!\nWe need to subtract the arrangement when these two people are together.\nLet's think of these two people as a single unit so there are 12 units.\nThe number of ways to arrange 12 units is 12!\nWe need to multiply this by 2 since these two people could switch places.\nThe total number of valid arrangements is 13! - 2*12! = 12!*(13-2) = 11x12!\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOne used-car salesperson receives a commission of $ 200 plus 4 percent of $ 1,000 less than the car\u2019s final sale price. Another car salesperson earns a straight commission of 4 percent of the car\u2019s final sale price. What is the final sale price of a car if both salespeople would earn the same commission for selling it?\n\n### Options:\nA. $ 5,000\nB. $ 6,000\nC. $ 8,000\nD. $ 10,000\nE. $ 12,000\n\n### Answer:\nThis question can be solved by TESTing THE ANSWERS.\nWe're given the pay rate of two different salespeople who sell cars:\n1) A commission of $ 200 plus 4 percent of $ 1,000 less than the car\u2019s final sale price.\n2) A straight commission of 6 percent of the car\u2019s final sale price.\nWe're asked for the final sale price of a car if both salespeople would earn the SAME commission for selling it?\nLet's TEST Answer B: $6,000\n1st salesperson = $200 + .04(6,000 - 1,000) = $200 + .04(5,000) = $200 + $200 = $400\n2nd salesperson = .06(6,000) = $360\nThese totals are NOT the same, so we can eliminate B. Looking at the two pay 'formulas', we can see that the 2nd salesperson will make more money than the 1st when the price of the car increases to a significant level, so we need a price that is HIGHER than $6,000. Since the difference in pay is relatively small in Answer B, we're likely looking for a number that is fairly close to $6,000 though...\nLet's TEST Answer C: $8,000\n1st salesperson = $200 + .04(8,000 - 1,000) = $200 + .04(7,000) = $200 + $280 = $480\n2nd salesperson = .06(8,000) = $480\nThese totals are the SAME, so this must be the answer.\nFinal Answer:\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAnnie and Sam set out together on bicycles traveling at 15 and 12 km per hour respectively. After 40 minutes, Annie stops to fix a flat tire. If it takes Annie 35 minutes to fix the flat tire and Sam continues to ride during this time, how many minutes will it take Annie to catch up with Sam assuming that Annie resumes riding at 15 km per hour?\n\n### Options:\nA. 20\nB. 40\nC. 60\nD. 80\nE. 100\n\n### Answer:\nAnnie gains 3 km per hour (or 1 km every 20 minutes) on Sam.\nAfter 40 minutes Annie is 2 km ahead.\nSam rides 1 km every 5 minutes.\nIn the next 35 minutes, Sam rides 7 km so Sam will be 5 km ahead.\nIt will take Annie 100 minutes to catch Sam.\nThe answer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA batsman makes a score of 64 runs in the 16th innings and thus increased his average by 3. Find his average after the 16th inning?\n\n### Options:\nA. 22\nB. 299\nC. 277\nD. 19\nE. 77\n\n### Answer:\nLet the average after the 16th inning be P.\nSo, the average after the 15th inning will be (P-3) Hence, 15(P-30) + 64 = 16P => P = 19.Answer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo sets A and B consists only of positive integers such that mean of set A is 70 . If set R consist of all the elements of both A and B such that mean of R is 80 then the mean of set B is =>\n\n### Options:\nA. [A] 65\nB. [B] 60\nC. [C] 70\nD. [D] 55\nE. [E] cannot be determined\n\n### Answer:\nFor this question, we have zero information about the size of two sets, sets AB. These two sets may have the same size or may be wildly different. Thus, the answer is (E), the mathematical answer cannot be determined. This is a very weak math question. As someone who writes GMAT practice questions, I would give this a grade of anD-as a question.\nAnswer E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a tap could fill entire tank in 20 hrs due to leakage, then in how much time\ntank can be emptied by leakage if tap can fill entire tank in 12 hrs without leakage\n\n### Options:\nA. 30hrs\nB. 24hrs\nC. 36hrs\nD. 48hrs\nE. 52hrs\n\n### Answer:\ntime take to fill[withleakage] =20hrs so workdone in 1hr=1/20\ntime tkae to fill[without leakage]=12hrs so workdone in 1hr=1/12\nif u subtract both u'll get time taken by leakage to empty...\n1/20-1/12=2/60 = 1/30 so 30hrs\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAdam's mother is 26 years older than him. Next year, however, she will be 3 times older than her son. How old is Adam's mother?\n\n### Options:\nA. 35 years\nB. 36 years\nC. 37 years\nD. 38 years\nE. 39 years\n\n### Answer:\nAt the present\nAdam is x years old.\nAdam's mother is y=x+26 years old.\nNext year\nAdam will be x+1 years old.\nAdams mother will be y+1=3 (x+1) years old.\nIf we combine the two equations,\ny=x+26, and\ny+1=3 (x+1), then\nx+26+1=3x+3\n2x=27-3\n2x=24\nx=12\nThis is Adam's age at the moment. Since his mother is 26 years older than him, her age is 12+26=38.\nANSWER: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe H.C.F. of two numbers is 12 and their L.C.M. is 600. If one of the number is 20, find the other?\n\n### Options:\nA. 100\nB. 360\nC. 120\nD. 200\nE. 150\n\n### Answer:\nOther number = 12*600/20= 360\nAnswer is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow much is 60% of 40 is greater than 4/5 of 25?\n\n### Options:\nA. 4\nB. 6\nC. 10\nD. 8\nE. 13\n\n### Answer:\n60/100) * 40 \u00e2\u20ac\u201c (4/5) * 25\n24 - 20 = 4\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRahul went to a shop and bought things worth Rs. 27, out of which 30 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?\n\n### Options:\nA. Rs 15\nB. Rs 12.10\nC. Rs 21.70\nD. Rs 16.80\nE. None of these\n\n### Answer:\nExplanation :\nLet the cost of the tax items = x\nGiven that tax rate = 6%\nCost of tax items, x*(6/100) = 30/100\nx = 5 rs\nNow non taxable item = total cost - cost for taxable item - tax\n= 27 - 5 - 0.30\n=21.70\nAnswer : C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the median and mean of the following test scores:\n75, 40, 100, 50, 45, 60, 50, 70, 45, 95\nWhich score falls in between the two scores?\n\n### Options:\nA. 40\nB. 50\nC. 60\nD. 70\nE. 75\n\n### Answer:\nList in order: 40,45,45,50,50,60,70,75,95,100\nThe median = (the average of two middle terms) = (50 + 60)/2 = 55.\nThe mean = (the sum)/(# of terms) = 630/10 = 63.\nThe Test Score between 55 and 63 is 60.\nAnswer: C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n75 percent of Andrea's living room floor is covered by a carpet that is 4 feet by 9 feet. What is the area of her living room floor?\n\n### Options:\nA. 48\nB. 180/7\nC. 50.4\nD. 60\nE. 90\n\n### Answer:\n75% of Area of the floor = 4*9 square feet = 36 square feet\ni.e. 100% Area of Floor = (36/75)*100 = 48 square feet\nAnswer: Option A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train leaves Delhi at 9 a.m. at a speed of 35 kmph. Another train leaves at 2 p.m. at a speed of 40 kmph on the same day and in the same direction. How far from Delhi, will the two trains meet?\n\n### Options:\nA. 229\nB. 288\nC. 600\nD. 888\nE. 1400\n\n### Answer:\nD = 35 * 5 = 175\nRS = 40 \u2013 35 = 5\nT = 175/5 = 35\nD = 40 * 35 = 1400 km\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nBy travelling at 40 kmph, a person reaches his destination on time. He covered two-third the total distance in one-third of the total time. What speed should he maintain for the remaining distance to reach his destination on time?\n\n### Options:\nA. 20 kmph\nB. 24 kmph\nC. 22 kmph\nD. 28 kmph\nE. 29 kmph\n\n### Answer:\nA\n20 kmph\nLet the time taken to reach the destination be 3x hours. Total distance = 40 * 3x = 120x km\nHe covered 2/3 * 120x = 80x km in 1/3 * 3x = x hours So, the remaining 40x km, he has to cover in 2x hours. Required speed = 40x/2x = 20 kmph.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the odd man out. 5,7,9,12,13\n\n### Options:\nA. 52\nB. 12\nC. 11\nD. 14\nE. 10\n\n### Answer:\nExplanation :\n5+2=7\n7+2=9\n9+2=11\n11+2=13\nHence, it is clear that 11 should have come instead of 12\nAnswer : Option C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how many years will a sum of money doubles itself at 5% per annum on simple interest?\n\n### Options:\nA. 80%\nB. 20%\nC. 28%\nD. 90%\nE. 30%\n\n### Answer:\nP = (P*5*R)/100\nR = 20%\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA tap can fill a tank in 6 hours. After half the tank is filled then 3 more similar taps are opened. What will be total time taken to fill the tank completely.\n\n### Options:\nA. 2 hours 30 mins\nB. 2 hours 45 mins\nC. 3 hours 30 mins\nD. 3 hours 45 mins\nE. None of these\n\n### Answer:\nExplanation:\nHalf tank will be filled in 3 hours\nLets calculate remaining half,\nPart filled by the four taps in 1 hour = 4*(1/6) = 2/3\nRemaining part after 1/2 filled = 1-1/2 = 1/2\n2/3:1/2::1:X\n=>X=(1/2\u22171\u221732)\n=>X=3/4hrs=45 mins\nTotal time = 3 hours + 45 mins = 3 hours 45 mins\nOption D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the simple interest on Rs. 3000 at 6 1/4% per annum for the period from\n4th Feb., 2005 to 18th April, 2005.\n\n### Options:\nA. Rs.36.50\nB. Rs.37.50\nC. Rs.35.50\nD. Rs.32.50\nE. Rs.33.50\n\n### Answer:\nTime = (24+31+18)days = 73 days = 73/365 years = 1/5 years.\nP = Rs.3000 and R = 6 \u00bc %p.a = 25/4%p.a\nS.I. = Rs.(3,000*(25/4)*(1/5)*(1/100))= Rs.37.50.\nRemark : The day on which money is deposited is not counted while the day on which money is withdrawn is counted\nAnswer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a theatre all rows have same no. Of . One family buys 10 tickets of first two row. 3 members want to sit in first row and 2 in second row. In how many ways they can be seated.\n\n### Options:\nA. 5400\nB. 5500\nC. 5600\nD. 5700\nE. 5800\n\n### Answer:\n10c3x10c2= 5400\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA family consists of grandparents, parents and three grandchildren. The average age of the grandparents is 67 years, that of the parents is 35 years and that of the grandchildren is 6 years. What is the average age of the family?\n\n### Options:\nA. 31 5/8 years\nB. 31 5/7 years\nC. 31 9/7 years\nD. 38 5/7 years\nE. 31 5/4 years\n\n### Answer:\nRequired Average = [(67 * 2) + (35 * 2 ) + (6 * 3)]/(2 + 2 + 3)\n= (134 + 70 + 18)/7\n= 31 5/7 years.\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average age of 40 passengers in a ferry is 35. What is the average age of the new group formed when combining the passengers with the 5 crew members of ferry whose average age is 25?\n\n### Options:\nA. 36.45\nB. 38.89\nC. 39.67\nD. 40.12\nE. 41.88\n\n### Answer:\nSum of ages of passengers= 40x35= 1400\nSum of ages of crew= 25x5= 125\nSum of ages of new group formed= 1525\nAverage=1525/45=38.89\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain characteristic in a large population has a distribution that is symmetric about the mean m. If 68 percent of the distribution lies within one standard deviation d of the mean, what percent W of the distribution is less than m +d ?\n\n### Options:\nA. 16%\nB. 32%\nC. 48%\nD. 84%\nE. 92%\n\n### Answer:\nD\nThe prompt says that 68% of the population lies between m-d and m+d.\nThus, 32% of the population is less than m-d or greater than m+d.\nSince the population is symmetric, half of this 32% is less than m-d and half is greater than m+d.\nThus, W=(68+16)% or (100-16)% of the population is less than m+d.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA, B and C rents a pasture for Rs.841. A put in 12 horses for 8 months, B 16 horses for 9 months and 18 horses for 6 months. How much should C pay?\n\n### Options:\nA. 270\nB. 279\nC. 276\nD. 261\nE. 262\n\n### Answer:\n12*8 :16*9 = 18*6\n8: 12: 9\n9/29 * 841 = 261\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nwhat is the Max number of rectangular boxes, each measuring 5 inches by 2 inches by 7 inches, that can be packed into a rectangular packing box measuring 15 inches by 20 inches by 35 inches, if all boxes are aligned in the same direction?\n\n### Options:\nA. 200\nB. 350\nC. 100\nD. 150\nE. 120\n\n### Answer:\nThe 5 inch side should be aligned to the 15 inch side ( 3 layer)\n2 inch side should be aligned to the 20 inch side. (10 layer)\n7 inch side should be aligned to the 35 inch side.(5 layer)\nMaximum number of rectangles =3*10*5=150\nAnswer is D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA dealer sold two of his cattle for Rs. 500 each. On one of them he lost 10% on the other, he gained 10%. His gain or loss percent in the entire transaction was:\n\n### Options:\nA. 10% loss\nB. 1% loss\nC. 1% gain\nD. Neither loss nor profit\nE. 2% gain\n\n### Answer:\nExplanation:\nLoss%= (common gain or loss % / 10)2 = (10/10)\u00b2 % = 1%. Answer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how many years does a sum of Rs. 3000 yield a simple interest of Rs. 12500 at 15% p.a.?\n\n### Options:\nA. 27.7 years\nB. 26.7 years\nC. 25.7 years\nD. 24.7 years\nE. 23.7 years\n\n### Answer:\nT = (100 * 12500)/(15 * 3000) = 27.7 years\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat should come in place of the question mark in the following questions?\n?\u204424 = 72\u2044\u221a?\n\n### Options:\nA. 12\nB. 16\nC. 114\nD. 144\nE. None of these\n\n### Answer:\n? \u00d7 \u221a? = 24 \u00d7 72 Squaring both the sides,\n(?2 \u00d7 ? ) = ?3 = (8 \u00d7 (3) \u00d7 (8 \u00d7 3) \u00d7 (8 \u00d7 9) \u00d7 (8 \u00d7 9)\n= 2(3)8(3)9(3)\n\u2234 ? = 2 \u00d7 8 \u00d7 9 = 144\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nn a Festival season Director informed his 20 staffs with their family to go for a one day tour. Package for one day is 750/- Some staffs are married and some are unmarried and some having their Kids. Director & 8 staffs are married with 2 kid each. What is the total package:\n\n### Options:\nA. 30000\nB. 38000\nC. 45000\nD. 33000\nE. 36000\n\n### Answer:\nTotal staffs = 20\nMarried staffs including Director = 9 *4= 36\nUnmarried Staff = 20-8 = 12\nTotal persons = 48\nTotal package = 48 * 750 = 36000\nAnswer is E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe numbers in which of the following pairs do NOT have a pair of distinct prime divisors in common?\n\n### Options:\nA. 10 and 20\nB. 12 and 18\nC. 24 and 16\nD. 21 and 63\nE. 22 and 88\n\n### Answer:\n16 has only the prime 2 (16=2^4) in its prime factorization, so it can not have a PAIR of distinct prime divisors in common with ANY of the numbers.\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich of the following values of A satisfies the inequality?\nA(A \u2013 2) = 5A \u2013 10\n\n### Options:\nA. A > 5 or A < 2\nB. 2 < A < 5\nC. 2 < A = 5\nD. A = 5, A = -2\nE. None of these\n\n### Answer:\nExplanation:\nA ( A \u2013 2) = 5 A \u2013 10\nA( A \u2013 2) = 5 ( A \u2013 2)\nA = 5 if A \u2013 2 > 0\nA = 5, A > 2\ni.e. 2 < A = 5\nANSWER: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMarla starts running around a circular track at the same time Nick starts walking around the same circular track. Marla completes 30 laps around the track per hour and Nick completes 15 laps around the track per hour. How many minutes after Marla and Nick begin moving will Marla have completed 4 more laps around the track than Nick?\n\n### Options:\nA. 5\nB. 16\nC. 12\nD. 15\nE. 20\n\n### Answer:\nMaria's rate - 30 laps per hour --> 30/60 laps/min\nNick's rate - 15 laps per hour --> 15/60 laps/min\nlets set equations:\n30/60*t=4 (since Maria had to run 4 laps before Nick would start)\n15/60*t=0 (Hick has just started and hasn't run any lap yet)\n(30/60-15/60)*t=4-0 (since Nick was chasing Maria)\nt=16 min needed Maria to run 4 laps\nAnswer : B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are two numbers. If 30% of the first number is added to the second number, then the second number increases to its six-fifth. What is the ratio of the first number to the second number?\n\n### Options:\nA. 1 : 4\nB. 4 : 5\nC. 3 : 5\nD. 5 : 8\nE. 2 : 3\n\n### Answer:\nLet the two numbers be x and y.\n(3/10) * x + y = (6/5) * y\n(3/10) * x = (1/5) * y\nx/y = 10/15 = 2/3\nThe answer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the odd man out. 1, 4, 9, 17, 25, 36, 49\n\n### Options:\nA. 1\nB. 9\nC. 17\nD. 49\nE. 36\n\n### Answer:\nExplanation :\nThe pattern is 1^2, 2^2, 3^2, 4^2, 5^2, 6^2, 7^2\nBut, instead of 4^2, 17 is given\nAnswer : Option C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a kilometer race, A beats B by 50 meters or 10 seconds. What time does A take to complete the race?\n\n### Options:\nA. 187 sec\nB. 190 sec\nC. 278 sec\nD. 268 sec\nE. 987 sec\n\n### Answer:\nTime taken by B run 1000 meters = (1000 * 10)/50\n= 200 sec.\nTime taken by A = 200 - 10\n=190 sec.\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA merchant gets a 5% discount on each meter of fabric he buys after the first 2,000 meters and a 7% discount on every meter after the next 1,500 meters. The price, before discount, of one meter of fabric is $2, what is the total amount of money the merchant spends on 4,500 meters of fabric?\n\n### Options:\nA. $8,617\nB. $8,710\nC. $8,810\nD. $8,835\nE. $8,915\n\n### Answer:\nfor first 2000 metres he does not get any discount\namount = 2*2000 = $4000\nfor next 1500 metres he gets 5% discount\namount = 2*1500 - (1/20)*3000 = $2850\nfor the nest 1000 metres he gets 7% discount\namount = 2*1000 - 7*20 = $1860\ntotal amount = $4000 + $2850 + $1860 = $8710\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe radius of a cylindrical vessel is 7cm and height is 5cm. Find the whole surface of the cylinder?\n\n### Options:\nA. 308 sq cm\nB. 528 sq cm\nC. 440 sq cm\nD. 132 sq cm\nE. 138 sq cm\n\n### Answer:\nr = 7 h = 5\n2\u03c0r(h + r) = 2 * 22/7 * 7(12) = 528\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA 6% stock yields 8%. The market value of the stock is:\n\n### Options:\nA. Rs. 48\nB. Rs. 75\nC. Rs. 96\nD. Rs. 133.33\nE. Rs. 143.33\n\n### Answer:\nLet the face value of the stock is Rs.100\nIt yields Rs.6\nMarket value of the stock=(6/8)*100=Rs.75\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain no. when divided by 50 leaves a remainder 25, what is the remainder if the same no.be divided by 15?\n\n### Options:\nA. 3\nB. 4\nC. 5\nD. 8\nE. 9\n\n### Answer:\nExplanation:\n50 + 25 = 75/15 = 5 (Remainder)\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOn his first 3 tests, Rajeev received an average score of N points. If on his fourth test, he exceeds his previous average score by 20 points, what is his average score for his first 4 tests?\n\n### Options:\nA. N\nB. N + 4\nC. N + 5\nD. N + 10\nE. N + 20\n\n### Answer:\nTotal points from first three tests: 3N\nPoints on fourth test: N + 20\nTotal points on all four tests: 3N + (N + 20) = 4N + 20\nAverage score for first four tests: (4N + 20)/4 = N + 5\nAnswer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe length of a rectangular plot is thrice its breadth. If the area of the rectangular plot is 675 sq m, then what is the breadth of the rectangular plot?\n\n### Options:\nA. 11\nB. 15\nC. 18\nD. 101\nE. 1322\n\n### Answer:\nLet the breadth of the plot be b m.\nLength of the plot = 3 b m\n(3b)(b) = 675\n3b2 = 675\nb2 = 225 = 15 (b > 0)\nb = 15 m.\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If three marbles are drawn what is the probability that one is yellow and two are red?\n\n### Options:\nA. 12/459\nB. 12/489\nC. 12/455\nD. 12/454\nE. 12/451\n\n### Answer:\nGiven that there are three blue marbles, four red marbles, six green marbles and two yellow marbles.\nWhen three marbles are drawn, the probability that one is yellow and two are red\n= (\u00b2C\u2081)(\u2074C\u2082)/\u00b9\u2075C\u2083\n= (2 * 4 * 3 * 3 * 2)/(1 * 2 * 15 * 14 * 13)\n= 12/455\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n(5568 / 87)1/3 + (72 x 2)1/2 = (?)1/2 ?\n\n### Options:\nA. 256\nB. 4\nC. \u221a2\nD. 16\nE. None\n\n### Answer:\nAnswer\n?)1/2 = (5568 / 87)1/3 + (72 x 2)1/2\n= (64)1/3 + (144)1/2\n\u2234 ? = (4 + 12)2 = 256\nCorrect Option: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAfter decreasing 24% in the price of an article costs Rs.684. Find the actual cost of an article?\n\n### Options:\nA. 218\nB. 777\nC. 900\nD. 2688\nE. 1991\n\n### Answer:\nCP* (76/100) = 684\nCP= 9 * 100 => CP = 900\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA watch which gains uniformly ,is 5 min,slow at 8 o'clock in the morning on sunday and it is 5 min 48 sec.fast at 8 p.m on following sunday. when was it correct?\n\n### Options:\nA. wednesday at 7:20 PM\nB. wednesday at 7:21 PM\nC. wednesday at 7:22 PM\nD. wednesday at 7:23 PM\nE. wednesday at 7:24 PM\n\n### Answer:\nThis sunday morning at 8:00 AM, the watch is 5 min. Slow, and the next sunday at 8:00PM it becomes 5 min 48 sec fast. The watch gains min in a time of (7\u00d724)+12 = 180 hours.\nTo show the correct time, it has to gain 5 min.\n54/5 min-> 180 hours\n5 min -> ?\n5/54/5x 180\n83 1/3 hrs = 72 hrs+11 1/3 hrs =3 days+11 hrs + 20 min\nSo the correct time will be shown on wednesday at 7:20 PM\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nLast year, Company X paid out a total of $1,050,000 in salaries to its 21 employees. If no employee earned a salary that is more than 25% greater than any other employee, what is the lowest possible salary that any one employee earned?\n\n### Options:\nA. $40,384.61\nB. $41,667\nC. $42,000\nD. $50,000\nE. $60,000\n\n### Answer:\nEmployee 1 earned $x(say)\nEmployee 2 will not earn more than $1.25x\nTherfore, to minimize the salary of any one employee, we need to maximize the salaries of the other 20 employees\n(1.25x*20)+x=1,050,000\nSolving for x=$40,384.61\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo trucks each 250m long are running in opposite directions on parallel paths. Their speeds are 30 km/hr and 20 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one?\n\n### Options:\nA. 77 sec\nB. 66 sec\nC. 48 sec\nD. 55 sec\nE. 36 sec\n\n### Answer:\nRelative speed = 20 + 30 = 50 km/hr.\n50 * 5/18 = 125/9 m/sec.\nDistance covered = 250 + 250 = 500 m.\nRequired time = 500 * 9/125 = 36 sec.\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe difference between the length and breadth of a rectangle is 28 m. If its perimeter is 120 m, then its area is:\n\n### Options:\nA. 704 m2\nB. 720 m2\nC. 620 m2\nD. 820 m2\nE. None\n\n### Answer:\nEXPLANATION\nWe have: (l \u00e2\u20ac\u201c b) = 28 and 2(l + b) = 120 or (l + b) = 60.\nSolving the two equations, we get: l = 44 and b = 16.\nArea = (l x b) = (44x 16) m2 = 704 m2.\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA solid yellow stripe is to be painted in the middle of a certain highway. If 1 gallon of paint covers an area of r square feet of highway, how many gallons of paint will be needed to paint a stripe of t inches wide on a stretch of highway m miles long? (1 mile = 5,280 feet and 1 foot = 12 inches)\n\n### Options:\nA. (5,280 mt) / 12 r\nB. (5,280 pt) / 12m\nC. (5,280 pmt) /12\nD. (5,280)(12m) / pt\nE. (5,280)(12p) / mt\n\n### Answer:\nGiven that: 1 gallon of paint covers an area ofrsquare feet. Question:how many gallonsof paint will be needed ...\nIn any case you will have:(total area in square feet)/(gallons per feet)=(total area in square feet)/r, so r must be in the denominator: eliminate all but A and D.\nNow, lets see where should be t: (area in square feet)=(width in feet)*(length in feet) --> width=tinchesas1 feet=12 inchesthent inches=t/12 feet, so (area in square feet)=(t/12) * (length in feet), so t must be in the nominator: only A is left.\nAnswer: A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA women travels from X to Y distance of 1000 miles in 10 hours. she returns to X in 4 hours. Find her average speed\n\n### Options:\nA. 300mph\nB. 150.2mph\nC. 142.8mph\nD. 200mph\nE. 111.01mph\n\n### Answer:\nSpeed from X to Y = 1000/10 = 100 mph\nSpeed from Y to X = 1000/4 = 250 mph\nAverage speed = 2*100*250 / 350 = 142.8mph\nAnswer is C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n120 students represent x percent of the boys at a school. If the boys at the school make up 30% of the total school population of x students, what is x?\n\n### Options:\nA. 120\nB. 150\nC. 180\nD. 200\nE. 250\n\n### Answer:\nLet B be the number of boys in the school.\n120 = xB/100\nB = 0.3x\n12000=0.3x^2\nx^2 = 40000\nx = 200\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe value of ((x \u2013 y)\u00b3 + (y - z)\u00b3 + (z \u2013 x)\u00b3)/(8 (x \u2013 y) (y \u2013 z) (z \u2013 x))\nis equal to :\n\n### Options:\nA. 0\nB. 1/12\nC. 3/8\nD. 1/4\nE. 1/3\n\n### Answer:\nSince (x \u2013 y) + (y \u2013 z) + (z \u2013 x) = 0,\nso (x \u2013 y)\u00b3 + (y \u2013 z)\u00b3 + (z \u2013 x)\u00b3= 3 (x \u2013 y) (y \u2013 z) (z \u2013 x).\n(3 (x \u2013 y) (y \u2013 z) (z \u2013 x))/(8(x \u2013 y) (y \u2013 z) (z \u2013 x)) = 3/8.\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA car dealership has 40 cars on the lot, 20% of which are silver. If the dealership receives a new shipment of 80 cars, 50% of which are not silver, what percentage of total number of cars are silver?\n\n### Options:\nA. 30%\nB. 35%\nC. 40%\nD. 45%\nE. 50%\n\n### Answer:\nThe number of silver cars is 0.2*40 + 0.5*80 = 48\nThe percentage of cars which are silver is 48/120 = 40%\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n10% people of a village in Sri Lanka died by bombardment, 20% of the remainder left the village on account of fear. If now the population is reduced to 3240, how much was it in the beginning?\n\n### Options:\nA. A)3800\nB. B)4200\nC. C)4400\nD. D)4500\nE. E)4600\n\n### Answer:\nX * (90/100) * (80/100) = 3240\nX = 4500\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe cash difference between the selling prices of an article at a profit of 4% and 6% is Rs. 3. The ratio of the two selling prices is?\n\n### Options:\nA. 52:56\nB. 52:53\nC. 52:28\nD. 52:19\nE. 52:20\n\n### Answer:\nLet C.P. of the article be Rs. x.\nThen, required ratio = 104% of x / 106% of x\n= 104/106 = 52/53\n=52:53\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThree grades of milk are 1 percent,4 percent and 3 percent fat by volume. If x gallons of the 1 percent grade, y gallons of the 2 percent grade, and z gallons of the 3 percent grade are mixed to give x+y+z gallons of a 1.5 percent grade, what is x in terms of y and z?\n\n### Options:\nA. y + 3z\nB. (y +z) / 4\nC. 2y + 3z\nD. 3y + z\nE. 4y + 3z\n\n### Answer:\nSoln:\nThe resulting equation is\n=> (.01x + .04y + .03z)/(x+y+z) = 1.5/100\n=> x + 4y + 3z = 1.5x + 1.5y + 1.5z\ntaking x to one side and y and z to other side we get\n=> x = 4y + 3z\nAns is E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nDue to construction, the speed limit along an 8-mile section of highway is reduced from 55 miles per hour to 35 miles per hour. Approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ?\n\n### Options:\nA. A) 4.99\nB. B) 8\nC. C) 10\nD. D) 15\nE. E) 24\n\n### Answer:\nOld time in minutes to cross 8 miles stretch = 8*60/55 = 8*12/11 = 8.72\nNew time in minutes to cross 8 miles stretch = 8*60/35 = 8*12/7 = 13.71\nTime difference = 4.99\nAns:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe time in a clock is 20 minute past 2. Find the angle between the hands of the clock.\n\n### Options:\nA. 60 degrees\nB. 120 degrees\nC. 45 degrees\nD. 50 degrees\nE. None of these\n\n### Answer:\nSolution:\nTime is 2:20. Position of the hands: Hour hand at 2 (nearly).\nMinute hand at 4\nAngle between 2 and 4 is 60 degrees [(360/12) * (4-2)]\nAngle made by the hour hand in 20 minutes is 10 degrees, since it turns through \u00bd degrees in a minute.\nTherefore, angle between the hands is 60 degrees - 10 degrees = 50 degrees\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n0, 1, 4, 9, 16, 25, 36, 49, ?\rWhat number should replace the question mark?\n\n### Options:\nA. 81\nB. 74\nC. 64\nD. 24\nE. 48\n\n### Answer:\nC 64\radd 0^2,1^2,2^2,......\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many times does the minute hand and the second hand make a straight line?\n\n### Options:\nA. 2844\nB. 2832\nC. 2855\nD. 2381\nE. 2831\n\n### Answer:\nmake a straight line 59 x 2 times = 118 times (both aligned, and in opposition) and there are 24 hours in a day, so in a day minutes and second hand make a straight line 24 x 118 times = 2832 times.\nso answer is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man can row a boat at 20 kmph in still water. If the speed of the stream is 9 kmph, what is the time taken to row a distance of 60 km downstream?\n\n### Options:\nA. 30/18 hours\nB. 37/13 hours\nC. 80/13 hours\nD. 30/13 hours\nE. 60/29 hours\n\n### Answer:\nSpeed downstream = 20 + 9 = 29 kmph.\nTime required to cover 60 km downstream\n= d/s = 60/29\n= 60/29 hours.\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nDrum X is 1/2 full of oil and drum Y, which has twice the capacity of drum X, is 1/4 full of oil. If all of the oil in drum X is poured into drum Y, then drum Y will be filled to what capacity?\n\n### Options:\nA. 1/2\nB. 2/3\nC. 3/4\nD. 5/6\nE. 7/8\n\n### Answer:\n(1/2)X = (1/4)Y\n(1/4)Y + (1/4)Y = (1/2)Y\nThe answer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how many different ways can the letters of the word 'PROFILE' be arranged in such a way that the vowels occupy only the odd positions ?\n\n### Options:\nA. 720\nB. 550\nC. 670\nD. 625\nE. 576\n\n### Answer:\nNumber of ways of arranging the vowels =4P3=4!=24.\nAlso, the 4 consonants can be arranged at the remaining 4 positions.\nNumber of ways of these arrangements =4P4=4!=24.\nTotal number of ways =(24*24)=576.\nAnswer is E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFour car rental agencies A, B, C and D rented a plot for parking their cars during the night. A parked 15 cars for 12 days, B parked 12 cars for 20 days, C parked 18 cars for 18 days and D parked 16 cars for 15 days. If A paid Rs. 1350 as rent for parking his cars, what is the total rent paid by all the four agencies?\n\n### Options:\nA. 2388\nB. 7380\nC. 1279\nD. 6150\nE. 2771\n\n### Answer:\nThe ratio in which the four agencies will be paying the rents = 15 * 12 : 12 * 20 : 18 * 18 : 16 * 15\n= 180 : 240 : 324 : 240 = 45 : 60 : 81 : 60\nLet us consider the four amounts to be 45k, 60k, 81k and 60k respectively.\nThe total rent paid by the four agencies = 45k + 60k + 81k + 60k= 246k\nIt is given that A paid Rs. 1350\n45k = 1350 => k = 30\n246k = 246(30) = Rs. 7380\nThus the total rent paid by all the four agencies is Rs. 7380.\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAn ore contains 25% of an alloy that has 90% iron. Other than this, in the remaining 75% of the ore, there is no iron. How many kilograms of the ore are needed to obtain 60 kg of pure iron?\n\n### Options:\nA. 250 kg\nB. 275 kg\nC. 300 kg\nD. 266.66 kg\nE. None\n\n### Answer:\nSolution: Let there is 100 kg of ore.\n25% ore contains 90% off Iron that means 25 kg contains;\n25*90/100 = 22.5 kg Iron.\n22.5 kg Iron contains 100 kg of ore.\nThen, 1 kg of iron contains = 25/100 kg ore;\nHence, 60 kg iron contains = 100*60/22.5 = 266.66 kg ore.\nAnswer: Option D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nis twice as fast as B. If B alone can do a piece of work in 30 days, in what time can A and B together complete the work?\n\n### Options:\nA. 13 days\nB. 10 days\nC. 16 days\nD. 11 days\nE. 18 days\n\n### Answer:\nB\n10 days\nA can do the work in 30/2 i.e., 15 days.\nA and B's one day's work = 1/15 + 1/30 = (2 + 1)/30 = 1/10\nSo A and B together can do the work in 10 days.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRon walks to a viewpoint and returns to the starting point by his car and thus takes a total time of 6 hours 45 minutes. He would have gained 2 hours by driving both ways. How long Q would it have taken for him to walk both ways.\n\n### Options:\nA. 8 h 45 min\nB. 7 h 45 min\nC. 6 h 45 min\nD. 5 h 30 min\nE. None of these\n\n### Answer:\n1.Walking to to a viewpoint+Driving back=6 hours 45 minutes\n2.Driving to a viewpoint+Driving back=6 hours 45 minutes - 2 hours=4 hours 45 minutes, thereforeone way driving=4 hours 45 minutes/2 =2 hours 22.5 minutes.\n3. From 1.one way driving=6 hours 45 minutes-2 hours 22.5 minutes=4 hours 22.5 minutes.\n4.Walking to to a viewpoint+Walking back Q=4 hours 22.5 minutes+4 hours 22.5 minutes=8 hours 45 minutes.\nAnswer: A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAlice and Heather are 20 miles apart and walk towards each other along the same route. Alice walks at constant rate that is 1 mile per hour faster than heather's constant rate of 5 miles/hour. If Heather starts her journey 24 minutes after Alice, how far from the original destination has Heather walked when the two meet?\n\n### Options:\nA. 4 miles\nB. 8 miles\nC. 10 miles\nD. 6 miles\nE. 12 mile\n\n### Answer:\nOriginal distance between S and H = 20 miles.\nSpeed of A = 5+1 = 6 mph, Speed of H = 5 mph.\nTime traveled by H = t hours ---> time traveled by A = t+24/60 = t+2/5 hours.\nNow, the total distances traveled by A and H = 20 miles ---> 6*(t+2/5)+5*t=20 ---> t= 8/5 hours. Thus H has traveled for 8/5 hours giving you a total distance for H = 5*8/5 = 8 miles.\nB is thus the correct answer.\nP.S.: based on the wording of the question, you should calculatehow far from theoriginal destination has Heather walkedwhen the two meet. 'Original destination' for H does not make any sense. Original destination for H was situated at a distance of 20 miles.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe length of the bridge, which a train 160 meters long and travelling at 45 km/hr can cross in 30 seconds, is:\n\n### Options:\nA. 239\nB. 277\nC. 215\nD. 88\nE. 232\n\n### Answer:\nSpeed = (45 * 5/18) m/sec = (25/2) m/sec. Time = 30 sec. Let the length of bridge be x meters. Then, (160 + X)/30\n= 25/2 ==> 2(160 + X) = 750 ==> X = 215 m.\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain tests consists 8 sections with 25 questions, numbered from 1 to 25, in each section. If a student answered all of the even-numbered questions correctly and 3/4 of the odd-numbered questions correctly, what was the total number of questions he answered correctly?\na. 150\nb. 172\nc. 174\nd. 175\ne. 176\n\n### Options:\nA. 174\nB. 150\nC. 180\nD. 175\nE. 190\n\n### Answer:\nEach set has 12 even and 13 odd numbered questions leading to total 96 even and 104 odd questions.\n96+3/4\u00e2\u02c6\u2014104=96+78=17496+3/4\u00e2\u02c6\u2014104=96+78=174\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the possible ways to make 3 digit numbers from 1 to 5 number(repetition is allowed)?\n\n### Options:\nA. 220\nB. 130\nC. 127\nD. 125\nE. 225\n\n### Answer:\nRepetition is allowed to make 3 digit number.So it is easy to calculate.\n5*5*5=125 ways.\nAnswer:option D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA leak in the bottom of a tank can empty the full tank in 6 hours. An inlet pipe fills water at the rate of 4 liters per minute. When the tank is full in inlet is opened and due to the leak the tank is empties in 8 hours. The capacity of the tank is?\n\n### Options:\nA. 2777\nB. 5760\nC. 2766\nD. 8987\nE. 2681\n\n### Answer:\n1/x - 1/6 = -1/8\nx = 24 hrs\n24 * 60 * 4 = 5760\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA collection of books went on sale, and 2/3 of them were sold for $4 each. If none of the 36 remaining books were sold, what was the total amount received for the books that were sold?\n\n### Options:\nA. $288\nB. $135\nC. $90\nD. $60\nE. $54\n\n### Answer:\nSince 2/3 of the books in the collection were sold, 1/3 were not sold. The 36 unsold books represent 1/3 of the total number of books in the collection, and 2/3 of the total number of books equals 2(36) or 72. The total proceeds of the sale was 72($4) or $288. The best answer is therefore A.\nAnswer: A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 865 in 4 years. The sum is:\n\n### Options:\nA. s. 665\nB. s. 690\nC. s. 698\nD. s. 700\nE. s. 720\n\n### Answer:\nS.I. for 1 year = Rs. (865 - 815) = Rs. 50.\nS.I. for 3 years = Rs.(50 x 3) = Rs. 150.\nPrincipal = Rs. (815 - 150) = Rs. 665.\nAnswer: Option A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe length of the bridge, which a train 130 m long and traveling at 45 km/hr can cross in 30 sec is?\n\n### Options:\nA. 240\nB. 235\nC. 245\nD. 250\nE. 260\n\n### Answer:\nSpeed = 45 * 5/18 = 25/2 m/sec.\nTime = 30 sec\nLet the length of bridge be x meters.\nThen, (130 + x)/30 = 25/2\nx = 245 m.\nAnswer: Option C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAverage of 15 results is 43. If the average of first seven results is 41 and average of last seven results is 45 Then find the eighth result?\n\n### Options:\nA. 41\nB. 39\nC. 43\nD. 45\nE. 47\n\n### Answer:\nOption 'C'\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a dairy farm, 40 cows eat 40 bags of husk in 40 days. In how many days one cow will eat one bag of husk?\n\n### Options:\nA. 32\nB. 36\nC. 38\nD. 40\nE. 50\n\n### Answer:\nAssume that in x days, one cow will eat one bag of husk.\nMore cows, less days (Indirect proportion)\nMore bags, more days (direct proportion)\nHence we can write as\n(cows)40:1\n(bags)1:40\nx:40\n=40\u00d71\u00d740=1\u00d740\u00d7x\n=x=40\nANSWER : D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a fuel station the service costs $1.75 per car, every liter of fuel costs 0.65$. Assuming that a company owns 12 cars and that every fuel tank contains 59 liters and they are all empty, how much money total will it cost to fuel all cars?\n\n### Options:\nA. 320.20$\nB. 380.20$\nC. 421.20$\nD. 451.20$\nE. 481.20$\n\n### Answer:\nTotal Cost = ( 1.75*12 ) + ( 0.65 * 12 * 59 ) = 481.20\nHence answer will be (E)\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA basket contains 6 blue, 6 red and 6 yellow marbles. If 6 marbles are extracted from the basket at random, what is the probability that a marble of each color is among the extracted?\n\n### Options:\nA. 2/21\nB. 3/25\nC. 1/6\nD. 9/34\nE. 11/24\n\n### Answer:\n18/18*12/17*6/16 = 9/34\nthe answer is (D)\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA polling company surveyed a certain country, and it found that 35% of that country\u2019s registered voters had an unfavorable impression of both of that state\u2019s major political parties and that 20% had a favorable impression only of Party T. If one registered voter has a favorable impression of both parties for every two registered voters who have a favorable impression only of Party B, then what percentage of the country\u2019s registered voters have a favorable impression of both parties (assuming that respondents to the poll were given a choice between favorable and unfavorable impressions only)?\n\n### Options:\nA. 15\nB. 20\nC. 30\nD. 35\nE. 45\n\n### Answer:\nS=100\nnot( T and B ) =35\nonly T=20\n(T and B)/B=1/2\nlet ( T and B ) =x\nonly B =2x\nso now, 20+35+x+2x=100\nx= 15\nA ans\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n300 + 5 \u00d7 8 = ?\n\n### Options:\nA. 820\nB. 340\nC. 420\nD. 209\nE. None of these\n\n### Answer:\n300 + 5 \u00d7 8 = ?\nor, ? = 300 + 40 = 340\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a class, there are 20 boys whose average age is decreased by 2 months, when one boy aged 21 years replaced by a new boy. The age of the new boy is?\n\n### Options:\nA. 14 years 8 months\nB. 15 years\nC. 16 years 4 months\nD. 17 years 8 months\nE. 17 years\n\n### Answer:\nTotal decrease = (20 x 2) months\n= 3 years 4 months\nAge of the new boy\n= 21 years - 3 years 4 months.\n= 17 years 8 months.\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe simple interest on a sum of money will be Rs.500 after 10 years. If the principal is trebled after 5 years what will be the total interest at the end of the tenth year?\n\n### Options:\nA. 700\nB. 800\nC. 900\nD. 1000\nE. 1100\n\n### Answer:\nP --- 10 ---- 500\nP --- 5 ----- 250\n3P --- 5 -----750\n------\n=> 1000\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n252 can be expressed as a product of primes as:\n\n### Options:\nA. 2 x 2 x 3 x 3 x 7\nB. 2 x 2 x 3 x 3 x 8\nC. 2 x 2 x 3 x 3 x 6\nD. 2 x 2 x 3 x 3 x 1\nE. 2 x 2 x 3 x 3 x 2\n\n### Answer:\nClearly, 252 = 2 x 2 x 3 x 3 x 7.\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nYouseff lives x blocks from his office. It takes him 1 minute per block to walk to work and 20 seconds per block to ride his bike to work. It is takes him exactly 12 minutes more to walk to work than to ride his bike to work, then x equals?\n\n### Options:\nA. 4\nB. 7\nC. 10\nD. 15\nE. 18\n\n### Answer:\nPlease follow posting guidelines, link is in my signatures.\nAs for your question, x/60 = blocks/time/block = block^2/time . This is not what you want. You are given x blocks and 60 seconds PER BLOCK. Thus you need to put it as 60*x to give you units of seconds as you are equating this to 720 (which is TIME in seconds.).\nThus the correct equation is : 60*x-20*x=7200 ----> 40x=720--> x = 18.\noption E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA woman started a business investing Rs. 70,000. Roja joined him after six months with an amount of Rs. 1,05,000 and Sachin joined them with Rs. 1.4 lakhs after another six months. The amount of profit earned should be distributed in what ratio among Akash, Roja and Sachin respectively, 3 years after Aman started the business ?\n\n### Options:\nA. 7:6:10\nB. 12:15:16\nC. 42:45:56\nD. None of these\nE. Cannot be determined\n\n### Answer:\nExplanation :\nAkash : Roja : Sachin = (70,000 x 36) : (1,05,000 x 30) : (1,40,000 x 24)\n= 12 : 15 : 16.\nAnswer : B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nX is able to do a piece of work in 14 days and Y can do the same work in 20 days. If they can work together for 5 days, what is the fraction of work completed?\n\n### Options:\nA. 15/28\nB. 17/28\nC. 13/28\nD. 19/28\nE. 11/28\n\n### Answer:\nExplanation :\nAmount of work X can do in 1 day = 1/14\nAmount of work Y can do in 1 day = 1/20\nAmount of work X and Y can do in 1 day = 1/14+ 1/20= 17/140\nAmount of work X and Y can together do in 5 days = 5 \u00d7 (17/140) = 17/28\nAnswer : Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOf the 200 students at University XYZ majoring in one or more of the engineering disciplines, 140 are majoring in electrical and 150 are majoring in mechanical. If at least 30 of the students are not majoring in either electrical or mechanical, then the number of students majoring in both electrical and mechanical could be any number from\n\n### Options:\nA. 30 to 70\nB. 70 to 100\nC. 90 to 110\nD. 130 to 150\nE. 150 to 170\n\n### Answer:\nif there are 140 students majoring in electrical then there must be 60 person not majoring electrical at all, since both of the student not majoring electrical and mechanical is at least 30, so the number of the student who are not majoring electrical but majoring mechanical will be at least 30.\nif there are 150 students majoring in mechanical there must be 50 students who are not majoring mechanical at all, since the number of the student who are not majoring electrical but majoring mechanical will be at least 30, hence the number of students both majoring mechanical and electrical will be at least 90\nso there must be at least 90 students who major in both\nsee the answers option the only possible answer is C !\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAverage age of students of an adult school is 46 years. 120 new students whose average age is 32 years joined the school. As a result the average age is decreased by 4 years. Find the number of students of the school after joining of the new students.\n\n### Options:\nA. 1200\nB. 120\nC. 360\nD. 168\nE. None of these\n\n### Answer:\nExplanation :\nLet the original no. of students be x.\nAccording to situation, 46x + 120*32 = (x + 120)36 \u21d2 x = 48\nSo, Required no. of students after joining the new students\n= x + 120 = 168.\nAnswer : D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the no.of ways of arranging the boy and 9 guests at a circular table so that the boy always sits in a particular seat?\n\n### Options:\nA. 3!\nB. 8!\nC. 7!\nD. 9!\nE. 11!\n\n### Answer:\nAns.(D)\nSol. Total number of persons = 10 Host can sit in a particular seat in one way. Now, remaining positions are defined relative to the host. Hence, the remaining can sit in 9 places in 9P9 = 9! Ways ... The number of required arrangements = 9! x 1= 9! = 9! ways\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJohn had a stock of 800 books in his bookshop. He sold 62 on Monday, 62 on Tuesday, 60 on Wednesday, 48 on Thursday and 40 on Friday. What percentage of the books were not sold?\n\n### Options:\nA. 26.5%\nB. 36.5%\nC. 71.7%\nD. 56.5%\nE. 70.0%\n\n### Answer:\nLet N be the total number of books sold. Hence\nN = 75 + 50 + 64 + 78 + 135 = 272\nLet M be the books NOT sold\nM = 960 - N = 960 - 402 = 688\nPercentage\nBooks not sold / total number of books = 688/960= 0.72 = 71.7%\ncorrect answer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo goods trains each 75 m long are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one?\n\n### Options:\nA. 2.3 sec\nB. 4.2 sec\nC. 48 sec\nD. 7.2 sec\nE. 9 sec\n\n### Answer:\nRelative speed = 45 + 30 = 75 km/hr.\n75 * 5/18 = 125/6 m/sec.\nDistance covered = 75 + 75 = 150 m.\nRequired time = 150 * 6/125 = 7.2 sec.\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nLamp A flashes every 6 seconds, Lamp B flashes every 8 seconds, Lamp C flashes every 10 seconds. At a certain instant of time all three lamps flash simultaneously. During the period of 5 minutes after that how many times will exactly two lamps flash? (Please include any flash of exactly two lights which occurs at the 5 minute mark.)\n\n### Options:\nA. 21\nB. 22\nC. 23\nD. 24\nE. 25\n\n### Answer:\n5 minutes is 300 seconds.\nLamp A and Lamp B will flash together every 24 seconds.\n300/24=12 plus remainder.\nIn the time period, Lamp A and Lamp B will flash together 12 times.\nLamp A and Lamp C will flash together every 30 seconds.\n300/30=10.\nIn the time period, Lamp A and Lamp C will flash together 10 times.\nLamp B and Lamp C will flash together every 40 seconds.\n300/40=7 plus remainder.\nIn the time period, Lamp B and Lamp C will flash together 7 times.\nAll three lights will flash together every 2*2*2*3*5=120 seconds.\n300/120=2 plus remainder.\nWe have counted these triple flashes three times, so we need to subtract three times the number of times that all three lights flash together.\nThe number of times that exactly two lights flash together is 12+10+7-6=23 times.\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA and B together can complete a piece of work in 4 days. If A alone can complete the same work in 12 days, in how many days can B alone complete that work?\n\n### Options:\nA. 22 days\nB. 4 days\nC. 13 days\nD. 6 days\nE. 9 days\n\n### Answer:\n(A + B)'s 1 day's work = (1/4). A's 1 day's work = (1/12).\nB's 1 day's work =((1/4)-(1/12))=(1/6)\nHence, B alone can complete the work in 6 days.\nAnswer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA 16% stock yielding 14% is quoted at:\n\n### Options:\nA. s. 83.33\nB. s. 110\nC. s. 114\nD. s. 120\nE. s. 140\n\n### Answer:\nIncome of Rs 14 on investment of Rs 100\nIncome of Rs 16 on investment of ?\n= (16*100)/14=114\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain business produced x rakes each month form November through February and shipped x/2 rakes at the beginning of each month from March through October. The business paid no storage costs for the rakes from November through February, but it paid storage costs of $0.40 per rake each month from March through October for the rakes that had not been shipped. In terms of x, what was the total storage cost, in dollars, that the business paid for the rakes for the 12 months form November through October?\n\n### Options:\nA. 0.40x\nB. 1.20x\nC. 5.60x\nD. 1.60x\nE. 3.20x\n\n### Answer:\nbecause we have a total of 4X\nAlso from Mar- Oct the rakes will be deducted by 1/8 X\nso\nIn Apr they pay for the storage 0.4 * 4X * 7/8\nIn May they pay for the storage 0.4 * 4X * 6/8\nIn Jun they pay for the storage 0.4 * 4X * 5/8\nIn Jul they pay for the storage 0.4 * 4X * 4/8\nIn Aug they pay for the storage 0.4 * 4X * 3/8\nIn Sep they pay for the storage 0.4 * 4X * 2/8\nIn Oct they pay for the storage 0.4 * 4X * 1/8\ntotal = 0.4 * 4X * 1/8 * [ 1+2+3+4+5+6+7]\n= 0.4 * X/2 * (28)\n= 5.6X\n(C)\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average age of husband, wife and their child 3 years ago was 25 years and that of wife and the child 5 years ago was 20 years. The present age of the husband is\n\n### Options:\nA. 22\nB. 40\nC. 34\nD. 21\nE. 11\n\n### Answer:\nExplanation:\nSum of the present ages of husband, wife and child = (25 x 3 + 3 x 3) years = 84 years.\nSum of the present ages of wife and child (20 x 2 + 5 x 2) years = 50 years.\nHusband's present age = (84 - 50) years = 34 years.\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nBani has only pennies, dimes, and nickels in a jar. The jar has at least 1 but no more than 4 pennies. If the jar has at least 1 nickel and 1 dime, which of the following could NOT be the total amount of money in the jar?\n\n### Options:\nA. 71\nB. 72\nC. 73\nD. 74\nE. 75\n\n### Answer:\nLet there be a pennies , b nickels and c dimes\nso total amount can be 1+5b+10c cents to 4+5b+10c\nas you can see the equation of total whenever divided by 5 would leave a remainder from 1 to 4 ( as pennies can only be from 1 to 4 and hence a is limited to values from 1 to 4)\nSo the total can never be divisible by 5 and hence only 75 that is c is the option which is divisible by 5.\nso answer is E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe smallest value of n, for which 2n+1 is not a prime number, is\n\n### Options:\nA. 3\nB. 4\nC. 5\nD. 6\nE. 7\n\n### Answer:\n(2\u00d71 + 1) = 3.\n(2\u00d72 + 1) = 5.\n(2\u00d73 + 1) = 7.\n(2\u00d74 + 1) = 9.\nwhich is not prime , n=4.\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA boat can travel 1.8 times the distance down the stream than up the stream in the same time. If the speed of the current is 3 KMPH, Find the speed of the boat in still water\n\n### Options:\nA. 5\nB. 10.5\nC. 15\nD. 20\nE. 25\n\n### Answer:\nSimple question, messy language.\nLets say boat's speed is B and current's speed is C.\nUpstream speed : B - C\nDownstream speed : B + C\nDistance will be the same both times. lets say D.\ngiven : time it takes upstream = 1.8 times time it takes downstream\nD/(B + C) = 1.8 * [D/(B - C)]\nSolving B = 3.5 C\ngiven : C is 3 KMPH\nSo B is 10.5 KMPH\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe marks obtained by Vijay and Amith are in the ratio 4:5 and those obtained by Amith and Abhishek in the ratio of 3:2. The marks obtained by Vijay and Abhishek are in the ratio of?\n\n### Options:\nA. 6:6\nB. 6:3\nC. 6:5\nD. 6:8\nE. 6:1\n\n### Answer:\n4:5\n3:2\n-------\n12:15:10\n12:10\n6:5\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJim is able to sell a hand-carved statue for $670 which was a 35% profit over his cost. How much did the statue originally cost him?\n\n### Options:\nA. $496.30\nB. $512.40\nC. $555.40\nD. $574.90\nE. $588.20\n\n### Answer:\n670 is the final price that is the selling price. now suppose, x is the cost price.\ntherefore 670 = 1.35 * x\nnow while doing x = 670/1.35 calculation. I saw that the answer choices begin with 5.\nSo i did 135 * 5 = 675. As 670 is less than 675. Therefore the quotient will be less than 5.\nWhich is only in the answer A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 4 (P's Capital) = 6 (Q's Capital) = 10 (R's Capital), then out of the total profit of Rs 4650, how much R will receive?\n\n### Options:\nA. 300\nB. 600\nC. 900\nD. 800\nE. 500\n\n### Answer:\nLet P's capital be p,\nQ's capital be q,\nand R's capital be r\nThen\n4p=6q=10r2p=3q=5r\u22ef(A)\nFrom (A),\nq=2p/3 \u22ef(1)\nr=2p/5 \u22ef(2)\np:q:r=p:2p/3:2p/5\n=15:10:6\nR's share =4650\u00d76/31=150\u00d76=900\nAnswer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAn urn contains 8 black and 2 white balls. Two balls are drawn from the urn one after the other\nwithout replacement. What is the probability that both drawn balls are black?\n\n### Options:\nA. 1/5\nB. 28/45\nC. 2/5\nD. 3/5\nE. 2/7\n\n### Answer:\nLet E and F denote respectively the events that first and second ball drawn\nare black. We have to find P(E n F) or P (EF).\nNow P(E) = P (black ball in first draw) = 8/10\nAlso given that the first ball drawn is black, i.e., event E has occurred, now there are 7 black balls and two white balls left in the urn. Therefore, the probability that the second ball drawn is black, given that the ball in the first draw is black, is nothing but the conditional probability of F given that E has occurred.\nThat is P(F|E) = 7/9\nBy multiplication rule of probability, we have\nP (E n F) = P(E) P(F|E)\n= 8/10 \u00d7 7/9 = 28/45\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA small, experimental plane has three engines, one of which is redundant. That is, as long as two of the engines are working, the plane will stay in the air. Over the course of a typical flight, there is a 1/3 chance that engine one will fail. There is a 70% probability that engine two will work. The third engine works only half the time. What is the probability that the plane will crash in any given flight?\n\n### Options:\nA. 7/12\nB. 1/4\nC. 1/2\nD. 7/24\nE. 17/24\n\n### Answer:\nIn probability questions the trap answer is just the multiple of the numbers in the question.\ni.e. if you multiply 1/3 * 1/4 * 1/2 = 1/24 is trap answer\nThe other trap answer could be 2/3 * 3/4 * 1/2 = 6/24 is trap answer\nSo lets say you have30 secsand you want to guess the answer then B, C are ruled out because they can be traps. You best guess is A, D, E. So you have 33% chances of being correct.\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOne pipe can fill a tank three times as fast as another pipe. If together the two pipes can fill the tank in 36 minutes, then the slower pipe alone will be able to fill the tank in\n\n### Options:\nA. 144 mins\nB. 140 mins\nC. 136 mins\nD. 132 mins\nE. 130 mins\n\n### Answer:\nExplanation:\nLet the slower pipe alone fill the tank in x minutes\nthen faster will fill in x/3 minutes.\nPart filled by slower pipe in 1 minute = 1/x\nPart filled by faster pipe in 1 minute = 3/x\nPart filled by both in 1 minute =1/x+3/x=1/36\n=>4/x=1/36\nx=36\u00e2\u02c6\u20144=144mins\nANSWER IS A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are 30 socks in a drawer. 60% of the socks are red and the rest are blue. What is the minimum number of socks that must be taken from the drawer without looking in order to be certain that at least two socks of the same colour have been chosen?\n\n### Options:\nA. 2\nB. 3\nC. 14\nD. 16\nE. 20\n\n### Answer:\n60% of 30 = 18.\nSo, there are 18 red socks and there are 12 blue socks.\nCheck out this possible cases once we have selected TWO socks:\ncase a: 2 red socks, in which case we have a pair of matching socks. DONE!\ncase b: 2 blue socks, in which case we have a pair of matching socks. DONE!\ncase c: 1 red sock and 1 blue sock. No matching socks, so we're not done yet.\nSince the first 2 cases result in a pair of matching socks, let's focus on case 3 and what happens when we select a 3rd sock.\nIf we have 1 red sock and 1 blue sock, then the next sock we select will EITHER match the red sock OR match the blue sock.\nIn both cases, we are guaranteed to have a pair of matching socks.\nSo, selecting 3 socks guarantees that we have a pair of matching socks.\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n8, 27, 64, 100, 125, 216, 343\n\n### Options:\nA. 64\nB. 100\nC. 125\nD. 216\nE. 343\n\n### Answer:\nThe pattern is 2 cube, 3 cube, 4 cube, 5 cube, 6 cube, 7 cube. But, 100 is not a perfect cube.\nanswer : B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many positive integers less than 5,000 are evenly divisible by neither 15 nor 20?\n\n### Options:\nA. 4,514\nB. 4,477\nC. 4,521\nD. 4,428\nE. 4,349\n\n### Answer:\nintegers less than 5000 divisible by 15 5000/15 =333.something , so 333\nintegers less than 5000 divisible by 20 5000/20 = 238.## , so 238\nwe have double counted some, so take LCM of 15 and 20 =105 and divide by 5000, we get 47. so all numbers divisible by 15 and 20 = 333 +238 -47 =524\nnow subtract that from 4999. 4999- 524 = 4477 answer B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFor any positive x, y and z if x is n% of y and z is m% of y then what percentage Q must x be of z?\n\n### Options:\nA. (n/m)%\nB. (m \u00d7 n)%\nC. (100 / [m \u00d7 n]) %\nD. (100 \u00d7 m/n)%\nE. (100 \u00d7 n/m)%\n\n### Answer:\nx is n% of y MEANS x= (n/100 )* y------------------------eq1\nz is m% of y MEANS z= (m/100 )* y------------------------eq2\nFind equation of xz\nsubstitute value of y from 2nd equation into Ist equation\nso x= (n/100)*(100z/m)\nso x= (n/m)z\nor x= (100n/m)z/100\nso answer Q is 100n/m %.E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nCar A leaves the airport at 9:00 am and travels at a constant rate of 30 km per hour. Car B leaves the airport at 9:30 am and travels in the same direction along the same highway at a constant rate of 34 km per hour. At what time will Car B be 12 km ahead of Car A?\n\n### Options:\nA. 3:45 pm\nB. 4:00 pm\nC. 4:15 pm\nD. 4:30 pm\nE. 4:45 pm\n\n### Answer:\nAt 9:30 am, Car A will be 15 km ahead of Car B.\nCar B travels at a rate 4 km per hour faster than Car A.\nCar B needs to travel 27 km more than Car A in order to be 12 km ahead.\nThis will take 27 km/4 km per hour=6.75 hours.\nCar B will be 12 km ahead at 4:15 pm.\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe units digit of (35)^(87) + (93)^(46) is:\n\n### Options:\nA. 2\nB. 4\nC. 6\nD. 8\nE. 0\n\n### Answer:\nStep 1: (35)^(87) can be broken up into (5)^87 x (7)^87. Each power of 7 ends in a units digit of either a 7,9,3 or 1. Each power of 5 ends in a 5. When you multiply 5 by any odd number you will end up with a units digit of 5.\nStep 2: (93)^(46) can be broken up into (3)^46 x (31)^46. Each power of 31 ends in a units digit of 1. Each power of 3 ends in a units digit of either 3,9,7 and 1. Since there is a pattern here where every 4th power of 3 ends in a units digit of 3, the 46th power of 3 would end in a units digit of 9. When you multiply 1 by 9 you end up with a units digit of 9.\nTherefore, the units digit we are looking for is 5 + 9 = 14. Units digit will be 4. Answer B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSum of 3 consecutive even no.'s is 26 more than the 1st no. of the series. Find the middle no.?\n\n### Options:\nA. 8\nB. twelve (12)\nC. 14\nD. 16\nE. 18\n\n### Answer:\nLet the numbers be x, x+2 and x+4 then\nx + x+2 + x+4 = x+26\n3x + 6 = x + 26\n2x = 20\n\\inline \\therefore x = 10\n\\inline \\therefore Middle number = x + 2 = 10+2 = 12\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJohn have a 630ml mixture of milk and water in the ratio 7:2. How much water must be added to make the ratio 7:3?\n\n### Options:\nA. 40 ml\nB. 60 ml\nC. 70 ml\nD. 80 ml\nE. 90 ml\n\n### Answer:\nconcentration of water in mixture1 =29 (since the ratio of milk and water = 7:2) ...(1)\nconcentration of water in pure water= 1 ...(2)\nNow the above mentioned items are mixed to form mixture2 where milk and water ratio = 7 : 3\n=> concentration of water in mixture2 =310\nBy rule of alligation,\nconcentration of water in mixture1 (29)\nconcentration of water in pure water (1)\nMean concentration\n(310)\n1\u2212310=710\n310\u221229=790\n=> Quantity of mixture1 : Quantity of water\n=710:790=110:190=1:19\nGiven that Quantity of mixture1 = 630 ml\n=> 630 : Quantity of water =1:19\n=> Quantity of water =630\u00d719=70 ml\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA 72 gallon solution of salt and water is 10% salt. How many gallons of water must be added to the solution in order to decrease the salt to 8% of the volume?\n\n### Options:\nA. 8\nB. 12\nC. 18\nD. 14\nE. 16\n\n### Answer:\nAmount of salt = 7.2\nAssume x gallons of water are added.\n7.2 / 72 + x = 8/100\n720 = 8x + 576\n8x = 144\nx = 18\nCorrect Option: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA container has a capacity of 20 gallons and is full of spirit. 4 gallons of spirit is drawn out and the container is again filled with water. This process is repeated 3 times. Find how much spirit is left in the resulting mixture finally?\n\n### Options:\nA. 6(257/525) gallons\nB. 6(346/625) gallons\nC. 6.5 gallons\nD. 6.25 gallons\nE. None of these\n\n### Answer:\nThere is a direct formula to calculate such repetition:\nLeft QTY / Orig QTY = ( (Orig QTY - Rep QTY) / Orig QTY )^n\nwhere n is number of times mixing done:\nLeft QTY / 20 = (20 -4)^3 / 20^3\nLeft QTY = 20 (16/20)^3\nLeft QTY = 20 ( 4/5 )^3\nLeft QTY = 10.24\nAnswer is E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe ratio of A and B is 5:3.After 2 years their ratio is 3:2.What is the age of B?\n\n### Options:\nA. 5\nB. 3\nC. 6\nD. 7\nE. 8\n\n### Answer:\nThe ratio of A and b is 5x and 3x years.\nAfter 2 years, their ratio will be 3 and 2.\n(i.e) (5x+2)/(3x+2)=3/2\n10x+4=9x+6\nx=2\nB's age=3x=3(2)=6 years\nAnswer is option C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA box contains four dime coins, of which two coins have heads on both their faces, one coin has tail on both its faces and the fourth coin is a normal one. A coin is picked at random and then tossed. If head is the outcome of the toss, then find the probability that the other face (hidden face) of the coin tossed is also a head.\n\n### Options:\nA. 3/4\nB. 1/5\nC. 2/5\nD. 3/5\nE. 4/5\n\n### Answer:\nThere are four ways (2 heads in one two-headed coin and 2 heads in the other two-headed coin)\nHow many ways can you get heads from this entire set of coins? There are five ways (four as identified above and one from the normal coin)\nTherefore probability = (number of ways to get heads from a two-headed coin)/(number of ways to get heads from any coin)\n= 4/5\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA cupcake recipe calls for 2 cups of sugar, and makes 2 dozen cupcakes. A caterer will supply cupcakes for 150 guests at a birthday party in which there should be at least 2 cupcakes per guest. What is the minimum amount of sugar needed?\n\n### Options:\nA. 24 cups\nB. 75 cups\nC. 2 cups\nD. 15 cups\nE. 250 cups\n\n### Answer:\nThe proportion equation can be used. Let C = sugar needed.\nNote: 12 = 1 dozen\nProportion: A/B = C/D\n2 cups of sugar (A) makes 24 cupcakes (B).\n(2)(150 guests) = 300 (D) is the least number cupcakes needed.\nProportion: 2/24 = C/300\nC = (2)(300)/24 = 600/24 = 24. At least 24 cups are needed.\nAnswer is A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 190 m long?\n\n### Options:\nA. 44\nB. 99\nC. 88\nD. 77\nE. 21\n\n### Answer:\n:\nSpeed = 45 * 5/18 = 25/2 m/sec\nTotal distance covered = 360 + 190 = 550 m\nRequired time = 550 * 2/25 = 44 sec\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA and B complete a work in 6 days. A alone can do it in 10 days. If both together can do the work in how many days?\n\n### Options:\nA. 3.75\nB. 4\nC. 2\nD. 8\nE. 7\n\n### Answer:\n1/6 + 1/10 = 8/30 = 4/15\n15/4 = 3.75 days\nANSWER A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJerry went to a shop and bought things worth Rs. 45, out of which 30 % went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?\n\n### Options:\nA. 19\nB. 19.7\nC. 21.3\nD. 29.5\nE. 39.7\n\n### Answer:\nTotal cost of the items he purchased = Rs.45\nGiven that out of this Rs.45, 30 % is given as tax\n=> Total tax incurred = 30 % = Rs.30/100\nLet the cost of the tax free items = x\nGiven that tax rate = 6%\n\u2234 (45\u221230/100\u2212x)6/100 = 30/100\n\u21d2 6(45 \u22120.3 \u2212x) = 30\n\u21d2 (45 \u2212 0.3 \u2212 x) = 5\n\u21d2 x = 45 \u2212 0.3 \u2212 5 = 39.7\nE)\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the time is currently 1:30 pm, what time will it be in exactly 642 hours?\n\n### Options:\nA. 3:30 am\nB. 4:30 am\nC. 5:30 am\nD. 6:30 am\nE. 7:30 am\n\n### Answer:\n642 = 26(24) + 18/24\nThe time will be 18 hours later than 1:30 pm which is 7:30 am.\nThe answer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSheila works 8 hours per day on Monday, Wednesday and Friday, and 6 hours per day on Tuesday and Thursday. She does not work on Saturday and Sunday. She earns $216 per week. How much does she earn in dollars per hour?\n\n### Options:\nA. 11\nB. 10\nC. 9\nD. 8\nE. 6\n\n### Answer:\nLet Sheila earn x dollars per hour\nSo, on Monday, Wednesday and Friday , she earns 8x each\nAnd, on Tuesday and Thursday, she earns 6x each\nIn total , over the week she should earn, 3(8x) + 2(6x) = 36x\nShe earns $216 per week\n36x =216\nx =6\nCorrect Option : E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nDuring a Pizza buffet where A eats more times 2.4 than B, and B eats 6 times less than C.find the leat number of times all the three has to eat\n\n### Options:\nA. 50\nB. 60\nC. 70\nD. 80\nE. 85\n\n### Answer:\nA eats more than B if B eats 1 times than the ratio of A and B is A:B is 2.4:1 or 12:5 and as B eat 6 times less the C the the ratio of B : C is 5:30 the the least number of times all three has eat is the LCM of A,B,C that is 60 ..\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nthe probability of a student possessing a ball point pen in exam is 3/5 & possessing an ink pen is 2/3. find his probability of possessing at least one of them\n\n### Options:\nA. 10/15\nB. 11/15\nC. 12/15\nD. 13/15\nE. 14/15\n\n### Answer:\nthe probability of a student possessing a ball point pen in exam is 3/5 .\nthe probability of a student not possessing a ball point pen in exam is 2/5 & possessing an ink pen is 2/3.\n& not possessing an ink pen is 1/3.\nhis probability of possessing none of them =2/5*1/3=2/15\nhis probability of possessing one of them =1-2/15 = 13/15\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA technician makes a round-trip to and from a certain service center by the same route. If the technician completes the drive to the center and then completes 50 percent of the drive from the center, what percent of the round-trip has the technician completed?\n\n### Options:\nA. 70\nB. 65\nC. 60\nD. 75\nE. 80\n\n### Answer:\nround trip means 2 trips i.e.to and fro. He has completed one i.e 50% completed. then he traveled another 50% of 50% i.e 25%. so he completed 50 +25 =75 % of total trip.\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain company assigns employees to offices in such a way that some of the offices can be empty and more than one employee can be assigned to an office. In how many ways can the company assign 4 employees to 2 different offices?\n\n### Options:\nA. 10\nB. 15\nC. 14\nD. 16\nE. 18\n\n### Answer:\nEach of three employee can be assigned to either of offices, meaning that each has 2 choices --> 2*2*2*2=2^4=16.\nAnswer: D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe price of a certain painting increased by 20% during the first year and decreased by 25% during the second year. The price of the painting at the end of the 2-year period was what percent of the original price?\n\n### Options:\nA. 102%\nB. 90%\nC. 120%\nD. 85%\nE. 95%\n\n### Answer:\nEasiest thing to do: Assume that price is 100\nPrice at the end of yr 1: 100+ 20 = 120\nPrice at the end of year 2 = 120 - 120*0.25 = 120*0.75 = 90\nHence required answer = (90/100)*100% = 90%\nAnswer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn school there are some bicycles and 4 wheeler wagons.one Tuesday there are 190 wheels in the campus.How many bicycles are there?\n\n### Options:\nA. 35\nB. 36\nC. 37\nD. 38\nE. 39\n\n### Answer:\nLet no. of bicycles be x\n& no. of wagons be y\nso, 2x+4y=190\nby solving, we get\nno. of bicycles=39 (wheels=>2*39=78)\nno. of wagons=28 (wheels=>4*28=112)\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe smallest value of n, for which 2n is not a prime number, is\n\n### Options:\nA. 2,3,4\nB. 1,3,5\nC. 2,5,6\nD. 4,8,9\nE. 12,14,16\n\n### Answer:\n(2\u00c3\u20141) = 2.\n(2\u00c3\u20142) = 4.\n(2\u00c3\u20143) = 6.\n(2\u00c3\u20144) = 8.\nwhich is not prime , n=2,3,4.\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a class of 52 students, 12 enrolled for both English and German. 22 enrolled for German. If the students of the class enrolled for at least one of the two subjects, then how many students enrolled for only English and not German?\n\n### Options:\nA. 30\nB. 10\nC. 18\nD. 28\nE. 32\n\n### Answer:\nTotal=English+German-Both+Neither --> 52=English+22-12+0 --> English=42 --> Only English=English-Both=42-12=30\nAnswer: A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA windmill is taking advantage of strong air currents in order to produce electrical energy. On a typical day the wind speed is around 20 mph and in that speed the windmill produces 600 kw/h (kilowatts per hour). On a stormy day a windmill produces 20% more energy. How much kw/h can three windmills produce in two hours on a stormy day?\n\n### Options:\nA. 2880.\nB. 4860.\nC. 5780\nD. 4320\nE. 6380.\n\n### Answer:\nNormal Day = 600 kw/h\nStormy Day = 600*1.2=720 kw/h\n3 windmills for 2 hours on stormy day\n720*3*2=4320\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a certain corporation, there are 300 male employees and 150 female employees. It is known that 40% of the male employees have advanced degrees and 40% of the females have advanced degrees. If one of the 450 employees is chosen at random, what is the probability this employee has an advanced degree or is female?\n\n### Options:\nA. 1/2\nB. 2/3\nC. 3/5\nD. 7/10\nE. 11/15\n\n### Answer:\nP(female) = 150/450 = 1/3\nP(male with advanced degree) = 0.4*300/450 = 120/450 = 4/15\nThe sum of the probabilities is 9/15 = 3/5\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average age of 3 girls is 16 years and their ages are in the proportion 1:2:3. The age of the youngest girl is?\n\n### Options:\nA. 12 years\nB. 7 years\nC. 9 years\nD. 10 years\nE. 8 years\n\n### Answer:\nTotal age of 3 boys = 16*3 =48\nratio of their ages = 1:2:3\nAge of the youngest =48*1/6 = 8 years\nAnswer is E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n(51+52+53+\u2026\u2026\u2026+100) is equal to:\n\n### Options:\nA. 2525\nB. 2975\nC. 3225\nD. 3775\nE. 3885\n\n### Answer:\n(51+52+53+\u2026\u2026\u2026+100) = (1+2+3+\u2026\u2026.+100)- (1+2+3+4+\u2026\u2026+50)\n= (100*101)/2 - (50*51)/2\n= (5050-1275)= 3775.\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo varieties of wheat - A and B costing Rs. 9 per kg and Rs. 15 per kg were mixed in the ratio 3 : 7. If 5 kg of the mixture is sold at 25% profit, find the profit made?\n\n### Options:\nA. Rs.16.90\nB. Rs.16.59\nC. Rs.16.60\nD. Rs.16.50\nE. Rs.18.50\n\n### Answer:\nLet the quantities of A and B mixed be 3x kg and 7x kg.\nCost of 3x kg of A = 9(3x) = Rs. 27x\nCost of 7x kg of B = 15(7x) = Rs. 105x\nCost of 10x kg of the mixture = 27x + 105x = Rs. 132x\nCost of 5 kg of the mixture = 132x/10x (5) = Rs. 66\nProfit made in selling 5 kg of the mixture = 25/100 (cost of 5 kg of the mixture) = 25/100 * 66 =Rs.16.50\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the price of a certain computer increased 30 percent from y dollars to 351 dollars, then 2y =\n\n### Options:\nA. 540\nB. 570\nC. 619\nD. 649\nE. 700\n\n### Answer:\nBefore Price increase Price = y\nAfter 30% Price increase Price = y+(30/100)*y= 1.3y = 351 (Given)\ni.e. y= 351/1.3 = $270\ni.e. 2y = 2*270 = 540\nAnswer: option A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOf the mutual funds on a \u201cselect list,\u201d 1/3 have 5-star ratings, and 2/5 of the remaining funds have 4-star ratings. If the remaining 400 funds on the list have 3-star ratings, how many funds are on the list?\n\n### Options:\nA. 500\nB. 750\nC. 1,000\nD. 1,200\nE. 1,500\n\n### Answer:\nC\nFraction of 5- and 4-star funds: 1/3 + (2/5)*(2/3) = 5/15 + 4/15 = 9/15\nFraction of 3-star funds = 1 - 9/15 = 6/15\n(6/15)*Total = 400\nTotal = 1000\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA researcher computed the mean, the median, and the standard deviation for a set of performance scores. If 10 were to be added to each score, which of these three statistics would change?\n\n### Options:\nA. The mean only\nB. The median only\nC. The mean and the median\nD. The standard deviation only\nE. The mean and the standard deviation\n\n### Answer:\nThe correct answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFor a certain cylinder, the diameter equals the height. If every length in this cylinder is decreased by 60%, then to the nearest integer, by what percent does the volume decrease?\n\n### Options:\nA. 22%\nB. 40%\nC. 60%\nD. 84%\nE. 94%\n\n### Answer:\nAgain, the exact dimensions of the cylinder do not matter, as long as every length increases by the same percent or same ratio. We now have a percent decrease, which means we subtract to construct our multiplier. A 60% decrease means we have a multiplier of 1 \u2013 0.60 = 0.4, and so k = 0.4 as well. For volume we need to cube the scale factor: k^3 = (0.4)^3 = 0.064 {approx} 0.06 approximately. That would be the multiplier for a 94% decrease, because 1 \u2013 0.94 = 0.06; therefore, the volume decreases by 94%. Answer = E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA boy has 5 pens out of which a pair is to be selected for an examination. At most, how many different pairs are possible?\n\n### Options:\nA. 20\nB. 10\nC. 5\nD. 40\nE. 10\n\n### Answer:\nN=5C2=5!/(3!2!)=5*2=10\nCorrect Option: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a certain sample of data has a mean of 15.0 and a standard deviation of 2.0, which of the following pairs contain two values that are each at least 2.5 standard deviations from the mean?\n\n### Options:\nA. (8.0; 16.5)\nB. (8.5; 21.0)\nC. (14.0; 26.5)\nD. (16.5; 26.0)\nE. (21.0; 26.5)\n\n### Answer:\n2.5 standard deviation equals to 2.5*2=5;\n2.5 standard deviations from the mean, so5 points, from the mean is the range from {mean-5} to {mean+5}, so from 10 to 20.\nThe correct answer choice must cover all this range: only answer choice B does this.\nAnswer: B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 0.4 of a number is equal to 0.06 of another number, the ratio of the numbers i\n\n### Options:\nA. 2 : 3\nB. 3 : 4\nC. 3 : 20\nD. 20 : 3\nE. None\n\n### Answer:\nSol.\n0.4A = 0.06 B \u21d4 A / B = 0.06 / 0.40 = 6/40 = 3/20.\n\u2234 A : B = 3 : 20.\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhen a plot is sold Rs. 18,700, the owner loses 15%. At what price must the plot be sold in order to gain 15%?\n\n### Options:\nA. Rs. 21,000\nB. Rs. 22,500\nC. Rs. 25,300\nD. Rs. 25,800\nE. None\n\n### Answer:\nSolution\n85 : 18700 = 115 : x or\tx = (18700 x 115 / 85)\n= 25300.\nHence, S.P. = Rs. 25300.\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a group of hats consisting of only blue hats, green hats, and purple hats, the ratio of blue hats to green hats to purple hats is 7:4:12. If there are a total of 161 hats in this group, how many of these hats are not blue?\n\n### Options:\nA. 28\nB. 42\nC. 48\nD. 112\nE. 76\n\n### Answer:\nSince the hats Blue, Green and Purple are in ratio of 7:4:12...The total no. of balls will be\n7x+4x+12x=161 or 23x=161...here 7x,4x and 12x represent hats of each type\n23x=161 so x=7...Blue hats =7*7=49...Not blue will be 161-49=112.\nAns D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRs.1010/- distributed among A,B and C such that on decreasing their shares by RS.25,RS.10 and RS.15 respectively, The balance money would be divided among them in the ratio 3:2:5. Then, A\u2019s share is:?\n\n### Options:\nA. Rs.255/-\nB. Rs.313/-\nC. Rs.365/-\nD. Rs.355/-\nE. Rs.345/-\n\n### Answer:\nA:B:C = 3:2:5\nTotal parts = 10\nA's share is = 3 parts\n10 -----> Rs.960/-\n3 -----> Rs.288/-\nA's total =288 + 25 = Rs.313/-\nB)\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA cycle is bought for Rs.900 and sold for Rs.1080, find the gain percent?\n\n### Options:\nA. 28%\nB. 20%\nC. 29%\nD. 27%\nE. 10%\n\n### Answer:\n900 ---- 180\n100 ---- ? => 20%\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMatt is touring a nation in which coins are issued in two amounts, 2\u00a2 and 5\u00a2, which are made of iron and copper, respectively. If Matt has twu iron coins and twu copper coins, how many different sums from 1\u00a2 to 14\u00a2 can he make with a combination of his coins?\n\n### Options:\nA. 8\nB. 11\nC. 9\nD. 4\nE. 12\n\n### Answer:\nThe total sum is 2*2 + 2*5 = 14\u00a2. If you can make each sum from 1 to 14 (1\u00a2, 2\u00a2, 3\u00a2, ..., 14\u00a2), then the answer would be 14 (maximum possible).\nNow, with 2\u00a2 and 5\u00a2 we cannot make 1\u00a2 and 3\u00a2. We also cannot make 13\u00a2 and 11\u00a2 (since total sum is 14\u00a2 we cannot remove 1\u00a2 or 3\u00a2 to get 13\u00a2 or 11\u00a2).\nAlso discarded 6 and 8, for lack of even numbers after 4\nSo, out of 14 sums 6 are for sure not possible, so the answer must be 14 - 6 = 8 sums or less. Only A fits.\nAnswer: A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe radius of the base of cone is 3 cm and height is 4 cm. Find the volume of the cone?\n\n### Options:\nA. 12\nB. 75\nC. 97\nD. 15\nE. 91\n\n### Answer:\n1/3 * \u03c0 * 3 * 3 * 4\n= 12 \u03c0\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSteve traveled the first 2 hours of his journey at 50 mph and the last 3 hours of his journey at 80 mph. What is his average speed of travel for the entire journey?\n\n### Options:\nA. 60 mph\nB. 68 mph\nC. 53.33 mph\nD. 64 mph\nE. 66.67 mph\n\n### Answer:\nAnswer\nAverage speed of travel = Total distance travelled/Total time taken\nTotal distance traveled by Steve = Distance covered in the first 2 hours + distance covered in the next 3 hours.\nDistance covered in the first 2 hours = speed * time = 50 * 2 = 100 miles.\nDistance covered in the next 3 hours = speed * time = 80 * 3 = 240 miles.\nTherefore, total distance covered = 100 + 240 = 340 miles.\nTotal time taken = 2 + 3 = 5 hours.\nHence, average speed = Total distance travelled/Total time taken=340/5 = 68 miles per hour.\nChoice B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAmy has to visit towns B and C in any order. The roads connecting these towns with her home are shown on the diagram. How many different routes can she take starting from A and returning to A, going through both B and C (but not more than once through each) and not travelling any road twice on the same trip?\n\n### Options:\nA. 1\nB. 8\nC. 9\nD. 2\nE. 7\n\n### Answer:\nExplanation:\nAmy can travel clockwise or anticlockwise on the diagram.\nClockwise, she has no choice of route from A to B, a choice of one out of two routes from B to C, and a choice of one out of two routes from C back to A. This gives four possible routes.\nSimilarly, anticlockwise sh\nAnswer: B) 8\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nCar X began traveling at an average speed of 35 miles per hour. After 48 minutes, car Y began traveling at an average speed of 39 miles per hour. When both cars had traveled the same distance, both cars stopped. How many miles did car X travel from the time car Y began traveling until both cars stopped?\n\n### Options:\nA. 105\nB. 140\nC. 175\nD. 210\nE. 245\n\n### Answer:\nIn 48 minutes, car X travels 28 miles.\nCar Y gains 4 miles each hour, so it takes 7 hours to catch car X.\nIn 7 hours, car X travels 245 miles.\nThe answer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n1100 boys and 700 girls are examined in a test; 31% of the boys and 23% of the girls pass. The percentage of the total who failed is ?\n\n### Options:\nA. A)63.3%\nB. B)52.4%\nC. C)81.2%\nD. D)75.4%\nE. E)72.11%\n\n### Answer:\nTotal number of students = 1100+700 = 1800\nNumber of students passed = (31% of 1100+23% of 700) = 341+161 = 502\nnumber of failures = 1298*100/1800= 72.11%\nAnswer is E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA sum of Rs. 2678 is lent into two parts so that the interest on the first part for 8 years at 3% per annum may be equal to the interest on the second part for 3 years at 5% per annum. Find the second sum?\n\n### Options:\nA. 1629\nB. 1648\nC. 2677\nD. 2986\nE. 2679\n\n### Answer:\n(x*8*3)/100 = ((2678 - x)*3*5)/100\n24x/100 = 40170/100 - 15x/100\n39x = 40170 => x = 1030\nSecond sum = 2678 \u00e2\u20ac\u201c 1030 = 1648\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nF and E are midpoints of AB and AD respectively. If the side of square ABCD is 8, what is the area of triangle CEF?\n\n### Options:\nA. 8\u221a2\nB. 9\u221a3\nC. 18\nD. 16\u221a2\nE. 24\n\n### Answer:\nArea of Shaded figure = Area of Square - (Area of Triangle AEF + Area of Triangle FBC + Area of Triangle EDC )\n= 8*8 - (1/2 * 4 * 4 + 1/2 * 4 * 8 + 1/2 * 4 * 8 )\n= 24.\nAnswer E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo-third of a positive number and 16/216 of its reciprocal are equal. Find the positive number.\n\n### Options:\nA. 9/25\nB. 14/4\nC. 4 /12\nD. 144/25\nE. 144/29\n\n### Answer:\nExplanation:\nLet the positive number be x.\nThen, 2/3 x = 16/216 * 1/x\nx2 = 16/216 * 3/2\n= 16/144\nx = \u221a16/144 =4 /12.\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOf the 60 electronics components that a factory must manufacture, 80 percent would be most e\u00a2 ciently manufactured by Machine A and the remaining 20 percent would be most efficiently manufactured by Machine B, though either machine could manufacture any of the 60 components. If 40 percent of the components were manufactured by Machine A and the remainder were manufactured by Machine B, what is thehighest possible number of components that were manufactured by the machine that would manufacture them the most efficiently?\n\n### Options:\nA. 30\nB. 32\nC. 33\nD. 35\nE. 36\n\n### Answer:\nA can manufacture 80 % of 60 efficiently, which is 48.\nB can manufacure 20 % of 60 efficiently, which is 12.\nNow 40 % of 60 are produced by A. This means 24 parts. Since A can produce 48 efficiently, all 24 are produced efficiently. Rest (36) is produced by B, which can produce max. 12 parts efficiently.\nHence parts that were produced efficiently = 12+24 = 36. (E).\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a group of ducks and cows, the total number of legs are 24 more than twice the no. of heads. Find the total no.of buffaloes.\n\n### Options:\nA. 10\nB. 12\nC. 16\nD. 17\nE. 18\n\n### Answer:\nLet the number of buffaloes be x and the number of ducks be y\n=> 4x + 2y = 2 (x + y) + 24\n=> 2x = 24 => x = 12\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind out the wrong number in the given sequence of numbers.\n1, 2, 6, 15, 31, 56, 93\n\n### Options:\nA. 2\nB. 6\nC. 15\nD. 93\nE. 91\n\n### Answer:\n1(result) + (1*1) = 2.\n2(result) + (2*2) = 6.\n6(result) + (3*3) = 15.\n15(result) + (4*4) = 31.\n31(result) + (5*5) = 56.\n56(result) + (6*6) = 92.\nNow we are getting 92 not 93.. So 93 is the wrong number of the given.\nanswer : D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWendy begins sanding a kitchen floor by herself and works for 7 hours. She is then joined by Bruce, and together the two of them finish sanding the floor in 2 hours. If Bruce can sand the floor by himself in 20 hours, how long would it take Wendy to sand the floor by herself?\n\n### Options:\nA. 9/80 hours\nB. 3/20 hours\nC. 20/3 hours\nD. 80/9 hours\nE. 10 hours\n\n### Answer:\nLet Wendy finishes sanding the floor alone in W hours while B be the hours for Bruce.\nThus in 1 hour Wendy finishes 1/w of the work while Bruce finishes 1/B of the work.\nIf wendy works for 7 hours and is then joined by Bruce to finish the work in 2 more hours,\n7/W + 2/W+2/B = 1 (1 denotes the total amount of work)\n9/W + 2/B =1 and given B =20 hours.\nThus W = 10 hours , E is the correct answer.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf two positive numbers are in the ratio 1/8 : 1/5, then by what percent is the second number more than the first?\n\n### Options:\nA. 67%\nB. 70%\nC. 60%\nD. 62%\nE. 65%\n\n### Answer:\nGiven ratio\n= 1/8 : 1/5 = 5 : 8\nLet first number be 5x and the second number be 8x.\nThe second number is more than first number by 3x.\nRequired percentage\n= 3x/5x * 100 = 60%.\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe regular price per can of a certain brand of soda is $0.55. If the regular price per can is discounted 25 percent when the soda is purchased in 24-can cases, what is the price of 70 cans of this brand of soda purchased in 24-can cases?\n\n### Options:\nA. $16.32\nB. $18.00\nC. $21.60\nD. $24.48\nE. $28.87\n\n### Answer:\nThe discounted price of one can of soda is (0.75)($0.55), or $0.4125\nTherefore, the price of 70 cans of soda at the discounted price would be (70)($0.4125) = 28.875\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n\u00e2\u02c6\u01611.5625 = ?\n\n### Options:\nA. 1.05\nB. 1.25\nC. 1.45\nD. 1.55\nE. 1.65\n\n### Answer:\nExplanation:\n1|1.5625( 1.25\n|1\n|-------\n22| 56\n| 44\n|-------\n245| 1225\n| 1225\n|-------\n| X\n|-------\n1.5625 = 1.25.\nANSWER IS B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA hostel had provisions for 250 men for 44 days. If 50 men left the hostel, how long will the food last at the same rate?\n\n### Options:\nA. 55\nB. 40\nC. 50\nD. 60\nE. 65\n\n### Answer:\nA hostel had provisions for 250 men for 44 days\nIf 50 men leaves the hostel, remaining men = 250 - 50 = 200\nWe need to find out how long the food will last for these 200 men.\nLet the required number of days = x days\nMore men, Less days (Indirect Proportion)\n(men) 250 : 200 :: x : 44\n250\u00d744=200x\n5\u00d744=4x\nx=5\u00d711=55\nANSWER A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe rate of Interest on a sum of money is 9% p.a. for the first 3 years, 4% p.a. for the next 4 years, and 5% for the period beyond 7 years. If the S.I, Occured on the sum for the total period of 8 years is Rs. 540/-, the sum is\n\n### Options:\nA. 1,125\nB. 2,000\nC. 2,100\nD. 2,250\nE. 2,540\n\n### Answer:\nExplanation:\nI1 = (P x 3 x 9)/100 = 10P/37\nI2 = (P x 4 x 4)/100 = 4P/25\nI3 = (P x 1 x 5)/100 = P/20\n10P/37 + 4P/25 + P/20 = 540\n12P/25 = 540\nP = 1125\nAnswer: Option A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFor an employee to qualify for early retirement at a certain company, the sum of the employee\u2019s age and years of service must be at least 74, If Sue was K years old when she was hired by the company, what is the minimum age at which she could possibly qualify for early retirement?\n\n### Options:\nA. K+37\nB. 2K+37\nC. (74+K)/2\nD. (74-K)/2\nE. 2(74-K)\n\n### Answer:\nLet y be the years of service at the company.\nAfter y years of service, Sue's age will be K + y.\nSue can retire when (K+y) + y = 74\ny = (74 - K)/2\nThen Sue's age will be K + y = K + (74 - K)/2 = (74+K) / 2\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nGrace packed 5 pairs of shoes, 3 pairs of pants, 8 shirts, and 3 jackets for her business trip. If an outfit consists of one of each item of clothing except shirts, of which she will wear 2, how many different outfits S can does Grace have available during her trip?\n\n### Options:\nA. 2,520\nB. 1,260\nC. 620\nD. 360\nE. 120\n\n### Answer:\nThe idea is to multiply the number of possibilities for each item of clothing with the different items. For the shirts you essentially choose 2 out of 8 so you should use the combination forumla (don't know how to use math symbols here).\nThis gives you S=5 x 3 x 28 x 3 = 1'260. Hence, solution B is correct.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA sun is divided among X, Y and Z in such a way that for each rupee X gets, Y gets 45 paisa and Z gets 50 paisa. If the share of Y is RS. 36, what is the total amount?\n\n### Options:\nA. 115\nB. 116\nC. 117\nD. 118\nE. 156\n\n### Answer:\nx:y:z = 100:45:50\n20:9:10\n9 --- 36\n39 --- ? => 156\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe length of a rectangle is two - fifths of the radius of a circle. The radius of the circle is equal to the side of the square, whose area is 100 sq.units. What is the area (in sq.units) of the rectangle if the rectangle if the breadth is 2 units?\n\n### Options:\nA. 140 sq.units\nB. 158 sq.units\nC. 8 sq.units\nD. 607 sq.units\nE. 815 sq.units\n\n### Answer:\nGiven that the area of the square = 100 sq.units\n=> Side of square = \u221a100= 10 units\nThe radius of the circle = side of the square = 10 units\nLength of the rectangle = 2/5 * 10 = 4 units\nGiven that breadth = 2 units\nArea of the rectangle = lb = 4 * 2 = 8 sq.units\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFrom a group of 3 CATS and 3 DOGS, 4 animals are to be randomly selected. What is the probability that equal numbers of cats and dogs will be selected?\n\n### Options:\nA. 1/5\nB. 2/5\nC. 4/5\nD. 3/5\nE. 1\n\n### Answer:\nUsing the first example, here is the probability of THAT EXACT sequence occurring:\nCCDD = (3/6)(2/5)(3/4)(2/3) = 36/360 = 1/10\nEach of the other 5 options will yield the exact SAME probability....\neg\nCDCD = (3/6)(3/5)(2/4)(2/3) = 36/360 = 1/10\nSo we have 6 different options that each produce a 1/10 chance of occurring.\n6(1/10) = 6/10 = 3/5\nFinal Answer:\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA company can manufacture 1000 phones in a day. One-fifth of the phones produced are defective and one-quarter of all phones produced are rejected by quality control technician. If one-tenth of the nondefective phones are rejected by mistake, and if all the phones not rejected are sold, then what percent of the phones sold by the company are defective?\n\n### Options:\nA. 4%\nB. 16%\nC. 24%\nD. 2%\nE. 8%\n\n### Answer:\nWe have 20% defective and 80% non-defective; we have 25% rejected and 75% not rejected. We also know that 1/10 of the non-defective ones (8%) are rejected, so 72% sold. This means that we have 3% sold that are defective and 17% rejected that are defective. Overall, we have 3%/75% or 1 of every 25 that are sold (not rejected) and defective. Correct Answer is A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train running at the speed of 60 km/hr crosses a pole in 36 seconds. What is the length of the train?\n\n### Options:\nA. 186 m\nB. 176 m\nC. 100 m\nD. 600 m\nE. 765 m\n\n### Answer:\nSpeed=(60 * 5/18) m/sec = (50/3) m/sec Length of the train\n= (Speed x Time) = (50/3 * 36) m\n= 600 m.\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTrain X and train Y pass one another traveling in opposite directions. Thirty minutes later they are 100 miles apart. If train X\u2019s constant speed is 40 miles per hour greater than train Y\u2019s, how far does train X travel during that time?\n\n### Options:\nA. 28\nB. 40\nC. 60\nD. 72\nE. 80\n\n### Answer:\nLet the rate of the Train Y be R\nThen the rate of the Train X will be R+40 (given)\nAs per relative rate concept, the rate at which they are increasing the distance between them is R+(R+40) [add the rates] i.e. 2R+40\nd=100 and t = 30 min i.e 30/60 hr\nusing RTD table, (2R+40) * 30/60 = 100 ==> R= 80 miles/hr\nSo the rate of train X is 120 miles/hr (since R+40)\nThe distance traveled by Train X in 30 min is R*T = 120 * 30/60 = 60 miles (C)\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo pipes A and B can separately fill a tank in 2 minutes and 15 minutes respectively. Both the pipes are opened together but 4 minutes after the start the pipe A is turned off. How much time will it take to fill the tank?\n\n### Options:\nA. 18\nB. 10\nC. 12\nD. 11\nE. 17\n\n### Answer:\n4/12 + x/15\n= 1\nx = 10\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJuan is a gold medalist in athletics. In the month of May, if Juan takes 12 seconds to run y yards, how many seconds will it take him to run x yards at the same rate?\n\n### Options:\nA. 10x/y\nB. 11x/y\nC. 9x/y\nD. 12x/y\nE. 13x/y\n\n### Answer:\nvelocity=distance/time;\nsince he ran at same rate both d tyms,\ny/12=x/t\nso t=12x/y\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe actual price of an article was Rs. 6000/- the successive discount on 10% and 20% then Finds the selling price\n\n### Options:\nA. Rs.3240/-\nB. Rs. 4320/-\nC. Rs.4230/-\nD. Rs.4200/-\nE. None of these\n\n### Answer:\nExplanation:\nNote: Selling price = MRP * (100 - d1)/100 * (100 - d2)/100 * -------------\nMRP = 6000/- , d1 = 10, d2 = 20\nSelling price = 6000 * (100 - 10)/100 * (100-20)/100 ==> 6000 * 90/100 * 80/100\n=> 48 * 90 = Rs. 4320/-\nAnswer: Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA rectangular grass field is 75 m * 55 m, it has a path of 2.5 m wide all round it on the outside. Find the area of the path and the cost of constructing it at Rs.2 per sq m?\n\n### Options:\nA. Rs.1350\nB. Rs.1327\nC. Rs.1328\nD. Rs.1397\nE. Rs.1927\n\n### Answer:\nArea = (l + b +2d) 2d\n= (75 + 55 +2.5 * 2) 2*2.5 => 675\n675 * 2 = Rs.1350\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo numbers are respectively 20% and 50% more than a third number. The percentage that is first of the second is?\n\n### Options:\nA. 77%\nB. 78%\nC. 79%\nD. 80%\nE. 81%\n\n### Answer:\nI II III\n120 150 100\n150----------120\n100-----------? => 80%\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain animal shelter has 28 cats and 46 dogs. How many dogs must be adopted and taken away from the animal shelter so that 70 percent of the animals in the shelter will be cats?\n\n### Options:\nA. 6\nB. 12\nC. 28\nD. 34\nE. 40\n\n### Answer:\n(28 + 46 - x)*0.7 = 28\nx = 34.\nAnswer: D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n45 men can complete a work in 18 days. Six days after they started working, 30 more men joined them. How many days will they now take to complete the remaining work?\n\n### Options:\nA. 6.6\nB. 10\nC. 15\nD. 7.2\nE. 8\n\n### Answer:\n45*18 men can complete the work in 1 day\n1 man's 1 day work = 1/810\n45 men 6 days work = 6*1/18 = 1/3\nremaining work = 1-1/3 = 2/3\n75 men's 1 day's work = 75/810 = 5/54\n2/3 work is done by them in 54/5 * 2/3 = 7.2 days\nAnswer is D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA reduction of 15% in the price of wheat enables a house wife to obtain 3 kgs more for Rs.500, what is the reduced price for kg?\n\n### Options:\nA. Rs.10\nB. Rs.15\nC. Rs.20\nD. Rs.25\nE. Rs.30\n\n### Answer:\nExplanation:\n500*(15/100) = 75 ---- 3\n? ---- 1 => Rs.25\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA rectangular box of volume V has width, depth and height in the ratio of 2:1:3 (in that order). What is the height as a function of V?\n\n### Options:\nA. (V/2)^(1/3)\nB. (2V/6)^(1/3)\nC. (9V/2)^(1/3)\nD. (4V/3)^(1/3)\nE. (4V/2)^(1/3)\n\n### Answer:\nWe are given width = 2, depth = 1, height = 3.\nThen Volume V = Width x Depth x Height = 2*1*3 = 6\ni.e. V = 6\nThe correct option should result in 3 (the height) on substituting the value of V=6.\nChecking options with V=6:\nA) (V/2)^(1/3) = (6/2)^(1/3) = 3^(1/3) INCORRECT ANSWER\nB) (2V/6)^(1/3) = (12/6)^(1/3) = 2^(1/3) INCORRECT ANSWER\nC) (9V/2)^(1/3) = (54/2)^(1/3) = 3 CORRECT ANSWER\nD) (4V/3)^(1/3) = (24/3)^(1/3) = 8^(1/3) = 2 INCORRECT ANSWER\nE) (4V/2)^(1/3) = (24/2)^(1/3) = 12^(1/3) INCORRECT ANSWER\nAnswer: Option C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 1st October is Sunday, then 1st November will be\n\n### Options:\nA. Saturday\nB. Thursday\nC. Wednesday\nD. Tuesday\nE. Monday\n\n### Answer:\nExplanation:\nGiven that 1st October is Sunday\nNumber of days in October = 31\n31 days = 3 odd days\n(As we can reduce multiples of 7 from odd days which will not change anything)\nHence 1st November = (Sunday + 3 odd days) = Wednesday\nAnswer: Option C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAt a certain stage of a soccer tournament, the score ratio of teams A, B and C was 3:4:5. Eventually, the score ratio of A to B has doubled while the score ratio of A to C has halved. If the final score of team C was 40, what was the final score W of team B?\n\n### Options:\nA. 1)8\nB. 2)10\nC. 3)20\nD. 4)40\nE. 5)80\n\n### Answer:\nA to B = 3 : 4\nSo, on doubling we get 6 : 4\nA to C = 3 : 5\nSo, on halving we get 1.5 : 5 or 3 : 10 or 6 : 20\nSo final ratio = 6 : 4 : 20.\nIf 20x = 40\n4x = 8\nHence, answer is A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA guy was asked to specify his age in years. He said, \u201cTake my age 8 years hence, multiply it by eight and subtract eight times of my age 8 years ago and get the half of the result and you will know my age.\u201d What was the age of that guy?\n\n### Options:\nA. 18\nB. 55\nC. 63\nD. 64\nE. 70\n\n### Answer:\nCurrent age of the guy = A years.\nThen, 8 (A + 8) \u2013 8 (A \u2013 8) = A\n(8A + 64) \u2013 (8A \u2013 64) = A\nA = 128/2 =64\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA car takes 6 hours to cover a distance of 288 Km. how much should the speed in Kmph be maintained to cover the same direction in 3/2th of the previous time?\n\n### Options:\nA. 50 Kmph\nB. 60 Kmph\nC. 32 Kmph\nD. 70 Kmph\nE. None\n\n### Answer:\nTime = 6\nDistence = 288\n3/2 of 6 hours = 6 * 3/2 = 9 Hours\nRequired speed = 288/9 = 32 Kmph\nC)\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJoe\u2019s average (arithmetic mean) test score across 4 equally weighted tests was 35. He was allowed to drop his lowest score. After doing so, his average test score improved to 40. What is the lowest test score that was dropped?\n\n### Options:\nA. 20\nB. 25\nC. 55\nD. 65\nE. 80\n\n### Answer:\nThe arithmetic mean of 4 equally weighted tests was 35. So what we can assume is that we have 4 test scores, each 35.\nHe dropped his lowest score and the avg went to 40. This means that the lowest score was not 35 and other three scores had given the lowest score 5 each to make it up to 35 too. When the lowest score was removed, the other 3 scores got their 5 back. So the lowest score was 3 *5 = 15 less than 35.\nSo the lowest score =35 - 15 = 20\nAnswer (A)\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf -1", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA and B complete a work in 4 days. A alone can do it in 8 days. If both together can do the work in how many days?\n\n### Options:\nA. 3.75 days\nB. 3.78 days\nC. 3.25 days\nD. 3.15 days\nE. 2.7 days\n\n### Answer:\n1/4 + 1/8 = 3/8\n8/3 = 2.7 days\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nCalculate the average of first 18 even numbers is?\n\n### Options:\nA. 21\nB. 29\nC. 19\nD. 14\nE. 10\n\n### Answer:\nExplanation:\nSum of 10 even numbers = 18 * 19 = 342\nAverage = 342/18 = 19\nAnswer: Option C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOn dividing 109 by a number, the quotient is 9 and the remainder is 1. Find the divisor.\n\n### Options:\nA. 12\nB. 14\nC. 16\nD. 18\nE. 22\n\n### Answer:\nd = (D-R)/Q\n= (109 - 1)/9\n= 108/9 = 12\nA)\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA card game called \u201chigh-low\u201d divides a deck of 52 playing cards into 2 types, \u201chigh\u201d cards and \u201clow\u201d cards. There are an equal number of \u201chigh\u201d cards and \u201clow\u201d cards in the deck and \u201chigh\u201d cards are worth 2 points, while \u201clow\u201d cards are worth 1 point. If you draw cards one at a time, how many ways can you draw \u201chigh\u201d and \u201clow\u201d cards to earn 5 points if you must draw exactly 3 \u201clow\u201d cards?\n\n### Options:\nA. 1\nB. 2\nC. 3\nD. 4\nE. 5\n\n### Answer:\nTo get a 5, you need one high and three lows (you could have had 2 highs and one low, but the constraint is that you must have three low cards)\nHLLL = 4!3! =4\n4! is the number of ways you can arrange these four spaces. divide by 3! because you you repeat three low cards\nANS:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a series of six consecutive odd numbers, the third number is 31. What is the fifth number?\n\n### Options:\nA. 35\nB. 33\nC. 45\nD. 31\nE. 29\n\n### Answer:\nLet the numbers be x, x + 1, x + 3, x + 5 and x + 7.\nGiven (x + 3) = 31\n=> x = 28\nThe fifth number = x + 7 = 28 + 7 = 35.\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the length of the wire required to go 15 times round a square field containing 69696 m^2.\n\n### Options:\nA. 15840\nB. 26480\nC. 15642\nD. 15640\nE. 15849\n\n### Answer:\na^2 = 69696 => a = 264\n4a = 1056\n1056 * 15 = 15840\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRavi and Kumar are working on an assignment. Ravi takes 6 hours to type 32 pages on a computer, while Kumar takes 5 hours to type 40 pages. How much time will they take, working together on two different computers to type an assignment of 110 pages?\n\n### Options:\nA. 7 hours 30 minutes\nB. 8 hours\nC. 8 hours 15 minutes\nD. 8 hours 25 minutes\nE. 7 hours 35 minutes\n\n### Answer:\nNumber of pages typed by Ravi in 1 hour =\t32/6\t=\t16/3\t.\nNumber of pages typed by Kumar in 1 hour =\t40/5\t= 8.\nNumber of pages typed by both in 1 hour =\t(16/3+ 8)\t=\t40/3\t.\nTherefore Time taken by both to type 110 pages =\t(\t110 x\t3/40\t)\thours\n= 8\t1/4 hours (or) 8 hours 15 minutes.\nOption C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo kinds of Vodka are mixed in the ratio 1:2 and 2:1 and they are sold fetching the profit 25% and 20% respectively. If the vodkas are mixed in equal ratio and the individual profit percent on them are increased by 4/3 and 5/3 times respectively, then the mixture will fetch the profit of\n\n### Options:\nA. 18%\nB. 20%\nC. 21%\nD. 25%\nE. Cannot be determined\n\n### Answer:\nAnswer: D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the C.I. on Rs. 15,625 for 9 months at 16% per annum compounded quarterly?\n\n### Options:\nA. Rs.1978\nB. Rs.1979\nC. Rs.1951\nD. Rs.1968\nE. Rs.1929\n\n### Answer:\nP = Rs. 15625, n = 9 months = 3 quarters, R = 16% p.a. per quarter.\nAmount = [15625 * (1 + 4/100)3]\n= (15625 * 26/25 * 26/25 * 26/25)\n= Rs. 17576 C.I.\n= 17576 - 15625 = Rs. 1951.\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a, b, and c are consecutive even positive integers, which of the following could be equal to a + b + c ?\n\n### Options:\nA. 141\nB. 200\nC. 624\nD. 391\nE. 412\n\n### Answer:\nThe key to answering this question quickly is to realize that a+b+c is a multiple of BOTH 2 and 3. With that information, you can quickly eliminate answer choices. If you don't recognize those two Number Properties though, then you can still get to the correct answer (but it will require a bit more work).\nWe're told that a, b and c are CONSECUTIVE EVEN INTEGERS, so we could write them algebraically as...\nA + (A+2) + (A+4) = 3A + 6\nWe know that 3A + 6 COULD equal one of those five answers; we just have to find it...\nCould 3A + 6 = 141\n3A = 135\nA = 45\nThis is NOT an EVEN INTEGER, so 141 is NOT the answer\nCould 3A + 6 = 200\n3A = 194\nA = 64.6666\nThis is NOT an EVEN INTEGER, so 200 is NOT the answer\nCould 3A + 6 = 624\n3A =618\nA = 206\nThis IS an EVEN INTEGER! The numbers would be 206, 208 and 210. This IS the answer\nFinal Answer:\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 20 liters of chemical X are added to 80 liters of a mixture that is 30% chemical X and 70% chemical Y, then what percentage of the resulting mixture is chemical X?\n\n### Options:\nA. 32%\nB. 35%\nC. 38%\nD. 41%\nE. 44%\n\n### Answer:\nThe amount of chemical X in the solution is 20 +0.3(80) = 44 liters.\n44 liters / 100 liters = 44%\nThe answer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA grocer has a sale of Rs 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs, 6500 ?\n\n### Options:\nA. 4991\nB. 2367\nC. 1976\nD. 1627\nE. 1981\n\n### Answer:\nExplanation:\nTotal sale for 5 months = Rs. (6435 + 6927 + 6855 + 7230 + 6562) = Rs. 34009.\nRequired sale = Rs.[(6500 x 6) - 34009]\n= Rs. (39000 - 34009)\n= Rs. 4991.\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n15 + sqrt(- 6 + 8\u00c3\u20145\u00c3\u00b74) =?\n\n### Options:\nA. 31\nB. 32\nC. 33\nD. 34\nE. 35\n\n### Answer:\nAccording to order of operations, inner brackets first where 8x5\u00c3\u00b74 is first calculated since it has a multiplication and a division.\n8x5\u00c3\u00b74 = 40\u00c3\u00b74 = 10\nHence\n15 + sqrt(- 6 + 8\u00c3\u20145\u00c3\u00b74) = 15+ sqrt(- 6 + 10)\n= 15 + sqrt(4) = 15 + 16 = 31\ncorrect answer A)31\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJanuary 1, 2007 was Monday. What day of the week lies on Jan. 1, 2008 ?\n\n### Options:\nA. Monday\nB. Tuesday\nC. wednesday\nD. Sunday\nE. None of these\n\n### Answer:\nSolution\nThe year 2007 is an ordinary year. So, it has 1 odd day.\n1st day of the year 2007 was Monday.\n1st day of the year 2008 will be 1 day beyond Monday.\nHence, it will be Tuesday. Answer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a - b = 4 and a2 + b2 = 30, find the value of ab.\n\n### Options:\nA. A)7\nB. B)12\nC. C)15\nD. D)18\nE. E)20\n\n### Answer:\nExplanation:\n2ab = (a2 + b2) - (a - b)2\n= 30 - 16 = 14\nab = 7\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA bullet train 220 m long is running with a speed of 59 kmph. In what time will it pass a man who is running at 7 kmph in the direction opposite to that in which the bullet train is going?\n\n### Options:\nA. 23 sec\nB. 15 sec\nC. 12 sec\nD. 11 sec\nE. 16 sec\n\n### Answer:\nC\n12 sec\nSpeed of the bullet train relative to man = (59 + 7) kmph\n= 66 *5/18 m/sec = 55/3 m/sec.\nTime taken by the bullet train to cross the man = Time taken by it to cover 220 m at (55/3) m / sec\n= (220 *3/55) sec = 12 sec\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe diameter of a garden roller is 1.4 m and it is 2 m long. How much area will it cover in 5 revolutions ? (use \u03c0 = 22\u20447)\n\n### Options:\nA. 40 m2\nB. 44 m2\nC. 48 m2\nD. 36 m2\nE. None of these\n\n### Answer:\nRequired area covered in 5 revolutions\n= 5 \u00d7 2\u03c0rh = 5 \u00d7 2 \u00d7 22\u20447 \u00d7 0.7 \u00d7 2 = 44 m2\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThirty percent of the members of a swim club have passed the lifesaving test. Among the members who havenotpassed the test, 5 have taken the preparatory course and 30 have not taken the course. How many members are there in the swim club?\n\n### Options:\nA. 60\nB. 80\nC. 50\nD. 120\nE. 140\n\n### Answer:\n30% of the members have passed the test, thus 70% have not passed the test.\nWe also know that 30+5=42 members have not passed the test, thus 0.7*Total=35 --> Total=50.\nAnswer: C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA is twice as good a work man as B and together they finish the work in 10 days. In how many days A alone can finish the work?\n\n### Options:\nA. 23\nB. 15\nC. 77\nD. 92\nE. 61\n\n### Answer:\nWC = 2:1\n2x + x = 1/10 => x = 1/30\n2x = 1/15\nA can do the work in 15 days.\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a triangle XYZ, XZ is the longest side, length of which is 1 unit more than YZ, which again has length 1 unit more than XY. If area of the triangle is 10 and the shortest side is 3. What are the lengths of the three sides?\n\n### Options:\nA. 1, 2, 5\nB. 3, 4, 5\nC. 4, 5, 6\nD. 7, 8, 9\nE. 5, 2, 4\n\n### Answer:\nXY=3\nYZ=1+XY = 4\nXZ=1+YZ=5\nB is the correct option.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n4,25,121,289,?\n\n### Options:\nA. 345\nB. 445\nC. 515\nD. 529\nE. 645\n\n### Answer:\nPrime numbers- 2,3,5,7,11,13,17,19,23.....\nSeries - 2^2,5^2,11^2,17^2,23^2\nSeries- 4, 25, 121, 289, 529.\nSo next term in series is- 529.\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a and b are integers and (2^a)(3^b) is a factor of 180^40, what is the largest possible value of ab?\n\n### Options:\nA. 2a\nB. 5a\nC. 20a\nD. 40a\nE. 80a\n\n### Answer:\n(2^a)(3^b) is a factor of 180^40\nWe need to find the largest possible value of ab.\nWe know that 180 = 2^2*5^1*3^2\nTherefore 180^40 will have 2 powers of 3 in it.\nHence in (2^a)(3^b), b has to 2\nTherefore value of ab = 2a\nCorrect Option: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the largest 4 digit number exactly divisible by 88?\n\n### Options:\nA. 8844\nB. 9944\nC. 7744\nD. 6644\nE. 5544\n\n### Answer:\nLargest 4 digit number = 9999\n9999 \u00f7 88 = 113, remainder = 55\nHence largest 4 digit number exactly divisible by 88\n= 9999 - 55 = 9944\nAnswer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe instructions state that Cheryl needs 4/9 square yards of one type of material and 2/3 square yards of another type of material for a project. She buys exactly that amount. After finishing the project, however, she has 6/12 square yards left that she did not use. What is the total amount of square yards of material Cheryl used?\n\n### Options:\nA. 1/12\nB. 1/9\nC. 2/3\nD. 1 1/9\nE. 11/18\n\n### Answer:\ntotal bought = 4/9+2/3\nleft part 6/12--->1/2\nso used part 4/9+2/3-1/2=11/18\nAns E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how many different ways can the letters of the word \"LEADING\" be arranged in such a way that the vowels always come together.\n\n### Options:\nA. W8\nB. 789\nC. 279\nD. 277\nE. 191\n\n### Answer:\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA sun is divided among X, Y and Z in such a way that for each rupee X gets, Y gets 45 paisa and Z gets 30 paisa. If the share of Y is RS. 54, what is the total amount?\n\n### Options:\nA. 166\nB. 105\nC. 178\nD. 177\nE. 210\n\n### Answer:\nx:y:z = 100:45:30\n20:9:6\n9 --- 54\n35 --- ? => 210\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a stationery store owner buys 50% more identically-priced calendars than she usually purchases, she will be given a 20% discount off the standard price. Her total cost would then be 120 times the dollar value of the standard price of one calendar. How many calendars does she usually purchase?\n\n### Options:\nA. 40\nB. 80\nC. 100\nD. 120\nE. 140\n\n### Answer:\nLet the Price is x per item\nand the final number of items she bought is y items\nSo to buy y items , the cost will be .8x (80% of original price , since there is a 20% discount on it)\n120*x = y*0.8*x\nSolving we get y =150\nnow to get the discount she bought 50% more than what she usually buys\nSo the number of items she usually buys is 50% less than 150\ni.e. original number of items she usually buys is = 150*(100/150) = 100\nHence Answer is (C)\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the average of the series : 256,254,350, 1110,1200 ?\n\n### Options:\nA. 129\nB. 308\nC. 634\nD. 207\nE. 174\n\n### Answer:\nAverage = (256+254+350+1110+1200) /5\n= 3170/5\n= 634\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a graduating class, 40 percent of the students are male. In this class, 50 percent of the male students and 40 percent of the female students are 25 years old or older. If one student in the class is randomly selected, approximately what is the probability that he or she will be less than 25 years old?\n\n### Options:\nA. 0.44\nB. 0.5\nC. 0.56\nD. 0.62\nE. 0.68\n\n### Answer:\nLet x be the total number of students.\nThe number students who are younger than 25 is 0.5*0.4x+0.6*0.6x = 0.56x\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf p+q=8z, then which of the following represents the average (arithmetic mean) of p, q, and z, in terms of z?\n\n### Options:\nA. 2z+1\nB. 3z\nC. 5z\nD. z/3\nE. 3z/2\n\n### Answer:\nPick any number like P=12, Q=12 and Z= 3 so that P+Q=8Z, now then the arithmetic mean will be (12+12+3)/3=9. Now, just look at the answers and put the value of Z there.\n(A) 2.3+1=7, no.\n(B) 3.3=9, it can be the answer, lets check us the other options\n(C) 5.3=15, no\n(D) 3/3=1 no\n(E) (3.3)/2=9/2, no\nso the answer will be B..\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOne year ago the ratio of Yamini\u2019s and Gamini\u2019s ages was 6 : 7 respectively. Four years hence this ratio would become 7 : 8. How old is Gamini?\n\n### Options:\nA. 35 years\nB. 30 years\nC. 31 years\nD. Cannot be determined\nE. None of these\n\n### Answer:\nY : G = 6 : 7; One year before\nY : G = 7 : 8; After 4 years\nNow, 1 \u2192 5\n\u2234 7 \u2192 35\nTherefore, the age of Gamini now is 35 + 1 = 36 years\nAnswer E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA and B together can do a piece of work in 8 days. If A alone can do the same work in 12 days, then B alone can do the same work in?\n\n### Options:\nA. 22 days\nB. 77 days\nC. 24 days\nD. 17 days\nE. 18 days\n\n### Answer:\nB = 1/8 \u2013 1/2 = 1/24 => 24 days\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRectangular tile each of size 35cm by 30cm must be laid horizontally on a rectangular floor of size 1000cm by 210cm,such that the tiles do not overlap and they are placed with edges jutting against each other on all edges. A tile can be placed in any orientation so long as its edges are parallel to the edges of floor. No tile should overshoot any edge of the floor. The maximum number of tiles that can be accommodated on the floor is:\n\n### Options:\nA. 600\nB. 400\nC. 200\nD. 500\nE. 100\n\n### Answer:\nArea of tile = 35*30 = 1050\nArea of floor = 1000*210 = 210000\nNo of tiles = 210000/1050 =200\nSo, the no of tile = 200\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFOG + FOG + FOG + FOG = 1468.\nIf F,O and G are digits in a three-digit number in the preceding equation the F + O + G = ?\n\n### Options:\nA. 11\nB. 12\nC. 13\nD. 14\nE. 16\n\n### Answer:\ngiven,FOG + FOG + FOG + FOG = 1468\n4(FOG)=1468\n=>FOG=367\nFace value of F is:3\nFace value of O is:6\nFace value of G is:7\nso F+O+G=3+6+7=16\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA sum of money is to be distributed among A, B, C, D in the proportion of 5:2:4:3. If C gets Rs. 1000 more than D, what is B's share?\n\n### Options:\nA. Rs.2029\nB. Rs.2028\nC. Rs.2000\nD. Rs.2022\nE. Rs.2021\n\n### Answer:\nLet the shares of A, B, C and D be 5x, 2x, 4x and 3x Rs. respectively.\nThen, 4x - 3x = 1000 => x = 1000.\nB's share = Rs. 2x = 2 * 1000\n= Rs.2000.\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSteve traveled the first 2 hours of his journey at 40 mph and the last 2 hours of his journey at 80 mph. What is his average speed of travel for the entire journey?\n\n### Options:\nA. 53.33 mph\nB. 56.67 mph\nC. 60 mph\nD. 64 mph\nE. 66.67 mph\n\n### Answer:\nAverage Speed = Total distance/ Total time = (40 * 2 + 80 * 2)/(2 + 2) = 240/4 = 60\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a(a + 2) = 35 and b(b + 2) = 35, where a \u2260 b, then a + b =\n\n### Options:\nA. -5\nB. -6\nC. -7\nD. -2\nE. -10\n\n### Answer:\ni.e. if a = 5 then b = -7\nor if a = -7 then b = 5\nBut in each case a+b = 5-7 = -2\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJane makes toy bears. When she works with an assistant, she makes 80 percent more bears per week and works 10 percent fewer hours each week. Having an assistant increases Jane\u2019s output of toy bears per hour by what percent R?\n\n### Options:\nA. 20%\nB. 80%\nC. 100%\nD. 180%\nE. 200%\n\n### Answer:\nC.\nLet's assume just Jane 40 bears per 40/hrs a week, so that is 1 bear/hr. With an assistant she makes 72 bears per 36 hours a week or 2 bears/hr ([40 bears * 1.8] / [40 hrs * .90]).\nR=[(2 - 1)/1] * 100% = 100%.C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf P/2 = Q/3 = R/4 then find P:Q:R\n\n### Options:\nA. 1:2:3\nB. 2:5:7\nC. 6:4:9\nD. 5:7:2\nE. 2:3:4\n\n### Answer:\nLet P/2 = Q/3 = R/4 = K\nP = 2K\nQ = 3K\nR = 4K\nP:Q:R = 2:3:4\nAnswer is E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe majority owner of a business received 25% of the profit, with each of 4 partners receiving 25% of the remaining profit. If the majority owner and two of the owners combined to receive $50,000, how much profit did the business make?\n\n### Options:\nA. $80,000\nB. $100,000\nC. $120,000\nD. $150,000\nE. $200,000\n\n### Answer:\nLet P be the total profit.\nP/4 + 1/2*(3P/4) = P/4 + 3P/8 = 5P/8 = 50000\nP = $80,000\nThe answer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man buys an article and sells it at a profit of 20%. If he had bought it at 20% less and sold it for Rs.50 less, he could have gained 25%. What is the cost price?\n\n### Options:\nA. 197\nB. 250\nC. 279\nD. 278\nE. 268\n\n### Answer:\nCP1 = 100 SP1 = 120\nCP2 = 80 SP2 = 80 * (125/100) = 100\n20 ----- 100\n50 ----- ? => 250\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nBy selling 16 pencils for a rupee a man loses 20%. How many for a rupee should he sell in order to gain 20%?\n\n### Options:\nA. 28\nB. 25\nC. 24\nD. 23\nE. 21\n\n### Answer:\n80% --- 16\n120% --- ?\n80/120 * 16 = 24\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man rides at the rate of 50km/hr. But stops 30minutes to change horses at the end of every 25th kilometer. How long will he take to go a distance of 250 kilometers?\n\n### Options:\nA. 5hr\nB. 6hr 30min\nC. 8hr 10min\nD. 7hr 20min\nE. 8hr\n\n### Answer:\nspeed of man = 50km/hr\nnumber of rests = (250/25)-1 = 9\ntime taken for the man = (250/50)+9*(20/60) = 8 hr\nAnswer is E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train when moves at an average speed of 40 kmph, reaches its destination on time. When its average speed becomes 35 kmph, then it reaches its destination 15 minutes late. Find the length of the journey\n\n### Options:\nA. 40km\nB. 50km\nC. 60km\nD. 70km\nE. 80km\n\n### Answer:\nDifference between timings = 15 min =0.25hr.\nLet the length of journey be x km.\nThen,\nx/35-x/40=0.25\n8x - 7x = 70\nx = 70km.\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIt costs a publishing company 50,000 dollars to make books. The 50,000 is a fixed cost or a cost that cannot change. To help the publishing company sell the books, a marketing company charges 4 dollars for each book sold. If the company charges 9 dollars per book, how many books should they sell to break even?\n\n### Options:\nA. 100\nB. 1000\nC. 10000\nD. 100000\nE. None\n\n### Answer:\nLet C be the cost of producing and selling x books\nLet R be the revenue made for selling x books\nR = selling price of 1 book \u00d7 number of books sold\nR = 9x\nC = fixed cost + variable cost\nvariable cost = fee charged for 1 book \u00d7 number of books sold\nvariable cost = 4x\nC = 50000 + 4x\nR = C\n9x = 50000 + 4x\n9x - 4x = 50000 + 4x - 4x\n5x = 50000\nx = 10000 since 5 \u00d7 10000 = 50000\nThe break even point is to sell 10000 books.\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf nn is a positive integer and (n+1)(n+3)(n+1)(n+3) is odd, then (n+2)(n+4)(n+2)(n+4) must be a multiple of which one of the following?\n\n### Options:\nA. 2\nB. 4\nC. 6\nD. 8\nE. 9\n\n### Answer:\n(n+1)(n+3)(n+1)(n+3) is odd only when both (n+1)(n+1) and (n+3)(n+3) are odd. This is possible only when nn is even.\nHence, n=2mn=2m, where mm is a positive integer. Then,\n(n+2)(n+4)=(2m+2)(2m+4)=2(m+1)2(m+2)=4(m+1)(m+2)(n+2)(n+4)=(2m+2)(2m+4)=2(m+1)2(m+2)=4(m+1)(m+2)\n=4 * (product of two consecutive positive integers, one which must be even)=4 * (product of two consecutive positive integers, one which must be even) =4 * (an even number), and this equals a number that is at least a multiple of 8=4 * (an even number), and this equals a number that is at least a multiple of 8\nHence, the answer is (D).\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\na, b, c, and d are positive consecutive even integers and a < b < c < d.\nIf the product of the highest and lowest numbers is six more than the sum of the middle numbers, what is the product of the smallest two numbers?\n\n### Options:\nA. 2\nB. 4\nC. 8\nD. 12\nE. 20\n\n### Answer:\nWe know the numbers must be consecutive even numbers, from the list 2, 4, 6, 8, 10, 12, 14, 16, and so on.\nThe product ad is 6 more than the sum bc. By testing some possible ad products (even numbers separated by two other even numbers), we can quickly see that the numbers have to be quite small: 6x12 is 72, much higher than any of the possible sums, and the products will go up much faster than the sums will.\nHowever, the lowest possible sequence gives an ad product of 2x8, or 16. And summing the middle numbers gives 10, exactly six less than the product. We have found the sequence: 2-4-6-8.\nThe answer, then, is the product of the smallest two numbers, or 2x4, which is 8 (option C).\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average of first five multiples of 4 is?\n\n### Options:\nA. 6\nB. 8\nC. 9\nD. 5\nE. 12\n\n### Answer:\nAverage = 4(1 + 2 + 3 + 4 + 5)/5\n= 60/5\n= 12.\nAnswer:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf Rs. 64 amount to Rs. 83.20 in 2 years, what will Rs. 86 amount to in 4 years at the same rate percent per annum ?\n\n### Options:\nA. Rs. 114.80\nB. Rs. 86.70\nC. Rs. 55.40\nD. Rs. 51.60\nE. None\n\n### Answer:\nSolution\nP = Rs. 64,S.I. = Rs. (83.20 - 64) = Rs. 19.20, T= 2 years.\nSo, rate = (100x19.20/64x2)= 15%.\nNow, P = Rs. 86, R = 15% ,T = 4 years.\n\u2234 S.I. = Rs.(86x15x4/100) Rs. 51.60.\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nBeth received 4/12 of the votes cast in a certian election. What franction of the other votes cast would she have needed in order to have received 1/2 of the votes cast?\n\n### Options:\nA. 1/5\nB. 2/7\nC. 3/10\nD. 7/20\nE. 2/8\n\n### Answer:\nLet the total votes be 12. Beth received 2 votes, other votes 12-4=8. In order to have received 1/2 of the votes she needed 6 votes so 2 more, which is 2/8 of the other votes.\nAnswer: E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere was a person who smoked a lot .One day he decided to quit his habbit,but he had 27 cigarettes with him.So he started smoking them one by one ,to finish them. He had the habit of smoking only 2/3rd of it and leaving the rest butt. Latter he found out that by joining 3 butts he can form 1 cigarette. So ,tell how many cigarettes in all he smoked.\n\n### Options:\nA. 30\nB. 40\nC. 50\nD. 60\nE. 45\n\n### Answer:\n27+9+3+1=40.\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average expenditure of a labourer for 10 months was 85 and he fell into debt. In the next 4 months by reducing his monthly expenses to 60 he not only cleared off his debt but also saved 30. His monthly income is\n\n### Options:\nA. 180\nB. 100\nC. 112\nD. 110\nE. None of the above\n\n### Answer:\nIncome of 10 months = (10 \u00d7 85) \u2013 debt\n= 850 \u2013 debt\nIncome of the man for next 4 months\n= 4 \u00d7 60 + debt + 30\n= 270 + debt\n\u2234 Income of 10 months = 1120\nAverage monthly income = 1120 \u00f7 10 = 112\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 2ab - c = 2a(b - c), which of the following must be true?\n\n### Options:\nA. a=0 and c=0\nB. a=1/2 and b=2\nC. b=1 and c=0\nD. a=1 or b=0\nE. a=1/2 or c=0\n\n### Answer:\n2ab - c = 2a(b - c)\n=> 2ab - c = 2ab - 2ac\n=> - c = - 2ac\n=> c = 2ac\n=> c - 2ac = 0\n=> c (1 - 2a) = 0\nEither c = 0 or 1 - 2a = 0 i.e. a = 1/2.\nHence, E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSolve the given two equations and find the inequality of X and Y. (a) x^4- 227= 398 and (b) y^2 + 321=346\n\n### Options:\nA. If x>y\nB. If x>=y\nC. If x < y\nD. If x<=y\nE. x=y or relationship cannot be established\n\n### Answer:\nSolution:-\nX=+5,-5 and Y= +5,-5\nComparing, we get X=Y, XY.\nTherefore, no relationship can be established between X and Y.\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAishwarya\u2019s mom was 28 years of age at the time of her birth, while her mom was 20 years old when her 2 years younger sister was born. The variance between the parents ages is :\n\n### Options:\nA. 10 years\nB. 11 years\nC. 15 years\nD. 9 years\nE. 4 years\n\n### Answer:\nA\n6 years\nMom\u2019s age when Aishwarya\u2019s sister was born = 20 years.\nDad\u2019s age when Aishwarya\u2019s sister was born = (28 + 2) years = 30 years.\nNeeded Variance = (30 \u2013 20) years = 10 years.\nAnswer is A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJohn makes $65 a week from his job. He earns a raise andnow makes $70 a week. What is the % increase?\n\n### Options:\nA. 7.69%\nB. 16.66%\nC. 17.8%\nD. 19%\nE. 21%\n\n### Answer:\nIncrease = (5/65)*100 = (1/13)*100 = 7.69%.\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe perimeter of a triangle is 44 cm and the in radius of the triangle is 2.5 cm. What is the area of the triangle?\n\n### Options:\nA. 76\nB. 88\nC. 66\nD. 55\nE. 35\n\n### Answer:\nArea of a triangle = r * s\nWhere r is the in radius and s is the semi perimeter of the triangle.\nArea of triangle = 2.5 * 44/2 = 55 cm2\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf xy \u2260 0 and x^2y^2 \u2212 xy = 30, which of the following could be y in terms of x?\nI. 6/x\nII. -5/x\nIII. 3/x\n\n### Options:\nA. I only\nB. II only\nC. I and II only\nD. I and III\nE. II and III\n\n### Answer:\n(x^2)(y^2) \u2013 xy - 30 = 0\n(xy \u2013 6)(xy + 5) = 0\nxy \u2013 6 = 0 or xy + 5 = 0\nxy = 6 or xy = -5\nSince we need y in terms of x, we can isolate y in both of our equations.\ny = 6/x or y = -5/x\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the least number of squares tiles required to pave the floor of a room 15 m 17 cm long and 9 m 2 cm broad?\n\n### Options:\nA. 814 tiles\nB. 800\nC. 100\nD. 200\nE. 456\n\n### Answer:\nLength of largest tile = H.C.F. of 1517 cm and 902 cm = 41 cm.\nArea of each tile = (41 x 41) cm2.\nRequired number of tiles = (1517 x 902)/41 x 41 = 814.\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 20 men can build a wall 66 meters long in 6 days, what length of a similar can be built by 86 men in 8 days?\n\n### Options:\nA. 49\nB. 39\nC. 29\nD. 19\nE. None of them\n\n### Answer:\nLet the required length be x meters\nMore men, More length built (Direct Proportion)\nLess days, Less length built (Direct Proportion)\nMen 20: 35\nDays 6: 3 : : 56 : x\nTherefore (20 x 6 x x)=(35 x 3 x 56)= x=(35 x 3 x 56)/120=49\nHence, the required length is 49 m.\nAnswer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSolve(0.76 \u00d7 0.76 \u00d7 0.76 \u2212 0.008)/(0.76 \u00d7 0.76 + 0.76 \u00d7 0.2 + 0.04)\n\n### Options:\nA. 0.56\nB. 0.71\nC. 0.45\nD. 0.67\nE. 0.71\n\n### Answer:\nOption 'A'\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nApproximately what percentage of the world\u2019s forested area is represented by Finland given that Finland has 53.42 million hectares of forested land of the world\u2019s 8.076 billion hectares of forested land.\n\n### Options:\nA. 0.0066%\nB. 0.066%\nC. 0.66%\nD. 6.6%\nE. 66%\n\n### Answer:\nSince 1 billion is 1000 million\nSoc changing all quantities to million\nFinland forest area =53.42 million hect.\nWorlds's forest area =8.076 billion hect.\n% =53.42*100/8.076*1000 =0.66%\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe price of sugar is increased by 20%. If the expenditure is not allowed to increase, the ratio between the reduction in consumption and the original consumption is :\n\n### Options:\nA. 1:3\nB. 1:4\nC. 1:6\nD. 1:5\nE. None\n\n### Answer:\nExplanation:\nReduction in consumption\n=(20/120\u00d7100)%=50/3%\nReduction in consumption/Original consumption=(50/3\u00d71/100)\n=1/6=1:6\nCorrect Option: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many 1/12s are there in 37 1/2?\n\n### Options:\nA. 350\nB. 450\nC. 500\nD. 650\nE. 700\n\n### Answer:\nRequired number = (75/2)/(1/12)\n= (75/2 x 12/1)\n= 450.\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe digit in units place of the product 81 x 82 x ..... x 89 is\n\n### Options:\nA. 0\nB. 2\nC. 6\nD. 8\nE. 9\n\n### Answer:\nSol.\nRequired digit = unit digit in (1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9) = 0.\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe ratio of the cost price and the selling price is 4:5. The profit percent is?\n\n### Options:\nA. 17\nB. 56\nC. 25\nD. 28\nE. 12\n\n### Answer:\nLet C.P. = Rs. 4x. Then, S.P. = Rs. 5x\nGain = (5x - 4x) = Rs. x\nGain % = (x * 100)/ 4x = 25%.\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average of five integers is 71, and none of these integers is greater than 100. If the average of three of the integers is 76, what is the least possible value of one of the other two integers?\n\n### Options:\nA. 5\nB. 15\nC. 20\nD. 21\nE. 27\n\n### Answer:\nWhen it comes to averages, we know thataverage value = (sum of n values)/n\nWe can rewrite this into a useful formula:sum of n values = (average value)(n)\nThe average of five integers is 71\nSo, the sum of ALL 5 integers = (71)(5) =355\nThe average of three of the integers is 65\nSo, the sum of the 3 integers = (76)(3) =228\nSo, the sum of the 2 REMAINING integers =355-228=127\nIf the sum of the 2 REMAINING integers =127, and we want to minimize one value, we must MAXIMIZE the other value.\n100 is the maximum value so let 1 integer = 100, which means the other must equal 27\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nP and Q started a business investing Rs, 85,000 and Rs. 15,000 respectively. In what ratio the profit named after 2 years bo divided between P and Q respectively ?\n\n### Options:\nA. 17:9\nB. 17:3\nC. 17:2\nD. 17:1\nE. 17:0\n\n### Answer:\nP : Q = 85000 : 15000 = 86 : 15 = 17 : 3\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn March, Kurt ran an average of 2 miles an hour. If by June he had increased his pace by 10 seconds per mile, then which of the following expresses the number of hours it would take Kurt to complete one mile in June?\n\n### Options:\nA. 3590/60^2\nB. 2410/60^2\nC. 1790/60^2\nD. 3586/60\nE. 60^2/3590\n\n### Answer:\nKurt ran at an average of 2 miles/hour in march. So to run 1 mile he would take 1/2 hours = (60 * 60)/2 seconds = 1800 seconds.\nIf he increases his speed by 10 seconds, he will complete a mile in 1790 seconds. Converting in hours = 1790/(60 * 60) = 1790/(60^2)\nANSWER: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf x is an integer, which of the following is a possible value of K=(x^2 +2x \u2013 7)/9?\n\n### Options:\nA. -2.4\nB. 0.268\nC. 1.166 repeating\nD. 4.555 repeating\nE. 8.125\n\n### Answer:\nx is an integer, which of the following is a possible value of K=(x^2 +2x \u2013 7)/9?\nUsed process of elimination\nA. -2.4\nwhen this is multiplied by 9, x is not an integer\nB. 0.268\nwhen this is multiplied by 9, x is not an integer\nC. 1.166 repeating\nwhen this is multiplied by 9, x is not an integer\nD. 4.555 repeating\nE. 8.125\nwhen this is multiplied by 9, x is not an integer\nAnswer choice D seems to fit.D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are 35 students in a hostel. If the no. of students increases by 2, the expenses of the mess increase by Rs.42/day while the average expenditure per head diminishes by Rs1. Find the original expenditure of the mess?\n\n### Options:\nA. s. 234.50\nB. s. 239.50\nC. s. 242.50\nD. s. 248.50\nE. s. 249.50\n\n### Answer:\nSuppose the average join the mess , total expenditure = 35x + 42\nNow, the average expenditure = (35x + 42)/ (35 + 2) = x \u2013 1\nor, 35x + 42 = 37x \u2013 37\nor, x = 39.50\nThus the original expenditure of the mess = 35 x 39.5 =1382.50\nTherefore x-1 = 38.5\nhence 42 x 38.5 = 1617\n1617-1382.50 = Rs. 234.50\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nI. a^2 - 9a + 20 = 0,\nII. 2b^2 - 5b - 12 = 0 to solve both the equations to find the values of a and b?\n\n### Options:\nA. a < b\nB. a \u2264 b\nC. the relationship between a and b cannot be established\nD. a > b\nE. a \u2265 b\n\n### Answer:\nI. (a - 5)(a - 4) = 0\n=> a = 5, 4\nII. (2b + 3)(b - 4) = 0\n=> b = 4, -3/2 => a \u2265 b\nOption E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe largest four-digit number which when divided by 4, 7 or 13 leaves a remainder of 3 in each case,is :\n\n### Options:\nA. 8739\nB. 9831\nC. 9834\nD. 9893\nE. 8976\n\n### Answer:\nSolution\nGreatest number of 4 digits is 9999. L.C.M. of 4, 7, and 13 = 364.\non dividing 9999 by 364, remainder obtained is 171.\nSo, greatest number of 4 digits divisible by 4,7, and 13 = (9999 - 171) = 9828.\nHence, required number = (9828 + 3) = 9831.Answer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf n = 3 x 4 x p, where p is a prime number greater than 3, how many different positive non-prime divisors does n have, excluding 1 and n?\n\n### Options:\nA. Six\nB. Seven\nC. Eight\nD. Nine\nE. Ten\n\n### Answer:\nN=Xa\u2217Yb where X and Y are prime,\nthen number of factors of N are given by the formula (a+1)(b+1) { Notice I have simply increased the powers of X and Y by one and then multiplied them. Also Make sure X and Y are DISTINCT primes)\nSo, in your question, n = 3 x 4 x p, where p is prime.\nI can n=31\u221722\u2217p^1\nor number of factors = (1+1) * (2+1) * (1+1) = 12.\nBut Notice we need to find Non prime and Other than 1 and n, so we have three prime numbers (2,3,p) , 1 and N.\nExcluding these, we have 12-5 = 7 such factors.\nHence Answer is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo trains are moving in the same direction at 72 kmph and 36 kmph. The faster train crosses a man in the slower train in 20 seconds. Find the length of the faster train?\n\n### Options:\nA. 270\nB. 277\nC. 200\nD. 257\nE. 271\n\n### Answer:\nRelative speed = (72 - 36) * 5/18 = 2 * 5 = 10 mps.\nDistance covered in 27 sec = 20 * 10 = 200 m.\nThe length of the faster train = 200 m.\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTogether, Andrea and Brian weigh p pounds; Brian weighs 8 pounds more than Andrea. Brian and Andrea's dog, Cubby, weighs p/4 pounds more than Andrea. In terms of p, what is Cubby's weight in pounds?\n\n### Options:\nA. p/2 - 10\nB. 3p/4 - 4\nC. 3p/2 - 5\nD. 5p/4 - 10\nE. 5p - 5\n\n### Answer:\nTogether, Andrea and Brian weigh p pounds --> A + B = p.\nBrian weighs 10 pounds more than Andrea --> B = A + 8 --> A + (A + 8) = p --> A = (p - 8)/2 = p/2 - 4.\nBrian and Andrea's dog, Cubby, weighs p/4 pounds more than Andrea --> C = A + p/4 = (p/2 - 4) + p/4 = 3p/4 -4.\nAnswer: B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a division sum, the remainder is 0. As student mistook the divisor by 12 instead of 21 and obtained 35 as quotient. What is the correct quotient ?\n\n### Options:\nA. 0\nB. 12\nC. 13\nD. 20\nE. 25\n\n### Answer:\n12*35=420\n420%21=20\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many two-digit whole numbers yield a remainder of 1 when divided by 10 and also yield a remainder of 1 when divided by 6?\n\n### Options:\nA. None\nB. One\nC. Two\nD. Three\nE. Four\n\n### Answer:\nThe possible number N can be written as follow:\nN = Multiple of LCM(6,10) + 1st such number\nN = 30x + 1\nPossible values = 1, 31, 61, 91\nAnswer : 3 such 2 digit number.\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA child must place 7 different toys in 4 different bins. If any of the toys can go in any of the bins, in how many ways can the child place the toys into the bins?\n\n### Options:\nA. 6^6\nB. 6^4\nC. 4^7\nD. 4^4\nE. 6^4-4^6\n\n### Answer:\nthere are 4 different bins and each of the toy can go to any of these bins..\nso answer 7\u00e2\u02c6\u20147\u00e2\u02c6\u20147\u00e2\u02c6\u20147\u00e2\u02c6\u20147\u00e2\u02c6\u20147\u00e2\u02c6\u20147=4^7\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n70% of the employees in a multinational corporation have VCD players, 83 percent have microwave ovens, 80 percent have ACs and 85 percent have washing machines. At least what percentage of employees has all four gadgets?\n\n### Options:\nA. (a) 15%\nB. (b) 5%\nC. (c) 10%\nD. (d) 18%\nE. (e) 25%\n\n### Answer:\nso 30% employees don't have VCD devices.\n17% employees don't have MO\n20% employees don't have ACs\n15% employees don't have WM\nSumm of employees that don't have some device = 30%+17%+20%+15% = 82% < 100%\nSo definitely at least 18% employees have 4 devices.\nans: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAn article is listed at Rs. 920. A customer pays Rs. 742.90 for it after getting two successive discounts. If the rate of first discount is 15%, the rate of 2nd discount is:\n\n### Options:\nA. 3%\nB. 5%\nC. 8%\nD. 12%\nE. None\n\n### Answer:\nSolution: MP = 920.\nAfter first discount Marked Price (MP) become,\n= 920 - 15% of 920 = 782.\nThe Selling Price (SP) = 742.90.\nLet second discount was x% on 782.\n782 - x% of 782 = 742.90\n782x/100 = 39.1\n782x = 3910\nx = 5%.\nSecond Discount = 5%.\nAnswer: Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nASvennumber is defined as a five-digit number which goes according to the following rules: the leftmost digit is even, any digit to the right of an even digit must be an odd digit, and any digit to the right of an odd digit can only be one of the digits 1 or 9. How many different 5-digit numbers areSvennumbers?\n\n### Options:\nA. 20\nB. 80\nC. 160\nD. 220\nE. 250\n\n### Answer:\nASvennumber is defined as a five-digit number which goes according to the following rules: the leftmost digit is even, any digit to the right of an even digit must be an odd digit, and any digit to the right of an odd digit can only be one of the digits 1 or 7. How many different 5-digit numbers areSvennumbers?\n4/9*5/10*2/10*2/10*2/10=160/9000\nE. 250\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the value of 72519 x 9999 = m?\n\n### Options:\nA. 456578972\nB. 436567874\nC. 653658791\nD. 725117481\nE. 357889964\n\n### Answer:\n72519 x 9999 = 72519 x (10000 - 1)\n= 72519 x 10000 - 72519 x 1\n= 725190000 - 72519\n= 725117481\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo numbers are in ratio P:Q. when 1 is added to both the numerator and the denominator, the ratio gets changed to R/S. again, when 1 is added to both the numerator and denominator, it becomes 1/2. Find the sum of P and Q.\n\n### Options:\nA. 3\nB. 4\nC. 5\nD. 6\nE. 7\n\n### Answer:\nSolution: If we go through normal method, It will be quite cumbersome,so,\nWe will solve this question through options.\nTaking option a: It has P+Q = 3. The possible value of P/Q is 1/2 or 2/1.\nUsing 1/2, we see that on adding 2 in both the numerator and denominator we get 3/4 (not required value.\nSimilarly we check for 2/1, this will also not give the required value.\nOPTION b:\nWe have 1/3 possible ratio.\nThen, we get the final value as 3/5 (not = to 1/2)\nHence, rejected.\nHere we have 1/4 or 2/3.\nChecking for 1/4 we get 3/6 = 1/2. Hence, the option is correct.\nOption c:\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA chair is bought for Rs.500/- and sold at a loss of 10% find its selling price\n\n### Options:\nA. Rs.450/-\nB. Rs.451/-\nC. Rs.440/-\nD. Rs.455/-\nE. Rs.445/-\n\n### Answer:\nLoss = 500*10/100 = 50\nS.P = C.P - Loss\n= 500- 50\n=Rs.450/-\nAnswer : A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train passes a man standing on the platform. If the train is 240 meters long and its speed is 72 kmph, how much time it took in doing so?\n\n### Options:\nA. 16 sec\nB. 14 sec\nC. 9 \u00bd sec\nD. 8 \u00bd sec\nE. 12 sec\n\n### Answer:\nD = 240\nS = 72 * 5/18 = 20 mps\nT = 240/20 = 12 sec\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average mark of the students of a class in a particular exam is 60. If 5 students whose average mark in that exam is 44 are excluded, the average mark of the remaining will be 80. Find the number of students who wrote the exam?\n\n### Options:\nA. 12\nB. 10\nC. 7\nD. 9\nE. 8\n\n### Answer:\nLet the number of students who wrote the exam be x.\nTotal marks of students = 60 x.\nTotal marks of (x - 5) students = 90(x - 5)\n60x - (5 * 44) = 80(x - 5)\n180 = 20x => x = 9\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA machine puts c caps on bottles in m minutes. How many W hours will it take to put caps on b bottles?\n\n### Options:\nA. 60bm/c\nB. W=bm/60c\nC. bc/60m\nD. 60b/cm\nE. b/60cm\n\n### Answer:\nThe machine puts c caps in m minutes or c caps in m/60 hours.\nRate = c/m/60 = 60c/m.\nTo put b caps the machine CCwill take:-\nTime = Work/Rate\nT = b/60c/m = bm/60c\nAnswer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man can swim in still water at 6 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is?\n\n### Options:\nA. 1.7\nB. 1.9\nC. 1.1\nD. 2\nE. 1.2\n\n### Answer:\nM = 6\nS = x\nDS = 6 + x\nUS = 6 - x\n6 + x = (6 - x)2\n6 + x = 12 -2x\n3x = 12-6=6\nx = 2\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the remainder when 1044 * 1047 * 1050 * 1053 is divided by 33?\n\n### Options:\nA. 3\nB. 27\nC. 30\nD. 21\nE. 18\n\n### Answer:\nExplanatory Answer\nUseful result pertaining to remainders\nYou can solve this problem if you know this rule about remainders.\nLet a number x divide the product of A and B.\nThe remainder will be the product of the remainders when x divides A and when x divides B.\nUsing this rule,\nThe remainder when 33 divides 1044 is 21.\nThe remainder when 33 divides 1047 is 24.\nThe remainder when 33 divides 1050 is 27.\nThe remainder when 33 divides 1053 is 30.\n\u2234 the remainder when 33 divides 1044 * 1047 * 1050 * 1053 is 21 * 24 * 27 * 30.\nNote: The remainder when a number is divided by a divisor 'd' will take values from 0 to (d - 1). It cannot be equal to or more than 'd'.\nThe value of 21 * 24 * 27 * 30 is more than 33.\nWhen the value of the remainder is more than the divisor, final remainder will be the remainder of dividing the product by the divisor.\ni.e., the final remainder is the remainder when 33 divides 21 * 24 * 27 * 30.\nWhen 33 divides 21 * 24 * 27 * 30, the remainder is 30.\nChoice C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRadha bought a watch for Rs. 144 and got a percentage of profit equal to the cost price of the watch. What is the cost price of the watch?\n\n### Options:\nA. Rs. 72\nB. Rs. 78\nC. Rs. 80\nD. Rs. 90\nE. Rs. 92\n\n### Answer:\nSP=144\nCP=x\nprofit %=x\nC.P.= (100/(100+gain%))*S.P.\nx=(100/100+x) *144\nx^2+100x=14400\nx^2+180x-80x-14400=0\n(x+180) (x-80)=0\nx=-180\nx=80\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain series is defined by the following recursive rule: Sb=K(Sb-1) , where k is a constant. If the 1st term of this series is 64 and the 25th term is 192, what is the 9th term?\n\n### Options:\nA. ROOT 2\nB. ROOT 3\nC. 64*ROOT 3\nD. 64*3^1/3\nE. 64*3^24\n\n### Answer:\nAns...D\nNo need for any GP formula here\nThe rule is that bth term is K times the (b-1)th term.\n1st = 64\n2nd = k.64\n3rd = k^2.64\n.\n.\n.\n9th term = k^8 *64\n.\n.\n.\nso 25th = k^24*64\nUsing this solve for k and substitute k in the equation for the 9th term\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFor any integer p, *p is equal to the product of all the integers between 1 and p, inclusive. How many prime numbers are there between *6 + 3 and *6 + 6, inclusive?\n\n### Options:\nA. One\nB. None\nC. Two\nD. Three\nE. Four\n\n### Answer:\nGenerally *p or p! will be divisible by ALL numbers from 1 to p. Therefore, *6 would be divisible by all numbers from 1 to 6.\n=> *6+3 would give me a number which is a multiple of 3 and therefore divisible (since *6 is divisible by 3)\nIn fact adding anyprimenumber between 1 to 6 to *6 will definitely be divisible.\nSo the answer is none (A)!\nSupposing if the question had asked for prime numbers between *6 + 3 and *6 + 11 then the answer would be 1. For *6 +3 and *6+ 13, it is 2 and so on...\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSam has forgotten his friend\u2019s seven-digit telephone number. He remembers the following: the first three digits are either 635 or 674, the number is odd, and the number nine appears once. If Sam were to use a trial and error process to reach his friend, what is the minimum number of trials he has to make before he can be certain to succeed ?\n\n### Options:\nA. 1000\nB. 2430\nC. 3402\nD. 3006\nE. None of these\n\n### Answer:\nExplanation :\nLet's check the number of ways for the first telephone number.\n6 3 5 - - - -\na) 6 3 5 9 - - -\n4 choices for last digit (1,3,5,7).\n9 * 9 choices for 5th and 6th digits together.\nSo, 9 * 9 * 4 choices = 324 ways.\nSimilarly,\nb.) 6 3 5 - 9 - - = 324 ways.\nc.) 6 3 5 - - 9 - = 324 ways.\nd.) 6 3 5 - - - 9 = 9 * 9 * 9 =729 ways.\nTotal= (324 + 324 + 324 + 729) = 1701.\nIt will be also the case with the phone number starting with 674.\nHence, the minimum number of trial required is 2 x 1701 = 3402.\nAnswer : C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA painting at an art gallery is framed such that the area of the square frame is 1/3 the area of the painting itself. If the diagonal line connecting corners of the frame has a length of 12, what is the area of the painting inside the frame?\n\n### Options:\nA. 10\nB. 20\nC. 30\nD. 40\nE. 54\n\n### Answer:\nSuppose side of the painting(which is a square) is a and side of the outer square(painting+frame) is b\nArea of painting = a^2 and we know that the area of the frame is (1/3) of that of the painting so\nArea of frame = (1/3) * a^2\nArea of Frame + Painting = a^2 + (1/3)*a^2 = (4/3)*a^2 which is equal to b^2\nLine connecting the corners of the frame is the diagonal of the outer square which is equal to b*sqrt2\nso, b * sqrt2 = 12\nso, b = 6 * sqrt2\nb^2 = 72\nwe know that b^2 = (4/3)*a^2\nso, a^2 = (3/4)*b^2 = (3/4)*72 = 54\nAnd area of painting = a^2 = 54\nSo, answer will be E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 4 (A's capital) = 6 (B's capital) = 8 (C's capital). Then the ratio of their capitals is?\n\n### Options:\nA. 6:4:5\nB. 6:4:3\nC. 6:4:2\nD. 6:2:3\nE. 6:5:3\n\n### Answer:\n4A = 6B = 8 C\nA:B:C = 1/4:1/6:1/8\n= 6:4:3\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA alone can finish a work in 10 days which B alone can finish in 15 days. If they work together and finish it, then out of a total wages of Rs.3000, A will get:\n\n### Options:\nA. Rs.1200\nB. Rs.1500\nC. Rs. 1800\nD. Rs.2000\nE. None of these\n\n### Answer:\nExplanation:\nRatio of working days of A : B = 10 : 15\nTherefore, their wages ratio = reverse ratio = 15 : 10\nTherefore, A will get 15 units of ratio\nTotal ratio = 25\n1 unit of ratio =3000/25 = 120\nSo, A\u2019s amount = 120 \u00d7 15 = Rs.1800.\nAnswer: Option C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the remainder when 121212.......(300) digits is divided by 99.\n\n### Options:\nA. 18\nB. 36\nC. 72\nD. 0\nE. 1\n\n### Answer:\n12/99=12\n1212/99=24\n121212/99=36\n.\n.\n.\n121212...(300)/99=(12*300)%99=36\nif they say 300 digits then (12*150)%99=18\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe price of a TV was increased by 30 percent. The new price was then increased by 20 percent. A single increase of what percent is equivalent to these two successive increases?\n\n### Options:\nA. 50%\nB. 60%\nC. 65%\nD. 56%\nE. 45%\n\n### Answer:\nconsider base price - $100\n25% increase = 1.30*100 = $130\nanother 20% increase on new price = 1.2* 130 = $156\nso final price of radio - $156\ntherefore a 56% increase\ncorrect option - D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe area of a rectangle plot is 460 square metres. If the length is 15% more than the breadth, what is the breadth of the plot?\n\n### Options:\nA. 10m\nB. 20m\nC. 50m\nD. 40m\nE. 30m\n\n### Answer:\nlb = 460 m power2...(Equation 1)\nLet the breadth = b\nThen length, l = b \u00d7 (100+15)/100 = 115b/100 ...(Equation 2)\nFrom Equation 1 and Equation 2,\n115b/100 \u00d7 b = 460\nb2 = 46000/115 = 400\n\u21d2 b = \u221a400 = 20 m\nAnswer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAccording to the directions on a packet of smoothie mix, 1 3-ounce packet of smoothie mix is to be combined with 10 ounces of water to make a smoothie. How many 3-ounce packets of smoothie mix are required to prepare 150 12-ounce smoothies?\n\n### Options:\nA. 120\nB. 150\nC. 180\nD. 240\nE. 600\n\n### Answer:\nThis question wasn't particularly grueling, but I think it's the first where I had the opportunity to solve it via theory andinspectionthat many on this board suggest as strategy on the GMAT. It actually came to me by accident. Basically, if we thought that the 3 packets of powder were included in the 12 ounces of water, that would mean we would need 150 packets of smoothie mix (along with 12(150) ounces of water for a total of 150 packets. However, we know, after a more careful reading of the stimulus, that the 3 ounces are NOT included in the 12 ounces. As such, the answer has to be LESS than 150 packets, since 150 would be too much powder considering you already have 150(12) ounces of water and need less packets than water to make a smoothie. As such, the only answer less than 150 is 120, A. Does this make sense? Or am I way off base?\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA list of numbers has six positive integers. Three of those integers are known: 4, 5 and 24 and three of those are unknown: x, y and z. The three unknowns are known to be distinct. It is also known that the mean of the list is 10 and the median lies between 7 and 8 (exclusive). Which of the following CANNOT be the value of any one of the unknowns?\n\n### Options:\nA. 13\nB. 12\nC. 11\nD. 10\nE. 5\n\n### Answer:\nMean = 10\nTherefore sum of the 6 digits = 6*10 = 60 -------- (1)\nThe 3 digits are 4,5 & 24 -------------- (2)\nNow, 7 < median < 8\n-> 7 < (sum of 2 digits)/2 < 8\n-> 14 < (sum of 2 digits) < 16\nTherefore the sum of 2 digits = 15.\nThe 2 digits whose sum is 15 & whose median is b/w 7 & 8 can be :\n1. 7, 8,\n2. 6, 9,\n3. 5, 10, or\nBut as soon as we take 4, 11 -> the series becomes 4,4,5,11,12,24 &\n11 pairs up with 5 to give median as 8.\nHence the number can't be 11 !!\nAnswer : C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMargaret is 9 years more than twice the age of his son. The age of son is 12. Find the age of mother and find the difference between their ages\n\n### Options:\nA. 21yrs\nB. 20yrs\nC. 30yrs\nD. 40yrs\nE. 50yrs\n\n### Answer:\nLet, age of son x=12\nMargaret is 9 years more than twice the age of his son, y = 9+2(x)\n=9+2(12)\n=9+24\n=33yrs\nDifference = 33 - 12\n=21yrs\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich of the following is(are) true for a@b=b@a?\nI. a@b=ab+ba\nII. a@b=(a+b+1)(a-b)\nIII. a@b=(a/b)+(b/a)\n\n### Options:\nA. only \u2160\nB. only \u2161\nC. only \u2162\nD. only \u2160\u2162\nE. only \u2161\u2162\n\n### Answer:\n-> If I. a@b=ab+ba, a@b=ab+ba=ba+ab=b@a (O).\nIf II. a@b=(a+b+1)(a-b), a@b=(a+b)(a-b)\u2260(b+a)/(b-a)=b@a (X).\nIf III.a@b=(a/b)+(b/a), a@b=(a/b)+(b/a)=(b/a)+(a/b)=b@a (O).\nThus, \u2160\u2162 are the answers. Therefore, D is the answer.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n2^8\u00d739+31=?\n\n### Options:\nA. 34545\nB. 65657\nC. 65567\nD. 45677\nE. 56782\n\n### Answer:\n256*39+31\n65567\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA trained covered x km at 40 kmph and another 2x km at 20 kmph. Find the average speed of the train in covering the entire 2x km.\n\n### Options:\nA. 16kmph\nB. 20kmph\nC. 25kmph\nD. 30kmph\nE. 35kmph\n\n### Answer:\nTotal time taken = x/40 + 2x/20 hours\n= 5x/40 = x/8 hours\nAverage speed = 2x/(x/8)\n= 16 kmph\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf x^3 + y^3 = 200, then the greatest possible value of x is between\n\n### Options:\nA. 2 and 3\nB. 3 and 4\nC. 4 and 5\nD. 5 and 6\nE. 7 and 8\n\n### Answer:\nfor the greatest possible value of x^3, we must minimize the value of y^3 i.e. lets say y^3 = 0\nthen we need to find a number x such that x^3 < 200. 5^3 = 125 and 6^3 = 216 so we can say that the maximum possible value of x can be a little more than 5 hence answer = between 5 and 6\nhence D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain car traveled twice as many miles from Town A to Town B as it did from Town B to Town C. From Town A to Town B, the car averaged 8 miles per gallon, and from Town B to Town C, the car averaged 18 miles per gallon. What is the average miles per gallon that the car achieved on its trip from Town A through Town B to Town C?\n\n### Options:\nA. 13\nB. 15.5\nC. 14\nD. 14.5\nE. 15\n\n### Answer:\nAns is B\nGiven d_ab = 2*d_bc\nlet d_ab = d and d_bc = x so d=2x\nfor average miles per gallon = (d+x)/((d/8)+(x/18)) = 15.5 (formula avg speed = total distance/ total time)\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many different ways can you select a pilot and a co pilot if you have 80 people to choose from?\n\n### Options:\nA. 199\nB. 200\nC. 398\nD. 4950\nE. 6320\n\n### Answer:\nYou are not just choosing two from 80. Each of the two people chosen fills a particular slot. The first filling the pilot slot and the second filling the copilot slot is different from the first filling the copilot slot and the second filling the pilot slot.\nSo the answer is in a sense (80C2) x 2 = 6320=E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nEach child has 12 crayons and 24 apples. If there are 18 children, how many crayons are there in total?\n\n### Options:\nA. 220\nB. 65\nC. 216\nD. 219\nE. 230\n\n### Answer:\n12*18=216.Answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA sells to B goods at five-thirds the rate of profit at which B has decided to sell it to C. C, on other hand sells it to D at one-third the rate of profit at which B sold it to C. If D gives Rs. 2145 to C at 10%, how much did A buy it for ?\n\n### Options:\nA. 1000\nB. 1100\nC. 1200\nD. 1300\nE. 1400\n\n### Answer:\nlet profit rate of b = x\nacc to question profit rate of a becomes 5/3 x\nand that of c= 1/3 x which is given as 10%\n1/3 x= 10\ntherefore x=30\nnow b=30% , a=50%\nnow we will find out c's price-\n11/10 * price = 2145\nprice = 1950\nin similar way we will find out b's price as we know that profit is 30%\ntherefore 130/100 * price = 1950\nso b 's price =1500\nsimilarly for a ('profit is 50%)\n150/100 * price = 1500\non solving it we get\na's price = 1000\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAlex deposited x dollars into a new account that earned 8 percent annual interest, compounded annually. One year later Alex deposited an additional x dollars into the account. If there were no other transactions and if the account contained w dollars at the end of two years, which of the following expresses x in terms of w ?\n\n### Options:\nA. w/(1+1.08)\nB. w/(1.08+1.16)\nC. w/(1.16+1.24)\nD. w/(1.08+1.08^2)\nE. w/(1.08^2+1.08^2)\n\n### Answer:\nAccount at the end of the first year would be 1.08x dollars. At this time x dollars was deposited, hence the account at the beginning of the second year would be (1.08x+x) dollars. Account at the end of the second year would be (1.08x+x)*1.08=w --> x(1.08^2+1.08)=w --> x=w/(1.08+1.08^2).\nAnswer: D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn an election a candidate who gets 60% of the votes is elected by a majority of 1040 votes. What is the total number of votes polled?\n\n### Options:\nA. A)4500\nB. B)5200\nC. C)6900\nD. D)7520\nE. E)6000\n\n### Answer:\nLet the total number of votes polled be x\nThen, votes polled by other candidate = (100-60)% of x = 40% of x\n60% of x - 40% of x = 1040\n20x/100 = 1040\nx = 1040*100/20 = 5200\nAnswer is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA boat can travel with a speed of 42 km/hr in still water. If the speed of the stream is 10 km/hr, find the time taken by the boat to go 94 km downstream\n\n### Options:\nA. 1 hour 40 min\nB. 2 hour 40 min\nC. 1 hour 20 min\nD. 1 hour 30 min\nE. 1 hour 50 min\n\n### Answer:\nSpeed of the boat in still water = 42 km/hr\nspeed of the stream = 10 km/hr\nSpeed downstream = (42+10) = 52 km/hr\nDistance travelled downstream = 94 km\nTime taken =distance/speed\n=94/52\n= 1.81 hours\n= 1 hour 50 min.\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n3 + 3 + 3 + 2 \u00d7 3^2 + 2 \u00d7 3^3 + 2 \u00d7 3^4 + 2 \u00d7 3^5 + 2 \u00d7 3^6 + 2 \u00d7 3^7 =\n\n### Options:\nA. 3^7\nB. 3^8\nC. 3^14\nD. 3^28\nE. 3^30\n\n### Answer:\nWe have the sum of 9 terms. Now, if all terms were equal to the largest term 2*3^7 we would have: sum=9*(2*3^7)=2*3^9=~3^10, so the actual sum is less than 3^10 and more than 3^7 (option A) as the last term is already more than that. So the answer is clearly B.\nAnswer: B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA milk man sells the milk at the cost price but he mixes the water in it and thus he gains 9.09%. The quantity of water in the mixture of 1 liter is\n\n### Options:\nA. 83.33 ml\nB. 83.03 ml\nC. 93.33 ml\nD. 63.03 ml\nE. 82.33 ml\n\n### Answer:\nExplanation:\nProfit (%) = 9.09 % = \\inline \\frac{1}{11}\nSince the ratio of water and milk is 1 : 11,\nTherefore the ratio of water is to mixture = 1:12\nThus the quantity of water in mixture of 1 liter = \\inline 1000\\times \\frac{1}{12} = 83.33 ml]\nAnswer: A) 83.33 ml\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA triangle has a perimeter 15. The two shorter sides have integer lengths equal to x and x + 1. Which of the following could be the length of the other side?\n\n### Options:\nA. 7\nB. 6\nC. 8\nD. 9\nE. 10\n\n### Answer:\nThe SHORTER sides have integral lengths equal to x and x + 1\nLet the longest side be 'a'\nSo, a + x + (x +1) = 15\na + 2x = 14.......eqn (1)\nWe know that the sum of the lengths of the shorter sides has to be more than the length of the longer one. i.e 2x+1> a\na =6\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHuey's Hip Pizza sells two sizes of square pizzas: a small pizza that measures 8 inches on a side and costs $10, and a large pizza that measures 12 inches on a side and costs $20. If two friends go to Huey's with $30 apiece, how many more square inches of pizza can they buy if they pool their money than if they each purchase pizza alone?\n\n### Options:\nA. 5 square inches\nB. 10 square inches\nC. 16 square inches\nD. 25 square inches\nE. 350 square inches\n\n### Answer:\nIn the first case each can buy one pizza of $10 and one pizza of $20.\nIn square inches that would be (8*8=64) for the small pizza and (12*12=144) for the large pizza. In total sq inches that would be (64+144)*2= 416 sq inches.\nIn the second case if they pool their money together they can buy 3 large pizzas. In terms of square inches that would be 3*144= 432 sq inches.\nHence, the difference is 16 square inches more (432-416).\nThe correct answer is C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man brought some eggs of which 10% are rotten. He gives 80% of the remainder to his neighbour. Now he left out with 36 eggs. Hw many eggs he brought\n\n### Options:\nA. 100\nB. 200\nC. 72\nD. 40\nE. 36\n\n### Answer:\nLet he bought 100 eggs.\nEggs after removing rotten one = 90.\nEggs given to neighbour = 80% of 90 = 72 eggs.\nNow he left with eggs = 90 - 72 = 18 eggs.\nNow,\nComparing,\n18 = 36\n1 = 36/18\nANSWER : OPTION B\n100 = 200.\nSo, he bought 200 eggs.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf an object travels at two feet per second, how many feet does it travel in one hour?\n\n### Options:\nA. 3488\nB. 3778\nC. 7200\nD. 1800\nE. 2881\n\n### Answer:\nExplanation:\nIf an object travels at 2 feet per second it covers 2x60 feet in one minute, and 2x60x60 feet in one hour.