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[ { "content": "Two friends plan to walk along a 43-km trail, starting at opposite ends of the trail at the same time. If Friend P's rate is 15% faster than Friend Q's, how many kilometers will Friend P have walked when they pass each other?\n\n['A)21', 'B)21.5', 'C)22', 'D)22.5', 'E)23']", "role": "user" }, { "content": "If Q complete x kilometers, then P completes 1.15x kilometers.\nx + 1.15x = 43\n2.15x=43\nx = 43/2.15 = 20\nThen P will have have walked 1.15*20=23 km.\nThe answer is E.", "role": "assistant" } ]

[ { "content": "In the coordinate plane, points (x, 1) and (5, y) are on line k. If line k passes through the origin and has slope 1/5, then what are the values of x and y respectively?\n\n['A)4 and 1', 'B)1 and 5', 'C)5 and 1', 'D)3 and 5', 'E)5 and 3']", "role": "user" }, { "content": "Line k passes through the origin and has slope 1/5 means that its equation is y=1/5*x.\nThus: (x, 1)=(5, 1) and (5, y) = (5,1) -->x=5 and y=1\nAnswer: C", "role": "assistant" } ]

[ { "content": "For all numbers p and q, the operation @ is defined by p@q = p^2 - pq. If xy ≠ 0, then which of the following can be equal to zero?\nI. x@y\nII. (xy)@y\nIII. x@(x + y)\n\n['A)II', 'B)I and II', 'C)I and III', 'D)II and III', 'E)All of the above']", "role": "user" }, { "content": "p@q = p^2 - pq=p(p-q).... so p@q will be zero if p=q or p=0.. but a cannot be equal to 0.. as per Q, x and y can take any int value except 0...\nnow lets look at the choices..\nwhen x=y, it will be 0... so ok...\nwhen we put xy=y, it is possible when x=1 and y any integer... so ok again\nwhen we put x=x+y.... only possibility when y=0 and it is given x and y cannot be 0....so not possible\nonly l and ll possible ans B....", "role": "assistant" } ]

[ { "content": "Carl is facing very difficult financial times and can only pay the interest on a $10,000 loan he has taken. The bank charges him a quarterly compound rate of 4%. What is the approximate interest he pays annually?\n\n['A)$1600', 'B)$2000', 'C)$2150', 'D)$2500', 'E)$12000']", "role": "user" }, { "content": "Usually, you are given the annual rate of interest and it is mentioned that it is annual rate.\nThe bank charges him a quarterly compounded ANNUAL rate of 16%.\nHere you find per quarter rate as (16/4)% = 4%\nI have actually never seen a question with quarter rate given but since this question did not mentionannual rate of interestand since the options did not make sense with 4% annual rate of interest, it is apparent that the intent was a 4% quarterly rate. So the bank charges 4% every quarter and compounds it in the next quarter. Had it been a simple quarterly rate, we would have just found 4 * 4% of 10,000 = $1600 as our answer.\nBut since, the interest is compounded, it will be a bit more than $1600. Option (A) looks correct.", "role": "assistant" } ]

[ { "content": "The speed at which a man can row a boat in still water is 25 kmph. If he rows downstream, where the speed of current is 11 kmph, what time will he take to cover 80 metres?\n\n['A)18 seconds', 'B)27 seconds', 'C)26 seconds', 'D)12 seconds', 'E)8 seconds']", "role": "user" }, { "content": "Speed of the boat downstream = 25 +11\n= 36 kmph\n= 36 * 5/18 = 10 m/s\nHence time taken to cover 80 m = 80/10\n= 8 seconds.\nAnswer:E", "role": "assistant" } ]

[ { "content": "There 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 6 possible combinations in which Jim and Ellen are not selected, what is the value of k?\n\n['A)8', 'B)9', 'C)10', 'D)11', 'E)12']", "role": "user" }, { "content": "There are k-2 members in the band, and k-4 members without Jim and Ellen.\n(k-4)C2 = 6\n(k-4)(k-5)/2 = 6\n(k-4)(k-5) = 12 = 4*3\nk = 8\nThe answer is A.", "role": "assistant" } ]

[ { "content": "If (x^2 + 4x - 11)/5 ≤ x + 1, then x could be represented by which of the following?\n\n['A)− 3 ≤ x ≤ 4', 'B)− 4 ≤ x ≤ 3', 'C)− 3 ≤ x ≤ 3', 'D)− 4 ≤ x ≤ − 3', 'E)3 ≤ x ≤ 4']", "role": "user" }, { "content": "IMO A is correct answer\nsolving through eqautions\nx^2 +4x-11<= 5x+5\n(x+3)(x-4)<=0", "role": "assistant" } ]

[ { "content": "Find the smallest number of five digits exactly divisible by 22,33,66 and 44.\n\n['A)10101', 'B)11000', 'C)10110', 'D)10111', 'E)10100']", "role": "user" }, { "content": "Smallest number of five digits is 10000.\nRequired number must be divisible by L.C.M. of 22,33,66,44 i.e 132,\nOn dividing 10000 by 132,we get 32 as remainder.\nTherefore, Required number = 10000 +( 132 – 32 ) = 10100.\nAnswer is E.", "role": "assistant" } ]

[ { "content": "The 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['A)16', 'B)20.5', 'C)17.5', 'D)20', 'E)4.5']", "role": "user" }, { "content": "Total 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", "role": "assistant" } ]

[ { "content": "If X and Y are digits and 8XY is a 3-digit number that is divisible by 2, which of the following is a possible product of X and Y?\n\n['A)15', 'B)31', 'C)12', 'D)27', 'E)91']", "role": "user" }, { "content": "Key to this question is to remember the fact that a number divisible by 2 must end with even OR 0 (i.e Y).\nIf Y had to be 0, product should also be 0 regardless of X.\nOtherwise, product is a multiple of 2. Only one answer choice meets the requirement.\nAns C.", "role": "assistant" } ]

[ { "content": "If Tim had lunch at $50 and he gave 20% tip, how much did he spend?\n\n['A)A)$60.00', 'B)B)$35.42', 'C)C)$60.60', 'D)D)$21.56', 'E)E)$78.45']", "role": "user" }, { "content": "The tip is 20% of what he paid for lunch.\ntip = 20% of 50.00 = (20/100)*50.00 = = $10.00\nTotal spent\n50.00 + 10.00 = $60.00\ncorrect answer is A)$60.00", "role": "assistant" } ]

[ { "content": "Rs. 825 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. 825 become in 3 years ?\n\n['A)Rs. 1020.80', 'B)Rs. 1025', 'C)Rs. 1055', 'D)Data inadequate', 'E)None of these']", "role": "user" }, { "content": "Solution\nS.I. = Rs.(956-825 )=Rs.131\nRate = (100x131/825x3) = 524/99%\nNew rate = (524/99 +4)% = 920/99%\nNew S.I. = Rs.(825 x 920/99 x 3/100) Rs. 230.\n∴ New amount = Rs.(825+230)= Rs. 1055.\nAnswer C", "role": "assistant" } ]

