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Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:5 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 result will not be 2 blue and 2 purple marbles? options: A)4/33 B)(5/36)^2 C)1/2 D)(31/36)^2 E)29/33 SOLUTION:Answer is 29/33. The probability of 2 blue and 2 purple marbles selected is 5C2.4C2/12C4 =4/33. Subtracting the above from 1 we get 29/33 E #### E QUESTION:In a tree, 3/7 of the birds are parrots while the rest are toucans. If 2/3 of the parrots are female and 7/10 of the toucans are female, what fraction of the birds in the tree are male? options: A)3/7 B)11/35 C)16/35 D)31/70 E)37/70 SOLUTION:Let x be the number of birds in the tree. The fraction of birds that are male parrots is (1/3)(3/7)=1/7. The fraction of birds that are male toucans is (3/10)(4/7)=6/35. The total fraction of male birds is 1/7 + 6/35 = 11/35. The answer is B. #### B QUESTION:Perimeter of the backwheel is 9 feet and front wheel is 7 feet at a certain distance. The front wheel gets 10 revolutions more than the back wheel. What is the distance? options: A)305 B)310 C)315 D)320 E)325 SOLUTION:If distance=d Number of revolutions by back wheel=d/9 & front wheel=d/7 (d/7)-(d/9)=10 ,2d=630 ,d=315 ANSWER:C #### C QUESTION:A man bought 20 shares of Rs. 50 at 5 discount, the rate of dividend being 13. The rate of interest obtained is: options: A)27% B)87% C)15% D)66% E)88% SOLUTION:Investment = Rs. [20 x (50 - 5)] = Rs. 900. Face value = Rs. (50 x 20) = Rs. 1000. Dividend = Rs. 27 x 1000 = Rs. 135. 2 100 Interest obtained = 135 x 100 % = 15% 900 View Answer Discuss in Forum Answer: C #### C QUESTION:John Purchased 1365 large bottles at $1.89 per bottle and 720 small bottles at $1.42 per bottle. What was the approximate average price paid per bottle? options: A)$1.63 B)$1.64 C)$1.68 D)$1.73 E)$1.76 SOLUTION:(1365*1.89+720*1.42)/(1365+720) =~1.73 Option (D) #### D QUESTION:An 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 46.5 meters. How many times did the ball bounce? options: A)5 B)6 C)7 D)8 E)9 SOLUTION:Going down = 16 m Going Up = 8 --> Total = 24 Going down = 8 --> Total = 32 Going Up = 4 --> Total = 36 Going down = 4 --> Total = 40 Going up = 2 --> Total = 42 Going down = 2 --> Total = 44 Going up = 1 --> Total = 45 Going down = 1 --> Total = 46 Going up = 0.5 --> Total = 46.5 (Caught) No of going downs = 5 .. ANSWER:A #### A QUESTION:The price of 10 bat is equal to that of 4 balls. The price of 15 balls and 2 bats together is Rs. 4000. The total price of 12 chairs and 3 balls is: options: A)Rs. 3200 B)Rs. 3500 C)Rs. 3700 D)Rs. 3900 E)Rs. 4000 SOLUTION:Let the cost of a chair and that of a table be Rs. x and Rs. y respectively. Then, 10x = 4y or y = 5 x. 2 15x + 2y = 4000 15x + 2 x 5 x = 4000 2 20x = 4000 x = 200. So, y = 5 x 200 = 500. 2 Hence, the cost of 12 chairs and 3 tables = 12x + 3y = Rs. (2400 + 1500) = Rs. 3900. D) #### D QUESTION:There are 8 people and 5 chairs. In how many different ways people can occupy the chairs? options: A)1640 B)1650 C)1660 D)1670 E)1680 SOLUTION:number of ways = 8*7*6*5 = 1680 Answer is E #### E QUESTION:If y ≠ 3 and 2h/y is a prime integer greater than 2, which of the following must be true? I. h = y II. y = 1 III. h and y are prime integers. options: A) None B) I only C) II only D) III only E) I and II SOLUTION:Note that we are asked which of the following MUST be true, not COULD be true. For such kind of questions if you can prove that a statement is NOT true for one particular set of numbers, it will mean that this statement is not always true and hence not a correct answer. So we should try to make the listed statements not true for some h and y (which satisfy y≠3 and 2h/y=prime>2). I. h = y --> not necessarily true: h=3 and y=2 (2h/y=3=prime>2); II. y=1 --> not necessarily true: h=3 and y=2 (2h/y=3=prime>2); III. h and y are prime integers --> not necessarily true: h=10 and y=4 (2h/y=5=prime>2). Answer: A. #### A QUESTION:A 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. options: A)252 B)240 C)300 D)924 E)None SOLUTION:Solution: Since, 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, [12!/(6!x 6!)]= 924 Answer: Option D #### D QUESTION:How many 3-digit even numbers are possible such that if one of the digits is 4, the next/succeeding digit to it should be 7? options: A)305 B)5 C)365 D)405 E)495 SOLUTION:470, 472, 474, 476, and 478, so total 5. Hence Option B. #### B QUESTION:If a is a digit in the number (a5,608 + 584)/88 = an integer, what is the value of a? options: A)2 B)1 C)3 D)7 E)9 SOLUTION:(a5,608 + 584)/88 = a6,192/88 Factors of 88 = (8)(11) Divisible by 8: if the last 3 digits of the number are divisible by 8. 192/8 = 24 => So, we want divisible by 11. Divisibe 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. a619-2 => a61-7 => a5-4 => a1 => 11/11. So a = 1. Answer: B #### B QUESTION:A man has some hens and cows. If the number of heads be 48 and the number of feet equals 140, then the number of hens will be: options: A)22 B)23 C)24 D)26 E)28 SOLUTION:let hens be x and cows be y now, feet: x*2+y*4=140 heads: x*1+y*1=48 implies, 2x+4y=140 and x+y=48 solving these two equations, we get x=26 and y=22 Therefore, hens are 26. ANSWER:D #### D QUESTION:An 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 options: A)50% B)40% C)33.5% D)37.5% E)None of these SOLUTION:Now, amount of petrol A = A⁄4 + A⁄8 = 3A⁄8 ∴ required% = 3A⁄ (8 × A) × 100 = 37.50% Answer D #### D QUESTION:A company has two types of machines, type R and type S. Operating at a constant rate a machine of R does a certain job in 36 hours and a machine of type S does the job in 36 hours. If the company used the same number of each type of machine to do job in 12 hours,how many machine R were used? options: A)3 B)4 C)6 D)9 E)12 SOLUTION:yes there is a typo in the question, I got the same ques on my GMAT PREP last week, and the questions goes as: A company has two types of machines,type R and type S.Operating at a constant rate a machine of R does a certain job in 36 hours and a machine of type S does the job in 36 hours .If the company used the same number of each type of machine to do job in2 hours,how many machine R were used? So for a job to be done in 2 hours R = 1/2 R_a(Rate of Machine R) = 1/36 R_s(Rate of Machine S) = 1/36 Lets say x machines are used to attain the desired rate, thus x/36+x/36 = 1/2 (Desired R =1/2 i.e. to complete the job in 2 hours) (x+x)/36 = 1/2 2x/36 = 1/2 x = 9. QA = 9 (ANSWER D) #### D QUESTION:If 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? options: A)41 B)42 C)43 D)44 E)45 SOLUTION:A two-digit number "cd" can be expressed algebraically as 10c+d. The sum of A + B = (10c+d)+(10d+c)=11(c+d). The only answer that is a multiple of 11 is 44. The answer is D. #### D QUESTION:If a > 0 and x is m percent of y, then, in terms of a, y is what percent of x? options: A)a) 100a B)b) 1/100a C)c) 1/a D)d) 10/a E)e) 10,000/a SOLUTION:x= a/100 * y So y= 100/a * x So y= (10000/a)/100 * x E #### E QUESTION:For the symbol, m”n=n^2−m for all values of m and n. What is the value of 4”2? options: A)5 B)3 C)2 D)1 E)0 SOLUTION:4”2= 4 - 4=0 Answer: E #### E QUESTION:There are 4 copies of 5 different pencils. In how many ways can they be arranged on a shelf? options: A)20!/4! B)20!/5(4!) C)20!/(4!)^5 D)20! E)5! SOLUTION:There are 4 copies of 5 different pencils.20!/((4!)^5) Answer - C #### C QUESTION:A 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? options: A)400 B)197 C)278 D)270 E)279 SOLUTION:2000 ---- 50 2000 ---- 40 x ----- 50 x*50 = 2000*40 x=1600 2000 ------- 400 Answer: A #### A QUESTION:The length of the bridge, which a train 140 metres long and travelling at 45 km/hr can cross in 30 seconds, is? options: A)876 m B)157 m C)235 m D)156 m E)167 m SOLUTION:Speed = [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. Answer: C #### C QUESTION:The average (arithmetic mean) of 24, 35, and 58 is 6 more than the average of 19, 51, and x. What is x? options: A)26 B)27 C)28 D)29 E)30 SOLUTION:The average of 24, 35, and 58 is 39. The average of 19, 51 and x is 33. Then 19 + 51 + x = 99. x = 29. The answer is D. #### D QUESTION:According to the directions on a can of frozen orange juice concentrate, 1 can of concentrate is to be mixed with 3 cans of water to make orange juice. How many 12 ounce cans of concentrate are required to prepare 160 six-ounce servings of orange juice? options: A)20 B)24 C)28 D)32 E)36 SOLUTION:1 X 12 ounce can of concentrate + 3 X 12 ounce cans of water = 48 ounces of the mixture. 48 ounces of mixture gives (48 / 6 ) = 8 servings. Thus 1 x 12 ounce can of concentrate is used to produce 8 servings of the mixture. To make 160 servings of the mixture, we need 160 / 8 = 20 cans of the concentrate. The answer is A. #### A QUESTION:A and B can do a piece of work in 50 days and 50 days respectively. They work together for 10 days and B leaves. In how many days the whole work is completed? options: A)30days B)35days C)40days D)44days E)45days SOLUTION:Explanation: (A+B)’s 10 days work = 10[1/50+1/50]=10[1+1/50]= 2/5 A complete remaining work in 2/5*50 = 20 Total work = 10+20= 30days Answer: Option A #### A QUESTION:If x is the smallest positive integer such that 4,536 multiplied by x is the square of an integer, then x must be options: A)12 B)21 C)16 D)17 E)14 SOLUTION:4536= 6*6*3*3*7*3, so we need one 7 and one 3 to make it a square of a number. so 7*3= 21 Ans: B #### B QUESTION:Working alone, Printers X, Y, and Z can do a certain printing job, consisting of a large number of pages, in 12, 16, and 18 hours, respectively. What is the ratio of the time it takes Printer X to do the job, working alone at its rate, to the time it takes Printers Y and Z to do the job, working together at their individual rates? options: A) 4/11 B) 1/2 C) 15/22 D) 144/17 E) 11/4 SOLUTION:P1 takes 12 hrs Rate for P2P3 together = 1/16 + 1/18 = 17/144 Therefore they take 144/17 Ratio = 144/17 = D #### D QUESTION:The prices of tea and coffee per kg were the same in june. In August the price of coffee shot up by 20% and that of tea dropped by 20%. if in August , a mixture containing equal quantities of tea and coffee costs 50/kg. how much did a kg of coffee cost in june ? options: A)45 B)50 C)40 D)35 E)30 SOLUTION:Let the price of tea and coffee be x per kg in June. Price of tea in August = 1.2x Price of coffee in August = 0.8x . In July the price of 1/2 kg (500gm) of tea and 1/2 kg (500gm) of coffee (equal quantities) = 50 1.2x(1/2) + 0.8x(1/2) = 50 => x =50 B #### B QUESTION:If a truck is traveling at a constant rate of 54 kilometers per hour, how many seconds will it take the truck to travel a distance of 600 meters? (1 kilometer = 1000 meters) options: A)18 B)24 C)30 D)36 E)40 SOLUTION:Speed = 54 Km/hr => 54,000 m/hr In one minute => 54000/60 = 900 meters In one sec => 900/60 = 15 meters Time = Total distance need to be covered / Avg. speed => 600/ 15 =40 and hence the Answer : E #### E QUESTION:Find the least number of complete years in which a sum of money put out at 15% compound interest will be more than double of itself? options: A)5 B)6 C)7 D)8 E)9 SOLUTION:5 years Answer: A #### A QUESTION:A sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 854 in 4 years. The sum is: . options: A)Rs. 650 B)Rs. 690 C)Rs. 698 D)Rs. 700 E)Rs. 720 SOLUTION:S.I. for 1 year = Rs. (854 - 815) = Rs. 39. S.I. for 3 years = Rs.(39 x 3) = Rs. 117. Principal = Rs. (815 - 117) = Rs. 698. Answer: Option C #### C QUESTION:What will be the ratio of simple interest earned by certain amount at the same rate of interest for 25 years and that for 40 years? options: A)5:8 B)7:5 C)3:8 D)Data inadequate E)None of these SOLUTION:Let the principal be P and rate of interest be R%. ∴ Required Ratio = [(P×R×25/100) /(P×R×40/100)]=25PR/40PR=25/40=5:8 Answer A #### A QUESTION:If P(A) = 5/7 and P (B) = 2/5, find P (A n B) if A and B are independent events. options: A)7/25 B)3/25 C)8/25 D)2/7 E)3/17 SOLUTION:P (A n B) = P(A) . P(B) P (A n B) = 5/7 . 2/5 P (A n B) = 2/7. D #### D QUESTION:If an organization were to sell n tickets for a theater production, the total revenue from ticket sales would be 20 percent greater than the total costs of the production. If the organization actually sold all but 5 percent of the n tickets, the total revenue from ticket sales was what percent greater than the total costs of the production? options: A)4% B)10% C)14% D)15% E)18% SOLUTION:Let Cost of PROD for 1 ticket = 1 So COP for n tickets = n So for selling n tickets, SP = 1.2 * n = 1.2n So SP of 1 ticket = 1.2 SP of 95% tickets = 1.2 * 0.95n So profit % = (1.2 * 0.95n - n)/n * 100 = 0.14 * 100 = 14% Answer - C #### C QUESTION:10 people can write 55 book in 12 days working 8 hour a day.then in how many day 198 can be written by 48 people? options: A)9 B)13 C)21 D)24 E)23 SOLUTION:work per day epr hour per person= 55/(12*8*10) // eq-1 people=48; let suppose day=p; per day work for 8 hours acc. to condition work per day epr hour per person= 198/(p*8*48) // eq-2 eq-1==eq-2; p= 9 ANSWER:A #### A QUESTION:Which of the following fractions is smaller than 17/50? options: A)2/5 B)11/34 C)43/99 D)8/21 E)9/20 SOLUTION:Answer B 17/50=0.34 11/34=0.323529 which is 0.01647 smaller than 0.34 #### B QUESTION:Sandy can do a job in 12 days and Molly can do the same job in 24 days. If they work together, in how many days will they complete the job? options: A)6 B)7 C)8 D)9 E)10 SOLUTION:Sandy can do 1/12 of the job each day. Molly can do 1/24 of the job each day. The combined rate is 1/12 + 1/24 = 1/8 of the job each day. The job will take 8 days. The answer is C. #### C QUESTION:A 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? options: A)287 m B)350 m C)187 m D)197 m E)186 m SOLUTION:Speed = 300/18 = 50/3 m/sec. Let the length of the platform be x meters. Then, (x + 300)/39 = 50/3 3x + 900 = 1950 => x = 350 m. Answer: B #### B QUESTION:A man's speed with the current is 12 km / hr and the speed of the current is 2 km / hr. The man's speed against the current i options: A)8 km / hr B)9 km / hr C)10 km / hr D)12.5 km / hr E)None SOLUTION:Sol. Man's rate in still in water = (12- 2) km / hr = 10km / hr. Man's rate against the current = (10 - 2) km / hr = 8 km / hr. Answer A #### A QUESTION:The Pinedale bus line travels at an average speed of 60 km/h, and has stops every 5 minutes along its route. Yahya wants to go from his house to the Pinedale Mall, which is 10 stops away. How far away, in kilometers, is Pinedale Mall away from Yahya's house? options: A)20 km B)30 km C)40 km D)50 km E)60 km SOLUTION:Number of stops in an hour: 60/5 = 12 Distance between stops: 60/12 = 5 km Distance between Yahya's house and Pinedale Mall: 5 x 10 = 50 km IMO, correct answer is "D." #### D QUESTION:A and B start from Opladen and Cologne respectively at the same time and travel towards each other at constant speeds along the same route. After meeting at a point between Opladen and Cologne, A and B proceed to their destinations of Cologne and Opladen respectively. A reaches Cologne 40 minutes after the two meet and B reaches Opladen 60 minutes after their meeting. How long did A take to cover the distance between Opladen and Cologne? options: A)1 hour B)1 hour 20 minutes C)2 hours 30 minutes D)1 hour 40 minutes E)2 hours 10 minutes SOLUTION:v1 and V2 are speeds. v1.t /60 = v2 v2.t/40 = v1 v1/v2 = 3/2 which train A would 60. 2/3 mins to cover the same distance 40 + 40 = 80 mins (ANS B) #### B QUESTION:A reduction of 20% in the price of salt enables a lady to obtain 10kgs more for Rs.300, find the original price per kg? options: A)s.7.7 B)s.7.4 C)s.7.5 D)s.7.1 E)s.7.9 SOLUTION:100*(20/100) = 20 --- 10 ? --- 1 => Rs.2 300 --- 80 ? --- 2 => Rs.7.5 Answer:C #### C QUESTION:The 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 ? options: A)240 B)270 C)295 D)360 E)300 SOLUTION:Explanation: Let the smaller number be x. Then larger number = (x + 1365). x + 1365 = 6x + 15 5x = 1350 x = 270 Smaller number = 270. ANSWER IS B #### B QUESTION:The edges of a cuboid are respectively 3cm, 4cm and 12 cm. Find the length of the diagonal of cuboid. options: A)9: 8 B)9: 5 C)9: 1 D)9: 2 E)9: 4 SOLUTION:a1 : a2 = 3 : 1 6 a12 : 6 a22 = 9: 1 Answer:C #### C QUESTION:If the Average (mean ) of 9 positive temperatures is x degrees fahrenheit, then the sum of the 3 greatest of these temperatures, in degrees Fahrenheit, could be options: A)8x B)4x C)5x/3 D)3x/2 E)3x/5 SOLUTION:Let the 5 numbers be 1,2,3,4,5,..9 (since no restrictions are given). There mean is 4 (x). Now the sum of greatest three would be 7+8+9=24 so the answer has to be 8x....that is option A #### A QUESTION:An aeroplane covers a certain distance at a speed of 100 kmph in 2 hours. To cover the same distance in 1 hours, it must travel at a speed of? options: A)100km/hr B)150km/hr C)200km/hr D)250km/hr E)300km/hr SOLUTION:Distance = 100*2 = 200 km Required speed = 200 *1 = 200km/hr Answer is C #### C QUESTION:A jeep 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? options: A)48 Kmph B)52 Kmph C)6o Kmph D)63 Kmph E)65 Kmph SOLUTION:Time = 6 Distance = 540 3/2 of 6 hours = 6 * 3/2 = 9 Hours Required speed = 540/9 = 60 Kmph C) #### C QUESTION:V and B are integers. The expression (V+1)(B+1) is even. What can be said about V and B? options: A)They are both even numbers. B)At least one of them is even. C)At least one of them is odd. D)They are both odd. E)Nothing can be said surly on V and B SOLUTION:Odd x Odd = Odd Odd x Even = Even Even x Even = Even To fulfill condition Either (V+1) or (B+1) needs to be Even So either V or B needs to be odd Or At least one of them is odd. At least one of them is odd=C #### C QUESTION:What is the median from the below series 92, 93, 88, 95, 88, 97, 87, and 98 options: A)80 B)82 C)92.25 D)98 E)100 SOLUTION:Ordering the data from least to greatest, we get: 87, 88, 88,92, 93, 95, 96, 98 The median quiz score was 92.25 (Four quiz scores were higher than 92.25 and four were lower.) C #### C QUESTION:Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 4 or 15 ? options: A)9/10 B)6/10 C)2/10 D)3/10 E)5/10 SOLUTION:Explanation: Here, S = {1, 2, 3, 4, ...., 19, 20}=> n(s) = 20 Let E = event of getting a multiple of 4 or 15 =multiples od 4 are {4, 8, 12, 16, 20} And multiples of 15 means multiples of 3 and 5 = {3, 6 , 9, 12, 15, 18, 5, 10, 15, 20}. = the common multiple is only (15). => E = n(E)= 6 Required Probability = P(E) = n(E)/n(S) = 6/20 = 3/10. Answer is D #### D QUESTION:Two taps can separately fill a cistern 5 minutes and 15 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? options: A)A)7 B)B)6 C)C)8 D)D)9 E)E)4.74 SOLUTION:1/5 + 1/15 - 1/x = 1/18 x = 4.74 Answer:E #### E QUESTION:In a college, 1 percent of students hate math, 2 percent of students hate English, 1 percent hate French and 4 percent hate German. Can you find out the percentage of students who hate all 4 subjects ? options: A)8% B)5% C)7% D)12% E)19% SOLUTION:A 8% of student hate all four subjects. #### A QUESTION:A 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? options: A)22 days B)4 days C)13 days D)6 days E)9 days SOLUTION:(A + B)'s 1 day's work = (1/4). A's 1 day's work = (1/12). B's 1 day's work =((1/4)-(1/12))=(1/6) Hence, B alone can complete the work in 6 days. Answer is D. #### D QUESTION:A 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? options: A)$503 B)$504 C)$505 D)$506 E)$507 SOLUTION:Explanation: Cash price = $21 000 Deposit = 10% × $21 000 = $2100 Loan amount = $21000 − $2100 = $18900 I=p*r*t/100 I=11340 Total amount = 18900 + 11340 = $30240 Regular payment = total amount /number of payments Answer: B #### B QUESTION:For 1rs 4p interest wat will be for 5000rs? options: A)350Rs B)450Rs C)200Rs D)30Rs E)448Rs SOLUTION:For 1rs , 4p interest for 5000rs, x x= 5000/1 * 4p ==> 20000 paise To express in rs, 20000/100 = 200rs ANSWER:C #### C QUESTION:William earned $3,200 per month as a teacher for the ten months from September to June. Then he took a job as a barista at a local café, where he earned $2,000 per month during July and August. What was his average monthly pay for the 12 months? options: A)$2,400 B)$2,800 C)$2,600 D)$3,000 E)$2,500 SOLUTION:E. William earned $3,200 × 10 = $32,000 as a teacher, and he earned $2,000 × 2 = $4,000 as a barista. So he earned $32,000 + $4,000 = $36,000 over the 12 months. Plug these values into the formula for the mean: mean=sum of values/number of values=>36.000/12=3.000 correct answer D)$3.000 #### D QUESTION:If 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 options: A) 478,823 B) 511,913 C) 531,875 D) 538,424 E) 569,114 SOLUTION:To know the unit digit you can multiply both digit number: 5 x 5 = 25 This eliminates A, B, D, and E, because the number must end with a 5 So the answer is C #### C QUESTION:In a group of ducks and cows, the total number of legs are 28 more than twice the number of heads. Find the total number of cows. options: A)12 B)14 C)16 D)18 E)20 SOLUTION:Let the number of ducks be d and number of cows be c Then, total number of legs = 2d + 4c = 2(d + 2c) total number of heads = c + d Given that total number of legs are 28 more than twice the number of heads => 2(d + 2c) = 28 + 2(c + d) => d + 2c = 14 + c + d => 2c = 14 + c => c = 14 i.e., total number of cows = 14 Answer is B. #### B QUESTION:A computer program generates a sequence of numbers a1, a2, a3, ... such that a1=1, a2=2, and ak=a(k-2)*4-1 for 2 < k < n for n=10. Find a6. options: A)19 B)27 C)31 D)36 E)41 SOLUTION:a1=1 a2=2 a3=1*4-1=3 a4=2*4-1=7 a5=3*4-1=11 a6=7*4-1=27 27 #### B QUESTION:There are 7 magazines lying on a table; 3 are fashion magazines and the other 4 are sports magazines. If 3 magazines are to be selected at random from the 8 magazines, what is the probability that at least one of the fashion magazines will be selected? options: A)1/2 B)7/8 C)32/35 D)11/12 E)13/14 SOLUTION:answer isB Total probability=7C3=48 4C3 +4C2*4C1+4C1*4C2=4+24+24=42 therefore the probability that at least one of the fashion magazines will be selected= 42/48=7/8 B #### B QUESTION:Find the remainder of the division (3^33)/7. options: A)2 B)3 C)4 D)5 E)6 SOLUTION:Find the pattern of the remainders after each power: (3^1)/7 remainder 3 (3^2)/7 remainder 2 (3^3)/7 remainder 6 (3^4)/7 remainder 4 (3^5)/7 remainder 5 (3^6)/7 remainder 1 -->this is where the cycle ends (3^7)/7 remainder 3 -->this is where the cycle begins again (3^8)/7 remainder 2 Continuing the pattern to (3^33)/7 gives us a remainder of 6 Final Answer: E) 6 #### E QUESTION:A total of 22 men and 30 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? options: A) 31 B) 31.5 C) 32.8 D) 32.5 E) 33 SOLUTION:Let Aw = average age of women Average = (Number of men X average age of men + Number of women X average age of women)/total number of people 35 * 52 = 22 * 38 + 30 * Aw =>1820 = 836 + 30 Aw => 30 Aw = 984 =>Aw = 32.8 Answer C #### C QUESTION:What percent of 180 is 45? options: A)0.25% B)4% C)25% D)40% E)250% SOLUTION:Here's an algebraic approach. Let p = the required percent. This means p/100 = the percent as a fraction. So, "What percent of 180 is 45?" becomes "(p/100) of 180 = 45 Or: (p/100)(180) = 45 Divide both sides by 180 to get: p/100 = 45/180 Simplify right side: p/100 = 1/4 Multiply both sides by 100 to get: p = 25 ANSWER:C #### C QUESTION:The smallest number which when divided by 20, 25, 35 and 40 leaves a remainder of 14, 19, 29 and 34 respectively is? options: A)1994 B)1494 C)1349 D)1496 E)1500 SOLUTION:LCM = 1400 1400 - 6 = 1394 ANSWER:C #### C QUESTION:In a certain apartment building, there are one-bedroom and two-bedroom apartments. The rental prices of the apartment depend on a number of factors, but on average, two-bedroom apartments have higher rental prices than do one-bedroom apartments. Let M be the average rental price for all apartments in the building. If M is $1,000 higher than the average rental price for all one-bedroom apartments, and if the average rental price for all two-bedroom apartments is $9,000 higher that M, then what percentage of apartments in the building are two-bedroom apartments? options: A)50% B)40% C)20% D)30% E)10% SOLUTION:Ratio of 2 Bedroom Apartment: 1 Bedroom Apartment = 1000 : 9000 -----> 1 : 9 Let total number of Apartments be X No. of 2 Bedroom Apartment = (1 / 10) * X percentage of apartments in the building are two-bedroom apartments ----> (1/10) * 100 ---> 10% Answer : E #### E <<<Examples ends QUESTION:All of the students of the Music High School are in the band, the orchestra, or both. 90 percent of the students are in only one group. There are 84 students in the band. If 60 percent of the students are in the band only, how many students are in the orchestra only? options: A)24 B)27 C)30 D)33 E)36 SOLUTION:60% of students are in the band only, so 30% of students are in the orchestra only. Since 10% of students are in both, then 70% of students are in the band which is 84 students. The number of students in the orchestra is (30/70)*84 = 36. The answer is E. #### E

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:A volunteer organization is recruiting new members. In the fall they manage to increase their number by 7%. By the spring however membership falls by 19%. What is the total change in percentage from fall to spring? options: A)16.16% B)15.55% C)14.44% D)13.33% E)12.22% SOLUTION:(100%+7%)*(100%-19%) = 1.07*.81 = 0.8667 1-0.8667 = 13.33% lost = -13.33% The Answer is D The organization has lost 13.33% of its total volunteers from fall to spring. #### D QUESTION:A bat is bought for Rs.400 and sold at a gain of 30% find its selling price? options: A)s.460/- B)s.480/- C)s.500/- D)s.520/- E)s.540/- SOLUTION:100 % ------> 400 (100 * 4 = 400) 130 % ------> 520 (130 * 4 = 520) Selling price = Rs.520/- Option 'D' #### D QUESTION:A company D has 15 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? options: A)200 B)125 C)180 D)152 E)250 SOLUTION:Let the total number of employees in the company be x % of secretaries = 15% % of salespeople = 45% % of of employees other than secretaries and salespeople = 100 - 60 = 40% But this number is given as 50 so 40% of x = 50 x = 125 Therefore there a total of 125 employees in the company D Correct answer - B #### B QUESTION:A construction company wants to number new houses using digit plates only. If the company puts an order for 912 plates, how many houses are to be given numbers? (The numbers of houses are consecutive and the number of the first house is 1). options: A)320 B)350 C)340 D)360 E)400 SOLUTION:You know that the answer is going to be three digits, and it's easy to figure out how many 1 and 2 digit numbers (9 and 90), so the real question is how many 3 digit number are there? 99+(912-9-90*2)/3=340 Answer : C #### C QUESTION:If December 3rd, 1999 is a Friday, what day is January 7th, 2000? options: A)Wednesday B)Thursday C)Friday D)Saturday E)Sunday SOLUTION:There is difference of 35 days from Dec. 3rd 1999 to Jan. 7th 2000. 35/7 has a remainder of 0. Jan. 7th is: Friday + 0 days = Friday The answer is C. #### C QUESTION:A bike covers a certain distance at the speed of 68km/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? options: A)85 km/h B)85.34 km/h C)87.67 km/h D)90.66 km/h E)90.64 km/h SOLUTION:Ans.(D) Sol. Total distance = 68 × 8 = 544 km Now speed = 544/6 = 90.66 km/h #### D QUESTION:A train 130 m long crosses a platform with a speed of 70 kmph in 20 sec; find the length of the platform? options: A)150 B)145 C)165 D)162 E)152 SOLUTION:D = 130 + x T = 20 S = 130+x/15 * 18/5 = 70 kmph. => (130+x) * 18 = 5250 => 130 + x = 292 => x= 162 m Answer: D #### D QUESTION:a milkman makes a profit of 20% on the sale of milk. If he were to add 10% water to the milk, by what % would his profit increase? options: A)50 % B)60 % C)70 % D)80 % E)40 % SOLUTION:let he sells 100 lit of milk @ 120 rs. means his cost price must b 100 to gain 20% profit. Nw he adds 10% milk ie total milk z 110 lit. Now he will get 132 rs. by selling 110 lit f milk (120*110/100) total profit = 32 rs increased profit =12 rs %age increase= 12/20= 60 % ANSWER:B #### B QUESTION:In 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? options: A)22 B)88 C)25 D)99 E)01 SOLUTION:A scores 60 while B score 40 and C scores 30. The number of points that C scores when B scores 100 = (100 * 30)/40 = 25 * 3 = 75. In a game of 100 points, B gives (100 - 75) = 25 points to C. Answer: C #### C QUESTION:When 3 fair coins are tossed simultaneously, in how many outcomes will the first and the last coin turn up heads? options: A)1 B)2 C)8 D)31 E)30 SOLUTION:Total outcome is 2^3 = 8 Favourable cases = H_ H The second place can be occupied by either H or T There are 2^1 =2 ways that can be done. Hence, the correct option is B #### B QUESTION:Today is Monday. After 61 days, it will be: options: A)SUNDAY B)SATURSDAY C)FRIDAY D)THURSDAY E)MONDAY SOLUTION:Each day of the week is repeated after 7 days. So, after 63 days, it will be Monday. After 61 days, it will be Saturday. Answer: Option B #### B QUESTION:What is the area of a square with perimeter 8P ? options: A) 16p^2 B) 4P^2 C) P^2/4 D) P/16 E) P^2/16 SOLUTION:Each side is 2p A = (2p)^2 = 4(p^2) Answer B #### B QUESTION:A number when divided by 779 gives a remainder 47. By dividing the same number by 19, what would be the remainder? options: A)9 B)8 C)7 D)6 E)5 SOLUTION:Number = ( 779 x a) + 47, where "a" is the quotient = (19 x 41 x a) + (19 x 2) + 9 = 19 x (41a + 2) + 9 = 19 x (New quotient) + 9 \inline \fn_jvn \therefore Required remainder = 9 Answer:A #### A QUESTION:3 candidates in an election and received 1136, 7636 and 11628 votes respectively. What % of the total votes did the winningcandidate got in that election? options: A)45% B)47% C)57% D)48% E)50% SOLUTION:Total number of votes polled = (1136 + 7636 + 11628) = 20400 So, Required percentage = 11628/20400 * 100 = 57% C #### C QUESTION:2, 4, 6, 8, 10, ? options: A)10 B)14 C)16 D)12 E)24 SOLUTION:The sequence is a series of even numbers, 2, 4, 6, 8, 10, 12.... Answer : D. #### D QUESTION:The HCF and LCM of two numbers m and n are respectively 6 and 210. If m + n = 72, then 1/m + 1/n is equal to options: A)1/35 B)3/35 C)5/37 D)2/35 E)None SOLUTION:Answer We have, m x n = 6 x 210 = 1260 ∴ 1/m + 1/n = (m + n)/mn = 72/1260 = 4/70 = 2/35 Correct Option: D #### D QUESTION:If 1 = 6 2 = 12 3 = 18 4 = 24 5 = 30 6 = 36 Then 24 = ? Hint: Its a logic Riddle not a mathematical riddle options: A)1 B)2 C)4 D)6 E)8 SOLUTION:C 24 As stated 4=24 => 24=4 Answer is C #### C QUESTION:A rectangle A has an area of 30 square centimeters. Square B has a perimeter of 16 centimeters. If square B is placed within square A and a random point is chosen within square A, what is the probability the point is not within square B? options: A)9/30 B)14/30 C)4/9 D)3/5 E)6/25 SOLUTION:I guess it's mean that square B is placed within rectangle A entirely. Since, the perimeter of B is 16, then its side is 16/4=4 and the area is 4^2=16; Empty space between the squares is 30-16=14 square centimeters, so if a random point is in this area then it won't be within square B: P=favorable/total=14/30. Answer: B. #### B QUESTION:A 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 Q apples did each person get before 45 people joined the feast? options: A)20. B)21. C)22. D)23. E)24. SOLUTION:Before solving it algebraically, let us prime factorize 1430 = 2*5*11*13. Since number of apples per person * total persons Q= 1430, the answer should be a factor of 1430. Only C is. And that's your answer.C #### C QUESTION:Compound interest earned on a sum for the second and the third years are Rs.1200 and Rs.1440 respectively. Find the rate of interest? options: A)65% p.a B)88% p.a C)20% p.a D)66% p.a E)44% p.a SOLUTION:Rs.1440 - 1200 = Rs.240 is the interest on Rs.1200 for one year. Rate of interest = (100 * 240) / (100 * 1) = 20% p.a Answer: C #### C QUESTION:The area of square ABCD above is 18. The shaded region is the intersection of the square and a circular region centered at C. What is the area of the shaded region? options: A)18−9/4∗π B)18−9/2∗π C)9+9/4∗π D)9+9/2∗π E)9/2−9/4∗π SOLUTION:=Square - Quarter circle =18- pi*18/4 =18- pi*9/2 ANSWER:B #### B QUESTION:The average age of a group of 12 students was 20. The average age increased by 2 years when two new students joined the group. What is the average age of the two new students who joined the group? options: A)22 years B)30 years C)34 years D)32 years E)None of these SOLUTION:Answer The average age of a group of 12 students is 20. Therefore, the sum of the ages of all 12 of them = 12 * 20 = 240 When two new students join the group, the average age increases by 2. New average = 22. Now, there are 14 students. Therefore, the sum of the ages of all 14 of them = 14 * 22 = 308 Therefore, the sum of the ages of the two new students who joined = 308 - 240 = 68 And the average age of each of the two new students = 68/2 = 34 years. Answer C #### C QUESTION:In 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? options: A)A)10 B)B)12 C)C)15 D)D)20 E)E)25 SOLUTION:the difference between the highest and lowest salaries is $100,000. So there are at least 2 people - say one with salary 0 and the other with 100k. No salary will be outside this range. Median = 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. Mean = 20k more than median so in our example, mean salary = 70k On the number line, 0........50k (median)........100k Mean = 70k So 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: 0....50k.....100k, 100k, 100k But 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: 0, ... 50k, 50k, 50k, 50k, ... 100k, 100k, 100k, 100k, 100k the median is not at 50k yet. Add another 3 people at 50k and another 2 at 100k to get 0, 50k, 50k, 50k, 50k, 50k, 50k, 50k, 100k, 100k, 100k, 100k, 100k, 100k, 100k Now the median is 50k and mean is 70k. Total number of people is 15. Answer (C) #### C QUESTION:The function g(p) is defined for integers p such that if p is even, g(p) = p/2 and if p is odd, g(p) = p + 5. Given that g(g(g(g(g(p))))) = 19, how many possible values for p would satisfy this equation? options: A)1 B)5 C)7 D)8 E)11 SOLUTION:Let me define terms: in g(p) = R p is argument, R is result, g() is function, in g(g(g(g(g(p))))), g1 is inner most, g5 is outermost for identification. From definition of function g, we can deduce that: If Result is even then two possibilities for argument = 1 Even 1 Odd If Result is odd then one possibility for argument = 1 Even Since final result = 19 = Odd Possibilities: g1:1 Even g2: 1*(Even,Odd ) =1 Even 1 Odd g3: 1*(Even,Odd) + 1 Even =2 Even 1 Odd g4: 2*(Even, Odd) + 1 Even =3 Even 2 Odd g5: 3*(Even, Odd) + 2 Even =5 Even 3 Odd = Total 8 Ans D it is! #### D QUESTION:If x ≠ 0 and (y^2 − xy)/x=y-x, which of the following expressions is equal to its opposite? options: A)x^2 B)x^2 – y^2 C)y^2 D)(y + x)^2 E)(x – y)^2 SOLUTION:(y^2 − xy)/x=y-x => y^2 − xy = xy -x^2 => x^2 - 2xy + y^2 = 0 => (x-y)^2 = 0 Answer E #### E QUESTION:Two 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 7 days? options: A)2/5 B)7/18 C)1/4 D)1/9 E)2/6 SOLUTION:A's one day's work = 1/30 B's one day's work = 1/45 (A + B)'s one day's work = 1/30 + 1/45 = 1/18 The part of the work completed in 7 days = 7 (1/18) = 7/18. ANSWER B #### B QUESTION:Two 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? options: A)95 minutes B)90 minutes C)88 minutes D)95 minutes E)None of these SOLUTION:Explanation : Let us consider that speed of train , first man and second man are respectively t, f and s. According to first given condition goods train crossed the first person moving in same direction in 20 sec. So length of the will be 20(t-f) Similarly train crossed the second man in 18 sec. So length of the train will be 18(t+s) on comparing these two equations, we get 20(t-f) = 18(t+s) => 2t = 20f + 18s => t = 10f + 9s Now it is given that After 10 min the train crossed the other person who is coming in opposite direction. So,If we consider this way of train as L then the next equation will be L = 600t (here 600 is used for 10 minutes) Finally as asked in the question the time required to meet the two man after the train has passed will be given by Time = (L-600 f)/(f+s) {here 600f is used for the distance traveled by first man in 10 minutes} => = (600t-600f) / (f+s) => = [600(10f+9s)-600f] / (f+s) => = 600(10f+9s-f) / (f+s) = 600 * 9(f+s) / (f+s) => =600*9 seconds => = 600*9/60min => = 90 minutes Hence (B) is the correct answer. Answer : B #### B QUESTION:A vendor bought toffees at 6 for a dollar. How many for a dollar must he sell to gain 20%? options: A)7 B)6 C)5 D)9 E)8 SOLUTION:C 5 C.P. of 6 toffees = $ 1 S.P. of 6 toffees = 120% of $ 1 = $ 6/5 For $ 6/5, toffees sold = 6. For $ 1. Toffees sold = 6 * 5/6 = 5 #### C QUESTION:An plane covers a certain distance at a speed of 240 kmph in 5 hours. To cover the same distance in 5/3 hours, it must travel at a speed of ? options: A)100 B)720 C)1100 D)940 E)860 SOLUTION:We know Distance = speed * time = 240 * 5 = 1200 km Now to cover 1200 km in 5/3 hrs , speed = distance / time = 1200 / (5/3) = 720 KMPH Ans- B #### B QUESTION:Find large number from below question The difference of two numbers is 1395. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder options: A)1245 B)1345 C)1455 D)1577 E)1671 SOLUTION:Let the smaller number be x. Then larger number = (x + 1395). x + 1395 = 6x + 15 5x = 1380 x = 276 Large number = 276+1395 = 1671 E #### E QUESTION:A train passes a station platform in 35 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? options: A)120 m B)225 m C)300 m D)360 m E)280 m SOLUTION:Speed = 54 x 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 metres. Then, (x + 300)/35 = 15 x + 300 = 525 x = 225 m.Answer: Option B #### B QUESTION:In each term of a sequence, 3 is added to get the next term. If the first term is 6, what is the 64th term? options: A) 192 B) 154 C) 134 D) 174 E) 120 SOLUTION:1rst term + 63 terms = 6 + 3+3+3+3+3+3+3+...+3 (63 times) 6 + (3 x 63) = 3 + 189 = 192 Answer A #### A QUESTION:A train 900 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? options: A)288 m B)256 m C)400 m D)278 m E)287 m SOLUTION:Speed = 78 * 5/18 = 65/3 m/sec. Time = 1 min = 60 sec. Let the length of the train be x meters. Then, (900 + x)/60 = 65/3 x = 400 m. Answer:C #### C QUESTION:If it is assumed that 50 percent of those who receive a questionnaire by mail will respond and 300 responses are needed, what is the minimum number of questionnaires that should be mailed? options: A)400 B)420 C)480 D)500 E)600 SOLUTION:Minimum no of mail to be sent for getting 300 responses at 50% = 300/0.5 = 600 Option E #### E QUESTION:Tanya prepared 4 different letters to 4 different addresses. For each letter, she prepared one envelope with its correct address. If the 3 letters are to be put into the four envelopes at random, what is the probability that only one letter will be put into the envelope with its correct address? options: A)1/24 B)1/8 C)1/4 D)1/3 E)3/8 SOLUTION:I hope you are familiar with basic probability fundas - Let's say you have just ONE letter and TWO envelopes ONE of which is correctly addressed and the other addressed incorrectly. What's the probability of putting the Letter in the correctly addressed envelope - To answer this question - we see IN HOW MANY WAYS can the letter be put into the envelope - you could put it (assuming you don't know which envelope is which) in either of the two - so in total you have TWO ways of shoving the letter in. However, there's only ONE way in which it can go into the correctly addressed envelope - so 1/2 is the prob of putting in correct envelope. This is easy. Now in our current problem - let's say we have just ONE letter but FOUR envelopes. Only one of these envelopes has the address corresponding to the letter. The remaining three envelopes are incorrectly addressed. So the probability that you will put the letter correctly is 1/4. Right? What happens if i ask you the reverse question? what is the prob for putting it in the incorrect envelope. Suddenly you have three envs that are incorrect so you can put the letter incorrectly with a prob of 3/4. Right? The whole problem can be broken down into Four Events that will fulfill the requirement of the question Event 1 - E1 We know that prob of putting ONE Letter correctly is 1/4. Now once ONE letter has been put CORRECTLY, what are you LEFT with? You are left with THREE ENVELOPES and the remaining THREE letters. Since the one letter has been put correctly (though technically we have just calculated the PROBABILITY that the first letter goes into the correct envelope) we have the remaining THREE Letters and THREE envelopes. Event 2 - E2 Let's take letter number 2 now - what is the probability that it LANDS in the INCORRECT envelope. Again by the same logic as above - there are 3 envelopes remaining out of which ONLY ONE has the correct address for LETTER number 2. The remaining 2 have INCORRECT address and LETTER NUMBER 2 could go in either of these 2 to meet our condition. Thus the probability of this event is 2/3 So till now what we have done is - we have calculated the prob of shoving Letter number 1 in correct env -- 1/4 we have calculated the prob of shoving Letter number 2 in INcorrect env --- 2/3 Event 3 - E3 Now let's take letter number 3 - again according to question we want to shove this in the WRONG envelope. There are 2 remaining envelopes and hence the prob of shoving this in the wrong env (or equally in the RIght env) is 1/2. Finally we come to event E4 - the Letter number 4. This has only one way of going in so its probability of being put into the WRONG envelope is 1. ok so we can see that our grand event is actually a combination of FOUR EVENTS happening - each with a probability of its own. So to calculate the total probability of the Grand Event itself we just multiply the individual probabilities since each event happens INDEPENDENTLY of each other Egrand = 1/4 * 2/3 * 1/2 * 1/1 = 1/12 However at this point - I must introduce one last element in this question -since there are FOUR Letters - what we saw above was JUST ONE SEQUENCE of events leading to the desired result. If we arbitrarily call the letters L1 thru L4, and let's say the above was an example in which we started by Picking up Letter L1 and worked thru the remaining letters, we could have equally well started out with letter L2 or L3 or L4. Thus since each of these events ARE MUTUALLY EXCLUSIVE, meaning THEY CAN NEVER HAPPEN ALL THE SAME TIME BUT ONLY ONE LETTER AT A TIME, to calculate the TOTAL PROBABILITY of we will add the individual probabilities 1/12 + 1/12 + 1/12 + 1/12 which works out to 1/8. B #### B QUESTION:The compound ratio of 2/3, 6/7, 1/3 and 1/8 is given by? options: A)1/48 B)1/42 C)1/40 D)1/41 E)1/43 SOLUTION:2/3 * 6/7 * 1/3 * 1/8 = 1/42 Answer: B #### B QUESTION:If a committee of 2 people is to be selected from among 4 married couples so that the committee does not include two people who are married to each other, how many such committees are possible? options: A)24 B)40 C)50 D)80 E)120 SOLUTION:Each couple can send only onerepresentativeto the committee. Let's see in how many ways we can choose 2 couples (as there should be 2 members) each to send onerepresentativeto the committee: 4C2=6. But these 2 chosen couples can send two persons (either husband or wife): 2*2=2^2=4. Total # of ways: 4C2*2^2=24. Answer: A #### A QUESTION:In how many ways can 6 boys and 3 girls be arranged at a table if 3 girls are never together? options: A)47520 B)45620 C)47888 D)42156 E)43210 SOLUTION:Total ways of arranging 10 person in a circle = 9! = 51840 ways If we consider three women as one, then we have 6+1=7 persons. Arranging these seven persons in circle will take = 6! = 720 ways And three women can arrange themselves in 3! ways Total ways in which three women sit together in circle = 6!*3! = 4320 ways Total ways in which three women doesn’t sit together in circle = 9! - 6!*3! = 51840 - 4320 = 47520 ways A #### A QUESTION:For any non-zero a and b that satisfy |ab| = -ab and |a| = -a, |b-4| + |ab-b| = options: A)ab-4 B)2b-ab-4 C)ab+4 D)ab-2b+4 E)4-ab SOLUTION:Given: |ab| = -ab and |a| = -a Question: |b-4| + |ab-b| = ? **** Looking at |ab| = -ab tells us that either one of a or b is negative. **** Looking at |a| = -a tells us that a must be negative **** Combine two observations: b is positive Let a=-1 and b=1 |b-4| + |ab-b| = |1-4| + |-1-1| = 5 Test a) |ab-4| = |(1)(-1)-4| = |-5|=5 Test b) 2b-ab-4 = (2)(1) - (-1) - 4 = -1 Test c) ab+4 = -1 + 4 = 3 Test d) ab-2b+4 = -1-2(1)+4=1 test e) 4-1=3 ANSWER=A #### A QUESTION:If f(f(n)) + f(n) = 2n+3, f(0) = 1 then f(2012) = ? options: A)2013 B)2088 C)270 D)1881 E)1781 SOLUTION:f (f(0)) + f(0) = 2(0) + 3 ⇒⇒ f(1) = 3-1 = 2, f(1) = 2 f(f(1)) + f(1) = 2(1) + 3 ⇒⇒ f(2) = 5-2 = 3, f(2) = 3 f(f(2)) + f(2) = 2(2) + 3 ⇒⇒ f(3) = 7-3 = 4, f(3) = 4 .............. f(2012) = 2013 Ans: A #### A QUESTION:A group of 55 adults and 70 children go for trekking. If there is meal for either 70 adults or 90 children and if 35 adults have their meal, find the total number of children that can be catered with the remaining food. options: A)33 B)54 C)18 D)45 E)01 SOLUTION:Explanation: As there is meal for 70 adults and 35 have their meal, the meal left can be catered to 35 adults. Now, 70 adults = 90 children 7 adults = 9 children Therefore, 35 adults = 45 children Hence, the meal can be catered to 45 children. ANSWER: D #### D QUESTION:By the how much is two-fifth of 300 greater than three -fifths of 125? options: A)15 B)3 C)5 D)45 E)None of these SOLUTION:Reqd no. = 2⁄5 × 300 - 3⁄5 × 125 = 120 - 75 = 45 Answer D #### D QUESTION:The size of the wooden block is 5 x 10 x 20 cm .How many such blocks will be required to construct a solid wooden cube of minimum size? options: A)6 B)8 C)12 D)16 E)18 SOLUTION:Explanation: Side of smallest cube = L.C.M of 5,10,20 = 20cm Volume of the cube = (20 x 20 x 20)cm3 = 8000 cm3 Volume of the block= (5 x 10 x 20) cm3 = 1000 cm3 Number of blocks = (8000/1000) = 8 Answer: B #### B QUESTION:Find the distance covered by a man walking for 42 min at a speed of 10km/hr? options: A)7km B)3km C)4km D)5km E)6km SOLUTION:Distance = 10*42/60 = 7 km Answer is A #### A QUESTION:What is the unit digit of (6!*3! / 3!*4!)? options: A)5 B)6 C)0 D)3 E)4 SOLUTION:(6!*3! /3!*4!) =(6! / 4!) =5*6 =30 Units digit of the above product will be equal to 0 Answer C #### C QUESTION:In a class of 50 students, 20 play SNOOKER, 15 play Cricket and 11 play Football. 7 play both SNOOKER and Cricket, 4 play Cricket and Football and 5 play SNOOKER and football. If 18 students do not play any of these given sports, how many students play exactly two of these sports? options: A)10 B)12 C)34 D)45 E)566 SOLUTION:Notice that7 play both SNOOKER and Cricket does not mean that out of those 7, some does not play Football too. The same for Cricket/Football and SNOOKER/Football. [color=#ffff00]{Total}={SNOOKER}+{Cricket}+{Football}-{HC+CH+HF}+{All three}+{Neither}For more check ADVANCED OVERLAPPING SETS PROBLEMS [/color] 50=20+15+11-(7+4+5)+{All three}+18 --> {All three}=2; Those who play ONLY SNOOKER and Cricket are 7-2=5; Those who play ONLY Cricket and Football are 4-2=2; Those who play ONLY SNOOKER and Football are 5-2=3; Hence, 5+2+3=10 students play exactly two of these sports. Answer: A. #### A QUESTION:How many numbers from 10 to 10000 are exactly divisible by 9? options: A)900 B)1000 C)1110 D)1200 E)1400 SOLUTION:10/9 = 1 and 10000/9 = 1111 ==> 1111 - 1 = 1110. Therefore 1110 Answer : C #### C QUESTION:Three numbers are in the ratio 1 : 2 : 3 and their H.C.F is 12. The numbers are options: A)4, 8, 12 B)5, 10,15 C)10, 20, 30 D)12, 24, 36 E)None SOLUTION:Solution Let the required numbers be x, 2x and 3x. Then, their H.C.F = x. So x = 12. The numbers are 12, 24, 36. Answer D #### D QUESTION:A 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? options: A)12.2 B)12.9 C)12.6 D)12.5 E)12.3 SOLUTION:Let the speed of the man in still water be a kmph and let the speed of the stream be b kmph. Now 30/(a + b) + 20/(a - b) = 4 and 45/(a + b) + 40/(a - b) = 7 Solving the equation, the speed of man in still water is 12.5 kmph. Answer: D #### D QUESTION:A certain kind of necklace is made from 9 gold, 6 blue, and 3 white beads. What is the maximum number of these necklaces that can be made from 36 beads of each color ? options: A)8 B)4 C)6 D)5 E)4 SOLUTION:Atleast 9 gold breads are needed to make a necklace, so irrespective of the combinations of blue and white beads, the number of necklaces that can be formed will be 36/9 =4 Answer:- E #### E QUESTION:Which of the following must be true? 1) Every prime number greater than 5 can be written as either as 8n+1 or 8n-1 2) Every prime number greater than 5 can be written as 4n+1 or 4n-1 3) Every number greater than 5 of the form 8n+1 or 8n-1 is a prime number. options: A)1,2,3 B)2,3 C)1,2 D)only 1 E)only 2 SOLUTION:Every prime number greater than 3 can be written in the form of 8n+1 or 8n-1 where n is an integer. So 1 can be possible. 3. This is not possible as 2 and 3 are being prime , we can't write then in the form of 8n+1 or 8n-1. C #### C QUESTION:If 4-X < (2+5X)/3, which of the following is correct? options: A)X < -5. B)X > -5. C)X > 5/4. D)-5 < X < 0. E)0 < X < 5. SOLUTION:4-X < (2+5X)/3 12-3X < 2+ 5X 10 < 8X 10/8<X 5/4<X C is the answer #### C QUESTION:The total marks obtained by a student in Mathematics and Physics is 50 and his score in Chemistry is 20 marks more than that in Physics. Find the average marks scored in Mathamatics and Chemistry together. options: A)15 B)25 C)35 D)45 E)55 SOLUTION:Let the marks obtained by the student in Mathematics, Physics and Chemistry be M, P and C respectively. Given , M + C = 50 and C - P = 20 M + C / 2 = [(M + P) + (C - P)] / 2 = (50 + 20) / 2 = 35. ANSWER:C #### C QUESTION:The income tax in country X is 8% of any income up to $5000. For incomes over $5,000, an 8% tax is imposed on the first $5,000, and a 10% tax is imposed on the portion of the total income in excess of $5000. If Perry paid $950 in income tax last month, then what was Perry's income? options: A)$10,500 B)$11,000 C)$13,000 D)$13,500 E)$14,000 SOLUTION:Given : For incomes over $5,000, an 8% tax is imposed on the first $5,000, and a 10% tax is imposed on the portion of the total income in excess of $5000. If Perry paid $950 in income tax last month, then what was Perry's income? for first 5000 , 8% tax then we get 400$ as tax. Now Perry paid 950$ tax... we need to check which option is going to yield 550$ on the remaining amount. A. $10,500 - 5000 = 5500 , then we get 10% tax , we get 550$... ( $10,500 - 5000 - here already for 5000$ we have calculated the tax and we need to tally for the remaining amount) 550+400 = 950$...hence this is the option. ANSWER :option A. #### A QUESTION:An art gallery owner is hanging paintings for a new show. Of the five paintings she has to choose from, she can only hang three on the main wall of the gallery. Assuming that she hangs as many as possible on that wall, in how many ways can she arrange the paintings? options: A)18 B)30 C)60 D)120 E)216 SOLUTION:Arrangment means permutations questions.. 5P3 = 5!/3! = 60. IMO option C is correct answer.. #### C QUESTION:Sachin 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? options: A)6 km B)8 km C)9 km D)11 km E)12 km SOLUTION:Let total distance =D=D Distance travelled at 4 kmph speed =(23)D=(23)D Distance travelled at 5 kmph speed =(1−23)D=(13)D=(1−23)D=(13)D Total time =1 hr 24 min = (60+24) min =8460=8460 hr =2115=2115 hr We know, Time=DistanceSpeedTime=DistanceSpeed Total time 2115=2/34D+1/35D2115=2/34D+1/35D 2115=2D12+D152115=2D12+D15 84=14D84=14D D=6 km Option A is correct #### A QUESTION:How many different positive integers exist between 10^3 and 10^4, the sum of whose digits is equal to 2? options: A)6 B)7 C)5 D)4 E)18 SOLUTION:So, the numbers should be from 1,000 to 10,000 The following two cases are possible for the sum of the digits to be 2: 1. Two 1's and the rest are 0's: 1,001 1,010 1,100 3 numbers. 2. One 2 and the rest are 0's: 2,000 1 number. Total = 4 numbers. Answer:D #### D QUESTION:Q. How many 9-digit even numbers less than 3,000,000 can be formed using the following digits: 1, 2, 2, 3, 5, 5, 6, 6, 7? options: A)180 B)140 C)210 D)270 E)300 SOLUTION:the number is less than 3000000 so we will have the digit on the left most side to be either 1 or 2 i.e your number can be 1 _ _ _ _ _ _ or 2 _ _ _ _ _ _ case 1 > 1 _ _ _ _ _ _ here the units digit can be either 2 or 6 when the units digit is 2 i.e 1 _ _ _ _ _ 2 number of ways this can be done would be 5! / 2! (as 5 is repeated twice) = 60 when the units digit is 6 i.e. 1 _ _ _ _ _ 6, number of ways would be 5!/(2! * 2!) {both 2 and 5 repeat twice} = 30 case 2 > 2 _ _ _ _ _ _ (here units digit may be 2 or 6) number of ways this can be done would be 5! / (2!) for 2 =60 and 5! / 2! for 6 ... = 60 adding all of these ... gives the answer 140 ... the explanation looks difficult but this technique helps if you are familiar with the concept of permutations when the numbers/alphabets repeat B #### B QUESTION:Working alone, A can complete a certain kind of job in 6 hours. A and D, working together at their respective rates, can complete one of these jobs in 4 hours. In how many hours can D, working alone, complete one of these jobs? options: A) 8 B) 10 C) 12 D) 14 E) 16 SOLUTION:Let total time taken by D to complete the job = D total time taken by A to complete the job = 6 Work done by A in an hour 1/A = 1/6 Working together A and D can complete the job in 4 hours 1/A + 1/D = 1/4 =>1/D = 1/4 - 1/A = 1/4 - 1/6 = 1/12 => D = 12 hours Answer C #### C QUESTION:210 school 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? options: A)25 B)40 C)50 D)60 E)75 SOLUTION:We 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. So, 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. #### B QUESTION:When an amount was distributed among 14 boys, each of them got $80 more than the amount received by each boy when the same amount is distributed equally among 18 boys. What was the amount? options: A)5050 B)5020 C)5040 D)5030 E)5075 SOLUTION:Let the total amount be Rs. X the, x/14 - x/18 = 80 ==> 2x/126 = 80 ==> x/63 = 63 x 80 = 5040. Hence the total amount is 5040. Answer C. #### C QUESTION:Jeni 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? options: A)423 B)325 C)142 D)171 E)127 SOLUTION:7C1 + 7C2+ 7C3+7C4+7C5+7C6+7C7 =127 . Answer: E #### E QUESTION:If 1st October is Sunday, then 1st November will be options: A)Saturday B)Thursday C)Wednesday D)Tuesday E)Monday SOLUTION:Explanation: Given that 1st October is Sunday Number of days in October = 31 31 days = 3 odd days (As we can reduce multiples of 7 from odd days which will not change anything) Hence 1st November = (Sunday + 3 odd days) = Wednesday Answer: Option C #### C QUESTION:The length, breadth and height of a room are in the ratio 12 : 4 : 4. If the breadth and height are halved while the length is doubled, then the total area of the four walls of the room will options: A)(a) remain the same B)(b) decrease by 13.64% C)(c) decrease by 15% D)(d) decrease by 18.75% E)(e) decrease by 30% SOLUTION:Length (L) = 12 Breadth (B) = 4 Height (H) = 4 Total Area of Walls = 2(BH + LH) = 2*(4*4 + 12*4) = 2*(16+48) = 128 Then, Finally Length (L) = 2*12 = 24 Breadth (B) = 4/2 = 2 Height (H) = 4/2 = 2 Total Area of Walls = 2(BH + LH) = 2*(2*2 + 24*2) = 2*(4+48) = 104 % change in Area of four walls = (Final Area-Initial Area)*100 /Initial Area i.e. % change in Area of four walls = (104-128)*100 /128=- 18.75% (Decrease) Answer: Option D #### D <<<Examples ends QUESTION:Mr. 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: options: A)broke even, B)lost 4 cents C)gained 4 cents D)lost 10 cents E)gained 10 cents SOLUTION:Solution: 20 % profit on $ 1.20 = $ 20/100 × 1.20 = $ 0.20 × 1.20 = $ 0.24 Similarly, 20 % loss on $ 1.20 = $ 20/100 × 1.20 = $ 0.20 × 1.20 = $ 0.24 Therefore, in one pipe his profit is $ 0.24 and in the other pipe his loss is $ 0.24. Since both profit and loss amount is same so, it’s broke even. Answer: A #### A

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:A 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? options: A)15/56 B)41/56 C)13/28 D)15/28 E)5/14 SOLUTION:The 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. Ways to select 6 out of total 8 = 8C6 Ways to select 4 out of 5 white balls = 5C4 Ways to select 2 out of 3 blue balls = 3C2 Thus the required probability = (5C4*3C2)/8C6 = 15/28. D is thus the correct answer. #### D QUESTION:If the average (arithmetic mean) of five consecutive negative integers is 2k – 1, what is the difference D between the greatest and least of the five integers? options: A)4K B)4k^2 -4k C)4-4k D)4 E)4k+4 SOLUTION:(n-2 + n - 1 + n + n + 1 + n + 2)/5 = 2k - 1 => n = 10k - 5 Greatest = n + 2 = 10k - 5 + 2 = 10k - 3 Least = n - 2 = 10k - 5 - 2 => Difference D= 10k - 3 - (10k - 7) = 4 Answer - D #### D QUESTION:If p and q are prime numbers, how many divisors does the product p^3 * q^6 have? options: A)9 B)12 C)18 D)28 E)36 SOLUTION:Lets take an example: find the number of factors of 100 try to represent 100 in least possible prime numbers 100= 2^2 * 5^2=p^a*q^b no of factors is given by the formula (a+1)* (b+1)=(2+1)(2+1)=9 similarly find the number of factors of p^3 * q^6--->a=3,b=6 (3+1)(6+1)=28 Ans D. #### D QUESTION:In how many ways can 6 boys and 3 girls be arranged at a table if 3 girls are never together? options: A)47520 B)45620 C)47888 D)42156 E)43210 SOLUTION:Total ways of arranging 10 person in a circle = 9! = 51840 ways If we consider three women as one, then we have 6+1=7 persons. Arranging these seven persons in circle will take = 6! = 720 ways And three women can arrange themselves in 3! ways Total ways in which three women sit together in circle = 6!*3! = 4320 ways Total ways in which three women doesn’t sit together in circle = 9! - 6!*3! = 51840 - 4320 = 47520 ways A #### A QUESTION:An 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.2400, what will be the difference between Q and R's share? options: A)8877 B)3000 C)7787 D)1799 E)1711 SOLUTION:4 --- 2000 5 --- ? => 3000 Answer: B #### B QUESTION:In 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? options: A)48400 B)48000 C)48100 D)48500 E)48600 SOLUTION:Assume that investment of C =x Then, investment of A =2x Investment of B =4x/3 A:B:C =2x:(4x)/3:x =2:4/3:1=6:4:3 B's share =157300×4/(6+4+3) =157300×4/13=12100×4=48400 Answer is A. #### A QUESTION:Two numbers A and B are such that the sum of 5% of A and 3% of B is two-third of the sum of 6% of A and 8% of B. Find the ratio of A : B. options: A)2 : 1 B)1 : 2 C)7 : 3 D)1 : 1 E)3 : 2 SOLUTION:Explanation: 5% of A + 3% of B = 2/3(6% of A + 8% of B) 5A/100 + 3B/100 = 2/3(6A/100+8B/100) ⇒5A + 3B = 2/3(6A + 8B) ⇒15A + 9B = 12A + 16B ⇒ 3A = 7B ⇒ AB = 7/3 ⇒ A:B=7:3 Answer: Option C #### C QUESTION:In how many different ways can change be provided for a one dollar bill using pennies (1 cent), nickels (5 cents), dimes (10 cents), and quarters (25 cents), if at least two of each type of coin must be included? options: A)0 B)6 C)8 D)10 E)15 SOLUTION:I. Case I = Four Quarters = this is impossible, because if we already have a dollar in quarters, then we cannot have any other coins. We cannot have all four coins represented if we have four quarters. Case I does not allow any ways. II. Case II = Three Quarters (75 cents) This does not allow for two each of the other coins. Case II does not allow any ways. III. Case III = Two Quarters (50 cents) This allows for 2-3 dimes. Subcase 1 = 2 Q, 3 D (80 cents) (2 ways) we could have 2-3 nickels Subcase 2 = 2 Q, 2 D (70 cents) (4 ways) we could have 2-5 nickels Case III allows for a total of 6 ways There's no other case, because we have to have at least two quarters and two dimes. The total over the cases equals Total = 0 + 0+ 6 =6 ways. OA =(B) #### B QUESTION:A dealer purchased an article at 3/4 of its list price and sold 50% more than the list price. Find his gain percent? options: A)120% B)190% C)100 percent D)200% E)101% SOLUTION:MP = 100 CP = 75 SP = 150 ------ 75 ---- 75 100 ---- ? => 100% Answer:C #### C QUESTION:A 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? options: A)8239 B)2900 C)2000 D)2393 E)2009 SOLUTION:Let the shares of A, B, C and D be 5x, 2x, 4x and 3x Rs. respectively. Then, 4x - 3x = 1000 => x = 1000. B's share = Rs. 2x = 2 * 1000 = Rs. 2000. Answer: C #### C QUESTION:If x is a positive integer, then the least value of x for which x! is divisible by 10 is? Can someone please explain intuitively what the question is asking? options: A)5 B)9 C)12 D)15 E)30 SOLUTION:In order x! to be divisible by 1,0, it should have at least 1 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 1. 5! = 120 has 1 trailing zeros. Answer: A #### A QUESTION:A batsman scored 120 runs whichincluded 3 boundaries and 8sixes. What % of his total score did he make by running between the wickets options: A)40 % B)50 % C)60 % D)70 % E)80 % SOLUTION:Number of runs made by running = 110 - (3 x 4 + 8 x 6) = 120 - (60) = 60 Now, we need to calculate 60 is what percent of 120. => 60/120 * 100 = 50 % B #### B QUESTION:A car covers a distance of 829 km in 7 hours. Find its speed? options: A)104 kmph B)289 kmph C)118 kmph D)277 kmph E)177 kmph SOLUTION:829/7 = 118 kmph Answer: C #### C QUESTION:A labourer was engaged for 25 days on the condition that for every day, he works, he will be paid Rs. 2 and for every day, he is absent he will be fined 50p. If he receives only Rs. 37•50, find the no. of days he was absent is_____ options: A)3 days B)4 days C)5 days D)6 days E)7 days SOLUTION:if a labour worked for 25 days he should get 50 Rs. but in this he is getting 13 Rs less. if he don't go for work for 1 day he will loose 2.5 Rs then no of days(Absent)=13/2.5=5.2. Means he was absent for 5 days ANSWER:C #### C QUESTION:By selling a watch for Rs.560/-, a man loses 20% what is that watch cost price options: A)s. 700/- B)s. 800/- C)s. 880/- D)s. 900/- E)s. 990/- SOLUTION:80 % ------> 560 (80 * 7 = 560) 100 % ------>700 (100 * 7 = 700) Cost price = Rs. 700/- A #### A QUESTION:When 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? options: A)3 B)8 C)12 D)32 E)35 SOLUTION:n = 5p + 1 = 6,11,16,21,26,31 n = 7q + 3 = 3,10,17,24,31 =>n = 39m + 31 To get this, we need to take LCM of co-efficients of p and q and first common number in series. So we need to add 8 more to make it 39m + 39 Answer - B #### B QUESTION:What is the decimal equivalent of (1/2)^2? options: A)0.0016 B)0.0625 C)0.16 D)0.25 E)0.5 SOLUTION:(1/2)² = (1/2)(1/2)= 1/4 APPROACH #1: use long division to divide 4 into 1 to get 1/4 = 0.25 D #### D QUESTION:Which of the following points is symmetric with y=x at (2,3)? options: A)(-2,-1) B)(-2,1) C)(2,1) D)(3,2) E)(-1,2) SOLUTION:We 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. (2,3) would become (3,2). Answer (D). #### D QUESTION:There are 2 red chips and 2 blue ones. When arranged in a row, they form a certain color pattern, for example RBRRB. How many color patterns? options: A)A)10 B)B)12 C)C)24 D)D)60 E)E)100 SOLUTION:Using anagram method: 4_3_2_1 R_R_B_B so.. 4!/Number of repeated letters (2!)(2!) = 6 ANS:D #### D QUESTION:If x > 3 and y < -3, then which of the following must be true ? options: A)x/y > 1 B)x/y < -1 C)x/y < 0 D)x + y > 0 E)xy > 0 SOLUTION:Pick x=3, y = -3 A) x/y > 1 - Incorrect as x/y = -1 B) x/y < -1 - Incorrect as x/y = -1 C) x/y < 0 -Correct. It will hold for all values x > 2 and y < -2 as x/y = -1 < 0 D) x + y > 0 - Incorrect. x + y = 0 E) xy > 0 - Incorrect. XY = -9 which is less than zero. D should be the answer. #### D QUESTION:A batsman scored 210 runs which included 3 boundaries and 8 sixes. What % of his total score did he make by running between the wickets options: A)40% B)50% C)65% D)71.4% E)75% SOLUTION:Number of runs made by running = 210 - (3 x 4 + 8 x 6) = 210 - (60) = 150 Now, we need to calculate 60 is what percent of 120. => 150/210 * 100 = 71.4 % D #### D QUESTION:A dishonest milkman wants to make a profit on the selling of milk. He would like to mix water (costing nothing) with milk costing Rs.46 per litre so as to make a profit of 20% on cost when he sells the resulting milk and water mixture for Rs.54 In what ratio should he mix the water and milk? options: A)1:20 B)1:10 C)1:8 D)1:45 E)6:11 SOLUTION:water = w (liter) Milk = m (liter) ==> Cost = Price x Quantity = 0.46m ==> Revenue = Price x Quantity = 0.54(m + w) ==> Profit =0.54(m+w) - 0.46m = 0.2*(0.46m)[20% of cost] ==> 0.54m + 0.54w - 0.46m = 0.092m ==> 0.012m = 0.54w ==> m/w = 0.54/0.012 = 45 --OR-- w/m = 1/45 D is correct. #### D QUESTION:Shekar scored 76, 65, 82, 47 and 85 marks in Mathematics, Science, Social studies, English and Biology respectively. What are his average marks? options: A)71 B)69 C)75 D)85 E)90 SOLUTION:Explanation : Average= (76+65+82+47+85)/5 = 355/5 =71 Hence average=71 Answer : A #### A QUESTION:A man can swim in still water at 7.5 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is? options: A)1.7 B)1.4 C)1.1 D)1.5 E)2.5 SOLUTION:M = 7.5 S = x DS = 7.5 + x US = 7.5 + x 7.5 + x = (7.5 - x)2 7.5 + x = 15 -2x 3x = 7.5 x = 2.5 Answer:E #### E QUESTION:Out of 8 consonants and 4 vowels, how many words of 3 consonants and 1 vowels can be formed? options: A)21005 B)10500 C)25200 D)5376 E)None of these SOLUTION:Solution Number of ways of selecting (3 consonants out of 8) and (1 vowels out of 4) 8c3 x 4c1= (8x7x6/3x2x1)x(4/1) =224 Number of group,each having 3 consonants and 1 vowels = 224 . Each group contains 4 letter. Number of ways of arranging 5 letters among themselves = 4 ! = (4 × 3 × 2 × 1) = 24 . So, Required number of words = (24 × 224) = 5376 .Answer D #### D QUESTION:{-10, -6, -5, -4, -2.5, -1, 0, 2.5, 4, 6, 7, 10} A number is to be selected at random from the set above. What is the probability that the number will be a solution to the equation (x-4)(x+9)(2X+5) = 0? options: A)1/12 B)1/6 C)1/4 D)1/3 E)1/2 SOLUTION:x = -2.5 Prob =1/12 Answer - A #### A QUESTION:If in a book a total of 3209 digits are used for numbering, then find out the total number of pages in the book. options: A)23777 B)69667 C)26976 D)2697 E)1079 SOLUTION:Explanation: Number of digits used in 1 digit numbers = 1*9 = 9 Number of digits used in 2 digit numbers = 2*90 = 180 Number of digits used in 3 digit numbers = 3*900 = 2700 Number of digits used in 1 digit numbers = 3209 – (9+180+2700) = 320 Hence, number of pages with 4 digit number = 320/4 = 80 Total number of pages = 1079 ANSWER: E #### E QUESTION:A seller mixed 4 dozen bananas costing Rs.12 per dozen with 6 dozen bananas at Rs.8 per dozen then what is the cost price of mixed bananas per dozen? options: A)Rs.6.40 B)Rs.10 C)Rs.9.6 D)Rs.10.2 E)None of the above SOLUTION:4 dozens of bananas cost is rs12 then 4*12=48 6 dozens of bananas cost is rs8 then 6*8=48 48+48/4+6=96/10=9.6 ANSWER:C #### C QUESTION:A watch was sold at a loss of 10%. If it was sold for Rs.500 more, there would have been a gain of 10%. What is the cost price? options: A)1000 B)2998 C)2500 D)2788 E)2991 SOLUTION:90% 110% -------- 20% ---- 500 100% ---- ? => Rs.2500 Answer:C #### C QUESTION:If a man buys 10 lollipops for $90 and sold them for $6 dollars determine his loss. options: A)50 B)60 C)70 D)20 E)90 SOLUTION:Cost of 10 lollipops = $80 Sold each lollipop for $6 So he sold 10 lollipops for $(10 × 6) = $60 Loss = $(80 – 60) = $20 answer :D Therefore, loss = $ 20. #### D QUESTION:If q is a positive integer and q^2 is divisible by 12, then the largest positive integer that must divide q ^3 is options: A) 2^3 B) 2^6 C) 3^3 D) 6^3 E) 12^2 SOLUTION:Since 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)) q^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 So, q will have a 2 and a 3. Or q will be a multiple of 6 So, largest possible integer than should divide q^3 is 6^3 So, Answer will be D #### D QUESTION:What percent is 2 gm of 1 kg? options: A)0.5 % B)0.2% C)1.5% D)2% E)3% SOLUTION:1 kg = 1000 gm 2/1000 × 100 = 200/1000 =1/5 = 0.2 % B) #### B QUESTION:Cole 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? options: A)66 B)70 C)72 D)75 E)78 SOLUTION:Let the distance one way be x Time from home to work = x/60 Time from work to home = x/100 Total time = 2 hrs (x/60) + (x/100)= 2 Solving for x, we get x = 75 Time from home to work in minutes= (75)*60/60 = 75 minutes Ans= D #### D QUESTION:An empty fuel tank is filled with brand Z gasoline. When the tank is half empty, it is filled with brand Y gasoline. When the tank is half empty again, it is filled with brand Z gasoline. When the tank is half empty again, it is filled with brand Y gasoline. At this time, what percent Q of the gasoline in the tank is brand Z? options: A)50% B)40% C)37.5% D)331⁄3% E)25% SOLUTION:Work with fraction of brand Z in the tank. 1st step: brand Z is 1 2nd step: brand Z is 1/2 3rd step: brand Z is (1/2)*(1/2) + 1/2 = 3/4 4th step: brand Z is (1/2)*(3/4) Q= 3/8 = 37.5% Answer (C) #### C QUESTION:What is the units digit of (52^5)(37^3)(71^9)? options: A)3 B)4 C)6 D)7 E)8 SOLUTION:The units digit of 52^5 is the units digit of 2^5 which is 2. The units digit of 37^3 is the units digit of 7^3 which is 3. The units digit of 71^9 is the units digit of 1^9 which is 1. The units digit of 2*3*1 is 6. The answer is C. #### C QUESTION:Among all sales staff at Listco Corporation, college graduates and those without college degrees are equally represented . Each sales staff member is either a level-1 or level-2 employee. Level-1 college graduates account for 15% of Listco's sales staff. Listco employs 60 level-1 employees, 30 of whom are college graduates. How many sales staff members without college degrees are level-2 employees ? options: A)46 B)42 C)56 D)70 E)58 SOLUTION:I'm going in on this one. So let's say that we have the following So we know that L1 = 60 and that C and L1 = 0.15X , we should set up a double set matrix btw but anyways, I'm just explaining the point with this problem. Now we are told that 0.15x = 30, therefore the grand total is 200. Now we know that L2 is 200 - 60 = 140. We also learn that C and No C are equally represented thus 100 each. Therefore No C and No L2 will be 100 - 30 = 70. Thus D is the correct answer choice #### D QUESTION:The tailor has a 10 meter long piece of fabric for which to sew a ball room dress. She has to cuts this fabric into strips of 200 centimeters each. How long will it take the tailor to complete this tasks if each 200 centimeter took 5 minutes to cut ? options: A)150 B)200 C)188 D)245 E)123 SOLUTION:The tailors would need to cut the fabric 49 times thus the total amount spent would be 245 minutes. The answer is D #### D QUESTION:The number of arrangements that can be made with the letters of the word MEADOWS so that the vowels occupy the even places? options: A)14 B)144 C)777 D)992 E)221 SOLUTION:The word MEADOWS has 7 letters of which 3 are vowels. -V-V-V- As 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. Hence the total ways are 24 * 6 = 144. Answer:B #### B QUESTION:If n is a natural number, then(6n^2+6n) is always divisible by? options: A)6 only B)6 and 12 C)12 only D)by 18 only E)None of these SOLUTION:(6n^2+6n)=6n(n+1), which is always divisible by 6 and 12 both, since n(n+1) is always even. Correct Option: B #### B QUESTION:The forth proportional to 2,4,6 is? options: A)8 B)12 C)15 D)18 E)22 SOLUTION:Let the fourth proportional to 2,4,6 be x then 2:4::6:x 2x = 4*6 x = 12 Answer is B #### B QUESTION:Solve for x if (log2)(1-x/2)=x-2. options: A)1 B)2 C)3 D)4 E)5 SOLUTION:(log2)(1-x/2)=x-2 or,log2-(x/2)log2=x-2 or,2log2-xlog2=2x-4 or,log4+4=2x+xlog2 or,4.60=2.3x i.e.x=2. ANSWER:B #### B QUESTION:A 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? options: A)4:7 B)4:0 C)4:3 D)4:1 E)4:2 SOLUTION:12:9 = 4:3 Answer: C #### C QUESTION:A 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? options: A)49/153 B)18/153 C)49/153 D)40/153 E)24/72 SOLUTION:Explanation: Total marbles in a box = 6 black + 8 red +4 green marbles = 18 marbles 2 marbles are drawn from 18 marbles at random. Therefore, n(S) = 18C2 = 153 ways Let A be the event that 2 marbles drawn at random are of the same color. Number of cases favorable to the event A is n(A) = 6C2 + 8C2 + 4C2 = 15+28+6= 49 Therefore, by definition of probability of event A, P(A) = n(A)/n(S) = 49/153 ANSWER:A #### A QUESTION:If inflation increases at a rate of 8 p.c.p.a. what will a 20 article cost at the end of two years? options: A)Between 20 and 21 B)Between 21 and 22 C)Between 22 and 23 D)Between 23 and 24 E)None of these SOLUTION:Required sum = 20(1+8/100)2=20×27×27/25×25=23.3 Answer D #### D QUESTION:Find the remainder of the division (3^33)/7. options: A)2 B)3 C)4 D)5 E)6 SOLUTION:Find the pattern of the remainders after each power: (3^1)/7 remainder 3 (3^2)/7 remainder 2 (3^3)/7 remainder 6 (3^4)/7 remainder 4 (3^5)/7 remainder 5 (3^6)/7 remainder 1 -->this is where the cycle ends (3^7)/7 remainder 3 -->this is where the cycle begins again (3^8)/7 remainder 2 Continuing the pattern to (3^33)/7 gives us a remainder of 6 Final Answer: E) 6 #### E QUESTION:Find the sum of all odd number upto 250. options: A)15345 B)15645 C)15625 D)15342 E)15683 SOLUTION:Explanation: Number of odd numbers upto 250 = n/2 = 250/2 = 125 Sum of first 125 odd numbers = (125)2 = 15625 Answer: Option C #### C QUESTION:A merchant purchased a jacket for $180 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’s gross profit on this sale? options: A)$0 B)$3 C)$4 D)$12 E)$15 SOLUTION:Let selling price = x So, x = 180 + 25x/100 Calculating above, x = 240 Selling price =240 20% Discount on Selling price = 192 So, profit = 192-180 = 12 Answer = D #### D QUESTION:In how many Q 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? options: A)720 B)864 C)900 D)936 E)1,296 SOLUTION:Total number of four letter passwords = 6*6*6*6= 1296 ------(1) Total number of passwords in which no letter repeats = 6C4*4!= 15*24=360------(2) therefore required value Q= (1)-(2)= 1296-360=936.D #### D QUESTION:A manufacturer of a certain product can expect that between 0.4 percent and 0.5 percent of the units manufactured will be defective. If the retail price is $2,500 per unit and the manufacturer offers a full refund for defective units, how much money can the manufacturer expect to need to cover the refunds on 20,000 units? options: A) Between $15,000 and $25,000 B) Between $30,000 and $50,000 C) Between $200,000 and $250,000 D) Between $150,000 and $250,000 E) Between $300,000 and $500,000 SOLUTION:Number of defective units is between = .4 % of 20000 and .5% of 20000 = 80 and 100 Retail Price per unit = 2500 $ Expected price of refund is between = 2500 x 80 and 2500 x 100 =2,00,000 and 2,50,000 dollars Answer C #### C QUESTION:What is the dividend. divisor 17, the quotient is 9 and the remainder is 5. options: A)140 B)142 C)146 D)158 E)160 SOLUTION:D = d * Q + R D = 17 * 9 + 5 D = 153 + 5 D = 158 #### D QUESTION:A number x is 4 times another number y. The percentage that y is less than x is options: A)12.5% B)75% C)80% D)11% E)1% SOLUTION:Say y=1 and x=4. Then y=1 is less than x=4 by (4-1)/4*100=3/4*100=75%. Answer: B. #### B QUESTION:In a 100 m race, A beats B by 10 m and C by 13 m. In a race of 180 m, B will beat C by: options: A)3 B)7 C)8 D)6 E)0 SOLUTION:A : B = 100 : 90. A : C = 100 : 87. \inline \fn_jvn {\color{Black}\therefore \frac{B}{C}=\left ( \frac{B}{A} \times \frac{A}{C}\right )=\left ( \frac{90}{100}\times \frac{100}{87} \right )=\frac{30}{29}} When B runs 30 m, C runs 29 m. When B runs 180 m, C runs \inline \fn_jvn {\color{Black}\left ( \frac{29}{30} \times 180\right )m}=174m \inline \fn_jvn {\color{Blue}\therefore } B beats C by (180 - 174) m = 6 m. Answer: D) 6m #### D QUESTION:The length of the longest tape in cm which can be used to measure exactly, the length 100cm; 2m25cm; and 7m80cm is: options: A)30 B)5 C)10 D)36 E)25 SOLUTION:The three lengths in cm are 100, 225 &780. HCF of 100, 225 &780 is 5. Hence, the answer is 5 cm. ANSWER:B #### B QUESTION:What was the day of the week on, 18th July, 1776? options: A)Thursday B)Wednesday C)Monday D)Saturday E)SUNDAY SOLUTION:16th July, 1776 = (1775 years + Period from 1st Jan, 1776 to 16th July, 1776) Counting of odd days : 1600 years have 0 odd day. 100 years have 5 odd days. 75 years = (18 leap years + 57 ordinary years) = [(18 x 2) + (57 x 1)] = 93 (13 weeks + 2 days) = 2 odd days. 1775 years have (0 + 5 + 2) odd days = 7 odd days = 0 odd day. Jan Feb Mar Apr May Jun Jul 31 + 29 + 31 + 30 + 31 + 30 + 16 = 198 days= (28 weeks + 4 days) Total number of odd days = (0 + 4) = 4. Required day was 'Thursday'. Answer:A #### A QUESTION:A 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.15,000 earned at the end of 2years from the startingof the business? options: A)s. 5,000 B)s. 4,500 C)s. 5,700 D)s. 6,500 E)s. 7,500 SOLUTION:A : B : C = (20,000 x 24) : (15,000 x 24) : (20,000 x 18) = 4 : 3 : 3. B's share = Rs. 15000 x 3/10 = Rs. 4,500. B #### B QUESTION:The H.C.F. of two numbers is 59 and the other two factors of their L.C.M. are 13 and 16. The larger of the two numbers is: options: A)678 B)944 C)456 D)323 E)899 SOLUTION:: Explanation: Clearly, the numbers are (59 x 13) and (59 x 16). {\color{Blue} \therefore } Larger number = (59 x 16) = 944. Answer: B)944 #### B QUESTION:If 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 72? options: A)24 B)36 C)12 D)18 E)16 SOLUTION:The greatest common divisor of n and 16 is 4 --> n is a multiple of 4 but not a multiple of 8. The greatest common divisor of n and 15 is 3 --> n is a multiple of 3 but not a multiple of 5. 72=2*3*3*2*2 is divisible by 12. therefore the greatest common divisor is 12 C #### C QUESTION:A candidate got 30% of the votes polled and he lost to his rival by 4000 votes. How many votes were cast? options: A)7500 B)2028 C)2775 D)10000 E)6851 SOLUTION:30%-----------L 70%-----------W ------------------ 40%----------4000 100%---------? => 10000 Answer:D #### D QUESTION:Two brothers Ram and Ravi appeared for an exam. The probability of selection of Ram is 5/7 and that of Ravi is 1/5. Find the probability that both of them are selected. options: A)2/35 B)2/3 C)7/35 D)1/7 E)7/5 SOLUTION:Let A be the event that Ram is selected and B is the event that Ravi is selected. P(A) = 5/7 P(B) = 1/5 Let C be the event that both are selected. P(C) = P(A) x P(B) as A and B are independent events: = 5/7 x 1/5 = 1/7 ANSWER:D #### D QUESTION:12. What is the dividend. divisor 17, the quotient is 9 and the remainder is 5. options: A)150 B)152 C)154 D)158 E)144 SOLUTION:D = d * Q + R D = 17 * 9 + 5 D = 153 + 5 D = 158 #### D QUESTION:A train running at a speed of 36 kmph crosses an electric pole in 12 seconds. In how much time will it cross a 350 m long platform? options: A)87 min B)82 min C)86 min D)47 min E)72 min SOLUTION:Let the length of the train be x m. When a train crosses an electric pole, the distance covered is its own length. So, x = 12 * 36 * 5 /18 m = 120 m. Time taken to cross the platform = (120 +350)/ 36 * 5/18 = 47 min. Answer:D #### D QUESTION:Two 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? options: A)Rs.12:29 B)Rs.18:90 C)Rs.16.28 D)Rs.16.50 E)Rs.82.09 SOLUTION:Let the quantities of A and B mixed be 3x kg and 7x kg. Cost of 3x kg of A = 9(3x) = Rs. 27x Cost of 7x kg of B = 15(7x) = Rs. 105x Cost of 10x kg of the mixture = 27x + 105x = Rs. 132x Cost of 5 kg of the mixture = 132x/10x (5) = Rs. 66 Profit made in selling 5 kg of the mixture = 25/100 (cost of 5 kg of the mixture) = 25/100 * 66 = Rs. 16.50 Answer:D #### D QUESTION:A bag contains 7 green and 8 white balls. If two balls are drawn simultaneously, the probability that both are of the same colour is ? options: A)7/17 B)7/22 C)7/18 D)7/19 E)7/15 SOLUTION:Drawing two balls of same color from seven green balls can be done in ⁷C₂ ways. Similarly from eight white balls two can be drawn in ⁸C₂ ways. P = 7C2/¹15C2 + 8C2/15C2 = 7/15 Answer: E #### E QUESTION:A vessel contains 20 liters of a mixture of milk and water in the ratio 3:2. 10 liters of the mixture are removed and replaced with an equal quantity of pure milk. If the process is repeated once more, find the ratio of milk and water in the final mixture obtained? options: A)9:1 B)4:7 C)7:1 D)2:5 E)5:6 SOLUTION:Explanation: Milk = 3/5 * 20 = 12 liters, water = 8 liters If 10 liters of mixture are removed, amount of milk removed = 6 liters and amount of water removed = 4 liters. Remaining milk = 12 - 6 = 6 liters Remaining water = 8 - 4 = 4 liters 10 liters of pure milk are added, therefore total milk = (6 + 10) = 16 liters. The ratio of milk and water in the new mixture = 16:4 = 4:1 If the process is repeated one more time and 10 liters of the mixture are removed, then amount of milk removed = 4/5 * 10 = 8 liters. Amount of water removed = 2 liters. Remaining milk = (16 - 8) = 8 liters. Remaining water = (4 -2) = 2 liters. The required ratio of milk and water in the final mixture obtained = (8 + 10):2 = 18:2 = 9:1. ANSWER IS A #### A <<<Examples ends QUESTION:5216 x 51 = ? options: A)266016 B)212016 C)266436 D)216314 E)None of these SOLUTION:Explanation : Normal way of multiplication may take time. Here are one alternative. 5216 x 51 = (5216 x 50) + 5216 = (5216 x 100/2) + 5216 = 521600/2 + 5216 = 260800 + 5216 = 266016. Answer : Option A #### A

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:A no.when divided by 220 gives a remainder 43, what remainder will beobtained by dividingthe same no.17? options: A)2 B)8 C)9 D)11 E)15 SOLUTION:220 + 43 = 263/17 = 8 (Remainder) B #### B QUESTION:A student scored an average of 65 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? options: A)86 B)165 C)76 D)125 E)26 SOLUTION:Given M + P + C = 65 * 3 = 195 --- (1) M + P = 90 * 2 = 180 --- (2) P + C = 70 * 2 = 140 --- (3) Where M, P and C are marks obtained by the student in Mathematics, Physics and Chemistry. P = (2) + (3) - (1) = 180 + 140 - 195 = 125 Answer:D #### D QUESTION:A man took loan from a bank at the rate of 12% p.a. S.I. After 3 years he had to pay Rs. 5400 interest only for the period. The principal amount borrowed by him was? options: A)15002 B)15001 C)15000 D)15007 E)15009 SOLUTION:Principal = (100 * 5400) / (12 * 3) = Rs. 15000.Answer:C #### C QUESTION:If five men together completes a job in 5 days then for the same job how many mens are required to complete it in a day. options: A)20 B)10 C)25 D)15 E)24 SOLUTION:work completed in a day by one men = 1/25 = (1/5)*(1/5) So it takes 25 men to complete this job = 25 * (1/25) = 1 Answer: C #### C QUESTION:Rahul went to a shop and bought things worth Rs. 28, 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? options: A)Rs 15 B)Rs 12.10 C)Rs 22.70 D)Rs 26.80 E)None of these SOLUTION:Explanation : Let the cost of the tax items = x Given that tax rate = 6% Cost of tax items, x*(6/100) = 30/100 x = 5 rs Now non taxable item = total cost - cost for taxable item - tax = 28 - 5 - 0.30 =22.70 Answer : C #### C QUESTION:M = {-6, -5, -4, -3, -2} T = {-3, -2, -1, 0, 1, 2, 3, 4} If 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? options: A)0 B)1/3 C)2/5 D)1/2 E)3/5 SOLUTION:We will have a negative product only if 1, 2, 3, or 4 are selected from set T. P(negative product) = 4/8 = 1/2 The answer is D. #### D QUESTION:Arjun started a business with Rs. 40,000 and is joined afterwards by Anoop with Rs.80, 000. After how many months did Anoop join if the profits at the end of the year are divided equally? options: A)3 B)4 C)5 D)6 E)7 SOLUTION:Suppose Anoop joined after 3 months. Then, 40000 * 12 = 80000 * (12 – x) => x = 6. ANSWER:D #### D QUESTION:What is the area of a square field whose diagonal of length 20 m? options: A)228 B)271 C)200 D)277 E)181 SOLUTION:d2/2 = (20 * 20)/2 = 200 Answer:C #### C QUESTION:Find the value of y from (12)^3 x 6^4 ÷ 432 = y? options: A)3452 B)2343 C)2435 D)2578 E)5184 SOLUTION:Given Exp. = (12)3 x 64 = (12)3 x 64 = (12)2 x 62 = (72)2 = 5184 432 12 x 62 E #### E QUESTION:Two brothers Ram and Ravi appeared for an exam. The probability of selection of Ram is 5/7 and that of Ravi is 1/5. Find the probability that both of them are selected. options: A)2/35 B)2/3 C)7/35 D)1/7 E)7/5 SOLUTION:Let A be the event that Ram is selected and B is the event that Ravi is selected. P(A) = 5/7 P(B) = 1/5 Let C be the event that both are selected. P(C) = P(A) x P(B) as A and B are independent events: = 5/7 x 1/5 = 1/7 ANSWER:D #### D QUESTION:A shop owner sells 40 Pencils and gains SP of 15 pencils. Find the gain %? options: A)55% B)40% C)50% D)60% E)78% SOLUTION:Gain=15 oranges Total 40 oranges CP 40-15=25 (15/25)*100 =60% Ans D #### D QUESTION:A tap can fill a tank in 2 hours. After half the tank is filled, two more similar taps are opened. What is the total time taken to fill the tank completely? options: A)1 hr 40 min B)4 hr C)3 hr D)1 hr 20 min E)2 hr 50 min SOLUTION:Explanation: 1 tap can fill the tank in 2 hours. Therefore 1 tap can fill half tank in 1 hours. 3 taps can fill the tank in 2/3 hour. Therefore 3 taps can fill half tank in 2/6 hour =20 minutes. Total time taken=1 hour 20 minutes Answer: Option D #### D QUESTION:A goods train runs at the speed of 72 km/hr and crosses a 150 m long platform in 26 sec. What is the length of the goods train? options: A)299 B)277 C)276 D)370 E)281 SOLUTION:Speed = 72 * 5/18 = 20 m/sec. Time = 26 sec. Let the length of the train be x meters. Then, (x + 150)/26 = 20 x = 370 m. Answer: D #### D QUESTION:In a bag there are a certain number of black 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 black balls to blue balls in the bag options: A)1:2 B)1:4 C)1:1 D)1:5 E)1:6 SOLUTION:since the probability of drawing a blue ball out of two picks is 1/2. the ratio of the blue ball to black balls should be 1:1 Answer : C #### C QUESTION:Set A: {1, 3, 4, 6, 9, 12, 16} If 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? options: A)3/14 B)2/7 C)9/14 D)5/7 E)1/35 SOLUTION:using probability you can solve: 3/7*2/6*1/5=1/35. Ans E #### E QUESTION:Find the value of x from the below equation? : 3x^2+5x+2 = 0 options: A)-1 B)1 C)2 D)3 E)4 SOLUTION:a = 3, b = 5, c = 2 x1,2 = (-5 ± √(52 - 4×3×2)) / (2×3) = (-5 ± √(25-24)) / 6 = (-5 ± 1) / 6 x1 = (-5 + 1)/6 = -4/6 = -2/3 x2 = (-5 - 1)/6 = -6/6 = -1 A #### A QUESTION:Annie has 100 cards numbered 1 through 100. If she deals four cards to Alex, without replacing any of them, what is the probability that Alex will get five consecutive numbers? options: A)95!/100! B)96!/100! C)(95! X 5!)/100! D)(96! X 5!)/100! E)(97! X 4!)/100! SOLUTION:Alex to get 4 consecutive cards in ascending order, to have 4 consecutive at the end is good enough. There are 97 consecutive numbers in 100: {1, 2, 3, 4, }, {2, 3, 4, 5}, ..., { 97, 98, 99, 100};{4!*97!}{100!}. Answer: E. #### E QUESTION:In a certain lottery drawing, two balls are selected at random from a container with 10 balls, numbered from 1 to 10, 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? options: A)$9 x 10^4 B)$9.90 x 10^6 C)$1.00 x 10^7 D)$1.05 x 10^7 E)$9.90 x 10^7 SOLUTION:The max product of any two balls can be 9 * 10 = 9900 = 9 * 10 If we multiply it by $1000 the max amount will be 9 * 10^4. A #### A QUESTION:If 0 < n < 1, what is the median of the values n, n^-1, n^2, n^1/2 and n^3? options: A)n B)n^-1 C)n^2 D)n^1/2 E)n^3 SOLUTION:A. To make the problem less confusing, I picked a number between 0 and 1 such as n = 1/4 and calculate: n = 1/4 n^-1 = 4 n^2 = 1/16 n^(1/2) = 1/2 n^3 = 1/8. From this, rearrange the number and the median is 1/4, which is n. Answer A #### A QUESTION:From 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? options: A)1/10 B)4/9 C)1/2 D)9/15 E)2/3 SOLUTION:The total number of ways to choose 2 children from 6 is 6C2 = 15 The number of ways to choose 1 boy and 1 girl is 3*3 = 9 P(1 boy and 1 girl) = 9/15 The answer is D. #### D QUESTION:A pipe can fill a cistern in 20 minutes whereas the cistern when fill can be emptied by a leak in 40 minutes. When both pipes are opened, find when the cistern will be full? options: A)17 minutes B)87 minutes C)40 minutes D)27 minutes E)11 minutes SOLUTION:1/20 - 1/40 = 1/40 40 minutes Answer:C #### C QUESTION:If a sum of money borrowed at 5 percent/annum SI amounts to Rs.1020 in 4 yrs, then the sum of money borrowed is? options: A)Rs. 850 B)Rs. 900 C)Rs. 980 D)Rs. 990 E)Rs. 1000 SOLUTION:Sol We have, A : Rs.1U2D Let the pr xnpal be R5 x Then mterest u — 12 : wzo — x Therefore, by u xglurmula. _umxx ’ Rx’: ( , _ma>< 1nzn—xv \4Ve|\a\e,Jc— 5“ :> ~(:51DD—S*(or6x:51UU or, J: : w 350 . The sum of money burrowed : Rs. 850 A) #### A QUESTION:The average of 6 no.'s is 3.95. The average of 2of them is 3.4, while the average of theother 2 is 3.85. What is the average of the remaining 2 no's? options: A)3.5 B)3.9 C)4.2 D)4.3 E)4.6 SOLUTION:Sum of the remaining two numbers = (3.95 * 6) - [(3.4 * 2) + (3.85 * 2)] = 23.70 - (6.8 + 7.7) = 23.70 - 14.5 = 9.20. Required average = (9.2 / 2) = 4.6. E #### E QUESTION:The sum of three consecutive odd numbers is 20 more than the first of these numbers. What is the middle number? options: A)3 B)6 C)9 D)12 E)15 SOLUTION:Sol. Let the numbers be x, x + 2 and x + 4. Then, x + (x + 2) + (x + 4) = x + 20 ⇔ 2x = 14 ⇔ x = 7. ∴ Middle number = x + 2 = 9. Answer C #### C QUESTION:A certain list consists of 21 different numbers. If n is in the list and n is 2 times the average (arithmetic mean) of the other 20 numbers in the list, then n is what fraction of the sum of the 21 numbers in the list? options: A)1/20 B)1/12 C)1/5 D)4/21 E)5/21 SOLUTION:series : a1, a2....a20,n sum of a1+a2+...+a20 = 20*x (x = average) so, n = 2*x Hence, a1+a2+..+a20+n = 22x So, the fraction asked = 2x/22x = 1/12 B #### B QUESTION:Anna left for city A from city B at 5.20 a.m. She traveled at the speed of 80 km/hr for 2 hrs 15 min. After that the speed was reduced to 60 km/hr. If the distance between two cities is 350 kms, at what time did Anna reach city A? options: A)10.21 B)10.27 C)10.25 D)10.23 E)60.25 SOLUTION:Distance covered in 2 hrs 15 min i.e., 2 1/4 hrs = 80 * 9/4 = 180 hrs. Time taken to cover remaining distance = (350 - 180)/60 = 17/6 hrs = 2 5/6 = 2 hrs 50 min Total time taken = (2 hrs 15 min + 2 hrs 50 min) = 5 hrs 5 min. So, Anna reached city A at 10.25 a.m. Answer: E #### E QUESTION:The current birth rate per thousand is 32, where as corresponding death rate is 10 per thousand. The net growth rate in terms of population increase in percent is given by? options: A)2.0% B)3.2% C)3.9% D)4% E)5.1% SOLUTION:Net growth on 1000 = 32-10 = 20 Net growth on 100 = 20*100/1000 = 2.0% Answer is A #### A QUESTION:The 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 : options: A)22 B)21 C)88 D)37 E)29 SOLUTION:Explanation: Lot the total number of workers be v Then, 8OOOv = (12000 * 7) + 6000 (v - 7) <=> 2000v = 42000 <=> v = 21 Answer: B) 21 #### B QUESTION:There are 200 cats in Cat-City. Out of the 200, 70 are street cats and the rest are domestic cats. 110 cats are gray, 25 out of the gray cats are NOT domestic ones. How many domestic cats are there which are not gray in Cat-City? options: A)90. B)45. C)50. D)40. E)25. SOLUTION:STREET-CAT DOMESTIC-Cat 70 130 (25gray+45other) 85gray+45other Answer:B #### B QUESTION:Walking with 4/5 of my usual speed, I miss the bus by 5 minutes. What is my usual time? options: A)35 min B)30 min C)25 min D)20 min E)40 min SOLUTION:Explanation: Speed Ratio = 1:4/5 = 5:4Time Ratio = 4:51 -------- 5 4 --------- ? è 20 ANSWER IS D #### D QUESTION:X is an even number and Y is a positive odd number. Which of the following expressions cannot be even? options: A)(XY)^Y B)X^3Y^3 C)X^3 D)XY E)Y^2 SOLUTION:If x is even, let x = 0 and see what happens. A. [(0)(Y)]^Y = 0 (EVEN - ELIMINATE) B. 0³Y³ = 0 (EVEN - ELIMINATE) C. 0³ = 0 (EVEN - ELIMINATE) D. (0)Y = 0 (EVEN - ELIMINATE) E. Y² Answer:E #### E QUESTION:If n is a positive integer, then n(n+1)(n+2) is even without any condition options: A)divisible by 3 only when n is odd B)divisible by 4 whenever n is even C)odd whenever n is odd D)even only when n is odd E)even only when n is even SOLUTION:n*(n+1)*(n+2)= +ve even integer divisible by 4 ( e.g 6,7&8) B #### B QUESTION:A customer pays 50 dollars for a coffee maker after a discount of 20 dollars What is the original price of the coffe maker? options: A)70 B)80 C)90 D)50 E)60 SOLUTION:Solution Let x be the original price. x - 20 = 50 x - 20 + 20 = 50 + 20 x + 0 = 70 x = 70 Answer A #### A QUESTION:The 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? options: A)15% B)32% C)44% D)62% E)80% SOLUTION:Assume 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 . So overall increase is from 100 to 144 is 44% Answer C #### C QUESTION:If a person walks at 16 km/hr instead of 12 km/hr, he would have walked 20 km more. The actual distance traveled by him is? options: A)50 B)65 C)70 D)61 E)60 SOLUTION:Let the actual distance traveled be x km. Then, x/12 = (x + 20)/16 x - 60 =>x = 60km. Answer: E #### E QUESTION:A man can do a piece of work in 5days, but with the help of his son, he can finish it in 3days. In what time can the son do it alone? options: A)5 B)5 1/2 C)7 1/2 D)6 E)9 1/2 SOLUTION:Son's 1day work = 1/3 - 1/5 = 2/15 Son alone can do the work in 15/2days = 7 1/2 days Answer is C #### C QUESTION:In a mixed college 160 students are there in one class. Out of this 160 students 1/4 students are girls. How many boys are there ? options: A)A)40 B)B)60 C)C)80 D)D)120 E)E)140 SOLUTION:Total Number of Students :160 Total Girls : 160*1/4 =40 Total Boys : 160-40 = 120 Answer is D #### D QUESTION:A sells a bicycle to B and makes a profit of 20%. B sells the same bicycle to C at a profit of 25%. If the final S.P. of the bicycle was Rs. 225, find out the cost price of the bicycle for A. options: A)237 B)126 C)971 D)611 E)150 SOLUTION:Explanation: ANSWER: E #### E QUESTION:What will be in unit's place digit of 3 to the power 34. options: A)1 B)6 C)3 D)0 E)9 SOLUTION:as 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.. ANSWER:E #### E QUESTION:A person was fined for exceeding the speed limit by 10 km/hr.Another person was also fined for exceeding the same speed limit by twice the same.If the second person was traveling at a speed of 35 km/hr,find the speed limit. options: A)487 B)15 C)76 D)29 E)12 SOLUTION:If x is speed limit, Speed of first person = x + 10 Speed of 2nd person = x + 20 But speed of 2nd person = 35 kmph x + 20 = 35 x = 15 kmph. so speed limit is 15 kmph option D Answer: B #### B QUESTION:The three competitors in a race have to be randomly chosen from a group of three men and three women. How many different such trios contain at least one woman? options: A)13 B)15 C)17 D)19 E)21 SOLUTION:The total number of ways to choose three runners 6C3 = 20 The number of trios with only males is 3C3 = 1 The number of trios which include at least one woman is 19. The answer is D. #### D QUESTION:According 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 6 - ounce cans of the concentrate are required to prepare 200 6-ounce servings of orange juice? options: A)25 B)34 C)50 D)67 E)100 SOLUTION:Orange juice concentrate: water::1:3 total quantity of orange juice = 200*6 = 1200 oz so Orange juice concentrate: water :: 300 oz:900 oz no. of 6 oz can = 300 oz/6 oz = 50 Answer C, 50 cans #### C QUESTION:present ages of A and B are in the ratio of 7:5 respectively. 5 years hence, the ratio of their ages will become 15:12 respectively . what A's present age in years? options: A)20 B)7/3 C)15/4 D)21/5 E)20/3 SOLUTION:A and B be 7x years and 5x years respectively (7x+5)/(5x+5)=15/12 4(7x+5)= 5(5x+5) x = 3/5 therefore A's present age : 7x=21/5 years correct answer(D) #### D QUESTION:The sale price sarees listed for Rs.528 after successive discount is 20% and 10% is? options: A)288 B)277 C)380 D)290 E)262 SOLUTION:528*(80/100)*(90/100) = 380 Answer: C #### C QUESTION:Angelo and Isabella are both salespersons. In any given week, Angelo makes $550 in base salary plus 8 percent of the portion of his sales above $4,000 for that week. Isabella makes 10 percent of her total sales for any given week. For what amount of weekly sales would Angelo and Isabella earn the same amount of money? options: A) 11,500 B) 24,500 C) 25,500 D) 26,500 E) 27,500 SOLUTION:OFFICIAL SOLUTION: The problem asks for the amount of weekly sales it takes for Angelo and Isabella to earn the same amount of money. You can write an equation that sets Angelo’s and Isabella’s weekly earnings equal to each other, with x representing weekly sales. Weekly earnings for each salesperson equal base salary plus commission. So Angelo’s earnings are 550 + (0.08)(x – 4,000), and Isabella’s are 0.10x. Set up the equation and solve: 550 + (0.08)(x – 4,000) = 0.10x Distribute the 0.08: 550 + 0.08x – 320 = 0.10x Combine terms and subtract 0.08x from both sides: 230 = 0.02x Divide both sides by 0.02: 11,500 = x Your answer is A. #### A QUESTION:In a consumer survey, 66% of those surveyed liked at least one of three products: 1, 2, and 3. 35% of those asked liked product 1, 30% liked product 2, and 20% liked product 3. If 8% 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? options: A)9 B)10 C)11 D)12 E)13 SOLUTION:35 + 30 + 20 = 85 This number includes some people counted twice and some people counted three times. 85 - 66 = 19, and this number represents people counted twice or three times. 8% of the people are counted two extra times. The percentage of people counted one extra time is 19 - 8(2) = 3. The percentage of people who liked more than one product is 8% + 3% = 11%. The answer is C. #### C QUESTION:If the sum of a set of 5 different positive prime numbers is 94, what is the difference between largest and smallest prime numbers between them? options: A)53 B)51 C)47 D)41 E)31 SOLUTION:All prime numbers apart from 2 are odd. Even + Even = Even Odd + Even = Odd Odd + Odd = Even We are given 5 different prime numbers, whose sum is 94 i.e even If we include 2, we will have 4 odd prime numbers and one even. This sum would be odd If we exclude 2, we will have 5 odd numbers. This sum would be even Hence 2 is included. The possible 5 no. are = 11+7+2+43+31 = 94 the difference between largest and smallest prime numbers between them = 43 - 2 = 41 Ans - D #### D QUESTION:A telephone company needs to create a set of 3-digit area codes. The company is entitled to use only digits 2, 4 and 8, which can be repeated. If the product of the digits in the area code must be even, how many different codes can be created? options: A)20 B)22 C)24 D)27 E)30 SOLUTION:Total # of codes possible is 3*3*3 = 27. Oit of those 27 codes Answer: D. #### D QUESTION:Find the largest 7 digit number which is exactly divisible by 88? options: A)9998765 B)9998907 C)9999944 D)9999954 E)9999968 SOLUTION:Largest 7 digit number is 9999999 After doing 9999999 ÷ 88 we get remainder 31 Hence largest 7 digit number exactly divisible by 88 = 9999999 - 31 = 9999968 E #### E QUESTION:On the independence day, bananas were be equally distributed among the children in a school so that each child would get two bananas. On the particular day 160 children were absent and as a result each child got two extra bananas. Find the actual number of children in the school? options: A)600 B)320 C)500 D)520 E)720 SOLUTION:Let the number of children in the school be x. Since each child gets 2 bananas, total number of bananas = 2x. 2x/(x - 160) = 2 + 2(extra) => 2x - 320 = x => x = 320. ANSWER:B #### B QUESTION:What is the greatest of 3 consecutive integers whose sum is 30 ? options: A)11 B)7 C)8 D)9 E)5 SOLUTION:The sum of three consecutive integers can be written as n + (n + 1) + (n + 2) = 3n + 3 If the sum is 24, we need to solve the equation 3n + 3 = 30; => 3n = 27; => n = 9 The greatest of the three numbers is therefore 9 + 2 = 11 Answer: A #### A QUESTION:Three 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? options: A) 8 B) 2 C) 6 D) 0 E) 12 SOLUTION:If B admitted 15 are overlapping with A admission of 17 But C does not overlap with anybody. Then no student will get nod from all the 3. Hence 0 student will get admission. Answer : D #### D QUESTION:A single letter is selected at random from the word 'SIMS'. The probability that it is a vowel is..?? options: A)1/4 B)3/11 C)4/11 D)3/7 E)1/2 SOLUTION:total vowels = 1, total number of letters = 4 so probability = 1/4 ANSWER:A #### A QUESTION:A certain number of workers can do a work in 25 days. If there were 10 workers more it could be finished in 10 days less. How many workers are there? options: A)15 B)30 C)28 D)24 E)32 SOLUTION:number of workers = 10* (25-10)/10 = 15 Answer is A #### A QUESTION:How many words with or without meaning, can be formed by using all the letters of the word, ‘POWER’, using each letter exactly once? options: A)700 B)720 C)750 D)800 E)120 SOLUTION:The word ‘POWER’ contains 5 different letters. Therefore, Required number of words= Number of arrangement of 5 letters, taken all at a time =5P5 = 5! = 5*4*3*2*1 = 120 ANSWER:E #### E QUESTION:An association of mathematics teachers has 1,260 members. Only 525 of these members cast votes in the election for president of the association. What percent of the total membership voted for the winning candidate if the winning candidate received 60 percent of the votes cast? options: A)75% B)58% C)42% D)34% E)25% SOLUTION:Total Number of members = 1260 Number of members that cast votes = 525 Since , winning candidate received 60 percent of the votes cast Number of votes for winning candidate = (60/100)*525 = 315 Percent of total membership that voted for winning candidate = (315/1260)*100 = 25% Answer E #### E QUESTION:Find the invalid no.from the following series 9, 16, 21, 28, 33, 37 options: A)13 B)18 C)40 D)37 E)25 SOLUTION:The differences between two successive terms from the beginning are 7, 5, 7, 5, 7, 5. So, 37 is wrong. Answer : D #### D QUESTION:An escalator moves towards the top level at the rate of 7 ft.sec and its length is 180 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. options: A)5sec B)25sec C)20sec D)15sec E)10sec SOLUTION:Explanation : Time taken to cover the entire length = tot.dist/resultant speed = 180/ (7+2) = 20sec Answer : C #### C QUESTION:On a ranch, a rancher can place a loop of rope, called a lasso, once in every 2 throws around a cow’s neck. What is the probability that the rancher will be able to place a lasso around a cow’s neck at least once in 4 attempts? options: A)3/4 B)5/8 C)7/8 D)11/16 E)15/16 SOLUTION:P(missing all 4)=(1/2)^4=1/16 P(success on at least one attempt)=1-1/16=15/16 The answer is E. #### E QUESTION:Based on this year's costs, an orchard grower budgets P dollars for planing N new trees next year. If the average cost of planting each tree were to decrease 50% from this year's cost, then the greatest number of trees that the orchard grower could plant next year using P dollars would be: options: A)100% less than N B)200% less than N C)Equal to N D)100% greater than N E)200% greater than N SOLUTION:Correct answer is (D). This year, the price of a tree is price1=P/N. If this price decreases by 50% it becomes Price2=P/N*0.5 Then with P dollars, you can grow P/Price2 trees i.e. P/(P/N*0.5) i.e. N/0.5 i.e. 2*N Which is 100% greater than N. #### D QUESTION:The 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 ? options: A)287 cm B)150.8 cm C)276 cm D)287 cm E)297 cm SOLUTION:Total height = 150 * 60 = 9000 cm. New average = [9000 - 5 * 146 + 5 * 156 ] / 60 = 150.8 cm. Answer:B #### B QUESTION:The cash difference between the selling prices of an article at a profit of 8% and 6% is Rs. 3. The ratio of the two selling prices is? options: A)52:56 B)52:53 C)52:50 D)54:53 E)52:51 SOLUTION:Let C.P. of the article be Rs. x. Then, required ratio = 108% of x / 106% of x = 108/106 = 54/53 = 54:53 Answer: D #### D QUESTION:A train 125 m long passes a man, running at 4 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is: options: A)49 kmph B)50 kmph C)51 kmph D)52 kmph E)54 kmph SOLUTION:Explanation: Speed of the train relative to man = (125/10) m/sec = (25/2) m/sec. [(25/2) x (18/5)] km/hr = 45 km/hr. Let the speed of the train be 'x' km/hr. Then, relative speed = (x - 4) km/hr. x - 4 = 45 => x = 49 km/hr. ANSWER IS A #### A QUESTION:Every student at Parcy School is in at least one of three clubs: horseback riding, embroidery, and country dancing, which are the only clubs in existence at the school. The ratio of the number of students in exactly two clubs to the number of students in exactly one club is 4:3, while the ratio of the number of students in exactly two clubs to the number of students in at least two clubs is 5:7. Which of the following could be the total number of students at Parcy School? options: A)63 B)69 C)74 D)82 E)86 SOLUTION:the total number of students at Parcy School The answer is 86 or any multiple of 43.E #### E <<<Examples ends QUESTION:What is the speed required for a car to cover a distance of 600 km in 5 hours? options: A)160 kmh B)140 kmh C)150 kmh D)130 kmh E)120 kmh SOLUTION:Speed= Distance / Time Speed = 600 / 5 = 140 Answer: B #### B

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:A and B together have Rs. 1210. If 4/15 of A's amount is equal to 2/5 of B's amount, how much amount does A have? options: A)576 B)800 C)726 D)484 E)500 SOLUTION:(4/15) * A = (2/5) * B A / B = 3 / 2 Therefore A's share is = (1210 * (3/5)) = 726 Ans - C #### C QUESTION:If 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. options: A)5 hours B)10 hours C)15 hours D)20 hours E)25 hours SOLUTION:1/5+2/8 + 3/x = 1 x =20 hours. ANSWER =D #### D QUESTION:Find the C.I. on a sum of Rs.1600 for 9 months at 20% per annum, interest being compounded quarterly? options: A)2528 B)2526 C)2522 D)2722 E)2426 SOLUTION:A = 1600(21/20)3 = 2522 Answer: C #### C QUESTION:The 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 6 minutes, then the area of the park (in sq. m) is: options: A)153601 B)153600 C)86400 D)153603 E)153604 SOLUTION:Perimeter = Distance covered in 6 min. =(12000/60) x 6m = 1200 m. Let length = 3x metres and breadth = 2x metres. Then, 2(3x + 2x) = 1200 or x = 120. Length = 360 m and Breadth = 240 m. Area = (360 x 240) m2 = 86400 m2. Answer: C #### C QUESTION:One-third of 1200 is what percent of 236 ? options: A)169.49 B)30 C)120.32 D)125.32 E)15.152 SOLUTION:Answer Let one-third of 1200 is N% of 236. ∵ 1200/3 = (N x 236)/100 ∴ N = (400 x 100) / 236= 169.49 Correct Option: A #### A QUESTION:If the sum of 7 consecutive negative integers is -70, what is the value of the 2nd number in the sequence? options: A)8 B)-9 C)-8 D)9 E)6 SOLUTION:if sum is -70, the average = median = -70/7 = -10 = which is the middle in the sequence. 7/2 = 3.5. When rounded up = 4. So -10 is the 4th in the sequence. 4th - 2nd = 2 numbers away. -10 + 2= -8 Answer: C #### C QUESTION:The 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? options: A)289 cm B)800 cm C)829 cm D)288 cm E)289 cm SOLUTION:Area of the square = s * s = 5(125 * 64) => s = 25 * 8 = 200 cm Perimeter of the square = 4 * 200 = 800 cm. Answer: B #### B QUESTION:Dana borrows 6000 pounds annually for her college education. If Dana gives her parents 2% of that amount back each month, how much will she still owe her parents after three years of college? options: A)13680 B)13885 C)14005 D)14280 E)14680 SOLUTION:dana borrows 6000 and returns 2% per month. so returns 120 per month. and 1440 per year. so dana owes 6000-1440=4560 per year. after 3 years she will owe 13680. Ans (A) #### A QUESTION:If Rs. 782 be divided into three parts, proportional to 1/2:2/3:3/4, then the first part is: options: A)Rs. 182 B)Rs. 190 C)Rs. 196 D)Rs. 204 E)Rs. 210 SOLUTION:Explanation: Given ratio =1/2:2/3:3/4=6:8:9 1st part = Rs. 782*6/23=Rs. 204 Answer is D #### D QUESTION:Anand and Deepak started a business investing Rs. 1000 and Rs. 5000 respectively. Out of a total profit of Rs. 2000, Deepak's share is: options: A)3776 B)1284.2 C)8400 D)1666.6 E)1671.8 SOLUTION:Ratio of their shares = 1000: 5000= 1:5 Deepak's share = 2000 * 5/6 = Rs. 1666.6. Answer: D #### D QUESTION:X can give Y 100 meters start and Z 200 meters start in X kilometer race. How much start can Y give Z in X kilometer race? options: A)112.2m B)216.3m C)111.12m D)213.27m E)222.40m SOLUTION:C 111.12 m X runs 1000 m while Y runs 900 m and Z runs 800 m. The number of meters that Z runs when Y runs 1000 m, = (1000 * 800)/900 = 8000/9 = 888.88 m. Y can give Z = 1000 - 888.88 = 111.12 m. #### C QUESTION:Ramu bought an old car for Rs. 40000. He spent Rs. 13000 on repairs and sold it for Rs. 64900. What is his profit percent? options: A)A)14% B)B)16% C)C)18% D)D)21.6% E)of these SOLUTION:Total CP = Rs. 40000 + Rs. 13000 = Rs. 53000 and SP = Rs. 64900 Profit(%) = (64900 - 53000)/55000 * 100 = 21.6% ANSWER:D #### D QUESTION:A train speeds past a pole in 15 seconds and a platform 140 meters long in 25 seconds. What is the length of the train (in meters)? options: A)190 B)200 C)210 D)220 E)230 SOLUTION:Let the length of the train be x meters. The speed of the train is x / 15. Then, x + 140 = 25*(x / 15) 10x = 2100 x = 210 meters The answer is C. #### C QUESTION:Tom opened a shop investing Rs.30000. Jose joined him 2 months later, investing Rs.45000. They earned a profit of Rs.72000 after completion of one year. What will be Jose's share of profit? options: A)20000 B)10000 C)25000 D)34000 E)40000 SOLUTION:SoL = ~s- So Anju’s share = [5/9] x 72000 = 40000 E #### E QUESTION:Renu can do a piece of work in 6 days, but with the help of her friend Suma , she can do it in 3 days. In what time Suma can do it alone? options: A)6 B)12 C)14 D)15 E)17 SOLUTION:Renu’s one day’s work = 1/6 Suma’s one day’s work = 1/3 - 1/6 = 1/6 Suma can do it alone in 6 days. ANSWER:A #### A QUESTION:There are two boxes,one containing 39 red balls & the other containing 26 green balls.you are allowed to move the balls b/w the boxes so that when you choose a box random & a ball at random from the chosen box,the probability of getting a red ball is maximized.this maximum probability is options: A)0.9 B)0.8 C)0.5 D)0.7 E)0.2 SOLUTION:Ans: Very interesting question. As we are allowed to move the balls, we keep only one red ball in first box and move all the remaining balls to the second box So fist box contains 1 redball, second box contains 38 red + 26 green = 64 balls Probability of choosing any box is 1/ 2. So probability of taking one red ball = 12×(1)+12(3864)≃0.8 Answer:B #### B QUESTION:A swimmer can swim in still water at 4 km/h. If the speed of the water current is 1 km/h, how many hours will the swimmer take to swim against the current for 6 km? options: A)1.2 B)1.4 C)1.6 D)1.8 E)2 SOLUTION:The swimmer can swim against the current at a speed of 4-1 = 3 km/h. The time it will take is 6/3 = 2 hours. The answer is E. #### E QUESTION:If x and y are integers and 4^(x-4) = 4^(y+4), what is y in terms of x? options: A)x - 8 B)x - 5 C)x - 2 D)x + 2 E)x + 6 SOLUTION:Answer: A 4^(x-4) = 4^(y+4) Since the base is the same, I isolated the equations and solved for y. x-4 = y+4 y=x-8 #### A QUESTION:A can do a work in 8 days. B can do the same work in 24 days. If both A & B are working together in how many days they will finish the work? options: A)3 B)5 C)4 D)2 E)6 SOLUTION:A rate = 1/8 B rate = 1/24 (A+B) rate = (1/8)+(1/24) = 1/6 A & B finish the work in 6days correct option is E #### E QUESTION:The 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? options: A)1 : 9 B)1 : 3 C)1 : 2 D)1 : 1 E)3 : 3 SOLUTION:Suppose age of Laxmi is x years. The difference of their ages \inline \therefore Ratio of their ages after 3 years = = = 12 : 36 = 1 : 3 Answer:B #### B QUESTION:There 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. options: A)18 B)99 C)12 D)07 E)11 SOLUTION:Let 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. a2 = 784 = (4)(196) = (22).(142) a = (2)(14) = 28 a = 2l, l = a/2 = 14 l = (7/3)s Therefore s = (3/7)(l) = 6 Circumference of the smaller circle = 2∏s = 12∏ cm. Answer: C #### C QUESTION:A 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: options: A)56 B)50 C)72 D)27 E)25 SOLUTION:Speed 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. Answer: B #### B QUESTION:The letters P,O,C and Y are rearranged to form the word 'Copy'. Find its probability. options: A)1/120 B)1/235 C)1/24 D)1/76 E)1/53 SOLUTION:Explanation : There are total 4 letters. The probability that P gets the first position is 1/4. The probability that O is in the second position is 1/3. Likewise, probability for C and Y are 1/2 and 1/1. Hence, the required probability is:- => (1/4) x (1/3) x (1/2) x 1. => 1/24. Answer : C #### C QUESTION:Three numbers are in the ratio 1 : 2 : 3 and their H.C.F is 12. The numbers are options: A)4, 8, 12 B)5, 10,15 C)10, 20, 30 D)12, 24, 36 E)None SOLUTION:Solution Let the required numbers be x, 2x and 3x. Then, their H.C.F = x. So x = 12. The numbers are 12, 24, 36. Answer D #### D QUESTION:In the following sequence: [x, y, z, 5, 7, 16, 28] each number is equal to the sum of the three numbers preceding it. What is x-y? options: A)6 B)3 C)4 D)5 E)7 SOLUTION:lets start from z, as per the question stem z + 5 + 7 = 16 -->> z= 4 similarly, y + 4 + 5 = 7 --> y = -2 similarly,, x + -2 + 4 = 5 --> x = 3 hence , x-y = 3+2 = 5 ANSWER:D #### D QUESTION:The 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? options: A)33 B)88 C)66 D)12 E)99 SOLUTION:Speed of the boat downstream = 15 + 3 = 18 kmph = 18 * 5/18 = 5 m/s Hence time taken to cover 60 m = 60/5 = 12 seconds. Answer: D #### D QUESTION:How many different subsets of the set {0, 1, 2, 3, 4, 5,6,} do not contain 0? options: A)A.66 B)B.57 C)C.31 D)D.32 E)E.58 SOLUTION:Number of subset Since we have 6 digits other than 0, we can take any numbers from the set of 6 to make a subset. Also it is a matter of selection and not arrangement.So we will consider combinations. 6c1+6c2+6c3+6c4+6c5+6c6=57 And one set is the NULL set having no elements in it so 57+1=58. ANSWER E. #### E QUESTION:12 buckets of water fill a tank when the capacity of each bucket is 49 litres. How many buckets will be needed to fill the same tank, if the capacity of each bucket is 7 litres? options: A)39 B)84 C)80 D)82 E)86 SOLUTION:Capacity of the tank = (12 × 49) litre Number of buckets required of capacity of each bucket is 17 litre = 12×49/7=12×7=84 Answer is B #### B QUESTION:Tanks P and B are each in the shape of a right circular cylinder. The interior of tank P has a height of 10 meters and a circumference of 8 meters, and the interior of tank B has a height of 8 meters and a circumference of 10 meters. The capacity of tank P is what percent of the capacity of tank B? options: A)75% B)80% C)100% D)120% E)125% SOLUTION:B. For P, r=8/2pi. Its capacity = (4pi)^2 * 10= 160pi For B, r=10/pi. Its capacity = (5pi)^2 *8 = 200pi P/B = 160pi/200pi = 0.8 #### B QUESTION:The average mark of the students of a class in a particular exam is 80. If 5 students whose average mark in that exam is 20 are excluded, the average mark of the remaining will be 92. Find the number of students who wrote the exam. options: A)15 B)25 C)30 D)45 E)55 SOLUTION:Let the number of students who wrote the exam be x. Total marks of students = 80 x. Total marks of (x - 5) students = 92(x - 5) 80x - (5 * 20) = 92(x - 5) 360 = 12x => x = 30 ANSWER:C #### C QUESTION:During a trip on an expressway, Son 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? options: A)8.5% B)50% C)x/12% D)60/x% E)500/x% SOLUTION:so Son drove (x-5) miles at 60mph and 5 miles at 30mph: (x-5)/60 + (10/60) = (X+5)/60 - current time to drive the whole distance if the entire trip @60mph than time = x/60 so to get percent [(X+5)/60 ]/[x/60] x100 =(x+5)/x *100 =100+500/x so increase of 500/x%[/u]=E #### E QUESTION:A 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? options: A)6 min B)8 min C)7 min D)9 min E)1 min SOLUTION:The combined rate of filling/emptying the tank = 1/10 - 1/6 = -1/15 Since the rate is negative, the tank will be emptied. A full tank would take 15 minutes to empty. Since the tank is only three-fifths full, the time is (3/5) * 15 = 9 minutes The answer is D. #### D QUESTION:Which of the following fractions is smaller than 17/50? options: A)2/5 B)11/34 C)43/99 D)8/21 E)9/20 SOLUTION:Answer B 17/50=0.34 11/34=0.323529 which is 0.01647 smaller than 0.34 #### B QUESTION:If the area of a circle is 81pi square feet, find its circumference. options: A)48 B)38 C)51 D)92 E)18 SOLUTION:The area is given by pi pi × r × r = 81 pi r × r = 81 ; hence r = 81 feet The circumference is given by 2 × pi × r = 2 × pi × 9 = 18 pi feet correct answer is E) 18 #### E QUESTION:A pump can fill a tank with a water in 2 hours. Because of a leak, it took 2 and 4/5 hours to fill the tank. The leak can drain all the water of the full tank in how many hours? options: A)4 B)5 C)6 D)7 E)8 SOLUTION:The rate of the pump + leak = 5/14 1/2 - leak's rate = 5/14 leak's rate = 1/2 - 5/14 = 1/7 The leak will empty the tank in 7 hours. The answer is D. #### D QUESTION:In the new budget the price of Petrol rose by 20%. By how much percent must a person reduce his consumption so that his expenditure on it does not increase? options: A)16.67% B)25% C)20.45% D)31.56% E)40% SOLUTION:Reduce in consumption = R/(100+R) *100% = 20/120 *100 = 16.67% Answer is A #### A QUESTION:if 8^25 divided by 7 then what is reminder options: A)25 B)1 C)0 D)2 E)3 SOLUTION:8^25/7 8 can be written as 7*1+1 (7*1+1)^25/7 (ax+1)^n/a always gives the remainder 1 here a=7,x=1,n=25 Hence remainder is 1 ANSWER:B #### B QUESTION:What percentage of numbers from 1 to 20 have squares that end in the digit 9? options: A)1 B)14 C)20 D)21 E)22 SOLUTION:Clearly, 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 18 are 3,7,13,17. Number of such numbers = 4. Required percentage = (4/18 * 100) = 22% ANSWER:E #### E QUESTION:A man can row 7 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? options: A)3.3 B)3.4 C)3.5 D)3.6 E)3.7 SOLUTION:M = 7 S = 1.2 DS = 7 + 1.2 = 8.2 US = 7 - 1.2 = 5.8 x/8.2 + x/5.8 = 1 x = 3.40.Answer: B #### B QUESTION:A bag contains an equal number of one rupee, 50 paise and 25 paise coins respectively. If the total value is 35, how many coins of each type are there? options: A)20 coin B)30 coins C)28 coins D)25 coins E)None of these SOLUTION:Let number of each type of coin = x. Then, 1 × x + .50 × x + .25x = 35 ⇒ 1.75x = 35 ⇒ x = 20 coin Answer A #### A QUESTION:85% of a number is added to 24, the result is the same number. Find the number? options: A)28 B)288 C)279 D)160 E)232 SOLUTION:(85/100) * X + 24 = X 3X = 480 X = 160 Answer:D #### D QUESTION:Two friends A and B apply for a job in the same company. The chances of A getting selected is 2/5 and that of B is 4/7. What is the probability that both of them get selected? options: A)8/38 B)8/32 C)8/35 D)8/31 E)6/38 SOLUTION:Explanation: P(A) = 2/5 P(B) = 4/7 E = {A and B both get selected} P(E) = P(A)*P(B) = 2/5 * 4/7 = 8/35 ANSWER: C #### C QUESTION:A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 15 seconds. The speed of the train is? options: A)35 B)50 C)88 D)66 E)22 SOLUTION:Speed of the train relative to man = (125/15) m/sec = (25/3) m/sec. [(25/3) * (18/5)] km/hr = 30 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 30 ==> x = 35 km/hr. Answer:A #### A QUESTION:By selling 99 pens, a trader gains the cost of 11 pens. Find his gain percentage? options: A)11 1/3% B)11 7/3% C)11 1/8% D)11 1/3% E)11 1/9% SOLUTION:Let the CP of each pen be Rs. 1. CP of 99 pens = Rs. 99 Profit = Cost of 11 pens = Rs. 11 Profit% = 11/99 * 100 = 11 1/9% Answer: E #### E QUESTION:P and Q entered into a partnership investing Rs. 16,000 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: options: A)Rs.2400 B)Rs.3000 C)Rs.3600 D)Rs.4800 E)Rs.3800 SOLUTION:A : B : C = (16000 x 3 + 11000 * 9) : (12000 * 3 + 17000 * 9) : (21000 * 6) = 147 : 189 : 126 = 7 : 9 : 6. Therefore, Difference of B and C’s shares = Rs. 26400 x 9/22 – 26400 x 6/22 = Rs.3600 ANSWER:C #### C QUESTION:Three people each took 5 tests. If the ranges of their scores in the 5 practice tests were 17, 28 and 34, what is the minimum possible range in scores of the three test-takers? options: A)a 17 B)b) 34 C)c) 35 D)d) 45 E)e) 80 SOLUTION:It is finding the minimum range between all their scores, if all test taker scores are between 0 and maximum range we will have: A- 0 and 17 B- 0 and 28 C- 0 and 35 therefore the minimum range is 34, it cant be any lower however you play with the numbers. B #### B QUESTION:15 ants can move 600 sugar cubes of 10 grams each to their home in 5 hours. Then how many sugar cubes of 5 grams each, will 20 ants move in 3 hours? options: A)360 B)480 C)720 D)960 E)1000 SOLUTION:D 15 ants move 600/5=120 sugar cubes of 10 grams in 1 hour. 5 grams sugar cubes will take less time to move. Thus if weight of the sugar cube is 5 grams, 15 ants will move 120 X 10 / 5 = 240 sugar cubes in 1 hour. More ants, more sugar cubes they can move. 20 ants will move 240 X 20 / 15 = 320 sugar cubes in 1 hour Thus in 3 hours, 20 ants will move 320 X 3 = 960 sugar cubes of 5 grams. #### D QUESTION:What is x if x + 3y = 33 and y = 10? options: A)1 B)2 C)3 D)4 E)5 SOLUTION:Substitute y by 10 in x + 3y = 33 x + 3(10) = 33 x + 30 = 33 If we substitute x by 3 in x + 30 = 33, we have 3 + 30 = 33. Hence x = 3 correct answer C #### C QUESTION:A can do a particular work in 6 days . B can do the same work in 8 days. A and B signed to do it for Rs. 3200. They completed the work in 3 days with the help of C. How much is to be paid to C? options: A)Rs. 380 B)Rs. 600 C)Rs. 420 D)Rs. 400 E)Rs. 480 SOLUTION:Explanation : Amount of work A can do in 1 day = 1/6 Amount of work B can do in 1 day = 1/8 Amount of work A + B can do in 1 day = 1/6 + 1/8 = 7/24 Amount of work A + B + C can do = 1/3 Amount of work C can do in 1 day = 1/3 - 7/24 = 1/24 work A can do in 1 day: work B can do in 1 day: work C can do in 1 day = 1/6 : 1/8 : 1/24 = 4 : 3 : 1 Amount to be paid to C = 3200 × (1/8) = 400 Answer : Option D #### D QUESTION:The difference of 2 digit number & the number obtained by interchanging the digits is 36. What is the difference the sum and the number if the ratio between the digits of the number is 1:2 ? options: A)6 B)8 C)9 D)10 E)12 SOLUTION:Let the number be xy. Given xy – yx = 36. This means the number is greater is than the number got on reversing the digits. This shows that the ten’s digit x > unit digit y. Also given ratio between digits is 1 : 2 => x = 2y (10x + y) – (10y +x) = 36 => x – y = 4 => 2y – y =4. Hence, (x + y) – (x – y) = 3y – y = 2y = 8 B #### B QUESTION:How much water must be added to 60 litres of milk at 1 1⁄2 litres for 20 so as to have a mixture worth 10 2⁄3 a litre? options: A)10 litres B)12 litres C)15 litres D)18 litres E)None of these SOLUTION:C.P. of 1 litre of milk = (20 × 2⁄3) = 40⁄3 ∴ Ratio of water and milk = 8⁄3 : 32⁄3 = 8 : 32 = 1 : 4 ∴ Quantity of water to be added to 60 litres of milk = (1⁄4 × 60) litres = 15 litres. Answer C #### C QUESTION:The average of first ten prime numbers which are odd is? options: A)15.2 B)15.7 C)15.4 D)15.8 E)15.5 SOLUTION:Sum of first 10 prime no. which are odd = 158 Average = 158/10 = 15.8 Answer:D #### D QUESTION:Two pipes A and B can fill a tank in 15 min and 20 min respectively. Both the pipes are opened together but after 4 min, pipe A is turned off. What is the total time required to fill the tank? options: A)14 min 80 sec B)14 min 48 sec C)14 min 42 sec D)14 min 40 sec E)14 min 43 sec SOLUTION:Part filled in 4 minutes = 4(1/15 + 1/20) = 7/15 Remaining part = 1 - 7/15 = 8/15 Part filled by B in 1 minute = 1/20 1/20 : 8/15 :: 1 ; x x = 8/15 * 1 * 20 = 10 2/3 min = 10 min 40 sec. The tank will be full in (4 min. + 10 min. 40 sec) = 14 min 40 sec. Answer:D #### D QUESTION:The number of students in 3 classes is in the ratio 2:3:4. If 12 students are increased in each class this ratio changes to 8:11:14. The total number of students in the three classes in the beginning was options: A)162 B)108 C)96 D)54 E)None SOLUTION:Solution: Let the number of students in the classes be 2x, 3x and 4x respectively; Total students = 2x+3x+4x = 9x. According to the question, (2x+12)/(3x+12) = 8/11 24x+96 = 22x+132 Or, 2x = 132-96 Or, x = 36/2 = 18 Hence, Original number of students, 9x = 9*18 = 162. Answer: Option A #### A QUESTION:At a dinner party, 5 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 R of different possible seating arrangements for the group? options: A)5 B)10 C)24 D)32 E)120 SOLUTION:Circular arrangements= (n-1)! Hence (4!) = 24=R Answer is C #### C QUESTION:The difference between the simple interest on a certain sum at the rate of 10%per annum for 2 years and compound interest which is compounded every 6 months is Rs.124.05. what is the principal sum options: A)124.05 B)124.09 C)124.04 D)124.06 E)124.02 SOLUTION:Explanation: Compound Interest on P at 10% for 2 years when interest is compounded half-yearly = Simple Interest on P at 10% for 2 years = Given that difference between compound interest and simple interest = 124.05 Answer:A #### A QUESTION:The probability that a number selected at random from the first 50 natural numbers is a composite number is? options: A)17/29 B)17/21 C)17/22 D)17/29 E)17/25 SOLUTION:The number of exhaustive events = 50C1 = 50. We have 15 primes from 1 to 50. Number of favourable cases are 34. Required probability = 34/50 = 17/25. Answer: E #### E QUESTION:A 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: options: A)28.97 B)28.0 C)28.47 D)27.47 E)29.47 SOLUTION:Explanation : After 10 days : 200 women had food for 25 days. Suppose 175 women had food for x days. Now, Less women, More days (Indirect Proportion) 175 : 200 :: 25 : x => 175 x x = 200 x 25 => x = 200 x 25 / 175 => x =28.47 Answer : C #### C QUESTION:A person purchased a TV set for Rs. 16000 and a DVD player for Rs. 1800. He sold both the items together for Rs. 31150. What percentage of profit did he make? options: A)30% B)75% C)40% D)70% E)None of these SOLUTION:The total CP = Rs. 16000 + Rs. 1800 = Rs. 17800 and SP = Rs. 31150 Profit(%) = (31150 - 17800)/17800* 100 = 75% ANSWER:B #### B QUESTION:Weight of M, D and I is 74. Sum of D and I is 46 greater than M. I is 60% less than D. What is D's weight. options: A)22 B)10 C)88 D)26 E)18 SOLUTION:M + D + I = 74 - - - (1) (D + I) - M = 46 - - - (2) I = 410410 D ⇒⇒ 5I = 2D ⇒⇒ I = 2D/5 - - - (3) Adding (1) and (2) we get 2D + 2I = 120 Substituting the value of I in the above equation, 2D+2(2D5)=1202D+2(2D5)=120 ⇒⇒ 14D = 600 ⇒⇒ D = 300/7 = 42.8 Ans:B #### B QUESTION:When 12 is divided by the positive integer k, the remainder is 7, for how many different values of k is this true? options: A)2 B)3 C)4 D)7 E)8 SOLUTION:When 20 is divided by k, remainder is 2 i.e. there are 2 balls leftover after grouping. so k must be greater than 2. It also means that 18 is completely divisible by k. Factors of 18 are 1, 2, 3, 6, 9, 18 Out of these, k can be 3, 6, 9 and 18. Answer (C) #### C QUESTION:Yesterday's closing prices of 2,640 different stocks listed on a certain stock exchange were all different from today's closing prices. The number of stocks that closed at a higher price today than yesterday was 20 percent greater than the number that closed at a lower price. How many of the stocks closed at a higher price today than yesterday? options: A) 484 B) 726 C) 1,100 D) 1,320 E) 1,440 SOLUTION:Lets consider the below - The number of stocks that closed at a higher price = H The number of stocks that closed at a lower price = L We understand from first statement -> H+L = 2640 ----(1) We understand from second statement -> H = (120/100)L => H = 1.2L ----(2) Solve eq (1)(2) to get H = 1440. E is my answer. #### E QUESTION:In a simultaneous throw of pair of dice .find the probability of getting the total more than 7? options: A)12/5 B)5/12 C)6/4 D)2/3 E)4/7 SOLUTION:Here n(S)=(6*6)=36 let E=event of getting a total more than 7 ={(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)} P(E)=n(E)/n(S)=15/36=5/12 Option B #### B QUESTION:Find the circumference and area of radius 13 cm. options: A)124 cm² B)531 cm² C)354 cm² D)584 cm² E)594 cm² SOLUTION:Area of circle = πr² = 22/7 × 13 × 13 cm² = 531 cm² ANSWER:B #### B <<<Examples ends QUESTION:What is 35% of 4/13 of 585? options: A)52 B)63 C)74 D)85 E)96 SOLUTION:This 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. The number 585 is between 540 and 630, so (1/9)*585 will be about 65. Keeping 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. The closest answer is 63, so this is the answer to choose. The answer is B. #### B

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:The residents of Town X participated in a survey to determine the number of hours per week each resident spent watching television. The distribution of the results of the survey had a mean of 21 hours and a standard deviation of 8 hours. The number of hours that Pat, a resident of Town X, watched television last week was between 1 and 2 standard deviations below the mean. Which of the following could be the number of hours that Pat watched television last week? options: A)30 B)20 C)11 D)14 E)6 SOLUTION:Given: mean=21 and SD=8 The number of hours that Pat watched television was between 1 and 2 standard deviations below the mean: 1 SD below the mean ismean-1*SD=13 and 2 SD below the mean ismean-2*SD=5, so the number of hours that Pat watched television was between 5 and 13 hours. Answer: C #### C QUESTION:The 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 6 years hence? options: A)22 B)77 C)70 D)98 E)72 SOLUTION:A + B = 60, A = 2B 2B + B = 60 => B = 20 then A = 40. 6 years, their ages will be 46 and 26. Sum of their ages = 46 + 26 = 72. Answer: E #### E QUESTION:If the average (arithmetic mean) of x + 2, x + 3, and x + 4 is 0, then x = options: A)–4 B)–3 C)–2 D)–1 E)0 SOLUTION:(x+2 + x+3 + x+4)/3 = 0 =>3x + 9 = 0 =>x = -3 Answer B #### B QUESTION:How many digits are required to number a book containing 250 pages? options: A)756 B)642 C)492 D)372 E)250 SOLUTION:9 pages from 1 to 9 will require 9 digits. 90 pages from 10 to 99 will require 90*2=180 digits. 250-(90+9)=151 pages will require 151*3=453 digits. The total number of digits is 9+180+453=642. The answer is B. #### B QUESTION:Train A leaves the station traveling at 30 miles per hour. Two hours later train В leaves the same station traveling in the same direction at 45 miles per hour. How many miles from the station was train A overtaken by train B? options: A)100 B)120 C)140 D)160 E)180 SOLUTION:After two hours, Train A is ahead by 60 miles. Train B can catch up at a rate of 15 miles per hour. The time to catch up is 60/15 = 4 hours. In 4 hours, train A travels another 30*4 = 120 miles for a total of 180 miles. The answer is E. #### E QUESTION:a man spends $2.6 for parking and $34.4 for petrol to travel in car from monday to friday.if he travel by public transport it costs $1.06,find the percentage of savings? options: A)75.6 B)85.6 C)85.7 D)95.7 E)105.7 SOLUTION:2.6+34.4=37 for 5 days 1.06*5=5.3 37-5.3=31.7 now the required saving percentage is (31.7/37)*100=85.6 ANSWER:B #### B QUESTION:How many 6-digits number are Palindromic numbers? A Palindromic number reads the same forward and backward, example options: A)100 B)610 C)729 D)900 E)1000 SOLUTION:The 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, 9∗10∗10∗1∗1∗1=9009∗10∗10∗1∗1∗1=900 Answer D #### D QUESTION:Sum of 3 consecutive even no.'s is 26 more than the 1st no. of the series. Find the middle no.? options: A)8 B)twelve (12) C)14 D)16 E)18 SOLUTION:Let the numbers be x, x+2 and x+4 then x + x+2 + x+4 = x+26 3x + 6 = x + 26 2x = 20 \inline \therefore x = 10 \inline \therefore Middle number = x + 2 = 10+2 = 12 B #### B QUESTION:Albert invested an amount of $8000 in a fixed deposit scheme for 2 years at compound interest rate 5% p.a. How much amount will Albert get on maturity of the fixed deposit? options: A)$8100 B)$8820 C)$8800 D)$8810 E)$8825 SOLUTION:Amount = 8000 x (1 + 5/100)^2) = 8000 x 21/20 x 21/20 =8820. Answer B)$8820 #### B QUESTION:Find the odd man out 4, 10, 22, 40, 84, 94 options: A)22 B)40 C)94 D)84 E)10 SOLUTION:Differnce is multiple of 6 4 and 10 diff is 6 10 and 22 diff is 12 22 and 40 diff is 18 40+24 = 64 but in series it is mentioned as 84 64+30 = 94 ANSWER:D #### D QUESTION:In how many different ways can the letters of the word 'OPTICAL' be arranged so that the vowels always come together? options: A)610 B)720 C)825 D)920 E)None of these SOLUTION:Explanation : The word 'OPTICAL' has 7 letters. It has the vowels 'O','I','A' in it and these 3 vowels should always come together. Hence these three vowels can be grouped and considered as a single letter. That is, PTCL(OIA). Hence we can assume total letters as 5. and all these letters are different. Number of ways to arrange these letters = 5! = [5 x 4 x 3 x 2 x 1] = 120 All The 3 vowels (OIA) are different Number of ways to arrange these vowels among themselves = 3! = [3 x 2 x 1] = 6 Hence, required number of ways = 120 x 6 = 720. Answer : Option B #### B QUESTION:In a family, there are six members A, B, C, D, E and F. A and B are a married couple, A being the male member. D is the only son of C, who is the brother of A. E is the sister of D. B is the daughter-in-law of F, whose husband has died. How many male members are there in the family ? options: A)1 B)9 C)3 D)4 E)6 SOLUTION:Explanation: A is a male and married to B. So, A is the husband and B is the wife. C is the brother of A. D is the son of C. E, who is the sister of D will be the daughter of C. B is the daughter-in-law of F whose husband has died means F is the mother of A. A is a male. B. the wife, is female. C. the brother, is male. D. the son, is male. E, the sister, is female. F, the mother, is a female. So, there are three males. Answer: C) 3 #### C QUESTION:A number when successively divided by 3,5 and 8 leaves remainders 1,4 and 7 respectively. Find the respective remainders R when the order of the divisors is reversed. options: A)8,5,3 B)R=4,2,1 C)R=3,2,1 D)R=6,4,2 E)None of above SOLUTION:My approach would be Three Divisors : 3, 5, 8 Three Remain: 1, 4, 7 Start from the bottom of the last column i.e. from the third remainder: Go up diagonally and multiply by the second divisor: 5*7 = 35 Go down and add the second remainder: 35 + 4 = 39 Go up diagonally and multiply by the first divisor: 39* 3 = 117 Go down and add the first remainder: 117 + 1 = 118 Divide 118 by 8, 5, 3 118/8 gives quotient = 14 and remainder = 6 14/5 gives quotient = 2 and remainder = 4 2/3 gives quotient = 0 and remainder = 2 Ans is D i.e. 6,4,2 #### D QUESTION:Find 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) options: A)Rs. 8167 B)Rs. 4261 C)Rs. 4269 D)Rs. 4266 E)Rs. 4262 SOLUTION:Explanation: CI = 14800{ [ 1 + 13.5/100]2 - 1 } = 14800 { [1 + 27/200]2 - 1 = 14800 { 2 + 27/200}{27/200} = (74)[2 + 27/200](27) = 1998[2 + 27/200] = 3996 + 269.73 = Rs. 4266 Answer:D #### D QUESTION:How many integers between 2000 and 3000 that have distinct digits and increase from left to right ? options: A)10 B)20 C)60 D)120 E)600 SOLUTION:Since the numbers must be distinct and increasing from left to right, The only arrangements we could come-up with are: 245_ --> 4 246_ --> 3 247_ --> 2 248_ --> 1 256_ --> 3 257_ --> 2 258_ --> 1 267_ --> 2 268_ --> 1 Number of integers =20 B #### B QUESTION:David 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 600 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 4,800. 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.? options: A)2400 B)3600 C)3000 D)2800 E)2500 SOLUTION:let the rate be x, then population of the bacteria after each hour can be given as 600,600x, 600(x^2), 600(x^3) now population at 4pm =4800 thus we have 600(x^3) = 4800 =8 thus x=2 therefore population at 3pm = 600(4) = 2400 Answer : A #### A QUESTION:90 students represent x percent of the boys at Jones Elementary School. If the boys at Jones Elementary make up 40% of the total school population of x students, what is x? options: A)125 B)150 C)225 D)250 E)500 SOLUTION:90 = (x/100)*(# boys) # boys = .4x substitute and solve: 90 = (x/100)*(.4x) 9000 = .4(x^2) 25000 = x^2 x=150 Answer: B #### B QUESTION:If P represents the product of the first 18 positive integers, then P is NOT a multiple of options: A)99 B)84 C)72 D)65 E)95 SOLUTION:Answer is E. Since prime factor of 95 is 5x19. 19 is a prime number and not part of the first 18 positive integers. A) 9 x 11 B) 12 x 7 C) 12 x 6 D) 13 x 5 E) 3 x 19 #### E QUESTION:The least number which when divided by 5, 6, 7 and 8 leaves a remainder 3, but when divided by 9 leaves no remainder, is options: A)1677 B)1683 C)2523 D)3363 E)None of these SOLUTION:Explanation: L.C.M of 5, 6, 7, 8 = 840 therefore Required Number is of the form 840k+3. Least value of k for which (840k+3) is divisible by 9 is k = 2 therefore Required Number = (840 x 2+3)=1683. Answer: B #### B QUESTION:A = {0, 1, -3, 6, -8, -10} B = {-1, 2, -4, 7, 6, -9} If 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? options: A)1/4 B)1/3 C)5/13 D)5/12 E)1/2 SOLUTION:For the product of 2 numbers to be negative either of them must be positive or negative: P(positive, negative) = 2/6*3/6 = 6/36; P(negative,positive ) = 3/6 * 3/6 = 9/36 P = 6/36 + 9/36 P = 15/36 P = 5/12 Answer: D #### D QUESTION:n is a whole number which when divided by 4 gives 3 as remainder. What will be the remainder when 2n is divided by 4? options: A)3 B)2 C)1 D)0 E)None of these SOLUTION:Let n=4q+3. 2n=8q+6=4(2q+1)+2 Thus, when 2n is divided by 4, the remainder is 2. Correct Option: B #### B QUESTION:In a exam there are 26 number of question. For one write question add 8 marks and for one wrong 5 marks subtract. One candidate answered all questions. His marks is 0. How many answers was correct? options: A)9 B)10 C)11 D)12 E)13 SOLUTION:let no. of right ques be x, then no. of wrong ques will be= 26 - x now, according to ques 8x - (26-x)5 = 0, hence x=10...no. of right ques is 10 ANSWER:B #### B QUESTION:Stacy has a 63 page history paper due in 3 days. How many pages per day would she have to write to finish on time? options: A)9 B)8 C)10 D)8.5 E)21 SOLUTION:63/3=21 Answer : E #### E QUESTION:What will come in place of the x in the following Number series? 73205, 6655, 605, 55, x options: A)35678 B)73205 C)75653 D)86554 E)87565 SOLUTION:(B) 5 x 11 = 55, 55 x 11 = 605, 605 x 11 = 6655, 6655 x 11 = 73205 #### B QUESTION:Set #1 = {A, B} Set #2 = {K, L, M, N, O, P} There 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? options: A)1/6 B)1/3 C)7/12 D)2/3 E)5/6 SOLUTION:So Not a vowel in Set-1 : 1/2 And not a vowel in Ser-2:5/6 Now, 1/2∗5/6=5/12 This is for not a vowel. Then for at least one vowel will be = 1−5/12=7/12 Answer will be C. #### C QUESTION:A 45° -45° - 90° right triangle has hypotenuse of length h. What is the area of the triangle R in terms of h? options: A)h/ √2 B)h/2 C)h/4 D)(h)^2 E)(h)^2/4 SOLUTION:IF...each of the two shorter sides = 3, then the hypotenuse = H = 3(root2). The AREA R= (1/2)(Base)(Height) = (1/2)(3)(3) = 9/2. So we're looking for an answer that = 9/2 when H = 3(root2). There's only one answer that matches... E #### E QUESTION:If the simple interest on Rs.3100 amount to Rs. 632.40 in 2 Years, What is the rate percent? options: A)11.2% B)10.2% C)12.2% D)13.2% E)18.2% SOLUTION:$632.40 = (3100*2*R)/100 R = 10.2% Answer: B #### B QUESTION:A 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? options: A)400 B)197 C)278 D)270 E)279 SOLUTION:2000 ---- 50 2000 ---- 40 x ----- 50 x*50 = 2000*40 x=1600 2000 ------- 400 Answer: A #### A QUESTION:Two, 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: options: A)2:3 B)4:3 C)7:3 D)9:3 E)4:2 SOLUTION:Let us name the trains as A and B. Then, (A's speed) : (B's speed) = b : a = 16 : 9 = 4 : 3. #### B QUESTION:There are 10 cans in the refrigerator. 5 of them are red and 5 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. options: A)410 B)490 C)493 D)455 E)445 SOLUTION:Answer: A. #### A QUESTION:A table is bought for Rs.1020/- and sold at Rs.750/- find the loss percentage options: A)26% Loss B)10% Gain C)20% Loss D)20% Gain E)30% Gain SOLUTION:Formula = (Selling price ~ Cost price)/Cost price * 100 = (750 ~ 1020)/1020 = 26% Loss A #### A QUESTION:George can do 3/5 of work in 9days.He then calls in pauls and they completed the work in 4days.How long paul would take long to complete the work? options: A)32 B)28 C)35 D)30 E)22 SOLUTION:George work is (5/3)*9 =15; 1 day work of george is 1/15 ; remaining is 2/5th; paul & george work is 5/2*4=10 ; their 1 day work is 1/10; and only paul work is (1/10)-(1/15)=30 ANSWER:D #### D QUESTION:If r is a positive integer and r^2 is divisible by 12, then the largest positive integer that must divide r ^3 is options: A) 2^3 B) 2^6 C) 3^3 D) 6^3 E) 12^2 SOLUTION:Since r is an integer so r 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 r^2 as a multiple of 12)) r^2 is divisible by 12 (12 = 2*2*3), So, r should have at least one 2 and one 3 so that r^2 has a 2^2 and two 3 So, r will have a 2 and a 3. Or r will be a multiple of 6 So, largest possible integer than should divide r^3 is 6^3 So, Answer will be D #### D QUESTION:A merchant marks his wares 40% more than the real price and allows 20% discount. His profit is: options: A)20% B)18% C)16% D)12% E)None of these SOLUTION:Let the CP = 100 Rs. Mark Price = 140 Discount = 20% Selling price 80/100 × 140 Hence profit = 12% Answer: D. #### D QUESTION:A car moves at 80 km/hr. What is the speed of the car in meters per second ? options: A)20 2/9m sec B)22 2/9m sec C)24 2/9m sec D)26 2/9m sec E)28 2/9m sec SOLUTION:Explanation: Speed=(80∗5/18)m/sec =200/9m/sec =22 2/9msec Option B #### B QUESTION:The difference between the ages of two persons is 10 years. Fifteen years ago, the elder one was twice as old as the younger one. The present age of the elder person is options: A)25 years B)30 years C)35 years D)40 years E)None SOLUTION:Sol. Let their ages of x years and (x + 10) years respectively. Then, (x + 10) - 15 = 2(x - 15) ⇔ x - 5 = 2x - 30 ⇔ x = 25. ∴ Present age of the elder person = (x + 10) = 35 years. Answer C #### C QUESTION:The compound ratio of 2/3, 6/7, 1/3 and 1/8 is given by? options: A)1/45 B)1/42 C)1/46 D)1/48 E)1/43 SOLUTION:2/3 * 6/7 * 1/3 * 1/8 = 1/42 Answer:B #### B QUESTION:A train 360 m long passed a pole in 30 sec. How long will it take to pass a platform 780 m long? options: A)76 sec B)89 sec C)87 sec D)95 sec E)16 sec SOLUTION:Speed = 360/30 = 12 m/sec. Required time = (360 + 780)/12 = 95 sec. Answer:D #### D QUESTION:If 13 = 13w/(1-w) ,then (3w)2 = options: A)1/4 B)1/2 C)1 D)2 E)3 SOLUTION:13-13w=13w 26w=13 w=1/2 3w=3/2 3w*2=3/2*2=3 ANSWER:E #### E QUESTION:How many odd integers X between 200 and 600 are there such that their tens digit is even? options: A)20 B)25 C)100 D)150 E)200 SOLUTION:The hundreds digit can take 4 values: 2, 3, 4 and 5; The tens digit can take 5 values: 0, 2, 4, 6 and 8; The units digit can take 5 values: 1, 3, 5, 7 and 9; Total X: 4*5*5=100. Answer: C. #### C QUESTION:For any integer k > 1, the term “length of an integer” 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 × 2 × 2 × 3. If x and y are positive integers such that x > 1, y > 1, and x + 3y < 920, what is the maximum possible sum of the length of x and the length of y? options: A)14 B)12 C)10 D)16 E)18 SOLUTION:we know that : x > 1, y > 1, and x + 3y < 1000, and it is given that length means no of factors. for any value of x and y, the max no of factors can be obtained only if factor is smallest noall factors are equal. hence, lets start with smallest no 2. 2^1 =2 2^2 =4 2^3=8 2^4=16 2^5=32 2^6=64 2^7=128 2^8=256 2^9=512 2^10 =1024 (it exceeds 920, so, x can't be 2^10) so, max value that X can take is 2^9 , for which has length of integer is 9. now, since x =512 ,x+3y<920 so, 3y<408 ==> y<136 so, y can take any value which is less than 136. and to get the maximum no of factors of smallest integer, we can say y=2^7 for 2^7 has length of integer is 7. SO, combined together : 9+7 = 16. D #### D QUESTION:A farmer spent $33 on feed for chickens and goats. He spent 40% money on chicken feed, which he bought at a 20% discount off the full price, and spent the rest on goat feed, which he bought at full price. If the farmer had paid full price for both the chicken feed and the goat feed, what amount would he have spent on the chicken feed and goat feed combined? options: A)$36.30 B)$38.50 C)$39.20 D)$39.50 E)$40.60 SOLUTION:A farmer spent 40% money on chicken feed, so he spent 0.4*$33=$13.2 on chicken feed, thus he spent the remaining 33-13.2=$19.8 on goat feed. Now, since he bought chicken feed at a 20% discount then the original price of it was x*0.8=$13.2 --> x=$16.5. Therefore if the farmer had paid full price for both the chicken feed and the goat feed, then he would he have spent 16.5+19.8=$36.3. Answer: A #### A QUESTION:The number of students in 3 classes is in the ratio 2:3:4. If 12 students are increased in each class this ratio changes to 8:11:14. The total number of students in the three classes in the beginning was options: A)162 B)108 C)96 D)54 E)None SOLUTION:Solution: Let the number of students in the classes be 2x, 3x and 4x respectively; Total students = 2x+3x+4x = 9x. According to the question, (2x+12)/(3x+12) = 8/11 24x+96 = 22x+132 Or, 2x = 132-96 Or, x = 36/2 = 18 Hence, Original number of students, 9x = 9*18 = 162. Answer: Option A #### A QUESTION:If q and r are even integers, which of the following is an odd integer? options: A)qr + 2 B)q(r − 1) C)q(q + 5) D)3q + 4r E)(q + 3)(r − 1) SOLUTION:If q and r are even integers, then: A. qr + 2: even + even = even B. q(r − 1): even(odd) = even C. q(q + 5): even(odd) = even D. 3q + 4r: even + even = even E. (q + 3)(r − 1): (odd)(odd) = odd. Answer is E. #### E QUESTION:A shopkeeper sells 20% of his stock at 10% profit ans sells the remaining at a loss of 5%. He incurred an overall loss of Rs. 450. Find the total worth of the stock? options: A)20029 B)22500 C)20289 D)20027 E)20026 SOLUTION:Let the total worth of the stock be Rs. x. The SP of 20% of the stock = 1/5 * x * 1.1 = 11x/50 The SP of 80% of the stock = 4/5 * x * 0.95 = 19x/25 = 38x/50 Total SP = 11x/50 + 38x/50 = 49x/50 Overall loss = x - 49x/50 = x/50 x/50 = 450 => x = 22500 Answer: B #### B QUESTION:If the sum of a set of 5 different positive prime numbers is 94, what is the difference between largest and smallest prime numbers between them? options: A)53 B)51 C)47 D)41 E)31 SOLUTION:All prime numbers apart from 2 are odd. Even + Even = Even Odd + Even = Odd Odd + Odd = Even We are given 5 different prime numbers, whose sum is 94 i.e even If we include 2, we will have 4 odd prime numbers and one even. This sum would be odd If we exclude 2, we will have 5 odd numbers. This sum would be even Hence 2 is included. The possible 5 no. are = 11+7+2+43+31 = 94 the difference between largest and smallest prime numbers between them = 43 - 2 = 41 Ans - D #### D QUESTION:A 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 1994. She ended on her options: A)thumb B)the index finger C)the middle finger D)the ring finger E)the little finger SOLUTION:Notice the pattern. The thumb lands up at numbers 1,9,17,25,33,... so every 8th number By this patter the thumb is also at number 1993 (multiple of 8 + 1) Hence 1994 has to be the index finger Answer is B #### B QUESTION:Two cylinders are of the same height. Their radii are in the ratio 1: 3. If the volume of the first cylinder is 40 cc. Find the volume of the second cylinder? options: A)120cc B)360cc C)450cc D)589C E)478cc SOLUTION:Explanation: r1 = x r2 = 3x Π * x2 * h = 40 Π9 x2h = 40 * 9 = 360cc Answer: B #### B QUESTION:If population of certain city increases at the rate of 5%. If population in 1981 was 231525, then population in 1978 was? options: A)120000 B)120029 C)187899 D)178968 E)200000 SOLUTION:X * (105/100) * (105/100) * (105/100) = 231525 X = 231525/1.157625 X = 200000 Answer:E #### E QUESTION:If the rectangular screen of a computer monitor is designed to have a length of x inches, a perimeter of P inches and an area of A square inches, which of these equations must be true? options: A)x^2 + Px + A = 0 B)x^2 - Px - 2A = 0 C)2x^2 + Px + 2A = 0 D)2x^2 - Px - 2A = 0 E)2x^2 - Px + 2A = 0 SOLUTION:Notice that we can discard options A, and C right away. The sum of 3 positive values Cannot be 0. Now, assume: Length =x = 1 inchand width = 1 inch; Perimeter =P = 4 inches; Area =A = 1 square inches. Plug the values of x, P, and A into the answer choices: only for E 2x^2 - Px + 2A = 2 - 4 + 2 = 0. Answer: E. #### E QUESTION:What percent is 400 gm of 1 kg? options: A)25% B)40% C)10% D)8% E)12% SOLUTION:1 kg = 1000 gm 400/1000 × 100 = 40000/1000 =40 % Answer is B #### B QUESTION:A 20 litre mixture of milk and water contains milk and water in the ratio 3 : 2. 10 litres of the mixture is removed and replaced with pure milk and the operation is repeated once more. At the end of the two removal and replacement, what is the ratio E of milk and water in the resultant mixture? options: A)17 : 3 B)9 : 1 C)3 : 17 D)5 : 3 E)11: 2 SOLUTION:he 20 litre mixture contains milk and water in the ratio of 3 : 2. Therefore, there will be 12 litres of milk in the mixture and 8 litres of water in the mixture. Step 1. When 10 litres of the mixture is removed, 6 litres of milk is removed and 4 litres of water is removed. Therefore, there will be 6 litres of milk and 4 litres of water left in the container. It is then replaced with pure milk of 10 litres. Now the container will have 16 litres of milk and 4 litres of water. Step 2. When 10 litres of the new mixture is removed, 8 litres of milk and 2 litres of water is removed. The container will have 8 litres of milk and 2 litres of water in it. Now 10 litres of pure milk is added. Therefore, the container will have 18 litres of milk and 2 litres of water in it at the end of the second step. Therefore, the ratio of milk and water is 18 : 2 or 9 : 1. Shortcut. We are essentially replacing water in the mixture with pure milk. Let W_o be the amount of water in the mixture originally = 8 litres. Let W_r be the amount of water in the mixture after the replacements have taken place. Then,{W_r}/{W_o}= (1-R/M)^n where R is the amount of the mixture replaced by milk in each of the steps, M is the total volume of the mixture and n is the number of times the cycle is repeated. Hence, {W_r}/{W_o} =(1/2)^2  =1/4 Therefore E,W_r ={W_o}/4= 8/4 = 2 litres.B #### B QUESTION:A 120 meter long train crosses a man standing on the platform in 6 sec. What is the speed of the train? options: A)229 B)108 C)278 D)72 E)112 SOLUTION:S = 120/6 * 18/5 = 72 kmph Answer: D #### D QUESTION:A, B and C invested Rs.6600, Rs.4400 and Rs.11000 respectively, in a partnership business. Find the share of A in profit of Rs.12100 after a year? options: A)Rs.3300 B)Rs.3100 C)Rs.3500 D)Rs.4200 E)Rs.3400 SOLUTION:6600:4400:11000 3:2:5 3/10 * 11000 = Rs.3300 AnswerA #### A QUESTION:If a number is exactly divisible by 11 and 13, which of the following types the number must be? options: A)Divisible by (11 + 13) B)Divisible by (13 - 11) C)Divisible by (11 x 13) D)Divisible by (13 ÷ 11) E)None SOLUTION:Answer LCM of 11 and 13 will be (11 x 13). Hence, if a number is exactly divisible by 11 x 13, then the same number must be exactly divisible by their LCM or by (11 x 13). Correct Option: C #### C QUESTION:A 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? options: A)4/8 B)9/2 C)7/6 D)9 E)2/21 SOLUTION:Explanation: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles. Probability that both marbles are blue = ³Câ‚‚/¹⁵Câ‚‚ = (3 * 2)/(15 * 14) = 1/35 Probability that both are yellow = ²Câ‚‚/¹⁵Câ‚‚ = (2 * 1)/(15 * 14) = 1/105 Probability that one blue and other is yellow = (³C₁ * ²C₁)/¹⁵Câ‚‚ = (2 * 3 * 2)/(15 * 14) = 2/35 Required probability = 1/35 + 1/105 + 2/35 = 3/35 + 1/105 = 1/35(3 + 1/3) = 10/(3 * 35) = 2/21 Answer: E #### E QUESTION:A company hired a printer to produce a total of x + 1 envelopes. The job consisted of two types of envelopes, 4¢ envelopes and 5¢ envelopes. If the company requested 3 more 4¢ envelopes than 5¢ envelopes, which of the following expressions denotes the cost, in cents, of the total x + 1 envelopes ? options: A)3x+32 B)5x-1 C)(7x+15)/2 D)(9x-4)/2 E)6x+2 SOLUTION:We can take X+1 = 9 X= 8 So 4c envelopes will be 6 and 5c envelopes will be 3 So total cost will be 39 Then that is our target Plug x =8 in answer choices Only B works Correct Answer : B #### B QUESTION:There are 35 kids in a play school. 26 kids play with white color balls and some kids play with yellow color balls and 19 kids play with both color balls. How many kids use yellow color balls? options: A)12 B)32 C)5 D)28 E)30 SOLUTION:number of kids playing with white color balls = 26 total number of kids in the play school = 35 number of kids playing with both white and yellow color balls = 19 we have to find, number of kids playing with yellow color balls 35 = 26 + n(B) - 19 35 + 19 - 26 = 28 Hence, Answer is 28 kids play with yellow color balls. ANSWER D #### D QUESTION:A team won 40 percent of its first 30 games in a particular season, and 80 percent of its remaining games. If the team won a total of 60 percent of its games that season, what was the total number of games that the team played? options: A)50 B)60 C)70 D)80 E)90 SOLUTION:60% is 20%-points above 40% and 20%-points below 80%. Thus the ratio of "the first 30 games" to "remaining games" is 1:1. So the team played a total of 30+30 = 60 games. The answer is B. #### B QUESTION:A 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? options: A)2km/hr B)3km/hr C)5km/hr D)7km/hr E)10km/hr SOLUTION:Time required = 5 hrs- 1hr = 4hr Required speed = 100/4 = 25km/hr Original speed = 100/5 = 20 km/hr Difference = 25-20 = 5 km/hr Answer is C #### C QUESTION:Weights of two friends Ram and Shyam are in the ratio 2:5. 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? options: A)17% B)10% C)21% D)16% E)None SOLUTION:Solution: given ratio of Ram and Shayam's weight = 2:5 Hence, (x-15)/(15-10) = 2/5 Or, x = 17%. Answer: Option A #### A QUESTION:In a garment industry, 12 men working 8 hours per day complete a piece of work in 10 days. To complete the same work in 8 days, working 20 hours a day, the number of men required is: options: A)4 B)5 C)6 D)8 E)9 SOLUTION:Explanation : Let the required number of men be x. Less days, More men (Indirect Proportion) More working hrs per day, Less men (Indirect Proportion) Days 8 : 10 Working Hrs 20 : 8 :: 12 : x => 8 x 20 x x = 10 x 8 x 12 => x = 10 x 8 x 12 / (8 x 20) => x = 6 Answer : C #### C QUESTION:How many four letter words are formed using the letters of the word POLICE? options: A)280 B)321 C)330 D)360 E)370 SOLUTION:The number of letters in the given word is four. The number of three letter words that can be formed using these four letters is 6P4 = 6 * 5 * 4 * 3 = 360. Answer: D #### D QUESTION:A 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 + 5 games? options: A)x + 3y/(n + 3) B)x + y/(n + 3) C)(x + 3y)/(n + 3) D)(nx + 3y)/(n + 5) E)(3x + ny)/(n + 3) SOLUTION:Total points in first n games = nx Total marks in next 3 games is 3y So, Average marks in n + 5 games = (nx+3y)/(n+5) Hence, correct answer will be (D) #### D <<<Examples ends QUESTION:How many seconds does a train 110 meters long, traveling at 54 km/h, take to completely cross a bridge of 160 meters in length? options: A)18 B)20 C)22 D)24 E)26 SOLUTION:54 km/h = 54000/3600 = 15 m/s Time = 270 / 15 = 18 seconds The answer is A. #### A