\nAnswer = 7200\nAnswer: C) 7200\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train 225 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is:\n\n### Options:\nA. 86\nB. 50\nC. 12\nD. 13\nE. 67\n\n### Answer:\nSpeed of the train relative to man = (225/10) m/sec = (45/2) m/sec. [(45/2) * (18/5)] km/hr = 81 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 81 ==> x = 86 km/hr.\nAnswer: Option A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf x > 3000, then the value of (x)/(2x-42) is closest to?\n\n### Options:\nA. 1/6\nB. 1/3\nC. 10/21\nD. 1/2\nE. 3/2\n\n### Answer:\nassume x = 3002\n(x)/(2x-42) = 3002 / (3002*2-42)\n=3002 / 5962\n= = 1/2\nAns - D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nLast year John earned m dollars at company X and was promised an n-percent raise for this year. If John is paid the promised amount and a $10,000 bonus at the end of this year, by what percent has his total salary(including his bonus) increased this year over last in terms of n and m?\n\n### Options:\nA. (mn + 10000)/m %\nB. (n + 10000)/m %\nC. (mn + 100,000)/100m %\nD. (mn + 1,000,000)/100m %\nE. (mn + 1,000,000)/m %\n\n### Answer:\nOld Salary = m dollars\nNew salary = M (1 + n/100) + 10,000\nNet increase = m*n/100 + 10,000\nPercentage change = (mn/100 + 10,000)*100/m\n= (mn + 1,000,000)/m%\nAnswer: E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo pipes A and B can fill a cistern in 12 and 24 minutes respectively, and a third pipe C can empty it in 36 minutes. How long will it take to fill the cistern if all the three are opened at the same time?\n\n### Options:\nA. 10 2/7 min\nB. 10 1/8 min\nC. 11 1/7 min\nD. 12 8/7 min\nE. 11 3/7 min\n\n### Answer:\n1/12 + 1/24 - 1/36\n= 7/72\n72/7 = 10 2/7\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe monthly incomes of A and B are in the ratio 5 : 2. B's monthly income is 12% more than C's monthly income. If C's monthly income is Rs. 15000, then find the annual income of A?\n\n### Options:\nA. 187888\nB. 276889\nC. 267777\nD. 504000\nE. 297112\n\n### Answer:\nB's monthly income = 15000 * 112/100 = Rs. 16800\nB's monthly income = 2 parts ----> Rs. 16800\nA's monthly income = 5 parts = 5/2 * 16800 = Rs. 42000\nA's annual income = Rs. 42000 * 12 = Rs.504000\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo numbers are in respectively 10% and 40% more than a third number. The ratio of the two numbers is?\n\n### Options:\nA. 11:14\nB. 7:9\nC. 17:25\nD. 15:26\nE. 2:3\n\n### Answer:\nLet the 3rd number be x\nThen, first number = 110% of x = 110x/100 = 11x/10\nsecond number = 140% of x = 140x/100 = 7x/5\nRatio of first two numbers = 11x/10 : 7x/5 = 11:14\nAnswer is A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA company conducted a survey about its two brands, A and B. x percent of respondents liked product A, (x \u2013 20) percent liked product B, 23 percent liked both products, and 23 percent liked neither product. What is the minimum number W of people surveyed by the company?\n\n### Options:\nA. 46\nB. 80\nC. W.90\nD. W.100\nE. 200\n\n### Answer:\n100 = x + x - 20 + 23 - 23\nx = 60,\nSo, Product A = 60%, Product B = 40%, Both = 23%, Neither = 23%\n23% of the total no. of people should be an integer. So, A,BC are out.\n60% of D and 40% of D are both integers. So, D satisfies all conditions.\nSo, answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a rectangular axis system, what is the area of a parallelogram with the coordinates: (5,7), (12,7), (2,3), (9,3) ?\n\n### Options:\nA. 21\nB. 28.\nC. 35.\nD. 49.\nE. 52.\n\n### Answer:\nArea of parallelogram = b*h.\nBase = Distance in x coordinates between (2,3) and (9,3) = 7\nHeight = Difference in y coordinates between (5,7) and (2,3) = 3.\nArea = 7*3 = 21.\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many ways are there to split a group of 6 girls into two groups of 3 girls each? (The order of the groups does not matter)\n\n### Options:\nA. 35\nB. 10\nC. 40\nD. 20\nE. 25\n\n### Answer:\nthe combination is 6C3 /2\n= 6!/3!*3!*2 = 20/2 =10\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA person travels from X to Y and vice versa. How long will it take to travel both the ways by bus?\n(A) It takes 15 hours in travelling from X to Y by train and returning by bus.\n(B) The distance between two places is 360 km.\n(C) He can save 3 hrs if he travels both the ways by train.\n\n### Options:\nA. A and B together\nB. B and C together\nC. A and C together\nD. Any two of them\nE. All statements are required\n\n### Answer:\nfrom x to y and y to x it takes 15hrs\nlet time taken by train be a and by bus be b\nso a+b=15\ntrain takes 3 hrs less i.e,\na+a=12\n2a=12\na=6\n6+b=15\nb=9\n2b=18hrs\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFrom a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee. In how many ways can it be done?\n\n### Options:\nA. 756\nB. 800\nC. 956\nD. 850\nE. 650\n\n### Answer:\nWe may have (3 men and 2 women) or (4 men and 1 woman) or (5 men only).\nRequired number of ways\t= (7C3 x 6C2) + (7C4 x 6C1) + (7C5)\n= (525 + 210 + 21)\n= 756.\nANSWER A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average marks of Riya,Siya,Lisa was 80. The average marks of Siya,Lisa,Hena was 85. If marks of Hena be 84, what was the mark of Riya?\n\n### Options:\nA. 39\nB. 69\nC. 37\nD. 42\nE. None of these\n\n### Answer:\nExplanation:\nR+S+L=80*3=240\nS+L+H=85*3=255\nAlso, marks of Hena=84\nmarks of Riya = 240+84-255 = 69\nAnswer: Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the value of 80641 x 9999 = m?\n\n### Options:\nA. 807518799\nB. 806436469\nC. 807538799\nD. 806329359\nE. 817431046\n\n### Answer:\n80641 x 9999 = 80641 x (10000 - 1)\n= 80641 x 10000 - 80641 x 1\n= 806410000 - 80641\n= 806329359\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich of the following describes all the values of x for which 8\u22124x < 18x\u221218?\n\n### Options:\nA. x > 5/7\nB. x < 5/11\nC. 5/11 < x\nD. x > 13/11\nE. 13/11 > x\n\n### Answer:\n8\u22124x < 18x\u221218\ni.e. 8+18 < 18x+4x\ni.e. 26 < 22x\ni.e. x>26/22\ni.e. x>13/11\nAnswer: Option D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA shopkeeper sold an book offering a discount of 5% and earned a profit of 42.5%. What would have been the percentage of profit earned if no discount was offered?\n\n### Options:\nA. 140\nB. 120\nC. 130\nD. 110\nE. 150\n\n### Answer:\nLet C.P. be $100.\nThen, S.P. = $142.50\nLet marked price be $x. Then, 95/100 x = 142.5\nx = 14250/95 = $150\nNow, S.P. = $150, C.P. = $100\nProfit % = 50%.\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe avg weight of A,B & C is 84 kg. If D joins the group, the avg weight of the group becomes 80 kg.If another man E who weights is 7 kg more than D Replaces A, Then the avgof B,C,D&E becomes 79 kg. What is the weight of A?\n\n### Options:\nA. 45\nB. 65\nC. 75\nD. 79\nE. 90\n\n### Answer:\nA + B + C = 3 *84 = 252\nA + B + C + D = 4 * 80 = 320 ---- (i)\nSo, D = 68& E = 68 + 7 = 75\nB + C + D +E = 79 * 4 = 316 --- (ii)\nFrom Eq. (i) & (ii)\nA-E = 320 \u2013 316 = 4\nA = E +4 = 75 + 4 = 79\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo stations P and Q are 110 km apart on a straight track. One train starts from P at 7 a.m. and travels towards Q at 20 kmph. Another train starts from Q at 8 a.m. and travels towards P at a speed of 25 kmph. At what time will they meet?\n\n### Options:\nA. 10.30\nB. 10\nC. 8.45\nD. 9.3\nE. 11\n\n### Answer:\nExplanation:\nAssume both trains meet after x hours after 7 am\nDistance covered by train starting from P in x hours = 20x km\nDistance covered by train starting from Q in (x-1) hours = 25(x-1)\nTotal distance = 110\n=> 20x + 25(x-1) = 110\n=> 45x = 135\n=> x= 3\nMeans, they meet after 3 hours after 7 am, ie, they meet at 10 am. Answer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA company assigns product codes consisting of all the letters in the alphabet.How many product codes are possible if the company uses at most 6 letters in its codes, and all letters can be repeated in any one code?\n\n### Options:\nA. A.321272406\nB. B.308915776\nC. C.11881376\nD. D.456976\nE. E.17576\n\n### Answer:\nThe no of ways in which the company can make codes of 1 letter : 26\n# for 2 letters : 26*26 = 676\n# for 3 letters : 26 * 26*26 =17576\n# for 4 letters : 26 * 26*26*26 =456976\n# for 5 letters : 26 * 26*26*26*26 =11881376\n# for 6 letters : 26 * 26*26*26*26*26 =308915776\nThe total : By adding all of them , 26+676+17576+456976+11881376+308915776=321272406\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average (arithmetic mean) of 4 positive integers is 40. If the average of 2 of these integers is 45, what is the greatest possible value that one of the other 2 integers can have?\n\n### Options:\nA. 55\nB. 69\nC. 100\nD. 109\nE. 115\n\n### Answer:\na + b + c + d =160\na + b = 90\nc + d =70\nGreatest possible = 69 (Just less than 1)\nAnswer = B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average (arithmetic mean) of 27, 32, and 64 is 6 less than the average of 29, 42, and x. What is x?\n\n### Options:\nA. 62\nB. 64\nC. 66\nD. 68\nE. 70\n\n### Answer:\nThe average of 27, 32, and 64 is 41.\nThe average of 29, 42 and x is 47.\nThen 29 + 42 + x = 141.\nx = 70.\nThe answer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nNumber of prime numbers between 10 and 20 is\n\n### Options:\nA. 4\nB. 5\nC. 6\nD. 7\nE. 9\n\n### Answer:\ntotal 4=1, 13, 17, 19\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA survey of n people in the town of Eros found that 50% of them preferred Brand A. Another survey of 100 people in the town of Angie found that 60% preferred Brand A. In total, 55% of all the people surveyed together preferred Brand A. What is the total number of people surveyed?\n\n### Options:\nA. 50\nB. 100\nC. 150\nD. 200\nE. 250\n\n### Answer:\nIt is simply a weighted average question. Since the given average of 50% and 60% is 55% (right in the middle), it means the number of people surveyed in Eros (n) is same as the number of people surveyed in Angie.\nSo n = 100\nTotal = 100 + 100 = 200\nAnswer (D)\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is:\n\n### Options:\nA. 127 m\nB. 277 m\nC. 245 m\nD. 217 m\nE. 219 m\n\n### Answer:\nSpeed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (130 + x)/30 = 25/2 => 2(130 + x) = 750 => x = 245 m.\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA team has to design a flag. The team has four yellow strips of cloth and five green strips of cloth that they must use as is to make the flag. How many different flags can the team design with the materials at hand?\n\n### Options:\nA. 24\nB. 120\nC. 126\nD. 140\nE. 156\n\n### Answer:\nThe # of permutations of total 4+5=9 strips where 4 are identical yellow and 5 are identical green is 9!/(4!*5!)=126 (note that they must use all the materials at hand, also I guess that the strips must be either only vertical or only horizontal).\nAnswer: C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how many ways can the letters of the word SPHERICAL be arranged such that all the vowels always appear together?\n\n### Options:\nA. 9!*6!\nB. 9!\nC. 7!*3!\nD. 9!*3!\nE. 6!*3!\n\n### Answer:\nThe 9 letters can be grouped into 6 consonants and one set of 3 vowels.\nThe number of ways to arrange 7 units is 7!\nThen, for each arrangement, the 3 vowels can be arranged in 3! ways.\nThe total number of arrangements is 7!*3!\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nKathleen can paint a room in 4 hours, and Anthony can paint an identical room in 5 hours. How many hours would it take Kathleen and Anthony to paint both rooms if they work together at their respective rates?\n\n### Options:\nA. 8/15\nB. 40/9\nC. 15/8\nD. 9/4\nE. 15/4\n\n### Answer:\n(1/4 + 1/5)t=2\nt= 40/9\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe probabilities of solving a question by 3students A, B & C are 1/2,1/3 &1/4, respectively. The probability that the problem will be solved is?\n\n### Options:\nA. 1/3\nB. 3/4\nC. 3/5\nD. 3/7\nE. 4/7\n\n### Answer:\nSol. First, we find the probability of not solving the problem x PTO x = (1 \u2014 D x - D x - D\n1 2 3 1 =iXiX71=4;\n1 3 Required probability 3/4\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAshwin rented a power tool from a rental shop. The rent for the tool was $25 for the first hour and $10 for each additional hour. If Ashwin paid a total of $125, excluding sales tax, to rent the tool, for how many hours did she rent it?\n\n### Options:\nA. 11\nB. 12\nC. 15\nD. 18\nE. 16\n\n### Answer:\n25 + 10n = 125\nn = 10\nTotal time = n+1 hrs = 10+1 hrs = 11 hrs\nAnswer : A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe curved surface of a sphere is 64 \u03c0 cm2. Find its radius?\n\n### Options:\nA. 9\nB. 8\nC. 4\nD. 5\nE. 6\n\n### Answer:\n4 \u03c0r2 = 64 => r = 4\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average of four consecutive odd numbers is 24. Find the largest number.\n\n### Options:\nA. 25\nB. 27\nC. 29\nD. 31\nE. 32\n\n### Answer:\nExplanation:\nLet the numbers are x, x+2, x+4, x+6, then\n=>x+(x+2)+(x+4)+(x+6)4=24\n=>4x+12)4=24\n=>x+3=24=>x=21\nSo largest number is 21 + 6 = 27\nAnswer: Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSuppose son name is 120,his brother name is 150 and his mother name is 230.find out his father's name???\n\n### Options:\nA. 190\nB. 210\nC. 230\nD. 240\nE. 260\n\n### Answer:\nsince difference between all name is =30\nso father's name will be 230+30=260.\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe consumption of diesel per hour of a bus varies directly as square of its speed. When the bus is travelling at 70 kmph its consumption is 1 litre per hour. if each litre costs $70 and other expenses per hous is $ 70, then what would be the minimum expenditure required to cover a distance of 700 Km?\n\n### Options:\nA. 1000\nB. 1500\nC. 1240\nD. 1630\nE. 1400\n\n### Answer:\n70 kmph consumption is 1 lt/hr\nso 700 km will take 10 hrs and the consumption is 10 lt for entire distance.\n1 lt costs $70\nso 10 lt costs $700\nextra expenses for 1 hr - $70\n10 hrs - $700\ntotal expense - $700 + $700 = $1400\nAnswer : E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo trains are running in opposite directions with the same speed. If the length of each train is 240 metres and they cross each other in 12 seconds, then the speed of each train (in km/hr) is:\n\n### Options:\nA. 68 km/hr.\nB. 32 km/hr.\nC. 34 km/hr.\nD. 35 km/hr.\nE. 72 km/hr.\n\n### Answer:\nLet the speed of each train be x m/sec.\nThen, relative speed of the two trains = 2x m/sec.\nSo, 2x = (240 + 240 )/12\n2x = 40\nx = 20.\nSpeed of each train = 10 m/sec = 20 x 18/5 km/hr = 72 km/hr.\nanswer :E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAaron will jog from home at 5 miles per hour and then walk back home by the same route at 10 miles per hour. How many miles from home can Aaron jog so that he spends a total of 3 hours jogging and walking?\n\n### Options:\nA. 15\nB. 18\nC. 10\nD. 12\nE. 14\n\n### Answer:\nxyt/(x+y)\nx= 5, y=10, t= 3\n5*10*3/5+10 = 150/50 = 10\nAnswer : C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA palindrome is a number that reads the same forward and backward, such as 464. How many odd five-digit numbers are palindromes?\n\n### Options:\nA. 40\nB. 400\nC. 500\nD. 5,000\nE. 100,000\n\n### Answer:\n5th digit 1,3,5,7,9\n4th digit 0 through 9\n3rd digit 0 through 9\ni.e 10*10*5 = 500 numbers\nfirst and second digit is going to be same as 4th and 5th. so it would still be 400 numbers.\nAnswer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a certain store, the profit is 150% of the cost. If the cost increases by 25% but the selling price remains constant, approximately what percentage of the selling price is the profit?\n\n### Options:\nA. 30%\nB. 70%\nC. 100%\nD. 50%\nE. 120%\n\n### Answer:\nLet C.P. = Rs. 100. Then, profit = Rs. 150, S.P. = Rs. 250\nNew C.P. = 125% of Rs. 100 = Rs. 125.\nNew S.P. = Rs. 250\nProfit = 250 - 125 = Rs. 125\nRequired percentage = 125/250 * 100 = 50%\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train sets off at 2 p.m. at the speed of 70 kmph. Another train starts at 3:30 p.m. in the same direction at the rate of 85 kmph. At what time the trains will meet?\n\n### Options:\nA. 10.18 p.m\nB. 10.29 p.m\nC. 10.30 p.m\nD. 10.38 p.m\nE. 10.32 p.m\n\n### Answer:\nD = 70 * 1 \u00bd = 105 km\nRS = 85 \u2013 70 = 15\nT = 105/15 = 7 h\n3.30 + 7 h = 10.30 p.m.\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe bus uses 80 gallons of fuel to fly 320 miles. At this rate, how many gallons of fuel are needed for a 800 mile bus?\n\n### Options:\nA. 100\nB. 300\nC. 150\nD. 200\nE. 50\n\n### Answer:\nNumber of gallons of fuel per mile = 320 /80 = 4 gallons per mile\nNumber of gallons of fuel for a 800 mile bus = 800/4= 200\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe area of sector of a circle whose radius is 12 metro and whose angle at the center is 42\u00b0 is?\n\n### Options:\nA. 52.5\nB. 52.9\nC. 52.8\nD. 52.1\nE. 52.2\n\n### Answer:\n42/360 * 22/7 * 12 * 12 = 52.8 m2\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSebastian bought a meal at a restaurant\nand left a 15% tip. With the tip, he paid\nexactly $36.11. How much did the meal cost without the tip?\n\n### Options:\nA. $28.98\nB. $29.91\nC. $30.40\nD. $30.60\nE. $30.85\n\n### Answer:\nThe tip is a percent increase of 15%, which is 115%. Let x equal the price before the tip.\nThus, 115% of this price equals $36.11:\n1.15x = 36.11\nDivide both sides by 1.15:=>x=36.11/1.15=31.40\ncorrect answer C)$31.40\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJohn distributes his pencil among his 4 friends Rose, Mary, Ranjan, and Rohit in the ratio 1/1 : 1/3 :1/4:1/5 . What is the minimum no. of pencils that the person should have?\n\n### Options:\nA. 45\nB. 65\nC. 98\nD. 107\nE. 198\n\n### Answer:\nRakesh : Rahul : Ranjan : Rohit = 1 / 1 : 1 / 3 : 1 / 4 : 1 / 5\nStep 1: At First we need to do is LCM of 2,3,4 and 5 is 60.\nStep 2: Then pencil are distributed in ratio among friends,\nRakesh = ( 1 / 1 x 60 ) = 60.\nRahul = ( 1 / 3 x 60 ) = 20.\nRanjan = ( 1 / 4 x 60 ) = 15.\nRohit = ( 1 / 5 x 60 ) = 12.\nStep 3: Total number of pencils are ( 60 x + 20 x + 15 x + 12 x) = 107 x.\nFor minimum number of pencils x = 1 .\nThe person should have at least 107 pencils.\nD)\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThree table runners have a combined area of 204 square inches. By overlapping the runners to cover 80% of a table of area 175 square inches, the area that is covered by exactly two layers of runner is 24 square inches. What is the area of the table that is covered with three layers of runner?\n\n### Options:\nA. 18 square inches\nB. 20 square inches\nC. 24 square inches\nD. 28 square inches\nE. 30 square inches\n\n### Answer:\nTotal = a + b + c - (sum of EXACTLY 2-group overlaps) - 2*(all three) + Neither\n80%*175 = 204 - 24 - 2*(all three) + 0\n2*(all three) = 204 - 24 - 140\nall three = 20\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the sum of the odd integers from 25 to 55, inclusive?\n\n### Options:\nA. 495\nB. 550\nC. 555\nD. 600\nE. 640\n\n### Answer:\nThe mean is 40.\nSum=Mean(# of elements)\nThere are 16 odd numbers between 25-55 inclusive. 16*40=640\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA car averages 45 mph for the first 4 hours of a trip and averages 75 mph for each additional hour. The average speed for the entire trip was 65 mph. How many hours long is the trip?\n\n### Options:\nA. 12\nB. 11\nC. 10\nD. 9\nE. 8\n\n### Answer:\nLet the time for which car averages 75 mph = t\n65*(t+4)= 45*4 + 75 t\n=>10 t= 80\n=> t = 8\nTotal duration of the trip = 8+4=12\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average age of 6 men increases by 3 years when two women are included in place of two men of ages 24 and 26 years. Find the average age of the women?\n\n### Options:\nA. 37\nB. 26\nC. 34\nD. 18\nE. 11\n\n### Answer:\nExplanation:\n24 + 26 + 6 * 3 = 68/2 = 34\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nConvert the 13/54 m/s into kilometers per hour?\n\n### Options:\nA. 1.7\nB. 1.5\nC. 0.86\nD. 1.1\nE. 1.2\n\n### Answer:\n13/54 m/s = 13/54 * 18/5 = 13/15\n= 0.86 kmph.\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the price of 50 toys is 1000, then what will the price of 20 toys ?\n\n### Options:\nA. 400\nB. 361\nC. 117\nD. 287\nE. 112\n\n### Answer:\nOne toy price = 1000/50 = 20\n20 toy price = 20 * 20 = 400\nAnswer : A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAfter allowing a discount of 15% on the marked price, the selling price is Rs. 6800 for an article. If it was sold at marked price, there would have been a profit of 60%. The cost price of the article is?\n\n### Options:\nA. Rs. 6400\nB. Rs. 5600\nC. Rs. 5000\nD. Rs. 4800\nE. None of these\n\n### Answer:\nGiven SP = Rs. 6800\nMarked price = [SP(100)]/(100 - d%) = (6800 * 100)/(100 - 15) = Rs. 8000\nIf SP = Rs. 8000, profit = 60%\nCP = [SP(100)]/(100 + 60) = (8000 * 100)/160 = Rs. 5000\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIce-ColdIce-cream factory produces only tricolor ice-cream products, where each ice-cream has three stripes of different colors. The factory uses the colors pink, purple, orange, silver, blue and GREEN. How many different ice-cream products have at least one stripe out of the following colors: pink, purple or orange (assume that the order of the stripes in a single ice-cream does not matter)?\n\n### Options:\nA. 12\nB. 14\nC. 18\nD. 19\nE. 20\n\n### Answer:\nIMO: D - 19\nThere are 6C3 = 20 ways to create different colored ice cream products. Out of these 20, only 1 (Silver, Blue, GREEN) will not contain at least one of the colors pink, purple, or orange. 20 - 1 = 19.\nThe other way would be to calculate the number of ice cream products that contain at least one of the colors pink, purple, or orange (PPO).\n#1: Pick one out of PPO and two out of SBP: 3C1 * 3C2 = 3 * 3 = 9\n#2: Pick two out of PPO and one out of SBP: 3C2 * 3C1 = 3 * 3 = 9\n#3: Pick three out of PPO: 3C3 = 1\n9 + 9 + 1 = 19\nanswer is D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWe give the following information about a race hedge.\nThere are 10 hurdles. The distance between consecutive two lines (that is to say which follow) is 9.14 m. There are 13.72 m between the starting line and the first line and the last hurdle between 14.02 m and line arrival. Each hurdle measures 106 cm in height.\nWhat is the length(in centimeters) of the track?\n\n### Options:\nA. 14060cm.\nB. 12060cm.\nC. 15060cm.\nD. 11060cm.\nE. None\n\n### Answer:\nSolution:\n[13.72+(9.14*9)+14.02+[(106\u00f7100)*10]] =>L=[13.72+82.26+14.02+10.6] =>L=120.6m = 12060cm.\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf y is an integer, then the least possible value of |23 - 8y| is\n\n### Options:\nA. 5\nB. 2\nC. 3\nD. 4\nE. 1\n\n### Answer:\nWe know that 8y is a multiple of 8, so let\u2019s first look at the multiples of 8 closest to 23. We have \u201c16\u201d and \u201c24\u201d. Let\u2019s subtract both of these from 23 and see which one produces the smallest result. When 2y = 16, y is 2 and when 3y = 24, y is 5. Let\u2019s start with letting y = 4.\n|23-8(2)|\n|23-16|\n|7| = 7\nNext, let\u2019s let y equal 3.\n|23-8(3)|\n|23-24|\n|-1| = 1\nWe see that the smallest possible value of |23-8y| is 1.\nAnswer E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train 1200 m long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 min, then the length of the tunnel is?\n\n### Options:\nA. 288 m\nB. 256 m\nC. 100 m\nD. 278 m\nE. 287 m\n\n### Answer:\nSpeed = 78 * 5/18 = 65/3 m/sec.\nTime = 1 min = 60 sec.\nLet the length of the train be x meters.\nThen, (1200 + x)/60\n= 65/3\nx = 500 m.\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a consumer survey, 85% of those surveyed liked at least one of three products: 1, 2, and 3. 50% of those asked liked product 1, 30% liked product 2, and 20% liked product 3. If 6% of the people in the survey liked all three of the products, what percentage of the survey participants liked more than one of the three products?\n\n### Options:\nA. 5\nB. 9\nC. 15\nD. 20\nE. 25\n\n### Answer:\nUse the forumla ;\nTotal = Group1 + Group2 + Group3 - (sum of 2-group overlaps) - 2*(all three) + Neither\n100 = 50 + 30 + 20 - ( sum of 2) -2(6) +15\n100 = 103-( sum of 2)\n3 = sum of 2\nso more than 1 = 9\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the smallest no. that should be added to 31110 to make it exactly divisible by 9?\n\n### Options:\nA. 1\nB. 3\nC. 5\nD. 6\nE. 9\n\n### Answer:\nIf a number is divisible by 9, the sum of its digits must be a multiple of 9.\nHere, 3+1+1+1+0=6, the next multiple of 9 is 9.\n3 must be added to 31110 to make it divisible by 9\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the personal income tax rate is lowered from 42% to 32%, what is the differential savings for a tax payer having an annual income before tax to the tune of $42400?\n\n### Options:\nA. $3500\nB. $5000\nC. $4240\nD. $7000\nE. $10000\n\n### Answer:\nSaving = (42-32)% of 42400 = 4240.\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAt a local supermarket, a box of cereal usually costs 18 dollars. This week, the supermarket sells the box of cereal for 12 dollars. How much money will you save if you buy this cereal at this supermarket?\n\n### Options:\nA. 5 dollars\nB. 3 dollars\nC. 6 dollars\nD. 2 dollars\nE. 4 dollar\n\n### Answer:\nSolution:\nIn this situation, there is a decrease in the price.\nSaving = 18 - 12 = 6 dollars\nOption C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nInsert the missing number. 34, 7, 37, 14, 40, 28, 43, (...)\n\n### Options:\nA. 31\nB. 42\nC. 46\nD. 56\nE. 68\n\n### Answer:\nExplanation :\nWe have two series here\n34, 37, 40, 43, ... (Increase by 3)\n7, 14, 28, ... (Multiply by 2)\nHence, next term is 28 \u00d7 2 = 56\nAnswer : Option D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn the city of San Durango, 60 people own cats, dogs, or rabbits. If 36 people owned cats, 40 owned dogs, 10 owned rabbits, and 12 owned exactly two of the three types of pet, how many people owned all three?\n\n### Options:\nA. 2\nB. 4\nC. 7\nD. 12\nE. 32\n\n### Answer:\nTotal = C + D + R - (CD + DR + CR) - 2CDR\n60 = 36 + 40 + 10 - (12) - 2x\nx = 7\nSo, answer will be C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n5/25= 10/50. which method did you use to determine whether this proportion is true or false?\n\n### Options:\nA. true\nB. neutral\nC. false\nD. not sure\nE. none\n\n### Answer:\n5/25= 10/50. cross multiplication: 5 * 50= 250, 10 *25 = 250,\nwe see that 250 are not equal to 250 so there is proportion. corrcet answer: (A)\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe perimeter of a triangle is 44 cm and the inradius of the triangle is 2.5 cm. What is the area of the triangle?\n\n### Options:\nA. 38 cm2\nB. 55 cm2\nC. 65 cm2\nD. 45 cm2\nE. 35 cm2\n\n### Answer:\nArea of a triangle = r * s\nWhere r is the inradius and s is the semi perimeter of the triangle.\nArea of triangle = 2.5 * 44/2 = 55 cm2\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA solution of X pounds of water and sugar is boiled until 20% of the water content evaporates. Originally w% of sugar was present in the solution. After evaporation, what percentage of the solution is sugar?\n\n### Options:\nA. 100w/(1-w)\nB. 80w/(1-w)\nC. 75w/(1-w)\nD. 100w/(80-0.2w)\nE. 100w/(80+0.2w)\n\n### Answer:\nWe'll go for the ALTERNATIVE approach since there are variables in all the answers (which means that any number could work). Since the question deals with percents, the easiest number to use is X = 100. Now let's say that w = 10. Before the evaporation we had 10 pound of sugar and 90 pounds of water. Since only water evaporated, after the evaporation the 10 pounds of sugar remained the same, but the water reduced by 20% of 90 (18 pounds), so we have only 72 pounds of water. 10 out of 82 is the fraction of sugar, so if we multiply it by 100 we get the percents. The correct answer is E: 100w/(80+0.2w) >>> 100x10 / 82\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf \u2018POOJA\u2019 is coded as \u2018SRRMD\u2019, then \u2018PRIYA\u2019 is coded as\n\n### Options:\nA. THGFE\nB. GVFED\nC. FREDCV\nD. SULBD\nE. SUUNF\n\n### Answer:\nP= 16 = 16+3 = 19 = S\nO = 15 =15+3 =18 = R\nSIMILARLY,\nP = 16 = 16+3 = 19 = S\nR = 18 = 18+3 = 21 = U\nI = 9 = 9+3 = 12 = L\nY = 25 = 25 +3 = 28 = B\nA = 1 = 1+3 = 4 = D\nSO ANS IS\nSULBD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA software programmer does 30% of the work in 80% of the time, and 80% of the work in the remaining 20% of the time. If the code he writes is X lines long and he was given one month (30 days) to accomplish the task, then, assuming that the programmer works at a constant rate in each of the two stages, How many lines of code were written in the last two weeks, in terms of X?\n\n### Options:\nA. 13x /15\nB. 15x/15\nC. 7x/15\nD. 2x/30\nE. 13x/30\n\n### Answer:\nTake X=30 lines\n80% of 30 = 24 lines\n20% of 30 = 6 lines\nW - R - T\n6 lines - r1 - 24 (first 80% of the 30 days)\n24 lines - r2 - 6 ( last 20% of the 20 days)\nr1 = 1/4r2 = 4\nNow Work in last 14 days = 6 days programmer worked at r2 + 8days programmer worked at r1\n=> 6 * 4 + 8 * 1/4 = 24 + 2 = 26\nInsert, X=30 in all options => C is the answer.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat are the last two digits of 5in2007th ?\n\n### Options:\nA. 75\nB. 65\nC. 55\nD. 25\nE. 05\n\n### Answer:\nJust keep track of the last two digits of the consecutive powers of 5 and note\nthat 5-2round- = 25 and 5 \u00d7 25 = 125.\ncorrect answer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nPavan travelled for 11 hours. He covered the first half of the distance at 30 kmph and remaining half of the distance at 25 kmph. Find the distance travelled by Pavan?\n\n### Options:\nA. 288\nB. 266\nC. 129\nD. 300\nE. 276\n\n### Answer:\nLet the distance travelled be x km.\nTotal time = (x/2)/30 + (x/2)/25 = 11 => x/60 + x/50 = 11 => (5x + 6x)/300 = 11\n=> x\n= 300 km\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many numbers from 2 to 11 are exactly divisible by 2?\n\n### Options:\nA. A)2\nB. B)3\nC. C)5\nD. D)7\nE. E)8\n\n### Answer:\n2/2 = 1 and11/2 = 5\n5 - 1 = 4\n4 + 1 = 5 Numbers.\nAnswer : C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe product of all the prime numbers less than 28 is closest to which of the following powers of 10?\n\n### Options:\nA. a) 10^9\nB. b) 10^8\nC. c) 10^7\nD. d) 10^6\nE. e) 10^8*2.23\n\n### Answer:\nGroup these numbers so as to get product close to a multiple of 10, so they can be rewritten as (2*5)(3*7)(11*19)(13*17)*23 or 10*21*209*221*23\nNow take out power of 10 from each number and rewrite\n10*10*100*100*10(1*2.1*2.09*2.21*2.3) or 10^7*(1*2.1*2.09*2.21*2.3)=2.23*10^8\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nEvery second Saturday and all Sundays are holidays. How many working days will be there in a\nmonth of 30 days beginning on a Saturday?\n\n### Options:\nA. 24\nB. 23\nC. 18\nD. 21\nE. 22\n\n### Answer:\nExplanation :\nMentioned month has begins on a Saturday and has 30 days\nSundays = 2nd, 9th, 16th, 23rd, 30th\n=> Total Sundays = 5\nSecond Saturdays = 8th and 22nd\nTotal Second Saturdays = 2\nTotal Holidays = Total Sundays + Total Second Saturdays = 5 + 2 = 7\nTotal days in the month = 30\nTotal working days = 30 - 7 = 23\nAnswer : Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe mean of 50 observations was 36. It was found later that an observation 48 was wrongly taken as 23. The corrected new mean is?\n\n### Options:\nA. 36.7\nB. 36.1\nC. 36.5\nD. 36.9\nE. 36.3\n\n### Answer:\nCorrect sum\n= (36 * 50 + 48 - 23)\n= 1825.\nCorrect mean = 1825/50\n= 36.5\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a 5 percent deposit that has been paid toward the purchase of a certain product is $70, how much more remains to be paid?\n\n### Options:\nA. $1120\nB. $1190\nC. $1260\nD. $1330\nE. $1400\n\n### Answer:\n95% remains to be paid so the remaining amount is 19*70=$1330.\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a group of cows and chickens, the number of legs was 18 more than twice the number of heads. The number of cows was:\n\n### Options:\nA. 5\nB. 7\nC. 9\nD. 12\nE. 14\n\n### Answer:\nLet the number of cows be x and their legs be 4x.\nLet the number of chicken be y and their legs be 2x.\nTotal number of legs = 4x + 2y.\nTotal number of heads = x + y.\nThe number of legs was 18 more than twice the number of heads.\nTherefore, 2 \u00d7 (x + y) + 18 = 4x + 2y.\nor, 2x + 2y + 18 = 4x + 2y.\nor, 2x + 18 = 4x [subtracting 2y from both sides].\nor, 18 = 4x \u2013 2x [subtracting 2x from both sides].\nor, 18 = 2x.\nor, x = 9 [dividing by 2 on both sides].\nTherefore, the number of cows = 9.\nCorrect Answer:C)9\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA waiter's salary consists of his salary and tips. During one week his tips were 5/3 of his salary. What fraction of his income came from tips ?\n\n### Options:\nA. 4/9\nB. 5/4\nC. 5/8\nD. 5/9\nE. 6/9\n\n### Answer:\nIncome = salary (s) +tips = s + s*5/3 = s*8/3\nTips = s*8/3\nfraction of his income came from tips = (s*5/3)/(s*8/3)= 5/8\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich of the following lines has x-intercept and y-intercept that are integers T?\n\n### Options:\nA. y=3x+1\nB. y=\u221ax+1\nC. y=-2/x\nD. y=x^2-1\nE. xy=1\n\n### Answer:\nValues that satisfy y=x^2-1 are (x,y)=(-1,0),(1,0),(0,-1). Hence, they are all integers T and the correct answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the least number which should be added to 2982 so that the sum is exactly divisible by 5, 6, 4, and 3?\n\n### Options:\nA. 14\nB. 18\nC. 22\nD. 26\nE. 30\n\n### Answer:\nL.C.M. of 5, 6, 4 and 3 = 60.\nWhen dividing 2982 by 60, the remainder is 42.\nThe number to be added = 60 - 42 = 18.\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA $74.95 lawn chair was sold for $59.95 at a special sale. By approximately what percent was the price decreased?\n\n### Options:\nA. 15%\nB. 20%\nC. 25%\nD. 60%\nE. 80%\n\n### Answer:\nListed selling price of chair = 74.95 $\nDiscounted selling price of chair = 59.95 $\nDiscount = 74.95 - 59.95 = 15 $\n% decrease in price of chair = (15/74.95) * 100% = 20 % approx\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA and B invests Rs.10000 each, A investing for 8 months and B investing for all the 12 months in the year. If the total profit at the end of the year is Rs.25000, find their shares?\n\n### Options:\nA. 22277\nB. 26782\nC. 22882\nD. 15000\nE. 28761\n\n### Answer:\nThe ratio of their profits A:B = 8:12 = 2:3\nShare of A in the total profit = 2/5 * 25000 = Rs.10000 Share of A in the total profit = 3/5 * 25000\n= Rs.15000\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA fair 2-sided coin is flipped 6 times. What is the probability that tails will be the result at least twice, but not more than 5 times?\n\n### Options:\nA. 5/8\nB. 3/4\nC. 7/8\nD. 57/64\nE. 15/16\n\n### Answer:\nTotal possible outcomes when coined is tossed 6 time=2^6=4*4*4=64\nTotal possible outcomes getting 2 or 3 or 4 or 5 tails= 6C2+6C3+6C4+6C5=(6*5)/2+(6*5*4)/(3*2)+(6*5)/2+6=15+20+15+6=56\nProbability of getting at least 2 but not more than 5 times tails=56/64=7/8\nAns=C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nYou have a pair of unbiased dices. You throw them together till you get a sum of 4 or 7.\nWhat is the probability that you get a sum of 4 before the sum of 7?\n\n### Options:\nA. 1/6\nB. 5/7\nC. 2/8\nD. 3/7\nE. 2/5\n\n### Answer:\nE\n2/5\nExplanation:\nThis problem can be solved with different approaches. Let us not go into the complicated generic stuff to avoid confusion and try to solve it with simpler means.\nLet us find the results separately. There can be 4 different results that give the sum of 5 and there can be 6 different results that give the sum of 7.\nThus, the probability that we get the sum of 4 before the sum of 7 will be:\n4/(4+6) = 4/10 = 2/5.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA 160 meter long train crosses a man standing on the platform in 6 sec. What is the speed of the train?\n\n### Options:\nA. 96 kmph\nB. 94 kmph\nC. 92 kmph\nD. 86 kmph\nE. 76 kmph\n\n### Answer:\nS = 160/6 * 18/5 = 96 kmph\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf A, B and C together can finish a piece of work in 4 days. A alone in 12 days and B in 18 days, then C alone can do it in?\n\n### Options:\nA. 6\nB. 5\nC. 7\nD. 9\nE. 2\n\n### Answer:\nC = 1/4 - 1/12 \u2013 1/18 = 1/9 => 9 days\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHarkamal purchased 9kg of grapes at the rate of 70 per kg and 9 kg of mangoes at the rate of 55 per kg. How much amount did he pay to the shopkeeper?\n\n### Options:\nA. A)1120\nB. B)1065\nC. C)1070\nD. D)1075\nE. E)1080\n\n### Answer:\nCost of 9 kg grapes = 70 \u00d7 9 = 630.\nCost of 9 kg of mangoes = 55 \u00d7 9 = 490.\nTotal cost he has to pay = 630 + 490 = 1120\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA sum fetched a total simple interest of Rs. 4016.25 at the rate of 9 p.c.p.a. in 5 years. What is the sum?\n\n### Options:\nA. 8000\nB. 8925\nC. 8500\nD. 8700\nE. 8750\n\n### Answer:\nP = (100*4016.25/9*5) ==>8925\nANSWER B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSomeone on a skateboard is traveling 10 miles per hour. How many feet does she travel in 20 seconds? (1 mile = 5280 feet)\n\n### Options:\nA. 292 ft\nB. 293.4 ft\nC. 295 ft\nD. 296 ft\nE. 297 ft\n\n### Answer:\nper second => 10*5280 ft/60*60 =14.67 ft\n20 seconds => 14.67 * 20 = 293.4 ft\nAnswer : B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA, B and C are entered into a partnership. A invested Rs.6500 for 6 months, B invested Rs.8400 for 5 months and C invested for Rs.10000 for 3 months. A is a working partner and gets 5% of the total profit for the same. Find the share of C in a total profit of Rs.7400.\n\n### Options:\nA. 1909\nB. 1900\nC. 1908\nD. 1905\nE. 1901\n\n### Answer:\n65 * 6 : 84 * 5 : 100 * 3\n26:28:20\nC share = 74000 * 95/100 = 7030 * 20/74 => 1900\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA container contains 20 liters of milk, From this container 2 liters of milk was taken out and replaced by water. This process was repeated further 2 times. How much milk is now contained by the container?\n\n### Options:\nA. 14.58 liters\nB. 20.16 liters\nC. 22.45 liters\nD. 26.95 liters\nE. 31.45 liters\n\n### Answer:\nAmount of milk left after 3 operations = 20 (1 - 2/20)^3 = 20 * 9/10 * 9/10 * 9/10 = 14.58 liters\nAnswer is A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAyesha's father was 31 years of age when she was born while her mother was 34 years old when her brother four years younger to her was born. What is the difference between the ages of her parents?\n\n### Options:\nA. 2 years\nB. 4 years\nC. 6 years\nD. 8 years\nE. 1 years\n\n### Answer:\nExplanation:\nMother's age when Ayesha's brother was born = 34 years.\nFather's age when Ayesha's brother was born = (31 + 4) years = 35 years.\nRequired difference = (35 - 34) years = 1 years.\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo students appeared at an examination. One of them secured 9 marks more than the other and his marks was 56% of the sum of their marks. The marks obtained by them are:\n\n### Options:\nA. 39, 30\nB. 41, 32\nC. 42, 33\nD. 43, 34\nE. 41, 44\n\n### Answer:\nC\nLet their marks be (x + 9) and x.\nThen, x + 9 = 56/100(x + 9 + x)\n25(x + 9) = 14(2x + 9)\n3x = 99\nx = 33\nSo, their marks are 42 and 33.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n100 identical coins each with probability 'pp' showing up heads & tossed.\n\n### Options:\nA. 13/101\nB. 11/101\nC. 51/101\nD. 53/102\nE. 54/101\n\n### Answer:\nLet aa be the number of coins showing heads\nThen, P(A=50)=P(A=51)P(A=50)=P(A=51)\n\u21d2100C50\u00d7P50\u00d7(1\u2212P)50\u21d2100C51\u00d7P51\u00d7(1\u2212P)49\u21d2100C50\u00d7P51\u00d7(1\u2212P)50=100C51\u00d7P\u21d251(1\u00e2\u02c6\u2032P)=50P\u21d2P=51/101\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf x2*square* \u2013 x \u2013 2 > 0, which of the following is the\nsolution set for x?\n\n### Options:\nA. x > \u20131\nB. x > 2\nC. \u20131 < x < 2\nD. x < \u20131 or x > 2\nE. No solutions are possible\n\n### Answer:\nBegin by treating the inequality x2 \u2013 x \u2013 2 > 0 as if it were an equation. Factor to find the zeros:\nx2 \u2013 x \u2013 2 = 0\n(x + 1)(x \u2013 2) = 0\nx = \u20131 and x = 2\nThe graph of this function is a parabola that crosses the x-axis at \u20131 and 2. This graph is\nconcave up because the coefficient of the x2 term (that is, a) is positive. The parabola dips\nbelow the x-axis when \u20131 < x < 2, so these values do not satisfy the equation. Therefore, the\ncorrect answer is D. (If you doubt this answer, note that when x = 0, x2 \u2013 x \u2013 2 = \u20132,\nwhich is less than 0. So 0 is not in the solution set.)\ncorrect answer D) x < \u20131 or x > 2\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA group of tourists wants to visit at least three of the four cities A, B, C, and D. How many travel itineraries can they make? All cities are connected to one another and please note that visiting the same cities in a different order counts as a different itinerary.\n\n### Options:\nA. 24\nB. 36\nC. 48\nD. 60\nE. 64\n\n### Answer:\nThe number of ways to choose three cities is 4C3=4.\nThe number of itineraries for each group of 3 cities is 3!.\nSo the number of itineraries to three cities is 4*3!=24.\nThe number of ways to choose four cities is 4C4=1.\nThe number of itineraries for the group of 4 cities is 4!.\nSo the number of itineraries to four cities is 4!=24.\nThe total number of itineraries is 24+24=48.\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average age of applicants for a new job is 31, with a standard deviation of 8. The hiring manager is only willing to accept applications whose age is within one standard deviation of the average age. What is the maximum number of different ages of the applicants?\n\n### Options:\nA. 8\nB. 14\nC. 15\nD. 17\nE. 30\n\n### Answer:\nwithin one standard deviation of the average age means 31 +/- 7\n23--31--39\nnumber of dif.ages -23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39\ntotal=17\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe difference between a number and its three fifth is 50. What is the number?\n\n### Options:\nA. 75\nB. 100\nC. 125\nD. 175\nE. 187\n\n### Answer:\nSol.\nLet the numbers be x.\nThen, x-3/5x = 50\n\u21d42/5x = 50\u21d4 x = (50x5/2) = 125.\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 12 men can reap 120 acres of land in 16 days, how many acres of land can 36 men reap in 32 days?\n\n### Options:\nA. 269\nB. 512\nC. 369\nD. 720\nE. 450\n\n### Answer:\n12 men 120 acres 16 days\n36 men ? 32 days\n120 * 36/12 * 32/16\n120 * 3 * 2\n120 * 6 = 720\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMary charges $8.50 per hour to clean a house. If she works 27 hours, how much\ndoes she earn in one week?\n\n### Options:\nA. $619.50\nB. $122.50\nC. $229.50\nD. $429.50\nE. $312.50\n\n### Answer:\nMultiply 27 hours x $8.50 =\nAnswer: $229.50\ncorrect answer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA city had 600 migrants in the year 2000. Since then, The number of migrants in a countrythe city has doubled every 3 years. If there were 600 migrants in the country in the year 2000, What was the increase in the population of migrants during the period from 2009 to 2012?\n\n### Options:\nA. 2400\nB. 4800\nC. 6600\nD. 8200\nE. 16400\n\n### Answer:\nThe population will increase in the following order:\n2000: 600\n2003: 1200\n2006: 2400\n2009: 4800\n2012: 9600\nDifference between 2009 and 2012 = 4800\nOption B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo pipes can fill a tank in 10 and 12 hours, while third pipe will make the tank empty in 20 hours. If all three pipes operate simultaneously. In how many hours the tank will be filled ?\n\n### Options:\nA. 5.5 Hours\nB. 7.5 Hours\nC. 8.5 Hours\nD. 9.5 Hours\nE. 6.5 Hours\n\n### Answer:\nIn 1 hour it fill 1/10 + 1/12 - 1/20 = 8/60\nSo fill tank fillup in 60/8 = 7.5 Hours\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA manufacturer sells a pair of glasses to a wholesale dealer at a profit of 18%. The wholesaler sells the same to retailer at a profit of 20%. The retailer in turn sells them to a customer for Rs. 30.09, there by earning a profit of 25%. The cost price for the manufacturer is?\n\n### Options:\nA. 19\nB. 10\nC. 17\nD. 18\nE. 12\n\n### Answer:\nLet the cost price for the manufacturer be Rs. x. Then, 125% of 120% of 118% of x\n= 30.09.\n125/100 * 120/100 * 118/100 * x\n= 3009/100\n177/100 x = 3009/100 => x = 17\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a colony of 70 residents, the ratio of the number of men and women is 4:3. Among the women, the ratio of the educated to the uneducated is 1:4. If the ratio of the number of education to uneducated persons is 8:27, then find the ratio of the number of educated and uneducated men in the colony?\n\n### Options:\nA. 1:4\nB. 3:5\nC. 3:9\nD. 3:7\nE. 1:3\n\n### Answer:\nNumber of men in the colony = 4/7 (70) = 40\nNumber of women in the colony = 3/7 (70) = 30\nNumber of educated women in the colony = 1/5 (30) = 6\nNumber of uneducated women in the colony = 4/5 (30) = 24\nNumber of educated persons in the colony = 8/35 (70) = 16\nAs 6 females are educated, remaining 10 educated persons must be men.\nNumber of uneducated men in the colony = 40 - 10 = 30\nNumber of educated men and uneducated men are in the ratio 10:30 => 1:3\nAnswer:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average of 25 results is 50. The average of first 12 of those is 14 and the average of last 12 is 17. What is the 13th result?\n\n### Options:\nA. 741\nB. 752\nC. 878\nD. 785\nE. 458\n\n### Answer:\nSolution: Sum of 1st 12 results = 12*14\nSum of last 12 results = 12*17\n13th result = x (let)\nNow,\n12*14+12*17+x = 25*50\nOr, x = 878.\nAnswer: Option C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA canoe has two oars, left and right. Each oar either works or breaks. The failure or non-failure of each oar is independent of the failure or non-failure of the other. You can still row the canoe with one oar. The probability that the left oar works is 3/5. The probability that the right oar works is also 3/5. What is the probability W that you can still row the canoe?\n\n### Options:\nA. 9/25\nB. 10/25\nC. 6/10\nD. 2/3\nE. 21/25\n\n### Answer:\nSimply look at the question from the other side. What is the probability that you can\u2019t row the canoe? This would be 2/5 x 2/5 = 4/25.\nUsing the idea that the probability of something happening is 1 \u2013 the probability that it doesn\u2019t happen, you can use the following equation to reach the right answer W: 1 \u2013 4/25 = 21/25.Answer choice E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWith what number must 6.2587 be multiplied in order to obtain the number 625.87?\n\n### Options:\nA. 1000\nB. 1,0000\nC. 100\nD. 100,000\nE. None of these\n\n### Answer:\nExplanation: The decimal must be moved two places to the right. To do this, we must multiply by a number with two zeroes. The correct answer is 100.The decimal must be moved two places to the right. To do this, we must multiply by a number with two zeroes. The correct answer is 100.\nAnswer : (C)\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA 300 m long train crosses a platform in 51 sec while it crosses a signal pole in 18 sec. What is the length of the platform?\n\n### Options:\nA. 287\nB. 350\nC. 828\nD. 277\nE. 550\n\n### Answer:\nSpeed = 300/18 = 50/3 m/sec.\nLet the length of the platform be x meters.\nThen, (x + 300)/5A = 50/3\n3x + 900 = 2550 => x = 550 m.\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many ways someone can make with 8 shirts and 6 pants?\n\n### Options:\nA. 50\nB. 45\nC. 55\nD. 52\nE. 48\n\n### Answer:\nIf you can only wear one shirt and one pair of pants, then you can make 8*6 = 48 combinations.\nAnswer:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA multiple choice question has 5 options. Choosing the correct option earns the student 1 marks. However choosing the wrong option incurs negative marks so that if a student chooses an option randomly, his expected score is 0. Suppose a student has successfully eliminated 2 incorrect options. His expected score if he chooses randomly among the remaining options is.\n\n### Options:\nA. 1/2\nB. 1/3\nC. 1/4\nD. 2/3\nE. 4/3\n\n### Answer:\nfor right ans 1 no is given and for wrong -.25\nso 1(1)+4(-.25)=0\nnow\n1(1)+2(-.25)=.5=1/2.\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThree candidates contested an election and received 1136, 7636 and 15628 votes respectively. What percentage of the total votes did the winning candidate got?\n\n### Options:\nA. 55%\nB. 64%\nC. 57%\nD. 58%\nE. 59%\n\n### Answer:\nTotal number of votes polled = (1136 + 7636 + 15628) = 24400\nSo, Required percentage = 15628/24400 * 100 = 64%\nANSWER : B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a group of ducks and Cows, the total number of legs are 16 more than twice the no. of heads. Find the total no.of buffaloes.\n\n### Options:\nA. 10\nB. 12\nC. 8\nD. 12\nE. 14\n\n### Answer:\nLet the number of buffaloes be x and the number of ducks be y\n=> 4x + 2y = 2 (x + y) + 16\n=> 2x = 16 => x = 8\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf you cut a 20ft piece of wood into two pieces making one piece 6ft longer than the other. What size is the smaller piece?\n\n### Options:\nA. 4ft\nB. 7ft\nC. 8ft\nD. 10ft\nE. 12ft\n\n### Answer:\nTotal length is 20ft, one piece is 6ft longer (x+6), leaving the other piece to figure out (x).\n(x)+ (x+4)=20\nx+x+6-6=20-6\n2x=14\n2x/2=14/2\nx=7\nThe piece is B) 7ft.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nEight friends go to see a movie at the local movie theater and sit in a row together. If there are two friends who refuse to sit next to each other, how many 8-person seating arrangements are possible?\n\n### Options:\nA. 5040\nB. 15,120\nC. 30,240\nD. 35,280\nE. 40,320\n\n### Answer:\nThe number of ways to arrange 8 people in a row is 8!\nFrom this we want to subtract all the arrangements where the two friends are next to each other. If we consider them as one unit, then the number of arrangements of this 2-person unit and the 6 other friends is 7! And the number of arrangements of the two friends within this unit are 2 because the two friends can switch places. So the total number of arrangements of the 8 friends with the 2-person unit together is 7!*2\nThe total number of permutations where these two friends are not seated next to each other is 8! - 7!*2 = 6*7! = 30,240\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIt takes John 10 minutes to walk to the car park and 45 to drive to work. At what time should he get out of the house in order to get to work at 9:00 a.m.?\n\n### Options:\nA. 5:44\nB. 7:35\nC. 7\nD. 5\nE. 6\n\n### Answer:\nThe time it takes John to get to work: time to walk to car park + time to drive\n25 + 45 = 70 minutes = 1 hour and 10 minutes\nJohn needs to get out of the house 1 hour and 10 minutes before 9:00 am at\n9:00 - 1:10 = 7:35 a.m.\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA student,after his teacher's question, chose a number, multiplied it by 2, then subtracted 138 from the result and got 102. What was the number he chose?\n\n### Options:\nA. 344\nB. 251\nC. 411\nD. 212\nE. 120\n\n### Answer:\nLet x be the number he chose, then\n2\u22c5x\u2212138=102\n2x=240\nx=120\ncorrect answer is E)120\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich of the following fractions is greater than 3/5 and less than 6/7?\n\n### Options:\nA. 7/8\nB. 1/3\nC. 2/3\nD. 1/3\nE. 6/7\n\n### Answer:\nExplanation :\nLCM of 5, 7, 2, 3, 3, 8 = 840\n3/5 = 504/840\n6/7 = 720/840\nHence, the question is to find out a number which is between the above numbers\nThe given choices are\n1/2 = 420/840\n2/3 = 560/840\n1/3 = 280/840\n7/8 = 735/840\nClearly, 560/840 = 2/3 . Answer : Option C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nKim has 7 pairs of shoes; each pair is a different color. If Kim randomly selects 2 shoes without replacement from the 14 shoes, what is the probability that she will select 2 shoes of the same color?\n\n### Options:\nA. 1/13\nB. 1/15\nC. 11/9\nD. 1/10\nE. 1/25\n\n### Answer:\nCan be tackled in this way as well: Probability of selecting any 1 out of 14 shoes = 14/14 = 1\nProbability of selecting the next shoe (out of 14 available) having the same color = 1/14 (as after selecting the 1st one, there is only 1 another shoe left with the same color).\nThus the total probability = 1*1/13=1/13.\nA is the correct answer.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo trains of length 100 m and 200 m are 90 m apart. They start moving towards each other on parallel tracks, at speeds 54 kmph and 72 kmph. After how much time will the trains meet?\n\n### Options:\nA. 21/9 sec\nB. 32/3 sec\nC. 18/7 sec\nD. 32/3 sec\nE. 53/2 sec\n\n### Answer:\nThey are moving in opposite directions, relative speed is equal to the sum of their speeds.\nRelative speed = (54 + 72)*5/18 = 7*5 = 35 mps.\nThe time required = d/s = 90/35 = 18/7 sec.\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA Complany provides health insurance that pays 50.0% of the cost, with a $180.00 deductible. This means that the employees pays the first $180.00, after which the insurance company pays 150.0%. How much will an employee pay if his total medical bill is $1400.00?\n\n### Options:\nA. $790\nB. $780\nC. $770\nD. $760\nE. $750\n\n### Answer:\nAmount employee pays = 180 + 50/100* (1400-180)\n= 180 + 50/100*1220\n= 180+610\n= $790\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nBy selling 100 pencil, a trader gains the cost of 33 Pencil. Find his gain percentage?\n\n### Options:\nA. 26 1/3%\nB. 51 1/3%\nC. 33 %\nD. 53 1/3%\nE. 34 1/3%\n\n### Answer:\nC\n33 %\nLet the CP of each pencil be Rs. 1.\nCP of 100 pens = Rs. 100\nProfit = Cost of 33 pencil = Rs. 33\nProfit% = 33/100 * 100 = 33 %\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA and B invested Rs.4000 and Rs.5000 and they get 20% profit at the end of year. Then share of B is\n\n### Options:\nA. Rs.1200\nB. Rs.1000\nC. Rs.1300\nD. Rs.1500\nE. Rs.1800\n\n### Answer:\nTotal invest is 9000\n20% gain of 9000 is 1800\nA:B=4:5\nB's share will be (5/9)*1800=1000\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat number has a 5:1 ratio to the number 10?\n\n### Options:\nA. 36\nB. 50\nC. 76\nD. 56\nE. 62\n\n### Answer:\n5:1 = x: 10\nx = 50\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA bike covers a certain distance at the speed of 16km/h in 2 hrs. If the bike was to cover the same distance in approximately 4 hrs, at what approximate speed should the bike travel?\n\n### Options:\nA. 8 km/h\nB. 9 km/h\nC. 7 km/h\nD. 6 km/h\nE. 10 km/h\n\n### Answer:\nAns.(A)\nSol. Total distance = 16 \u00d7 2 = 32 km\nNow speed = 32/4 = 8 km/h\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nPresent ages of X and Y are in the ratio 5:6 respectively. Ten years hence this ratio will become 6:7 respectively. What is X's present age in years?\n\n### Options:\nA. 35\nB. 36\nC. 50\nD. 39\nE. 40\n\n### Answer:\nLet the present ages of X and Y be 5x and 6x years respectively.\nThen, (5x + 10)/(6x + 10) = 6/7\n7(5x +10) = 6(6x +10) => 35x+70= 36x+60 => x=10\nX's present age = 5x = 5*10 = 50\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA car drives 40 miles on local roads at 20 mph, and 180 miles on the highway at 60 mph, what is the average speed of the entire trip?\n\n### Options:\nA. 36 mph\nB. 40 mph\nC. 44 mph\nD. 52 mph\nE. 58 mph\n\n### Answer:\nExplanations\n1) In phase #1 of the trip, the car traveled 40 mi at 20 mph. That time of this phase was:\ntime = distance/rate = (40 mi)/(20 mph) = 2 hr\nIn phase #2 of the trip, the car traveled 180 mi at 60 mph. That time of this phase was:\ntime = distance/rate = (180 mi)/(60 mph) = 3 hr\nThe total distance of the trip = 40 mi + 180 mi = 220 mi\nThe total time of the trip = 2 hr + 3 hr = 5 hr\nThe average speed of trip is given by\nspeed = distance/time = (220 mi)/(5 hr) = 44 mph\nAnswer: C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe tax on a commodity is diminished by 20% but its consumption is increased by 5%. Find the decrease percent in the revenue derived from it?\n\n### Options:\nA. 12%\nB. 14%\nC. 16%\nD. 20%\nE. 22%\n\n### Answer:\nExplanation:\n100 * 100 = 10000\n80 * 105 = 8400\n10000------- 1600\n100 ------- ? = 16%\nC)\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nfind value for x from below equation? x + 1 = -3\n\n### Options:\nA. 1\nB. -4\nC. -1\nD. 2\nE. 3\n\n### Answer:\n1. Subtract 1 from both sides:\nx + 1 - 1 = -3 - 1\n2. Simplify both sides:\nx = -4\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe present ages of three persons are in the proportion of 4 : 7 : 9. Eight years ago, the sum of their ages was 96. Find their present ages.\n\n### Options:\nA. 24,42,54\nB. 8,20,28\nC. 16,28,36\nD. 16,28,46\nE. None of these\n\n### Answer:\nLet the present ages of three persons be 4K,7K and 9K respectively.\n(4K - 8) + (7K - 8) + (9K - 8) = 96\n20K = 120\nK = 6\nTherefore, then present ages are 24,42,54.\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many integers Q are prime numbers in the range 200 < Q < 220?\n\n### Options:\nA. 1\nB. 2\nC. 3\nD. 4\nE. 5\n\n### Answer:\nMy friend, every single odd number greater than can be written either as 4Q+1 or as 4Q+3. If you divide any odd number by 4, you will get a remainder of either 1 or 3. That's not a rule unique to prime numbers at all.\nThe 6Q+1 or 6Q-1 rule is basically every odd number that is not divisible by three, so it narrows the search a little.\nHere's how I thought about the problem. First, eliminate all the even numbers and the odd multiples of 5 in that range. That leaves us with:\n{201, 203, 207, 209, 211, 213, 217, 219}\nEliminate the four multiples of 3. Notice that 21 is a multiple of 3, so 210 is also a multiple of 3. If we add or subtract 3 or 9, we get more multiples of three. When we eliminate those, we are left with.\n{203, 209, 211, 217}\nNow, notice that a cool thing about this range is that 210 is also a multiple 7 (again, because 21 is a multiple of 7). This means that\n210 - 7 = 203\n210 + 7 = 217\nThose two numbers are also multiples of 7, so eliminate them from the list. Now, we are left with\n{209, 211}.\nWe've already checked all the prime numbers less than 10, so we know that neither of these numbers is divisible by anything less than 10. We have to check 11 now. We know that 22 is a multiple of 11, so 220 is also a multiple of 11. This means that\n220 - 11 = 209\nis also a multiple of 11. We can eliminate this from the list also.\nThat leaves us with just 211. There's no zero option in the question, so this must be a prime number.\nAnswer = (A)\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat sum of money will produce Rs.70 as simple interest in 4 years at 3 1/2 percent?\n\n### Options:\nA. 266\nB. 500\nC. 287\nD. 26\nE. 281\n\n### Answer:\n70 = (P*4*7/2)/100\nP = 500\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFor a certain set, the value range of its members is 96.8. A new set is created from the members of the old set as follows: 12 is subtracted from a member of the old set, and the result is divided by 4. The resulting value is a member of the new set. If this operation is done for each member of the old set, what is the range of values of the members of the new set?\n\n### Options:\nA. 21.2\nB. 24.2\nC. 36.3\nD. 48.4\nE. 96.8\n\n### Answer:\nLet x and z be the smallest and largest of the original set, respectively.\nz - x = 96.8\nThe smallest and largest members of the new set will be (x-12) / 4 and (z-12) / 4.\nThen the range is (z-12) / 4 - (x-12) / 4 = (z-x) / 4 = 96.8 / 4 = 24.2\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA third of Arun\u2019s marks in mathematics exeeds a half of his marks in english by 80.if he got 240 marks In two subjects together how many marks did he got inh english?\n\n### Options:\nA. 120,60\nB. 180,60\nC. 180,90\nD. 120,40\nE. None of them\n\n### Answer:\nLet Arun\u2019s marks in mathematics and english be x and y\nThen 1/3x-1/2y=30\n2x-3y=180\u2026\u2026>(1)\nx+y=240\u2026\u2026.>(2)\nsolving (1) and (2)\nx=180\nand y=60\nAnswer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n8^9 - 8^2 is approximation of which of the following?\n\n### Options:\nA. 9^7\nB. 9^8\nC. 9^9\nD. 9^11\nE. 8^9\n\n### Answer:\n=> Since 8^2 is a small number compared to 8^9, it can be disregarded. Thus, 8^9-8^2=8^9 is derived and the answer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich of the following describes all values of x for which 2\u2013x^2 >= 0?\n\n### Options:\nA. x >= 1\nB. x <= \u20131\nC. 0 <= x <= 2\nD. x <= \u20131 or x >= 1\nE. \u20132 <= x <= 2\n\n### Answer:\nWhich of the following describes all values of x for which 2\u2013x^2 >= 0?\n(A) x >= 1\nPlugged in 2. 2\u2013(3)^2 >= 0 -7>=0? NO. Wrong\n(B) x <= \u20131\nPlugged in -3. 2\u2013(-3)^2 >= 0 -7>=0? NO. Wrong\n(C) 0 <= x <= 2\nPlugged in 0, 1, and 2. All of them work. But E is better because it describes all the values of x\n(D) x <= \u20131 or x >= 1\nA and B answer this. Wrong.\n(E) \u20132 <= x <= 2\nX is a positive or negative fraction or a zero.\nx = -2 x = 2 x = 0\nPlug all of them. They work.\nAnswer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nDivide 71 into 2 parts such that 1 part exceeds the other by 8. What are the 2 no.'s in that part?\n\n### Options:\nA. 27\nB. 29\nC. 31\nD. 32\nE. 37\n\n### Answer:\nLet $let n$ be the smaller and 71 - n be the larger number. Now, since the larger number exceeds the smaller number by 7, we can form the equation\nlarger number \u2013 smaller number = 7\nwhich is equivalent to\nSimplifying, we have 71 - 2n = 7. This gives us 2n = 78 which implies that the larger number is . The smaller is 71-39=31.\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the odd man out\n25, 49, 81, 121, 144, 169\n\n### Options:\nA. 49\nB. 121\nC. 144\nD. 169\nE. 25\n\n### Answer:\n144 is square of 12 which is even number where as all others are squares of odd numbers.\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn the xy-plane, the point (-2, -1) is the center of a circle. The point (1, -1) lies inside the circle and the point (-2, 4) lies outside the circle. If the radius r of the circle is an integer, then r =\n\n### Options:\nA. 6\nB. 5\nC. 4\nD. 3\nE. 2\n\n### Answer:\nAn easy way to solve this question will be just to mark the points on the coordinate plane.\nYou'll see that the distance between the center (-2, -1) and the point inside the circle (1, -1) is 3 units\n(both points are on y=-1 line so the distance will simply be 1-(-2)=3)\nSo the radius must be more than 3 units.\nThe distance between the center (-2,-1) and the point outside the circle (-2,4) is 5 units\n(both points are on x=-2 line so the distance will simply be 4-(-1)=5)\nSo the radius must be less than 5 units, which implies 3 < r < 5, thus as r is an integer then r=4.\nAnswer: C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n10 men can complete a piece of work in 35 days. In how many days can 7 men complete that piece of work?\n\n### Options:\nA. 23 days\nB. 46 days\nC. 22 days\nD. 29 days\nE. 50 days\n\n### Answer:\nE\n50 days\n10 * 35 = 7 * x => x = 50 days\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nPipes A and B can fill a cistern in 20 and 60 minutes respectively. They are opened an alternate minutes. Find how many minutes, the cistern shall be full?\n\n### Options:\nA. 30\nB. 45\nC. 32\nD. 18\nE. 19\n\n### Answer:\n:\n1/20 + 1/60 = 1/15\n15 * 2 = 30.Answer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n900 men have provisions for 15 days. If 200 more men join them, for how many days will the provisions last now?\n\n### Options:\nA. 12.88\nB. 12.6\nC. 12.55\nD. 12.21\nE. 12.27\n\n### Answer:\n900*15 = 1100*x\nx = 12.27.Answer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat amount does Kiran get if he invests Rs.8000 at 10% p.a. compound interest for two years, compounding done annually?\n\n### Options:\nA. 2999\nB. 2787\nC. 2097\nD. 9680\nE. 2886\n\n### Answer:\nA= P{1 + R/100}n\n=> 8000{1 + 10/100}2\n= Rs.9680\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA, B and C enter into a partnership. A invests 3 times as much as B invests and 2/3 of what C invests. At the end of the year, the profit earned is Rs. 55000. What is the share of C?\n\n### Options:\nA. Rs. 12250\nB. Rs. 13375\nC. Rs. 16750\nD. Rs. 15000\nE. None of these\n\n### Answer:\nExplanation:\nLet the investment of C be Rs. x.\nThe inverstment of B = Rs.(2x/3)\nThe inverstment of A = Rs. (3 \u00d7 (2/3)x) = Rs. (2x)\nRatio of capitals of A, B and C = 2x : 2x/3 : x = 6 : 2 : 3\nC's share = Rs. [(3/11) \u00d7 55000] = Rs. 15000\nAnswer: Option D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn the standard formulation of a flavored drink the ratio by volume of flavoring to corn syrup to water is 1 : 12 : 30. In the sport formulation, the ratio of flavoring to corn syrup is three times as great as in the standard formulation, and the ratio of flavoring to water is half that of the standard formulation. If a large bottle of the sport formulation contains 8 ounces of corn syrup, how many ounces of water does it contain?\n\n### Options:\nA. 45\nB. 50\nC. 55\nD. 60\nE. 120\n\n### Answer:\nF:C:W\n1:12:30\nSport version:\nF:C\n3:12\nF:W\n1:60\nOR 3:180\nSo C:F:W = 12:3:180\nC/W = 12/180 = 3 ounces/x ounces\nx = 8*180/12 = 120 ounces of water\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe sum of two numbers is 40 and their product is 350. What will be the sum of their reciprocals?\n\n### Options:\nA. 4/35\nB. 8/75\nC. 75/4\nD. 75/8\nE. 75/6\n\n### Answer:\n(1/a)+(1/b)=(a+b)/ab=40/350=4/35\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the value of\n(10)150\u00f7(10)146\n\n### Options:\nA. 10\nB. 100\nC. 1000\nD. 10000\nE. None of these\n\n### Answer:\nExplanation:\n=(10)150/(10)146=10(4)=10000\nOption D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man can row downstream at the rate of 30 Kmph and upstream at 10 Kmph. Find the man\u2019s rate in still water and rate of current?\n\n### Options:\nA. 10\nB. 8.0\nC. 9.5\nD. 9.0\nE. 8.25\n\n### Answer:\nRate of still water = 1/2 (down stream + upstream)\n= 1/2 (30 + 10) = 20 Kmph\nrate of current = 1/2 (down stream - upstream)\n= 1/2 (30 - 10)\n= 1/2 (20)\n= 10 kmph\nAnswer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA sum fetched a total simple interest of $4016.25 at the rate of 9 p.c.p.a. in 5 years. What is the sum?\n\n### Options:\nA. $8829\nB. $2840\nC. $6578\nD. $7782\nE. $8925\n\n### Answer:\nE\n8925\nPrincipal\n= $100 x 4016.25/9 x 5\n= $401625/45\n= $8925.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn 1998 the profits of company N were 10 percent of revenues. In 1999, the revenues of company N fell by 20 percent, but profits were 15 percent of revenues. The profits in 1999 were what percent of the profits in 1998?\n\n### Options:\nA. 80%\nB. 105%\nC. 120%\nD. 124.2%\nE. 138%\n\n### Answer:\nLet's TEST:\n1998\nRevenues= $100\nProfits = $10\nNext we're told that, in 1999, revenue FELL by 20%, but profits were 15% of revenues. Using the numbers from 1998 (above), we end up with...\n1999\nRevenues = $80\nProfits = $12\nWe're asked to compare the profits in 1999 to the profits in 1998 (as a percentage):\n$12/$10 = 1.2 = 120%\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA chemical lab is scheduled to go through two air ventilation systems, a basic system and a more advanced system that takes forty minutes and 2 hours respectively to fully ventilate the room. If both ventilation systems were to operate at the same time with their respective constant rates, how many hours would it take to fully ventilate the chemical lab?\n\n### Options:\nA. 1/2\nB. 1/3\nC. 2/5\nD. 5/4\nE. 3/2\n\n### Answer:\nThe rate of the basic system is 1 room/ (2/3 of an hour) = 3/2 rooms per hour\nThe rate of the advanced system is 1/2 of a room per hour\nThe combined rate is 2 rooms per hour.\nThe time to ventilate one room is 1/2 of an hour.\nThe answer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA chair is bought for Rs.600/- and sold at a loss of 5% find its selling price\n\n### Options:\nA. s.570/-\nB. s.550/-\nC. s.560/-\nD. s.590/-\nE. s.580/-\n\n### Answer:\n100 % ------> 600 (100 * 6 = 600)\n95 % ------> 540 (95 * 6 = 570)\nSelling price = Rs.540/-\nA)\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a no. when divided by 44, gives 432 as quotient and 0 as remainder. What will be the remainder when dividing the same no. by 35\n\n### Options:\nA. 1\nB. 3\nC. 5\nD. 7\nE. 9\n\n### Answer:\nP \u00c3\u00b7 44 = 432\n=> P = 432 * 44 = 19008\nP / 35 = 19008 / 35 = 543, remainder = 3\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nEvaluate: 10010 - 12*3*2 = ?\n\n### Options:\nA. 30002\nB. 70002\nC. 50002\nD. 90002\nE. 10002\n\n### Answer:\nAccording to order of operations, 12?3?2 (division and multiplication) is done first from left to right\n12**2 = 4* 2 = 8\nHence\n10010 - 12*3*2 = 10010 - 8 = 10002\ncorrect answer E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the average of the series : 212, 152, 142, 132 and 112?\n\n### Options:\nA. 129\nB. 150\nC. 267\nD. 207\nE. 174\n\n### Answer:\nAverage = (212+152+142+132+112)/5\n= 750/5\n= 150\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nLast year, the price of a vacation package was P. At the beginning of this year, the price went up 20%. Lucas used a travel voucher to purchase the vacation package at 30% off this year\u2019s price. In terms of P, how much did Lucas pay?\n\n### Options:\nA. P + 10\nB. 1.1*P\nC. 1.12*P\nD. 0.80*P\nE. 0.84*P\n\n### Answer:\nLast year price = P;\nThis year price = 1.2P;\nLucas used a travel voucher to purchase the vacation package at 30% off this year\u2019s price, thus he paid (1 - 0.3)*1.2P = 0.84P.\nAnswer: E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOne fourth of one third of two fifth of a number is 15. What will be40% of that number\n\n### Options:\nA. 140\nB. 150\nC. 180\nD. 200\nE. 220\n\n### Answer:\nExplanation:\n(1/4) * (1/3) * (2/5) * x = 15\nthen x = 15 * 30 = 450\n40% of 450 = 180\nAnswer: Option C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich of the following represents the profit from the investment of x dollars at n percent compound annual interest for 5 years?\n\n### Options:\nA. x (1+n/100)^5 - x\nB. 4x (1+n/100)^4 - x\nC. 6x (1+n/100)^6 - x\nD. 2x (1+n/100)^2 - x\nE. x (1+n/100)^7 - x\n\n### Answer:\nAmount after 5 years compounded yearly = x (1+n/100)^5\nThus profit = Final amount - original principle = x (1+n/100)^5 - x . Answer : A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA property was originally on a 99 years lease and two thirds of the time passed is equal to the four fifth of the time to come.how many years are there to go.\n\n### Options:\nA. 33\nB. 80\nC. 79\nD. 27\nE. 111\n\n### Answer:\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJosh spends a total of $5.5 buying S items in the convenience store. If each of the items is either a 5 cents single bubblegum, or a 50 cents bubblegum pack, then S may be which of the following?\n\n### Options:\nA. 99\nB. 100\nC. 101\nD. 112\nE. 113\n\n### Answer:\nS items in the convenience store$5.5 = 550 cents\n550 = 50a + 5b\n=>110 = 10a + b\nb = 110 - 10a = 10(11-a)\nHence b is even and multiple of 10.\nPossible values of b:\nb = 10,20,30,40,50,60,70,80,90,100\na = 11,9,8,7,6,5,4,3,2,1\nThe total (a+b) is 21,29,38,47,56,65,74,83,92,101\nThe only option is 101. Hence C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich of the list following is a prime number ?\n\n### Options:\nA. 29\nB. 81\nC. 91\nD. 93\nE. 10\n\n### Answer:\nA\n29\nClearly, 29 is a prime number.\nAnswer is A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are two alloys madeup of copper and aluminium. In the first alloy copper is half as much as aluminium and in the second alloy copper is thrice as much as aluminium. How many times the second alloy must be mixed with first alloy to get the new alloy in which\ncopper is twice as much as aluminium?\n\n### Options:\nA. 2\nB. 3\nC. 4\nD. 5\nE. 6\n\n### Answer:\nfirst alloy second alloy\nC Al C Al\nRequired alloy\nC Al\n2 1\nThus, Copper in first alloy = 1/3\ncopper in second alloy = 3/4\ncopper in required alloy =2/3\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train is 360 meter long is running at a speed of 45 km/hour. In what time will it pass a bridge of 140 meter length?\n\n### Options:\nA. 27 seconds\nB. 29 seconds\nC. 40 seconds\nD. 11 seconds\nE. 12 seconds\n\n### Answer:\nSpeed = 45 Km/hr = 45*(5/18) m/sec = 25/2 m/sec\nTotal distance = 360+140 = 500 meter\nTime = Distance/speed\n= 500 * (2/25) = 40 seconds\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain lab experiments with white and brown mice only. In one experiment, 2/3 of the mice are white. If there are 9 brown mice in the experiment, how many mice in total are in the experiment?\n\n### Options:\nA. 39\nB. 33\nC. 27\nD. 21\nE. 10\n\n### Answer:\nLet total number of mice = M\nNumber of white mice = 2/3 M\nNumber of brown mice = 1/3 M = 9\n=> M = 27\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n5 men are equal to as many women as are equal to 8 boys. All of them earn Rs.60 only. Men\u00e2\u20ac\u2122s wages are?\n\n### Options:\nA. 6Rs\nB. 7Rs\nC. 8Rs\nD. 4Rs\nE. 1Rs\n\n### Answer:\n5M = xW = 8B\n5M + xW + 8B ----- 60 Rs.\n5M + 5M + 5M ----- 60 Rs.\n15M ------ 60 Rs. => 1M = 4Rs.\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA number has exactly 32 factors out of which 4 are not composite. Product of these 4 factors (which are not composite) is 30. How many such numbers W are possible?\n\n### Options:\nA. 2\nB. 4\nC. 6\nD. 3\nE. Not possible\n\n### Answer:\nFirstly , we should note that 1 is NEITHER a prime nor a composite number.The first composite number is 4.Thus, when the problem states that there are 4 factors that are not composite, these nos are 1,2,3,5. Thus, the given number = 2^a*3^b*5^c. Also, (a+1)*(b+1)*(c+1) = 32. We can break down 32 into 3 integers as : 2*2*8 or 4*4*2\nAlso, the only possible combinations for a,b,c are : 3,3,1 OR 1,1,7. Thus, each combination has 3 possible orders and we have a total W of 6 possibilities.\nC.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA person has uncovered a secret that was a mystery for ages. He transfers the data into his hard drive and encrypts the drive with a password. Then, he writes a line on a paper to remember the password.\nThe line says 'You force heaven to be empty'.\nCan you decrypt the line to reveal the password if you know that the password is seven characters long that comprise of just letters and numbers?\n\n### Options:\nA. M472BMT\nB. U472BMT\nC. S472BMT\nD. D472BMT\nE. V472BMT\n\n### Answer:\nB\nThe password is U472BMT.\nRead aloud the line and you will sound something like \"U Four Seven 2 B M T\".\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe product of the prime integers between 53 and 60, inclusive, is:\n\n### Options:\nA. 50! \u2013 40!\nB. 178,239\nC. 2,303\nD. 2,021\nE. 2,000\n\n### Answer:\nonly prime number bet ween 53 and 60 inclusive are 53, 57, 59\nthus 53*57 * 59= 178,239\nAns: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAlice\u2019s take-home pay last year was the same each month, and she saved the same fraction of her take-home pay each month. The total amount of money that she had saved at the end of the year was 2 times the amount of that portion of her monthly take-home pay that she did NOT save. If all the money that she saved last year was from her take-home pay, what fraction of her take-home pay did she save each month?\n\n### Options:\nA. 1/7\nB. 1/6\nC. 1/5\nD. 1/4\nE. 1/3\n\n### Answer:\nSuppose the portion of her salary that she saved is X\nand the remaining portion is Y\nX+Y= total take home salary\ngiven, 12X = 2Y\nor 6X = Y\nTotal take-home salary= X+ 6X= 7X\nhence, she saved 1/7-th portion of her take home salary\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA, B and C started a business with capitals of Rs. 8000, Rs. 10000 and Rs. 12000 respectively. At the end of the year, the profit share of B is Rs. 1800. The difference between the profit shares of A and C is?\n\n### Options:\nA. 720\nB. 266\nC. 155\nD. 600\nE. 441\n\n### Answer:\nRatio of investments of A, B and C is 8000 : 10000 : 12000 = 4 : 5 : 6\nAnd also given that, profit share of B is Rs. 1800\n=> 5 parts out of 15 parts is Rs. 1800\nNow, required difference is 6 - 4 = 2 parts\nRequired difference = 2/5 (1800) = Rs. 720\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA student scored an average of 80 marks in 3 subjects: Physics, Chemistry and Mathematics. If the average marks in Physics and Mathematics is 90 and that in Physics and Chemistry is 70, what are the marks in Physics?\n\n### Options:\nA. 11\nB. 66\nC. 77\nD. 80\nE. 71\n\n### Answer:\nGiven M + P + C = 80 * 3 = 240 --- (1)\nM + P = 90 * 2 = 180 --- (2)\nP + C = 70 * 2 = 140 --- (3)\nWhere M, P and C are marks obtained by the student in Mathematics, Physics and Chemistry.\nP = (2) + (3) - (1) = 180 + 140 - 240 = 80\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nDonna, Chris, and Austin have a total of $93 in their wallets. Donna has $7 more than Chris. Austin has 3 times what Donna has. How much do they have in their wallets?\n\n### Options:\nA. Donna $10 -Chris $45 -Austin $90\nB. Donna $20-Chris $13 -Austin $60\nC. Donna $30 -Chris $34-Austin $70\nD. Donna $40 -Chris $56 -Austin $100\nE. Donna $50 -Chris $23 -Austin $80\n\n### Answer:\nLet the amount in Chris\u2019s wallet be $x\nDonna has $7 more than Chrish's wallet = $(x + 7)\nAustin has 3 times than Donna's wallet = $3(x + 7)\nAccording to the problem, Donna, chris, and Austin have a total of $93 in their wallets.\nTherefore,\nx + (x + 7) + 3(x + 7) = 93\nx + x + 7 + 3x + 21 = 93\n5x + 28 = 93\n- 28 -28 (subtract 28 from both sides)\n5x = 65\nor, 5x/5 = 65/5 (Divide both sides by 5)\nx = 13\nAmount in Chris wallet = $x = $13\nAmount in Donna's wallet = $(x + 7) = $(13 + 7) = $20\nAmount in Austin 's wallet = $3(x + 7) = $3(13 + 7) = $3(20) = $ 60\nAnswer: Amount in Chris\u2019s wallet: $13\nAmount in Donna's wallet: $20\nAmount in Austin's wallet: $60\ncorrect answer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich of the following is a prime number\n\n### Options:\nA. 18\nB. 20\nC. 19\nD. 16\nE. 24\n\n### Answer:\nClearly, 19 is a prime number.\nOption C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA shopkeeper sells 400 metres of cloth for Rs. 18000 at a loss of Rs.5 per metre. Find his cost price for one metre of cloth?\n\n### Options:\nA. Rs.59\nB. Rs.58\nC. Rs.09\nD. Rs.50\nE. Rs.13\n\n### Answer:\nSP per metre = 18000/400\n= Rs. 45 Loss per metre\n= Rs. 5 CP per metre = 45 + 5\n= Rs.50\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a flight of 600 km, an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by 200 km/hr and the time of flight increased by 30 minutes. The duration of the flight is:\n\n### Options:\nA. 1 hour\nB. 2 hours\nC. 3 hours\nD. 4 hours\nE. 5 hours\n\n### Answer:\nLet the duration of the flight be x hours\n600/x - 600 (x+1/2)= 200\n600/x - 1200/(2x+1) = 200\nx(2x + 1) = 3\n2x2 + x - 3 = 0\n(2x + 3)(x - 1) = 0\nx can't be negative hence x=1\nx = 1 hr.\nDuration =1 hr\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo airplanes take off from one airfield at noon. One flies due east at 202 miles per hour while the other flies directly northeast at 283 miles per hour. Approximately how many miles apart are the airplanes at 2 p.m.?\n\n### Options:\nA. 166\nB. 332\nC. 400\nD. 483\nE. 404\n\n### Answer:\nE\nIn two hours:\nthe plane flying East will be 404 miles away from airport.\nthe other plane will be 566 miles away from airport.\n566/404 = ~1.4 = ~sqrt(2)\nThis means that planes formed a right isocheles triangle => sides of such triangles relate as 1:1:sqrt(2) => the planes are 404 miles apart. E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat number times (1\u20444)^2 will give the value of 4^3?\n\n### Options:\nA. 4\nB. 16\nC. 64\nD. 256\nE. 1024\n\n### Answer:\nx*(1/4)^2 = 4^3\nx = 4^2*4^3 = 4^5 = 1024\nThe answer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nthe age of a and b are in the ratio 4:5 and of b and c in the ratio 3:2.the youngedt of three is\n\n### Options:\nA. a\nB. b\nC. c\nD. can't say\nE. none\n\n### Answer:\na:b => 4:5 3*(a:b)=> 12:15\nb:c=>3:2 5*(b:c)=> 15:10\na:b:c =>12:15:10\nTherefore youngest is c.\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 47, the how old is B?\n\n### Options:\nA. 7\nB. 9\nC. 18\nD. 11\nE. 10\n\n### Answer:\nExplanation:\nLet C's age be x years. Then, B's age = 2x years. A's age = (2x + 2) years.\n(2x + 2) + 2x + x = 47\n\u21d2 5x = 45\n\u21d2 x = 9.\nHence, B's age = 2x = 18 years.\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nEleven years ago Tina was half as old as Ike will be in 4 years. If Ike is m years old now, how old is Tina now, in terms of m?\n\n### Options:\nA. 4m - 11\nB. m/2 + 13\nC. 1/(2m - 22)\nD. (4m + 11)/2\nE. 2m-7\n\n### Answer:\nIke's current age = m\nIke's age after 4 years = m + 4\nTina age 11 years ago =(m+4)/2\nTina's current age = (m+4)/2 + 11 = (m+4+22)/2= m/2+13\nAns B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n3 buffaloes eat as much as 4 cows or 2 oxen. At a farm, there are 15 buffaloes, 8 oxen, and 24 cows. The fodder for these cattle is available for 48 days. If 40 more cows and 15 more buffaloes are brought in, how many days will the fodder last?\n\n### Options:\nA. 20\nB. 24\nC. 28\nD. 32\nE. 36\n\n### Answer:\n2 oxen = 3 buffaloes = 4 cows\nAlso: 15 buffaloes + 8 oxen + 24 cows\n= 10 oxen + 8 oxen + 12 oxen = 30 oxen\nThere is enough fodder for 1 oxen for 30*48 days.\n40 cows + 15 buffaloes = 20 oxen + 10 oxen = 30 oxen\nThe new total is equal to 60 oxen instead of 30 oxen.\n30*48 / 60 oxen = 24 days\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRodrick mixes a martini that has a volume of 'n' ounces having 40% Vermouth and 60% Gin by volume. He wants to change it so that the martini is 50% Vermouth by volume. How many ounces of Gin must he add?\n\n### Options:\nA. n/6\nB. n/3\nC. 3n/5\nD. 5n/6\nE. 8n/5\n\n### Answer:\n4 ounces is vermouth\n6 ounces of gin...\nTotal volume 10.\nTo make vermouth account for 50% of total volume the new volume must be....\nx*0.5=4\nx=8 ounces....\nSo now you see that he must add 2 ounces of gin...\nPlug in 6 for n in the answer choices and look for answer 2\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the average (arithmetic mean) of a and b is 140, and the average of b and c is 100, what is the value of a \u2212 c?\n\n### Options:\nA. \u2212220\nB. \u2212100\nC. 100\nD. 135\nE. 80\n\n### Answer:\na+b = 280\nb+c = 200\na-c = 80.\nIMO option E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man invests some money partly in 9% stock at 96 and partly in 12% stock at 120. To obtain equal dividends from both, he must invest the money in the ratio:\n\n### Options:\nA. 3:4\nB. 3:5\nC. 4:5\nD. 16:15\nE. 12:13\n\n### Answer:\nFor an income of $1 in 9% stock at 96, investment =$(96/9)=32/3\nFor an income of $1 in 12% stock at 120, investment =$(120/12)\n=$10\nRatio of investment=32/3:10\n=16:15\nOption D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA freight train starts from Los Angeles and heads for Chicago at 40 mph. Two hours later a\npassenger train leaves the same station for Chicago traveling 60 mph. How long before the\npassenger train overtakes the freight train?\n\n### Options:\nA. 6hours\nB. 5hours\nC. 9ours\nD. 2hours\nE. 4 hours\n\n### Answer:\nRead the problem. It is a time, rate, and distance problem. (Use D=r*t)\nThe question asks, \u201chow long?\u201d (which means time) for the passenger train.\nLet t=the time it takes the passenger train to overtake the freight train\nt+2=the number of hours the freight train had traveled when overtaken.\nDraw a sketch and make a table.\nTime Rate Distance\nFreight t+2- 40 mph- 40(t+2)\nPassengert- 60 mph-60t\nEquation: When the passenger train overtakes the freight train, they have both traveled\nthe same distance. Write each of their distances in terms of ratetime (as seen in the\ntable above), then set them equal to each other to create an equation. Then solve the\nequation.\n40(t+2)=60t\n40t+80=60t\n80=20t\nt=4\nThe answer: It takes the passenger train 4 hours to overtake the freight train.\nCheck by substituting 4 into the original equation.\n40(4+2)=60(4)\n40(6)=240\n240=240\ntrue\nThus, 4 hours is the correct answer.\ncorrect answer E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man can row downstream at the rate of 24 Kmph and upstream at 7 Kmph. Find the man\u2019s rate in still water and rate of current?\n\n### Options:\nA. 8.5\nB. 8.0\nC. 9.5\nD. 9.0\nE. 8.25\n\n### Answer:\nRate of still water = 1/2 (down stream + upstream)\n= 1/2 (24 + 7) = 15.5 Kmph\nrate of current = 1/2 (down stream - upstream)\n= 1/2 (24 - 7)\n= 1/2 (17)\n= 8.5 kmph\nAnswer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSekar started a business investing Rs.25,000 in 1999. In 2000, he invested an additional amount of Rs.10,000 and Rajeev joined him with an amount of Rs.35,000. In 2001, Sekar invested another additional amount of Rs.10,000 and Jatin joined them with an amount of Rs.35,000. What will be Rajeev's share in the profit of Rs.2,70,000 earned at the end of 3 years from the start of the business in 1999?\n\n### Options:\nA. Rs.45,000\nB. Rs.50,000\nC. Rs.90,000\nD. Rs.75,000\nE. none\n\n### Answer:\nSolution\nSekar:Rajeev:Jatin=\t(25000\u00d712+35000\u00d712+45000\u00d712):(35000\u00d724) : (35000\u00d712)\n= 1260000 : 840000 : 420000\n= 3 : 2 : 1.\nRajeev's share\t=Rs.(270000\u00d72/6)\n= Rs.90000.\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man can row 7 \u00bd kmph in still water.if in a river running at 1.5 km/hr an hour,it takes him 50 minutes to row to a place and back,how far off is the place?\n\n### Options:\nA. 1.5 km\nB. 1 km\nC. 2.5km\nD. 2 km\nE. 3 km\n\n### Answer:\nSpeed downstream =(7.5+1.5)km/hr=9 km/hr;\nSpeed upstream=(7.5-1.5)kmph=6kmph.\nLet the required distance be x km.then,\nx/9+x/6=50/60.\n2x+3x=(5/6*18)\n5x=15\nx=3.\nHence,the required distance is 3km.\nAnswer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the value of 72515 x 9999 = m?\n\n### Options:\nA. 345434667\nB. 246465757\nC. 465767867\nD. 725077485\nE. 645354643\n\n### Answer:\n72515 x 9999 = 72515 x (10000 - 1)\n= 72515 x 10000 - 72515 x 1\n= 725150000 - 72515\n= 725077485\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a person walks at 14 km/hr instead of 10 km/hr, he would have walked 20 km more. The actual distance travelled by him is:\n\n### Options:\nA. 50 km\nB. 56 km\nC. 70 km\nD. 80 km\nE. 85 km\n\n### Answer:\nLet the actual distance travelled be x km.\nThen,\tx/10\t=\t(x + 20)/14\n=14x = 10x + 200\n4x = 200\nx = 50 km.\nAnswer :A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a(a + 2) = 120 and b(b + 2) = 120, where a \u2260 b, then a + b =\n\n### Options:\nA. -4\nB. -6\nC. -2\nD. -10\nE. -8\n\n### Answer:\ni.e. if a = 10 then b = -12\nor if a = -12 then b = 10\nBut in each case a+b = -12+10 = -2\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 16 hours respectively. The ratio of their speeds is?\n\n### Options:\nA. 4:7\nB. 4:3\nC. 4:0\nD. 4:2\nE. 4:6\n\n### Answer:\nLet us name the trains A and B.\nThen, (A's speed) : (B's speed)\n= \u221ab : \u221aa = \u221a16 : \u221a9\n= 4:3\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA pack of baseball cards consists of 12 outfielder cards and 8 infielder cards. What is the lowest number of outfielder cards that would have to be removed from the pack so that no more than 20 percent of the pack would be outfielder cards?\n\n### Options:\nA. 10\nB. 5\nC. 6\nD. 7\nE. 8\n\n### Answer:\nlet the number of O card to be removed=X\nthen remaning cards=12-X\nnow this 12-X cards should count less than 20% of toatal Ocards\n12-X<.2*12\nX>12-2.4\nX>9.6\nX=10\nAns A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n78 persons can repair a road in 12 days, working 5 hours a day. In how many days will 30 persons, working 6 hours a day, complete the work?\n\n### Options:\nA. 10\nB. 13\nC. 26\nD. 15\nE. 16\n\n### Answer:\nLet the required number of days be x.\nLess persons, More days (Indirect Proportion)\nMore working hours per day, Less days (Indirect Proportion)\nPersons\t30\t:\t78\t:: 12 : x\nWorking hours/day\t6\t:\t5\n30 x 6 x x = 78 x 5 x 12\nx =\t(78 x 5 x 12)/(30 x 6)\nx = 26.\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf x% of y is 100 and y% of z is 200, then find the relation between x and z.\n\n### Options:\nA. z = x\nB. 2z = x\nC. z = 2x\nD. z =x2\nE. None of above\n\n### Answer:\nExplanation:\nIt is , y% of z = 2(x% of y)\n=> yz/100 = 2xy/100\n=> z = 2x\nAnswer: Option C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFive years ago, the average age of A and B was 15 years. Average age of A, B and C today is 20 years. How old will C be after 15 years?\n\n### Options:\nA. 30\nB. 35\nC. 40\nD. 50\nE. 60\n\n### Answer:\nExplanation :\n(A + B), five years ago = (15 * 2) = 30 years.\n(A+B), now = (30+5*2)years=40 years.\n(A + B + C), now = (20 x 3) years =60 years.\nC, now = (60 - 40) years = 20 years.\nC, after 15 years = (20 + 15) years =35 years.\nAnswer : B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe digits of a three-digit number A are written in the reverse order to form another three-digit number B. If B>A and B-A is perfectly divisible by 7, then which of the following is necessarily true?\n\n### Options:\nA. 100 A\nc \u2013 a = 14 is not possible as the maximum difference between c and a = 9 \u2013 1 = 8 only.\nSo c \u2013 a = 7.\nIf c = 9, a = 2\nc = 8, a = 1\nb can take any value from 0 to 9\nTherefore, minimum value of abc = 109, maximum value = 299\nFrom the given options, option B satisfies this.\nCorrect option: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the odd man out\n4, 9,16, 36, 64, 144\n\n### Options:\nA. 144\nB. 16\nC. 9\nD. 36\nE. 4\n\n### Answer:\n9 is square of 3 which is odd number where as all others are squares of even numbers.\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAfter taking N tests, each containing 100 questions, John had an average of 70% of correct answers. How much does John need to score on the next test to make his average equal 74%?\nM13-03.\n\n### Options:\nA. N\u221235\nB. N+72\nC. 2N+76\nD. 2N+70\nE. 2N\u221235\n\n### Answer:\nSay N=1.\nSo, after 1 test John has 70 correct answers.\nIn 2 tests, so in 200 questions he needs to have 0.74*200=148 correct answers, so in the second test he must get 148-70=78 questions correctly.\nNow, plug N=1 into the answer choices to see which one yields 78. Only option D fits.\nAnswer: C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA student completes a 3 part exam as follows. The student completes sections A in 4 minutes and takes an equal time to complete the two remaining sections. What is the ratio of time spent on section C to section A if the total duration is 1 hour?\n\n### Options:\nA. 10:3\nB. 9:2\nC. 7:1\nD. 8:3\nE. 11:2\n\n### Answer:\nThe time spent on section B and section C is 28 minutes each.\nThe ratio of C to A is 28:4 = 7:1\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe distance between two cities A and B is 465 Km. A train starts from A at 8 a.m. and travel towards B at 60 km/hr. Another train starts from B at 9 a.m and travels towards A at 75 Km/hr. At what time do they meet?\n\n### Options:\nA. 09\nB. 07\nC. 12\nD. 05\nE. 03\n\n### Answer:\nExplanation:\nSuppose they meet x hrs after 8 a.m\nthen,\n[Distance moved by first in x hrs] + [Distance moved by second in (x-1) hrs] = 465\nTherefore, 60x + 75(x-1) = 465\n=> x=3.\nSo,they meet at (8+4) i.e, 12 noon\nAnswer: C)\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf f(x) = k(x - k) and k is a constant, what is the value of f(6) - f(2), in terms of k?\n\n### Options:\nA. 1\nB. 4k\nC. 7k - 1\nD. k^2 + k\nE. k^2 - k\n\n### Answer:\nFirst, distribute f(x). k(x - k) = kx - k^2. Now evaluate f(6) and f(2):\nf(6) = k(6) - k^2 = 6k - k^2\nf(2) = 2k - k^2\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the probability of getting at least one six in a single throw of three unbiased dice?\n\n### Options:\nA. 1/6\nB. 125/216\nC. 1/36\nD. 81/216\nE. 91/216\n\n### Answer:\nFind the number of cases in which none of the digits show a '6'.\ni.e. all three dice show a number other than '6', 5 * 5 *5 = 125 cases.\nTotal possible outcomes when three dice are thrown = 216.\nThe number of outcomes in which at least one die shows a '6' = Total possible outcomes when three dice are thrown - Number of outcomes in which none of them show '6'.\n= 216 - 125 = 91.\nThe required probability = 91/216.\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the perimeter of a regular polygon with sides of length 15 cm and internal angles measuring 145\u00b0 each?\n\n### Options:\nA. 96 cm\nB. 108 cm\nC. 120 cm\nD. 132 cm\nE. 154.28 cm\n\n### Answer:\nSum of all interior angles is given by:\n180(n-2) = n is number of sides\n180(n-2) = 145*n\nfrom here\nn = 10.28\nSo perimeter becomes 15*10.28= 154.28\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSouju's age is 150% of what it was 10 years ago, but 75% of what it will be after 10 years. What is her present age?\n\n### Options:\nA. 25 years\nB. 27years\nC. 30 years\nD. 42 years\nE. 66 years\n\n### Answer:\nLet the age before 10 years =x. Then,\n150x/100=x+10\n\u00e2\u2021\u2019150x=100x+1000\n\u00e2\u2021\u2019x=1000/50=20\nPresent age =x+10=20+10=30\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIncome of A is 25% more than the income of B. What is the income of B in terms of income of A?\n\n### Options:\nA. 80%\nB. 75%\nC. 78.66%\nD. 71.25%\nE. None of these\n\n### Answer:\nExplanation:\nOne of the most basic questions.\nLet income of B be 100. Income of A is 25% more than income of B which means Income of A becomes 125\nNow income of B in terms of A = 100/125 *100 = 80%\nANSWER A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA miniature gumball machine contains 4 blue, 3 green, and 3 red gumballs, which are identical except for their colors. If the machine dispenses three gumballs at random, what is the probability that it dispenses one gumball of each color?\n\n### Options:\nA. 2/5\nB. 3/5\nC. 3/10\nD. 7/30\nE. 11/30\n\n### Answer:\nThe total number of ways to dispense 3 gumballs is 10C3=120.\nThe number of ways to choose one of each color is 4*3*3=36.\nP(dispensing one of each color)=36/120=3/10.\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe diameter of a wheel of cycle is 21 cm. It moves slowly along a road. How far will it go in 500 revolutions?\n\n### Options:\nA. 260 m\nB. 290 m\nC. 320 m\nD. 330 m\nE. 380 m\n\n### Answer:\nIn revolution, distance that wheel covers = circumference of wheel Diameter of wheel = 21 cm\nTherefore, circumference of wheel = \u03c0d\n= 22/7 \u00d7 21\n= 66 cm\nSo, in 1 revolution distance covered = 66 cm\nIn 500 revolution distance covered = 66 \u00d7 500 cm\n= 33000 cm\n= 33000/100 m\n= 330 m\nAnswer : option D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA sells his goods 50% cheaper than B but 50% dearer than C. The cheapest is?\n\n### Options:\nA. A\nB. B\nC. C\nD. D\nE. ALL\n\n### Answer:\nAnswer: Option C\nLet b = 100\na = 50\nc * (150/100) = 50\n3c = 100\nc = 33.3 then 'c' cheapest\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the last non-zero digit of 30^2345\n\n### Options:\nA. 1\nB. 2\nC. 3\nD. 4\nE. 5\n\n### Answer:\n30^2345=(3*10)^2345=3^2345*10^2345\nso 30^2345 has 2345 zeroes,the last non-zero digit of 30^2345 will be same as unit digit of 3^2345\n3^2345=3^(4*586+1)=> 3^1=3\nlast non-zero digit of 30^2345= 3\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich of the following leads to the correct mathematical solution for the number of ways that the letters of the word BANANA could be arranged to create a six-letter code?\n\n### Options:\nA. 6!\nB. 6! \u2212 (3! + 2!)\nC. 6! \u2212 (3! \u00d7 2!)\nD. 6!/(3! + 2!)\nE. 6!/(3! \u00d7 2!)\n\n### Answer:\nNumber of letters in word 'BANANA' = 6.\nThe letters 'A' and 'N' appear 3 times and 2 times respectively in the word 'BANANA'.\nTherefore the mathematical solution for number of ways that the letters of the word BANANA can be arranged to create six-letter code\n= 6!/(3!*2!)\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many cubes of 3cm edge can be cut out of a cube of 18cm edge\n\n### Options:\nA. 36\nB. 232\nC. 216\nD. 484\nE. None of these\n\n### Answer:\nExplanation:\nnumber of cubes=(18 x 18 x 18) / (3 x 3 x 3) = 216\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFor any integer k > 1, the term \u201clength of an integer\u201d refers to the number of positive prime factors, not necessarily distinct, whose product is equal to k. For example, if k = 24, the length of k is equal to 4, since 24 = 2 \u00d7 2 \u00d7 2 \u00d7 3. If x and y are positive integers such that x > 1, y > 1, and x + 3y < 980, what is the maximum possible sum of the length of x and the length of y?\n\n### Options:\nA. 16\nB. 14\nC. 18\nD. 10\nE. 20\n\n### Answer:\nwe know that : x > 1, y > 1, and x + 3y < 980,\nand it is given that length means no of factors.\nfor any value of x and y, the max no of factors can be obtained only if factor is smallest no all factors are equal.\nhence, lets start with smallest no 2.\n2^1 =2\n2^2 =4\n2^3=8\n2^4=16\n2^5=32\n2^6=64\n2^7=128\n2^8=256\n2^9=512\n2^10 =1024 (it exceeds 1000, so, x can't be 2^10)\nso, max value that X can take is 2^9 , for which has length of integer is 9.\nnow, since x =512 ,x+3y<980\nso, 3y<468\n==> y<156\nso, y can take any value which is less than 162. and to get the maximum no of factors of smallest integer, we can say y=2^7\nfor 2^7 has length of integer is 7.\nSO, combined together : 9+7 = 16.\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man is 18 years older than his son. In eight years, his age will be twice the age of his son. The present age of this son is\n\n### Options:\nA. 5 years\nB. 10 years\nC. 15 years\nD. 20 years\nE. 25 years\n\n### Answer:\nExplanation:\nLet's Son age is x, then Father age is x+18.\n=> 2(x+8) = (x+18+8)\n=> 2x+16 = x+26\n=> x = 10 years\nAnswer: Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nlog3 N+log15 N what is 3 digit number N that will be whole number\n\n### Options:\nA. 3375\nB. 7292\nC. 8291\nD. 3929\nE. 2727\n\n### Answer:\nNo of values N can take is 1\n15^3=3375\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA regular octagon is inscribed in a circle. If A and B are adjacent vertices of the pentagon and O is the center of the circle, what is the value of \u2220OAB ?\n\n### Options:\nA. 48 degrees\nB. 54 degrees\nC. 67.5 degrees\nD. 84 degrees\nE. 108 degrees\n\n### Answer:\nits a regular pentagon so divide the globe by 8.\n= 360/8\n= 45\n45 would be the angle at O.\nAngles at A and B are equivalent, so\n45 + 2x = 180\n2x = 135\nx = 67.5\nAngles OAB and OBA will be 67.5 degrees each.\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe difference of the squares of two consecutive even integers is divisible by which of the following integers ?\n\n### Options:\nA. 3\nB. 4\nC. 6\nD. 7\nE. 9\n\n### Answer:\nLet the two consecutive even integers be 2n and (2n + 2). Then,\n(2n + 2)2 = (2n + 2 + 2n)(2n + 2 - 2n)\n= 2(4n + 2)\n= 4(2n + 1), which is divisible by 4.\nANSWER B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nBy selling 45 lemons for Rs 40, a man loses 20 %. How many should he sell for Rs 24 to gain 20 % in the transaction ?\n\n### Options:\nA. 16\nB. 18\nC. 20\nD. 22\nE. 25\n\n### Answer:\nExplanation:\nLet S.P. of 45 lemons be Rs. x.\nThen, 80 : 40 = 120 : x or x =40X120/80=60\nFor Rs.60, lemons sold = 45\nFor Rs.24, lemons sold =45/60X24=18.\nANSWER IS B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nCarol spends 1/4 of her savings on a stereo and 1/3 less than she spent on the stereo for a television. What fraction of her savings did she spend on the stereo and television?\n\n### Options:\nA. 1/4\nB. 2/7\nC. 5/12\nD. 1/2\nE. 7/12\n\n### Answer:\nTotal Savings = S\nAmount spent on stereo = (1/4)S\nAmount spent on television = (1-1/3)(1/4)S = (2/3)*(1/4)*S = (1/6)S\n(Stereo + TV)/Total Savings = S(1/4 + 1/6)/S = 5/12\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRamu bought an old car for Rs. 42000. He spent Rs. 13000 on repairs and sold it for Rs. 60900. What is his profit percent?\n\n### Options:\nA. 10.7%\nB. 19%\nC. 18%\nD. 14%\nE. 16%\n\n### Answer:\nTotal CP = Rs. 42000 + Rs. 13000\n= Rs. 55000 and SP\n= Rs. 60900\nProfit(%) = (60900 - 55000)/55000 * 100\n= 10.7%\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSam is training for the marathon. He drove 12 miles from his home to the Grey Hills Park and then ran 5 miles to Red Rock, retraced his path back for 2 miles, and then ran 3 miles to Rock Creek. If he is then n miles from home, what is the range of possible values for n?\n\n### Options:\nA. 1 \u2264 n \u226423\nB. 3 \u2264 n \u226421\nC. 6 \u2264 n \u226418\nD. 5 \u2264 n \u226419\nE. 9 \u2264 n \u226415\n\n### Answer:\nANSWER: C To find the maximum and minimum range for his distance from home, assume that he traveled either directly toward his home or directly away from his home. The range then is between 12+5-2+3=18 for the maximum, and 12-5+2-3=6 for the minimum, so C is the answer\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA and B invested in a business. They earned some profit which they divided in the ratio of 2:3. If A invested Rs.40, 000, the amount invested by B is:\n\n### Options:\nA. Rs. 65,000\nB. Rs. 70,000\nC. Rs. 80,000\nD. Rs. 90,000\nE. Rs. 60,000\n\n### Answer:\nInvested by B = 40000/2*3 = 60000\nAnswer : E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nBy selling 12 toffees for a rupee, a man loses 20%. How many for a rupee should be sell to get a gain of 20%?\n\n### Options:\nA. 5\nB. 8\nC. 10\nD. 15\nE. 20\n\n### Answer:\nExplanation:\nLet S.P. of 12 toffees be Rs. x.\nThen, 80:1 = 120:x or x = 120/180 = 3/2\nFor Rs. 3/2, toffees sold = 12.\nFor Re. 1, toffees sold = 12 * 2/3 = 8\nANSWER IS B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA basketball player practices 2 hours a day Monday through Friday. How many hours must he practice Saturday and Sunday combined if he wants to practice an average (arithmetic mean) of 3 hours a day for the seven day week?\n\n### Options:\nA. 8\nB. 9\nC. 10\nD. 11\nE. 12\n\n### Answer:\nTotal number of hours practiced Mon through Fri: 5*2 = 10\nTotal number of hours that will be practiced in a 7 day week considering 3 hours a day average: 7*3 = 21\nthus 21-10 = 11 hours still need to be practiced (on Sat and Sun combined)\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the simple interest on Rs. 3000 at 6 1/4% per year for the period from 4th Feb., 2005 to 18th April, 2005.\n\n### Options:\nA. 36.5\nB. 33.5\nC. 35.5\nD. 37.5\nE. None of them\n\n### Answer:\nTime = (24+31+18)days = 73 days = 73/365 years = 1/5 years.\nP = Rs.3000 and R = 6 \u00bc %p.a = 25/4%p.a\nTherefore, Simple Interest. = Rs.(3,000*(25/4)*(1/5)*(1/100))= Rs.37.50.\nAnswer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA quadratic function f(x) attains its minimum value of -15 at x=3. If f(0)=5, find the value of f(9).\n\n### Options:\nA. 65\nB. 55\nC. -25\nD. 75\nE. 25\n\n### Answer:\nExplanation :\nAny quadratic equation can be written as f(x) = \u03b1(x-k)2 - \u03b2\nGiven that minimum value of f(x) is -15 at x=3\nf(x) is minimum when x=k => k=3\n-15=-\u03b2 => \u03b2= 15\nAlso given that f(0) = 5\n=> 5 = \u03b1(0-3)2 - 15 => \u03b1= 20/9\nHence, f(9)=20/9(9-3)2 - 15 = 65\nAnswer : A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWithout any stoppages a person travels a certain distance at an average speed of 40 km/hr and with stoppages he covers the same distance at an average of 20 km/hr. How many minutes per hour does he stop?\n\n### Options:\nA. 15 minute\nB. 20 minutes\nC. 30 minutes\nD. 45 minutes\nE. None of these\n\n### Answer:\nExplanation :\nIn one hour the distance covered at actual speed = 40km and with stoppages it covers only 20 km\nso to travel 20 km at original speed i.e. 20 = 40*t, so t = 1/2 hour = 30\nminutes\nAnswer \u2013 C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf two numbers are in the ratio 2:3. If 10 is added to both of the numbers then the ratio becomes 3:4 then find the smallest number?\n\n### Options:\nA. 10\nB. 20\nC. 25\nD. 30\nE. 35\n\n### Answer:\n2:3\n2x + 10 : 3x + 10 = 3 : 4\n4[2x + 10] = 3[3x + 10]\n8x + 40 = 9x + 30\n9x - 8x = 40 - 30\nx = 10\nThen smallest number is = 2\n2x = 20\nB)\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTen years ago, P was half of Q's age. If the ratio of their present ages is 3:4, what will be the total of their present ages?\n\n### Options:\nA. 35\nB. 38\nC. 37\nD. 36\nE. 30\n\n### Answer:\nLet present age of P and Q be 3x and 4x respectively.\nTen years ago, P was half of Q's age\n\u21d2(3x\u221210)=12(4x\u221210)\u21d26x\u221220=4x\u221210\u21d22x=10\u21d2x=5\nTotal of their present ages\n=3x+4x=7x=7\u00d75=35\nAnswer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn what time will a railway train 65 m long moving at the rate of 36 kmph pass a telegraph post on its way?\n\n### Options:\nA. 8 sec\nB. 7 sec\nC. 2 sec\nD. 6.5 sec\nE. 9 sec\n\n### Answer:\nT = 65/36 * 18/5\n= 6.5 sec\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are 7 pairs of socks and 2 socks are worn from that such that the pair of socks worn are not of the same pair. what is the number of pair that can be formed.\n\n### Options:\nA. 40\nB. 49\nC. 41\nD. 56\nE. 42\n\n### Answer:\nFirst of all you should remember that there is a difference in left and right sock.\nnow no. of way to select any of the sock = 7\nand for second = 6\nso total methods = 7*6 = 42\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn what time will a train 100 m long cross an electric pole, it its speed be 126 km/hr?\n\n### Options:\nA. 2.5\nB. 2.9\nC. 2.4\nD. 2.85\nE. 2.1\n\n### Answer:\nSpeed = 126 * 5/18 = 35 m/sec\nTime taken = 100/35\n= 2.85 sec.\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhen positive integer n is divided by 5, the remainder is 1. When n is divided by 7, the remainder is 3. What is the smallest positive integer k such that k+n is a multiple of 39?\n\n### Options:\nA. 3\nB. 8\nC. 12\nD. 32\nE. 35\n\n### Answer:\nn = 5p + 1 = 6,11,16,21,26,31\nn = 7q + 3 = 3,10,17,24,31\n=>n = 39m + 31\nTo get this, we need to take LCM of co-efficients of p and q and first common number in series.\nSo we need to add 8 more to make it\n39m + 39\nAnswer - B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nArun borrowed a sum for 4 years on S.I. at 12%. The total interest paid was Rs. 360. Find the Principal.\n\n### Options:\nA. 120\nB. 360\nC. 480\nD. 560\nE. 750\n\n### Answer:\nP=100\u00d7SI/RT=100\u00d7360/12\u00d74\n=100\u00d730/4\n=25\u00d730\n=750\nOption E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train travels from station A to station B. If the train leaves station A and makes 75 km/hr, it arrives at station B 48 minutes ahead of scheduled. If it made 50 km/hr, then by the scheduled time of arrival it would still have 40 km more to go to station B. Find:\nA) The distance between the two stations;\nB) The time it takes the train to travel from A to B according to the schedule;\nC) The speed of the train when it's on schedule.\n\n### Options:\nA. 34\nB. 27\nC. 26\nD. 28\nE. 60\n\n### Answer:\nLet xx be the scheduled time for the trip from A to B. Then the distance between A and B can be found in two ways. On one hand, this distance equals 75(x\u22124860)75(x\u22124860) km. On the other hand, it is 50x+4050x+40 km. So we get the equation:\n75(x\u22124860)=50x+4075(x\u22124860)=50x+40\nx=4x=4 hr is the scheduled travel time. The distance between the two stations is 50\u22c54+40=24050\u22c54+40=240 km. Then the speed the train must keep to be on schedule is 2404=602404=60 km/hr.\nAnswer:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA , B , and C started a partnership business by investing $27,000 , $72,000 , and $81,000 respectively. At the end of the year , the profit was distributed among them. If C's share of profit is $18,000, what is the total profit?\n\n### Options:\nA. $24,000\nB. $32,000\nC. $40,000\nD. $48,000\nE. $56,000\n\n### Answer:\nA:B:C = 27000:72000:81000 which is a ratio of 3:8:9.\nLet the total profit be x.\nx * 9/20 = 18000\nx = 18000*20/9 = 40,000.\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the arithmetic mean of seventy-five numbers is calculated, it is 35. if each number is increased by 5, then mean of new numbers is :\n\n### Options:\nA. 22\nB. 40\nC. 88\nD. 27\nE. 11\n\n### Answer:\nExplanation:\nLet the numbers are\nBy Hypothesis , ......(i)\nMean of new numbers =\nBy (i)\nAnswer: B) 40\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the median from the below series\n77, 72, 68, 76, 78, 88, 84, 86, and 81\n\n### Options:\nA. 72\nB. 76\nC. 78\nD. 77\nE. 81\n\n### Answer:\nOrdering the data from least to greatest, we get:\n68, 72, 76, 77, 78, 81, 84, 86, 88\nThe median numbers was 78. (Four number were higher than 78 and four were lower.)\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich of the following is between 27/37 and 29/35?\n\n### Options:\nA. 1/3\nB. 3/8\nC. 1/2\nD. 5/8\nE. 7/9\n\n### Answer:\nI see this as a POE (Process of Elimination) and Ballparking (Estimation) question. Not sure if this is the most efficient, but it worked:\n1) I estimate 27/37 to be ~3/4+ (approximately slightly greater than 3/4)\n2) I estimate 29/35 to be ~4/5+ (approximately slightly greater than 4/5)\n3) So now I'm looking for an answer choice that is .75 < x < .80\nIt should be pretty easy to identify which answer choices are less than .75 (or 3/4) if you have had practice with fractions.\nA) clearly wrong - it's less than 3/4\nB) also clearly wrong - it's less than 3/4\nC) also clearly wrong - it's less than 3/4\nD) also clearly wrong - it's less than 3/4\nI would just stop here and select E. But to verify:\nE) 7/9 ~ .77 which is greater than .75 and less than .80\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMangala completes a piece of work in 12 days, Raju completes the same work in 36 days. If both of them work together, then the number of days required to complete the work is\n\n### Options:\nA. 6 days\nB. 7 days\nC. 8 days\nD. 9 days\nE. 11 days\n\n### Answer:\nIf A can complete a work in x days and B can complete the same work in y days, then, both\nof them together can complete the work in x y/ x+ y days.\nThat is, the required No. of days = 12 \u00c3\u2014 36/48 = 9 days.\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA semicircular shaped window has diameter of 63cm. Its perimeter equals\n\n### Options:\nA. 162\nB. 766\nC. 298\nD. 277\nE. 198\n\n### Answer:\nExplanation:\nperimeter of window = {\\color{Blue} \\Pi }r+2r\n= [{(22/7) * (63/2)} +63]\n= 99+63\n= 162 cm\nAnswer: A) 162\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf pq > 0, which of the following must be negative?\n\n### Options:\nA. p/q\nB. -p/q\nC. -p/-q\nD. -p * -q\nE. pq\n\n### Answer:\nGiven pq> 0 So both will be the positive integers. If both are positive, then A,C,D,E also positive.\nAnswer :B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf q = 50! + 1, which of the following cannot be a prime factor of q?\nI. 11\nII. 29\nIII. 41\n\n### Options:\nA. I\u200b only\nB. III only\nC. II and III\nD. I and II\nE. I\u200b, II, and III\n\n### Answer:\nThe numbers 11, 29, and 41 are all factors of 50!\nTherefore they can not be factors of 50! + 1.\nThe answer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe difference between a two digit number and the number obtained by interchanging the positions of its digits is 36. What is the difference between the two digits of that number?\n\n### Options:\nA. 2\nB. 3\nC. 4\nD. 8\nE. 9\n\n### Answer:\nSolution\nLet the ten's digit be x and units digit be y.\nThen, (10x+y) - (10y+x)= 36\t\u2039=\u203a9(x - y) = 36\n\u2039=\u203ax - y = 4.\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the value of 4^5+4^8?\n\n### Options:\nA. 4^12\nB. 4^35\nC. 17(4^5)\nD. 8^12\nE. 65(4^5)\n\n### Answer:\n4^5+4^8\n=4^5(1+4^3)\n=4^5 * 65\nAnswer E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo trains 121 meters and 165 meters in length respectively are running in opposite directions, one at the rate of 80 km and the other at the rate of 65 kmph. In what time will they be completely clear of each other from the moment they meet?\n\n### Options:\nA. 7.18\nB. 7.12\nC. 7.1\nD. 7.15\nE. 7.11\n\n### Answer:\nT = (121 + 165)/ (80 + 65) * 18/5\nT = 7.15\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe value of a machine depreciates at the rate of 10% every year. It was purchased 3 years ago. If its present value is Rs. 8748, its purchase price was :\n\n### Options:\nA. 12003\nB. 12000\nC. 12002\nD. 12289\nE. 12019\n\n### Answer:\nExplanation:\n= Rs.12000\nAnswer: B) 12000\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA carpenter worked alone for 1 day on a job that would take him 6 more days to finish. He and another carpenter completed the job in 5 more days. How many days would it have taken the second carpenter to do the complete job working alone?\n\n### Options:\nA. 4.5\nB. 7.5\nC. 9.5\nD. 17.5\nE. 24.5\n\n### Answer:\nA carpenter worked only 1 day on something that takes him 6 MORE days.\nMeans;\nCarpenter finishes his work in 7 days.\nLet his buddy finish the same task in x days.\nRespective rates per day:\n1/7 AND 1/x\nTo complete 1 work:\nFirst guy worked for 5 days @ rate=1/7 per day.\nSecond one worked for 5 days @ rate=1/x per day\nExpression:\nDays*Rate=Work\n5*1/7+5*1/x=1\n5x+35=7x\n2x=35\nx=17.5 days.\nAns:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAt a certain college there are twice as many history majors as English majors and three times as many history majors as mathematics majors. What is the ratio of the number of english majors to the number of mathematics majors?\n\n### Options:\nA. 6 to 1\nB. 2 to 3\nC. 3 to 2\nD. 1 to 5\nE. 1 to 6\n\n### Answer:\nThis is how I translated the question:\nAt a certain college there are twice as many english majors as history majors\nH = 2E\nand three times as many english majors as mathematics majors.\nH = 3M\nWhat is the ratio of the number of history majors to the number of mathematics majors?\nWhat is E:M?\nJust set E equal to each other to get the ratio in terms of E and M.\n2E = 3M\nE/M = 3/2\nThe answer is 3:2\nAnswer : C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThomas bought a pack of eleven computers for Rs. 500000 and sold it for Rs.550000. What is the % of profit he is making per computer?\n\n### Options:\nA. 10\nB. 14\nC. 19\nD. 21\nE. 25\n\n### Answer:\nThe cost of buying a single computer= Rs(500000/11)=Rs. 45454.5\nThe cost of selling a selling computer=Rs(550000/11)=Rs. 50000.0\nProfit per computer=Rs.(50000-45454.5)=Rs. 4545.5\nThe % of profit in selling a single computer=(4545.5/45454.5)*100=10%\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the number of divisors of 1728.?\n\n### Options:\nA. 26\nB. 27\nC. 28\nD. 29\nE. 30\n\n### Answer:\n1728= 2^6 * 3^3\nHence the Number of factors = (6+1) x (3+1) = 7 x 4 = 28.\nWe know that if a number represented in standard form (a^m *b^n) , then the number of factors Is given by (m+1)(n+1).\nAnswer is 28\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf $100 invested at a certain rate of simple interest amounts to $140 at the end of 3 years,How much will $150 amount to at the same rate of interest in 6 years?\n\n### Options:\nA. $190\nB. $180\nC. $200\nD. $240\nE. $270\n\n### Answer:\n100 amounts to 140 in 3 years.\ni.e (principal + interest ) on 120 in 3 years = 140\n100 + 100*(r/100)*(3) = 140 => r = 40/3\n150 in 6 years = principal + interest\n= 150 + 150*(r/100)*(6)\n= 270\nAnswer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nBob invested $2000 in fund A and $1000 in fund B. Over the next two years, the money in Fund A earned a total interest of 12 percent for the two years combined and the money in fund B earned 30 percent annual interest compounded annually. Two years after bob made these investments. Bob's investment in fund A was worth how much more than his investment in fund B?\n\n### Options:\nA. $500\nB. $550\nC. $600\nD. $650\nE. $700\n\n### Answer:\nBob earned 2000*(1+0.12) in total by fund A and earned 1000*(1+0.3)^2 in total by fund B.\nSo 2000*(1.12) - 1000*(1.69)= 550.\nThe answer is, therefore, (B).\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat least number must be added to the least number of six digits so that the resulting number may be a perfect square.\n\n### Options:\nA. 489\nB. 267\nC. 278\nD. 199\nE. 111\n\n### Answer:\nThe least number of six digits = 100000 3 10 00 00 317 9 61 100 61 627 3900 4389 \u2013 489 Least number to be added = 489.\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe area of a square is equal to five times the area of a rectangle of dimensions 50 cm * 10 cm. What is the perimeter of the square?\n\n### Options:\nA. 289 cm\nB. 200 cm\nC. 829 cm\nD. 288 cm\nE. 289 cm\n\n### Answer:\nArea of the square = s * s\n= 5(50 * 10)\n=> s = 50\n= 50 cm\nPerimeter of the square\n= 4 * 50\n= 200 cm.\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe total age of A and B is 15 years more than the total age of B and C. C is how many years younger than A ?\n\n### Options:\nA. 12\nB. 27\nC. 15\nD. 18\nE. 11\n\n### Answer:\n(A+B) - (B+C) = 15\nA - C = 15.\nC is younger than A by 15 years.\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe total marks obtained by a student in Mathematics and Physics is 60 and his score in Chemistry is 20 marks more than that in Physics. Find the average marks scored in Mathamatics and Chemistry together.\n\n### Options:\nA. 40\nB. 28\nC. 29\nD. 26\nE. 20\n\n### Answer:\nLet the marks obtained by the student in Mathematics, Physics and Chemistry be M, P and C respectively.\nGiven , M + C = 60 and C - P = 20 M + C / 2\n= [(M + P) + (C - P)] / 2\n= (60 + 20) / 2 = 40.\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 1 + 9 + 11 = 1, Then what is the value of\n12 + 11 + 9 = ?\n\n### Options:\nA. 9\nB. 11\nC. 12\nD. 13\nE. 10\n\n### Answer:\nE\nEquation 1 + 9 + 11 = 1 can be derived from\nOne (o) + nine (n) + eleven (e) = one => 1\nSimilarly for equation,\n12 + 11 + 9\nTwelve (t) + eleven (e) + nine (n) => ten (10)\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf f is a function defined for all k by f(k) = k^5 /16, what is f(3k) in terms of f(k)?\n\n### Options:\nA. 1/8 f(k)\nB. 5/8 f(k)\nC. 244 f(k)\nD. 243 f(k)\nE. 323 f(k)\n\n### Answer:\nf(k) = k^5 /16\nf(3k) = (3k)^5/16 = 243 * k^5 /16 = 243 * (k^5 /16) = 243 f(k).\nSo answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n3x^2-6x+3 = 0 Find the above equation find the value of x\n\n### Options:\nA. 0\nB. 1\nC. 2\nD. 3\nE. 4\n\n### Answer:\na = 3, b = -6, c = 3\nx1,2 = (6 \u00b1 \u221a( (-6)2 - 4\u00d73\u00d73)) / (2\u00d73) = (6 \u00b1 \u221a(36-36)) / 6 = (6 \u00b1 0) / 6\nx1 = x2 = 1\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf x^2 - y^2 = 2xy, then (x+y)^2 =\n\n### Options:\nA. 2x^2\nB. 3x^2\nC. 4xy\nD. 2y^2\nE. -y^2\n\n### Answer:\nIts B\nx^2 -y^2 = 2xy\nx^2 = 2xy + y^2\nAdd x^2 on both sides we get\nx^2 +x^2 = x^2 +y^2 +2xy\n2x^2 = (x+y)^2\nCorrect Option : A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA jar contains 8 marbles consisting of an equal number of red, green, and blue marbles. Four marbles are removed from the jar and discarded. What is the probability that only two colors will remain in the jar after the four marbles have been removed?\n\n### Options:\nA. 1/495\nB. 1/165\nC. 3/70\nD. 1/35\nE. 11/20\n\n### Answer:\nJar contains {4-red, 4-green, 4-blue} marbles. We are asked to find the probability that after removing 4 marbles only 2 colours remain in the jar, i.e., the probability of removing EITHER red, OR green, OR blue.\nSample space = 8C4 = 495.\nProbability of choosing 4 red = 4C4/8C4 = 1/70.\nProbability of choosing 4 green = 4C4/8C4 = 1/70.\nProbability of choosing 4 blue = 4C4/8C4 = 1/70.\nRequired probability = 1+1+1/70 = 3/70 Ans (C).\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many boxes do we need if we have to carry 250 apples into boxes that each hold 25 apples?\n\n### Options:\nA. A)9\nB. B)5\nC. C)7\nD. D)10\nE. E)None of the above\n\n### Answer:\nSol.\nApples 250\nEach carries 25\n= 250/25\n= 10\nAnswer : D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n7, 35, 56, 91, 126\nIn the sequence above, each term is related with the others. Which of the following could not be a term in the sequence?\n\n### Options:\nA. 398\nB. 259\nC. 322\nD. 686\nE. 847\n\n### Answer:\nSimplifying the question into easier words we just need to find which of the numbers is not divisible by 7\nclearly the answer is 398 because if we divide 398 by 7 we get a remainder of 56.85\nCorrect answer - A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe speed of the boat in still water in 12 kmph. It can travel downstream through 54 kms in 3 hrs. In what time would it cover the same distance upstream?\n\n### Options:\nA. 8 hours\nB. 6 hours\nC. 4 hours\nD. 5 hours\nE. 9 hours\n\n### Answer:\nStill Water=12km/hr\nDownstream=54/3=18km/hr\nUpstream=>> still water=(u+v/2) =>> 12=u+18/2 = 6km/hr\nSo time taken in upstream = 545/6 =9hrs\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n24 oz of juice P and 25 oz of juice F are mixed to make smothies X and Y . The ratio of p to F in smothie X is 4 is to 1 and that in Y is 1is to 5.How many ounces of juice P are contained in the smothie X?\n\n### Options:\nA. 5\nB. 10\nC. 15\nD. 20\nE. 25\n\n### Answer:\nEasy way to solve this question is start from the answer and then conform the information provided in the question.\nwe can start from option D i.e 20 ... as a quantity of juice P in X because it is the only one option that gets divided by 4 is 20 ... since in the X the juice P to F ratio is 4:1\nthis gives us that quantity of juice P in X = 20 therefore quantity of Juice F will be 5 ... hence ratio = 4:1\nThis will lead to quantity of juice P in X = 4 and quantity of Juice F = 20 ... hence ratio 1:5\nif we calculate total Juice P = 24 and total of juice V = 25\nit fits because totals are same as what mentioned in the question ...\nthus ans is D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThree years ago the average age of a family of six members was 19 years. A boy have been born, the average age of the family is the same today. What is the age of the boy?\n\n### Options:\nA. 1\nB. 4\nC. 3\nD. 8\nE. 6\n\n### Answer:\n6 * 22 = 132\n7 * 19 = 133\n--------------\n1\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMaxwell leaves his home and walks toward Brad's house at the same time that Brad leaves his home and runs toward Maxwell's house. If the distance between their homes is 72 kilometers, Maxwell's walking speed is 6 km/h, and Brad's running speed is 12 km/h. What is the distance traveled by Maxwell when they meet in the middle?\n\n### Options:\nA. 14\nB. 24\nC. 16\nD. 18\nE. 20\n\n### Answer:\nConsider Max starts from Point A and Brad Starts from Point B and move towards each other.\nAssume they shall meet at point O after Time 'T'. The question asks us to find OA.\nFrom the question stem we can make out :- Distance OA = 50km - Distance OB\n=> 6xT = 72 - 12xT (i.e distance =Speed x Time)\n=> 18T = 72\nHence T = 4\nOA = 6 x 4 = 24 Km\nAnswer : B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the least number which when divided by 20,25,35 and 40 leaves remainders 14,19,29 and 34 respectively.\n\n### Options:\nA. 1394\nB. 1294\nC. 1194\nD. 1094\nE. None of them\n\n### Answer:\nHere,(20-14) = 6,(25 \u2013 19)=6,(35-29)=6 and (40-34)=6.\nTherefore, Required number = (L.C.M. of 20,25,35,40) \u2013 6 =1394.\nAnswer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIncome and expenditure of a person are in the ratio 8 : 7. If the income of the person is Rs. 40000, then find his savings?\n\n### Options:\nA. 5000\nB. 6000\nC. 7000\nD. 8000\nE. 9000\n\n### Answer:\nLet the income and the expenditure of the person be Rs. 8x and Rs. 7x respectively.\nIncome, 8x = 40000\n=> x = 5000\nSavings = Income - expenditure\n= 8x - 7x = x\nSo, savings =Rs.5000.\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n135 kg of an alloy A is mixed with 145 kg of alloy B. If alloy A has lead and tin in the ratio 3:5 and alloy B has tin and copper in the ratio 2:3, then the amount of tin in the new alloy is?\n\n### Options:\nA. 100.6kg\nB. 142kg\nC. 135kg\nD. 110.8kg\nE. 114kg\n\n### Answer:\nQuantity of tin in 135kg of A = 135*5/8 = 84kg\nQuantity of tin in 145kg of B = 145*2/5 = 58kg\nQuantity of tin in the new alloy = 84+58 = 142kg\nAnswer is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe ratio of two numbers is 3 : 4 and their H.C.F. is 4. Their L.C.M. is:\n\n### Options:\nA. 12\nB. 16\nC. 24\nD. 48\nE. 50\n\n### Answer:\nLet the numbers be 3x and 4x. Then, their H.C.F. = x. So, x = 4.\nSo, the numbers 12 and 16.\nL.C.M. of 12 and 16 = 48.\nanswer :D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train 400 m long can cross an electric pole in 20 sec and then find the speed of the train?\n\n### Options:\nA. 34\nB. 56\nC. 72\nD. 35\nE. 32\n\n### Answer:\nLength = Speed * time\nSpeed = L/T\nS = 400/20\nS = 20 M/Sec\nSpeed= 20*18/5 (To convert M/Sec in to Kmph multiply by 18/5)\nSpeed = 72 Kmph\nAnswer: Option C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nQ as a percentage of P is equal to P as a percentage of (P + Q). Find Q as a percentage of P.\n\n### Options:\nA. 62%\nB. 50%\nC. 75%\nD. 66%\nE. 65%\n\n### Answer:\nExplanation :\nIF P+Q=62%\nANSWER IS A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average weight of a group of boys is 30 kg. After a boy of weight 35 kg joins the group, the average weight of the group goes up by 1 kg. Find the number of boys in the group originally ?\n\n### Options:\nA. 4\nB. 5\nC. 6\nD. 7\nE. 8\n\n### Answer:\nLet the number off boys in the group originally be x.\nTotal weight of the boys = 30x\nAfter the boy weighing 35 kg joins the group, total weight of boys = 30x + 35\nSo 30x + 35 + 31(x + 1) = > x = 4.\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhen positive integer H is divided by positive integer B, the result is 4.35. Which of the following could be the reminder when H is divided by B?\n\n### Options:\nA. 13\nB. 14\nC. 15\nD. 16\nE. 17\n\n### Answer:\nthe remainder will be obtained from the decimal part when H is divided by B i.e. 0.35\n0.35 = 35/100 = 7/20 so possible remainders are 7,14,21,28. Only option B-14 satisfies this\nPS: for B-14 H=174 and B=40\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFor what value(s) of n is the following equation satisfied: 2n-6-n = 5n+6-4n\n\n### Options:\nA. a. -5\nB. b. 0 only\nC. c. 5/2 only\nD. d. No value\nE. e. Any value\n\n### Answer:\n2n-6-n = 5n+6-4n\nn - 6 = n + 6\n-6 = 6, which is false.\nSo, no n satisfies given equation.\nAnswer: D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAn article is bought for Rs.695 and sold for Rs.900, find the gain percent?\n\n### Options:\nA. 30 1/3%\nB. 33 1/3%\nC. 23 1/3%\nD. 35 1/3%\nE. 29 69/139%\n\n### Answer:\nE\n29 69/139%\n695 ---- 205\n100 ---- ? => 29 69/139%\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train 140 m long, running with a speed of 63 km/hr will pass a tree in?\n\n### Options:\nA. 18 sec\nB. 6 sec\nC. 8 sec\nD. 15 sec\nE. 7 sec\n\n### Answer:\nSpeed = 63 * 5/18 = 35/2 m/sec\nTime taken = 140 * 2/35 = 8 sec\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe percentage profit earned by selling an article for Rs. 1920 is equal to the percentage loss incurred by selling the same article for Rs. 1280. At what price should the article be sold to make 25% profit?\n\n### Options:\nA. Rs. 2000\nB. Rs. 2200\nC. Rs. 2400\nD. Data inadequate\nE. Cannot be determined\n\n### Answer:\nExplanation :\nLet the C.P. of the article be Rs. x\nGiven that % profit earned by selling article at Rs. 1920 = % loss incurred by selling article at Rs. 1280\n(1920\u2212x/x)\u2217100 = (x\u22121280/x)\u2217100\n=> 1920 - x = x - 1280\n=> 2x = 3200\n=> x = 1600\nS.P. for 25% profit = Rs. 1600 + 25% of Rs. 1600 = Rs. 1600*(125/100) = Rs. 2000\nAnswer : A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat should come in place of the question mark (?) in each of the following questions ?\n12 + 22 + 32 + ... + 102 = ?\n\n### Options:\nA. 400\nB. 625\nC. 380\nD. 385\nE. 370\n\n### Answer:\nExplanation :\nSum of the squares of first 'n' natural number = n(n+l)(2n+l)/6 Put n = 10. 10x 11x21/6=55x7=385.\nAnswer : Option D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA biker covered half the distance between two towns in 2 hr 30 min. After that he increased his speed by 2 km/hr. He covered the second half of the distance in 2 hr 20 min. Find the distance between the two towns and the initial speed of the biker.\n\n### Options:\nA. 140\nB. 120\nC. 130\nD. 150\nE. 160\n\n### Answer:\nLet x km/hr be the initial speed of the biker, then his speed during the second part of the trip is x + 2 km/hr. Half the distance between two cities equals 23060\u22c5x km and 22060\u22c5(x+2) km. From the equation: 23060\u22c5x=22060\u22c5(x+2) we get x=28 km/hr.\nThe intial speed of the biker is 28 km/h.\nHalf the distance between the two towns is\n2h30min\u00d728=2.5\u00d728=70.\nSo the distance is 2\u00d770=140 km.\nAnswer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf p, q, and r are consecutive integers such that p > q > r and the sum of p, q, and r is a multiple of 10, which of the following could be the value of p?\n\n### Options:\nA. 0\nB. 1\nC. 9\nD. 10\nE. 12\n\n### Answer:\nWe're given a very specific set of restrictions in this prompt:\n1) P, Q and R are CONSECUTIVE INTEGERS\n2) P > Q > R\n3) P+Q+R = a multiple of 10\nWe're asked which of the 5 answer COULD be the value of P given these restrictions. Rather than staring at the screen or doing layered math, we canbrute forcethe answers until we find one that fits these restrictions..\nAnswer A: P = 0\nIn this case, the numbers would be 0, -1, and -2. The sum = -3 which is NOT a multiple of 10. Eliminate A.\nAnswer B: P = 1\nIn this case, the numbers would be 1, 0, and -1. The sum = 0 which IS a multiple of 10. B IS the answer.\nFinal Answer:\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA company has found that when x units of a product are manufactured and sold, its revenue is given by x 2 + 100 x dollars and its costs are given by 240 x + 500 dollars. How many units must be produced and sold to make a profit of 10,000 dollars? (HINT: profit = revenue - costs)\n\n### Options:\nA. 192\nB. 193\nC. 194.\nD. 195\nE. 196\n\n### Answer:\nLet us use profit = revenue - costs to find a formula for the profit P\nP = ( x 2 + 100 x ) - ( 240 x + 500 )\nSubstitute P in the above equation by 10,000 dollars to obtain\n10000 = x 2 - 140 x - 500\nWrite the equation in standard form and solve for x\nx 2 - 140 x - 10500 = 0\nSolve the above equation for x\nx = 194.10 and x = -54.01\nThe number of units to produce must be positive, so\nx = 194.\nAs an exercise, check that for the above value of x the profit is approximately (because of the rounding) equal to 10,000.\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the least number of five digits which is exactly divisible by 12, 15 and 18?\n\n### Options:\nA. 1080\nB. 10080\nC. 10025\nD. 11080\nE. 12000\n\n### Answer:\nLCM = 180\n180) 10000 (55\n9900\n---------\n100\n10000 + 180 - 100 = 10080\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSet S consists of integers {2,3,4,5}. If two numbers are chosen from set S at random, what is the probability that the product of 2 numbers is more than 10?\n\n### Options:\nA. 1/2\nB. 1/4\nC. 2/5\nD. 3/7\nE. 1/6\n\n### Answer:\nNumber of ways you can choose 2 from 4 = 4C2 = 6\nE = event of getting the 2 numbers product is more than 10 = (3,4),(3,5),(4,5) = 3\nprobability = 3/6 = 1/2\nAnswer is A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA goods train runs at the speed of 72 kmph and crosses a 350 m long platform in 26 seconds. What is the length of the goods train?\n\n### Options:\nA. 230 m\nB. 140 m\nC. 160 m\nD. 170 m\nE. None of these\n\n### Answer:\nExplanation:\nSpeed =[ 72 x (5/18) ]m/sec= 20 m/sec.\nTime = 26 sec.\nLet the length of the train be x metres.\nThen,[ (x+350)/26 ]= 20\n=> x + 350 = 520\n=> x = 170. Answer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a division sum, the divisor is ten times the quotient and five times the remainder. If the remainder is 44, the dividend is?\n\n### Options:\nA. 4320\nB. 4325\nC. 4330\nD. 4884\nE. 4336\n\n### Answer:\nDivisor = (5 * 44) = 220\n= 10 * Quotient = Divisor\n=> Quotient = 220/10 = 22\nDividend = (Divisor * Quotient) + Remainder\nDividend = (220 * 22) + 44 = 4884\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat will be the ratio of simple interest earned by certain amount at the same rate of interest for 7 years and that for 11 years?\n\n### Options:\nA. 8 : 11\nB. 9 : 11\nC. 7 : 11\nD. Data inadequate\nE. None of these\n\n### Answer:\nLet the principal be P and rate of interest be R%.\n\u2234 Required Ratio = [(P\u00d7R\u00d77/100) /(P\u00d7R\u00d711/100)]=1PR/11PR=7/11=7:11\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIt takes printer A 4 more minutes more than printer B to print 40 pages. Working together, the two printers can print 50 pages in 6 minutes. How long will it take Printer A to print 120 pages?\n\n### Options:\nA. 12\nB. 18\nC. 20\nD. 24\nE. 36\n\n### Answer:\nIf it takes 4 more minutes for A to print 40 pages than it takes B,\nit takes 5 more minutes for A to print 50 pages than it takes B.\nThus if b is the number of minutes than B takes to print 50 pages,\nwe can write:\n1/b+1/(b+5)=1/6 (since in 1 minute, they print 1/6th of the 50 page job)\n6(2b+5)=b(b+5)\nb^2-7b-30=0\n(b-10)(b+3)=0\nb=10\nThus it takes A 15 minutes to print 50 pages and 15*120/50=36 minutes to print 120 pages (ANSWER E)\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a certain game of dice, the player\u2019s score is determined as a sum of four throws of a single die. The player with the highest score wins the round. If more than one player has the highest score, the winnings of the round are divided equally among these players. If Jim plays this game against 26 other players, what is the probability of the minimum score that will guarantee Jim some monetary payoff?\n\n### Options:\nA. 41/50\nB. 1/221\nC. 1/1296\nD. 1/84\nE. 1/42\n\n### Answer:\nToguaranteethat Jim will get some monetary payoff he must score the maximum score of 6+6+6+6=24, because if he gets even one less than that so 23, someone can get 24 and Jim will get nothing.\nP(24)=1/6^4=1/1296.\nAnswer: C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling alongthe oundary of the park at the speed of 12 km/hr completes one round in 8 min, then the area of the park (in sq. m) is?\n\n### Options:\nA. 123400 m\nB. 145500 m\nC. 153600 m\nD. 186400 m\nE. 165700 m\n\n### Answer:\nPerimeter = Distance covered in 8 min. = 12000 x 8 m = 1600 m.\n60\nLet length = 3x metres and breadth = 2x metres.\nThen, 2(3x + 2x) = 1600 or x = 160.\nLength = 480 m and Breadth = 320 m.\nArea = (480 x 320) m2 = 153600 m\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich of the following is equivalent to the pair of inequalities x + 7 > 10 and x - 1 <= 5 ?\n\n### Options:\nA. 2 < x < 16\nB. 2 <= x < 4\nC. 3 < x <= 6\nD. 4 < x <= 8\nE. 4 <= x <= 16\n\n### Answer:\nSolution:\nLet\u2019s isolate x in both inequalities, starting with x + 7 > 10.\nx + 7 > 10\nx > 3\nNext we isolate x in the inequality x \u2013 1 \uf0a3 5.\nx \u2013 1 <= 5\nx <= 6\nBringing these two inequalities together we know:\n3 < x <= 6\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat sum of money will produce Rs.70 as simple interest in 4 years at 3 1/2 percent?\n\n### Options:\nA. 288\nB. 500\nC. 299\nD. 2766\nE. 2912\n\n### Answer:\n70 = (P*4*7/2)/100\nP = 500.Answer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRobert is travelling on his cycle andhas calculated to reach point A at 2 PM. if he travels at 10 kmph, he will reach there at 12Pm if he travels at 15 kmph. At what speed musthe travel to reach A at 1 PM?\n\n### Options:\nA. 8 kmph\nB. 10 kmph\nC. 12 kmph\nD. 14 kmph\nE. 16 kmph\n\n### Answer:\nLet the distance travelled by x km.\nThen, x - x = 2\n10 15\n3x - 2x = 60\nx = 60 km.\nTime taken to travel 60 km at 10 km/hr = 60 hrs = 6 hrs.\n10\nSo, Robert started 6 hours before 2 P.M. i.e., at 8 A.M.\nRequired speed = 60 kmph. = 12 kmph.\n5\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the compound interest on a certain sum of money for 6 years at 10% per annum be Rs. 993, what would be the simple interest?\n\n### Options:\nA. Rs. 880\nB. Rs. 890\nC. Rs. 1800\nD. Rs. 900\nE. None\n\n### Answer:\nLet P = Principal\nA - Amount\nWe have a = P(1 + R/100)3 and CI = A - P\nATQ 993 = P(1 + R/100)3 - P\n? P = 3000/-\nNow SI @ 10% on 3000/- for 6 yrs = (3000 x 10 x 6)/100\n= 1800/-\nAnswer: C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average of eleven ten prime numbers which are odd is?\n\n### Options:\nA. 17.72\nB. 18.52\nC. 19.63\nD. 16.53\nE. 15.63\n\n### Answer:\nExplanation:\nSum of first 11 prime no. which are odd = 195\nAverage = 195/11 = 17.72\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA reduction of 24% in the price of salt enables a lady to obtain 10kgs more for Rs.100, find the original price per kg?\n\n### Options:\nA. 2.8\nB. 3.2\nC. 2.5\nD. 2.1\nE. 2.9\n\n### Answer:\n100*(24/100) = 24 --- 10\n? --- 1 => Rs.2.4\n100 --- 76\n? --- 2.4 => Rs.3.2\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThree medical experts, working together at the same constant rate, can write an anatomy textbook in 32 days. How many additional experts, working together at this same constant rate, are needed to write the textbook in 24 days?\n\n### Options:\nA. 1\nB. 2\nC. 3\nD. 4\nE. 5\n\n### Answer:\nEach expert can write 1/96 of the book per day.\nTo complete the book in 24 days, we need 96/24 = 4 experts, thus 1 more expert is needed.\nThe answer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAn bus covers a certain distance at aspeed of 150 kmph in 5 hours. To cover the same distance in 1hr, it must travel at a speed of?\n\n### Options:\nA. 560 km/h\nB. 450 km/h\nC. 779 km/h\nD. 723 km/h\nE. 720 km/h\n\n### Answer:\nDistance = (150 x 5) = 750 km.\nSpeed = Distance/Time\nSpeed = 750/(5/3) km/hr. [We can write 1 hours as 5/3 hours]\nRequired speed = 750 x 3/5 km/hr = 450 km/hr.\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe cost price of 13 articles is equal to the selling price of 11 articles. Find the profit percent?\n\n### Options:\nA. 78 2/11%\nB. 18 2/11%\nC. 88 2/11%\nD. 58 2/11%\nE. 68 2/11%\n\n### Answer:\nExplanation:\n13 CP = 11 SP\n11 --- 2 CP\n100 --- ? =>18 2/11%\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn an intercollegiate competition that lasted for 3 days, 150 students took part on day 1, 110 on day 2 and 140 on day 3. If 75 took part on day 1 and day 2 and 25 took part on day 2 and day 3 and 15 took part on all three days, how many students took part only on day 2?\n\n### Options:\nA. 50\nB. 35\nC. 45\nD. 25\nE. 60\n\n### Answer:\nDay 1&2 = 75; Only Day 1&2 (75 -15) = 60,\nDay 2&3 = 25; Only Day 2&3 (25 -15) = 10,\nOnly Day 2 = 110 - (60+10+15) = 25\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA student multiplied a number by 3/5 instead of 5/3. What is the percentage error.\n\n### Options:\nA. 64%\nB. 65%\nC. 66%\nD. 67%\nE. None of these\n\n### Answer:\nExplanation:\nLet the number be x,\nthen,\n5/3\u22123/5=16/15x\nError% =\n(16/15x\u22173/5\u2217100)\nOption A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRamu rides his bike at an average speed of 45 km/hr and reaches his desitination in four hours. Somu covers the same distance in six hours. If Ramu covered his journey at an average speed which was 9 km/hr less and Somu covered his journey at an average speed which was 10 km/hr more, then the difference in their times taken to reach the destination would be (in minutes).\n\n### Options:\nA. 22 min\nB. 30 min\nC. 87 min\nD. 26 min\nE. 11 min\n\n### Answer:\nExplanation:\nDistance travelled by Ramu = 45 x 4 = 180 km\nSomu travelled the same distance in 6 hours.\nHis speed = 180/6 = 30 km/hr\nHence in the conditional case, Ramu's speed = 45 - 9 = 36 km/hr and Somu's speed = 30 + 10 = 40km/hr.\nTherefore travel time of Ramu and Somu would be 5 hours and 4.5 hours respectively.\nHence difference in the time taken = 0.5 hours = 30 minutes.\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA and B can do a piece of work in 8 days. With the help of C they finish the work in 4 days. C alone can do that piece of work in?\n\n### Options:\nA. 40 days\nB. 20 days\nC. 8 days\nD. 60 days\nE. 40 days\n\n### Answer:\nC\n8 days\nC = 1/4 \u2013 1/8 = 1/8 => 8 days\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n24 oz of juice P and 25 oz of juice V are mixed to make smothies E and Y . The ratio of p to V in smothie E is 4 is to 1 and that in Y is 1is to 5.How many ounces of juice P are contained in the smothie E?\n\n### Options:\nA. 5\nB. 10\nC. 15\nD. 20\nE. 25\n\n### Answer:\nThe ratio of p to V in smothie E is 4 is to 1 and that in Y is 1is to 5. p1 + p2 = 24\nv1 + v2 = 25\np1 = 4v1\np2 = v2/5\n4v1 + v2/5 = 24\nv1 + v2 = 25\n4v2 - v2/5 = 76\n19v2/5 = 76 => v2 = 20\n=> v1 = 5\n=> p1 = 20\nAnswer - D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSolve the equation for x : 6x - 87 + 3x = 4 + 9 - x\n\n### Options:\nA. 12\nB. 5\nC. 10\nD. 9\nE. 3\n\n### Answer:\nC\n10\n9 x + x = 13 + 87\n10 x = 100 => x = 10\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average weight of a group of 30 friends increases by 10 kg when the weight of additional 30 friends was added. If average weight of the whole group after including the additional 30 members is 40 kg, what is the average weight of the additional friends?\n\n### Options:\nA. 50 kg\nB. 60 kg\nC. 61 kg\nD. 62 kg\nE. 91 kg\n\n### Answer:\nlet a=avg. wt. of additional 30 friends\noriginal total weight=(30 friends)(30 kg avge)=900kg\n(900+30a)/(30+30)=40 kg avge\na=50 kg\nAnswer - A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA trader purchased two colour televisions for a total of Rs. 35000. He sold one colour television at 30% profit and the other 40% profit. Find the difference in the cost prices of the two televisions if he made an overall profit of 32%?\n\n### Options:\nA. Rs. 21000\nB. Rs. 17500\nC. Rs. 19000\nD. Rs. 24500\nE. None of these\n\n### Answer:\nLet the cost prices of the colour television sold at 30% profit and 40% profit be Rs. x and Rs. (35000 - x) respectively.\nTotal selling price of televisions = x + 30/100 x + (35000 - x) + 40/100 (35000 - x)\n=> 130/100 x + 140/100 (35000 - x) = 35000 + 32/100 (35000)\nx = 28000\n35000 - x = 7000\nDifference in the cost prices of televisions = Rs. 21000\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the two-digit number?\nI. Sum of the digits is 7.\nII. Difference between the number and the number obtained by interchanging the digits is 9.\nIII. Digit in the ten's place is bigger than the digit in the unit's place by 1.\n\n### Options:\nA. I and II\nB. II and III\nC. I and III only\nD. All\nE. I and II as well as I and III\n\n### Answer:\nAnswer: Option E\nExplanation:\nLet the tens and units digit be x and y respectively.\nI. x + y = 7.\nII. (10x + y) - (10y + x) = 9 x - y = 1.\nIII. x - y = 1.\nThus, I and II as well as I and III give the answer.\nCorrect answer is (E).\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe amount of electrical current that flows through a wire is inversely proportional to the resistance in that wire. A wire originally carries 4 amperes of electrical current. Then the resistance is reduced to one-sixth of its original value. How many amperes of electrical current will flow through the wire?\n\n### Options:\nA. 2/3\nB. 4\nC. 16\nD. 24\nE. 32\n\n### Answer:\nGiven that, I\u221d1/R, I*R is a constant value.\nI1*R1 = I2*R2\nI1*R1 = I2*R1/6\nI2 = 6*I1 = 24 amperes\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe ratio of investments of two partners P and Q is 7:5 and the ratio of their profits is 7:10. If P invested the money for 5 months, find for how much time did Q invest the money?\n\n### Options:\nA. 22\nB. 6\nC. 17\nD. 10\nE. 88\n\n### Answer:\n7*5: 5*x = 7:10\nx = 10\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn what time a sum of money double itself at 8% per annum simple interest?\n\n### Options:\nA. 33 1/8%\nB. 33 1/3%\nC. 83 1/3%\nD. 33 4/3%\nE. 12 1/2%\n\n### Answer:\nP = (P*8*R)/100\nR = 12 1/2%\nAnswer:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSneh's age is 1/6th of her father's age. Sneh's father's age will be twice of Vimal's age after 10 years. If Vimal's eighth birthday was celebrated two years before, what is Sneh's present age?\n\n### Options:\nA. 24 years\nB. 30 years\nC. 6 2/3 years\nD. 32 years\nE. None of these\n\n### Answer:\nVimal's age after 10 years = (8+2+10)years\n= 20 years.\nSneh's father age after 10 years = 40 years (Twice than Vimal's age after 10yr)\nSneh's father Present age = 30 years (40yrs -10yrs)\nTherefore Sneh's age\t= (1/6 * 30)years\n= 5 years.\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhen all the students in a school are made to stand in rows of 50, 25 such rows are formed. If the students are made to stand in rows of 30, how many such rows will be formed ?\n\n### Options:\nA. 41\nB. 36\nC. 38\nD. 19\nE. 21\n\n### Answer:\nExplanation:\nTotal number of students = 50 x 25\nWhen arranged in rows of 30, number of rows formed are,\n= 41.\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn one hour a boat goes 22 km long the stream and 12 km against the stream.The speed of the boat in still water is?\n\n### Options:\nA. 17\nB. 18\nC. 16\nD. 15\nE. 11\n\n### Answer:\nSpeed in still water A = \u00bd ( 22+12) km/hr A= 17 kmph\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average of first 10 natural numbers is?\n\n### Options:\nA. 4.9\nB. 5.5\nC. 2.7\nD. 5.1\nE. 2.5\n\n### Answer:\nExplanation:\nSum of 10 natural no. = 110/2 = 55\nAverage = 55/10 = 5.5\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA cyclist covers a distance of 750 m in 2 min 30 sec. What is the speed in km/hr of the cyclist?\n\n### Options:\nA. 9km/hr\nB. 7km/hr\nC. 12km/hr\nD. 15km/hr\nE. 18km/hr\n\n### Answer:\nSpeed = { 750 } m/sec =5 m/sec = { 5 * 18 } km/hr =18km/hr\nAns:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFive friends, Peter, Eric, Melyssa, Tony, and Carl, are pooling their money to buy a $1300 item. Peter has twice as much money as Melyssa. Tony has $60 more than Peter. Carl has 20% more than Tony and Eric has twice as much as Peter. If they put all their money together and spend the $1300, they will have $38 left. How much money does Peter have?\n\n### Options:\nA. $300\nB. $270\nC. $320\nD. $350\nE. $220\n\n### Answer:\nP= 2M ; T= P+60 ; C= 1.2(T); P=(E/2)\nP+M+T+C+E-1300=38\nP+0.5P+P+60+1.2(P+20)+2P = 1338\nP+0.5P+P+60+1.2P+24+2P = 1338\nP+0.5P+P+1.2P+2P+84 = 1338\nP+0.5P+P+1.2P+2P = 1254\n5.7P = 1254\nP=220\nAnswer:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a train, travelling at a speed of 90 kmph, crosses a pole in 5 sec, then the length of train is?\n\n### Options:\nA. 125 m\nB. 104 m\nC. 140 m\nD. 152 m\nE. 150 m\n\n### Answer:\nD = 90 * 5/18 * 5 = 125 m\nANSWER A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAn bus covers a certain distance at a speed of 240 kmph in 5 hours. To cover the samedistance in 1hr, it must travel at a speed of?\n\n### Options:\nA. 600 km/hr\nB. 720 km/hr\nC. 730 km/hr\nD. 750 km/hr\nE. 760 km/hr\n\n### Answer:\nDistance = (240 x 5) = 1200 km.\nSpeed = Distance/Time\nSpeed = 1200/(5/3) km/hr. [We can write 1 hours as 5/3 hours]\nRequired speed = 1200 x 3 km/hr = 720 km/hr.\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA polling company found that, of 300 households surveyed, 120 spent at least $100 per month on both gasoline and electricity, 60 spent at least $100 per month on gasoline but not on electricity, and for every household that did not spend at least $100 per month on gasoline or electricity, 4 spent at least $100 per month on electricity but not on gasoline. How many of the 300 households did not spend at least $100 per month on either gasoline or electricity?\n\n### Options:\nA. 24\nB. 30\nC. 36\nD. 90\nE. 96\n\n### Answer:\nFor every household that did not spend at least $100 per month on gasoline or electricity = P ,\n4 spent at least $100 per month on electricity but not on gasoline = 4P\nSpent = 300 - P\nagain spent = 60+120+4P\nNow,\n300 - P = 60+120+4P\nor, 5P = 120\nor, P = 24 (Answer)\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nsowdharya had 90 currency notes in all, some of which are of Rs 95 denomination and the remaining of Rs 45 denomination. The total amount of all these currency notes was Rs. 5000. How much amount (in Rs) did she have in the denomination of Rs 45?\n\n### Options:\nA. 75\nB. 72\nC. 71\nD. 76\nE. 73\n\n### Answer:\nLet the number of 45-rupee notes = x\nThen, the number of 95-rupee notes = (90 \u2013 x)\n45x + 95(90 \u2013 x) = 5000 : x = 71\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow long does a train 110 meters long running at the speed of 72 km/hour take to cross a bridge 132 meters in length ?\n\n### Options:\nA. 22.1 seconds\nB. 12.1 seconds\nC. 17.1 seconds\nD. 12.9 seconds\nE. 11.1 seconds\n\n### Answer:\nSpeed = 72 km/hour = 72*(5/18) m/sec\n= 20 m/sec\nTotal distance to be covered = 110+132 = 142 meters\nTime = Distance/Speed\n= 242/20 = 12.1 seconds\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn the following sequence: [x, y, z, 5, 7, 16, 28] each number is equal to the sum of the three numbers succeding it. What is x+y?\n\n### Options:\nA. 113\nB. 213\nC. 163\nD. 213\nE. 131\n\n### Answer:\nlets start from z, as per the question stem\nz =5+7+16 =28\n-->> z= 28\nsimilarly, y =28+5+7\n--> y = 40\nsimilarly,, x =40+28+5\n--> x =73\nhence , x+y =73+40 = 113 --> x+y=113\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn the xy-coordinate plane, the graph of y = -x^2 + 9 intersects line L at (p,4) and (t,-7). What is the least possible value of the slope of line L?\n\n### Options:\nA. 6\nB. 2\nC. -2\nD. -6\nE. -5.5\n\n### Answer:\nWe need to find out the value of p and L to get to the slope.\nLine L and Graph y intersect at point (p,5). hence, x= p and Y=5 should sactisfy the graph. soliving\n5 = -p2 +9\np2 = 4\np = + or - 2\nsimillarly point (t,-7) should satisfy the equation. hence x=t and Y=-7.\n-7 = -t2+9\nt = +or - 4\nconsidering p = -2 and t =4, the least slope is (-7-4)/(4-2) = -5.5\nIMO option E is correct answer.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf P * Q implies (P2 + Q2), 8 * (3 * 2) = ?\n\n### Options:\nA. 239\nB. 278\nC. 233\nD. 2697\nE. 771\n\n### Answer:\nExplanation:\nWe have, P * Q = (P2 + Q2) ......... Given\n8 * (3 * 2) = ?\n8 * 13 = (64 +169) = 233\nANSWER: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a workshop there are 4 kinds of beds, 3 kinds of closets, 2 kinds of shelves and 7 kinds of chairs. In how many ways can a person decorate his room if he wants to buy in the workshop one closet, one bed and one of the following: a chair or a shelf?\n\n### Options:\nA. A)168.\nB. B)80.\nC. C)56.\nD. D)108.\nE. E)16.\n\n### Answer:\nways to select one closet = 3\nways to select one bed = 4\nways to select one of the following: a chair or a closet = 7+2 = 10\nways to select all of them together = 3*4*9 = 108\nAnswer : D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the sum of the different positive prime factors of 380?\n\n### Options:\nA. 5\nB. 10\nC. 15\nD. 17\nE. 26\n\n### Answer:\nPrime factorization of 380\n=38 * 10\n=2*19 * 10\n=2*19 * 2*5\n=2^2 * 5 * 19\nSum of the different positive prime factors of 380 = 2+5+19\n=26\nAnswer E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train starts from Delhi at 6.00 a.m. and reaches Meerut at 10 a.m. The other train starts from Meerut at 8 a.m. and reaches Delhi at 11.30 a.m. If the distance between Delhi and Meerut is 200 km, then at what time did the two trains meet each other?\n\n### Options:\nA. 8.56 a.m\nB. 8.46 a.m\nC. 7.56 a.m\nD. 8.30 a.m\nE. None of these\n\n### Answer:\nThe Speed of the train starting from Delhi = 200/4 = 50 km/h\nThe Speed of train starting from Meerut = 200/3.5 = 400/7 km/h\nSuppose the two trains meet x hours after 6.00 am\nThen x X 50 + (x - 2) x 400/7 = 200\nor, 350x + 400x - 800 = 1400\nor, 750x = 2200\nor, x = 2200/750 = 2h 56 min\nHence, the required time = 8.56 am\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo trains 140 m and 200 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is?\n\n### Options:\nA. 10.9 sec\nB. 8.64 sec\nC. 53.8 sec\nD. 10.8 sec\nE. 10.4 sec\n\n### Answer:\nRelative speed = 60 + 40 = 100 km/hr.\n= 100 * 5/18 = 250/9 m/sec.\nDistance covered in crossing each other = 140 + 200 = 240 m.\nRequired time = 240 * 9/250 = 8.64 sec.\nAnswer: B:\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nComplete the sequence:\nB D H N ?\n\n### Options:\nA. M\nB. V\nC. S\nD. D\nE. Z\n\n### Answer:\nB+2=D\nD+4=H\nH+6=N\nB+8=V\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a certain sample of data has a mean of 31.0 and a standard deviation of 2.0, which of the following pairs contain two values that are each at least 2.5 standard deviations from the mean?\n\n### Options:\nA. (27.0; 36.5)\nB. (24.5; 38.0)\nC. (28.0; 32.5)\nD. (26.5; 35.0)\nE. (29.0; 32.5)\n\n### Answer:\nThe standard deviation is 2, so 2.5 standard deviations would be (2.5)(2) = 5.\nThe values between 26 and 36 are within 2.5 standard deviations from the mean.\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nxy+yz=63\nxz+yz=23\nfind x+y+z ?\n\n### Options:\nA. 23\nB. 24\nC. 25\nD. 26\nE. 27\n\n### Answer:\ntake z as common term in second equation\nie z(x+y)=23\nnow as 23 is prime no therefore its factors must be 1 and 23.\nnow as x,y,z is integer no therefore z= 1 as sum of two integer cannot be equal to 1.\n=> z= 1 and x + y = 23\ntherefore x+y+z = 1 + 23 = 24.\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 5 (A's capital) = 8 (B's capital) = 10 (C's capital). Then the ratio of their capitals is?\n\n### Options:\nA. 8:5:4\nB. 8:5:18\nC. 8:5:12\nD. 8:5:14\nE. 8:5:11\n\n### Answer:\n5A = 8B = 10 C\nA:B:C = 1/5:1/8:1/10\n= 8:5:4\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a certain game, a large container is filled with red, yellow, green, and blue beads worth, respectively, 7, 5, 3, and 2 points each. A number of beads are then removed from the container. If the product of the point values of the removed beads is 30,870,000, how many red beads were removed?\n\n### Options:\nA. 1\nB. 2\nC. 3\nD. 4\nE. 5\n\n### Answer:\n30,870,000\n= 2^4 * 5^4 * 3087\n= 2^4 * 3 * 5^4 * 1029\n= 2^4 * 3^2 * 5^4 * 343\n= 2^4 * 3^2 * 5^4 * 7^3\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA can do a work in 6 days. B can do the same work in 8 days. Both A&B together will finish the work and they got $1000 from that work. Find their shares?\n\n### Options:\nA. 600,400\nB. 600,800\nC. 300,700\nD. 800,200\nE. 550,450\n\n### Answer:\nRatio of their works A:B = 6:8\nRatio of their wages A:B = 3:4\nA's share = (3/5)1000 = 600\nB's share = (4/5)1000 = 800\ncorrect option is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOn a game show, a contestant spins three four wheels; each wheel is numbered 1 to 7. What is the probability that the contestant will spin all tens?\n\n### Options:\nA. 1/2401\nB. 2/5\nC. 1\nD. 9\nE. 63\n\n### Answer:\nAll 7s:\n1st wheel = 7= 1/7\n2nd wheel = 7 = 1/7\n3rd wheel = 7 = 1/7\n4th wheel = 7 = 1/7\n(1/7)(1/7)(1/7)(1/7) = 1/2401\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA and B together can do a work In 4 days. A alone can do it in 12 days. What time B will take to do the work alone?\n\n### Options:\nA. 6 days\nB. 8 days\nC. 12 days\nD. 10 days\nE. 5 days\n\n### Answer:\nExplanation:\nA and B 1day's work = 1/6\nA alone can do 1day's work = 1/12\nwhat time B will take to do the work alone?\nB = (A+B) - A = (1/6) - (1/12) = 12 Days\nAnswer: Option C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA metallic sphere of radius 12 cm is melted and drawn into a wire, whose radius of cross section is 16 cm. What is the length of the wire?\n\n### Options:\nA. 6\nB. 7\nC. 8\nD. 9\nE. 10\n\n### Answer:\nVolume of the wire (in Cylindrical shape) is equal to the volume of the sphere.\n\u03c0(16)2 * h = (4/3)\u03c0 (12)3 => h = 9 cm\nAnswer: Option E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA student has to select 3 subject out of 6 subjects M,B,H,U,L. If he has chosen M, what is the probability of B being chosen ?\n\n### Options:\nA. 2/5\nB. 1/5\nC. 3/5\nD. 7/5\nE. None of these\n\n### Answer:\nExplanation :\nOut of 6 subjects, one subject M has already been chosen. Ramaining 2 subjects are to be choden from rest (6-1) i.e 5 subjects.\nWithout restriction, no. of selections = 5C2.\nWith restriction, no. of selection of B from rest 4 subject = 4C1.\n=> Probability\n= Selections with restriction / Selections without restriction\n= 4C1 / 5C2 .\n= 2 / 5.\nHence, the probability of subject B being chosen is 2 / 5.\nAnswer : A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThree cards are drawn successively, without replacement from a pack of 52 well shuffled cards.\nWhat is the probability that first two cards are queens and the third card drawn is an ace?\n\n### Options:\nA. 2/5525\nB. 3/5525\nC. 2/5525\nD. 2/5526\nE. 4/5525\n\n### Answer:\nLet Q denote the event that the card drawn is queen and A be the event that\nthe card drawn is an ace. Clearly, we have to find P (QQA)\nNow P(Q) = 4/52\nAlso, P (Q|Q) is the probability of second queen with the condition that one queen has\nalready been drawn. Now there are three queen in (52 - 1) = 51 cards.