[ { "content": "q is a positive integer and multiple of 2; p = 4^q, what is the remainder when p is divided by 10?\n\n['A)10', 'B)6', 'C)4', 'D)0', 'E)It Cannot Be Determined']", "role": "user" }, { "content": "It is essential to recognize that the remainder when an integer is divided by 10 is simply the units digit of that integer. To help see this, consider the following examples:\n4/10 is 0 with a remainder of 4\n14/10 is 1 with a remainder of 4\n5/10 is 0 with a remainder of 5\n105/10 is 10 with a remainder of 5\nIt is also essential to remember that the q is a positive integer and multiple of 2. Any integer that is a multiple of 2 is an even number. So, q must be a positive even integer.\nWith these two observations, the question can be simplified to:what is the units digit of 4 raised to an even positive integer?\nThe units digit of 4 raised to an integer follows a specific repeating pattern:\n4^1 = 4\n4^2 = 16\n4^3 = 64\n4^4 = 256\n4^(odd number) --> units digit of 4\n4^(even number) --> units digit of 6\nThere is a clear pattern regarding the units digit. 4 raised to any odd integer has a units digit of 4 while 4 raised to any even integer has a units digit of 6.\nSince q must be an even integer, the units digit of p=4^q will always be 6. Consequently, the remainder when p=4^q is divided by 10 will always be 6.\nIn case this is too theoretical, consider the following examples:\nq=2 --> p=4^q=16 --> p/10 = 1 with a remainder of 6\nq=4 --> p=4^q=256 --> p/10 = 25 with a remainder of 6\nq=6 --> p=4^q=4096 --> p/10 = 409 with a remainder of 6\nq=8 --> p=4^q=65536 --> p/10 = 6553 with a remainder of 6\nAnswer: B.", "role": "assistant" } ]

[ { "content": "If q is the square of a positive integer, which of the following must be equal to the square of the next positive integer?\n\n['A)√n + 1', 'B)n + 1', 'C)n^2 + 1', 'D)q + 2√q + 1', 'E)n^2 + 2n + 1']", "role": "user" }, { "content": "If q is the square of a positive integer, which of the following must be equal to the square of the next positive integer?\nq = (x)^2 where x is a positive integer\nTo calculate -\n(x+1)^2 = x^2 + 2x + 1\nroot(q) = x\nAns - q + 2 root(q) + 1\nThis should be D", "role": "assistant" } ]

[ { "content": "Rs. 5600 is divided into three parts A, B and C. How much A is more than C if their ratio is 1/7:1/7:1/14?\n\n['A)300', 'B)992', 'C)1120', 'D)552', 'E)312']", "role": "user" }, { "content": "1/7:1/7:1/14 = 2:2:1\n1/5*5600 = 1120\n2240-1120 = 1120\nAnswer: C", "role": "assistant" } ]

[ { "content": "If a/b=3/4 and 8a+5b=22,then find the value of a.\n\n['A)1/2', 'B)3/2', 'C)5/2', 'D)4/2', 'E)7/2']", "role": "user" }, { "content": "(a/b)=3/4 b=(4/3) a.\nTherefore, 8a+5b=22 = 8a+5*(4/3) a=22  8a+(20/3) a=22\n=44a = 66 = a=(66/44)=3/2\nAnswer is B.", "role": "assistant" } ]

[ { "content": "Given that k/l < 1, and both k and l are positive integers, which one of the following must be greater than 1?\n\n['A)k/l^2', 'B)k^2/l', 'C)k^2/l^2', 'D)l/k', 'E)√(k/l)']", "role": "user" }, { "content": "Since k/l is a fraction l must always be > 1\nGiven -\nWhich one of the following must be greater than 1\nWe can get the result one only when the denominator in k/l ( Which is less than 1 ) becomes numerator..\nAmong the given options only (D) has the required characteristic we are looking for...\nHence answer will be (D)", "role": "assistant" } ]

[ { "content": "Mike took 5 mock tests before appearing for the GMAT. In each mock test he scored 10 points more than the previous mock test. If he scored 760 on the GMAT and his average score for the mocks and the GMAT was 716.67, what was the difference in the score of his last mock and his GMAT score?\n\n['A)20', 'B)32', 'C)40', 'D)50', 'E)60']", "role": "user" }, { "content": "One way to do this would be weighted average method..\n1) let the average of 5 mocks be x...\nso take it as a mix of5 quantitites of xand1 quantity of 760resulting in an average of 716.67...\nBy alligation/weighted average..\nthe difference in 760 and 716.67 is 5/6 of difference of 760 and x..\n760-716.67 = 5/6 * (760-x)\n760-x= 43.33*6/5=52...\nso x = 708..\nthe last of mock test will be 708+10+10=728...\nso ans = 760-728=32\nB", "role": "assistant" } ]

[ { "content": "John found that the average of 15 numbers is 40. If 10 is added to each number then the mean of number is?\n\n['A)50', 'B)45', 'C)65', 'D)78', 'E)64']", "role": "user" }, { "content": "(x+x1+...x14)/15 = 40\n50\nOption A", "role": "assistant" } ]

[ { "content": "A person is traveling at 20 km/hr and reached his destiny in 2.5 hr then find the distance?\n\n['A)53 km', 'B)55 km', 'C)52 km', 'D)60 km', 'E)50 km']", "role": "user" }, { "content": "T = 2.5 hrs = 5/2 hrs\nD= T*S = 20*5/2 = 50 km\nAnswer is E", "role": "assistant" } ]

[ { "content": "The first five numbers in a regular sequence are 4, 10, X, 46, and 94. What is x ?\n\n['A)28', 'B)26', 'C)30', 'D)22', 'E)24']", "role": "user" }, { "content": "it is a good Q to learn to pick up number properties in the given set, even if we do not get a Q on these line in actuals..\nwhen we see the sequence 4, 10, x, 46, and 94, we see that each succeeding number is some value more than twice the previous number..\n10=2*4+2..\nx=2*10+2 = 22..\nand so on..\nso next number= 22\nD", "role": "assistant" } ]

[ { "content": "Tim has 350 pounds of cement in 100, 50, and 25 pound bags. He has an equal number of each size bag. How many bags of cement does Tim have?\n\n['A)2', 'B)4', 'C)6', 'D)8', 'E)10']", "role": "user" }, { "content": "Let the number of each sized bag = c\r100c + 50c + 25c = 350\r175c = 350\rc = 2\rTherefore, Tim has 3c = 6 bags of cement\rAnswer: C", "role": "assistant" } ]

[ { "content": "What is the least value of x, So that 2x5475 is divisible by 9\n\n['A)7', 'B)8', 'C)4', 'D)3', 'E)2']", "role": "user" }, { "content": "Explanation:\nThe sum of the digits of the number is divisible by 9.\nThen the number is divisible by 9.\n2 + x + 5 + 4 + 7 + 5 = 23 + x\nLeast value of x may be '4',\nSo that the total 23 + 4 = 27\nis divisible by 9.\nAnswer: Option C", "role": "assistant" } ]