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:If k^2 = h^2, which of the following must be true? options: A)k = m B)|k| = |h| C)k = |m| D)k = -|m| E)k = -m SOLUTION:Solution: We are given that k^2 = h^2, and we can start by simplifying the equation by taking the square root of both sides. √k^2 = √h^2 When we take the square root of a variable squared, the result is the absolute value of that variable. Thus: √k^2 = √h^2 is |k| = |h| Note 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. Answer: E #### E QUESTION:The number of defects in the first five cars to come through a new production line are 9, 7, 10, 4, and 8, respectively. If the sixth car through the production line has either 3, 7, or 12 defects, for which of theses values does the mean number of defects per car for the first six cars equal the median? I. 3 II. 7 III. 12 options: A)I only B)II only C)III only D)I and III only E)I, II, and III SOLUTION:C for 7 we will have mean as 7.16(approx) and median as 7 but for 3 we will have mean and median = 6.5 and for 12 we will have median and mean =8 #### C QUESTION:Find the circumference and area of radius 13 cm. options: A)124 cm² B)531 cm² C)354 cm² D)584 cm² E)594 cm² SOLUTION:Area of circle = πr² = 22/7 × 13 × 13 cm² = 531 cm² ANSWER:B #### B QUESTION:Because of weight limits, a lorry can carry a maximum of 20 crates of apples. The weight of a crate of oranges is 3434 the weight of a crate of apples. If 10 crates of apples were loaded into the lorry, what is the maximum number of crates of oranges that the lorry can still accommodate? options: A)8 B)9 C)12 D)13 E)14 SOLUTION:There's still room for 10 crates of apples. The weight of 10 crates of apples is the same as the weight of 10∗(4/3)=13 1/3 crates of oranges. Because the number of crates has to be an integer, the lorry can accommodate a maximum of 13 crates of oranges. Answer: D #### D QUESTION:A 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, 70 percent of books that were loaned out are returned and there are 63 books in the special collection at that time, how many books of the special collection were loaned out during that month? options: A)20 B)30 C)35 D)40 E)55 SOLUTION:I didn't understand How did we get 100? Total = 75 books. 65% of books that were loaned out are returned --> 100%-70%=30% of books that were loaned out are NOT returned. Now, there are 63 books, thus 76-63=12 books are NOT returned. {loaned out}*0.30=7 --> {loaned out}=40. Answer: D. #### D QUESTION:If f(x)=x^2 and x is a positive integer, which of the following will not be the value of f(f(x))? options: A)1 B)16 C)81 D)256 E)144 SOLUTION:f(x)=x^2 f(f(x)) = (x^2)^2 =x^4 A. 1 , x=1 B. 16 , x=2 C. 81 , x=3 E. 144 f(x)=12 Square root of 12 is not a positive integer . Hence 144 can not be the value of f(f(x)) . D. 256 , x=4 Answer E #### E QUESTION:864.942 - ? + 45.76 = 547.905 options: A)A)899.015 B)B)752.804 C)C)714.642 D)D)362.797 E)of these SOLUTION:Explanation: 362.797 Answer: Option D #### D QUESTION:A bat is bought for Rs.200 and sold at a gain of 20% find its selling price options: A)A)Rs.460/- B)B)Rs.270/- C)C)Rs.280/- D)D)Rs.240/- E)E)Rs.520/- SOLUTION:100 % ------> 200 (100 * 2 = 200) 120 % ------> 240 (120 * 2 = 240) Selling price = Rs.240/- Answer : D #### D QUESTION:A man swims downstream 72 km and upstream 45 km taking 9 hours each time; what is the speed of the current? options: A)1.9 B)1.5 C)1.2 D)1.6 E)1.1 SOLUTION:72 --- 9 DS = 8 ? ---- 1 45 ---- 9 US = 5 ? ---- 1 S = ? S = (8 - 5)/2 = 1.5 Answer:B #### B QUESTION:A trader has 50 kg of pulses, part of which he sells at 8 per cent profit and the rest at 18 per cent profii. He gains 14 per cent on the whole. What is the quantity sold at 18 per cent profit? options: A)30 kg B)25 kg C)20 kg D)40 kg E)none of these SOLUTION:Ratio of quantities sold at 8% profit and 18% profit =>4:6 = 2:3 Therefore,the quantity sold at 18% profit =>50/(2 + 3) x 3 =>30 kg ANSWER:A #### A QUESTION:A is twice as good a work man as B and together they finish the work in 14 days. In how many days A alone can finish the work? options: A)5 days B)21 days C)15 days D)25 days E)30 days SOLUTION:Explanation: WC = 2:1 2x + x = 1/14 => x = 1/42 2x = 1/21 A can do the work in 21 days. Answer: B #### B QUESTION:If k is the sum of the digits of integer m, and m=12n, where n is an integer, which of the following must be true? options: A)k is not divisible by 9 B)The sum of the digits of k is divisible by 3 C)m is a multiple of 2k D)k is a multiple of 9 E)k is a multiple of 6 SOLUTION:m= 12n i.e n =1,2,3 ,4 etc or -1,-2.-3 ,-4 then m =12,24,36,48 or -12 ,-24 ,-36 ,-48 then k 3,6 9,12 or -(1+2) , -(4+2) , -(3+6) ,-(4+8) . ans B #### B QUESTION:A solution of 60 ounces of sugar and water is 20% sugar. How much water must be added to make a solution that is 5% sugar? options: A)20 ounces B)80 ounces C)100 ounces D)120 ounces E)180 ounces SOLUTION:20% sugar in 60 oz solution; Sugar = 60*20/100 = 12 oz Water = 60-12 = 48 oz Now; let's add "x" oz of water in the solution; Total solution = 60+x oz Sugar = 12 oz.(Sugar's amount will not change as we are not adding or subtracting sugar) 12 = (60+x) * 5/100 60+x = 240 x = 240 - 60 = 180 oz Answer: "E" #### E QUESTION:Mice can multiply very fast. Adult mice can give birth once every month, and baby mice grow into adult mice in just two months after they are born. If you would buy a baby mouse just after it was born, how many mice would you have in 10 months? options: A)1 B)2 C)3 D)4 E)5 SOLUTION:One. You cannot have more mice if you start with one! Answer A #### A QUESTION:Find the value of 72515 x 9999 = m? options: A)345434667 B)246465757 C)465767867 D)725077485 E)645354643 SOLUTION:72515 x 9999 = 72515 x (10000 - 1) = 72515 x 10000 - 72515 x 1 = 725150000 - 72515 = 725077485 D #### D QUESTION:A, 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? options: A)3:4:8 B)3:4:7 C)3:4:5 D)3:4:1 E)3:4:0 SOLUTION:A:B:C = (40000 * 36) : (80000 * 12 + 40000 * 24) : (120000 * 24 + 40000 * 12) = 144:192:336 = 3:4:7 Answer: B #### B QUESTION:A bookseller has two display windows. She plans to display 5 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? options: A)24 B)72 C)720 D)336 E)420 SOLUTION:The left window will have permutations of the 5 fiction books, so the number of possibilities for that window is permutations = 5! = (5)(4)(3)(2)(1) = 120 The right window will have permutations of the 3 non-fiction books, so the number of possibilities for that window is permutations = 3! = (3)(2)(1) = 6 Any 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 120*6 = 720 Answer: C. #### C QUESTION:The average (arithmetic mean) of 24, 35, and 58 is 6 more than the average of 19, 51, and x. What is x? options: A)26 B)27 C)28 D)29 E)30 SOLUTION:The average of 24, 35, and 58 is 39. The average of 19, 51 and x is 33. Then 19 + 51 + x = 99. x = 29. The answer is D. #### D QUESTION:In 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. options: A)144 B)24 C)576 D)48 E)16 SOLUTION:4 black chess pieces can be arranged in 4! ways and 4 white pieces can be arranged in 4! ways. W_W_W_W Number of ways = 4!*4! = 24 * 24 = 576 Answer C #### C QUESTION:A boat having a length 8 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: options: A)12 kg B)60 kg C)72 kg D)160 kg E)None of these SOLUTION:Explanation: Volume of water displaced = (8 x 2 x 0.01) m3 = 0.16 m3. ∴ Mass of man = Volume of Water displaced x Density of water = (0.16 x 1000)kg = 160 kg. Answer: D #### D QUESTION:The percentage profit earned by selling an article for $1920 is equal to the percentage loss incurred by selling the same article for $1280. At what price should the article be sold to make 25% profit? options: A)$3000 B)$1000 C)$2000 D)$5000 E)$6000 SOLUTION:C $2000 Let C.P. be $x. Then, (1920 - x)/x * 100 = (x - 1280)/x * 100 1920 - x = x - 1280 2x = 3200 => x = 1600 Required S.P. = 125 % of $1600 = 125/100 * 1600 = $2000. #### C QUESTION:A hiker 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 at 1 mile faster than 2nd day for same hours. How many miles in total did she walk? options: A)63 B)44 C)58 D)60 E)62 SOLUTION:First day - 18 miles with 3 miles per hours then total - 6 hours for that day Second day - 4 miles per hour and 5 hours - 20 miles Third day - 5 miles per hour and 5 hours - 25 miles Total 18+20+25 = 63 Answer: option A. #### A QUESTION:Look at this series: 14, 28, 20, 40, 32, 64, ... What number should come next? options: A)52 B)56 C)96 D)128 E)None SOLUTION:Explanation: This is an alternating multiplication and subtracting series: First, multiply by 2 and then subtract 8. Answer: Option B #### B QUESTION:A shopkeeper buys mangoes at the rate of 5 a rupee and sells them at 3 a rupee. Find his net profit or loss percent? options: A)66 2/3 % B)33 7/3 % C)33 1/3 % D)33 5/8 % E)34 1/3 % SOLUTION:The total number of mangoes bought by the shopkeeper be 15. If he buys 5 a rupee, his CP = 3 He selling at 3 a rupee, his SP = 5 Profit = SP - CP = 5 - 3 = 2 Profit Percent = 2/3 * 100 = 66 2/3 % Answer: A #### A QUESTION:For any 5 given numbers, which of the following is always equivalent to adding the 3 numbers together and then dividing the sum by 3? I. Ordering the 3 numbers numerically, from highest to lowest, and then selecting the middle number. II. Dividing each of the numbers by 3 and then adding the results together. III. Multiplying each number by 6, adding the resulting products together, and then dividing the sum by 9. options: A)I only B)II only C)I and II only D)II and III only E)None of the above SOLUTION:Let the 3 numbers be x, y and z. Question: Which of the following is equivalent to (x + y + z)/3 I. Ordering the 3 numbers numerically, from highest to lowest, and then selecting the middle number. --> Not always equivalent Eg: 111 and 141 II. Dividing each of the numbers by 3 and then adding the results together. --> x/3 + y/3 + z/3 = (x + y + z)/3 --> Equivalent III. Multiplying each number by 6, adding the resulting products together, and then dividing the sum by 9. --> (6x + 6y + 6z)/9 = 2(x + y + z)/3 --> Not equivalent Answer: C #### C QUESTION:A can run 3 Kms in 3 min 18 sec and B can run same distance in 3 min 40 sec, then by how much distance A can beat B? options: A)300 m B)220 m C)280 m D)195 m E)295 m SOLUTION:Distance travelled=3000m Time taken by A=3 m 18 s Time taken by B=3 m 40 sec=220 sec speed of B=3000m/220 s=150/11 m/s Difference between time of A and B=22 sec when time will be 3 m 18 s A will have travelled 3000m but B need 22 sec more to finish. Distance travelled by B in 22 sec=(150/11)*22=300 m Hence, A beat B by 300 m ANSWER:A #### A QUESTION:8^100 is divisible by 17. Find the remainder? options: A)10 B)12 C)16 D)18 E)20 SOLUTION:This 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. So divide 100 by 16 and find the remainder. Remainder = 4 Therefore, 100 = (16 × 6) + 4 Now this problem can be written as 810017 = 816×6+417 = (816)6×8417 Now this problem simply boils down to (1)6×8417 = 8417 84 = 82×82, we need to find the remainder when 64 × 64 is divisible by 17. Or 13 × 13 = 169. When 169 is divided by 17, remainder is 16. C #### C QUESTION:If C.P. of 28 books is equal to S.P of 30 books , then your gain or loss is ? options: A)23 1/3 gain % B)30 10/23 loss % C)6.67 loss % D)30 1/3 loss % E)40 1/3 loss % SOLUTION:Say the cost price of 28 books is $28 so $1 for a book. The cost of 30 books would be $30, and the selling price of 30 books would be 28$, hence the loss = ($30 - $28)/$30 = ~6.67%. Answer: C. #### C QUESTION:8 chess players take part in a tournament. Every player plays twice with each of his opponents. How many games are to be played? options: A)66 B)52 C)58 D)55 E)56 SOLUTION:Though 2*(8C2) 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. The first guy has to play 2 matches with the rest of 7, so he'll play 14 matches. Similarly, second guy has to play with the rest of 6 as his 2 games with the first guy are already played. So he plays 12 matches. This continues like this and the total matches are 14+12+10...+2 14+12+...+2 = 2(7+6+...+1) = 2((7*8)/2) = 7*8 =56. ANSWER:E #### E QUESTION:On flipping 3 coins together what is the outcomes for exactly one head and one tail? options: A){HHH, HTH, THH, TTH, THT, HTT} B){HHT, HTH, THH, TTH, THT, TTT} C){HHT, HTH, THH, TTH, THT, HTT} D){HHT, HTH, THH, TTH, THT, TTT} E)None SOLUTION:Sample space, S = {HHH, HHT, HTH, THH, TTH, THT, HTT, TTT} Favorable outcomes for at least two heads = favorable outcomes for one head and one tail and favorable outcomes for more than one head and one tail. = {HHT, HTH, THH, TTH, THT, HTT} C #### C QUESTION:The 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? options: A)3 dm B)4 dm C)5 dm D)6 dm E)7 dm SOLUTION:33 + 43 + 53 = a3 => a = 6 ANSWER:D #### D QUESTION:factor: 3y (x-3)-2(x-3) options: A)(x-3)-2(x-3) B)(x-3)power2 C)(x-3)(3y-2) D)3y(x-3) E)x-3 SOLUTION:3y(x-3)-2(x-3), = (x-3)(3y-2). Answer: (C) #### C QUESTION:HOW 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 10% options: A)36 B)40 C)32 D)42 E)45 SOLUTION:Let the weight of tea(25 per kg) to be used - X The total cost of the blend - total cost of 25 RS tea + total cost of 30 RS tea - 25X + 900 ( as the total weight of 30 RS tea is already given i.e 30) total weight of the blend = X + 30 ( which should be sold per 30 RS and result in 10% profit) The equation follows like this 25X + 900 + (10 % of (25X + 900)) = 30( X + 30) 25X + 900 +2.5 X + 90 = 30 X + 900 27.5 X + 990 = 30 X + 900 2.5 X = 90 X= 90/2.5 = 36 ANSWER:A #### A QUESTION:In 10 years, A will be twice as old as B was 10 years ago. If A is now 6 years older than B the present age of B is options: A)37 B)36 C)39 D)40 E)41 SOLUTION:let present age of A be a and B be b a+10 = 2*(b-10) => 2b-a = 30 ......(i) a = b+6 =>2b-b-6 = 30 b=36 so the present age of b is 36 years ANSWER:B #### B QUESTION:A 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 45 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? options: A)40 B)45 C)50 D)55 E)60 SOLUTION:A- B = 120 Miles B - C = 60 Miles Avg Speed = 45 Miles Time taken for A-B 3t and B-C be t avg speed = (120+60) / Total time 45 = 180/4t t = 60 B-C = 60 mph Answer E #### E QUESTION:P is three times as fast as Q and working together, they can complete a work in 12 days. In how many days can Q alone complete the work? options: A)11 days B)16 days C)13 days D)15 days E)19 days SOLUTION:B 16 days P = 3Q P + Q = 3Q + Q = 4Q These 4Q people can do the work in 12 days, which means Q can do the work in 48 days. Hence, P can do the work in 16 days. #### B QUESTION:In how many ways can the letters of the word REPORT be arranged? options: A)1206 B)360 C)2520 D)3000 E)3478 SOLUTION:REPORT has 6 words, but R is repeated two times. Thus ways = 6! / 2! = 360 ways B #### B QUESTION:Zachary is helping his younger brother, Sterling, learn his multiplication tables. For every question that Sterling answers correctly, Zachary gives him 3 pieces of candy. For every question that Sterling answers incorrectly, Zachary takes away two pieces of candy. After 6 questions, if Sterling had answered 2 more questions correctly, he would have earned 31 pieces of candy. How many of the 6 questions did Zachary answer correctly? options: A)6 B)7 C)8 D)9 E)10 SOLUTION:i got two equations: 3x-2y=25 x+y=6 3x-2(6-x)=25 3x-12+2x=25 5x=37 x=7.4 or between 7 and 8. (ANS B) #### B QUESTION:If a and b are positive integers of C such that a/b=2.86, which of the following must be a divisor of a? options: A)10 B)B.13 C)18 D)26 E)50 SOLUTION:The prompt gives us a couple of facts to work with: 1) A and B are positive INTEGERS 2) A/B = 2.86 We 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). The simplest place to start is with... A = 286 B = 100 286/100 = 2.86 These values are NOT the smallest possible values though (since they're both even, we can divide both by 2)... A = 143 B = 50 143/50 = 2.86 There 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.... Since 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. Final Answer: B #### B QUESTION:The cost price of an article is 70% of the marked price. Calculate the gain percent after allowing a discount of 10%. options: A)13.6% B)28.6% C)35.6% D)42.3% E)none SOLUTION:Sol. Let marked price = Rs. 100. Then, C.P. = Rs. 70. S.P = Rs. 90. ∴ Gain % = [20/70 * 100]% = 28.6%. Answer B #### B QUESTION:The 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 10%. By approximately what percent would the output of the factory now have to be decreased in order to restore the original output? options: A)17% B)24% C)30% D)32% E)79% SOLUTION:take it as original output =100. to meet demand increase by 10%, then output=110. to meet holiday demand , new output increase by 10% then output equals 121 To restore new holidy demand output to original 100. final -initial/final*100 =21/121*100=8/33*100=17% approxiamately. option A is correct. #### A QUESTION:A milk man has 30 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: options: A)20% B)25% C)33.33% D)35% E)None of these SOLUTION:Explanation: when 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 30 liters of milk. Therefore, profit percentage = 35 %. Answer: D #### D QUESTION:If a(a + 5) = 6 and b(b + 5) = 6, where a ≠ b, then a + b = options: A) −5 B) −2 C) 2 D) 46 E) 48 SOLUTION:a(a + 5) = 6 and b(b + 5) = 6 => a, b must be integers and if a is -6 or 1, b will be 1 and -6 respectively => a+b = -5 Ans: A #### A QUESTION:A 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 : options: A)16000 B)18000 C)20000 D)30000 E)None of these SOLUTION:Explanation: Number of bricks =Courtyard area /1 brick area =(1800×1200 /12×6)=30000 Option D #### D QUESTION:Six consecutive traffic signals each show either red or green. How many different arrangements of the six signals are possible? options: A)90 B)79 C)64 D)57 E)36 SOLUTION:Since 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. We're told that 6 consecutive traffic signals each show either red or green. We're asked how many different arrangements of the 6 signals are possible. Total Options: 64 Final Answer: C #### C QUESTION:All the milk in container A which was filled to its brim was poured into two containers B and C. The quantity of milk in container B was 62.5% less than the capacity of container A. If 150 liters was now transferred from C to B, then both the containers would have equal quantities of milk. What was the initial quantity of milk in container A? options: A)1200 B)1723 C)1129 D)2613 E)1372 SOLUTION:A B has 62.5% or (5/8) of the milk in A. Therefore, let the quantity of milk in container A(initially) be 8k. Quantity of milk in B = 8k - 5k = 3k. Quantity of milk in container C = 8k - 3k = 5k Container: A B C Quantity of milk: 8k 3k 5k It is given that if 150 liters was transferred from container C to container B, then both the containers would have equal quantities of milk. 5k - 150= 3k + 150 => 2k = 300 => k = 150 The initial quantity of milk in A = 8k = 8 * 150= 1200 liters. #### A QUESTION:There are 10 fictions and 6 non-fictions. How many cases are there such that 2 fictions and 2 non-fictions are selected from them? options: A)90 B)120 C)675 D)180 E)200 SOLUTION:Number of ways of selecting 2 fiction books = 10C2 Number of ways of selecting 2 non fiction books = 6C2 10C2 * 6C2 = 45 * 15 = 675 Answer: C #### C QUESTION:In 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 150? options: A)15 B)75 C)25 D)18 E)12 SOLUTION:A scores 60 while B score 40 and C scores 30. The number of points that C scores when B scores 100 = (100 * 30)/40 = 25 * 3 = 75. In a game of 100 points, B gives (150 - 75) = 75 points to C. Answer:B #### B QUESTION:P is three times as fast as Q and working together, they can complete a work in 12 days. In how many days can Q alone complete the work? options: A)16 B)77 C)88 D)55 E)778 SOLUTION:P = 3Q P + Q = 3Q + Q = 4Q These 4Q people can do the work in 12 days, which means Q can do the work in 48 days. Hence, P can do the work in 16 days. Answer:A #### A QUESTION:Pump 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). options: A)2 hours 2 minutes B)3 hours 5 minutes C)4 hours 6minutes D)5 hours 7 minutes E)7 hours 9 minutes SOLUTION:In 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 1/5 + 1/8 = 13 / 40 of a tank Since 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 (13/40) t = 1 t = 40 / 13 = 39/13 + 1/13 hours = 3 hours and (1/13)*60 minutes = 3 hours 5 minutes (rounded to the nearest minute) correct answer B #### B QUESTION:What is the sum of the different positive prime factors of 960? options: A)5 B)10 C)15 D)17 E)21 SOLUTION:Prime factorization of 960 =96 * 10 =16*6 * 10 =4*4 * 2*3 * 2*5 =2*2 * 2*2 * 2* 3 * 2*5 =2^6 * 3 * 5 Sum of the different positive prime factors of 960 = 2+3+5 =10 Answer B #### B QUESTION:In a certain city, 60% of the registered voters are democrats and the rest are republicans.In a mayoral race, if 70% 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? options: A)a) 50% B)b) 53% C)c) 54% D)d) 55% E)e) 57% SOLUTION:Let total voters = 100 so D= 60, vote for the mayor 60*75%=45 (60*3/4) R= 40, vote for the mayor 40*20%= (40*1/5) 45+8=53 53/100*100=55% D #### D QUESTION:If A and B are two prime numbers bigger than 2, which of the following can't be true? (1) A + B is an even number. (2) A - B is also a Even number. (3) A^B is also a prime number. options: A)1 only. B)2 only. C)3 only. D)2 and 3 only. E)1, 2 and 3. SOLUTION:Answer is D : 2 and 3 only (1) A + B is an even number. : All primes beyond 2 are odd, so odd+odd = even, so true (2) A - B is also a Even number. : True (3) A^B is also a prime number. : Beats the property of primes, so false Ans : C #### C QUESTION:What is the average of first 21 multiples of 7 ? options: A)49 B)77 C)66 D)57 E)50 SOLUTION:Required average = 7(1+2+....+21) / 21 (7/21)X ( (21x22) / 2 ) (because sum of first 21 natural numbers) = 77 ANSWER IS B #### B QUESTION:The forth proportional to 1,2,3 is? options: A)2 B)4 C)8 D)9 E)6 SOLUTION:Let the fourth proportional to 1,2,3 be x then 1:2::3:x 1x = 2*3 x = 6 Answer is E #### E QUESTION:A reward of $1400 was divided among a group of 36 rescue workers such that each male in the group received $50. How much did each of the 16 females receive? options: A)$10 B)$12.50 C)$25 D)$37.50 E)$50 SOLUTION:x = amount each female received amount each male received = 50 number of females = 16 number of males = 36 - 16 = 20 total to males = 20(50) = 1000 total to females = 16x reward = total to males + total to females 1400 = 1000 + 16x 1400 - 1000 = 16x 400 = 16x 25 = x Answer: C #### C QUESTION:If 0.75: x :: 5:12, then x is equal to: options: A)1.12 B)1.16 C)1.8 D)1.3 E)None of these SOLUTION:Explanation: (x * 5) = (0.75 *12) X=9/5 = 1.80 Answer: C #### C QUESTION:How 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? options: A)482 B)725 C)992 D)837 E)923 SOLUTION:20000(11/10)4 - 20000(6/5)2 = 482 Answer:A #### A QUESTION:The H.C.F of two numbers is 23 and the other two factors of their L.C.M are 13 and 14. The larger of the two numbers is: options: A)276 B)299 C)322 D)345 E)355 SOLUTION:Clearly, the numbers are (23 * 13) and (23 * 14). Larger number = (23 * 14) = 322. ANSWER:C #### C QUESTION:The 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 ? options: A)3600 B)3890 C)88798 D)2789 E)2891 SOLUTION:Explanation: Manager's monthly salary Rs. (1600 * 21 - 1500 * 20) = Rs. 3600. Answer: A) 3600 #### A QUESTION:If 4a = 16b and 9b = 14c, Find a:b:c? options: A)52:13:7 B)13:7:52 C)7:13:52 D)64:14:9 E)None of these SOLUTION:Explanation: (4a = 16b ==> a/b = 16/4) and (9b = 14c ==> b/c = 14/9) ==> a:b = 16:4 and b:c = 14:9 a:b:c = 64:14:9 Answer: Option D #### D QUESTION:2 chairs and 1 table cost $110. 4 chairs and 1 table cost $166. How much does one chair cost? options: A)26 B)56 C)110 D)28 E)54 SOLUTION:Let the cost of 1 chair = x, let the cost of 1 table = y 2x + y = 110 y = 110 - 2x Again, 4x + y = 166 4x + (110 - 2x) = 166 4x + 110 - 2x = 166 2x + 110 = 166 2x = 56 x = 28 Answer: D #### D QUESTION:Due to construction, the speed limit along an 5-mile section of highway is reduced from 60 miles per hour to 40 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 ? options: A)A) 3.12 B)B) 2.5 C)C) 10 D)D) 15 E)E) 24 SOLUTION:Old time in minutes to cross 5 miles stretch = 5*60/60 = 5*1/1 = 5 New time in minutes to cross 5 miles stretch = 5*60/40 = 5*3/2 = 7.5 Time difference = 2.5 Ans:B #### B QUESTION:A man can swim in still water at 4.5 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is? options: A)1.7 B)1.4 C)1.1 D)1.5 E)1.9 SOLUTION:M = 4.5 S = x DS = 4.5 + x US = 4.5 + x 4.5 + x = (4.5 - x)2 4.5 + x = 9 -2x 3x = 4.5 x = 1.5 Answer:D #### D <<<Examples ends QUESTION:4 professors and 6 students are being considered for membership on a supervisory committee which must consist of 3 people. If the committee has to include at least 2 professor, how many ways can this committee be formed? options: A)36 B)64 C)72 D)80 E)100 SOLUTION:you count up combinations twice. 4*9*8... and let me name 6 with students A,B,C,..,F after choosing a professor, when you choose Student A and B, you can choose A first, then B. Or B first, then A. Both combination are same. I don't think that's the only mistake. 64 is a factor of = 2^2*4^2 144 is a factor of = 2^4*3^2. These are very different numbers and you cannot divide 144 with something to get to 64. #### B

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:Difference between a two-digit number and the number obtained by interchanging the two digits is 36, what is the difference between two numbers options: A)2 B)4 C)8 D)12 E)14 SOLUTION:Explanation: Let the ten digit be x, unit digit is y. Then (10x + y) - (10y + x) = 36 => 9x - 9y = 36 => x - y = 4. Option B #### B QUESTION:A person crosses a 600 m long street in 5 minutes. What is his speed in km per hour? options: A)7.9 B)7.3 C)7.8 D)7.2 E)7.1 SOLUTION:distance = 600 meter time = 5 minutes = 5 x 60 seconds = 300 seconds Speed = distancetime=600300=2m/s=2×185 km/hr=365 km/hr=7.2 km/hr Answer :D #### D QUESTION:The ratio between a two-digit number and the sum of the digits of that number is 4 : 1.If the digit in the unit's place is 3 more than the digit in the ten’s place, what is the number? options: A)47 B)36 C)58 D)25 E)14 SOLUTION:Let the ten's digit be x. Then, unit's digit = (x + 3). Sum of the digits = x + (x + 3) = 2x + 3. Number = l0x + (x + 3) = llx + 3. 11x+3 / 2x + 3 = 4 / 1 => 11x + 3 = 4 (2x + 3) => 3x = 9 => x = 3. Hence, required number = 11x + 3 = 36. Answer is B. #### B QUESTION:Rs.8000 become Rs.9261 in a certain interval of time at the rate of 5% per annum of C.I. Find the time? options: A)4 B)6 C)2 D)3 E)8 SOLUTION:9261 = 8000(21/20)N (21/20)3 = (21/20)N => N = 3 ANSWER D #### D QUESTION:How much water must be added to a 30 quarts of a 75% acid solution to reduce it to a 15% solution of acid? options: A)120 qts B)220 qts C)320 qts D)420 qts E)520 qts SOLUTION:I’m adding water, so we have WATER + WATER = WATER Starting off with 30 quarts and adding x quarts, we should end up with (30 + x) quarts 30 + x = (30 + x) The problem describes the solution in terms of acid, we have set it up in terms of water. So, we have to change the percentages and put them in the problem. .25(30) + x = .85(30 + x) Again, we multiply both sides of the equation by 100 to get rid of the decimal point. 25(30) + 100x = 85(30 + x) 750 + 100x = 2550 + 85x 15x = 1800 x = 120 qts correct answer A #### A QUESTION:In a 8 x 8 chess board what is the total number of squares. options: A)238 B)204 C)678 D)169 E)161 SOLUTION:Ans: The total number of squares in a n x n chess board is equal to "the sum of first n natural number squares" i.e., n(n+1)(2n+1)6n(n+1)(2n+1)6 So Substituting 8 in the above formula we get 204 Answer:B #### B QUESTION:How 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. options: A)1875 B)2000 C)2375 D)2500 E)3875 SOLUTION:Number of combo with 4 as first digit + Number of combos with 4 as second digit = 1*4*5*5*5 + 3*5*5*5 = 2375 ANSWER:C #### C QUESTION:a, b, c and d are four consecutive numbers. If the sum of a and dis 111, what is the product of b and c? options: A)2652 B)2578 C)2534 D)3080 E)4234 SOLUTION:Here d = a + 3 a + a + 3 = 111 2a = 108 a = 54 So, numbers are 54, 55, 56 and 57 ∴ b × c= 55 × 56 = 3080 D #### D QUESTION:If -5 < x < 7 and -6 < y < 3, which of the following specifies all the possible values of xy? options: A)-42 < xy < 30 B)-42 < xy < 24 C)-28 < xy < 18 D)-24 < xy < 21 E)-24 < xy < 24 SOLUTION:The 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. Therefore -42 < xy < 30. Answer: A. #### A QUESTION:A dishonest milkman wants to make a profit on the selling of milk. He would like to mix water (costing nothing) with milk costing Rs.46 per litre so as to make a profit of 20% on cost when he sells the resulting milk and water mixture for Rs.54 In what ratio should he mix the water and milk? options: A)1:20 B)1:10 C)1:8 D)1:45 E)6:11 SOLUTION:water = w (liter) Milk = m (liter) ==> Cost = Price x Quantity = 0.46m ==> Revenue = Price x Quantity = 0.54(m + w) ==> Profit =0.54(m+w) - 0.46m = 0.2*(0.46m)[20% of cost] ==> 0.54m + 0.54w - 0.46m = 0.092m ==> 0.012m = 0.54w ==> m/w = 0.54/0.012 = 45 --OR-- w/m = 1/45 D is correct. #### D QUESTION:f, 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? options: A) 20 B) 19 C) 18 D) 16 E) 15 SOLUTION:When 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. b + d cannot be 15, hence E is the answer. #### E QUESTION:If A:B:C = 2:3:4, then find AB:BC:CA options: A)5:9:24 B)6:9:24 C)7:9:24 D)8:9:24 E)None of these SOLUTION:Explanation: Let A = 2x, B = 3x, C = 4x, then, AB=2x3x=23BC=3x4x=34CA=4x2x=21=>AB:BC:CA=23:34:21=8:9:24 Answer: D #### D QUESTION:A certain list has an average of 6 and a standard deviation of B (B is positive). Which of the following pairs of data when added to the list, must result in a list of 102 data with standard deviation less than B? options: A)(-6;0) B)(0;0) C)(0;6) D)(0;12) E)(6;6) SOLUTION:Standard deviation shows how much variation there is from the mean. A low standard deviation indicates that the data points tend to be very close to the mean, whereas high standard deviation indicates that the data are spread out over a large range of values. So when we add numbers, which are far from the mean we are stretching the set making SD bigger and when we add numbers which are close to the mean we are shrinking the set making SD smaller. According to the above adding two numbers which are closest to the mean will shrink the set most, thus decreasing SD by the greatest amount. Closest to the mean are 6 and 6 (actually these numbers equal to the mean) thus adding them will definitely shrink the set, thus decreasing SD. E) #### E QUESTION:The average temperature for Wednesday, Thursday and Friday was 40oC. The average for Thursday, Friday and Saturday was 41oC. If temperature on Saturday was 42oC, what was the temperature on Wednesday? options: A)39oC B)44oC C)38oC D)41oC E)None SOLUTION:Solution: Average temperature for Wednesday, Thursday and Friday = 40oC Total temperature = 3*40 = 120oC Average temperature for Thursday, Friday and Saturday = 41oC Total temperature = 41*3 = 123oC Temperature on Saturday = 42oC Now, (Thursday + Friday + Saturday) - (Wednesday + Thursday + Friday) = 123-120; Saturday - Wednesday = 3 Wednesday = 42-3 = 39oC. Answer: Option A #### A QUESTION:For my anniversary, I decided to surprise my wife. Since she is a voracious reader, I decided to collect a lot of books for her. On the first day of the month, I bought one book, on the second, I bought two and on the third, I bought three. This process went on till the anniversary and on the day, I had 190 books with me to gift her. Can you calculate, on which day is our anniversary? options: A)31 B)28 C)19 D)33 E)25 SOLUTION:C 19rd day 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 + 14 + 15 + 16 + 17 + 18 + 19 = 190 Thus our anniversary falls on the 19rd day of the month. You can apply other formulas to shorten the process but that is the simplest way to do it. #### C QUESTION:Solution Y is 30 percent liquid X and 70 percent water. If 2 kilograms of water evaporate from 8 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? options: A)30% B)33 1/3% C)37 1/2% D)40% E)50% SOLUTION:Initial solution => 8 kg (x:w :: 2.4:5.6) After evaporation Initial solution => 6 kg (x:w:: 2.4:3.6) New solution => 2 kg (x:w::0.6:1.4) Mixing (Initial solution + New solution) => 6 kg (2.4:3.6)+ 2 kg (0.6:1.4) = = 8 kg [(2.4+0.6) : (3.6+1.4)] = 8 kg (x : water :: 3kg : 5 kg) Hence % of x = 3/8 = 37.5% ANSWER:C #### C QUESTION:A 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 35% impurities to the product. Find the net profit percentage of the dealer? options: A)44% B)40% C)68.75% D)56.25% E)36% SOLUTION:The dealer uses weight which is 20% less than the real weight. or (1- 1/5) or 4/5 of real weight. It means that he is selling $4 worth of product for $5. The dealer then further added 35% impurities to the product. It means that he is selling $5 worth of product for $6.75. So his profit is $6.75-$4 = $2 and his profit percent is (2.75/4)*100 = 68.75% Answer:- C #### C QUESTION:Two pipes A&B can fill a tank in 24 min and 32 min respectively. If both the pipes are opened simultaneously, after how much time B should be closed so that the tank is full in 18 min. options: A)8 min B)3 min C)21 min D)23 min E)24 min SOLUTION:3/4 tank is filled by A in 18 mins. then balance 1/4 tank is filled by B in 32*1/4 = 8 mins. ANSWER:A #### A QUESTION:A dishonest dealer professes to sell goods at the cost price but uses a false weight and gains 25%. Find his false weight age? options: A)2288 B)277 C)800 D)2878 E)211 SOLUTION:25 = E/(1000 - E) * 100 1000 - E = 4E 1000 = 5E => E = 200 1000 - 200 = 800.Answer: C #### C QUESTION:If y is the smallest positive integer such that 11,025 multiplied by y is the square of an integer, then y must be options: A)2 B)4 C)6 D)7 E)14 SOLUTION:i just tried plugging in the numbers and found out that 4*11025 = 44, 100, which is a square of 210 B #### B QUESTION:There 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? options: A)12 B)23 C)28 D)80 E)84 SOLUTION:The number of ways in which one can travel from P to R = 3 × 4 = 12 Answer is A #### A QUESTION:If 5^10 x 2^10 = 10^n what is the value of n? options: A)16 B)14 C)12 D)10 E)18 SOLUTION:5^10*2^10 = 10^n or 10^10 =10^n n=10 D #### D QUESTION:Rahul 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? options: A)Rs 15 B)Rs 12.10 C)Rs 21.70 D)Rs 16.80 E)None of these SOLUTION:Explanation : Let the cost of the tax items = x Given that tax rate = 6% Cost of tax items, x*(6/100) = 30/100 x = 5 rs Now non taxable item = total cost - cost for taxable item - tax = 27 - 5 - 0.30 =21.70 Answer : C #### C QUESTION:The average of 11 numbers is 11. 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 options: A)10.4 B)11.5 C)81.5 D)11.5 E)21.5 SOLUTION:Explanation: Middle numbers = [(10.5 x 6 + 11.4 x 6) - 11 x 11] = 10.4. Answer: A #### A QUESTION:If a, b, and c are consecutive positive even integers and a > b > c, which of the following could be equal to a - b - c ? options: A)6 B)2 C)-1 D)-3 E)-4 SOLUTION:a = 2n (n>=3), b = 2n - 2, c = 2n - 4 a -b -c = 2n - (2n-2) - (2n-4) = 6 - 2n <= 0 since n >=3 , even -> E ANSWER:E #### E QUESTION:In how many ways can the letters of the CHEATER be arranged options: A)20160 B)2520 C)360 D)80 E)None of these SOLUTION:Explanation: As we can see the letter "E" is twice in given word, so Required Number =7!/2!=7∗6∗5∗4∗3∗2!/2!=2520 Option B #### B QUESTION:If a company allocates 15 percent of its budget to advertising, 10 percent to capital improvements, and 60 percent to salaries, what fraction of its budget remains for other allocations? options: A)4/5 B)3/5 C)3/20 D)1/5 E)1/10 SOLUTION:15 + 10 + 60 = 85% 100 - 85 = 15% to all others C #### C QUESTION:Becky, Merry and John want to share a chocolate bar evenly. What part of the bar will each of them take? What part of the bar will Becky and Merry have together? options: A)1/3 B)2/3 C)2/4 D)None of these E)Cannot be determined SOLUTION:Solution The children need to divide the bar into three pieces. So everyone will take 1/3 of the chocolate bar. Two girls together will have two pieces, hence, mathematically speaking, they will have 2/3 of the bar Answer B #### B QUESTION:The ages of two person differ by 12 years. If 5 years ago, the elder one be 5 times as old as the younger one, their present ages(in years) are respectively options: A)30, 10 B)25, 5 C)29, 9 D)50, 30 E)20, 8 SOLUTION:Let their ages be x and (x + 12) years. Then, 5(x - 5) = (x + 12 - 5) => 4x = 32 =>x =8 Their present ages are 20 years and 8 year. ANSWER:E #### E QUESTION:How 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 ? options: A)3.5 years B)4 years C)4.5 years D)5 years E)None of these SOLUTION:Solution Time =(100*81/450*4.5) years =4 years Answer B #### B QUESTION:A trader has 50 kg of pulses, part of which he sells at 8 per cent profit and the rest at 18 per cent profii. He gains 14 per cent on the whole. What is the quantity sold at 18 per cent profit? options: A)30 kg B)25 kg C)20 kg D)40 kg E)none of these SOLUTION:Ratio of quantities sold at 8% profit and 18% profit =>4:6 = 2:3 Therefore,the quantity sold at 18% profit =>50/(2 + 3) x 3 =>30 kg ANSWER:A #### A QUESTION:One half of the people at the game wore the team colors. Two thirds of those people wore team hats as well. One fourth of those with team colors and team hats had banners to wave. Twenty five people had team colors and banners, but no hats. One hundred people had only banners. If there were 1824 people at the game, how many had banners? options: A)177 B)277 C)377 D)477 E)577 SOLUTION:1/2 x 1824 = 912 with team colors 2/3 x 912 = 608 with hats and colors 1/4 x 608 = 152 with hats, colors, and banners 152 + 100 + 25 = 277 with banners correct answer B #### B QUESTION:A girl has to make pizza with different toppings. There are 8 different toppings. In how many ways can she make pizzas with 2 different toppings? options: A)16 B)56 C)112 D)28 E)38 SOLUTION:In 8 different toppings, selecting 2 diff toppings = 8c2 formula is n!/(n-c)! n = total number of toppings C = number chosen in a grouping. n=8 and c=2 so we get 8!/(8-2)! = (8*7*6*5*4*3*2*1)/(6*5*4*3*2*1) = 8*7 =56 ANSWER:B #### B QUESTION:The 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) options: A)Rs.20043.94 B)Rs.20043.95 C)Rs.20043.91 D)Rs.20043.98 E)Rs.20043.87 SOLUTION:Explanation: Let the rate of interest be R% p.a. (49500)(3)(R)/100 = 17820 495R = 5940 R = 12 CI on Rs.49500 at 12% p.a. for three years = 49500{[1 + 12/100]3 - 1} = 69543.936 - 49500 = Rs.20043.94 when rounded off to two decimal places. Answer: A #### A QUESTION:If x and y are different integers, both divisible by 11, then which is not necessarily true? options: A)x^2 + y^2 is divisible by 11 B)x - y is divisible by 11 C)xy is divisible by 11 D)x + y is divisible by 11 E)x + y is divisible by 22 SOLUTION:Let x = 11k and let y = 11j. Then x+y = 11(k+j) and k+j could be even or odd. Thus 11(k+j) is not necessarily divisible by 22. The answer is E. #### E QUESTION:If each data point in a certain set Q is increased by a factor of 20, what happens with the set's standard deviation? options: A)Doesn't Change B)Decreases by Factor 20 C)Can't be determined D)Increases by 20 E)Increases by Factor 20 SOLUTION:Standard deviation questions will always be conceptual in nature, because the GMAT does not require that you be able to calculate standard deviation.Veritasteaches a concept known as themapping strategyfor data sufficiency, which helps make a problem like this easily understandable. The mapping strategy is just looking at data sufficiency with sets of numbers like you would look at a map. Moving left and right on the map does not change the map's scale (which represents standard deviation in this analogy), just as adding or subtracting the same value in all numbers of a set does not change that set's standard deviation. For example, the set: 2, 5, 8, 11 has the same standard deviation of that same set after adding 5 to each number: 7, 10, 13, 16. Multiplying and dividing the entire set by a number other than 1, however, does affect standard deviation, and it does so proportionately. Multiplying by a number with an absolute value greater than 1 is like zooming in on a map...the standard deviation increases. Consider that same set multiplied by 2: 4, 10, 16, 22....this has a larger standard deviation than 2, 5, 8, 11. The opposite goes for division - dividing each number in a set of numbers by a number with an absolute value greater than 1 will reduce standard deviation, like zooming out on a map reduces the map's scale. Here because each number was multiplied by a factor of 20, the standard deviation will increase proportionately, giving us answer choice E #### E QUESTION:If 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? options: A)Y2 = xz B)Y2 = xy C)Y2 = Yz D)Y3 = xz E)Y5 = xY SOLUTION:X = (Y*NR)/100 Y = (Z*NR)/100 X/Y = NR/100 Y/Z = NR/100 X/Y = Y/Z Y2 = XZ.Answer:A #### A QUESTION:Two sides of a triangle have lengths q and y and meet at a right angle. If the perimeter of the triangle is 4q, what is the ratio of q to y ? options: A)a) 2 : 3 B)b) 3 : 4 C)c) 4 : 3 D)d) 3 : 2 E)e) 2 : 1 SOLUTION:Ahhhh....my bad. Thank you, you're correct. 8q = 6y --> q/y = 3/4. Actually B is the right answer. #### B QUESTION:At the end of three years what will be the compound interest at the rate of 10% p.a. on an amount of Rs.20000? options: A)6620 B)9278 C)2782 D)5772 E)5286 SOLUTION:A = 20000(11/10)3 = 26620 = 20000 ---------- 6620 Answer: A #### A QUESTION:What approximate value should come in place of the question mark (?) in each of the following equations ? 27.874 x 15.01 3 = ? options: A)135 B)137 C)139 D)28 E)27 SOLUTION:Explanation : 27.9 x 15 3 = 27 - 9 x 5 = 139.5 Answer : Option C #### C QUESTION:A 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 120 km downstream? options: A)60/18 B)30/29 C)60/12 D)60/13 E)30/82 SOLUTION:Speed downstream = 20 + 6 = 26 kmph. Time required to cover 60 km downstream = d/s = 120/26 = 60/13 hours. Answer:D #### D QUESTION:A wildlife preserve is being planned for 6,000 rhinoceroses. The preserve is to contain a total of 10,000 acres of watering area, plus 100 acres of grazing area for each rhinoceros. If the number of rhinoceroses is expected to increase by 10 percent, how many thousand acres should the preserve have in order to provide for the increased population? options: A) 340 B) 330 C) 670 D) 310 E) 300 SOLUTION:Number of rhinos = 6000 Watering area = 10,000 acres Number of rhino to increase by 10 percent ,then number of rhino = 6600 Grazing area for a rhino = 100 Total grazing area for 6600 rhinos= 6600 * 100 = 6,60,000 Total area required for the wildlife preserve = 6,60,000 + 10,000 = 6,70,000 = 670 * 1000 Answer C #### C QUESTION:A 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 G will the work get over? options: A)60 B)70 C)G=75 D)G=80 E)100 SOLUTION:We can also use the concept of man-days here 100 days -->10men so the job includes 100*10=1000 man-days After 20 days 1/4 of Job is completed so 1/4 X 1000 man-days=250 man-days Job is done Now the Balance Job=1000-250=750 man-days worth of Job Since 2 men are fired so B/L men=8 Therefore Total no. of days of Job=750 man-day/8 days = 375/4=94 days (approx.) Now since this is total and Ques. is asking for additional no. of days, So 94-20=74 days The nearest approx. to answer is 75 Ans: C (75 days) #### C QUESTION:The 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: options: A)83.08 B)114 C)114.75 D)124 E)124.75 SOLUTION:Face Value = Rs. 6000. Dividend = 10.5%. Annual Income = Rs. 756. Brokerage per Rs. 100 = Rs. 0.25. Dividend is always paid on the face value of a share. Face Value * Dividend / (Market Value + Brokerage per Rs. 100) = Annual income. = 6000 * 10.5 / 756 = Market Value of Rs. 100 stock + Brokerage per Rs. 100. = Market Value of Rs. 100 stock + Brokerage per Rs. 100 = Rs. 83.33. = Market Value of Rs. 100 stock = Rs. 83.33 - Re. 0.25. = Market Value of Rs. 100 stock = Rs. 83.08 answer : A #### A QUESTION:A store reduced the price of all items in the store by 12% 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? options: A)80.0 B)79.2 C)81.0 D)81.1 E)81.9 SOLUTION:consider price of the all items as $100 after a initial reduction of 12% price becomes = 0.88 *100 = $ 88 after the final reduction of 10% price becomes = 0.9* 88 = $ 79.2 price of all items on second day is 79.2% of price on first day correct answer option B #### B QUESTION:Find the simple interest on Rs. 73,000 at 16 2/3% per year for 9 months. options: A)7500 B)6500 C)8125 D)9125 E)None of them SOLUTION:P = Rs.73000,R = 50/3% p.a and T = 9/12 years = 3/4years. Simple Interest = (P*R*T)/100 = Rs.(73,000*(50/3)*(3/4)*(1/100))= Rs.9125 Answer is D. #### D QUESTION:Mr. 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. options: A)s. 5266 B)s. 5396 C)s. 5228 D)s. 5218 E)s. 52192 SOLUTION:Explanation: Let us assume Mr. Karan borrowed amount is Rs. A. (the principal) By formula of simple interest, S.I. = PRT / 100 Where P = The principal, R = Rate of interest as a %, T = Time in years S.I. = (P * 6 * 9)/100 = 54 P/100 Amount = Principal + S.I. 8310 = P + (54P/100) 8310 = (100P + 54P)/100 8310 = 154P/100 P = (8310 * 100)/154 = Rs. 5396.104 ANSWER: B #### B QUESTION:In how many Q 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? options: A)720 B)864 C)900 D)936 E)1,296 SOLUTION:Total number of four letter passwords = 6*6*6*6= 1296 ------(1) Total number of passwords in which no letter repeats = 6C4*4!= 15*24=360------(2) therefore required value Q= (1)-(2)= 1296-360=936.D #### D QUESTION:The maximum number of students among them 100 pens and 50 pencils can be distributed in such a way that each student get the same number of pens and same number of pencils? options: A)50 B)75 C)69 D)79 E)82 SOLUTION:number of pens = 100 number of pencils = 50 Required number of students = H.C.F. of 100 and 50 = 50 Answer is A #### A QUESTION:In a class of 100 students, there are 50 who play soccer, 45 who play basketball, and 50 who play volleyball. Only 15 of these students play all three sports. Everyone plays at least one of these sports. How many of the students play exactly two of these sports? options: A)15 B)20 C)25 D)30 E)35 SOLUTION:Let S1 be the number of students who play exactly one of the three sports; S2 - the number of students who play exactly two of the three sports; and let S3 be the number of students who play all three sports. We know that S3 = 15 and S1 + S2 + S3 = 100 (the total number of students). Also in the sum 50+45+50 (soccer players + basketball players + volleyball players), each student who plays exactly one sport is counted once, the ones who play exactly two sports are counted twice, and those who play all three sports are counted three times. Thus, 50 + 45 + 50 = S1 + 2S2 + 3S3. Note that S2 = (S1 + 2S2 + 3S3) − (S1 + S2 + S3) − 2S3 = 15 correct answer A #### A QUESTION:which of the following is a prime number ? options: A)17 B)18 C)15 D)20 E)25 SOLUTION:Clearly, 17 is a prime number. Option A #### A QUESTION:The average of three consecutive odd numbers is 12 more than one third of the first of these numbers. What is the last of the three numbers? options: A)15 B)17 C)19 D)21 E)23 SOLUTION:x,x+2,x+4 are three odd numbers (x+x+2+x+4)/3=12+(x/3) x=15 last no.=x+4=19 ANSWER:C #### C QUESTION:A 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: options: A)35.55 km/hr B)36 km/hr C)71 km/hr D)71.11 km/hr E)70 km/hr SOLUTION:Total time taken =((160/64)+(160/80))hrs=9/2hrs. Average speed =(320 x2/9)km/hr= 71.11 km/hr. ANSWER D #### D QUESTION:If 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? options: A)3:2 B)2:1 C)3:3 D)1:2 E)6:1 SOLUTION:8M + 2B = 4(1M + 1B) 8M + 2B = 4M + 4B 4M = 2B The required ratio of work done by a man and a boy = 2:4=1:2 D #### D QUESTION:In a company, 58% of all its employees earn lesser than $50,000; 66% earn more than $40,000; 17% earn $45,000; 3% earn $48,000. What is the median salary options: A)42,000 B)43,000 C)44,000 D)45,000 E)46,000 SOLUTION:as only amount mentioned in the question and in the options is $45000 ($48000 not mentioned) Rest amounts are in the form of greater than or lesser than , Hence C $45000 answer is D #### D QUESTION:One card is drawn at random from a pack of 48 cards. What is the probability that the card drawn is a face card? options: A)1/4 B)1/7 C)1/8 D)1/5 E)2/5 SOLUTION:Clearly, there are 52 cards, out of which there are 12 face cards. P (getting a face card) = 12/48 = 1/4 A #### A QUESTION:The area of sector of a circle whose radius is 12 metro and whose angle at the center is 39° is? options: A)40m2 B)45m2 C)49m2 D)51m2 E)55m2 SOLUTION:39/360 * 22/7 * 12 * 12 = 49m2 Answer:C #### C QUESTION:Given 2 numbers; 16 and x, the LCM and HCF of both numbers is 144 and 2 respectively. Find x? options: A)16 B)28 C)15 D)13 E)18 SOLUTION:HCF x LCM = Product of Numbers 2 x 144 = 16 x x x = (2 x 144) / 16 x = 18 ANSWER : E #### E QUESTION:Yearly subscription to professional magazines cost a company $840.00. To Make a 30% cut in the magazine budget, how much less must be spent? options: A)654 B)655 C)656 D)588 E)658 SOLUTION:total cost 840 840*30/100=252 so the cut in amount is 252 the less amount to be spend is 840-252=588 ANSWER:D #### D QUESTION:A car traveled 448 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? options: A)14 B)18 C)21 D)22 E)27 SOLUTION:Let the speed in highway be h mpg and in city be c mpg. h = c+6 h miles are covered in 1 gallon 462 miles will be covered in 462/h. Similarly c miles are covered in 1 gallon 336 miles will be covered in 336/c. Both should be same (as car's fuel capacity does not change with speed) => 336/c = 448/h => 336/c = 448/(c+6) => 336c+336*6=448c =>c=336*6/112=18 Answer B. #### B QUESTION:Set X consists of all two-digit primes and set Y consists of all positive even multiples of 5 less than 100. If the two sets are combined into one, what will be the range of the new set? options: A) 87 B) 89 C) 90 D) 92 E) 95 SOLUTION:Set X = {11, 13, 17,............., 83, 89, 97} Set Y = {10, 20, 30,..............., 70, 80, 90} Combining two sets, say Set Z Set Z = { 10,11, 13, 17, 20,30,..................., 70, 80, 83, 89, 90, 97} Range = Max Value - Min Value Range (Z) = 97 - 10 = 87 OA A is the answer. #### A QUESTION:Two 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 2:3 and 3:1 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. options: A)99:61 B)99:160 C)61:160 D)61:99 E)99:160 SOLUTION:Vessel A = 300 gallons --> milk = 120, water = 180; Vessel B = 500 gallons --> milk = 375, water = 125; Vessel A + B = 800 gallons --> milk = 495, water 305. The ratio = 495/305 --> reduce by 5 = 99/61. Answer: A. #### A QUESTION:Can you find the smallest non fractional number such that If the number gets divided by 9 , we get the remainder of 1; If the number gets divided by 10 , we get the remainder of 2 If the number gets divided by 11 , we get the remainder of 3; If the number gets divided by 12 , we get the remainder of 4. options: A)1450 B)1300 C)1205 D)2501 E)1978 SOLUTION:E.option E As we know LCM of the numbers 9 10 11 & 12 is 1980. So if i divide 1980 by any of the four number , it gives remainder as 0. Now to get reminder as desired, is should be 2 short of 1978. (3-1,4-2,5-3,6-4 ) Ans:option E #### E QUESTION:How many 4's are there in the following series which are preceded by 7, but are not preceded by 8? 3 4 5 7 4 3 7 4 8 5 4 3 7 4 9 8 4 7 2 7 4 1 3 6 options: A)1 B)2 C)3 D)4 E)More than four SOLUTION:count 1 - - - - - - 7 4 3 count 2------------748 count 3------------749 count 4------------741 ANSWER:D #### D <<<Examples ends QUESTION:A man bought an article and sold it at a gain of 5 %. If he had bought it at 5% less and sold it for Re 5 less, he would have made a profit of 10%. The C.P. of the article was options: A)960 B)980 C)900 D)970 E)1000 SOLUTION:Explanation: Let original Cost price is x Its Selling price = (105/100) * x = 21x/20 New Cost price = (95/100) * x = 19x/20 New Selling price = (110/100 )* (19x/20 )= 209x/200 [(21x/20) - (209x/200)] = 1 => x = 1000 Answer: E) Rs 1000 #### E

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:At a dinner party, 7 people are to be seated around a circular table. Two seating arrangement 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? options: A)5 B)10 C)720 D)32 E)120 SOLUTION:Has to be C. Simple formula: There are (n - 1)! ways to arrange n distinct objects in a circle hence (7-1)! = 6!= 720 #### C QUESTION:A 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? options: A)300 B)320 C)350 D)345 E)568 SOLUTION:Speed = [300 / 18] m/sec = 50/3 m/sec. Let the length of the platform be x meters. Then, x + 300 / 39 = 50/3 3(x + 300) = 1950 è x = 350 Answer: Option C #### C QUESTION:By selling an article at Rs.700, a shopkeeper makes a profit of 25%. At what price should he sell the article so as to make a loss of 25%? options: A)s.600 B)s.480 C)s.500 D)s.450 E)s.420 SOLUTION:SP = 700 Profit = 25% CP = (SP)*[100/(100+P)] = 700 * [100/125] = 560 Loss = 25% = 25% of 560 = Rs.140 SP = CP - Loss = 560 - 140 = Rs.420 ANSWER:E #### E QUESTION:A 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? options: A)13 B)25 C)17 D)12 E)11 SOLUTION:11 cartons total 7 large boxes (7 * 8 = 56 boxes) 4 small boxes (4 *10 = 40 boxes 11 total cartons and 96 boxes #### E QUESTION:Printer 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? options: A)10 pm B)1 pm C)2 pm D)3 pm E)4 pm SOLUTION:Work done by P in 1 hour = 1/8 Work done by Q in 1 hour = 1/10 Work done by R in 1 hour = 1/12 Work done by P,Q and R in 1 hour = 1/8 + 1/10 + 1/12 = 37/120 Work done by Q and R in 1 hour = 1/10 + 1/12 = 22/120 = 11/60 From 9 am to 11 am, all the Printer were operating. Ie, they all operated for 2 hours and work completed = 2 × (37/120) = 37/60 Pending work = 1- 37/60 = 23/60 Hours taken by Q an R to complete the pending work = (23/60) / (11/60) = 23/11 which is approximately equal to 2 Hence the work will be completed approximately 2 hours after 11 am ; ie around 1 pm B #### B QUESTION:The annual interest rate earned by an investment increased by 10 percent from last year to this year. If the annual interest rate earned by the investment this year was 13 percent, what was the annual interest rate last year? options: A)1% B)1.1% C)9.1% D)11.81% E)11.50% SOLUTION:13=1.1*x X=11.81% Answer D) #### D QUESTION:Find the area of a cuboid of length 10cm , breadth 8 cm . and height 6cm. options: A)400 cm cube B)410 cm cube C)420 cm cube D)430 cm cube E)480 cm cube SOLUTION:Area of a cuboid = lxbxh =10cm x 8cm x 6cm = 480 cm cube answer :E #### E QUESTION:To furnish a room in a model home an interior decorator is to select 2 chairs and 2 tables from the collection of chairs and tables in a warehouse that are all different from each other. If there are 5 chairs in the warehouse and if 150 different combinations are possible, how many tables w are there in the warehouse? options: A)6 B)8 C)10 D)15 E)30 SOLUTION:Total number of ways to choose 2 chairs from 5 w= 5C2=10 Total number of combination=150 That means we need get 15 combinations from the selection of tables.... Screening through the answers.... 6C2=15..... 15*10=150 Answer is 6... A #### A QUESTION:The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 10 and 12. The larger of the two numbers is: options: A)276 B)299 C)322 D)345 E)395 SOLUTION:Clearly, the numbers are (23 x 10) and (23 x 12). Larger number = (23 x 12) = 276. Answer: Option A #### A QUESTION:If 12 men can reap 120 acres of land in 36 days, how many acres of land can 54 men reap in 54 days? options: A)267 B)766 C)810 D)868 E)812 SOLUTION:12 men 120 acres 36 days 54 men ? 54 days 120 * 54/12 * 54/36 10 * 54 * 3/2 54 * 15 = 810 Answer:C #### C QUESTION:In a certain school, 20% of students are below 8 years of age. The number of students above 8 years of age is 2/3 of the number of students of 8 years of age which is 48. What is the total number of students in the school? options: A)200 B)300 C)600 D)700 E)100 SOLUTION:E 100 Let the number of students be x. Then, Number of students above 8 years of age = (100 - 20)% of x = 80% of x. 80% of x = 48 + 2/3 of 48 80/100x = 80 x = 100. #### E QUESTION:In how many ways can 5 boys and 3 girls sit around a table in such a way that no two girls sit together? options: A)1000 B)1400 C)1440 D)1800 E)1900 SOLUTION:The 5 boys can be seated around a table in 4! Ways. In between them there are 5 places. The 3 girls can be placed in the 5 places in 5P3 ways. Therefore, Required number of ways= 4!* 5P3 =24*60 =1440 ANSWER:C #### C QUESTION:What inequality represents the condition 1<x<13? options: A)|x|<3 B)|x+5|<4 C)|x-7|<6 D)|-5+x|<4 E)|3+x|<5 SOLUTION:1<x<13 represents segment with length: 13-1 = 12 center: (13+1)/2 = 7 For any |x-a|<b a is a center and b is a half of length. So, |x-7|<12/2 represents our inequality (answer C) #### C QUESTION:A gardener increased the length of a rectangle-shaped garden by 20 percent and decreased its width by 10 percent. The area of the new garden options: A)has increased by 20 percent B)has increased by 12 percent C)has increased by 8 percent D)is exactly the same as the old area E)cannot be expressed in percentage terms without actual numbers SOLUTION:Let L be the original length and let W be the original width. The original area was L*W. The new area is 0.9W*1.2L = (0.9)(1.2)L*W = 1.08*L*W The answer is C. #### C QUESTION:9823 + x = 13200, then x is ? options: A)3327 B)3237 C)3337 D)3377 E)None of these SOLUTION:Answer x = 13200 - 9823 = 3377 Option: D #### D QUESTION:There are 200 questions in a 3 hr examination. Among these questions there are 50 mathematics problems. It is suggested that twice as much time be spent on each maths problem as for each other question. How many minutes should be spent on mathematics problems options: A)36 minutes B)60 minutes C)72 minutes D)100 minutes E)None of these SOLUTION:Explanation : Let x = minutes spent on a non-math problem then 2x = minutes spent on a math problem x(200-50) + 2x(50) = 180 x(150) + 2x(50) = 180 150x + 100x = 180 250x = 180 x = 0.72 minutes Time to spend on math problems: 2x(50)=100x = 100(0.72) = 72 minutes Answer : C #### C QUESTION:A firm has 5 senior partners and 7 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.) options: A)145 B)155 C)165 D)175 E)185 SOLUTION:The number of ways to form a group of 3 is 12C3 = 220 The number of groups with no senior partner is 7C3 = 35 The number of groups with at least one senior partner is 220-35 = 185 The answer is E. #### E QUESTION:The sum of the first 50 positive even integers is 2550. What is the sum Q of even integers from 102 to 200 inclusive? options: A)5100 B)7550 C)10100 D)15500 E)20100 SOLUTION:My solution is: First 50 even integers: 2 4 6 8 <...> Integers from 102 to 200 102 104 106 108 <...> We 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: Q=2550+(100*50)=7550.B #### B QUESTION:There are two sections C and D of a class, consisting of 18 and 22 students respectively. If the average weight of sections C is 20 kg and that of sections D is 18 kg. Find the average weight of the whole class options: A)18.7 B)18.8 C)18.9 D)19.9 E)None SOLUTION:Solution Total weight of(18+22)Students = (18x20+22x18)Kg = 756 kg. Average weight of the whole class = (756 /40 ) = 18.90. Answer C #### C QUESTION:What will come in place of the x in the following Number series? 18, 22, 30, 46 ,78, X options: A)35 B)56 C)142 D)87 E)98 SOLUTION:(C) The pattern is +4, +8, +16, +32, +64 So the missing term is = 142 #### C QUESTION:The average of first 10 odd numbers is? options: A)22 B)10 C)98 D)66 E)88 SOLUTION:Sum of 10 odd no. = 100 Average = 100/10 = 10 Answer:B #### B QUESTION:A jar is filled with red, white, and blue tokens that are equivalent except for their color. The chance of randomly selecting a red token, replacing it, then randomly selecting a white token is the same as the chance of randomly selecting a blue token. If the number of tokens of every color is a multiple of 8, what is the smallest possible total number of tokens in the jar? options: A) 9 B) 12 C) 15 D) 18 E) 21 SOLUTION:(Red / Total Coins)*(White / Total Coins) = (Blue / Total Coins) í.ẹ. Red*White = Blue*Total Coins Let, Red = 3a White = 3b Blue = 3c Total Coins = 3(a+b+c) í.ẹ. 3a * 3b = 3c*3(a+b+c) í.ẹ. a*b = c*(a+b+c) For smallest values of a, b and c 2*3 = 1*(1+2+3) í.ẹ. Minimum Total Coins = 3*(1+2+3) = 15 Answer: Option C #### C QUESTION:Two trains of equal lengths take 12 sec and 24 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? options: A)18 sec B)12 sec C)17 sec D)21 sec E)16 sec SOLUTION:Speed of the first train = 120/12 = 10 m/sec. Speed of the second train = 120/24 = 5 m/sec. Relative speed = 10 + 5 = 15 m/sec. Required time = (120 + 120)/15 = 16 sec. Answer: E #### E QUESTION:Which letter will come exactly between the tenth letter from your left and the seventh letter from your right. Without changing any order in the original from the alphabet? options: A)U B)Y C)O D)Y E)R SOLUTION:10th letter from your left is J 7th letter from your right is T The mid letter between J and T is O. Answer: Option 'C' #### C QUESTION:A sum of money is put out at compound interest for 2 years at 20%. It would fetch Rs.723 more if the interest were payable half-yearly, then it were pay able yearly. Find the sum. options: A)22200 B)21897 C)28799 D)30000 E)32782 SOLUTION:P(11/10)^4 - P(6/5)^2 = 723 P = 30000 Answer: D #### D QUESTION:At 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? options: A)404 B)452 C)444 D)468 E)422 SOLUTION:312 + 222 - 112 (since 112 is counted twice )= 422 E is the answer #### E QUESTION:A rectangular grassy plot 110 m. by 65 m has a gravel path 2.5 m wide all round it on the inside. Find the cost of gravelling the path at 60 paise per sq. metre options: A)s510 B)s780 C)s880 D)s480 E)s980 SOLUTION:area of the plot=110m*65m=7150sq.m area of plot excluding gravel=105m*60m=6300sq.m area of gravel =7150sq.m-6300sq.m =850sq.m cost of building it = 850sq.m*60 = 51000p in Rs =51000/100=Rs510 ANSWER:A #### A QUESTION:An 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 1/4 %, then the amount invested at 11% was? options: A)12500 B)37500 C)29977 D)26777 E)19871 SOLUTION:Let the sum invested at 9% be Rs. x and that invested at 11% be Rs. (100000 - x). Then, (x * 9 * 1)/100 + [(100000 - x) * 11 * 1]/100 = (100000 * 37/4 * 1/100) (9x + 1100000 - 11x) = 37000/4 = 925000 x = 87500 Sum invested at 9% = Rs. 87500 Sum invested at 11% = Rs. (100000 - 87500) = Rs. 12500. Answer: A #### A QUESTION:A retail item is offered at a discount of d percent (where d > 10), with a 5% state sales tax assessed on the discounted purchase price. If the state sales tax were not assessed, what percent discount from the item’s original retail price, in terms of d, would result in the same final price? options: A)d+5/1.05 B)d/1.05 +5 C)1.05d-5 D)d-5/1.05 E)1.05(p – 5) SOLUTION:Let x be the price of the item. Final price after discount and sales tax = x * (1 - d/100) * 1.05 Let e be the percent discount which would result in the same final price. Then, x * (1 - d/100) * 1.05 = x * (1 - e/100) => 1.05 - 1.05d/100 = 1 - e/100 => e/100 = 1.05d/100 - .05 => e = 1.05d - 5 Hence ,option C is correct. #### C QUESTION:A car covers a distance of 829 km in 7 hours. Find its speed? options: A)104 kmph B)289 kmph C)118 kmph D)277 kmph E)177 kmph SOLUTION:829/7 = 118 kmph Answer: C #### C QUESTION:Find the odd man out 32, 34, 42, 46, 58, 59, 60, 66 options: A)31 B)41 C)67 D)59 E)61 SOLUTION:as 59 is only odd number. ANSWER:D #### D QUESTION:If the number 481*673 is completely divisible by 9, what is the the smallest whole number in place of *? options: A)4 B)5 C)6 D)7 E)8 SOLUTION:Let x be the smallest whole number in place of * 481x673 is completely divisible by 9 => (4+8+1+x+6+7+3) is divisible by 9 => (29+x) is divisible by 9 x should be the smallest whole number. Hence, (29+x)=36 =>x=36−29=7 Answer is D. #### D QUESTION:597**6 is divisible by both 3 and 11. The non-zero digits in the Hundred’s and ten’s places are respectively: options: A)3 and 6 B)7 and 9 C)2 and 6 D)4 and 7 E)None SOLUTION:Solution : Let the given number be 597xy6. Then (5+9+7+x+y+6)=(27+x+y) must be divisible by 3 And, (6+x+9)-(y+7+5)=(x-y+3) must be either 0 or divisible by 11. x-y+3=0 => y=x+3 27+x+y) =>(27+x+x+3) =>(30+2x) => x = 3 and y = 6. Answer A #### A QUESTION:The average age of a group of 10 persons was decreased by 3 years when one person, whose age was 46 years, was replaced by a new person. Find the age of the new person? options: A)18 B)56 C)16 D)17 E)14 SOLUTION:Initial average age of the 10 persons be P. Age of the new person Q. Sum of the ages of the initial 10 persons = 10P New average = (P-3) 10(P-3) = 10P - 46 + Q => Q = 16 Answer:C #### C QUESTION:A worker's daily wage is increased by 40% and the new wage is $28 per day. What was the worker's daily wage before the increase? options: A)$18 B)$20 C)$22 D)$24 E)$25 SOLUTION:Let x be the daily wage before the increase. 1.4x = $28 x = $20 The answer is B. #### B QUESTION:A team consists of 4 boys and 3 girls. If you pick two persons at the same time, what's the probability that one person is boy and other one is girl ? options: A)2/7 B)5/7 C)4/7 D)3/7 E)1/2 SOLUTION:P(1st b, 2nd g) = 4/7*3/6 = 4/14; P(1st g, 2nd b) = 3/7*4/6 = 4/14. P = 4/14 + 4/14 = 4/7. Answer: C. #### C QUESTION:A train 480 m in length crosses a telegraph post in 16 seconds. The speed of the train is? options: A)22 kmph B)108 kmph C)54 kmph D)71 kmph E)88 kmph SOLUTION:S = 480/16 * 18/5 = 108 kmph Answer:B #### B QUESTION:The 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 10%. By approximately what percent would the output of the factory now have to be decreased in order to restore the original output? options: A)17% B)24% C)30% D)32% E)79% SOLUTION:take it as original output =100. to meet demand increase by 10%, then output=110. to meet holiday demand , new output increase by 10% then output equals 121 To restore new holidy demand output to original 100. final -initial/final*100 =21/121*100=8/33*100=17% approxiamately. option A is correct. #### A QUESTION:The ratio of two quantities is 2 to 3. If each of the quantities is increased by 4, what is the ratio of these two new quantities? options: A)5/5 B)It cannot be determined from the information given. C)11/5 D)12/5 E)13/5 SOLUTION:let the actual ratio be 2k/3k, increase numerator and denominator by 4=> 2k+4/3k+4 Until the value of k is unknown we can not determine the actual ratio. OR let the actual be 3/4. After increasing 4 => 7/8 let the actual be 6/8. After increasing 4 => 10/12 Therefore without actual quantities we cannot determine the actual ratio. Answer : B #### B QUESTION:Calculate the distance covered by 350 revolutions of a wheel of radius 25.3 cm. options: A)558.6 m B)556.6 m C)516.6 m D)156.6 m E)256.6 m SOLUTION:In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 350 resolutions. =350 * 2 * 22/7 * 25.3 = 55660 cm = 556.6 m ANSWER:B #### B QUESTION:The odds against ram solving the problem are 6 to 3 and the odds in favour of krishna solving the same are 7 to 5. What is the chance that it will be solved when they both try? options: A)1/4 B)5/21 C)16/21 D)23/28 E)13/18 SOLUTION:Odds against Ram are 6:3 so probability that he will solve the problem is 1/3. Odds in favor of Krishna are 7:5 so probability that he will solve it is 7/12 It will be solved means that either Ram or Krishna or both will be able to solve it. P(A or B) = P(A) + P(B) - P(A and B) = 1/3 + 7/12 - (1/3)*(7/12) = 13/18 E #### E QUESTION:If a particular player is always chosen, in how many ways can a cricket-be chosen out of 15 players? options: A)1123 B)1234 C)1452 D)1356 E)1365 SOLUTION:A particular player is always chosen, it means that 10 players are selected out of the remaining 14 players. =. Required number of ways = 14C10 = 14C4 = 14!/4!x19! = 1365 E #### E QUESTION:A train after traveling for 50km meets with an accident and then proceeds at 3/4 of its former speed and arrives at its destination 35 minutes late . Had the accident occurred 24 km farther, it would have reached the destination only 25 minutes late. What is the speed T of the train. options: A)a) 45 B)b) 33 C)c) 48 D)d) 55 E)e) 61 SOLUTION:Let y be the balance distance to be covered and x be the former speed. A train after traveling for 50km meets with an accident and then proceeds at 3/4 of its former speed and arrives at its destination 35 minutes late so, y/(3x/4) - y/x = 35/60 4y/3x - y/x = 7/12 y/x(4/3-1)=7/12 y/x*1/3=7/12 y/x=7/4 4y-7x=0 ........ 1 Had the accident occurred 24 km farther, it would have reached the destination only 25 minutes late so, (y-24)/(3x/4) - (y-24)/x = 25/60 4(y-24)/3x - (y-24)/x = 5/12 (y-24)/x (4/3-1) = 5/12 (y-24)/x *1/3 = 5/12 (y-24)*12 = 3x*5 (y-24)*4 = 5x 4y-5x = 96 ....... 2 eq2 - eq1 2x=96 x=48=T Ans = C #### C QUESTION:A 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? options: A)22 B)80 C)40 D)77 E)12 SOLUTION:800*(25/100) = 200 ---- 5 ? ---- 1 => Rs.40 Answer: C #### C QUESTION:Two 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? options: A)22 B)30 C)48 D)99 E)12 SOLUTION:Relative speed = 90 + 30 = 120 km/hr. 120 * 5/18 = 100/3 m/sec. Distance covered = 500 + 500 = 1000 m. Required time = 1000 * 3/100 = 30 sec. Answer: B #### B QUESTION:A sum 's' is divided into 4 parts. second person gets Rs 10 more than first.3rd person is Rs 10 more than second,4th is 10 more than 3rd.how much amount do 1st person get.? options: A)x = (s-60)/4 B)x = (s-60)/5 C)x = (s-60)/3 D)x = (s-60)/2 E)x = (s-60)/6 SOLUTION:let x be amount getting by first person, second person gets x +10,third person gets x + 20,fourth person gets x + 30, now s = (x)+(x+10)+(x+20)+(x+30) s = 4x + 60 s - 60 = 4x or x = (s-60)/4 ANSWER:A #### A QUESTION:Last year, the price per transaction of certain company increases P percent from the year before, and the number of transactions increase N percent from the year before. Total revenue is simply the number of transactions times the price per transaction. Assume this one transaction is this company's only source of revenue. Which of the following is the percent increase in revenue last year, from the year before? options: A)P∗N % B)(P+N) C)(P+N+P∗N/100) % D)(P+N-P∗N/100) % E)(P+N+P∗N/100)^2 % SOLUTION:Assume x = price per transaction for previous year y = price per transaction for this year Relationship between x and y y =x (1+P/100) Similarly, if n1= no. of transactions for last year n2 = no. of transactions for this year n2 = n1(1+N/100) Now, the question is [(n2y- n1x) /n1x] * 100 n2y = n1x(1+P/100)(1+N/100) So, [(n2y - n1x)/n1x] * 100 = (n1x[(1+P/100) (1+N/100) - 1]/ n1x) * 100 D is the answer. #### D QUESTION:If x is 20 percent greater than 98, then x = options: A)68 B)70.4 C)86 D)105.6 E)117.6 SOLUTION:x=98*1.2=117.6 So the answer is E. #### E QUESTION:In a theater, the first row has 15 seats and each row has 2 more seats than previous row. If the last row has 53 seats, what is the total number of seats in the theater? options: A)600 B)640 C)680 D)720 E)760 SOLUTION:The number of seats in the theater is 15 + (15+2) + ...+ (15+38)= 20(15) + 2(1+2+...+19)= 20(15) + 2(19)(20)/2= 20(15+19) = 20(34) = 680 The answer is C. #### C QUESTION:In a village the average age of n people is 42 years. But after the verification it was found that the age of a person had been considered 20 years less than the actual age, so the new average, after the correction,increased by 1. The value of n is? options: A)11 B)20 C)28 D)17 E)13 SOLUTION:Explanation: It is the same as a person with 20 years more age replaces an existing person of the group ( or village) Since the total age of the village having n persons, is being increased by 20 years and the average age of village is being increased by 1 year, hence there are total 20 people in the village. Alternatively : ( n x 42 ) + 20 = ( n x 43 ) => n=20 Answer: B #### B QUESTION:What is the area of a square with perimeter 8P ? options: A) 16p^2 B) 4P^2 C) P^2/4 D) P/16 E) P^2/16 SOLUTION:Each side is 2p A = (2p)^2 = 4(p^2) Answer B #### B QUESTION:Look at this series: 5.2, 4.8, 4.4, 4, ... What number should come next? options: A)3 B)3.3 C)3.5 D)3.6 E)None SOLUTION:Explanation: In this simple subtraction series, each number decreases by 0.4. Answer: Option D #### D QUESTION:Six persons A,B,C,D,E &F went to soldier cinema. There are six consecutive seats. A sits in the first seat followed by B, followed by C and so on. If A taken on of the six seats, then B should sit adjacent to A. C should sit adjacent to A or B. D should sit adjacent to A, B or C and so on. How many possibilities are there ? options: A)30 B)32 C)34 D)36 E)38 SOLUTION:First we have to arrange A, there is 1 method for it, for second person B, there are 2 methods one left and one right, for third 2 methods are there same as for B similarly for others, so total number of methods = 1*2*2*2*2*2 = 32 ANSWER:B #### B QUESTION:10 chess players take part in a tournament. Every player plays twice with each of his opponents. How many games are to be played? options: A)90 B)98 C)35 D)99 E)80 SOLUTION:Though 2*(10C2) 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. The first guy has to play 2 matches with the rest of 9, so he'll play 18 matches. Similarly, second guy has to play with the rest of 8 as his 2 games with the first guy are already played. So he plays 16 matches. This continues like this and the total matches are 18+16+14...+2 18+16+...+2 = 2(9+8+...+1) = 2((9*10)/2) = 9*10 = 90. ANSWER:A #### A QUESTION:The number of new words that can be formed by rearranging the letters of the word 'ALIVE' is ? options: A)118 B)290 C)119 D)139 E)132 SOLUTION:Number of words which can be formed = 5! - 1 = 120 - 1 = 119. Answer:C #### C QUESTION:For Consecutive integers x, y and z, where x > y > z, which of the following CANNOT be the value of (x2−y2)∗(y2−z2)(x^2−y^2)∗(y^2−z^2) ? options: A)63 B)99 C)195 D)276 E)323 SOLUTION:2 ways: 1) x-odd y-even z-odd (odd^2−even^2)(even^2−odd^2)=even 2) x-even y-odd z-even (even^2−odd^2)(odd^2−even^2)=even The only even answer we have is D) 276 #### D QUESTION:Pipe 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? options: A)1.5 B)2 C)2.5 D)3 E)3.5 SOLUTION:The part filled by A + B + C in 1 hour = 1/6 + 1/4 + 1/12 = 12/24 = 1/2 All the three pipes together will fill the tank in 2 hours. The answer is B. #### B QUESTION:The present population of a town is 240. Population increase rate is 10% p.a. Find the population of town after 1 years? options: A)100 B)120 C)200 D)220 E)264 SOLUTION:P = 240 R = 10% Required population of town = P*(1 + R/100)^T = 240*(1 + 10/100) = 240*(11/10) = 264 Answer is E #### E QUESTION:A certain shade of gray paint is obtained by mixing 3 parts of white paint with 5 parts of black paint. If 2 gallons of the mixture is needed and the individual colors can be purchased only in one gallon or half gallon cans, what is the least amount of paint W, in gallons, that must be purchased in order to measure out the portions needed for the mixture? options: A)2 B)2 1/2 C)3 D)3 1/2 E)4 SOLUTION:Given W:B = 3:5 That means say 3 gallons of white paint + 5 gallons of black paint = 8 gallons of paint mixture. But we want least amount of whiteblack paints for minimum of 2 gallons of mixture, so lets reduce keeping same ratio, 1.5 : 2.5 gives 1.5 + 2.5 = 4 gallons of mixture, but we want only 2 gallons, lets further reduce 0.75: 1.25 gives 1+1.5 =2.5 gallons of mixture. This looks ok, but lets reduce further just to be sure 0.375: 0.625 gives 0.5 + 1 = 1.5 gallons of mixture, thats less than 2 gallons of mixture, so not acceptable. So correct ans is 2.5 gallons. B #### B QUESTION:In how many ways can the letters of the word "PROBLEC" be rearranged to make 7 letter words such that none of the letters repeat? options: A)4! B)5! C)7! D)8! E)9! SOLUTION:There are seven positions to be filled. The first position can be filled using any of the 7 letters contained in PROBLEM. The second position can be filled by the remaining 6 letters as the letters should not repeat. The third position can be filled by the remaining 5 letters only and so on. 758 Therefore, the total number of ways of rearranging the 7 letter word = 7*6*5*4*3*2*1 = 7! Ways. C #### C QUESTION:What is the 4 digit number 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? options: A)1100 B)1200 C)1349 D)1430 E)1340 SOLUTION:First digit is 1/3 second digit => The numbers can be 1 & 3, 2& 6, 3 & 9. First + second = third => we can eliminate 3 & 9 since 3 + 9 = 12. Last is 3 times the second => we can eliminate option 2 & 6 since 3 * 6 = 18. Hence the number is 1349 C #### C QUESTION:There are 6 identical pens and 9 identical books. In how many different ways can a person select at least one object from this set? options: A)15 B)30 C)69 D)78 E)90 SOLUTION:We can select from 0 to 6 pens and from 0 to 9 books. Thus the total possible ways to select objects is 7*10 = 70 We must subtract 1 for the case with 0 pens and 0 books. The answer is C. #### C QUESTION:The 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.8600. If his salary for the month of May is Rs.6500, find his salary for the month of January? options: A)s.4100 B)s.4270 C)s.4500 D)s.4550 E)s.2500 SOLUTION:Sum of the salaries of the person for the months of January, February, March and April = 4 * 8000 = 32000 ----(1) Sum of the salaries of the person for the months of February, March, April and May = 4 * 8600 = 34400 ----(2) (2)-(1) i.e. May - Jan = 2400 Salary of May is Rs.6500 Salary of January = Rs.4100 Answer:A #### A QUESTION:The weight of a hollow sphere is directly dependent on its surface area. The surface area of a sphere is 4π·R^2, where R is the radius of the sphere. If a hollow sphere of radius 0.15 cm made of a certain metal weighs 8 grams, a hollow sphere of radius 0.3 cm made of the same metal would weigh how many grams T? options: A)T=16 B)T=32 C)T=64 D)128 E)512 SOLUTION:Weight directly proportional to 4 pi r^2 Now, 4pi is constant, so, weight is directly proportional to r^2. When radius = 0.15, weight = 8, so (0.15) ^ 2 proportional to 8; (0.15)^2 * 4 proportional to 8*4, solving further (0.15)^2 * 2 ^2 = (0.15*2)^2 = 0.3 ^ 2; so answer = 32 (B) #### B <<<Examples ends QUESTION:There is a 30 % chance of rain and a 70% chance of shine. If it rains there is a 50% chance that Bob will cancel his picnic but if the sun is shining he will definitely have his picnic. What is the chance that Bob will have his picnic? options: A)70 % B)75 % C)80 % D)85 % E)90 % SOLUTION:Chance of no picnic+chance of picnic= 100% ... (i) Chance of picnic=100%-Chance of no picnic ... (ii) Chance of no picnic= 50% of 30%= 15% Therefore, According to (ii), Chance of picnic= 100%-15%= 85%. Answer D #### D

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:When the price of an article was reduced by 35% its sale increased by 80%. What was the net effect on the sale? options: A)17% increase B)44% decrease C)60% increase D)66% increase E)66% decrease SOLUTION:if n items are sold for $p each, revenue is $np. If we reduce the price by 35%, the new price is 0.65p. If we increase the number sold by 80%, the new number sold is 1.8n. So the new revenue is (0.65p)(1.8n) = 1.17np, which is 1.17 times the old revenue, so is 17% greater. ANSWER:A #### A QUESTION:The sum of 55 consecutive integers is 5555. What is the greatest integer in the set? options: A)126 B)128 C)130 D)132 E)134 SOLUTION:Let x be the first integer in the set, then x+54 is the largest integer. The sum is: x+(x+1)+(x+2)+...+(x+54) = 55x + 54*55/2 = 55(x+27) Then x+27=101 x=74 The largest integer in the set is 74+54=128 The answer is B. #### B QUESTION:The sum of 33 consecutive integers is 3333. What is the greatest integer in the set? options: A)113 B)115 C)117 D)119 E)121 SOLUTION:Let x be the first integer in the set, then x+32 is the largest integer. The sum is: x+(x+1)+(x+2)+...+(x+32) = 33x + 32*33/2 = 33(x+16) Then x+16=101 x=85 The largest integer in the set is 85+32=117 The answer is C. #### C QUESTION:A 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 options: A)6 ½ sec B)7 ½ sec C)8 sec D)13 ½ sec E)9 sec SOLUTION:Explanation: Speed of train = 132 ×(5/18) m/sec = 110/3 m/sec. Distance covered in passing the platform = (200 + 295) m = 495 m. Time taken =495 ×(3/110) sec =27/2 sec = 13 ½ sec Answer: Option D #### D QUESTION:if page of chemistry book is 30 more than page of physics book.if ratio of pages is 5:3.a child torn 15 pages of chemistry book.calculate new ratio. options: A)1:1 B)2:1 C)5:4 D)4:3 E)2:3 SOLUTION:chemistry page=5x, physics page=3x 5x-3x=30,2x=30,x=15 chemistry page=75, physics page=45 after torn 15 page of chemistry=60 ratio become 60/45=4:3 answer D #### D QUESTION:Mr. 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. options: A)s. 5266 B)s. 5396 C)s. 5228 D)s. 5218 E)s. 52192 SOLUTION:Explanation: Let us assume Mr. Karan borrowed amount is Rs. A. (the principal) By formula of simple interest, S.I. = PRT / 100 Where P = The principal, R = Rate of interest as a %, T = Time in years S.I. = (P * 6 * 9)/100 = 54 P/100 Amount = Principal + S.I. 8310 = P + (54P/100) 8310 = (100P + 54P)/100 8310 = 154P/100 P = (8310 * 100)/154 = Rs. 5396.104 ANSWER: B #### B QUESTION:Martin bought 5 packet milk at an average price (arithmetic mean) of 20¢. If Martin returned two packet to the retailer, and the average price of the remaining millk packet was 12¢, then what is the average price, in cents, of the two returned milk packets? options: A)30 B)31 C)32 D)33 E)34 SOLUTION:Total price of 5 packet milk=5*20=100 Total price of 3 packet milk=3*12=36 Total price of 2 packet returned milk=100-36=64 Average price of 2 packet milk=64/2=32 Correct option Answer:C #### C QUESTION:A certain list consists of 21 different numbers. If n is in the list and n is 2 times the average (arithmetic mean) of the other 20 numbers in the list, then n is what fraction of the sum of the 21 numbers in the list? options: A)1/20 B)1/12 C)1/5 D)4/21 E)5/21 SOLUTION:series : a1, a2....a20,n sum of a1+a2+...+a20 = 20*x (x = average) so, n = 2*x Hence, a1+a2+..+a20+n = 22x So, the fraction asked = 2x/22x = 1/12 B #### B QUESTION:Calculate the largest 3 digit number which is exactly divisible by 89? options: A)911 B)969 C)979 D)977 E)971 SOLUTION:Largest 4 digit number is 999 After doing 999 ÷ 89 we get remainder 20 Hence largest 3 digit number exactly divisible by 89 = 999 - 20 = 979 C #### C QUESTION:What will come in place of the x in the following Number series? 12, 38, 116, 350, 1052, x options: A)2450 B)2560 C)3200 D)3400 E)3158 SOLUTION:12 12 × 3 + 2 = 38 38 × 3 + 2 = 116 116 × 3 + 2 = 350 350 × 3 + 2 = 1052 1052 × 3 + 2 = 3158 E #### E QUESTION:A store reduced the price of all items in the store by 9% 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? options: A)80.0 B)80.9 C)81.0 D)81.1 E)81.9 SOLUTION:consider price of the all items as $100 after a initial reduction of 9% price becomes = 0.91 *100 = $ 91 after the final reduction of 10% price becomes = 0.9* 91 = $ 81.9 price of all items on second day is 81.9% of price on first day correct answer option E #### E QUESTION:A reduction of 48% in the price of bananas would enable a man to obtain 64 more for Rs.40, what is reduced price per dozen? options: A)2.6 B)8.6 C)7.6 D)3.6 E)1.6 SOLUTION:Explanation: 40*(48/100) = 19.2 --- 64 ? --- 12 => Rs.3.6 Answer: D #### D QUESTION:If p, q and r are positive integers and satisfy x = (p + q -r)/r = (p - q + r)/q = (q + r - p)/p, then the value of x is? options: A)1/2 B)1 C)-1/2 D)-1 E)0 SOLUTION:When two or more ratios are equal, each of the ratios are equal to sum of the numerators divided by the sum of the denominators, provided sum of the denominators is non-zero. Hence, x = (p + q -r)/r = (p - q + r)/q = (q + r - p)/p => x = (p + q - r + p - q + r + q + r - p) / (r + q + p) => x = (r + q + p) / (r + q + p) = 1 p + q + r is non-zero. ANSWER:B #### B QUESTION:A man spends Rs. 1900 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 . 5200 a year. What is his average monthly income? options: A)2075 B)2175 C)2275 D)2375 E)2475 SOLUTION:Explanation: Total expenditure for the first 3 months = 3 × 1900 = 5700 Total expenditure for 4 months = 4 × 1550 = 6200 Total expenditure for 5 months = 5 × 1800 = 9000 Total expenditure and saving (which is income for one year) = 5700 + 6200 + 9000 + 5200 = Rs. 25200 So, Average monthly income = 26100/12 = Rs. 2175 Answer B #### B QUESTION:The average weight of a group of persons increased from 48 kg to 51 kg, when two persons weighing 78 kg and 93 kg join the group. Find the initial number of members in the group? options: A)87 B)67 C)23 D)75 E)25 SOLUTION:Let the initial number of members in the group be n. Initial total weight of all the members in the group = n(48) From the data, 48n + 78 + 93 = 51(n + 2) => 51n - 48n = 69 => n = 23 Therefore there were 23 members in the group initially. Answer: C #### C QUESTION:A man purchases 8 pens for Rs.9 and sells 9 pens for Rs.8, how much profit or loss does he make? options: A)30.98%loss B)20.98%loss C)20.97%loss D)20.68%loss E)20.98%loss SOLUTION:81 ---- 17 100 ----- ? è 20.98%loss Answer: B #### B QUESTION:m:n = 5: 8 , n: p = 6 : 7 , m:n:p = ? options: A)30 : 48 : 54 B)30 : 48 : 56 C)30 : 48 : 50 D)30 : 48 : 52 E)30 : 48 : 58 SOLUTION:m:n = 5: 8 n: p = 6 : 7 m:n:p =30 : 48 : 56 Answer : B #### B QUESTION:Six 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 5, what is the probability that one of the two cards drawn is numbered 3 ? options: A)1/3 B)1/2 C)1/4 D)1/5 E)1/6 SOLUTION:(3,2) (2,3) (4,1) (1,4) – only 4 possible scenarios for sum to be 5. One from this 4 has already happened. From this four cases, only in two we have 3. So, the probability is 2 chances out of 4 that the one that occurred had 3: P=2/4.=1/2 Answer: B. #### B QUESTION:A man bought 20 shares of Rs. 50 at 5 discount, the rate of dividend being 13. The rate of interest obtained is: options: A)27% B)87% C)15% D)66% E)88% SOLUTION:Investment = Rs. [20 x (50 - 5)] = Rs. 900. Face value = Rs. (50 x 20) = Rs. 1000. Dividend = Rs. 27 x 1000 = Rs. 135. 2 100 Interest obtained = 135 x 100 % = 15% 900 View Answer Discuss in Forum Answer: C #### C QUESTION:One packet of flower seeds was enough to just fill the area of the smaller garden in #3. How many packets of seed are needed for the larger garden? Round each answer to the nearest square foot before continuing. options: A)1 seed packet B)2 seed packets C)3 seed packets D)4 seed packets E)5 seed packets SOLUTION:3.14 x 32 = 28.26 sq. ft. area of small garden 28 sq. ft. rounded 3.14 x 62 = 113.04 sq. ft. area of large garden 113 sq. ft. rounded 113 ÷ 28 = 4.04 or 4 seed packets (rounded) correct answer D #### D QUESTION:Bat is bought for Rs.400 and sold at a gain of 20% find its selling price? options: A)Rs.320 B)Rs.350 C)Rs.370 D)Rs.480 E)None of these SOLUTION:Explanation : 100 % = 400 (100 * 4 = 400)120 % = 480 (120 * 4 = 480)Selling price = Rs.480/- Answer : D #### D QUESTION:The arithmetic mean of set P is zero. If Q = {-2.22; -1.96; -1.68; 1.62; 1.94; 2.16} is the subset of P consisting of all those elements in P which are more than two but less than three standard deviations away from the arithmetic mean of P, what could be equal to the standard deviation of P? options: A)0.54 B)0.77 C)0.82 D)0.97 E)1.62 SOLUTION:This is a fairly straightforward question that can be solved quickly by just applying the options We are provided with Mean, m= 0 and Q = {-2.22; -1.96; -1.68; 1.62; 1.94; 2.16} is the subset of P Q consists of all those elements in P that are more than 2 but less than 3 SDs away from the arithmetic mean of P If an element is 1 PD away from the mean, we can write it as either m + PD or m - PD Similarly, if an element is 2 PDs away from the mean, we can write it as either m + 2*PD or m - 2*PD So, if these elements lie within 2 and 3 PDs of mean, m=0 we can find which one of these values of PD satisfies each value within Q Only PD = 0.77 does Answer : B #### B QUESTION:A honey bee flies for 10 seconds, from a daisy to a rose. It immediately continues to a poppy, flying for 6 additional seconds. The distance the bee passed, flying from the daisy to the rose is 18 meters longer than the distance it passed flying from the rose to the poppy. The bee flies to the poppy at 3 meters per second faster than her speed flying to the rose. The bee flies how many meters per second from the daisy to the rose? options: A)1.4 B)1.5 C)1.6 D)1.8 E)1.0 SOLUTION:Let the speed be 's' and let the distance between rose and poppy be 'x' The problem boils down to: Rose to Poppy: s+3=x/6 ------- 1 Daisy to Rose: s=(x+18)/10------ 2 so from 1 we can re write x as x=6s+18 substitute the value of x in 2 gives us s=1.8 m/s D #### D QUESTION:What is the least possible product of 4 different integers, each of which has a value between –1 and 10, inclusive? options: A)–5040 B)–3600 C)–720 D)–600 E)–120 SOLUTION:Maximize the total product with a -ve sign so -1 * 10 * 9 * 8 = 720 * -1 = -720 Answer is C. #### C QUESTION:A football matches has been organized in such a fashion, every participating team plays a match against every other team once and only once. If 36 matches are totally played, how many teams participated? options: A)7 B)8 C)9 D)10 E)11 SOLUTION:For a match u need 2 teams. Suppose there are totally 'n'teams. Now we have to choose 2 teams out of 'n' teams. nC2 = 36; Solve to get n=9. n(n-1)/2 = 36 9(9-1)/2 = 36 9(8)/2 = 36 72/2 = 36 So, answer is 9 If 36 matches are totally played. ANSWER:C #### C QUESTION:Three pipes of same capacity can fill a tank in 8 hours. If there are only two pipes of same capacity, the tank can be filled in? options: A)15 hours B)12 hours C)76 hours D)16 hours E)81 hours SOLUTION:The part of the tank filled by three pipes in one hour = 1/8 => The part of the tank filled by two pipes in 1 hour = 2/3 * 1/8 = 1/12. The tank can be filled in 12 hours. Answer: B #### B QUESTION:A 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? options: A)33 B)277 C)40 D)88 E)11 SOLUTION:The total CP = Rs. 16000 + Rs. 6250 = Rs. 22250 and SP = Rs. 31150 Profit(%) = (31150 - 22250)/22250 * 100 = 40% Answer: C #### C QUESTION:If 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? options: A)41 B)42 C)43 D)44 E)45 SOLUTION:A two-digit number "cd" can be expressed algebraically as 10c+d. The sum of A + B = (10c+d)+(10d+c)=11(c+d). The only answer that is a multiple of 11 is 44. The answer is D. #### D QUESTION:Ram purchased a TV and a DVD Player for Rs. 25000 and Rs. 5000 respectively. He sold the DVD Player at a loss of 4 percent and TV at a profit of 10 percent. Overall he make a.? options: A)2200 B)2500 C)2800 D)2300 E)2000 SOLUTION:Let the SP of the TV and the DVD Player be Rs. r and Rs. m respectively. r = 25000(1 + 10/100) = 25000 + 2500 m = 5000(1 - 4/100) = 5000 - 200 Total SP - Total CP = r + m - (25000 + 5000) = 2500 - 200 = Rs. 2300 As this is positive, an overall profit of Rs. 2300 was made. Answer: D #### D QUESTION:what is the least number. which should be added to 221 to make it a perfect square? options: A)5 B)8 C)4 D)6 E)7 SOLUTION:221+4=225 15^2 ANSWER:C #### C QUESTION:If n is a positive integer, which of the following is a possible value of |36 - 5n|? options: A)7 B)14 C)12 D)15 E)20 SOLUTION:When 36>5n, then |36- 5n| = 71- 5n = (36-5n) + 1 = {multiple of 5} + 1 When 36<=5n, then |36- 5n| = -(71- 5n) = (36-70) - 1 = {multiple of 5} - 1 So, the correct answer must be 1 greater or 1 less than a multiple of 5. Only B fits. Answer: B #### B QUESTION:A 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.157. Find the unknown rate of two blankets? options: A)420 B)550 C)490 D)450 E)520 SOLUTION:10 * 157 = 1570 3 * 100 + 5 * 150 = 1050 1570 – 1050 = 520 Answer:E #### E QUESTION:Free notebooks were distributed equally among children of a class. The number of notebooks each child got was one-eighth of the number of children. Had the number of children been half, each child would have got 16 notebooks. Total how many notebooks were distributed? options: A)502 B)512 C)523 D)521 E)500 SOLUTION:Let n be the total number of children. More children, less notebooks(Indirect proportion) If the number children = n, number of books each child will get = n/8 If the number children = n/2, number of books each child will get = 16 Hence we can write as children n:n/2}::16:n/8 ⇒n×n/8=n/2×16 ⇒n8=16/2=8 ⇒n=8×8=64 Then, total number of notebooks those were distributed = n×n/8=(64×64)/8=64×8=512 Answer is B. #### B QUESTION:If 63 percent of a class answered the first question on a certain test correctly, 49 percent answered the second question on the test correctly, and 20 percent answered neither of the questions correctly, what percent answered both correctly? options: A)22% B)24% C)26% D)28% E)32% SOLUTION:63% answered the first question correctly and 20% answered neither correctly. Then 17% missed the first question but answered the second question correctly. Then the percent who answered both correctly is 49% - 17% = 32%. The answer is E. #### E QUESTION:A park square in shape has a 3 metre wide road inside it running along its sides. The area occupied by the road is 1764 square metres. What is the perimeter along the outer edge of the road? options: A)576 metres B)589 metres C)600 metres D)700 metres E)None SOLUTION:Solution Let the length of the outer edges be x metres. Then, length of the inner edge = ( x - 6)m. ∴ x2 - (x-6)2 = 1764 ‹=› x2-(x2-12x+36)= 1764 ‹=›12x = 1800 ‹=›x = 150. ∴ Required perimeter = (4x)m ‹=› (4 x 150)m = 600m. Answer C #### C QUESTION:Three people are playing cards. What is the probability that a card drawn from a pack of 52 cards will be a diamond or a king? options: A)1/3 B)2/11 C)4/13 D)5/13 E)5/14 SOLUTION:Here, n(S) = 52 There are 13 cards of diamond (including one king) and there are 3 more kings. Let E = event of getting a diamond or a king. Then, n(E) = (13 + 3) = 16 P (E) = 16 / 52 = 4/13 C #### C QUESTION:(128.5 x 32) + (13.8 x 30) = ? x 25 options: A)524.48 B)556.02 C)574.36 D)181.04 E)595.46 SOLUTION:Explanation : ? = (128.5 x 32) + (13.8 x 30)/25 = 4112 + 414/25 = 181.04 Answer : Option D #### D QUESTION:A person borrows Rs. 6000 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. options: A)120 rs B)150 rs C)160 rs D)180 rs E)200 rs SOLUTION:Gain in 2 years = [(6000*6*2)/100]-[(6000*4*2)/100] 720-480=240 Gain in 1 year =(240/2)=120 rs ANSWER:A #### A QUESTION:A gardener increased the length of a rectangle-shaped garden by 20 percent and decreased its width by 10 percent. The area of the new garden options: A)has increased by 20 percent B)has increased by 12 percent C)has increased by 8 percent D)is exactly the same as the old area E)cannot be expressed in percentage terms without actual numbers SOLUTION:Let L be the original length and let W be the original width. The original area was L*W. The new area is 0.9W*1.2L = (0.9)(1.2)L*W = 1.08*L*W The answer is C. #### C QUESTION:Simplify: 244 x 301 options: A)73144 B)73143 C)73200 D)72956 E)73444 SOLUTION:244 x 301 = 244 x (300 + 1) = 73200 + 244 =73444 Answer is E #### E QUESTION:Find the compound interest on Rs. 7500 at 4% per annum for 2 years, compounded annually. options: A)Rs. 610 B)Rs. 612 C)Rs. 614 D)Rs. 616 E)None of these SOLUTION:Explanation: Amount=[7500×(1+4100)2]=(7500×2625×2625)=8112 So compound interest = (8112 - 7500) = 612 Answer: B #### B QUESTION:what is the smallest integer that is multiple of 3,7 and 20 options: A)141 B)180 C)130 D)122 E)420 SOLUTION:Correct Answer :E It is the lcm of 3,7 and 20 which is 420 #### E QUESTION:A 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? options: A)2 months B)7 months C)8 months D)10 months E)12 months SOLUTION:Explanation: 7 * 8 : 9 * x = 8:9 => x= 7 months ANSWER:B #### B QUESTION:If n = 2.0767 and n* is the decimal obtained by rounding n to the nearest hundredth, what is the value of n* – n? options: A) -0.0053 B) -0.0003 C) 0.0007 D) 0.0047 E) 0.0033 SOLUTION:n*=2.08 n*-n=2.08-2.0767 0.0033 Answer: E #### E QUESTION:The average of 20 results is 65 and the average of other 65 results is 20 . what is the average of all the results? options: A)30 B)25 C)48 D)50 E)None SOLUTION:Answer Sum of 85 result = sum of 20 result + sum of 65 result. = 20 x 65 + 65 x 20 = 2600 Correct Option: A #### A QUESTION:The average weight of a group of 30 friends increases by 3 kg when the weight of their 3 football coaches was added. If average weight of the group after including the weight of the 3 football coach is 33 kg, what is the average weight of their football coaches ? options: A)31 kg B)63 kg C)61 kg D)62 kg E)91 kg SOLUTION:let c=coach's avg. weight original total weight=(30 friends)(30 kg avge)=900kg (900+3c)/(30+3)=33 kg avg. c=63 kg Answer B #### B QUESTION:A car traveled 448 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? options: A)14 B)18 C)21 D)22 E)27 SOLUTION:Let the speed in highway be h mpg and in city be c mpg. h = c+6 h miles are covered in 1 gallon 462 miles will be covered in 462/h. Similarly c miles are covered in 1 gallon 336 miles will be covered in 336/c. Both should be same (as car's fuel capacity does not change with speed) => 336/c = 448/h => 336/c = 448/(c+6) => 336c+336*6=448c =>c=336*6/112=18 Answer B. #### B QUESTION:The true discount on a bill of Rs.4320 is Rs.720.The banker's discount is options: A)862 B)864 C)866 D)868 E)None of these SOLUTION:Solution P.W = Rs.(4320 - 720) = Rs. 3600 S.I on Rs. 4320 =Rs.(720/3600 x 4320) = Rs. 864. Answer B #### B QUESTION:Thin rectangular slab of potato was cut into two pieces for an osmosis lab. One piece is 50mm greater than the other. If the original uncut slab is 600mm, what is the length of the other piece of the potato after it is cut. options: A)550 B)275 C)50 D)300 E)250 SOLUTION:piece one as p1, and piece two as p2. p2+50=p1 as eq.a p1+p2=600 as eq.b substitute eq. a into eq.b, resulting in (p2+50) + p2=600mm. Group like terms, p2+p2=600-50 (2*p2/2)=550/2 solves to p2= 275. Ansewr is B. #### B QUESTION:A vendor sold two things at same cost of 16 RS with one item at 25%profit and other at 20%loss,by this transaction he made profit or loss by how much options: A)0.60 loss B)0.70 loss C)0.80 loss D)0.50 loss E)0.40 loss SOLUTION:CP when profit of 25% = 12.8 CP when loss of 20% = 20 Total CP = 32.8 Total SP = 32.00 Total loss = 0.80 ANSWER:C #### C QUESTION:John 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? options: A) 24 B) 34.8 C) 37.8 D) 40 E) 84 SOLUTION:The difference between the amounts John paid and Jane paid is the deference between 15% of p and 15% of 0.9p: 0.15p - 0.15*0.9p = 0.60 --> 15p - 13.5p = 60 --> p = 40. Answer: D. #### D QUESTION:A boat can move upstream at 25 kmph and downstream at 35 kmph, then the speed of the current is? options: A)5 B)9 C)4 D)1 E)3 SOLUTION:US = 25 DS = 35 M = (35 - 25)/2 = 5 Answer: A #### A QUESTION:The ratio of the ages of Mini and Minakshi is 4 : 3. The sum of their ages is 14 years. The ratio of their ages after 8 years will be options: A)5 : 3 B)8 : 11 C)8 : 7 D)6 : 5 E)3 : 11 SOLUTION:Let Mini’s age = 4x and Minakshi’s age = 3x Then 4x + 3x = 14 x = 2 Mini’s age = 8 years And Minakshi’s age = 6 years Ratio of their ages after 8 years = (8 + 8) : (6 + 8) = 16 : 14 = 8 : 7 ANSWER:C #### C QUESTION:In a 1000 m race, A beats B by 200 meters or 25 seconds. Find the speed of B? options: A)8 B)9 C)7 D)5 E)2 SOLUTION:Since A beats B by 200 m or 25 seconds, i t implies that B covers 200 m in 25 seconds. Hence speed of B = 200/25 = 8 m/s. Answer: A #### A QUESTION:Three different containers contain 496 litres, 403 litres and 713 litres of mixture of milk and water respectively. What is the biggest measure can measure all the different quantities exactly ? options: A)29 litres B)31 litres C)35 litres D)19 litres E)26 litres SOLUTION:M1 = 496 litres M2 = 403 litres M3 = 713 litres Required measurement = H.C.F. of M1,M2,M3 = 31 litres Answer is B #### B QUESTION:What approximate value should come in plce of question mark (?) in the following equations ? 728.038 x 54.978 - 72.016 x 85.250 = ? options: A)31400 B)32700 C)33900 D)34400 E)32400 SOLUTION:Explanation : ? = 728 x 55 - 72 x 85.25 = 40040 - 6138 = 339900 Answer : Option C #### C QUESTION:The G.C.D of 1.08, 0.42 and 0.9 is options: A)0.19 B)0.1 C)0.06 D)0.11 E)0.12 SOLUTION:Explanation: Given numbers are 1.08 , 0.42 and 0.90 H.C.F of 108, 42 and 90 is 6 [because G.C.D is nothing but H.C.F] therefore H.C.F of given numbers = 0.06 Answer: C) #### C QUESTION:Pants, Shorts and Shirts in a dresser are in the ratio of 7: 7: 10. If there are 14 Pants, the number of Shirts in the dresser is: options: A)14 B)7 C)20 D)70 E)35 SOLUTION:Explanation : Let Pants = 7x, Shorts = 7x & Shirts = 10x. Now, 7x = 14 hence x = 2. Number of Apples = 10x = 20. Answer : C #### C QUESTION:A four-character password consists of one letter of the alphabet and three different digits between 1 and 9, inclusive. The letter must appear as the second or third character of the password. How many different passwords are possible? options: A)5,040 B)18,720 C)26,208 D)37,440 E)52,000 SOLUTION:4 character password: DLDD First digit can be chosen in 9 ways. The letter can be chosen in 26 ways. Next digit can be chosen in 8 ways. Next digit can be chosen in 7 ways. This gives us 9*26*8*7ways Now, the letter can also be DDLD so there will be another 9*26*8*7 ways Total = 9*26*8*7*2 = 26,208 ways C #### C QUESTION:For my anniversary, I decided to surprise my wife. Since she is a voracious reader, I decided to collect a lot of books for her. On the first day of the month, I bought one book, on the second, I bought two and on the third, I bought three. This process went on till the anniversary and on the day, I had 253 books with me to gift her. Can you calculate, on which day is our anniversary? options: A)31 B)28 C)23 D)33 E)22 SOLUTION:E 22rd day 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 + 14 + 15 + 16 + 17 + 18 + 19 + 20 + 21 + 22 = 253 Thus our anniversary falls on the 22rd day of the month. You can apply other formulas to shorten the process but that is the simplest way to do it. #### E QUESTION:What is the place value of 7 in the numeral 2734? options: A)450 B)500 C)700 D)800 E)840 SOLUTION:Option 'C' 7 * 100 = 700 #### C QUESTION:Two different solutions of alcohol with respective proportions of alcohol to water of 3:1 and 2:3 were combined. What is the concentration of alcohol in the new solution if the first solution was 4.6 times the amount of the second solution? options: A)62.0 B)65.25 C)68.75 D)70.15 E)72.35 SOLUTION:SOL: Lets assume that 46L of sol1 was mixed with 10L of sol2. Alcohol in Sol1: 46*3/4 = 34.5L Alcohol in Sol2: 10*2/5 = 4L Total Alcohol in the mixed solution of 56L = 34.5 + 4 = 38.5L Alcohol concentration in the new sol: (38.5/56)*100 = 68.75% ANSWER:C #### C QUESTION:The probability of rain showers in Barcelona on any given day is 0.3. What is the probability that it will rain on exactly one out of three straight days in Barcelona? options: A)0.441 B)0.072 C)0.432 D)0.72 E)0.288 SOLUTION:IMO This is just for first day! It can rain on 2nd day or 3 rd day (and not rain on other days) in 3 consecutive days! Hence, 0.3*0.7*0.7 + 0.7*0.3*0.7 + 0.7*0.7*0.3 = 0.441 Option - A #### A QUESTION:How many numbers from 10 to 40 are exactly divisible by 3? options: A)13 B)15 C)16 D)10 E)18 SOLUTION:12, 15, 18, 21, 24, 27, 30, 33, 36, 39. 10 Numbers. 10/3 = 3 and 40/3 = 13 ==> 13 - 3 = 10. Therefore 10 digits D) #### D <<<Examples ends QUESTION:If in a triangle, the area is numerically equal to the perimeter, then the radius of the inscribed circle of the triangle is options: A)1 B)2 C)3 D)4 E)5 SOLUTION:Solution Radius = Area / Semi perimeter = [Area x 2 / Area] = 2. Answer B #### B

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:A, 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? options: A)2399 B)2889 C)2830 D)2878 E)3000 SOLUTION:Explanation: 60*5:36*6:75*3 100: 72: 75 100/247 * 7410 = 3000 Answer: E #### E QUESTION:Excluding stoppages, the speed of a train is 55 kmph and including stoppages it is 40 kmph. Of how many minutes does the train stop per hour? options: A)82 B)16 C)12 D)82 E)18 SOLUTION:Explanation: T = 15/55 * 60 = 16 Answer: Option B #### B QUESTION:Ramu bought an old car for Rs. 42000. He spent Rs. 13000 on repairs and sold it for Rs. 64900. What is his profit percent? options: A)19% B)11% C)18% D)218% E)14% SOLUTION:Total CP = Rs. 42000 + Rs. 13000 = Rs. 55000 and SP = Rs. 64900 Profit(%) = (64900 - 55000)/55000 * 100 = 18% Answer:C #### C QUESTION:If in a triangle, the area is numerically equal to the perimeter, then the radius of the inscribed circle of the triangle is options: A)1 B)2 C)3 D)4 E)5 SOLUTION:Solution Radius = Area / Semi perimeter = [Area x 2 / Area] = 2. Answer B #### B QUESTION:The quantities S and T are positive and are related by the equation S=K/T, where k is a constant. If the value of S increases by 60 percent, then the value of T decreases by what percent? options: A)25% B)33 ¹/₃% C)50% D)66 ²/₃% E)75% SOLUTION:We can assign numbers: lets say S = 2, K = 6 (constant) and T = 3 (so that S=K/T) Now increasing S by 50% gives S=4, K remains constant, so T = 2 (6/2=3) decrease in T= 1, percent decrease in T = (1/4)*100 = 25% Answer A #### A QUESTION:The value of ((x – y)³ + (y - z)³ + (z – x)³)/(21 (x – y) (y – z) (z – x)) is equal to : options: A)0 B)1/12 C)1/7 D)1/4 E)1/3 SOLUTION:Since (x – y) + (y – z) + (z – x) = 0, so (x – y)³ + (y – z)³ + (z – x)³= 3 (x – y) (y – z) (z – x). (3 (x – y) (y – z) (z – x))/(21(x – y) (y – z) (z – x)) = 1/7. ANSWER:C #### C QUESTION:In 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 W percentage of those asked favoured more than one of the 3 proposals. options: A) 10 B) 12 C) 17 D) 22 E) 30 SOLUTION:Bunuel, my answer for exactly 2 people was 17 and this was my approach: 100%=(A+B+C)-(AnB+AnC+BnC)-5%+22% which leads me to W=100%=(50+30+20)-(at least 2 people)-5%+22%.C #### C QUESTION:w,x,y,z is an arithmetic sequence, which of the following options also qualifies as an arithmetiv sequence? I. w-6,x-6,y-6,z-6 II. 5w,2x,3y,5z III. 5w,5x,5y,5z options: A)II and III B)III only C)I and III D)I and II E)II only SOLUTION:lets look at the three choices... I. w-6,x-6,y-6,z-6 since the difference is constant, it is an arithmetic sequence... II. 5w,2x,3y,5z since the difference is not constant, it is not an arithmetic sequence III. 5w,5x,5y,5z since the difference is constant it is an arithmetic sequence... Answer is A) #### A QUESTION:Find the area of right angled triangle whose hypotenuse is 15 cm and one of the sides is 12 cm. options: A)34 cm² B)38 cm² C)54 cm² D)56 cm² E)64 cm² SOLUTION:AB² = AC² - BC² = 15² - 12² = 225 - 144 = 81 Therefore, AB = 9 Therefore, area of the triangle = ¹/₂ × base × height = ¹/₂ × 12 × 9 = 54 cm² ANSWER : C #### C QUESTION:What is the remainder when you divide 2^200-1 by 7? options: A)1 B)2 C)3 D)4 E)5 SOLUTION:answer is C. this is very similar to the 32^32^32-1 divided by 7 question. #### C QUESTION:A cistern has a leak which would empty the cistern in 20 minutes. A tap is turned on which admits 6 liters a minute into the cistern, and it is emptied in 24 minutes. How many liters does the cistern hold? options: A)480 B)487 C)720 D)729 E)268 SOLUTION:1/x - 1/20 = -1/24 x = 120 120 * 6 = 720 Answer:C #### C QUESTION:A part-time employee whose hourly wage was increased by 10 percent decided to reduce the number of hours worked per week so that the employee's total weekly income would remain unchanged. By what percent should the number of hours worked be reduced? options: A)9.09 B)10 C)11 D)12 E)13 SOLUTION:Let original hourly wage be x and let the no of hours worked be y Total wage will be =x*y After the increment the wage will be=1.1 x Now we need to find number of hours worked so that x*y=1.1x*z i.e z=x* y/1.1x= 1/1.1 y %decrease = (y-1/1.1y)/y *100= 1-1/1.1 *100 =9.09% Thus my answer is A. #### A QUESTION:If a tire rotates at 400 revolutions per minute when the car is traveling 120km/h, what is the circumference of the tire? options: A)2 meters B)6 meters C)5 meters D)3 meters E)7 meters SOLUTION:400 rev / minute = 400 * 60 rev / 60 minutes = 24,000 rev / hour 24,000 * C = 120,000 m : C is the circumference C = 5 meters correct answer C #### C QUESTION:The forth proportional to 1,2,3 is? options: A)2 B)4 C)8 D)9 E)6 SOLUTION:Let the fourth proportional to 1,2,3 be x then 1:2::3:x 1x = 2*3 x = 6 Answer is E #### E QUESTION:A certain company retirement plan has arule of 70provision that allows an employee to retire when the employee's age plus years of employment with the company total at least 70. In what year could a female employee hired in 1989 on her 32nd birthday first be eligible to retire under this provision? options: A)2008 B)2004 C)2005 D)2006 E)2007 SOLUTION:She must gain at least 70 points, now she has 32 and every year gives her two more points: one for age and one for additional year of employment, so 32 + 2*(# of years) = 70 --> (# of years) = 19 --> 1989+19=2008. Answer: A. #### A QUESTION:Two numbers are respectively 20% and 25% more than a third number. The percentage that is first of the second is? options: A)98% B)56% C)96% D)964% E)16% SOLUTION:I II III 120 125 100 125----------120 100-----------? => 96% Answer:C #### C QUESTION:There are six leopards and one sheep. Leopard can eat sheep but since as the land is magical, the leopards who eats the sheep , turns into sheep and then can be eaten by the remaining leopard(s). If we leave them for some time then how many sheep and leopard will be there , when we come back ? options: A)4 leopard and one sheep B)5 leopard and one sheep C)6 leopard and one sheep D)7 leopard and one sheep E)None SOLUTION:Solution: 5 leopard and one sheep since all animal are rational , once 1st leopard eats the sheep all the rest of leopard would know about this. Answer B #### B QUESTION:A and B starts a business with Rs.8000 each, and after 8 months, B withdraws half of his capital . How should they share the profits at the end of the 18 months? options: A)18:11 B)18:13 C)23:12 D)11:9 E)11:10 SOLUTION:A invests Rs.8000 for 18 months, but B invests Rs.8000 for the first 8 months and then withdraws Rs.4000. So, the investment of B for remaining 10 months is Rs.4000 only. A : B 8000*18 : (8000*8) + (4000*10) 144000 : 104000 A:B = 18:13 ANSWER:B #### B QUESTION:A girl has exactly 5 quarters, 9 dimes, and 10 nickels in her pocket. If she withdraws a number of these coins at random, how many coins would she have to withdraw to ensure that she has at least a 50 percent chance of withdrawing at least one quarter? options: A)2 B)3 C)4 D)5 E)6 SOLUTION:When the probability of NOT drawing a quarter is 50% or less, then the probability of drawing a quarter is at least 50%. P(not drawing a quarter with 2 coins) = 19/24 * 18/23 = 57/92 > 50% P(not drawing a quarter with 3 coins) = 57/92 * 17/22 = 969/2024 < 50% The answer is B. #### B QUESTION:Select the non termination decimal among the following. options: A)5/3 B)3/4 C)4/5 D)7/8 E)9/10 SOLUTION:A. Non terminating decimal means that 5/3 = 1.66666 and so on. #### A QUESTION:There are 2 red chips and 2 blue ones. When arranged in a row, they form a certain color pattern, for example RBRRB. How many color patterns? options: A)A)10 B)B)12 C)C)24 D)D)60 E)E)100 SOLUTION:Using anagram method: 4_3_2_1 R_R_B_B so.. 4!/Number of repeated letters (2!)(2!) = 6 ANS:D #### D QUESTION:If Ajay drives at 4/5th of his usual speed to his office, he is 6 minutes late. What is his usual time to reach his office? options: A)38 B)27 C)24 D)19 E)17 SOLUTION:Explanation: Let t be his usual time to reach his office and v be his usual speed. v = d/t ……….(d is the distance Ajay travels while going to his office) vt = d At v1 = 4v/5 ; t1 = t + 6 4v/5 = d/(t + 6) 4v/5* (t + 6) = d 4v/5* (t + 6) = vt On solving we get, t = 24 minutes ANSWER:C #### C QUESTION:I. m-14, m, m, m, m+14 II. b, b+1, b+2, b+3, b+4 III. c, c, c, c, c The data sets I, II, and III above are ordered from greatest standard deviation to least standard deviation in which of the following? options: A)I, II, III B)I, III, II C)II, III, I D)III, I, II E)III, II, I SOLUTION:S.D is a non-negative entity. Also, for a given set with all the elements same, the S.D is Zero(It is zero even if there is only one element in the set too). From the given sets, we can see that the last set has a standard deviation of zero. Also, because the other sets can not have all the terms equal for any values of m or b, thus the S.D for the third set(III) has to be the minimum. Select the option which has III in the end. A. #### A QUESTION:A photo-mat shop charges $0.50 for the first photo inside a film, and 40% cents less for each additional photo. How many photos can we develop with $24 if each film contains 36 photos? options: A)2 films and 6 photos B)5 films and 6 photos C)5 films and 14 photos D)6 films and 4 photos E)6 films and 28 photos SOLUTION:1st photo = 0.50 Subsequent = 0.50*0.6=0.3 Price of 1 full film=0.50+0.3*35=11 Price of 2 full film = 11*2=22 24-22=2 2=0.5+0.3x x=5 24--->2 full films and 1+5=6 photos Answer: A #### A QUESTION:In what time will a train 100 m long cross an electric pole, it its speed be 54 km/hr? options: A)2.5 B)2.9 C)6.67 D)2.8 E)2.1 SOLUTION:Speed = 54 * 5/18 = 15 m/sec Time taken = 100/15 = 6.67 sec. Answer:C #### C QUESTION:In a group of 28 junior high school students, 7 take French, 9 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? options: A)7 B)6 C)9 D)4 E)8 SOLUTION:E 8 Add 7 + 9 + 4 to get 20. Then subtract 21 from the total students ⇒ 28 – 20 = 8. Answer is E #### E QUESTION:The maximum number of students among them 100 pens and 50 pencils can be distributed in such a way that each student get the same number of pens and same number of pencils? options: A)50 B)75 C)69 D)79 E)82 SOLUTION:number of pens = 100 number of pencils = 50 Required number of students = H.C.F. of 100 and 50 = 50 Answer is A #### A QUESTION:A part of certain sum of money is invested at 16% 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? options: A)5:4 B)1:4 C)3:1 D)3:5 E)3:4 SOLUTION:12:16 = 3:4 ANSWER:E #### E QUESTION:What 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 ? options: A)1288 B)2797 C)3944 D)1299 E)1082 SOLUTION:Let the side of the square plot be 'a' ft. Given area of the plot (a x a) = 289 => a = 17 Length of the fence = Perimeter of the plot = 4a = 68 ft. Cost of building the fence = 68 x 58 = Rs. 3944. Answer: C #### C QUESTION:If an article is sold at 19% profit instead of 12% profit, then the profit would be $84 more. What is the cost price? options: A)$900 B)$1200 C)$1500 D)$1800 E)$2100 SOLUTION:7% * cost price = $84 1% * cost price = $84 / 7 = $12 The cost price is $1200. The answer is B. #### B QUESTION:In what time will a train 100 metres long cross an electric pole, if its speed be 144 km/hr? options: A)2.5 sec B)4.25 Sec C)5 sec D)12.5 sec E)None SOLUTION:Solution Speed = (144 x 5 /18) m/sec = 40 m / sec Time taken = (100 /40) sec = 2.5 sec. Answer A #### A QUESTION:If a sum of money borrowed at 5 percent/annum SI amounts to Rs.1020 in 4 yrs, then the sum of money borrowed is? options: A)Rs. 850 B)Rs. 900 C)Rs. 980 D)Rs. 990 E)Rs. 1000 SOLUTION:Sol We have, A : Rs.1U2D Let the pr xnpal be R5 x Then mterest u — 12 : wzo — x Therefore, by u xglurmula. _umxx ’ Rx’: ( , _ma>< 1nzn—xv \4Ve|\a\e,Jc— 5“ :> ~(:51DD—S*(or6x:51UU or, J: : w 350 . The sum of money burrowed : Rs. 850 A) #### A QUESTION:There 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? options: A)12 B)23 C)28 D)80 E)84 SOLUTION:The number of ways in which one can travel from P to R = 3 × 4 = 12 Answer is A #### A QUESTION:A certain family has 3 sons: Richard is 6 years older than David, and David is 8 years older than Scott. If in 8 years, Richard will be twice as old as Scott, then how old was David 7 years ago? options: A) 8 B) 10 C) 12 D) 14 E) 7 SOLUTION:Let's say Age of Richard isR Age of David isD Age of Scott isS Now Richard is 6 years older than David, i.e. R = D +6 David is 8 years older than Scott i.e. D = S +8 If in 8 years, Richard will be twice as old as Scott i.e. R+8 = 2x(S+8) i.e. R+8 = 2S + 16 i.e. R = 2S+8 But R = D+6 = (S+8)+6 = S+14 therefore, 2S + 8 = S +14 i.e. S = 6 i.e. R = 20 i.e. D = 14 Now, how old was David 7 years ago? i.e. D-7 = 14-7 = 7 years Answer: Option E #### E QUESTION:In how many years will a sum of money doubles itself at 30% per annum on simple interest? options: A)7% B)3% C)5% D)8% E)2% SOLUTION:P = (P*30*R)/100 R = 3% Answer:B #### B QUESTION:If Rahul rows 15 km upstream in 3 hours and 21 km downstream in 3 hours, then the speed of the stream is options: A)5 km/hr B)4 km/hr C)2 km/hr D)1 km/hr E)None of these SOLUTION:Explanation: Rate upstream = (15/3) kmph Rate downstream (21/3) kmph = 7 kmph. Speed of stream (1/2)(7 - 5)kmph = 1 kmph Answer: D #### D QUESTION:All the students of class are told to sit in circle shape. Here the boy at the 8 th position is exactly opposite to 33 th boy. Total number of boys in the class? options: A)40 B)50 C)28 D)38 E)48 SOLUTION:As half the circle shape consist of 33-8=25 boys, So total number of boys in full circle=2*25=50 ANSWER: B #### B QUESTION:John walking at 4 Kmph reaches his office 8 minutes late. If he walks at 6 Kmph, he reaches there 9 minutes earlier. How far is the office from his house? options: A)3 2/5 Km B)3 1/5 Km C)4 1/5 Km D)5 1/5 Km E)None SOLUTION:Formula = S1*S2/S2-S1 * T1+T2/60 = 4*6/2 * 17/6 = 24/2 * 17/60 = 17/5 = 3 2/5 Km A #### A QUESTION:In 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? options: A)160 B)175 C)180 D)195 E)215 SOLUTION:Suppose the man works overtime for x hours. Now, working hours in 4 weeks = (5 X 8 X 4) = 160. 160 X 2.40 + x X 3.20 = 432 3.20 X = 432 - 384 = 48 x = 15. Hence, total hours of work = (160 + 15) = 175 Answer: Option B #### B QUESTION:In a theater, the first row has 15 seats and each row has 2 more seats than previous row. If the last row has 53 seats, what is the total number of seats in the theater? options: A)600 B)640 C)680 D)720 E)760 SOLUTION:The number of seats in the theater is 15 + (15+2) + ...+ (15+38)= 20(15) + 2(1+2+...+19)= 20(15) + 2(19)(20)/2= 20(15+19) = 20(34) = 680 The answer is C. #### C QUESTION:The ratio of cats to dogs to birds to fish is 3:4:5:6. There are no other types of animals in the pet store. which of the following cannot be the total number of animals in the store? options: A)36 B)54 C)72 D)90 E)101 SOLUTION:The parts add up to 3 + 4 + 5 + 6 = 18, so we know that any possible number of total answers must be a multiple of 18. All five answer choices are multiples of 18: (A) 36 = 18*2 (B) 54 = 18*3 (C) 72 = 18*4 (D) 90 = 18*5 (E) 101 = not a multiple of 18 ans is E #### E QUESTION:M = {-6, -5, -4, -3, -2} T = {-3, -2, -1, 0, 1, 2, 3, 4} If 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? options: A)0 B)1/3 C)2/5 D)1/2 E)3/5 SOLUTION:We will have a negative product only if 1, 2, 3, or 4 are selected from set T. P(negative product) = 4/8 = 1/2 The answer is D. #### D QUESTION:he L.C.M. of two numbers is 48. The numbers are in the ratio 2 : 3. Then sum of the number is: options: A)30 B)40 C)38 D)36 E)39 SOLUTION:Let the numbers be 2x and 3x. Then, their L.C.M. = 6x. So, 6x = 48 or x = 8 The numbers are 16 and 24. Hence, required sum = (16 + 24) = 40. Answer: Option B #### B QUESTION:A 45° -45° - 90° right triangle has hypotenuse of length h. What is the area of the triangle E in terms of h? options: A)h/ √2 B)h/2 C)h/4 D)(h)^2 E)(h)^2/4 SOLUTION:IF...each of the two shorter sides = 3, then the hypotenuse = H = 3(root2). The AREA E= (1/2)(Base)(Height) = (1/2)(3)(3) = 9/2. So we're looking for an answer that = 9/2 when H = 3(root2). There's only one answer that matches... E #### E QUESTION:The average age of three boys is 40 years and their ages are in proportion 6:10:8. What is the age in years of the youngest boy? options: A)8 B)10 C)7 D)6 E)5 SOLUTION:6x + 10x + 8x = 40 x =1.6 6x = 10 Answer:B #### B QUESTION:Which of the following inequalities is equivalent to −4 < x < 8? options: A)|x - 1| < 7 B)|x + 2| < 6 C)|x + 3| < 5 D)|x - 2| < 6 E)None of the above SOLUTION:We know that |x| < a means -a < x < a, where Sum of lower limit of x (i.e -a) and the upper limit of x (i.e a), is 0 Given is, -4 < x < 8, let's say by adding y to this inequality we will get into the above format -4+y < x+y < 8+y Now, to move this into the mod format, we need to have (-4+y) + (8+y) = 0 => y = -2 Thus, -6< x-2 < 6 => |x-2| < 6. Hence, answer is D #### D QUESTION:How many numbers between 11 and 90 are divisible by 7 ? options: A)23 B)11 C)22 D)32 E)15 SOLUTION:The required numbers are 14, 21, 28, 35, .... 77, 84. This is an A.P. with a = 14 and d = (21 - 14) = 7. Let it contain n terms. Then, Tn = 84 => a + (n - 1) d = 84 => 14 + (n - 1) x 7 = 84 or n = 11. Required number of terms = 11 ANSWER B 11 #### B QUESTION:In 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: options: A)12 km/hr B)11 km/hr C)10 km/hr D)8 km/hr E)15 km/hr SOLUTION:EXPLANATION Let speed of the boat in still water = a and speed of the stream = b Then a + b = 14 a - b = 8 Adding these two equations, we get 2a = 22 => a = 11 ie, speed of boat in still water = 11 km/hr ANSWER IS B #### B QUESTION:Out of 8 consonants and 4 vowels, how many words of 3 consonants and 1 vowels can be formed? options: A)21005 B)10500 C)25200 D)5376 E)None of these SOLUTION:Solution Number of ways of selecting (3 consonants out of 8) and (1 vowels out of 4) 8c3 x 4c1= (8x7x6/3x2x1)x(4/1) =224 Number of group,each having 3 consonants and 1 vowels = 224 . Each group contains 4 letter. Number of ways of arranging 5 letters among themselves = 4 ! = (4 × 3 × 2 × 1) = 24 . So, Required number of words = (24 × 224) = 5376 .Answer D #### D QUESTION:If the ratio of boys to girls in a class is B and the ratio of girls to boys is G; then 3 (B + G) is ? options: A)Equal to 3 B)Less than 3 C)More than 3 D)Less than 1/3 E)none of these SOLUTION:Let number of boys = x Let number of girls = y Therefore x/y = B and y/x = G 3(B + G) = 3[(x/y) + (y/x)] = 3[(x2 + y2)/xy] > 3 ANSWER:C #### C QUESTION:The averge score of a cricketer for ten matches is 66 runs. If the average for the first six matches is 54. Then find the average for the last four matches? options: A)66 B)83.5 C)84 D)95 E)76 SOLUTION:sum of last 4 matches = (10 × 66) – (6 × 54)= 336 Average = 336/4 = 84 ANSWER:C #### C QUESTION:Two squares are chosen at random on a chessboard. What is the probability that they have a side in common? options: A)1/18 B)64/4032 C)63/64 D)1/9 E)1/4 SOLUTION:Explanation : No of ways of selecting two squares from 64 squares on the chess board is 64C2. Three cases arise: case 1: when first square is any of the four corner ones In this case second square can be chosen in 2 ways no of ways of selecting two squares: 4*2 = 8 case2: when first square is any of the 24 squares on the side of the chess board other than the corner ones the second square can be chosen in 3 ways no of ways of selecting two squares: 24*3 = 72 case 3: the first square is any of the 36 remaining squares the second square can be chosen in 4 ways no of ways of selecting two squares: 36*4 = 144 Total no of ways of selecting two adjacent squares = 8 + 72 + 144 = 224 So required probability = 224/64C2 = 224/4032 = 1/18 Answer : A #### A QUESTION:An seller earns an income of Re 3 on the first day of his business. On every subsequent day, he earns an income which is just thrice of that made on the previous day. On the 15th day of business, he earns an income of: options: A)19 B)22 C)25 D)20 E)36 SOLUTION:2nd day he earns = 3(2 – 3) 3rd day he earns = 3(3 – 3) On 15th day he earns 3(15 -3) = 36 rupees ANSWER:E #### E QUESTION:A store reduced the price of all items in the store by 9% 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? options: A)80.0 B)80.9 C)81.0 D)81.1 E)81.9 SOLUTION:consider price of the all items as $100 after a initial reduction of 9% price becomes = 0.91 *100 = $ 91 after the final reduction of 10% price becomes = 0.9* 91 = $ 81.9 price of all items on second day is 81.9% of price on first day correct answer option E #### E QUESTION:The average marks of a class of 30 students is 50 and that of another class of 50 students is 60. Find the average marks of all the students? options: A)56.25 B)52.9 C)52.1 D)52.3 E)42.5 SOLUTION:Sum of the marks for the class of 30 students = 30 * 50 = 1500 Sum of the marks for the class of 50 students = 50 * 60 = 3000 Sum of the marks for the class of 80 students = 1500 + 3000 = 4500 Average marks of all the students = 4500/80 = 56.25 Answer:A #### A QUESTION:On a certain road, 10% of the motorists exceed the posted speed limit and receive speeding tickets, but 60% of the motorists who exceed the posted speed limit do not receive speeding tickets. What percent of the motorists on that road exceed the posted speed limit? options: A)10.5% B)12.5% C)15% D)25% E)30% SOLUTION:suppose there are X motorists. 10% of them exceeded the speed limit and received the ticket, i.e. X/10. Again, suppose total no. of motorists who exceeded the speed limit are Y. 60% of Y exceeded the speed limit but didn't received the ticket, i.e. 3Y/5. it means 2Y/5 received the ticket. hence, 2Y/5 = X/10 or Y/X=1/4 or Y/X * 100= 1/4 * 100= 25% D #### D QUESTION:If A,B,C are three integers and AB+C is even ; which of the following must be true? A)C is even B)B is even C)AB is even options: A)I only B)II only C)III only D)II,III only E)None of the above SOLUTION:If AB is Odd then C will not even. O+E = O If B is even AB is even always. But If C is Odd E+O = O None of the above are true #### E QUESTION:Which of the following will give a non-integer on taking cube root? options: A)–64 B)–1 C)8 D)9 E)27 SOLUTION:all except 9, square root of 9 is 3 which is an integer but cube root is not an integer so answer is D #### D QUESTION:When the positive integer k is divided by the positive integer n , the remainder is 13. If k/n = 81.2 , what is the value of n? options: A)9 B)20 C)55 D)70 E)81 SOLUTION:Here's an approach that's based on Number Properties and a bit ofbrute forcemath: We're told that K and N are both INTEGERS. Since K/N = 81.2, we can say that K = 81.2(N) N has tomultiply outthe .2 so that K becomes an INTEGER. With the answers that we have to work with, N has to be a multiple of 5. Eliminate A and E. With the remaining answers, we can TEST THE ANSWERS and find the one that fits the rest of the info (K/N = 81.2 and K/N has a remainder of 11) Answer B: If N = 20, then K = 1624; 1624/20 has a remainder of 4 NOT A MATCH Answer C: If N = 55, then K = 4466; 4466/55 has a remainder of 11 MATCH. Final Answer: B #### B QUESTION:Insert the missing number 100,91,....,76,70 options: A)82 B)83 C)84 D)81 E)80 SOLUTION:Missing number: 83 Answer: B #### B QUESTION:The cash difference between the selling prices of an article at a profit of 2% and 6% is Rs 3. The ratio of two selling prices is options: A)51:53 B)52:53 C)53:54 D)54:55 E)None of these SOLUTION:Explanation: Let the Cost price of article is Rs. x Required ratio = (102% of x) / (106% of x) =102/106 =51/53 = 51:53. Answer: A #### A QUESTION:Tom and Linda stand at point A. Linda begins to walk in a straight line away from Tom at a constant rate of 4 miles per hour. One hour later, Tom begins to jog in a straight line in the exact opposite direction at a constant rate of 9 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? options: A)60 B)72 C)84 D)90 E)216 SOLUTION:E is the answer.... D = TS where D=distance, T=Time and S=Speed To travel half distance, (2+4T) = 9T ==> T = 2/5 ==> 24 minutes To travel double distance, 2(2+4T) = 9T ==> 4 ==> 240 minutes Difference, 216 minutes E #### E QUESTION:The population of a town is 8100. It decreases annually at the rate of 10% p.a. What was its population 2 years ago? options: A)9000 B)8000 C)8500 D)9500 E)10000 SOLUTION:Formula : ( After =100 denominator Ago = 100 numerator) 8100 × 100/90 × 100/90 = 10000 E) #### E QUESTION:A girl has to make pizza with different toppings. There are 8 different toppings. In how many ways can she make pizzas with 2 different toppings? options: A)16 B)56 C)112 D)28 E)38 SOLUTION:In 8 different toppings, selecting 2 diff toppings = 8c2 formula is n!/(n-c)! n = total number of toppings C = number chosen in a grouping. n=8 and c=2 so we get 8!/(8-2)! = (8*7*6*5*4*3*2*1)/(6*5*4*3*2*1) = 8*7 =56 ANSWER:B #### B <<<Examples ends QUESTION:For each positive integer,the quantitySn is defined such thatSn+2=(Sn)^2 -S(n+2).in addition ,S2=1.then which of the following must be true. options: A)a)S4 +S3 +1=0 B)b)(S1)^2 +S4 +2=0 C)c) ifS1=-1thenS4 is also equal to-1. D)d) ifS4 =-7thenS1=-2. E)e) ifS1 =-3thenS4=-7 SOLUTION:Since all the answers include S4, let's start from there. S4=S2^2-S3 S3=S1^2-S2 Substituting S3 into the first equation we get: S4=S2^2-(S1^2-S2) Since S2=1 S4=1-(S1^2-1) S4=2-S1^2 We need S1^2 in order to calculate S4. E) provides S1 and from there we can calculate S4: S4=2-(-3)^2 S4=-7 Correct. As a side note, I would be very careful with answers in the formif S4=x then S1=y(such as option D ), as we are dealing with S1^2 (not S1), S1 can have two different values and it can not be determined for sure which root is the right answer. For example: If S4=-7 then S1=3 : if we substitute S4 with - 7 we get: -7=2-S1^2 S1^2=9 now S1 can be +/-3 !! E #### E

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:The ratio, by weight, of coffee to mate to water in a certain cup of coffee is 6:2:15. The coffee is altered so that the ratio of coffee to mate is halved while the ratio of coffee to water is doubled. If the altered coffee will contain 16 grams of mate, how many grams of water does it contain after alteration? options: A)12 B)15 C)30 D)60 E)100 SOLUTION:c:m:w = 6:2:15 new c:m = 1/2(6/2) = 3:2 new c:w = 2(6:15) = 12:15 = 4:5 so new m:c:w = 2:3 4:5 = 8:12:15 ( notice how i combined the two ratios by multiplication by 3 and 4 of respective ratios) m = 16 g Let T = total amount of c + m + w then 8 / (8+12+15)T = 16 x 35/8 = 70g then w = 15/35 x 70 = 30g Answer C #### C QUESTION:A farmer used 1,034 acres of land for beans, wheat, and corn in the ratio of 5 : 2 : 4, respectively. How many Y acres were used for corn? options: A) 188 B) 258 C) 376 D) 470 E) 517 SOLUTION:consider 5x acres of land used for bean consider 2x acres of land used for wheat consider 4x acres of land used for corn Total given is 1034 acres 11x =1034 x = 94 land used for corn Y= 4 * 94 = 376 correct option - C #### C QUESTION:There are 7000 people in the particular village , among them 30% are educated and out of these 28% are doing agriculture and out of them 50% are woman's. Then find out the number of woman's who are educated and doing agriculture? options: A)294 B)235 C)350 D)288 E)580 SOLUTION:Total number of people in the village = 7000; out of them 30% educated = 2100; out of them 28% doing agriculture = 588; out of them 50% are woman's = 294. #### A QUESTION:John can complete a given task in 10 days. Jane will take only 20 days to complete the same task. John and Jane set out to complete the task by beginning to work together. However, Jane was indisposed 4 days before the work got over. In how many days did the work get over from the time John and Jane started to work on it together? options: A)8 B)9 C)8.5 D)9.5 E)10.5 SOLUTION:In such questions, you need to start from the end. Last 4 days John works alone and completes 4 * (1/10) = 2/5 of the work. So 3/5 of the work should have been completed by the two of them together before Jane left. Their combined rate of work is 1/20 + 1/12 = 8/60 Time taken to complete 4/5 of the work = (3/5)/(8/60) = 9/2 days. So total number of days taken to complete the work =9/2 + 4 = 8.5 days. C #### C QUESTION:How much water must be added to 64 litres of milk at 1 1⁄2 litres for 20 so as to have a mixture worth 10 2⁄3 a litre? options: A)16 litres B)12 litres C)15 litres D)18 litres E)None of these SOLUTION:C.P. of 1 litre of milk = (20 × 2⁄3) = 40⁄3 ∴ Ratio of water and milk = 8⁄3 : 32⁄3 = 8 : 32 = 1 : 4 ∴ Quantity of water to be added to 64 litres of milk = (1⁄4 × 64) litres = 16 litres. Answer A #### A QUESTION:A man can swim in still water at 7.5 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is? options: A)1.7 B)1.4 C)1.1 D)1.5 E)2.5 SOLUTION:M = 7.5 S = x DS = 7.5 + x US = 7.5 + x 7.5 + x = (7.5 - x)2 7.5 + x = 15 -2x 3x = 7.5 x = 2.5 Answer:E #### E QUESTION:The 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: options: A)5:2 B)7:3 C)9:2 D)13:4 E)3:4 SOLUTION:Let the age of father and son 10 years ago be 3x and x years respectively. Then, (3x + 10) + 10 = 2[(x + 10) + 10] 3x + 20 = 2x + 40 => x = 20. Required ratio = (3x + 10):(x + 10) = 70:30 = 7:3 ANSWER:B #### B QUESTION:Two cards are drawn together from a pack of 52 cards. The probability that one is a spade and one is a heart, is: options: A)13/109 B)13/162 C)13/111 D)13/102 E)13/112 SOLUTION:Let S be the sample space. Then, n(S) = \inline {\color{Black}52C_{2} }=(52 x 51)/(2 x 1) = 1326. Let E = event of getting 1 spade and 1 heart. n(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. P(E) = n(E)/n(S) = 169/1326 = 13/102. Answer: D) 13/102 #### D QUESTION:Which of the following is NOT a prime number? options: A)21 B)31 C)41 D)11 E)51 SOLUTION:Ans is A A prime number has itself and 1 as the only factors. e.g. 2, 3, 7, 11, 19. Factors of 21 = {1 , 3 , 7 , 21} => 21 is not a prime number #### A QUESTION:A flagpole 18 meters high casts a shadow of length 45 meters. If a building under similar conditions casts a shadow of length 50 meters, what is the height of the building (in meters)? options: A)16 B)20 C)24 D)28 E)32 SOLUTION:The height:length ratio will be equal in both cases. 18 / 45 = x / 50 x = 20 The answer is B. #### B QUESTION:A problem is given to three students whose chances of solving it are 1/2, 1/3 and 1/4 respectively. What is the probability that the problem will be solved? options: A)2/4 B)3/4 C)4/5 D)5/6 E)6/7 SOLUTION:consider A,B,C events and AA,BB,CC not solving the problems now P(1)=1/2, P(B)=2/3 and P(C)=1/4 Not solving events =1/2*2/3*3/4 ==>1-1/4= 3/4 ANSWER B #### B QUESTION:Indu gave Bindu Rs.3750 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? options: A)5 B)6 C)9 D)3 E)1 SOLUTION:3750 = D(100/4)2 D = 6 Answer: B #### B QUESTION:A 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? options: A)230 m B)210 m C)260 m D)320 m E)330 m SOLUTION:Relative speed = (120 + 80) km/hr = (200 x(5/18))m/sec = (500/9)m/sec. Let the length of the other train be x metres. Then, (x + 290)/9 = 500/9 x + 290 = 500 x = 210. B #### B QUESTION:Six persons A,B,C,D,E &F went to soldier cinema. There are six consecutive seats. A sits in the first seat followed by B, followed by C and so on. If A taken on of the six seats, then B should sit adjacent to A. C should sit adjacent to A or B. D should sit adjacent to A, B or C and so on. How many possibilities are there ? options: A)30 B)32 C)34 D)36 E)38 SOLUTION:First we have to arrange A, there is 1 method for it, for second person B, there are 2 methods one left and one right, for third 2 methods are there same as for B similarly for others, so total number of methods = 1*2*2*2*2*2 = 32 ANSWER:B #### B QUESTION:If the sum of two positive integers is 20 and the difference of their squares is 40, what is the product of the two integers? options: A)108 B)99 C)128 D)135 E)143 SOLUTION:Let the 2 positive numbers x and y x+ y = 20 -- 1 x^2 - y^2 = 40 => (x+y)(x-y)=40 -- 2 Using equation 1 in 2 , we get => x-y = 2 -- 3 Solving equation 1 and 3 , we get x= 11 y= 9 Product = 11*9 = 99 Answer B #### B QUESTION:in 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 9 people all together .how many people can sit in a bus? options: A)52 B)49 C)95 D)90 E)66 SOLUTION:Right Side =15 seat Left Side =15-3 (3 few seat in right side)= 12 seat Total= 15+12= 27 People can seat in 27 seat= 27*3=81 People can seat in Last Seat = 9 Total People can seat= 81+9=90 ANSWER:D #### D QUESTION:Consider 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. 6300 interest only for the period. The principal amount borrowed by her was options: A)Rs. 2000 B)Rs. 17500 C)Rs. 15000 D)Rs. 20000 E)None of these SOLUTION:Explanation : Principal = Rs. (100×6300 / 12×3) => Rs. 17500. Answer : B #### B QUESTION:A sun is divided among X, Y and Z in such a way that for each rupee X gets, Y gets 50 paisa and Z gets 40 paisa. If the share of X is RS. 30, what is the total amount? options: A)67 B)55 C)62 D)47 E)57 SOLUTION:x:y:z = 100:50:40 10:5:4 10 --- 30 19 --- ? => 57 Answer: E #### E QUESTION:One day, Raviraj left home and cycled 20 Km southwards, turned right and cycled 10 km and turned right and cycled 20 Km and turned left and cycled 20 Km. How many kilometres will he have to cycle to reach his home straight ? options: A)50 B)30 C)40 D)60 E)80 SOLUTION:Raviraj starts from home at A, moves 20 Km in south upto B. Then he turns right and moves 10 Km upto C, then he turns right and moves 20 Km upto D, then he turns lefts and moves 20 Km upto E. So from image it is clear that, if he moves straight then he will have to move AD+DE, AD = BC = 10 Km So, he will have to move 10 + 20 = 30 Km ANSWER B #### B QUESTION:A 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? options: A)5 B)7 C)3 D)1/2 E)4 SOLUTION:Explanation: M = 4 S = 2 US = 4 - 2 = 2 D = 6 T = 6/2 = 3 Answer: C #### C QUESTION:If q is a positive integer and q^2 is divisible by 12, then the largest positive integer that must divide q ^3 is options: A) 2^3 B) 2^6 C) 3^3 D) 6^3 E) 12^2 SOLUTION:Since 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)) q^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 So, q will have a 2 and a 3. Or q will be a multiple of 6 So, largest possible integer than should divide q^3 is 6^3 So, Answer will be D #### D QUESTION:A family pays $700 per year for an insurance plan that pays 60 percent of the first $1,000 in expenses and 100 percent of all medical expenses thereafter. In any given year, the total amount paid by the family will equal the amount paid by the plan when the family's medical expenses total how much? options: A)$1,000 B)$1,200 C)$1,500 D)$1,800 E)$2,200 SOLUTION:Assuming the medical expenses are $1000 or more, the family pays $700 + $400 = $1100. The total amount paid by insurance plan for the first $1000 of expenses is $600. The insurance will pay another $500 when the medical expenses are $1500. The answer is C. #### C QUESTION:Pants, Shorts and Shirts in a dresser are in the ratio of 7: 7: 10. If there are 14 Pants, the number of Shirts in the dresser is: options: A)14 B)7 C)20 D)70 E)35 SOLUTION:Explanation : Let Pants = 7x, Shorts = 7x & Shirts = 10x. Now, 7x = 14 hence x = 2. Number of Apples = 10x = 20. Answer : C #### C QUESTION:The positive integers p and q leave remainders of 2 and 3, respectively, when divided by 6. p > q. What is the remainder when p – q is divided by 6? options: A)5 B)4 C)3 D)2 E)1 SOLUTION:Let's test out some values of p and q that satisfy the given information. p leaves are remainder of 2 when divided by 6 So, p COULD equal 8 q leaves are remainder of 3 when divided by 6 So, q COULD equal 3 What is the remainder when p – q is divided by 6? So, p - q = 8 - 3 = 5, and when we divide 5 by 6, we get 0 with remainder 5 Answer: A #### A QUESTION:If two integers x,y (x>y) are selected from -5 to 6 (inclusive), how many cases are there? options: A)62 B)66 C)70 D)74 E)78 SOLUTION:There are 12 integers from -5 to 6 inclusive. 12C2 = 66. The answer is B. #### B QUESTION:A license plate in the country Kerrania consists of four digits followed by two letters. The letters A, B, and C are used only by government vehicles while the letters D through Z are used by non-government vehicles. Kerrania's intelligence agency has recently captured a message from the country Gonzalia indicating that an electronic transmitter has been installed in a Kerrania government vehicle with a license plate starting with 79. If it takes the police 9 minutes to inspect each vehicle, what is the probability that the police will find the transmitter within three hours? options: A) 18/79 B) 1/6 C) 1/25 D) 19/900 E) 1/900 SOLUTION:Everything is correct except that you assumed the letters can't be repeated. It can be repeated. AA BB CC AB, AC, BC, BA, CA, CB. Thus; total government vehicles = (10)^2*(3)^2 = 100*9 = 900 Vehicles inspected within 3 hours = 60*3/9 = 19 P = 19/900 Ans:D #### D QUESTION:How many different subsets of the set {0, 1, 2, 3, 4, 5,6,} do not contain 0? options: A)A.66 B)B.57 C)C.31 D)D.32 E)E.58 SOLUTION:Number of subset Since we have 6 digits other than 0, we can take any numbers from the set of 6 to make a subset. Also it is a matter of selection and not arrangement.So we will consider combinations. 6c1+6c2+6c3+6c4+6c5+6c6=57 And one set is the NULL set having no elements in it so 57+1=58. ANSWER E. #### E QUESTION:Find the one which does not belong to that group ? options: A)3 B)4 C)5 D)9 E)7 SOLUTION:Explanation: 3, 5, 9 and 7 are odd numbers, but not 4. ANSWER IS B #### B QUESTION:How many words with or without meaning, can be formed by using all the letters of the word, ‘ORANGE’, using each letter exactly once? options: A)700 B)720 C)750 D)800 E)820 SOLUTION:The word ‘ORANGE’ contains 6 different letters. Therefore, Required number of words= Number of arrangement of 6 letters, taken all at a time =6P6 = 6! = 6*5*4*3*2*1 = 720 ANSWER:B #### B QUESTION:3 pig’s and 10 hens are brought for Rs.1200. If the average price of a hen be Rs.30. What is the average price of a pig. options: A)300 B)350 C)400 D)425 E)275 SOLUTION:Explanation: Average price of a hen = Rs.30 total price of 10 hens = 10*30 = Rs.300 But total price of 3 pigs and 10 hens = Rs. 1200 Total price of 3 pigs is = 1200 - 300 = 900 Average price of a pig = 900/3 = Rs. 300 Answer: A #### A QUESTION:A 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? options: A)200 B)992 C)772 D)662 E)552 SOLUTION:Profit on first article = 20% of 1000 = 200. This is equal to the loss he makes on the second article. That, is he makes neither profit nor loss. Answer: A #### A QUESTION:The avg weight of A,B & C is 70 kg. If D joins the group, the avg weight of the group becomes 70 kg.If another man E who weights is 3 kg more than D Replaces A, Then the avgof B,C,D&E becomes 68 kg. What is the weight of A? options: A)81 B)65 C)75 D)89 E)90 SOLUTION:A + B + C = 3 *70 = 210 A + B + C + D = 4 * 70 = 280 ---- (i) So, D = 70& E = 70 + 3 = 73 B + C + D +E =68 * 4 = 272 --- (ii) From Eq. (i) & (ii) A-E = 280 –272 = 8 A = E +8 = 73 + 8 = 81 Answer : A #### A QUESTION:If grapes are 92% water and raisins are 20% water, then how much did a quantity of raisins, which currently weighs 15 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.) options: A)25 pounds B)46 pounds C)150 pounds D)100 pounds E)146 pounds SOLUTION:Since 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*15 --> x = 150. Answer: C. #### C QUESTION:Calculate the speed of a boat in still water (in km/hr) if in one hour, the boat goes 10 km/hr downstream and 4 km/hr upstream. options: A)7 kmph B)8 kmph C)9 kmph D)7 kmph E)6 kmph SOLUTION:Speed in still water = (10 + 4)1/2 kmph = 7 kmph. answer :A #### A QUESTION:The G.C.D of 1.08, 0.42 and 0.9 is options: A)0.19 B)0.1 C)0.06 D)0.11 E)0.12 SOLUTION:Explanation: Given numbers are 1.08 , 0.42 and 0.90 H.C.F of 108, 42 and 90 is 6 [because G.C.D is nothing but H.C.F] therefore H.C.F of given numbers = 0.06 Answer: C) #### C QUESTION:A batsman scored 120 runs whichincluded 3 boundaries and 8sixes. What % of his total score did he make by running between the wickets options: A)40 % B)50 % C)60 % D)70 % E)80 % SOLUTION:Number of runs made by running = 110 - (3 x 4 + 8 x 6) = 120 - (60) = 60 Now, we need to calculate 60 is what percent of 120. => 60/120 * 100 = 50 % B #### B QUESTION:The price for a loaf of bread in April was $1.20, in May the price was $1.27, and in June the price was $1.08. If 2/3 as much bread was sold in April as in May, and twice as much was sold in June as in April, what was the average price for a loaf of bread sold during the three-month period? options: A)$1.18 B)$1.17 C)$1.16 D)$1.15 E)$1.14 SOLUTION:Let x be the number of loaves sold in May. Then 2x/3 loaves were sold in April and 4x/3 loaves were sold in June. The average price was (2x/3)(120) + 127x + (4x/3)(108) / (2x/3 + x + 4x/3) = (80 + 127 + 144) / (3) = 351/3 = $1.17 The answer is B. #### B QUESTION:If a is a positive integer, which of the following could NOT be the square of a? options: A) 5,008,644 B) 5,004,169 C) 4,999,696 D) 4,995,225 E) 4,990,752 SOLUTION:A number ending with 2 can never be a perfect square. Units digit of a perfect square must be: 1,4,9,6,5 Answer E) #### E QUESTION:A person borrows Rs. 6000 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. options: A)120 rs B)150 rs C)160 rs D)180 rs E)200 rs SOLUTION:Gain in 2 years = [(6000*6*2)/100]-[(6000*4*2)/100] 720-480=240 Gain in 1 year =(240/2)=120 rs ANSWER:A #### A QUESTION:By selling an article for 96, double profit is obtained than the profit that would have been obtained by selling it for 84. What is the cost price of the article? options: A)72.0 B)75.0 C)70.00 D)68.00 E)None of these SOLUTION:Let the cost price of the article be x. Then,2(84 –x) = 96 – x l68 – 2x= 96 – x \ x = 72 Answer A #### A QUESTION:Three workers have a productivity ratio of 3 to 5 to 6. 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 8th 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? options: A)12 to 1 B)6 to 1 C)5 to 1 D)20 to 7 E)1 to 5 SOLUTION:The fastest worker who does 6 units of job worked for all 10 hours, so he did 6*10=60 units of job; The slowest worker who does 3 unit of job worked for only 4+3=7 hours (first 4 hours and last 3 hours), so he did 3*7=21 The ratio thus is 60 to 21, or 20 to 7. Answer: D. #### D QUESTION:A rope of which a calf is tied is increased from 12 m to 23 m, how much additional grassy ground shall it graze? options: A)1298 B)1228 C)1210 D)1782 E)1762 SOLUTION:π (232 – 122) = 1210 Answer:C #### C QUESTION:If 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? options: A)3:2 B)2:2 C)3:4 D)1:2 E)6:1 SOLUTION:B 2:2 6M + 2B = 4(1M + 1B) 6M + 2B = 4M + 4B 2M = 2B The required ratio of work done by a man and a boy = 2:2 #### B QUESTION:A 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. options: A)Rs.240 B)Rs.350 C)Rs.340 D)Rs.390 E)Rs.370 SOLUTION:Explanation: (3*8 + 2*4):(4*8 + 5*4) 8:13 8/21 * 630 = 240 ANSWER IS A #### A QUESTION:An 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.2400, what will be the difference between Q and R's share? options: A)8877 B)3000 C)7787 D)1799 E)1711 SOLUTION:4 --- 2000 5 --- ? => 3000 Answer: B #### B QUESTION:The true discount on a bill of Rs. 2360 is Rs. 360. What is the banker's discount? options: A)Rs. 432 B)Rs. 425 C)Rs. 412 D)Rs. 442 E)None of these SOLUTION:Explanation : F = Rs. 2360 TD = Rs. 360 PW = F - TD = 2360 - 360 = Rs. 2000 True Discount is the Simple Interest on the present value for unexpired time =>Simple Interest on Rs. 2000 for unexpired time = Rs. 360 Banker's Discount is the Simple Interest on the face value of the bill for unexpired time = Simple Interest on Rs. 2360 for unexpired time =360/2000 × 2360 = 0.18 × 2160 = Rs. 425 Answer : Option B #### B QUESTION:In Town X, 64 percent of the population are employed, and 45 percent of the population are employed males. What percent of the employed people in Town X are females? options: A)16% B)25% C)30% D)40% E)52% SOLUTION:We are asked to find the percentage of females in employed people. Total employed people 64%, out of which 45 are employed males, hence 19% are employed females. (employed females)/(total employed people)=19/64=30% Answer: C. #### C QUESTION:A horse is tethered to one corner of a rectangular grassy field 36 m by 20 m with a rope 12 m long. Over how much area of the field can it graze? options: A)154 cm2 B)113 m2 C)123 m2 D)115 m2 E)None of these SOLUTION:Area of the shaded portion = 1⁄4 × π × (12)2 = 113 m2 Answer B #### B QUESTION:By selling 20 pens for a rupee a man loses 30%. How many for a rupee should he sell in order to gain 30%? options: A)8.76 B)10.76 C)8.76 D)9.76 E)5.76 SOLUTION:70% --- 20 130% --- ? 70/130 * 20 = 10.76 Answer: B #### B QUESTION:The base of pyramid P is an isosceles right triangle whose leg is 3. If the height of P is 4, what is the volume of P? options: A)36 B)18 C)12 D)8 E)6 SOLUTION:Volume of a pyramid is given by V=1/3Ah, where A is the area of the triangular base and h is the height of the pyramid. Area of triangular base = 1/2 * 3*3 = 9/2 So, V = 1/3 * 9/2 *4 = 6 Option E #### E QUESTION:2+2+2²+2³ ... +2^9 options: A)2^9 B)2^10 C)2^16 D)2^35 E)2^37 SOLUTION:2+2=2^2 2^2+2^2=(2^2)*(1+1)=2^3 2^3+2^3=(2^3)*(1+1)=2^4 so you can notice the pattern... in the end you will have 2^9+2^9, which will give you 2^10 Answer B #### B QUESTION:Tim and Élan are 120 miles away from one another. They are starting to move towards each other simultaneously, Tim at a speed of 10 Mph and Élan at a speed of 5 Mph. If every hour they double their speeds, what is the distance that Tim will pass until he meets Élan? options: A)30 miles. B)35 miles. C)45 miles. D)60 miles. E)80 miles. SOLUTION:Tim and Elan will meet at the same time while their ratio of speed is 2:1 respectively.So their individual distance traveled ratio will be same. Plugging in the answer choice Only Answer Choice E meet the 2:1(Tim:Elan=80:40) ratio of maintaining total distance traveled 120 miles So Correct answer E #### E QUESTION:A shopkeeper buys mangoes at the rate of 6 a rupee and sells them at 4 a rupee. Find his net profit or loss percent? options: A)33 1/8 % B)33 7/3 % C)50 % D)33 5/8 % E)34 1/3 % SOLUTION:The total number of mangoes bought by the shopkeeper be 24. If he buys 6 a rupee, his CP = 4 He selling at 4 a rupee, his SP = 6 Profit = SP - CP = 6 - 4 = 2 Profit Percent = 2/4 * 100 = 50 % Answer: C #### C QUESTION:If the simple interest on a sum of money for 2 years at 5% per annum is Rs. 52, what is the compound interest on the same sum at the rate and for the same time? options: A)s. 53.30 B)s. 53.22 C)s. 51.219 D)s. 53.18 E)s. 51.10 SOLUTION:Explanation: Sum = (52 * 100) / (2 * 5) = Rs. 520 Amount = [520 * (1 + 5/100)2] = Rs. 573.3 C.I. = (573.3 - 520) = Rs. 53.30. Answer:A #### A QUESTION:For every integer n ≥ 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(99) – g(97)? options: A)98 B)100 C)0 D)99 E)97 SOLUTION:g(99) = 1*3*5*7*9*...*99 g(97) = 1*3*5*7*9*...*97 g(99) - g(97) = 1*3*5*7*9*...*99 - 1*3*5*7*9*...*97 = 1*3*5*7*9*...*97*(99 - 1) = 1*3*5*7*9*...*97*98 hence:A. #### A QUESTION:A reduction of 46% in the price of bananas would enable a man to obtain 64 more for Rs.40, what is reduced price per dozen? options: A)2.45 B)8.45 C)7.45 D)3.45 E)1.45 SOLUTION:Explanation: 40*(46/100) = 18.4 --- 64 ? --- 12 => Rs.3.45 Answer: D #### D QUESTION:A 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 ? options: A)1000 B)1100 C)1200 D)1300 E)1400 SOLUTION:let profit rate of b = x acc to question profit rate of a becomes 5/3 x and that of c= 1/3 x which is given as 10% 1/3 x= 10 therefore x=30 now b=30% , a=50% now we will find out c's price- 11/10 * price = 2145 price = 1950 in similar way we will find out b's price as we know that profit is 30% therefore 130/100 * price = 1950 so b 's price =1500 similarly for a ('profit is 50%) 150/100 * price = 1500 on solving it we get a's price = 1000 ANSWER:A #### A QUESTION:The 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 40 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 ? options: A)87 B)95 C)99 D)100 E)103 SOLUTION:The average score in an examination of 10 students of a class is 60 --> the total score = 10*60 = 600; The 5 smallest scores have an average of 55 --> the total score of the 5 smallest scores = 275. From above, the total score of the 5 largest scores = 600 - 275 = 325. Say the 5 largest scores are a, b, c, d, and e (where a<b<c<d<e, since each of the top five scorers had distinct scores). We want to maximize e. To maximize e, we need to minimize a, b, c, and d. The least value of a, is 55 (The least score of the top 5 , a, should be equal to the highest of the bottom 5 and to minimize the highest of the bottom 5, all scores from the bottom 5 should be equal). In this case the least values of b, c, and d are 56, 57, and 58 respectively: a + b + c + d + e = 55 + 56 +57 + 58 + e = 325; e = 99. Answer: C. #### C QUESTION:Find large number from below question The difference of two numbers is 1395. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder options: A)1245 B)1345 C)1455 D)1577 E)1671 SOLUTION:Let the smaller number be x. Then larger number = (x + 1395). x + 1395 = 6x + 15 5x = 1380 x = 276 Large number = 276+1395 = 1671 E #### E QUESTION:The larger interior angle of a parallelogram is 90° more than its smaller interior angle. What is the measure of the smaller interior angle of the parallelogram? options: A)90° B)75° C)60° D)45° E)30° SOLUTION:let smaller be x ,larger becomes x+90... total of all angles=360 so 4x+180=360 and x=45 ANSWER:D #### D QUESTION:A group of 7 fishermen chartered a boat for a day to fish for flounder. The boat costs x dollars per day to rent. If the group can find 2 more fishermen on the docks who are willing to come aboard and share the rental costs, how much less will the rental cost be per person in terms of x? options: A)x/70 B)2x/63 C)3x/70 D)3x/10 E)3x/7 SOLUTION:cost of boat per day = x cost per person =x/7 if three more persons afre there, cost =x/9 difference = x/7-x/9 =2x/63 Ans B #### B QUESTION:The cost of a one-family home was $ 120,000 in 1980. In 1988, the price had increased to $ 168,000. What was the percent increase in the cost of the home? options: A)60% B)50% C)55% D)40% E)33.3% SOLUTION:Increase = 168000-120000 = 48000 % increase = 48000*100/120000 = 40% Answer: option D #### D QUESTION:A train passes a station platform in 50 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? options: A)180 m B)200 m C)240 m D)320 m E)450 m SOLUTION:Sol. Speed = [54 * 5/18] m/sec = 15 m/sec. Length of the train = (15 * 20) m = 300 m. Let the length of the platform be x metres. Then, x + 300 / 50 = 15 ⇔ x + 300 = 750 ⇔ x = 450 m. Answer E #### E QUESTION:A, 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? options: A)3002 B)3000 C)3018 D)3019 E)3012 SOLUTION:60*5:36*6:75*3 100: 72: 75 100/247 * 7410 = 3000 Answer: B #### B <<<Examples ends QUESTION:On return from a business trip Mr. Chidambaram was to be picked up from the railway station by his coachman. Someone he managed a train connection earlier and thus arrived two hours too early. Immediately on arrived he rang up home for the coach and was told that it had just left in order to be exactly in time for the train by which he was scheduled to come. To save the time he started walking homeward at 3kmph. On the way he met the coachman who brought him home an hour before schedule. How far is the Mr. Chidambaram’s house from the railway station? options: A)22 B)18 C)99 D)27 E)11 SOLUTION:Very good questions. Appeared in Puzzles book of Ravi Nirula. Let the train's correct time is 9.00 am. Now chidambaram reached the station at 7 am and he was informed that the coachman (car) left at 7 am. So car takes 2 hours to reach the station. This car expected to reach home at 11 am. But the car after picking up chidambaram, reached home 1 hour early. i.e., 10 am. So car has travelled 3 hours and 1.5 hours towards the station. So it picked him up at 8.30 am. Car saved distance equivalent to 30 minutes. but this distance is covered by Chidambaram by walk. He took 1.5 hours to cover this distance. So Car speed is 3 times that of his walking speed. Car speed = 3 × 3 = 9 km. We know that car takes 2 hours to reach station. So the distance = 9 × 2 = 18 km. Answer:B #### B