\nTherefore P(Q|Q) = 3/51\nP(A|QQ) is the probability of third drawn card to be an ace, with the condition\nthat two queens have already been drawn. Now there are four aces in left 50 cards.\nTherefore P(A|QQ) = 4/50\nBy multiplication law of probability, we have\nP(QQA) = P(Q) P(Q|Q) P(A|QQ)\n= 4/52 \u00d7 3/51 \u00d7 4/50\n= 2/5525.\nA)\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the average marks of all the students in 2 separate classes, if the average marks of students in the first class of 58 students is 67 and that of another class of 52 students is 82.\n\n### Options:\nA. 74.1\nB. 56.3\nC. 67.8\nD. 79.7\nE. 19.4\n\n### Answer:\nSum of the marks for the class of 58 students = 58 * 67 = 3886\nSum of the marks for the class of 52 students = 52 * 82 = 4264\nSum of the marks for the class of 110 students =\n3886 + 4262 = 8150\nAverage marks of all the students = 4200/80\n= 74.1\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are 12 balls in a jar: 6 red, 2 blue and 4 green. If a single ball is drawn from the jar, what is the probability of that it is either blue or red?\n\n### Options:\nA. 1/12\nB. 1/4\nC. 1/2\nD. 2/3\nE. 3/4\n\n### Answer:\nBlue + Red =8\nTotal number of balls is 6+2+4=12\nSo the answer is 8/12=2/3\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a certain code language, '3a, 2b, 7c' means 'Truth is Eternal';\n'7c, 9a, 8b, 3a' means 'Enmity is not Eternal' and\n'9a, 4d, 2b, 8b' means 'Truth does not perish'.\nWhich of the following means 'enmity' in that language ?\n\n### Options:\nA. 3\nB. 9\nC. 8\nD. 6\nE. 2\n\n### Answer:\nExplanation:\nJustification:\nIn the second and third statements, the common code is '9a' and the common word is 'not'.\nSo, '9a' means 'not'.\nIn the first and second statements, the common codes are '7c' and '3a' and the common words are 'is' and 'Eternal'.\nSo, in the second statement, '8b' means 'enmity'.\nAnswer: C) 8b\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe price of commodity X increases by 40 cents every year, while the price of commodity Y increases by 15 cents every year. In 2001, the price of commodity X was $4.20 and the price of commodity Y was $6.30. In which year will the price of commodity X be 15 cents more than the price of commodity Y?\n\n### Options:\nA. 2010\nB. 2011\nC. 2012\nD. 2013\nE. 2014\n\n### Answer:\nThe price of commodity X increases 25 cents each year relative to commodity Y.\nThe price difference is $2.10 and commodity X needs to be 15 cents more than commodity Y.\n$2.25 / 25 cents = 9 years\nThe answer is 2001 + 9 years = 2010.\nThe answer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain business produced x rakes each month form November through February and shipped x/2 rakes at the beginning of each month from March through October. The business paid no storage costs for the rakes from November through February, but it paid storage costs of $0.50 per rake each month from March through October for the rakes that had not been shipped. In terms of x, what was the total storage cost, in dollars, that the business paid for the rakes for the 12 months form November through October?\n\n### Options:\nA. 0.40x\nB. 1.20x\nC. 1.40x\nD. 1.60x\nE. 3.20x\n\n### Answer:\nbecause we have a total of 4X\nAlso from Mar- Oct the rakes will be deducted by 1/8 X\nso\nIn Apr they pay for the storage 0.5 * 4X * 7/8\nIn May they pay for the storage 0.5 * 4X * 6/8\nIn Jun they pay for the storage 0.5 * 4X * 5/8\nIn Jul they pay for the storage 0.5 * 4X * 4/8\nIn Aug they pay for the storage 0.5 * 4X * 3/8\nIn Sep they pay for the storage 0.5 * 4X * 2/8\nIn Oct they pay for the storage 0.5 * 4X * 1/8\ntotal = 0.5 * 4X * 1/8 * [ 1+2+3+4+5+6+7]\n= 0.5 * X/2 * (28)\n= 7.0X\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe product of the squares of two positive integers is 9. How many pairs of positive integers satisfy this condition?\n\n### Options:\nA. 0\nB. 1\nC. 2\nD. 3\nE. 4\n\n### Answer:\nAns:B - 1 pairs\n(x\u02c62)(y\u02c62) = 9 [square root both sides]\nxy = 3\n3 = 1x3, 3x1\nCancel the repeats\nThis leaves us with exactly 1 options.\nHence, B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a question on division with zero remainder, a candidate took 12 as divisor instead of 21. The quotient obtained by him was 35. The correct quotient is/\n\n### Options:\nA. 20\nB. 22\nC. 24\nD. 26\nE. 27\n\n### Answer:\nNumber = (35 * 12) = 420\nCorrect quotient = 420/21 = 20\nA)\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average earning of amechanic for the first 4days of a week is Rs.53 and for the last four days is Rs.22. If heearns Rs.20 on the fourth day, his average earning forthe whole week is?\n\n### Options:\nA. s. 10\nB. s. 20\nC. s. 30\nD. s. 40\nE. s. 50\n\n### Answer:\nTotal earning for the week = Sum of earning of first four days + Sum of earning of last four days - Earning of 4th day\n= 4 x 53 + 4 x 22 -20\n= Rs. 280\n\u00e2\u02c6\u00b4 Average earning = 280/ 7\n= Rs. 40\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf I walk at 5 km/h, I miss the bus by 12 minutes. If I walk at 6 km/h, I reach 15 minutes before the arrival of the bus. How far I walk to reach the bus stand ?\n\n### Options:\nA. 11.0 km\nB. 13.8 km\nC. 11.5 km\nD. 12.5 km\nE. 13.5 km\n\n### Answer:\nd = product of speed difference of time /difference of speed\nd = 5x6/60[12\u00e2\u02c6\u2019(\u00e2\u02c6\u201915)/6-5]\n[Here, \u00e2\u20ac\u201cve sign indicates before the schedule time]\n\u00e2\u2021\u2019 d = 13.5 km\nAnswer E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA case contains c cartons. Each carton contains b boxes, and each box contains 400 paper clips. How many paper clips are contained in 2 cases?\n\n### Options:\nA. 400bc\nB. 400b/c\nC. 800bc\nD. 800b/c\nE. 800/bc\n\n### Answer:\n2 cases * c cartons/case * b boxes/carton * 400 clips/box = 800bc paper clips\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man can row upstream at 25 kmph and downstream at 45 kmph, and then find the speed of the man in still water?\n\n### Options:\nA. 65\nB. 86\nC. 35\nD. 78\nE. 38\n\n### Answer:\nUS = 25\nDS = 45\nM = (45 + 25)/2\n= 35\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a group of 25 factory workers, 13 have brown eyes. Six of the women do not have brown eyes. How many of the 11 men have brown eyes.\n\n### Options:\nA. 10\nB. 9\nC. 8\nD. 7\nE. 5\n\n### Answer:\nTotal number of worker (M+W): 25\nNo. of men (M): 11 (Inferred fromHow many of the 11 men)\nNo. of women (W): 14\nTotal no. of workers who have brown eyes (B): 13\nNo. of women who do not have brown eyes: 6\nTherefore, no. of women who have brown eyes: W - 6 = 14 - 6 = 8\nRemaining 5 are men. (B - 8= 13 - 8= 5)\nSo 5 out of 11 men have brown eyes.\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\na man have 4 goat,2 sheep and 3 buffalo.he have to take three cattle out one each.with two available door.in how many ways he can out three cattle?\n\n### Options:\nA. 72\nB. 12\nC. 36\nD. 48\nE. 24\n\n### Answer:\nfrom, fundamental principle of calculate\nsimple,4*2*3*2=48ways\nanswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo trains are running at 40 km/hr and 20 km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 8 sec. What is the length of the fast train?\n\n### Options:\nA. 27 7/6\nB. 277/5\nC. 27 7/2\nD. 400/9\nE. 27 7/1\n\n### Answer:\nRelative speed = (40 - 20) = 20 km/hr.\n= 20 * 5/ 18 = 50/9 m/sec.\nLength of faster train = 50/9 * 8 = 400/9\n= 27 7/9 m.\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhen 2/9 of the votes on a certain resolution have been counted, 3/4 of those counted are in favor of the resolution. What fraction w of the remaining votes must be against the resolution so that the total count will result in a vote of 2 to 1 against the resolution?\n\n### Options:\nA. 11/14\nB. 13/18\nC. 4/7\nD. 3/7\nE. 3/14\n\n### Answer:\nIf we use variable for total votes there will be too many fractions to manipulate with, so pick some smart #: let set total # of votes is 18.\n2/9 of the votes on a certain resolution have been counted--> 4 counted and 18-4=14 votes left to be counted;\n3/4 of those counted are in favor of the resolution--> 3 in favor and 1 against;\nRatio of those who voted against to those who voted for to be 2 to 1 there should be total of 18*2/3=12 people who voted against, so in the remaining 14 votes there should be 12-1=11 people who voted against. Thus w=11/14 of the remaining votes must be against.\nAnswer: A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average salary of all the workers in a workshop is Rs.8000. The average salary of 7 technicians is Rs.14000 and the average salary of the rest is Rs.6000. The total number of workers in the workshop is\n\n### Options:\nA. 20\nB. 21\nC. 22\nD. 23\nE. 28\n\n### Answer:\nSolution\nLet the toatl number of workers be x.\nThen 8000x=(14000 x 7) + 6000 (x -7)\nx= 28.\nAnswer E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n. A car covers a distance of 742 km in 7 hours. Find its speed?\n\n### Options:\nA. 104\nB. 55\nC. 148\nD. 150\nE. 159\n\n### Answer:\n742/5 = 148 kmph\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe ratio between the presents of the A and B is 2:3. If B is 5 years older than A, what will be the ratio of the ages of A and B after 5 years?\n\n### Options:\nA. 3:4\nB. 1:2\nC. 2:3\nD. 5:6\nE. 1:3\n\n### Answer:\nLet A and B ages will be 2x and 3x\n3x - 2x = 5\nx = 5\nRequired ratio = 2x+5 : 3x+5 = 15:20 = 3:4\nAnswer is A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAt what time between 5 and 6 o' clock are the hands of a 3 minutes apart ?\n\n### Options:\nA. 24min\nB. 44min\nC. 14min\nD. 21min\nE. 74min\n\n### Answer:\nIn this type of problems the formuae is\n(5*x+ or - t)*12/11\nHere x is replaced by the first interval of given time. Here x is 5.\nt is spaces apart\nCase 1 : (5*x + t) * 12/11\n(5*5 + 3) * 12/11\n28 * 12/11 = 336/11= min\ntherefore the hands will be 3 min apart at 31 5/11 min past 5.\nCase 2 : (5*x - t) * 12/11\n(5*5 -3 ) * 12/11\n22 *12/11 = 24 min\ntherefore the hands will be 3 min apart at 24 min past 5\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nCan you replace the question mark with the correct number, given the pair of numbers exhibits similar relationship?\n? : 3839 :: 11 : 1209\n\n### Options:\nA. 6\nB. 16\nC. 26\nD. 36\nE. 46\n\n### Answer:\nFormular used :\npow(x,3) - pow(x,2) - 1\n11*11*11 - 11*11 - 1\n1331 - 121 - 1\n1209\nSimilarly, we can solve\npow($x,3) - pow($x,2) - 1 = 3839\nThis condition holds true for number-16.\ncorrect answer is B)16\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n(0.15)(power 3) - (0.1)(power 3)/ (0.15)(power 2) + 0.015 + (0.1)(power 2) is:\n\n### Options:\nA. 0.68\nB. 0.08\nC. 0.05\nD. 0.06\nE. None of them\n\n### Answer:\nGiven expression\n= (0.15) (power 3) - (0.1)(power 3) / (0.15)(power 2) + (0.15 x 0.1) + (0.1)(power 2)\n= a (power 3) - b(power 3) / a(power 2) + ab + b(power 2)\n= (a - b)\n= (0.15 - 0.1)\n= 0.05\nAnswer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhen positive integer n is divided by 5, the remainder is 1. When n is divided by 7, the remainder is 3. What is the smallest positive integer k such that k + n is a multiple of 70.\n\n### Options:\nA. 3\nB. 4\nC. 12\nD. 32\nE. 35\n\n### Answer:\nFirst, let us say I have a number n which is divisible by 5 and by 7. We all agree that it will be divisible by 35, the LCM of 5 and 7.\nNow, if I have a number n which when divided by 5 gives a remainder 1 and when divided by 7 gives a remainder 1, we can say the number is of the form\nn = 5a + 1 e.g. 5 + 1, 10 + 1, 15 + 1, 20 + 1, 25 + 1, 30 + 1, 35 + 1 etc\nand\nn = 7b + 1 e.g. 7 + 1, 14 + 1, 21 + 1, 28 + 1, 35 + 1 etc\nSo when it is divided by the LCM, 35, it will give 1 as remainder (as is apparent above)\nNext, if I have a number n which when divided by 5 gives a remainder 1 and when divided by 7 gives a remainder 3, we can say the number is of the form\nn = 5a + 1\nand\nn = 7b + 3\nNow, the only thing you should try to understand here is that when n is divided by 5 and if I say the remainder is 1, it is the same as saying the remainder is -4. e.g. When 6 is divided by 5, remainder is 1 because it is 1 more than a multiple of 5. I can also say it is 4 less than the next multiple of 5, can't I? 6 is one more than 5, but 4 less than 10.\nTherefore, we can say n = 5x - 4 and n = 7y - 4 (A remainder of 3 when divided by 7 is the same as getting a remainder of -4)\nNow this question is exactly like the question above. So when you divide n by 70, remainder will be -4 i.e. n will be 4 less than a multiple of 70. So you must add 4 to n to make it a multiple of 70\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA bat is bought for Rs.400 and sold at a gain of 20% find its selling price\n\n### Options:\nA. Rs.430/-\nB. Rs.480/-\nC. Rs.400/-\nD. Rs.580/-\nE. Rs.600/-\n\n### Answer:\n100 % ------> 400 (100 * 4 = 400)\n120 % ------> 480 (120 * 4 = 480)\nSelling price = Rs.480/-\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that atleast one bulb is good.\n\n### Options:\nA. 125/129\nB. 125/121\nC. 125/126\nD. 125/122\nE. 125/124\n\n### Answer:\nExplanation:\nRequired probability = 1 - 1/126 = 125/126\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are two examinations rooms A and B. If 10 students are sent from A to B, then the number of students in each room is the same. If 20 candidates are sent from B to A, then the number of students in A is double the number of students in B. The number of students in room A is?\n\n### Options:\nA. 128\nB. 276\nC. 100\nD. 277\nE. 110\n\n### Answer:\nLet the number of students in rooms A and B be x and y respectively.\nThen, x - 10 = y + 10 \u21d2 x - y = 20 .... (i)\nand x + 20 = 2(y - 20) \u21d2 x - 2y = -60 .... (ii)\nSolving (i) and (ii) we get: x = 100 , y = 80.\n\u2234 The required answer A = 100.\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe sum of three consecutive even numbers is 42. Find the middle number of the three?\n\n### Options:\nA. 14\nB. 15\nC. 52\nD. 25\nE. 32\n\n### Answer:\nAnswer: Option A\nThree consecutive even numbers (2P - 2), 2P, (2P + 2).\n(2P - 2) + 2P + (2P + 2) = 42\n6P = 42 => P = 7.\nThe middle number is: 2P = 14.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn an exam, Amar scored 64 percent, Bhavan scored 36 percent and Chetan 44 percent. The maximum score awarded in the exam is 800. Find the average mark scored by all the three boys?\n\n### Options:\nA. 384\nB. 656\nC. 443\nD. 324\nE. 534\n\n### Answer:\nAverage mark scored by all the three boys =\n[64/100 (800) + 36/100 (800) + 44/100 (800)] / 3 = 384\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a box, there are 3 grey, 5 brown and 2 yellow pencils. One pen is picked up randomly. What is the probability that it is neither brown nor yellow?\n\n### Options:\nA. 2/5\nB. 3/5\nC. 3/10\nD. 3/4\nE. 3/11\n\n### Answer:\nExplanation :\nNeither brown nor yellow means the pencils drawn is grey.\nTotal number of outcomes = (3+5+2) = 10.\nNumber of Favourable outcomes = 3 = Number of grey pencils.\nHence, Probability of the event = 3/10 = 3/10.\nAnswer : C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA sum was put at simple interest at certain rate for 3 years. Had it been put at 1% higher rate it would have fetched Rs. 66 more. The sum is: A. Rs. 2,400 B. Rs. 2,100 C. Rs. 2,200 D.Rs. 2,480\n\n### Options:\nA. 2000\nB. 2100\nC. 2200\nD. 2300\nE. 2400\n\n### Answer:\n1 percent for 3 years= 66\n1 percent for 1 year = 22\n=> 100 percent = 2200\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOf the three-digit integers greater than 800, how many have two digits that are equal to each other and the remaining digit different from the other two?\n\n### Options:\nA. 90\nB. 82\nC. 80\nD. 45\nE. 36\n\n### Answer:\nLet the three digit number be represented as X Y Z.\nThere are 3 cases:\nCase I.[ X=Y ]Z is not equal to XY :XXZorYYZ\nX can be either 7, 8 or 9, so digit at X can be chosen in 3 ways\nAfter X is chosen, Y can be chosen in 1 way\nAfter XY are chosen, Z can be chosen in 9 ways\nThus, possible No of digits = (3 ways) * (1 way) * (9 ways) = 27 ....(1)\n[example numbers: 774,779,882,993 etc]\nCase II.[ X=Z ]Y is not equal to XZ:XYXorZYZ\nX can be either 7, 8 or 9, so digit at X can be chosen in 3 ways\nAfter X is chosen, Z can be chosen in 1 way\nAfter XZ are chosen, Z can be chosen in 9 ways\nThus, possible No of digits = (3 ways) * (9 ways) * (1 way) = 27 ....(2)\n[example numbers: 747,797,828,939 etc]\nCase III.[ Y =Z ]X is not equal to YZ :XYYorXZZ\nX can be either 7, 8 or 9, so digit at X can be chosen in 3 ways\nAfter X is chosen, Y can be chosen in 9 ways\nAfter Y is chosen, Z can have 1 way\nThus, possible No of digits = (3 ways) * (1 way) * (9 ways) = 27 ....(3)\n[example numbers: 744,799,822,933 etc]\nTherefore, total numbers of possible digits [sum of Case (1), (2)(3) above] = 27 + 27 + 27 - 1 = 80\nOne digit is subtracted from total number of possible digits to eliminate one possibility of XYZ = 700 to satisfy the condition that digit > 800.\nAnswer:(B)\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRoberto has three children: two girls and a boy. All were born on the same date in different years. The sum of the ages of the two girls today is smaller than the age of the boy today, but a year from now the sum of the ages of the girls will equal the age of the boy. Three years from today, the difference between the age of the boy and the combined ages of the girls will be\n\n### Options:\nA. 1\nB. 2\nC. 3\nD. \u20132\nE. \u20131\n\n### Answer:\ngirl1: g1, girl2: g2, boy:b, these are the symbols for their ages today.\ng1+g2", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a light flashes every 6 seconds, how many times will it flash in 2/5 of an hour?\n\n### Options:\nA. 181\nB. 211\nC. 241\nD. 271\nE. 301\n\n### Answer:\nIn 2/5 of an hour there are 24*60 = 1440 seconds\nThe number of 6-second intervals = 1440/6 = 240\nAfter the first flash, there will be 240 more flashes for a total of 241.\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJohn walking at 4 Kmph reaches his office 8 minutes late. If he walks at 6 Kmph, he reaches there 10 minutes earlier. How far is the office from his house?\n\n### Options:\nA. 3 2/5 Km\nB. 3 3/5 Km\nC. 4 1/5 Km\nD. 5 1/5 Km\nE. None\n\n### Answer:\nFormula = S1*S2/S2-S1 * T1+T2/60\n= 4*6/2 * 18/6\n= 24/2 * 18/60\n= 18/5 = 3 3/5 Km\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn an election, candidate X got 75% of the total valid votes. If 15% of the total votes were declared invalid and the total numbers of votes is 560000, find the number of valid vote polled in favour of candidate?\n\n### Options:\nA. 280000\nB. 300000\nC. 355000\nD. 356000\nE. 357000\n\n### Answer:\nTotal number of invalid votes = 15 % of 560000\n= 15/100 \u00d7 560000\n= 8400000/100\n= 84000\nTotal number of valid votes 560000 \u2013 84000 = 476000\nPercentage of votes polled in favour of candidate X = 75 %\nTherefore, the number of valid votes polled in favour of candidate X = 75 % of 476000\n= 75/100 \u00d7 476000\n= 35700000/100\n= 357000\nE)\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThis is how Edward\u2019s Lotteries work. First, 9 different numbers are selected. Tickets with exactly 7 of the 9 numbers randomly selected are printed such that no two tickets have the same set of numbers. Finally, the winning ticket is the one containing the 7 numbers drawn from the 9 randomly. There is exactly one winning ticket in the lottery system. How many tickets can the lottery system print?\n\n### Options:\nA. 9C7\nB. 9P3\nC. 9C9\nD. 9C6\nE. 69\n\n### Answer:\nsince we have to select random 7 numbers from 9 and they all are distinct. i think it should be 9C7 or A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are seven thieves. They stole diamonds from a diamond merchant and ran away. While running, night sets in and they decide to rest in the jungle.\nWhen everybody was sleeping, two of them woke up and decided to divide the diamonds equally among themselves. But when they divided the diamonds equally, one diamond is left.\nSo they woke up the 3rd thief and tried to divide the diamonds equally again but still one diamond was left. Then they woke up the 4th thief to divide the diamonds equally again, and again one diamond was left. This happened with the 5th and 6th thief \u2013 one diamond was still left.\nFinally, they woke up the 7th thief and this time the diamonds were divided equally.\nHow many diamonds did they steal in total?\n\n### Options:\nA. 700\nB. 721\nC. 702\nD. 703\nE. None of the above\n\n### Answer:\nWe need a number that is a multiple of 7 that will give a remainder of 1 when divided by 2, 3, 4, 5, and 6. The least common multiple of these numbers is 60. So, we need a multiple of 7 that is 1 greater than a multiple of 60.\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf r = 2^4 * 5^2 * 7 and s = 2^3 * 3^2 * 5, which of the following is equal to the greatest common divisor of r and s?\n\n### Options:\nA. 2 * 5\nB. 2^2 * 5\nC. 2^3 * 5^2\nD. 2*3*5*7\nE. 2^3 * 3^2 * 5^2 * 7\n\n### Answer:\nGCD = product of prime factors raised to the least power = 2^3 * 5\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf x is negative and y is positive, which of the following cannot be positive?\n\n### Options:\nA. -xy\nB. x^2/y\nC. x^4/y\nD. -x^3*y\nE. -x/-y\n\n### Answer:\n- * - = +\n+ / - = -\n-x/-y is negative.\nAnswer : E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA window 2 inches wide is placed on the back of a rectangular painted area with dimensions 8 inches by 12 inches. What is the area of the window, in square inches?\n\n### Options:\nA. 44\nB. 96\nC. 128\nD. 144\nE. 168\n\n### Answer:\nThis question is an example of a 'punch out' question - we have to find the area of EVERYTHING, then 'punch out' the part that we don't want.\nWe're told that a window 2 inches wide is placed around a rectangular painted area with dimensions 8 inches by 12 inches. We're asked for the area of the window, in square inches.\nArea of a rectangle = (length)(width)\nSo the area of the window is... (8)(12) = 96\nThe window 'adds' 2 inches to the top, bottom, left and right 'sides' of the painted area, so the area of EVERYTHING is...\n(8+2+2)(12+2+2) = (12)(16) = 196\nWhen we 'punch out' the area of the painted area, we'll be left with the area of the window:\n192 - 96 = 96\nFinal Answer:\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind compound interest on Rs. 8000 at 15% per annum for 2 years 4 months, compounded annually.\n\n### Options:\nA. Rs 309\nB. Rs 319\nC. Rs 3109\nD. Rs 109\nE. Rs 209\n\n### Answer:\nTime = 2 years 4 months = 2(4/12) years = 2(1/3) years.\nAmount = Rs'. [8000 X (1+\u00ac(15/100))2 X (1+((1/3)*15)/100)]\n=Rs. [8000 * (23/20) * (23/20) * (21/20)]\n= Rs. 11109.\t.\n:. C.I. = Rs. (11109 - 8000) = Rs. 3109.\nANSWER C 3109\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo men starting from the same place walk at the rate of 5 kmph and 5.5 kmph respectively. What time will they take to be 5.5 km apart, if they walk in the same direction?\n\n### Options:\nA. 11 hrs\nB. 14 hrs\nC. 15 hrs\nD. 17 hrs\nE. None\n\n### Answer:\nSol.\nto be 0.5 km apart, they take 1 hour.\nTo be 5.5 km apart, they take [1/0.5 * 5.5] hrs = 11 hrs.\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain company assigns employees to offices in such a way that some of the offices can be empty and more than one employee can be assigned to an office. In how many ways can the company assign 4 employees to 2 different offices?\n\n### Options:\nA. 5\nB. 16\nC. 7\nD. 8\nE. 9\n\n### Answer:\nAns. Each employee can go into any of the two offices. Thus we have\n=> 2 * 2 * 2 * 2= 16\nAnswer : B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are 1500 jelly beans divided between two jars, Jar X and Jar Y. If there are 200 fewer jelly beans in jar X than three times the number of beans in jar Y, how many beans are in jar X?\n\n### Options:\nA. 1050\nB. 1075\nC. 1100\nD. 1125\nE. 1150\n\n### Answer:\nX+Y=1500 so Y=1500-X\nX=3Y-200\nX=3(1500-X)-200\n4X=4300\nX=1075\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA mixture of 150 liters of wine and water contains 20% water. How much more water should be added so that water becomes 25% of the new mixture?\n\n### Options:\nA. 87 liters\nB. 17 liters\nC. 10 liters\nD. 17 liters\nE. 16 liters\n\n### Answer:\nNumber of liters of water in150 liters of the mixture = 20% of 150 = 20/100 * 150 = 30 liters.\nP liters of water added to the mixture to make water 25% of the new mixture.\nTotal amount of water becomes (30 + P) and total volume of mixture is (150 + P).\n(30 + P) = 25/100 * (150 + P)\n120 + 4P = 150 + P => P = 10 liters.\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n16 people can write 52 book in 12 days working 8 hour a day.then in how many day 206 can be written by 64 people?\n\n### Options:\nA. 309/26\nB. 309/28\nC. 309/22\nD. 319/26\nE. 339/26\n\n### Answer:\nwork per day epr hour per person= 52/(12*8*16) // eq-1\npeople= 64; let suppose day=p; per day work for 8 hours\nacc. to condition\nwork per day epr hour per person= 206/(p*8*64) // eq-2\neq-1==eq-2;\np= 309/26\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the number 52,1n9, where n represents the tens digit, is a multiple of 3, then the value of n could be which of the following?\n\n### Options:\nA. 6\nB. 5\nC. 3\nD. 1\nE. 0\n\n### Answer:\nMaybe you are misreading the question but it is saying that 52,1n9 is a multiple of 3 and not necessarily n is a multiple of 3.\nThe sum of the digits 5 + 2 + 1 + n + 9 must be a multiple of 3\n17 + n must be a multiple of 3\nsubstituting the numbers n must = 1\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA car averages 65 mph for the first 5 hours of a trip and averages 75 mph for each additional hour. The average speed for the entire trip was 60 mph. How many hours long is the trip?\n\n### Options:\nA. 9\nB. 8\nC. 7\nD. 6\nE. 5\n\n### Answer:\nLet the time for which car averages 75 mph = t\n60*(t+5)= 65*4 + 70 t\n=>10t= 40\n=> t = 4\nTotal duration of the trip = 5+4=9\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA cube has a volume of 343 cubic feet. If a similar cube is twice as long, twice as wide, and twice as high, then the volume, in cubic feet of such cube is?\n\n### Options:\nA. 24\nB. 48\nC. 64\nD. 2744\nE. 100\n\n### Answer:\nVolume = 343 = side^3\ni.e. Side of Cube = 7\nNew Cube has dimensions 14, 14, and 14 as all sides are twice of teh side of first cube\nVolume = 14*14*14 = 2744 square feet\nAnswer: option D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf two dice are thrown together, the probability of getting an even number on one die and an odd number on the other is?\n\n### Options:\nA. 1/8\nB. 1/2\nC. 1/6\nD. 1/1\nE. 1/5\n\n### Answer:\nThe number of exhaustive outcomes is 36.\nLet E be the event of getting an even number on one die and an odd number on the other. Let the event of getting either both even or both odd then\n= 18/36 = 1/2\nP(E)\n= 1 - 1/2 = 1/2.\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA pair of prime numbers that can be expressed in the form {p, (p + 6)} is de\ufb01ned as a pair of \u201csexy primes.\u201d A \u201csexy triplet\u201d is a group of three primes that can be expressed in the form {p, (p + 6), (p + 12)}. All of the following prime numbers are the middle term of a sexy triplet EXCEPT\n\n### Options:\nA. 11\nB. 13\nC. 17\nD. 19\nE. 23\n\n### Answer:\n{x-6, x, x+6} all must be primes. Substitute options for x to check whether this will hold true. If x=19, then x+6=25, which is not a prime.\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf p and q are positive integers, how many integers are larger than pq and smaller than p(q + 5)?\n\n### Options:\nA. 3\nB. P + 2\nC. p \u2013 2\nD. 2p \u2013 1\nE. 5p - 1\n\n### Answer:\nThe number of integers between x and y, where x>y is (x-y)-1. For example, the number of integers between 1 and 5 is (5-1)-1=3: 2, 3, and 4.\nThus, the number of integers between pq and p(q+5)=pq+5p is (pq+5p-pq)-1=5p-1.\nAnswer: E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat will be the ans of that 126th term in the series abbcccdddd......???\n\n### Options:\nA. m\nB. n\nC. o\nD. q\nE. p\n\n### Answer:\nuse formula n(n+1)/2=126\n15*16=2*126\nso 15 th letter is p\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWorker A takes 8 hours to do a job. Worker B takes 10 hours to do the same Job.How long should it take both A and B, working together but independently, to do the same job?\n\n### Options:\nA. 40/9 days\nB. 9 days\nC. 40 days\nD. 94 days\nE. 7 days\n\n### Answer:\nA\u2019s 1 hour's work = 1/8\nB's 1 hour's work = 1/10\n(A + B)'s 1 hour's work = (1/8) +(1/10)=9/40\nBoth A and B will finish the work in 40/9 days.\nAns: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf annual decrease in the population of a town is 10% and the present number of people is 500 what will the population be in 1 year?\n\n### Options:\nA. 450\nB. 310\nC. 250\nD. 410\nE. 390\n\n### Answer:\nPopulation in 1 year = 500(1 - 10/100) = 500*90/100 = 450\nAnswer is A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nKamal started a business with Rs.25000 and after 4 months, Kiran joined him with Rs.60000. Kamal received Rs.58000 including 10% of profit as commission for managing the business. What amount did Kiran receive?\n\n### Options:\nA. 72000\nB. 720\nC. 82000\nD. 92000\nE. 7200\n\n### Answer:\nRatio of the profits = 25000*12 : 60000*8\n= 25*12 : 60*8\t= 5*3 : 12:2 = 5 : 4*2\n= 5:8\nLet the total profit = x.\nThen Kamal received 10x/100 = x/10 as commission for managing the business\nRemaining profit = x- x/10 = 9x/10 which is shared in the ration 5:8\nKamal's share = x/10 + (9x/10) * (5/13) = 58000\n=> x + 9x(5/13) = 580000\n=> x(1 + 45/13) = 580000\n=> x ( 58/13) = 580000\n=> x ( 1/13) = 10000\n=> x = 130000\nKiran's share = 130000 - 58000 = 72000\nAnswer is A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n5+8\n\n### Options:\nA. 8\nB. 13\nC. 28\nD. 6\nE. 2\n\n### Answer:\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA shopkeeper labeled the price of his articles so as to earn a profit of 30% on the cost price. He then sold the articles by offering a discount of 10% on the labeled price. What is the actual percent profit earned in the deal?\n\n### Options:\nA. 18%\nB. 20%\nC. 17%\nD. 18%\nE. None of these\n\n### Answer:\nExplanation:\nLet the CP of the article = Rs.100.\nThen labeled price = Rs.130.\nSP = Rs.130- 10% of 130 = Rs.130-13 = Rs.117.\nGain = Rs.117 \u2013 Rs.100 = Rs.17\nTherefore, gain/profit percent = 17%.\nAnswer: Option C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA can do a work in 6 days. B can do the same work in 4 days. Both A&B together will finish the work and they got $2000 from that work. Find their shares?\n\n### Options:\nA. 600,400\nB. 500,500\nC. 300,700\nD. 800,1200\nE. 550,1450\n\n### Answer:\nRatio of their works A:B = 6:4\nRatio of their wages A:B = 2:3\nA's share = (2/5)2000 = 800\nB's share = (3/5)2000 = 1200\ncorrect option is D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average age of husband, wife and their child 3 years ago was 27 years and that of wife and the child 5 years ago was 20 years. The present age of the husband is:\n\n### Options:\nA. 40\nB. 25\nC. 30\nD. 35\nE. 48\n\n### Answer:\nSum of the present ages of husband, wife and child = (27 * 3 + 3 * 3) = 90 years.\nSum of the present age of wife and child = (20 * 2 + 5 * 2) = 50 years.\nHusband's present age = (90 - 50) = 40 years.\nANSWER A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich of the following has the most number of divisors?\n\n### Options:\nA. 99\nB. 101\nC. 176\nD. 182\nE. 107\n\n### Answer:\n99 = 1 x 3 x 3 x 11\n101 = 1 x 101\n176 = 1 x 2 x 2 x 2 x 2 x 11\n182 = 1 x 2 x 7 x 13\nSo, divisors of 99 are 1, 3, 9, 11, 33, .99\nDivisors of 101 are 1 and 101\nDivisors of 176 are 1, 2, 4, 8, 11, 16, 22, 44, 88 and 176\nDivisors of 182 are 1, 2, 7, 13, 14, 26, 91 and 182.\nAnswer: Option C\nHence, 176 has the most number of divisors.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe amount of an investment will double in approximately 70/ p years, where p is the percent interest, compounded annually. If Thelma invests $ 40,000 in a long-term CD that pays 5 percent interest, compounded annually, what will be the approximate total value of the investment when Thelma is ready to retire 42 years later?\n\n### Options:\nA. $ 280,000\nB. $ 320,000\nC. $ 360,000\nD. $ 450,000\nE. $ 540,000\n\n### Answer:\nThe amount of an investment will double in approximately 70/ p years, where p is the percent interest, compounded annually. If Thelma invests $ 40,000 in a long-term CD that pays 5 percent interest, compounded annually, what will be the approximate total value of the investment when Thelma is ready to retire 42 years later?\nThe investment gets doubled in 70/p years. Therefore, the investment gets doubled in 70/5= every 14 years. After 42 years, the investment will get doubled 42/14= 3 times.\nSo the amount invested will get doubled thrice.\nSo, 40000 *2 = 80000\n80000*2 = 160000\n160000*2 = 320000\nHence, the answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf A speaks the truth 30% of the times, B speaks the truth 40% of the times. What is the probability that at least one will tell the truth\n\n### Options:\nA. 0.58\nB. 0.9\nC. 1.9\nD. 2.2\nE. 2.3\n\n### Answer:\nprobability of A speaks truth p(A)=3/10;false=7/10\nprobability of B speaks truth p(B)=4/10;false=6/10.For given qtn\nAns=1-(neither of them tell truth).Because A & B are independent events\n=1-[(7/10)*(6/10)]=1-42/100=1-0.42=0.58\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA rectangular-shaped carpet that measures x feet by y feet is priced at $50. What is the cost of the carpet, in dollars per square yard? (1 square yard = 9 square feet)\n\n### Options:\nA. xy/360\nB. 9xy/40\nC. 40xy/9\nD. 450xy\nE. 450/(xy)\n\n### Answer:\nThe area of the carpet in feet is xy.\nThe area in square yards is xy / 9.\nThe price per square yard is 50 / (xy/9) = 450/(xy).\nThe answer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAn office supply store stocks two sizes of notebooks, each in five colors: blue, green, yellow, red, or pink. The store packs the notebooks in packages that contain either 4 notebooks of the same size and the same color or 4 notebooks of the same size and of 4 different colors. If the order in which the colors are packed is not considered, how many different packages of the types described above are possible?\n\n### Options:\nA. 10\nB. 12\nC. 20\nD. 24\nE. 28\n\n### Answer:\nFirst let's consider the small notebooks.\nThere are 5 ways to choose notebooks of the same color.\nThe number of ways to choose four notebooks with different colors is 5C4=5.\nThere are 10 different packages we can make with the small notebooks.\nWe can use the same process to find 10 different packages with large notebooks.\nThe total number of different packages is 20.\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA store sells chairs and tables. If the price of 2 chairs and 1 table is 60% of the price of 1 chair and 2 tables, and the price of 1 table and 1 chair is $60, what is the price, in dollars, of 1 table? (Assume that every chair has the same price and every table has the same price.)\n\n### Options:\nA. 105/2\nB. 45\nC. 44\nD. 52\nE. 50\n\n### Answer:\nLET C= CHAIR ; T =TABLE\n2C+1T = 0.6 (1C + 2T) OR C( 2-0.6) = 1.2T -1T OR 1.4C = 0.2 T THEREFORE C= 0.2/1.4 T = 1/7 T\nIC +1T =60 OR 1/7T + 1T =60 THEREFORE T= 60*7/8 = 105/2\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo whales are moving in the same direction at 60 kmph and 42 kmph. The faster whale manages to cross the other whale in 14 seconds. Find the length of the faster whale in meters.\n\n### Options:\nA. 110 m\nB. 45 m\nC. 70 m\nD. 120 m\nE. 113 m\n\n### Answer:\nRelative speed = ( 60 - 42 ) * 5 / 18 = 5 mps.\nDistance covered in 14 seconds = 14 * 5 = 70 m.\nThe length of the faster whale = 70m.\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe length of a rectangular plot is thrice its width. If the area of the rectangular plot is 588 sq meters, then what is the width (in meters) of the rectangular plot?\n\n### Options:\nA. 14\nB. 16\nC. 18\nD. 20\nE. 22\n\n### Answer:\nArea = L*W = 3W^2 = 588\nW^2 = 196\nW = 14\nThe answer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average of a set of five distinct integers is 370. If each number is less than 2,000, and the median of the set is the greatest possible value, what is the sum of the two smallest numbers?\n\n### Options:\nA. -4,494\nB. -3,997\nC. -3,494\nD. -4,144\nE. The answer cannot be determined from the information given\n\n### Answer:\nSum of the set = 370*5=1850 Each number is less than 2000 and median of the set is the greatest possible value.\nTherefore last 3 numbers can be 1999,1998 and 1997. Their sum=5994.\nTherefore sum of two smallest numbers= 1850-5994= -4144\nAnswer=D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOf the goose eggs laid at a certain pond, 1/4 hatched and 4/5 of the geese that hatched from those eggs survived the first month. Of the geese that survived the first month, 3/5 did not survive the first year. If 120 geese survived the first year and if no more than one goose hatched from each egg, how many goose eggs were laid at the pond?\n\n### Options:\nA. 1200\nB. 1300\nC. 1400\nD. 1500\nE. 1600\n\n### Answer:\nLet x be the number of eggs that were laid.\n(2/5)(4/5)(1/4)x = 120\n(8/100)x = 120\nx = 1500\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe probability of having a girl is identical to the probability of having a boy. In a family with five children, what is the probability that all the children are of the same gender?\n\n### Options:\nA. 1/16\nB. 1/4\nC. 1/8\nD. 1/12\nE. 1/25\n\n### Answer:\nThere are two cases. All boys and all girls\ncase 1. all boys.\n1/2*1/2*1/2*1/2*1/2= 1/32\ncase 2 .all girls.\n1/2*1/2*1/2*1/2*1/2=1/32\nWe will add the cases to get 1/16\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA shopkeeper buys two articles for Rs.1000 each and then sells them, making 20% profit on the first article and 20% loss on second article. Find the net profit or loss percent?\n\n### Options:\nA. 200\nB. 88\nC. 77\nD. 66\nE. 51\n\n### Answer:\nProfit on first article = 20% of 1000 = 200.\nThis is equal to the loss he makes on the second article. That, is he makes neither profit nor loss.\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWorking in a South Side studio at a constant rate, Kanye can drop a full-length platinum LP in 5 weeks. Working at his own constant rate, Common can drop a full-length platinum LP in x weeks. If the two emcees work together at their independent rates, they can drop a full-length platinum compilation LP in 2 weeks. Assuming no efficiency is lost or gained from working together, how many weeks would it take Common, working alone, to drop a full-length platinum LP?\n\n### Options:\nA. 3 and 1/3 weeks\nB. 3 weeks\nC. 2 and 1/2 weeks\nD. 2 and 1/3 weeks\nE. 2 weeks\n\n### Answer:\nVERITAS PREPOFFICIAL SOLUTION:\nNow, while your instinct may be to Go! and speed through your initial read of this rate problem, remember: slow motion (is) better than no motion. As you read each sentence, you should start jotting down variables and relationships so that by the time you get to the question mark you have actionable math on your noteboard and you don\u2019t have to read the question all over again to get started. You should be thinking:\nWorking in a South Side studio at a constant rate, Kanye can drop a full-length platinum LP in 5 weeks.\nRate (K) = 1 album / 5 weeks\nWorking at his own constant rate, Common can drop a full-length platinum LP in x weeks.\nRate (C) = 1 album / x weeks\nIf the two emcees work together\u2026\nI\u2019m adding these rates, so their combined rate is 1/5 + 1/x\n\u2026they can drop a full-length platinum compilation LP in 2 weeks.\nAnd they\u2019re giving me the combined rate of 1 album / 2 weeks, so 1/5 + 1/x = 1/2\nAssuming no efficiency is lost or gained from working together, how many weeks would it take Common, working alone, to drop a full-length platinum LP?\nI\u2019m using that equation to solve for Common\u2019s time, so I\u2019m solving for x.\nNow by this point, that slow motion has paid off \u2013 your equation is set, your variable is assigned, and you know what you\u2019ve solving for. Your job is to solve for x, so:\n1/5 + 1/x = 1/2, so let\u2019s get the x term on its own:\n1/x = 1/2 \u2013 1/5. and we can combine the two numeric terms by finding a common denominator of 10:\n1/x = 5/10 \u2013 2/10\n1/x = 3/10, and from here you have options but let\u2019s cross multiply:\n10 = 3x, so divide both sides by 3 to get x alone:\n10/3 = x, and that doesn\u2019t look like the answer choices so let\u2019s convert to a mixed number: 3 and 1/3 (there\u2019s that number again), for answer choice A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a convention where they distributes prizes. In how many ways can 3 prizes be distributed among 4 boys when a boy gets any number of prizes?\n\n### Options:\nA. 58\nB. 60\nC. 64\nD. 68\nE. 90\n\n### Answer:\nIn this case, repetitions are allowed, so all the three prizes can be given in 4 ways, i.e. (4 x 4 x 4) ways = 4*3 ways = 64 ways\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA taxi company charges $1.25 for the first quarter of a mile and fifteen cents for each additional quarter of a mile. What is the maximum distance someone could travel with $4.90?\n\n### Options:\nA. 4 miles\nB. 4 1/4 miles\nC. 4 3/4 miles\nD. 5 1/2 miles\nE. 6 1/3 miles\n\n### Answer:\nIf we start out with $4.90 and have to spend $1.25 for the first quarter-mile, we will have $3.65 left to spend on quarter-mile intervals.\nSince $3.65/$0.15 = 24.33 we can buy 24.33 more quarter-miles, and will travel 25.33 quarter miles in all:\n25.33 \u00d7 1/4 =6 1/3 miles.\nThe correct answer is choice (E).\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo trains each 250 m in length are running on the same parallel lines in opposite directions with the speed of 90 kmph and 70 kmph respectively. In what time will they cross each other completely?\n\n### Options:\nA. 15 sec\nB. 19 sec\nC. 12 sec\nD. 10 sec\nE. 11.25 sec\n\n### Answer:\nExplanation:\nD = 250 m + 250 m = 500 m\nRS = 90 + 70 = 160 * 5/18 = 400/9\nT = 500 * 9/400 = 11.25 sec\nAnswer: Option E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the ratio in which rice at Rs. 7.20 a kg be mixed with rice at Rs. 5.70 a kg to produce a mixture worth Rs. 6.30 a kg.\n\n### Options:\nA. 2:7\nB. 2:3\nC. 2:0\nD. 2:1\nE. 2:2\n\n### Answer:\nExplanation:\nBy the rule of alligation:\nCost of 1 kg rice of 1st kind Cost of 1 kg rice of 2nd kind\n{\\color{Blue} \\therefore } Required ratio = 60 : 90 = 2 : 3\nAnswer: B) 2:3\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJadeja rented a power tool from a rental shop. The rent for the tool was $13 for the first hour and $8 for each additional hour. If Jadeja paid a total of $133, excluding sales tax, to rent the tool, for how many hours did she rent it?\n\n### Options:\nA. 14\nB. 19\nC. 16\nD. 13\nE. 12\n\n### Answer:\n13 + 8n = 133\nn = 15\nTotal time = n+1 hrs = 15+1 hrs = 16 hrs\nAnswer : C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nExactly 3/7 of the people in the room are under the age of 21, and exactly 5/10 of the people in the room are over the age of 65. If the total number of the people in the room is greater than 50 and less than 100, how many people in the room are under the age of 21?\n\n### Options:\nA. 21\nB. 35\nC. 39\nD. 30\nE. 65\n\n### Answer:\nThe total number of the people in the room must be a multiple of both 7 and 10 (in order 3/7 and 5/10 of the number to be an integer), thus the total number of the people must be a multiple of LCM of 7 and 10, which is 70.\nSince, the total number of the people in the room is greater than 50 and less than 100, then there are 70 people in the room.\nTherefore there are 3/7*70=30 people in the room under the age of 21.\nAnswer: D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn year Y imported machine tools accounted for 60 percent of total machine-tools sales in the United States, and Japanese imports accounted for 30 percent of the sales of imported machine tools. If the total sales of machine tools imported from Japan that year was x billion dollars, then the total sales of all machine tools in the United States was how many billion dollars?\n\n### Options:\nA. 55x/9\nB. 50x/9\nC. 60x/9\nD. 65x/9\nE. 75x/9\n\n### Answer:\nSales of imported tools = 60% of the total sales = 0.60*{total} = 3{total}/5;\nSales of Japanese tools = 30% of the sales of imported tools = 3/10*3{total}/5 = 9{total}/50.\nSince the sales of of Japanese tools was x, then 9{total}/50 = x -->9 {total} = 50x\n{total} = 50x/9\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAt what rate percent on simple interest will Rs.1750 amount to Rs.2000 in 4 years?\n\n### Options:\nA. 4 %\nB. 3.57 %\nC. 2 6/7 %\nD. 5 %\nE. 6 %\n\n### Answer:\nExplanation:\n250 = (1750x4xR)/100\nR = 3.57 %\nAnswer: Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf (5^5)(9^3)=3(15^x), what is the value of x?\n\n### Options:\nA. 5\nB. 9\nC. 11\nD. 13\nE. 15\n\n### Answer:\n(5^5)(9^3)=3(15^x)\n=> 5^5 * 3^6 = 3 * 3^x * 5^x\n=> 5^5 * 3^6 = 3^(x+1) * 5^x\nValue of x = 5\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nCity A to city B, Andrew drove for 1hr at 46 mph and for 3 hours at 60 mph. What was the average speed for the whole trip?\n\n### Options:\nA. 56.5\nB. 57.5\nC. 61\nD. 61.5\nE. 62.5\n\n### Answer:\nThe total distance is 1\u00d746+3\u00d760=226\nAnd the total time is 4 hours. Hence,\nAverage Speed=(Total Distance/Total Time)\n=226/4=56.5\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nGiven that x = 2^b \u2013 (8^35 + 16^5), which of the following values for b yields the lowest value for |x|?\n\n### Options:\nA. 104\nB. 105\nC. 106\nD. 107\nE. 125\n\n### Answer:\n8^35 + 16^5 = 2^105 + 2^20\nCompared to 2^105, the value of 2^20 is negligible.\n2^105 - (2^105 +2^20) will minimize the value of |x|.\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the odd pair of numbers\n1) 55 - 42\n2) 69 - 56\n3) 48 - 34\n4) 95 - 82\n5) 45 - 32\n\n### Options:\nA. 55-42\nB. 69-56\nC. 48-34\nD. 95-82\nE. 45-32\n\n### Answer:\nminus the numbers\n55-42=13\n69-56=13\n48-34=14\n95-82=13\n45-32=13\nhere 48-34 = 14 which is not similar to the other, so 48 - 34 is the odd pair of numbers. correct answer (C)\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA company, Chauncy Co., has an annual travel budget of $53,000. The accounting department estimates that transportation expenses will increase 5 percent in the coming year, and nontransportation travel expenses will increase by 15 percent in the coming year. Last year, Chauncy Co. spent $19,500 on transportation-related expenses, and $35,000 on nontransportation travel expenses. If the annual travel budget does not increase this year, and if the accounting department\u2019s estimates are correct, how far over the annual travel budget will expenses be this year?\n\n### Options:\nA. Expenses will not go over the budget.\nB. $500\nC. $4,225\nD. $7,725\nE. $60,725\n\n### Answer:\nannual travel budget of $53,000\nLet, Transportation expenses = T = 19500\nand Non-Transportation expenses = N=35000\ni.e. Increased Transportation expenses = 1.05T = 20475\nand Increased Non-Transportation expenses = 1.15N = 40250\nTotal Expense = 20475+40250 = 60725\nExpense over Budget = Budget - expense = 53000-60725 = 7725\nAnswer: Option D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nX can do a piece of work in 40days. He works at it for 8days and then Y finished it in 28 days. How long will Y take to complete the work?\n\n### Options:\nA. 10\nB. 12\nC. 15\nD. 18\nE. 35\n\n### Answer:\nWork done by X in 8days = 8*1/40 = 1/5\nRemaining work = 1 - 1/5 = 4/5\n4/5 work is done by Y in 28 days\nWhole work will be done by Y in 28*5/4 = 35 days\nAnswer is E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAt Jefferson Elementary School, the number of teachers and students (kindergarten through sixth grade) totals 510. The ratio of students to teachers is 16 to 1. Kindergarten students make up 1/4 of the student population and fifth and sixth graders account for 1/3 of the remainder. Students in first and second grades account for 1/4 of all the students. If there are an equal number of students in the third and fourth grades, then the number of students in third grade is how many greater or fewer than the number of students in kindergarten?\n\n### Options:\nA. 12 greater\nB. 17 fewer\nC. 28 fewer\nD. 36 fewer\nE. 52 fewer\n\n### Answer:\nSoln>> from the given ratio of 16:1 u can derive that ter are 480 students\nKG= 1/4 * 480 =120\n5th and 6th graders = 1/3 * 384= 128 (1/3 of remainder)\n1st and 2nd grade = 1/4 * 480 =120 ( 1/4 of all students)\nequal number of students in 3rd and 4th => 480 - 344= 136 and 136/2=68 each since equal number\n(344 is the sum of remaining students)\nthus 120-68 =52>>> therfore answer is 28 fewer\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf positive integer n is divisible by both 4 and 18, then n must be divisible by which of the following?\n\n### Options:\nA. 8\nB. 13\nC. 18\nD. 24\nE. 48\n\n### Answer:\nA number divisible by both 4,18 is 36 which s divisible by 18.\nIMO : Answer C 18\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train 575 m long crosses a tunnel of length 325 in 90 sec. What is the speed of the train in kmph.\n\n### Options:\nA. 28\nB. 32\nC. 36\nD. 24\nE. 30\n\n### Answer:\nTotal distance traveled = Length of train + Length of tunnel = 575 + 325 = 900\nTime taken to cross the tunnel = 90 sec.\nSpeed in kmph = distance/time *18/5 = 900/90 * 18/5\n= 180/5 = 36 kmph\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nY and Z are in a relay race. Y runs the first leg of the course in 58 seconds. Z runs the second leg of the course in 26 seconds. What was the average time they took to run a leg of the course?\n\n### Options:\nA. 39\nB. 40\nC. 41\nD. 42\nE. 43\n\n### Answer:\n(58 seconds +26 seconds)/2= 42 seconds\nCorrect option is: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTrain X crosses a stationary train Y in 60 seconds and a pole in 25 seconds with the same speed. The length of the train X is 300 m. What is the length of the stationary train Y?\n\n### Options:\nA. 185 m\nB. 420 m\nC. 167 m\nD. 176 m\nE. 168 m\n\n### Answer:\nLet the length of the stationary train Y be LY\nGiven that length of train X, LX = 300 m\nLet the speed of Train X be V.\nSince the train X crosses train Y and a pole in 60 seconds and 25 seconds respectively.\n=> 300/V = 25 ---> ( 1 )\n(300 + LY) / V = 60 ---> ( 2 )\nFrom (1) V = 300/25 = 12 m/sec.\nFrom (2) (300 + LY)/12 = 60\n=> 300 + LY = 60 (12) = 720\n=> LY = 720 - 300 = 420 m\nLength of the stationary train = 420 m\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe events A and B are independent, the probability that event A occurs is greater than 0, and the probability that event A occurs is twice the probability that event B occurs. The probability that at least one of events A and B occurs is 5 times the probability that both events A and B occur. What is the probability that event A occurs?\n\n### Options:\nA. 1/45\nB. 1/2\nC. 1/8\nD. 2/3\nE. 2/11\n\n### Answer:\nLet us say probability of A occuring is a.\nLet us say probability of B occuring is b.\na = 2b\nProbability (either A or B or both) = 5 times Probability (A and B)\na*(1-b) + b*(1-a) + ab = 5*ab\nSubstituting a=2b in the second equation:\n2b*(1-b) + b*(1-2b) + 2b*b = 5*2b*b\n3b-2b^2 = 110b^2\n3b = 12b^2\nb = 3/12 = 1/4\nSo, a = 2b = 1/2\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nlexus car agency has 135 cars.he sold some cars at 9% profit and rest at 36% profit thus he gains 17% on the sale of all his cars.the no. of cars sold at 36% profit is?\n\n### Options:\nA. 36\nB. 37\nC. 38\nD. 39\nE. 40\n\n### Answer:\nratio of 36% profit cars to 9% profit cars = 8:19\nso no. of cars sold at 36% profit = 135*8/27= 40 cars\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo pipes can fill a tank in 8 minutes and 5 minutes. An outlet pipe can empty the tank in 12 minutes. If all the pipes are opened when the tank is empty, then how many minutes will it take to fill the tank?\n\n### Options:\nA. 30 minutes\nB. 17 minutes\nC. 15 minutes\nD. 10 minutes\nE. 14 minutes\n\n### Answer:\nPart of the filled by all the three pipes in one minute\n= 1/8 + 1/5 - 1/12 = (15 + 24 - 10)/120 = 29/120\nSo, the tank becomes full in 14 minutes.\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n0.014\u00d70.014= ?\n\n### Options:\nA. 0.000196\nB. 0.00196\nC. 19.6\nD. 196\nE. NONE\n\n### Answer:\nSolution\nSum of decimals places= 6.\n14\u00d714\t= 196.\n= s0.014\u00d70.014\n= 0.000196\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwenty percent of the skiers that tried out for the ski patrol were selected. Of those that were not selected, 7 skiers were CPR certified and 17 were not. How many skiers tried out for the ski patrol?\n\n### Options:\nA. 30\nB. 50\nC. 60\nD. 70\nE. 80\n\n### Answer:\nNot Selected = 80%\nIf total is x.\nThen 0.8x=7+17=24\nx=30\nHence answer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n12, 14, x, 10\nThe median of the list of positive integers above is 11. Which of the following could be the average (arithmetic mean) of the list?\n\n### Options:\nA. 3\nB. 5.5\nC. 11\nD. 7\nE. 7.5\n\n### Answer:\nGivenThe median of the list of positive integers above is 11\nSo arranging the numbers from lowest to highest, avg of 2 middle terms needs to be 11\nso the sequence will be x 10 12 14\nLets say x = 8, which gives us mean = sum/4 = 11\nC is correct\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the compound interest on $ 56,000 at 20% per annum for 9 months, compounded quarterly\n\n### Options:\nA. 2532\nB. 2552\nC. 6524\nD. 8827\nE. 9512\n\n### Answer:\nPrincipal = $ 56000; Time = 9 months =3 quarters;\nRate = 20% per annum = 5% per quarter.\nAmount = $ [56000 x (1+(5/100))^3] = $ 64827.\nCI. = $ (64827 - 56000) = $ 8827.\nAnswer D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n111 = O\n222 = E\n333 = T\n444 = S\nReading and analyzing the above, can you find out the following ?\n555 = ?\n\n### Options:\nA. J\nB. A\nC. M\nD. K\nE. O\n\n### Answer:\nE\nO\n1 * 1 * 1 = One\n2 * 2 * 2 = Eight\n3 * 3 * 3 = Twenty seven\n4 * 4 * 4 = Sixty Four\nFor all the above, you can see that the first letter of the sum is the code.\nThus 5 * 5 * 5 = One twenty five\nThus 555 = O.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf x is the median of the set {8/2, 11/3, 27/9, 21/5, x}, x could be\n\n### Options:\nA. 4\nB. 17/5\nC. 16/5\nD. 30/7\nE. 31/7\n\n### Answer:\nThe median is the middle number once all the numbers are arranged in increasing/decreasing order.\nWe see that\n11/3 = 3.something,\n28/9 = 3.something\n21/5 = 4.something\n9/2 = 4.something\nSo x should greater than the smallest two numbers and smaller than the greatest two numbers. We can see that x = 4 is possible. (First look at the simplest option or the middle option since options are usually arranged in increasing/decreasing order)\nAnswer (A)\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a series of six consecutive even numbers, the sum of the second and sixth numbers is 24. What is the fourth number?\n\n### Options:\nA. 8\nB. 12\nC. 6\nD. 14\nE. None of these\n\n### Answer:\nLet the numbers be x, x + 2, x + 4, x + 6, x + 8 and x + 10.\nGiven (x + 2) + (x + 10) = 24\n=> 2x + 12 = 24 => x = 6\nThe fourth number = x + 6 = 6 + 6 = 12.\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAnne traveled from City A to City B in 4 hours, and her speed was between 35 miles per hour and 50 miles per hour. John traveled from City A to City B along the same route in 2 hours, and his speed was between 50 miles per hour and 90 miles per hour. Which of the following could be the distance, in miles, from City A to City B?\n\n### Options:\nA. 95\nB. 115\nC. 125\nD. 135\nE. 170\n\n### Answer:\nIn four hours Anne must travel 4 times her speed\nso Anne's possible distances =\n4(35 -50) or 140-200 miles\nin two hours John travels 2 times his speed or\n2(50-90) or 100-180 miles\nthe statement is only true if both distances are possible,\nso you can tell its between or equal to\n140-180\nE is the answer.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n7 speakers gathered to deliver speeches on two topics. Even though 7 speeches were initially planned to be delivered, due to lack of time only 2 speeches were finally decided to be delivered. Topics are to be spoken in a specific order and the speeches differ with respect to speaker or topic. How many such two speeches are possible?\n\n### Options:\nA. 2\nB. 49\nC. 50\nD. 47\nE. 1024\n\n### Answer:\n1)there are 7 speeches in ONE topic and 7 in OTHER..\n2)there is a specific order for topics, so\na) both the topics are to be spoken on- so ONE from each\nb) the order does not matter since there is ONLY one specific order..\nso 7C1\u22177C1=7\u22177=49\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a certain city, 60% of the registered voters are democrats and the rest are republicans.In a mayoral race, if 75% of the registered voters who are democrats and 20% of the registered voters who are republicans are expected to vote for candidate A,What % of the registered voters are expected to vote for candidate A?\n\n### Options:\nA. 50%\nB. 53%\nC. 54%\nD. 55%\nE. 57%\n\n### Answer:\nLet total voters = 100\nso D= 60, vote for the mayor 60*75%=45 (60*3/4)\nR= 40, vote for the mayor 40*20%= (40*1/5)\n45+8=53\n53/100*100=53%\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAverage of five numbers is 12, and the sum of three of the numbers is 39, what is the average of the other 2 numbers?\n\n### Options:\nA. 9.5\nB. 8.5\nC. 7.5\nD. 11.5\nE. 10.5\n\n### Answer:\nLet the five numbers be a, b, c, d, e. Then their average is (a+b+c+d+e)/5=12\ra+b+c=39\r(39+d+e)/5=12\r39+d+e=60\rd+e=21\raverage=21/2=10.5\rAns E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man rides at the rate of 20km/hr. But stops 20minutes to change horses at the end of every 30th kilometer. How long will he take to go a distance of 120 kilometers?\n\n### Options:\nA. 5hr\nB. 6hr 30min\nC. 8hr 10min\nD. 7hr\nE. 9hr\n\n### Answer:\nspeed of man = 20km/hr\nnumber of rests = (120/30)-1 = 3\ntime taken for the man = (120/20)+3*(20/60) = 7 hr\nAnswer is D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo trains are moving at 50 kmph and 70 kmph in opposite directions. Their lengths are 170 m and 100 m respectively. The time they will take to pass each other completely is?\n\n### Options:\nA. 3 sec\nB. 8 sec\nC. 9 sec\nD. 5 sec\nE. 7 sec\n\n### Answer:\n70 + 50 = 120 * 5/18 = 100/3 mps\nD = 170 + 100 = 270 m\nT = 270 * 3/100 = 8 sec\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many distinct four-digit numbers can be formed by the digits {1, 2, 3, 4, 5, 5, 6, 6}?\n\n### Options:\nA. 280\nB. 360\nC. 486\nD. 560\nE. 606\n\n### Answer:\nOption 1: each group of 4 different digits will produce 4!=24 four-digit numbers\n- Option 2: each group of 4 digits that contains two 5's will produce 4!/2=12 four-digit numbers\n- Option 3: same with option 2 -> 4!/2=12 four-digit numbers\n- Option 4: 4!/4=6 four-digit numbers\nIn total, there are: 15*24 + 10*12 + 10*12 + 1*6 = 606 four-digit numbers.\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train sets off at 2 p.m. at the speed of 70 kmph. Another train starts at 4:00 p.m. in the same direction at the rate of 85 kmph. At what time the trains will meet?\n\n### Options:\nA. 10.18 p.m\nB. 11.00 p.m\nC. 10.30 p.m\nD. 10.38 p.m\nE. 10.32 p.m\n\n### Answer:\nD = 70 * 1 \u00bd = 105 km\nRS = 85 \u2013 70 = 15\nT = 105/15 = 7 h\n4.00 + 7 h = 11.00 p.m.\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 5 toys cost Rs, 234, what do 35 toys cost?\n\n### Options:\nA. 1645\nB. 1564\nC. 1546\nD. 1638\nE. None of them\n\n### Answer:\nLet the required cost be Rs. x. Then,\nMore toys, More cost\t(Direct Proportion)\n= x=(35 X 234)/5 =1638\nAnswer is D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain characteristic in a large population has a distribution that is symmetric about the mean m. 60 percent of the distribution lies within one standard deviation d of the mean. If the shelf\u2019s average life is 7.2 years and the standard deviation is 2.8 years, what percent of the distribution has more than 10.0 years as a shelf\u2019s average life?\n\n### Options:\nA. 10%\nB. 12%\nC. 14%\nD. 15%\nE. 17%\n\n### Answer:\nAverage = 7.2\nSD = 2.8\n7.2 - 2.8 < 60% of distribution < 7.2 + 2.8\n4.4 < 60% of distribution < 10.0\n30% is outside this range.\nGiven: Distribution is symmetric. So 15% of distribution is less than 7.5 and the other 15% of distribution is greater than 10.0.\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n81,162,49,98,25,50,64\n\n### Options:\nA. 126\nB. 127\nC. 129\nD. 128\nE. 131\n\n### Answer:\n81*2=162\n49*2=98\n25*2=50\n64*2=128\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average of first ten prime numbers which are odd is?\n\n### Options:\nA. 15.5\nB. 15.7\nC. 15.2\nD. 15.8\nE. 15.1\n\n### Answer:\nSum of first 10 prime no. which are odd = 158\nAverage = 158/10 = 15.8\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf A : B= 1 : 2 and B : C = 3 : 4, then A : B : C is:\n\n### Options:\nA. 9:6:4\nB. 1:2:3\nC. 3:6:9\nD. 12:25:87\nE. 3:5:7\n\n### Answer:\nA:B=1:2, B:C=3:4, A:B:C=3\u00c3\u20143:3\u00c3\u20142:1\u00c3\u20144\n\u00e2\u2021\u2019 9:6:4\nAnswer: A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe no. of girls in a class are seven times the no. of boys, which value cannever be the of total students?\n\n### Options:\nA. 23\nB. 25\nC. 30\nD. 36\nE. 39\n\n### Answer:\nLet the boys are X, then girls are 7X, total = X+7X = 8X\nSo it should be multiple of 8, 30 is not a multiple of 8.\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nhree persons A, B and C divide a certain amount of money such that A's share is Rs. 4 less than half of the total amount, B's share is Rs. 8 more than half of what is left and finally C takes the rest which is Rs. 14. Find the total amount they initially had with them?\nA. Rs. 61 B. Rs. 85\n\n### Options:\nA. 20\nB. 20\nC. 30\nD. 80\nE. 33\n\n### Answer:\nLet the total amount be Rs. p.\nLet shares of A and B be Rs. x and Rs. y respectively.\nC's share was Rs. 14\nwe have, x + y + 14 = p ----- (1)\nFrom the given data, x = (p/2) - 4 ----- (2)\nRemaining amount = p - (p/2 - 4) => p/2 + 4.\ny = 1/2(p/2 + 4) + 8 => p/4 + 10 ----- (3)\nFrom (1), (2) and (3)\np/2 - 4 + p/4 + 10 + 14 = p\n3p/4 + 20 = p\np/4 = 20 => p = Rs. 80.\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man whose bowling average is 12.4, takes 8 wickets for 26 runs and there by decreases his average by 0.4. the number of wickets taken by him before his last match is?\n\n### Options:\nA. 173\nB. 174\nC. 175\nD. 176\nE. 177\n\n### Answer:\n12.4*x+26=(8+x)12\nsolve equation x=175\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many numbers are there between 20 and 60 which are divisible by 3 and the total of two digits is 9?\n\n### Options:\nA. 2\nB. 3\nC. 4\nD. 5\nE. 6\n\n### Answer:\nSince number are\n27,36,45,54\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind value of X: 5216 \u00d7 51 = X\n\n### Options:\nA. 265016\nB. 343546\nC. 266016\nD. 353546\nE. 457632\n\n### Answer:\nNormal way of multiplication may take time. Here is one alternative.\n5216\u00d751=(5216\u00d750)+5216=(5216\u00d71002)+5216=5216002+5216=260800+5216=266016\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many numbers between 11 and 90 are divisible by 7 ?\n\n### Options:\nA. 23\nB. 11\nC. 22\nD. 32\nE. 15\n\n### Answer:\nThe required numbers are 14, 21, 28, 35, .... 77, 84.\nThis is an A.P. with a = 14 and d = (21 - 14) = 7.\nLet it contain n terms.\nThen, Tn = 84 => a + (n - 1) d = 84\n=> 14 + (n - 1) x 7 = 84 or n = 11.\n\uf05cRequired number of terms = 11\nANSWER B 11\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain car averages 25 miles per gallon of gasoline when driven in the city and 35 miles per gallon when driving on the highway. According to these rates, which of the following is closest to the number of miles per gallon that the car averages when it is driven 10 miles in the city and then 50 miles on the highway?\n\n### Options:\nA. 28\nB. 30\nC. 33\nD. 36\nE. 38\n\n### Answer:\n10*1/25 gpm+50*1/35 gpm=1.82 total gallons\n60 total miles/1.82 total gallons=32.9 average mpg\nC. 33\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the least number to be subtracted from 11, 15, 21 and 30 each so that the resultant numbers become proportional?\n\n### Options:\nA. 7\nB. 6\nC. 3\nD. 4\nE. 9\n\n### Answer:\nLet the least number to be subtracted be 'x', then 11 - x, 15 - x, 21 - x and 30 - x are in proportion.\n<=> (11 - x):(15 - x) = (21 - x):(30 -x)(21 - x)\nFrom the options, when x = 3\n=> 8 * 27 = 12 * 18 => then x = 3. => (11 - x)(30 - x) = (15 - x)(21 - x)\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n5 men are equal to as many women as are equal to 8 boys. All of them earn Rs.90 only. Men\u00e2\u20ac\u2122s wages are?\n\n### Options:\nA. Rs.6\nB. Rs.6.5\nC. Rs.8\nD. Rs.5\nE. Rs.2\n\n### Answer:\nAnswer: Option A\n5M = xW = 8b\n5M + xW + 8b ----- 90 Rs.\n5M + 5M + 5M ----- 90 Rs.\n15M ------ 90 Rs. => 1M = 6Rs.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 6 men and 2 boys working together, can do four times as much work per hour as a man and a boy together. Find the ratio of the work done by a man and that of a boy for a given time?\n\n### Options:\nA. 3:2\nB. 2:2\nC. 3:4\nD. 1:2\nE. 6:1\n\n### Answer:\nB\n2:2\n6M + 2B = 4(1M + 1B)\n6M + 2B = 4M + 4B\n2M = 2B\nThe required ratio of work done by a man and a boy = 2:2\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n? x 240 = 173 x 240\n\n### Options:\nA. 173\nB. 685\nC. 865\nD. 495\nE. 534\n\n### Answer:\nLet y x 240 = 173 x 240\nThen y = (173 x 240) / 240\n=173\nANSWER :A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train 260 m long passed a pole in 26 sec. How long will it take to pass a platform 650 m long?\n\n### Options:\nA. 91 sec\nB. 89 sec\nC. 54 sec\nD. 27 sec\nE. 22 sec\n\n### Answer:\nSpeed = 260/26 = 10 m/sec.\nRequired time = (260 + 650)/10\n= 91 sec.\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the sum of natural numbers between 90 and 100\n\n### Options:\nA. 1045\nB. 4860\nC. 5000\nD. 5500\nE. 5550\n\n### Answer:\na = first number\nl = last number\nSn = n/2[a + l]\nbetween 90 and 100 numbers = 11 => 100 - 90 = 10 + 1 = 11\nSn = 11/2 \u00c3\u2014 190 = 11 \u00c3\u2014 95 = 1045\nAnswer : A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n4 dice are thrown simultaneously on the board. Find the probability show the same face.\n\n### Options:\nA. 1/113\nB. 1/115\nC. 1/216\nD. 2/113\nE. 3/111\n\n### Answer:\nThe total number of elementary events associated to the random experiments of throwing four dice simultaneously is:\n=6\u00d76\u00d76\u00d76=64=6\u00d76\u00d76\u00d76=64\nn(S)=64n(S)=64\nLet XX be the event that all dice show the same face.\nX={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)}X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)}\nn(X)=6n(X)=6\nHence required probability,\n=n(X)n(S)=664=n(X)n(S)=664\n=1/216\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA lent Rs. 5000 to B for 2 years and Rs. 3000 to C for 4 years on simple interest at the same rate of interest and received Rs. 1540 in all from both of them as interest. The rate of interest per annum is?\n\n### Options:\nA. 7%\nB. 12%\nC. 74%\nD. 10%\nE. 45%\n\n### Answer:\nLet the rate be R% p.a. Then,\n(5000 * R * 2)/100 + (3000 * R * 4)/100 = 1540\n100 R + 120 R = 1540\nR = 7%\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If two marbles are picked at random, what is the probability that they are either red or green?\n\n### Options:\nA. 53/105\nB. 43/105\nC. 42/105\nD. 32/105\nE. 46/105\n\n### Answer:\ngiven that there are three blue marbles, four red marbles, six green marbles and two yellow marbles. Probability that both marbles are red = 4C\u00e2\u201a\u201a/\u00c2\u00b9\u00e2\u0081\u00b5C\u00e2\u201a\u201a = (3 * 2)/(15 * 14) = 3/21\nProbability that both are green = 6C\u00e2\u201a\u201a/\u00c2\u00b9\u00e2\u0081\u00b5C\u00e2\u201a\u201a = (2 * 1)/(15 * 14) = 1/105\nProbability that one red and other is green = (4C\u00e2\u201a\u0081 * 6C\u00e2\u201a\u0081)/\u00c2\u00b9\u00e2\u0081\u00b5C\u00e2\u201a\u201a = (2 * 3 * 2)/(15 * 14) = 27/105\nRequired probability = 3/21 + 1/105 + 27/105\n= 43/105\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHaving scored 99 runs in the 19th inning, a cricketer increases his average score by 4. What will be his average score after 19 innings?\n\n### Options:\nA. 28\nB. 27\nC. 26\nD. 22\nE. 24\n\n### Answer:\nExplanation :\nLet the average score of the first 18 innings be n\n18n + 99 = 19(n+4)=> n = 23\nSo, Average score after 19th innings = x+4 =27.\nAnswer : B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSushil got thrice as many marks in English as in Science. His total marks in English, Science and Maths are 152. If the ratio of his marks in English and Maths is 1:5, find his marks in Science?\n\n### Options:\nA. 8\nB. 77\nC. 66\nD. 55\nE. 31\n\n### Answer:\nS:E = 1:3\nE:M = 1:5\n------------\nS:E:M = 1:3:15\n1/19 * 152 = 8\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOne-tenth of the students at a nursery school are 4 years old or older. If 20 students have not yet reached their third birthday, and a total of 50 students are not between 3 years old and 4 years old, how many children are in the nursery school?\n\n### Options:\nA. 150\nB. 300\nC. 450\nD. 490\nE. 620\n\n### Answer:\nx/10 students are > 4 yrs\n20 students are < 3 yrs\nx/10+ 20 = 50\nx/10 = 30\nx = 300\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSimplify (3^y + 3^y + 3^y + 3^y + 3^y) (5^y + 5^y + 5^y)\n\n### Options:\nA. 15^y+1\nB. 12^y+1\nC. 16^y + 9^y\nD. 12^y\nE. 4^y * 12^y\n\n### Answer:\nA\n(3^y + 3^y + 3^y + 3^y + 3^y) (5^y + 5^y + 5^y)\n(5*3^y)(3*5^y)\n15*15^y=15^(y+1)..\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n155 liters of a mixture of milk and water contains in the ratio 3:2. How much water should now be added so that the ratio of milk and water becomes 3:4?\n\n### Options:\nA. 12 liters\nB. 62 liters\nC. 41 liters\nD. 50 liters\nE. 34 liters\n\n### Answer:\nMilk = 3/5 * 155 = 93 liters\nWater = 62 liters\n93 : (62+P) = 3:4\n186 + 3P = 372 => P = 62\n62 liters of water are to be added for the ratio become 3:4.\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf x/y = 9/8, Then (8x + 7y) / (8x \u00e2\u20ac\u201c 7y) = ?\n\n### Options:\nA. 8\nB. 7\nC. 10\nD. 9\nE. 6\n\n### Answer:\nAnswer\nDividing numerator as well as denominator by y, we get\nGiven Exp. = (8x + 7y) / (8x \u00e2\u20ac\u201c 7y) = (8x/y + 7) / (8x/y \u00e2\u20ac\u201c 7)\nSince x/y = 9/8\nthis implies that\n=[(8*9)/8 +7]/[(8*9)/8 -7)]\n= (9+ 7) / (9 - 7)\n= 8\nOption: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf x and y are different integers and x^2 = xy, which of the following must be true ?\nI. y = 0\nII. x = 0\nIII. x = -y\n\n### Options:\nA. I only\nB. II only\nC. III only\nD. I and III only\nE. I, II, and III\n\n### Answer:\nAnswer choice A is correct.\nThe question gives you x^2=xy\nyou can simplify that as x^2-xy=0\nx(x-y)=0 the solution will be either x=0 or x=y, since x and y are different integers x cannot equal y, that leaves you x=0 to be the only answer.\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average weight of 18 boys in a class is 50.25 kg and that of the remaining 8 boys is 45.15 kg. Find the average weights of all the boys in the class.\n\n### Options:\nA. 48.68077\nB. 42.25983\nC. 50\nD. 51.25388\nE. 52.25\n\n### Answer:\nExplanation:\nAverage weight of 18 boys = 50.25\nTotal weight of 18 boys = 50.25 \u00d7 18\nAverage weight of remaining 8 boys = 45.15\nTotal weight of remaining 8 boys = 45.15 \u00d7 8\nTotal weight of all boys in the class = (50.25 \u00d7 18)+ (45.15 \u00d7 8)\nTotal boys = 18 + 8 = 26\nAverage weight of all the boys = (50.25\u00d718)+(45.15\u00d78)/26\n=48.68077\nAnswer: Option A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many different arrangements of letters are possible if three letters are chosen from the letters A through J and the letters E and A must be among the letters selected?\n\n### Options:\nA. 36\nB. 39\nC. 42\nD. 45\nE. 48\n\n### Answer:\nBesides A and E, there are 8 letters and we can choose one of them.\n8C1 = 8\nThree letters can be arranged in 3! ways.\nThe number of arrangements is 8*3! = 48\nThe answer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe letters B,G,I,N and R are rearranged to form the word 'Bring'. Find its probability.\n\n### Options:\nA. 1/120\nB. 1/235\nC. 1/24\nD. 1/76\nE. 1/53\n\n### Answer:\nExplanation :\nThere are total 5 letters. The probability that B gets the first position is 1/5.\nThe probability that G is in the second position is 1/4.\nLikewise, probability for I,N and G are 1/3, 1/2 and 1/1.\nHence, the required probability is:-\n=> (1/5) x (1/4) x (1/3) x (1/2) x 1.\n=> 1/120.\nAnswer : A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe perimeter of one square is 48 cm and that of another is 20 cm. Find the perimeter and the diagonal of a square which is equal in area to these two combined?\n\n### Options:\nA. 13\u221a7\nB. 13\u221a2\nC. 13\u221a8\nD. 13\u221a9\nE. 12\u221a2\n\n### Answer:\n4a = 48 4a = 20\na = 12 a = 5\na2 = 144 a2 = 25\nCombined area = a2 = 169 => a = 13\nd = 13\u221a2\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA hall is 24 meters long and 12 meters wide. If the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls, what is the volume of the hall (in cubic meters)?\n\n### Options:\nA. 1896\nB. 1912\nC. 2108\nD. 2304\nE. 2524\n\n### Answer:\n2HL + 2HW = 2LW\nH = LW / (L+W)\nVolume = LWH = (LW)^2 / (L+W) = 2304\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average marks of a class of 28 students is 40 and that of another class of 50 students is 60. Find the average marks of all the students?\n\n### Options:\nA. 52.2\nB. 59.5\nC. 52.8\nD. 52.5\nE. 52.1\n\n### Answer:\nSum of the marks for the class of 28 students = 28 * 40 = 1120\nSum of the marks for the class of 50 students = 50 * 60 = 3000\nSum of the marks for the class of 78 students =\n1120 + 3000 = 4120\nAverage marks of all the students = 4120/78\n= 52.8\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA family has two children. find the probability that both the children are girls given that at least\none of them is a girl?\n\n### Options:\nA. 1/2\nB. 1by3\nC. 3/5\nD. 3/7\nE. 3/11\n\n### Answer:\nLet b stand for boy and g for girl. The sample space of the experiment is\nS = {(g, g), (g, b), (b, g), (b, b)}\nLet E and F denote the following events :\nE : \u2018both the children are girls\u2019\nF : \u2018at least one of the child is a girl\u2019\nThen E = {(g,g)} and F = {(g,g), (g,b), (b,g)}\nNow E n F = {(g,g)}\nThus P(F) = 3/4\nand P (E n F )= 1/4\nTherefore P(E|F) = P(E \u2229 F)/P(F) = (1/4)/(3/4) = 1/3\nB)\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow much more would Rs.20000 fetch, after two years, if it is put at 20% p.a. compound interest payable half yearly than if is put at 20% p.a. compound interest payable yearly?\n\n### Options:\nA. 482\nB. 442\nC. 552\nD. 662\nE. 526\n\n### Answer:\n20000(11/10)4 - 20000(6/5)2 = 482\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a group of 10 doctors, 3 doctors are only pediatricians; the others are surgeons or general practitioners - but not both. A team of 3 doctors is to be chosen which must have at least 1 pediatrician, how many different teams can be chosen?\n\n### Options:\nA. 85\nB. 140\nC. 60\nD. 80\nE. 75\n\n### Answer:\nThe problem asks for a combination, since order doesn't matter. Now, selecting r items from a set of n gives the Combination Formula: nCr= n!/r!(n-r)!\nn = 10\nr = 3\nSo, total teams is 10C3 = 10!/(3!(10 - 3)!) = 120, and\nn = 10 - 3 = 7\nr = 3\nfor teams without a pediatrician is 7C3 = 7!/(3!(7 - 3)!) = 35,\nso, teams with at least 1 pediatrician = 120 - 35 = 85\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA store sells chairs and tables. If the price of 2 chairs and 1 table is 60% of the price of 1 chair and 2 tables, and the price of 1 table and 1 chair is $96, what is the price, in dollars, of 1 table? (Assume that every chair has the same price and every table has the same price.)\n\n### Options:\nA. 81\nB. 84\nC. 85\nD. 88\nE. 90\n\n### Answer:\nLET C= CHAIR ; T =TABLE\n2C+1T = 0.6 (1C + 2T) OR C( 2-0.6) = 1.2T -1T OR 1.4C = 0.2 T THEREFORE C= 0.2/1.4 T = 1/7 T\nIC +1T =96 OR 1/7T + 1T =96 THEREFORE T= 96*7/8 = 84\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nPeter invests a sum of money and gets back an amount of $ 815 in 3 years . David invests an equal amount of money and gets an amount of $850 in 4 years. If both amounts were invested at the same rate (simple interest ) What was the sum of money invested ?\n\n### Options:\nA. 670\nB. 664\nC. 698\nD. 744\nE. 710\n\n### Answer:\nSince both Peter and David invested the same amount of money at the same rate, they would earn same interest per year.\nDavid invested for one year more than Peter and hence he got interest amount for one more year.\nInterest earned per year = Amount received by David - Amount received by Peter = 850 - 815 = 35\nInterest earned for 3 years = 35*3 =105\nAmount invested = 815 - 105= 710\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAntonio works in a bakery. He made cookies that cost $3 and made $300. How many customer did he have?\n\n### Options:\nA. 100 customers\nB. 185 customers\nC. 250 customers\nD. 200customers\nE. 270 customers\n\n### Answer:\nA cookie costs $3 adding another one is $6. 300 divided by 6 is 50x 2 is 100. He had 100 customers.\nThe correct answer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAravamudhan, Balakrishnan and Chinnan work in a developing software company in starting level positions. However their salaries are different. Aravamudhan's salary to Balakrishnan's salary and Balakrishnan's salary to Chinnan's salary are in the ratio 4:3. If the total salary of all the three employees is Rs.29230, what is the salary of Chinnan?\n\n### Options:\nA. Rs.12640\nB. Rs.9480\nC. Rs.7110\nD. Rs.8660\nE. Rs.9660\n\n### Answer:\nmaking them in equal proportion of Aravind:Bala:Cinnana=16:12:9\nand given total salary 37*x=29230\nx=790\nChinnana salary is 9*790=7110\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nGoldenrod and No Hope are in a horse race with 7 contestants. How many different arrangements of finishes are there if No Hope always finishes before Goldenrod and if all of the horses finish the race?\n\n### Options:\nA. 5040\nB. 2520\nC. 1200\nD. 240\nE. 210\n\n### Answer:\nAll 7 horses can finish the race in 7! way (assuming no tie).\nIf no tie is possible between No Hope and Goldenrod, then in half of these cases No Hope will be before Goldenrod and in half of these cases after (not necessarily right before or right after). How else? So, there are 7!/2=2520 different arrangements of finishes where No Hope always finishes before Goldenrod.\nAnswer: B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man invests Rs. 6,000 at the rate of 5% per annum. How much more should he invest at the rate of 8%, so that he can earn a total of 6% per annum?\n\n### Options:\nA. Rs. 1200\nB. Rs. 1300\nC. Rs. 1500\nD. Rs. 3000\nE. None of these\n\n### Answer:\nExplanation :\nInterest on Rs.6000 at 5% per annum = ( 6000 \u00d7 5 \u00d7 1) / 100 = Rs. 300\nLet his additional investment at 8% = x\nInterest on Rs.x at 8% per annum = ( x \u00d7 8 \u00d7 1 ) / 100 = 2x/25.\nTo earn 6% per annum for the total, interest = (6000 + x) \u00d7 6 \u00d7 1/100.\n=> 300 + 2x/25 = (6000 + x) \u00d7 6 \u00d7 1/100.\n=> 30000 + 8x = (6000 + x) \u00d7 6.\n=> 30000 + 8x = 36000 + 6x.\n=> 2x=6000.\n=> x=3000.\nAnswer : D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA can do a piece of work in 4hours. B and C together can do it in 3 hours, while A and C together can do it in 2 hours. How long will B alone take to do it?\n\n### Options:\nA. 8 hours\nB. 10 hours\nC. 12 hours\nD. 24 hours\nE. 30 hours\n\n### Answer:\nA's 1 hour work= 1/4\n(B+C)'s 1 hour work= 1/3\n(A+C)'s 1 hour work= 1/2\n(A+B+C)'s 1 hour work= (1/4+1/3)=7/12\nB's 1hour's work= (7/12-1/2)= 1/12\nB alone will take 12 hours to do the work.\ncorrect option is C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA girl swims downstream 48 km and upstream 16 km taking 8 hours each time; what is the speed of the current?\n\n### Options:\nA. 2.0\nB. 2.1\nC. 2.2\nD. 2.3\nE. 2.4\n\n### Answer:\n48 --- 8 DS = 6\n? ---- 1\n16 ---- 8 US = 2\n? ---- 1 S = ?\nS = (6 - 2)/2 = 2\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe ratio of radius of a circle and the side of a square is 2 : 9. Find the ratio of their areas:\n\n### Options:\nA. 2 : 1\nB. 4 : 7\nC. 8 : 77\nD. 4 : 81\nE. None\n\n### Answer:\nradius/side = 2/9\n\u00e2\u2021\u2019 area of circle/area of square= 4/81\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nEach shelf of a bookcase contained 11 books. If the librarian took out 30 books and rearranged the remaining books so that all shelves but the last one contained 7 books and that last shelf contained 5 books, how many shelves does the bookcase have?\n\n### Options:\nA. 5\nB. 6\nC. 7\nD. 8\nE. 9\n\n### Answer:\nLet x be the number of shelves.\n11x - 30 = 7(x-1) + 5\n4x = 28\nx = 7\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA dog takes 5 leaps for every 7 leaps of a hare. If one leap of the dog is equal to 3 leaps of the hare, the ratio of the speed of the dog to that of the hare is :\n\n### Options:\nA. 16 : 7\nB. 15 : 7\nC. 20 : 7\nD. 7 :15\nE. 14 : 7\n\n### Answer:\nExplanation:\nDog : Hare = (5*3) leaps of hare : 7 leaps of hare = 15 : 7\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n3/x + 3x = 3(x-9)\n\n### Options:\nA. -9\nB. -1/6\nC. -1/9\nD. 1/9\nE. 9\n\n### Answer:\nWe can solve - expand the right side, multiply by x on both sides and then subtract away the 3x^2 terms:\n(3/X) + 3x = 3(x-9)\n(3/x) + 3x = 3x - 18\n3 + 3x^2 = 3x^2 - 18x\n3 = -18x\n-1/6 = x\nand to confirm, you can plug that answer back into the original equation to see that it makes the left and right sides equal.\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train 110 m long is running with a speed of 60 km/hr. In what time will it pass a man who is running at 6 km/hr in the direction opposite to that in which the train is going?\n\n### Options:\nA. 9\nB. 7\nC. 5\nD. 4\nE. 6\n\n### Answer:\nSpeed of train relative to man = 60 + 6 = 66 km/hr.\n= 66 * 5/18 = 55/3 m/sec.\nTime taken to pass the men = 110 * 3/55\n= 6 sec.\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the sum of the numbers between 1 and 10, inclusive?\n\n### Options:\nA. 85\nB. 95\nC. 100\nD. 105\nE. 55\n\n### Answer:\nSol. add all the numbers between 1 and 10.\nFinal Answer =E, 55.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFrom a group of 4 boys and 4 girls, 2 children are to be randomly selected. What is the probability that 1 boy and 1 girl will be selected?\n\n### Options:\nA. 1/2\nB. 2/3\nC. 3/5\nD. 4/7\nE. 5/9\n\n### Answer:\nThe total number of ways to choose 2 children from 8 is 8C2 = 28\nThe number of ways to choose 1 boy and 1 girl is 4*4 = 16\nP(1 boy and 1 girl) = 16/28 = 4/7\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA jogger running at 9 km/hr along side a railway track is 240 m ahead of the engine of a 120 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger?\n\n### Options:\nA. 30\nB. 35\nC. 36\nD. 37\nE. 38\n\n### Answer:\nSpeed of train relative to jogger = 45 - 9 = 36 km/hr.\n= 36 * 5/18 = 10 m/sec.\nDistance to be covered = 240 + 120 = 360 m.\nTime taken = 360/10 = 36 sec.\nAnswer: Option C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA brick measures 20 cm * 10 cm * 7.5 cm how many bricks will be required for a wall 24 m * 2 m * 0.75 m?\n\n### Options:\nA. 22377\nB. 27782\nC. 27891\nD. 24000\nE. 18771\n\n### Answer:\n24 * 2 * 0.75 = 20/100 * 10/100 * 7.5/100 * x\n24 = 1/100 * x => x = 24000\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA,B,C can complete a piece of work in 18,6,12 days. Working together, they complete the same work in how many days?\n\n### Options:\nA. 2\nB. 4/5\nC. 7/9\nD. 36/11\nE. 24/7\n\n### Answer:\nA+B+C 1day work = 1/18 + 1/6 + 1/12 = 11/36\nA,B,C together will complete the job in 36/11 days\nAnswer is D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA box contains 5 black, 10 white and 8 yellow marbles. 4 marbles are drawn from the box at random. What is the probability that all three marbles are of the same color?\n\n### Options:\nA. 224/8855\nB. 225/8855\nC. 245/8855\nD. 285/8855\nE. 244/8855\n\n### Answer:\nExplanation:\nTotal marbles in a box = 5 black +10 white + 8 yellow marbles = 23 marbles\n4 marbles are drawn from 23 marbles at random. Therefore,\nn(S) = 23C4 = 8855 ways\nLet A be the event that 4 marbles drawn at random are of the same color. Number of cases favorable to the event A is\nn(A) = 5C4 + 10C4 + 8C4 = 5 +210 + 70= 285\nTherefore, by definition of probability of event A,\nP(A) = n(A)/n(S) =285/8855\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat approximate value should come in place of question mark (?) in the following equation\n287.532 + 1894.029 \u2013 857.48 = 743.095 + ?\n\n### Options:\nA. 870\nB. 790\nC. 580\nD. 770\nE. 890\n\n### Answer:\n? = 285 + 1895 \u2013 855 \u2013 745 or, ? = 580\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA walks around a circular field at the rate of one round per hour while B runs around it at the rate of six rounds per hour. They start in the same direction from the same point at 7.30 a.m. They shall first cross each other at:\n\n### Options:\nA. 5.30 a.m\nB. 6.42 a.m\nC. 7.55 a.m\nD. 7.42 a.m\nE. None\n\n### Answer:\nSol.\nSince A and B move in the same direction along the circle, so they will first meet each other when there is a difference of one round between the two\nRelative speed of A and B = (6-1) = 5 rounds per hour.\nTime taken to complete one round at this speed = 1/5 hr = 12 min.\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn the coordinate plane, points (x, 1) and (7, y) are on line k. If line k passes through the origin and has slope 1/7, then x - y =\n\n### Options:\nA. 6\nB. 7\nC. 5\nD. 8\nE. 3\n\n### Answer:\nLine k passes through the origin and has slope 1/7 means that its equation is y=1/7*x.\nThus: (x, 1)=(7, 1) and (7, y) = (7,1) --> x-y=7-1=6.\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA boat can move upstream at 20 kmph and downstream at 35 kmph, then the speed of the current is?\n\n### Options:\nA. 5 kmph\nB. 7.5 kmph\nC. 8 kmph\nD. 9 kmph\nE. 4 kmph\n\n### Answer:\nUS = 20\nDS = 35\nM = (35 - 20)/2 = 7.5\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 35 percent of 400 is 20 percent of x, then what is 70 percent of x?\n\n### Options:\nA. 200\nB. 490\nC. 700\nD. 900\nE. 1,400\n\n### Answer:\n35/100(400) = 2/10(x)\nX = 700..\n70 percent of x =70/100(700) =490\nOption B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nCost is expressed by the formula tb^4. If b is doubled, the new cost E is what percent of the original cost?\n\n### Options:\nA. E=200\nB. E=600\nC. E=800\nD. E=1600\nE. 50\n\n### Answer:\nOriginal Cost E, C1=t1*b1^4\nNew Cost C2= t2*b2^4....only b is doubled so t2=t1 and b2=2b1\nC2=t2*(2b1)^4\n=16(t1*b1^4)\n=16C1\n16 times C1=>1600% of C1\nAns D=1600\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo trains of equal length 120 metres move in the same direction. The faster train completely\novertakes the slower one in 15 seconds. If the slower train were to move at half its speed, the over\ntaking would take in 10 seconds. At what speeds are the 2 trains moving ?\n\n### Options:\nA. 24,22\nB. 32,16\nC. 30,18\nD. 28,14\nE. None of these\n\n### Answer:\nExplanation :\nThe total distance covered for over taking = length of the two trains = 120 +120 = 240\nSpeed of faster train be x m/s and slower train be y m/s\nIn the first case Relative speed = x-y\nRelative Speed = Distance / Time taken = x-y = 240/15 = 16 m/s(1)\nIn the second case, the slower train moves at half its speed\nRelative Speed = x-0.5y = 240/10 = 24 m/s ..(2)\nSolving equation 1 & 2 we get x = 32 and y = 16 .\nThe speed of the faster and slower trains are 32 m/s and 16 m/s respectively\nAnswer : B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf x is a positive integer, then the least value of x for which x! is divisible by 10,000 is?\nCan someone please explain intuitively what the question is asking?\n\n### Options:\nA. 5\nB. 9\nC. 12\nD. 15\nE. 20\n\n### Answer:\nIn order x! to be divisible by 1,000, it should have at least 3 trailing zeros. A trailing 0 in factorial of a number is produced by 2 and 5 in it: 2*5 = 10. So, we need 10 to be in x! at least in power of 3.\n5! = 120 has 1 trailing zeros.\n10! will have 2 trailing zeros.\n15! will have 3 trailing zeros.\n20! will have 5 trailing zeros.\nAnswer: E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo pipes A and B can separately fill a tank in 10 and 15 minutes respectively. A third pipe C can drain off 45 liters of water per minute. If all the pipes are opened, the tank can be filled in 15 minutes. What is the capacity of the tank?\n\n### Options:\nA. 450\nB. 540\nC. 542\nD. 829\nE. 279\n\n### Answer:\n1/10 + 1/15 - 1/x = 1/15\nx = 10\n10 * 45 = 450\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA car mechanic purchased four old cars for Rs. 1 lakh. He spent total 2 lakh in the maintenance and repairing of these four cars. what is the average sale price of the rest three cars to get 60% total profit if he has already sold one of the four cars at Rs. 1.2 lakh?\n\n### Options:\nA. 1.8 lakh\nB. 1.2 lakh\nC. 1.9 lakh\nD. 8.1 lakh\nE. 6.1 lakh\n\n### Answer:\nExplanation:\nTotal cost of 4 cars = 1+2 = 3 lakh\nTotal SP of 4 cars = 3 x 1.6 = 4.8 lakh\nSP of 1 car = 1.2 lakh\nSP of rest 3 cars = 4.8 - 1.2 = 3.6 lakh\nAverage SP of all the 3 cars = 1.2 lakh\nAnswer: B)\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe 4 sticks in a complete bag of Pick-Up Sticks are all straight-line segments of negligible width, but each has a different length: 1 inch, 2 inches, 3 inches, and 4 inches, respectively. If Tommy picks a stick at random from each of 3 different complete bags of Pick-Up Sticks, what is the probability S that Tommy CANNOT form a triangle from the 3 sticks?\n\n### Options:\nA. 11/32\nB. 13/32\nC. 15/32\nD. 17/32\nE. 19/32\n\n### Answer:\nIn order to form a triangle, the sum of two sides must be greater than the third side.\nSo we can choose the combination of numbers which will NOT result in a triangle.\nFavorable outcomes:\n1,1,4 (4>1+1): 3 ways of arriving at this (1,1,4), (1,4,1), (4,1,1) or\n1,2,4 (4>1+2): 6 ways of arriving at this (1,2,4), (1,4,2), (2,1,4), (2,4,1), (4,1,2), (4,2,1) which is same as 3!\n1,3,4 (4=1+3): 6 ways of arriving at this\n2,2,4 (4=2+2): 3 ways of arriving at this\n1,1,3 (3>1+1): 3 ways of arriving at this\n1,2,3 (3=1+2): 6 ways of arriving at this\n1,1,2 (2+1+1): 3 ways of arriving at this\nOverall favourable outcomes: 30\nTotal outcomes: 4*4*4 = 64 (4 ways of choosing a stick from each of the 3 bags)\nProbability S that a triangle is not formed = 30/64 = 15/32\nC is the correct option here.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train moves fast a telegraph post and a bridge 264 m long in 8 sec and 20 sec respectively. What is the speed of the train?\n\n### Options:\nA. 89.2 km/hr\nB. 79.9 km/hr\nC. 99.2 km/hr\nD. 79.2 km/hr\nE. 72.2 km/hr\n\n### Answer:\nLet the length of the train be x m and its speed be y m/sec.\nThen, x/y = 8 => x = 8y\n(x + 264)/20 = y\ny = 22\nSpeed = 22 m/sec = 22 * 18/5\n= 79.2 km/hr.\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA trader marks his articles 20% more than the cost price. If he allows 20% discount, then find his gain or loss percent?\n\n### Options:\nA. 6%\nB. 8%\nC. 5%\nD. 2%\nE. 4%\n\n### Answer:\nLet CP of an article = RS. 100\nMP= Rs. 120\nDiscount = 20%\nSP = M[(100 - d%)/100] = 120(80/100) = Rs. 96\nClearly, the trader gets 4% loss.\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are two positive numbers in the ratio 5:8. If the larger number exceeds the smaller by 15, then find the smaller number?\n\n### Options:\nA. 25\nB. 81\nC. 86\nD. 16\nE. 27\n\n### Answer:\nLet the two positive numbers be 5x and 8x respectively.\n8x - 5x = 15\n3x = 15 => x = 5\n=> Smaller number = 5x = 25.\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are 6 red balls,8 blue balls and 7 green balls in a bag. If 5 are drawn with replacement, what is the probability at least three are red?\n\n### Options:\nA. 312/16808\nB. 312/16807\nC. 312/16805\nD. 312/16838\nE. 312/16111\n\n### Answer:\nAt least 3 reds means we get either : 3 red or 4 red or 5 red. And this is a case of replacement.\ncase 1 : 3 red balls : 6/21 x 6/21 x 6/21 x 15/21 x 15/21\ncase 2 : 4 red balls : 6/21 x 6/21 x 6/21 x 6/21 x 15/21\ncase 3 : 5 red balls : 6/21 x 6/21 x 6/21 x 6/21 x 6/21\nTotal probability = = (6/21 x 6/21 x 6/21 x 15/21 x 15/21)+(6/21 x 6/21 x 6/21 x 6/21 x (15 )/21)+ (6/21 x 6/21 x 6/21 x 6/21 x 6/21)\n= 312/16807\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJohn is going with 10 friends on a trip to Sidney for spring break. Airfare and hotel costs a total of $12100.00 for the group of 11 friends. How much does each person have to pay for their hotel and airfare?\n\n### Options:\nA. $1010\nB. $1100\nC. $1110\nD. $1101\nE. $1200\n\n### Answer:\nAnswer= B\nThe total cost of the trip ($12100.00) divided by 11 equals $1100.00.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man's speed with the current is 20 kmph and speed of the current is 5 kmph. The Man's speed\nagainst the current will be\n\n### Options:\nA. 11 kmph\nB. 10 kmph\nC. 14 kmph\nD. 17 kmph\nE. None of these\n\n### Answer:\nExplanation:\nSpeed with current is 20,\nspeed of the man + It is speed of the current\nSpeed in s\u019fll water = 20 - 5 = 15\nNow speed against the current will be\nspeed of the man - speed of the current\n= 15 - 5 = 10 kmph\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nConvert the following units:\n(a) 60 cm\u00b2 in mm\u00b2\n\n### Options:\nA. 600 mm\u00b2\nB. 1600 mm\u00b2\nC. 6000 mm\u00b2\nD. 600 mm\u00b2\nE. 6600 mm\u00b2\n\n### Answer:\n60 cm\u00b2 in mm\u00b2\n1 cm = 10 mm\n1 cm\u00b2 = 100 mm\u00b2\nTherefore, 60 cm\u00b2 = 60 \u00d7 100 mm\u00b2\n= 6000 mm\u00b2\nANSWER : OPTION C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average weight of 25 boys sitting in a class had some value. A new boy added to them whose weight was 46 kg only. Due to his arrival, the average weight of all the boys decreased by 5 kg. Find the average weight of first 25 boys?\n\n### Options:\nA. 150\nB. 152\nC. 176\nD. 180\nE. 182\n\n### Answer:\n25x + 46 = 26(x \u2013 5)\nx = 176\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA motorcyclist goes from Bombay to Pune, a distance of 288 kms at an average of 32 kmph speed. Another man starts from Bombay by car 2 \u00bd hours after the first, and reaches Pune \u00bd hour earlier. What is the ratio of the speed of the motorcycle and the car?\n\n### Options:\nA. 1:2\nB. 1:5\nC. 1:4\nD. 2:3\nE. 1:8\n\n### Answer:\nT = 288/32 = 9 h\nT = 9 - 3 = 6\nTime Ratio = 9:6 = 3:2\nSpeed Ratio = 2:3\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a mixture of 45 litres the ratio of milk to water is 4:1. Additional 3 litres of water is added to the mixture. Find the ratio of milk to water in the resulting mixture.\n\n### Options:\nA. 2/1\nB. 4/1\nC. 2/3\nD. 3/4\nE. 3/1\n\n### Answer:\nGiven that Milk/Water=4x/x and 4x+x=45 --> x=9.\nThus Milk=4x=36 liters and Water=x=9 liters.\nNew ratio = 36/(9+3) = 36/12 = 3/1.\nAnswer: E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA tourist purchased a total of $1,550 worth of traveler\u2019s checks in $10 and $50 denominations, During the trip the tourist cashed 7 checks and then lost all of the rest. If the number of $10 checks cashed was one more or one less than the number of $50 checks cashed, what is the minimum possible value of the checks that were lost?\n\n### Options:\nA. $1,430\nB. $1,320\nC. $1,290\nD. $1,270\nE. $1,150\n\n### Answer:\nsince total cashed checks = 7 ans $10 check cashed = one less or more than $50 checks\nTherefore either $10 checks = 3 and $50 checks = 4 OR $10 checks = 4 and $50 checks = 3\nusing this information 1st option gives us the maximum cashed value therefore if we negate this value from total value we will get minimum value of which checks have lost\nTherfore 1550 - 230 = 1320 hence answer is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo numbers x and y are such that the sum of 3% of x and 4% of y is one-third of the sum of 2% of of x and 8% of y. Find the ratio of x : y.\n\n### Options:\nA. 3:8\nB. 6:7\nC. 4:7\nD. 2:5\nE. None of these\n\n### Answer:\nExplanation :\nSolution: 3% of x+ 4% of y=1/3(2% of x+8% of y)\n3x/100 + 4y/100 = 2x/300 + 8y/300\n(3x+4y)3 = 2x+8y\n7x = 4y\nx/y = 4/7\nAnswer : C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA, B and C are entered into a partnership. A invested Rs.6500 for 6 months, B invested Rs.8400 for 5 months and C invested for Rs.10000 for 3 months. A is a working partner and gets 5% of the total profit for the same. Find the share of C in a total profit of Rs.7400?\n\n### Options:\nA. 2998\nB. 1900\nC. 2788\nD. 2662\nE. 1122\n\n### Answer:\n65 * 6 : 84 * 5 : 100 * 3\n26:28:20\nC share = 74000 * 95/100 = 7030 * 20/74\n=> 1900\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n2,345\n2,354\n2,435\n.....\n....\n+5,432\nThe addition problem above shows four of the 24 different integers that can be formed by using each of the digits 2,3,4,5 exactly once in each integer. What is the sum of these 24 integers?\n\n### Options:\nA. 81,218\nB. 85,546\nC. 89,928\nD. 93,324\nE. 97,716\n\n### Answer:\nIn each of the units, tens, hundreds, and thousands place, each digit will appear 6 times.\nThen the sum equals 6(2222)+6(3333)+6(4444)+6(5555) = 93,324\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA 300 meter long train crosses a platform in 48 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform?\n\n### Options:\nA. 500\nB. 289\nC. 350\nD. 882\nE. 281\n\n### Answer:\nSpeed = [300 / 18] m/sec = 50/3 m/sec.\nLet the length of the platform be x meters.\nThen, x + 300 / 48 = 50/3\n3(x + 300) = 2400 \u00e8 x = 500m.\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOn a map the distance between two mountains is 312 inches. The actual distance between the mountains is 136 km. Ram is camped at a location that on the map is 25 inch from the base of the mountain. How many km is he from the base of the mountain?\n\n### Options:\nA. 10.89\nB. 14.81\nC. 14.8\nD. 14.82\nE. 14.12\n\n### Answer:\nExplanation:\nSince 312 inch = 136 km\nSo 1 inch = 136/312 km\nSo 25 inch = (136 \u00c3\u2014 25)/ 312 = 10.89 km\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFor a race a distance of 224 meters can be covered by P in 28 seconds and Q in 32 seconds. By what distance does P defeat Q eventually?\n\n### Options:\nA. 26m\nB. 32m\nC. 24m\nD. 28m\nE. None of these\n\n### Answer:\nExplanation:\nThis is a simple speed time problem. Given conditions:\n=>Speed of P= 224/28 = 8m/s\n=>Speed of Q=224/32 = 7m/s\n=>Difference in time taken = 4 seconds\nTherefore, Distance covered by P in that time= 8m/s x 4 seconds = 32 metres\nANSWER: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nBy selling 100 pens, a trader gains the cost of 40 pens. Find his gain percentage?\n\n### Options:\nA. 40%\nB. 50%\nC. 60%\nD. 70%\nE. 30%\n\n### Answer:\nLet the CP of each pen be Rs. 1.\nCP of 100 pens = Rs. 100\nProfit = Cost of 40 pens\n= Rs. 40\nProfit% = 40/100* 100\n= 40%\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average age of a group of n people is 14 years old. One more person aged 32 joins the group and the new average is 15 years old. What is the value of n?\n\n### Options:\nA. 13\nB. 14\nC. 15\nD. 16\nE. 17\n\n### Answer:\n14n + 32 = 15(n+1)\nn = 17\nThe answer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the average (arithmetic mean) of the four numbers K, 2K + 3, 3K \u2013 5 and 5K + 1 is 85, what is the value of K?\n\n### Options:\nA. 11\nB. 15 3/4\nC. 31\nD. 23\nE. 25 3/10\n\n### Answer:\nK + 2K +3 + 3K - 5 + 5K +1 = 11K -1\n(11K -1)/4 = 85\n11K = 85 * 4 +1 = 340 +1 = 341\nK = 253 / 11 = 31.\nAnswer C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIt rained on exactly 7 of the days during Jane's summer holiday trip. On\neach day that it rained, it rained either in the morning or the afternoon\nbut not both. There were exactly 5 afternoons when it did not rain and\nexactly 6 mornings when it did not rain. How many days did the trip\nlast?\n\n### Options:\nA. 7\nB. 8\nC. 9\nD. 10\nE. 11\n\n### Answer:\nLet M be the number of days it rained in the morning; A - the number of\ndays it rained in the afternoon; and let N be the number of days when it did not rain.\nWe have M + A = 7 (days when it rained); M + N = 5 (afternoons when it did not\nrain); and A + N = 6 (mornings when it did not rain). Adding the equations we get\n2(M + A + N) = 18, M + A + N = 9.\ncorrect answer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe probability that A speaks truth is 3/5 and that of B speaking truth is 4/7. What is the probability that they agree in stating the same fact?\n\n### Options:\nA. 18/35\nB. 18/35\nC. 18/39\nD. 18/31\nE. 18/32\n\n### Answer:\nIf both agree stating the same fact, either both of them speak truth of both speak false.\nProbability = 3/5 * 4/7 + 2/5 * 3/7\n= 12/35 + 6/35 = 18/35\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many four digit numbers have no repeat digits, do not contain zero, and have a sum of digits F equal to 28?\n\n### Options:\nA. 14\nB. 24\nC. 28\nD. 48\nE. 96\n\n### Answer:\nFirst, look for all 4 digits without repeat that add up to 28. To avoid repetition, start with the highest numbers first.\nStart from the largest number possible 9874.\nThen the next largest number possible is 9865.\nAfter this, you'll realize no other solution. Clearly the solution needs to start with a 9 (cuz otherwise 8765 is the largest possible, but only equals 26). With a 9, you also need an 8 (cuz otherwise 9765 is the largest possible, but only equals 27). With 98__ only 74 and 65 work.\nSo you have two solutions. Each can be rearranged in 4!=24 ways. So F=24+24=48.D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhen a plot is sold for Rs. 18,700, the owner loses 15%. At what price must that plot be sold in order to gain 15%?\n\n### Options:\nA. 25300\nB. 22000\nC. 21000\nD. 23560\nE. 24540\n\n### Answer:\nsell at 18700 he got a loss of 15% means, This 18700 is 85% not 100%.\nTo get 1% : 18700/85=220; Then 220 is 1%.\nTo get 100% : 220*100=22000.\nTo get 115% : 220*115=25300.\nANSWER :A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average number of shirts with Salman, Ambani and Dalmiya is 60, if all of them reached a shopping mall in Delhi and purchased 3 shirts each of them then average number of shirt each of them now has\n\n### Options:\nA. 66\nB. 63\nC. 62\nD. 64\nE. 61\n\n### Answer:\nRequired average\n= Old average + New average\n= 60 + 3 = 63\nanswer :B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nEvaluate: 19 + sqrt(- 2 + 12\u00c3\u20146\u00c3\u00b79) =?\n\n### Options:\nA. 51\nB. 53\nC. 55\nD. 57\nE. 59\n\n### Answer:\nAccording to order of operations, inner brackets first where 12x6\u00c3\u00b79 is first calculated since it has a multiplication and a division.\n12x6\u00c3\u00b79 = 72\u00c3\u00b79 = 8\nHence\n19 + sqrt(- 2 + 12\u00c3\u20146\u00c3\u00b79) = 19+ sqrt(- 2 + 8)\n= 19 + sqrt(6) = 19 + 36 = 55\ncorrect answer C)55\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the numbers which are in the ratio 3:2:4 such that the sum of the first and the second added to the difference of the third and the second is 21.\n\n### Options:\nA. 9, 6, 16\nB. 9, 6, 19\nC. 9, 6, 16\nD. 9, 6, 12\nE. 9, 6, 11\n\n### Answer:\nLet the numbers be a, b and c.\na:b:c = 3:2:4\nGiven, (a + b) + (c - b) = 21\n=> a + c = 21\n=> 3x + 4x = 21 => x = 3\na, b, c are 3x, 2x, 4x\na, b, c are 9, 6, 12.\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf T = 5/9 * (K - 32), and if T = 75, then what is the value of K?\n\n### Options:\nA. 158\nB. 161\nC. 164\nD. 167\nE. 170\n\n### Answer:\nK-32=9T/5\nK=9T/5 + 32\nK=9(75)/5 + 32 = 167\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the area of circle whose radius is 7m?\n\n### Options:\nA. 124 sq m\nB. 154 sq m\nC. 145 sq m\nD. 167 sq m\nE. 180 sq m\n\n### Answer:\nr = 7\nArea of Circle =\u220fr2\n= (22/7)(7)(7)\n= 154 sq m.Answer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow much time will take for an amount of Rs. 400 to yield Rs. 81 as interest at 4.5% per annum of simple interest?\n\n### Options:\nA. 4 1/2 years\nB. 6 1/2years\nC. 7 1/2years\nD. 12 1/2years\nE. 15 1/2years\n\n### Answer:\nTime = (100 * 81) / (400 * 4.5) = 4 1/2years\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nEvaluate: 50 - 12\u00f74\u00d72 =\n\n### Options:\nA. 44\nB. 54\nC. 16\nD. 27\nE. 30\n\n### Answer:\nAccording to order of operations, 12\u00f74\u00d72 (division and multiplication) is done first from left to right\n12\u00f74\u00d72 = 3 \u00d7 2 = 6\nHence\n50 - 12\u00f74\u00d72 = 50 - 6 = 44\ncorrect answer A)44\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIt takes Joey the postman 1 hours to run a 2 mile long route every day. He delivers packages and then returns to the post office along the same path. If the average speed of the round trip is 6 mile/hour, what is the speed with which Joey returns?\n\n### Options:\nA. 9\nB. 12\nC. 13\nD. 14\nE. 15\n\n### Answer:\nlet his speed for one half of the journey be 3 miles an hour\nlet the other half be x miles an hour\nnow,\navg speed =5 mile an hour\n2*2*x/3+x=6\n4x=6x+18=>2x=18\nx=9\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe speed of the boat in still water in 12 kmph. It can travel downstream through 42 kms in 3 hrs. In what time would it cover the same distance upstream?\n\n### Options:\nA. 8 hours\nB. 6 hours\nC. 4.2 hours\nD. 5 hours\nE. 6 hours\n\n### Answer:\nStill Water=12km/hr\nDownstream=42/3=14km/hr\nUpstream=>> still water=(u+v/2) =>> 12=u+14/2 = 10km/hr\nSo time taken in upstream = 42/10 =4.2hrs\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAt a dinner party, 8 people are to be seated around a circular table. 2 seating arrangements are considered different only when the positions of the people are different relative to each other. what is the total number of different possible seating arrangements for the group?\n\n### Options:\nA. 5\nB. 10\nC. 24\nD. 32\nE. 5040\n\n### Answer:\nSoln: Since the arrangement is circular and 2 seating arrangements are considered different only when the positions of the people are different relative to each other, we can find the total number of possible seating arrangements, by fixing one person's position and arranging the others.\nThus if one person's position is fixed, the others can be arranged in 7! = 5040 ways.\nAns is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA number, x is chosen at random from the set of positive integers less than 20. What is the probability that (18/x) > x?\n\n### Options:\nA. 1/5\nB. 2/9\nC. 3/19\nD. 4/19\nE. 7/9\n\n### Answer:\nNumber x has to be chosen from numbers 1-19\n(18/x) > x\n=> 18 > x^2\n=>x^2 - 18 < 0\nx can have 2 values only 1 , 2 , 3 , 4\nTherefore , probability = 4 / 19\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a class of 140 students, 60% of them passed. By what percent is the number of students who passed more than the number of failed students?\n\n### Options:\nA. 80%\nB. 20%\nC. 40%\nD. 50%\nE. None of these\n\n### Answer:\nNumber of students passed = 60% of 140 = 60/100 * 140 = 84\nNumber of students failed = 140 - 84 = 56.\nRequired percentage = 28/56 * 100 = 50%.\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA cricketer scored 152 runs which included 12 boundaries and 2 sixes. What percent of his total score did he make by running between the wickets.\n\n### Options:\nA. 46.2%\nB. 54.54 %\nC. 60.52%\nD. 70%\nE. None of these\n\n### Answer:\nExplanation :\nNumber of runs made by running = 152 - (12 x 4 + 2 x 6)\n= 152 - (60)\n= 92\nNow, we need to calculate 92 is what percent of 152.\n=> 92/152 * 100 = 60.52 %\nAnswer : C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a mayoral election, Candidate X received 1/5 more votes than candidate Y, and Candidate Y received 1/2 fewer votes than Z. If Z received 20,000 votes how many votes did candidate X received?\n\n### Options:\nA. 12000\nB. 22000\nC. 24000\nD. 26000\nE. 32000\n\n### Answer:\nZ=20 --> Y received 1/2 fewer votes than Z --> Y=Z-1/2*Z=10;\nX received 1/5 more votes than Y --> X=Y+1/5*Y=12.\nAnswer: A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train leaves Delhi at 9 a.m. at a speed of 30 kmph. Another train leaves at 2 p.m. at a speed of 40 kmph on the same day and in the same direction. How far from Delhi, will the two trains meet?\n\n### Options:\nA. 229\nB. 277\nC. 600\nD. 275\nE. 221\n\n### Answer:\nD = 30 * 5 = 150\nRS = 40 \u2013 30 = 10\nT = 150/10 = 15\nD = 40 * 15 = 600 km.,Answer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf k is an integer and 0.0010101 x 10^k is greater than 10, what is the least possible value of k?\n\n### Options:\nA. 2\nB. 3\nC. 4\nD. 5\nE. 6\n\n### Answer:\n0.0010101 * 10^k > 10\nWe need to move the decimal point to the right 4 places to get 10.101\nThis is equivalent to multiplying by 10^4.\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a group of 150 readers who read science fiction or literacy works or both, 120 read science fiction and 90 read literacy works. How many read both science fiction and literacy works?\n\n### Options:\nA. 70\nB. 60\nC. 90\nD. 100\nE. 110\n\n### Answer:\nConsider total number of reader n(S U L) = 150\nPeople who read science fiction n(S) = 120\nPeople who read literacy works n(L) = 90\nboth science fiction and literacy n(S \u00e2\u02c6\u00a9 L) = ?\nn(S U L) = n(S)+ n(L) - n(S \u00e2\u02c6\u00a9 L)\n150 = 120 + 90- n(S \u00e2\u02c6\u00a9 L)\nn(S \u00e2\u02c6\u00a9 L) = 210 -150\nn(S \u00e2\u02c6\u00a9 L) = 60\nSO People read both science fiction and literacy works are 160\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many words can be formed by using all letters of the word \u2018ILLINOIS\u2019 ?\n\n### Options:\nA. 40230\nB. 40320\nC. 30420\nD. 20340\nE. 40240\n\n### Answer:\nSolution\nThe word ILLINOIS contains 8 different letters.\nRequired number of words = 8P8 = 8 ! = (8 x 7 x 6 x 5 x 4 x 3 x 2 x 1) = 40320\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSiddharth wants to borrow Rs.7000 at rate of interest 6% p.a. at S.I and lend the same amount at C.I at same rate of interest for two years. What would be his income in the above transaction?\n\n### Options:\nA. s.21.60\nB. s.21.68\nC. s.25.2\nD. s.21.98\nE. s.21.29\n\n### Answer:\nAmount of money Siddharth borrowed at S.I at 6% p.a. for two years = Rs.7,000\nHe lend the same amount for C.I at 6% p.a. for two years.\n=> Siddharth's income = C.I - S.I\n= p[1 + r/ 100]n - p - pnr/100\n= p{ [1 + r/ 100]2 - 1 - nr/100\n= 7,000{ [1 + 6/100]2 - 1 - 12/100}\n= 7,000 {(1.06)2- 1 - 0.12} = 7,000(1.1236 - 1 - 0.12)\n= 7,000 (0.0036) = 7 * 3.6\n= Rs.25.2\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA, B and C invested Rs.6300, Rs.4200 and Rs.10500 respectively, in a partnership business. Find the share of A in profit of Rs.12100 after a year?\n\n### Options:\nA. Rs.3630\nB. Rs.2840\nC. Rs.3200\nD. Rs.5600\nE. Rs.5700\n\n### Answer:\n6300:4200:10500\n3:2:5\n3/10 * 12100 = 3630\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n12 chess players take part in a tournament. Every player plays twice with each of his opponents. How many games are to be played?\n\n### Options:\nA. 190\nB. 132\nC. 210\nD. 220\nE. 225\n\n### Answer:\nThough 2*(12C2) is the correct approcah to do this, but for people like me who find Perm, Comb n Prob a nightmare, an easy approach can be used.\nThe first guy has to play 2 matches with the rest of 11, so he'll play 22 matches.\nSimilarly, second guy has to play with the rest of 10 as his 2 games with the first guy are already played. So he plays 20 matches.\nThis continues like this and the total matches are 22+20+18...+2\n22+20+...+2 = 2(11+10+...+1) = 2((11*12)/2) = 11*12 = 132.\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA company has 17 equally qualified applicants for 4 open positions. How many different groups of 4 applicants can be chosen by the company to fill the positions if the order of selection does not matter?\n\n### Options:\nA. 2380\nB. 2400\nC. 2420\nD. 2440\nE. 2460\n\n### Answer:\n17C4=2380\nThe answer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA can do a piece of work in 80 days. He works at it for 10 days & then B alone\nfinishes the remaining work in 42 days. In how much time will A and B, working\ntogether, finish the work?\n\n### Options:\nA. 122days\nB. 41days\nC. 80days\nD. 42days\nE. 30days\n\n### Answer:\nWork done by A in 10 days=10/80=1/8\nRemaining work=(1-(1/8))=7/8\nNow, work will be done by B in 42 days.\nWhole work will be done by B in (42*8/7)=48 days\nTherefore, A's one day's work=1/80\nB\u2019s one day's work=1/48\n(A+B)'s one day's work=1/80+1/48=8/240=1/30\nHence, both will finish the work in 30 days.\nanswer E 30days\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many multiples of 2 are there between 1 and 58, exclusive?\n\n### Options:\nA. 21\nB. 22\nC. 24\nD. 26\nE. 28\n\n### Answer:\n28\nmultiples of 2 between 1 and 58 exclusive.\nfrom 2 * 1 upto 2*28, (1,2,3,4,...,28). Hence, 28 multiples !\ncorrect option is E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAnnie and Sam set out together on bicycles traveling at 15 and 12 km per hour respectively. After 40 minutes, Annie stops to fix a flat tire. If it takes Annie 25 minutes to fix the flat tire and Sam continues to ride during this time, how many minutes will it take Annie to catch up with Sam assuming that Annie resumes riding at 15 km per hour?\n\n### Options:\nA. 20\nB. 40\nC. 60\nD. 80\nE. 100\n\n### Answer:\nAnnie gains 3 km per hour (or 1 km every 20 minutes) on Sam.\nAfter 40 minutes Annie is 2 km ahead.\nSam rides 1 km every 5 minutes.\nIn the next 25 minutes, Sam rides 5 km so Sam will be 3 km ahead.\nIt will take Annie 60 minutes to catch Sam.\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If three marbles are drawn what is the probability that one is yellow and two are red?\n\n### Options:\nA. 24/455\nB. 3/91\nC. 12/455\nD. 15/91\nE. None of these\n\n### Answer:\nGiven that there are three blue marbles, four red marbles, six green marbles and two yellow marbles.\nWhen three marbles are drawn, the probability that one is yellow and two are red\n= (\u00b2C\u2081)(\u2074C\u2082)/\u00b9\u2075C\u2083\n= (2 * 4 * 3 * 3 * 2)/(1 * 2 * 15 * 14 * 13) = 12/455\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are 12 intermediate stations between two places A and B. Find the number of ways in which a train can be made to stop at 4 of these intermediate stations so that no two stopping stations are consecutive?\n\n### Options:\nA. 108\nB. 112\nC. 126\nD. 140\nE. None of these\n\n### Answer:\nExplanation :\nInitially, let's remove the 4 stopping stations\nThen we are left with 8 non-stopping stations (=12-4) as shown below\n(non-stopping stations are marked as 1,2 ... 8)\nNow there are 9 positions (as marked by * in the above figure) to place the 4 stopping stations\nsuch that no two stopping stations are consecutive\nThis can be done in 9C4 ways\nHence, required number of ways = 9C4\n=((9)(8)(7)(6)/(4)(3)(2)(1))=126\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFive pieces of wood have an average length of 120cm and a median length of 140cm. What is the maximum possible length, in cm, of the shortest piece of wood?\n\n### Options:\nA. a) 90\nB. b) 100\nC. c) 110\nD. d) 130\nE. e) 140\n\n### Answer:\nA. 90\nsum of all lengths of all 5 pieces of wood = 124 * 5 = 600\n3rd piece (sorted in increasing length) length = 140 (median)\nfor sum of first 2 wood length to become max, last two should be least.\nlet 4th, 5th wood also have length 140 each.\ntotal of last 3 = 140 * 3 = 420\nsum of first 2 = 600 - 420 = 180\neach of these 2 will have length 180/2 = 90\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAn aeroplane covers a certain distance at a speed of 240 kmph in 5 hours. To cover the same distance in 1 hours, it must travel at a speed of:\n\n### Options:\nA. 150\nB. 720\nC. 160\nD. 80\nE. 12\n\n### Answer:\nExplanation:\nSpeed = Distance/Time\nSpeed =1200(5/3)km/hr\nRequired speed =(1200*(3/5))km/hr=720 km/hr\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA grocer buys apples for 81\u00a2 per pound. If 10% of the apples goes bad and he still wants to make a 20% profit over his purchase price, what should be the sales price?\n\n### Options:\nA. 100\u00a2\nB. 108\u00a2\nC. 110\u00a2\nD. 95\u00a2\nE. 99\u00a2\n\n### Answer:\nfor making calculation simple let us consider he buys 10pounds @ 81/pound=810\u00a2 in total .\n10% apples lost...means 9 pounds left.\nfurther he wants 20% profit on 810 \u00a2\nmeans he wants to earn 972\u00a2\nsales price should be 972/9=\u00a2 108\nAns B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nBruno and Sacha are running in the same direction around a stadium. Sacha runs at a constant speed of 6 meters per second, and Bruno runs at a constant speed of 5 meters per second. At a certain point Sacha overtakes Bruno. If three minute afterward, Sacha stops and waits for Bruno to reach him, then how many seconds does he have to wait?\n\n### Options:\nA. 12\nB. 24\nC. 36\nD. 60\nE. 72\n\n### Answer:\nthe difference of the speed is 1m per second so in three minute Sacha will be 180 m ahead of Bruno..\nBruno will cover this in 180/5=36 secs..\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA fair sided die labeled 1 to 6 is tossed three times. What is the probability the sum of the 3 throws is 16?\n\n### Options:\nA. 1/6\nB. 7/216\nC. 1/36\nD. 9/216\nE. 11/216\n\n### Answer:\nthe total number of possible outcomes is, of course, 6^3.\nFortunately, there are only two combinations of three dice throws that will give you a sum of 16:\n5, 5, 6\n4, 6, 6\n(I have a hard time remembering a real GMAT question that would give you 12, as the number of potential combinations is indeed inordinately large and difficult to map out.)\nHowever, our denominator counts out the number of throwing sequences (permutations) and not just combinations, so we will need to do the same. Effectively there are three throwing sequences for either combination:\n6, 5, 5\n5, 6, 5\n5, 5, 6\n4, 6, 6\n6, 4, 6\n6, 6, 4\nSo 6 throwing sequences we want divided by 6^3 throwing sequences we could get gives us 1/(6^2) or 1/36.\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo goods train each 500 m long are running in opposite directions so parallel tracks.Their speeds are 45 kmph and 30 kmph respectively.Find the time taken by the slower train to pass the driver of the first one\n\n### Options:\nA. 12 sec\nB. 24 sec\nC. 48 sec\nD. 60 sec\nE. 65 sec\n\n### Answer:\nonly need length of slower train which is L=500m\nrelative sped (both are opposite direction)\ns=45+30=75kmph\n75*5/18=125/6 m/s\ntime =dist/speed\n=(500*6)/125=24 sec\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the length of the wire required to go 15 times round a square field containing 69696 m2?\n\n### Options:\nA. 15840\nB. 19879\nC. 27997\nD. 15842\nE. 15823\n\n### Answer:\na2 = 69696 => a = 264\n4a = 1056\n1056 * 15\n=15840\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a match, awards are given to each of 11 members of the team and a trophy to the team. In all winning team gets 2.75kg weight awards. If the weight of match wining trophy is 1.275kg, what the weight of each player giving weight of trophy ?\n\n### Options:\nA. 134.09 gms\nB. 144.09 gms\nC. 154.09 gms\nD. 164.09 gms\nE. 174.09 gms\n\n### Answer:\nTotal weight of all the awards for winning team is 2.75kg = 2750gms\ntrophy weight is 1.275 kg=1275gms\nnow rest weight = 2750-1275= 1475gms\nrest weight divided in 11 players is = 1475/11 = 134.09 gms\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a race with 30 runners where 6 trophies will be given to the top 6 runners (the trophies are distinct: first place, second place, etc), how many ways can this be done?\n\n### Options:\nA. 6^6 ways\nB. 8^9 ways\nC. 7^8 ways\nD. 8^7 ways\nE. 8^6 ways\n\n### Answer:\n6 people can be prized with distinct prizes in 6^6 ways\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n18 chess players take part in a tournament. Every player plays twice with each of his opponents. How many games are to be played?\n\n### Options:\nA. 230\nB. 274\nC. 306\nD. 354\nE. 424\n\n### Answer:\n2*18C2 = 2*153 = 306\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich number is the odd one out in the list ?\n\n### Options:\nA. 38442\nB. 78426\nC. 84029\nD. 67626\nE. 72927\n\n### Answer:\nC\n84029\nAll the others are three digit numbers followed by their square root, eg 729 followed by its square root, 27.\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average marks of a class of 30 students is 40 and that of another class of 50 students is 60. Find the average marks of all the students?\n\n### Options:\nA. 52.6\nB. 52.4\nC. 52.1\nD. 52.5\nE. 52.9\n\n### Answer:\nSum of the marks for the class of 30 students = 30 * 40 = 1200\nSum of the marks for the class of 50 students = 50 * 60 = 3000\nSum of the marks for the class of 80 students =\n1200 + 3000 = 4200\nAverage marks of all the students = 4200/80 = 52.5.Answer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich of the following inequalities is equivalent to 40 + 6x > -3x - 11x + 20?\n\n### Options:\nA. x < 1\nB. x < -1\nC. x < 3\nD. x < -3\nE. x < 4\n\n### Answer:\nYou can work with the inequality in the same way as you do when you have the equal to sign. You can take terms to the other side by flipping their sign, you can multiply/divide the inequality by the same term on both sides of the equation etc.\nThe only important thing to note is the following:\nWhen you multiply/divide by a negative number, the sign of the inequality flips.\nTo illustrate,\n40 + 6x > -3x - 11x + 20\n40 + 20 > - 20x (Correct)\n60 > - 20x (Correct)\n-3 > x (Correct)\nthe correct option is D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe area of a square field 3136 sq m, if the length of cost of drawing barbed wire 3 m around the field at the rate of Rs.1.50 per meter. Two gates of 1 m width each are to be left for entrance. What is the total cost?\n\n### Options:\nA. 278\nB. 279\nC. 999\nD. 287\nE. 287\n\n### Answer:\na2 = 3136 => a = 56\n56 * 4 * 3 = 672 \u2013 6 = 666 * 1.5\n= 999\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAshley paid 5 dollars for 1 notebook and 1 pencil. If both prices were integers, how many pencils did Ashley buy if she paid 93 dollars for the pencils and for 15 notebooks?\n\n### Options:\nA. 6.\nB. 16.\nC. 18\nD. 21\nE. 26\n\n### Answer:\n5 = 1P + 1 N\n93 = XP + 15N, where X is the number of pencils\nPossible prices for 1P & 1N (integers):\nN = 1 P = 4 then 15N = 15, 4X = 93 - 15 = 78, X = 19.5 (not an integer)\nN = 2 P = 3 then 15N = 30, 3X = 93 - 30 = 63, X = 21 (the answer we were looking for, no need to continue calculations)\nN = 3 P = 2\nN = 4 P =1\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRobert is traveling from one end of a forest to the other. In order to find his way back, he is leaving morsels of bread in the following pattern: 2 morsels of milk, 3 morsels of white, and 1 morsel of rye. The pattern repeats after he leaves the morsel of rye. If Robert drops 2,000 morsels of bread, what are the last 3 morsels of bread that he drops?\n\n### Options:\nA. rye \u2212 milk \u2212 milk\nB. milk \u2212 milk \u2212 white\nC. white \u2212 rye \u2212 milk\nD. white \u2212 white \u2212 white\nE. white \u2212 white \u2212 rye\n\n### Answer:\nIn a single round Robert drops 6 morsels.\nRemainder (2000/6) = 2\nFinal action = 2 drops of milk --> Options B, C, D and E can be eliminated\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nShare Rs.4200 among John, Jose & Binoy in the ration 2 : 4 : 6.Find the amount received by John?\n\n### Options:\nA. 900\nB. 980\nC. 1200\nD. 1240\nE. 1400\n\n### Answer:\nAmount received by sanjay.\n4 / 12 X 4200 = 1400= ( related ratio / sum of ratio ) x Total amount\nSo, the Amount received by sanjay is 1400.\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA driver of auto rickshaw makes a profit of 20% on every trip when he carries 3 passengers and the price of petrol is Rs. 30 a litre. Find the % profit for the same journey if he goes for 4 passengers per trip and the price of petrol reduces to Rs. 24 litres?\n\n### Options:\nA. 40%.\nB. 60%.\nC. 80%.\nD. 100%.\nE. 120%.\n\n### Answer:\n20% of 30 = 6 rupee profit\n36/3 = 12 rupee per passenger\n12*4 = 48\n48 - 24 = 24.\nso profit = 100%.\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe Coen family consists of a father, a mother, two children and a dog. A photographer is about to take the family's picture. How many different arrangements (of standing in a row) does the photographer have, if it is known that the father insists of standing by his first child?\n\n### Options:\nA. 12\nB. 24\nC. 30\nD. 48\nE. 120\n\n### Answer:\nWe need to find the number of arrangements of Father, Mother, Child-1, Child-2, and a Dog, so that F and C1 are always together.\nConsider F and C1 to be one unit, then we would have total of four units: {FC1}, {M}, {C2}, {D}. The number of arrangements of these four units is 4!, but F and C1 within their unit can be arranged in 2 ways: {FC1} or {C1F}, so total number of arrangements is 4!*2=48.\nAnswer: D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe radius of a cone is 8 m, height 6 m. Find the slant height?\n\n### Options:\nA. 5\nB. 10\nC. 15\nD. 20\nE. 25\n\n### Answer:\nCone slant height (l) = \u221ar(power2)+h(power2)\n= \u221a64+36 = 10 m.\nAnswer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the odd man out. 2, 3, 5, 9, 12, 17, 23\n\n### Options:\nA. 12\nB. 9\nC. 23\nD. 2\nE. 3\n\n### Answer:\nExplanation :\n2\n2 + 1 = 3\n3 + 2 = 5\n5 + 3 = 8\n8 + 4 = 12\n12 + 5 = 17\n17 + 6 = 23\nie, 8 should have come in place of 9\nAnswer : Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThree numbers are in the ratio 1 : 2 : 3 and their H.C.F is 12. The numbers are\n\n### Options:\nA. 4, 8, 12\nB. 5, 10, 15\nC. 10, 20, 30\nD. 12, 24, 36\nE. None of these\n\n### Answer:\nExplanation:\nLet the required numbers be x, 2x, 3x. Then, their H.C.F =x. so, x= 12\nThe numbers are 12, 24, 36. Answer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSpandy travels from X to Y at a speed od 40 kmph and returns by increasing his speed by 50%. What is his average speed for the whole journey?\n\n### Options:\nA. 36 kmph\nB. 45 kmph\nC. 48 kmps\nD. 45 kmps\nE. 42 kmps\n\n### Answer:\nExplanation :\nLet the distance between X and Y be x km.\nTime taken from X to Y @ 40 km/h=(x/40)hours\nTime taken from Y to X @ 60 km/h=(x/60)hours\nAverage speed=2x/((x/40)+(x/60))= 48 km/h.\nAnswer : C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe difference between the compound interest and simple interest on a certain sum at 20% per annum for 2years is $500. Find the sum?\n\n### Options:\nA. $10000\nB. $50000\nC. $15200\nD. $12500\nE. $15000\n\n### Answer:\nLet the sum be $x\nC.I. = x(1+20/100)^2 - x = 35x/100\nS.I. = (X*20*2)/100 = 2x/5\nC.I.- S.I. = (35x/100)-(2x/5) = 5x/100\n5x/100 = 500\nx = 10000\nAnswer is A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAn inspector rejects 0.08% of the meters as defective, How many meters he examine to reject 2 meteres\n\n### Options:\nA. 1300\nB. 1400\nC. 2400\nD. 2500\nE. 2600\n\n### Answer:\nIt means that 0.08% of x = 2\n(8100\u00d7100 \u00d7x)=2\nx=2\u00d7100\u00d71008\nx=2500\nANSWER :D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nNails and screws are manufactured at a uniform weight per nail and a uniform weight per screw. If the total weight of one screw and one nail is half that of 6 screws and one nail, then the total weight of 3 screws, and 3 nails is how many times that of 2 screws and 4 nails?\n\n### Options:\nA. a. 4\nB. b. 5/2\nC. c. 2\nD. d. 3/2\nE. e. 5/4\n\n### Answer:\nlet the weight of nail be n and that of screw be s..\nso s+w=1/2 * (6s+1n)...\nor 1n = 4s..\nlets see the weight of 3 s and 3n= 3s+3*4s=15s..\nand weight of 2s and 4n= 2s+4*2s=10s..\nratio= 15s/10s=15/10=3/2\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe age of man is three times the sum of the ages of his two sons. Eight years hence,his age will be double of the sum of the ages of his sons.The father\u00e2\u20ac\u2122s present age is :\n\n### Options:\nA. 40 years\nB. 45 years\nC. 50 years\nD. 55 years\nE. 72 years\n\n### Answer:\nSolution\nLet the sum of present ages of the two sons be x years.\nThen,father's present age = 3x years.\n\u00e2\u02c6\u00b4 (3x + 8)=2 (x +16) \u00e2\u2021\u201d 3x + 8 = 2x + 32 \u00e2\u2021\u201d x =24.\nHence,father's present age = 72 years. Answer E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThree numbers are in the ratio 5 : 6 : 7. The sum of its longest and smallest numbers equals the sum of the third number and 48. Find the third number?\n\n### Options:\nA. 18\nB. 76\nC. 48\nD. 27\nE. 12\n\n### Answer:\nLet the numbers be 5x, 6x, 7x.\nLargest number = 7x.\nSmallest number = 5x.\nThird number = 6x.\n7x + 5x = 6x + 48\n6x = 48 => third number is 48.\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOne cutting machine cuts 100 metal bars in 30 minutes.Another machine does the same job in 30 seconds.What time will it take if both machines are put on the same work ?\n\n### Options:\nA. 25.0 seconds\nB. 29.5 seconds\nC. 30.0 seconds\nD. 30.5 seconds\nE. 30.7 seconds\n\n### Answer:\nBy guess it is clear that the time taken will be less than 30 seconds and very near to it. Therefore, answer 29.5 seconds will be correct. Answer-B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average (arithmetic mean) of four different positive integers is 15. If the first of these integers in 3 times the second integer and the second integer is 2 less than the third integer, what is the least possible value of the fourth integer?\n\n### Options:\nA. 8\nB. 4\nC. 3\nD. 2\nE. 1\n\n### Answer:\nLet the second integer be x and the fourth be a.\nThen [3x + x + (x+2) + a]/4 =15\n=> 5x + 2 + a = 60\n=> 5x + a = 58\n=> a = 58 - 5x\nFrom the above equation we can see that a is minimum when x is maximum, provided both are positive\nThe maximum value that x can take in the above equation while still keeping a positive is x=10\nThis gives us a= 58 - 50 =8\nTherefore the minimum value that the fourth integer can have is 8. Option A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n12 points lie on a circle. How many cyclic quadrilaterals can be drawn by using these points?\n\n### Options:\nA. 334\nB. 377\nC. 495\nD. 766\nE. 261\n\n### Answer:\nExplanation:\nFor any set of 4 points we get a cyclic quadrilateral. Number of ways of choosing 4 points out of 12 points is \\inline {\\color{Black}12C_4{}} = 495.\nTherefore, we can draw 495 quadrilaterals\nAnswer: C) 495\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA father said to his son, \"I was as old as you are at the present at the time of your birth\". If the father's age is 20 years now, the son's age five years back was:\n\n### Options:\nA. 9 years.\nB. 8 years.\nC. 7 years.\nD. 5 years.\nE. 6 years.\n\n### Answer:\nLet the son's present age be x years. Then, (20- x) = x\n2x = 20\nx = 10.\nSon's age 5 years back (10 - 5) = 5 years.\nAnswer: Option D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA candidate got 32% of the votes polled and he lost to his rival by 1908 votes. How many votes were cast?\n\n### Options:\nA. 5100\nB. 5200\nC. 5300\nD. 5400\nE. 5500\n\n### Answer:\nLet x be the total number of votes.\n0.32x + 1908 = 0.68x\n0.36x = 1908\nx = 1908/0.36 = 5300\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMixture A is 30 percent alcohol, and mixture B is 60 percent alcohol. If the two are poured together to create a 4-gallon mixture that contains 40 percent alcohol, approximately how many gallons of mixture A are in the mixture?\n\n### Options:\nA. 0.8\nB. 0.7\nC. 0.6\nD. 0.5\nE. 0.4\n\n### Answer:\n(60-50)/(50-30) = Qa/Qb\n10/20= Qa/Qb\n1/2 = Qa/Qb\nQa = (1/6) * 4 = 4/6 = 1/2 = 0.50\nAnswer : D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a fuel station the service costs $2.75 per car, every liter of fuel costs 0.65$. Assuming that a company owns 12 cars and that every fuel tank contains 55 liters and they are all empty, how much money total will it cost to fuel all cars?\n\n### Options:\nA. 320$\nB. 380$\nC. 420$\nD. 450$\nE. 462$\n\n### Answer:\n12*2.75 + 0.65*12*55 = 462 hence - E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nEach of the products produced yesterday was checked by worker x or worker y. 0.5% of the products checked by worker x are defective and 0.8% of the products checked by worker y are defective. If the total defective rate of all the products checked by worker x and worker y is 0.55%, what fraction of the products was checked by worker y?\n\n### Options:\nA. 1/3\nB. 1/4\nC. 1/5\nD. 1/6\nE. 1/8\n\n### Answer:\nx: 0.5% is 0.05%-points from 0.55%.\ny: 0.8% is 0.25%-points from 0.55%.\nTherefore the ratio of products checked by y:x is 1:5.\nThus, worker y checked 1/6 of the products.\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man rides at the rate of 20km/hr. But stops 10minutes to change horses at the end of every 25th kilometer. How long will he take to go a distance of 175 kilometers?\n\n### Options:\nA. 9hr\nB. 8 hr 30 min\nC. 9hr 45min\nD. 6hr 20min\nE. 8hr 40min\n\n### Answer:\nspeed of man = 20km/hr\nnumber of rests = (175/25)-1 = 6\ntime taken for the man = (175/20)+6*(10/60) = 9 hr 45 min\nAnswer is C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf G is a negative integer, which of the following must be a negative integer?\n\n### Options:\nA. G + 1\nB. G/2+3\nC. G^4\nD. G \u2013 y\nE. G^11\n\n### Answer:\nWe need to check each option here:\nA. G + 1\nThis will depend on the value of G. Nothing can be said\nB. G/2+3\nThis will depend on the value of G. Nothing can be said\nC. G^4\nThis will always be positive. Even powers of negative numbers are positive and odd powers are negative\nD. G \u2013 y\nThis will depend on the value of G. Nothing can be said\nE. G^11\nThis will always be negative. Even powers of negative numbers are positive and odd powers are negative\nCorrect Option: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSakshi can do a piece of work in 20 days .Tanya is 25% more efficient than Sakshi. the number of days taken by tanya to do the same piece of work is?\n\n### Options:\nA. 25days\nB. 45days\nC. 24days\nD. 16days\nE. 36days\n\n### Answer:\nThe ratio of times taken by Sakshi and Tanya=125:100=5:4.\nsuppose Tanya takes x days to do the work.\n5:4::20:x\nx=(4*20)/5\nx=16 days\nTanya can do work in 16 days\nAnswer(D)\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFor any integer k > 1, the term \u201clength of an integer\u201d refers to the number of positive prime factors, not necessarily distinct, whose product is equal to k. For example, if k = 24, the length of k is equal to 4, since 24 = 2 \u00d7 2 \u00d7 2 \u00d7 3. If x and y are positive integers such that x > 1, y > 1, and x + 3y < 940, what is the maximum possible sum of the length of x and the length of y?\n\n### Options:\nA. 24\nB. 22\nC. 16\nD. 18\nE. 20\n\n### Answer:\nwe know that : x > 1, y > 1, and x + 3y < 940,\nand it is given that length means no of factors.\nfor any value of x and y, the max no of factors can be obtained only if factor is smallest noall factors are equal.\nhence, lets start with smallest no 2.\n2^1 =2\n2^2 =4\n2^3=8\n2^4=16\n2^5=32\n2^6=64\n2^7=128\n2^8=256\n2^9=512\n2^10 =1024 (opps//it exceeds 1000, so, x can't be 2^10)\nso, max value that X can take is 2^9 , for which haslength of integeris 9.\nnow, since x =512 ,x+3y<940\nso, 3y<428\n==> y<428/3\nso, y can take any value which is less than 428/3. and to get the maximum no of factors of smallest integer, we can say y=2^7\nfor 2^7 has length of integer is 7.\nSO, combined together : 9+7 = 16.\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a committee of 4 people is to be selected from among 5 married couples so that the committee does not include two people who are married to each other, how many such committees are possible?\n\n### Options:\nA. 20\nB. 40\nC. 50\nD. 80\nE. 120\n\n### Answer:\nEach couple can send only onerepresentativeto the committee. Let's see in how many ways we can choose 4 couples (as there should be 4 members) each to send onerepresentativeto the committee: 5C4=5.\nBut these 4 chosen couples can send two persons (either husband or wife): 2*2*2=2^3=8.\nTotal # of ways: 5C3*2^3=40.\nAnswer: B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how many ways can 5 letters be posted in 3 post boxes, if any number of letters can be posted in all of the three post boxes?\n\n### Options:\nA. 5 C 3\nB. 5 P 3\nC. 5(3)\nD. 3(5)\nE. 2(5)\n\n### Answer:\nExplanatory Answer\nSampling with replacement\nThe first letter can be posted in any of the 3 post boxes. Therefore, we have 3 possibilities.\nSimilarly, the second, the third, the fourth and the fifth letter can each be posted in any of the 3 post boxes.\nEach of the 5 letters has 3 possibilities because we can post any number of letters in all of the boxes.\nTherefore, the total number of ways the 5 letters can be posted in 3 boxes is 3 * 3 * 3 * 3 * 3 = 3(5)\nChoice D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many multiples of 5 are there between 5 to 100?\n\n### Options:\nA. 9\nB. 18\nC. 17\nD. none of these\nE. Cannot be determined\n\n### Answer:\nExplanation :\nAs you know, multiples of 5 are integers having 0 or 5 in the digit to the extreme right (i.e. the units place).\nSo the numbers are 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95.\nAnswer : B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA can complete a work in 12days and B can do the same work in 6days. If A after doing 3days, leaves the work, find in how many days B will do the remaining work?\n\n### Options:\nA. 2 1/2days\nB. 4 1/2days\nC. 6 1/2days\nD. 7 1/2days\nE. 10 1/2days\n\n### Answer:\nThe required answer = (12-3)*6 / 12 = 54/12 = 4 1/2days\nAnswer is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average weight of 5 person's increases by 10.0 kg when a new person comes in place of one of them weighing 40 kg. What might be the weight of the new person?\n\n### Options:\nA. 76 kg\nB. 76.5 kg\nC. 90 kg\nD. Data inadequate\nE. None of these\n\n### Answer:\nExplanation:\nTotal weight increased = (5 x 10.00) kg = 50 kg.\nWeight of new person = (40 + 50) kg = 90 kg.\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe area of a rectangular field is equal to 300 square meters. Its perimeter is equal to 70 meters. Find the width of this rectangle.\n\n### Options:\nA. W = 27\nB. W = 15\nC. W = 38\nD. W =43\nE. W = 13\n\n### Answer:\nL * W = 300 : area , L is the length and W is the width.\n2 L + 2 W = 70 : perimeter\nL = 35 - w : solve for L\n(35 - W) * W = 300 : substitute in the area equation\nW = 15 and L = 20 : solve for W and find L using L = 35 - w.\ncorrect answer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat percent of a day is six hours?\n\n### Options:\nA. 20.83%\nB. 25%\nC. 18x2/3%\nD. 22x1/2%\nE. None of these\n\n### Answer:\nExplanation :\nRequired percentage = (6/24100)%\n= 25%.\nAnswer : B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many bricks, each measuring 25 cm x 11.25 cm x 6 cm, will be needed to build a wall of 8 m x 6 m x 22.5 cm?\n\n### Options:\nA. 6400\nB. 6410\nC. 6440\nD. 6500\nE. 6800\n\n### Answer:\nNumber of bricks = Volume of Wall/Volume of Bricks\n=800x600x22.5/21x11.25x6= = 6400\nanswer :A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nEddy and Freddy start simultaneously from city A and they travel to City B and City C respectively. Eddy takes 3 hours and Freddy takes 4 hours to complete the journey. If the distance between City A and City B is 450 kms and City A and City C is 300 kms. What is the ratio of their average speed of travel? (Eddy: Freddy)\n\n### Options:\nA. 8/3\nB. 2/1\nC. 8/5\nD. 5/8\nE. 5/3\n\n### Answer:\nDistance traveled by Eddy = 600 km\nTime taken by Eddy = 3 hours\nAverage speed of Eddy = 450/3 = 150 km/hour\nDistance traveled by Freddy = 300 km\nTime taken by Freddy = 4 hours\nAverage speed of Freddy = 300/4 = 75 km/hour\nRatio of average speed of Eddy to Freddy = 150/75 = 2/1\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA car takes 6 hours to cover a distance of 540 Km. how much should the speed in Kmph be maintained to cover the same direction in 3/2th of the previous time?\n\n### Options:\nA. 50 Kmph\nB. 60 Kmph\nC. 65 Kmph\nD. 70 Kmph\nE. None\n\n### Answer:\nTime = 6\nDistence = 540\n3/2 of 6 hours = 6 * 3/2 = 9 Hours\nRequired speed = 540/9 = 60 Kmph\nB)\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJill invests $10000 in an account that pays an annual rate of 3.96%, compounding semi-annually. Approximately how much E does she have in her account after two years?\n\n### Options:\nA. $10079.44\nB. E=$10815.83\nC. $12652.61\nD. $14232.14\nE. $20598.11\n\n### Answer:\nPS. I guess one can use simple interest to solve cause the answer choices are quite spread between you can easily arrive at something near 8%\nHence B the answer\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 8 men and 2 boys working together, can do four times as much work per hour as a man and a boy together. Find the ratio of the work done by a man and that of a boy for a given time?\n\n### Options:\nA. 3:2\nB. 2:1\nC. 3:3\nD. 1:2\nE. 6:1\n\n### Answer:\n8M + 2B = 4(1M + 1B)\n8M + 2B = 4M + 4B\n4M = 2B\nThe required ratio of work done by a man and a boy = 2:4=1:2\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA sum of money at simple interest amounts to Rs. 825 in 3 years and to Rs. 854 in 4 years. The sum is?\n\n### Options:\nA. Rs. 738\nB. Rs. 638\nC. Rs. 650\nD. Rs. 730\nE. Rs. 735\n\n### Answer:\nS.I. for 1 year = (854 - 825) = Rs. 29\nS.I. for 3 years = 29 * 3 = Rs. 87\nPrincipal = (825 - 87) = Rs. 738.\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf S + A < S - A < A - S, which of the following is correct?\n\n### Options:\nA. A < S < 0.\nB. S < A < 0.\nC. S < 0 < A.\nD. 0 < B < A.\nE. B > A > 0.\n\n### Answer:\nCheck first inequality\nS + A < S - A\nA<-A\nA is -ve\nCheck another equality\nS - A < A - S\n-2A<-2S\nA>S\nCombining both 0>A>S\nOption B fits only\nAns B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich of the following fractions Q has a decimal equivalent that is a terminating decimal?\n\n### Options:\nA. 10/189\nB. 15/196\nC. 16/225\nD. 25/144\nE. 39/128\n\n### Answer:\nThe fraction Q will terminate if and only if the denominator has prime divisors only 2 and 5 or both.\nA. 10/189 = 10/(3*3*3*7) Non-term.\nB. 15/196 = 15/(2*2*7*7) Non-term.\nC. 16/225 = 16/(5*5*3*3) Non-term.\nD. 25/144 = 25/(2*2*2*7) Non-term.\nE. 39/128 = 39/(2^7) Terminatingbecause only 2 in denominator.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the rate percent when the simple interest on Rs.9100 amount to Rs.455 in 3 Years?\n\n### Options:\nA. 3.7%\nB. 5.7%\nC. 6.7%\nD. 8.7%\nE. 9.7%\n\n### Answer:\n455 = (4100*3*R)/100\nR = 3.7%\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe median annual household income in a certain community of 21 households is $50,000. If the mean income of a household increases by 10% per year over the next 2 years, what will the median M income in the community be in 2 years?\n\n### Options:\nA. $50,000\nB. $60,000\nC. $60,500\nD. $65,000\nE. Cannot be determined\n\n### Answer:\nAnswer is E, because there are different numbers in the set and we are not sure which side of the numbers in the set will be increased so the mean M is increase by 10%. It could be the case that small number of higher end incomes increased a little or many low end incomes increased - it cannot be identified.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nClaire has a total of 80 pets consisting of gerbils and hamsters only. One-quarter of the gerbils are male, and one-third of the hamsters are male. If there are 25 males altogether, how many gerbils does Claire have?\n\n### Options:\nA. 39\nB. 50\nC. 54\nD. 57\nE. 36\n\n### Answer:\nG+H =80 ...1 ; G/4 +H/3 =25 ....2 OR 3G +4H =25*12 =300\nG =80-H OR 3(80-H) +4H =300 H = 300-240 =60 THEN G= 96-60 =36\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA ship sails 4 degrees north, then 13 S. then 17 N. then 24 S. and has finally 11 degrees of south latitude. What was her latitude at starting ?\n\n### Options:\nA. 5\nB. 1\nC. 2\nD. 3\nE. None of these\n\n### Answer:\nLet x = the latitude sought.\nThen marking the northings +, and the southings -;\nBy the statement x + 4 - 13 + 17 - 24 = -11\nAnd x = 5.\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a no. when divided by 44, gives 432 as quotient and 0 as remainder. What will be the remainder when dividing the same no. by 34\n\n### Options:\nA. 2\nB. 3\nC. 5\nD. 7\nE. 9\n\n### Answer:\nP \u00c3\u00b7 44 = 432\n=> P = 432 * 44 = 19008\nP / 34 = 19008 / 34 = 559, remainder = 2\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are 24 Kids in a classroom. 12 Kids are wearing socks and 8 are wearing Shoes. 6 Kids are wearing both.\nHow many are Bare Feet ?\n\n### Options:\nA. 10\nB. 20\nC. 40\nD. 50\nE. 70\n\n### Answer:\nA\n10\n12 kids wear socks\n8 kids wear shoes\n6 wear both.\n12 \u2013 6 = 6 (wear only socks)\n8 \u2013 6 = 2 (wear only shoes)\n6 (wear both)\nhence, 24 -14 = 10\n10 kids are with bare feet.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train of length 240 metres takes 60 seconds to cross a tunnel of length 450 metres. What is the speed of the train in km/hr?\n\n### Options:\nA. 10 km/hr.\nB. 20 km/hr.\nC. 30 km/hr.\nD. 40 km/hr.\nE. None\n\n### Answer:\nSol.\nSpeed = [240 + 450 / 60] m/sec = [690/ 60 * 18/5] km/hr = 41.4 km/hr.\nAnswer E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA bag is filled with pennies and nickels in the ratio of 5 to 3. There are 30 nickles in the bag, how many coins are there in that bag?\n\n### Options:\nA. 40\nB. 50\nC. 65\nD. 70\nE. 80\n\n### Answer:\nA ratio of pennies to nickels of 5 to 3 means that we can write the number of pennies and nickels in the form\nnumber of pennies = 5x and number of nickels = 3x\nBut we know the number of nickels, 30. Hence\n3x = 30\nSolve for x\nx = 10\nThe total number of coins is given by\n5x + 3x = 8x = 8 \u00d7 10 = 80\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nP, Q and R can do a work in 20, 30 and 60 days respectively. How many days does it need to complete the work if P does the work and he is assisted by Q and R on every third day?\n\n### Options:\nA. 10 days\nB. 14 days\nC. 15 days\nD. 9 days\nE. 19 days\n\n### Answer:\nExplanation :\nAmount of work P can do in 1 day = 1/20\nAmount of work Q can do in 1 day = 1/30\nAmount of work R can do in 1 day = 1/60\nP is working alone and every third day Q and R is helping him\nWork completed in every three days = 2 \u00d7 (1/20) + (1/20 + 1/30 + 1/60) = 1/5\nSo work completed in 15 days = 5 \u00d7 1/5 = 1\nIe, the work will be done in 15 days\nAnswer : Option C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 13 kmph and 21 kmph respectively. When they meet, it is found that one train has traveled 60 km more than the other one. The distance between the two stations is?\n\n### Options:\nA. 477\nB. 408\nC. 279\nD. 276\nE. 291\n\n### Answer:\n1h ----- 5\n? ------ 60\n12 h\nRS = 13 + 21 = 34\nT = 12\nD = 34 * 12 = 408.Answer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nEach shelf of a bookcase contains 24 books. If the librarian took out 34 books and rearranged the remaining books so that all shelves but the last one contained 16 books and the last shelf contained 22 books, how many shelves does the bookcase have?\n\n### Options:\nA. A)4\nB. B)5\nC. C)6\nD. D)8\nE. E)9\n\n### Answer:\nDenoting x the number of the shelves,\nwe can build an equation: 24x=16(x\u22121)+22+34\nSolving the equation, we get x=5\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA baker filled with a measuring cup with 1/2 cup water. He poured 1/2 of the water into the batter, and then spilled 1/8 of the water on the floor. How much water will the baker needed to add what is left in the cup to have 50% more than what he started with?\n\n### Options:\nA. 1/8 cup\nB. 3/8 cup\nC. 1/4 cup\nD. 1/2 cup\nE. 5/8 cup\n\n### Answer:\n1/2 is the original water in cup .half in batter.So left is 1/4 out which 1/8 is spilled out.So again left with 1/8.\nso 50% more than what he started was = 1/2+1/2*(1/2)=3/4\nAmount of water needed to add = 6/8 - 1/8=5/8\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average marks in mathematics scored by the pupils of a school at the public examination were 39. If four of these pupils who actually scored 5, 12, 15 and 19 marks at the examination had not been sent up, the average marks for the school would have been 44. Find the number of pupils sent up for examination from the school?\n\n### Options:\nA. 25\nB. 20\nC. 30\nD. 35\nE. 40\n\n### Answer:\n39x = 5 + 12 + 15 + 19 + (x \u00e2\u20ac\u201c 4)44\nx = 25\nANSWER A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n7^6n -1^ 6n When n is an integer > 0 is divisible by\n\n### Options:\nA. 112\nB. 127\nC. 145\nD. 187\nE. 185\n\n### Answer:\n127\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA, B, C subscribe Rs. 50,000 for a business. A subscribes Rs. 4000 more than B and B Rs. 5000 more than C. Out of a total profit of Rs. 35,000, A receives:\n\n### Options:\nA. Rs. 8400\nB. Rs. 11,900\nC. Rs. 13,600\nD. Rs. 14,700\nE. Rs. 13700\n\n### Answer:\nLet C = x.\nThen, B = x + 5000 and A = x + 5000 + 4000 = x + 9000.\nSo, x + x + 5000 + x + 9000 = 50000\n3x = 36000\nx = 12000\nA : B : C = 21000 : 17000 : 12000 = 21 : 17 : 12.\nA's share = Rs. (35000 x\t21/50) = Rs. 14,700.\nTHE CORRECT ANSWER IS D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average of 10 numbers is calculated as 21. It is discovered later on that while calculating the average, one number namely 36 was wrongly read as 26. The correct average is?\n\n### Options:\nA. A)16\nB. B)18\nC. C)19\nD. D)22\nE. E)24\n\n### Answer:\nExplanation:\n10 * 21 + 36 \u2013 26 = 220=>220/10 = 22\nD)\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man was engaged on a job for 30 days on the condition that he would get a wage of Rs. 10 for the day he works, but he have to pay a fine of Rs. 2 for each day of his absence. If he gets Rs. 216 at the end, he was absent for work for ... days.\n\n### Options:\nA. 7 days\nB. 5 days\nC. 3 days\nD. 4 days\nE. 8 days\n\n### Answer:\nThe equation portraying the given problem is:\n10 * x \u2013 2 * (30 \u2013 x) = 216 where x is the number of working days.\nSolving this we get x = 23\nNumber of days he was absent was 7 (30-23) days.\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the greatest prime factor of 8!7! + 7!6! ?\n\n### Options:\nA. 7\nB. 11\nC. 13\nD. 17\nE. 19\n\n### Answer:\n8!7! + 7!6! = 7!6!(8*7+1) = 7!*6!*57 = 7!*6!*3*19\nThe answer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe radius of a cylinder is 8 m, height 13 m. The volume of the cylinder is:\n\n### Options:\nA. 2200\nB. 2614.9\nC. 3300\nD. 1100\nE. 4400\n\n### Answer:\nCylinder volume = \u00cf\u20acr(power2)h\n= 22/7 \u00c3\u2014 8 \u00c3\u2014 8 \u00c3\u2014 13\n= 2614.9 m(power3)\nAnswer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMaxwell leaves his home and walks toward Brad's house at the same time that Brad leaves his home and runs toward Maxwell's house. If the distance between their homes is 20 kilometers, Maxwell's walking speed is 4 km/h, and Brad's running speed is 6 km/h, what is the distance traveled by Brad?\n\n### Options:\nA. 12\nB. 18\nC. 20\nD. 24\nE. 30\n\n### Answer:\nTime taken = Total Distance / Relative Speed\nTotal Distance = 20 kms\nRelative Speed (Opposite side) (As they are moving towards each other speed would be added ) = 6+ 4 = 10 kms/hr\nTime taken = 20 / 10 = 2 hrs\nDistance traveled by Brad = Brad's speed * time taken = 6 * 2 = 12 kms... Answer - A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nCalculate the area of a triangle, if the sides are 13 cm, 12 cm and 5 cm, what is its area?\n\n### Options:\nA. 36 cm2\nB. 35 cm2\nC. 30 cm2\nD. 32 cm2\nE. 31 cm2\n\n### Answer:\nThe triangle with sides 13 cm, 12 cm and 5 cm is right angled, where the hypotenuse is 13 cm.\nArea of the triangle = 1/2 * 12 * 5 = 30 cm2\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA dealer purchased an article at 3/4 of its list price and sold 50% more than the list price. Find his gain percent?\n\n### Options:\nA. 106%\nB. 200%\nC. 100%\nD. 170%\nE. 104%\n\n### Answer:\nMP = 100\nCP = 75\nSP = 150\n------\n75 ---- 75\n100 ---- ? => 100%\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf n is a positive integer and the greatest common divisor of n and 16 is 4, and the greatest common divisor of n and 15 is 3, which of the following is the greatest common divisor of n and 96?\n\n### Options:\nA. 20\nB. 22\nC. 24\nD. 12\nE. 36\n\n### Answer:\nThe greatest common divisor of n and 16 is 4 --> n is a multiple of 4 but not a multiple of 8.\nThe greatest common divisor of n and 15 is 3 --> n is a multiple of 3 but not a multiple of 5.\n96=2*3*4*4 is divisible by 12. therefore the greatest common divisor is 12\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf x < y < z and y-x > 3, where x is an even integer and y and z are odd integers, what is the least possible value of z - x?\n\n### Options:\nA. 7\nB. 6\nC. 8\nD. 9\nE. 10\n\n### Answer:\nWe have:\n1) x3\n3) x=2k (x is an even number)\n4) y=2n+1 (y is an odd number)\n5) z=2p+1 (z is an odd number)\n6) z-x=? least value\nz-x=2p+1-2k=2p-2k+1=2(p-k)+1 - that means that z-x must be an ODD number.\nwe are asked to find the least value, so we have to pick the least numbers\nsince y is odd and x is even, y-x must be odd. since y-x>3, the least value for y-x must be 5, the least value for x must be 2, and, thus, the least possible value for y must be 7 (y-2=5, y=7)\n2<7", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA, B and C enter into partnership. A invests some money at the beginning, B invests double the amount after 6 months, and C invests thrice the amount after 8 months. If the annual gain be Rs.18900. A's share is?\n\n### Options:\nA. 6300\nB. 2765\nC. 6000\nD. 1298\nE. 1261\n\n### Answer:\nx* 12 : 2x* 6: 3x* 4\n1:1:1\n1/3 * 18900 = 6300\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nEvaluate: 98612 / 22*11*70 = ?\n\n### Options:\nA. 700.4\nB. 704.4\nC. 740.4\nD. 744.4\nE. 700.0\n\n### Answer:\nAccording to order of operations, 22?11?70 (division and multiplication) is done first from left to right\n22/11 = 2* 70 = 140\nHence\n98612 / 24*11*70 = 98612 / 140 = 704.4\ncorrect answer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nUsing all the letters of the word \"NOKIA\", how many words can be formed, which begin with N and end with A?\n\n### Options:\nA. 7\nB. 6\nC. 8\nD. 9\nE. 3\n\n### Answer:\nThere are five letters in the given word.\nConsider 5 blanks ....\nThe first blank and last blank must be filled with N and A all the remaining three blanks can be filled with the remaining 3 letters in 3! ways.\nThe number of words = 3! = 6.\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhen a Bike is sold for Rs. 63,000, the owner loses 10%. At what price must that Bike be sold in order to gain 10%?\n\n### Options:\nA. 74000\nB. 75000\nC. 76000\nD. 77000\nE. 78000\n\n### Answer:\n90 : 63000 = 110 : x\nx = (63000 x 110)/90 = 77,000.\nHence, S.P. = Rs. 77,000.\nAnswer: Option D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a room filled with 6 people, all 6 people have exactly 2 siblings in the room. If two individuals are selected from the room at random, what is the probability that those two individuals are NOT siblings?\n\n### Options:\nA. 3/5\nB. 3/7\nC. 4/7\nD. 5/6\nE. 7/12\n\n### Answer:\nThe 6 people consist of two sets of 3 siblings.\nThe number of ways to choose 2 people is 6C2 = 15.\nThe number of ways to choose 2 from the first group of siblings is 3C2 = 3.\nThe number of ways to choose 2 from the second group of siblings is 3C2 = 3.\nThe number of ways to choose 2 people who are siblings is 3+3 = 6.\nThe number of ways to choose 2 people who are not siblings is 15-6=9.\nP(the two people are not siblings) = 9/15 = 3/5\nThe answer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJohn and Jane went out for a dinner and they ordered the same dish. Both used a 10% discount coupon. John paid a 15% tip over the original price of the dish, while Jane paid the tip over the discounted price for the coupon. If John paid $0.60 more than Jane, what was the original price of the dish?\n\n### Options:\nA. 24\nB. 34.8\nC. 37.8\nD. 40\nE. 84\n\n### Answer:\nThe difference between the amounts John paid and Jane paid is the deference between 15% of p and 15% of 0.9p:\n0.15p - 0.15*0.9p = 0.60 --> 15p - 13.5p = 60 --> p = 40.\nAnswer: D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJohn purchased a grinder and a mobile for Rs. 15000 &Rs. 8000 respectively. He sold the grinder at a loss of 5% and the mobile phone at a profit of 10%. Overall how much he make a profit.