[ { "content": "Square P is inscribed in circle Q. If the perimeter of P is 40, what is the circumference of Q?\n\n['A)11√ 2π', 'B)10√ 2π', 'C)9√ 2π', 'D)8√ 2π', 'E)7√ 2π']", "role": "user" }, { "content": "square forms two right angled triangles.\nAny time we have a right angle triangle inside a circle, the hypotenuse is the diameter.\nhypotenuse here = diagonal of the square = 10 sqrt(2) = diameter\n=> radius = 5 sqrt(2)\nCircumference of the circle = 2pi r = 10 pi sqrt(2)\nAnswer is B.", "role": "assistant" } ]

[ { "content": "A debtor reached an agreement with his creditor to repay a loan by making a monthly payment which is double of the amount she paid the previous month. If the debtors first payment was $200, and he is expected to pay back 51200, how many months will it take to fully repay the loan?\n\n['A)9', 'B)10', 'C)9', 'D)12', 'E)10']", "role": "user" }, { "content": "First payment--$200\nTotal amount to be repaid--$25600\nFirst month payment--$200\nSecond month payment( double the previous month payment)--$200*2=$400\nThird month payment( double the previous month payment)--$400*2=$800\nFourth month payment( double the previous month payment)--$800*2=$1600\nFifth month payment( double the previous month payment)--$1600*2=$3200\nSixth month payment( double the previous month payment)--$3200*2=$6400\nSeventh month payment( double the previous month payment)--$6400*2=$12800\nEight month payment( double the previous month payment)--$12800*2=$25600\nNinth month payment( double the previous month payment)--$25600*2=$51200\nAnswer is A", "role": "assistant" } ]

[ { "content": "As a bicycle salesperson, James earns a fixed salary of $30 per week plus $6 per bicycle for the first 6 bicycles he sells, $12 per bicycle for the next 6 bicycles he sells, and $18 per bicycle for every bicycle sold after first 12. This week, he earned more than twice as much as he did last week. If he sold x bicycles last week and y bicycles this week, which of the following statements must be true?\nI. y<2x\nII. y>x\nIII. y>3\n\n['A)I,II only', 'B)I only', 'C)II,III only', 'D)II only', 'E)III only']", "role": "user" }, { "content": "II. y>x --> since this week, James earned more than he did last week and the total salary is in direct relationship with the # of bicycle sold, then y (# of bicycle sold this week) must be more than x (# of bicycle sold last week);\nIII. y>3 --> if James sold 3 bicycles this week then this week he earned 30+3*6=$48, which cannot be more than twice as much as he earned the last week, since the minimum salary is fixed to $30. So y must be more than 3;\nI. y<2x --> is not always true.\nAnswer: C", "role": "assistant" } ]

[ { "content": "A school currently maintains a fixed number of students per class. If the ratio of students per class were to be increased by 1, 10 fewer classes would be run for a total of 120 students. What is the current ratio Q of students per class?\n\n['A)Q=3', 'B)Q=4', 'C)6', 'D)8', 'E)12']", "role": "user" }, { "content": "Another way to look at the problem...\nSince the total is 120, RATIO * CLASSES = R*C = 120.....(i)\nwe are looking where ratio increases by 1 and # of classes decreases by 10 = (R+1)(C-10) = RC+C-10R-10=120....(ii)\n(ii)-(i)....\nC=10R+10 = 10(R+1).......\nso # of classes has to be multiple of 10\nAS RC=120.... 10(R+1)*R = 120...................R(R+1) = 12..\nso 12 is a multiple of consecutive numbers ONLY 3 *4 fits in..... and R=3\nA", "role": "assistant" } ]

[ { "content": "A survey reveals that the average income of a company’s customers is $45,000 per year. If 50 customers respond to the survey and the average income of the wealthiest 10 of those customers is $95,000, what is the average income of the other 40 customers?\nIs there a way to solve this using weighted average concept instead of doing tedious calculations?\n\n['A) $32,500', 'B) $35,000', 'C) $37,500', 'D) $42,500', 'E) $50,000']", "role": "user" }, { "content": "let x be the average of 40 customers\n40*x + 10* 95000 = 50*45000\nsolving this we have x= 32500\nAnswer is A.", "role": "assistant" } ]

[ { "content": "The slant height of a cone is 35 cm and radius of the base is 14cm, find the curved surface of the cone.\n\n['A)4150', 'B)1780', 'C)1540', 'D)1500', 'E)6100']", "role": "user" }, { "content": "π * 14 * 35= 1540\nAnswer:C", "role": "assistant" } ]

[ { "content": "A cheese factory sells its cheese in rectangular blocks. A normal block has a volume of 8 cubic feet. If a small block has half the width, half the depth, and half the length of a normal block, what is the volume of cheese in a small block in cubic feet?\n\n['A)1', 'B)5', 'C)4', 'D)6', 'E)2']", "role": "user" }, { "content": "Volume of cube=lbh=8\nNew cube l ,b, h are decreases of .5l, .5b,.5h\nNew volume of cube =.5l*.5b*.5h=.125*lbh\n=.125*8\n=1\nAnswer: A", "role": "assistant" } ]

[ { "content": "In a new housing development, trees are to be planted along the sidewalk of a certain street. Each tree takes up one square foot of sidewalk space, and there are to be 20 feet between each tree. How many trees can be planted if the road is 148 feet long?\n\n['A)8', 'B)9', 'C)10', 'D)11', 'E)16']", "role": "user" }, { "content": "Let T be the number of trees. Then the length required for trees on the sidewalk will be 1*T= T\nTo maximize the number of trees, the number of 20 feet spaces between trees should be 1 less than total number of trees.\nFor example, If there are 3 trees, then there should be 2 spaces between them.\nSo the number of 20 feet spaces will be T-1. Then, the length of sidewalk required for 20 feet spaces will be 20*(T-1)\nIt is given that total length of sidewalk is 148 feet.\nor 20(T-1)+T = 148\nor 20T-20+T = 148\nor 21T = 168\nor T=8\nAnswer:-A", "role": "assistant" } ]

[ { "content": "What will be the difference in simple and compound interest on 2000 after three years at the rate of 10 percent per annum?\n\n['A)160', 'B)42', 'C)62', 'D)20', 'E)None of these']", "role": "user" }, { "content": "For 3 years:\nDiff.=Sum×(rate)2(300+rate)/(100)3\n= 2000×10×10×310/100×100×100 = 62\nAnswer C", "role": "assistant" } ]

[ { "content": "A $500 investment and a $1,500 investment have a combined yearly return of 19 percent of the total of the two investments. If the $500 investment has a yearly return of 7 percent, what percent yearly return does the $1,500 investment have?\n\n['A)9%', 'B)10%', 'C)23%', 'D)21%', 'E)22%']", "role": "user" }, { "content": "The equation we can form the question :\nReturn on Total Investment = Sum of individual Investments\n(500+1500)(19)=(500∗7)+(1500x), where x is the return on investment of 1500.\nSolving the equation, we get x = 23% ( Option C )\tANSWER:C", "role": "assistant" } ]