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:If x and y are prime numbers such that x > y > 3, then x^2 − y^2 must be divisible by which one of the following numbers? options: A) 3 B) 4 C) 5 D) 9 E) 12 SOLUTION:If x=8 and y=6, then x^2-y^2=28 and 28 is divisible only by 4 from the options, thus it must be correct. Answer: B. #### B QUESTION:A man can row upstream at 10 kmph and downstream at 20 kmph, and then find the speed of the man in still water? options: A)11 B)77 C)25 D)88 E)34 SOLUTION:US = 20 DS = 30 M = (30 + 20)/2 = 25 Answer:C #### C QUESTION:A shopkeeper sold an article for 240 after giving 20% discount on the labelled price and made 20% profit on the cost price. What would have been the percentage profit,had he not given the discount’? options: A)25% B)50% C)23% D)28% E)None of these SOLUTION:Cost price = 240×100/120= 200 S.P. at no discount = 240×100/80 = 300 ∴ % profit = 100×100/200 = 50 % Answer B #### B QUESTION:A book is bought for $60 and sold for $75. What is the profit in percentage? options: A)12 B)15 C)20 D)25 E)30 SOLUTION:75/60 = 1.25 The answer is D. #### D QUESTION:A and B can do a piece of work in 11 days. With the help of C they finish the work in 5 days. C alone can do that piece of work in? options: A)15.5 days B)19.5 days C)17.5 days D)9.2 days E)18.5 days SOLUTION:C = 1/5 – 1/11 = 6/55 => 9.2 days ANSWER:D #### D QUESTION:What least number mustbe subtracted from 427398 so that remaining no.is divisible by 15 options: A)3 B)5 C)7 D)8 E)9 SOLUTION:Explanation: On dividing 427398 by 15 we get the remainder 3, so 3 should be subtracted Answer: Option A #### A QUESTION:In 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? options: A)A)1:5 B)B)1:1 C)C)1:8 D)D)1:9 E)E)1:3 SOLUTION:Number of men in the colony = 5/7 * 70 = 50. Number of women in the colony = 2/7 * 70 = 20. Number educated women in the colony = 1/5 * 30 = 6. Number of uneducated women in the colony = 4/5 * 50 = 24. Number of educated persons in the colony = 8 /35 * 70 = 16. As 6 females are educated, remaining 10 educated persons must be men. Number of uneducated men in the colony = 50 - 10 = 40. Number of educated men and uneducated men are in the ratio 10 : 40 i.e., 1:4. Answer:A #### A QUESTION:One pipe can fill a pool four times faster than a second pipe. When both pipes are opened, they fill the pool in eight hours. How long would it take to fill the pool if only the faster pipe is used? options: A)5 hr B)8 hr C)10 hr D)16 hr E)20 hr SOLUTION:fast pipe + slow pipe = together One pipe fills the pool four times faster than the other pipe so, hourly fill rates: 1/x + 1/4x = 1/8 Let x = number of hours it would take the fast pipe to fill the pool thus, x=10 hours Answer: C #### C QUESTION:If r, s, and t are three different positive integers whose sum is prime, which of the following statements could be true? options: A)Each of r + s, r + t, and s + t is prime. B)Each of r + 3, s + 3, and t + 3 is prime. C)Each of r, s, and t is prime. D)The average (arithmetic mean) of r, s, and t is prime. E)r + s = t SOLUTION:the question asks could be!!!! this means that if at least one option works, it is the answer. 3, 7, 19 satisfies the condition, since 29 is a prime number. Since the question asks for a could be - we know automatically that C is the answer. #### C QUESTION:Six persons A,B,C,D,E &F went to soldier cinema. There are six consecutive seats. A sits in the first seat followed by B, followed by C and so on. If A taken on of the six seats, then B should sit adjacent to A. C should sit adjacent to A or B. D should sit adjacent to A, B or C and so on. How many possibilities are there ? options: A)30 B)32 C)34 D)36 E)38 SOLUTION:First we have to arrange A, there is 1 method for it, for second person B, there are 2 methods one left and one right, for third 2 methods are there same as for B similarly for others, so total number of methods = 1*2*2*2*2*2 = 32 ANSWER:B #### B QUESTION:Line W has the equation 3x + y = 7. Which of the following lines is perpendicular to Line W? options: A) y = 3x + 4 B) y = –3x – 6 C) y = (1/3)x – 1 D) y = (–1/3)x + 2 E) y = (–7/3)x – 5 SOLUTION:I first rewrote the equation in the standard y=mx+b form. Therefore, Line W as presented, 3x + y = 7, can be rewritten as follows: y=-3x+7. Thought process next is what line would be perpendicular to Line W? Any line with a reciprocal of the slope but in the opposite direction. The reciprocal of any fraction/integer is 1 over that number/integer. Therefore the reciprocal of -3 is -1/3 - need to drop the negative sign because the line would kinda run parallel and we want perpendicular. Scan the answers choices and notice C as the only one. #### C QUESTION:The average age of the district level hockey team of eleven is 35 years.The average age gets increased by 1 year when the coach age is also included.what is the age of the coach ? options: A)43 yrs. B)44 yrs. C)45 yrs. D)47 yrs. E)46 yrs. SOLUTION:Explanation: Total age of players in team = 35 x 11 = 385 When coach is included, total members = 12, Avg age increases by one becomes 23 Total age when coach is included = 36x12 = 432 Age of coach = 432-385 = 47 yrs. Answer:D #### D QUESTION:If in a triangle, the area is numerically equal to the perimeter, then the radius of the inscribed circle of the triangle is options: A)1 B)2 C)3 D)4 E)5 SOLUTION:Solution Radius = Area / Semi perimeter = [Area x 2 / Area] = 2. Answer B #### B QUESTION:After decreasing 50% in the price of an article costs Rs.620. Find the actual cost of an article? options: A)2777 B)2987 C)1200 D)1240 E)1671 SOLUTION:CP* (50/100) = 620 CP= 12.4 * 100 => CP = 1240 Answer: D #### D QUESTION:In measuring the sides of a rectangle, one side is taken 16% in excess and other 5% in deficit. Find the error percentage in the area calculated from these measurements. options: A)3.5% B)2.4% C)10.2% D)5% E)2.6% SOLUTION:Say both sides of the rectangle are equal to 100 (so consider that we have a square). In this case the area is 100*100=10,000. Now, the area obtained with wrong measurements would be 116*95=11,020, which is 10.2% greater than the actual area. Answer: C. #### C QUESTION:A certain Social Security recipient will receive an annual benefit of $12,000 provided he has annual earnings of $9,360 or less, but the benefit will be reduced by $1 for every $3 of annual earnings over $9,360. What amount of total annual earnings would result in a 55 percent reduction in the recipient's annual Social Security benefit? (Assume Social Security benefits are not counted as part of annual earnings.) options: A)$15,360 B)$17,360 C)$25,560 D)$21,360 E)$27,360 SOLUTION:For every $3 earn above $9360, the recipient loses $1 of benefit. OR For every $1 loss in the benefit, the recipient earns $3 above $9360 If earning is; 9360+3x Benefit = 12000-x Or the vice versa If benefit is 12000-x, the earning becomes 9360+3x He lost 50% of the benefit; Benefit Received= 12000-0.55*12000 = 12000-6600 x=5400 Earning becomes 9360+3x=9360+3*5400=25560 Ans:C #### C QUESTION:The number 95 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 options: A)9 B)10 C)15 D)18 E)17 SOLUTION:The only possible sum for 4 different squares of an integer with total sum number is 95 are : 49 + 36 + 9 + 1 = 95 which are the square from numbers : 7, 6, 3, 1 (total sum number is 17) or 81 + 9 + 4 + 1 = 95 which are the square from numbers : 9, 3, 2, 1 (total sum number is 15) hence the answer is (E) #### E QUESTION:How many five digit numbers can be formed by using the digits 0,1,2,3,4,5 such that the number is divisible by 4? options: A)288 B)173144 C)144 D)297 E)2181 SOLUTION:Explanation: If a number has to be divisible by 4, the last two digit of that number should be divisible by 4. So _ _ _ x y. Here xy should be a multiple of 4. There are two cases: Case 1: xy can be 04, 20 or 40 In this case the remaining 3 places can be filled in 4×3×2 = 24. So total 24×3 = 72 ways. Case 2: xy can be 12, 24, 32, 52. In this case, left most place cannot be 0. So left most place can be filled in 3 ways. Number of ways are 3×3×2 = 18. Total ways = 18×4 = 72. Total ways = 144 Answer:C #### C QUESTION:A train running at a speed of 36 kmph crosses an electric pole in 12 seconds. In how much time will it cross a 350 m long platform? options: A)25 B)15 C)18 D)47 E)26 SOLUTION:Let the length of the train be x m. When a train crosses an electric pole, the distance covered is its own length. So, x = 12 * 36 * 5 /18 m = 120 m. Time taken to cross the platform = (120 +350)/ 36 * 5/18 = 47 min. Answer:D #### D QUESTION:Find the value of 1/(3+1/(3+1/(3-1/3))) options: A)21/89 B)89/27 C)27/89 D)1/14 E)1/56 SOLUTION:1/[3 + (1/(3+1/(3 - 1/3)))] => 1/[3 + 1/(3 + 1/(8/3))] => 1/[3 + 1/(3 + 3/8)] => 1/[3 + 8/27] => 1/(89/27) => 27/89 C #### C QUESTION:Indu gave Bindu Rs.3750 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? options: A)5 B)6 C)9 D)3 E)1 SOLUTION:3750 = D(100/4)2 D = 6 Answer: B #### B QUESTION:A grocer has a sale of Rs. 4435, Rs. 4927, Rs. 4855, Rs. 5230 and Rs. 4562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 4500? options: A)s. 1991 B)s. 2991 C)s. 3991 D)s. 4991 E)s. 5991 SOLUTION:Explanation: Total sale for 5 months = Rs. (4435 + 4927 + 4855 + 5230 + 4562) = Rs. 24009. Required sale = Rs. [ (4500 x 6) – 24009 ] = Rs. (27000 – 24009) = Rs. 2991. Answer B #### B QUESTION:in 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? options: A)11101 B)11110 C)10111 D)11011 E)11010 SOLUTION:4+3=7 since base is 7 so it will become 0 giving 1 carry to next digits(so 4+7=0) 3+4 + 1 carry from above step= 1 and 1 carry to next digit 2+5 + 1 carry to next digit= 1 and 1 carry 1+6= 11 so ans=11110 ANSWER:B #### B QUESTION:Sum of 3 consecutive even no.'s is 26 more than the 1st no. of the series. Find the middle no.? options: A)8 B)twelve (12) C)14 D)16 E)18 SOLUTION:Let the numbers be x, x+2 and x+4 then x + x+2 + x+4 = x+26 3x + 6 = x + 26 2x = 20 \inline \therefore x = 10 \inline \therefore Middle number = x + 2 = 10+2 = 12 B #### B QUESTION:In case N is the only individual sewing on committee B, which among the following shouldserve on committee A? options: A)V and U B)V and T C)U and S D)O and P E)T and U SOLUTION:O and P should serve on A ANSWER:D #### D QUESTION:A man lent money of Rs. 2500 on simple interest for rate on interest being same as number of years. If he got Rs. 900 as interest amount at the end of the period then what is the rate of interest? options: A)6% B)4% C)5% D)3% E)2% SOLUTION:Explanation : SI = pnr SI = (2500*3r*3r)=900 r2 = 25 r = 5% Answer : C #### C QUESTION:In a Private Company 20 Nos. staffs are employed. In a Festival season their Boss give festival allowance to all. He says his accountant to calculate for 30 days @ 100. Also he says balance payment will give to driver and cleaning staff and to be adjust from petty cash. He had given Rs.65000/- to the accountant. How much amount will taken from Petty cash? options: A)A)1000 B)B)3000 C)C)3500 D)D)2500 E)E)2250 SOLUTION:For 20 staffs: 300*100*20 = 60000 for driver and cleaning staff: 300*100*2 =6000 From petty Cash : 1000 Answer is 1000 Answer is A #### A QUESTION:Amit and Ian paint a wall in alternating shifts. First Amit paints alone, then Ian paints alone, then Amit paints alone, etc. During each of his shifts, Amit paints 1/2 of the remaining unpainted area of the wall, while Ian paints 1/3 of the remaining unpainted area of the wall during each of his shifts. If Amit goes first, what fraction of the wall's area will remain unpainted after Amit has completed his 2th shift? options: A)1/27 B)1/54 C)1/81 D)1/6 E)1/216 SOLUTION:Fraction of area unpainted after FIRST shift of Amit = 1-(1/2) = 1/2 Fraction of area unpainted after FIRST shift of Ian = (1/2)-(1/3)(1/2) = (2/3)(1/2) Fraction of area unpainted after SECOND shift of Amit = (1/2)(2/3)(1/2)=1/6 Answer: option D #### D QUESTION:Mary travels the first 9 hours of her journey at 40 mph speed and the remaining 6 hours at 30 mph speed. What is the average speed of Mary's travel in mph? options: A)32 mph B)34 mph C)36 mph D)35 mph E)31 mph SOLUTION:Explanation : Average speed=Total Distance/Time. Total distance travelled by mary = Distance covered in the first 9 hours + Distance covered in the next 6 hours. Distance covered in the first 9 hours = 9×40=360 miles Distance covered in the next 6 hours= 6×30=180 miles Therefore, total distance travelled = 360+180=540 miles. The total time taken = 9+6=15hours. Hence, the average speed =540/15= 36 mph. Answer : C #### C QUESTION:If y ≠ 3 and 2x/y is a prime integer greater than 2, which of the following must be true? I. x = y II. y = 1 III. x and y are prime integers. options: A)None B)I only C)II only D)III only E)I and II SOLUTION:given 2x/y is prime and greater than 2. => 2x/y could be any of the following 3,5,7.... => 2x/y is odd and prime (as 2 is the only even prime number and its not in this set) 1. x = y , can't be true if x=y , 2x/y = 2 which is not odd and prime. 2. y=1. can't be true. if y=1,2x/y = 2x = even which is not odd & prime. 3. x and y are prime integers, need not be true. lets say 2x/y = 3 and say y=2 prime =>x = 6/2 = 3 prime satisfies the given condition here. but when 2x/y = 3 and y=5 prime => x = 15/2 not prime My Answer is A #### A QUESTION:In a class, the average age of 28 boys is 12 years and the average of 20 girls is 8 years. what is the average age of the whole class? options: A)10.3 Years B)12.3 Years C)12.6 Years D)13 Years E)15 Years SOLUTION:Total age of 48 students (28X 12+20 X 8) = 496 Average = 496/48 = 10.3 Years A #### A QUESTION:Find the best average of the first 10 multiples of 7.... options: A)30.5 B)38.5 C)40 D)43.5 E)55.5 SOLUTION:the exp is - 7(1+2+3+4+5+6+7+8+9+10)/10 => 7(10(10+1)/10*2 => 7(110)/10*2 = 38.5 ANSWER B #### B QUESTION:In how many ways the letters in the word MANAGEMENT can be arranged such that A’s does not come together. options: A)181440 B)191440 C)171440 D)182440 E)185440 SOLUTION:Methods to arrange all the letters leaving A = 8*7*6*5*4*3*2*1/(2*1)*(2*1)*(2*1)= 5040 Now between these 8 letters , there are 9 places so methods to place A and A in these positions = 9*8/2*1 = 36 thus total methods are 5040*36 = 181440 ANSWER:A #### A QUESTION:A and B started a business investing Rs. 24,000 and Rs 18,000 respectively. In what ratio the profit earned after 2 years be divided between A and B respectively? options: A)4 : 3 B)9:2 C)18:20 D)1:4 E)18:4 SOLUTION:A: B =24000 : 18000 = 8 : 6 = 4 : 3 ANSWER:A #### A QUESTION:John 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? options: A)54 B)55 C)56 D)57 E)58 SOLUTION:Let there be a pennies , b nickels and c dimes so total amount can be 1+5b+10c cents to 4+5b+10c as 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) So the total can never be divisible by 5 and hence only 55 that is c is the option which is divisible by 5. so answer is B #### B QUESTION:The average (arithmetic mean) of 24, 35, and 58 is 6 more than the average of 19, 51, and x. What is x? options: A)26 B)27 C)28 D)29 E)30 SOLUTION:The average of 24, 35, and 58 is 39. The average of 19, 51 and x is 33. Then 19 + 51 + x = 99. x = 29. The answer is D. #### D QUESTION:In a park there are two ponds with both brown ducks and green ducks. In the smaller pond there are 30 ducks and in the larger pond there are 50 ducks. If 20% of the ducks in the smaller pond are green and 12% of the ducks in the larger pond are green, then what percentage of ducks are green? options: A)13% B)14% C)15% D)16% E)17% SOLUTION:Number of ducks in small pond = 30 green ducks in small pond = 20 % of 30 = 6 ducks Number of ducks in large pond = 50 green ducks in large pond = 12 % of 50 = 6 ducks Total number of ducks = 30 + 50 = 80 total number of green ducks = 6 + 6 = 12 ducks percentage of green ducks = 12/80 * 100 = 15% Answer: C #### C QUESTION:The first republic day of the India was celebrated on 26th January,1950. It was options: A)221 B)28 C)276 D)20 E)22 SOLUTION:1-1-1 AD fall on Monday. We calculate the number of odd days till 24th december, 1995. Number of odd days till 1600 years = 0 1601 to 1700 = 5 1701 to 1800 = 5 1801 to 1900 = 5 49 years contains = 37 normal + 12 leap years =12 × 2 + 37 = 61 odd days = 61/7 = 5 odd days 25th January 1950 = 25/7 = 4 odd days Total odd days =15 + 5 + 4 = 24/7 = 3 odd days So 26th January,1950 is Thursday Answer:B #### B QUESTION:A car is traveling 72 kilometers per hour. How many meters does the car travel in one minute? options: A)1,200 meters / minute B)1,300 meters / minute C)1,450 meters / minute D)1,550 meters / minute E)1,650 meters / minute SOLUTION:Convert hour into minutes ( 1 hour = 60 minutes) and kilometers into meters (1 km = 1000 m) and simplify 72 kilometers per hour = 72 km/hr = (72 * 1000 meters) / (60 minutes) = 1,200 meters / minute correct answer A #### A QUESTION:how many square are there between 2001....2300 I don't remember the exact series. options: A)1 B)4 C)2 D)3 E)5 SOLUTION:series was from 2001 to 2300 45^2=2025 46^2=2116 47^2=2209 48^2=2304 (so exclude 48) so ans is 3 (45,46 and 47) ANSWER:D #### D QUESTION:A watch was sold at a loss of 10%. If it was sold for Rs.500 more, there would have been a gain of 10%. What is the cost price? options: A)1000 B)2998 C)2500 D)2788 E)2991 SOLUTION:90% 110% -------- 20% ---- 500 100% ---- ? => Rs.2500 Answer:C #### C QUESTION:In a friendship gang Angel has 3 gang, in how many ways can he invite one or more of the gang to his house? options: A)58 B)5 C)12 D)9 E)7 SOLUTION:Angel can select one or more than one of his 8 gang. => Required number of ways = 2^3 – 1= 7. E #### E QUESTION:The population of a town is 176400. If it increase at the rate of 5% per annum. What was its population 5 years ago? options: A)152460 B)214560 C)138214 D)210000 E)200000 SOLUTION:population 2 years ago = 176400/(1 + 5/100)^5 Answer is C #### C QUESTION:Two pipes can fill the cistern in 10hr and 12 hr respectively, while the third empty it in 20hr. If all pipes are opened simultaneously, then the cistern will be filled in options: A)7.5 hr B)8 hr C)8.5 hr D)10 hr E)None of these SOLUTION:Solution: Work done by all the tanks working together in 1 hour. 1/10+1/12−1/20=2/15 Hence, tank will be filled in 15/2=7.5 hour Option(A) #### A QUESTION:A number x is multiplied with itself and then added to the product of 4 and x. If the result of these two operations is 5, what is the value of x? options: A)-4 B)-2 C)2 D)1 and -5 E)Cannot be determined. SOLUTION:A number x is multiplied with itself --> X^2 added to the product of 4 and x --> X^2+4X If the result of these two operations is -4 --> X^2+4X=5 i.e X^2+4X-5=0 is the Quadratic equation which needs to be solved. (X-1)(X+5) = 0 Hence X=1. C=-5 IMO D #### D QUESTION:A man took loan from a bank at the rate of 12% p.a. simple interest. After 3 years he had to pay Rs. 5400 interest only for the period. The principal amount borrowed by him was: options: A)Rs. 2000 B)Rs. 10,000 C)Rs. 15,000 D)Rs. 20,000 E)Rs. 26,000 SOLUTION:Principal = Rs.(100 x 5400)/(12x3) = Rs. 15000. Answer: Option C #### C QUESTION:√(36)^2 options: A)6 B)14 C)36 D)21 E)None of these SOLUTION:explanation √(36)^2 =? or, ? = 36 Answer C #### C QUESTION:A bookseller has two display windows. She plans to display 5 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? options: A)24 B)72 C)720 D)336 E)420 SOLUTION:The left window will have permutations of the 5 fiction books, so the number of possibilities for that window is permutations = 5! = (5)(4)(3)(2)(1) = 120 The right window will have permutations of the 3 non-fiction books, so the number of possibilities for that window is permutations = 3! = (3)(2)(1) = 6 Any 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 120*6 = 720 Answer: C. #### C QUESTION:A, B and C shared the profit in a business in the ratio 5 : 7 : 8. They had partnered for 14 months, 2 months and 7 months respectively. What was the ratio of their investments? options: A)10:12:14 B)12:24:28 C)20:22:12 D)5:49:16 E)None of these SOLUTION:Explanation : Ratio in which A,B and C shared the profit = 5 : 7 : 8 Assume that the ratio of their investment = a:b:c Then 14a : 2b : 7c = 5 : 7 : 8 Good to go, we got the equation. Now it's a matter of time to find a, b and c 14a/2b = 5/7 => 98a = 10b => b = 98a/10 = 49a/5 ---(1) 14a/7c =5/8 => 2a/c =5/8 => 16a = 5c => c = 16a/5 ---(2) a : b : c = a : 49a/5 : 16a/5 = 1 : 49/20 : 16/5 = 5 : 49 : 16. Answer : Option D #### D QUESTION:How many two digit numbers of distinct digits can be formed by using digits 1, 2, 3, 4, 5, 6 and 7 such that the numbers are divisible by 9? options: A)4 B)5 C)6 D)7 E)8 SOLUTION:A number will be divisible by 9 if sum of all the digits of the number is divisible by 9 Here the Possible sum of the two distinct digits can be 9 only in order to satisfy the given condition If sum of Digits = 9, No. = 27, 36, 45, 54, 63, 72 --- 6 Cases Answer: option C #### C QUESTION:The number of digits of the smallest number, which when multiplied by 7 gives the result consisting entirely of nines is options: A)3 B)5 C)6 D)8 E)9 SOLUTION:Sol. By hit and trial, we find that a number exactly divisible by 7 and consisting entirely of nines is 999999. Number of digits in it = 6. Answer C #### C QUESTION:Two-third of two-fifth of three-fourth of a number is 36. What is the square root of four-fifth of that number? options: A)9 B)12 C)14 D)16 E)18 SOLUTION:Explanation: We have, 2/3 * 2/5 * 3/4 * X = 36 X = 180 Now, 4/5 * X ===> 4/5 * 180 = 144 √144 = 12 ANSWER: B #### B QUESTION:Find the value of y from the given equation. 9^y = 3^12, what is y? options: A)3 B)5 C)7 D)8 E)6 SOLUTION:3^2y = 3^12 2y=12, therefore y=6 E #### E QUESTION:What is the sum of all remainders obtained when the first 120 natural numbers are divided by 9? options: A)397 B)401 C)403 D)405 E)399 SOLUTION:A positive integer can give only the following 9 remainders when divided by 9: 1, 2, 3, 4, 5, 6, 7, 8, and 0. 1 divided by 9 gives the remainder of 1; 2 divided by 9 gives the remainder of 2; ... 8 divided by 9 gives the remainder of 8; 9 divided by 9 gives the remainder of 0. We'll have 11 such blocks, since 99/9=11. The last will be: 91 divided by 9 gives the remainder of 1; 92 divided by 9 gives the remainder of 2; ... 98 divided by 9 gives the remainder of 8; 99 divided by 9 gives the remainder of 0. The last number, 100, gives the remainder of 1 when divided by 9, thus the sum of all remainders will be: 11(1+2+3+4+5+6+7+8+0)+1=405. Answer: D. #### D QUESTION:If the equation x^2−x=k has at least one solution, which of the following must be true? options: A)k ≥-1/4 B)k < −9 C)k = 9 D)k ≤ 9 E)k ≥ −9 SOLUTION:x^2−x=k => x^2−x - k = 0 For a quadratic equation to have at least one solution, its discriminant (b^2-4ac) should be non-negative. b^2-4ac ≥0 => 1- 4*1*(-k) ≥0 =>1 + 4k ≥0 => k ≥ -14 Answer A #### A QUESTION:Albert 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 options: A)Rs. 8510 B)Rs. 22050 C)Rs. 8730 D)Rs. 8820 E)None of these SOLUTION:Explanation: =>(20000×(1+5/100)2) =>20000×21/20×21/20 =>22050 Option B #### B QUESTION:In a certain animal shelter, the ratio of the number of catsto the number of dogs is 15 to 7. If 16 additional dogs were to be taken in by the shelter, the ratio of the number of cats to the number of dogs would be 15 to 11. How many cats are in the shelter? options: A)15 B)25 C)30 D)45 E)60 SOLUTION:This ratio question can be solved in a couple of different ways. Here's an Algebraic approach... We're told that the ratio of the number of cats to the number of dogs is 15:7. We're then told that 16 more dogs are added to this group and the ratio becomes 15:11. We're asked for the number of cats. Algebraically, since the number of cats is a multiple of 15 and the number of dogs is a multiple of 7, we can write this initial relationship as... 15X/7X When we add the 16 cats and factor in the 'ending ratio', we have an equation.... 15X/(7X+16) = 15/11 Here we have 1 variable and 1 equation, so we can solve for X.... (15X)(11) = (7X+16)(15) (X)(11) = (7X+16)(1) 11X = 7X + 16 4X = 16 X = 4 With this X, we can figure out the initial number of dogs and cats... Initial dogs = 15X = 15(4) = 60 Final Answer: D #### D QUESTION:Krishna's monthly expenditure was decreased by 50% and subsequently increased by 50%. How much percent does he loss? options: A)25 % B)50 % C)75 % D)85 % E)None of these SOLUTION:Explanation : Let the original expenditure = Rs. 100. New final expenditure = 150% of (50% of Rs. 100) = Rs.(150/10050/100100) = Rs. 75. Decrease = 100- 75 = 25 % Answer : A #### A QUESTION:There are 40 students in a certain geometry class. If two thirds of the students are boys and three fourths of the boys are under six feet tall, how many boys in the class are under six feet tall? options: A)6 B)12 C)20 D)24 E)27 SOLUTION:40*2/3 *3/4= 20 Answer: C #### C QUESTION:How many 3 digit positive integers T exist that when divided by 7 leave a remainder of 5? options: A)128 B)142 C)143 D)141 E)129 SOLUTION:Minimum three digit number is 100 and maximum three digit number is 999. The first three digit number that leaves remainder 5 when divided by 7 is 103. 14 * 7 = 98 +5 = 103 The second three digit number that leaves remainder 5 when divided by 7 is 110. 15 * 7 = 105 +5 =110 The third three digit number that leaves remainder 5 when divided by 7 is 117 and so on The last three digit number that leaves remainder 5 when divided by 7 is 999 142 * 7 = 994 + 5 = 999 Therefore, we identify the sequence 103,110,117.....999 use the formula of last term Last term = first term + (n - 1) * common difference you will get the answer 129 that is definitely E. #### E QUESTION:The basic one-way air fare for a child aged between 3 and 10 years costs half the regular fare for an adult plus a reservation charge that is the same on the child's ticket as on the adult's ticket. One reserved ticket for an adult costs $216 and the cost of a reserved ticket for an adult and a child (aged between 3 and 10) costs $327. What is the basic fare for the journey for an adult? options: A)$111 B)$52.5 C)$210 D)$58.5 E)$6 SOLUTION:Explanatory Answer Step 1: Assign variables and frame equations Let the basic fare for the child be $X. Basic one-way air fare of a child costs half the regular fare for an adult Therefore, the basic fare for an adult = 2(basic one-way airfare for a child) = $2X. Reservation charge is the same on the child's ticket as on the adult's ticket. Let the reservation charge per ticket be $Y Hence, an adult ticket will cost (Basic fare + Reservation charges) = 2X + Y = $216 ..... (1) And ticket for an adult and a child will cost (2X + Y) + (X + Y) = 3X + 2Y = $327 .... (2) Step 2: Solve the equations and determine basic fare for an adult Multiply equation (1) by 2: 4X + 2Y = 432 .... (3) Subtract equation (2) from equation (3): (4X + 2Y = 432) - (3X + 2Y = 327) ∴ X = $105. The basic fare of an adult ticket = 2X = 2*105 = $210 Answer C #### C QUESTION:P and Q started a business with respective investments of Rs. 4 lakhs and Rs. 10 lakhs. As P runs the business, his salary is Rs. 5000 per month. If they earned a profit of Rs. 2 lakhs at the end of the year, then find the ratio of their earnings? options: A)1:8 B)1:6 C)2:1 D)1:1 E)1:7 SOLUTION:Ratio of investments of P and Q is 2 : 5 Total salary claimed by P = 12 * 5000 = Rs. 60000 Total profit = Rs. 2 lakhs. Profit is to be shared = Rs. 140000 Share of P = (2/7) * 140000 = Rs. 400000 Share of Q = Rs. 100000 Total earnings of P = (60000 + 40000) = Rs. 100000 Ratio of their earnings = 1:1 Answer:D #### D QUESTION:A, B and C can do a piece of work in 20, 30 and 60 days respectively. In how many days can A do the work if he is assisted by B and C on every third day? options: A)20 B)18 C)12 D)14 E)15 SOLUTION:A's 2 day's work = 1/20 x 2 = 1/10 (A + B + C)'s 1 day's work = 1/20 + 1/30 + 1/60 = (3+2+1)/60 = 1/10 Work done in 3 days = A's 2 day's work + (A + B + C)'s 1 day's work Work done in 3 days = 1/10 + 1/10 Now, work is done in 3 days = 2/10 = 1/5 So, 1/5 cork is done in 3 days. So, work will be done in (3 x 5) = 15 days. So, correct answer is E #### E QUESTION:A policeman noticed a criminal from a distance of 180 km. The criminal starts running and the policeman chases him. The criminal and the policeman run at the rate of 8 km and 10 km per hour respectively. What is the distance between them after 3 minutes ? options: A)100 m B)80 m C)130 m D)150 m E)None of these SOLUTION:Explanation : Solution: Relative speed = (10 - 8) = 2 km/hr. Distance covered in 3 minutes = (2 * 3/60) km = 1/10 km = 100 m. .'. Distance between the criminal and policeman = (180 - 100) m = 80 m. Answer : B #### B <<<Examples ends QUESTION:How many seconds will a 500 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? options: A)299 meters B)278 meters C)500 meters D)276 meters E)299 meters SOLUTION:Let length of tunnel is x meter Distance = 800+x meter Time = 1 minute = 60 seconds Speed = 78 km/hr = 78*5/18 m/s = 65/3 m/s Distance = Speed*Time 800+x = (65/3) * 60 800+x = 20 * 65 = 1300 x = 1300 - 800 = 500 meters Answer: C #### C

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:A, B, K start from the same place and travel in the same direction at speeds of 30 km/hr, 40 km/hr, 160 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? options: A)5.0 B)5.5 C)6.0 D)6.5 E)7.0 SOLUTION:In 2 hours, A travels 60 km. B can catch A at a rate of 10 km/hr, so B catches A 6 hours after B starts. So A and B both travel a distance of 240 km. C needs 1.5 hours to travel 240 km, so C leaves 6.5 hours after A. The answer is D. #### D QUESTION:The area of the largest circle that can be drawn inside a square of side 98 Cm in length is: options: A)8600 B)3646 C)7546 D)7636 E)1606 SOLUTION:Radius of required circle = 49 Cm its area = 22/7 × 49 × 49 154 × 49 = 7546 Cm(power)2 Answer is C. #### C QUESTION:A box contains four cents, of which two centss have heads on both their faces, one cent has tail on both its faces and the fourth cent is a normal one. A cent 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 cent tossed is also a head. options: A)4/5 B)3/5 C)2/5 D)3/4 E)1/2 SOLUTION:There are four ways (2 heads in one two-headed cent and 2 heads in the other two-headed cent) How many ways can you get heads from this entire set of cents? There are five ways (four as identified above and one from the normal coin) Therefore probability = 4/5 Option A #### A QUESTION:The Simple Interest on Rs. 7300 from 11 May, 1987 to 10 September 1987 ( Both day Include ) at 5% per annum is : options: A)120 B)123 C)125 D)128 E)130 SOLUTION:Time from 11 May to 10 September, 1987 =21+30+31+31+10 = 123 days Time : 123 days = 123/365 year S.I =(7300x123x5)/(365x100)=Rs.123 answer :B #### B QUESTION:If a man rows at the rate of 5 kmph in still water and his rate against the current is 3.5 kmph,then the man’s rate along the current is : options: A)4.25 kmph B)6 kmph C)6.5 kmph D)8.5 kmph E)None of these SOLUTION:Solution Let the rate along the current be x kmph.Then,1/2(x + 3.5) = 5 or x = 6.5 kmph. Answer C #### C QUESTION:What is the smallest positive integer K such that the product of 450 x K is a perfect square? options: A)3 B)9 C)15 D)25 E)63 SOLUTION:A perfect square, is just an integer that can be written as the square of some other integer. For example 16=4^2, is a perfect square. Now, 450 = 3^2 * 5^2 *3 , so if k=3 then 450k = (3 * 5 * 3)^2, which is a perfect square (basically the least positive value of k must complete only the power of 7 to even power as powers of other primes are already even). Answer: A. #### A QUESTION:Salesperson 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? options: A)$21,000 B)$18,000 C)$15,000 D)$ 14,500 E)$4,000 SOLUTION:sometime, setting up an equation is an easy way to go with: 350 + 0.06 (x - 1000) = 0.08 x x = 14,500 Ans : D #### D QUESTION:A man buys an item at Rs. 600 and sells it at the loss of 20 percent. Then what is the selling price of that item options: A)Rs. 480 B)Rs. 760 C)Rs. 860 D)Rs. 960 E)None of these SOLUTION:Explanation: Here always remember, when ever x% loss, it means S.P. = (100 - x)% of C.P when ever x% profit, it means S.P. = (100 + x)% of C.P So here will be (100 - x)% of C.P. = 80% of 600 = 80/100 * 600 = 480 Option A #### A QUESTION:Seller selling an apple for Rs.18, a Seller loses 1/6th of what it costs him. The CP of the apple is? options: A)10 B)12 C)19 D)18 E)20 SOLUTION:SP=18Loss=CP19Loss=CP−SP=CP−18⇒CP19=CP−18⇒18 CP19=18⇒CP19=1⇒CP=19 C #### C QUESTION:Indu gave Bindu Rs.3750 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? options: A)5 B)6 C)9 D)3 E)1 SOLUTION:3750 = D(100/4)2 D = 6 Answer: B #### B QUESTION:Given a collection of points P in the plane a 1-set is a point in P that can be separated from the rest by a line; i.e the pint lies on one side of the line while the others lie on the other side. The number of 1-sets of P is denoted by n1(P) . The maximum value of n1(P) over all configurations P of 4 points in the plane is options: A)1 B)2 C)3 D)4 E)5 SOLUTION:maximum no of 1-sets will be the no of points itself...as in even a simple configuration we can separate one point from others to make it 1-set ANSWER:A #### A QUESTION:Set 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? options: A)a) L(1 + K / 5) B)b) L * (K/100) - 20L C)c) 20L(1+K/100) D)d) 20(1+K/100)-19L E)e) L*(K/5)-19 SOLUTION:Let's assume the value of new element to bea. So converting the word problem into equation, (19*L + a) / (19 + 1) = L + k ==> after solving the equation we will get a (value of newly added element) = L + 20K But according to the answer options, problem writer wanted to conveyk% percent rise in average value. If we consider this case than resulting equation will be, (19*L + a) / ( 19+1 ) = L + (K/100)*L ==> 19L + a = 20 [ L + KL/100] ==> a= 20L + KL/5 -19L ==> a= L + KL/5 , which is equivalent to option [A] #### A QUESTION:If a two-digit positive integer has its digits reversed, the resulting integer differs from the original by 36. By how much do the two digits differ? options: A) 3 B) 4 C) 5 D) 6 E) 7 SOLUTION:Given that (10a + b) - (10b + a) = 36 --> 9a - 9b =36 --> a - b = 4. Answer: B. #### B QUESTION:A 25% stock yielding 20% is quoted at: options: A)s. 83.33 B)s. 110 C)s. 112 D)s. 125 E)s. 140 SOLUTION:Income of Rs 20 on investment of Rs 100 Income of Rs 25 on investment of ? = (25*100)/20=125 ANSWER:D #### D QUESTION:If a mixture is 3⁄7 alcohol by volume and 4⁄7 water by volume, what is the ratio of the volume of alcohol to the volume of water in this mixture? options: A)3⁄7 B)4⁄7 C)3⁄4 D)4⁄3 E)7⁄4 SOLUTION:Should be a sub-600 level Q.. volume= {3/7}/{4/7}=3/4 ANSWER:C #### C QUESTION:The population of a town is 10000. It increases annually at the rate of 10% p.a. What will be its population after 2 years? options: A)12300 B)12350 C)12100 D)12500 E)12600 SOLUTION:Formula : ( After =100 denominator Ago = 100 numerator) 10000 × 110/100 × 110/100 = 12100 C #### C QUESTION:A coin is tossed live times. What is the probability that there is at the least one tail? options: A)1/15 B)31/32 C)1/10 D)30/32 E)25/27 SOLUTION:Probability of getting least one tail at the coin tossed five times. = There is not even a single tail. = 1/32 ; P(T) = 1 - 1/32 = 31/32 ANSWER B #### B QUESTION:If a - b =6 and a2+b2=48 , find the value of ab. options: A)6 B)8 C)10 D)12 E)2 SOLUTION:Explanation: We know 2ab=(a2+b2)−(a−b)2 2ab=48−36=12 =>ab=6 Option E #### E QUESTION:If SAGE is coded as 4657 and COT is coded as 333. How is GATE coded? options: A)5637 B)5367 C)5763 D)6573 E)6753 SOLUTION:g-5 a-6 e-7 from the code gate t - 3 from bat ANSWER:A #### A QUESTION:18 business executives and 7 chairmen meet at a conference. If each business executive shakes the hand of every other business executive and every chairman once, and each chairman shakes the hand of each of the business executives but not the other chairmen, how many handshakes would take place? options: A)144 B)131 C)279 D)90 E)45 SOLUTION:there are 18 business exec and in each handshake 2 business execs are involved. hence 18C2=153 Also, each of 18 exec will shake hand with every 7 other chairmen for total of 126 handshake. total=153+126=279 ANS: C #### C QUESTION:What is the perimeter of a triangle with sides 7 and 4 that has the maximum possible area? options: A)11 + √5 B)11 + √6 C)11 + 4√7 D)11 + √65 E)11 + 3√17 SOLUTION:We can maximize the area of the triangle by making these two sides the base and the height of a right angle triangle. Then the third side is the hypotenuse with a length of √(49+16) = √65 The perimeter is 11 + √65 The answer is D. #### D QUESTION:Two trains are moving in opposite directions with speed of 210 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 options: A)56 B)48 C)47 D)26 E)24 SOLUTION:Explanation: Relative speed = 210+90 = 300 km/hr (Since both trains are moving in opposite directions) Total distance = 1.1+.9 = 2km Time = 2/300 hr = 1/150 hr = 3600/150 seconds =24 seconds Answer: Option E #### E QUESTION:A conference is to have eight presentations over the course of one day, consisting of three long presentations, and five short presentations. If the conference organizer doesn't want consecutive long presentations, and the conference is to start with a short presentation, how many schedules of presentations are possible? options: A)1200 B)7200 C)2880 D)5760 E)11520 SOLUTION:S*S*S*S*S* 5 short presentations can be arranged in 5!=120 ways. As for 3 long presentations: each can be placed instead of any of the 5 star, so in C35=10C53=10 ways, and they also can be arranged in 3!=6 ways. Total = 120*10*6 = 7,200 Ans:B #### B QUESTION:If a > 0 and x is m percent of y, then, in terms of a, y is what percent of x? options: A)a) 100a B)b) 1/100a C)c) 1/a D)d) 10/a E)e) 10,000/a SOLUTION:x= a/100 * y So y= 100/a * x So y= (10000/a)/100 * x E #### E QUESTION:A boat can move upstream at 15 kmph and downstream at 35 kmph, then the speed of the current is? options: A)5 B)6 C)10 D)8 E)9 SOLUTION:US = 15 DS = 35 M = (35 - 15)/2 = 10 Answer: C #### C QUESTION:There 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? options: A)980 B)1150 C)1360 D)1540 E)1720 SOLUTION:The number of ways to choose two teams is 17C2 = 17*16/2 = 136 The total number of games in the season is 10*136 = 1360. The answer is C. #### C QUESTION:Find the value of x from the below equation? : 3x^2+5x+2 = 0 options: A)-1 B)1 C)-2 D)2 E)-3 SOLUTION:a = 3, b = 5, c = 2 x1,2 = (-5 ± √(52 - 4×3×2)) / (2×3) = (-5 ± √(25-24)) / 6 = (-5 ± 1) / 6 x1 = (-5 + 1)/6 = -4/6 = -2/3 x2 = (-5 - 1)/6 = -6/6 = -1 A #### A QUESTION:The difference between the squares of two consecutive odd integers is a square<1000 whose root equals the combined sum of the digits of the two integers. What is the sum of the digits M of the larger integer? options: A)M=2 B)M=5 C)M=8 D)10 E)11 SOLUTION:Really hard. But let's start with few concepts: 1. Square of an odd integer will be odd. 2. Difference of odd and odd will be even. 3. Any odd integer can be expressed as difference of two squares. 4. An even integer can be expressed as difference of two squares only if that even integer is a multiple of 4. Assume two odd integers to be (2x-1) and (2x+1). Difference of their squares = (2x+1)^2 - (2x-1)^2 = 4x^2 + 1 + 4x - (4x^2 + 1 - 4x) = 4x^2 + 1 + 4x - 4x^2 - 1 + 4x = 8x Now root of 8x needs to be an integer such that it is equal to the sum of the digits of the two odd integers. 8 = 2^3, so x needs to be such that itcompletesa perfect square. If we find x, we can find the value of 2x+1 (larger integer) and then sum of its digits. Let's check the options, starting with c. For sum to be 8, few possibilities are: 17, 35, 53, 71 If we take 17, the pair is 15 and 17, meaning x = 8. 8x = 64 root of 64 = 4 but 4 is not equal to 1+5+1+7. Reject. If we take 35, the pair is 33 and 35, meaning x = 17. 8x = 8*17 Reject since perfect square is not possible. If we take 53, the pair is 51 and 53, meaning x = 26. 8x = 8*26 Reject since perfect square is not possible. If we take 71, the pair is 69 and 71, meaning x = 35. 8x = 8*35 Reject since perfect square is not possible. I tried each option and the possibilities and then got lost. Then, it occurred to me that I was only checking 2-digit integers. What about 3-digits? Starting with option a, only 2-digit odd integer whose sum is 2 is 101. If we take 101, the pair is 99 and 101, meaning x = 50. 8x = 8*50 = 400 root of 400 = 20 which is indeed equal to 9+9+1+1. Answer (A). #### A QUESTION:A man buys an item at Rs. 750 and sells it at the loss of 20 percent. Then what is the selling price of that item options: A)Rs. 660 B)Rs. 760 C)Rs. 600 D)Rs. 960 E)None of these SOLUTION:Explanation: Here always remember, when ever x% loss, it means S.P. = (100 - x)% of C.P when ever x% profit, it means S.P. = (100 + x)% of C.P So here will be (100 - x)% of C.P. = 80% of 750 = 80/100 * 750 = 600 Option C #### C QUESTION:A man buys $50 shares in a company which pays 10% dividend. If the man gerts 12.5% on his investment, at what price did he buy the shares? options: A)37.5 B)40 C)50 D)48 E)52 SOLUTION:Dividend on 1 share = $(10/100*50) =$5 $12.5 is an income on an investment of $100 $5 is an income on an investment of $(100*2/25*5)=40 Thus, cost of 1 share =$40 ANSWER B #### B QUESTION:Becky, Merry and John want to share a chocolate bar evenly. What part of the bar will each of them take? What part of the bar will Becky and Merry have together? options: A)1/3 B)2/3 C)2/4 D)None of these E)Cannot be determined SOLUTION:Solution The children need to divide the bar into three pieces. So everyone will take 1/3 of the chocolate bar. Two girls together will have two pieces, hence, mathematically speaking, they will have 2/3 of the bar Answer B #### B QUESTION:A person's present age is two-fifth of the age of his mother. After 8 years, he will be one-half of the age of his mother. How old id the mother at present? options: A)32 years B)36 years C)40 years D)48 years E)58 years SOLUTION:Let the mother's present age be x years. Then, the person's present age = 2/5 x years. (2/5 x + 8) = 1/2 (x + 8) 2(2x + 40) = 5(x + 8) => x = 40 ANSWER:C #### C QUESTION:A 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? options: A)2km/hr B)3km/hr C)5km/hr D)7km/hr E)10km/hr SOLUTION:Time required = 5 hrs- 1hr = 4hr Required speed = 100/4 = 25km/hr Original speed = 100/5 = 20 km/hr Difference = 25-20 = 5 km/hr Answer is C #### C QUESTION:If 6^w is a factor of (10!)^2, What is the greatest possible value of w ? options: A)2 B)4 C)6 D)8 E)10 SOLUTION:w 10!= 10*9*8*7*6*5*4*3*2*1 = 2*5*3*3*2*2*2*7*2*3*5*2*2*3*2 = 2^8*3^4*5^2*7 6= 2*3 Therefore only the exponents of 2 and 3 are relevant, 2^8 or 3^4 -> higher number counts = 8 -> Answer Choice D #### D QUESTION:Two 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 options: A)42 B)36 C)28 D)20 E)24 SOLUTION:Explanation: Distance covered = 120+120 = 240 m Time = 12 s Let the speed of each train = v. Then relative speed = v+v = 2v 2v = distance/time = 240/12 = 20 m/s Speed of each train = v = 20/2 = 10 m/s = 10×36/10 km/hr = 36 km/hr Answer: Option B #### B QUESTION:If a coin is tossed three times, what is the probability that on the first toss the coin lands on tails and then lands on heads the next two tosses? options: A)1/8 B)1/3 C)1/4 D)1/2 E)1 SOLUTION:P(THH) = 1/2*1/2*1/2=1/8 The answer is A. #### A QUESTION:If w is a positive integer, then 3^w + 3^(w +1) = options: A)4^a B)3^a − 1 C)3^(2a) + 1 D)3^a*(a − 1) E)4(3^w) SOLUTION:3^w + 3^(w +1) = 3^w + (3^w * 3^1) = 3^w (1 + 3) = 3^w(4) Ans. E) 4(3^w) #### E QUESTION:Which of the statements is true for 3111 & 1714 options: A)11 B)88 C)66 D)17 E)16 SOLUTION:Answer:B #### B QUESTION:The ratio between a two-digit number and the sum of the digits of that number is 4 : 1.If the digit in the unit's place is 3 more than the digit in the ten’s place, what is the number? options: A)47 B)36 C)58 D)25 E)14 SOLUTION:Let the ten's digit be x. Then, unit's digit = (x + 3). Sum of the digits = x + (x + 3) = 2x + 3. Number = l0x + (x + 3) = llx + 3. 11x+3 / 2x + 3 = 4 / 1 => 11x + 3 = 4 (2x + 3) => 3x = 9 => x = 3. Hence, required number = 11x + 3 = 36. Answer is B. #### B QUESTION:A 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 ? options: A)115 B)117 C)116 D)114 E)112 SOLUTION:Explanation: Length = 6 m 24 cm = 624 cm Width = 4 m 32 cm = 432 cm HCF of 624 and 432 = 48 Number of square tiles required = (624 x 432)/(48 x 48) = 13 x 9 = 117. Answer IS B #### B QUESTION:When the numerator of a fraction is decreased by 25% and its denominator is decreased by 20%, the new fraction obtained is 3/4. Find the original fraction? options: A)5/4 B)4/7 C)5/6 D)6/7 E)None of these SOLUTION:Let the fraction be x/y. When the numerator decreased by 25% and the denominator decreased by 20%. (x * 3/4)/(y * 4/5) = 3/4 => x/y = 3/4 * (4/5)/(3/4) = 4/5 ANSWER:E #### E QUESTION:If an organization were to sell n tickets for a theater production, the total revenue from ticket sales would be 20 percent greater than the total costs of the production. If the organization actually sold all but 5 percent of the n tickets, the total revenue from ticket sales was what percent greater than the total costs of the production? options: A)4% B)10% C)14% D)15% E)18% SOLUTION:Let Cost of PROD for 1 ticket = 1 So COP for n tickets = n So for selling n tickets, SP = 1.2 * n = 1.2n So SP of 1 ticket = 1.2 SP of 95% tickets = 1.2 * 0.95n So profit % = (1.2 * 0.95n - n)/n * 100 = 0.14 * 100 = 14% Answer - C #### C QUESTION:How 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? options: A)482 B)725 C)992 D)837 E)923 SOLUTION:20000(11/10)4 - 20000(6/5)2 = 482 Answer:A #### A QUESTION:Narendra started a business, investing 30000. Six months later, Chandan joined him with 15000. If they make a profit of 10000 at the end of the year, what should be the share of Narendra? options: A)Rs.7000 B)Rs.8000 C)Rs.8500 D)Rs.8600 E)Rs.8700 SOLUTION:The ratio of their investments = 30000 × 12 : 15000 × 6 = 4 : 1. :. Narendra’s share on profit of Rs.10000 = 10000 × 4/5 = Rs.8000. B) #### B QUESTION:If a, b, and c are consecutive positive even integers and a > b > c, which of the following could be equal to a + b - c ? options: A)6 B)2 C)-1 D)-3 E)-4 SOLUTION:consectutive even , X , X + 2 , X + 4 where X = Even now subtract X + (X+2) - (X+4) doing this leaves us with X -2 what even number can we substitute in X to yield an answer choice B works 2 (plug in 4 for X) #### B QUESTION:The compound ratio of 5:1, 3:1 and 2:5? options: A)6:1 B)1:3 C)1:5 D)1:1 E)1:6 SOLUTION:5/1 * 3/1 * 2/5 = 30/5 6:1 Answer: A #### A QUESTION:Zaya purchase 13 jars in a store then she returned 10 jars to store .Now how many jars she had? options: A)A)5 B)B)11 C)C)19 D)D)3 E)E)4 SOLUTION:13-10=3. Answer is D #### D QUESTION:A 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 five years back was: options: A)14 B)16 C)19 D)22 E)24 SOLUTION:Let the son's present age be x years. Then, (42 - x) = x 2x = 42. x = 21. Son's age 5 years back (21 - 5) = 16 years. answer :B #### B QUESTION:On Sunday morning, Pugsley and Wednesday are trading pet spiders. If Pugsley were to give Wednesday four of his spiders, Wednesday would then have four times as many spiders as Pugsley does. But, if Wednesday were to give Pugsley five of her spiders, Pugsley would now have five fewer spiders than Wednesday had before they traded. How many pet spiders does Pugsley have before the trading game commences? options: A)6 B)7 C)8 D)10 E)12 SOLUTION:If Pugsley were to give Wednesday four of his spiders, Wednesday would then have five times as many spiders as Pugsley does: (w + 4) = 4(p - 4) If Wednesday were to give Pugsley five of her spiders, Pugsley would now have five fewer spiders than Wednesday had before they traded: p + 5 = w - 5 Solving gives p = 10 and w = 20. Answer: D. #### D QUESTION:Express the ratio 3 2/3 : 7 1/3 in its simplest form. options: A)1:21 B)1:1 C)2:1 D)1:2 E)2:11 SOLUTION:Solution We first convert the mixed numbers 3 2/3 and 7 1/3 into fractions 3 2/3 = 3*3 / 3 + 2 / 3 = 11 / 3 7 1/3 = 7*3 / 3 + 1 / 3 = 22 / 3 The ratio 3 2/3 : 7 1/3 can be expressed as 11 / 3 ÷ 22 / 3 = 11 / 3 × 3 / 22 Simplify = 11 / 22 = 1 / 2 The ratio is 1 / 2 or 1:2 ANSWER IS D #### D QUESTION:A number is said to be a “digifac” if each of its digits is a factor of the number itself. What is the sum N of the missing digits of the following five-digit digifac: 9, 5, 3 _ _ ? options: A) 5 B) 7 C) 9 D) 10 E) 14 SOLUTION:Here, the term “digifac” should look intimidating. You probably haven’t studied digifacs before, so how should you approach this problem? Well, keep in mind that digifacs aren’t being tested; in fact, the author of this question just made that term up, and then defined it for you. What makes this question hard is that the non-challenge-seeker (I think I just made that term up, too…) will see the unfamiliar term “digifac” and lose faith immediately. “I don’t know what that is!” She who finds the challenge in the GMAT fun, however, will read the definition and think “got it – I need to find the two digits that ensure that 9, 5, and 3 are both factors of the overall number, and that the remaining two digits are also factors”. And work from there. The number must be divisible by 5, so the only units digits that work are 0 or 5. And the number must be divisible by 9 (and also 3), so we need the sum N of all digits to be a multiple of 9. 9 + 5 + 3 = 17, so our only options are to get the sum to 18 (by adding 1) or to 27 (by adding 10). A quick glance at the answer choices shows that 0 1 isn’t an option. Why not? That would require 0 to be one of the digits…and 0 isn’t a factor of anything. So the units digit must be 5, making the tens digit 5, and we have 95,355. That number is a multiple of 5, 3, and 9, so it works:the correct answer is D, and more importantly this fun challenge required no “trivial” information about digifacs…that term only existed to obscure the link between the given information and the path to the answer.D #### D QUESTION:If a company gains 10 %, the wholesale dealer 15 % and the retailer 25 %, then find the cost of production of a table if the retail price was Rs 1265 options: A)800 B)700 C)750 D)850 E)900 SOLUTION:cost P = 125/100 * 115/100 * 110/100 = 1265 253/160p=1265==> p =800 ANSWER A #### A QUESTION:The average weight of 20 girls increases by 2 kg when a new girl comes in place of one of them weighing 40 kg. What might be the weight of the new girl? options: A)85 kg B)90 kg C)80 kg D)75 kg E)70 kg SOLUTION:Total weight increased = 20 x 2 kg = 40 kg. Weight of new person = 40 + 40 kg =80 kg Answer : C #### C QUESTION:If a trader sold two cars each at Rs. 325475 and gains 10% on the first and loses 10% on the second, then his profit or loss percent on the whole is? options: A)1.44% B)1.74% C)1.84% D)1.47% E)1.00% SOLUTION:SP of each car is Rs. 325475, he gains 10% on first car and losses 10% on second car. In this case, there will be loss and percentage of loss is given by = [(profit%)(loss%)]/100 = (10)(10)/100 % = 1.00% Answer:E #### E QUESTION:Carmen made a sculpture from small pieces of wood. The sculpture is 2 feet 10 inches tall.Carmen places her sculpture on a base that is 2 inches tall. How tall are the sculpture andbase together? options: A)3.1 feet B)3.2 feet C)3.3 feet D)3.0 feet E)3.5 feet SOLUTION:we know 1 feet =12 inch then 2 feet =24 inch 24+10=34 then 34+2=36 36/12=3.0 feet ANSWER:D #### D QUESTION:A box contains nine slips that are each labeled with one number: 1, 2, 3, 5, 8, 13, 21, and 55. Two of the slips are drawn at random from the box without replacement. What is the probability that the sum of the numbers on the two slips is equal to one of the numbers left in the box? options: A)7/72 B)1/6 C)7/36 D)5/28 E)21/36 SOLUTION:Probability = No: of desired outcomes / Total No: of outcomes. You are picking two slips out of 8 slips. So Total No: of outcomes = 8C2 = 28 Desired outcome : sum of the numbers on the two slips is equal to one of the numbers left in the box. How many such outcomes are there? If you look at the numbers closely, you will see that the following pair of numbers will give you the desired outcome. (1,2) (2,3) (3,5) (5,8) (8,13) . There are 5 such pairs. If the two numbers which I pick is from any of these 5 pairs, then I get my desired outcome. So No: of desired outcomes = 5 Probability = 5/28 Answer :D #### D QUESTION:What is the smallest possible common multiple of three integers, all larger than 53? options: A)27. B)54. C)846. D)19,656. E)21,924. SOLUTION:The Least common positive multiple would be for the immediate least number(s) after 53 i.e 54. Since nowhere is it stated that the three integers must be different, the integers could be 54,54 and 54... leading to least possible positive common multiple to be 54. Answer B. #### B QUESTION:If a point (x,y) is randomly selected within the square shown in the figure above, (the vertices are on 1,1 1,-1, -1,1 -1,-1) what are the R odds that x^2+y^2>1? options: A)1. pi/4 B)2. R=pi/16 C)3. R=1-pi/4 D)4. 1-pi/16 E)5.4-pi SOLUTION:area of the square will be 4, and the area of circle with center (0,0) and radius 1 will be pi. then succesful outcomes = 4 - pi (the area where x2+y2 will be greater than 1) total outcomes = 4 therefore probability = (4-pi)/4 C #### C QUESTION:A train 330 m long passed a pole in 11 sec. How long will it take to pass a platform 760 m long? options: A)76 sec B)89 sec C)87 sec D)35 sec E)36 sec SOLUTION:Speed = 330/11 = 30 m/sec. Required time = (330 + 760)/30 = 36 sec. Answer:E #### E QUESTION:A batch of cookies was divided among three tins: 2/3 of all the cookies were placed in either the blue tin 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 T of the cookies that were placed in the other tins were placed in the green tin? options: A)15/2 B)9/4 C)5/9 D)7/5 E)9/7 SOLUTION:Blue tin or red tin: 2/3 (N) Red tin: (1/3)N Blue tin: (1/4)N What the last statment meant, is it wants this fraction: (# of cookies in green tin)/(# of cookies in red and green tin) # of cookies in green tin = 2N/3 - N/4 = 8N- 3N/12 = 5N/12 # of cookies in red and green tin = N/3 + 5N/12 = 9N/12 Fraction T= 5N/12 * 12/9N = 5/9 (C) #### C QUESTION:A hen leaps 3 leaps for every 2 leaps of a duck, but 4 leaps of the duck are equal to 3 leaps of the hen. What is the ratio of the speed of the hen to that of the duck? options: A)2:1 B)3:4 C)4:3 D)1:4 E)5:6 SOLUTION:Given; 4 duck = 3 hen; Or, duck/hen = 3/4; Let hen's 1 leap = 4 meter and ducks 1 leap = 3 meter. Then, ratio of speed of hen and duck = 4*3/3*2 = 2:1''Answer: 2:1; #### A QUESTION:There are four prime numbers written in ascending order. The product of first three is 385 and that of last three is 1001. The last number is: options: A)9 B)13 C)15 D)12 E)19 SOLUTION:Explanation: abc/bcd=385/1001=>a/d=5/13 So d = 13 Option B #### B QUESTION:The sides AB, BC & CA of a triangle ABC have 3, 4 and 5 interior points respectively on them. Find the number of triangles that can be constructed using these points as vertices. options: A)220. B)205. C)250 D)105 E)225 SOLUTION:different ways.. 1) EASIEST approach.. lets see how many total can be made if none of the points were colliner that is NO three were in one line = 12C3 = 12!/9!3! = 220... Due to collinear, extra triangles considered above = 3C3 + 5C3 +4C3 = 1+10+4 = 15.. total = 220-15 = 205 ANSWER:B #### B QUESTION:On a certain day, mangrov farm harvested 4267 apples. If mangrov distributes his apples evenly across 7 different retail shops, how many apples would remain with him. Options: options: A)1 apple B)2 apple C)3 apple D)4 apple E)5 apple SOLUTION:This is equivalent to finding the first number that is divisible by 7 that occurs before 4267. In order to divide the sum in 7 parts, the amount must be divisible by 7 Divisibility rule of 7: The sum of the digits must be divisible by 7 Sum of digits of 4267 = 19 and 7 is divisible by 7. Hence, we need to remove 5 to this number for it to be divisible by 7 Correct Option:E #### E <<<Examples ends QUESTION:Three numbers are in the ratio 5 : 6 : 8. The sum of its longest and smallest numbers equals the sum of the third number and 49. Find the third number? options: A)A)54 B)B)75 C)C)48 D)D)42 E)E)63 SOLUTION:Let the numbers be 5x, 6x, 8x. Largest number = 8x. Smallest number = 5x. Third number = 6x. 8x + 5x = 6x + 49 7x = 49 =>x=7 6x=42=> third number is 42. Answer:D #### D

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:The maximum numbers of students among them 891 pens and 810 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is options: A)91 B)81 C)1001 D)1911 E)None SOLUTION:olution Required number of students. = H.C.F of 891 and 810. ‹=› 81. Answer B #### B QUESTION:Find the area of trapezium whose parallel sides are 20 cm and 18 cm long, and the distance between them is 15 cm options: A)178 cm2 B)179 cm2 C)285 cm2 D)167 cm2 E)197 cm2 SOLUTION:Area of a trapezium = 1/2 (sum of parallel sides) * (perpendicular distance between them) = 1/2 (20 + 18) * (15) = 285 cm2 Answer: C #### C QUESTION:Walking with 4/5 of my usual speed, I arrive at the bus stop 8 minutes later than normal. How many minutes does it take to walk to the bus stop at my usual speed? options: A)20 B)24 C)28 D)32 E)36 SOLUTION:Let t = usual time = distance / usual speed t + 8 = distance / (4* usual speed/5) = (5 * distance) / (4 * usual speed) = 5t/4 t = 32 The answer is D. #### D QUESTION:What is the HCF of 2/3, 5/9 and 6/5 options: A)1/45 B)2/45 C)4/15 D)8/45 E)9/45 SOLUTION:Explanation: HCF of Fractions = HCF of Numerators/LCM of Denominators = (HCF of 2, 5, 6)/(LCM of 3, 9, 5) = 1/45 Answer: Option A #### A QUESTION:Two employees X and Y are paid a total of Rs. 800 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week? options: A)s.200.63 B)s.250.63 C)s.290.63 D)s.300.63 E)s.363.63 SOLUTION:Let the amount paid to X per week = x and the amount paid to Y per week = y Then x + y = 800 But x = 120% of y = 120y/100 = 12y/10 ∴12y/10 + y = 800 ⇒ y[12/10 + 1] = 800 ⇒ 22y/10 = 800 ⇒ 22y = 8000 ⇒ y = 8000/22 =Rs.363.63 E) #### E QUESTION:Difference between two numbers is 5, six times of the smaller lacks by 6 from the four times of the greater. Find the numbers? options: A)8 B)9 C)7 D)5 E)4 SOLUTION:Explanation: x – y = 5 4x – 6y = 6 x = 12 y = 7 Answer:C #### C QUESTION:34. The side surface of a cylinder is rolled with a rectangular plate. If the perimeter of the circular base Is 6 feet, and the diagonal of the rectangular plate was 10 ft. What is height of the of the cylinder? options: A)7 B)10 C)8 D)12 E)15 SOLUTION:Think of a Pringles can. If you took off the bottom and top and cut a slit down the length, it would flatten to a rectangle. The dimensions of the rectangle are the height of the can and the circumference of the circle. Since you know both, one side and thehypothenuse use pythagoreans theorem or properties of 3-4-5 triangles to solve for the other side, 8. Correct answer C. #### C QUESTION:A city with a population of 160,080 is to be divided into 8 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? options: A)18,200 B)18,300 C)18,400 D)18,500 E)18,600 SOLUTION:The minimum possible population occurs when all the other districts have a population that is 10% greater than the least populated district. Let p be the population of the least populated district. Then 160,080 = p + 7(1.1)p 8.7p=160,080 p = 18,400 The answer is C. #### C QUESTION:The U.S. Defense Department has decided that the Pentagon is an obsolete building and that it must be replaced with an upgraded version: the Hexagon. The Secretary of Defense wants a building that is exactly 70 feet high and 200 feet on a side, and that has a hexagonal bull's-eye cutout in the center (somewhat like the current one) that is 25 feet on a side. What will be the volume of the new building in cubic feet? options: A)3,937,500 cubic feet B)15,750 cubic feet C)11550√3 cubic feet D)7,160,947 cubic feet E)3,937,500√3 cubic feet SOLUTION:Volume of the Hexagon with side 200 and height 70 = Area * height = 6*(sqrt(3)/4)(200^2)(70) Volume of the center bull's eye that is similar in shape of a hexagon but side 25 = 6 * (sqrt(3)/4)(25^2)*70 Volume of the building = 6*(sqrt(3)/4)(200^2)(70) - 6 * (sqrt(3)/4)(25^2)*70=7,160,947 Answer is D #### D QUESTION:A motor cyclist participant of a race says "We drove with the speed of 10 miles an hour one way, but while returning because of less traffic we drove on the same route with 17 miles per hour." What was their average speed in the whole journey? options: A)10 miles/hour B)12 miles/hour C)11 miles/hour D)12.6 miles/hour E)14 miles/hour SOLUTION:2xy/x+y=12.6 miles/hour ANSWER:D #### D QUESTION:In how many ways can the letters of the word "PROBLEC" be rearranged to make 7 letter words such that none of the letters repeat? options: A)4! B)5! C)7! D)8! E)9! SOLUTION:There are seven positions to be filled. The first position can be filled using any of the 7 letters contained in PROBLEM. The second position can be filled by the remaining 6 letters as the letters should not repeat. The third position can be filled by the remaining 5 letters only and so on. 758 Therefore, the total number of ways of rearranging the 7 letter word = 7*6*5*4*3*2*1 = 7! Ways. C #### C QUESTION:A contractor is engaged for 30days on the condition thathe receives Rs.25 for each day he works &is fined Rs.7.50 for each day is absent. He gets Rs.425 in all. For how many days was he absent? options: A)8 B)10 C)15 D)17 E)19 SOLUTION:30 * 25 = 750 425 ----------- 325 25 + 7.50 = 32.5 325/32.5 = 10 B #### B QUESTION:The true discount on a bill of Rs. 2560 is Rs. 360. What is the banker's discount? options: A)Rs. 432 B)Rs. 422 C)Rs. 419 D)Rs. 442 E)None of these SOLUTION:Explanation : F = Rs. 2560 TD = Rs. 360 PW = F - TD = 2560 - 360 = Rs. 2200 True Discount is the Simple Interest on the present value for unexpired time =>Simple Interest on Rs. 2200 for unexpired time = Rs. 360 Banker's Discount is the Simple Interest on the face value of the bill for unexpired time = Simple Interest on Rs. 2160 for unexpired time =360/2200 × 2560 = 0.16 × 2560 = Rs. 419 Answer : Option C #### C QUESTION:A 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 55% 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? options: A) 7/12 B) 1/4 C) 1/2 D) 7/24 E) 17/24 SOLUTION:In probability questions the trap answer is just the multiple of the numbers in the question. i.e. if you multiply 1/3 * 1/4 * 1/2 = 1/24 is trap answer The other trap answer could be 2/3 * 3/4 * 1/2 = 6/24 is trap answer So 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. C #### C QUESTION:If December 3rd, 1999 is a Friday, what day is January 7th, 2000? options: A)Wednesday B)Thursday C)Friday D)Saturday E)Sunday SOLUTION:There is difference of 35 days from Dec. 3rd 1999 to Jan. 7th 2000. 35/7 has a remainder of 0. Jan. 7th is: Friday + 0 days = Friday The answer is C. #### C QUESTION:An order was placed for the supply of a carpet whose breadth was 6 m and length was 1.44 times the breadth. What be the cost of a carpet whose length and breadth are 40% more and 25% more respectively than the first carpet. Given that the ratio of carpet is Rs. 45 per sq m? options: A)4882.40 B)8082.40 C)4002.40 D)4082.40 E)9082.40 SOLUTION:Explanation: Length of the first carpet = (1.44)(6) = 8.64 cm Area of the second carpet = 8.64(1 + 40/100) 6 (1 + 25/100) = 51.84(1.4)(5/4) sq m = (12.96)(7) sq m Cost of the second carpet = (45)(12.96 * 7) = 315 (13 - 0.04) = 4095 - 12.6 = Rs. 4082.40 Answer: Option D #### D QUESTION:Consider two statements Statement 1 => If R is an integer and R=2p+1 where p is not an integer. Statement 2 => If S is an integer and S=2q where q is not an integer Which of the following correctly specifies the Even/Odd nature of R and S respectively options: A)1) Odd,Even B)2) Odd,Odd C)3) Even,Odd D)4) Even,Even E)5) Cannot be determined SOLUTION:answer will be E R = integer R = 2p+1 = integer here p can be any n/2 and n can be even or odd , matters alot 2 get cancelled out if n were even R would odd if n odd R would be even ANSWER IS E #### E QUESTION:In 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 $841,000 invested in preferred stocks, what is the total amount of money invested in the fund? options: A)$1,974,000 B)$2,538,000 C)$3,264,000 D)$3,826,000 E)$4,205,000 SOLUTION:Portion invested in preferred stock = 3/5 * 1/3 = 1/5 1/5 of fund = 841--- Fund = 5 * 841--- Here, we can avoid the math and simply look at 5 * 1 -> 5. Only option E has 5 in it. Answer (E). #### E QUESTION:At a meeting of the 8 Joint 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 8 Chiefs of Staff be seated around a circular table? options: A)120 B)480 C)960 D)2520 E)5080 SOLUTION:Bunuel, I'm also a little confused with the number of arrangements of n distinct objects in a circle. Why is it given by (n-1)!. In theveritasanswer they say:answer E (5080), should be the number of ways to arrange all 7 without the seating restriction given. Is this incorrect?E #### E QUESTION:If x and y are perfect squares, then which five of the following is not necessarily a perfect square? options: A)x^2 B)xy C)4x D)x+y E)x^5 SOLUTION:If x=y=1^2=1, then each option but A is a perfect square, therefore A is NOT necessarily a perfect square. Answer: A. #### A QUESTION:Rahim bought 65 books for Rs.1150 from one shop and 50 books for Rs.920 from another. What is the average price he paid per book ? options: A)Rs.17 B)Rs.18 C)Rs.12 D)Rs.11 E)Rs.10 SOLUTION:Average price per book = (1150 + 920) / (65 + 50) = 2070 / 115 = Rs.18 Answer:B #### B QUESTION:The difference of 2 digit number & the number obtained by interchanging the digits is 36. What is the difference the sum and the number if the ratio between the digits of the number is 1:2 ? options: A)6 B)8 C)9 D)10 E)12 SOLUTION:Let the number be xy. Given xy – yx = 36. This means the number is greater is than the number got on reversing the digits. This shows that the ten’s digit x > unit digit y. Also given ratio between digits is 1 : 2 => x = 2y (10x + y) – (10y +x) = 36 => x – y = 4 => 2y – y =4. Hence, (x + y) – (x – y) = 3y – y = 2y = 8 B #### B QUESTION:In 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 16 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)? options: A)144 B)150 C)156 D)162 E)168 SOLUTION:Initially the number of gold coins and silver coins is 2k and 6k. After adding gold coins, the number of coins is 3k and 6k. Thus k = 16 and the total number of coins is 9k = 144. The answer is A. #### A QUESTION:Find the average of all numbers between 2 and 63 which are divisible by 5 options: A)15 B)20 C)25 D)32.5 E)35 SOLUTION:Explanation: Average=(5+10+15+20+25+30+35+40+45+50+55+60)/12=390/12=32.5 Answer: Option D #### D QUESTION:Ten years ago A was half of B in age. If the ratio of their present ages is 3 : 4, what will be the total of their present ages options: A)30 B)35 C)37 D)41 E)42 SOLUTION:Explanation: Let A's age 10 years ago = x years. Then, B's age 10 years ago = 2x years. (x + 10) / (2x+ lO) = 3/4 => x = 5. So, the total of their present ages =(x + 10 + 2x + 10) = (3x + 20) = 35 years Option B #### B QUESTION:What percent of 200 is 55? options: A)0.25% B)4% C)25% D)27.5% E)250% SOLUTION:200*x /100 = 55 x = 27.5 Ans: D #### D QUESTION:What will be the ratio of simple interest earned by certain amount at the same rate of interest for 2 years and that for 8 years? options: A)3 : 2 B)1 : 3 C)2 : 3 D)3 : 1 E)1 : 4 SOLUTION:Explanation : Simple Interest = PRT/100 Here Principal(P) and Rate of Interest (R) are constants Hence, Simple Interest ∝ T Required Ratio = Simple Interest for 2 years/Simple Interest for 8 years =T1/T2 =2/8 =1/4 =1:4 Answer : Option E #### E QUESTION:The length of a room is 5.5 m and width is 3.75 m. What is the cost of paying the floor by slabs at the rate of $400 per sq. metre. options: A)$8250 B)$8350 C)$8650 D)$8450 E)$8500 SOLUTION:Area =5.5×3.75 sq. metre. Cost for 1 sq. metre. = $400 Hence, total cost =5.5×3.75×400= $8250 A #### A QUESTION:12 is 6% of a, and 6 is 12% of b. c equals b/a. What is the value of c? options: A)1 / 2 B)1 / 3 C)1 / 4 D)1 /6 E)1 / 12 SOLUTION:6a/100 = 12 a = 200 12b/100 = 6 b = 50 c = b/a = 50 / 200 = 1/4 The answer is C. #### C QUESTION:If x < y < z and y - x > 5, where x is an even integer and y and z are odd integers, what is the least possible value D of z - x? options: A)6 B)7 C)8 D)9 E)10 SOLUTION:x<y<z To find the least possible value for z-x; we need to find the values for z and x that can be closest to each other. If x is some even number, then what could be minimum possible odd z. If x is some even number y-x>5; y>x+5; minimum value for y=x+5+2=x+7[Note: x+5 is as even+odd=odd and nearest odd greater than x+5 is x+5+2] Minimum value for z=y+2=x+7+2=x+9 [Note: z=y+2 because both z and y are odd. Difference between two odd numbers is 2] D=z-x = x+9-x= 9 Ans:D #### D QUESTION:Three friends (Caleb, Jerry and Elvis) are employees of a company. Their respective salaries are in the ratio of 3 : 4 : 6. Jerry and Elvis's salaries together is Rs. 10000. By what percent is Elvis's salary than that of Sarah? options: A)500%. B)400%. C)300%. D)200%. E)100%. SOLUTION:Explanation: Let the salaries be 3x, 4x and 6x respectively. Then,4x + 6x = 10000 => x = 1000. Caleb's salary = Rs. 3000, , Jerry's salary = Rs. 4000, and and Elvis's salary Rs. 6000. Excess of Elvis's salary over Caleb's=[ (3000 /3000) x 100] = 100%. Answer: E #### E QUESTION:36 men can complete a piece of work in 18 days. In how many days will 27 men complete the same work? options: A)56 B)28 C)45 D)24 E)45 SOLUTION:D 24 Let the required number of days be x. Less men, More days (Indirect Proportion) 27 : 36 :: 18 : x <-> 27 x x = 36 x 18 x = (36 x 18)/27 x = 24 #### D QUESTION:From a pack of 52 cards, 1 card is drawn at random. Find the probability of a face card drawn options: A)4/13 B)1/52 C)1/4 D)1/5 E)None of above SOLUTION:Explanation: Total number of cases = 52 Total face cards = 16 [favourable cases] So probability = 16/52 = 4/13 Answer: A #### A QUESTION:Mohan 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? options: A)A)Rs.520 B)B)Rs.594 C)C)Rs.596 D)D)Rs.595 E)None of these SOLUTION:Explanation: Price of 10 kgs of rice at Rs.26/kg = 10x26 = Rs.260 Price of 8 kgs of pulses at Rs.26/kg = 10x26 = Rs.260 Therefore, Total amount = Rs.260+Rs.260 = Rs.520. Answer: Option A #### A QUESTION:What is the perimeter of a triangle with sides 5 and 4 that has the maximum possible area? options: A)9 + 3√2 B)9 + √41 C)16 D)9 + √37 E)9 + 3√6 SOLUTION:We can maximize the area of the triangle by making these two sides the base and the height of a right angle triangle. Then the third side is the hypotenuse with a length of √(25+16) = √41 The perimeter is 9 + √41 The answer is B. #### B QUESTION:Five drainage pipes, each draining water from a pool at the same constant rate, together can drain a certain pool in 12 days. How many additional pipes T, each draining water at the same constant rate, will be needed to drain the pool in 4 days? options: A) 6 B) 9 C) 10 D) 12 E) 15 SOLUTION:This is an inverse proportional problem...... 5 pipes in 12 days; So for 4 days, it will be = 12 x 5 / 4 = 15 So, T=15-5 = 10.C #### C QUESTION:Monica 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 4 muffins remained. How many guests did Monica plan on? options: A)3. B)4. C)5. D)6. E)7. SOLUTION:Let x be the number of guests. Number of muffins prepared = 5x + 2 Number of muffins eaten + Number of muffins remaining = Number of muffins prepared 6(x - 1) + 4 = 5x + 2 6x - 4 = 5x + 2 x = 6 Answer: D #### D QUESTION:A sum of Rs. 800 amounts to Rs. 920 in 8 years at simple intere interest rate is increased by 8%, it would amount to bow mucb ? options: A)Rs 990 B)Rs 995 C)Rs 997 D)Rs 992 E)Rs 999 SOLUTION:S.l. = Rs. (920 - 800) = Rs. 120; p = Rs. 800, T = 3 yrs. _ . R = ((100 x 120)/(800*3) ) % = 5%. New rate = (5 + 3)% = 8%. New S.l. = Rs. (800*8*3)/100 = Rs. 192. :. New amount = Rs.(800+192) = Rs. 992 Answer is D. #### D QUESTION:If a two-digit positive integer has its digits reversed, the resulting integer differs from the original by 36. By how much do the two digits differ? options: A) 3 B) 4 C) 5 D) 6 E) 7 SOLUTION:Given that (10a + b) - (10b + a) = 36 --> 9a - 9b =36 --> a - b = 4. Answer: B. #### B QUESTION:Which of the following inequalities is equivalent to −4 < x < 8? options: A)|x - 1| < 7 B)|x + 2| < 6 C)|x + 3| < 5 D)|x - 2| < 6 E)None of the above SOLUTION:We know that |x| < a means -a < x < a, where Sum of lower limit of x (i.e -a) and the upper limit of x (i.e a), is 0 Given is, -4 < x < 8, let's say by adding y to this inequality we will get into the above format -4+y < x+y < 8+y Now, to move this into the mod format, we need to have (-4+y) + (8+y) = 0 => y = -2 Thus, -6< x-2 < 6 => |x-2| < 6. Hence, answer is D #### D QUESTION:A family consists of two grandparents, two parents and three grandchildren. The average age of the grandparents is 65 years, that of the parents is 45 years and that of the grandchildren is 8 years. What is the average age of family? options: A)6/7years B)B)31 C)C)30 D)D)33 E)E)35 SOLUTION:Required average = (65 x 2 + 45 x 2 + 8 x 3 )/(2 + 2 + 3) = (130 + 90 + 24)/7 =244/7 = 34 6/7years. Answer is A #### A QUESTION:A 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? options: A)276 Marks B)200 Marks C)186 Marks D)187 Marks E)167 Marks SOLUTION:30% ------------ 50 45% ------------ 25 ---------------------- 15% ------------- 75 30% -------------- ? 150 + 50 = 200 Marks Answer: B #### B QUESTION:An amount of money is to be distributed among Faruk, Vasim and Ranjith in the ratio 3 : 5 : 8. If Vasims share is Rs. 1500, what is the difference between Faruk's and Ranjith's shares? options: A)s 1200 B)s 1500 C)s 1600 D)s 1900 E)s 1700 SOLUTION:Explanation : Let P = Faruk, Q = Vasim, R = Ranjith Let P = 3x, Q = 5x and R = 8x. Then, 5x = 1500 ? x = 300. P=900,Q=1500 and R = 2400. Hence, (R - p) = (2400 - 900) = 1500 Answer : B #### B QUESTION:What distance will be covered by a bus moving at 126 kmph in 10 seconds? options: A)287 B)600 C)350 D)276 E)207 SOLUTION:126 kmph = 126 * 5/18 = 35 mps D = Speed * time = 35 * 10 = 350 m. Answer:C #### C QUESTION:A certain league has five divisions. The respective divisions had 6, 7, 8, 9 and 11 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? options: A) 81 B) 83 C) 85 D) 86 E) 89 SOLUTION:Overall, there can be 81 minuses. Tus, it is A. #### A QUESTION:As part of a promotion designed to attract visitors, an amusement park gives out 24,600 free tickets per year. Usually, the number of tickets given away each month is constant. Due to an employee error, only 10,000 tickets were given out in the first four months of the year. How many tickets should the amusement park give out in the fifth month so that it will begin the sixth month back on its regular giveaway schedule? options: A)205 B)207 C)220 D)225 E)250 SOLUTION:24600/12=2050 2050*5=10250 10250-10000=250 Answer E #### E QUESTION:How many quarters are equal to 7 dollars? options: A)1 B)28 C)12 D)9 E)7 SOLUTION:7 * 4 = 28 quarters Answer : B #### B QUESTION:The average age of 39 students in a group is 14 years. When teacher's age is included to it, the average increases by one. What is the teacher's age in years ? options: A)35 years B)45 years C)51 years D)54 years E)None of these SOLUTION:Explanation: Age of the teacher = (40 * 15 - 39 * 14) years = 54 years. Answer: D #### D QUESTION:Find the greatest number which on dividing 6215 and 7373, leaves a reminder of 23 and 29 respectively options: A)125 B)127 C)129 D)131 E)144 SOLUTION:Explanation: In this type of question, its obvious we need to calculate the HCF, trick is HCF of (6215 - 23) and (7373 -29) = HCF (6192, 7344) = 144 Option E #### E QUESTION:If Juan takes 16 seconds to run y yards, how many seconds will it take him to run x yards at the same rate? options: A)16x/y B)16y/x C)x/(16y) D)16/(xy) E)xy/16 SOLUTION:This problem is testing us on the Rate x Time = Distance relationship. This relationship also tells us that Rate = Distance/Time and Time = Distance/Rate. Ultimately, we are looking for how many seconds it will take Juan to run x yards. Thus, the equation we’ll use is: Time = Distance/Rate. We know the distance is x yards, and we need to find Juan’s rate. We can find Juan’s rate as follows: Rate = Distance/Time = y yards/16 seconds Using that rate, we need to determine how long it takes him to run x yards at the same rate. So we have: Time = Distance/Rate Time = x yards/(y yards/16 seconds) Time = (x yards) x (16seconds/y yards) Time = 16x/y seconds Answer A. #### A QUESTION:If 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%? options: A)3 B)8 C)9 D)6 E)4 SOLUTION:96% ---- 12 144% ---- ? 96/144 * 12 = 8 Answer: B #### B QUESTION:An office supply store stocks two sizes of notebooks, each in six colors: orange, 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? options: A)20 B)24 C)32 D)36 E)42 SOLUTION:First let's consider the small notebooks. There are 6 ways to choose notebooks of the same color. The number of ways to choose four notebooks with different colors is 6C4=15. There are 21 different packages we can make with the small notebooks. We can use the same process to find 21 different packages with large notebooks. The total number of different packages is 42. The answer is E. #### E QUESTION:A straight line in the xy-plane has a slope of 2 and a y-intercept of 2. On this line, what is the x-coordinate of the point whose y-coordinate is 550 ? options: A)249 B)498 C)676 D)823 E)274 SOLUTION:slope of 2 and a y-intercept of 2 y-coordinate is 550 y = 2x + 2 548 = 2x x = 274 Answer: E. 274 #### E QUESTION:Two numbers are in the ratio 3 : 4. If the sum of numbers is 63, find the numbers. options: A)26,37 B)25,38 C)27,36 D)28,35 E)29,34 SOLUTION:Sum of the terms of the ratio = 3 + 4 = 7 Sum of numbers = 63 Therefore, first number = 3/7 × 63 = 27 Second number = 4/7 × 63 = 36 Therefore, the two numbers are 27 and 36. Answer:C #### C QUESTION:If a positive odd integer N has p positive factors, how many positive factors will 3N have ? options: A)p B)2p C)P+1 D)2p+1 E)Cannot be determined SOLUTION:I have added some extra text to make this question more GMAT-like: Let's TEST some values of N Try N = 3 The factors of 3 are {1, 3}. Here, p =2 So, 2N = (2)(3) = 6 The factors of 6 are {1, 2, 3, 6}. So, we have a total of4 Now check the answer choices: A) p =2No good. We want an output of4. ELIMINATE B) 2p = (2)(2) = 4. PERFECT! KEEP B C) P+1 =2+ 1 = 3 No good. We want an output of4. ELIMINATE D) 2p+1 = (2)(2) + 1 = 5 No good. We want an output of4. ELIMINATE E) Cannot be determined. POSSIBLE. KEEP E Let's TEST another value of N Try N = 7 The factors of 7 are {1, 7}. Here, p =2 So, 2N = (2)(7) = 14 The factors of 14 are {1, 2, 7, 14}. So, we have a total of4 Now check the REMAINING answer choices: B) 2p = (2)(2) =4. PERFECT! KEEP B E) Cannot be determined. POSSIBLE. KEEP E Let's TEST one more (non-prime) value of N Try N = 9 The factors of 9 are {1, 3, 9}. Here, p =3 So, 2N = (2)(9) = 18 The factors of 18 are {1, 2, 3, 6, 9}. So, we have a total of6 Now check the REMAINING answer choices: B) 2p = (2)(3) =6. PERFECT! KEEP B E) Cannot be determined. POSSIBLE. KEEP E At this point, it SEEMS LIKELY that the correct answer is C #### C QUESTION:The average of five numbers is 27. If one number is excluded, the average becomes 21. The excluded number is? options: A)48 B)49 C)50 D)51 E)52 SOLUTION:Excluded number = (27 * 5) - (21 * 4) = 135 - 84 = 51. Answer: D #### D QUESTION:A father is four times as old as his son. In twenty years, he'll be twice as old. How old are they now? options: A)5,40 B)10,40 C)20,40 D)10,30 E)15,30 SOLUTION:If F is age of father and s is age of son f=4s f+20 = 2*(s+20) 4s+20 = 2s+40 2s=20 s=10 F=40 ANSWER:B #### B QUESTION:The 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? options: A)9 B)4 C)8 D)5 E)3 SOLUTION:S = 4 M = x DS = x + 4 US = x - 4 6/(x + 4) + 6/(x - 4) = 2 x = 8 Answer:C #### C QUESTION:A is the average (arithmetic mean) of the first 7 positive multiples of 4 and B is the median of the first 3 positive multiples of positive integer n. If the value of A^2 – B^2 is zero, what is the value of n? options: A)2 B)4 C)6 D)8 E)10 SOLUTION:If A^2 - B^2 = 0, then let's assume that A = B. A must equal the 4th positive multiple of 4, thus A = 16, which also equals B. B is the second positive multiple of n, thus n = 16/2 = 8. The answer is D. #### D QUESTION:The 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.8600. If his salary for the month of May is Rs.6500, find his salary for the month of January? options: A)s.4100 B)s.4270 C)s.4500 D)s.4550 E)s.2500 SOLUTION:Sum of the salaries of the person for the months of January, February, March and April = 4 * 8000 = 32000 ----(1) Sum of the salaries of the person for the months of February, March, April and May = 4 * 8600 = 34400 ----(2) (2)-(1) i.e. May - Jan = 2400 Salary of May is Rs.6500 Salary of January = Rs.4100 Answer:A #### A QUESTION:What is the difference between the local value of 1 and 2 in the number 2124? options: A)70 B)75 C)20 D)80 E)60 SOLUTION:Explanation: 100 – 20 = 80 Answer: D #### D QUESTION:How many of the integers between 25 and 45 are even ? options: A)21 B)20 C)11 D)10 E)9 SOLUTION:Number start between 25 to 45 is 20 numbers half of them is even..which is 10 ANSWER:D #### D QUESTION:On a certain day, Tim invested $600 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’s investment in the first 2 years was how much greater than the total amount of interest earned by Lana’s investment in the first 2 years? options: A)$5 B)$15 C)$44 D)$100 E)$105 SOLUTION:Compounded 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. With respect to the problem at hand, at the end of two years, Tim would have 600(1.10)^2 = 600(1.21) = 726 and Lana would have 800(1.05)^2 = 800(1.1025) = 882 Thus, Tim earned 126 dollars, while Lana earned 82 dollars The difference is $44 and the answer is C. #### C QUESTION:6x + 2y = -4 4x + y = 1 In the system of equations above, what is the value of x? options: A)5 B)4 C)3 D)2 E)1 SOLUTION:6x + 2y = -4 can be written as 3x + y = -2 Let's subtract the second equation from this equation. -x = -3 x = 3 The answer is C. #### C <<<Examples ends QUESTION:Can you find the smallest non fractional number such that If the number gets divided by 9 , we get the remainder of 1; If the number gets divided by 10 , we get the remainder of 2 If the number gets divided by 11 , we get the remainder of 3; If the number gets divided by 12 , we get the remainder of 4. options: A)1450 B)1300 C)1205 D)2501 E)1978 SOLUTION:E.option E As we know LCM of the numbers 9 10 11 & 12 is 1980. So if i divide 1980 by any of the four number , it gives remainder as 0. Now to get reminder as desired, is should be 2 short of 1978. (3-1,4-2,5-3,6-4 ) Ans:option E #### E

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:What is the smallest number which when diminished by 20, is divisible 15, 30, 45 and 60? options: A)200 B)220 C)240 D)322 E)342 SOLUTION:Required Number = (LCM of 15, 30, 45 and 60) + 20 = 180 + 20 = 200 Option A #### A QUESTION:In 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. options: A)10 B)9 C)8 D)7 E)5 SOLUTION:Total number of worker (M+W): 25 No. of men (M): 11 (Inferred fromHow many of the 11 men) No. of women (W): 14 Total no. of workers who have brown eyes (B): 13 No. of women who do not have brown eyes: 6 Therefore, no. of women who have brown eyes: W - 6 = 14 - 6 = 8 Remaining 5 are men. (B - 8= 13 - 8= 5) So 5 out of 11 men have brown eyes. E #### E QUESTION:The ratio between the number of sheep and the number of horses at the Stewart farm is 1 to 7, If each horse is fed 230 ounces of horse food per day and the farm needs a total 12,880 ounces of horse food per day, what is the number of sheep in the farm? options: A)18 B)28 C)32 D)56 E)8 SOLUTION:Let the number of sheeps and horses be 1x and 7x. Now total number of horses = total consumption of horse food/consumption per horse = 12880/230 = 56, which is equal to 7x. => x = 8 Sheeps = 1x = 1*8 = 8. Hence E #### E QUESTION:Mice can multiply very fast. Adult mice can give birth once every month, and baby mice grow into adult mice in just two months after they are born. If you would buy a baby mouse just after it was born, how many mice would you have in 10 months? options: A)1 B)2 C)3 D)4 E)5 SOLUTION:One. You cannot have more mice if you start with one! Answer A #### A QUESTION:A 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? options: A)15% B)20% C)25% D)27% E)40% SOLUTION:Total time for travelling 120 miles @ 60 mph = 120/60 = 2 hour = 120 minutes. Given, 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. #### D QUESTION:On day one, a store sold 125 bags. On each of the next d days, the company sold 83 bags. If the average daily sales of bags over this time period (including day one) is 90 bags, what is the value of d? options: A)4 B)5 C)6 D)7 E)8 SOLUTION:125 + 83d = 90(d+1). 7d = 35. d = 5. The answer is B. #### B QUESTION:A palindrome is a number that reads the same forward and backward, such as 242. How many even thirteen-digit numbers are palindromes? options: A)40 B)400 C)500 D)5,000 E)40,000,000 SOLUTION:if the palindrome must be even, it must begin and end in 2,4 6 and 8 ( 4 ways) e.g 22122,44144. The middle number in the thirteen-digit could be 0-9 ( 10 ways), e.g 2222225222222, 2864228224682 The 2nd and fourth numbers , the 3rd and 5th, 4th and 6th, 5th and 7th must also be same i.e 0-9( 10 ways) we thus have, 4 *10*10*10*10 *10*10= 4000000.E #### E QUESTION:The product of all the prime numbers less than 20 is closest to which of the following powers of 10 ? options: A)10^9 B)10^8 C)10^7 D)10^6 E)10^5 SOLUTION:We should find the approximate value of 2*3*5*7*11*13*17*19 to some power of 10. # of different approximations are possible. Approach #1: 2*5=10; 3*7=~20 (actually more than 20); 11*19=~200 (actually more than 200); 13*17=~200 (actually more than 200); 2∗3∗5∗7∗11∗13∗17∗19≈10∗20∗200∗200=8∗106≈107 Answer: C. Approach #2: 2*5=10 3*17=~50 (actually more than 50); 7*13=~100 (actually less than 100); 11*19=~200 (actually more than 200) 2∗3∗5∗7∗11∗13∗17∗19≈10∗50∗100∗200=107. Answer: C. #### C QUESTION:If the price of a certain bond on May 1st was 2/3 the price of the bond on June 1st and the price of the bond on July 1st was 25% greater than the price of the bond on May 1st. then the price of the bond on June 1st st was what percent of the average (arithmetic mean) price of the bond on May 1st and July 1st? options: A)50% B)75% C)120% D)133 1/3% E)150% SOLUTION:The price on June 1st = 12 (assume); The price on May 1st = 2/3*12 = 8; The price on July 1st = 8*1.25 = 10. The average price of the bond on May 1st and July 1st = (8+10)/2 = 9. The price of the bond on June 1st (12) is 4/3 times (134%) the average price of the bond on May 1st and July 1st. Answer: D. #### D QUESTION:Two 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? options: A)11 B)408 C)2881 D)287 E)221 SOLUTION:1h ----- 5 ? ------ 60 12 h RS = 13 + 21 = 34 T = 12 D = 34 * 12 = 408 Answer:B #### B QUESTION:If each side of a right triangle is increased by 10% and the base(b) is half of the height, find the percentage change in its area? options: A)26% B)21% C)15% D)18% E)12% SOLUTION:a =1/2 x b x h or 1/2 x 2a x a(for simplification) New h = 220a / 100 = 22a / 10 New b =(110a x 100) ==11a/10 New area = 1/2 (22a x 11a) / (10 x 10) = (121a²/100) increased area== (121a²/100) - a² Increase %= [(21a²/100 ) x (1/a² ) x 100]% = 21% answer :B #### B QUESTION:A man invested Rs. 1552 in a stock at 97 to obtain an income of Rs. 128. The dividend from the stock is: options: A)7.5% B)8% C)9.7% D)10% E)None of these SOLUTION:By investing Rs. 1552, income = Rs. 128 By investing Rs. 97, income = Rs. (128/1552 * 97) = Rs. 8 Dividend = 8% Answer = B #### B QUESTION:In 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.] options: A) 0.22 B) 0.44 C) 0.55 D) 22 E) 55 SOLUTION:A dozen eggs cost as much as a pound of rice --> 12 eggs = 1 pound of rice = 33 cents; A half-liter of kerosene costs as much as 8 eggs --> 4 eggs = 1/2 liters of kerosene. How many cents does a liter of kerosene cost --> 1 liter of kerosene = 8 eggs = 8/12*33 = 22 cents. Answer: D. #### D QUESTION:A man lent money of Rs. 2500 on simple interest for rate on interest being same as number of years. If he got Rs. 900 as interest amount at the end of the period then what is the rate of interest? options: A)6% B)4% C)5% D)3% E)2% SOLUTION:Explanation : SI = pnr SI = (2500*3r*3r)=900 r2 = 25 r = 5% Answer : C #### C QUESTION:Calculate the rate on a principal of Rs.1500 which yields a simple interest of Rs. 220.50 in 3 Years? options: A)6.9% B)2.9% C)9.9% D)5.9% E)4.9% SOLUTION:220.50 = (1500*3*R)/100 R = 4.9% Answer: E #### E QUESTION:A train 100 meters long completely crosses a 300 meters long bridge in 45 seconds. What is the speed of the train is? options: A)32 B)55 C)6 D)78 E)81 SOLUTION:S = (100 + 300)/45 = 400/45 * 18/5 = 32 Answer: A #### A QUESTION:A train running at the speed of 60 km/hr crosses a pole in 9 sec. What is the length of the train? options: A)296 m B)267 m C)297 m D)150 m E)255 m SOLUTION:Speed = 60 * 5/18 = 50/3 m/sec Length of the train = speed * time = 50/3 * 9 = 150 m Answer:D #### D QUESTION:The 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? options: A) 24 B) 26 C) 30 D) 46 E) 50 SOLUTION:carrrots = (carrrots + kiwi + x)*0.3 24 = (30 + 24 + x)*0.3 x = 26. Answer: B. #### B QUESTION:On a map, 1.5 inches represent 24 miles. How many miles approximately is the distance if you measured 48 centimeters assuming that 1-inch is 2.54 centimeters? options: A)174.2 B)212 C)288.1 D)296 E)302 SOLUTION:1.5 inch = 2.54*1.5 cm. So, 2.54*1.5 represents 24 miles. So for 48 cm.: 48/(2.54*1.5) = x / 24 ---> x = 24*47/(3.81) = 302 Answer will be E. #### E QUESTION:A 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? options: A)$40 B)$60 C)$80 D)$90 E)$100 SOLUTION:Purchase price = 120 Selling price = x 120 + 0.4*x = x 0.6*x = 120 x = 200 Profit = 200 - 150 = 50 ANSWER:A #### A QUESTION:A, B and C shared profits in ratio of 3 : 7 : 6. Theypartnered for 14months, 8months and 7months respectively. What was he ratio of their investments ? options: A)12 : 49 : 64 B)20 : 49 : 64 C)10 : 19 : 64 D)20 : 29 : 64 E)30 : 29 : 63 SOLUTION:Simply multiply profit sharing ratio with investment ratio to get investment amount ratio. Let X is the total investment ⇒14 x = 3 ⇒ 8 x = 7 ⇒ 7x = 8 ⇒ Final investment ratio = 12 : 49 : 64 A #### A QUESTION:If x is a positive integer, then the least value of x for which x! is divisible by 10 is? Can someone please explain intuitively what the question is asking? options: A)5 B)9 C)12 D)15 E)30 SOLUTION:In order x! to be divisible by 1,0, it should have at least 1 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 1. 5! = 120 has 1 trailing zeros. Answer: A #### A QUESTION:If the perimeter of a rectangular garden is 600 m, its length when its breadth is 100 m is? options: A)299 m B)777 m C)200 m D)167 m E)128 m SOLUTION:2(l + 100) = 600 => l = 200 m Answer:C #### C QUESTION:A 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 21 months? options: A)18:11 B)18:15 C)21:11 D)18:121 E)18:112 SOLUTION:A invests Rs.8000 for 21 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. A : B 8000*21 : (8000*4) + (4000*14) 168000 : 88000 A:B = 21:11.Answer:C #### C QUESTION:Ramu bought an old car for Rs. 40000. He spent Rs. 13000 on repairs and sold it for Rs. 64900. What is his profit percent? options: A)A)14% B)B)16% C)C)18% D)D)21.6% E)of these SOLUTION:Total CP = Rs. 40000 + Rs. 13000 = Rs. 53000 and SP = Rs. 64900 Profit(%) = (64900 - 53000)/55000 * 100 = 21.6% ANSWER:D #### D QUESTION:There 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. options: A)1 B)2 C)3 D)4 E)9 SOLUTION:145 divided by 12 = 12x12+1. That is, 1 banana will be extra after distributing 12 bananas to each candidate (12 in number). Answer A. #### A QUESTION:Consider a sequence of numbers given by the expression 7 + (a - 1) * 5, where n runs from 1 to 80.What is the sum of this series ? options: A)409 B)1636 C)16360 D)16000 E)15360 SOLUTION:terms in this sequence are 7,12,17----402 now since this is an a.p. with a common difference of 5. therefore its sum can be given as a(f+l)/2----------------1) a= total no. of terms =80 f= first term=7 l= last term=402 subsituting values in the expression 1 we have 80(7+402)/2 = 40(409) =16360=C #### C QUESTION:Two angles of a triangle have ratio 5:3, and the third angle is the difference of the other two. Find the smallest angle of such a triangle in degrees. options: A)16 B)18 C)20 D)24 E)36 SOLUTION:The angles are 5x, 3x, and (5x-3x) = 2x [note that 2x is the smallest angle] the angles of a triangle add up to 180, so 5x+3x+2x=180 10x = 180 x = 18 2x is the smallest angle, so 2*18 = 36 is the smallest angle E #### E QUESTION:Find the length of the longest pole that can be placed in a room 12 m long 8m broad and 9m high. options: A)13 B)14 C)15 D)16 E)17 SOLUTION:Length of longest pole = Length of the diagonal of the room = sqrt(12^2+8^2+9^2= sqrt(289)= 17 m. Answer is E. #### E QUESTION:5020−(502÷100.4)=? options: A)15 B)20 C)5015 D)25 E)35 SOLUTION:Explanation: =5020−(502/1004×10) =5020−5=5015 Option C #### C QUESTION:If s and t are positive integers such that s/t = 84.15, which of the following could be the remainder when s is divided by t ? options: A)2 B)4 C)8 D)20 E)9 SOLUTION:s/t= 84.15 s = 84.15t s = (84 + 0.15)t s = 84t + (15/100)t s = 84t + (3/20)t So remainder will be multiple of 3. The only multiple of 3 is 9. Ans. E #### E QUESTION:John professes to sell his goods at the cost price but he made use of 800 grams instead of a kg, what is the gain percent? options: A)12 1/3% B)12 1/4% C)12 2/3% D)12 2/1% E)12 1/2% SOLUTION:800 --- 100 100 --- ? => 12 1/2% Answer:E #### E QUESTION:Two taps can separately fill a cistern 8 minutes and 12 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? options: A)7 B)8 C)6.5 D)9 E)5 SOLUTION:1/8 + 1/12 - 1/x = 1/18 x = 72/11 = 6.5 Answer: C #### C QUESTION:The 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: options: A)3 months B)4 months C)5 months D)6 months E)7 months SOLUTION:S.I. on Rs. 1600 = T.D. on Rs. 1680. Rs. 1600 is the P.W. of Rs. 1680, i.e., Rs. 80 is on Rs. 1600 at 15%. Time = (100x80)/(1600x15)= 1/3 year = 4 months answer : B #### B QUESTION:A lady has fine gloves and hats in her closet- 18 blue, 32 red, and 25 yellow. The lights are out and it is totally dark. In spite of the darkness, she can make out the difference between a hat and a glove. She takes out an item out of the closet only if she is sure that if it is a glove. How many gloves must she take out to make sure she has a pair of each color? options: A)50 B)8 C)60 D)42 E)32 SOLUTION:in the first case the lady takes up 32 red colour then he takes up 24 y (cause he should take up pair) then he takes up 1y+1blue then 2blue(cause to make sure he has a pair of each color in hand) 32+24+2+2=60 ANSWER:C #### C QUESTION:The average monthly income of P and Q is Rs. 5100. The average monthly income of Q and R is 6250 and the average monthly income of P and R is Rs. 5200. The monthly income of P is? options: A)A)Rs.4050 B)B)Rs.4000 C)C)Rs.4029 D)D)Rs.4027 E)E)Rs.4020 SOLUTION:Let P, Q and R represent their respective monthly incomes. Then, we have: P + Q = (5050 * 2) = 10200 --- (i) Q + R = (6250 * 2) = 12500 --- (ii) P + R = (5200 * 2) = 10400 --- (iii) Adding (i), (ii) and (iii), we get: 2(P + Q + R) = 33100 = P + Q + R = 16550 --- (iv) Subtracting (ii) from (iv), we get, P = 4050. P's monthly income = Rs.4050. Answer: A #### A QUESTION:Kate and her boyfriend Ben, completed the painting of their new apartment together in 6 days.If they were to work separately, how long will it take each of them to complete it, if Ben can complete the painting 5 days earlier than Kate. options: A)6 and 11 B)5 and 10 C)10 and 15 D)8 and 13 E)6 and 10 SOLUTION:Work = (A)(B)/(A+B) where A and B are the individual times of each entity. Here, 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. Answers E, A and C are illogical, since the individual times must both be greater than 10 days. so we can TEST the values for Answers B and D. Using the values for Answers C and D... Answer C: (10)(15)/(10+15) = 150/25 = 6 This is a match Final Answer: C #### C QUESTION:A man can row upstream 10 kmph and downstream 30 kmph. Find the rate of the stream and man rate in still water. options: A)15,20 B)30,20 C)1,20 D)20,20 E)10,20 SOLUTION:Explanation: Please remember, If a is rate downstream and b is rate upstream Rate of current = 1/2(a-b) Rate in still water = 1/2(a+b) => Rate of current = 1/2(30-10) = 10 kmph => Rate in still water = 1/2(30+10) = 20 kmph Option E #### E QUESTION:An investor receives a total combined return of 7% on his two different investments. On his $40,000 investment he receives a return of 6%. What is the return on his $20,000 investment? options: A)7.25% B)7.5% C)8% D)8.5% E)9% SOLUTION:0.06 * 40000 + 20000x = 0.07(60000) solving for x give x = 9% option E #### E QUESTION:A 9-meter long wire is cut into two pieces. If the longer piece is then used to form a perimeter of a square, what is the probability that the area of the square will be more than 4 if the original wire was cut at an arbitrary point? options: A)1/5 B)2/7 C)2/9 D)3/10 E)4/11 SOLUTION:The longer wire will form a square with an area more than 4 if the wire is cut at a point within one meter of either end. The probability of this is 2/9. The answer is C. #### C QUESTION:How many ONE letter words are formed using the letters of the word WALK? options: A)1 B)16 C)7 D)4 E)2 SOLUTION:The number of letters in the given word is 4. The number of ONE letter words that can be formed using these four letters is 4P1=4*1=4 Answer:D #### D QUESTION:The ratio between the present ages of P and Q is 6:7. If Q is 4 years old than P, what will be the ratio of the ages of P and Q after 4 years options: A)A)3:4 B)of these C)C)4:3 D)inadequate E)B)3:5 SOLUTION:Let P's age and Q's age be 6x and 7x years respectively. Then, 7x - 6x = 4 => x = 4 Required ratio = (6x + 4) : (7x + 4) 28 : 32 = 7:8 ANSWER:B #### B QUESTION:Last year Sandy saved 10% of her annual salary. This year, she made 10% more money than last year, and she saved 15% of her salary. The amount saved this year was what percent of the amount she saved last year? options: A)142% B)150% C)165% D)176% E)188% SOLUTION:Let last year's salary be x. Last year, Sandy save 0.1x This year, Sandy saved 0.15*1.1x = 0.165x 0.165x / 0.1x = 1.65 = 165% The answer is C. #### C QUESTION:An aeroplane covers a certain distance at a speed of 100 kmph in 2 hours. To cover the same distance in 1 hours, it must travel at a speed of? options: A)100km/hr B)150km/hr C)200km/hr D)250km/hr E)300km/hr SOLUTION:Distance = 100*2 = 200 km Required speed = 200 *1 = 200km/hr Answer is C #### C QUESTION:During a behavioral experiment in a psychology class, each student is asked to compute his or her lucky number by raising 7 to the power of the student's favorite day of the week (numbered 1 through 7 for Monday through Sunday respectively), multiplying the result by 3, and adding this to the doubled age of the student in years, rounded to the nearest year. If a class consists of 28 students, what is the probability that the median lucky number in the class will be a non-integer? options: A)0% B)10% C)20% D)30% E)40% SOLUTION:Student's age is integral value. In question, we are multiplying student's age by 2 and adding some 3* 7^x something over there. It means Even (2* age of students) + Odd (3) * 7 ^x (where x is day of week). We know that 7^x is always odd. (e.g. 7, 49, 243, 1701, and repeat). => 3* odd is again odd. 2 * age of students is always even. So final equation is even +odd = odd. Avg of any number of odd digits or any number of even digits can never be non integral value. So 0% is the answer A. #### A QUESTION:In how many different ways can the letters of the word 'OPTICAL' be arranged so that the vowels always come together? options: A)610 B)720 C)825 D)920 E)650 SOLUTION:Explanation: The word 'OPTICAL' has 7 letters. It has the vowels 'O','I','A' in it and these 3 vowels should always come together. Hence these three vowels can be grouped and considered as a single letter. That is, PTCL(OIA). Hence we can assume total letters as 5 and all these letters are different. Number of ways to arrange these letters =5!=5×4×3×2×1=120=5!=5×4×3×2×1=120 All the 3 vowels (OIA) are different Number of ways to arrange these vowels among themselves =3!=3×2×1=6=3!=3×2×1=6 Hence, required number of ways =120×6=720 ANSWER IS B #### B QUESTION:1/3, 1/2, 1/4, 2 1/3, 3 1/2, 4 1/4, 4 1/3, 6 1/2, ? options: A)8 1/4 B)9 1/4 C)8 1/2 D)8 1/3 E)6 1/4 SOLUTION:there are 3 series--- 1/3,2 1/3,4 1/3. 1/2,3 1/2,6 1/2. 1/4,4 1/4,? ans 8 1/4 ANSWER:A #### A QUESTION:A shopkeeper sells 20% of his stock at 10% profit ans sells the remaining at a loss of 5%. He incurred an overall loss of Rs. 450. Find the total worth of the stock? options: A)20029 B)22500 C)20289 D)20027 E)20026 SOLUTION:Let the total worth of the stock be Rs. x. The SP of 20% of the stock = 1/5 * x * 1.1 = 11x/50 The SP of 80% of the stock = 4/5 * x * 0.95 = 19x/25 = 38x/50 Total SP = 11x/50 + 38x/50 = 49x/50 Overall loss = x - 49x/50 = x/50 x/50 = 450 => x = 22500 Answer: B #### B QUESTION:What is the sum of all the multiples of 10 between 0 and 75? options: A)500 B)620 C)450 D)340 E)280 SOLUTION:The multiples of 10 between 0 and 99 are 10, 20, 30, 40, 50, 60, 70. If these are all added together, the result is 280. Final Answer: E #### E QUESTION:131,95,70,54, ? options: A)42 B)45 C)44 D)40 E)39 SOLUTION:131 - 95 = 36 = 6^2 95 - 70 = 25 = 5^2 70 - 54 = 16 = 4^2 so we can write 54 - x = 09 = 3^2 , where x is the next number x = 54 - 9 = 45 so the next number will be 45 ANSWER:B #### B QUESTION:In 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? options: A)8200 B)7500 C)7000 D)8000 E)8400 SOLUTION:Equal number of candidates appeared in each state. In state A, 6% candidates got selected. In state B, 7% candidates got selected. Given that 80 more candidates got selected in state B than A. Therefore, 1% of candidates appeared in each state =80 Answer: Option D = 100% of candidates appeared in each state =80×100=8000 i.e., number of candidates appeared from each state = 8000 #### D QUESTION:The 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? options: A)27 B)30 C)31 D)33 E)34 SOLUTION:The total of seven numbers = 7X18 = 126 The total of first 3 and last 3 numbers is = 3 X 14+3 X 19 = 99 So, the middle number is (126 - 99 ) = 27 A #### A QUESTION:In the xy-coordinate system, line k passes through points (-8m, 0) and (0, 2m). Which of the following is a possible equation of line k? options: A)y = -4x + 2m B)y = 1/4*x - 8m C)y = 4x + 2m D)y = 1/4*x + 2m E)y = -1/4*x - 8m SOLUTION:The slope of the line is 2m/8m=1/4. The y-intercept is 2m. the equation of the line is: y = 1/4*x +2m The answer is D. #### D QUESTION:The smallest number which when diminished by 7, is divisible by 12, 16, 18, 21 and 28 is options: A)1008 B)1015 C)1022 D)1032 E)1043 SOLUTION:Required Number = (L.C.M of 12, 16, 18,21,28)+7 = 1008 + 7 = 1015 Answer: B #### B QUESTION:Express 50 mps in kmph? options: A)172 B)160 C)150 D)180 E)120 SOLUTION:25 * 18/5 = 180 kmph Answer:D #### D QUESTION:A 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? options: A)246 m B)240 m C)257 m D)577 m E)567 m SOLUTION:Speed = (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 #### B QUESTION:The probability that Alex will solve a problem is 1/5. What is the probability that he solves at least one problem out of 4 problems? options: A)64/125 B)256/625 C)64/625 D)369/625 E)359/625 SOLUTION:The probability that Alex will not solve a problem = 4/5. The probability that Alex will not solve 10 problems = (4/5)4 = 256/625. Hence, the probability that Alex will solve at least one problem = 1 - 256/625 = 369/625. ANSWER:D #### D QUESTION:Q=(429)^2 * 237 * (1243)^3 is thrice of ? options: A)33605 * 31960 * (1243)^2 B)33654 * 538219 * (1243)^2 C)33891 * 533247 * (1243)^2 D)34122 * 532004 * (1243)^2 E)34606 * 534572 * (1243)^2 SOLUTION:Q=(429)^2*237*(1243)^3 is an odd number. Among answer choices only C is an odd number, (so thrice C also will be an odd number). Answer: C. #### C QUESTION:The value of (34.31*0.473*1.5)/(0.0673*23.25*7.57) is close to options: A)2 B)1.15 C)2.01 D)2.06 E)2.35 SOLUTION:(34.31*0.473*1.5)/(0.0673*23.25*7.57) = 24.343/11.845 = 2.06 ANSWER:D #### D QUESTION:A 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? options: A)Rs:567 B)Rs:518 C)Rs:519 D)Rs:500 E)Rs:520 SOLUTION:P - 340 = (P*4*8)/100 P = 500 Answer:D #### D QUESTION:It 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: options: A)1:3 B)2:4 C)9:3 D)7:8 E)3:4 SOLUTION:Let the speed of the train be x km/hr and that of the car be y km/hr. Then, 120/x + 480/y= 8 1/x + 4/y = 1/15 ....(i) And, 200/x + 400/y = 25/3 1/x + 2/y = 1/24 ....(ii) Solving (i) and (ii), we get: x = 60 and y = 80. Ratio of speeds = 60 : 80 = 3 : 4. answer :E #### E QUESTION:The LCM and HCF of two numbers are 8 and 48 respectively. If one of them is 24, Find the other ? options: A)12 B)14 C)15 D)16 E)20 SOLUTION:HCF x LCM = Product of Numbers 8 x 48 = 24 x the other number other number = (8 x 48) / 24 other number = 16 ANSWER : D #### D QUESTION:In how many different ways can the letters of the word ‘INDIGO’ be arranged ? options: A)420 B)520 C)620 D)720 E)820 SOLUTION:D 720 Required number of arrangements = 6! = 720 #### D QUESTION:In a country where everyone wants a boy, each family continues having babies till they have a boy. After some time, what is the proportion of boys to girls in the country? (Assuming probability of having a boy or a girl is the same) options: A)1:2 B)3:5 C)1:1 D)3:7 E)2:4 SOLUTION:C 1:1 This is a very simple probability question in a software interview. This question might be a little old to be ever asked again but it is a good warm up. Assume there are C number of couples so there would be C boys. The number of girls can be calculated by the following method. Number of girls = 0*(Probability of 0 girls) + 1*(Probability of 1 girl) + 2*(Probability of 2 girls) + … Number of girls = 0*(C*1/2) + 1*(C*1/2*1/2) + 2*(C*1/2*1/2*1/2) + … Number of girls = 0 + C/4 + 2*C/8 + 3*C/16 + … Number of girls = C (using mathematical formulas; it becomes apparent if you just sum up the first 4-5 terms) The proportion of boys to girls is 1 : 1. #### C <<<Examples ends QUESTION:How many numbers between 100 and 600 are divisible by 2, 3, and 7 together? options: A)112 B)77 C)267 D)12 E)99 SOLUTION:Explanation: As the division is by 2, 3, 7 together, the numbers are to be divisible by: 2*3*7 = 42 The limits are 100 and 600 The first number divisible is 42*3 = 126 To find out the last number divisible by 42 within 600: 600/42 = 14.28 Hence, 42*14 = 588 is the last number divisible by 42 within 600 Hence, total numbers divisible by 2, 3, 7 together are (14 – 2) = 12 ANSWER: D #### D

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:Twenty four men can do a work in 32 days. How many men are required to complete the work in 12 days? options: A)32 B)10 C)64 D)40 E)60 SOLUTION:C 64 We have M1 D1 = M2 D2 So, 24 * 32 = M2 * 12 => M2 = 64. Answer is C #### C QUESTION:A 250 m long train is running at a speed of 55 Km/hr. It crossed a platform of length 520 m in ? options: A)40.4 sec B)40.5 sec C)50.4 sec D)50.5 sec E)60.4 SOLUTION:Speed = 55 Km/hr (to convert km/hr in to M/s) = 55 x 5/18 M/s Distance = 250 m + 520 m ( If questions is about train crossing a post you need to consider only the length of Train, ) = 770 m Time = Distance / Speed = 770 x 18 / (5 x 55) = 50.4 sec correct Answer: option a #### A QUESTION:An aptitude test contains 4 questions from verbal reasoning, 5 questions from simple mathematics and 6 questions testing knowledge of English. Three questions are selected at random from the list of questions. The probability that all of them are from simple mathematics section, is: options: A)2/91 B)1/22 C)3/22 D)2/77 E)None of these SOLUTION:Explanation : Let S be the sample space. Then, n(S) = number of ways of selecting 3 questions out of 15= 15C3= (15 x 14 x 13)/(3 x 2 x 1)= 455 Let E = event of getting all the 3 questions from simple mathematics section. n(E) = 5C3 = 5C2 = (5 x 4)/(2 x 1) = 10 P(E) = n(E)/n(S) = 10/455 = 2/91 . Answer : A #### A QUESTION:A man divides $8600 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? options: A)A)$200 B)B)$1000 C)C)$800 D)D)$1011.76 E)E)$400 SOLUTION:Let the share of each nephews be $X. Then, share of each daughter=$4X, share of each son= $5X. So, 4*4X+4*4X+2*X=8600 16X+16X+2X=8600 34X=8600, X=252.94. Daughter receives four times of nephew so 4 * 252.94 = 1011.76. So Each Daughter receives $800. answer is option D) $1011.76. #### D QUESTION:Each digit 1 through 5 is used exactly once to create a 5-digit integer. If the 3 and the 4 cannot be adjacent digits in the integer, how many 5-digit integers are possible? options: A)48 B)66 C)72 D)78 E)90 SOLUTION:Total number of 5 digit numbers that can be formed = 5! = 120. Total number of 5 digit numbers in which 3 and 4 are adjacent = 48. This can be calculated by taking 3 and 4 as a pair and considering positions where they can appear. Number of 5 digit numbers in which 3 and 4 are not adjacent = Total number of 5 digit numbers - Total number of 5 digit numbers in which 3 and 4 are adjacent. Ans = 120 - 48 = 72 C #### C QUESTION:A tradesman by means of his false balance defrauds to the extent of 10%? in buying goods as well as by selling the goods. What percent does he gain on his outlay? options: A)29% B)17% C)44% D)46% E)21% SOLUTION:g% = 10 + 10 + (10*10)/100 = 21% Answer: E #### E QUESTION:A person starts walking at a speed of 5km/hr through half the distance, rest of the distance he covers with aspeed 4km/hr. Total time of travel is 36 hours. What is the maximum distance he can cover? options: A)20km B)40km C)60km D)80km E)160km SOLUTION:t=d/s, so 36=x/2*1/5+x/2*1/4(because half distance with 5 km/ph, and remaining half with 4km/hr) 36=x(18/80) x=160km ANSWER:E #### E QUESTION:Excluding stoppages, the speed of a bus is 64 kmph and including stoppages, it is 50 kmph. For how many minutes does the bus stop per hour? options: A)15.5 B)12.3 C)10.5 D)10.12 E)13.12 SOLUTION:Due to stoppages, it covers 14 km less. Time taken to cover 14 km = ((14/64)×60) = 13.12 min. Option(E) is correct #### E QUESTION:A no. when divided by the sum of 555 and 445 gives 2times their difference as quotient & 30 as remainder. Find the no. is? options: A)122443 B)154546 C)165454 D)186545 E)220030 SOLUTION:(555 + 445) * 2 * 110 + 30 = 220000 + 30 = 220030 E #### E QUESTION:What is the sum of the first 22 natural numbers (starting from 1)? options: A)223 B)233 C)243 D)253 E)263 SOLUTION:The sum of n natural numbers = n*(n+1) / 2 = 22*23/2 = 253 The answer is D. #### D QUESTION:A 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? options: A)600,400 B)500,500 C)300,700 D)800,1200 E)550,1450 SOLUTION:Ratio of their works A:B = 6:4 Ratio of their wages A:B = 2:3 A's share = (2/5)2000 = 800 B's share = (3/5)2000 = 1200 correct option is D #### D QUESTION:3,10,29,66,__ options: A)125 B)165 C)145 D)127 E)112 SOLUTION:3=1*1*1+2 10=2*2*2+2 29=3*3*3+2 66=4*4*4+2 Similarly 5*5*5+2=127 ANSWER:D #### D QUESTION:If a cloth merchant sells ‘a’ metres of cloth for Rs.x, then what is the selling price of ‘b’ metres of cloth? options: A)Rs.(b*x) B)Rs.{(b*x)/a} C)Rs.{(a*b)/x} D)None of these E)Cannot be determined SOLUTION:Explanation: Cost of ‘a’ metres of cloth = Rs.x. Therefore, each metre of cloth costs Rs. (x/a). The cost of ‘b’ metres of cloth = Rs. b*(x/a) = Rs. {(b*x)/a} ANSWER B #### B QUESTION:In boring a well 50 m deep, the cost is Rs.4/– for the first meter. The cost of each successive meter increases by Rs.2/–. What is the cost of boring the entire well? options: A)1650 B)2650 C)3650 D)4650 E)2850 SOLUTION:For successive meters the cost of boring will be 4, 6, 8, 10, ......., which forms an arithmetic series with terms n=50, first term a=4 & difference d=2 So Sum=(n/2)[2a+(n-1)d]= Total cost of boring =(50/2)[2*4+(50-1)*2]=25(8+98) = 2650 ANSWER:B #### B QUESTION:The tax on a commodity is diminished by 20% and its consumption increased by 15%. The effect on revenue is? options: A)7% decrease B)8% decrease C)9% decrease D)6% decrease E)4% decrease SOLUTION:100 * 100 = 10000 80 * 115 = 9200 ----------- 10000-----------800 100-----------? => 8% decrease Answer: B #### B QUESTION:A beauty pageant is being held with 50 competitors (one from each state in the USA). Each competitor has an equal chance of winning the competition. Four competitors will be chosen, and each will win either 1st, 2nd, 3rd, or 4th place. What is the probability California, Florida, and Hawaii will win three of the four places? options: A)3/100 B)3/5 C)1/100 D)1/4,900 E)1/5 SOLUTION:Combination Formula: nCr = n!/(r!(n - r)!), where n is the population/set, and r is the sample/subset. Total number possible = 50C4 - 50!/(4!(50 - 4)!) = 230,300 Number CA possible = 1C1 = 1 Number FL possible = 1C1 = 1 Number HI possible = 1C1 = 1 Number other possible = 47C1 = 47 Probability Formula: P(A) = (Number Favorable Outcomes)/(Total Number Possible Outcomes) P(CA, FL, HI) = (1C1)(1C1)(1C1)(47C1)/50C4 = 47/230,300 = 1/4,900 Answer: D #### D QUESTION:If a number is formed by writing integers 1 to 150 one after another, like 12345...150. How many digits does this integer consists of? options: A)150 B)339 C)342 integers D)359 E)362 SOLUTION:1-digit integers Number of 1-digit integers (1 to 9) = 9 - 1 + 1 = 9 Number of digits used = (9)(1) = 9 2-digit integers Number of 2-digit integers (10 to 99) = 99 - 10 + 1 = 90 Number of digits used = (90)(2) = 180 3-digit integers Number of 3-digit integers (100 to 150) = 150 - 100 + 1 = 51 Number of digits used = (51)(3) = 153 TOTAL # of digits uses = 9 + 180 + 153 = 342 Answer: C #### C QUESTION:Two 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? options: A)54 B)77 C)36 D)88 E)21 SOLUTION:Let the speed of each train be x m/sec. Then, relative speed of the two trains = 2x m/sec. So, 2x = (120 + 120)/8 => x = 15 Speed of each train = 15 m/sec. = 15 * 18/5 =- 54 km/hr.Answer: A #### A QUESTION:One 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? options: A)187 min B)177 min C)144 min D)189 min E)166 min SOLUTION:Let the slower pipe alone fill the tank in x min. Then, faster pipe will fill it in x/3 min. 1/x + 3/x = 1/36 4/x = 1/36 => x = 144 min. Answer:C #### C QUESTION:The ratio between v and y is 7/9; v and y are increased by 4, what is the ratio between the new values of v and y? options: A)7/9 B)14/9 C)7/18 D)11/13 E)It Cannot Be Determined SOLUTION:Ratio = 7k/9k = 7/9, 14/18, etc. v and y are increased by 4 --> (7k + 4)/(9k + 4) New ratio can be 11/13, 18/22, etc. Answer: E #### E QUESTION:Two 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 19 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? options: A)565 B)444 C)676 D)420 E)663 SOLUTION:1h ----- 3 ? ------ 60 12 h RS = 16 + 19 = 35 T = 12 D = 35 * 12 =420 Answer: D #### D QUESTION:A two-digit number is such that the product of the digits is 8. When 18 is added to the number, then the digits are reversed. The number is: options: A)22 B)73 C)99 D)42 E)11 SOLUTION:Explanation: Just go in reverse order. Check the options with th subtracting 18 from each option for getting reverse number. 42 – 18 = 24 (which is in reverse). So answer is 42. Answer D #### D QUESTION:A dealer purchases 15 articles for Rs. 25 and sells 12 articles for Rs. 35. Find the profit percentage? options: A)80% B)50% C)75% D)40% E)53% SOLUTION:L.C.M of 15 and 12 = 60 CP of 60 articles = Rs. 100 (25 * 4) SP of 60 articles = Rs. 175 (35 * 5) Profit percentage = (175 - 100)/100 * 100 = 75% Answer: C #### C QUESTION:If a particular player is always chosen, in how many ways can a cricket-be chosen out of 15 players? options: A)1236 B)1345 C)1358 D)1321 E)1365 SOLUTION:A particular player is always chosen, it means that 10 players are selected out of the remaining 14 players. =. Required number of ways = 14C10 = 14C4 = 14!/4!x19! = 1365 E #### E QUESTION:What is the area of a square field whose diagonal of length 12 m? options: A)288 B)72 C)200 D)112 E)178 SOLUTION:d2/2 = (12 * 12)/2 = 72 Answer: B #### B QUESTION:A 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 A. The store sold the first 150 copies in the first week at 80% more than A, and then over the next month, sold a 100 more at 20% more than A. Finally, to clear shelf space, the store sold the remaining copies to a bargain retailer at 40% less than A. What was the bookstore’s net percent profit or loss on the entire lot of 400 books? options: A) 30% loss B) 10% loss C) 10% profit D) 20% profit E) 60% profit SOLUTION:[[A(150)(1.8)+A(100)(1.2)+A(150)(0.6)]/400A] - 1 [50[(3)(1.8) + (2)(1.2) + (3)(0.6)] / (50)(8)] - 1 [(5.4 + 2.4 + 1.8)/8] - [8/8] +1.6/8 +20% answer is D #### D QUESTION:A pair of articles was bought for $50 at a discount of 50%. What must be the marked price of each of the article? options: A)$25 B)$12.50 C)$29.65 D)$35.95 E)$45.62 SOLUTION:S.P. of each of the article = 50/2 = $25 Let M.P = $x 50% of x = 25 x = 25*.5 =$12.50 Answer is B #### B QUESTION:If Mel saved more than $10 by purchasing a sweater at a 15 percent discount, what is the smallest amount the original price of the sweater could be, to the nearest dollar? options: A)45 B)67 C)75 D)83 E)150 SOLUTION:We are told that 15 percent discount from the original price is more than $10: 0.15*{price} > 10; {price} > 1,000/15; {price} > 66 2/3. Answer: B. #### B QUESTION:A number lock on a suitcase has 3 wheels each labelled with 10 digits from 0 to 9. If opening of the lock is a particular sequence of three digits with no repeats, how many such sequences will be possible? options: A)720 B)760 C)680 D)780 E)880 SOLUTION:On first wheel there can be 10 digits. On the second wheel there will be one of the 9 digits and on the third wheel there will be 8 digits. Therefore, the number of numbers is 10 x 9 x 8 = 720 ANSWER:A #### A QUESTION:A certain culture of bacteria quadruples every hour. If a container with these bacteria was half full at 8:00 a.m., at what time was it one-eighth full? options: A)9:00 a.m. B)7:00 a.m. C)6:00 a.m. D)4:00 a.m. E)2:00 a.m. SOLUTION:To go from one-eighth (1/8) full to half (1/2) full culture of bacteria should quadruple: 1/8*4=1/2, as it quadruples every hour then container was one-eighth full at 8:00 a.m -1 hour = 7:00 a.m. Answer: B. #### B QUESTION:An electric pump can fill a tank in 5 hours. Because of a leak in the tank, it took 10hours to fill the tank. If the tank is full, how much time will the leak take to empty it? options: A)10hours B)12hours C)8hours D)5hours E)15hours SOLUTION:Work done by the leak in 1 hour = 1/5 - 1/10 = 1/10 The leak will empty the tank in 10hours Answer is A #### A QUESTION:The H.C.F of two numbers is 23 and the other two factors of their L.C.M are 15 and 16. The larger of the two numbers is: options: A)338 B)278 C)322 D)368 E)121 SOLUTION:Clearly, the numbers are (23 * 15) and (23 * 16). Larger number = (23 * 16) = 368. Answer: D #### D QUESTION:7+2=56 6+3=48 5+5=45 2+1=4 4+9=?? Solve it? options: A)92 B)48 C)42 D)38 E)72 SOLUTION:x+y=x[y+(x-1)]=x^2+xy-x 7+2=7[2+(7-1)]=49+14-7=56 6+3=6[3+(6-1)]=36+18-6=48 5+5=5[5+(5-1)]=25+25-5=45 2+1=2[1+(2-1)]=4+2-2=4 4+9=4[9+(4-1)]=16+36-4=48 Answer :B #### B QUESTION:A tour group of 25 people paid a total of $630 for entrance to a museum. If this price included a 10% sales tax, and all the tickets cost the same amount, what was the face value of each ticket price without the sales tax? Choices options: A)$22.68 B)$23.94 C)$24 D)$25.20 E)$30 SOLUTION:A. #### A QUESTION:A man travels 100km by train at 60km/hr, 200km by ship at 20km/hr, 300km by aeroplane at 100km/hr and 100km by car at 50km/hr. What is the average speed for the entire distance? options: A)35.3km/hr B)42km/hr C)48.9km/hr D)52.6km/hr E)27.6km/hr SOLUTION:Total distance traveled = 100+200+300+100 = 700km Total time taken = 100/60 + 200/20 + 300/100 + 100/50 = 16.67 hrs Average speed = 700/16.67 = 42km/hr approximately ; Answer is B #### B QUESTION:In what ratio should a mixture of milk and water in the ratio of 3:4 be mixed with another mixture of milk and water in the ratio 5:2 so that the resultant mixture contains equal quantities of milk and water? options: A)3:1 B)3:5 C)7:8 D)7:9 E)9:11 SOLUTION:First mixture: milk and water in the ratio of 3x:4x. Second mixture: milk and water in the ratio 5y:2y. We want their mixture to have equal quantities of milk and water: 3x + 5y = 4x + 2y --> x/y = 3. Answer: A. #### A QUESTION:A and B can do a piece of work in 3 days, B and C in 4 days, C and A in 6 days. How long will C take to do it? options: A)23 days B)16 days C)11 days D)24 days E)35 days SOLUTION:D 24 days 2c = ¼ + 1/6 – 1/3 = 1/12 c = 1/24 => 24 days #### D QUESTION:The wages earned by Robin is 50% 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? options: A)18.75% B)23% C)30% D)50% E)7% SOLUTION:Let wage of Erica = 10 Wage of Robin = 1.5*10 = 15 Wage of Charles = 1.6 *10 = 16 Percentage by which wage earned by Charles is more than that earned by Robin = (16-15)/15 * 100% = 1/15 * 100% =7% Answer E #### E QUESTION:The cost price of a radio is Rs.1500 and it was sold for Rs.1230, find the loss %? options: A)18% B)12% C)22% D)24% E)21 SOLUTION:1500 ---- 270 100 ---- ? => 18% Answer:A #### A QUESTION:When 30 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? options: A)3 : 4 B)4 : 3 C)3 : 2 D)Data inadequate E)None of these SOLUTION:Let the first and the second numbers be x and y respect then y + 30% of x = 140% of y or, y + 0.3x = 1.4y or, 0.3x = 0.4y ∴ x : y = 0.4 : 0.3 = 4 : 3 Answer B #### B QUESTION:Three 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 twice, no apples were left.How many apples were there? options: A)62 B)63 C)64 D)65 E)66 SOLUTION:Whenever 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 6 times. So answer is (2^6)-1=63. ANSWER:B #### B QUESTION:By investing in 1623% stock at 64, one earns Rs. 1600. The investment made is options: A)s. 9600 B)s. 7500 C)s. 5640 D)s. 6144 E)s. 6760 SOLUTION:Explanation : Market Value = Rs.64 Face Value is not given and hence take it as Rs.100 16 2/3% of the face value = 50/3 ie, to earn 50/3, investment = Rs.64 Hence, to earn Rs.1600, investment needed = 64×3×1600/50=6144 Answer : Option D #### D QUESTION:The average weight of 19 students is 15kg. by the admission of a new student the average weight is reduced to 14.9 kg. the weight of the new student is ? options: A)10.6 kg B)10.8 kg C)11 kg D)13 kg E)None SOLUTION:Answer Weight of new student = Total weight of all 20 students - Total weight of initial 19 students = (20 x 14.9 - 19 x 15) kg = 13 kg. Correct Option: D #### D QUESTION:What is the cost of leveling the field in the form of parallelogram at the rate of Rs.50/10 sq.metre, whose base & perpendicular distance from the other side being 54m & 24m respectively? options: A)Rs. 6000 B)Rs. 6300 C)Rs. 6400 D)Rs. 6480 E)Rs. 7000 SOLUTION:Area of the parallelogram = Length of the base * Perpendicular height = 54 * 24 = 1296 m. Total cost of levelling = Rs. 6480 D #### D QUESTION:A man can row upstream at 29km/hr and down stream at 15km/hr find mans rate of the current ? options: A)9.8km/hr B)3.6km/hr C)8.9km/hr D)7km/hr E)5.9km/hr SOLUTION:given upstream(u) =29km/hr down stream (v)= 15km/hr rate of the current =1/2(u-v) =1/2(29-15)=7km/hr Answer is (D) #### D QUESTION:A company has two types of machines, type R and type S. Operating at a constant rate a machine of R does a certain job in 36 hours and a machine of type S does the job in 36 hours. If the company used the same number of each type of machine to do job in 12 hours,how many machine R were used? options: A)3 B)4 C)6 D)9 E)12 SOLUTION:yes there is a typo in the question, I got the same ques on my GMAT PREP last week, and the questions goes as: A company has two types of machines,type R and type S.Operating at a constant rate a machine of R does a certain job in 36 hours and a machine of type S does the job in 36 hours .If the company used the same number of each type of machine to do job in2 hours,how many machine R were used? So for a job to be done in 2 hours R = 1/2 R_a(Rate of Machine R) = 1/36 R_s(Rate of Machine S) = 1/36 Lets say x machines are used to attain the desired rate, thus x/36+x/36 = 1/2 (Desired R =1/2 i.e. to complete the job in 2 hours) (x+x)/36 = 1/2 2x/36 = 1/2 x = 9. QA = 9 (ANSWER D) #### D QUESTION:Two trains of equal lengths take 9 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? options: A)10 B)11.3 C)13 D)14 E)15 SOLUTION:Speed of the first train = 120/9 = 13.3 m/sec. Speed of the second train = 120/15 = 8 m/sec. Relative speed = 13.3 + 8 = 21.3 m/sec. Required time = (120 + 120)/21.3 = 11.3 sec. Answer: Option B #### B QUESTION:14 times a number gives 210. The number is options: A)11 B)12 C)15 D)None E)Cannot be determined SOLUTION:Explanation: Let the number be 'N' 14×N=210⇒N=15 Correct Option: C #### C QUESTION:An 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.3600, what will be the difference between Q and R's share? options: A)2788 B)4500 C)7282 D)2782 E)2729 SOLUTION:4 --- 3600 5 --- ? => 4500 Answer:B #### B QUESTION:A 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, the how old is B? options: A)7 years. B)8 years. C)9 years. D)10 years. E)11 years. SOLUTION:EXPLANATION Let C’s age be x years. Then, B’s age = 2x years. A’s age = (2x + 2) years. (2x + 2) + 2x + x = 27 5x = 25 x = 5. Hence, B’s age = 2x = 10 years. Answer D #### D QUESTION:A university needs to select an eight-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 5 students hold membership in both organizations, how many different committee are possible? options: A)215 B)275 C)325 D)385 E)495 SOLUTION:student government + the student advisory board consists of 9 + 8 = 17 members. 5 students hold membership in both, so they were counted twice. The total number of people to choose from is 17 - 5 = 12 The number of ways to choose 8 members from 12 is 12C8 = 495 The answer is E. #### E QUESTION:A tyre has two punctures. The first puncture alone would have made the tyre flat in 9 minutes and the second alone would have done it in 6 minutes. If air leaks out at a constant rate, how long does it take both the punctures together to make it flat ? options: A)315min B)325min C)335min D)345min E)None of these SOLUTION:Explanation: Do not be confused, Take this question same as that of work done question's. Like work done by 1st puncture in 1 minute and by second in 1 minute. Lets Solve it: 1 minute work done by both the punctures = (19+16)=(518) So both punctures will make the type flat in (185)mins=335mins Answer: C #### C QUESTION:A train 300 m long is running at a speed of 99 km/hr. In what time will it pass a bridge 195 m long? options: A)17 B)18 C)19 D)20 E)21 SOLUTION:Speed = 99 * 5/18 = 55/2 m/sec Total distance covered = 300 + 195 = 495 m Required time = 495 * 2/55 = 18 sec Answer: B #### B QUESTION:The 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? options: A)Rs.4538 B)Rs.4518 C)Rs.4518 D)Rs.4530 E)Rs.4517 SOLUTION:Area of the four walls = 2h(l + b) Since there are doors and windows, area of the walls = 2 * 12 (15 + 25) - (6 * 3) - 3(4 * 3) = 906 sq.ft. Total cost = 906 * 5 = Rs.4530 Answer: D #### D QUESTION:A river 7m deep and 75 m wide is flowing at the rate of 4 kmph the amount of water that runs into the sea per minute is? options: A)54996.5 B)32296.5 C)34996.5 D)34996.5 E)31255.5 SOLUTION:Rate of water flow-4kmph--4000/60--66.66 m/min depth of river--7m width of river--75m vol of water per min--66.66 *7*75---34996.5 Answer C #### C QUESTION:Two 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 90 kmph. After how much time will the trains meet? options: A)20/8 sec B)20/4 sec C)5/2 sec D)22/7 sec E)60/7 sec SOLUTION:They are moving in opposite directions, relative speed is equal to the sum of their speeds. Relative speed = (54 + 90)*5/18 = 8*5 = 40 mps. The time required = d/s = 100/40 = 5/2 sec.Answer:C #### C QUESTION:There are 14 people in a room. If each person shakes hands with exactly 3 other people, what is the total number of handshakes? options: A)18 B)21 C)35 D)42 E)56 SOLUTION:Note that each handshake includes two people. The total number of handshakes is 14*3/2 = 21 The answer is B. #### B QUESTION:A corporation ten times its annual bonus to 25 of its employees. What percent of the employees’ new bonus is the increase? options: A)25% B)44% C)38% D)9% E)90% SOLUTION:Let the annual bonus be X. A corporation triples its annual bonus. So new bonus = 10X. Increase = 10X-X =9X The increase is what percent of the employees’ new bonus = (9X/10X)*100 = 90% Hence E. #### E QUESTION:If the simple interest on a sum of money for 2 years at 5% per annum is Rs. 52, what is the compound interest on the same sum at the rate and for the same time? options: A)s. 53.30 B)s. 53.22 C)s. 51.219 D)s. 53.18 E)s. 51.10 SOLUTION:Explanation: Sum = (52 * 100) / (2 * 5) = Rs. 520 Amount = [520 * (1 + 5/100)2] = Rs. 573.3 C.I. = (573.3 - 520) = Rs. 53.30. Answer:A #### A QUESTION:Machine W can produce x units in 3/4 of the time it takes machine N to produce x units. Machine N can produce x units in 2/3 the time it takes machine O to produce x units. If all three machines are working simultaneously, what fraction of the total output is produced by machine N? options: A) 1/2 B) 1/3 C) 4/13 D) 8/29 E) 6/33 SOLUTION:Let the following be true: W makes x in time t Then the following follows: N makes x in 4t/3 O makes x in 3/2(4t/3) = 2t M:N:O = 1:4/3:2=3:4:6 So N=4/(3+4+6)=4/13=C #### C QUESTION:The true discount on a bill of Rs.8640 is Rs.1440.The banker's discount is options: A)1428 B)1528 C)1628 D)1728 E)None of these SOLUTION:Solution P.W = Rs.(8640 - 1440) = Rs. 720 S.I on Rs. 8640 =Rs.(1440/7200 x 8640) = Rs. 1728. Answer D #### D QUESTION:If S = {50, 72, 108, 120, 205}, how much less is the mean of the numbers in S than the median of the numbers in S? options: A)2 B)3 C)5 D)8 E)9 SOLUTION:Mean = (50 + 72 + 108 + 120 + 205)/5 = 111 Median = 108 Difference = 111-108 = 3 Option B #### B QUESTION:Average of first five multiples of 2 is options: A)9 B)6 C)13 D)15 E)16 SOLUTION:Explanation: Average=2(1+2+3+4+5)5=6 Answer: Option B #### B QUESTION:The 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? options: A)8 B)2 C)9 D)4 E)6 SOLUTION:Explanation: [15000 * (1 + R/100)2 - 15000] - (15000 * R * 2)/100 = 96 15000[(1 + R/100)2 - 1 - 2R/100] = 96 15000[(100 + R)2 - 10000 - 200R]/10000 = 96 R2 = (96 * 2)/3 = 64 => R = 8 Rate = 8% Answer: Option A #### A <<<Examples ends QUESTION:$378 is divided among A, B, and C so that A receives half as much as B, and B receives half as much as C. How much money is C's share? options: A)$200 B)$208 C)$216 D)$224 E)$232 SOLUTION:Let the shares for A, B, and C be x, 2x, and 4x respectively. 7x = 378 x = 54 4x = 216 The answer is C. #### C

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:How many even integers n, such that 20<=n<=200 are of the form 3k+4, where k is any natural number? options: A)26 B)30 C)34 D)38 E)42 SOLUTION:The first number is 22 = 16+6(1). We can continue adding 6 to make a list: 22, 28, 34,... The last number is 196 = 16+6(30) There are 30 numbers in the list. The answer is B. #### B QUESTION:If the selling price of 5 books is same as the cost price of 10 books. Find the gain or loss percentage? options: A)50% B)100% C)45% D)55% E)65% SOLUTION:Let the C.P of each book be Re 1. Then, S.P of 5 books= C.P of 10 books= Rs. 10 Now, C.P of 5 books= Rs.5, S.p of 5 books= Rs 10 Gain = Rs ( 10 -5 ) = Rs 5. Gain% = ( 5/5× 100 ) % = 100% Answer : B #### B QUESTION:The product of n^2 consecutive positive integers is always divisible by options: A)n^2 -1 B)(n+1)! C)2n +1 D)n^2 + 1 E)n! SOLUTION:Plug in some vlues and check - Product of first 2 number is 2*1 Product of first 3 number is 3*2*1 Product of first 4 number is 4*3*2*1 Product of first 5 number is 5*4*3*2*1 So, The product of first n natural numbers is always divisible by n! , answer will be (A) #### A QUESTION:In a tree, 3/7 of the birds are parrots while the rest are toucans. If 2/3 of the parrots are female and 7/10 of the toucans are female, what fraction of the birds in the tree are male? options: A)3/7 B)11/35 C)16/35 D)31/70 E)37/70 SOLUTION:Let x be the number of birds in the tree. The fraction of birds that are male parrots is (1/3)(3/7)=1/7. The fraction of birds that are male toucans is (3/10)(4/7)=6/35. The total fraction of male birds is 1/7 + 6/35 = 11/35. The answer is B. #### B QUESTION:Let S be the set of permutations of the sequence 2, 3, 4, 5, 6 for which the first term is not 2. A permutation is chosen randomly from S. The probability that the second term is 5 is given by a/b (in lowest terms). What is a+b? options: A)5 B)6 C)11 D)16 E)19 SOLUTION:The number of possible permutation without 2 in the first digit is 4X4X3X2X1=96 ways. The number of possible permutations with 5 in the second term is= 3X3X2X1=18 ways. 18c1/96c1 = 18/96= 3/16= > a+b=19. ANSWER:E #### E QUESTION:When 732 is subtracted form the square of a number, the answer that is obtained is 5280. What is the number? options: A)228 B)103 C)286 D)122 E)102 SOLUTION:Explanation: Let the number be x x2 - 732 = 5280 x2 = 5280 + (70+3)2 = 5280 + 4900 + 420 + 9 = 10609 = 10000 + 2(100)(3) + 32 = (100 + 3)2 x = 100 + 3 = 103. Answer: B #### B QUESTION:How many points (x, y) lie on the line segment between (22, 12 2/3) and (16, 17 2/3) such that x and y are both integers? options: A)1 B)5 C)7 D)8 E)9 SOLUTION:slope = (17 2/3 - 12 2/3) / (16 - 22) = -5/6 y = mx + b => 12 2/3 = -22*5/6 + b => b = 31 y = -5x/6 + 31 Only integer values work, and the only multiples of 6 between 16 and 22 for x values is 18, thus 1 point. A #### A QUESTION:How many seconds will a 500 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? options: A)25 B)30 C)40 D)45 E)35 SOLUTION:Speed of the train relative to man = (63 - 3) km/hr = 60 km/hr =(60 x(5/18)) m/sec =50/3 m/sec. Therefore Time taken to pass the man =(500 x(3/50))sec = 30 sec. Answer :B #### B QUESTION:If john makes a contribution to a charity fund at school, the average contribution size will increase by 50% reaching $75 per person. If there were 6 other contributions made before john's, what is the size of his donation? options: A)$225 B)$150 C)$200 D)$250 E)$450 SOLUTION:Cavg = average contribution before John Cavg*1.5 = 75, therefore the average cont is $50 before John. If he needs to increase the average contribution by $25, he must put in $25 for each of the 6 people. so $150. But, he also has to put in the average for himself (the seventh person), so add $75. So $225 is your answer. Answer A #### A QUESTION:In traveling from a dormitory to a certain city, a student went 1/5 of the way by foot, 2/3 of the way by bus, and the remaining 14 kilometers by car. What is the distance, in kilometers, from the dormitory to the city? options: A)30 B)45 C)60 D)90 E)105 SOLUTION:Whole trip = distance by foot + distance by bus + distance by car x = 1/5x + 2/3x + 14 x - 13/15x = 14 2/15x = 14 => so x = (15/2)*14 = 105Km Answer E #### E QUESTION:The 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? options: A)1/64 B)1/9 C)1/16 D)1/25 E)1/2 SOLUTION:There are two cases. All boys and all girls case 1. all boys. 1/2*1/2*1/2*1/2*1/2*1/2*1/2= 1/128 case 2 .all girls. 1/2*1/2*1/2*1/2*1/2*1/2*1/2=1/128 We will add the cases to get 1/64 #### A QUESTION:How many different positive integers exist between 10^3 and 10^4, the sum of whose digits is equal to 2? options: A)6 B)7 C)5 D)4 E)18 SOLUTION:So, the numbers should be from 1,000 to 10,000 The following two cases are possible for the sum of the digits to be 2: 1. Two 1's and the rest are 0's: 1,001 1,010 1,100 3 numbers. 2. One 2 and the rest are 0's: 2,000 1 number. Total = 4 numbers. Answer:D #### D QUESTION:In how many ways can the letters of the word REGULATION be arranged such that all the vowels always appear together? options: A)10!*5! B)10!*6! C)10! D)6!*5! E)5!*5! SOLUTION:The 10 letters can be grouped into 5 consonants and one set of 5 vowels. The number of ways to arrange 6 units is 6! Then, for each arrangement, the 5 vowels can be arranged in 5! ways. The total number of arrangements is 6!*5! The answer is D. #### D QUESTION:Sum of 3 consecutive even no.'s is 34 more than the 1st no. of the series. Find the middle no.? options: A)8 B)12 C)14 D)16 E)18 SOLUTION:Let the numbers be x, x+2 and x+4 then x + x+2 + x+4 = x+34 3x + 6 = x + 34 2x = 28 \inline \therefore x = 14 \inline \therefore Middle number = x + 2 = 14+2 = 16 D #### D QUESTION:A work which could be finished in 12 days was finished 3 days earlier after 10 more men joined. The number of men employed was? options: A)22 B)20 C)88 D)71 E)10 SOLUTION:x ------- 12 (x + 10) ---- 6 x * 12 = (x + 10)6 x = 10 \Answer: E #### E QUESTION:In climbing a round pole of 80 meters height, a monkey climbs 5 meters in a minute and slips 2 meters in the alternate minute. To get to the top of the pole, the monkey would take : options: A)51 minutes B)54 minutes C)58 minutes D)61 minutes E)63 minutes SOLUTION:a monkey climbs 5 meters in one min & slips 2m in other min. therefore the monkey reach 3meters in 2min 3m=2min 25*3m=25*2min - >75m=50min hence the remaining 5m jumps the monkey in 1min to reach original height so 51 min ANSWER:A #### A QUESTION:Howmany three digits odd numbers can be formed using the digits 4,5,6,7,8,9 (repetition of digits not allowed) options: A)60 B)75 C)65 D)55 E)45 SOLUTION:There are 3 ways of filling the unit place of the number. The remaining ten's and 100's place canbe filled in 5ways and 4 ways respectively. Required number of numbers =3x5x4=60. Ans: A #### A QUESTION:Danny 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 192, what is the area of the side face of the box? options: A)13 B)16 C)18 D)29 E)32 SOLUTION:Lets suppose length= l, breadth= b, depth= d Front face area= l*w = 1/2 w*d (l=1/2 d or d=2l) top face area= w*d side face area= w*d = 1.5 d*l (w=1.5l) Volume = l*w*d= 192 l*1.5l*2l= 192 l=4 Side face area= l*d= l*2l= 4*2*4 =32 E is the answer #### E QUESTION:In a college, the ratio of the number of boys to girls is 8 : 5. If there are 300 girls, the total number of students in the college is options: A)420 B)520 C)620 D)780 E)820 SOLUTION:Explanation: Let the boy are 8x and Girls are 5x => 5x = 300 => x = 60 Total students = 8x+5x = 13x = 13(60) = 780 Option D #### D QUESTION:The average height of 35 boys in a class was calculated as 185cm. 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).? options: A)178.27 cm B)183.29 cm C)978.29 cm D)178.89 cm E)176.29 cm SOLUTION:Calculated average height of 35 boys = 185 cm. Wrong total height of 35 boys = 185 * 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 = 185 cm - (166 cm - 106 cm)/35 =185 cm - 60 /35 cm = 185 cm - 1.71 cm = 183.29 cm. Answer: B #### B QUESTION:What percent of 7.2 kg is 18 gms ? options: A)25 B)66 C)288 D)19 E)17 SOLUTION:Explanation: Required percentage = (18/7200 * 100)% = 1/4% = 0.25% Answer: A) .25% #### A QUESTION:In a college 1/5th of the girls and 1/8th of the boys took part in a social camp. What of the total number of student in the college took part in the camp ? options: A)13/40 B)13/80 C)2/13 D)Data inadequate E)None SOLUTION:Answer Out of the 5 girls, 1 took part in the camp. Out of the 8 boys, 1 took part in the camp. ∴ 2/13 of total number of students took part in the camp. Correct Option: C #### C QUESTION:On final examination a student's average (arithmetic mean) score on 4 subjects is 90. What must be his score on a 5th subject for his average score on the 5 subjects to be 92? options: A)60 B)70 C)80 D)90 E)100 SOLUTION:(4*90+x)/5=92 x=(5*92)-(4*90) x= 460 - 360 total score required 460 - 360=100 Correct answer is E #### E QUESTION:John and Beth each drove from Smallville to Crown City by different routes. John drove an an average speed of 40 miles per hour and completed the trip in 30 minutes. Beth's route was 5 miles longer, and it took her 20 minutes more than John to complete the trip. How many miles per hour was Beth's average speed on this trip? options: A) 24 B) 30 C) 48 D) 54 E) 75 SOLUTION:Speed = Distance/Time Distance for John = Speed * Time = 40 * 1/2 = 20 miles Distance for Beth = Distance for John +5 = 20+5 = 25 miles Time taken by Beth = Time taken by John + (1/3 hour) = 1/2+1/3 = 5/6 Speed of Beth = D/T = 25/(5/6) = 25*6/5 = 30 miles per hour Hence, B is the answer. #### B QUESTION:How many leading zeros (zeros after the decimal point but before the first nonzero digit of a number) are in 1/6!? options: A)2 B)3 C)5 D)6 E)9 SOLUTION:7! = 720 1/1000 < 1/720< 1/100 0.001 < 1/720 < 0.01 So 1/720 has 2 leading zeros Answer: A #### A QUESTION:The probability that a man will be alive for 10more yrs is 1/3 & the probability that his wife will alive for 10 more yrs is 5/8. The probability that none of them will be alive for 10 more yrs, is options: A)1/8 B)1/4 C)2/3 D)3/4 E)2 SOLUTION:Sol. Required probability = Pg.) x P(B) = (1— D x(1 —I) =: x 1=1/4 Ans.(B) #### B QUESTION:With 630 ml mixture of milk & water in the ratio 7:2. How much water mustbe added to make the ratio 7:3? options: A)60 ml B)80 ml C)70 ml D)90 ml E)92 ml SOLUTION:concentration of water in mixture1 =2/9 (since the ratio of milk and water = 7:2) ...(1) concentration of water in pure water= 1 ...(2) Now the above mentioned items are mixed to form mixture2 where milk and water ratio = 7 : 3 => concentration of water in mixture2 =3/10 By rule of alligation, concentration of water in mixture1 (2/9) concentration of water in pure water (1) Mean concentration (3/10) 1−3/10=7/10 =1:19 => Quantity of water =630×1/9=70 ml C #### C QUESTION:The ratio of number of boys and girls in a school is 3:5. If there are 320 students in the school, find the number of girls in the school? options: A)150 B)250 C)300 D)200 E)280 SOLUTION:Let the number of boys and girls be 3x and 5x Total students = 320 Number of girls in the school = 5*320/8 = 200 Answer is D #### D QUESTION:In how many ways can the letters of the word REPORT be arranged? options: A)1206 B)360 C)2520 D)3000 E)3478 SOLUTION:REPORT has 6 words, but R is repeated two times. Thus ways = 6! / 2! = 360 ways B #### B QUESTION:The ratio between the speeds of two Bullet trains is 7: 8. If the second Bullet train runs 440 kms in 5 hours, then the speed of the first train is: options: A)89.25 km/hr. B)77 km/hr. C)90.25 km/hr. D)94.25 km/hr. E)96.25 km/hr. SOLUTION:Let the speed of two bullet trains be 7x and 8x km/hr. Then, 8x = (440/5) = 88 x = (88/8) = 11 Hence, speed of first bullet train = (7 x 11) km/hr = 77 km/hr. B #### B QUESTION:Find 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.15of money? options: A)1500 B)1800 C)2100 D)1950 E)2200 SOLUTION:P = 15(100/10)2 => P = 1500 ANSWER:A #### A QUESTION:At 9 am a car (A) began a journey from a point, traveling at 40 mph. At 10 am another car (B) started traveling from the same point at 60 mph in the same direction as car (A). At what time will car B pass car A? options: A)12 pm B)1 pm C)2 pm D)3 pm E)4 pm SOLUTION:After t hours the distances D1 traveled by car A is given by D1 = 40 t Car B starts at 10 am and will therefore have spent one hour less than car A when it passes it. After (t - 1) hours, distance D2 traveled by car B is given by D2 = 60 (t-1) When car B passes car A, they are at the same distance from the starting point and therefore D1 = D2 which gives 40 t = 60 (t-1) Solve the above equation for t to find t = 3 hours Car B passes car A at 9 + 3 = 12 pm Answer A #### A QUESTION:Which of the following lines has x-intercept and y-intercept that are integers T? options: A)y=3x+1 B)y=√x+1 C)y=-2/x D)y=x^2-1 E)xy=1 SOLUTION:Values 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. #### D QUESTION:C and D enter into partnership with capital as 7:9. At the end of 8 months, C withdraws. If they receive the profits in the ratio of 8:9 find how long D's capital was used? options: A)months B)months C)months D)months E)months SOLUTION:7 * 8 : 9 * x = 8:9 => x= 7 ANSWER:D #### D QUESTION:The 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? options: A)2197 B)1267 C)1750 D)2267 E)1262 SOLUTION:Explanation: C.I. = [4000 * (1 + 10/100)2 - 4000] = (4000 * 11/10 * 11/10 - 4000) = Rs. 840. Sum = (420 * 100)/(3 * 8) = Rs. 1750 Answer:C #### C QUESTION:A train consists of 12 boggies, each boggy 15 metres long. The train crosses a telegraph post in 18 seconds. Due to some problem, three boggies were detached. The train now crosses a telegraph post in options: A)18 sec B)12 sec C)15 sec D)20 sec E)13.5 sec SOLUTION:Length of train = 12 × 15 = 180 m. Then, speed of train = 180⁄18 = 10 m/s Now, length of train = 9 × 15 = 135m ∴ Required time = 135⁄10 = 13.5 sec. Answer E #### E QUESTION:Uncle Bruce is baking chocolate chip cookies. He has 36 ounces of dough (with no chocolate) and 14 ounces of chocolate. How many ounces of chocolate are left over if he uses all the dough but only wants the cookies to consist of 20% chocolate? options: A) 3 B) 6 C) 7.2 D) 5 E) 9 SOLUTION:Answer is D. x/x+36=1/5 x=9 14-9=5 #### D QUESTION:A 10-by-8 inch piece of paper is used to form the lateral surface of a cylinder. If the entire piece of paper is used to make the lateral surface, which of the following must be true of the two possible cylinders that can be formed? options: A)The volume of the cylinder with height 10 is 80/pi cubic inches greater than the volume of the cylinder with height 6. B)The volume of the cylinder with height 8 is 80/pi cubic inches greater than the volume of the cylinder with height 10. C)The volume of the cylinder with height 10 is 80pi cubic inches greater than the volume of the cylinder with height 6. D)The volume of the cylinder with height 8 is 80pi cubic inches greater than the volume of the cylinder with height 10. E)The volume of the cylinder with height 8 is 240/pi cubic inches greater than the volume of the cylinder with height 10. SOLUTION:Pretty straightforward. Plug in the values to compute the volume of the cylinder. Keep in mind 8 and 10 are the circumference of the base and not the radius. B is the right answer. #### B QUESTION:It is required to seat 7 boys and 4 girls in a row so that the girls occupy the even places. How many such arrangements are possible? options: A)86,288 B)86,214 C)86,400 D)86,328 E)86,368 SOLUTION:Total number of candidates = 6 + 5 = 11. In the row of 11 positions, the even places are 2nd, 4th, 6th,8th,10th. Now, number of even places = 5. Number of girls to occupy the even places = 5. Even places can be filled = P (5, 5) ways. Number of boys = 6. The remaining 6 places can be filled by 6 boys = P (6, 6) ways By the fundamental principle of counting: The required number of seating arrangements P(5, 5) x P(6, 6) = 5! x 6! = 120 x 720 = 86,400 ANSWER:C #### C QUESTION:f a < b < c , which of the following must be true? (I) a < b^2 (II) b − a < c (III) a^2 < b^2 < c^2 options: A)None B)I only C)II only D)III only E)II and III SOLUTION:(I) a < b^2. Not necessarily true fractions: try a=1/3 and b=1/2. (II) b − a < c. Not necessarily true: try a=-1, b=0, and c=1. (III) a^2 < b^2 < c^2. Not necessarily true: try a=-1, b=0, and c=1. None of the options must be true. Answer: A. #### A QUESTION:Of the following values of n, the value of (-1/7 )^(-n) will be greatest for n = options: A)3 B)2 C)0 D)-2 E)-3 SOLUTION:imo -2 (-17)^-2= 1/(1/49)=49 oops i meant 2 B #### B QUESTION:In a maths test, students were asked to find 5/16 of a certain number. One of the students by mistake found 5/6th of that number and his answer was 200 more than the correct answer. Find the number. options: A)384 B)76 C)26 D)28 E)11 SOLUTION:Explanation: Let the number be x. 5*x/6 = 5*x/16 + 200 25*x/48 = 200 x = 384 ANSWER: A #### A QUESTION:An order was placed for the supply of a carpet whose breadth was 6 m and length was 1.44 times the breadth. What be the cost of a carpet whose length and breadth are 40% more and 25% more respectively than the first carpet. Given that the ratio of carpet is Rs. 45 per sq m? options: A)Rs.4082.67 B)Rs.4082.99 C)Rs.4082.29 D)Rs.4082.40 E)Rs.4082.12 SOLUTION:Length of the first carpet = (1.44)(6) = 8.64 cm Area of the second carpet = 8.64(1 + 40/100) 6 (1 + 25/100) = 51.84(1.4)(5/4) sq m = (12.96)(7) sq m Cost of the second carpet = (45)(12.96 * 7) = 315 (13 - 0.04) = 4095 - 12.6 = Rs.4082.40 Answer:D #### D QUESTION:Find the length of the longest pole that can be placed in a room 12 m long 8m broad and 9m high. options: A)13 B)14 C)15 D)16 E)17 SOLUTION:Length of longest pole = Length of the diagonal of the room = sqrt(12^2+8^2+9^2= sqrt(289)= 17 m. Answer is E. #### E QUESTION:If a particular player is always chosen, in how many ways can a cricket-be chosen out of 15 players? options: A)1236 B)1345 C)1358 D)1321 E)1365 SOLUTION:A particular player is always chosen, it means that 10 players are selected out of the remaining 14 players. =. Required number of ways = 14C10 = 14C4 = 14!/4!x19! = 1365 E #### E QUESTION:One-third of 1200 is what percent of 236 ? options: A)169.49 B)30 C)120.32 D)125.32 E)15.152 SOLUTION:Answer Let one-third of 1200 is N% of 236. ∵ 1200/3 = (N x 236)/100 ∴ N = (400 x 100) / 236= 169.49 Correct Option: A #### A QUESTION:If a is a digit in the number (a5,608 + 584)/88 = an integer, what is the value of a? options: A)2 B)1 C)3 D)7 E)9 SOLUTION:(a5,608 + 584)/88 = a6,192/88 Factors of 88 = (8)(11) Divisible by 8: if the last 3 digits of the number are divisible by 8. 192/8 = 24 => So, we want divisible by 11. Divisibe 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. a619-2 => a61-7 => a5-4 => a1 => 11/11. So a = 1. Answer: B #### B QUESTION:In an intercollegiate competition that lasted for 3 days, 175 students took part on day 1, 210 on day 2 and 150 on day 3. If 80 took part on day 1 and day 2 and 70 took part on day 2 and day 3 and 20 took part on all three days, how many students took part only on day 1? options: A)25 B)45 C)55 D)70 E)30 SOLUTION:Day 1&2 = 80; Only Day 1&2 (80-20) = 60, Day 2&3 = 70; Only Day 2&3 (70-20) = 50, Only Day 1 = 175 - (60+50+20) = 45 Answer:B #### B QUESTION:Sandy can do a job in 6 days and Molly can do the same job in 12 days. If they work together, in how many days will they complete the job? options: A)4 days B)6 days C)8 days D)2 days E)9 days SOLUTION:Sandy can do 1/6 of the job each day. Molly can do 1/12 of the job each day. The combined rate is 1/6 + 1/12 = 1/4 of the job each day. The job will take 4 days. The answer is A. #### A QUESTION:The value of x + x(xx) when x = 2 is: options: A)36 B)16 C)18 D)64 E)10 SOLUTION:x + x(xx) Put the value of x = 2 in the above expression we get, 2 + 2(22) = 2 + 2(2 × 2) = 2 + 2(4) = 2 + 8 = 10 #### E QUESTION:Mark drove for 1/2 of the trip, and Justin drove for 1/4 of the trip. Gina and Kaitlyn divided the rest of the driving evenly between them. If the entire trip was 128 miles, how many miles did Kaitlyn drive? options: A)26 miles B)16 miles C)20 miles D)18 miles E)17 miles SOLUTION:1/2 x 128 = 64 miles Mark drove 1/4 x 128 = 32 miles Justin drove 64 + 32 = 96 miles driven 128 - 96 = 32 miles left 32 ÷ 2 = 16 miles driven by Kaitlyn correct answer B #### B QUESTION:A 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? options: A)288 B)266 C)120 D)287 E)212 SOLUTION:Speed = (12/10 * 60) km/hr = (72 * 5/18) m/sec = 20 m/sec. Length of the train = 20 * 6 = 120 m. Answer: C #### C QUESTION:Solution X is 30% chemical A and 70% chemical B by volume. Solution Y is 40% chemical A and 60% chemical B by volume. If a mixture of X and Y is 36% chemical A, what percent of the mixture is Solution X? options: A)30% B)35% C)40% D)45% E)50% SOLUTION:The volume of the mixture be X+Y. 0.3X +0.4Y=0.36(X+Y) X=2Y/3 X/(X+Y)=(2Y/3) / (5Y/3)=2/5=40%. The answer is C. #### C QUESTION:The cost price of 13 articles is equal to the selling price of 11 articles. Find the profit percent? options: A)18 2/18% B)18 2/11% C)18 2/91% D)18 9/11% E)12 2/11% SOLUTION:13 CP = 11 SP 11 --- 2 CP 100 --- ? =>18 2/11% Answer: B #### B QUESTION:In a certain sequence of 8 numbers, each number after the first is 1 more than the previous number. If the first number is −4, how many of the numbers in the sequence are positive? options: A)None B)One C)Two D)Three E)Four SOLUTION:Non - Negative ( zero to positive infinity ) Solution to the question : -4,-3,-2,-1,0 , 1,2,3 Hence ans is 3 ..option D #### D QUESTION:The average weight of A, B and C is 75 kg. If the average weight of A and B be 88 kg and that of B and C be 72 kg, then the weight of B is: options: A)60 kg B)59 kg C)62 kg D)63 kg E)61 kg SOLUTION:EXPLANATION Let A, B, C represent their respective weights. Then, we have: A + B + C = (75 x 3) = 225 …. (i) A + B = (88 x 2) = 176 …. (ii) B + C = (72 x 2) = 144 ….(iii) Adding (ii) and (iii), we get: A + 2B + C = 288 …. (iv) Subtracting (i) from (iv), we get : B = 63. B’s weight = 63 kg. Answer D #### D QUESTION:The 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? options: A)7 B)4 C)6 D)9 E)3 SOLUTION:65*(90/100)*((100-x)/100) = 56.16 x = 4% Answer: B #### B QUESTION:A person bought 20 kg of rice at Rs 10.50 per kg and 30 kgs at Rs 12 per kg. He mixed the two and sold the mixture at Rs 11.40 per kg. What was the gain in his deal(in Rs)? options: A)0 B)20 C)75 D)5 E)10 SOLUTION:Explanation : Gain = 50 * 11.40 - (20*10.5 + 30*12) = 0 Answer : A #### A QUESTION:The true discount on a bill of Rs.8640 is Rs.1440.The banker's discount is options: A)1428 B)1528 C)1628 D)1728 E)None of these SOLUTION:Solution P.W = Rs.(8640 - 1440) = Rs. 720 S.I on Rs. 8640 =Rs.(1440/7200 x 8640) = Rs. 1728. Answer D #### D QUESTION:How 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? options: A)22 B)30 C)88 D)266 E)121 SOLUTION:Speed of train relative to man = 63 - 3 = 60 km/hr. = 60 * 5/18 = 50/3 m/sec. Time taken to pass the man = 500 * 3/50 = 30 sec. Answer:B: #### B QUESTION:With out any halt a train travels a certain distance with an average speed of 66 km ph , and with halts it covers the same distance at an average speed of 33 kmph. When it is traveling with halts, how many minutes/per hour does the train halt on an average ? options: A)48 min. B)12min. C)60min. D)18min. E)19min. SOLUTION:With halt in 1 hour the train travels 60km With out halt for traveling same distance it take 66/33= 2/1 = 120 minutes :. 60 minutes is the halting time per hour ANSWER:C #### C QUESTION:List I: 3, 6, 14, 19 List II: x, 3, 14, 8, 19 options: A) 6 B) 7 C) 8 D) 9 E) 10 SOLUTION:We start by calculating the median of the numbers of list I: 3, 6, 14, 19. We see that the numbers in the list are in order already and, since we have an even number of numbers, the median is the average of the two middle numbers. median = (6 + 14)/2 median = 20/2 median = 10 The median of list I is 7. Looking at list II: x, 3, 6, 14, 19, we see that we have an odd number of terms. Thus, when the list is ordered from least to greatest the median must be the middle term. Since the medians of the two lists must be equal, we know that the median of list II must be 10 and therefore x is 10. The answer is E. #### E QUESTION:A 16% stock yielding 10% is quoted at : options: A)83.33 B)110 C)112 D)120 E)160 SOLUTION:Solution To earn Rs. 10, money invested = Rs. 100. To earn Rs. 16, money invested = Rs.(100/10X16) = Rs. 160. ∴ Market value of Rs. 100 stock =Rs. 160 Answer E #### E QUESTION:The 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 80 feet wide by 150 feet long by 10 feet deep and is currently at 100% capacity, how long will it take to drain the pool? options: A)1400 B)1600 C)1800 D)1500 E)2000 SOLUTION:volume of pool = 80*150*10 cu.ft ,100% full = 60*100*10*1 cu.ft water is available to drain. draining capacity =60 cu.ft /min therefore time taken = 80*150*10*1/ 60 min= 2000 min E #### E <<<Examples ends QUESTION:Susan, Tim, Matt and Kim need to be seated in 4 identical chairs in straight line so that Susan is seated always left to Tim. How many such arrangements are possible ? options: A)360 B)12 C)80 D)240 E)60 SOLUTION:Total # of arrangement of 4 people is 4!. In half of the cases Susan will be seated left to Tim and in half of the cases Susan will be seated right to Tim (why should one seating arrangement have more ways to occur than another?). So, # of arrangements to satisfy the given condition is 4!/2=12. Answer: B. #### B