\n\n### Options:\nA. s. 90\nB. s. 120\nC. s. 200\nD. s. 50\nE. s. 290\n\n### Answer:\nLet the SP of the refrigerator and the mobile phone be Rs. r and Rs. m respectively.\nr = 15000(1 - 5/100) = 15000 - 750\nm = 8000(1 + 10/100) = 8000 + 800\nTotal SP - Total CP = r + m - (15000 + 8000) = -750 + 800 = Rs. 50\nAs this is positive, an overall profit of Rs. 50 was made.\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow long will a car take to run round a circular field of radius 2/\u03c0 metres. If car runs at the rate of 8km/hr ?\n\n### Options:\nA. 2.5 sec.\nB. 10 sec.\nC. 3 sec\nD. 2 sec\nE. 1.8 sec\n\n### Answer:\nSpeed = 8 km/hr = 8*5/18 = 20/9 m/sec\ndistance = 2\u03c0r=2\u03c0*2/\u03c0=4 m\ntime taken = 4*9/20 = 1.8 sec.\nAnswer E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA computer store offers employees a 20% discount off the retail price. If the store purchased a computer from the manufacturer for $1000 dollars and marked up the price 20% to the final retail price, how much would an employee save if he purchased the computer at the employee discount (20% off retail price) as opposed to the final retail price.\n\n### Options:\nA. $1,000\nB. $960\nC. $240\nD. $200\nE. $150\n\n### Answer:\nCost price=1000\nProfit=20% =20% of 1000=200\nselling price=CP+ Profit\nSP=1200\na Discount of 20% to employees means 20% off on 1200\nso 20% of 1200= 240\nso a employee thinks he saved 240..\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a code word is defined to be a sequence of different letters chosen from the 8 letters A, B, C, D, E, F, G, AND H, what is the ratio of the number of 5-letter code words to the number of 4-letter code words?\n\n### Options:\nA. 4\nB. 8\nC. 5\nD. 10\nE. 12\n\n### Answer:\nMethod #1: Using the permutation formula\n# of 5 letter code words:\nnPr = n! / (n \u2013 r)! = 8! / (8 \u2013 5)! = 8*7*6*5*4\n# of 4 letter code words:\nnPr = 8! / (8 \u2013 4)! = 8*7*6*5\n# of 5 words / # of 4 words = (8*7*6*5*4)/(8*7*6*5) = 4 = 4\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain bag contains 60 balls \u2014 22 white, 10 green, 7 yellow, 15 red, and 6 purple. If a ball is to be chosen at random, what is the probability that the ball will be neither red nor purple?\n\n### Options:\nA. 0.09\nB. 0.65\nC. 0.54\nD. 0.85\nE. 0.91\n\n### Answer:\nAccording to the stem the ball can be white, green or yellow, so the probability is (white + green + yellow)/(total) = (22 + 10 + 17)/60 = 39/60 = 0.65.\nAnswer: B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA factory produces 5500 toys per week. If the workers at this factory work 5 days a week and if these workers make the same number of toys everyday, how many toys are produced each day?\n\n### Options:\nA. 1100 toys\nB. 5487 toys\nC. 6113 toys\nD. 2354 toys\nE. 1375 toys\n\n### Answer:\nTo find the number of toys produced every day, we divide the total number of toys produced in one week (of 5 days) by 5.\n5500 /5 = 1100 toys\ncorrect answer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the average marks of three batches of 47, 60 and 45 students respectively is 50, 55, 60, then the\naverage marks of all the students is\n\n### Options:\nA. 54.48\nB. 54.93\nC. 54.6\nD. 54.58\nE. None of these\n\n### Answer:\nExplanation:\n=(47*50+60*55+45*60)/(47+60+45)=54.93\nAnswer: Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAn integer is said to be \u201cdiverse\u201d if no two of its digits are the same. For example, 327 is \u201cdiverse\u201d but 404 is not. How many \u201cdiverse\u201d two digit numbers are there ?\n\n### Options:\nA. 70\nB. 72\nC. 81\nD. 90\nE. 91\n\n### Answer:\nA two digit number has to be formed from digits 0 to 9 such that unit's digit and ten's digit are not same.\nThe unit's digit can have 10 values from 0 to 9.\nTen's digit can have 9 values from 1 to 9\nSo total number of two digit numbers will be 9 x 10 = 90\nBut there are 9 numbers which are not diverse.\n11,22,33,44,55,66,77,88,99\nso, the number of diverse two digit numbers will be 90-9 = 81\nAnswer:- C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA set consist of 2l-1 element. What is the number of subsets of this set which contain at most l-1 elements?\n\n### Options:\nA. 2^(2l-2)\nB. 2^(2l) - 2\nC. 2^(2l) -1\nD. 2^(2l)\nE. 2^(2l-1)\n\n### Answer:\nI used l=3, so then we have\n5!/2!3! + 5!/4!1! + 5!/0!5!\n10 + 5 + 1 = 16\nSo our target is 16\nNow replace in answer choices\nA gives us 2^4 = 16\nHence A is the correct option\nRead carefully it says at most so keep in mind that picking a small number such as 3 will help you save time since you have to list fewer outcomes\nAvoid 2 since you will get 1 arrangement (l-1) and may be risky since 1 is a number with certain unique properties\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA can do a piece of work in 90 days & Y can do it in 80 days. They began working together but A leaves after some days and then B completed the remaining work in 46 days. The number of days after which A left the work was?\n\n### Options:\nA. 12 days\nB. 18 days\nC. 16 days\nD. 19 days\nE. 21 days\n\n### Answer:\nA and B did the work for some days.\nAfter that , B completed the remaining work in 46 days .\nIn 46 days, word done by B =\n1\n80\nx 46 =\n23\n45\nRemaining work = 1 \u2013 23/45\n= 17/45\nRemaining work is done by both A and B together =\n17/45x 90 x 80/90 + 80\n= 16 days\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe speed of a train is 90 kmph. What is the distance covered by it in 10 minutes?\n\n### Options:\nA. 15 kmph\nB. 18 kmph\nC. 85 kmph\nD. 17 kmph\nE. 99 kmph\n\n### Answer:\n90 * 10/60\n=15 kmph\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how many years will a sum of money doubles itself at 25% per annum on simple interest?\n\n### Options:\nA. 8%\nB. 2%\nC. 3%\nD. 4%\nE. 5%\n\n### Answer:\nP = (P*25*R)/100\nR = 4%\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAt what price must an article costing Rs.47.50 be marked in order that after deducting 5% from the list price. It may be sold at a profit of 25% on the cost price?\n\n### Options:\nA. 62.5\nB. 62.9\nC. 62.6\nD. 62.1\nE. 22.4\n\n### Answer:\nCP = 47.50\nSP = 47.50*(125/100) = 59.375\nMP*(95/100) = 59.375\nMP = 62.5\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAn aeroplane covers a certain distance of 480 Kmph in 4 hours. to cover the same distance in 4 1/3 hours, it Must travel at a speed of\n\n### Options:\nA. 440\nB. 540\nC. 443\nD. 740\nE. 250\n\n### Answer:\nSpeed of aeroplane = 480 Kmph\nDistance travelled in 4 hours\n= 480 * 4 = 1920 Km\nSpeed of aeroplane to acver 1920 Km in 13/3\n= 1920*3/13 = 443 Km\nAnswer C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nLook at this series: 544, 509, 474, 439,404, 369, 334, ... What number should come next?\n\n### Options:\nA. 206\nB. 299\nC. 306\nD. 507\nE. 404\n\n### Answer:\n299\nThis is a simple subtraction series. Each number is 35 less than the previous number.\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIt is the New Year and Mandy has made a resolution to lose weight this year. She plans to exercise and do yoga. For exercise she plans to workout at the gym and ride her bicycle in the ratio of 2:3 everyday. She will also do yoga in the ratio, yoga:exercise = 2:3. If she rides her bike for 20 minutes, how much time will she spend doing yoga? (rounded to minutes)\n\n### Options:\nA. 10 min.\nB. 33 min.\nC. 17 min.\nD. 23 min.\nE. 25 min.\n\n### Answer:\nThe ratio is 2:3 = gym:ride, so (20)(3/2) = 30 minutes at the gym, and 30 + 20 = 50 minutes exercise, so (2/3)(50) = 33 minutes yoga.\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a sequence of 8 consecutive odd integers with increasing values has 1 as its 7th term, what is the sum of the terms of the sequence?\n\n### Options:\nA. -48\nB. -32\nC. -16\nD. 16\nE. 32\n\n### Answer:\nLet x be the first term.\nThen x + 12 = 1 and x = -11\nThe sum is: x + (x+2) +...+ (x+14) =\n8x + 2(1+2+...+7) = 8x + 2(7)(8) / 2 = 8(-11) + 56 = -32\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA cistern is normally filled in 8 hours but takes two hours longer to fill because of a leak in its bottom. If the cistern is full, the leak will empty it in?\n\n### Options:\nA. 33\nB. 88\nC. 40\nD. 99\nE. 11\n\n### Answer:\n1/8 - 1/x = 1/10\nx = 40\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf x, y, and z are positive integers and 3x = 7y = 5z, then the least possible value of x + y + z is\n\n### Options:\nA. 15\nB. 25\nC. 71\nD. 35\nE. 45\n\n### Answer:\ngiven 3x=7y=5z\nx+y+z in terms of x\n= x+(3x/7)+(3x/5) = 71x/35\nnow checking with each of the answers and see which value gives a minimum integer value.\nA x = 35/71*15 , not an integer\nB,D,E can be ruled out similarly.\nC is minimum value as x = 71*35/71 = 35\nAnswer is C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo men and three women working 7 hours a day finish a work in 5 days. Four men and four women working 3 hours a day complete the work in 7 days. The number of days in which only 7 men working 4 hours a day will finish the work is?\n\n### Options:\nA. 5 days\nB. 3 days\nC. 2 days\nD. 9 days\nE. 10 days\n\n### Answer:\nAnswer: Option A\n2M + 3W ----- 35 h\n4M + 4W ------- 21 h\n7M -------? d\n70M + 105W = 84M +84M\n21W = 14M => 2M = 3W\n4 * 35 = 7 * x => x = 20 hours\n20/4 = 5 days\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf n is an integer and 5^n > 4,000,000, what is the least possible value of n?\n\n### Options:\nA. 7\nB. 8\nC. 9\nD. 10\nE. 11\n\n### Answer:\nWhen you separate the 4000000 into factors of 5 and 2 you get - > 10^6 x 2^2 = 5^6 x 2^8\n2 to the ^ 8 = 256 so its 256 x 5^6\nthat means 5^6 x 5^x must be greater\n5^x > 256\n5^1=5\n5^2=25\n5^3= 125\n5^4= 625 - > so x must be at least 4\n5^(6+4)= 5^10\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich of the following equations passes through the points (2,4) and (-3,-6)\n\n### Options:\nA. y = (1/2)x - 2\nB. y = 2x + 3\nC. y = (-1/2)x + 2\nD. y = 2x + 4\nE. y = 4x - 4\n\n### Answer:\nFind slope first = (y1-y2)/(x1-x2) = (-6-4)/(-3-2) = 2\nUsing the point (2,4) in options\nwe get,\ny = 4x - 4 as right answer.\nAns- E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMeena wrote number starting from 1 till 19999.Then how many digits did she write ?\n\n### Options:\nA. 87889\nB. 88889\nC. 89889\nD. 88789\nE. 88989\n\n### Answer:\n1-9=>1*9 digits\n10-99=>2*90=180(numbers between 10-99 is 90 where each no has 2 digits)\n100-999=>3*900=2700\n1000-9999=>4*9000\n10000-19999=>5*10000\nso ans is 88889\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA car is purchased on hire-purchase. The cash price is $21 000 and the terms are a deposit of 10% of the price, then the balance to be paid off over 60 equal monthly instalments. Interest is charged at 12% p.a. What is the monthly instalment?\n\n### Options:\nA. $503\nB. $504\nC. $505\nD. $506\nE. $507\n\n### Answer:\nExplanation:\nCash price = $21 000\nDeposit = 10% \u00d7 $21 000 = $2100\nLoan amount = $21000 \u2212 $2100\n= $18900\nI=p*r*t/100\nI=11340\nTotal amount = 18900 + 11340 = $30240\nRegular payment = total amount /number of payments\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a 4-member subcommittee is to be formed from a certain 6-member committee, how many different such subcommittee are possible?\n\n### Options:\nA. 6\nB. 15\nC. 20\nD. 60\nE. 216\n\n### Answer:\nAnother way:\n1st member can be selected in 6 ways\n2nd can be selected in 5 ways\n3rd can be selected in 4 ways\n4th can be selected in 3 ways\nSo total ways : 360\nBut to avoid the similar scenarios 360/4!=15\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA pet store regularly sells pet food at a discount of 10 percent to 30 percent from the manufacturer\u2019s suggested retail price. If during a sale, the store discounts an additional 20 percent from the discount price, what would be the lowest possible price of a container of pet food that had a manufacturer\u2019s suggested retail price o f $ 35.00?\n\n### Options:\nA. $ 10.00\nB. $ 11.20\nC. $ 14.40\nD. $ 16.00\nE. $ 19.60\n\n### Answer:\nFor retail price = $35\nFirst maximum discounted price = 35 - 30% of 35 = 35-10.5 = 24.5\nPrice after additional discount of 20% = 24.5 - 20% of 24.5 = 24.5- 4.9 = 19.6\nAnswer: Option E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man is walking at a speed of 10 km per hour. After every kilometre, he takes rest for 5 minutes. How much time will be take to cover a distance of 5 kilometres?\n\n### Options:\nA. 48 min.\nB. 50 min.\nC. 45 min.\nD. 55 min.\nE. None of these\n\n### Answer:\nRest time = Number of rest \u00d7 Time for each rest\n= 4 \u00d7 5 = 20 minutes\nTotal time to cover 5km\n= (5\u204410 \u00d7 60)minutes + 20 minutes = 50 minutes\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n50 litres of diesel is required to travel 600 km using a 800 cc engine. If the volume of diesel required to cover a distance varies directly as the capacity of the engine, then how many litres of diesel is required to travel 800 km using 1200 cc engine?\n\n### Options:\nA. 80 litres\nB. 90 litres\nC. 100 litres\nD. 170 litres\nE. None of these\n\n### Answer:\nExplanatory Answer\nTo cover a distance of 800 kms using a 800 cc engine, the amount of diesel required = 800/600*50 = 66.67 litres.\nHowever, the vehicle uses a 1200 cc engine and the question states that the amount of diesel required varies directly as the engine capacity.\ni.e., for instance, if the capacity of engine doubles, the diesel requirement will double too.\nTherefore, with a 1200 cc engine, quantity of diesel required = 1200/800*66.67 = 100 litres.\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n476 ** 0 is divisible by both 3 and 11.The non zero digits in the hundred's and ten's places are respectively:\n\n### Options:\nA. 8 and 8\nB. 8 and 5\nC. 8 and 7\nD. 7 and 5\nE. 8 and 3\n\n### Answer:\nExplanation:\nLet the number be 476ab0\n476ab0 is divisible by 3\n=> 4 + 7 + 6 + a + b + 0 is divisible by 3\n=> 17 + a + b is divisible by 3 ------------------------(i)\n476ab0 is divisible by 11\n[(4 + 6 + b) -(7 + a + 0)] is 0 or divisible by 11\n=> [3 + (b - a)] is 0 or divisible by 11 --------------(ii)\nSubstitute the values of a and b with the values given in the choices and select the values which satisfies both Equation 1 and Equation 2.\nif a=6 and b=2,\n17 + a + b = 17 + 6 + 2 = 25 which is not divisible by 3 --- Does not meet equation(i).Hence this is not the answer\nif a=8 and b=2,\n17 + a + b = 17 + 8 + 2 = 27 which is divisible by 3 --- Meet equation(i)\n[3 + (b - a)] = [3 + (2 - 8)] = -3 which is neither 0 nor divisible by 11---Does not meet equation(ii).Hence this is not the answer\nif a=6 and b=5,\n17 + a + b = 17 + 6 + 5 = 28 which is not divisible by 3 --- Does not meet equation (i) .Hence this is not the answer\nif a=8 and b=5,\n17 + a + b = 17 + 8 + 5 = 30 which is divisible by 3 --- Meet equation 1\n[3 + (b - a)] = [3 + (5 - 8)] = 0 ---Meet equation 2\nSince these values satisfies both equation 1 and equation 2, this is the answer\nAnswer: D) 8 and 5\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the smallest no. which must be added to 532869 so as to obtain a sum which is divisible by 9?\n\n### Options:\nA. 9\nB. 2\nC. 1\nD. 3\nE. 6\n\n### Answer:\nFor 532869 , 5+3+2+8+6+9=33\n3 must be added to 532869 to make it divisible by 9.\nNow ,5+3+2+8+7+2=27=> 27 is a multiple of 9 and hence 532869 is also divisible by 9\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the product of the integers a, b, c and d is 546 and if 1 < a < b < c < d, what is the value of b+c?\n\n### Options:\nA. 273\nB. 185\nC. 21\nD. 10\nE. 4\n\n### Answer:\nMake prime factorization of 546: 546=2*3*7*13.\nNow, since given that 1 < a < b < c < d, then a=2, b=3, c=7 and d=13 --> b+c=3+7=10.\nAnswer: D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a : b = 2 : 3 and b : c = 5 : 7, then find a : b : c.\n\n### Options:\nA. 10 : 15 : 27\nB. 10 : 15 : 21\nC. 10 : 15 : 22\nD. 10 : 15 : 12\nE. 10 : 15 : 28\n\n### Answer:\na : b : c = (2 x 5) : ( 3 x 5) : (3 x 7) = (10) : (15) : (21)\nAnswer:\tA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf there are only 2 wheelers and 4 wheelers parked in a school located at the heart of the city, find the number of 4 wheelers parked there if the total number of wheels is 82?\n\n### Options:\nA. 11\nB. 12\nC. 13\nD. 20\nE. 25\n\n### Answer:\nfour wheeler=20*4=80(max)\n2 wheel=1\nso no of 4 wheeler=20\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe price of sugar is increased by 4%. By how much percent should a home maker reduce her consumption of sugar to have no extra expenditure?\n\n### Options:\nA. (300/103) %\nB. (400/104) %\nC. (100/107)%\nD. (7/100)%\nE. (100/700)%\n\n### Answer:\nOld price = $100 (assume);\nOld consumption = 1 kg (assume).\nNew price = $104.\nWe want the spendings to remain at $100.\n(New consumption)*104 = 100 --> (New consumption) = 100/104 kg.\nPercent decrease = Change/Original *100 = (1 - 100/104)/1*100 = 400/104%.\nAnswer: B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf Leo gains 10 pounds, he will weigh 50% more than his sister Kendra. Currently their combined weight is 140 pounds. What is Leo's current weight?\n\n### Options:\nA. 80\nB. 90\nC. 100\nD. 110\nE. 120\n\n### Answer:\nL+K = 140 and so K = 140-L\nL+10 = 1.5K = 1.5(140-L)\n2.5L = 200\nL = 80\nThe answer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTough and Tricky questions: Work/Rate Problems.\nA group of 4 junior lawyers require 4 hours to complete a legal research assignment. How many hours would it take a group of three legal assistants to complete the same research assignment assuming that a legal assistant works at two-thirds the rate of a junior lawyer?\nSource: Chili Hot GMAT\n\n### Options:\nA. 13\nB. 10\nC. 9\nD. 8\nE. 5\n\n### Answer:\n# of people times the # of hours:\n4*4 = 16 --> 4 lawyers do 16worksin 4 hours.\n3*8/3 = 24/3 = 8 --> 3 assistants do 8 worksin 8/3 hours (2/3*5= 10/3)\nSo, since the amount of work the assistants do is half the work the lawyers do, the time will be double, soANS D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nsuppose that jody drove 80 miles in 2 hours. dividing 80 by 2 tells us how many mile jody drove in each hour. the unit for this rate are miles per hour(miles/hr). if we divide 2 by 80 what information would this give us? give an interpretation of the rate. what unit would be used for this rate?\n\n### Options:\nA. mile/hours\nB. hours/mile\nC. minutes/mile\nD. km/hours\nE. none\n\n### Answer:\nspeed= distance/time, here speed=distance covered in 1 hour. total distance 80 miles divided by total time 2 hours= 80/2. miles/ hour= 40 mile/hour. jody drove 40 miles in hour. correct answer : (B)\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a recent survey at a local deli, it was observed that 3 out of 5 customers bought a bagel and 5 out of 7 customers bought a coffee. Some customers bought both. If 5 customers are selected, what are the chances that at least 1 customer bought a coffee and a bagel?\n\n### Options:\nA. 27/343\nB. 3/7\nC. 27/125\nD. 329/411\nE. 9/125\n\n### Answer:\nLet us take 7*5=35 as the total number of customers. So 7*3=21 customers bought a bagel and 5*5=25 customers bought a coffee.\nchances that at least 1 customer bought a coffee and a bagel = 1 - chances that no customer bought a coffee and a bagel\nchances that no customer bought a coffee and a bagel= 24/35*23/34*22/33*21/32*20/31=82/411\nchances that at least 1 customer bought a coffee and a bagel= 1 - 82/411 = 329/411\nAnswer D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTeams A, B, C and D were in a baseball tournament. Each team played each other team once. Team A beat team D. Teams A, B and C won the exact same number of games. How many games did team D lose?\n\n### Options:\nA. 2\nB. 3\nC. 4\nD. 6\nE. 7\n\n### Answer:\nThere are 4 teams and each team played each other team once. That tells us 2 facts:\n\uf0b7 Each team played 3 games\n\uf0b7 4 teams played a total of 6 games.\nSince there are only 6 games, only 6 total wins are possible. Since A, B and C won the exact same number of games, they either all won 1 game or all won 2 games. Let\u2019s examine both scenarios:\nScenario #1: A, B and C each won 1 game. In this scenario, D must have won all 3 games it played. That contradicts with the fact that A beat D. So, scenario 1 is not possible. So, it has to be scenario #2.\nScenario #2: A, B and C each 2 games. In this scenario, D won 0 games. That means D lost all 3 games it played.\ncorrect answer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is 2 2/3 - 1 1/4 divided by 1/2 - 1/4 ?\n\n### Options:\nA. 17/36\nB. 36/17\nC. 17/6\nD. 17/3\nE. 51/4\n\n### Answer:\n2 2/3 - 1 1/4 = 8/3 - 5/4 = (32 - 15 )/12 = 17/12\n1/2 - 1/4 = (2-1)/4 = 1/4\nSo 17/12/1/4 = 17/12 *4 = 17/3\nAnswer - D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSP of a book is Rs. 450 he gets a loss of 10%, find CP of the book?\n\n### Options:\nA. Rs.300\nB. Rs.450\nC. Rs.500\nD. Rs.600\nE. Rs.640\n\n### Answer:\nFind cost price\nLet C.P. of book = x and S.P. = Rs. 450\nS.P. of book = C.P. \u2013 (10% of C.P.)\nS.P. = x \u2013 (0.10x)\n450 = 0.9 x\nx i.e cost price = Rs.500\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJagan went to another town covering 240 km by car moving at 60 kmph. Then he covered 400km by train moving at 100 kmph and then rest 200 km he covered by a bus moving at 50 kmph. The average speed during the whole journey was ?\n\n### Options:\nA. 80 kmph\nB. 60 kmph\nC. 10 kmph\nD. 70 kmph\nE. 90 kmph\n\n### Answer:\nExplanation:\nBy car 240 km at 60 kmph\nTime taken = 240/60 = 4 hr.\nBy train 240 km at 60 kmph\nTime taken = 400/100 = 4 hr.\nBy bus 240 km at 60 kmph\nTime taken = 200/50 = 4 hr.\nSo total time = 4 + 4 + 4 = 12 hr.\nand total speed = 240+400+200 = 840 km\nAverage speed of the whole journey = 840/12 = 70 kmph.\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOne night a certain hotel rented 1/2 of its rooms, including 2/3 of their air conditioned rooms. If 3/5 of its rooms were air conditioned, what percent of the rooms that were not rented were air conditioned?\n\n### Options:\nA. 25%\nB. 30%\nC. 35%\nD. 40%\nE. 50%\n\n### Answer:\nThe rooms which were not rented is 1/2\nThe AC rooms which were not rented is (1/3)*(3/5) = 1/5\nThe percentage of unrented rooms which were AC rooms is (1/5) / (1/2) = 2/5 = 40%\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a library, there are certain number of books on a shelf, ranging between 75 and 100. 1/6th of them are fiction and 12.5% of them are non-fiction. Find the number of books.\n\n### Options:\nA. 376\nB. 96\nC. 26\nD. 198\nE. 178\n\n### Answer:\nExplanation:\n12.5% can be written as 1/8th\nSince 1/6th of the books are fiction and 1/8th are non-fiction, the total number of books must be exactly divisible by 6 and 8 and should be between 75 and 100.\nTherefore, 96 is the only number, which fulfills the above criteria.\nNote that the question doesn't imply that there are ONLY two varieties of books.\nANSWER: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many seconds will a train 120 meters long take to cross a bridge 150 meters long if the speed of the train is 36 kmph?\n\n### Options:\nA. 17 sec\nB. 21 sec\nC. 25 sec\nD. 27 sec\nE. 29 sec\n\n### Answer:\nD = 120 + 150 = 270\nS = 36 * 5/18 = 10 mps\nT = 270/10 = 27 sec\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a group of 25 factory workers, 14 have brown eyes. Six of the women do not have brown eyes. How many of the 11 men have brown eyes.\n\n### Options:\nA. 10\nB. 9\nC. 8\nD. 7\nE. 6\n\n### Answer:\nTotal number of worker (M+W): 25\nNo. of men (M): 11 (Inferred fromHow many of the 11 men)\nNo. of women (W): 14\nTotal no. of workers who have brown eyes (B): 14\nNo. of women who do not have brown eyes: 6\nTherefore, no. of women who have brown eyes: W - 6 = 14 - 6 = 8\nRemaining 6 are men. (B - 8= 14- 8= 6)\nSo 6 out of 11 men have brown eyes.\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA, B and C play a cricket match. The ratio of the runs scored by them in the match is A:B = 5:3 and B:C = 5:2. If the total runs scored by all of them are 60, the runs scored by B are?\n\n### Options:\nA. 20.23\nB. 20.13\nC. 30.93\nD. 19.56\nE. 10.93\n\n### Answer:\nA:B = 5:3\nB:C = 5:2\nA:B:C = 25:15:6\n15/46 * 60 = 19.56\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat will come in place of the x in the following Number series? 12, 38, 116, x,\n\n### Options:\nA. 2643\nB. 350\nC. 3456\nD. 7554\nE. 3158\n\n### Answer:\n12\n12 \u00c3\u2014 3 + 2 = 38\n38 \u00c3\u2014 3 + 2 = 116\n116 \u00c3\u2014 3 + 2 = 350\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\na circular wheel radius is 1.75m.for covering 11k.m how much time it revolve?\n\n### Options:\nA. 10\nB. 100\nC. 1000\nD. 10000\nE. 50\n\n### Answer:\ndistance traveled in 1 round=perimeter={2*22/7*175/100}m\n=11 m\ntotal no. of revolution in covering 11 km=11000/11=1000\nanswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJill\u2019s compact disc player randomly plays a song, so that no song is repeated before the entire album is played. If Bill plays a disc with 18 songs, what are the chances that the third song he hears will be his favorite?\n\n### Options:\nA. 1/18\nB. 1/12\nC. 1/11\nD. 3/14\nE. 1/3\n\n### Answer:\nThe player plays the songs on the album at random, so there are 18 songs that can be the third one played. Only 1 of these ways will result in Bill's favorite song being the third one played.\nTotal outcomes ==> 18\nTotal positive outcomes ==> 1\nCorrect answer is A) 1/18\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo pipes A and B can fill a cistern in 37 1/2 minutes and 45 minutes respectively. Both pipes are opened. The cistern will be filled in just half an hour, if the pipe B is turned off after?\n\n### Options:\nA. 8\nB. 9\nC. 6\nD. 4\nE. 1\n\n### Answer:\nLet B be turned off after x minutes. Then, part filled by (A + B) in x min + part filled by A in (30 - x) min = 1.\nx(2/75 + 1/45) + (30- x) 2/75 = 1\n11x + 180 - 6x = 225 => x = 9\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA dog takes 3 leaps for every 7 leaps of a hare. If one leap of the dog is equal to 3 leaps of the hare, the ratio of the speed of the dog to that of the hare is :\n\n### Options:\nA. 9:7\nB. 9:9\nC. 9:6\nD. 9:1\nE. 9:2\n\n### Answer:\nExplanation:\nDog : Hare = (3*3) leaps of hare : 7 leaps of hare = 9 : 7.\nAnswer: A) 9:7\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many Z ways can you group 3 people from 4 sets of twins if no two people from the same set of twins can be chosen?\n\n### Options:\nA. 3\nB. 16\nC. 28\nD. 32\nE. 56\n\n### Answer:\nWays to select 3 people from 8 people (4 twins x 2) = 8C3 = 56\nWays to select 1 twin + 1 people = 4C1*6C1 = 24\nWays to select a group 3 people from 4 sets of twins if no two people from the same set of twins can be chosen Z= 56 - 24 = 32\nAns: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn an increasing sequence of 10 consecutive integers, the sum of the first 5 integers is 555. What is the sum of the last 5 integers in the sequence?\n\n### Options:\nA. 585\nB. 580\nC. 575\nD. 570\nE. 565\n\n### Answer:\nAll 5 integers are 5 numbers larger than in the first sum (eg. 1 becomes 6, 2 7...). 5*5=25+555=580\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA small company employs 3 men and 5 women. If a team of 3 employees is to be randomly selected to organize the company retreat, what is the probability that the team will have exactly 2 women?\n\n### Options:\nA. 1/14\nB. 1/7\nC. 2/7\nD. 5/7\nE. 1/2\n\n### Answer:\nTotal ways to choose 4 employees from 8 employees = 8C3\nTwo women = 5C2\nTwo Men = 3C1\nP = (5C2 * 3C1)/8C2 = 5/7 hence D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n45 men working 8 hours per day dig 30 m deep. How many extra men should be put to dig to a depth of 50 m working 6 hours per day?\n\n### Options:\nA. 77\nB. 66\nC. 50\nD. 55\nE. 44\n\n### Answer:\n(45 * 8)/30 = (x * 6)/50 => x =100\n100 \u2013 45 = 55\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA, B and C are partners in a business. Their capitals are respectively, Rs.5000, Rs.6000 and Rs.4000. A gets 30% of the total profit for managing the business. The remaining profit is divided among three in the ratio of their capitals. In the end of the year, the profit of A is Rs.200 more than the sum of the profits of B and C. Find the total profit.\n\n### Options:\nA. 1987\nB. 2799\nC. 3288\nD. 3000\nE. 2982\n\n### Answer:\nA:B:C = 5:6:4\nLet the total profit = 100 - 30 = 70\n5/15 * 70 = 70/3\nA share = 70/3 + 30 = 160/3\nB + C share = 100 - 160/3 = 140/3\nA-(B+C) = 160/3 - 140/3 = 20/3\n20/3 ---- 200\n100 ---- ? => 3000\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA is twice efficient as B and together they do the same work in as much time as C and D together. If C and D can complete the work in 20 and 30 daysrespectively, working alone ,then in how many days A can complete the work individually:\n\n### Options:\nA. 12 days\nB. 18 days\nC. 24 days\nD. 30 days\nE. None of these\n\n### Answer:\nExplanation:\nA + B = C + D\n| | | |\nRatio of efficiency 10x + 5x 9x + 6x\n|________| |_________|\n15x 15x\nTherefore , ratio of efficiency of A:C =10:9\nTherefore, ratio of days taken by A:C = 9:10\nTherefore, number of days taken by A = 18 days\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nhow many prime no. are there from 0 to 50?\n\n### Options:\nA. 14\nB. 15\nC. 16\nD. 17\nE. 19\n\n### Answer:\nwe calculate it manually.we know the definition of prime no.prime no. should only have two distinct\u00e2\u20ac\u2039 natural no. divisor 1 and itself.\nnote:1 is not a prime no.\n2,3,5,7,11,13,17,19,23,29,31,37,41,43,47\ntotal no.=15\nanswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nDan has a membership at a local gym that also gives classes three nights a week. On any given class night, Dan has the option of taking yoga, weight training, or kickboxing classes. If Dan decides to go to either one or two classes per week, how many different combinations T of classes are available?\n\n### Options:\nA. 3\nB. T=6\nC. T=7\nD. T=9\nE. T=12\n\n### Answer:\nI think it should be E only.\nNo where it is given that he attends different classes on each day.\nExperts please provide your views.\n--- EDITED my Response. It was a typo. I meant 12 is the answer.\nIf only Day 1 : 3 options\nIf Day 1 and Day 2 : 3*3 = 9 Options\nSo, Total = 3+9= 12.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nfind the number, difference between number and its 3/5 is 60.\n\n### Options:\nA. 150\nB. 153\nC. 154\nD. 155\nE. 156\n\n### Answer:\nExplanation:\nLet the number = x,\nThen, x-(3/5)x = 60,\n=> (2/5)x = 60 => 2x = 60*5,\n=> x = 150\nAnswer: Option A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are 3 numbers A, B and C. If A:B = 3/4, B:C = 4/5, C:D = 5/6, then A:D will be?\n\n### Options:\nA. 1 : 2\nB. 2 : 3\nC. 3 : 5\nD. 4 : 7\nE. 4 : 9\n\n### Answer:\nSol. A : B = 3 : 4, B : C = 4 : 5, C : D = 5 : 6\n\u2234A\u2236B\u2236C\u2236D= 3 : 4 : 5 : 6.\nThus, A : D = 3 : 6 or, 1 : 2\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA & B started a partnership business. A's investment was thrice the investment of B and the period of his investment was two times the period of investments of B. If B received Rs 4500 as profit , what is their total profit?\n\n### Options:\nA. 28000\nB. 30000\nC. 31500\nD. 34000\nE. None of these\n\n### Answer:\nExplanation :\nSuppose B's investment = x. Then A's investment= 3x\nSuppose Bs period of investment = y, then A's period of investment = 2y\nA : B = 3x * 2y : xy\n= 6 : 1\nTotal profit * 1/7 = 4500\n=> Total profit = 4500*7 = 31500. Answer : Option C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf n = 8p, where p is a prime number greater than 2, how many different positive even divisors does n have, including n ?\n\n### Options:\nA. Two\nB. Three\nC. Four\nD. Six\nE. Eight\n\n### Answer:\nIf n = 8p, where p is a prime number greater than 2, how many different positive even divisors does n have, including n ?\n(A) Two\n(B) Three\n(C) Four\n(D) Six\n(E) Eight\nSince we cannot have two correct answers just pick a prime greater than 2, and see how many different positiveevendivisors will 8p have.\np = 3 --> 8p = 24--> 24 has 6 even divisors: 2, 4, 6, 8, 12, 24.\nAnswer: D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nLaura can paint 1/x of a certain room in 20 minutes. What fraction Z of the same room can Joseph paint in 20 minutes if the two of them can paint the room in an hour, working together at their respective rates?\n\n### Options:\nA. 1/(3x)\nB. 3x/(x-3)\nC. (x \u2013 3)/(3x)\nD. x/(x-3)\nE. (x-3)/x\n\n### Answer:\nOptions with variables are often done by plugging in numbers.\nBoth working together can paint the room in 1 hr so if their individual rates were equal, each would take 2 hours alone.\n2 hours is 120 mins so in 20 mins each would complete Z=120/20 = 1/6th of the room alone.\nSo if x = 6 (Laura completes 1/6th of the room in 20 mins), the correct option will give 1/6. (Joseph will also paint 1/6th of the room if their rates are same)\nIf you put x = 6 in the options, only option (C) will give 1/6\nAnswer (C)\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo tests had the same maximum mark. The pass percentages in the first and the second test were 40% and 45% respectively. A candidate scored 222 marks in the second test and failed by 39 marks in that test. Find the pass mark in the first test?\n\n### Options:\nA. 768\nB. 232\nC. 246\nD. 625\nE. 224\n\n### Answer:\nLet the maximum mark in each test be M.\nThe candidate failed by 36 marks in the second test.\npass mark in the second test = 222 + 39 = 252\n45/100 M = 261\nPass mark in the first test = 40/100 M = 40/45 * 261 = 232\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are some balloons in party, 1/3rd blasted by kids . Then 2/5th of the remaining by men , then 2/3rd of the remaining by women . At last 20 were remaining . How many balloons were in total ?\n\n### Options:\nA. 150\nB. 27\nC. 28\nD. 26\nE. 91\n\n### Answer:\nSol:\n45\nIf x persons were there in total , then\nx \u00d7 (1 \u2013 1/3)\u00d7 (1 \u2013 2/5) \u00d7(1 \u2013 2/3) = 20\nx\u00d72/3 \u00d7 3/5 \u00d7 1/3 = 20\nx = 150\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA and B complete a work in 3 days. A alone can do it in 9 days. If both together can do the work in how many days?\n\n### Options:\nA. 3.75 days\nB. 4.75 days\nC. 3.25 days\nD. 3.15 days\nE. 2.75 days\n\n### Answer:\n1/3 + 1/9 = 4/9\n9/4 = 4.75 days\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAfter decreasing 20% in the price of an article costs Rs.600. Find the actual cost of an article?\n\n### Options:\nA. 775\nB. 620\nC. 53\nD. 530\nE. 220\n\n### Answer:\nCP* (80/100) = 600\nCP= 7.75 * 100 => CP = 775\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average mark of the students of a class in a particular exam is 80. If 5 students whose average mark in that exam is 60 are excluded, the average mark of the remaining will be 90. Find the number of students who wrote the exam.\n\n### Options:\nA. 22\nB. 27\nC. 15\nD. 99\nE. 21\n\n### Answer:\nLet the number of students who wrote the exam be x.\nTotal marks of students = 80 x.\nTotal marks of (x - 5) students = 90(x - 5)\n80x - (5 * 60) = 90(x - 5)\n150 = 10x => x = 15.Answer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOn a map, 1 centimeter represents 25 kilometers. Two cities 425 kilometers apart would be separated on the map by how many centimeters?\n\n### Options:\nA. 25\nB. 17\nC. 19\nD. 310\nE. 280\n\n### Answer:\nX=425/25= 17\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many digits will be there to the right of the decimal point in the product of 95 and .02554 ?\n\n### Options:\nA. 6\nB. 7\nC. 4\nD. 5\nE. 8\n\n### Answer:\nproduct of 95 and .02554 is 2.4263.\nTherefore number of digits to right of decimal point is 4\nAnswer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nEvaluate : (2.39)(power 2) - (1.61) (power 2) / 2.39 - 1.61\n\n### Options:\nA. 4\nB. 6\nC. 8\nD. 2\nE. 10\n\n### Answer:\nGiven Expression = a(power 2) - b(power 2) / a-b\n= (a + b)(a - b) / (a-b)\n= (a + b) = (2.39 + 1.61) = 4.\nAnswer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe length of a train and that of a platform are equal. If with a speed of 90 k/hr, the train crosses the platform in one minute, then the length of the train (in meters) is?\n\n### Options:\nA. 278\nB. 272\nC. 892\nD. 750\nE. 298\n\n### Answer:\nSpeed = [90 * 5/18] m/sec = 25 m/sec; Time\n= 1 min.\n= 60 sec.\nLet the length of the train and that of the platform be x meters.\nThen, 2x/60 = 25 \u00e8 x = 25 * 60 / 2\n= 750\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe mean of (54,825)^2 and (54,827)^2 =\n\n### Options:\nA. (54,821)^2\nB. (54,821.5)^2\nC. (54,820.5)^2\nD. (54,826)^2 + 1\nE. (54,821)^2 \u2013 1\n\n### Answer:\n54825^2 = (54826-1)^2 = 54826^2 + 1^2 - 2*54826*1\n54827^2 = (54826+1)^2 = 54826^2 +1^2 + 2*54826*1\nTaking the average of above 2 , we get (54826)^2 +1\nhence the answer is D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe number of boys in a class is three times the number of girls. Which one of the following numbers cannot represent the total number of children in the class ?\n\n### Options:\nA. 48\nB. 44\nC. 42\nD. 40\nE. 4\n\n### Answer:\nremaining are divisible by 4\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 28% of a number exceeds 18% of it by 7.2, then find the number?\n\n### Options:\nA. 50\nB. 34\nC. 55\nD. 60\nE. 90\n\n### Answer:\nUse the elimination method to find the correct option.\nOf all the options only 90 fits\n28% of 90 = 25.2\n18% of 90 = 16.2\n25.2 - 16.2 = 7.2\nRequired number is 90.\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe no. of girls in a class are seven times the no. of boys, which value cannever be the of total students?\n\n### Options:\nA. 3\nB. 4\nC. 8\nD. 9\nE. 12\n\n### Answer:\nLet the boys are X, then girls are 7X, total = X+7X = 8X\nSo it should be multiple of 8, 30 is not a multiple of 8.\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe speed of a car is 10 km in the first hour and 60 km in the second hour. What is the average speed of the car?\n\n### Options:\nA. 79 kmph\nB. 85 kmph\nC. 35 kmph\nD. 23 kmph\nE. 14 kmph\n\n### Answer:\nS = (10 + 60)/2\n= 35 kmph\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA 1200 m long train crosses a tree in 120 sec, how much time will I take to pass a platform 700 m long?\n\n### Options:\nA. 177\nB. 190\nC. 178\nD. 124\nE. 121\n\n### Answer:\nL = S*T\nS= 1200/120\nS= 10 m/Sec.\nTotal length (D)= 1900 m\nT = D/S\nT = 1900/10\nT = 190 Sec\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA person can walk at a constant rate of 8mph and can bike at a rate of 16mph. If he wants to travel 88 miles in 8 hours using bike and walking at their constant rates, how much distance would he require to walk?\n\n### Options:\nA. 20\nB. 30\nC. 40\nD. 60\nE. 72\n\n### Answer:\nTotal distance = 88\nDistance = Speed * Time\nWalking speed = s1 = 8\nWalking time = t1\nBike speed = s2 = 16\nTime traveled in bike = t2\nd1 + d2 = 88\ns1t1 + s2t2 = 88\n8*t1 + 16*t2 = 88\nt1 + 2*t2 = 11 ----- (1)\nGiven: t1 + t2 = 8 ----- (2)\n(1) - (2) --> t2 = 3 and t1 = 8 - 3 = 5\nWalking distance = s1*t1 = 8*5 = 40\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn an examination 60% failed in Math and 40% failed in French. If 15% failed in both. What % of students passed in both.\n\n### Options:\nA. 25%\nB. 15%\nC. 20%\nD. 30%\nE. 10%\n\n### Answer:\nPassed in Math = 100 - 60 = 40%\nPassed in French = 100 - 40 = 60%\nStudents who passed Math or French = 100 -15 = 85%\nStudents passed in Math and French = (Passed in Math) + (Passed in French) - (Students who passed Math or French) = 60+40-85 =15%\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf x^2 - 4 = 0 and x < 0, which of the following must be equal to 0 ?\n\n### Options:\nA. x^2 - 9x\nB. x^2 - 9x + 20\nC. x^2 - 2x + 3\nD. x^2 + 2x - 3\nE. x^2 + 5x + 6\n\n### Answer:\nx^2-4 = 0\nx= +2 or x = -2\nif we substitute x= -2 in the equation x^2 +5x+6 = 4-10+6 = 0\nE is also the answer\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA bus stops for taking passengers. The speed of the bus with stoppages is 36 km/hr and without stoppages is 45 km/hr.For how many minutes bus stopped per hour?\n\n### Options:\nA. 10 min\nB. 11 min\nC. 12 min\nD. 13 min\nE. None of these\n\n### Answer:\nExplanation :\nIt takes 9 km less due to stoppages. Time spend in stoppages=(9/45)*60=12 min\nAnswer : C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nPaul's income is 40% less than Rex's income, Quentin's income is 20% less than Paul's income, and Sam's income is 40% less than Paul's income. If Rex gave 60% of his income to Sam and 40% of his income to Quentin, sam's new income would be what fraction of Quentin's new income?\n\n### Options:\nA. 11/12\nB. 12/11\nC. 13/19\nD. 12/19\nE. 11/19\n\n### Answer:\nMAKE R = 10\nP = 0.6R = 6\nQ = 0.8P = 4.8\nS= 0.6P = 3.6\nFOR THAT WE GET S = 9.6\nAND Q 8.8\nSO 9.6/8.8= 1.2/1.1\nAns:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn each of the following questions a number series is given with one term missing. Choose the correct alternative that will continue the same pattern and fill in the blank spaces.\n2, 7, 14, ?, 34, 47\n\n### Options:\nA. 31\nB. 23\nC. 36\nD. 31\nE. 33\n\n### Answer:\nB\n23\nThe given sequence is +5, +7, +9, \u2014\u2014\nie. 2+ 5 = 7, 7 + 7 = 14, 14 + 9 = 23\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 2 cards are selected at random from the deck of 52 cards then What is the probability of one of the selected cards will be King and other will be Jack?\nA deck of cards has a total of 52 cards, consisting of 4 suits; (spades(Black), hearts(Red), diamond(Red)s, and clubs(Black)); and 13 cards including 1 king, 1 queen and 1 jack in each suit\n\n### Options:\nA. 8/2652\nB. 1/2652\nC. 18/2652\nD. 12/2652\nE. 6/2652\n\n### Answer:\n2 possible cases:\nKing - Jack or Jack -King (4 kings and 4 Jacks).\nEither way,\nthe total probability = 2( King -Jack) = 2 (4/52 * 4/51) = 18/2652. C is the correct answer.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nKathleen can paint a room in 2 hours, and Anthony can paint an identical room in 7 hours. How many hours would it take Kathleen and Anthony to paint both rooms if they work together at their respective rates?\n\n### Options:\nA. 28/9\nB. 4/3\nC. 15/8\nD. 9/4\nE. 15/4\n\n### Answer:\n(1/2 + 1/7)t=2\nt=28/9\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat will come in place of the x in the following Number series? 25, 100, x, 1600, 6400\n\n### Options:\nA. 2345\nB. 3579\nC. 6400\nD. 6799\nE. 8646\n\n### Answer:\n(C)\n25 x 4 = 100, 100 x 4 = 400, 400 x 4 = 1600, 1600 x 4 = 6400.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average number of shirts with Salman, Ambani and Dalmiya is 60, if all of them reached a shopping mall in Delhi and purchased 6 shirts each of them then average number of shirt each of them now has\n\n### Options:\nA. 66\nB. 63\nC. 62\nD. 64\nE. 61\n\n### Answer:\nRequired average\n= Old average + New average\n= 60 + 6 = 66\nanswer :A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe perimeter of an isosceles right triangle is 4 + 4 sq rt 2. What is the length of the hypotenuse of the triangle?\n\n### Options:\nA. 2.82\nB. 2\nC. 3\nD. 4\nE. 5\n\n### Answer:\nside of triangle is a then perimeter = a+ a +a.sqrt2 ( right angle and pythagorus) =2a +a .sqrt 2 = 4 + 4 Sqrt2 or,\na. ( 2+ sqrt2) = 4(1 + sqrt2) a= 4.( 1+sqrt2)/2+sqrt2 =4*2.414/3.414 = then hypotenuse = 2.82\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA trade analyst announced 8% reduction in the unit price of bike. As a result, the sales volume went up by 20%. What was the net effect on the sales revenue?\n\n### Options:\nA. no change\nB. decreases by 10.4%\nC. increases by 10.4%\nD. increases by 10%\nE. None of these\n\n### Answer:\nExplanation :\nReduction of price = (100 -8)% = 92% = 0.92\nIncrease of sale = (100+20)% = 120% = 1.20\nTotal effect = 0.92 X 1.20 = 110.4%, Increases by 10.4%\nAnswer : C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA waitress's income consists of her salary and tips.During one week ,her tips were 7/4 of her salary.What fraction of her income for the week came from tips?\n\n### Options:\nA. 1/9\nB. 1/6\nC. 2/3\nD. 4/9\nE. 7/11\n\n### Answer:\nHer tips were 7/4 of her salary.\nLet's say her salary =$4\nThis mean her tips = (7/4)($4) =$7\nSo, her TOTAL INCOME =$4+$7=$11\nWhat fraction of her income for the week came from tips\n$7/$11= 7/11\n= E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf green means red, red means yellow, yellow means blue, blue means orange and orange means green, what is the colour of leaf ?\n\n### Options:\nA. Red\nB. Green\nC. Yellow\nD. Orange\nE. Pink\n\n### Answer:\nExplanation:\nThe colour of leaf is 'green' and as given 'orange' means 'green'.\nso, the colour of leaf is 'red'.\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many digits will be there to the right of the decimal point in the product of 89.635 and .02218?\n\n### Options:\nA. 5\nB. 6\nC. 7\nD. 8\nE. 9\n\n### Answer:\nExplanation :\nSum of decimal places = 3 + 5 = 8\nThe last digit to the extreme right is zero (Since 5 x 8 = 40)\nHence, there will be 7 significant digits to the right of the decimal point. Answer : Option C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a simultaneous throw of pair of dice .find the probability of getting the total more than 7?\n\n### Options:\nA. 12/5\nB. 5/12\nC. 6/4\nD. 2/3\nE. 4/7\n\n### Answer:\nHere n(S)=(6*6)=36\nlet E=event of getting a total more than 7\n={(2,6),(3,5),(3,6),(4,4),(4,5),(4,6),(5,3),(5,4),(5,5),(5,6),(6,2),(6,3),(6,4),(6,5),(6,6)}\nP(E)=n(E)/n(S)=15/36=5/12\nOption B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a, b, and c are consecutive odd positive integers and a < b < c, which of the following could be equal to c - b - a+2 ?\n\n### Options:\nA. -1\nB. 3\nC. -4\nD. -1/2\nE. -1/3\n\n### Answer:\nlet we put values. a=1, b=3, c=5\n5-3-1=1\n1+2 =3\nAnswer :B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average of a couple was 23Yrs when they were married 5Yrs ago.The avg age of\nthe couple and a child, who was born during the interval, is 20Yrs now. How old is the\nchild now ?\n\n### Options:\nA. 2 Yrs\nB. 4 Yrs\nC. 3 Yrs\nD. 1 Yrs\nE. None of these\n\n### Answer:\n(a+b-5-5)/2=23;\na+b=56;\na+b+c/3=20;\nsolving both c=4\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich of these lines in the xy-plane does not contain any point with two negative coordinates?\n\n### Options:\nA. y = 3x\nB. y = x + 8\nC. y = x^2 - 4\nD. y = x^3 + 2x\nE. y = x^2\n\n### Answer:\nx^2 is 0 when x is 0 and positive for all other values of x.\nThe answer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMangala completes a piece of work in 10 days, Raju completes the same work in 40 days. If both of them work together, then the number of days required to complete the work is?\n\n### Options:\nA. 8 days\nB. 10 days\nC. 12 days\nD. 14 days\nE. 16 days\n\n### Answer:\nIf A can complete a work in x days and B can complete the same work in y days, then, both\nof them together can complete the work in x y/ x+ y days.\nThat is, the required No. of days = 10 \u00d7 40/50 = 8 days\nA)\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf e > a and L < a, which of the following cannot be true?\n\n### Options:\nA. d + L = 14\nB. d - L = 7\nC. d - L = 1\nD. a - e = 9\nE. a + d = 9\n\n### Answer:\nIs the answer D?\nIf e>a, then e-a>0 (always positive). The converse would be a-e<0 (always negative). Option D states that a-e=9, which can never be true.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo trains running in opposite directions cross a man standing on the platform in 35 seconds and 28 seconds respectively and they cross each other in 32 seconds. The ratio of their speeds is:\n\n### Options:\nA. 3 : 1\nB. 4: 3\nC. 3 : 8\nD. 3 : 25\nE. 3 : 4\n\n### Answer:\nLet the speeds of the two trains be x m/sec and y m/sec respectively. Then, length of the first train = 35 x meters, and length of the second train = 28 y meters. (35 x + 28 y) / (x + y) = 32\n==> 35 x + 28 y = 32 x + 32 y ==> 3 x = 4 y ==> x/y = 4/3\nAnswer: Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWith a uniform speed a car covers the distance in 8 hours. Had the speed been increased by 4 km/hr, the same distance could have been covered in 7 1/2 hours. What is the distance covered?\n\n### Options:\nA. 187 km\nB. 480 km\nC. 278 km\nD. 297 km\nE. 671 km\n\n### Answer:\nLet the distance be x km. Then,\nx/(7 1/2) - x/8 = 4\n2x/15 - x/8 = 4 => x = 480 km.\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n8 liters of solution is removed from 20% milk solution and 8 liters of water is added to the solution. The resulting solution has 16% milk in it. What was the initial quantity of the 20% milk solution?\n\n### Options:\nA. 40 Ltrs\nB. 50\nC. 60\nD. 70\nE. 80\n\n### Answer:\nAllegation method.\nConcentration of Alcohol in original sol - 20%\nConcentration of Alcohol in water -- 0%\nConcentration of Alcohol in final sol -- 16%\nAfter applying allegation as shown in figure they have to be mixed in 4:1 part\n1 part is given as 8 ltr, so total initial volume is 5 part = 5*8 = 40 Ltrs\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n4.036 divided by 0.04 gives :\n\n### Options:\nA. 100.8\nB. 100.2\nC. 100.5\nD. 100.9\nE. 100.7\n\n### Answer:\n= 4.036/0.04\n= 403.6/4\n= 100.9\nAnswer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSimplfy\n4b - [b -(a+b) - {b - (b - a+b)} + 2a]\n\n### Options:\nA. a\nB. 2a\nC. 4a\nD. 0\nE. 3b\n\n### Answer:\nExplanation:\n4b-[b-(a+b)-{b-(b-a+b)}+2a]\n=4b-[b-a-b-{b-(2b-a)}+2a]\n=4b-[-a-{b-2b+a}+2a]\n=4b-[-a-{-b+a}+2a]\n=4b-[-a+b-a+2a]\n=4b-[-2a+b+2a]\n=4b-b\n=3b\nOption E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the greatest number which leaves the same remainder when it divides 25, 57 and 105.\n\n### Options:\nA. 23\nB. 28\nC. 18\nD. 16\nE. 12\n\n### Answer:\nExplanation:\n105 - 57 = 48\n57 - 25 = 32\n105 - 25 = 80\nThe H.C.F of 32, 48 and 80 is 16.\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat percent of the different arrangements of the letters of the word ABACUS are those in which the vowels appear together?\n\n### Options:\nA. 10%\nB. 20%\nC. 40%\nD. 50%\nE. 60%\n\n### Answer:\nThe total number of different arrangements are 6!/2=360. We divide here by 2, since we have two same letters A.\nLetters A, A, and U are vowels. Put them together and consider as one object. So, we have 4 different objects (AAU) B C S. The number of different arrangements of them are 4!=24. And we have 3 possibilities to arrange vowels: AAU, AUA, UAA. Therefore, we have 24*3=72 different arrangements.\nHence, 72/360*100%=20%.\nThe correct answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nConsider a lady took a loan from a bank at the rate of 12% p.a. simple interest. After 3 years she had to pay Rs. 8100\ninterest only for the period. The principal amount borrowed by her was\n\n### Options:\nA. Rs. 22500\nB. Rs. 10000\nC. Rs. 15000\nD. Rs. 20000\nE. None of these\n\n### Answer:\nExplanation :\nPrincipal = Rs. (100\u00d78100 / 12\u00d73)\n=> Rs. 22500.\nAnswer : A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA fair coin is tossed 9 times. What is the probability of getting more heads than tails in 9 tosses?\n\n### Options:\nA. 1/2\nB. 63/128\nC. 4/7\nD. 61/256\nE. 63/64\n\n### Answer:\nOn each toss, the probability of getting a head is 1/2 and the probability of getting a tail is 1/2.\nThere is no way to get the same number of heads and tails on an odd number of tosses.\nThere will either be more heads or more tails.\nThen there must be more heads on half of the possible outcomes and more tails on half of the possible outcomes.\nP(more heads) = 1/2\nThe answer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are two circles of different radii. The are of a square is 784 sq cm and its side is twice the radius of the larger circle. The radius of the larger circle is seven - third that of the smaller circle. Find the circumference of the smaller circle.\n\n### Options:\nA. 87\u220f cm\nB. 56\u220f cm\nC. 12\u220f cm\nD. 16\u220f cm\nE. 75\u220f cm\n\n### Answer:\nLet the radii of the larger and the smaller circles be l cm and s cm respectively. Let the side of the square be a cm.\na2 = 784 = (4)(196) = (22).(142)\na = (2)(14) = 28\na = 2l, l = a/2 = 14\nl = (7/3)s\nTherefore s = (3/7)(l) = 6 Circumference of the smaller circle = 2\u220fs = 12\u220f cm.\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n7 liters of a 22 percent solution of alcohol in water are mixed with 3 liters of an 11 percent alcohol in water solution. What is the percentage of alcohol in the new solution?\n\n### Options:\nA. 17.5%\nB. 17.8%\nC. 18.1%\nD. 18.4%\nE. 18.7%\n\n### Answer:\nThe total amount of alcohol is 0.22(7) + 0.11(3) = 1.87 liters.\nThe percentage is 1.87 / 10 = 18.7 / 100 which is 18.7%\nThe answer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe sum of the ages of a father and son is 45 years. Five years ago, the product of their ages was four times the fathers age at that time. The present age of father and son\n\n### Options:\nA. 34,11\nB. 35,10\nC. 36,9\nD. 40,5\nE. 41,5\n\n### Answer:\nExplanation:\nLet sons age = x years. Then fathers age = (45 - x)years.\n(x\u20145)(45\u2014x\u20145) = 4(45- x - 5) hence (x\u20145) = 4 so x = 9\nTheir ages are 36 years and 9 years.\nAnswer: Option C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf x > 0, x/40 + x/20 is what percent of x?\n\n### Options:\nA. 6%\nB. 25%\nC. 37 1/2%\nD. 60%\nE. 75 %\n\n### Answer:\nJust plug and chug. Since the question asks for percents, pick 100. (but any number will do.)\n100/40 + 100/20= 2.5+5=7.5\n7.5 is 75% of 100=E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA walks around a circular field at the rate of one round per hour while B runs around it at the rate of six rounds per hour. They start in the same direction from the same point at 7.30 a.m. They shall first cross each other at?\n\n### Options:\nA. 12 min\nB. 16 min\nC. 18 min\nD. 15 min\nE. 19 min\n\n### Answer:\nSince A and B move in the same direction along the circle, so they will first meet each other when there is a difference of one round between the two.\nRelative speed of A and B = 6 - 1 = 5 rounds per hour.\nTime taken to complete one round at this speed\n= 1/5 hr\n= 12 min.\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe length of each side of square A is increased by 100 percent to make square B. If the length of the side of square B is increased by 25 percent to make square C, by what percent is the area of square C greater than the sum of the areas of squares A and B?\n\n### Options:\nA. 75%\nB. 25%\nC. 10%\nD. 45%\nE. 180%\n\n### Answer:\nLet length of each side of square A be 10\nArea of A = 10^2 = 100\nSince , length of each side of square A is increased by 100 percent to make square B\nlength of each side of square B = 2*10 = 20\nArea of B = 20^2 = 400\nSince , length of the side of square B is increased by 25 percent to make square C\nlength of each side of square C= 1.25*20 = 25\nArea of C= 25^2 = 625\nDifference in areas of C and cummulative areas of A and B = 625 -(400+100) = 225\npercent is the area of square C greater than the sum of the areas of squares A and B = (225/500) * 100 % = 45%\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFor her customer feedback score, Jess wants to average at or above an 8.0 rating. For the month of June, she received the following scores: 7, 8, 8, 7, 9, 9, 6, 7, 8 and 7. By what percent did she fall short of her goal?\n\n### Options:\nA. 4%\nB. 5%\nC. 8%\nD. 10%\nE. 12%\n\n### Answer:\nExpected minimum rating = 8\nDeviation from the expected minimum rating = (-1 + 0 + 0 - 1 + 1 + 1 - 2 - 1 + 0 - 1)/10 = -4/10 = -0.4\nCurrent rating is 0.4 less than 8.\nPercentage = (0.4/8)*100 = 5%\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nfind value for x from below equation? x + 1 = 5\n\n### Options:\nA. -5\nB. -4\nC. 4\nD. 3\nE. 2\n\n### Answer:\n1. Subtract 1 from both sides:\nx + 1 - 1 = 5 - 1\n2. Simplify both sides:\nx = 4\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nPradip spends 40 per cent of his monthly income on food items, and 50 per cent of the remaining on clothes and conveyance. He saves one-third of the remaining amount after spending on food, clothes and conveyance. If he saves 19,200 every year,what is his monthly income?\n\n### Options:\nA. 24,000\nB. 12,000\nC. 16,000\nD. 20,000\nE. None of these\n\n### Answer:\nFood items = 40%\nClothes + conveyance = 1\u20442 of 60% = 30%\n1\u20443 of 30% = 19,200\u204412 \u21d2 10% = 1600\n\u2234 100% = 16,000\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTo make 552185 divisible by 8, what is the least whole number that should be added to it?\n\n### Options:\nA. 3\nB. 7\nC. 9\nD. 6\nE. 4\n\n### Answer:\nA number is divisible by 8 if the number formed by the last three digits is divisible by 8.\nHere, 552185=185(no formed by last three digit)\nthe next multiple of 8 is 192\n7 must be added to 552185 to make it divisible by 8\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n64, 81, 100, 144, 196, ?, F ind the missing number(?).\n\n### Options:\nA. 225\nB. 220\nC. 230\nD. 238\nE. 278\n\n### Answer:\nThe series consists of squares of consecutive composite numbers.\nAnswer : A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA dishonest dealer professes to sell goods at the cost price but uses a weight of 600 grams per kg, what is his percent?\n\n### Options:\nA. 11\nB. 25\nC. 66\nD. 88\nE. 11\n\n### Answer:\n600 --- 400\n100 --- ? => 66%\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n27 * 27* 27 * 27 = 3^ ?\n\n### Options:\nA. 7\nB. 12\nC. 5\nD. 6\nE. 8\n\n### Answer:\n3^3 * 3^3 * 3^3 * 3^3 = 3^ (3+3+3+3) = 3^12\nAnswer : 12\nOption : B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA person can swim in still water at 4 km/h. If the speed of water 2 km/h, how many hours will the man take to swim back against the current for 14km?\n\n### Options:\nA. 3\nB. 6\nC. 8\nD. 9\nE. 7\n\n### Answer:\nM = 4\nS = 2\nUS = 4 - 2 = 2\nD = 14\nT = 14/2 = 7\nAnswer:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are 600 students in a school. The ratio of boys and girls in this school is 3:5. Find the total of girls & boys are there in this school?\n\n### Options:\nA. 320\nB. 345\nC. 375\nD. 380\nE. 400\n\n### Answer:\nIn order to obtain a ratio of boys to girls equal to 3:5, the number of boys has to be written as 3 x and the number of girls as 5 x where x is a common factor to the number of girls and the number of boys. The total number of boys and girls is 600. Hence\n3x + 5x = 600\nSolve for x\n8x = 600\nx = 75\nNumber of boys\n3x = 3 \u00d7 75 = 225\nNumber of girls\n5x = 5 \u00d7 75 = 375\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?\n\n### Options:\nA. 37\nB. 240\nC. 288\nD. 267\nE. 211\n\n### Answer:\nSpeed = (54 * 5/18) m/sec = 15 m/sec. Length of the train = (15 x 20)m = 300 m. Let the length of the platform be x meters. Then, (x + 300)/36 = 15 ==> x + 300 = 540 ==> x = 240 m.Answer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nArun's Ice Cream Shop sells ice cream at x cents a scoop. For an additional y cents, a customer can add 4 toppings to his or her sundae. How much would a sundae with 4 scoops and 4 toppings cost, in terms of x and y?\n\n### Options:\nA. 3x+y\nB. 5x+y\nC. 6x+y\nD. 4x+y\nE. 7x+y\n\n### Answer:\nAnswer A 4x+y\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA computer program generates a single digit by a random process, according to which the probability of generating any digit is directly proportional to the reciprocal of one more than that digit. If all digits are possible to generate, then the probability E of generating an odd prime digit is between\n\n### Options:\nA. 0 and 1/6\nB. 1/6 and 1/3\nC. 1/3 and 1/2\nD. 1/2 and 2/3\nE. 2/3 and 5/6\n\n### Answer:\nK (1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/7 + 1/8 + 1/9+ 1/10) =1\nNote that 1/10 is least value and is equal to 0.1 so we can write above series as\nK (1+0.5+0.3+0.25+0.2+0.16+0.5+residual) = 1\nK=1/3+\nP (3 or 5 or 7) =K*13/24\nRequired probability E= 13/24 \u00d7 1/3+ = 4+/24 > 1/6\nAnswer should be B\nP.s. 3+ denotes a value little greater than 3 .\nSame for 4+.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n15 men take 21 days of 8 hours each to do a piece of work. How many days of 6 hours each would 21 women take to do the same. If 3 women do as much work as 2 men?\n\n### Options:\nA. 20\nB. 10\nC. 30\nD. 40\nE. 50\n\n### Answer:\nC\n30\n3W = 2M\n15M ------ 21 * 8 hours\n21 W ------ x * 6 hours\n14 M ------ x * 6\n15 * 21 * 8 = 14 * x * 6\nx = 30\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the sum of three consecutive even numbers is 44 more than the average of these numbers, then the largest of these numbers is?\n\n### Options:\nA. 20\nB. 24\nC. 22\nD. 26\nE. 27\n\n### Answer:\nExplanation:\nLet the smallest of these number be x. The other two numbers are (x + 2) and (x + 4).\nx + (x + 2) + (x + 4) = (X + (X+2) + (x+4)) / 3 + 44\n3x + 3*(x + 2) + 3*(x + 4) = x + (x + 2) + (x + 4) + 132\n9x + 18 = 3x + 138\n6x = 120\nx = 20\nTherefore, the largest number is 24.\nANSWER B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe length of the bridge, which a train 130 metres long and travelling at 54 km/hr can cross in 30 seconds, is:\n\n### Options:\nA. 200 m\nB. 225 m\nC. 320 m\nD. 250 m\nE. 240 m\n\n### Answer:\nSpeed = [54 X 5/18] m/sec = [15/1] m/sec\nTime = 30 sec\nLet the length of bridge be x metres.\nThen, (130 + x)/30 = 15 => (130 + x) = 450 => x = 450-130 = 320m\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSimple interest on a certain amount is 9/16 of the principal. If the numbers representing the rate of interest in percent and time in years be equal, then time, for which the principal is lent out, is :\n\n### Options:\nA. 6 1/2\nB. 7 1/2\nC. 8\nD. 9 1/2\nE. None\n\n### Answer:\nSol.\nLet sum = x. Then, S.I. = 9/16 x.\nLet rate = R% and time = R years.\n\u2234 [x * R * R / 100] = 9x / 16 \u21d4 R\u00b2 = 900/16\n\u21d4 R = 30/4 = 7 1/2\nHence, time = 7 1/2 years.\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many two-digit numbers yield a remainder of 3 when divided by both 4 and 14?\n\n### Options:\nA. 0\nB. 1\nC. 2\nD. 3\nE. 4\n\n### Answer:\nEasier to start with numbers that are of the form 14p+3 ---> 17,31,45,59,73,87.\nOut of these 3 (31,59,87) are also of the form 4q+3. Thus 3 is the answer. D is the correct answer.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a games hour 4 different types of players came to the ground? cricket 16, hokey 12, football 18, softball 13. How many players are present in the ground?\n\n### Options:\nA. 70\nB. 52\nC. 62\nD. 59\nE. 50\n\n### Answer:\ntotal number of players= 16+12+18+13= 59\nAnswer is D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a number is subtracted from its square we get 272. Find the number?\n\n### Options:\nA. 7\nB. 21\nC. 19\nD. 15\nE. 17\n\n### Answer:\nx^2 \u00e2\u20ac\u201c x = 272\n=> x =17\nAnswer E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA positive number x is multiplied by 4, and this product is then divided by 3. If the positive square root of the result of these two operations equals x, what is the value of x ?\n\n### Options:\nA. 9/4\nB. 3/2\nC. 4/3\nD. 1/3\nE. 1/2\n\n### Answer:\nWe need to produce an equation from the information given in the problem stem. We are first given that x is multiplied by 2 and then the product is divided by 3. This gives us:\n2x/3\nNext we are given that the positive square root of the result (which is 2x/3) is equal to x. This gives us\n\u221a(2x/3) = x\n2x/3 = x^2\n2x = 3x^2\n3x^2 \u2013 2x = 0\nx(3x \u2013 2) = 0\nx = 0 or\n3x \u2013 2 = 0\n3x = 2\nx = 1/3\nBecause x is positive, x = 1/3. The answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA firm has 4 senior partners and 6 junior partners. How many different groups of 3 partners can be formed in which at least one member of the group is a senior partner. (2 groups are considered different if at least one group member is different)\n\n### Options:\nA. 48\nB. 100\nC. 120\nD. 288\nE. 600\n\n### Answer:\nTotal no of groups of 3 members (including junior and senior) = 10C3\nTotal no of groups of 3 members (only juniors) = 6C3\nTotal no of groups of 3 members (at least 1 senior) = 10C3 - 6C3 = 120 - 20 =100\nans:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nBy investing in 16 % stock at 64, one earns Rs. 1500. The investment made is:\n\n### Options:\nA. 5760\nB. 7667\nC. 4445\nD. 4566\nE. 3344\n\n### Answer:\nExplanation:\nTo earn Rs., investment = Rs. 64.\nTo earn Rs. 1500, investment = = Rs. 5760.\nAnswer: C) 5760\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf x and y are positive integers such that y is a multiple of 5 and 3x + 8y = 700, then x must be a multiple of which of the following?\n\n### Options:\nA. 3.\nB. 6.\nC. 7.\nD. 8.\nE. 10.\n\n### Answer:\nIf y is a multiple of 5, then 8y is also a multiple of 5.\n3x = 700 - 8y\n700 - 8y is even and it is a multiple of 5.\nThus x must also be even and a multiple of 5.\nTherefore x must be a multiple of 10.\nThe answer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average of first 50 non-zero positive integers is\n\n### Options:\nA. 11.5\nB. 25.5\nC. 22\nD. 25\nE. 27\n\n### Answer:\nExplanation :\nSum of first n non-zero positive integers n(n + 1)/2\nSo, average of first n non-zero positive integers n(n + 1)/2n = (n + 1)/2\n=> (50 + 1)/2 = 25.5\nAnswer : B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA woman has four blouses of different colors, three skirts of different colors, and two different pairs of shoes. She refuses to wear her pink blouse with her green skirt. How many different blouseskirt-shoe combinations could she wear?\n\n### Options:\nA. 8\nB. 22\nC. 16\nD. 17\nE. 18\n\n### Answer:\ntotal ways = 4*3*2=24..\nnow its better to find the ways in which the pink blose and green skirty are together and subtract from total to get the answer..\nthe ways in which the pink blose and green skirty are together=1*1*2=2..\ntotal ways =24-2=22..\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n18% of 680 - ? = 68.7\n\n### Options:\nA. 44.1\nB. 32.4\nC. 66.5\nD. 75.2\nE. 53.7\n\n### Answer:\nE\n53.7\n(18 *680)/100 - ? = 68.7\n? = 122.4 - 68.7\n? = 53.7\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo dice are thrown simultaneously. What is the probability of getting two numbers whose product is even?\n\n### Options:\nA. 1/2\nB. 3/8\nC. 3/4\nD. 5/16\nE. 9/16\n\n### Answer:\nIn a simultaneous throw of two dice, we have n(S) = (6 x 6) = 36.\nThen, E\t= {(1, 2), (1, 4), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 2), (3, 4),\n(3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 2), (5, 4), (5, 6), (6, 1),\n(6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}\nn(E) = 27.\nP(E) =\tn(E)/n(S)\t=\t27/36\t=\t3/4\t.\nAnswer : C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train 700 m long passes a man, running at 20 km/hr in the same direction in which the train is going, in 40 sec. The speed of the train is?\n\n### Options:\nA. 40 km/hr\nB. 41 km/hr\nC. 42 km/hr\nD. 43 km/hr\nE. 44 km/hr\n\n### Answer:\nSpeed of the train relative to man = 700/40 = 35/2 m/sec.\n= 35/2 * 18/5 = 63 km/hr\nLet the speed of the train be x km/hr. Then, relative speed = (x - 20) km/hr.\nx - 20 = 63 => x = 43 km/hr.\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 3 men or 4 women can reap a field in 43 days how long will 7 men and 5 women take to reap it?\n\n### Options:\nA. 9\nB. 12\nC. 15\nD. 18\nE. 19\n\n### Answer:\nExplanation:\n3 men reap 1/43 field in 1 day\n1 man reap 1/(3 x 43)\n4 women reap 1/43 field in 1 day\n1 woman reap 1/(43 x 4)\n7 men and 5 women reap (7/(3 x 43)+ 5/(4 x 43)) =1/12 in 1 day\n7 men and 5 women will reap the field in 12 days\nAnswer: Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nin a certain flower shop, which stocks four types of flowers, there are 1/4 as many violets as carnations, and 1/4 as many tulips as violets. If there are equal numbers of roses and tulips, what percent of the flowers in the shop are carnations?\n\n### Options:\nA. 31\nB. 30\nC. 29\nD. 28\nE. 27.27\n\n### Answer:\nGiven :-\nViolets - C/4\nCarnations - C\nTulip - C/16\nRose - C/16\nTotal flowers in terms of C = C/4+C+C/16+C/16 = 22C/6\nPercentage of Carnations = C/22C/6 *100 =27.27\nAnswer E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf I walk at 8 km/h, I miss the bus by 14 minutes. If I walk at 9 km/h, I reach 16 minutes before the arrival of the bus. How far I walk to reach the bus stand ?\n\n### Options:\nA. 3.4 km\nB. 2.9 km\nC. 2.4 km\nD. 2.6 km\nE. 2.8 km\n\n### Answer:\nd = product of speed difference of time /difference of speed\nd = 8 X 9/60[14\u00e2\u02c6\u2019(\u00e2\u02c6\u201916)/9-8]\n[Here, \u00e2\u20ac\u201cve sign indicates before the schedule time]\n\u00e2\u2021\u2019 d = 2.4 km\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nwhat is next no. 11 23 47 83 131 191 263 347 443 551???\n\n### Options:\nA. 171\nB. 181\nC. 191\nD. 201\nE. 671\n\n### Answer:\n11+12*1=23\n23+12*2=47\n47+12*3=83\n83+12*4=131\n131+12*5=191\n191+ 12*6=263\n263+12*7=347\n347+12*8=443\n443+12*9=551\n551+12*10=671\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain debt will be paid in 65 installments from January 1 to December 31 of a certain year. Each of the first 20 payments is to be $410; each of the remaining payments is to be $65 more than each of the first 20 payments. What is the average (arithmetic mean) payment that will be made on the debt for the year?\n\n### Options:\nA. 443\nB. 455\nC. 465\nD. 468\nE. 475\n\n### Answer:\nTotal number of installments = 65\nPayment per installment for the first 20 installments = 410\nPayment per installment for the remaining 45 installments = 410+65=475\nAverage = (20*410 + 45*475)/65 = 455\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a party every person shakes hands with every other person. If there were a total of 171 handshakes in the party then what is the number of persons present in the party ?\n\n### Options:\nA. 15\nB. 16\nC. 17\nD. 18\nE. 19\n\n### Answer:\nExplanation :\nLet the number of persons be n\n\u00e2\u02c6\u00b4 total handshakes = nC2 = 171\nn(n-1)/2 = 171 \u00e2\u02c6\u00b4 n = 19\nAnswer : Option E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nExpress a speed of 16 kmph in meters per second?\n\n### Options:\nA. 10 mps\nB. 8 mps\nC. 4 mps\nD. 7 mps\nE. 2 mps\n\n### Answer:\n16 * 5/18\n= 4 mps\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe area of a rectangle is 15 square centimeters and the perimeter is 16 square centimeters. What are the dimensions of the rectangle?\n\n### Options:\nA. 2&4\nB. 3&5\nC. 4&6\nD. 5&7\nE. 6&8\n\n### Answer:\nLet x and y be the length and width of the rectangle. Using the formulas for the area and the perimeter, we can write two equations.\n15 = x y and 16 = 2 x + 2 y\nSolve the second equation for x\nx = 8 - y\nSubstitute x in the equation 15 = x y by 8 - y to rewrite the equation as\n15 = (8 - y) y\nSolve for y to find\ny = 3 and y = 5\nUse x = 8 - y to find x\nwhen y = 3 , x = 5 and when y = 5 , x = 3.\nThe dimensions of the rectangle are 3 and 5.\ncorrect answer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the radius of the circum circle of the triangle whose sides are 5, 12 and 13 units respectively?\n\n### Options:\nA. 2 units\nB. 12 units\nC. 6.5 units\nD. 6 units\nE. 7.5 units\n\n### Answer:\nsides of triangle are 5,12,13\ni.e triangle is right angled,hypotenuse=13\nin case of a right angled triangle, the hypotenuse is the diameter of the circumcircle\nso radius of the circum circle=13/2=6.5 units\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train covers a distance of 12 km in 10 min. If it takes 4 sec to pass a telegraph post, then the length of the train is?\n\n### Options:\nA. 20\nB. 110\nC. 120\nD. 80\nE. 60\n\n### Answer:\nSpeed = (12/10 * 60) km/hr = (72 * 5/18) m/sec = 20 m/sec.\nLength of the train = 20 * 4= 80 m.\nAnswer: Option D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf P is a prime number greater than 5, what is the remainder when P^2 is divided by 8.\n\n### Options:\nA. 4\nB. 3\nC. 2\nD. 1\nE. Cannot be determined\n\n### Answer:\nHere is the algebraic approach..\nthese prime numbers are of teh form 6n+1 or 6n-1..\nso P= 6n+1..\nP^2=(6n+1)2=36n^2+12n+1\nNow 36n^2+12n=4n(9n+3)\nif n is even... 4n will be div by 8....\nif n is odd.. 4n will be div by 4 and 9n+3 will become even and be div by 2,hence 4n*(9n+3) will be div by 4*2=8..\nso in P^2=36n^2+12n+1 only 1 is left, Remainder = 1.\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA company D has 15 percent of the employees are secretaries and 10 percent are salespeople. If there are 120 other employees of Company D, how many employees does Company D have?\n\n### Options:\nA. 200\nB. 160\nC. 180\nD. 152\nE. 250\n\n### Answer:\nLet the total number of employees in the company be x\n% of secretaries = 15%\n% of salespeople = 10%\n% of of employees other than secretaries and salespeople = 100 - 25 = 75%\nBut this number is given as 120\nso 75% of x = 120\nx = 160\nTherefore there a total of 160 employees in the company D\nCorrect answer - B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n2 trains starting at the same time from 2 stations 200 km apart and going in opposite direction cross each other at a distance of 110 km from one of the stations. What is the ratio of their speeds\n\n### Options:\nA. 11:9\nB. 13:9\nC. 17:9\nD. 21:9\nE. None of these\n\n### Answer:\nExplanation:\nWe know total distance is 200 Km\nIf both trains crossed each other at a distance of 110 km then one train covered 110 km and other 90 km [110+90=200km]\nSo ratio of their speed = 110:90 = 11:9\nOption A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 15% of 40 is greater than 25% of a number by 2, the number is\n\n### Options:\nA. 14\nB. 16\nC. 18\nD. 20\nE. 22\n\n### Answer:\nExplanation:\n15/100 * 40 - 25/100 * x = 2 or x/4 = 4 so x = 16\nOption B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRamesh can finish a work in 20 days and Sushil in 25 days. They both work together for 5 days and then Sushil goes away. In how many days will Ramesh complete the remaining work?\n\n### Options:\nA. 22 days\nB. 68 days\nC. 77 days\nD. 11 days\nE. 88 days\n\n### Answer:\n(5 + x)/20 + 5/25 = 1 => x = 11 days\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA garrison of 2000 men has provisions for 54 days. At the end of 15 days, a reinforcement arrives, and it is now found that the provisions will last only for 20 days more. What is the reinforcement?\n\n### Options:\nA. 1900\nB. 2776\nC. 8888\nD. 1666\nE. 1878\n\n### Answer:\n2000 ---- 54\n2000 ---- 39\nx ----- 20\nx*20 = 2000*39\nx = 3900\n2000\n-------\n1900\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the equation x^2\u22126x=2k has at least one solution, which of the following must be true?\n\n### Options:\nA. k > 9\nB. k < \u22129\nC. k = 9\nD. k \u2264 9\nE. k \u2265 \u22129/2\n\n### Answer:\nx^2\u22126x=2k\n=> x^2\u22126x - 2k = 0\nFor a quadratic equation to have at least one solution, its discriminant (b^2-4ac) should be non-negative.\nb^2-4ac \u22650\n=> 36 - 4*1*(-2k) \u22650\n=> 36 + 8k \u22650\n=> k \u2265 -9/2\nAnswer E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA group of students was interviewed for that if it was asked whether or not they speak French and / or English. Among those who speak French, 10 speak English well, while 40 of them do not speak English. If 75% of students do not speak French, how many students were surveyed?\n\n### Options:\nA. 210\nB. 225\nC. 200\nD. 250\nE. 300\n\n### Answer:\nNumber of students who speak French are 40 + 10 = 50\nOf total students, the percentage of students who do not speak French was 75% --> percentage of who do is 25%\n50-------25%\nx ------- 100%\nx = 50*100/25 = 200 = number of all students\nAnswer is C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the rate percent when the simple interest on Rs.800 amount to Rs.160 in 4 Years?\n\n### Options:\nA. 5\nB. 6\nC. 7\nD. 8\nE. 9\n\n### Answer:\n160 = (180*4*R)/100\nR = 5%.Answer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf an object travels at nine feet per second, how many feet does it travel in one hour?\n\n### Options:\nA. 30\nB. 300\nC. 720\nD. 1800\nE. 32400\n\n### Answer:\nSpeed = 9 feet per second.\n1 Hour= 60X60 Seconds = 3600 Seconds.\nTotal no of feet traveled in 1 hour = 3600X9 = 32400\nAnswer E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA bag contains equal number of Rs.5, Rs.2 and Re.1 coins. If the total amount in the bag is Rs.1152, find the number of coins of each kind?\n\n### Options:\nA. 337\nB. 268\nC. 144\nD. 772\nE. 997\n\n### Answer:\nLet the number of coins of each kind be x.\n=> 5x + 2x + 1x = 1152\n=> 8x = 1152 => x = 144\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThree 6 faced dice are thrown together. The probability that exactly two dice show the same number on them is ?\n\n### Options:\nA. 5/16\nB. 5/12\nC. 5/87\nD. 5/56\nE. 5/38\n\n### Answer:\nUsing question number 11 and 12, we get the probability as\n1 - (1/36 + 5/9) = 5/12\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn the floor of a particular kitchen owned by an abstract artist, each row of tiles to the right of the first row contains two fewer tiles than the row directly to its left. If there are nine rows in all and a total of 270 tiles in the floor, how many tiles does the leftmost row contain?\n\n### Options:\nA. 38\nB. 56\nC. 60\nD. 64\nE. 68\n\n### Answer:\nThis question can be solved in a variety of ways: with algebra, by TESTing THE ANSWERS and by using a great Number Property shortcut involving consecutive integers.\nWe're given a few facts to work with:\n1) There are 9 rows of tiles.\n2) When going from 'left to right', each row contains TWO FEWER tiles than the one next to it.\n3) There are a total of 270 tiles\nWe're asked how many tiles the left-most most row holds (meaning the one with the MOST tiles).\nTo start, 270 is divisible by 9, so we can figure out the AVERAGE number of tiles per row. That is 270/9 = 30. Since we're dealing with a set of 9 consecutive integers that differ by 2 each, we know that the '5th row' will have 30 tiles (the average). Then we just have to 'add 2s' until we get to the first row...\n30 +2 +2 +2 +2 = 38.\nFinal Answer:\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA ship sails out to a mark at the rate of 18 kmph. and sails back at the rate of 14 kmph. The average rate of sailing is ?\n\n### Options:\nA. 5 km/hr\nB. 12 km/hr\nC. 16 km/hr\nD. 25 km/hr\nE. None\n\n### Answer:\nAnswer\nAverage = ( 2uv / u +v ) km/hr\n= ( 2 x 18 x 14 ) / (18 +14 ) km/hr.\n= 16 km/hr.\nCorrect Option: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA, Band C can do a piece of work in 35 days, 20 days and 55 days respectively, working alone. How soon can the work be done if A is assisted by Band C on alternate days?\n\n### Options:\nA. 7 days\nB. 8 days\nC. 9 days\nD. 10 days\nE. 16 days\n\n### Answer:\n(A+B)'s 1 day's work = 1/35+1/20 = 11/140\n(A+C)'s 1 day's work = 1/35+1/55 = 18/385\nwork done in 2 day's = 11/140+18/385 = 48/383\n48/383th work done in 2 days\nwork done= 383/48*2 = 16 days (approx)\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train 220 m long is running with a speed of 60 km/hr. In what time will it pass a man who is running at 6 km/hr in the direction opposite to that in which the train is going?\n\n### Options:\nA. 12\nB. 6\nC. 7\nD. 8\nE. 9\n\n### Answer:\nSpeed of train relative to man = 60 + 6 = 66 km/hr.\n= 66 * 5/18 = 55/3 m/sec.\nTime taken to pass the men = 220 * 3/55 = 12 sec.\nAnswer: Option A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many even multiples of 45 are there between 449 and 901?\n\n### Options:\nA. 5\nB. 6\nC. 9\nD. 10\nE. 11\n\n### Answer:\n450 = 10*45\n900 = 20*45\nThe even multiples are 45 multiplied by 10, 12, 14, 16, 18, and 20 for a total of 6.\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFor all positive integers m, [m]=3m when m is odd and [m]=(1/2)*m when m is even. What is [5]*[6] equivalent to?\n\n### Options:\nA. [45]\nB. [30]\nC. [15]\nD. [5]\nE. [50]\n\n### Answer:\n[5]*[6] = 15*3 = 45 = [15]\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man goes from A to B at a speed of 20 kmph and comes back to A at a speed of 30 kmph. Find his average speed for the entire journey?\n\n### Options:\nA. 19 kmph\nB. 24 kmph\nC. 17 kmph\nD. 12 kmph\nE. 16 kmph\n\n### Answer:\nDistance from A and B be 'd'\nAverage Speed = total distance/total time\nAverage Speed = (2d)/[(d/20) + (d/30)]\n= (2d)/[5d/60) => 24 kmph.\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFor an upcoming charity event, a male vocalist has agreed to sing 7 out of 9 \u201cold songs\u201d and 5 out of 8 \u201cnew songs.\u201d How many ways can the singer make his selection?\n\n### Options:\nA. 25\nB. 50\nC. 150\nD. 480\nE. 161.28\n\n### Answer:\n=9C7*8C5\n=9*8/5*8*7/5\n=161.28\nAns = E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many shots of 1cm radius can be prepared from a sphere of 2cm radius?\n\n### Options:\nA. 3\nB. 8\nC. 27\nD. 88\nE. 99\n\n### Answer:\n4/3 \u00cf\u20ac * 2 * 2 * 2 = 4/3 \u00cf\u20ac * 1 * 1 * 1 * x\nx = 8\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nwhat is the remainder when 789456123 is divided by 999\n\n### Options:\nA. 349\nB. 359\nC. 369\nD. 379\nE. 389\n\n### Answer:\nthere is a simple trick for 99 or 999..u have to add the digits from right side for 99 you will select the last 2 digits and add with next two last digits and go on..similarly for 999 u will add last three digits then its next two last digits and so on..\nso you will get 123 + 456 +789 =1368 again select last 3 and add them u will get 368 + 001 i.e 369\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo numbers are in the ratio 3 : 4. If their L.C.M. is 84. what is sum of the numbers?\n\n### Options:\nA. 49\nB. 56\nC. 76\nD. 84\nE. 85\n\n### Answer:\nExplanation:\nLet the numbers be 3x and 4x\nLCM of 3x and 4x = 12x (Since LCM of 3 and 4 is 12. Hence LCM of 3x and 4x is 12x)\nGiven that LCM of 3x and 4x is 84\n=> 12x =84\n=> x = 84/12 = 7\nSum of the numbers\n= 3x + 4x\n= 7x\n= 7 x 7 = 49\nAnswer: Option A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the speed of the train in km/hr whose length is 360 metres which passes a pole in 18 seconds?\n\n### Options:\nA. 59/9 km/hr\nB. 50/9 km/hr\nC. 25/6 km/hr\nD. 55/18 km/hr\nE. 60/18 km/hr\n\n### Answer:\nSpeed=(18x5/18)=5 m/sec.\nLength of the train= 360 metre\nTime=18s\nSpeed=length / time\nSpeed=(360/8)=20 m/sec = 20*5/18 km/hr = 50/9 km/hr\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average of first 40 prime numbers is?\n\n### Options:\nA. 15.41\nB. 16.41\nC. 15.61\nD. 15\nE. 16.91\n\n### Answer:\nExplanation:\nAverage = (2+3+5+7+11+13+17+19+23+29+31+37)/12= 197/12= 16.41(Approx)\nAnswer is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the greatest number that will divide 28, 128 and 147 leaving 10, 2 and 3 as remainders respectively\n\n### Options:\nA. 19\nB. 17\nC. 13\nD. 9\nE. 18\n\n### Answer:\nExplanation:\nAnswer will be HCF of (28-10, 128-2, 147-3)\nHCF of (18, 126, 144) = 18\nOption E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n6x \u2212 12 = 6y\n5y + 5x = 10\nWhich of the following is the number of solutions to the system of equations shown above?\n\n### Options:\nA. More than three\nB. Exactly three\nC. Exactly two\nD. Exactly one\nE. None\n\n### Answer:\n6x \u2212 12 = 6y\n=> 6x - 6y = 12\n=> x- y =2 -- 1\n5y + 5x = 10\n=>x + y = 2 -- 2\nFrom equation 1 and 2 , we get\n2x = 4\n=> x=2\ny=0\nTherefore , the given system will have Exactly one solution\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n80% of the students of a village is 1600. The total students of the school is?\n\n### Options:\nA. 2000\nB. 2500\nC. 3000\nD. 1800\nE. 2200\n\n### Answer:\nX * (80/100) = 1600\nX = 20 * 100\nX = 2000\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe sum of ages of 5 children born at theintervals of 3 years each is 50 years. what is the age of the youngest child?\n\n### Options:\nA. 4\nB. 5\nC. 9\nD. 8\nE. 10\n\n### Answer:\nthe age of children x, (x+3), (x+6) , (x+9) and (x+12) years.\nx+(x+3)+(x+6)+(x+9)+(x+12)= 50\n5x= 20 , x=4. correct answer (A)\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSuresh borrowed some money at the rate of 6% p.a. for the first three years, 9% p.a. for the next five years and 13% p.a. for the period beyond eight years. If the total interest paid by him at the end of 11 years is Rs.8160, how much money did he borrow?\n\n### Options:\nA. Rs.8500\nB. Rs.6000\nC. Rs.8000\nD. Rs.9000\nE. Rs.7000\n\n### Answer:\nusing the formula S.I=P*T*R/100\n(x*6*3/100)+(x*9*5/100)+(x*13*3/100)=8160\nx=8000\ni.e money borrowed is Rs.8000\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA & B partner in a business , A contribute 1/4 of the capital for 15 months & B received 2/3 of the profit . For how long B's money was used\n\n### Options:\nA. 12 months\nB. 10 months\nC. 14 months\nD. 16 months\nE. None of these\n\n### Answer:\nExplanation :\nB received 2/3 of the profit\n=> A : B = 1 : 2\nLet the total capital = x\nThen A's capital = x/4\nB's capital = x \u2013 x/4 = 3x/4\nAssume B's money was used for b months\nThen A:B = (x/4)*15 : (3x/4)*b = 1 : 2\n=> 15/4 : 3b/4 = 1 : 2\n=> 15 : 3b = 1 : 2\n=> 5 : b = 1 : 2\n=> 5/b = 1/ 2\n=> b = 5*2 = 10. Answer : Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many numbers of 5 digits can be formed with the digits 0, 1, 2, 3, 4, 6 & 8 with no digit being repeated in the same number?\n\n### Options:\nA. 2170\nB. 2160\nC. 4396\nD. 4500\nE. 3500\n\n### Answer:\nAs we have 5 digits.. and having no repeation..\nFor the first digit can't be \"0\".. so, possibilities are 6..\nfor the second digit the possibilities are 6 including \"0\" also..\nfor the third digit there are 5 possibilities\nfor the fourth digit 4 possibilities\nfor the fifth digit 3 possibilities..\nso, total no.of numbers can form is 6*6*5*4*3=2160\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThree friends, returning from a movie, stopped to eat at a restaurant. After dinner, they paid their bill and noticed a bowl of mints at the front counter. Sita took one-third of the mints, but returned four because she had a momentary pang of guilt. Fatima then took one-fourth of what was left but returned three for similar reason. Eswari then took half of the remainder but threw two back into the bowl. The bowl had only 17 mints left when the raid was over. How many mints were originally in the bowl?\n\n### Options:\nA. 38\nB. 31\nC. 41\nD. None of these\nE. Cannot be determined\n\n### Answer:\nExplanation :\nLet there be x mints originally in the bowl.\nSita took 1/3 but returned 4. So, noe the bowl haa (2x/3) + 4 mints\nFatima took 1/4 of the remainder but returned 3. So, the bawl now has (3/4)((2x/3) + 4) + 3 mints.\nEshwari took half of the remainder that is (1/2) [ (3/4) ( (2x/3) + 4 ) + 3 ]\nShe returns 2, so the bawl now has\n=> (1/2) [ (3/4) ( (2x/3) + 4) + 3 ] + 2 = 17.\n=> x = 48.\nAnswer : D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe dimensions of a room are 25 feet * 15 feet * 12 feet. What is the cost of white washing the four walls of the room at Rs. 5 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each?\n\n### Options:\nA. 4338\nB. 4536\nC. 4538\nD. 4530\nE. 4531\n\n### Answer:\nArea of the four walls = 2h(l + b)\nSince there are doors and windows, area of the walls = 2 * 12 (15 + 25) - (6 * 3) - 3(4 * 3) = 906 sq.ft.\nTotal cost = 906 * 5 = Rs. 4530\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average age of a husband and a wife is 23 years when they were married five years ago but now the average age of the husband, wife and child is 20 years(the child was born during the interval). What is the present age of the child?\n\n### Options:\nA. 7 years\nB. 9 years\nC. 6 years\nD. 4 years\nE. 5 years\n\n### Answer:\n28 * 2 = 56\n20 * 3 = 60\n-----------\n4 years\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA shopkeeper expects a gain of 22.5% on his cost price. If in a week, his sale was of Rs. 343, what was his profit?\n\n### Options:\nA. s. 63\nB. s. 69\nC. s.72\nD. s.75\nE. s.90\n\n### Answer:\nC.P. = Rs. (100/122.5)x343\n= Rs. (1000/1225)x343\n= Rs. 280\nProfit = Rs. (343 - 280) = Rs. 63.\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the smallest number which when divided by 13 and 17 leaves respective remainders of 3 and 7.\n\n### Options:\nA. 187\nB. 211\nC. 207\nD. 219\nE. 227\n\n### Answer:\nLet 'N' is the smallest number which divided by 13 and 17 leaves respective remainders of 3 and 7.\nRequired number = (LCM of 13 and 17) - (common difference of divisors and remainders) = (221) - (10) = 211.\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man is 22 years older than his son. In two years, his age will be twice the age of his son. The present age of the son is?\n\n### Options:\nA. 20\nB. 25\nC. 27\nD. 22\nE. 91\n\n### Answer:\nLet the son's present age be x years.\nThen, man's present age = (x + 22) years.\n(x + 22) + 2 = 2(x + 2) x + 24 = 2x + 4 => x = 20.\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how much time will a train of length 100 m, moving at 36 kmph cross an electric pole?\n\n### Options:\nA. 27\nB. 29\nC. 17\nD. 10\nE. 86\n\n### Answer:\nConvert kmph to mps. 36 kmph = 36 * 5/18 = 10 mps.\nThe distance to be covered is equal to the length of the train.\nRequired time t = d/s = 100/10 = 10 sec.\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how many different ways can 4 physics, 2 math and 3 chemistry books be arranged in a row so that all books of the same branch are together?\n\n### Options:\nA. 1242\nB. 1728\nC. 1484\nD. 1734\nE. 1726\n\n### Answer:\nSoln:\n= 3! * 4! * 2! * 3!\n= 1728\nAns is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA runs twice as fast as B and gives B a start of 64m.How long should the racecourse be so that A and B might reach in the same time?\n\n### Options:\nA. 75 m.\nB. 128 m.\nC. 150 m.\nD. 100 m.\nE. None of the above\n\n### Answer:\nratio of speeds of a and b is 2:1\nb is 64m away from a but we know that a covers 1 meter(2-1) more in every second than b\nthe time taken for a to cover 64m is 64/1=64m\nso the total time taken by a and b to reach =2*64=128m\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA bat is bought for Rs.440 and sold at a gain of 20% find its selling price\n\n### Options:\nA. s.430/-\nB. s.480/-\nC. s.400/-\nD. s.528/-\nE. s.600/-\n\n### Answer:\n100 % ------> 440\n120 % ------> 440*120/100\nSelling price = Rs.528/-\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many 4 digit number contain number 2 ?\n\n### Options:\nA. 3168\nB. 3268\nC. 3368\nD. 3468\nE. 3568\n\n### Answer:\ntotal 4 digit no. = 9*10*10*10 = 9000\nnot containing 2 = 8*9*9*9 = 5832\ntotal 4 digit number contain 2 = 9000 - 5832 = 3168\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n6x \u2212 24 = 6y\n5y + 5x = 15\nWhich of the following is the number of solutions to the system of equations shown above?\n\n### Options:\nA. Exactly one\nB. Exactly three\nC. Exactly two\nD. More than three\nE. None\n\n### Answer:\n6x \u2212 24 = 6y\n=> 6x - 6y = 24\n=> x- y =4 -- 1\n5y + 5x = 15\n=>x + y = 3 -- 2\nFrom equation 1 and 2 , we get\n2x = 7\n=> x=3.5\ny=.5\nTherefore , the given system will have Exactly one solution\nAnswer : A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA bike covers a certain distance at the speed of 62km/h in 8 hrs. If the bike was to cover the same distance in approximately 6 hrs, at what approximate speed should the bike travel?\n\n### Options:\nA. 85 km/h\nB. 82.66 km/h\nC. 87.67 km/h\nD. 90.25 km/h\nE. 90.64 km/h\n\n### Answer:\nAns.(B)\nSol. Total distance = 62 \u00d7 8 = 496 km\nNow speed = 496/6 = 82.66 km/h\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA particular library has 75 books in a special collection, all of which were in the library at the beginning of the month. These book are occasionally loaned out through an inter-library program. If, by the end of the month, 80 percent of books that were loaned out are returned and there are 64 books in the special collection at that time, how many books of the special collection were loaned out during that month?\n\n### Options:\nA. 20\nB. 30\nC. 35\nD. 40\nE. 55\n\n### Answer:\nthere are 11 books less(75-64) which represents 20% of the loaned books (100-80)\nSo total loaned out books = 55\nAnswer E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nBeth received 2/5 of the votes cast in a certain election. What fraction of the other votes cast would she have needed in order to have received 2/3 of the votes cast?\n\n### Options:\nA. 1/5\nB. 2/7\nC. 3/10\nD. 7/20\nE. 4/9\n\n### Answer:\nLet the total votes be 100. Beth received 40 votes, other votes 100-40=60. In order to have received 1/2 of the votes she needed 200/3 votes so 80/3 more, which is 4/9 of the other votes.\nAnswer: E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMangala completes a piece of work in 10 days, Raju completes the same work in 40 days. If both of them work together, then the number of days required to complete the work is?\n\n### Options:\nA. 8 days\nB. 12 days\nC. 14 days\nD. 16 days\nE. 18 days\n\n### Answer:\nIf A can complete a work in x days and B can complete the same work in y days, then, both\nof them together can complete the work in x y/ x+ y days.\nThat is, the required No. of days = 10 \u00d7 40/50 = 8 days\nA)\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRamu bought an old car for Rs. 45000. He spent Rs. 12000 on repairs and sold it for Rs. 80000. What is his profit percent?\n\n### Options:\nA. 16%\nB. 17%\nC. 40%\nD. 58%\nE. 13%\n\n### Answer:\nTotal CP = Rs. 45000 + Rs. 12000\n= Rs. 57000 and SP = Rs. 80000\nProfit(%)\n= (80000 - 57000)/57000 * 100\n= 40%\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere is a 20% chance that Lions will not win at all during the whole season. There is a 20% chance that Federer will not play at all in the whole season. What is the greatest possible probability that the Lions will win and Federer will play during the season?\n\n### Options:\nA. A)55%\nB. B)60%\nC. C)70%\nD. D)72%\nE. E)80%\n\n### Answer:\nThere is a 20% chance that Lions will not win at all during the whole season\nWe can infer that there is 80% chance Lions will win .\nSimilarly There is a 20% chance that Federer will not play at all in the whole season\nWe can also infer that there is 80% chance that Federer will play.\nAnswer E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo pipes P and Q can fill a cistern in 12 and 14 minutes respectively. Both are opened together, but at the end of 3 minutes the first is turned off. How much longer will the cistern take to fill?\n\n### Options:\nA. 11 1/2 min\nB. 11 1/4 min\nC. 11 2/4 min\nD. 11 1/5 min\nE. 10 1/2 min\n\n### Answer:\n3/12 + x/14 = 1\nx= 10 1/2\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA straight fence is to be constructed from posts 9 inches wide and separated by lengths of chain 5 feet long. If a certain fence begins and ends with a post, which of the following couldnotbe the length of the fence in feet? (12 inches = 1 foot)\n\n### Options:\nA. 17\nB. 28\nC. 35\nD. 39\nE. 40\n\n### Answer:\nThe fence begins and ends with a post: {post = 0.5 feet}{chains = 5 feet}{post = 0.5 feet}...{chains = 5 feet}{post = 0.5 feet}\nThe minimum length is with 2 posts = 0.5 + 5 + 0.5 = 6 feet. To increase the fence, each time we should add{post = 0.5 feet}{chains = 5 feet}, so 5.5 feet. Thus, the lengths could be:\n9 feet;\n9 + 5.5 = 14.5 feet;\n11.5 + 5.5 = 20 feet;\n17 + 5.5 = 25.5 feet;\n22.5 + 5.5 = 31 feet;\n28 + 5.5 = 34.5 feet;\n33.5 + 5.5 = 41 feet.\n...\nWe skipped 40 feet.\nAnswer: E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the compound interest and the amount on Rs.8000 at 5% per annum for 3 years when C.I is reckoned yearly?\n\n### Options:\nA. 2661\nB. 1651\nC. 1267\nD. 1627\nE. 1261\n\n### Answer:\nExplanation:\nA = 8000(21/20)3\n= 9261\n= 8000\n---------\n1261\nAnswer:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain store sold pens for $0.35 each and pencils for $0.25 each. If a customer purchased both pens and pencils from the store for a total of $3.50, what total number of pens and pencils did the customer purchase?\n\n### Options:\nA. 8\nB. 9\nC. 10\nD. 11\nE. 12\n\n### Answer:\nAnswer: Algebraically, the question looks like this: 2.5 = 0.35x + 0.25y There are six possible numbers of pens that fit that requirement:\n1 pen: $0.35\n2 pens: $0.70\n3 pens: $1.05\n4 pens: $1.40\n5 pens: $1.75 balance can fetch 7 pencils for $0.25 each. That's 5 pens and 7 pencils for a total of 12 pens and pencils. Choice (E) is correct.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nPipe A can fill a tank in 7 hours, pipe B in 14 hours and pipe C in 42 hours. If all the pipes are open,in how many hours will the tank be filled ?\n\n### Options:\nA. 4\nB. 4.2\nC. 4.5\nD. 4.3\nE. 4.1\n\n### Answer:\n1/7+1/14+1/42=10/42=1/4.2. so 4.2 hrs\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe arithmetic mean and standard deviation of a certain normal distribution are 17.5 and 2.5, respectively. What value is exactly 2 standard deviations less than the mean?\n\n### Options:\nA. 10.5\nB. 11\nC. 11.5\nD. 12\nE. 12.5\n\n### Answer:\nMean = 17.5\nTwo standard deviations is 2.5 + 2.5 = 5.0\nThere could be two calues for this.\nMean + two standard deviations = 22.5\nMean - Two standard deviations = 12.5\nAnswer choice has 12.5 and so E is the answer.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAverage age of boys in a class is 16 years and average age of girls is 15 years, what is the average age of all\n\n### Options:\nA. 15.5\nB. 15\nC. 16\nD. Cant be computed\nE. 17\n\n### Answer:\nExplanation:\nAs number of girls and boys is not given so result cant be computed\nAnswer: Option D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSuppose we have six marbles: 3 blue marbles, 2 red marbles, and one green marble. Suppose we are going to put them into three cups: a black cup, a white cup, and a purple cup. We could put all six in any cup and leave two cups empty; or we could put marbles in two cups and leave one cup empty; or we could put some marbles in each of the three cups. How many combinations are possible?\n\n### Options:\nA. 90\nB. 180\nC. 360\nD. 540\nE. 720\n\n### Answer:\n# ways to distribute Blue marbles(3) is :\n1 in each cup= 1\n2 in one cup and 1 in other=6\nall 3 in one cup = 3\ntotal 1+6+3=10 possibilities\n# ways to distribute Red marbles(2) is :\n1 in each cup = 3 ways\nall in one cup = 3ways\ntotal 6ways.\n# ways to distribute Green marbles(1) is :\n3 ways\ntotal number of ways = 10*6 *3 = 180 ANS:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo taps can separately fill a cistern 10 minutes and 15 minutes respectively and when the waste pipe is open, they can together fill it in 78 minutes. The waste pipe can empty the full cistern in?\n\n### Options:\nA. 8 min\nB. 7 min\nC. 5 min\nD. 9 min\nE. 6.5 min\n\n### Answer:\n1/10 + 1/15 - 1/x\n= 1/78\nx = 6.5\nAnswer:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA dealer professing to sell his goods at cost price, uses 900gm weight for 1 kg. His gain percent is\n\n### Options:\nA. 13%\nB. 12 1/3%\nC. 11 1/9%\nD. 10%\nE. 12%\n\n### Answer:\nGain % = ( Error/ (( True value) - Error)) *100 %\n= (1000gm -900gm) / (1000 -100)* 100 %\n= 100/900*100%\n= 100/9\n= 11 1/9 %\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf E is the product of all positive integers less than 31, than what is the greatest integer k for which E/18^k is an integer?\n\n### Options:\nA. 3\nB. 6\nC. 7\nD. 14\nE. 26\n\n### Answer:\n30!E must be divisible by (3*3*2)^k.\nAs I will find a lot of 2's among 30!'s factors I will focus on the 3's (that also occurs twice instead of only once as a factor in 18).\nEvery multiple of 3 will provide me with atleast one factor of 3. There aren't that many so I list them quickly.\n3 6 9*\n12 15 18*\n21 24 27**\n30\nThe stars are marked as they are multiples of 9* or 27** and thus provides two or three 3's respectively.\n3=3 (occurs 10 times) +10\n3*3=9 (occurs 3 times) +3(adding just one additional three each as they were not counted for in the multiples of 3)\n3*3*3=27 (occurs 1 time) +1 (again, adding just one as they were previously not counted)\nTotal: 14.\nFor every k we add two 3's. So we must divide 14 by 2 to get the highest integer K before we receive a non-integer result.\nAnswer: 7 -> Answer choice: C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average of seven numbers is 22. The average of first three numbers is 14 and the average of last three numbers is 19. What is the middle number?\n\n### Options:\nA. 27\nB. 55\nC. 31\nD. 34\nE. 35\n\n### Answer:\nThe total of seven numbers = 7X22 = 154\nThe total of first 3 and last 3 numbers is = 3 X 14+3 X 19 = 99\nSo, the middle number is (154 - 99 ) = 55\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo trains are running in opposite directions with the same speed. If the length of each train is 250 m and they cross each other in 10 sec, then the speed of each train is?\n\n### Options:\nA. 30\nB. 31\nC. 36\nD. 25\nE. 90\n\n### Answer:\nLet the speed of each train be x m/sec.\nThen, relative speed of the two trains = 2x m/sec.\nSo, 2x = (250 + 250)/10 => x =25\nSpeed of each train = 25 m/sec.\n= 25 * 18/5 =90 km/hr.\nAnswer: Option E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA candidate got 31% of the votes polled and he lost to his rival by 2451 votes. How many votes were cast?\n\n### Options:\nA. 6150\nB. 6250\nC. 6350\nD. 6450\nE. 6550\n\n### Answer:\nLet x be the total number of votes.\n0.31x + 2451 = 0.69x\n0.38x = 2451\nx = 2451/0.38 = 6450\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the smallest five digit number that is divisible by 16, 36, 40, and 54?\n\n### Options:\nA. 10200\nB. 10500\nC. 10800\nD. 11000\nE. 11400\n\n### Answer:\n16 = 2^4\n36 = 2^2 * 3^2\n40 = 2^3 * 5\n54 = 2 * 3^3\nLCM = 2^4 * 3^3 * 5 = 2160\nThe smallest five-digit number that is a multiple of 2160 is 5*2160 = 10,800\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich of these lines in the xy-plane does not contain any point with two negative coordinates?\n\n### Options:\nA. y = 4x\nB. y = x + 6\nC. y = x^2 - 5\nD. y = x^3 + 3x\nE. y = 2x^4\n\n### Answer:\n2x^4 is 0 when x is 0 and positive for all other values of x.\nThe answer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe greatest common factor of positive integers m and n is 14. What is the greatest common factor of (2m^2, 2n^2)?\n\n### Options:\nA. 14\nB. 28\nC. 196\nD. 392\nE. 784\n\n### Answer:\nm = 14j and n = 14k, where the greatest common factor of j and k is 1.\n2m^2 = 2*14*14*j^2 and 2n^2 = 2*14*14*k^2\nThe greatest common factor of 2m^2 and 2n^2 is 2*14*14 = 392\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nConvert the following unit:\n6.5 hectares in m\u00c2\u00b2\n\n### Options:\nA. 55000 m\u00c2\u00b2\nB. 80000 m\u00c2\u00b2\nC. 70000 m\u00c2\u00b2\nD. 67500 m\u00c2\u00b2\nE. 65000 m\u00c2\u00b2\n\n### Answer:\n6.5 hectares in m\u00c2\u00b2\n1 hectare = 10000 m\u00c2\u00b2\nTherefore, 6.5 hectares = 6.5 \u00c3\u2014 10000 m\u00c2\u00b2\n= 65000 m\u00c2\u00b2\nANSWER : OPTION E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOf the 120 passengers on Flight 750, 55% are female. 10% of the passengers sit in first class, and the rest of the passengers sit in coach class. If 1/3 of the passengers in first class are male, how many females are there in coach class?\n\n### Options:\nA. 44\nB. 48\nC. 50\nD. 52\nE. 58\n\n### Answer:\nNumber of passengers on flight = 120\nNumber of female passengers= .5*120 = 66\nNumber of passengers in first class = (10/100)* 120 = 12\nNumber of passengers in coach class = (90/100)* 120 = 108\nNumber of male passengers in first class = 1/3 * 12 = 4\nNumber of female passengers in first class = 12-4 = 8\nNumber of female passengers in coach class = 66 - 8 = 58\nAnswer E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMary's income is 60% more Than Tim's income and Tim's income is 10% less than Juan's income.What % of Juan's income is Mary's income.\n\n### Options:\nA. 144%\nB. B.120%\nC. 96%\nD. 80%\nE. 64%\n\n### Answer:\nEven I got 96%\nJ = 100\nT = 100*0.9 = 90\nM = 90*1.6 = 144\nIf Mary's income is x percent of J\nM = J*x/100\nx = M*100/J = 144*100/100 = 144\nAns:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe ratio between the perimeter and the width of a rectangle is 5:1. If the area of the rectangle is 150 square centimeters, what is the length of the rectangle in centimeters?\n\n### Options:\nA. 15\nB. 16\nC. 17\nD. 18\nE. 19\n\n### Answer:\nPerimeter = 2(W+L) = 5W\n3W = 2L\nW = 2L/3\nWL = 150\n2L^2/3 = 150\nL^2 = 225\nL = 15 cm\nThe answer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA contract is to be completed in 46 days sad 117 men were said to work 8 hours a day. After 33 days, (4/7) of the work is completed. How many additional men may be employed so that the work may be completed in time, each man now working 9 hours a day?\n\n### Options:\nA. 91\nB. 87\nC. 85\nD. 81\nE. None of them\n\n### Answer:\nRemaining work = (1-(4/7) =(3/7)\nRemaining period = (46 - 33) days = 13days\nLet the total men working at it be x.\nLess work, Less men\t(Direct Proportion)\nLess days, More men\t(Indirect Proportion)\nMore Hours per Day, Less men\t(Indirect Proportion)\nWork (4/7): (3/7)\nDays 13:33 } : : 117: x\nHrs/day 9 : 8\nTherefore (4/7) x 13 x 9 x x =(3/7) x 33 x 8 x 117 or x=(3 x 33 x 8 x 117)/(4 x 13 x 9)=198\nAdditional men to be employed = (198 - 117) = 81.\nAnswer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the smallest positive perfect square that is divisible by 9, 21, and 49?\n\n### Options:\nA. 225\nB. 324\nC. 441\nD. 529\nE. 900\n\n### Answer:\nThe number needs to be divisible by 3^2, 3*7, and 7^2.\nThe smallest such perfect square is 3^2*7^2 = 441\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn what time will a train 60 m long cross an electric pole, it its speed be 144 km/hr?\n\n### Options:\nA. 2.5 sec\nB. 2.8 sec\nC. 7.5 sec\nD. 2.3 sec\nE. 1.5 sec\n\n### Answer:\nSpeed = 144 * 5/18\n= 40 m/sec\nTime taken = 60/40\n= 1.5 sec.\nAnswer:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA grocer has a sale of Rs. 6345, Rs. 6927, Rs.6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 6500?\n\n### Options:\nA. Rs. 3000\nB. Rs. 4991\nC. Rs. 5991\nD. Rs. 6001\nE. NOne\n\n### Answer:\nSol.\nTotal sale for 5 months = Rs. (6435 + 6927 + 6855 + 7230 + 6562)\n= Rs. 34009.\n\u2234 Required sale = Rs.[(6500 x 6) - 34009]\n= Rs. (39000 - 34009)\n= Rs. 4991.\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA statue is being carved by a sculptor. The original piece of marble weighed 200 kg. In the first week 20 percent is cut away. In the second week 25 percent of the remainder is cut away. In the third week the statue is completed when 35 percent of the remainder is cut away. What is the weight of the final statue?\n\n### Options:\nA. 97.5 kg\nB. 103 kg\nC. 108 kg\nD. 125 kg\nE. 117 kg\n\n### Answer:\nA\n97.5 kg\n250 \u00c3\u2014 0.8 \u00c3\u2014 0.75 \u00c3\u2014 0.65 = 97.5 kg.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the least number of squares tiles required to pave the floor of a room 15 m 17 cm long and 9 m 2 cm broad?\n\n### Options:\nA. 814\nB. 800\nC. 100\nD. 200\nE. 456\n\n### Answer:\nLength of largest tile = H.C.F. of 1517 cm and 902 cm = 41 cm.\nArea of each tile = (41 x 41) cm2.\nRequired number of tiles = (1517 x 902)/41 x 41 = 814.\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a division sum, the remainder is 6 and the divisor is 5 times the quotient and is obtained by adding 2 to the thrice of the remainder. The dividend is\n\n### Options:\nA. 86\nB. 90\nC. 92\nD. 94\nE. 96\n\n### Answer:\nDivisor = (6 * 3) + 2 = 20\n5 * Quotient = 20\nQuotient = 4.\nDividend = (Divisor * Quotient) + Remainder\nDividend = (20 * 4) + 6 = 86.\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how many ways can the integer 800 be expressed as a product of two different positive integers?\n\n### Options:\nA. 10\nB. 7\nC. 5\nD. 4\nE. 2\n\n### Answer:\n800=(2^5)*(5^2)\nSince 800 is not a perfect square, no of ways=7\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhen a certain number X is divided by 61, the remainder is 24. What is the remainder when X is divided by 5?\n\n### Options:\nA. 2\nB. 3\nC. 4\nD. 5\nE. 6\n\n### Answer:\nWhen a certain number X is divided by 61, the remainder is 24. What is the remainder when X is divided by 5?\nPutting a value say x = 24 we get remainder as 24 when divided by 61.\nWhen 24 divided by 5 we get 4 as remainder.\nC is the answer.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the ratio of the curved surfaces of two cylinders of same heights if their radii are in the ratio 1:2?\n\n### Options:\nA. 1:2\nB. 2:3\nC. 2:9\nD. 2:1\nE. 2:2\n\n### Answer:\n1:2\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 16 kmph and 21 kmph respectively. When they meet, it is found that one train has traveled 60 km more than the other one. The distance between the two stations is?\n\n### Options:\nA. 444 km\nB. 400 km\nC. 450 km\nD. 500 km\nE. 550 km\n\n### Answer:\n1h ----- 5\n? ------ 60\n12 h\nRS = 16 + 21 = 37\nT = 12\nD = 37 * 12 = 444\nANSWER A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich of the following expressions CAN be equal to 0 when x^2 \u221216= 0 ?\n\n### Options:\nA. x^2 \u2212 6x + 9\nB. x^2 \u2212 4x + 3\nC. x^2 \u2212 x \u2212 2\nD. x^2 \u2212 7x + 6\nE. x^2 \u2212 5x + 4\n\n### Answer:\nx^2 \u2212 16 = 0\nx=-4 or x=4\nOnle one choice results in a possibility of 0 when you plug in -4 or 4 for x except rest of all\nx^2 \u2212 5x + 4\nAnswer is E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhen positive integer x is divided by positive integer y, the result is 59.32. What is the sum E of all possible 2-digit remainders for x/y?\n\n### Options:\nA. 560\nB. 616\nC. 672\nD. 728\nE. 784\n\n### Answer:\nans B 616...\nremainders = .32=32/100=8/25=16/50 and so on..\nso two digit remainders are 16+24+32+....+96..\nE=8(2+3+4....+12)=616.B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe banker's gain of a certain sum due 2 years hence at 10% per annum is Rs. 24. The present worth is:\n\n### Options:\nA. 480\nB. 520\nC. 600\nD. 960\nE. 840\n\n### Answer:\nT.D. = B.G. x 100 / Rate x Time\n= Rs.(24 x 100/10 x 2)= Rs. 120.\nP.W. =(100 x T.D./Rate x Time)\n= Rs.(100 x 120/10 x 2)= Rs. 600.\nCorrect answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhen the price of sugar was increased by 32%, a family reduced its consumption in such a way that the expenditure on sugar was only 10% more than before. If 30 kg were consumed per month before, find the new monthly consumption.\n\n### Options:\nA. 20 kg\nB. 25 kg\nC. 30 kg\nD. 35 kg\nE. None of these\n\n### Answer:\nSince, expenditure = price \u00d7 consumption\n\u2234 110% of 30 = 132\u2044100 \u00d7 new consumption\n\u21d2 110\u2044100 \u00d7 30 = 132\u2044100 \u00d7 new consumption\n\u21d2 New consumption = 25 kg\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA person purchased a TV set for Rs. 16000 and a DVD player for Rs. 6250. He sold both the items together for Rs. 36490\n. What percentage of profit did he make?\n\n### Options:\nA. 64%\nB. 49%\nC. 40%\nD. 70%\nE. 90%\n\n### Answer:\nThe total CP = Rs. 16000 + Rs. 6250\n= Rs. 22250 and SP = Rs. 36490\nProfit(%) = (36490 - 22250)/22250 * 100\n= 64%\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how many ways can a group of 5 men and women be made out of a total of 7 men and 3 women?\n\n### Options:\nA. 63\nB. 90\nC. 126\nD. 45\nE. 135\n\n### Answer:\nRequired number of ways=7c5 x 3c2\n=7c2 x 3c1\n=63\nANSWER A 63\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train covers a distance of 12 km in 10 min. If it takes 6 sec to pass a telegraph post, then the length of the train is?\n\n### Options:\nA. 288\nB. 277\nC. 120\nD. 285\nE. 121\n\n### Answer:\nSpeed = (12/10 * 60) km/hr = (72 * 5/18) m/sec = 20 m/sec.\nLength of the train = 20 * 6 = 120 m.\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJack spent 1/6 of his lifetime in adolescence. His facial hair started growing after 1/12 more of his life. He successfully married his girlfriend Diana after 1/7 more of his life. Their son was born after 5 years from then. The son lived just 1/2 of what Jack lived. Jack dies four years after his son died.\nHow long did Jack live ?\n\n### Options:\nA. 75\nB. 90\nC. 45\nD. 80\nE. 84\n\n### Answer:\nE\n84\nExplanation:\nLet us assume that jack lived for p years.\np/6 + p/12 + p/7 + 5 + p/2 + 4 = x\n=> p = 84.\nTherefore, Jack lived for 84 years.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJohn completes a piece of work in 320 days, Rose completes the same work in 480 days. If both of them work together, then the number of days required to complete the work is?\n\n### Options:\nA. 190\nB. 192\nC. 194\nD. 196\nE. 198\n\n### Answer:\nIf A can complete a work in x days and B can complete the same work in y days, then, both\nof them together can complete the work in x y/ x+ y days.\nThat is, the required No. of days = 320 \u00d7 480/800 = 192 days\nAnswer is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe area of a rectangle is x2 + 4x -12. What are the dimensions of the rectangle (length and width)?\n\n### Options:\nA. x + 6 , x + -2\nB. x + 7 , x + -2\nC. x + 8 , x + -2\nD. x + 9 , x + -2\nE. none\n\n### Answer:\nSolution\nThe main idea is to factor x2 + 4x -12\nSince -12 = -2 \u00d7 6 and -2 + 6 = 4\nx2 + 4x -12 = ( x + -2) \u00d7 ( x + 6)\nSince the length is usually longer, lenth = x + 6 and width = x + -2\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a shop, the marked price of an article is worked out in such a way that it generates a profit of 33133313. What should be the discount percent allowed on the marked price during a sale, so that the final profit made is 20%?\n\n### Options:\nA. 13 1/3\nB. 12 1/2\nC. 10%\nD. 8 1/2\nE. 6 2/3\n\n### Answer:\nsoln:-\nlets consider the cost price of an article as $60 (take a number whose 33.33% can be calculated easily)\nso marked price = 1.3333*60 = 80\nprofit to be earned = 20%\nfinal selling price = 1.2*60 = 72\ntherefore discount to be given = 8/80 = 10%\nanswer - C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe length of a rectangle is three times of its width. If the length of the diagonal is 8\u221a10 then find the perimeter of the rectangle.\n\n### Options:\nA. 77 cm\nB. 88 cm\nC. 64 cm\nD. 11 cm\nE. 18 cm\n\n### Answer:\nLet Breadth = x cm,\nthen, Length = 3x cm\nx2+(3x)2=(810\u2212\u2212\u221a)2=>10x2=640=>x=8\nx2+(3x)2=(810)2=>10x2=640=>x=8\nSo, length = 24 cm and breadth = 8 cm\nPerimeter = 2(l+b)\n= 2(24+8) = 64 cm\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind how many positive integers less than 10,000 are there such thatthe sum of the digits of the no. is divisible by 3?\n\n### Options:\nA. 3468\nB. 2378\nC. 2875\nD. 3334\nE. 3579\n\n### Answer:\nIf sum of the digits is divisible by 3, the number is divisible by 3.\nTherefore, required number of non-negative integers is equal to count of numbers less than 10,000 which are divisible by 3.\nSuch numbers are (3, 6, 9, ... , 9999) (arithmetic progression with first term=3, last term=9999, common difference=3).\nCount of such numbers =\n9999\n3\n=\n3333\n99993=3333\nBut zero is also divisible by 3.\nThis makes our total count 3334\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn what time will a railway train 30 m long moving at the rate of 36 kmph pass a telegraph post on its way?\n\n### Options:\nA. 5 sec\nB. 4 sec\nC. 3 sec\nD. 6 sec\nE. 1 sec\n\n### Answer:\nT = 30/36 * 18/5 = 3 sec\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe sum of two consecutive number is 49. Which is the larger number?\n\n### Options:\nA. 42\nB. 43\nC. 25\nD. 45\nE. 46\n\n### Answer:\nLet consecutive number be x, x+1\nTherefore sum of the consecutive number is x + x+1=49\n2x+1=49\n2x=48\nx=24\nTherefore larger number is x+1=25\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a room there are 11 people. Each person shook hands with every other person. How many hand shakes were there?\n\n### Options:\nA. 52\nB. 53\nC. 54\nD. 55\nE. 56\n\n### Answer:\n11C2 = 55\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nExcluding stoppages, the speed of a bus is 70 km/hr and including stoppages, it is 40 km/hr. For how many minutes does the bus stop per hour?\n\n### Options:\nA. 118 min\nB. 10 min\nC. 18 min\nD. 16 min\nE. 25 min\n\n### Answer:\nDue to stoppages, it covers 30 km less.\nTime taken to cover 30 km = 30/70 * 60\n= 25 min.\nAnswer:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMaxwell leaves his home and walks toward Brad's house. One hour later, Brad leaves his home and runs toward Maxwell's house. If the distance between their homes is 74 kilometers, Maxwell's walking speed is 4 km/h, and Brad's running speed is 6 km/h. What is the total time it takes Maxwell before he meets up with Brad?\n\n### Options:\nA. 3\nB. 4\nC. 5\nD. 6\nE. 8\n\n### Answer:\nTotal Distance = 74 kms\nMaxwell Speed = 4 kms/hr\nMaxwell travelled for 1hour before Brad started , therefore Maxwell traveled for 4 kms in 1 hour.\nTime taken = Total Distance / Relative Speed\nTotal Distance after Brad started = 70 kms\nRelative Speed (Opposite side) (As they are moving towards each other speed would be added ) = 6+ 4 = 10 kms/hr\nTime taken to meet Brad after Brad Started = 70 / 10 = 7 hrs\nDistance traveled by Maxwell = Maxwell's speed * time taken = 4 * 7 = 28+4 = 32 kms...\nTherefore Total Time taken by Maxwell to meet Brad = Distance travelled by Maxwell / Maxwell's Speed = 32 /4 = 8 hrs ... Answer E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSeats for Mathematics, Physics and Biology in a school are in the ratio 5:7:8. There is a proposal to increase these seats by 40%, 50% and 75% respectively. What will be the ratio of increased seats?\n\n### Options:\nA. 2:3:4\nB. 2:3:8\nC. 2:3:0\nD. 2:3:1\nE. 2:3:9\n\n### Answer:\nOriginally, let the number of seats for Mathematics, Physics and Biology be 5x, 7x and 8x respectively. Number of increased sears are (140% of 5x), (150% of 7x) and (175% of 8x)\ni.e., (140/100 * 5x), (150/100 * 7x) and (175/100 * 8x)\ni.e., 7x, 21x/2 and 14x\nRequired ratio = 7x:21x/2:14x\n= 14x : 21x : 28x = 2:3:4\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the sum of 5 consecutive integers is y, which of the following must be true?\nI. y is an even number\nII. y is an odd number\nIII. y is a multiple of 5\n\n### Options:\nA. I only\nB. II only\nC. III and II only\nD. I and III\nE. III only\n\n### Answer:\nI. If you start off with an even number, the sum (y) is even, and if you start off with an odd number the sum (x) is odd. Therefore this is not always true.\nII. Same as above. This need not be always true.\nIII. Say, the first number is p. Then the sum of the five numbers = p + (p+1) + (p+2)...... + (p+4)\n= 5p + 10 = 5 (p+2) => divisible by 5. There this must be true in all cases.\nTherefore E is the answer.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a partnership between A, B and C. A's capital is Rs.5000. If his share of a profit of Rs.800 is Rs.200 and C's share is Rs.130, what is B's capital?\n\n### Options:\nA. 11758\nB. 11756\nC. 11753\nD. 11750\nE. 11751\n\n### Answer:\n200 + 130 = 330\n800 - 330 = 470\n200 ---- 5000\n470 ---- ? => 11750\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nArea of four walls of a room is 99 m2. The length and breadth of the room are 7.5 m and 3.5m respectively. The height of the room is:\n\n### Options:\nA. 2.5m\nB. 3.5m\nC. 1.5m\nD. 4.5m\nE. 5.5m\n\n### Answer:\n2(7.5+3.5)\u00d7h = 99\n2(11)h = 99\n22h = 99\nh = 99/22 = 9/2 = 4.5 m\nAnswer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA fruit salad mixture consists of apples, peaches, and grapes. There are 2 times as many pounds of apples as grapes and 3 times as many pounds of peaches as grapes. If a mixture that has an average (arithmetic mean) of 9 pounds per fruit, how many more pounds of apples than grapes does the mixture have?\n\n### Options:\nA. 15\nB. 12\nC. 9\nD. 6\nE. 3\n\n### Answer:\nA+P+G= 9*2\nA=2G\nP=3G\n3G+2G+G= 9*2\nG= 9*2/6= 3\nA= 3*2=6\nDifference = 6-3=3\n'E' is the answer\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTom and Linda stand at point A. Linda begins to walk in a straight line away from Tom at a constant rate of 2 miles per hour. One hour later, Tom begins to jog in a straight line in the exact opposite direction at a constant rate of 7 miles per hour. If both Tom and Linda travel indefinitely, what is the positive difference, in minutes, between the amount of time it takes Tom to cover half of the distance that Linda has covered and the amount of time it takes Tom to cover twice the distance that Linda has covered?\n\n### Options:\nA. 60\nB. 56\nC. 84\nD. 90\nE. 108\n\n### Answer:\nB is the answer....\nD = TS where D=distance, T=Time and S=Speed\nTo travel half distance, (2+2T) = 7T ==> T = 2/5 ==> 24 minutes\nTo travel double distance, 2(2+2T) = 7T ==> 2 ==>80 minutes\nDifference, 56 minutes\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRavi's average (arithmetic mean) test score on 4 tests is 78. What must be the student's score on a 5th test for the Ravi's average score on the 5 tests to be 80?\n\n### Options:\nA. 80\nB. 82\nC. 84\nD. 86\nE. 88\n\n### Answer:\nE. 88\nRavi must score at least an 80 for sure. If he scores an 8, then he will need to score 2 pots for each of the 4 other tests tomake upthe difference. They each were at 78 (at least the average is, but this is a small point and doesn't matter to the answer). So 4 tests that were each 2 points short of the 80 average that is desired means the next test must be 8 points higher than the desired average, so 80+8 = 88.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJolene entered an 14-month investment contract that guarantees to pay 2 percent interest at the end of 6 months, another 3 percent interest at the end of 12 months, and 4 percent interest at the end of the 18 month contract. If each interest payment is reinvested in the contract, and Jolene invested $10,000 initially, what will be the total amount of interest paid during the 18-month contract?\n\n### Options:\nA. $506.00\nB. $726.24\nC. $900.00\nD. $920.24\nE. $926.24\n\n### Answer:\nIf interest were not compounded in every six months (so if interest were not earned on interest) then we would have (2+3+4)=9% simple interest earned on $10,000, which is $900. So, you can rule out A, B and C right away.\nInterest earned after the first time interval: $10,000*2%=$200;\nInterest earned after the second time interval: ($10,000+$200)*3%=$300+$6=$306;\nInterest earned after the third time interval: ($10,000+$200+$306)*4%=$400+$8+(~$12)=~$420;\nTotal: 200+306+(~420)=~$506.00\nAnswer: A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n5n + 2 > 12 and 7n - 12 < 44; n must be between which numbers?\n\n### Options:\nA. 2 and 8\nB. 2 and 6\nC. 0 and 9\nD. 2 and 7\nE. 2 and 9\n\n### Answer:\n5n+2 > 12\n5n > 10\nn > 2\n7n-12 < 44\n7n < 56\nn < 8\nSo n must be between 2 and 8\n2 < n < 8\ncorrect answer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man rows his boat 78 km downstream and 56 km upstream, taking 4 hours each time. Find the speed of the stream?\n\n### Options:\nA. 6\nB. 5\nC. 7\nD. 8\nE. 3\n\n### Answer:\nSpeed downstream = d/t = 78/(4) = 20 kmph\nSpeed upstream = d/t = 56/(4) = 14 kmph\nThe speed of the stream = (20 - 14)/2 = 3 kmph\nAnswer:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nx varies inversely as square of y. Given that y = 2 for x = 1. The value of x for y = 6 will be equal to?\n\n### Options:\nA. 1/6\nB. 1/3\nC. 1/0\nD. 1/9\nE. 1/5\n\n### Answer:\nGiven x = k/y2, where k is a constant.\nNow, y = 2 and x = 1 gives k = 4.\nx = 4/y2 => x = 4/62, when\ny = 6 => x = 4/36 = 1/9.\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average price of three items of furniture is Rs. 15000. If their prices are in the ratio 2:4:6, the price of the cheapest item is?\n\n### Options:\nA. 2379\nB. 2889\nC. 9288\nD. 9000\nE. 7500\n\n### Answer:\nLet their prices be 3x, 5x and 7x.\nThen, 2x + 4x + 6x = (15000 * 3) or x = 3750.\nCost of cheapest item = 2x = Rs. 7500.\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nX and Y are integers, X is even and negative, Y is odd and positive. Which of the following could be false?\n1. (X + Y) is an odd number.\n2. Y^(X + Y) is an integer.\n3. X^Y is a positive number.\n\n### Options:\nA. 2 only\nB. 3 only\nC. 1 and 3 only\nD. 2 and 3 only\nE. 1, 2 and 3\n\n### Answer:\nUsing the properties for even and odd numbers along with positive and negatives,\n1. (X + Y) is an odd number : even + odd is always a odd number, so eliminate 1\n2. Y^(X + Y) is an integer. : an odd and positive number could be raised to power of either positive or negative, so not conclusive, eliminate 2\n3. X^Y is a positive number. : a negative number raised to power of odd number is always negative.\nAnswer : B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a cinema hall for the matinee show which started at 2.30 pm and ended at 5.30 pm the vehicle parking lot had only three wheelers (auto rickshaws) and four wheelers. Today the wheels of the vehicles parked was counted and found to be 240. What could be the number of three wheelers parked therein ?\n\n### Options:\nA. 10\nB. 48 wheelers\nC. 37\nD. 97\nE. 12\n\n### Answer:\n3X + 4y = 240\nby substitute through options 48 is correct\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich of the following can be a perimeter t of a triangle inscribed in a circle of radius 1?\nI. 0.001\nII. 0.010\nIII. 0.100\n\n### Options:\nA. I only\nB. III only\nC. II and III only\nD. I, II, and III\nE. Not I, II, or III\n\n### Answer:\nYes,the length of any side of a triangle must be larger than the positive difference of the other two sides, but smaller than the sum of the other two sides.\nBut how do you use the above property to solve the question?\nThe lower limit of the perimeter of an inscribed triangle in a circle of ANY radius is 0: t>0.\nAnswer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe dimensions of a room are 25 feet * 15 feet * 12 feet. What is the cost of white washing the four walls of the room at Rs. 9 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each?\n\n### Options:\nA. s.4538\nB. s.8154\nC. s.4518\nD. s.4530\nE. s.4517\n\n### Answer:\nArea of the four walls = 2h(l + b)\nSince there are doors and windows, area of the walls = 2 * 12 (15 + 25) - (6 * 3) - 3(4 * 3) = 906 sq.ft.\nTotal cost = 906 * 9 = Rs.8154\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat number should replace the question mark? 2, 16, 4, 14, 6, 12, ---?\n\n### Options:\nA. 8\nB. 10\nC. 12\nD. 14\nE. 16\n\n### Answer:\nAnswer: A\n2, 16, 4, 14, 6, 12, 8?\nThere are two alternate sequences: +2 and -2.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the area of a cuboid of length 8cm , breadth 10 cm . and height 12cm.\n\n### Options:\nA. 900 cm cube\nB. 910 cm cube\nC. 920 cm cube\nD. 930 cm cube\nE. 960 cm cube\n\n### Answer:\nArea of a cuboid = lxbxh =8cm x 10cm x 12cm = 960 cm cube\nanswer :E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo numbers A and B are such that the sum of 5% of A and 4% of B is two-third of the sum of 6% of A and 8% of B. Find the ratio of A : B.\n\n### Options:\nA. 2:1\nB. 1:2\nC. 1:1\nD. 4:3\nE. 5:6\n\n### Answer:\n5% of A% of B = 2/3 (6% of A + 8% of B)\n5A/100 = 4B/100 = 2/3(6A/100 + 8B/100)\n=>3A=4B\nA/B=4/3\nA:B=4:3\nANSWER D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich of the following does NOT have a decimal equivalent that is a terminating decimal?\n\n### Options:\nA. 1/2^25\nB. 5^3/2^7\nC. 3^8/6^10\nD. 3^9/6^7\nE. 6^8/10^10\n\n### Answer:\nFor a fraction to have terminating decimal, it must either have only 2 and/or 5 in the denominator. All other values in the denominator leads to non terminating decimal values\nHence,\n1. A has 2 in the denominator, Hence it is terminating\n2. B is also terminating\n3. 3^8/(6^10) can be written as 3^8/ (2^10 * 3^10) => 1/(2^10 * 3^2). There is 3 in the denominator. Hence it is non terminating decimal\n4. 3^9/(2^7 * 3^7) => 3^2/2^7. Hence Terminating\n5. Has both 2 & 5 in the denominator. Hence Terminating.\nOption C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAt 3:00 pm, a car has driven 30 miles east. It will continue to drive east at 0.6 minutes per mile and then turn around and drive at 0.6 minutes per mile back to its original starting point. How far can it drive before turning around in order to arrive back to its original starting point by 3:40 pm?\n\n### Options:\nA. a) 10\nB. b) 11\nC. c) 55/3\nD. d) 13\nE. e) 14\n\n### Answer:\n0.8 minutes --> 1 mile\n1 minute --> 1/0.6 = 10/6 = 5/3 miles/minute\nDistance covered in 40 minutes = 5/3 * 40 = 200/3 miles\nDistance covered in the current direction = Distance covered from the opposite direction (since car returns back to starting point)\nLet x be the miles driven before turning\n30 + x = 200/3 - x\n2x = 200/3 -30\nx = 55/3\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA water tank has three taps A, B and C. Tap A, when opened,can fill the water tank alone in 4 hours. Tap B, when opened, can fill the water tank alone in 6 hours and tap C, when opened, can empty the water tank alone in 3 hours. If taps A, B and C are opened simultaneously, how long will it take to fill the tank completely?\n\n### Options:\nA. 10 hours\nB. 8 hours\nC. 18 hours\nD. 12 hours\nE. None of these\n\n### Answer:\nRequired time to fill the tank\n= 1 /(1/4+1/6)\u22121/3=1 /5/12\u22121/3=1 /1/12=12h\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA dishonest dealer professes to sell goods at the cost price but uses a false weight and gains 25%. Find his false weight age?\n\n### Options:\nA. 7\nB. 9\nC. 8\nD. 4\nE. 5\n\n### Answer:\n25 = E/(1000 - E) * 100\n1000 - E = 4E\n1000 = 5E => E = 200\n1000 - 200 = 8\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are 9 person among whom 2 are brother. The total no.of ways in which these persons can be seated around a round table so that exactly 1person sit between the brothers, is equal to?\n\n### Options:\nA. 4!*2!\nB. 7!*2!\nC. 6!*2!\nD. 2!*1!\nE. 5!*1!\n\n### Answer:\nTotal number of ways = 6!*2!.\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn Town X, 60 percent of the population are employed, and 48 percent of the population are employed males. What percent of the employed people in Town X are females?\n\n### Options:\nA. 16%\nB. 20%\nC. 31%\nD. 40%\nE. 52%\n\n### Answer:\nWe are asked to find the percentage of females in employed people.\nTotal employed people 60%, out of which 48 are employed males,hence 12% are employed females.\n(employed females)/(total employed people)=12/60=1/5=20%\nAnswer: B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n10 men can complete a piece of work in 15 days and 15 women can complete the same work in 12 days. If all the 10 men and 15 women work together, in how many days will the work get completed?\n\n### Options:\nA. 6\nB. 7 2\u20443\nC. 6 2\u20443\nD. 6 1\u20443\nE. None of these\n\n### Answer:\n10 men + 15 women in 1 day do 1\u204415 + 1\u204412 = 9\u204460 work\n\\ Time taken = 60\u20449 days = 62\u20443 days\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFor a finite sequence of non zero numbers, the number of variations in the sign is defined as the number of pairs of consecutive terms of the sequence for which the product of the two consecutive terms is negative. What is the number of variations in sign for the sequence 10, -3, 20, 5, -4, 6, -7 , 12?\n\n### Options:\nA. 1\nB. 2\nC. 3\nD. 4\nE. 5\n\n### Answer:\nThe questions basically asks: how many pairs of consecutive terms are there in the sequence such that the product of these consecutive terms is negative.\n10*(-3)=-30=negative;\n-3*20=-60=negative;\n5*(-4)=-20=negative.\n6 * (-7) = -42 > negative\n-7 * 12 = -84 >>negative\nSo there are 5 pairs of consecutive terms.\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe length of the bridge, which a train 150 metres long and travelling at 54 km/hr can cross in 30 seconds, is?\n\n### Options:\nA. 340 m.\nB. 350 m.\nC. 320 m.\nD. 330 m.\nE. 360 m.\n\n### Answer:\nSpeed = [54X 5/18] m/sec = [15] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (130 + x)/30\n= 15 => (130 + x)/30\n= 320 => x\n= 320 m.\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nCole drove from home to work at an average speed of 60 kmh. He then returned home at an average speed of 100 kmh. If the round trip took a total of 2 hours, how many minutes did it take Cole to drive to work?\n\n### Options:\nA. 66\nB. 70\nC. 72\nD. 75\nE. 78\n\n### Answer:\nLet the distance one way be x\nTime from home to work = x/60\nTime from work to home = x/100\nTotal time = 2 hrs\n(x/60) + (x/100)= 2\nSolving for x, we get x = 75\nTime from home to work in minutes= (75)*60/60 = 75 minutes\nAns= D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOut of 18 points in a plane, no three are in the same straight line except five points which are collinear. How many straight lines can be formed by joining them ?\n\n### Options:\nA. 124\nB. 144\nC. 134\nD. 142\nE. 143\n\n### Answer:\nThe number of straight lines formed joining the 18 points, taking 2 at a time = 18C2=153. Number of straight lines formed by joining the 5 points, taking 2 at a time =5C2=10. But 5 collinear point, when joined pairwise give only one line. Required number of straight lines =153-10+1 =144. Answer :B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n3, 5, 7, 11, 13, 17, 19, ____\n\n### Options:\nA. 25\nB. 36\nC. 23\nD. 49\nE. 27\n\n### Answer:\nThe sequence is a series of prime numbers, 3, 5, 7, 11, 13, 17, 19, 23....\nAnswer : C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the average of all prime numbers between 1 and 10\n\n### Options:\nA. 2.5\nB. 1.35\nC. 4.25\nD. 6.12\nE. 7.13\n\n### Answer:\nPrime numbers between 1 and 10 are 2,3,5,7\nRequired average = (2+3+5+7)/4 = 17/4 = 4.25\nAnswer is C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA group of students decided to collect as many paise from each member of group as is the number of members. If the total collection amounts to Rs. 13.69, the number of the member is the group is:\n\n### Options:\nA. 57\nB. 67\nC. 37\nD. 87\nE. 97\n\n### Answer:\nMoney collected =(13.69 x 100) paise = 1369 paise\nnumbers of members = 1369 squareroot = 37\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nP works 25% more efficiently than Q and Q works 50% more efficiently than R. To complete a certain project, P alone takes 50 days less than Q alone. If, in this project P alone works for 60 days and then Q alone works for 130 days, in how many days can R alone complete the remaining work?\n\n### Options:\nA. 50 days\nB. 83.6 days\nC. 100 days\nD. 150 days\nE. 80 days\n\n### Answer:\nP works 25% more efficiently than Q: Something that takes Q 5 days, takes P 4 days\nQ works 50% more efficiently than R: Something that takes R 7.5 days, takes Q 5 days\nP alone takes 50 days less than Q: For every 4 days P works, Q has to work an extra day. Hence P alone can do it in 200 days and Q alone in 250 days and hence R alone in 380 days\nP works for 60 days--> 60/200 work done => 30%\nQ works for 130 days--> 130/250 work done => 52%\n22% work left ... R alone will take 22% * 380 = 83.6 days\nAnswer is (B)\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 0.75: x :: 5:7, then x is equal to:\n\n### Options:\nA. 1.05\nB. 1.16\nC. 1.2\nD. 1.3\nE. None of these\n\n### Answer:\nExplanation:\n(x * 5) = (0.75 *7)\nX=5.25/5 = 1.05\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA person takes 20 minutes more to cover a certain distance by decreasing his speed by 20%. What is the time taken to cover the distance at his original speed?\n\n### Options:\nA. 1 hour 40 minutes\nB. 1 hour 38 minutes\nC. 1 hour 20 minutes\nD. 1 hour 44 minutes\nE. 2 hour 20 minutes\n\n### Answer:\nLet the distance and original speed be d km and k kmph respectively.\nd/0.8k - d/k = 20/60 => 5d/4k - d/k = 1/3\n=> (5d - 4d)/4k = 1/3 => d = 4/3 k\nTime taken to cover the distance at original speed\n= d/k = 4/3 hours = 1 hour 20 minutes.\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n2 pipes A and B can separately fill a cistern in 10 and 15 mins respectively. A person opens both the pipes together when the cistern should have been was full he findsthe waste pipe open. He then closes the waste pipe and in another 4 mins the cistern was full. In what time can the waste pipe empty the cistern when fill?\n\n### Options:\nA. 1/5\nB. 1/3\nC. 2/7\nD. 3/5\nE. 3/11\n\n### Answer:\n1/10 + 1/15 = 1/6 * 4 = 2/3\n1 - 2/3 = 1/3\n1/10 + 1/15 - 1/x = 1/3\nx = 8\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe cricket team of 11members is 25yrs old & the wicket keeper is 3 yrs older. If the ages ofthese 2are excluded, the average age of theremaining players is 1 year less than the average age of the whole team. What is the average age of the team ?\n\n### Options:\nA. 21\nB. 22\nC. 23\nD. 25\nE. 28\n\n### Answer:\nLet the average age of the whole team be x years.\n11x - (25 + 28) = 9 (x - 1)\n=> 11x - 9x = 44\n=> 2x = 44\n=> x = 22.\nSo, average age of the team is 22 years.\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA, B, C subscribe Rs. 50,000 for a business. If A subscribes Rs. 4000 more than B and B Rs. 5000 more than C, out of a total profit of Rs. 35,000, what will be the amount A receives?\n\n### Options:\nA. 14200\nB. 14700\nC. 14800\nD. 14500\nE. None of these\n\n### Answer:\nExplanation :\nTotal amount invested = 50000\nAssume that investment of C = x.\nThen investment of B = 5000 + x ,\nInvestment of A = 4000 + 5000 + x = 9000 + x\nx + 5000+x + 9000 + x = 50000\n=> 3x + 14000 = 50000\n=> 3x = 50000 \u2013 14000 = 36000\n=> x = 36000/3 = 12000\n=> Investment of C = x = 12000 ,\nInvestment of B = 5000 + x = 17000,\nInvestment of A = 9000 + x = 21000\nRatio of the investment of A : B : C = 21000 : 17000 : 12000 = 21 : 17 : 12\nShare of A = Total Profit * 21/50 = 35000 * 21/50 = 700*21 = 14700, Answer : Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a village of 2,600 people, 800 people are over 70 years old and 850 people are female. It is known that 40 percent of the females are younger than 70 years old. If no one in the village is 70 years old, what is the probability that a person chosen at random is either a male or younger than 70 years old?\n\n### Options:\nA. 221/250\nB. 199/250\nC. 33/50\nD. 8/25\nE. 209/260\n\n### Answer:\nThe number of people younger than 70 years old is 2600-800 = 1800\nThe number of females older than 70 years old is 0.6*850 = 510\nThen the number of males older than 70 years old is 800 - 510 = 290.\nThe number of people who are either male or younger than 70 is 1800+290 = 2090.\nP(a person is younger than 70 or male) = 2090/2600 = 209/260\nThe answer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAnnika hikes at a constant rate of 12 minutes per kilometer. She has hiked 2.75 kilometers east from the start of a hiking trail when she realizes that she has to be back at the start of the trail in 40 minutes. If Annika continues east, then turns around and retraces her path to reach the start of the trail in exactly 40 minutes, for how many kilometers total did she hike east?\n\n### Options:\nA. 3.625\nB. 3.5\nC. 3\nD. 3.04\nE. 4\n\n### Answer:\nSet up two R x T =D cases.\n1. 1/12 km/ min x T = 2.75\nfrom which T= 33 mins.\nWe know total journey time now is 40 +33 =73.\nThe rate is the same ie 1/12km/min.\nset up second R x T =D case.\n1/12 km/min x 73 = 6.08 km\nNow the total journey would be halved as distance would be same in each direction. 6.08/2 =3.04\nD.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nfind S.P when CP=56.25,gain=20%.\n\n### Options:\nA. Rs 66.50\nB. Rs 65.50\nC. Rs 67.50\nD. Rs 69.50\nE. Rs 68.50\n\n### Answer:\nSP =20% of Rs 56.25 ,=Rs{(120/100)*56.25}=Rs67.50\nAnswer is C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a is an odd integer and b is an odd integer which of the following must not be an odd integer :\n\n### Options:\nA. a/b\nB. ab\nC. 2a+b\nD. 2(a+b)\nE. 3a/b\n\n### Answer:\nonly when two odd number added then we get even number.\nTherefore answer is D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA person goes to his office at 1/3rd of the speed at which he returns from his office. If the avg speed during the whole trip is 12m/h. what is the speedof the person while he was going to his office?\n\n### Options:\nA. 8km/h\nB. 12km/h\nC. 14km/h\nD. 16km/h\nE. 17km/h\n\n### Answer:\nu = k , v= 3k\n\\inline \\therefore \\frac{2uv}{u+v}\\: \\: \\Rightarrow \\frac{2\\times k\\times 3k}{(k+3k)}=12\n\\inline \\Rightarrow 1.5k = 12\n\\inline \\Rightarrow k=8km/h\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJoe needs to paint all the airplane hangars at the airport, so he buys 360 gallons of paint to do the job. During the first week, he uses 1/4 of all the paint. During the second week, he uses 1/4 of the remaining paint. How many gallons of paint has Joe used?\n\n### Options:\nA. 18\nB. 157\nC. 175\nD. 216\nE. 250\n\n### Answer:\nTotal paint initially = 360 gallons\nPaint used in the first week = (1/4)*360 = 90 gallons.\nRemaning paint = 270 gallons\nPaint used in the second week = (1/4)*270 = 67 gallons\nTotal paint used = 157 gallons.\nOption B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nNotebooks are sold in packages of four or seven only. If Wilson bought 69 notebooks exactly, what could be the number of large packs Wilson bought?\n\n### Options:\nA. 3\nB. 4\nC. 7\nD. 8\nE. 9\n\n### Answer:\nLet number of packs of four = f\nlet number of packs of seven = s\n4f + 7s = 69\nNow , we need to test for values of s .\nSince sum 69 is odd and 4f will always be even , e can't be even .\nNow , we can test for values e = 3 , 7 and 9\n4*5 + 7*7 = 20 + 49 = 69\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf X-Y = 2X-2Z, X-2Y = 4Z and X+Y+Z = 21, what is the value of Y/Z?\n\n### Options:\nA. -4.5.\nB. -2.\nC. -1.7.\nD. -0.667.\nE. 2.5.\n\n### Answer:\nX-Y = 2X-2Z\nY= -X+2Z---------- 1\nX-2Y = 4Z\nX-4Z= 2Y--------- 2\nAdding equation 1 from equation 2\n-2Z= 3Y\nY/Z= -0.667\nD is the answer\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a certain government school, 40% of students are below 10 years of age. The number of students above 10 years of age is 5/6 th of the number of students of 10 years age which is 36. What is the total number of students in the school ?\n\n### Options:\nA. 100\nB. 72\nC. 110\nD. 135\nE. 145\n\n### Answer:\nExplanation :\nSolution: let the number of students be x. then, number of students of or above 10 years = (100-40)% of x = 60% of x.\n.'. 60% of x = 36 +5/6 *36\n=>60/100 * x = 66\n=>x = 110\nAnswer : C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nif india=90 and france=146 then england equals to?\n\n### Options:\nA. 215\nB. 216\nC. 217\nD. 218\nE. 219\n\n### Answer:\nI=9 N=14 D=4 I=9 A=1\n(9*1)+(14*2)+(4*3)+(9*4)+(1*5) = 90\nMultiply code of each lettr wid 1 2 3 in dat order...\nSimilarly france wil b\n(6*1)+(18*2)+(1*3)+(14*4)+(3*5)+(5*6)= 146\nIn dat manner england will be 219\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train running at the speed of 40 km/hr crosses a pole in 27 seconds. What is the length of the train?\n\n### Options:\nA. 250\nB. 300\nC. 350\nD. 400\nE. 450\n\n### Answer:\nSpeed=(40 * 5/18) m/sec = (100/9) m/sec Length of the train = (Speed x Time) = (100/9 *29 ) m\n= 300 m.\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat percent is 1 gm of 1 kg?\n\n### Options:\nA. 0.1 %\nB. 1%\nC. 1.5%\nD. 2%\nE. 3%\n\n### Answer:\n1 kg = 1000 gm\n1/1000 \u00d7 100 = 100/1000\n=1/10 = 0.1 %\nA)\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the ratio of the volumes of a right cylinder to that of a right cone having equal diameters?\n\n### Options:\nA. 1:3\nB. 3:1\nC. 2:3\nD. 3:2\nE. None of these\n\n### Answer:\nSOLUTION :\nvolume of cylinder : volume of cone\npr2h : 1/3 pr2h = 3 : 1\nANSWER IS B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo pipes A and B can fill a tank in 12 and 24 minutes respectively. If both the pipes are used together, then how long will it take to fill the tank?\n\n### Options:\nA. 8 min\nB. 28 min\nC. 18 min\nD. 5 min\nE. 6min\n\n### Answer:\nExplanation :\nPart filled by pipe A in 1 minute= 1/12\nPart filled by pipe B in 1 minute= 1/24\nPart filled by pipe A and pipe B in 1 minute= 1/12+1/24=1/8\ni.e., both the pipe together can fill the tank in 8 minutes\nAnswer is A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively . If they cross each other in 25 seconds, what is the ratio of their speeds?\n\n### Options:\nA. 1:3\nB. 4:1\nC. 2:3\nD. 3:2\nE. 3:4\n\n### Answer:\nLet the speed of the trains be x and y respectively\nlength of train1 = 27x\nlength of train2 = 17y\nRelative speed= x+ y\nTime taken to cross each other = 25 s\n= (27x + 17 y)/(x+y) = 25\n= (27x + 17 y)/ = 25(x+y)\n= 2x = 8y\n=x/y = 8/2 = 4/1 i.e 4:1\nAnswer :B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nBert and Rebecca were looking at the price of a condominium. The price of the condominium was 100% more than Bert had in savings, and separately, the same price was also 60% more than Rebecca had in savings. What is the ratio of what Bert has in savings to what Rebecca has in savings.\n\n### Options:\nA. 1:5\nB. 2:5\nC. 3:5\nD. 4:5\nE. 1:1\n\n### Answer:\nSuppose bert had 100 so price becomes 200 , this 200 = 1.6 times R's saving .. so R's saving becomes 125\nSo required ratio is 100:125=4:5\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA take twice as much time as B or thrice as much time to finish a piece of work. Working together, they can finish the work in 5 days. B can do the work alone in?\n\n### Options:\nA. 19\nB. 12\nC. 11\nD. 30\nE. 114\n\n### Answer:\nSuppose A, B and C take x, x/2 and x/3 respectively to finish the work.\nThen, (1/x + 2/x + 3/x) = 1/5\n6/x = 1/5 => x = 30\nSo, B takes 15 hours to finish the work.\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind a sum for first 8 prime numbers?\n\n### Options:\nA. 22\nB. 28\nC. 59\nD. 77\nE. 84\n\n### Answer:\nRequired sum = (2 + 3 + 5 + 7 + 11+13+17+19) = 77\nNote: 1 is not a prime number\nOption D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n5 3 -2 -5 -3 2....What is the sum of first thirty number sequence?\n\n### Options:\nA. 0\nB. 1\nC. 2\nD. 3\nE. 4\n\n### Answer:\n5 3 -2 -5 -3 2 5 3 -2 -5 -3 2 5 3 -2 -5 -3 2 5 3 -2 -5 -3 2 5 3 -2 -5 -3 2\n=> 50-50=0.\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRobert spent $120 in buying raw materials, $195 in buying machinery and 10% of the total amount he had as cash with him. What was the total amount?\n\n### Options:\nA. A)$150\nB. B)$210\nC. C)$350\nD. D)$160\nE. E)$200\n\n### Answer:\nLet the total amount be x\nthen, (100-10)% of x = 120+195\n90% of x = 315\n90x/100 = 315\nx = $350\nAnswer is C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe breath of a rectangular landscape is 6 times its length. There is a playground in it whose area is 4200 square mtr & which is 1/7 th of the total landscape. What is the breath of the landscape?\n\n### Options:\nA. 520\nB. 420\nC. 320\nD. 550\nE. 450\n\n### Answer:\nSol. 6x * x =7* 4200\nx = 70\nLength = 6* 70 = 420 B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA side of beef lost 35 percent of its weight in processing. If the side of beef weighed 545 pounds after processing, how many pounds did it weigh before processing?\n\n### Options:\nA. 191\nB. 355\nC. 737\nD. 838\nE. 1,560\n\n### Answer:\nLet weight of side of beef before processing = x\n(65/100)*x = 545\n=> x = (545 * 100)/65 = 838\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe sum of the mean, the median, and the range of the set {5,6,7} equals which one of the following values?\n\n### Options:\nA. 18\nB. 14\nC. 16\nD. 12\nE. 10\n\n### Answer:\nHere Mean => 5+6+7/3 => 6\nmedian => 6\nand range => 7-1 => 6\nhence sum => 6+6+6=> 18\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAt what rate percent on simple interest will a sum of money double itself in 30 years?\n\n### Options:\nA. 3 1/3%\nB. 3 5/3%\nC. 3 1/9%\nD. 3 1/5%\nE. 3 1/7%\n\n### Answer:\nP = (P*30*R)/100\nR = 3 1/3%\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nKurt, a French painter, has 9 jars of paint: 4 jars of yellow paint, 2 jars of red paint, and 3 jars of brown paint. Kurt pours the contents of 3 jars of paint into a new container to make a new color, which he will name according to the following conditions:\nThe paint will be namedBrun Yif it contains 2 jars of brown paint and no yellow.\nThe paint will be namedBrun Xif the paint contains 3 jars of brown paint.\nThe paint will be namedJaune Xif the paint contains at least 2 jars of yellow.\nThe paint will be namedJaune Yif the paint contains exactly 1 jar of yellow.\nWhat is the probability M that the new color will be one of theJaunecolors?\n\n### Options:\nA. 5/42\nB. 37/42\nC. 1/21\nD. 4/9\nE. 5/9\n\n### Answer:\nI get B.\nJaune Y = (4 choose 1)*(5 choose 2) = 4*10 = 40\nJaune X = (4 choose 2)*(5 choose 1) + (4 choose 3) = 6*5 + 4 = 34\nTotal combinations = 9 choose 3 = 84\nProbability of Jaune MM = (40 + 34)/84 = 37/42.B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a mixture of 45 litres, the ratio of acid to base is 3 : 2. How much base must be added to make the ratio 9: 11?\n\n### Options:\nA. 10 lts\nB. 15 lts\nC. 17 lts\nD. 20 lts\nE. 22 lts\n\n### Answer:\nLet M = 3K,W = 2K\nThus, 3K + 2K = 45\n=> K=9\n=> acid = 27 litres and base = 18 litres.\nNow suppose x litres of base is added to the mixture such that\n27/(18 + X) = 9/11\n=>162 +9X = 297\n=> 9X = 135\n=> X = 15\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average age of A, B and C is 27 years. If the average age of A and C is 29 years, what is the age of B in years ?\n\n### Options:\nA. 19\nB. 35\nC. 20\nD. 32\nE. 23\n\n### Answer:\nAge of B = Age of (A + B + C) \u00e2\u20ac\u201c Age of (A + C) = 27 \u00c3\u2014 3 \u00e2\u20ac\u201c 29 \u00c3\u2014 2 = 81 \u00e2\u20ac\u201c 58 = 23 years\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many seconds will a train 100 meters long take to cross a bridge 250 meters long if the speed of the train is 36 kmph?\n\n### Options:\nA. 54 sec\nB. 35 sec\nC. 25 sec\nD. 45 sec\nE. 24 sec\n\n### Answer:\nD = 100 + 250 = 350\nS = 36 * 5/18 = 10 mps\nT = 350/10 = 35 sec\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a mixture of 60 liters, the ratio of milk and water is 2:1. What amount of water must be added to make the ratio of milk and water as 1:2?\n\n### Options:\nA. 76 liters\nB. 86 liters\nC. 60 liters\nD. 34 liters\nE. 18 liters\n\n### Answer:\n2:1 --- 60\n1:2\n2:4\n---------------\n3\n3 ----------- 60\n3 ----------- ? => 60 liters\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe password for a computer account has to consist of exactly eight characters. Characters can be chosen from any of the following: letter of the alphabet, numerical digits from 0 to 9, a hyphen, or the exclamation mark. Upper-case letters (e.g., A) are considered different from lower-case letters (e.g., a), and characters can be repeated. Given these rules, how many different passwords are possible?\n\n### Options:\nA. 2^9\nB. 2^14\nC. 2^18\nD. 2^40\nE. 2^48\n\n### Answer:\n26 letters in the alphabet, 26*2 = 52 letters, since the password is case-sensitive. Accounting for possibilities of the other special characters we have;\n26+26+10+1+1 = 64, or 2^6 possibilities per character of the password.\nTotal number of possible combinations: (2^6)^8 = 2^48\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA company produces 72000 bottles of water everyday. If a case can hold 9 bottles of water .How many cases are required by the company to hold its one day production\n\n### Options:\nA. 2000\nB. 4500\nC. 5000\nD. 8000\nE. 9000\n\n### Answer:\nNumber of bottles that can be held in a case = 9.\nNumber of cases required to hold 72000 bottles = 72000/9=8000 cases.\nSo the answer is D =8000\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many five letter combinations can be formed using the letters of the word CARTS?\n\n### Options:\nA. 12\nB. 20\nC. 60\nD. 120\nE. 200\n\n### Answer:\nThe number of letters in the given word is four.\nThe number of five letter combinations that can be formed using these five letters is\n= 5 * 4 * 3 * 2 * 1= 120.\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn filling a room with gas 100 m * 10 m * 10 m the volumes of gas will be?\n\n### Options:\nA. 100 cu.m\nB. 1000 cu.m\nC. 10000 cu.m\nD. 100000 cu.m\nE. 10000000 cu.m\n\n### Answer:\n100 * 10 * 10 = 10000\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSuppose you want to buy three loaves of bread that cost $1.50 each\nand a jar of peanut butter that costs $4. A jar of jelly is $2.75, but you\ndon\u2019t need any jelly. You have $10. How much money will you have left\nover?\n\n### Options:\nA. $1.50\nB. $2.50\nC. $3.50\nD. $4.50\nE. $5.50\n\n### Answer:\nThe jelly is extra information. 10.00 \u2013 3 x 1.50 \u2013 4.00 =\n10.00 \u2013 4.50 \u2013 4.00 = 1.50.\nYou have $1.50 left.\ncorrect answer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the height of the triangle?\nI.\tThe area of the triangle is 20 times its base.\nII.\tThe perimeter of the triangle is equal to the perimeter of a square of side 10 cm.\n\n### Options:\nA. I alone sufficient while II alone not sufficient to answer\nB. II alone sufficient while I alone not sufficient to answer\nC. Either I or II alone sufficient to answer\nD. Both I and II are not sufficient to answer\nE. Both I and II are necessary to answer\n\n### Answer:\nEXPLANATION\nI. A = 20 x B \u21d21-div-1by2 x B x H = 20 x B\u21d2H = 40.\nI alone gives the answer.\nII gives, perimeter of the triangle = 40 cm.\nThis does not give the height of the triangle.\nanswer is (A).\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many odd factors does 210 have?\n\n### Options:\nA. 3\nB. 4\nC. 5\nD. 6\nE. 8\n\n### Answer:\nStart with the prime factorization: 210 = 2*3*5*7\nFor odd factors, we put aside the factor of two, and look at the other prime factors.\nset of exponents = {1, 1, 1}\nplus 1 to each = {2, 2, 2}\nproduct = 2*2*2 = 8\nTherefore, there are 8 odd factors of 210. In case you are curious, they are {1, 3, 5, 7, 15, 21, 35, and 105}\nAnswer: E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man has some hens and cows. If the number of heads be 48 and the number of feet equals 140, then the number of cows will be:\n\n### Options:\nA. 30\nB. 23\nC. 24\nD. 26\nE. 22\n\n### Answer:\nExplanation:\nLet the number of hens be x and the number of cows be y.\nThen, x + y = 48 .... (i)\nand 2x + 4y = 140 x + 2y = 70 .... (ii)\nSolving (i) and (ii) we get: x = 26, y = 22.\nThe required answer = 22.\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nDuring the first two weeks of January, the total rainfall in Springdale was 35 inches. If the rainfall during the second week was 1.5 times the rainfall during the first week, what was the rainfall during the second week of January?\n\n### Options:\nA. 5 inches\nB. 6 inches\nC. 9 inches\nD. 10 inches\nE. 21 inches\n\n### Answer:\nTotal rainfall in 2 weeks = 35 inches.\nAssume the rainfall in second week = 1.x\nRainfall in first week = x\nTotal rainfall = 2.5x = 35 inches\nx = 14 and 1.5x = 21\nRainfall during second week = 21 inches\nOption E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA project has three test cases. Three teams are formed to study the three different test cases. James is assigned to all three teams. Except for James, each researcher is assigned to exactly one team. If each team has exactly 7 members, then what is the exact number of researchers required?\n\n### Options:\nA. 23\nB. 20\nC. 21\nD. 22\nE. 19\n\n### Answer:\nalternatively, we have\n7*3-2( because james is included in all the three teams)\n=19\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nX and Y invest Rs.21000 and Rs.17500 respectively in a business. At the end of the year, they make a profit of Rs.26400. What is the share of X in the profit?\n\n### Options:\nA. Rs.14400\nB. Rs.26400\nC. Rs.12000\nD. Rs.12500\nE. None of these\n\n### Answer:\nExplanation :\nRatio of the investment = 21000 : 17500 = 210 : 175 = 42 : 35 = 6 : 5\nShare of X in the profit = 26400 * (6/11) = 2400 * 6 = 14400 .. Answer : Option A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n45 girls and 60 boys are present at a party. There are 17 girl-boy are in relationship among them. If a girl and a boy is selected at random, what is the probability that they will be a couple?\n\n### Options:\nA. 1/200\nB. 1/100\nC. 90/2900\nD. 17/2700\nE. 1/20\n\n### Answer:\nIn how many ways we can select a girl and a boy from 45 lady and 60 gentlemen? In 45*60 = 2,700 ways.\nWe have a total of 17 couples so, the probability of selecting a couple is 17/2,700 = 17/2700.\nAns- D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWith a uniform speed a car covers the distance in 8 hours. Had the speed been increased by 3 km/hr, the same distance could have been covered in 7 1/2 hours. What is the distance covered?\n\n### Options:\nA. 360 km\nB. 480 km\nC. 278 km\nD. 297 km\nE. 671 km\n\n### Answer:\nLet the distance be x km. Then,\nx/(7 1/2) - x/8 = 3\n2x/15 - x/8 = 3 => x = 360 km.\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn the xy plane line m has the equation 4x + y = t. Line n passes through the origin and is perpendicular to line m. If point p has the coordinates (r, r+1) and is on both line n and m what is the value of r?\n\n### Options:\nA. -4/3\nB. 1/4\nC. -4\nD. 3/4\nE. 4/3\n\n### Answer:\nThe equation of line m is y=-4x+t. Now, since line n is perpendicular to line m, then its slope is negative reciprocal of the slope of line m, so the slope of n is 1/4. Next, as line n passes through the origin (0, 0) and has the slope of 1/4 then its equation is y=1/4*x.