[ { "content": "Find the constant k so that : -x2 - (k + 11)x - 8 = -(x - 2)(x - 4)\n\n['A)11', 'B)12', 'C)17', 'D)14', 'E)15']", "role": "user" }, { "content": "-x2 - (k + 11)x - 8 = -(x - 2)(x - 4) : given\n-x2 - (k + 11)x - 8 = -x2 + 6x - 8\n-(k + 11) = 6 : two polynomials are equal if their corresponding coefficients are equal.\nk = -17 : solve the above for k\ncorrect answer C", "role": "assistant" } ]

[ { "content": "A positive whole number has factors of 3 and 5. The number MUST be divisible by: I. 15 II. 30 III. 60\n\n['A)I & II', 'B)III', 'C)I & III', 'D)II & III', 'E)II']", "role": "user" }, { "content": "15 , 30 is not divisible by 60.But 60 is divisible by 3,5,15,30\nSo answer is III\nAnswer : B", "role": "assistant" } ]

[ { "content": "Krishan and Nandan jointly started a business. Krishan invested six times as Nandan did and invested his money for double time as compared to Nandan. Nandan earned Rs. 6000. If the gain is proportional to the money invested and the time for which the money is invested then the total gain was?\n\n['A)Rs.78000', 'B)Rs.48000', 'C)Rs.6000', 'D)Rs.82000', 'E)Rs.32000']", "role": "user" }, { "content": "6:1\n2:1\n------\n12:1\n1 ----- 6000\n13 ----- ? => Rs.78,000\nAnswer: A", "role": "assistant" } ]

[ { "content": "There are 8 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['A)10', 'B)30', 'C)28', 'D)60', 'E)90']", "role": "user" }, { "content": "10 players are there.\ntwo players play one game with one another.\nso 8C2=8*7/2\n=28\nSO OPTION C is correct", "role": "assistant" } ]

[ { "content": "A pipe takes a hours to fill the tank. But because of a leakage it took 2 times of its original time. Find the time taken by the leakage to empty the tank\n\n['A)50 min', 'B)60 min', 'C)90 min', 'D)80 min', 'E)120 min']", "role": "user" }, { "content": "pipe a can do a work 60 min.\nlets leakage time is x;\nthen\n1/60 -1/x=1/120\nx=120 min\nANSWER:E", "role": "assistant" } ]

[ { "content": "Today is 22 days before Mariah's graduation. If she graduates on a Friday, what day of the week is it today?\n\n['A)Monday', 'B)Friday', 'C)Tuesday', 'D)Thursday', 'E)Sunday']", "role": "user" }, { "content": "Each weekday is repeated every 7 days. 22 divided by 7 is 3, with a remainder of 1. Therefore, 22 days before the graduation occurs 1 day before the weekday of the graduation. Answer: D", "role": "assistant" } ]

[ { "content": "Suppose a, b, and c are positive integers with a < b < c such that\n1/a\n+\n1/b\n+\n1/c\n= 1. What is\na + b + c?\n\n['A)1', 'B)4', 'C)9', 'D)11', 'E)no such integers exist']", "role": "user" }, { "content": "First note that we must have 1/a < 1, so a > 1. Since 1/a > 1/b > 1/c, we\nmust also have 1/a > 1/3; so a < 3. Thus, a/ 2. Now 1/b + 1/c = 1/2 where 2 < b < c.\nSimilar to before, 1/b > 1/4, so b < 4. Thus, b = 3. With a = 2 and b = 3 we have\n1/2+1/3+1/c = 1, which is satisfied when c = 6. To conclude, a+b+c = 2+3+6 = 11.\ncorrect answer D", "role": "assistant" } ]

[ { "content": "The age of man is three times the sum of the ages of his two sons.Four years hence,his age will be double of the sum of the ages of his sons.The father’s present age is :\n\n['A)36 years', 'B)45 years', 'C)50 years', 'D)55 years', 'E)75 years']", "role": "user" }, { "content": "Solution\nLet the sum of present ages of the two sons be x years.\nThen,father's present age = 3x years.\n∴ (3x + 4)=2 (x +8) ⇔ 3x + 4 = 2x + 16 ⇔ x =12.\nHence,father's present age = 36 years. Answer A", "role": "assistant" } ]

[ { "content": "A bottle of coke contains 200gm in place of 1kg of fluid. Find the actual % difference, given a 10% gain on initial fluid?\n\n['A)32.5%', 'B)112.5%', 'C)35%', 'D)40%', 'E)50%']", "role": "user" }, { "content": "fluid price of 200gm = 100+10 = 110\nDifference = 110-20 = 90\n% of difference = 90*100/80 =112.5 %\nAnswer is B", "role": "assistant" } ]

[ { "content": "A person can walk at a constant rate of 8mph and can bike at a rate of 16mph. If he wants to travel 64 miles in 8 hours using bike and walking at their constant rates, how much distance would he require to walk?\n\n['A)20', 'B)30', 'C)48', 'D)64', 'E)72']", "role": "user" }, { "content": "Total distance = 64\nDistance = Speed * Time\nWalking speed = s1 = 8\nWalking time = t1\nBike speed = s2 = 16\nTime traveled in bike = t2\nd1 + d2 = 64\ns1t1 + s2t2 = 64\n8*t1 + 16*t2 = 64\nt1 + 2*t2 = 8 ----- (1)\nGiven: t1 + t2 = 8 ----- (2)\n(1) - (2) --> t2 = 0 and t1 = 8 - 0 = 8\nWalking distance = s1*t1 = 8*8 = 64\nAnswer: D", "role": "assistant" } ]

[ { "content": "5358 x 51 = ?\n\n['A)273258', 'B)273268', 'C)273348', 'D)273358', 'E)None of these']", "role": "user" }, { "content": "Explanation:\n5358 x 51\t= 5358 x (50 + 1)\n= 5358 x 50 + 5358 x 1\n= 267900 + 5358\n= 273258.\nANSWER IS A", "role": "assistant" } ]

[ { "content": "3 persons (1 couple and 1 single) are seated at random in a row of 5 chairs. What is the probability that the couple does not sit together?\n\n['A)5/7', 'B)4/5', 'C)2/5', 'D)3/5', 'E)11/8']", "role": "user" }, { "content": "Let's find the probability that a couple sits together (right next to each other) and subtract that value from 1.\nTotal # of ways 3 persons C1C1, C2C2 and SS to be seated in a row of 5 seats is 5!2!=605!2!=60. Consider this, we are interested in arrangement of C1, C2, S, E, EC1, C2, S, E, E, so in arrangement of 5 letters out of which 2 E's are identical (E denotes an empty seat);\n# of ways for a couple to sit together is 4!2!∗2=244!2!∗2=24. Consider a couple as a single unit: {C1,C2}, S, E, E{C1,C2}, S, E, E, so we have total of 4 units out of which 2 E's are identical, # of arrangement of these units is 4!2!4!2!, but C1C1, C2C2 within their unit can be arranged in 2 ways ({C1,C2}{C1,C2} or {C2,C1}{C2,C1}), so total # of arrangement for this case is 4!2!∗2=244!2!∗2=24;\nP=1−2460=35P=1−2460=35.\nAnswer: D.", "role": "assistant" } ]