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:A dealer purchases 15 articles for Rs. 25 and sells 12 articles for Rs. 35. Find the profit percentage? options: A)80% B)50% C)75% D)40% E)53% SOLUTION:L.C.M of 15 and 12 = 60 CP of 60 articles = Rs. 100 (25 * 4) SP of 60 articles = Rs. 175 (35 * 5) Profit percentage = (175 - 100)/100 * 100 = 75% Answer: C #### C QUESTION:When a certain number X is divided by 143, the remainder is 45. Which of the following numbers, if added to X, would result in a number divisible by 14? options: A)7 B)21 C)34 D)8 E)55 SOLUTION:So the number given is N = 143Q + 45 If this number is divided by 13, the remainder would be R[(143Q + 45)/13] Since 143 is divisible by 13 , the product 143Q gives no remainder This means the remainder of 45/13 should be the remainder of the entire number N which is 6 To make it divisible by 13 , the smallest number that can be added = 14 - 6 = 8 Correct Option : D #### D QUESTION:Two-third of two-fifth of three-fourth of a number is 36. What is the square root of four-fifth of that number? options: A)9 B)12 C)14 D)16 E)18 SOLUTION:Explanation: We have, 2/3 * 2/5 * 3/4 * X = 36 X = 180 Now, 4/5 * X ===> 4/5 * 180 = 144 √144 = 12 ANSWER: B #### B QUESTION:The least number of complete years in which a sum of money put out at 20% C.I. will be more than doubled is? options: A)7 B)4 C)5 D)3 E)1 SOLUTION:Explanation: P(1 + 20/100)n > 2P or (6/5)n > 2 Now, (6/5 * 6/5 * 6/5 * 6/5) > 2. So, n = 4 years. Answer:B #### B QUESTION:A train running at the speed of 60 km/hr crosses a pole in 15 sec. What is the length of the train? options: A)356 B)250 C)127 D)279 E)150 SOLUTION:Speed = 60 * 5/18 = 50/3 m/sec Length of the train = speed * time = 50/3 * 15 = 250 m Answer: B #### B QUESTION:There 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? options: A)8/12 B)6/16 C)4/16 D)6/10 E)4/10 SOLUTION:w = m+4 w+m = 20 m+4+m = 20 2m = 16 m = 8 w = 12 ratio:8:12 Ans: A #### A QUESTION:The distance light travels in one year is approximately 5,870,000,000,000 miles. The distance light travels in 100 years is: options: A)587 × 10<10>(exponent) miles B)587 × 10<-12> (exponent) miles C)587 × 10<-10>(exponent) miles D)587 × 10<12>(exponent) miles E)587 × 10<8>(exponent) miles SOLUTION:The distance of the light travels in 100 years is: 5,870,000,000,000 × 100 miles. = 587,000,000,000,000 miles. = 587 ×10<12>(exponent) miles #### D QUESTION:A cab driver 5 days income was $200, $150, $750, $400 , $500. Then his average income is? options: A)$420 B)$410 C)$400 D)$390 E)$380 SOLUTION:avg = sum of observations/number of observations avg income=(200+150+750+400+500)/5 = 400 Answer is C #### C QUESTION:The ratio between a two-digit number and the sum of the digits of that number is 4 : 1.If the digit in the unit's place is 3 more than the digit in the ten’s place, what is the number? options: A)47 B)36 C)58 D)25 E)14 SOLUTION:Let the ten's digit be x. Then, unit's digit = (x + 3). Sum of the digits = x + (x + 3) = 2x + 3. Number = l0x + (x + 3) = llx + 3. 11x+3 / 2x + 3 = 4 / 1 => 11x + 3 = 4 (2x + 3) => 3x = 9 => x = 3. Hence, required number = 11x + 3 = 36. Answer is B. #### B QUESTION:At a particular graduation party with 300 guests, 70% of the guests brought gifts, and 40% of the female guests brought gifts. If 45 males did not bring gifts to the party, how many females did bring gifts? options: A)18 B)30 C)42 D)68 E)70 SOLUTION:the correct method total = 300.. 70% of 300 = 210 got gifts.. 90 did not get gift, out of which 48 are males, so remaining 90-45=50 are females.. But 40% females brought gift, so 60% did not get it.. so 60% = 45, 100%= 45*100/60= 75.. ans 40% of 75 =30 B #### B QUESTION:Given that 268x74= 19632, find the value of 2.68x.74. options: A)1.9632 B)1.0025 C)1.5693 D)1.0266 E)None SOLUTION:Solution Sum of decimals places =(2+2) = 4. Therefore, = 2.68×.74 = 1.9632 Answer A #### A QUESTION:A train passes a man standing on the platform. If the train is 170 meters long and its speed is 72 kmph, how much time it took in doing so? options: A)3 1/2 sec B)3 5/2 sec C)3 7/2 sec D)8 1/2 sec E)3 1/8 sec SOLUTION:D = 170 S = 72 * 5/18 = 20 mps T = 170/20 = 8 1/2 sec Answer: D #### D QUESTION:If a point (x,y) is randomly selected within the square shown in the figure above, (the vertices are on 1,1 1,-1, -1,1 -1,-1) what are the R odds that x^2+y^2>1? options: A)1. pi/4 B)2. R=pi/16 C)3. R=1-pi/4 D)4. 1-pi/16 E)5.4-pi SOLUTION:area of the square will be 4, and the area of circle with center (0,0) and radius 1 will be pi. then succesful outcomes = 4 - pi (the area where x2+y2 will be greater than 1) total outcomes = 4 therefore probability = (4-pi)/4 C #### C QUESTION:What is x if x + 3y = 33 and y = 10? options: A)1 B)2 C)3 D)4 E)5 SOLUTION:Substitute y by 10 in x + 3y = 33 x + 3(10) = 33 x + 30 = 33 If we substitute x by 3 in x + 30 = 33, we have 3 + 30 = 33. Hence x = 3 correct answer C #### C QUESTION:In 1 hour, a boat goes 5 km along the stream and 9 km against the stream. The speed of the boat in still water (in km/hr) is : options: A)3 km/hr. B)2 km/hr. C)7 km/hr. D)8 km/hr. E)5 km/hr. SOLUTION:Speed in still water = 1/2(9 + 5) km/hr = 7 km/hr. ANSWER :C #### C QUESTION:How many seconds will a 900 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? options: A)22 B)54 C)99 D)77 E)12 SOLUTION:Speed of train relative to man = 63 - 3 = 60 km/hr. = 60 * 5/18 = 50/3 m/sec. Time taken to pass the man = 900 * 3/50 = 54 sec. Answer: B #### B QUESTION:Alice and Bob will throw three dice each. The score is the sum of points on all three dice. If Alice scores 17 in her attempt what is the probability that Bob will outscore Alice in his attempt? options: A)1/216 B)5/216 C)7/216 D)1/36 E)5/36 SOLUTION:The total number of ways the dice can land is 6*6*6=216. Bob must get a score of 18=6+6+6. There is only 1 way to do this. P(Bob wins)=1/216 The answer is A. #### A QUESTION:An article is bought for Rs.675 and sold for Rs.900, find the gain percent? options: A)33 1/7% B)33 2/3% C)33 1/3% D)37 1/3% E)23 1/3% SOLUTION:675 ---- 225 100 ---- ? => =33 1/3% Answer:C #### C QUESTION:AB +BA ___ 121 In the addition problem above, A and B represent digits in two different two-digit numbers. What is the sum of A and B? options: A)6 B)8 C)9 D)11 E)14 SOLUTION:two ways to do it.. 1) straight logic.. we can see that ones digit is 1 when units digit B and A are added.. answer has to be 1 in the units digit.. only 11 fits in.. 2) BA=10B+A, and AB=10A+B.. it is given that BA+AB=121.. or 10B+A +10A+B=121.. 11(A+B)=121.. so A+B=11.. ANSWER:D #### D QUESTION:Which number should replace both the asterisks in (* /21) x (*/84) = 1 ? options: A)21 B)42 C)63 D)72 E)168 SOLUTION:Let (y/21) x (y/84) = 1 y^2 = 21 x 84 = 21 x 21 x 4 y = (21 x 2) = 42 The answer is B. #### B QUESTION:Find out Difference between SI and CI if p=1000000 r=4% ant t=3 yr? options: A)4864 B)4854 C)4844 D)4868 E)4866 SOLUTION:p=1000000, r=4% annual , t=3 yr SI = p*r*t/100 = 1000000*4*3/100 = 120000 CI = p[(1+ r/100)^t -1] = 1000000[(1+ 4/100)^3 -1] = 124864 difference = CI - SI = 124864 - 120000 = 4864 ANSWER:A #### A QUESTION:A and B are two partially filled buckets of water. If 7 liters are transferred from A to B, then A would contain one-third of the amount of water in B. Alternatively, if 7 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? options: A)77/5 B)13 C)17 D)21 E)23 SOLUTION:Let Bucket A be A and Bucket B be B Scenario 1 A-7 = 1/3 (B+7) ----> 3A-21 =B+7 Scenario 2 B-7 = 1/2 (A+7) -----> 2B-14 = A+7 From Scenario 1, B = 3A-28 Substitute B with this information in Stmt 2 2 (3A-28) -14 = A+7 ------> 6A -56-14 = A+7 ------> 6A- A = 70+7 ---> 5A= 77 A= 77/5, Answer choice A #### A QUESTION:If the simple interest on a sum of money for 2 years at 5% per annum is Rs. 50, what is the compound interest on the same sum at the rate and for the same time? options: A)Rs.51.25 B)Rs.51.26 C)Rs.51.22 D)Rs.51.98 E)Rs.51.11 SOLUTION:Sum = (50 * 100) / (2 * 5) = Rs. 500 Amount = [500 * (1 + 5/100)2] = Rs. 551.25 C.I. = (551.25 - 500) = Rs. 51.25. Answer: A #### A QUESTION:If u r genius solve it:- 70 * 17 = 11 60 * 16 = 15 50 * 15 = ? options: A)2 B)12 C)6 D)8 E)10 SOLUTION:Logic: 70*17=1190=1+1+9+0=11 60*16=960=9+6+0=15 50*15=750=7+5+0=? Answer : B #### B QUESTION:In a division sum, the remainder is 6 and the divisor is 5 times the quotient and is obtained by adding 7 to the thrice of the remainder. The dividend is options: A)74 B)78 C)86 D)92 E)106 SOLUTION:Divisor = (6 * 3) + 7 = 25 5 * Quotient = 25 Quotient = 5. Dividend = (Divisor * Quotient) + Remainder Dividend = (20 * 5) + 6 = 106. E) #### E QUESTION:A girl goes to her school from her house at a speed of 6km/hr and returns at a speed of 4 km/hr. If she takes 10 hours in going and coming back, the distance between her school and house is options: A)12 kms B)16 kms C)20 kms D)24 kms E)None of above SOLUTION:Let distance be D 10 = D/4 + D/6 Answer : D #### D QUESTION:The 323rd term of the series a, b , b, c, c, c, d, d, d, d, e, e, e, e, e, .... is options: A)u B)v C)w D)y E)z SOLUTION:a is one time, b,2 times so on... so 323=n(n+1)/2.. 0r n(n+1)= 646... now 25*26=650...24*25<646 so n= 25. and 25th alphabet is Y. ans D #### D QUESTION:50% of a number is added to 120, the result is the same number. Find the number? options: A)240 B)288 C)1687 D)997 E)121 SOLUTION:(50/100) * X + 120 = X X = 240 Answer:A #### A QUESTION:log3 N+log12 N what is 3 digit number N that will be whole number options: A)6291 B)7292 C)1728 D)1929 E)1727 SOLUTION:No of values N can take is 1 12^3=1728 ANSWER:C #### C QUESTION:How many numbers from 10 to 1000 are exactly divisible by 9? options: A)100 B)10 C)11 D)12 E)14 SOLUTION:10/9 = 1 and 1000/9 = 111 ==> 111 - 1 = 100. Therefore 100 Answer : A #### A QUESTION:The cash difference between the selling prices of an article at a profit of 2% and 6% is Rs 3. The ratio of two selling prices is options: A)51:53 B)52:53 C)53:54 D)54:55 E)None of these SOLUTION:Explanation: Let the Cost price of article is Rs. x Required ratio = (102% of x) / (106% of x) =102/106 =51/53 = 51:53. Answer: A #### A QUESTION:Claire 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? options: A)39 B)50 C)66 D)57 E)60 SOLUTION:G+H =90 ...1 ; G/4 +H/3 =25 ....2 OR 3G +4H =25*12 =300 G =90-H OR 3(90-H) +4H =300 H = 300-270 =30 THEN G= 96-30 =66 C #### C QUESTION:How many kilograms of sugar costing Rs.9 per kg must be mixed with 27 kg of sugar costing Rs.7 per Kg so that there may be a gain of 10% by selling the mixture at Rs.9.24 per Kg? options: A)36 Kg B)42 Kg C)54 Kg D)63 Kg E)None of these SOLUTION:Solution Ratio of quantities of 1st and 2nd kind = 14 : 6 = 7 : 3. Let x kg of sugar of 1st kind be mixed with 27 kg of 2nd kind. Then, 7 : 3 = x : 27 or x = (7 x 27 / 3) = 63 kg Answer D #### D QUESTION:A $84.95 lawn chair was sold for $59.95 at a special sale. By approximately what percent was the price decreased? options: A)15% B)20% C)25% D)29% E)80% SOLUTION:Listed selling price of chair = 84.95 $ Discounted selling price of chair = 59.95 $ Discount = 84.95 - 59.95 = 25 $ % decrease in price of chair = (25/84.95) * 100% = 29 % approx Answer D #### D QUESTION:A man buys Rs. 20 shares paying 9% dividend. The man wants to have an interest of 12% on his money. What is the market value of each share? options: A)Rs.12 B)Rs.18 C)Rs.15 D)Rs.21 E)Rs.25 SOLUTION:Explanation : Face value of each share = Rs.20 Dividend per share = 9% of 20 = 9×20/100=9/5 He needs to have an interest of 12% on his money ie, Money Paid for a share 9×12/100=9/5 Money Paid for a share=9/5×100/12=15 ie, Market Value of the share = Rs.15 Answer : Option C #### C QUESTION:A certain quantity of 45% solution is replaced with 25% solution such that the new concentration is 35%. What is the fraction of the solution that was replaced? options: A)1/4 B)1/3 C)1/2 D)2/3 E)3/4 SOLUTION:Let's say that the total original mixture A is 100 ml The original mixture A thus has 45 ml of alcohol out of 100 ml of solution You want to replace some of that original mixture A with another mixture B that contains 25 ml of alcohol per 100 ml. Thus, the difference between 45 ml and 25 ml is 20 ml per 100 ml of mixture. This means that every time you replace 100 ml of the original mixture A by 100 ml of mixture B, the original alcohol concentration will decrease by 20%. The question says that the new mixture, let's call it C, must be 35% alcohol, a decrease of only 10%. Therefore, 10 out of 20 is 1/2 and C is the answer. #### C QUESTION:In a maths test, students were asked to find 5/16 of a certain number. One of the students by mistake found 5/6th of that number and his answer was 200 more than the correct answer. Find the number. options: A)384 B)76 C)26 D)28 E)11 SOLUTION:Explanation: Let the number be x. 5*x/6 = 5*x/16 + 200 25*x/48 = 200 x = 384 ANSWER: A #### A QUESTION:Jayant opened a shop investing Rs. 30,000. Madhu joined him 2 months later, investing Rs. 45,000. They earned a profit of Rs. 60,000 after completion of one year. What will be Madhu's share of profit? options: A)Rs. 27,000 B)Rs. 24,000 C)Rs. 30,000 D)Rs. 36,000 E)None of these SOLUTION:30,000 *12=45,000*8 1:1 Madhu's share=1/2*60,000 i.e. Rs. 30,000 ANSWER:C #### C QUESTION:If the cost price of 50 articles is equal to the selling price of 40 articles, then the gain or loss percent is? options: A)22 B)65 C)78 D)33 E)25 SOLUTION:Given that, cost price of 50 article is equal to selling price of 40 articles. Let cost price of one article = Rs. 1 Selling price of 40 articles = Rs. 50 But Cost price of 40 articles = Rs. 40 Therefore, the trader made profit.\Percentage of profit = 10/40 * 100 = 25% Answer:E #### E QUESTION:A code is to be made by arranging 6 letters. Three of the letters used will be the letter A, two of the letters used will be the letter B and one of the letters used will be the letter C . If there is only one way to present each letter, how many different codes are possible? options: A)230 B)360 C)420 D)840 E)5,040 SOLUTION:we have 6 letters out of which 3 are of one kind, 2 are of another kind.. so total ways = 6!/2!1!=360 ans B #### B QUESTION:In a recent head-to-head run-off election, 12,000 absentee ballets were cast. 1/2 of the absentee ballets were thrown out and 1/2 of the remaining absentee ballets were cast for Candidate A. How many absentee votes did Candidate B receive? options: A)2,000 B)3,000 C)6,000 D)8,000 E)9,000 SOLUTION:1/2 * 1/2 (total absentee votes) = 1/4 (total votes)=1/4*12000=3000 Answer is B #### B QUESTION:The length W of a rectangle is decreased by 15% and its width is increased by 40%. Does the area of the rectangle decrease or increase and by what percent? options: A)Decreases by 19% B)Decreases by 25% C)Increases by 6% D)Increases by 19% E)Increases by 25% SOLUTION:Let the length W of the rectangle be 100x, and width be 100y. Area = 100x * 100y = 10000xy Now after the change Length = 85x, and width = 140 y. Area = 11900xy % Change = (11900xy - 10000xy)/(10000xy) = 19 % Increase. Hence D. #### D QUESTION:What is the sum of all the numbers which divides 100 ? options: A)408 B)102 C)816 D)916 E)416 SOLUTION:You first have to know all the divisor of 100. They are 2,4,5,10,20,25,50 and 100. If you add all these numbers together, you get 408. Final Answer: A #### A QUESTION:In how many ways can a group of 11 friends be seated round 2 tables if one of the tables can seat 7 and the other can seat 4 people? options: A)11C6 * 9! *4! B)11C3 * 6! *3! C)15C4 * 9! *3! D)15C2 * 10! *3! E)16C5 * 10! *4! SOLUTION:7 people can be selected from 11 people in 11C7 ways. Remaining 4 people can be selected from 4 people in 4C4 ways. Now, arranging 7 people on a round table = (7-1) ! = 6! Arranging 4 people on a round table = (4-1) ! = 3! Hence, total number of ways = 11C7 * 6! * 4C4 * 3! = 11C3 * 6! * 3! B #### B QUESTION:A and B together can do a piece of work in 8 days. If A alone can do the same work in 20 days, then B alone can do the same work in? options: A)0.075 days B)0.45 days C)0.55 days D)0.25 days E)0.15 days SOLUTION:B = 1/8 – 1/22 =0.075 days ANSWER:A #### A QUESTION:What is the next number of the following sequence 2, 12, 4, 24, 8, 48, (...) options: A)10 B)12 C)16 D)20 E)22 SOLUTION:The series is 2*6=12 12/3=4 4*6=24 24/3=8 8*6=48 48/3=16 ANSWER: C #### C QUESTION:The value of 0.1 x 0.1 x 0.1 + 0.02 x 0.02 x 0.02 is: 0.2 x 0.2 x 0.2 + 0.04 x 0.04 x 0.04 options: A)0.0125 B)0.125 C)0.25 D)0.5 E)None of these SOLUTION:Explanation: Given expression = (0.1)3 + (0.02)3=1= 0.125 23 [(0.1)3 + (0.02)3] =8 Answer- B #### B QUESTION:In a exam there are 26 number of question. For one write question add 8 marks and for one wrong 5 marks subtract. One candidate answered all questions. His marks is 0. How many answers was correct? options: A)9 B)10 C)11 D)12 E)13 SOLUTION:let no. of right ques be x, then no. of wrong ques will be= 26 - x now, according to ques 8x - (26-x)5 = 0, hence x=10...no. of right ques is 10 ANSWER:B #### B QUESTION:There are 9 people in the room. There are two pairs of siblings within that group. If we choose two people, what is the probability that they will not be siblings? options: A)12/18 B)17/18 C)2/9 D)1/18 E)4/18 SOLUTION:we have XXXXXBBCC We have to take into the account when we have XX, XB, XC So 5/9*4/8 5/9*2/8 and 5/9*2/8 note we need to multiply these by 2 (except the first) b/c we can have BX and CX. 20+20+20 --> 60/72 --> 30/36 --> 15/18 then next is BC 2/9*2/8 --> 4/72 2/36 1/18 --> multiply this by 2 b/c of CB so 2/18+15/18 --> 17/18 ANSWER:B #### B QUESTION:Last year Sandy saved 10% of her annual salary. This year, she made 10% more money than last year, and she saved 15% of her salary. The amount saved this year was what percent of the amount she saved last year? options: A)142% B)150% C)165% D)176% E)188% SOLUTION:Let last year's salary be x. Last year, Sandy save 0.1x This year, Sandy saved 0.15*1.1x = 0.165x 0.165x / 0.1x = 1.65 = 165% The answer is C. #### C QUESTION:The 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? I. c > a II. c = a III. c < a options: A)I only B)II only C)III only D)I and II only E)II and III only SOLUTION:Let q = 10% then l = 100/11 % let b = 100 then a = 110 after increasing a by l and decreasing b yq we get c= 108 therefore c<a C it is answer #### C QUESTION:The velocity of a falling object in a vacuum is directly proportional to the amount of time the object has been falling. If after 5 seconds an object is falling at a speed of 90 miles per hour, how fast will it be falling after 18 seconds? options: A)18 miles per hour B)90 miles per hour C)216 miles per hour D)324 miles per hour E)5400 miles per hour SOLUTION:Since Velocity is proportional to Time Velocity =k*Timewhere k is the constant of proportionality Time= 5 seconds Velocity = 5k = 90 miles per Hour i.e. k = 18 i.e. The relation between Velocity and Time becomes Velocity =18*Time Time= 18 seconds Velocity = 18*18 = 324 miles per hour Answer: Option D #### D QUESTION:H.C.F. of 513, 1134 and 1215 is options: A)27 B)21 C)76 D)42 E)33 SOLUTION:H.C.F. of 513, 1134 and 1215 = 3 × 3 × 3 = 27 Answer: Option A #### A QUESTION:From 6 positive numbers and 6 negative numbers, how many groups F of 4 numbers, yielding a positive product, can be formed? options: A)720 B)625 C)30 D)960 E)255 SOLUTION:Potential combinations of 4 numbers that will yield positive product ++++ 4C6 ---- 4C6 ++-- 2C6*2C6 4C6 + 4C6 + 2C6*2C6 F=15 +15 + 15*15 = 255=E #### E QUESTION:If x = 3^9 and x^x = 3^k, what is k? options: A)3^11 B)3^13 C)3^25 D)3^27 E)3^81 SOLUTION:Solution: We know that x=3^9 which implies x^x = (3^9)^(3^9) = 3^(9 * 3^9) [because (x^y)^z = x^(y*z))] so 3^(3^2 * 3^9) = 3^(3^(2+9)) [because x^a * x^b = x^(a+b)] therefore x^x = 3^(3^11) Given that x^x=3^k so 3^(3^11) = 3^k Since the base is same the exponent will also be same therefore k = 3^11 Answer: A #### A QUESTION:Find the cost of fencing around a circular field of diameter 32 m at the rate of Rs.2 a meter? options: A)201 B)132 C)772 D)592 E)261 SOLUTION:2 * 22/7 * 16 = 100.5 100.5 * 2 = Rs.201 Answer: A #### A QUESTION:If A,B,C are three integers and AB+C is even ; which of the following must be true? A)C is even B)B is even C)AB is even options: A)I only B)II only C)III only D)II,III only E)None of the above SOLUTION:If AB is Odd then C will not even. O+E = O If B is even AB is even always. But If C is Odd E+O = O None of the above are true #### E QUESTION:If 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. options: A)5 hours B)10 hours C)15 hours D)20 hours E)25 hours SOLUTION:1/5+2/8 + 3/x = 1 x =20 hours. ANSWER =D #### D QUESTION:If p is a positive integer and p^2 is divisible by 12, then the largest positive integer that must divide p ^3 is options: A)2^3 B)2^6 C)3^3 D)6^3 E)12^2 SOLUTION:Since p is an integer so p 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 p^2 as a multiple of 12)) p^2 is divisible by 12 (12 = 2*2*3), So, p should have at least one 2 and one 3 so that p^2 has a 2^2 and two 3 So, p will have a 2 and a 3. Or p will be a multiple of 6 So, largest possible integer than should divide p^3 is 6^3 So, Answer will be D #### D QUESTION:Find out the next word in the series below... FAG, GAF, HAI, IAH, ...? options: A)GAK B)JAK C)HGF D)JAH E)KHG SOLUTION:In first FAG it was reodering the first and last letters and these are the continuous alphabets ANSWER:B #### B QUESTION:Consider a sequence of numbers given by the expression 7 + (a - 1) * 5, where n runs from 1 to 80.What is the sum of this series ? options: A)409 B)1636 C)16360 D)16000 E)15360 SOLUTION:terms in this sequence are 7,12,17----402 now since this is an a.p. with a common difference of 5. therefore its sum can be given as a(f+l)/2----------------1) a= total no. of terms =80 f= first term=7 l= last term=402 subsituting values in the expression 1 we have 80(7+402)/2 = 40(409) =16360=C #### C QUESTION:The ages of two persons differ by 20 years. If 5 years ago, the elder one be 5 times as old as the younger one, their present ages (in years) are respectively options: A)18 years B)88 years C)77 years D)10 years E)17 years SOLUTION:Let their ages be x and (x + 20) years. 5 (x - 5) = (x + 20 - 5) or 4x = 40 or x = 10. Their present ages are 30 years and 10 years Answer:D #### D QUESTION:In 10 years, P will be as old as Q is now. Twenty years ago, Q was twice as old as P was then. How old is P now? options: A)30 B)35 C)40 D)45 E)50 SOLUTION:Q = P+10 Q-20 = 2(P-20) P-10 = 2P-40 P = 30 The answer is A. #### A QUESTION:The profit earned by selling on article for 900 is double the loss incurred when the same article is sold for 450. At what price should the article be sold to make 25% profit? options: A)750 B)800 C)850 D)860 E)890 SOLUTION:Let ‘x’ be the CP of the article; Then 900 – x = 2(x – 450); :. x= 600. 25% of 600 = 150 :. New SP = 600 + 150 = 750 Option 'A' #### A <<<Examples ends QUESTION:The area of a circle is increased by 800%. By what percent has the diameter of the circle increased? options: A)100% B)200% C)300% D)600% E)800% SOLUTION:A diameter of 2 it's radius = 1 it's area = (1^2)pi = 1pi Answer A: If we increase that diameter 100%, we have.... A diameter of 4 it's radius = 2 it's area = (2^2)pi = 4pi This area has increased (4 pi - 1pi)/1pi = 3pi/1pi = 3 = 300% Answer B: If we increase the diameter 200%, we have... A diameter of 6 it's area = 3 it's area = (3^2)pi = 9pi This area has increased (9pi - 1pi)/1pi = 8 pi/1pi = 8 = 800% ANSWER:E #### E

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:If the length of an edge of cube M is thrice the length of an edge of cube N, what is the ratio of the volume of cube N to the volume of cube M? options: A)2/13 B)1/27 C)1/5 D)1/9 E)1/8 SOLUTION:The length of cube N = 1; The length of cube M = 3; The ratio of the volume of cube N to the volume of cube M = 1^3/3^3 = 1/27 Answer : B #### B QUESTION:There is a 10% chance that Tigers will not win at all during the whole season. There is a 30% 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? options: A)A)55% B)B)60% C)C)80% D)D)72% E)E)70% SOLUTION:There is a 10% chance that Tigers will not win at all during the whole season We can infer that there is 90% chance Tigers will win . Similarly There is a 30% chance that Federer will not play at all in the whole season We can also infer that there is 70% chance that Federer will play. Answer E #### E QUESTION:Zoey 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? options: A)$3 B)$2 C)$9 D)$1 E)$4 SOLUTION:Zoey 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. #### D QUESTION:A certain sum of money doubles itself in 10 years in how much many years will it trible itself at the same rate? options: A)20 years B)28 years C)24 years D)27 years E)57 years SOLUTION:100 ---- 100 --- 10 100 --- 10 -------------------- 300 ---- 20 years Answer:A #### A QUESTION:A car crosses a 720 m long bridge in 2 minutes. What is the speed of car in km per hour? options: A)20.5 km/hr B)21.6 km/hr C)31.6 km/hr D)15.6 km/hr E)22.3 km/hr SOLUTION:Speed = 720 m/sec. 360/60m/s = 6 m/sec. Converting m/sec to km/hr (see important formulas section) =6 x 18/5 km/hr 5 = 21.6 km/hr B #### B QUESTION:If 1 > 1 - ab > 0, which of the following must be true? I. a/b > 0 II. ab < 1 III. a/b < 2 options: A)I only B)II only C)III only D)I and II only E)I and III only SOLUTION:MANHATTAN GMATOFFICIAL SOLUTION: You can manipulate the original compound inequality as follows, making sure to perform each manipulation on every term: 1 > 1 - ab > 0 0 > -a b > -1 Subtract 1 from all three terms. 0 < ab < 1 Multiply all three terms by -1 and flip the inequality signs. Therefore 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. Therefore, the correct answer is (D). #### D QUESTION:If two numbers are in the ratio 2:3. If 10 is subtracted from both of the numbers then the ratio becomes 2:4 then find the biggest number? options: A)20 B)22 C)27 D)28 E)30 SOLUTION:Given Ratio => 2:3 2x - 10 : 3x - 10 = 2 : 4 4[2x - 10] = 2[3x - 10] 8x - 40 = 6x - 20 8x - 6x = 40 - 20 x = 10 Then biggest number is = 3x 3x = 30 Ans = E #### E QUESTION:A fruit seller had some oranges. He sells 20% oranges and still has 380 oranges. How many oranges he had originally? options: A)475 B)700 C)220 D)400 E)None of these SOLUTION:Explanation : He sells 20% of oranges and still there are 380 oranges remaining => 80% of oranges = 380 ⇒ (80 × Total Oranges)/100 = 380 ⇒ Total Oranges/100 = 4.75 ⇒ Total Oranges = 4.75 × 100 = 475 Answer : Option A #### A QUESTION:If a positive odd integer N has p positive factors, how many positive factors will 3N have ? options: A)p B)2p C)P+1 D)2p+1 E)Cannot be determined SOLUTION:I have added some extra text to make this question more GMAT-like: Let's TEST some values of N Try N = 3 The factors of 3 are {1, 3}. Here, p =2 So, 2N = (2)(3) = 6 The factors of 6 are {1, 2, 3, 6}. So, we have a total of4 Now check the answer choices: A) p =2No good. We want an output of4. ELIMINATE B) 2p = (2)(2) = 4. PERFECT! KEEP B C) P+1 =2+ 1 = 3 No good. We want an output of4. ELIMINATE D) 2p+1 = (2)(2) + 1 = 5 No good. We want an output of4. ELIMINATE E) Cannot be determined. POSSIBLE. KEEP E Let's TEST another value of N Try N = 7 The factors of 7 are {1, 7}. Here, p =2 So, 2N = (2)(7) = 14 The factors of 14 are {1, 2, 7, 14}. So, we have a total of4 Now check the REMAINING answer choices: B) 2p = (2)(2) =4. PERFECT! KEEP B E) Cannot be determined. POSSIBLE. KEEP E Let's TEST one more (non-prime) value of N Try N = 9 The factors of 9 are {1, 3, 9}. Here, p =3 So, 2N = (2)(9) = 18 The factors of 18 are {1, 2, 3, 6, 9}. So, we have a total of6 Now check the REMAINING answer choices: B) 2p = (2)(3) =6. PERFECT! KEEP B E) Cannot be determined. POSSIBLE. KEEP E At this point, it SEEMS LIKELY that the correct answer is C #### C QUESTION:A certain culture of bacteria quadruples every hour. If a container with these bacteria was half full at 8:00 a.m., at what time was it one-eighth full? options: A)9:00 a.m. B)7:00 a.m. C)6:00 a.m. D)4:00 a.m. E)2:00 a.m. SOLUTION:To go from one-eighth (1/8) full to half (1/2) full culture of bacteria should quadruple: 1/8*4=1/2, as it quadruples every hour then container was one-eighth full at 8:00 a.m -1 hour = 7:00 a.m. Answer: B. #### B QUESTION:45 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? options: A)80 litres B)90 litres C)120 litres D)170 litres E)None of these SOLUTION:Explanatory Answer To cover a distance of 800 kms using a 800 cc engine, the amount of diesel required = 800/600*45 = 60 litres. However, the vehicle uses a 1200 cc engine and the question states that the amount of diesel required varies directly as the engine capacity. i.e., for instance, if the capacity of engine doubles, the diesel requirement will double too. Therefore, with a 1200 cc engine, quantity of diesel required = 1200/800*60 = 90 litres. Answer B #### B QUESTION:Two cogged wheels of which one has 32 cogs and other 54 cogs, work into each other. If the latter turns 80 times in three quarters of a minute, how often does the other turn in 8 seconds? options: A)22 B)24 C)99 D)27 E)17 SOLUTION:Explanation: Less Cogs more turns and less time less turns Number of turns required=80 × × = 24 times Answer: B) 24 #### B QUESTION:The present ages of three persons are in the proportion of 4 : 7 : 9. Eight years ago, the sum of their ages was 76. Find their present ages. options: A)20,35,45 B)8,20,28 C)16,28,36 D)16,28,46 E)None of these SOLUTION:Let the present ages of three persons be 4K,7K and 9K respectively. (4K - 8) + (7K - 8) + (9K - 8) = 76 20K = 100 K = 5 Therefore, then present ages are 20,35,45. ANSWER:A #### A QUESTION:220% of a number X is 44. What is 44% of X. options: A)8.8 B)8.9 C)6.6 D)7.7 E)None SOLUTION:Solution: Given, 220% of X = 44 Or, X = 20. Thus, 44% of 20 = (44 *20) /100 = 8.8 Answer: Option A #### A QUESTION:Find the largest 7 digit number which is exactly divisible by 88? options: A)9998765 B)9998907 C)9999944 D)9999954 E)9999968 SOLUTION:Largest 7 digit number is 9999999 After doing 9999999 ÷ 88 we get remainder 31 Hence largest 7 digit number exactly divisible by 88 = 9999999 - 31 = 9999968 E #### E QUESTION:A train running at a speed of 36 kmph crosses an electric pole in 12 seconds. In how much time will it cross a 350 m long platform? options: A)44 sec B)49 sec C)42 sec D)47 sec E)None of these SOLUTION:Let the length of the train be x m. When a train crosses an electric pole, the distance covered is its own length. So, x = 12 * 36 * 5 /18 m = 120 m. Time taken to cross the platform = (120 +350)/ 36 * 5/18 = 47 min. ANSWER:D #### D QUESTION:Xavier, Yvonne, and Zelda each try independently to solve a problem. If their individual probabilities for success are 1/4, 2/3 and 5/8, respectively, what is the probability that Xavier and Yvonne, but not Zelda, will solve the problem? options: A)1/16 B)7/8 C)9/64 D)5/64 E)3/64 SOLUTION:P(Xavier will solve)=1/4 P(Yvonne will solve)=2/3 P(Zelda will NOT solve) = 1- 5/8 = 3/8. Now, we need to multiply all this Ps to find an answer: p= (1/4)*(2/3)*(3/8) = 1/16. Ans. A. #### A QUESTION:Pipe 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? options: A)1.5 B)2 C)2.5 D)3 E)3.5 SOLUTION:The part filled by A + B + C in 1 hour = 1/6 + 1/4 + 1/12 = 12/24 = 1/2 All the three pipes together will fill the tank in 2 hours. The answer is B. #### B QUESTION:The probability that a number selected at random from the first 50 natural numbers is a composite number is? options: A)17/29 B)17/21 C)17/22 D)17/29 E)17/25 SOLUTION:The number of exhaustive events = 50C1 = 50. We have 15 primes from 1 to 50. Number of favourable cases are 34. Required probability = 34/50 = 17/25. Answer: E #### E QUESTION:If the product of the integers a, b, c, and d is 1,155 and if a > b > c > d > 1, then what is the value of a – d? options: A)2 B)8 C)10 D)11 E)14 SOLUTION:1155 = 3 * 5 * 7 * 11 a = 11 d = 3 a - d = 8 Answer is B #### B QUESTION:How 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? options: A)5 B)4 C)20 D)25 E)30 SOLUTION:Since each desired number is divisible by 5, so we must have 5 at the unit place. So, there is 1 way of doing it. The tens place can now be filled by any of the remaining 5 digits (2, 3, 6, 7, 9). So, there are 5 ways of filling the tens place. The hundreds place can now be filled by any of the remaining 4 digits. So, there are 4 ways of filling it. Required number of numbers = (1 x 5 x 4) = 20. ANSWER C #### C QUESTION:Bookman purchased 55 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 360, how many paperback copies were sold? options: A)8 B)10 C)12 D)19 E)16 SOLUTION:The bookman had 10 hardback ad 55-10=45 paperback copies; 14 copies were sold, hence 55-14=41 copies were left. Let # of paperback copies left be p then 10p+20(41-p)=560 --> 10 p=260 --> p=26 # of paperback copies sold is 45-26=19 Answer: D #### D QUESTION:The compound and the simple interests on a certain sum at the same rate of interest for two years are Rs.11730 and Rs.10200 respectively. Find the sum. options: A)33498 B)17000 C)2665 D)28876 E)313 SOLUTION:The simple interest for the first year is 10200/2 is Rs.5100 and compound interest for first year also is Rs.5100. The compound interest for second year on Rs.5100 for one year So rate of the interest = (100 * 1530)/ (5100 * 1) = 30% p.a. So P = (100 * 10200)/ (30 * 2) = Rs.17000 Answer:B #### B QUESTION:In 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 ? options: A)160 B)170 C)175 D)195 E)180 SOLUTION:Suppose the man works overtime for x hours. Now, working hours in 4 weeks = (5 x 8 x 4) = 160. 160 x 2.40 + x x 3.20 = 432 3.20x = 432 - 384 = 48 x = 15. Hence, total hours of work = (160 + 15) = 175. ANSWER :C #### C QUESTION:A trader bought a car at 20% discount on its original price. He sold it at a 40% increase on the price he bought it. What percent of profit did he make on the original price? options: A)18% B)22% C)12% D)92% E)14% SOLUTION:Original price = 100 CP = 80 S = 80*(140/100) = 112 100 - 112 = 12% Answer: C #### C QUESTION:Find 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 options: A)2:0 B)2:3 C)2:1 D)2:2 E)2:8 SOLUTION:By the rule of alligation: Cost of 1 kg rice of 1st kind Cost of 1 kg rice of 2nd kind Required ratio = 60 : 90 = 2 : 3 Answer: B #### B QUESTION:Jack 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? options: A)3/14 B)1/7 C)0 D)1/2 E)12/21 SOLUTION:METHOD-1 Probability that the number on first die is 7 = 0 Probability that the number on Second die is 7 = 1/7 [Because 1 out of 7 faces is 7] Probability that Both Dice result in odd numbers = (0)*(1/7) = 0 Answer: Option C #### C QUESTION:What is the perimeter of a square with area 9p^2/25 ? options: A)3p/4 B)3p^2/4 C)12p/5 D)3p^2 E)4p/3 SOLUTION:Area of square, (side)^2 = (3p/5)^2 Therefore side of the square = 3p/5 Perimeter of square = 4*side = 4* (3p/5) = 12p/5 Answer is C. #### C QUESTION:An oratorical society consists of six members, and at an upcoming meeting, the members will present a total of four speeches. If no member presents more than two of the four speeches, in how many different orders could the members give speeches? options: A)720 B)1080 C)1170 D)1470 E)1560 SOLUTION:You need to remember that of the 3 people, 1 is going twice and two are going once. Since one of the 3 is going once, there are 3C1 possibilities for the double speaker. So, to convert your work to the correct answer, you need to multiply: 240 * 3C1 = 240 * 3 = 720. ANS:A #### A QUESTION:A 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 G will the work get over? options: A)60 B)70 C)G=75 D)G=80 E)100 SOLUTION:We can also use the concept of man-days here 100 days -->10men so the job includes 100*10=1000 man-days After 20 days 1/4 of Job is completed so 1/4 X 1000 man-days=250 man-days Job is done Now the Balance Job=1000-250=750 man-days worth of Job Since 2 men are fired so B/L men=8 Therefore Total no. of days of Job=750 man-day/8 days = 375/4=94 days (approx.) Now since this is total and Ques. is asking for additional no. of days, So 94-20=74 days The nearest approx. to answer is 75 Ans: C (75 days) #### C QUESTION:The 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? options: A)2^9 B)2^14 C)2^18 D)2^40 E)2^48 SOLUTION:26 letters in the alphabet, 26*2 = 52 letters, since the password is case-sensitive. Accounting for possibilities of the other special characters we have; 26+26+10+1+1 = 64, or 2^6 possibilities per character of the password. Total number of possible combinations: (2^6)^8 = 2^48 ANSWER:E #### E QUESTION:A dishonest dealer professes to sell his goods at Cost Price but still gets 30% profit by using a false weight. What weight does he substitute for a kilogram? options: A)769 1/7 grams B)769 3/13 grams C)769 8/3 grams D)769 1/3 grams E)769 1/13 grams SOLUTION:If the cost price is Rs.100, then to get a profit of 30%, the selling price should be Rs.130. If 130kg are to be sold, and the dealer gives only 100kg, to get a profit of 30%. How many grams he has to give instead of one kilogram(1000 gm). 130 gm ------ 100 gm 1000 gm ------ ? (1000 * 100)/130 = 769 3/13 grams. Answer:B #### B QUESTION:A, 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.2400? options: A)s.800 B)s.810 C)s.820 D)s.900 E)s.920 SOLUTION:2400 * 1/3 = 800 Option A #### A QUESTION:Two alloys A and B are composed of two basic elements. The ratios of the compositions of the two basic elements in the two alloys are 5:3 and 1:2, respectively. A new alloy X is formed by mixing the two alloys A and B in the ratio 4:3. What is the ratio of the composition of the two basic elements in alloy X? options: A)1:1 B)2:3 C)5:2 D)4:3 E)None of these SOLUTION:Explanation : Let,the actual amount of A and B be 4x and 3x respectively. Amount of 1st basic element in the new alloy T is (5/8)*4x + (1/3)*3x = (7x)/2. Similarly, the amount of 2nd basic element in the new alloy T is (3/8)*4x + (2/3)*3x= (7x)/2. So, the ratio of 1st basic element to 2nd basic element is [(7x)/2 ] / [ 7x/2] = 1/1 = 1:1. Answer : A #### A QUESTION:A car traveling at a certain constant speed takes 2 seconds longer to travel 1 kilometer than it would take to travel 1 kilometer at 900 kilometers per hour. At what speed, in kilometers per hour, is the car traveling? options: A)671.5 B)600 C)672.5 D)673 E)773.5 SOLUTION:Many approaches are possible, one of them: Let the distance be 1 kilometer. Time to cover this distance at 900 kilometers per hour is 1/900 hours = 3,600/900 seconds = 4 seconds; Time to cover this distance at regular speed is 900+2=902 seconds = 902/3,600 hours = 1/600 hours; So, we get that to cover 1 kilometer 1/600 hours is needed --> regular speed 600 kilometers per hour (rate is a reciprocal of time or rate=distance/time). Answer: B. #### B QUESTION:What is the probability that a leap year has 53 Sundays and 52 Mondays? options: A)1/9 B)1/8 C)1/3 D)1/7 E)1/2 SOLUTION:A leap year has 52 weeks and two days Total number of cases = 7 Number of favourable cases = 1 i.e., {Saturday, Sunday} Required Probability = 1/7 Answer:D #### D QUESTION:A train 150 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: options: A)22 B)50 C)99 D)288 E)59 SOLUTION:Speed of the train relative to man = (150/10) m/sec = (15) m/sec. [(15) * (18/5)] km/hr = 54 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 54 ==> x = 59 km/hr.Answer: E #### E QUESTION:If a cloth merchant sells ‘a’ metres of cloth for Rs.x, then what is the selling price of ‘b’ metres of cloth? options: A)Rs.(b*x) B)Rs.{(b*x)/a} C)Rs.{(a*b)/x} D)None of these E)Cannot be determined SOLUTION:Explanation: Cost of ‘a’ metres of cloth = Rs.x. Therefore, each metre of cloth costs Rs. (x/a). The cost of ‘b’ metres of cloth = Rs. b*(x/a) = Rs. {(b*x)/a} ANSWER B #### B QUESTION:A 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 ? options: A)115 B)117 C)116 D)114 E)112 SOLUTION:Explanation: Length = 6 m 24 cm = 624 cm Width = 4 m 32 cm = 432 cm HCF of 624 and 432 = 48 Number of square tiles required = (624 x 432)/(48 x 48) = 13 x 9 = 117. Answer IS B #### B QUESTION:The difference between simple and compound interest on Rs. 1600 for one year at 10% per annum reckoned half-yearly is? options: A)8 B)3 C)9 D)4 E)2 SOLUTION:S.I. = (1600 * 10 * 1)/100 = Rs. 160 C.I. = [1600 * (1 + 5/100)2 - 1600] = Rs. 164 Difference = (164 - 160) = Rs.4. Answer:D #### D QUESTION:How much is 90% of 40 is greater than 4/5 of 25? options: A)29 B)776 C)66 D)16 E)99 SOLUTION:(90/100) * 40 – (4/5) * 25 36 - 20 = 16 Answer: D #### D QUESTION:A 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. He was afraid of forgetting his PIN. He wrote down the number 125 in his diary to remember his PIN. He also wrote out the way to calculate 125 : "Multiply the card number by PIN. Divide the product by 997. The remainder is 125". Once, Prafull saw his diary in which Pinaki wrote this number 125. Prafull did a lot of purchasing, as he now knows Pinaki's PIN. What is Pinaki's PIN? options: A)874 B)872 C)876 D)875 E)879 SOLUTION:Explanation : Let, the PIN is x. According to the question, The card number =996 and Remainder =125. Thus, (996 × x)/997=125. =>x= 872. Answer : B #### B QUESTION:A, 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 4 days before the completion of the work. In how many days was the work completed? options: A)32 B)88 C)67 D)11 E)66 SOLUTION:One 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 4 days = 4*(1/24 + 1/30) = 3/10 Remaining work = 7/10 The number of days required for this initial work = 7 days. The total number of days required = 4 + 7 = 11 days. Answer:D #### D QUESTION:A 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? options: A)4 B)5 C)34 D)7 E)9 SOLUTION:7 * 8 : 9 * x = 8:9 => x= 7 Answer:D #### D QUESTION:The number of cars present at a particular time was measured at 4,999 different locations on Tuesday and on Wednesday. The number of locations that had more cars on Wednesday was 20% higher than the number of locations that had more cars on Tuesday. How many of the locations had more cars on Tuesday? options: A)1,159 B)1,333 C)1,860 D)2,160 E)2,272 SOLUTION:The question states that all these 4,999 locations were measured twice, once on each day. It also breaks the 4,999 into two groups, the higher-on-Tuesday locations and the higher-on-Wednesday locations, which we can call T and W. Therefore, we can write two equations: For each of the first and second day count of locations, T + W = 4999 But, for the second day count, W = 1.20 T i.e. for Second day count, T + 1.20T = 4999 i.e. 2.20 T = 4999 i.e. T = 2272 E #### E QUESTION:If a(a + 7) = 18 and b(b + 7) = 18, where a ≠ b, then a + b = options: A) −48 B) −2 C) 2 D) −7 E) 48 SOLUTION:a(a + 7) = 18 and b(b + 7) = 18 => a, b must be integers and if a is -9 or 2, b will be 2 and -9 respectively => a+b = -7 Ans: D #### D QUESTION:If the price of petrol increases by 44, by how much must a user cut down his consumption so that his expenditure on petrol remains constant? options: A)25% B)20% C)16.67% D)33.33% E)None of these SOLUTION:Explanation : let us assume before increase the petrol will be Rs. 100. After increase it will be Rs (100+44) i.e 144. Now, his consumption should be reduced to :- =(144−100)/144 ∗ 100. Hence, the consumption should be reduced to 30.6%. Answer : E #### E QUESTION:Two mechanics were working on your car. One can complete the given job in 5 hours, but the new guy takes eight hours. They worked together for the first two hours, but then the first guy left to help another mechanic on a different job. How long will it take the new guy to finish your car? options: A)7/4 B)4/3 C)14/5 D)10/3 E)17/5 SOLUTION:Rate(1)=1/5 Rate(2)=1/8 Combined = 13/40 Work done in 2 days=13/20 Work left = 7/20 Rate * Time = Work left 1/8 * Time = 7/20 Time=14/5 C #### C QUESTION:Anderson has a phone plan that charges a monthly rate of $50 for the first 1,000 minutes plus $0.25 for each additional minute. Which of the following functions models Anderson’s plan for all m > 1,000, with m as the number of minutes per month and f(m) as the monthly charge? options: A)f(m) = 0.25m B)f(m) = 0.25m + 50 C)f(m) = 0.25m – 200 D)f(m) = 0.25m – 950 E)f(m) = 0.25m + 1,000 SOLUTION:For m > 1,000 — that is, beyond 1,000 minutes of usage — the plan charges a usage fee based on the number of minutes used plus a flat rate of $50. With this information, you can create the following function: f(m) = Usage fee + 50 The usage fee is $0.25 per minute; however, the first 1,000 minutes are already paid for. So the usage fee is 0.25(m – 1,000). Plug this value into the preceding function and simplify: f(m) = 0.25(m – 1,000) + 50 f(m) = 0.25m – 250 + 50 f(m) = 0.25m – 200 correct answer C)f(m) = 0.25m – 200 #### C QUESTION:The 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 6 years hence? options: A)22 B)77 C)70 D)98 E)72 SOLUTION:A + B = 60, A = 2B 2B + B = 60 => B = 20 then A = 40. 6 years, their ages will be 46 and 26. Sum of their ages = 46 + 26 = 72. Answer: E #### E QUESTION:Carmelo and LeBron participate in a six-person footrace on the basketball court during All-Star Weekend. If all six contestants finish (including Charles Barkley) and there are no ties, how many different arrangements of finishes are there in which Carmelo defeats LeBron? options: A)5040 B)2520 C)360 D)120 E)42 SOLUTION:6! = 720 720/2=360 half the time carmelo is in front, vice versa Answer: (C) 360 #### C QUESTION:Vijay's salary is Rs. 21,600 per month. In the first month of the year, he spends 30% of his income on clothing, 20% of the remaining on entertainment and some percentage of the remaining on food. He saves of the amount he spends. Find the percentage of spending on food as a percentage of saving. options: A)180% B)124% C)160% D)154% E)140% SOLUTION:Let monthly income be = x on clothing =.3x on entertainment = .2(.7x) =.14x on food = (.16x)k saving =( .3x .14x .16xk)*13 solving we get k =.31.16 putting the value and we get ...... on the food =.31x ,and saving =.25x %on food / %on saving = .06x/.25x =24% correct answer - B #### B QUESTION:The 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. 28,000 is made? options: A)Rs. 1,10,000 B)Rs. 1,20,000 C)Rs. 1,24,000 D)Rs. 1,21,000 E)None of these SOLUTION:The value of the machine after two years = 0.8 * 0.8 * 1,50,000 = Rs. 96,000 SP such that a profit of Rs. 24,000 is made = 96,000 + 28,000 = Rs. 1,24,000 ANSWER:C #### C QUESTION:The price of a T.V. set worth Rs. 30000 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? options: A)22678 B)26699 C)29000 D)19000 E)26711 SOLUTION:Money paid in cash = Rs. 1000 Balance payment = (30000 - 1000) = Rs. 29000 Answer: C #### C QUESTION:Five 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 four of the carpenters work together at their respective rates ? options: A)11/15 B)3/5 C)11/30 D)47/75 E)5/9 SOLUTION:Farmer A, B, C, and D A's rate: 1/3 job/hour B's rate: 1/4 job/hour C's rate: 1/5 job/hour D's rate: 1/7 job/hour By intuition we know that the three fastest farmers are A B and C. As such (1/3 + 1/4 + 1/5)*(4/5) = ? 47/75 or (D) #### D QUESTION:Sangakara and Ponting select batting by using a dice, but dice is biased. So to resolve,Ponting takes out a coin. What is the probability that coin shows correct option? options: A)1/2 B)1/6 C)1/12 D)6/10 E)3/10 SOLUTION:as coin has only two faces then probability must be 1/2 ANSWER:A #### A QUESTION:Eight children — A, B, C, D, E, F, G and H — are going to sit in eight 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? options: A)600 B)720 C)10080 D)14320 E)14800 SOLUTION:for such questions , we can treat both as one then total person=7.. these 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 ans C #### C QUESTION:The 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? options: A)6 B)5 C)8 D)9 E)4 SOLUTION:S = 4 M = x DS = x + 4 US = x - 4 6/(x + 4) + 6/(x - 4) = 2 x = 8.Answer: C #### C QUESTION:The average weight of 8 person's 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? options: A)80 kg B)85 kg C)90 kg D)100 kg E)110 kg SOLUTION:Total weight increased = (8 x 2.5) kg = 20 kg. Weight of new person = (65 + 20) kg = 85 kg. B) #### B QUESTION:How many cubes of 5cm edge can be cut out of a cube of 20cm edge options: A)36 B)64 C)216 D)484 E)None of these SOLUTION:Explanation: number of cubes=(20 x 20 x 20) / (5 x 5 x 5) = 64 Answer: B #### B QUESTION:The average of runs of a cricket player of 10 innings was 40. How many runs must he make in his next innings so as to increase his average of runs by 4? options: A)87 B)16 C)10 D)84 E)17 SOLUTION:Average after 11 innings = 44 Required number of runs = (44* 11) - (40* 10) = 484- 400 = 84. Answer: D #### D QUESTION:HCF and LCM two numbers are 12 and 396 respectively. If one of the numbers is 36, then the other number is? options: A)36 B)66 C)132 D)264 E)152 SOLUTION:12 * 396 = 36 * x x = 132 ANSWER:C #### C QUESTION:The cross-section of a cannel is a trapezium in shape. If the cannel is 12 m wide at the top and 8 m wide at the bottom and the area of cross-section is 690 sq m, the depth of cannel is? options: A)39 B)28 C)27 D)69 E)71 SOLUTION:1/2 * d (12 + 8) = 690 d = 69 Answer: D #### D QUESTION:The ratio between a two-digit number and the sum of the digits of that number is 4 : 1.If the digit in the unit's place is 3 more than the digit in the ten’s place, what is the number? options: A)47 B)36 C)58 D)25 E)14 SOLUTION:Let the ten's digit be x. Then, unit's digit = (x + 3). Sum of the digits = x + (x + 3) = 2x + 3. Number = l0x + (x + 3) = llx + 3. 11x+3 / 2x + 3 = 4 / 1 => 11x + 3 = 4 (2x + 3) => 3x = 9 => x = 3. Hence, required number = 11x + 3 = 36. Answer is B. #### B <<<Examples ends QUESTION:Two numbers are respectively 20% and 50% more than a third number. The ratio of the two numbers is: options: A)4:5 B)3:5 C)6:8 D)3:5 E)5:4 SOLUTION:third number be x. first no = 120% of x = 6x/5 second no = 150% of x = 3x/2 ratio in first two nos = (6x/5:3x/2)=> 4:5 ANSWER A #### A

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:In the number 10,0AB, A and B represent the tens and units digits, respectively. If 11,0AB is divisible by 55, what is the greatest possible value of B × A? options: A)0 B)5 C)10 D)15 E)25 SOLUTION:You should notice that 55*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=15 (next number won't have 110 as the first 3 digits so we have only two options 0 and 25). Answer: E. ! Please post PS questions in the PS subforum:gmat-problem-solving-ps-140/ Please post DS questions in the DS subforum:gmat-data-sufficiency-ds-141/ No posting of PS/DS questions is allowed in the mainMath forum. D #### D QUESTION:The average of 6 no.'s is 3.95. The average of 2of them is 3.4, while the average of theother 2 is 3.85. What is the average of the remaining 2 no's? options: A)2.3 B)2.5 C)3.5 D)3.6 E)4.6 SOLUTION:Sum of the remaining two numbers = (3.95 * 6) - [(3.4 * 2) + (3.85 * 2)] = 23.70 - (6.8 + 7.7) = 23.70 - 14.5 = 9.20. Required average = (9.2 / 2) = 4.6. E #### E QUESTION:How many days will there be from 26th January,1996 to 15th May,1996(both days included)? options: A)102 B)103 C)111 D)120 E)201 SOLUTION:Explanation : Number of days from 26-Jan-1996 to 15-May-1996 (both days included) = 6(Jan) + 29(Feb) + 31 (Mar) + 30(Apr)+ 15(May) = 111 Answer : Option C #### C QUESTION:Six children — A, B, C, D, E and F— are going to sit in six chairs in a row. The children B & 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? options: A)240 B)720 C)1440 D)4320 E)4800 SOLUTION:for such questions , we can treat both as one then total person=5. these 5 can be arranged in 5! ways.. but within these 5 , one consists of two people who can be arranged in 2 ways BF or FB.. so ans =5!*2=240 ans A #### A QUESTION:One out of every 600 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? options: A)60,000 B)5,000 C)10,000 D)50,000 E)52,000 SOLUTION:20 broken glasses indicates that 10*10= 100 defected bulbs are present. 100 defected bulbs indicates that 100*600= 60,000 light bulbs are present. A is the answer #### A QUESTION:A military garrison in a wild frontier has 600 men who have provisions to last 25 weeks. At the end of 6 weeks they are joined by another 300 men. How long will the provisions last? options: A)13 1/3 B)12 1/3 C)38 D)36 E)12 3/4 SOLUTION:Total provisions=600*25*7=105000 Provisions used for in 6 weeks=6*7*600=25200 remaining provisions=79800 remaining provisions need to be split between 900(600+300) people. Number of provisions per person= 79800/900 we need to find the answer in terms of weeks=(79800/900)/7=38 Answer:C #### C QUESTION:The 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? options: A)600 cm B)800 cm C)400 cm D)1000 cm E)None of these SOLUTION:Area of the square = s * s = 5(125 * 64) => s = 25 * 8 = 200 cm Perimeter of the square = 4 * 200 = 800 cm. ANSWER:B #### B QUESTION:The average weight of a class of 20 boys was calculated to be 58.4 kgs and it was later found that one weight was misread as 56 kg instead of 66 kg. What is the correct weight? options: A)58kgs B)58.85kgs C)58.9kgs D)59kgs E)59.85kgs SOLUTION:Actual total weight is (20X 58.4 - 56 + 66) = 1178 Kgs Actual average weight is 1178/20 = 58.9kgs C #### C QUESTION:8k8 + k88 -------- 1,6t6 If k and t represent non-zero digits within the integers above, what is t? options: A)6 B)7 C)8 D)9 E)17 SOLUTION:8k8 k88 -------- 16t6 Trial 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 t=6. Answer: A. #### A QUESTION:A train passes a man standing on the platform. If the train is 160 meters long and its speed is 72 kmph, how much time it took in doing so? options: A)6 ½ sec B)6 ½ sec C)9 ½ sec D)8 sec E)7 ½ sec SOLUTION:D 8 sec D = 160 S = 72 * 5/18 = 20 mps T = 160/20 = 8 sec #### D QUESTION:If grapes are 92% water and raisins are 20% water, then how much did a quantity of raisins, which currently weighs 10 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.) options: A)25 pounds B)46 pounds C)92 pounds D)100 pounds E)146 pounds SOLUTION:Since 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*10 --> x = 100. Answer: D. #### D QUESTION:A fruit vendor purchased 20 dozens of bananas at Rs. 15 per dozen. But one-fourth of the bananas were rotten and had to be thrown away. He sold two-third of the remaining bananas at Rs. 22.50 per dozen. At what price per dozen should he sell the remaining bananas to make neither a profit nor a loss? options: A)17 B)15 C)11 D)16 E)12 SOLUTION:CP of 20 dozen of bananas = 15 * 20 = Rs. 300 Number of bananas which are rotten = 1/4 * 20 = 5 dozen. SP of two-third of remaining bananas = (2/3 * 15) * 22.5 = Rs. 225 SP of remaining 5 dozens of bananas to make no profit and no loss =(300 - 225) = Rs. 75. SP of 1 dozen bananas = 75/5 = Rs. 15. Answer: B #### B QUESTION:If Leo gains 10 pounds, he will weigh 50% more than his sister Kendra. Currently their combined weight is 160 pounds. What is Leo's current weight? options: A)80 B)86 C)92 D)98 E)104 SOLUTION:L+K = 160 and so K = 160-L L+10 = 1.5K = 1.5(160-L) 2.5L = 230 L = 92 The answer is C. #### C QUESTION:Andrew started saving at the beginning of the year and had saved $180 by the end of the year. He continued to save and by the end of 2 years had saved a total of $540. Which of the following is closest to the percent increase in the amount Andrew saved during the second year compared to the amount he saved during the first year? options: A)11% B)25% C)44% D)56% E)100% SOLUTION:Percent increase in the amount Andrew saved during the second year compared to the amount he saved during the first year. Percentage Change = ( Change in value / Original value ) * 100 Percentage Change = [ (Saving in 2nd year - Saving in 1st year ) / Saving in 1st year ] * 100 Saving in 2nd year + Saving in 1st year = 540 Saving in 2nd year + 180 = 540 Saving in 2nd year = 540 - 180 = 360 Change in Value = 360 - 180 = 180 Original Value = 180 Percentage Increase = (180 / 180 ) * 100 = 100%..... Answer E...... #### E QUESTION:A number when divided by 128 gives a remainder 34, what remainder will be obtained by dividing the same number 19? options: A)7 B)6 C)9 D)10 E)3 SOLUTION:Explanation: 128 + 34 = 162/19 = 10 (Remainder) Answer: D #### D QUESTION:If a and b are both prime numbers greater than 10, which of the following CANNOT be true? I. ab is an even number. II. The difference between a and b equals 117. III. The sum of a and b is even. options: A)I only B)I and II only C)I and III only D)II and III only E)I, II and III SOLUTION:CONCEPT: Prime Numbers greater than 10 will all be ODD I. ab is an even number - Can't be True because both a and b are ODD II. The difference between a and b equals 117 - Can't be True because both a and b are ODD and Difference of two Odd No. must be EVEN III. The sum of a and b is even - This will be True because both a and b are ODD and Sum of two Odd No. must be EVEN ANSWER:B #### B QUESTION:A took 15 seconds to cross a rectangular field diagonally walking at the rate of 52 m/min and B took the same time to cross the same field along its sides walking at the rate of 68m/min. The area of the field is? options: A)33 B)60 C)88 D)27 E)26 SOLUTION:Explanation: length of the diagonal = 52*(15/60) =13m sum of length and breadth = 68*(15/60) = 17m \inline {\color{Black}\sqrt{l^{2}+b^{2}}=13 \; or\; l+b=17 } area =lb = 1/2[(2lb)] = 1/2[(l+b)² - (l²+b²)] = 1/2[17² -169] =1/2*120 = 60 sq meter Answer: B) 60 #### B QUESTION:If M is the least positive integer that is divisible by every integer from 4 to 12 inclusive, then M/11 is = options: A) 40320 B) 27720 C) 20160 D) 6720 E) 2520 SOLUTION:The integer should be divisible by: 4, 5, 6, 7, 8, 9, 10, 11 and 12, that is 2^2, 5, 2*3, 7, 2^3, 3^2, 2*5, 11, 3*2^2. The least common multiple of these integers is the product of 11, 7, 5, 3^2 and 2^3. Then, M/11 is (11 * 7 * 5 * 3^2 * 2^3)/11 = 7*5*9*8 = 2520. Answer: E. #### E QUESTION:A 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 35% impurities to the product. Find the net profit percentage of the dealer? options: A)44% B)40% C)68.75% D)56.25% E)36% SOLUTION:The dealer uses weight which is 20% less than the real weight. or (1- 1/5) or 4/5 of real weight. It means that he is selling $4 worth of product for $5. The dealer then further added 35% impurities to the product. It means that he is selling $5 worth of product for $6.75. So his profit is $6.75-$4 = $2 and his profit percent is (2.75/4)*100 = 68.75% Answer:- C #### C QUESTION:A present value of a machine is $400. Its value depletiation rate is 25% per annum then find the machine value after 2 years? options: A)$125 B)$100 C)$200 D)$215 E)$225 SOLUTION:P= $400 R = 25% T = 2 years Machine value after 2 years = P[(1-R/100)^T] =400*3/4 * 3/4 =$225 approximately Answer is E #### E QUESTION:If x:y=9:4 then (7x-3y) : (7x+3y)=? options: A)51:76 B)6:13 C)51:75 D)51:76 E)None of these SOLUTION:Explanation: x/y = 9/4 (Given) (7x − 3y)/(7x + 3y) 7(x/y) − 3/7(x/y)+3 ( on dividing Nr and Dr by y) (7(9/4) − 3)/(7(9/4) + 3) (63/4 − 3/1)/(63/4 + 3/1) [(63 − 12)/4]/[(63 + 12)/4] = 51/75 (7x-3y) : (7x+3y) = 51:75 Answer: Option C #### C QUESTION:The average of first 10 odd numbers is? options: A)22 B)10 C)98 D)66 E)88 SOLUTION:Sum of 10 odd no. = 100 Average = 100/10 = 10 Answer:B #### B QUESTION:Envelopes 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 $7.60? options: A)426 B)430 C)443 D)470 E)486 SOLUTION:I think first we should see in what group envelopes value less, so that we can buy as many as we can with a specific amount of money: -the 100 pack costs 1.5$, meaning 0.015$ per envelope -the 50 pack costs 1$, meaning 0.02$ per envelope -the single envelope costs 0.03$ per envelope Thus, 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. Having 7.6$, we can buy as many as 4 packs of 100 (4 x 1.5$ = 6$). We then have 1.6 $ left. so we buy 1 pack of 50 for 1$. We now have 0.6$ left, so we buy 20 individual envelopes. If we add up the numbers, we get 400+50+20=470 envelopes. Answer D #### D QUESTION:Find the fourth proportional to 2.8 , 3.4 and 5.2? options: A)5.98 B)6.14 C)6.29 D)6.31 E)5.64 SOLUTION:Formula = fourth proportion =(b x c)/a a=2.8 , b=3.4 and c=5.2 (3.4 x 5.2)/2.8=6.31 D #### D QUESTION:A basketball coach is choosing her starting lineup from a team of 11 girls. 7 of the girls are post players and 4 are guards. If she chooses 3 post players and 2 guards, how many different lineups can be made? options: A)210 B)220 C)240 D)260 E)270 SOLUTION:(7c3)*(4c2) [7!/(3!*4!)]*[4!/(2!*2!)] 35*6 210 A #### A QUESTION:A train travelling at a speed of 75 mph enters a tunnel 31/2 miles long. The train is 1/4 mile long. How long does it take for the train to pass through the tunnel from the moment the front enters to the moment the rear emerges? options: A)2.5 min B)3 min C)3.2 min D)3.5 min E)4 min SOLUTION:Total distance = (7/2 + 1/4) miles = 15/4 miles time taken = 15/4*75 hrs =1/20 hrs = 3 min ANSWER B #### B QUESTION:One train is traveling 72 kmph and other is at 10 meters a second. Ratio of the speed of the two trains is? options: A)5:4 B)5:6 C)2:1 D)5:4 E)5:1 SOLUTION:72 * 5/18 = 10 20:10 => 2:1 Answer: C #### C QUESTION:How many different eight letter words can be formed (the words need not be meaningful) using the letters of the word MEDITERRANEAN such that the first letter is E and the last letter is R? options: A)59 B)11!/(2!*2!*2!) C)56 D)76 E)11!/(3!*2!*2!*2!) SOLUTION:E- -R We are left with the following 11 letters: {M, D, I, T, R, EE, AA, NN} out of which 8 are distinct: {M, D, I, T, R, E, A, N}. We should consider two cases: 1. If the two middle letters are the same, we'd have 3 words: EEER, EAAR and ENNR. 2. If the two middle letters are distinct, then we are basically choosing 2 letters out of 8 when the order of the selection matters, so it's 8P2 = 56. Total = 56 + 3 = 76. Answer: D. #### D QUESTION:At the end of three years what will be the compound interest at the rate of 10% p.a. on an amount of Rs.20000? options: A)6620 B)9278 C)2782 D)5772 E)5286 SOLUTION:A = 20000(11/10)3 = 26620 = 20000 ---------- 6620 Answer: A #### A QUESTION:Agatha 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? options: A) 32 B) 30 C) 29 D) 28 E) 27 SOLUTION:5n + 10m = 460 n > m Pick an easy number to work with. suppose n=30. Then you have 150. You need another 310 and that means you need m=31 which is greater than n. Therefore, n > 30. The only answer choice where n> 30 is if n = 32. A is the answer. #### A QUESTION:A 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 12 miles per gallon, and from Town B to Town C, the car averaged 14 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? options: A)13 B)13.5 C)14 D)14.5 E)15 SOLUTION:Ans is E Given d_ab = 2*d_bc let d_ab = d and d_bc = x so d=2x for average miles per gallon = (d+x)/((d/12)+(x/14)) = 15 (formula avg speed = total distance/ total time) #### E QUESTION:A dealer purchased an article at 3/4 of its list price and sold 50% more than the list price. Find his gain percent? options: A)120% B)190% C)100 percent D)200% E)101% SOLUTION:MP = 100 CP = 75 SP = 150 ------ 75 ---- 75 100 ---- ? => 100% Answer:C #### C QUESTION:A 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? options: A)12/489 B)12/452 C)12/455 D)12/429 E)12/292 SOLUTION:Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles. When three marbles are drawn, the probability that one is yellow and two are red = (²C₁)(⁴C₂)/¹⁵C₃ = (2 * 4 * 3 * 3 * 2)/(1 * 2 * 15 * 14 * 13) = 12/455 Answer: C #### C QUESTION:A 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? options: A)15/56 B)41/56 C)13/28 D)15/28 E)5/14 SOLUTION:The 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. Ways to select 6 out of total 8 = 8C6 Ways to select 4 out of 5 white balls = 5C4 Ways to select 2 out of 3 blue balls = 3C2 Thus the required probability = (5C4*3C2)/8C6 = 15/28. D is thus the correct answer. #### D QUESTION:A 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 210 items for $150 each, what will her monthly salary be? options: A)$1,500 B)$1,800 C)$2,100 D)$2,500 E)$2,800 SOLUTION:Ans : 1000+ 7.5 % * 150 * (210-50) = $ 2800 ANSWER:E #### E QUESTION:Listed below are the mean temperatures measured in the Tokharian desert in a certain month. What is the median temperature E in that particular month? Mean Temp (C°) No. of days 29 --------------------> 5 30 --------------------> 11 31 --------------------> 8 32 --------------------> 6 options: A)29 B)30 C)30.5 D)31 E)32 SOLUTION:to find out median===>they must be arranged in ascending order. 29 29 29...(5 times)30 30 30 30.....(11 times)31 31 31.....(8 times)32 32 32 .....(6 times) total days=5+11+8+6=30 therefore 30 numbers ...median E will be==>mean of 15 and 16 th place temperature===>(30+30)/2=30 hence B #### B QUESTION:In 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? options: A)39 B)24 C)28 D)26 E)30 SOLUTION:x x+4 x+8 x+12 x+16 x+20 x+24 x+28 x+32 x+36 10x+180=340 10x=160 x=16 3rd question = x+8 = 16+8 = 24 Answer B #### B QUESTION:A retailer buys 100 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 % ? options: A)110 B)175 C)212 D)218 E)220 SOLUTION:let the market price of each pen be $1 then, Cost Price of 100 pens = $ 36 Selling Price of 100 pens =99% of $100=$ 99 profit %=((63*100)/36) %=175% Answer B #### B QUESTION:Ifaequals the sum of the even integers from 2 to 60, inclusive, andbequals the sum of the odd integers from 1 to 59, inclusive, what is the value of a - b ? options: A)1 B)10 C)30 D)20 E)21 SOLUTION:This is a solution from Beatthegmat: even numbers: (60-2)/2 + 1 = 30 even integers. (60+2)/2 = 31 is the average of the even set. sum = avg*(#of elements) = 31*30 = 930 = a odd numbers: (59-1)/2 + 1 = 30 odd integers. (59+1)/2 = 30 is the average of the odd set. sum = avg*(#of elements) = 30*30 = 900 = b a-b = 930 - 900 = 30. Answer : C #### C QUESTION:On a map the distance between two mountains is 310 inches. The actual distance between the mountains is 136 km. Ram is camped at a location that on the map is 34 inch from the base of the mountain. How many km is he from the base of the mountain? options: A)14.83 B)14.81 C)14.91 D)14.82 E)14.12 SOLUTION:Explanation: Since 310 inch = 136 km So 1 inch = 136/310 km So 34 inch = (136 × 34)/ 310 = 14.91 km Answer: C #### C QUESTION:Find 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 options: A)2:0 B)2:3 C)2:1 D)2:2 E)2:8 SOLUTION:By the rule of alligation: Cost of 1 kg rice of 1st kind Cost of 1 kg rice of 2nd kind Required ratio = 60 : 90 = 2 : 3 Answer: B #### B QUESTION:Given 2 numbers; 16 and x, the LCM and HCF of both numbers is 144 and 2 respectively. Find x? options: A)16 B)28 C)15 D)13 E)18 SOLUTION:HCF x LCM = Product of Numbers 2 x 144 = 16 x x x = (2 x 144) / 16 x = 18 ANSWER : E #### E QUESTION:A 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? options: A)28.5 B)46 C)30 D)Data inadequate E)None of these SOLUTION:Giving no discount to customer implies selling the product on printed price. Suppose the cost price of the article is 100. Then printed price = 100×(100+38.7)/(100−5) =146 Hence, required % Profit = 146 – 100 = 46% Answer B #### B QUESTION:A man starts walking at 3 pm . he walks at a speed of 4 km/hr on level ground and at a speed of 3 km/hr on uphill , 6 km/hr downhill and then 4 km/hr on level ground to reach home at 9 pm. What is the distance covered on one way? options: A)12 B)66 C)77 D)88 E)91 SOLUTION:lets us consider t1 = time taken on level road. t2 = uphill. t3 = down hill; the distance traveled uphill and down hill same so t2*3 = 6*t3; => t2 = 2t3;---> (1) total time = 2*t1 + t2 + t3 = 6 hours ---> (2) 2t1+3t3 = 6 -->(3) total distance = 2*(4t1) + 3*t2+ 6*t3 ---> (4) substitute (1) in (4) 8t1 + 12t3 => 4(2t1+3t3) then from (3) the total distance will become 4*6= 24 => one way distance = 12km Answer: A #### A QUESTION:How much is 80% of 60 is greater than 4/5 of 25? options: A)15 B)28 C)16 D)12 E)73 SOLUTION:(80/100) * 60 – (4/5) * 25 48 - 20 = 28 Answer: B #### B QUESTION:There 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 T that the number of men is equal to that of women? options: A)T=18/35 B)16/35 C)14/35 D)13/35 E)12/35 SOLUTION:METHOD- 1: Favorable outcomes (i.e. No. of Men= No. of Women =2) = 4C2 * 4C2 = 6*6 = 36 Total ways of selecting 4 out of 8 Students = 8C4 = 8! / (4! * 4!) = 70 Probability = 36/70 = 18/35 A METHOD-2:Also see the mistake done by the person who posted this question Probability of First selected person being Man = 4/8 Probability of Second selected person being Man = 3/7 Probability of First selected person being Woman = 4/6 Probability of Second selected person being Woman = 3/5 i.e. Probability = (4/8)*(3/7)*(4/6)*(3/5) *[4!/(2!*2!)]= 18/35 The important part for the readers is to understand the reason of multiplying[4!/(2!*2!)]here When 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 The 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! A #### A QUESTION:If 0.75: x :: 5:9, then x is equal to: options: A)1.12 B)1.16 C)1.2 D)1.35 E)None of these SOLUTION:Explanation: (x * 5) = (0.75 *9) X=6.75/5 = 1.35 Answer: D #### D QUESTION:The number of students in 3 classes is in the ratio 2:3:4. If 12 students are increased in each class this ratio changes to 8:11:14. The total number of students in the three classes in the beginning was options: A)162 B)108 C)96 D)54 E)None SOLUTION:Solution: Let the number of students in the classes be 2x, 3x and 4x respectively; Total students = 2x+3x+4x = 9x. According to the question, (2x+12)/(3x+12) = 8/11 24x+96 = 22x+132 Or, 2x = 132-96 Or, x = 36/2 = 18 Hence, Original number of students, 9x = 9*18 = 162. Answer: Option A #### A QUESTION:A is 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? options: A)10 days B)77 days C)66 days D)55 days E)54 days SOLUTION:A can do the work in 30/2 i.e., 15 days. A and B's one day's work = 1/15 + 1/30 = (2 + 1)/30 = 1/10 So A and B together can do the work in 10 days. Answer: A #### A QUESTION:A 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? options: A)230 B)783 C)291 D)112 E)221 SOLUTION:Relative speed = 120 + 80 = 200 km/hr. = 200 * 5/18 = 500/9 m/sec. Let the length of the other train be x m. Then, (x + 270)/9 = 500/9 => x = 230. Answer:A #### A QUESTION:If 1+2+3+...+n=n (n+1), then 3 (1+3+5+....+79)=? options: A)4500 B)4250 C)4350 D)4800 E)4150 SOLUTION:Explanation : To solve this use the formula of AP, Sn= (n/2)(a+l) ................(1) To find n, use => Tn= a+(n-1)d => 79=1+(n-1)2 => n=40 Use value of n in (1) then, Sn = (40/2)(1+79) = 1600 Ans:- 3(Sn) = 4800 Answer : D #### D QUESTION:In a garden, there are yellow and green flowers which are straight and curved. If the probability of picking a green flower is 2/3 and picking a straight flower is 1/2, then what is the probability of picking a flower which is yellow and straight options: A)1/6 B)1/8 C)1/4 D)3/4 E)7/8 SOLUTION:Good question. So we have a garden where all the flowers have two properties: color (green or yellow) and shape (straight or curved). we're told that 2/3 of the garden is green, so, since all the flowers must be either green or yellow, we know that 1/3 are yellow. We're also told there is an equal probability of straight or curved, 1/2. We want to find out the probability of something being yellow and straight, Pr( Yellow and Straight ). So 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) = 1/3 * 1/2 = 1/6, or A. #### A QUESTION:Two pipes can fill a tank in 10 hours & 12 hours respectively. While 3rd pipe empties the full tank n 20 hours. If all the three pipes operate simultaneously,in how much time will the tank be filled? options: A)6 hrs 43 min B)2 hrs 25 min C)7 hrs 30 min D)6 hrs 32 min E)7 hrs 10 min SOLUTION:tank filled in 1 hr = 1/10 + 1/12 - 1/20 = 8/60 = 2/15 part so full tank is filled in 15/2 hrs = 7 hr 30 min.. ANSWER:C #### C QUESTION:Two trains start from P and Q respectively and travel towards each other at a speed of 50 km/hr and 40 km/hr respectively. By the time they meet, the first train has traveled 100 km more than the second. The distance between P and Q is? options: A)767 km B)975 km C)678 km D)900 km E)546 km SOLUTION:At the time of meeting, let the distance traveled by the second train be x km. Then, distance covered by the first train is (x + 100) km. x/40 = (x + 100)/50 50x = 40x + 4000 => x = 400 So, distance between P and Q = (x + x + 100)km =900 km. Answer: D #### D QUESTION:Excluding stoppages, the speed of a train is 45 kmph and including stoppages it is 34 kmph. Of how many minutes does the train stop per hour? options: A)E982 B)27 C)12 D)14.6 E)28 SOLUTION:Explanation: T = 11/45 * 60 = 14.6 Answer: Option D #### D QUESTION:Two trains 141 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? options: A)7.16 B)7.59 C)7.12 D)7.15 E)7.11 SOLUTION:T = (141 + 165)/ (80 + 65) * 18/5 T = 7.59 Answer: B #### B QUESTION:There are 136 employees in Company X. If the number of employees who birth in June is the greatest, what is the least possible number of the employees in the company who birth in June? options: A)15 B)11 C)12 D)13 E)14 SOLUTION:IMO 15 Take each answer choice and substract it from 136 and the divided this with 11. A #### A QUESTION:Operation#is defined as adding a randomly selected two digit multiple of 10 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? options: A)0% B)10% C)20% D)30% E)40% SOLUTION:Any multiple of 10 is even. Any two-digit prime number is odd. (even+odd)/2 is not an integer. Thus # does not yield an integer at all. Therefore P=0. Answer: A. #### A QUESTION:Five 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 14 years? options: A)30 B)34 C)40 D)50 E)60 SOLUTION:Explanation : (A + B), five years ago = (15 * 2) = 30 years. (A+B), now = (30+5*2)years=40 years. (A + B + C), now = (20 x 3) years =60 years. C, now = (60 - 40) years = 20 years. C, after 14 years = (20 + 14) years =34 years. Answer : B #### B QUESTION:Each of the 20 boxes in a certain shipment weighs either 10 pounds or 20 pounds, and the average (arithmetic mean) weight of the boxes in the shipment is 18 pounds. If the average weight of the boxes in the shipment is to be reduced to 15 pounds by removing some of the 20-pound boxes, how many 20-pound boxes must be removed? options: A)10 B)12 C)14 D)16 E)18 SOLUTION:If the average of 10-pound and 20-pound boxes is 18, the ratio of 10-pound boxes:20-pound boxes is 1:4. So out of 20 boxes, 4 are 10-pound boxes and 16 are 20-pound boxes. If the average of 10 and 20-pound boxes is to be 15, the ratio of 10-pound boxes:20-pound boxes should be 1:1. The number of 10 pound boxes remains the same so we still have 4 of them. To get a ratio of 1:1, the number of 20-pound boxes must be 4. We need to remove 12 of the 20-pound boxes. The answer is B. #### B QUESTION:The length of the longest rod that can fit in a cubical room of 4 m side is? options: A)3:8 B)3:1 C)3:0 D)3:2 E)3:5 SOLUTION:3:1 Answer:B #### B QUESTION:A train running at the speed of 36 km/hr crosses a pole in 9 seconds. What is the length of the train? options: A)286 B)278 C)90 D)150 E)287 SOLUTION:Speed=(36 * 5/18) m/sec = (10) m/sec Length of the train = (Speed x Time) = (10 * 9) m = 90 m. Answer:C #### C QUESTION:A can be divided by 11 with no remainder. Which of the following expressions could be divided by 11 leaving a remainder of 1? options: A)A-20. B)A-12. C)A-9. D)A-10. E)A-13. SOLUTION:We could use the following logic: since A is a multiple of 11, we could very well say A = 11K (where K is 1,2...n). The condition here should now be 11K + 1 = <operation> such that it gives us an integer 11k +1 = A -20 => A = 11K + 21 Not divisible by 11 11K +1 = A -12 => A = 11K + 31 Not Divisible by 11 11K +1 = A -9 => A = 11K + 10 Not Divisible by 11 11K +1 = A -10 => A = 11K + 11Divisible by 11 11K +1 = A -13 => A = 11K + 14 Not Divisible by 11 Answer therefore is A -10 (D) #### D QUESTION:In 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 options: A)37 B)38 C)39 D)40 E)41 SOLUTION:let present age of A be a and B be b a+10 = 2*(b-10) => 2b-a = 30 ......(i) a = b+9 =>2b-b-9 = 30 b=39 so the present age of b is 39 years ANSWER:C #### C <<<Examples ends QUESTION:The price of an item is discounted 10 percent on day 1 of a sale. On day 2, the item is discounted another 15 percent, and on day 3, it is discounted an additional 20 percent. The price of the item on day 3 is what percentage of the sale price on day 1? options: A)28% B)40% C)68% D)70% E)72% SOLUTION:Let initial price be 1000 Price in day 1 after 10% discount = 900 Price in day 2 after 15% discount = 765 Price in day 3 after 20% discount = 612 So, Price in day 3 as percentage of the sale price on day 1 will be = 612/900*100 => 68% Answer will definitely be (C) #### C

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:When 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 36. options: A)5 B)4 C)12 D)32 E)35 SOLUTION:First, 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. Now, 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 n = 5a + 1 e.g. 5 + 1, 10 + 1, 15 + 1, 20 + 1, 25 + 1, 30 + 1, 35 + 1 etc and n = 7b + 1 e.g. 7 + 1, 14 + 1, 21 + 1, 28 + 1, 35 + 1 etc So when it is divided by the LCM, 35, it will give 1 as remainder (as is apparent above) Next, 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 n = 5a + 1 and n = 7b + 3 Now, 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. Therefore, 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) Now this question is exactly like the question above. So when you divide n by 36, remainder will be -4 i.e. n will be 4 less than a multiple of 36. So you must add 5 to n to make it a multiple of 36 A #### A QUESTION:Insert the missing number 3, 7, 6, 5, 9, 3, 12, 1, 15, ... options: A)18 B)33 C)-1 D)3 E)-3 SOLUTION:3, 7, 6, 5, 9, 3, 12, 1, 15, ... has two different series 1) 3, 6, 9, 12, 15..... 2) 7, 5, 3, 1, ..... -1 is the next number ANSWER:C #### C QUESTION:Two cards are drawn together from a pack of 52 cards. The probability that one is a spade and one is a heart, is: options: A)13/109 B)13/162 C)13/111 D)13/102 E)13/112 SOLUTION:Let S be the sample space. Then, n(S) = \inline {\color{Black}52C_{2} }=(52 x 51)/(2 x 1) = 1326. Let E = event of getting 1 spade and 1 heart. n(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. P(E) = n(E)/n(S) = 169/1326 = 13/102. Answer: D) 13/102 #### D QUESTION:Using all the letters of the word "LAKSHMI", how many words can be formed, which begin with L and end with I? options: A)111 B)145 C)110 D)119 E)120 SOLUTION:There are five letters in the given word. Consider 7 blanks .... The first blank and last blank must be filled with L and I all the remaining three blanks can be filled with the remaining 5 letters in 5! ways. The number of words = 5! = 120. Answer:E #### E QUESTION:A 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.? options: A)30 min B)35 min C)45 min D)50 min E)55 min SOLUTION:there are 9 hours in between 9 a.m. to 6 p.m. 9*5=45 minutes. ANSWER:C #### C QUESTION:Jenna rode her bike to school at 5 kph, but rode home at 15 kph. What was her average speed traveling to and from school? options: A)5 kph B)7 kph C)10 kph D)13 kph E)15 kph SOLUTION:(5 kph +15 kph)/2 =10 kph Correct answer is: C #### C QUESTION:Distance 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? options: A)67.0 km /hr B)67.2 km /hr C)69.0 km /hr D)69.2 km /hr E)None SOLUTION:Solution Required average speed =(2xy / x+y)km/hr = 2 x 84 x 56 /(84 + 56) = (2 x 84 x 85 /140) = 67.2 km/hr. Answer B #### B QUESTION:Find large number from below question The difference of two numbers is 1375. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder options: A)1235 B)1345 C)1678 D)1767 E)1647 SOLUTION:Let the smaller number be x. Then larger number = (x + 1375). x + 1375 = 6x + 15 5x = 1360 x = 272 Large number = 272+1375 = 1647 E #### E QUESTION:If the cost price of 60 boxes is equal to the selling price of 50 boxes, the gain percent is options: A)5 B)10 C)15 D)20 E)25 SOLUTION:Let C.P. of each box be Re. 1. Then, C.P. of 50 boxes = Rs. 50; S.P. of 50 boxes = Rs. 60. Gain % = 10/50 * 100 = 20% Answer:D #### D QUESTION:In the interior of a forest, a certain number of apes equal to the square of one-eighth of the total number are playing and having great fun. The remaining sixteen apes are on a hill and the echo of their shrieks by the adjoining hills frightens them. They came and join the apes in the forest and play with enthusiasm. What is the total number of apes? options: A)32 B)16 C)64 D)80 E)16 or 48 SOLUTION:Let total number be x No in the interior = (x/8)^2 No outside = 16 So : x - (x/8)^2=16 x^2-64x+16*64=0 (x-32)^2=0 x=32 A #### A QUESTION:what is the sum of all 5 digits numbers which can be formed with the digits 0,1,2,3,4 without repetition options: A)2599980 B)2699980 C)2799980 D)2509980 E)2499980 SOLUTION:There is a simplest formula for solving these type of questions when we are using numbers along with 0 for finding sum. i,e........(sum of numbers)*{(n-1)!*(111...........n times)-(n-2)!*(111..........(n-1)times) } so,here by putting the values as, (0+1+2+3+4){(5-1)!*(11111)-(5-2)!*1111} = 10{(4!*11111)-(3!*1111)} = 10{266664-6666} = 2599980 ANSWER:A #### A QUESTION:A no.when divided by 220 gives a remainder 43, what remainder will beobtained by dividingthe same no.17? options: A)2 B)8 C)9 D)11 E)15 SOLUTION:220 + 43 = 263/17 = 8 (Remainder) B #### B QUESTION:In a class, the average age of 28 boys is 12 years and the average of 20 girls is 8 years. what is the average age of the whole class? options: A)10.3 Years B)12.3 Years C)12.6 Years D)13 Years E)15 Years SOLUTION:Total age of 48 students (28X 12+20 X 8) = 496 Average = 496/48 = 10.3 Years A #### A QUESTION:A bag contains 8 red and 3 white balls. One ball is drawn at random. What is the probability that the ball drawn is white? options: A)4/7 B)2/3 C)8/11 D)1/4 E)5/7 SOLUTION:Total number of balls = 8+3 = 11 number of white balls = 8 Probability = 8/11 = 8/11 Answer is C #### C QUESTION:The total number of plums that grow during each year on a certain plum tree is equal to the number of plums that grew during the previous year, less the age of the tree in years (rounded down to the nearest integer). During its 5th year, the plum tree grew 50 plums. If this trend continues, how many plums will it grow during its 6th year? options: A)40 B)42 C)45 D)48 E)54 SOLUTION:1st year : 0-1 (age), we take age = 0 (as the question says that we have to(rounded down to the nearest integer)) 2ndyear : 1-2 (age), we take age = 1 3rd year : 2-3 (age), we take age = 2 4th year : 3-4 (age), we take age = 3 5th year : 4-5 (age), we take age = 4 6th year : 5-6 (age), we take age = 5 Thus for the 5th year = 50, 6th year = 50-5 = 45. The correct answer is C. #### C QUESTION: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: options: A)3:5 B)2:1 C)16:15 D)4:5 E)None of these SOLUTION:Explanation: For an income of Re. 1 in 9% stock at 96, investment = Rs. 96/9 = Rs.32/3 For an income Re. 1 in 12% stock at 120, investment = Rs. 120/12 = Rs. 10. Ratio of investments =(32/3) : 10 = 32 : 30 = 16 : 15. Answer: C #### C QUESTION:If 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 6-letter code words to the number of 5-letter code words? options: A)5 to 4 B)3 to 2 C)2 to 1 D)5 to 1 E)6 to 1 SOLUTION:Number of ways to form 6-letter code: 10!/4! = 10*9*8*7*6*5 Number of ways to form 5-letter code: 10!/5! = 10*9*8*7*6 Ratio: 5 to 1 Answer : D #### D QUESTION:Sandy can do a job in 12 days and Molly can do the same job in 24 days. If they work together, in how many days will they complete the job? options: A)6 B)7 C)8 D)9 E)10 SOLUTION:Sandy can do 1/12 of the job each day. Molly can do 1/24 of the job each day. The combined rate is 1/12 + 1/24 = 1/8 of the job each day. The job will take 8 days. The answer is C. #### C QUESTION:69 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? options: A)20 B)23 C)24 D)25 E)26 SOLUTION:According to the chain rule, M1 x T1 = M2 x T2 Therefore, 69 x 12 x 5 = 30 x 6 x X X = 23 Hence, the number of days = 23. ANSWER:B #### B QUESTION:A, 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? options: A)14700 B)14500 C)14900 D)14300 E)14000 SOLUTION:Total amount invested = 50000 Assume that investment of C =x. Then investment of B =5000+x, Investment of A =4000+5000+x=9000+x x+5000+x+9000+x=50000 ⇒3x+14000=50000 ⇒3x=50000–14000=36000 ⇒x=36000/3=12000 Investment of C =x=12000 Investment of B =5000+x=17000 Investment of A =9000+x=21000 Ratio of the investment of A, B and C =21000:17000:12000 =21:17:12 Share of A = Total profit ×21/50 =35000×21/50=700×21=14700 Answer is A. #### A QUESTION:A 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? options: A)5 hr 30 mins B)7 hr 30 mins C)4hr 30 mins D)2 hr 30 mins E)3 hr 30 mins SOLUTION:Explanation: A tap can fill a tank in 12 hours. Therefore the tap can fill half the tank in 6 hours. One tap take time to fill half of the tank = 6 hrs 4 taps take time to fill half of the tank = 6/4 hrs = 1 hr 30 mins Total time taken to fill the tank = 6 hr+1 hr 30 min = 7 hr 30 mins Answer : B #### B QUESTION:Express a speed of 90 kmph in meters per second? options: A)10 mps B)76 mps C)26 mps D)97 mps E)25 mps SOLUTION:90 * 5/18 = 25 mps Answer:E #### E QUESTION:According to the directions on a can of frozen orange juice concentrate, 1 can of concentrate is to be mixed with 3 cans of water to make orange juice. How many 12 ounce cans of concentrate are required to prepare 160 six-ounce servings of orange juice? options: A)20 B)24 C)28 D)32 E)36 SOLUTION:1 X 12 ounce can of concentrate + 3 X 12 ounce cans of water = 48 ounces of the mixture. 48 ounces of mixture gives (48 / 6 ) = 8 servings. Thus 1 x 12 ounce can of concentrate is used to produce 8 servings of the mixture. To make 160 servings of the mixture, we need 160 / 8 = 20 cans of the concentrate. The answer is A. #### A QUESTION:Two mechanics were working on your car. One can complete the given job in six hours, but the new guy takes 9 hours. They worked together for the first two hours, but then the first guy left to help another mechanic on a different job. How long will it take the new guy to finish your car? options: A)7/4 B)32/9 C)15/4 D)10/3 E)17/5 SOLUTION:Rate(1)=1/6 Rate(2)=1/9 Combined = 5/18 Work done in 2 days=5/9 Work left = 4/9 Rate * Time = Work left 1/8 * Time = 4/9 Time=32/9 B #### B QUESTION:A man buys a cycle for Rs.1400 and sells it at a loss of 18%. What is the selling price of the cycle? options: A)Rs.1148 B)Rs.1160 C)Rs.1190 D)Rs.1202 E)NONE SOLUTION:Solution S.P = 82% of Rs.1400 = Rs.(82/100×1400) Rs.1148. Answer A #### A QUESTION:Rectangle A has sides a and b, and rectangle B has sides c and d. If a/c=b/d=4/5, what is the ratio of rectangle A’s area to rectangle B’s area? options: A)5/4 B)25/16 C)4/5 D)16/25 E)16/5 SOLUTION:The area of rectangle A is ab. c=5a/4 and d=5b/4. The area of rectangle B is cd=25ab/16. The ratio of rectangle A's area to rectangle B's area is ab / (25ab/16) = 16/25. The answer is D. #### D QUESTION:Find the average of all the numbers between 6 and 34 which are divisible by 5 options: A)18 B)20 C)24 D)30 E)40 SOLUTION:Exp. Multiples of 5 between 6 and 34 are 10,15,20,25,30 Average = (10+15+20+25+30)/5 =5(10+30)/2*5 = 40/2 =20 Answer:B #### B QUESTION:Two bus tickets from city A to B and three tickets from city A to C cost Rs. 385 but three tickets from city A to B and two tickets from city A to C cost Rs. 365. What are the fares for cities B and C from A ? options: A)s. 4, Rs. 23 B)s. 13, Rs. 17 C)s. 15, Rs. 14 D)s. 17, Rs. 13 E)s. 65, Rs. 85 SOLUTION:If fares for cities B and C from A are x and y respectively, then 2x+3y=385 or 6x+9y= 1155 3x+2y =365 or 6x+4y= 730 subtracting 5y = 425 y= Rs 85 Hence E. Rs. 65, Rs. 85 ANSWER:E #### E QUESTION:When a merchant imported a certain item, he 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 $94.50, what was the total value of the item? options: A)$2,350 B)$2,850 C)$3,250 D)$3,400 E)$3,750 SOLUTION:Let x be the value in excess of $1,000. 0.07x = 94.5 x = $1,350 The total value was $1,350 + $1,000 = $2,350. The answer is A. #### A QUESTION:When 3 is added to half of one-third of one-fifth of a number, the result is one-fifteenth of the number. Find the number? options: A)32 B)81 C)60 D)27 E)90 SOLUTION:Explanation: Let the number be 3 + 1/2[1/3(a/5)] = a/15 => 3 = a/30 => a = 90 Answer:E #### E QUESTION:In 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? options: A)150 B)100 C)280 D)360 E)496 SOLUTION:Explanation: Let the number of students be x. Then, Number of students above 8 years of age = (100 - 20)% of x = 80% of x. 80% of x = 48 +2/3 of 48 80/100x=80 x=100 Answer: B #### B QUESTION:A family consists of two grandparents, two parents and three grandchildren. The average age of the grandparents is 65 years, that of the parents is 45 years and that of the grandchildren is 8 years. What is the average age of family? options: A)6/7years B)B)31 C)C)30 D)D)33 E)E)35 SOLUTION:Required average = (65 x 2 + 45 x 2 + 8 x 3 )/(2 + 2 + 3) = (130 + 90 + 24)/7 =244/7 = 34 6/7years. Answer is A #### A QUESTION:In Hockey game, one player throws two fair, six-sided die at the same time. If the player receives at least a five or a one on either die, that player wins. What is the probability that a player wins after playing the game once? options: A)1/3 B)4/9 C)5/9 D)2/3 E)3/4 SOLUTION:In Hockey game, Probably the easiest approach would be to find the probability of the opposite event and subtract it from 1: P(win) = 1- P(not win) = 1 - 4/6*4/6 = 5/9. Answer: C. #### C QUESTION:#p is defined as 2p-20 for any number p. What is p, if #(#(#p))=6? options: A)–108 B)–44 C)10 D)16 E)18.25 SOLUTION:#p = 2p-20 --->#(#p) = 2(2p-20)-20 = 4p-60 and thus #(4p-60) = 2(4p-60)-20 = 8p-140 = 6 ---> 8p= 146 ---> p = 18.25, E is the correct answer. #### E QUESTION:A 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 67 ounces of nuts, representing a mixture of both brands, and 15 ounces of the mixture are almonds, how many ounces of Brand Q's Deluxe mixed nuts are used? options: A) 16 B) 20 C) 32 D) 44 E) 48 SOLUTION:lets say x ounces of P is mixed with Q. => 67-x ounces of Q is present in the mixture (as the total = 67 ounces) given total almond weight = 15 ounces (20x/100)+(25/100)(67-x) = 15 => x = 35 => 67-35 = 32 ounces of Q is present in the mixture. Answer is C. #### C QUESTION:In Set T, the average (arithmetic mean) equals the median T. Which of the following must be true? I. Set T consists of evenly spaced numbers. II. Set T consists of an odd number of terms. III. Set T has no mode. IV. None of the above. options: A)I only B)I and II C)II and III D)I, II, and III E)IV only SOLUTION:This is a very good 'trap question'. Consider Set A= { 0,0,0,0 } Mean=Median=Mode=0- Eliminates 1,2 and 3 OR Consider Set B= {1,2,2,3 } Mean=Median=Mode=2- Eliminates 1,2 and 3 If you think that only in 'consecutive integers' the average is equal to the median T you might fall for 'D'. Ans: E #### E QUESTION:Find the least number with which 16200 should be multiplied, to make it a perfect cube. options: A)36 B)48 C)45 D)360 E)55 SOLUTION:16200 = 23 * 34 * 52 A perfect cube has a property of having the indices of all its prime factors divisible by 3. Required number = 32 * 5 = 45. ANSWER:C #### C QUESTION:In 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 150? options: A)15 B)75 C)25 D)18 E)12 SOLUTION:A scores 60 while B score 40 and C scores 30. The number of points that C scores when B scores 100 = (100 * 30)/40 = 25 * 3 = 75. In a game of 100 points, B gives (150 - 75) = 75 points to C. Answer:B #### B QUESTION:In a certain voting district, 40 percent of registered voters live in Town A and the rest live in Town B. In the last election, 70 percent of the registered voters from Town A voted. If equal numbers of registered voters from both towns voted, approximately what percent of the registered voters from Town B voted? options: A)72% B)47% C)42% D)34% E)28% SOLUTION:Town A is 40%, therefore town B must be 60% Town A registered voters:0.70∗0.40=0.28 Town B registered voters: 0.60x=0.28 --> x=28/60 which is a little bit less than 50 percent ANSWER:B #### B QUESTION:Two roads XY and YZ of 15 metres and 20 metres length respectively are perpendicular to each other. What is the distance between X & Z by the shortest route? options: A)35 metres B)30 metres C)24 metres D)25 metres E)None of these SOLUTION:XYZ is a right-angled triangle XZ =√15(2)+20(2)=√=625=25m Answer D #### D QUESTION:A 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 120 km downstream? options: A)60/18 B)30/29 C)60/12 D)60/13 E)30/82 SOLUTION:Speed downstream = 20 + 6 = 26 kmph. Time required to cover 60 km downstream = d/s = 120/26 = 60/13 hours. Answer:D #### D QUESTION:If the two hands in a clock are 15 minutes divisions apart,then the angle between them is options: A)3° B)18° C)24° D)90° E)None of these SOLUTION:In a clock, each minute makes 6° ∴ 15 minutes will make 6 × 15 = 90° Answer D #### D QUESTION:the egg vendor calls on his 1st customer and sells his half his eggs and half an egg.to the 2nd customer he sells half of what he had left and half an egg,and to the 3rd customer he sells half of what he had then left and half an egg.by the way he did not break any eggs.in the end 3 eggs were remainig.how many did he start out with? options: A)21 B)31 C)41 D)51 E)61 SOLUTION:He start out with 31eggs. In the end, he have 3eggs left. So, 3*2 +1= 7 7*2 +1= 15 15*2 +1= 31 31eggs he had initially. ANSWER:B #### B QUESTION:If one-third of one-fourth of a number is 15, then three-tenth of that number is options: A)35 B)15 C)60 D)54 E)57 SOLUTION:Let the number be x. then 1/3 of ¼ of x=15 X=15x12=180 The required number=(3/10)*180=54 ANSWER D 54 #### D QUESTION:In what time a debt of Rs.7920 due may be cleared by immediate cash down payment of Rs.3600 at 1/2% per month options: A)10years B)20years C)30years D)40years E)50years SOLUTION:Explanation: PW=100x Amount/100+(RxT) Answer: B #### B QUESTION:A, 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. options: A)1200 B)1400 C)2660 D)1600 E)1800 SOLUTION:A is a working member and for that, he receive 5% of the profit = 5% of 7400 = 5*7400/100 = 370 Remaining amount = 7400-370 = 7030 Ratio of their investments = 6500*6 : 8400*5 : 10000*3 = 65*6 : 84*5 : 100*3 = 13*6 : 84 : 20*3 = 13*2 : 28 : 20 = 13 : 14 : 10 Share of B in the profit = 7030 * (14/37) = 190*14 = 2660 Answer is C #### C QUESTION:From a pack of 52 cards, two cards are drawn together at random. What is the probability that the one is heart and other two is diamond? options: A)238/5525 B)176/5534 C)253/5523 D)234/5525 E)1/5525 SOLUTION:Solution Let S be the sample space. Then, n(S) = 52C3 = 22100 Let E = event of getting 1 face card. n(E) = number of ways of choosing 1 face card out of 26 =13C1 * 13C2= 13*72 = 936 P(E) = n(E) / n(S) = 936 / 22100 = 234/5525 = 234/5525. Answer D #### D QUESTION:A 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? options: A)2 1/2days B)4 1/2days C)6 1/2days D)7 1/2days E)10 1/2days SOLUTION:The required answer = (12-3)*6 / 12 = 54/12 = 4 1/2days Answer is B #### B QUESTION:For every integer n ≥ 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(99) – g(97)? options: A)98 B)100 C)0 D)99 E)97 SOLUTION:g(99) = 1*3*5*7*9*...*99 g(97) = 1*3*5*7*9*...*97 g(99) - g(97) = 1*3*5*7*9*...*99 - 1*3*5*7*9*...*97 = 1*3*5*7*9*...*97*(99 - 1) = 1*3*5*7*9*...*97*98 hence:A. #### A QUESTION:By 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? options: A)116.68 B)116.11 C)116.19 D)116.66 E)116.1 SOLUTION:Explanation: Let the cost of the brand be Rs. X per kg. C.P. of 5 kg = (2 * 200 + 3 * x) = Rs. (400 + 3x) S.P of 5 kg = Rs. (5 * 177) = Rs. 885 [885 - (400 + 3x)]/(400 + 3x) * 100 = 18 24250 - 150x = 3600 + 27x 177x = 20650 => x = 116 2/3 So, cost of the other brand = Rs. 116.66. Answer: D #### D QUESTION:76^77 /7 remainder is ? options: A)5 B)6 C)7 D)8 E)9 SOLUTION:as, 4^3/3=64/3 remainder=1 and also 4/3=1 and 5^3/3 remainder=2 and also 5/3=2 so it does not matter on the power value so the answer will be 76/7 remainder=6 ANSWER:B #### B QUESTION:There are two sections C and D of a class, consisting of 18 and 22 students respectively. If the average weight of sections C is 20 kg and that of sections D is 18 kg. Find the average weight of the whole class options: A)18.7 B)18.8 C)18.9 D)19.9 E)None SOLUTION:Solution Total weight of(18+22)Students = (18x20+22x18)Kg = 756 kg. Average weight of the whole class = (756 /40 ) = 18.90. Answer C #### C QUESTION:How many 4 letter combinations can be made from the letters of the word VERMONT if the first letter has to be a vowel and the last letter has to be a consonant, and each letter can be used only once? options: A)21 B)42 C)120 D)600 E)200 SOLUTION:Vowel: E O Consonants: V R M N T First letter can be filled in 2 Ways ( As the question states thatfirst letter has to be a vowel) Fourth letter can be filled in 5 Ways ( As the question states thatthe last letter has to be a consonant) Now since each letter can be used only once, and 2 letters out of 7 letters are already used in First and fourth letter Second letter can be filled in 5 Ways Third letter can be filled in 4 Ways So, Total number of ways = 2 Ways x 5 Ways x 4 ways x 5 ways = 200 Answer E #### E QUESTION:Which of the following number will completely divide (49^15)-1? options: A)8 is the number B)6 C)22 D)12 E)14 SOLUTION:x^n - 1 will be divisible by x+1 only when n is even. 49^15 - 1 = (7^2)^15 - 1 = 7^30 - 1 which is divisible by 7+1 i.e. 8 Answer is A #### A QUESTION:5.005/4.004 = options: A)1.05 B)1.50015 C)1.501 D)1.5015 E)1.25 SOLUTION:5.005/4.004 = 5005/4004 = 5(1001)/4(1001) = 5/4 = 1.25 The answer is E. #### E QUESTION:What is the greatest possible length that can be used to measure exactly the following Lengths 7m, 3m 85cm, 12m 95cm? options: A)25 cms B)30 cms C)35 cms D)38 cms E)45 cms SOLUTION:HCF of 7m, 3m 85cm, 12m 95cm is 35 cms. ANSWER:C #### C QUESTION:A, 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 B? options: A)2160 B)3000 C)3018 D)3019 E)3012 SOLUTION:60*5:36*6:75*3 100: 72: 75 72/247 * 7410 = 2160 Answer: A #### A QUESTION:A dishonest dealer professes to sell goods at the cost price but uses a weight of 600 grams per kg, what is his percent? options: A)75% B)67% C)29% D)55% E)45% SOLUTION:600 --- 400 100 --- ? => 67% Answer: B #### B QUESTION:Sonika deposited Rs.4500 which amounted to Rs.8400 after 2 years at simple interest. Had the interest been 4% more. She would get how much? options: A)9680 B)8790 C)8760 D)9020 E)5000 SOLUTION:(4500*2*4)/100 = 360 8400 -------- 8760 Answer: C #### C QUESTION:Frank the Fencemaker needs to fence in a rectangular yard. He fences in the entire yard, except for one full side of the yard, which equals 40 feet. The yard has an area of 480 square feet. How many feet offence does Frank use? options: A)14 B)47 C)54 D)180 E)64 SOLUTION:Area = Length x Breadth 480 = 40 x Breadth So, Breadth = 12 Units Fencing required is - Breadth + Breadth + Length 12 + 12 + 40 => 64 feet Answer must be (E) 64 #### E QUESTION:A train travels at the rate of 10 miles/hr for the first hour of a trip, at 20 miles/hr for the second hour, at 30 miles/hr for the third hour and so on. How many hours will it take the train to complete a 210-mile journey? Assume that the train makes no intermediate stops. options: A)6 B)6.5 C)7 D)7.5 E)5 SOLUTION:A train travels at the rate of 10 miles/hr for the first hour of a trip, at 20 miles/hr for the second hour, at 30 miles/hr for the third hour and so on. How many hours will it take the train to complete a 210-mile journey? Assume that the train makes no intermediate stops. I think the easiest way to solve this problem would be simply to count the number of miles it travels per hour (and in total) Hour miles/hour Total miles 1 10 10 2 20 30 3 30 60 4 40 100 5 50 150 6 60 210 It takes a total of nine hours to cover the 210 mile distance. ANSWER: A 6 #### A QUESTION:A person crosses a 600 m long street in 5 minutes. What is his speed in km per hour? options: A)7.1 B)7.2 C)7.5 D)7.4 E)7.3 SOLUTION:distance = 600 meter time = 5 minutes = 5 x 60 seconds = 300 seconds Speed = distance/time=600/300=2m/s=2×18/5 km/hr=36/5 km/hr=7.2 km/hr Answer is B. #### B QUESTION:WHEN A PERSON SELLS TWO ITEMS $1656 each, ONE AT A GAIN OF 20% AND OTHER AT A LOSS OF 20%.THEN THE SELLER INCURS A LOSS OR GAIN OF: options: A)no loss no gain B)20 % profit C)4% loss D)2% profit E)2% loss. SOLUTION:The 2 items are sold at 1656 each , one at a profit of 20% and the other at a loss of 20% So the original rates of the items are 1380 and 2070 respectively So the total he spend for those 2 items is 3450 but he ended up in selling them with (1656*2) 3312 So the loss is 3450 - 3312 = 138 The loss percentage is (138/3450) *100 = 4% loss - Answer C #### C QUESTION:Two representatives must be selected from each of two groups of students. One group consists of four men and one woman, and the other group consists of two women and one man. What is the probability that 2 men and 2 women will be selected ? options: A)1/6 B)1/4 C)2/7 D)7/15 E)1/2 SOLUTION:Group 1: 4 Men and 1 Woman Group 2: 1 Men and 2 Woman Need: 2 Men and 2 women Case 1: 2 Men from Group 1 and 2 women from group 2 - 4C2*2C2 = 6 ways Case 2: 1 Men and 1 Woman from Group 1 and 1 Man and 1 women from group 2 - 4*1*1*2 = 8 ways Total Favorable cases = 6+8 = 14 Total Possible ways of selecting students 2 from each group = 5C2*3C2 = 10*3 = 30 Probability = 14/30 = 7/15 Answer : Option D #### D <<<Examples ends QUESTION:If 20 men can build a wall 112 metres long in 6 days, what length of a similar wall can be built by 40 men in 3 days? options: A)65mtr. B)52mtr C)70mtr. D)112mtr. E)17mtr. SOLUTION:20 men is 6 days can build 112 metres 25 men in 3 days can build = 112*(40/20)x(3/6) = 112 meters Answer: D. #### D

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:Anil does a work in 90 days, Bittu in 40 days and Chintu in 12 days. They work one after another for a day each, starting with Anil followed by Bittu and then by Chintu. If the total wages received are Rs 360 and Anil, Bittu, Chintu share them in the ratio of the work done, find their respective individual wages. options: A)Rs 40, Rs 60 and Rs 260 B)Rs 36, Rs 81 and Rs 243 C)Rs 42, Rs 86 and Rs 232 D)Rs 38, Rs 88 and Rs 234 E)none of these SOLUTION:Let the total work done be 360 units. Therefore, work done by Anil, Bittu and Chintu in single day are 4 units, 9 units and 30 units respectively. Each of them working for 9 days Anil and Bittu will be able to complete 4 units and 9 units of their work on the 9th day but Chintu will be doing remaining 3 units of work. Hence, individual work done by them to complete the whole work is 36 units, 81 units and 243 units till the end of 9th day for each of them. Thus, respective wages on the basis of work done is Rs 36, Rs 81 and Rs 243 respectively for Anil, Bittu and Chintu. ANSWER:B #### B QUESTION:The difference of the squares of two consecutive even integers is divisible by which of the following integers ? options: A)6 B)4 C)2 D)5 E)1 SOLUTION:Let the two consecutive even integers be 2n and (2n + 2). Then, (2n + 2)^2 = (2n + 2 + 2n)(2n + 2 - 2n) = 2(4n + 2) = 4(2n + 1), which is divisible by 4. ANSWER B #### B QUESTION:In the simple subtraction problem below, some single digits (not necessarily distinct) are replaced by letters. Find the value of 2*A + 2*B + 4*C*D. A9C5 - 2B79 -------------- 633D options: A)50 B)52 C)66 D)48 E)46 SOLUTION:A9C5 -2B79 ---------- 6336 since,15-9=6. from there,D=6 and solving all,we get A=8,B=5,C=1. So 2*8+2*5+4*1*6=50 ANSWER:A #### A QUESTION:In 6 years, A will be thrice as old as B was 4 years ago. If A is now 6 years older than B, find the present age of B. options: A)16 years B)24 years C)8 years D)12 years E)18 years SOLUTION:let present age of A be A let presennt age of B be B in 6 yrs A+6:B+6=3(B-4):B=6 ie A+6=3(B-4) but given A=B+6 so B+6+6=3(B-4) B=12 ANSWER:D #### D QUESTION:If 50 apprentices can finish a job in 4 hours, and 30 journeymen can finish the same job in 7 hours, how much of the job should be completed by 10 apprentices and 15 journeymen in one hour? options: A)17/140 B)29/180 C)26/143 D)1/5 E)39/121 SOLUTION:50 apprentices can finish the job in 4 hours,thus: 10 apprentices can finish the job in 4*5 = 20 hours; In 1 hour 10 apprentices can finish 1/20 of the job. 30 journeymen can finish the same job in 4,5 hours,thus: 15 journeymen can finish the job in 7*2 = 14 hours; In 1 hour 15 journeymen can finish 1/14 of the job. Therefore, in 1 hour 10 apprentices and 15 journeymen can finish 1/20+1/14=17/140 of the job. Answer: A #### A QUESTION:Twelve telegenic contestants with a variety of personality disorders are to be divided into two “tribes” of five members each, tribe A and tribe B, for a competition. How many distinct groupings of two tribes are possible? options: A)120 B)126 C)792 D)1200 E)1260 SOLUTION:My ans is 12C5 = 792 C #### C QUESTION:Ashok 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? options: A)66 B)74 C)78 D)80 E)None of these SOLUTION:Explanation: Number of subjects = 6 Average of marks in 6 subjects = 74 Therefore total marks in 6 subjects = 74 * 6 = 444 Now, No. of subjects = 5 Total marks in 5 subjects = 74 * 5 = 370 Therefore marks in 6th subject = 444 – 370 = 74 ANSWER B #### B QUESTION:Two pipes can fill a tank in 14 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 ? options: A)5.5 Hours B)7.5 Hours C)8.5 Hours D)9.5 Hours E)6.5 Hours SOLUTION:In 1 hour it fill 1/14 + 1/12 - 1/20 = 2/19 So fill tank fill up in 19/2= 9.5 Hours ANSWER:D #### D QUESTION:A 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? options: A)1687 B)1478 C)1480 D)14000 E)1500 SOLUTION:25*12: 30*12: 35*8 15:18:14 14/47 * 47000 = 14000 Answer: D #### D QUESTION:A train of 30 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? options: A)6 B)3.3 C)4 D)9 E)2 SOLUTION:D = 30 * 60 + 1500 = 3300 m T = 3300/60 * 18/5 = 198 sec = 3.3 mins Answer:B #### B QUESTION:It costs a man 75 dollars to buy the things that he needs to make hotdogs. The city allows him to sell his hotdog somewhere near the city hall. However, the city hall charges him 1 dollar for each hotdog sold Calculate the break even point if the price he charges for 1 hotdog is $1.50 options: A)140 B)150 C)160 D)170 E)180 SOLUTION:Let x be the number of hotdogs sold Let C be the cost of buying and selling x hotdogs Let R be the revenue made for selling x hotdogs R = selling price of 1 hotdog × number of hotdogs sold R = 1.50x C = fixed cost + variable cost variable cost = fee charged for 1 hotdog × number of hotdogs sold variable cost = 1x C = 75 + 1x R = C 1.50x = 75 + 1x 1.50x - 1x = 75 + 1x - 1x 0.5x = 75 x = 150 since 0.5 × 150 = 75 The break even point is to sell 150 hotdogs. Answer B #### B QUESTION:What should come in place of the question mark (‘?) in the following equation? 18 2⁄5 of 150.8 + ? = 8697.32 – 3058.16 options: A)2764.44 B)2864.34 C)1864.44 D)2684.44 E)None of these SOLUTION:? = 8697.32 – 3058.16 – 92⁄5 × 150.8 = 5639.16 – 2774.72 = 2864.44 Answer E #### E QUESTION:The 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? options: A)6 B)5 C)8 D)9 E)4 SOLUTION:S = 4 M = x DS = x + 4 US = x - 4 6/(x + 4) + 6/(x - 4) = 2 x = 8.Answer: C #### C QUESTION:A 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? options: A)45 B)40 C)35 D)30 E)50 SOLUTION:Explanation: Let the total number of students = x The average marks increased by 1/2 due to an increase of 83 - 63 = 20 marks. But total increase in the marks = 1/2×x=x/2 Hence we can write as x/2=20 ⇒x=20 x 2=40 Answer: Option B #### B QUESTION:What is the speed of the train in km/hr whose length is 360 metres which passes a pole in 18 seconds? options: A)59/9 km/hr B)50/9 km/hr C)25/6 km/hr D)55/18 km/hr E)60/18 km/hr SOLUTION:Speed=(18x5/18)=5 m/sec. Length of the train= 360 metre Time=18s Speed=length / time Speed=(360/8)=20 m/sec = 20*5/18 km/hr = 50/9 km/hr Answer: B #### B QUESTION:A standard Veggiematik machine can chop 36 carrots in 4 minutes. How many carrots can 6 standard Veggiematik machines chop in 5 minutes? options: A)36 B)54 C)108 D)270 E)324 SOLUTION:ONE Veggiematik machine can chop 36 carrots in 4 minutes So, ONE Veggiematik machine can chop (1.5)(36) carrots in (1.5)(4) minutes In other words, ONE Veggiematik machine can chop 54 carrots in5minutes So,SIXVeggiematik machines can chop (5)(54) carrots in5minutes In other words, SIX Veggiematik machines can chop 270 carrots in5minutes Answer D #### D QUESTION:6x − 12 = 6y 5y + 5x = 10 Which of the following is the number of solutions to the system of equations shown above? options: A)More than three B)Exactly three C)Exactly two D)Exactly one E)None SOLUTION:6x − 12 = 6y => 6x - 6y = 12 => x- y =2 -- 1 5y + 5x = 10 =>x + y = 2 -- 2 From equation 1 and 2 , we get 2x = 4 => x=2 y=0 Therefore , the given system will have Exactly one solution D #### D QUESTION:What annual payment dischargea debit of Rs.12900, due in 4yrs.At 5% rate? options: A)2000 B)2200 C)3000 D)3400 E)3500 SOLUTION:A.P.=(200X12900)/[4(200+5X3)]=3000 Ans Alternative 100+105+110+115=12900 430=12900 100=12900/(430)X100=3000 C #### C QUESTION:If P represents the product of the first 16 positive integers, then P is not a multiple of: options: A)a) 99 B)b) 84 C)c) 72 D)d) 65 E)e) 57 SOLUTION:a) 99 = 9*11 b) 84 = 4*7*3 c) 72 =9*8 d) 65 = 5*13 e) 45 =9*5 since 11 is not there in first 15 positive numbers it is the only possibility A #### A QUESTION:If ‘+’ means ‘×’, ‘-‘ means ‘+’, ‘×’ means ‘÷’ and ‘÷’ means ‘-‘ then find the value of; 6 – 9 + 8 × 3 ÷ 15 = options: A)6 B)10 C)12 D)-2 E)15 SOLUTION:E 15 #### E QUESTION:Two numbers are in the ratio 3 : 4. If their L.C.M. is 48. what is sum of the numbers? options: A)28 B)56 C)76 D)84 E)85 SOLUTION:Explanation: Let the numbers be 3x and 4x LCM of 3x and 4x = 12x (Since LCM of 3 and 4 is 12. Hence LCM of 3x and 4x is 12x) Given that LCM of 3x and 4x is 48 => 12x = 48 => x = 48/12 = 4 Sum of the numbers = 3x + 4x = 7x = 7 x 4 = 28 Answer: Option A #### A QUESTION:A student took five papers in an examination, where the full marks were the same for each paper. His marks in these papers were in the proportion of 6 : 7 : 8 : 9 : 10. In all papers together, the candidate obtained 60% of the total marks. Then the number of papers in which he got more than or equal to 60% marks is options: A)4 B)3 C)2 D)1 E)5 SOLUTION:Here we can assume that one subject is of 100 marks so total there are 5 subjects => 100*5 = 500. Now according to the question he secured 60 % of those which is 60%of 500 = 300 marks in total. The ratio between the marks is given as 6 : 7 : 8 : 9 : 10 , so now we can distribute 300 marks according to the ratio. Total ratio = 40 For 6 : (300/40)*6 = 45 Similarly , we will get for others as 52.5 , 60 , 62.5 , 75. Hence , there are 3 subject where he secured more that 60 %. The answer is 3. B #### B QUESTION:A batsman scored 120 runs whichincluded 3 boundaries and 8sixes. What % of his total score did he make by running between the wickets options: A)40 % B)50 % C)60 % D)70 % E)80 % SOLUTION:Number of runs made by running = 110 - (3 x 4 + 8 x 6) = 120 - (60) = 60 Now, we need to calculate 60 is what percent of 120. => 60/120 * 100 = 50 % B #### B QUESTION:Find the smallest number which when divided by 13 and 16 leaves respective remainders of 2 and 5. options: A)128 B)197 C)127 D)182 E)091 SOLUTION:Explanation: Let 'N' is the smallest number which divided by 13 and 16 leaves respective remainders of 2 and 5. Required number = (LCM of 13 and 16) - (common difference of divisors and remainders) = (208) - (11) = 197. Answer:B #### B QUESTION:Find the compound interest on Rs. 7500 at 4% per annum for 2 years, compounded annually. options: A)Rs. 610 B)Rs. 612 C)Rs. 614 D)Rs. 616 E)None of these SOLUTION:Explanation: Amount=[7500×(1+4100)2]=(7500×2625×2625)=8112 So compound interest = (8112 - 7500) = 612 Answer: B #### B QUESTION:The total car population in a Mumbai is 2,94,00 out of which 1,50,00 are made by Honda. Out of every 100 Honda cars, 98 are red in color, but only 53% of the total car population is red. Find the % of non-Honda cars that are red options: A)2.54% B)4.56% C)6.125% D)7.134% E)8.341% SOLUTION:Total Car.29.10 i.e., Honda +non Honda = 29400 Given: Whim. tractor .150W Now,5346 of 2..00 = Honda +Red Non-Honda 29400 .:4 =15582 Thus...El Mall... 1.0 Now Honda 15582 flow, Non-. Honda =15582 - 15.582-14700=8B2 96 non-Honda =1=1.100 = 6.125% C #### C QUESTION:The effective annual rate of interest corresponding to a nominal rate of 6% per annum payable half-yearly is? options: A)6.06% B)6.07% C)6.08% D)6.09% E)6.19% SOLUTION:Amount 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% ANSWER:D #### D QUESTION:Distances from you to Man united is written below. CHELSEA and ARSENAL are 700 kms away SPURS 1800 kms away WOLVES 200 kms away Based on the system , How far should it be to MANCITY ? options: A)1100 miles. B)3100 miles. C)2100 miles. D)5100 miles. E)4100 miles. SOLUTION:Solution: 2100 miles. Each vowel equivalent to 500 and each consonant equivalent to -200 Answer C #### C QUESTION:How many words can be formed by using all letters of the word “BIHAR” options: A)452 B)320 C)365 D)456 E)120 SOLUTION:The word BIHAR contains 5 different letters. Required number of words = 5p5 = 5! = (5x4x3x2x1) = 120 Ans: E #### E QUESTION:The product of two numbers is 192 and the sum of these two numbers is 28. What is the smaller of these two numbers? options: A)10 B)12 C)14 D)15 E)16 SOLUTION:Solution Let the number be x and (28 - x) = Then, x (28 - x) = 192 ‹=›x2 - 28x + 192 = 0. ‹=›(x - 16) (x - 12) = 0 ‹=›x = 16 or x = 12. Answer B #### B QUESTION:If a and b are positive integers of C such that a/b=2.86, which of the following must be a divisor of a? options: A)10 B)B.13 C)18 D)26 E)50 SOLUTION:The prompt gives us a couple of facts to work with: 1) A and B are positive INTEGERS 2) A/B = 2.86 We 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). The simplest place to start is with... A = 286 B = 100 286/100 = 2.86 These values are NOT the smallest possible values though (since they're both even, we can divide both by 2)... A = 143 B = 50 143/50 = 2.86 There 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.... Since 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. Final Answer: B #### B QUESTION:A rectangle A has an area of 30 square centimeters. Square B has a perimeter of 16 centimeters. If square B is placed within square A and a random point is chosen within square A, what is the probability the point is not within square B? options: A)9/30 B)14/30 C)4/9 D)3/5 E)6/25 SOLUTION:I guess it's mean that square B is placed within rectangle A entirely. Since, the perimeter of B is 16, then its side is 16/4=4 and the area is 4^2=16; Empty space between the squares is 30-16=14 square centimeters, so if a random point is in this area then it won't be within square B: P=favorable/total=14/30. Answer: B. #### B QUESTION:The 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? options: A)18/35 B)18/18 C)18/19 D)18/17 E)18/12 SOLUTION:If both agree stating the same fact, either both of them speak truth of both speak false. Probability = 3/5 * 4/7 + 2/5 * 3/7 = 12/35 + 6/35 = 18/35 Answer:A #### A QUESTION:Conversation between two mathematicians: First: I have three children. The product of their ages is 36. If you sum their ages, it is exactly same as my neighbor's door number on my left. The second mathematician verifies the door number and says that it is not sufficient. Then the first says "Ok one more clue is that my youngest is really the youngest". Immediately the second mathematician answers. Can you answer the question asked by the first mathematician? What are the children ages? options: A)6,6, 1 B)6,6, 2 C)6,5, 1 D)6,5, 2 E)6,6, 3 SOLUTION:Possible options for same sum of ages ( 13 here)with product of ages as 36 are 2,2,9 and 6,6,1 but in case of 2,2,9 youngest is not really youngest as two children of age 2 years are twins. whereas in case of 6,6,1 youngest is really youngest. so 6,6, 1 is correct. ANSWER:A #### A QUESTION:The 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: options: A)377 B)267 C)268 D)750 E)271 SOLUTION:Speed = [90 * 5/18] m/sec = 25 m/sec; Time = 1 min. = 60 sec. Let the length of the train and that of the platform be x meters. Then, 2x/60 = 25 è x = 25 * 60 / 2 = 750 .Answer: D #### D QUESTION:On a summer camp, 25% of the campers paid $110 each, 35% paid $80 each and the rest paid $65 each. What percentage of the total amount paid came from the campers who paid $80? options: A)18% B)21% C)33.35 D)33.3% E)37.5% SOLUTION:let the total no of campers be 100 total amount = (25*110)+(35*80)+(40*65) = 2750+2800+2600= $8150 required percentage = (2800/8150)*100=33.35% C #### C QUESTION:Find the principle on a certain sum of money at 5% per annum for 2 2/5 years if the amount being Rs.1120? options: A)1000 B)289 C)209 D)280 E)892 SOLUTION:1120 = P [1 + (5*12/5)/100] P= 1000 Answer: A #### A QUESTION:0---:-|---:--|-:--:-|--:---|-:----1 On the number line above, the segment from 0 to 1 has been divided into fifths, as indicated by the large tick marks, and also into sevenths, as indicated by the small tick marks. What is the LEAST possible distance Z between any two of the tick marks? options: A)1/70 B)1/35 C)2/35 D)1/12 E)1/7 SOLUTION:divisions are 0 1/7 2/7 3/7 4/7 5/7 6/7 1 1/5 2/5 3/5 4/5 5/5 expressing the same in terms of the lcm of 5,7 ,i.e 35 0 7/35 14/35 21/35 28/35 35/35 5/35 10/35 15/35 20/35 25/35 30/35 by comparing the divisions with each other we can see 1/35 is the shortest possible distance between any two selected divisions. Z=1/35 Answer is B. #### B QUESTION:A basket contains 10 apples and 20 oranges out of which 3 apples and 5 oranges are defective. If we choose two fruits at random, what is the probability that either both are oranges or both are non defective? options: A)316/439 B)316/438 C)316/435 D)316/299 E)316/199 SOLUTION:Let A be the event of getting two oranges and B be the event of getting two non-defective fruits. and be the event of getting two non-defective oranges Answer: C) 316/435 #### C QUESTION:If x^2 - 1 = 0 and x < 0, which of the following must be equal to 0 ? options: A) x^2 - 9x B) x^2 - 9x + 20 C) x^2 - 2x + 3 D) x^2 + 2x + 1 E) x^2 + 5x + 6 SOLUTION:x^2-1 = 0 x= +1 or x = -1 if we substitute x= -1 in the equation x^2 +2x+1 = 1-2+1 = 0 D is also the answer #### D QUESTION:The area of a parallelogram is 162sq m and its altitude is twice the corresponding base. Then the length of the base is? options: A)8 B)9 C)7 D)62 E)2 SOLUTION:2x * x = 162 => x= 9 Answer: B #### B QUESTION:Find value of x (11^2 + 12^2 + 13^2 + ... + 20^2) = x options: A)1200 B)1340 C)1234 D)1203 E)2485 SOLUTION:(11^2 + 12^2 + 13^2 + ... + 20^2) = (1^2 + 2^2 + 3^2 + ... + 20^2) - (1^2 + 2^2 + 3^2 + ... + 10^2) 6 = 20 x 21 x 41 - 10 x 11 x 21 6 6 = (2870 - 385) = 2485 E #### E QUESTION:A man can do a job in 5 days. His father takes 20 days and his son finishes it in 25 days. How long will they take to complete the job if they all work together? options: A)6.3 B)6.9 C)3.5 D)6.1 E)6.2 SOLUTION:1 day work of the three persons = (1/5 + 1/20 + 1/25) = 29/100 So, all three together will complete the work in 100/29 = 3.5 days. Answer:C #### C QUESTION:During a clearance sale, a retailer discounted the original price of its TVs by 20% 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? options: A)40% B)45% C)55% D)60% E)64% SOLUTION:VERITAS PREPOFFICIAL SOLUTION: D. 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 80% 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 80% that they did pay, which can be made easier by looking at what the customer does pay: 80% of the 80% sale price. Using fractions, that means they pay: 4/5*(4/5) of the original price, which nets to 0.64 of the original price, or 64%. E #### E QUESTION:If 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? options: A)41 B)42 C)43 D)44 E)45 SOLUTION:A two-digit number "cd" can be expressed algebraically as 10c+d. The sum of A + B = (10c+d)+(10d+c)=11(c+d). The only answer that is a multiple of 11 is 44. The answer is D. #### D QUESTION:In a Quiz the points in each round for the first,second and third were 1000,50,20 . No other points were given. Sam participated in several rounds in the competition and the product of his score was 50000. In How many rounds did he participate? options: A)Cannot be determined B)43 C)3 D)6 E)10 SOLUTION:Correct answer is A because we are given that there won't be any points awarded for rounds other than 1st three position. Thus, it may happen that he played 100 rounds out of only 7 rounds were there in which he was awarded some points. #### A QUESTION:A card is drawn at random from a pack of 52 cards. What is the probability that it is neither a spade nor a jack? options: A)9/13 B)4/13 C)2/13 D)6/13 E)5/13 SOLUTION:There are 13 spades including a jack and 3 more jacks of other suits. Probability of getting spade or a jack: = (13 + 3)/52 = 16/52 = 4/13 Therefore, the probability of getting neither a spade nor a jack: = 1 − 4/13 = 9/13 ANSWER:A #### A QUESTION:The 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: options: A)51:52 B)52:53 C)51:53 D)52:55 E)53:54 SOLUTION:Explanation: Let C.P. of the article be Rs. x. Then, required ratio = 104% of x / 106% of x = 104/106 = 52/53 = 52:53 ANSWER IS B #### B QUESTION:What percent of 180 is 45? options: A)0.25% B)4% C)25% D)40% E)250% SOLUTION:Here's an algebraic approach. Let p = the required percent. This means p/100 = the percent as a fraction. So, "What percent of 180 is 45?" becomes "(p/100) of 180 = 45 Or: (p/100)(180) = 45 Divide both sides by 180 to get: p/100 = 45/180 Simplify right side: p/100 = 1/4 Multiply both sides by 100 to get: p = 25 ANSWER:C #### C QUESTION:In how many ways can five boys and three girls sit in a row such that all boys sit together? options: A)A)2888 B)B)2885 C)C)2880 D)D)2876 E)E)2224 SOLUTION:Treat all boys as one unit. Now there are four students and they can be arranged in 4! ways. Again five boys can be arranged among themselves in 5! ways. Required number of arrangements = 4! * 5! = 24 * 120 = 2880. Answer:C #### C QUESTION:Bob 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? options: A)20 B)24 C)27 D)30 E)40 SOLUTION:Many 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. #### D QUESTION:The average (arithmetic mean) of the 5 positive integers k, m, r, s, and t is 10, and k < m < r < s < t. If t is 20, what is the greatest possible value of the median of the 5 integers? options: A)16 B)18 C)13 D)20 E)22 SOLUTION:We need to find the median which is the third value when the numbers are in increasing order. Since k<m<r<s<t, the median would be r. The average of the positive integers is 10 which means that in effect, all numbers are equal to 10. If the largest number is 20, it is 10 more than 20. We need r to be maximum so k and m should be as small as possible to get the average of 10. Since all the numbers are positive integers, k and m cannot be less than 1 and 2 respectively. 1 is 9 less than 10 and 2 is 8 less than 10 which means k and m combined are 17 less than the average. 20 is already 10 more than 10 and hence we only have 17 - 10 = 7 extra to distribute between r and s. Since s must be greater than r, r can be 10+3 = 13 and s can be 10+4 = 14. So r is 13. Answer (C) #### C QUESTION:If f is a function defined for all k by f(k) = k^3 /16, what is f(2 k) in terms of f(k)? options: A)1/8 f(k) B)8 f(k) C)2 f(k) D)10 f(k) E)32 f(k) SOLUTION:f(k) = k^3 /16 f(2k) = (2k)^3 /16 =8 * k^3/16 = 8 x (k^3 /16) = 8 f(k). So answer is B. #### B QUESTION:After an ice began to melt out from the freezer, in the first hour lost 3/4, in the second hour lost 3/4 of its remaining. If after two hours, the volume is 0.3 cubic inches, what is the original volume of the cubic ice, in cubic inches? options: A)2.5 B)3.0 C)4.8 D)6.5 E)8.0 SOLUTION:Let initial volume of ice be = x Ice Remaining after 1 hour = x - 0.75x = 0.25x Ice Remaining after 2 hour = (1/4)x - (3/4 * 1/4 * x) = (1/16)x (1/16)x = 0.3 x = 4.8 Alternate solution: Try to backsolve. Initial volume = 4.8 After one hour --> (1/4)4.8 = 1.2 After two hours --> (1/4)1.2 = 0.3 Answer: C #### C QUESTION:A started a bussiness with a sum of Rs. 14000. After 4 months, B entered with an amount of Rs. 12000 and A added another 2,000 in the business. After 6 months, C entered with Rs. 20000 and 'B' withdrew Rs. 2000 from the business. What will be C's share of profit out of a total profit of Rs. 94000 at the end of 2 years. options: A)Rs. 376000 B)Rs. 204000 C)Rs. 36000 D)Rs. 18000 E)Rs. 260000 SOLUTION:Investments-- A=14000x4+16000x20=376000 B=12000x2+10000x18=204000 C=20000x18=360000 So C's Share = 94000xC/(A+B+C)=36000 ANSWER:C #### C QUESTION:Income and expenditure of a person are in the ratio 5 : 4. If the income of the person is Rs. 18000, then find his savings? options: A)Rs.3600 B)Rs.3629 C)Rs.3279 D)Rs.3629 E)Rs.3283 SOLUTION:Let the income and the expenditure of the person be Rs. 5x and Rs. 4x respectively. Income, 5x = 18000 => x = 3600 Savings = Income - expenditure = 5x - 4x = x So, savings =Rs.3600. Answer: A #### A QUESTION:A baker filled with a measuring cup with 1/3 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? options: A)1/8 cup B)3/8 cup C)11/24 cup D)1/2 cup E)7/8 cup SOLUTION:1/3 is the original water in cup .half in batter.So left is 1/6 out which 1/8 is spilled out.So again left with 1/24. so 50% more than what he started was = 1/3+1/2*(1/3)=1/2 Amount of water needed to add = 1/2 - 1/24=11/24 C #### C QUESTION:In how many different number of ways a combination of 3 men and 2 women can be selected from 6 men and 5 women? options: A)10 B)20 C)30 D)40 E)50 SOLUTION:6C3 = 6!/(3! . 3!) = (6 × 5 × 4)/(3 × 2) = 5 × 4 = 20 B) #### B QUESTION:In what time will a train 100 m long cross an electric pole, it its speed be 144 km/hr? options: A)2.5 sec B)2.8 sec C)8.5 sec D)2.2 sec E)4.5 sec SOLUTION:Speed = 144 * 5/18 = 40 m/sec Time taken = 100/40 = 2.5 sec. Answer:A #### A QUESTION:A vendor bought Headphones at 5 for Rs 100.How many for Rs 100 must he sell to gain 50%? options: A)8 B)3 C)5 D)6 E)None SOLUTION:C.P. of 9 Headphones= Rs100 S.P. of 9 Headphones = 150% of Rs 100 = Rs150 For Rs.150 , Headphones sold = 9. For Rs. 100,Pens sold=(9/150)*100=6 Answer: Option D #### D QUESTION:A salt manufacturing company produced a total of 5000 tonnes of salt in January of a particular year. Starting from February its production increased by 180 tonnes every month over the previous months until the end of the year. Find its average monthly production for that year? options: A)2989 B)2765 C)6000 D)2989 E)9772 SOLUTION:Total production of salt by the company in that year = 5000 + 5180 + 5360 + .... + 6980 = 72060. Average monthly production of salt for that year = 72060/12 = 6005. Answer:C #### C QUESTION:A bakery has 6 employees. It pays annual salaries of $19,000 to each of 2 employees, $21,000 to 1 employee, and $22,000 to each of the remaining 3 employees. Which number is closest to the average (arithmetic mean) annual salary of these employees? options: A)$20,200 B)$20,500 C)$20,800 D)$21,000 E)$21,400 SOLUTION:average = 2(19000)+(21000)+3(22000) / 6 = $20,833 The answer is C. #### C QUESTION:In a class of 50 students, 20 play SNOOKER, 15 play Cricket and 11 play Football. 7 play both SNOOKER and Cricket, 4 play Cricket and Football and 5 play SNOOKER and football. If 18 students do not play any of these given sports, how many students play exactly two of these sports? options: A)10 B)12 C)34 D)45 E)566 SOLUTION:Notice that7 play both SNOOKER and Cricket does not mean that out of those 7, some does not play Football too. The same for Cricket/Football and SNOOKER/Football. [color=#ffff00]{Total}={SNOOKER}+{Cricket}+{Football}-{HC+CH+HF}+{All three}+{Neither}For more check ADVANCED OVERLAPPING SETS PROBLEMS [/color] 50=20+15+11-(7+4+5)+{All three}+18 --> {All three}=2; Those who play ONLY SNOOKER and Cricket are 7-2=5; Those who play ONLY Cricket and Football are 4-2=2; Those who play ONLY SNOOKER and Football are 5-2=3; Hence, 5+2+3=10 students play exactly two of these sports. Answer: A. #### A QUESTION:John 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 65 miles per hour, what is v in miles per hour? options: A)30 B)40 C)50 D)55 E)70 SOLUTION:HiBunuel THe question seems incorrect. it should not be 80% at the speed of 80. However if it's 20% at the speed of 80, Answer comes out 55. The question is correct. Here's the explanation: Let distance be D. We can find the total timeequate it, which comes as: 0.8D / 80 + 0.2D / v = D / 65 => v = 55 (Option D). #### D <<<Examples ends QUESTION:Let n~ be defined for all positive integers n as the remainder when (n - 1)! is divided by n. What is the value of 30~ ? options: A)1 B)0 C)2 D)8 E)31 SOLUTION:n~ = (n-1)! so 30~ = (30-1)! = 29! when 29!/30 we have 16*2 inside 29! hence 30 gets cancelled and we get remainder as 0 B #### B