\nPoint (r, r+1) lies on line n means that (r+1)=1/4*r --> r=-4/3.\nAnswer: A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSubtracting 10% from X is the same as multiplying X by what number?\n\n### Options:\nA. 12\nB. 90\nC. 26\nD. 27\nE. 18\n\n### Answer:\nX - (10/100) X = X * ?\n? = 90%\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow much 60% of 50 is greater than 40% of 30?\n\n### Options:\nA. 18\nB. 91\nC. 11\nD. 17\nE. 12\n\n### Answer:\n(60/100) * 50 \u2013 (40/100) * 30\n30 - 12 = 18\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA taxi company charges $1.40 for the first quarter of a mile and fifteen cents for each additional quarter of a mile. What is the maximum distance someone could travel with $4.90?\n\n### Options:\nA. 4 miles\nB. 4 1/4 miles\nC. 4 3/4 miles\nD. 5 1/2 miles\nE. 6 miles\n\n### Answer:\nIf we start out with $4.90 and have to spend $1.40 for the first quarter-mile, we will have $3.50 left to spend on quarter-mile intervals.\nSince $3.50/$0.15 = 23.33, we can buy 23.33 more quarter-miles, and will travel 24.33 quarter miles in all:\n24.33 \u00d7 1/4 = 6 miles.\nThe correct answer is choice (E).\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf $30,000 interest is invested in 10 percent simple annual interest for 2 years, which of the following represents the total amount of interest, in dollars, that will be earned by this investment in the 2 years?\n\n### Options:\nA. $6000\nB. $4000\nC. $5000\nD. $3000\nE. $2000\n\n### Answer:\n30000*10/100*2 = $6000\nAnswer : A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMalar and Roja combined will complete a task in 35 days, but Malar alone can complete same work in 60 days. Calculate in how many days Roja can complete this work ?\n\n### Options:\nA. 85 days\nB. 45 days\nC. 90 days\nD. 84 days\nE. 95 days\n\n### Answer:\nMalar - 35 days =>1/35\nRoja - 60 days =>1/60\nMalar one day work = 1/35-1/60\n=1/84\n==>84 days\nANSWER D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf difference between compound interest and simple interest on a sum at 10% P.a. for 2 years is Rs.150 then sum is\n\n### Options:\nA. s.15000\nB. s.15100\nC. s.15800\nD. s.16000\nE. s.16200\n\n### Answer:\np(r/100)^2=C.I-S.I\nP(10/100)^2=150\n15000\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many seconds will a train 100 meters long take to cross a bridge 180 meters long if the speed of the train is 36 kmph?\n\n### Options:\nA. 22 sec\nB. 27 sec\nC. 25 sec\nD. 24 sec\nE. 28 sec\n\n### Answer:\nExplanation:\nD = 100 + 180 = 280\nS = 36 * 5/18 = 10 mps\nT = 280/10 = 28 sec\nAnswer: Option E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA cistern normally takes 6 hours to be filled by a tap but because of a leak, 2 hours more. In how many hours will the leak empty a full cistern ?\n\n### Options:\nA. 20 hours\nB. 24 hours\nC. 26 hours\nD. 18 hours\nE. None of these\n\n### Answer:\n\u2235 cistern fill in 6 hours.\n\u2234 in 1 hour, filled part = 1\u20446th\nNow, due to leakage, filled part in 1 hour = 1\u20448th\nPart of the cistern emptied, due to leakage in 1 hour\n= 1\u20446 - 1\u20448 = 1\u204424th\n\u2234 The leakage will empty the full cistern in 24 hrs.\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJack and Dick work at a hospital with 4 other workers. For an internal review, 2 of the 6 workers will be randomly chosen to be interviewed. What is the probability that Jack and Dick will both be chosen?\n\n### Options:\nA. A)1/3\nB. B)1/4\nC. C)1/15\nD. D)3/8\nE. E)2/3\n\n### Answer:\nTotal number of people = 6\nProbability of selecting Jack first and then Dick is 1/6\u22171/5=1/30\nProbability of selecting Dick first and then Jack is 1/6\u22171/5=1/30\nTherefore probability of selecting Jack and Dick for the review is 1/30+1/30=1/15\nAnswer is C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nI buy coffee from 3 different shops at Rs.150,Rs.140,Rs.130 per kg and mix them in proportion 8:5:3.At what price per kg must I sell the mixture to make a profit of 25%?\n\n### Options:\nA. 168.906\nB. 178.906\nC. 188.906\nD. 198.906\nE. 158.906\n\n### Answer:\ntotal=16x kg, tot cp=2290x\nsp should be=2862.5x\nso sp/kg=178.906\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIt takes printer A 4 more minutes more than printer B to print 40 pages. Working together, the two printers can print 50 pages in 6 minutes. How long will it take Printer A to print 100 pages?\n\n### Options:\nA. 12\nB. 18\nC. 20\nD. 24\nE. 30\n\n### Answer:\nIf it takes 4 more minutes for A to print 40 pages than it takes B,\nit takes 5 more minutes for A to print 50 pages than it takes B.\nThus if b is the number of minutes than B takes to print 50 pages,\nwe can write:\n1/b+1/(b+5)=1/6 (since in 1 minute, they print 1/6th of the 50 page job)\n6(2b+5)=b(b+5)\nb^2-7b-30=0\n(b-10)(b+3)=0\nb=10\nThus it takes A 15 minutes to print 50 pages and 15*100/50=30 minutes to print 100 pages (ANSWER E)\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a circuit board factory, all circuit boards that pass a verification process are certified. Every board that fails the verification process is indeed faulty, but 1/8 of those that pass are also faulty.\nApproximately how many faulty circuit boards exist in a group of 400 circuit boards where 64 fail inspection?\n\n### Options:\nA. 106\nB. 192\nC. 200\nD. 256\nE. 264\n\n### Answer:\nTotal of 400 boards. All that fail verification are indeed faulty. So the 64 are indeed faulty. 1/8 those that pass are also faulty.\nFrom the 400 we know 64 fail. So 336 must pass. Of these 1/8 are faulty. 336 divided by 8 gives you 42.\nWhat one must do now is to add to the 42 which were not detected the actually detected faulty ones, namely the 64.\nTotal faulty: 106.\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn 10 years,A will be 5 times as old as B was 10 years ago.If A is now 9 years older than B,the present age of B is :\n\n### Options:\nA. 17.25 Years\nB. 29 Years\nC. 39 Years\nD. 49 Years\nE. 59 Years\n\n### Answer:\nSolution\nLet B's present age = x years.Then,A's present age =(x +9) years.\n\u00e2\u02c6\u00b4 (x + 9)+ 10 = 5 (x - 10) \u00e2\u2021\u201d x + 19 = 5x- 50 \u00e2\u2021\u201d 4x = 69.\nx = 17.25\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRobin is traveling from one end of a forest to the other. In order to find her way back, she is leaving morsels of bread in the following pattern: 2 morsels of RICE , 3 morsels of white, and 1 morsel of rye. The pattern repeats after she leaves the morsel of rye. If Robin drops 2,000 morsels of bread, what are the last 3 morsels of bread that she drops?\n\n### Options:\nA. rye \u2212 wheat \u2212 wheat\nB. RY-R-R\nC. white \u2212 rye \u2212 wheat\nD. white \u2212 white \u2212 white\nE. white \u2212 white \u2212 rye\n\n### Answer:\nQ is nothing BUT asking about remainder..\ntotal morsels thrown before the pattern is repeated = 2+3+1 = 6..\nso REMAINDER when 2000 is div by 6..\n1998 is EVEN and also div by 3, so remainder is 2..\nLast 3 of morsels are 1998-1999-2000\nso he uses the last of morsel of pattern in 1998 two of the first morsels of the pattern in 1999 and 2000, and the pattern is R, R, W, W, W, RY..\nans RY-R-R\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo trains are running at 40 km/hr and 20 km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 7 sec. What is the length of the fast train?\n\n### Options:\nA. 27 7/6\nB. 27 7/5\nC. 27 7/2\nD. 350/9\nE. 27 7/1\n\n### Answer:\nRelative speed = (40 - 20) = 20 km/hr.\n= 20 * 5/ 18 = 50/9 m/sec.\nLength of faster train = 50/9 * 7 = 350/9\n= 350/9 m.\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe ratio of men to women in the Snyder community choir is 4 to 5. The ratio of men to women in the Leigh community choir is 5 to 6. If the two choirs merged, the ratio of men to women in the combined choir would be 22 to 27. If Snyder has 4 more men and 6 more women than Leigh, how many women are in the Snyder choir?\n\n### Options:\nA. 20\nB. 24\nC. 30\nD. 32\nE. 34\n\n### Answer:\nUse simultaneous equations / By combination\n4x = 5y + 4\n5x = 6y + 6\nMultiply (1) by 6\nMultiply (2) by -5\nGet rid of y, and x = 6\nThen 5x = 30\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTotal value of the quantity sold for item C is what per cent of the total value of the quantity sold for Item E?\n\n### Options:\nA. 30\nB. 60\nC. 100\nD. 80\nE. 90\n\n### Answer:\nE\n90\nTotal value of the quantity sold for item C = Rs(45 \u00d7 7.5 \u00d7 100)\n= Rs 33750\nTotal value of the quantity sold for item E = Rs(15 \u00d7 25 \u00d7 100) = Rs 37500\n\u2234 Required percentage = 33750/37500X 100 = 90\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many values of c in x^2 - 5x + c, result in rational roots which are integers?\n\n### Options:\nA. 23\nB. 27\nC. 25\nD. 12\nE. 82\n\n### Answer:\nExplanation:\nBy the quadratic formula, the roots of x2\u22125x+c=0x2\u22125x+c=0 are \u2212(\u22125)\u00b1\u221252\u22124(1)(c)\u2212\u2212\u2212\u2212\u2212\u2212\u2212\u2212\u2212\u2212\u2212\u221a2(1)\u2212(\u22125)\u00b1\u221252\u22124(1)(c)2(1) = 5\u00b125\u22124c\u2212\u2212\u2212\u2212\u2212\u2212\u221a25\u00b125\u22124c2\nTo get rational roots, 25\u22124c25\u22124c should be square of an odd number. Why? because 5 + odd only divided by 2 perfectly.\nNow let 25 - 4c = 1, then c = 6\nIf 25 - 4c = 9, then c = 4\nIf 25 - 4c = 25, then c = 0 and so on...\nSo infinite values are possible.\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a, b, and c are integers and a*b^2/c is a positive even integer, which of the following must be true?\nI. c is even\nII. ab > 4\nIII. ab is even\n\n### Options:\nA. I only\nB. III only\nC. I and II\nD. I and III\nE. I, II, and III\n\n### Answer:\nTwo ways this can happen: 1- Even/ Even= Even or 2- Even/Odd= Even\nSo Ab MUST be even, with either A or B being even, Ab does not have to be positive, as B could be negative and once it is raised to 2 it becomes positive again, and of course, C could be Odd or Even as described above.\nIII only.letter B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA set of consecutive positive integers beginning with 1 is written on the blackboard. A student came along and erased one number. The average of the remaining numbers is 35*7/17. What was the number erased?\n\n### Options:\nA. 7\nB. 8\nC. 6\nD. 5\nE. 4\n\n### Answer:\nExplanation :\nLet the higher number be n and x be the number erased.\nThen((n(n+1)/2)+x)/(n+1) = 35*7/17 = 602/17\nHence, n = 69 and x =7 satisfy the above conditions.\nAnswer : A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA can complete a certain job in 7 days. B is 40% more efficient than A. In how many days can B complete the same job?\n\n### Options:\nA. 5\nB. 6.25\nC. 7\nD. 7.5\nE. 4.8\n\n### Answer:\nLet, Total Work Unit = 70 Units\nA can finish in 7 days = 70 unit work\ni.e. A can finish in 1 days = 10 unit work\ni.e. B can finish in 1 days = 10+(40/100)*10 = 14 unit work\nDays in which B will complete the work alone = 70/14 = 5 days\nAnswer: Option A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nLittle John had $7.10. He spent $1.05 on sweets and gave to his two friends $1.00 each. How much money was left?\n\n### Options:\nA. $4.85\nB. $4.15\nC. $4.65\nD. $4.55\nE. $4.05\n\n### Answer:\nJohn spent and gave to his two friends a total of\n1.05 + 1.00 + 1.00 = $3.05\nMoney left\n7.10 - 3.05 = $4.05\nAnswer :E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf n = 2\u00d73\u00d75\u00d77\u00d711\u00d713\u00d715, then which of the following statements must be true?\nI. n^2 is divisible by 600\nII. n + 19 is divisible by 19\nIII. (n + 4)/2 is even\n\n### Options:\nA. I only\nB. II only\nC. I and III\nD. III only\nE. None of the above\n\n### Answer:\nStatement I: 600 = (2^3)*(3)*(5^2) this is true.\nStatement 2: this is NOT true.\nStatement 3: (n+4)/2 = n/2 + 2, So this is true.\nHence option (C).\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the speed of x meters per second is equivalent to the speed of Y mile per hour, what is y in terms of x? (1 mile = 1609.34 meter)\n\n### Options:\nA. 1.21x\nB. 1.33x\nC. 2.23x\nD. 2.84x\nE. 3.13x\n\n### Answer:\nx meters per second -->\n--> 3,600x meters per hour(as there are 3,600 seconds in one hour);\n--> 3,600x/1,609.34=2.236x miles per hour (as there are 1,609.34 meters in one mile).\nAnswer: C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train 600 m long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 min, then the length of the tunnel is?\n\n### Options:\nA. 298 m\nB. 268 m\nC. 700 m\nD. 267 m\nE. 181 m\n\n### Answer:\nSpeed = 78 * 5/18 = 65/3 m/sec.\nTime = 1 min = 60 sec.\nLet the length of the train be x meters.\nThen, (600 + x)/60 = 65/3\nx = 700 m.\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo cars are traveling towards each other. If car A is traveling at a speed of 50 mph and car B is traveling 12% slower, how much time will it take the cars to meet if the initial distance between the two is 705 miles?\n\n### Options:\nA. Six hours and 30 minutes.\nB. Seven hours and 30 minutes.\nC. Eight hours and 20 minutes.\nD. Nine hours and 15 minutes.\nE. Ten hours and 20 minutes.\n\n### Answer:\nsince they are travelling towards each other, the total speed is 50 mph + 50*0.88 = 94 mph (0.88 since, the other car is 12% less than first one)\nDistance to be covered is 705, so time taken = distance/speed = 705/94 = 7.5 hours or 7 hours and 30 mins.\nAnswer is B: Seven hours and 30 minutes.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average age of 'a' boys is \u2018b\u2019 years and of \u2018n\u2019 girls \u2018c\u2019 years. The average age of all together is?\n\n### Options:\nA. (ab \u2013 nc)/ (a + n) years\nB. (ab + nc)/ (a - n) years\nC. (ab + nc)/ (a + n) years\nD. (ab \u2013 nc)/ (a - n) years\nE. None of these\n\n### Answer:\n(ab + nc) / (a+ n)\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA sum of money is divided among A, B, C & D in the ratio 3:5:8:9 respectively. If the share of D Rs.1872 more than the share of A, then what is the total amount of money of B & C together?\n\n### Options:\nA. Rs. 4000\nB. Rs. 4056\nC. Rs. 4060\nD. Rs. 4100\nE. Rs. 4150\n\n### Answer:\nSol. Share of B + C = -3 x (5 + 8) = Rs. 4056\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n252 can be expressed as a product of primes as :\n\n### Options:\nA. 2 x 2 x 3 x 3 x 7\nB. 2 x 2 x 2 x 3 x 7\nC. 3 x 3 x 3 x 3 x 7\nD. 2 x 3 x 3 x 3 x 7\nE. 2 x 3 x 7 x 3 x 2\n\n### Answer:\n252 = 2 x 2 x 3 x 3 x 7.\nanswer :A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA and B starts a business with Rs.8000 each, and after 4 months, B withdraws half of his capital . How should they share the profits at the end of the 18 months?\n\n### Options:\nA. 18:11\nB. 18:16\nC. 18:10\nD. 18:14\nE. 14:11\n\n### Answer:\nA invests Rs.8000 for 18 months, but B invests Rs.8000 for the first 4 months and then withdraws Rs.4000. So, the investment of B for remaining 14 months is Rs.4000 only.\nA : B\n8000*18 : (8000*4) + (4000*14)\n14400 : 88000\nA:B = 18:11\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average age of 3 boys is 15 years and their ages are in the proportion 1:2:3. The age of the youngest boy is?\n\n### Options:\nA. 10 years\nB. 12 years\nC. 15 years\nD. 18 years\nE. 7.5 years\n\n### Answer:\nTotal age of 3 boys = 15*3 = 45\nratio of their ages = 1:2:3\nAge of the youngest = 45*1/6 = 7.5 years\nAnswer is E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n0.0006688/0.0000150 x 19.85 = ?\n\n### Options:\nA. 850\nB. 900\nC. 950\nD. 1000\nE. 2000\n\n### Answer:\nExplanation :\n? = 6688/150 x 19.85 = 45 x 20 = 900\nAnswer : Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA group of workers was put on a job. From the second day onwards, one worker was withdrawn each day. The job was finished when the last worker was withdrawn. Had no worker been withdrawn at any stage, the group would have finished the job in 55% of the time. How many workers were there in the group?\n\n### Options:\nA. 33\nB. 38\nC. 23\nD. 10\nE. 27\n\n### Answer:\nExplanation:\nIt can be solved easily through option.\n\\inline \\left ( 10+9+8+....+1 \\right )=10\\left ( 10\\times \\frac{55}{100} \\right )\n55 = 55 Hence correct\nAlternatively:\n\\inline \\frac{n(n+1)}{2}=n\\times \\frac{55n}{100}\n=> n= 10\nIn Both cases total work is 55man-days.\nAnswer: D) 10\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhen 33 is divided by the positive integer k, the remainder is 3, for how many different values of k is this true?\n\n### Options:\nA. 1\nB. 2\nC. 3\nD. 4\nE. 5\n\n### Answer:\nThis means that 30 must be a multiple of k.\nThe factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30.\nOut of these, k can be 5, 6, 10, 15, and 30.\nThe answer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA letter lock consists of three rings each marked with six different letters. The number of distinct unsuccessful attempts to open the lock is at the most\n\n### Options:\nA. 200\nB. 215\nC. 220\nD. 230\nE. 240\n\n### Answer:\nSince each ring consists of six different letters, the total number of attempts possible with the three rings is = 6 * 6 * 6 = 216. Of these attempts, one of them is a successful attempt.\nMaximum number of unsuccessful attempts = 216 - 1 = 215\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAt the store, Sam bought a shirt and a toaster. There was a 5% sales tax on each item, and with tax, Sam paid a total of K. If the price of the toaster before tax was T, what, in terms of K and T, is the price of the shirt before tax?\n\n### Options:\nA. 0.95(K \u2013 T)\nB. 0.95K \u2013 T\nC. 0.95(K \u2013 1.05T)\nD. (K \u2013 T)/1.05\nE. (K/1.05) \u2013 T\n\n### Answer:\n1.05S + 1.05T = K\n1.05S = K - 1.05T\nS = (K/1.05) - T\nThe answer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a km race, A beats Bby 28 metres or 7 seconds. Find A's timeoverthe course\n\n### Options:\nA. 4 min\nB. 3 min. 3sec\nC. 4 min.4 sec\nD. 5 min. 3 sec\nE. 4 min. 3 sec\n\n### Answer:\nClearly, B covers 28 m in 7 seconds.\n:. B's time over the course = (278 x 1000) sec = 250 seconds.\n:. A's time over the course = (250 - 7-) sec = 243 sec\n= 4 min. 3 sec.\nOption E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn Solution P, the proportion of water to alcohol is 5:1. In Solution Q, the proportion of water to alcohol is 2:1. If the two solutions are combined, what is the concentration of alcohol in the new solution if the original solutions were mixed in equal amounts?\n\n### Options:\nA. 21%\nB. 23%\nC. 25%\nD. 27%\nE. 29%\n\n### Answer:\nLet V be the total volume of the new solution.\nThe amount of alcohol added from Solution P is (1/6)*V/2=(1/12)*V\nThe amount of alcohol added from Solution Q is (1/3)*V/2=(1/6)*V\nThe total amount of alcohol in the new solution is (1/12+1/6)*V=(1/4)*V\nThe alcohol concentration is 1/4=25%\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train 300 m long can cross an electric pole in 15 sec and then find the speed of the train?\n\n### Options:\nA. 65 Kmph\nB. 70 Kmph\nC. 72Kmph\nD. 75 Kmph\nE. 78 Kmph\n\n### Answer:\nLength = Speed * time\nSpeed = L/T\nS = 300/15\nS = 20 M/Sec\nSpeed= 20*18/5 (To convert M/Sec in to Kmph multiply by 18/5)\nSpeed = 72 Kmph\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich of the following CANNOT be true if the sum of k consecutive integers is 0, where k \u2265 1 ?\nI. The product of the k integers is positive\nII. The smallest of the k integers is zero\nIII. The largest of the k integers is negative\n\n### Options:\nA. I only\nB. II only\nC. III only\nD. I and III\nE. I, II and III\n\n### Answer:\nfor the sum of k consecutive integers to be 0 we have at least k=1 as 0\nor if k=3 then 1,0,-1\n1) product will be 0 every time......Not True\n2)as stated earlier if k=1 as 0 then 0 is the highest as well lowest number.....Could be True\n3) largest number can only be 0 if K=1 or any +ve integer if K>1--------->largest integer be -ve Never true.\nAns D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nDavid has d books, which is 3 times as many as Jeff and 2/3 as many as Paula. How many books do the three of them have altogether, in terms of d?\n\n### Options:\nA. 5/6*d\nB. 7/3*d\nC. 17/2*d\nD. 7/2*d\nE. 9/2*d\n\n### Answer:\nAlthough we could plug in a real value for d, the problem can be just as easily solved by setting up equations. However, let\u2019s start by defining some variables. Since we are given that David has d books, we can use variable d to represent how many books David has.\nnumber of books David has = d\nnumber of books Jeff has = j\nnumber of books Paula has = p\nWe are given that David has 3 times as many books as Jeff. We can now express this in an equation.\nd = 3j\nd/3 = j\nWe are also given that David has \u00bd as many books as Paula. We can also express this in an equation.\nd = (2/3)p\n3d/2 = p\nNotice that we immediately solved forj in terms of d and p in terms of d. Getting j and p in terms of d is useful when setting up our final expression. We need to determine, in terms of d, the sum of the number of books for David, Jeff, and Paula. Thus, we have:\nd + d/3 + 3d/2\n=17d/2\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA and B complete a work in 6 days. A alone can do it in 10 days. If both together can do the work in how many days?\n\n### Options:\nA. 8 days\nB. 12 days\nC. 15 days\nD. 16 days\nE. 3.75 days\n\n### Answer:\nExplanation:\n1/6 + 1/10 = 8/30 = 4/15\n15/4 = 3.75 days\nAnswer E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a function they are distributing noble prize. In how many ways can 3 prizes be distributed among 8 boys when a boy gets any no. of prizes?\n\n### Options:\nA. 55\nB. 512\nC. 510\nD. 540\nE. 70\n\n### Answer:\nAns.(B)\nSol. In this case, repetitions are allowed, so all the three prizes can be given in 8 ways, i.e. (8 x 8x 8) ways = 83 ways = 512 ways Or nr ways = 83 ways = 512 ways\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a coin has an equal probability of landing heads up or tails up each time it is flipped , what is the probability that the coin will land Tails up exactly once in 3 consecutive flips ?\n\n### Options:\nA. 0.125\nB. 0.375\nC. 0.325\nD. 0.5\nE. 0.666\n\n### Answer:\nTotal number of ways in which H or T can appear in 3 tosses of coin is\n= 2 * 2 * 2 = 8 ways\nFor 2 T and 1 TH\nThus probability is\n= P(HTT) + P(TTH) + P(THT)\n= 1/8 + 1/8 + 1/8\n= 3/8\n= .375\nAnswer :B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAmong the first 1 million numbers, 40 is a number that is pretty unique.\nCan you find out why ?\n\n### Options:\nA. 36\nB. 31\nC. 45\nD. 39\nE. 40\n\n### Answer:\nE\n40\nThe number 40 (Forty) is the only number in one million numbers whose letters are arranged in the order they are arranged in English alphabets as well.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the perimeter of a rectangular garden is 1200 m, its length when its breadth is 240 m is?\n\n### Options:\nA. 338 m\nB. 778 m\nC. 200 m\nD. 276 m\nE. 360 m\n\n### Answer:\n2(l + 240)\n= 1200 => l\n= 360 m\nAnswer:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe circumferences of two circles are 264 meters and 352 meters. Find the difference between the areas of the larger and the smaller circles.\n\n### Options:\nA. 388\nB. 277\nC. 4312\nD. 2887\nE. 2992\n\n### Answer:\nLet the radii of the smaller and the larger circles be s m and l m respectively.\n2\u220fs = 264 and 2\u220fl = 352\ns = 264/2\u220f and l = 352/2\u220f\nDifference between the areas = \u220fl2 - \u220fs2\n= \u220f{1762/\u220f2 - 1322/\u220f2}\n= 1762/\u220f - 1322/\u220f\n= (176 - 132)(176 + 132)/\u220f\n= (44)(308)/(22/7) = (2)(308)(7) = 4312 sq m.Answer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAfter successive discounts of 20%, 10% and 5% a certain good is sold for Rs. 6600. Find the actual price of the good.\n\n### Options:\nA. s. 6000\nB. s. 9000\nC. s. 10800\nD. s. 9649\nE. s. 9980\n\n### Answer:\nLet actual price was 100.\nAfter three successive discount this will become,\n100 ==20% discount => 80 ==10% discount => 72 ==5% discount = 68.4\nNow Compare,\n68.4 = 6600\n1 = 6600/68.4\n100 = (6600*100)/68.4 = Rs. 9649.\nAnswer: Option D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFor an agricultural experiment, 300 seeds were planted in one plot and 200 were planted in a second plot. If exactly 20 percent of the seeds in the first plot germinated and exactly 35 percent of the seeds in the second plot germinated, what percent of the total number of seeds germinated?\n\n### Options:\nA. 12%\nB. 26%\nC. 29%\nD. 30%\nE. 60%\n\n### Answer:\nIn the first plot 20% of 300 seeds germinated, so 0.20 x 300 = 60 seeds germinated.\nIn the second plot, 35% of 200 seeds germinated, so 0.35 x 200 = 70 seeds germinated.\nSince 60 + 70 = 130 seeds germinated out of a total of 300 + 200 = 500 seeds, the percent of seeds that germinated is (130/500) x 100%, or 26%.\nAnswer: B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA and B together can do a piece of work in 8 days. If A alone can do the same work in 12 days, then B alone can do the same work in?\n\n### Options:\nA. 24\nB. 30\nC. 35\nD. 12\nE. 10\n\n### Answer:\nb=188-1/2 = 1/24\n=>24 days\nANSWER A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf x*y = xy \u2013 2(x + y) for all integers x and y, then 2* (\u20133) =\n\n### Options:\nA. \u201316\nB. \u201311\nC. \u20134\nD. 4\nE. 16\n\n### Answer:\nThe quickest (rather only) way is to apply the given formula:\n2*(-3) = 2*(-3) - 2 (2 + (-3) ) = -6 +2 = -4\nOption (C)\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are 5 periods in each working day of a school. In how many ways can one organize 4 subjects such that each subject is allowed at least one period?\n\n### Options:\nA. 240\nB. 250\nC. 260\nD. 280\nE. None of these\n\n### Answer:\n4 subjects can be arranged in 5 periods in 5P4 ways.\nRemaining 1 period can be arranged in 4P1 ways.\nTwo subjects are alike in each of the arrangement. So we need to divide by 2! to avoid overcounting.\nTotal number of arrangements = (5P4 x 4P1)/2! = 240\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAn empty fuel tank to a car was filled with A type of petrol. When the tank was half empty, it was filled with B type of petrol. Again when the tank was half empty, it was filled with A type of petrol. When the tank was half empty again,it was filled\n\n### Options:\nA. 50%\nB. 40%\nC. 33.5%\nD. 37.5%\nE. None of these\n\n### Answer:\nNow, amount of petrol A = A\u20444 + A\u20448 = 3A\u20448\n\u2234 required% = 3A\u2044 (8 \u00d7 A) \u00d7 100 = 37.50%\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFox jeans regularly sell for $15 a pair and Pony jeans regularly sell for $18 a pair. During a sale these regular unit prices are discounted at different rates so that a total of $9 is saved by purchasing 5 pairs of jeans: 3 pairs of Fox jeans and 2 pairs of Pony jeans. If the sum of the two discounts rates is 50 percent, what is the discount rate on Pony jeans?\n\n### Options:\nA. 9%\nB. 10%\nC. 110%\nD. 120%\nE. 150%\n\n### Answer:\nx discount on Pony jeans, (0.5-x) discount on Fox jeans.\nSet the equation: 3*15(0.5-x)+2*18x=9 --> x=1.5=150%\nAnswer: E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the average (arithmetic mean) of all the multiples of ten from 10 to 170 inclusive?\n\n### Options:\nA. 90\nB. 80\nC. 100\nD. 105\nE. 110\n\n### Answer:\n10 and 190 inclusive would mean there are 17 terms.\nNo need to add up all the terms and further divide by 17 since the terms are evenly spaced in ascending order from 10, 20, 30........170\nThe middle term is the average which is the tenth term = 80\nB is the answer.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train 360 m long is running at a speed of 42 km/hr. In what time will it pass a bridge 140 m long?\n\n### Options:\nA. 40 sec\nB. 29 sec\nC. 26 sec\nD. 27 sec\nE. 43 sec\n\n### Answer:\nSpeed = 42 * 5/18 = 35/3 m/sec\nTotal distance covered = 360 + 140 = 500 m\nRequired time = 500 * 3/35\n= 43 sec\nAnswer:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train crosses a platform of 150 m in 15 sec, same train crosses another platform of length 250 m in 20 sec. then find the length of the train?\n\n### Options:\nA. 150m\nB. 157m\nC. 750m\nD. 850m\nE. 350m\n\n### Answer:\nLength of the train be \u2018X\u2019\nX + 150/15 = X + 250/20\n4X + 600 = 3X + 750\nX = 150m\nAnswer:A:\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average weight of 49 students in a class is 52 kg. 5 of them whose average weight is 48 kg leave the class and other 5 students whose average weight is 54 kg join the class. What is the new average weight (in kg) of the class ?\n\n### Options:\nA. 51 1\u20443\nB. 52 30/49\nC. 52 1\u204449\nD. 43.42\nE. None of these\n\n### Answer:\nTotal weight of 49 students\n= 49 \u00d7 52 = 2548 kg\nTotal weight of 5 students who leave\n= 5 \u00d7 48 = 240 kg\nTotal weight of 5 students who join\n= 5 \u00d7 54 = 270 kg\nTherefore, new total weight of 49 students\n= 2548 \u2013 240 + 270 = 2578\n\u21d2 New average weight = 2578\u204449 = 52 30/49 kg\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf equation |x/2| + |y/2| = 1 encloses a certain region on the coordinate plane, what is the area of this region?\n\n### Options:\nA. 8\nB. 50\nC. 100\nD. 200\nE. 400\n\n### Answer:\nThe equation can be reduced to intercept form as |x/2| + |y/2| = 1, so these are lines in four quadrants with x and y intercept as 2, so it is a rhombus with diagonals of 4 each and hence area = 1/2*d1*d2 = 1/2*4*4= 8. Answer A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nBuses leave town B at 3 pm and every 10 hours after that. Buses leave town C at 4pm and every 15 hours after that. If the buses follow this schedule beginning on a Monday, what is the earliest day D on which the buses leave at the same time.\n\n### Options:\nA. D=Tuesday\nB. D=Wednesday\nC. Thursday\nD. Sunday\nE. D=The busses will never leave at the same time\n\n### Answer:\nThe answer is E.\nI think the best way to do it is to look at the times on a 24 hour clock. Town B busses start at 15:00, and Town C start at 16:00. If you think about it that way, then for Town B you'd add 10 hours each time, and the number will always end in a 5. Town C you'd add 15 hours each time, and the numbers would always end in a 1 or 6. So you can see they'd never coincide.\nAlternatively, you could see that if they left at the same time, they'd coincide every 30 hours, but since C is one hour ahead of B, every 30 hours C will still be one hour ahead of B.E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAt the end of year X, automobile installment credit accounted for 35% of all outstanding consumer installment credit. At that time automobile finance companies extended $40 billion of credit, or 1/3 of the automobile installment credit. How many billion dollars of consumer installment credit was outstanding at that time?\n\n### Options:\nA. 120\nB. 300\nC. 401.36\nD. 350.15\nE. 342.86\n\n### Answer:\nSystem of Equations\na = (35/100) c\n(1/3) a = 40 --> a = 120\nSubstitution\n120 = (35/100) c\nc = (100/35) 120\nAnswer\n- 120/35 * 100\nThe Correct Answer is E.\n- 342.86\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe present ages of three persons in proportions 5 : 6 : 4. Five years ago, the sum of their ages was 60. Find their present ages (in years).\n\n### Options:\nA. 8, 20, 28\nB. 16, 28, 36\nC. 25,30,20\nD. 18, 24, 32\nE. None of these\n\n### Answer:\nExplanation:\nLet their present ages be 5x, 6x and 4x years respectively.\nThen, (5x - 5) + (6x - 5) + (4x - 5) = 60\n15x-15 = 60\nx = 5\nTheir present ages are 5x = 25 years, 6x = 30 years and 4x = 20 years respectively.\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe rate of increase of the price of sugar is observed to be three percent more than the inflation rate expressed in percentage. The price of sugar, on January 1, 1994, is Rs. 25 per kg. The inflation rate for the years 1994 and 1995 are expected to be 12% each. The expected price of sugar on January 1, 1996 would be\n\n### Options:\nA. 33.06\nB. 34.1\nC. 34.2\nD. 24.6\nE. None of these\n\n### Answer:\nExplanation :\nIncrease in the price of sugar = (12+3)= 15%\nHence, price of the sugar on Jan 1, 1996\n=> (25 * 115 * 115)/( 100 * 100 ) = Rs 33.06.\nAnswer : A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSet S has a mean of 10 and a standard deviation of 1.5. We are going to add two additional numbers to Set S. Which pair of numbers would decrease the standard deviation the most?\n\n### Options:\nA. {2, 10}\nB. {9, 11}\nC. {10, 18}\nD. {7, 13}\nE. {16, 16}\n\n### Answer:\nanswer B,C, and E mean is not 10 therefore not accepted . D mean is 10 but S.D is more. therefore accepted\nanswer is B mean is 10 and S.D decreases minimum.\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA shopkeeper bought 600 oranges and 400 bananas. He found 15% of oranges and 5% of bananas were rotten. Find the percentage of fruits in good condition?\n\n### Options:\nA. 92.5%\nB. 89.0%\nC. 85.2%\nD. 96.8%\nE. 78.9%\n\n### Answer:\nTotal number of fruits shopkeeper bought = 600 + 400 = 1000\nNumber of rotten oranges = 15% of 600\n= 15/100 \u00d7 600\n= 9000/100\n= 90\nNumber of rotten bananas = 5% of 400\n= 20\nTherefore, total number of rotten fruits = 90 + 20= 110\nTherefore Number of fruits in good condition = 1000 - 110 = 890\nTherefore Percentage of fruits in good condition = (890/1000 \u00d7 100)%\n= (89000/1000)%\n= 89.0%\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nEach writer for the local newspaper is paid as follows: a dollars for each of the first z stories each month, and a + b dollars for each story thereafter, where a > b. How many more dollars will a writer who submits z + a stories in a month earn than a writer who submits z+ b stories?\n\n### Options:\nA. (a \u2013 b)( a + b + z)\nB. a \u2013 b\nC. a^2 \u2013 b^2\nD. z( a \u2013 b)\nE. az + bz \u2013 az\n\n### Answer:\ntotal earned for z+a stories =a + a(a+b)\ntotal earned for z+b stories =a+ b(a+b)\ndifference = a+a(a+b) -a -b(a+b)\n=(a+b)(a-b) =a^2-b^2\nanswer is C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA hiker walking at a constant rate of 4 miles per hour is passed by a cyclist travelling in the same direction along the same path at a constant rate of 16 miles per hour. the cyclist stopswaits for the hiker 5 min after passing her while the hiker continues to walk at her constant rate. how many minutes must the cyclist wait until the hiker catches up\n\n### Options:\nA. 6 2/3\nB. 15\nC. 20\nD. 25\nE. 26 2/3\n\n### Answer:\nHere is how I did it:\nThe cyclist travels 16 miles in 60 mins, so in 5 mins he will travel [(16*5)/60] miles, which equals 4/3 miles in 5 mins.\nNow the hiker travels 4 miles in 60 mins. To travel 4/3 miles, he will take [(60*4/3)/4] = 20 mins.\nhence 20-5=15 mins\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe length of a rectangular plot is 20 metres more than its breadth. If the cost of fencing the plot @ Rs. 26.50 per metre is Rs. 5300, what is the length of the plot in metres?\n\n### Options:\nA. 333\nB. 200\nC. 288\nD. 276\nE. 1999\n\n### Answer:\nLet length of plot = L meters, then breadth = L - 20 meters\nand perimeter = 2[L + L - 20] = [4L - 40] meters\n[4L - 40] * 26.50 = 5300\n[4L - 40] = 5300 / 26.50 = 200\n4L = 240\nL = 240/4= 60 meters.\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAfter decreasing 24% in the price of an article costs Rs.912. Find the actual cost of an article?\n\n### Options:\nA. 1218\nB. 2777\nC. 1200\nD. 2688\nE. 1991\n\n### Answer:\nCP* (76/100) = 912\nCP= 12 * 100 => CP = 1200\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf g and s are positive integers such that (2^g)(4^s) = 16, then 2g + s =\n\n### Options:\nA. 2\nB. 3\nC. 4\nD. 5\nE. 6\n\n### Answer:\nlets get the eq into simplest orm..\n(2^g)(4^s) = 16..\n(2^g)(2^2s) = 2^4..\nor g+2s=4..\nsince g and s are positive integers, only g as 2 and s as 1 satisfy the Equation..\nso 2g+s=2*2+1=5..\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA group of 55 adults and 70 children go for trekking. If there is meal for either 70 adults or 90 children and if 28 adults have their meal, find the total number of children that can be catered with the remaining food.\n\n### Options:\nA. 33\nB. 54\nC. 18\nD. 17\nE. 01\n\n### Answer:\nExplanation:\nAs there is meal for 70 adults and 28 have their meal, the meal left can be catered to 42 adults.\nNow, 70 adults = 90 children\n7 adults = 9 children\nTherefore, 42 adults = 54 children\nHence, the meal can be catered to 54 children.\nANSWER: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA room is 18 meters long, 15 meters wide 12 meters in height. The longest possible rod which can be placed in the room is\n\n### Options:\nA. 25.28 meters\nB. 24.28 meters\nC. 23.28 meters\nD. 26.28 meters\nE. 20.28 meters\n\n### Answer:\nSquare root of 18^2+15^2+12^2...(Diognal) which is square root of 639 that lies 25<\u221a639<26. Hence the answer should be A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJonathan\u2019s grandparents lend $10,000 to Jonathan at a simple annual interest rate of 10%. He pays them back 5 years later. How much do they receive?\n\n### Options:\nA. 10,000\u22170.1^5\nB. 10,000\u22170.5\nC. 10,000\u22171.5\nD. 10,000\u22171.1^5\nE. (10,000\u22170.1)^5\n\n### Answer:\nLet the principal be $1\nSo Interest for the $1 for 5 years at 10% Pa is -\n1\u22175\u221710/100 => 0.50\nNow Principal is $1 and Interest is $ 0.50 , so Amount to be returned is - $1 + $0.50 => $1.50\nSo, for $ 10,000 , amount to be returned is 10,000 * 1.50; Answer is (C)\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA pupil's marks were wrongly entered as 73 instead of 45. Due to that the average marks for the class got increased by half. The number of pupils in the class is :\n\n### Options:\nA. 56\nB. 80\nC. 20\nD. 25\nE. 26\n\n### Answer:\nLet there be x pupils in the class.\nTotal increase in marks = (X*1/2) = X/2.\nX/2 = (73 - 45)\n=> X/2 = 28\n=> X = 56.\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf X is the sum of first 50 positive even integers and Y is the sum of first 50 positive odd integers, what is the value of x-y?\n\n### Options:\nA. 0\nB. 25\nC. 50\nD. 75\nE. 100\n\n### Answer:\nFirst even minus first odd = 2-1 = 1;\nThe sum of first 2 even integers minus the sum of first 2 odd integers = (2+4)-(1+3) = 2;\nThe sum of first 3 even integers minus the sum of first 3 odd integers = (2+4+6)-(1+3+5) = 3;\n...\nWe can see the patterns here, so the sum of first 50 positive even integers minus the sum of first 50 positive odd integers will be 50.\nAnswer: C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe moon revolves around the earth at a speed of approximately 1.05 kilometers per second. This approximate speed is how many kilometers per hour?\n\n### Options:\nA. 60\nB. 61.2\nC. 62.5\nD. 3,780\nE. 3,672\n\n### Answer:\nmoon revolves around the earth at a speed of 1.02kilometers per second.\none hour equal to 60 minutes.\none minute equals to 60 seconds. so one hour equals to 3600seconds.\nso one hour, speed= 1.05*3600=3780kilometers per hour.\nOption D is correct\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe ages of two persons differ by 16 years. 6 years ago, the elder one was 3 times as old as the younger\none. What are their present ages of the elder person\n\n### Options:\nA. 15\nB. 20\nC. 25\nD. 30\nE. 35\n\n### Answer:\nExplanation:\nLet's take the present age of the elder person = x\nand the present age of the younger person = x \ufffd 16\n(x \ufffd 6) = 3 (x-16-6)\n=> x \ufffd 6 = 3x \ufffd 66\n=> 2x = 60\n=> x = 60/2 = 30\nAnswer: Option D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n80 is what percent of 40?\n.\n\n### Options:\nA. 0.2%\nB. 2%\nC. 200%\nD. 20%\nE. 500%\n\n### Answer:\n80= x*40/100\nx = 200%\nAns; C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man saves 20% of his monthly salary. If an account of dearness of things he is to increase his monthly expenses by 20%, he is only able to save Rs. 250 per month. What is his monthly salary?\n\n### Options:\nA. 5000\nB. 2999\nC. 2878\nD. 6250\nE. 2771\n\n### Answer:\nIncome = Rs. 100\nExpenditure = Rs. 80\nSavings = Rs. 20\nPresent Expenditure 80*(20/100) = Rs. 96\nPresent Savings = 100 \u00e2\u20ac\u201c 96 =Rs. 4\n100 ------ 4\n? --------- 250 => 6250\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA semicircle has a radius of 9. What is the approximate perimeter of the semicircle?\n\n### Options:\nA. 16\nB. 25\nC. 33\nD. 46\nE. 58\n\n### Answer:\nThe perimeter of a circle is 2*pi*r.\nThe perimeter of a semicircle is 2*pi*r/2 + 2r = pi*r + 2r\nThe perimeter is pi*9 + 2*9 which is about 46.\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo trains of equal length, running with the speeds of 60 and 40 kmph, take 36 seconds to cross each other while they are running in the same direction. What time will they take to cross each other if they are running in opposite directions?\n\n### Options:\nA. 10 sec\nB. 16 sec\nC. 19 sec\nD. 7.2 sec\nE. 13 sec\n\n### Answer:\nRS = 60 -40 = 20 * 5/18 = 100/18\nT = 36\nD = 36 * 100/18 = 200\nRS = 60 + 40 = 100 * 5/18\nT = 200 * 18/500 = 7.2 sec\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA building contractor employs 20 male, 15 female and 5 child workers. To a male worker he pays Rs.25 per day, to a female worker Rs.20 per day and a child worker Rs.8 per day. The average wage per day paid by the contractor is?\n\n### Options:\nA. 24\nB. 21\nC. 20\nD. 22\nE. 25\n\n### Answer:\n20 15 5\n25 20 8\n500 + 300 + 40 = 840/40 = 21\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average age of a class of 32 students is 16 yrs. if the teacher's age is also included, the average increases by one year. Find the age of the teacher\n\n### Options:\nA. 49 Years\nB. 51 Years\nC. 53 Years\nD. 54 Years\nE. 55 Years\n\n### Answer:\nTotal age of students is 32X16 = 512 Years\nTotal age inclusive of teacher = 33X (16+1) = 561\nSo, Teacher's age is 561-512 = 49 Yrs\nThere is a shortcut for these type of problems\nTeacher's age is 16+(33X1) = 49 Years\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJanuary 1, 2004 was a Thursday, what day of the week lies on January 1 2005.\n\n### Options:\nA. Saturday\nB. Monday\nC. Saturday\nD. Tuesday\nE. Wednesday\n\n### Answer:\nExplanation:\nGiven that January 1, 2004 was Thursday.\nOdd days in 2004 = 2 (because 2004 is a leap year)\n(Also note that we have taken the complete year 2004 because we need to find out the odd days from 01-Jan-2004 to 31-Dec-2004, that is the whole year 2004)\nHence January 1, 2005 = (Thursday + 2 odd days) = Saturday\nAnswer: Option C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn order to obtain an income of Rs. 650 from 10% stock at Rs. 96, one must make an investment of\n\n### Options:\nA. 3100\nB. 6220\nC. 6210\nD. 6240\nE. 6670\n\n### Answer:\nMarket Value = Rs. 96.\nRequired Income = Rs. 650.\nHere face value is not given. Take face value as Rs.100 if it is not given in the question\nTo obtain Rs.10 (ie,10% of the face value 100), investment = Rs.96\nTo obtain Rs.650, investment = 96/10\u00d7650=6240\nAnswer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA boy has 9 trousers and 15 shirts. In how many different ways can he select a trouser and a shirt?\n\n### Options:\nA. 100\nB. 140\nC. 104\nD. 135\nE. 125\n\n### Answer:\nThe boy can select one trouser in nine ways.\nThe boy can select one shirt in 12 ways.\nThe number of ways in which he can select one trouser and one shirt is 9 * 15 = 135 ways.\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFor dinner at a restaurant, there are x + 1 choices of appetizers, y + 1 main courses, and z choices of dessert. How many total possible choices are there if you choose 1 appetizer, 1 main course, and 1 dessert for your meal?\n\n### Options:\nA. x + y + z + 1\nB. xyz + xz\nC. xyz+xz+yz+z\nD. xyz + 1\nE. xyz + 1/2\n\n### Answer:\nx +1 appetizers,\ny + 1 main courses,\nz dessert\nRequired: 1 appetizer, 1 main course, and 1 dessert\nNumber of ways possible = (x+1)C1*(y+1)C1*zC1 {NC1 = N! / (N-1)!*1! = N}\nHence, number of ways = (x+1)(y+1)z = (yz+z)(x+1)=xyz+xz+yz+z\nCorrect Option: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA box contains 100 balls, numbered from 1 to 100. If three balls are selected at random and with replacement from the box, what is the probability K that the sum of the three numbers on the balls selected from the box will be odd?\n\n### Options:\nA. 1/4\nB. 3/8\nC. 1/2\nD. 5/8\nE. 3/4\n\n### Answer:\nThe sum of the three numbers on the balls selected from the box to be odd one should select either three odd numbered balls (Odd+Odd+Odd=Odd) or two even numbered balls and one odd numbered ball (Even+Even+Odd=Odd);\nP(OOO)=(1/2)^3;\nP(EEO)=3*(1/2)^2*1/2=3/8 (you should multiply by 3 as the scenario of two even numbered balls and one odd numbered ball can occur in 3 different ways: EEO, EOE, or OEE);\nSo finally K=1/8+3/8=1/2.\nAnswer: C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the third proportional to 3 and 9?\n\n### Options:\nA. 10\nB. 12\nC. 27\nD. 19\nE. 20\n\n### Answer:\nFormula = Third proportional = (b \u00d7 b)/a\nA = 3 and B = 9\n(9 x 9)/ 3 = 81/3 = 27\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOn a certain day, orangeade was made by mixing a certain amount of orange juice with an equal amount of water. On the next day, orangeade was made by mixing the same amount of orange juice with twice the amount of water. On both days, all the orangeade that was made was sold. If the revenue from selling the orangeade was the same for both days and if the orangeade was sold at $0.48 per glass on the first day, what was the price per glass on the second day?\n\n### Options:\nA. $015\nB. $0.20\nC. $0.30\nD. $0.32\nE. $0.45\n\n### Answer:\nOn the first day 1 unit of orange juice and 1 unit of water was used to make 2 units of orangeade;\nOn the second day 1 unit of orange juice and 2 units of water was used to make 3 units of orangeade;\nSo, the ratio of the amount of orangeade made on the first day to the amount of orangeade made on the second day is 2 to 3. Naturally the ratio of the # of glasses of orangeade made on the first day to the # of glasses of orangeade made on the second day is 2 to 3.\nWe are told thatthe revenue from selling the orangeade was the same for both daysso the revenue from 2 glasses on the first day equals to the revenue from 3 glasses on the second day.\nSay the price of the glass of the orangeade on the second day was $x then 2*0.48=3*x --> x=$0.32.\nAnswer: D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn order to obtain an income of Rs. 900 from 20% stock at Rs. 102, one must make an investment of\n\n### Options:\nA. Rs.6000\nB. Rs.4590\nC. Rs.4560\nD. Rs.4500\nE. Rs.4570\n\n### Answer:\nExplanation :\nMarket Value = Rs. 102.\nRequired Income = Rs. 900.\nHere face value is not given. Take face value as Rs.100 if it is not given in the question\nTo obtain Rs.20(ie,20% of the face value 100), investment = Rs.102\nTo obtain Rs.900, investment = 102/20\u00c3\u2014900=Rs.4590\nAnswer : Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf p and q are prime numbers, how many divisors does the product p^3 * q^6 have?\n\n### Options:\nA. 9\nB. 12\nC. 18\nD. 28\nE. 36\n\n### Answer:\nLets take an example: find the number of factors of 100\ntry to represent 100 in least possible prime numbers\n100= 2^2 * 5^2=p^a*q^b\nno of factors is given by the formula (a+1)* (b+1)=(2+1)(2+1)=9\nsimilarly find the number of factors of p^3 * q^6--->a=3,b=6\n(3+1)(6+1)=28 Ans D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man divides $6800 Among 4 Sons, 4 Daughters and 2 Nephews. If each daughter receives four times as much as each nephews and each son receives five times as much as each nephews, how much does each daughter receive?\n\n### Options:\nA. A)$200\nB. B)$1000\nC. C)$800\nD. D)$1200\nE. E)$400\n\n### Answer:\nLet the share of each nephews be $X.\nThen, share of each daughter=$4X, share of each son= $5X.\nSo, 4*4X+4*4X+2*X=6800\n16X+16X+2X=8600\n34X=6800, X=200.\nDaughter receives four times of nephew so 4 * 200 = 800.\nSo Each Daughter receives $800. answer is option C) $800.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n40% of Ram's marks is equal to 20% of Rahim's marks which percent is equal to 30% of Robert's marks. If Robert's marks is 80, then find the average marks of Ram and Rahim?\n\n### Options:\nA. 93\nB. 77\nC. 68\nD. 90\nE. 62\n\n### Answer:\nGiven, 40% of Ram's marks = 20% of Rahim's marks = 30% of Robert's marks.\nGiven, marks of Robert = 80\n30% of 80 = 30/100 * 8 = 24\nGiven, 40% of Ram's marks = 24.\n=> Ram's marks = (24 * 100)/40 = 60\nAlso, 20% of Rahim's marks = 24\n=> Rahim's marks = (24 * 100)/20 = 120\nAverage marks of Ram and Rahim = (60 + 120)/2 = 90.\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAndrew has a certain number of coins in his pocket. He has three times as many dimes as quarters and six times as many nickels as dimes. A nickel is worth $0.05, a dime is worth $0.10 and a quarter is worth $0.25. If he has a total of $10.15, then which of the following represents the number of dimes in Nickles\u2019s pocket?\n\n### Options:\nA. 9\nB. 10\nC. 18\nD. 112\nE. 116\n\n### Answer:\nE.\nLet number of quarters be q. Therefore , dimes are 3q and nickels are 18q.\nTotal value = 18q(.05) + 3q(0.1) + .25q =1.45q\nGiven total value = 10.15\ntherefore, 1.45q=10.15 or q=7\nNumber of dimes = 18q or 116\nAnswer : E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nLine Q has the equation 5y \u2013 3x = 30. If Line S is perpendicular to Q, has an integer for its y-intercept, and intersects Q in the second quadrant, then how many possible Line S\u2019s exist? (Note: Intersections on one of the axes do not count.)\n\n### Options:\nA. 22\nB. 33\nC. 36\nD. 41\nE. 58\n\n### Answer:\n5y - 3x = 30 and so y = 3x/5 + 6\nWhen x = 0, then y = 6.\nWhen y = 0, then x = -10\nThe slope is 3/5, so the slope of line S is -5/3.\nThrough the point (-10, 0), 0 = -5(-10)/3 + c\nThe y-intercept is c = -50/3 < -16.\nThus the perpendicular line S can have y-intercepts from -16 up to 5.\nThe number of possible lines is 16 + 5 + 1 = 22\nThe answer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a cricket match, five batsmen A, B, C, D and E scored an average of 36 runs. D Scored 5 more than E; E scored 8 fewer than A; B scored as many as D and E combined; and B and C scored 107 between them. How many runs did E score ?\n\n### Options:\nA. 62\nB. 45\nC. 28\nD. 20\nE. 25\n\n### Answer:\nExplanation:\nTotal runs scored = (36 x 5) = 180.\nLet the runs scored by E be x.\nThen, runs scored by D = x + 5; runs scored by A = x + 8;\nruns scored by B = x + x + 5 = 2x + 5;\nruns scored by C = (107 - B) = 107 - (2x + 5) = 102 - 2x.\nSo, total runs = (x + 8) + (2x + 5) + (102 - 2x) + (x + 5) + x = 3x + 120.\nTherefore 3x + 120 =180 3X = 60 x = 20.\nAnswer: Option D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA boatman can row 96 km downstream in 8 hr. If the speed of the current is 4 km/hr, then find in what time he will be able to cover 8 km upstream ?\n\n### Options:\nA. 3 hrs\nB. 7 hrs\nC. 9 hrs\nD. 2 hrs\nE. 6 hrs\n\n### Answer:\nExplanation:\nSpeed in downstream = 96/8 = 12 kmph\nSpeed of current = 4 km/hr\nSpeed of the boatman in still water = 12 \u00e2\u20ac\u201c 4 = 8 kmph\nSpeed in upstream = 8 \u00e2\u20ac\u201c 4 = 4 kmph\nTime taken to cover 8 km upstream = 8/4 = 2 hours.\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf two students are made to sit in a row, then 6 don't have seats. If 6 students are made to sit in a row, then three rows are empty. How many students have to sit a row such that each row has equal number of students and all students are seated?\n\n### Options:\nA. 0\nB. 3\nC. 4\nD. 5\nE. 9\n\n### Answer:\nLet there be a rows.\nThen 2a + 6 = 6(a-3) [equating the number of students]\n=> a= 6\nand total number of students = 18\nTherefore 3 students much sit in each row such that each row has an equal number of students and all students are seated.\nOption (B)\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo people measure each other's height, the height of the taller person is H and the height of the other person is L. If the difference in their heights is equal to the average height, what is the Value of H/L\n\n### Options:\nA. 1/3.\nB. 1/2.\nC. 2.\nD. 3.\nE. 6.\n\n### Answer:\nDifference = Average\nH - L = (H + L)/2,\nSolving for H/L gives 3. A quick check, H be 21 and L be 7, 21- 7= (21 + 7 )/2\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf b is an integer greater than 6, which of the following must be divisible by 3?\n\n### Options:\nA. b (b+3) (b-5)\nB. b (b+2) (b-1)\nC. b (b+1) (b-4)\nD. b (b+4) (b-2)\nE. b (b+5) (b-6)\n\n### Answer:\nanything in the form of (b-1) (b) (b+1) is divisible by 3. in other word, a product of any 3 consecutive intevers is divisible by 3.\nb (b+1) (b-4) = b (b+1) ((b-1)-3) is equivalant to (b-1) (b) (b+1)\nb (b+2) (b-1) is equivalant to (b+1) missing.\nb (b+3) (b-5) is equivalant to (b-1) missing and b repeating.\nb (b+4) (b-2) is equivalant to odd/even consqcutive integers\nb (b+5) (b-6) is equivalant to (b+1) missing and b repeating.\nAnswer : C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a and b are positive integers of Y such that a/b=2.86, which of the following must be a divisor of a?\n\n### Options:\nA. 10\nB. B.13\nC. 18\nD. 26\nE. 50\n\n### Answer:\nThe prompt gives us a couple of facts to work with:\n1) A and B are positive INTEGERS\n2) A/B = 2.86\nWe can use these facts to figure out POSSIBLE values of A and B. The prompt asks us for what MUST be a divisor of A. Since we're dealing with a fraction, A and B could be an infinite number of different integers, so we have to make both as SMALL as possible; in doing so, we'll be able to find the divisors that ALWAYS divide in (and eliminate the divisors that only SOMETIMES divide in).\nThe simplest place to start is with...\nA = 286\nB = 100\n286/100 = 2.86\nThese values are NOT the smallest possible values though (since they're both even, we can divide both by 2)...\nA = 143\nB = 50\n143/50 = 2.86\nThere is no other way to reduce this fraction, so A must be a multiple of 143 and B must be an equivalent multiple of 50. At this point though, the value of B is irrelevant to the question. We're asked for what MUST divide into A....\nSince A is a multiple of 143, we have to 'factor-down' 143. This gives us (11)(13). So BOTH of those integers MUST be factors of A. You'll find the match in the answer choices.\nFinal Answer:\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo trains of length 90 m and 100 m are 200 m apart. They start moving towards each other on parallel tracks, at speeds 71 kmph and 89 kmph. After how much time will the trains meet?\n\n### Options:\nA. 47/10\nB. 46/10\nC. 45/10\nD. 42/10\nE. 43/10\n\n### Answer:\nThey are moving in opposite directions, relative speed is equal to the sum of their speeds.\nRelative speed = (71 + 89)*5/18 = 44.4mps.\nThe time required = d/s = 200/44.4= 45/10 sec.\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nif f(f(X))=81. then. value of x=?\nwhen f(X)=2X-1+f(X-1). is not equal to zero and f(X=0)=0\n\n### Options:\nA. 2\nB. 3\nC. 4\nD. 5\nE. 6\n\n### Answer:\nf(X=0) = 0\nf(X=1) = 2*1-1+f(1-1)\n= 2-1+0\n= 1\nf(X=2) = 2*2-1+f(2-1)\n= 4-1+1\n= 4\nf(X=3) = 2*3-1+f(3-1)\n= 6-1+4\n= 9\n===>f(X=n) = n^2\nf(f(X)) = 81\nX = sqrt(sqrt(81)) = 3\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n50% of Ram's marks is equal to 20% of Rahim's marks which percent is equal to 30% of Robert's marks. If Robert's marks is 80, then find the average marks of Ram and Rahim?\n\n### Options:\nA. 70\nB. 97\nC. 84\nD. 90\nE. 76\n\n### Answer:\nGiven, 50% of Ram's marks = 20% of Rahim's marks = 30% of Robert's marks.\nGiven, marks of Robert = 80\n30% of 80 = 30/100 * 8 = 24\nGiven, 50% of Ram's marks = 24.\n=> Ram's marks = (24 * 100)/50 =48\nAlso, 20% of Rahim's marks = 24\n=> Rahim's marks = (24 * 100)/20 = 120\nAverage marks of Ram and Rahim = (48 + 120)/2 = 84.\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe positive number a is q percent greater than the positive number b, which is l percent less than a itself. If a is increased by l percent, and the result is then decreased by q percent to produce a positive number c, which of the following could be true?\nI. c > a\nII. c = a\nIII. c < a\n\n### Options:\nA. I only\nB. II only\nC. III only\nD. I and II only\nE. II and III only\n\n### Answer:\nLet q = 10% then l = 100/11 %\nlet b = 100 then a = 110\nafter increasing a by l and decreasing b yq we get c= 108\ntherefore c", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 34 men completed 2/5th of a work in 8 days working 9 hours a day. How many more man should be engaged to finish the rest of the work in 6 days working 9 hours a day?\n\n### Options:\nA. 100\nB. 102\nC. 104\nD. 106\nE. 108\n\n### Answer:\nUsing the chain rule,\nM1 x T1 = M2 x T2\nThus, (34 x 8 x 9) / 2/5 = (M2 x 6 x 9) / 3/5\nM2 = 68.\nTherefore, required number of men = (68 + 34) = 102\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n20 people with two sisters among them want to sit around a round table such that the two sisters are exactly separated by one person sitting in between them. Find the probability.\n\n### Options:\nA. 1/19\nB. 2/29\nC. 3/29\nD. 4/29\nE. 5/29\n\n### Answer:\n20 people in which 2 sisters are there and the condition is that 2 sisters should be seperated by 1 person\n(s1 p s2) be 1 set\nthen 20-3 persons => 17 persons + 1 set= 18\n18 can be arranged in 17! ways bcz it is circular permutuation\nthe 2 sis can be arranged in 2! ways\nand the p place can be filled in 18 ways\nand the total permutations are 19!\nprobability is = (2!*18*17!)/(19!)\n= 2/19\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf x = y^2, and x and y are positive integers, which of the following numbers could be the value of x?\n\n### Options:\nA. 9,827\nB. 10,816\nC. 11,433\nD. 12,908\nE. 13,482\n\n### Answer:\nThe square of an integer can have a units digit of 0, 1, 4, 5, 6, or 9.\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhen running a mile during a recent track meet, Nuria was initially credited with a final time of 4 minutes, 44 seconds. Shortly after her run, officials realized that the timing mechanism malfunctioned. The stopwatch did not begin timing her until 11/25 of a minute after she began to run. If the time was otherwise correct, how long did it actually take Nuria to run the mile?\n\n### Options:\nA. 4 minutes, 17.6 seconds\nB. 4 minutes, 21.8 seconds\nC. 4 minutes, 43.56 seconds\nD. 5 minutes, 10.4 seconds\nE. 4 minutes, 44.44 seconds\n\n### Answer:\nOne approach:\nThe watch starts to work after Nuria began his running. It means the time should be greater than credited 4 minutes, 44 seconds. The only number is 5 minutes, 10.4 seconds.\nAnother approach:\n11/25 close to 30 second when added to the 4 minutes, 44 seconds, it means it passes 5 minute.\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe ratio of boys to girls in Class A is 3 to 4. The ratio of boys to girls in Class B is 4 to 6. If the two classes were combined, the ratio of boys to girls in the combined class would be 17 to 22. If Class A has one more boy and two more girls than class B, how many girls are in Class A?\n\n### Options:\nA. 8\nB. 9\nC. 10\nD. 11\nE. 12\n\n### Answer:\nSince it is given that the ratio of boys to girls in Class A is 3 to 4 - so we can quickly eliminate the answer choices which are not multiples of 4.\nso ans can either be 8 0r 12.\nWith 8 as answer - no of girls = 8\nWith 12 as answer - no of girls = 12\nNow Class A has one more boy and two more girls than class B and also the ratio of boys to girls in Class B is 4 to 5.\nSo we are looking for number of girls in B to be divisible by 5.\nWith 8 as answer -> Girls = 8-2 = 6. (Not possible)\nWith 12 as answer -> Girls = 12-2 = 5.\nSo, answer = 11. ( D)\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain lab experiments with white and brown mice only. In one experiment, 2/3 of the mice are white. If there are 7 brown mice in the experiment, how many mice in total are in the experiment?\n\n### Options:\nA. 39\nB. 33\nC. 26\nD. 21\nE. 10\n\n### Answer:\nLet total number of mice = M\nNumber of white mice = 2/3 M\nNumber of brown mice = 1/3 M = 7\n=> M = 21\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA thief goes away with a SANTRO car at a speed of 40 kmph. The theft has been discovered after half an hour and the owner sets off in a bike at 50 kmph when will the owner over take the thief from the start?\n\n### Options:\nA. 2\nB. 5\nC. 7\nD. 5\nE. 8\n\n### Answer:\nExplanation:\n|-----------20--------------------|\n50 40\nD = 20\nRS = 50 \u2013 40 = 10\nT = 20/10 = 2 hours\nAnswer: Option A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average weight of a class of 24 students is 35 kg. If the weight of the teacher be included, the average rises by 400 g. The weight of the teacher is\n\n### Options:\nA. 45\nB. 50\nC. 55\nD. 60\nE. 65\n\n### Answer:\nOption A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA carton contains 25 bulbs, 8 of which are defective. What is the probability that if a sample of 4 bulbs is chosen, exactly 2 of them will be defective ?\n\n### Options:\nA. (8/25) x (7/24) x (17/23) x (16/22)\nB. (4C2) x (8/25) x (7/24) x (17/23) x (16/22)\nC. (8/26) x (8/24) x (17/33) x (16/22)\nD. None of these\nE. Cannot be determined\n\n### Answer:\nExplanation :\nThe probability that exactly two bulbs are defective and exactly two are not defective will be given by\n(4C2) x (8/25) x (7/24) x (17/23) x (16/22)\nAnswer : B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA and B are two circles. The radius of A is four times as large as the diameter of B. What is the ratio between the areas of the circles?\n\n### Options:\nA. 1:8.\nB. 1:2.\nC. 1:24.\nD. 1:64.\nE. 1:6.\n\n### Answer:\nGiven : The radius of A is 4 times as large as the diameter of B. => R(a) = 4*D(b) = 4*2*R(b) = 8R(b). The radius are in ratio of 1:8 thus the area will be in the ratio of square of radius. 1:64. Hence D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 4 men can colour 48 m long cloth in 2 days, then 8 men can colour 36 m long cloth in\n\n### Options:\nA. 0.75 day\nB. 2 days\nC. 1.2 days\nD. 4 days\nE. 5 days\n\n### Answer:\nThe length of cloth painted by one man in one day = 48 / 4 \u00d7 2 = 6 m\nNo. of days required to paint 36 m cloth by 6 men = 36/ 6 \u00d7 8 = 0.75 day.\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA and B invests Rs.3000 and Rs.4000 respectively in a business. If A doubles his capital after 6 months. In what ratio should A and B divide that year's profit?\n\n### Options:\nA. 8:8\nB. 9:8\nC. 9:9\nD. 9:5\nE. 9:1\n\n### Answer:\n(3*6 + 6*6): (4*12)\n54:48 => 9:8\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA and B entered into a partnership investing Rs.25000 and Rs.30000 respectively. After 4 months C also joined the business with an investment of Rs.35000. What is the share of C in an annual profit of Rs.47000?\n\n### Options:\nA. 1687\nB. 1478\nC. 1480\nD. 14000\nE. 1500\n\n### Answer:\n25*12: 30*12: 35*8\n15:18:14\n14/47 * 47000 = 14000\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA number of 47 marbles is to be divided and contain with boxes. If each box is to contain 3, 4, or 5 marbles, what is the largest possible number of boxes?\n\n### Options:\nA. 10\nB. 12\nC. 15\nD. 16\nE. 17\n\n### Answer:\nTo maximize # of boxes we should minimize marbles per box: 14*3+1*5=47 --> 14+1=15.\nAnswer: C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man has some hens and cows. If the number of heads be 46 and the number of feet equals 140, then the number of hens will be:\n\n### Options:\nA. 22\nB. 23\nC. 24\nD. 26\nE. 28\n\n### Answer:\nlet hens be x and cows be y\nnow,\nfeet: x*2+y*4=140\nheads: x*1+y*1=46\nimplies, 2x+4y=140 and x+y=46\nsolving these two equations, we get x=22 and y=24\nTherefore, hens are 22.\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the 28th digit to the right of the decimal point in the decimal form of 4/11?\n\n### Options:\nA. 3\nB. 4\nC. 5\nD. 6\nE. 7\n\n### Answer:\n4/11 = 0.363636...\nThe even numbered positions in the decimal expansion are all 6.\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n60 boys can complete a work in 40 days.how many men need to complete twice the work in 20 days\n\n### Options:\nA. 160\nB. 170\nC. 180\nD. 190\nE. 240\n\n### Answer:\none man can complete the work in 40*60=2400 days = one time work\nto Complete the work twice it will be completed in\nlet M be the no. of worker assign for this therefore the eqn becomes\nM*20=2*2400\nM=240 workers\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIt takes one machine to paint 1000 sq.m. surface in 24 minutes.Another machine does the same job in 40 seconds.How much time will it take if both machines are put on the same work?\n\n### Options:\nA. 10.0 seconds\nB. 20.0 seconds\nC. 38.9 seconds\nD. 40.0 seconds\nE. 52.0 seconds\n\n### Answer:\nBy guess it is clear that the time taken will be less than 40 seconds and very near to it. Therefore, answer 38.9 seconds will be correct. Answer-C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nLast year 26 members of a certain club traveled to England, 26 members traveled to France, and 32 members traveled to Italy. Last year 6 members of the club traveled to both England and France, no members traveled to both England and Italy, and 11 members traveled to both France and Italy. How many members of the club traveled to at least one of these three countries last year?\n\n### Options:\nA. 52\nB. 71\nC. 67\nD. 73\nE. 79\n\n### Answer:\nn(E or F or I) = n(E) + n(F) + n(I) - n(E and F) - n(F and I) - n(I and E) +n(E and F and I)\nn(E or F or I) = 26 + 26 + 32 - 6 - 11 - 0 + 0\nWhy is the number of people who traveled to E and F and I 0? Because no one traveled to both England and France. So obviously, no one would have traveled to England, France and Italy.\nn(E or F or I) = 67\nAnswer (C)\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRam professes to sell his goods at the cost price but he made use of 800 grms instead of a kg, what is the gain percent?\n\n### Options:\nA. 25%\nB. 11 1/8%\nC. 11 9/9%\nD. 11 5/9%\nE. 11 1/5%\n\n### Answer:\n800 --- 200\n100 --- ? => 25%\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many of the following numbers are divisible by 132?\n264, 396, 462, 792, 968, 2178, 5184, 6336,528,1320\n\n### Options:\nA. 4\nB. 5\nC. 6\nD. 7\nE. 8\n\n### Answer:\nExplanation:\nA number is divisible by 132, if it is divisible by each one of 11, 3 and 4.\nClearly, 968 is not divisible by 3. None of 462 and 2178 is divisible by 4.\nAlso, 5184 is not divisible by 11.\nEach one of remaining 6 is divisible by each one of 11, 3 and 4 and therefore, by 132.\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA customer pays 50 dollars for a coffee maker after a discount of 20 dollars\nWhat is the original price of the coffe maker?\n\n### Options:\nA. $50\nB. $60\nC. $70\nD. $80\nE. $90\n\n### Answer:\nLet x be the original price.\nx - 20 = 50\nx - 20 + 20 = 50 + 20\nx + 0 = 70\nx = 70\ncorrect answer is C)$70\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the radius of a circle is decreased 30%, what happens to the area?\n\n### Options:\nA. 51% decrease\nB. 20% decrease\nC. 36% decrease\nD. 40% decrease\nE. 50% decrease\n\n### Answer:\nArea of Square = Pi* radius^2\nNew Radius = 0.7 * old radius\nso new area = (0.7)^2 old area => 0.49 of old area => 49% old area\nAns : A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf two sides of a triangle have lengths 1 and 5, which of the following could be the perimeter of the triangle?\nI. 9\nII. 15\nIII. 19\n\n### Options:\nA. None\nB. I only\nC. II only\nD. II and III only\nE. I, II, and III\n\n### Answer:\nThe length of any side of a triangle must be larger than the positive difference of the other two sides, but smaller than the sum of the other two sides.\nTherefore:\n(5-1) < {third side} < (5+1).\n4 < {third side} < 6.\nPerimeter = {third side} + 1 + 5 = {third side} + 6.\n10 < {perimeter} < 12.\nanswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf m=9^(x\u22121), then in terms of m, 3^(4x\u22122) must be which of the following?\n\n### Options:\nA. m/3\nB. 9m\nC. 9m^2\nD. m^2/3\nE. m^2/9\n\n### Answer:\n3(4x\u22122)=3^2(2x\u22121)=9(2x\u22121)=9\u22179(2x\u22122)=9\u2217(9(x\u22121))2=9m\nAnswer: C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIt takes 40 identical printing presses 15 hours to print 500,000 papers. How many hours would it take 30 of these printing presses to print 500,000 papers?\n\n### Options:\nA. 16\nB. 18\nC. 20\nD. 21\nE. 24\n\n### Answer:\n40 printing presses can do 1/15 of the job each hour.\n30 printing presses can do 3/4*1/15 = 1/20 of the job each hour.\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA circle graph shows how the MegaTech corporation allocates its Research and Development budget: 12% microphotonics; 24% home electronics; 15% food additives; 29% genetically modified microorganisms; 8% industrial lubricants; and the remainder for basic astrophysics. If the arc of each sector of the graph is proportional to the percentage of the budget it represents, how many degrees of the circle are used to represent basic astrophysics research?\n\n### Options:\nA. 43\u00b0\nB. 10\u00b0\nC. 18\u00b0\nD. 36\u00b0\nE. 52\u00b0\n\n### Answer:\nHere all percentage when summed we need to get 100% . As per data 12+24+15+29+8 = 88%.\nSo remaining 12% is the balance for the astrophysics.\nSince this is a circle all percentage must be equal to 360 degrees.\n100% ---- 360 degrees\nThen 12% will be 43 degrees..\nIMO option A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo out of ten employees are capable of doing a certain task. Sixty percent of the five employees, including the two who are capable, are assigned to a project involving this task. what percentage of employees assigned to the project are not capable?\n\n### Options:\nA. 43.33%\nB. 66.66%\nC. 13.33%\nD. 38.33%\nE. 23.33%\n\n### Answer:\nGiven 60% of 10 employees including 2 who are capable of doing task.\n60% of 10 employeees\n= 60/100 * 10\n= 6 employees\n===> 2 employees who are capable of doing the task and four employee who is not capable.\npercentage of employees assigned who are not capable\n= 4/6 * 100\n= 66.66%\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man ran 20 miles in 2 hours 2 minutes. What was the average speed of the man in miles per hour?\n\n### Options:\nA. 9.72 miles / hour\nB. 9.73 miles / hour\nC. 9.75 miles / hour\nD. 9.78 miles / hour\nE. 9.79 miles / hour\n\n### Answer:\nWe first convert the time of 2 hours 2 minutes in minutes\n2 hours 2 minutes = 2* 60 + 2 = 122 minutes\nAverage speed S is given by distance / time. Hence\nS = 20 miles / 122 minutes = 0.163mile / minute\n= 9.78 miles / hour\ncorrect answer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nwhich of the following could be the greatest common factor of positive integers 10 and 15 ? I) 5 II) 4 III) 2\n\n### Options:\nA. II only\nB. I only\nC. III only\nD. I,II only\nE. I,III only\n\n### Answer:\n10=2*5\n15=3*5\nGCF =5\nAnswer : B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA 70 cm long wire is to be cut into two pieces so that one piece will be 2/5th of the other, how many centimeters will the shorter piece be?\n\n### Options:\nA. 10\nB. 20\nC. 30\nD. 40\nE. 50\n\n### Answer:\n1: 2/5 = 5: 2\n2/7 * 70 = 20\nANSWER B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a room are five chairs to accommodate 3 people, one person to a chair. How many seating arrangements are possible?\n\n### Options:\nA. 45\nB. 60\nC. 72\nD. 90\nE. 120\n\n### Answer:\nI actually solved this problem by the following thoughts (derived from factorials):\nFirst Person: 5 Chairs to choose\nSecond Person: 4 Chairs to choose\nThird Person: 3 Chairs to choose\nThen I simply multiplied this values and got the answer. Basically it\u2019s 5! \u2013 2!.=60\nAnswer: B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nif the price of a book is first decreased by 30% and then increased by 20%, then the net change in the price will be :\n\n### Options:\nA. 10\nB. 16\nC. 37\nD. 29\nE. 22\n\n### Answer:\nExplanation:\nLet the original price be Rs. 100.\nDecreased by 30% = 70\nThen increased 20% on Rs 70 = 70 + 14 = 84\nNet change in price = 100 - 84 = 16\nAnswer : B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a family with 3 children, the parents have agreed to bring the children to the pet store and allow each child to choose a pet. This pet store sells only dogs, cats, and monkeys. If each child chooses exactly one animal, and if more than one child can choose the same kind of animal, how many different arrangements of animals could the family leave with?\n\n### Options:\nA. 6\nB. 8\nC. 9\nD. 10\nE. 12\n\n### Answer:\nThe question has a catch.. It would seem on the face of it it would be 3 x 3 x3 = 27 arrangements, but what it is asking is how many arrangements the family leaves with.. so that is going to be\nPick all 3 = 1 way\nPick all of a kind = 3 x 1 = 3 ways\nPick 2 of a kind = 3 x 1 x 2 = 6 ways\nTotal of 10\nANS:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the percentage gain if a shop owner sells 39 mtr of fabric and gains Cost Price of 12 meters?\n\n### Options:\nA. 20.5%\nB. 23.5%\nC. 21.5%\nD. 13.5%\nE. 32.5%\n\n### Answer:\nLet cost of each metre be Rs. 100.\nTherefore, cost price of 12m cloth = 12*100 =1200\ncost price of 39m cloth = 39*100 = 3900\nSince the trader made the CP of 12m from the sale of 39m therefore\nProfit on sale of 39m = cost price of 12 m cloth = 1200\nSelling price of 39m = 3900+1200 = 5100\nProfit % = 23.5%\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nStalin and Heather are 20 miles apart and walk towards each other along the same route. Stalin walks at constant rate that is 1 mile per hour faster than heather's constant rate of 5 miles/hour. If Heather starts her journey 20 minutes after Stalin, how far from the original destination has Heather walked when the two meet?\n\n### Options:\nA. 4 miles\nB. 6 miles\nC. 9 miles\nD. 10 miles\nE. 12 mile\n\n### Answer:\nOriginal distance between S and H = 20 miles.\nSpeed of S = 5+1 = 6 mph, Speed of H = 5 mph.\nTime traveled by H = t hours ---> time traveled by S = t+20/60 = t+2/6 hours.\nNow, the total distances traveled by S and H = 20 miles ---> 6*(t+2/6)+5*t=20 ---> t= 8/11 hours. Thus H has traveled for 8/11 hours giving you a total distance for H = 5*8/11 ~ 4 miles.\nA is thus the correct answer.\nP.S.: based on the wording of the question, you should calculatehow far from theoriginal destination has Heather walkedwhen the two meet. 'Original destination' for H does not make any sense. Original destination for H was situated at a distance of 20 miles.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn business, A and C invested amounts in the ratio 4:2, whereas the ratio between amounts invested by A and B was 4:1, If Rs 20,000 was their profit, how much amount did A receive.\n\n### Options:\nA. 13333\nB. 26758\nC. 45896\nD. 14639\nE. 89576\n\n### Answer:\nExplanation:\nA:B = 4:1 = 4:1\n=> A:C = 4:2 = 4:2\n=> A:B:C = 4:1:2\nA share = (4/6)*20000\n= 13333\nOption A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA goods train runs at a speed of 72 kmph and crosses a 270 m long platform in 26 seconds.What is the length of the goods train?\n\n### Options:\nA. 230 m\nB. 250 m\nC. 260 m\nD. 270 m\nE. 240 m\n\n### Answer:\ns=270+x/t\n72*5/18=270+x/26\nx=250\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe present ratio between the ages of Paul and Ben is 5:2. In 4 years time Paul will be 28. What is the present age of Ben?\n\n### Options:\nA. 13\nB. 12\nC. 11\nD. 15\nE. 10\n\n### Answer:\nLet the present ages of Paul and Ben be 5x years and 2x years respectively\n4x+4 = 28\n4x = 24\nx = 6\nBen's age = 2x = 12 years\nAnswer is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA collection of books went on sale, and 2/3 of them were sold for $3.25 each. If none of the 20 remaining books were sold, what was the total amount received for the books that were sold?\n\n### Options:\nA. $130\nB. $185\nC. $175\nD. $165\nE. $155\n\n### Answer:\nIf 20 books constitute 1/3rd of the total, then 2/3rd of the total = 40 books\nAmount received for sold books = 40 * 3.25 = $130\nAnswer :A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many such three letter passwords can exist?\n\n### Options:\nA. 216\nB. 26C6 *3\nC. (26C6)^3\nD. ((26C6)^3) *63\nE. 215\n\n### Answer:\n1st ring: 6 out of 26 alphabets can be selected in 26C6 ways.\nAnd is for 2nd and 3rd ring.\nAlso, these 3 set of 6 letters can be arranged amongst themselves in 63 ways.\nHence, total number of 3 letter passwords = 26C6 * 26C6 *26C6 *63 ways.\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe workforce of Company X is 50% female. The company hired 20 additional male workers, and as a result, the percent of female workers dropped to 50%.How many employees did the company have after hiring the additional male workers?\n\n### Options:\nA. 225\nB. 220\nC. 230\nD. 235\nE. 240\n\n### Answer:\nlet x be the total worker then 0.5x =female worker and 0.5x is male worker then 20 male worker added\n05x/(0.5x +20) = 50/100 or 50x = 50*( 0.5x+100) = 25x+ 5000 or 25x = 5000 , x = 5000/25=200\ntotal worker = 200 +20= 220\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a class, 30 students pass in English and 20 students in Math, while some students among these pass in both. How many more students do only English as compared to those doing only Maths?\n\n### Options:\nA. 10\nB. 15\nC. 20\nD. 25\nE. Indeterminate\n\n### Answer:\nLet us consider tht x student are tohse who passed in both English and Maths...\nSo first we remove x student from both of them\nTherefore,\nEnglish = 30-x\nMaths = 20-x\nNow, Number of Students more in English = (30-x)-(20-x)\n= 30-x-20+x\n= 10\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is difference between biggest and smallest fraction among 2/3, 3/4, 4/5 and 5/3\n\n### Options:\nA. 2/5\nB. 3/5\nC. 1/6\nD. 1\nE. None of these\n\n### Answer:\nExplanation:\n2/3 = .66, 3/4 = .75, 4/5 = .8 and 5/3 = 1.66\nSo biggest is 5/3 and smallest is 2/3\nTheir difference is 5/3 - 2/3 = 3/3 = 1\nOption D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA building contractor employs 20 male, 15 female and 5 child workers. To a male worker he pays Rs.25 per day, to a female worker Rs.20 per day and a child worker Rs.8 per day. The average wage per day paid by the contractor is?\n\n### Options:\nA. 28\nB. 21\nC. 29\nD. 27\nE. 13\n\n### Answer:\n20 15 5\n25 20 8\n500 + 300 + 40 = 840/40 = 21\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 10 gallons of grape juice are added to 50 gallons of a mixture, which contains 10 percent grape juice then what percent of the resulting mixture is grape juice?\n\n### Options:\nA. 14%\nB. 25%\nC. 28%\nD. 34%\nE. 50%\n\n### Answer:\nOFFICIAL SOLUTION:\nIf we start with 40 gallons of a mixture that is 10% grape juice, then we have:\n50 \u00d7 0.10 = 5 gallons of grape juice.\n50 \u00d7 0.90 = 45 gallons of other components.\nIf we add 10 gallons of grape juice, we will end up with 15 gallons of grape juice and 45 gallons of other components, and we will have a total of 60 gallons of the mixture.\nSo 15/60 of the new mixture is grape juice. Now we convert this to a percent:Percent Grape Juice = 25/100= 25%.\nThe correct answer is choice (B)\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man bets on no. 16 on a roulette wheel 14 times and losses each time. On the 15th span he does a quick calculation and finds out that the no. 12 had appeared twice in the 14 spans and is therefore, unable to decide whether to bet on 16 or 12 in the 15th span. Which will give him the best chance and what are the odds of winning on the bet that he takes?\n\n### Options:\nA. 23:41\nB. Either ;35:1\nC. 41:54\nD. 35:43\nE. 12:31\n\n### Answer:\nEach of the span is an independent event and the outcome of the 15th span will not depend on the outcome of the earlier spans.\nEither ;35:1\nB)\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn one hour, a boat goes 4 km/hr along the stream and 2 km/hr against the stream. The speed of the boat in still water (in km/hr) is:\n\n### Options:\nA. 3 km/hr\nB. 4 km/hr\nC. 5 km/hr\nD. 6 km/hr\nE. 8 km/hr\n\n### Answer:\nUpstream relative speed is u + v=4km/hr\nDownstream speed is u-v = 2\nWhere u = speed of boat in still water and v is speed of stream\nThen adding two equations u+v + u-v =4+2\n2u=6\nFinally, u=3.\nANSWER : A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA company, Chauncy Co., has an annual travel budget of $50,000. The accounting department estimates that transportation expenses will increase 5 percent in the coming year, and nontransportation travel expenses will increase by 15 percent in the coming year. Last year, Chauncy Co. spent $19,500 on transportation-related expenses, and $35,000 on nontransportation travel expenses. If the annual travel budget does not increase this year, and if the accounting department\u2019s estimates are correct, how far over the annual travel budget will expenses be this year?\n\n### Options:\nA. Expenses will not go over the budget.\nB. $500\nC. $4,225\nD. $5,725\nE. $10,725\n\n### Answer:\nannual travel budget of $50,000\nLet, Transportation expenses = T = 19500\nand Non-Transportation expenses = N=35000\ni.e. Increased Transportation expenses = 1.05T = 20475\nand Increased Non-Transportation expenses = 1.15N = 40250\nTotal Expense = 20475+40250 = 60725\nExpense over Budget = Budget - expense = 50000-60725 = 10725\nAnswer: Option E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average of first five multiples of 3 is\n\n### Options:\nA. 3\nB. 6\nC. 9\nD. 12\nE. 15\n\n### Answer:\nSolution\nAverage\t= 3(1+2+3+4+5) / 5\n= 45 / 5.\n= 9.\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe present age of the father is 4years more than 4 times the age of his son. 4 years hence, father's age will be 20 years more than twice the age of the son. Find the present age of the father?\n\n### Options:\nA. 25\nB. 56\nC. 45\nD. 36\nE. 44\n\n### Answer:\nLet the son's present age be x years\nfather's present age = (4x+4)\n4x+4+4 = 2(x+4)+10\n4x+8 = 2x+18\nx = 5\nfather's present age = 4x+4 = 4*10+4 = 44 years\nAnswer is E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nBill\u2019s compact disc player randomly plays a song, so that no song is repeated before the entire album is played. If Bill plays a disc with 17 songs, what are the chances that the third song he hears will be his favorite?\n\n### Options:\nA. 1/17\nB. 1/12\nC. 1/11\nD. 3/14\nE. 1/3\n\n### Answer:\nThe player plays the songs on the album at random, so there are 17 songs that can be the third one played. Only 1 of these ways will result in Bill's favorite song being the third one played.\nTotal outcomes ==> 17\nTotal positive outcomes ==> 1\nCorrect answer is A) 1/17\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe cost price of a radio is Rs.1500 and it was sold for Rs.1230, find the loss %?\n\n### Options:\nA. 18%\nB. 19%\nC. 28%\nD. 38%\nE. 58%\n\n### Answer:\n1500 ---- 270\n100 ---- ? => 18%\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRs.385 were divided among X,Y,Z in such a way that X had Rs.20 more than Y and Z had Rs 15 more than X . How much was Y\u2019s share?\n\n### Options:\nA. Rs.130\nB. Rs.145\nC. Rs.154\nD. Rs.160\nE. Rs.164\n\n### Answer:\nLet Y gets Rs x. Then We can say X gets Rs (x + 20 ) and Y gets Rs ( x + 35) .\nx + 20 + x + x + 35 = 385\n3x = 330\nx = 110 .\nR\u2019s share = Rs ( 110 + 35 ) = Rs.145\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe cost price of 30 articles is the same as the selling price of x articles. If the profit is 25%, what is x?\n\n### Options:\nA. 18\nB. 20\nC. 22\nD. 24\nE. 26\n\n### Answer:\nLet the cost price = y\nThe cost price of 30 articles = 30y\nThe selling price of x articles = 1.25y*x\n1.25y*x = 30y\nx = 30 / 1.25 = 24\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the greatest number which on dividing 1657 and 2037 leaves remainders 6 and 5 respectively.\n\n### Options:\nA. 127\nB. 157\nC. 147\nD. 137\nE. None of them\n\n### Answer:\nRequired number = H.C.F. of (1657 - 6) and (2037 - 5) = H.C.F. of 1651 and 2032\n_______\n1651 ) 2032 ( 1 1651\n1651_______\n381 ) 1651 ( 4\n1524_________\n127 ) 381 ( 3\n381\n0\nRequired number = 127.\nAnswer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a certain boys camp, 20% of the total boys are from school A and 30% of those study science. If there are 28 boys in the camp that are from school A but do not study science then what is the total number of boys in the camp?\n\n### Options:\nA. 70\nB. 245\nC. 150\nD. 200\nE. 350\n\n### Answer:\nSince 30% of the boys from school A study science, then 70% of the boys from school A do NOT study science and since 20% of the total number of boys are from school A, then 0.2*0.7 = 0.14, or 14% of the boys in the camp are from school A and do not study science.\nWe are told that this number equals to 28, so 0.14*{total} = 28 --> {total} = 200.\nAnswer: D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a factory, there are 90% technicians and 10% non-technicians. If the 90% of the technicians and 10% of non-technicians are permanent employees, then the percentage of workers who are temporary is?\n\n### Options:\nA. 62%\nB. 57%\nC. 52%\nD. 82%\nE. 42%\n\n### Answer:\nTotal = 100\nT= 90 NT= 10\n90*(10/100)=910*(90/100)=9\n9 + 9 = 18=> 100 - 18 = 82%\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average age of four children in a family is 12 years. If the spacing between their ages is 4 years, the age of the youngest child is ?\n\n### Options:\nA. 6 years\nB. 7 years\nC. 8 years\nD. 9 years\nE. None\n\n### Answer:\nAnswer\nLet the age of youngest child be y.\nso from question y + (y + 4) + (y + 8) + (y + 12) = 4 x 12\n\u21d2 4y + 24= 48\n\u2234 y = 6 years\nCorrect Option: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nPriya covers journey from kavali to nellore by car at average speed of 80 Km/hr. She returns back by scooty with an average speed of 40 Km/hr. Find her average speed during the whole journey?\n\n### Options:\nA. 50Km/hr\nB. 53.33Km/hr\nC. 60Km/hr\nD. 66Km/hr\nE. 72km/hr\n\n### Answer:\nExplanation:\nAverage speed = 2 xy/x+y\n= 2*80*40/120\n= 53.33 Km/hr\nAnswer: Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA bat is bought for Rs.400 and sold at a gain of 20% find its selling price\n\n### Options:\nA. Rs.480/-\nB. Rs.500/-\nC. Rs.520/-\nD. Rs.540/-\nE. Rs.560/-\n\n### Answer:\n100 % ------> 400 (100 * 4 = 400)\n120 % ------> 480 (120 * 4 = 480)\nSelling price = Rs.480/-\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSum of two numbers is 15. Two times of the first exceeds by 5 from the three times of the other. Then the numbers will be?\n\n### Options:\nA. 5\nB. 9\nC. 11\nD. 13\nE. 15\n\n### Answer:\nExplanation:\nx + y = 15\n2x \u2013 3y = 5\nx = 10 y = 5\nA)\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAmit and Ananthu can do a work in 15 days and 25 days respectively. Amit started the work and left after 3 days. Ananthu took over and completed the work. In how many days was the total work completed?\n\n### Options:\nA. 28 days\nB. 20 days\nC. 23 days\nD. 25 days\nE. 27 days\n\n### Answer:\nAmit\u2019s one day\u2019s work= 1/15\nAmit\u2019s 3 day\u2019s work = 1/15 *3 = 1/5\nWork left= 1-1/5 = 4/5\nAnanthu\u2019s one day\u2019s work= 1/25\nAnanthu can do work in = 4/5 *25 = 20/1 days\nSo total days = 25+3 = 28 days\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a 4 person race, medals are awarded to the fastest 3 runners. The first-place runner receives a gold medal, the second-place runner receives a silver medal, and the third-place runner receives a bronze medal. In the event of a tie, the tied runners receive the same color medal. (For example, if there is a two-way tie for first-place, the top two runners receive gold medals, the next-fastest runner receives a silver medal, and no bronze medal is awarded). Assuming that exactly three medals are awarded, and that the three medal winners stand together with their medals to form a victory circle, how many different victory circles are possible?\n\n### Options:\nA. 24\nB. 52\nC. 96\nD. 144\nE. 648\n\n### Answer:\nGold can be awarded in 4 ways, then silver can be awarded in 3 ways and Bronze in 2 ways.\ntherefore the total number of ways are : 4*3*2=24ways of awarding the medals and the same number of ways of forming the circle.\nThis is when there is no tie. And if there is tie, for example all three receive the GOLD or the Silver or the Bronze, then there are 4 more cases. which implies 24*4=96. ANS:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA garrison of 400 men had a provision for 31 days. After 28 days 280 persons re-enforcement leave the garrison. Find the number of days for which the remaining ration will be sufficient?\n\n### Options:\nA. 10 days\nB. 20 days\nC. 5 days\nD. 25 days\nE. 15 days\n\n### Answer:\n400 --- 31\n400 --- 3\n120 --- ?\n400*3 = 120*x => x =10 days\nANSWER A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA club with a total membership of 30 has formed 3 committees, M, S and R, which have 8, 12 and 5 members respectively. If no members of committee M is on either of the other 2 committees, what is the greatest possible number of members in the club who are on none of the committees?\n\n### Options:\nA. 5\nB. 7\nC. 8\nD. 10\nE. 12\n\n### Answer:\n{total} = {M} + {S} + {R} - {Both} + {Neither}\nWe want to maximize Neither, so Both has to be as large as possible. The max of {Both} is 5 because {R} = 5.\n30 = 8 + 12 + 5 - 5 + Neither\nNeither = 10\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOf the 200 students at University XYZ majoring in one or more of the engineering disciplines, 130 are majoring in electrical and 150 are majoring in mechanical. If at least 30 of the students are not majoring in either electrical or mechanical, then the number of students majoring in both electrical and mechanical could be any number from\n\n### Options:\nA. 30 to 70\nB. 70 to 100\nC. 110 to 130\nD. 130 to 150\nE. 150 to 170\n\n### Answer:\nlower point = Sum in each - total possible = 150+130- (200-30) = 280-170 =110...\nhigher point = entire 130 majoring in electrical major in mechanical too , so = 130..\nrange = 110 to 130\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA bus travel 5/7 of its speed covers 42 km in 1 hr 40 min48 sec. What is theactual speed of the bus ?\n\n### Options:\nA. 20 km/hr\nB. 35 km/hr\nC. 40 km/hr\nD. 53 km/hr\nE. 55 km/hr\n\n### Answer:\nTime = 1 hr 40 min 48 sec = 1hr +4060hr+483600hr=1+23+175=12675hrdistance = 42 kmspeed=distancetime=42(12675)=42\u00d775126\u21d257 of the actual speed = 42\u00d775126\u21d2actual speed = 42\u00d775126\u00d775=42\u00d71518=7\u00d7153=7\u00d75=35 km/hr\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average height of 35 boys in a class was calculated as 183cm. It has later found that the height of one of the boys in the class was wrongly written as 166 cm whereas his actual height was 106 cm. Find the actual average height of the boys in the class (Round off your answer to two decimal places).?\n\n### Options:\nA. 178.27 cm\nB. 181.29 cm\nC. 978.29 cm\nD. 178.89 cm\nE. 176.29 cm\n\n### Answer:\nCalculated average height of 35 boys = 183 cm.\nWrong total height of 35 boys = 183 * 35 cm. This was as a result of an actual height of 106 cm being wrongly written as 166 cm. Correct total height of 35 boys = 183 cm - (166 cm - 106 cm)/35\n= 183 cm - 60 /35 cm\n= 183 cm - 1.71 cm = 181.29 cm.\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo trains are running at 40 km/hr and 20 km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 2 sec. What is the length of the fast train?\n\n### Options:\nA. 11 1/9 m\nB. 11 7/4 m\nC. 11 7/2 m\nD. 11 7/9 m\nE. 11 7/7 m\n\n### Answer:\nRelative speed = (40 - 20) = 20 km/hr.\n= 20 * 5/ 18 = 50/9 m/sec.\nLength of faster train = 50/9 * 2 = 100/9 = 11 1/9 m.Answer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSunil invested $ 2600 fir 3 years and $ 1200 for 5 years at the same rate of Simple Interest. If the total interest from these investments is $ 930, what is the rate of interest?\n\n### Options:\nA. 2 3/4%\nB. 5 1/3%\nC. 5 1/2%\nD. 6 3/4%\nE. 3 2/4%\n\n### Answer:\n(2600x3xR)/100+(1200x5xR)/100=930\n138R=930\nR= 6 3/4%\nAnswer is D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the least value of x. So that 23x58 is divisible by 3.\n\n### Options:\nA. 2\nB. 0\nC. 1\nD. 3\nE. 4\n\n### Answer:\nExplanation:\nThe sum of the digits of the number is divisible by 3, then the number is divisible by3.\n2 + 3 + x + 5 + 8 = 18 + x\nLeast value of x may be 0\nTherefore 18 + 0 = 18 is divisible by 3.\nAnswer: Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nLinda spent 3/4 of her savings on furniture and the rest on a TV. If the TV cost her $300, what were her original savings?\n\n### Options:\nA. $1200\nB. $1300\nC. $1400\nD. $1800\nE. $1900\n\n### Answer:\nIf Linda spent 3/4 of her savings on furnitute, the rest\n4 / 4 - 3 / 4 = 1 / 4 on a TV\nBut the TV cost her $300. So 1 / 4 of her savings is $300. So her original savings are 4 times $300 = $1200\ncorrect answer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA goods train runs at the speed of 72 kmph and crosses a 230 m long platform in 26 seconds. What is the length of the goods train?\n\n### Options:\nA. 230 m\nB. 270m\nC. 643m\nD. 832m\nE. 290m\n\n### Answer:\nSpeed =\t(72 x\t5/18)m/sec\t= 20 m/sec.\nTime = 26 sec.\nLet the length of the train be x metres.\nThen,\tx + 230/26\t= 20\nx + 230 = 520\nx = 290.\nAnswer:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA security guard at a certain store is instructed to check the receipt of one out of every five customers as they are leaving the store. If, on the guard's shift, 12 customers leave the store, how many different samples of customers could have been selected to have their receipts checked?\n\n### Options:\nA. 20\nB. 66\nC. 59\nD. 90\nE. 100\n\n### Answer:\nto choose the sample of 2 customers from 12. it can be done 12C2 possible ways.\nSo the answer is B. 66\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAnnie will be half as old as Larry in 3 years. Annie will also be one-third as old as Jerome in 5 years. If Jerome is 10 years older than Larry, how old is Annie?\n\n### Options:\nA. 3\nB. 8\nC. 19\nD. 26\nE. 34\n\n### Answer:\nJ = L+10\n(1) 2(A+3) = L+3\n(2) 3(A+5) = J+5 = L+15\nLet's subtract equation (1) from equation (2)\nA+9 = 12\nA = 3\nThe answer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average age of a group of 5 members is 20 years. Two years later, a new member joins the group. The average age of the group becomes 21 years. What is the age of the new member ?\n\n### Options:\nA. 16 years\nB. 21 years\nC. 22 years\nD. 23 years\nE. 24 years\n\n### Answer:\nThe average age of the 5 members is 20 years\n=> The sum of the ages of the 5 members is 20*5 = 100 years\nOnce the new member joins, the average age becomes 21 years.\nLet the age of the new member be x.\nThen (110+x)/6 = 21\n=> x = 16 years\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\njudith is practicing her dance steps along with her friends. In a particular sequence, all of them form a row. At that point, judithis standing on the 5th position from either end of the row.\nCan you find out how many girls are practicing together?\n\n### Options:\nA. 4\nB. 9\nC. 7\nD. 6\nE. 8\n\n### Answer:\nAs judith is 5th from either end of the row, it means that 4 girls are on one of her sides and 4 are present on the other.\n4 + 4 + 1(judith herself) = 9.\nHence,9 girls are practicing the dance together.\ncorrect answer is B)9\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe speed at which a man can row a boat in still water is 6 km/hr. If he rows downstream, where the speed of current is 3 km/hr, how many seconds will he take to cover 80 meters?\n\n### Options:\nA. 28\nB. 32\nC. 36\nD. 40\nE. 44\n\n### Answer:\nThe speed of the boat downstream = 6 + 3 = 9 km/hr\n9 km/hr * 5/18 = 2.5 m/s\nThe time taken to cover 80 meters = 80/2.5 = 32 seconds.\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA childrens identification code consists of a vowel followed by a 3-digit number greater than 200. Exactly 2 of the 3 digits in the code should be identical. How many different codes is it possible to form?\n\n### Options:\nA. 211\nB. 216\nC. 1075\nD. 1080\nE. 2160\n\n### Answer:\nA childrens identification code will be of the type -,-,-,-\nfirst digit can be selected from any of the 5 vowels in 5C1 ways\nnow for the remaining three digit lets consider the following two cases\ncase 1: when the number is greater than 200 but less than 300\nnumber will be of the type 2,_,_. now suppose repeating number is same as first digit number i.e. 2. and the third number is one of the remaining 9 numbers (we are rejecting 2 here, because it will result in 222, which is not acceptable as per the given condition). thus these two number can arrange themselves in two blank spaces in 2! ways. hence total number of numbers in which repeating digit is same as the first digit = 1.9.2! =18\nnow, suppose that repeating number is different than first digit. thus possible case in this case are 8 as listed below:\n211\n233\n244\n255\n266\n277\n288\n299\nhere again we have rejected 200( because number must be greater than 200) and 222 ( exactly two repeating digits are allowed)\nthus total possible cases are 18 + 8 =26\ncase 2: number ranging from 300 to 999\nhere for first digit we have 7 cases (3,4,5,6,7,8,9)\nnow if the repeating number is same as the first number then we will have 18 cases ( same reasoning as mentioned in the previous case)\nif the repeating number is different than first digit number then we will have 9 cases ( because here number ending with two zeros are allowed)\nhence total number of ways = 7(18+9) = 189\nthus different number of codes = 5(189+26) = 1075\nhence C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA shopkeeper buys two articles for Rs.1000 each and then sells them, making 15% profit on the first article and 15% loss on second article. Find the net profit or loss percent?\n\n### Options:\nA. 200\nB. 150\nC. 282\nD. 202\nE. 270\n\n### Answer:\nProfit on first article = 15% of 1000 = 150.\nThis is equal to the loss he makes on the second article. That, is he makes neither profit nor loss.\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA bullock cart has to cover a distance of 80km in 10hrs. If it covers half of the journey in 3/5th time. what should be its speed to cover the remaining distance in the time left.\n\n### Options:\nA. 8 km/h\nB. 10 km/h\nC. 12 km/h\nD. 14 km/h\nE. 16 km/h\n\n### Answer:\nTime left = 10 - 3/5*10\n= 4 hr 10 km/h\nspeed =40 km /4 hr\n=10 kmph\nAnswer : B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA drum contains 4 red balls, 3 blue balls and 2 white balls. Three balls are removed (no replacement) what is the probability that there will be one of each?\n\n### Options:\nA. 22\nB. 21\nC. 24\nD. 25\nE. 28\n\n### Answer:\n4*3*2 / 9*8*7.\nThere is a 4/9 chance of taking a red ball first; if you do, ther'es a 3/8 chance of taking a blue ball next, and if you get that far, there's a 2/7 chance of getting a white ball third.\nOr you might get white first, blue second and red third: 2/9, followed by 3/8 and then 4/7. No matter what order it might occur, the multiplication will always be (4*3*2)/(9*8*7).\nSince 4*2 = 8 and 3 is a factor of 9, you can cancel out the entire top row to leave 1 / (3*1*7) ie. 1 chance in 21.\nanswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSuppose you want to arrange your English, Hindi, Mathematics, History, Geography and Science books on a shelf. In how many ways can you do it?\n\n### Options:\nA. 700\nB. 710\nC. 720\nD. 740\nE. 750\n\n### Answer:\nWe have to arrange 6 books.\nThe number of permutations of n objects isn!=n.(n\u22121).(n\u22122)...2.1n!=n.(n\u22121).(n\u22122)...2.1\nHere n=6n=6 and therefore, number of permutations is 6.5.4.3.2.1=6.5.4.3.2.1= 720\nOption is C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA straight pipe 6 yard in length was marked off in fourths and also in thirds. If the pipe was then cut into separate pieces at each of these markings, which of the following gives all the different lengths of the pieces, in fractions of a yard?\n\n### Options:\nA. 1/6 and 1/4 only\nB. 1/4 and 1/3 only\nC. 1/6, 1/4, and 1/3\nD. 1/12, 1/6 and 1/4\nE. 1/12, 1/6, and 1/3\n\n### Answer:\nSince we want to find the fractions, we can assume some other length of the pipe which will make calculation easier. Take the length of the pipe to be 12-meter long (the least common multiple of 3 and 4.\nIn this case the branch would be cut at3,4, 6,8, and 9meters (in black are given fourths of the length and in red thirds of the length).\nDistinct lengths would be: 3=3/12=1/4, 4-3=1=1/3 meters long pieces.\nAnswer: B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many multiples of 2 are there between 10 and 52, 10 and 52 inclusive?\n\n### Options:\nA. 27\nB. 25\nC. 24\nD. 21\nE. 22\n\n### Answer:\n2 multiples are ...10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,...,\nthe answer is =22\nAnswer is E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are two concentric circles with radii 8 and 6. If the radius of the outer circle is increased by 25% and the radius of the inner circle decreased by 50%, by what percent does the area between the circles increase?\n\n### Options:\nA. 225\nB. 250\nC. 275\nD. 300\nE. 325\n\n### Answer:\nThe area of a circle is piR^2, where R is the radius.\nThe area of the big circle is 64pi.\nThe area of the small circle is 36pi.\nThe area A1 between the circles is 28pi.\nWhen the big circle's radius increases, the new area is 100pi.\nWhen the small circle's radius decreases, the new area is 9pi.\nThe area A2 between the circles is 91pi.\nThe ratio of A2/A1 is 91/28 = 3.25 which is an increase of 225%.\nThe answer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n0.99999999/1.0001\u22120.99999991/1.0003\n\n### Options:\nA. 10^(-8\nB. 3*10^(-8)\nC. 3*10^(-4)\nD. 2*10^(-4)\nE. 10^(-4)\n\n### Answer:\nlook at the options closely\nA. 0.00000001\nB. 0.00000003\nC. 0.0003\nD. 0.0002\nE. 0.0001\nOnly one option is an even number, the rest odd (an esoteric sort of even/odd number)\nboth fractions in the question are odds\nodd minus odd is always even.\nSo answer must be even.\nOnly D is even.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train can travel 50% faster than a car. Both start from point A at the same time and reach point B at 75 kms away from A at the same time. On the way, however, the train lost about 12.5 minutes while stopping at the stations. The speed of the car is?\n\n### Options:\nA. 110 km/hr\nB. 145 km/hr\nC. 151 km/hr\nD. 180 km/hr\nE. 120 km/hr\n\n### Answer:\nE\nLet speed of the car be x km/hr.\nThen, speed of the train = 150/100 x = 3/2 x km/hr.\n75/x - 75/(3/2 x) = 125/(10 * 60)\n75/x - 50/x = 5/24 = 120 km/hr.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a school having roll strength 286, the ratio of boys and girls is 8:5. If 22 more girls get admitted into the school, the ratio of boys and girls becomes\n\n### Options:\nA. 12:7\nB. 10:7\nC. 8:7\nD. 4:3\nE. none\n\n### Answer:\nSolution: Boys: girls = 8:5; (let the boys = 8x; girl = 5x)\nTotal strength = 286;\n8x+5x = 286;\n13x = 286;\nOr, x = 286/13 = 22;\nBoys = 176 and girls = 110;\n22 more girls get admitted then number of girls become,\n(5x+22) = 110+22 = 132;\nNow, new ratio of boys and girls = 176:132 = 4:3.\nAnswer: Option D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMr. Srinivas saves one coin of 5 on first day of the\nweek, three coins of 5 on the second day of the week.\nFive coins of 5 on third day and so on. How much money will he has at the end of the week?\n\n### Options:\nA. 238\nB. 245\nC. 2867\nD. 987\nE. 111\n\n### Answer:\nNumber of\n5 coins with him at the end of week = 5 \u00d7 (1 + 3 + 5 + 7 + 9 + 11 + 13) = 5 \u00d7 (sum of first 7 odd numbers) (By using the formula discussed earlier). \u2234 Sum of all numbers = 5 \u00d7 72 = 245.\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain company reported that the revenue on sales increased 30 % from 2000 to 2003, and increased 80 % from 2000 to 2005. What was the approximate percent increase in revenue for this store from 2003 to 2005?\n\n### Options:\nA. 50 %\nB. 40 %\nC. 35 %\nD. 32 %\nE. 39 %\n\n### Answer:\nAssume the revenue in 2000 to be 100. Then in 2003 it would be 130 and and in 2005 180, so from 2003 to 2005 it increased by (180-130)/130=50/130= 39%\nAnswer: E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAn amount of money is to be divided between P, Q and R in the ratio of 3:7:12. If the difference between the shares of P and Q is Rs.3200, what will be the difference between Q and R's share?\n\n### Options:\nA. 2788\nB. 4000\nC. 7282\nD. 2782\nE. 2729\n\n### Answer:\n4 --- 3200\n5 --- ? => 4000\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nfind the number, difference between number and its 3/5 is 50.\n\n### Options:\nA. 120\nB. 123\nC. 124\nD. 125\nE. 126\n\n### Answer:\nExplanation:\nLet the number = x,\nThen, x-(3/5)x = 50,\n=> (2/5)x = 50 => 2x = 50*5,\n=> x = 125\nAnswer: Option D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWorker A takes 5 hours to do a job. Worker B takes 15 hours to do the same job. How long it take both A & B, working together but independently, to do the same job?\n\n### Options:\nA. 15/4\nB. 40/9\nC. 50/9\nD. 60/9\nE. 80/9\n\n### Answer:\none day work of A = 1/5\none day work of B = 1/15\nso one day work of A and B together = 1/5 + 1/15 = 4/15\nso total days required = 15/4\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe length of a room is 5.5 m and width is 3.75 m. Find the cost of paying the floor by slabs at the rate of Rs. 400 per sq.metre.\n\n### Options:\nA. Rs. 15,000\nB. Rs. 8,250\nC. Rs. 15,600\nD. Rs. 16,500\nE. None\n\n### Answer:\nSolution\nArea of the floor\t= (5.5 x 3.75)m\u00b2\n= 20.635m \u00b2\nCost of paying\t= Rs. (400 x 20.625)\n= Rs.8,250.\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe area of a circular field is 17.56 hectares. Find the cost of fencing it at the rate of Rs. 6 per metre approximately\n\n### Options:\nA. 4457\nB. 4567\nC. 4235\nD. 4547\nE. 8915\n\n### Answer:\nExplanation:\nArea = (17.56 x 10000) m2= 175600 m2.\n\u03a0R2 = 175600 \u21d4 (R)2 = (175600 x (7/22)) \u21d4 R = 236.37 m.\nCircumference = 2\u03a0R = (2 x (22/7) x 236.37) m =1485.78 m.\nCost of fencing = Rs. (1485.78 x 6) = Rs. 8915.\nAnswer: Option E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are 202 lights which are functional and each is controlled by a separate On/Off switch. Two children A and B start playing with the switches. A starts by pressing every third switch till he reaches the end. B, thereafter, presses every fifth switch till he too reaches the end. If all switches were in Off position at the beggining, How many lights are switched On by the end of this operation?\n\n### Options:\nA. 93\nB. 94\nC. 92\nD. 96\nE. 95\n\n### Answer:\nEditing my solution:\nNumber of switches = 202\nNumber of switches turned on by A: 3, 6, ... 201 = 67\nNumber of switches turned on by B: 5, 10, ....200 = 40\nFew switches are turned on by A and later turned off by B: LCM(3,5) = 15x = 15, 30,....90 = 6.\nSubtract the above 6 switches from both A and B as they are turned off.\nNumber of switches that are turned on = (67- 6) + (40 - 6) = 95\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe mean of 50 observations was 36. It was found later that an observation 48 was wrongly taken as 23. The corrected new mean is ?\n\n### Options:\nA. 33.3\nB. 36.5\nC. 26.5\nD. 16.5\nE. 86.5\n\n### Answer:\nCorrect Sum = (36 * 50 + 48 - 23) = 1825.\nCorrect mean = = 1825/50 = 36.5\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf n is an integer and n^4 is divisible by 32, which of the following could be the remainder when n is divided by 32?\n\n### Options:\nA. 2\nB. 4\nC. 5\nD. 6\nE. 10\n\n### Answer:\nGiven:\nn^4/32 = int\nn^4/2^5 = int\n1/2(n/2)^4 = int\ntry n= int = 2,4,6,8... because n/2 must be an integer\nn=2 wont work because 1/2(n/2)^4 needs to be an integer.\nn=4, result = 1/2 (2)^4 = 8, so the remainder of n/32 = remainder of 8/32 = 8 (not an option)\nn=8, result = 1/2(8/2)^4 = 1/2(4)^4 = 1/2x16x16= 16x8, so the remainder of n/32 = remainder of 16x8/32 = 4 (option B)\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA sum of money is divided among A, B, C & D in the ratio 3:5:8:9 respectively. If the share of D Rs.1872 more than the share of A, then what is the total amount of money of B & C together?\n\n### Options:\nA. 3000\nB. 4056\nC. 5000\nD. 5400\nE. 5600\n\n### Answer:\nSol. Share of B + C = -3 x (5 + 8) = Rs. 4056\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA, B, C hired a car for Rs. 520 and used it for 7, 8 and 11 hours respectively. Hire charges paid by B were?\n\n### Options:\nA. 127\nB. 160\nC. 287\nD. 237\nE. 111\n\n### Answer:\nA : B : C = 7 : 8 : 11.\nHire charges paid by B = Rs. (520 * 8/26) = Rs. 160.\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA person travels equal distances with speeds of 3 km/hr, 4 km/hr and 5 km/hr and takes a total time of 54 minutes. The total distance is?\n\n### Options:\nA. 1 km\nB. 2 km\nC. 3 km\nD. 3.4 km\nE. 5 km\n\n### Answer:\nD\n3 km\nLet the total distance be 3x km.\nThen, x/3 + x/4 + x/5 = 54/60\n47x/60 = 54/60 => x = 1.14\nTotal distance = 3 * 1.14 = 3.4 km.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf -3x < 9, which of the following must be true?\n\n### Options:\nA. x < -3\nB. x < -2\nC. x > -3\nD. x > -2\nE. x > 0\n\n### Answer:\n-3x < 9\n=> -x < 3\n=> x > - 3\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTo mail a package, the rate is 10 cents for the first pound and 5 cents for each additional pound. Two packages weighing 3 pounds and 5 pounds, respectively can be mailed seperately or combined as one package. Which method is cheaper and how much money is saved?\n\n### Options:\nA. Combined, with a saving of 5 cents\nB. Combined, with a saving of 10 cents\nC. Combined, with a saving of 15 cents\nD. Separately, with a saving of 5 cents\nE. Separately, with a saving of 10 cents\n\n### Answer:\n3 pounds cost = 10+2*5 = 20\n5 pounds cost = 10+4*5 = 30\nTotal = 50\n8 pounds cost = 10+ 7*5 =45\nAnswer : A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe population of locusts in a certain swarm doubles every two hours. If 4 hours ago there were 1,000 locusts in the swarm, in approximately how many hours will the swarm population exceed 128,000 locusts?\n\n### Options:\nA. 12\nB. 8\nC. 4\nD. 10\nE. 16\n\n### Answer:\n- 4 hours: 1,000\n-2 hours: 2,000\nNow: 4,000\n+ 2 hours: 8,000\n+ 4 hours: 16,000\n+ 6 hours: 32,000\n+ 8 hours: 64,000\n+ 10 hours: 128,000\nAnswer : D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nBy selling an umbrella for Rs. 300, a shop keeper gains 20%. During a clearance sale, the shopkeeper allows a discount of 10% on the marked price. His gain percent during the sale is:\n\n### Options:\nA. 7\nB. 7.5\nC. 8\nD. 9\nE. 10\n\n### Answer:\nExplanation:\nMarked price = Rs. 300\nC.P. = 100/120 * 300 = Rs. 250\nSale price = 90% of Rs. 300 = Rs. 270\nRequired gain % = 20/250 * 100 = 8%.\nANSWER IS C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA car takes 6 hours to cover a distance of 504 Km. how much should the speed in Kmph be maintained to cover the same direction in 3/2th of the previous time?\n\n### Options:\nA. 48 Kmph\nB. 50 Kmph\nC. 52 Kmph\nD. 56 Kmph\nE. 60 Kmph\n\n### Answer:\nTime = 6\nDistence = 504\n3/2 of 6 hours = 6 * 3/2 = 9 Hours\nRequired speed = 504/9 = 56 Kmph\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOf the families in City X in 1994, 40 percent owned a personal computer. The number of families in City X owning a computer in 1998 was 30 percent greater than it was in 1994, and the total number of families in City X was 4 percent greater in 1998 than it was in 1994. what percent of the families in City X owned a personal computer in 1998?\n\n### Options:\nA. 50%\nB. 52%\nC. 56%\nD. 70%\nE. 74%\n\n### Answer:\nSay a 100 families existed in 1994 then the number of families owning a computer in 1994 - 40\nNumber of families owning computer in 1998 = 40 * 130/100 = 52\nNumber of families in 1998 = 104\nThe percentage = 52/104 * 100 = 50%.\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf x^2 + y^2 = 13 and xy = 3, then (x \u2212 y)^2 =\n\n### Options:\nA. 7\nB. 11\nC. 14\nD. 17\nE. 20\n\n### Answer:\nbut you cannot take xy+ 3 to mean xy=-3..\nonly if xy+3=0, it will mean xy=-3..\nrest your solution is perfect and you will get your correct answer as 13-2*3=7..\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA cement mixture is composed of 3 elements. By weight, 1/3 of the mixture is sand, 1/2 of the mixture is water, and the remaining 8 pounds of the mixture is gravel. What is the weight of the entire mixture in pounds?\n\n### Options:\nA. 30\nB. 36\nC. 42\nD. 46\nE. 48\n\n### Answer:\nLet the total weight be x.\nSand content= (1/3)x\nWater content= (1/2)x\nGravel=x-(1/3)x-(1/2)x=(1/6)x=8\nx=48\nThen answer will be E=48\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nEach of the 11 letters A, H, I, M, O, T, U, V, W, X and Z appears same when looked at in a mirror. They are called symmetric letters. Other letters in the alphabet are asymmetric letters. How many four letter computer passwords can be formed (no repetition allowed) with at least one symmetric letter?\n\n### Options:\nA. 2,145\nB. 6,435\nC. 326,040\nD. 12,870\nE. 25,740\n\n### Answer:\nSince we are given atleast one symmetric letter in the three letter word we can take the following cases\n1. All four\n2. One symmetry and other three non\n3. Two symmetry and other two non\n4. Three symmetry and one non\n4. All the three letters can be arranged in 24 ways\n( 11c4 + 11c1 * 15c3 + 11c2 * 15c2 + 11c3 *15c1 ) * 6\n(330 +5005 + 5775+2475 ) * 24\n326,040\nIMO option C is the correct answer..\nOA please...will correct if I missed anything.. C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf n is a positive integer and n^2 is divisible by 36, then the largest positive integer that must divide n is\n\n### Options:\nA. 6\nB. 12\nC. 24\nD. 36\nE. 48\n\n### Answer:\nThe question asks aboutthe largest positive integer that MUST divide n, not COULD divide n. Since the least value of n for which n^2 is a multiple of 72 is 12 then the largest positive integer that MUST divide n is 12.\nComplete solution of this question is given above. Please ask if anything remains unclear.\nI spent a few hours on this one alone and I'm still not clear. I chose 12 at first, but then changed to 48.\nI'm not a native speaker, so here is how I interpreted this question:the largest positive integer that must divide n=the largest positive factor of n. Since n is a variable (i.e. n is moving), so is its largest factor. Please correct if I'm wrong here.\nI know that if n = 12, n^2 = 144 = 2 * 72 (satisfy the condition). When n = 12, the largest factor of n is n itself, which is 12. Check: 12 is the largest positive number that must divide 12 --> true\nHowever if n = 48, n^2 = 48 * 48 = 32 * 72 (satisfy the condition too). When n = 48, the largest factor of n is n itself, which is 48. Check: 48 is the largest positive number that must divide 48 --> true\nSo, I also notice that the keyword isMUST, notCOULD. The question is, why is 48 notMUST divide 48, but instead onlyCOULD divide 48? I'm not clear right here. Why is 12MUST divide 12? What's the difference between them?\nOnly restriction we have on positive integer n is that n^2 is divisible by 72. The least value of n for which n^2 is divisible by 72 is 12, thus nmustbe divisible by 12 (n is in any case divisible by 12). For all other values of n, for which n^2 is divisible by 72, n will still be divisible by 12. This means that n is always divisible by 12 if n^2 is divisible by 72.\nNow, ask yourself: if n=6, is n divisible by 48? No. So, n is not always divisible by 48.\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how much time will a train of length 110 m, moving at 36 kmph cross an electric pole?\n\n### Options:\nA. sec\nB. sec\nC. sec\nD. sec\nE. sec\n\n### Answer:\nConvert kmph to mps. 36 kmph = 36 * 5/18 = 10 mps.\nThe distance to be covered is equal to the length of the train.\nRequired time t = d/s = 110/10 = 11 sec.\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a recent election, Ms. Robinson received 3200 voters cast by independent voters, that is, voters not registered with a specific political party. She also received 10 percent of the votes cast by those voters registered with a political party. IF N is the total number of votes cast in the election and 40 percent of the votes cast were cast by independent voters, which of the following represents the number of votes that Mrs. Robbins received?\n\n### Options:\nA. 0.06N+3200\nB. 0.1N+7200\nC. 0.4N+7200\nD. 0.1N+8000\nE. 0.06N+8000\n\n### Answer:\n40% of N are independent voters, hence 60% of N are not independent voters. From this group she received 10% votes so, 0.1*0.6*N plus 3,200 votes from independents: total=0.1*0.6*N+3,200=0.06*N+3,200.\nAnswer: A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA women sells 3 different size(in kgs) packs of sugar which are multiples of 1.A person who buys sugar should buy all types of packs.4 different people buys 20,21,23,29 kgs .what will the maximum and minimum amounts a person can buy??\n\n### Options:\nA. 22\nB. 33\nC. 34\nD. 54\nE. 85\n\n### Answer:\npacket are 11,6 and 7\n7+7+6=20\n7+7+7=21\n6+6+11=23\n7+11+11=29\nand min 6+6+6=18\nand max 11+11+11=33\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a - b = 3 and a^2 + b^2 = 29, find the value of ab.\n\n### Options:\nA. 12\nB. 15\nC. 10\nD. 18\nE. 13\n\n### Answer:\n2ab = (a^2 + b^2) - (a - b)^2\n= 29 - 9 = 20\nab = 10.\nAnswer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA brick measures 20cm*10cm*7.5cm how many bricks will be required\rfor a wall 25m*2m*0.75m ?\n\n### Options:\nA. 24000\nB. 23000\nC. 22000\nD. 25000\nE. 27000\n\n### Answer:\n25*2*0.75=20/100*10/100*0.75/100*X\r25=1/100*X\rX=25000\rAnswer :D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTickets numbered from 1 to 20 are mixed and then a ticket is selected randomly. What is the probability that the selected ticket bearsa number which is a multiple of 3?\n\n### Options:\nA. 1/5\nB. 2/5\nC. 3/10\nD. 3/7\nE. 1/7\n\n### Answer:\nHere, S = [1, 2, 3, 4, \u2026., 19, 20]\nLet E = event of getting a multiple of 3 = [3, 6, 9, 12, 15, 18]\nP (E) = n (E) / n (S) = 6 / 20 = 3/10\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA shopkeeper loses 15%,if an article is sold for Rs. 102. What should be the selling price of the article to gain 20%?\n\n### Options:\nA. 221\nB. 144\nC. 666\nD. 888\nE. 212\n\n### Answer:\nGiven that SP = Rs. 102 and loss = 15%\nCP = [100(SP)]/(100 - l%) = (100 * 102)/85 = 20 * 6 = Rs. 120.\nTo get 20% profit, New SP = [(100 + p%)CP]/100 = (120 * 120)/100 = Rs. 144\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many positive three-digit integers are divisible by both 5 and 7?\n\n### Options:\nA. 10\nB. 15\nC. 18\nD. 20\nE. 26\n\n### Answer:\nA number to be divisible by both 5 and 7 should be divisible by the least common multiple of 5 and 7 so by 35.\nMultiples of 35 between 100 and 999, inclusive is\n(last-first)/multiple+1=(980-105)/35+1=25+1=26\nAnswer: E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo boys starts from the same place walking at the rate of 5.5 kmph and 7.5 kmph respectively in the same direction. What time will they take to be 32 km apart?\n\n### Options:\nA. 18\nB. 16\nC. 19\nD. 15\nE. 34\n\n### Answer:\nExplanation:\nRelative speed = 7.5 - 5.5 = 2 kmph (because they walk in the same direction)\ndistance = 32 km\ntime = distance / speed=32/2=16 hr\nAnswer :B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA grocer has a sale of Rs. 3435, Rs. 3927, Rs. 3855, Rs. 4230 and Rs. 3562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 3500?\n\n### Options:\nA. s. 1991\nB. s. 2991\nC. s. 3991\nD. s. 4991\nE. s. 5991\n\n### Answer:\nExplanation:\nTotal sale for 5 months = Rs. (3435 + 3927 + 3855 + 4230 + 3562) = Rs. 19009.\nRequired sale = Rs. [ (3500 x 6) \u00e2\u20ac\u201c 19009 ]\n= Rs. (21000 \u00e2\u20ac\u201c 19009)\n= Rs. 1991.\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA rectangular table seats 3 people on each of two sides, with every person directly facing another person across the table. If six people choose their seats at random, what is probability that any two of them directly face other?\n\n### Options:\nA. 1/5\nB. 1/8\nC. 1/7\nD. 15/56\nE. 4/7\n\n### Answer:\nA B C\n------------\n| TABLE |\n------------\nD E F\nA to F are 6 people.\nProb to select any 1 person = 1\nProb to select the person opposite to the chosen person = 1/5\nFor ex. If we select A as the person than prob of choosing D is 1/5.\nHence, answer will be A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA student is to take her final exams in two subjects. The probability that she will pass the first subject is 3/4 and the probability that she will pass the second subject is 2/3. What is the probability that she will pass one exam or the other exam?\n\n### Options:\nA. 5/12\nB. 1/2\nC. 7/12\nD. 5/7\nE. 11/12\n\n### Answer:\nLet the two subjects be X (probability of passing 3/4) and Y (probability of passing 2/3)\nThe probability of passing in X only is 3/4 times 1/3 (failing in Y) = 1/4\nThe probability of passing in Y only is 2/3 times 1/4 (failing in X) = 1/6\nTherefore the total probability = 1/4 + 1/6 = 5/12\nHence A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe probability that a number selected at random from the first 50 natural numbers is a composite number is ?\n\n### Options:\nA. 17/29\nB. 17/25\nC. 17/27\nD. 17/29\nE. 17/89\n\n### Answer:\nThe number of exhaustive events = \u2075\u2070C\u2081 = 50.\nWe have 15 primes from 1 to 50.\nNumber of favourable cases are 34.\nRequired probability = 34/50 = 17/25\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man has Rs. 720 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?\n\n### Options:\nA. 33\nB. 38\nC. 135\nD. 90\nE. 28\n\n### Answer:\nLet number of notes of each denomination be x.\nThen x + 5x + 10x = 720\n\u21d2 16x = 720\n\u2234 x = 45.\nHence, total number of notes = 3x = 135\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo tables are purchased for the total cost of Rs. 5000. First table is sold at 40% profit and second at 40% loss. If selling price is same for both the tables, what is the cost price of the table that was sold at profit?\n\n### Options:\nA. Rs. 1500.\nB. Rs. 2500.\nC. Rs. 3500.\nD. Rs. 4500.\nE. Rs. 5500.\n\n### Answer:\nAns: 140% of cost price of first table = 60% of cost price of second table.\nTherefore, Cost price of first table : Cost price of second table\n= 60 : 140 = 3 : 7\nTherefore, Cost price of first table = 3/10\u00d7 5000 = Rs. 1500.\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA tank is filled by three pipes with uniform flow. The first two pipes operating simultaneously fill the tank in the same during which the tank is filled by the third pipe alone. The second pipe fills the tank 5 hours faster than the first pipe and 4 hours slower than the third pipe. The time required by the first pipe is?\n\n### Options:\nA. 17\nB. 27\nC. 15\nD. 19\nE. 16\n\n### Answer:\nSuppose, first pipe alone takes x hours to fill the tank. Then, second and third pipes will take (x - 5) and (x - 9) hours respectively to fill the tank.\n1/x + 1/(x - 5) = 1/(x - 9)\n(2x - 5)(x - 9) = x(x - 5)\nx2 - 18x + 45 = 0\n(x- 15)(x - 3) = 0 => x = 15\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a 100 m race, A runs at 8km per hour. If A gives B a start of 4 m and still him by 15 seconds, what is the speed of B ?\n\n### Options:\nA. 5.56 km/hr.\nB. 5.06 km/hr.\nC. 5.76 km/hr.\nD. 6.76 km/hr.\nE. 5.72 km/hr.\n\n### Answer:\nTime taken by A to cover 100 m =(60 X 60 / 8000)\tx 100 sec = 45 sec.\nB covers (100 - 4) m = 96 m in (45 + 15) sec = 60 sec.\nB's speed = (96 x 60 x 60)/(60 x 1000)km/hr = 5.76 km/hr.\nAnswer is C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many four digit numbers can be formed using the digits {1, 3, 4, 5, 7,9}(repetition of digits is not allowed)?\n\n### Options:\nA. 360\nB. 729\nC. 365\nD. 735\nE. 345\n\n### Answer:\nThe given digits are six.\nThe number of four digit numbers that can be formed using six digits is \u2076P\u2084\n= 6 * 5 * 4 * 3 = 360.\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA and B started a business in partnership investing Rs.20,000 and Rs.15,000 respectively. After 6months, C joined them with Rs.20,000. Whatwill be B's share in total profit of Rs.22,000 earned at the end of 2years from the startingof the business?\n\n### Options:\nA. s. 5,000\nB. s. 5,500\nC. s. 5,700\nD. s. 6,600\nE. s. 7,500\n\n### Answer:\nA : B : C = (20,000 x 24) : (15,000 x 24) : (20,000 x 18) = 4 : 3 : 3.\nB's share = Rs. 22000 x\t3/10\t= Rs. 6,600.\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a class there are 20 boys and 24 girls. In how many ways can a boy and a girl be selected?\n\n### Options:\nA. 508\nB. 480\nC. 800\nD. 570\nE. 503\n\n### Answer:\nWe can select one boy from 20 boys in 20 ways.\nWe select one girl from 24 girls in 24 ways\nWe select a boy and girl in 20 * 24 ways i.e., = 480 ways.\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the cost of fencing around a circular field of diameter 28 m at the rate of Rs.1.50 a meter?\n\n### Options:\nA. 299\nB. 132\nC. 269\nD. 267\nE. 262\n\n### Answer:\n2 * 22/7 * 14 = 88\n88 * 1 1/2\n= Rs.132\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average of a set of five distinct integers is 350. If each number is less than 2,000, and the median of the set is the greatest possible value, what is the sum of the two smallest numbers?\n\n### Options:\nA. -4,244\nB. -3,997\nC. -3,494\nD. -3,194\nE. The answer cannot be determined from the information given\n\n### Answer:\nSum of the set = 350*5=1750 Each number is less than 2000 and median of the set is the greatest possible value.\nTherefore last 3 numbers can be 1999,1998 and 1997. Their sum=5994.\nTherefore sum of two smallest numbers= 1750-5994= -4244\nAnswer=A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOn a certain day, orangeade was made by mixing a certain amount of orange juice with an equal amount of water. On the next day, orangeade was made by mixing the same amount of orange juice with twice the amount of water. On both days, all the orangeade that was made was sold. If the revenue from selling the orangeade was the same for both days and if the orangeade was sold at $0.50 per glass on the first day, what was the price per glass on the second day?\n\n### Options:\nA. $0.15\nB. $0.20\nC. $0.33\nD. $0.40\nE. $0.45\n\n### Answer:\nOn the first day 1 unit of orange juice and 1 unit of water was used to make 2 units of orangeade;\nOn the second day 1 unit of orange juice and 2 units of water was used to make 3 units of orangeade;\nSo, the ratio of the amount of orangeade made on the first day to the amount of orangeade made on the second day is 2 to 3. Naturally the ratio of the # of glasses of orangeade made on the first day to the # of glasses of orangeade made on the second day is 2 to 3.\nWe are told thatthe revenue from selling the orangeade was the same for both daysso the revenue from 2 glasses on the first day equals to the revenue from 3 glasses on the second day.\nSay the price of the glass of the orangeade on the second day was $x then 2*0.5=3*x --> x=$0.33.\nAnswer: C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe price of commodity X increases by 30 cents every year, while the price of commodity Y increases by 20 cents every year. If in 2001, the price of commodity X was $4.20 and the price of commodity Y was $4.50, in which year will commodity X cost 90 cents more than the commodity Y?\n\n### Options:\nA. 2010\nB. 2011\nC. 2012\nD. 2013\nE. 2014\n\n### Answer:\nThe cost of commodity X increases by 10 cents per year relative to commodity Y.\nThe price of X must gain 30 + 90 = $1.20 cents on commodity Y, which will take 12 years.\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe ratio of the volumes of two cubes is 2744 : 1331. What is the ratio of their total surface areas?\n\n### Options:\nA. 196 : 121\nB. 81 : 127\nC. 181 : 196\nD. 81 : 161\nE. 81 : 182\n\n### Answer:\nExplanation:\nRatio of the sides = \u00b3\u221a2744 : \u00b3\u221a1331 = 14 : 11\nRatio of surface areas = 14^2 : 11^2 = 196 : 121\nAnswer: Option A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the next number of the following sequence.\n8, 8, 6, 2,.... ?\n\n### Options:\nA. -4\nB. -5\nC. -6\nD. -7\nE. -8\n\n### Answer:\n8-(2*0) = 8\n8-(2*1) = 6\n6-(2*2) = 2\n2-(2*3) = -4\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a and b are the two values of t that satisfy\nthe equation t2 \u2013 6t + 8 = 0, with a > b, what is the value of a \u2013 b?\n\n### Options:\nA. 2\nB. 4\nC. 6\nD. 8\nE. 10\n\n### Answer:\nFactor the left side of the equation:\nt2 \u2013 6t + 8 = 0\n(t \u2013 2)(t \u2013 4) = 0\nSplit this equation into two equations and solve:\nt \u2013 2 = 0 t \u2013 4 = 0\nt = 2 t = 4\nThus, a = 4 and b = 2. So a \u2013 b = 4 \u2013 2 = 2.\ncorrect answer A)2\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n30 men can do a work in 40 days. When should 16 men leave the work so that the entire work is completed in 40 days after they leave the work?\n\n### Options:\nA. 87 days\nB. 14 days\nC. 55 days\nD. 44 days\nE. 22 days\n\n### Answer:\nTotal work to be done = 30 * 40 = 1200\nLet 16 men leave the work after 'P' days, so that the remaining work is completed in 40 days after they leave the work.\n40P + (16 * 40) = 1200\n40P = 560 => P = 14 days\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhen 242 is divided by a certain divisor the remainder obtained is 4. When 698 is divided by the same divisor the remainder obtained is 8. However, when the sum of the two numbers 242 and 698 is divided by the divisor, the remainder obtained is 7. What is the value of the divisor?\n\n### Options:\nA. 5\nB. 17\nC. 13\nD. 23\nE. None of these\n\n### Answer:\nlet that divisor be x\nsince remainder is 4 or 8 it means divisor is greater than 8.\nnow 242-4=238 =kx (k is an integer and 234 is divisble by x)\nsimilarly 698-8=690 = lx (l is an integer and 689 is divisible by x)\nadding both 698 and 242\n= (238+690)+4+8\n=x(k+l) + 12\nwhen we divide this number by x then remainder will be equal to remainder of (12 divided by x) = 7 hence x = 12-7 = 5\nhence A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nConvert 700 miles into meters?\n\n### Options:\nA. 784596\nB. 1126538\nC. 804670\nD. 784596\nE. 864520\n\n### Answer:\n1 mile = 1609.34 meters\n700mile = 700*1609.34 = 1126538 meters\nAnswer is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nPipe A can fill a tank in 6 hours, pipe B in 8 hours, and pipe C in 24 hours. If all the pipes are open, in how many hours will the tank be filled?\n\n### Options:\nA. 2.5\nB. 3\nC. 3.5\nD. 4\nE. 4.5\n\n### Answer:\nThe part filled by A + B + C in 1 hour\n= 1/6 + 1/8 + 1/24\n= 8/24 = 1/3\nAll the three pipes together will fill the tank in 3 hours.\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf, in a baseball game, a single picher can decide to throw either a 100mph fastball or 60 mph knuckleball on any pitch, how much less time, in seconds, does the batter have from when the ball is released as a fastball than when the ball is released as a knuckle ball? (Assume where the batter's point of contact is exactly 60ft away from the pitcher's release point. 5280 ft = 1 mile.)\n\n### Options:\nA. 6/22s\nB. 7/22s\nC. 8/22s\nD. 9/22s\nE. 15/22s\n\n### Answer:\nOne conversion to know is = 1 mile = 5280 ft\nTime taken for fastball = (60 / (100 * 5280)) * 60 * 60 = 9/22\nTime taken for knuckle ball = (60 / (60 * 5280)) * 60 * 60 = 15/22\nQn is the difference between the time taken by the two balls => 15/22 - 9/22 = 6/22\nOption A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nPoints A, B, and C lie, in that order, on a straight railroad track. The distance from point A to point B is twice the distance from point B to point C. A train traveled from point A to point C without stopping. The train's average speed when traveling from point A to point B was 150 miles per hour and the train's average speed when traveling from point B to point C was 100 miles per hour. What was the train's average speed, in miles per hour, when traveling from point A to point C?\n\n### Options:\nA. 22.5\nB. 21.43\nC. 25.5\nD. 26.5\nE. 27.5\n\n### Answer:\nAverage speed = distance/time\nBecause we are looking for average speed we can pick a distance for the variable d.\nSpeed A-B = 150\nSpeed B-C = 100\nAverage Speed = total distance/total rate\nrate = distance/time\nA====================B==========C\nIf A-B is twice the length of B-C then let A-B = 2d and let B-C = d\nAverage speed = 3d/(2d/150) + (d/100)\n3d/(4d/300 + (3d/300)\n3d/(7d/50)\n150d/7d\nAverage speed = 21.43\nANSWER: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a fair coin is tossed five times, what is the probability of getting exactly four heads in a row?\n\n### Options:\nA. 1/64\nB. 1/32\nC. 1/16\nD. 1/8\nE. 1/4\n\n### Answer:\nP(HHHHT) = 1/32\nP(THHHH) = 1/32\nThe sum of these probabilities is 2/32 = 1/16\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe traffic lights at 3 different roads change after every 14 sec, 72 sec, 108 sec respectively. If they all change simultaneously at 9:15 AM then at what time will they again change simultaneously.\n\n### Options:\nA. 9:22:12\nB. 9:42:15\nC. 10:15:24\nD. 9:40:12\nE. 10:01:20\n\n### Answer:\nLCM of 14,72,108 = 1512 = 25mnts 12sec\nThe lines will change every 25m 12sec\nThe light will change again after 9:15 AM is = 9:15+0:25:12 = 9:40:12\nAnswer is D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA box contains 22 electric bulbs, out of which 4 are defective. Two bulbs are chosen at random from this box. The probability that at least one of these is defective is\n\n### Options:\nA. 4/19\nB. 7/19\nC. 12/19\nD. 21/99\nE. 26/77\n\n### Answer:\nSolution\nP( None is defective)\n= 18C2 / 22C2\n= 51/77\nP( at least one is defective)\n= (1- 51/77)\n= 26/77.\nAnswer E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAA is two digit number then m times its cube of AA has 1 in its tens place then what is m.\n\n### Options:\nA. 3\nB. 4\nC. 5\nD. 6\nE. 7\n\n### Answer:\nwhen AA=11\n7*(11)^3= 7*1331= 9317\nm=7\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe L.C.M of two numbers is 2310 and their H.C.F is 30. If one number is 210 the Other is\n\n### Options:\nA. 330\nB. 300\nC. 270\nD. 250\nE. 350\n\n### Answer:\nThe other number\n= L.C.M * H.C.F/given number\n= 2310*30/210 = 330\nAnswer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a theater, the first row has 17 seats and each row has 3 more seats than previous row. If the last row has 44 seats, what is the total number of seats in the theater?\n\n### Options:\nA. 265\nB. 275\nC. 285\nD. 295\nE. 305\n\n### Answer:\nThe number of seats in the theater is\n17 + (17+3) + ...+ (17+27)=\n10(17) + 3(1+2+...+9)=\n10(17) + 3(9)(10)/2= 170 + 135 = 305\nThe answer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFour extra-large sandwiches of exactly the same size were ordered for m students, where m > 7. Three of the sandwiches were evenly divided among the students. Since 4 students did not want any of the fourth sandwich, it was evenly divided among the remaining students. If Carol ate one piece from each of the four sandwiches, the amount of sandwich that she ate would be what fraction of a whole extra-large sandwich?\n\n### Options:\nA. (6m-21)/[m(m-7)]\nB. (4m-21)/[m(m-7)]\nC. (8m-21)/[m(m-5)]\nD. (10m-21)/[m(m-5)]\nE. (4m-15)/[m(m-5)]\n\n### Answer:\nThree of the sandwiches were evenly divided among the students\ni.e. Amount of Sandwiches with each students = 3/m\nAmount of 4th Sandwich with remaining (m-7) students = 1/(m-7)\nThe amount of Sandwich that carol ate = 3/m + 1/(m-7) = (3m-21+m)/[m(m-7)] = (4m-21)/[m(m-7)]\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOne pipe can fill a tank three times as fast as another pipe. If together the two pipes can fill the tank in 38 minutes, then the slower pipe alone will be able to fill the tank in\n\n### Options:\nA. 144 mins\nB. 140 mins\nC. 136 mins\nD. 152 minw\nE. None of these\n\n### Answer:\nExplanation:\nLet the slower pipe alone fill the tank in x minutes\nthen faster will fill in x/3 minutes.\nPart filled by slower pipe in 1 minute = 1/x\nPart filled by faster pipe in 1 minute = 3/x\nPart filled by both in 1 minute =\n1/x+3/x=1/38\n=>4/x=1/38\nx=38\u22174=152mins\nOption D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n4 buses runs between Chennai and Mysore. If a man goes from Chennai to Mysore by a bus and comes back to Mysore by another bus, then the total possible ways are\n\n### Options:\nA. 4\nB. 8\nC. 12\nD. 16\nE. None of these\n\n### Answer:\nSince the man can go in 4 ways and can back in 3 ways. Therefore total number of ways are 4 x3 = 12ways.\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA diet contains 400 grams of a mixture of two foods, food X and food Y. Food X contains 10 percent protein and food Y contains 15 percent protein. If a diet provides exactly 50 grams of protein daily, how many grams of food X are in the mixture?\n\n### Options:\nA. 120\nB. 140\nC. 150\nD. 160\nE. 200\n\n### Answer:\nLet x be the number of grams of food X in the mixture.\n0.1x + 0.15(400-x) = 50\n0.05x = 10\nx = 200\nThe answer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA and B start a business with Rs.6000 and Rs.8000 respectively. Hoe should they share their profits at the end of one year?\n\n### Options:\nA. 3:8\nB. 3:4\nC. 3:5\nD. 3:2\nE. 3:1\n\n### Answer:\nThey should share the profits in the ratio of their investments.\nThe ratio of the investments made by A and B\n=6000 : 8000 => 3:4\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many times digit 6 is used while writing numbers from 150 to 1000?\n\n### Options:\nA. 648\nB. 300\nC. 252\nD. 225\nE. 26\n\n### Answer:\nThere are 100 numbers which begin with 600\nNext, In every 10 numbers such as 100 to 110, 110 to 120, 120 to 130 6 comes at least once. Number of such intervals = End limit - First no. / interval. Our range of numbers is 100 - 1000\n1000 - 100 = 900/10 = 90\nNumber of 10s interval in this is 90. So 90 '6s'\nSo far we have calculated 190.\nThe total now comes to 280. The nearest to which is 252. Hence C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe distance between Delhi and Mathura is 110 kms. A starts from Delhi with a speed of 20 kmph at 7 a.m. for Mathura and B starts from Mathura with a speed of 25 kmph at 8 p.m. from Delhi. When will they meet?\n\n### Options:\nA. 11 a.m\nB. 10 a.m\nC. 77 a.m\nD. 55 a.m\nE. 65 a.m\n\n### Answer:\nD = 110 \u2013 20 = 90\nRS = 20 + 25 = 45\nT = 90/45 = 2 hours\n8 a.m. + 2 = 10 a.m.\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train covers a distance of 12 km in 10 min. If it takes 6 sec to pass a telegraph post, then the length of the train is?\n\n### Options:\nA. 100\nB. 110\nC. 120\nD. 121\nE. 123\n\n### Answer:\nSpeed = (12/10 * 60) km/hr = (72 * 5/18) m/sec = 20 m/sec.\nLength of the train = 20 * 6 = 120 m.\nAnswer: Option C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAt what approximate time between 4 and 5 am will the hands of a clock be at right angle?\n\n### Options:\nA. 4 : 40 am\nB. 4 : 38 am\nC. 4 : 35 am\nD. 4 : 39 am\nE. None of these\n\n### Answer:\nHere H \u00d7 30 = 4 \u00d7 30 = 120\u00b0.\n(Since initially the hour hand is at 4. \u2234 H = 4).\nRequired angle A = 90\u00b0 and since, H \u00d7 30 > A\u00b0 so, there will be two timings.\nRequired time T = 2\u204411(H \u00d7 30 \u00b1 A) minutes past H.\n\u2234 One timing = 2\u204411(4 \u00d7 30 + 90) minutes past 4\n= 382\u204411 minutes past 4.\nOr 4 : 38 approx.\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that atleast one bulb is good?\n\n### Options:\nA. 125/167\nB. 125/118\nC. 125/126\nD. 125/128\nE. 125/129\n\n### Answer:\nRequired probability\n= 1 - 1/126 = 125/126\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nDifference of 2 numbers is 1660. If 7.5% of one number is 12.5% of the other number, find the 2 numbers?\n\n### Options:\nA. 125,150\nB. 5124,4515\nC. 4150,2490\nD. 3250,4510\nE. 1254,3210\n\n### Answer:\nLet the numbers be x and y\n7.5% of x = 12.5% of y\nx = 125y/75 = 5y/3\nx-y = 1660\n5y/3 - y = 1660\ny = 2490\nx = 5y/3 = 4150\nAnswer is C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA person got Rs.48 more when he invested a certain sum at compound interest instead of simple interest for two years at 8% p.a. Find the sum?\n\n### Options:\nA. 7500\nB. 2776\nC. 2877\nD. 2667\nE. 2671\n\n### Answer:\nP = (d * 1002) / R2\n=> (48 * 100 * 100) / 8 * 8 = Rs.7500\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe organizers of a week-long fair have hired exactly eight security guards to patrol the fairgrounds at night for the duration of the event. Exactly three guards are assigned to patrol the grounds every night, with no guard assigned consecutive nights. If the fair begins on a Monday, how many different groups of 3 guards will be available to patrol the fairgrounds on the following Saturday night?\n\n### Options:\nA. 6\nB. 8\nC. 10\nD. 12\nE. 14\n\n### Answer:\nFor any given day, only the guards patrolling on the previous day won't be available. So, 3 guards who patrolled on Friday won't be available. We are thus left with 5 guards.\nTo choose 3 out of 5, we will have 5C3 = 10 different groups.\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA can do a work in 60 days. He works for 15 days and later B alone completes the work in 30 days. In what time will they together complete the work?\n\n### Options:\nA. 24 days\nB. 25 days\nC. 30 days\nD. 32 days\nE. None of these\n\n### Answer:\nlet A can do a work in = 1/60 days\nhe does 15 days so work done by A in 15 days= (15) * (1/60) = 1/4\nremaining work is = 1- 1/4= 3/4\nB's one day work is =1/30\nso 3/4 work is done by B in=(3/4) * (1/30) = 1/40 days\ntime require to complete the work is= 1/60 + 1/40 = 5/120\n5/120 = 1/24\nso 24 days require to complete the work together.\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nX Y\n+Y X\n________\nThe sum of the two digit numbers above is a three digit number PQ6, where each letter X, Y, P, and Q represents a different non zero digit. Which of the following can be the value of X?\nI)\t7\nII)\t8\nIII)\t9\n\n### Options:\nA. I only\nB. II only\nC. III only\nD. I , II and III\nE. I and II only\n\n### Answer:\nit can be a combination of 9,7 or 8,8\nI choose D as an answer.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA bat is bought for Rs.400 and sold at a gain of 20% find its selling price?\n\n### Options:\nA. Rs.460/-\nB. Rs.480/-\nC. Rs.500/-\nD. Rs.520/-\nE. Rs.540/-\n\n### Answer:\n100 % ------> 400 (100 * 4 = 400)\n120 % ------> 480 (120 * 4 = 480)\nSelling price = Rs.480/-\nOption 'B'\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nLook at this series: 0.6, 0.3, ____, 0.075, 0.0375, ... What number should fill the blank?\n\n### Options:\nA. 0.015\nB. 1.15\nC. 0.15\nD. 0.25\nE. 0.35\n\n### Answer:\nThis is a simple multiplication series. Each number is multiple by 1/2.\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat ratio must a shopkeepermix Peas and Soybean of Rs.16 and Rs. 25/kg, As to obtain a mixture of Rs.22?\n\n### Options:\nA. 10 : 7\nB. 9 : 8\nC. 1 : 2\nD. 13 : 11\nE. 14 : 8\n\n### Answer:\nCorrect option: (C)\nUse rule of alligation, to determine the ratio\nThe required ratio of Soybean and Peas = 3 : 6 = 1 :2\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA fair coin is tossed repeatedly. If heads appears on first 5 tosses what is the probability that tail appears on the next two tosses?\n\n### Options:\nA. 1/6\nB. 1/5\nC. 1/3\nD. 1/4\nE. 1/6\n\n### Answer:\nExplanation :\nLike mentioned in the question, the coin is fair. So chance of appearing of head and tail on each toss is same and each toss is independent from the previous one. So the chance of appearing tail on the next two tosses is still 1/2 each.\n1/2 * 1/2 = 1/4\nAnswer : D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nDue to construction, the speed limit along an 10-mile section of highway is reduced from 55 miles per hour to 20 miles per hour. Approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ?\n\n### Options:\nA. A) 6.24\nB. B) 8\nC. C) 10\nD. D) 19.1\nE. E) 24\n\n### Answer:\nOld time in minutes to cross 10 miles stretch = 10*60/55 = 10*12/11 = 10.9\nNew time in minutes to cross 10 miles stretch = 10*60/20 = 10*3 = 30\nTime difference = 19.1\nAns:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nBob wants to run a mile in the same time as his sister. If Bob\u2019s time for a mile is currently 10 minutes and his sister\u2019s time is currently 8 minutes 30 seconds, by what percent does Bob need to improve his time in order run a mile in the same time as his sister?\n\n### Options:\nA. 3%\nB. 15%\nC. 8%\nD. 10%\nE. 12%\n\n### Answer:\nBob's time = 600 secs.\nHis sis' time = 510 secs.\nPercent increase needed = (640-510/600) * 100 = 90/600 * 100 = 15%. Ans (B).\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat are the next two numbers in this sequence?\n7, 14, 17, 21, 27, 28, 35, 37, ?\n\n### Options:\nA. 40\nB. 41\nC. 42\nD. 43\nE. 44\n\n### Answer:\nthese are digits which are either multiples of 7 or containing the digit 7.\ns0 next numbers are 42\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the sides of a rectangle are increased by 35%, what is the percentage increase in the area?\n\n### Options:\nA. 38.25%\nB. 40.25%\nC. 82.25%\nD. 50%\nE. 65%\n\n### Answer:\nIf sides are a and b, after increase sides would be 1.35a and 1.35 b.\nPercentage increase in area = (1.35a*1.35b - ab) *100/ab = 82.25\nAnswer : C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA sum of money amounts to Rs.9800 after 5 years and Rs.12005 after 8 years at the same rate of simple interest. The rate of interest per annum is\n\n### Options:\nA. 15%\nB. 12%\nC. 8%\nD. 7%\nE. 5%\n\n### Answer:\nExplanation :\nSimple Interest for 3 years = (Rs.12005 - Rs.9800) = Rs.2205\nSimple Interest for 5 years = 22053\u00d75=Rs.3675\nPrincipal(P) = (Rs.9800 - Rs.3675) = Rs.6125\nR = 100\u00d7SI/PT\n=100\u00d73675/6125\u00d75\n=12%\nAnswer : Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the common ratio of three numbers in G.P whose product is 216 and the sum of the products taken in pairs is 114.\n\n### Options:\nA. 2 or \u00bd\nB. 2/3 or 3/2\nC. \u00be or 4/3\nD. 4 or \u00bc\nE. 5 or 1/5\n\n### Answer:\nLet the terms be a/r, a , ar\na/r *a * ar = a 3 =216, a =6\n(a/r*a )+ (a*ar) + (ar*a/r ) =114, a 2/r + a 2 r + a 2 =114\na 2 ( 1/r + r +1 ) = 114, 36[( 1+ r 2 +r )/r] =114\n6 [( 1 +r 2+ r )/r ]= 19, 6 r 2 -13 r + 6 = 0,\nOn solving, r = 2/3 or 3/2\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhile playing a certain dice game, Chris wins if the sum of the two dice is 10, at which point the game is over. If the game allows Chris three rolls in an attempt to win, what is the probability that Chris will win?\n\n### Options:\nA. 1/2\nB. 17/36\nC. 190/827\nD. 11/36\nE. 25/216\n\n### Answer:\nProbability of winning game = 1- Probability of losing game\nProbability of losing game = (Probability of not getting sum 7 in any of the three attempts)\nWays of getting sum 10 = (4,6)(5,5)(6,4)= 3 ways\nTotal ways of getting outcome on two dice =6*6=36\nProbability of getting sum as 10 in any attempt =3/36=1/12\nProbability of NOT getting sum as 10 in any attempt = 1-(1/12)= 11/12\nProbability of losing game =(11/12)*(11/12)*(11/12)=637/827\nI.e. Probability of wining game = 1-(637/827) = 190/827\nAnswer : Option C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain ball team has an equal number of right- and left-handed players. On a certain day, two-thirds of the players were absent from practice. Of the players at practice that day, one-third were right handed. What is the ratio of the number of right-handed players who were not at practice that day to the number of left handed players who were not at practice?\n\n### Options:\nA. 1/3\nB. 2/3\nC. 7/5\nD. 5/7\nE. 3/2\n\n### Answer:\nSay the total number of players is 18, 9 right-handed and 9 left-handed.\nOn a certain day, two-thirds of the players were absent from practice --> 12 absent and 6 present.\nOf the players at practice that day, one-third were right-handed --> 6*1/3=2 were right-handed and 4 left-handed.\nThe number of right-handed players who were not at practice that day is 9-2=7.\nThe number of left-handed players who were not at practice that days is 9-4=5.\nThe ratio = 7/5.\nAnswer: C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n12 year old Manick is three times as old as his brother Rahul. How old will Manick be when he is twice as old as Rahul ?\n\n### Options:\nA. 16\nB. 27\nC. 21\nD. 10\nE. 11\n\n### Answer:\nManick's present age = 12 years, Rahul's present age = 4 years.\nLet Manick be twice as old as Rahul after x years from now.\nThen, 12 + x = 2 (4 + x) 12 + x = 8 + 2x x = 4.\nHence, Manick's required age = 12 + x = 16 years.\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA worker makes a toy in every 2h. If he works for 120h, then how many toys will he make ?\n\n### Options:\nA. 40\nB. 60\nC. 45\nD. 39\nE. None\n\n### Answer:\nNo. of toys = 120/2 = 60\nAnswer : B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nLinda bought 3 notebooks at $1.20 each; a box of pencils at $1.50 and a box of pens at $1.70. How much did Linda spend?\n\n### Options:\nA. $6.80\nB. $8.40\nC. $7.70\nD. $4.70\nE. $3.90\n\n### Answer:\nLinda spent\n1.20 ? 3 = $3.60 on notebooks\nThe total amount of money that Linda spent is equal to\n3.60 + 1.50 + 1.70 = $6.80\ncorrect answer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe faces of pyramid are to be painted by 4 different colors. In how many ways can be this be done?\n\n### Options:\nA. A.720\nB. B.256\nC. C.24\nD. D.12\nE. E.36\n\n### Answer:\nIf I have to paint 4 sides with 4 different colour...\nFirst face can have 4c1 options,\n2nd would have 3c1, and subsequent ones would have 2c1 and 1 options respectively.\nTotal options = 4c1 x 3c1 x 2c1 x 1 = 24 distinct ways\nCorrect answer - C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThree faces of a fair die are Yellow, two faces red and two blue.The die is tossed three\ntimes. The probability that the colours, yellow, red and blue appear in the first, second and\nthird tosses respectively is\n\n### Options:\nA. 1/36\nB. 1/18\nC. 1/32\nD. 1/37\nE. None of these\n\n### Answer:\nProbability of getting yellow color = P(Y) = 3/6 = 1/2\nProbability of getting red color = P(R) = 2/6 = 1/3\nProbability of getting blue color = P(B) = 2/6=1/3\nSo, the probability that the colors yellow, red and blue appear in first, second and third toss respectively= P(Y \u2229 R \u2229 B) = P(Y) x P(R) x P(B) = 1/2 x 1/3 x 1/3 = 1/18\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA speaks the truth in 75% of cases and B in 80% of cases. In what percent of cases are they likely to contradict each other in narrating the same event?\n\n### Options:\nA. 0.225\nB. 0.37\nC. 0.32\nD. 0.35\nE. 0.55\n\n### Answer:\nDifferent possible cases of contradiction occurs when A speaks the truth and B does not speak the truth or A does not speak the truth and B speaks the truth.\n(3/4 x 1/5) + (1/4 x 1/5) = 7/20 = 35%\n= 0.35\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe entrance fee for a fair is $5 for persons under the age of 18, and 20% more for persons older. Each ride at the fair costs $0.50. If Joe goes with her 6 years old twin brothers, and they each took 3 rides in total. How much money does Joe end up spending at the fair?\n\n### Options:\nA. 16\nB. 20.5\nC. 17.5\nD. 20\nE. 4.5\n\n### Answer:\nTotal entrance fee is (2*$5) + (1.20*5)= $16\nTotal rides fee is (0.50*3)*3= $4.50\nTotal money spent is $20.50\nAnswer is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the principal sum?\nI. The sum amounts to Rs. 690 at S.I.\nII. Total year is 8 years.\nIII. The rate of interest is 5% p.a.\n\n### Options:\nA. I and III only\nB. II and III only\nC. I and II only\nD. Any two of the three\nE. All I, II and III\n\n### Answer:\nExplanation:\nClearly, all the three statements are needed to solve this question\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe side of a square has the length of 9. What is the area of the region shaded?\n\n### Options:\nA. 48-8\u03c0\nB. 48-6 \u03c0\nC. 24+6\u03c0\nD. 16+8\u03c0\nE. 64-9\u03c0\n\n### Answer:\nThe area of a square whose side is 9 \u2013 (the area of a square whose side is 4 + the area of the semi-circle whose side is 4) = the area of the region shaded\nThe correct answer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nwhat is the compound interest on rs:80,000 for 4 months at the rate of 5% per annum\n\n### Options:\nA. 1341.69\nB. 1342.69\nC. 1343.69\nD. 1344.69\nE. 1345.69\n\n### Answer:\nit is monthly compound\nrate=5/12% per month\n80000*(1+5/1200)^4-80000=1341.69\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nLet us say that a table tennis tournament was going on with knock out terms which means the one who loses the match is out of the tournament. 450 players took part in that tournament.\nHow many matches were played?\n\n### Options:\nA. 449 matches.\nB. 88 matches.\nC. 77 matches.\nD. 66 matches.\nE. 55 matches.\n\n### Answer:\nSolution:\n449 matches.\nThe number of matches will always sum up to one less than the number of players in a knock out tournament. You may calculate it in any manner. Thus 449 matches were played.\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the dividend. divisor 16, the quotient is 6 and the remainder is 2\n\n### Options:\nA. 86\nB. 87\nC. 88\nD. 89\nE. 90\n\n### Answer:\nC = d * Q + R\nC = 16 * 6 + 2\nC = 86 + 2\nC = 88\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJohn distributes his pencil among his 4 friends Rose, Mary, Ranjan, and Rohit in the ratio 1/2 : 1/3 :1/3:1/5 . What is the minimum no. of pencils that the person should have?\n\n### Options:\nA. 41\nB. 65\nC. 70\nD. 77\nE. 98\n\n### Answer:\nRakesh : Rahul : Ranjan : Rohit = 1 / 2 : 1 / 3 : 1 / 3 : 1 / 5\nStep 1: At First we need to do is LCM of 2,3,3 and 5 is 30.\nStep 2: Then pencil are distributed in ratio among friends,\nRakesh = ( 1 / 2 x 30 ) = 15.\nRahul = ( 1 / 3 x 30 ) = 10.\nRanjan = ( 1 / 3 x 30 ) = 10.\nRohit = ( 1 / 5 x 30 ) = 6.\nStep 3: Total number of pencils are ( 15 x + 10 x + 10 x + 6 x) = 41 x.\nFor minimum number of pencils x = 1 .\nThe person should have at least 41 pencils.\nA)\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe Snow Lovers Ski Team is comprised of 4 men and 8 women. If a team of 5 skiers is to be randomly selected to pack the skis into the bus, what is the probability that the team will have exactly 3 women?\n\n### Options:\nA. 14/33\nB. 7/33\nC. 2/7\nD. 13/73\nE. 12/27\n\n### Answer:\nCombination Probability Formula: nCr = n!/[r!(n-r)!]\nTotal possible, select 5 people from 12 people = 12C5 = 12!/[5!(12 - 5)!] = 792.\nTo have 3 women there must be 2 men, select 2 men from 4 = 4C2 = 6.\nAnd, select 3 women from 8 = 8C3 = 56.\n3 women and 2 men = (6)(56) = 336\nProbability = (number outcomes favorable)/(total number outcomes) = 336/792 = 14/33\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTruck X is 13 miles ahead of Truck Y, which is traveling the same direction along the same route as Truck X. If Truck X is traveling at an average speed of 47 miles per hour and Truck Y is traveling at an average speed of 53 miles per hour, how long will it take Truck Y to overtake and drive 5 miles ahead of Truck X?\n\n### Options:\nA. 2 hours\nB. 2 hours 20 minutes\nC. 2 hours 30 minutes\nD. 2 hours 45 minutes\nE. 3 hours\n\n### Answer:\nRelative speed = 53-47 = 6 miles per hour\nDist required = 13+5 = 18 miles\nTime taken to overtake = 18/6 = 3 hours.\nE is the answer.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds. Its length is:\n\n### Options:\nA. 110 m\nB. 120 m\nC. 190 m\nD. 150 m\nE. 180 m\n\n### Answer:\nAnswer: Option D\nLet the length of the train be x meters and its speed be y m/sec.\nThey, x / y = 15 => y = x/15\nx + 100 / 25 = x / 15\nx = 150 m.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA hare and a jackal are running a race. Three leaps of the hare are equal to four leaps of the jackal. For every three leaps of the hare, the jackal takes five leaps. Find the ratio of the speed of the hare to the speed of the jackal.\n\n### Options:\nA. 6:7\nB. 4:5\nC. 5:8\nD. 25:64\nE. 3:5\n\n### Answer:\nThe hare takes 3 leaps and the jackal takes 5 leaps.\n1 hare leap = 4/3 jackal leaps\nThus the hare's 3 leaps = 3*(4/3) = 4 jackal leaps.\nThe ratio of their speeds is 4:5.\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA metallic sphere of radius 12 cm is melted and drawn into a wire, whose radius of cross section is 8 cm. What is the length of the wire?\n\n### Options:\nA. 16 cm\nB. 24 cm\nC. 28 cm\nD. 36 cm\nE. 39 cm\n\n### Answer:\nVolume of the wire (in Cylindrical shape) is equal to the volume of the sphere.\n\u03c0(8)^2 * h = (4/3)\u03c0 (12)^3 => h\n= 36 cm\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average monthly salary of 20 employees in an organisation is Rs. 1500. If the manager's salary is added, then the average salary increases by Rs. 100. What is the manager's monthly salary?