[ { "content": "In 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 8 customers are selected, what are the chances that at least 1 customer bought a coffee and a bagel?\n\n['A)27/343', 'B)3/7', 'C)27/125', 'D)199/245', 'E)9/125']", "role": "user" }, { "content": "Let 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*17/28=46/245\nchances that at least 1 customer bought a coffee and a bagel= 1 - 46/245 = 199/245\nAnswer D.", "role": "assistant" } ]

[ { "content": "|x+3| – |4-x| = |8+x| How many S solutions will this equation have?\n\n['A)0', 'B)1', 'C)2', 'D)3', 'E)4']", "role": "user" }, { "content": "|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", "role": "assistant" } ]

[ { "content": "The output of a factory was increased by 10% 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['A)20%', 'B)24%', 'C)30%', 'D)32%', 'E)79%']", "role": "user" }, { "content": "Let initial output is O then after 10% increase it will be 1.1O and after 20% increase on this new output the latest output will be 1.1O * 1.20 = 1.32O\nNow we have to decrease the output by some percentage so that the new output is same as the starting output (O)\nso, 1.32O * (1-x/100) = O\n=> x = 24.24%\nSo, answer will be B", "role": "assistant" } ]

[ { "content": "In a graduate physics course, 70 percent of the students are male and 30 percent of the students are married. If two-sevenths of the male students are married, what fraction of the male students is single?\n\n['A)2/7', 'B)1/3', 'C)1/2', 'D)2/3', 'E)5/7']", "role": "user" }, { "content": "let assume there are 100 students of which 70 are male and 30 are females\nif 30 are married then 70 will be single.\nnow its given that two-sevenths of the male students are married that means 2/7 of 70 = 20 males are married\nif 30 is the total number of students who are married and out of that 20 are males then the remaining 10 will be females who are married.\ntotal females = 70\nmarried males = 20\nthen single males = 70-20 = 50\nwe need to find the fraction of male students who are single i.e single male students / total male student\n= 50/70 = 5/7 [E]", "role": "assistant" } ]

[ { "content": "The cost of painting the whole surface area of a cube at the rate of 13 paise per Sq.cm is Rs. 343.98. Then the volume of the cube is\n\n['A)8500 cm3', 'B)9000 cm3', 'C)9250 cm3', 'D)9261 cm3', 'E)None']", "role": "user" }, { "content": "Solution\nSurface area\t= (34398 / 13)\n‹=›2646cm3\n‹=›6a2= 2646\n‹=›a2= 441\n‹=›a = 21.\nSo,volume =(21x21x21)cm3= 9261cm3.\nAnswer D", "role": "assistant" } ]

[ { "content": "A man sold 20 articles for $60 and gained 20%. How many articles should he sell for $50 to incur a loss 20%?\n\n['A)25', 'B)36', 'C)40', 'D)50', 'E)48']", "role": "user" }, { "content": "Production cost per article: $60*(100%-20%) / 20 = $2.40\nRequired production costs for a loss of 20%: $50*(100% + 20%) = $60\nNumber of articles to be sold for $60 to incur a 20% loss: $60 / $2.40 = 25\nThus, solution A is correct.", "role": "assistant" } ]

[ { "content": "A 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['A)3:5', 'B)2:1', 'C)16:15', 'D)4:5', 'E)None of these']", "role": "user" }, { "content": "Explanation:\nFor an income of Re. 1 in 9% stock at 96, investment = Rs. 96/9 = Rs.32/3\nFor an income Re. 1 in 12% stock at 120, investment = Rs. 120/12 = Rs. 10.\nRatio of investments =(32/3) : 10 = 32 : 30 = 16 : 15.\nAnswer: C", "role": "assistant" } ]

[ { "content": "A, B, C rent a pasture. A puts 10 oxen for 7 months, B puts 12 oxen for 5 months and C puts 15 oxen for 3 months for grazing. If the rent of the pasture is Rs. 175, how much must C pay as his share of rent?\n\n['A)Rs. 45', 'B)Rs. 50', 'C)Rs. 55', 'D)Rs. 60', 'E)Rs. 65']", "role": "user" }, { "content": "Explanation:\nA : B : C = (10 x 7) : (12 x 5) : (15 x 3) = 70 : 60 : 45 = 14 : 12 : 9.\nC's rent = Rs.(175 x\t9/35)= Rs. 45.\nANSWER IS A", "role": "assistant" } ]

[ { "content": "A train 500 m long can cross an electric pole in 20 sec and then find the speed of the train?\n\n['A)95 Kmph', 'B)90 Kmph', 'C)92 Kmph', 'D)95 Kmph', 'E)98 Kmph']", "role": "user" }, { "content": "Length = Speed * time\nSpeed = L/T\nS = 500/20\nS = 25 M/Sec\nSpeed= 25*18/5 (To convert M/Sec in to Kmph multiply by 18/5)\nSpeed = 90 Kmph\nANSWER:B", "role": "assistant" } ]

[ { "content": "The smallest number when increased by \" 1 \" is exactly divisible by 6,9,15,35,45 is:\n\n['A)631', 'B)630', 'C)359', 'D)629', 'E)600']", "role": "user" }, { "content": "LCM = 630\n630 - 1 = 629\nANSWER:D", "role": "assistant" } ]

[ { "content": "How many keystrokes are needed to type the numbers from 1 to 500?\n\n['A)1156', 'B)1392', 'C)1480', 'D)1562', 'E)1788']", "role": "user" }, { "content": "There are 9 one-digit numbers from 1 to 9.\nThere are 90 two-digit numbers from 10 to 99.\nThere are 401 three-digit numbers from 100 to 500.\n9 + 90(2) + 401(3) = 1392\nThe answer is B.", "role": "assistant" } ]

[ { "content": "In a two-digit number, the digit in the unit's place is four times the digit in ten's place and the sum of the digits is equal to 10. What is the number?\n\n['A)82', 'B)41', 'C)14', 'D)56', 'E)28']", "role": "user" }, { "content": "Let the ten's digit be x. then, unit's digit = 4x\ntherefore x + 4x = 10 ==> 5x = 10 ==> x = 2\nso ten's digit is 2 and unit's digit is 8, so the number is 28\nso the correct answer is option E) 28", "role": "assistant" } ]

[ { "content": "The edge of a cube is 7a cm. Find its surface?\n\n['A)24a8', 'B)24a4', 'C)24a1', 'D)24a2', 'E)294a2']", "role": "user" }, { "content": "6a2 = 6 * 7a * 7a = 294a2\nAnswer:E", "role": "assistant" } ]

[ { "content": "A shop sells chocolates It is used to sell chocolates for Rs.2 each but there were no sales at that price.When it reduced the price all the chocolates sold out enabling the shopkeeper to realize Rs 164.90 from the chocolates alone If the new price was not less than half the original price quoted How many chocolates were sold?\n\n['A)1.9', 'B)1.7', 'C)1.2', 'D)1.5', 'E)1.6']", "role": "user" }, { "content": "16490 = 2 × 5 × 17 × 97\nNow now chocolate price should be greater than 1 and less than 2. So 2 x 5 x 17 = 170\nSo Total chocolates sold = 97 and New chocolate price = Rs.1.7\nAnswer:\tB", "role": "assistant" } ]