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:If John invested $ 1 at 5 percent interest compounded annually, the total value of the investment, in dollars, at the end of 5 years would be options: A)(1.5)^4 B)(1.05)^5 C)(1.05)^4 D)1 + (0.05)^4 E)1 + 4(0.05) SOLUTION:In this prompt, the answer choices show that we don't actually have to calculate anything - we just need to 'format' the calculation correctly. We're told that the interest is COMPOUNDED ANNUALLY, so we need the Compound Interest Formula, with a Principal of $1, an R of 5% (which would 'translate' as .05) and a T of . We'd have.... Answer :B #### B QUESTION:How many figures are required to number the pages the pages of a book containing 365 pages? options: A)987 B)977 C)967 D)897 E)997 SOLUTION:1 to 9 = 9 * 1 = 9 10 to 99 = 90 * 2 = 180 100 to 365 = 266 * 3 = 798 ----------- 987 ANSWER:A #### A QUESTION:During the last four years, a large truck company purchased diesel at rates of $1.2, $1.4, $1.6 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? options: A)$2.5 B)$2.55 C)$1.51 D)$3.25 E)$3.0 SOLUTION:finding the Harmonic mean here. HM = 4/(1/12 + 1/14 + 1/16 + 1/21) = 15.1 C #### C QUESTION:An art gallery owner is hanging paintings for a new show. Of the five paintings she has to choose from, she can only hang three on the main wall of the gallery. Assuming that she hangs as many as possible on that wall, in how many ways can she arrange the paintings? options: A)18 B)30 C)60 D)120 E)216 SOLUTION:Arrangment means permutations questions.. 5P3 = 5!/3! = 60. IMO option C is correct answer.. #### C QUESTION:Richard has to paint a mural with seven horizontal stripes. He only has enough paint for four brown stripes, four green 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? options: A)120 B)350 C)1470 D)2,520 E)5,040 SOLUTION:Number of ways to choose 2 colors among 7 - 7c2 Number of ways that the chosen colors can be painted for 7 horizontal stripes - 2 (either (4,3) or (3,4)) Now the order, the number of ways in which a particular color among the 2 chosen colors can be painted for 4 stripes is - 7c4 [Note: We don't need to calculate the ways for the remaining 3 stripes as they are obvious and already counted under this] Total number of combinations - 7c2 * 2* 7c4 = 1470 C #### C QUESTION:A train 150 meters long takes 6 seconds to cross a man walking at 5 kmph in the direction opposite to that of the train. Find the speed of the train. options: A)45 kmph B)50 kmph C)85 kmph D)60 kmph E)70 kmph SOLUTION:Explanation: Let the speed of the train be x kmph. Speed of the train relative to man = (x + 5) kmph = (x + 5) ×5/18 m/sec. Therefore 150/((x+5)×5/18)=6 <=> 30 (x + 5) = 2700 <=> x = 85 Speed of the train is 85 kmph. Answer: Option C #### C QUESTION:Two trains 200m and 250m long run at the speed of 72kmph and 18kmph in opposite directions in parallel tracks. The time which they take to cross each other is? options: A)5.6sec B)8.9sec C)10.8sec D)12.6sec E)18 sec SOLUTION:Relative speed = 72+18 = 90 kmph * 5/18 = 25 m/s Distance covered in crossing each other = 200+250 = 450m Required time = 450*1/25 = 18 sec Answer is E #### E QUESTION:John professes to sell his goods at the cost price but he made use of 800 grams instead of a kg, what is the gain percent? options: A)12 1/3% B)12 1/4% C)12 2/3% D)12 2/1% E)12 1/2% SOLUTION:800 --- 100 100 --- ? => 12 1/2% Answer:E #### E QUESTION:An seller earns an income of Re 3 on the first day of his business. On every subsequent day, he earns an income which is just thrice of that made on the previous day. On the 15th day of business, he earns an income of: options: A)19 B)22 C)25 D)20 E)36 SOLUTION:2nd day he earns = 3(2 – 3) 3rd day he earns = 3(3 – 3) On 15th day he earns 3(15 -3) = 36 rupees ANSWER:E #### E QUESTION:Uncle Bruce is baking chocolate chip cookies. He has 36 ounces of dough (with no chocolate) and 14 ounces of chocolate. How many ounces of chocolate are left over if he uses all the dough but only wants the cookies to consist of 20% chocolate? options: A) 3 B) 6 C) 7.2 D) 5 E) 9 SOLUTION:Answer is D. x/x+36=1/5 x=9 14-9=5 #### D QUESTION:Frank the Fencemaker needs to fence in a rectangular yard. He fences in the entire yard, except for one full side of the yard, which equals 40 feet. The yard has an area of 480 square feet. How many feet offence does Frank use? options: A)14 B)47 C)54 D)180 E)64 SOLUTION:Area = Length x Breadth 480 = 40 x Breadth So, Breadth = 12 Units Fencing required is - Breadth + Breadth + Length 12 + 12 + 40 => 64 feet Answer must be (E) 64 #### E QUESTION:A 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 ? options: A)90 B)70 C)50 D)80 E)60 SOLUTION:Let number of notes of each denomination be x. Then x + 5x + 10x = 480 16x = 480 x = 30. Hence, total number of notes = 3x = 90. Answer is A. #### A QUESTION:In a certain school, 20% of students are below 8 years of age. The number of students above 8 years of age is 2/3 of the number of students of 8 years of age which is 48. What is the total number of students in the school? options: A)200 B)300 C)600 D)700 E)100 SOLUTION:E 100 Let the number of students be x. Then, Number of students above 8 years of age = (100 - 20)% of x = 80% of x. 80% of x = 48 + 2/3 of 48 80/100x = 80 x = 100. #### E QUESTION:A 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? options: A)5.2 hrs B)2.9 hrs C)1.9 hrs D)7.5 hrs E)1.4 hrs SOLUTION:Net part filled in 1 hour = (1/3 - 1/5) = 2/15 The cistern will be filled in 15/2 hrs i.e., 7.5 hrs. Answer:D #### D QUESTION:A certain league has five divisions. The respective divisions had 6, 7, 8, 9 and 11 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? options: A) 81 B) 83 C) 85 D) 86 E) 89 SOLUTION:Overall, there can be 81 minuses. Tus, it is A. #### A QUESTION:The average marks of a class of 30 students is 50 and that of another class of 50 students is 60. Find the average marks of all the students? options: A)56.25 B)52.9 C)52.1 D)52.3 E)42.5 SOLUTION:Sum of the marks for the class of 30 students = 30 * 50 = 1500 Sum of the marks for the class of 50 students = 50 * 60 = 3000 Sum of the marks for the class of 80 students = 1500 + 3000 = 4500 Average marks of all the students = 4500/80 = 56.25 Answer:A #### A QUESTION:The amount of water (in ml) that should be added to reduce 9 ml. Lotion, containing 50% alcohol, to a lotion containing 45% alcohol, is? options: A)1 B)4 C)5 D)6 E)7 SOLUTION:4.5 4.5 45% 55% 45% ----- 4.5 55% ------? => 5.5 - 4.5 = 1 ml ANSWER:A #### A QUESTION:The difference between simple interest and C.I. at the same rate for Rs.5000 for 2 years in Rs.72. The rate of interest is? options: A)11 B)12 C)77 D)85 E)65 SOLUTION:5000 = 72(100/R)2 5 R2 = 720 => R = 12.Answer:B #### B QUESTION:A certain set of numbers has an average (arithmetic mean) of 50 and a standard deviation of 50.5. If c 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 c and n? options: A)-200 B)-130 C)-104 D)51 E)305 SOLUTION:2 standard deviations from the average is frommean - 2*SDtomean + 2*SD, thus from 50-2*50.5=51 to 50+2*50.5=151: -51 < c < 151 -51 < n < 151 -102 < c+n < 302. Only option D is in this range. Answer: D. #### D QUESTION:A 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 70% total profit if he has already sold one of the four cars at Rs. 1.2 lakh? options: A)1.8 lakh B)1.3 lakh C)1.9 lakh D)8.1 lakh E)6.1 lakh SOLUTION:Explanation: Total cost of 4 cars = 1+2 = 3 lakh Total SP of 4 cars = 3 x 1.7 = 5.1 lakh SP of 1 car = 1.2 lakh SP of rest 3 cars = 5.1 - 1.2 = 3.9 lakh Average SP of all the 3 cars = 1.3 lakh Answer: B) #### B QUESTION:The 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? options: A)14/33 B)7/33 C)2/7 D)13/73 E)12/27 SOLUTION:Combination Probability Formula: nCr = n!/[r!(n-r)!] Total possible, select 5 people from 12 people = 12C5 = 12!/[5!(12 - 5)!] = 792. To have 3 women there must be 2 men, select 2 men from 4 = 4C2 = 6. And, select 3 women from 8 = 8C3 = 56. 3 women and 2 men = (6)(56) = 336 Probability = (number outcomes favorable)/(total number outcomes) = 336/792 = 14/33 Answer: A #### A QUESTION:34. The side surface of a cylinder is rolled with a rectangular plate. If the perimeter of the circular base Is 6 feet, and the diagonal of the rectangular plate was 10 ft. What is height of the of the cylinder? options: A)7 B)10 C)8 D)12 E)15 SOLUTION:Think of a Pringles can. If you took off the bottom and top and cut a slit down the length, it would flatten to a rectangle. The dimensions of the rectangle are the height of the can and the circumference of the circle. Since you know both, one side and thehypothenuse use pythagoreans theorem or properties of 3-4-5 triangles to solve for the other side, 8. Correct answer C. #### C QUESTION:If 10 litres of an oil of Rs.55 per litres be mixed with 5 litres of another oil of Rs.66 per litre then what is the rate of mixed oil per litre? options: A)Rs.49.17 B)Rs.51.03 C)Rs.58.66 D)Rs.55.33 E)None of the above SOLUTION:55*10 = 550 66*5 = 330 880/15 = 58.66 ANSWER:C #### C QUESTION:A 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? options: A)10 min past 7pm on wednesday B)20 min past 7pm on wednesday C)20 min past 9pm on wednesday D)26 min past 7pm on wednesday E)20 min past 4pm on wednesday SOLUTION:This 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 (7×24)+12 = 180 hours. To show the correct time, it has to gain 5 min. So the correct time will be shown on wednesday at 7:20 PM Answer: B #### B QUESTION:What is the unit digit of (6!*3! / 3!*4!)? options: A)5 B)6 C)0 D)3 E)4 SOLUTION:(6!*3! /3!*4!) =(6! / 4!) =5*6 =30 Units digit of the above product will be equal to 0 Answer C #### C QUESTION:The area of a parallelogram is 128sq m and its altitude is twice the corresponding base. Then the length of the base is? options: A)8 B)9 C)7 D)62 E)2 SOLUTION:2x * x = 128 => x= 8 Answer: A #### A QUESTION:A parking garage rents parking spaces for $12 per week or $30 per month. How much does a person save in a year by renting by the month rather than by the week? options: A) $140 B) $160 C) $220 D) $240 E) $264 SOLUTION:12$ per week! An year has 52 weeks. Annual charges per year = 52* 12 = 624$ 30$ per month! An year has 12 months. Annual charges per year = 12 * 30 = 360$ 624 - 360 = 264 Ans E #### E QUESTION:The workforce of Company Samsung is 60% 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? options: A)180 B)170 C)160 D)150 E)145 SOLUTION:let x be the total worker then 0.6x =female worker and 0.4x is male worker then 20 male worker added 06x/(0.4x +20) = 50/100 or 60x = 50*( 0.4x+100) = 20x+ 5000 or 40x = 5000 , x = 125 total worker = 125+20= 145 E #### E QUESTION:If it takes 70 workers 3 hours to disassemble the exhibition rides at a small amusement park, how many hours would it take 30 workers to do this same job? options: A)40/3 B)11 C)7 D)7/3 E)9/7 SOLUTION:70 Workers = 3 hours then, 1 Worker = 3*70 Hours 30 Workers = (3*70) /(30) = 7 ANSWER:C #### C QUESTION:9 - 3 ÷ 1/3 + 4 = ? options: A)4 B)3 C)6 D)9 E)12 SOLUTION:9 - 3 1/3 + 4 =9-3÷1/3+4 =9-(3X3) +4 =9-9+4 =4 CORRECT ANSWER : A #### A QUESTION:Two persons A and B can complete a piece of work in 30 days and 60 days respectively. If they work together, what part of the work will be completed in 10 days? options: A)1/8 B)1/3 C)1/6 D)1/2 E)5/3 SOLUTION:A's one day's work = 1/30 B's one day's work = 1/60 (A + B)'s one day's work = 1/30 + 1/60 = 1/20 The part of the work completed in 10 days = 10 (1/20) = 1/2. Answer:D #### D QUESTION:a bank was to give a loan out to a newly married couple for 800,000 with no interest for 2 years and raise the price to 900,000 after 2 years. what is the interest rate? options: A)17% B)13% C)12% D)7% E)6% SOLUTION:for 0 years = (900,000- 800,000) = 100,000. for 2 years = (100,000 x 2)/2= 100,000 Principal = (800,000 - 100,000) = 700,000. Hence, rate = (100 x 100,000)/(700,000x2) = 7% ANSWER: D #### D QUESTION:If 5 workers collect 48 kg of cotton in 4 days, how many kg of cotton will 9 workers collect in 2 days? options: A)47.6 kg B)52.6 kg C)59.6 kg D)56.6 kg E)57.6 kg SOLUTION:(3 * 5)/48 = (9 * 2)/ x x = 57.6 kg ANSWER:E #### E QUESTION:Two 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: options: A)68 km/hr. B)32 km/hr. C)34 km/hr. D)35 km/hr. E)72 km/hr. SOLUTION:Let the speed of each train be x m/sec. Then, relative speed of the two trains = 2x m/sec. So, 2x = (240 + 240 )/12 2x = 40 x = 20. Speed of each train = 10 m/sec = 20 x 18/5 km/hr = 72 km/hr. answer :E #### E QUESTION:John was thrice as old as Tom 6 yrs back. He will be 5/3 times as old as Tom 6 years hence. How old is Tom today? options: A)8 years B)10 years C)12 years D)14 years E)15 years SOLUTION:Sol. RMBflSk -6 = 3 (Ravi - 6) ...(j) and Rupesh + 6 = | (Ravi + 6) ...(ii) Solving both the equations we get, Ravi = 12 years. C #### C QUESTION:The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along theoundary 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? options: A)124545 m B)134561 m C)156787 m D)15450 m E)153600 m SOLUTION:Perimeter = Distance covered in 8 min. = 12000 x 8 m = 1600 m. 60 Let length = 3x metres and breadth = 2x metres. Then, 2(3x + 2x) = 1600 or x = 160. Length = 480 m and Breadth = 320 m. Area = (480 x 320) m2 = 153600 m E #### E QUESTION:Excluding 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? options: A)9 B)10 C)12 D)20 E)8 SOLUTION:Due to stoppages, it covers 9 km less. Time taken to cover 9 km =(9/54x 60)min = 10 min. Answer :B #### B QUESTION:In 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? options: A)8200 B)7500 C)7000 D)8000 E)8400 SOLUTION:Equal number of candidates appeared in each state. In state A, 6% candidates got selected. In state B, 7% candidates got selected. Given that 80 more candidates got selected in state B than A. Therefore, 1% of candidates appeared in each state =80 Answer: Option D = 100% of candidates appeared in each state =80×100=8000 i.e., number of candidates appeared from each state = 8000 #### D QUESTION:An order was placed for the supply of a carper whose length and breadth were in the ratio of 3 : 2. Subsequently, the dimensions of the carpet were altered such that its length and breadth were in the ratio 7 : 3 but were was no change in its parameter. Find the ratio of the areas of the carpets in both the cases. options: A)8:9 B)8:7 C)8:1 D)8:2 E)8:8 SOLUTION:Let the length and breadth of the carpet in the first case be 3x units and 2x units respectively. Let the dimensions of the carpet in the second case be 7y, 3y units respectively. From the data,. 2(3x + 2x) = 2(7y + 3y) => 5x = 10y => x = 2y Required ratio of the areas of the carpet in both the cases = 3x * 2x : 7y : 3y = 6x2 : 21y2 = 6 * (2y)2 : 21y2 = 6 * 4y2 : 21y2 = 8 : 7 Answer:B #### B QUESTION:Two 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 5 seconds.What is the length of the fast trian? options: A)23 m B)23 2/9 m C)27m D)27 7/9m E)29 7/9m SOLUTION:relative speed=20kmph=50/9m/sec length of the train=50/9*5=250/9=27 7/9m ANSWER:D #### D QUESTION:If x, y, and z are consecutive positive integers greater than 1, not necessarily in that order, then which of the following is (are) true? I. x > z II. 2x+ 2y > 2z III. yz > xz IV. xy > y + z options: A) I only B) II only C) II and III only D) II and IV only E) III and IV only SOLUTION:we do not know the values or the relative values but that the three are consecutive.. so the max difference in any two number is 2 and min 1.. lets see the choices.. I. x > z... we do not know the values or the relative values... need not be true.. II. 2x+ 2y > 2z or x+ y > z we take the worst case that z is teh largest and x and y are lowest possible..... so 2+3>4.. 5>4.. always true III. yz > xz we do not know the values or the relative values between x and y..need not be true IV. xy > y + z xy-y>z or y(x-1)>z... again lets take the worst scenario.. we 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 only ii is true ans B #### B QUESTION:A man buys Rs. 20 shares paying 9% dividend. The man wants to have an interest of 12% on his money. What is the market value of each share? options: A)Rs.12 B)Rs.18 C)Rs.15 D)Rs.21 E)Rs.25 SOLUTION:Explanation : Face value of each share = Rs.20 Dividend per share = 9% of 20 = 9×20/100=9/5 He needs to have an interest of 12% on his money ie, Money Paid for a share 9×12/100=9/5 Money Paid for a share=9/5×100/12=15 ie, Market Value of the share = Rs.15 Answer : Option C #### C QUESTION:A certain sum amounts to Rs.1525 in 3 years and Rs.1875 in 5 years. Find the rate % per annum? options: A)6.76% B)3.76% C)5.26% D)5.76% E)4.76% SOLUTION:3 --- 1525 5 --- 1875 -------------- 2 --- 350 N = 1 I = 75 R = ? P = 1525 - 225 = 1300 75 = (1300*1*R)/100 R = 5.76% ANSWER:D #### D QUESTION:If f(f(n)) + f(n) = 2n+3, f(0) = 1 then f(2012) = ? options: A)2013 B)2088 C)270 D)1881 E)1781 SOLUTION:f (f(0)) + f(0) = 2(0) + 3 ⇒⇒ f(1) = 3-1 = 2, f(1) = 2 f(f(1)) + f(1) = 2(1) + 3 ⇒⇒ f(2) = 5-2 = 3, f(2) = 3 f(f(2)) + f(2) = 2(2) + 3 ⇒⇒ f(3) = 7-3 = 4, f(3) = 4 .............. f(2012) = 2013 Ans: A #### A QUESTION:40, 45, 50, 55, 60, 75, 75, 90, 100, 100. The list above shows the scores of 10 schoolchildren on a certain test. If the standard deviation of the 10 scores is 21.2, rounded to the nearest tenth, how many of the scores are more than 1 standard deviation below the mean of the 10 scores? options: A)1 B)2 C)3 D)4 E)5 SOLUTION:The average of {40, 45, 50, 55, 60, 75, 75, 90, 100, 100} is 69. 1 standard deviation below the mean is 69 - 21.2 = 47.8. Hence there are two scores (40 and 45) more than 1 standard deviation below the mean. Answer B. #### B QUESTION:A boat having a length 8 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: options: A)12 kg B)60 kg C)72 kg D)160 kg E)None of these SOLUTION:Explanation: Volume of water displaced = (8 x 2 x 0.01) m3 = 0.16 m3. ∴ Mass of man = Volume of Water displaced x Density of water = (0.16 x 1000)kg = 160 kg. Answer: D #### D QUESTION:A train running at a speed of 36 km/h passes an electric pole in 14 seconds. In how many seconds will the whole train pass a 370-meter long platform? options: A)45 B)47 C)49 D)51 E)53 SOLUTION:Let the length of the train be x meters. When a train crosses an electric pole, the distance covered is its own length x. speed = 36 km/h = 36000 m / 3600 s = 10 m/s x = 14 * 10 = 140 m. The time taken to pass the platform = (140 +370)/ 10 = 51 seconds The answer is D. #### D QUESTION:Find the area of a parallelogram with base 24 cm and height 16 cm? options: A)198 cm2 B)384 cm2 C)279 cm2 D)128 cm2 E)297 cm2 SOLUTION:Area of a parallelogram = base * height = 24 * 16 = 384 cm2 Answer:B #### B QUESTION:All of the citizens of a country have a four-character or five-character national identification code that is created using the 26 letters of the alphabet and the 10 digits from 0 to 9. What is the maximum number of citizens who can be designated with these codes? options: A)37(36^4) B)36^9 C)35(36^5) D)37(36^5) E)35(36^9) SOLUTION:The number of possible 4-digit codes is 36^4. The number of possible 5-digit codes is 36^5. The total sum is 36^4 + 36^5 = 36^4(1+36) = 37(36^4) The answer is A. #### A QUESTION:Mike 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 14 miles, how many miles was Mike's ride? options: A)28 B)30 C)32 D)34 E)36 SOLUTION:The cost of Annie's ride was 2.5+5+(0.25*14) = $11 Let x be the distance of Mike's ride. The cost of Mike's ride is 2.5+(0.25*x) = 11 0.25*x = 8.5 x = 34 miles The answer is D. #### D QUESTION:A 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? options: A)45 B)40 C)35 D)30 E)50 SOLUTION:Explanation: Let the total number of students = x The average marks increased by 1/2 due to an increase of 83 - 63 = 20 marks. But total increase in the marks = 1/2×x=x/2 Hence we can write as x/2=20 ⇒x=20 x 2=40 Answer: Option B #### B QUESTION:Three unbiased coins are tossed. What is the probability of getting at most two heads? options: A)3/4 B)7/8 C)3/8 D)5/6 E)9/11 SOLUTION:Here S = {TTT, TTH, THT, HTT, THH, HTH, HHT, HHH} Let E = event of getting at most two heads. Then E = {TTT, TTH, THT, HTT, THH, HTH, HHT}. P(E)=n(E)/n(S) =7/8 The answer should be B #### B QUESTION:John throws a coin until a series of six consecutive heads or three consecutive tails appears. What is the probability that the game will end after the seventh throw? options: A)1/64 B)2/16 C)3/16 D)7/16 E)9/16 SOLUTION:Let's consider the routes that would lead to ending the game on the fourth toss. In order to be a win at that point, tosses #2#3#4 would all have to be the same, either H or T, and in order for the game NOT to end on the third toss, the first toss would have to be different from the other four. Thus, the only two possible sequences are H-T-T-T-T-T ----> P = (1/2)^7= 1/128 T-H-H-H-H-H ----> P = (1/2)^7= 1/128 Either one of these would satisfy the condition, so we could have one or the other. OR means add in probability. 1/128 + 1/128 = 2/128 = 1/64 Answer(A). #### A QUESTION:The product of all the prime numbers less than 20 is closest to which of the following powers of 10 ? options: A)10^9 B)10^8 C)10^7 D)10^6 E)10^5 SOLUTION:We should find the approximate value of 2*3*5*7*11*13*17*19 to some power of 10. # of different approximations are possible. Approach #1: 2*5=10; 3*7=~20 (actually more than 20); 11*19=~200 (actually more than 200); 13*17=~200 (actually more than 200); 2∗3∗5∗7∗11∗13∗17∗19≈10∗20∗200∗200=8∗106≈107 Answer: C. Approach #2: 2*5=10 3*17=~50 (actually more than 50); 7*13=~100 (actually less than 100); 11*19=~200 (actually more than 200) 2∗3∗5∗7∗11∗13∗17∗19≈10∗50∗100∗200=107. Answer: C. #### C QUESTION:Six children — A, B, C, D, E, and F — are going to sit in six chairs in a row. Child E must be somewhere to the left of child F. How many possible configurations are there for the children? options: A)60 B)180 C)240 D)360 E)720 SOLUTION:If we wanted, we could make this one extremely difficult, counting out all kinds of possibilities in several different cases. Instead, we are going to make this ridiculously easy. First of all, with absolutely no restrictions, how many ways can the six children be arranged on the six chairs? That’s a permutation of the 6 items —- 6P6 = 6! = 720. That’s the total number of arrangements with no restrictions. Of course, those 720 arrangements have all kinds of symmetry to them. In particular, in all of those arrangements overall, it’s just as likely for E to be to the left of F as it is for E to be to the right of F. Therefore, exactly half must have E to the right of F, and exactly half must have E to the left of F. Therefore, exactly (1/2)*720 = 360 of the arrangements have E to the left of F. Answer = D. #### D QUESTION:If xy not equal 0 and x^2*y^2 -xy = 20, which of the following could be y in terms of x? I. 1/2x II. -5/x III. 4/x options: A)II B)II and III C)I &II D)III E)IV SOLUTION:x2y2 - xy = 20 x2y2-xy-20 = 0 (xy-4)(xy+5)=0 xy = 4 or xy=-5 y = 4/x or y = -5/x II and III only B #### B QUESTION:Rahul 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? options: A)19 B)19.7 C)20 D)21.1 E)23 SOLUTION:Total cost of the items he purchased = Rs.25 Given that out of this Rs.25, 30 Paise is given as tax => Total tax incurred = 30 Paise = Rs.30/100 Let the cost of the tax free items = x Given that tax rate = 6% ∴ (25−30/100−x)6/100 = 30/100 ⇒ 6(25 −0.3 −x) = 30 ⇒ (25 − 0.3 − x) = 5 ⇒ x = 25 − 0.3 − 5 = 19.7 B) #### B QUESTION:From a total of 5 boys and 6 girls, how many 4-person committees can be selected if the committee must have exactly 2 boys and 2 girls? options: A)16 B)24 C)60 D)120 E)150 SOLUTION:Answer=E=150 No of 4 person committees that can be formed=5C2*6C2=150 Answer E #### E QUESTION:150 candies are distributed to children with the same number of candies for each child. What can’t be the range which includes the number of children? options: A)1~10 B)10~20 C)20~30 D)45~55 E)55~65 SOLUTION:150 = 2*3*5^2 There are factors in each range except for 55~65 The answer is E. #### E QUESTION:A bag contains 50 black balls and 10 white balls. One ball is drawn at random. What is the probability that the ball is white? options: A)1 B)1/6 C)1/3 D)1/2 E)None of these SOLUTION:Explanation: Total cases = 50 + 10 = 60 Favourable cases = 10 So probability = 10/60 = 1/6 Answer: B #### B QUESTION:Workers 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? options: A)350 B)400 C)500 D)550 E)590 SOLUTION:N * 50 = (325000 - 300000) = 25000 N = 25000 / 50 = 500 C #### C QUESTION:A 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? options: A)400 B)991 C)881 D)771 E)551 SOLUTION:2000 ---- 50 2000 ---- 40 x ----- 50 x*50 = 2000*40 x=1600 2000 ------- 400 Answer: A #### A QUESTION:14 times a number gives 210. The number is options: A)11 B)12 C)15 D)None E)Cannot be determined SOLUTION:Explanation: Let the number be 'N' 14×N=210⇒N=15 Correct Option: C #### C QUESTION:Find large number from below question The difference of two numbers is 1375. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder options: A)1235 B)1345 C)1678 D)1767 E)1647 SOLUTION:Let the smaller number be x. Then larger number = (x + 1375). x + 1375 = 6x + 15 5x = 1360 x = 272 Large number = 272+1375 = 1647 E #### E <<<Examples ends QUESTION:If the speed of the boat in still water is 12km/hr and the speed of the stream is 5km/hr. Find the time taken to travel 34kms down stream. options: A)4 hrs. B)1 hrs. C)3 hrs. D)2 hrs. E)5 hrs. SOLUTION:DS =speed of the boat + speed of the stream 5+12 =17km/hr. Time taken to cover 34km down stream =34/17 =2hrs. Answer : D #### D

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:A milkman purchases the milk at Rs. x per litre and sells it at Rs. 2x per litre still he mixes 2 litres water with every 6 litres of pure milk. What is the profit percentage? options: A)116% B)166.66% C)60% D)100% E)150% SOLUTION:Explanation: Let the cost price of 1 litre pure milk be Re.1, then {6 litres(milk)->cp=Rs.6, 2 litres(water)->cp=Rs.0}->cp=Rs.6 only and 8 litre mixture ->SP -> 8 x 2 = Rs.16 Profit %= [16/6 -6]x100=100/6=166.66% ANSWER IS B #### B QUESTION:If A:B is 3:4 and B:C is 4:5 then A:C is equal to options: A)1:3 B)3:5 C)3:4 D)3:7 E)1:5 SOLUTION:The two ratios given are having the same number 4 for B in both the ratios. Hence- A:B = 3:4 B:C = 4:5 => A:C = 3:5 Answer B #### B QUESTION:N and M are each 3-digit integers. Each of the numbers 3,4, 5, 6, 7, and 8 is a digit of either N or M. What is the smallest possible positive difference between N and M? options: A)59 B)49 C)58 D)113 E)131 SOLUTION:You have 6 digits: 3, 4, 5, 6, 7, 8 Each 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. The first digit (hundreds digit) of both numbers should be consecutive integers Now 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 3 and 8 in the hundreds places and reserve them for the tens places . Now what are the options? Try 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. 487 and 536 (difference is 49) or Try and make a pair with (6** and 7**). Make the 6** number as large as possible and make the 7** number as small as possible. We get 685 and 734 (difference is 49) B #### B QUESTION:If x is 20 percent greater than 98, then x = options: A)68 B)70.4 C)86 D)105.6 E)117.6 SOLUTION:x=98*1.2=117.6 So the answer is E. #### E QUESTION:A and B started a business and invested in 4:5 ratio.after 3 month A takes back 1/4 part of his investment and B takes back 1/5 part of his investment.after 10 month there is profit of 76000 rs.calculate the profit share of A. options: A)35000 B)43000 C)33000 D)46000 E)38000 SOLUTION:let A invested 4x rs. and B invested 5x rs. ratio of A and B investment={(4x*3)+[4x-1/4*4x]*7}:{(5x*3)+[5x-1/5*5x]*7} =(12x+21x):(15x+28x)=33:43. total profit=76000 rs. share profit of A=[76000*33/76]rs.=33000 rs. answer C #### C QUESTION:A grocer has a sale of Rs. 4435, Rs. 4927, Rs. 4855, Rs. 5230 and Rs. 4562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 4500? options: A)s. 1991 B)s. 2991 C)s. 3991 D)s. 4991 E)s. 5991 SOLUTION:Explanation: Total sale for 5 months = Rs. (4435 + 4927 + 4855 + 5230 + 4562) = Rs. 24009. Required sale = Rs. [ (4500 x 6) – 24009 ] = Rs. (27000 – 24009) = Rs. 2991. Answer B #### B QUESTION:Find the principle on a certain sum of money at 5% per annum for 2 2/5 years if the amount being Rs.1792? options: A)1600 B)2777 C)2889 D)27670 E)2771 SOLUTION:1792 = P [1 + (5*12/5)/100] P= 1600.Answer:A #### A QUESTION:John bought 2 shares and sold them for $90 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 options: A) a profit of $10 B) a profit of $8 C) a loss of $8 D) a loss of $20 E) neither a profit nor a loss SOLUTION:$ Profit of the share sold at 20% profit = 120-90 20-? $10 profit on the sale of 1 share. $ Loss of the share sold at 20% loss= 80-90 20-? $30 loss on the sale of 1 share. 10-30=Loss of $20 Answer: D #### D QUESTION:Three business people wish to invest in a new company. Each person is willing to pay one third of the total investment. After careful calculations, they realize that each of them would pay $2,200 less if they could find two more equal investors. How much is the total investment in the new business? options: A)$11,000 B)$50,000 C)$16,500 D)$ 6,600 E)$ 3,600 SOLUTION:Total Investment between 5: (x/5) Total investment including 2200 less between 3 people(x-(2200*3))/3 Set both eq. equal to each other. 16,500 Answer C) #### C QUESTION:The sum of the present ages of a father and his son is 60 years. Six years ago, father's age was five times the age of the son. After 6 years, son's age will be options: A)12 years B)20 years C)25 years D)28 years E)None SOLUTION:Solution Let the present ages of son and father be x and (60 - x) years respectively. Then, (60 - x) - 6 = 5(x - 6) = 54 - x = 5x - 30 ‹=›6x = 84 ‹=›x= 14. ∴Son's age after 6 years = (x + 6) = 20 years. Answer B #### B QUESTION:The 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's present age is : options: A)50 years B)46 years C)20 years D)45 years E)30 years SOLUTION:Let the sum of present ages of the two sons be x years. then father's present age =3x years. (3x+5)=2(x+10) 3x+5=2x+20 x=15. Hence, father's present age =45 years. Answer is D #### D QUESTION:A 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? options: A)500bc B)500b/c C)1000bc D)1000b/c E)1000/bc SOLUTION:2 cases * c cartons/case * b boxes/carton * 500 clips/box = 1000bc paper clips The answer is C. #### C QUESTION:If (1 – 1.5)N = 1, then N = options: A) −400 B) −140 C) −2 D) 4 E) 400 SOLUTION:(1 – 1.5)N = 1 Simplify to get: -0.5N = 1 Rewrite as (-1/2)N = 1 Multiply both sides by -2 to get: N = -2 Answer: C #### C QUESTION:During a recent track meet, Peter ran x meters of the 100 meter dash in 9 seconds; running at the same rate, how many seconds will it take Peter to run z meters of the 200 meter dash? options: A)9/xz B)9zx C)9x/z D)9z/x E)xz/9 SOLUTION:Speed of Peter = x/9 meters per second Time needed to run z meters = DISTANCE/SPEED = z / (x/9) =9z/x Option D The values 100m and 200m have no role to play here and are just given to confuse you. #### D QUESTION:A bag contains 6 white and 4 black balls .2 balls are drawn at random. find the probability that they are of same colour. options: A)15/7 B)4/17 C)7/18 D)19/6 E)7/15 SOLUTION:Let S be the sample space Then n(S)=no of ways of drawing 2 balls out of (6+4)=10c2=(10*9)/(2*1)=45 Let E=event of getting both balls of same colour Then n(E)=no of ways(2 balls out of six) or(2 balls out of 4) =(6c2+4c2)=(6*5)/(2*1)+(4*3)/(2*1)=15+6=21 P(E)=n(E)/n(S)=21/45=7/15 Option E #### E QUESTION:An investor receives a total combined return of 7% on his two different investments. On his $40,000 investment he receives a return of 6%. What is the return on his $20,000 investment? options: A)7.25% B)7.5% C)8% D)8.5% E)9% SOLUTION:0.06 * 40000 + 20000x = 0.07(60000) solving for x give x = 9% option E #### E QUESTION:For any non-zero a and b that satisfy |ab| = ab and |C| = -c |b - 4| + |ab - b| = ? options: A)a) ab - 4 B)b) b - 2b + 4 C)c) ab + 4 D)d) 2b - ab - 4a E)e) 4 - ab SOLUTION:|a| = -a Suggests that 'a' is Negative |ab| = ab Suggests that 'ab' is Positive 'ab' is Positive Suggests that 'a' and 'b' have same Sign i.e. either both positive or both negative But since 'a' is Negative therefore 'b' is Negative too. Since b is negative so |b - 4| = -b+4 Since ab is Positive and b is Negative so |ab - b| = ab - b i.e. |b - 4| + |ab - b| = -b+4 + ab - b =ab - 2b + 4 Answer: Option B #### B QUESTION:A CAN FINISH A WORK IN 12 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? options: A)4 B)5 1/2 C)6 D)8 E)NONE OF THESE SOLUTION:B'S 10 DAY'S WORK=(1/15*10)=2/3 REMAINING WORK = (1-2/3)=1/3 NOW, 1/18 WORK IS DONE BY A IN 1 DAY 1/3 WORK IS DONE BY A IN (12*1/3)=4 DAYS. CORRECT OPTION:A #### A QUESTION:A can run 3 Kms in 3 min 18 sec and B can run same distance in 3 min 40 sec, then by how much distance A can beat B? options: A)300 m B)220 m C)280 m D)195 m E)295 m SOLUTION:Distance travelled=3000m Time taken by A=3 m 18 s Time taken by B=3 m 40 sec=220 sec speed of B=3000m/220 s=150/11 m/s Difference between time of A and B=22 sec when time will be 3 m 18 s A will have travelled 3000m but B need 22 sec more to finish. Distance travelled by B in 22 sec=(150/11)*22=300 m Hence, A beat B by 300 m ANSWER:A #### A QUESTION:An 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 1/4 %, then the amount invested at 11% was? options: A)12500 B)37500 C)29977 D)26777 E)19871 SOLUTION:Let the sum invested at 9% be Rs. x and that invested at 11% be Rs. (100000 - x). Then, (x * 9 * 1)/100 + [(100000 - x) * 11 * 1]/100 = (100000 * 37/4 * 1/100) (9x + 1100000 - 11x) = 37000/4 = 925000 x = 87500 Sum invested at 9% = Rs. 87500 Sum invested at 11% = Rs. (100000 - 87500) = Rs. 12500. Answer: A #### A QUESTION:A train running at the speed of 60 km/hr crosses a pole in 15 seconds. Find the length of the train? options: A)250 meter B)876 meter C)167 meter D)719 meter E)169 meter SOLUTION:Speed = 60*(5/18) m/sec = 50/3 m/sec Length of Train (Distance) = Speed * Time (50/3) * 15 = 250 meter Answer: A #### A QUESTION:How 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? options: A)24 sec B)30 sec C)27 sec D)28 sec E)29 sec SOLUTION:Speed of train relative to man = 63 - 3 = 60 km/hr. = 60 * 5/18 = 50/3 m/sec. Time taken to pass the man = 400 * 3/50 = 24 sec. Answer:A #### A QUESTION:The C.P of 15 books is equal to the S.P of 18 books. Find his gain% or loss%? options: A)16 2/3% loss B)100/3% loss C)50/3% profit D)100/3% loss E)200/3% loss SOLUTION:Explanation: 15 CP = 18 SP 18 --- 3 CP loss 100 --- ? => 16 2/3% loss ANSWER IS A #### A QUESTION:A 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 24 on Wednesday, what would be the value of D calculated on the following Saturday? options: A)3450 B)3860 C)4220 D)4670 E)5040 SOLUTION:On Saturday, the value would be 7*6*5*24 = 5040 The answer is E. #### E QUESTION:We bought 85 hats at the store. Blue hats cost $6 and green hats cost $7. The total price was $600. How many green hats did we buy? options: A)A)36 B)B)90 C)C)40 D)D)42 E)E)44 SOLUTION:Let B be the number of blue hats and let G be the number of green hats. B+G=85. B=85-G. 6B+7G=600. 6(85-G)+7G=600. 510-6G+7G=600. G=600-510=90. The answer is B. #### B QUESTION:A 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? options: A)17 kmph B)45 kmph C)86 kmph D)197 kmph E)15 kmph SOLUTION:Let the distance to be travelled to catch the bus be x km x/30 - x/40 = 30/60 => (4x - 3x)/120 = 1/2 => x = 60 km By traavelling 30 kmph time taken = 60/30 = 2 hours By 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. Answer:B #### B QUESTION:A six-sided die is rolled once. What is the probability that the number rolled is an even number greater than 2? options: A)1/4 B)2/4 C)1/2 D)1/3 E)2/3 SOLUTION:Out 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 (number of even numbers greater than 2) / 6 = 2 / 6 = 1 / 3 correct answer D #### D QUESTION:the egg vendor calls on his 1st customer and sells his half his eggs and half an egg.to the 2nd customer he sells half of what he had left and half an egg,and to the 3rd customer he sells half of what he had then left and half an egg.by the way he did not break any eggs.in the end 3 eggs were remainig.how many did he start out with? options: A)21 B)31 C)41 D)51 E)61 SOLUTION:He start out with 31eggs. In the end, he have 3eggs left. So, 3*2 +1= 7 7*2 +1= 15 15*2 +1= 31 31eggs he had initially. ANSWER:B #### B QUESTION:121,112,...?..,97,91,86 options: A)99 B)104 C)102 D)108 E)100 SOLUTION:121. 112. 104. 97. 91. 86 the decreasing difference is reducing by 1 at each step so,missing no. will be 104 answer B #### B QUESTION:Large, medium and small ships are used to bring water. 4 large ships carry as much water as 7 small ships; 3 medium ships carry as much water as 2 large ships and 1 small ship. If 15 large, 7 medium and 14 small ships, each made 36 journeys to bring a certain quantity of water, then in how many journeys will 12 large, 14 medium and 21 small ships bring the same quantity of water? options: A)29 B)30 C)20 D)50 E)55 SOLUTION:Explanation : Here, Large, Medium and Small ships are denoted by the symbol L, M and S. Now, according to the question, 4L = 7S. ------(i) 3M = 2L + S. ------(ii) Using above equations, the ratios of the capacity of the Large, Medium and Small ships are :- 7: 6 : 4. Let, the number of journeys required be x. Since, quantity of water remains the same, so :- =((15×7+7×6+14×4)36) = x (12×7+14×6+21×4). =>((15×7+7×6+14×4)36) / (12×7+14×6+21×4)= x =>x=7308/252 =>x=29. Answer : A #### A QUESTION:Three math classes: X, Y, and Z, take an algebra test. The average score in class X is 83. The average score in class Y is 76. The average score in class Z is 85. The average score of all students in classes X and Y together is 79. The average score of all students in classes Y and Z together is 81. What is the average score for all the three classes, taken together? options: A)81 B)81.5 C)82 D)84.5 E)None of these SOLUTION:Explanation : Let the number of students in classes X, Y and Z be a, b and c respectively. Then Total of X = 83a Total of Y = 76b Total of Z = 85c And , (83a + 76b) / (a + b) = 79. i.e 4a = 3b. Also, (76b + 85c) / (b + c) = 81. i.e 4c = 5b. Hence, b= (4/3)a, c =(5/4)b = (5/4) x (4/3)a = (5/3)a. Average of X, Y and Z = (83a + 76b + 85c ) / (a + b + c). => 83a+76∗(4/3)a+85∗(5/3)a /a+(4/3)a+(5/3)a . => 978/12 => 81.5 Answer : B #### B QUESTION:Pipe A runs 10 liters of water per minute into a tank that has a total volume of 1,200 liters. Pipe B fills an half the tank in 1 hours. Working together how long will it take both pipes to fill the tank ? options: A)2 hours and 36 minutes B)1.5 hours C)9 hours and 12 minutes D)15 hours E)1 hour and 12 minutes. SOLUTION:Pipe A has a rate of 10 liters per minute which equals a rate of 600 liters per hour. Pipe B has a rate of 400 liters per hour. 400 + 600 (A+B) = Together they have a rate of 1000 liters per hour. 1200 (The tank ) / 1000 = 6/5 = 1 hour and 12 minutes Answer -E #### E QUESTION:If m=9^(x−1), then in terms of m, 3^(4x−6) must be which of the following? options: A)m/3 B)9m C)9m^2 D)m^2/3 E)m^2/9 SOLUTION:m = 9 ^ (X-1) m = 3 ^ (2x-2) m^2 = 3 ^ (4x-4) m^2/9 = 3 ^ (4x-6) Answer E #### E QUESTION:a, b, c, and d are positive consecutive even integers and a < b < c < d. If 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? options: A)2 B)4 C)8 D)12 E)20 SOLUTION:We know the numbers must be consecutive even numbers, from the list 2, 4, 6, 8, 10, 12, 14, 16, and so on. The 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. However, 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. The answer, then, is the product of the smallest two numbers, or 2x4, which is 8 (option C). #### C QUESTION:If 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? options: A)4/5 km B)4/6 km C)4/9 km D)4/1 km E)4/3 km SOLUTION:x/3 – x/4 = 4/60 x = 4/5 km Answer: A #### A QUESTION:Rajan and Rakesh started a business and invested Rs. 20,000 and Rs. 25,000 respectively. After 4 months Rakesh left and Mukesh joined by investing Rs. 15,000. At the end of the year there was a profit of Rs. 4,600. What is the share of Rajan? options: A)2000 B)2100 C)2200 D)2300 E)2400 SOLUTION:Ratio of share of Rajan, Rakesh nd Mukesh => 20000:25000:15000 =>4:5:3 =>4*12 : 5*4 : 3*8 [Since Rakesh left after 4 months nd Mukesh joined after 4 months...] => 12:5:6 Share of Rajan => 4600*12/23 = 2400 ANSWER:E #### E QUESTION:The length of a train and that of a platform are equal. If with a speed of 72 k/hr, the train crosses the platform in one minute, then the length of the train (in meters) is? options: A)227 B)299 C)276 D)600 E)211 SOLUTION:Speed = [72 * 5/18] m/sec = 20 m/sec; Time = 1 min. = 60 sec. Let the length of the train and that of the platform be x meters. Then, 2x/60 = 20 è x = 20 * 60 / 2 = 600 Answer: D #### D QUESTION:A lady bought five books namely A,B,C,D,E to distribute her 3 child. How many ways she can distribute books? options: A)3^3 B)3^4 C)3^5 D)3^6 E)3^2 SOLUTION:3*3*3*3*3 3^5 ANSWER:C #### C QUESTION:A 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 66 books in the special collection at that time, how many books of the special collection were loaned out during that month? options: A)20 B)30 C)35 D)45 E)55 SOLUTION:there are 9 books less(75-66) which represents 20% of the loaned books (100-80) So total loaned out books = 45 Answer D #### D QUESTION:8^100 is divisible by 17. Find the remainder? options: A)8 B)12 C)16 D)18 E)20 SOLUTION:This 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. So divide 100 by 16 and find the remainder. Remainder = 4 Therefore, 100 = (16 × 6) + 4 Now this problem can be written as 810017 = 816×6+417 = (816)6×8417 Now this problem simply boils down to (1)6×8417 = 8417 84 = 82×82, we need to find the remainder when 64 × 64 is divisible by 17. Or 13 × 13 = 169. When 169 is divided by 17, remainder is 16. C #### C QUESTION:The perimeter of one face of a cube is 48 cm. Its volume will be: options: A)125cm3 B)400cm3 C)250cm3 D)625cm3 E)None of these SOLUTION:Explanation: Edge of cude = 48/4 = 12 cm Volume = a*a*a = 12*12*12 = 1728 cm cube Option E #### E QUESTION:jhon has 10 choclates, jennifer has 5 choclates. Totally how many choclates they have in all? options: A)5 B)10 C)15 D)20 E)14 SOLUTION:10+5=15. Answer is C #### C QUESTION:What will be the ratio of simple interest earned by certain amount at the same rate of interest for 2 years and that for 10 years? options: A)3 : 2 B)1 : 3 C)2 : 3 D)1 : 5 E)2 : 1 SOLUTION:Explanation : Simple Interest = PRT/100 Here Principal(P) and Rate of Interest (R) are constants Hence, Simple Interest ∝ T Required Ratio = Simple Interest for 2 years/Simple Interest for 10 years =T1/T2 =2/10 =1/5 =1:5 Answer : Option D #### D QUESTION:A 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? options: A)276 Marks B)200 Marks C)186 Marks D)187 Marks E)167 Marks SOLUTION:30% ------------ 50 45% ------------ 25 ---------------------- 15% ------------- 75 30% -------------- ? 150 + 50 = 200 Marks Answer: B #### B QUESTION:Given that 268x74= 19632, find the value of 2.68x.74. options: A)1.9632 B)1.0025 C)1.5693 D)1.0266 E)None SOLUTION:Solution Sum of decimals places =(2+2) = 4. Therefore, = 2.68×.74 = 1.9632 Answer A #### A QUESTION:If Rs.450 amount to Rs.540 in 4 years, what will it amount to in 6 years at the same rate % per annum? options: A)s.575 B)s.595 C)s.590 D)s.580 E)s.585 SOLUTION:80 = (450*4*R)/100 R = 5% I = (450*6*5)/100 = 135 450 + 135 = 585 ANSWER:E #### E QUESTION:A 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? options: A)12 B)13 C)46 D)37 E)26 SOLUTION:16x + 85 = 17(x + 3) x = 34 + 3 = 37 Answer: D #### D QUESTION:A and B started a business investing Rs. 24,000 and Rs 18,000 respectively. In what ratio the profit earned after 2 years be divided between A and B respectively? options: A)4 : 3 B)9:2 C)18:20 D)1:4 E)18:4 SOLUTION:A: B =24000 : 18000 = 8 : 6 = 4 : 3 ANSWER:A #### A QUESTION:Find the invalid no.from the following series 15, 16, 33, 105, 424, 2124, 12756 options: A)16 B)33 C)105 D)424 E)2124 SOLUTION:2nd term = (1st term) * 1 + 1 = 15 *1 + 1 = 16. 3rd term = (2nd term) * 2 + 2 = 16 * 2 + 2 = 34 4th term = (3th term) *3 + 3 = 34 * 3 + 3 = 105 5th term = (4th term) * 4 + 4 = 105 * 4 + 4 = 424 6th term = (5th term) * 5 + 5 = 424 * 5 + 5 = 2125 3th term should 34 instead of 33. B #### B QUESTION:John 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? options: A)17 B)18 C)19.7 D)21 E)27 SOLUTION:Total cost of the items he purchased = Rs.25 Given that out of this Rs.25, 30 Paise is given as tax => Total tax incurred = 30 Paise = Rs.30/100 Let the cost of the tax free items = x Given that tax rate = 6% ∴ (25−30/100−x)6/100 = 30/100 ⇒ 6(25 −0.3 −x) = 30 ⇒ (25 − 0.3 − x) = 5 ⇒ x = 25 − 0.3 − 5 = 19.7 C) #### C QUESTION:If P(A) = 5/7 and P (B) = 2/5, find P (A n B) if A and B are independent events. options: A)7/25 B)3/25 C)8/25 D)2/7 E)3/17 SOLUTION:P (A n B) = P(A) . P(B) P (A n B) = 5/7 . 2/5 P (A n B) = 2/7. D #### D QUESTION:An investor invests in a new fund. The fund averages 20% growth annually for the first three years, but it loses 40% of its value in the fourth year. At the end of four years, the value of the fund is approximately what percent of the original amount? options: A)91.23% B)95.56% C)97.86% D)101.45% E)103.68% SOLUTION:0.6*1.2^3 = 1.0368 The answer is E. #### E QUESTION:At 9 am a car (A) began a journey from a point, traveling at 40 mph. At 10 am another car (B) started traveling from the same point at 60 mph in the same direction as car (A). At what time will car B pass car A? options: A)12 pm B)1 pm C)2 pm D)3 pm E)4 pm SOLUTION:After t hours the distances D1 traveled by car A is given by D1 = 40 t Car B starts at 10 am and will therefore have spent one hour less than car A when it passes it. After (t - 1) hours, distance D2 traveled by car B is given by D2 = 60 (t-1) When car B passes car A, they are at the same distance from the starting point and therefore D1 = D2 which gives 40 t = 60 (t-1) Solve the above equation for t to find t = 3 hours Car B passes car A at 9 + 3 = 12 pm Answer A #### A QUESTION:Together, 15 type A machines and 7 type B machines can complete a certain job in 4 hours. Together 8 type B machines and 15 type C machines can complete the same job in 11 hours. How many W hours would it take one type A machine, one type B machine, and one type C machine working together to complete the job (assuming constant rates for each machine)? options: A) 22 hours B) 30 hours C) 44 hours D) 60 hours E) It cannot be determined from the information above. SOLUTION:Say the rates of machines A, B and C are a, b, and c, respectively. Together 15 type A machines and 7 type B machines can complete a certain job in 4 hours --> 15a + 7b = 1/4; Together 8 type B machines and 15 type C machines can complete the same job in 11 hours --> 8b + 15c = 1/11. Sum the above: 15a + 15b + 15c = 1/4 + 1/11 = 15/44 --> reduce by 15: a + b + c = 1/44 --> so, the combined rate of the three machines is 1/44 job/hour --> time is reciprocal of the rate, thus machines A, B and C can do the job W in 44 hours. Answer: C. #### C QUESTION:A 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? options: A)6 months B)8 months C)10 months D)7 months E)12 months SOLUTION:Explanation: 7 * 8 : 9 * x = 8:9 => x= 7 ANSWER IS D #### D QUESTION:A football coach must choose 4 freshers from a team of 11 players. How many different ways can the coach choose the freshers? options: A)330 B)650 C)729 D)800 E)890 SOLUTION:Choose 4 starters from a team of 11 players. Order is not important. \inline {\color{Black} 11C_{4}}= 330 A #### A QUESTION:A man sitting in a train which is traveling at 50 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.? options: A)50 kmph B)58 kmph C)62 kmph D)65 kmph E)75 kmph SOLUTION:Relative speed = 280/9 m / sec = ((280/9)*(18/5)) kmph = 112 kmph. Speed of goods train = (112 - 50) kmph = 62 kmph. Answer : C. #### C QUESTION:The 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: options: A)279 B)283 C)308 D)318 E)342 SOLUTION:Other number = (11 x 7700)/275 = 308. Answer: Option C #### C QUESTION:What is the HCF of 2/3, 5/9 and 6/5 options: A)1/45 B)2/45 C)4/15 D)8/45 E)9/45 SOLUTION:Explanation: HCF of Fractions = HCF of Numerators/LCM of Denominators = (HCF of 2, 5, 6)/(LCM of 3, 9, 5) = 1/45 Answer: Option A #### A QUESTION:The ratio, by weight, of coffee to sugar to water in a pot of coffee is 7:3:15. 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? options: A)12 B)13 C)14 D)15 E)16 SOLUTION:The new ratio of coffee to sugar is 3.5:3 The new ratio of coffee to water is 14:15. The new ratio of coffee to sugar to water is 14:12:15. If there are 12 grams of sugar, then there are (15/12)*12=15 grams of water. The answer is D. #### D QUESTION:A bag contains 7 green and 8 white balls. If two balls are drawn simultaneously, the probability that both are of the same colour is ? options: A)7/17 B)7/22 C)7/18 D)7/19 E)7/15 SOLUTION:Drawing two balls of same color from seven green balls can be done in ⁷C₂ ways. Similarly from eight white balls two can be drawn in ⁸C₂ ways. P = 7C2/¹15C2 + 8C2/15C2 = 7/15 Answer: E #### E QUESTION:A and B undertake to do a piece of work for Rs. 1200. 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 B. options: A)250 B)450 C)750 D)800 E)None of them SOLUTION:C's 1 day's work = 1/3-(1/6+1/8)=24 A : B : C = Ratio of their 1 day's work = 1/6:1/8:1/24= 4 : 3 : 1. A’s share = Rs. (1200 *4/8) = Rs.600, B's share = Rs. (1200 *3/8) = Rs. 450 C's share = Rs. [1200 - (300 + 225») = Rs. 150. Answer is B #### B QUESTION:The area of sector of a circle whose radius is 12 metro and whose angle at the center is 42° is? options: A)52.7 m2 B)57.8 m2 C)52.8 m2 D)72.8 m2 E)52.8 m2 SOLUTION:42/360 * 22/7 * 12 * 12 = 52.8 m2 Answer: C #### C QUESTION:log3 N+log5 N what is 3 digit number N that will be whole number options: A)629 B)729 C)829 D)125 E)727 SOLUTION:No of values N can take is 1 5^3=125 ANSWER:D #### D <<<Examples ends QUESTION:161?85?65?89=100 then use + or - in place of ? and take + as m,- as n then find value of m-n options: A)3 B)-1 C)1 D)-3 E)2 SOLUTION:161-85-65+89=100 so m=1, n=2 => (m-n)=-1 ANSWER:B #### B

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:How many kg of pure salt must be added to 100kg of 10% solution of salt and water to increase it to a 15% solution? options: A)A)5.8 B)B)1.3 C)C)9.6 D)D)12.5 E)E)7.9 SOLUTION:Amount salt in 100kg solution = 10*100/100 = 10 kg Let x kg of pure salt be added then(10+x)/(100+x)=15/100 200+20x=300+3x 17x = 100 x = 5.8 Answer is A #### A QUESTION:If Leo gains 10 pounds, he will weigh 50% more than his sister Kendra. Currently their combined weight is 160 pounds. What is Leo's current weight? options: A)80 B)86 C)92 D)98 E)104 SOLUTION:L+K = 160 and so K = 160-L L+10 = 1.5K = 1.5(160-L) 2.5L = 230 L = 92 The answer is C. #### C QUESTION:Positive Integer A gives the remainder of 18 when divided by another positive Integer B. If A/B = 147.24, what is the value of B? options: A)96 B)75 C)48 D)25 E)12 SOLUTION:.24 of B = Remainder .24 of B = 18 B = (18*100) / 24 = 75. B #### B QUESTION:In a two digit number, the digit in the units place is three times the digit in ten's place and sum of the digits is equal to 8. What is the number? options: A)26 B)28 C)32 D)36 E)38 SOLUTION:Solution Let the ten digits be x. Then,units digit=3x Therefore x + 3x = 8 ‹=›4x = 8 ‹=›x= 2. So, ten's digit = 2, unit's digit = 6. Hence, the required number is 26. Answer A #### A QUESTION:A family made a down payment of $20 and borrowed the balance on a set of encyclopedias that cost $120. The balance with interest was paid in 7 monthly payments of $15.2 each and a final payment of $7. The amount of interest paid was what percent of the amount borrowed? options: A) 6% B) 12% C) 13.4% D) 16% E) 20% SOLUTION:interest paid = 15.2*7+7 - 100 = 13.4 % off the balance = (13.4/100) * 100 = 13.4 % Answer is C. #### C QUESTION:In how many ways a committee consisting of 5 men and 6 women can be formed from 8 men and 10 women? options: A)266 B)86400 C)11760 D)5040 E)None of these SOLUTION:Here, 5 men out of 8 men and 6 women out of 10 women can be chosen in 8C5 × 10C6 ways, i.e., 11760 ways. Answer C #### C QUESTION:A bike covers a certain distance at the speed of 67km/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? options: A)89.33 km/h B)85.34 km/h C)87.67 km/h D)90.25 km/h E)90.64 km/h SOLUTION:Ans.(A) Sol. Total distance = 67 × 8 = 536 km Now speed = 536/6 = 89.33 km/h #### A QUESTION:8, 24, 12, 36, 18, 54, (....) options: A)72 B)68 C)108 D)27 E)86 SOLUTION:8 × 3 = 24 24 ÷ 2 = 12 12 × 3 = 36 36 ÷ 2 = 18 18 × 3 = 54 54 ÷ 2 = 27 Answer is D. #### D QUESTION:A train 2000 m long can cross an electric pole in 25 sec and then find the speed of the train? options: A)322 B)324 C)326 D)328 E)330 SOLUTION:Length = Speed * time Speed = L/T S = 2000/25 S = 80 M/Sec Speed= 80*18/5 (To convert M/Sec in to Kmph multiply by 18/5) Speed = 324 Kmph Answer: B #### B QUESTION:A trader bought a car at 20% discount on its original price. He sold it at a 40% increase on the price he bought it. What percent of profit did he make on the original price? options: A)12% B)19% C)15% D)14% E)22% SOLUTION:Original price = 100 CP = 80 S = 80*(140/100) = 112 100 - 112 = 12% Answer:A #### A QUESTION:At Company K, 15 percent of the employees are secretaries and 60 percent are salespeople. If there are 30 other employees of Company K, how many employees does Company K have? options: A) 160 B) 120 C) 190 D) 200 E) 400 SOLUTION:Let the total number of employees in the company be x % of secretaries = 15% % of salespeople = 60% % of of employees other than secretaries and salespeople = 100 - 75 = 25% But this number is given as 30 so 25% of x = 30 x = 120 Therefore there a total of 120 employees in the company K Correct answer - B #### B QUESTION:A train consists of 12 boggies, each boggy 15 metres long. The train crosses a telegraph post in 18 seconds. Due to some problem, three boggies were detached. The train now crosses a telegraph post in options: A)18 sec B)12 sec C)15 sec D)20 sec E)13.5 sec SOLUTION:Length of train = 12 × 15 = 180 m. Then, speed of train = 180⁄18 = 10 m/s Now, length of train = 9 × 15 = 135m ∴ Required time = 135⁄10 = 13.5 sec. Answer E #### E QUESTION:If x and y are different integers and x^2 = xy, which of the following must be true ? I. x = y II. y = 0 III. x = 0 options: A)I only B)II only C)III only D)I and III only E)I, II, and III SOLUTION:Answer choice A is correct. The question gives you x^2=xy you can simplify that as x^2-xy=0 x(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. Answer C #### C QUESTION:An electric pump can fill a tank in 5 hours. Because of a leak in the tank, it took 10hours to fill the tank. If the tank is full, how much time will the leak take to empty it? options: A)10hours B)12hours C)8hours D)5hours E)15hours SOLUTION:Work done by the leak in 1 hour = 1/5 - 1/10 = 1/10 The leak will empty the tank in 10hours Answer is A #### A QUESTION:A train crosses a platform in 15 sec, same train crosses another platform of length 250 m in 20 sec. If the speed of the train is 15 m/sec then find the length of the platform? options: A)277m B)180m C)165m D)278m E)175m SOLUTION:Length of the train be ‘X’ (X + 250)/20 = 15 X = 50m Let the length of the platform be y (y + 50)/15 = (50 + 250)/20 4y + 200 = 900 X = 1750m Answer: E #### E QUESTION:If the sum of two numbers is 22 and the sum of their squares is 386, then the product of the numbers is options: A)40 B)49 C)80 D)88 E)90 SOLUTION:Sol. Let the numbers be x and y. Then, (x+y) = 22 and x2 + y2 = 386. Now, 2xy = (x+y)2 - (x2 + y2) = (22)2 - 386= 484 - 386= 98 xy = 49. Answer B #### B QUESTION:Solve x^2 – 7x = 0 options: A)(0,7) B)(0,3) C)(0,2) D)(0,5) E)(0,6) SOLUTION:This quadratic factors easily: Copyright © Elizabeth Stapel 2002-2011 All Rights Reserved x^2 – 7x = 0 x(x – 7) = 0 x = 0 or x – 7 = 0 x = 0 or x = 7 The solution is x = 0, 7 Ans: A #### A QUESTION:In 1970 there were 8,902 women stockbrokers in the United States. By 1978 the number had increased to 24,947. Approximately what was the percent increase? options: A) 45% B) 125% C) 145% D) 150% E) 180% SOLUTION:The percent increase is (24947-8902)/8902=16045/8902=1.80 So the approximate answer is E #### E QUESTION:A is twice as good a workman as B and together they complete a work in 12 days. In how many days A alone can do the work? options: A)32 B)33 C)34 D)35 E)36 SOLUTION:A’s one day’s work : B’s one day’s work= 2:1 (A+B)’s one day’s work= 1/12 B’s one day’s work= 1/12 *1/3 = 1/36 B alone can do the work in 36 days ANSWER:E #### E QUESTION:A train 120 m long passed a pole in 6 sec. How long will it take to pass a platform 360 m long? options: A)20 sec B)21 C)22 D)23 E)24 SOLUTION:Speed = 120/6 = 20 m/sec. Required time = (120 + 360)/20 = 24 sec. Answer:E #### E QUESTION:A man cheats while buying as well as while selling. While buying he takes 11% more than what he pays for and while selling he gives 20% less than what he claims to. Find the profit percent, if he sells at 9.09% below the cost price of the claimed weight. options: A)19.81% B)20% C)37.5% D)25% E)42.86% SOLUTION:There is a one step calculation method too. It requires more thought but is faster. The man takes 11% more than what he pays for. So if he claims to take 100 pounds, he pays $100 but he actually takes 111 pounds for which he will take from the customer $111. Hence, in effect, there is a 11% mark up. While selling, he sells 30% less. This means, he claims to sell 100 pounds and gets $100 but actually sells only 70 pounds and should have got only $70 for it. So this is again a mark up of $30 on $70. But he also sells at 9.09% less i.e. gives a discount of 1/11. (1 + m1%)(1 + m2%)(1 - d%) = (1 + p%) 11/10 * 10/7 * 10/11 = (1 + p%) profit % = 42.86%E #### E QUESTION:A bus from city M is traveling to city N at a constant speed while another bus is making the same journey in the opposite direction at the same constant speed. They meet in point P after driving for 2 hours. The following day the buses do the return trip at the same constant speed. One bus is delayed 24 minutes and the other leaves 36 minutes earlier. If they meet 24 miles from point P, what is the distance Q between the two cities? options: A)48 B)72 C)96 D)120 E)192 SOLUTION:Hmmm I did this question a while ago and got it wrong so trying again Rate x time = distance. For the initial trip lets the distance Q to the midpoint be represented by P. EQN1: R x 2 = P For the second trip we know one bus left late and one left early. Together this is just a tricky way of saying one bus left an hour after the other. We know the total trip takes 4 hours (since getting to P is 2 hours). The second trip can be represented by: Since the trip takes 4 hours if a bus leaves one hour early, the reminaining 3 hours are split between the two buses, ie. 1 + 3/2 = 2.5 EQN2: R x 2.5 = P + 24 EQN2-EQN1 : 0.5R=24 R=48 So the distance is rate x time = 48 x 4 = 192. ANS = E #### E QUESTION: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? options: A)20/67 B)20/63 C)20/19 D)20/18 E)20/28 SOLUTION:Required probability = (⁵C₃ . ⁴C₁)/⁹C₄ = (10 * 4)/126 = 20/63 Answer: B #### B QUESTION:Find the average marks of all the students in 2 separate classes, if the average marks of students in the first class of 55 students is 60 and that of another class of 48 students is 58 options: A)55.1 B)51.1 C)53.1 D)52.1 E)59.1 SOLUTION:Sum of the marks for the class of 55 students = 55 * 60 = 3300 Sum of the marks for the class of 48 students = 48 * 58 = 2784 Sum of the marks for the class of 103 students = 3300 + 2784 = 6084 Average marks of all the students = 6084/103 = 59.1 Answer:E #### E QUESTION:Solution X is 30% chemical A and 70% chemical B by volume. Solution Y is 40% chemical A and 60% chemical B by volume. If a mixture of X and Y is 36% chemical A, what percent of the mixture is Solution X? options: A)30% B)35% C)40% D)45% E)50% SOLUTION:The volume of the mixture be X+Y. 0.3X +0.4Y=0.36(X+Y) X=2Y/3 X/(X+Y)=(2Y/3) / (5Y/3)=2/5=40%. The answer is C. #### C QUESTION:A company hired a printer to produce a total of x + 1 envelopes. The job consisted of two types of envelopes, 4¢ envelopes and 5¢ envelopes. If the company requested 3 more 4¢ envelopes than 5¢ envelopes, which of the following expressions denotes the cost, in cents, of the total x + 1 envelopes ? options: A)3x+32 B)5x-1 C)(7x+15)/2 D)(9x-4)/2 E)6x+2 SOLUTION:We can take X+1 = 9 X= 8 So 4c envelopes will be 6 and 5c envelopes will be 3 So total cost will be 39 Then that is our target Plug x =8 in answer choices Only B works Correct Answer : B #### B QUESTION:There are 7 magazines lying on a table; 3 are fashion magazines and the other 4 are sports magazines. If 3 magazines are to be selected at random from the 8 magazines, what is the probability that at least one of the fashion magazines will be selected? options: A)1/2 B)7/8 C)32/35 D)11/12 E)13/14 SOLUTION:answer isB Total probability=7C3=48 4C3 +4C2*4C1+4C1*4C2=4+24+24=42 therefore the probability that at least one of the fashion magazines will be selected= 42/48=7/8 B #### B QUESTION:If the product of the integers j, k, l and m is 770, and if 1 < j< k< l< m, what is the value of j+ m? options: A)10 B)13 C)16 D)18 E)21 SOLUTION:770 = 2 * 5 * 7 * 11 So j= 2, k= 5, l= 7, m= 11 j+ m= 2 + 11 = 13 Answer - B #### B QUESTION:A person's salary is getting reduced by 20%. What percentage should be added to get back his original salary? options: A)25% B)50% C)75% D)85% E)95% SOLUTION:Salary he get after reduced 20% = 100-20% = 80% So,percentage should be added to get back his salary = (20/80)*100 = 25% ANSWER:A #### A QUESTION:An article is bought for Rs.600 and sold for Rs.500, find the loss percent? options: A)16 2/5% B)16 8/3% C)16 2/7% D)16 2/3% E)12 2/3% SOLUTION:600 ---- 100 100 ---- ? => 16 2/3% Answer: D #### D QUESTION:The sum of the non-prime numbers between 10 and 20, non-inclusive, is options: A)60 B)75 C)90 D)105 E)120 SOLUTION:sum of consecutive integers from 11 to 19, inclusive ====> (A1 + An)/2 * # of terms = (11 + 19)/2 * 9 = 15 *9 = 135 sum of non-prime numbers b/w 10 and 20, non inclusive ===> 135 - 60 (i.e., 11 + 13 + 17 + 19, being the prime #s in the range) = 75 Answer: B #### B QUESTION:How much time will it take for an amount of Rs. 900 to yield Rs. 81 as interest at 4.5% per annum of simple interest? options: A)2 years B)3 years C)1 year D)4 years E)5 years SOLUTION:Explanation: P = Rs.900 SI = Rs.81 T = ? R = 4.5% T= (100×SI)/PR = (100×81)/(900×4.5) = 2 years Answer: Option A #### A QUESTION:A school has received 60% of the amount it needs for a new building by receiving a donation of $500 each from people already solicited. People already solicited represent 50% 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? options: A)$200 B)$333.33 C)$100.25 D)$277.78 E)$377.00 SOLUTION:Let us suppose there are 100 people. 50% of them donated $25000 ( 500 * 50 ) $25000 is 60% of total amount. So total amount = 25000 * 100/60 Remaining amount is 40% of total amount. 40% of total amount = 25000 * (100/60) * (40/100) = 50000/3 This amount has to be divided by 50( remaining people are 50 ) So per head amount is 50000/3 / 50 = 32000/180 = 333.33; ANSWER:B #### B QUESTION:A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train? options: A)120 metres B)180 metres C)324 metres D)150 metres E)100 meters SOLUTION:Speed=60 x5/18m/sec=50/3 m/sec. Length of the train = (Speed x Time). Length of the train = 50/3 x 9m = 150 m. ANSWER:D #### D QUESTION:The residents of the town A participated in a survey to determine the number of hours per week each resident spent watching television. The distribution of the results of the survey had a mean of 21 hours and a standard deviation of 6 hours. The number of hours that Pat, a resident of town A, watched television last week was between 1 and 2 standard deviations below the mean. Which of the following could be the number of hours that Pat watched television last week? options: A)- 30 B)- 20 C)- 6 D)- 12 E)- 16 SOLUTION:(21-6*2)<number of hours that Pat watched television last week <(21-6*1) =9<W<15 12=C. #### C QUESTION:Two 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 options: A)18% B)20% C)25% D)23% E)Cannot be determined SOLUTION:Answer: C. #### C QUESTION:A buffet costs rs300. owner reduced the price 20% less. he got profit of 25% on its revenue. what is the percentage increase in number of customers? options: A)56% B)57% C)58% D)45% E)35% SOLUTION:let assume he sells 1 buffet daily, now then 300*1 = revenue (eq -1) if he reduced his price by 20% then , 240*(customer) = 125/100*revenue customer = 1.25*300/240 = 1.56 means 56 % increase in customer. ANSWER:A #### A QUESTION:An article is bought for Rs.675 and sold for Rs.900, find the gain percent? options: A)33 1/8% B)33 1/1% C)33 1/3% D)33 2/3% E)32 1/3% SOLUTION:675 ---- 225 100 ---- ? => 33 1/3% Answer:C #### C QUESTION:Kamal will complete work in 20 days. If Suresh is 25% more efficient than Kamal, he can complete the work in --- days. options: A)11 B)12 C)13 D)15 E)16 SOLUTION:Work done by Kamal in 1 day = 1/20 Work done by Suresh in 1 day = (1/20) × (125/100) = 5/80 = 1/16 => Suresh can complete the work in 16 days Answer is E. #### E QUESTION:an article with cost price of 192 is sold at 25% profit. what is the selling price? options: A)198 B)200 C)204 D)240 E)210 SOLUTION:sp=1.25*192=240 ANSWER:D #### D QUESTION:A can do a job in 16 days and B can do it in 30 days. A and B working together will finish twice the amount of work in ------- days? options: A)28 4/5 days B)25 4/5 days C)22 4/5 days D)20 4/5 days E)21 4/5 days SOLUTION:1/16 + 1/30 = 46/480 =23/240 240/23=11 2/5 *2 = 22 4/5 days ANSWER:C #### C QUESTION:A 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? options: A)13 B)21 C)77 D)88 E)11 SOLUTION:20 15 5 25 20 8 500 + 300 + 40 = 840/40 = 21' Answer: B #### B QUESTION:The fourth proportional to 5, 8, 15 is: options: A)15 B)5 C)24 D)8 E)28 SOLUTION:Let the fourth proportional to 5, 8, 15 be x. Then, 5 : 8 : 15 : x = 5x = (8 x 15) x = (8 x 15)/5= 24. Answer is C. #### C QUESTION:The 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? options: A)65 B)21 C)78 D)67 E)51 SOLUTION:Let the total number of workers be x. Then, 8000x = (12000 * 7) + 6000(x - 7) = 2000x = 42000 = x = 21. Answer: B #### B QUESTION:When Professor Wang looked at the rosters for this term's classes, she saw that the roster for her economics class (E) had 20 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 4 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? options: A)30 B)44 C)42 D)46 E)50 SOLUTION:Total # of students 20+28+18-(9+7+10)+4=44. Answer: B. #### B QUESTION:It takes Kannan 10 minutes to walk to the car park and 110 min 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.? options: A)8:50 a.m B)5:50 a.m C)7:50 a.m D)6:50 a.m E)7:00 a.m SOLUTION:The time it takes Kannan to get to work: time to walk to car park + time to drive 10 + 110 = 120 minutes = 2 hours Kannan needs to get out of the house 2 hours before 9:00 am at 9:00 - 2:00 = 7:00 a.m correct answer E #### E QUESTION:Anil does a work in 90 days, Bittu in 40 days and Chintu in 12 days. They work one after another for a day each, starting with Anil followed by Bittu and then by Chintu. If the total wages received are Rs 360 and Anil, Bittu, Chintu share them in the ratio of the work done, find their respective individual wages. options: A)Rs 40, Rs 60 and Rs 260 B)Rs 36, Rs 81 and Rs 243 C)Rs 42, Rs 86 and Rs 232 D)Rs 38, Rs 88 and Rs 234 E)none of these SOLUTION:Let the total work done be 360 units. Therefore, work done by Anil, Bittu and Chintu in single day are 4 units, 9 units and 30 units respectively. Each of them working for 9 days Anil and Bittu will be able to complete 4 units and 9 units of their work on the 9th day but Chintu will be doing remaining 3 units of work. Hence, individual work done by them to complete the whole work is 36 units, 81 units and 243 units till the end of 9th day for each of them. Thus, respective wages on the basis of work done is Rs 36, Rs 81 and Rs 243 respectively for Anil, Bittu and Chintu. ANSWER:B #### B QUESTION:Calculate how long it will take a swimmer to swim a distance of 8km against the current of a river which flows at 1.4km/hr, given that he can swim in still water at 3km/h options: A)20 seconds B)3 C)4 D)1 E)5 SOLUTION:swim in still water at = 3 speed of river= 1.4 US = 3 - 1.4= 1.6 Distance = 8 T = 8/1.6 = 5 Answer: E #### E QUESTION:A 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 C on this shipment? options: A)a) $100 B)b) $115 C)c) $125 D)d) $130 E)e) $135 SOLUTION:I recommend one should use fractions to solve this one rather than converting it into decimals Sol: 1500 heads -> $600 1 head -> $600/1500 1 head -> $(2/5) 25% more of (2/5) -> 125/100 * 2/5 = $(1/2) He sold 2/3*1500 = 1000 heads for $(1/2) per head Total revenue by selling 1000 heads = 1000 * 1/2 = $500 Heads left: 500 Cost per head: 90% of the previous price: 90/100 * 1/2 = $(9/20) Total revenue by selling 500 heads = 9/20 * 500 = 225 Total revenue after selling 1500 cabbage heads - 225+500 = $725 Money spent on the purchase: $600 Profit C= 725-600 = $125 Ans:C #### C QUESTION:The average age of a husband and his wife was 23 years at the time of their marriage.After 5 years they have a one year old child.The average of the family is now? options: A)18 years B)23 years C)29 years D)26 years E)19 years SOLUTION:sum of the present age of husband, wife and child =(23*2+5*2)+1 = 57 years required average = 57/3 = 19 years. Answer :E #### E QUESTION:Two cars start at the same time from opposite ends of a highway that is 333 miles long. One car is riding at 54 mph and the second car is riding at 57 mph. How long after they begin will they meet? options: A)1 B)2 C)3 D)4 E)5 SOLUTION:As cars are moving in opposite directions their speeds will be added. So their relative speeds: 57+54 = 111 mph Total distance to be covered = 333 miles. Time taken would be: 333 miles/111 mph = 3 hours C is the answer. #### C QUESTION:A company wants to spend equal amounts of money for the purchase of two types of computer printers costing $350 and $200 per unit, respectively. What is the fewest number of computer printers that the company can purchase? options: A)9 B)10 C)11 D)12 E)13 SOLUTION:The smallest amount that the company can spend is the LCM of 350 and 200, which is 1400 for each, which is total 2800. The number of 1st type of computers which costing $350 = 1400/350 = 4. The number of 2nd type of computers which costing $200 = 1400/200 = 7. Total = 4+7 = 11 Answer is C. #### C QUESTION:A bike covers a certain distance at the speed of 65km/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? options: A)85 km/h B)85.34 km/h C)86.66 km/h D)90.25 km/h E)90.64 km/h SOLUTION:Ans.(C) Sol. Total distance = 65 × 8 = 520 km Now speed = 520/6 = 86.66 km/h #### C QUESTION:If n is an integer greater than 8, which of the following must be divisible by 3? options: A)1. n (n+1) (n-4) B)2. n (n+2) (n-1) C)3. n (n+3) (n-5) D)4. n (n+4) (n-2) E)5. n (n+5) (n-6) SOLUTION:We need to find out the number which is divisible by three, In every 3 consecutive integers, there must contain 1 multiple of 3. So n+4 and n+1 are same if we need to find out the 3's multiple. replace all the numbers which are more than or equal to three 1. n (n+1) (n-4) = > n(n+1)(n-1) = > (n-1)n(n+1) 2. n (n+2) (n-1) = > n(n+2)(n-1) = > (n-1)n(n+1) 3. n (n+3) (n-5) = > n(n+0)(n-2) = > (n-2)n(n) 4. n (n+4) (n-2) = > n(n+1)(n-2) = > (n-2)n(n+1) 5. n (n+5) (n-6) = > n(n+2)(n-0) = > (n)n(n+2) from the above onlyoption Ais product of consecutive three numbers. C #### C QUESTION:What is the difference between the local value of 3 and 9 in the number 23974? options: A)430 B)377 C)288 D)277 E)210 SOLUTION:Explanation: 300 – 90 = 210 Answer: E #### E QUESTION:A 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 40 years now, the son's age 10 years back was: options: A)10 years B)19 years C)33 years D)38 years E)39years SOLUTION:Let the son's present age be x years. Then, (40 - x) = x 2x = 40. x = 20 Son's age 5 years back (20 - 10) = 10 years. Answer:A #### A QUESTION:If |4x+6| = 50, what is the sum of all the possible values of x? options: A)2 B)-2 C)4 D)-3 E)6 SOLUTION:There will be two cases 4x+6= 50 or 4x+6 = -50 => x =11 or x= -14 sum of both the values will be -14 +11 = -3 Answer is D #### D QUESTION:A cyclist covers a distnce of 750 m in 2 min 30 sec. What is the speed in km/hr of the cyclist? options: A)28 km/hr B)18 km/hr C)20 km/hr D)22 km/hr E)24 km/h4 SOLUTION:Speed = { 750 } m/sec =5 m/sec = { 5 * 18 } km/hr =18km/hr Option B #### B QUESTION:Water 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 162 grams of water? options: A) 16 B) 72 C) 112 D) 128 E) 144 SOLUTION:Solution: We 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 162 grams of water. 2x + 16x = 162 18x = 162 x = 9 Since x is 9, we know that there are 16 x 9 = 144 grams of oxygen in 162 grams of water. Answer E. #### E QUESTION:A large petrol tank has two inlet tubes (a large one and a small one) and one outlet tube. It takes 3 hours to fill the tank with the large inlet tube. On the other hand, it takes 6 hours to fill the tank with the small inlet tube. The outlet tube allows the full tank to be emptied in 9 hours. What fraction of the tank (initially empty) will be filled in 0.64 hours if all three tubes are in operation? Give your answer to two decimal places (e.g., 0.25, 0.5, or 0.75). options: A)1 hour B)2 hour C)3 hour D)4 hour E)5 hour SOLUTION:In one hour, Soln 1: the large inlet tube fills 1 / 3 of the tank; the small inlet tube fills 1 / 6 of the tank; the outlet tube empties 1 / 9 of the tank; and therefore all three tubes together fill [ (1 / 3) + (1 / 6) − (1 / 9) ] of the tank. Fraction of the tank that will be filled in 0.64 hours = 0.64 [ (1 / 3) + (1 / 6) − (1 / 9) ] = 0.25. Soln 2: Let V be the total volume of the tank. From equation (1), Flow Rate (large inlet tube) = V / 3 Flow Rate (small inlet tube) = V / 6 Flow Rate (outlet tube) = V / 9. Substituting in equation (2), Rate of Accumulation in tank = (V / 3) + (V / 6) − (V / 9). Using the above result in equation (1), Time required to fill the complete tank = V / [ (V / 3) + (V / 6) − (V / 9) ]. Note that V cancels out on simplifying the above expression. Fraction of the tank that will be filled in 0.64 hours = 0.64 [ (1 / 3) + (1 / 6) − (1 / 9) ] = 0.25. #### A QUESTION:If y = ||x – 3| – 2|, for how many values of x is y = 5? options: A)2 B)1 C)3 D)4 E)5 SOLUTION:y = ||x – 3| – 2| can be 4 only and only when X-3= +/-7. so there are 2 values of X Answer : A #### A QUESTION:If (x + 1) times (2x + 1) is an odd integer, then x must be options: A)an odd integer B)an even integer C)a prime number D)a composite number E)a negative integer SOLUTION:(x + 1) times (2x + 1) means (x + 1) * (2x + 1).. (x + 1)*(2x + 1)= 2x^2+3x+1... for 2x^2+3x+1 to be odd, 3x+1 should be odd.. hence 3x should be even, which further leads to x as even.. so x is even integer.. ANSWER:B #### B QUESTION:What is the area of a square with perimeter 12P ? options: A) 16p^2 B) 4P C) 9P^2 D) P/16 E) P^2/16 SOLUTION:Each side is 3p A = (3p)^2 = 9p^2 Answer C #### C QUESTION:The area of an isosceles trapezoid with sides of length 5 and bases of length 6 and 12 is? options: A)44 B)42 C)40 D)38 E)36 SOLUTION:Isosceles trapezoid indicates that if we draw perpendicular from two vertex of the smaller side, the longer side with side 12 will be divided into 3 parts= 6, 3 and 3 (Making one square and two right triangles) For the right triangle, height will be= (5^2-3^2)^1/2= 4 And the area of trapezoid = 1/2 (B1+B2)H= 1/2*18*4= 36 E #### E <<<Examples ends QUESTION:30 liters of a mixture contains milk and water in the ratio 2:1. If 5 liters of this mixture be replaced by 5 liters of milk, the ratio of milk to water in the new mixture would be? options: A)3:2 B)3:1 C)4:1 D)5:2 E)2:1 SOLUTION:Quantity of milk in 30 liters if mix = 30*2/3 =20 liters Quantity of milk in 35 liters of new mix = 20+5 = 25 liters Quantity of water in it = 35-25 = 10 liters Ratio of milk and water in new mix = 25:10 = 5:2 Answer is D #### D

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:In a mixed college 160 students are there in one class. Out of this 160 students 3/5 students are girls. How many boys are there ? options: A)A)40 B)B)64 C)C)80 D)D)120 E)E)140 SOLUTION:Total Number of Students :160 Total Girls : 160*3/5 =96 Total Boys : 160-96= 64 Answer is B #### B QUESTION:Two 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: options: A)68 km/hr. B)32 km/hr. C)34 km/hr. D)35 km/hr. E)72 km/hr. SOLUTION:Let the speed of each train be x m/sec. Then, relative speed of the two trains = 2x m/sec. So, 2x = (240 + 240 )/12 2x = 40 x = 20. Speed of each train = 10 m/sec = 20 x 18/5 km/hr = 72 km/hr. answer :E #### E QUESTION:Of the families in City X in 1956, 25 percent owned a personal computer. The number of families in City X owning a computer in 1960 was 15 percent greater than it was in 1956, and the total number of families in City X was 5 percent greater in 1956 than it was in 1960. what percent of the families in City X owned a personal computer in 1960? options: A)50% B)51.22% C)5.26% D)7.20% E)27.38% SOLUTION:Say a 100 families existed in 1956 then the number of families owning a computer in 1956 - 25 Number of families owning computer in 1960 = 25 * 115/100 = 28.75 Number of families in 1960 = 105 The percentage = 28.75/105 * 100 = 27.38%. Option: E #### E QUESTION:How many 4's are there in the following series which are preceded by 7, but are not preceded by 8? 3 4 5 7 4 3 7 4 8 5 4 3 7 4 9 8 4 7 2 7 4 1 3 6 options: A)1 B)2 C)3 D)4 E)More than four SOLUTION:count 1 - - - - - - 7 4 3 count 2------------748 count 3------------749 count 4------------741 ANSWER:D #### D QUESTION:A man can row downstream at 20 kmph and upstream at 10 kmph. Find the speed of the man in still water and the speed of stream respectively? options: A)3 B)5 C)6 D)4 E)9 SOLUTION:Let the speed of the man in still water and speed of stream be x kmph and y kmph respectively. Given x + y = 20 --- (1) and x - y = 10 --- (2) From (1) & (2) 2x = 30 => x = 15, y = 5. Answer: B #### B QUESTION:A number is said to be a “digifac” if each of its digits is a factor of the number itself. What is the sum N of the missing digits of the following five-digit digifac: 9, 5, 3 _ _ ? options: A) 5 B) 7 C) 9 D) 10 E) 14 SOLUTION:Here, the term “digifac” should look intimidating. You probably haven’t studied digifacs before, so how should you approach this problem? Well, keep in mind that digifacs aren’t being tested; in fact, the author of this question just made that term up, and then defined it for you. What makes this question hard is that the non-challenge-seeker (I think I just made that term up, too…) will see the unfamiliar term “digifac” and lose faith immediately. “I don’t know what that is!” She who finds the challenge in the GMAT fun, however, will read the definition and think “got it – I need to find the two digits that ensure that 9, 5, and 3 are both factors of the overall number, and that the remaining two digits are also factors”. And work from there. The number must be divisible by 5, so the only units digits that work are 0 or 5. And the number must be divisible by 9 (and also 3), so we need the sum N of all digits to be a multiple of 9. 9 + 5 + 3 = 17, so our only options are to get the sum to 18 (by adding 1) or to 27 (by adding 10). A quick glance at the answer choices shows that 0 1 isn’t an option. Why not? That would require 0 to be one of the digits…and 0 isn’t a factor of anything. So the units digit must be 5, making the tens digit 5, and we have 95,355. That number is a multiple of 5, 3, and 9, so it works:the correct answer is D, and more importantly this fun challenge required no “trivial” information about digifacs…that term only existed to obscure the link between the given information and the path to the answer.D #### D QUESTION:A goods train runs at the speed of 72 kmph and crosses a 270 m long platform in 26 seconds. What is the length of the goods train? options: A)230 m B)250m C)643m D)832m E)270m SOLUTION:Speed = (72 x 5/18)m/sec = 20 m/sec. Time = 26 sec. Let the length of the train be x metres. Then, x + 270/26 = 20 x + 270 = 520 x = 250. Answer:B #### B QUESTION:Two 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? options: A)9:36 B)9:31 C)9:35 D)9:37 E)9:32 SOLUTION:1/4 : 3/4 = (1:3)5 = 5:15 1/5 : 4/5 = (1:4)4 = 4:16 ------ 9:31 Answer: B #### B QUESTION:The 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? options: A)8% B)7% C)10% D)12% E)4% SOLUTION:Option E Explanation: 65*(90/100)*((100-x)/100) = 56.16 x = 4% #### E QUESTION:What is the sum of natural numbers between 50 and 100 options: A)4800 B)4860 C)3825 D)5500 E)5550 SOLUTION:a = first number l = last number Sn = n/2[a + l] between 50 and 100 numbers = 51 => 100 - 50 = 50 + 1 = 51 Sn = 51/2 × 150 = 51 × 75 = 3825 Answer : C #### C QUESTION:In 10 years, A will be twice as old5as B was 10 years ago. If A is now 8 years older than B, the present age of B is options: A)35 B)37 C)38 D)41 E)42 SOLUTION:Explanation: Let B's age = x years. Then, As age = (x+ 8) years. (x+8+10)=2(x—10) hence x=38. Present age of B = 38 years Answer: Option C #### C QUESTION:For 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 181? options: A)3820 B)5740 C)6580 D)7360 E)9200 SOLUTION:100 + 102 + ... + 180 = 100*41 + (2+4+...+80) = 100*41 + 2*(1+2+...+40) = 100*41 + 2(40)(41)/2 = 100*41 + 40*41 = 140(41) = 5740 The answer is B. #### B QUESTION:When the positive integer y is divided by 9, the remainder is 5. What is the remainder when 3y is divided by 9? options: A)0 B)1 C)3 D)4 E)6 SOLUTION:Lets take the number as y when y is divided by 9 the remainder is 5 hence y can be written as y=9k +5 Multiplying by 3 will give 3y = 27k + 15 we can also write 3y = 27k + 9 + 6 Now 27k and 9 are divisible by 9 leaving the remainder as 6 hence E is the answer. #### E QUESTION:A 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? options: A)22 B)28 C)120 D)287 E)278 SOLUTION:Let 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=25×6012.5=2×60=120 Answer : C #### C QUESTION:What is the remainder when 103 * 505 * 607 is divided by 9 options: A)6 B)18 C)2 D)4 E)7 SOLUTION:103/9==> Remainder=4 505/9==> Remainder=1 607/9==> Remainder=4 =4*4*1=16/9==> Remainder=7 Answer: E #### E QUESTION:Y and Z start a business with Rs.3000 and Rs.6000 respectively. How should they share their profits at the end of one year? options: A)4:1 B)1:3 C)1:4 D)1:5 E)1:2 SOLUTION:They should share the profits in the ratio of their investments. The ratio of the investments made by Y and Z = 3000 : 6000 => 1:2 . Answer:E #### E QUESTION:The population of a town increased from 1,75,000 to 2,62,500 in a decade. What is the average percent increase of population per year? options: A)5% B)6% C)7% D)2% E)8% SOLUTION:increase = 262500 - 175000 = 87500 % increase in 10 yrs = 87500/175000*100 = 50% avg = 50/10 = 5% ANSWER A #### A QUESTION:36 men can complete a piece of work in 18 days. In how many days will 27 men complete the same work? options: A)56 B)28 C)45 D)24 E)45 SOLUTION:D 24 Let the required number of days be x. Less men, More days (Indirect Proportion) 27 : 36 :: 18 : x <-> 27 x x = 36 x 18 x = (36 x 18)/27 x = 24 #### D QUESTION:.05% of cans of beans that go down a conveyor belt are sealed improperly and must be disposed of. How many cans of beans must pass down a conveyor belt for 5 cans to be sealed improperly? options: A)500 B)5000 C)4000 D)2500 E)10000 SOLUTION:Let the number of total cans of beans be x Then, .05% of x=5 (5/100)*(1/100)*x=5 x=10000 Answer is E #### E QUESTION:If x^2 − 2x − 15 = (x + r)( x + s) for all values of x, and if r and s are constants, then which of the following is a possible value of r − s? options: A)8 B)2 C)− 2 D)− 3 E)− 5 SOLUTION:Given: x^2 − 2x − 15 = (x + r)( x + s) Factor to get: (x - 5)(x + 3) = (x + r)( x + s) Rewrite as: (x + -5)(x + 3) = (x + r)( x + s) So, it's possible that r = -5 and s = 3 Here, r - s = (-5) - 3 = -8 Try REVERSING the factorization: x^2 − 2x − 15 = (x + r)( x + s) Factor to get: (x + 3)(x - 5) = (x + r)( x + s) Rewrite as: (x + 3)(x + -5) = (x + r)( x + s) So, it's possible that r = 3 and s = -5 Here, r - s = 3 - (-5) = 8 Answer: A #### A QUESTION:If 3 persons can do 3 times of a particular work in 3 days, then, 7 persons can do 7 times of that work in? options: A)3 days B)5 days C)7 days D)11 days E)12 days SOLUTION:That is, 1 person can do one time of the work in 3 days. Therefore, 7 persons can do 7 times work in the same 3 days itself. A) #### A QUESTION:The sum of two numbers is 16. The difference is 4. What are the two numbers?Let x be the first number. Ley y be the second number x + y = 16 x - y = 4 options: A)10 and 6 B)10 and 5 C)10 and 4 D)10 and 3 E)10 and 2 SOLUTION:Solution Let x be the first number. Ley y be the second number x + y = 16 x - y = 4 Solve the system of equations by elimination Adding the left sides and the right sides gives: x + x + y + -y = 16 + 4 2x = 20 x = 10 Since x + y = 16, 10 + y = 16 10 + y = 16 10 - 10 + y = 16 - 10 y = 6 The numbers are 10 and 6 Answer A #### A QUESTION:Carol and Jordan draw rectangles of equal area. If Carol's rectangle measures 12 inches by 15 inches and Jordan's rectangle is 6 inches long, how wide is Jordan's rectangle, in inches? options: A)24 B)26 C)28 D)30 E)32 SOLUTION:Area of first rectangle is 12*15=180 hence area of second would be 6x=180x x=30 answer is D #### D QUESTION:How many integers from 0 to 50 inclusive have a remainder of 3 when divided by 6? options: A)5 B)6 C)7 D)8 E)9 SOLUTION:The numbers should be of the form 6c+3. The minimum is 3 when c=0. The maximum is 45 when c=7. There are 8 such numbers. The answer is D. #### D QUESTION:Ravi can do a piece of work in 30 days while Prakash can do it in 40 days. In how many days will they finish it together? options: A)17 1/7 B)17 1/9 C)17 1/2 D)17 1/7 E)17 1/5 SOLUTION:1/30 + 1/40 = 7/120 120/7 = 17 1/7 days Answer: A #### A QUESTION:If 0.003^5 is represented in its shortest possible decimal form, how many 0’s to the right of the decimal point does it contain? options: A)9 B)10 C)11 D)12 E)13 SOLUTION:0.003^5= (3*10^-3)^5 = 243*10^-15 = 0.243*10^-12 which would have 12 zeros to the right of the decimal point. The answer is D. #### D QUESTION:Two 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: options: A)39,30 B)41,32 C)42,33 D)43,34 E)35,36 SOLUTION:Let their marks be (x + 9) and x. then x+9 = 56/100(x+9+x) 3x=99 x=33 their marks 42 and 33 ANSWER C #### C QUESTION:Six cards numbered from 1 to 6 are placed in a cardboard box . 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 10, what is the probability that one of the two cards drawn is numbered 5 ? options: A)1/2 B)1/4 C)1/5 D)1/6 E)1/3 SOLUTION:(6,4) (4,6) (5,5) – only 3 possible scenarios for sum to be 10. One from this 5 has already happened. From this three cases, only in one we have 5. So, the probability is 1 chances out of 3 that the one that occurred had 5: P=1/3. Answer: E. #### E QUESTION:A policeman noticed a criminal from a distance of 180 km. The criminal starts running and the policeman chases him. The criminal and the policeman run at the rate of 8 km and 10 km per hour respectively. What is the distance between them after 3 minutes ? options: A)100 m B)80 m C)130 m D)150 m E)None of these SOLUTION:Explanation : Solution: Relative speed = (10 - 8) = 2 km/hr. Distance covered in 3 minutes = (2 * 3/60) km = 1/10 km = 100 m. .'. Distance between the criminal and policeman = (180 - 100) m = 80 m. Answer : B #### B QUESTION:If x and y are positive integers, and 4x^2=3y, then which of the following must be a multiple of 8? I. x^2 II. y^2 III. xy options: A)I only B)II only C)III only D)I and II only E)I, II and III SOLUTION:4x^2 = 3y since x,y are positive integers, x^2 = x*x is divisible by 3 -> x is divisible by 3 and y is divisible by x^2 -> x^2 and y is divisible by 9 -> y^2 is divisible by 9 (1),(2), and (3) must be true Answer is C #### C QUESTION:A group of men decided to do a work in 20 days, but 8 of them became absent. If the rest of the group did the work in 28 days, Find the original number of men? options: A)60 B)28 C)40 D)50 E)25 SOLUTION:Original number of men = 8*28 / (28-20) = 28 Answer is B #### B QUESTION:There are two batches A and B of a class. Batch A consists of 36 students and batch B consists of 44 students. Find the average weight of whole class, if average weight of batch A is 40 kg and that of batch B is 35 kg. options: A)29.23 kg B)32.56 kg C)35.66 kg D)37.25 kg E)NONE OF THE ABOVE SOLUTION:Given: Average weight of batch A = 40 kg , average weight of batch B = 35 kg 1) First find the total weight of all students - Weight of batch A = (36 x 40) = 1440 - Weight of batch B = (44 x 35) = 1540 Total weight of all students = (1440 + 1540) = 2980 kg 2) Find average weight of whole class (Batch A + Batch B) students = (36 + 44) = 80 students Average Weight = Total weight of all the students / No. of Students = 2980 / 80 = 37.25 kg ANSWER IS D #### D QUESTION:The average of first 10 odd numbers is? options: A)22 B)10 C)98 D)66 E)88 SOLUTION:Sum of 10 odd no. = 100 Average = 100/10 = 10 Answer:B #### B QUESTION:A man can row a boat at 20 kmph in still water. If the speed of the stream is 7 kmph, what is the time taken to row a distance of 60 km downstream? options: A)30/18 hours B)37/13 hours C)80/13 hours D)20/9 hours E)30/43 hours SOLUTION:Speed downstream = 20 + 7 = 27 kmph. Time required to cover 60 km downstream = d/s = 60/27 = 20/9 hours. Answer: D #### D QUESTION:In a box of 9 pens, a total of 3 are defective. If a customer buys 2 pens selected at random from the box, what is the probability that neither pen will be defective? options: A)2/9 B)3/10 C)4/11 D)5/12 E)6/13 SOLUTION:# defective pens = 3 # good pens = 6 Probability of the 1st pen being good = 6/9 Probability of the 2nd pen being good = 5/8 Total probability = 6/9 * 5/8 = 5/12 The answer is D. #### D QUESTION:The CI on Rs 30000 at 7% per annum for a certain period is 4347.The period is ? options: A)2 B)3 C)1 D)6 E)5 SOLUTION:I year 2100 II year 2100+147=2247 2100+2247=4347 So 2 Years Answer A #### A QUESTION:The guidelines at a certain college specify that for the introductory English class, the professor may choose one of six specified novels, and choose two plays from a list of 5 specified plays. Thus, the reading list for this introductory class has one novel and two plays. How many different reading lists could a professor create within these parameters? options: A)50 B)55 C)60 D)65 E)70 SOLUTION:6C1*5C2 = 6*10 = 60 The answer is C. #### C QUESTION:A train crosses a platform of 120 m in 15 sec, same train crosses another platform of length 250 m in 20 sec. then find the length of the train? options: A)150 B)88 C)270 D)62 E)52 SOLUTION:Length of the train be ‘X’ X + 120/15 = X + 250/20 4X + 480 = 3X + 750 X = 270m Answer: C #### C QUESTION:How many kilograms of sugar costing Rs.9 per kg must be mixed with 27 kg of sugar costing Rs.7 per Kg so that there may be a gain of 10% by selling the mixture at Rs.9.24 per Kg? options: A)36 Kg B)42 Kg C)54 Kg D)63 Kg E)None of these SOLUTION:Solution Ratio of quantities of 1st and 2nd kind = 14 : 6 = 7 : 3. Let x kg of sugar of 1st kind be mixed with 27 kg of 2nd kind. Then, 7 : 3 = x : 27 or x = (7 x 27 / 3) = 63 kg Answer D #### D QUESTION:At the end of three years what will be the compound interest at the rate of 10% p.a. on an amount of Rs.20000? options: A)Rs.6620 B)3378 C)2768 D)2999 E)2771 SOLUTION:A = 20000(11/10) 3 = 26620 = 20000 ---------- 6620 Answer: A #### A QUESTION:40, 45, 50, 55, 60, 70, 75, 100, 100, 100. The list above shows the scores of 10 schoolchildren on a certain test. If the standard deviation of the 10 scores is 22.3, rounded to the nearest tenth, how many of the scores are more than 1 standard deviation below the mean of the 10 scores? options: A)1 B)2 C)3 D)4 E)5 SOLUTION:The average of {40, 45, 50, 55, 60, 70, 75, 100, 100, 100} is 69.5. 1 standard deviation below the mean is 69.5 - 22.3 = 47.2. Hence there are two scores (40 and 45) more than 1 standard deviation below the mean. Answer B. #### B QUESTION:Three seventh of a number is 12 more than 40% of that number. What will be the 10% of that number? options: A)A)148 B)B)210 C)C)21 D)D)248 E)E)258 SOLUTION:3/7 x – 40/100 x = 12 x = 35 * 12 35 * 12 * 10/100 = 42/2 = 21 ANSWER:C #### C QUESTION:Mr. 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 options: A)$145 B)$250 C)$300 D)$175 E)$150 SOLUTION:Let the 1st paycheck be x(integer).Mr. Rodger got a weekly raise of $145. so after completing the 1st week she will get $ (x+145).similarly after completing the 2nd week she will get $(x+145)+$145.=$(x+145+145=$(x+290). so in this way end of every week her salary will increase by $145. correct answer will be (A) #### A QUESTION:A man bets on no.16 on a roulette wheel 14times 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 istherefore, unable to decide whether to bet on 16 or 12 in the 15th span. Which will give him the best chance and what r the odds of winning on the bet that he takes? options: A)35:1 B)Either ;35:1 C)Either 70;35:1 D)Either 55;45:1 E)Either 65;35:5 SOLUTION:Each of the span is an independent event and the outcome of the 15th span will not depend on the outcome of the earlier spans. Either ;35:1 B) #### B QUESTION:A box contains four silver 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. options: A)1/5 B)2/5 C)3/5 D)4/5 E)3/4 SOLUTION:There are four ways (2 heads in one two-headed coin and 2 heads in the other two-headed coin) How 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) Therefore probability = 4/5 Option D #### D QUESTION:A train of 25 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 1.0 km long? options: A)2.5 B)3 C)5 D)7 E)9 SOLUTION:D = 25 * 60 + 1000 = 2500 m T = 2500/60 * 18/5 = 150 sec = 2.5 mins Answer: A #### A QUESTION:A can complete a work in 15 days and B can do the same work in 9days. If A after doing 5days, leaves the work, find in how many days B will do the remaining work? options: A)2days B)4days C)6days D)7days E)10days SOLUTION:The required answer = (15-5)*9 / 15 = 40/10 = 6days Answer is C #### C QUESTION:a and b are positive integers less than or equal to 9 and multiple of 4. If a and b are assembled into the seven-digit number abaabab, which of the following must be a factor of abaabab? options: A)3 B)4 C)5 D)7 E)8 SOLUTION:The last two digit of the number are ab. Both a and b are multiple of 4,thus the last two digits are divisible by 4, which makes the number abaabab divisible by 4. Thus 4 is always a factor of abaabab. Answer: B #### B QUESTION:A train covers a distance of 12 km in 10 min. If it takes 12 sec to pass a telegraph post, then the length of the train is? options: A)178 m B)240 m C)120 m D)168 m E)178 m SOLUTION:Speed = (12/10 * 60) km/hr = (72 * 5/18) m/sec = 20 m/sec. Length of the train = 20 * 12 = 240 m. Answer: B #### B QUESTION:Ravi and sunil are partners in a business. Ravi invests Rs.12,000 for 4 months and Sunil invested Rs.10000 for 5 months then after one year ratio of their profits will be options: A)1:3 B)2:3 C)24:25 D)20:22 E)3:4 SOLUTION:=(12000*4):(10000*5) =48000:50000 =24:25 ANSWER:C #### C QUESTION:A certain restaurant offers 6 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? options: A)8 B)12 C)15 D)21 E)27 SOLUTION:As dessert platter should contain equal number of kinds of cheese and fruits, desert can contain: A. 2 kinds of cheese and 2 kinds of fruits --> 6C2*2C2=15*1=15 B. 1 kind of cheese and 1 kind of fruit --> 6C1*2C1=6*2=12 A+B=15+12=27 Answer: E. #### E QUESTION:In an election between two candidates, 10% of votes are were declares invalid. First candidate got 10800 votes which were 60% of the total valid votes . The total number of votes enrolled in that election was: options: A)9000 B)98000 C)60000 D)11000 E)12000 SOLUTION:100 % - 10 % = 90 % 54%-36%=18% 18% ------> 10800 ( 18 × 600 = 10800) 100% -------> 60000 votes (100 × 600 = 60000) C #### C QUESTION:An order was placed for the supply of a carpet whose breadth was 6 m and length was 1.44 times the breadth. What be the cost of a carpet whose length and breadth are 40% more and 25% more respectively than the first carpet. Given that the ratio of carpet is Rs. 45 per sq m? options: A)4882.40 B)8082.40 C)4002.40 D)4082.40 E)9082.40 SOLUTION:Explanation: Length of the first carpet = (1.44)(6) = 8.64 cm Area of the second carpet = 8.64(1 + 40/100) 6 (1 + 25/100) = 51.84(1.4)(5/4) sq m = (12.96)(7) sq m Cost of the second carpet = (45)(12.96 * 7) = 315 (13 - 0.04) = 4095 - 12.6 = Rs. 4082.40 Answer: Option D #### D QUESTION:If 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? options: A)ft + rk B)(ft + rk)/2 C)t/f + k/r D)(ft + rk)/(t + k) E)(ft + rk)/(t - k) SOLUTION:Average Speed = Total Distance /Total Time Taken Total Distance travelled in t hours = ft Total Distance travelled in s hours = rk Total Time taken = t+k Therefore , Average Speed = (ft+tk)/(t+k) Answer D #### D QUESTION:Calculate the speed of a boat in still water (in km/hr) if in one hour, the boat goes at 13 km/hr downstream and 4 km/hr upstream. options: A)4.5 kmph B)9.5 kmph C)7.5 kmph D)8.5 kmph E)5.5 kmph SOLUTION:Speed in still water = (13 + 4)1/2 kmph = 8.5 kmph. answer :D #### D QUESTION:A man can swim in still water at 7.5 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is? options: A)1.7 B)1.4 C)1.1 D)1.5 E)2.5 SOLUTION:M = 7.5 S = x DS = 7.5 + x US = 7.5 + x 7.5 + x = (7.5 - x)2 7.5 + x = 15 -2x 3x = 7.5 x = 2.5 Answer:E #### E QUESTION:If 24 men can do a piece of work in 25 hours, in how many hours will 15 men do it ? options: A)40 hours B)45 hours C)50 hours D)55 hours E)60 hours SOLUTION:Let the required number of hours be x. Then, Less men, More hours (Indirect Proportion) 15 : 24 : : 25 : x<=>(15 x x) =(24 x 25)<=>(24 x 25)/15 = 40 Hence, 15 men can do it in 60 hours Answer is A. #### A QUESTION:At present, the ratio between the ages of Akbar and Denial is 4:3. After 6 years, Arun’s age will be 26 years. What is the age of Deepak at present? options: A)5 B)10 C)15 D)20 E)25 SOLUTION:Sol. Let the present ages of Akbar and Danial be 4x years and 3x years respectively. Then, 4x + 6 =26 ⇔ 4x = 20 ⇔ x = 5. ∴ Deepak’s age = 3x =15 years. Answer C #### C QUESTION:If 0 < M < Y, M is an odd number and Y is a prime number, which of the following can be the value of M + Y ? options: A)11. B)13. C)17. D)10. E)7. SOLUTION:If m is odd ,implies m(odd)+y(odd/even prime)=(Even/Odd) If Y is even, the 2 is the even prime , therefore y=2m=1 since 0<M<Y therefore M+Y =3. But 3 is not an option which implies y is odd, Now M(odd)+Y(odd)=Even 10 is the only option that is even=D #### D QUESTION:A can complete a project in 10 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? options: A)15 B)19 C)20 D)21 E)22 SOLUTION:A's 1day work=1/10; B's 1day work=1/30; (A+B) 1day work=(1/10+1/30)=2/15; It is given that A leaves the work 10 days before completion of the project.. Thus,B alone does the remaining job in 10 days. So,In 10 days ,B can do 1/3 w .. Thus,(A+B) have worked (1-1/3)=2/3 w.. (A+B)can do 2/15 work in 1 day... They did 2/3 w in 5 days. Total days=(5+10) = 15 ANSWER:A #### A QUESTION:The banker's discount on Rs.1800 at 48% per annum is equal to the true discount on Rs.1872 for the same time at the same rate. Find the time? options: A)1 months B)4 months C)5 months D)6 months E)7 months SOLUTION:Solution S.I on Rs.1800 = T.D on Rs.1872. P.W on Rs.1872 is Rs.1800. Rs.72 is S.I on Rs. 1800 at 48%. Time =(100x72 / 48x1800) = 1/12 year = 1 months. Answer A #### A QUESTION:find value for x from below equation? x + 1 = 3 options: A)-5 B)-4 C)4 D)3 E)2 SOLUTION:1. Subtract 1 from both sides: x + 1 - 1 = 3 - 1 2. Simplify both sides: x = 2 E #### E QUESTION:A 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? options: A)12.6 kmph B)17.5 kmph C)12.8 kmph D)12.5 kmph E)14.5 kmph SOLUTION:Let the speed of the man in still water be a kmph and let the speed of the stream be b kmph. Now 30/(a + b) + 20/(a - b) = 4 and 45/(a + b) + 40/(a - b) = 7 Solving the equation, the speed of man in still water is 12.5 kmph. Answer: D #### D QUESTION:in 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 9 people all together .how many people can sit in a bus? options: A)52 B)49 C)95 D)90 E)66 SOLUTION:Right Side =15 seat Left Side =15-3 (3 few seat in right side)= 12 seat Total= 15+12= 27 People can seat in 27 seat= 27*3=81 People can seat in Last Seat = 9 Total People can seat= 81+9=90 ANSWER:D #### D <<<Examples ends QUESTION:Tom opened a shop investing Rs.30000. Jose joined him 2 months later, investing Rs.45000. They earned a profit of Rs.54000 after completion of one year. What will be Jose's share of profit? options: A)10000 B)12000 C)13000 D)14000 E)30000 SOLUTION:SoL = ~s- So Anju’s share = [5/9] x 54000 = 30000 E #### E

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:Two Trains A and B start simultaneously from stations 500 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? options: A) 112 B) 133 C) 150 D) 250 E) 288 SOLUTION:Since we know the distance (500) and the combined rate (100), we plug it into the formula: Distance = Rate * Time 500 = 100 * Time We can solve for the time they will meet cause we added the rate of Train A and Train B together. So the time will be 500/100 from dividing 100 on both sides to isolate Time in the equation above. Time will be 5 hours so now you can plug that in for Train A’s distance. Distance = Rate * Time Distance = 50 * 5 Distance = 250 according to answer choice D. #### D QUESTION:A carpenter makes 4 bunk beds every day. A military school needs to organize a place to sleep for 143 soldiers. If there are 5 carpenters working on the job, how many whole days in advance should they receive the order and start working in order to finish the right number of beds assuming that each bunk- bed is used by two soldiers? options: A)3. B)4. C)5. D)6. E)7. SOLUTION:I believe it is C because if 1C makes 3 beds in 1 day then: 1C's rate = 3/1 So 5c's = 3/1 * 5 = 15/1 = 15 beds in a day. Since we have 173 soldiers who need beds and bunk beds come in pairs, 72 is the least amount of beds needed. Time = Amount / Rate Time = 72 / (15/1) = 72/15, simplifying we get 72/15 = 24/5 = 4.7 So, in order for the carpenters to be able to finish they need 5 whole days. At first I made the mistake of thinking how many whole days it took them to finish (as in ignore the partial day) but the prompt clarifiesdays in advance, meaning how many days would they need to finish so even if they finish early, theyusedthat day. C #### C QUESTION:10 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 ? options: A)4 hours a day B)5 hours a day C)6 hours a day D)7 hours a day E)8 hours a day SOLUTION:Explanation: More Men, Less Hours {Indirect Proportion} Less Days, More Hours {Indirect Proportion} [men 15 10 days 12 18] ::7:x =>x∗15∗12=10∗18∗7 =>x=10∗18∗7/ 15∗12 =>x=7 Option D #### D QUESTION:Ramu bought an old car for Rs. 42000. He spent Rs. 13000 on repairs and sold it for Rs. 64900. What is his profit percent? options: A)17% B)19% C)18% D)14% E)16% SOLUTION:Total CP = Rs. 42000 + Rs. 13000 = Rs. 55000 and SP = Rs. 64900 Profit(%) = (64900 - 55000)/55000 * 100 = 18% Answer: C #### C QUESTION:For every integer n ≥ 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(99) – g(97)? options: A)98 B)100 C)0 D)99 E)97 SOLUTION:g(99) = 1*3*5*7*9*...*99 g(97) = 1*3*5*7*9*...*97 g(99) - g(97) = 1*3*5*7*9*...*99 - 1*3*5*7*9*...*97 = 1*3*5*7*9*...*97*(99 - 1) = 1*3*5*7*9*...*97*98 hence:A. #### A QUESTION:Howmany three digits odd numbers can be formed using the digits 4,5,6,7,8,9 (repetition of digits not allowed) options: A)60 B)75 C)65 D)55 E)45 SOLUTION:There are 3 ways of filling the unit place of the number. The remaining ten's and 100's place canbe filled in 5ways and 4 ways respectively. Required number of numbers =3x5x4=60. Ans: A #### A QUESTION:What is the tens digit of 36^12? options: A)1 B)3 C)5 D)7 E)9 SOLUTION:36^10 = 6^24 (6^2)=6*6 = 36 (6^3)= 36*6 = .16 (6^4)= .16*6 = ..96 (6^5) = ..96*6 = ..76 (6^6) = ..76*6 = ...56 (6^7) = ....56*6 = ....36 If you see there is a pattern here in tens digits 3,1,9,7,5,3,1 and so on... Continue the pattern up to 6^24 ( dont actually calculate full values) and answer is E: 9 #### E QUESTION:If y exceeds x by 22%, then x is less than y by? options: A)18 2/8% B)18 8/3% C)18 2/61% D)76 2/3% E)17 2/3% SOLUTION:X=100 y=122 122------22 100-------? => 18 2/61% Answer:C #### C QUESTION:If YWVSQ is 25 - 24 - 21 - 19 - 17, Then MLIGF options: A)13 - 11 - 9 - 7 - 8 B)13 - 11 - 9 - 7 - 6 C)13 - 11 - 9 - 7 - 7 D)13 - 11 - 9 - 7 - 3 E)13 - 11 - 9 - 7 - 1 SOLUTION:MLIGF = 13 - 11 - 9 - 7 - 8 Note: this is a dummy question. Dont answer these questions Answer:A #### A QUESTION:For any non-zero a and b that satisfy |ab| = ab and |a| = -a, |b-3| + |ab-b| = options: A)ab-4+b B)2b-ab-4 C)ab+4 D)ab-2b+5 E)4-ab SOLUTION:Given: |ab| = ab and |a| = -a Question: |b-3| + |ab-b| = ? **** Looking at |ab| = ab tells us that a and b are either both positive or negative **** Looking at |a| = -a tells us that a must be negative **** Combine two observations: a and b are both negative values Let a=-1 and b=-1 |b-4| + |ab-b| = |-1-3| + |1-(-1)| = 5 Test a) ab-4 = (-1)(-1)-4 = -5 Test b) 2b-ab-4 = (2)(-1) - (1) - 4 = -7 Test c) ab+4 = 1 + 4 = 5 Answer: C #### C QUESTION:A man swims downstream 72 km and upstream 45 km taking 9 hours each time; what is the speed of the current? options: A)1.7 B)1.5 C)1.2 D)1.1 E)1.9 SOLUTION:72 --- 9 DS = 8 ? ---- 1 45 ---- 9 US = 5 ? ---- 1 S = ? S = (8 - 5)/2 = 1.5 Answer: B #### B QUESTION:A person starts walking at a speed of 5km/hr through half the distance, rest of the distance he covers with aspeed 6km/hr. Total time of travel is 9 hours. What is the maximum distance he can cover? options: A)20km B)40km C)60km D)80km E)90km SOLUTION:t=d/s, so 9=x/2*1/5+x/2*1/6(because half distance with 5 km/ph, and remaining half with 6km/hr) 9=x(18/120) x=60km ANSWER:C #### C QUESTION:The tax on a commodity is diminished by 20% and its consumption increased by 15%. The effect on revenue is? options: A)7% decrease B)8% decrease C)9% decrease D)6% decrease E)4% decrease SOLUTION:100 * 100 = 10000 80 * 115 = 9200 ----------- 10000-----------800 100-----------? => 8% decrease Answer: B #### B QUESTION:Three unbiased coins are tossed. What is the probability of getting 3 heads and 1 Tail? options: A)3/4 B)1/4 C)3/8 D)1/2 E)1/8 SOLUTION:Let, H --> Head , T --> Tail Here S = {TTT, TTH, THT, HTT, THH, HTH, HHT, HHH} Let E = event of getting 3 heads Then E = {HHH,HTH,THH,HHT} P(E) = n(E)/n(S) =4/8 = 1/2 Answer is D #### D QUESTION:A miniature gumball machine contains 5 blue, 3 green, and 2 red gumball, 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? options: A)1/10 B)1/8 C)1/6 D)1/5 E)1/4 SOLUTION:The total number of ways to dispense 3 gumballs is 10C3=120. The number of ways to choose one of each color is 5*3*2=30. P(dispensing one of each color)=30/120=1/4. The answer is E. #### E QUESTION:A train running at the speed of 30 km/hr crosses a pole in 6 sec. What is the length of the train? options: A)20 m B)70 m C)50 m D)Cannot be determined E)None of these SOLUTION:Speed = 30 * 5/18 = 25/3 m/sec Length of the train = speed * time = 25/3 * 6 = 50 m ANSWER:C #### C QUESTION:There is a 30 % chance of rain and a 70% chance of shine. If it rains there is a 50% chance that Bob will cancel his picnic but if the sun is shining he will definitely have his picnic. What is the chance that Bob will have his picnic? options: A)70 % B)75 % C)80 % D)85 % E)90 % SOLUTION:Chance of no picnic+chance of picnic= 100% ... (i) Chance of picnic=100%-Chance of no picnic ... (ii) Chance of no picnic= 50% of 30%= 15% Therefore, According to (ii), Chance of picnic= 100%-15%= 85%. Answer D #### D QUESTION:Anitha had 80 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. 4000. How much amount (in Rs) did she have in the denomination of Rs 45? options: A)3500 B)72 C)2000 D)3000 E)4000 SOLUTION:Let the number of 45-rupee notes = x Then, the number of 95-rupee notes = (80 – x) 45x + 95(80 – x) = 4000 or x + 2(80 – x) = 95 or x = 72. ANSWER:B #### B QUESTION:How many three letter words are formed using the letters of the word TIME? options: A)28 B)21 C)26 D)24 E)29 SOLUTION:The number of letters in the given word is four. The number of three letter words that can be formed using these four letters is ⁴P₃ = 4 * 3 * 2 = 24. Answer: D #### D QUESTION:A grocer buys apples for 63¢ 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? options: A)66¢ B)70¢ C)75¢ D)77¢ E)84¢ SOLUTION:for making calculation simple let us consider he buys 10 pounds @ 63/pound=630¢ in total . 10% apples lost...means 9 pounds left. further he wants 20% profit on 630 ¢ means he wants to earn 756¢ sales price should be 756/9==¢ 84 ANSWER:E #### E QUESTION:Which of the following cannot be the range of a set consisting of 5 odd multiples of 11? options: A)44 B)88 C)45 D)176 E)352 SOLUTION:Solution: sequence of 11 lets say sequence is 11n, 11(n+1), 11(n+2), 11(n+3), 11(n+4) so range is 11n+44-11n = 44 if we put the different values of n we will get different but the range will be multiple of 44 and only 45 is not multiple of 44 Answer : C #### C QUESTION:1/2+[(2/3*3/8)+4]-7/16= options: A)29/16 B)19/16 C)69/16 D)9/13 E)0 SOLUTION:1/2+[(2/3*3/8)+4]-7/16= 1/2+[(1/4)+4]-7/16= 1/2+[17/4]-7/16= 8/16 + 68/16 - 7/16 = 69/16 C #### C QUESTION:When positive integer x is divided by positive integer y, the result is 59.32. What is the sum W of all possible 2-digit remainders for x/y? options: A)560 B)616 C)672 D)728 E)784 SOLUTION:ans B 616... remainders = .32=32/100=8/25=16/50 and so on.. so two digit remainders are 16+24+32+....+96.. W=8(2+3+4....+12)=616 #### B QUESTION:Two sides of a triangle have lengths x and t and meet at a right angle. If the perimeter of the triangle is 4x, what is the ratio of x to t ? options: A)a) 2 : 3 B)b) 3 : 4 C)c) 4 : 3 D)d) 3 : 2 E)e) 2 : 1 SOLUTION:Ahhhh....my bad. Thank you, you're correct. 8x = 6t --> x/t = 3/4. Actually B is the right answer. #### B QUESTION:At 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? options: A)2 B)7 C)C)120 D)D)144 E)E)720 SOLUTION:The number of arrangements of n distinct objects in a row is given by n! The number of arrangements of n distinct objects in a circle is given by (n−1)! "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: R=n!-n=(n−1)! (n−1)!=(7−1)!=720 Answer: E #### C QUESTION:Find the fraction which has the same ratio to 2/13 that 5/34 has to 7/48. options: A)240/1587 B)240/1545 C)240/1547 D)240/1542 E)240/1512 SOLUTION:P : 2/13 = 5/34 : 7/48 As the product of the means is equal to the product of the extremes. P*7/48 = 2/13 * 5/34 P*7/48 = 10/442 P = 480/3094 => P = 240/1547 Answer: C #### C QUESTION:A candidate got 35% of the votes polled and he lost to his rival by 2250 votes. How many votes were cast? options: A)7500 B)7508 C)7528 D)7527 E)7232 SOLUTION:35%-----------L 65%-----------W ------------------ 30%----------2250 100%---------? => 7500 Answer:A #### A QUESTION:A, B and C have Rs.500 between them, A and C together have Rs.200 and B and C Rs.320. How much does C have? options: A)50 B)78 C)267 D)20 E)27 SOLUTION:A+B+C = 500 A+C = 200 B+C = 320 -------------- A+B+2C = 520 A+B+C = 500 ---------------- C = 20 Answer: D #### D QUESTION:How 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? options: A)24 sec B)30 sec C)27 sec D)28 sec E)29 sec SOLUTION:Speed of train relative to man = 63 - 3 = 60 km/hr. = 60 * 5/18 = 50/3 m/sec. Time taken to pass the man = 400 * 3/50 = 24 sec. Answer:A #### A QUESTION:Two 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: options: A)68 km/hr. B)32 km/hr. C)34 km/hr. D)35 km/hr. E)72 km/hr. SOLUTION:Let the speed of each train be x m/sec. Then, relative speed of the two trains = 2x m/sec. So, 2x = (240 + 240 )/12 2x = 40 x = 20. Speed of each train = 10 m/sec = 20 x 18/5 km/hr = 72 km/hr. answer :E #### E QUESTION:A can run 288 metre in 28 seconds and B in 32 seconds. By what distance A beat B? options: A)38 metre B)28 metre C)23 metre D)15 metre E)36 metre SOLUTION:Clearly, A beats B by 4 seconds Now find out how much B will run in these 4 seconds Speed of B = Distance/Time taken by B=288/32=9 m/s Distance covered by B in 4 seconds = Speed × time =9×4=36 metre i.e., A beat B by 36 metre Answer is E #### E QUESTION:What 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? options: A)1200 B)1256 C)1349 D)1456 E)1590 SOLUTION:First digit is 1/3 second digit => The numbers can be 1 & 3, 2& 6, 3 & 9. First + second = third => we can eliminate 3 & 9 since 3 + 9 = 12. Last is 3 times the second => we can eliminate option 2 & 6 since 3 * 6 = 18. Hence the number is 1349 C #### C QUESTION:walking at ¾ of his usual speed ,a man is late by 2 ½ hr. the usual time is. options: A)7 B)8 ½ C)7 ½ D)7 ¾ E)9 ½ SOLUTION:Usual speed = S Usual time = T Distance = D New Speed is ¾ S New time is 4/3 T 4/3 T – T = 5/2 T=15/2 = 7 ½ Answer is C. #### C QUESTION:40% of x is greater than 1/3rd of x by 110.what is x? options: A)1100 B)2100 C)1300 D)1650 E)1400 SOLUTION:4x/10-x/3=110 1x/15=110 x=1650 ANSWER:D #### D QUESTION:The current birth rate per thousand is 42, where as corresponding death rate is 22 per thousand. The net growth rate in terms of population increase in percent is given by? options: A)2.0% B)3.2% C)3.9% D)4% E)5.1% SOLUTION:Net growth on 1000 = 42-22 = 20 Net growth on 100 = 20*100/1000 = 2.0% Answer is A #### A QUESTION:The 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: options: A)5:2 B)7:3 C)9:2 D)13:4 E)3:4 SOLUTION:Let the age of father and son 10 years ago be 3x and x years respectively. Then, (3x + 10) + 10 = 2[(x + 10) + 10] 3x + 20 = 2x + 40 => x = 20. Required ratio = (3x + 10):(x + 10) = 70:30 = 7:3 ANSWER:B #### B QUESTION:√(36)^2 options: A)6 B)14 C)36 D)21 E)None of these SOLUTION:explanation √(36)^2 =? or, ? = 36 Answer C #### C QUESTION:If c is 14% of a and 40% of b, what percent of a is b? options: A) 2.5% B) 15% C) 25% D) 35% E) 250% SOLUTION:Answer = D 14a/100 = 40b/100 b = 14a/40 = 35a/100 = 35% #### D QUESTION:Find the odd man out. 18, 7, 12, 24, 48, 34, 46 options: A)16 B)46 C)24 D)11 E)7 SOLUTION:Explanation : 7 is the only odd number in the given series Answer : Option E #### E QUESTION:In X game of billiards, X can give Y 20 points in 45 and he can give Z 30 points in 45. How many points can Y give Z in X game of 100? options: A)30 B)20 C)25 D)40 E)50 SOLUTION:X scores 45 while Y score 40 and Z scores 30. The number of points that Z scores when Y scores 100 = (100 * 30)/25 = 60. In X game of 100 points, Y gives (100 - 60) = 40 points to C. D #### D QUESTION:Find large number from below question The difference of two numbers is 1375. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder options: A)1235 B)1345 C)1678 D)1767 E)1647 SOLUTION:Let the smaller number be x. Then larger number = (x + 1375). x + 1375 = 6x + 15 5x = 1360 x = 272 Large number = 272+1375 = 1647 E #### E QUESTION:How many numbers from 29 to 79 are exactly divisible by 11? options: A)4 B)6 C)8 D)5 E)7 SOLUTION:Numbers=(79/11)-(29/11) =7-2 =5 numbers Option D is answer #### D QUESTION:A set consist of 2k-1 element. What is the number of subsets of this set which contain at most k-1 elements? options: A)2^(2k-2) B)2^(2k) - 2 C)2^(2k) -1 D)2^(2k) E)2^(2k-1) SOLUTION:I used k=3, so then we have 5!/2!3! + 5!/4!1! + 5!/0!5! 10 + 5 + 1 = 16 So our target is 16 Now replace in answer choices A gives us 2^4 = 16 Hence A is the correct option Read 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 Avoid 2 since you will get 1 arrangement (k-1) and may be risky since 1 is a number with certain unique properties #### A QUESTION:A 140 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? options: A)35 B)20 C)47 D)36 E)40 SOLUTION:1: 2/5 = 5: 2 2/7 * 140 =40 Answer:E #### E QUESTION:Concentrated 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? options: A)24. B)28. C)36. D)42. E)48. SOLUTION:concentrated pineapple juice since height of a tube is 15 inches , the tubes can fit only in one way . now, diameter of each tube = 5 inches therefore, 4*2 can be put in each wooden box in 3 boxes 3*4*2 can be accommodated = 24=A #### A QUESTION:A man rows his boat 65 km downstream and 45 km upstream, taking 2 1/2 hours each time. Find the speed of the stream? options: A)5 kmph B)4 kmph C)9 kmph D)8 kmph E)1 kmph SOLUTION:Speed downstream = d/t = 65/(2 1/2) = 26 kmph Speed upstream = d/t = 45/(2 1/2) = 18 kmph The speed of the stream = (26 - 18)/2 = 4 kmph Answer:B #### B QUESTION:A family made a down payment of $300 and borrowed the balance on a set of encyclopedias that cost $750. The balance with interest was paid in 9 monthly payments of $57 each and a final payment of $21. The amount of interest paid was what percent of the amount borrowed? options: A) 6% B) 12% C) 14% D) 18.66% E) 20% SOLUTION:interest paid = 57*9+21 - 450 = 84 % off the balance = (84/450) * 100 = 18.66% Answer is D. #### D QUESTION:The value of a 10.5% stock, in which an income of Rs.756 is derived by investing Rs.9000, brokerage being% is : options: A)Rs. 113.5 B)Rs. 119.7 C)Rs. 124.75 D)Rs. 130.75 E)Rs. 134.45 SOLUTION:For an income of Rs.756, investment = Rs.9000 For an income of Rs., investment = = Rs.125 For a Rs.100 stock, investment = Rs.125. Market value of Rs. 100 stock = = Rs. 124.75 C #### C QUESTION:The simple interest on a certain sum of money for 2 l/2 years at 12% per year is Rs. 40 less than the simple interest on the same sum for 3 ½ years at 10% per year. Find the sum. options: A)800 B)700 C)600 D)500 E)None of them SOLUTION:Let the sum be Rs. x Then, ((x*10*7)/(100*2)) – ( (x*12*5)/(100*2)) = 40 = (7x/20)-(3x/10)=40 x = (40 * 20) = 800. Hence, the sum is Rs. 800. Answer is A. #### A QUESTION:The sum of money will be double itself in 30years and simple interest find rate of interest? options: A)A)2.33% B)B)3.33% C)C)4.33% D)D)5.33% E)E)6.33% SOLUTION:T = 30 years P= principle amount = x A = total amount = 2x SI = simple interest = A-P = 2x-x = x R = 100SI/PT = 100x/30x =3.33% Answer is B #### B QUESTION:At a certain health club, 30 percent of the members use both the pool and sauna, but 50 percent of the members who use the pool do not use the sauna. What percent of the members of the health club use the pool? options: A)33 1/3% B)46 2/3% C)50% D)62 1/2% E)75% SOLUTION:P = pool S = sauna given P+S = 30 then let only S be x and only P will be 100 - (30+x) = 70 -x 50% of (70-x) = x => 35 - 0.5x = x => x = 23 1/3% so only P = 70 -23 1/3 = 46 2/3% Answer B #### B QUESTION:A 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. 230 per month. What is his monthly salary? options: A)5000 B)5750 C)2878 D)2990 E)2771 SOLUTION:Income = Rs. 100 Expenditure = Rs. 80 Savings = Rs. 20 Present Expenditure 80*(20/100) = Rs. 96 Present Savings = 100 – 96 =Rs. 4 100 ------ 4 ? --------- 230 => 5750 Answer: B #### B QUESTION:Albert invested amount of 16000 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 options: A)Rs. 17640 B)Rs. 8620 C)Rs. 8730 D)Rs. 8820 E)None of these SOLUTION:Explanation: =>(16000×(1+5/100)2) =>16000×21/20×21/20 =>17640 Option A #### A QUESTION:A is 16th position and 29th from down of the people who passed. 5 failed , 6 didn't give . how many boys are there in the class? options: A)52 B)53 C)54 D)55 E)56 SOLUTION:A is 16th position, means = 15 + A 29th from down, means = A + 28 Total passed = A + 15 + 28 = 44 Total failed = 5 Didn't give = 6 Therefore, total boys = 44 + 5 + 6 = 55 ANSWER:D #### D QUESTION:It will take 16 days for Mary to complete a certain task alone. She worked for 8 days before she was joined by her sister. both of them completed the remaining task in 2 and half days. if her sister had joined her when she started the task, how many days would it have taken? options: A)6 B)8 C)2 D)5 E)4 SOLUTION:Explanation: Mary and her sister complete half work in 2.5 days => they can complete whole work in 5 days Answer: Option D #### D QUESTION:The speed of light is approximately 93 * 10^5 miles per second. This approximate speed is how many miles per hour? options: A) 3,35 * 10^8 B)70 * 10^7 C) 11 * 10^8 D) 16 * 10^8 E) 70 * 10^8 SOLUTION:The easiest way to answer this question is by POE, it does not require any calculation (answered in 30seconds). In one hour there are 3600 seconds, therefore speed in miles/hour will be. (.93*10^5)*3600 = (.93*10^5)*(3.6*10^3) = some number*10^8... The key is realizing that thesome numberhas to be bigger thatn .93(because .93*3.6), and the only answer that fits that is A #### A QUESTION:Calculate the HCF of 64, 318, 250 options: A)6 B)5 C)4 D)3 E)2 SOLUTION:Explanation: Lets solve this question by factorization method. 64=2 x 2 x 2 x 2 x 2 x 2, 318=2 × 3 × 53, 250=2 × 5 × 5 × 5 So HCF will be minimum term present in all three, i.e. 2×32=18 Answer: Option E #### E QUESTION:What least number must be subtracted from 7538 so that remaining no.is divisible by 14 options: A)3 B)5 C)6 D)8 E)9 SOLUTION:Explanation: On dividing 7538 by 14 we get the remainder 6, so 6 should be subtracted Option C #### C QUESTION:When the price of an article was reduced by 35% its sale increased by 80%. What was the net effect on the sale? options: A)17% increase B)44% decrease C)60% increase D)66% increase E)66% decrease SOLUTION:if n items are sold for $p each, revenue is $np. If we reduce the price by 35%, the new price is 0.65p. If we increase the number sold by 80%, the new number sold is 1.8n. So the new revenue is (0.65p)(1.8n) = 1.17np, which is 1.17 times the old revenue, so is 17% greater. ANSWER:A #### A QUESTION:The 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? options: A)8939 B)8383 C)8389 D)4530 E)9392 SOLUTION:Explanation: Area of the four walls = 2h(l + b) Since there are doors and windows, area of the walls = 2 * 12 (15 + 25) - (6 * 3) - 3(4 * 3) = 906 sq.ft. Total cost = 906 * 5 = Rs. 4530 Answer: Option D #### D QUESTION:A tank contains 10,000 gallons of a solution that is 5 percent sodium chloride by volume. If 5,500 gallons of water evaporate from the tank, the remaining solution will be approximately what percent sodium chloride? options: A) 1.25% B) 3.75% C) 6.25% D) 6.67% E) 11.11% SOLUTION:The 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 10,000-5,500=4,500 gallons and sodium chloride is 500 gallons (5% of initial solution of 10,000 gallons) then sodium chloride is 500/4,500*100=~11.11% of the remaining solution of 4,500 gallons. Answer: E. #### E QUESTION:There 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? options: A)90. B)80. C)50. D)40. E)25. SOLUTION:STREET-CAT DOMESTIC-Cat 70 130 (20gray+50other) 90gray+40other Answer:D #### D QUESTION:What is the are of an equilateral triangle of side 8 cm? options: A)64√5 B)64√9 C)16√3 D)64√3 E)64√2 SOLUTION:Area of an equilateral triangle = √3/4 S2 If S = 8, Area of triangle = √3/4 * 8 * 8 = 16√3 cm2; Answer: C #### C QUESTION:If x is an integer and y = 3x + 5, which of the following CANNOT be a divisor of y? options: A)4 B)12 C)2 D)7 E)6 SOLUTION:For any value of x, the expression 3x + 5 would never be divisible by 3,6,9...... onwards So answer = 6 = E #### E <<<Examples ends QUESTION:A can do a piece of work in 10 days and B can do it in 15 days and C can do it 20 days. They started the work together and B leaves after 2 days and C leaves after 4 days from the beginning. How long will work lost? options: A)3 2/3 B)5 2/3 C)6 2/3 D)4 2/3 E)7 2/3 SOLUTION:x/10 + 2/15 + 4/20 = 1 x = 40/60*10 = 6 2/3 Answer: C #### C

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:Rs.12320 were divided among W, X & Y in such a way that W had Rs.640 more than X and Y had Rs 480 more than X . How much was X’s share? options: A)Rs.4590 B)Rs.4610 C)Rs.4620 D)Rs.4630 E)Rs.4640 SOLUTION:Let X gets Rs x. Then We can say W gets Rs (x + 640 ) and Y gets Rs ( x + 560) . x + 640 + x + x + 1120 = 12320 3x = 10560 x = 3520 . C’s share = Rs ( 3520+1120 ) = Rs.4640 E #### E QUESTION:The value of 489.1375 x 0.0483 x 1.956/0.0873 x 92.581 x 99.749 is closest to: options: A)0.48 B)5.8 C)0.58 D)0.058 E)0.0058 SOLUTION:= 489.1375 x 0.0483 x 1.956/0.0873 x 92.581 x 99.749 = 489 x 0.05 x 2/0.09 x 93 x 100 = 489/9 x 93 x 10 = 163/279 x 1/10 = 0.58/10 = 0.058 (or) 0.06. Answer is D. #### D QUESTION:Monica 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 4 muffins remained. How many guests did Monica plan on? options: A)3. B)4. C)5. D)6. E)7. SOLUTION:Let x be the number of guests. Number of muffins prepared = 5x + 2 Number of muffins eaten + Number of muffins remaining = Number of muffins prepared 6(x - 1) + 4 = 5x + 2 6x - 4 = 5x + 2 x = 6 Answer: D #### D QUESTION:If a card is drawn from a well shuffled pack of cards, the probability of drawing a spade or a king is options: A)4/17 B)4/16 C)4/15 D)4/13 E)4/12 SOLUTION:P(SᴜK) = P(S) + P(K) - P(S∩K), where S denotes spade and K denotes king. P(SᴜK) = 13/52 + 4/52 - 1/52 = 4/13 Answer:D #### D QUESTION:Pipe A can fill a tank in 8 hours, pipe B in 4 hours and pipe C in 24 hours. If all the pipes are open, in how many hours will the tank be filled? options: A)1.9 hour B)2.1 hour C)4.7 hour D)2.4 hour E)3.2 hour SOLUTION:Part filled by pipe A in 1 hour =1/8 Part filled by pipe B in 1 hour =1/4 Part filled by pipe C in 1 hour =1/24 Part filled by pipes A,B,C together in 1 hour=1/8+1/4+1/24=10/24 i.e, pipes A,B,C together can fill the tank in = 24/10 hr =2.4 hour. ANSWER:D #### D QUESTION:Murali 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 3 : 3? options: A)16 B)48 C)277 D)92 E)11 SOLUTION:Let the distances between city A to B and B to C be 3x km and 3x km respectively. Total time taken to cover from A to C = (3x)/40 + (3x)/60 = (9x + 6x)/120 = 15x/120 = x/8 Average speed = (3x + 3x)/(x/8) = 48 kmph. Answer:B #### B QUESTION:If the integer N = 139,k50 where k is the hundreds digit, N can NEVER be divisible by which of the following? options: A)2 B)3 C)4 D)6 E)9 SOLUTION:It is divisible by 2 irrespective of k value as unit digit's value is even(0). It can be divisible by 3 for k values 2,5,8 as sum will be divisible by 3 It can be divisible by 6 if divisible by 2 and 3. It can be divisible by 9 for k value 2 as sum will be divisible by 9. Therefore answer is 4 as number is divisible if last two digits are divisible.In this case 50(No) Hence answer C #### C QUESTION:A train is running at a speed of 40 km/hr and it crosses a post in 18 seconds. What is the length of the train? options: A)metres B)metres C)metres D)metres E)metres SOLUTION:Explanation: Speed of the train, v = 40 km/hr = 40000/3600 m/s = 400/36 m/s Time taken to cross, t = 18 s Distance Covered, d = vt = (400/36)× 18 = 200 m Distance covered is equal to the length of the train = 200 m Answer: Option C #### C QUESTION:Which of the following options is an appropriate approximate value in the following equation’? 3 4/3 of 155.83+22% of 1547= ? - 504.7 options: A)1855.94 B)1557.94 C)1257.94 D)1837.94 E)1857.94 SOLUTION:3 4/3 of 155.83+22% of 1547= ? - 504.7 1012.9+340.34= ? - 504.7 1012.9+340.34 +504.7= ? ≈ 1857.94 Answer E #### E QUESTION:Two pipes can fill the cistern in 10hr and 12 hr respectively, while the third empty it in 20hr. If all pipes are opened simultaneously, then the cistern will be filled in options: A)7.5 hr B)8 hr C)8.5 hr D)10 hr E)None of these SOLUTION:Solution: Work done by all the tanks working together in 1 hour. 1/10+1/12−1/20=2/15 Hence, tank will be filled in 15/2=7.5 hour Option(A) #### A QUESTION:The 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? options: A)7:9 B)7:3 C)7:2 D)7:9 E)7:1 SOLUTION:Let the age of father and son 10 years ago be 3x and x years respectively. Then, (3x + 10) + 10 = 2[(x + 10) + 10] 3x + 20 = 2x + 40 => x = 20. Required ratio = (3x + 10):(x + 10) = 70:30 = 7:3 Answer:B #### B QUESTION:If grapes are 92% water and raisins are 20% water, then how much did a quantity of raisins, which currently weighs 10 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.) options: A)25 pounds B)46 pounds C)92 pounds D)100 pounds E)146 pounds SOLUTION:Since 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*10 --> x = 100. Answer: D. #### D QUESTION:Given that 268x74= 19632, find the value of 2.68x.74. options: A)1.9632 B)1.0025 C)1.5693 D)1.0266 E)None SOLUTION:Solution Sum of decimals places =(2+2) = 4. Therefore, = 2.68×.74 = 1.9632 Answer A #### A QUESTION:A basket has 5 apples and 4 oranges. Three fruits are picked at random. The probability that at least 2 apples are picked is? options: A)25/42 B)25/46 C)25/41 D)25/49 E)25/23 SOLUTION:Total fruits = 9 Since there must be at least two apples, (⁵C₂ * ⁴C₁)/⁹C₃ + ⁵C₃/⁹C₃ = 25/42. Answer:A #### A QUESTION:The 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 options: A)153550 m^2 B)153600 m^2 C)153700 m^2 D)153800 m^2 E)153900 m^2 SOLUTION:Explanation: Perimeter = Distance covered in 8 min. = 12000 x 8 m = 1600 m. 60 Let length = 3x metres and breadth = 2x metres. Then, 2(3x + 2x) = 1600 or x = 160. Length = 480 m and Breadth = 320 m. Area = (480 x 320) m2 = 153600 m^2. Option B #### B QUESTION:Each of the positive integers a and c is a four-digit integer. If each of the digits 0 through 9 appears in one of these three integers, what is the maximum possible value of the sum of a and c? options: A)18695 B)18325 C)18365 D)18395 E)18485 SOLUTION:According to the stem we should use the digits 0 through 9 to construct 2 four-digit integers, so that their sum is as big as possible. To maximize the sum, maximize the thousands digits of a and c, so make them 9 and 8. Next, maximize hundreds digits. Make them 7 and 6 . Next maximize 10's digit place by 5 and 4 Use the remaining digits (3,and 2) for units digits. So, a would be 9753,and c would be 8642. 9753 + 8642 = 18395 Answer: D. #### D QUESTION:walking at ¾ of his usual speed ,a man is late by 2 ½ hr. the usual time is. options: A)7 B)8 ½ C)7 ½ D)7 ¾ E)9 ½ SOLUTION:Usual speed = S Usual time = T Distance = D New Speed is ¾ S New time is 4/3 T 4/3 T – T = 5/2 T=15/2 = 7 ½ Answer is C. #### C QUESTION:a fruit vender buys 4 varieties of apple costing rs. 140,rs.150,rs.160 and rs.170 per kg in the ratio 2:3:4:1 and mixes all the four varieties and sells at 50% profit. What is the selling price per kg of apple? options: A)225 B)228 C)230 D)231 E)235 SOLUTION:CP = 140*2+150*3+160*4+170*1=1540 SP = 1.5*1540=2310 Total no.of kgs=2+3+4+1=10 SP per kg=2310/10=231 ANSWER:D #### D QUESTION:In 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 options: A)37 B)38 C)39 D)40 E)41 SOLUTION:let present age of A be a and B be b a+10 = 2*(b-10) => 2b-a = 30 ......(i) a = b+9 =>2b-b-9 = 30 b=39 so the present age of b is 39 years ANSWER:C #### C QUESTION:Two trains are moving in opposite directions with speed of 210 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 options: A)56 B)48 C)47 D)26 E)24 SOLUTION:Explanation: Relative speed = 210+90 = 300 km/hr (Since both trains are moving in opposite directions) Total distance = 1.1+.9 = 2km Time = 2/300 hr = 1/150 hr = 3600/150 seconds =24 seconds Answer: Option E #### E QUESTION:5 - [5 - {5 - 5(5 + 5)}] = ? options: A)5 B)-45 C)45 D)50 E)60 SOLUTION:Explanation: => ? = 5 - [5 - {5 - 5 × 10}] = 5 - [5 - (-45)] = 5 - (50) = - 45 Answer: Option B #### B QUESTION:A retail item is offered at a discount of d percent (where d > 10), with a 5% state sales tax assessed on the discounted purchase price. If the state sales tax were not assessed, what percent discount from the item’s original retail price, in terms of d, would result in the same final price? options: A)d+5/1.05 B)d/1.05 +5 C)1.05d-5 D)d-5/1.05 E)1.05(p – 5) SOLUTION:Let x be the price of the item. Final price after discount and sales tax = x * (1 - d/100) * 1.05 Let e be the percent discount which would result in the same final price. Then, x * (1 - d/100) * 1.05 = x * (1 - e/100) => 1.05 - 1.05d/100 = 1 - e/100 => e/100 = 1.05d/100 - .05 => e = 1.05d - 5 Hence ,option C is correct. #### C QUESTION:How many 4-letter word with or without meaning can be formed out of the letters of the word 'LOGARITHMS' if repetition of letters is not allowed options: A)5040 B)1254 C)4510 D)1203 E)4510 SOLUTION:'LOGARITHMS' contains 10 different letters Required number of words = Number of arrangements of 100 letters taking 4 at a time = 10P4 = 10 * 9 * 8 * 7 = 5040 Ans: A #### A QUESTION:Sum of the numbers from 1 to 25 is options: A)210 B)325 C)320 D)105 E)None of these SOLUTION:Explanation: Sum of first n natural numbers = 1 + 2 + 3 + ..... n = n(n+1)/2 Substitute n = 25. So S20=25×26/2=325 Correct Option: B #### B QUESTION:Which of the following is closest to (8!-7!)/(8!+7!)? options: A)0.01 B)0.8 C)0.2 D)1 E)10 SOLUTION:(8!-7!)/(8!+7!) 7! (8-1)/7! (8+1) 7/9 = 0.8 (approximately) B is the answer #### B QUESTION:If x + y = 8 and y − 3x = 7, then what is the value of y-x? options: A)1/7 B)3 C)15 D)15/2 E)60/7 SOLUTION:x+y=8 ...equation 1 -3x+y=7 ...equation 2 adding both the equations -2x+2y=15=>y-x=15/2 correct answer option D #### D QUESTION:You are filling up your car with gas. Your tank can hold 19 gallons. Your car started with x gallons in it. You paid $20 in gas. What was the cost of gas per gallon? options: A)19/20 B)x/20 C)(19-x)/20 D)x-19)/20 E)19+20/x SOLUTION:Amount of gas you added to your car: 19-x Price per gallon: (19-x)/20 Answer: C #### C QUESTION:The timing of a college is from 12 p.m to 4.20 p.m. Five lectures are held in the given duration and a break of 5 minutes after each lecture is given to the students. Find the duration of each lecture. options: A)52 minutes B)45 minutes C)30 minutes D)48 minutes E)44 minutes SOLUTION:Explanation: Total time a student spends in college = 4 hours 20 minutes = 260 minutes As there are 5 lectures, the number of breaks between lectures is 4. Total time of the break = 20 minutes Hence, the duration of each lecture is = (260 – 20)/5 = 48 minutes ANSWER D #### D QUESTION:If x and y are integers and 4^(x-4) = 4^(y+4), what is y in terms of x? options: A)x - 8 B)x - 5 C)x - 2 D)x + 2 E)x + 6 SOLUTION:Answer: A 4^(x-4) = 4^(y+4) Since the base is the same, I isolated the equations and solved for y. x-4 = y+4 y=x-8 #### A QUESTION:A 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? options: A)15/56 B)41/56 C)13/28 D)15/28 E)5/14 SOLUTION:The 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. Ways to select 6 out of total 8 = 8C6 Ways to select 4 out of 5 white balls = 5C4 Ways to select 2 out of 3 blue balls = 3C2 Thus the required probability = (5C4*3C2)/8C6 = 15/28. D is thus the correct answer. #### D QUESTION:One fast typist type some matter in 2hrs and another slow typist type the same matter in 3hrs. If both do combine in how much time they will take to finish. options: A)10 B)11 C)12 D)13 E)14 SOLUTION:Fast's 1 hr work = 1/2 slow's 1 hr work = 1/3 1/2 + 1/3 = 5/6 they ll finish in 6/5hrs= 1 1/5 ==> 1 hr 12 mins ANSWER:C #### C QUESTION:What is the least possible product of 4 different integers, each of which has a value between –1 and 10, inclusive? options: A)–5040 B)–3600 C)–720 D)–600 E)–120 SOLUTION:Maximize the total product with a -ve sign so -1 * 10 * 9 * 8 = 720 * -1 = -720 Answer is C. #### C QUESTION:The probability that a brand A widget is defective is x, the probability that a brand B widget is defective is 0.06, and the probability that a brand C widget is defective is 0.08. There are 40 brand A widgets, 35 brand B widgets, 25 brand C widgets, and nothing else in a container. If a widget is selected at random from the container, the probability that the widget selected is defective is 0.053. What is the value of x? options: A)0.03 B)0.04 C)0.048 D)0.05 E)0.12 SOLUTION:Probability of Brand A defective is x Probability of Brand B defective is 0.06 which 6/100. Which tells you there are 2 defective piece in a lot of 33, for 35 lot it is approx - 2.12 Probability of Brand C defective is 0.08 which 8/100. Which tells you there are 2 defective piece in a lot of 25 Total = 40 + 25 + 25 = 100 Probability of having defective piece in a lot of 100 ( All brands ) = 0.053 Hence 5.3 defective piece out 100 lot. So 40x + 2.12 + 2 = 5.3 x = 0.03 ANSWER :Opt A. #### A QUESTION:If a positive odd integer N has p positive factors, how many positive factors will 3N have ? options: A)p B)2p C)P+1 D)2p+1 E)Cannot be determined SOLUTION:I have added some extra text to make this question more GMAT-like: Let's TEST some values of N Try N = 3 The factors of 3 are {1, 3}. Here, p =2 So, 2N = (2)(3) = 6 The factors of 6 are {1, 2, 3, 6}. So, we have a total of4 Now check the answer choices: A) p =2No good. We want an output of4. ELIMINATE B) 2p = (2)(2) = 4. PERFECT! KEEP B C) P+1 =2+ 1 = 3 No good. We want an output of4. ELIMINATE D) 2p+1 = (2)(2) + 1 = 5 No good. We want an output of4. ELIMINATE E) Cannot be determined. POSSIBLE. KEEP E Let's TEST another value of N Try N = 7 The factors of 7 are {1, 7}. Here, p =2 So, 2N = (2)(7) = 14 The factors of 14 are {1, 2, 7, 14}. So, we have a total of4 Now check the REMAINING answer choices: B) 2p = (2)(2) =4. PERFECT! KEEP B E) Cannot be determined. POSSIBLE. KEEP E Let's TEST one more (non-prime) value of N Try N = 9 The factors of 9 are {1, 3, 9}. Here, p =3 So, 2N = (2)(9) = 18 The factors of 18 are {1, 2, 3, 6, 9}. So, we have a total of6 Now check the REMAINING answer choices: B) 2p = (2)(3) =6. PERFECT! KEEP B E) Cannot be determined. POSSIBLE. KEEP E At this point, it SEEMS LIKELY that the correct answer is C #### C QUESTION:If the sum of two positive integers is 20 and the difference of their squares is 40, what is the product of the two integers? options: A)108 B)99 C)128 D)135 E)143 SOLUTION:Let the 2 positive numbers x and y x+ y = 20 -- 1 x^2 - y^2 = 40 => (x+y)(x-y)=40 -- 2 Using equation 1 in 2 , we get => x-y = 2 -- 3 Solving equation 1 and 3 , we get x= 11 y= 9 Product = 11*9 = 99 Answer B #### B QUESTION:In a clock (Conventional clock with numbers 1 to 12 in order)is cut into 3 pieces such that the sum of each piece in AP with a common difference of 1. What is the count of numbers in each piece? and what are the numbers? options: A)25 B)26 C)27 D)28 E)29 SOLUTION:Sum of the 12 numbers=1+2+3+......+12=12*13/2=78 So we have to divide it into 3 slots such that the sum is 78 and sum of each slot is in AP, thus the 3 slots are 25,26,27. So the numbers can be: 3+4+5+6+7=25 8+9+10=27 11+12+1+2=26 ANSWER:B #### B QUESTION:There were two candidates in an election. Winner candidate received 60% of votes and won the election by 288 votes. Find the number of votes casted to the winning candidate? options: A)776 B)864 C)299 D)257 E)125 SOLUTION:W = 60% L = 40% 60% - 40% = 20% 20% -------- 288 60% -------- ? => 864 Answer:B #### B QUESTION:The juice stall at the circus stocked just 2 brands of orange juice tetra packs. Brand A costs $1 per pack and brand B costs $1.5 per pack. Last week , brand A contributed to m% of stall’s revenue and accounted for n% of sales of juice tetra packs. Which of the following expresses m in terms of n? options: A)100n/(150 – n) B)200n/(250-n) C)200n/(300-n) D)250n/(400-n) E)300n/(500-n) SOLUTION:Let the number of units sold be 100. Then n units of A are sold and (100-n) units of B are sold. Total revenue= Revenue due to A + Revenue due to B = (No.of units of A sold * Cost/unit of A) + (No.of units of B sold * cost/unit of B) = n *1 + (100-n) *1.5 = n + (150-1.5n) --- (1) 2. But we know, revenue due to A = m%. of the total revenue --- (2) 3. To express m in terms of n we need to relate (1) and (2) 4. m% = n / ( n + (150-1.5n)) or m= 100n / 150-0.5n = 200n/(300-n) ANSWER:C #### C QUESTION:Anderson has a phone plan that charges a monthly rate of $50 for the first 1,000 minutes plus $0.25 for each additional minute. Which of the following functions models Anderson’s plan for all m > 1,000, with m as the number of minutes per month and f(m) as the monthly charge? options: A)f(m) = 0.25m B)f(m) = 0.25m + 50 C)f(m) = 0.25m – 200 D)f(m) = 0.25m – 950 E)f(m) = 0.25m + 1,000 SOLUTION:For m > 1,000 — that is, beyond 1,000 minutes of usage — the plan charges a usage fee based on the number of minutes used plus a flat rate of $50. With this information, you can create the following function: f(m) = Usage fee + 50 The usage fee is $0.25 per minute; however, the first 1,000 minutes are already paid for. So the usage fee is 0.25(m – 1,000). Plug this value into the preceding function and simplify: f(m) = 0.25(m – 1,000) + 50 f(m) = 0.25m – 250 + 50 f(m) = 0.25m – 200 correct answer C)f(m) = 0.25m – 200 #### C QUESTION:When 3 is added to half of one-third of one-fifth of a number, the result is one-fifteenth of the number. Find the number? options: A)32 B)81 C)60 D)27 E)90 SOLUTION:Explanation: Let the number be 3 + 1/2[1/3(a/5)] = a/15 => 3 = a/30 => a = 90 Answer:E #### E QUESTION:Calculate the circumference of a circular field whose radius is 10 centimeters. options: A)20 π cm B)19 π cm C)28 π cm D)25 π cm E)30 π cm SOLUTION:Circumference C is given by C = 2πr = 2π*10 = 20 π cm Answer: A #### A QUESTION:Find the value of x: x² + 4x + 4. options: A)2 B)4 C)-2 D)-4 E)0 SOLUTION:That quadratic is factored as follows: x² + 4x +4 = (x+2)(x+2). Lesson 17. Now, it is easy to see that the second factor will be 0 when x = -2. The solution is: x = -2 C #### C QUESTION:A sum of Rs. 125000 amounts to Rs. 15500 in 4 years at the rate of simple interest. What is the rate of interest? options: A)3% B)2% C)1% D)6% E)7% SOLUTION:S.I. = (15500 - 12500) = Rs. 3000\ Rate = (100 * 3000) / (12500 * 4) = 6% Answer: D #### D QUESTION:A 16% stock yielding 10% is quoted at : options: A)83.33 B)110 C)112 D)120 E)160 SOLUTION:Solution To earn Rs. 10, money invested = Rs. 100. To earn Rs. 16, money invested = Rs.(100/10X16) = Rs. 160. ∴ Market value of Rs. 100 stock =Rs. 160 Answer E #### E QUESTION:The probability that A speaks truth is 15/23 and that of B speaking truth is 17/29. What is the probability that they agree in stating the same fact? options: A)182/395 B)129/289 C)197/353 D)479/667 E)None of these SOLUTION:If both agree stating the same fact, either both of them speak truth of both speak false. Probability = 15/23 * 17/29 + 14/23 * 16/29 = 255/667 + 224/667 = 479/667 ANSWER:D #### D QUESTION:If 4,5qD + 8,737 = 13,qD3, where q and D are distinct digits, what is the value of D – q? options: A)6 B)4 C)3 D)2 E)1 SOLUTION:4500+10q+d+8737=13003+100q+10d 13237+10 q+d=13003+100q+10d 234=90q+9d 26=10 q+d d=6 ^ q=2 ==> d-q= 4 ANSWER B #### B QUESTION:In a kilometer race, A can give B a 100 m start and C a 150 m start. How many meters start can B give to C? options: A)50 B)50/9 C)8500/9 D)500/9 E)None of these SOLUTION:A can give B a 100 m start and C a 150m. Start means when A runs 1000m, B runs 900m and C runs 850m. When B runs 1000m, C will run 1000 x (850/900) m (i.e. 8500/9 m) Thus, B can give C a start of - 1000 - (8500/9), i.e. 500/9 m. Answer: D #### D QUESTION:If the equation x^2−x=k has at least one solution, which of the following must be true? options: A)k ≥-1/4 B)k < −9 C)k = 9 D)k ≤ 9 E)k ≥ −9 SOLUTION:x^2−x=k => x^2−x - k = 0 For a quadratic equation to have at least one solution, its discriminant (b^2-4ac) should be non-negative. b^2-4ac ≥0 => 1- 4*1*(-k) ≥0 =>1 + 4k ≥0 => k ≥ -14 Answer A #### A QUESTION:There are 9 teams in a certain league and each team plays each of the other teams exactly once. What is the total number of games played? options: A)24 B)25 C)28 D)32 E)36 SOLUTION:9C2 = 36 The answer is E #### E QUESTION:A person crosses a 600 m long street in 5 minutes. What is his speed in km per hour? options: A)7.9 B)7.3 C)7.8 D)7.2 E)7.1 SOLUTION:distance = 600 meter time = 5 minutes = 5 x 60 seconds = 300 seconds Speed = distancetime=600300=2m/s=2×185 km/hr=365 km/hr=7.2 km/hr Answer :D #### D QUESTION:The 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.1950. The perimeter of the plot is? options: A)126 B)156 C)190 D)300 E)260 SOLUTION:Sol. Let width = x, Length = (10+x) Perimeter = 2(x+(10+x)) = 2(2x=10) & 2(2x+10)*6.5 = 1950 X = 70 Required perimeter = 2(70+80) = 300 D #### D QUESTION:What is the 4 digit number 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? options: A)1244 B)1532 C)1349 D)1423 E)1543 SOLUTION:First digit is 1/3 second digit => The numbers can be 1 & 3, 2& 6, 3 & 9. First + second = third => we can eliminate 3 & 9 since 3 + 9 = 12. Last is 3 times the second => we can eliminate option 2 & 6 since 3 * 6 = 18. Hence the number is 1349 C #### C QUESTION:A 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? options: A)1/2 B)1/4 C)3/8 D)5/12 E)2/5 SOLUTION:The probability for each ball to be drawn third is equal. Then the probability a red ball is drawn third is 4/16 = 1/4. The answer is B. #### B QUESTION:A man whose speed is 6.5 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 2.5 kmph, find his average speed for the total journey ? options: A)1 kmph B)5 kmph C)5.5 kmph D)4 kmph E)7 kmph SOLUTION:Explanation: Speed of Man = 6.5 kmph Speed of stream = 2.5 kmph Speed in DownStream = 9 kmph Speed in UpStream = 4 kmph Average Speed = (2 x 9 x 4)/13 = 5.5 kmph. Answer: C #### C QUESTION:The 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? I. c > a II. c = a III. c < a options: A)I only B)II only C)III only D)I and II only E)II and III only SOLUTION:Let q = 10% then l = 100/11 % let b = 100 then a = 110 after increasing a by l and decreasing b yq we get c= 108 therefore c<a C it is answer #### C QUESTION:A bucket full of nuts was discovered by the crow living in the basement. The crow eats a sixth of the total number of nuts in 4 hours. How many hours i total will it take the crow to finish a quarter of the nuts? options: A)6 B)8 C)10 D)12 E)14 SOLUTION:In one hour, the crow eats 1/24 of the nuts. (1/4) / (1/24) = 6 hours The answer is A. #### A QUESTION:Mr. 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 options: A)$145 B)$250 C)$300 D)$175 E)$150 SOLUTION:Let the 1st paycheck be x(integer).Mr. Rodger got a weekly raise of $145. so after completing the 1st week she will get $ (x+145).similarly after completing the 2nd week she will get $(x+145)+$145.=$(x+145+145=$(x+290). so in this way end of every week her salary will increase by $145. correct answer will be (A) #### A QUESTION:If f is a function defined for all k by f(k) = k^3 /16, what is f(2 k) in terms of f(k)? options: A)1/8 f(k) B)8 f(k) C)2 f(k) D)10 f(k) E)32 f(k) SOLUTION:f(k) = k^3 /16 f(2k) = (2k)^3 /16 =8 * k^3/16 = 8 x (k^3 /16) = 8 f(k). So answer is B. #### B QUESTION:Which 2 digit number has its digits reversed when you double it and take 1? options: A)33 B)34 C)35 D)36 E)37 SOLUTION:reverse it and you get 73 which is 2*37-1. ANSWER:E #### E QUESTION:If -2/(a - 6) = 4/(a + 4), then a = ? options: A)2/3 B)1/2 C)5/3 D)8/3 E)7/3 SOLUTION:Multiply all terms of the given equation by (a - 6)(a + 4), simplify and solve (a - 6)(a + 4)[ -2/(a - 6) ] = (a - 6)(a + 4) [ 4/(a + 4) ] - 2 (a + 4) = 4 (a - 6) a = 8/3 correct answer D #### D QUESTION:There are 16 teams in a tournament. If during the first round, each team plays every other team exactly once, how many games will be played in the first round? options: A)15 B)30 C)120 D)240 E)256 SOLUTION:Number of ways to pick 2 teams from a total of 16 = 16C2 = 16!/14!*2! = 120. Hence C. #### C QUESTION:In a market, a dozen eggs cost as much as a pound of rice, and a half-liter of kerosene costs as much as 8 eggs. If the cost of each pound of rice is $0.33, then how many E cents does a liter of kerosene cost? [One dollar has 100 cents.] options: A) 0.33 B) 0.44 C) 0.55 D) 44 E) 55 SOLUTION:Main thing to remember is answer is asked in cents, however when we calculate, it comes up as 0.44 $ Just multiply by 100, Answer E= 44.D #### D QUESTION:If the sides of a triangle are 26 cm, 24 cm and 10 cm, what is its area? options: A)120 cm2 B)187 cm2 C)178 cm2 D)189 cm2 E)176 cm2 SOLUTION:The triangle with sides 26 cm, 24 cm and 10 cm is right angled, where the hypotenuse is 26 cm. Area of the triangle = 1/2 * 24 * 10 = 120 cm2 Answer: A #### A QUESTION:The 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? options: A)289 cm B)800 cm C)829 cm D)288 cm E)289 cm SOLUTION:Area of the square = s * s = 5(125 * 64) => s = 25 * 8 = 200 cm Perimeter of the square = 4 * 200 = 800 cm. Answer: B #### B <<<Examples ends QUESTION:Envelopes 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 $7.90? options: A)426 B)430 C)443 D)480 E)486 SOLUTION:I think first we should see in what group envelopes value less, so that we can buy as many as we can with a specific amount of money: -the 100 pack costs 1.5$, meaning 0.015$ per envelope -the 50 pack costs 1$, meaning 0.02$ per envelope -the single envelope costs 0.03$ per envelope Thus, 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. Having 7.9$, we can buy as many as 4 packs of 100 (4 x 1.5$ = 6$). We then have 1.9 $ left. so we buy 1 pack of 50 for 1$. We now have 0.9$ left, so we buy 30 individual envelopes. If we add up the numbers, we get 400+50+30=480 envelopes. Answer D #### D