\n\n### Options:\nA. 2000\nB. 3000\nC. 3600\nD. 4800\nE. 4000\n\n### Answer:\nManager's monthly salary\n= Rs. (1600 * 21 - 1500 * 20) = Rs. 3600\nANSWER C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average of 11 numbers is 10.9. If the average of the first six numbers is 10.5 and that of the last six numbers is 11.4, then the middle number is\n\n### Options:\nA. 71.5\nB. 11.5\nC. 81.5\nD. 11.5\nE. 21.5\n\n### Answer:\nExplanation:\nMiddle numbers = [(10.5 x 6 + 11.4 x 6) - 10.9 x 11] = (131.4 - 119-9) = 11.5.\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA right circular cylinder has a height of 22 and a radius of 5. A rectangular solid with a height of 15 and a square base, is placed in the cylinder such that each of the corners of the solid is tangent to the cylinder wall. Liquid is then poured into the cylinder such that it reaches the rim. What is the volume of the liquid?\n\n### Options:\nA. 500(\u03c0 \u2013 3)\nB. 500(\u03c0 \u2013 2.5)\nC. 500(\u03c0 \u2013 2)\nD. 550(\u03c0 \u2013 1.5)\nE. 500(\u03c0 \u2013 1)\n\n### Answer:\n[quote=Bunuel]A right circular cylinder has a height of 20 and a radius of 5. A rectangular solid with a height of 15 and a square base, is placed in the cylinder such that each of the corners of the solid is tangent to the cylinder wall. Liquid is then poured into the cylinder such that it reaches the rim. What is the volume of the liquid?\nThe square base has sides of sqrt(50) due to the 45-45-90 triangle\n22*25*pi - 15*sqrt(50)^2\n=550(\u03c0 \u2013 1.5)\nD. 500(\u03c0 \u2013 1.5)\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many times are the hands of a clock at right angle in a day?\n\n### Options:\nA. 22\nB. 44\nC. 41\nD. 21\nE. 40\n\n### Answer:\nCorrect Answer : B\nIn 12 hour hands of clock are at right angle 22 times\nIn 24 hour hands of clock are at right angle 44 times\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train,130 metres long travels at a speed of 45 km/hr crosses a bridge in 30 seconds. What is the length of the bridge?\n\n### Options:\nA. 210\nB. 225\nC. 235\nD. 245\nE. 260\n\n### Answer:\nSpeed =45 km/hr=45\u00d75/18 m/s =12.5 m/s Distance travelled = (Speed x Time)\nDistance travelled = 12.5\u00d730=375 m\nlength of the bridge = 375-130 = 245 m\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA glucose molecule contains 6 carbon, 12 hydrogen and 6 oxygen atoms. During photosynthesis, green plants create glucose daily. If, over a period of 15 days, an eucalyptus plant (a green plant) creates 15,000 molecules of glucose then approximately how many more atoms of hydrogen than carbon are created on average per day?\n\n### Options:\nA. 60,000\nB. 6,000\nC. 2,500\nD. 250\nE. 0\n\n### Answer:\nSolution:\nWe know that 15,000 glucose molecules are created over a period of 15 days. Therefore 15,000/15 = 1,000 glucose molecules are created on average per day.\nEach glucose molecule contains 6 carbon atoms and 12 hydrogen atoms. So 1,000 glucose molecules contain 6 \u00d7 1,000 = 6,000 carbon atoms and 12 \u00d7 1,000 = 12,000 hydrogen atoms. The difference is 12,000 \u2013 6,000 = 6,000.\nThe correct answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA positive whole number has factors of 3 and 5. The number MUST be divisible by: I. 15 II. 30 III. 60\n\n### Options:\nA. I & II\nB. III\nC. I & III\nD. II & III\nE. II\n\n### Answer:\n15 , 30 is not divisible by 60.But 60 is divisible by 3,5,15,30\nSo answer is III\nAnswer : B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a consumer survey, 88% of those surveyed liked at least one of three products: 1, 2, and 3. 55% of those asked liked product 1, 40% liked product 2, and 20% liked product 3. If 7% of the people in the survey liked all three of the products, what percentage of the survey participants liked more than one of the three products?\n\n### Options:\nA. 15\nB. 20\nC. 25\nD. 30\nE. 35\n\n### Answer:\n55 + 40 + 20 = 115\nThis number includes some people counted twice and some people counted three times.\n115 - 88 = 27, and this number represents people counted twice or three times.\n7% of the people are counted two extra times.\nThe percentage of people counted one extra time is 27 - 7(2) = 13.\nThe percentage of people who liked more than one product is 7% + 13% = 20%.\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nBy selling 99 pens, a trader gains the cost of 33 pens. Find his gain percentage?\n\n### Options:\nA. 33 1/3%\nB. 68 1/3%\nC. 28 1/3%\nD. 18 1/3%\nE. 11 1/3%\n\n### Answer:\nExplanation:\nLet the CP of each pen be Rs. 1.\nCP of 99 pens = Rs. 99\nProfit = Cost of 33 pens = Rs. 33\nProfit% = 33/99 * 100 = 33 1/3%\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf (c - a)/(c - b) = 3, then (5b - 5a)/(c - a) =\n\n### Options:\nA. 0.5\nB. 1\nC. 1.5\nD. 3.33\nE. 2.5\n\n### Answer:\nLet's say c=7, b=5, a=1 so that our 1st expression holds true. Now, ibsert those numbers in the second expression and we'll get 3.33\nAnswer D (hopefully )))\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf X = the product of five distinct prime numbers, how many factors does X have besides 1 and itself?\n\n### Options:\nA. 24\nB. 30\nC. 36\nD. 42\nE. 48\n\n### Answer:\nSince X has 5 distinct prime factors, X has a total of 2^5 = 32 factors.\nBesides 1 and itself, X has 30 factors.\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe variable x is inversely proportional to the square of the variable y. If y is divided by 6a, then x is multiplied by which of the following?\n\n### Options:\nA. 1/36a\nB. 1/36a^2\nC. 1/6a\nD. 36a\nE. 36a^2\n\n### Answer:\ninitially - did x= 1/y^2\nBut this yielded the wrong answer,\nI then re examined the question and tried y^2/x =1\nWhich I then got y = SQR(X)\nsubbing into y/6a I got answer E)\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe ages of two persons differ by 16 years. 6 years ago, the elder one was 3 times as old as the younger one. What are their present ages of the elder person\n\n### Options:\nA. 11\nB. 66\nC. 28\nD. 30\nE. 99\n\n### Answer:\nLet's take the present age of the elder person = x\nand the present age of the younger person = x \u2013 16\n(x \u2013 6) = 3 (x-16-6)\n=> x \u2013 6 = 3x \u2013 66\n=> 2x = 60\n=> x = 60/2 = 30\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA can run a kilometer race in 4 1/2 min while B can run same race in 5 min. How many meters start can A give B in a kilometer race, so that the race mat end in a dead heat?\n\n### Options:\nA. 299m\nB. 287m\nC. 279m\nD. 100m\nE. 277m\n\n### Answer:\nA can give B (5 min - 4 1/2 min) = 30 sec start.\nThe distance covered by B in 5 min = 1000 m.\nDistance covered in 30 sec = (1000 * 30)/300 = 100 m.\nA can give B 100m start.\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nGiven that 268x74= 19832, find the value of 2.68x.74.\n\n### Options:\nA. 1.9832\nB. 1.0025\nC. 1.5693\nD. 1.0266\nE. None\n\n### Answer:\nSolution\nSum of decimals places\t=(2+2)\n= 4.\nTherefore,\t= 2.68\u00d7.74\n= 1.9832\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA local bank that has 11 branches uses a two-digit code to represent each of its branches. The same integer can be used for both digits of a code, and a pair of two-digit numbers that are the reverse of each other (such as 17 and 71) are considered as two separate codes. What is the fewest number of different integers required for the 11 codes?\n\n### Options:\nA. 3\nB. 11 ( 2 integers 4 codes)\nC. 5\nD. 6\nE. 7\n\n### Answer:\nPick any two integer.\nIntegers: 12\nCode: 11, 12, 21, 22 = 4 Codes\nAdd one more integer: 3\n13, 31, 33, 23, 32 = 5 Codes\nAdd one more integer: 4\n44, 14, 41, 24, 42, 34, 43 = 7 Codes\nTotal = 16 Codes. Enough. Answer: B\n4 integers create 11 codes.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n8^100 is divisible by 17. Find the remainder?\n\n### Options:\nA. 10\nB. 12\nC. 16\nD. 21\nE. 26\n\n### Answer:\nThis is an extremely difficult problem to solve with out Fermat's little theorem. By applying Fermat's little theorem , We know that 816 when divided by 17, the remainder is 1.\nSo divide 100 by 16 and find the remainder. Remainder = 4\nTherefore, 100 = (16 \u00d7 6) + 4\nNow this problem can be written as 810017 = 816\u00d76+417 = (816)6\u00d78417\nNow this problem simply boils down to (1)6\u00d78417 = 8417\n84 = 82\u00d782, we need to find the remainder when 64 \u00d7 64 is divisible by 17. Or 13 \u00d7 13 = 169. When 169 is divided by 17, remainder is 16.\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train 200 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is:\n\n### Options:\nA. 45 km/hr\nB. 50 km/hr\nC. 77 km/hr\nD. 55 km/hr\nE. 56 km/hr\n\n### Answer:\nSpeed of the train relative to man = (200/10) m/sec = 20 m/sec. [20 * (18/5)] km/hr = 72 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 72==> x = 77 km/hr.\nANSWER: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThree 6 faced dice are thrown together. The probability that exactly two dice show the same number on them is -.\n\n### Options:\nA. 5/12\nB. 4/13\nC. 5/17\nD. 3/12\nE. 8/9\n\n### Answer:\nUsing question number 11 and 12, we get the probability as\n1 - (1/36 + 5/9) = 5/12\nANSWER A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe area of Circle O is added to its diameter. If twice the circumference of Circle O is then subtracted from this total, the result is 8. What is the diameter of Circle O?\n\n### Options:\nA. 4/\u03c0\nB. 4\nC. 8\nD. 10\nE. 6\n\n### Answer:\narea+diameter-2*circumference=8\npi*r^2+2r=8+2*2pi*r\nisolate r and get r(pi*r+2)=8+4pi*r\nr=(8+4pi*r)/(pi*r+2) =>4(pi*r+2)/(pi*r+2)\nr=4\nDiameter = 2r = 8\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJohn and Lewis leave Chennai for Bangalore simultaneously at 6 P.M in the evening driving in two cars at speeds of 50 mph and 70 mph respectively. As soon as Lewis reaches Bangalore he returns back to Chennai along the same route and meets John on the way back. If the distance between the two cities is 140 miles, how far from Chennai did John and Lewis meet?\n\n### Options:\nA. 110 miles\nB. 130 miles\nC. 100 miles\nD. 125 miles\nE. 25 mlies\n\n### Answer:\nTime taken by Lewis to reach Bangalore = 140/70 = 2 hours\nIn 2 hours, John travels 50*2 = 100 miles\nSo distance at which they meet should be greater than 100 miles.\nOnly C satisfies.\nAnswer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nin a bus left side are 15 seats available,3 few seats in right side because in rear exit door .Each seat hold 3 people.In addition ,there is a seat back can sit 8 people all together .how many people can sit in a bus?\n\n### Options:\nA. 52\nB. 49\nC. 95\nD. 88\nE. 89\n\n### Answer:\nRight Side =15 seat\nLeft Side =15-3 (3 few seat in right side)= 12 seat\nTotal= 15+12= 27\nPeople can seat in 27 seat= 27*3=81\nPeople can seat in Last Seat = 8\nTotal People can seat= 81+8=89\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSolve below question 2x + 1 = -17\n\n### Options:\nA. 7\nB. -9\nC. 10\nD. -1\nE. 2\n\n### Answer:\n1. Subtract 1 from both sides:\n2x + 1 - 1 = -17 - 1\n2. Simplify both sides:\n2x = -18\n3. Divide both sides by 2:\n4. Simplify both sides:\nx = -9\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n1 \u00f7 [1 + 1 \u00f7 {1 + 1 \u00f7 (1 \u00f7 1)}] = ?\n\n### Options:\nA. 5/3\nB. 4/3\nC. 2/3\nD. 1/3\nE. 1/5\n\n### Answer:\nExplanation:\n1 \u00f7 [1 + 1 \u00f7 {1 + 1 \u00f7 (1 \u00f7 1)}]\n= 1 \u00f7 [1 + 1 \u00f7 {1 + 1 \u00f7 1}]\n= 1 \u00f7 [1 + 1 \u00f7 {1 + 1}]\n= 1 \u00f7 [1 + 1 \u00f7 2]\n= 1 \u00f7 [1 + (1/2)] = 1 \u00f7 3/2 = 1 \u00d7 3/2 = 1 \u00d7 2/3 = 2/3\nAnswer: Option C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain company assigns employees to offices in such a way that some of the offices can be empty and more than one employee can be assigned to an office. In how many ways can the company assign 3 employees to 4 different offices?\n\n### Options:\nA. 52\nB. 64\nC. 32\nD. 11\nE. 12\n\n### Answer:\nEach of three employee can be assigned to either of offices, meaning that each has 2 choices --> 4*4*4=4^3=64.\nAnswer: B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average price of three items of furniture is Rs. 12000. If their prices are in the ratio 3:5:7, the price of the cheapest item is?\n\n### Options:\nA. 2379\nB. 2889\nC. 9288\nD. 7200\nE. 28311\n\n### Answer:\nLet their prices be 3x, 5x and 7x.\nThen, 3x + 5x + 7x = (12000 * 3) or x = 2400.\nCost of cheapest item = 3x = Rs. 7200.\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man can row with a speed of 15 kmph in still water. If the stream flows at 5 kmph, then the speed in downstream is?\n\n### Options:\nA. 27\nB. 23\nC. 20\nD. 28\nE. 12\n\n### Answer:\nM = 15\nS = 5\nDS = 15 + 5 = 20\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the difference between compound interest (interest compounded yearly) and simple interest on a certain sum at the rate 20% p.a. after 3 years is Rs.1280 then what is the principal?\n\n### Options:\nA. 7900\nB. 8,000\nC. 10,000\nD. 8,300\nE. 9,300\n\n### Answer:\nlet p is the principal,so p([120/100]^3-1)-p*20/100*3=1280\np[728/1000-3/5]=1280\np=1280*5*1000/728*5-3000=10000\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat number has a 5:1 ratio to the number 10?\n\n### Options:\nA. 42\nB. 50\nC. 55\nD. 62\nE. 65\n\n### Answer:\nExplanation:\n5:1 = x: 10\nx = 50\nANSWER IS B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the average (arithmetic mean) of 5 positive temperatures is y degrees Fahrenheit, then the sum of the 3 greatest of these temperatures, in degrees Fahrenheit, could be:\n\n### Options:\nA. 6y\nB. 4y\nC. 5y/3\nD. 3y/2\nE. 3y/5\n\n### Answer:\nThe sum of three greatest should be more than sum of two lowest.\nThe total sum is; 5y\nA. 6y; 6y is more than 5y. Not possible.\nB. 4y; 5y-4y=y(Possible)\nC. 5y/3; 10y/3; 10y/3 > 5y/3. Not possible\nD. 3y/2; 7y/2; 7y/2 > 3y/2. Not possible\nE. 3y/5; 22y/5; 22y/5 > 3y/5. Not possible.\nAns:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a three digit number, the hundred digit is 2 more than the tens digit and the units digit is 2 less than the tens digit. If the sum of the digits is 18, find the number?\n\n### Options:\nA. 867\nB. 864\nC. 385\nD. 946\nE. 549\n\n### Answer:\nB\n864\nLet the three digit numbers be 100a + 10b + c\na = b + 2\nc = b - 2\na + b + c = 3b = 18 => b = 6\nSo a = 8 and b = 4\nHence the three digit number is: 864\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe owner of a furniture shop charges his customer 24% more than the cost price. If a customer paid Rs. 8339 for a computer table, then what was the cost price of the computer table?\n\n### Options:\nA. 2882\nB. 2277\nC. 2697\nD. 6725\nE. 2681\n\n### Answer:\nCP = SP * (100/(100 + profit%))\n= 8339(100/124)\n= Rs. 6725.\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSuppose that f(x) is a function such that for every real number x,i)f(x)+f(1-x) = 14 and (ii) f(1+x) = 3+f(x). Then f(x)+f(-x)\nmust equal\n\n### Options:\nA. 8\nB. 9\nC. 10\nD. 11\nE. 12\n\n### Answer:\nSince (ii) holds for every real number x, it will remain valid if we replace x with\n-x. Therefore, f(1-x) = 3+f(-x). Now, from (i), 14 = f(x)+f(1-x) = f(x)+3+f(-x)\nso that f(x) + f(-x) = 14-3 = 11. (Observe that f(x) = 3x + 4 satisfies the conditions\nin the problem.)\ncorrect answer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFor the set { 3, 3, 4, 4, 5, 5, x}, which of the following values of x will most increase the standard deviation?\n\n### Options:\nA. (-3)^2\nB. 2\nC. 3\nD. 4\nE. 5\n\n### Answer:\nStandard Deviation Step 1, as pointed out by others, is to find out the mean = 4\nStep 2, For each number: subtract the Mean and square the result =\n(1-4)^2=(-3)^2\n(2-4)^2=(-2)^2\n(3-4)^2 =(-1)^2\n(4-4)^2=(.0)^2\n(5-4)^2=(1)^2\nClearly (1-4)^2=(-3)^2 will give you the greatest value among all the other options.\nHence A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo trains A and B starting from two points and travelling in opposite directions, reach their destinations 9 hours and 4 hours respectively after meeting each other. If the train A travels at 110kmph, find the rate at which the train B runs.\n\n### Options:\nA. 40\nB. 165\nC. 120\nD. 80\nE. 100\n\n### Answer:\nIf two objects A and B start simultaneously from opposite points and, after meeting, reach their destinations in \u2018a\u2019 and \u2018b\u2019 hours respectively (i.e. A takes \u2018a hrs\u2019 to travel from the meeting point to his destination and B takes \u2018b hrs\u2019 to travel from the meeting point to his destination), then the ratio of their speeds is given by:\nSa/Sb = \u221a(b/a)\ni.e. Ratio of speeds is given by the square root of the inverse ratio of time taken.\nSa/Sb = \u221a(4/9) = 2/3\nThis gives us that the ratio of the speed of A : speed of B as 2:3.\nSince speed of A is 110 kmph, speed of B must be 110*(3/2) = 165 kmph\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a student loses 5 kilograms, he will weigh twice as much as his sister. Together they now weigh 110 kilograms. What is the student's present weight in kilograms?\n\n### Options:\nA. 71\nB. 72\nC. 73\nD. 74\nE. 75\n\n### Answer:\nLet x be the weight of the sister.\nThen the student's weight is 2x+5.\nx + (2x+5) = 110\n3x = 105\nx = 35 kg\nThen the student's weight is 75 kg.\nThe answer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn an election, candidate Douglas won 60 percent of the total vote in Counties X and Y. He won 72 percent of the vote in County X. If the ratio of people who voted in County X to County Y is 2: 1, what percent of the vote did candidate Douglas win in County Y?\n\n### Options:\nA. 18%\nB. 30%\nC. 36%\nD. 48%\nE. 54%\n\n### Answer:\ngiven voters in ratio 2:1\nlet X has 200 votersY has 100 voters\nfor X 72% voted means 72*200=144 votes\ncombined for XY has 300 voters and voted 60% so total votes =180\nbalance votes=180-144=36\nAs Y has 100 voters so 36 votes means 36% of votes required\nAns C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA sum of Rs 1162.00 is divided among A, B and C such that 4 times A\u2019s share is equal to 5 times B\u2019s share and 7 times C\u2019s share. What is the share of C?\n\n### Options:\nA. 280\nB. 285\nC. 270\nD. 295\nE. 255\n\n### Answer:\ngiven 4x=5y=7z\nso x:y=5:4\ny:z=7:5\nx:y:z=35:28:20\nc share=20*1162/(35+28+20) =280.\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how many different number of ways 3 men and 2 women can sit on a shopa which can accommodate persons?\n\n### Options:\nA. A)60\nB. B)70\nC. C)1\nD. D)5\nE. E)2\n\n### Answer:\n5p1 = 5\nOption 'D'\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA bag contains 12 white and 18 black balls. 2balls are drawn in succession. What is the probability that first is white and second is black?\n\n### Options:\nA. 35/145\nB. 36/145\nC. 36/140\nD. 36/141\nE. 31/142\n\n### Answer:\nThe probability that first ball is white:\n=12C130C1=12C130C1\n=1230=1230\n=25=25\nSince, the ball is not replaced; hence the number of balls left in bag is 29.\nHence, the probability the second ball is black:\n=18C129C1=18C129C1\n=1829=1829\nRequired probability,\n=(25)\u00d7(1829)=(25)\u00d7(1829)\n=36/145\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain bag contains 100 balls \u2014 50 white, 30 green, 10 yellow, 7 red, and 3 purple. If a ball is to be chosen at random, what is the probability that the ball will be neither red nor purple?\n\n### Options:\nA. 0.9\nB. 0.75\nC. 0.6\nD. 0.8\nE. 0.5\n\n### Answer:\nAccording to the stem the ball can be white, green or yellow, so the probability is (white + green + yellow)/(total) = (50 + 30 + 10)/100 = 90/100 = 0.9.\nAnswer is A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA tank is filled in SIXTEEN hours by three pipes A, B and C. Pipe A is twice as fast as pipe B, and B is twice as fast as C. How much time will pipe B alone take to fill the tank?\n\n### Options:\nA. 56 hours\nB. 28 hours\nC. 55 hours\nD. 66 hours\nE. 47 hours\n\n### Answer:\n1/A + 1/B + 1/C = 1/16 (Given)\nAlso given that A = 2B and B = 2C\n=> 1/2B + 1/B + 2/B = 1/16\n=> (1 + 2 + 4)/2B = 1/16\n=> 2B/7 = 16\n=> B = 56 hours.\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRavi and Kavi start a business by investing \u00e2\u201a\u00b9 3000 and \u00e2\u201a\u00b9 72000, respectively. Find the ratio of their profits at the end of year.\n\n### Options:\nA. 2 : 24\nB. 5 : 24\nC. 7 : 24\nD. 1 : 24\nE. 3 : 24\n\n### Answer:\nRatio of profit = Ratio of investments\n= 3000 : 72000 = 1 : 24\nAnswer : D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nLook at this series: 15, 15, 27, 27, 39, 39, 51, 51, 63, 63, ? ... What number should fill the blank?\n\n### Options:\nA. 51\nB. 39\nC. 75\nD. 15\nE. None\n\n### Answer:\nExplanation: In this simple addition with repetition series, each number in the series repeats itself, and then increases by 12 to arrive at the next number.\nAnswer: Option C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many times the keys of a writer have to be pressed in order to write first 200 counting no's?\n\n### Options:\nA. 452\nB. 462\nC. 472\nD. 482\nE. 492\n\n### Answer:\n1 to 9 = 9 * 1 = 9\n10 to 99 = 90 * 2 = 180\n100 to 200 = 101 * 3 = 303\n-----------\n492\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a - b = 3 and a(power 2) + b(power 2) = 39, find the value of ab.\n\n### Options:\nA. 15\nB. 8\nC. 4\nD. 10\nE. 3\n\n### Answer:\n2ab = (a(power 2) + b(power 2) - (a - b)(power 2)\n= 39 - 9 = 30\nab = 15.\nAnswer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe sum of ages of 5 children born at the intervals of 3 years each is 50 years. What is the age of the youngest child?\n\n### Options:\nA. None of these\nB. 11 years\nC. 10 years\nD. 8 years\nE. 4 years\n\n### Answer:\nExplanation:\nLet the ages of children be x, (x + 3), (x + 6), (x + 9) and (x + 12) years.\nThen, x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 50\n\u21d2 5x = 20\n\u21d2 x = 4.\nAge of the youngest child = x = 4 years.\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn 1982 and 1983, Company B\u2019s operating expenses were $11.0 million and $14.0 million, respectively, and its revenues were $15.6 million and $18.8 million, respectively. What was the percent increase in Company B\u2019s profit (revenues minus operating expenses) from 1982 to 1983 ?\n\n### Options:\nA. 3%\nB. 16 2/3%\nC. 25%\nD. 4 1/3%\nE. 60%\n\n### Answer:\nProfit in 1982 = 15.6 - 11 = 4.6 million $\nProfit in 1983 = 18.8 - 14 = 4.8 million $\nPercentage increase in profit = (4.8-4.6)/4.6 * 100 %\n= 4 1/3%\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA person took some amount with some interest for 3 years, but increase the interest for 1%, he paid Rs.120/- extra, then how much amount he took?\n\n### Options:\nA. s.5500/-\nB. s.6000/-\nC. s.4000/-\nD. s.7000/-\nE. s.8000/-\n\n### Answer:\nExplanation:\n3 years = Rs.120/-\nyear = 120/3\nRate of Interest = 1%\n100/1% \u00d7 120/3 = Rs.4000/-\nP = Rs.4000/-\nAnswer: Option C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhen a 160 meters long rod is cut down into small pieces of length 3.2 meters each. Then how many pieces are available ?\n\n### Options:\nA. 52\nB. 50\nC. 62\nD. 67\nE. 69\n\n### Answer:\nAnswer\nNo. of pieces = Total length / Length of each piece\n= 160/3.2\n= 50\nOption: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOne hour after Yolanda started walking from X to Y, a distance of 31 miles, Bob started walking along the same road from Y to X. If Yolanda\u00e2s walking rate was 1 miles per hour and Bob\u00e2s was 2 miles per hour, how many miles had Bob walked when they met?\n\n### Options:\nA. 19\nB. 20\nC. 22\nD. 21\nE. 19.5\n\n### Answer:\nLet t be the number of hours that Bob had walked when he met Yolanda. Then, when they met, Bob had walked 4t miles and Yolanda had walked (t + 1) miles. These distances must sum to 31 miles, so 2t + (t + 1) = 31, which may be solved for t as follows\n2t + (t + 1) = 31\n2t + t + 1 = 31\n3t = 30\nT = 10 (hours)\nTherefore, Bob had walked 2t = 2(10) = 20 miles when they met. The best answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFor all positive integers m, [m]=3m when m is odd and [m]=(1/2)*m when m is even. What is [9]*[10] equivalent to?\n\n### Options:\nA. [25]\nB. [135]\nC. [30]\nD. [90]\nE. [45]\n\n### Answer:\n[9]*[10] = 27*5 = 135 = 3*45 = [45]\nThe answer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA full stationary oil tank that is a right circular cylinder has a radius of 100 feet and a height of 25 feet. Oil is pumped from the stationary tank to an oil truck that has a tank that is a right circular cylinder until the truck's tank is completely filled. If the truck's tank has a radius of 7 feet and a height of 10 feet, how far (in feet) did the oil level drop in the stationary tank?\n\n### Options:\nA. 0.07\nB. 0.049\nC. 0.7\nD. 0.49\nE. 4.9\n\n### Answer:\nThe volume of oil pumped to the tank = The volume of oil taken away from stationary cylinder.\npi*49*10 = pi*h*100*100 (h is distance that the oil level dropped)\nh = 490/10,000 = 49/1000 = 0.049 ft\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average mark of the students of a class in a particular exam is 80. If 5 students whose average mark in that exam is 40 are excluded, the average mark of the remaining will be 90. Find the number of students who wrote the exam.\n\n### Options:\nA. 22\nB. 27\nC. 25\nD. 99\nE. 21\n\n### Answer:\nLet the number of students who wrote the exam be x.\nTotal marks of students = 80 x.\nTotal marks of (x - 5) students = 90(x - 5)\n80x - (5 * 40) = 90(x - 5)\n250 = 10x => x = 25.Answer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the value of (P + Q)/(P - Q) if P/Q is 7?\n\n### Options:\nA. 4/3\nB. 2/3\nC. 2/6\nD. 7/8\nE. 8/7\n\n### Answer:\n(P + Q)/(P - Q) = [(P/Q) + 1]/[(P/Q) - 1]\n= (7 + 1)/(7 - 1)\n= 8/6\n= 4/3\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the C.I. on a sum of Rs.1600 for 9 months at 20% per annum, interest being compounded quarterly?\n\n### Options:\nA. Rs.1652\nB. Rs.2569\nC. Rs.4587\nD. Rs.479\nE. Rs.2522\n\n### Answer:\nExplanation:\nA = 1600(21/20)3 = Rs.2522\nAnswer:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAjay had purchased a second hand scooter for 18,000 and spent Rs.1800 for repairs. After one year he wanted to sell the scooter. At what price should he sell it to gain 100/9%, if 100/11% is to be deducted at the end of every year on account of deprecation?\n\n### Options:\nA. Rs.18000\nB. Rs.19800\nC. Rs.20000\nD. Rs.22500\nE. Rs.23500\n\n### Answer:\nCost Price =Rs.18000.\nCost on Reparing = Rs. 1800.\nSo, Total cost = 18000 +1800 = 19800.\nDepreciation = 100/11% = 9.09%.\nGain = 100/9% = 11.11%.\nAfter depreciation, the cost price would be = 19800 - 9.09% of 19800 = Rs. 18000\nSP to gain 11.11% = 18000 + 11.11% of 18000 = 18000 + 1999.8 = Rs. 20,000.\nANSWER : C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA boatman goes 3 km against the current of the stream in 3 hour and goes 1 km along the current in 30 minutes. How long will it take to go 3 km in stationary water?\n\n### Options:\nA. 5 hours\nB. 4 hours\nC. 3 hours\nD. 2 hours\nE. 1 hours\n\n### Answer:\nExplanation:\nSpeed upstream = 3/3 = 1 km/hr\nSpeed downstream = 1/(30/60)= 2 km/hr\nSpeed in still water = 1/2(2+1)= 3/2 km/hr\nTime taken to travel 3 km in still water = 3/(3/2) = 6/3 = 2 hours\nAnswer: Option D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\ncircular path of 13 m radius has marginal walk 2 m wide all round it. Find the cost of leveling the walk at 25p per m2?\n\n### Options:\nA. 44\nB. 55\nC. 66\nD. 78\nE. 49\n\n### Answer:\n\u03c0 (152 - 132) = 176\n176 * 1/4 = Rs.44.Answer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain sum of money amounts to Rs. 1008 in 2 years and to Rs.1164 in 3 \u00bd years. Find the sum and rate of interests.\n\n### Options:\nA. 13%\nB. 12%\nC. 25%\nD. 18%\nE. 52%\n\n### Answer:\nS.I. for 1 \u00bd years = Rs.(1164-1008) = Rs.156.\nS.l. for 2 years = Rs.(156*(2/3)*2)=Rs.208\nPrincipal = Rs. (1008 - 208) = Rs. 800.\nNow, P = 800, T = 2 and S.l. = 208.\nRate =(100* 208)/(800*2)% = 13%\nAnswer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn an xy-coordinate plane, a line is defined by y = kx + 1. If (3, b), (a, 4), and (a, b+1) are three points on the line, where a and b are unknown, then k = ?\n\n### Options:\nA. 1/2\nB. 1\nC. 3/2\nD. 2/3\nE. 5/2\n\n### Answer:\nb=3k+1...(1)\nb+1=ak+1...(2)\n4=ak+1...(3)\nTaking (2) and (3)\n4=b+1\nb=3\nTaking (1)\n3=3k+1\nk=2/3\nAnswer : D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nthere are five red shoe and 4 green. if one draw randomly a shoe then what is the probability of getting red\n\n### Options:\nA. 1/9\nB. 2/9\nC. 3/9\nD. 4/9\nE. 5/9\n\n### Answer:\nprob of getting red shoe = 5/9\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe difference between the length and breadth of a rectangle is 42 m. If its perimeter is 280 m, then its area is:\n\n### Options:\nA. 1520 m2\nB. 4250 m2\nC. 4459 m2\nD. 4092 m2\nE. None\n\n### Answer:\nEXPLANATION\nWe have: (l \u00e2\u20ac\u201c b) = 42 and 2(l + b) = 280 or (l + b) = 140.\nSolving the two equations, we get: l = 91 and b = 49.\nArea = (l x b) = (91x 49) m2 = 4459 m2.\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA total of 3000 chocolates were distributed among 120 boys and girls such that each boy received 2 chocolates and each girl received 3 chocolates. Find the respective number of boys and girls?\n\n### Options:\nA. 22\nB. 60\nC. 77\nD. 26\nE. 23\n\n### Answer:\nLet the number of boys be x.\nNumber of girls is 120 - x.\nTotal number of chocolates received by boys and girls = 2x + 3(120 - x) = 300\n=> 360 - x = 300 => x = 60.\nSo, the number of boys or girls is 60.\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA tank contains 6,500 gallons of a solution that is 5 percent sodium chloride by volume. If 2,500 gallons of water evaporate from the tank, the remaining solution will be approximately what percent sodium chloride?\n\n### Options:\nA. 5.12%\nB. 6.12%\nC. 7.12%\nD. 8.12%\nE. 9.12%\n\n### Answer:\nWe start with 6,500 gallons of a solution that is 5% sodium chloride by volume. This means that there are 0.05 x 6,500 = 325 gallons of sodium chloride.\nWhen 2,500 gallons of water evaporate we are left with 4,000 gallons of solution. From here we can determine what percent of the 4,000 gallon solution is sodium chloride.\n(sodium chloride/total solution) x 100 = ?\n(325/4,000) x 100 = ?\n0.0812 x 100 = ?\n= 8.12%\nAnswer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn an interview , the probability of appointing Husband is 1/5 while that of wife is\n\u00bc.find probability that only one of them get selected in interview.\n\n### Options:\nA. 3/20\nB. 4/20\nC. 5/20\nD. 6/20\nE. 7/20\n\n### Answer:\np(H)=1/5\np(w)=1/4\nP(H bar)=1-1/5=4/5\np(w bar)=1-1/4=3/4\nRequired probability=p(H)*p(w bar)+p(w)*p(H bar)\n1/5*3/4+1/4*4/5\n7/20\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA person buys an article at Rs.500. At what price should he sell the article so as to make a profit of 20%?\n\n### Options:\nA. 600\nB. 887\nC. 256\nD. 654\nE. 712\n\n### Answer:\nCost price = Rs.500\nprofit = 20% of 500 = Rs.100\nSelling price = Cost price + Profit\n= 500 + 100 = 600\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThree interviewers, A, B, and C are interviewing 40 applicants. Only with three interviewers' admission can an applicant be admitted. If interviewer B admitted 15 applicants, A admitted 17 applicants, and C admitted 20 applicants, at least how many applicants get the admission?\n\n### Options:\nA. 8\nB. 2\nC. 6\nD. 0\nE. 12\n\n### Answer:\nIf B admitted 15 are overlapping with A admission of 17 But C does not overlap with anybody.\nThen no student will get nod from all the 3.\nHence 0 student will get admission.\nAnswer : D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA basket has 5 apples and 4 oranges. Three fruits are picked at random. The probability that at least 2 apples are picked is?\n\n### Options:\nA. 25/42\nB. 25/49\nC. 25/46\nD. 25/48\nE. 35/49\n\n### Answer:\nTotal fruits = 9\nSince there must be at least two apples,\n(\u2075C\u2082 * \u2074C\u2081)/\u2079C\u2083 + \u2075C\u2083/\u2079C\u2083\n= 25/42.\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA semicircle has a radius of 11. What is the approximate perimeter of the semicircle?\n\n### Options:\nA. 45\nB. 51\nC. 57\nD. 63\nE. 69\n\n### Answer:\nThe perimeter of a circle is 2*pi*r.\nThe perimeter of a semicircle is 2*pi*r/2 + 2r = pi*r + 2r\nThe perimeter is pi*11 + 2*11 which is about 57.\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nBobby bought 2 shares, and which he sold for $96 each. If he had a profit of 20% on the sale of one of the shares but a loss of 20% on the sale of the other share, then on the sale of both shares Bobby had...\n\n### Options:\nA. a profit of 10\nB. a profit of 8\nC. a loss of 8\nD. a loss of 10\nE. neither a profit nor a loss\n\n### Answer:\nCost of the first stock: 96/1.2=80, so profit from it 96-80=16\nCost of the second stock: 96/0.8=120, so loss from it 96-120=-24\nOverall loss 16-24=-8\nAnswer: C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average of first five multiples of 3 is?\n\n### Options:\nA. 2\nB. 9\nC. 8\nD. 6\nE. 3\n\n### Answer:\nAverage = 3(1 + 2 + 3 + 4 + 5)/5\n= 45/5\n= 9.\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many integers Z are prime numbers in the range 200 < Z < 220?\n\n### Options:\nA. 1\nB. 2\nC. 3\nD. 4\nE. 5\n\n### Answer:\nMy friend, every single odd number greater than can be written either as 4Z+1 or as 4Z+3. If you divide any odd number by 4, you will get a remainder of either 1 or 3. That's not a rule unique to prime numbers at all.\nThe 6Z+1 or 6Z-1 rule is basically every odd number that is not divisible by three, so it narrows the search a little.\nHere's how I thought about the problem. First, eliminate all the even numbers and the odd multiples of 5 in that range. That leaves us with:\n{201, 203, 207, 209, 211, 213, 217, 219}\nEliminate the four multiples of 3. Notice that 21 is a multiple of 3, so 210 is also a multiple of 3. If we add or subtract 3 or 9, we get more multiples of three. When we eliminate those, we are left with.\n{203, 209, 211, 217}\nNow, notice that a cool thing about this range is that 210 is also a multiple 7 (again, because 21 is a multiple of 7). This means that\n210 - 7 = 203\n210 + 7 = 217\nThose two numbers are also multiples of 7, so eliminate them from the list. Now, we are left with\n{209, 211}.\nWe've already checked all the prime numbers less than 10, so we know that neither of these numbers is divisible by anything less than 10. We have to check 11 now. We know that 22 is a multiple of 11, so 220 is also a multiple of 11. This means that\n220 - 11 = 209\nis also a multiple of 11. We can eliminate this from the list also.\nThat leaves us with just 211. There's no zero option in the question, so this must be a prime number.\nAnswer = (A)\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man swims downstream 76 km and upstream 48 km taking 4 hours each time; what is the speed of the current?\n\n### Options:\nA. 3 kmph\nB. 1.5 kmph\nC. 3.5 kmph\nD. 6.5 kmph\nE. 7:3kmph\n\n### Answer:\nExplanation:\n76 --- 4 DS = 19\n? ---- 1\n48 ---- 4 US = 12\n? ---- 1 S = ?\nS = (19 - 12)/2 = 3.5\nAnswer: Option C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nPipe A fills a swimming pool in 4 hours. Pipe B empties the pool in 6 hours. If pipe A was opened at 7:00 am and Pipe B at 8:00 am, at what time will the pool be full?\n\n### Options:\nA. 16:00\nB. 18:00\nC. 19:00\nD. 20:00\nE. 17:00\n\n### Answer:\nPipe A fills the pool in 4 hrs.\n1 hour's work : 1/4\nPipe B empties the pool in 6 hrs.\n1 hour's work : 1/6\nTogether if they work, 1 hour's work = 1/4 -1/6 = 1/12\nGiven : Pipe A started at 7:00 a.m and Pipe B at 8:00 a.m\nPool filled after 1 hour by Pipe A : 1/4 or 3/12\nAfter 8:00 a.m\nPool filled after 1 hour with both the pipes on : 1/12\nPool filled after 9 hours with both pipes on : 9/12\nPool filled in 1 hour + Pool filled in 9 hours = 3/12 +9/12 =1\nTherefore, it takes 10 hrs to fill the pool\nAs Pipe A started at 7:00 a.m, pool is full at 17:00 hrs\nAnswer : E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA boy has 11 trousers and 12 shirts. In how many different ways can he select a trouser and a shirt?\n\n### Options:\nA. 120ways\nB. 138ways\nC. 140ways\nD. 132ways\nE. 150ways\n\n### Answer:\nThe boy can select one trouser in 11 ways.\nThe boy can select one shirt in 12 ways.\nThe number of ways in which he can select one trouser and one shirt is 11 * 12\n= 132 ways.\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA car started running at a speed of 28 km/hr and the speed of the car was increased by 2 km/hr at the end of every hour. Find the total distance covered by the car in the first 10 hours of the journey.\n\n### Options:\nA. 37 km\nB. 76 km\nC. 25 km\nD. 15 km\nE. 30 km\n\n### Answer:\nA\n37 km\nThe total distance covered by the car in the first 10 hours = 28 + 30 + 32 + 34 + 36 + 38 + 40 + 42 + 44 + 46 = sum of 10 terms in AP whose first term is 28 and last term is 46 = 10/2 [28 + 46] = 370 km.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA can do a piece of work in 20 days. B in 15 days A and C in 12 days. In how many days can A finish the work if he is assisted by B on one day and C on the next, alternately?\n\n### Options:\nA. 9 days\nB. 8 days\nC. 5 days\nD. 54 days\nE. 2 days\n\n### Answer:\nA + B = 1/20 + 1/15 = 7/60\nA + C = 1/20 + 1/12 = 8/60\n7/60 + 8/60 = 15/60 = 1/4\n4 days * 2 = 8 days\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nEighteen years ago, a father was three times as old as his son. Now the father is only twice as old his son. Then the sum of the present ages of the son and the father is:\n\n### Options:\nA. 53\nB. 108\nC. 77\nD. 107\nE. 109\n\n### Answer:\nExplanation:\nLet the present ages of the father and son be 2x and x years respectively.\nThen, (2x - 18) = 3(x - 18) => x = 36\nRequired sum = (2x + x) = 108 years.\nAnswer: Option D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWorkers at a campaign office have 3000 fliers to send out. If they send out 1/5 of them in the morning and 1/4 of the remaining ones out during the afternoon, how many are left for the next day?\n\n### Options:\nA. 1800\nB. 800\nC. 1100\nD. 1200\nE. 1900\n\n### Answer:\n(1/5)*3000 = 600\nRemaining = 3000-600 = 2400\n(1/4) of remaining = (1/4)*2400 = 600\nRemaining now = 2400-600 = 1800\nAnswer: Option A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA tree increases annually by 1\u20445 th of its height. If its height today is 50 cm, what will be the height after 2 years?\n\n### Options:\nA. 64 cm\nB. 84 cm\nC. 72 cm\nD. 64 cm\nE. 74 cm\n\n### Answer:\nExplanation:\nThis problem is similar to the problems we saw in compound interest.\nWe can use the formulas of compound interest here as well.\nRate of increase = 1/5 \u00d7 100 = 20%\nHeight after 2 years = P(1+R/100)T\n= 50(1 + 20/100)2 = 50(1 + 1/5)2\n= 50(6/5)2 = (50 \u00d7 6 \u00d7 6)/(5 \u00d7 5) = 2 \u00d7 6 \u00d7 6 = 72 cm\nAnswer: Option C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA pair of articles was bought for $50 at a discount of 40%. What must be the marked price of each of the article?\n\n### Options:\nA. $25\nB. $15\nC. $29.65\nD. $35.95\nE. $45.62\n\n### Answer:\nS.P. of each of the article = 50/2 = $25\nLet M.P = $x\n60% of x = 25\nx = 25*.6 =$15\nAnswer is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn her backyard, Florry grows only yellow roses and white roses. Some of the rose bushes have flowers of both colors, and some have flowers of one color only. The number of rose bushes that have only yellow roses is 50% greater than the number of rose bushes that have only white roses. If there are yellow roses on 80% of Florry's rose bushes, then what percent of her bushes have only yellow roses?\n\n### Options:\nA. 20\nB. 30\nC. 50\nD. 70\nE. 80\n\n### Answer:\nlet, the number of bushes with only yellow flowers be x\nso, number of bushes with only yellow flowers will be 1.5x\nif total number of bushes of flowers= T\nthen total number of bushes with yellow flowers= 0.8T\nwe can say that total number of bushes with yellow flowers+ bushes with only white flowers= total number of bushes with flowers\nso, 0.8T+x=T\nx=0.2T\nso, 1.5x=0.3T\n30% flowers are yellow flowers\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe total age of A and B is 11 years more than the total age of B and C. C is how many year younger than A\n\n### Options:\nA. A)11\nB. B)12\nC. C)13\nD. D)14\nE. E)15\n\n### Answer:\nExplanation:\nGiven that A+B = 11 + B + C\n=> A \u2013 C = 11 + B \u2013 B = 11\n=> C is younger than A by 11 years\nAnswer: Option A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind out the square of a number which when doubled exceeds its one sixth by 11 ?\n\n### Options:\nA. 36\nB. 25\nC. 19\nD. 26\nE. 17\n\n### Answer:\nA\nLet the number be p, then the square will be p^2\nAccording to question:\n2p = (p/6) + 11\n=> 12p = p + 66\n=> p = 6\np^2 = 6^2 = 36.\nAnswer : A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe manager of a theater noted that for every 10 admissions tickets sold, the theater sells 3 bags of popcorn at 2.40 $ each, 4 sodas at 1.50 $ each and 2 candy bars at 1.00$ each. To the nearest cent, what is the average (arithmetic mean) amount of these snacks sales per ticket sold?\n\n### Options:\nA. 1.48$\nB. 1.52$\nC. 1.60$\nD. 1.64$\nE. 1.70$\n\n### Answer:\nFor every 10 tickets amount of snacks sold is 3*2.40+4*1.5+2*1=$15.2, hence amount of the snacks sales per ticket is $15.2/10=~$1.52.\nAnswer: B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how many different number of ways a Committee of 4 person of can be selected from 6 boys and 4girls such that at least 1 girl is included in the committee\n\n### Options:\nA. 195\nB. 200\nC. 80\nD. 15\nE. NONE OF THESE\n\n### Answer:\n1G 3B 2G 2B 3G B 4G\n= (4C1*6C3)+(4C2*6C2)+(4C3*6C1)+4C4\n= (4*20)+(6*150+(4*6)+1\n= 80+90+24+1=195\nTotal 5M 3W\n10C4=210\n6C4=15\nAt least one girl = total - with out girl\nAt least one girl = 210-15=195\nA)\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf two dice are thrown together, the probability of getting an even number on one die and an odd number on the other is?\n\n### Options:\nA. 1/4\nB. 1/2\nC. 1/8\nD. 1/0\nE. 1/1\n\n### Answer:\nThe number of exhaustive outcomes is 36.\nLet E be the event of getting an even number on one die and an odd number on the other. Let the event of getting either both even or both odd then = 18/36 = 1/2\nP(E) = 1 - 1/2 = 1/2.\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo pipes A and B can separately fill a cistern in 10 and 15 minutes respectively. A person opens both the pipes together when the cistern should have been was full he finds the waste pipe open. He then closes the waste pipe and in another 4 minutes the cistern was full. In what time can the waste pipe empty the cistern when fill?\n\n### Options:\nA. 2 min\nB. 8 min\nC. 9 min\nD. 3 min\nE. 5 min\n\n### Answer:\n1/10 + 1/15 = 1/6 * 4 = 2/3\n1 - 2/3 = 1/3\n1/10 + 1/15 - 1/x = 1/3\nx = 8\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain football coach allows his quarterback to call three plays in a row. If the quarterback can choose from 3 passing plays, 4 running plays, and 2 trick plays, how many different E arrangements of plays can be run, if the same play can\u2019t be run more than once?\n\n### Options:\nA. 24\nB. 125\nC. 243\nD. 504\nE. 729\n\n### Answer:\nNumber of E ways to choose the first play: 9\nSecond play: 8\nThird:7\n9*8*7= 504.D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe membership of a committee consists of 3 science teachers, 4 Mathematics teachers, and 2 Social Studies teachers. If 2 committee members are to be selected at random to write the committee\u2019s report, what is the probability that the two members selected will both be science teachers?\n\n### Options:\nA. 1/12\nB. 1/3\nC. 2/9\nD. 1/14\nE. 1/24\n\n### Answer:\nProbability of first member an science teacher = 3/9\nProbability of second member an science teacher = 2/8\nProbability of both being english teacher = 3/9 x 2/8 =1/12 (A)\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA gives B a start of 10 metres in a 100 metre race and still beats him by 1.25 seconds. How long does B take to complete the 100 metre race if A runs at the rate of 10 m/sec?\n\n### Options:\nA. 8 seconds\nB. 10 seconds\nC. 16.67 seconds\nD. 12.5 seconds\nE. None\n\n### Answer:\nSolution:\nA gives B a start of 10 metres in a 100 metre race. This means that when A runs 100 metres, B runs only 90 metres.\nDespite that start, A beats B by 1.25 seconds.\nAs A is running at the speed of 10 m/sec, he will take 10 seconds to complete the 100 metre race. And B takes 10 + 1.25 = 11.25 seconds to cover 90 metres.\nTherefore, the speed at which B is running = 8 m/sec.\nRunning at 8 m/sec, B will take = 12.5 seconds to complete the 100 metre race.\nHence the correct answer is D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOne week, a certain truck rental lot had a total of 20 trucks, all of which were on the lot Monday morning. If 50% of the trucks that were rented out during the week were returned to the lot on or before Saturday morning of that week, and if there were at least 16 trucks on the lot that Saturday morning, what is the greatest number of different trucks that could have been rented out during the week?\n\n### Options:\nA. 18\nB. 16\nC. 12\nD. 14\nE. 8\n\n### Answer:\nN - Not rented trucks; R - Rented trucks\nN + R = 20\nN + R/2 = 16\nR = 8\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average of 11 results is 45, if the average of first five results is 49 and that of the last seven is 52. Find the fifth result?\n\n### Options:\nA. 114\nB. 116\nC. 117\nD. 118\nE. 119\n\n### Answer:\n1 to 11 = 11 * 45 = 495\n1 to 5 = 5 * 49 = 245\n5 to 11 = 7 * 52 = 364\n5th = 245 + 364 \u2013 495=114\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nArjun and Sajal are friends . each has some money. If Arun gives Rs. 30 to Sajal, the Sajal will have twice the money left with Arjun. But, if Sajal gives Rs. 10 to Arjun, the Arjun will have thrice as much as is left with Sajal. How much money does Sajal have?\n\n### Options:\nA. Rs 34\nB. Rs 35\nC. Rs 36\nD. Rs 37\nE. Rs 38\n\n### Answer:\nIf arun had x rs , and sejal had y rs, then\n2*(x-30) = y+30 or 2x-60= y+30 or y= 2x-90\nand\nx+10 = 3*(y-10)= 3*(2x-90-10)=6x-300\nor\n5x=310\nx= 310/5 = 62 Rs with Arjun\ny= 2x-90 = Rs 34 with Sajal\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich of these must the factor of the product of four consecutive even integers:-\n1) 48\n2) 64\n3) 96\n4) 192\n5) 80\n\n### Options:\nA. 1,2 only\nB. 2,3 only\nC. 1,2,3 only\nD. 1,2,3,4 only\nE. All of them\n\n### Answer:\n80 is not factor.... It has to have one 5.\nAnswer is D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf x < 0 and 0 < y < 1, which of the following has the greatest value H?\n\n### Options:\nA. x^2\nB. (xy)^2\nC. (x/y)^2\nD. x^2/y\nE. x^2*y\n\n### Answer:\nGiven, x < 0 and 0 < y < 1\nLet, x = -2 and y = 1/2\nA. x^2 = (-2)^2 =4\nB. (xy)^2 = (-2*1/2)^2 =1\nC. (x/y)^2 = {-2/(1/2)}^2 = (-4)^2 =16\nD. x^2/y = (-2)^2 / (1/2) = 4*2 =8\nE. x^2*y = (-2)^2*(1/2) =2\nAnswer: option C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAfter the recall of defective by Telvin inc 2 years ago, its share price has since lost 12%. However, after the launch of its new product 1 year ago its stock price has appreciated by 6%, bringing its share price to $25. What was its share price 2 years ago?\n\n### Options:\nA. 28\nB. 26.8\nC. 56.6\nD. 27.2\nE. 25.7\n\n### Answer:\n-12+6-(12*6)/100=-6.72% net decrease\nlet initial price be Y\nY(1-6.72/100)=25\nY=25/0.9328 = ~26.8\nAns is B)\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAt a certain conference, 42% of the attendees registered at least two weeks in advance and paid their conference fee in full. If 40% of the attendees who paid their conference fee in full did not register at least two weeks in advance, what percent of conference attendees registered at least two weeks in advance?\n\n### Options:\nA. 18.0%\nB. 62.0%\nC. 79.2%\nD. 70.0%\nE. 82.0%\n\n### Answer:\nRefer to the table in the attachment:\nLet x= No. of members who have paid in Full\n40 % members paid in full and did not register in advance = 0.4x\n42 % registerd in advance and paid in full.\nSo if total No. of members = 100, then 42 members paid Full and registered in advance.\nHence total members who paid full amount = 0.4x + 42 =x\n0.6x =42\nHence x = 70\ni.e. 80 out of 100 or 70 %\nAns. D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA 5\" cube is painted in all its faces and then it is cut down into 1\" blocks. How many 1\" blocks\nare there even without a single face being painted?\n\n### Options:\nA. 16 blocks\nB. 20 blocks\nC. 27 blocks\nD. 36 blocks\nE. 64 blocks\n\n### Answer:\nThe unpainted blocks are the interior blocks.\nThese blocks form a 3\" cube on the inside.\nThe number of unpainted blocks is 3*3*3 = 27 blocks.\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf it is 6:27 in the evening on a certain day, what time in the morning was it exactly 2,879,277 minutes earlier? (Assume standard time in one location.)\n\n### Options:\nA. 6:22\nB. 6:24\nC. 6:27\nD. 6:30\nE. 6:32\n\n### Answer:\n6:27 minus 2,879,277 in any way must end with 0.\nThe only answer choice which ends with 0 is D.\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe current of a stream runs at the rate of 4 kmph. A boat goes 6 km and back to the starting point in 2 hours, then find the speed of the boat in still water?\n\n### Options:\nA. 9\nB. 4\nC. 8\nD. 5\nE. 3\n\n### Answer:\nS = 4\nM = x\nDS = x + 4\nUS = x - 4\n6/(x + 4) + 6/(x - 4) = 2\nx = 8\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRachel and Sarah spent $8 for gasoline, $15.65 for their lunch, and $5 apiece for gifts for Grandma.\nGrandma gave each of them $10. If the girls left home with a total of $50, how much do they have for\nthe return trip?\n\n### Options:\nA. $36.35\nB. $26.35\nC. $16.35\nD. $46.35\nE. $56.35\n\n### Answer:\n$50 + $20 = $70 what they left with\nplus $10 to each\n$8 + $15.65 + $10 = $33.65 what they spent\n(gifts are $5 + $5)\n$70 - $33.65 = $36.35 left\ncorrect answer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nInteger x is equal to the product of all even numbers from 2 to 60, inclusive. If Q is the smallest prime number that is also a factor of x-1, then which of the following expressions must be true?\n\n### Options:\nA. 030\n\n### Answer:\nQ Smallest prime factor is greater than 29. So answer is E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n20 throws of a die produces following results\nSCORE -- NUMBER OF OCCURRENCES\n---1-------------------4\n---2-------------------3\n---3-------------------5\n---4-------------------2\n---5-------------------2\n---6-------------------4\nWhat is the probability P that one more throw to this series will increase the mean score?\n\n### Options:\nA. 1/6\nB. 1/3\nC. 1/2\nD. 2/3\nE. 5/6\n\n### Answer:\nI get the mean as 67/20 --> 3.35. Thus in order to raise this mean we would need a 4,5,or 6.\nThus probability P is 1/2.C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man can row 30 km downstream and 20 km upstream in 4 hours. He can row 45 km downstream and 40 km upstream in 7 hours. Find the speed of man in still water?\n\n### Options:\nA. 12.8 kmph\nB. 12.7 kmph\nC. 12.6 kmph\nD. 12.5 kmph\nE. 12.3 kmph\n\n### Answer:\nLet the speed of the man in still water be a kmph and let the speed of the stream be b kmph.\nNow 30/(a + b) + 20/(a - b) = 4 and 45/(a + b) + 40/(a - b) = 7\nSolving the equation, the speed of man in still water is 12.5 kmph.\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe number of new words that can be formed by rearranging the letters of the word 'RAM' is ?\n\n### Options:\nA. 5\nB. 10\nC. 120\nD. 6\nE. 8\n\n### Answer:\nNumber of words which can be formed\n= 3! - 1 = 6- 1\n= 5.\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAccording to the direction on a can of frozen orange juice concentrate is to be mixed with 3 cans of water to make orange juice . How many 12 - ounce cans of the concentrate are required to prepare 272 6-ounce servings of orange juice?\n\n### Options:\nA. 25\nB. 34\nC. 50\nD. 67\nE. 100\n\n### Answer:\nOrange juice concentrate: water::1:3\ntotal quantity of orange juice = 272*6 = 1632 oz\nso Orange juice concentrate: water :: 408 oz:1224 oz\nno. of 12 oz can = 408 oz/12 oz = 34\nAnswer B, 34 cans\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat Is The Next Number\n12 13 15 17 111 113 117 119 123 ?\n\n### Options:\nA. 154\nB. 220\nC. 129\nD. 428\nE. 224\n\n### Answer:\nC\n129.\nThese are the first 10 prime numbers (2, 3, 5...) prefixed with a 1\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA room 5m 55cm long and 3m 74cm broad is to be paved with square tiles.Find the least number of square tiles required to cover the floor?\n\n### Options:\nA. 122\nB. 123\nC. 828\nD. 122\nE. 176\n\n### Answer:\nArea of the room=(544 * 374)\nsize of largest square tile= H.C.F of 544 & 374 = 34 cm\nArea of 1 tile = (34 x 34)\nNumber of tiles required== [(544 x 374) / (34 x 34)] = 176\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAt the start of an experiment, a certain population consisted of 3 animals. At the end of each month after the start of the experiment, the population size was double its size at the beginning of that month. Which of the following represents the population size at the end of 11 months?\n\n### Options:\nA. 2^3\nB. 3^2\nC. 2(3^10)\nD. 3(2^11)\nE. 3(10^2)\n\n### Answer:\n3*2^n where n is the #of month --> 3*2^11 Answer (D)\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the greatest 6-digit number when divided by 7 ,8 , 9, and 10 leaves a remainder of 5, 6, 7, and 8 respectively?\n\n### Options:\nA. 456788\nB. 678910\nC. 997479\nD. 997919\nE. 997920\n\n### Answer:\nWhen you divide a positive integer by 10, the remainder will just be the units digit. We know the remainder is 8 when we divide by 10, so A is the only possible answer.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nk = 2^n + 5, where n is an integer greater than 1. If k is divisible by 9, which of the following MUST be divisible by 9?\n\n### Options:\nA. 2^n - 8\nB. 2^n - 4\nC. 2^n\nD. 2^n + 4\nE. 2^n + 5\n\n### Answer:\nGiven: k, M and N are integers\nIf k is a divisor of both N and M, then k is a divisor of N+M (and N\u2013M and M\u2013N)\nWe're told that 9 is a divisor of 2^n + 5\nWe also know that 9 is a divisor of9.\nSo, applying the aboverule, 9 is a divisor of 2^n + 5 +9, and 9 is a divisor of 2^n + 5 -9 = 2^n-4\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n10 women can complete a work in 7 days and 10 children take 14 days to complete the work. How many days will 5 women and 10 children take to complete the work?\n\n### Options:\nA. 2\nB. 1\nC. 7\nD. 6\nE. 4\n\n### Answer:\n1 women's 1 day work = 1/70\n1 child's 1 day work = 1/140\n(5 women + 10 children)'s 1 day work\n= (5/10 + 10/140) = (1/14 + 1/14) = 1/7\n5 women and 10 children will complete the work in 7 days.\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe cost price of 20 articles is the same as the selling price of x articles. If the profit is 25%, then the value of x is:\n\n### Options:\nA. 15\nB. 16\nC. 18\nD. 25\nE. 24\n\n### Answer:\nExplanation:\nLet C.P. of each article be Re. 1 C.P. of x articles = Rs. x.\nS.P. of x articles = Rs. 20.\nProfit = Rs. (20 - x).\n(20-X/X X100=25)\n2000 - 100x = 25x\n125x=2000\nx=16\nANSWER IS B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn the City 45% of the population lived in the East at the Beginning of the Year and the rest of the City lived in the West. During the Same Year, the population of City grew by 5.0%. If the population in the West grew by 2.5%, by how much did the population grow in the remaining side?\n\n### Options:\nA. 5.9%\nB. 2.5%\nC. 5.0%\nD. 8.2%\nE. 7.5%\n\n### Answer:\nRatio of population in City = East:West :: 45%:45% = 1:1\nMean growth = 5%\nWest Growth: 2.5%\nEast Growth = ??\nEast-------------Average--------------West\n? __(1n)_____5.0%_____(1n)_____2.5%\nSince:\n2.5+1n=5\nn=2.5\nTherefore:\nEast=5+1n\nEast=5+2.5\nThat is the population grew in East Side of the town is 7.5%\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 2 < x < 7 and 8 << y < 9, then the lowest possible value for xy is\n\n### Options:\nA. between 60 and 70\nB. between 0 and 60\nC. 0\nD. between 0 and -70\nE. less than -70\n\n### Answer:\nIf 2 < x < 7 and 8 << y < 9,\nSay y = 8.9 (8<", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train passes a station platform in 36 sec and a man standing on the platform in 23 sec. If the speed of the train is 54 km/hr. What is the length of the platform?\n\n### Options:\nA. 767 m\nB. 240 m\nC. 195 m\nD. 176 m\nE. 186 m\n\n### Answer:\nSpeed = 54 * 5/18 = 15 m/sec.\nLength of the train = 15 * 23 = 345 m.\nLet the length of the platform be x m . Then,\n(x + 345)/36 = 15 => x = 195 m.\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many different subsets of the set {10, 14, 13, 24} are there that contain an odd number of elements?\n\n### Options:\nA. 3\nB. 6\nC. 8\nD. 10\nE. 12\n\n### Answer:\nAnswer = C = 8\n{10}\n{14}\n{13}\n{24}\n{10, 14, 13}\n{14, 13, 24}\n{10, 13, 24}\n{10, 14, 24}\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nUBA Capital recently bought Brand new vehicles for office use. UBA capital only went for Toyota and Honda and bought more of Toyota than Honda at the ratio of 4:6. If 40% of the Toyota bought and 60% of the Honda bought were SUV\u00c3\u00a2\u00e2\u201a\u00ac\u00e2\u201e\u00a2s. How many SUV\u00c3\u00a2\u00e2\u201a\u00ac\u00e2\u201e\u00a2s did UBA capital buy in the aforementioned purchase?\n\n### Options:\nA. 66%\nB. 64%\nC. 68%\nD. 69%\nE. 52%\n\n### Answer:\nlet total no of Vehicles bought be 100, Toyota 40 and Honda 60, so total number of SUV's bought for Toyota and Honda respectively 40* 40/100=16 and 60* 60/100=36\nso total 52 SUV's were bought out of 100 Vehicles bought..so required % is 52%\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe price of lunch for 15 people was $206.00, including a 15 percent gratuity for service. What was the average price per person, EXCLUDING the gratuity?\n\n### Options:\nA. $11.73\nB. $12.48\nC. $13.80\nD. $14.00\nE. $15.87\n\n### Answer:\nTake the initial price before the gratuity is 100\nThe gratuity is calculated on the final price, so as we assumed the final bill before adding gratuity is 100 so gratuity is 15% of 100 is 15 so the total price of meals is 115 so the given amount i.e 206 is for 115 then we have to calculate for 100\nfor 115 206\nfor 100 x\nso by cross multiplication we get 115x=100*206 => x=100*206/110 by simplifying we get x as 187.27 which is the price of lunch before gratuity so the gratuity is 18.73 so\nas the question ask the average price person excluding gratuity is 187.27/15=12.48 so our answer is B)\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a particular player is always chosen, in how many ways can a cricket-be chosen out of 15 players?\n\n### Options:\nA. 1123\nB. 1234\nC. 1452\nD. 1356\nE. 1365\n\n### Answer:\nA particular player is always chosen, it means that 10 players are selected out of the remaining 14 players.\n=. Required number of ways = 14C10 = 14C4\n= 14!/4!x19! = 1365\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf |r|=\u2212r, which of the following must be true?\n\n### Options:\nA. x\u22650\nB. r\u22640\nC. x2>x\nD. x3<0\nE. 2x", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMr. Jones is the Chairman of a committee. In how many ways can a committee of 5 be chosen from 10 people given that Mr. Jones must be one of them?\n\n### Options:\nA. 126\nB. 252\nC. 459\nD. 3024\nE. 4126\n\n### Answer:\nTotal Ways of choosing the committee = Total Ways of choosing 4 out of 9 candidates leaving Mr.Jones as one of the selected candidate in advance\nTotal Ways of choosing 4 out of 9 candidates = 9C4 = 9!/(5!*4!) = 126\nAnswer: option A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a and b are digits, and the number a99,99b/88 = an integer, what are the values of a and b?\n\n### Options:\nA. a = b = 7\nB. a = b = 6\nC. a = b = 3\nD. a = b = 1\nE. a = b = 2\n\n### Answer:\na99,99b, divisible by 88.\nFactors of 88 = (8)(11)\nDivisible by 8: if the last 3 digits of the number are divisible by 8.\n99b/8 => 992/8 = 124 => b = 2\nDivisibe by 11: subtract the last digit from the number, over and over again, as necessary. If the remaining number is divisible by 11, the original number is divisible by 11.\na9999-2 => a999-7 => a99-2 => a9-7 => a2 => 22/11 = 2.\nSo a = 2.\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man counted his animals, 80 heads and 260 legs (ducks and goats). how many goats are there?\n\n### Options:\nA. 30\nB. 40\nC. 50\nD. 60\nE. 70\n\n### Answer:\nlet no of ducks=d and no of goat=g\nd+g=80(heads)----------> eq 1\neach duck has 2 legs and goat has 4 legs\n2d+4g=260 and divide 2d+4g=260 by 2 we get d+2g=130 -----------> eq2\nsubtract eq1 from eq2\nwe get no of goats=50\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA bottle is 80% full. The liquid in the bottle consists of 60% guava juice and 40% pineapple juice. The remainder of the bottle is then filled with 70 lm of rum. How much guava is in the bottle?\n\n### Options:\nA. 155 ml\nB. 158 ml\nC. 165 ml\nD. 168 ml\nE. 175 ml\n\n### Answer:\nif the Bottle is 100ml:\nwe have 48% Guava, 32% Pineapple, and 20% Rum.\nNow, is the bottle 20% of rum is represented by 70 ml. So, we have to find for the same bottle 48% guava is what ml?\ntherefore, Guava= (70*48)/20= 168 ml\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn the Hillside summer camp there are 50 children. 90% of the children are boys and the rest are girls. The camp administrator decided to make the number of girls only 5% of the total number of children in the camp. How many more boys must she bring to make that happen?\n\n### Options:\nA. 50\nB. 45.\nC. 40.\nD. 30.\nE. 25.\n\n### Answer:\nGiven there are 50 students , 90% of 50 = 45 boys and remaining 5 girls.\nNow here 90% are Boys and 10% are Girls.\nNow question is asking about how many boys do we need to add, to make the girls percentage to 5 or 5%..\nIf we add 50 to existing 45 then the count will be 95 and the girls number will be 5 as it.\nNow boys are 95% and girls are 5%. ( out of 100 students = 95 boys + 5 girls ).\nAnswer: option A is correct.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nExpress a speed of 18 kmph in meters per second?\n\n### Options:\nA. 5 mps\nB. 10 mps\nC. 6 mps\nD. 7 mps\nE. 12 mps\n\n### Answer:\n18 * 5/18\n= 5 mps\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA cuboid of dimension 24cm x 9cm x 8 cm is melted and smaller cubers are of side 3 cm is formed.find how many such cubes can be formed ?\n\n### Options:\nA. 64\nB. 56\nC. 48\nD. 40\nE. 47\n\n### Answer:\nExplanation:\nVolume of cuboid = (24 x 9 x 8) cm = 1728 cu.cm\nVolume of small cube = (3 x 3 x 3) cm = 27 cu.cm\nSo,\nNo. of small cubes formed = 1728/27 = 64.\nANSWER IS A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the average (arithmetic mean) of x, y, and 40 is 5 greater than the average of x, y, 40, and 60, find the average of x and y.\n\n### Options:\nA. 100\nB. 110\nC. 120\nD. 140\nE. 150\n\n### Answer:\nconsider the statement \"9 is 5 greater than 4\": 9 = 4 + 5\nsimilarly,\nthe average of x, y, and 40 = (the average of x, y, 40, and 60) + 5\n(x+y+40)/3 = (x+y+40+60)/4 + 5\n(x+y+40)/3 = (x+y+100)/4 + 5\nget a common denominator on the right side\n(x+y+40)/3 = (x+y+100)/4 + 20/4\n(x+y+40)/3 = (x+y+100+20)/4\n(x+y+40)/3 = (x+y+120)/4\ncross multiply\n4(x+y+40) = 3(x+y+120)\n4x+4x+160 = 3x+3y+360\ncollect like terms\n4x-3x+4y-3y = 360 - 160\nx + y = 200\nthus\n(x+y)/2 = 200/2\n(x+y)/2 = 100\nthe average of x and y is 100\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich of the following fractions is greater than 4/5 and less than 9/10?\n1. 4/5 2. 9/10 3. 1/2 4.3/4 5. 3/5 6. 8/9\n\n### Options:\nA. 4/5\nB. 9/10\nC. 1/2\nD. 3/4\nE. 3/5\n\n### Answer:\n4/5= 0.80, 9/10 = 0.90, 1/2= 0.5, 3/4= 0.75, 3/5=0.66, 1/10= 0.1.\nClearly, 0.75 lies between 0.80 and 0.90.\nTherefore, 3/4 lies between 4/5 and 9/10.\nAnswer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nEqual amount of water were poured into two empty jars of different capacities, which made one jar 1/6 full and other jar 1/5 full. If the water in the jar with lesser capacity is then poured into the jar with greater capacity, what fraction of the larger jar will be filled with water?\n\n### Options:\nA. 1/7\nB. 2/7\nC. 1/3\nD. 7/12\nE. 2/3\n\n### Answer:\nSame amount of water made bigger jar 1/6 full, thenthe same amount of water(stored for a while in smaller jar) were added to bigger jar, so bigger jar is 1/6+1/6=2/6= 1/3 full.\nAnswer: C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo trains are running in opposite directions in the same speed. The length of each train is 120 meter. If they cross each other in 12 seconds, the speed of each train (in km/hr) is\n\n### Options:\nA. 42\nB. 36\nC. 28\nD. 20\nE. 15\n\n### Answer:\nExplanation:\nDistance covered = 120+120 = 240 m\nTime = 12 s\nLet the speed of each train = v. Then relative speed = v + v = 2v\n2v = distance/time = 240/12 = 20 m/s\nSpeed of each train = v = 20/2 = 10 m/s\n= 10 \u00d7 36/10 km/hr = 36 km/hr.\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA can do a piece of work in 16 days. When he had worked for 2 days B joins him. If the complete work was finished in 8 days. In how many days B alone can finish the work?\n\n### Options:\nA. 18\nB. 77\nC. 66\nD. 55\nE. 12\n\n### Answer:\n8/16 + 6/x = 1\nX = 12 days\nAnswer:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe owner of a local jewellery store hired three watchmen to guard his diamonds, but a thief still got in and stole some diamonds. On the way out, the thief met each watchman, one at a time. To each he gave 1/3 of the diamonds he had then, and 3 more besides. He escaped with 3 diamonds. How many did he steal originally?\n\n### Options:\nA. 198\nB. 199\nC. 200\nD. None of these\nE. Cannot be determined\n\n### Answer:\nExplanation :\nSince, thief escaped with 3 diamond,\nBefore 3rd watchman, he had ( 3 + 3 ) x 3 = 18 diamonds.\nBefore 2nd watchman, he had ( 18 + 3 ) x 3 = 63 diamonds.\nBefore 1st watchman, he had ( 63 + 3 ) x 3 = 198 diamonds.\nAnswer : A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe speed of a car is 90 km in the first hour and 60 km in the second hour. What is the average speed of the car?\n\n### Options:\nA. 72 kmph\nB. 75 kmph\nC. 30 kmph\nD. 80 kmph\nE. 85 kmph\n\n### Answer:\nExplanation:\nS = (90 + 60)/2 = 75 kmph\nANSWER IS B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the value of x in 8.5 \u2013 { 5 \u00bd \u2013 [7 \u00bd + 2.8]/x}*4.25/(0.2)^2 = 306\n\n### Options:\nA. 3.2\nB. 3.4\nC. 3.5\nD. 4.1\nE. 4.2\n\n### Answer:\n8.5-{5.5-(7.5+(2.8/x))}*(4.25/0.04) = 306\n\uf0f3 8.5-{5.5-{(7.5x+2.8)/x)}*(425/4) = 306\n\uf0f3 8.5-{(5.5x-7.5x-2.8)/x}*(425/4) = 306\n\uf0f3 8.5-{(-2x-2.8)/x}*106.25 = 306\n\uf0f3 8.5-{(-212.5x-297.5)/x} = 306\n\uf0f3 (306-221)x = 297.5 \uf0f3 x =(297.5/85) = 3.5.\nANSWER C 3.5\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA work can be finished in 30 days by twenty women. The same work can be finished in fifteen days by 10 men. The ratio between the capacity of a man and a woman is\n\n### Options:\nA. 1:3\nB. 4:1\nC. 2:3\nD. 2:1\nE. 2:4\n\n### Answer:\nWork done by 20 women in 1 day = 1/30\nWork done by 1 woman in 1 day = 1/(30\u00d720)\nWork done by 10 men in 1 day = 1/15\nWork done by 1 man in 1 day = 1/(15\u00d710)\nRatio of the capacity of a man and woman =1/(15\u00d710) : 1/(30\u00d720) = 1/150 : 1/600\n= 1/1 :1/4 = 4:1\nOption B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTough and Tricky questions: Functions. Let a be a positive integer. Let n#a equal n^(2a) if a is odd and n^(a) if a is even. Then (2#3) + (3#2) \u2013 (3#3) is equal to\n\n### Options:\nA. 64\nB. -656\nC. 128\nD. 512\nE. 1522\n\n### Answer:\nAnswer:\n2^6 + 3^2 - 3^6 = 2^6 = -656\nANs B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA bakery has 6 employees. It pays annual salaries of $16,000 to each of 2 employees, $18,000 to 1 employee, and $19,000 to each of the remaining 3 employees. Which number is closest to the average (arithmetic mean) annual salary of these employees?\n\n### Options:\nA. $17,200\nB. $17,500\nC. $17,800\nD. $18,000\nE. $18,400\n\n### Answer:\naverage = 2(16000)+(18000)+3(19000) / 6 = $17,833\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA, B, C together started a business. A invested Rs.2000 for 5 months B invested Rs.8000 for 6 months and C Rs.14000 for 3 months. If they get a total profit of Rs.2500. Find the share of A?\n\n### Options:\nA. 2999\nB. 3000\nC. 2777\nD. 2999\nE. 250\n\n### Answer:\n1*5:4*6:7*3\n5: 24: 21\n5/50 * 2500 = 250\nAnswer:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTanks A and B are each in the shape of a right circular cylinder. The interior of tank A has a height of 10 meters and a circumference of 9 meters, and the interior of tank B has a height of 9 meters and a circumference of 10 meters. The capacity of tank A is what percent of the capacity of tank B?\n\n### Options:\nA. 75%\nB. 90%\nC. 100%\nD. 120%\nE. 125%\n\n### Answer:\nThe radius of tank A is 9/(2*pi).\nThe capacity of tank A is 10*pi*81 / (4*pi^2) = 405 / (2*pi)\nThe radius of tank B is 10 / (2*pi).\nThe capacity of tank B is 9*pi*100 / (4*pi^2) = 450 / (2*pi)\nTank A / Tank B = 405/450 = 9/10 = 90%\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJamshid and Irwin decided to make up their own version of basketball. In addition to being able to score 2-point baskets, they created ways to score 5-, 11-, and 13-point baskets. If at halftime the product of the point values of Irwin\u2019s baskets was 2,420, how many 11-point baskets T did Irwin score?\n\n### Options:\nA. 0\nB. 1\nC. 2\nD. 3\nE. 4\n\n### Answer:\nFirst thing I noticed was that all these numbers are prime...\nPrime factorization gives the following\nStep 1:2*1210\nStep 2:2*11*110\nStep 4:2*11*11*10\nStep 5:2*11*11*2*5\nSo he scored T=2 11-point baskets in my opinion.\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRaman mixed 24 kg of butter at Rs. 150 per kg with 36 kg butter at the rate of Rs. 125 per kg. At what price per kg should he sell the mixture to make a profit of 40% in the transaction?\n\n### Options:\nA. Rs.129\nB. Rs.120\nC. Rs.189\nD. Rs.178\nE. Rs.126\n\n### Answer:\nCP per kg of mixture = [24(150) + 36(125)]/(24 + 36)\n= Rs. 135\nSP = CP[(100 + profit%)/100]\n= 135 * [(100 + 40)/100]\n= Rs.189.\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA veterinarian surveys 26 of his patrons. He discovers that 14 have dogs, 10 have cats, and 5 have fish. Four have dogs and cats, 3 have dogs and fish, and one has a cat and fish. If no one has all three kinds of pets, how many patrons have none of these pets?\n\n### Options:\nA. 5\nB. 6\nC. 8\nD. None of these\nE. Cannot determined\n\n### Answer:\n7 + 4 + 0 + 3 + 1 + 5 + 1 + x = 26\n21 + x = 26\nx = 5 patrons have none of these animals\nA)\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe area of a parallelogram is 98sq m and its altitude is twice the corresponding base. Then the length of the base is?\n\n### Options:\nA. 8\nB. 9\nC. 7\nD. 6\nE. 5\n\n### Answer:\n2x * x = 98 => x= 7\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man misses a bus by 40 minutes if he travels at 30 kmph. If he travels at 40 kmph, then also he misses the bus by 10 minutes. What is the minimum speed required to catch the bus on time?\n\n### Options:\nA. 43 kmph\nB. 45 kmph\nC. 47 kmph\nD. 49 kmph\nE. 42 kmph\n\n### Answer:\nB\nLet the distance to be travelled to catch the bus be x km\nx/30 - x/40 = 30/60 => (4x - 3x)/120 = 1/2 => x = 60 km\nBy traavelling 30 kmph time taken = 60/30 = 2 hours\nBy taking 2 hours, he is late by 40 min. So, he has to cover 60 km in at most speed = 60/(4/3) = 45 kmph.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA dress on sale in a shop is marked at $D. During the discount sale its price is reduced by 15%. Staff are allowed a further 10% reduction on the discounted price. If a staff member buys the dress what will she have to pay in terms of D ?\n\n### Options:\nA. 0.75D\nB. 0.76D\nC. 0.765D\nD. 0.775D\nE. 0.805D\n\n### Answer:\nSuccessive doscounts = - a - b +ab/100\nPutting the values,\nTotal discount = -15 - 10 + 150/100 = -25 + 1.5 = 23.5% discount\nHence the final price of the dress = D - 0.235D = 0.765D\nCorrect Option: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n5 nouns, 5 verbs and 3 adjectives are written on blackboard.we can form sentence by choosing 1 from each available set without caring it makes sense or not.what is the number of ways of doing this??\n\n### Options:\nA. 360\nB. 390\nC. 420\nD. 450\nE. 540\n\n### Answer:\nwe have to choose one from each set. 1 from 5 nouns and 1 from 5 verbs and 1 from 3 adjectives.\nthen we have to arrange 3 different sets in 3! ways.\nso,\n5c1*5c1*3c1*3!=450\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind a sum for first 4 prime number'ss?\n\n### Options:\nA. 18\nB. 12\nC. 30\nD. 17\nE. 36\n\n### Answer:\nRequired sum = (2 + 3 + 5 + 7) = 17\nNote: 1 is not a prime number\nOption D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA jogger running at 9 km/hr along side a railway track is 240 m ahead of the engine of a 100 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger?\n\n### Options:\nA. 28 sec\nB. 16 sec\nC. 34 sec\nD. 18 sec\nE. 17 sec\n\n### Answer:\nSpeed of train relative to jogger = 45 - 9 = 36 km/hr.\n= 36 * 5/18 = 10 m/sec.\nDistance to be covered = 240 + 100 = 340 m.\nTime taken = 340/10 = 34 sec.\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 4 hours and 10 hours respectively. The ratio of their speeds is\n\n### Options:\nA. 4 : 9\nB. 4 : 3\nC. 4 : 12\nD. 4 : 8\nE. 5 : 2\n\n### Answer:\nLet us name the trains as A and B. Then, (A's speed) : (B's speed) = b : a = 10 : 4 = 5 : 2.\rAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe speed of a boat in upstream is 60 kmph and the speed of the boat downstream is 190 kmph. Find the speed of the boat in still water and the speed of the stream?\n\n### Options:\nA. 10\nB. 99\nC. 77\nD. 55\nE. 65\n\n### Answer:\nSpeed of the boat in still water = (60+190)/2 = 125 kmph. Speed of the stream\n= (190-60)/2\n= 65 kmph.\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf you have 8 New Year greeting cards and you want to send them to 3 of your friends, in how many ways can this be done?\n\n### Options:\nA. 336\nB. 720\nC. 340\nD. 670\nE. None\n\n### Answer:\nSolution\nWe have to find number of permutations of 3 objects out of 8 objects. This number is 8P3=8(8-1)(8-2)=8*7*6=336\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA salesman\u00e2\u20ac\u2122s terms were changed from a flat commission of 5% on all his sales to a fixed salary of Rs.1000 plus 2.5% commission on all sales exceeding Rs. 4,000. If his remuneration as per new scheme was Rs. 500 more than that by the previous schema, his sales were worth?\n\n### Options:\nA. s. 14,000\nB. s. 12,000\nC. s.16,000\nD. s. 40,000\nE. s. 50,000\n\n### Answer:\n[1000 + (X-4000) * (2.5/100)] - X * (5/100) = 600\nX = 16000\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the area of a square field whose diagonal of length 18 m?\n\n### Options:\nA. 120 sq m\nB. 250 sq m\nC. 200 sq m\nD. 180 sq m\nE. 100 sq m\n\n### Answer:\nd2/2 = (18 * 18)/2 = 180\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA clock is set right at 12 noon on Monday. It losses 1/2% on the correct time in the first week but gains 1/4 on the true time during the second week. The time shown on Monday after two weeks will be\n\n### Options:\nA. 12:25:12\nB. 11:34:48\nC. 12:50:24\nD. 12:24:16\nE. None of these\n\n### Answer:\nSolution: Time lost over two weeks = 25% a week time(given that 1/2% clock loses in first week and in the second week it gains 1/4% on true time)\nA week = 168 hours\nHence, clock lost = 0.42 hours = 25.2 minutes or 25 minute 12 seconds.\nThus, correct time = 12:25:12.\nAnswer: Option A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n7% of the total quantity of rice is lost in grinding when a country has to import 6 million tonnes, but when only 7 3/4% is lost, it can import 3 million tonnes. Find the quantity of rice grown in the country.\n\n### Options:\nA. 200\nB. 300\nC. 400\nD. 450\nE. 560\n\n### Answer:\nLet x be the total grown quantity of wheat. According to the question\n(7%of x)+ 64 31 %of x)+3 7x 31x => 100+ 6 = 400 + 3 1200 x = \u2014 400 million tonnes rice grown\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nthe first flight out of Phoenix airport had a late departure. If the next three flights departed on-time, how many subsequent flights need to depart from Phoenix on-time, for the airport's on-time departure rate to be higher than 90%?\n\n### Options:\nA. 6\nB. 7\nC. 9\nD. 10\nE. 11\n\n### Answer:\nWe need on-time departure rate to be higher than 9/10, so it should be at least 10/11 which means that 10 out of 11 flights must depart on time. Since for now 3 out of 4 flights departed on time then 10\u22123=7 subsequent flights need to depart on-time.\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nBy selling a house for Rs.45000, it was found that 1/8 of the outlay was gained, what ought the selling to price to have been in order to have lost 5 p.c?\n\n### Options:\nA. 38008\nB. 38000\nC. 38029\nD. 380219\nE. 38012\n\n### Answer:\nCP + CP/8 = 45000\nCP = 40000\nSP = 40000*(95/100) = 38000\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a man travels f miles an hour for t hours and r miles an hour for k hours, what is his average rate in miles per hour for the entire distance traveled?\n\n### Options:\nA. ft + rk\nB. (ft + rk)/2\nC. t/f + k/r\nD. (ft + rk)/(t + k)\nE. (ft + rk)/(t - k)\n\n### Answer:\nAverage Speed = Total Distance /Total Time Taken\nTotal Distance travelled in t hours = ft\nTotal Distance travelled in s hours = rk\nTotal Time taken = t+k\nTherefore , Average Speed = (ft+tk)/(t+k)\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man is trying 2 different pairs of pants &6 different shirts. How many combinations of 1 pair of pants &1 shirt are possible?\n\n### Options:\nA. 10\nB. 12\nC. 16\nD. 19\nE. 21\n\n### Answer:\nUse a tree diagram to illustrate the possible selections. In the diagram, use P1 and P2 to represent the pants and S1, S2, S3, S4, S5, and S6 to represent the shirts.\nUsing the Fundamental Counting Principle, 2 \u00d7 6 = 12 outfits are possible.\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the least number which when divided by 33 and 8 leaves a remainder of 2 in each case.\n\n### Options:\nA. 266\nB. 268\nC. 270\nD. 272\nE. 274\n\n### Answer:\nThe least number which when divided by different divisors leaving the same remainder in each case\n= LCM(different divisors) + remainder left in each case.\nHence the required least number\n= LCM(33, 8) + 2 = 266.\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are 8 students. 4 of them are men and 4 of them are women. If 4 students are selected from the 8 students. What is the probability R that the number of men is equal to that of women?\n\n### Options:\nA. R=18/35\nB. 16/35\nC. 14/35\nD. 13/35\nE. 12/35\n\n### Answer:\nMETHOD-1:\nFavorable outcomes (i.e. No. of Men= No. of Women =2) = 4C2 * 4C2 = 6*6 = 36\nTotal ways of selecting 4 out of 8 Students = 8C4 = 8! / (4! * 4!) = 70\nProbability = 36/70 = 18/35\nA\nMETHOD-2:Also see the mistake done by the person who posted this question\nProbability of First selected person being Man = 4/8\nProbability of Second selected person being Man = 3/7\nProbability of First selected person being Woman = 4/6\nProbability of Second selected person being Woman = 3/5\ni.e. Probability = (4/8)*(3/7)*(4/6)*(3/5) *[4!/(2!*2!)]= 18/35\nThe important part for the readers is to understand the reason of multiplying[4!/(2!*2!)]here\nWhen we take the probability of each case like we have have taken in this method then it always include ARRANGEMENTS as well and so we have to take every arrangement of the events as well\nThe arrangement of these 4 events can be done in 4! ways but since the second man can't be selected before 1st so we have to exclude their arrangement by dividing by 2! and similarly since the second Woman can't be selected before 1st so we have to exclude their arrangement by dividing by 2!\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a village there are 150 men and 90 women in present time.if in next year population will be P=(a^2 +b^2)^1/2 , and in every year men are reduces 12%.what is population of after 2 year.\n\n### Options:\nA. 139\nB. 141\nC. 142\nD. 143\nE. 144\n\n### Answer:\nnext year total population=[150^2+90^2]^.5=174.92=175\nman decreased by 11% so total man =150*.88=132\nwomen will be= 175-132=43\nso population after two years= [135^2+43^2]^.5=138.8=139\nso population after two year= 139\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIF x is an integer greater than 6, then all the following must be divisible by 3 EXCEPT\n\n### Options:\nA. 3x^3\nB. x(x+1)(x+2)\nC. 9x\nD. 9x^2\nE. x+3\n\n### Answer:\n*any number multiplied by 3, will be divided by 3\nfor option E if we put value x=7, 7+3=10 is not divisible by 3\nAnswer : E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA jet plane is rising vertically with a velocity of 10 m/s. It has reached a certain height when the pilot drops a coin, which takes 4 sec to hit the ground. Assuming that there is no resistance to the motion of the coin, the height of the place and the velocity of the coin on impact with the ground are:\n\n### Options:\nA. 38.4 m, 28.7 m/s\nB. 38.4 m, 29.2 m/s\nC. 26.5 m, 13.5 m/s\nD. 26.5 m, 28.7 m/s\nE. 26 m\n\n### Answer:\nThe coin will move up with the initial velocity of 10 m/s till it comes to rest. Time taken is given by:\n0=10\u00e2\u02c6\u20199.8t\n\u00e2\u2021\u2019t=10/9.8 sec.\nTime taken to reach the ground from the highest point:\n=4\u00e2\u02c6\u201910/9.8\n=29.2/9.8 sec\nVelocity of coin on impact\n=0+9.8\u00c3\u2014(29.2/9.8)\n=29.2 m/s\nIf 'h' is the height from which the coin dropped.\nThen\n29.2^2\u00e2\u02c6\u201910^2=2\u00c3\u20149.8\u00c3\u2014h\n\u00e2\u2021\u2019h = 38.4 m\nAnswer : B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how many ways can 3 postcards can be posted in 5 postcards?\n\n### Options:\nA. 50\nB. 120\nC. 125\nD. 130\nE. 100\n\n### Answer:\nFirst card can go into any of the five boxes, Second can go into any of the five boxes.\nThird card also can go into any of the five boxes\nNumber of ways=5*5*5=125 ways\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the probability of rolling a total of 5 with a single roll of two fair six-sided dice, each with the distinct numbers 1 through 6 on each side?\n\n### Options:\nA. 1/12\nB. 1/6\nC. 2/7\nD. 1/3\nE. 1/9\n\n### Answer:\nTotalsample spacefrom two fair six-sided dice is 36.\nThere are six possible ways to be 5 i.e. (1+4), (2+3), (3+2), (4+1)\nSo, total probability is 4/36 or 1/9.\nAnswer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn an examination 35% of the students passed and 546 failed. How many students appeared for the examination?\n\n### Options:\nA. A)540\nB. B)400\nC. C)700\nD. D)650\nE. E)840\n\n### Answer:\nLet the number of students appeared be x\nthen, 65% of x = 546\n65x/100 = 546\nx = 546*100/65 = 840\nAnswer is E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo musicians, Maria and Perry, work at independent constant rates to tune a warehouse full of instruments. If both musicians start at the same time and work at their normal rates, they will complete the job in 120 minutes. However, if Perry were to work at twice Maria\u2019s rate, they would take only 20 minutes. How long would it take Perry, working alone at his normal rate, to tune the warehouse full of instruments?\n\n### Options:\nA. 1 hr 20 min\nB. 1 hr 45 min\nC. 2 hr\nD. 2 hr 20 min\nE. 1 hr\n\n### Answer:\nSol:\nLets Perry Rate be P and Rate of Maria be M\n(rate)*(time)= Work or rate = work/time\nfirst equation=> P+M = 1/120\nconverting it to hrs P+M= 1/(60/120) => 2\nsecond equation => M+2M =>1/20\nconverting it to hrs 3M=1/(20/60) =>1/(1/3) =>3\ntherefore M= 1 and P=1\nRate of Perry = 1\ntime= work/rate (work = 1 job)\nTime= 1 hrs\nAnswer : E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a division sum, the divisor is ten times the quotient and five times the remainder. If the remainder is 6, the dividend is:\n\n### Options:\nA. 92\nB. 94\nC. 96\nD. 98\nE. 100\n\n### Answer:\nDivisor = (5 * 6) = 30\n= 10 * Quotient = Divisor\n=> Quotient = 30/10 = 3\nDividend = (Divisor * Quotient) + Remainder\nDividend = (30 * 3) + 6 = 96.\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRavi can do a piece of work in 11 days while Prakash can do it in 22 days. In how many days will they finish it together?\n\n### Options:\nA. 5 7/3 days\nB. 7 1/3days\nC. 5 1/9 days\nD. 5 7/3 days\nE. 4 7/9 days\n\n### Answer:\n1/11 + 1/22 = 3/22\n22/3 = 7 1/3 days\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nBrittany's income is 12 percent more than Tina's income, and Tina's income is 15 percent less than Jean's income. What percent of Jean's income is Brittany's income?\n\n### Options:\nA. 95.2%\nB. 91.2%\nC. 96.2%\nD. 94.2%\nE. 92.2%\n\n### Answer:\nJean's income = 100 (assume);\nTina's income = 85 (15 percent less than Jean's income);\nBrittany's income = 95.2 (12 percent more than Tina's income).\nThus, Brittany's income (95.2) is 95.2% of Jean's income (100).\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIt takes 6 beavers 10 hours to build a certain dam, working at a uniform rate. If three beavers start to build the same dam at 8:00 AM, and one beaver per hour is added beginning at 6:00 PM, at what time will the dam be complete?\n\n### Options:\nA. 7:30 PM\nB. 8:00 PM\nC. 9:00 PM\nD. 10:00 PM\nE. 11:00 PM\n\n### Answer:\nThe rate of 1 beaver is 1/60.\nThe amount of work done by 3 beavers in 10 hours is 3/60 *10 = 30/60\nIn the next hour, 4 beavers do 4/60 for a total of 34/60.\nIn the next hour, 5 beavers do 5/60 for a total of 39/60.\nIn the next hour, 6 beavers do 6/60 for a total of 45/60.\nIn the next hour, 7 beavers do 7/60 for a total of 52/60.\nIn the next hour, 8 beavers do 8/60 for a total of 60/60.\nThe dam will be completed at 11:00 pm.\nThe answer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf (-6)^(2x) = 6^(7 + x) and x is an integer, what is the value of x ?\n\n### Options:\nA. 5\nB. 4\nC. 3\nD. 8\nE. 7\n\n### Answer:\nSince x is an integer, (-6)^2x is always positive.\nSo, 6^2x = 6^(7 + x)\n2x = 7 + x\nx = 7\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe ratio, by weight, of coffee to sugar to water in a pot of coffee is 5:2:15. The ratio is then altered so that the ratio of coffee to sugar is halved while the ratio of coffee to water is doubled. If the altered pot of coffee contains 12 grams of sugar, how many grams of water does it contain after alteration?\n\n### Options:\nA. 22.5\nB. 20\nC. 17.5\nD. 15\nE. 12.5\n\n### Answer:\nThe new ratio of coffee to sugar is 2.5:2 = 5:4\nThe new ratio of coffee to water is 10:15.\nThe new ratio of coffee to sugar to water is 10:8:15.\nIf there are 12 grams of sugar, then there are (15/8)*12=22.5 grams of water.\nThe answer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the greatest possible straight line distance, in inches, between any two points on a rectangular box that is 5 inches wide, 3 inches long, and 4 inches high?\n\n### Options:\nA. 2\u221a5\nB. 5\nC. 5\u221a2\nD. 10\nE. 50\n\n### Answer:\nThe maximum possible distance in a cuboid is the diagonal.\nDiagonal length = sqrt(length^2 + breadth^2 + height^2) = sqrt(50)\n= 5\u221a2\n(Option C)\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe radius of a semicircle is 7. What is the approximate perimeter of the semicircle?\n\n### Options:\nA. 36\nB. 25\nC. 15\nD. 28\nE. 37\n\n### Answer:\nperimeter of a circle =2pi*r\nperimeter of a semicircle = pi*r + 2r\naprox perimiter = 3.14*7 + 2*7 = 35.98 approximately 36\nanswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA hollow iron pipe is 21 cm long and its external diameter is 8 cm. If the thickness of the pipe is 1 cm and iron weighs , then the weight of the pipe is\n\n### Options:\nA. 3.496 kg\nB. 3.696 kg\nC. 3.690 kg\nD. 9.696 kg\nE. 3.296 kg\n\n### Answer:\nExplanation:\nExternal radius = 4 cm,\nInternal radius = 3 cm.\nVolume of iron = =\nWeight of iron = (462 x 8)gm = 3696 gm = 3.696 kg\nAnswer: B) 3.696 kg\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the compound ratio of (1:2), (2:3) and (3:4) is\n\n### Options:\nA. 1:2\nB. 3:5\nC. 5:7\nD. 1:4\nE. 2:1\n\n### Answer:\nRequired ratio = 1/2 * 2/3 * 3/4 = 1/4 = 1:4\nAnswer is D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain number of two digits is three times the sum of its digits and if 45 be added to it, the digits are reversed. Then number is\n\n### Options:\nA. 21\nB. 23\nC. 27\nD. 72\nE. 57\n\n### Answer:\nSol.\nLet the ten's digit be x and unit's digit be y.\nThen, 10x + y = 3(x+y) \u21d2 7x - 2y = 0\n10x + y + 45 = 10y + x \u21d2 y - x = 5\nSolving (i) and (ii), we get : x = 2 and y = 7.\n\u2234 Required number = 27.\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man sold 20 articles for $60 and gained 20%. How many articles should he sell for $70 to incur a loss 20%?\n\n### Options:\nA. 45\nB. 35\nC. 40\nD. 50\nE. 48\n\n### Answer:\nProduction cost per article: $60*(100%-20%) / 20 = $2.40\nRequired production costs for a loss of 20%: $70*(100% + 20%) = $84\nNumber of articles to be sold for $84 to incur a 20% loss: $84 / $2.40 = 35\nThus, solution B is correct.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA person covered one-fourth of the total distance at 26 kmph and remaining distance at 24 kmph. What is the average speed for the total distance?\n\n### Options:\nA. 21 (1/8)kmph\nB. 21 (1/3)kmph\nC. 21 (7/3)kmph\nD. 27 (1/3)kmph\nE. 21 (1/8)kmph\n\n### Answer:\nLet the total distance be x km\ntotal time taken = (x/4)/16 + (3x/4)/24 = x/64 + x/32 = 3x/64\nAverage speed = x/(3x/64) = 64/3kmph\n= 21 (1/3)kmph.\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMurali travelled from city A to city B at a speed of 40 kmph and from city B to city C at 60 kmph. What is the average speed of Murali from A to C given that the ratio of distances between A to B and B to C is 2 : 3?\n\n### Options:\nA. 50 kmph\nB. 60 kmph\nC. 40 kmph\nD. 70 kmph\nE. 80 kmph\n\n### Answer:\nA\nLet the distances between city A to B and B to C be 2x km and 3x km respectively.\nTotal time taken to cover from A to C\n= (2x)/40 + (3x)/60 = (6x + 6x)/120 = 12x/120 = x/10 Average speed = (2x + 3x)/(x/10) = 50 kmph.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe numerator of a certain fraction is 8 less than the denominator. If 3 is added to the numerator and 3 is subtracted from the denominator, the fraction becomes 3/4. Find the original fraction?\n\n### Options:\nA. 24.5\nB. 28.5\nC. 30\nD. Data inadequate\nE. None of these\n\n### Answer:\nExplanation:\nLet C.P. be Rs. 100.\nThen, S.P. = Rs. 123.50\nLet marked price be Rs. x. Then, 95/100 x = 123.50\nx = 12350/95 = Rs. 130\nNow, S.P. = Rs. 130, C.P. = Rs. 100\nProfit % = 30%.\nAnswer: Option C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 2^z is a factor of 27!, which of the following could be the value of z?\nI. 22\nII. 23\nIII. 24\n\n### Options:\nA. I \u200b only\nB. II only\nC. I\u200b and II\nD. I, II, and III\nE. None\n\n### Answer:\n27! contains all numbers from 1 to 27. To find the factor with the highest power of 2, we count the number of multiples of 2, 4, 8 and 16.\nMultiples of 2 = 13\nMultiples of 4 = 6\nMultiples of 8 = 3\nMultiples of 16 = 1\nTotal count = 23\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nCity I City II\tCity III\tCity IV\tCity V\tCity VI\nCity I\nCity II\nCity III\nCity IV\nCity V\nCity VI\nIn the table above, what is the least number of table entries that are needed to show the mileage between each city and each of the other five cities?\n\n### Options:\nA. 14\nB. 15\nC. 13\nD. 12\nE. 11\n\n### Answer:\nEasy way to go about this problem is we have 6*6 = 36 enteries in table the least number of enteries would be (36 - 6) /2 since 6 enteries represent the distances between same points .\nAlternatively this can be solved as combination problem.\nCorrect Answer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the area of a square field whose diagonal of length 14 m?\n\n### Options:\nA. 160 sq m\nB. 140 sq m\nC. 200 sq m\nD. 400 sq m\nE. 180 sq m\n\n### Answer:\nd2/2 = (14 * 14)/2 = 140\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man buys an article and sells it at a profit of 10%. If he had bought it at 10% less and sold it for Rs.55 less, he could have gained 15%. What is the cost price?\n\n### Options:\nA. 197\nB. 375\nC. 846\nD. 278\nE. 268\n\n### Answer:\nCP1 = 100 SP1 = 110\nCP2 = 90 SP2 = 90 * (115/100) = 103.5\n6.5 ----- 100\n55 ----- ? => 846\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe perimeter of a square is equal to the perimeter of a rectangle of length 19 cm and breadth 14 cm. Find the circumference of a semicircle whose diameter is equal to the side of the square. (Round off your answer to two decimal places)\n\n### Options:\nA. 22.78\nB. 23.54\nC. 23.5\nD. 24.55\nE. 25.93\n\n### Answer:\nLet the side of the square be a cm.\nPerimeter of the rectangle = 2(19 + 14) = 66 cm\nPerimeter of the square = 66 cm\ni.e. 4a =66\nA = 16.5\nDiameter of the semicircle = 16.5 cm\nCircumference of the semicircle\n= 1/2(\u220f)(16.5)\n= 1/2(22/7)(16.5) = 25.93 cm to two decimal places\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn the third grade of Windblown School there are 108 students, one third of them failed the math test and 1/6 failed that literature test. At least how many students failed both tests?\n\n### Options:\nA. 0.\nB. 6.\nC. 8.\nD. 10\nE. 12\n\n### Answer:\nOne third of them failed the math test = 1/3 of 108 = 36. Passed in math test = 82.\nAnd 1/6 failed that literature test = 18.\nIt is a possible scenario that these 18 (failed in literature) were the ones who passed the math test. So in this case, no one failed in both.\nHence A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n\u221a[200\u221a[200\u221a[200\u2026\u2026..\u221e]]] = ?\n\n### Options:\nA. 200\nB. 10\nC. 1\nD. 20\nE. 2\n\n### Answer:\nLet \u221a[200\u221a[200\u221a[200\u2026\u2026..\u221e]]] = x ; Hence \u221a200x = x\nSquaring both sides 200x = x\u00b2 \u00de x (x \u2013 200) = 0\n\u00de x = 0 or x \u2013 200 = 0 i.e. x = 200\nAs x cannot be 0, x = 200.\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf (1+f)g=g, which of the following must be true?\n\n### Options:\nA. f=-1 or g=0\nB. f=0 or g=0\nC. f=1 or g=1\nD. f=-1 or g=-1\nE. f=0 or g=1\n\n### Answer:\nBy only having fg=0, we cannot say answer is B as A and E options also satisfy the condition fg=0. ans B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA, B and C enter into a partnership and their shares are in the ratio 1/2 : 1/3 : 1/4. After 2 months, A withdraws half of his capital and after 10 months, a profit of Rs. 378 is divided among them. What is B's share ?\n\n### Options:\nA. 144\nB. 378\nC. 217\nD. 299\nE. 277\n\n### Answer:\nExplanation:\nRatio of initial investments = 1/2 : 1/3 : 1/4 = 6 : 4 : 3.\nLet their initial investments be 6x, 2x and 3x respectively.\nA : B : C = (6x * 2 + 3x * 10) : (4x * 12) : (3x * 12) = 42 : 48 : 36 = 7 : 8 : 6.\nB's share = = Rs. 144.\nAnswer: A) 144\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA baker filled with a measuring cup with 3/4 cup water. He poured 1/2 of the water into the batter, and then spilled 2/8 of the water on the floor. How much water will the baker needed to add what is left in the cup to have 50% more than what he started with?\n\n### Options:\nA. 1/8 cup\nB. 3/8 cup\nC. 1/4 cup\nD. 1/2 cup\nE. 8/8 cup\n\n### Answer:\n3/4 is the original water in cup .half in batter.So left is 3/8 out which 2/8 is spilled out.So again left with 1/8.\nso 50% more than what he started was = 3/4+1/2*(3/4)=9/8\nAmount of water needed to add = 9/8 - 1/8=8/8\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA woman invested $1,000, part at 5% and the rest at 6%. Her total investment with interest at the end of the year was $1,054. How much did she invest at 5%?\n\n### Options:\nA. $500\nB. $600\nC. $700\nD. $900\nE. $950\n\n### Answer:\net x be the portion invested at 5% and\nLet (1-x) be the rest which is invested at 6%\nThe question states that the return after 1 year is (1054/1000)-1 = 0.054 = 5.4%\nWe want to find the dollar amount invested in X\nUsing our defined variables, put together the equation and solve for x (the percentage of 1000 invested at 5%)\n0.05x+0.06(1-x)= 0.054\n(0.05)x +0.06 - (0.06)x = 0.054\n-0.01x = -0.006\nx= -0.006/-0.01 = 6/10 = 60%\nSo X = 60% of the 1000 which is 600\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow much time will an express train of length 200 m moving at a speed of 72 kmph take to cross another express train of length 300 m, moving at 36 kmph in the same direction?\n\n### Options:\nA. sec\nB. sec\nC. sec\nD. sec\nE. sec\n\n### Answer:\nThe distance to be covered = Sum of their lengths = 200 + 300 = 500 m.\nRelative speed = 72 -36 = 36 kmph = 36 * 5/18 = 10 mps.\nTime required = d/s = 500/10 = 50 sec.\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn what ratio must a grocer mix two varieties of pulses costing Rs.15 and Rs.20 per kg respectively so as to get a mixture worth Rs.16.50 per Kg?\n\n### Options:\nA. 3 : 7\nB. 5 : 7\nC. 7 : 3\nD. 7 : 5\nE. None\n\n### Answer:\nSolution\nRequired ratio = 3.50 : 1.50 = 35 : 15 = 7 : 3.\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAmong the employees of a certain company, 52 percent of the employees are male and 48 percent are female. In this company 70 percent of the male employees are married and 50 percent of the female employees are married. If one employee in the company is randomly selected, approximately what is the probability that he or she is NOT married?\n\n### Options:\nA. 0.3\nB. 0.4\nC. 0.5\nD. 0.6\nE. 0.7\n\n### Answer:\nTotal Males = 52\nTotal Female = 48\nTotal = 100\nNot married Male = 30% = 15.6\nNot marries Female = 50% = 24\nTotal = 39.6\nProbability = 39.6/100 = .396 = approx .4\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf Rs. 595 be divided among A, B, C in such a way that A gets 2/3 of what B gets and B gets 1/4 of what C gets, then their shares are respectively?\n\n### Options:\nA. s.420\nB. s.360\nC. s.389\nD. s.368\nE. s.323\n\n### Answer:\n(A = 2/3 B and B = 1/4 C) = A/B = 2/3 and B/C = 1/4\nA:B = 2:3 and B:C = 1:4 = 3:12\nA:B:C = 2:3:12\nA;s share = 595 * 2/17 = Rs. 70\nB's share = 595 * 3/17 = Rs. 105\nC's share = 595 * 12/17 =Rs.420.\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat ratio must a shopkeepermix Peas and Soybean of Rs.16 and Rs. 25/kg, As to obtain a mixture of Rs.20 ?\n\n### Options:\nA. 10 : 7\nB. 9 : 8\nC. 5 : 4\nD. 13 : 11\nE. 14 : 8\n\n### Answer:\nCorrect option: (C)\nUse rule of alligation, to determine the ratio\nThe required ratio of Soybean and Peas = 5 : 4\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe population of a city is 160,000. If it increases at the rate of 6% per annum, then what will be its population 2 years hence?\n\n### Options:\nA. 268942\nB. 186935\nC. 179776\nD. 167425\nE. None of these\n\n### Answer:\nExplanation:\nPopulation after n years = P [1 + (R/100)]2\nPopulation after 2 years = 160000 * [1 + 6/100]2 = (160000 x 53/50 x 53/50) = 179776\nANSWER: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n10x + 2y = -6\n8x + y = 3\nIn the system of equations above, what is the value of x?\n\n### Options:\nA. -6\nB. -4\nC. -2\nD. 2\nE. 4\n\n### Answer:\n10x + 2y = -6 can be written as 5x + y = -3\nLet's subtract the second equation from this equation.\n-3x = -6\nx = 2\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the are of an equilateral triangle of side 16 cm?\n\n### Options:\nA. 64\u221a8 cm2\nB. 64\u221a1 cm2\nC. 68\u221a3 cm2\nD. 64\u221a3 cm2\nE. 24\u221a3 cm2\n\n### Answer:\nArea of an equilateral triangle\n= \u221a3/4 S2\nIf S = 16, Area of triangle\n= \u221a3/4 * 16 * 16\n= 64\u221a3 cm2;\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA sun is divided among X, Y and Z in such a way that for each 2 rupees X gets, Y gets 80 paisa and Z gets 60 paisa. If the share of Y is RS. 40, what is the total amount?\n\n### Options:\nA. 160\nB. 155\nC. 150\nD. 170\nE. 165\n\n### Answer:\nx:y:z = 200:80:60\n10:4:3\n4 --- 40\n17 --- ? => 170\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many 4 digit numbers can be formed with the digits 0, 1, 2, 3, 4, 5, 6 and 5?\n\n### Options:\nA. a. 220\nB. b. 249\nC. c. 432\nD. d. 216\nE. e. 288\n\n### Answer:\nTaking Question with it's same language as given\nTo make number divisible by 5, the unit digit should be either 0 or 5 only\nCase 1: If unit digit is fixed as zero\nWith two6s The choice to fill the remaining three digits = 3C2 x 5 = 15\nWith all remaining 3 digits different, The choice to fill the remaining three digits = 6 x 5 x 4= 120\nTotal Such cases = 120+15 = 135\nCase 2: If unit digit is fixed as Five\nWith two6s and one0The choice to fill the remaining three digits = 2 [6605 or 6065]\nWith two6s and without0The choice to fill the remaining three digits = 3C2 x 4 = 12\nWith all remaining 3 digits different, and one0The choice to fill the remaining three digits = 2 (ways to place zero) x 5 x 4= 40\nWith all remaining 3 digits different, and without0The choice to fill the remaining three digits = 3 x 5 x 4= 60\nTotal Such cases = 2+12+40+60 = 114\nTotal numbers = 135+114 = 220\nANSWER OPTION A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOne-fourth of a number is greater than one-fifth of the number succeeding it by 1. Find the number.\n\n### Options:\nA. 24\nB. 42\nC. 36\nD. 48\nE. 50\n\n### Answer:\nnumber is 24\nas 1/4 th of 24= 6\n1/5 th of 25(24+1) =5\n6=5+1\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAn urn contains 5 red, 6 blue and 8 green balls. 3 balls are randomly selected from the urn, find the probability that the drawn ball are blue?\n\n### Options:\nA. 20/969\nB. 20/875\nC. 21/876\nD. 3/512\nE. 2/9\n\n### Answer:\nSample space = no. of ways 3 balls were drawn from urn = 19C3 = 969\nNo. ways 3 blue balls were drawn from bag = 6C3 = 20\nProbability = 20 / 969\nAns - A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo trains of length 200 m and 280 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively. In what time will they be clear of each other from the moment they meet?\n\n### Options:\nA. 22 sec\nB. 77 sec\nC. 76 sec\nD. 20 sec\nE. 24 sec\n\n### Answer:\nRelative speed = (42 + 30) * 5/18 = 4 * 5 = 20 mps.\nDistance covered in passing each other = 200 + 280 = 480 m.\nThe time required = d/s = 480/20 = 24 sec.\nAnswer:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA shipment of 8 television sets contains 2 black-and-white sets and 7 color sets. If 2 television sets are to be chosen at random from this shipment, what is the probability that at least 1 of the 2 sets chosen will be a black-and-white set?\n\n### Options:\nA. 1/7\nB. 1/4\nC. 5/14\nD. 11/28\nE. 13/28\n\n### Answer:\nI get 1/4, which is not in the answer choices.\nthe probability of getting at least one b/w TV is 1-(the probability of getting 2 color TVs)\n1-C(7,2)/C(8/2)=7/28=1/4\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA snail, climbing a 42 feet high wall, climbs up 4 feet on the first day but slides down 2 feet on the second. It climbs 4 feet on the third day and slides down again 2 feet on the fourth day. If this pattern continues, how many days will it take the snail to reach the top of the wall?\n\n### Options:\nA. 20\nB. 26\nC. 32\nD. 39\nE. 51\n\n### Answer:\ntotal transaction in two days = 4-2 = 2 feet\nin 38 days it will climb 38 feet\non the 39th day , the snail will climb 4 feet , thus reaching the top\ntherefore , total no of days required =39\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many seconds will a 400 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?\n\n### Options:\nA. 20\nB. 30\nC. 40\nD. 24\nE. 60\n\n### Answer:\nSpeed of train relative to man = 63 - 3 = 60 km/hr.\n= 60 * 5/18 = 50/3 m/sec.\nTime taken to pass the man = 400 * 3/50 = 24 sec.\nAnswer: Option D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nGiven three boxes I, II and III, each containing two coins. In box I, both coins are 1 rupee\ncoins, in box II, both are 2 rupee coins and in the box III, there is one 1 rupee and one 2 rupee coin.\nA person chooses a box at random and takes out a coin. If the coin is of 1 rupee, what is the\nprobability that the other coin in the box is also of 1 rupee?\n\n### Options:\nA. 1/5\nB. 2/3\nC. 2/7\nD. 3/7\nE. 2/5\n\n### Answer:\nLet E1, E2 and E3 be the events that boxes I, II and III are chosen, respectively.\nThen P(E1) = P(E2) = P(E3) = 1/3\nAlso, let A be the event that \u2018the coin drawn is of 1 rupee'\nThen P(A|E1) = P(a 1 rupee coin from bag I) = 2/2 = 1\nP(A|E2) = P(a 1 rupee coin from bag II) = 0\nP(A|E3) = P(a 1 rupee coin from bag III) = 1/2\nthe probability that the other coin in the box is of 1 rupee\n= the probability that 1 rupee coin is drawn from the box I.\n= P(E1|A)\nfrom Bayes' theorem, we know that\nP(E1|A) = [P(E1 )P(A|E1 )]/ [P(E1 )P(A|E1 )+P(E2 )P(A|E2 )+P(E3 )P(A|E3 )]\n= (1/3 \u00d7 1)/(1/3 \u00d7 1 + 1/3 \u00d7 0 + 1/3 \u00d7 1/2)\n= (1/3)/(1/3 \u00d7 1 + 1/3 \u00d7 0 + 1/3 \u00d7 1/2)\n= (1/3)/(1/3 \u00d7 1/6) = (1/3)/(3/6) = (1/3)/2 = 2/3\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe area of a square field 3136 sq m, if the length of cost of drawing barbed wire 3 m around the field at the rate of Rs.1.50 per meter. Two gates of 1 m width each are to be left for entrance. What is the total cost?\n\n### Options:\nA. Rs.500\nB. Rs.250\nC. Rs.896\nD. Rs.789\nE. Rs.999\n\n### Answer:\nExplanation:\na^2 = 3136 => a = 56\n56 * 4 * 3 = 672 \u2013 6 = 666 * 1.5 =Rs. 999\nAnswer : E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe radius of a cone is 14 m, slant height is 20 m. Find the curved surface area?\n\n### Options:\nA. 770\nB. 550\nC. 110\nD. 880\nE. 330\n\n### Answer:\nCone curved surface area = \u03c0rl\n22/7 \u00d7 14 \u00d7 120 = 44 \u00d7 20 = 880 m(power2)\nAnswer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich of the following leads to the correct mathematical solution for the number of ways that the letters of the word TIE could be arranged to create a three-letter code?\n\n### Options:\nA. 3!\nB. 3! \u2212 (3! + 2!)\nC. 3! \u2212 (2!)\nD. 3!/(3! + 2!)\nE. 3!/(3! \u00d7 2!)\n\n### Answer:\nTIE - three letters can be arranged in 3! ways\nsince 'there is no repetition'\n3!\nAns. A) 3!\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 8 < x < 9, and x^2 = (10 \u2013 y)(10 + y), which of the following is a possible value for y?\n\n### Options:\nA. \u20137\nB. \u20136\nC. 3\nD. 4\nE. 5\n\n### Answer:\nGiven : 8 64 Y^2 = 25 satisfies the above equation.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo persons A and B can complete a piece of work in 30 days and 45 days respectively. If they work together, what part of the work will be completed in 4 days?\n\n### Options:\nA. 2/5\nB. 1/6\nC. 1/4\nD. 1/9\nE. 2/9\n\n### Answer:\nA's one day's work = 1/30\nB's one day's work = 1/45\n(A + B)'s one day's work = 1/30 + 1/45 = 1/18\nThe part of the work completed in 4 days = 4 (1/18) = 2/9.\nANSWER E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA 300 m long train crosses a platform in 42 sec while it crosses a signal pole in 18 sec. What is the length of the platform?\n\n### Options:\nA. 286 m\nB. 350 m\nC. 277 m\nD. 400 m\nE. 267 m\n\n### Answer:\nSpeed = 300/18 = 50/3 m/sec.\nLet the length of the platform be x meters.\nThen, (x + 300)/42 = 50/3\nx = 400 m.\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA, B and C can do a piece of work in 24, 30 and 40 days respectively. They start the work together but C leaves 4 days before the completion of the work. In how many days is the work done?\n\n### Options:\nA. 22 days\nB. 77 days\nC. 88 days\nD. 11 days\nE. 18 days\n\n### Answer:\nx/24 + x/30 + x/40 = 1\nx = 11 days\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the mean proportional between 64 & 81?\n\n### Options:\nA. A)59\nB. B)61\nC. C)63\nD. D)72\nE. E)67\n\n### Answer:\nFormula = \u221aa\u00d7b\nA = 64 and B = 81\n\u221a64\u00d781 = 8 \u00d7 9 = 72\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nLet a,b,c and d be the result of rounding off 7382.196 to the nearest thousand, hundred, ten and one, respectively. Which of the following statements is true?\n\n### Options:\nA. d", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf x dollars is invested at 10 percent for one year and y dollars is invested at 8 percent for one year, the annual income from the 10 percent investment will exceed the annual income from the 8 percent investment by $48. If $1500 is the total amount invested, how much is invested at 8 percent?\n\n### Options:\nA. a. $280\nB. b. $566.67\nC. c. $892\nD. d. $1108\nE. e. $1200\n\n### Answer:\n2 equations with 2 unknowns\n10x / 100 - 8y / 100 = 48\nand\nx + y = 1500\nSolving these 2 equations, x = 933.33 and y = 566.67\nAnswer B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nCheese, bologna, and peanut butter sandwiches were made for a picnic in a ratio of 5 to 7 to 8. If a total of 360 sandwiches were made, how many Cheese sandwiches\nwere made?\n\n### Options:\nA. 15\nB. 30\nC. 90\nD. 42\nE. 48\n\n### Answer:\nFor deciding such task we should calculate all parts 5 + 7 + 8 = 20 parts\nand we should calculate how many sandwiches holds 1 part:\n360 / 20 = 18 sandwiches in one part\nFor cheese we have 5 parts so:\n5 * 18 = 90\nAnswer is C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA Prototype fuel-efficient car (P-Car) is estimated to get 70% more miles per gallon of gasoline\nthan does a traditional fuel-efficient car (T-Car). However, the P-Car requires a special type\nof gasoline that costs 30% more per gallon than does the gasoline used by a T-Car. If the two\ncars are driven the same distance, what percent less than the money spent on gasoline for the\nT-Car is the money spent on gasoline for the P-Car?\n\n### Options:\nA. 16 2/3%\nB. 23.53 %\nC. 50%\nD. 60%\nE. 66 2/3 %\n\n### Answer:\nAssumption\nMiles/Gallon\nT = 100\nP = 170 ( 70% more)\n$/gallon\nT = 100\nP = 130 (30% more)\nMiles\n100 for both\nCost = (Miles X $/ Gallon)/ M/gallon\nT = 100\nP = 76.47\nHence 100 - 76.47 = 23.53%\nAns B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain factory produces buttons and buckles at a uniform weight. If the total weight of 2 buttons and 2 buckles is one third of 11 buckles and 3 buttons, then the weight of 3 buttons and 2 buckles is how many times that of 4 buckles and 6 buttons?\n\n### Options:\nA. 7/15.\nB. 4/9.\nC. 6/11.\nD. 1/2.\nE. 8/15.\n\n### Answer:\n2buttons + 2buckles = 1/3(11buckles + 3buttons)\n6buttons + 6buckles = 11buckles + 3buttons\n3buttons = 5buckles\nWeight of 3buttons and 2buckles = 5buckles + 2buckles = 7buckles\nWeight of 6buttons and 5buckles = 10buckles + 4buckles = 14buckles\n(3buttons and 2buckles) = x * (6buttons and 5buckles)\n7 = x*14\nx = 7/14=1/2\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a group of 25 factory workers, 18 have brown eyes. Six of the women do not have brown eyes. How many of the 11 men have brown eyes.\n\n### Options:\nA. 10\nB. 9\nC. 8\nD. 7\nE. 4\n\n### Answer:\nTotal number of worker (M+W): 25\nNo. of men (M): 11 (Inferred fromHow many of the 11 men)\nNo. of women (W): 14\nTotal no. of workers who have brown eyes (B): 18\nNo. of women who do not have brown eyes: 6\nTherefore, no. of women who have brown eyes: W - 6 = 14 - 6 = 8\nRemaining 10 are men. (B - 8= 18 - 8= 10)\nSo 10 out of 11 men have brown eyes.\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA password of a computer used three digits where they are from 0 and 9. What is the probability that the password solely consists of prime numbers and zero?\n\n### Options:\nA. 1/32\nB. 1/16\nC. 1/8\nD. 2/5\nE. 1/2\n\n### Answer:\nWe have three digits can be used for password -0,2,3,5,7.\nAssuming that the numbers can be repeated any number of times in the password, probability of selecting any one of them is 5/10 (out of 10 digits from 0-9)\nSo, 5/10 * 5/10 * 5/10 =1/8 (C)\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 4a = 5b and ab \u22600, what is the ratio of a/5 to b/4?\n\n### Options:\nA. 125/64\nB. 25/16\nC. 1\nD. 4/5\nE. 64/125\n\n### Answer:\nA nice fast approach is the first find a pair of numbers that satisfy the given equation: 4a = 5b\nHere's one pair: a =5 and b =4\nWhat is the ratio of a/5 to b/4?\nIn other words, what is the value of (a/5)/(b/4)?\nPlug in values to get: (a/5)/(b/4) = (5/5)/(4/4)\n= 1/1\n= 1\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how many ways can 22 books on English and 20 books on Hindi be placed in a row on a shelf so that two books on Hindi may not be together?\n\n### Options:\nA. 4586\nB. 5896\nC. 2415\nD. 1771\nE. 1881\n\n### Answer:\nIn order that two books on Hindi are never together, we must place all these books as under:\nH E H E H E H\u2026.. H E H\nWhere H denotes the position of Hindi book and E that of English book.\nSince there are 22 books on English, the number of places marked E are 23.\nNow, 20 places out of 23 can be chosen in 23C20 = 23C3 = 23*22*21\n3*2*1\n= 1771 ways.\nHence the number of ways = 1771 ways\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe banker's discount on Rs. 1600 at 15% per annum is the same as true discount on Rs. 1680 for the same time and at the same rate. The time is?\n\n### Options:\nA. 4 months\nB. 6 months\nC. 8 months\nD. 9 months\nE. 1 months\n\n### Answer:\nS.I. on Rs. 1600 = T.D. on Rs. 1680.\nRs. 1600 is the P.W. of Rs. 1680, i.e., Rs. 80 is on Rs. 1600 at 15%.\nTime =(100 x 80/1600 x 15)year\n=1/3\tyear = 4 months.\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAt Jefferson Elementary School, the number of teachers and students (kindergarten through sixth grade) totals 510. The ratio of students to teachers is 16 to 1. Kindergarten students make up 1/8 of the student population and fifth and sixth graders account for 1/3 of the remainder. Students in first and second grades account for 1/4 of all the students. If there are an equal number of students in the third and fourth grades, then the number of students in third grade is how many greater or fewer than the number of students in kindergarten?\n\n### Options:\nA. 8 greater\nB. 17 fewer\nC. 28 fewer\nD. 36 fewer\nE. 44 fewer\n\n### Answer:\nSoln>> from the given ratio of 16:1 u can derive that ter are 480 students\nKG= 1/8* 480 =60\n5th and 6th graders = 1/3 * 384= 128 (1/3 of remainder)\n1st and 2nd grade = 1/4 * 480 =120 ( 1/4 of all students)\nequal number of students in 3rd and 4th => 480 - 344= 136 and 136/2=68 each since equal number\n(344 is the sum of remaining students)\nthus 60-68 =-8>>> therfore answer is 8 greater\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nInteger x is equal to the product of all even numbers from 2 to 60, inclusive. If y is the smallest prime number that is also a factor of x-1, then which of the following expressions must be true?\n\n### Options:\nA. 030\n\n### Answer:\nx = the product of all even numbers from 2 to n, where n is any even integer value from 2 to 60 including.\nIf x = 2, x - 1 = 2! -1\nIf x = 2x4, x - 1 = 2! (2^2) - 1\nIf x = 2x4x6, x - 1 = 3! (2^3) - 1\nIf x = 2x4x6x8, x - 1 = 4! (2^4) - 1\n.\n.\n.\n.\nIf x = 2x4x6x.......x60, x - 1 = 30! (2^30) - 1\nLets find y, a smallest prime factor of (x-1):\nIf y were 2, [(30!) (2^30) -(1)] would be divisible by 2 however thats not the case.\nIf y were 3, [(30!) (2^30) -(1)] would be divisible by 3 however thats not the case.\nIf y were 5, [(30!) (2^30) -(1)] would be divisible by 5 however thats not the case.\n.\n.\n.\n.\n.\nIf y were 29, [(30!) (2^30) -(1)] would be divisible by 29 however thats not the case.\nIf none of the primes under 31 is a factor of (x-1), (x-1) must have a prime factore above 30.\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA WNBA player just signed a new contract in which she will earn a 5% increase in base pay from last year to this year. Last year, she did not have a performance bonus; but this year, she will have the opportunity to earn up to a $40,000 performance bonus. If she earns the full performance bonus, her new effective salary will be a 7% raise over last year. What will her new salary be if she earns the full performance bonus?\n\n### Options:\nA. 2,120,000\nB. 2,140,000\nC. 2,180,000\nD. 2,240,000\nE. 2,260,000\n\n### Answer:\nlet x = last year's salary\nthe new base pay + 40,000 = the new effective pay\n(1+.05)*x + 40,000 = (1+.07)*x\n1.05x + 40,000 = 1.07x\n40,000 = .02x\n2,000,000 = x\nthus the new salary = (1+.07)*2,000,000 = 2,140,000\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf we multiply the digits of a number until we get a single digit, then which is the only two digit number which require multiplication of digits more than 3 times?\n\n### Options:\nA. 77\nB. 67\nC. 87\nD. 97\nE. 57\n\n### Answer:\n77 =7*7 =49\n49 =4*9 =36\n36 =3*6 =18\n18 =1*8 =8\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nCream costs twice as much as skim milk. A certain brand of milk is 1/5 cream and 4/5 skim milk. What fraction of the cost of this brand is due to the cream?\n\n### Options:\nA. 1/3\nB. 2/3\nC. 1/4\nD. 3/4\nE. 2/5\n\n### Answer:\nLet x be the cost of the skim milk in the mixture.\nThe cost of the cream is (1/4)*x*2 = x/2.\nThe total cost is x+x/2 = 3x/2 and the fraction due to the cream is (x/2) / (3x/2) = 1/3\nThe answer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSet S consists of all prime numbers less than 10. If two numbers are chosen from et S at random, what is the probability that the product of these numbers will be greater than the product of the numbers which were not chosen?\n\n### Options:\nA. 1/3\nB. 2/3\nC. 1/2\nD. 7/10\nE. 4/5\n\n### Answer:\nPrime integers below 10: 2, 3, 5, 7\nTotal outcomes: Number of ways you can choose 2 from 4 = 4C2=6pairs4C2=6pairs\nNo. of ways for Event: Pairs that will have products greater than product of pairs not selected i.e. (3,5), (3,7), (5,7) =3pairs=3pairs\nProbability = number of ways/Total outcomes =3/6=1/2=3/6=1/2\nHence choice(C) is correct.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRahul's mother is the only daughter of Monika's father. How is Monika's husband related to Rahul ?\n\n### Options:\nA. Uncle\nB. Father\nC. Grandfather\nD. Brother\nE. SISTER\n\n### Answer:\nExplanation:\nClearly, the only daughter or Monika's father is Monika herself\nSo, Rahul's mother is Monika\nThus, Monika's husband is the father of Rahul.\nAnswer: B) Father\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf money is invested at r percent interest, compounded annually, the amount of the investment will double in approximately 54/r years. If Joe's parents invested $5,000 in a long-term bond that pays 6 percent interest, compounded annually, what will be the approximate total amount of the investment 18 years later, when Joe is ready for college?\n\n### Options:\nA. $20000\nB. $15000\nC. $12000\nD. $10000\nE. $9000\n\n### Answer:\nSince investment doubles in 54/r years, then for r=6 it'll double in 54/6=~9 years (we are not asked about the exact amount so such an approximation will do). Thus after 18 years investment will become $5,000*2=$10,000 .\nAnswer: D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the sum of the prime factors of 121 and the prime factors of 7434\n\n### Options:\nA. 27\nB. 67\nC. 57\nD. 37\nE. 47\n\n### Answer:\nThe prime factors of 7434are 3*3*2*7\nThe prime factors of 121 are 11*11\n3+3+2+7+11+11 = 37. D is the correct answer\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA 270 m long train running at the speed of 120 km/hr crosses another train running in opposite direction at the speed of 80 km/hr in 9 sec. What is the length of the other train?\n\n### Options:\nA. 230 m\nB. 240 m\nC. 260 m\nD. 320 m\nE. 520 m\n\n### Answer:\nRelative speed = 120 + 80 = 200 km/hr.\n= 200 * 5/18 = 500/9 m/sec.\nLet the length of the other train be x m.\nThen, (x + 270)/9 = 500/9 => x = 230.\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA mixture of 70 litres of milk and water contains 10% water. How many litres of water should be added to the mixture so that the mixture contains 12 1/2% water?\n\n### Options:\nA. 2 litres\nB. 3 litres\nC. 5 litres\nD. 7 litres\nE. 8 litres\n\n### Answer:\nQuantity of milk in the mixture = 90/100 (70) = 63 litres.\nAfter adding water, milk would form 87 1/2% of the mixture.\nHence, if quantity of mixture after adding x liters of water,\n(87 1/2) / 100 x = 63 => x = 72\nHence 72 - 70 = 2 litres of water must be added.\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train 360 m long is running at a speed of 60 km/hr. In what time will it pass a bridge 140 m long?\n\n### Options:\nA. 40 sec\nB. 30 sec\nC. 26 sec\nD. 27 sec\nE. 34 sec\n\n### Answer:\nSpeed = 60 * 5/18 = 50/3 m/sec\nTotal distance covered = 360 + 140 = 500 m\nRequired time = 500 * 3/50\n= 30 sec\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe sale price of an article including the sales tax is Rs. 616. The rate of sales tax is 10%. If the shopkeeper has made a profit of 25%, then the cost price of the article is:\n\n### Options:\nA. 500\nB. 277\nC. 222\nD. 448\nE. 111\n\n### Answer:\nExplanation:\n110% of S.P. = 616\nS.P. = (616 * 100)/110 = Rs. 560\nC.P = (100 * 560)/125 = Rs. 448\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThree numbers are in the ratio 3:5:7. The largest number value is 42. Find difference between Smallest & largest number is?\n\n### Options:\nA. 20\nB. 24\nC. 26\nD. 28\nE. 30\n\n### Answer:\n== 3:5:7\nTotal parts = 15\n= The largest number value is 42\n= The largest number is = 7\n= Then 7 parts -----> 42 ( 7 * 6 = 42 )\n= smallest number = 3 & Largest number = 7\n= Difference between smallest number & largest number is = 7 - 3 = 4\n= Then 4 parts -----> 24 (4 * 6 = 24)\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwenty four men can do a work in 35 days. How many men are required to complete the work in 21 days?\n\n### Options:\nA. 22\nB. 40\nC. 277\nD. 26\nE. 12\n\n### Answer:\nWe have M1 D1 = M2 D2\nSo, 24 * 35 = M2 * 21 => M2 = 40.\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train 360 m long is running at a speed of 72 km/hr. In what time will it pass a bridge 140 m long?\n\n### Options:\nA. 40 sec\nB. 29 sec\nC. 25 sec\nD. 27 sec\nE. 34 sec\n\n### Answer:\nSpeed = 72 * 5/18 = 20 m/sec\nTotal distance covered = 360 + 140 = 500 m\nRequired time = 500 * 1/20\n= 25 sec\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nKiran started a business investing Rs. 20,000. After 4 months, Sanket joined with a capital of Rs. 12000. At the end of the year, they earn a profit of Rs. 14,000. Find what will be the share of Sanket in the profit?\n\n### Options:\nA. Rs. 4000\nB. Rs. 4007\nC. Rs. 4001\nD. Rs. 4002\nE. Rs. 4047\n\n### Answer:\nExplanation:\nKiran : Sanket = (20000 * 12) : (12000 * 8) = 5 : 2\nSanket's share = Rs. 14,000 * (2/7) = Rs. 4000\nANSWER: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe surface area of a sphere is same as the curved surface area of a right circular cylinder whose height and diameter are 6 cm each. The radius of the sphere is\n\n### Options:\nA. 3 cm\nB. 4 cm\nC. 6 cm\nD. 8 cm\nE. None\n\n### Answer:\nSolution\n4\u00ce R2\t= 2\u00ce 3x6\n\u00e2\u2021\u2019 R2 = (3x6/2)\n\u00e2\u2021\u2019 9\n\u00e2\u2021\u2019 R = 3 cm.\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAt a certain conference, 150 students spoke one or more of the following languages: Spanish, English, and French. If 51 students spoke Spanish, 90 spoke English, 65 spoke French, and 32 spoke only 2 languages, how many students spoke three different languages?\n\n### Options:\nA. 7\nB. 9\nC. 12\nD. 15\nE. 18\n\n### Answer:\n150=51+90+65-32-2x\nx=12\nC. 12\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow much time will a train of length 200 m moving at a speed of 72 kmph take to cross another train of length 300 m, moving at 36 kmph in the same direction?\n\n### Options:\nA. 50 sec\nB. 25 sec\nC. 40 sec\nD. 65 sec\nE. 60 sec\n\n### Answer:\nExplanation:\nThe distance to be covered = Sum of their lengths = 200 + 300 = 500 m.\nRelative speed = 72 -36 = 36 kmph = 36 * 5/18 = 10 mps.\nTime required = d/s = 500/10 = 50 sec.\nANSWER IS A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAn bus covers a certain distance at a speed of 250 kmph in 5 hours. To cover the samedistance in 1hr, it must travel at a speed of?\n\n### Options:\nA. 1520 km/hr\nB. 1250 km/hr\nC. 1256 km/hr\nD. 1231 km/hr\nE. 1220 km/hr\n\n### Answer:\nDistance = (250 x 5) = 1250 km.\nRequired speed = 1250km/hr.\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a motorist had driven 1 hour longer on a certain day and at an average rate of 4 miles per hour faster, he would have covered 70 more miles than he actually did. How many more miles would he have covered than he actually did if he had driven 2 hours longer and at an average rate of 10 miles per hour faster on that day?\n\n### Options:\nA. 100\nB. 120\nC. 140\nD. 150\nE. 160\n\n### Answer:\nCase 1:\nlet rate = R, Time = T, and Distance =D\nso D=RT\nCase 2:\n(D+70)=(R+4)(T+1)\nCase 3:\n(D+X)=(R+10)(T+2)\nX=140\nAns C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe ratio 6 : 5 expressed as a percent equals\n\n### Options:\nA. 12.5%\nB. 40%\nC. 120%\nD. 125%\nE. None\n\n### Answer:\nSolution\n6 : 5\t= 6/ 5\n= (6/5 x 100)%.\n= 120 %.\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nif Juan takes 12 seconds to run y yards, how many seconds will it take him to run x yards at the same rate?\n\n### Options:\nA. 11x/y\nB. 11y/x\nC. x/11y\nD. 12x/y\nE. xy/11\n\n### Answer:\nAnswer is D\nThe rate of running hards: 12 minutes per y hards.\nThus the time for running x hards = x hards * 12 minutes/y hards = 12x/y\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n8k8\n+ k88\n--------\n1,6r6\nIf k and r represent non-zero digits within the integers above, what is r?\n\n### Options:\nA. 6\nB. 7\nC. 8\nD. 9\nE. 17\n\n### Answer:\n8k8\nk88\n--------\n16r6\nTrial and error or just plug-in method might be the shortest way to solve this problem. Though you can narrow down the possible values of k to just two: 7 and 8 --> 8**+7**=16** or 8**+8**=16** (k can not be less than 7 or 9, as the result won't be 16**). After that it's easy to get that k=7 and r=6.\nAnswer: A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nCompany C produces toy trucks at a cost of $5.00 each for the first 100 trucks and $3.50 for each additional truck. If 500 toy trucks were produced by Company C and sold for $20.00 each, what was Company C\u2019s gross profit?\n\n### Options:\nA. $7,250\nB. $8,500\nC. $8,100\nD. $8,250\nE. $8,600\n\n### Answer:\nCost of 500 trucks: (100 * 5 ) + (400 * 3.5) = 500 + 1400 =$ 1900\nRevenue : 500 * 20 = $10000\nProfit: 10000 - 1900 = $ 8100\nOption C is correct\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAt present, the ratio between the ages of Arun and Deepak is 4:5. After 5 years, Arun's age will be 25 years. What is the age of Deepak at present?\n\n### Options:\nA. 18\nB. 20\nC. 25\nD. 23\nE. 22\n\n### Answer:\nLet the present ages of Arun and Deepak be 4x and 3x years respectively.\nThen, 4x + 5 = 25 => x = 5\nDeepak's age = 5x = 25 years.\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf n = 3p, where p is a prime number greater than 2, how many different positiveevendivisors does n have, including n ?\n\n### Options:\nA. Two\nB. Three\nC. Four\nD. Six\nE. Eight\n\n### Answer:\nThis is an interesting question because we are immediately given the option to insert any prime number we wish for p. Since this is a problem-solving question, and there can only be one correct answer, we can select any value for p, as long as it is a prime number greater than 2. We always want to work with small numbers, so we should select 3 for p. Thus, we have:\nn = 4 x 3\nn = 12\nNext we have to determine all the factors, or divisors, of P. Remember the term factor is synonymous with the term divisor.\n1, 12, 6, 2, 4, 3\nFrom this we see that we have 4 even divisors: 12, 6, 2, and 4.\nIf you are concerned that trying just one value of p might not substantiate the answer, try another value for p. Let\u2019s say p = 5, so\nn = 4 x 5\nn = 20\nThe divisors of 20 are: 1, 20, 2, 10, 4, 5. Of these, 4 are even: 20, 2, 10 and 4. As we can see, again we have 4 even divisors.\nNo matter what the value of p, as long as it is a prime number greater than 2, n will always have 4 even divisors.\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the ones digit of 73^353\n\n### Options:\nA. 3\nB. 5\nC. 6\nD. 7\nE. 9\n\n### Answer:\nThe units digit of 73^353 will be the same as the units digit of 3^353.\n3^1=3 --> the units digit is 3;\n3^2=9 --> the units digit is 9;\n3^3=27 --> the units digit is 7;\n3^4=81 --> the units digit is 1;\n3^5=243 --> the units digit is 3 AGAIN;\n...\nSo, as you can see the units digit repeats in blocks of 4: {3, 9, 7, 1}, {3, 9, 7, 1}, ... Now, since 353=352+1=(multiple of 4)+1, then the units digit of 3^353 will be the first number in the pattern thus 3.\nAnswer:A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train covers a distance of 54 km in 15 min. If it takes 8 sec to pass a telegraph post, then the length of the train is?\n\n### Options:\nA. 470\nB. 480\nC. 490\nD. 500\nE. 510\n\n### Answer:\nSpeed = (54/15 * 60) km/hr = (216 * 5/18) m/sec = 60 m/sec.\nLength of the train = 60 * 8 = 480 m.\nAnswer: Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFor all positive integers m and v, the expression m \u0398 v represents the remainder when m is divided by v. What is the value of (( 88 \u0398 33 ) \u0398 17 ) - ( 90 \u0398 (33 \u0398 17)) ?\n\n### Options:\nA. 0\nB. 1\nC. 2\nD. 3\nE. 4\n\n### Answer:\n(( 88 \u0398 33 ) \u0398 17 )\nThe remainder of 88 divided by 33 is 22;\nThe remainder of 22 divided by 17 is 5;\n( 98 \u0398 (33 \u0398 17))\nThe remainder of 33 divided by 17 is 16;\nThe remainder of 98 divided by 16 is 2.\n5 - 2 = 3.\nAnswer: D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 854 in 4 years. The sum is:\n\n### Options:\nA. Rs. 650\nB. Rs. 690\nC. Rs. 698\nD. Rs. 700\nE. Rs. 740\n\n### Answer:\nS.I. for 1 year = Rs. (854 - 815) = Rs. 39.\nS.I. for 3 years = Rs.(39 x 3) = Rs. 117.\nPrincipal = Rs. (815 - 117) = Rs. 698.\nAnswer: Option C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAt a tanning salon, customers are charged $10 for their first visit in a calendar month and $4 for each visit after that in the same calendar month. In the last calendar month, 100 customers visited the salon, of which 30 made a second visit, and 10 made a third visit. All other customers made only one visit. If those visits were the only source of revenue for the salon, what was the revenue for the last calendar month at the salon?\n\n### Options:\nA. $1220\nB. $1160\nC. $1300\nD. $1340\nE. $1880\n\n### Answer:\nI get B. This question seems too straightforward for 600+. Am I missing something?\n100 first-time visits --> 100(10) = $1000\n30 + 10 = 40 subsequent visits --> 40(4) = $160\nTotal revenue: 1000+ 160 = $1160\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA is thrice as good as B in work. A is able to finish a job in 60 days less than B. They can finish the work in - days if they work together.\n\n### Options:\nA. 18 days\nB. 22 \u00bd days\nC. 24 days\nD. 26 days\nE. 23 days\n\n### Answer:\nIf A completes a work in 1 day, B completes the same work in 3 days\nHence, if the difference is 2 days, B can complete the work in 3 days\n=> if the difference is 60 days, B can complete the work in 90 days\n=> Amount of work B can do in 1 day= 1/90\nAmount of work A can do in 1 day = 3 \u00d7 (1/90) = 1/30\nAmount of work A and B can together do in 1 day = 1/90 + 1/30 = 4/90 = 2/45\n=> A and B together can do the work in 45/2 days = 22 \u00bd days\nAnswer : B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe area of a sector of a circle of radius 5 cm formed by an arc of length 3.5 cm is?\n\n### Options:\nA. 0.35 cm2\nB. 17.5 cm2\nC. 8.75 cm2\nD. 55 cm2\nE. 50 cm2\n\n### Answer:\nExplanation:\n(5 * 3.5)/2 = 8.75\nANSWER IS C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a rectangular axis system, what is the area of a parallelogram with the coordinates: (4,4), (7,4), (5,9), (8,9) ?\n\n### Options:\nA. 21.\nB. 28.\nC. 5.\nD. 49.\nE. 52.\n\n### Answer:\nDelta x will give us the dimension of one side of the parallelogram = 5-4= 1 unit\nDelta y will give us the dimension of the other side of parallelogram = 9-4=5 unit\nArea of parallelogram = 1*5 = 5\nANSWER IS C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe ratio of the ages of Mini and Minakshi is 4 : 3. The sum of their ages is 21 years. The ratio of their ages after 8 years will be\n\n### Options:\nA. 2 : 3\nB. 20 : 17\nC. 5 : 4\nD. 3 : 5\nE. 6 : 11\n\n### Answer:\nLet Mini\u2019s age = 4x and Minakshi\u2019s age = 3x\nThen 4x + 3x = 21\nx = 3\nMini\u2019s age = 12 years\nAnd Minakshi\u2019s age = 9 years\nRatio of their ages after 8 years = (12 + 8) : (9 + 8) = 20 : 17\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJill works as a waitress at the local diner where she earns an hourly wage of $4.00 per hour and a standard tip rate of 15% of the cost of the orders she serves. If she worked three 8-hour shifts this week and averaged $40 in orders per hour, how much did Jill earn this week?\n\n### Options:\nA. 280\nB. 300\nC. 240\nD. 350\nE. 400\n\n### Answer:\nJill earns 4 dollars/hour and the hourly tip is (3/20)*40.\nJill thus earns 4*8+8*2*3 per day(or 4(8)+6(8)=10(8)=80).\nJill has worked for 3 days -> 80*3=240.\nThis matches answer choice C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nBy selling a bicycle for Rs. 2,850, a shopkeeper gains 14%. If the profit is reduced to 8%, then the selling price will be:\n\n### Options:\nA. Rs. 2,600\nB. Rs. 2,700\nC. Rs. 2,800\nD. Rs. 3000\nE. NOne\n\n### Answer:\nSolution: Let Cost Price was X.\nX + 14% of X = 2850\nX + 14X/100 = 2850\nX + 0.14X = 2850\n1.14X = 2850\nX = 2500.\nSo, Cost Price = Rs. 2500.\nNow, Selling Price When profit remains at 8%,\n= 2500 + 8% of 2500\n= Rs. 2700.\nShort-Cut\nCP of bicycle = 100/114*2850 = Rs. 2500;\nSP for a profit of 8% = 108/100*2500 = Rs. 2700.\nAnswer: Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain sum amounts to Rs.7350 in 2 years and to Rs.8575 in 3 years.find the sum and rate percent\n\n### Options:\nA. 3488\nB. 7789\nC. 5400\nD. 2887\nE. 1881\n\n### Answer:\nExplanation:\nInterest for 1 year is the same whether it's simple interest or the compound interest.\nNow interest of third year = 8575 - 7350 = 1225; means principal for this interest is 7350 if comound interest is takenIf 7350 is the principal interest = 1225\nif 100 is the principal interest =(1225/7350) * 100 = 50/3 %\nWhen a thing increases for two successive times the overall increase on initial amount = a + b + (a * b)/100\nTherefore overall interest for two years = 50/3 + 50/3 + [(50/3)*(50/3)]/100 = 325/9 %\nTherefore amount after 2 years = 100 + 325/9 = 1225/9\nIf 1225/9 is the amount principal =100\nif 7350 is the amount principal =(900/1225)*7350 =5400\nSo sum = 5400; Rate = 50/3 %\nAnswer: C) 5400\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo trains are running in opposite directions in the same speed. The length of each train is 120 meter. If they cross each other in 4 seconds, the speed of each train (in km/hr) is\n\n### Options:\nA. 42\nB. 36\nC. 108\nD. 120\nE. 124\n\n### Answer:\nExplanation:\nDistance covered = 120+120 = 240 m\nTime = 4 s\nLet the speed of each train = v. Then relative speed = v+v = 2v\n2v = distance/time = 240/4 = 60 m/s\nSpeed of each train = v = 60/2 = 30 m/s\n= 30\u00d736/10 km/hr = 108 km/hr\nAnswer: Option C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are 100 students in 3 sections A, B and C of a class. The average marks of all the three sections was 84. The average of B and C was 87.5 and the average marks of students in A section was\n\n### Options:\nA. 20\nB. 37\nC. 28\nD. 11\nE. 12\n\n### Answer:\nExplanation:\nNumbers of students in section A = x\n\u00e2\u02c6\u00b4 Numbers of students in section B and C = (100 \u00e2\u20ac\u201c x)\n\u00e2\u02c6\u00b4 x 70 + (100 \u00e2\u20ac\u201c x) 87.5 = 84 100\n=> 70x + 87.5 100 \u00e2\u20ac\u201c 87.5x = 8400\n=> 8750 \u00e2\u20ac\u201c 17.5x = 8400\n=> 17.5x = 8750 \u00e2\u20ac\u201c 8400 => x = 20.\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the square root of p^2 is an integer, which of the following must be true?\nI. p^2 has an odd number of factors\nII. p^2 can be expressed as the product of an even number of prime factors\nIII. p has an even number of factors\n\n### Options:\nA. I\nB. II\nC. III\nD. I and II\nE. II and III\n\n### Answer:\nI. p^2 is a perfect square and a perfect square has pairs of factors and '1' with it. The total number of factors is odd\nII. If p = 3 then p^2 = 9. The prime factors will always remain even as the p is an integer and the pairs have to come out of square root to make p an integer.\nIII. This is not true always. Let us say p = 4, it has three factors: 1, 2 and 4. Hence it will not hold true always.\nHence D is the answer.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSimplify : 5793405 x 9999\n\n### Options:\nA. 57928256595\nB. 59278256595\nC. 57928262559\nD. 59722422582\nE. None of them\n\n### Answer:\n5793405x9999=5793405(10000-1)=57934050000-5793405=57928256595.\nAnswer is A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nVillage P\u2019s population is 800 greater than Village Q's population. If Village Q\u2019s population were reduced by 700 people, then Village P\u2019s population would be 7 times as large as Village Q's population. What is Village Q's current population?\n\n### Options:\nA. 910\nB. 920\nC. 930\nD. 940\nE. 950\n\n### Answer:\nP = Q+800.\nP=7(Q-700).\n7(Q-700)=Q+800.\n6Q=5700.\nQ=950.\nThe answer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the lowest positive integer that is divisible by 8 through 11, inclusive?\n\n### Options:\nA. 999\nB. 7811\nC. 6555\nD. 9200\nE. 7920\n\n### Answer:\nThe integer should be divisible by: 8, 9, 10 and 11. The least common multiple of these integers is LCM=8*9*10*11=7920\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA fair red coin with sides marked heads and tails is to be tossed eight times. What is the probability that the coin will land tails side up more than five times?\n\n### Options:\nA. A)37/256\nB. B)56/256\nC. C)65/256\nD. D)70/256\nE. E)81/256\n\n### Answer:\nLanding on tails more than 5 times means tails has to hit 6, 7 or 8 times.\n8!/6!2! = 7*4 = 28\n8!/7!1! = 8\n8!/8! = 1\n28 + 8 + 1 = 37/256\nans:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAt Company X, senior sales representatives visit the home office once every 18 days, and junior sales representatives visit the home office once every 12 days. The number of visits that a junior sales representative makes in a 2-year period is approximately what percent greater than the number of visits that a senior representative makes in the same period?\n\n### Options:\nA. 10%\nB. 25%\nC. 33%\nD. 50%\nE. 67%\n\n### Answer:\nEach 36-day period, senior representatives visit the home office 2 times while junior representatives visit 3 times, thus 50% more.\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA student committee on academic integrity has 72 ways to select a president and vice president from a group of candidates. The same person cannot be both president and vice president. How many candidates are there?\n\n### Options:\nA. 7\nB. 8\nC. 9\nD. 10\nE. 11\n\n### Answer:\nxC1 * (x-1)C1=72\nx^2 -x -72 =0\n(X-9) (X+8) = 0\nX= 9 , -8\n-8 can't possible.\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind value of X: (422+404)^2\u2212(4\u00d7422\u00d7404)=X.\n\n### Options:\nA. 234\nB. 267\nC. 324\nD. 356\nE. 577\n\n### Answer:\nGiven Equation is in the form (a+b)2\u22124ab where a=422 and b=404\nHence answer\n=(a+b)2\u22124ab=(a\u2212b)2=(422\u2212404)2=182=324\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe radius of a circular wheel is 1.75 m, how many revolutions will it make in traveling 1 km?\n\n### Options:\nA. 1000\nB. 817\nC. 278\nD. 268\nE. 280\n\n### Answer:\n2 * 22/7 * 1.75 * x\n= 11000\nx = 1000\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA set consist of 2k-1 element. What is the number of subsets of this set which contain at most k-1 elements?\n\n### Options:\nA. 2^(2k-2)\nB. 2^(2k) - 2\nC. 2^(2k) -1\nD. 2^(2k)\nE. 2^(2k-1)\n\n### Answer:\nI used k=3, so then we have\n5!/2!3! + 5!/4!1! + 5!/0!5!\n10 + 5 + 1 = 16\nSo our target is 16\nNow replace in answer choices\nA gives us 2^4 = 16\nHence A is the correct option\nRead carefully it says at most so keep in mind that picking a small number such as 3 will help you save time since you have to list fewer outcomes\nAvoid 2 since you will get 1 arrangement (k-1) and may be risky since 1 is a number with certain unique properties\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA manufacturer of a certain type of screw rejects any screw whose length is less than 2.47 centimeters or greater than 2.5 + 0.03 centimeters. If k represents the length of a screw, in centimeters, which of the following inequalities specifies all the lengths of screws that are acceptable?\n\n### Options:\nA. |k + 0.03| > 2.5\nB. |k \u2014 0.03| <= 2.5\nC. |k \u2014 2.5| > 0.03\nD. |k \u2014 2.5| >= 0.06\nE. 2|k \u2014 2.5| <= 0.06\n\n### Answer:\nSo, let's go through this step by step:\nrejects any screw whose length is less than 2.47 centimeters or greater than 2.5 + 0.03 centimeters.\nIn other words, any screw that is less than: 2.47 or greater than 2.50 + 0.03 =2.53will be rejected.\nIf k represents the length of a screw\nIn other words, K is an acceptable screw that must fall within the acceptable range of 2.47 to 2.53, So:\n2.47 \u2264 K \u2264 2.53\nYou can rule out answers with < or > as opposed to \u2264 or \u2265 because the length cannot be LESS than 2.47 or GREATER than 2.53. In other words, 2.47 and 2.53 are acceptable lengths.\nLet's look at (E):\n2|k \u2014 2.5| <= 0.06 or |k \u2014 2.5| <= 0.03\nFor the positive case: k - 2.5 \u2264 0.03 ===>k \u2264 2.53\nFor the negative case: -(k - 2.5) \u2264 0.03 ===> -k +2.5 \u2264 0.03 ===> - k \u2264 -2.47 ===>k \u2265 2.47\n2.47 \u2264\u00a0k \u2264 2.53\n(E)\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 1535/1038 = a+1/[b+1 /{c+(d+1/e)}]. Find a*b*c*d*e?\n\n### Options:\nA. 165/2\nB. 175/2\nC. 178/3\nD. 187 by 2\nE. 197/2\n\n### Answer:\nby expanding 1535/1038 make form like a+1/[b+1/{c+(d+ 1/e)}\n=1+(497/1038) now a=1\n=1+{1/(1038/497)}\n=1+{1/(2+42/497)}\n=1+{1/(2+1/(497/42)} now b= 2 similarly expand\nc=11 d= 1 e=34/8\nfinally a*b*b*c*d*e\n1*2*11*1*34/8\n187/2\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA and B invests Rs.10000 each, A investing for 8 months and B investing for all the 12 months in the year. If the total profit at the end of the year is Rs.45000, find their shares?\n\n### Options:\nA. s.17000, Rs.2500\nB. s.18000, Rs.35059\nC. s.16000, Rs.27000\nD. s.14000, Rs.25000\nE. s.18000, Rs.27000\n\n### Answer:\nThe ratio of their profits A:B\n= 8:12 = 2:3\nShare of A in the total profit\n= 2/5 * 45000\n= Rs.18000 Share of A in the total profit = 3/5 * 45000\n= Rs.27000\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhen E is divided by 5, the remainder is 3. When y is divided by 5, the remainder is 4. What is the remainder when E + y is divided by 5?\n\n### Options:\nA. 0\nB. 1\nC. 2\nD. 3\nE. 4\n\n### Answer:\nIn my view the answer should be C\nE/5 has Remainder=3 -> E = 5 x Q + 3\nY/5 has a Remainder=4 -> Y = 5 x Q + 3\nCombining both\n((5 x Q1 + 3) + (5 x Q2 + 3))/5 =\n5(Q1+Q2)/5 + 7/5 =\nQ1+Q2 + 7/5\n7/5 = 1+ 2/5 => Remainder 2\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nCompound interest of Rs.3000 at 10% per annum for 1 l/2years will be (interest compounded half yearly).\n\n### Options:\nA. Rs.473\nB. Rs.374\nC. Rs.495\nD. Rs.347\nE. None of the above\n\n### Answer:\n10% interest per annum will be 5% interest half yearly for 3 terms( 1 1/2 years)\nSo compound interest=3000[1+(5/100)]^3 - 3000=3000[(21/20)^3 -1]\n=3000(9261-8000)/8000\n=3*1261/8\n=472.8 ~ 473\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nCara took out a charge account at the General Store and agreed to pay 5% simple annual interest. If she charges $54 on her account in January, how much will she owe a year later, assuming she does not make any additional charges or payments?\n\n### Options:\nA. $55.70\nB. $56.20\nC. $56.70\nD. $57.20\nE. $57.70\n\n### Answer:\n1.05*$54=$56.70\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n9, 16, 18, 25, 36,49\n\n### Options:\nA. 9\nB. 16\nC. 18\nD. 25\nE. 36\n\n### Answer:\nEach of the numbers except 18, is perfect square.\nAnswer: Option C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe number 90 can be written as the sum of the squares of 3 different positive integers. What is the sum of these 3 integers?\n\n### Options:\nA. 17\nB. 16\nC. 15\nD. 14\nE. 13\n\n### Answer:\n7^2+5^2+4^2=49+25+16 = 90\n7+5+4 =16\nHence answer is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFrom a salary of an officer, 10% is deducted as house rent, 15% of the rest he spend on children's education and 10% of the balance he spends on clothes. Then, he is left with Rs. 4131. Find his total salary?\n\n### Options:\nA. 6000\nB. 3788\nC. 9009\nD. 6788\nE. 2772\n\n### Answer:\nSuppose his total salary be Rs.x, then\n90% of 85% of 90% of x = 4131\n\\inline \\Rightarrow \\frac{90}{100}\\times \\frac{85}{100}\\times \\frac{90}{100}\\times x=4131\n\\inline \\therefore x=\\frac{4131\\times 100\\times 100\\times 100}{90\\times 85\\times 90}=6000\nHence , the salary of the officer is Rs.6000\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nDuring the second quarter of 1984, a total of 2,976,000 domestic cars were sold. If this was 24% greater than the number sold during the first quarter of 1984, how many were sold during the first quarter ?\n\n### Options:\nA. 714,240\nB. 2,261,760\nC. 2,400,000 cars\nD. 3,690,240\nE. 3,915,790\n\n### Answer:\nLet number of cars sold in 1st quarter = x\nNumber of cars sold in 2nd quarter = 24% greater than the number sold during the first quarter = (1 + 24/100)x = 1.24 x\n1.24 x = 2,976,000\n=> x = 2,400,000\nSo, answer will be C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nCharlie, a painter, has 9 jars of paint: 4 are violet, 2 are yellow, and the rest are brown. Charlie will combine 3 jars of paint into a new container to make a new colour, which he will name according to the following conditions:\n1) C1, if the paint contains 2 jars of brown paint and no violet paint\n2) C2, if the paint contains 3 jars of brown paint.\n3) J1, if the paint contains at least 2 jars of violet paint\n4) J2, if the paint contains exactly 1 jar of violet paint\nWhat is the probability that the new colour will be a shade of J (J1 or J2)?\n\n### Options:\nA. 37/42\nB. 35/42\nC. 37/21\nD. 74/21\nE. 42/37\n\n### Answer:\nthe probability that it would be J1 or J2 is same as 1-()probability that it is C1 or C2\nFor C1-3C2(Brown)*2C1(Yellow)=3*2=6\nFor C2-3C3(all brown)=1\nTotal=9C3=84\n1-7/84=77/84= 37/42\nAnswer : A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a - b = 3 and\na2+b2=29\n, then find the value of ab\n\n### Options:\nA. 7\nB. 8.5\nC. 10\nD. 12\nE. 14\n\n### Answer:\nExplanation:\n2ab=(a2+b2)\u2212(a\u2212b)2\n=> 2ab = 29 - 9 = 20\n=> ab = 10\nOption C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n5, 11, 17, 25, 33, 43, ?\n\n### Options:\nA. 44\nB. 26\nC. 58\nD. 59\nE. 53\n\n### Answer:\nE\n53\nThe sequence is +6, +6, +8, +8, +10, ....\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWinners will be announced the following day at 9 AM Pacific/1 PM Eastern Time.\nIf A, X, Y, and Z are unique nonzero digits in the equation:\nXY\n*YX\n____\nAYZ\nAnd Y > X, the 2-digit number XY = ?\n\n### Options:\nA. 13\nB. 21\nC. 23\nD. 24\nE. 25\n\n### Answer:\nThe reasoning is as follows:-\nB) can't be answer because Yxwill give 3 digit numbermiddle digit is Y\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf w is a positive integer, then 3^w + 3^(w +1) =\n\n### Options:\nA. 4^a\nB. 3^a \u2212 1\nC. 3^(2a) + 1\nD. 3^a*(a \u2212 1)\nE. 4(3^w)\n\n### Answer:\n3^w + 3^(w +1)\n= 3^w + (3^w * 3^1)\n= 3^w (1 + 3)\n= 3^w(4)\nAns. E) 4(3^w)\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe sum of the present ages of a father and his son is 57 years. Six years ago, father's age was four times the age of the son. After 6 years, son's age will be:\n\n### Options:\nA. 17\nB. 18\nC. 19\nD. 20\nE. 21\n\n### Answer:\nLet the present ages of son and father be x and (57 - x) years respectively.\nThen, (57 - x) - 6 = 4(x - 6)\n51 - x = 4x - 24\nx = 15\nThe son's age after 6 years will be 21.\nThe answer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n7^6 + 7^6 + 7^6 + 7^6 =\n\n### Options:\nA. 7^7\nB. 4^6\nC. 4^8\nD. 4^9\nE. 4^12\n\n### Answer:\nHi shakticnb,\nCertain Quant questions on the GMAT are just about 'organizing' the information in a specific way. If you find yourself getting confused by a prompt, think about how you might change the way that the information is presented to you.\nHere, for example, we're asked for....\n7^6 + 7^6 + 7^6 + 7^6 =\nNow, the GMAT doesn't really expect us to calculate this sum (but we could if we had to), but we are expected to find a way to organize this information... If, instead of all of those exponents, we had...\nX + X + X + X =\nWhat would the sum be?\nClearly, it would be 4(X) = 4X.....since we're just combining 'like' terms. Take that same idea with this prompt and you have...\n7^6 + 7^6 + 7^6 + 7^6 =\n7(7^6)\nThis can be re-written as...\n(7^1)(7^6)\n...and now we can use exponent rules; since we're MULTIPLYING 'bases' that are the same, we ADD the exponents...\n(7^1)(7^6) = 7^7\nFinal Answer:\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe H.C.F of two numbers is 17 and their L.C.M is 5134. If one of the numbers is 289, then the other is?\n\n### Options:\nA. 302\nB. 304\nC. 306\nD. 308\nE. 310\n\n### Answer:\nOther number = (17 * 5134)/289\n= 302.\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAyesha\u2019s father was 38 years of age when she was born while her mother was 34 years old when her brother four years younger to her was born. What is the difference between the ages of her parents?\n\n### Options:\nA. 2 years\nB. 4 years\nC. 6 years\nD. 8 years\nE. None\n\n### Answer:\nEXPLANATION\nMother\u2019s age when Ayesha\u2019s brother was born = 34 years.\nFather\u2019s age when Ayesha\u2019s brother was born = (38 + 4) years = 42 years.\nRequired difference = (42 \u2013 34) years = 8 years.\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA car averages 55 mph for the first 4 hours of a trip and averages 70 mph for each additional hour. The average speed for the entire trip was 60 mph. How many hours long is the trip?\n\n### Options:\nA. 6\nB. 8\nC. 11\nD. 12\nE. 14\n\n### Answer:\nIn 4hr journey = 55*4 = 220mph\nLet in the next additional hour journey = 70*x =70x mph\nSo, (220+70x)/(4+x)= 60\n=> 220+70x = 240+60x\n=> 10x = 20\n=> x = 2h\nSo the trip is (4+x)=> 6 hours long\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a certain company, the ratio of the number of managers to the number of non-managers in any department must always be greater than 7 : 37. In the company, what is the maximum number of non-managers in a department that has 11 managers?\n\n### Options:\nA. 56\nB. 57\nC. 58\nD. 59\nE. 60\n\n### Answer:\n11/7 * 37 = 58.1\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOne man traveled a distance of 61 km in 9hrs. He traveled partly on footat 4 km/hr and partly on bicycle ta 9 km/hr. The distance traveled on foot is?\n\n### Options:\nA. 8 km\nB. 12 km\nC. 16 km\nD. 18 km\nE. 20 km\n\n### Answer:\nLet the distance travelled on foot be x km.\nThen, distance travelled on bicycle = (61 -x) km.\nSo, x + (61 -x) = 9\n4 9\n9x + 4(61 -x) = 9 x 36\n5x = 80\nx = 16 km.\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n3 no.'s A, B & C are in the ratio of 12:15:25. If sum of these no.'s is 312, find the ratio between the difference of B & A & the difference of C & B.\n\n### Options:\nA. 2 : 5\nB. 3 : 10\nC. 4 : 5\nD. 4 : 7\nE. 5 : 11\n\n### Answer:\nWe have, a = 12, b = 15, c = 25 and x = 312.\nax_ 12 X 312\na+b+c 12+15+25\n\u2014 72,\nbx _ 15 X 312 B \u2014 \u2014 90 a +b+c 12 + 15+ 25 cx 25 X 312 And, C =\na+b+c 12 + 15+ 25\n...B-A=18 andC-B=60\n- 150\nThus, their ratio = 18 : 60 or 3 : 10\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nGiven that 0 < a < b < c < d, which of the following the largest ?\n\n### Options:\nA. (c+d) / (a+b)\nB. (a+d) / (b+c)\nC. (b+c) / (a+d)\nD. (b+d) / (a+c)\nE. None of these\n\n### Answer:\nExplanation :\nFor the fraction to be largest, denominator should be minimum and numerator should be maximium.\nHere a and b is minimum which is in denominator of option 1. and c and d is maximum which is also in the numerator of option 1.\nHence 1.) (c+d) / (a+b\nAnswer : A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a boat 25 persons were sitting. Their average weight increased one kilogram when One man goes and a new man comes in. The weight of the new man is 70kgs. Find the Weight of the man who is going ?\n\n### Options:\nA. 45\nB. 66\nC. 44\nD. 33\nE. 61\n\n### Answer:\nWeight increased per person is 1 kg. Total increase in weight = 25 kgs Weight of new man is 70 kgs, (Which means his weight is 25 kgs heavier) The weight of the old man was 70 \u2013 25 = 45 kgs\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain college's enrollment at the beginning of 1992 was 20 percent greater than it was at the beginning of 1991, and its enrollment at the beginning of 1993 was 25 percent greater than it was at the beginning of 1992. The college's enrollment at the beginning of 1993 was what percent greater than its enrollment at the beginning of 1991 ?\n\n### Options:\nA. 47.5%\nB. 44%\nC. 50%\nD. 35%\nE. 38%\n\n### Answer:\nSuppose enrollment in 1991 was 100\nThen enrollment in 1992 will be 120\nAnd enrollment in 1993 will be 120*1.25=150\nIncrease in 1993 from 1991 = 150-100= 50\nAnswer : C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo numbers are 30% and 37% are less than a third number .How much percent is the second number less than the first?\n\n### Options:\nA. 10\nB. 15\nC. 20\nD. 30\nE. 35\n\n### Answer:\nI II III\n70 63 100\n70 -------- 7\n100 ------ ? => 10%\nANSWER A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA driver covers a certain distance by car driving at 60 km/hr and returns back to the starting point riding on a scooter at 10 km/hr. What was the average speed for the whole journey?\n\n### Options:\nA. 14.2 km/h\nB. 17.1 km/h\nC. 19.3 km/h\nD. 21.7 km/h\nE. 23.5 km/h\n\n### Answer:\ntime 1 = d / 60\ntime 2 = d / 10\ntotal time = d/60 + d/10 = 7d/60\naverage speed = total distance / total time = 2d / (7d/60) = 17.1 km/h\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFor the positive integers x, x + 2, x + 4, x + 7, and x + 27, the mean is how much greater than the median?\n\n### Options:\nA. 0\nB. 1\nC. 2\nD. 4\nE. 7\n\n### Answer:\nMean = (x + x+2 + x+4 + x+7 + x+27)/5\n=(5x+40)/5\n=x+8\nMedian = x+4\nThus Mean - Median = x+8 - (x+4)\n=4\nAnswer = D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA 180 meter long train crosses a man standing on the platform in 6 sec. What is the speed of the train?\n\n### Options:\nA. 228\nB. 108\nC. 1266\nD. 188\nE. 211\n\n### Answer:\nS = 180/6 * 18/5 = 108 kmph\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain sum becomes four times itself at simple interest in eight years. In how many years does it become ten times itself?\n\n### Options:\nA. 24\nB. 55\nC. 77\nD. 99\nE. 01\n\n### Answer:\nLet the sum be Rs. x, then it becomes Rs. 4x in eight years Rs. 3x is the interest on x for eight years.\nR = (100 * 3x)/(x * 8) = 300/8 %\nIf the sum becomes ten times itself, then interest is 9x.\nThe required time period = (100 * 9x)/(x * 300/8) = (100 * 9x * 8)/(x * 300) = 24 years.Answer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nKamal obtained 81, 68, 82, 69 and 90 marks(out of 100) in English, Mathematics, Physics, Chemistry and Biology. What are his average marks?\n\n### Options:\nA. 65\nB. 69\nC. 72\nD. 75\nE. NOne\n\n### Answer:\nSol.\nAverage\n= 81 + 68 + 82 + 69 + 90 / 5)\n= (390 / 5)\n= 78.\nAnswer E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSolve for x: 2x \u2013 y = (3/4)x + 6.\n\n### Options:\nA. (y + 6)/5\nB. 4(y + 6)/5\nC. (y + 6)\nD. 4(y - 6)/5\nE. 6(y-4)/5\n\n### Answer:\n2x \u2013 y = (3/4)x + 6.\nor, 2x - (3/4)x = y + 6.\nor, (8x -3x)/4 = y + 6.\nor, 5x/4 = y + 6.\nor, 5x = 4(y + 6).\nor, 5x = 4y + 24.\nor, x = (4y + 24)/5.\nTherefore, x = 4(y + 6)/5\ncorrect answer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many integers from 0 to 44, inclusive, have a remainder of 1 when divided by 3 ?\n\n### Options:\nA. 13\nB. 16\nC. 17\nD. 18\nE. 19\n\n### Answer:\nExplanation:\n1 also gives 1 remainder when divided by 3, another number is 4, then 7 and so on.\nHence we have an arithmetic progression: 1, 4, 7, 10,..... 43, which are in the form 3n+1.\nNow we have to find out number of terms.\ntn=a+(n-1)d, where tn is the nth term of an AP, a is the first term and d is the common difference.\nso, 43 = 1+(n-1)3\nor, (n-1)3 = 42\nor, n-1 = 12\nor, n = 13\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the length of the wire required to go 10 times round a square field containing 53824 m2.\n\n### Options:\nA. 15840\nB. 9280\nC. 2667\nD. 8766\nE. 66711\n\n### Answer:\na2 = 53824 => a = 232\n4a = 928\n928 * 10 = 9280\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf e is a positive integer and 10^e \u2013 74 in decimal notation has digits whose sum is 440, what is the value of e?