[ { "content": "A board 7ft. 9 inches long is divided into 3 equal parts . What is the length of each part?\n\n['A)31 inches', 'B)32 inches', 'C)33 inches', 'D)34 inches', 'E)35 inches']", "role": "user" }, { "content": "7 ft 9 in is 84 + 9 = 93 inches. so 93/3 = 31 inches or 2 ft. 7 inch.\nANSWER:A", "role": "assistant" } ]

[ { "content": "Find the number of zeroes in the expression 15*32*25*22*40*75*98*112*125\n\n['A)12', 'B)9', 'C)14', 'D)7', 'E)6']", "role": "user" }, { "content": "(3*5)*(2*2*2*2*2)*(5*5)*(2*11)*(2*2*2*2*5)*(5*5*3)*(2*7*7)*(2*2*2*2*7)*(5*5*5)\nthere are 9 (5*2) pairs which gives zero\nso.no of zeros 9\nANSWER:B", "role": "assistant" } ]

[ { "content": "The diagonals of a rhombus are 18 cm and 22 cm. Find its area?\n\n['A)277', 'B)266', 'C)198', 'D)288', 'E)212']", "role": "user" }, { "content": "1/2 * 18 * 22 = 198\nAnswer: C", "role": "assistant" } ]

[ { "content": "If rupee one produces rupees nine over a period of 40 years, find the rate of simple interest?\n\n['A)22 1/8 %', 'B)22 3/2 %', 'C)28 1/2 %', 'D)22 1/2 %', 'E)32 1/2 %']", "role": "user" }, { "content": "9 = (1*40*R)/100\nR = 22 1/2 %\nAnswer:D", "role": "assistant" } ]

[ { "content": "A 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['A)32:99', 'B)8:21', 'C)32:45', 'D)34:89', 'E)35:21']", "role": "user" }, { "content": "A : B\n(6000*4)+(3000*8) : (12000*6)+(9000*6)\n48000 : 126000\n8 : 21\nAnswer:B", "role": "assistant" } ]

[ { "content": "A train covers a distance of 10km in 10 min. If it takes 6 sec to pass a telegraph post, then the length of the train is?\n\n['A)m', 'B)m', 'C)m', 'D)m', 'E)m']", "role": "user" }, { "content": "Speed = (10/10 * 60) km/hr\n= (60 * 5/18) m/sec = 50/3 m/sec.\nLength of the train = 50/3 * 6\n= 100 m.\nAnswer:C", "role": "assistant" } ]

[ { "content": "The rental charge for a car is 34 cents for the first 1/4 mile driven and 6 cents for every 1/5 mile driven over the initial 1/4 mile. If a man paid $1.24 in rental charges, how many miles did he drive?\n\n['A)2.5', 'B)3.0', 'C)3.25', 'D)3.75', 'E)4.0']", "role": "user" }, { "content": "Total Rent = Rent for the first 0.25 mile + Rent After 0.25 mile\nRent for the first 0.25 mile = 34 cents\nRent After 0.25 mile = [6 cent/(1/5 mile)]*(x - 0.25) = 30(x-0.25)\nTherefore, Total Rent = 35 + 30(x - 0.25)\n124 = 34 + 30(x - 0.25)\n90 = 30(x - 0.25)\n3 = x - 0.25\nx = 3 + 0.25 = $3.25 C", "role": "assistant" } ]

[ { "content": "A question paper consists of three sections 4,5 and 6 questions respectively. Attempting one question from each section is compulsory but a candidate need not attempt all the questions. In how many ways can a candidate attempt the questions?\n\n['A)209', 'B)(4!-1)*(5!-1)*(6!-1)', 'C)119', 'D)29295', 'E)None']", "role": "user" }, { "content": "Solution:\nAt least 1 question from each section is compulsory, so from the 1st section the candidate can attempt 1 or 2 or 3 or 4 questions.\nIn each section each question can be dealt with in 2 ways, i.e. either he attempts it or leaves it.\nSo far 4 question there are 2 *2 *2 *2 ways to attempt. As he has to attempt at least 1 question, the total number of ways in which he can attempt questions from 1st section is 24−1.\nSimilarly for the 2nd section there are 25−1 ways in which he can attempt and for the 3rd section there are 26−1 ways.\nThe ways in which the attempts one or more questions in any section is independent of the number of ways in which he attempts one or more questions from the other sections.\nThus, total number of ways\nAnswer: Option D", "role": "assistant" } ]

[ { "content": "10 women can complete a work in 9 days and 10 children take 12 days to complete the work. How many days will 6 women and 7 children take to complete the work?\n\n['A)4', 'B)5', 'C)7', 'D)8', 'E)2']", "role": "user" }, { "content": "1 women's 1 day work = 1/90\n1 child's 1 day work = 1/120\n(6 women + 7 children)'s 1 day work\n= (6/90 + 7/120) = 1/8\n6 women and 7 children will complete the work in 8 days.\nD", "role": "assistant" } ]

[ { "content": "Three numbers are in the ratio 5 : 6 : 7. The sum of its longest and smallest numbers equals the sum of the third number and 54. Find the third number?\n\n['A)A)37', 'B)B)85', 'C)C)48', 'D)D)43', 'E)E)54']", "role": "user" }, { "content": "Let the numbers be 5x, 6x, 7x.\nLargest number = 7x.\nSmallest number = 5x.\nThird number = 6x.\n7x + 5x = 6x + 54\n6x = 54 => third number is 54.\nAnswer: Option E", "role": "assistant" } ]

[ { "content": "At the end of a business conference the nine people present all shake hands with each other once. How many handshakes will there be altogether ?\n\n['A)20', 'B)45', 'C)36', 'D)90', 'E)95']", "role": "user" }, { "content": "number of handshakes = 9C2= 9*8/2 = 36\nANSWER:C", "role": "assistant" } ]

[ { "content": "Sum of the squares of three numbers is 351 and the sum of their products taken two at a time is 245. Find the sum?\n\n['A)20', 'B)22', 'C)25', 'D)26', 'E)29']", "role": "user" }, { "content": "(a + b + c)2 = a2 + b2 + c2 + 2(ab +bc + ca) = 351 + 2* 245\na + b + c = √841 = 29\nE", "role": "assistant" } ]

[ { "content": "What is the are of an equilateral triangle of side 16 cm?\n\n['A)64√6 cm2', 'B)64√3 cm2', 'C)64√9 cm2', 'D)34√3 cm2', 'E)24√3 cm2']", "role": "user" }, { "content": "Area of an equilateral triangle = √3/4 S2\nIf S = 16, Area of triangle = √3/4 * 16 * 16\n= 64√3 cm2;\nAnswer: D", "role": "assistant" } ]