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:A train 500 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? options: A)298 m B)279 m C)500 m D)289 m E)800 m SOLUTION:Speed = 78 * 5/18 = 65/3 m/sec. Time = 1 min = 60 sec. Let the length of the train be x meters. Then, (500 + x)/60 = 65/3 x = 800 m. Answer: E #### E QUESTION:The 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 51 kmph, find the speed of the stream? options: A)12 kmph B)13 kmph C)14 kmph D)15 kmph E)17 kmph SOLUTION:The ratio of the times taken is 2:1. The ratio of the speed of the boat in still water to the speed of the stream = (2+1)/(2-1) = 3/1 = 3:1 Speed of the stream = 51/3 = 17 kmph ANSWER:E #### E QUESTION:In a certain aquarium, the number of red fish is three times the number of the green fish, and the number of blue fish is half the number of the red fish. If the ratio of green fish to red fish were to be doubled, and the ratio of red fish to blue fish were to be doubled, then the ratio of blue fish to green fish in that aquarium would be options: A)3:2 B)1:1 C)1:2 D)3:4 E)3:8 SOLUTION:Lots of little places to make a mistake or panic here. =) R = 3G B = R/2 G/R = 1/3 ----> Doubled G/R = 2/3 R/B = 2 ----> Doubled R/B = 4 B/G = (B/R)*(R/G) = (1/4)*(3/2) = 3/8 ANSWER:E #### E QUESTION:A bank offers 3% compound interest calculated on quarter-yearly basis. A customer deposits $ 15000 each in 1st month. At the end of the year, the amount he would have gained by way of interest is? options: A)200 B)150 C)455 D)300 E)600 SOLUTION:Amount = (15000)* (1 + (3/4*100))^4 Amount = 15000 * (1+ 0.0075)^4 = 15455 ------(for investment in 1st month) Interest = 15455-15000 = 455.............. Ans -C #### C QUESTION:A train running at the speed of 60 km/hr crosses a pole in 30 seconds. What is the length of the train? options: A)500 m B)620 m C)872 m D)150 m E)765 m SOLUTION:Speed=(60 * 5/18) m/sec = (50/3) m/sec Length of the train = (Speed x Time) = (50/3 * 30) m = 500 m. Answer: A #### A QUESTION:What will be the cost of building a fence around a square plot with area equal to 144 sq ft, if the price per foot of building the fence is Rs. 58? options: A)2784 B)2287 C)2977 D)2668 E)1298 SOLUTION:Let the side of the square plot be a ft. a2 = 144=> a = 12 Length of the fence = Perimeter of the plot = 4a = 48 ft. Cost of building the fence = 48 * 58 = Rs. 2784. Answer:A #### A QUESTION:If a quarter kg of onions costs 80 paise, how many paise will 100 gm cost? options: A)32 paise B)65 paise C)56 paise D)87 paise E)15 paise SOLUTION:Explanation: Let the required cost be x paise. Less weight, Less cost (Direct proportion) 250 : 100 : : 80 : x 250 * x = (100 * 80) x = (100 * 80) / 250 x = 32 ANSWER: A #### A QUESTION:If A:B:C = 2:3:4, then find AB:BC:CA options: A)5:9:24 B)6:9:24 C)7:9:24 D)8:9:24 E)None of these SOLUTION:Explanation: Let A = 2x, B = 3x, C = 4x, then, AB=2x3x=23BC=3x4x=34CA=4x2x=21=>AB:BC:CA=23:34:21=8:9:24 Answer: D #### D QUESTION:Two alloys A and B are composed of two basic elements. The ratios of the compositions of the two basic elements in the two alloys are 5:3 and 1:2, respectively. A new alloy X is formed by mixing the two alloys A and B in the ratio 4:3. What is the ratio of the composition of the two basic elements in alloy X? options: A)1:1 B)2:3 C)5:2 D)4:3 E)None of these SOLUTION:Explanation : Let,the actual amount of A and B be 4x and 3x respectively. Amount of 1st basic element in the new alloy T is (5/8)*4x + (1/3)*3x = (7x)/2. Similarly, the amount of 2nd basic element in the new alloy T is (3/8)*4x + (2/3)*3x= (7x)/2. So, the ratio of 1st basic element to 2nd basic element is [(7x)/2 ] / [ 7x/2] = 1/1 = 1:1. Answer : A #### A QUESTION:A shopkeeper sells 20% of his stock at 10% profit ans sells the remaining at a loss of 5%. He incurred an overall loss of Rs. 400. Find the total worth of the stock? options: A)30000 B)20000 C)23000 D)21020 E)28211 SOLUTION:Explanation: Let the total worth of the stock be Rs. x. The SP of 20% of the stock = 1/5 * x * 1.1 = 11x/50 The SP of 80% of the stock = 4/5 * x * 0.95 = 19x/25 = 38x/50 Total SP = 11x/50 + 38x/50 = 49x/50 Overall loss = x - 49x/50 = x/50 x/50 = 400 => x = 20000 Answer: B #### B QUESTION:How many even multiples of 45 are there between 449 and 901? options: A)5 B)6 C)9 D)10 E)11 SOLUTION:450 = 10*45 900 = 20*45 The even multiples are 45 multiplied by 10, 12, 14, 16, 18, and 20 for a total of 6. The answer is B. #### B QUESTION:If x is negative and y is positive, which of the following cannot be positive? options: A)x/y B)-x*y C)-x/y D)x^2+y E)x^6+y SOLUTION:- /+ = - x/y is negative. Answer : A #### A QUESTION:A and B are two circles. The radius of A is thrice as large as the diameter of B. What is the ratio between the areas of the circles? options: A)1:18. B)1:20. C)1:4. D)1:36. E)1:16. SOLUTION:Given : The radius of A is thrice as large as the diameter of B. => R(a) = 3*D(b) = 3*2*R(b) = 6R(b). The radius are in ratio of 1:6 thus the area will be in the ratio of square of radius. 1:36. Hence D. #### D QUESTION:A train 280 m long, running with a speed of 63 km/hr will pass a tree in? options: A)18 sec B)16 sec C)19 sec D)11 sec E)12 sec SOLUTION:: Speed = 63 * 5/18 = 35/2 m/sec Time taken = 280 * 2/35 = 16 sec Answer: B #### B QUESTION:A bus covered a distance of 250 km, partly at an average speed of 40 kmph and partly at 60 kmph. If the total time taken is 5 hours, then the distance covered at 40 kmph is options: A)130 km B)120km C)100km D)140km E)none of these SOLUTION:Let the partial distance covered at 40 kmph be X Let the another partial distance covered at 60 kmph be (250 - x) Thus, x/40 - (250 - x)/60 = 5 or, x/40 + (250 - x)/60 = 5 or, (3x + 500 - 2x)//120 = 5 or 500 + x = 600 x=100 ANSWER:C #### C QUESTION:Three pipes, A, B, & C are attached to a tank. A & B can fill it in 20 & 30 minutes respectively while C can empty it in 20 minutes. If A, B & C are kept open successively for 1 minute each, how soon will the tank be filled? options: A)2 hours B)4 hours C)1 hour 30 min D)5 hours E)6 hours SOLUTION:in three minute 1/20+1/30-1/20=2/60 = 1/30 part is filled 3 min--------1/30 parts x min--------- 1 part(full) x=90 min =1 hour 30 min ANSWER:C #### C QUESTION:Population of a city in 20004 was 1000000. If in 2005 there isan increment of 15% , in 2006 there is a decrements of 35 % and in 2007 there is an increment of 45%, then find the population of city atthe end of the year 2007 options: A)1056787 B)1076658 C)1079767 D)1079977 E)1083875 SOLUTION:Required population = P (1 + R1/100)(1 - R2/100)(1 + R3/100) = P (1 + 15/100)(1 - 35/100)(1 + 45/100) = 1083875 E #### E QUESTION:If six persons sit in a row, then the probability that three particular persons are always together is ? options: A)1/3 B)1/9 C)1/5 D)1/7 E)1/1 SOLUTION:Six 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 #### C QUESTION:A train after traveling for 50km meets with an accident and then proceeds at 3/4 of its former speed and arrives at its destination 35 minutes late . Had the accident occurred 24 km farther, it would have reached the destination only 25 minutes late. What is the speed T of the train. options: A)a) 45 B)b) 33 C)c) 48 D)d) 55 E)e) 61 SOLUTION:Let y be the balance distance to be covered and x be the former speed. A train after traveling for 50km meets with an accident and then proceeds at 3/4 of its former speed and arrives at its destination 35 minutes late so, y/(3x/4) - y/x = 35/60 4y/3x - y/x = 7/12 y/x(4/3-1)=7/12 y/x*1/3=7/12 y/x=7/4 4y-7x=0 ........ 1 Had the accident occurred 24 km farther, it would have reached the destination only 25 minutes late so, (y-24)/(3x/4) - (y-24)/x = 25/60 4(y-24)/3x - (y-24)/x = 5/12 (y-24)/x (4/3-1) = 5/12 (y-24)/x *1/3 = 5/12 (y-24)*12 = 3x*5 (y-24)*4 = 5x 4y-5x = 96 ....... 2 eq2 - eq1 2x=96 x=48=T Ans = C #### C QUESTION:The average weight of a class of 20 boys was calculated to be 58.4 kgs and it was later found that one weight was misread as 56 kg instead of 66 kg. What is the correct weight? options: A)58kgs B)58.85kgs C)58.9kgs D)59kgs E)59.85kgs SOLUTION:Actual total weight is (20X 58.4 - 56 + 66) = 1178 Kgs Actual average weight is 1178/20 = 58.9kgs C #### C QUESTION:How many words with or without meaning, can be formed by using all the letters of the word, ‘POWER’, using each letter exactly once? options: A)700 B)720 C)750 D)800 E)120 SOLUTION:The word ‘POWER’ contains 5 different letters. Therefore, Required number of words= Number of arrangement of 5 letters, taken all at a time =5P5 = 5! = 5*4*3*2*1 = 120 ANSWER:E #### E QUESTION:a, b, c and d are four consecutive numbers. If the sum of a and dis 111, what is the product of b and c? options: A)2652 B)2578 C)2534 D)3080 E)4234 SOLUTION:Here d = a + 3 a + a + 3 = 111 2a = 108 a = 54 So, numbers are 54, 55, 56 and 57 ∴ b × c= 55 × 56 = 3080 D #### D QUESTION:in how many possible ways you can write 3240 as product of 3 positive integers a, b, c . options: A)450 B)420 C)350 D)320 E)300 SOLUTION:3240 => 2^3 * 3^4 * 5^1 a => 2^x1 * 3^y1 * 5^z1 b => 2^x2 * 3^y2 * 5^z2 c => 2^x3 * 3^y3 * 5^z3 a * b * c = 3240 x1 + x2 + x3 = 3 => 5C2 y1 + y2 + y3 = 4 => 6C2 z1 + z2 + z3 = 1 => 3C2 5C2 * 6C2 * 3C2 = 10 * 15 * 3 = 450 ANSWER:A #### A QUESTION:How long does a train 110 m long running at the speed of 72 km/hr takes to cross a bridge 132 m length? options: A)12.6 B)12.0 C)12.1 D)12.3 E)12.2 SOLUTION:Speed = 72 * 5/18 = 20 m/sec Total distance covered = 110 + 132 = 242 m. Required time = 242/20 = 12.1 sec.Answer: B #### B QUESTION:The second of two numbers is two less than three times the first. Find the numbers if there sum is 74. options: A)7-19 B)8-20 C)10-16 D)15-9 E)19-55 SOLUTION:We are looking for two numbers. #1 - x #2 - 3x – 2 The sum is 74. #1 + #2 = 74 Substituting x + 3x – 2 = 74 4x – 2 =74 4x = 76 x = 19 The first number is 19, the second number is two less than three times 19 or 55. correct answer E #### E QUESTION:In 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 20% of the total number of children in the camp. How many more boys must she bring to make that happen? options: A)35. B)45. C)40. D)30. E)25. SOLUTION:Given there are 50 students , 90% of 50 = 45 boys and remaining 5 girls. Now here 90% are Boys and 10% are Girls. Now question is asking about how many boys do we need to add, to make the girls percentage to or 20%.. If we add 35 to existing 45 then the count will be 80 and the girls number will be 20 as it. Now boys are 80% and girls are 20%. ( out of 100 students = 80 boys + 20 girls ). IMO option A is correct. #### A QUESTION:An 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? options: A)18 B)24 C)30 D)45 E)60 SOLUTION:First let's consider the small notebooks. There are 5 ways to choose notebooks of the same color. The number of ways to choose four notebooks with different colors is 5C4=5. There are 10 different packages we can make with the small notebooks. We can use the same process to find 10 different packages with medium and large notebooks. The total number of different packages is 30. The answer is C. #### C QUESTION:A person bought 20 kg of rice at Rs 10.50 per kg and 30 kgs at Rs 12 per kg. He mixed the two and sold the mixture at Rs 11.40 per kg. What was the gain in his deal(in Rs)? options: A)0 B)20 C)75 D)5 E)10 SOLUTION:Explanation : Gain = 50 * 11.40 - (20*10.5 + 30*12) = 0 Answer : A #### A QUESTION:At what rate of annual simple interest,a certain sum will amount to four times in 15 year? options: A)15% B)17.5% C)20% D)25% E)35% SOLUTION:r=? t=15 yrs SI=p*r*t/100 Amount = SI+p = 4p (p*r*15/100)+p = 4p p(15r/100 + 1) = 4p 15r + 100 = 400 15r = 300 r = 20% ANSWER:C #### C QUESTION:Yesterday's closing prices of 2,640 different stocks listed on a certain stock exchange were all different from today's closing prices. The number of stocks that closed at a higher price today than yesterday was 20 percent greater than the number that closed at a lower price. How many of the stocks closed at a higher price today than yesterday? options: A) 484 B) 726 C) 1,100 D) 1,320 E) 1,440 SOLUTION:Lets consider the below - The number of stocks that closed at a higher price = H The number of stocks that closed at a lower price = L We understand from first statement -> H+L = 2640 ----(1) We understand from second statement -> H = (120/100)L => H = 1.2L ----(2) Solve eq (1)(2) to get H = 1440. E is my answer. #### E QUESTION:Two sides of a triangle have lengths x and t and meet at a right angle. If the perimeter of the triangle is 4x, what is the ratio of x to t ? options: A)a) 2 : 3 B)b) 3 : 4 C)c) 4 : 3 D)d) 3 : 2 E)e) 2 : 1 SOLUTION:Ahhhh....my bad. Thank you, you're correct. 8x = 6t --> x/t = 3/4. Actually B is the right answer. #### B QUESTION:Can you deduce the pattern and find the next number in the series? 3, 24,81, 192, __? options: A)276 B)277 C)278 D)279 E)375 SOLUTION:Solution: 375 Explanation: 3 = 1^1^1 + 1^1^1 + 1^1^1 24 = 2^2^2 + 2^2^2 + 2^2^2 81 = 3^3^3 + 3^3^3 + 3^3^3 192 = 4^4^4 + 4^4^4 + 4^4^4 Thus the next number will be 375 =5^5^5 + 5^5^5 + 5^5^5 Answer E #### E QUESTION:Several people are sitting around a round table playing a card game with a deck of 67 cards. Each person is dealt one card per deal, and the cards are dealt in a clockwise fashion. If Martin is dealt both the first card of the deck and the last card of the deck, which of the following could be the total number of people sitting at the table? options: A)4 B)5 C)7 D)11 E)13 SOLUTION:Let n be the number of people at the table. If Martin gets the first and the last card, it means Martin got one more card than the others. Thus 67/n has a remainder of 1 and so 67-1 = 66 is a multiple of n. The answer is D. #### D QUESTION:How many positive integers less than 100 have a remainder of 3 when divided by 13? options: A)6 B)7 C)8 D)9 E)3 SOLUTION:We have to include 3 also.As 13*0 + 3 =3 If somebody says to divide 3 by 13 ,we will be telling we have 0 quotient and remainder as 3. Answer is E #### E QUESTION:In how many different ways can the letters of the word ‘INDIGO’ be arranged ? options: A)420 B)520 C)620 D)720 E)820 SOLUTION:D 720 Required number of arrangements = 6! = 720 #### D QUESTION:A four digit number divisible by 7 becomes divisible by 3 when 19 is added to it. The largest such number is : options: A)4461 B)4473 C)4479 D)4487 E)4491 SOLUTION:Out of all the 5 options, only 4487 is NOT divisible by 3. All others are divisible So Answer = D (No further calculation required) Addition of any two non-divisible numbers by 3 gives the resultant divisible by 3 19 is non-divisible by 3; we are adding a number to that so that the resultant becomes divisible by 3 Applying the above rule,It means that the number which we are going to add should be non-divisible by 3 So comes the answer = 4487 Answer : D #### D QUESTION:Which number should replace both the asterisks in (* /18) x (*/162) = 1 ? options: A)27 B)36 C)54 D)72 E)90 SOLUTION:Let (y/18) x (y/162) = 1 y^2 = 18 x 162 = 18 x 18 x 9 y = (18 x 3) = 54 The answer is C. #### C QUESTION:Which one of the following numbers is exactly divisible by 12? options: A)A)12 B)B)13 C)C)14 D)D)15 E)E)16 SOLUTION:12/12=1 answer is A #### A QUESTION:The average weight of 4 students decreases by 8 kg when one of them weighing 96 kg is replaced by a new student. The weight of the student is options: A)62 kg B)60 kg C)64 kg D)72 kg E)None of these SOLUTION:Explanation : Let the weight of student be x kg. Given, Difference in average weight = 8 kg => (96-x)/4 = 8 => x = 64 Answer : C #### C QUESTION:In September, John sold 2323 more soap than in February. In November, he sold 5 percent more than in September. John's November sales were what percent greater than his February sales? options: A)10/3% B)65% C)214/3 % D)75% E)514/3% SOLUTION:Let february sale= x september sale= x+2/3x= 5x/3 November sale= 5x+3 + 5*5/100*3x 21/12x= 1.75 x Hence November sale is 75% > February sale D is the answer #### D QUESTION:A rectangular with dimensions 25 inches by 35 inches is to be divided into squares of equal size. Which of the following could be a length of a side of the squares? options: A)a) 5 inches B)b) 6 inches C)c) 7 inches D)d) 8 inches E)e) 10 inches SOLUTION:you need to divide the width and length of the rectangular to equal pieces where L = W you can solve this using GCF 25=5*5 35=5*7 GCF = 5 P.S you can make squares with side of 5 Answer : A #### A QUESTION:The average age of a family of 5 members is 20 years. If the age of the youngest member be 10 years then what was the average age of the family at the time of the birth of the youngest member? options: A)13.5 B)14 C)15 D)12.5 E)None SOLUTION:Solution: At present the total age of the family = 5*20 =100. The total age of the family at the time of the birth of the youngest member, =[100−10−(10*4)]=50. Therefore, average age of the family at the time of birth of the youngest member, = 50/4 = 12.5. Answer: Option D #### D QUESTION:A train travelling at a speed of 75 mph enters a tunnel 31/2 miles long. The train is 1/4 mile long. How long does it take for the train to pass through the tunnel from the moment the front enters to the moment the rear emerges? options: A)2.5 min B)3 min C)3.2 min D)3.5 min E)4 min SOLUTION:Total distance = (7/2 + 1/4) miles = 15/4 miles time taken = 15/4*75 hrs =1/20 hrs = 3 min ANSWER B #### B QUESTION:To 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. options: A)530 B)675 C)330 D)987 E)854 SOLUTION:Let x e 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: 3⋅25+(x−3)⋅30=75+30(x−3) Therefore: 25x=75+30(x−3)−100 25x=75+30x−90−100 190−75=30x−25 115=5x x=23 So the company worked 23 days and they made 23⋅25+100=675 pieces. #### B QUESTION:TOM traveled the entire 60 miles trip. If he did the first 12 miles of at a constant rate 24 miles per hour and the remaining trip of at a constant rate 48 miles per hour, what is the his average speed, in miles per hour? options: A)20mph B)24mph C)30mph D)40mph E)42mph SOLUTION:avg speed = total distance/ total time = (d1+d2)/(t1+t2) = (12+48) / ((12/24)+(48/48)) = 60*2/3 = 40mph D #### D QUESTION:There are 1000 students in a school and among them 25 % of them attends chess class. 50% of the students who are in the chess class are also enrolled for swimming. No other students are interested in swimming so how many will attend the swimming class if all enrolled attends? options: A)1 B)10 C)125 D)50 E)20 SOLUTION:25% of 1000 gives 250. so 250 attends chess and 50% of 250 gives 125 so 125 enrolled for swimming Answer: C #### C QUESTION:Tickets 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? options: A)1/11 B)2/13 C)3/10 D)4/15 E)5/16 SOLUTION:Here, S = [1, 2, 3, 4, …., 19, 20] Let E = event of getting a multiple of 3 = [3, 6, 9, 12, 15, 18] P (E) = n (E) / n (S) = 6 / 20 = 3/10 C #### C QUESTION:Two 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? options: A)10.6 B)27 C)10.4 D)10.8 E)10.1 SOLUTION:Relative speed = 60 + 40 = 100 km/hr. = 100 * 5/18 = 250/9 m/sec. Distance covered in crossing each other = 300 + 450 = 750 m. Required time = 700 * 9/250 = 27 sec. Answer: B #### B QUESTION:The average runs scored by a batsman in 22 matches is 28. In the next 13 matches the batsman scored an average of 15 runs. Find his average in all the 35 matches? options: A)31.23 B)25.12 C)36.25 D)23.17 E)27.66 SOLUTION:Total score of the batsman in 22 matches = 616. Total score of the batsman in the next 13 matches = 195. Total score of the batsman in the 35 matches = 811. Average score of the batsman = 811/35 = 23.17. Answer: D #### D QUESTION:(3 x 10^2) + (2 x 10) + 4 = options: A)302400 B)32400 C)30240 D)3240 E)324 SOLUTION:When you multiply a number by 10 you just add a zero => 3 x 10^2 => add 2 zeros => 3 x 10^2 = 300 =>2 x 10 = 20 => 4 = 4 =>3 x 10^2 + 2 x 10 + 4 = 300 + 20 + 4 = 324 => answer is E ( 324) #### E QUESTION:Out 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? options: A)17/65 B)17/29 C)17/21 D)P(EᴜP) =17/20 E)17/212 SOLUTION:n(S) = 20 n(Even no) = 10 = n(E) n(Prime no) = 8 = n(P) P(EᴜP) = 10/20 + 8/20 - 1/20 = 17/20.Answer:D #### D QUESTION:Bookman purchased 40 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 300, how many paperback copies were sold? options: A)6 B)4 C)8 D)10 E)12 SOLUTION:The bookman had 10 hardback ad 40-10=30 paperback copies; 14 copies were sold, hence 40-14=26 copies were left. Let # of paperback copies left be p then 10p+20(26-p)=300 --> 10 p=220 --> p=22 # of paperback copies sold is 30-22=8 Answer: C #### C QUESTION:If December 3rd, 1999 is a Friday, what day is January 7th, 2000? options: A)Wednesday B)Thursday C)Friday D)Saturday E)Sunday SOLUTION:There is difference of 35 days from Dec. 3rd 1999 to Jan. 7th 2000. 35/7 has a remainder of 0. Jan. 7th is: Friday + 0 days = Friday The answer is C. #### C QUESTION:X, Y, and Z are consecutive numbers and X > Y > Z. Also, X + 3Y + 3Z = 5Y + 8. What is the value of Z? options: A)2 B)3 C)4 D)5 E)6 SOLUTION:If X, Y, and Z are consecutive numbers and X > Y > Z, then Y = Z+1 and X = Z+2. X + 3Y + 3Z = 5Y + 8 Z+2+3Z+3+3Z = 5Z+5+8 2Z = 8 Z = 4 The answer is C. #### C QUESTION:In measuring the sides of a rectangle, one side is taken 16% in excess and other 5% in deficit. Find the error percentage in the area calculated from these measurements. options: A)3.5% B)2.4% C)10.2% D)5% E)2.6% SOLUTION:Say both sides of the rectangle are equal to 100 (so consider that we have a square). In this case the area is 100*100=10,000. Now, the area obtained with wrong measurements would be 116*95=11,020, which is 10.2% greater than the actual area. Answer: C. #### C QUESTION:A paint store mixes 3/4 pint of red paint and 2/3 pint of white paint to make a new paint color called Perfect Pink. How many pints of red paint would be needed to make 35 pints of Perfect Pink paint? options: A)9 B)16 C)19 D)25 1/3 E)28 1/2 SOLUTION:3/4 pint is required to make 3/4 + 2/3 = 17/12 pint of perfect pink so 17/12 pint requires 3/4 pint of red.. 1 pint will require 3/4 * 12/17=9/17.. 35 pints will require 9/17 * 35= 19 pints.. C #### C QUESTION:Myra drove at an average speed of 30 miles per hour for some time and then at an average speed of 60 miles/hr for the rest of the journey. If she made no stops during the trip and her average speed for the entire journey was 50 miles per hour, for what fraction of the total time did she drive at 30 miles/hour? options: A)The average speed is 1/5 miles per hour. B)The average speed is 1/3 miles per hour. C)The average speed is 2/5 miles per hour. D)The average speed is 2/3 miles per hour. E)The average speed is 3/5 miles per hour. SOLUTION:We know the average speed and must find the fraction of time taken at a particular speed. t1/t2 = (A2 – Aavg)/(Aavg – A1) t1/t2 = (60 – 50)/(50 – 30) = 1/2 So out of a total of 3 parts of the journey time, she drove at 30 mph for 1 part and at 60 mph for 2 parts of the time. Fraction of the total time for which she drove at 30 mph is 1/3. ANSWER (B) #### B QUESTION:If the wheel is 15 cm then the number of revolutions to cover a distance of 1056 cm is? options: A)18 B)11.2 C)14 D)12 E)91 SOLUTION:2 * 22/7 * 15 * x = 1056 => x = 11.2 Answer: B #### B QUESTION:In 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. What is the duration of the flight ? options: A)3 hours B)2.4 hours C)1.4 hours D)1 hour E)None of these SOLUTION:Explanation: Let the duration of the flight be x hours. Then 600x−600x+12=200600x−12002x+1=200x(2x+1)=32x2+x−3=0=>(2x+3)(x−1)=0 Neglecting the negative value for x we get x = 1 Answer: D #### D QUESTION:A 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. What is the total distance traveled by the man? options: A)5.78 B)5.79 C)5.76 D)5.74 E)5.721 SOLUTION:M = 6 S = 1.2 DS = 7.2 US = 4.8 x/7.2 + x/4.8 = 1 x = 2.88 D = 2.88 * 2 = 5.76.Answer: C #### C QUESTION:What percent is 20% of 25%? options: A)20% B)30% C)50% D)60% E)80% SOLUTION:Required percentage = 20%/25% * 100 = 20/25 * 100 = 80% Answer is E #### E QUESTION:The owner of a furniture shop charges his customer 24% more than the cost price. If a customer paid Rs. 8587 for a computer table, then what was the cost price of the computer table? options: A)7297 B)2977 C)2871 D)6925 E)2981 SOLUTION:Explanation: CP = SP * (100/(100 + profit%)) = 8587(100/124) = Rs. 6925. Answer: D #### D QUESTION:The 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? options: A)Rs.4538 B)Rs.4518 C)Rs.4518 D)Rs.4530 E)Rs.4517 SOLUTION:Area of the four walls = 2h(l + b) Since there are doors and windows, area of the walls = 2 * 12 (15 + 25) - (6 * 3) - 3(4 * 3) = 906 sq.ft. Total cost = 906 * 5 = Rs.4530 Answer: D #### D QUESTION:A, B and C invested Rs.6600, Rs.4400 and Rs.11000 respectively, in a partnership business. Find the share of A in profit of Rs.12100 after a year? options: A)Rs.3300 B)Rs.3100 C)Rs.3500 D)Rs.4200 E)Rs.3400 SOLUTION:6600:4400:11000 3:2:5 3/10 * 11000 = Rs.3300 AnswerA #### A <<<Examples ends QUESTION:Three seventh of a number is 12 more than 40% of that number. What will be the 10% of that number? options: A)A)148 B)B)210 C)C)21 D)D)248 E)E)258 SOLUTION:3/7 x – 40/100 x = 12 x = 35 * 12 35 * 12 * 10/100 = 42/2 = 21 ANSWER:C #### C

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:Two trains of length 100 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? options: A)10 sec B)32 sec C)82 sec D)20 sec E)19 sec SOLUTION:Relative speed = (42 + 30) * 5/18 = 4 * 5 = 20 mps. Distance covered in passing each other = 100 + 280 = 380m. The time required = d/s = 380/20 = 19 sec. Answer:E #### E QUESTION:In how many ways 3 boys and 3 girls can be seated in a row so that boys and girls are alternate? options: A)69 B)70 C)71 D)72 E)73 SOLUTION:number of ways = 2*3!*3! = 72 Answer is D #### D QUESTION:The length of a rectangle is increased to 2 times its original size and its width is increased to 3 times its original size. If the area of the new rectangle is equal to 1800 square meters, what is the area of the original rectangle? options: A)300 square meters B)400 square meters C)500 square meters D)600 square meters E)700 square meters SOLUTION:If L and W be the original length and width of the rectangle and its area is given by L ? W After increase the length becomes 2 L and the width becomes 3 W. The area is then given by (2 L) ? (3 W) and is known. Hence (2 L) ? (3 W) = 1800 Solve the above equation to find L ? W 6 L ? W = 1800 L ? W = 1800 / 6 = 300 square meters , area of original rectangle correct answer A #### A QUESTION:If a certain number X is divided by 82, the reminder is 5. what is the reminder when X+13 is divided by 41? options: A)3 B)18 C)6 D)16 E)5 SOLUTION:X can be written as 82K + 5 or X = 5,87,169,etc. X + 13 = 82K + 5+13= 82K +18 or X + 13 = 18,100, 182 etc. When divided by 41, we will get the remainder 18. B #### B QUESTION:A shopkeeper buys two articles for Rs.1000 each and then sells them, making 10% profit on the first article and 10% loss on second article. Find the net profit or loss percent? options: A)200 B)100 C)276 D)280 E)279 SOLUTION:Profit on first article = 10% of 1000 = 100. This is equal to the loss he makes on the second article. That, is he makes neither profit nor loss. Answer: B #### B QUESTION:A merchant who marked his goods up by 50% subsequently offered a discount of 20% on the marked price. What is the percentage profit that the merchant made after offering the discount? options: A)30% B)125% C)25% D)20% E)16.66% SOLUTION:Explanatory Answer The easiest way to solve these kinds of problems is to assume a value for the merchant's cost price. To make calculations easy, it is best to assume the cost price to be $100. The merchant marks his goods up by 50%. Therefore, his marked price (quoted price) = cost price + mark up. Marked price = $100 + 50% of $100 = 100 + 50 = $150. The merchant offers a discount of 20% on his marked price. Discount offered = 20% of 150 = $30. Therefore, he finally sold his goods for $150 - $30 = $ 120. We assumed his cost to be $100 and he sold it finally for $120. Therefore, his profit = $20 on his cost of $ 100. Hence, his % profit = profit/cost price * 100 = 20/100 * 100 = 20%. Choice D #### D QUESTION:The lunch menu at a certain restaurant contains 4 different entrees and 5 different side dishes. If a meal consists of 1 entree and 2 different side dishes, how many different meal combinations Q could be chosen from this menu? options: A)10 B)20 C)40 D)80 E)100 SOLUTION:Q=4C1 * 5C2 = 4 * (5*4*3!)/(3!2!) = 4 * 10 = 40 Answer - C #### C QUESTION:The cross-section of a cannel is a trapezium in shape. If the cannel is 10 m wide at the top and 6 m wide at the bottom and the area of cross-section is 640 sq m, the depth of cannel is? options: A)34 B)97 C)37 D)80 E)22 SOLUTION:1/2 * d (10 + 6) = 640 d = 80 Answer: D #### D QUESTION:$500 will become $1000 in 6 years find the rate of interest? options: A)A)16.67% B)B)20% C)C)25% D)D)30% E)E)50% SOLUTION:SI = simple interest = A-P = 1000-500 = $500 R = 100SI/PT = 100*500/500*6 =16.67% Answer is A #### A QUESTION:Find the distance covered by a man walking for 42 min at a speed of 10km/hr? options: A)7km B)3km C)4km D)5km E)6km SOLUTION:Distance = 10*42/60 = 7 km Answer is A #### A QUESTION:log(a(a(a)^1/4)^1/4)^1/4 here base is a. options: A)0 B)21/64 C)1 D)22/63 E)23/65 SOLUTION:log(a(a(a^1/4)^1/4)^1/4 => log(a(a^1+1/4)^1/4)^1/4 => log(a(a^5/4)^1/4)^1/4 =>log(a(a^5/16)^1/4 =>log(a^1+5/16)^1/4 =>log(a^21/16)^1/4 =>log(a^21/64) =>21/64 log(a) =>21/64 ANSWER:B #### B QUESTION:The compound ratio of 5:1, 3:1 and 2:5? options: A)6:1 B)1:3 C)1:5 D)1:1 E)1:6 SOLUTION:5/1 * 3/1 * 2/5 = 30/5 6:1 Answer: A #### A QUESTION:A marketing survey of Anytown found that the ratio of trucks to sedans to motorcycles was 3:7:2, respectively. Given that there are 11,200 sedans in Anytown, how many motorcycles are there? options: A)1260 B)2100 C)3600 D)3200 E)5200 SOLUTION:Let the total number of trucks = 3x total number of sedans = 7x total number of motorcycles = 2x total number of sedans = 11200 => 7x = 11200 => x = 1600 total number of motorcycles =2x = 2*1600 =3200 Answer D #### D QUESTION:In how many ways a committee of 10 men and 8 women can be made out of total of 15 men and 12 women? options: A)336/987 B)1001/165 C)1245/789 D)3256/789 E)256/85 SOLUTION:Required number of ways = 15C10 * 12C8 = 15C5 * 12C4 = 3003/495 = 1001/165 Answer is B #### B QUESTION:20 people are there, they are shaking hands together, how many hand shakes possible,if they are in pair of cyclic sequence. options: A)19 B)20 C)21 D)22 E)23 SOLUTION:in case of cycle no of handshakes = no of persons hence ans = 20 ANSWER:B #### B QUESTION:Set A contains three different positive odd integers and three different positive even integers. Set B contains two different positive odd integers and three different positive even integers. If one integer from set A and one integer from set B are chosen at random, what is the probability that the product of the chosen integers is even? options: A)3/5 B)2/5 C)1/2 D)4/5 E)19/25 SOLUTION:There can be an odd product only if both integers are odd. P(odd product) = 1/2*2/5 = 1/5 P(even product) = 1 - 1/5 = 4/5 The answer is D. #### D QUESTION:Positive integer y is 50 percent of 50 percent of positive integer x, and y percent of x equals 9. What is the value of x? options: A)20 B)60 C)100 D)120 E)150 SOLUTION:y = 0.5*0.5*x = x/4 y%*x = 9 (y/100)*x = 9 (x/400)*x = 9 x^2 = 9*400 x = 60 The answer is B. #### B QUESTION:A 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: options: A)5% B)8% C)10% D)12% E)6% SOLUTION:C.P. of 56 kg rice = Rs. (26 x 20 + 30 x 36) = Rs. (520 + 1080) = Rs. 1600. S.P. of 56 kg rice = Rs. (56 x 30) = Rs. 1680. Gain =(80/1600x 100)% = 5%. Answer is A. #### A QUESTION:Dacid obtained 45, 35, 52, 47 and 55 marks (out of 100) in English, Mathematics, Physics, Chemistry and Biology. What are his average marks? options: A)79 B)99 C)47 D)89 E)45 SOLUTION:Average = (45+35+ 52+ 47+55)/5 = 234/5 = 47. Answer:C #### C QUESTION:A goods train runs at the speed of 72 km/hr and crosses a 300 m long platform in 26 sec. What is the length of the goods train? options: A)382 B)782 C)278 D)270 E)220 SOLUTION:Speed = 72 * 5/18 = 20 m/sec. Time = 26 sec. Let the length of the train be x meters. Then, (x + 300)/26 = 20 x = 220 m. Answer: E #### E QUESTION:A 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? options: A)19 cm2 B)30 cm2 C)17 cm2 D)18 cm2 E)12 cm2 SOLUTION:The circumference of the circle is equal to the permeter of the rectangle. Let l = 6x and b = 5x 2(6x + 5x) = 2 * 22/7 * 3.5 => x = 1 Therefore l = 6 cm and b = 5 cm Area of the rectangle = 6 * 5 = 30 cm2 Answer:B #### B QUESTION:10 men can prepare 20 toys in 12 days working 15 hours a day. Then in how many days can 24 men prepare 32 toys working 20 hrs a day? options: A)4 days B)10 days C)20 days D)25 days E)26 days SOLUTION:Explanation: 10*12*15/20 = 24*20*x/32 X=4 Answer: Option A #### A QUESTION:A company wants to spend equal amounts of money for the purchase of two types of computer printers costing $350 and $200 per unit, respectively. What is the fewest number of computer printers that the company can purchase? options: A)9 B)10 C)11 D)12 E)13 SOLUTION:The smallest amount that the company can spend is the LCM of 350 and 200, which is 1400 for each, which is total 2800. The number of 1st type of computers which costing $350 = 1400/350 = 4. The number of 2nd type of computers which costing $200 = 1400/200 = 7. Total = 4+7 = 11 Answer is C. #### C QUESTION:A person walking at 4 Kmph reaches his office 8 minutes late. If he walks at 6 Kmph, he reaches there 8 minutes earlier. How far is the office from his house? options: A)3 1/5 Km B)2 1/5 Km C)4 Km D)4 1/5 Km E)3 3/5 Km SOLUTION:Formula = S1*S2/S2-S1 * T1+T2/60 = 4*6/2 * 16/6 = 24/2 * 16/60 = 8 * 2/5 = 16/5 = 3 1/5 Km A #### A QUESTION:In how many ways can a cricket eleven be chosen out of a batch of 15 players ? options: A)1365 B)5263 C)4512 D)7845 E)1549 SOLUTION:Required number of ways = 15c11 = 15c(15-11) = 11c4 = 15x14x13x12/4x3x2x1 = 1365. Ans: A #### A QUESTION:If the set S is composed of the following numbers {99, 100, 100, 105, 106, 115, 124}, which of the following is largest? options: A)The average (arithmetic mean) of set S B)The median of set S C)The mode of set S D)The range of set S E)The standard deviation of set S SOLUTION:A) 99, 100, 100, 105, 106, 115, 124 = 749 and its mean is 749/7 = 107. B) The list is of 7 numbers and median is 105. C) Mode is number of repetition of a number in the list , here it is 100. D) Range = Max value - min value = 124 -99 = 25. E) SD = square root of (sum of ( mean of series - number)^2 ) / n => < 100 IMO option A is correct answer.. #### A QUESTION:A company has 2 directors and 5 managers. How many different committees with 5 people can be chosen having at least 1 director? options: A)500 B)720 C)4500 D)20 E)55 SOLUTION:atleast one means exactly one and more than one. different committees with 5 people can be chosen having at least 1 director is (2c1*5c4) + (2c2*5c3) = 20; Hence D. #### D QUESTION:A table is bought for Rs.1020/- and sold at Rs.750/- find the loss percentage options: A)26% Loss B)10% Gain C)20% Loss D)20% Gain E)30% Gain SOLUTION:Formula = (Selling price ~ Cost price)/Cost price * 100 = (750 ~ 1020)/1020 = 26% Loss A #### A QUESTION:A 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? options: A)5 hr 30 mins B)7 hr 30 mins C)4hr 30 mins D)2 hr 30 mins E)3 hr 30 mins SOLUTION:Explanation: A tap can fill a tank in 12 hours. Therefore the tap can fill half the tank in 6 hours. One tap take time to fill half of the tank = 6 hrs 4 taps take time to fill half of the tank = 6/4 hrs = 1 hr 30 mins Total time taken to fill the tank = 6 hr+1 hr 30 min = 7 hr 30 mins Answer : B #### B QUESTION:A 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? options: A)276 Marks B)200 Marks C)186 Marks D)187 Marks E)167 Marks SOLUTION:30% ------------ 50 45% ------------ 25 ---------------------- 15% ------------- 75 30% -------------- ? 150 + 50 = 200 Marks Answer: B #### B QUESTION:What number should replace the question mark? 16, 23, 19, 19, 22, 15, 25, ? options: A)11 B)12 C)13 D)14 E)15 SOLUTION:A 11 There are two alternate sequences + 3 and - 4 #### A QUESTION:Which of the following cannot be the range of a set consisting of 5 odd multiples of 7? options: A)56 B)112 C)224 D)448 E)425 SOLUTION:Solution: sequence of 7 lets say sequence is 7n, 7(n+1), 7(n+2), 7(n+3), 7(n+4) so range is 7n+28-7n = 28 if we put the different values of n we will get different but the range will be multiple of 28 and only 425 is not multiple of 28 Answer : E #### E QUESTION:Find the average of all prime numbers between 10 and 30. options: A)30 B)33.6 C)39.8 D)18.6 E)None SOLUTION:Sol. There are six prime numbers between 10 and 30. They are 11, 13, 17, 19, 23, 29 ∴ Required average = [11+ 13+ 17+19+ 23+ 29 / 6] = 112/ 6 = 18.6 Answer D #### D QUESTION:In 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? options: A)80% B)105% C)120% D)112% E)138% SOLUTION:0,112R = x/100*0.1R Answer D #### D QUESTION:Mr. Ram is on tour and he has Rs 360 for his expenses. If he exceeds his tour by 4 days he must cut down daily expenses by Rs 3. The number of days of Mr. Ram's tour programme is options: A)28 Days B)24 Days C)22 Days D)20 Days E)None of these SOLUTION:Solution: Let Ram under takes a tour of x days. Then, expenses for each day = 360/x 360/x+4=360/x−3 x=20x=20 and −24−24 Hence, x= 20 days. Option(D) #### D QUESTION:If the perimeter of a rectangular garden is 600 m, its length when its breadth is 150 m is? options: A)150 m B)778 m C)200 m D)276 m E)971 m SOLUTION:2(l + 150) = 600 => l = 150 m Answer:A #### A QUESTION:A retailer sold an appliance for $100. If the retailer's gross profit on the appliance was 25 percent of the retailer's cost for the appliance, how many dollars was the retailer's gross profit? options: A)$10 B)$16 C)$20 D)$24 E)$25 SOLUTION:Let P be the original price paid by the retailer. 1.25*P = 100 P = 80 The profit is $20. The answer is C. #### C QUESTION:An investment compounds annually at an interest rate of 33.34% What is the smallest investment period by which time the investment will more than triple in value? options: A)1 B)2 C)3 D)5 E)4 SOLUTION:Assume initial amount is x Annual Interest is 34.1% so after 1 year the amount will become x * (100+33.34)/100 => x*4/3 now we need to find n for x * (4/3)^n = 3x or in other words n = 4 E #### E QUESTION:A train running at a speed of 36 kmph crosses an electric pole in 12 seconds. In how much time will it cross a 350 m long platform? options: A)44 sec B)49 sec C)42 sec D)47 sec E)None of these SOLUTION:Let the length of the train be x m. When a train crosses an electric pole, the distance covered is its own length. So, x = 12 * 36 * 5 /18 m = 120 m. Time taken to cross the platform = (120 +350)/ 36 * 5/18 = 47 min. ANSWER:D #### D QUESTION:Michele invests 500 of her money in a mutual fund that quickly goes sour, losing 25% of its value each day for a week. Which of the following COULD be the value of Michele’s investment at the close-of-business any day that week? options: A)$0.00 B)$133.00 C)$250.05 D)$66.74 E)$10000.00 SOLUTION:Suppose she invests n$ in the starting then in the subesequent days the money left after the day will be n/4, n/8, n/16, n/32 So, answer will be D #### D QUESTION:How long will it take for a sum of money to grow from Rs.1000 to Rs.5,000, if it is invested at 20% p.a simple interest? options: A)8 years B)20 years C)72 years D)56 years E)None SOLUTION:In this case, Rs. 1000 has become Rs.5000. Therefore, the interest earned = 5000 – 1000 =4000 Interest for Rs 1000 @ 20% for 1 year = 200 200 - 1 4000 - ? => 20 years Answer : B #### B QUESTION:The largest natural number by which the product of three consecutive even natural numbers is always divisible, is options: A)16 B)24 C)48 D)96 E)78 SOLUTION:Solution Required number = (2×4×6) = 48. Answer C #### C QUESTION:If x^2 + y^2 = 13 and xy = 3, then (x − y)^2 = options: A)7 B)11 C)14 D)17 E)20 SOLUTION:but you cannot take xy+ 3 to mean xy=-3.. only if xy+3=0, it will mean xy=-3.. rest your solution is perfect and you will get your correct answer as 13-2*3=7.. Answer A #### A QUESTION:A 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 27 times, A has killed: options: A)60 birds B)72 birds C)30 birds D)80 birds E)20 birds SOLUTION:Let the total number of shots be x. Then, Shots fired by A =(5/8)x Shots fired by B =(3/8)x Killing shots by A =(1/3)of (5/8)x=(5/24)x Shots missed by B =(1/2) of (3/8)x =(3/16)x 3x/16= 27 or x =(27 x 16)/3= 144. Birds killed by A =(5x/24) =(5/24*144)= 30. Answer is C. #### C QUESTION:How many two digit numbers of distinct digits can be formed by using digits 1, 2, 3, 4, 5 and 6 such that the numbers are divisible by 9? options: A)1 B)2 C)4 D)6 E)8 SOLUTION:CONCEPT: A number will be divisible by 9 if sum of all the digits of the number is divisible by 9 Here the Possible sum of the two distinct digits can be 9 only in order to satisfy the given condition If sum of Digits = 9, No. =36, 45, 54, 63 --- 4 Cases Answer: option C #### C QUESTION:Line R has the equation 3x + y = 7. Which of the following lines is perpendicular to Line R? options: A) y = 3x + 4 B) y = –3x – 6 C) y = (1/3)x – 1 D) y = (–1/3)x + 2 E) y = (–7/3)x – 5 SOLUTION:I first rewrote the equation in the standard y=mx+b form. Therefore, Line R as presented, 3x + y = 7, can be rewritten as follows: y=-3x+7. Thought process next is what line would be perpendicular to Line R? Any line with a reciprocal of the slope but in the opposite direction. The reciprocal of any fraction/integer is 1 over that number/integer. Therefore the reciprocal of -3 is -1/3 - need to drop the negative sign because the line would kinda run parallel and we want perpendicular. Scan the answers choices and notice C as the only one. #### C QUESTION:A 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? options: A)246 m B)240 m C)257 m D)577 m E)567 m SOLUTION:Speed = (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 #### B QUESTION:A bike covers a certain distance at the speed of 67km/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? options: A)89.33 km/h B)85.34 km/h C)87.67 km/h D)90.25 km/h E)90.64 km/h SOLUTION:Ans.(A) Sol. Total distance = 67 × 8 = 536 km Now speed = 536/6 = 89.33 km/h #### A QUESTION:In a room there are 11 people. Each person shook hands with every other person. How many hand shakes were there? options: A)52 B)53 C)54 D)55 E)56 SOLUTION:11C2 = 55 The answer is D. #### D QUESTION:The area of a square is 4489 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. options: A)5:28 B)5:19 C)5:12 D)5:13 E)43:134 SOLUTION:Let the length and the breadth of the rectangle be l cm and b cm respectively. Let the side of the square be a cm. a2 = 4489 a = 67 L = 2a and b = a - 24 b : l = a - 24 : 2a = 43 : 134 Answer:E #### E QUESTION:In an election between 2 candidates, 50% of the voters cast their votes, out of which 10% of the votes were declared invalid. A candidate got 5000 votes which were 50% of the total valid votes. Find the total number of votes enrolled in that election? options: A)16200 B)18000 C)17500 D)15823 E)15000 SOLUTION:Let the total number of votes enrolled be x. Then, number of votes cast = 50% of x. Valid votes = 90% of (50% of x) 50% of (90% of (50% of x)) = 4050 (50/100)*(90/100)*(50/100)x = 4050 x = 18000 Answer is B #### B QUESTION:Sam is training for the marathon. He drove 12 miles from his home to the Grey Hills Park and then ran 6 miles to Red Rock, retraced his path back for 2 miles, and then ran 5 miles to Rock Creek. If he is then n miles from home, what is the range of possible values for n? options: A)1 ≤ n ≤23 B)3 ≤ n ≤21 C)5 ≤ n ≤19 D)6 ≤ n ≤18 E)9 ≤ n ≤15 SOLUTION:ANSWER: 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+6-2+5=21 for the maximum, and 12-6+2-5=3 for the minimum, so B is the answer #### B QUESTION:If a tire rotates at 400 revolutions per minute when the car is traveling 120km/h, what is the circumference of the tire? options: A)2 meters B)6 meters C)5 meters D)3 meters E)7 meters SOLUTION:400 rev / minute = 400 * 60 rev / 60 minutes = 24,000 rev / hour 24,000 * C = 120,000 m : C is the circumference C = 5 meters correct answer C #### C QUESTION:A train running at 1/3 of its own speed reached a place in 9 hours. How much time could be saved if the train would have run at its own speed? options: A)8hrs B)10hrs C)12hrs D)15hrs E)6hrs SOLUTION:time taken if run its own speed = 1/3*9 =3 hrs Time saved = 9 - 3 = 6 hrs Answer : E #### E QUESTION:The 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? options: A)1: 96 B)1: 98 C)1: 97 D)1: 95 E)1: 91 SOLUTION:Let the length and the breadth of the rectangle be 4x cm and 3x respectively. (4x)(3x) = 6912 12x2 = 6912 x2 = 576 = 4 * 144 = 22 * 122 (x > 0) => x = 2 * 12 = 24 Ratio of the breadth and the areas = 3x : 12x2 = 1 : 4x = 1: 96. Answer:A #### A QUESTION:By selling an article for 96, double profit is obtained than the profit that would have been obtained by selling it for 84. What is the cost price of the article? options: A)72.0 B)75.0 C)70.00 D)68.00 E)None of these SOLUTION:Let the cost price of the article be x. Then,2(84 –x) = 96 – x l68 – 2x= 96 – x \ x = 72 Answer A #### A QUESTION:Find the L.C.M of 2^2 * 3^3 * 5 *7^2*11, 2^3 * 3^2* 5^2* 7^4*11, 2 * 3* 5^3* 7^4*11 options: A)2^3 * 3^3 * 5^3 * 7^4 * 11 B)2^2*3^3*5^3 * 7^4 * 11 C)2^2*3^3*5^2 * 7^4 * 11 D)2^3*3^3*5^2* 7^4 * 11 E)2^3*3^3*5^2* 7^3 * 11 SOLUTION:L.C.M= product of the highest powers of 2,3,5,7 and 11=2^3 * 3^3 * 5^3 * 7^4 * 11 Answer (A) #### A QUESTION:A coin is weighted so that the probability of heads on any flip is 0.1, while the probability of tails is 0.9. If the coin is flipped 5 times independently, which of the following represents the probability that tails will appear no more than twice? options: A)(0.1)^5 + 5(0.1)^4(0.9) + 10(0.1)^3(0.9)^2 B)(0.1)^5 + 4(0.1)^4(0.9) + 6(0.1)^3(0.9)^2 C)(0.6)^5 + 3(0.6)^4(0.4) + 2(0.6)^3(0.4)^2 D)(0.6)^5 + 2(0.6)^4(0.4) + (0.6)^3(0.4)^2 E)(0.6)^5 + (0.6)^4(0.4) + (0.6)^3(0.4)^2 SOLUTION:Probability of Head, P(H) = 0.1 Probability of Tail, P(T) = 0.9 Tail will appear NO more than twice i.e. favourable cases 2 Tails and 3 Heads, Probability = 5C2*(0.1)^3*(0.9)^2 1 Tail and 4 Heads, Probability = 5C1*(0.1)^4*(0.9)^2 0 Tail and 5 Heads, Probability = (0.1)^5 Required Probability = Sum of all Favourable cases = (0.1)^5 + 5(0.1)^4(0.9) + 10(0.1)^3(0.9)^2 Answer: option A #### A QUESTION:What is the sum of the first 22 natural numbers (starting from 1)? options: A)223 B)233 C)243 D)253 E)263 SOLUTION:The sum of n natural numbers = n*(n+1) / 2 = 22*23/2 = 253 The answer is D. #### D QUESTION:a, b, c and d are four consecutive numbers. If the sum of a and dis 111, what is the product of b and c? options: A)2652 B)2578 C)2534 D)3080 E)4234 SOLUTION:Here d = a + 3 a + a + 3 = 111 2a = 108 a = 54 So, numbers are 54, 55, 56 and 57 ∴ b × c= 55 × 56 = 3080 D #### D QUESTION:Equal weights of two alloys containing tin, copper and lead in the ratio 6:8:7 and 1:2:4 are melted and mixed together. What is the ratio of tin, copper and lead in the resultant alloy? options: A)11:8:3 B)3:1:8 C)17:28:27 D)9:4: 11 E)9:14: 11 SOLUTION:Let the weight of the two alloys be w each Required ratio = (6w/21+1w/7): (8w/21+2w/7 ): (7w/21+4w/7) = 9w/21 : 14w/21 : 11w/21 = 9:14: 11 ANSWER:E #### E QUESTION:Jemma takes 2 hours to swim the 4 miles from buoy A to buoy B. Tired from her swim, she then continues to buoy C at half her previous speed. If buoy C is 6 miles away from buoy B, how many more hours will pass before Jemma reaches Buoy C? options: A)4 B)5 C)6 D)7 E)8 SOLUTION:Time taken for Jemma to reach buoy B is 2 hours. The distance between the buoys is 4 miles. Distance travelled/time taken = Average speed Hence the average speed to travel the distance is 2m/hr Now, she would have to travel 6 miles . However as she is tired the speed is half or 1m/hr Hence, it will take her 6 hours (Option C) #### C QUESTION:In a exam there are 26 number of question. For one write question add 8 marks and for one wrong 5 marks subtract. One candidate answered all questions. His marks is 0. How many answers was correct? options: A)9 B)10 C)11 D)12 E)13 SOLUTION:let no. of right ques be x, then no. of wrong ques will be= 26 - x now, according to ques 8x - (26-x)5 = 0, hence x=10...no. of right ques is 10 ANSWER:B #### B QUESTION:44×98×101=? options: A)435512 B)434431 C)548654 D)543286 E)546543 SOLUTION:44×(100-2)×(100+1) (4400-88)×(100+1) 4312×(100+1) 431200+4312=435512 answer A #### A <<<Examples ends QUESTION:If n = 9^11 – 9, what is the units digit of n? options: A)0 B)1 C)4 D)6 E)8 SOLUTION:Always 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 #### A

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:A train 240 m long passed a pole in 24 sec. How long will it take to pass a platform 500 m long? options: A)65sec B)70sec C)74sec D)80sec E)85sec SOLUTION:Speed = 240/24 = 10 m/sec. Required time = (240 + 500)/10 = 74 sec. Answer:C #### C QUESTION:Pipe A that can fill a tank in an hour and pipe B that can fill the tank in half an hour are opened simultaneously when the tank is empty. Pipe B is shut 10 minutes before the tank overflows. When will the tank overflow? options: A)37 mins B)35 mins C)40 mins D)32 mins E)36 mins SOLUTION:The last 10 minutes only pipe A was open. Since it needs 1 hour to fill the tank, then in 10 minutes it fills 1/5th of the tank, thus 5/6 of the tank is filled with both pipes open. The combined rate of two pipes is 1 + 2 = 3 tanks/hour, therefore to fill 5/6th of the tank they need (time) = (work)/(rate) = (5/6)/3 = 5/18 hours = 27 minutes. Total time = 10+ 27= 37 minutes. Answer: A. #### A QUESTION:A car crosses a 600 m long bridge in 5 minutes. Whatis the speed of car in km per hour? options: A)7 km/hr B)7.2 km/hr C)7.4 km/hr D)7.8 km/hr E)8.9 km/hr SOLUTION:Speed = 600 m/sec. 5 x 60 = 2 m/sec. Converting m/sec to km/hr (see important formulas section) = 2 x 18 km/hr 5 = 7.2 km/hr B #### B QUESTION:What simple interest will produce Rs.84000 as in 4 years at 3 1/2 percent? options: A)11500 B)12660 C)15220 D)11760 E)16520 SOLUTION:(84000*4*7/2)/100 = i i = 11760 Answer: D #### D QUESTION:A question paper consists of two sections A and B having respectively 3 and 4 questions.Four questions are to be solved to qualify in that paper.It is compulsory to solve at least one question from section A and 2 questions from section B .In how many ways can a candidate select the questions to qualify in that paper? options: A)30 B)40 C)42 D)44 E)46 SOLUTION:here two cases are possible. case 1) 1 question from section A and 3 question from section B are solved = 3C1.4C3 case 2) 2 question from section A and 2 question from section B are solved = 3C2.4C2 thus total number of ways = 3C1.4C3 + 3C2.4C2 = 30 ANS:A #### A QUESTION:Benny 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 nine kids? options: A)8 B)9 C)3 D)7 E)10 SOLUTION:cost of each apple = 4 dollars Apples that Benny can buy with the amount she has=360/4 = 90. Apples that each kid gets evenly = 90/9 =10 Apples. So the answer is E=10 #### E QUESTION:A 200 meter long train crosses a platform in 50 seconds while it crosses a signal pole in 42 seconds. What is the length of the platform? options: A)39.9 B)37.88 C)35 D)38.88 E)38.09 SOLUTION:Speed = [200 / 42] m/sec = 100/21 m/sec. Let the length of the platform be x meters. Then, x + 200 / 50 = 100/21 21(x + 200) = 5000 è x = 38.09 m. Answer: E #### E QUESTION:A, 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 C's share. options: A)Rs. 3240 B)Rs. 2520 C)Rs. 2880 D)Rs. 3360 E)None of these SOLUTION:Explanation: Let C's investment = Rs. x B's investment = Rs. (x - 3000) A's investment = Rs. (x - 3000 + 6000) = Rs. (x + 3000) Now, (A + B + C)'s investment = Rs. 72000 => x + (x - 3000) + (x + 3000) = 72000 => 3x = 72000 => x = 24000 Hence, A's investment = Rs. 27000 B's investment = Rs. 21000 C's investment = Rs. 24000 Ratio of the capitals of A, B and C = 27000 : 21000 : 24000 = 9 : 7 : 8 A's share = Rs. [(8/24) × 8640] = Rs. 2880 Answer: Option C #### C QUESTION:Find the compound interest on $30000 in 2years at 4% per annum, the interest being compounded half-yearly? options: A)$645.56 B)$824.32 C)$954.26 D)$2472.96 E)$1020.45 SOLUTION:Principle = $10000 Rate = 2% half yearly = 4 half years Amount = 30000*(1 + 2/100)^4 = 30000 * 51/50 * 51/50 * 51/50 * 51/50 = $32472.96 C.I. = 32472.96-10000 = $2472.96 Answer is D #### D QUESTION:John 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? options: A)54 B)55 C)56 D)57 E)58 SOLUTION:Let there be a pennies , b nickels and c dimes so total amount can be 1+5b+10c cents to 4+5b+10c as 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) So the total can never be divisible by 5 and hence only 55 that is c is the option which is divisible by 5. so answer is B #### B QUESTION:A rocket soars for 12 seconds at 150 meters per second. It then plummets 600 meters in 3 seconds. What is the average speed of the rocket in meters per second? options: A)140 B)150 C)155 D)160 E)175 SOLUTION:When soaring, the rocket travels a total distance of 1800m(150m/s for 12s) While plummeting the rockets travel distance of 600m in 3s The total distance traveled is 2400m(1800 + 600) The time taken to travel this distance is 15s(12 + 3) Average speed = 2400/15 = 160 ANS: (Option D) #### D QUESTION:A division of a company consists of five men and five women. If two of these employees are randomly selected as representatives of the division, what is the probability that both representatives will be female? options: A)2/5 B)2/7 C)2/9 D)2/11 E)2/13 SOLUTION:Total number of ways to select 2 members = 10C2 = 45 Total number of ways to select 2 females = 5C2 = 10 P(two females) = 10/45 = 2/9 The answer is C. #### C QUESTION:A 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 50 years now, the son's age five years back was? options: A)18years B)19years C)20years D)21years E)22years SOLUTION:Let the son's present age be x years. Then, (50 - x) = x 2x = 50. x = 25. Son's age 5 years back (25 - 5) = 20 years. C) #### C QUESTION:The average of twelve numbers is 7. The average of first nine numbers is 6 and the average of last two numbers is 10. What is the middle number? options: A)A)9 B)B)10 C)C)12 D)D)7 E)E)13 SOLUTION:The total of twelve numbers = 12X7 = 84 The total of first 9 and last 2 numbers is = 9 X 6+2 X 10 = 74 So, the middle number is (84 - 74 ) = 10 B #### B QUESTION:what is the smallest integer that is multiple of 7, 12 and 20 options: A)141 B)180 C)130 D)122 E)420 SOLUTION:Correct Answer :E It is the lcm of 7, 12 and 20 which is 420 #### E QUESTION:What will come in place of the x in the following Number series? 1, 2, 12, 7, 23, 12, 34, x options: A)14 B)15 C)16 D)17 E)18 SOLUTION:There are two series here 1, 12, 23, 34, ... (Increase by 11) 2, 7, 12, ... (Increase by 5) Hence, next term is 12 + 5 = 17 Correct Answer Choice is D #### D QUESTION:What is the HCF of 2/3, 5/9 and 6/5 options: A)1/45 B)2/45 C)4/15 D)8/45 E)9/45 SOLUTION:Explanation: HCF of Fractions = HCF of Numerators/LCM of Denominators = (HCF of 2, 5, 6)/(LCM of 3, 9, 5) = 1/45 Answer: Option A #### A QUESTION:If 1 > 1 - ab > 0, which of the following must be true? I. a/b > 0 II. ab < 1 III. a/b < 2 options: A)I only B)II only C)III only D)I and II only E)I and III only SOLUTION:MANHATTAN GMATOFFICIAL SOLUTION: You can manipulate the original compound inequality as follows, making sure to perform each manipulation on every term: 1 > 1 - ab > 0 0 > -a b > -1 Subtract 1 from all three terms. 0 < ab < 1 Multiply all three terms by -1 and flip the inequality signs. Therefore 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. Therefore, the correct answer is (D). #### D QUESTION:The average score of a cricketer for five matches is 45 runs. If the average for first three matches is 30, then average for last two matches is options: A)33.25 B)32.25 C)67.5 D)60.5 E)45.5 SOLUTION:Explanation: =(45×5)−(30×3)/2 =(225 −90)4=67.5 Answer: Option C #### C QUESTION:Calculate the time it will take for a train that is 240 meter long to pass a bridge of 130 meter length, if the speed of the train is 50 km/hour ? options: A)21.64 seconds B)22.64 seconds C)23.64 seconds D)26.64 seconds E)35.64 seconds SOLUTION:Speed = 35 Km/hr = 50*(5/18) m/sec = 13.89 m/sec Total distance = 240+130 = 370 meter Time = Distance/speed = 370 * (1/13.89) = 26.64 seconds Answer: D #### D QUESTION:Milk contains 5% water. What content of pure milk should be added to 10 liters of milk to reduce this to 2%? options: A)10liters B)15liters C)20liters D)18liters E)22liters SOLUTION:Quantity of water in 10 liters = 5% of 10 liters = 0.5 liters Let x liters of pure milk be added. Then, 0.5/(10+x) = 2/100 2x = 30 x=15 liters Answer is B #### B QUESTION:what is the integer among the following that represents a sum of 3 consecutive even integers? options: A)200 B)303 C)400 D)554 E)588 SOLUTION:Sum of three consecutive Even Integers must be a multiple of 2 as well as a multiple of 3 because such a sum is always 3 times the middle number (applicable to all equally spaced numbers) Divisibility of 3: Sum of the digits of the number must be divisible by 3 Divisibility of 2: Unit digit of the number must be divisible by 2 A. 200NOT A MULTIPLE OF 3 SO RULED OUT B. 303NOT A MULTIPLE OF 2 SO RULED OUT C. 400NOT A MULTIPLE OF 3 SO RULED OUT D. 554NOT A MULTIPLE OF 3 SO RULED OUT E. 588A MULTIPLE OF BOTH 2 AND 3 SO THE CORRECT ANSWER!!! #### E QUESTION:In how many ways can the letters of the CHEATER be arranged options: A)20160 B)2520 C)360 D)80 E)None of these SOLUTION:Explanation: As we can see the letter "E" is twice in given word, so Required Number =7!/2!=7∗6∗5∗4∗3∗2!/2!=2520 Option B #### B QUESTION:What inequality represents the condition 1<x<13? options: A)|x|<3 B)|x+5|<4 C)|x-7|<6 D)|-5+x|<4 E)|3+x|<5 SOLUTION:1<x<13 represents segment with length: 13-1 = 12 center: (13+1)/2 = 7 For any |x-a|<b a is a center and b is a half of length. So, |x-7|<12/2 represents our inequality (answer C) #### C QUESTION:At a particular graduation party with 300 guests, 70% of the guests brought gifts, and 40% of the female guests brought gifts. If 45 males did not bring gifts to the party, how many females did bring gifts? options: A)18 B)30 C)42 D)68 E)70 SOLUTION:the correct method total = 300.. 70% of 300 = 210 got gifts.. 90 did not get gift, out of which 48 are males, so remaining 90-45=50 are females.. But 40% females brought gift, so 60% did not get it.. so 60% = 45, 100%= 45*100/60= 75.. ans 40% of 75 =30 B #### B QUESTION:Find out the wrong number in the given sequence of numbers. 1, 2, 6, 15, 31, 55 options: A)55 B)6 C)15 D)31 E)91 SOLUTION:1(result) + (1*1) = 2. 2(result) + (2*2) = 6. 6(result) + (3*3) = 15. 15(result) + (4*4) = 31. 31(result) + (5*5) = 56. Now we are getting 56 not 55.. So 55 is the wrong number of the given. answer : A #### A QUESTION:Sandy purchased 20 dozen toys at the rate of $360 per dozen. Sandy sold each toy at the rate of $30.60. What was the percentage profit? options: A)1% B)2% C)3% D)4% E)5% SOLUTION:A dozen toys cost $360, so each toy cost $30. selling price / cost price = 30.60 / 30 = 1.02 The percentage profit is 2%. The answer is B. #### B QUESTION:A boy has 9 trousers and 10 shirts. In how many different ways can he select a trouser and a shirt? options: A)100 B)102 C)104 D)108 E)90 SOLUTION:The boy can select one trouser in nine ways. The boy can select one shirt in 12 ways. The number of ways in which he can select one trouser and one shirt is 9 * 10 = 90 ways. E #### E QUESTION:A 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? options: A)4 sec B)6 sec C)7 sec D)3 sec E)2 sec SOLUTION:Speed of train relative to man = 60 + 6 = 66 km/hr. = 66 * 5/18 = 55/3 m/sec. Time taken to pass the men = 110 * 3/55 =6 sec. Answer:B #### B QUESTION:Given that 268x74= 19632, find the value of 2.68x.74. options: A)1.9632 B)1.0025 C)1.5693 D)1.0266 E)None SOLUTION:Solution Sum of decimals places =(2+2) = 4. Therefore, = 2.68×.74 = 1.9632 Answer A #### A QUESTION:Amit and Ian paint a wall in alternating shifts. First Amit paints alone, then Ian paints alone, then Amit paints alone, etc. During each of his shifts, Amit paints 1/2 of the remaining unpainted area of the wall, while Ian paints 1/3 of the remaining unpainted area of the wall during each of his shifts. If Amit goes first, what fraction of the wall's area will remain unpainted after Amit has completed his 2th shift? options: A)1/27 B)1/54 C)1/81 D)1/6 E)1/216 SOLUTION:Fraction of area unpainted after FIRST shift of Amit = 1-(1/2) = 1/2 Fraction of area unpainted after FIRST shift of Ian = (1/2)-(1/3)(1/2) = (2/3)(1/2) Fraction of area unpainted after SECOND shift of Amit = (1/2)(2/3)(1/2)=1/6 Answer: option D #### D QUESTION:16 men can complete a piece of work in 25 days. In how many days can 15 men complete that piece of work? options: A)26.7 days B)77 days C)20 days D)88 days E)44 days SOLUTION:16 * 25 = 15 * x => x = 26.7 days Answer: A #### A QUESTION:A, B and C invests Rs.4000, Rs.2000 and Rs.6000 in a business. After one year A removed his money; B and C continued the business for two more year. If the net profit after 3 years be Rs.3300, then A's share in the profit is? options: A)6000 B)4000 C)2000 D)600 E)300 SOLUTION:4*12 : 2*36 : 4*36 2: 3: 6 2/11 * 3300 = 600 Answer: D #### D QUESTION:A boat can travel with a speed of 22 km/hr in still water. If the speed of the stream is 5 km/hr, find the time taken by the boat to go 81 km downstream options: A)5 hours B)4 hours C)3 hours D)2 hours E)None of these SOLUTION:Explanation : Speed of the boat in still water = 22 km/hr speed of the stream = 5 km/hr Speed downstream = (22+5) = 27 km/hr Distance travelled downstream = 81 km Time taken = distance/speed = 81/27 = 3 hours. Answer : Option C #### C QUESTION:If a is Negative integers and b is positive integers and a ≠ 0 which of the following equal 0 ? options: A)a-b B)a^2+b^2 C)a*b D)a/b E)a^2-b^2 SOLUTION:All options Except E gives Non-zero answer. a should be negative integers and b should be an positive integers. (E)a^2-b^2 If b=0,a^2-b^2=a^2. a is negative integers. Any square of the negative integers gives us a positive numbers. So The option E is answer #### E QUESTION:If a wagon wheel had 10 more spokes, the angle between them would decrease by 6 degrees. Can you identify the number of spokes in the wheel? options: A)20 spokes B)10 spokes C)30 spokes D)15 spokes E)25 spokes SOLUTION:A 20 spokes 360/S = A 360/(S +10) = A – 6 Thus there are 20 spokes in the wheel. #### A QUESTION:In a History examination, the average for the entire class was 80 marks. If 10% of the students scored 35 marks and 20% scored 90 marks, what was the average marks of the remaining students of the class ? options: A)22 B)27 C)75 D)29 E)271 SOLUTION:Explanation: Let the number of students in the class be 100 and let this required average be x. Then, (10 * 95) + (20 * 90) + (70 * x) = (100 * 80) => 70x = 8000 - (950 + 1800) = 5250 => x = 75. Answer: C) 75 #### C QUESTION:. The average of first ten prime numbers which are odd is? options: A)22.9 B)28.1 C)12.9 D)15.8 E)11.2 SOLUTION:Explanation: Sum of first 10 prime no. which are odd = 158 Average = 158/10 = 15.8 Answer:D #### D QUESTION:Find 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.15of money? options: A)1500 B)1992 C)9921 D)2798 E)2789 SOLUTION:P = 15(100/10)2 => P = 1500 Answer: A #### A QUESTION:When 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 ? options: A)339 B)349 C)369 D)359 E)Data inadequate SOLUTION:Explanation: x = 13p + 11 and x = 17q + 9 13p + 11 = 17q + 9 17q - 13p = 2 q = 2 + 13p 17 The least value of p for which q = 2 + 13p is a whole number is p = 26 17 x = (13 x 26 + 11) = (338 + 11) = 349 Answer: B #### B QUESTION:If 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? I. 14.5 II. 15.3 III. 9.5 options: A)I only B)I and II only C)II only D)III only E)I and III only SOLUTION:Mean = 12 SD = 1.3 2 SD above mean = 12+2*1.3 = 14.6 2 SD below mean = 12-2*1.3 = 9.4 14.5 and 9.5 lies in the range of 2SD from mean Answer: Option C #### C QUESTION:If -2/(a - 6) = 4/(a + 4), then a = ? options: A)2/3 B)1/2 C)5/3 D)8/3 E)7/3 SOLUTION:Multiply all terms of the given equation by (a - 6)(a + 4), simplify and solve (a - 6)(a + 4)[ -2/(a - 6) ] = (a - 6)(a + 4) [ 4/(a + 4) ] - 2 (a + 4) = 4 (a - 6) a = 8/3 correct answer D #### D QUESTION:If x = y^2, and x and y are positive integers, which of the following numbers could be the value of x? options: A)10,573 B)11,908 C)12,322 D)13,924 E)14,537 SOLUTION:The square of an integer can have a units digit of 0, 1, 4, 5, 6, or 9. The answer is D. #### D QUESTION:Which of the following must be true? 1) Every prime number greater than 5 can be written as either as 8n+1 or 8n-1 2) Every prime number greater than 5 can be written as 4n+1 or 4n-1 3) Every number greater than 5 of the form 8n+1 or 8n-1 is a prime number. options: A)1,2,3 B)2,3 C)1,2 D)only 1 E)only 2 SOLUTION:Every prime number greater than 3 can be written in the form of 8n+1 or 8n-1 where n is an integer. So 1 can be possible. 3. This is not possible as 2 and 3 are being prime , we can't write then in the form of 8n+1 or 8n-1. C #### C QUESTION:How many 5-digit positive integers exist the sum of whose digits are odd? options: A)36000 B)38000 C)45000 D)90000 E)None SOLUTION:Solution: There are 9�104 = 90000, 5-digit positive integers. Out of these 90000 positive integers, the sum of the digits of half of the numbers will add up to an odd number and the remaining half will add up to an even number. Hence, there are 90000 /2= 45000, 5-digit positive integers whose sum add up to an odd number. Answer: Option C #### C QUESTION:A bag contains 8 red and 3 white balls. One ball is drawn at random. What is the probability that the ball drawn is white? options: A)4/7 B)2/3 C)8/11 D)1/4 E)5/7 SOLUTION:Total number of balls = 8+3 = 11 number of white balls = 8 Probability = 8/11 = 8/11 Answer is C #### C QUESTION:A train travels at the rate of 10 miles/hr for the first hour of a trip, at 20 miles/hr for the second hour, at 30 miles/hr for the third hour and so on. How many hours will it take the train to complete a 210-mile journey? Assume that the train makes no intermediate stops. options: A)6 B)6.5 C)7 D)7.5 E)5 SOLUTION:A train travels at the rate of 10 miles/hr for the first hour of a trip, at 20 miles/hr for the second hour, at 30 miles/hr for the third hour and so on. How many hours will it take the train to complete a 210-mile journey? Assume that the train makes no intermediate stops. I think the easiest way to solve this problem would be simply to count the number of miles it travels per hour (and in total) Hour miles/hour Total miles 1 10 10 2 20 30 3 30 60 4 40 100 5 50 150 6 60 210 It takes a total of nine hours to cover the 210 mile distance. ANSWER: A 6 #### A QUESTION:The 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 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? options: A)3 B)4 C)5 D)6 E)7 SOLUTION:For 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 4 guards. To choose 3 out of 4, we will have 4C3 = 4 different groups. The answer is B. #### B QUESTION:A 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? options: A)13 B)21 C)77 D)88 E)11 SOLUTION:20 15 5 25 20 8 500 + 300 + 40 = 840/40 = 21' Answer: B #### B QUESTION:The average height of 35 boys in a class was calculated as 185cm. 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).? options: A)178.27 cm B)183.29 cm C)978.29 cm D)178.89 cm E)176.29 cm SOLUTION:Calculated average height of 35 boys = 185 cm. Wrong total height of 35 boys = 185 * 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 = 185 cm - (166 cm - 106 cm)/35 =185 cm - 60 /35 cm = 185 cm - 1.71 cm = 183.29 cm. Answer: B #### B QUESTION:Find the odd man out. 1, 3, 9, 12, 19, 29 options: A)12 B)9 C)1 D)3 E)29 SOLUTION:12 is an even number. All other given numbers are odd Answer is A #### A QUESTION:By selling 8 pencils for a rupee a man loses 10%. How many for a rupee should he sell in order to gain 10%? options: A)6.54 B)9.45 C)7.34 D)6.67 E)5.09 SOLUTION:90% --- 8 110% --- ? 90/110 * 8 = 6.54 Answer: A #### A QUESTION:1 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? options: A)12/9 days B)15/4 days C)82/8 days D)22/76 days E)3/2 days SOLUTION:1M = 6W ---- 20 days 12M + 8W -----? 72W + 8 W = 80W ---? 6W ---- 20 80 -----? 6 * 20 = 80 * x => x = 3/2 days Answer:E #### E QUESTION:The average of six number is 3.95. The average of two of them is 3.8, while the average of the other two is 3.85. what is the average of the remaining two number ? options: A)4.5 B)4.2 C)4.7 D)4.8 E)None of these SOLUTION:solution: Sum of the remaining two numbers = (3.95 × 6) - [(3.8 × 2) + (3.85 ×2)] =23.70 -(7.6 + 7.7) = 23.70 - 15.3 = 8.4. ∴ Required average =8.4/2 = 4.2 Answer B #### B QUESTION:69 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? options: A)20 B)23 C)24 D)25 E)26 SOLUTION:According to the chain rule, M1 x T1 = M2 x T2 Therefore, 69 x 12 x 5 = 30 x 6 x X X = 23 Hence, the number of days = 23. ANSWER:B #### B QUESTION:Three clocks were set to true time and starts to run together, makes a beep sound at intervals of 8,10 and 12 minutes respectively. In 2 days, how many times do they will make the sound together ? options: A)12 B)15 C)25 D)30 E)35 SOLUTION:Explanation : The clocks make sound at intervals of 8, 10 and 12 minutes respectively. The LCM of 8,10 and 12 is 120. So, the clocks will make sound together after every 120 minutes. i.e., after every 2 hours. In 2 days(48 hours), they will make the sound together (48/2) = 24 times. At the end of 2nd day, they will make one more beep together. Therefore, totally (24+1) 25 times beep sound is made together. Hence the answer is 25 times. Answer : C #### C QUESTION:If 1 = 6 2 = 12 3 = 18 4 = 24 5 = 30 6 = 36 Then 24 = ? Hint: Its a logic Riddle not a mathematical riddle options: A)1 B)2 C)4 D)6 E)8 SOLUTION:C 24 As stated 4=24 => 24=4 Answer is C #### C QUESTION:A man is 22 years older than his son. In THREE years, his age will be THRICE the age of his son. The present age of this son is options: A)8 years B)2 years C)7 years D)8 years E)5 years SOLUTION:Let's Son age is x, then Father age is x+22. => 3(x+3) = (x+22+3) => 3x+9 = x+25 => 2x = 16 years = 8 YEARS Answer: D #### D QUESTION:Of the 400 members at a health club, 260 use the weight room and 300 use the pool. If at least 60 of the members do not use either, then the number of members using both the weight room and the pool must be between: options: A)40 to 100 B)80 to 140 C)160 to 260 D)220 to 260 E)220 to 300 SOLUTION:260-X+X+300-X+GT60 = 400 =>X = GT 620-400 => X = GT 220 => X >= 220 (Here GT means Greater than) So Min value of X is 220 coming to options D/E X's maximum value cannot exceed 260 as per the venn diagramsince 'W' circle cannot accomodate 'X' More than 260 ANSWER:D #### D QUESTION:Alex age after 13years will be 10 times his age 10years back. What is the present age of Alex? options: A)15 B)13 C)20 D)21 E)26 SOLUTION:Let Alex's present age be x Alex's age after 17 years = x+17 Alex's age 10 years back = x-10 x+17= 10(x-10) x = 13 Rajeev's present age = 13 years Answer is B #### B QUESTION:If the perimeter of a rectangular garden is 600 m, its length when its breadth is 100 m is? options: A)299 m B)777 m C)200 m D)167 m E)128 m SOLUTION:2(l + 100) = 600 => l = 200 m Answer:C #### C QUESTION:A retailer buys 80 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 % ? options: A)110 B)115 C)112 D)118 E)120 SOLUTION:let the market price of each pen be $1 then, Cost Price of 80 pens = $ 36 Selling Price of 80 pens =99% of $80=$ 79.20 profit %=((43.20*100)/36) %=120% Answer E)120 #### E QUESTION:A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 15 seconds. The speed of the train is? options: A)35 B)50 C)88 D)66 E)22 SOLUTION:Speed of the train relative to man = (125/15) m/sec = (25/3) m/sec. [(25/3) * (18/5)] km/hr = 30 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 30 ==> x = 35 km/hr. Answer:A #### A QUESTION:A 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 W on this shipment? options: A)a) $100 B)b) $115 C)c) $125 D)d) $130 E)e) $135 SOLUTION:I recommend one should use fractions to solve this one rather than converting it into decimals Sol: 1500 heads -> $600 1 head -> $600/1500 1 head -> $(2/5) 25% more of (2/5) -> 125/100 * 2/5 = $(1/2) He sold 2/3*1500 = 1000 heads for $(1/2) per head Total revenue by selling 1000 heads = 1000 * 1/2 = $500 Heads left: 500 Cost per head: 90% of the previous price: 90/100 * 1/2 = $(9/20) Total revenue by selling 500 heads = 9/20 * 500 = 225 Total revenue after selling 1500 cabbage heads - 225+500 = $725 Money spent on the purchase: $600 Profit W= 725-600 = $125 Ans:C #### C <<<Examples ends QUESTION:With 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? options: A)9000 cubic meters B)10500 cubic meters C)11750 cubic meters D)12000 cubic meters E)12500 cubic meters SOLUTION:D. 12000 cubic meters. If 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. Now, if valve 1 admits x cubic meter of water per minute then the capacity of pool will be 120x and also 80 (x+50). or, 120x = 80 (x + 50). or x = 100. Hence, the capacity of pool = 120x = 12000 cubic meters. #### D

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:A boy has 9 trousers and 10 shirts. In how many different ways can he select a trouser and a shirt? options: A)100 B)102 C)104 D)108 E)90 SOLUTION:The boy can select one trouser in nine ways. The boy can select one shirt in 12 ways. The number of ways in which he can select one trouser and one shirt is 9 * 10 = 90 ways. E #### E QUESTION:A car covers a distance of 624 km in 3 hours. Find its speed? options: A)104 kmph B)194 kmph C)208 kmph D)174 kmph E)101 kmph SOLUTION:624/3 =208 kmph Answer:C #### C QUESTION:Three numbers are in the ratio 3:4:5 and their L.C.M. is 600. Their H.C.F is? options: A)10 B)30 C)40 D)50 E)60 SOLUTION:Let the numbers be 3x,4x and 5x their L.C.M. = 60x 60x =600 x = 10 The numbers are 3*10 , 4*10 , 5*10 Hence required H.C.F. = 10 Answer is A #### A QUESTION:Which of the following are orthogonal pairs? a. 3i+2j b. i+j c. 2i-3j d. -7i+j ??? options: A)a,b B)a,c C)b,c D)a,d E)b,d SOLUTION:a. 3i+2j and c. 2i-3j are orthogonal pair. as the dot product of two vectors is zero;so they are orthogonal. ANSWER:B #### B QUESTION:Two friends run the New York City marathon, one friend finishes the marathon in 400 minutes while the second friend finishes the marathon in 625 minutes. What is the ratio of their speed? options: A)10 : 12 B)1 : 2 C)5 :10 D)20 : 25 E)None SOLUTION:Solution Let us name the friends as A and B. = ( Friend A'S speed) : (Friend B's speed) =√b : √a = √400 : √625 = 20 : 25 Answer D #### D QUESTION:A school’s annual budget for the purchase of student computers increased by 70% this year over last year. If the price of student computers increased by 30% this year, then the number of computers it can purchase this year is what percent greater than the number of computers it purchased last year? options: A)30% B)30.77% C)36% D)37% E)38% SOLUTION:Pick numbers. Lats year: budget = $100, price = $1 --> the number of computers purchased = 100/1 = 100; This year: budget = $170, price = $1.3 --> the number of computers purchased = 170/1.3 = ~130.77 Increase in the number of computers purchased = 30.77%. Answer: B. #### B QUESTION:If $600 is deposited into a savings account at an annual interest rate of 4% that compounds monthly, what is the value of the investment after 7 years? options: A)$750.00 B)$823.50 C)$973.25 D)$100.25 E)$793.49 SOLUTION:Using CI Formula: A=P(1+r/n)^n*t A=600(1+4/7)^4*7 A=793.49 Option: E #### E QUESTION:There 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? options: A)15624 B)16478 C)17953 D)19655 E)28958 SOLUTION:15624 A #### A QUESTION:Enrollment in City College in 1980 was 83 1/3 percent of enrollment in 1990. What was the percent increase in the college’s enrollment from 1980 to 1990? options: A)10% B)16 2/3 % C)20% D)25% E)183 1/3% SOLUTION:Let 100 is the enrollment in 1990. Enrollment in 1980= 83.3 % increase= (Increase from 1980 to 1990)/Enrollment in 1983 =>16.7*100/83.3 =20% ANSWER:C #### C QUESTION:Tickets 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? options: A)2/7 B)3/8 C)3/10 D)4/11 E)5/13 SOLUTION:Here, S = [1, 2, 3, 4, …., 19, 20] Let E = event of getting a multiple of 3 = [3, 6, 9, 12, 15, 18] P (E) = n (E) / n (S) = 6 / 20 = 3/10 C #### C QUESTION:Which of the following CANNOT be a product of two distinct positive integers x and y? options: A)x B)y C)3y + 2x D)y - x E)yx SOLUTION:In 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 take x = 1 and y = 2 and work with the options xy = 2 A) x take x =2, y = 1 B) y take x = 1 y = 2 C) 3y + 2x Seems tricky, lets see other options and then come back to it. D) 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? E) yx Always true You don't even have to worry what C is ! ans D #### D QUESTION:A and B r 2 men who enter into business and they invest Rs 1000, Rs 2000respectively. How will they divide the income of Rs 5000 options: A)3336,1667 B)3339,1667 C)3333,1666 D)3333,1668 E)3333,1669 SOLUTION:they invested in the ratio 1:2 a's share =1/3*5000=1666 b's share=2/3*5000=3333 ANSWER:C #### C QUESTION:If a > 0 and x is m percent of y, then, in terms of a, y is what percent of x? options: A)a) 100a B)b) 1/100a C)c) 1/a D)d) 10/a E)e) 10,000/a SOLUTION:x= a/100 * y So y= 100/a * x So y= (10000/a)/100 * x E #### E QUESTION:A person starts walking at a speed of 5km/hr through half the distance, rest of the distance he covers with aspeed 4km/hr. Total time of travel is 36 hours. What is the maximum distance he can cover? options: A)20km B)40km C)60km D)80km E)160km SOLUTION:t=d/s, so 36=x/2*1/5+x/2*1/4(because half distance with 5 km/ph, and remaining half with 4km/hr) 36=x(18/80) x=160km ANSWER:E #### E QUESTION:Which one of the following is not a prime number? options: A)31 B)61 C)71 D)91 E)101 SOLUTION:91 is divisible by 7. So, it is not a prime number. answer :D #### D QUESTION:A 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.5 per sq m? options: A)6500 B)2779 C)2779 D)3900 E)2781 SOLUTION:Area = (l + b – d) d (80 + 60 – 10)10 => 1300 m2 1300 * 5 = Rs.6500 Answer:A #### A QUESTION:A man sells 45 lemons for Rs 40 and loses 20%. At how much price should he sell 24 lemons to the next customer to make a 20% profit? options: A)37 B)299 C)72 D).32 E)01 SOLUTION:Explanation: Let cost price of lemons be x. Selling price of lemons becomes CP - loss. =>SP=x-(20/100)x =>40=x(80/100) =>50 So 45 lemons cost Rs 50 Cost of 1 lemon = 50/45 Rs Cost of 24 lemons = (50/45)*24 =80/3 Rs Selling Price of 24 lemons =(80/3)+(20/100)(80/3)=Rs 32 ANSWER:D #### D QUESTION:A man walking at a constant rate of 9 miles per hour is passed by a woman traveling in the same direction along the same path at a constant rate of 15 miles per hour. The woman stops to wait for the man 3 minutes after passing him, while the man continues to walk at his constant rate. How many minutes must the woman wait until the man catches up? options: A)1 B)2 C)3 D)4 E)5 SOLUTION:When the woman passes the man, they are aligned (m and w). They are moving in the same direction. After 5 minutes, the woman (W) will be ahead the man (M): m------M---------------W w In the 5 minutes, after passing the man, the woman walks the distance mW = wW, which is 3*15/60 =15/20 miles and the man walks the distance mM, which is 3*9/60 = 9/20 mile. The difference of 15/20 - 9/20 =3/10 miles (MW) will be covered by the man in (3/10)/9 = 1/30 of an hour, which is 2 minutes. Answer B. #### B QUESTION:A word is defined as a sequence of five dots arranged in a row. Each dot is colored either red, yellow, or blue. How many distinct words can be formed? options: A)124 B)150 C)212 D)243 E)316 SOLUTION:3^5 = 243 The answer is D. #### D QUESTION:Rs. 5887 is divided between Shyam and Ram, such that Shyam's share at the end of 9 years is equal to Ram's share at the end of 11 years, compounded annually at the rate of 5%. Find the share of Shyam. options: A)2088 B)2000 C)3087 D)None of these E)Cannot be determined SOLUTION:Solution: Shyam's share * (1+0.05)9 = Ram's share * (1 + 0.05)11 Shyam's share / Ram's share = (1 + 0.05)11 / (1+ 0.05)9 = (1+ 0.05)2 = 441/400 Therefore Shyam's share = (441/841) * 5887 = 3087. Answer C #### C QUESTION:The sum of a certain number and its reciprocal is equal to 2,9. What is the absolute value of the difference of this number and its reciprocal ? options: A)2,2 B)1,2 C)0,3 D)0,4 E)2,1 SOLUTION:x + 1/x = 2.9 x-1/x = y Add two equations 2x = 2.9 + y So when 2.9 and correct answer choice are added, the final digit should be even So eliminate A, B and D Substitute y=0.3 x=1.6 1.6+1/1.6 is not equal to 2.9 Substitute y = 2.1 So x=2.5 2.5+1/2.5 =2.9 ANSWER:E #### E QUESTION:In a group of pigs and hens, the number of legs are 22 more than twice the number of heads. The number of pigs is options: A)5 B)7 C)10 D)12 E)11 SOLUTION:Explanation: Let the number of pigs be x and the number of hens be y. Then, 4x + 2y = 2 (x + y) + 22 4x + 2y = 2x + 2y + 22 2x = 22 x = 11 Answer: E #### E QUESTION:A 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? options: A)12 min B)17 min C)19 min D)11 min E)16 min SOLUTION:Since 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. Relative speed of A and B = 6 - 1 = 5 rounds per hour. Time taken to complete one round at this speed = 1/5 hr = 12 min. Answer: A #### A QUESTION:Arun has certain number of books. It is not less than 15 and not more than 30. If he wants to give these books equally to 2 of his friends, then 1 book will remain. If he wants to give these books equally to 3 of his friends, then 2 books will remain. If he wants to give these books equally to 4 of his friends, then 3 books will remain. What is the number of books he had? options: A)23 B)24 C)25 D)26 E)27 SOLUTION:Explanation : If he wants to give these books equally to 2 of his friends, then 1 book will remain, it means possible number of books = 15,17,19,21,23,25,27,29 If he wants to give these books equally to 3 of his friends, then 2 books will remain, it means possible number of books = 17,20,23,26,29 If he wants to give these books equally to 4 of his friends, then 3 book will remain, it means possible number of books = 15,19,23,27 Hence ,the common number is only 23 so it will be answer. Answer : A #### A QUESTION:On dividing a number by 999, the quotient is 366 and the remainder is 103. The number is: options: A)364724 B)365387 C)365737 D)366757 E)366767 SOLUTION:Required number= 999*366+103 = (1000-1)*366+103 = 366000-366+103 = 365737. ANSWER:C #### C QUESTION:A can do a job in 18 days and B can do it in 30 days. A and B working together will finish twice the amount of work in ------- days? options: A)22 1/8 B)22 1/2 C)22 1/1 D)22 1/5 E)22 1/9 SOLUTION:1/18 + 1/30 = 8/90 = 4/45 45/4 = 11 ¼ *2 = 22 1/2 days Answer:B #### B QUESTION:A batsman in his 15th inning makes a score of 75 and their by increasing his average by 3. What is his average after the 15th inning? options: A)31 B)32 C)33 D)34 E)35 SOLUTION:14x + 75 = 15(x + 3) x = 30 + 3 = 33 Answer:C #### C QUESTION:There are 7 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? options: A)21 B)30 C)45 D)60 E)90 SOLUTION:7 players are there. two players play one game with one another. so 7C2=7*6/2 =21 SO OPTION A is correct #### A QUESTION:One side of a rectangular field is 15m and one of its diagonal is 17m. Find the area of field? options: A)120 sq. m B)140 sq. m C)125 sq. m D)130 sq. m E)110 sq. m SOLUTION:Other side = [(17 x 17) - (15 x 15)] = (289 - 225) = 8m Area = 15 x 8 =120 sq. m ANSWER:A #### A QUESTION:Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 3 or 5? options: A)5/20 B)9/25 C)8/20 D)9/20 E)6/20 SOLUTION:Explanation: Here, S = {1, 2, 3, 4, ...., 19, 20}. Let E = event of getting a multiple of 3 or 5 = {3, 6 , 9, 12, 15, 18, 5, 10, 20} answer 9/20 Answer D #### D QUESTION:The average of twelve numbers is 7. The average of first nine numbers is 6 and the average of last two numbers is 10. What is the middle number? options: A)A)9 B)B)10 C)C)12 D)D)7 E)E)13 SOLUTION:The total of twelve numbers = 12X7 = 84 The total of first 9 and last 2 numbers is = 9 X 6+2 X 10 = 74 So, the middle number is (84 - 74 ) = 10 B #### B QUESTION:Convert 700 miles into meters? options: A)784596 B)1126538 C)804670 D)784596 E)864520 SOLUTION:1 mile = 1609.34 meters 700mile = 700*1609.34 = 1126538 meters Answer is B #### B QUESTION:If y ≠ 3 and 2h/y is a prime integer greater than 2, which of the following must be true? I. h = y II. y = 1 III. h and y are prime integers. options: A) None B) I only C) II only D) III only E) I and II SOLUTION:Note that we are asked which of the following MUST be true, not COULD be true. For such kind of questions if you can prove that a statement is NOT true for one particular set of numbers, it will mean that this statement is not always true and hence not a correct answer. So we should try to make the listed statements not true for some h and y (which satisfy y≠3 and 2h/y=prime>2). I. h = y --> not necessarily true: h=3 and y=2 (2h/y=3=prime>2); II. y=1 --> not necessarily true: h=3 and y=2 (2h/y=3=prime>2); III. h and y are prime integers --> not necessarily true: h=10 and y=4 (2h/y=5=prime>2). Answer: A. #### A QUESTION:A 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? options: A)75 B)100 C)125 D)150 E)175 SOLUTION:Let x be the total length of the trip. 0.1x + 30 miles + 0.5x = x 30 miles = 0.4x x = 75 miles The answer is A. #### A QUESTION:Rates for having a manuscript typed at a certain typing service are $5 per page for the first time a page is typed and $4 per page each time a page is revised. If a certain manuscript has 100 pages, of which 30 were revised only once, 20 were revised twice, and the rest required no revisions, what was the total cost of having the manuscript typed? options: A)$760 B)$750 C)$810 D)$800 E)$780 SOLUTION:50 pages typed 1x 30 pages typed 2x (original + one revision) 20 pages typed 3x (original + two revisions) 50(5)+30(5+4)+20(5+4+4)=250+270+260=780 Answer - E #### E QUESTION:20, 19, 17, ?, 10, 5 options: A)14 B)15 C)13 D)18 E)17 SOLUTION:A 14 The Pattern is - 1, - 2, -3, ... #### A QUESTION:If n = 30! + 27, then n is divisible by which of the following? I. 25 II. 27 III. 29 options: A)None B)I only C)II only D)I and II E)II and III SOLUTION:27 divides 30! so 27 also divides 30! + 27. 25 and 29 divide 30! so they do not divide 30! + 27. The answer is C. #### C QUESTION:If the volume of two cubes are in the ratio 64:1, the ratio of their edges is: options: A)3:1 B)3:2 C)3:5 D)4:1 E)None of these SOLUTION:Explanation: Let the edges be a and b of two cubes, then a3/b3=64/1 =>(a/b)3=(4/1)3 a/b=4/1 =>a:b=4:1 Option D #### D QUESTION:P beats Q by 250 meter in a kilometer race. Find Q's speed if P's speed is 16 meter/sec. options: A)21 meter/sec B)7 meter/sec C)12 meter/sec D)18 meter/sec E)28 meter/sec SOLUTION:P's speed = 16m/s P's distance = 1000m (as it is a km race) t = 1000/16 = 62.5 sec Q's distance = 1000-250= 750m Q's time to complete this distance is also 62.5 sec. Q's speed = dist/time = 750/62.5 = 12 m/s Hence C is the answer. #### C QUESTION:The total number of plums that grow during each year on a certain plum tree is equal to the number of plums that grew during the previous year, less the age of the tree in years (rounded down to the nearest integer). During its 5th year, the plum tree grew 50 plums. If this trend continues, how many plums will it grow during its 6th year? options: A)40 B)42 C)45 D)48 E)54 SOLUTION:1st year : 0-1 (age), we take age = 0 (as the question says that we have to(rounded down to the nearest integer)) 2ndyear : 1-2 (age), we take age = 1 3rd year : 2-3 (age), we take age = 2 4th year : 3-4 (age), we take age = 3 5th year : 4-5 (age), we take age = 4 6th year : 5-6 (age), we take age = 5 Thus for the 5th year = 50, 6th year = 50-5 = 45. The correct answer is C. #### C QUESTION:The market value of a certain machine decreased by 20 percent of its purchase price each year. If the machine was purchased in 1982 for its market value of $8,000, what was its market value two years later? options: A) $8,000 B) $5,600 C) $3,200 D) $2,400 E) $4,800 SOLUTION:E. Market value in 1982= $ 8000 Market value in 1983 = $ 8000- ($ 8000 x 20/100) = 8000-1600= $ 6400 Market value in 1984 = Market value in 1983 - (20 % of $8000)= 6400-1600 = $4800 #### E QUESTION:The least number which when increased by 4 each divisible by each one of 22, 32, 36 and 54 is : options: A)427 B)859 C)860 D)4320 E)None of these SOLUTION:Solution Required number = (L.C.M. of 24, 32, 36, 54) - 4 = 864 - 4 = 860. Answer C #### C QUESTION:Here 10 programmers, type 10 lines within 10 minutes then 60 lines can type within 60 minutes. How many programmers are needed? options: A)16 B)10 C)6 D)60 E)50 SOLUTION:10 10 programmer 10 line 10 mins. 10 programmer 20 line 20 mins. . . . .10 programmer 60 line 60 mins. ANSWER:D #### D QUESTION:A railway half ticket costs half the full fare and the reservation charge is the same on half ticket as on full ticket. One reserved first class ticket from Chennai to Trivandrum costs Rs. 216 and one full and one half reserved first class tickets cost Rs. 327. What is the basic first class full fare and what is the reservation charge? options: A)Rs. 105 and Rs. 6 B)Rs. 216 and Rs. 12 C)Rs. 210 and Rs. 12 D)Rs. 210 and Rs. 6 E)None SOLUTION:Explanatory Answers Let half of the full basic fare be Rs. X. Therefore, full basic fare is Rs. 2X. Let the reservation charge be Rs. Y per ticket. Now, one full reservation ticket would cost 2X (basic fare) + Y (reservation charge) 2X + Y = 216 --- (1) The total basic fare for one half and one full ticket = X + 2X = 3X and the total reservation charge is 2Y. Hence, 3X + 2Y = 327 --- (2) Solving (1) and (2) we get, X = 105 and Y = 6 Hence, the full basic fare is 2X = Rs. 210 and the reservation charge is Y = Rs. 6 Answer D #### D QUESTION:The navy pilots are practicing flight formations. 200 pilots are practicing flying in rectangles. They want to make a rectangular formation with X planes in a row and Y planes in a column. If the number of airplanes in a row is no less than 5 and no more than 40, how many different combinations of rectangular shapes are possible? options: A)6 B)7 C)8 D)9 E)10 SOLUTION:firstly factors of 200 = 1,2,4,5,8,10,20,25,40,50,100,200 the question says each row will have airplanes not less than 5 and not more than 40, therefore, we should be interested in the factors starting from 5 til 40 (inclusive) 5(in each row) * 40(number of columns) =200, similarly 8 * 25 10 * 20 20 * 10 25 * 8 40 * 5 total possibilities = 6 option A #### A QUESTION:A 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? options: A) 1.25% B) 3.75% C) 6.25% D) 6.67% E) 15% SOLUTION:The 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. Answer: E. #### E QUESTION:A 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? options: A)285 m B)240 m C)277 m D)765 m E)176 m SOLUTION:Speed = (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)/39 = 15 ==> x + 300 = 585 ==> x = 285 m. Answer: A #### A QUESTION:The sum of money at compound interest amounts to thrice itself in 3 years. In how many years will it be 9 times itself? options: A)7 B)1 C)8 D)6 E)9 SOLUTION:100 ---- 300 --- 3 900 --- 3 ---- 6 years Answer:D #### D QUESTION:105,100,...,90,85,80,75 Insert the missing number options: A)95 B)78 C)83 D)84 E)none of the above SOLUTION:Missing number : 95 Answer : A #### A QUESTION:Find the area of trapezium whose parallel sides are 20 cm and 18 cm long, and the distance between them is 15 cm options: A)178 cm2 B)179 cm2 C)285 cm2 D)167 cm2 E)197 cm2 SOLUTION:Area of a trapezium = 1/2 (sum of parallel sides) * (perpendicular distance between them) = 1/2 (20 + 18) * (15) = 285 cm2 Answer: C #### C QUESTION:Find the average of first 4 multiples of 11? options: A)10 B)12.6 C)27.5 D)31.3 E)40.8 SOLUTION:average = (11+22+33+44)/4 = 27.5 Answer is C #### C QUESTION:A two-digit number is such that the product of the digits is 8. When 18 is added to the number, then the digits are reversed. The number is: options: A)22 B)73 C)99 D)42 E)11 SOLUTION:Explanation: Just go in reverse order. Check the options with th subtracting 18 from each option for getting reverse number. 42 – 18 = 24 (which is in reverse). So answer is 42. Answer D #### D QUESTION:A sum of Rs.1420 is divided into 13 students so that each boy gets Rs.120 while each girl gets Rs.100. Find the number of boys and number of girls options: A)8B, 5G B)5B, 8G C)4B, 9G D)9B, 4G E)6B, 7G SOLUTION:120B+100G=1420-----i B+G=13-------ii from i 100B+20B+100G=1420 100(B+G)+20B=1420 100(13)+20B=1420 By simplifing we get B=6;G=7 ANSWER:E #### E QUESTION:How many cuboids of length 5 m, width 3 m and height 2 m can be farmed from a cuboid of 18 m length, 15 m width and 2 m height. options: A)106 B)109 C)108 D)101 E)104 SOLUTION:(18 × 15 × 12)/(5 × 3 × 2) = 108 Answer is C. #### C QUESTION:Calculate the percentage increase in the area of a square if each of its sides is increased by 15%? options: A)32.25% B)39.25% C)36.25% D)35.25% E)31.25% SOLUTION:Assume original length = 100m by 50m original area = 100*50= 5000 15% increase on each side l = 100 + 15 = 115 w = 50 + 7.5 = 57.5 new area = 115*57.5= 6612.5 increase in area = 6612.5 - 5000 = 1612.5 %increase =21% Answer A #### A QUESTION:The 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? options: A)3 B)7 C)8 D)5 E)1 SOLUTION:S = 4 M = x DS = x + 4 US = x - 4 6/(x + 4) + 6/(x - 4) = 2 x = 8 Answer:C #### C QUESTION:a goes to place x and b goes to place y. after a travelled 180 km more than b they together meet at a point between xy. they together had their lunch for half an hour. after that a took 2 hrs to reach x and b took 4.5 hrs to reach y. find distance between x and y? options: A)900km B)540km C)720km D)820km E)920km SOLUTION:let speed of A be-------Sa let speed of B be--------Sb let the distance covered by B while going to position XY be-----------x so distance covered by A in same time while going to XY is----------180 +x(it's given in the question) so total distance b/w X and Y is=x+(x+180) while going to position XY :- time taken by A = time taken by B (x+180)/Sa= x/Sb Sa/Sb=(x+180)/x---------------------1 After lunch:- A.C.T(according to question) Sa=x/2 Sb=(x+180)/4.5 dividing Sa/Sb=(x*4.5) / ((x+180)*2)--------------------2 equating equations 1 and 2 9/4 = (x+180)^2 / x^2 now taking square root on both sides we get 3/2 = (x+180) / x x=360 therefore distance between x and y =x+(x+180)=900km ANSWER:A #### A QUESTION:A car after covering ½ of a journey of 100 km develops engine trouble and later travels at ½ of its original speed. As a result, it arrives 2 hours late than its normal time. What is the normal speed of the car is? options: A)287 B)27 C)28 D)25 E)28 SOLUTION:[50/x + 50/(x/2)] – 100/x = 2 x = 25 Answer: D #### D QUESTION:A man purchased 3 blankets @ Rs.100 each, 4 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? options: A)A)600 B)B)350 C)C)450 D)D)470 E)E)500 SOLUTION:Explanation: 10 * 150 = 1500 3 * 100 + 4 * 150 = 900 1500 – 900 = 600 A #### A QUESTION:The speed of a car is 50 km in the first hour and 60 km in the second hour. What is the average speed of the car? options: A)79 kmph B)85 kmph C)55 kmph D)23 kmph E)14 kmph SOLUTION:S = (55 + 60)/2 = 55 kmph Answer:C #### C QUESTION:Two letters from the word KYANTKAR are selected at random. What is the probability that at least one of the selected letters is a consonant? options: A)14/27 B)15/28 C)27/28 D)16/28 E)30/28 SOLUTION:There are 6 consonants and 2 vowels in KYANTKAR . probability that at least one of the selected letters is a consonant = 1 - (Probability of both vowels) Probability of both vowels = 2C2/8C2 = 1/28 So,Answer is 1 - 1/28 = 27/28 Answer : C #### C QUESTION:The missing term in the sequence 2, 3, 5, 7, 11, ... 17, 19 is options: A)11 B)13 C)15 D)17 E)18 SOLUTION:Sequence is contain prime numbers. Final sequence : 2,3,5,7,11,13,17,19 ANSWER:B #### B QUESTION:Set #1 = {A, B} Set #2 = {K, L, M, N, O, P} There 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? options: A)1/6 B)1/3 C)7/12 D)2/3 E)5/6 SOLUTION:So Not a vowel in Set-1 : 1/2 And not a vowel in Ser-2:5/6 Now, 1/2∗5/6=5/12 This is for not a vowel. Then for at least one vowel will be = 1−5/12=7/12 Answer will be C. #### C QUESTION:The C.P of 15 books is equal to the S.P of 18 books. Find his gain% or loss%? options: A)16 2/3% loss B)100/3% loss C)50/3% profit D)100/3% loss E)200/3% loss SOLUTION:Explanation: 15 CP = 18 SP 18 --- 3 CP loss 100 --- ? => 16 2/3% loss ANSWER IS A #### A <<<Examples ends QUESTION:If y ≠ 3 and 2a/y is a prime integer greater than 2, which of the following must be true? I. xa= y II. y = 1 III. a and y are prime integers. options: A) None B) I only C) II only D) III only E) I and II SOLUTION:Note that we are asked which of the following MUST be true, not COULD be true. For such kind of questions if you can prove that a statement is NOT true for one particular set of numbers, it will mean that this statement is not always true and hence not a correct answer. So we should try to make the listed statements not true for some x and y (which satisfy y≠3 and 2x/y=prime>2). I. a = y --> not necessarily true: a=3 and y=2 (2a/y=3=prime>2); II. y=1 --> not necessarily true: a=3 and y=2 (2a/y=3=prime>2); III. a and y are prime integers --> not necessarily true: a=10 and y=4 (2a/y=5=prime>2). Answer: A. #### A

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:In 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 10P pots? options: A)M/10 B)6/M C)600M D)M/6 E)10M SOLUTION:The time it takes to wash 10P pots is 10M minutes which is 10M / 60 = M/6 hours. The answer is D. #### D QUESTION:There exists exactly one positive value of k such that the line y = kx intersects the parabola y = x2 + x + 4 at exactly one point. Compute the intersection point. options: A)(2,10) B)(5,10) C)(7,10) D)(3,10) E)(1,10) SOLUTION:If the line is tangent, then we must have that x2 + x + 4 = kx has a unique solution in x, or x2 + (1 - k)x + 4 = 0 has a unique solution. Thus, (1 - k)2- 16 = 0, or (1- k) = 4. Therefore, k = -3 or k = 5. Taking k = 5, we have that y = 5x intersects y = x2 + x + 4 when x = 2, and the intersection point is (2, 10) . correct answer A #### A QUESTION:What is 2/5 of 5/9 of 1/2? options: A)1/4 B)1/9 C)9/16 D)5/8 E)16/9 SOLUTION:2/5 * 5/9 * 1/2= 1/9 Answer: B #### B QUESTION:A 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 options: A)4/19 B)7/19 C)12/19 D)21/99 E)26/77 SOLUTION:Solution P( None is defective) = 18C2 / 22C2 = 51/77 P( at least one is defective) = (1- 51/77) = 26/77. Answer E #### E QUESTION:How many odd 4-digit positive integers W that are multiples of 5 can be formed without using the digit 3? options: A)648 B)729 C)900 D)1296 E)3240 SOLUTION:I choose A. Possible n° of 1st digit: 8 (0 can't be the first number, or else it wouldn't have 4 digits. 3 is exlcuded) Possible n° of 2nd digit: 9 (3 is excluded) Possible n° of 3rd digit: 9 (3 is excluded) Possible n° 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) So, W=8*9*9*1=648 (A) #### A QUESTION:A square, with perimeter 40, is inscribed in a circle. What is the area of the circle? options: A)50π B)40π C)30π D)25π E)35π SOLUTION:Area of circuscribed circle = pi/2*area of square Area of square = (40/4)^2 = 10^2= 100 Area of circle = pi/2*100=50pi Answer : A #### A QUESTION:The average age of 30 students in a class is 14 years. If the age of teacher is also included, the average becomes 15 years, find the age of the teacher. options: A)43 B)44 C)45 D)47 E)48 SOLUTION:Explanation: If teacher's age is 14 years, there is no change in the average. But teacher has contributed 1 year to all the students along with maintaining his age at 15. Age of teacher = Average age of all + Total increase in age = 15 + (1 x 30 ) = 45 years Answer:C #### C QUESTION:If x, 3, 5, 7 are there and the range and median of them are the same, what is the value of x? options: A)0 B)1 C)2 D)5 E)4 SOLUTION:Try taking the values of x as you suggested and then see if the median and the range are equal. Once you do that, you will get the answer yourself. Tried substituting values starting with 3, 5, 7... only x = 5 satisfies the condition. D #### D QUESTION:Which number is the odd one out? 159 248 951 357 122 582 options: A)951 B)246 C)325 D)147 E)852 SOLUTION:A 951 In the rest there is the same difference between each digit, eg: 9(–4) 5 (–4)1 #### A QUESTION:A 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? options: A)1350 B)8837 C)2377 D)3772 E)3881 SOLUTION:Area = (l + b +2d) 2d = (75 + 55 +2.5 * 2) 2*2.5 => 675 675 * 2 = Rs.1350 Answer: A #### A QUESTION:The avg weight of A,B & C is 70 kg. If D joins the group, the avg weight of the group becomes 70 kg.If another man E who weights is 3 kg more than D Replaces A, Then the avgof B,C,D&E becomes 68 kg. What is the weight of A? options: A)81 B)65 C)75 D)89 E)90 SOLUTION:A + B + C = 3 *70 = 210 A + B + C + D = 4 * 70 = 280 ---- (i) So, D = 70& E = 70 + 3 = 73 B + C + D +E =68 * 4 = 272 --- (ii) From Eq. (i) & (ii) A-E = 280 –272 = 8 A = E +8 = 73 + 8 = 81 Answer : A #### A QUESTION:Three positive integers a, b, and c are such that their average is 24 and a ≤ b ≤ c. If the median is (a + 11), what is the least possible value of c? options: A)23 B)25 C)27 D)29 E)31 SOLUTION:Solution: We know that the average value is 24 therefore (a+b+c)/3 = 24 so a+b+c = 72 and b = a + 11 therefore a + (a + 11) + c = 72 The least value of c is when c = b so take c = a + 11 hence, a + (a + 11) + (a + 11) = 72 i.e., a = 50/3 a non integer therefore c is not equal to b so take c = b+1 therefore c = a+12 a + (a + 11) + (a + 12) = 72 i.e., a= 49/3 again a non integer therefore c is not equal to b+1 next take c= b+2 therefore c = a+13 a + (a + 11) + (a + 13) = 72 i.e., a=48/3 = 16 hence, a = 16, b = 27, and c = 29 Answer: D #### D QUESTION:A thief is spotted by a policeman from a distance of 300metres. When the policeman starts the chase, the thief also starts running. If the speed of the thief be 16km/hr and that of the policeman 20km/hr, how far the thief will have run before he is overtaken ? options: A)A)1km B)B)500m C)C)650m D)D)750m E)E)1200m SOLUTION:Relative speed of the policeman = 20-16 = 4 km/hr time taken by policeman to cover 300m = (300/1000)*(1/4) = 3/40 hr In 3/40 hr the thief covers a distance of 48/40 km = 6/5 km = 1200m Answer is E #### E QUESTION:Out of 7 people working on a project, 4 are graduates. If 3 people are selected at random, what is the probability that there is at least one graduate among them? options: A)19/20 B)24/25 C)29/30 D)34/35 E)39/40 SOLUTION:P(no graduates) = 3C3 / 7C3 = 1/35 P(at least one graduate) = 1- 1/35 = 34/35 The answer is D. #### D QUESTION:At a party, everyone shook hands with everybody else. There were 66 handshakes. How many people were at the party? options: A)15 B)18 C)11 D)12 E)19 SOLUTION:D 12 If there are n people, the first person will shake hand with n-1 persons, the second with n-2, the third with n-3, and the (n-1)th person with n-(n-1)=1 person means the last person. Hence, total handshakes are (n-1)+(n-2)+(n-3)+….+3+2+1 Which can be equated using n(n-1)/2=66 Hence, n=12 #### D QUESTION:If x^2 > x^3 > x^1, which of the following could NOT be the value of x? options: A)-0.5 B)-1.2 C)-1/5 D)-2/3 E)-0.1 SOLUTION:x^2 > x^3 > x^1 1)Here we have an even power of a variable (x) that is greater than both a larger odd power of the variable x and a smaller odd power of the variable x. This can be possible only if the base is negative; therefore, the variable, x, must be a negative number. 2) Now if the variable x is negative, the higher power results in a smaller number if x<-1, and a higher power results in a larger number if 0>x>-1. With this information, we know that x is a negative number less than -1; therefore, B (-1.2) is the only option that does not fall within this category. #### B QUESTION:How many bricks, each measuring 125 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? options: A)1280 B)2400 C)5500 D)7400 E)3400 SOLUTION:Number of bricks = Volume Of the wall / Volume of 1 brick = (800 x 600 x 22.5) / (125 x 11.25 x 6) = 1280 ANSWER:A #### A QUESTION:Which of the following CANNOT be a value of 8/(x–8)? options: A)-1 B)-1/2 C)0 D)2 E)8 SOLUTION:The question doesn't ask for the value of x here, but for the possible results of the equation. If 8/(x-8) = 0, then the numerator must be 0. But since the numerator is 8, the fraction can not be equal to 0. The answer is C. #### C QUESTION:What is the remainder when you divide 2^200+2 by 7? options: A)1 B)2 C)3 D)6 E)5 SOLUTION:answer is D. this is very similar to the 32^32^32+2 divided by 7 question. #### D QUESTION:The 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? options: A)15% B)32% C)44% D)62% E)80% SOLUTION:Assume 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 . So overall increase is from 100 to 144 is 44% Answer C #### C QUESTION:Two 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? options: A)26 km/hr B)17 km/hr C)60 km/hr D)77 km/hr E)46 km/hr SOLUTION:Let the speed of the slower train be x m/sec. Then, speed of the train = 2x m/sec. Relative speed = ( x + 2x) = 3x m/sec. (100 + 100)/8 = 3x => x = 25/3. So, speed of the faster train = 50/3 = 50/3 * 18/5 = 60 km/hr. Answer:C #### C QUESTION:What is the units digit of (3^5)(4^13)? options: A)2 B)4 C)6 D)7 E)8 SOLUTION:-> The ones place of (~3)^n repeats after 4 times like 39713. The ones place of (~4)^n repeats after 2 times like 464. Then, 3^5=3^4*1+13^1., 4^13=4^2*6+1=4^1=~4 which is (3^5)(4^13) (3^1)(~4)=(~3)(~4)=~2. Therefore, the answer is A. #### A QUESTION:A delegation of 5 members has to be formed from 3 ladies and 5 gentlemen. In how many ways the delegation can be formed, if 2 particular ladies are always included in the delegation? options: A)20 B)30 C)37 D)40 E)39 SOLUTION:There are three ladies and five gentlemen and a committee of 5 members to be formed. Number of ways such that two ladies are always included in the committee = ⁶C₃ = (6 * 5 * 4)/6 = 20. Answer:A #### A QUESTION:A perfect cube is an integer whose cube root is an integer. For example, 27, 64 and 125 are perfect cubes. If p and q are perfect cubes, which of the following will not necessarily be a perfect cube? options: A)8p B)pq C)pq + 27 D)-p E)(p - q)^6 SOLUTION:A. since p is a perfect cube and 8 is a perfect cube, 8p will be a perfect cube. reject. B. since p is a perfect cube and q is a perfect cube, pq will be a perfect cube. reject. C. Hold. D. since p is a perfect cube, -p will also be a perfect cube. reject. E. (p-q)^6, is a perfect cube, so reject. By elimination C is the answer. Check say p = 1, q=8, then 8+27 = 35 --> not a perfect cube. ANSWER:C #### C QUESTION:36 men can complete a piece of work in 18 days. In how many days will 27 men complete the same work? options: A)26 B)22 C)12 D)24 E)20 SOLUTION:Explanation: Let the required number of days be x More men, less days (indirect proportion) Hence we can write as (men) 36 : 27 :: x : 18 ⇒36×18=27 × x ⇒12×18=9 × x ⇒12×2=x ⇒x=24 Answer: Option D #### D QUESTION:In each term of a sequence, 3 is added to get the next term. If the first term is 6, what is the 64th term? options: A) 192 B) 154 C) 134 D) 174 E) 120 SOLUTION:1rst term + 63 terms = 6 + 3+3+3+3+3+3+3+...+3 (63 times) 6 + (3 x 63) = 3 + 189 = 192 Answer A #### A QUESTION:A 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? options: A)767 m B)240 m C)187 m D)176 m E)186 m SOLUTION:Speed = 54 * 5/18 = 15 m/sec. Length of the train = 15 * 20 = 300 m. Let the length of the platform be x m . Then, (x + 300)/36 = 15 => x = 240 m. Answer:B #### B QUESTION:Find the invalid no.from the following series 3, 7, 15, 27, 63, 127, 255 options: A)18 B)19 C)27 D)29 E)31 SOLUTION:Go on multiplying the number by 2 and adding 1 to it to get the next number.So, 27 is wrong. C #### C QUESTION:If the speed of the boat in still water is 12km/hr and the speed of the stream is 5km/hr. Find the time taken to travel 34kms down stream. options: A)4 hrs. B)1 hrs. C)3 hrs. D)2 hrs. E)5 hrs. SOLUTION:DS =speed of the boat + speed of the stream 5+12 =17km/hr. Time taken to cover 34km down stream =34/17 =2hrs. Answer : D #### D QUESTION:How many numbers amongst the numbers 5 to 30 are there which are exactly divisible by 6 but not by 4? options: A)Nil B)1 C)2 D)3 E)More than 3 SOLUTION:6,12,18,24,30 are divisible by 6. 12, 24 are divisible by 4 also. So there are 3 numbers exactly divisible by 6 but not by 4 ANSWER:D #### D QUESTION:In a group of ducks and cows, the total number of legs are 32 more than twice the number of heads. Find the total number of cows. options: A)12 B)14 C)16 D)18 E)20 SOLUTION:Let the number of ducks be d and number of cows be c Then, total number of legs = 2d + 4c = 2(d + 2c) total number of heads = c + d Given that total number of legs are 32 more than twice the number of heads => 2(d + 2c) = 32 + 2(c + d) => d + 2c = 16 + c + d => 2c = 16 + c => c = 16 i.e., total number of cows = 16 Answer is C. #### C QUESTION:A train travelling at a speed of 75 mph enters a tunnel 31/2 miles long. The train is 1/4 mile long. How long does it take for the train to pass through the tunnel from the moment the front enters to the moment the rear emerges? options: A)2.5 min B)3 min C)3.2 min D)3.5 min E)4 min SOLUTION:Total distance = (7/2 + 1/4) miles = 15/4 miles time taken = 15/4*75 hrs =1/20 hrs = 3 min ANSWER B #### B QUESTION:For 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 [1.988] = 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 ? options: A)0 B)1 C)27 D)54 E)Cannot be determined SOLUTION:It cannot be determined.As we do not know the actual value of K. however minimum value of k is sq.rt of 3^2*4^2*5^2 = 60 * any integer K=[lCM of 80 and 45] * (any integer) for value of k(60) * any integer unit value will be always zero . A #### A QUESTION:24 oz of juice P and 25 oz of juice V are mixed to make smothies M and Y . The ratio of p to V in smothie M is 4 is to 1 and that in Y is 1is to 5.How many ounces of juice P are contained in the smothie M? options: A)5 B)10 C)15 D)20 E)25 SOLUTION:The ratio of p to V in smothie M is 4 is to 1 and that in Y is 1is to 5.p1 + p2 = 24 v1 + v2 = 25 p1 = 4v1 p2 = v2/5 4v1 + v2/5 = 24 v1 + v2 = 25 4v2 - v2/5 = 76 19v2/5 = 76 => v2 = 20 => v1 = 5 => p1 = 20 Answer - D #### D QUESTION:Tim and Élan are 120 miles away from one another. They are starting to move towards each other simultaneously, Tim at a speed of 10 Mph and Élan at a speed of 5 Mph. If every hour they double their speeds, what is the distance that Tim will pass until he meets Élan? options: A)30 miles. B)35 miles. C)45 miles. D)60 miles. E)80 miles. SOLUTION:Tim and Elan will meet at the same time while their ratio of speed is 2:1 respectively.So their individual distance traveled ratio will be same. Plugging in the answer choice Only Answer Choice E meet the 2:1(Tim:Elan=80:40) ratio of maintaining total distance traveled 120 miles So Correct answer E #### E QUESTION:A fill pipe can fill 1/3 of cistern in 20 minutes in how many minutes, it can fill 3/4 of the cistern? options: A)15 min B)45 min C)25 min D)40 min E)50 min SOLUTION:1/3 of the cistern can fill in 20 min 3/4 of the cistern can fill in = 20*3*3/4 = 45min Answer is B #### B QUESTION:A 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? options: A)7000 B)7029 C)7290 D)7010 E)7102 SOLUTION:Let the sum be Rs. x. (x * 18 * 2)/100 - (x * 12 * 2)/100 = 840 => 36x/100 - 24x/100 =840 => 12x/100 = 840 => x = 7000. Answer:A #### A QUESTION:For a lottery, three numbers are drawn, each from 1 to 40. A player can win if the product of his or her three numbers is odd. Initially, the same number may be picked up to three times. Later, the rules are changed so that each number may only be picked once. Approximately how much does this reduce a person's probability of winning? options: A)01 B)025 C)115 D)125 E)5 SOLUTION:(1/2)∗(1/2)∗(1/2))−((1/2)∗(19/39)∗(18/38))((1/2)∗(1/2)∗(1/2))−((1/2)∗(19/39)∗(18/38)) ((1/8)−(9/78))((1/8)−(9/78)) (0.125−approx.0.1111)(0.125−approx.0.1111) Approximately 0.010.01 ANSWER :A #### A QUESTION:In 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? options: A)16% B)25% C)33% D)40% E)52% SOLUTION:Total employed people 12%, out of which 80 are employed males, hence 40% are employed females. (employed females)/(total employed people)=40/120=1/3=33% Answer: C. #### C QUESTION:Three people (1 couple and 1 single) are seated at random in a row of 4 chairs. What is the probability that the couple does not sit together? options: A)3/7 B)1/2 C)2/5 D)3/4 E)5/12 SOLUTION:The total number of arrangements of 3 people is 4*3*2 = 24 Let's think of the couple as a single unit. The number of arrangements when the couple sits together is 3*2*2 = 12. Note that we multiply by 2 because the couple can switch places with each other. The number of ways the couple won't sit together is 24 - 12 = 12 P(couple won't sit together) = 12/24 = 1/2 The answer is B. #### B QUESTION:f a < b < c , which of the following must be true? (I) a < b^2 (II) b − a < c (III) a^2 < b^2 < c^2 options: A)None B)I only C)II only D)III only E)II and III SOLUTION:(I) a < b^2. Not necessarily true fractions: try a=1/3 and b=1/2. (II) b − a < c. Not necessarily true: try a=-1, b=0, and c=1. (III) a^2 < b^2 < c^2. Not necessarily true: try a=-1, b=0, and c=1. None of the options must be true. Answer: A. #### A QUESTION:The present population of a town is 4032. Population increase rate is 20% p.a. Find the population of town before 2 years? options: A)2500 B)2800 C)3500 D)3600 E)2050 SOLUTION:P = 4032 R = 20% Required population of town = P/(1 + R/100)^T = 4032/(1 + 20/100)^2 = 4032/(6/5)^2 = 2800(approximately) Answer is B #### B QUESTION:In a partnership between A, B and C. A's capital is Rs.5000. If his share of a profit of Rs.800 is Rs.300 and C's share is Rs.130, what is B's capital? options: A)19878 B)12798 C)6166 D)11750 E)22073 SOLUTION:300 + 130 = 430 800 - 430 = 370 300 ---- 5000 370 ---- ? => 6166 Answer: C #### C QUESTION:What least number must be subtracted from 9679 so that the remaining number is divisible by 15? options: A)3 B)1 C)16 D)4 E)15 SOLUTION:On dividing 9679 by 15, we get remainder = 4. Required number be subtracted = 4 ANSWER:D #### D QUESTION:If e is an integer, what is the greatest possible value for e that would still make the following statement true: 11*10^e < 1/10 ? options: A) –4 B) –3 C) –2 D) –1 E) 0 SOLUTION:Just putting values, the LHS becomes e=0 --> 11 e=-1 --> 11/10 e=-2 --> 11/100 e=-3 --> 11/1000 Anything lower will be smaller than 11/1000. e=-2, equality does not hold but it does for e=-3. Answer is B. #### B QUESTION:A man took a loan at rate of 12% per annum simple interest. After 3 years he had to pay 9000 interest. The principal amount borrowed by him was. options: A)Rs 14000 B)Rs 25000 C)Rs 16000 D)Rs 17000 E)None of these SOLUTION:Explanation: S.I.=P∗R∗T/100 =>P=S.I.∗100/R∗T =>P=9000∗100/12∗3=Rs25000 Option B #### B QUESTION:A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long? options: A)40 sec B)65 sec C)18 sec D)16 sec E)17 sec SOLUTION:Speed = 45 * 5/18 = 25/2 m/sec Total distance covered = 360 + 140 = 500 m Required time = 500 * 2/25 = 40 sec Answer:A #### A QUESTION:In the simple subtraction problem below, some single digits (not necessarily distinct) are replaced by letters. Find the value of 2*A + 2*B + 4*C*D. A9C5 - 2B79 -------------- 633D options: A)50 B)52 C)66 D)48 E)46 SOLUTION:A9C5 -2B79 ---------- 6336 since,15-9=6. from there,D=6 and solving all,we get A=8,B=5,C=1. So 2*8+2*5+4*1*6=50 ANSWER:A #### A QUESTION:If a : b = 5 : 9 and b : c = 4: 7, find a : b : c options: A)63:36:20 B)36:20:63 C)20:63:36 D)20:36:63 E)None of them SOLUTION:a:b=5:9 and b:c=4:7= (4X9/4): (7x9/4) = 9:63/4 a:b:c = 5:9:63/4 =20:36:63. Answer is D. #### D QUESTION:What is the perimeter of a square field whose diagonal is 8√2? options: A)82 m B)32 m C)27 m D)26 m E)76 m SOLUTION:4a = 32 m Answer: B #### B QUESTION:The average weight of A, B and C is 30 kg. If the average weight of A and B be 25 kg and that of B and C be 28 kg, then the weight of B is: options: A)14 kg B)15 kg C)18 kg D)19 kg E)16 kg SOLUTION:EXPLANATION Let A, B, C represent their respective weights. Then, we have: A + B + C = (30 x 3) = 90 …. (i) A + B = (25 x 2) = 50 …. (ii) B + C = (28 x 2) = 56 ….(iii) Adding (ii) and (iii), we get: A + 2B + C = 106 …. (iv) Subtracting (i) from (iv), we get : B = 16. B’s weight = 16 kg. Answer E #### E QUESTION:A girl goes to her school from her house at a speed of 6km/hr and returns at a speed of 4 km/hr. If she takes 10 hours in going and coming back, the distance between her school and house is options: A)12 kms B)16 kms C)20 kms D)24 kms E)None of above SOLUTION:Let distance be D 10 = D/4 + D/6 Answer : D #### D QUESTION:38 69 22 43 31 47 13 82 Which of the following numbers is greater than three fourths of the numbers but less than one fourth of the numbers in the list above? options: A)56 B)69 C)70 D)71 E)73 SOLUTION:Arrange the numbers in ascending order: 13, 22, 31, 38, 43, 47, 69, 82 (Just cross check the count to ensure that you didn't miss anything) How many numbers do we see? 8, alright. What's (1/4)8? 2. What's (3/4)8? 6. We're asked to find a number that are greater than 6 numbers in the list AND smaller than the remaining two. 13, 22, 31, 38, 43, 47, 69, 82 13, 22, 31, 38, 43, 47: Find a number greater than any of these numbers. 69, 82: Find a number smaller than any of these numbers. Only 56 fits the description. Ans:A #### A QUESTION:A 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 49 grams of protein daily, how many grams of food X are in the mixture? options: A)160 B)180 C)200 D)220 E)240 SOLUTION:Let x be the number of grams of food X in the mixture. 0.1x + 0.15(400-x) = 49 0.05x = 11 x = 220 The answer is D. #### D QUESTION:For any positive integer n, the sum of the first n positive integers equals n(n+1)/2. What is the sum z of all the even integers between 99 and 301? options: A)10,100 B)20,200 C)22,650 D)40,200 E)45,150 SOLUTION:I would solve it in a different way. First of all, total number of even integers between 99 and 301 are, (301-99)/2 = 202/2=101 Average = (301+99)/2 = 400/2 = 200 Sum z= Average*total count = 200*101 = 20,200 Answer is B #### B QUESTION:P = {105, 106, 107, 108, 109, x} Set P above consists of 6 integers. For what value of x are the mode, the median and the average equal? options: A)105 B)106 C)107 D)108 E)109 SOLUTION:Mode of a set is the number with max frequency. Median for an even numbered set is the average of middle terms. Average or mean is the sum of the set/No. of elements in the set. Going from the answer choices, if we use 107 as the missing number. The set becomes {105, 106, 107, 107, 108, 109} Now the mode, median and mean are all same, 107 ANS (Option C) #### C QUESTION:A man can swim in still water at 7.5 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is? options: A)1.7 B)1.4 C)1.1 D)1.5 E)2.5 SOLUTION:M = 7.5 S = x DS = 7.5 + x US = 7.5 + x 7.5 + x = (7.5 - x)2 7.5 + x = 15 -2x 3x = 7.5 x = 2.5 Answer:E #### E QUESTION:In 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? options: A)70 B)52 C)62 D)59 E)50 SOLUTION:total number of players= 16+12+18+13= 59 Answer is D #### D QUESTION:If the sum of 5 consecutive integers is y, which of the following must be true? I. y is an even number II. y is an odd number III. y is a multiple of 5 options: A) I only B) II only C) III and II only D) I and III E) III only SOLUTION:I. 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. II. Same as above. This need not be always true. III. Say, the first number is p. Then the sum of the five numbers = p + (p+1) + (p+2)...... + (p+4) = 5p + 10 = 5 (p+2) => divisible by 5. There this must be true in all cases. Therefore E is the answer. #### E QUESTION:210 school 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? options: A)25 B)40 C)50 D)60 E)75 SOLUTION:We 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. So, 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. #### B QUESTION:What is the greatest of 3 consecutive integers whose sum is 30 ? options: A)11 B)7 C)8 D)9 E)5 SOLUTION:The sum of three consecutive integers can be written as n + (n + 1) + (n + 2) = 3n + 3 If the sum is 24, we need to solve the equation 3n + 3 = 30; => 3n = 27; => n = 9 The greatest of the three numbers is therefore 9 + 2 = 11 Answer: A #### A QUESTION:A 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? options: A)6%. B)7.5%. C)9.2%. D)10.5%. E)14%. SOLUTION:Denominator: 340+10+3.2+6.8=360 Numerator: 340(1-.80-.06)+3.2 340(0.14)+3.2 47.6+3.2 50.8 Ratio: 50.8/360=0.14 Answer: E #### E QUESTION:If X is to be chosen at random from the integers between 1 to 6, inclusive, and Y is to be chosen at random from the integers between 7 and 11, inclusive, what is the probability that X + Y will be even? options: A)1/2 B)2/3 C)3/4 D)4/5 E)5/6 SOLUTION:X+Y will be even if X and Y are both even or both odd. P(X and Y are both even) = 3/6*2/5 = 1/5 P(X and Y are both odd) = 3/6*3/5 = 3/10 P(X+Y is even) = 1/5 + 3/10 = 1/2 The answer is A. #### A QUESTION:A crate measures 4 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? options: A)2 B)4 C)6 D)8 E)12 SOLUTION:To fit the cylinder with largest radius inside this cuboid , we should make the base of the crate as wide as possible so we will take the base as 12 feet by 8 feet Now since the limiting number in the base is 8 feet; therefore a cylinder {we can visualise that a cylinder's width is its diameter } can only fit inside the crate if it is 8 feet or less. Therefore the radius of the cylinder will become Diameter 2===>8/2=4 Diameter ANSWER:D #### D <<<Examples ends QUESTION:A sum of money deposited at C.I. amounts to Rs.3000 in 3 years and to Rs.3600 in 4 years. Find the rate percent? options: A)25% B)5% C)10% D)15% E)20% SOLUTION:3000 --- 600 100 --- ? => 20% Answer: E #### E

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:John had a stock of 700 books in his bookshop. He sold 50 on Monday, 82 on Tuesday, 60 on Wednesday, 48 on Thursday and 40 on Friday. What percentage of the books were not sold? options: A)26.5% B)50% C)46.5% D)56.5% E)60% SOLUTION:Let N be the total number of books sold. Hence N = 50 + 82 + 64 + 78 + 135 = 280 Let M be the books NOT sold M = 700 - N = 700 - 280 = 420 Percentage Books not sold / total number of books = 420/700= 0.60 = 60% correct answer E #### E QUESTION:The difference between a number and its three-fifths is 50.What is the number? options: A)75 B)100 C)125 D)Cannot be determined E)None of these SOLUTION:Suppose the number is N. Then N - 3⁄5N = 50 ⇒ 2N⁄5 = 50 ∴ N=50×52=125 Answer.C #### C QUESTION:In a joint business, the capital of A, B and C were Rs. 45000, Rs. 30000 and Rs. 22500 respectively. A withdrew half of his capital after 4 months. After 9 months of this withdrawal, there was a total profit of Rs. 28400. Find the A share of profit? options: A)10600 B)10400 C)10200 D)12200 E)14200 SOLUTION:Given A=45000 B=30000 C=22500 A:B:C= 450:300:225 As A withdrew its half of capital after 4 months,it can withdraw 22500 rupees But before 4 months, it is 45000 only and the profit is calculated after withdrwal it is almost 9+4=13 months.For that 9 months, the capital for A is half of its original capital, So A= 450*4+ 225*9= 1800+2025= 3825 Similarly, B= 300*13=3900 Similarly,C= 225*13= 2925 Therefore, ratio of A:B:C= 3825: 3900 : 2925= 51:52:39 A's share=51/142(28400)=10200 ANSWER:C #### C QUESTION:An enterprising businessman earns an income of Re 5 on the first day of his business. On every subsequent day, he earns an income which is just thrice of that made on the previous day. On the 10th day of business, he earns an income of: options: A)21 B)22 C)20 D)45 E)30 SOLUTION:2nd day he earns = 3(2 – 5) 3rd day he earns = 3(3 – 5) On 20th day he earns 3(20 -5) = 45 rupees ANSWER:D #### D QUESTION:if log 2 = 0.30103, the number of digits in 2128 is options: A)22 B)39 C)88 D)28 E)11 SOLUTION:Explanation: log(2128) = 128log(2) = 128 × 0.30103 ≈ 38.4 ie, its characteristic = 38 Hence, number of digits in 2128 = 38+1 = 39 Answer: Option B #### B QUESTION:A toy store regularly sells all stock at a discount of 10 percent. If an additional 10 percent were deducted from the discount price during a special sale, what would be the lowest possible price of a toy costing $10 before any discount? options: A) $7.20 B) $8.00 C) $8.10 D) $8.27 E) $9.00 SOLUTION:sale price = (original price - 10% decrease) - 10% decrease price = [10 * (90/100)] * (90/100) = 10 * (.90) * (.90) = 9 * .90 = 8.10 The answer is C. #### C QUESTION:Find large number from below question The difference of two numbers is 1395. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder options: A)1245 B)1345 C)1455 D)1577 E)1671 SOLUTION:Let the smaller number be x. Then larger number = (x + 1395). x + 1395 = 6x + 15 5x = 1380 x = 276 Large number = 276+1395 = 1671 E #### E QUESTION:A 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. 63 more. The sum is: A. Rs. 2,400 B. Rs. 2,100 C. Rs. 2,200 D.Rs. 2,480 options: A)2000 B)2100 C)2200 D)2300 E)2400 SOLUTION:1 percent for 3 years= 63 1 percent for 1 year = 21 => 100 percent = 2100 ANSWER:B #### B QUESTION:There are 9 teams in a certain league and each team plays each of the other teams exactly once. What is the total number of games played? options: A)24 B)25 C)28 D)32 E)36 SOLUTION:9C2 = 36 The answer is E #### E QUESTION:The maximum number of students among them 100 pens and 50 pencils can be distributed in such a way that each student get the same number of pens and same number of pencils? options: A)50 B)75 C)69 D)79 E)82 SOLUTION:number of pens = 100 number of pencils = 50 Required number of students = H.C.F. of 100 and 50 = 50 Answer is A #### A QUESTION:A sum of Rs.48000 is invested at a compound interest for three years, the rate of interest being 10% p.a., 20% p.a. and 25% p.a. for the 1st, 2nd and the 3rd years respectively. Find the interest received at the end of the three years. options: A)28880 B)31200 C)28770 D)29990 E)12770 SOLUTION:Let A be the amount received at the end of the three years. A = 48000[1 + 10/100][1 + 20/100][1 + 25/100] A = (48000 * 11 * 6 * 5)/(10 * 5 * 4) A = Rs.79200 So the interest = 79200 - 48000 = Rs.31200 Answer: B #### B QUESTION:In what ratio should a variety of Rice costing Rs. 20 per kg be mixed with another variety of Rice costing Rs. 31.50 per kg to obtain a mixture costing Rs. 23.75 per kg? options: A)16 : 30 B)30 : 14 C)16 : 31 D)31 : 15 E)15 : 31 SOLUTION:Let us say the ratio of the quantities of cheaper and dearer varieties = x : y By the rule of allegation, x/y = (31.50 - 23.75) / (23.75 - 20) = 31/15 ANSWER:D #### D QUESTION:A basket contains 10 apples and 20 oranges out of which 3 apples and 5 oranges are defective. If we choose two fruits at random, what is the probability that either both are oranges or both are non defective? options: A)316/439 B)316/438 C)316/435 D)316/299 E)316/199 SOLUTION:Let A be the event of getting two oranges and B be the event of getting two non-defective fruits. and be the event of getting two non-defective oranges Answer: C) 316/435 #### C QUESTION:From a group of 16 astronauts that includes 7 people with previous experience in space flight, a 3-person crew is to be selected so that exactly 1 person in the crew has previous experience in space flight. How many different crews of this type are possible? options: A)270 B)252 C)272 D)292 E)285 SOLUTION:number of astronauts with previous experience = 7 Remaining =9 we need to pick exactly one from the first group and 2 from the second group (7C1)*(9C2) =7*36= 252 Answer : B #### B QUESTION:The cost price of an article is 70% of the marked price. Calculate the gain percent after allowing a discount of 10%. options: A)13.6% B)28.6% C)35.6% D)42.3% E)none SOLUTION:Sol. Let marked price = Rs. 100. Then, C.P. = Rs. 70. S.P = Rs. 90. ∴ Gain % = [20/70 * 100]% = 28.6%. Answer B #### B QUESTION:Excluding stoppages,the speed of the bus is 54kmph and including stoppages,it is 27kmph. For how many minutes does the bus stop per hr options: A)12 min B)11 min C)13 min D)20 min E)30 min SOLUTION:Due to stoppages,it covers 27km less. time taken to cover 27 km is [27/54 *60] min = 30min Answer is E. #### E QUESTION:A can do a job in 18 days and B can do it in 30 days. A and B working together will finish twice the amount of work in ------- days? options: A)22 1/8 B)22 1/2 C)22 1/1 D)22 1/5 E)22 1/9 SOLUTION:1/18 + 1/30 = 8/90 = 4/45 45/4 = 11 ¼ *2 = 22 1/2 days Answer:B #### B QUESTION:Calculate the circumference of a circular field whose radius is 6 centimeters. options: A)2 π cm B)1 π cm C)15 π cm D)12 π cm E)19 π cm SOLUTION:Circumference C is given by C = 2πr = 2π*6 = 12 π cm Answer: D #### D QUESTION:A train passes a platform in 34 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 options: A)280 meter B)240 meter C)210 meter D)200 meter E)None of these SOLUTION:Explanation: Speed of the train = 54 km/hr = (54×10)/34 m/s = 15 m/s Length of the train = speed × time taken to cross the man = 15×20 = 300 m Let the length of the platform = L Time taken to cross the platform = (300+L)/15 => (300+L)/15 = 34 => 300+L = 15×34 = 510 => L = 510-300 = 210 meter Answer: Option C #### C QUESTION:A and B together invested Rs. 20,000 in a business. At the end of the year, out of total profit is Rs. 5,000 B's share was Rs. 2000. A's investment was options: A)s. 4,500 B)s. 8,250 C)s. 10,500 D)s. 11,250 E)s. 12,000 SOLUTION:A+B=20000 total profit=5000 5000-2000=3000 3000;2000=3:2 then 3*20000/5=12000 ANSWER:E #### E QUESTION:Find the missing in the series: 70, 56, 45, 41,___ options: A)22 B)287 C)2679 D)276 E)2771 SOLUTION:Answer:D #### D QUESTION:If P gets 25% more than Q, then by what percent does Q get less than P? options: A)60% B)22% C)12% D)20% E)13% SOLUTION:Let Q get 1 unit. 25% of 1 unit = 1/4 = 0.25 P gets (1 + 0.25) i.e., 1.25 units. Difference = (1.25 - 1) = 0.25 Required percentage = 0.25/1.25 * 100 = 1/5 * 100 = 20% Answer: C #### C QUESTION:How long will it take for a sum of money to grow from Rs.1000 to Rs.5,000, if it is invested at 20% p.a simple interest? options: A)8 years B)20 years C)72 years D)56 years E)None SOLUTION:In this case, Rs. 1000 has become Rs.5000. Therefore, the interest earned = 5000 – 1000 =4000 Interest for Rs 1000 @ 20% for 1 year = 200 200 - 1 4000 - ? => 20 years Answer : B #### B QUESTION:If a(a - 8) = 9 and b(b -8) = 9, where a ≠ b, then a + b = options: A)−48 B)−2 C)8 D)9 E)48 SOLUTION:i.e. if a = -1 then b = 9 or if a =9 then b = -1 But in each case a+b = -1+9= 8 Answer: option C #### C QUESTION:36 men can complete a piece of work in 18 days. In how many days will 27 men complete the same work? options: A)12 B)18 C)22 D)24 E)none of these SOLUTION:Let the required number of days be x. Less men, More days (Indirect Proportion) 27 : 36 :: 18 : x 27 * x = 36 * 18 x = (36 * 18)/27 x = 24. Answer is D. #### D QUESTION:The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is? options: A)38 B)2767 C)245 D)277 E)232 SOLUTION:Speed = [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. Answer:C #### C QUESTION:Find the smallest number which should be multiplied with 520 to make it a perfect square options: A)337 B)297 C)266 D)116 E)130 SOLUTION:Explanation: 520 = 26 * 20 = 2 * 13 * 22 * 5 = 23 * 13 * 5 Required smallest number = 2 * 13 * 5 = 130 130 is the smallest number which should be multiplied with 520 to make it a perfect square. Answer: E #### E QUESTION:Walking 4/3 of his usual rate, a boy reaches his school 4 min early. Find his usual time to reach the school? options: A)22 B)16 C)27 D)28 E)20 SOLUTION:Speed Ratio = 1:4/3 = 3:4 Time Ratio = 4:3 1 -------- 4 4 --------- ? 16 m.Answer:B #### B QUESTION:Mice can multiply very fast. Adult mice can give birth once every month, and baby mice grow into adult mice in just two months after they are born. If you would buy a baby mouse just after it was born, how many mice would you have in 10 months? options: A)1 B)2 C)3 D)4 E)5 SOLUTION:One. You cannot have more mice if you start with one! Answer A #### A QUESTION:If a certain coin is flipped, the probability that the coin will land heads is 1/2. If the coin is flipped 6 times, what is the probability that it will land heads up on the first 4 flips but not on the last 2 flips? options: A)1/8 B)1/16 C)1/32 D)1/64 E)1/128 SOLUTION:P(HHHHTT) = 1/2*1/2*1/2*1/2*1/2*1/2 = 1/64 The answer is D. #### D QUESTION:The salary of A, B, C, D, E is Rs. 8000, Rs. 5000, Rs. 16000, Rs. 7000, Rs. 9000 per month respectively, then the average salary of A, B, C, D, and E per month is options: A)Rs. 7000 B)Rs. 8000 C)Rs. 8500 D)Rs. 9000 E)None SOLUTION:Answer Average salary = 8000 + 5000 + 16000 + 7000 + 9000 / 5 = Rs. 9000 Correct Option: D #### D QUESTION:A starts business with Rs.3500 and after 5 months, B joins with A as his partner. After a year, the profit is divided in the ratio 2 : 3. What is B’s contribution in the Capital ? options: A)24887 B)20778 C)23788 D)9000 E)2811 SOLUTION:Explanation: A invested Rs.3500 for 12 months. Let B joined with investment x. And he invested for 12 - 5 = 7 months. So there profit ratio = (3500 × 12) : (7x) = 2 : 3 ⇒ x = 9000 Answer: D #### D QUESTION:A can do a job in 30days and B in 40days. If they work on it together for 10 days, then the fraction of the work that is left is? options: A)2/11 B)3/13 C)5/12 D)7/10 E)6/15 SOLUTION:A's 1 day work = 1/30 B's 1day work = 1/40 A+B 1day work = 1/30 + 1/40 = 7/120 A+B 4days work = 7/120*10 = 7/12 Remaining work = 1 - 7/12 = 5/12 Answer is C #### C QUESTION:In what time will a train 100 m long cross an electric pole, it its speed be 144 km/hr? options: A)2.5 sec B)4.25 sec C)5 sec D)12.5 sec E)12 sec SOLUTION:Speed = 144 * 5/18 = 40 m/sec Time taken = 100/40 = 2.5 sec. ANSWER:A #### A QUESTION:Today is Monday. After 61 days, it will be: options: A)SUNDAY B)SATURSDAY C)FRIDAY D)THURSDAY E)MONDAY SOLUTION:Each day of the week is repeated after 7 days. So, after 63 days, it will be Monday. After 61 days, it will be Saturday. Answer: Option B #### B QUESTION:Find the value of 3 + 2 • (8 – 3) options: A)(a) 25 B)(b) 13 C)(c) 17 D)(d) 24 E)(e) 15 SOLUTION:3 + 2 • (8 – 3) = 3 + 2 (5) = 3 + 2 × 5 = 3 + 10 = 13 Answer: (D) #### D QUESTION:Mr. Das decided to walk down the escalator of a mall. He found that if he walks down 26 steps, he requires 30seconds to reach the bottom. However, if he steps down 34 stair she would only require 18 seconds to get to the bottom. If the time is measured from the moment the top step begins to descend to the time he steps off the last step at the bottom, find out the height of the stair way insteps? options: A)5 B)6 C)7 D)8 E)9 SOLUTION:here when he step down 26 steps he has 30 seconds for remaining steps. if he step down 34 stairs he has only 18 sec. 30-18=12 12 secs for 8 steps.. 18 secs for 12 steps. 12+34=46 so ans is 46.. ANSWER:B #### B QUESTION:If i walk with 30 miles/hr i reach 1 hour before and if i walk with 20 miles/hr i reach 1 hour late.Find the distance between 2 points and the exact time of reaching destination is 11 am then find the speed with which it walks. options: A)120 MILES B)130 MILES C)140 MILES D)150 MILES E)160 MILES SOLUTION:LET ORIGINAL SPEED BE V AND TIME TAKEN BE T... AS DISTANCE BETWEEN TWO POINTS IS CONSTANT, 30*(T-1)=20*(T+1)=V*T HENCE, V=24MILE/HR T=5 HRS DISTANCE BETWEEN TWO POINTS IS 120 MILES ANSWER:A #### A QUESTION:If a is an odd integer and b is an even integer which of the following must be an integer : options: A)a/b B)ab C)2a+b D)2(a+b) E)option B C and D SOLUTION:a= odd = e.g 3 b=even = e.g 6 A. odd/even for example 3/6 = 0.5 no even no odd B. odd * even = 3 * 6 = 18 even C. 2*odd + even = even + even even D. 2(even + odd) = 2(odd) even Hence E it is. #### E QUESTION:a, b, c, d, and e are five consecutive numbers in increasing order of size. Deleting one of the five numbers from the set decreased the sum of the remaining numbers in the set by 20%. Which one of the following numbers Q was deleted? options: A) a B) b C) c D) d E) e SOLUTION:a+b+c+d+e => 1+2+3+4+5=15 Q=20%*15= 3 =>C #### C QUESTION:The sum of 33 consecutive integers is 3333. What is the greatest integer in the set? options: A)113 B)115 C)117 D)119 E)121 SOLUTION:Let x be the first integer in the set, then x+32 is the largest integer. The sum is: x+(x+1)+(x+2)+...+(x+32) = 33x + 32*33/2 = 33(x+16) Then x+16=101 x=85 The largest integer in the set is 85+32=117 The answer is C. #### C QUESTION:John walking at 4 Kmph reaches his office 8 minutes late. If he walks at 6 Kmph, he reaches there 9 minutes earlier. How far is the office from his house? options: A)3 2/5 Km B)3 1/5 Km C)4 1/5 Km D)5 1/5 Km E)None SOLUTION:Formula = S1*S2/S2-S1 * T1+T2/60 = 4*6/2 * 17/6 = 24/2 * 17/60 = 17/5 = 3 2/5 Km A #### A QUESTION:A box contains nine slips that are each labeled with one number: 1, 2, 3, 5, 8, 13, 21, and 55. Two of the slips are drawn at random from the box without replacement. What is the probability that the sum of the numbers on the two slips is equal to one of the numbers left in the box? options: A)7/72 B)1/6 C)7/36 D)5/28 E)21/36 SOLUTION:Probability = No: of desired outcomes / Total No: of outcomes. You are picking two slips out of 8 slips. So Total No: of outcomes = 8C2 = 28 Desired outcome : sum of the numbers on the two slips is equal to one of the numbers left in the box. How many such outcomes are there? If you look at the numbers closely, you will see that the following pair of numbers will give you the desired outcome. (1,2) (2,3) (3,5) (5,8) (8,13) . There are 5 such pairs. If the two numbers which I pick is from any of these 5 pairs, then I get my desired outcome. So No: of desired outcomes = 5 Probability = 5/28 Answer :D #### D QUESTION:What is the remainder when 14,451 × 15,654 × 16,783 is divided by 5? options: A)1 B)3 C)2 D)4 E)5 SOLUTION:Only the unit's digit of the product will decide the remainder when divided by 5. Hence, 1*4*3= will give units digit as 2 So, whatever be the number, if it ends in 2, the remainder after dividing with 5 will be 2. Option C #### C QUESTION:If the sum of the interior angles of a regular polygon measures up to 1080 degrees, then how many sides does the polygon have? options: A)10 B)16 C)8 D)11 E)14 SOLUTION:one of the interior angle = 180 - 360/n sum of the interior angles is = n (180 - 360/n) given n(180 - 360/n)=1080 180n - 360 = 1080 180n = 1440 n = 1440/180 = 8 ANSWER:C #### C QUESTION:A cyclist covers a distance of 750 m in 2 min 30 sec. What is the speed in km/hr of the cyclist? options: A)9km/hr B)7km/hr C)12km/hr D)15km/hr E)18km/hr SOLUTION:Speed = { 750 } m/sec =5 m/sec = { 5 * 18 } km/hr =18km/hr Ans:E #### E QUESTION:The LCM and HCF of two numbers are 100 and 10 respectively. Find the larger of the two numbers if their sum is 110. options: A)100 B)12 C)35 D)466 E)56 SOLUTION:There are 2 approaches in solving this. Methode 1. HCF * LCM = The Actual Number. 100* 10= 1000 So the answer which we are looking for has to be a factor of 1000. So among the options shortlist the answers by eliminating those numbers which is not divisible by 1000. and then take the highest number as the answer as the question asks abt the highest number. answer is A #### A QUESTION:How many integers between 2000 and 3000 that have distinct digits and increase from left to right ? options: A)10 B)20 C)60 D)120 E)600 SOLUTION:Since the numbers must be distinct and increasing from left to right, The only arrangements we could come-up with are: 245_ --> 4 246_ --> 3 247_ --> 2 248_ --> 1 256_ --> 3 257_ --> 2 258_ --> 1 267_ --> 2 268_ --> 1 Number of integers =20 B #### B QUESTION:A sells a bicycle to B and makes a profit of 20%. B sells the same bicycle to C at a profit of 25%. If the final S.P. of the bicycle was Rs. 225, find out the cost price of the bicycle for A. options: A)237 B)126 C)971 D)611 E)150 SOLUTION:Explanation: ANSWER: E #### E QUESTION:5 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 result will not be 2 blue and 2 purple marbles? options: A)4/33 B)(5/36)^2 C)1/2 D)(31/36)^2 E)29/33 SOLUTION:Answer is 29/33. The probability of 2 blue and 2 purple marbles selected is 5C2.4C2/12C4 =4/33. Subtracting the above from 1 we get 29/33 E #### E QUESTION:A lady bought five books namely A,B,C,D,E to distribute her 3 child. How many ways she can distribute books? options: A)3^3 B)3^4 C)3^5 D)3^6 E)3^2 SOLUTION:3*3*3*3*3 3^5 ANSWER:C #### C QUESTION:Which of the following will give a non-integer on taking cube root? options: A)–64 B)–1 C)8 D)9 E)27 SOLUTION:all except 9, square root of 9 is 3 which is an integer but cube root is not an integer so answer is D #### D QUESTION:Let B represent a set of four distinct prime numbers. If the sum of the numbers in B is even and x is a member of B, then what is the least possible value that x can be? options: A)1 B)2 C)3 D)5 E)7 SOLUTION:We are told that B is a set of four distinct prime numbers, and the sum of the numbers in B 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. If 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 B must be odd to yield an even sum. Since all the members of the set must be odd prime numbers, the answer is the smallest odd prime number, which is 3. The correct answer is choice (C). Note:1 is not a prime number. #### C QUESTION:Excepting ‘seldom’ which means – rarely, infrequently and not often, is the antonym. options: A)22 B)278 C)267 D)176 E)971 SOLUTION:Answer:D #### D QUESTION:Two roads XY and YZ of 15 metres and 20 metres length respectively are perpendicular to each other. What is the distance between X & Z by the shortest route? options: A)35 metres B)30 metres C)24 metres D)25 metres E)None of these SOLUTION:XYZ is a right-angled triangle XZ =√15(2)+20(2)=√=625=25m Answer D #### D QUESTION:If 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? options: A)7 days B)3 days C)9 days D)8 days E)2 days SOLUTION:C 9 days C = 1/4 - 1/12 – 1/18 = 1/9 => 9 days #### C QUESTION:The speed of a subway train is represented by the equation z=s^2+2s for all situations where 0≤s≤7, 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 4 seconds? options: A)4 B)9 C)39 D)48 E)63 SOLUTION:Given: z=s^2+2s for 0≤s≤7 z(4) = 4^2 + 2*4 = 24 z(7) = 7^2 + 2*7 = 63 Therefore z(7) - z(3) = 63 - 24 = 39 km/hr Option C #### C QUESTION:Aman 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 ? options: A)2:3:9 B)24:25:36 C)7:6:10 D)12 : 15 : 16 E)None of these SOLUTION:Explanation: Aman : Rakhi : Sagar =(70000×36)=(70000×36) :(105000×30):(105000×30) :(140000×24):(140000×24) =12:15:16=12:15:16. ANSWER IS D #### D QUESTION:The roof of an apartment building is rectangular and its length is 4 times longer than its width. If the area of the roof is 900 feet squared, what is the difference between the length and the width of the roof? options: A)38. B)40. C)42. D)44. E)45. SOLUTION:Let the width= x x*4x=900 x^2= 225 x= 15 Length= 4*15= 60 difference= 60-15= 45 E is the answer #### E QUESTION:There is a 30 % chance of rain and a 70% chance of shine. If it rains there is a 50% chance that Bob will cancel his picnic but if the sun is shining he will definitely have his picnic. What is the chance that Bob will have his picnic? options: A)70 % B)75 % C)80 % D)85 % E)90 % SOLUTION:Chance of no picnic+chance of picnic= 100% ... (i) Chance of picnic=100%-Chance of no picnic ... (ii) Chance of no picnic= 50% of 30%= 15% Therefore, According to (ii), Chance of picnic= 100%-15%= 85%. Answer D #### D QUESTION:Working at their respective constant rates, Paul, Abdul and Adam alone can finish a certain work in 3, 4, and 5 hours respectively. If all three work together to finish the work, what fraction R of the work will be done by Adam? options: A) 1/4 B) 12/47 C) 1/3 D) 5/12 E) 20/47 SOLUTION:Let the total work be 60 units. Pual does 60/3 =20 units of work per hr. abdul does 15 units per hr and adam does 12 units per hr. If all work together they do (20 + 15 + 12) units per hr = 47 units per hr. So the time taken to finish the work = 60/47 hrs. adam will do 60/47 * 12 units of work in 60/47 hr . fraction of work adam does =work done by adam / total work R>( 60/47 *12)/60 =12/47 Answer B #### B QUESTION:The probability that A speaks truth is 15/23 and that of B speaking truth is 17/29. What is the probability that they agree in stating the same fact? options: A)182/395 B)129/289 C)197/353 D)479/667 E)None of these SOLUTION:If both agree stating the same fact, either both of them speak truth of both speak false. Probability = 15/23 * 17/29 + 14/23 * 16/29 = 255/667 + 224/667 = 479/667 ANSWER:D #### D QUESTION:A 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? options: A)267 B)2667 C)200 D)269 E)265 SOLUTION:When the second train leaves Mumbai the first train covers 40 * 1 = 40 km So, the distance between first train and second train is 40 km at 10.00am Time taken by the trains to meet = Distance / relative speed = 40 / (50 -40) = 4 hours So, the two trains meet at 2 p.m. The two trains meet 4 * 50 = 200 km away from Mumbai. Answer:C #### C QUESTION:60 persons like apple. 7 like orange and mango dislike apple. 10 like mango and apple and dislike orange. 4 like all. How many people like apple? options: A)47 B)46 C)54 D)58 E)67 SOLUTION:orange+mango-apple=7 mango+apple-orange=10 apple=60 orange+mango+apple=4 60+10+4-7=67 like apple ANSWER:E #### E <<<Examples ends QUESTION:A 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 1.2 km long? options: A)2 mins 14 sec B)2 mins 34 sec C)162 sec D)244 sec E)2 mins 44 sec SOLUTION:D = 25 * 60 + 1200 = 2700 m T = 2700/60 * 18/5 = 162 sec ANSWER:C #### C

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:An investment of d dollars at k percent simple annual interest yields $600 over a 2 year period. In terms of d, what dollar amount invested at the same rate will yield $2,400 over a 3 year period? options: A)(2d)/3 B)(3d)/4 C)(4d)/3 D)(3d)/2 E)(8d)/3 SOLUTION:600 dollars in 2 years means 300 dollars in 1 year. To get 2400 dollars' it will take 8 years. To get 2400 in 3 years, we need 8/3 times money. Answer is E. #### E QUESTION:Eight children — A, B, C, D, E, F, G and H — are going to sit in eight 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? options: A)600 B)720 C)10080 D)14320 E)14800 SOLUTION:for such questions , we can treat both as one then total person=7.. these 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 ans C #### C QUESTION:There exists exactly one positive value of k such that the line y = kx intersects the parabola y = x2 + x + 4 at exactly one point. Compute the intersection point. options: A)(2,10) B)(5,10) C)(7,10) D)(3,10) E)(1,10) SOLUTION:If the line is tangent, then we must have that x2 + x + 4 = kx has a unique solution in x, or x2 + (1 - k)x + 4 = 0 has a unique solution. Thus, (1 - k)2- 16 = 0, or (1- k) = 4. Therefore, k = -3 or k = 5. Taking k = 5, we have that y = 5x intersects y = x2 + x + 4 when x = 2, and the intersection point is (2, 10) . correct answer A #### A QUESTION:Which of the following options is the possible total number of people in a hall given that the number of people is a multiple of both 4 and 20.? options: A)28 B)60 C)32 D)36 E)44 SOLUTION:the number of people are a multiple of both 7 and 13, so it must be divisible by 7 and 13. using the elimination method look for a number that is both divisible by 7 and 13, of all the options only 60 is divisible by 4 and 20. [ 60/4=15 and 60/20=3] answer :B #### B QUESTION:If x and y are prime numbers such that x > y > 3, then x^2 − y^2 must be divisible by which one of the following numbers? options: A) 3 B) 7 C) 5 D) 9 E) 12 SOLUTION:If x=6 and y=4, then x^2-y^2=20and 20 is divisible only by 5 from the options, thus it must be correct. Answer: C. #### C QUESTION:An article is bought for Rs.700 and sold for Rs.900, find the gain percent? options: A)33 1/8% B)33 8/3% C)28 4/7% D)35 1/3% E)32 1/3% SOLUTION:700 ---- 200 100 ---- ? => 28 4/7% Answer: C #### C QUESTION:In a college, the ratio of the number of boys to girls is 8 : 5. If there are 300 girls, the total number of students in the college is options: A)420 B)520 C)620 D)780 E)820 SOLUTION:Explanation: Let the boy are 8x and Girls are 5x => 5x = 300 => x = 60 Total students = 8x+5x = 13x = 13(60) = 780 Option D #### D QUESTION:A train 410 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long? options: A)40 sec B)50 sec C)44 sec D)49 sec E)60 sec SOLUTION:Speed = 45 * 5/18 = 25/2 m/sec Total distance covered = 410 + 140 = 550 m Required time = 550 * 2/25 = 44 sec Answer:C #### C QUESTION:On flipping 3 coins together what is the outcomes for at least one tail, three tail and three head? options: A)1/7 B)3/8 C)3/11 D)4/13 E)5/8 SOLUTION:Sample space, S = {HHH, HHT, HTH, THH, TTH, THT, HTT, TTT} Favorable outcomes for at least two heads = favorable outcomes for exactly two heads and favorable outcomes for more than two heads = {HHT,HHH,THH,HTH,TTT} 5/8 E #### E QUESTION:A bike covers a certain distance at the speed of 65km/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? options: A)85 km/h B)85.34 km/h C)86.66 km/h D)90.25 km/h E)90.64 km/h SOLUTION:Ans.(C) Sol. Total distance = 65 × 8 = 520 km Now speed = 520/6 = 86.66 km/h #### C QUESTION:Two trains of equal are running on parallel lines in the same direction at 44 km/hr and 36 km/hr. The faster train passes the slower train in 36 sec. The length of each train is? options: A)40 m B)72 m C)80 m D)82 m E)84 m SOLUTION:Let the length of each train be x m. Then, distance covered = 2x m. Relative speed = 44 - 36 = 8 km/hr. = 8 * 5/18 = 20/9 m/sec. 2x/36 = 20/9 => x = 40. ANSWER:A #### A QUESTION:Evaluate 25% of 450 + 45% of 250 options: A)225 B)242 C)252 D)262 E)272 SOLUTION:Explanation: = (25/100) * 450 + (45/100) * 250 = 225 Option A #### A QUESTION:present ages of A and B are in the ratio of 7:5 respectively. 5 years hence, the ratio of their ages will become 15:12 respectively . what A's present age in years? options: A)20 B)7/3 C)15/4 D)21/5 E)20/3 SOLUTION:A and B be 7x years and 5x years respectively (7x+5)/(5x+5)=15/12 4(7x+5)= 5(5x+5) x = 3/5 therefore A's present age : 7x=21/5 years correct answer(D) #### D QUESTION:Of the 150 employees at company X, 80 are full-time, and 100 have worked at company X for at least a year. There are 20 employees at company X who aren’t full-time and haven’t 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? . options: A)20 B)30 C)50 D)80 E)100 SOLUTION:150 employees 80 are full-time 100 have worked at company X for at least a year 20 employees at company X who aren’t full-time and haven’t 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? 150-80=70 employees not full time 70-20= 50 employees not full time who worked over a year 100 employees have worked at company X for at least a year-50 employees not full time who worked over a year = 50 full-time employees of company X have worked at the company for at least a year ANSWER:C #### C QUESTION:Which of the following is closest to 1/6+1/66+1/666 options: A)1/4.5 B)1/7 C)1/5.67 D)1/9 E)1/8 SOLUTION:1/6+1/66+1/666=0.16+0.015+0.0015=0.1765=1/5.665 Answer C #### C QUESTION:A die is tossed. Find the probability of getting a multiple of 2 ? options: A)1/5 B)2/3 C)1/6 D)1/3 E)1/2 SOLUTION:S = {1,2,3,4,5,6} E= event of getting a multiple of 2 = {2,4,6} P(E) = 3/6 = 1/2 Answer is E #### E QUESTION:a goes to place x and b goes to place y. after a travelled 180 km more than b they together meet at a point between xy. they together had their lunch for half an hour. after that a took 2 hrs to reach x and b took 4.5 hrs to reach y. find distance between x and y? options: A)900km B)540km C)720km D)820km E)920km SOLUTION:let speed of A be-------Sa let speed of B be--------Sb let the distance covered by B while going to position XY be-----------x so distance covered by A in same time while going to XY is----------180 +x(it's given in the question) so total distance b/w X and Y is=x+(x+180) while going to position XY :- time taken by A = time taken by B (x+180)/Sa= x/Sb Sa/Sb=(x+180)/x---------------------1 After lunch:- A.C.T(according to question) Sa=x/2 Sb=(x+180)/4.5 dividing Sa/Sb=(x*4.5) / ((x+180)*2)--------------------2 equating equations 1 and 2 9/4 = (x+180)^2 / x^2 now taking square root on both sides we get 3/2 = (x+180) / x x=360 therefore distance between x and y =x+(x+180)=900km ANSWER:A #### A QUESTION:Sangakara and Ponting select batting by using a dice, but dice is biased. So to resolve,Ponting takes out a coin. What is the probability that coin shows correct option? options: A)1/2 B)1/6 C)1/12 D)6/10 E)3/10 SOLUTION:as coin has only two faces then probability must be 1/2 ANSWER:A #### A QUESTION:Two 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 6 sec. What is the length of the fast train? options: A)27 7/6 B)27 7/5 C)277/2 D)300/9 E)27 7/1 SOLUTION:Relative speed = (40 - 20) = 20 km/hr. = 20 * 5/ 18 = 50/9 m/sec. Length of faster train = 50/9 * 6 = 300/9 = 300/9 m. Answer:D #### D QUESTION:You need to climb 10 stairs. At each support, you can walk one stair or you can jump two stairs. In what number alternative ways you'll climb ten stairs? options: A)99 B)79 C)55 D)89 E)66 SOLUTION:D #### D QUESTION:A 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 24 on Wednesday, what would be the value of D calculated on the following Saturday? options: A)3450 B)3860 C)4220 D)4670 E)5040 SOLUTION:On Saturday, the value would be 7*6*5*24 = 5040 The answer is E. #### E QUESTION:A number x is 4 times another number y. The percentage that y is less than x is options: A)12.5% B)75% C)80% D)11% E)1% SOLUTION:Say y=1 and x=4. Then y=1 is less than x=4 by (4-1)/4*100=3/4*100=75%. Answer: B. #### B QUESTION:In one hour, a boat goes 9 km along the stream and 5 km against the stream. The speed of the boat in still water (in km/hr) is: options: A)2 B)4 C)7 D)12 E)15 SOLUTION:Sol. Speed in still water = 1/2 (9+5) kmph = 7 kmph. Answer C #### C QUESTION:There are 7000 people in the particular village , among them 30% are educated and out of these 28% are doing agriculture and out of them 50% are woman's. Then find out the number of woman's who are educated and doing agriculture? options: A)294 B)235 C)350 D)288 E)580 SOLUTION:Total number of people in the village = 7000; out of them 30% educated = 2100; out of them 28% doing agriculture = 588; out of them 50% are woman's = 294. #### A QUESTION:Five 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 four of the carpenters work together at their respective rates ? options: A)11/15 B)3/5 C)11/30 D)47/75 E)5/9 SOLUTION:Farmer A, B, C, and D A's rate: 1/3 job/hour B's rate: 1/4 job/hour C's rate: 1/5 job/hour D's rate: 1/7 job/hour By intuition we know that the three fastest farmers are A B and C. As such (1/3 + 1/4 + 1/5)*(4/5) = ? 47/75 or (D) #### D QUESTION:if price of t.v set is reduced by 25%, then its sale increases by 75%, find net effect on sale value options: A)31 B)32 C)46 D)47 E)48 SOLUTION:- a + b + ((-a)(b)/100) = -25+75+(-25*75)/100 = -25+75-19 =31 ANSWER:A #### A QUESTION:When m is divided by 9, the remainder is 2. When m is divided by 13, the remainder is 3. If 1 < m < 300, what is the greatest possible value of m? options: A)173 B)203 C)233 D)263 E)293 SOLUTION:13*9 = 117 Let's start with 3, and keep adding 13 until we find a number with the form 9k+2. 3, 16, 29 = 9*3+2 The next possible number is 29 + 117 = 146 The next possible number is 146 + 117 = 263 The next possible number would be greater than 300. The answer is D. #### D QUESTION:A right circular cylinder has a height of 21 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? options: A)500(π – 3) B)500(π – 2.5) C)510(π – 1.5) D)500(π – 2) E)500(π – 1) SOLUTION:[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? The square base has sides of sqrt(50) due to the 45-45-90 triangle 21*25*pi - 15*sqrt(50)^2 =510(π – 1.5) C. 510(π – 1.5) #### C QUESTION:Insert the missing number 3, 7, 6, 5, 9, 3, 12, 1, 15, ... options: A)18 B)33 C)-1 D)3 E)-3 SOLUTION:3, 7, 6, 5, 9, 3, 12, 1, 15, ... has two different series 1) 3, 6, 9, 12, 15..... 2) 7, 5, 3, 1, ..... -1 is the next number ANSWER:C #### C QUESTION:(17)3.75 x (17)? = 178 options: A)2.29 B)2.75 C)4.25 D)4.5 E)None of these SOLUTION:Solution let (17)3.75 * (17)x = 178. then, (17)3.5 + x = (17)8. ∴ 3.75 + x = 8 ⇔ x = (8 - 3.75) ⇔ x = 4.25 Answer C #### C QUESTION:Find the smallest number which when divided by 11 and 12 leaves respective remainders of 2 and 3. options: A)131 B)197 C)207 D)219 E)227 SOLUTION:Let 'N' is the smallest number which divided by 11 and 12 leaves respective remainders of 2 and 3. Required number = (LCM of 11 and 12) - (common difference of divisors and remainders) = (132) - (1) = 131. ANSWER:A #### A QUESTION:Find the area of a parallelogram with base 20 cm and height 10 cm? options: A)287 cm2 B)887 cm2 C)200 cm2 D)250 cm2 E)668 cm2 SOLUTION:Area of a parallelogram = base * height = 20 * 10 = 200 cm2 Answer: C #### C QUESTION:Find the curved surface area, if the radius of a cone is 28 m and slant height is 30 m? options: A)2550 B)2640 C)3960 D)4280 E)5490 SOLUTION:Cone curved surface area = Ï€rl 22/7 × 28 × 30 = 88 × 30 = 2640 m(power2) Answer is B. #### B QUESTION:In an examination, a pupil's average marks were 63 per paper. If he had obtained 20 more marks for his Geography paper and 2 more marks for his History paper, his average per paper would have been 65. How many papers were there in the examination ? options: A)12 B)27 C)26 D)11 E)22 SOLUTION:Let the number of papers be x. Then, 63x + 20 + 2 = 65x or 2x = 22 or x = 11. Answer: D #### D QUESTION:A train 150 m long running at 72 kmph crosses a platform in 25 sec. What is the length of the platform? options: A)287 B)298 C)350 D)726 E)267 SOLUTION:D = 72 * 5/18 = 25 = 500 – 150 = 350 Answer: C #### C QUESTION:Speed of a boat in standing water is 16 kmph and the speed of the stream is 2 kmph. A man rows to a place at a distance of 6840 km and comes back to the starting point. The total time taken by him is: options: A)914.2 hours B)900 hours C)915 hours D)868.6 hours E)915 hours SOLUTION:Explanation: Speed downstream = (16 + 2) = 18 kmph Speed upstream = (16 - 2) = 14 kmph Total time taken = 6840/18 + 6840/14 = 380 + 488.6 = 868.6 hours Answer: Option D #### D QUESTION:If there are three sum of money P, Q and R so that P is the simple interest on Q and Q is the simple interest of R, rate % and time are same in each case, then the relation of P, Q and R is given by options: A)P2 = QR B)Q2 = PR C)R2 = PQ D)PQR = 100 E)None of these SOLUTION:P = Q×r×t/100 and Q = R×r×t/100 ⇒ P/Q=Q/R=r×t/100 ∴ Q2 = PR. Answer B #### B QUESTION:The simple interest on Rs.15000 at a certain rate of interest in five years is Rs.7200. Find the compound interest on the same amount for two years at the same rate of interest. options: A)3052.82 B)3015.24 C)3052.24 D)3018.24 E)3052.23 SOLUTION:R = 100 I / PT => R = (100 * 7200)/ (15000 * 5) = 9.6% CI = P{ [1 + R /100]n - 1} = 15000 { [ 1 + 9.6 / 100]^2 - 1} = Rs.3018.24 Answer:D #### D QUESTION:The value of Underrot 32pi/4 + Underrot 25 is most nearly equal to which of the following integers? (Please refer to the picture below for the exact version of the question) options: A)6 B)35 C)41 D)30 E)23 SOLUTION:Under root (32pi/4) ~ 25 Under root (25) = 5 Hence, 25+5 = 30 is the approx answer. D is the correct answer. #### D QUESTION:If w and t are integers and w^2 – t^2 is an odd integer, which of the following must be an even integer? I. w + t + 2 II. w^2 + 2wt + t^2 III. w^2 + t^2 options: A)None B)I only C)II only D)III only E)I, II, and III SOLUTION:w^2–t^2 is an odd integer means that either w is even and t is odd or w is odd and t is even. Check all options: I. w + t + 2 --> even+odd+even=odd or odd+even+even=odd. Discard; II. w^2 + 2wt + t^2 --> even+even+odd=odd or odd+even+even=odd. Discard; III. w^2 + t^2 --> even+odd=odd or odd+even=odd. Discard. Answer: A. #### A QUESTION:The total marks obtained by a student in Mathematics and Physics is 50 and his score in Chemistry is 20 marks more than that in Physics. Find the average marks scored in Mathamatics and Chemistry together. options: A)15 B)25 C)35 D)45 E)55 SOLUTION:Let the marks obtained by the student in Mathematics, Physics and Chemistry be M, P and C respectively. Given , M + C = 50 and C - P = 20 M + C / 2 = [(M + P) + (C - P)] / 2 = (50 + 20) / 2 = 35. ANSWER:C #### C QUESTION:Which of the following values of R gives the greatest value for the expression R/(R-2)? options: A)5.5 B)4.5 C)3.5 D)2.5 E)1.5 SOLUTION:5.5/(5.5 - 2) = 11/7 (~1.57) 4.5/(4.5 - 2) = 9/5 (1.8) 3.5/(3.5 - 2) = 7/3 (~2.33) 2.5/(2.5-2) = 5 1.5/(1.5 - 2) = -3 Thus, the answer is D. #### D QUESTION:Jerry wrote down all the positive integers that have at most 7 digits and contain only the digits 0 and 1. How many times did he write down the digit 1 ? options: A)128 B)224 C)288 D)448 E)512 SOLUTION:Jerry wrote down a total of 27 − 1 = 127 numbers (0 is missing). Add 0 to the numbers Jerry wrote. We divide the resulting 128 numbers in pairs. If x is one of the numbers Jerry wrote then we put it in pair with 1111111 − x (whose digits are also 0s and 1s). For example 1100101 is paired with 11010. In this way, we divide the numbers into 64 distinct pairs so that each number appears exactly once. Note that there are exactly 7 digits 1 in each pair. So, Jerry wrote the digit 1 exactly 64 × 7 = 448 times. correct answer D #### D QUESTION:A, B and C enter into a partnership. A initially invests Rs. 25 lakhs and adds another Rs. 10 lakhs after one year. B initially invests Rs. 35 lakhs and withdraws Rs. 10 lakhs after 2 years and C invests Rs. 30 lakhs. In what ratio should the profits be divided at the end of 3 years ? options: A)11:10:15 B)20:17:23 C)19:19:18 D)5:4:9 E)None of these SOLUTION:Explanation: A:B:CA:B:C =(25 lakhs××1)+(35 lakhs××2) :(35 lakhs××2+25 lakhs××1) :(30 lakhs××3) = 95 lakhs : 95 lakhs : 90 lakhs =19:19:18=19:19:18. ANSWER IS C #### C QUESTION:In a box of 16 pens, a total of 3 are defective. If a customer buys 2 pens selected at random from the box, what is the probability that neither pen will be defective? options: A)1/6 B)2/9 C)6/20 D)13/20 E)3/4 SOLUTION:Method- 1 There are 9 fine pieces of pen and 3 defective in a lot of 16 pens i.e. Probability of first pen NOT being defective = (13/16) i.e. Probability of Second pen NOT being defective = (12/15) [15 pen remaining with 12 defective remaining considering that first was defective] Probability of Both pen being NON-defective = (12/15)*(13/16) = 13/20 Answer: option D #### D QUESTION:Find 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.15of money? options: A)1500 B)2999 C)2772 D)2987 E)2661 SOLUTION:P = 15(100/10)2 => P = 1500.Answer:A #### A QUESTION:In a group of ducks and cows, the total number of legs are 28 more than twice the number of heads. Find the total number of cows. options: A)12 B)14 C)16 D)18 E)20 SOLUTION:Let the number of ducks be d and number of cows be c Then, total number of legs = 2d + 4c = 2(d + 2c) total number of heads = c + d Given that total number of legs are 28 more than twice the number of heads => 2(d + 2c) = 28 + 2(c + d) => d + 2c = 14 + c + d => 2c = 14 + c => c = 14 i.e., total number of cows = 14 Answer is B. #### B QUESTION:Enrollment in City College in 1980 was 210 percent of enrollment in 1990. What was the percent increase in the college’s enrollment from 1980 to 1990? options: A)- 10% B)- 16 2/3 % C)- 52.38% D)- 25% E)- 183 1/3% SOLUTION:Assume 100 enrollments present in 1990 210 % of 1990 = enrollments on 1980 enrollments on 1980 = 210 % change = (enrollment in 1990 - enrollment in 1980)*100/(enrollment in 1980) =(100 - 210) *100 / 210 = -11000 / 210 = - 52.38 % Ans - C #### C QUESTION:How much pure alcohol should be added to 400ml of a 15% solution to make the strength of solution 26%? options: A)100 ml B)60 ml C)120 ml D)130 ml E)150 ml SOLUTION:we can also go by answer choices Tke 100 ml for eg 400 (old)+100 (new concentr)ml 500*26/100 = 130 ml (30ml is de old concentration +100 ml (newly added) Answer D #### D QUESTION:The average salary of all the workers in a workshop is Rs. 8000. The average salary of 7 technicians is Rs. 16000 and the average salary of the rest is Rs. 6000. The total number of workers in the workshop is options: A)20 B)21 C)22 D)35 E)NONE SOLUTION:Sol. Let the total number of workers be x. Then, 8000x = (16000 × 7) + 6000 ( x – 7) ‹=› 2000x = 70000 ‹=› x = 35. Answer D #### D QUESTION:Find the smallest number which when divided by 13 and 16 leaves respective remainders of 2 and 5. options: A)128 B)197 C)127 D)182 E)091 SOLUTION:Explanation: Let 'N' is the smallest number which divided by 13 and 16 leaves respective remainders of 2 and 5. Required number = (LCM of 13 and 16) - (common difference of divisors and remainders) = (208) - (11) = 197. Answer:B #### B QUESTION:There 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? options: A)15624 B)16478 C)17953 D)19655 E)28958 SOLUTION:15624 A #### A QUESTION:Sum of the numbers from 1 to 25 is options: A)210 B)325 C)320 D)105 E)None of these SOLUTION:Explanation: Sum of first n natural numbers = 1 + 2 + 3 + ..... n = n(n+1)/2 Substitute n = 25. So S20=25×26/2=325 Correct Option: B #### B QUESTION:A man can row upstream at 10kmph and downstream at 18 kmph. The speed of the stream is options: A)2.5 km/hr B)4 km/hr C)5 km/hr D)10.5 km/hr E)None SOLUTION:Sol. Speed of stream = 1/2(18 -10) kmph = 4 kmph. Answer B #### B QUESTION:A father is four times as old as his son. In twenty years, he'll be twice as old. How old are they now? options: A)5,40 B)10,40 C)20,40 D)10,30 E)15,30 SOLUTION:If F is age of father and s is age of son f=4s f+20 = 2*(s+20) 4s+20 = 2s+40 2s=20 s=10 F=40 ANSWER:B #### B QUESTION:In how many ways a committee consisting of 3 men and 2 women can be formed from 4 men and 9 women? options: A)A)144 B)B)15 C)C)20 D)D)18 E)E)21 SOLUTION:Required number of ways = 4C3*9C2 = 4*36 = 144 Answer is A #### A QUESTION:Ravi'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? options: A) 80 B) 82 C) 84 D) 86 E) 88 SOLUTION:E. 88 Ravi 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. #### E QUESTION:At the beginning of year 1, an investor puts pp dollars into an investment whose value increases at a variable rate of xnxn per year, where nn is an integer ranging from 1 to 3 indicating the year. If 85<xn<11085<xn<110 for all nn between 1 and 3, inclusive, then at the end of 3 years, the value of the investment must be between? options: A)$p and $2p B)$2pand $5p C)$5p and $10p D)$10p and $ 25p E)$25p and $75p SOLUTION:Since the min rate of interest is 86% the min value of investment will be (1+0.86)^3*p = (1.86^3)*p. Similarly max value will be (2.1)^3*p. 2.1^3 is 9.5 or you can guess little over 8 so 10p may be good estimate. 1.86^3 is trickier to estimate. I knew root(3) = 1.73. So 1.86^2 is close to 3 and 3*1.8 is 5.4. So 5p is a close lower bound. So range is 5p to 10p. Answer C. #### C QUESTION:An electric pump can fill a tank in 3 hours. Because of a leak in the tank, it took 3 hours 30 min to fill the tank. In what time the leak can drain out all the water of the tank and will make tank empty ? options: A)10 hours B)13 hours C)17 hours D)21 hours E)25 hours SOLUTION:Explanation: We can get the answer by subtrating work done by leak in one hour by subtraction of filling for 1 hour without leak and with leak, as Work done for 1 hour without leak = 1/3 Work done with leak = 3 1/2=7/2 Work done with leak in 1 hr=2/7 Work done by leak in 1 hr=1/3=2/7=1/21 So tank will be empty by the leak in 21 hours. ANSWER IS D #### D QUESTION:What is the next number of the following sequence 2, 12, 4, 24, 8, 48, (...) options: A)10 B)12 C)16 D)20 E)22 SOLUTION:The series is 2*6=12 12/3=4 4*6=24 24/3=8 8*6=48 48/3=16 ANSWER: C #### C QUESTION:AB +BA ___ 121 In the addition problem above, A and B represent digits in two different two-digit numbers. What is the sum of A and B? options: A)6 B)8 C)9 D)11 E)14 SOLUTION:two ways to do it.. 1) straight logic.. we can see that ones digit is 1 when units digit B and A are added.. answer has to be 1 in the units digit.. only 11 fits in.. 2) BA=10B+A, and AB=10A+B.. it is given that BA+AB=121.. or 10B+A +10A+B=121.. 11(A+B)=121.. so A+B=11.. ANSWER:D #### D QUESTION:What is 35% of 4/13 of 845? options: A)58 B)69 C)80 D)91 E)102 SOLUTION:This 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 845, or 1/9 of 845. 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. The number 845 is a bit more than 810, so (1/9)*845 will be a bit more than 90. Keeping 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. The closest answer is 91, so this is the answer to choose. The answer is C. #### C QUESTION:850 students took the test on English and Maths. 35% students failed in english and 45% failed in maths. 40% of those who passed in maths also passed in english, then how many students failed in both ? options: A)a) 162 B)b) 138 C)c) 60 D)d) 17 E)e) 12 SOLUTION:Passed in english = 65% Passed in maths = 55% Passed in both = 40% of 55% = 2/5 * (55%) = 22% Passed in (English + Maths - Both + Neither) = 100% 65 + 55 - 22 + Neither = 100 Neither = 100 - 98 = 2% = 0.02 * 850 = 17 Answer: D #### D QUESTION:If a train, travelling at a speed of 180 kmph, crosses a pole in 5 sec, then the length of train is? options: A)250 m B)112 m C)117 m D)125 m E)123 m SOLUTION:A A = 180 * 5/18 * 5 = 250 m #### A <<<Examples ends QUESTION:The price of an article has been reduced by 25%. In order to restore the original price the new price must be increased by? options: A)33 1/3 % B)9 1/11 % C)11 1/9 % D)66 2/3 % E)None SOLUTION:100 75 ------- 75 ------- 25 100 ------ ? => 33 1/3% ANSWER:A #### A