\n\n### Options:\nA. 40\nB. 44\nC. 45\nD. 46\nE. 50\n\n### Answer:\nAnswer E = 50\nWe have (10^e)-74, where the sum of the digits is 440.\n100-74 = 26, so we already have 2+6 = 8 from the 440.\nBecause we have a power of 10, we will have numbers like 100, 1000, 10000 and so on. This minus 74 rests 26 and a lot of 9s. E.g: 1000-74 = 9926.\nSo dividing the 432/9 = 48, that`s the number of 9s. and we have 2 other numbers (2 and 6) wich were 00 before the subtraction.\nSo we have 48 + 2 as an e = 50\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA boat moves upstream at the rate of 1 km in 20 minutes and down stream 1 km in 15 minutes. Then the speed of the current is :\n\n### Options:\nA. 1 kmph\nB. 0.5 kmph\nC. 3 kmph\nD. 2.5 kmph\nE. 3.5 kmph\n\n### Answer:\nRate upstream = (1/20 *60) = 3 kmph\nRate down stream = 1/15 * 60 = 4 kmph\nRate of the current = \u00bd (4-3) = 0.5 kmph\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe value of (4x10^7)(7x10^8) is closest to which of the following?\n\n### Options:\nA. 10^15\nB. 10^12\nC. 10^13\nD. 10^14\nE. 10^17\n\n### Answer:\nmultiplying these we get,\n28 x 10^7 x 10^8\n= 2.8x 10^16\nwhich is closer to 10^17\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how many ways can 5 different candies be distributed in 4 identical baskets?\n\n### Options:\nA. 120\nB. 51\nC. 24\nD. 5^4\nE. 4^5\n\n### Answer:\n5-N-N-N : 5C5 = 1 - OK\n4-1-N-N : 5C4 *1C1 = 5 - OK\n3-2-N-N : 5C3*2C2 = 10 - OK\n3-1-1-N : 5C3*2C1*1C1 = 20 - NO - only 10, once you decide to split the remaining two after choosing the 3 before, no factor of 2 needed\n2-2-1-N : 5C2*3C2*1C1 = 30 - NO - it is 15 = 30/2; baskets being identical, doesn't matter which group of 2 you choose first\n2-1-1-1 : 5C2*3*2*1 = 60 - NO - only 10, because you only choose those 2 to be placed together, all the other three you put in different baskets, no choices\nTotal of 1 + 5 + 10 + 10 + 15 + 10 = 51.\nAnswer B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is x if x + 3y = 10 and y = 3?\n\n### Options:\nA. 1\nB. 2\nC. 3\nD. 4\nE. 5\n\n### Answer:\nSubstitute y by 3 in x + 3y = 10\nx + 3(3) = 10\nx + 9 = 10\nIf we substitute x by 1 in x + 9 = 10, we have 1 + 9 = 10. Hence\nx = 1 correct answer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nLinda spent 4/5 of her savings on furniture and the rest on a TV. If the TV cost her $100, what were her original savings?\n\n### Options:\nA. $900\nB. $300\nC. $500\nD. $700\nE. $800\n\n### Answer:\nIf Linda spent 4/5 of her savings on furniture, the rest\n5 / 5 - 4 / 5 = 1 / 5 on a TV\nBut the TV cost her $100. So 1 / 5 of her savings is $100. So her original savings are 5 times $100 = $500\ncorrect answer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 15 machine can finish a job in 36 days, then how many more machines would be needed to finish the job in one -fourth less time?\n\n### Options:\nA. a. 5\nB. b. 8\nC. c. 10\nD. d. 12\nE. e. 16\n\n### Answer:\nYou might think of this in a management context - we can use the principle of 'person-hours' to solve any problem where we have identical workers. So, using simpler numbers, suppose you know that 6 identical employees, working simultaneously, would finish a job in 5 hours. Then that job requires 6*5 = 30 total hours of person-work. If instead you wanted the job done in 3 hours, you'd assign 30/3 = 10 employees to do the job, because you want to get a total of 30 hours of work from the employees.\nWe can solve this problem identically. If 15 machines (identical ones, I assume) work simultaneously for 36 days, they will do a total of 15*36 machine-days of work. So the job requires 15*36 days of machine work in total. We instead want the job done in 1/4 less time, so in 27 days. So we'll need 15*36/27 = 20 machines, or 5 additional machines.\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nPipes A and B can fill a tank in 2 and 3 hours. Pipe C can empty it in 6 hours. If all pipes are opened together, then the tank will be filled in?\n\n### Options:\nA. 3/2hr\nB. 1/2hr\nC. 1hr\nD. 9/7hr\nE. 5/3hr\n\n### Answer:\nNet part filled in 1 hour = 1/2 + 1/3 - 1/6 = 2/3\nThe tank will be full in 3/2 hr\nAnswer is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the sum of all 3 digit numbers that leave a remainder of '2' when divided by 3?\n\n### Options:\nA. 897\nB. 164,850\nC. 164,749\nD. 149,700\nE. 156,720\n\n### Answer:\nExplanatory Answer\nStep 1: Identify the series\nThe smallest 3 digit number that will leave a remainder of 2 when divided by 3 is 101.\nThe next couple of numbers that will leave a remainder of 2 when divided by 3 are 104 and 107.\nThe largest 3 digit number that will leave a remainder of 2 when divided by 3 is 998.\nIt is evident that any number in the sequence will be a 3 digit positive integer of the form (3n + 2).\nSo, the given numbers are in an Arithmetic sequence with the first term being 101 and the last term being 998 and the common difference being 3.\nStep 2: Compute the sum\nSum of an Arithmetic Progression (AP) = [first term + last term/2]n\nWe know the first term: 101\nWe know the last term: 998.\nThe only unknown is the number of terms, n.\nIn an A.P., the nth term an = a1 + (n - 1)*d\nIn this case, therefore, 998 = 101 + (n - 1)* 3\nOr 897 = (n - 1) * 3\n(n - 1) = 299 or n = 300.\nSum of the AP will therefore, be [101+998/2]\u2217300 = 164,850\nChoice B is the correct answer.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a barrel of juice there is 20 liters; in a barrel of beer there are 80 liters. If the price ratio between barrels of juice to a barrel of beer is 3:4, what is the price ratio between one liter of juice and one liter of beer?\n\n### Options:\nA. 3:2.\nB. 2:1.\nC. 3:1.\nD. 4:3.\nE. 3:4\n\n### Answer:\nPrice of 20 L juice= 3x\n1L= 3x/20\nPrice of 80 L beer= 4x\n1L= 4x/80\nRatio of 1 L price = 3x/20/4x/80= 3:1\nC is the answer\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf money is invested at r percent interest, compounded annually, the amount of investment will double in approximately 70/r years. If Pat's parents invested $ 7000 in a long term bond that pays 8 percent interest, compounded annually, what will be the approximate total amount of investment 18 years later, when Pat is ready for college?\n\n### Options:\nA. $28000\nB. $15000\nC. $12000\nD. $10000\nE. $9000\n\n### Answer:\nSince investment doubles in 70/r years then for r=8 it'll double in 70/8=~9 years (we are not asked about the exact amount so such an approximation will do). Thus in 18 years investment will double twice and become ($7,000*2)*2=$28,000 (after 9 years investment will become $7,000*2=$14,000 and in another 9 years it'll become $14,000*2=$28,000).\nAnswer: A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA clock store sold a certain clock to a collector for 45 percent more than the store had originally paid for the clock. When the collector tried to resell the clock to the store, the store bought it back at 25 percent of what the collector had paid. The shop then sold the clock again at a profit of 55 percent on its buy-back price. If the difference between the clock's original cost to the shop and the clock's buy-back price was $180, for how much did the shop sell the clock the second time?\n\n### Options:\nA. $149.55\nB. $134.56\nC. $175.43\nD. $158.65\nE. $255.45\n\n### Answer:\nNow, in the question above, lets say the original cost of the clock to store was C$ and then it sold the same to the collector at 45% profit.\nThis means the clocks' selling price was C (1.45) and this becomes cost price for the collector.\nNow, when the collector tries to sell the same clock to the store, the store buys it for 25% the price at which the collector bought it.\nThus, you get = 1.45*0.25*C = 0.3625 C\nFurthermore, the store sells the clock for the second time for 55% profit and thus the selling price of the clock becomes = cost price of the clock for the store at buy-back * 1.55 = 1.55 * 0.3625 C\nFinally given that C - 0.3625 C = 180 ----> C = 282.35$\nThus, the cost of the clock the second time around = 1.55*0.3625 C = 1.55 * 0.3625 * 282.35 = 158.65$. Hence D is the correct answer.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the odd man out. 49, 65, 81, 144, 169, 225, 441\n\n### Options:\nA. 49\nB. 65\nC. 81\nD. 144\nE. 169\n\n### Answer:\nExplanation :\nEach of the given numbers except 65 is a perfect square\nAnswer : Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe value of a laptop depreciates at the rate of 30% every year. It was purchased 2 years ago. If its present value is Rs. 3430, its purchase price was\n\n### Options:\nA. 6000\nB. 6500\nC. 7000\nD. 7500\nE. 8000\n\n### Answer:\nExplanation:\n= Rs.7000\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOne pipe can fill a tank three times as fast as another pipe. If together the two pipes can fill the tank in 39 minutes, then the slower pipe alone will be able to fill the tank in\n\n### Options:\nA. 144 mins\nB. 140 mins\nC. 136 mins\nD. 156 minw\nE. None of these\n\n### Answer:\nExplanation:\nLet the slower pipe alone fill the tank in x minutes\nthen faster will fill in x/3 minutes.\nPart filled by slower pipe in 1 minute = 1/x\nPart filled by faster pipe in 1 minute = 3/x\nPart filled by both in 1 minute =\n1/x+3/x=1/39\n=>4/x=1/39\nx=39\u22174=156 mins\nOption D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA cyclist bikes x distance at 8 miles per hour and returns over the same path at 10 miles per hour. What is the cyclist's average rate for the round trip in miles per hour?\n\n### Options:\nA. 8.1\nB. 8.9\nC. 8.6\nD. 8.3\nE. 9.0\n\n### Answer:\nDistance = d1 = x miles\nSpeed = s1 = 8 miles per hour\nTime = t1 = Distance/ Speed = x/8\n2. Going from B to A\nDistance = d2 = x miles\nSpeed = s2 = 10 miles per hour\nTime = t2 = Distance/ Speed = x/10\n3. Average Speed = Total Distance/Total Time\nTotal Distance = x + x = 2x\nTotal Time = x/10 + x/8 = x (1/10 + 1/8) = =9x/40\nSpeed = 2x/(9x/40) = 80/9\n= 8.9\nAnswer : B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe no. of girls in a class are seven times the no. of boys, which value cannever be the of total students?\n\n### Options:\nA. 3\nB. 5\nC. 8\nD. 9\nE. 11\n\n### Answer:\nLet the boys are X, then girls are 7X, total = X+7X = 8X\nSo it should be multiple of 8, 30 is not a multiple of 8.\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow long does a train 165 meters long running at the rate of 90 kmph take to cross a bridge 660 meters in length?\n\n### Options:\nA. 33\nB. 72\nC. 55\nD. 82\nE. 62\n\n### Answer:\nExplanation:\nT = (660 + 165)/90 * 18/5\nT = 33\nAnswer: Option A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo brothers took the GMAT exam, the higher score is X and the lower one is Y. If the difference between the two scores is equal to their average, what is the value of X/Y ?\n\n### Options:\nA. 3.\nB. 2.\nC. 1/2.\nD. 1/3.\nE. There isn't enough data to answer the question.\n\n### Answer:\nAnswer is A : 3\nX - Y = (X + Y)/2\nSolving for X/Y =3\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a certain lottery drawing, two balls are selected at random from a container with 50 balls, numbered from 1 to 50, inclusive. If the winner of the lottery is awarded a cash prize in the amount of $1,000 times the product of the numbers on the two selected balls, which of the following is a possible amount of the cash prize given to the winner?\n\n### Options:\nA. $9.85 x 10^6\nB. $2.45 x 10^6\nC. $1.00 x 10^7\nD. $1.05 x 10^7\nE. $9.90 x 10^7\n\n### Answer:\nThe max product of any two balls can be 49 * 50 = 2450 = 2.45 * 10^3\nIf you multiply it by $1000 the max amount will be 2.45 * 10^6.\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA sum of money deposited at compound interest (compounded yearly) amounts to $1210 in 2 years and to $1452 in 3 years. What is the interest rate?\n\n### Options:\nA. 20%\nB. 10%\nC. 60%\nD. 70%\nE. 30%\n\n### Answer:\n1452 - 1210 = 242\n242 / 1210 = 0.2 = 20%\nThe answer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAn analysis of the monthly incentives received by 5 salesmen : The mean and median of the incentives is $7000. The only mode among the observations is $12,000. Incentives paid to each salesman were in full thousands. What is the difference between Q the highest and the lowest incentive received by the 5 salesmen in the month?\n\n### Options:\nA. $4000\nB. $5000\nC. $9000\nD. $11,000\nE. $13,000\n\n### Answer:\nBreak down the question in to steps:\nStep #1: incentives received by 5 salesmen -->abcde\nStep #2: mean and median of the incentives is $7000: via number properties --> total incentives = 7,000 * 5 = 35, 000ab7,000de\nStep #3: only mode among the observations is $12,000: mode is the value that appears most often in a set of data. Therefore 12,000 must occur more then once and since 12,000 is larger than the mean (7,000) the most it can occur is twice in our list. If we place the numbers in ascending order we haveab7,00012,00012,000\nStep #4: What is the difference between the highest and the lowest incentive:\n- The total paid has to equal mean * # of numbers = 7,000 * 5 = 35 000.\n- The three values we have so far (12,000 12,000 and 7, 000) equal 31,000.\n- Therefore the first two numbers( ab) must equal 4, 000\n- There is only one mode which is 12,000, therefore 4,000 must be equal to a set of two numbers that are not the and a < b\nif a = 1,000 b = 3,000 --> difference Q between the highest and the lowest incentive = 12,000 - 1,000 =11, 000\nno other options for a or b to fit the criteria\nFinal List:1,0003,0007,00012,00012,000\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf b/x = 7/4 and b/y =7/ 5, then (y -x) =\n\n### Options:\nA. b/2\nB. b/7\nC. 2b\nD. 3b/7\nE. b\n\n### Answer:\nRatio 1:\n4b = 7x\nRatio 2:\n5b = 7y\ny -x = b/7\nAnswer is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOf the three-digit positive integers whose three digits are all different and nonzero, how many are odd integers greater than 700?\n\n### Options:\nA. 84\nB. 91\nC. 100\nD. 105\nE. 243\n\n### Answer:\nNumber of combinations for type 1 : 1*7*4 = 28\nNumber of combinations for type 2: 1*7*5 = 35\nNumber of combinations for type 3 : 1*7*4 = 28\nThus, total numbers possible = 28+35+28 = 91.\nB is thus the correct answer\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA person has to cover a distance of 10km in 1hour. If he covers one half of the distance in half of the total time; to cover the remaining distance in the remaining time, his speed must be?\n\n### Options:\nA. 5km/hr\nB. 8km/hr\nC. 10km/hr\nD. 12km/hr\nE. 15km/hr\n\n### Answer:\nRemaining distance = 5km\nRemaining time = 1/2 * 60 = 30min = 1/2 hour\nRequired speed = 5*2 = 10km/hr\nAnswer is C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe arithmetic mean of the set S = {5, K, 4, 10, M, 5} is 6. If K and M are integers, and K \u2260 M, what is the median of the numbers in the set?\n\n### Options:\nA. 4\nB. 4.5\nC. 5\nD. 5.5\nE. 6\n\n### Answer:\nThe sum of the numbers is 6*6 = 36\nK+M = 36 - 10 - 5 - 5 - 4 = 12\nSince K \u2260 M, K and M do not equal 6.\nThus one of the two numbers is 5 or less and one is 7 or more.\nThen middle two numbers in the set are 5 and 5.\nThe median is 5.\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe sum of two numbers is 65. Their difference is 5. The bigger number is\n\n### Options:\nA. 20\nB. 25\nC. 30\nD. 35\nE. 45\n\n### Answer:\nX + Y = 65\nX - Y = 5\nAdding 2X = 70 ==> X = 35 and Y = 65 - 35 = 30\nBigger number is X = 35\nAnswer D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA wire in the form of a circle of radius 3.5 m is bent in the form of a rectangule, whose length and breadth are in the ratio of 6 : 5. What is the area of the rectangle?\n\n### Options:\nA. 17 cm2\nB. 30 cm2\nC. 18 cm2\nD. 19 cm2\nE. 15 cm2\n\n### Answer:\nThe circumference of the circle is equal to the permeter of the rectangle.\nLet l = 6x and b = 5x 2(6x + 5x) = 2 * 22/7 * 3.5\n=> x = 1\nTherefore l = 6 cm and b = 5 cm Area of the rectangle\n= 6 * 5\n= 30 cm2\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nCereal A is 11% sugar by weight, whereas healthier but less delicious Cereal B is 2% sugar by weight. To make a delicious and healthy mixture that is 4% sugar, what should be the ratio of Cereal A to Cereal B, by weight?\n\n### Options:\nA. 2:5\nB. 1:3\nC. 2:7\nD. 3:4\nE. 1:5\n\n### Answer:\n2% is 2%-points below 4% and 11% is 7%-points above 4%.\nThe ratio of A:B should be 2:7.\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a division sum, the quotient is 120, the divisor 456 and the remainder 333, find the dividend?\n\n### Options:\nA. 23504\nB. 34545\nC. 55053\nD. 23434\nE. 23456\n\n### Answer:\nExplanation:\n120 * 456 + 333 = 55053\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAt the end of the first quarter, the share price of a certain mutual fund was 30 percent higher than it was at the beginning of the year. At the end of the second quarter, the share price was 75 percent higher than it was at the beginning of the year. What was the percent increase in the share price from the end of the first quarter to the end of the second quarter?\n\n### Options:\nA. 20%\nB. 25%\nC. 30%\nD. 34.6%\nE. 40%\n\n### Answer:\nAnother method is to use the formula for 2 successive percentage changes:\nTotal = a + b + ab/100\n75 = 30 + b + 30b/100\nb = 34.6\nAnswer (D)\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe mass of 1 cubic meter of a substance is 200 kg under certain conditions. What is the volume in cubic centimeters of 1 gram of this substance under these conditions? (1 kg =1,000 grams and 1 cubic meter = 1,000,000 cubic centimeters)\n\n### Options:\nA. 1\nB. 2\nC. 3\nD. 4\nE. 5\n\n### Answer:\n200 kg - 1 cubic meter;\n200,000 g - 1 cubic meter;\n200,000 g - 1,000,000 cubic centimeters;\n1 g - 1,000,000/200,000 = 10/2 = 5 cubic centimeters.\nAnswer: E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many terms are there in 2,4,8,16\u2026\u20261024?\n\n### Options:\nA. 10\nB. 14\nC. 16\nD. 18\nE. 20\n\n### Answer:\nClearly 2,4,8,16\u2026\u2026..1024 form a GP. With a=2 and r = 4/2 =2.\nLet the number of terms be n . Then\n2 x 2n-1 =1024 or 2n-1 =512 = 29.\n\uf05cn-1=9 or n=10.\nANSWER A 10\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nExpress a speed of 72 kmph in meters per second?\n\n### Options:\nA. 10 mps\nB. 76 mps\nC. 20 mps\nD. 97 mps\nE. 16 mps\n\n### Answer:\n72 * 5/18\n= 20 mps\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the length of the wire required to go 12 times round a square field containing 104976 m2.\n\n### Options:\nA. 15840\nB. 3388\nC. 2667\nD. 8766\nE. 15552\n\n### Answer:\na2 = 104976 => a = 324\n4a = 1296\n1296 * 12 = 15552\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nKelly and Jody packed boxes with books. If Jody packed 40% of the total number of boxes, what was the ratio of the number of boxes Kelly packed to the number that Jody packed?\n\n### Options:\nA. 1 to 6\nB. 1 to 4\nC. 2 to 5\nD. 3 to 5\nE. 3 to 2\n\n### Answer:\nExplanation:\nIf Jody packed 40% of the boxes then Kelly packed 60%. The ratio of the number of boxes Kelly packed to the number Jody packed is thus 60%/40%=3/2\nAnswer: Option E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMary can do a piece of work in 11 days. Rosy is 10% more efficient than Mary. The number of days taken by Rosy to do the same piece of work is?\n\n### Options:\nA. 10\nB. 15\nC. 20\nD. 25\nE. 30\n\n### Answer:\nRatio of times taken by Mary and Rosy = 110:100 =11:10\nSuppose Rosy takes x days to do the work.\n11:10 :: 11:x => x= 10 days.\nHence, Rosy takes 10 days to complete the work.\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA and B are two multiples of 14, and Q is the set of consecutive integers between A and B, inclusive. If Q contains 12 multiples of 14, how many multiples of 7 are there in Q?\n\n### Options:\nA. 20\nB. 21\nC. 22\nD. 23\nE. 24\n\n### Answer:\nHalfway between the multiples of 14, there will be another multiple of 7.\nThe total number of multiples of 7 is 12+11 = 23.\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf x and y are positive integers and y \u2260 1, then xy(y \u22121) is\n\n### Options:\nA. Always even\nB. Always odd\nC. Odd only when x is odd\nD. Even only when y is even\nE. Odd only when xy is odd\n\n### Answer:\nExpression is xy(y-1). We can ignore x and only work with y.\nIf y = even -> entire expression is even since anything multiplied by even is even\nIf y = odd, y-1 -> even -> entire expression is even since anything multiplied by even is even\nHence, entire expression will always be even.\nAnswer (A).\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the rate percent when the simple interest on Rs.800 amount to Rs.400 in 2 Years?\n\n### Options:\nA. 5%\nB. 6%\nC. 2%\nD. 25%\nE. 1%\n\n### Answer:\nInterest for 2yrs = 400\nInterest for 1yr = 200\nInterest rate = 200/800 x 100 = 25%\nAnswer : D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf Yury has been writing programming code for 16 hours at a rate of 5 lines of code per 20 seconds, how many lines of code has he written?\n\n### Options:\nA. 126(10^2)\nB. 126(10^3)\nC. 144(10^2)\nD. 1.26(10^7)\nE. .126(10^9)\n\n### Answer:\n5 LINES IN 20 SECONDS\nSO FOR 1 MINUTE ( 5 X 3 = 15 LINES )\nI HOUR = 60 MINUTES\n15 X 60 = 900 LINES IN AN HOUR\n16 HOURS = 900 X 16 = 144(10^2)\nANSWER C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRs.1500 is divided into two parts such that if one part is invested at 6% and the other at 5% the whole annual interest from both the sum is Rs.85. How much was lent at 5%?\n\n### Options:\nA. 399\nB. 700\nC. 288\nD. 500\nE. 211\n\n### Answer:\n(x*5*1)/100 + [(1500 - x)*6*1]/100 = 85\n5x/100 + 90 \u2013 6x/100 = 85\nx/100 = 5\n=> x = 500\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn doing a division of a question with zero remainder, a candidate took 12 as divisor instead of 21. The quotient obtained by him was 35. The correct quotient is\n\n### Options:\nA. 0\nB. 12\nC. 13\nD. 20\nE. None\n\n### Answer:\nSol.\nDividend = (12 x 35) = 420.\nNow, dividend = 420 and divisor = 21.\n\u2234 Correct quotient = 420 / 21 = 20.\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average weight of 20 persons sitting in a boat had some value. A new person added to them whose weight was 45 kg only. Due to his arrival, the average weight of all the persons decreased by 5 kg. Find the average weight of first 20 persons?\n\n### Options:\nA. 55\nB. 56\nC. 57\nD. 58\nE. 60\n\n### Answer:\n20x + 45 = 21(x \u2013 5)\nX=60\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHariprasad and Madhusudan started a business, investing sums in the ratio of 2 : 3. If Hariprasad had invested an additional amount of 10,000 the ratio of Hariprasad's investment to Madhusudan's investment would have been 3 : 2. What was the amount invested by Hariprasad?\n\n### Options:\nA. 8000\nB. 12000\nC. 9000\nD. Data inadequate\nE. None of these\n\n### Answer:\nLet the initial investments of Hariprasad and Madhusudan be 2x and 3x,respectively.\nFrom the question,\n2x+10000/3x=32\nor, 4x + 20000 = 9x\n\\ x = 4000\n\\ Amount invested by Hariprasad = 2x = 8000\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nwhat is the value of y if the greatest common divisor of (y-4)!,(y+1)!, and (y+2)! is 720.\n\n### Options:\nA. 12\nB. 10\nC. 9\nD. 7\nE. 8\n\n### Answer:\nGCD of (y-4)!,(y+1)!, and (y+2)! is 720. Find y.\nBest way to find n is substitute each of the answer and find out the correct one.\nOnly option B gave the correct answer.\nOption B: 10 and find GCD or 6!, 11! and 12!. 6! itself is 720 and 6! which is contained in the other two factorials. This satisfies the condition, hence answer is 10.\nAnswer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nConsider there is an elevator and you are at the upside and coming down using elevator. You walk 20 steps and then you stop, then you reach to the ground in 10 minutes. If you walk 10 steps and then stop, then you reach to the ground in 20 minutes. What is the speed of the elevator and How many steps are there??\n\n### Options:\nA. 1 step/min\nB. 2 step/min\nC. 3 step/min\nD. 4 step/min\nE. 5 step/min\n\n### Answer:\nLet e be the speed of the elevator, n be the no. of steps\nn = 20 + 10*e = 10+20*e\ne=1\nn=30\nNo. of steps : 30\nSpeed : 1 step/min\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe greatest number of four digits which is divisible by 15, 25, 40 and 75 is:\n\n### Options:\nA. 9000\nB. 9400\nC. 9600\nD. 9800\nE. 9200\n\n### Answer:\nGreatest number of 4-digits is 9999.\nL.C.M. of 15, 25, 40 and 75 is 600.\nOn dividing 9999 by 600, the remainder is 399.\nRequired number (9999 - 399) = 9600.\nAnswer: Option C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a certain fish pond, 1 out of every 120 bass are caught. If 3 out of every 4 caught bass are fried for dinner, and there are 9 fried bass for dinner, how many bass total are there in the pond?\n\n### Options:\nA. 5,000\nB. 700\nC. 500\nD. 1,222\nE. 1,440\n\n### Answer:\nProportions: Let B = bass, and Bc = bass caught, and Bcf = caught fried bass.\n9Bcf/xBc = 3Bcf/4Bc\nxBc = 12Bc\n12Bc/yB = 1Bc/120B\nyB = 1,440B\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf an amount of Rs 42,240 is distributed equally\namongst 22 persons, how much amount would each\nperson get?\n\n### Options:\nA. Rs 1905\nB. Rs 1920\nC. Rs 745\nD. Rs 765\nE. None\n\n### Answer:\nRequired amount =42240/22 = Rs 1920\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe population of a town is 8000. It decreases annually at the rate of 20% p.a. What will be its population after 2 years?\n\n### Options:\nA. 4300\nB. 4500\nC. 5120\nD. 5230\nE. 5366\n\n### Answer:\nFormula :\n( After =100 denominator\nAgo = 100 numerator)\n8000 \u00d7 80/100 \u00d7 80/100 = 5120\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe length of the bridge, which a train 130 m long and traveling at 45 km/hr can cross in 30 sec is?\n\n### Options:\nA. 227\nB. 268\nC. 245\nD. 299\nE. 271\n\n### Answer:\nSpeed = 45 * 5/18 = 25/2 m/sec.\nTime = 30 sec\nLet the length of bridge be x meters.\nThen, (130 + x)/30 = 25/2\nx = 245 m.\nAnswer:C:\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\na, b, c, d, and e are five consecutive numbers in increasing order of size. Deleting one of the five\nnumbers from the set decreased the sum of the remaining numbers in the set by 20%. Which one of\nthe following numbers E was deleted?\n\n### Options:\nA. a\nB. b\nC. c\nD. d\nE. e\n\n### Answer:\na+b+c+d+e => 1+2+3+4+5=15\n20%*15= 3 =>C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 36 men can do a piece of work in 25 hours, in how many hours will 13 men\ndo it ?\n\n### Options:\nA. 65 hours\nB. 69 hours\nC. 30 hours\nD. 62 hours\nE. 66 hours\n\n### Answer:\nLet the required number of hours be x. Then,\nLess men, More hours\t(Indirect Proportion)\n13 : 36 : : 25 : x\t\uf0f3(13 x x) = (36 x 25)\t\uf0f3(36 x 25)/13= 69\nHence, 15 men can do it in 60 hours.\nAnswer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man can do a piece of work in 5 days, but with the help of his son he can do it in 3 days. In what\ntime can the son do it alone ?\n\n### Options:\nA. 712days\nB. 612days\nC. 512days\nD. 412days\nE. None of these\n\n### Answer:\nExplanation:\nIn this type of question, where we have one person work and together work done. Then we can easily\nget the other person work just by subtracting them. As\nSon's one day work =\n(13\u221215)=(5\u2212315)=215\nSo son will do whole work in 15/2 days\nwhich is =\n712days\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo trains of equal length, running with the speeds of 60 and 40 kmph, take 50 seconds to cross each other while they are running in the same direction. What time will they take to cross each other if they are running in opposite directions?\n\n### Options:\nA. 10 sec\nB. 16 sec\nC. 13 sec\nD. 67 sec\nE. 13 sec\n\n### Answer:\nRS = 60 -40 = 20 * 5/18 = 100/18\nT = 50\nD = 50 * 100/18 = 2500/9\nRS = 60 + 40 = 100 * 5/18\nT = 2500/9 * 18/500 = 10 sec\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n60% of a number is added to 120, the result is the same number. Find the number?\n\n### Options:\nA. 300\nB. 200\nC. 400\nD. 500\nE. 600\n\n### Answer:\n(60/100) * X + 120 = X\n2X = 600\nX = 300\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe jogging track in a sports complex is 900 m in circumference. Sunil and Sachin start from the same point and walk in opposite directions at 5.4 km/hr and 3.6km/hr respectively. They will meet for the first time in?\n\n### Options:\nA. 2.98 min\nB. 5.7 min\nC. 6.0 min\nD. 6.3 min\nE. 7.2 min\n\n### Answer:\nClearly, the two will meet when they are 900m apart.\nTo be (5.4+ 3.6) = 9.0 km apart, they take 1 hour.\nTo be 900 m apart, they take\n= (900/9000 * 60) min\n= 6.00 min.\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe units digit of (10)^(87) + (5)^(46) is:\n\n### Options:\nA. 2\nB. 4\nC. 6\nD. 8\nE. 0\n\n### Answer:\nany power of anything ending in 5 always has a units digit of 5. So the first term has a units digit of 5. Done.\nThe second term anything power to 10 unit digit will be zero\nthen 5 + 0 = 5,\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOut of first 28 natural numbers, one number is selected at random. The probability that it is either an even number or a prime number is -.\n\n### Options:\nA. 1/2\nB. 16/19\nC. 4/5\nD. 22/28\nE. 3/5\n\n### Answer:\nn(S) = 28\nn(Even no) = 14 = n(E)\nn(Prime no) = 9 = n(P)\nP(E\u1d1cP) = 14/28 + 9/28 - 1/28 = 22/28\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn an election between two candidates, one got 55% of the total valid votes, 20% of the votes were invalid. If the total number of votes was 7500, the number of valid votes that the other candidate got, was:\n\n### Options:\nA. 2700\nB. 2900\nC. 3000\nD. 3100\nE. 3300\n\n### Answer:\nNumber of valid votes = 80% of 7500 = 6000.\nValid votes polled by other candidate = 45% of 6000\n=45/100 x 6000 = 2700\nANSWER :A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe can empty 3 gallons per minute. All the three pipes working together can fill the tank in 15 minutes. The capacity of the tank is:\n\n### Options:\nA. 60\nB. 100\nC. 120\nD. 180\nE. 200\n\n### Answer:\nWork done by the waste pipe in 1 min = 1/15-(1/20+1/24)\n=-1/40\nvolume of whole = (3*40)=120 gallons\nANSWER C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man buys 12 lts of liquid which contains 10% of the liquid and the rest is water. He then mixes it with 10 lts of another mixture with 30% of liquid. What is the % of water in the new mixture?\n\n### Options:\nA. 80.91\nB. 76.45\nC. 77.45\nD. 74.45\nE. 73.45\n\n### Answer:\n10% in 12 lts is 1.2. So water = 12-1.2 = 10.8 lts. 30% of 10 lts = 3. So water in 2nd mixture = 10-3 = 7 lts. Now total quantity = 12 + 10 = 22 lts. Total water in it will be 10.8 + 7 = 17.8 lts. % of water = (100*17.8)/22 = 80.91. Answer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe side of a square is increased by 25% then how much % does its area increases?\n\n### Options:\nA. 52.65\nB. 56.25\nC. 50.75\nD. 42.75\nE. 52.75\n\n### Answer:\na = 100 a2 = 10000\na = 125 a2 = 15625\n----------------\n10000 --------- 5625\n100 -------? => 56.25 %\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn an examination 35% of the students passed and 520 failed. How many students appeared for the examination?\n\n### Options:\nA. A)540\nB. B)400\nC. C)800\nD. D)650\nE. E)840\n\n### Answer:\nLet the number of students appeared be x\nthen, 65% of x = 520\n65x/100 = 520\nx = 520*100/65 = 800\nAnswer is C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n10^25 - 260 is divisible by all of the following except:\n\n### Options:\nA. A.10\nB. B.8\nC. C.5\nD. D.4\nE. E.2\n\n### Answer:\nThe last three digits ( 1000 - 260 ) 740\n740 is divisible by 10,4,2,5\n740 is not evenly divisible by 8 so the answer is B) 8\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA and B can together finish a work in 40days. They worked together for 10days and then B left. After another 21 days, A finished the remaining work. In how many days A alone can finish the job?\n\n### Options:\nA. 10\nB. 25\nC. 60\nD. 30\nE. 28\n\n### Answer:\nA+B 10days work = 10*1/40 = 1/4\nRemaining work = 1-1/4 = 3/4\n3/4 work is done by A in 21 days\nwhole work will be done by A in 21*4/3 = 28 days\nAnswer is E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe food in a camp lasts for 25 men for 40 days. If ten more men join, how many days will the food last?\n\n### Options:\nA. 40 days\nB. 29 days\nC. 60 days\nD. 50 days\nE. 45 days\n\n### Answer:\none man can consume the same food in 25*40 = 1000 days.\n10 more men join, the total number of men = 35\nThe number of days the food will last = 1000/35 = 29 days.\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe value of a machine depreiates at the rate of 10% per annum. If its present is Rs.1,62,000 what will be its worth after 2 years ? What was the value of the machine 2 years ago ?\n\n### Options:\nA. Rs.200000\nB. Rs.100000\nC. Rs.500000\nD. Rs.300000\nE. Rs.800000\n\n### Answer:\nValue of the machine after 2 years\n=Rs.[162000*(1-(10/100))^2] = Rs.[162000*(9/10)*(9/10)]\n=Rs. 131220\nValue of the machine 2 years ago\n= Rs.[162000/(1-(10/100)^2)]=Rs.[162000*(10/9)*(10/9)]=Rs.200000\nAnswer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nCalculate the average mark scored by Andrea if he had the following scores in an examination: 66, 60, 72, 77, 55 and 85 marks (out of 100) in English, Mathematics, Chemistry, Biology, French Language and Physics respectively?\n\n### Options:\nA. 74\nB. 76\nC. 70\nD. 67\nE. 69.2\n\n### Answer:\nExplanation:\nAverage mark = 66+60+72+77+55+85/6=69.2\nAnswer: Option E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere r 4 prime numbers in ascending order. The multiplication of first 3 is 385 and that of last 3is 1001. what is the last number is\n\n### Options:\nA. 12\nB. 15\nC. 16\nD. 13\nE. 18\n\n### Answer:\nExplanation:\nabcbcd=3851001=>ad=513\nabcbcd=3851001=>ad=513\nSo d = 13\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are between 120 and 130 cards in a collection of cards. If they are counted out 3 at a time, there are 2 left over, but if they are counted out 4 at a time, there is 1 left over. How many cards are in the collection?\n\n### Options:\nA. 121\nB. 123\nC. 125\nD. 127\nE. 129\n\n### Answer:\nThe numbers with the form 4n+1 are 121, 125, and 129.\nOnly 125 has the form 3k+2.\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe speed of a boat in still water is 60kmph and the speed of the current is 30kmph. Find the speed downstream and upstream?\n\n### Options:\nA. 40, 68 kmph\nB. 40, 30 kmph\nC. 90, 60 kmph\nD. 40, 60 kmph\nE. 90, 30 kmph\n\n### Answer:\nSpeed downstream = 60 + 30 = 90 kmph\nSpeed upstream = 60 - 30 = 30 kmph\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA dealer purchased an article at 3/4 of its list price and sold 50% more than the list price. Find his gain percent?\n\n### Options:\nA. 180%\nB. 189%\nC. 100%\nD. 109%\nE. 120%\n\n### Answer:\nMP = 100\nCP = 75\nSP = 150\n------\n75 ---- 75\n100 ---- ? => 100%\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe weights of three boys are in the ratio 4 : 5 : 6. If the sum of the weights of the heaviest and the lightest boy is 45 kg more than the weight of the third boy, what is the weight of the lightest boy?\n\n### Options:\nA. 39 kg\nB. 36 kg\nC. 32 kg\nD. 31 kg\nE. 96 kg\n\n### Answer:\nLet the weights of the three boys be 4k, 5k and 6k respectively.\n4k + 6k = 5k + 45\n=> 5k = 45 => k = 9\nTherefore the weight of the lightest boy\n= 4k = 4(9) = 36 kg.\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA person bought an article and sold it at a loss of 10%. If he had bought it for 20% less and sold it for Rs.75 less, he could have gained 25%. What is the cost price?\n\n### Options:\nA. 250\nB. 277\nC. 299\nD. 266\nE. 292\n\n### Answer:\nCP1 = 100 SP1 = 90\nCP2 = 80 SP2 = 80 * (140/100) = 112\n22 ----- 100\n55 ----- ? => Rs.250.Answer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average age of husband, wife and their child 3 years ago was 24 years and that of wife and the child 5 years ago was 20 years. The present age of the husband is\n\n### Options:\nA. 31 years\nB. 40 years\nC. 50 years\nD. 55 years\nE. None\n\n### Answer:\nSolution\nSum of the present ages of husband, wife and child\t= (24x3+3x3) years\n= 81 years.\nSum of the present ages of wife and child\t= (20x2+5x2) years\n= 50 years.\n\u00e2\u02c6\u00b4 Husband's present age\t= (81 - 50) years\n= 31 years.\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many total number of ways in which n distinct objects can be put into two different boxes is\n\n### Options:\nA. n2\nB. 2n\nC. 2n\nD. 3n\nE. None of these\n\n### Answer:\nLet the two boxes be B1 and B2. There are two choices for each of the n objects. So, the total number of ways is\n2 \u00d7 2 \u00d7.....\u00d7 2 (n times ) = 2n\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train running at the speed of 142 km/hr crosses a pole in 12 seconds. Find the length of the train.\n\n### Options:\nA. 540\nB. 288\nC. 200\nD. 340\nE. 712\n\n### Answer:\nSpeed = 162*(5/18) m/sec = 45m/sec\nLength of Train (Distance) = Speed * Time\n45 * 12 = 540 meter\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRoger can read a book in k minutes. What part of the book can he read in 4 minutes? (k>8)\n\n### Options:\nA. 8+k\nB. 8/k\nC. k/8\nD. (k+ 8)/k\nE. (k-8) / k\n\n### Answer:\nLet's sayk = 24\nThat is, it takes 24 minutes to read the entire book.\nSo, in 8 minutes, Roger can read1/3of the book\nSo, we're looking for the answer choice that yields an OUTPUT of1/3whenk = 24\nA) 8+24=32ELIMINATE\nB) 8/24=1/3KEEP\nC)24/8 =3ELIMINATE\nD) (24+ 8)/24=32/24 = 4/3ELIMINATE\nE) (24-8) /24=16/24 = 2/3ELIMINATE\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nBy selling an umbrella for Rs. 300, a shop keeper gains 20%. During a clearance sale, the shopkeeper allows a discount of 10% on the marked price. His gain percent during the sale is?\n\n### Options:\nA. 5\nB. 6\nC. 8\nD. 9\nE. 1\n\n### Answer:\nMarked price = Rs. 300\nC.P. = 100/120 * 300 = Rs. 250\nSale price = 90% of Rs. 300 = Rs. 270\nRequired gain % = 20/250 * 100 = 8%.\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA sum of Rs.66000 is divided into three parts such that the simple interests accrued on them for six, two and eleven years respectively may be equal. Find the amount deposited for 11 years.\n\n### Options:\nA. 6500\nB. 2000\nC. 4500\nD. 3000\nE. 6000\n\n### Answer:\nLet the amounts be x, y, z in ascending order of value. As the interest rate and interest accrued are same for 2 years 6 years and 11 years i.e. 2x = 6y = 11z = k.\nL.C.M. of 2,6,11 = 66 So x:y:z: = 33000 : 11000 :6000\nThe amount deposited for 11 years = 6000\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nYour town has a population of 1260. Every three people have a car. How many cars are in your town?\n\n### Options:\nA. 400\nB. 410\nC. 420\nD. 430\nE. 450\n\n### Answer:\nEvery three person has a car, then the number of cars in the town could be calculated by the division of number of people over the person-to-car ratio.\nthe number of cars in the town=1260/(3/1)=1260/3=420 cars\nSo the correct choice is C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA can finish a piece of work in 5 days. B can do it in 10 days. They work together for 1 day and then A goes away. In how many days will B finish the work?\n\n### Options:\nA. 8 days\nB. 5 days\nC. 6 days\nD. 7 days\nE. 9 days\n\n### Answer:\n1/5 + (1 + x)/10 = 1 => x = 7 days\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRs.280 contained in a box consists of one rupee, 50 paisa and 25 paisa coins in the ratio 4:5:6. What is the number of 25 paisa coins?\n\n### Options:\nA. 210\nB. 266\nC. 120\nD. 299\nE. 267\n\n### Answer:\n4x 5x 6x\n100 50 25\n400x + 250x + 150x = 28000\nx = 35\n6x = 210\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe length of the rectangular field is double its width. Inside the field there is square shaped pond 8m long. If the area of the pond is 1/2 of the area of the field. What is the length of the field?\n\n### Options:\nA. 13\nB. 16\nC. 34\nD. 43\nE. 42\n\n### Answer:\nExplanation:\nA/2 = 8 * 8 => A = 8 * 8 * 2\nx * 2x = 8 * 8 * 2\nx = 8 => 2x = 16\nAnswer: Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe speed of a train is 120 kmph. What is the distance covered by it in 8 minutes?\n\n### Options:\nA. 15 kmph\nB. 11 kmph\nC. 16 kmph\nD. 18 kmph\nE. 12 kmph\n\n### Answer:\n120 * 8/60\n= 16 kmph\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSet S contains exactly 10 numbers and has an average (arithmetic mean) of 6.2. If one of the numbers in Set S is increased by 6, while all other numbers remain the same, what is the new average of Set S?\n\n### Options:\nA. 6.6\nB. 6.7\nC. 6.8\nD. 6.85\nE. 6.9\n\n### Answer:\nOld set S - Total is avg * no of elements = 6.2*10 = 62\nIf one number is increased by 6 then total increased to 62+6=68\nNew avg - 68/10 = 6.8.\nHence answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nCalculate the L.C.M of 1/5, 6/ 7, 5/6, 3/5 is :\n\n### Options:\nA. 15\nB. 30\nC. 20\nD. 40\nE. 10\n\n### Answer:\nRequired L.C.M =L.C.M. of 1, 6, 5, 3/H.C.F. of 5, 7, 6, 5 =30/1=30\nAnswer is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRitesh and Co. generated revenue of Rs. 1,800 in 2006. This was 12.5% of its gross revenue. In 2007, the gross revenue grew by Rs. 2,500. What is the percentage increase in the revenue in 2007?\n\n### Options:\nA. 17.36%\nB. 20%\nC. 25%\nD. 50%\nE. None of these\n\n### Answer:\nExplanation :\nGiven, Ritesh and Co. generated revenue of Rs. 1,800 in 2006 and that this was 12.5% of the gross revenue.\nHence, if 1800 is 12.5% of the revenue, then 100% (gross revenue) is:\n=>(100/12.5)\u00d71800.\n=>14,400.\nHence, the total revenue by end of 2007 is Rs. 14,400. In 2006, revenue grew by Rs. 2500. This is a growth of:\n=>(2500/14400)\u00d7100.\n=>17.36%.\nAnswer : A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe value of a scooter depreciates in such a way that its value of the end of each year is 3/4 of its value of the beginning of the same year. If the initial value of the scooter is Rs.40,000, what is the value at the end of 1 year?\n\n### Options:\nA. 3277\nB. 2977\nC. 30000\nD. 6077\nE. 17112\n\n### Answer:\nExplanation: 40,000*(3/4)^1\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a and d are both integers, a>d, and -3c>19, then the largest value of d would be?\n\n### Options:\nA. -5\nB. -6\nC. -7\nD. -8\nE. -10\n\n### Answer:\nNo, your thinking is incorrect. When we know that a>d and a<-6.33, the largest value of a can be -7 while if a=-7, then largest value of d < -7 will be -8.For negative numbers, -7 > -8 and -8> -10.\nYou are right in saying that d can take any value less than -7 ---> d could be -8, -9, -10 .... and out of all these values, -8 is the greatest.\nLook at the numbers on the number line. For any 2 numbers, the ones on the right are greater than the ones on the left:\n.......-11 -10 -9 -8 -7 -6 -5 ..... 0 1 2 3 4 5 6 ... (-11< -10, -10< -8, 4< 5 etc).\nSo, as per the question if d", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFor an integer n greater than 1, n* denotes the product of all the integers from 1 to n inclusive. How many prime numbers are there between 6*+2 and 6*+6, inclusive ?\n\n### Options:\nA. 1\nB. None of the above\nC. 2\nD. 3\nE. 4\n\n### Answer:\nGiven that n* denotes the product of all the integers from 1 to n, inclusive so, 6* + 2 = 6! + 2 and 6* + 6 = 6! + 6.\nNow, notice that we can factor out 2 our of 6! + 2 so it cannot be a prime number, we can factor out 3 our of 6! + 3 so it cannot be a prime number, we can factor out 4 our of 6! + 4 so it cannot be a prime number, ... The same way for all numbers between 6! + 2 and 6! +7, inclusive. Which means that there are no primes in this range.\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA larger cube has 8 cubic inch as a volume and in the cube there are 8 smaller cubes such that their volume is 1 cubic inch. What is the difference between the surface areas\u2019 sum of the 8 smaller cubes and the surface area of the larger cube, in square inch?\n\n### Options:\nA. 24\nB. 64\nC. 81\nD. 108\nE. 120\n\n### Answer:\nVolume of larger cube = 8 = 2^3\nSide of larger cube = 2\nVolume of smaller cube = 1 --> Side of smaller cube = 1\nSurface area of larger cube = 6 * 2^2 = 24\nSurface area of 27 smaller cubes = 8 * 6 * 1 = 48\nDifference = 48 - 24 = 24\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nPipe B that can fill a tank in an hour and pipe A that can fill the tank in half an hour are opened simultaneously when the tank is empty. Pipe A is shut 15 minutes before the tank overflows. When will the tank overflow?\n\n### Options:\nA. 32 mins\nB. 35 mins\nC. 40 mins\nD. 30 mins\nE. 36 mins\n\n### Answer:\nThe last 15 minutes only pipe B was open. Since it needs 1 hour to fill the tank, then in 15 minutes it fills 1/4th of the tank, thus 3/4 of the tank is filled with both pipes open.\nThe combined rate of two pipes is 1 + 2 = 3 tanks/hour, therefore to fill 3/4th of the tank they need (time) = (work)/(rate) = (3/4)/3 = 1/4 hours = 15 minutes.\nTotal time = 15 + 15 = 30 minutes.\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJohn purchased a fridge and a mobile for Rs. 15000 &Rs. 8000 respectively. He sold the fridgeat a loss of 4% and the mobile phone at a profit of 10%. Overall how much he make a profit.\n\n### Options:\nA. 139\nB. 160\nC. 200\nD. 220\nE. 250\n\n### Answer:\nLet the SP of the refrigerator and the mobile phone be Rs. r and Rs. m respectively.\nr = 15000(1 - 4/100) = 15000 - 600\nm = 8000(1 + 10/100) = 8000 + 800\nTotal SP - Total CP = r + m - (15000 + 8000) = -600 + 800 = Rs. 200\nAs this is positive, an overall profit of Rs. 200 was made.\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nCONVERT 2.0 hectares in ares\n\n### Options:\nA. 130 ares.\nB. 160 ares.\nC. 180 ares.\nD. 200 ares.\nE. 250 ares.\n\n### Answer:\n2.0 hectares in ares\n1 hectare = 100 ares\nTherefore, 2.0 hectares = 2.0 \u00d7 100 ares\n= 200 ares.\nANSWER- D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nManoj borrowed Rs.4200 from Anwar at 6% p.a. simple interest for three years. He then added some more money to the borrowed sum and lent it to Ramu for the same time at 9% p.a. simple interest. If Manoj gains Rs.824.85 by way of interest on the borrowed sum as well as his own amount from the whole transaction, then what is the sum lent by him to Ramu?\n\n### Options:\nA. 22877\nB. 5855\nC. 2778\nD. 6787\nE. 1771\n\n### Answer:\nLet the sum lent by Manoj to Ramu be Rs.P.\nAmount gained by Manoj = P. 3.9 /100 = 4200.3.6/100 = Rs.824.85\n27P = 75600 = 82485\nP = (82485 + 75600)/27 = 3055 + 2800 = Rs.5855\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the angle between the two hands at 8.20 O'clock?\n\n### Options:\nA. 150 degree\nB. 120 degree\nC. 130 degree\nD. 250 degree\nE. 320 degree\n\n### Answer:\nangle=|11/2(min)-30(hrs)|\n=|11/2(20)-30(8)|\n=|110-240|\n=130 deg\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe speed of a bus increases by 2 kmph after every one hour. If the distance travelled in the first one hour was 35 km, what was the total distance travelled in 12 hours?\n\n### Options:\nA. 550\nB. 500\nC. 552\nD. 560\nE. 580\n\n### Answer:\nDist 1st hr = 35 km\nspeed of bus by 2 kmph 2nd hr = 37 km\n3rd hr = 39 km\ntot = 35+37+39+....(12 terms)\n12/2(2*35+(12-1)2]\n=6*92\n= 552\nANSWER C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nCalculate the amount that an investor needs to be invest to earn $1005 in interest in 12 months if the investor plans to invest x dollars in a savings account that pays interest at an annual rate of 11% compounded semi-annually?\n\n### Options:\nA. 8000\nB. 8100\nC. 8900\nD. 8600\nE. 8400\n\n### Answer:\nthe approach is substitution,\nour interest requirement is $1005 after 12 months, 2 compounding period.\ncalculate the compound interest on each option and find out the one that yields 460 in 12 months\n8900 yielded $1005\nusing the formula\nA = P(1 + r/n)nt\nhence answer is C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 6 (A's capital) = 8 (B's capital) = 10 (C's capital). Then the ratio of their capitals is?\n\n### Options:\nA. 20:15:15\nB. 20:15:10\nC. 20:15:12\nD. 20:15:11\nE. 20:15:13\n\n### Answer:\n6A = 8B = 10 C\nA:B:C = 1/6:1/8:1/10\n= 20:15:12.Answer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn an examination, a student scores 4 marks for every correct answer and loses 1 mark for every wrong answer. If he attempts all 75 questions and secures 125 marks, the number of questions he attempts correctly, is :\n\n### Options:\nA. 38\nB. 40\nC. 26\nD. 25\nE. 11\n\n### Answer:\nExplanation:\nLet the number of correct answers be x.\nThen numbers of incorrect answers will be 75 \u2013 x\nWe get 4x \u2013 (75 \u2013 x)\u00d71= 125\nOn solving the equation we get x= 40\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the area of square field whose side of length 15 m?\n\n### Options:\nA. 225\nB. 2878\nC. 277\nD. 266\nE. 279\n\n### Answer:\n15 * 15\n= 225 sq m\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow much 60% of 50 is greater than 40% of 30?\n\n### Options:\nA. 18\nB. 13\nC. 15\nD. 20\nE. 25\n\n### Answer:\nExplanation:\n(60/100) * 50 \u00e2\u20ac\u201c (40/100) * 30\n30 - 12 = 18\nAnswer is A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe profit obtained by selling an article for Rs. 57 is the same as the loss obtained by selling it for Rs. 43. What is the cost price of the article?\n\n### Options:\nA. Rs. 40\nB. Rs. 50\nC. Rs. 49\nD. Rs. 59\nE. None of these\n\n### Answer:\nS.P 1- C.P = C.P \u2013 S.P 2\n57 - C.P = C.P - 43\n2 C.P = 57 + 43;\nC.P = 100/2 = 50\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAn incredible punch is composed of buttermilk, orange juice, and brandy. How many pints of orange juice are required to make 7 1\u20442 gallons of punch containing twice as much buttermilk as orange juice and three times as much orange juice as brandy? (1 Gallon = 8 Pints )\n\n### Options:\nA. 16\nB. 18\nC. 20\nD. 22\nE. 24\n\n### Answer:\n1 gallon = 8 pints\n7.5 gallons = 60 pints\nButtermilk = 2 orange\norange = 3 brandy\nbuttermilk+orange+brandy = 60\n2orange+orange+1/3 orange = 60\n10 orange = 180\norange = 18 pints\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA sports equipment store sold ping pong rackets for a total of $637. If the average (arithmetic mean) price of a pair of rackets is $9.8, how many pairs were sold?\n\n### Options:\nA. 50\nB. 100\nC. 65\nD. 500\nE. 980\n\n### Answer:\nAverage price for a pair of rackets = $9.8\nTotal cost = $9.8*x = $637\nx = 65 pairs were sold.\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nDavid's Bank's saving amount is decreased 10% due to loan payment and current balance is Rs.90000. Find the actual balance before deduction?\n\n### Options:\nA. 8000\nB. 8500\nC. 9000\nD. 9500\nE. 100000\n\n### Answer:\n10% decreased\n90% Balance = 90000\n100% = 90000/90*100 = 100000\nAnswer : E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhen E is divided by 9, the remainder is 4. All of the following are possible values of E, except for which of the following?\n\n### Options:\nA. 13\nB. 31\nC. 49\nD. 57\nE. 67\n\n### Answer:\nThe number can be expressed in the form of 9x+4 where x can 0,1,2,3,4....\nby evaluating the answer choices carefully we can clearly observe that 57 is the only number which can't be expressed E in the form of 9x+4\nIn other words we can also say that the (answer - 4) will not be divisible by 9.57 is the number which doesn't follow this condition\nCorrect Answer - D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo carpenters, working in the same pace, can build 2 desks in two hours and a half. How many desks can 4 carpenters build in 3 hours?\n\n### Options:\nA. 2.4.\nB. 3.6.\nC. 4.8.\nD. 5.5.\nE. 6.4\n\n### Answer:\nW = 2 desks\nT = 2.5 hrs\nRate of 2 carpenters = 2\u00d7R\nRate = work done/ time\n2xR = 2/2.5\nR = 1/2.5 = 2/5 (this is the rate of each carpenter)\nWork done by 4 carpenters in 3 hrs = 4 \u00d7 rate of each carpenter x time = 4\u00d7 2/5 \u00d7 3 =4.8 desks\nC is the correct answer.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFor all numbers a and b, the operationis defined by ab = (a + 2)(b \u2013 3).\nIf 3y = \u201330, then y =\n\n### Options:\nA. \u201315\nB. \u20136\nC. -3\nD. 6\nE. 15\n\n### Answer:\n(3+2)(y-3)=-30..\nx-3=-6..\nx=-3\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat profit percent is made by selling an article at a certain price, if by selling at 2/3rd of that price, there would be a loss of 20%?\n\n### Options:\nA. 85 %\nB. 26 %\nC. 10 %\nD. 20 %\nE. 15 %\n\n### Answer:\nExplanation:\nSP2 = 2/3 SP1\nCP = 100\nSP2 = 80\n2/3 SP1 = 80\nSP1 = 120\n100 --- 20 => 20%\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf both 5^2 and 3^3 are factors of n x (2^5) x (12^2) x (7^3) x (10), what is the smallest possible positive value of n?\n\n### Options:\nA. 15\nB. 45\nC. 75\nD. 125\nE. 150\n\n### Answer:\n(2^5) x (12^2) x (7^3) x (10) has two appearances of 3 (in 12^2) and one appearance of 5 (in the 10).\nThus n must include at least 3 * 5 = 15\nThe answer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA photo-mat shop charges $0.55 for the first photo inside a film, and 20% cents less for each additional photo. How many photos can we develop with $52.58 if each film contains 36 photos?\n\n### Options:\nA. 4 films and 12 photos\nB. 5 films and 6 photos\nC. 5 films and 14 photos\nD. 6 films and 4 photos\nE. 2 films and 28 photos\n\n### Answer:\n1st photo = 0.55\nSubsequent = 0.55*0.6=0.33\nPrice of 1 full film=0.55+0.33*35=12.1\nPrice of 4 full film = 12.1*4=48.4\n52.58-48.4=4.18\n4.18=0.55+0.33x\nx=11\n52.58--->2 full films and 1+11=28 photos\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf x and y are two-single digit integers such that x < 40 and y<7, which of the following is closest to the maximum possible value of xy ?\n\n### Options:\nA. 700\nB. 2,800\nC. 4,000\nD. 7,000\nE. 63\n\n### Answer:\nTo get the maximum possible value of xy, we need maximize the value of both x and y\nmax x can be = 9 (given x is a two-digit integer < 40)\nmax y can be = 7 (given y is a two-digit integer < 7)\nxy = 9*7 = 63\nAnswer (E)\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRon walks to a viewpoint and returns to the starting point by his car and thus takes a total time of 6 hours 45 minutes. He would have gained 2 hours by driving both ways. How long W would it have taken for him to walk both ways.\n\n### Options:\nA. 8 h 45 min\nB. 7 h 45 min\nC. 6 h 45 min\nD. 5 h 30 min\nE. None of these\n\n### Answer:\n1.Walking to to a viewpoint+Driving back=6 hours 45 minutes\n2.Driving to a viewpoint+Driving back=6 hours 45 minutes - 2 hours=4 hours 45 minutes, thereforeone way driving=4 hours 45 minutes/2 =2 hours 22.5 minutes.\n3. From 1.one way driving=6 hours 45 minutes-2 hours 22.5 minutes=4 hours 22.5 minutes.\n4.Walking to to a viewpoint+Walking back W=4 hours 22.5 minutes+4 hours 22.5 minutes=8 hours 45 minutes.\nAnswer: A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFor a bake sale, Simon baked 2n more pies than Theresa. Theresa baked half as many pies as Roger, who baked 1313n pies. No other pies were baked for the sale. What fraction of the total pies for sale did Roger bake?\n\n### Options:\nA. 1/16\nB. 1/8\nC. 3/16\nD. 3/8\nE. 13/16\n\n### Answer:\nS : Simon\nT : Theresa\nR : Roger\nLet Theresa baked A.\nAs per question, we have S = A + 2n\nR = 2A = n/3 or A = n/6\nNow, Total = A + (A+2n) + 2A = 8n/3\nFraction, (n/3) / (8n/3) = 1/8\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOf the 5 numbers, whose average is 100, the first is one-fourth of the sum of the last 4. The first number is?\n\n### Options:\nA. 83.3\nB. 80\nC. 78.63\nD. 56.98\nE. 67.85\n\n### Answer:\nLet the first number be x\nsum of the 5 numbers = x+5x = 6x\n6x/5 = 100\nx = 100*5/6 = 83.3\nAnswer is A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n(A% of 4B + B% of A) is equal to ?\n\n### Options:\nA. A% of B\nB. B% of A\nC. 5% of AB\nD. AB% of 3\nE. None\n\n### Answer:\nAnswer\nA% of 4B + B% of A =4AB/100 + AB/100\n= 5AB/100 = 5% of AB\nCorrect Option: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average monthly income of A and B is Rs. 5050. The average monthly income of B and C is Rs. 6250 and the average monthly income of A and C is Rs. 5200. What is the monthly income of A?\n\n### Options:\nA. 1000\nB. 1500\nC. 2000\nD. 3000\nE. 4000\n\n### Answer:\nLet monthly income of A = a\nmonthly income of B = b\nmonthly income of C = c\na + b = 2 \u00d7 5050 .... (Equation 1)\nb + c = 2 \u00d7 6250 .... (Equation 2)\na + c = 2 \u00d7 5200 .... (Equation 3)\n(Equation 1) + (Equation 3) - (Equation 2)\n=> a + b + a + c - (b + c) = (2 \u00d7 5050) + (2 \u00d7 5200) - (2 \u00d7 6250)\n=> 2a = 2(5050 + 5200 - 6250)\n=> a = 4000\ni.e., Monthly income of A = 4000\nAnswer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the difference between the largest number and the least number written with the digits 6, 3, 2, 5?\n\n### Options:\nA. 6084\nB. 4176\nC. 2077\nD. 2721\nE. 1812\n\n### Answer:\nExplanation:\n2356\n6532\n------------\n4176\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nDuring a certain two-week period, 80 percent of the movies rented from a video store were comedies, and of the remaining movies rented, there were 4 times as many dramas as action movies. If no other movies were rented during that two-week period and there were A action movies rented, then how many comedies, in terms of A, were rented during that two-week period?\n\n### Options:\nA. 5 A\nB. 15 A\nC. 20 A\nD. 1/25 A\nE. 30 A\n\n### Answer:\nMovies: 80 % comedies. 20 % remaining genre.\nNow in this 20 %, there are only 2 categories. Action movies and Drama Movies.\nIf Action = x; Drama movies = 4x. Total 5x.\n5x = 20; x = 4\nAction movies: 4 %\nDrama movies: 16 %\nwe can say that out of 100z,:\ncomedies: 80z\naction: 4z\ndrama: 16 z\nNow action movies wereA\nThis means:\nA = 4z.\nz = (A/4)\nComedies: 80z = 80 * (A/4)\n20 A\nC is the answer.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the number of ways in which 8 different beads can be arranged to form a necklace.\n\n### Options:\nA. 30\nB. 20\nC. 2520\nD. 60\nE. 80\n\n### Answer:\nSince in forming a necklace clockwise and anticlockwise arrangements are not different, therefore,8 beads can be arranged to form a necklace in(8-1)! /2ways\n= 7*6*5*4*3*2/2 = 2520 ways\nAnswer is C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn August,a cricket team that played 120 matches won 22% of the games it played.After a continuous winning streak,this team raised its average to 52%.How many matches did the team win to attain this average?\n\n### Options:\nA. 40\nB. 52\nC. 68\nD. 75\nE. 98\n\n### Answer:\nlet the no of matches played more=x\nso,\n(120+x)*52/100=26.4+x\nby solving we get x=75\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA and B are two partially filled buckets of water. If 6 liters are transferred from A to B, then A would contain one-third of the amount of water in B. Alternatively, if 6 liters are transferred from B to A, B would contain one-half of the amount of water in A. Bucket A contains how many liters of water?\n\n### Options:\nA. 66/5\nB. 13\nC. 17\nD. 21\nE. 23\n\n### Answer:\nLet Bucket A be A and Bucket B be B\nScenario 1\nA-6 = 1/3 (B+6) ----> 3A-18 =B+6\nScenario 2\nB-6 = 1/2 (A+6) -----> 2B-12 = A+6\nFrom Scenario 1, B = 3A-24\nSubstitute B with this information in Stmt 2\n2 (3A-24) -12 = A+6 ------> 6A -48-12 = A+6 ------> 6A- A = 60+6 ---> 5A= 66\nA= 66/5, Answer choice A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo trains, one from P to Q and the other from Q to P, start simultaneously. After they meet, the trains reach their destinations after 49 hours and 16 hours respectively. The ratio of their speeds is\n\n### Options:\nA. 4:1\nB. 4:2\nC. 4:5\nD. 4:3\nE. 4:7\n\n### Answer:\nRatio of their speeds = Speed of first train : Speed of second train\n= \u221a16\u2212\u2212\u221a49\n= 4:7\nAnswer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf n is an even integer, then which of the following must be an odd integer?\n\n### Options:\nA. 2n\nB. 3n\nC. 3n + n^2 + 2\nD. n^2 + 1\nE. 2n + n^2\n\n### Answer:\nAnswer: D\nA: 2n = even\nB: 3n = even\nC: 3n + n^2 + 2 = even\nD: n^2 + 1 = odd\nE: 2n + n^2 = even\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain team has 16 members, including Joey. A three-member relay team will be selected as follows: one of the 16 members is to be chosen at random to run first, one of the remaining 15 members is to be chosen at random to run second, and one of the remaining 14 members is to be chosen at random to run third. What is the probability that Joey will be chosen to run second or third?\n\n### Options:\nA. 1/4\nB. 2/5\nC. 1/6\nD. 2/7\nE. 1/8\n\n### Answer:\nEach member has an equal probability to run second (1/16) or third (1/16).\nThe probability that Joey runs second or third is 1/16 + 1/16 = 1/8\nThe answer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJanuary 1, 2007 was Monday. What day of the week lies on Jan. 3, 2008?\n\n### Options:\nA. Monday\nB. Thursday\nC. Wednesday\nD. Friday\nE. Sunday\n\n### Answer:\nThe year 2007 is an ordinary year. So, it has 1 odd day.\nday of the year 2007 was Monday\nday of the year 2008 will be 3 days beyond Monday\nHence, It will be Thursday. answer : B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n4 men and 12 boys finish a piece of work in 4 days, 7 men and 6 boys do it in 5 days. The ratio between the efficiencies of a man and boy is?\n\n### Options:\nA. 18:19\nB. 17:19\nC. 15:19\nD. 18:14\nE. 18:11\n\n### Answer:\n4M + 12B ----- 4 days\n7M + 6B ------- 5 days\n16M + 48B = 35M + 30B\n18B = 19M => 5M = 6B\nM: B = 18:19\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOne morning after sunrise, Suresh was standing facing a pole. The shadow of the pole fell exactly to his right. To which direction was he facing?\n\n### Options:\nA. East\nB. West\nC. South\nD. North\nE. 2891\n\n### Answer:\nExplanation:\nSun rises in the east in the morning. Since the shadow of Suresh falls to his right. So he is facing South.\nAnswer: C) South\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSolve 7y \u2013 5 = 3y + 11\n\n### Options:\nA. 4\nB. 6(1/3)\nC. 7(1/3)\nD. 3\nE. 9(1/3)\n\n### Answer:\nSol.\n7y \u2013 5 = 3y + 11\n=> 7y \u2013 3y = 11 + 5\n=> 4y = 16 => x = 4\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nEvery year an amount increases by 1/8th of itself. How much will it be after two years if its present value is Rs.64000?\n\n### Options:\nA. 81000\nB. 29899\nC. 26798\nD. 27799\nE. 27781\n\n### Answer:\n64000* 9/8 * 9/8 = 81000.Answer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat will be the cost of building a fence around a square plot with area equal to 25 sq ft, if the price per foot of building the fence is Rs. 58?\n\n### Options:\nA. 1160\nB. 1251\nC. 1102\nD. 1352\nE. 1450\n\n### Answer:\nLet the side of the square plot be a ft.\na2 = 25 => a = 5\nLength of the fence = Perimeter of the plot = 4a = 20 ft.\nCost of building the fence = 20 * 58 = Rs. 1160.\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFesdus goes out cycling outdoors. He travels at an average speed of 3km/h, to the top of the hill where the midpoint of the trip is. Going down hill, Juan travels at an average speed of 9km/h. Which of the following is the closest approximation of Fesdus's average speed, in kilometers per hour, for the round trip?\n\n### Options:\nA. 4.2\nB. 4.5\nC. 7.6\nD. 3.6\nE. 2.2\n\n### Answer:\nSince we're not given a distance to work with, we can TEST any distance that we like. Here, since the speeds are 3 km/hour and 9 km/hour, using a multiple of both 3 and 9 would make the math easiest.\nLet's set the Distance up the hill at 36 km.\nSo, going uphill, we have....\nD = (R)(T)\n36 = (3)(T)\n36/3 = 13 = T\n13 hours to go uphill\nGoing downhill, we have....\nD = (R)(T)\n36 = (9)(T)\n36/9 = 4 = T\n4 hours to go downhill\nTotal Distance = 120 km\nTotal Time = 13+4 = 17 hours\nAverage Speed = 72/17 = 4.2 km/hour\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the average of first 4 multiples of 5?\n\n### Options:\nA. 10\nB. 12.5\nC. 22.5\nD. 31.3\nE. 40.8\n\n### Answer:\naverage = (5+10+15+20)/4 = 12.5\nAnswer is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA and B can complete a job in 30 and 20 days respectively. They start working together and B leaves 5 days before the work is finished. In how many days is the total work finished?\n\n### Options:\nA. 15\nB. 6\nC. 5\nD. 4\nE. 3\n\n### Answer:\nA and B can do the job in 30 and 20 days individually, so together they will take 30*20/(30 + 20) = 600/50 = 12 days.\nThe work that A can do in 5 days is 1/6th. So, A left when 5/6th of the work was done or A left after (5/6)*12 = 10 days\nTotal time taken = 10 + 5 = 15 days.\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRavi and Kavi start a business by investing \u00e2\u201a\u00b9 4000 and \u00e2\u201a\u00b9 72000, respectively. Find the ratio of their profits at the end of year.\n\n### Options:\nA. 2 : 28\nB. 5 : 28\nC. 7 : 18\nD. 1 : 18\nE. 3 : 18\n\n### Answer:\nRatio of profit = Ratio of investments\n= 4000 : 72000 = 1 : 18\nAnswer : D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMy brother is 3 years elder to me. My father was 28 years of age when my sister was born while my mother was 26 years of age when I was born. If my sister was 4 years of age of when my brother was born, then, what was the age of my father and mother respectively when my brother was born?\n\n### Options:\nA. 32 yrs, 23 yrs\nB. 32 yrs, 29 yrs\nC. 35 yrs, 29 yrs\nD. 35 yrs, 33 yrs\nE. none\n\n### Answer:\nSol.\nClearly, my brother was born 3 years before I was born and 4 years after my sister was born.\nSo, father's age when brother was born = (28 + 4) = 32 years.\nmother's age when was born = (26 - 3) years = 23 years.\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe Royal Hawaiian Hotel decorates its Rainbow Christmas Tree with non-flashing white lights and a series of colored flashing lights - red, blue, green, orange, and yellow. The red lights turn red every 20 seconds, the blue lights turn blue every 30 seconds, the green lights turn green every 45 seconds, the orange lights turn orange every 60 seconds, and yellow lights turn yellow every 1 minute and 20 seconds. The manager plugs the tree in for the first time on December 1st precisely at midnight and all lights begin their cycle at exactly the same time. If the five colored lights flash simultaneously at midnight, what is the next time E all five colored lights will all flash together at the exact same time?\n\n### Options:\nA. 0:03 AM\nB. 0:04 AM\nC. 0:06 AM\nD. 0:12 AM\nE. 0:24 AM\n\n### Answer:\nTime taken by each light to on\nRed = 20 secs\nBlue = 30 secs\nGreen = 45 secs\nOrange = 60 secs\nYellow = 80 secs\nWe need to take LCM to find the time all five colored lights will flash together.\nLCM = 720 secs\n=12 mins\n=0.12 AM\nAns = D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich of the following inequalities is always true for any real number 'a' and 'b'?\n\n### Options:\nA. |a+b| >= |(|a|-|b|)|\nB. |a-b| <= |(|a|-|b|)|\nC. |a-b| = |(|a|-|b|)|\nD. |a-b| >= |(|a|-|b|)|\nE. |a-b| <= |a|-|b|\n\n### Answer:\nThe answer here is D. One of the fundamental properties of absolute value is subadditivity, and this is a reverse triangle inequality, which is equivalent to subadditivity. So this means that difference of two any elements is something (some number) which is greater than or equal to the difference of the each element taken on itself separately, i.e. |a-b| >= |(|a|-|b|)|\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a card is drawn from a well shuffled pack of cards, the probability of drawing a spade or a king is\n\n### Options:\nA. 4/17\nB. 4/16\nC. 4/15\nD. 4/13\nE. 4/12\n\n### Answer:\nP(S\u1d1cK) = P(S) + P(K) - P(S\u2229K), where S denotes spade and K denotes king.\nP(S\u1d1cK) = 13/52 + 4/52 - 1/52\n= 4/13\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nBalloons are bought at 8 for Rs.10/- and sold at 10 for Rs.8/-. Find the gain or loss percentage?\n\n### Options:\nA. 36% Loss\nB. 36% Gain\nC. 18% Loss\nD. 18% Gain\nE. 19% Loss\n\n### Answer:\nExplanation:\n8 Balloons -----> Rs.10/-\n10 Balloons ----> Rs.8/-\nNote: In every time same in the cost price articles and selling price articles.\n10(8 10) ==> 80 100 = Cost price\n8(10 8) ==> 80 64 = Selling price\nThen, 36/100 \u00d7 100 = 36 % Loss\nAnswer: Option A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe list price of an article is Rs.65. A customer pays Rs.56.16 for it. He was given two successive discounts, one of them being 10%. The other discount is?\n\n### Options:\nA. 3%\nB. 4%\nC. 5%\nD. 6%\nE. 7%\n\n### Answer:\n65*(90/100)*((100-x)/100) = 56.16\nx = 4%\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAt a conference table, 5 employees gather around a table. One of the employees is the manager and he sits at the head of the table. Two of the employees sit on either side of the table. How many different seating arrangements can be made with these five employees?\n\n### Options:\nA. 5\nB. 10\nC. 24\nD. 32\nE. 120\n\n### Answer:\nHead's sit is fixed. Now 4 people is left with 4 seats.\n4 people can sit on 4 seats in 4! ways or 24 ways.\nAns is C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe ratio between the speeds of two trains is 7: 9. If the second train runs 540 kms in 3 hours, then the speed of the first train is ?\n\n### Options:\nA. 140 km/hr\nB. 130 km/hr\nC. 110 km/hr\nD. 120 km/hr\nE. None of these\n\n### Answer:\nExplanation:\nLet the speeds of two trains be 7X and 9X km/hr.\n9/X=540/3=>X=20Km/hr\nSo speed of first train is 20*7 = 140 km/hr\nOption A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat percent is 36 paisa's of 12 rupees?\n\n### Options:\nA. 2 %\nB. 3 %\nC. 4 %\nD. 5 %\nE. 6 %\n\n### Answer:\n12 Rupees = 1200 paisa's\n36/1200 \u00d7 100 = 3/12\n12/3 = 3 %\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA magician holds one six-sided die in his left hand and two in his right. What is the probability the number on the dice in his left hand is greater than the sum of the dice in his right?\n\n### Options:\nA. 7/108\nB. 5/54\nC. 1/9\nD. 2/17\nE. 1/4\n\n### Answer:\nThe least sum of the numbers of the two dice in the right hand is 2. The maximum sum of the numbers on these two dice can be 5, for the left hand dice to be able to have a greater number.\nTherefore the number on the dice in the left hand must be 3 or more.\nNumber of ways to get a sum of 2 with the two dice in the right hand= 1\nNumber of ways to get a sum of 3 with the two dice in the right hand= 2\nNumber of ways to get a sum of 4 with the two dice in the right hand= 3\nNumber of ways to get a sum of 5 with the two dice in the right hand= 4\nTherefore required probability = P(two right dice have a sum of 2)*P(left dice has 3) + P(right dice have sum of 2 or 3)*P(left dice has 4) + P(two right dice have a sum of 2,3, or 4)*P(left dice has 5) + P(two right dice have a sum of 2,3,4,or 5)*P(left dice has 6)\n= (1/36)*(1/6) + (3/36)*(1/6) + (6/36)*(1/6) + (10/36)*(1/6)\n= (1/216) * (1+3+6+10)\n= 20/216\n= 5/54\nOption B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the average of four tenths and two thousandths\n\n### Options:\nA. 0.2022\nB. 0.3325\nC. 0.201\nD. 0.2012\nE. 0.2114\n\n### Answer:\nExplanation:\nFour tenths = 0.4\ntwo thousandths = 0.002\nThe average is (0.4 + 0.002)/2 = 0.201\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nf, b, c, and d are positive integers. If the remainder is 9 when f is divided by b, and the remainder is 5 when c is divided by d, which of the following is NOT a possible value for b + d?\n\n### Options:\nA. 20\nB. 19\nC. 18\nD. 16\nE. 15\n\n### Answer:\nWhen f is divided by b remainder is 9 that means b is greater than or equals to 10, similarly d is greater than or equals to 6.\nb + d cannot be 15, hence E is the answer.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n10 machines, each working at the same constant rate, together can complete a certain job in 12 days. How many additional machines, each working at the same constant rate, will be needed to complete the Job in 8 days?\n\n### Options:\nA. 2\nB. 3\nC. 4\nD. 5\nE. 8\n\n### Answer:\nAnother solution which is faster is Since each machine works at a constant rate. The time needs to bought down from 12 to 8. So the new time is 2/3 of the original time. Thus to achieve this we need the rate to be 3/2 of original.\nSo 3/2* 10 = 15\nSo we need 15-10 = 5 more machines.\nAnswer : D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA group of 4 students bought movie tickets in one row next to each other. If Bob and Lisa are in this group, what is the probability that Bob and Lisa will each sit next to only one of the three other students from the group?\n\n### Options:\nA. 5.55%\nB. 16.67%\nC. 15.75%\nD. 20.45%\nE. 25%\n\n### Answer:\nThe question basically asks about the probability that Bob and Lisa sit at the ends.\nThe total # of sitting arrangements is 4!.\nDesired arrangement is either BYZL or LYZB. Now, YZ can be arranged in 2! ways, therefore total # of favorable arrangements is 2*2!.\nP=(favorable)/(total)=(2*2!)/4!=1/6.\nAnswer: B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a and b are positive integers, and a=5b+20, the greatest common divisor of a and b CANNOT be\n\n### Options:\nA. 2\nB. 4\nC. 5\nD. 6\nE. 10\n\n### Answer:\nIf b is 2, 4, 5, or 10, then GCD of a and b is 2, 4, 5, and 10 respectively. So, by POE the answer must be D.\nStill: if b is a multiple of 6, then a is 20 greater than a multiple of 6, so not a multiple of 6, so both of them cannot be divisive by 6.\nAnswer: D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the average (arithmetic mean) of 8 consecutive odd integers is 414, then the least of these integers is\n\n### Options:\nA. a) 407\nB. b) 518\nC. c) 519\nD. d) 521\nE. e) 525\n\n### Answer:\nA very helpful rule to know in arithmetic is the rule that in evenly spaced sets, average = median. Because the average will equal the median in these sets, then we quickly know that the median of this set of consecutive odd integer numbers is 414.\nThere are 8 numbers in the set, and in a set with an even number of terms the median is just the average of the two most median terms (here the 4th and 5th numbers in the set). This means that numbers 4 and 5 in this set are 413 and 415. Because we know that number 4 is 413, we know that the smallest number is 3 odd numbers below this, which means that it is 3*2 = 6 below this (every odd number is every other number). Therefore 413-6 = 407, answer choice A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA bat is bought for Rs.400 and sold at a gain of 20% find its selling price\n\n### Options:\nA. Rs.500/-\nB. Rs.480/-\nC. Rs.430/-\nD. Rs.490/-\nE. Rs.500/-\n\n### Answer:\n100 % ------> 400 (100 * 4 = 400)\n120 % ------> 480 (120 * 4 = 480)\nSelling price = Rs.480/-\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA 90 cm long wire is to be cut into two pieces so that one piece will be 2/7th of the other, how many centimeters will the shorter piece be?\n\n### Options:\nA. A)73\nB. B)20\nC. C)83\nD. D)21\nE. E)52\n\n### Answer:\nExplanation:\n1: 2/7 = 7: 2\n2/9 * 90 = 20\nAnswer: Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nif 5+6+4=010530\nand 2+4+8=021040\nand 3+5+9=021155\nand 4+6+7=020954....\nthen 2+7+5=??????\n\n### Options:\nA. 051070\nB. 051770\nC. 051074\nD. 151070\nE. 071070\n\n### Answer:\nif 5+6+4=010530\nand 2+4+8=021040\nand 3+5+9=021155\nand 4+6+7=020954....\nthen 2+7+5=??????\n051070\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe smallest number which when diminished by 7, is divisible by 12, 16, 18, 21 and 28 is\n\n### Options:\nA. 2333\nB. 1015\nC. 2683\nD. 2693\nE. 1113\n\n### Answer:\nExplanation:\nRequired Number = (L.C.M of 12, 16, 18,21,28)+7\n= 1008 + 7\n= 1015\nAnswer: B) 1015\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA basketball team composed of 12 players scored 100 points in a particular contest. If none of the individual players scored fewer than 7 points, what is the greatest number of points T that an individual player might have scored?\n\n### Options:\nA. 7\nB. 13\nC. 16\nD. 21\nE. 23\n\n### Answer:\nGeneral rule for such kind of problems:\nto maximize one quantity, minimize the others;\nto minimize one quantity, maximize the others.\nThus to maximize the number of points of one particular player minimize the number of points of all other 11 players.\nMinimum number of points for a player is 7, so the minimum number of points of 11 players is 7*11=77.\nTherefore, the maximum number of points T for 12th player is 100-77=23.\nAnswer: E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA team scored a total of 126 points. If each player on the team scored at least 14 points, then what is the greatest possible number of players on the team?\n\n### Options:\nA. A)6\nB. B)7\nC. C)8\nD. D)9\nE. E)10\n\n### Answer:\n126/14=9 plus remainder.\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man whose speed is 4.5 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 1.5 kmph, find his average speed for the total journey?\n\n### Options:\nA. 8\nB. 4\nC. 3\nD. 2\nE. 6\n\n### Answer:\nM = 45\nS = 1.5\nDS = 6\nUS = 3\nAS = (2 * 6 * 3) /9 = 4\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the number of square tiles to cover the floor of a room measuring 4.5 m * 9.5 m leaving 0.25 m space around the room. A side of square tile is given to be 25 cms?\n\n### Options:\nA. 422\nB. 576\nC. 429\nD. 428\nE. 413\n\n### Answer:\nFloor area to be covered by tiles = 4 * 9 = 36\ntiles area = 0.25 * 0.25 =0.0625\nNo. of tiles = 36/0.0625 = 576\nAnswer : B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nReena took a loan of Rs. 1400 with simple interest for as many years as the rate of interest. If she paid Rs. 432 as interest at the end of the loan period, what was the rate of interest?\n\n### Options:\nA. 8.55%\nB. 5.55%\nC. 4.55%\nD. 6.55%\nE. 7.55%\n\n### Answer:\nLet rate = R% and time = R years.\nThen, (1400 * R * R) / 100 = 432\n14R2 = 432\nR2 = 30.8 => R = 5.55\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a shower, 6 cm of rain falls. The volume of water that falls on 1.5 hectares of ground is:\n\n### Options:\nA. 75 cu. m\nB. 900 cu. m\nC. 750 cu. m\nD. 9000 cu. m\nE. 7.50 cu. m\n\n### Answer:\n1 hectare = 10000 sq mtr\nThe volume of water that falls on 1.5 hectares of ground = 0.06*1.5*10000 = 900 cub mtr .\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?\n\n### Options:\nA. 126\nB. 217\nC. 150\nD. 277\nE. 212\n\n### Answer:\nSpeed=(60 * 5/18) m/sec = (50/3) m/sec Length of the train = (Speed x Time) = (50/3 * 9) m = 150 m. Answer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA dishonest shopkeeper professes to sell pulses at the cost price, but he uses a false weight of 970gm. for a kg.His gain is \u2026%.\n\n### Options:\nA. 3.09%\nB. 5.36%\nC. 4.26%\nD. 6.26%\nE. 7.26%\n\n### Answer:\nHis percentage gain is 100*30/970 as he is gaining 30 units for his purchase of 970 units.\nso 3.09%.\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe sum of a number and the number preceding it is 33. By how much is two less than six times the\nnumber?\n\n### Options:\nA. 196\nB. 94\nC. 90\nD. 100\nE. 120\n\n### Answer:\ntwo numbers must be 16 and 17\n16+17=33\nrequired number is 17\nsix times of this number= 6*17=102\ntwo less than 102= 102-2= 100\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n(7 + 7 + 7 \u00f7 7) / (5 + 5 + 5 \u00f7 5) = ?\n\n### Options:\nA. 1\nB. 1 / 5\nC. 15 / 11\nD. 3 / 11\nE. None\n\n### Answer:\nAnswer\nGiven expression = (7 + 7 + 7 \u00f7 7) / (5 + 5 + 5 \u00f7 5)\n= (14 + 1) / (10 + 1)\n=15 / 11\nOption: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many diagonals does a 63-sided convex polygon have?\n\n### Options:\nA. 1890\nB. 1953\nC. 3780\nD. 3843\nE. 3906\n\n### Answer:\nA 63-sided convex polygon has 63 vertices.\nIf we examine a single vertex, we can see that we can connect it with 60 other vertices to create a diagonal. NOTE: there are 60 options because we can't connect the vertex to ITSELF, and we can't connect it to its ADJACENT vertices, since this would not create a diagonal.\nIf each of the 63 vertices can be connected with 60 vertices to create a diagonal then...\n...the total number of diagonals = (63)(60) = 3780\nHOWEVER, before we select answer choice C, we must recognize that we have counted every diagonal TWICE.\nFor example, we might connect vertex A with vertex F and count that as 1 diagonal, and at the same time we connect vertex F with vertex A and count that as 1 diagonal. Of course these diagonals are the SAME.\nTo account for counting each diagonal twice, we must divide 3780 by 2 to get: 1890\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are three foam generators in the factory, each of the first two can generate 14 liters of foam in one hour and the third can generate 20 liters in an hour. The three generators start working together at the same time and after one hour and a half one of the first generators stops working and two hours after that the third generator stops working and only one generator is left. If 5 hours after they all started to work the last generator stops working, how many liters of foam were generated?\n\n### Options:\nA. 120.\nB. 132.\nC. 146.\nD. 161.\nE. 166.\n\n### Answer:\nLet the foam generators capacity be -\nA = 14 lit/hr\nB = 14 lit/hr\nC = 20 lit/hr\nTotal foam generation in 1 hour will be 48 lit ( 14 + 14 + 20 ) ; since in 1 and 1/2 hr they will generate 48 + 24 => 72 litres...\nNow one of the first generators stops working ( Say A stops working ) , so we have -\nB = 14 lit/hr\nC = 20 lit/hr\nTotal foam generation in 2 hour will be 68 litres {2 (14+20)}\nThe third generator stops working and now only B works for the remaining time 1 and 1/2 ( 5 - 1 and 1/2 - 2 )...\nFoam generated by B will be 3/2 * 14 => 21 litres\nSo, total foam generated will be 161 Litres ( 72 + 68 + 21 ) ; hence answer will be (D)\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the price of gold increases by 40%, find by how much the quantity of ornaments must be reduced, so that the expenditure may remain the same as before?\n\n### Options:\nA. 331/8%\nB. 26.67%\nC. 28.5%\nD. 332/3%\nE. 131/3%\n\n### Answer:\n100\n140\n------\n140-------40\n100-------? => 28.5%\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nGrace packed 5 pairs of shoes, 3 pairs of pants, 8 shirts, and 3 jackets for her business trip. If an outfit consists of one of each item of clothing except shirts, of which she will wear 2, how many different outfits F can does Grace have available during her trip?\n\n### Options:\nA. 2,520\nB. 1,260\nC. 620\nD. 360\nE. 120\n\n### Answer:\nThe idea is to multiply the number of possibilities for each item of clothing with the different items. For the shirts you essentially choose 2 out of 8 so you should use the combination forumla (don't know how to use math symbols here).\nThis gives you F=5 x 3 x 28 x 3 = 1'260. Hence, solution B is correct.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAnand and Deepak started a business investing Rs. 6,000 and Rs. 8,000 respectively. Out of a total profit of Rs.4,600. Deepak's share is?\n\n### Options:\nA. s. 2600.31\nB. s. 2628.57\nC. s. 2450.32\nD. s. 3400.41\nE. s. 2400.32\n\n### Answer:\nRatio of their shares = 6000 : 8000 = 3 : 4\nDeepak's share = Rs. (4600 * 4/7) = Rs. 2628.57 ANSWER \"B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nCarina has 115 ounces of coffee divided into 5- and 10-ounce packages. If she has 2 more 5-ounce packages than 10-ounce packages, how many 10-ounce packages does she have?\n\n### Options:\nA. 5\nB. 7\nC. 6\nD. 4\nE. 3\n\n### Answer:\nLets say 5 and 10 ounce packages be x and y respectively.\nGiven that, 5x+10y=115 and x=y+2. What is the value of y.\nSubstituting the x in first equation, 5y+10+10y=85 ->y=105/15.=7\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf two dice are thrown together, the probability of getting a doublet on the dice is\n\n### Options:\nA. 1/6\nB. 1/5\nC. 1/4\nD. 1/3\nE. 1/2\n\n### Answer:\nThe number of exhaustive outcomes is 36.\nLet E be the event of getting doublet on the dies is 6/36 = 1/6\nP(E) = 1/6.\nA)\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich of the following is closer to (22!+21!)/(22!-21!)?\n\n### Options:\nA. 49\nB. 36\nC. 1\nD. 16\nE. 25\n\n### Answer:\nNotice that 22! = (22)(21!), so we can factor out 21! from top and bottom.\n(22!+21!)/(22!-21!)=[21!(22+1)]/[21!(22-1)]\n= (22+1)/(21-1)\n= 23/21\n\u2248 1\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man has Rs. 480 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?\n\n### Options:\nA. 90\nB. 94\nC. 96\nD. 97\nE. 99\n\n### Answer:\nLet number of notes of each denomination be x.\nThen x + 5x + 10x = 480\n16x = 480\nx = 30.\nHence, total number of notes = 3x = 90.\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTom drives from town T to town B, driving at a constant speed of 60 miles per hour. From town B Tom immediately continues to town C. The distance between T and B is twice the distance between B and C. If the average speed of the whole journey was 36 mph, then what is Tom's speed driving from B to C in miles per hour?\n\n### Options:\nA. 12\nB. 20\nC. 24\nD. 30\nE. 36\n\n### Answer:\nLet's assume that it takes 4 hours to go from point T to B. Then the distance between them becomes 240 which makes distance between B and C 120. (240+120)/(4+x) gives us the average speed which is 36. You find x=6. So the question simplifies itself to 120/6=20\nHence the answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA town's oldest inhabitant is x years older than the sum of the ages of the Lee triplets. If the oldest inhabitants is now J years old, how old will one of the triplets W be in 20 years?\nJ-X-40/3 is my answers.\nJ = X + L + L + L is the initial situation\nAfter 20 years\nJ + 20 = X + L + L + L + 60 ...20 years for each triplet so 60 years totally.\nJ - X - 40/ 3 = L is my answer.\nWhat wrong am i doing ? Since the age asked is after 20 years i also consider adding 20 years to J .\n\n### Options:\nA. (J - 50)/3\nB. 3(J + 20)/x\nC. (J + x - 50)/3\nD. (J - x + 60)/3\nE. (J + x - 20)/3\n\n### Answer:\nhere it goes:\nOldest inhabitant = sum of age of triplets + X\nJ = 3L + X so L = (J - X)/3\nAfter 20 years = L + 20\n= (J - X)/3 + 20\nW= (J - X + 60)/3=D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a stack of cards, 9 cards are blue and the rest are red. If 2 cards are to be chosen at random from the stack without replacement, the probability that the cards chosen will both be blue is 9/11. What is the number of cards in the stack?\n\n### Options:\nA. 10\nB. 11\nC. 12\nD. 15\nE. 18\n\n### Answer:\nThis question can be solved by TESTing THE ANSWERS.\nWe're told that we have 9 blue cards and an unknown number of red cards. We're also told that if 2 cards are to be chosen at random from the stack WITHOUT replacement, then the probability that the cards chosen will BOTH be BLUE is 9/11. We're asked for the TOTAL number of cards.\nNormally, when TESTing THE ANSWERS, we should start with either B or D. Answer B looks easier, so let's start there.\nAnswer A: 10 total cards\nWith 10 total cards, and 9 blue cards, the probability of pulling two blue cards is...\n(9/10)(8/9) = 72/90~ 9/11\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAt a conference, the only events scheduled for the day are seminars and breaks. All seminars are the same length and are 10 times as long as each break. A break must be between two consecutive seminars. If the first seminar begins at 9:00 a.m. and the third one ends at 11:20 a.m., how long will the conference last if there are a total of 6 seminars that day?\n\n### Options:\nA. hours and 15 minutes\nB. hours and 20 minutes\nC. hours and 25 minutes\nD. hours and 30 minutes\nE. hours and 35 minutes\n\n### Answer:\nWell its like this S B S B S B S B S B S\nthe interval between 9 am to 11:40 am is 160 min having 3 seminars and 2 breaks .If 1 break is of 5 min than time for 3 seminars = 160 - 2*5=150\nTime of 1 seminar =150 /3=50 min .\nSo calculating for 6 seminars and 5 breaks ,total time comes out to be 5 hrs and 20 min .\nAnswer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many words, with or without meaning, can be formed using all letters of the word EQUATION using each letter exactly once?\n\n### Options:\nA. 38,320\nB. 39,320\nC. 40,320\nD. 38,400\nE. 39,400\n\n### Answer:\nThe Word EQUATION has exactly 8 letters which are all different.\nTherefore the number of words that can be formed = Number of permutations of 8 letters taken all at a time.\n= P (8, 8) = 8!\n= 8 \u00d7 7 x 6 \u00d7 5 x 4 x 3 x 2 \u00d7 1\n= 40,320\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA shopkeeper buys mangoes at the rate of 4 a rupee and sells them at 3 a rupee. Find his net profit or loss percent?\n\n### Options:\nA. 33 1/8 %\nB. 33 8/3 %\nC. 33 1/3 %\nD. 93 1/3 %\nE. 43 1/3 %\n\n### Answer:\nThe total number of mangoes bought by the shopkeeper be 12.\nIf he buys 4 a rupee, his CP = 3\nHe selling at 3 a rupee, his SP = 4\nProfit = SP - CP = 4 - 3 = 1\nProfit Percent = 1/3 * 100 = 33 1/3 %\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf A and B are two prime numbers bigger than 2, which of the following can be true?\n(1) A + B is an even number.\n(2) A x B is also a prime number.\n(3) A^B is also a prime number.\n\n### Options:\nA. 1 only.\nB. 2 only.\nC. 3 only.\nD. 2 and 3 only.\nE. 1, 2 and 3.\n\n### Answer:\nAnswer is D : 2 and 3 only\n(1) A + B is an even number. : All primes beyond 2 are odd, so odd+odd = even, so true\n(2) A x B is also a prime number. : Beats the property of primes, so false\n(3) A^B is also a prime number. : Beats the property of primes, so false\nAns :A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nElvin's monthly telephone bill is the sum of the charge for the calls he made during the month and a fixed monthly charge for Internet service. Elvin's total telephone bill for January was $46 and Elvin's total telephone bill for February was 76$. If Elvin's charge for the calls he made in February was twice the charge for the calls he made in January, what is Elvin's fixed monthly charge for Internet service?\n\n### Options:\nA. $5\nB. $10\nC. $14\nD. $16\nE. $28\n\n### Answer:\nBill = Fixed Charge + Charge of Calls made\nin Jan, Bill = Fixed Charge(Let, y) + Charge of calls made in Jan (Let, x) = $46\nin Feb, Bill = Fixed Charge (Let, y) + Charge of calls made in Feb (Then, 2x) = $76\ni.e. x+y = 46\nand 2x+y = 76\nTake the difference if two equations\ni.e. (2x+y) - (x+y) = 76 - 46\ni.e. x = 30\ni.e. Fixed Monthly Charge, y = 16\nAnswer: Option\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFor positive integers k and n, the k-power remainder of n is defined as r in the following equation:\nn = k^w + r, where w is the largest integer such that r is not negative. For instance, the 3-power remainder of 13 is 4, since 13 = 3^2 + 4. In terms of k and w, what is the largest possible value of r that satisfies the given conditions?\n\n### Options:\nA. (k \u2013 1)k^w \u2013 1\nB. k^w \u2013 1\nC. (k + 1)k^w \u2013 1\nD. k^(w+1) \u2013 1\nE. (k + 1)k^(w+1) \u2013 1\n\n### Answer:\nn = k^w + r, where w is the largest integer such that r is not negative\nThis means k^w <= n, and k^(w+1) > n\nSo n lies between k^w and k^(w+1)\nNow, r = n - k^w, which means r is the distance between n and k^w\nThis distance is maximised at the highest possible value of n, which can be just below k^(w+1)\nSo n = k^(w+1) - 1, as n is an integer\nTherefore, highest value of r = n - k^w = k^(w+1) - 1 - k^w = (k - 1)k^w - 1\nA is the correct\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe H.C.F of two numbers is 8. Which one of the following can never be their L.C.M?\n\n### Options:\nA. 8\nB. 12\nC. 60\nD. 72\nE. None\n\n### Answer:\nSolution\nH.C.F of two numbers divides their L.C.M exactly.\nClearly, 8 is not a factor of 60.\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSum of the squares of three numbers is 522 and the sum of their products taken two at a time is 131. Find the sum?\n\n### Options:\nA. 20\nB. 22\nC. 25\nD. 27\nE. 28\n\n### Answer:\n(a + b + c)2 = a2 + b2 + c2 + 2(ab +bc + ca) = 522 + 2* 131\na + b + c = \u221a784 = 28\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe value of a 10.5% stock, in which an income of Rs.756 is derived by investing Rs.9000, brokerage being% is :\n\n### Options:\nA. 110.43\nB. 120.65\nC. 124.75\nD. 134.56\nE. 165.9\n\n### Answer:\nFor an income of Rs.756, investment = Rs.9000\nFor an income of Rs., investment = = Rs.125\nFor a Rs.100 stock, investment = Rs.125.\nMarket value of Rs. 100 stock = = Rs. 124.75\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nGeorge does 3/5th of a piece of work in 9 days. He then calls in Paul , and they finish the work in 4 days. How long would Paul take to do the work by himself?\n\n### Options:\nA. 30\nB. 40\nC. 50\nD. 60\nE. 70\n\n### Answer:\n100% work will be done by George in 15 days\n(1/15)9+(1/15+1/x)4=1\nsolving this eqn.\nwe get x=30\nhence Paul take to do the work in 30 days\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe greatest possible length which can be used to measure exactly the length 6m, 4m 20cm, 4m is\n\n### Options:\nA. 20\nB. 27\nC. 35\nD. 87\nE. 98\n\n### Answer:\nExplanation:\nRequired Length = H.C.F of 600 cm, 420 cm and 400 c\n= 20 cm.\nAnswer: A) 20 cm\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMixture A is 10 percent alcohol, and mixture B is 40 percent alcohol. If the two are poured together to create a 4-gallon mixture that contains 20 percent alcohol, approximately how many gallons of mixture A are in the mixture?\n\n### Options:\nA. 1.6\nB. 1.7\nC. 1.8\nD. 1.9\nE. 2.0\n\n### Answer:\n(40-20)/(20-15) = Qa/Qb\n20/10 = Qa/Qb\n2/1 = Qa/Qb\nQa = (2/5) * 4 = 8/5 = 1.6 approx\nAnswer : A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain company has budgeted $1380 for entertainment expenses for the year, divided into 12 equal monthly allocations. If by the end of the third month, the total amount spent on entertainment was $400, how much was the company under budget or over budget?\n\n### Options:\nA. $55 under budget\nB. $30 under budget\nC. $30 over budget\nD. $55 over budget\nE. $90 over budget\n\n### Answer:\nThe budget for 3 months is (3/12)*$1380 = $345\nThe company is $55 over budget.\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo trains, each 100 m long, moving in opposite directions, cross other in 5 sec. If one is moving twice as fast the other, then the speed of the faster train is?\n\n### Options:\nA. 22\nB. 96\nC. 60\nD. 88\nE. 12\n\n### Answer:\nLet the speed of the slower train be x m/sec.\nThen, speed of the train = 2x m/sec.\nRelative speed = ( x + 2x) = 3x m/sec.\n(100 + 100)/5 = 3x => x = 40/3.\nSo, speed of the faster train = 80/3 = 80/3 * 18/5 = 96 km/hr.\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA rectangular carpet has an area of 60 sq.m. If its diagonal and longer side together equal 5 times the shorter side, the length of the carpet is:\n\n### Options:\nA. 5m\nB. 12m\nC. 13m\nD. 14.5m\nE. 15.5m\n\n### Answer:\nLet, length= x meters and breadth= y meters\nThen xy=60 and (x2+y2) + x= 5\nTherefore, x=60 and (x2+y2)= (5y-x)2\nOr xy=60 and 24y2-10xy=0.\nTherefore, 24y2-10*60=0 or y2= 25 or =5.\nTherefore, x= (60/5)m= 12m. So, length of the carpet = 12m\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe tax on a commodity is diminished by 20% and its consumption increased by 15%. The effect on revenue is?\n\n### Options:\nA. 7% decrease\nB. 8% decrease\nC. 9% decrease\nD. 6% decrease\nE. 4% decrease\n\n### Answer:\n100 * 100 = 10000\n80 * 115 = 9200\n-----------\n10000-----------800\n100-----------? => 8% decrease\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn Plutarch Enterprises, 70% of the employees are marketers, 10% are engineers, and the rest are managers. Marketers make an average salary of $50,000 a year, and engineers make an average of $80,000. What is the average salary for managers if the average for all employees is also $80,000?\n\n### Options:\nA. $80,000\nB. $130,000\nC. $240,000\nD. $370,000\nE. $320,000\n\n### Answer:\nFor sake of ease, let's say there are 10 employees: 7 marketers, 1 engineers, and 2 manager.\nAverage company salary * Number of employees = Total company salary\n>>> $80,000 * 10 = $800,000\nSubtract the combined salaries for the marketers (7 * $50,000) and the engineers ( $80,000)\n>>> $800,000 - $350,000 - $80,000 = $370,000.\nThe correct answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSix computers, each working at the same constant rate, together can process a certain amount of data in 6 days. How many additional computers, each working at the same constant rate, will be needed to process the same amount of data in 4 days?\n\n### Options:\nA. 3\nB. 5\nC. 6\nD. 9\nE. 12\n\n### Answer:\nExplanation: If six computers require 6 days to process the data, thats\na total of 36 computer-days the product of 6 and 6. If you change the number\nof computers or the number of days, 36 will have to remain the product, whether\nthat means 36 days of one computer or one day with 36 computers.\nIn 4 days, the number of computers is:\n4c = 36\nc = 9\n9 computers is 3 more than the 6 that it took to do the job in 6 days, so\nthe correct choice is (A).\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe length of a rectangle is three - fifths of the radius of a circle. The radius of the circle is equal to the side of the square, whose area is 1225 sq.units. What is the area (in sq.units) of the rectangle if the rectangle if the breadth is 10 units?\n\n### Options:\nA. 240 sq.units\nB. 140 sq.units\nC. 120 sq.units\nD. 130 sq.units\nE. 150 sq.units\n\n### Answer:\nGiven that the area of the square = 1600 sq.units\n=> Side of square = \u221a1600 = 40 units\nThe radius of the circle = side of the square = 35 units Length of the rectangle = 3/5 * 40 = 24units\nGiven that breadth = 10 units\nArea of the rectangle = lb = 24* 10 = 240 sq.units\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man has Rs. 480 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?\n\n### Options:\nA. 45\nB. 60\nC. 75\nD. 90\nE. 80\n\n### Answer:\nBy verifying options ,we can solve this problem.\nGiven that no. of denominations are equal i.e.,3(like one rupee,5 rupee and 10 rupee notes)\n45/3=15 i.e 15*1+15*5+15*10 =240\n...\n..\n90/3=30 i.e.,30*1+30*5+30*10 =480\nanswer is 90.\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nCompound X contains elements A and B at an approximate ratio, by weight, of 2:10. Approximately how many grams of element B are there in 300 grams of compound X?\n\n### Options:\nA. 54\nB. 162\nC. 250\nD. 270\nE. 322\n\n### Answer:\ntotal number of fractions =2+10=12\nelement B constitutes =10 out of 12 parts of X\nSo in 300 gms of X have 300*10/12=250 gms of B\nand 300-250=50 gms of A.\ncross check:- A/B = 50/250 =2/10 (as given)\nAns C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nChoose any 4 desserts from a menu of 10?\n\n### Options:\nA. 120\nB. 140\nC. 180\nD. 210\nE. 240\n\n### Answer:\n10c4 = 210\nAnswer is D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man buys Rs. 20 shares paying 9% dividend. The man wants to have an interest of 12% on his money. The market value of each share is:\n\n### Options:\nA. 12\nB. 13\nC. 14\nD. 15\nE. 18\n\n### Answer:\nDividend on Rs 20 = 9/100*20 = 9/5\nis 12 income 100\n9/5 is an income on Rs (100/12*9/5) = Rs 15\nANSWER D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA garrison of 2000 men has provisions for 54 days. At the end of 15 days, a reinforcement arrives, and it is now found that the provisions will last only for 20 days more. What is the reinforcement?\n\n### Options:\nA. 1898\nB. 9801\nC. 1987\nD. 1900\nE. 8373\n\n### Answer:\n2000 ---- 54\n2000 ---- 39\nx ----- 20\nx*20 = 2000*39\nx = 3900\n2000\n-------\n1900\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe cross-section of a cannel is a trapezium in shape. If the cannel is 16 m wide at the top and 4 m wide at the bottom and the area of cross-section is 700 sq m, the depth of cannel is?\n\n### Options:\nA. 76\nB. 28\nC. 27\nD. 80\nE. 70\n\n### Answer:\n1/2 * d (16 + 4) = 700\nd = 70\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA paint crew gets a rush order to paint 80 houses in a new development. They paint the first y houses at a rate of x houses per week. Realizing that they'll be late at this rate, they bring in some more painters and paint the rest of the houses at the rate of 1.25x houses per week. The total time E it takes them to paint all the houses under this scenario is what fraction of the time it would have taken if they had painted all the houses at their original rate of x houses per week?\n\n### Options:\nA. 0.8(80 \u2013 y)\nB. 0.8 + 0.0025y\nC. 80/y \u2013 1.25\nD. 80/1.25y\nE. 80 \u2013 0.25y\n\n### Answer:\nThis may be a case of bad numberpicking but it worked for me.\n80 houses. Let's say that y=40 houses are painted at the rate x=10 houses per week <=> 1/10 week per house. 40*1/10 = 4 houses per week will be painted at this rate.\n80-y = 80-40 = 40 houses are to be painted at the faster rate. X*1,25=12,5 houses per week <=> 1/12,5 weeks per house * 40 houses = 40/12,5 = 80/25 = 320/100 = 3,2 weeks.\nWhich means finishing all houses at normal rate E=> 2*4 = 8 weeks. Faster rate = 4+3,2 = 7,2 weeks.\n7,2/8 = 9/10 = 0,9. Insert y=40 in equations and it is clear that only (B) gives us 0,9.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA basketball team scored x points per game in its first n games of the season, and in all the following games it scored an average (arithmetic mean) of y points per game. What was the average number of points per game in its first n + 7 games?\n\n### Options:\nA. x + 3y/(n + 3)\nB. x + y/(n + 3)\nC. (x + 3y)/(n + 3)\nD. (nx + 3y)/(n + 7)\nE. (3x + ny)/(n + 3)\n\n### Answer:\nTotal points in first n games = nx\nTotal marks in next 3 games is 3y\nSo, Average marks in n + 7 games = (nx+3y)/(n+7)\nHence, correct answer will be (D)\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 27, then how old is B?\n\n### Options:\nA. 76 years\nB. 88 years\nC. 55 years\nD. 10 years\nE. 15 years\n\n### Answer:\nLet C's age be x years.\nThen, B's age = 2x years.\nA's age = (2x + 2) years.\n(2x + 2) + 2x + x = 27\n5x = 25 => x = 5\nHence, B's age = 2x = 10 years.Answer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAlice and Bob race around a running track. Alice runs at a constant rate of one lap every 5 minutes and Bob runs at a constant rate of one lap every 6 minutes. If they both start at the same time, how many minutes will it take for Alice to get exactly one lap ahead of Bob?\n\n### Options:\nA. 30\nB. 32\nC. 35\nD. 36\nE. 40\n\n### Answer:\nLet x be the number of minutes it takes for Alice to get one lap ahead.\nThen Alice ran x/5 laps and Bob ran x/6 laps.\nx/5 = 1+x/6\n6x=30+5x\nx=30\nThe answer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThree cars A,B and C started at same point and time. After A reach 50 km, B and C are backward by 10km and 20 km. When B reach 200km, find the position of A and C?\n\n### Options:\nA. 240 and 160km\nB. 170 and 230 km\nC. 180 and 240 km\nD. 235 and 165 km\nE. 250 and 150 km\n\n### Answer:\nExplanation:\nA:B = 50 : 40 = 5 : 4\nA:C = 50 : 30 = 5 : 3\n=>B:C = 4:3\nWhen B covers 40 km , C Covers 30 km\nWhen B covers 200 km , C Covers\n=> 150 km\nWhen B covers 40 km , A Covers 50 km\nWhen B covers 200 km , A Covers\n=> 250 km\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA bag contains 5 white balls, 4 black balls, and 3 red balls. One by one, three balls are drawn out without replacement. What is the probability that the third ball is red?\n\n### Options:\nA. 1/2\nB. 1/4\nC. 3/8\nD. 5/16\nE. 2/5\n\n### Answer:\nThe probability for each ball to be drawn third is equal.\nThen the probability a red ball is drawn third is 3/12 = 1/4.\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe forth proportional to 5,10,20 is?\n\n### Options:\nA. 20\nB. 40\nC. 45\nD. 80\nE. 35\n\n### Answer:\nLet the fourth proportional to 5,10,20 be x\nthen 5:10::20:x\n5x = 10*20\nx = 40\nAnswer is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the cp of 12 rubbers is equal to the sp of 8 rubbers, the gain %is ?\n\n### Options:\nA. 25%\nB. 30%\nC. 50%\nD. 70%\nE. 80%\n\n### Answer:\n(Explanation:Friends, we know we will need gain amount to get gain percent, right.\nSo lets get gain first.\nLet the cost price of 1 pen is Re 1 Cost of 8 pens = Rs 8 Selling price of 8 pens = 12\nGain = 12 - 8 = 4 Gain%=(GainCost*100)%=(48*100)%=50%\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSripad has scored average of 68 marks in three objects. In no subjects has he secured less than 58 marks. He has secured more marks in Maths than other two subjects. What could be his maximum score in Maths ?\n\n### Options:\nA. 79\nB. 28\nC. 38\nD. 27\nE. 88\n\n### Answer:\nAssuming Sripad has scored the least marks in subject other than science,\nThen the marks he could secure in other two are 58 each.\nSince the average mark of all the 3 subject is 68.\ni.e (58+58+x)/3 = 68\n116 + x = 204\nx = 88 marks.\nTherefore, the maximum marks he can score in maths is 88.\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf x is to be chosen at random from the set {1,2,3,4} and y is to be chosen at random from the set {3,4,5}, what`s the probability that xy will be even?\n\n### Options:\nA. 1/6\nB. 2/3\nC. 1/2\nD. 1/3\nE. 5/6\n\n### Answer:\nThe product to be even either one or both must be even, so:\nP(x=even OR y=even)=P(x=even)+P(y=even)-P(x=even AND y=even)=2/4+1/3-2/4*1/3=2/3;\nOr: P(xy=even)=1-P(xy=odd)=1-2/4*2/3=2/3, so basically we find the probability of the product to be odd (which happens when both x and y are odd) and subtract it from 1.\nAnswer: B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n1=5,2=25,3=253,4=150,5=225 then 150=?\n\n### Options:\nA. 1\nB. 255\nC. 4\nD. 445\nE. 235\n\n### Answer:\n1=5,2=25,3=253,4=150,5=225 then 150=?\n150=4\ncheck the fourth eqn.\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo trains of length 100 m and 200 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 54 kmph and 72 kmph. In how much time will the trains cross each other?\n\n### Options:\nA. 80/9\nB. 80/7\nC. 80/2\nD. 80/1\nE. 80/3\n\n### Answer:\nRelative speed = (54 + 72)* 5/18 = 7 * 5 = 35 mps.\nThe time required = d/s = (100 + 100 + 200)/35\n= 400/35 = 80/7 sec.\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFor the past 3 weeks, Rikki has gone to the gym an average of 2 times per week. After 1 more week, the average number of times Rikki goes to the gym increases to 3 times per week. How many times did Rikki visit the gym during the most recent week?\n\n### Options:\nA. 7\nB. 3\nC. 6\nD. 2\nE. 4\n\n### Answer:\nTotal times per week over 3 weeks = 3*2 = 6\nTotal times per week over 4 weeks = 4*3 = 12\nNumber of visits in most recent week = 12-6 = 6 visits\nAnswer is C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA and B are two stations 390 km apart. A train starts from A at 10 a.m. and travels towards B at 65 kmph. Another train starts from B at 11 a.m. and travels towards A at 35 kmph. At what time do they meet?\n\n### Options:\nA. 2.15 pm\nB. 2.15 am\nC. 3.15 pm\nD. 3.15 am\nE. None of them\n\n### Answer:\nSuppose they meet x hours after 10 a.m. Then,\n(Distance moved by first in x hrs) + [Distance moved by second in (x-1) hrs]=390.\n65x + 35(x-1) = 390 => 100x = 425 => x =\t17/4\nSo, they meet 4 hrs.15 min. after 10 a.m i.e., at 2.15 p.m.\nAnswer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA car traveled 281 miles in 4 hours 41 minutes. What was the average speed of the car in miles per hour?\n\n### Options:\nA. 100 miles / hour\nB. 90 miles / hour\nC. 70 miles / hour\nD. 60 miles / hour\nE. 30 miles / hour\n\n### Answer:\nWe first convert the time of 4 hours 41 minutes in minutes\n4 hours 41 minutes = 4 ? 60 + 41 = 281 minutes\nAverage speed S is given by distance / time. Hence\nS = 281 miles / 281 minutes = 1 mile / minute\n= 60 miles / hour\ncorrect answer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nEight cubes, each with a volume of 512 cm^3, are joined to form one large cube. What is the surface area of the large cube?\n\n### Options:\nA. 4096 sq cm\nB. 1536 sq cm\nC. 1024 sq cm\nD. 2048 sq cm\nE. 512 sq cm\n\n### Answer:\nvolume = a x a x a = a ^3\nvolume of cube = 8 x 512 = 4096 cm^3\n4096 = a^3\na = 16\nsurface area of cube = 6 a^2 = 6 x 16^2 = 1536\nAnswer is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo pipes A and B can fill a tank in 12 hours and 15 hours respectively. If both the pipes are opened simultaneously, how much time will be taken to fill the tank?\n\n### Options:\nA. 20 hours\nB. 15 hours\nC. 10 hours\nD. 12 hours\nE. 7 4/9 hours\n\n### Answer:\nPart filled by A in 1 hour = 1/12\nPart filled by B in 1 hour = 1/15\nPart filled by (A+B) in 1 hour = 1/12 + 1/15 = 9/60\nBoth the pipes together fill the tank in 60/9 = 7 4/9 hours\nAnswer is E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf each side of a square is increased by 25%, find the percentage change in its area?\n\n### Options:\nA. 65.25\nB. 56.25\nC. 65\nD. 56\nE. 25\n\n### Answer:\nlet each side of the square be a , then area = a x a\nNew side = 125a / 100 = 5a / 4\nNew area =(5a x 5a) / (4 x 4) = (25a\u00b2/16)\nincreased area== (25a\u00b2/16) - a\u00b2\nIncrease %= [(9a\u00b2/16 ) x (1/a\u00b2 ) x 100]% = 56.25%\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe division of a whole number N by 10 gives a quotient of 15 and a remainder of 2. Find N.\n\n### Options:\nA. 152\nB. 197\nC. 597\nD. 997\nE. 297\n\n### Answer:\nAccording to the division process of whole numbers, N can be written, using multiplication, as follows\nN = quotient *divisor + remainder = 15* 10 + 2 = 152 correc answer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAt a loading dock, each worker on the night crew loaded 1/2 as many boxes as each worker on the day crew. If the night crew has 4/5 as many workers as the day crew, what fraction of all the boxes loaded by the two crews did the day crew load?\n\n### Options:\nA. 1/2\nB. 2/5\nC. 3/5\nD. 4/5\nE. 5/7\n\n### Answer:\nMethod: X = No. of boxes loaded by day crew.\nBoxes by night crew = 1/2 * 4/5 X = 2/5 X\n% loaded by day crew = X/(X + 2/5X) = 5/7\nAnswer E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat annual payment will discharge a debt of Rs. 1025 due in 2 years at the rate of 5% compound interest?\n\n### Options:\nA. 551.28\nB. 551.25\nC. 551.2\nD. 551.23\nE. 551.21\n\n### Answer:\nLet each installment be Rs. x. Then,\nx/(1 + 5/100) + x/(1 + 5/100)2 = 1025\n820x + 1025 * 441\nx = 551.25\nSo, value of each installment = Rs. 551.25.Answer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf an article is sold at 19% profit instead of 12% profit, then the profit would be Rs. 105 more. What is the cost price?\n\n### Options:\nA. 1509\nB. 1528\nC. 1500\nD. 1598\nE. 1512\n\n### Answer:\nLet the cost price of an article be Rs. x.\n(19% of x) - (12% of x) = 105\n19x/100 - 12x/100 = 105 => 7x = 105 * 100\n=> x = 1500\nCost price = Rs. 1500.Answer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA sequence of numbers a1a1, a2a2, a3a3,\u2026. is defined as follows: a1=3a1=3, a_2 = 5, and every term in the sequence after a2a2 is the product of all terms in the sequence preceding it, e.g, a3=(a1)(a2)a3=(a1)(a2) and a4=(a1)(a2)(a3)a4=(a1)(a2)(a3). If an=tan=t and n>2n>2, what is the value of an+2an+2 in terms of t?\n\n### Options:\nA. 4t\nB. t^2\nC. t^3\nD. t^4\nE. t^8\n\n### Answer:\nAn = (A1)(A2)......(An-1) = t\nAn+1 = t * An = t^2\nAn+2 = t * An * An+1 = t * t * t^2 = t^4\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA, B and C can do a piece of work in 24, 30 and 40 days respectively. They start the work together but C leaves 4 days before the completion of the work. In how many days is the work done?\n\n### Options:\nA. 15 days\nB. 14 days\nC. 13 days\nD. 11 days\nE. 10 days\n\n### Answer:\nExplanation:\nx/24 + x/30 + x/40 = 1\nx = 11 days\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n12 spheres of the same size are made from melting a solid cylinder of 8 cm diameter and 27 cm height. What is the diameter of each sphere?\n\n### Options:\nA. 2 cm\nB. 4 cm\nC. 6 cm\nD. 8 cm\nE. 10 cm\n\n### Answer:\nVolume of cylinder = pi*r^2*h\nVolume of a sphere = 4*pi*R^3 / 3\n12*4*pi*R^3 / 3 = pi*r^2*h\nR^3 = r^2*h / 16 = 27 cm^3\nR = 3 cm\nD = 6 cm\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how many different ways can five people be seated on a five-seat bench if two of them must sit next to each other?\n\n### Options:\nA. 24\nB. 48\nC. 120\nD. 240\nE. 480\n\n### Answer:\n5 people can sit in 5! ways.\nIf 2 of them must sit next to each other, they can sit in 4! ways.\nNow, these 2 persons who sit next to each other , can sit in 2! ways.\nTherefore, total different ways in which 5 people can sit are 2! x 4! = 48.\nCorrect answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are 200 cats in Cat-City. Out of the 200, 70 are street cats and the rest are domestic cats. 110 cats are gray, 20 out of the gray cats are NOT domestic ones. How many domestic cats are there which are not gray in Cat-City?\n\n### Options:\nA. 90.\nB. 80.\nC. 50.\nD. 40.\nE. 25.\n\n### Answer:\nSTREET-CAT DOMESTIC-Cat\n70 130\n(20gray+50other) 90gray+40other\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIs y is a positive number? Statement\u20131: 2x+y > 27; Statement\u20132: x\u20133y < 24\n\n### Options:\nA. 22\nB. 62\nC. 28\nD. 16\nE. 11\n\n### Answer:\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAt a certain organisation, the number of male members went up by 12% in the year 2001 from year 2000, and the number of females members went down by 4% in the same time period. If the total membership at the organisation went up by 1.2% from the year 2000 to 2001, what was the ratio of male members to female members in the year 2000?\n\n### Options:\nA. 1:2\nB. 1:3\nC. 2:3\nD. 3:2\nE. 2:1\n\n### Answer:\nmen increase by 12% ==> 1.12M = males in 2001\nwomen decrease by 4% ==> 0.96F = women in 2001\ntotal employees increase by 1.2% ==> 1.012*(M + F) = total number of employees in 2001\nObviously\n(males in 2001) + (females in 2001) = total number of employees in 2001\n1.12M + 0.96F = 1.012*(M + F)\n1.12M + 0.96F = 1.012M + 1.012F\n1.12M - 1.012M = 1.012F - 0.96F\n0.108M = 0.052F\nM/F = (0.052)/(0.108) = 52/108 = 1/2\nAnswer =(A)\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere is 60 lit of milk and water in which milk forms 84%.Howmuch water must be added to this solution to make it solution in which milk forms 50%\n\n### Options:\nA. 40.8\nB. 19.75\nC. 20.75\nD. 21.75\nE. 22.75\n\n### Answer:\n60*84/100=50.40 lit milk that is 9.60 lit water\nlet x lit water will be added then\n(60+x)*50/100=50.40\nso x=40.8\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf n is a positive integer, which one of these following numbers must have a remainder of 3 when\ndivided by any of the numbers 4, 5, and 6?\n\n### Options:\nA. 125n + 3\nB. 240n + 3\nC. 380n + 3\nD. 590n + 3\nE. 700n + 3\n\n### Answer:\nThe numbers 4, 5, and 6 all divide 240 so they all divide 240n.\nWhen we divide (240n + 3) by 4, 5, or 6, the remainder must be 3.\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a two-digit positive integer has its digits reversed, the resulting integer differs from the original by 63. By how much do the two digits differ?\n\n### Options:\nA. 3\nB. 4\nC. 5\nD. 6\nE. 7\n\n### Answer:\nGiven that (10a + b) - (10b + a) = 63 --> 9a - 9b =63 --> a - b = 7.\nAnswer: E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe simple interest on a sum of money is 4/9 of the principal. Find the rate percentage and time, if both are numerically equal.\n\n### Options:\nA. 6 1/3 % and 6 2/3 years\nB. 6 2/3 % and 6 1/3 years\nC. 6 2/3 % and 6 2/3 years\nD. 6 1/3 % and 6 1/3 years\nE. 6 % and 6 2/3 years\n\n### Answer:\nLet sum = Rs. x. Then, S.l. = Rs. 4x/9\nLet rate = R% and time = R years.\nThen, (x*R*R)/100=4x/9 or R^2 =400/9 or R = 20/3 = 6 2/3.\nRate = 6 2/3 % and\nTime = 6 2/3 years = 6 years 8 months\nAnswer is C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA can finish a piece of work in 5 days. B can do it in 10 days. They work together for two days and then A goes away. In how many days will B finish the work?\n\n### Options:\nA. 4\nB. 5\nC. 6\nD. 8\nE. 2\n\n### Answer:\n2/5 + (2 + x)/10 = 1 => x = 4 days\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA sum of money placed at C.I. interest doubles itself in 5 years. It will amount to eight times itself at the same rate of interest in?\n\n### Options:\nA. 7 years\nB. 10 years\nC. 15 years\nD. 20 years\nE. 25 years\n\n### Answer:\nP(1 + R/100)5 = 2P => (1 + R/100)5 = 2\nLet P(1 + R/100)n = 8P\n=> (1 + R/100)n = 8 = 23 = {(1 + R/100)5}3\n=> (1 + R/100)n = (1 + R/100)15 => n = 15 Required time = 15 years.\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn the decimal notation of number (223)3(223)3, what is the third digit to the right of the decimal point?\n\n### Options:\nA. 0\nB. 1\nC. 2\nD. 4\nE. 8\n\n### Answer:\nBecause (2/23)3<(2/20)3=(1/10)3=0.001, the third digit to the right of the decimal point in the decimal notation of (2/23)3 is 0.\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a person walks at 15 km/hr instead of 10 km/hr, he would have walked 10km more. The actual distance traveled by him is?\n\n### Options:\nA. 50 km\nB. 30 km\nC. 18 km\nD. 16 km\nE. 97 km\n\n### Answer:\nLet the actual distance traveled be x km. Then,\nx/10 = (x + 10)/15\n5x - 150 =>x = 30 km.\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe sum of ages of 5 children born at the intervals of 3 years each is 50 years. What is the age of the youngest child?\n\n### Options:\nA. 4 years\nB. 8years\nC. 10 years\nD. 12 years\nE. None of these\n\n### Answer:\nLet the ages of children be x, (x + 3), (x + 6), (x + 9) and (x + 12) years.\nThen, x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 50\n5x = 20\nx = 4.\nAge of the youngest child = x = 4 years.\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n1100 male students and 700 female students are examined in a monthly test; 42% of the male students and 30% of the female students only pass in the examination. Find the percentage of the total failed?\n\n### Options:\nA. 62*2/3\nB. 40*2/3\nC. 55*2/3\nD. 50*2/3\nE. 35*2/3\n\n### Answer:\nTotal number = 1100 + 700 = 1800.\ntot students passed = (42% of 1100 + 30% of 700) - (462 + 210) = 672.\nNumber of failures = 1800-672 = 1128.\nPercentage of failure = (1128/1800 * 100 )% = 62 * 2/3 %.\nANSWER A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe price of 10 chairs is equal to that of 4 tables. The price of 15 chairs and 2 tables together is Rs. 4000. The total price of 12 chairs and 3 tables is:\n\n### Options:\nA. Rs. 3500\nB. Rs. 3750\nC. Rs. 3840\nD. Rs. 3900\nE. None\n\n### Answer:\nEXPLANATION\nLet the cost of a chair and that of a table be Rs. x and Rs. y respectively.\nThen, 10x = 4y or y = 5b/2 x\n15x + 2y = 4000\n15x + 2 x 5/2 x= 4000\n20x = 4000\nx = 200.\nSo, y = 172 = 500.\nHence, the cost of 12 chairs and 3 tables = 12x + 3y\n= Rs. (2400 + 1500)\n= Rs. 3900.\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man can row upstream at 45km/hr and down stream at 36km/hr find mans rate of the current ?\n\n### Options:\nA. 6.3km/hr\nB. 9.6km/hr\nC. 4.5km/hr\nD. 5.9km/hr\nE. 9.8km/hr\n\n### Answer:\ngiven upstream(u) =45km/hr\ndown stream (v)= 36km/hr rate of the current =1/2(u-v) =1/2(45-36)=4.5km/hr\nAnswer is (C)\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe area of a triangle will be when a = 1m, b = 2m, c = 3m, a, b, c being lengths of respective sides.\n\n### Options:\nA. 0 sq m\nB. 3 sq m\nC. 2 sq m\nD. 6 sq m\nE. 9 sq m\n\n### Answer:\nS = (1 + 2 + 3)/2 = 3\n=> No triangle exists\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe probability that a computer company will get a computer hardware contract is 3/4 and the probability that it will not get a software contract is 5/9. If the probability of getting at least one contract is 4/5, what is the probability that it will get both the contracts?\n\n### Options:\nA. 11/30\nB. 31/60\nC. 41/80\nD. 51/120\nE. 71/180\n\n### Answer:\nLet, A \u2261 event of getting hardware contract\nB \u2261 event of getting software contract\nAB \u2261 event of getting both hardware and software contract.\nP(A) = 3/4, P(~B) =5/9\n=> P(B) = 1- (5/9) = 4/9.\nA and B are not mutually exclusive events but independent events. So,\nP(at least one of A and B ) = P(A) + P(B) - P(AB).\n=> 4/5 = (3/4) + (4/9) - P(AB).\n=> P(AB) = 71/180.\nHence, the required probability is 71/180.\nThe answer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the price of gold increases by 50%, find by how much the quantity of ornaments must be reduced, so that the expenditure may remain the same as before?\n\n### Options:\nA. 331/8%\nB. 331/3%\nC. 381/3%\nD. 351/3%\nE. 231/3%\n\n### Answer:\n100\n150\n------\n150-------50\n100-------? => 331/3%\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA company conducted a survey about its two brands, A and B. x percent of respondents liked product A, (x \u2013 20) percent liked product B, 23 percent liked both products, and 23 percent liked neither product. What is the minimum number Q of people surveyed by the company?\n\n### Options:\nA. 46\nB. Q.80\nC. Q.90\nD. Q.100\nE. 200\n\n### Answer:\n100 = x + x - 20 + 23 - 23\nx = 60,\nSo, Product A = 60%, Product B = 40%, Both = 23%, Neither = 23%\n23% of the total no. of people should be an integer. So, A,BC are out.\n60% of D and 40% of D are both integers. So, D satisfies all conditions.\nSo, answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain candy store sold lollipops for $0.90 each and pieces of individually wrapped saltwater taffy for $0.20 each. If a customer purchased both lollipops and taffy from the store, and spent a total of $3.90, what total number of lollipops and saltwater taffy did the customer purchase?\n\n### Options:\nA. 6\nB. 7\nC. 8\nD. 9\nE. 10\n\n### Answer:\nwe can take numbers, as price of lollipop 9, 2 for taffy and 39 total for ease.\nNow we can determine quickly that total number should range between 39/9 <= N <=39/2, so ans should be between 4 and 20.\nNow solving the expression 9A+2B =39\nfirst possibility with 1 lollipop, 15 taffy we get $3.90 total amount, but 1+15=16, and 16 is not an option.\nSo next choice, for 9A+2B =39 would come by decreasing 39 in multiple of 9 and checking divisibility of that number by 2. this way we get\n3 lollipop, 6 taffy would be $3.90 total, 3*0.90 + 6*0.20= 3.90\nHence total number is 3 + 6 = 9\nAns D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man bought a computer at 30% discount on its original price. He sold it at a 520% increase on the price he bought it. What percent of profit did he make on the original price?\n\n### Options:\nA. 1%\nB. 2%\nC. 3%\nD. 4%\nE. 5%\n\n### Answer:\nOriginal price = 100\nCP = 70\nS = 70*(150/100) = 105\n105 - 100 = 5%\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a certain sequence, the first term is 7, and each successive term is 1 more than the reciprocal of the term that immediately precedes it. What is the fifth term in this sequence?\n\n### Options:\nA. 13/8\nB. 39/24\nC. 8/5\nD. 5/8\nE. 8/13\n\n### Answer:\nlet five terms in the sequence be a,b,c,d,e\na=7\nb= 1+1/7=8/7\nc=1+7/8= 15/8\nd= 1+8/15 = 24/15\ne= 1+15/24 = 39/24\nhence answer should be B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man spends 10% of his income in house rent, 20% of the rest on his children\u2019s education, 25% of the rest miscellaneous causes. If he now posses Rs. 1944 then his income is?\n\n### Options:\nA. Rs.3600\nB. Rs.4000\nC. Rs.4500\nD. Rs.3000\nE. Rs.5000\n\n### Answer:\nX * (90/100) * (80/100) * (75/100) = 1944\nX * 0.9 * 0.8 * 0.75\nX = 1944/0.54\nX = 3600\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the sum of all the multiples of 10 between 0 and 99?\n\n### Options:\nA. 500\nB. 620\nC. 450\nD. 340\nE. 440\n\n### Answer:\nThe multiples of 10 between 0 and 99 are 10, 20, 30, 40, 50, 60, 70, 80, and 90. If these are all added together, the result is 450.\nFinal Answer:\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn what ratio must tea at Rs.62 per Kg be mixed with tea at Rs. 72 per Kg so that the mixture must be\nworth Rs. 64.50 per Kg?\n\n### Options:\nA. 1 : 2\nB. 2 : 1\nC. 3 : 1\nD. 1 : 3\nE. None of these\n\n### Answer:\nExplanation :\nBy the rule of alligation, we have\nCost of 1 kg of 1st kind tea Cost of 1 kg tea of 2nd kind tea\n62 72\nMean Price\n64.5\n72-64.5=7.5 64.5-62=2.5\nRequired Ratio = 7.5 : 2.5 = 3 : 1\nAnswer : Option C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe product A of the first 10 prime numbers is closest to which of the following?\n\n### Options:\nA. 6.5 x 10^7\nB. 6.5 x 10^8\nC. 6.5 x 10^9\nD. 6.5 x 10^10\nE. 6.5 x 10^11\n\n### Answer:\nThe first 10 primes are: 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29.\nSo, we need to find approximate value of 2*3*5*7*11*13*17*19*23*29.\n# of different approximations are possible. For example:\n2*5=10\n3*17=~50 (actually more than 50);\n7*13=~100 (actually less than 100);\n11*19=~200 (actually more than 200)\n23*29=667=A\n2*3*5*7*11*13*17*19=~10*50*100*200*667=10^7*667=6.67*10^9.\nAnswer: C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA driver of auto rickshaw makes a profit of 20% on every trip when he carries 3 passengers and the price of petrol is Rs. 30 a litre. Find the % profit for the same journey if he goes for 4 passengers per trip and the price of petrol reduces to Rs. 24 litres? (revenue per passenger is same)\n\n### Options:\nA. 20%\nB. 33.33%\nC. 100%\nD. 65.66%\nE. Data inadequate\n\n### Answer:\nSolution: Assume the cost price = 100 and selling price = 120.\nThen, when price of petrol is reduced;\nCost price become 60 and selling price = 160;\nProfit increased = 100%.\nAnswer: Option C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many positive numbers not greater than 4300 can be formed using the digits 0,1,2,3,4 where repeatation is allowed?\n\n### Options:\nA. 576\nB. 575\nC. 620\nD. 640\nE. 660\n\n### Answer:\n1 digit = 5\n2 digits = 4* 5 = 20\n3 digits = 4*5*5= 100\nNow,4 digit number till 4000 can have digits 1,2,3 in thousands place ( total choices = 3 )\n0,1,2,3,4 in hundreds ,tens and ones place\nI.e 3*5*5*5 = 375\nNow From 4000 to 4299 = 1*3*5*5 =75\nTotal = 5+20+100+375+75+1 =576 (1 for 4300)\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo trains 160 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is?\n\n### Options:\nA. 10.52 sec\nB. 18.8 sec\nC. 14.52 sec\nD. 10.8 sec\nE. 11.52 sec\n\n### Answer:\nRelative speed = 60 + 40 = 100 km/hr.\n= 100 * 5/18 = 250/9 m/sec.\nDistance covered in crossing each other = 160 + 160 = 320 m.\nRequired time = 320 * 9/250 = 288/25 = 11.52 sec.\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA certain club has 10 members, including Parry. One of the 10 members is chosen at random to be the president, one of the remaining 9 members is to be chosen at random to be the secretary, and one of the remaining 8 members is to be chosen at random to be the treasurer. What is the probability that parry will be either the member chose to be secretary or the member chose to be treasurer?\n\n### Options:\nA. 1/720\nB. 1/80\nC. 1/10\nD. 1/9\nE. 1/5\n\n### Answer:\nIn order to become a secretary the person cannot be chosen as a president. This can be done in 9/10 ways. Then to become a secretary this person's probability is 1/9\nProbability to become a secretary = (9/10 * 1/9) = 1/10\nSimilar concept for treasurer. Probability of not president = 9/10, Probability of not secretary = 8/9, probability of treasurer 1/8\nprobability to become a treasurer = (9/10 * 8/9 * 1/8) = 1/10\nSince, the problem is saying parry secretary OR Treasurer it is addition: 1/10 + 1/10 = 1/5=E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJake remembers only the last three letters of his four-letter Klingon name. If he is sure that the first letter is neither \"N\" nor \"X\", and assuming that there are only 15 letters in the Klingon alphabet, what is the probability that he will give the correct name when asked for it by the space attendant?\n\n### Options:\nA. A)8/100\nB. B)9/100\nC. C)1/8\nD. D)1/13\nE. E)9/10\n\n### Answer:\nTotal letters 15, out of which the first letter is anything of 10 but N or X...\nSo there are 13 possible letters for first place..\nAnd only one of them is correct..\nSo 1/13\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAnand and Deepak started a business investing Rs. 3500 and Rs. 7000 respectively. Out of a total profit of Rs. 2000, Deepak's share is:\n\n### Options:\nA. 1333.3\nB. 2687.1\nC. 1200.6\nD. 1580.2\nE. 2671\n\n### Answer:\nRatio of their shares = 3500 : 7000 = 1:2\nDeepak's share = 2000* 2/3 = Rs. 1333.3.\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn an election a candidate who gets 60% of the votes is elected by a majority of 900 votes. What is the total number of votes polled?\n\n### Options:\nA. A)4500\nB. B)5200\nC. C)6900\nD. D)7520\nE. E)6000\n\n### Answer:\nLet the total number of votes polled be x\nThen, votes polled by other candidate = (100-60)% of x = 40% of x\n60% of x - 40% of x = 900\n20x/100 = 900\nx = 900*100/20 = 4500\nAnswer is A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a/b = 1/3, b/c = 2, c/d = 1/2, d/e = 3 and e/f = 1/2, then what is the value of abc/def ?\n\n### Options:\nA. 27/4\nB. 27/8\nC. 3/4\nD. 3/8\nE. 1/4\n\n### Answer:\nSay a = 3. Then:\na/b = 1/3 --> b = 9;\nb/c = 2 --> c = 9/2;\nc/d = 1/2 --> d = 9;\nd/e = 3 --> e = 3;\ne/f = 1/2 --> f = 6.\nabc/def = (3*9*9/2)/(9*3*6) = 3/4.\nAnswer: C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn the table above, what is the least number of table entries that are needed to show the mileage between each city and each of the other five cities?\n\n### Options:\nA. 15\nB. 21\nC. 25\nD. 30\nE. 36\n\n### Answer:\nTotal number of entries 6*6(6rows*6columns) =36\nNow 6 entries are representing mileage with the city itself so subtract that => 36-6\nMinimum entries required = half the Total = 30/2 = 15\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nLinda spent 3/4 of her savings on furniture and the rest on a TV. If the TV cost her $200, what were her original savings?\n\n### Options:\nA. $500\nB. $600\nC. $700\nD. $800\nE. $900\n\n### Answer:\nIf Linda spent 3/4 of her savings on furnitute, the rest\n4 / 4 - 3 / 4 = 1 / 4 on a TV\nBut the TV cost her $200. So 1 / 4 of her savings is $200. So her original savings are 4 times $200 = $800\ncorrect answer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe H.C.F. of two numbers is 12 and their L.C.M. is 600. If one of the number is 12, find the other?\n\n### Options:\nA. 100\nB. 600\nC. 120\nD. 200\nE. 150\n\n### Answer:\nOther number = 12*600/12= 600\nAnswer is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nLindsay can paint 1/x of a certain room in one hour. If Lindsay and Joseph, working together at their respective rates, can paint the room in two hours, what fraction of the room can Joseph paint in 20 minutes?\n\n### Options:\nA. 1/6x\nB. x/(x-6)\nC. (x-2)/6x\nD. x/(x-2)\nE. (x-2)/x\n\n### Answer:\nLet J be Joseph's rate per hour.\n1/x + J = 1/2 of a room per hour\nJ = 1/2 - 1/x, of a room per hour\nIn 20 minutes Joseph can paint 1/3*(1/2-1/x) = 1/6-1/3x = (x-2)/6x\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf one root of the equation 2x^2 + 3x \u2013 k = 0 is 5, what is the value of k?\n\n### Options:\nA. 65\nB. 79\nC. 68\nD. 87\nE. 90\n\n### Answer:\nWe just enter this root into the equation in order to recieve an equation to find the answer!\n2*5^2+3*5-k=0\nk=50+15=65\nThe answer is A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMatt is touring a nation in which coins are issued in two amounts, 2\u00a2 and 5\u00a2, which are made of iron and copper, respectively. If Matt has twuenty iron coins and thuenty copper coins, how many different sums from 1\u00a2 to 140\u00a2 can he make with a combination of his coins?\n\n### Options:\nA. 137\nB. 140\nC. 166\nD. 136\nE. 2\n\n### Answer:\nThe total sum is 20*2 + 20*5 = 140\u00a2. If you can make each sum from 1 to 140 (1\u00a2, 2\u00a2, 3\u00a2, ..., 140\u00a2), then the answer would be 140 (maximum possible).\nNow, with 2\u00a2 and 5\u00a2 we cannot make 1\u00a2 and 3\u00a2. We also cannot make 139\u00a2 and 137\u00a2 (since total sum is 140\u00a2 we cannot remove 1\u00a2 or 3\u00a2 to get 139\u00a2 or 137\u00a2).\nSo, out of 140 sums 4 are for sure not possible, so the answer must be 140 - 4 = 136 sums or less. Only A fits.\nAnswer: D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nEvaluate: 1234562- 12*3*2 = ?\n\n### Options:\nA. 32435453\nB. 1234554\nC. 76768786\nD. 97979797\nE. 75868656\n\n### Answer:\nAccording to order of operations, 12?3?2 (division and multiplication) is done first from left to right\n12**2 = 4* 2 = 8\nHence\n1234562 - 12*3*2 = 1234562 - 8 = 1234554\ncorrect answer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nBill bought 100 packets of candy. He was able to sell 1/2 of them at a 20% profit, another 1/4 of them at zero profit and the remainder was sold at a 5% loss. Find the total profit or loss made by Bill after selling those 100 packets. A packet sold at a loss had a price of $9.\nPlease provide an intuitive answer if possible. Thanks!!\n\n### Options:\nA. 0\nB. Profit of $87.5\nC. Loss of $25\nD. Profit of $80\nE. Profit of $85\n\n### Answer:\nA packet sold at a 10% loss had a price of $9, thus the cost of a packet is $10.\n50 packets was sold at a 20% profit --> gives profit of 10*0.2*50 = $100.\n25 packets was sold at a 5% loss --> gives loss of 10*0.05*25 = $12.5.\nThe overall Profit is $100 - $12.5 = $87.5.\nAnswer: B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA shopkeeper sold an article at $100 with 10% profit. Then find its cost price?\n\n### Options:\nA. $120\nB. $100\nC. $91\nD. $72\nE. $69\n\n### Answer:\ncost price = selling price *100/(100+profit)\nC.P. = 100*100/110 = $91(approximately)\nAnswer is C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJohn has 6 people in his group of friends. How many different ways can he invite one or more of them to his house?\n\n### Options:\nA. 56\nB. 97\nC. 63\nD. 65\nE. 71\n\n### Answer:\nJohn can select one or more of his group of 6\n=> Required number of ways = 2^6 \u2013 1= 63.\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThree partners A,B,C invested 360000rs.,378000rs. and 414000rs.in a business.at the end of one year,there is profit of 64000rs.then calculate the profit share of C.\n\n### Options:\nA. 24000\nB. 23000\nC. 28000\nD. 2750\nE. 2880\n\n### Answer:\nratio of A,B,C investment=360000:378000:414000=20:21:23.\ntotal profit=64000 rs.\nshare of C=[64000\u00d723/64]=23000 rs.\nanswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf z is a multiple of 9702, what is the remainder when z^2 is divided by 4?\n\n### Options:\nA. 0\nB. 1\nC. 2\nD. 3\nE. It depends on z.\n\n### Answer:\n2 is a factor of 9702, so 2 is a factor of z.\nThen 2^2 = 4 is a factor of z^2.\nThen the remainder when z^2 is divided by 4 is 0.\nThe answer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat will be the cost of building a fence around a square plot with area equal to 289 sq ft, if the price per foot of building the fence is Rs. 58?\n\n### Options:\nA. 3944\nB. 39288\nC. 288\nD. 266\nE. 1881\n\n### Answer:\nLet the side of the square plot be a ft.\na2 = 289 => a = 17\nLength of the fence = Perimeter of the plot = 4a = 68 ft.\nCost of building the fence = 68 * 58 = Rs. 3944.Answer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the selling price of 50 articles is equal to the cost price of 40 articles, then the loss or gain percent is?\n\n### Options:\nA. 20\nB. 98\nC. 66\nD. 54\nE. 12\n\n### Answer:\nLet C.P. of each article be Re. 1.\nThen, C.P. of 50 articles = Rs. 50;\nS.P. of 50 articles = Rs. 40.\nLoss % = 10/50 * 100 = 20%\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many numbers are divisible by both 2 and 3 up to 300?\n\n### Options:\nA. 50\nB. 100\nC. 150\nD. 200\nE. 250\n\n### Answer:\nDivide 300 by 6, as the numbers which are divisible by both 2 and 3 are also divisible by 6.\nThe quotient obtained after dividing 300 by 6 is 50, hence answer is 50.\nOption A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSix persons in an organization including A and B were to be divided in two groups of 3 members each. The total number of groups containing both A and B is what fraction of the total number of groups which can be formed?\n\n### Options:\nA. 3/10\nB. 1/70\nC. 3/14\nD. 1/10\nE. 11/14\n\n### Answer:\nThe fraction is nothing but the probability..\nNumber to choose 3 out of 6= 6C3\nNumber to choose A and B and 2 from remaining 4=4C2..\nprob of A and B choosen=4C2/6C3=3/10\nAnswer : A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA shopkeeper expects a gain of 22.5% on his cost price. If in a week, his sale was of Rs. 441, what was his profit?\n\n### Options:\nA. s. 64\nB. s. 69\nC. s.72\nD. s.75\nE. s.81\n\n### Answer:\nC.P. = Rs. (100/122.5)x441\n= Rs. (1000/1225)x441\n= Rs. 360\nProfit = Rs. (441 - 360) = Rs. 81.\nAnswer:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe total weight of nine nougat nuggets is 7 oz. What is the average (arithmetic mean) weight of one such nougat nugget?\n\n### Options:\nA. 0.18 oz.\nB. 0.5 oz.\nC. 1.8 oz.\nD. 0.77 oz.\nE. 18 oz\n\n### Answer:\nAverage = Total/Number of items\n= 7/9 = 0.77.\nHence, D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAn investment of $3000 was made in a certain account and earned interest that was compounded annually. The annual interest rate was fixed for the duration of the investment, and after 12 years the $3000 increased to $12000 by earning interest. In how many years after the initial investment was made the $3000 have increased to $24000 by earning interest at that rate?\n\n### Options:\nA. 16\nB. 22\nC. 20\nD. 18\nE. 30\n\n### Answer:\nIn 12 years the investment quadrupled (from $3,000 to $12,000).\nThus, at the same rate compounded annually, it would need additional 12/2=6 years to double (from $12,000 to $24,000).\nTherefore, 12+6=18 years are needed $3,000 to increase to $24,000.\nAnswer: D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA sum of money becomes 7/6 of itself in 5 years at a certain rate of simple interest. The rate per annum is?\n\n### Options:\nA. 20/7\nB. 20/3\nC. 23/6\nD. 10/3\nE. 10/7\n\n### Answer:\nLet sum = x. Then, amount = 7x/6\nS.I. = 7x/6 - x = x/6; Time = 5 years.\nRate = (100 * x) / (x * 6 * 5) = 10/3 %.\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJohn left home and drove at the rate of 50 mph for 2 hours. He stopped for lunch then drove for another 3 hours at the rate of 55 mph to reach his destination. How many miles did John drive?\n\n### Options:\nA. 235 miles.\nB. 245 miles.\nC. 255 miles.\nD. 265 miles.\nE. 275 miles.\n\n### Answer:\nThe total distance D traveled by John is given by\nD = 50 * 2 + 3 * 55 = 265 miles.\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAt an elementary school, 70% of the faculty members are women and 40% of the faculty members are married. If 1\u20443 of the men are single, what fraction of the women are married?\n\n### Options:\nA. 5\u20447\nB. 7\u204410\nC. 2/7\nD. 7\u204430\nE. 5\u204470\n\n### Answer:\n--------------------M------W--------Total\nMarrried----------20-----20---------40\nNot married-----10-----50---------60\nTotal-------------30-----70--------100\nneed married woman/total woman, so 20/70=2/7\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA secret can be told only 2 persons in 5 minutes .the same person tells to 2 more persons and so on . How long will take to tell it to 768 persons ?\n\n### Options:\nA. 25 min\nB. 32 min\nC. 33 min\nD. 34 min\nE. 35 min\n\n### Answer:\nat start one person will tell to 2 persons, it will take 5 min, now that 1+2 = 3 persons will tell this to next 6 persons, then 1+2+6 = 9 persons will tell to next 18 persons, then 1+2+6+18 = 27 persons to 54 similarly 1+2+6+18+54 = 81 persons will tell this to 162 persons similarly 1+2+6+18+54+162 = 243 persons will tell this to 486 persons, upto this step total persons who have listened this secret = 2+6+18+54+162+486 = 728, and total time taken upto this step = 5*6 = 30 min, now next 5 min will be sufficient to tell this message to next 40 persons so total time taken = 35 min\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf $10 is invested at x percent simple annual interest for n years, which of the following represents the total amount of interest, in dollars, that will be earned by this investment in the n years?\n\n### Options:\nA. 10n(x/100)\nB. 10,000(x/100)^n\nC. 10,000n(x/100)\nD. 10,000(1+x/100)^n\nE. 10,000n(1+x/100)\n\n### Answer:\nI think answer D is for compound interest (which i assumed)\nand answer A is for simple interest because it is not compounding.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nLast year, for every 100 million vehicles that traveled on a certain highway, 50 vehicles were involved in accidents. If 5 billion vehicles traveled on the highway last year, how many of those vehicles were involved in accidents? (1 billion = 1,000,000,000)\n\n### Options:\nA. 800\nB. 850\nC. 900\nD. 500\nE. 1000\n\n### Answer:\nTo solve we will set up a proportion. We know that \u201c100 million vehicles is to 50 accidents as 5 billion vehicles is to x accidents\u201d. To express everything in terms of \u201cmillions\u201d, we can use 5,000 million rather than 5 billion. Creating a proportion we have:\n100/50 = 5,000/x\nCross multiplying gives us:\n100x = 2,000 * 50\nx = 20 * 50 = 1000\nAnswer : E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a certain deck of cards, each card has a positive integer written on it, in a multiplication game a child draws a card and multiplies the integer on the card with the next large integer. If the each possible product is between 15 and 270, then the least and greatest integer on the card would be\n\n### Options:\nA. 3 and 15\nB. 3 and 20\nC. 4 and 13\nD. 4 and 16\nE. 5 and 14\n\n### Answer:\nGiven: 1515 --> so, the least value is 4. Test for the largest value: if x=16 then\nx(x+1)=16*17=272>270\nAnswer: D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nBy mixing two brands of tea and selling the mixture at the rate of Rs. 177 per kg. a shopkeeper makes a profit of 18%. If to every 2 kg of one brand costing Rs. 200 per kg, 3 kg of the other brand is added, then how much per kg does the other brand cost?\n\n### Options:\nA. Rs. 110\nB. Rs. 120\nC. Rs. 140\nD. None of these\nE. Not determined\n\n### Answer:\nExplanation:\nLet the cost of the brand be Rs. X per kg.\nC.P. of 5 kg = (2 * 200 + 3 * x) = Rs. (400 + 3x)\nS.P of 5 kg = Rs. (5 * 177) = Rs. 885\n[885 - (400 + 3x)]/(400 + 3x) * 100 = 18\n24250 - 150x = 3600 + 27x\n177x = 20650 => x = 116 2/3\nSo, cost of the other brand = Rs. 116.66.\nAnswer is D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat percent is 2 minutes 24 seconds of an hour?\n\n### Options:\nA. 6%\nB. 8%\nC. 4%\nD. 2%\nE. 9%\n\n### Answer:\n2mt 24s =144s\n(144*100)/(60*60)=4%\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA student traveled 25 percent of the distance of the trip alone, continued another 40 miles with a friend, and then finished the last half of the trip alone. How many miles long was the trip?\n\n### Options:\nA. 120\nB. 140\nC. 160\nD. 180\nE. 200\n\n### Answer:\nLet x be the total length of the trip.\n0.25x + 40 miles + 0.5x = x\n40 miles = 0.25x\nx = 160 miles\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAll the water in container A which was filled to its brim was poured into two containers B and C. The quantity of water in container B was 62.5% less than the capacity of container A. If 151 liters was now transferred from C to B, then both the containers would have equal quantities of water. What was the initial quantity of water in container A?\n\n### Options:\nA. 1289\nB. 1198\nC. 281\nD. 1208\nE. 282\n\n### Answer:\nExplanation:\nB has 62.5% or (5/8) of the water in A. Therefore, let the quantity of water in container A(initially) be 8k.\nQuantity of water in B = 8k - 5k = 3k.\nQuantity of water in container C = 8k - 3k = 5k\nContainer: A B C\nQuantity of water: 8k 3k 5k\nIt is given that if 151 liters was transferred from container C to container B, then both the containers would have equal quantities of water.\n5k - 151 = 3k + 151 => 2k = 302 => k = 151\nThe initial quantity of water in A = 8k = 8 * 151 = 1208 liters.\nAnswer: Option D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n|x+3| \u2013 |4-x| = |8+x| How many K solutions will this equation have?\n\n### Options:\nA. 0\nB. 1\nC. 2\nD. 3\nE. 4\n\n### Answer:\n|x| = x when x >= 0 (x is either positive or 0)\n|x| = -x when x < 0 (note here that you can put the equal to sign here as well x <= 0 because if x = 0,\n|0| = 0 = -0 (all are the same)\nSo the '=' sign can be put with x > 0 or with x < 0. We usually put it with 'x > 0' for consistency.A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nGill drives 120 miles from Los Angeles to San Diego to fetch a package. On her way there she drives at 40 miles per hour. On her way back she drives 50% faster. What is Gill's average velocity W for the round trip?\n\n### Options:\nA. 24 miles per hour\nB. 48 miles per hour\nC. 50 miles per hour\nD. 53 1/3 miles per hour\nE. 68 miles per hour\n\n### Answer:\nHere's an Average Speed question in which the prompt gives you almost all of the immediate numbers needed to work with.\nDriving from LA to SD, we have a distance of 120 miles and a speed of 40 miles/hour.\nD = (R)(T)\n120 = (40)(T)\n120/40 = 3 = T\n3 hours to drive to SD\nOn the way back, she drives 50% FASTER. Gill's return speed is (1.5)(40) = 60 miles/hour.\nD = (R)(T)\n120 = (60)(T)\n120/60 = 2 = T\n2 hours to drive to SD\nTotal Distance = 240 miles\nTotal Time = 3+2 = 5 hours\nAverage Speed = 240/5 = 48 miles/hour\nFinal Answer:\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe jogging track in a sports complex is 726 m in circumference. Deepak and his wife start from the same point and walk in opposite directions at 4.5 km/hr and 3.75 km/hr respectively. They will meet for the first time in?\n\n### Options:\nA. 4.9 min\nB. 5.28 min\nC. 5.5 min\nD. 6 min\nE. 7 min\n\n### Answer:\nClearly, the two will meet when they are 726 m apart.\nTo be (4.5 + 3.75) = 8.25 km apart, they take 1 hour.\nTo be 726 m apart, they take (100/825 * 726/1000) hrs = (242/2750 * 60) min = 5.28 min.\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many such 3's are there in the following number sequence which are immediately Preceded by an odd number and immediately followed by an even number ? 5 3 8 9 4 3 7 2 3 8 1 3 8 4 2 3 5 7 3 4 2 3 6\n\n### Options:\nA. 1\nB. 2\nC. 3 three\nD. 4\nE. More than four\n\n### Answer:\nA is followed by B means : A comes first,B comes next\nA preceded by B means : B comes first, A comes next\nThe sets which satisfy the condition is: 5 3 8\n1 3 8\n7 3 4\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJohnny makes $3.25 per hour at his work. If he works 8 hours, how much money will he earn?\n\n### Options:\nA. $30\nB. $54\nC. $26\nD. $12\nE. $9.60\n\n### Answer:\n3.25*8=26. Answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the least number must be added to 228712 so that remaining no.is divisible by 9?\n\n### Options:\nA. 5\nB. 3\nC. 1\nD. 6\nE. 2\n\n### Answer:\nOn dividing 228712 by 9 we get the remainder 4, so 5 should be subtracted\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWe have 7770 balls available, and there is 1 ball on d top of rack and then 3 balls on d 1st floor behind the top rack (horizontal rack) and then 6 balls on 2nd floor then 10 balls on 3rd floor,\nHow many floors can be accomdated with the given no of balls...???\n\n### Options:\nA. 36\nB. 35\nC. 34\nD. 33\nE. 32\n\n### Answer:\n1+3+6+10+........=7770 sum of triangular number\nn*(n+1)*(n+2)/6 gives 35\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA circular metal plate of even thickness has 12 holes of radius 1 cm drilled into it. As a result the plate lost 1/6th its original weight. The radius of the circular plate is\n\n### Options:\nA. 16sqrt2\nB. 8sqrt2\nC. 32sqrt2\nD. sqrt72\nE. sqrt82\n\n### Answer:\nArea of 12 holes=12*Pi*1^2=12*Pi\nAs 12*Pi=(1/6)th weight,so total Area of Plate=12*Pi/(1/6)=72*Pi\nIf r=radius of the plate,then its Area=Pi*r^2=72*Pi, So r=Sqrt72\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAn athlete runs 200 metres race in 24 seconds. His speed is :\n\n### Options:\nA. 20 km/hr\nB. 24 km/hr\nC. 28.5 km/hr\nD. 30 km/hr\nE. None of these\n\n### Answer:\nSpeed = 200/24 m/sec=25/3 m/sec=(25/3*18/5)km/hr=30 km/hr.\nCorrect Option: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMachine A and machine B are each used to manufacture 550 sprockets. It takes machine A 10 hours longer to produce 550 sprockets than machine B. Machine B produces 10 percent more sprockets per hour than machine A. How many sprockets per hour does machine A produces?\n\n### Options:\nA. 6\nB. 5\nC. 7\nD. 8\nE. 9\n\n### Answer:\nMachine B: Takes x hours to produce 550 sprockets\nMachine A: Takes (x+10) hours to produce 550 sprockets\nMachine B: In 1 hour, B makes 550/x sprockets\nMachine A: In 1 hour, A makes 550/(x+10) sprockets\nEquating:\n1.1(550/(x+10)) = 550/x\n605/(x+10) = 550/x\n605x = 550x+5500\n55x = 5500\nx = 100\nA makes 550/(110) = 5 sprockets per hour\nAnswer : B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOn 8th Feb, 1995 it was Wednesday. The day of the week on 8th Feb, 1994 was\n\n### Options:\nA. wednesday\nB. Tuesday\nC. Thursday\nD. Friday\nE. None\n\n### Answer:\n1994 being an ordinary year, it has 1 odd day. So, the day on 8th Feb, 1995 is one day beyond the day on 8th Feb, 1994. But, 8th Feb, 1995 was Wednesday. 8th Feb, 1994 was Tuesday.\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFrom the starting point in a boat race, one competitor started to sail north at a speed of 1.1 Km/h, the other competitor started to sail west at a speed of 1.2 Km/h. What is the distance in Km between the two competitors after 5 hours?\n\n### Options:\nA. 8.1\nB. 12.\nC. 12.5.\nD. 14.\nE. 15.4.\n\n### Answer:\nBoth competitors are sailing making angle of 90 degrees.\nAfter 5 hrs one competitor will cover a distance of = 1.1 *5= 5.5 KM\nAnd, other competitor will cover a distance of = 1.2*5= 6KM\ndistance between them after 5 hrs = (5.5^2+ 6^2)^1/2= 8.1 KM\nA is the answer\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a 300 member association consisting of men and women, exactly 20% of men and exactly 25 % women are homeowners. What is the least number of members who are homeowners?\n\n### Options:\nA. 79\nB. 77\nC. 85\nD. 83\nE. 61\n\n### Answer:\nSolution simple\nOut of 300 20% are male i.e 60 and 25% are female i.e 75 , so total homeowner is 135.\nNow min number homeowner is 60 and max is 135 so question ask us to find least and 61 has least value among all option.\nSo ans is 61.\nAnswer : E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOn Saturday morning, John will begin a camping vacation and he will return home at the end of the first day on which it rains. If on the first three days of the vacation the probability of rain on each day is 0.6, what is the probability that Malachi will return home at the end of the day on the following Monday?\n\n### Options:\nA. 0.096\nB. 0.125\nC. 0.128\nD. 0.512\nE. 0.64\n\n### Answer:\nRe-phrasing the question:\nWhat is the probability of: Saturday: No rain, Sunday: No rain, Monday: Rain\nProbability of rain = 0.6\nTherefore, probability of no rain = 0.4\n0.6*0.6*0.4 = 0.096\nHence A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe price of a book is increased from $300 to $360. What is the % of increase in its price?\n\n### Options:\nA. 10%\nB. 20%\nC. 40%\nD. 50%\nE. 60%\n\n### Answer:\nExplanation: Change in the price = Rs 360 \u2013 Rs 300\n= Rs 60\nPercentage of increase = Change in the price Initial Price\n* 100.\nPercentage increase in price =( 60 300\n) *100 = 20%\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf x is less than y by 50% then y exceed x by:\n\n### Options:\nA. 33.33%\nB. 100%\nC. 75%\nD. 66.66%\nE. None of these\n\n### Answer:\nUsing formula (x/(100-x)*100) where x is Percentage decrease (here it is 25%)\n=> 50(100-50)*100\n=100%\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA special lottery is to be held to select a student who will live in the only deluxe room in a hostel. There are 100 Year-III, 150 Year-II and 200 Year-I students who applied.\nEach Year-III's name is placed in the lottery 3 times; each Year-II's name, 2 times and Year-I's name, 1 time. What is the probability that a Year-III's name will be chosen?\n\n### Options:\nA. 1/8\nB. 2/9\nC. 2/7\nD. 3/8\nE. 3/9\n\n### Answer:\nExplanation :\nTotal names in the lottery,\n=3\u00d7100+2\u00d7150+200\n=800.\nNumber of Year-III's names,\n=3\u00d7100\n=300.\nThe required probability,\n=300/800.\n=3/8.\nAnswer : D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe length of the bridge, which a train 180 metres long and travelling at 45 km/hr can cross in 30 seconds, is?\n\n### Options:\nA. 245\nB. 777\nC. 282\nD. 195\nE. 288\n\n### Answer:\nSpeed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (180 + x)/30 = 25/2 => 2(180 + x) = 750 => x = 195 m.\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the square root of 36, divided by 6?\n\n### Options:\nA. 9\nB. 36\nC. 122\nD. 6\nE. 1\n\n### Answer:\nSquare root is a number times itself\nSquare root of 36=6, 6/6=1\n(E)1\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n16,25,36,72,144,196,225\n\n### Options:\nA. 36\nB. 196\nC. 225\nD. 144\nE. 72\n\n### Answer:\nEach of the numbers except 72 is a perfect square.\nanswer :E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a stack of boards at a lumber yard, the 13th board counting from the top of the stack is immediately below the 12th board counting from the bottom of the stack. how many boards are in the stack?\n\n### Options:\nA. 33\nB. 23\nC. 25\nD. 32\nE. 42\n\n### Answer:\n1 2 3 ....\n..............13 12 ................. 1\nSo the number of boards = 13+10 =23.\nOption: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA woman has three blouses of different colors, four skirts of different colors, and two different pairs of shoes. She refuses to wear her pink blouse with her green skirt. How many different blouseskirt-shoe combinations could she wear?\n\n### Options:\nA. 8\nB. 12\nC. 16\nD. 17\nE. 22\n\n### Answer:\ntotal ways = 3*4*2=24..\nnow its better to find the ways in which the pink blose and green skirty are together and subtract from total to get the answer..\nthe ways in which the pink blose and green skirty are together=1*1*2=2..\ntotal ways =24-2=22..\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA can do a job in 3 days less time than B. A works at it alone for 4 days and then B takes over and completes it. If altogether 14 days were required to finish the job, how many days would each of them take alone to finish it?\n\n### Options:\nA. 17 days, 20 days\nB. 12 days, 15 days\nC. 13 days, 16 days\nD. 14 days, 11 days\nE. None of these\n\n### Answer:\nLet B can finish the work in x days.\nThen A can finish the work in (x \u2013 3) days.\nB\u2019s one day\u2019s work = 1\u2044xth work.\nA\u2019s one day\u2019s work = 1\u2044(x - 3)th work.\nA\u2019s 4 days\u2019 work = 4\u2044(x - 3)th work.\nRemaining work = 1 - 4\u2044(x - 3) = x\u22127 /x\u22123\nThe remaining work done by B in 14 \u2013 4 = 10 days.\nNow, in 10 days, work done by B = x\u22127/x\u22123th work.\n\u2234 in 1 day, work done by B = 110(x\u22127/x\u22123) th work.\nand 1/10(x\u22127/x\u22123)=1/x\n\u21d2 x = 15 days\n\u2234 B \u2192 15 days and A \u2192 12 days\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf x is a positive even number, then each of the following is even odd EXCEPT\n\n### Options:\nA. (x + 3)(x + 5)\nB. x^2 +4\nC. x^2 + 6x + 9\nD. 3x^2 + 4\nE. 5(x + 3)\n\n### Answer:\nSince it is given tht x is even number, so any integer multiplied with x will also be even..\nso, we should concentrate only on other terms..\nlets see the choices..\nA. (x + 3)(x + 5)\nWe have two terms with x and each is added with a odd number..\neach bracket becomes odd and Odd*Odd=Odd\nB. x^2 + 5\nhere we are adding an Odd number to even.. so E + O=O\nC. x^2 + 6x + 9\nhere we are again adding an Odd number to even.. so E +E + O=O\nD. 3x^2 + 4\nhere we are adding an Even number to even.. so E + E=E..\nso tjis is our answer\nE. 5(x + 3)\nagain O*O=O\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man has Rs. 480 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?\n\n### Options:\nA. 45\nB. 60\nC. 75\nD. 90\nE. 95\n\n### Answer:\nLet number of notes of each denomination be x.\nThen x + 5x + 10x = 480\n16x = 480\nx = 30.\nHence, total number of notes = 3x = 90.\nAnswer: Option D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe can empty 3 gallons per minute. All the three pipes working together can fill the tank in 15 minutes. The capacity of the tank is?\n\n### Options:\nA. 299\nB. 2767\nC. 120\nD. 287\nE. 261\n\n### Answer:\nWork done by the waste pipe in 1 minute = 1/15 - (1/20 + 1/24) = - 1/40\nVolume of 1/40 part = 3 gallons\\\nVolume of whole = 3 * 40 = 120 gallons.