[ { "content": "Each of the following equations W has at least one solution EXCEPT\n\n['A)W=–2^n = (–2)^-n', 'B)2^-n = (–2)^n', 'C)2^n = (–2)^-n', 'D)(–2)^n = –2^n', 'E)(–2)^-n = –2^-n']", "role": "user" }, { "content": "While it is possible to reason out which of these choices must not work, we may not have time or the confidence to do so. However, this problem has variable in its answer choice, and relatively simple math. Therefore, an easy alternative is picking numbers.\nSince we're dealing with exponents, we want to keep things as easy as possible. Hence, we'll start with the easiest exponent possible: n = 1. A, B, and C are not solved (x^-n = 1/(x^n), so we're comparing integers to fractions), but choices D and E both end up valid, eliminating them from contention.\nIn the process of doing this, however, we've uncovered a major clue to our next step: A, B, and C, all compared integers to fractions, and the only integer equal to it's reciprocal is 1, which is equal to 1/1. This, in turn, tells us the we need to pick n = 0. Remember, for all non-zero x, x^0 = 1.\nIf we plug n = 0 into choices B and C, we end up with 1 = 1 both times. Choice A, however, results in the false 1 = -1. Thus, we conclude that the first choice has no valid solutions, and is therefore the correct answer.", "role": "assistant" } ]

[ { "content": "If the population of a certain country increases at the rate of one person every 40 seconds, by how many persons does the population increase in 1 hour?\n\n['A)90', 'B)120', 'C)150', 'D)180', 'E)160']", "role": "user" }, { "content": "Answer = 1.5 * 60 = 90\nAnswer is A", "role": "assistant" } ]

[ { "content": "A 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['A)288', 'B)180', 'C)288', 'D)277', 'E)265']", "role": "user" }, { "content": "Length of the train be ‘X’\nX + 120/15 = X + 180/18\n6X + 720 = 5X + 900\nX = 180m .Answer: B", "role": "assistant" } ]

[ { "content": "Find the area of a rhombus whose side is 25 cm and one of the diagonals is 30 cm?\n\n['A)272 sq.cm', 'B)267 sq.cm', 'C)286 sq.cm', 'D)251 sq.cm', 'E)600 sq.cm']", "role": "user" }, { "content": "Consider the rhombus ABCD. Let the diagonals intersect at E. Since diagonals bisect at right angles in a rhombus.\nBE2 + AE2 = AB2\n252 = 152 + AE2 AE\n= √(625 - 225)\n= √400 = 20,\nAC = 20 + 20 = 40 cm.\nArea of a rhombus\n= 1/2 * d1d2\n= 1/2 * 40 * 30\n= 600 sq.cm.\nAnswer:E", "role": "assistant" } ]

[ { "content": "How long does a train 110 m long running at the speed of 72 km/hr takes to cross a bridge 132 m length?\n\n['A)12.8 sec', 'B)12.1 sec', 'C)12.2 sec', 'D)12.6 sec', 'E)11.1 sec']", "role": "user" }, { "content": "Speed = 72 * 5/18 = 20 m/sec\nTotal distance covered = 110 + 132 = 242 m.\nRequired time = 242/20 = 12.1 sec.\nAnswer: B", "role": "assistant" } ]

[ { "content": "The 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['A)120', 'B)1250', 'C)1200', 'D)1100', 'E)1150']", "role": "user" }, { "content": "60 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", "role": "assistant" } ]

[ { "content": "From 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. What is the probability of having 0 woman in committee ?\n\n['A)7/36', 'B)9/144', 'C)1/36', 'D)1/18', 'E)5/18']", "role": "user" }, { "content": "We may have (3 men and 2 women) = (7C3 x 6C2) = 525\nor (4 men and 1 woman) = (7C4 x 6C1) = 210\nor (5 men only) = (7C5) = 21\nRequired ways = 756\nProbability of having 0 woman in committee = 21 / 756 =1/36\nans - C", "role": "assistant" } ]

[ { "content": "A 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['A)20/69', 'B)20/63', 'C)20/65', 'D)20/61', 'E)20/62']", "role": "user" }, { "content": "Required probability = (10 * 4)/126 = 20/63.Answer: B", "role": "assistant" } ]

[ { "content": "A train passes a station platform in 32 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['A)228', 'B)240', 'C)887', 'D)166', 'E)180']", "role": "user" }, { "content": "Speed = 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)/32 = 15 => x = 180 m.\nAnswer: E", "role": "assistant" } ]

[ { "content": "If |w|=−w, which of the following must be true?\n\n['A)x≥0', 'B)w≤0', 'C)x2>x', 'D)x3<0', 'E)2x<x']", "role": "user" }, { "content": "|w| =-w means absolute value of w is equal to negative of w. Since absolute value cannot be negative hence negative of w should result in a non negative number. It means w is a non positive number i.e. w<0. Answer is B", "role": "assistant" } ]

[ { "content": "Two 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['A)8%', 'B)9%', 'C)10%', 'D)11%', 'E)12%']", "role": "user" }, { "content": "Explanation:\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%Explanation:\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%\nOption C", "role": "assistant" } ]

[ { "content": "How many numbers from 39 to 79 are exactly divisible by 11?\n\n['A)5', 'B)7', 'C)4', 'D)11', 'E)12']", "role": "user" }, { "content": "39/11 = 1 and 79/11 = 7 ==> 7 - 3 = 4 Numbers\nAnswer : C", "role": "assistant" } ]

[ { "content": "It is found that the volume of a cube is numerically equal to its surface area. Then the measure of its edge in meters is:\n\n['A)4', 'B)6', 'C)8', 'D)9', 'E)cannot be determined']", "role": "user" }, { "content": "if edge of cube = a\nvolume of cube = a^3\nsurface area = 6(a^2)\nthen\na^3 = 6(a^2)\na = 6\nANSWER:B", "role": "assistant" } ]

[ { "content": "if there are 30 cans out of them one is poisned if a person tastes very little he will die within 14 hours so if there are mice to test and 24 hours to test, how many mices are required to find the poisned can?\n\n['A)3', 'B)2', 'C)6', 'D)1', 'E)7']", "role": "user" }, { "content": "as we know only one can is poisoned so try mice every can n notice the time\nfor ex suppose for ist can time was 12:05 then after 5 min test for can 2 means 12:10..n if 1st can contain poision then according to time it can be cleared..\nANSWER:D", "role": "assistant" } ]

[ { "content": "How long does a train 165 meters long running at the rate of 72 kmph take to cross a bridge 660 meters in length?\n\n['A)28', 'B)41.25', 'C)55', 'D)18', 'E)12']", "role": "user" }, { "content": "T = (660 + 165)/72 * 18/5\nT = 41.25\nAnswer: B", "role": "assistant" } ]

[ { "content": "A particular store purchased a stock of turtleneck sweaters and marked up its cost by 20%. During the New Year season, it further marked up its prices by 25% of the original retail price. In February, the store then offered a discount of 15%. What was its profit on the items sold in February?\n\n['A)27.5%', 'B)30%', 'C)35%', 'D)37.5%', 'E)40%']", "role": "user" }, { "content": "Assume the total price = 100x\nPrice after 20% markup = 120x\nPrice after 25%further markup = 1.25*120x = 150x\nPrice after the discount = 0.85*150x = 127.5x\nHence total profit = 27.5%\nOption A", "role": "assistant" } ]