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:Divide Rs.32000 in the ratio 3:3? options: A)12000, 20000 B)12000, 200098 C)16000, 16000 D)12000, 20006 E)12000, 20001 SOLUTION:3/6 * 32000 = 16000 5/6 * 32000 = 16000 Answer: C #### C QUESTION:If A(k)=(k+1)^k, and k=1, what is the value of A(A(A(k-1)))? options: A)0 B)2 C)1 D)6 E)9 SOLUTION:A(A(A(0)))=A(A(0))=A(0)=1. Thus, the answer is C. #### C QUESTION:f, 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? options: A) 20 B) 19 C) 18 D) 16 E) 15 SOLUTION:When 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. b + d cannot be 15, hence E is the answer. #### E QUESTION:A train running at the speed of 60 km/hr crosses a pole in 9 seconds. Find the length of the train. options: A)150 meter B)250 meter C)200 meter D)480 meter E)153 meter SOLUTION:Speed = 60*(5/18) m/sec = 50/3 m/sec Length of Train (Distance) = Speed * Time (50/3) * 9 = 150 meter Answer:A #### A QUESTION:What will be the fraction of 20% options: A)1/4 B)1/5 C)1/10 D)1/11 E)None of above SOLUTION:Explanation: It will 20*1/100 = 1/5 Option B #### B QUESTION:Average of first five multiples of 3 is options: A)9 B)11 C)13 D)15 E)17 SOLUTION:Explanation: Average=3(1+2+3+4+5) / 5=45 / 5=9 Option A #### A QUESTION:Today Joelle opened an interest-bearing savings account and deposited $5,000. If the annual interest rate is 4 percent compounded interest, and she neither deposits nor withdraws money for exactly 2 years, how much money will she have in the account? options: A)$5200 B)$5408 C)$5208 D)$5608 E)$5808 SOLUTION:Interest for 1st year = 5000*4/100 = 200 Interest for 2nd year = 5200 *4/100 = 208 Total =5000+200+208 = 5408 Answer : B #### B QUESTION:Katherine invested a certain sum of money in a bank that paid simple interest. The amount grew to $350 at the end of 2 years. She waited for another 3 years and got a final amount of $425. What was the principal amount that she invested at the beginning? options: A)$360 B)$380 C)$300 D)$280 E)$275 SOLUTION:What shall be the rate of interest.? Does that is not required for the calculation? Not really! Keep in mind that the interest earned each year will be the same in Simple Interest. At the end of 2 years, Amount = $350 At the end of 5 years, Amount = $425 This means she earned an interest of $75 in 3 years. Or $25 in each year. We know that the interest earned each year will be the same. Therefore she must have earned $50 in 2 years. Hence Principal Amount = $350 - $50 = $300 Option C #### C QUESTION:A boat can travel with a speed of 22 km/hr in still water. If the speed of the stream is 5 km/hr, find the time taken by the boat to go 81 km downstream options: A)5 hours B)4 hours C)3 hours D)2 hours E)None of these SOLUTION:Explanation : Speed of the boat in still water = 22 km/hr speed of the stream = 5 km/hr Speed downstream = (22+5) = 27 km/hr Distance travelled downstream = 81 km Time taken = distance/speed = 81/27 = 3 hours. Answer : Option C #### C QUESTION:Tough and Tricky questions: Mixture Problems. A drink holding 6 ounces of an alcoholic drink that is 1 part rum to 2 parts coke is added to a jug holding 35 ounces of an alcoholic drink that is 1 part rum to 3 parts coke. What is the ratio of rum to coke in the resulting mixture? options: A)2:5 B)5:15 C)3:5 D)4:7 E)14:5 SOLUTION:Answer = B) 5:15 ........................ Rum ..................... Coke ................. Total First Drink ........... 2 ............................ 4 ..................... 6 (Ratio 1:2) Second Drink ....... 8 ............................. 24 ................... 32 (Ratio 1:3) Total .................. 10 ............................. 28 .................... 38 Ratio = 10:30 = 5:15 B #### B QUESTION:As part of a promotion designed to attract visitors, an amusement park gives out 24,600 free tickets per year. Usually, the number of tickets given away each month is constant. Due to an employee error, only 10,000 tickets were given out in the first four months of the year. How many tickets should the amusement park give out in the fifth month so that it will begin the sixth month back on its regular giveaway schedule? options: A)205 B)207 C)220 D)225 E)250 SOLUTION:24600/12=2050 2050*5=10250 10250-10000=250 Answer E #### E QUESTION:Which of the following has the most number of divisors? options: A)99 B)101 C)176 D)182 E)179 SOLUTION:Explanation: 99 = 1 x 3 x 3 x 11 101 = 1 x 101 176 = 1 x 2 x 2 x 2 x 2 x 11 182 = 1 x 2 x 7 x 13 So, divisors of 99 are 1, 3, 9, 11, 33, .99 Divisors of 101 are 1 and 101 Divisors of 176 are 1, 2, 4, 8, 11, 16, 22, 44, 88 and 176 Divisors of 182 are 1, 2, 7, 13, 14, 26, 91 and 182. Hence, 176 has the most number of divisors. Answer: C #### C QUESTION:A 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: options: A)5.30 a.m B)6.42 a.m C)7.55 a.m D)7.42 a.m E)None SOLUTION:Sol. Since 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 Relative speed of A and B = (6-1) = 5 rounds per hour. Time taken to complete one round at this speed = 1/5 hr = 12 min. Answer D #### D QUESTION:Which of the following options is the possible total number of people in a hall given that the number of people is a multiple of both 4 and 20.? options: A)28 B)60 C)32 D)36 E)44 SOLUTION:the number of people are a multiple of both 7 and 13, so it must be divisible by 7 and 13. using the elimination method look for a number that is both divisible by 7 and 13, of all the options only 60 is divisible by 4 and 20. [ 60/4=15 and 60/20=3] answer :B #### B QUESTION:If A = B/C, -1 < C < 0 and 4 < B, which of the following is correct? options: A)A > 4. B)0 < A <4. C)-4 < A < 0. D)A < -4. E)A < -20. SOLUTION:B is +veC is -ve Eliminate AB For min. value max. numerator and minimize dinominator take B=4.1A=-0.9 A=4.1/-0.9 A<-4 Ans D #### D QUESTION:The average of first ten prime numbers which are odd is? options: A)15.2 B)15.7 C)15.4 D)15.8 E)15.5 SOLUTION:Sum of first 10 prime no. which are odd = 158 Average = 158/10 = 15.8 Answer:D #### D QUESTION:What will be the difference between simple and compound interest at 10% per annum on a sum of Rs. 1000 after 4 years? options: A)64.19 B)64.12 C)62.1 D)64.1 E)64.11 SOLUTION:S.I. = (1000 * 10 * 4)/100 = Rs. 400 C.I. = [1000 * (1 + 10/100)4 - 1000] = Rs. 464.10 Difference = (464.10 - 400) = Rs. 64.10 Answer: D #### D QUESTION:On dividinng 109 by a number, the quotient is 9 and the remainder is 1. Find the divisor. options: A)12 B)14 C)15 D)16 E)17 SOLUTION:d = (D-R)/Q = (109 - 1)/9 = 108/9 = 18 A #### A QUESTION:Average between two sets of numbers is closer to the set withmore numbers? options: A)70 B)80 C)90 D)95 E)98 SOLUTION:If 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 3×90+2×805=4305=86.3×90+2×805=4305=86. Here, 90 has a weight of 3 => it occurs 3 times. Whereas 80 has a weight of 2 => it occurs 2 times. So the average is closer to 90 than to 80 as we have just calculated. B #### B QUESTION:Mary'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? options: A) 124% B) 102% C) 96% D) 80% E) 64% SOLUTION:Juan's income = 100 (assume); Tim's income = 60 (40 percent less than Juan's income); Mary's income = 102 (70 percent more than Tim's income). Thus, Mary's income (102) is 102% of Juan's income (100). Answer: B. #### B QUESTION:The area of a triangle will be when a = 1m, b = 1m, c = 2m, a, b, c being lengths of respective sides? options: A)2 B)7 C)5 D)3 E)4 SOLUTION:S = (1 + 1 + 2)/2 = 2 Answer: A #### A QUESTION:There 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? options: A)8 B)10 C)12 D)14 E)15 SOLUTION:Number of ways in which one can travel from P to R =3×4=12 Answer: Option C #### C QUESTION:Out of a classroom of 6 boys and 5 girls, the teacher randomly chooses a president for the student board, a vice president, and a secretary. What is the probability that only girls will be selected for all three positions? options: A)2/33 B)4/33 C)2/165 D)4/165 E)7/165 SOLUTION:The number of ways to choose three people is 11C3=165. The number of ways to choose three girls is 5C3=10. P(only girls are chosen)=10/165=2/33 The answer is A. #### A QUESTION:An electric pump can fill a tank in 5 hours. Because of a leak in the tank, it took 10hours to fill the tank. If the tank is full, how much time will the leak take to empty it? options: A)10hours B)12hours C)8hours D)5hours E)15hours SOLUTION:Work done by the leak in 1 hour = 1/5 - 1/10 = 1/10 The leak will empty the tank in 10hours Answer is A #### A QUESTION:The 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? options: A)1/2 B)3/4 C)3/5 D)3/7 E)4/9 SOLUTION:Sol. First, we find the probability of not solving the problem x PTO x = (1 — D x - D x - D 1 2 3 1 =iXiX71=4; 1 3 Required probability 3/4 B #### B QUESTION:What is the remainder when you divide 2^200-1 by 7? options: A)1 B)2 C)3 D)4 E)5 SOLUTION:answer is C. this is very similar to the 32^32^32-1 divided by 7 question. #### C QUESTION:Anand and Deepak started a business investing Rs. 4,500 and Rs. 6,000 respectively. Out of a total profit of Rs. 420. Deepak's share is? options: A)s. 280 B)s. 310 C)s. 240 D)s. 840 E)s. 400 SOLUTION:Ratio of their shares = 4500 : 6000 = 3 : 4 Deepak's share = Rs. (420 * 4/7) = Rs. 240 ANSWER "C #### C QUESTION:Lionel left his house and walked towards Walt's house, 48 miles away. Four hours later, Walt left his house and ran towards Lionel's house. If Lionel's speed was 3 miles per hour and Walt's 6 miles per hour, how many miles had Lionel walked when he met Walt? options: A)12 B)16 C)20 D)24 E)28 SOLUTION:In the first 4 hours Lionel at the rate of 3 miles per hour covered distance=rate*time=4*3=12 miles. So, the distance between him and Walt was 48-12=36 miles when Walt left his house. Now, their combined rate to cover this distance was 3+6=9 miles per hour, hence they will meet (they will cover that distance) in time=distance/rate=36/9=4 hours. Total time that Lionel was walking is 4+4=8 hours, which means that he covered in that time interval distance=rate*time=3*8=24 miles. Answer: D. #### D QUESTION:A train 250 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: options: A)95 km/hr B)50 km/hr C)54 km/hr D)55 km/hr E)56 km/hr SOLUTION:Speed of the train relative to man = (250/10) m/sec = 25 m/sec. [(25 * (18/5)] km/hr = 90km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 90 ==> x = 95 km/hr. ANSWER: A #### A QUESTION:How many times in a day, the hands of a clock are straight? options: A)22 B)44 C)48 D)24 E)36 SOLUTION:The hands of a clock point in opposite directions (in the same straight line, making an angle 180° 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. The hands of a clock coincide(0° 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. So In 24 hours, the hands come in opposite direction or coincide 44 times. This is already given as a formula and it's is better to learn the answer by heart as 44 which can save time in competitive exams.(However you should know the theory behind). Answer: Option B #### B QUESTION:If x = y^2, and x and y are positive integers, which of the following numbers could be the value of x? options: A)10,573 B)11,908 C)12,322 D)13,924 E)14,537 SOLUTION:The square of an integer can have a units digit of 0, 1, 4, 5, 6, or 9. The answer is D. #### D QUESTION:A certain no. when divided by 50 leaves a remainder 25, what is the remainder if the same no.be divided by 15? options: A)3 B)4 C)5 D)8 E)9 SOLUTION:Explanation: 50 + 25 = 75/15 = 5 (Remainder) C #### C QUESTION:The 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? options: A)18−9∗π B)12−3∗π C)9+9/4∗π D)9+9/2∗π E)9/2−9/4∗π SOLUTION:=Square - Quarter circle =12- pi*12/4 =12- pi*3 ANSWER:B #### B QUESTION:Nitin 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. 13260, how much money did he borrow? options: A)13000 B)80288 C)2668 D)2600 E)2781 SOLUTION:Let the sum be Rs. x. Then, [(x * 6 * 3)/100] + [(x * 9 * 5)/100] + [(x * 13 * 3)/100] = 13260 18x + 45x + 39x = (13260* 100) 102x = 1326000 => x = 13000. Answer:A #### A QUESTION:By travelling at 60 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? options: A)30 kmph B)28 kmph C)26 kmph D)24 kmph E)22 kmph SOLUTION:Let the time taken to reach the destination be 3x hours. Total distance = 60 * 3x = 180x km He covered 2/3 * 180x = 120x km in 1/3 * 3x = x hours So, the remaining 60x km, he has to cover in 2x hours. Required speed = 60x/2x =30 kmph. Answer: A #### A QUESTION:If a, b, and c are integers and ab^2/c is a positive even integer, which of the following must be true? I. ab is even II. ab > 0 III. c is even options: A)I only B)II only C)I and II D)I and III E)I, II, and III SOLUTION:ab2/c is positive which means a and C >0 or a and c<0 since b2 is positive Case 1 - a=3 b=2 c=3 or c=6 where ab2 /2 would be even when c= 3 or c=6 lets see III option where C is even as per our assumption C can be even and odd, hence it is out. lets see option II ab>0 a and b can positive or negative hence sign of ab cannot be determined hence it is out So options B,C,D,E are gone and ans is A #### A QUESTION:A train passes a platform in 34 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 options: A)280 meter B)240 meter C)210 meter D)200 meter E)None of these SOLUTION:Explanation: Speed of the train = 54 km/hr = (54×10)/34 m/s = 15 m/s Length of the train = speed × time taken to cross the man = 15×20 = 300 m Let the length of the platform = L Time taken to cross the platform = (300+L)/15 => (300+L)/15 = 34 => 300+L = 15×34 = 510 => L = 510-300 = 210 meter Answer: Option C #### C QUESTION:A merchant purchased a jacket for $180 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’s gross profit on this sale? options: A)$0 B)$3 C)$4 D)$12 E)$15 SOLUTION:Let selling price = x So, x = 180 + 25x/100 Calculating above, x = 240 Selling price =240 20% Discount on Selling price = 192 So, profit = 192-180 = 12 Answer = D #### D QUESTION:In 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 140800, how many purple chips were selected? options: A)1 B)2 C)3 D)4 E)5 SOLUTION:140800 = 1*5^2*8^3*11 The factors of 8 must come from the purple point value, so there are 3 purple chips. The answer is C. #### C QUESTION:In a sports club with 27 members, 17 play badminton and 19 play tennis and 2 do not play either. How many members play both badminton and tennis? options: A)7 B)8 C)9 D)10 E)11 SOLUTION:Let x play both badminton and tennis so 17-x play only badminton and 19-x play only tennis. 2 play none and there are total 30 students. hence, (17-x)+(19-x)+x+2=27 38-2x+x=27 38-x=27 x=11 So 8 members play both badminton and tennis. E #### E QUESTION:If 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? options: A)3:2 B)2:1 C)3:3 D)1:2 E)6:1 SOLUTION:8M + 2B = 4(1M + 1B) 8M + 2B = 4M + 4B 4M = 2B The required ratio of work done by a man and a boy = 2:4=1:2 D #### D QUESTION:A 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? options: A)3 B)7.5 C)2.25 D)1.5 E)4 SOLUTION:M = 9 S = x DS = 9 + x US = 9 - x 9 + x = (9 - x)2 9 + x = 18 -2x 3x = 9 x = 3 ANSWER:A #### A QUESTION:85% of a number is added to 24, the result is the same number. Find the number? options: A)28 B)288 C)279 D)160 E)232 SOLUTION:(85/100) * X + 24 = X 3X = 480 X = 160 Answer:D #### D QUESTION:In the formula V = 1/(2r)^2, if r is halved, then V is multiplied by ? options: A)64 B)1/8 C)1 D)4 E)1/64 SOLUTION:Say r=2 => V1 = 1/16 when r=1; V2 = 1/4 V2 = 4*V1. Answer : D #### D QUESTION:If |x + 132| = 32 what is the sum of all the values of x. options: A)-264 B)200 C)-64 D)0 E)-328 SOLUTION:There will be two cases x+132 = 32 and x+132 = -32 Solve for x => x=32-132=> x=-100 or x= -32 - 132 => x= -164 The sum of both values will be -164 + -100 = -264 Answer is A #### A QUESTION:6 men, 8 women and 6 children complete a job for a sum of Rs.950. If their individual wages are in the ratio 4:3:2, the total money earned by the children is options: A)Rs. 150 B)Rs. 170 C)Rs. 180 D)Rs. 190 E)None of these SOLUTION:Explanation: Ratio of wages of 6 men, 8 women and 6 children = 6 x 4 : 8 x 3 : 6 x 2 = 24 : 24 : 12 = 2 : 2 : 1 Money earned by children = 950 x (1/5) = Rs. 190 Answer: Option D #### D QUESTION:The average age of three boys is 15 years and their ages are in proportion 3:5:7. What is the age in years of the youngest boy? options: A)7 B)9 C)11 D)13 E)14 SOLUTION:Explanation: 3x + 5x + 7x = 45 x =3 3x = 9 B) #### B QUESTION:A jar contains 12 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? options: A)1/495 B)1/165 C)1/81 D)11/31 E)3/220 SOLUTION:Jar 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. Sample space = 12C3 = 220. Probability of choosing 3 red = 3C3/12C3 = 1/220. Probability of choosing 3 green = 3C3/12C3 = 1/220. Probability of choosing 3 blue = 3C3/12C3 = 1/220. Required probability = 1+1+1/220 = 3/220 Ans (E). #### E QUESTION:A four-digit code can consist of the digits 0 ~ 9 except that it does not contain the digits 1, 2, 4, and 6 at all. If repeated digits are allowed, what is the probability that it has at least one even digit? options: A)23/24 B)31/36 C)55/64 D)65/81 E)75/121 SOLUTION:P(no even digits) = 2/3*2/3*2/3*2/3 = 16/81 P(at least one even digit) = 1 - 16/81 = 65/81 The answer is D. #### D QUESTION:Three math classes: X, Y, and Z, take an algebra test. The average score in class X is 83. The average score in class Y is 76. The average score in class Z is 85. The average score of all students in classes X and Y together is 79. The average score of all students in classes Y and Z together is 81. What is the average score for all the three classes, taken together? options: A)81 B)81.5 C)82 D)84.5 E)None of these SOLUTION:Explanation : Let the number of students in classes X, Y and Z be a, b and c respectively. Then Total of X = 83a Total of Y = 76b Total of Z = 85c And , (83a + 76b) / (a + b) = 79. i.e 4a = 3b. Also, (76b + 85c) / (b + c) = 81. i.e 4c = 5b. Hence, b= (4/3)a, c =(5/4)b = (5/4) x (4/3)a = (5/3)a. Average of X, Y and Z = (83a + 76b + 85c ) / (a + b + c). => 83a+76∗(4/3)a+85∗(5/3)a /a+(4/3)a+(5/3)a . => 978/12 => 81.5 Answer : B #### B QUESTION:3 workers transfer a tool weighing 120kg in 12 seconds. How many men are required to transfer it in 9 seconds? options: A)4 B)5 C)6 D)7 E)8 SOLUTION:We have, M1D1H1 = M2D2H2 3*120*12 = M2*120*9 M2 = 3*120*12/120*9 = 4 ANSWER:A #### A QUESTION:If m and n are positive integers, and m=2n and k=9m, then - options: A)k is a factor of m. B)2m is a factor of k. C)3m is a factor of k/2. D)m/2 is a factor of k. E)k is a factor of m/2. SOLUTION:m=2n --> m is even. k=9m --> m is factor of k, thus m/2 = integer must also be a factor of k. Answer: D. #### D QUESTION:Cities M and N are 600km apart. Bus A starts from city M towards N at 9AM and bus B starts from city N towards M at the same time. Bus A travels the first one-third of the distance at a speed of 40kmph, the second one-third at 50kmph and the third one-third at 60kmpr. Bus B travels the first one-third of the total time taken at a speed of 40kmph, the second one-third at 50kmph and the third one-third at 60kmph. When and where will the two buses cross each other? options: A)300 kms from A B)280 kms from A C)305 kms from A D)295 kms from A E)265 kms from A SOLUTION:DETAILED SOLUTION Bus A Travels 200km @ 40kmph the next 200km @ 50kmph and the final 200km @ 60kmph So, Bus A will be at a distance of 200km from city M after 5 hours, and at a distance of 400km after 9 hours, and reach N after 12 hours and 20 mins Bus B Travels at an overall average speed of 50kmph, so will take 12 hours for the entire trip. So, Bus B will travel 160 kms in the first 4 hours 200 kms in the next 4 hours and 240 in the final 4 hours So, both buses cross each other when they are in their middle legs. After 5 hours, bus A will be at a position 200kms from city M. At the same time, bus B will be at a distance 210kms from city N (4 * 40 + 50). The distance between them will be 190kms (600 - 200 - 210). Relative speed = Sum of the the two speeds = 50 + 50 = 100 kmph. Time taken = 190/100 = 1.9 hours. = 1 hour and 54 minutes. So, the two buses will meet after 6 hours and 54 minutes. Bus B will have travelled 210 + 95 = 305 kms. So, the two buses will meet at a point that is 305 kms from City N and 295 kms from city A. CORRECT ANSWER D #### D QUESTION:A spirit and water solution is sold in a market. The cost per liter of the solution is directly proportional to the part (fraction) of spirit (by volume) the solution has. A solution of 1 liter of spirit and 1 liter of water costs 40 cents. How many cents does a solution of 1 liter of spirit and 2 liters of water cost? options: A)40 B)33 C)50 D)51 E)52 SOLUTION:Yes, ensure that you understand the relation thoroughly! Cost per liter = K * Fraction of Spirit 40 cents is the cost of 2 liters of solution (1 part water, 1 part spirit). So cost per liter is 20 cents. Fraction of spirit is 1/2. 20 = K * (1/2) K = 40 Cost per liter = 40 * (1/3) (1 part spirit, 2 parts water) Cost for 3 liters = 40 * (1/3) * 3 = 40 cents A. 40 cents #### A QUESTION:By selling an article at Rs.700, a shopkeeper makes a profit of 25%. At what price should he sell the article so as to make a loss of 25%? options: A)s.600 B)s.480 C)s.500 D)s.450 E)s.420 SOLUTION:SP = 700 Profit = 25% CP = (SP)*[100/(100+P)] = 700 * [100/125] = 560 Loss = 25% = 25% of 560 = Rs.140 SP = CP - Loss = 560 - 140 = Rs.420 ANSWER:E #### E QUESTION:The surface area of a sphere is 4πR2, where R is the radius of the sphere. If the area of the base of a hemisphere is 3, what is the surface area T of that hemisphere? options: A) 6/π B) 9/π C) 6 D) 9 E) 12 SOLUTION:Given Area of the base of a hemisphere is 3 = PI * R^2 Thus R = Sqrt ( 3 / PI ) . Surface area of whole sphere = 4*PI*R^2 . = 4 * PI * 3 / PI = 12 . Since the hemisphere is half of a sphere the Surface area of the hemisphere = 12 / 2 = 6 ( curved part , not including the flat rounded base ) . But the total surface area = 6 + Area of the base of a hemisphere . = 6 + 3 = 9. Answer is D !! #### D QUESTION:A, 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 1/3rd 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? options: A)1/3 B)2/9 C)9/46 D)7/19 E)1/6 SOLUTION:The first thing to notice is that A is faster than B and B is faster than C. Since 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. If A works for 2 days, B works for 1 day and C works for only 2/3 of the day. Therefore total work done = (2*2) + (1*1) + (1/3*1/3) = 46/9 Proportion of work done by B = (1*1) / (46/9) = 9/46 Hence Answer C. #### C QUESTION:At the end of a business conference the ten people present all shake hands with each other once. How many handshakes will there be altogether ? options: A)20 B)45 C)55 D)90 E)85 SOLUTION:Explanation: Clearly, total number of handshakes = (9+ 8 + 7 + 6 + 5 + 4 + 3 + 2+1) = 45. Answer: B #### B QUESTION:TOM traveled the entire 60 miles trip. If he did the first 12 miles of at a constant rate 24 miles per hour and the remaining trip of at a constant rate 48 miles per hour, what is the his average speed, in miles per hour? options: A)20mph B)24mph C)30mph D)40mph E)42mph SOLUTION:avg speed = total distance/ total time = (d1+d2)/(t1+t2) = (12+48) / ((12/24)+(48/48)) = 60*2/3 = 40mph D #### D QUESTION:What annual payment dischargea debit of Rs.12900, due in 4yrs.At 5% rate? options: A)2000 B)2200 C)3000 D)3400 E)3500 SOLUTION:A.P.=(200X12900)/[4(200+5X3)]=3000 Ans Alternative 100+105+110+115=12900 430=12900 100=12900/(430)X100=3000 C #### C QUESTION:In how many ways can 5 people, A, B, C, D, E, be seated in a row such that C and D are not seated next to each other as well as A and B are not seated next to each other? options: A)384 B)396 C)576 D)24 E)696 SOLUTION:Number of total arrangements = 5! Restriction 1= ABCD not next to each other --> let say AB and CD are considered as one unit, respectively Restriction 2= AB is not the same as BA + CD is not the same as DC --> the number will increase by 2*2 Total number of arrangements - Number out of restrictions = Result 5! - (4!*2*2) = 120 - (24*2*2) = 24 Answer D #### D QUESTION:Rs. 5887 is divided between Shyam and Ram, such that Shyam's share at the end of 9 years is equal to Ram's share at the end of 11 years, compounded annually at the rate of 5%. Find the share of Shyam. options: A)2088 B)2000 C)3087 D)None of these E)Cannot be determined SOLUTION:Solution: Shyam's share * (1+0.05)9 = Ram's share * (1 + 0.05)11 Shyam's share / Ram's share = (1 + 0.05)11 / (1+ 0.05)9 = (1+ 0.05)2 = 441/400 Therefore Shyam's share = (441/841) * 5887 = 3087. Answer C #### C QUESTION:A certain university will select 1 of 3 candidates eligible to fill a position in the mathematics department and 2 of 10 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? options: A)42 B)70 C)140 D)135 E)315 SOLUTION:1 of 3 will be chosen for the math 2 of 10 will be chosen for the computer None of the 3 chosen people can be in more than one departments. We can choose any of the 3 candidates for the math dep., which gives as 3 selections. We can choose 2 of the 10 candidates for the computer dep., which gives us 2 selections and 8 rejections. So, the way to find how many different selections of 2 candidates we can have for the computer dep., we do: 10! /2!*8!= (9*10) / 2 = 90 / 2 = 45. We are multiplying our individual selections: 3*45 = 135 In the bolded part, we don't have to multiply all of the numbers, as those in 8! are included in 10!, so we simplify instead. Ans D #### D QUESTION:R campers fished for 2 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? options: A)2m + n(R-m) B)(2m + n(R-m))/3 C)(2m + n(m-R))/3 D)(2m + n)/2 E)(2m + n)/R SOLUTION:m of the campers caught 2 fish apiece in 2 hours --> total fish caught by m campers = 2m; The rest caught a combined total of n fish. Total fish caught in 2 hours = 2m+n --> per hour (2m+n)/2. Answer: D. #### D <<<Examples ends QUESTION:An amount of money is to be distributed among Faruk, Vasim and Ranjith in the ratio 3 : 5 : 9. If Vasims share is Rs. 1500, what is the difference between Faruk's and Ranjith's shares? options: A)s 1800 B)s 1500 C)s 1600 D)s 1900 E)s 1700 SOLUTION:Explanation : Let P = Faruk, Q = Vasim, R = Ranjith Let P = 3x, Q = 5x and R = 9x. Then, 5x = 1500 ? x = 300. P=900,Q=1500 and R = 2700. Hence, (R - p) = (2700 - 900) = 1800 Answer : A #### A

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:If a cloth merchant sells ‘a’ metres of cloth for Rs.x, then what is the selling price of ‘b’ metres of cloth? options: A)Rs.(b*x) B)Rs.{(b*x)/a} C)Rs.{(a*b)/x} D)None of these E)Cannot be determined SOLUTION:Explanation: Cost of ‘a’ metres of cloth = Rs.x. Therefore, each metre of cloth costs Rs. (x/a). The cost of ‘b’ metres of cloth = Rs. b*(x/a) = Rs. {(b*x)/a} ANSWER B #### B QUESTION:What is the ratio of y to x if (x + 3y) / ( x - y) = 5/4? options: A)-15/4 B)-5/3 C)1/17 D)3/5 E)15/1 SOLUTION:Solving for y/x gives, 1/17 (C) #### C QUESTION:By selling an article at Rs.600, a profit of 25% is made. Find its cost price? options: A)Rs.486 B)Rs.455 C)Rs.487 D)Rs.480 E)Rs.489 SOLUTION:SP = 600 CP = (SP)*[100/(100+P)] = 600 * [100/(100+25)] = 600 * [100/125] = Rs.480 Answer: D #### D QUESTION:There 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? options: A)320 B)345 C)375 D)380 E)400 SOLUTION:In 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 3x + 5x = 600 Solve for x 8x = 600 x = 75 Number of boys 3x = 3 × 75 = 225 Number of girls 5x = 5 × 75 = 375 C #### C QUESTION:A mixture contains alcohol and water in the ratio 4 : 3. If 9 litres of water is added to the mixture, the ratio becomes 4: 5. Find the quantity of alcohol in the given mixture options: A)15 litres B)10 litres C)30 litres D)22 litres E)18 litres SOLUTION:Let the quantity of alcohol and water be 4x litres and 3x litres respectively 4x/(3x+9)=4/5 20x=4(3x+9) 8x=36 x=4.5 Quantity of alcohol = (4 x 4.5) litres = 18 litres. Answer is E #### E QUESTION:A work could be completed in 100days by x workers. However, due to the absence of 10workers, it was completed in 110days. The original no.of workers was: options: A)90 B)100 C)110 D)130 E)140 SOLUTION:sax Letlheo g alnumberofworkers hex x workers can do the wor - 100 days (x — 10) workers can do the work in 110 days 4 100x 1u1x— 10) 1100 Q x 110 C #### C QUESTION:The number which exceeds 16% of it by 63 is : options: A)75 B)52 C)58 D)60 E)62 SOLUTION:Solution Solution Let the number be x. x-16% of x =63 x-16/100x =63 x-4/25x=63 21/25x=63 x=(63x25/21)= 75 Answer A #### A QUESTION:The average of five numbers is 27. If one number is excluded, the average becomes 21. The excluded number is? options: A)48 B)49 C)50 D)51 E)52 SOLUTION:Excluded number = (27 * 5) - (21 * 4) = 135 - 84 = 51. Answer: D #### D QUESTION:The amount of water (in ml) that should be added to reduce 9 ml. Lotion, containing 50% alcohol, to a lotion containing 45% alcohol, is? options: A)1 B)4 C)5 D)6 E)7 SOLUTION:4.5 4.5 45% 55% 45% ----- 4.5 55% ------? => 5.5 - 4.5 = 1 ml ANSWER:A #### A QUESTION:The 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? options: A)Rs.4538 B)Rs.4518 C)Rs.4518 D)Rs.4530 E)Rs.4517 SOLUTION:Area of the four walls = 2h(l + b) Since there are doors and windows, area of the walls = 2 * 12 (15 + 25) - (6 * 3) - 3(4 * 3) = 906 sq.ft. Total cost = 906 * 5 = Rs.4530 Answer: D #### D QUESTION:The average height of 30 students in a class was calculated as 177 cm. It has later found that the height of one of the students in the class was incorrectly written as 151 cm whereas the actual height was 106 cm. What was the actual average height of the students in the class? options: A)176.5 cm B)175.5 cm C)174.5 cm D)173.5 cm E)172.5 cm SOLUTION:The total height was 45 cm too much. The average height should be reduced by 45 cm/30 = 1.5 cm The answer is B. #### B QUESTION:the egg vendor calls on his 1st customer and sells his half his eggs and half an egg.to the 2nd customer he sells half of what he had left and half an egg,and to the 3rd customer he sells half of what he had then left and half an egg.by the way he did not break any eggs.in the end 3 eggs were remainig.how many did he start out with? options: A)21 B)31 C)41 D)51 E)61 SOLUTION:He start out with 31eggs. In the end, he have 3eggs left. So, 3*2 +1= 7 7*2 +1= 15 15*2 +1= 31 31eggs he had initially. ANSWER:B #### B QUESTION:By selling 33 meters of cloth , one gains the selling price of 11 metres . Find the gain percent . options: A)50 B)45 C)40 D)60 E)55 SOLUTION:(Selling Price of 33m)-(Cost Price of 33m)=Gain=Selling Price of 11m Selling Price of 22m = Cost Price of 33m Let Cost Price of each meter be $1 , Then, Cost Price of 22m= $22, Selling Price of 22m=$33. Gain%=[(11/22)*100]%=50% Answer A) 50. #### A QUESTION:If the number 24*32 is completely divided by 6. what is the smallest whole number in the place of * ? options: A)4 B)3 C)1 D)2 E)5 SOLUTION:Solution The number is divisible by 6 means it must be divisible by 2 and 3. Since the number has 2 as its end digit it is divisible by 2. Now, 2+4+x+3+2=11+x which must be divisible by 3. Thus x=1 Answer C #### C QUESTION:If 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? options: A)1 B)2 C)5 D)7 E)14 SOLUTION:Try with the options - A. If BC = 1 , both B and C must be 1 B. 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 C. 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 D. If BC = 6 , then we can have the following possibilities i. 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 ii. 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 E. 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 Thus answer is (D) #### D QUESTION:The function f(Z) represents the number of ways that prime numbers can be uniquely summed to form a certain number Z such that Z = a + b + c + d… where those summed variables are each prime and a ≤ b ≤ c ≤ d ... For instance f(8) = 3 and the unique ways are 2 + 2 + 2 + 2 and 2 + 3 + 3 and 3 + 5. What is f(12)? options: A)4 B)5 C)6 D)9 E)7 SOLUTION:Its better to start with 2 and check whether sum of two primes is primes is even. 1) 2(6 times) 2) 2(3 times) + 3(2 times) 3) 2(2 times) + 3 + 5 4) 2 + 3 + 7 5) 2 + 5 + 5 6) 3(4 times) 7) 5 + 7 Answer: E #### E QUESTION:How many words with or without meaning, can be formed by using all the letters of the word, ‘ORANGE’, using each letter exactly once? options: A)700 B)720 C)750 D)800 E)820 SOLUTION:The word ‘ORANGE’ contains 6 different letters. Therefore, Required number of words= Number of arrangement of 6 letters, taken all at a time =6P6 = 6! = 6*5*4*3*2*1 = 720 ANSWER:B #### B QUESTION:If 3 women can color 180 m long cloth in 2 days, then 5 women can color 300 m long cloth in? options: A)2 days B)3 days C)5 days D)1 day E)4 days SOLUTION:The length of cloth painted by one woman in one day = 180/ 3× 2 = 30 m No. of days required to paint 300 m cloth by 5 women = 300/ 5 × 30 = 2 days Answer : A #### A QUESTION:A sum of Rs.4000 is invested at a compound interest for three years, the rate of interest being 10% p.a., 20% p.a. and 25% p.a. for the 1st, 2nd and the 3rd years respectively. Find the interest received at the end of the three years. options: A)2888 B)3120 C)2877 D)2600 E)1277 SOLUTION:Let A be the amount received at the end of the three years. A = 4000[1 + 10/100][1 + 20/100][1 + 25/100] A = (4000 * 11 * 6 * 5)/(10 * 5 * 4) A = Rs.6600 So the interest = 6600 - 4000 = Rs.2600 Answer: D #### D QUESTION:Divide $ 1162 among A, B, C in the ratio 35 : 28 : 20. options: A)490,490,490 B)360,392,460 C)490,382,280 D)260,160,60 E)492,390,280 SOLUTION:Sum of ratio terms = (35 + 28 + 20) = 83. A's share = $ (1162 x (35/83))= $ 490; B's share = $ (1162 x(28/83))= $. 392; C's share = $ (1162 x (20/83))= $ 280. Option C #### C QUESTION:The average of 6 no.'s is 3.95. The average of 2of them is 3.4, while the average of theother 2 is 3.85. What is the average of the remaining 2 no's? options: A)3.5 B)3.9 C)4.2 D)4.3 E)4.6 SOLUTION:Sum of the remaining two numbers = (3.95 * 6) - [(3.4 * 2) + (3.85 * 2)] = 23.70 - (6.8 + 7.7) = 23.70 - 14.5 = 9.20. Required average = (9.2 / 2) = 4.6. E #### E QUESTION:If population of certain city increases at the rate of 5%. If population in 1981 was 138915, then population in 1978 was? options: A)120000 B)228788 C)266891 D)267689 E)127791 SOLUTION:X * (105/100) * (105/100) * (105/100) = 138915 X = 138915/1.157625 X = 120000 Answer:A #### A QUESTION:A plane flying north at 500 kmph passes over a city at 12 noon. A plane flying east at the same attitude passes over the same city at 12.30 pm. The plane is flying east at 400 kmph. To the nearest hundred km, how far apart are the two planes at 2 pm? options: A)600 km B)1000 km C)1100 km D)1200 km E)1300 km SOLUTION:The plane flying north would have traveled for 2 hours at 2 PM. It travels at 500 kmph. Hence, the plane flying north would have covered 1000 kms from the city at 2 PM. The plane flying east would have traveled for 1.5 hours at 2 PM. It travels at 400 kmph. Hence, the plane flying east would have covered 1.5*400 = 600 kms from the city at 2 PM. The two planes are flying at right angles to each other. The shortest distance between the two planes is the length of the hypotenuse of the right triangle whose legs are the distances covered by the two planes. Hence, distance = 1000square + 200 square = 1166 km The nearest 100 km distance between the two planes = 1200 kms. Answer D #### D QUESTION:Which of the following is NOT a prime number? options: A)21 B)31 C)41 D)11 E)51 SOLUTION:Ans is A A prime number has itself and 1 as the only factors. e.g. 2, 3, 7, 11, 19. Factors of 21 = {1 , 3 , 7 , 21} => 21 is not a prime number #### A QUESTION:A, 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.2430? options: A)s.800 B)s.810 C)s.820 D)s.900 E)s.920 SOLUTION:2430 * 1/3 = 810 Option B #### B QUESTION:You 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. options: A)180 B)181 C)182 D)178 E)168 SOLUTION:add the max weights 52+50+78=180 ANSWER:A #### A QUESTION:For any positive integer n, the length of n is defined as the number of prime factors whose product is n. For example, the length of 75 is 3, since 75 = 3 * 5 * 5. How many two-digit positive integers have length 6? options: A)None B)One C)Two D)Three E)Four SOLUTION:The best (quickest) way I can think of to get the answer, is start with 2^6, then move on from there. 2^6=64 2^5*3=96 Obviously 2^5*5 will be more than 2 digits, as will 2^4*3^2. So 64 and 96 are it. Answer is 2 (C). #### C QUESTION:A machine P completes a certain amount of work in 12 hrs and machine Q completes the same work in x hrs if both machines works together to complete the same work in 8 hrs then what is x? options: A)12 hrs B)18 hrs C)24 hrs D)32 hrs E)34 hrs SOLUTION:Explanation: P’s 1hr work = 1/12 Q’s 1 hr work = 1/x (A+B)’s 1 hr work = 1/8 = 1/12+1/x => x = 24 hrs Answer: Option C #### C QUESTION:In 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? options: A)A)1:5 B)B)1:1 C)C)1:8 D)D)1:9 E)E)1:3 SOLUTION:Number of men in the colony = 5/7 * 70 = 50. Number of women in the colony = 2/7 * 70 = 20. Number educated women in the colony = 1/5 * 30 = 6. Number of uneducated women in the colony = 4/5 * 50 = 24. Number of educated persons in the colony = 8 /35 * 70 = 16. As 6 females are educated, remaining 10 educated persons must be men. Number of uneducated men in the colony = 50 - 10 = 40. Number of educated men and uneducated men are in the ratio 10 : 40 i.e., 1:4. Answer:A #### A QUESTION:Virat buys an old car for Rs. 40000 and spends Rs. 4000 on its repairs. If he sells the car for Rs. 60000, his gain percent is: options: A)3 (4/7) % B)11 (1/9) % C)12 (2/3) % D)12% E)36.36% SOLUTION:Explanation: C.P. = Rs. (40000 + 4000) = Rs. 44000 S.P. = Rs. 60000. Gain% = ( (16000 / 44000) * 100 ) % = 36.36% ANSWER E #### E QUESTION:If there is an equal probability of a child being born a boy or a girl, what is the probability that a couple who have 4 children have two children of the same sex and one of the opposite sex? options: A)1/3 B)2/3 C)1/4 D)1/2 E)3/5 SOLUTION:No of ways of selecting a gender - 2C1 No of ways of selecting any 2 children out of 4 = 4C2 Total possible outcomes - 2^4 (each child can be either a girl or a boy) Probability=2C1*4C2/2^4= 2*4/2*2*2*2=8/16=1/2 Ans=D #### D QUESTION:A retailer buys a radio for Rs 225. His overhead expenses are Rs 30. He sellis the radio for Rs 300. The profit percent of the retailer is options: A)10% B)50% C)25% D)17.6% E)None of these SOLUTION:Explanation: cost price = (225 + 30) = 255 sell price = 300 gain = (45/255)*100 = 17.6%. Answer: D #### D QUESTION:Two 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? options: A)270 B)277 C)200 D)257 E)271 SOLUTION:Relative speed = (72 - 36) * 5/18 = 2 * 5 = 10 mps. Distance covered in 27 sec = 20 * 10 = 200 m. The length of the faster train = 200 m. Answer: C #### C QUESTION:A machine manufactures notebooks in a series of five colors: red, blue, black, white, and yellow. After producing a notebook of one color from that series, it produces a notebook of the next color. Once five are produced, the machine repeats the same pattern. If the machine began a day producing a red notebook and completed the day by producing a black notebook, how many notebooks could have been produced that day? options: A)27 B)34 C)50 D)61 E)78 SOLUTION:A machine manufactures notebooks in a series of five colors: red, blue, black, white, and yellow. Machine starts manufacturing Red and ended on Black. This means that either machine has manufactured 3, 8, 13, 18, 23, 28, 33, 38, 43, 48, 53, 58, 63, 68, 73, 78 Only 78 is given in the options. So answer = 78 ANSWER:E #### E QUESTION:A 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 49 grams of protein daily, how many grams of food X are in the mixture? options: A)160 B)180 C)200 D)220 E)240 SOLUTION:Let x be the number of grams of food X in the mixture. 0.1x + 0.15(400-x) = 49 0.05x = 11 x = 220 The answer is D. #### D QUESTION:There 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? options: A)8 B)10 C)12 D)14 E)15 SOLUTION:Number of ways in which one can travel from P to R =3×4=12 Answer: Option C #### C QUESTION:The 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. 25,000 is made? options: A)Rs. 1,10,000 B)Rs. 1,20,000 C)Rs. 1,24,000 D)Rs. 1,21,000 E)None of these SOLUTION:The value of the machine after two years = 0.8 * 0.8 * 1,50,000 = Rs. 96,000 SP such that a profit of Rs. 25,000 is made = 96,000 + 25,000 = Rs. 1,21,000 ANSWER:D #### D QUESTION:The simple interest at x% for x years will be Rs. x on a sum of: options: A)x B)x^2 C)100x D)100x^2 E)50x^2 SOLUTION:Explanation : P = ? R = x% Simple Interest,SI = x T = x years P=100× SI/RT=100 × x / x × x=100/x Answer : Option C #### C QUESTION:The volume of a cube is 3375 cc. Find its surface. options: A)1350 B)1150 C)1456 D)1254 E)1489 SOLUTION:a3 = 3375 => a = 15 6a2 = 6 * 15 * 15 = 1350 Answer: A #### A QUESTION:What is value of (P + Q)/(P - Q) if P/Q = 7 ? options: A)1/3 B)2/3 C)4/3 D)5/3 E)None of these SOLUTION:Explanation: (P + Q)/(P - Q) = (P/Q+1)/(P/Q - 1) = (7 +1)/(7 - 1) = 4/3. Answer: C #### C QUESTION:A 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 10 years back was: options: A)10 years. B)14 years. C)17 years. D)16 years. E)12 years. SOLUTION:Let the son's present age be x years. Then, (44 - x) = x 2x = 44. x = 22 Son's age 10 years back (22 - 10) = 12 years. ANSWER :E #### E QUESTION:A train is 288 meter long is running at a speed of 29 km/hour. In what time will it pass a bridge of 101 meter length? options: A)48.29 B)50 C)26.8 D)45.29 E)30 SOLUTION:Speed = 29 Km/hr = 29*(5/18) m/sec = 145/18 m/sec Total distance = 288+101 = 389 meter Time = Distance/speed = 389 * (18/145) = 48.29 seconds. Answer: A #### A QUESTION:The 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? options: A)9% B)4% C)6% D)3% E)5% SOLUTION:65*(90/100)*((100-x)/100) = 56.16 x = 4% Answer:B #### B QUESTION:The ratio between the present ages of P and Q is 6:7. If Q is 4 years old than P, what will be the ratio of the ages of P and Q after 4 years options: A)A)3:4 B)of these C)C)4:3 D)inadequate E)B)3:5 SOLUTION:Let P's age and Q's age be 6x and 7x years respectively. Then, 7x - 6x = 4 => x = 4 Required ratio = (6x + 4) : (7x + 4) 28 : 32 = 7:8 ANSWER:B #### B QUESTION:David covered a distance of 50 miles on his first trip. On a later trip he traveled 75 miles while going six times as fast. His new time compared with the old time was: options: A)twice as much B)three times as much C)the same D)half as much E)a fourth as much SOLUTION:Let t be the time of the first trip. On the later trip, David can travel 300 miles in time t. The trip of 75 miles takes t/4. The answer is E. #### E QUESTION:If 0 < a < b and k = (2a + 8b)/b , which of the following must be true? options: A)k < 2 B)k < 7 C)k < 10 D)k > 10 E)k > 11 SOLUTION:Here's another approach: k = (2a + 8b)/b = 2a/b + 8b/b = 2(a/b) + 8 Since 0 < a < b, we know that a/b is less than 1, which means that 2(a/b) is some number less than 2. So, we get k = (some number less than 2) + 8 From here, we can see that k must be less than 10 Answer: C #### C QUESTION:A computer program generates a sequence of numbers a1, a2, a3, ... such that a1=1, a2=2, and ak=a(k-2)*4-1 for 2 < k < n for n=10. Find a6. options: A)19 B)27 C)31 D)36 E)41 SOLUTION:a1=1 a2=2 a3=1*4-1=3 a4=2*4-1=7 a5=3*4-1=11 a6=7*4-1=27 27 #### B QUESTION:If a wagon wheel had 10 more spokes, the angle between them would decrease by 6 degrees. Can you identify the number of spokes in the wheel? options: A)20 spokes B)10 spokes C)30 spokes D)15 spokes E)25 spokes SOLUTION:A 20 spokes 360/S = A 360/(S +10) = A – 6 Thus there are 20 spokes in the wheel. #### A QUESTION:A, 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 $900 was the net sum to be paid for the entire work, what was the average daily wage of B? options: A)$144 B)$90 C)$60 D)$54 E)$48 SOLUTION:The correct answer is C. #### C QUESTION:What is the difference between the local values of 4 in the number 54404? options: A)2992 B)3996 C)2877 D)2077 E)1211 SOLUTION:Explanation: 4000 – 4 = 3996 Answer:B #### B QUESTION:A car dealership has 40 cars on the lot, 15% of which are silver. If the dealership receives a new shipment of 80 cars, 30% of which are not silver, what percentage of total number of cars are silver? options: A)20% B)25% C)30% D)35% E)40% SOLUTION:The number of silver cars is 0.15*40 + 0.3*80 = 30 The percentage of cars which are silver is 30/120 = 25% The answer is B. #### B QUESTION:A bottle contains a certain solution. In the bottled solution, the ratio of water to soap is 3:4, and the ratio of soap to salt is five 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? options: A)9:32 B)9:30 C)32:9 D)19:32 E)18:30 SOLUTION:Water:soap = 3:4 Soap:Salt=15:20 => For 15 soap, salt = 20 => For 4 Soap, salt = (20/15)*4 = 80/15=16/3 So, water:soap:salt = 3:4:16/3= 9:12:16 After open container, water:soap:salt =4.5:12:16 So, water:salt = 4.5:16 = 9:32 ANSWER:A #### A QUESTION:At a party, there were seven times as many females as males and twice times as many adults as children. Which of the following could NOT be the number of people at the party? options: A)384 B)258 C)215 D)120 E)72 SOLUTION:Five times as many females as males --> F = 7M. Three times as many adults as children --> (F + M) = 2C. The number of people at the party = F + M + C = 2C + C = 3C. The number of people at the party must be a multiple of 3. The only answer choice which is NOT a multiple of 3 is C. Answer: C. #### C QUESTION:If 0.60: x : : 6 : 4, then x is equal to options: A)0.1 B)0.4 C)0.82 D)0.8 E)None SOLUTION:Sol. (x×6) = (0.60×4) ⇒ x = 2.4/6 = 0.40. Answer B #### B QUESTION:Two men started from the same place walk at the rate of 10kmph and 12kmph respectively. What time will they take to be 20 km apart, if they walk in the same direction? options: A)5hours B)10hours C)8hours D)10hours E)12hours SOLUTION:To be 2km apart they take 1 hour To be 10km apart they take = 1/2 * 20 =10 hours Answer is B #### B QUESTION:A 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 ? options: A)34 B)40 C)68 D)88 E)None of these SOLUTION:Solution We have : l = 20 ft and lb = 680 sq. ft. So, b = 34 ft. ∴ Length of fencing = (l + 2b) = (20 + 68) ft = 88 ft. Answer D #### D QUESTION:What will be the difference between simple and compound interest at 10% per annum on a sum of Rs. 1000 after 4 years? options: A)Rs.64.18 B)Rs.64.67 C)Rs.64.08 D)Rs.64.10 E)Rs.64.22 SOLUTION:S.I. = (1000 * 10 * 4)/100 = Rs. 400 C.I. = [1000 * (1 + 10/100)4 - 1000] = Rs. 464.10 Difference = (464.10 - 400) = Rs. 64.10 Answer: D #### D QUESTION:It takes one machine 3 hours to complete a production order and another machine 3 hours to complete the same order. How many hours would it take both amhcines working simultaneously at their respective rates to complete the order? options: A)a) 7/12 B)b) 1 1/2 C)c) 1 5/7 D)d) 3 1/2 E)e) 1 1/2 SOLUTION:RT = W Given: R = 1/3 + 1/3 = 2/3 T = ? W = 1 T = 1 / (2/3) = 3/2 = 1 1/2 Answer: E #### E QUESTION:Two numbers are respectively 20% and 50% more than a third number. The ratio of the two numbers is: options: A)4:5 B)3:5 C)6:8 D)3:5 E)5:4 SOLUTION:third number be x. first no = 120% of x = 6x/5 second no = 150% of x = 3x/2 ratio in first two nos = (6x/5:3x/2)=> 4:5 ANSWER A #### A QUESTION:A tank can supply water to a village for 30 days. If a leak at the bottom of the tank drains out 15 liters per day, the supply lasts for 20 days only. For how many days will the supply last if the leak drains out 20 liters per day? options: A)12 B)14 C)15 D)16 E)18 SOLUTION:Losing 15 liters per day results in a loss of 300 liters in 20 days. So, those 300 liters were for 10 days, making daily consumption of the village 30 liters per day. Thus the capacity of the tank is 30*30 = 900 liters. Losing 20 liters plus 30 liters gives 50 liters per day. At this rate the supply will last 900/50 = 18 days. The answer is E. #### E QUESTION:A 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 24 times, A has killed: options: A)27 birds B)72 birds C)30 birds D)80 birds E)20 birds SOLUTION:Let the total number of shots be x. Then, Shots fired by A =(5/8)x Shots fired by B =(3/8)x Killing shots by A =(1/3)of (5/8)x=(5/24)x Shots missed by B =(1/2) of (3/8)x =(3/16)x 3x/16= 27 or x =(24 x 16)/3= 128. Birds killed by A =(5x/24) =(5/24*128)= 27. Answer is A #### A QUESTION:The sum of two numbers is 20. The larger number is four less than twice the smaller number. What are the two numbers? options: A)7 and 12 B)8 and 12 C)9 and 12 D)10 and 12 E)None of these SOLUTION:Let x and y be the two numbers such that x is larger than y. The statement "the larger number is four less than twice the smaller number" may be formulated by x = 2y - 4 We use the sum of the two numbers to write a second equation. x + y = 20 Substitute x by 2y - 4 in x + y = 20 to obtain 2y - 4 + y = 20 Solve for y to find y = 8 and x = 2y - 4 = 12 Answer B #### B QUESTION:For any 5 given numbers, which of the following is always equivalent to adding the 3 numbers together and then dividing the sum by 3? I. Ordering the 3 numbers numerically, from highest to lowest, and then selecting the middle number. II. Dividing each of the numbers by 3 and then adding the results together. III. Multiplying each number by 6, adding the resulting products together, and then dividing the sum by 9. options: A)I only B)II only C)I and II only D)II and III only E)None of the above SOLUTION:Let the 3 numbers be x, y and z. Question: Which of the following is equivalent to (x + y + z)/3 I. Ordering the 3 numbers numerically, from highest to lowest, and then selecting the middle number. --> Not always equivalent Eg: 111 and 141 II. Dividing each of the numbers by 3 and then adding the results together. --> x/3 + y/3 + z/3 = (x + y + z)/3 --> Equivalent III. Multiplying each number by 6, adding the resulting products together, and then dividing the sum by 9. --> (6x + 6y + 6z)/9 = 2(x + y + z)/3 --> Not equivalent Answer: C #### C QUESTION:On 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? options: A) 8 B) 12 C) 24 D) 32 E) 36 SOLUTION:Jan 1 = C Feb 1 = C - 3 March 1 = C - 6 April 1 = C - 9 May 1 = C - 12 June 1 = C - 15 July 1 = C - 18 Aug 1 = C - 21 Sept 1 = C - 24 Difference between stock on September 1 than were in stock on January 1 will be - C - ( C - 24 )= 24 Hence answer will be (C) #### C <<<Examples ends QUESTION:If x and y are integers such that (x+1)^2 is less than or equal to 16 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? options: A) -16 B) -10 C) 0 D) 14 E) 16 SOLUTION:(x+1)^2 <= 16 x <= 3 x >= -5 (y-1)^2< 64 y < 9 y > -7 Max possible value of xy is -5 × -6 = 30 minimum possible value of xy is -5 × 8 = -40 -40 + 30 = -10 Answer : B #### B

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:The students of a particular class were given two tests for evaluation. Twenty Five percent of the class cleared both the tests and forty five percent of the students were able to clear the first test. You have to calculate the percentage of those students who passed the first test and were also able to pass the second test. How will you do it? options: A)48% B)55% C)60% D)71% E)80% SOLUTION:C 60% In all such cases where you have to find out the probability of anything with an already given situation, you have to use the formula for conditional probability. In this case, you have to find out the probability that the second test was passed by a student given that he passed the first test already. Therefore, P(Second/First) = P (First and Second)/ P (First) = 0.25/0.42 =0.60 =60 % #### C QUESTION:The ratio of two numbers is 3 : 4 and their H.C.F. is 4. Their L.C.M. is: options: A)12 B)24 C)34 D)48 E)54 SOLUTION:Let the numbers be 3x and 4x. Then, their H.C.F. = x. So, x = 4. So, the numbers 12 and 16. L.C.M. of 12 and 16 = 48.Answer: Option D #### D QUESTION:A bag contains an equal number of one rupee, 50 paise and 25 paise coins respectively. If the total value is 175, how many coins of each type are there? options: A)20 coins B)30 coins C)50 coins D)100 coins E)None of these SOLUTION:Let number of each type of coin = x. Then, 1 × x + .50 × x + .25x = 175 ⇒ 1.75x = 175 ⇒ x = 100 coins Answer D #### D QUESTION:A 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? options: A)12 B)13 C)14 D)15 E)16 SOLUTION:w:x:y = 100:30:20 20:6:4 20 --- 10 30 --- ? => 15 Answer:D #### D QUESTION:Three numbers are in the ratio 1:3:5 and their H.C.F is 5. The numbers are? options: A)5, 15, 35 B)5, 15, 30 C)5, 15, 25 D)5, 15, 40 E)5, 15, 20 SOLUTION:Let the required numbers be x, 3x and 5x. Then, their H.C.F = x. So, x = 5. The numbers are 5, 15, 25. Answer: C #### C QUESTION:In how many ways can a group of 11 friends be seated round 2 tables if one of the tables can seat 7 and the other can seat 4 people? options: A)11C6 * 9! *4! B)11C3 * 6! *3! C)15C4 * 9! *3! D)15C2 * 10! *3! E)16C5 * 10! *4! SOLUTION:7 people can be selected from 11 people in 11C7 ways. Remaining 4 people can be selected from 4 people in 4C4 ways. Now, arranging 7 people on a round table = (7-1) ! = 6! Arranging 4 people on a round table = (4-1) ! = 3! Hence, total number of ways = 11C7 * 6! * 4C4 * 3! = 11C3 * 6! * 3! B #### B QUESTION:How many kg of salt at 42 paise per kg must a man mix with 25 kg of salt at 24 paise per kg so that he may, on selling the mixture at 40 paise per kg gain 25% on the outlay? options: A)15 kg B)18 kg C)20 kg D)24 kg E)None of these SOLUTION:Here, cost price of mixture = 100×100/100+25 = 32 paise ∴q1q2=32−24/42−32=810=45 and hence q1 = 4⁄5 × 25 = 20 kg Answer C #### C QUESTION:In Township K, 1/5 of the housing units are equipped with cable television . If 1/10 of the housing units , including 1/3 of those that are equipped with cable television , are equipped with videocassette recorders ,what fraction of the housing units have neither cable television nor videocassette recorders ? options: A)23/30 B)11/15 C)7/10 D)1/6 E)2/15 SOLUTION:Let total Housing Units = 5x. As per question, Equipped with Cable TV = x Equipped with VCR = x/2, which includes x/3 CTV. So, only VCR = x/2 - x/3 = x/6. So, Cable TV + VCR = x + x/6 = 7x/6 No Cable TV and VCR = 5x - 7x/6 = 23x/6. Fraction = 23x/(6 * 5x) = 23/30. Hence, A #### A QUESTION:The 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). options: A)8, 20, 28 B)16, 28, 36 C)25,30,20 D)18, 24, 32 E)None of these SOLUTION:Explanation: Let their present ages be 5x, 6x and 4x years respectively. Then, (5x - 5) + (6x - 5) + (4x - 5) = 60 15x-15 = 60 x = 5 Their present ages are 5x = 25 years, 6x = 30 years and 4x = 20 years respectively. Answer: C #### C QUESTION:Let the number which when multiplied by 11 is increased by 300. options: A)14 B)20 C)26 D)28 E)30 SOLUTION:Solution Let the number be x . Then, 11x - x = 300 ‹=›10x = 300 x ‹=› 30. Answer E #### E QUESTION:An accurate clock shows 8 o'clock in the morning. Through how may degrees will the hour hand rotate when the clock shows 2 o'clock in the afternoon? options: A)267 B)180 C)287 D)177 E)911 SOLUTION:Angle traced by the hour hand in 6 hours =(360/12)*6 Answer: B #### B 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? options: A)(-5, -3) B)(-5, 3) C)(5, -3) D)(3, -5) E)(3, 5) SOLUTION:The 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? I marked the tricky part in red. It seems c is anegativenumber and d is a positive number. This means Vertex #1 = (c, d) is in QII (that is, negative x and positive y) Vertex #2 = (c, -d) is in QIII (that is, both xy negative) Vertex #3 = (-c, -d) is in QIV (that is y is negative, but x is positive) That means the last vertex should be in the first quadrant --- the only first quadrant point is (5, 3), answer =E. #### E QUESTION:John is filling out the office space for his employees. There are 8 people in his office, and he must assign 8 employees to the following positions: 2 next to his cabin, 2 near the gate, 2 in center, and 2 near coffee machine. Only 2 employees are secretary and can sit next to his cabin, and they cannot sit anywhere else. The other employees can sit anywhere they like. How many different groupings are possible? options: A)100 B)90 C)80 D)70 E)60 SOLUTION:Secretary can sit in 2C2 ways = 1 Near the gate we can have 6C2 combinations (2 secretaries are already having a place) In the center we can have 4 C2 employees as 4 already have a place Near coffee machine we can have 2C2 employees as all other place are taken Number of selection = 2C2 * 6C2 * 4C2 * 2C2 = 90 Ans: B #### B QUESTION:The ratio between a two-digit number and the sum of the digits of that number is 4 : 1.If the digit in the unit's place is 3 more than the digit in the ten’s place, what is the number? options: A)47 B)36 C)58 D)25 E)14 SOLUTION:Let the ten's digit be x. Then, unit's digit = (x + 3). Sum of the digits = x + (x + 3) = 2x + 3. Number = l0x + (x + 3) = llx + 3. 11x+3 / 2x + 3 = 4 / 1 => 11x + 3 = 4 (2x + 3) => 3x = 9 => x = 3. Hence, required number = 11x + 3 = 36. Answer is B. #### B QUESTION:3,10,29,66,__ options: A)125 B)165 C)145 D)127 E)112 SOLUTION:3=1*1*1+2 10=2*2*2+2 29=3*3*3+2 66=4*4*4+2 Similarly 5*5*5+2=127 ANSWER:D #### D QUESTION:Weights of two friends Ram and Shyam are in the ratio 2:5. 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? options: A)17% B)10% C)21% D)16% E)None SOLUTION:Solution: given ratio of Ram and Shayam's weight = 2:5 Hence, (x-15)/(15-10) = 2/5 Or, x = 17%. Answer: Option A #### A QUESTION:What percent of 7.2 kg is 18 gms ? options: A)25 B)66 C)288 D)19 E)17 SOLUTION:Explanation: Required percentage = (18/7200 * 100)% = 1/4% = 0.25% Answer: A) .25% #### A QUESTION:A fruit seller sells mangoes at the rate of Rs.16 per kg and thereby loses 12%. At what price per kg, he should have sold them to make a profit of 20%? options: A)Rs.21.81 B)Rs.12 C)Rs.12.25 D)Rs.12.31 E)None SOLUTION:Solution 88 : 16 = 120 : x x= (16×120/88) = Rs.21.81 Hence, S.p per Kg = Rs.21.81 Answer A #### A QUESTION:Mr. loyd wants to fence his Square shaped land of 150Sqft each side.If a pole is laid every 30ft how many poles do he need? options: A)20 B)30 C)40 D)50 E)60 SOLUTION:If each side is 120 feet..then total perimeter is 150*4=600 poles every 20 feet hence no of poles= 600/20=30 ANSWER:B #### B QUESTION:In 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 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 Ms. Robbins received? options: A)0.06N + 3,200 B)0.1N + 7,200 C)0.4N + 7,200 D)0.1N + 8,000 E)0.06N + 7,000 SOLUTION:total vote = N vote cast by independent voters = 0.4 N vote cast by registered voters = 0.6 N vote received by Ms. Robbins = 7000 + 10% of vote be registered voters = 7000 + 0.06 N Answer choice E #### E QUESTION:Andrew travelling to 7 cities. Gasoline prices varied from city to city. What is the median gasoline price? options: A)$1 B)$1.84 C)$2.54 D)$2.65 E)$3 SOLUTION:Ordering the data from least to greatest, we get: $1.61, $1.75, $1.79, $1.84, $1.96, $2.09, $2.11 The median gasoline price is $1.84. (There were 3 states with higher gasoline prices and 3 with lower prices.) B #### B QUESTION:The average expenditure of a labourer for 6 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 i options: A)70 B)72 C)75 D)78 E)80 SOLUTION:Income of 6 months = (6 × 85) – debt = 510 – debt Income of the man for next 4 months = 4 × 60 + debt + 30 = 270 + debt ∴ Income of 10 months = 780 Average monthly income = 780 ÷ 10 = 78 Answer D #### D QUESTION:A trader cheats both his supplier and customer by using faulty weights. When he buys from the supplier, he takes 10% more than the indicated weight. When he sells to his customer, he gives the customer a weight such that 10% of that is added to the weight, the weight claimed by the trader is obtained. If he charges the cost price of the weight that he claims, find his profit percentage. options: A)20% B)21% C)21.33% D)22.109% E)23% SOLUTION:Lets say the indicated weight is x for $10 but the trader actually get 1.1x for $10 now he tells to the customer that its 1.1(1.1x) = 1.21x and charges the price accordingly i.e. 1.21x * 10/ x = 12.1 so profit % = (12.1-10)/ 10 = 0.21 = 21% ANSWER:B #### B QUESTION:To 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. options: A)600 B)500 C)575 D)655 E)675 SOLUTION:Let x 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: 3⋅25+(x−3)⋅30=75+30(x−3) Therefore: 25x=75+30(x−3)−100 25x=75+30x−90−100 190−75=30x−25 115=5x x=23 So the company worked 23 days and they made 23⋅25+100=675 pieces. So answer is E. #### E QUESTION:Three 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? options: A) 8 B) 2 C) 6 D) 0 E) 12 SOLUTION:If B admitted 15 are overlapping with A admission of 17 But C does not overlap with anybody. Then no student will get nod from all the 3. Hence 0 student will get admission. Answer : D #### D QUESTION:A1, A2 and A3 enter into a partnership in the ratio 7/2 : 4/3 : 6/5 . After 4 months, A1 increases his share 50%. If the total profit at the end of one year be Rs. 21,600, then A2's share in the profit is: options: A)3000 B)3200 C)3450 D)4000 E)3570 SOLUTION:Ratio of initial investments = 7/2 : 4/3 : 6/5 = 105 : 40 : 36. Let the initial investments be 105x, 40x and 36x. => A1 : A2 : A3 = 105x x 4 + 150/100 x 105x x 8 : (40x x 12) : (36x x 12) = 1680x : 480x : 432x = 35 : 10 : 9. Hence, A2's share = Rs. 21600 x 10/54 = Rs. 4000. Answer : D #### D QUESTION:x and y are positive integers of h. If 1/x + 1/y < 2, which of the following must be true? options: A) x + y > 4 B) xy>1 C) x/y + y/x < 1 D) (x - y)^2 > 0 E) None of the above SOLUTION:Answer is B: 1/X + 1/Y < 2 The maximum value of 1/X is 1 because if X equals any other number greater than one it will be a fraction. The same is true with 1/Y. So 1/X and 1/Y will always be less than 2 as long as both X and Y are not both equal to one at the same time. Another way of putting it is: X*Y>1.B #### B QUESTION:A batsman in his 11th inning makes a score of 69 and their by increasing his average by 1. What is his average after the 11th inning? options: A)58 B)59 C)68 D)69 E)78 SOLUTION:10x + 69 = 11(x + 1) x = 58 + 1 = 59 Answer:B #### B QUESTION:For a finite sequence of non zero numbers, the number of variations in 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 3, -3, 2, 5, -4, -6 ? options: A)1 B)2 C)3 D)4 E)5 SOLUTION:Given sequence: {1, -3, 2, 5, -4, -6} The questions basically asks: how manypairs of consecutive termsare there in the sequence such that the product of these consecutive terms is negative. 1*(-3)=-3=negative; -3*2=-6=negative; 2*5=10=positive; 5*(-4)=-20=negative; (-4)*(-6)=24=positive. So there are 3 pairs of consecutive terms of the sequence for which the product is negative. Answer: A. #### A QUESTION:Jaclyn buys $60 000 worth of debentures in a company. She earns 9.5% p.a. simple interest, paid to her quarterly (that is, every 3 months). If the agreed period of the debenture was 18 months: calculate the amount of interest Jaclyn will earn for each quarter options: A)1187.5 B)1234 C)1289 D)1425 E)None of these SOLUTION:Explanation: I=(p x r x t)/100 = 60000*9.5/100*(18/12)^1/6 = 1425 Answer: D #### D QUESTION:Circular gears P and Q start rotating at the same time at constant speeds. Gear P makes 10 revolutions per minute and Gear Q makes 40 revolutions per minute. How many seconds after the gears start rotating will gear Q have made exactly 45 more revolutions than gear P? options: A)45 B)80 C)90 D)100 E)120 SOLUTION:Gear Q makes 30 more revolutions each 60 seconds. The time to make 45 = 30*1.5 more revolutions is 60*1.5 = 90 seconds. The answer is C. #### C QUESTION:The greatest possible length which can be used to measure exactly the length 7m, 3m 85cm, 12 m 95 cm is options: A)15 cm B)25 cm C)35 cm D)42 cm E)43 cm SOLUTION:Explanation: Required Length = H.C.F of 700 cm, 385 cm and 1295 c = 35 cm. Answer: C #### C QUESTION:The 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? options: A)65 B)21 C)78 D)67 E)51 SOLUTION:Let the total number of workers be x. Then, 8000x = (12000 * 7) + 6000(x - 7) = 2000x = 42000 = x = 21. Answer: B #### B QUESTION:A number when successively divided by 3,5 and 8 leaves remainders 1,4 and 7 respectively. Find the respective remainders R when the order of the divisors is reversed. options: A)8,5,3 B)R=4,2,1 C)R=3,2,1 D)R=6,4,2 E)None of above SOLUTION:My approach would be Three Divisors : 3, 5, 8 Three Remain: 1, 4, 7 Start from the bottom of the last column i.e. from the third remainder: Go up diagonally and multiply by the second divisor: 5*7 = 35 Go down and add the second remainder: 35 + 4 = 39 Go up diagonally and multiply by the first divisor: 39* 3 = 117 Go down and add the first remainder: 117 + 1 = 118 Divide 118 by 8, 5, 3 118/8 gives quotient = 14 and remainder = 6 14/5 gives quotient = 2 and remainder = 4 2/3 gives quotient = 0 and remainder = 2 Ans is D i.e. 6,4,2 #### D QUESTION:Convert 50miles into yards? options: A)25630 yards B)35200 yards C)88000 yards D)42560 yards E)41520 yards SOLUTION:1 mile = 1760 yards 50 miles = 50*1760 = 88000 yards Answer is C #### C QUESTION:8k8 + k88 -------- 1,6t6 If k and t represent non-zero digits within the integers above, what is t? options: A)6 B)7 C)8 D)9 E)17 SOLUTION:8k8 k88 -------- 16t6 Trial 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 t=6. Answer: A. #### A QUESTION:Two 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 2:3 and 3:1 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. options: A)99:61 B)99:160 C)61:160 D)61:99 E)99:160 SOLUTION:Vessel A = 300 gallons --> milk = 120, water = 180; Vessel B = 500 gallons --> milk = 375, water = 125; Vessel A + B = 800 gallons --> milk = 495, water 305. The ratio = 495/305 --> reduce by 5 = 99/61. Answer: A. #### A QUESTION:The true discount on a bill of Rs. 2560 is Rs. 360. What is the banker's discount? options: A)Rs. 432 B)Rs. 422 C)Rs. 419 D)Rs. 442 E)None of these SOLUTION:Explanation : F = Rs. 2560 TD = Rs. 360 PW = F - TD = 2560 - 360 = Rs. 2200 True Discount is the Simple Interest on the present value for unexpired time =>Simple Interest on Rs. 2200 for unexpired time = Rs. 360 Banker's Discount is the Simple Interest on the face value of the bill for unexpired time = Simple Interest on Rs. 2160 for unexpired time =360/2200 × 2560 = 0.16 × 2560 = Rs. 419 Answer : Option C #### C QUESTION:A recycling facility is staffed by 9 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’s wages account for 1/9 of all wages paid at the facility, what is the value of n? options: A)8/7 B)8 C)9/8 D)7 E)5 SOLUTION:Say each floor worker is paid $x, then the manager is paid $xn. Total salary would be 9x+xn and we are told that it equals to 9xn: 9x+xn=9xn --> reduce by x: 9+n=9n -->8n=9 n = 9/8 Answer: C #### C QUESTION:Rovert traveled a distance of 30 km, covering the first 10 km in x minutes, the next 10 km in y minutes and the last 10 km in z minutes. If he totally took 3y minutes to cover the whole distance, then which of the following cannot be true? Assume x , y and z are different. options: A)z=3x B)x=3z C)y=2x D)x=2y E)y=3x SOLUTION:Rovert Travelled for x,y and for z min. Total Time : x + y + z Which is equal to : 3y Equating both sides we get x+y+z = 3y => x+z =2y ........ Eqn 1 Looking out at options D Says x =2y Using it in Eqn 1 2y + z = 2y => Z = 0 mins, Which I guess is not possible. The Ans isD #### D QUESTION:If MAPLE is coded as VOKZN then how will CAMEL be coded? options: A)OVNZF B)OUNZX C)OVNZX D)XZNVO E)XZNVV SOLUTION: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 Z Y X W V U T S R Q P O N M L K J I H G F E D C B A So each alphabet is replaced by the above rule and also whole word is reversed i.e MAPLE - after just replacing each alphabet (by above rule) we get NZKOV,then we reverse this word again and we get VOKZN. so this way CAMEL becomes OVNZX ANSWER:C #### C QUESTION:What least number must be subtracted from 7538 so that remaining no.is divisible by 14 options: A)3 B)5 C)6 D)8 E)9 SOLUTION:Explanation: On dividing 7538 by 14 we get the remainder 6, so 6 should be subtracted Option C #### C QUESTION:Out of four consonants and three vowels, how many words can be made so that each word contains two consonants and three vowels? options: A)480 B)540 C)600 D)720 E)900 SOLUTION:4C2 x 3C3 x 5! = 720 The answer is D. #### D QUESTION:Which of the following CANNOT be a value of 8/(x–8)? options: A)-1 B)-1/2 C)0 D)2 E)8 SOLUTION:The question doesn't ask for the value of x here, but for the possible results of the equation. If 8/(x-8) = 0, then the numerator must be 0. But since the numerator is 8, the fraction can not be equal to 0. The answer is C. #### C QUESTION:Two 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? options: A)22 B)98 C)60 D)88 E)12 SOLUTION:Let the speed of the slower train be x m/sec. Then, speed of the train = 2x m/sec. Relative speed = ( x + 2x) = 3x m/sec. (100 + 100)/8 = 3x => x = 25/3. So, speed of the faster train = 50/3 = 50/3 * 18/5 = 60 km/hr. Answer:C #### C QUESTION:In a Private Company 20 Nos. staffs are employed. In a Festival season their Boss give festival allowance to all. He says his accountant to calculate for 30 days @ 100. Also he says balance payment will give to driver and cleaning staff and to be adjust from petty cash. He had given Rs.65000/- to the accountant. How much amount will taken from Petty cash? options: A)1000 B)3000 C)3500 D)2500 E)2250 SOLUTION:For 20 staffs: 300*100*20 = 60000 for driver and cleaning staff: 300*100*2 =6000 From petty Cash : 1000 Answer is 1000 #### A QUESTION:A 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 ? options: A)A)1km B)B)300m C)C)650m D)D)750m E)E)800m SOLUTION:Relative speed of the policeman = 20-15 = 5 km/hr time taken by policeman to cover 100m = (100/1000)*(1/5) = 1/50 hr In 1/50 hr the thief covers a distance of 15/50 km = 3/10 km = 300m Answer is B #### B QUESTION:A train 250 m long running at 72 kmph crosses a platform in 20 sec. What is the length of the platform? options: A)150m B)200m C)250m D)270m E)300 m SOLUTION:D = 72 * 5/18 = 20 = 400 – 250 = 150m ANSWER:A #### A QUESTION:In how many ways can 4 men & 3 women can be made from a gang of 6 men & 7 women ? options: A)10 hr B)50 C)20 D)250 E)260 SOLUTION:Explanation: 6C4 * 7C3 = 50 B #### B QUESTION:Two 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 75 percent in profit, And Errol lost all the money he had remaining. What percentage of Arthur's fortune currently remains? options: A)93% B)97% C)100% D)107% E)99% SOLUTION:Say Arthur's fortune was $100. Then: A = 20*1.5*1.1 = 33 B = 20*1.5*1.1 = 33 C = 20*1.5*0.4 = 12 D = 20*0.6*1.75 = 21 E = 0 Total 33 + 33 + 12 + 21 = 99. Answer: E. #### E QUESTION:A guy was asked to specify his age in years. He said, “Take my age 6 years hence, multiply it by six and subtract six of my age 6 years ago and you will know my age.” What was the age of that guy? options: A)18 B)35 C)53 D)69 E)72 SOLUTION:Current age of the guy = A years. Then, 6 (A + 6) – 6 (A – 6) = A (6A + 36) – (6A – 36) = A A = 72 E #### E QUESTION:Cars P and Q are approaching each other on the same highway. Car P is moving at 46 mph northbound and Car Q is moving at 54 mph southbound. At 2:00 pm, they are approaching each other and 190 miles apart. Eventually they pass each other. At what clock time are they moving away from each other and 35 miles apart? options: A) 3:30 pm B) 3:45 pm C) 4:00 pm D) 4:15 pm E) 4:30 pm SOLUTION:Total distance, which should be covered by both cars is 190+35=225 miles. Let t be the time so the equation will be 46t+54t=225 thus, t=2.25 hours Answer: D #### D QUESTION:The 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? options: A)Rs. 8400 B)Rs. 8721 C)Rs. 8856 D)Rs. 9000 E)None of these SOLUTION:Explanation: Actual price = 95% of 90% of 85% of Rs. 12000 = 95/100 * 90/100 * 85/100 * 12000 = Rs. 8721. ANSWER IS B #### B QUESTION:Sheena has a pet frog and it is growing fast and eating more flies each day. When she first brought it home on Monday it ate 3 flies, Tuesday it ate 6, Wednesday it ate 9, and Friday it ate 15. How many flies did her frog eat on Thursday? options: A)12 B)14 C)10 D)11 E)13 SOLUTION:A) 12. The frog started eating 3 more flies each day. 3 +3 =6 6+3=9 9+3=12 12+3=15 #### A QUESTION:72 hens cost Rs. __ 96.7__. Then what does each hen cost, where two digits in place of ‘__’ are not visible or are written in illegible hand? options: A)Rs. 3.23 B)Rs. 5.11 C)Rs. 5.51 D)Rs. 7.22 E)None SOLUTION:Explanation : The best way to solve this question is to multiply the alternatives by 72 and find which one gives the middle three digits 96.7. To cut time, you can choose to multiply 72 by integer values only, e.g. 72 × 3 = 216, 72 × 5 = 360 and 72 × 7 = 504. It must be remembered that the decimal part of the answer will be multiplied by 72 and the actual answer will increase . Let us now roughly multiply the decimal values of the options also by 72, e.g. 72 x 0.2 = 14.4, 72 × 0.1 = 7.2 and 72 × 0.5 = 36. So, option (1) will yield (216 + 14) = 230 (approximately), option(2) will yield (360 + 7) = 367 (approximately), option(3) will yield (360 + 36) = 396 (approximately), and option(4) will yield (504 + 14) = 528 (approximately). Of these only option (3) satisfies our requirement of 2nd and 3rd digits being 96. Answer : C #### C QUESTION:A can do a work in 40days, B in 60days. A alone start the work after 10days he left work. In how many days B can finish the work? options: A)20days B)15days C)30days D)45days E)50days SOLUTION:10days work of A = 10/40 = 1/4 remaining work = 1-1/4 = 3/4 B can finish 3/4 work = 60*3/4 = 45days Answer is D #### D QUESTION:Carmen made a sculpture from small pieces of wood. The sculpture is 2 feet 10 inches tall.Carmen places her sculpture on a base that is 2 inches tall. How tall are the sculpture andbase together? options: A)3.1 feet B)3.2 feet C)3.3 feet D)3.0 feet E)3.5 feet SOLUTION:we know 1 feet =12 inch then 2 feet =24 inch 24+10=34 then 34+2=36 36/12=3.0 feet ANSWER:D #### D QUESTION:Aishwarya’s 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 : options: A)10 years B)11 years C)15 years D)9 years E)4 years SOLUTION:A 6 years Mom’s age when Aishwarya’s sister was born = 20 years. Dad’s age when Aishwarya’s sister was born = (28 + 2) years = 30 years. Needed Variance = (30 – 20) years = 10 years. Answer is A #### A QUESTION:In 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 = options: A)6 B)7 C)5 D)8 E)3 SOLUTION:Line k passes through the origin and has slope 1/7 means that its equation is y=1/7*x. Thus: (x, 1)=(7, 1) and (7, y) = (7,1) --> x-y=7-1=6. Answer: A #### A QUESTION:A 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? options: A)12 min B)17 min C)19 min D)11 min E)16 min SOLUTION:Since 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. Relative speed of A and B = 6 - 1 = 5 rounds per hour. Time taken to complete one round at this speed = 1/5 hr = 12 min. Answer: A #### A QUESTION:If c and d are prime numbers, which of the following CANNOT be the sum of c and d? options: A)5 B)9 C)13 D)23 E)33 SOLUTION:All answer choices but D are odd. In order odd number to be the sum of two prime numbers one must be even, so 2, and another odd. Now, 23=2+21. Since 21 is not a prime then 23 cannot be written as the sum of two prime numbers. Answer: D #### D QUESTION:The amount of water (in ml) that should be added to reduce 9 ml. Lotion, containing 50% alcohol, to a lotion containing 45% alcohol, is? options: A)1 B)4 C)5 D)6 E)7 SOLUTION:4.5 4.5 45% 55% 45% ----- 4.5 55% ------? => 5.5 - 4.5 = 1 ml ANSWER:A #### A QUESTION:When 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? options: A)10 B)20 C)30 D)40 E)50 SOLUTION:Asha=25 Nisha =n Usha =3n Asha=2a Nisha =a Usha =34 The difference of all ages must be same 25-2a=n-a=3n-34 We will get two equation 2n+a=34 n+a=25 From the equation we will get n=9 and a=16 The ages are Asha=2a=32 Nisha =16 and Usha =34 Sum of the ages =100 (32+x)+(16+x)+(34+x)=100 82+3x=100 3x=18 x=6 Age of Usha =34+6=40 ANSWER:D #### D QUESTION:A meal cost $ 35.50 adn there was no tax. If the tip was more than 5 pc but less than 8pc of the price, then the total amount paid should be: options: A)40-42 B)39-41 C)38-40 D)37-38 E)36-37 SOLUTION:5%(35.5) = 1.775 8%(35.5) = 2.84 total amount could have been 35.5+1.775 and 35.5+2.84 => could have been between 37.275 and 38.34 => approximately between 37 and 38 Answer is B.D #### D <<<Examples ends QUESTION:Less than half of a committee that is to be formed out of certain group, are to be men. If there are 100 possible ways of forming the committee, then the number of men in the committee can be, options: A)2 B)3 C)4 D)5 E)cannot be determined SOLUTION:1. Let there be m men and w women out of which the committee is formed. 2. mCn * wCr = 100, where n is the number of men chosen and r is the number of women chosen 3. The possible products for LHS of (2) are, 100 * 1, 50 * 2, 25 * 4, 20 * 5, 10 * 10 4. Since the number of women is greater than the number of men, the first three products in (3) can be rejected as they would not satisfy this condition. 5. In the case of the fourth product, 20 * 5 may be given by 6C3 * 5C1. Though this may satisfy the condition with 3 women and 1 man, 1 man is not in the choices given. 6. The last product 10 * 10 may be given by 5C2 * 5C3 with 2 men and 3 women. This satisfies the condition and also 2 men is one of the choices given. Therefore the answer is choice A. #### A

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:The residents of Town X participated in a survey to determine the number of hours per week each resident spent watching television. The distribution of the results of the survey had a mean of 21 hours and a standard deviation of 8 hours. The number of hours that Pat, a resident of Town X, watched television last week was between 1 and 2 standard deviations below the mean. Which of the following could be the number of hours that Pat watched television last week? options: A)30 B)20 C)11 D)14 E)6 SOLUTION:Given: mean=21 and SD=8 The number of hours that Pat watched television was between 1 and 2 standard deviations below the mean: 1 SD below the mean ismean-1*SD=13 and 2 SD below the mean ismean-2*SD=5, so the number of hours that Pat watched television was between 5 and 13 hours. Answer: C #### C QUESTION:Find the invalid no.from the following series 15 46 63 71 75 77 78 options: A)32 B)35 C)46 D)49 E)67 SOLUTION:In 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. 46 C #### C QUESTION:A rectangular parking space is marked out by painting three of its sides. If the length of the unpainted side is 9 feet, and the sum of the lengths of the painted sides is 37 feet, find out the area of the parking space in square feet? options: A)124 sq.ft. B)120 sq.ft. C)126 sq.ft. D)129 sq.ft. E)132 sq.ft. SOLUTION:Let l = 9 ft. Then l + 2b = 37 => 2b = 37 - l = 37 - 9 = 28 => b = 28/2 = 14 ft Area = lb = 9 × 14 = 126 sq. ft. Answer is C. #### C QUESTION:What is the speed required for a car to cover a distance of 600 km in 5 hours? options: A)160 kmh B)140 kmh C)150 kmh D)130 kmh E)120 kmh SOLUTION:Speed= Distance / Time Speed = 600 / 5 = 140 Answer: B #### B QUESTION:A candidate got 35% of the votes and lost to the rival by 1350 votes. How many votes were cast? options: A)4000 B)4500 C)5000 D)5500 E)6000 SOLUTION:35%-----------L 65%-----------W ------------------ 30% = 1350 10% = 450 100% of the votes = 4500 Answer: B #### B QUESTION:A person saves 10% of his income. If his income is increased by 20% and he saves 15% of the new income, by what percent his savings will increase? options: A)80% B)90% C)70% D)60% E)50% SOLUTION:Ans. Let previous income = Rs. 100 Previous savings = 10% of Rs. 100 = Rs. 10 Increased income = Rs. 100 + 20% of Rs. 100 = Rs. 120 Increased savings = 15% of Rs. 120 = Rs. 18 Therefore, Increase in savings = Rs. 18 - Rs. 10 = Rs. 8 Therefore, Percent increase in savings = 8/10 x 100 = 80% Answer A #### A QUESTION:It is known that no more than 7 children will be attending a party. What is the smallest number of cookies that must be brought to the party so that each child receives the same number of cookies? options: A)220 B)250 C)320 D)420 E)560 SOLUTION:No more than 7 children attending the party means the number of children could be 1,2,3,4,5,6,7. We need to find a number that is divisible by each of these. Out of the choices given only 420 is divisible by each of these numbers. Hence , answer is D. #### D QUESTION:A train 120 m long passed a pole in 6 sec. How long will it take to pass a platform 360 m long? options: A)20 sec B)21 C)22 D)23 E)24 SOLUTION:Speed = 120/6 = 20 m/sec. Required time = (120 + 360)/20 = 24 sec. Answer:E #### E QUESTION:Speed of a boat in standing water is 16 kmph and the speed of the stream is 2 kmph. A man rows to a place at a distance of 6840 km and comes back to the starting point. The total time taken by him is: options: A)914.2 hours B)900 hours C)915 hours D)868.6 hours E)915 hours SOLUTION:Explanation: Speed downstream = (16 + 2) = 18 kmph Speed upstream = (16 - 2) = 14 kmph Total time taken = 6840/18 + 6840/14 = 380 + 488.6 = 868.6 hours Answer: Option D #### D QUESTION:if price of t.v set is reduced by 25%, then its sale increases by 75%, find net effect on sale value options: A)31 B)32 C)46 D)47 E)48 SOLUTION:- a + b + ((-a)(b)/100) = -25+75+(-25*75)/100 = -25+75-19 =31 ANSWER:A #### A QUESTION:In three annual examinations, of which the aggregate marks of each was 500, a student secured average marks 45% and 55% in the first and the second yearly examinations respectively. To secure 70% average total marks, it is necessary for him in third yearly examination to secure marks : options: A)300 B)350 C)400 D)450 E)550 SOLUTION:total marks:1500 for three exams 70% of 1500=1050 first exam marks=45% of 500=225 second exam marks=55% of 500=275 let X be the third exam marks 225 + 275 + X =1050 X=550 ANSWER:E #### E QUESTION:In a certain pond, 50 fish were caught, tagged, and returned to the pond. A few days later, 50 fish were caught again, of which 8 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 is the approximate number of fish in the pond? options: A) 400 B) 625 C) 1,250 D) 2,500 E) 312 SOLUTION:total fish = x percentage of second catch = (8/50)*100 = 16% so, x * 16% = 50 x = 312 ans.E #### E QUESTION:A certain deck of cards contains 2 blue 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 green? options: A)15/28 B)1/4 C)9/16 D)1/32 E)1/16 SOLUTION:The question asks they will both be not green. Considering that these are draws without replacement there are following possibilities : draw 1, draw 2 ===== ===== 1) Not green, green; 2) green, Not green; 3) green, green; 4) Not green, not green; The 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 green P(4) = 6/8*5/7=15/28 1- [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 A #### A QUESTION:The area of a parallelogram is 162sq m and its altitude is twice the corresponding base. Then the length of the base is? options: A)8 B)9 C)7 D)62 E)2 SOLUTION:2x * x = 162 => x= 9 Answer: B #### B QUESTION:Sally, Mark, Sarah, Steve and Jim are inheriting the money from their grandmother. She left them $527,500 to split equally between all of them. If the money is split equally, how much money will each person receive? options: A)$135,875 B)$52,700 C)$127,900 D)$105,500 E)$105,000 SOLUTION:There are 5 people inheriting the money. We have to take the total of the inheritance and divide it by 5 for each person receiving money. $527,500 / 5 = $105,500. Therefore the correct answer is D. #### D QUESTION:Ten years ago, a mother was four times older than her daughter. After ten years, the mother will be twice older than daughter. The present age of the daughter is options: A)22 B)21 C)24 D)20 E)19 SOLUTION:Let the mother’s present age be ’x’ Let the daughter’s age be ’y’; 10 years ago; (x - 10) = 4(y - 10) or x - 4y = - 30.. (1) 10 years later; (x + 10) = 2(y + 10) or x - 2y = 10.. (2) Solving (1) & (2) y = 20 ANSWER:D #### D QUESTION:The 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? options: A)2^9 B)2^14 C)2^18 D)2^40 E)2^48 SOLUTION:26 letters in the alphabet, 26*2 = 52 letters, since the password is case-sensitive. Accounting for possibilities of the other special characters we have; 26+26+10+1+1 = 64, or 2^6 possibilities per character of the password. Total number of possible combinations: (2^6)^8 = 2^48 ANSWER:E #### E QUESTION:A certain list has an average of 6 and a standard deviation of B (B is positive). Which of the following pairs of data when added to the list, must result in a list of 102 data with standard deviation less than B? options: A)(-6;0) B)(0;0) C)(0;6) D)(0;12) E)(6;6) SOLUTION:Standard deviation shows how much variation there is from the mean. A low standard deviation indicates that the data points tend to be very close to the mean, whereas high standard deviation indicates that the data are spread out over a large range of values. So when we add numbers, which are far from the mean we are stretching the set making SD bigger and when we add numbers which are close to the mean we are shrinking the set making SD smaller. According to the above adding two numbers which are closest to the mean will shrink the set most, thus decreasing SD by the greatest amount. Closest to the mean are 6 and 6 (actually these numbers equal to the mean) thus adding them will definitely shrink the set, thus decreasing SD. E) #### E QUESTION:If x is to be chosen at random from the set {5,6,7,8} and y is to be chosen at random from the set {7,8,9}, what`s the probability that xy will be even? options: A)1/6 B)1/3 C)1/2 D)5/6 E)2/3 SOLUTION:The product to be even either one or both must be even, so: P(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; Or: 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. Answer: E. #### E QUESTION:The H.C.F. of two numbers is 5 and their L.C.M. is 150. If one of the numbers is 25, then the other is: options: A)30 B)28 C)24 D)20 E)35 SOLUTION:Product of two nos = product of HCF and LCM Let one number = x => 25 * x = 5 * 150 x=5*150/25=30 ANSWER A #### A QUESTION:10^(600) ÷ 10^(580) = ? options: A)10^10 B)10^20 C)10^22 D)10^23 E)10^24 SOLUTION:10^(600) ÷ 10^(580) = 10^ (600-580) = 10^20 Answer : B #### B QUESTION:A train 150 m long pass a telegraph pole in 5 seconds. Find the speed of the train options: A)66 km/hr B)108 km/hr C)72 km/hr D)79.2 km/hr E)None SOLUTION:Sol. Speed = [150/5] m/sec = [30 * 18/5] km/hr = 108 km/hr. Answer B #### B QUESTION:The total number of plums that grow during each year on a certain plum tree is equal to the number of plums that grew during the previous year, less the age of the tree in years (rounded down to the nearest integer). During its 5th year, the plum tree grew 50 plums. If this trend continues, how many plums will it grow during its 6th year? options: A)40 B)42 C)45 D)48 E)54 SOLUTION:1st year : 0-1 (age), we take age = 0 (as the question says that we have to(rounded down to the nearest integer)) 2ndyear : 1-2 (age), we take age = 1 3rd year : 2-3 (age), we take age = 2 4th year : 3-4 (age), we take age = 3 5th year : 4-5 (age), we take age = 4 6th year : 5-6 (age), we take age = 5 Thus for the 5th year = 50, 6th year = 50-5 = 45. The correct answer is C. #### C QUESTION:Maddie has 15 apples, if she give 8 to mike, how many does she have left? options: A)1 B)7 C)3 D)4 E)5 SOLUTION:15-8=7 B. 7 #### B QUESTION:I. a^2 - 9a + 20 = 0, II. 2b^2 - 5b - 12 = 0 to solve both the equations to find the values of a and b? options: A)If a < b B)If a ≤ b C)If the relationship between a and b cannot be established D)If a > b E)If a ≥ b SOLUTION:I. (a - 5)(a - 4) = 0 => a = 5, 4 II. (2b + 3)(b - 4) = 0 => b = 4, -3/2 => a ≥ b Option E #### E QUESTION:A grocer buys apples for 63¢ 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? options: A)66¢ B)70¢ C)75¢ D)77¢ E)84¢ SOLUTION:for making calculation simple let us consider he buys 10 pounds @ 63/pound=630¢ in total . 10% apples lost...means 9 pounds left. further he wants 20% profit on 630 ¢ means he wants to earn 756¢ sales price should be 756/9==¢ 84 ANSWER:E #### E QUESTION:What least number mustbe subtracted from 427398 so that remaining no.is divisible by 15 options: A)3 B)5 C)6 D)8 E)9 SOLUTION:Explanation: On dividing 427398 by 15 we get the remainder 3, so 3 should be subtracted Option A #### A QUESTION:A runner runs the 40 miles from Marathon to Athens at a constant speed. Halfway through the run she injures her foot, and continues to run at half her previous speed. If the second half takes her 11 hours longer than the first half, how many hours did it take the runner to run the second half? options: A)14 B)15 C)18 D)22 E)33 SOLUTION:The runner runs the first 20 miles at speed v and the second 20 miles at speed v/2. The time T2 to run the second half must be twice the time T1 to run the first half. T2 = 2*T1 = T1+11 T1 = 11 and so T2 = 22. The answer is D. #### D QUESTION:In a tree, 3/7 of the birds are parrots while the rest are toucans. If 2/3 of the parrots are female and 7/10 of the toucans are female, what fraction of the birds in the tree are male? options: A)3/7 B)11/35 C)16/35 D)31/70 E)37/70 SOLUTION:Let x be the number of birds in the tree. The fraction of birds that are male parrots is (1/3)(3/7)=1/7. The fraction of birds that are male toucans is (3/10)(4/7)=6/35. The total fraction of male birds is 1/7 + 6/35 = 11/35. The answer is B. #### B QUESTION:An bus covers a certain distance at a speed of 100 kmph in 5 hours. To cover the samedistance in 1hr, it must travel at a speed of? options: A)500 km/hr B)640 km/hr C)656 km/hr D)731 km/hr E)720 km/hr SOLUTION:Distance = (100 x 5) = 500 km. Required speed = 500 km/hr. A #### A QUESTION:An apple orchard grows red and green apples. On the first day of harvest, 496 apples are collected. There are three times as many red apples as there are green apples. How many green apples were harvested? options: A)99 B)112 C)118 D)124 E)130 SOLUTION:Let x be the number of green apples. There were 496 total apples; there are three times as many red apples as green apples. Therefore, x + 3x = 496 4x = 496 x = 124 Answer: D #### D QUESTION:The 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 options: A)20 B)21 C)22 D)23 E)24 SOLUTION:Solution Let the toatl number of workers be x. Then 8000x=(12000 x 7) + 6000 (x -7) 2000x =42000 x= 21. Answer B #### B QUESTION:a number divided by 44 leaves remainder 12 what is the remainder when same number divided by 12 options: A)7 B)8 C)9 D)10 E)11 SOLUTION:add 44+12=56 now 56divided by 12 so we get 8 as reaminder ANSWER:B #### B QUESTION:Find the middle one when The sum of three consecutive even numbers is 36? options: A)10 B)12 C)14 D)16 E)18 SOLUTION:3 consecutive numbers can be a - 1, a, a + 1 So sum of numbers = 3a = 36. Hence a = 12. B #### B QUESTION:A courier charges for packages to a certain destination are 65 cents for the first 250 grams and 10 cents for each additional 100 grams or part thereof. What could be the weight in grams of a package for which the charge is $2.05? options: A)980 B)1130 C)1440 D)1610 E)1820 SOLUTION:The charge is 65 cents for the first 250 grams. This leaves a charge of $2.05 - $0.65 = $1.40 The charge for the next 1300 grams is $1.30 which leaves a charge of $0.10 The weight is somewhere between 1550 and 1650. The answer is D. #### D QUESTION:If the price of a TV is first decreased by 20% and then increased by 45%, then the net change in the price will be : options: A)4% increase B)10% increase C)10% decrease D)16% increase E)None of these SOLUTION:Explanation : Solution: let the original price be Rs. 100. New final price = 145% of(80% of 100) =Rs. 145/100 * 80/100 * 100 = Rs. 116. .'. Increase = 16% Answer : D #### D QUESTION:The area of a circular field is 17.56 hectares. Find the cost of fencing it at the rate of Rs. 6 per metre approximately options: A)4457 B)4567 C)4235 D)4547 E)8915 SOLUTION:Explanation: Area = (17.56 x 10000) m2= 175600 m2. ΠR2 = 175600 ⇔ (R)2 = (175600 x (7/22)) ⇔ R = 236.37 m. Circumference = 2ΠR = (2 x (22/7) x 236.37) m =1485.78 m. Cost of fencing = Rs. (1485.78 x 6) = Rs. 8915. Answer: Option E #### E QUESTION:In the xy-coordinate system, line k passes through points (-7m, 0) and (0, 3m). Which of the following is a possible equation of line k? options: A)y = -7/3*x + 3m B)y = 3/7*x - 7m C)y = 7/3*x + 3m D)y = 3/7*x + 3m E)y = -3/7*x - 7m SOLUTION:The slope of the line is 3m/7m=3/7. The y-intercept is 3m. the equation of the line is: y = 3/7*x +3m The answer is D. #### D QUESTION:The difference between the simple interest on a certain sum at the rate of 10%per annum for 2 years and compound interest which is compounded every 6 months is Rs.124.05. what is the principal sum options: A)124.05 B)124.09 C)124.04 D)124.06 E)124.02 SOLUTION:Explanation: Compound Interest on P at 10% for 2 years when interest is compounded half-yearly = Simple Interest on P at 10% for 2 years = Given that difference between compound interest and simple interest = 124.05 Answer:A #### A QUESTION:Fox 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? options: A)9% B)56.6% C)11% D)12% E)15% SOLUTION:You 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 3(15) = 45 - Fox 2(18) = 36 - Pony The total discount discount is $3 and you are asked to find the percent discount of pony jeans, so 45(18 - X)/100 + 36(X)/100 = 3 or 45*18 -45*x + 36*x =3*100 or 9x = -3*100 +45*18 x= 510/9 = 56.6% B #### B QUESTION:The value of 0.1 x 0.1 x 0.1 + 0.02 x 0.02 x 0.02 is: 0.2 x 0.2 x 0.2 + 0.04 x 0.04 x 0.04 options: A)0.0125 B)0.125 C)0.25 D)0.5 E)None of these SOLUTION:Explanation: Given expression = (0.1)3 + (0.02)3=1= 0.125 23 [(0.1)3 + (0.02)3] =8 Answer- B #### B QUESTION:A 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? options: A)4 B)5 C)6 D)7 E)8 SOLUTION:If n is a perfect square and a perfect cube, then n = a^6 for some integer a. The numbers are 1^6=1, 2^6=64, 3^6= 729, 4^6=4096, 5^6=15,625. The answer is B. #### B QUESTION:The mean of 50 observations was 36. It was found later that an observation 48 was wrongly taken as 23. The corrected new mean is options: A)76.5 B)36.5 C)46.5 D)16.5 E)26.5 SOLUTION:Explanation: Correct Sum = (36 * 50 + 48 - 23) = 1825. Correct mean = = 1825/50 = 36.5 Answer: B #### B QUESTION:A train sets off at 9:00 am at the speed of 70 km/h. Another train starts at 10:30 am in the same direction at the rate of 80 km/h. At what time will the second train catch the first train? options: A)7:00 B)8:00 C)9:00 D)10:00 E)11:00 SOLUTION:In one hour and thirty minutes the first train travels 105 km. The second train catches the first train at a rate of 80 km/h - 70 km/h = 10 km/h. The second train will catch the first train in 105/10 = 10.5 hours, so at 9:00 pm. The answer is C. #### C QUESTION:o 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 33×13%33×13%, and finished the work 1 day earlier than it was planned. A) What is the area of the grass field? B) How many days did it take to mow the whole field? C) How many days were scheduled initially for this job? options: A)387 B)39 C)37 D)20 E)28 SOLUTION:Hint: See problem 20 and solve by yourself. Answer: A) 120 hectares; B) 7 days; C) 8 days. Answer:D #### D QUESTION:Find the perimeter and area of the rectangle of length 17 cm and breadth 13 cm. options: A)221 cm2 B)211 cm2 C)231 cm2 D)236 cm2 E)241 cm2 SOLUTION:Given: length = 17 cm, breadth = 13 cm Perimeter of rectangle = 2 (length + breadth) = 2 (17 + 13) cm = 2 × 30 cm = 60 cm We know that the area of rectangle = length × breadth = (17 × 13) cm22 = 221 cm2 ANSWER :A #### A QUESTION:385, 462, 572, 396, 429, 671, 264 options: A)385 B)429 C)671 D)264 E)None of these SOLUTION:Solution In each number except 429,the middle digit is the sum of the other two. Answer B #### B QUESTION:Among the two clocks, clock A gains 20 seconds per minute. If clock A and B are set at 2 0'clock, when clock A is at 7:20, what does clock B show? options: A)5:30 B)6:00 C)5:45 D)6:20 E)3:30 SOLUTION:Clock A gains 20 seconds per minute, 1200 seconds per hour or 20 minutes per hour. The two clocks show 2:00 at 2 0'clock At 3:00 - Clock B is at 3:00 Clock A is at 3:20 (1 hour + gains 20 minutes) AT 4:00 - Clock B is at 4:00 Clock A is at 4:40 (2 hours + gains 40 minutes) In 4 hours the clock A gains 4*20=80 minutes or 1 hour 20 minutes If clock A is at 7:20 the clock B is at 6:00 Answer is B #### B QUESTION:If the height of a cone is increased by 100% then its volume is increased by? options: A)200% B)300% C)100% D)500% E)350% SOLUTION:Height of=>100% so increased by 100% ANSWER C #### C QUESTION:If the price of rice rises from Rs. 6 per kg to Rs. 8 per kg, to have no increase in his expenditure on rice, a person will have to reduce his consumption of sugar by options: A)12 % B)19 % C)25 % D)32 % E)36 % SOLUTION:Explanation: Let original consumption = 100 kg and consumption = y kg. So, 100 x 6 = y x 8 y = 75 kg Reduction in consumption = 25 %. ANSWER: C #### C QUESTION:There are 7 magazines lying on a table; 3 are fashion magazines and the other 4 are sports magazines. If 3 magazines are to be selected at random from the 8 magazines, what is the probability that at least one of the fashion magazines will be selected? options: A)1/2 B)7/8 C)32/35 D)11/12 E)13/14 SOLUTION:answer isB Total probability=7C3=48 4C3 +4C2*4C1+4C1*4C2=4+24+24=42 therefore the probability that at least one of the fashion magazines will be selected= 42/48=7/8 B #### B QUESTION:In a park there are two ponds with both brown ducks and green ducks. In the smaller pond there are 30 ducks and in the larger pond there are 50 ducks. If 20% of the ducks in the smaller pond are green and 12% of the ducks in the larger pond are green, then what percentage of ducks are green? options: A)13% B)14% C)15% D)16% E)17% SOLUTION:Number of ducks in small pond = 30 green ducks in small pond = 20 % of 30 = 6 ducks Number of ducks in large pond = 50 green ducks in large pond = 12 % of 50 = 6 ducks Total number of ducks = 30 + 50 = 80 total number of green ducks = 6 + 6 = 12 ducks percentage of green ducks = 12/80 * 100 = 15% Answer: C #### C QUESTION:A train 125 m long passes a man, running at 4 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is: options: A)49 kmph B)50 kmph C)51 kmph D)52 kmph E)54 kmph SOLUTION:Explanation: Speed of the train relative to man = (125/10) m/sec = (25/2) m/sec. [(25/2) x (18/5)] km/hr = 45 km/hr. Let the speed of the train be 'x' km/hr. Then, relative speed = (x - 4) km/hr. x - 4 = 45 => x = 49 km/hr. ANSWER IS A #### A QUESTION:A, B and C can do a piece of work in 7 days, 14 days and 28 days respectively. How long will they taken, if all the three work together? options: A)6 days B)4 days C)8 days D)5 days E)1 days SOLUTION:1/7 + 1/14 + 1/28 = 7/28 = 1/4 => 4 days Answer: B #### B QUESTION:UBA Capital recently bought Brand new vehicles for office use. UBA capital only went for Toyota and Honda and bought less of Toyota than Honda at the ratio of 7:3. If 70% of the Toyota bought and 30% of the Honda bought were SUV’s. How many SUV’s did UBA capital buy in the aforementioned purchase? options: A)76% B)58% C)68% D)89% E)49% SOLUTION:let total no of Vehicles bought be 100, Toyota 70 and Honda 30, so total number of SUV's bought for Toyota and Honda respectively 70* 70/100=49 and 30* 30/100=9 so total 58 SUV's were bought out of 100 Vehicles bought..so required % is 58% ANSWER:B #### B QUESTION:In a college, the ratio of the number of boys to girls is 8 : 5. If there are 300 girls, the total number of students in the college is options: A)420 B)520 C)620 D)780 E)820 SOLUTION:Explanation: Let the boy are 8x and Girls are 5x => 5x = 300 => x = 60 Total students = 8x+5x = 13x = 13(60) = 780 Option D #### D QUESTION:On a map, 3.5 inches represent 35 miles. How many miles approximately is the distance if you measured 127 centimeters assuming that 1-inch is 2.54 centimeters? options: A)515 B)500 C)525 D)530 E)535 SOLUTION:1 inch = 2.54 cm 3.5 inch = 2.54 * 3.5 cm 8.89 cm = 35 miles 127 cms = 35/8.89*127= 500 miles Answer : B #### B QUESTION:By 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? options: A)22388 B)38000 C)27888 D)27288 E)28112 SOLUTION:Explanation: CP + CP/8 = 45000 CP = 40000 SP = 40000*(95/100) = 38000 Answer: B #### B QUESTION:A “Sophie Germain” 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 9 is options: A)3 B)7 C)21 D)189 E)267 SOLUTION:In that case, the Sophie prime numbers greater than 9 are 11,23,47,59, .. which yields units digit as 1,3,7 and 9 Product would be 1 x 3 x 7x9 =189 Answer should be D #### D QUESTION:If n = 2.0254 and n* is the decimal obtained by rounding n to the nearest hundredth, what is the value of n* – n? options: A) -0.0053 B) -0.0003 C) 0.0007 D) 0.0046 E) 0.0153 SOLUTION:n*=2.03 n*-n=2.03-2.0254 0.0046 Answer: D #### D QUESTION:After a mathematics exam, 20 percent of the students reported that they didn't study, while 20 percent of the students who didn't study refused to admit they hadn't studied. What percent of the students didn't study? options: A)15% B)50% C)35% D)20% E)25% SOLUTION:Statement: 20% of Students (S) Reported they Didn't Study (RDS). Of the students who didn't study (DS) 20% refused to admit they didn't study (notRDT). [Note: A Venn Diagram is useful to visualize the problem.] Solution: Sample space is 100%. S = 100% RDS/S = 20% notRDS/DS = 20% => 100% - 20% => RDS/DS = 80% DS/S = (20)/(80)% = 25% Answer: E #### E QUESTION:What is the number which when multiplied by 13 is increased by 180? options: A)13 B)15 C)23 D)35 E)45 SOLUTION:13 × 15 = 195 Answer: B #### B QUESTION:In a certain game, you perform three tasks. You flip a quarter, and success would be tails. You roll a single die, and success would be a six. You pick a card from a full playing-card deck, and success would be picking a spades card. If any of these task are successful, then you win the game. What is the probability of winning? options: A)1/48 B)11/16 C)11/12 D)5/16 E)23/48 SOLUTION:First lets get the overview Event 1(A) = Flipping the quarter( Probability of both winning/loosing = 1/2) Event 2(B) = Rolling a dice( Probability of winning = 1/6 ;Probability of loosing= 1 - 1\6 =5\6) Event 3(C) = Drawing a card( SPADES) Probability of winning = 13/52=3/4 ;Probability of loosing= 1 - 3/4 =1/4) So now as above we have three events A,BC. 1st method(This is lengthy method) Possible cases in which it's a win( the highlighted green event is a win and red is loose. 1.ABC= 1/2*5/6*3/4 OR 2.ABC= 1/2*1/6*3/4 OR 3.ABC= 1/2*5/6*1/4 OR 4.ABC= 1/2*1/6*3/4 OR 5.ABC= 1/2*5/6*1/4 OR 6.ABC= 1/2*5/6*1/4 OR 7.ABC= 1/2*1/6*1/4 As we now OR means add Adding up all of them we'll get the probability of winning ie 11/16 Answer : B #### B QUESTION:7+2+2^2+2^3+2^4+2^5=？ options: A)(2^3-1)(2^3+1) B)2^6+5 C)2^5-1 D)2^5+1 E)2^5-2 SOLUTION:From 7+2+2^2+2^3+2^4+2^5=69, 2^6+5=69 the correct answer is B. #### B <<<Examples ends QUESTION:A candidate got 35% of the votes polled and he lost to his rival by 2250 votes. How many votes were cast? options: A)7500 B)3600 C)8900 D)9000 E)5000 SOLUTION:35%-----------L 65%-----------W ------------------ 30%----------2250 100%---------? => 7500 ANSWER A #### A

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:. A car covers a distance of 390 km in 4 hours. Find its speed? options: A)104 B)55 C)66 D)98 E)100 SOLUTION:390/4 = 98 kmph Answer: D #### D QUESTION:Ram 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. options: A)12 , 18 B)8 , 10 C)18 , 20 D)20 , 25 E)None of these SOLUTION:Explanation : Let speed of ram and shakil be x and y resp. Case 1 : Ram gives a start of 200m and beats Shakil by 1 minute. 2000/x - 1800/y= -60 2000/x= 1800/y -60---------------------(1) Case2: Ram gives Shakil a start of 6 min and is beaten by 1000 meters distance travelled by shakil in 6 minutes= (6*60*y) meters = 360y meters 1000/x = (2000- 360y)/y------------------(2) Solve equation 1 and 2 to obtain x and y Answer is x = 8 minutes, y = 10 minutes Hence (B) is the corret answer. Answer : B #### B QUESTION:A crow leaves its nest, and flies back and forth from its nest to a nearby ditch to gather worms. The distance between the nest and the ditch is 200 meters. In one and a half hours, the crow manages to bring worms to its nest 15 times. What is the speed of the crow in kilometers per hour? options: A)1 B)2 C)3 D)4 E)6 SOLUTION:The distance between the nest and the ditch is 200 meters. 15 times mean = A crow leaves its nest, and flies back ( going and coming back) i.e. 2 times we get total 30 rounds. So the distance is 30 * 200 = 6000. D = ST 6000/1.5 = T , I think we can take 6000 meters as 6 km, then only we get T = 4.( 1000 meters = 1 km) D) #### D QUESTION:The difference of the squares of two consecutive even integers is divisible by which of the following integers ? options: A)6 B)4 C)2 D)5 E)1 SOLUTION:Let the two consecutive even integers be 2n and (2n + 2). Then, (2n + 2)^2 = (2n + 2 + 2n)(2n + 2 - 2n) = 2(4n + 2) = 4(2n + 1), which is divisible by 4. ANSWER B #### B QUESTION:Danny 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 192, what is the area of the side face of the box? options: A)13 B)16 C)18 D)29 E)32 SOLUTION:Lets suppose length= l, breadth= b, depth= d Front face area= l*w = 1/2 w*d (l=1/2 d or d=2l) top face area= w*d side face area= w*d = 1.5 d*l (w=1.5l) Volume = l*w*d= 192 l*1.5l*2l= 192 l=4 Side face area= l*d= l*2l= 4*2*4 =32 E is the answer #### E QUESTION:To 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. options: A)530 B)675 C)330 D)987 E)854 SOLUTION:Let x e 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: 3⋅25+(x−3)⋅30=75+30(x−3) Therefore: 25x=75+30(x−3)−100 25x=75+30x−90−100 190−75=30x−25 115=5x x=23 So the company worked 23 days and they made 23⋅25+100=675 pieces. #### B QUESTION:A political candidate collected $1,749 from a fund raising dinner. If each supporter contributed at least $50, what is the greatest possible number of contributors at the dinner? options: A)33 B)34 C)35 D)36 E)37 SOLUTION:Nearest to 1749≈1750 175/50=35 (Caution: Collection is 1750 - 1 = 1749) Counting 1 less = 50*34 = 1700 >> 49 remains which will be adjusted with the 34 members 51* 34 = 1734 >> 15 remains which will be adjusted with 15 members 52 * 15 + 51 * 19 = 780 + 969 = 1749 Answer = B #### B QUESTION:Find the length of the wire required to go 12 times round a square field containing 104976 m2. options: A)15840 B)3388 C)2667 D)8766 E)15552 SOLUTION:a2 = 104976 => a = 324 4a = 1296 1296 * 12 = 15552 Answer: E #### E QUESTION:There are two inlets and one outlet to a cistern. One of the inlets takes 4 hours to fill up the cistern and the other inlet takes twice as much time to fill up the same cistern. Both of the inlets are turned on at 8:30 AM with the cistern completely empty, and at 10:30AM, the outlet is turned on and it takes 1 more hour to fill the cistern completely. How much time does the outlet working alone takes to empty the cistern when the cistern is full? options: A)2 hours B)2.5 hours C)3 hours D)3.5 hours E)8 hours SOLUTION:The combined inflow rate of the two inlets is 1/4 + 1/8 = 3/8 cistern/hour. Thus, working together, it takes 8/3 hours (time is reciprocal of rate) to fill the cistern. From 8:30 AM to 10:30 AM, so in 2 hours, the inlet pipes will fill (time)*(rate) =2*3/8 = 3/4 th of the cistern . Then the outlet is turned on and the remaining 1/4 th of the cistern is filled in 1 hour. Letting x to be the rate of the outlet, we would have: 3/8 - x = 1/4 --> x = 1/8 cistern/hour, which means that it takes 8 hours the outlet working alone to empty the cistern. Answer: E. #### E QUESTION:If n is the square of a positive integer, which of the following must be equal to the square of the next positive integer? . options: A)√n + 1 B)n + 1 C)n^2 + 1 D)n + 2√n + 1 E)n^2 + 2n + 1 SOLUTION:Let a= +ve integer such that n= a^2 (a+1)= next +ve integer (a+1)^2 = a^2 + 1 + 2a and a=n^(1/2) Therefore , (a+1)^2=n+1+2*n^(1/2) Answer D #### D QUESTION:4 bells first begin to toll together with an intervals of 5, 10, 15 & 20 sec. How many times does they toll together in an hr? options: A)50 B)60 C)70 D)80 E)90 SOLUTION:5|5, 10, 15, 20 2|1, 2, 3, 4 |1, 1, 3, 2 L.C.M of 5, 10, 15, 20 is 60 60 times B #### B QUESTION:Two numbers are in the ratio 3:5. If 9 be subtracted from each, they are in the ratio of 3:2. The first number is: options: A)A)3 B)B)98 C)C)34 D)D)35 E)E)62 SOLUTION:(3x-9):(5x-9) = 3:2 x = 1 => 3x = 3 Answer:A #### A QUESTION:The area of a triangle is with base 18m and height 6m? options: A)88 m2 B)10 m2 C)66 m2 D)54 m2 E)31 m2 SOLUTION:1/2 * 18 * 6 = 54 m2 Answer: D #### D QUESTION:If a(a - 8) = 9 and b(b -8) = 9, where a ≠ b, then a + b = options: A)−48 B)−2 C)8 D)9 E)48 SOLUTION:i.e. if a = -1 then b = 9 or if a =9 then b = -1 But in each case a+b = -1+9= 8 Answer: option C #### C QUESTION:At an international conference, “Yellow” world countries and “Blue” world countries are the only participants. The ratio of “Yellow” world participants to “Blue” world participants is 3:2. If one-third of “Yellow” world participants are left-handed and two-thirds of “Blue” world participants are left-handed, then what is the fraction of the participants who are left-handed? options: A)7 B)7/15 C)5/8 D)9/2 E)4/6 SOLUTION:Yellow: Blue = 3:2 Let Yellow = 3x and Blue = 2x 1/3 of Yellow are left handed => 1/3 * 3x = 3x/3 Yellow left handed 2/3 of Blue are left handed => 2/3 *2x = 4x/3 blue left handed fraction of participants who are left handed = total left handed/ total participants = (yellow left handed + blue left handed)/total participants = (3x/3 + 4x/3)/(3x+2x) = (7x/15x) = 7/15 Answer : B #### B QUESTION:A company plans to gradually replace its fleet of 20 cars with newer models. At the end of every year starting with 2000 it retires 5 of its old cars and buys 6 new models.How many years did it take before the number of older cars left in the company's fleet was less than 50 percent of the fleet? options: A)6 B)3 C)2 D)4 E)5 SOLUTION:Total fleet--20 End of year 2000 -- (retires 5 and buys 6) total fleet--21(15 old 6 new). End of year 2001 -- (retires 5 and buys 6) total fleet--22(10 old 12 new). Answer is C--after 2 years the company has a total of 22 cars (10 old 12 new), the old cars are already less than 50% of its fleet. #### C QUESTION:The ages of Patrick and Michael are in the ratio of 3 : 5 and that of Michael and Monica are in the ratio of 3 : 5. If the sum of their ages is 147, what is the difference between the ages of Patrick and Monica? options: A)48 B)47 C)46 D)49 E)52 SOLUTION:let their ages are 9x,15x and 25x respectively. difference between the ages of Patrick and Monica = 25x-9x=16x where 49x=147 or x=3 so diff in ages = 16x=16*3=48 yrs ANSWER:A #### A QUESTION:The least number of complete years in which a sum of money put out at 20% C.I. will be more than doubled is? options: A)7 B)4 C)5 D)3 E)1 SOLUTION:Explanation: P(1 + 20/100)n > 2P or (6/5)n > 2 Now, (6/5 * 6/5 * 6/5 * 6/5) > 2. So, n = 4 years. Answer:B #### B QUESTION:By the how much is two-fifth of 300 greater than three -fifths of 125? options: A)15 B)3 C)5 D)45 E)None of these SOLUTION:Reqd no. = 2⁄5 × 300 - 3⁄5 × 125 = 120 - 75 = 45 Answer D #### D QUESTION:A city with a population of 160,080 is to be divided into 8 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? options: A)18,200 B)18,300 C)18,400 D)18,500 E)18,600 SOLUTION:The minimum possible population occurs when all the other districts have a population that is 10% greater than the least populated district. Let p be the population of the least populated district. Then 160,080 = p + 7(1.1)p 8.7p=160,080 p = 18,400 The answer is C. #### C QUESTION:A sum of money lent out at S.I. amounts to a total of $480 after 2 years and to $680 after a further period of 5 years. What was the initial sum of money that was invested? options: A)$360 B)$380 C)$400 D)$420 E)$440 SOLUTION:S.I for 5 years = $680 - $480 = $200 The S.I. is $40/year S.I. for 2 years = $80 Principal = $480 - $80 = $400 The answer is C. #### C QUESTION:The ages of two persons differ by 24 years. If 5 years ago, the elder one be 5 times as old as the younger one, their present ages (in years) are respectively options: A)20,20 B)20,10 C)25,15 D)35,11 E)None of these SOLUTION:Explanation: Let their ages be x and (x + 24) years. 5 (x - 5) = (x + 24 - 5) or 4x = 44 or x = 11. Their present ages are 35 years and 11 years Option D #### D QUESTION:How many 0's are there in the binary form of 6*1024 + 4*64 + 2 options: A)6 B)7 C)8 D)10 E)9 SOLUTION:6*1024 + 4*64 + 2 = 6144+256 +2 = 6402 in binary code 6402 base 10 = 11001 000000 10 in base 2. so 9 zeros are there. ANSWER:E #### E QUESTION:A person starts walking at a speed of 5km/hr through half the distance, rest of the distance he covers with aspeed 6km/hr. Total time of travel is 9 hours. What is the maximum distance he can cover? options: A)20km B)40km C)60km D)80km E)90km SOLUTION:t=d/s, so 9=x/2*1/5+x/2*1/6(because half distance with 5 km/ph, and remaining half with 6km/hr) 9=x(18/120) x=60km ANSWER:C #### C QUESTION:A meal cost $ 35.50 adn there was no tax. If the tip was more than 5 pc but less than 8pc of the price, then the total amount paid should be: options: A)40-42 B)39-41 C)38-40 D)37-38 E)36-37 SOLUTION:5%(35.5) = 1.775 8%(35.5) = 2.84 total amount could have been 35.5+1.775 and 35.5+2.84 => could have been between 37.275 and 38.34 => approximately between 37 and 38 Answer is B.D #### D QUESTION:The difference between the compound interest compounded annually and simple interest for 2 years at 20% per annum is Rs.144. Find the principal? options: A)3377 B)2997 C)3600 D)2799 E)7719 SOLUTION:P = 144(100/5)2 => P = 3600 Answer:C #### C QUESTION:How many different pairs of positive integers (a, b) satisfy the equation 1/a+1/b=34/57 ? options: A)6 B)3 C)2 D)1 E)5 SOLUTION:There 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. So, we start with a=1, we get b as -ve. out a=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) a=3, we get b as 3. Yes (Now we have 3 possible solutions) a=4, we get b as fraction. Out a=5, we get b again as some fraction. Out a=6 already taken. We have A,B options left. C,D,E are out. A is 6. To have 6 as the answer, we will need one more pair like2,6and one more solution where a=b. When a=b, we have only 1 solution = 5. So, one more solution, where a=b is not possible. So, answer will be E. #### E QUESTION:A man can swim in still water at 4.5 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is? options: A)1.09 B)1.6 C)1.2 D)1.5 E)1.1 SOLUTION:M = 4.5 S = x DS = 4.5 + x US = 4.5 + x 4.5 + x = (4.5 - x)2 4.5 + x = 9 -2x 3x = 4.5 x = 1.5 Answer: D #### D QUESTION:At Joes Steakhouse the hourly wage for a chef is 20% 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 $6.50 per hour, how much less than a manager does a chef earn each hour? options: A)$2.6 B)$2.40 C)$3.40 D)$4.40 E)$5.40 SOLUTION:Manager wages per hour = $6.50 Dishwasher wages per hour = half of manager's wages. = 1/2($6.50) ==> $3.25 Chef wages per hour = 20% greater than Dishwasher wages --> 20% of $3.25 = (20*($3.25)) /100 --> ($65)/100 --> $0.65 Therefore, Chef wages per hour = $3.25 + $0.65 ==> $3.9 Difference of wages between manager and chef = $6.50 - $3.9 ==> $2.6 ANSWER:A #### A QUESTION:The difference between the length and breadth of a rectangle is 23 m. If its perimeter is 206 m, then its area is : options: A)1520 m2 B)2420 m2 C)2480 m2 D)2520 m2 E)None of these SOLUTION:Solution We have : (l - b) = 23 and 2 (l + b) = 206 or (l + b) = 103. Solving the two equations, we get, l = 63 and b = 40. ∴ Area = (l × b) = (63 × 40) m2 = 2520 m2. Answer D #### D QUESTION:The average marks of a class of 20 students is 40 and that of another class of 50 students is 60. Find the average marks of all the students? options: A)44.28 B)54.28 C)34.28 D)64.28 E)74.28 SOLUTION:Sum of the marks for the class of 20 students = 20 * 40 = 800 Sum of the marks for the class of 50 students = 50 * 60 = 3000 Sum of the marks for the class of 70 students = 800 + 3000 = 3800 Average marks of all the students = 3800/70 = 54.28 ANSWER:B #### B QUESTION:By selling an article at Rs.600, a profit of 25% is made. Find its cost price? options: A)228 B)200 C)279 D)480 E)221 SOLUTION:SP = 600 CP = (SP)*[100/(100+P)] = 600 * [100/(100+25)] = 600 * [100/125] = Rs.480.Answer:D #### D QUESTION:A 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? options: A)30/18 hours B)37/13 hours C)80/13 hours D)30/13 hours E)60/29 hours SOLUTION:Speed downstream = 20 + 9 = 29 kmph. Time required to cover 60 km downstream = d/s = 60/29 = 60/29 hours. Answer: E #### E QUESTION:Eight years ago, Rhea was half of Rick in age. If the ratio of their present ages is 3:4, what is the total of their present ages? options: A)25 years B)28 years C)32 years D)26 years E)28 years SOLUTION:let rhea age be x rick age be y given x-8=1/2(y-8)......a also given x/y=(3/4) =>x=3/4(y).......b by solving a and b we get y=16 x=12 then x+y=12+16=28 ANSWER:B #### B QUESTION:A tank has both an inlet pipe and an outlet pipe. Working alone, the inlet pipe can fill up the tank in 4 hours. Working alone, the outlet pipe can empty out the tank in 10 hours. If it is desired that the tank should be filled, from empty, exactly 6 hours after the inlet pipe is turned on at 9:30am, then at what time should the outlet pipe be opened ? options: A)8:30am B)9:30am C)10:00am D)10:30am E)11:30am SOLUTION:In 6 hours the inlet pipe will pump in water equal to 6*1/4 = 6/4 of the pool. So, 2/4 more than necessary, which should be compensated by the outlet pipe. To pump out 2/4 of the water the outlet pipe needs 20/4 = 5 hours. Therefore, the outlet pipe should be opened at 9:30am + 6 hours - 5 hours = 10:30am. Answer: D #### D QUESTION:A 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? options: A)400bc B)400b/c C)800bc D)800b/c E)800/bc SOLUTION:2 cases * c cartons/case * b boxes/carton * 400 clips/box = 800bc paper clips The answer is C. #### C QUESTION:The average age of a group of 10 students was 24. The average age increased by 2 years when two new students joined the group. What is the average age of the two new students who joined the group? options: A)22 years B)36 years C)32 years D)44 years E)None of these SOLUTION:The total age of 10 students with average 24 = 240 The total age of 12 students with average 26 = 312 The total age of 2 new students = 72 Their average =36 Correct Option B #### B QUESTION:Randy can rebuild an automobile engine in b hours. Alvin can rebuild the same engine in a hours. If Randy and Alvin work together at their respective rates to rebuild the engine, which of the following represents the portion of the job that Randy will not have to complete? options: A)ab/(a+b) B)(a-b)/(a+b) C)b/(b+a) D)a/(a+b) E)b/(a-b) SOLUTION:Randy can do the job in a hrs, Alvin can do the job in b hrs. When they work together, you need to find the fraction of work that Randy doesn't need to do i.e. the fraction that will be done by Alvin. Ratio of Randy's speed:Alvin's speed = b:a (since time taken by them is in the ratio a:b) So Randy does a/(a+b) of the work and Alvin does b/(a+b) of the work. Answer (C). #### C QUESTION:Two 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? options: A)10 sec B)16 sec C)19 sec D)7.2 sec E)13 sec SOLUTION:RS = 60 -40 = 20 * 5/18 = 100/18 T = 36 D = 36 * 100/18 = 200 RS = 60 + 40 = 100 * 5/18 T = 200 * 18/500 = 7.2 sec Answer: D #### D QUESTION:The population of a village is 7800. It increases annually at the rate of 18% p.a. What will be its population after 2 years? options: A)10000 B)12000 C)13000 D)10860 E)14400 SOLUTION:Formula : ( After =100 denominator Ago = 100 numerator) 7800 × 118/100 × 118/100 = 10860 D #### D QUESTION:A sum of Rs. 12,500 amounts to Rs. 15,500 in 4 years at the rate of simple interest. What is the rate of interest? options: A)3% B)4% C)5% D)6% E)None of these SOLUTION:S.I. = Rs. (15500 - 12500) = Rs. 3000. Rate =((100 x 3000)/(12500 x 4))% = 6% Answer :D #### D QUESTION:At a dinner party, 5 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 R of different possible seating arrangements for the group? options: A)5 B)10 C)24 D)32 E)120 SOLUTION:Circular arrangements= (n-1)! Hence (4!) = 24=R Answer is C #### C QUESTION:What will be the cost of building a fence around a square plot with area equal to 144 sq ft, if the price per foot of building the fence is Rs. 58? options: A)2784 B)2287 C)2977 D)2668 E)1298 SOLUTION:Let the side of the square plot be a ft. a2 = 144=> a = 12 Length of the fence = Perimeter of the plot = 4a = 48 ft. Cost of building the fence = 48 * 58 = Rs. 2784. Answer:A #### A QUESTION:The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 13 and 14. The larger of the two numbers is options: A)276 B)299 C)312 D)322 E)None SOLUTION:Solution Clearly, the numbers are (23 x 13) and (23 x 14). Larger number = (23 x 14) = 322. Answer D #### D QUESTION:The inverse ratio of 4: 2: 1 is? options: A)2:4:8 B)2:3:9 C)2:3:2 D)2:3:6 E)2:3:1 SOLUTION:1/4: 1/2: 1/1 = 2:4:8 Answer:A #### A QUESTION:3, 5, 7, 11, 13, 17, 19, ____ options: A)25 B)36 C)23 D)49 E)27 SOLUTION:The sequence is a series of prime numbers, 3, 5, 7, 11, 13, 17, 19, 23.... Answer : C. #### C QUESTION:Two 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 ? options: A)10.7 Seconds B)10.8 Seconds C)10.9 Seconds D)11.8 Seconds E)None of these SOLUTION:Explanation: Relative Speed = 60+40 = 100 Kmph = 100*(5/18) = 250/9 m/sec Distance to be covered = 140 + 160 = 300 metres Time = Distance/Speed Time=300∗9/250=54/5=10.8 seconds Option B #### B QUESTION:What percent is 400 gm of 1 kg? options: A)25% B)40% C)10% D)8% E)12% SOLUTION:1 kg = 1000 gm 400/1000 × 100 = 40000/1000 =40 % Answer is B #### B QUESTION:Baby Isabel plays with blocks. Each block is 3.9 inches tall. She has a collection of 32 blocks. If she could stack all of the blocks up one on top of the other, how many inches tall would her tower of blocks be? options: A)67" B)124.8" C)106" D)120" E)151.7" SOLUTION:3.9"*32=124.8". Answer is B. #### B QUESTION:A retailer buys 140 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 % ? options: A)105 B)155 C)125 D)185 E)285 SOLUTION:let the market price of each pen be $1 then, Cost Price of 140 pens = $ 36 Selling Price of 140 pens =99% of $140=$ 138.60 profit %=((102.60*100)/36) %=285% Answer E #### E QUESTION:Find the Missing Number 1, 2, 4, 10, 16, 40, 64 (Successive terms are related) options: A)100 B)200 C)300 D)90 E)80 SOLUTION:Well, the pattern looked REALLY familiar to me, like it's a binary progression. And it is...but with a twist. 2^0 = 1 2^1 = 2 2^2 = 4 2^3 = 8 2^4 = 16 2^5 = 32 2^6 = 64 You'll note that all the numbers up there match your sequence...except for 2^3 = 8 (10 in your sequence) and 2^5 = 32 (40 in your sequence). BUT, if you convert 8 to base 8, you get 10. And if you convert 32 to base 8, you get 40. Which indicates that every other number starting with the first one is expressed in base 10 and every other number starting with the second number is expressed in base 8. If this is true, then you next number would be: 2^7 = 128 That is the base 10 number. Since this number should be expressed in base 8 (following the pattern), it should be 200. ANSWER:A #### A QUESTION:Albert buys 4 horses and 9 cows for Rs. 13,400. If he sells the horses at 10% profit and the cows at 20% profit, then he earns a total profit of Rs. 1880. The cost of a horse is: options: A)Rs. 1000 B)Rs. 2000 C)Rs. 2500 D)Rs. 3000 E)Rs. 3500 SOLUTION:Let C.P. of each horse be Rs. x and C.P. of each cow be Rs. y. Then, 4x + 9y = 13400 -- (i) And, 10% of 4x + 20% of 9y = 1880 2/5 x + 9/5 y = 1880 => 2x + 9y = 9400 -- (ii) Solving (i) and (ii), we get : x = 2000 and y = 600. Cost price of each horse = Rs. 2000. ANSWER:B #### B QUESTION:Rs.525 among A, B and C such that B may get 2/3 of A and C together get. Find the share of C? options: A)127 B)150 C)177 D)167 E)122 SOLUTION:A+B+C = 590 5A = 6B = 8C = x A:B:C = 1/5:1/6:1/8 = 24:20:15 15/59 * 590 = Rs.150 Answer:B #### B QUESTION:John was thrice as old as Tom 6 yrs back. He will be 5/3 times as old as Tom 6 years hence. How old is Tom today? options: A)10 B)11 C)12 D)14 E)15 SOLUTION:Sol. RMBflSk -6 = 3 (Ravi - 6) ...(j) and Rupesh + 6 = | (Ravi + 6) ...(ii) Solving both the equations we get, Ravi = 12 years. C #### C QUESTION:Victor'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 R would it take Victor to complete 10 jobs without any supervision? options: A)34 B)52 C)60 D)70 E)92 SOLUTION:Rate when supervised = (job)/(time) = 1/t. Rate when unsupervised = (job)/(time) = 1/(t+3). For 144/2=72 days he is supervised and for 144/2=72 days he is unsupervised and does 36 jobs: 72/t + 72/(t+3) = 36 --> t=3 days --> t+3 = 6 days. Victor to complete 10 jobs without any supervision will need R 10(t + 3) = 60 days. Answer: C. #### C QUESTION:Equal weights of two alloys containing tin, copper and lead in the ratio 6:8:7 and 1:2:4 are melted and mixed together. What is the ratio of tin, copper and lead in the resultant alloy? options: A)11:8:3 B)3:1:8 C)17:28:27 D)9:4: 11 E)9:14: 11 SOLUTION:Let the weight of the two alloys be w each Required ratio = (6w/21+1w/7): (8w/21+2w/7 ): (7w/21+4w/7) = 9w/21 : 14w/21 : 11w/21 = 9:14: 11 ANSWER:E #### E QUESTION:A man rows his boat 65 km downstream and 45 km upstream, taking 2 1/2 hours each time. Find the speed of the stream? options: A)5 kmph B)4 kmph C)9 kmph D)8 kmph E)1 kmph SOLUTION:Speed downstream = d/t = 65/(2 1/2) = 26 kmph Speed upstream = d/t = 45/(2 1/2) = 18 kmph The speed of the stream = (26 - 18)/2 = 4 kmph Answer:B #### B QUESTION:In a box of 8 pens, a total of 3 are defective. If a customer buys 2 pens selected at random from the box, what is the probability that neither pen will be defective? options: A)2/10 B)3/11 C)4/13 D)5/14 E)6/17 SOLUTION:P(neither pen is defective) = 5/8*4/7 = 5/14 The answer is D. #### D QUESTION:1/3, 1/2, 1/4, 2 1/3, 3 1/2, 4 1/4, 4 1/3, 6 1/2, ? options: A)8 1/4 B)9 1/4 C)8 1/2 D)8 1/3 E)6 1/4 SOLUTION:there are 3 series--- 1/3,2 1/3,4 1/3. 1/2,3 1/2,6 1/2. 1/4,4 1/4,? ans 8 1/4 ANSWER:A #### A QUESTION:In a family, there are six members A, B, C, D, E and F. A and B are a married couple, A being the male member. D is the only son of C, who is the brother of A. E is the sister of D. B is the daughter-in-law of F, whose husband has died. How many male members are there in the family ? options: A)1 B)9 C)3 D)4 E)6 SOLUTION:Explanation: A is a male and married to B. So, A is the husband and B is the wife. C is the brother of A. D is the son of C. E, who is the sister of D will be the daughter of C. B is the daughter-in-law of F whose husband has died means F is the mother of A. A is a male. B. the wife, is female. C. the brother, is male. D. the son, is male. E, the sister, is female. F, the mother, is a female. So, there are three males. Answer: C) 3 #### C QUESTION:In an intercollegiate competition that lasted for 3 days, 175 students took part on day 1, 210 on day 2 and 150 on day 3. If 80 took part on day 1 and day 2 and 70 took part on day 2 and day 3 and 20 took part on all three days, how many students took part only on day 1? options: A)25 B)45 C)55 D)70 E)30 SOLUTION:Day 1&2 = 80; Only Day 1&2 (80-20) = 60, Day 2&3 = 70; Only Day 2&3 (70-20) = 50, Only Day 1 = 175 - (60+50+20) = 45 Answer:B #### B QUESTION:A fruit salad mixture consists of apples, peaches, and grapes. There are 3 times as many pounds of apples as grapes and 2.5 times as many pounds of peaches as grapes. If a mixture that has an average (arithmetic mean) of 39 pounds per fruit, how many more pounds of apples than grapes does the mixture have? options: A)5 B)12 C)19 D)36 E)50 SOLUTION:A+P+G= 39*3 A=3G P=2.5G 3G+2.5G+G= 39*3 G=39*3/6.5= 18 A= 6*3=54 Difference = 36 'D' is the answer #### D QUESTION:A sum of money when distributed among friends is in the ratio of 3:4:5, if the amount is the larger 3digit number divisible by 24, what is the share of 3rd person? options: A)400 B)410 C)420 D)430 E)440 SOLUTION:Largest 3 digit number divisible by 24= 984 So their shares are (984*3/12=246) , (984*4/12=328) , (984*5/12=410) ANSWER:B #### B QUESTION:Today Jim is twice as old as Fred, and Sam is 2 years younger than Fred. Six years ago Jim was 7 times as old as Sam. How old is Jim now? options: A)8 B)12 C)16 D)20 E)24 SOLUTION:We're asked how old Jim is NOW. We're given three facts to work with: 1) Today, Jim is TWICE as old as Fred 2) Today, Sam is 2 years younger than Fred 3) Six years ago, Jim was 7 times as old as Sam. let's TEST Answer D: 20 IF....Jim is currently 20 years old.... Fred is 10 years old Sam is 8 years old 6 years ago, Jim was 14 and Sam was 2, so Jim WAS 7 times Sam's age. This is an exact MATCH for what we were told, so this MUST be the answer. D #### D <<<Examples ends QUESTION:Evaluate : (2.39)(power 2) - (1.61) (power 2) / 2.39 - 1.61 options: A)4 B)6 C)8 D)2 E)10 SOLUTION:Given Expression = a(power 2) - b(power 2) / a-b = (a + b)(a - b) / (a-b) = (a + b) = (2.39 + 1.61) = 4. Answer is A. #### A

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:If x is less than y by 45% then y exceed x by: options: A)33.33% B)25% C)81.81% D)66.66% E)None of these SOLUTION:Using formula (x/(100-x)*100) where x is Percentage decrease (here it is 25%) => 45/(100-45)*100 =81.81% ANSWER:C #### C QUESTION:A man has Rs. 320 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 ? options: A)37 B)38 C)60 D)90 E)28 SOLUTION:Let number of notes of each denomination be x. Then, x + 5x + 10x = 320 16x = 320 x = 20. Hence, total number of notes = 3x = 60. Answer:C #### C QUESTION:Due to 10% decrease in the price of sugar and John can buy 5kg more sugar in Rs100 , then find the CP of sugar? options: A)Rs.2(1/9) B)Rs.2(2/9) C)Rs.3(1/9) D)Rs.1(1/9) E)Rs.2(2/5) SOLUTION:Here r = 10 % ,x = 100 and A = 5 kg Actual price of sugar = 10*100/((100-10 )*5) = Rs.2(2/9) B #### B QUESTION:The average expenditure of a labourer for 6 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 i options: A)70 B)72 C)75 D)78 E)80 SOLUTION:Income of 6 months = (6 × 85) – debt = 510 – debt Income of the man for next 4 months = 4 × 60 + debt + 30 = 270 + debt ∴ Income of 10 months = 780 Average monthly income = 780 ÷ 10 = 78 Answer D #### D QUESTION:Two 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? options: A)29 B)29 C)60 D)19 E)12 SOLUTION:Let the speed of the slower train be x m/sec. Then, speed of the train = 2x m/sec. Relative speed = ( x + 2x) = 3x m/sec. (100 + 100)/8 = 3x => x = 25/3. So, speed of the faster train = 50/3 = 50/3 * 18/5 = 60 km/hr. Answer:C #### C QUESTION:Plane leaves from Chelsea every 35 minutes from West Ham airport. Air hostess told Frank Lampard that the plane had left 25 minutes ago and the next plane for Chelsea will leave at 7:00 p.m. At what time air hostess convey this information to Frank Lampard? options: A)5:35 p.m B)6:50 p.m C)7:35 p.m D)8:35 p.m E)9:35 p.m SOLUTION:Explanation: Time of Frank Lampard last missed plane = 7:00 p.m - 35 min = 6:25 p.m As this information has been given to Frank Lampard 25 minutes after the plane has already left, the air hostess gave the information at 6:25 p.m + 25 min = 6:50 p.m Answer B #### B QUESTION:3 candidates in an election and received 5136, 7636 and 11628 votes respectively. What % of the total votes did the winningcandidate got in that election? options: A)45% B)48% C)57% D)59% E)61% SOLUTION:Total number of votes polled = (5136 + 7636 + 11628) = 24400 So, Required percentage = 11628/24400 * 100 = 48% B #### B QUESTION:Consider a sequence of numbers given by the expression 7 + (q - 1) * 5, where n runs from 1 to 80.What is the sum of this series ? options: A)409 B)1636 C)16360 D)16000 E)15360 SOLUTION:terms in this sequence are 7,12,17----402 now since this is an a.p. with a common difference of 5. therefore its sum can be given as q(a+l)/2----------------1) q= total no. of terms =80 a= first term=7 l= last term=402 subsituting values in the expression 1 we have 80(7+402)/2 = 40(409) =16360=C #### C QUESTION:A train passes a station platform in 36 seconds and a man standing on the platform in 24 seconds. If the speed of the train is 54 km/hr, what is the length of the platform? options: A)180 B)240 C)288 D)267 E)211 SOLUTION:Speed = (54 * 5/18) m/sec = 15 m/sec. Length of the train = (15 x 24)m = 360 m. Let the length of the platform be x meters. Then, (x + 360)/36 = 15 ==> x + 360 = 540 ==> x = 180 m.Answer: A #### A QUESTION:A bag contains 7 red, 2 green balls. 3 balls are drawn randomly. What is the probability that balls drawn contain exactly two green balls? options: A)1/7 B)2/9 C)1/12 D)4/17 E)2/3 SOLUTION:Total number of balls = 7+2 = 9 n(S) = 9C3 = 9*8*7 / 3*2 = 84 n(E) = 2C2* 7C1 = 7 Probability = 7/84 = 1/12 Answer is C #### C QUESTION:The average age of a committee of 8 members is 40 years. A member aged 55 years retired and his place was taken by another member aged 39 years . The average age of present committee is; options: A)39 years B)38 years C)36 years D)35 years E)34 years SOLUTION:Exp. Total age of the committee = 40*8 = 320, Total age when a member is retired and a new one was joined = 320-55 +39, =304 Average age of present committee = 304/8 = 38. Answer: B #### B QUESTION:A rectangular farm has to be fenced one long side, one short side and the diagonal. If the cost of fencing is Rs.15 per meter. The area of farm is 1200 m2 and the short side is 30 m long. How much would the job cost? options: A)1276 B)1200 C)2832 D)1800 E)1236 SOLUTION:Explanation: l * 30 = 1200 è l = 40 40 + 30 + 50 = 120 120 * 15 = 1800 Answer: Option D #### D QUESTION:The product of the prime numbers between 0 and 20 is closest to... options: A)10^5 B)10^6 C)10^7 D)10^8 E)10^9 SOLUTION:Write out the primes 1 - 20 2 x 3 x 5 x 7 x 11 x 13 x 17 x 19 Round the numbers off in multiples of 5. Try to alternate rounding up and down 5 x 5 x 5 x 5 x 10 x 10 x 20 x 20 25 x 25 x 10 x 10 x 20 x 20 pull out 10 from each number 10^6 (2.5 x 2.5 x 2 x 2) 10^6 (5 x 4) 10^7 (2) round off the 2. answer is C #### C QUESTION:When a number is divided by 6 &then multiply by 12 the answer is 9 what is the no.? options: A)4.5 B)5 C)5.5 D)5.8 E)6 SOLUTION:if $x$ is the number, x/6 * 12 = 9 => 2x = 9 => x = 4.5 A #### A QUESTION:Shekhar 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’s share in the profit of Rs. 1,50,000 earned at the end of 3 years from the start of the business in 1999?. options: A)Rs. 10000 B)Rs. 20000 C)Rs. 30000 D)Rs. 40000 E)Rs. 50000 SOLUTION:Shekhar : Rajeev : Jatin = (25000 X 12 + 35000 X 12 + 45000 X 12) : (35000 X 24) : (35000 X 12) = 1260000 : 840000 : 420000 = 3 : 2 : 1. Rajeev’s share = Rs.(150000×2/6) = Rs. 50000 Answer E #### E QUESTION:If a × b = 2a - 3b + ab, then 4 × 5 + 5 × 4 is equal to : options: A)31 B)32 C)43 D)45 E)26 SOLUTION:Explanation: 4 × 5 + 5 × 4 = (2 × 4 - 3 × 5 + 4 × 5) + ( 2 × 5 - 3 × 4 + 5 × 4) = (8 -15 + 20 + 10 - 12 +20) = 31. Answer: A #### A QUESTION:A tank can supply water to a village for 30 days. If a leak at the bottom of the tank drains out 15 liters per day, the supply lasts for 20 days only. For how many days will the supply last if the leak drains out 20 liters per day? options: A)12 B)14 C)15 D)16 E)18 SOLUTION:Losing 15 liters per day results in a loss of 300 liters in 20 days. So, those 300 liters were for 10 days, making daily consumption of the village 30 liters per day. Thus the capacity of the tank is 30*30 = 900 liters. Losing 20 liters plus 30 liters gives 50 liters per day. At this rate the supply will last 900/50 = 18 days. The answer is E. #### E QUESTION:The product of two numbers is 220 and the sum of their squares is 289. The sum of the number is? options: A)A)23 B)B)25 C)C)27 D)D)31 E)E)35 SOLUTION:Let the numbers be x and y. Then, xy = 220 and x2 + y2 = 289. (x + y)2 = x2 + y2 + 2xy = 289 + (2 x 220) = 729 x + y = 27. Option C #### C QUESTION:Find the area of a rhombus whose side is 25 cm and one of the diagonals is 30 cm? options: A)602 sq.cm B)620 sq.cm C)200 sq.cm D)605 sq.cm E)600 sq.cm SOLUTION:Consider the rhombus ABCD. Let the diagonals intersect at E. Since diagonals bisect at right angles in a rhombus. BE2 + AE2 = AB2 252 = 152 + AE2 AE = √(625 - 225) = √400 = 20, AC = 20 + 20 = 40 cm. Area of a rhombus = 1/2 * d1d2 = 1/2 * 40 * 30 = 600 sq.cm. Answer: E #### E QUESTION:What annual payment dischargea debit of Rs.12900, due in 4yrs.At 5% rate? options: A)2000 B)2200 C)3000 D)3400 E)3500 SOLUTION:A.P.=(200X12900)/[4(200+5X3)]=3000 Ans Alternative 100+105+110+115=12900 430=12900 100=12900/(430)X100=3000 C #### C QUESTION:There are 680 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? options: A)425 B)345 C)375 D)380 E)400 SOLUTION:In 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 680. Hence 3x + 5x = 680 Solve for x 8x = 680 x = 85 Number of boys 3x = 3 × 85 = 255 Number of girls 5x = 5 × 85 = 425 A #### A QUESTION:If the diagonal of a rectangle is 17cm long and its perimeter is 46 cm. Find the area of the rectangle? options: A)122 sq.cm B)120 sq.cm C)277 sq.cm D)118 sq.cm E)119 sq.cm SOLUTION:let length = x and breadth = y then 2(x+y) = 46 x+y = 23 x²+y² = 17² = 289 now (x+y)² = 23² x²+y²+2xy= 529 289+ 2xy = 529 xy = 120 area = xy = 120 sq.cm Answer: B #### B QUESTION:A tank is filled in SIX 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? options: A)56 hours B)28 hours C)55 hours D)66 hours E)21 hours SOLUTION:1/A + 1/B + 1/C = 1/6 (Given) Also given that A = 2B and B = 2C => 1/2B + 1/B + 2/B = 1/6 => (1 + 2 + 4)/2B = 1/6 => 2B/7 = 6 => B = 21 hours. Answer: E #### E QUESTION:The radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 500 resolutions? options: A)287 m B)704 m C)278 m D)298 m E)286 m SOLUTION:In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 500 resolutions. = 500 * 2 * 22/7 * 22.4 = 70400 cm = 704 m Answer:B #### B QUESTION:A work can be finished in 14 days by thirty women. The same work can be finished in fifteen days by forteen men. The ratio between the capacity of a man and a woman is options: A)3:4 B)4:3 C)2:1 D)3:2 E)4:5 SOLUTION:Work done by 20 women in 1 day = 1/14 Work done by 1 woman in 1 day = 1/(14×30) Work done by 14 men in 1 day = 1/15 Work done by 1 man in 1 day = 1/(15×14) Ratio of the capacity of a man and woman =1/(15×14) : 1/(14×30) = 1/15 : 1/30 = 1/3 :1/6 = 1/1=1/2=2:1 Answer is C #### C QUESTION:Pump 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). options: A)2 hours 2 minutes B)3 hours 5 minutes C)4 hours 6minutes D)5 hours 7 minutes E)7 hours 9 minutes SOLUTION:In 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 1/5 + 1/8 = 13 / 40 of a tank Since 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 (13/40) t = 1 t = 40 / 13 = 39/13 + 1/13 hours = 3 hours and (1/13)*60 minutes = 3 hours 5 minutes (rounded to the nearest minute) correct answer B #### B QUESTION:The perimeter of one square is 48 cm and that of another is 36 cm. Find the perimeter and the diagonal of a square which is equal in area to these two combined? options: A)13√4 B)13√2 C)23√2 D)12√4 E)15√2 SOLUTION:4a = 48 4a = 36 a = 12 a = 9 a2 = 144 a2 = 81 Combined area = a2 = 225 => a = 15 d = 15√2 Answer: E #### E QUESTION:A gardener increased the length of a rectangle-shaped garden by 20 percent and decreased its width by 10 percent. The area of the new garden options: A)has increased by 20 percent B)has increased by 12 percent C)has increased by 8 percent D)is exactly the same as the old area E)cannot be expressed in percentage terms without actual numbers SOLUTION:Let L be the original length and let W be the original width. The original area was L*W. The new area is 0.9W*1.2L = (0.9)(1.2)L*W = 1.08*L*W The answer is C. #### C QUESTION:P is three times as old as Q. In 10 years, P will be twice as old as Q. How old was P three years ago? options: A)27 B)30 C)33 D)36 E)39 SOLUTION:P = 3Q so Q = P/3 P+10 = 2(Q+10) = 2(P/3+10) P/3 = 10 P = 30 Three years ago, P was 27. The answer is A. #### A QUESTION:By selling 50 mangoes, a shopkeeper gains the price of 10 mangoes. His gain per cent is options: A)25% B)35% C)20% D)23% E)30% SOLUTION:Suppose S.P of 50 mangoes = Rs 50 Therefore, Gain = Rs 10 => C.P = Rs 40 Gain % = 10/40 x 100 = 25% Gain = 25% ANSWER:A #### A QUESTION:John and David work at a hospital with 8 other workers. For an internal review, 2 of the 8 workers will be randomly chosen to be interviewed. What is the probability that John and David will both be chosen? options: A)1/30 B)1/25 C)1/20 D)1/28 E)1/30 SOLUTION:Probability that John and David will both be chosen out of 8 workers = (2/8)*(1/7) = 1/28 Answer D #### D QUESTION:John was thrice as old as Tom 6 yrs back. He will be 5/3 times as old as Tom 6 years hence. How old is Tom today? options: A)8 years B)10 years C)12 years D)14 years E)15 years SOLUTION:Sol. RMBflSk -6 = 3 (Ravi - 6) ...(j) and Rupesh + 6 = | (Ravi + 6) ...(ii) Solving both the equations we get, Ravi = 12 years. C #### C QUESTION:529 is a perfect square. When x is added to the square root of 529, the result is also a perfect square. What is x? options: A)1 B)2 C)3 D)4 E)5 SOLUTION:529 is 23*23 here A 23+1 = 24 B 23+2 = 25 C 23+3 = 26 D 23+4 = 27 E 23+5= 28 so, B is the only addition that gives a perfect square. so x=3 then the answer is B #### B QUESTION:Subtracting 10% from X is the same as multiplying X by what number? options: A)80% B)90% C)10% D)50% E)60% SOLUTION:Explanation: X - (10/100) X = X * ? ? = 90% ANSWER IS B #### B QUESTION:If k is an integer and 121 < k^2 < 225, then k can have at most how many values? options: A)3 B)4 C)5 D)6 E)8 SOLUTION:given k is an integer 121 < k^2 < 225 11 < | k| < 15 K=-12,-13,-14,12,13,14 ANSWER:D #### D QUESTION:We bought 85 hats at the store. Blue hats cost $6 and green hats cost $7. The total price was $600. How many green hats did we buy? options: A)A)36 B)B)90 C)C)40 D)D)42 E)E)44 SOLUTION:Let B be the number of blue hats and let G be the number of green hats. B+G=85. B=85-G. 6B+7G=600. 6(85-G)+7G=600. 510-6G+7G=600. G=600-510=90. The answer is B. #### B QUESTION:If C and D are positive integers, and the remainder obtained when C is divided by D is the same as the remainder obtained when D is divided by C, which of the following is a possible value of CD? options: A) 62 B) 55 C) 48 D) 31 E) 25 SOLUTION:I am not too sure on this. I guess it is possible only when C and D are both same. If they are both same, CD must be a perfect square. 25 is a perfect square. Ans:E #### E QUESTION:When the price of a radio was reduced by 20%, its sale increased by 80%. What was the net effect on the sale? options: A)44% increase B)44% decrease C)66% increase D)75% increase E)None of these SOLUTION:Let the original price be x and sale be of y units. Then, the revenue collected initially = x × y Now, new price = 0.8x, new sale = 1.8y Then, new revenue collected = 1.44xy % increase in revenue = 0.44xy/xy×100 = 44% increase Answer A #### A QUESTION:A team of eight entered for a shooting competition. The best marks man scored 82 points. If he had scored 92 points, the average scores for. The team would have been 86. How many points altogether did the team score? options: A)662 B)678 C)652 D)642 E)721 SOLUTION:8 * 86 = 688 – 10 = 678 ANSWER:B #### B QUESTION:Consider below info to be a table: AMOUNT OF BACTERIA TIME - AMOUNT 1PM - 10gms 4PM - x gms 7PM - 10.0 gms Data 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 ? options: A)12.0 B)12.1 C)10.0 D)12.3 E)12.4 SOLUTION:let say the factor is x, the at 7PM quantity = 10 (i.e. quantity @1PM)* x^2 =10.0 => x^2 =1.00 or x = 1.0 => @4PM quantity = 10x =10*1.0 =10. Answer C #### C QUESTION:A store’s selling price of $2500 for a certain printer would yield a profit of 40 percent of the store’s cost for the printer. What selling price would yield a profit of 50 percent of the printer’s cost? options: A) $2400 B) $2464 C) $2650 D) $2478 E) $2800 SOLUTION:1.4x = 2500 x=2500/1.4 so, 1.5X = 2500*1.5/1.4= 2478 Answer:- D #### D QUESTION:Imagine John has 2 blue balls, 3 green balls, 1 black ball and 4 red balls. How many ways can he arrange the balls lining them up? options: A)10!/(2!)2 1! B)10!/2! 1! 3! 1! C)10!/4! 4! D)9!/4! 3! 2! E)10!/4! 3! 2! SOLUTION:n items of which p are alike of one kind, q alike of the other, r alike of another kind and the remaining are distinct can be arranged in a row in n!/p!q!r! ways. John has 10 balls which are 4 red balls, 3 green balls, 2 blue balls and 1 black ball. Number of arrangements = 9!/(2!)2 3! Answer: E #### E QUESTION:Ravi and Kavi start a business by investing ₹ 4000 and ₹ 72000, respectively. Find the ratio of their profits at the end of year. options: A)2 : 28 B)5 : 28 C)7 : 18 D)1 : 18 E)3 : 18 SOLUTION:Ratio of profit = Ratio of investments = 4000 : 72000 = 1 : 18 Answer : D #### D QUESTION:The sum of 33 consecutive integers is 3333. What is the greatest integer in the set? options: A)113 B)115 C)117 D)119 E)121 SOLUTION:Let x be the first integer in the set, then x+32 is the largest integer. The sum is: x+(x+1)+(x+2)+...+(x+32) = 33x + 32*33/2 = 33(x+16) Then x+16=101 x=85 The largest integer in the set is 85+32=117 The answer is C. #### C QUESTION:The total marks obtained by a student in Mathematics and Physics is 80 and his score in Chemistry is 20 marks more than that in Physics. Find the average marks scored in Mathamatics and Chemistry together. options: A)40 B)30 C)25 D)50 E)None of these. SOLUTION:Let the marks obtained by the student in Mathematics, Physics and Chemistry be M, P and C respectively. Given , M + C = 80 and C - P = 20 M + C / 2 = [(M + P) + (C - P)] / 2 = (80 + 20) / 2 = 50. ANSWER:D #### D QUESTION:A 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? options: A)21 (1/3) kmph B)25 (1/3) kmph C)29 (1/3) kmph D)20 (1/3) kmph E)24 (1/3) kmph SOLUTION:A Let the total distance be x km total time taken = (x/4)/16 + (3x/4)/24 = x/64 + x/32 = 3x/64 Average speed = x/(3x/64) = 64/3kmph = 21 (1/3)kmph. #### A QUESTION:If the integer n has exactly three positive divisors, including 1 and n, how many positive divisors does n^3 have? options: A)7 B)5 C)6 D)8 E)9 SOLUTION:take the example of 4... it has 3 positive divisors (1,2,4) Now, take the example of 64... it has only 7 divisors.. so A is the ans #### A QUESTION:Coconuts were purchased at 150 per hundred and sold at 2 per coconut. If 2000 coconuts were sold, what was the total profit made? options: A)500 B)1000 C)1500 D)2000 E)None of these SOLUTION:C.P. for one coconut = 150⁄100 = 3⁄2 S.P. for one coconut = 2 Profit on one coconut = 2 - 3⁄2 = 1⁄2 ∴ Profit on 2000 coconut = 1⁄2 × 2000 = 1000 Answer B #### B QUESTION:If the sum of the interior angles of a regular polygon measures 1440o, how many sides does the polygon have? options: A)10 sides B)8 sides C)12 sides D)9 sides E)None of these SOLUTION:Explanatory Answer Step 1: Compute sum of all interior and exterior angles The sum of an exterior angle and an interior angle of a polygon = 180o. The sum of all the exterior angles of a polygon = 360o. From the question stem: sum of all interior angles of the given polygon = 1440o. Therefore, sum of all the interior and all exterior angles of the polygon = 1440 + 360 = 1800o. Step 2: Compute number of sides If there are 'n' sides to this polygon, then the sum of all the exterior and interior angles = 180 * n = 1800o. Therefore, n = 10. Alternative Approach : Using formula Sum of all interior angles of a convex polygon = (n - 2)* 180 So, (n - 2) * 180 = 1440 n - 2 = 8 n = 10 Choice A #### A QUESTION:A cube is painted red on all faces. It is then cut into 27 equal smaller cubes. How many J cubes are painted on only 2 faces? options: A)12 B)8 C)6 D)10 E)16 SOLUTION:1) Draw a simple cube 2) 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. 3) Remember that the OUTSIDE of the cube is the part that's painted.... The 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. J=4 + 4 + 4 = 12. Answer A #### A QUESTION:On a ferry, there are 27 cars and 13 trucks. The cars have an average mass of 1100 kg and the trucks have an average mass of 3000 kg. What is the average mass of all 40 vehicles on the ferry? options: A)1515.5 B)1616.5 C)1717.5 D)1818.5 E)1919.5 SOLUTION:The total mass of the vehicles is 27*1100+13*3000=68700 The average mass is 68700/40=1717.5 The answer is C. #### C QUESTION:Due to 10% decrease in the price of sugar and John can buy 5kg more sugar in Rs100 , then find the CP of sugar? options: A)Rs. 1(2/9) B)Rs. 2(2/9) C)Rs. 2(1/9) D)Rs. 4(2/9) E)Rs. 3(1/9) SOLUTION:Here r = 10 % ,x = 100 and A = 5 kg Actual price of sugar = 10*100/((100-10 )*5) = Rs. 2(2/9) B #### B QUESTION:The cash difference between the selling prices of an article at a profit of 2% and 6% is Rs 3. The ratio of two selling prices is options: A)51:53 B)52:53 C)53:54 D)54:55 E)None of these SOLUTION:Explanation: Let the Cost price of article is Rs. x Required ratio = (102% of x) / (106% of x) =102/106 =51/53 = 51:53. Answer: A #### A QUESTION:In how many ways can the letters of the word CAVERN be arranged in a row so that the vowels appear in alphabetic order? options: A)360 B)720 C)620 D)180 E)36 SOLUTION:Two letters can be arranged in 2! ways. only one combination EIU is required. 6 letters can be arranged in 6! ways. thus 6!/ 2! * 1 = 360. A #### A QUESTION:A bicyclist travels uphill from town A to town B for 2 hours at an average speed of 5 miles per hour and returns along the same road at an average speed of 6 miles per hour. What is the bicyclist’s average speed for the round trip, in miles per hour? options: A)(a) 60/11 B)(b) 5 C)(c) 26/5 D)(d) 27/5 E)(e) 28/5 SOLUTION:from the uphill we can find out the distance = 5*2 = 10 average speed = total distance/total time = 20/ (2+ (10/6)) = 60/11 Answer is A. #### A QUESTION:A student scores 55% marks in 8 papers of 100 marks each. He scores 15% of his total marks in English. How much does he score in English? options: A)55 B)66 C)77 D)44 E)None of these SOLUTION:Given student scores 55% marks in english in 8 papers of 100 marks each. so,his total marks are (55*800)/100 =>440 15% of his 440 marks is 440*(15/100)=>66 so,he scored 66 marks in english. ANSWER:B #### B QUESTION:If the sum of two numbers is 24 and the sum of their squares is 404, then the product of the numbers is options: A)40 B)44 C)80 D)86 E)90 SOLUTION:Sol. Let the numbers be x and y. Then, (x+y) = 24 and x2 + y2 = 404. Now, 2xy = (x+y)2 - (x2 + y2) = (24)2 - 404 = 576- 404 = 172 xy = 86. Answer D #### D QUESTION:If a number 105 divides into n with no remainder, which of the following must be a factor of n? options: A)2 B)4 C)6 D)7 E)11 SOLUTION:105 / n = k (with k an integer) (7)(5)(3) / n = k n must have a 7 in his prime factorization to divide 105 without remainder. answer D #### D QUESTION:A man travelled from the village to the post office at the rate of 25kmph and walked backed at the rate of 4 kmph. If the whole journey took 5 hours 48 minutes, find the distance of the post office from the village? options: A)10km B)50km C)30km D)25km E)20km SOLUTION:Average speed = 2xy/x+y = 2*25*4/25+4 = 200/29km/hr Distance travelled in 5hr 48mnts = 200/9 * 29/5 = 40km Distance of the post office from the village = 40/2 = 20km Answer is E #### E QUESTION:Given a circular wheel of 3.62 m radius how many revolutions will the will make to travel a distance of 1 km? options: A)22754.3 B)22254.2 C)25754.2 D)22753.2 E)22254.2 SOLUTION:2 * 22/7 * 3.62 * x = 22754.3 x = 1000 Answer: A #### A QUESTION:If a is an odd integer and b is an even integer which of the following must be an integer : options: A)a/b B)ab C)2a+b D)2(a+b) E)option B C and D SOLUTION:a= odd = e.g 3 b=even = e.g 6 A. odd/even for example 3/6 = 0.5 no even no odd B. odd * even = 3 * 6 = 18 even C. 2*odd + even = even + even even D. 2(even + odd) = 2(odd) even Hence E it is. #### E QUESTION:Mary 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? options: A)24/64 B)32/64 C)36/64 D)40/64 E)42/64 SOLUTION:Expected value of one die is 1/6*(1+2+3+4+5+6)=3.5. Expected value of three dice is 3*3.5=10.5. Mary 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. That's because the probability distribution is symmetrical for this case: The probability of getting the sum of 3 (min possible sum) = the probability of getting the sum of 18 (max possible sum); The probability of getting the sum of 4 = the probability of getting the sum of 17; The probability of getting the sum of 5 = the probability of getting the sum of 16; ... The probability of getting the sum of 10 = the probability of getting the sum of 11; Thus the probability of getting the sum from 3 to 10 = the probability of getting the sum from 11 to 18 = 1/2. Answer: B. #### B QUESTION:A train passes a station platform in 30 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? options: A)120 m B)240 m C)168 m D)75 m E)60 m SOLUTION:Speed = 54 * 5/18 = 15 m/sec. Length of the train = 15 * 20 = 300 m. Let the length of the platform be x m . Then, (x + 300)/30 = 15 => x = 60 m Answer: E #### E QUESTION:In how many ways can the letters of the CHEATER be arranged options: A)20160 B)2520 C)360 D)80 E)None of these SOLUTION:Explanation: As we can see the letter "E" is twice in given word, so Required Number =7!/2!=7∗6∗5∗4∗3∗2!/2!=2520 Option B #### B <<<Examples ends QUESTION:Robert 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? options: A)8 kmph B)10 kmph C)12 kmph D)16 kmph E)18 kmph SOLUTION:Let the distance travelled by x km. Then, x - x = 2 10 15 3x - 2x = 60 x = 60 km. Time taken to travel 60 km at 10 km/hr = 60 hrs = 6 hrs. 10 So, Robert started 6 hours before 2 P.M. i.e., at 8 A.M. Required speed = 60 kmph. = 12 kmph. 5 C #### C