\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nS is the infinite sequence S1 = 2, S2 = 22, S3 = 222,...Sk = Sk\u20131 + 2(10k\u20131). If p is the sum of the first 30 terms of S, what is the ninth digit of p, counting right to left from the units digit?\n\n### Options:\nA. 1\nB. 2\nC. 4\nD. 6\nE. 9\n\n### Answer:\nC\nSum of unit digits of first 30 terms = 60\nSum of tens digits of first 30 terms = 58\nSum of thousands digits of first 30 terms = 56\nand so on..\np1 = 0\np2 = (6+58) = 4\np3 = (6+56) = 2\np4 = (6+54) = 0\np5 = (6+52) = 8\np6 = (5+50) = 5\np7 = (5+48) = 3\np8 = (5+46) = 1\np9 = (5+44) = 9\nANSWER: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 3^x*4^y = 1,594,323 and x \u2013 y = 13, then x = ?\n\n### Options:\nA. 10\nB. 11\nC. 12\nD. 13\nE. 14\n\n### Answer:\nSince 1,594,323 is an odd number, it is not a multiple of 4.\nThis means that y must equal zero.\nSince x - y = 13 and y = 0, then x = 13.\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo goods trains each 500 m long are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one?\n\n### Options:\nA. 40\nB. 45\nC. 48\nD. 51\nE. 44\n\n### Answer:\nRelative speed = 45 + 30 = 75 km/hr.\n75 * 5/18 = 125/6 m/sec.\nDistance covered = 500 + 500 = 1000 m.\nRequired time = 1000 * 6/125 = 48 sec.\nAnswer: Option C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA father said to his son, \"I was as old as you are at the present at the time of your birth\". If the father's age is 38 years now, the son's age five years back was:\n\n### Options:\nA. 14\nB. 67\nC. 56\nD. 89\nE. 34\n\n### Answer:\nLet the son's present age be x years. Then, (38 - x) = x\n2x = 38.\nx = 19.\nSon's age 5 years back (19 - 5) = 14 years.\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn doing a division of a question with zero remainder,a candidate\ntook 12 as divisor instead of 21.The quotient obtained by him was 35.\nThe correct quotient is?\n\n### Options:\nA. 12\nB. 21\nC. 20\nD. 35\nE. 10\n\n### Answer:\nDividend=12*35=420.\nNow dividend =420 and divisor =21.\nTherefore correct quotient =420/21=20.\nANSWER C 20\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn one hour, a boat goes 13 km along the stream and 5 km against the stream. The speed of the boat in still water (in km/hr) is:\n\n### Options:\nA. 2\nB. 4\nC. 9\nD. 12\nE. 15\n\n### Answer:\nSol.\nSpeed in still water = 1/2 (13+5) kmph = 9 kmph.\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man can row with a speed of 15 kmph in still water. If the stream flows at 20 kmph, then the speed in downstream is?\n\n### Options:\nA. 27\nB. 27\nC. 20\nD. 99\nE. 35\n\n### Answer:\nM = 15\nS = 25\nDS = 15 + 25 = 35\nAnswer:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a office work is distribute between p persons. If 1/5 members are absent then work increased for each person is?\n\n### Options:\nA. 13.28%\nB. 14.28%\nC. 15.28%\nD. 16.28%\nE. 25%\n\n### Answer:\nlet total % of work is 100%\ntotal person=p\n1/5 person are absent of total person . so absent person is 1/5p ie p/5.\nleft person is, p-p/5=4p/5.\np person do the work 100%\n1 person do the work 100*p%\n4p/5 person do the work (100*p*5)/4p%=125%\nwork increased for each person is=(125-100)%=25%\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nBob bikes to school every day at a steady rate of x miles per hour. On a particular day, Bob had a flat tire exactly halfway to school. He immediately started walking to school at a steady pace of y miles per hour. He arrived at school exactly t hours after leaving his home. How many miles is it from the school to Bob's home?\n\n### Options:\nA. (x + y) / t\nB. 2(x + t) / xy\nC. 2xyt / (x + y)\nD. 2(x + y + t) / xy\nE. x(y + t) + y(x + t)\n\n### Answer:\nSay the distance to school is 10 miles, x=5 miles per hour and y=1 miles per hour, then:\nTime Bob spent biking would be 5/5=1 hour, and time he s pent walking would be 5/1=5 hours, so t=1+5=6 hours.\nNow, plug x=5, y=1, and t=6 into the answer choices to see which one yields the distance of 10 miles. Only answer choice C fits.\nAnswer: C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train 400 m long can cross an electric pole in 20 sec and then find the speed of the train?\n\n### Options:\nA. 88 Kmph\nB. 89 Kmph\nC. 72 Kmph\nD. 16 Kmph\nE. 18 Kmph\n\n### Answer:\nLength = Speed * time\nSpeed = L/T\nS = 400/20\nS = 20 M/Sec\nSpeed= 20*18/5 (To convert M/Sec in to Kmph multiply by 18/5)\nSpeed = 72 Kmph\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA father said to his son, \"I was as old as you are at present at the time of your birth.\" If the father's age is 40 years now, the son's age 10 years back was?\n\n### Options:\nA. 12yr\nB. 15yr\nC. 14yr\nD. 10yr\nE. 20yr\n\n### Answer:\nLet the son's present age be x years\nThen, 40-x = x\nx = 20\nSon's age 10 years back = 20-10 = 10years\nAnswer is D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat number has a 5:1 ratio to the number 10?\n\n### Options:\nA. 74\nB. 50\nC. 94\nD. 59\nE. 48\n\n### Answer:\nAnswer: Option B\nExplanation:\n5:1 = x: 10\nx = 50\nAnswer: Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSeven fencers participate in a fencing championship. Assuming all competitors have an equal chance of winning, how many possibilities are there with respect to how a first-place and second-place medal can be awarded?\n\n### Options:\nA. 30\nB. 36\nC. 42\nD. 48\nE. 49\n\n### Answer:\n7*6 = 42\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the sum of two numbers is 30 and the sum of their squares is 840, then the product of the numbers is\n\n### Options:\nA. 40\nB. 44\nC. 80\nD. 88\nE. 30\n\n### Answer:\nSol.\nLet the numbers be x and y.\nThen, (x+y) = 30 and x2 + y2 = 840.\nNow, 2xy = (x+y)2 - (x2 + y2)\n= (30)2 - 840= 900 - 840= 60\nxy = 30.\nAnswer E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf P is a prime number greater than 5, what is the remainder when P^2 is divided by 6.\n\n### Options:\nA. 4\nB. Cannot be determined\nC. 2\nD. 6\nE. 1\n\n### Answer:\ntake square of any prime number\nremainder will be 1\nAns E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTina has 5 socks and 3 pair of shoes. How many combinations does Barbara have, if she doesn\u2019t wear 2 specific socks with 1 specific pair of shoes?\n\n### Options:\nA. 4\nB. 7\nC. 10\nD. 11\nE. 13\n\n### Answer:\nTotal no of combinations available is= 5 Socks X 3 pair of shoes = 15\nEliminate the 2 socks X 1 pair of shoes combo = 2 which gives.......>> 15-2=13\nANSWER: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow must a grocer mix 4 types of peanuts worth 54 c, 72 c, $1.2 and $1.44 per pound so as to obtain a mixture at 96 cents per pound?\n\n### Options:\nA. 8:4:4:7\nB. 24:12:12:50\nC. 4:8:7:4\nD. 16:42:28:10\nE. Cannot be uniquely determined\n\n### Answer:\nAs we know Sum of (Respective Quantity x Respective Price) = Total Price = Average price x Total Quantity\nOption 1\nRatio of quantity mixed - 8a:4a:4a:7a\nTotal quantity = 23a parts (8+4+4+7)\n(8a.9 + 4a.12 + 4a.20 + 7a.24) = 16.23a\n368a = 368a\nLHS = RHS\nThus option 1 satisfy the condition\nOption 2\nRatio of quantity mixed - 24a:12a:12a:50a or 12a:6a:6a:25a\nTotal quantity = 49a parts\n(12a.9 + 6a.12 + 6a.20 + 25a.24) = 16.49a\n900a = 784a\nLHS is not equal to RHS\nThus option 2 does not satisfy the condition\nOption 3\nRatio of quantity mixed - 4a:8a:7a:4a\nTotal quantity = 23a parts\n(4a.9 + 8a.12 + 7a.20 + 4a.24) = 16.23a\n368a = 368a\nLHS = RHS\nThus option 3 satisfy the condition\nAs we are asked a unique case, a problem can't have two solutions. Thus answer is it Cannot be uniquely determined\nAnswer E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n25.25/2000 is equal to:\n\n### Options:\nA. 1.012526\nB. 0.012625\nC. 0.12526\nD. 0.12625\nE. 0.12725\n\n### Answer:\n25.25/2000 = 2525/200000\n= 0.012625\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n3x^2-6x+3 = 0\nFind the above equation find the value of x\n\n### Options:\nA. 0\nB. 1\nC. 2\nD. 4\nE. 5\n\n### Answer:\na = 3, b = -6, c = 3\nx1,2 = (6 \u00b1 \u221a( (-6)2 - 4\u00d73\u00d73)) / (2\u00d73) = (6 \u00b1 \u221a(36-36)) / 6 = (6 \u00b1 0) / 6\nx1 = x2 = 1\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFor a group of n people, k of whom are of the same sex, the (n-k)/n expression yields an index for a certain phenomenon in group dynamics for members of that sex. For a group that consists of 20 people, 6 of whom are females, by how much does the index for the females exceed the index for the males in the group?\n\n### Options:\nA. 0.4\nB. 0.0625\nC. 0.2\nD. 0.25\nE. 0.6\n\n### Answer:\nIndex for females = (20-6)/20 = 7/10 = 0.7\nIndex for males = (20-14/20 = 3/10 = 0.3\nIndex for females exceeds males by 0.7 - 0.3 = 0.4\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA 300 meter long train crosses a platform in 39 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform?\n\n### Options:\nA. 177\nB. 166\nC. 350\nD. 198\nE. 161\n\n### Answer:\nSpeed = [300 / 18] m/sec = 50/3 m/sec.\nLet the length of the platform be x meters.\nThen, x + 300 / 39 = 50/3\n3(x + 300) = 1950 \u00e8 x = 350m.\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA, B, C enter into a partnership investing Rs. 35,000, Rs. 45,000 and Rs. 55,000 respectively. The respective shares of A, B, C in annual profit of Rs. 40,500 are?\n\n### Options:\nA. Rs. 10,500, Rs. 13,500, Rs. 16,500\nB. Rs. 10,500, Rs. 13,500, Rs. 16,509\nC. Rs. 10,500, Rs. 13,500, Rs. 16,555\nD. Rs. 10,500, Rs. 13,500, Rs. 16,506\nE. Rs. 10,500, Rs. 13,500, Rs. 16,504\n\n### Answer:\nA:B:C = 35000 : 45000 : 55000 = 7:9:11\nA's share = 40500 * 7/27 = Rs. 10500\nB's share = 40500 * 9/27 = Rs. 13500\nC's share = 40500 * 11/27 = Rs. 16500\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how many ways can the letters of the word ABACUS be rearranged such that the vowels always appear together?\n\n### Options:\nA. 6! / 2!\nB. 3! * 3!\nC. 4! / 2!\nD. (4! * 3!) / 2!\nE. (3! * 3!) / 2!\n\n### Answer:\nExplanatory Answer\nStep 1: Group the vowels as one unit and rearrange\nABACUS is a 6 letter word with 3 of the letters being vowels.\nBecause the 3 vowels have to appear together, let us group the AAU as one unit.\nThere are 3 consonants in addition to one unit of vowels.\nThese 4 elements can be rearranged in 4! ways.\nStep 2: Rearrange the letters within the unit containing the vowels\nThe 3 vowels can rearrange among themselves in 3!/2! ways as \"a\" appears twice.\nHence, the total number of rearrangements in which the vowels appear together is 4!\u22173!/2!\nChoice D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the population of a certain country increases at the rate of one person every 15 seconds, by how many persons does the population increase in 60 minutes?\n\n### Options:\nA. 80\nB. 100\nC. 150\nD. 240\nE. 300\n\n### Answer:\nSince the population increases at the rate of 1 person every 15 seconds, it increases by 4 people every 60 seconds, that is, by 4 people every minute. Thus, in 60 minutes the population increases by 60 x 4 = 240 people.\nAnswer. D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average age of a class of 39 students is 15 years. If the age of the teacher be included, then the average increases by3 months. Find the age of the teacher.\n\n### Options:\nA. 20\nB. 23\nC. 25\nD. 21\nE. 22\n\n### Answer:\nTotal age of 39 persons = (39 x 15) years\n= 585 years.\nAverage age of 40 persons= 15 yrs 3 months\n= 61/4 years.\nTotal age of 40 persons = (61/4 )x 40) years= 610 years.\n:. Age of the teacher = (610 - 585) years=25 years.\nAnswer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA monkey ascends a greased pole 20 metres high. He ascends 2 metres in first minute and slips down 1 metre in the alternate minute. In which minute, he reaches the top ?\n\n### Options:\nA. 21st\nB. 22nd\nC. 23rd\nD. 24th\nE. 37th\n\n### Answer:\nIn 2 minutes, he ascends = 1 metre\n\u00e2\u02c6\u00b4 18 metres, he ascends in 36 minutes.\n\u00e2\u02c6\u00b4 He reaches the top in 37th minute.\nAnswer E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTo fill a tank, 25 buckets of water is required. How many buckets of water will be required to fill the same tank if the capacity of the bucket is reduced to two-fifth of its present ?\n\n### Options:\nA. 65.5\nB. 63.5\nC. 60.5\nD. 61.5\nE. 62.5\n\n### Answer:\nLet the capacity of 1 bucket = x.\nThen, the capacity of tank = 25x.\nNew capacity of bucket = 2/5 x\nTherefore, Required number of buckets = (25x)/(2x/5)\n= (25x) x 5/2x\n= 125/2\n= 62.5\nAnswer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n6/8 of the population of the country of Venezia lives in Montague Province, while the rest lives in Capulet Province. In the upcoming election, 80% of Montague residents support Romeo, while 70% of Capulet residents support Juliet; each resident of Venezia supports exactly one of these two candidates. Rounded if necessary to the nearest percent, the probability that a Juliet supporter chosen at random resides in Capulet is\n\n### Options:\nA. 28%\nB. 54%\nC. 45%\nD. 72%\nE. 78%\n\n### Answer:\nTotal population = 80 (assume).\n6/8*80=60 people from Montague.\n2/8*80=20 people from Capulet.\n0.2*60=12 people from Montague support Juliet.\n0.7*20=14 people from Capulet support Juliet.\nThe probability that a Juliet supporter chosen at random resides in Capulet is 14/(12+14)=~54\nAnswer: B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average weight of 16 children in a class is 50.25 kg and that of the remaining 8 children is 45.15 kg. Find the average weights of all the children in the class.\n\n### Options:\nA. A)48.55\nB. B)49\nC. C)51\nD. D)61\nE. E)62\n\n### Answer:\nRequired average\n= (50.25 x 16 + 45.15 x 8)/(16 + 8)\n= (804 + 361.20)/24\n= 1165.20/24\n= 48.55kg\nAnswer is A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOne boy forgot the lastdigit of a 7 digit telephone no. If he randomly dialthe final 3 digits after correctly dialing the 1st four, then what is the chance of dialing the correct no.?\n\n### Options:\nA. 2/995\nB. 1/998\nC. 1/1000\nD. 1/1100\nE. 1/1200\n\n### Answer:\nit is given that last 3 digits are randomly dialed\nThen, each of the digit can be selected out of 10 digits in 10 ways. Hence, required probability\n= 1/(10)3 = 1/1000\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average of five numbers id 27. If one number is excluded, the average becomes 25. The excluded number is\n\n### Options:\nA. 25\nB. 27\nC. 30\nD. 35\nE. None\n\n### Answer:\nSolution\nExcluded number\t= (27 x 5 ) - ( 25 x 4)\n= 135 - 100\n= 35.\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n4 male and 6 female can cultivate a field in 8 days, 7 male and 3 female can cultivate a field in 10 days. then how many days will take to cultivate a field if 10 female works?\n\n### Options:\nA. 120/19\nB. 130/19\nC. 140/19\nD. 120/18\nE. 120/17\n\n### Answer:\n4 male+6female in 8 days=> 32 male+48 female in 1day\n7male+ 3 female in 10 days =>70 male+30 female in 1 day\n.:32 male+48 female=70 male+30 female\n18 female=38 male\n1 female= 38/18 male=19/9 male\nnow,4 male+6 female=4 male+6*(19/9)=50/3 male=150/9 male\nwe have to find for 10 female workers= 10*(19/9)=190/9 male\nmore men ,fewer days wud be req to finish work\nmale days\n150/9 8\n190/9 x\nso, x/8=(150/9)/(190/9)\nx=120/19\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the probability of rolling a nine with two, fair, six-sided dice?\n\n### Options:\nA. 1/6\nB. 1/9\nC. 2/13\nD. 1/12\nE. 5/36\n\n### Answer:\nThere are 4 ways to roll a nine: 3 and 6, 6 and 3, 4 and 5, 5 and 4 with two six-sided dice. There are 6 times 6 = 36 ways to roll two dice. The probability of rolling a 9 is thus 4/36 = 1/9. B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a is a positive integer and 10^a \u2013 74 in decimal notation has digits whose sum is 440, what is the value of a?\n\n### Options:\nA. 40\nB. 44\nC. 45\nD. 46\nE. 50\n\n### Answer:\nAnswer E = 50\nWe have (10^a)-74, where the sum of the digits is 440.\n100-74 = 26, so we already have 2+6 = 8 from the 440.\nBecause we have a power of 10, we will have numbers like 100, 1000, 10000 and so on. This minus 74 rests 26 and a lot of 9s. E.g: 1000-74 = 9926.\nSo dividing the 432/9 = 48, that`s the number of 9s. and we have 2 other numbers (2 and 6) wich were 00 before the subtraction.\nSo we have 48 + 2 as an a = 50\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA cube is painted red on all faces. It is then cut into 27 equal smaller cubes. How many P cubes are painted on only 2 faces?\n\n### Options:\nA. 12\nB. 8\nC. 6\nD. 10\nE. 16\n\n### Answer:\n1) Draw a simple cube\n2) Draw 9 squares on each face of the cube (so that it looks like a Rubik's Cube) - this is what the cube will look like when it's cut into 27 equal smaller cubes.\n3) Remember that the OUTSIDE of the cube is the part that's painted....\nThe mini-cubes with 2 painted sides are ALL on the edge of the cube, in themiddleof the edge. There are 4 in front, 4 in back and 4 more on thestripthat runs around the left/top/right/bottom of the cube. P=4 + 4 + 4 = 12. Answer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf x represents the sum of all the positive three-digit numbers that can be constructed using each of the distinct nonzero digits a, b, and c exactly once, what is the largest integer by which x must be divisible?\n\n### Options:\nA. 3\nB. 6\nC. 11\nD. 22\nE. 222\n\n### Answer:\nMaybe there is a faster way to do it but I did it like this:\nHow many ways can you arrange abc?\nabc\nacb\nbac\nbca\ncab\ncba\nwhich are equivalent to:\n100a + 10b + c\n100a + 10c + b\n100b + 10a + c\n100b + 10c + a\n100c + 10a + b\n100c + 10b + a\nif you add them all together you get 222a + 222b + 222c\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA shopkeeper sold an article for Rs 2524.36. Approximately what was his profit percent if the cost price of the article was Rs 2400\n\n### Options:\nA. 4%\nB. 5%\nC. 6%\nD. 7%\nE. 8%\n\n### Answer:\nExplanation:\nGain % = (125.36*100/2400) = 5.2 % = 5% approx\nOption B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe speed of a car increases by 2 kms after every one hour. If the distance travelling in the first one hour was 45 kms. what was the total distance traveled in 12 hours?\n\n### Options:\nA. 252 kms\nB. 152 kms\nC. 672 kms\nD. 752 kms\nE. 152 kms\n\n### Answer:\nExplanation:\nTotal distance travelled in 12 hours =(45+47+49+.....upto 12 terms)\nThis is an A.P with first term, a=45, number of terms,\nn= 12,d=2.\nRequired distance = 12/2[2 x 45+{12-1) x 2]\n=6(112)\n= 672 kms.\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man purchased 3 blankets @ Rs.100 each, 5 blankets @ Rs.150 each and two blankets at a certain rate which is now slipped off from his memory. But he remembers that the average price of the blankets was Rs.150. Find the unknown rate of two blankets?\n\n### Options:\nA. 300\nB. 350\nC. 450\nD. 470\nE. 500\n\n### Answer:\nExplanation:\n10 * 150 = 1500\n3 * 100 + 5 * 150 = 1050\n1500 \u2013 1050 = 450\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat percentage loss will a merchant incur if he marks his goods up by x% over his cost price and then offers a discount of x% on his selling price?\n\n### Options:\nA. 0 %\nB. 2x/100 %\nC. x^2/100 %\nD. x %\nE. 2x %\n\n### Answer:\nAnswer is C.\nTaking smart numbers:\nLet, C.P = 100$ and X = 20% over C.P\nthen Mark Up = 120$\nAfter discount of X%\nS.P= 80% of 120\nS.P = 96$\nTherefore Loss is 4$ and hence Loss in % = 4%\nPlugging numbers in options.\nA. 0 % ---------------------------Not truebecause loss is 4%\nB. 2x/100 % --------------------2*20/100 = 0.4%.Hence Not True\nC. x^2/100 % ------------------ 20^2/100 = 4%.True ANSWER IS C\nD. x % --------------------------- 20%.Hence Not True\nE. 2x % -------------------------- 2*20 = 40%.Hence Not True ANSWER IS C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nP and Q started a business investing Rs 10000 and Rs 15000 resp. In what ratio the profit earned after 2 years be divided between P and Q respectively.\n\n### Options:\nA. 2:7\nB. 2:6\nC. 17:6\nD. 2:3\nE. 7:8\n\n### Answer:\nExplanation:\nIn this type of question as time frame for both investors is equal then just get the ratio of their investments.\nP:Q = 10000:15000\n= 10:15\n= 2:3\nOption D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train 140 m long passes a man,running at 6 kmph in the direction opposite to that of the train,in 6 seconds.The speed of the train is\n\n### Options:\nA. 54 kmph\nB. 60 kmph\nC. 66 kmph\nD. 72 kmph\nE. 78 kmph\n\n### Answer:\nspeed of train relative to man: 140/6 * 18/5 km/hr\n= 84 km/hr\nlet speed of train= x\ntherefore x+6 = 84\nx= 84-6\nx=78 km/hr\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average of a group of men is increased by 5 years when a person aged of 18 years is replaced by a new person of aged 38 years. How many men are there in the group?\n\n### Options:\nA. 3\nB. 4\nC. 5\nD. 6\nE. 7\n\n### Answer:\nSolution: Let N be the no. of persons in the group.\nRequired number of person is given by;\nMember in group* aged increased = difference of replacement\nN*5 = 38-18\nOr, 5N = 20\nOr, N = 4.\nAnswer: Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA bag contains 3 blue and 5 white marbles. One by one, marbles are drawn out randomly until only two are left in the bag. What is the probability Z that out of the two, one is white and one is blue?\n\n### Options:\nA. 15/56\nB. 41/56\nC. 13/28\nD. 15/28\nE. 5/14\n\n### Answer:\nThe required probability Z= probability of choosing 6 balls out of the total 8 in such a way that we remove 4 out of 5 white and 2 out of 3 blue balls.\nWays to select 6 out of total 8 = 8C6\nWays to select 4 out of 5 white balls = 5C4\nWays to select 2 out of 3 blue balls = 3C2\nThus the required probability = (5C4*3C2)/8C6 = 15/28.\nD is thus the correct answer.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 4x + 3y = 8 and y-3x = 8, then what is the value of x + 4y?\n\n### Options:\nA. 1/7\nB. 16\nC. 15\nD. 52/7\nE. 60/7\n\n### Answer:\n4x+3y=8 ...equation 1\n-3x+y=8 ...equation 2\nadding both the equations\nx+4y=16\ncorrect answer option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAMOUNT OF BACTERIA PRESENT\nTime Amount\n1:00 P.M. 14.0 grams\n4:00 P.M. x grams\n7:00 P.M. 18.4 grams\nData for a certain biology experiment are given in the table above. If the amount of bacteria present increased by the same fraction during each of the two 3-hour periods shown, how many grams of bacteria were present at 4:00 P.M.?\n\n### Options:\nA. 14.0\nB. 16.1\nC. 16.0\nD. 12.3\nE. 12.4\n\n### Answer:\nThe question says that bacteria increased by same fraction, not by same amount in 2 intervals of 3 hours.\nLet X represent the amount of bacteria present at 4:00 PM. Since the fractional increase must remain constant from 1 to 4pm as it is from 4pm to 7pm:\nFractional increase from 1 PM to 4 PM = X / 14.0\nFractional increase from 4 PM to 7 PM = 18.4 / X\nX \\ 14 = 18.4 \\ X\nX^2 = 18.4 * 14\nX = 16\nanswer : C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nStatement : A large majority of the work force in India is unorganised. Most of them earn either the minimum or uncertain wages while others are engaged in sundry jobs.\nConclusions :\nI. The workers in the organised sector get better facilities and stay longer in their jobs.\nII. Some workers in the unorganised sector of the work force have a regular and fixed income.\n\n### Options:\nA. Only conclusion I follows\nB. Only conclusion II follows\nC. Either I or II follows\nD. Neither I nor II follows\nE. Both I and II follow\n\n### Answer:\nExplanation:\nConclusion I is not stated in the statement.\nOnly Conclusion II follows.\nOption B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA girl scout was selling boxes of cookies. In a month, she sold both boxes of chocolate chip cookies ($1.25 each) and boxes of plain cookies ($0.75 each). Altogether, she sold 1,585 boxes for a combined value of $1,587.75. How many boxes of plain cookies did she sell?\n\n### Options:\nA. 0\nB. 233\nC. 500\nD. 695\nE. 787\n\n### Answer:\nLet #plain cookies sold be X then #chocolate cookies = (total cookies-X)\nEquating for X\n(0.75)*X +(1.25)*(1585-X)=1587.75\n=>x=787\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the area of the quadrilateral of one of its diagonals is 20 cm and its off sets 9 cm and 6 cm?\n\n### Options:\nA. 128\nB. 150\nC. 882\nD. 272\nE. 121\n\n### Answer:\n1/2 * 20(9 + 6) = 150 cm2\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSum of 3 consecutive even no.'s is 26 more than the 1st no. of the series. Find the middle no.?\n\n### Options:\nA. 10\nB. 12\nC. 14\nD. 17\nE. 18\n\n### Answer:\nLet the numbers be x, x+2 and x+4 then\nx + x+2 + x+4 = x+26\n3x + 6 = x + 26\n2x = 20\n\\inline \\therefore x = 10\n\\inline \\therefore Middle number = x + 2 = 10+2 = 12\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a certain region, the number of children who have been vaccinated against rubella is twice the number who have been vaccinated against mumps. The number who have been vaccinated against both is twice the number who have been vaccinated only against mumps. If 4,000 have been vaccinated against both, how many have been vaccinated only against rubella?\n\n### Options:\nA. 2,5000\nB. 8,000\nC. 10,000\nD. 15,000\nE. 17,500\n\n### Answer:\nUse a single variable as far as possible.\nNumber vaccinated only against mumps = x\nNumber vaccinated against both = 2x = 4000 (so x = 2000)\nThen, number vaccinated against mumps (including both) = x + 2x = 3x\nNumber vaccinated against rubella = 2*3x = 6x\nThen, number vaccinated against only rubella = 6x - 2x = 4x = 4*2000 = 8,000\nAnswer (B)\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA guy was asked to specify his age in years. He said, \u201cTake my age 4 years hence, multiply it by four and subtract four times of my age 4 years ago and you will know my age.\u201d What was the age of that guy?\n\n### Options:\nA. 18\nB. 15\nC. 13\nD. 32\nE. 40\n\n### Answer:\nCurrent age of the guy = A years.\nThen, 4 (A + 4) \u2013 4 (A \u2013 4) = A\n(4A + 16) \u2013 (4A \u2013 16) = A\nA = 32\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHalf the people on a bus get off at each stop after the first, and no one gets on after the first stop. If only one person gets off at stop number 3, how many people got on at the first stop?\n\n### Options:\nA. 128\nB. 64\nC. 32\nD. 16\nE. 8\n\n### Answer:\nBefore stop 3, there were 2 passengers on the bus.\nBefore stop 2, there were 4 passengers on the bus.\nBefore stop 1, there were 8 passengers on the bus.\nThe answer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nExcluding stoppages, the average speed of a bus is 60 km/hr and including stoppages, the average speed of the bus is 40 km/hr. For how many minutes does the bus stop per hour?\n\n### Options:\nA. 15 min\nB. 18 min\nC. 16 min\nD. 20 min\nE. 26 min\n\n### Answer:\nIn 1hr, the bus covers 60 km without stoppages and 40 km with stoppages.\nStoppage time = time take to travel (60 - 40) km i.e 20 km at 60 km/hr.\nstoppage time = 20/60 hrs\n= 20 min\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn what time will a train 100 m long cross an electric pole, it its speed be 162 km/hr?\n\n### Options:\nA. 2.5\nB. 2.9\nC. 2.4\nD. 2.8\nE. 2.22\n\n### Answer:\nSpeed = 162 * 5/18 = 45 m/sec\nTime taken = 100/45\n= 2.22 sec.\nAnswer:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf f(x)=x^2 and x is a positive integer, which of the following CAN be the value of f(f(x))?\n\n### Options:\nA. 25\nB. 17\nC. 81\nD. 144\nE. 258\n\n### Answer:\nf(x)=x^2\nf(f(x)) = (x^2)^2\nf(f(3) = (3^2)^2 = 81\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\ny =2x^2 +2bx + 512 cuts the x axis at (h, 0) and (k, 0). If h and k are integers, what is the least value of b?\n\n### Options:\nA. 256\nB. -256\nC. -128\nD. -64\nE. -257\n\n### Answer:\nAs the curve cuts the x-axis at (h,0) and (k,0). Therefore h,k are the roots of the quadratic equation.\nFor the quadratic equation is in the form ofax^2+bx+c=0,\nThe product of the roots =c/a= 512/2=256 and the sum of the roots =-b/a=-b\n256 can be expressed as product of two numbers in the following ways:\n1 * 256\n2 * 128\n4 * 64\n8 * 32\n16 * 16\nThe sum of the roots is maximum when the roots are 1 and 256 and the maximum sum is 1 + 256 = 257.\nThe least value possible for b is therefore -257.\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSushil got thrice as many marks in English as in Science. His total marks in English, Science and Maths are 162. If the ratio of his marks in English and Maths is 3:5, find his marks in Science?\n\n### Options:\nA. 24\nB. 18\nC. 20\nD. 25\nE. 16\n\n### Answer:\nS:E = 1:3\nE:M = 3:5\n------------\nS:E:M = 3:9:15\n3/27 * 162 = 18\nANSWER B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nDuring a trip on an expressway, Lon drove a total of x miles. His average speed on a certain 5-mile section of the expressway was 30 miles per hour, and his average speed for the remainder of the trip was 60 miles per hour. His travel time for the x-mile trip was what percent greater than it would have been if he had traveled at a constant rate of 60 miles per hour for the entire trip?\n\n### Options:\nA. 8.5%\nB. 50%\nC. x/12%\nD. 60/x%\nE. 500/x%\n\n### Answer:\nso Lon drove (x-5) miles at 60mph and 5 miles at 30mph:\n(x-5)/60 + (10/60) = (X+5)/60 - current time to drive the whole distance\nif the entire trip @60mph than time = x/60\nso to get percent [(X+5)/60 ]/[x/60] x100\n=(x+5)/x *100\n=100+500/x\nso increase of 500/x%[/u]=E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nEach month, after Jill pays for rent, utilities, food, and other necessary expenses, she has one fifth of her net monthly salary left as discretionary income. Of this discretionary income, she puts 30% into a vacation fund, 20% into savings, and spends 35% on eating out and socializing. This leaves her with $102 dollar, which she typically uses for gifts and charitable causes. What is Jill\u2019s net monthly salary?\n\n### Options:\nA. $3400\nB. $3200\nC. $6000\nD. $6400\nE. $9600\n\n### Answer:\nlet x be the monthly salary\n15%of 1/5*x=102\nx=3400\nanswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a class there are 55 pupil, out of them 10 are in debate only and 18 in singing only. Then how many in both?\n\n### Options:\nA. 132\nB. 26\nC. 17\nD. 11\nE. 12\n\n### Answer:\nExplanation:Total pupil = 55\nDebate + Singing = 10 + 18 = 28\nThe intersection for two = 55 \u00e2\u20ac\u201c 10 \u00e2\u20ac\u201c 28 = 17 play both games.\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a group of Peacocks and cows, the total number of legs are 36 more than twice the no. of heads. Find the total no.of buffaloes.\n\n### Options:\nA. 10\nB. 19\nC. 12\nD. 16\nE. 18\n\n### Answer:\nLet the number of buffaloes be x and the number of ducks be y\n=> 4x + 2y = 2 (x + y) + 36\n=> 2x = 36 => x = 18\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe ratio of the volumes of two cubes is 125 : 216. What is the ratio of their total surface areas?\n\n### Options:\nA. 25:36\nB. 12:25\nC. 25:46\nD. 18:22\nE. 12:24\n\n### Answer:\nRatio of the sides = \u00c2\u00b3\u00e2\u02c6\u0161125 : \u00c2\u00b3\u00e2\u02c6\u0161216\n= 5 : 6\nRatio of surface areas =25:36\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n250 men work for 16 days and finish a work. How many men would do a job 3 times the previous one in 20 days?\n\n### Options:\nA. 700\nB. 666\nC. 600\nD. 400\nE. 800\n\n### Answer:\nNumber of men needed to finish the required work (variation, proportion method ) =3*16*250/20 =600 Answer : C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA furniture dealer purchased a desk for $120 and then set the selling price equal to the purchase price plus a markup that was 40% of the selling price. If the dealer sold the desk at the selling price, what was the amount of the dealer's gross profit from the purchase and the sale of the desk?\n\n### Options:\nA. $40\nB. $60\nC. $80\nD. $90\nE. $100\n\n### Answer:\nPurchase price = 120\nSelling price = x\n120 + 0.4*x = x\n0.6*x = 120\nx = 200\nProfit = 200 - 150 = 50\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn 1979 approximately 1/3 of the 32.3 million airline passengers traveling to or from the United States used Kennedy Airport. If the number of such passengers that used Miami Airport was 1/2 the number that used Kennedy Airport and 4 times the number that used Logan Airport, approximately how many millions of these passengers used Logan Airport that year?\n\n### Options:\nA. 18.6\nB. 9.3\nC. 6.2\nD. 1.33\nE. 1.6\n\n### Answer:\nnumber of\npassengers using Kennedy airport = 32/3 =~10.67\nPassengers using Miami airport = 10.67/2=~5.34\npassengers using logan airport = 5.34/4 =~1.33\nso D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nExactly 12% of the reporters for a certain wire service cover local politics in Country X. If 40% of the reporters who cover politics for the wire service do not cover local politics in Country X, what percent of the reporters for the wire service do not cover politics?\n\n### Options:\nA. 20%\nB. 42%\nC. 44%\nD. 80%\nE. 84%\n\n### Answer:\nLet's assume there are 100 reporters --> 12 reporters cover local politics.\nNow, as 40% of the reporters who cover all politics do not cover local politics then the rest 60% of the reporters who cover politics do cover local politics, so if there are x reporters who cover politics then 60% of them equal to 12 (# of reporters who cover local politics): 0.6x=12 --> x=20, hence 20 reporters cover politics and the rest 100-20=80 reporters do not cover politics at all.\nAnswer: D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a division sum, the remainder is 6 and the divisor is 5 times the quotient and is obtained by adding 12 to the thrice of the remainder. The dividend is\n\n### Options:\nA. 74\nB. 78\nC. 86\nD. 126\nE. 98\n\n### Answer:\nDivisor = (6 * 3) + 12 = 30\n5 * Quotient = 30\nQuotient = 6.\nDividend = (Divisor * Quotient) + Remainder\nDividend = (20 * 6) + 6 = 126.\nD)\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a 200-mile trip, the first 50 miles were completed at 40 mph. If the average speed for the whole trip was 50 mph, what was the average speed in the last 150 miles?\n\n### Options:\nA. 592/11 mph\nB. 594/11 mph\nC. 596/11 mph\nD. 598/11 mph\nE. 600/11 mph\n\n### Answer:\nThe time to complete the first 50 miles was (50 miles / 40 mph) = (5/4) hours.\nThe time to complete the whole trip was (200 miles / 50 mph) = (4) hours.\nThe time to complete the last 150 miles was (4) - (5/4) = (11/4) hours.\nThe average speed in the last 150 miles was (150 miles / (11/4) hours) = 600/11 mph.\nThe answer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJacob is now 13 years younger than Michael. If 9 years from now Michael will be twice as old as Jacob, how old will Jacob be in 4 years?\n\n### Options:\nA. 8\nB. 7\nC. 15\nD. 21\nE. 25\n\n### Answer:\nJacob=x years, Michael=x+13 years\n9 years from now,\n2(x+9)=x+22\n2x+18=x+22\nx=4\nx+4=8 years\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a family, the father took 1/4 of the cake and he had 3 times as much as each of the other members had. The total number of family members is\n\n### Options:\nA. 3\nB. 7\nC. 10\nD. 12\nE. 15\n\n### Answer:\n1-1/4 = remain cake 3/4\n3/4*3 = 9/4\n9/4+1/4 = 10\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich of the following equations has a solution in common with 2x^2 - 5x - 42?\n\n### Options:\nA. 2x^2 + 8x - 42 = 0\nB. x^2 - 14x + 24 = 0\nC. 2x^2 - 8x + 8 = 0\nD. x^2 + 13x + 13 = 0\nE. none of the above\n\n### Answer:\nGiven : 2x^2 - 5x - 42 => (2x + 7) (x - 6) = 0 => -7/2 and 6 are the roots..\nA. 2x^2 + 8x - 42 = 0 => (2x - 6) (x + 7)\nB. x^2 - 14x + 24 = 0 => (x - 6) (x - 8)\nC. x^2 + 13x + 13 = 0 => (2x -7) ( x - 1)\nD. x^2 + 13x + 13 = 0 => (x + 6) (x + 7)\nNone of the answer equations have exactly both the same roots as the question equation, but at least one of them does share one of the two roots.\nSo IMO \"B\" is correct answer... because it shares the one root (part of the solution), -3, from the (x+3) portion of its factoring\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf x=3y=4z, what is z+y, in terms of x?\n\n### Options:\nA. 3x/5\nB. 4x/9\nC. 11x/13\nD. 7x/12\nE. 5x/11\n\n### Answer:\nx=3y=4z\nx/4 = z\nand y = x/3\nz+y = x/4 + x/3 = 7x/12\nAnswer is D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA car is traveling 75 kilometers per hour. How many meters does the car travel in one minute?\n\n### Options:\nA. 1250m/min\nB. 1360m/min\nC. 2560m/min\nD. 1670m/min\nE. 1890m/min\n\n### Answer:\nConvert hour into minutes ( 1 hour = 60 minutes) and kilometers into meters (1 km = 1000 m) and simplify\n75 kilometers per hour = 75 km/hr\n= (75 \u00d7 1000 meters) / (60 minutes) = 1,250 meters / minute\ncorrect answer is A)1250m/min\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA vessel of capacity 90 litres is fully filled with pure milk. Nine litres of milk is removed from the vessel and replaced with water. Nine litres of the solution thus formed is removed and replaced with water. Find the quantity of pure milk in the final milk solution?\n\n### Options:\nA. 23:89\nB. 72.9\nC. 38:3\nD. 78:3\nE. 79:3\n\n### Answer:\nExplanation:\nLet the initial quantity of milk in vessel be T litres.\nLet us say y litres of the mixture is taken out and replaced by water for n times, alternatively.\nQuantity of milk finally in the vessel is then given by [(T - y)/T]n * T\nFor the given problem, T = 90, y = 9 and n = 2.\nHence, quantity of milk finally in the vessel\n= [(90 - 9)/90]2 (90) = 72.9 litres.\nAnswer: Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn the rectangular coordinate system, points (16, 0) and (\u2013 16, 0) both lie on circle C. What is the maximum possible value of the radius of C ?\n\n### Options:\nA. 2\nB. 4\nC. 8\nD. 16\nE. None of the above\n\n### Answer:\nD\nIt takes 3 distinct points to define a circle. Only 2 are given here.\nThe two points essentially identify a single chord of the circle C. Since no other information is provided, however, the radius of the circle can essentially be anything. All this information tell us is that the radius isgreater 16 D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA can do in 6 day and B can do in 8 and C can do in 12 days but b left after working for 6 days for how many no of day A and C shluld work ?\n\n### Options:\nA. 2 days\nB. 1 day\nC. 3 days\nD. 4 days\nE. 5 days\n\n### Answer:\nB for one day work is 1/8\nhe worked for 6 days, so 6*1/8=3/4 work will be completed.\nremaining work is 1-3/4=1/4\nA and C can complete the work in 4 days\nbut there is only 1/4 work that is to be completed, so A and C can complete 1/4 work in 1 day..\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwelve contestants at the county fair have entered their cakes to be judged in the cake decorating competition. A purple ribbon, blue ribbon, red ribbon, and white ribbon will be given to the first, second, third, and fourth place competitors, respectively. How many different ways are there to award the four ribbons to the contestants?\n\n### Options:\nA. 8!(4!*4!)\nB. 12!(8!*4!)\nC. 8!/4!\nD. 12!/8!\nE. 12!/4!\n\n### Answer:\nThe mistake you are doing is that you are neglecting the 4! ways in you can arrange 4 contestants for the 4 prizes.\nNumber of ways you can select 4 people out of 12 = 12C4\nOnce you select the 4 people, you have the following arrangement, PBRW (PBRW being the 4 prizes) but the same group of people can also be chosen against BRWP etc. Thus you get 4! ways of arranging 4 prizes.\nThus total possible ways = 12C4*4! = 12!/8!. D is the correct answer.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n9.99 x 9.9 x 9 \u00f7 9.9 \u00f7 0.3 = ?\n\n### Options:\nA. 276\nB. 299\nC. 310\nD. 3.33\nE. 365\n\n### Answer:\nExplanation:\n? = (9.99 x 9.9 x 9)/(9.9 x 0.9 x 0.3) = 3.33\nAnswer: Option D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe difference between the place value and the face value of 6 in the numeral 856973 is\n\n### Options:\nA. 5994\nB. 6973\nC. 973\nD. 1000\nE. 7000\n\n### Answer:\n(Place value of 6) - (Face value of 6) = (6000 - 6) = 5994\nANSWER A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man has Rs. 480 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?\n\n### Options:\nA. 70\nB. 80\nC. 90\nD. 100\nE. 110\n\n### Answer:\nExplanation:\nLet number of notes of each denomination be x.\nThen x + 5x + 10x = 480\n16x = 480\nx = 30.\nHence, total number of notes = 3x = 90.\nC)\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA clock loses a minute every three hours for 4 days and gains 2% in the subsequent 6 days. If it was set right on Friday at 11 AM, what will be the time at the end of 10 days?\n\n### Options:\nA. 01:54:40 PM\nB. 01:56:24 PM\nC. 12:46:40 PM\nD. 11:54:24 AM\nE. 01:20:48 PM\n\n### Answer:\nLoses 8 minutes each day.\nso total loss = 4\u00d78 = 32min\nsubsequent 6 days = 6\u00d748\u00d760 minutes\n1% gain = ( 6\u00d724\u00d760)/100 = 172.8 minutes\nso, total gain = 172.8 - 32 = 140.8 min = 140 + 0.8 min = 2 Hours 20 minutes + 0.4 \u00d7 60 seconds = 2 Hours 20 min + 48 seconds\n10 days later the clock should be 2 Hours 20 min + 48 seconds\nso time , 01:20:48 pm (Answer E)\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average age of husband, wife and their child 3 years ago was 21 years and that of wife and the child 5 years ago was 20 years. The present age of the husband is\n\n### Options:\nA. 22 years\nB. 40 years\nC. 50 years\nD. 55 years\nE. None\n\n### Answer:\nSolution\nSum of the present ages of husband, wife and child\t= (21x3+3x3) years\n= 72 years.\nSum of the present ages of wife and child\t= (20x2+5x2) years\n= 50 years.\n\u00e2\u02c6\u00b4 Husband's present age\t= (72 - 50) years\n= 22 years.\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are 145 bananas lying in a shop which is to be divided equally among 12 candidates. Find the extra number of bananas lying with the shop owner after distribution.\n\n### Options:\nA. 1\nB. 2\nC. 3\nD. 4\nE. 9\n\n### Answer:\n145 divided by 12 = 12x12+1. That is, 1 banana will be extra after distributing 12 bananas to each candidate (12 in number). Answer A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the two-digit integers A and B are positive and have the same digits, but in reverse order, which of the following could be the sum of A and B?\n\n### Options:\nA. 41\nB. 42\nC. 43\nD. 44\nE. 45\n\n### Answer:\nA two-digit number \"cd\" can be expressed algebraically as 10c+d.\nThe sum of A + B = (10c+d)+(10d+c)=11(c+d).\nThe only answer that is a multiple of 11 is 44.\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn what time will a train 100 meters long cross an electric pole, if its speed is 360 km/hr\n\n### Options:\nA. 1 second\nB. 4.5 seconds\nC. 3 seconds\nD. 2.5 seconds\nE. None of these\n\n### Answer:\nExplanation:\nFirst convert speed into m/sec\nSpeed = 360*(5/18) = 100 m/sec\nTime = Distance/speed\n= 100/100 = 1 second\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how many ways can 3 hats be formed out of 3 blue hats and 10 red hats?\n\n### Options:\nA. 12\nB. 302\nC. 1\nD. 250\nE. 286\n\n### Answer:\nTotal number of hats = 13\rPossible number of formations = 13C3 = 286\rCorrect answer is E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAyush was born two years after his father's marriage. His mother is five years younger than his father but 20 years older than Ayush who is 15 years old. At what age did the father get married ?\n\n### Options:\nA. 20years\nB. 21years\nC. 22years\nD. 23years\nE. 25years\n\n### Answer:\nExplanation:\nAyush's present age = 15 years.\nHis mother's present age = (15 + 20) years = 35 years.\nAyush's father's present age = (35 + 5) years = 40 years.\nAyush's father's age at the time of Ayush's birth = (40 - 15) years = 25 years.\nTherefore Ayush's father's age at the time of marriage = (25 - 2) years = 23 years.\nAnswer: D) 23 year\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train 240 m in length crosses a telegraph post in 16 seconds. The speed of the train is?\n\n### Options:\nA. 50\nB. 54\nC. 52\nD. 56\nE. 58\n\n### Answer:\nExplanation:\nspeed= Distance/ Time\nS = 240/16 * 18/5 = 54 kmph\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat number has a 5:1 ratio to the number 9?\n\n### Options:\nA. 45\nB. 50\nC. 88\nD. 52\nE. 12\n\n### Answer:\n5:1 = x: 9\nx = 45\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRs.705 is divided amongst A, B, C so that 3 times A's share, 5 times B's share and 4 times C's share are all equal. Find B's share?\n\n### Options:\nA. 177\nB. 150\nC. 180\nD. 716\nE. 616\n\n### Answer:\nA+B+C = 705\r3A = 5B = 4C = x\rA:B:C = 1/3:1/5:1/4\r= 20:12:15\r12/47 * 705\r= Rs.180\rAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf e is a positive integer, Which of the following options must be divisible by 2?\n\n### Options:\nA. (e\u22121)*e*(e+1)\nB. e^2*(e\u22125)\nC. e^2*(e\u22125)\nD. (e^2\u22122)\nE. e(e+2)^3\n\n### Answer:\noption A) (e\u22121)*e*(e+1) which represents the product of three consecutive integers\nthe product of 3 consecutive integers is divisible by both 2 and 3.\nAnswer is A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the L.C.M of 20,50,100\n\n### Options:\nA. 400\nB. 200\nC. 600\nD. 800\nE. 1000\n\n### Answer:\n20=2^2*5 50=2*5^2 100=2^4*5^2\nL.C.M=2^4*5^2=400\nAnswer=(A)\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe third proportional to 1 and 5 is?\n\n### Options:\nA. 8\nB. 27\nC. 24\nD. 25\nE. 3\n\n### Answer:\n(5*5)/1 = 25\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nLisa is buying candy at the grocery store, and has $15 on hand. M&M's are $4.50, Snickers are $6.00, Reese's are $5.50, and Milky Way's are $7.25. Of the following, which of the 5 options could Lisa buy to have $4.00 leftover for a Coffee at Starbucks?A\n\n### Options:\nA. 2 M&M's (9)\nB. 2 Snickers (12)\nC. 2 Reese's (11)\nD. 2 Milky Way's (14.50)\nE. A & C\n\n### Answer:\nThe correct answer must be the Sum of 2 correct candies with a remainder of at least $4\nA=(2*4.50+4) = $13 ($15 on hand is enough)\nB=(2*6+4) =$16 ($15 on hand is not enough)\nC=(2*5.50+4) = $15 (exactly enough on hand)\nD=(2*7.25+4) = $18.50 ($15 on hand is not enough)\nE= A & C (Total of both candies and $4 coffee is $15 or less) *Correct Answer*\nThe Correct Answer is E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nBob finishes the first half of an exam in one-thirds the time it takes him to finish the second half. If the whole exam takes him an hour, how many minutes does he spend on the first half of the exam?\n\n### Options:\nA. 20\nB. 24\nC. 27\nD. 30\nE. 40\n\n### Answer:\nMany times, it is easiest to think of problems like this conceptually (as opposed to formulaically). Conceptually, if the first half of the exam takes 1/3's the time of the second half (3/3's), we can see that the hour the entire exam took to finish can be broken down into fifth's. (Another way to look at this problem is via ratio's - first half is 1:5 and the second half is 3:5). With each fifth of an hour being 15 minutes (60/4), the first half of the exam would have taken 30 minutes. Correct answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA house seller can deduct 5 percent from the total sales value. If he has sold 5 houses, and the price of two houses is between $100,000 and $250,000, one of them is $300,000 house, two houses are between $500,000 and 750,000, what is the range of his revenue?\n\n### Options:\nA. 800\nB. 850\nC. 875\nD. 880\nE. 900\n\n### Answer:\n(1) 2(100)+300+2(500) = 1500\n1500*0.95=1425 (Revenue considering the minimum values with the discount)\n(2) 2(250)+300+2(750) = 2300 (Revenue considering the maximum values without the discount)\nSo, the the revenue range could be = 2300 - 1425 = 875\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the cost of fencing around a circular field of diameter 20 m at the rate of Rs.1.50 a meter?\n\n### Options:\nA. 287\nB. 94.2\nC. 156\nD. 158\nE. 267\n\n### Answer:\n2 * 22/7 * 10 = 62.8\n62.8 * 1 1/2 = Rs.94.2\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nCalculate how many ways a woman who has 4 bags and 6 books can put the books in her bag?\n\n### Options:\nA. 4296\nB. 4056\nC. 4016\nD. 4096\nE. 3096\n\n### Answer:\nFirst books can be put in 4 ways, similarly second, third , forth, fifth and sixth book also can be put in 4 ways.\nSo total number of ways = 4 x 4 x 4 x 4 x 4 x 4 = 4096\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThree partners A, B, C in a business invested money such that 3(A\u00e2\u20ac\u2122s capital) = 2(B\u00e2\u20ac\u2122s capital) = 5(C\u00e2\u20ac\u2122s capital) then, The ratio of their capitals is\n\n### Options:\nA. 63 : 45 : 34\nB. 63 : 54 : 34\nC. 36 : 54 : 28\nD. 63 : 45 : 35\nE. 10 : 15 : 6\n\n### Answer:\nExplanation:\nLet 3(A\u00e2\u20ac\u2122s capital) = 2(B\u00e2\u20ac\u2122s capital) = 5(C\u00e2\u20ac\u2122s capital) = Rs.x\nThen, A\u00e2\u20ac\u2122s capital = Rs x/3, B\u00e2\u20ac\u2122s capital = Rs. x/2 and C\u00e2\u20ac\u2122s capital = Rs. x/5.\nA : B : C = x/3 : x/2 : x/5\n10 : 15 : 6\nAnswer: Option E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average weight of a group of boys is 30 kg. After a boy of weight 35 kg joins the group, the average weight of the group goes up by 1 kg. Find the number of boys in the group originally ?\n\n### Options:\nA. 4\nB. 5\nC. 6\nD. 7\nE. 9\n\n### Answer:\nLet the number off boys in the group originally be x.\nTotal weight of the boys = 30x\nAfter the boy weighing 35 kg joins the group, total weight of boys = 30x + 35\nSo 30x + 35 + 31(x + 1) = > x = 4.\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAfter a storm deposits 120 billion gallons of water into the city reservoir, the reservoir is 60% full. If the original contents of the reservoir totaled 240 billion gallons, the reservoir was approximately what percentage full before the storm?\n\n### Options:\nA. 40%\nB. 48%\nC. 54%\nD. 58%\nE. 65%\n\n### Answer:\nWhen the storm deposited 120 billion gallons, volume of water in the reservoir = 240 + 120 = 360 billion gallons\nIf this is only 60% of the capacity of the reservoir, the total capacity of the reservoir = 360/0.6 = 600 billion gallons\nTherefore percentage of reservoir that was full before the storm = (240/600)*100 = 40%\nOption C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhen positive integer n is divided by 3, the remainder is 1. When n is divided by 8, the remainder is 5. What is the smallest positive integer p, such that (n + p) is a multiple of 15?\n\n### Options:\nA. 1\nB. 2\nC. 5\nD. 19\nE. 20\n\n### Answer:\nWhen positive integer n is divided by 3, the remainder is 1 i.e., n=3x+1\nvalues of n can be one of {1, 4, 7, 10, 13, 16, 19, 22..............49, 52, 59..................}\nSimilarly,\nWhen n is divided by 8, the remainder is 5..i.e., n=7y+5\nvalues of n can be one of {5, 13, 21, 29, 37, 45, 53, 61........}\ncombining both the sets we get\nn={13, 37, ...........}\nWhat is the smallest positive integer p, such that (n + p) is a multiple of 15 or 15x\nin case of n=13 p=2\nso for min value of p, we take min value of n.\nB is the answer.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered. If the area of the field is 680 sq. feet, how many feet of fencing will be required ?\n\n### Options:\nA. 34\nB. 40\nC. 68\nD. 88\nE. None of these\n\n### Answer:\nSolution\nWe have : l = 20 ft and lb = 680 sq. ft. So, b = 34 ft.\n\u2234 Length of fencing = (l + 2b) = (20 + 68) ft = 88 ft. Answer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n70,76, 74,85,90,105,105,130,130,130\nThe list consists of the times in seconds that it took each of the 10 school children to run a distance of 400 mts . If the standard deviation of the 10 running times is 22.4, rounded to the nearest tenth of a second, how many of the 10 running times are more than 1 standard deviation below the mean of the 10 running times.\n\n### Options:\nA. 1\nB. 2\nC. 3\nD. 4\nE. 5\n\n### Answer:\nHow many of the 10 running times are more than one SD below the meanmeans how many data points from given 10 are less thanmean-1SD.\nWe are given that SD=22.4, so we should find mean --> mean=100 --> there are only 3 data points below 100-22.4=77.6, namely 70 75, and 74.\nAnswer: C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the arithmetic mean of seventy five numbers is calculated, it is 35. If each number is increased by 5, then mean of new number is?\n\n### Options:\nA. 22\nB. 40\nC. 28\nD. 21\nE. 27\n\n### Answer:\nA.M. of 75 numbers = 35\nSum of 75 numbers = 75 * 35 = 2625\nTotal increase = 75 * 5 = 375\nIncreased sum = 2625 + 375 = 3000\nIncreased average = 3000/75\n= 40.\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the next number of the following sequence\n108,58,50,8,?\n\n### Options:\nA. 40\nB. 50\nC. 30\nD. 42\nE. 35\n\n### Answer:\n108-58=50\n58-50=8\n50-8=42\ntherefore next no. is 42\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMarch 11, 2003 is a Tuesday. What will be the day on which march 11 2004 comes??\n\n### Options:\nA. Thursday\nB. Friday\nC. Saturday\nD. Sunday\nE. Monday\n\n### Answer:\n2004 is a leap year that means 29 days in feb.\nso march 11,2003 to march 11, 2004 will be 366 days.\n366/7=52 weeks + 2 days. Hence Thursday\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA candidate appearing for an examination has to secure 35% marks to pass paper I. But he secured only 42 marks and failed by 23 marks. What is the maximum mark for paper I?\n\n### Options:\nA. 110\nB. 120\nC. 186\nD. 140\nE. 150\n\n### Answer:\nhe secured 42 marks nd fail by 23 marks so\ntotal marks for pass the examinatn=65\nlet toal marks x\nx*35/100=65\nx=186\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA rectangular photograph is surrounded by a border that is 1 inch wide on each side. The total area of the photograph and the border is M square inches. If the border had been 7 inches wide on each side, the total area would have been (M + 264) square inches. What is the perimeter of the photograph, in inches?\n\n### Options:\nA. 8\nB. 12\nC. 16\nD. 20\nE. 24\n\n### Answer:\nLet x and y be the width and length of the photograph.\n(x+2)(y+2)=M and so (1) xy + 2x + 2y + 4 = M\n(x+14)(y+14)=M and so (2) xy + 14x + 14y + 196 = M+264\nLet's subtract equation (1) from equation (2).\n12x + 12y + 192 = 264\n2x + 2y = 12, which is the perimeter of the photograph.\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf n + 15 is a positive odd integer, which of the following must be true about the sum of the next four integers?\n\n### Options:\nA. It is a multiple of 3\nB. It is a multiple of 4\nC. It is a prime number\nD. It is a multiple of 5\nE. It is a multiple of 2\n\n### Answer:\nn+15 is a positive odd integer. This means n will be an odd integer\nThe next 4 integers would be: n + 15, n + 16, n + 17, n + 18\nSum = 4n + 56\nThis sum will always be even.\nOption B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA piece of work can finish by a certain number of men in 100 days. If however, there were 10 men less, it would take 10 days more for the work to be finished. How many men were there originally?\n\n### Options:\nA. 75\nB. 82\nC. 100\nD. 110\nE. 120\n\n### Answer:\nOriginally let there be x men.\nLess men, more days (Indirect)\n:. (x-10): x : : 100 :110 or x-10/x = 100/110\nor 11x-110 = 10x or x =110\nSo, originally there were 110 men.\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSome articles were bought at 6 articles for Rs. 5 and sold at 5 articles for Rs. 6. Gain percent is:\n\n### Options:\nA. 30%\nB. 32%\nC. 34%\nD. 35%\nE. 44%\n\n### Answer:\nSuppose, number of articles bought = L.C.M. of 6 and 5 = 30.\nC.P. of 30 articles = Rs.5/6x30= Rs. 25.\nS.P. of 30 articles = Rs.6/5x 30= Rs. 36.\nGain % =\t11/25x 100% = 44%.\nAnswer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich of the following equations describes a line that is perpendicular to y=x+5?\n\n### Options:\nA. y = x \u2212 5\nB. y = \u22121 \u2212 x\nC. y = 5x\nD. y = 5x+1\nE. y = 1/x + 5\n\n### Answer:\nTwo perpendicular lines have slopes that are inverse reciprocals of each other.\nThe slope of y=x+5 is 1 so the slope of a perpendicular line will be -1.\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man has Rs. 160 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?\n\n### Options:\nA. 30\nB. 60\nC. 75\nD. 90\nE. 105\n\n### Answer:\nAnswer : A\nLet number of notes of each denomination be x.\nThen, x + 5x + 10x = 160\n16x = 160\nx = 10.\nHence, total number of notes = 3x = 30.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a box there are 5 red balls and 6 blue balls. What is the probability of drawing at least one red ball when drawing 3 consecutive balls randomly?\n\n### Options:\nA. 201/202\nB. 164/165\nC. 256/259\nD. 98/103\nE. 115/217\n\n### Answer:\nP(at least one red) = 1 - P(no red, so 3 blue) = 1- 3/11*2/10*1/9 = 164/165.\nAnswer is B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe probability that B can shoot a target two out of two times is 0.5. What is the probability that the target will be missed by B immediately after such two shots?\n\n### Options:\nA. 0.25\nB. 0.5\nC. 0.75\nD. 0.4\nE. 0.8\n\n### Answer:\nSuppose there are total 'x' shots.\nB shoots 2 out of 2 times. means out of x shots (x>2) B shots 2 out of 2 ----> B shots at least 2 out of x.\ntherefore, 2/x = 0.5 (given)\nthe target will be missed by B immediately after such two shots : this means he can shot just twice ...the third shot cannot happen which means he missed (x-2) shots.\nthus, the probabilty of missing just after 2 shots is (x-2)/x.\n(x-2)/x = 1 - 2/x\n= 1 - 0.5\n= 0.5\nAnswer : B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nEric, Nick and Archi make contributions to the Society Of Nature Protection in the ratio of 5:3:2.5. If altogether they contribute 5145 Nis, how much more money does Nick contribute than Archi?\n\n### Options:\nA. 128 Nis\nB. 212 Nis\nC. 234 Nis\nD. 245 Nis\nE. 288 Nis\n\n### Answer:\nNormalising the fraction from 5:3:2.5 to 10:6:5 (Eric: Nick:Archi)\nGiven Nick contributes one unit more than Archi and one unit of 5145/(10+6+5) = 245\nAnswer is D: 245 Nis\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA boy was asked to multiply a number by 25. He instead multiplied the next number by 52 and got the answers 324 more than the correct answer. The number to be multiplied was\n\n### Options:\nA. 10\nB. 12\nC. 15\nD. 25\nE. 14\n\n### Answer:\nLet the number be x.\nThen, 52 x - 25 x\t= 324\n\u2039=\u203a 27 x = 324\nx= 12.\nAnswer :B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nExcluding stoppages, the speed of a bus is 54 kmph and including stoppages, it is 45 kmph. For how many minutes does the bus stop per hour?\n\n### Options:\nA. 9\nB. 10\nC. 12\nD. 20\nE. 22\n\n### Answer:\nDue to stoppages, it covers 9 km less.\nTime taken to cover 9 km = (9/54 x 60) min = 10 min.\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJerry received a 10% raise each month for two consecutive months. What was his starting salary if after the two raises his salary is $1452?\n\n### Options:\nA. $1,200\nB. $1,300\nC. $1,331\nD. $1,380\nE. $1,403\n\n### Answer:\nS * 1.1 * 1.1 = 1452 so,\nS = 1200\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA grocer has a sale of Rs. 7435, Rs. 7920, Rs. 7855, Rs. 8230 and Rs. 7560 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 7500?\n\n### Options:\nA. 500\nB. 2000\nC. 5000\nD. 6000\nE. 7000\n\n### Answer:\nTotal sale for 5 months = Rs. (7435 + 7920 + 7855 + 8230 + 7560) = Rs. 39000.\nRequired sale = Rs. [ (7500 x 6) - 39000 ]\n= Rs. (45000 - 39000)\n= Rs. 6000\nAnswer: Option D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSouju's age is 125% of what it was 10 years ago, but 83 1/3% of what it will be after 10 years. What is her present age?\n\n### Options:\nA. 50 years\nB. 62 years\nC. 56 years\nD. 60 years\nE. 76 years\n\n### Answer:\nLet the age before 10 years =x. Then,\n125x/100=x+10\n\u00e2\u2021\u2019125x=100x+1000\n\u00e2\u2021\u2019x=1000/25=40\nPresent age =x+10=40+10=50\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nLet y = 2m + x^2 and m = 5x + 5. If m^2 =100, then which of the following can be a value of 2y + 3m?\n\n### Options:\nA. 83\nB. 63\nC. 93\nD. 73\nE. 53\n\n### Answer:\nm^2 = 100 => m=10\n10= 5x+5 => x=1\ny= 2*10+1^2 = 21\n2y+3m = 2*21+3*10 = 93\nAnswer : C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe C.P of 15 books is equal to the S.P of 18 books. Find his gain% or loss%?\n\n### Options:\nA. 16 2/3% loss\nB. 100/3% loss\nC. 50/3% profit\nD. 100/3% loss\nE. None of these\n\n### Answer:\nExplanation:\n15 CP = 18 SP\n18 --- 3 CP loss\n100 --- ? => 16 2/3% loss\nANSWER IS A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are between 90 and 100 cards in a collection of cards. If they are counted out 3 at a time, there is 1 left over, but if they are counted out 4 at a time, there is 1 left over. How many cards are in the collection?\n\n### Options:\nA. 91\nB. 93\nC. 95\nD. 97\nE. 99\n\n### Answer:\nThe numbers with the form 4n+1 are 93 and 97.\nOnly 97 has the form 3k+1.\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n1+3=2 2+3=10 3+3=30 4+3=68 5+3=??\n\n### Options:\nA. 110\nB. 120\nC. 130\nD. 140\nE. 150\n\n### Answer:\n1^3+3-2=2,\n2^3+3-1=10,\n3^3+3-0=30,\n4^3+3+1=68,\n5^3+3+2=130\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe result when a number subtracted from 100 is the same as the number added to 40. what is the number?\n\n### Options:\nA. 70\nB. 65\nC. 80\nD. 140\nE. 60\n\n### Answer:\nAnswer\nLet the number be x.\nThen, x - 40= 100- x\n\u00e2\u2021\u2019 2x = 100+ 40= 140\n\u00e2\u2021\u2019 2x = 140\n\u00e2\u02c6\u00b4 x = 70\nCorrect Option: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n1500 is increased by 20%. Find the final number.\n\n### Options:\nA. 1500\nB. 1800.\nC. 1900\nD. 1700\nE. 1660\n\n### Answer:\nFinal number = Initial number + 20%(original number) = 1500 + 20%(1500) = 1500 + 300 = 1800.\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe sum of a number and its square is 1406. What is the number?\n\n### Options:\nA. 1409\nB. 1402\nC. 1221\nD. 1406\nE. 8828\n\n### Answer:\nExplanation:\nBy option Verification 37 + 37 \u00d7 37 = 1406\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n5,9,18,31,52,__\n\n### Options:\nA. 79\nB. 80\nC. 86\nD. 82\nE. 83\n\n### Answer:\n(9+5) +4 = 18\n(16+9) +6 = 31\n(28+16)+8 = 52\n(48+28)+10 = 86\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are 12 stations between Ernakulam and Chennai. How many second class tickets have to be printed, so that a passenger can travel from one station to any other station?\n\n### Options:\nA. 132\nB. 145\nC. 165`\nD. 400\nE. 300\n\n### Answer:\nThe total number of stations= 12\nFrom 12 Stations we have to choose any two stations and the direction of travel (Ernakulam to Chennai is different from Chennai to Ernakulam) in 12P2 ways.\n12P2= 12*11= 870\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If two marbles are drawn at random, what is the probability that at least one is green?\n\n### Options:\nA. 23/35\nB. 23/356\nC. 23/36\nD. 23/32\nE. 23/31\n\n### Answer:\nGiven that there are three blue marbles, four red marbles, six green marbles and two yellow marbles.\nProbability that at least one green marble can be picked in the random draw of two marbles = Probability that one is green + Probability that both are green\n= (\u2076C\u2081 * \u2079C\u2081)/\u00b9\u2075C\u2082 + \u2076C\u2082/\u00b9\u2075C\u2082\n= (6 * 9 * 2)/(15 * 14) + (6 * 5)/(15 * 14) = 36/70 + 1/7\n= 46/70 = 23/35\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA grocer stacked oranges in a pile. The bottom layer was rectangular with 5 rows of 5 oranges each. In the second layer from the bottom, each orange rested on 4 oranges from the bottom layer, and in the third layer, each orange rested on 4 oranges from the second layer. Which of the following is the maximum number of oranges that could have been in the third layer?\n\n### Options:\nA. 2\nB. 4\nC. 6\nD. 7\nE. 9\n\n### Answer:\nBottom Layer = 5 x 5 = 25\nIInd Layer = (5-1) x (5-1) = 16\nIIIrd Layer = (4-1) x (4-1) = 9\nAnswer = 9 = E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nthere is a equilateral triangle whose area is A.another triangle is formed by joining the mid points.this process is continued.find the sum of these areas.\n\n### Options:\nA. A/3\nB. 2A/3\nC. A\nD. 4A/3\nE. 5A/3\n\n### Answer:\nArea of equilateral triangle =(root(3)/4)*a^2=A(given)\nside of triangle=a\nnow side is a/2\nthen total area A+A/4 +A/16-------\nA/1-(1/4)=A*4/3 is total area\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe number of bacteria in a petri dish increased by 50 percent every 2 hours. If there were 108 million bacteria in the dish at 4: 00 p.m., at what time were there 32 million bacteria in the dish?\n\n### Options:\nA. 6: 00 p.m.\nB. 8: 00 p.m.\nC. 10: 00 a.m.\nD. 8: 00 a.m.\nE. 11: 00 a.m.\n\n### Answer:\nGiven:\nhe number of bacteria in a petri dish increased by 50 percent every 2 hours\nThere were 108 million bacteria in the dish at 4: 00 p.m\nSince the bacteria is increasing by 50% every 2 hours, this means that the number is multiplied by 1.5 every 2 hours.\nRequired: At what time were there 32 million bacteria in the dish?\nAssume that there were n intervals of 2 hours between 32 million and 108 million.\n32 * (1.5)^n = 108\n(3/2)^n = 108/32 = 27/8 = (3/2)^3\nHence n = 3 intervals.\nEach interval was of 2 hours. Therefore, the number of hours = 6\nSubtracting 6 hours from 4 PM, we get 10 AM as the answer.\nOption C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 100% of j is equal to 25% of k, 150% of k is equal to 50% of l, and 125% of l is equal to 75% of m, then 20% of m is equal to what percent of 200% of j ?\n\n### Options:\nA. 0.35\nB. 3.5\nC. 350\nD. 35\nE. 3500\n\n### Answer:\nIMO answer should be 350...\nconsider j=10, then k=50, l=150 and m=350....\n20% of 350, comes out to be 70....\n200% of 10 is 20....\n(70*100)/20=350....\nAns : C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nBen\nips a fair coin repeatedly. Given that Ben's first coin\nip is heads, compute the probability\nBen\nips two heads in a row before Ben\nips two tails in a row.\n\n### Options:\nA. 2/3\nB. 3/3\nC. 1/3\nD. 1/1\nE. 2/2\n\n### Answer:\nIf Ben successfully\nips two heads in a row, then Ben must have\nipped the coin an\neven number of times. If Ben successfully\nips two tails in a row, then he must have\nipped\nthe coin an odd number of times. However, the coin must have been\nipped at least twice. The\ndesired probability is therefore\n(1/3)/(1/2)=2/3\ncorrect answer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA person travelled from his house to office at 20km/hr and office to house at 80km/hr. Then find the average speed?\n\n### Options:\nA. 32km/hr\nB. 40km/hr\nC. 48km/hr\nD. 50km/hr\nE. 62km/hr\n\n### Answer:\nAverage speed = (2*20*80)/(20+80)\r= 32km/hr\rAnswer is A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nCalculate the distance covered by 150 revolutions of a wheel of radius 20.5 cm.\n\n### Options:\nA. 293.3 m\nB. 197.3 m\nC. 193.3 m\nD. 143.3 m\nE. 198.3 m\n\n### Answer:\nIn one resolution, the distance covered by the wheel is its own circumference. Distance covered in 500 resolutions.\n= 150 * 2 * 22/7 * 20.5 = 19328.57 cm = 193.3 m\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a and b are consecutive integers (b>a), which of the following statements could be false? 1. a^3+b is always even number. 2. ab is even number 3. (a + b) is always an odd number.\n\n### Options:\nA. II only\nB. III only\nC. I only\nD. I,II only\nE. II,III only\n\n### Answer:\n2^3+3 =8+3 = 11 Option I false\nodd*even = even. Option II is true\nodd + even = odd. Option III is true\nAnswer : C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA dog travelled for 2 hours. He covered the first half of the distance at 10 kmph and remaining half of the distance at 5 kmph. Find the distance travelled by the dog?\n\n### Options:\nA. 20 km\nB. 16 km\nC. 6 km\nD. 3 km\nE. 61 km\n\n### Answer:\nLet the distance travelled be x km.\nTotal time = (x/2)/10 + (x/2)/5 = 2 => x/20 + x/10\n= 2 => (1x + 2x)/20 = 2 => x\n= 20 km\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFor any positive integer n, the sum of the first n positive integers equals [n(n+1)]/2.\nWhat is the sum of all the even integers between 99 and 201?\n\n### Options:\nA. 6540\nB. 7650\nC. 8760\nD. 9870\nE. 10,980\n\n### Answer:\n100 + 102 +...+ 200 = 51*100 + (2+4...+100) = 51*100 + 2(1+2+...+50) =\n51*100 + 2(50)(51)/2 = 150*51 = 7650\nThe answer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAravind had $ 2100 left after spending 30 % of the money he took for shopping. How much money did he\ntake along with him?\n\n### Options:\nA. 2000\nB. 2300\nC. 3000\nD. 3200\nE. 3400\n\n### Answer:\nLet the money he took for shopping be m.\nMoney he spent = 30 % of m\n= 30/100 \u00d7 m\n= 3/10 m\nMoney left with him = m \u2013 3/10 m = (10m \u2013 3m)/10 = 7m/10\nBut money left with him = $ 2100\nTherefore 7m/10 = $ 2100\nm = $ 2100\u00d7 10/7\nm = $ 21000/7\nm = $ 3000\nTherefore, the money he took for shopping is $ 3000.\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAnnie will be half as old as Larry in 3 years. Annie will also be one-third as old as Jerome in 5 years. If Jerome is 11 years older than Larry, how old is Annie?\n\n### Options:\nA. 4\nB. 8\nC. 19\nD. 26\nE. 34\n\n### Answer:\nJ = L+11\n(1) 2(A+3) = L+3\n(2) 3(A+5) = J+5 = L+16\nLet's subtract equation (1) from equation (2)\nA+9 = 13\nA = 4\nThe answer is A.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe captain of a cricket team of 11 members is 26 years old and the wicket keeper is 3 years older. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. What is the average age of the team?\n\n### Options:\nA. 23 years\nB. 24 years\nC. 25 years\nD. None of these\nE. Cannot be determined\n\n### Answer:\nExplanation: Let the average age of the whole team by x years.\n11x - (26 + 29) = 9(x -1)\n11x - 9x = 46\n2x = 46\nx = 23.\nSo, average age of the team is 23 years.\nAnswer: Option A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train running at a speed of 36 kmph crosses an electric pole in 12 seconds. In how much time will it cross a 360 m long platform?\n\n### Options:\nA. 37 min\nB. 55 min\nC. 48 min\nD. 67 min\nE. 45 min\n\n### Answer:\nC\n48 min\nLet the length of the train be x m.\nWhen a train crosses an electric pole, the distance covered is its own length.\nSo, x = 12 * 36 * 5 /18 m = 120 m.\nTime taken to cross the platform = (120 +360)/ 36 * 5/18 = 48 min.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe Tens digit of a two digit number is 4 times of its unit digit and the sum of the digits be 10. Then the first number is\n\n### Options:\nA. 67\nB. 73\nC. 53\nD. 82\nE. 89\n\n### Answer:\nLet the number be 10x + y\nAccording to the question\nx = 4y\nx + y = 10\n4y + y = 10\nor y = 2\nand x = 8\nSo required number is = 10*8 + 2 = 82\nanswer :D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man counted his animals, 80 heads and 240 legs (ducks and goats). how many goats are there?\n\n### Options:\nA. 30\nB. 40\nC. 50\nD. 60\nE. 70\n\n### Answer:\nlet no of ducks=d and no of goat=g\nd+g=80(heads)----------> eq 1\neach duck has 2 legs and goat has 4 legs\n2d+4g=240 and divide 2d+4g=240 by 2 we get d+2g=120 -----------> eq2\nsubtract eq1 from eq2\nwe get no of goats=40\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA shopkeeper sells 400 metres of cloth for Rs. 18000 at a loss of Rs.5 per metre. Find his cost price for one metre of cloth?\n\n### Options:\nA. Rs. 45\nB. Rs. 40\nC. Rs. 35\nD. Rs. 50\nE. None of these\n\n### Answer:\nSP per metre = 18000/400 = Rs. 45 Loss per metre = Rs. 5 CP per metre = 45 + 5 = Rs. 50\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man\u2019s speed with the current is 15 km/hr and the speed of the current is 2.5 km/hr.The man\u2019s speed against the current is :\n\n### Options:\nA. 8.5 km/hr\nB. 9 km/hr\nC. 10 km/hr\nD. 12.5 km/hr\nE. None of these\n\n### Answer:\nSolution\nMan\u2019s rate in still water =(15-2.5) km/hr = 12.5 km/hr.\nMan\u2019s rate against the current = (12.5-2.5)km/hr = 10 km/hr. Answer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nEle, the circus Elephant, is currently three times older than Lyn, the circus Lion. In 6 years from now, Lyn the circus Lion will be exactly half as old as Ele, the circus Elephant. How old is Ele today?\n\n### Options:\nA. 17\nB. 16\nC. 14\nD. 13\nE. 18\n\n### Answer:\nEle, the circus Elephant, is currently three times older than Lyn, the circus Lion.\nEle = 3*Lyn\nUsually, ages are integers so there is a good possibility that the age of Ele is 18 (the only option that is a multiple of 3).\nThen age of Lyn would be 6. In 6 yrs, Ele would be 24 and Lyn would be 12 - so Lyn would be half as old as Ele.\nAnswer (E)\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a camp, food was was sufficient for 2000 people for 54 days. After 15 days, more people came and the food last only for 20 more days. How many people came?\n\n### Options:\nA. 1900\nB. 1800\nC. 1940\nD. 2000\nE. None of these\n\n### Answer:\nExplanation :\nGiven that food was sufficient for 2000 people for 54 days\nHence, after 15 days, the remaining food was sufficient for 2000 people for 39 days (\u2235 54 - 15 = 39)\nLet x number of people came after 15 days.\nThen, total number of people after 15 days = (2000 + x)\nThen, the remaining food was sufficient for (2000 + x) people for 20 days\nMore men, Less days (Indirect Proportion)\n\u21d2Men 2000:(2000+x)}:: 20 : 39\n\u21d22000 \u00d7 39 = (2000 + x)20\n\u21d2 100 \u00d7 39 = (2000 + x)\n\u21d2 3900 = 2000 + x\nx = 3900 \u2212 2000 = 1900. Answer : Option A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRunning at their respective constant rates, machine X takes 2 days longer to produce w widgets than machine Y. At these rates, if the two machines together produce 5/4 w widgets in 3 days, how many days would it take machine X alone to produce 4w widgets?\n\n### Options:\nA. 4\nB. 6\nC. 8\nD. 24\nE. 12\n\n### Answer:\nLet Y produce w widgets in y Days\nHence, in 1 day Y will produce w/y widgets.\nAlso, X will produce w widgets in y+2 days (given, X takes two more days)\nHence, in 1 day X will produce w/y+2 widgets.\nHence together X and Y in 1 day will produce {w/y + w/y+2} widgets.\nTogether X and Y in 3 days will produce = 3 * [{w/y + w/y+2}] widgets.\nIt is given that in 3 days together they produce (5/4)w widgets.\nEquating, 3 * [{w/y + w/y+2}] = (5/4)w\nTake out w common and move 3 to denominator of RHS\nw{1/y + 1/(y+2)} = (5/12)w\nCanceling w from both sides\n{1/y + 1/(y+2)} = 5/12\n2y+2/y(y+2) = 5/12\n24y+24=5y^2 + 10y\n5y^2-14y-24=0\n5y^2-20y+6y-24=0\n5y(y-4)+6(y-4)=0\n(5y+6)+(y-4)=0\ny=-6/5 or y=4\nDiscarding y=-6/5 as no of days cannot be negative\ny=4\nhence it takes Y, 4 days to produce w widgets.\nTherefore, it will take X (4+2)=6 days to produce w widgets.\nHence it will take X 4*6=24 days to produce 4w widgets.\nAnswer : D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train covers a distance of 12 km in 10 minutes. If it takes 6 seconds to pass a telegraph post, then the length of the train is\n\n### Options:\nA. 100m\nB. 120m\nC. 140m\nD. 160m\nE. 170cm\n\n### Answer:\nExplanation:\nSpeed =12/10x 60 km/hr = 72 x5/18m/sec = 20 m/sec.\nLength of the train = (Speed x Time) = (20 x 6) m = 120 m\nAnswer: Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf pq represents a positive two digit number, where p and q are single digit integers, which of the following cannot be true?\n\n### Options:\nA. p+q =9\nB. (p)(q)=9\nC. p-q = 9\nD. q-p= 9\nE. p/q = 9\n\n### Answer:\n(A) pq = 45 or 63 or 27\n(B) pq = 33 or 19\n(C) 90\n(D) impossible\n(E) pq = 91\n(D) is impossible because 09 is not a valid two digit number --- if there's a zero in the ten's place, that's just 9, a single digit number. Therefore, no valid two digit number would satisfy (D).\nans D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nStatement: The authorities in Society X are cracking down on street hawkers, blaming them for traffic jams near their society.\nActions:\nI. Street hawkers should not be allowed during peak hours\nII. Street hawkers should be warned and asked not to create chaos.\n\n### Options:\nA. Only I follows\nB. Only II follows\nC. Either I or II follows\nD. Neither I nor II follows\nE. Both I and II follow\n\n### Answer:\nExplanation: Here a situation of traffic jam is depicted and the actions mentioned, give different ways for improving the situation.\nANSWER IS B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRose's grade was 70th percentile of the 60 grades for her class. Of the 40 grades from another class, 16 were higher than Rose's, and the rest were lower. If no other grade was the same as Rose's grade, then Rose's grade was what percentile of the grades of the two classes of two classes combined?\n\n### Options:\nA. 66th\nB. 70th\nC. 74th\nD. 82nd\nE. 85th\n\n### Answer:\n66th/70th/74th/82nd/85th\nCorrect option: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOf the students at a certain high school, 90 percent took a course in algebra or geometry and 30 percent took courses in both. If the percent of students who took a course in algebra was 2 times the percent of students who took a course in geometry, what percent of the students took a course in algebra but not geometry?\n\n### Options:\nA. 50%\nB. 40%\nC. 45%\nD. 35%\nE. 30%\n\n### Answer:\nYou can also just use the formula\nn(A or B) = n(A) + n(B) - n(A and B)\n90 = 2X + X - 30\nX = 40\n2X = 80\nThis is the number of people who took algebra including those who took both. To get the number of people who took only algebra, 80 - 30 = 50%\nAnswer (A)\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRam professes to sell his goods at the cost price but he made use of 900 grms instead of a kg, what is the gain percent?\n\n### Options:\nA. 11 1/8%\nB. 11 1/5%\nC. 11 1/9%\nD. 11 12%\nE. 11 5/9%\n\n### Answer:\n900 --- 100\n100 --- ? => 11 1/9%\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRs.1170 is divided so that 4 times the first share, thrice the 2nd share and twice the third share amount to the same. What is the value of the third share?\n\n### Options:\nA. Rs.589\nB. Rs.518\nC. Rs.519\nD. Rs.540\nE. Rs.528\n\n### Answer:\nA+B+C = 1170\n4A = 3B = 2C = x\nA:B:C = 1/4:1/3:1/2 = 3:4:6\n6/13 * 1170 = Rs.540\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nToday is Monday. A person wants to meet a lawyer and as that lawyer is busy he asks him to come three days after the before day of the day after tomorrow? On which day the lawyer asks the person to come?\n\n### Options:\nA. SUNDAY\nB. MONDAY\nC. TUESDAY\nD. WEDNESDAY\nE. FRIDAY\n\n### Answer:\nToday is Monday\nafter three days--->Thursday\nnow, (thursday)after before day--->Wednesday\nthen, (Wednesday)day after tomorrow--->Friday\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n63 + 5 * 12 / (180/3) = ?\n\n### Options:\nA. 22\nB. 77\nC. 29\nD. 64\nE. 21\n\n### Answer:\n63 + 5 * 12 / (180/3) = 63 + 5 * 12 / (60)\n= 63 + (5 * 12)/60 = 63 + 1 = 64.Answer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA bad habit milkman to sell his milk at cost price but he mixes it with water and thereby gains 25%. Find the percentage of mixture water ?\n\n### Options:\nA. 20\nB. 30\nC. 35\nD. 40\nE. 45\n\n### Answer:\ncp of 1 lr = 1 rs\nmix = (100/125*1) = 4/5\nratio of milk to water = 4/5:1/5 = 4:1\n=>percentage of mix = (1/5*100) = 20\nANSWER A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are six different models that are to appear in a fashion show. Two are from Europe, two are from South America, and two are from North America. If all the models from the same continent are to stand next to each other, how many ways can the fashion show organizer arrange the models?\n\n### Options:\nA. 72\nB. 48\nC. 64\nD. 24\nE. 8\n\n### Answer:\nLet's say that Models of Europe are represented by E1 and E2 respectively\nLet's say that Models of South America are represented by S1 and S2\nLet's say that Models of North America are represented by Na and N2\nSo we have to define the total ways of entries of E1 E2 S1 S2 N1 N2\nWe have to keep E1 E2 together and similarly N1 N2 together and similarly S1 S2 together so make three groups of two models from same region each\nArrangement of these three Group can be done in 3! ways\nArrangement of Models within Group can be done in 2!x2!x2! ways\ni.e. Total Ways of Arranging the models so that they are grouped as per region together = (3!)*(2!x2!x2!) = 6*8 = 48\nAnswer: Option B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the lowest positive integer that is divisible by each of the integers 1 through 10 inclusive?\n\n### Options:\nA. 420\nB. 840\nC. 1260\nD. 2520\nE. 5020\n\n### Answer:\nWe have to find the LCM of 1, 2, 3, 2^2, 5, 2*3, 7, 2^3, 3^2, and 2*5.\nThe LCM is 1*2^3*3^2*5*7= 2520\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFrom a pack of cards two cards are drawn one after the other, with replacement. The probability that the first is a red card and the second is a king is?\n\n### Options:\nA. 1/26\nB. 1/25\nC. 1/87\nD. 1/17\nE. 1/12\n\n### Answer:\nLet E1 be the event of drawing a red card.\nLet E2 be the event of drawing a king .\nP(E1 \u2229 E2) = P(E1) . P(E2)\n(As E1 and E2 are independent)\n= 1/2 * 1/13 = 1/26\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA scientist has a set of weights {1Kg, 2Kg, 4Kg, 8Kg, 16Kg, 32Kg}. This set is good enough to weight any object having an integral weight between 1Kg and 63Kg (Eg. 19 Kg = 16Kg + 2Kg + 1Kg). If the 4 Kg weight is lost, how many weights between 1Kg & 63Kg can no longer be measured ?\n\n### Options:\nA. 16\nB. 32\nC. 48\nD. 64\nE. 80\n\n### Answer:\nTotal # of ways to distribute SSEGT among 5 sisters (without restriction) is 5!2!=605!2!=60;\nThe # of ways when the youngest niece gets G is: 4!2!=124!2!=12 (give G to youngest and then distribute SSET among 4 sisters).\nSo, # of ways when youngest niece doesn't get G is: 60\u221212=4860\u221212=48.\nAnswer: 48.\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nArun purchased 30 kg of wheat at the rate of Rs. 11.50 per kg and 20 kg of wheat at the rate of 14.25 per kg. He mixed the two and sold the mixture. Approximately what price per kg should be sell the mixture to make 30% profit?\n\n### Options:\nA. 66.3\nB. 76.3\nC. 86.3\nD. 16.3\nE. 36.3\n\n### Answer:\nExplanation:\nC.P. of 50 kg wheat = (30 * 11.50 + 20 * 14.25) = Rs. 630.\nS.P. of 50 kg wheat = 130% of Rs. 630 = 130/100 * 630 = Rs. 819.\nS.P. per kg = 819/50 = Rs. 16.38 = 16.30.\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the number 97215 * 6 is completely divisible by 11, then the smallest whole number in place of * will be:\n\n### Options:\nA. 2\nB. 4\nC. 6\nD. 3\nE. 8\n\n### Answer:\nD\n3\nGiven number = 97215x6\n(6 + 5 + 2 + 9) - (x + 1 + 7) = (14 - x), which must be divisible by 11.\nx = 3\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a flight of 600 km, an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by 200 km/hr and the time of flight increased by 30 minutes. The duration of the flight is\n\n### Options:\nA. 3 hr.\nB. 5 hr.\nC. 2 hr.\nD. 7 hr.\nE. 1 hr.\n\n### Answer:\nE\n1 hr.\nLet the duration of the flight be x hours.\nThen, 600/x - 600/0.5x = 200\n--> 600/x - 1200/(2x+1) = 200\n--> x(2x + 1) = 3\n--> 2x^2 + x - 3 = 0\n--> (2x + 3)(x - 1) = 0\n--> x = 1 hr.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nBy using the numbers 1, 3, 4, 6 and 9 only once, how many five digit numbers can be made that are divisible by 8?\n\n### Options:\nA. 3\nB. 12\nC. 6\nD. 18\nE. 42\n\n### Answer:\nA number to be divisible by 8 must end with 08, 16, 24,32 ,40 or 72.\nSo, there are the following cases possible:\n349-16 --> the first three digits can be arranged in 3=6 ways.\nTotal = 6 = 6.\nAnswer: C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a ring of diameter 4 inches moves at the rate of x inches/min and another ring of diameter 12 inches moves at the rate of y inches/min, and if they both cover a distance at the same time then find the value of x in terms of y?\n\n### Options:\nA. 6y/2\nB. 3y/4\nC. 5y/2\nD. 2y/4\nE. 1y/3\n\n### Answer:\nt=S1/V1=S2/V2\nor 4/x=12/y\nor x=4y/12=1y/3\nAnswer is E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a jar there are balls in different colors: blue, red, green and yellow.\nThe probability of drawing a blue ball is 1/4.\nThe probability of drawing a red ball is 1/5.\nThe probability of drawing a green ball is 1/10.\nIf a jar cannot contain more than 50 balls, how many yellow balls are in the Jar?\n\n### Options:\nA. 5.\nB. 7.\nC. 9.\nD. 10.\nE. 17.\n\n### Answer:\nWe need to get some number which is less than 50 and exactly divisible by 4,5 and 10\nLets take LCM of three balls 4,5 and 10 =20.\nThe probability of drawing a blue ball is 1/4...For every 8 balls we get 1 BLUE ball then out of 20 balls we get 5 BLUE balls.\nThe probability of drawing a red ball is 1/5...For every 5 balls we get 1 RED ball then out of 20 balls we get 4 REB balls.\nThe probability of drawing a green ball is 1/10. For every 10 balls we get 1 GREEN ball then out of 20 balls we get 2 GREEN BALLS.\nThen out of 20 - ( 5 + 4 + 2 ) = 9 YELLOW balls.\nIMO option C is correct.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nx^2 + dx + 72 = 0 has two distinct integer roots; how many values are possible for d?\n\n### Options:\nA. 3\nB. 6\nC. 8\nD. 12\nE. 24\n\n### Answer:\nFor a quadratic equation ax^2+dx+c=0, we know that -d/a is sum of roots and c/a is product of roots.\nThe quadratic equation here is x^2 + dx + 72 = 0, where product of roots is 72.\nIf we find all the factors of 72, we have the answer.\nBy prime factorization, we get 72= 2^3*3^2.\nWe know that total factors are (3+1)*(2+1) = 12 (Reason: with 2^n, we have n+1 possibilities. n^0 to n^n. so n+1)=D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMr Sridharan invested money in two schemes A and B,offering compound interest @ 8 p.c.p.a. and 9 p.c.p.a.respectively. If the total amount of interest accured through the two schemes together in two years was 4818.30 and the total amount invested was 27,000, what was the amount invested in Scheme A?\n\n### Options:\nA. 15,000\nB. 13,500\nC. 12,000\nD. Cannot be determined\nE. None of these\n\n### Answer:\nLet, in scheme A, Sridharan invest x.\nThen, his investment in scheme B = (27000 \u2013 x).\nNow,\nx(1+8100)2+(2700\u2212x)(1+9100)2\n\u2013 27000 = 4818.30\nor, x(1.08)2 + (27000 \u2013 x)(1.09)2 = 31818.30\nor, 1.1664x + 32078.7 \u2013 1.1881x = 31818.30\nor, 0.0217x = 260.4\nor, x = 260.4\u20440.0217 = 12000\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA doctor prescribed 18 cubic centimeters of a certain drug to a patient whose body weight was 105 pounds. If the typical dosage is 2 cubic centimeters per 15 pounds of the body weight, by what percent was the prescribed dosage greater than the typical dosage?\n\n### Options:\nA. 8%\nB. 9%\nC. 11%\nD. 12.5%\nE. 14.28%\n\n### Answer:\nTypical dosage is Dose : weight :: 2: 15.\nNow if weight is 105 (Multiplying factor is 7: (105/15)) then typical dosage would be 2 *7 = 14 cc.\nDosage = 18 cc. Dosage is greater by 2 cc.\n% dosage is greater: (2 / 14)*100 = 14.28 %\nE is the answer.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat will come in place of the x in the following Number series? 5,28,57,88,125\n\n### Options:\nA. 190\nB. 180\nC. 166\nD. 189\nE. 191\n\n### Answer:\n28=23+5\n57=29+28\n88=31+57\n125=37+88\n166=41+125\n=166\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n1,236\n1,263\n1,326\n.....\n....\n+6,321\nThe addition problem above shows four of the 24 different integers that can be formed by using each of the digits 1,2,3,6 exactly once in each integer. What is the sum of these 24 integers?\n\n### Options:\nA. 63,332\nB. 67,772\nC. 71,112\nD. 75,552\nE. 79,992\n\n### Answer:\nIn each of the units, tens, hundreds, and thousands place, each digit will appear 6 times.\nThen the sum equals 6(1111)+6(2222)+6(3333)+6(6666) = 79,992\nThe answer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average of 11numbers is 500. Out of 11numbers the average of first 6no. is 50, and last 6numbers is 60 then find 6th number?\n\n### Options:\nA. 95\nB. 80\nC. 110\nD. 120\nE. 72\n\n### Answer:\n6th number = sum of 1st 6no.s + sum of last 6no.s - sum of 11no.s\nanswer = 6*50+6*60-11*50 = 110\nAnswer is C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are 10 women and 9 men in a certain club. If the club is to select a committee of 2 women and 2 men, how many different such committees are possible?\n\n### Options:\nA. 120\nB. 720\nC. 1,060\nD. 1,620\nE. 1,980\n\n### Answer:\nAnswer is E. Can somebody tell me what answer I may have found if I had added the 10C2 and 9C2 (45+36=81)?\nI'm guessing that would've been the number of 2-member committees which had men and women separately. Is that right?\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRahul and Sham together can complete a task in 35 days, but Rahul alone can complete same work in 60 days. Calculate in how many days Sham can complete this work ?\n\n### Options:\nA. 84 days\nB. 82 days\nC. 76 days\nD. 68 days\nE. 60 days\n\n### Answer:\nExplanation:\nAs Rahul and Sham together can finish work in 35 days.\n1 days work of Rahul and Sham is 1/35\nRahul can alone complete this work in 60 days,\nSo, Rahul one day work is 1/60\nClearly, Sham one day work will be = (Rahul and Sham one day work) - (Rahul one day work)\n=1/35-1/60\n=1/84\nHence Sham will complete the given work in 84 days.\nANSWER IS A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOf the 30 employees of a certain company, 10 are accountants. 2 employees of the company will be selected at random. Which of the following is closest to the probability that neither of the employees selected will be an accountant?\n\n### Options:\nA. P(E)=0.43\nB. 0.36\nC. 0.31\nD. 0.52\nE. 0.63\n\n### Answer:\nWe can Solve this by two ways:\neither find the probability by = 1-(both accountant+atleast one accountant)\nor direct from = P(both non accountant)\nsecond is easier but requires calculation if don't do the approximation.\nSo probability= (20/30)*(19/29) = 0.43\nso the answer is A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA person want to give his money of $4500 to his 4 children A,B,C,D in the ratio 2:4:5:4. What is the A+B share?\n\n### Options:\nA. $1000\nB. $2000\nC. $1800\nD. $1500\nE. $1600\n\n### Answer:\nA's share = 4500*2/15 = $600\nB's share = 4500*4/15 = $1200\nA+B = $1800\nAnswer is C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train moves past a post and a platform 264 m long in 8 seconds and 20 seconds respectively. What is the speed of the train?\n\n### Options:\nA. 79.0\nB. 79.2\nC. 79.5\nD. 79.7\nE. 79.6\n\n### Answer:\nLet x is the length of the train and v is the speed\nTime taken to move the post = 8 s\n=> x/v = 8\n=> x = 8v --- (1)\nTime taken to cross the platform 264 m long = 20 s\n(x+264)/v = 20\n=> x + 264 = 20v ---(2)\nSubstituting equation 1 in equation 2, we get\n8v +264 = 20v\n=> v = 264/12 = 22 m/s\n= 22\u00d736/10 km/hr = 79.2 km/hr\nAnswer is B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA wire can be bent in the form of a circle of radius 56cm. If it is bent in the form of a square, then its area will be\n\n### Options:\nA. 7744\nB. 8844\nC. 5544\nD. 4444\nE. 3444\n\n### Answer:\nlength of wire = 2 PieR= 2 *(22/7 )*56 = 352 cm\nside of the square = 352/4 = 88cm\narea of the square = 88*88 = 7744 sq cm Answer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average of 3 consecutive odd numbers is 30. What is the difference between the highest and lowest numbers?\n\n### Options:\nA. 5\nB. 6\nC. 8\nD. 4\nE. 3\n\n### Answer:\nLet the numbers be x, x+2, x+4\nThen, (x+ x+2+ x+4)/3 = 30\nx = 28\nRequired answer is = 28+4-28 = 4\nAnswer is D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThree pipes of same capacity A,B,C can fill a tank in 24 hours. If there are only two pipes A and B of same capacity, the tank can be filled in?\n\n### Options:\nA. 12\nB. 24\nC. 6\nD. 36\nE. 8\n\n### Answer:\nThe part of the tank filled by three pipes in one hour\n= 1/24\n=> The part of the tank filled by two pipes in 1 hour\n= 2/3 * 1/24 = 1/36.\nThe tank can be filled in 36 hours.\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA student got 72% in math and 84% in history. To get an overall average of 75%, how much should the student get in the third subject?\n\n### Options:\nA. 65%\nB. 67%\nC. 69%\nD. 71%\nE. 73%\n\n### Answer:\n72 + 84 + x = 3*75\nx = 69\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA local club has between 24 and 57 members. The members of the club can be separated into groups of which all but the final group, which will have 3 members, will have 4 members. The members can also be separated into groups so that all groups but the final group, which will have 3 members, will have 5 members. If the members are separated into as many groups of 6 as possible, how many members will be in the final group? (Source: Bell Curves)\n\n### Options:\nA. 6\nB. 5\nC. 3\nD. 2\nE. 1\n\n### Answer:\nCase 1: Final group = 3; Rest of the group = 4A; Number of members = 4A + 3\nCase 2: Final group = 3; Rest of the group = 5B; Number of members = 5B + 3\n4A + 3 = 5B + 3\n4A = 5B --> Possible values = 20, 40, 60, ........ --> But only 40 satisfies the given conditions\nNumber of members = 40 + 3 = 43\nWhen divided into groups of 6, final group will have 1 member (6*7 + 1).\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is 990*990?\n\n### Options:\nA. 974,169\nB. 974,219\nC. 974,549\nD. 980,100\nE. 985,369\n\n### Answer:\nif you take a base of 1000 then 990 is 10 less than 1000\nto get the product of 990 x 990 write like this\n990- 10( as 10 less than base1000)\n990- 10\nnow 10 x 10 = 100\nand 990-10 = 980\nso 990 x 990 = 980100 ... (bingo the answer is D . you can even have a shortcut ...... 10 x 10 = 100... only answer choice has last three digits as 100.. so no need to calculate 990-10 . after you get 10 x 10 you can straight way pick answer choice D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA person can row at 9 kmph and still water. He takes 4 1/2 hours to row from A to B and back. What is the distance between A and B if the speed of the stream is 1 kmph?\n\n### Options:\nA. 24 km\nB. 76 km\nC. 99 km\nD. 77 km\nE. 20 km\n\n### Answer:\nLet the distance between A and B be x km.\nTotal time = x/(9 + 1) + x/(9 - 1) = 4.5\n=> x/10 + x/8 = 9/2 => (4x + 5x)/40 = 9/2 => x = 20 km.\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe present ages of three persons are in the proportion of 4 : 7 : 9. Eight years ago, the sum of their ages was 56. Find their present ages.\n\n### Options:\nA. 20,35,45\nB. 8,20,28\nC. 16,28,36\nD. 16,28,46\nE. None of these\n\n### Answer:\nLet the present ages of three persons be 4K,7K and 9K respectively.\n(4K - 8) + (7K - 8) + (9K - 8) = 56\n20K = 80\nK = 4\nTherefore, then present ages are 16,28,36.\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFor every positive integer n, the nth term of sequence is given by an= 1/n - 1/(n+1). What is the sum of the first 75 terms?\n\n### Options:\nA. 25/26\nB. 40/41\nC. 75/76\nD. 150/151\nE. 151/75\n\n### Answer:\na1 = 1 - 1/2\na2 = 1/2 - 1/3\na3 = 1/3 - 1/4\netc...\na75 = 1/75 - 1/76\nThe sum of these terms is 1-1/76 = 75/76\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat day of the week does May 28 2006 fall on\n\n### Options:\nA. Saturday\nB. Monday\nC. Sunday\nD. Thursday\nE. Tuesday\n\n### Answer:\nExplanation :\n28th May 2006 = (2005 years + period from 1-Jan-2006 to 28-May-2006)\nWe know that number of odd days in 400 years = 0\nHence the number of odd days in 2000 years = 0 (Since 2000 is a perfect multiple of 400)\nNumber of odd days in the period 2001-2005\n= 4 normal years + 1 leap year\n= 4 x 1 + 1 x 2 = 6\nDays from 1-Jan-2006 to 28-May-2006 = 31 (Jan) + 28 (Feb) + 31 (Mar) + 30 (Apr) + 28(may)\n= 148\n148 days = 21 weeks + 1 day = 1 odd day\nTotal number of odd days = (0 + 6 + 1) = 7 odd days = 0 odd day\n0 odd day = Sunday\nHence May 28 2006 is Sunday\nAnswer : Option C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo trains 140 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is?\n\n### Options:\nA. 10.6 sec\nB. 18.8 sec\nC. 14.8 sec\nD. 10.8 sec\nE. 11.8 sec\n\n### Answer:\nRelative speed = 60 + 40 = 100 km/hr.\n= 100 * 5/18 = 250/9 m/sec.\nDistance covered in crossing each other = 140 + 160 = 300 m.\nRequired time = 300 * 9/250 = 54/5 = 10.8 sec.\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJames celebrated his 23rd Birthday on 2016 but he was strangely born in 1950. How can this be possible?\n\n### Options:\nA. 1250\nB. 1850\nC. 1980\nD. 1950\nE. 1750\n\n### Answer:\nD\nI was born in Hospital whose room number is 1950.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train covers a distance of 1250 km in 25hrs. Find the speed of the train?\n\n### Options:\nA. 30km/hr\nB. 40km/hr\nC. 50km/hr\nD. 60km/hr\nE. 100km/hr\n\n### Answer:\nSpeed = 1250/25 = 50km/hr\nAnswer is C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe numerator of a certain fraction is 8 less than the denominator. If 3 is added to the numerator and 3 is subtracted from the denominator, the fraction becomes 3/4. Find the original fraction?\n\n### Options:\nA. 3/16\nB. 3/28\nC. 3/11\nD. 3/19\nE. 3/29\n\n### Answer:\nThe denominator be P, the numerator will be (P - 8).\nThe fraction will be (P - 8)/P.\nAdding 3 to the numerator and subtracting 3 from the denominator, (P - 8 + 3)/(P - 3) = 3/4.\n(P - 5)/(P - 3) = 3/4\nP = 20 - 9 => P = 11.\nThe fraction is: 3/11.\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo numbers are less than third number by 30% and 37% respectively. How much percent is the second number less than by the first\n\n### Options:\nA. 8%\nB. 10%\nC. 9%\nD. 11%\nE. 12%\n\n### Answer:\nLet the third number is x.\nthen first number = (100-30)% of x\n= 70% of x = 7x/10\nSecond number is (63x/100)\nDifference = 7x/10 - 63x/100 = 7x/10\nSo required percentage is, difference is what percent of first number\n(7x/100 * 10/7x * 100 )% = 10% ANSWER :B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the integer n has exactly three positive divisors, including 1 and n, how many positive divisors does n^3 have?\n\n### Options:\nA. 7\nB. 5\nC. 6\nD. 8\nE. 9\n\n### Answer:\ntake the example of 4...\nit has 3 positive divisors (1,2,4)\nNow, take the example of 64...\nit has only 7 divisors..\nso A is the ans\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average of 7 numbers is 26. If each number be multiplied by 5. Find the average of new set of numbers?\n\n### Options:\nA. A)110\nB. B)122\nC. C)120\nD. D)125\nE. E)130\n\n### Answer:\nExplanation:\nAverage of new numbers = 26 * 5 = 130\nAnswer: Option E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSam bought 2Q steaks for W dollars. Jerome buys R steaks for a 50% discount, how much will the steaks cost him in cents?\n\n### Options:\nA. 50RW/Q.\nB. 50QR/W.\nC. 25RQ/W.\nD. 25RW/Q.\nE. RW/(4Q).\n\n### Answer:\nSam bought 2Q steaks for W dollars, so 1 steak = W/2Q\nJerome buys R steaks for a 50% discount: r* (W/4Q)\nin cents the answer will be : r* (100 W/4Q)= 25 RW/ Q=D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFox jeans regularly sell for $15 a pair and Pony jeans regularly sell for $18 a pair. During a sale these regular unit prices are discounted at different rates so that a total of $3 is saved by purchasing 5 pairs of jeans: 3 pairs of Fox jeans and 2 pairs of Pony jeans. If the sum of the two discounts rates is 18 percent, what is the discount rate on Pony jeans?\n\n### Options:\nA. 9%\nB. 56.6%\nC. 11%\nD. 12%\nE. 15%\n\n### Answer:\nYou know that Fox jeans costs $15, and Pony jeans costs $18, you also know that 3 pairs of Fox jeans and 2 pairs of Pony jeans were purchased. So\n3(15) = 45 - Fox\n2(18) = 36 - Pony\nThe total discount discount is $3 and you are asked to find the percent discount of pony jeans,\nso 45(18 - X)/100 + 36(X)/100 = 3 or 45*18 -45*x + 36*x =3*100 or 9x = -3*100 +45*18\nx= 510/9 = 56.6%\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOf the six-digit positive integers that have no digits equal to zero, how many have two digits that are equal to each other and the remaining digit different from the other two?\n\n### Options:\nA. 2443200\nB. 3643200\nC. 5443200\nD. 1443200\nE. 2163200\n\n### Answer:\nOf the six-digit positive integers that have no digits equal to zero, how many have two digits that are equal to each other and the remaining digit different from the other two?\nA. 24\nB. 36\nC. 72\nD. 144\nE. 216\nChoosing the digit for p - 9 ways;\nChoosing the digit for q - 8 ways;\nChoosing the digit for r - 7ways;\nChoosing the digit for s - 6ways;\nChoosing the digit for t - 5ways;\n# of permutations of 3 digits in ppqrst - 6!/2!\nTotal: 9*8*7*6*5*6!/2!=5443200.\nAnswer: C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe least number, which when divided by 12, 15, 20 and 54 leaves in each case a remainder of 8 is:\n\n### Options:\nA. 504\nB. 536\nC. 544\nD. 548\nE. 568\n\n### Answer:\nRequired number = (L.C.M. of 12, 15, 20, 54) + 8\n= 540 + 8\n= 548.\nAnswer: Option D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJim is able to sell a hand-carved statue for $620 which was a 25% profit over his cost. How much did the statue originally cost him?\n\n### Options:\nA. $496.00\nB. $512.40\nC. $555.40\nD. $574.90\nE. $588.20\n\n### Answer:\n620 = 1.25*X\nX = 620/1.25 = 496.00\nwhich rounds to $496.00, which is (A).\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf Rs.10 be allowed as true discount on a bill of Rs.110 at the end of a certain time , then the discount allowed on the same sum due at the end of double the time is\n\n### Options:\nA. 18.20\nB. 18.33\nC. 18\nD. 18.3\nE. None of these\n\n### Answer:\nExplanation:\nPresent worth = Amount - TrueDiscount\n= 110 -10 = Rs.100\nSI on Rs.100 for a certain time = Rs.10\nSI on Rs.100 for doube the time = Rs.20\nTrueDiscount on Rs.120 = 120 - 100 = Rs.20\nTrueDiscount on Rs.110 = (110x 20/120) = Rs.18.33\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many diagonals does a 60-sided convex polygon have?\n\n### Options:\nA. 960\nB. 1280\nC. 1710\nD. 2560\nE. 3420\n\n### Answer:\nA 60-sided convex polygon has 60 vertices.\nIf we examine a single vertex, we can see that we can connect it with 57 other vertices to create a diagonal. Note that we can't connect the vertex to itself and we can't connect it to its adjacent vertices, since this would not create a diagonal.\nIf each of the 60 vertices can be connected with 57 vertices to create a diagonal then the total number of diagonals would be (60)(57) = 3420\nHowever, we must recognize that we have counted every diagonal twice.\nTo account for counting each diagonal twice, we must divide 3420 by 2 to get 1710.\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the one which does not belong to that group ?\n\n### Options:\nA. 237\nB. 232\nC. 223\nD. 426\nE. 111\n\n### Answer:\nExplanation:\n525 => 5 52,\n39 => 3 32,\n24 => 2 22,\n636 => 6 62. The above pattern is not followed in 426.\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n7500 + (1250 / 50)\n\n### Options:\nA. 7500\nB. 7525\nC. 7550\nD. 8000\nE. None of these\n\n### Answer:\nExplanation:\nAs per BODMAS rule first we will solve the terms in the bracket then other.\n= 7500 + (25) = 7525\nOption B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA telephone number contains 10 digit, including a 3-digit area code. Bob remembers the area code and the next 5 digits of the number. He also remembers that the remaining digits are not 0, 1, 2, 5, 6, or 7. If Bob tries to find the number by guessing the remaining digits at random, the probability that he will be able to find the correct number in at most 2 attempts is closest to which of the following?\n\n### Options:\nA. 1/2\nB. 1/4\nC. 1/8\nD. 1/16\nE. 1/32\n\n### Answer:\nThere are 4*4 = 16 possibilities.\nBob has 2 chances so the probability is 2/16 = 1/8.\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the value of x. (47% of 1442 - 36% of 1412) + 63 = x?\n\n### Options:\nA. 1\nB. 2\nC. 3\nD. 5\nE. 7\n\n### Answer:\nC) 3\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe C.P of 8 books is equal to the S.P of 16 books. Find his gain% or loss%?\n\n### Options:\nA. 60%\nB. 50%\nC. 70%\nD. 90%\nE. 55%\n\n### Answer:\nexplanation:\n8 CP = 16 SP\n16 --- 8 CP loss\n100 --- ? => 50% loss\nAnswer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIF 2+3=10 ; 2+5=27 ; 2+7=53 Then 2+11=?\n\n### Options:\nA. 124\nB. 129\nC. 128\nD. 125\nE. 120\n\n### Answer:\n2^0 + 3^2= 1 + 9 = 10\n2^1 + 5^2= 2 + 25 = 27\n2^2 + 7^2= 4 + 49 = 53\nand\n2^3 + 11^2= 8 + 121 = 129\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA reading list for a certain course consists of 10 books, of which 5 are poems and the rest are novels. Each student is required to read a selection of 4 books from the list, including at most 2 novels. How many selections of 4 books satisfy the requirements?\n\n### Options:\nA. 90\nB. 115\nC. 130\nD. 144\nE. 155\n\n### Answer:\nAns: B\nSolution: Selection requires at most 2 novels, means=\n0N4P + 1N3P + 2N2P\n5c0*5c4+ 5c1*5c3 + 5c2*5c2\n= 5+ 50 + 100\n= 155\nAns: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nConcentrated pineapple juice comes inside a cylinder tube with a radius of 2.5 inches and a height of 15 inches. The tubes are packed into wooden boxes, each with dimensions of 11 inches by 10 inches by 31 inches. How many tubes of concentrated pineapple juice, at the most, can fit into 3 wooden boxes?\n\n### Options:\nA. 24.\nB. 28.\nC. 36.\nD. 42.\nE. 48.\n\n### Answer:\nconcentrated pineapple juice since height of a tube is 15 inches , the tubes can fit only in one way .\nnow, diameter of each tube = 5 inches\ntherefore, 4*2 can be put in each wooden box\nin 3 boxes 3*4*2 can be accommodated\n= 24=A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 6,15 and 24 are factors of T, which of the following is the largest number that must divide evenly into T?\n\n### Options:\nA. 30\nB. 48\nC. 60\nD. 80\nE. 120\n\n### Answer:\nYou can verify which the following numbers are divisible by 6,15,24 simultaneously\nBy elimination you will find that only the number 120 satisfies this condition.\nSo, the answer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe L.C.M of two numbers is 48. The numbers are in the ratio 1:4. The sum of numbers is:\n\n### Options:\nA. 28\nB. 30\nC. 40\nD. 50\nE. 60\n\n### Answer:\nLet the numbers be 1x and 4x.\nThen, their L.C.M = 4x. So, 4x = 48 or x = 12.\nThe numbers are 12 and48.\nHence, required sum = (12+ 48) = 60.\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the remainder when 570 is divided by 6?\n\n### Options:\nA. 1\nB. 5\nC. 4\nD. 0\nE. 2\n\n### Answer:\nExplanation:\n52 = 25, on division by 6, the remainder is 1.\n53 = 125, on division by 6, the remainder is 5.\n54 = 625, on division by 6, the remainder is 1.\n55 = 3125, on division by 6, the remainder is 5.\nHence, for 5 (2x) on division by 6, the remainder is 1, and for 5(2x-1) on division by 6, the remainder is 5.\nTherefore, for 570, on division by 6, the remainder is 1.\nANSWER: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the tens digit of positive integer x is 6 and the tens digit of positive integer y is 6, how many possible values of the tens digit of 2(x+y) can there be?\n\n### Options:\nA. 2\nB. 3\nC. 4\nD. 5\nE. 6\n\n### Answer:\nWe only need to consider the tens and ones digits of x and y, and the last two digits can be represented as 60 + p and 60 + q respectively.\n2(60+p+60+q)= 240 + 2(p + q).\n2(p+q) can range from 0 up to a maximum value of 36 when p=q=9.\nThen the tens and ones digits of 2(x+y) can range from 40 up to 76.\nThere can be 4 possibilities for the tens digit.\nThe answer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n19.19/2000 is equal to:\n\n### Options:\nA. 1.01252633\nB. 0.01262533\nC. 0.12526333\nD. 0.012793333\nE. 0.12725333\n\n### Answer:\n19.19/2000 = 2525/200000\n= 0.012793333\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTea worth Rs.126 per kg are mixed with a third variety in the ratio 1: 1 : 2. If the mixture is worth Rs.157 per kg, the price of the third variety per kg will be\n\n### Options:\nA. Rs.179.50\nB. Rs.1700\nC. Rs. 175.50\nD. Rs. 180\nE. None\n\n### Answer:\nSolution\nSince first second varieties are mixed in equal proportions, so their average price = Rs.(126+135/2) = Rs.130.50\nSo, the mixture is formed by mixing two varieties, one at Rs. 130.50 per kg and the other at say, Rs. x per kg in the ratio 2 : 2, i.e., 1 : 1. We have to find x.\nx-157/22.50 = 1 =\u00e2\u20ac\u00ba x - 157 = 22.50 =\u00e2\u20ac\u00ba x=179.50.\nHence, price of the third variety = Rs.179.50 per kg.\nAnswer A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA paper is in a square form whose one side is 20 cm. Two semi circles are drawn on its opposites as diameters. If these semi circles are cut down what is the area of the remaining paper?\n\n### Options:\nA. 8.76\nB. 8.79\nC. 8.75\nD. 8.74\nE. 8.72\n\n### Answer:\n(5 * 3.5)/2 = 8.75\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man sells a horse for Rs.200 and loses something, if he had sold it for Rs.620, his gain would have been double the former loss. Find the cost price of the horse?\n\n### Options:\nA. 140\nB. 162\nC. 160\nD. 150\nE. 71\n\n### Answer:\nCP = SP + 1CP = SP - g\n200 + x = 620 - 2x\n3x = 420 => x = 140\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n3 buffaloes eat as much as 4 cows or 2 oxen. At a farm there are 15 buffaloes, 8 oxen and 24 cows. The fodder for these cattle is available for 24days. If 8 more cows & 9 more buffaloes are brought in, how long will the fodder last?\n\n### Options:\nA. 10\nB. 13\nC. 15\nD. 18\nE. 21\n\n### Answer:\nSol. 2 oxen = 3 buffaloes = 4 cows 8 oxen = 16 cows and 15 buffaloes = 20 cows 16 cows + 20 cows + 24 cows = 60 cows Since fodder is available for 60 cows for 24 days\nSo fodder will be available for (60 + 8 + 12) = 80 cows c 24x60 .0 .\nfor-^\u2014=18 days.\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nP can do a work in 24 days. Q can do the samework in 9 days & R can do the same work in 12 days. Q & R start the work and leave after 3 days. P finishes the remaining work in how many days.\n\n### Options:\nA. 8\nB. 10\nC. 14\nD. 16\nE. 19\n\n### Answer:\nWork done by P in 1 day = 1/24\nWork done by Q in 1 day = 1/9\nWork done by R in 1 day = 1/12\nWork done by Q and R in 1 day = 1/9 + 1/12 = 7/36\nWork done by Q and R in 3 days = 3\u00d77/36 = 7/12\nRemaining work = 1 \u2013 7/12 = 5/12\nNumber of days in which P can finish the remaining work = (5/12) / (1/24) = 10\nB\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are two sections Y and Z of a class, consisting of 288 and 352 students respectively. If the average weight of sections Y is 320 kg and that of sections Z is 280 kg. Find the average weight of the whole class\n\n### Options:\nA. 297.5\nB. 298.0\nC. 298.5\nD. 299.0\nE. None\n\n### Answer:\nSolution\nTotal weight of(288+352)Students\t= (288x320+352x280)Kg\n= 1,90,720 kg.\nAverage weight of the whole class\t= (190720 / 640)\n= 298.00.\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how many ways can 4 men & 3 women can be made from a gang of 7 men & 8 women ?\n\n### Options:\nA. 91\nB. 94\nC. 89\nD. 10\nE. 19\n\n### Answer:\nExplanation:\n7C4 * 8C3 = 91\nA\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many numbers from 10 to 46 are exactly divisible by 3?\n\n### Options:\nA. 13\nB. 12\nC. 16\nD. 17\nE. 18\n\n### Answer:\n12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45.\n12 Numbers.\n10/3 = 3 and 46/3 = 15 ==> 15 - 3 = 12. Therefore 12 digits\nB)\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich of the following could be the sum of the reciprocals of two prime numbers?\n\n### Options:\nA. 7/13\nB. 11/12\nC. 12/10\nD. 23/50\nE. 19/77\n\n### Answer:\n12/10 it is\n6/5=(1/2) + (1/5)\nAnswer - C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo trains, each 160 m long, moving in opposite directions, cross other in 8 sec. If one is moving twice as fast the other, then the speed of the faster train is?\n\n### Options:\nA. 26 km/hr\nB. 17 km/hr\nC. 60 km/hr\nD. 77 km/hr\nE. 96 km/hr\n\n### Answer:\nLet the speed of the slower train be x m/sec.\nThen, speed of the train = 2x m/sec.\nRelative speed = ( x + 2x) = 3x m/sec.\n(160 + 160)/8 = 3x => x = 40/3.\nSo, speed of the faster train = 80/3 = 80/3 * 18/5\n= 96 km/hr.\nAnswer:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA, B and C invested Rs.6300, Rs.4200 and Rs.10500 respectively, in a partnership business. Find the share of A in profit of Rs.12100 after a year?\n\n### Options:\nA. 3630\nB. 2879\nC. 289\nD. 279\nE. 2928\n\n### Answer:\n6300:4200:10500\n3:2:5\n3/10 * 12100 = 3630\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nX does a work in 10 days. Y does the same work in 15 days. In how many days they together will do the same work?\n\n### Options:\nA. 10\nB. 15\nC. 3\nD. 6\nE. 12\n\n### Answer:\nX's 1day's work= 1/10\nY's 1 day's work=1/15\n(X+Y)'s 1day's work= (1/10+1/15)=1/6\nboth together will finish the work in 6 days.\ncorrect option is D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThere are 8 balls in a bucket, 4 balls are blue and 4 balls are red. If two ball chosen randomly , how many chances there are at least one blue ball will present?\n\n### Options:\nA. 21\nB. 25\nC. 16\nD. 22\nE. 20\n\n### Answer:\nTwo ball will be chosen. At least 1 blue ball\nTotal ways = 8C2 = 28\nTotal without any blue ball = 4C2 = 6\nHence ways in which at least one blue will be present = 28 - 6 = 22\nCorrect option: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe distance from City A to City B is 120 miles. While driving from City A to City B, Cara drives at a constant speed of 30 miles per hour. Dan leaves City A 90 minutes after Cara. What is the minimum constant speed in miles per hour that Dan must exceed in order to arrive in City B before Cara?\n\n### Options:\nA. 42\nB. 44\nC. 46\nD. 48\nE. 50\n\n### Answer:\nThe time it takes Cara to drive to City B is 120 / 30 = 4 hours.\nDan needs to take less than 2.5 hours for the trip.\nDan needs to exceed a constant speed of 120 / 2.5 = 48 miles per hour.\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nEnvelopes can be purchased for $1.50 per pack of 100, $1.00 per pack of 50, or $0.03 each. What is the greatest number of envelopes that can be purchased for $6.30?\n\n### Options:\nA. 426\nB. 430\nC. 443\nD. 410\nE. 486\n\n### Answer:\nI think first we should see in what group envelopes value less, so that we can buy as many as we can with a specific amount of money:\n-the 100 pack costs 1.5$, meaning 0.015$ per envelope\n-the 50 pack costs 1$, meaning 0.02$ per envelope\n-the single envelope costs 0.03$ per envelope\nThus, we have to buy as many 100 packs as we can, then as meny of 50 packs as we can and the remaining envelopes are single ones.\nHaving 6.3$, we can buy as many as 4 packs of 100 (4 x 1.5$ = 6$). We then have 0.3 $ left. so we buy 10 individual envelopes. If we add up the numbers, we get 400+10=410 envelopes. Answer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn 2008, the profits of Company M were 5 percent of revenues. In 2009, the revenues of Company N fell by 20 percent, but profits were 15 percent of revenues. The profits in 2009 were what percent of the profits in 2008?\n\n### Options:\nA. 80%\nB. 105%\nC. 124%\nD. 240%\nE. 138%\n\n### Answer:\nthe profit 0f 2009 in terms of 2008 = 0.8*15/5*100=240%\nD\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe cost of an item was reduced from its usual selling price of $23.99 to $18.99. Which of the following is closest to the percent decrease in the price of the item?\n\n### Options:\nA. 17%\nB. 21%\nC. 24%\nD. 25%\nE. 42%\n\n### Answer:\nThe price decreased by 23.99 - 8.99 = $5.\n$5 is a bit more than 20% of original price of $24.\nAnswer: B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJohn want to buy a $100 Trouser at the store, but he think it\u2019s too expensive. Finally, it goes on sale for $20. What is the percent decrease?\n\n### Options:\nA. 20%\nB. 30%\nC. 40%\nD. 70%\nE. 80%\n\n### Answer:\nThe is always the difference between our starting and ending points. In this case, it\u2019s 100 \u2013 20 = 80. The \u201coriginal\u201d is our starting point; in this case, it\u2019s 100. (80/100)*100 = (0.8)*100 = 80%.\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nwhat is rate of interest if principal.amount be 400,simple interest 180 and time 2year.\n\n### Options:\nA. 10\nB. 12.5\nC. 25\nD. 22.5\nE. 14.5\n\n### Answer:\ns.i=(p*r*t)/100\n180=800r/100\nr=180/8=22.5%\nanswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the next number of the following sequence\n10,8,18,16,34,32,....\n\n### Options:\nA. 44\nB. 66\nC. 55\nD. 77\nE. 48\n\n### Answer:\n10\n10-2=8\n8+10=18\n18-2=16\n16+18=34\n34-2=32\n32+34=66\nanswer will be 66\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n80% of a number is added to 120, the result is the same number. Find the number?\n\n### Options:\nA. 600\nB. 288\nC. 1687\nD. 997\nE. 121\n\n### Answer:\n(80/100) * X + 120 = X\n2X = 1200\nX = 600\nAnswer:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nVijay bought 160 shirts at the rate of Rs. 225 per shirt. The transport expenditure was Rs. 1400. He paid an octroi at the rate of Rs. 1.75 per shirt and labour charges were Rs. 320. What should be the selling price of one shirt, if he wants a profit of 10%?\n\n### Options:\nA. 282\nB. 229\nC. 277\nD. 285\nE. 261.25\n\n### Answer:\nTotal CP per shirt = 225 + 1400/160 + 1.75 + 320/160 = Rs. 237.5\nSP = CP[(100 + profit%)/100]\n= 237.5 * [(100 + 10)/100] = Rs. 261.25.\nAnswer:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA retailer bought a machine at a wholesale price of $90 and later on sold it after a 10% discount of the retail price. If the retailer made a profit equivalent to 20% of the whole price, what is the retail price of the machine?\n\n### Options:\nA. 81\nB. 100\nC. 120\nD. 135\nE. 160\n\n### Answer:\nMy solution: Wholesale Price= 90\nRetail Price, be = x\nHe provides 10 % discount on Retail price= x-10 x/100\nThis Retail price = 20 % profit on Wholesale price\nx-10 x/100 = 90+ 1/5(90)\nx=120;\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n2 hours after train A leaves Lucknow a train B leaves the same stationtraveling in the same direction at an average speed of 36 km/hr. After traveling 6 hrsthe train B overtakes the train A. What is the average speed of the train A?\n\n### Options:\nA. 22.5 km/hr\nB. 16 km/hr\nC. 27 km/hr\nD. 18 km/hr\nE. None of these\n\n### Answer:\nExplanation :\nTotal distance covered by B=36*6=216kmTotal time taken by A to cover same distance=2+6=8 hrsaverage speed of A=216/8=27 km/hr\nAnswer : C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhen four fair dice are rolled simultaneously, in how many outcomes will at least one of the dice show 3?\n\n### Options:\nA. 233\nB. 671\nC. 287\nD. 279\nE. 171\n\n### Answer:\nExplanation:\nWhen 4 dice are rolled simultaneously, there will be a total of 6 x 6 x 6 x 6 = 1296 outcomes.\nThe number of outcomes in which none of the 4 dice show 3 will be 5 x 5 x 5 x 5 = 625 outcomes.\nTherefore, the number of outcomes in which at least one die will show 3 = 1296 \u2013 625 = 671\nAnswer: B) 671\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf 625^(-x) + 25^(-x) + 5^(-4x) = 15, what is the value of x?\n\n### Options:\nA. -4\nB. -1/4\nC. 0\nD. 1/4\nE. 4\n\n### Answer:\nWe're told that 625^(-X) + 25^(-2X) + 5^(-4X) = 15. We're asked for the value of X.\nSince each of the calculated terms MUST be positive (regardless of what the exponent is), we can use thebasesto our advantage.....\nWith Answer A, we'd have 625^4, which is MUCH BIGGER than 15 (and we'd be adding to that big number). Eliminate A.\nWith Answer E, we'd have 625^(-4), which would create a TINY fraction (and we'd add some other fractions to it, so the total would be MUCH TOO SMALL). Eliminate E.\nWith Answer D, we'd have 625^(-1/4), which will also be a fraction (just not as tiny as the one in answer E), but the total would still be TOO SMALL. Eliminate D.\nWith Answer C, anything to the '0 power' is 1, so we'd have 1+1+1 = 3. This is not 15. Eliminate C.\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is x if x + 2y = 10 and y = 1?\n\n### Options:\nA. A)10\nB. B)8\nC. C)6\nD. D)4\nE. E)2\n\n### Answer:\nx = 10 - 2y\nx = 10 - 2.\nx = 8\nAnswer : B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many 7-digits number are Palindromic numbers? A Palindromic number reads the same forward and backward, example 1234321.\n\n### Options:\nA. 100\nB. 610\nC. 729\nD. 9000\nE. 1000\n\n### Answer:\nTake the task of building palindromes and break it intostages.\nStage 1: Select the 7th digit\nWe can choose 1, 2, 3, 4, 5, 6, 7, 8, or 9\nSo, we can complete stage 1 in 9ways\nStage 2: Select the 6th digit\nWe can choose 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9\nSo, we can complete stage 2 in10ways\nStage 3: Select the 5th digit\nWe can choose 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9\nSo, we can complete stage 3 in10ways\nStage 4: Select the 5th digit\nWe can choose 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9\nSo, we can complete stage 4 in10ways\nIMPORTANT: At this point, the remaining digits are alreadylocked in.\nStage 5: Select the hundreds digit\nThis digit must be the SAME as the thousands digit (which we already chose in stage 2)\nSo, we can complete this stage in1way.\nStage 6: Select the tens digit\nThis digit must be the SAME as the thousands digit (which we already chose in stage 2)\nSo, we can complete this stage in1way.\nStage 7: Select the units digit\nThis digit must be the SAME as the ten-thousands digit (which we already chose in stage 1)\nSo, we can complete this stage in1way.\nBy theFundamental Counting Principle(FCP), we can complete all 5 stages (and thus build a 7-digit palindrome) in(9)(10)(10)(10)(1)(1)(1)ways (= 9000 ways)\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA can finish a work in 72days, B in 9days and C in 2days, B and C start the work but are forced to leave after 3 days. The remaining work was done by A in?\n\n### Options:\nA. 30days\nB. 12days\nC. 6days\nD. 7days\nE. 8days\n\n### Answer:\nB+C 1day work = 1/9 + 1/12 = 7/36\nwork done by B and C in 3days = 7/36 * 3 = 7/12\nRemaining work = 1 - 7/12 = 5/12\n1/24 work is done by A in 1day\n5/12 work is done by A in 72*5/12 = 30days\nAnswer is A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA bowl of fruit contains 10 apples and 23 oranges. How many oranges must be removed so that 50% of the pieces of fruit in the bowl will be apples?\n\n### Options:\nA. 3\nB. 13\nC. 14\nD. 17\nE. 20\n\n### Answer:\nNumber of apples = 10\nnumber of oranges = 23\nlet number of oranges that must be removed so that 50% of pieces of fruit in bowl will be apples = x\nTotal number of fruits after x oranges are removed = 10+(23-x) = 33-x\n10/(33-x) = 5/10\n=>20 = 33-x\n=>x= 13\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRamu rides his bike at an average speed of 45 km/hr and reaches his desitination in four hours. Somu covers the same distance in five hours. If Ramu covered his journey at an average speed which was 9 km/hr less and Somu covered his journey at an average speed which was 10 km/hr more, then the difference in their times taken to reach the destination would be (in minutes).\n\n### Options:\nA. 65 minutes\nB. 66 min\nC. 56 minutes\nD. 69 minutes\nE. 46 minutes\n\n### Answer:\nDistance travelled by Ramu = 45 * 4 = 180 km\nSomu travelled the same distance in 5 hours.\nHis speed = 180/5 = 36 km/hr\nHence in the conditional case, Ramu's speed = 45 - 9 = 36 km/hr and Somu's speed = 36 + 10 = 46km/hr.\nTherefore travel time of Ramu and Somu would be 5 hours and 3.9 hours respectively. Hence difference in the time taken = 1.1 hours = 66 minutes.\nANSWER:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf k is an integer and 121 < k^2 < 225, then k can have at most how many values?\n\n### Options:\nA. 3\nB. 4\nC. 5\nD. 6\nE. 8\n\n### Answer:\ngiven k is an integer\n121 < k^2 < 225\n11 < | k| < 15\nK=-12,-13,-14,12,13,14\nANSWER:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFind the value of a/b + b/a, if a and b are the roots of the quadratic equation x2 + 10x +5 = 0?\n\n### Options:\nA. 6\nB. 42\nC. 24\nD. 18\nE. 95\n\n### Answer:\na/b + b/a = (a2 + b2)/ab = (a2 + b2 + a + b)/ab\n= [(a + b)2 - 2ab]/ab\na + b = -10/1 = -10\nab = 5/1 = 5\nHence a/b + b/a = [(-10)2 - 2(5)]/5 = 90/5 = 18.\nD)\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man saves Rs. 200 at the end of each year and lends the money at 5% compound interest. How much will it become at the end of 3 years?\n\n### Options:\nA. Rs. 565.25\nB. Rs. 635\nC. Rs. 662.02\nD. Rs. 666.50\nE. Rs. 686.50\n\n### Answer:\nAmount = [200(1 + 5/100)3 + 200(1 + 5/100)2 + 200(1 + 5/100)]\n= [200 * 21/20(21/20 * 21/20 + 21/20 + 1)] = Rs. 662.02\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAt Joel\u2019s bookstore, the current inventory is 40% historical fiction. Of the historical fiction books, 40% are new releases, while 20% of the other books are new releases. What fraction of all new releases are the historical fiction new releases?\n\n### Options:\nA. 4/25\nB. 8/23\nC. 2/5\nD. 8/14\nE. 2/3\n\n### Answer:\nlet there be 100 books in all\nHistoric fiction books = 40% of total = 40\nOther books = 60\nNew historic fiction = 40% of 40 = 16\nOther new books = 20% of 60 = 12\ntotal new books = 28\nfraction = 16/28 = 8/14\nAns: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAn auction house charges a commission of 25% on the first $50,000 of the sale price of an item, plus 10% on the amount of of the sale price in excess of $50,000. What was the price of a painting for which the house charged a total commission of $24,000?\n\n### Options:\nA. $115,000\nB. $165,000\nC. $215,000\nD. $240,000\nE. $365,000\n\n### Answer:\nSay the price of the house was $x, then 0.25*50,000+0.1*(x-50,000)=24,000 --> x=$165,000 (25% of $50,000 plus 10% of the amount in excess of $50,000, which is x-50,000, should equal to total commission of $24,000).\nAnswer: B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA sun is divided among X, Y and Z in such a way that for each rupee X gets, Y gets 45 paisa and Z gets 30 paisa. If the share of Y is RS. 18, what is the total amount?\n\n### Options:\nA. 70\nB. 105\nC. 178\nD. 177\nE. 169\n\n### Answer:\nx:y:z = 100:45:30\n20:9:6\n9 --- 18\n35 --- ? => 70\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe cost of producing x tools by a company is given by\nC(x) = 2000 x + 5500 (in $)\na) What is the cost of 100 tools?\n\n### Options:\nA. 215500 $\nB. 205800 $\nC. 125900 $\nD. 226500 $\nE. 205500 $\n\n### Answer:\nSolution\nC(100) = 2000*100 + 5500 = 205500 $\nAnswer E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo trains of length 100 m and 200 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 90 kmph and 72 kmph. After how much time will the trains meet?\n\n### Options:\nA. 20/8 sec\nB. 20/9 sec\nC. 20/7 sec\nD. 22/7 sec\nE. 60/7 sec\n\n### Answer:\nThey are moving in opposite directions, relative speed is equal to the sum of their speeds.\nRelative speed = (90 + 72)*5/18 = 9*5 = 45 mps.\nThe time required = d/s = 100/45 = 20/9 sec.Answer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA and B can together complete a piece of work in 4 days. If A alone can complete the same work in 12 days, in how many days can B alone complete that work ?\n\n### Options:\nA. 4 days\nB. 5 days\nC. 6 days\nD. 7 days\nE. 8 days\n\n### Answer:\nExplanation:\n(A+B)'s 1 day work = 1/4\nA's 1 day work = 1/12\nB's 1 day work =\n(1/4\u22121/12)=3\u22121/12=1/6\nSo B alone can complete the work in 6 days\nOption C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nRahim bought 50 books for Rs.1000 from one shop and 40 books for Rs.800 from another. What is the average price he paid per book ?\n\n### Options:\nA. 28\nB. 20\nC. 27\nD. 29\nE. 21\n\n### Answer:\nAverage price per book\n= (1000+ 800) / (50 + 40)\n= 1800 / 90\n= Rs.20\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn a bag there are coins of 50 paisa, 25 paisa and one rupee in the proportion 10:8:2. If there are in all Rs.90, the number of 50 paisa coins is?\n\n### Options:\nA. 120\nB. 110\nC. 90\nD. 80\nE. 100\n\n### Answer:\n10x 8x 2x\n50 25 100\n500x + 200x + 200x = 4200\n900x = 9000\nx = 10 => 10x = 100\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWorking alone, machine X can manufacture 1,000 nails in 16 hours. Working together, machines X and Y can manufacture 1,000 nails in 5 hours. How many hours does it take machine Y to manufacture 1,000 nails working alone?\n\n### Options:\nA. 3 9/17\nB. 5 1/3\nC. 7\nD. 7 3/11\nE. 8 4/7\n\n### Answer:\nrate of machine x = 1000/16\n(1000/16 + y)5=1000\ny=200-125/2=275/2\n275/2 * t = 1000\nt=7 3/11\nD. 7 3/11\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf there are 156 laborers in a crew, and on a certain day, 70 were present. Calculate the percentage that showed up for work? (round to the nearest tenth).\n\n### Options:\nA. 45.9%\nB. 43.9%\nC. 42.9%\nD. 41.9%\nE. 44.9%\n\n### Answer:\n70/156*100=44.87\n44.9%\ncorrect answer E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nwhat comes next?\n7, -35, -34, -3, 15, 16, 4\n\n### Options:\nA. -20\nB. -15\nC. 5\nD. 21\nE. 33\n\n### Answer:\n7*-5=-35, then -35+1=-34\n-3*-5=15,then 15+1=16\nso 4*-5=-20\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA tank is filled in eight hours by three pipes A, B and C. Pipe A is twice as fast as pipe B, and B is twice as fast as C. How much time will pipe B alone take to fill the tank?\n\n### Options:\nA. 22\nB. 28\nC. 77\nD. 12\nE. 21\n\n### Answer:\n1/A + 1/B + 1/C = 1/8 (Given)\nAlso given that A = 2B and B = 2C\n=> 1/2B + 1/B + 2/B = 1/8\n=> (1 + 2 + 4)/2B = 1/8\n=> 2B/7 = 8\n=> B = 28 hours.Answer: B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich one of the following numbers is divisible by 11?\n\n### Options:\nA. 4823718\nB. 8423718\nC. 8432718\nD. 4832718\nE. 4852718\n\n### Answer:\nExplanation:\n4832718 = (4+3+7+8) \u2013 (8+2+1) = 11\nSo, the given number is divisible by 11\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nPositive integer x has y factors; 3x has 3 factors; Which of the following values can y take?\nI. 1\nII. 2\nIII. 3\n\n### Options:\nA. I or II\nB. I only is true\nC. II only is true\nD. II or III\nE. I or III\n\n### Answer:\nSquares have odd number of factors.The square which is a multiple of 3 is 9.\n3 has factors 1,3 .\nTherefore 2 factors\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n1/0.05 is equal to\n\n### Options:\nA. 25.5\nB. 2.5\nC. 25\nD. 20\nE. None of these\n\n### Answer:\nExplanation:\n1/0.05 = (1 * 100)/5 = 100/5 = 20\nOption D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe area of a rectangular field is equal to 750 square meters. Its perimeter is equal to 110 meters. Find the width of this rectangle.\n\n### Options:\nA. 5\nB. 10\nC. 15\nD. 20\nE. 25\n\n### Answer:\nL * W = 750 : area , L is the length and W is the width.\n2 L + 2 W = 110 : perimeter\nL = 55 - w : solve for L\n(55 - W) * W = 750 : substitute in the area equation\nW = 25 and L = 30\ncorrect answer E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA and B put in Rs.300 and Rs.400 respectively into a business. A reinvests into the business his share of the first year's profit of Rs.210 where as B does not. In what ratio should they divide the second year's profit?\n\n### Options:\nA. 39:40\nB. 39:48\nC. 39:43\nD. 39:46\nE. 39:42\n\n### Answer:\n3: 4\nA = 3/7*210 = 90\n390: 400\n39:40\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe price of a cycle is reduced by 25 per cent. The new price is reduced by a further 50 per cent. The two reductions together are equal to a single reduction of\n\n### Options:\nA. 45%\nB. 62.5%\nC. 35%\nD. 32.5%\nE. 30%\n\n### Answer:\nPrice = p\ninitially price reduced by 25% which means new price is 3/4P\nNow on this new price further 50percent is reduced which means the new price is merely 50percent of 3/4P\n==> (3/4)x(1/2)P = 3/8P is the new price after both deduction which is 37.5percent of the original value P. This implies this entire series of deduction is worth having discounted 62.5% of P. So answer is B = 62.5%\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nPipe A can fill a tank in 5 hours, pipe B in 10 hours and pipe C in 30 hours. If all the pipes are open, in how many hours will the tank be filled?\n\n### Options:\nA. 2\nB. 2.2\nC. 3\nD. 3.5\nE. 4\n\n### Answer:\nPart filled by A + B + C in 1 hour = 1/5 + 1/10 + 1/30 = 1/3\nAll the three pipes together will fill the tank in 3 hours.\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how many ways letters of the word POLICIES be arranged?\n\n### Options:\nA. 45326\nB. 28763\nC. 20160\nD. 45693\nE. 54823\n\n### Answer:\nPOLICIES has 8 letters, out of which I repeated 2 times. Hence total ways = 8! / 2! = 20160ways\nC\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the cost price of 12 pencils is equal to the selling price of 8 pencils, the gain percent is:\n\n### Options:\nA. 30\nB. 40\nC. 50\nD. 60\nE. 70\n\n### Answer:\nC\n50%\nLet C.P. of each pencil be $ 1.\nThen, C.P. of 8 pencils = $8; S.P. of 8 pencils = $12.\nGain % = 4/8 * 100 = 50%\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe perimeter of a triangle is 22 cm and the inradius of the triangle is 3.5 cm. What is the area of the triangle?\n\n### Options:\nA. 22\nB. 35\nC. 77\nD. 54\nE. 38\n\n### Answer:\nArea of a triangle = r * s\nWhere r is the inradius and s is the semi perimeter of the triangle.\nArea of triangle = 3.5 * 22/2\n= 38.5 cm2\nAnswer:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMr. loyd wants to fence his Square shaped land of 120Sqft each side.If a pole is laid every 10ft how many poles do he need?\n\n### Options:\nA. 20\nB. 30\nC. 48\nD. 50\nE. 60\n\n### Answer:\nIf each side is 120 feet..then total perimeter is 120*4=480\npoles every 10 feet hence no of poles= 480/10=48\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA cistern has a leak which would empty the cistern in 20 minutes. A tap is turned on which admits 4 liters a minute into the cistern, and it is emptied in 24 minutes. How many liters does the cistern hold?\n\n### Options:\nA. 480\nB. 266\nC. 287\nD. 1661\nE. 211\n\n### Answer:\n1/x - 1/20 = -1/24\nx = 120\n120 * 4 = 480\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nCan you replace the question mark with the number to complete the series, provided the pair of numbers exhibits a similar relationship?\n? : 4623 :: 9 : 647\n\n### Options:\nA. ?= 17\nB. 18\nC. 13\nD. 10\nE. 20\n\n### Answer:\nA\n17\nThe relationship holds for below formula :\npow(x,3) - pow(x,2) - 1\n=> 9*9*9 - 9*9 - 1\n=> 729 - 81 - 1\n=> 647\nSimilarly,\n17*17*17 - 17*17 - 1\n=> 4913 - 289 - 1\n=> 4623\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf a farmer wants to plough a farm field on time, he must plough 120 hectares a day. For technical reasons he ploughed only 85 hectares a day, hence he had to plough 2 more days than he planned and he still has 40 hectares left. What is the area of the farm field and how many days the farmer planned to work initially?\n\n### Options:\nA. 483\nB. 720\nC. 885\nD. 645\nE. 287\n\n### Answer:\nLet x be the number of days in the initial plan. Therefore, the whole field is 120\u22c5x hectares. The farmer had to work for x+2 days, and he ploughed 85(x+2) hectares, leaving 40 hectares unploughed. Then we have the equation:\n120x=85(x+2)+40\n35x=210\nx=6\nSo the farmer planned to have the work done in 6 days, and the area of the farm field is 120\u22c56=720 hectares.\ncorrect answer is B)720\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe jogging track in a sports complex is 1040 m in circumference. Kapil and his wife start from the same point and walk in opposite directions at 7.5 km/hr and 3.7 km/hr respectively. They will meet for the first time in?\n\n### Options:\nA. 3.12 min\nB. 3.74 min\nC. 4.25 min\nD. 4.90 min\nE. 5.57 min\n\n### Answer:\nClearly, the two will meet when they are1040 m apart.\nTo be (7.5 + 3.7) = 11.2 km apart, they take 1 hour. THat is 60 minutes.\nTo be 1040m apart, they take\n= (1040/11200 * 60) min\n= 5.57 min.\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nthe sum of 2nd and 19th term of A.P. is equal to the sum of 8th , 15th and 12 th term . find the term which is 0\n\n### Options:\nA. 12\nB. 13\nC. 14\nD. 15\nE. 16\n\n### Answer:\nt2 + t19 = t8 + t15 + t12\n=> a+d + a+18d = a+7d + a+14d + a+11d\n=> a + 13d = 0\n=> t14 = 0 i.e. 14th term is zero.\nANSWER:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nTwo trains of equal length are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. The faster train passes the slower train in 36 seconds. The length of each train is:\n\n### Options:\nA. 50 m\nB. 72 m\nC. 80 m\nD. 82 m\nE. 84 m\n\n### Answer:\nLet the length of each train be x metres.\nThen, distance covered = 2x metres.\nRelative speed = (46 - 36) km/hr\n(10 x (5/18) ) m/s = 25/9 m/s\n2x/36 = 25/9\n2x=100\nx=50\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nGopi gives Rs. 90 plus one turban as salary to his servant for one year. The servant leaves after 9 months and receives Rs. 45 and the turban. Find the price of the turban.\n\n### Options:\nA. 27\nB. 36\nC. 29\nD. 90\nE. 11\n\n### Answer:\nLet the price of turban be x.\nThus, for one year the salary = (90 + x)\nFor 9 months he should earn 3434 (90 + x).\nNow he gets one turban and Rs. 45.\nThus, 3434 (90 + x) = 45 + x or 270 + 3x = 180 + 4x or x = 90\nAnswer:D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSam invested Rs. 15000 @ 10% per annum for one year. If the interest is compounded half-yearly, then the amount received by Sam at the end of the year will be?\n\n### Options:\nA. 16537.52\nB. 16537.29\nC. 16537.5\nD. 16537.2\nE. 16537.11\n\n### Answer:\nP = Rs. 15000; R = 10% p.a. = 5% per half-year; T = 1 year\n= 2 half-year\nAmount = [15000 * (1 + 5/100)2]\n= (15000 * 21/20 * 21/20)\n= Rs.16537.50\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nLook at this series: 1000, 200, 40, ... What number should come next?\n\n### Options:\nA. 8\nB. 10\nC. 15\nD. 20\nE. 25\n\n### Answer:\n1000/5=200\n200/5=40\n40/5=8\nANSWER:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMr. Jones sold two pipes at $1.20 each. Based on the cost, his profit one was 20% and his loss on the other was 20%. On the sale of the pipes, he:\n\n### Options:\nA. broke even\nB. lost 10 cents\nC. lost 4 cents\nD. gained 10 cents\nE. gained 4 cents\n\n### Answer:\n20 % profit on $ 1.20\n= $ 20/100 \u00d7 1.20\n= $ 0.20 \u00d7 1.20\n= $ 0.24\nSimilarly, 20 % loss on $ 1.20\n= $ 20/100 \u00d7 1.20\n= $ 0.20 \u00d7 1.20\n= $ 0.24\nTherefore, in one pipe his profit is $ 0.24 and in the other pipe his loss is $ 0.24.\nSince both profit and loss amount is same so, it\u2019s broke even.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how many different number of ways 3 boys and 2 girls can sit on a bench?\n\n### Options:\nA. 720\nB. 730\nC. 740\nD. 750\nE. 120\n\n### Answer:\nnpn = n!\n5p5 = 5 \u00d7 4 \u00d7 3 \u00d7 2 \u00d7 1 = 120\nE\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhat is the area of square field whose side of length 13 m?\n\n### Options:\nA. 225\nB. 662\nC. 169\nD. 882\nE. 21\n\n### Answer:\n13 * 13\n= 169 sq m\nAnswer:C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nCereal A is 10% sugar by weight, whereas healthier but less delicious Cereal B is 3% sugar by weight. To make a delicious and healthy mixture that is 4% sugar, what should be the ratio of Cereal A to Cereal B, by weight?\n\n### Options:\nA. 2:9\nB. 2:7\nC. 1:6\nD. 1:4\nE. 1:3\n\n### Answer:\n(10/100)A+(3/100)B = (4/100)(A+B)\n6A =B\n=> A/B = 1/6\nAnswer is C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf you multiply all the numbers on your mobile phone except 0 and 9, what is the answer?\n\n### Options:\nA. 25869\nB. 48586\nC. 40320\nD. 58964\nE. 45698\n\n### Answer:\nWe have to multiply 1 to 8 to find the answer.\nTherefore 1*2*3*4*5*6*7*8=40320\nAnswer is C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA man sells a car to his friend at 11% loss. If the friend sells it for Rs.54000 and gains 20%, the original C.P.of the car was :\n\n### Options:\nA. Rs.25561.80\nB. Rs.37500.80\nC. Rs.50561.80\nD. Rs.60000\nE. None of these\n\n### Answer:\nExplanation:\nS.P = Rs.54,000. Gain earned = 20%\nC.P = Rs.[100/120\u00c3\u201454000]\n=Rs. 45000\nThis is the price the first person sold to the second at at loss of 11%.\nNow S.P = Rs.45000 and loss = 11%\nC.P. Rs.[100/89\u00c3\u201445000]= Rs.50561.80.\nCorrect Option : C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many three digit numbers W are divisible by 78 or 91?\n\n### Options:\nA. 17\nB. 19\nC. 20\nD. 21\nE. 22\n\n### Answer:\nThe answer will be 19.\nExplanation:\n78= 2*3*13 now multiples of 78, 156 ....780, now 1000-780 = 220 only two more muktiples of 78 can exists. So total number of 3 digit Multiples of 78 are 9+2=11\n91= 13*7--Total number of three digit multiples --9\nNo remember we have a common multiples as well-- 13*7*6=91*6=546\nSo total number of multiples W--11+9 -1 =19.\nHence Answer is 19.B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSix cards numbered from 1 to 6 are placed in an empty bowl. First one card is drawn and then put back into the bowl; then a second card is drawn. If the cards are drawn at random and if the sum of the numbers on the cards is 6, what is the probability that one of the two cards drawn is numbered 3 ?\n\n### Options:\nA. 1/3\nB. 1/2\nC. 1/5\nD. 3/5\nE. 4/5\n\n### Answer:\n(5,1) (1,5) (4,2) (2,4) (3,3) \u2013 only 5 possible scenarios for sum to be 6. One from this 5 has already happened.\nFrom this five cases, only in one we have 3. So, the probability is 1 chances out of 5 that the one that occurred had 3: P=1/5.\nAnswer: C.\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA sum of money lent out at S.I. amounts to a total of $520 after 2 years and to $820 after a further period of 5 years. What was the initial sum of money that was invested?\n\n### Options:\nA. $340\nB. $360\nC. $380\nD. $400\nE. $420\n\n### Answer:\nS.I for 5 years = $820 - $520 = $300\nThe S.I. is $60/year\nS.I. for 2 years = $120\nPrincipal = $520 - $120 = $400\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA part of certain sum of money is invested at 9% per annum and the rest at 12% per annum, if the interest earned in each case for the same period is equal, then ratio of the sums invested is?\n\n### Options:\nA. 4:2\nB. 4:8\nC. 4:3\nD. 4:0\nE. 4:9\n\n### Answer:\n12:9\n= 4:3\nAnswer: C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe average of five numbers is 27. If one number is excluded, the average becomes 25. The excluded number is?\n\n### Options:\nA. 12\nB. 72\nC. 23\nD. 35\nE. 28\n\n### Answer:\nExcluded number = (27 * 5) - (25 * 4)\n= 135 - 100\n= 35.\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA daughter lent $750 to her mother to help pay her rent. At the end of the month, the daughter received y dollars more than than the amount that was lent due to interest. The mother also gave her daughter an additional $5 for goodwill. In terms of y, what fraction of the total amount that the daughter received was the goodwill amount?\n\n### Options:\nA. (5y-1)/(755-y)\nB. 5/(755+y)\nC. 5y/(755+y)-1\nD. 5y/(755+y)\nE. 5y\n\n### Answer:\nThe amount of money the daughter received was (750 + 5+ y) dollars. The $5 goodwill gift as a fraction of the amount received was, therefore, 5/(755+y).\nAnswer: B.\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nP beats Q by 5 seconds in a race of 1000 m and Q beats R by 5 metres in a race of 100 m. By how many seconds does P beats R in a race of 1000 m?\n\n### Options:\nA. 5 sec\nB. 7 sec\nC. 10 sec\nD. Can't be determined\nE. None of these\n\n### Answer:\nExplanation :\nIf P takes t seconds to run 1000 m, then Q takes (t+5) sec.\nIn (t+5) sec Q runs 100 m whereas R runs only 950 m.\nR runs 1000 m in (1000/950)x(t+5)sec.\nP takes t seconds to cover 1000m , while R takes (20t/19+100/95)sec.\nFrom the data given, we cannot determine t .\nAnswer : D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJohn has 6 friends who want to ride in his new car that can accommodate only 5 people at a time (John plus 4 passengers). How many different combinations of 4 passengers can be formed from John's 6 friends?\n\n### Options:\nA. 3\nB. 8\nC. 10\nD. 15\nE. 20\n\n### Answer:\n6C4 = 15\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn 1990 the budgets for projects Q and V were $700,000 and $780,000, respectively. In each of the next 10 years, the budget for Q was increased by $30,000 and the budget for V was decreased by $10,000. In which year was the budget for Q equal to the budget for V ?\n\n### Options:\nA. 1992\nB. 1993\nC. 1994\nD. 1995\nE. 1996\n\n### Answer:\nLet the no of years it takes is x.\n700+30x = 780-10x --> 40x = 80 and x=2.\nThus, it happens in 1992.\nA.\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA shop that sells phone accessories had the following sales: 10 thousand earbuds at $10 each, 5300 phone cases at $12 each and 450 power banks at $50 each. What % of the shop's revenue is from power banks?\n\n### Options:\nA. 11.1%\nB. 12.1%\nC. 10.1%\nD. 9.1%\nE. 13.1%\n\n### Answer:\nCorrect Answer: B\nThe company's total revenue from earbuds=10000*$10=$100000\nThe company's total revenue from phone cases=5300*$12=$63600\nThe company's total revenue from power banks=450*$50=$22500\nThe combined total of all sales=$186100\nTherefore % of power banks sales=22500/186100*100= 12.1%\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIn how many ways can you line up 7 wrestlers in a row if one of them, Houdidi, cannot be in the middle or at the either end?\n\n### Options:\nA. 1,850\nB. 929\nC. 828\nD. 724\nE. 2,880\n\n### Answer:\nSince Houdini cannot be placed in the middle or at either end (3 spots), then he can choose 4 spots to sit. The remaining 6 apples can be placed in in 6! ways. Thus the # of arrangements is 4*6! = 2,880.\nAnswer: E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA 14 cm long wire is to be cut into two pieces so that one piece will be 2/5th of the other, how many centimeters will the shorter piece be?\n\n### Options:\nA. 12\nB. 20\nC. 88\nD. 77\nE. 4\n\n### Answer:\n1: 2/5 = 5: 2\n2/7 * 14 = 4\nAnswer: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA straight line is formed using two points A(3,3) and B(6,6). Another point P(x,y) lies between A and B such that AP/BP = 2. What are the coordinates of P?\n\n### Options:\nA. (7/2, 7/2)\nB. (4, 4)\nC. (21/5, 21/5)\nD. (9/2, 9/2)\nE. (5, 5)\n\n### Answer:\nThe equation of the straight line is y = x, so the x- and y-coordinates of P are the same.\nThe x, y coordinates are 2/3 of the distance from 3 to 6.\nx = 3 + (6-3)*(2/3) = 3 + 2 = 5 = y\nThe answer is E.\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 160 m long?\n\n### Options:\nA. 41.6 sec\nB. 11 sec\nC. 88 sec\nD. 19 sec\nE. 10 sec\n\n### Answer:\nSpeed = 45 * 5/18 = 25/2 m/sec\nTotal distance covered = 360 + 160 = 520 m\nRequired time = 520 * 2/25 = 41.6 sec\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nBarbara has 8 shirts and 12 pants. How many clothing combinations does Barbara have, if she doesn\u2019t wear 2 specific shirts with 3 specific pants?\n\n### Options:\nA. 126\nB. 120\nC. 101\nD. 112\nE. 115\n\n### Answer:\n8 shirts\n9 pants\nwe can combine 2 shirts with (12-3) pants\n2*9=18\nwe can combine the other shirts (6) with any pants (9)\n9*12=54\nThus total :108+18=126\tANS:A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nJohn has 10 pairs of matched socks. If he loses 3 individual socks, what is the greatest number of pairs of matched socks he can have left?\n\n### Options:\nA. 7\nB. 8\nC. 5\nD. 4\nE. 3\n\n### Answer:\nBecause we have to maximize the pair of matched socks, we will remove 1 pairs(2 socks) out of 10 pairs 1 sock from the 2th pair.\nThus the no of matching socks pair remaining = 10 - 2 = 8\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA volume of 11780 l water is in a container of sphere. How many hemisphere of volume 4l each will be required to transfer all the water into the small hemispheres?\n\n### Options:\nA. 2812\nB. 8231\nC. 2734\nD. 4222\nE. 2945\n\n### Answer:\na volume of 4l can be kept in 1 hemisphere\ntherefore, a volume of 11780l can be kept in (11780/4) hemispheres\nans.2945\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nBy the how much is two-fifth of 150 greater than three -fifths of 25?\n\n### Options:\nA. 15\nB. 3\nC. 45\nD. 30\nE. None of these\n\n### Answer:\nReqd no. = 2\u00e2\u0081\u201e5 \u00c3\u2014 150 - 3\u00e2\u0081\u201e5 \u00c3\u2014 25\n= 60 - 15 = 45\nAnswer C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nIf the sum of a number and its square is 342, What is the number?\n\n### Options:\nA. 16\nB. 77\nC. 25\nD. 87\nE. 18\n\n### Answer:\nExplanation:\nLet the integer be x.\nThen, x + x2 = 342\nx2 + x - 342 = 0\n(x + 19) (x \u2013 18) = 0\nx = 18\nANSWER: E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA 300 meter long train running at the speed of 120 kmph crosses another train running in the opposite direction at the speed of 80 kmph in 9 seconds.What is the lenght of other train.\n\n### Options:\nA. 210m\nB. 220m\nC. 230m\nD. 240m\nE. 200m\n\n### Answer:\nRelative speeds=(120+80)km/hr\n=200km/hr=(200*5/18)m/s=(500/9)m/s\nlet length of train be xm\nx+300/9=500/9\nx=200\nAns is 200m\nANSWER:E\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\n((1^m)/(5^m))((1^16)/(4^16)) = 1/(2(10)^31)\nWhat is m?\n\n### Options:\nA. 17\nB. 18\nC. 34\nD. 31\nE. 36\n\n### Answer:\n((1^m)/(5^m))((1^16)/(4^16)) = 1/(2(10)^31)\n((1/5)^m ) * ((1/2)^32) = 1/ (2 * (2*5)^31))\n2^36 will cancel out,since 1 can be written as 1^35 ,So (1/5)^m= (1/5)^31\n((1/5)^m ) * ((1/2)^32) = 1/[(2^32)*(5^31)]\nSo, m=31\nAnswer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAt the end of three years what will be the compound interest at the rate of 10% p.a. on an amount of Rs.30000?\n\n### Options:\nA. 9930\nB. 1879\nC. 2779\nD. 2672\nE. 2782\n\n### Answer:\nA = 30000(11/10)^3\n= 39930\n= 30000\n----------\n9930\nAnswer: A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nHow many digits will be there to the right of the decimal point in the product of 95.75 and .02554 ?\n\n### Options:\nA. 5\nB. 6\nC. 7\nD. 8\nE. 9\n\n### Answer:\nEXPLANATION\nSum of decimal places = 7.\nSince the last digit to the extreme right will be zero (since 5 x 4 = 20), so there will be 6 significant digits to the right of the decimal point.\nAnswer B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nBefore lunch, a painter can paint a wall at a rate of r square feet per minute. The same painter, after lunch and a cup of coffee, can paint the same wall at a rate r + 1 square feet per minute, and the same wall would be finished in 30 seconds less time. What is the value of r?\n\n### Options:\nA. 1/3\nB. 3\nC. 1/2\nD. 1\nE. 2\n\n### Answer:\nConvert 30 seconds to 1/2 minute\nEquation: 1/r = 1/(r + 1) + 1/2\nPlug options into the equation:\nD fits: 1/1 = 1/(1 + 1) + 1/2\nAnswer: D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nThe graphs of the two linear equations ax + by = c and bx - ay = c, where a, b and c are all not equal to zero,\n\n### Options:\nA. are parallel\nB. intersect at one point but not perpendicular\nC. intersect at two points\nD. perpendicular\nE. none of the above\n\n### Answer:\nfind the slopes of the two lines\na x + b y = c , slope m1 = - a / b\nb x - a y = c , slope m2 = b / a\nm1*m2 = (- a / b)(b / a) = - 1\nThe two lines are perpendicular\nANSWER : D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nSimplify: (4 \u2013 5) \u2013 (13 \u2013 18 + 2).\n\n### Options:\nA. 5\nB. 4\nC. -3\nD. 2\nE. -1\n\n### Answer:\n(4 \u2013 5) \u2013 (13 \u2013 18 + 2).\n= -1-(13+2-18).\n= -1-(15-18).\n= -1-(-3).\n= -1+3.\n= 2.\ncorrect answer D\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA store has 10 bottles of juice, including 5 bottles of apple juice. In the evening, 6 bottles of juice are sold one by one. What is the probability of selling 4 bottles of apple juice among the 6 bottles? Assume that every bottle has an equal chance of being bought.\n\n### Options:\nA. 2/7\nB. 3/11\nC. 4/15\nD. 5/21\nE. 6/25\n\n### Answer:\nThe total number of ways to sell 6 bottles from 10 is 10C6 = 210.\nThe number of ways to sell 4 bottles of apple juice is 5C4*5C2 = 5*10 = 50\nP(selling 4 bottles of apple juice) = 50/210 = 5/21\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA is a positive integer. when a is divided by 4 the remainder is 3, and when divided by 9 the remainder is 1. what is the remainder if a is divided by 52?\n\n### Options:\nA. Between 1 and5, inclusive\nB. Between 10 and15, inclusive\nC. 5\nD. Between 8 and 12, inclusive\nE. Between 4 and 8, inclusive\n\n### Answer:\nGiven the integer a\n4a+3= 9a+5\nStart 4a+3 -->7, 11, 15,...59,....\nOf these only 55 fit the description 9a+5. The remainder when divided by 52 is 7. So answer is E).\nAnswer = E)\nThe answer is: E<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nOf the 65 cars on a car lot, 45 have air-bag, 30 have power windows, and 12 have both air-bag and power windows. How many of the cars on the lot have neither air-bag nor power windows?\n\n### Options:\nA. 8\nB. 2\nC. 10\nD. 15\nE. 18\n\n### Answer:\nTotal -Neither = All Air bag + All Power Windows - Both\nor 65 - Neither = 45 + 30 -12 = 63.\n=> Neither = 2, hence B.\nAnswer : B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nMangala completes a piece of work in 12 days, Raju completes the same work in 18 days. If both of them work together, then the number of days required to complete the work is?\n\n### Options:\nA. 5.2 days\nB. 6.2 days\nC. 7.2 days\nD. 8.2 days\nE. 9.2 days\n\n### Answer:\nIf A can complete a work in x days and B can complete the same work in y days, then, both\nof them together can complete the work in x y/ x+ y days.\nThat is, the required No. of days = 12 \u00c3\u2014 18/30 = 7.2 days.\nC)\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA and B started a partnership business investing some amount in the ratio of 3 : 5. C joined then after 3 months with an amount equal to that of B. In what proportion should the profit at the end of one year be distributed among A, B and C?\n\n### Options:\nA. 4 : 9 : 8\nB. 5 : 7 : 4\nC. 6 : 10 : 7.5\nD. 7 : 9: 4\nE. 5 : 4 : 8\n\n### Answer:\nLet the initial investments of A and B be 3x and 5x.\nA : B : C = (3x x 12) : (5x x 12) : (5x x 9) = 36 : 60 : 45\n= 6 : 10 : 7.5.\nANSWER :C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nWhich of the following is the lowest positive integer that is divisible by 4, 5, 6, 7, 8, 9, and 10?\n\n### Options:\nA. 1680\nB. 1950\nC. 2230\nD. 2520\nE. 2870\n\n### Answer:\nThe number needs to be divisible by 2^2, 5, 2*3, 7, 2^3, 3^2, and 2*5.\nThe lowest positive integer is 7 * 2^3 * 3^2 * 5 = 2520\nThe answer is D.\nThe answer is: D<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nA student chose a number, multiplied it by 2, then subtracted 138 from the result and got 104. What was the number he chose?\n\n### Options:\nA. 123\nB. 121\nC. 277\nD. 267\nE. 120\n\n### Answer:\nLet xx be the number he chose, then\n2\u00e2\u2039\u2026x\u00e2\u02c6\u2019138=104 2\u00e2\u2039\u2026x\u00e2\u02c6\u2019138=104\nx=121\nAnswer:B\nThe answer is: B<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nAngelina walked 250 meters from her home to the grocery at a constant speed. She then walked 360 meters to the gym at double the speed. She spent 70 seconds less on her way from the grocery to the gym than on her way from home to the grocery. What was Angelina's speed, in meters per second, from the grocery to the gym?\n\n### Options:\nA. 2\nB. 3\nC. 4\nD. 6\nE. 12\n\n### Answer:\nlet the speed be X...\nso time taken from home to grocery= 250/x..\nthe speed to gym = 2x..\nso time taken = 360/2x=180/x..\nits given 250/x-180/x=70..\n70/x=70..\nx=1m/secs..\nso grocery to gym=2*1=2m/s...\nAnswer : A\nThe answer is: A<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nFred and Sam are standing 35 miles apart and they start walking in a straight line toward each other at the same time. If Fred walks at a constant speed of 2 miles per hour and Sam walks at a constant speed of 5 miles per hour, how many miles has Sam walked when they meet?\n\n### Options:\nA. 5\nB. 9\nC. 25\nD. 30\nE. 45\n\n### Answer:\nrelative distance =35 miles\nrelative speed =2+5 =7 miles per hour\ntime taken =35/7=5 hours\ndistance travelled by sam =5*5=25 miles=C\nThe answer is: C<|end_of_text|>", + "Below is a MCQ that you will need to answer. Write an answer that fully explains your reasoning.\n\n### Question:\nBefore being simplified, the instructions for computing income tax in Country R were to add 2 percent of one's annual income to the average (arithmetic mean) of 100 units of Country R's currency and 1 percent of one's annual income. Which of the following represents the simplified formula for computing the income tax, in Country R's currency, for a person in that country whose annual income is A?\n\n### Options:\nA. 50+A/200\nB. 50+3A/100\nC. 50+A/40\nD. 100+A/50\nE. 100+3A/100\n\n### Answer:\nthe simplified formula for computing the income tax, in Country R's currency, for a person in that country\nannual income is A:50+A/40\nANSWER:C\nThe answer is: C<|end_of_text|>" + ], + "desc_act": false, + "group_size": 128, + "modules_in_block_to_quantize": null, + "quant_method": "gptq", + "sym": true, + "true_sequential": true + }, + "rms_norm_eps": 1e-05, + "rope_scaling": null, + "rope_theta": 500000.0, + "tie_word_embeddings": false, + "torch_dtype": "bfloat16", + "transformers_version": "4.41.2", + "unsloth_version": "2024.6", + "use_cache": true, + "vocab_size": 128256 +}