[ { "content": "Half of 2 percent written as decimal is\n\n['A)0.01', 'B)0.5', 'C)0.05', 'D)0.005', 'E)None of these']", "role": "user" }, { "content": "Explanation:\nIt will be 1/2(2%) = 1/2(2/100) = 2/200 = 0.01\nOption A", "role": "assistant" } ]

[ { "content": "If books bought at prices ranging from Rs. 98 to Rs. 195 are sold at prices ranging from Rs. 120 to Rs 215, what is the greatest possible profit that might be made in selling 13 books ?\n\n['A)Rs. 1650', 'B)Rs. 3000', 'C)Rs. 1521', 'D)Rs. 1400', 'E)Rs. 1560']", "role": "user" }, { "content": "The 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 13 books = 98*13 = Rs. 1,274\nMaximum selling price of 13 books = 215 *13 = Rs. 2,795\nSo, maximum profit = 2795 - 1274 = Rs. 1,521\nANSWER : OPTION C", "role": "assistant" } ]

[ { "content": "Two 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['A)40', 'B)90', 'C)120', 'D)80', 'E)100']", "role": "user" }, { "content": "If two objects A and B start simultaneously from opposite points and, after meeting, reach their destinations in ‘a’ and ‘b’ hours respectively (i.e. A takes ‘a hrs’ to travel from the meeting point to his destination and B takes ‘b hrs’ to travel from the meeting point to his destination), then the ratio of their speeds is given by:\nSa/Sb = √(b/a)\ni.e. Ratio of speeds is given by the square root of the inverse ratio of time taken.\nSa/Sb = √(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", "role": "assistant" } ]

[ { "content": "I bought three toys for my triplet boys (one for each). I placed the toys in the dark store. One by one each boy went to the store and pick the toy. What is the probability that no boy will choose his own toy?\n\n['A)1/3', 'B)2/3', 'C)3/3', 'D)4/3', 'E)5/3']", "role": "user" }, { "content": "Solution:\n1/3\nAssuming T1 is the Toy for brother1, T2 is the toy for brother2 and T3 is the toy for brother3.\nFollowing are the possible cases for toys distribution:\nBoy1 Boy2 Boy3\nT1 T2 T3\nT1 T3 T2\nT2 T1 T3\nT2 T3 T1 .... (A)\nT3 T1 T2 .... (B)\nT3 T2 T1\nIn both steps (A) & (B), no one gets the correct toy.\nTherefore probability that none brother can get the own toy is 2/6 = 1/3\nAnswer A", "role": "assistant" } ]

[ { "content": "A man, a woman and a boy can complete a job in 3 days, 4 days and 12 days respectively. How many boys must assist 1 man and 1 woman to complete the job in 1/4th of a day?\n\n['A)10', 'B)41', 'C)31', 'D)21', 'E)22']", "role": "user" }, { "content": "Explanation:\n1 man’s 1 day’s work = 1/3, ¼ day’s work = 1/3 × ¼ = 1/12\n1 woman’s 1 day’s work = ¼, ¼ day’s work = ¼ × ¼ = 1/16\n1 boy’s 1 day’s work = 1/12, ¼ day’s work = 1/12 × ¼ = 1/48\nLet ‘x’ be the No. of boys required.\nThen, (1 man + 1 woman + x boy)’s ¼ day’s work 1/12 + 1/16 + x/48 = 1\n= (4 + 3 + x)/48 = 1\ni.e. 7 + x= 48 and x = 41.\nAnswer: Option B", "role": "assistant" } ]

[ { "content": "At present, the ratio between the ages of Amit and Dhiraj is 5 : 4. After 6 years, Amit’s age will be 26 years. What is the age of Dhiraj at present?\n\n['A)16', 'B)77', 'C)566', 'D)197', 'E)161']", "role": "user" }, { "content": "Explanation:\nLet the present ages of Amit and Dhiraj be 5x years and 4x years respectively. Then,\n5x + 6 = 26\n5x = 20\nx = 4\nDhiraj’s age = 4x = 16 years\nANSWER: A", "role": "assistant" } ]

[ { "content": "A 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['A)9:6', 'B)9:8', 'C)9:1', 'D)9:9', 'E)9:5']", "role": "user" }, { "content": "(3*6 + 6*6): (4*12)\n54:48 => 9:8.Answer:B", "role": "assistant" } ]

[ { "content": "If 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['A)I only', 'B)II only', 'C)III only', 'D)I and II', 'E)II and III']", "role": "user" }, { "content": "The 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'", "role": "assistant" } ]

[ { "content": "If each side of a square is increased by 25%, find the percentage change in its area?\n\n['A)65.25', 'B)56.25', 'C)65', 'D)56', 'E)25']", "role": "user" }, { "content": "let 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) = (25a²/16)\nincreased area== (25a²/16) - a²\nIncrease %= [(9a²/16 ) x (1/a² ) x 100]% = 56.25%\nAnswer: B", "role": "assistant" } ]

[ { "content": "If the sum and difference of two numbers are 20 and 8 respectively, then the difference of their square is:\n\n['A)12', 'B)28', 'C)160', 'D)180', 'E)18']", "role": "user" }, { "content": "Let the numbers be x and y.\nThen, x + y = 20 and x - y = 8\nx2 - y2 = (x + y)(x - y) = 20 * 8 = 160.\nANSWER:C", "role": "assistant" } ]

[ { "content": "If $500 is deposited into a savings account at an annual interest rate of 5% that compounds monthly, what is the value of the investment after 10 years?\n\n['A)$750.00', 'B)$823.50', 'C)$973.25', 'D)$1000.25', 'E)$1100.00']", "role": "user" }, { "content": "ROI = 5% per annum compounded Monthly\nTenure, n = 10 years = 120 month\nPrincipal = $500\n5% per annum compounded monthly will be a little more than 5% at end of an year compounded anually = 6% per annum (approx)\nin 10 years the among simple rate will increase by 60% but at coumpound rate the amount wil increase more by 60%\nThis question can only be solved by approximation\n60% of $500 = $300\ni.e. amount after 10 years will be a little more than 500+300 = $800\ni.e. B option seems the closest possible answer\nAnswer: option B", "role": "assistant" } ]

[ { "content": "Two jars contain milk and water in the ratio 5: 4 and 2: 1 regpectively. What volume should be taken out from the first jar if volumes have to be taken out from both jars so as to fill up a third 30 l jar with milk to water in the ratio 1: 1 ?\n\n['A)7.5 l', 'B)15 l', 'C)22.5 l', 'D)It is impossible', 'E)none of these']", "role": "user" }, { "content": "In both jars concentration of milk is more than 50%.\nTherefore, in jar three concentration of milk cannot be 50%.\nHence, we cannot decide the volumes\nANSWER:D", "role": "assistant" } ]