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:The mean of 50 observations was 36. It was found later that an observation 48 was wrongly taken as 23. The corrected new mean is options: A)35.2 B)36.1 C)36.5 D)39.1 E)None SOLUTION:Sol. Therefore correct sum = ( 36 × 50 + 48 – 23) = 1825. Therefore correct mean = 1825 / 50 = 36.5. Answer C #### C QUESTION:The number of female students in a college in the previous year was 400. If in the current year the number of male students in the college doubled over that of the previous year but the proportion of male students halved, then what is the number of female students in the college in the current year? options: A)200 B)600 C)900 D)1600 E)2000 SOLUTION:Let x be the number of male students last year. The number of male students this year is 2x. Let y be the number of female students this year. x/400 = 2(2x/y) y = 1600 The answer is D. #### D QUESTION:16 men can complete a piece of work in 25 days. In how many days can 15 men complete that piece of work? options: A)26.7 days B)77 days C)20 days D)88 days E)44 days SOLUTION:16 * 25 = 15 * x => x = 26.7 days Answer: A #### A QUESTION:217 + 2.017 + 0.217 + 2.0017 = ? options: A)229.3657 B)229.7563 C)229.6357 D)229.5637 E)221.2357 SOLUTION:217 2.017 0.217 + 2.0017 -------- 221.2357 --------- Answer is E. #### E QUESTION:The vertex of a rectangle are (1, 0), (9, 0), (1, 2) and (9, 2) respectively. If line L passes through the origin and divided the rectangle into two identical quadrilaterals, what is the slope of line L? options: A)5 B)4 C)1/2 D)1/5 E)1/8 SOLUTION:If line L divides the rectangle into two identical quadrilaterals, then it must pass through the center (5, 1). The slope of a line passing through (0,0) and (5, 1) is 1/5. The answer is D. #### D QUESTION:A shopkeeper sold an article offering a discount of 5% and earned a profit of 21.6%. What would have been the percentage of profit earned if no discount was offered? options: A)60% B)28% C)30% D)56% E)73% SOLUTION:Let C.P. be Rs. 100. Then, S.P. = Rs. 121.60 Let marked price be Rs. x. Then, 95/100 x = 121.60 x = 12160/95 = Rs. 128 Now, S.P. = Rs. 128, C.P. = Rs. 100 Profit % = 28%. Answer: B #### B QUESTION:An association of mathematics teachers has 1,260 members. Only 525 of these members cast votes in the election for president of the association. What percent of the total membership voted for the winning candidate if the winning candidate received 60 percent of the votes cast? options: A)75% B)58% C)42% D)34% E)25% SOLUTION:Total Number of members = 1260 Number of members that cast votes = 525 Since , winning candidate received 60 percent of the votes cast Number of votes for winning candidate = (60/100)*525 = 315 Percent of total membership that voted for winning candidate = (315/1260)*100 = 25% Answer E #### E QUESTION:A sun is divided among X, Y and Z in such a way that for each rupee X gets, Y gets 50 paisa and Z gets 40 paisa. If the share of X is RS. 30, what is the total amount? options: A)67 B)55 C)62 D)47 E)57 SOLUTION:x:y:z = 100:50:40 10:5:4 10 --- 30 19 --- ? => 57 Answer: E #### E QUESTION:S 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? options: A) The median of S is prime. B) The median of T is prime C) The median of S is equal to the median of T. D) The sum of the terms in S is prime. E) The sum of the terms in T is prime. SOLUTION:Here 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? (A) The median of S is prime. Thismust 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. (B) The median of T is prime. Thismay 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. (C) The median of S is equal to the median of T. Under 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. (D) The sum of the terms in S is prime. Thismay 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. (E) The sum of the terms in T is prime. Thismust 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. D #### D QUESTION:How many factors does 35^2 have? options: A)2 B)8 C)24 D)25 E)26 SOLUTION:36^2 = 6*6*6*6 = 2^4*3^4 Total factors = (4+1)*(4+1) = 6*4 = 24 Answer C. #### C QUESTION:A, B, K start from the same place and travel in the same direction at speeds of 30 km/hr, 40 km/hr, 160 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? options: A)5.0 B)5.5 C)6.0 D)6.5 E)7.0 SOLUTION:In 2 hours, A travels 60 km. B can catch A at a rate of 10 km/hr, so B catches A 6 hours after B starts. So A and B both travel a distance of 240 km. C needs 1.5 hours to travel 240 km, so C leaves 6.5 hours after A. The answer is D. #### D QUESTION:If set A={2,2,2,....,n times} , set B={3,3,3,3....m times} and set C={13,13,13...k time} , then in terms of m,n and k , how many possible subsets from sets A,B, and C can be created ? options: A)a) k(n+m+mn)+ k B)b) (1+n+m+mn)(k+1) C)c) k^2(mn+n/m) D)d) kmn(k+m+n) E)e) None of the above. SOLUTION:a) how many 2's are included? b) how many 3's are included? and c) how many 11's are included? For 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. NOTICE 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. The 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: (mn + m + n + 1)(k + 1). Mike B #### B QUESTION:In 2000, a town had 1300 males and 1400 females. In 2015, the same town had 56500 males and 60000 females. By approximately what percent did the ratio of males to females increase from 2000 to 2015. options: A)0.4% B)0.7% C)0.9% D)1.1% E)1.4% SOLUTION:2000: males/females = 1300/1400 =3900/4200 2015: males/females = 56500/60000 =3955/4200 ASIDE: It's useful to write both ratios with the same denominator. This allows us to IGNORE the denominator and focus solely on the numerators. So, our ratio went from 3900/4200 to 3955/4200 Ignoring the denominators, we went from 3900 to 3955 The percent change = 100(difference in values)/(original value) = (100)(3955-3900)/3900 = (100)(55)/3900) = (100)(0.0141) ≈ 1.41... Answer: E #### E QUESTION:Out of 12 students in a class, 7 are wearing blue shirts, 3 are wearing green shirts, and 2 are wearing red shirts. Four students are to be selected at random. What is the probability that at least one is wearing a green shirt? options: A)25/33 B)31/44 C)41/55 D)53/66 E)65/77 SOLUTION:Total possible ways to choose 4 students out of 12 = 12C4 = 495 The number of ways to choose 4 students with no green shirts = 9C4 = 126 P(no green shirts) = 126/495 = 14/55 P(at least 1 green shirt) = 1 - 14/55 = 41/55 The answer is C. #### C QUESTION:A rectangular box of volume x has width, depth and height in the ratio of 5:1:2 (in that order). What is the width as a function of x? options: A)(4x/12)^(1/2) B)(10x/4)^(1/2) C)(5x)^(1/2) D)(2x/5)^(1/2) E)(4x/3)^(1/2) SOLUTION:We are given width = 5, depth = 1, height = 2 Then Volume x = Width x Depth x Height = 5*1*2 = 10 i.e. x = 10 i.e. The correct option should result in 5 (the width) on substituting the value of x=10 Checking options with x=10 A) (4x/12)^(1/2) = (4*10/12)^(1/2) = (40/12)^(1/2) INCORRECT ANSWER B) (10x/4)^(1/2) = (10*10/4)^(1/2) = 25^(1/2) = 5 CORRECT ANSWER C) (5x)^(1/2) = (5*10)^(1/2) = 50^(1/2) INCORRECT ANSWER D) (2x/5)^(1/2) = (2*10/5)^(1/2) = 4^(1/2) = 2 INCORRECT ANSWER E) (4x/3)^(1/2) = (4*10/3)^(1/2) = 40/3^(1/2) INCORRECT ANSWER Answer: Option B #### B QUESTION:Two persons start running simultaneously around a circular track of length 300 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? options: A)76 seconds B)16 seconds C)18 seconds D)27 seconds E)19 seconds SOLUTION:Time taken to meet for the first time anywhere on the track = length of the track / relative speed = 300 / (15 + 25)5/18 = 300* 18 / 40 * 5 = 27 seconds. Answer: D #### D QUESTION:Which of the following inequalities is equivalent to −1 < x < 5? options: A)|x - 1| < 7 B)|x + 2| < 3 C)|x + 3| < 5 D)|x - 2| < 3 E)None of the above SOLUTION:We know that |x| < a means -a < x < a, where Sum of lower limit of x (i.e -a) and the upper limit of x (i.e a), is 0 Given is, -1 < x < 5, let's say by adding y to this inequality we will get into the above format -1+y < x+y < 5+y Now, to move this into the mod format, we need to have (-1+y) + (5+y) = 0 => y = -2 Thus, -3< x-2 < 3 => |x-2| < 3. Hence, answer is D #### D QUESTION:An 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 12-meter platform and caught it after it had traveled 35.65 meters. How many times did the ball bounce? options: A)5 B)6 C)7 D)8 E)9 SOLUTION:Ans: 6 Division of total diatance travelled will be 12+12+6+3+1.5+.75+0.4 ANS B #### B QUESTION:Walking across campus, a student interviewed a group of students. 35% of the students took a finance class last semester, 45% took a marketing class last semester, and 50% 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? options: A)40% B)30% C)25% D)15% E)10% SOLUTION:{Total} = {finance} + {marketing} - {both} + {neither} 100 = 35 + 45 - {both} + 50 {both} = 30%. The answer is B. #### B QUESTION:Ramu bought an old car for Rs. 40000. He spent Rs. 13000 on repairs and sold it for Rs. 64900. What is his profit percent? options: A)17% B)22.4% C)18% D)14% E)16% SOLUTION:Total CP = Rs. 40000 + Rs. 13000 = Rs. 53000 and SP = Rs. 64900 Profit(%) = (64900 - 53000)/53000 * 100 = 22.4% Answer: B #### B QUESTION:If 0 < m < 1 < n< 7, which of the following must be less than 1? I.m/n II. mn III. n - m options: A)II,III only B)I,III only C)I only D)III only E)II only SOLUTION:n > 1. So, option II, III is not possible. So, Option I is correct. Answer : C #### C QUESTION:The average of first 10 odd numbers is? options: A)22 B)10 C)98 D)66 E)88 SOLUTION:Sum of 10 odd no. = 100 Average = 100/10 = 10 Answer:B #### B QUESTION:Carol is four times Alice’s age but only twice as old as Betty. Alice is thirty-six years younger than Carol. How old is Betty? options: A)36 B)39 C)42 D)48 E)24 SOLUTION:Beyond the obvious Algebra approach to this question, it can also be solved by TESTing THE ANSWERS. We're told 3 facts about the relative ages of 3 people: 1) Carol's age is 4 times Alice's age 2) Carol's age is 2 times Betty's age 3) Carol is 36 years older than Alice We're asked for BETTY'S age. Since Carol is TWICE Betty's age, Betty is clearly younger than Carol, so we'll TEST smaller answer first. IF.... Betty = 24 Then Carol = 2(24) = 48 Then Alice = 48 - 36 = 12 AND 48/4 =12 All of these values mesh perfectly with the facts and with one another, so Betty MUST be 24 E #### E QUESTION:The expression (11.98 x 11.98 + 11.98 x x + 0.02 x 0.02) will be a perfect square for x equal to: options: A)0.04 B)0.004 C)0.4 D)0.0004 E)None of them SOLUTION:Given expression = (11.98)(power 2) + (0.02)(power 2) + 11.98 x x. For the given expression to be a perfect square, we must have 11.98 x (x) = 2 x 11.98 x 0.02 or x = 0.04 Answer is A #### A QUESTION:There are 3 teams each with 8 basket players. How many combinations are there if we were to pick 2 players from the 3 teams such that no team was picked twice? options: A)50 B)23 C)192 D)28 E)45 SOLUTION:There are altogether three arrangements, which are we can select two members each from team A and B, each from team A and C, and each from team B and C. For each arrangement, there are altogether 64 possibilities (8*8) since each team has 8 players. So there are a total of 192 possibilities (64*3). I hope this method is easier for you to understand. #### C QUESTION:In what ratio water be mixed with milk costing Rs.12 per liter to obtain a mixture worth of Rs.8 per litre? options: A)2:7 B)1:2 C)2:9 D)2:2 E)2:6 SOLUTION:Answer with Explanation: By the rule of allegation, i. C.P of 1 liter of water = 0 ii. C.P of 1 liter of milk = 12 iii. Mean price (p) = 8 iv. d – m = 12-8 = 4 v. m – c = 8-0 = 8  Ratio of water and milk = 4 : 8 = 1 : 2 Answer:B #### B QUESTION:A is older than B by 5years. Seven years hence, thrice A's age shall be equal to four times that of B. Find their present ages. options: A)14, 7 B)10, 5 C)13, 8 D)12, 8 E)8, 12 SOLUTION:Explanation: Let the present ages of A and B be 'a' and 'b' respectively. 3(a + 7)= 4( (b +7 ) --- (1) =>3a-4b=7 -------(1) a-b = 5 -------(2) Solving (1) and (2) we get b=8 Substituting b = 8 in second equation, we get a= 13. Answer : C => 2a = 32 => a = 16. Answer: C #### C QUESTION:If 36 men can do a piece of work in 25 hours, in how many hours will 10 men do it? options: A)22 B)38 C)60 D)88 E)90 SOLUTION:Explanation: Let the required no of hours be x. Then Less men , More hours (Indirect Proportion) \inline \fn_jvn \therefore 10:36 ::25:x \inline \fn_jvn \Leftrightarrow (10 x X)=(36 x 25) \inline \fn_jvn \Leftrightarrow \inline \fn_jvn x=\frac{36\times 25}{10}=90 Hence, 10 men can do it in 90 hours. Answer: E) 90 #### E QUESTION:In power plant, If 36 men can do a piece of work in 25 hours, in how many hours will 15 men do it ? options: A)40 hours B)50 hours C)60 hours D)70 hours E)None of these SOLUTION:Explanation : Let the required number of hours be x. Then, Less men, More hours (Indirect Proportion) 15 : 36 : : 25 : x => (15 * x) = (36 * 25) x=(36 x 25)/15 = 60 Hence, 15 men can do it in 60 hours. Answer : C #### C QUESTION:The 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? options: A)1/36a B)1/36a^2 C)1/6a D)36a E)36a^2 SOLUTION:initially - did x= 1/y^2 But this yielded the wrong answer, I then re examined the question and tried y^2/x =1 Which I then got y = SQR(X) subbing into y/6a I got answer E) #### E QUESTION:In a game of 80 points; A can give B 5 points and C 15 points. Then how many points B can give C in a game of 60 ? options: A)B can give C 1 points B)B can give C 4 points C)B can give C 2 points D)B can give C 6 points E)B can give C 8 points SOLUTION:A: B = 80 : 75, A : C = 80 : 65. B/C = ( B/ A * A/C) = (75 / 80 * 80 / 65) = 15/13 = 60 /52 = 60: 5 Therfore ,In a game of 60, B can give C 8 points. Answer is E. #### E QUESTION:If q is a positive integer and q^2 is divisible by 12, then the largest positive integer that must divide q ^3 is options: A) 2^3 B) 2^6 C) 3^3 D) 6^3 E) 12^2 SOLUTION:Since 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)) q^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 So, q will have a 2 and a 3. Or q will be a multiple of 6 So, largest possible integer than should divide q^3 is 6^3 So, Answer will be D #### D QUESTION:A 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? options: A)22 days B)4 days C)13 days D)6 days E)9 days SOLUTION:(A + B)'s 1 day's work = (1/4). A's 1 day's work = (1/12). B's 1 day's work =((1/4)-(1/12))=(1/6) Hence, B alone can complete the work in 6 days. Answer is D. #### D QUESTION:What will be the difference between simple and compound interest at 8% per annum on a sum of Rs. 1000 after 4 years? options: A)64.19 B)64.12 C)40.5 D)64.1 E)64.11 SOLUTION:S.I. = (1000 * 8 * 4)/100 = Rs. 320 C.I. = [1000 * (1 + 8/100)4 - 1000] = Rs. 360.5 Difference = (360.5 - 320) = Rs. 40.5 Answer: C #### C QUESTION:A retailer buys a radio for Rs 225. His overhead expenses are Rs 15. He sellis the radio for Rs 300. The profit percent of the retailer is options: A)10% B)50% C)25% D)52% E)None of these SOLUTION:Explanation: cost price = (225 + 15) = 240 sell price = 300 gain = (60/240)*100 = 25%. Answer: C #### C QUESTION:If x is divisible by 2 and 7, which of the following must divide evenly into x? I. 60 II. 32 III. 14 options: A)I,II only B)I,III only C)I only D)III only E)II only SOLUTION:If x is divisible by 2,7 means it will be = or > 14, 28,42 etc... That are not divisible by 60, 32. So, the answer is D #### D QUESTION:The capacity of a tank of dimensions (8m x 6m x 2.5m)is options: A)120 litres B)1200 litres C)12000 litres D)120000 litres E)None of these SOLUTION:Explanation: capacity of atank =volume of tank = (8 x 100 x 6 x 100 x 2.5 x 100)/1000 litres = 120000 litres Answer: D #### D QUESTION:Two persons start from two places 160 km apart at the same time with velocities 50 km/hr and 30 km/hr. move in opposite direction. Where they meet ? options: A)90 km from A B)50 km from B C)100 km from A D)70 km from B E)None of these SOLUTION:Explanation : Solution: d = 160, v1 = 50, v2 = 30 relative speed vr = v1 + v2 = 50 + 30 = 80. the distance covered by them will be indirectly proportional to their distance of the persons of meeting from A = 160*50/(50+30) km = 160*5/8 = 100 km. Answer : C #### C QUESTION:In the equation x^2+kx+1=0, x is a variable and k is a constant. If the quadratic equation has two distinct real roots, which of the following could be true? I) k=0 II) k=−1 III) k=−3 options: A)I only B)III only C)I and II only D)II and III only E)I and III only SOLUTION:Please format the question properly. Per the question, x^2+kx+1=0 with k=constant. For a quadratic equation (ax2+bx+c=0) to have 2 distinct roots ---> D=b2−4ac>0 ---> k^2−4>0 --->k<−2or k>2 . Only III falls in these ranges. B is the correct answer. #### B QUESTION:In a recent election, Ms. Robinson received 8000 voters 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 40 percent of the votes cast were cast by independent voters, which of the following represents the number of votes that Mrs. Robbins received? options: A) 0.06N+3200 B) 0.1N+7200 C) 0.4N+7200 D) 0.12N+8000 E) 0.06N+8000 SOLUTION:40% of N are independent voters, hence 60% of N are not independent voters. From this group she received 20% votes so, 0.2*0.6*N plus 8,000 votes from independents: total=0.2*0.6*N+8,000=0.12*N+8,000. Answer: D. #### D QUESTION:A Cone, a hemisphere and a cylinder stand on equal bases and have the same height .Find ratio of their volumes. options: A)2:1:3 B)2:1:4 C)1:2:3 D)4:1:7 E)5:1:8 SOLUTION:Let R be the radius of each Height of the hemisphere = Its radius = R. Height of each = R. Ratio of volumes = (1/3)∏ R2 x R : (2/3)∏R3 : ∏ R2 x R = 1:2:3 ANSWER C 1:2:3 #### C QUESTION:Evaluate : (2.39)(power 2) - (1.61) (power 2) / 2.39 - 1.61 options: A)4 B)6 C)8 D)2 E)10 SOLUTION:Given Expression = a(power 2) - b(power 2) / a-b = (a + b)(a - b) / (a-b) = (a + b) = (2.39 + 1.61) = 4. Answer is A. #### A QUESTION:In order to obtain an income of Rs. 580 from 15% stock at Rs. 100, one must make an investment of options: A)5363 B)6240 C)8700 D)5600 E)2732 SOLUTION:To obtain Rs. 10, investment = Rs. 100. To obtain Rs. 580, investment = = Rs. 8700. Answer: C #### C QUESTION:A man can row upstream at 5km/hr and down stream at 13km/hr find mans rate in still water ? options: A)7.5km/hr B)3.5km/hr C)9km/hr D)4km/hr E)5km/hr SOLUTION:given upstream(u) =5km/hr down stream (v)= 13km/hr rate in still water =1/2(u+v)=1/2(5+13)=9km/hr Answer is (C) #### C QUESTION:The H.C.F. of two numbers is 5 and their L.C.M. is 150. If one of the numbers is 25, then the other is: options: A)30 B)28 C)24 D)20 E)35 SOLUTION:Product of two nos = product of HCF and LCM Let one number = x => 25 * x = 5 * 150 x=5*150/25=30 ANSWER A #### A QUESTION:Harkamal 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? options: A)1055 B)1050 C)1057 D)1060 E)1070 SOLUTION:Cost of 8 kg grapes = 70 × 8 = 560. Cost of 9 kg of mangoes = 55 × 9 = 490. Total cost he has to pay = 560 + 490 = 1055. A #### A QUESTION:In 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? options: A)23000 B)22000 C)20000 D)25000 E)30000 SOLUTION:Winner - Looser 55% - 45% If 3000 people change their mind and vote for the loser: Winner - Looser 45% - 55% Thus 3,000 people compose 10% of all voters, which means that the total number of votes is 30,000. Answer: E. #### E QUESTION:In a Private Company 20 Nos. staffs are employed. In a Festival season their Boss give festival allowance to all. He says his accountant to calculate for 30 days @ 100. Also he says balance payment will give to driver and cleaning staff and to be adjust from petty cash. He had given Rs.65000/- to the accountant. How much amount will taken from Petty cash? options: A)A)1000 B)B)3000 C)C)3500 D)D)2500 E)E)2250 SOLUTION:For 20 staffs: 300*100*20 = 60000 for driver and cleaning staff: 300*100*2 =6000 From petty Cash : 1000 Answer is 1000 Answer is A #### A QUESTION:Working at their respective constant rates, Paul, Abdul and Adam alone can finish a certain work in 3, 4, and 5 hours respectively. If all three work together to finish the work, what fraction R of the work will be done by Adam? options: A) 1/4 B) 12/47 C) 1/3 D) 5/12 E) 20/47 SOLUTION:Let the total work be 60 units. Pual does 60/3 =20 units of work per hr. abdul does 15 units per hr and adam does 12 units per hr. If all work together they do (20 + 15 + 12) units per hr = 47 units per hr. So the time taken to finish the work = 60/47 hrs. adam will do 60/47 * 12 units of work in 60/47 hr . fraction of work adam does =work done by adam / total work R>( 60/47 *12)/60 =12/47 Answer B #### B QUESTION:What is the measure of the radius of the circle that circumscribes a triangle whose sides measure 11, 60 and 61? options: A)6.5 B)12.5 C)28 D)30.5 E)40 SOLUTION:Some of pyhtagron triplets we need to keep it in mind. Like {( 2,3,5) , ( 5,12,13) ,( 7, 24,25), ( 11, 60,61). So now we know the triangle is an right angle triangle. The circle circumscribes the triangle. The circumraduis of the circle that circumscribes the right angle triangle = hypotanse / 2 = 61 / 2 = 30.5 Ans. D #### D QUESTION:A, B and C invested Rs.6600, Rs.4400 and Rs.11000 respectively, in a partnership business. Find the share of A in profit of Rs.12100 after a year? options: A)Rs.3300 B)Rs.3100 C)Rs.3500 D)Rs.4200 E)Rs.3400 SOLUTION:6600:4400:11000 3:2:5 3/10 * 11000 = Rs.3300 AnswerA #### A QUESTION:Average 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 550. The income of the deceased was? options: A)Rs. 692.80 B)Rs. 820 C)Rs. 990 D)Rs. 1385 E)None SOLUTION:Answer Income of the deceased = Total income of 4 members - total income of remaining 3 members. = 735 x 4 - 550 x 3 Rs. = 1290 Rs. Correct Option: E #### E QUESTION:What annual payment will discharge a debt of Rs. 1025 due in 2 years at the rate of 5% compound interest? options: A)Rs. 560 B)Rs. 560.75 C)Rs. 551.25 D)Rs. 550 E)Rs. 560 SOLUTION:Explanation: Present worth of Rs. x due T years hence is given by Present Worth (PW) = x/(1+R/100)T Let x be the annual payment Then, present worth of x due 1 year hence + present worth of x due 2 year hence = 1025 x(1 + 5/100)1 + x(1 + 5/100)2 = 1025 x/(21/20) + x/(21/20)2 = 1025 20x/21 + 400x/441 = 1025 820x/441 = 1025 x = (1025 × 441)/820 = (205 × 441)/164 = Rs. 551.25 Answer: Option C #### C QUESTION:A certain elevator has a safe weight limit of 1950 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 190 pounds and the average weight of the others being 200 pounds? options: A)7 B)8 C)9 D)10 E)11 SOLUTION:Lets assume there are 2X people. Half of them have average weight of 190 and other half has 200. Maximum Weight is = 1950 So 190*X + 200*X = 1950 => 390X = 1950 => X is approximately equal to 5. So total people is 2*5 = 10 Answer D. #### D QUESTION:The cost price of an article is 70% of the marked price. Calculate the gain percent after allowing a discount of 10%. options: A)13.6% B)28.6% C)35.6% D)42.3% E)none SOLUTION:Sol. Let marked price = Rs. 100. Then, C.P. = Rs. 70. S.P = Rs. 90. ∴ Gain % = [20/70 * 100]% = 28.6%. Answer B #### B QUESTION:A furniture manufacturer has two machines, but only one can be used at a time. Machine W is utilized during the first shift and Machine B during the second shift, while both work half of the third shift. If Machine W 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? options: A)14 B)13 C)11 D)9 E)7 SOLUTION:'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. To finish a work Machine W say 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 #### D QUESTION:Minute hand overlaps hour hand in 65 mins. In how many days it will gain 1440 hours ? options: A)58.384 days B)59.384 days C)57.384 days D)69.384 days E)55.384 days SOLUTION:In this problem , it has considered that 65 mins = 1hr so mins has increased by 5 mins so multiply 5*24=120 mins extra , That is now per day it adds 2hr extra so divide 1440/26=59.384 days ANSWER:B #### B QUESTION:How many numbers between 300 and 500 begin or end with 3? options: A)20 B)60 C)100 D)110 E)120 SOLUTION:How many numbers between 300 and 500 begin or end with 3? Just think that those numbers are: i) The ones ending in 3: 303, 313, 323, ... , 493 --> 20 numbers ii) The ones beginning in 3: 300, 301, 302, 303, ... , 393, ... , 399 --> 100 numbers BUT 10 out of the first 20 numbers are repeated in the second set. THEREFORE, the solution is 110 numbers. Answer: D #### D QUESTION:From a pack of cards two cards are drawn one after the other, with replacement. The probability that the first card is a spade and the second card is a jack is? options: A)1/50 B)1/13 C)1/26 D)1/52 E)1/4 SOLUTION:Probability of a spade = 13/52 = 1/4 Probability of a jack = 4/52 = 1/13 Probability of both = P1*P2 = 1/(4*13) = 1/52 Answer is D. #### D QUESTION:A man buys an article for rs.27.50 and sells it for rs.28.50. find his gain percentage. options: A)4 B)2 C)1 D)3 E)None of them SOLUTION:cost price=rs27.50, sp=rs 28.50 gain=rs(28.50 –27.50)=rs1.10 so gain%={(1.10/27.50)*100}=4% Answer is A. #### A QUESTION:What is the sum of the different positive prime factors of 960? options: A)5 B)10 C)15 D)17 E)21 SOLUTION:Prime factorization of 960 =96 * 10 =16*6 * 10 =4*4 * 2*3 * 2*5 =2*2 * 2*2 * 2* 3 * 2*5 =2^6 * 3 * 5 Sum of the different positive prime factors of 960 = 2+3+5 =10 Answer B #### B QUESTION:Find the number of solutions for 3x+4y=60, if x and y are positive integers options: A)1 B)2 C)3 D)4 E)5 SOLUTION:3x+4y=60 =>x=(60-4y)/3 as x and y are positive integers, put y=1,2,3,... & find x y=3,x=16 y=6,x=12 y=9,x=8 y=12,x=4 (x,y)=(4,12),(8,9),(12,6),(16,3) only 4 solution ANSWER:D #### D QUESTION:After running a series of television advertisements, a leading beverage producer saw its sales increase by 25% to $3 million dollars per month. Prior to the advertising campaign, about how many dollars in sales did the company average per day? options: A)$1.25 million B)$80,000 C)$750,000 D)$27,000 E)$10,000 SOLUTION:Let sales in previous month = X 1.25 X=2,000,000 5/4 X= 2,000,000 ..........> X=2,400,000 sales per day= 2,400,000/30= less than 80,000 Answer:B #### B QUESTION:The perimeters of two squares are 80 cm and 64 cm. Find the perimeter of a third square whose area is equal to the difference of the areas of the two squares. options: A)42cm B)44cm C)46cm D)48cm E)49cm SOLUTION:Explanation: Side of first square = (80/4) = 20 cm; Side of second square = (64/4)cm = 16 cm. Area of third square = [(20)2 - (16)2] cm2 = (400 - 256) cm2 = 144 cm2. Side of third square = (144)(1/2) cm = 12 cm. Required perimeter = (12 x 4) cm = 48 cm. Answer: Option D #### D <<<Examples ends QUESTION:The 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? options: A)289 cm B)800 cm C)829 cm D)288 cm E)289 cm SOLUTION:Area of the square = s * s = 5(125 * 64) => s = 25 * 8 = 200 cm Perimeter of the square = 4 * 200 = 800 cm. Answer: B #### B

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:A 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 : options: A)1 kmph B)2 kmph C)3 kmph D)1.3 kmph E)3.5 kmph SOLUTION:Rate upstream = (1/25 *60) = 2.4 kmph Rate dowm stream = 1/12 * 60 = 5 kmph Rate of the current = ½ (5-2.4) = 1.3 kmph ANSWER:D #### D QUESTION:When 100 is divided by positive integer x, the remainder is 4. What is the remainder when 196 is divided by x? options: A)2 B)3 C)4 D)6 E)8 SOLUTION:f100/x leaves a reminder 4 then (100-4) i.e. 96 is divisible by x So (100+96)/x leaves a reminder rem(100/x)+rem(96/x)=> 4+0=4 Answer :C #### C QUESTION:If n is an integer and 102n^2 is less than or equal to 8100, what is the greatest possible value of n? options: A)7 B)8 C)9 D)10 E)11 SOLUTION:102 * n^2 <=8100 n^2 <=8100/102 which will be less than 81 since 8100/100 = 81 which is the square of 9 Next closest value of n where n^2<=81 is 8 Ans B #### B QUESTION:The average weight of a group of 30 friends increases by 2 kg when the weight of their football coach was removed. If average weight of the group after removing the weight of the football coach is 28 kg, what is the weight of their football coach? options: A)31 kg B)60 kg C)61 kg D)62 kg E)88 kg SOLUTION:let c=coach's weight original total weight=(30 friends)(30 kg avge)=900kg (900-c)/(30-1)=28 kg avge c=88 kg Answer - E #### E QUESTION:Three partners A, B, C in a business invested money such that 3(A’s capital) = 6(B’s capital) = 9(C’s capital) then, The ratio of their capitals is options: A)63 : 45 : 34 B)6 : 3 : 2 C)36 : 54 : 28 D)63 : 45 : 35 E)None of these SOLUTION:Explanation: Let3(A’s capital) = 6(B’s capital) = 9(C’s capital) = Rs.x Then, A’s capital = Rs x/3, B’s capital = Rs. x/6 and C’s capital = Rs. x/9. A : B : C = x/3 : x/6 : x/9 6 : 3 : 2 Answer: Option B #### B QUESTION:The 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. 16000, then find the annual income of A? options: A)Rs. 537600 B)Rs. 180000 C)Rs. 201600 D)Rs. 504000 E)None of these SOLUTION:B's monthly income = 16000 * 112/100 = Rs. 17920 B's monthly income = 2 parts ----> Rs. 17920 A's monthly income = 5 parts = 5/2 * 17920 = Rs. 44800 A's annual income = Rs. 44800 * 12 = Rs. 537600 ANSWER:A #### A QUESTION:A can do a job in 30days and B in 40days. If they work on it together for 10 days, then the fraction of the work that is left is? options: A)2/11 B)3/13 C)5/12 D)7/10 E)6/15 SOLUTION:A's 1 day work = 1/30 B's 1day work = 1/40 A+B 1day work = 1/30 + 1/40 = 7/120 A+B 4days work = 7/120*10 = 7/12 Remaining work = 1 - 7/12 = 5/12 Answer is C #### C QUESTION:In a sequence of 40 numbers, each term, except for the first one, is 7 less than the previous term. If the greatest term in the sequence is 282, what is the smallest term in the sequence? options: A)2 B)-2 C)0 D)8 E)9 SOLUTION:Which term is the greatest? The first or the last? It is given to you that every term is 7 less than the previous term. Hence as you go on, your terms keep becoming smaller and smaller. The first term is the greatest term. An = 282 + (40 - 1)*(-7) An = 282 - 273 = 9 E #### E QUESTION:The positive integer x has a factor of 16. If the square root of x is > 16, which of the following could equal x/16? options: A)13 B)14 C)15 D)16 E)17 SOLUTION:Given: x=16k (where k is a positive integer) and √x=√16k >16 --> x=16k>16^2 --> divide by 16. So as x/16=k=integer>16, then x/16 can be 17, 18, ... Answer: E. #### E QUESTION:Plane leaves from Chelsea every 35 minutes from West Ham airport. Air hostess told Frank Lampard that the plane had left 25 minutes ago and the next plane for Chelsea will leave at 7:00 p.m. At what time air hostess convey this information to Frank Lampard? options: A)5:35 p.m B)6:50 p.m C)7:35 p.m D)8:35 p.m E)9:35 p.m SOLUTION:Explanation: Time of Frank Lampard last missed plane = 7:00 p.m - 35 min = 6:25 p.m As this information has been given to Frank Lampard 25 minutes after the plane has already left, the air hostess gave the information at 6:25 p.m + 25 min = 6:50 p.m Answer B #### B QUESTION:The 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? options: A)Rs. 120,002 B)Rs. 1,20,000 C)Rs. 1,20,00 D)Rs. 1,20,028 E)Rs. 1,20,011 SOLUTION:Explanation: The value of the machine after two years = 0.8 * 0.8 * 1,50,000 = Rs. 96,000 SP such that a profit of Rs. 24,000 is made = 96,000 + 24,000 = Rs. 1,20,000 Answer: B #### B QUESTION:How 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 ? options: A)3.5 years B)4 years C)4.5 years D)5 years E)None of these SOLUTION:Solution Time =(100*81/450*4.5) years =4 years Answer B #### B QUESTION:If i walk with 30 miles/hr i reach 1 hour before and if i walk with 20 miles/hr i reach 1 hour late.Find the distance between 2 points and the exact time of reaching destination is 11 am then find the speed with which it walks. options: A)120 MILES B)130 MILES C)140 MILES D)150 MILES E)160 MILES SOLUTION:LET ORIGINAL SPEED BE V AND TIME TAKEN BE T... AS DISTANCE BETWEEN TWO POINTS IS CONSTANT, 30*(T-1)=20*(T+1)=V*T HENCE, V=24MILE/HR T=5 HRS DISTANCE BETWEEN TWO POINTS IS 120 MILES ANSWER:A #### A QUESTION:A took 15 seconds to cross a rectangular field diagonally walking at the rate of 52 m/min and B took the same time to cross the same field along its sides walking at the rate of 68m/min. The area of the field is? options: A)33 B)60 C)88 D)27 E)26 SOLUTION:Explanation: length of the diagonal = 52*(15/60) =13m sum of length and breadth = 68*(15/60) = 17m \inline {\color{Black}\sqrt{l^{2}+b^{2}}=13 \; or\; l+b=17 } area =lb = 1/2[(2lb)] = 1/2[(l+b)² - (l²+b²)] = 1/2[17² -169] =1/2*120 = 60 sq meter Answer: B) 60 #### B QUESTION:Angelo and Isabella are both salespersons. In any given week, Angelo makes $550 in base salary plus 8 percent of the portion of his sales above $4,000 for that week. Isabella makes 10 percent of her total sales for any given week. For what amount of weekly sales would Angelo and Isabella earn the same amount of money? options: A) 11,500 B) 24,500 C) 25,500 D) 26,500 E) 27,500 SOLUTION:OFFICIAL SOLUTION: The problem asks for the amount of weekly sales it takes for Angelo and Isabella to earn the same amount of money. You can write an equation that sets Angelo’s and Isabella’s weekly earnings equal to each other, with x representing weekly sales. Weekly earnings for each salesperson equal base salary plus commission. So Angelo’s earnings are 550 + (0.08)(x – 4,000), and Isabella’s are 0.10x. Set up the equation and solve: 550 + (0.08)(x – 4,000) = 0.10x Distribute the 0.08: 550 + 0.08x – 320 = 0.10x Combine terms and subtract 0.08x from both sides: 230 = 0.02x Divide both sides by 0.02: 11,500 = x Your answer is A. #### A QUESTION:Of the 11 temporary employees in a certain company, 4 will be hired as permanent employees. If 5 of the 11 temporary employees are women, how many of the possible groups of 4 employees consist of 3 women and one man? options: A)22 B)35 C)60 D)70 E)105 SOLUTION:another approach : one scenario : [WWWM] now we have 5 ways for the first women , 4 ways for the 2nd women and , 3 ways for the third women. and 6 ways to select one man so 5*4*3*6 = 360 now the three women are same so combinations with win them are irrelevant the 3 women can we arranged in 3! ways hence 360/3!= 360/6= 60 C #### C QUESTION:A can complete a work in 15 days and B can do the same work in 9days. If A after doing 5days, leaves the work, find in how many days B will do the remaining work? options: A)2days B)4days C)6days D)7days E)10days SOLUTION:The required answer = (15-5)*9 / 15 = 40/10 = 6days Answer is C #### C QUESTION:Abhijit started a business investing 2000. Anuja joined him after 8 months with an amount of 6000 and Sunil joined them with 60,000 after another 4 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? options: A)6 : 13 : 90 B)5 : 12 : 90 C)5 : 11 : 80 D)6 : 11 : 90 E)12 : 6 : 90 SOLUTION:Ratio of their investments = 2 × 36 : 6 × 22 : 60 × 18 = 6 : 11 : 90 Answer D #### D QUESTION:A, 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 $900 was the net sum to be paid for the entire work, what was the average daily wage of B? options: A)$144 B)$90 C)$60 D)$54 E)$48 SOLUTION:The correct answer is C. #### C QUESTION:A train running at the speed of 60 km/hr crosses a pole in 15 sec. What is the length of the train? options: A)356 B)250 C)127 D)279 E)150 SOLUTION:Speed = 60 * 5/18 = 50/3 m/sec Length of the train = speed * time = 50/3 * 15 = 250 m Answer: B #### B QUESTION:Boy sells a book for Rs. 450 he gets a loss of 10 %, To gain 10 %, what should be the SP? options: A)Rs.320 B)Rs.450 C)Rs.550 D)Rs.640 E)Rs.680 SOLUTION:Find Selling Price to gain 10 %. Now, we are asked to find selling price to gain 10% profit. Hint: Selling Price = (100 + Gain%) × C.P. 100 Selling Price = (100 + 10) × 500 100 Selling Price = (110) × 500 100 Therefore, selling Price = Rs.550 C #### C QUESTION:A factory has three types of machines, each of which works at its own constant rate. If 7 Machine As and 11 Machine Bs can produce 305 widgets per hour, and if 8 Machine As and 22 Machine Cs can produce 600 widgets per hour, how many widgets could one machine A, one Machine B, and one Machine C produce in one 8-hour day? options: A)400 B)440 C)550 D)625 E)700 SOLUTION:Let Machine A produce A widgets per hour. B produce B widgets per hour and C produce C widgets per hour. 7A+11B=305 ---(1) 8A+22C=600 ---(2) Dividing (2) by 2 4A+11C=300.....(3) Adding (1)(3) 11A+11B+11C = 605 A+B+C=55 per hour So for eight hrs = 55*8 = 440 = Answer = B #### B QUESTION:If k is a non-negative integer and 15^k is a divisor of 823,435 then 5^k - k^5 = options: A)0 B)1 C)35 D)120 E)245 SOLUTION:8+2+3+4+3+5 = 25, so this number is not divisible by 3 and thus not divisible by 15. Therefore, k=0 5^k - k^5 =1-0=1 The answer is B. #### B QUESTION:By how much is two-fifth of 350 greater than four- seventh of 210 ? options: A)95 B)110 C)20 D)None of these E)Cannot be determined SOLUTION:Solution 2/5of 350 - 4/7of 210 = 20. Answer C #### C QUESTION:The average of 11numbers is 50. Out of 11numbers the average of first 6no. is 58, and last 6numbers is 65 then find 6th number? options: A)A)188 B)B)65 C)C)58 D)D)62 E)E)48 SOLUTION:6th number = sum of 1st 6no.s + sum of last 6no.s - sum of 11no.s answer = 6*58+6*65-11*50= 188 Answer is A #### A QUESTION:The 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 options: A)20 B)21 C)22 D)28 E)NONE SOLUTION:Sol. Let the total number of workers be x. Then, 8000x = (14000 × 7) + 6000 ( x – 7) ‹=› 2000x = 56000 ‹=› x = 28. Answer D #### D QUESTION:A two digit number reversed and multiplied by 4 is 3 more than the original digit. what is the digit? options: A)61 B)62 C)63 D)64 E)66 SOLUTION:If no is xy , then 10x+y = 4*(10y+x)-3= 40y +4x-3 6x-39y +3 =0 2x-13y +1 =0 13 y =2x+1 when y=1, x=6 so number is 61. ANSWER:A #### A QUESTION:If n is the square of a positive integer, which of the following must be equal to the square of the next positive integer? . options: A)√n + 1 B)n + 1 C)n^2 + 1 D)n + 2√n + 1 E)n^2 + 2n + 1 SOLUTION:Let a= +ve integer such that n= a^2 (a+1)= next +ve integer (a+1)^2 = a^2 + 1 + 2a and a=n^(1/2) Therefore , (a+1)^2=n+1+2*n^(1/2) Answer D #### D QUESTION:A 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. options: A)310 meter B)335 meter C)345 meter D)350 meter E)375 meter SOLUTION:Explanation: Speed = Distance/time = 300/18 = 50/3 m/sec Let the length of the platform be x meters then Distance=Speed∗Timex+300=50/3 X 39 =>3(x+300)=1950=>x=350 meters ANSWER IS D #### D QUESTION:If 6 (A's capital) = 8 (B's capital) = 16 (C's capital). Then the ratio of their capitals is? options: A)8:15:16 B)8:15:68 C)8:6:3 D)20:15:11 E)20:15:19 SOLUTION:6A = 8B = 16 C A:B:C = 1/6:1/8:1/16 = 8:6:3 Answer: C #### C QUESTION:The cross-section of a cannel is a trapezium in shape. If the cannel is 10 m wide at the top and 6 m wide at the bottom and the area of cross-section is 640 sq m, the depth of cannel is? options: A)22 B)28 C)27 D)80 E)21 SOLUTION:1/2 * d (10 + 6) = 640 d = 80 Answer:D #### D QUESTION:If x and y are positive integers greater than 1 such that x – y and x/y are both even integers, which of the following numbers must be non-prime integers? I. x II. x + y III. y/x options: A)I only B)II only C)III only D)I and II E)I ,II and III SOLUTION:Ans: from the conditions given to us we get x>y and the min value of y can be 2 , therefore x will be a multiple of 4 so both I and ii will always be non-prime but iii will not be an integer. Answer (D). #### D QUESTION:The product of all the prime numbers less than 25 is closest to which of the following powers of 10? options: A)10^9 B)10^8 C)10^7 D)10^8 E)10^5 SOLUTION:Quickly approximate 2, 3, 5, 7, 11, 13, 17, 19,23 =2.2 *10^8 D #### D QUESTION:A 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 2.8% on their total annual charges made on the credit card, then what was the customer's annual charge? options: A)$40,000 B)$45,000 C)$50,000 D)$55,000 E)$60,000 SOLUTION:The customer receives $75 for the first $5000. The customer receives $125 for the next $5000. Let x be the total amount of the customer's annual charge. $200 + 0.03(x-10,000)=0.028x 0.002x=100 x=50,000 The answer is C. #### C QUESTION:Find the highest common factor of 36 and 84. options: A)4 B)6 C)12 D)18 E)19 SOLUTION:36 = 22 x 32 84 = 22 x 3 x 7 H.C.F. = 22 x 3 = 12. Answer: Option C #### C QUESTION:Machine Z takes 2 more hours than machine B to make 20 widgets. If working together, the machines can make 25 widgets in 3 hours, how long will it take machine Z to make 40 widgets? options: A) 5 B) 6 C) 8 D) 10 E) 12 SOLUTION:i approached this one by plugging in numbers...started with C. if 40 are made in 8 hours, then 20 are made in 4 hours. so time of Z is 4, and time of B is 2. rate together: 20/4 + 20/2 = 5+10 = 15. so in 1 hour, together make 15 widgets. in 3 hours = 45. way too much. we can eliminate right away C, B, and A - because B and A reduces the time - the total # of widgets made will be even higher. now between D and E -> try only one ..if it doesn't work, then the other one is the answer. i picked E: 12h to make 40 widgets, and 6 hours to make 20. this is the time of Z. time of B=4 hours. 20/6 + 20/4 = 10/3 + 20/4 find LCM of 3 and 4 = 12. multiply first by 4, and second by 3: 40+60/12 = 100/12 divide by 4: 25/3 so this is the rate given. E is the correct answer #### E QUESTION:Today is Monday.After 61 days,it will be options: A)Wednesday B)Saturday C)Tuesday D)Thursday E)None of these SOLUTION:Solution Each day of the week is repeated after 7 days So,after 63 days,it will be Monday. ∴ After 61 days,it will be Saturday. Answer B #### B QUESTION:An office 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? options: A)5 B)10 C)15 D)20 E)25 SOLUTION:Total Employees: 6 Female: 5 Male: 1 committee of 3 with inclusion of Male Number of ways Female can be selected : 5C2 = 10 For male it should be 6C1 or 6C6 6C1= 6 6C6= 1 ANS= 10 B #### B QUESTION:If the radius of a circle that centers at the origin is 5, how many J points on the circle have integer coordinates? options: A) 4 B) 8 C) 12 D) 15 E) 20 SOLUTION:I understand this might not be required but I used the equation of a circle. Since the origin is at 0, x^2+y^2=5^2. X,Y could be +/- (0,5 or 5,0) - 4 possibilities. X,Y could be +/- (3,4 or 4,3) - 8 possibilities. Ans: J=C #### C QUESTION:Jim and Reneey will play one game of Rock, Paper, Scissors. In this game, each will select and show a hand sign for one of the three items. Rock beats Scissors, Scissors beat Paper, and Paper beats Rock. Assuming that both Jim and Reneey have an equal chance of choosing any one of the hand signs, what is the probability that Jim will win? options: A)5/6 B)2/3 C)1/2 D)5/12 E)1/3 SOLUTION:1/3 probability of jim winning is basically the sum of three probabilities: probability of jim picking rock and reneey picking scissors = 1/3*1/3 = 1/9 probability of jim picking scissors and reneey picking paper = 1/3*1/3=1/9 probability of jim picking paper and reneey picking rock = 1/3*1/3=1/9 1/9 + 1/9 + 1/9 = 3/9 = 1/3=E #### E QUESTION:575.104 x 15.98 ÷ 9.001 + 21.25 = ? options: A)983.578 B)1043.65 C)1033.65 D)656.112 E)456.512 SOLUTION:Explanation: ? = 575.104 x 15.98 ÷ 9.001 + 21.25 ≈ (575.104 x 16/9) + 21.25 ≈ 1022.40 + 21.25 ≈ 1043.65 Answer: Option B #### B QUESTION:A shopkeeper purchased 70 kg of potatoes for Rs. 420 and sold the whole lot at the rate of Rs. 6.50 per kg. What will be his gain percent? options: A)8 1/9 % B)8 7/3 % C)8 1/3 % D)2 1/3 % E)8 3/3 % SOLUTION:C.P. of 1 kg = 420/7 = Rs. 6 S.P. of 1 kg = Rs. 6.50 Gain % = 0.50/6 * 100 = 25/3 = 8 1/3 %.Answer: C #### C QUESTION:A can do a half of certain work in 70 days and B one third of the same in 35 days. They together will do the whole work in. options: A)17 days B)97 days C)19 days D)60 days E)15 days SOLUTION:A = 140 days B = 105 days 1/140 + 1/105 = 7/420 = 1/60 =>60 days Answer: D #### D QUESTION:Based on this year's costs, an orcharde grower budgets P dollars for planing N new trees next year. If the average cost of planting each tree were to increase 50% from this year's cost, then the greatest number of trees that the orchard grower could plant next year using P dollars would be options: A)33% less than N B)25% less than N C)equal to N D)20% greater than N E)25% greater than SOLUTION:Correct answer is (A). This year, the price of a tree is price1=P/N. If this price increases by 50% it becomes price2=P/N*1.50 Then with P dollars, you can grow P/price2 tress i.e. P/(P/N*1.50) i.e. N/1.5 i.e. .67% less* A #### A QUESTION:A sum amounts to Rs.8820 in 2 years at the rate of 5% p.a. If interest was compounded yearly then what was the principal? options: A)s.4000 B)s.5000 C)s.4500 D)s.4800 E)s.8000 SOLUTION:CI=8820,R=5,N=2 CI=P[1+R/100]^2 =P[1+5/100]^2 8820=P[21/20]^2 8820[20/21]^2 8000 ANSWER:E #### E QUESTION:The 40 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? options: A)4 B)6 C)8 D)9 E)10 SOLUTION:The formula is Total = A+B+C - sum of exactly two + 2*all three + neither 21+18+19-x-2*5=40 solving for x you get 8 Answer C #### C QUESTION:Today is Tuesday. 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? options: A)Saturday B)MONDAY C)TUESDAY D)WEDNESDAY E)FRIDAY SOLUTION:Today is Tuesday after three days--->Friday now, (Friday)after before day--->Thursday then, (Thursday)day after tomorrow--->Saturday ANSWER:A #### A QUESTION:Two pipes can fill the cistern in 10hr and 12 hr respectively, while the third empty it in 20hr. If all pipes are opened simultaneously, then the cistern will be filled in options: A)7.5 hr B)8 hr C)8.5 hr D)10 hr E)None of these SOLUTION:Solution: Work done by all the tanks working together in 1 hour. 1/10+1/12−1/20=2/15 Hence, tank will be filled in 15/2=7.5 hour Option(A) #### A QUESTION:How many multiples of 5 are there between 50 and 500 ? options: A)128 B)91 C)89 D)61 E)60 SOLUTION:It should be mentioned whether 50 and 500 are inclusive. If 50 and 500 are inclusive, then the answer is (500-50)/5+1=91. If 50 and 500 are NOT inclusive, then the answer is (495-55)/5+1=89. Since OA is C, then we have NOT inclusive case. #### C QUESTION:How many days will there be from 26th January,1996 to 15th May,1996(both days included)? options: A)102 B)103 C)111 D)120 E)None of these SOLUTION:Explanation : Number of days from 26-Jan-1996 to 15-May-1996 (both days included) = 6(Jan) + 29(Feb) + 31 (Mar) + 30(Apr)+ 15(May) = 111.. Answer : Option C #### C QUESTION:In a certain aquarium, the number of red fish is three times the number of the green fish, and the number of blue fish is half the number of the red fish. If the ratio of green fish to red fish were to be doubled, and the ratio of red fish to blue fish were to be doubled, then the ratio of blue fish to green fish in that aquarium would be options: A)3:2 B)1:1 C)1:2 D)3:4 E)3:8 SOLUTION:Lots of little places to make a mistake or panic here. =) R = 3G B = R/2 G/R = 1/3 ----> Doubled G/R = 2/3 R/B = 2 ----> Doubled R/B = 4 B/G = (B/R)*(R/G) = (1/4)*(3/2) = 3/8 ANSWER:E #### E QUESTION:Before January, the price of a dress was D and the price of a matching pair of shoes was H. In January, the price of the dress increased by 40% and the price of the shoes increased by 50%. In March, Roberta bought both items with a 30% discount. If D = 6H, which of the following represents the amount that Roberta paid? options: A)D + 40 B)D + H – 1 C)D + 2H D)6.93H E)1.21D SOLUTION:before Discount price was: 1.4D+1.5H After Discount: 1.4D +1.5H-.42D-.45H substitute D=6H final value: 6.93H Ans Is D #### D QUESTION:The average marks of a class of 20 students is 40 and that of another class of 50 students is 60. Find the average marks of all the students? options: A)44.28 B)54.28 C)34.28 D)64.28 E)74.28 SOLUTION:Sum of the marks for the class of 20 students = 20 * 40 = 800 Sum of the marks for the class of 50 students = 50 * 60 = 3000 Sum of the marks for the class of 70 students = 800 + 3000 = 3800 Average marks of all the students = 3800/70 = 54.28 ANSWER:B #### B QUESTION:A train passes a station platform in 50 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? options: A)180 m B)200 m C)240 m D)320 m E)450 m SOLUTION:Sol. Speed = [54 * 5/18] m/sec = 15 m/sec. Length of the train = (15 * 20) m = 300 m. Let the length of the platform be x metres. Then, x + 300 / 50 = 15 ⇔ x + 300 = 750 ⇔ x = 450 m. Answer E #### E QUESTION:if log 7 = 0.845098, the number of digits in 7128 is options: A)100 B)120 C)109 D)280 E)110 SOLUTION:Explanation: log(7128) = 128log(7) = 128 × 0.845098 ≈ 108.17 ie, its characteristic = 108 Hence, number of digits in 2128 = 108+1 = 109 Answer: Option D #### D QUESTION:The cost price of 7 articles is equal to the selling price of 5 articles. What is the profit percent? options: A)10% B)20% C)30% D)40% E)50% SOLUTION:5*SP = 7*CP SP = 1.4*CP The profit percent is 40%. The answer is D. #### D QUESTION:If the simple interest on a sum of money for 2 years at 5% per annum is Rs. 52, what is the compound interest on the same sum at the rate and for the same time? options: A)s. 53.30 B)s. 53.22 C)s. 51.219 D)s. 53.18 E)s. 51.10 SOLUTION:Explanation: Sum = (52 * 100) / (2 * 5) = Rs. 520 Amount = [520 * (1 + 5/100)2] = Rs. 573.3 C.I. = (573.3 - 520) = Rs. 53.30. Answer:A #### A QUESTION:If four coins are tossed, the probability of getting two heads and two tails is ? options: A)3/8 B)3/6 C)3/1 D)3/2 E)3/4 SOLUTION:Since four coins are tossed, sample space = 24 Getting two heads and two tails can happen in six ways. n(E) = six ways p(E) = 6/24 = 3/8 Answer: A #### A QUESTION:For a certain art exhibit, a museum sold admission tickets to a group of 30 people every 5 minutes from 9:00 in the morning to 4:55 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 3 times as many regular admission tickets were sold as student tickets, what was the total revenue from ticket sales that day? options: A)$24960 B)$25920 C)$28080 D)$28500 E)$29160 SOLUTION:From 9:00 in the morning to 4:55 in the afternoon, inclusive there are 8*12=96 five-minute intervals, thus total of 96*30 tickets were sold. Say x student and 3x regular tickets were sold, then x+3x=96*30 --> x=24*30 and 3x=3*(24*30)=24*90. Therefore, the total revenue from ticket sales that day was 24*30*6+24*90*10=$25,920. Answer: B. #### B QUESTION:In 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? options: A)12 B)3 C)5 D)8 E)10 SOLUTION:Let the number of buffaloes be x and the number of ducks be y. Then 4x+2y=2(x+y)+24 =>x=12 ANSWER A 12 #### A QUESTION:George can do 3/5 of work in 9days.He then calls in pauls and they completed the work in 4days.How long paul would take long to complete the work? options: A)32 B)28 C)35 D)30 E)22 SOLUTION:George work is (5/3)*9 =15; 1 day work of george is 1/15 ; remaining is 2/5th; paul & george work is 5/2*4=10 ; their 1 day work is 1/10; and only paul work is (1/10)-(1/15)=30 ANSWER:D #### D QUESTION:Let X be the smallest positive integer such that 10 and 14 are factors of 250 + X, so the value of X is: options: A)0 B)10 C)20 D)30 E)40 SOLUTION:You can calculate the LCM (10,14) = 70. After that you should check which of the possible X values will result in a number divisible by 70. The only possibility for this is 30 ( because 250 + 30 = 280 = 70*4) Answer D #### D QUESTION:What percent is 400 gm of 1 kg? options: A)25% B)40% C)10% D)8% E)12% SOLUTION:1 kg = 1000 gm 400/1000 × 100 = 40000/1000 =40 % Answer is B #### B QUESTION:How many integers between 2000 and 3000 that have distinct digits and increase from left to right ? options: A)10 B)20 C)60 D)120 E)600 SOLUTION:Since the numbers must be distinct and increasing from left to right, The only arrangements we could come-up with are: 245_ --> 4 246_ --> 3 247_ --> 2 248_ --> 1 256_ --> 3 257_ --> 2 258_ --> 1 267_ --> 2 268_ --> 1 Number of integers =20 B #### B <<<Examples ends QUESTION:A goods train runs at the speed of 72 kmph and crosses a 250m long platform in 26seconds. what is the length of the goods train? options: A)230 m B)240 m C)260 m D)270 m E)250 m SOLUTION:Speed =(72 *5/18)m/sec= 20 m/sec. then (x+250)/26=20 x+250 =520 x=520-250 then x=270 Answer: D #### D

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:If x is divisible by 2, 14, and 11, which of the following must be the least multiple of x? options: A)308 B)154 C)70 D)44 E)0 SOLUTION:We are looking for the LCM (which is not 0) of 2, 11, 14: 2 * 11 * 7 = 154 ANSWER:B #### B QUESTION:In a class, there are 20 boys whose average age is decreased by 2 months, when one boy aged 17 years replaced by a new boy. The age of the new boy is? options: A)14 years 8 months B)15 years C)13 years 8 months D)17 years 10 months E)17 years SOLUTION:Total decrease = (20 x 2) months = 3 years 4 months Age of the new boy = 17 years - 3 years 4 months. = 13 years 8 months. ANSWER:C #### C QUESTION:Two numbers are in the ratio of 1 : 2. If 8 be added to both, their ratio changes to 3 : 5. The greater number is options: A)20 B)24 C)28 D)32 E)36 SOLUTION:Let the ratio be X : Y, Given X/Y = 1/2 , (X + 8)/(Y + 8) = 3/5 => X = 16 And Y = 32 ANSWER:D #### D QUESTION:A 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 : options: A)Rs.80 B)Rs.115.20 C)Rs.120 D)Rs.125.40 E)None of these SOLUTION:Explanation: For an income of Rs. 10, investment = Rs. 96. For an income of Rs. 12, investment = (96/10x12) =115.20 Answer: B #### B QUESTION:Find the smallest number which when divided by 13 and 16 leaves respective remainders of 2 and 5. options: A)128 B)197 C)127 D)182 E)091 SOLUTION:Explanation: Let 'N' is the smallest number which divided by 13 and 16 leaves respective remainders of 2 and 5. Required number = (LCM of 13 and 16) - (common difference of divisors and remainders) = (208) - (11) = 197. Answer:B #### B QUESTION:A sum of Rs.1420 is divided into 13 students so that each boy gets Rs.120 while each girl gets Rs.100. Find the number of boys and number of girls options: A)8B, 5G B)5B, 8G C)4B, 9G D)9B, 4G E)6B, 7G SOLUTION:120B+100G=1420-----i B+G=13-------ii from i 100B+20B+100G=1420 100(B+G)+20B=1420 100(13)+20B=1420 By simplifing we get B=6;G=7 ANSWER:E #### E QUESTION:The triplicate ratio of 1:3 is? options: A)1:0 B)1:8 C)1:27 D)1:2 E)1:1 SOLUTION:13: 33 = 1:27 Answer: C #### C QUESTION:A certain club has 10 members, including Tarry. 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 Tarry will be either the member chose to be secretary or the member chose to be treasurer? options: A)1/720 B)1/80 C)1/10 D)1/9 E)1/5 SOLUTION:In 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 Probability to become a secretary = (9/10 * 1/9) = 1/10 Similar concept for treasurer. Probability of not president = 9/10, Probability of not secretary = 8/9, probability of treasurer 1/8 probability to become a treasurer = (9/10 * 8/9 * 1/8) = 1/10 Since, the problem is saying Tarry secretary OR Treasurer it is addition: 1/10 + 1/10 = 1/5=E #### E QUESTION:If a certain manager had received a 5% raise instead of the 8% raise that she actually received, her salary would have been $60,500. What was her actual salary after the raise? options: A)55,000 B)58,806 C)59,290 D)62228.52 E)61,620 SOLUTION:No need of getting involved with decimals ..just work in fractions .. salary(let X) included 5% increase can be written as (1+5/100)X=60500 X=60500/1.05------>57619.05 if there is 8% rise in 57619.05 then the salary now is 8% of 57619.05 8*57619.05/100=4609.52 then toal salary after increment=57619.05+4609.52----->62228.52 Ans D #### D QUESTION:what is the sum of all 5 digits numbers which can be formed with the digits 0,1,2,3,4 without repetition options: A)2599980 B)2699980 C)2799980 D)2509980 E)2499980 SOLUTION:There is a simplest formula for solving these type of questions when we are using numbers along with 0 for finding sum. i,e........(sum of numbers)*{(n-1)!*(111...........n times)-(n-2)!*(111..........(n-1)times) } so,here by putting the values as, (0+1+2+3+4){(5-1)!*(11111)-(5-2)!*1111} = 10{(4!*11111)-(3!*1111)} = 10{266664-6666} = 2599980 ANSWER:A #### A QUESTION:A 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? options: A)230 B)288 C)267 D)256 E)298 SOLUTION:Relative speed = 120 + 80 = 200 km/hr. = 200 * 5/18 = 500/9 m/sec. Let the length of the other train be x m. Then, (x + 270)/9 = 500/9 => x = 230. Answer: A #### A QUESTION:2 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? options: A)1/5 B)1/3 C)2/7 D)3/5 E)3/11 SOLUTION:1/10 + 1/15 = 1/6 * 4 = 2/3 1 - 2/3 = 1/3 1/10 + 1/15 - 1/x = 1/3 x = 8 B #### B QUESTION:A bag contains 6 green jacks and 24 white jacks. One jack is drawn at random. What is the probability that the jack is white? options: A)3/4 B)4/5 C)7/8 D)1 E)None of these SOLUTION:Explanation: Total cases = 6 + 24 = 30 Favourable cases = 24 So probability = 24/30 = 4/5 Answer: A #### A QUESTION:Anitha had 80 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. 4000. How much amount (in Rs) did she have in the denomination of Rs 45? options: A)3500 B)72 C)2000 D)3000 E)4000 SOLUTION:Let the number of 45-rupee notes = x Then, the number of 95-rupee notes = (80 – x) 45x + 95(80 – x) = 4000 or x + 2(80 – x) = 95 or x = 72. ANSWER:B #### B QUESTION:The average of first six multiples of 3 is options: A)10.5 B)6 C)9 D)12 E)15 SOLUTION:Solution Average = 3(1+2+3+4+5+6) / 6 = 63 / 6. = 10.5. Answer A #### A QUESTION:The MegaTek Corporation is displaying its distribution of employees by department in a circle graph. The size of each sector of the graph representing a department is proportional to the percentage of total employees in that department. If the section of the circle graph representing the manufacturing department takes up 252° of the circle, what percentage of MegaTek employees are in manufacturing? options: A)20% B)25% C)30% D)35% E)70% SOLUTION:ANSWER: E 252° divided by 360° equals 0.7, therefore the sector is equal to 70% of the total #### E QUESTION:A, 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? options: A)3999 B)7799 C)2500 D)2772 E)2912 SOLUTION:A:B:C = 2/3:1/6:1/6 = 4:1:1 x * 2/100 * 2/3 = 200 B capital = 15000*1/6 = 2500.Answer: C #### C QUESTION:If 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%? options: A)6 B)8 C)6 D)5 E)4 SOLUTION:96% ---- 12 144% ---- ? 96/144 * 12 = 8 Answer:B #### B QUESTION:In a recent election, James received 5 percent of the 2,000 votes cast. To win the election, a candidate needed to receive more than 50 percent of the vote. How many additional votes would James have needed to win the election? options: A)901 B)989 C)990 D)991 E)1,001 SOLUTION:James = (5/100)*2000 = 100 Votes to win = (50/100)*Total Votes +1 = (50/100)*2000 +1 = 1001 Remaining Voted needed to win election = 1001 - 100 = 901 Answer: option A #### A QUESTION:What is the greatest positive integer x such that 7^x is a factor of 343^10? options: A)5 B)9 C)10 D)20 E)30 SOLUTION:343^10 = (7^3)^10 = 7^30 ANSWER:E #### E QUESTION:If 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? options: A)3:2 B)2:1 C)3:3 D)1:2 E)6:1 SOLUTION:8M + 2B = 4(1M + 1B) 8M + 2B = 4M + 4B 4M = 2B The required ratio of work done by a man and a boy = 2:4=1:2 D #### D QUESTION:Howmany three digits odd numbers can be formed using the digits 4,5,6,7,8,9 (repetition of digits not allowed) options: A)60 B)75 C)65 D)55 E)45 SOLUTION:There are 3 ways of filling the unit place of the number. The remaining ten's and 100's place canbe filled in 5ways and 4 ways respectively. Required number of numbers =3x5x4=60. Ans: A #### A QUESTION:Find the one which does not belong to that group ? options: A)3 B)4 C)5 D)9 E)7 SOLUTION:Explanation: 3, 5, 9 and 7 are odd numbers, but not 4. ANSWER IS B #### B QUESTION:A ball is bought for Rs.400 and sold at a gain of 20% find its selling price? options: A)Rs.480/- B)Rs.490/- C)Rs.500/- D)Rs.520/- E)Rs.540/- SOLUTION:100 % ------> 400 (100 * 4 = 400) 120 % ------> 480 (120 * 4 = 480) Selling price = Rs.480/- A #### A QUESTION:Set W includes elements {8, 2, 11, x, 3, y} and has a mean of 7 and a median of 5.5. If x < y, then which of the following is the maximum possible value of x? options: A)0 B)1 C)2 D)3 E)4 SOLUTION:First, reach to the point of getting the equation W: x + y = 18 It should take about 20 seconds. Then Substitute the answer choices into the equation. I don't know what the answer choices in this case are. But I'm sure, you would be able to eliminate at least 2 or 3 answer choices. (about 10 seconds). Say you are left with 2 answer choices. (If you are short on time, guess One of the two and you'll have a 50% probability of getting it right.) The Median (of 6 numbers) = 5.5. See if the AVERAGE of any two numbers among (2,3,8,11) results in the median. In this case, it does for 3 and 8. (15 seconds). Once you know that the numbers that contribute towards Median are 3 and 8, and not x or y, then given x < y, x≤3. (about 10 seconds)=D #### D QUESTION:curie bakes 5 cookies for 5 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? options: A)1 B)2 C)3 D)4 E)5 SOLUTION:curie made 5*5 cookies = 25 cookies. 2 friends eat 3 cookies, leaving 9 remaining for 2 friends. 9 is not divisible by 2. The 2 friends ate a cumulative number of cookies less than 9 that must be divisible by 2, because the number is the same. The nearest multiple of 2 is 8. 9-8=1 A is the correct answer #### A QUESTION:A train is moving at a speed of 50km/hr and its length is 500m. Find the time taken by it to pass a man standing near the railway line? options: A)30sec B)45sec C)36sec D)29sec E)52sec SOLUTION:Speed of the train = 50*5/18 = 250/18 m/sec Distance moved in passing the standing man = 500m Required time taken = 500/(250/18) = 500*18/250 = 36sec Answer is C #### C QUESTION:In what time will a railway train 75 m long moving at the rate of 50 kmph pass a telegraph post on its way? options: A)3 B)5.4 C)4.3 D)6.5 E)7 SOLUTION:T = 75/50 * 18/5 = 5.4 sec Answer:B #### B QUESTION:A 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? options: A)12 min B)17 min C)19 min D)11 min E)16 min SOLUTION:Since 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. Relative speed of A and B = 6 - 1 = 5 rounds per hour. Time taken to complete one round at this speed = 1/5 hr = 12 min. Answer: A #### A QUESTION:For each month of a given year except December, a worker earned the same monthly salary and donated one-tenth of that salary to charity. In December, the worker earned N times his usual monthly salary and donated one-third of his earnings to charity. If the worker's charitable contributions totaled one-eighth of his earnings for the entire year, what is the value of N? options: A)8/5 B)5/2 C)3 D)33/25 E)4 SOLUTION:Let monthly salary for each of the 11 months except December was x, then 11x*1/10 + Nx*1/3 = 1/8(11x + Nx); 11/10 + N/3 = 1/8(11 + N) 33+10N/30= 11+N/8 =>264+80N= 330+30N=>50N=66 N = 66/50=33/25 Answer: D. #### D QUESTION:A sports equipment store sold ping pong rackets for a total of $490. If the average (arithmetic mean) price of a pair of rackets is $9.8, how many pairs were sold? options: A)50 B)100 C)490 D)500 E)980 SOLUTION:Average price for a pair of rackets = $9.8 Total cost = $9.8*x = $490 x = 50 pairs were sold. ANSWER:A #### A QUESTION:A Fruit store sells four varieties of Mangoes. A,B,C & D. IF A Costs 15% less than B, and C costs 20% less than A,and D costs 25% less than C what percent of B's cost is D? options: A)40% B)38% C)44% D)46% E)51% SOLUTION:Soln:- B=100 A 15% less than B = 85 C 20% less than A = 68 D 25% less than C = 51 D is what percent of B = D/B * 100 = 51/100 * 100 = 51% ANSWER:E #### E QUESTION:Find the cost of fencing around a circular field of diameter 32 m at the rate of Rs.2 a meter? options: A)201 B)132 C)772 D)592 E)261 SOLUTION:2 * 22/7 * 16 = 100.5 100.5 * 2 = Rs.201 Answer: A #### A QUESTION:The ratio of boarders to day students at a school was originally 2 to 5. However, after a number of new boarders join the initial 120 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? options: A)30 B)50 C)70 D)80 E)90 SOLUTION:Let x be the number of new boarders. The ratio changed from 2:5 = 4:10 up to 1:2 = 5:10. 120 / (120+x) = 4/5 x = 30 The answer is A. #### A QUESTION:Marla starts running around a circular track at the same time Nick starts walking around the same circular track. Marla completes 20 laps around the track per hour and Nick completes 10 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? options: A)5 B)8 C)24 D)15 E)20 SOLUTION:Maria's rate - 20 laps per hour --> 20/60 laps/min Nick's rate - 10 laps per hour --> 10/60 laps/min lets set equations: 20/60*t=4 (since Maria had to run 4 laps before Nick would start) 10/60*t=0 (Hick has just started and hasn't run any lap yet) (20/60-10/60)*t=4-0 (since Nick was chasing Maria) t=24 min needed Maria to run 4 laps Answer : C #### C QUESTION:The center of a circle is (5, -2). (5, 7) is outside the circle, and (2, -2) is inside the circle. If the radius, r, is an integer, how many possible values are there for r? options: A) 4 B) 2 C) 2 D) 10 E) 12 SOLUTION:r must be greater than 3 and smaller than 9, hence r=4,5,6,7 or 8. Answer A #### A QUESTION:Two roads XY and YZ of 15 metres and 20 metres length respectively are perpendicular to each other. What is the distance between X & Z by the shortest route? options: A)35 metres B)30 metres C)24 metres D)25 metres E)None of these SOLUTION:XYZ is a right-angled triangle XZ =√15(2)+20(2)=√=625=25m Answer D #### D QUESTION:A rectangular mat has an area of 120 sq.metres and perimeter of 46 m. The length of its diagonal is: options: A)19m B)17m C)15m D)16m E)20m SOLUTION:rectangular area = l × b = 120 and perimeter = 2(l+b) = 46 l+b = 23 (l-b)power2 - 4lb = (23)power2 - 4 × 120 = (529-480) = 49 = l-b = 7 l+b = 23, l-b = 7, we get l = 15, b = 8 Diagonal = √152+82 √225+64 => √289 = 17m Answer is B. #### B QUESTION:The population of a city increases by 6% per year but due to migration it decrease by 1% per years. What will be the percentage increase in population in 3 years? options: A)9% B)9.27% C)27% D)15.76% E)None of these SOLUTION:Actual increase in population=5% Let, earlier population=100 then the population after 3 years =100(1+5/100)^3=115.7625 ∴Required percentage=15.7625% ANSWER:D #### D QUESTION:A 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? options: A)-3 B)-2 C)1 D)2 E)3 SOLUTION:Q=-3*a^2=3(3a+2) a= -2 or -1 a=-2=B #### B QUESTION:A man invested Rs. 1552 in a stock at 97 to obtain an income of Rs. 128. The dividend from the stock is: options: A)8% B)6% C)9% D)10% E)11% SOLUTION:Rs 1552 income = Rs 128 By investing Rs 97 income = 128/1552*97 = Rs 8 Divdend = 8% ANSWER A #### A QUESTION:A and B start from Opladen and Cologne respectively at the same time and travel towards each other at constant speeds along the same route. After meeting at a point between Opladen and Cologne, A and B proceed to their destinations of Cologne and Opladen respectively. A reaches Cologne 40 minutes after the two meet and B reaches Opladen 60 minutes after their meeting. How long did A take to cover the distance between Opladen and Cologne? options: A)1 hour B)1 hour 20 minutes C)2 hours 30 minutes D)1 hour 40 minutes E)2 hours 10 minutes SOLUTION:v1 and V2 are speeds. v1.t /60 = v2 v2.t/40 = v1 v1/v2 = 3/2 which train A would 60. 2/3 mins to cover the same distance 40 + 40 = 80 mins (ANS B) #### B QUESTION:P and Q can do a work in 30 days. Q and R can do the same work in 24 days and R and P in 20 days. They started the work together, but Q and R left after 12 days. How many days more will P take to finish the work? options: A)12 B)15 C)18 D)20 E)22 SOLUTION:Let work done by P in 1 day = p, Work done by Q in 1 day = q, Work done by R in 1 day = r p + q = 1/30 q + r = 1/24 r + p = 1/20 Adding all the above, 2p + 2q + 2r = 1/30 + 1/24+ 1/20 = 15/120 = 1/8 => p + q + r = 1/16 => Work done by P,Q and R in 1 day = 1/16 Work done by P, Q and R in 12 days = 12 × (1/16) = 12/16 = 3/4 Remaining work = 1 = 3/4 = 1/4 Work done by P in 1 day = Work done by P,Q and R in 1 day - Work done by Q and R in 1 day = 1/16 – 1/24 = 1/48 Number of days P needs to work to complete the remaining work = (1/4) / (1/48) = 12 Option A #### A QUESTION:The mean of 50 observations was 41. It was found later that an observation 48 was wrongly taken as 23. The corrected new mean is options: A)35.2 B)36.1 C)36.5 D)41.5 E)None SOLUTION:Sol. Therefore correct sum = ( 41 × 50 + 48 – 23) = 2075. Therefore correct mean = 2075 / 50 = 41.5. Answer D #### D QUESTION:Two 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 42 minutes. The waste pipe can empty the full cistern in? options: A)8 min B)7 min C)5 min D)9 min E)4 min SOLUTION:1/10 + 1/15 - 1/x = 1/42 x = 7 Answer: B #### B QUESTION:Excluding stoppages, the speed of a bus is 64 kmph and including stoppages, it is 50 kmph. For how many minutes does the bus stop per hour? options: A)15.5 B)12.3 C)10.5 D)10.12 E)13.12 SOLUTION:Due to stoppages, it covers 14 km less. Time taken to cover 14 km = ((14/64)×60) = 13.12 min. Option(E) is correct #### E QUESTION:There 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? options: A)980 B)1150 C)1360 D)1540 E)1720 SOLUTION:The number of ways to choose two teams is 17C2 = 17*16/2 = 136 The total number of games in the season is 10*136 = 1360. The answer is C. #### C QUESTION:The function f is defined for all positive integers n by the following rule: f(n) is the product of the distinct prime factors of n. If f(n) < 75 and n is not prime, what is the greatest possible value of f(n)? options: A)72 B)69 C)65 D)60 E)58 SOLUTION:Since we need the largest value of f (n), we will start with the largest option. Option A: 2*2*2*2*2*2 = . This is not a product of distinct prime numbers. Hence incorrect Option B: 69 = 3*23. This is a product of distinct prime numbers. Rest all the options are smaller that 69. Correct Option: B #### B QUESTION:A train is running with a speed of 60 kmph and its length is 110 metres. Calculate the time by which it will pass a man running opposite with speed of 6 kmph options: A)2 second B)4 second C)6 second D)8 second E)10 second SOLUTION:Explanation: From the given question, we will first calculate the speed of train relative to man, => ( 60 + 6 ) = 66 km/hr ( we added 6 because man is running opposite ) Convert it in metre/second =66×5/18 =55/3m/sec Time it will take to pass man =110×3/55 =6 seconds ANSWER IS C #### C QUESTION:What was the principal , if at 5% per annum the interest after 10 years amounted to Rs.3100 less than the sum lent? options: A)6200 B)3000 C)3000 D)2000 E)1000 SOLUTION:P - 2336 = (P*10*5)/100 P = 6200 Answer: A #### A QUESTION:If the average marks of three batches of 56, 60 and 45 students respectively is 50, 55, 60, then the average marks of all the students is options: A)54.48 B)54.68 C)54.65 D)54.58 E)None of these SOLUTION:Explanation: (56×50)+(60×55)+(45×60)/(56+60+46)=54.65 Answer: Option C #### C QUESTION:An 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? options: A)23777 B)35000 C)29977 D)26777 E)19871 SOLUTION:Let the sum invested at 9% be Rs. x and that invested at 11% be Rs. (100000 - x). Then, (x * 9 * 1)/100 + [(100000 - x) * 11 * 1]/100 = (100000 * 29/3 * 1/100) (9x + 1100000 - 11x)/100 = 29000/3 = 9700 (9x + 1100000 - 11x) = 970000 x = 65000 Sum invested at 9% = Rs. 65000 Sum invested at 11% = Rs. (100000 - 65000) = Rs. 35000. Answer: B #### B QUESTION:John has taken four (4) tests that have an average of 81. In order to bring his course grade up to a ‘B’, he will need to have a final average of 87. What will he need to average on his final two tests to achieve this grade? options: A)87 B)90 C)92 D)94 E)99 SOLUTION:87-81=6*4=24 points 2*87=174 174+24=198 points to be scored in the 2 tests. Avg of 2 tests = 198/2=99 Answer: E Traditional Method: Total scored till now 81*4=324 Total score to avg 87 in 6 tests = 87*6=522 Total to be scored on 2 tests = 522-324=198 Avg on 2 tests = 198/2 = 99 Answer E #### E QUESTION:J is faster than P. J and P each walk 24 km. Sum of the speeds of J and P is 7 kmph. Sum of time taken by them is 14 hours. Then J speed is equal to options: A)22 B)14 C)6 D)8 E)16 SOLUTION:Given J > P J + P = 7, only options are (6, 1), (5, 2), (4, 3) From the given options, If J = 4 the P = 3. Times taken by them = 244+243=14 Answer:B #### B QUESTION:Find out Difference between SI and CI if p=1000000 r=4% ant t=3 yr? options: A)4864 B)4854 C)4844 D)4868 E)4866 SOLUTION:p=1000000, r=4% annual , t=3 yr SI = p*r*t/100 = 1000000*4*3/100 = 120000 CI = p[(1+ r/100)^t -1] = 1000000[(1+ 4/100)^3 -1] = 124864 difference = CI - SI = 124864 - 120000 = 4864 ANSWER:A #### A QUESTION:Each student at a certain university is given a four-character identification code, the rest two characters of which are digits between 0 and 9, inclusive, and the last two characters of which are selected from the 26 letters of the alphabet. If characters may be repeated and the same characters used in a different order constitute a different code, how many different identification codes can be generated following these rules? options: A)135,200 B)67,600 C)64,000 D)60,840 E)58,500 SOLUTION:First two parts for the code, are digits between 0-9, therefore, 10 options for the first part of the code, and as characters may be repeated, 10 options for the second part as well Therefore, we have 10 X 10 possibilities for the first and second part of the code Last two parts of the code, are characters selected from the 26 letters of the alphabet, therefore, 26 options for the third part of the code, and as characters may be repeated, 26 options for the fourth part as well Therefore, we have 26 X 26 possibilities for the third and fourth part of the code so, in all total no. of different identification codes generated following these rules = 10 X 10 X 26 X 26 = 67600 Answer B #### B QUESTION:P = {105, 106, 107, 108, 109, x} Set P above consists of 6 integers. For what value of x are the mode, the median and the average equal? options: A)105 B)106 C)107 D)108 E)109 SOLUTION:Mode of a set is the number with max frequency. Median for an even numbered set is the average of middle terms. Average or mean is the sum of the set/No. of elements in the set. Going from the answer choices, if we use 107 as the missing number. The set becomes {105, 106, 107, 107, 108, 109} Now the mode, median and mean are all same, 107 ANS (Option C) #### C QUESTION:If 10^(z-1)< 0.000125 <10^z, what is the value of an integer z? options: A)-4 B)-3 C)-2 D)3 E)4 SOLUTION:-> Multiply 10^6- > (10^6){10^(z-1)}<125<(10^6)(10^z) -> 125 is bigger than 100 -> (10^6)(10^(z-1))=100 -> 10^(6+z-1)=10^2, z+5=2 -> z=-3 Thus, the answer is B #### B QUESTION:7^1+7^2+7^3+...........+7^2015 find out how many numbers present which unit place contain 3 ? options: A)502 B)503 C)504 D)505 E)506 SOLUTION:7^3,7^7,7^11,7^15,7^19.........7^2015 contains last digit=3. Now,we see 3,7,11,15....2015 are in AP tn=a+(n-1)d 2015=3+(n-1)4 2015=3+4n-4 4n=2016 n=504 ANSWER:C #### C QUESTION:The 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. 9540, what is the length of the plot in metres? options: A)20 B)200 C)300 D)400 E)100 SOLUTION:Let length of plot = L meters, then breadth = L - 20 meters and perimeter = 2[L + L - 20] = [4L - 40] meters [4L - 40] * 26.50 = 9540 [4L - 40] = 9540 / 26.50 = 360 4L = 400 L = 400/4= 100 meters. Answer: E #### E QUESTION:A is half good a work man as B and together they finish a job in 32 days. In how many days working alone B finish the job? options: A)98 days B)21 days C)48 days D)18 days E)19 days SOLUTION:WC = 1:2 2x + x = 1/32 => x = 1/96 2x = 1/96 => 48 days Answer:C #### C QUESTION:If c = 9/25, w = 15/32, and m + w + c = 1, which of the following gives the values of m, w, and c in increasing order? options: A)c, m, w B)c, w, m C)m, w, c D)m, c, w E)w, m, c SOLUTION:Answer D - m, c, w c ~ 1/3 w ~ 1/2 and m+w+c = 1 hence m ~ 1/6 Hence increasing order would be m -> c -> w Aswer D #### D QUESTION:A 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. 6900? options: A)s. 4991 B)s. 5991 C)s. 6001 D)s. 6991 E)s. 7391 SOLUTION:total fr 5 mnths=(6435+6927+6855+7230+6562)=Rs34009. Reqd.sale=Rs.[(6900*6)-34009] = Rs.(41400-34009) = Rs.7391. ANSWER:E #### E QUESTION:The average of runs of a cricket player of 10 innings was 40. How many runs must he make in his next innings so as to increase his average of runs by 4? options: A)87 B)16 C)10 D)84 E)17 SOLUTION:Average after 11 innings = 44 Required number of runs = (44* 11) - (40* 10) = 484- 400 = 84. Answer: D #### D <<<Examples ends QUESTION:In a maths test, students were asked to find 5/16 of a certain number. One of the students by mistake found 5/6th of that number and his answer was 200 more than the correct answer. Find the number. options: A)384 B)76 C)26 D)28 E)11 SOLUTION:Explanation: Let the number be x. 5*x/6 = 5*x/16 + 200 25*x/48 = 200 x = 384 ANSWER: A #### A

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:In what time will a train 200 m long cross an electric pole, it its speed be 144 km/hr? options: A)2.5 sec B)2.9 sec C)3.5 sec D)7.5 sec E)5 sec SOLUTION:Speed = 144 * 5/18 = 40 m/sec Time taken = 200/40 = 5 sec. Answer: E #### E QUESTION:If a and b are prime numbers, which of the following CANNOT be (x + y)? options: A)5 B)9 C)13 D)16 E)23 SOLUTION:All answer choices but E are odd. In order odd number to be the sum of two prime numbers one must be even, so 2, and another odd. Now, 23=2+21. Since 21 is not a prime then 23 cannot be written as the sum of two prime numbers. Answer: E. #### E QUESTION:A money lender lent a total of $1600 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 $1600, how much did he lend to each of the two customers? options: A)700; 1100 B)1072; 528 C)1000; 800 D)1200; 800 E)None of the above SOLUTION:The method given above is the one given in the book. However the method I used was (1*x*5)/100 + (1600-x)*6/100 = 1600*5.67/100 Simplifying we get x= 528 B #### B QUESTION:A crew can row a certain course up the stream in 84 minutes; they can row the same course down stream in 7 minutes less than they can row it in still water. How long would they take to row down with the stream options: A)45 or 23 minutes B)73 or 12 minutes C)77 minutes D)19 minutes E)25 minutes SOLUTION:A method has been discussed here to nullify the calculations though. All I can input here is, speed of a crew in still water = 1/2 ( speed upstream + speed downstream) approximating this for time, t = 1/2(84+ (t-7)) giving t = 77 C #### C QUESTION:Two numbers are in the ratio of 7:6. If 18 be subtracted from each, they are in the ratio of 6:5. Find the numbers? options: A)5,9 B)7,9 C)4,7 D)7,6 E)6,9 SOLUTION:(7x-18):(6x-18) = 6:5 x = 1 => 7,6 Answer: D #### D QUESTION:The difference between a number and its three-fifths is 50.What is the number? options: A)75 B)100 C)125 D)Cannot be determined E)None of these SOLUTION:Suppose the number is N. Then N - 3⁄5N = 50 ⇒ 2N⁄5 = 50 ∴ N=50×52=125 Answer.C #### C QUESTION:A sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 878 in 4 years. The sum is: options: A)500 B)698 C)626 D)910 E)None SOLUTION:Sol. S.I. for 1 year = Rs. (878 - 815) = Rs. 63. S.I. for 3 years = Rs. (63 * 3) = Rs. 189. ∴ Principal = Rs. (815 - 189) = Rs. 626 Answer C #### C QUESTION:If 4x + y = 8 and −2x + y = 13, then what is the value of 2x + 2y? options: A)1/7 B)3 C)15 D)21 E)60/7 SOLUTION:4x + y = 8 −2x + y = 13 Adding both the equations --> 2x + 2y = 21 Answer: D #### D QUESTION:If w<0, which of the following must be true? options: A)–100 < w < 100 B)w ≤ –1 C)w ≤ 1 D)w^2 ≥ 1/4 E)–100 < w < 0 SOLUTION:w is a negative number. A. –100 < w < 100w can be a negative number less than -100 B. w ≤ –1w can be a fraction, in which case it would be greater than -1 C. w ≤ 1must be true since 1 is positive and w is negative D. w^2 ≥ 1/4not true if w is a negative fraction like -1/5 E. –100 < w < 0w can be a negative number less than -100=C #### C QUESTION:The average weight of 29 students is 28 kg. By the admission of a new student, the average weight is reduced to 27.4 kg. The weight of the new student is options: A)22 kg B)21.6 kg C)22.4 kg D)10 kg E)None of these SOLUTION:Exp . The total weight of 29 students = 29* 28 The total weight of 30 students = 30* 27.4 Weight of the new student = ( 30*27.4 – 29*28) = 822 - 812 = 10 Answer:D #### D QUESTION:A swimming pool 9 m wide and 12 m long is 1 m deep on the shallow side and 4 m deep on the deeper side. Its volume is: options: A)260 B)262 C)270 D)272 E)None of these SOLUTION:Explanation: Volume will be length * breadth * height, but in this case two heights are given so we will take average, Volume=(12∗9∗(1+4 /2))m312∗9∗2.5m3=270m3 Option C #### C QUESTION:Sum of 3 consecutive even no.'s is 30 more than the 1st no. of the series. Find the middle no.? options: A)8 B)12 C)14 D)16 E)18 SOLUTION:Let the numbers be x, x+2 and x+4 then x + x+2 + x+4 = x+30 3x + 6 = x + 30 2x = 24 \inline \therefore x = 12 \inline \therefore Middle number = x + 2 = 12+2 = 14 C #### C QUESTION:Which number should replace both the asterisks in (* /18) x (*/162) = 1 ? options: A)27 B)36 C)54 D)72 E)90 SOLUTION:Let (y/18) x (y/162) = 1 y^2 = 18 x 162 = 18 x 18 x 9 y = (18 x 3) = 54 The answer is C. #### C QUESTION:A, 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? options: A)14 days B)21 days C)22 days D)11 days E)43 days SOLUTION:D 11 days x/24 + x/30 + x/40 = 1 x = 11 days #### D QUESTION:The difference between the compound interest compounded annually and simple interest for 2 years at 20% per annum is Rs.144. Find the principal? options: A)3377 B)2997 C)3600 D)2799 E)7719 SOLUTION:P = 144(100/5)2 => P = 3600 Answer:C #### C QUESTION:A right triangle ATC has to be constructed in the xy-plane so that the right angle is at A and AT is parallel to x axis. The coordinates of A, T and C are integers and satisfy the inequalities -1 ≤ x ≤ 7 and 1 ≤ y ≤ 7. How many different triangles can be constructed with these properties? options: A)63 B)336 C)567 D)3024 E)5040 SOLUTION:All the cordinates are integer hence, possible AT values are {-1,0}, {-1,1} ....{-1,7}: 8 ways .... {7,-1}, {7,0} ......{7,6}: 8 ways 9*8 ways = 72 for AC values can be {1,2}, {1,3} .... {1,7} : 6ways ...... {7,1}, {7,2} ..... {7,6} : 6 ways 7*6 = 42 Total = 72 * 42 = 3024 hence D #### D QUESTION:The average monthly salary of 20 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 ? options: A)3700 B)3890 C)88798 D)2789 E)2891 SOLUTION:Explanation: Manager's monthly salary Rs. (1700 * 21 - 1600 * 20) = Rs. 3700. Answer: A) 3700 #### A QUESTION:The length of a room is 5.5 m and width is 3.75 m. Find the cost of paving the floor by slabs at the rate of Rs. 1200 per sq. metre. options: A)Rs. 15000 B)Rs. 15550 C)Rs. 24750 D)Rs. 16500 E)None of these SOLUTION:Solution Area of the floor = (5.5 × 3.75) m2 = 20.625 m2 ∴ Cost of paving = Rs. (1200 × 20.625) = 24750. Answer C #### C QUESTION:Two numbers are in the ratio 3 : 4. If their L.C.M. is 48. what is sum of the numbers? options: A)28 B)56 C)76 D)84 E)85 SOLUTION:Explanation: Let the numbers be 3x and 4x LCM of 3x and 4x = 12x (Since LCM of 3 and 4 is 12. Hence LCM of 3x and 4x is 12x) Given that LCM of 3x and 4x is 48 => 12x = 48 => x = 48/12 = 4 Sum of the numbers = 3x + 4x = 7x = 7 x 4 = 28 Answer: Option A #### A QUESTION:A person purchased a TV set for Rs. 16000 and a DVD player for Rs. 1800. He sold both the items together for Rs. 31150. What percentage of profit did he make? options: A)30% B)75% C)40% D)70% E)None of these SOLUTION:The total CP = Rs. 16000 + Rs. 1800 = Rs. 17800 and SP = Rs. 31150 Profit(%) = (31150 - 17800)/17800* 100 = 75% ANSWER:B #### B QUESTION:The 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? options: A)30 Years B)49 Years C)51 Years D)55 Years E)57 Years SOLUTION:Total age of students is 32X16 = 512 Years Total age inclusive of teacher = 33X (16+1) = 561 So, Teacher's age is 561-512 = 49 Yrs There is a shortcut for these type of problems Teacher's age is 16+(33X1) = 49 Years B) #### B QUESTION:A coin is tossed 6 times. What is the probability of getting exactly 5 heads? options: A)3/8 B)3/16 C)5/16 D)3/32 E)7/64 SOLUTION:The number of possible outcomes is 2^6 = 64 There are 6 ways to get exactly 5 heads. P(exactly 5 heads) = 6/64 = 3/32 The answer is D. #### D QUESTION:Question: What is the remainder when R=(1!)!^3 + (2!)^3 + (3!)^3 + … + (432!)^3 is divided by 144? options: A) 0 B) 25 C) 49 D) 81 E) 100 SOLUTION:144 =12 *12 (1!)^3=1 2!=2, therefore (2!)^3=2*2*2=8 3!=6, therefore (3!)^3=6*6*6=216 4!=24 therefore (4!)^3= 24*24*24 which is completely divisible by 144 thus from 4! onwards each term will be divisible by 144 and will leave the remainder of 0 now the remainder when R=(1!)^3 + (2!)^3 + (3!)^3 + … + (432!)^3 is divided by 144 is same as, when 1+8+216 =225 is divided by 144 now remainder when 225 is divided by 144 is 81. hence answer should be D #### D QUESTION:Sum of three numbers 264, If the first number be twice then second and third number be one third of the first, then the second number is options: A)70 B)71 C)72 D)73 E)74 SOLUTION:Explanation: Let the second number is x, then first is 2x, and third is 1/3(2x) =>2x+x+2x/3=264 <=>11x/3=264 =>x=72 Answer: Option C #### C QUESTION:In what ratio P:Q should the Mixture P of milk and water in the ratio of 5:3 be mixed with another Mixture Q of milk and water in the ratio 1:3 so that the resultant mixture contains equal quantities of milk and water? options: A)5:2 B)4:3 C)3:2 D)2:1 E)4:1 SOLUTION:(5/8)*P +(1/4)*Q = (3/8)*P+(3/4)*Q 2P=4Q P/Q = 2/1 The answer is D. #### D QUESTION:In 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 : 24. In the company, what is the maximum number of non-managers in a department that has 8 managers? options: A)26 B)27 C)28 D)29 E)30 SOLUTION:8/7 * 24 = 27.4 The answer is B. #### B QUESTION:A palindrome is a number that reads the same forward and backward, such as 242. How many even thirteen-digit numbers are palindromes? options: A)40 B)400 C)500 D)5,000 E)40,000,000 SOLUTION:if the palindrome must be even, it must begin and end in 2,4 6 and 8 ( 4 ways) e.g 22122,44144. The middle number in the thirteen-digit could be 0-9 ( 10 ways), e.g 2222225222222, 2864228224682 The 2nd and fourth numbers , the 3rd and 5th, 4th and 6th, 5th and 7th must also be same i.e 0-9( 10 ways) we thus have, 4 *10*10*10*10 *10*10= 4000000.E #### E QUESTION:The average age of a husband and his wife was 23 years at the time of their marriage.After 5 years they have a one year old child.The average of the family is now? options: A)18 years B)23 years C)29 years D)26 years E)19 years SOLUTION:sum of the present age of husband, wife and child =(23*2+5*2)+1 = 57 years required average = 57/3 = 19 years. Answer :E #### E QUESTION:Andrew travelling to 7 cities. Gasoline prices varied from city to city. What is the median gasoline price? options: A)$1 B)$1.84 C)$1.92 D)$2.13 E)$2.15 SOLUTION:Ordering the data from least to greatest, we get: $1.61, $1.75, $1.79, $1.84, $1.96, $2.09, $2.11 The median gasoline price is $1.84. (There were 3 states with higher gasoline prices and 3 with lower prices.) B #### B QUESTION:A horse is tethered to one corner of a rectangular grassy field 36 m by 20 m with a rope 12 m long. Over how much area of the field can it graze? options: A)154 cm2 B)113 m2 C)123 m2 D)115 m2 E)None of these SOLUTION:Area of the shaded portion = 1⁄4 × π × (12)2 = 113 m2 Answer B #### B QUESTION:The 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? options: A)20 years B)21 years C)22 years D)23 years E)24 years SOLUTION:Explanation: Let the average age of the whole team by x years. 11x – (24 + 27) = 9(x -1) 11x – 9x = 42 2x = 42 x = 21. So, average age of the team is 21 years. Answer B #### B QUESTION:Anand 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 options: A)Rs 9600 B)Rs 8500 C)Rs 8450 D)Rs 8400 E)None of these SOLUTION:Explanation: Ratio of their shares = 22500 : 35000 =9 : 14 Deepak's share = Rs.(13800×14/23) = Rs. 8400 Option D #### D QUESTION:Murali 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 3 : 3? options: A)16 B)48 C)277 D)92 E)11 SOLUTION:Let the distances between city A to B and B to C be 3x km and 3x km respectively. Total time taken to cover from A to C = (3x)/40 + (3x)/60 = (9x + 6x)/120 = 15x/120 = x/8 Average speed = (3x + 3x)/(x/8) = 48 kmph. Answer:B #### B QUESTION:The length of the bridge, which a train 150 metres long and travelling at 45 km/hr can cross in 30 seconds, is? options: A)76 m B)178 m C)225 m D)187 m E)176 m SOLUTION:Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (150 + x)/30 = 25/2 => 2(150 + x)= 750 => x = 225 m. Answer: C #### C QUESTION:On 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 0.5, what is the probability that Malachi will return home at the end of the day on the following Monday? options: A)0.008 B)0.125 C)0.128 D)0.512 E)0.64 SOLUTION:Re-phrasing the question: What is the probability of: Saturday: No rain, Sunday: No rain, Monday: Rain Probability of rain = 0.5 Therefore, probability of no rain = 0.5 0.5*0.5*0.5 = 0.125 Hence B #### B QUESTION:In a LAB experiment, a 100 ml compound of element X and element Y needs to be increased to 150 ml by adding some quantity of element X, and some quantity of element Y. If the original compound contains 30% of element X, how much (in ml) of element Y must be added so that element X will be exactly one third of the resulting mixture ? options: A)40 ml B)100/3 ml C)30 ml D)20/3 ml E)10 ml SOLUTION:There are 0.3*100=30 ml of element X in the initial solution. We need X to be 1/3rd of 150 ml in the resulting solution, so 50 ml. Thus out of 50 ml of solution added, 20 must be X (in order it to become 50 ml) ans the remaining 30 must be Y. Answer: C #### C QUESTION:How many different positive integers exist between 10^3 and 10^4, the sum of whose digits is equal to 2? options: A)6 B)7 C)5 D)4 E)18 SOLUTION:So, the numbers should be from 1,000 to 10,000 The following two cases are possible for the sum of the digits to be 2: 1. Two 1's and the rest are 0's: 1,001 1,010 1,100 3 numbers. 2. One 2 and the rest are 0's: 2,000 1 number. Total = 4 numbers. Answer:D #### D QUESTION:A 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 35% impurities to the product. Find the net profit percentage of the dealer? options: A)44% B)40% C)68.75% D)56.25% E)36% SOLUTION:The dealer uses weight which is 20% less than the real weight. or (1- 1/5) or 4/5 of real weight. It means that he is selling $4 worth of product for $5. The dealer then further added 35% impurities to the product. It means that he is selling $5 worth of product for $6.75. So his profit is $6.75-$4 = $2 and his profit percent is (2.75/4)*100 = 68.75% Answer:- C #### C QUESTION:Three people candidates contested an election and they received 1136, 7636 and 11628 votes respectively. What is the percentage of the total votes did the winning candidate get? options: A)40% B)45% C)57% D)58% E)60% SOLUTION:tot no of votes = (1136+7636+11628) = 20400 req = > (11628/20400 * 100) = > 57% ANSWER C #### C QUESTION:Half of 5 percent written as decimal is options: A)5 B)0.5 C)0.05 D)0.025 E)None of these SOLUTION:Explanation: It will be 1/2(5%) = 1/2(5/100) = 5/200 = 0.025 Answer: Option D #### D QUESTION:When 2/3 of the garments in the shipment were inspected, 28 of the garments passed inspection and the remaining 2 garments failed. How many of the un inspected garments must pass inspection in order that 90 percent of the garments in the shipment pass? options: A)10 B)9 C)13 D)7 E)5 SOLUTION:B = 9 2/3x= 30 x=45 for 90% approval we need 41 garments approved. already approved = 28 we need 13 more. Answer : C #### C QUESTION: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 6%. What was its profit on the items sold in February? options: A)27.5% B)30% C)35% D)37.5% E)41% SOLUTION:Assume the total price = 100x Price after 20% markup = 120x Price after 25%further markup = 1.25*120x = 150x Price after the discount = 0.94*150x = 141x Hence total profit = 41% Option E #### E QUESTION:How many even multiples of 45 are there between 449 and 901? options: A)5 B)6 C)9 D)10 E)11 SOLUTION:450 = 10*45 900 = 20*45 The even multiples are 45 multiplied by 10, 12, 14, 16, 18, and 20 for a total of 6. The answer is B. #### B QUESTION:For which of the following values of n is (500+n)/n NOT an integer? options: A) 1 B) 2 C) 3 D) 4 E) 5 SOLUTION:Solution: This problem is easiest solved by plugging in each answer choice. A) (500 + 1)/1 = 501/1 = 501 Answer choice A yields an integer. B) (500 + 2)/2 = 502/2 = 251 Answer choice B yields an integer. C) (500 + 3)/3 = 503/3 = 167, remainder 2 Answer choice C DOES NOT yield an integer. Although we believe answer choice C is correct, we should still test the other answer choices. D) (500 + 4)/4 = 504/4 = 126 Answer choice D yields an integer. E) (500 + 5)/5 = 505/5 = 101 Answer choice E yields an integer. Thus, the correct answer is answer choice C. #### C QUESTION:There 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 20% of all the students at Morse have cars, how many students are in the three lower grades? options: A)600 B)900 C)1200 D)1350 E)1500 SOLUTION:Let x be the number of students in the lower three grades. 0.1x + 150 = 0.2(x+300) 0.1x = 900 x = 900 The answer is B. #### B QUESTION:Goldenrod 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? options: A) 720 B) 360 C) 120 D) 24 E) 21 SOLUTION:no hope finishing before goldenrod= 1/2 of the times therefore the different L arrangements are 1/2* 6! = 360 = B #### B QUESTION:16.02 × 0.1 = ? options: A)0.1602 B)0.001602 C)1.6021 D)0.01602 E)None of these SOLUTION:16.02 × 0.1 = 1.602 The answer is C. #### C QUESTION:If 6111309× 3145208 × K^2 is divisible by 3, which of the following could be the value of K? options: A)30 B)4 C)5 D)66 E)All of these SOLUTION:The first term divisible by 3, so any term could be the third term. Answer =(E) #### E QUESTION:The cost of an item was reduced from its usual selling price of $23.99 to $16.99. Which of the following is closest to the percent decrease in the price of the item? options: A)17% B)21% C)24% D)29% E)42% SOLUTION:The price decreased by 23.99 - 16.99 = $7. $7 is a bit more than 29% of original price of $24. Answer: D. #### D QUESTION:If U 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, U, 0, 1, 3, K, 7}? I. -1.5 II. -2 III. 0 options: A) I only B) II only C) III only D) I and III only E) None SOLUTION:If U 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 #### E QUESTION:For the set { 3, 3, 4, 4, 5, 5, x}, which of the following values of x will most increase the standard deviation? options: A)(-3)^2 B)2 C)3 D)4 E)5 SOLUTION:Standard Deviation Step 1, as pointed out by others, is to find out the mean = 4 Step 2, For each number: subtract the Mean and square the result = (1-4)^2=(-3)^2 (2-4)^2=(-2)^2 (3-4)^2 =(-1)^2 (4-4)^2=(.0)^2 (5-4)^2=(1)^2 Clearly (1-4)^2=(-3)^2 will give you the greatest value among all the other options. Hence A #### A QUESTION:Victor'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 R would it take Victor to complete 10 jobs without any supervision? options: A)34 B)52 C)60 D)70 E)92 SOLUTION:Rate when supervised = (job)/(time) = 1/t. Rate when unsupervised = (job)/(time) = 1/(t+3). For 144/2=72 days he is supervised and for 144/2=72 days he is unsupervised and does 36 jobs: 72/t + 72/(t+3) = 36 --> t=3 days --> t+3 = 6 days. Victor to complete 10 jobs without any supervision will need R 10(t + 3) = 60 days. Answer: C. #### C QUESTION:The number of people who purchased book A is twice the number of people who purchased book B. The number of people who purchased both books A and B is 500, which is twice the number of people who purchased only book B. What is the number of people C who purchased only book A? options: A)250 B)500 C)750 D)1000 E)1500 SOLUTION:This is best solved using overlapping sets or a Venn Diagram. We know that A = 2B, and that 500 people purchased both A and B. Further, those purchasing both was double those purchasing B only. This gives us 250 people purchasing B only. With the 500 that pruchased both, we have a total of 750 that purchased B and this is 1/2 of those that purchased A. So, 1500 purchased A. Less the 500 that purchased both, C=1000 purchased A only. (This is much simpler to solve using the Venn diagram). Correct answer is D. 1000 #### D QUESTION:If A and B are two prime numbers bigger than 2, which of the following can't be true? (1) A + B is an even number. (2) A - B is also a Even number. (3) A^B is also a prime number. options: A)1 only. B)2 only. C)3 only. D)2 and 3 only. E)1, 2 and 3. SOLUTION:Answer is D : 2 and 3 only (1) A + B is an even number. : All primes beyond 2 are odd, so odd+odd = even, so true (2) A - B is also a Even number. : True (3) A^B is also a prime number. : Beats the property of primes, so false Ans : C #### C QUESTION:A marching band of 240 musicians are to march in a rectangular formation with s rows of exactly t musicians each. There can be no less than 8 musicians per row and no more than 30 musicians per row. How many different rectangular formations Z are possible? options: A)3 B)Z=4 C)Z=5 D)Z=6 E)Z=8 SOLUTION:The combinations could be {(1,240),(2,120),(3,80),(4,60),(5,48),(6,40),(8,30),(10,24),(12,20),)15,16),(16,15),(20,12),(24,10),(30,8),(40,6),(48,5),(60,4),(80,3),(120,2),(240,1)} Of these we are told 8<=t<=30 So we can remove these pairs, and we are left only with. {(8,30,(10,24),(12,20),(15,16),(16,15),(20,12),(24,10),(30,8)} Hence 8.E #### E QUESTION:A train is running at a speed of 40 km/hr and it crosses a post in 18 seconds. What is the length of the train? options: A)metres B)metres C)metres D)metres E)metres SOLUTION:Explanation: Speed of the train, v = 40 km/hr = 40000/3600 m/s = 400/36 m/s Time taken to cross, t = 18 s Distance Covered, d = vt = (400/36)× 18 = 200 m Distance covered is equal to the length of the train = 200 m Answer: Option C #### C QUESTION:Which one the following fractions has the biggest value? options: A)211/711 B)201/711 C)191/711 D)221/711 E)181/711 SOLUTION:All options have the same denominator 711. If denominator is same, the fraction with the biggest value will be the one with the biggest numerator. Answer (D). #### D QUESTION:The forth proportional to 1,2,3 is? options: A)2 B)4 C)8 D)9 E)6 SOLUTION:Let the fourth proportional to 1,2,3 be x then 1:2::3:x 1x = 2*3 x = 6 Answer is E #### E QUESTION:Two cogged wheels of which one has 32 cogs and other 54 cogs, work into each other. If the latter turns 80 times in three quarters of a minute, how often does the other turn in 8 seconds? options: A)22 B)24 C)99 D)27 E)17 SOLUTION:Explanation: Less Cogs more turns and less time less turns Number of turns required=80 × × = 24 times Answer: B) 24 #### B QUESTION:A rectangular with dimensions 35 inches by 45 inches is to be divided into squares of equal size. Which of the following could be a length of a side of the squares? options: A)a) 4 inches B)b) 6 inches C)c) 5 inches D)d) 8 inches E)e) 10 inches SOLUTION:you need to divide the width and length of the rectangular to equal pieces where L = W you can solve this using GCF 35=5*7 45=3*3*5 GCF = 5 P.S you can make squares with side of 5 Answer : C #### C QUESTION:40 liters of a mixture is created by mixing Liquid P and Liquid Q in the ratio 5:3. How many liters of Liquid Q must be added to make the ratio 5:6? options: A)5 B)8 C)10 D)12 E)15 SOLUTION:Let x be the amount of liquid Q to be added. (3/8)*40 + x = (6/11)*(40+x) 1320 + 88x = 1920 + 48x 40x = 600 x = 15 The answer is E. #### E QUESTION:A 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? options: A)400 B)991 C)881 D)771 E)551 SOLUTION:2000 ---- 50 2000 ---- 40 x ----- 50 x*50 = 2000*40 x=1600 2000 ------- 400 Answer: A #### A QUESTION:Seven 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? options: A)7 years B)5 years C)3 years D)8 years E)10 years SOLUTION:Explanation: Average of the family of two numbers 7 years ago = 25 = (25+ 7) * 2 = 64 years Average age of the family of three members at present = 23 years = 23 * 3 = 69 YEARS Age of child = 69 - 64 = 5 years Answer: Option B #### B QUESTION:The average (arithmetic mean) of 24, 35, and 58 is 6 more than the average of 19, 51, and x. What is x? options: A)26 B)27 C)28 D)29 E)30 SOLUTION:The average of 24, 35, and 58 is 39. The average of 19, 51 and x is 33. Then 19 + 51 + x = 99. x = 29. The answer is D. #### D <<<Examples ends QUESTION:A man sells 45 lemons for Rs 40 and loses 20%. At how much price should he sell 24 lemons to the next customer to make a 20% profit? options: A)37 B)299 C)72 D).32 E)01 SOLUTION:Explanation: Let cost price of lemons be x. Selling price of lemons becomes CP - loss. =>SP=x-(20/100)x =>40=x(80/100) =>50 So 45 lemons cost Rs 50 Cost of 1 lemon = 50/45 Rs Cost of 24 lemons = (50/45)*24 =80/3 Rs Selling Price of 24 lemons =(80/3)+(20/100)(80/3)=Rs 32 ANSWER:D #### D

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:The batting average of a particular batsman is 60 runs in 46 innings. If the difference in his highest and lowest score is 150 runs and his average excluding these two innings is 58 runs, find his highest score. options: A)179 B)208 C)210 D)223 E)229 SOLUTION:Explanation: Total runs scored by the batsman = 60*46 = 2760 runs Now excluding the two innings the runs scored = 58*44 = 2552 runs Hence the runs scored in the two innings = 2760 – 2552 = 208 runs. Let the highest score be x, hence the lowest score = x – 150 x + (x - 150) = 208 2x = 358 x = 179 runs ANSWER A #### A QUESTION:The average of four consecutive even numbers is 27. Find the largest of these numbers. options: A)28 B)30 C)32 D)34 E)36 SOLUTION:Given: Consider the consecutive even numbers as : x, (x + 2), (x + 4) and (x+ 6) Average = Sum of Quantities/Number of Quantities = [x + (x + 2) + (x + 4) + (x + 6)] /4= (4x + 12) /4 = 27 Simplifying we get, x = 24 Therefore, Largest number = (x + 6) = (24 + 6) = 30 Smallest number = 24 ANSWER IS B #### B QUESTION:In a recent head-to-head run-off election, 12,000 absentee ballets were cast. 1/6 of the absentee ballets were thrown out and 3/5 of the remaining absentee ballets were cast for Candidate A. How many absentee votes did Candidate B receive? options: A)2,000 B)3,000 C)4,000 D)8,000 E)9,000 SOLUTION:5/6 * 2/5 (total absentee votes) = 1/3 (total votes)=1/3*12000=4000 Answer is C #### C QUESTION:The population of a town is 7500. It decreases annually at the rate of 10% p.a. What was its population 2 years ago? options: A)9300 B)8000 C)8500 D)9500 E)10000 SOLUTION:Formula : ( After =100 denominator Ago = 100 numerator) 7500 × 100/90 × 100/90 = 9259 A) #### A QUESTION:A mixture contains alcohol and water in the ratio 4 : 3. If 9 litres of water is added to the mixture, the ratio becomes 4: 5. Find the quantity of alcohol in the given mixture options: A)15 litres B)10 litres C)30 litres D)22 litres E)18 litres SOLUTION:Let the quantity of alcohol and water be 4x litres and 3x litres respectively 4x/(3x+9)=4/5 20x=4(3x+9) 8x=36 x=4.5 Quantity of alcohol = (4 x 4.5) litres = 18 litres. Answer is E #### E QUESTION:A certain university will select 1 of 7 candidates eligible to fill a position in the mathematics department and 2 of 8 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? options: A)42 B)70 C)140 D)196 E)315 SOLUTION:Ans: 196 7C1 * 8C2 Answer D) #### D QUESTION:If 144/0.144 = 14.4/x, then the value of x is: options: A)0.144 B)1.44 C)0.0144 D)0.014 E)0.00144 SOLUTION:=144/0.144 = 14.4/x =144 x 1000/144 =14.4/x =x = 14.4/1000 = 0.0144 Answer is C. #### C QUESTION:If (a-3)(b-2) =0, which of the following must be true ? I. a=3 and b=2 II. if a is not = 3, then b=2 III. if a=3, then b is not=2 options: A)I only B)II only C)III only D)I and II E)II and III SOLUTION:(a-3)(b-2)=0 So either a=3 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. The answer is B. #### B QUESTION:Running at their respective constant rate, machine X takes 2 days longer to produce w widgets than machines Y. AT these rates, if the two machines together produce 5w/4 widgets in 3 days, how many days would it take machine X alone to produce 4w widgets. options: A)4 B)6 C)8 D)10 E)24 SOLUTION:I am getting 12. E. Hope havent done any calculation errors.. approach.. let y=no. of days taken by Y to do w widgets. Then X will take y+2 days. 1/(y+2) +1/y = 5/12(5/12 is because (5/4)w widgets are done in 3 days. So, x widgets will be done in 12/5 days or 5/12 th of a widget in a day) Solving, we have y = 4 =>X takes 6 days to doing x widgets. So, he will take 24 days to doing 4w widgets. Answer : E #### E QUESTION:A worker is paid a regular rate of Rs.10 for completing a survey. The worker completes 50 surveys per week. For any survey involving the use of her cellphone, she is paid at a rate of that is 30% higher than her regular rate. If she completed 35 surveys involving the use of her cellphone, how much did she get that week? options: A)605 B)505 C)105 D)100 E)200 SOLUTION:earning 35 surveys using her cell phone = 13*35 = 455 balance 15 surveys = 10 x 15 = 150 Total = 455+150 = 605 Answer : A #### A QUESTION:By selling 150 mangoes, a fruit-seller gains the selling price of 30 mangoes. Find the gain percent? options: A)28% B)25% C)23% D)45% E)15% SOLUTION:SP = CP + g 150 SP = 150 CP + 30 SP 120 SP = 150 CP 120 --- 30 CP 100 --- ? => 25% Answer: B #### B QUESTION:In the xy-coordinate system, what is the slope of the line that goes through point (2, 4) and is equidistant from the two points P = (9, 3) and Q = (5, 9)? options: A)0.1 B)0.2 C)0.3 D)0.4 E)0.5 SOLUTION:First, get the middle coordinate between (9,3) and (5,9). x = 9 + (5-9)/2 = 7 y = 3 + (9-3)/2 = 6 Second, get the slope of (7,6) and (2,4). m = 6-4 / 7-2 = 2/5 = 0.4 Answer: D #### D QUESTION:Two 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? options: A)9:36 B)9:31 C)9:35 D)9:37 E)9:32 SOLUTION:1/4 : 3/4 = (1:3)5 = 5:15 1/5 : 4/5 = (1:4)4 = 4:16 ------ 9:31 Answer: B #### B QUESTION:A cycle is bought for Rs.900 and sold for Rs.1125, find the gain percent? options: A)27% B)20% C)80% D)30% E)25% SOLUTION:900 ---- 225 100 ---- ? => 25% Answer: E #### E QUESTION:John weighs twice as much as Susan. Susan's weight is 60% of Sam's weight. Mark weighs 50% of Lynn's weight. Lynn weighs 190% of John's weight. Which of these 5 people weighs the least? options: A)John B)Susan C)Sam D)Mark E)Lynn SOLUTION:Let J – John’s weight S – Susan’s weight M – Mark’s weight A – Sam’s weight L – Lynn’s weight J = 2S S = 0.6A M = 0.5L L = 1.9J Let us convert these weights to one variable S = J/2 A = S/0.6 = J/1.2 = 5J/6 L = 1.9J M = 0.5 * 1.9J = 0.95J So Susan has the least weight. Answer - B #### B QUESTION:Two trains each 170m in length each, are running on two parallel lines in opposite directions. If one goes at the speed of 55km/h while the other travels at 50km/h. how long will it take for them to pass each other completely. options: A)15 sec B)11.6 sec C)31.6 sec D)12.6 sec E)23 sec SOLUTION:Explanation: D = 170 m + 170 m = 340 m RS = 55 + 50 = 105 * 5/18 = 146/5 T = 340 * 5/146 = 11.6 sec Answer: Option B #### B QUESTION:In 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 4P pots? options: A)M/15 B)15M C)15/M D)4M/15 E)15/4M SOLUTION:The time it takes to wash 4P pots is 4M minutes which is 4M / 60 = M/15 hours. The answer is A. #### A QUESTION:Find out Difference between SI and CI if p=1000000 r=4% ant t=3 yr? options: A)4864 B)4854 C)4844 D)4868 E)4866 SOLUTION:p=1000000, r=4% annual , t=3 yr SI = p*r*t/100 = 1000000*4*3/100 = 120000 CI = p[(1+ r/100)^t -1] = 1000000[(1+ 4/100)^3 -1] = 124864 difference = CI - SI = 124864 - 120000 = 4864 ANSWER:A #### A QUESTION:A certain sum amount to $1400 in 2 yrs and $2000 in five years on certain fixed simple interest. In how many yrs would the amount be $1840 had it been put at the rate of interest compounded annually? options: A)4.5 B)3.5 C)3 D)2 E)1 SOLUTION:We can form equations as following: Initial amount = P, Total amount after interest = T, Interest per year = I T = P+I Given T1 = P+2I = 1400 T2 = P+ 5I = 2000 From this we get, P = 1000I = 200 $ Now we know that simple interest is<Compound interest ( CI = SI only after 1st year if CI is compounded annually) consider simple interest - after 1st yer it is 200$ , after 2nd years it is 400$ and after 3rd year it is 600$. To get a 440 $ compound interest the duration have to be > 1 year and < 3 years. Only option fitting : Option D. #### D QUESTION:If it takes 70 workers 3 hours to disassemble the exhibition rides at a small amusement park, how many hours would it take 30 workers to do this same job? options: A)40/3 B)11 C)7 D)7/3 E)9/7 SOLUTION:70 Workers = 3 hours then, 1 Worker = 3*70 Hours 30 Workers = (3*70) /(30) = 7 ANSWER:C #### C QUESTION:How many diagonals does a 62-sided convex polygon have? options: A)1829 B)2356 C)3458 D)3843 E)4820 SOLUTION:A 62-sided convex polygon has 62 vertices. If 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. If 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 However, we must recognize that we have counted every diagonal twice. To account for counting each diagonal twice, we must divide 3658 by 2 to get 1829. The answer is A. #### A QUESTION:There are 22 students in a class. In how many different ways can a committee of 3 students be formed? options: A)1180 B)1320 C)1540 D)1760 E)1920 SOLUTION:22C3 = 22*21*20 / 6 = 1540 The answer is C. #### C QUESTION:What is the remainder when 14,451 × 15,654 × 16,783 is divided by 5? options: A)1 B)3 C)2 D)4 E)5 SOLUTION:Only the unit's digit of the product will decide the remainder when divided by 5. Hence, 1*4*3= will give units digit as 2 So, whatever be the number, if it ends in 2, the remainder after dividing with 5 will be 2. Option C #### C QUESTION:In how much time would the simple interest on a certain sum be 0.125 times the principal at 10% per annum? options: A)1 1/4 B)1 1/6 C)1 1/0 D)1 1/5 E)1 5/1 SOLUTION:Let sum = x. Then, S.I. = 0.125x = 1/8 x, R = 10% Time = (100 * x) / (x * 8 * 10) = 5/4 = 1 1/4 years.Answer: A #### A QUESTION:Mangala completes a piece of work in 10 days, Raju completes the same work in 20 days. If both of them work together, then the number of days required to complete the work is? options: A)8 days B)10 days C)20/3 days D)14 days E)16 days SOLUTION:If A can complete a work in x days and B can complete the same work in y days, then, both of them together can complete the work in x y/ x+ y days. That is, the required No. of days = 10 × 20/30 = 20/3 days C) #### C QUESTION:In an engineering class that contained 150 students, the final exam consisted of 2 questions. Three fifths of the students answered the first question correctly. If four fifths of the remainder answered the second question correctly, how many students answered both questions incorrectly? options: A)4 B)6 C)10 D)12 E)24 SOLUTION:1st Question : Three fifths of the students answered the first question correctly - so 3/5∗150=90 2nd Question : four fifths of the remainder answered the second question correctly so 4/5∗(150−90)=4/5∗60=48 total students who answered at least one Q correct =90+48=138 so students who answered BOTH incorrectly = 150−138=12 ANSWER:D #### D QUESTION:The number of cars present at a particular time was measured at 4,999 different locations on Tuesday and on Wednesday. The number of locations that had more cars on Wednesday was 20% higher than the number of locations that had more cars on Tuesday. How many of the locations had more cars on Tuesday? options: A)1,159 B)1,333 C)1,860 D)2,160 E)2,272 SOLUTION:The question states that all these 4,999 locations were measured twice, once on each day. It also breaks the 4,999 into two groups, the higher-on-Tuesday locations and the higher-on-Wednesday locations, which we can call T and W. Therefore, we can write two equations: For each of the first and second day count of locations, T + W = 4999 But, for the second day count, W = 1.20 T i.e. for Second day count, T + 1.20T = 4999 i.e. 2.20 T = 4999 i.e. T = 2272 E #### E QUESTION:The population of a village is 7800. It increases annually at the rate of 18% p.a. What will be its population after 2 years? options: A)10000 B)12000 C)13000 D)10860 E)14400 SOLUTION:Formula : ( After =100 denominator Ago = 100 numerator) 7800 × 118/100 × 118/100 = 10860 D #### D QUESTION:Expenditures of a Company (in Lakh Rupees) per Annum Over the given Years. Year Item of Expenditure Salary Fuel and Transport Bonus Interest on Loans Taxes 1998 288 98 3.00 23.4 83 1999 342 112 2.52 32.5 108 2000 324 101 3.84 41.6 74 2001 336 133 3.68 36.4 88 2002 420 142 3.96 49.4 98 The total amount of Fuel paid by the company during the given period is approximately what percent of the total amount of salary paid during this period? options: A)A)0.5% B)B)1% C)C)1.25% D)D)3% E)E)4% SOLUTION:Required percentage = (288 + 342 + 324 + 336 + 420) = [ 17 x 100 ] % 1710 ~= 1%. Answer : B #### B QUESTION:How many kilograms of sugar costing Rs.9 per kg must be mixed with 27 kg of sugar costing Rs.7 per Kg so that there may be a gain of 10% by selling the mixture at Rs.9.24 per Kg? options: A)36 Kg B)42 Kg C)54 Kg D)63 Kg E)None of these SOLUTION:Solution Ratio of quantities of 1st and 2nd kind = 14 : 6 = 7 : 3. Let x kg of sugar of 1st kind be mixed with 27 kg of 2nd kind. Then, 7 : 3 = x : 27 or x = (7 x 27 / 3) = 63 kg Answer D #### D QUESTION:A 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: options: A)59 7/12 min. past 3 B)4 p.m. C)58 7/12 min. past 3 D)58 7/11 min. past 4 E)2 3/11 min. past 4 SOLUTION:Time from 7 a.m. to 4.15 p.m. = 9 hrs 15 min. = 37/4 hrs. 3 min. 5 sec. of this clock = 3 min. of the correct clock. 37/720 hrs of this clock =1/20 hrs of the correct clock. 37/4 hrs of this clock =1/20 x 720/37 x 37/4 hrs of the correct clock. = 9 hrs of the correct clock. The correct time is 9 hrs after 7 a.m. i.e., 4 p.m. Answer: B #### B QUESTION:George and Mark can paint 720 boxes in 20 days. Mark and Harry in 24 days and Harry and George in 15 days. George works for 4 days, Mark for 8 days and Harry for 8 days. The total number of boxes painted by them is options: A)28 B)H C)27 D)29 E)271 SOLUTION:Answer:B #### B QUESTION:A 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? options: A)2 1/2days B)4 1/2days C)6 1/2days D)7 1/2days E)10 1/2days SOLUTION:The required answer = (12-3)*6 / 12 = 54/12 = 4 1/2days Answer is B #### B QUESTION:There are 100 apples in a bag of which 98% are green and the rest red. How many green apples do you need to remove so that only 96% of the apples are green? options: A)40 B)8 C)15 D)25 E)50 SOLUTION:98−x/100−x=96100 Or, 9800−100x=9600−96x Or, 200=4x Or, x=50 ANSWER:E #### E QUESTION:217 + 2.017 + 0.217 + 2.0017 = ? options: A)229.3657 B)229.7563 C)229.6357 D)229.5637 E)221.2357 SOLUTION:217 2.017 0.217 + 2.0017 -------- 221.2357 --------- Answer is E. #### E QUESTION:An bus covers a certain distance at a speed of 100 kmph in 5 hours. To cover the samedistance in 1hr, it must travel at a speed of? options: A)500 km/hr B)640 km/hr C)656 km/hr D)731 km/hr E)720 km/hr SOLUTION:Distance = (100 x 5) = 500 km. Required speed = 500 km/hr. A #### A QUESTION:Envelopes 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 $7.60? options: A)426 B)430 C)443 D)470 E)486 SOLUTION:I think first we should see in what group envelopes value less, so that we can buy as many as we can with a specific amount of money: -the 100 pack costs 1.5$, meaning 0.015$ per envelope -the 50 pack costs 1$, meaning 0.02$ per envelope -the single envelope costs 0.03$ per envelope Thus, 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. Having 7.6$, we can buy as many as 4 packs of 100 (4 x 1.5$ = 6$). We then have 1.6 $ left. so we buy 1 pack of 50 for 1$. We now have 0.6$ left, so we buy 20 individual envelopes. If we add up the numbers, we get 400+50+20=470 envelopes. Answer D #### D QUESTION:In how many ways a committee consisting of 3 men and 2 women can be formed from 4 men and 7 women? options: A)A)84 B)B)15 C)C)20 D)D)18 E)E)21 SOLUTION:Required number of ways = 4C3*7C2 = 4*21 = 84 Answer is A #### A QUESTION:Tough and Tricky questions: Combinations. Three students - 2 boys and 1 girls - are to sit side by side for a makeup exam. How many ways could they arrange themselves given that no two boys and no two girls can sit next to one another? options: A)2 B)4 C)72 D)240 E)720 SOLUTION:2!*1!*2 = 2*1*2 = 4 ways. Ans. B) 4 #### B QUESTION:12,31,68,129,220,? options: A)129 B)220 C)387 D)347 E)520 SOLUTION:2*2*2 + 4 = 12 3*3*3 +4 = 31 4*4*4 + 4 = 68 5*5*5 + 4 = 129 6*6*6 + 4 = 220 7 *7 *7 + 4 = 347 ANSWER : D #### D QUESTION:What is the smallest possible common multiple of three integers, all larger than 53? options: A)27. B)54. C)846. D)19,656. E)21,924. SOLUTION:The Least common positive multiple would be for the immediate least number(s) after 53 i.e 54. Since nowhere is it stated that the three integers must be different, the integers could be 54,54 and 54... leading to least possible positive common multiple to be 54. Answer B. #### B QUESTION:If the price of an article went up by 20%, then by what percent should it be brought down to bring it back to its original price? options: A)16 2/3% B)16 4/3% C)16 7/3% D)16 6/3% E)16 2/3% SOLUTION:Let the price of the article be Rs. 100. 20% of 100 = 20. New price = 100 + 20 = Rs. 120 Required percentage = (120 - 100)/120 * 100 = 20/120 * 100 = 50/3 = 16 2/3%. Answer:A #### A QUESTION:If n = 3p, where p is a prime number greater than 2, how many different positiveevendivisors does n have, including n ? options: A) Two B) Three C) Four D) Six E) Eight SOLUTION:This 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: n = 4 x 3 n = 12 Next we have to determine all the factors, or divisors, of P. Remember the term factor is synonymous with the term divisor. 1, 12, 6, 2, 4, 3 From this we see that we have 4 even divisors: 12, 6, 2, and 4. If you are concerned that trying just one value of p might not substantiate the answer, try another value for p. Let’s say p = 5, so n = 4 x 5 n = 20 The 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. No matter what the value of p, as long as it is a prime number greater than 2, n will always have 4 even divisors. The answer is B. #### B QUESTION:A rectangle A has an area of 30 square centimeters. Square B has a perimeter of 16 centimeters. If square B is placed within square A and a random point is chosen within square A, what is the probability the point is not within square B? options: A)9/30 B)14/30 C)4/9 D)3/5 E)6/25 SOLUTION:I guess it's mean that square B is placed within rectangle A entirely. Since, the perimeter of B is 16, then its side is 16/4=4 and the area is 4^2=16; Empty space between the squares is 30-16=14 square centimeters, so if a random point is in this area then it won't be within square B: P=favorable/total=14/30. Answer: B. #### B QUESTION:A 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? options: A)5 B)6 C)21 D)8 E)9 SOLUTION:Speed of train relative to man = (60 + 6) km/hr = 66 km/hr [66 * 5/18] m/sec = [55/3] m/sec. Time taken to pass the man = [385 * 3/55] sec = 21 sec Answer: C #### C QUESTION:What annual payment will discharge a debt of Rs. 1030 due in 2 years at the rate of 5% compound interest? options: A)553.94 B)551.25 C)534.33 D)543.33 E)646.33 SOLUTION:Explanation: Let each installment be Rs. x. Then, x/(1 + 5/100) + x/(1 + 5/100)2 = 1030 820x + 1030 * 441 x = 553.94 So, value of each installment = Rs. 553.94 Answer: Option A #### A QUESTION:A, 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? options: A)3999 B)7799 C)2500 D)2772 E)2912 SOLUTION:A:B:C = 2/3:1/6:1/6 = 4:1:1 x * 2/100 * 2/3 = 200 B capital = 15000*1/6 = 2500.Answer: C #### C QUESTION:Farm Tax is levied on the 45% of the cultivated Land. The tax department collected total $ 3840 through the farm Tax from the village of Mr. willam. Mr. willam paid only $ 480 as farm tax. The percentage of total land of Mr. willam over the total taxable land of the village is : options: A)15% B)25% C)15.125% D)27.78% E)none SOLUTION:Only trick n this question is to ignore 45% information as farm tax is levied uniformly in the village and that includes Mr William's land. What percentage of tax Mr William paid ? This will be equal to the percentage of total cultivated land he holds over the total cultivated land in the village. That leads to (480/3840)x100 =12.5%in percentage terms. But the question asks ratio between his total land to total cultivated land. Hence the answer is 12.5%x (100/45) = 27.78% and the answer is not there in the options. The correct answer is (D). #### D QUESTION:a is the hundreds digit of the three digit integer x, b is the tens digit of x, and c is the units digit of x. 2a = b = 4c, and a > 0. What is the difference between the two greatest possible values of x? Tip: Dont stop till you have exhausted all answer choices to arrive at the correct one. options: A)124 B)241 C)394 D)421 E)842 SOLUTION:Ratio of a:b:c= 2:4:1 Two possible greatest single digit values for b are 8 and 4 if b is 8, then x= 482 if b is 4, then x= 241 difference= 482-241= 241 B is the answer #### B QUESTION:A basket has 5 apples and 5 oranges. Three fruits are picked at random. What is the probability that at least 2 apples are picked? options: A)1/2 B)3/5 C)3/8 D)4/9 E)7/10 SOLUTION:The total possible choices are 10C3 = 120 The ways to choose 3 apples: 5C3 = 10 The ways to choose 2 apples: 5C2 * 5C1 = 50 P(at least 2 apples) = 60/120 = 1/2 The answer is A. #### A QUESTION:Length of a rectangular plot is 28 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? options: A)54 m B)64 m C)74 m D)84 m E)94 m SOLUTION:Let breadth = x metres. Then, length = (x + 28) metres. Perimeter = 5300 m = 200 m. 26.50 2[(x + 28) + x] = 200 2x + 28 = 100 2x = 72 x = 36. Hence, length = x + 28 = 64 m B #### B QUESTION:which of the following could be the greatest common factor of positive integers 10 and 15 ? I) 5 II) 4 III) 2 options: A)II only B)I only C)III only D)I,II only E)I,III only SOLUTION:10=2*5 15=3*5 GCF =5 Answer : B #### B QUESTION:A 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? options: A)96 km B)100 km C)106 km D)116 km E)126 km SOLUTION:Distance covered in first two hours = 10 × 2 = 20 km Distance covered in next two hours = 12 × 2 = 24 km Distance covered in next two hours = 14 × 2 = 48 km Distance covered in first six hours 20 + 24 + 48 = 92 km Remaining distance = 8 km 92 + 8 = 100 km Answer B #### B QUESTION:A certain list consists of 21 different numbers. If n is in the list and n is 5 times the average (arithmetic mean) of the other 20 numbers in the list, then n is what fraction of the sum of the 21 numbers in the list? options: A)1/20 B)1/6 C)1/5 D)4/21 E)5/21 SOLUTION:series : a1, a2....a20,n sum of a1+a2+...+a20 = 20*x (x = average) so, n = 5*x Hence, a1+a2+..+a20+n = 25x So, the fraction asked = 5x/25x = 1/5 Answer C #### C QUESTION:The juice stall at the circus stocked just 2 brands of orange juice tetra packs. Brand A costs $1 per pack and brand B costs $1.5 per pack. Last week , brand A contributed to m% of stall’s revenue and accounted for n% of sales of juice tetra packs. Which of the following expresses m in terms of n? options: A)100n/(150 – n) B)200n/(250-n) C)200n/(300-n) D)250n/(400-n) E)300n/(500-n) SOLUTION:Let the number of units sold be 100. Then n units of A are sold and (100-n) units of B are sold. Total revenue= Revenue due to A + Revenue due to B = (No.of units of A sold * Cost/unit of A) + (No.of units of B sold * cost/unit of B) = n *1 + (100-n) *1.5 = n + (150-1.5n) --- (1) 2. But we know, revenue due to A = m%. of the total revenue --- (2) 3. To express m in terms of n we need to relate (1) and (2) 4. m% = n / ( n + (150-1.5n)) or m= 100n / 150-0.5n = 200n/(300-n) ANSWER:C #### C QUESTION:How much time will a train of length 400 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? options: A)40 sec B)50 sec C)60 sec D)70 sec E)80 sec SOLUTION:The distance to be covered = Sum of their lengths = 400 + 300 = 700 m. Relative speed = 72 -36 = 36 kmph = 36 * 5/18 = 10 mps. Time required = d/s = 700/10 = 70 sec. ANSWER:D #### D QUESTION:To fill a cistern, pipes A,B and C take 20 minutes, 15 minute and 12 minutes resp. The time in minutes that the three pipes together will take to fill the cistern is options: A)5 B)6 C)8 D)3 E)9 SOLUTION:A 5 #### A QUESTION:For any positive integer n, the length of n is defined as the number of prime factors whose product is n. For example, the length of 75 is 3, since 75 = 3 * 5 * 5. How many two-digit positive integers have length 6? options: A)None B)One C)Two D)Three E)Four SOLUTION:The best (quickest) way I can think of to get the answer, is start with 2^6, then move on from there. 2^6=64 2^5*3=96 Obviously 2^5*5 will be more than 2 digits, as will 2^4*3^2. So 64 and 96 are it. Answer is 2 (C). #### C QUESTION:John was thrice as old as Tom 6 yrs back. He will be 5/3 times as old as Tom 6 years hence. How old is Tom today? options: A)8 years B)10 years C)12 years D)14 years E)15 years SOLUTION:Sol. RMBflSk -6 = 3 (Ravi - 6) ...(j) and Rupesh + 6 = | (Ravi + 6) ...(ii) Solving both the equations we get, Ravi = 12 years. C #### C QUESTION:Given a collection of points P in the plane a 1-set is a point in P that can be separated from the rest by a line; i.e the pint lies on one side of the line while the others lie on the other side. The number of 1-sets of P is denoted by n1(P) . The maximum value of n1(P) over all configurations P of 4 points in the plane is options: A)1 B)2 C)3 D)4 E)5 SOLUTION:maximum no of 1-sets will be the no of points itself...as in even a simple configuration we can separate one point from others to make it 1-set ANSWER:A #### A QUESTION:If the product of two positive integers is 144, which of the following could be the LCM and HCF of the two numbers? I. LCM : 24; HCF : 6 II. LCM : 18; HCF : 8 III. LCM : 16; HCF : 9 options: A)I only B)II and III only C)I and II only D)I and III only E)I, II and III SOLUTION:We need to keep two things in mind here: 1. Product of two numbers = LCM*HCF 2. LCM should be a multiple of HCF Only Statement I follows these two rules. Correct Option A #### A QUESTION:If x and y are integers and x + y = 3, which of the following must be true? options: A)If x < 0, then y > 0. B)x and y are consecutive integers. C)If x > 0, then y < 0. D)Both x and y are even. E)Both x and y are less than 5. SOLUTION:In option C if x > 0,then y<0 means x is +ve and y is -ve In option B if x < 0, then y>0 means y is +ve and x is -ve, both are same and satisfying x+y = 5. How option A is right could you explain #### A QUESTION:In the interior of a forest, a certain number of apes equal to the square of one-eighth of the total number are playing and having great fun. The remaining sixteen apes are on a hill and the echo of their shrieks by the adjoining hills frightens them. They came and join the apes in the forest and play with enthusiasm. What is the total number of apes? options: A)32 B)16 C)64 D)80 E)16 or 48 SOLUTION:Let total number be x No in the interior = (x/8)^2 No outside = 16 So : x - (x/8)^2=16 x^2-64x+16*64=0 (x-32)^2=0 x=32 A #### A QUESTION:A 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? options: A)25 days B)24 C)22 days D)27 days E)21 days SOLUTION:B 24 days B = 1/8 – 1/2 = 1/24 => 24 days #### B <<<Examples ends QUESTION:A question paper consists of two sections A and B having respectively 3 and 4 questions.Four questions are to be solved to qualify in that paper.It is compulsory to solve at least one question from section A and 2 questions from section B .In how many ways can a candidate select the questions to qualify in that paper? options: A)30 B)40 C)42 D)44 E)46 SOLUTION:here two cases are possible. case 1) 1 question from section A and 3 question from section B are solved = 3C1.4C3 case 2) 2 question from section A and 2 question from section B are solved = 3C2.4C2 thus total number of ways = 3C1.4C3 + 3C2.4C2 = 30 ANS:A #### A

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:Lisa plays a dice game in which she rolls two, fair, six-sided dice two times. If her second roll matches her first roll, she wins. What is the probability that she wins if her first roll was 10? options: A)1/6 B)5/36 C)1/9 D)1/12 E)1/18 SOLUTION:There are 3 ways to roll a 10 with two six-sided dice: 4 and 6, 6 and 4, 5 and 5. You only count 5 and 5 once. There are 6*6=36 ways to roll two six-sided dice. Thus the probability of rolling a 10 is 3/36 = 1/12. D #### D QUESTION:The area of a triangle is with base 4m and height 5m? options: A)15 B)19 C)56 D)10 E)36 SOLUTION:Explanation: Area=1/2*b*h 1/2 * 4 * 5 = 10 m^2 Answer : D #### D QUESTION:A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train? options: A)120 metres B)180 metres C)324 metres D)150 metres E)100 meters SOLUTION:Speed=60 x5/18m/sec=50/3 m/sec. Length of the train = (Speed x Time). Length of the train = 50/3 x 9m = 150 m. ANSWER:D #### D QUESTION:In a certain parking lot, 4% of the cars are towed for parking illegally. However 80% of the cars which are parked illegally are not towed. What percentage of cars in the parking lot are parked illegally? options: A)20% B)25% C)30% D)35% E)40% SOLUTION:Let x be the number of cars and let y be the number of cars parked illegally. 4%*x = 20%*y y/x = 1/5 = 20% The answer is A. #### A QUESTION:Helen went to the stationers and bought things worth Euro 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? options: A)Euro 15 B)Euro 15.7 C)Euro 19.7 D)Euro 20 E)None SOLUTION:Explanation: Let the amount taxable purchases be Euro x. Then, 6% of x = 30/100 x = (30/100 x 100/6) = 5. Cost of tax free items = Euro [25 - (5 + 0.30)] = Euro 19.70 Answer: Option C #### C QUESTION:Carl drove from his home to the beach at an average speed of 80 kilometers per hour and returned home by the same route at an average speed of 70 kilometers per hour. If the trip home took 1/2 hour longer than the trip to the beach, how many kilometers k did Carl drive each way? options: A) 350 B) 345 C) 320 D) 280 E) 240 SOLUTION:Let us backsolve here. The answer option has to be divisible by 7 to give us 1/2. Let us try k=280 km. Time taken will be 3.5 hours and 4 hours. Hence D is the answer. #### D QUESTION:Nitin 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. 13260, how much money did he borrow? options: A)13000 B)80288 C)2668 D)2600 E)2781 SOLUTION:Let the sum be Rs. x. Then, [(x * 6 * 3)/100] + [(x * 9 * 5)/100] + [(x * 13 * 3)/100] = 13260 18x + 45x + 39x = (13260* 100) 102x = 1326000 => x = 13000. Answer:A #### A QUESTION:Number A is randomly selected from a set of all primes between 10 and 40, inclusive. Number K is selected from a set of all multiples of 5 between 10 and 40 inclusive. What is the probability that A+K is odd? options: A) 1/2 B) 2/3 C) 3/4 D) 4/7 E) 5/8 SOLUTION:All primes except 2 are odd, thus A must be odd. For A + K = odd + K to be odd, K must be even. There are 7 multiples of 5 between 10 and 40, inclusive: 10, 15, 20, 25, 30, 35, and 40. Out of them 3 (15, 25, and 35) are odd. Therefore the probability that A + K is odd is 4/7. Answer: D. #### D QUESTION:A 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? options: A)1.99 km B)2.88 km C)4.49 km D)2.99 km E)7.88 km SOLUTION:M = 6 S = 1.2 DS = 6 + 1.2 = 7.2 US = 6 - 1.2 = 4.8 x/7.2 + x/4.8 = 1 x = 2.88 Answer: B #### B QUESTION:What least value must be assigned to * so that th number 197*5462 is divisible by 9? options: A)2 B)4 C)6 D)1 E)3 SOLUTION:Let the missing digit be x Sum of digits = (1+9+7+x+5+4+6+2)=34+x For 34+x to be divisible by 9 , x must be replaced by 2 The digit in place of x must be 2. ANSWER A 2 #### A QUESTION:James took a 3-hour bike ride. In the second hour he traveled 6 miles, which was 20 percent farther than he traveled the first hour. If he traveled 25 percent farther in the third hour than he did in the second hour, how many miles did jose travel during the entire ride? options: A)54.0 B)54.9 C)18.5 D)57.0 E)63.0 SOLUTION:Let the distance travelled in the first hour be x. Thus, 1.2x = 6, x = 5. Now, the distance travelled in the 3rd hour = 6+1/4∗6=7.5 The only option ending with a 0.5 in the decimal place is C. ANSWER:C #### C QUESTION:A Baker decides to make a cake of 5 layers, one of strawberry, chocolate, butterscoch, vanila and pista. Baker decides not to put the layers of butterscoch and vanila next to each other as they both are white in colour. How many different type of such cakes can he make? options: A)5! - (4!×2!) B)4! - (6!×2!) C)3! - (2!×4!) D)4! - (4!×2!) E)5! × (4!×3!) SOLUTION:We can find the answer by substracting the number of arrangements in which V and B comes together from the total number of arrangements of 5 layers. Arrangements in which V and B comes next to each other: We can consider V and B as a single object having 2! Variations(VB and BV). VB, S, C, P can be arranged in 4! Ways. In total there are 4!×2! Ways of arranging 5 layers with B and V layers coming next to each other. Required answer = A. 5! - (4!×2!) #### A QUESTION:The average (arithmetic mean) of the integers from 100 to 400, inclusive, is how much greater than the average of the integers from 50 to 250, inclusive? options: A) 100 B) 175 C) 200 D) 125 E) 300 SOLUTION:For an AP the mean or average of series is average of first and last term. So, average of numbers between 100 to 400, inclusive = (100+400)/2 = 250 average of numbers between 50 to 250, inclusive = (50+250)/2 = 150 difference = 250 - 150 = 100 Answer is A #### A QUESTION:A company wants to spend equal amounts of money for the purchase of two types of computer printers costing $350 and $200 per unit, respectively. What is the fewest number of computer printers that the company can purchase? options: A)9 B)10 C)11 D)12 E)13 SOLUTION:The smallest amount that the company can spend is the LCM of 350 and 200, which is 1400 for each, which is total 2800. The number of 1st type of computers which costing $350 = 1400/350 = 4. The number of 2nd type of computers which costing $200 = 1400/200 = 7. Total = 4+7 = 11 Answer is C. #### C QUESTION:The present population of a town is 240. Population increase rate is 10% p.a. Find the population of town after 1 years? options: A)100 B)120 C)200 D)220 E)264 SOLUTION:P = 240 R = 10% Required population of town = P*(1 + R/100)^T = 240*(1 + 10/100) = 240*(11/10) = 264 Answer is E #### E QUESTION:If the average (arithmetic mean) of five consecutive negative integers is 2k – 1, what is the difference D between the greatest and least of the five integers? options: A)4K B)4k^2 -4k C)4-4k D)4 E)4k+4 SOLUTION:(n-2 + n - 1 + n + n + 1 + n + 2)/5 = 2k - 1 => n = 10k - 5 Greatest = n + 2 = 10k - 5 + 2 = 10k - 3 Least = n - 2 = 10k - 5 - 2 => Difference D= 10k - 3 - (10k - 7) = 4 Answer - D #### D QUESTION:The 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 ? options: A)3600 B)3890 C)88798 D)2789 E)2891 SOLUTION:Explanation: Manager's monthly salary Rs. (1600 * 21 - 1500 * 20) = Rs. 3600. Answer: A) 3600 #### A QUESTION:There are three vessels of equal capacity .Vessel A contains Milk and water in the ratio 4:3 ;Vessel B contains Milk and water in the ratio 2:1 and Vessel C contains Milk and water in the ratio 3:2 .If the mixture in all the three vessels is mixed up.What will be the ratio of milk and water ? options: A)9:6 B)3:2 C)118:126 D)193:122 E)201:132 SOLUTION:m=portion of milk in solution m=(4/7+2/3+3/5)/3➡193/315 315-193=122 122/315=portion of water in solution ratio of milk to water=193/122 ANSWER:D #### D QUESTION:A watch was sold at a loss of 10%. If it was sold for Rs.196 more, there would have been a gain of 4%. What is the cost price? options: A)s:1000 B)s:1067 C)s:1278 D)s:1028 E)s:1400 SOLUTION:90% 104% -------- 14% ---- 196 100% ---- ? => Rs:1400 Answer: E #### E QUESTION:Given a collection of points P in the plane a 1-set is a point in P that can be separated from the rest by a line; i.e the pint lies on one side of the line while the others lie on the other side. The number of 1-sets of P is denoted by n1(P) . The maximum value of n1(P) over all configurations P of 4 points in the plane is options: A)1 B)2 C)3 D)4 E)5 SOLUTION:maximum no of 1-sets will be the no of points itself...as in even a simple configuration we can separate one point from others to make it 1-set ANSWER:A #### A QUESTION:Ayesha'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? options: A)2 years B)4 years C)6 years D)8 years E)1 years SOLUTION:Explanation: Mother's age when Ayesha's brother was born = 34 years. Father's age when Ayesha's brother was born = (31 + 4) years = 35 years. Required difference = (35 - 34) years = 1 years. Answer: E #### E QUESTION:If U 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, U, 0, 1, 3, K, 7}? I. -1.5 II. -2 III. 0 options: A) I only B) II only C) III only D) I and III only E) None SOLUTION:If U 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 #### E QUESTION:A 10-by-8 inch piece of paper is used to form the lateral surface of a cylinder. If the entire piece of paper is used to make the lateral surface, which of the following must be true of the two possible cylinders that can be formed? options: A)The volume of the cylinder with height 10 is 80/pi cubic inches greater than the volume of the cylinder with height 6. B)The volume of the cylinder with height 8 is 80/pi cubic inches greater than the volume of the cylinder with height 10. C)The volume of the cylinder with height 10 is 80pi cubic inches greater than the volume of the cylinder with height 6. D)The volume of the cylinder with height 8 is 80pi cubic inches greater than the volume of the cylinder with height 10. E)The volume of the cylinder with height 8 is 240/pi cubic inches greater than the volume of the cylinder with height 10. SOLUTION:Pretty straightforward. Plug in the values to compute the volume of the cylinder. Keep in mind 8 and 10 are the circumference of the base and not the radius. B is the right answer. #### B QUESTION:In 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 11 percent of revenues. The profits in 2009 were what percent of the profits in 2008? options: A)80% B)105% C)88% D)124.2% E)138% SOLUTION:x = profits r= revenue x/r = 0,1 x= 10 r=100 2009: r=80 x/80 = 0,11 = 11/100 x= 80*11/100 x= 8.8 8.8/10 = 0.88 = 88%, Answer C #### C QUESTION:If f(x)= 5x^3- 2x+8 and h(y)= 4y-4, then h(f(x)) = options: A)11x^2+4x+4 B)11x^2-12x+44 C)8x^3-8x+32 D)30x^3+4x+4 E)20x^3-8x+28 SOLUTION:h(f(x)) = 4(f(x)) -4 = 4(5x^3- 2x+8) - 4 = 20x^3-8x+28 =>E #### E QUESTION:A man rows his boat 90 km downstream and 70 km upstream, taking 3 hours each time. Find the speed of the stream? options: A)76 kmph B)6 kmph C)3.5 kmph D)4.5 kmph E)4 kmph SOLUTION:Speed downstream = d/t = 90/(3) = 30 kmph Speed upstream = d/t = 70/(3) = 23 kmph The speed of the stream = (30 - 23)/2 = 3.5 kmph Answer:C #### C QUESTION:If we know that a positive integer is a multiple of 4, how many (distinct) possibilities are there for the last digit of the integer? options: A)3 B)4 C)5 D)6 E)7 SOLUTION:the last digit of the integer may be any of (0,2,4,6,8) so, 1/5 ANSWER:C #### C QUESTION:If john makes a contribution to a charity fund at school, the average contribution size will increase by 50% reaching $75 per person. If there were 6 other contributions made before john's, what is the size of his donation? options: A)$225 B)$150 C)$200 D)$250 E)$450 SOLUTION:Cavg = average contribution before John Cavg*1.5 = 75, therefore the average cont is $50 before John. If he needs to increase the average contribution by $25, he must put in $25 for each of the 6 people. so $150. But, he also has to put in the average for himself (the seventh person), so add $75. So $225 is your answer. Answer A #### A QUESTION:The simple interest on Rs.15000 at a certain rate of interest in five years is Rs.7200. Find the compound interest on the same amount for two years at the same rate of interest. options: A)3052.82 B)3015.24 C)3052.24 D)3018.24 E)3052.23 SOLUTION:R = 100 I / PT => R = (100 * 7200)/ (15000 * 5) = 9.6% CI = P{ [1 + R /100]n - 1} = 15000 { [ 1 + 9.6 / 100]^2 - 1} = Rs.3018.24 Answer:D #### D QUESTION:If 4x = 8^y, which of the following expresses x in terms of y? options: A)2^(y-2) B)2^(y-1) C)2^(3y-2) D)2^(2y-3) E)2^y SOLUTION:By exponential simplification. 4 = 2^2 and 8=2^3 therefore (2^2)x=(2^3)^y gives x=(2^3y)/(2^2) further simplified to x=(2^3y)(2^-2) which gives x=2^(3y-2) (because exponential is additive in multiplication. i.e. a^b*a^c=a^(b+c). Answer: C #### C QUESTION:In how many different number of ways 4 boys and 2 girls can sit on a bench? options: A)700 B)710 C)720 D)800 E)820 SOLUTION:npn = n! 6p6 = 6 × 5 × 4 × 3 × 2 × 1 = 720 C) #### C QUESTION:How many integers between 323,700 and 458,600 have tens digit 1 and units digit 3? options: A)10,300 B)10,030 C)1,353 D)1,352 E)1,349 SOLUTION:There is one number in hundred with 1 in the tens digit and 3 in the units digit:13, 113, 213, 313, ... The difference between 323,700 and 458,600 is 458,600-323,700=134,900 - one number per each hundred gives 134,900/100=1,349 numbers. Answer: E. #### E QUESTION:A metallic sphere of radius 12 cm is melted and drawn into a wire, whose radius of cross section is 4 cm. What is the length of the wire? options: A)116 cm B)144 cm C)168 cm D)173 cm E)189 cm SOLUTION:Volume of the wire (in Cylindrical shape) is equal to the volume of the sphere. π(4)^2 * h = (4/3)π (12)^3 => h = 144 cm Answer:B #### B QUESTION:In a group of 28 junior high school students, 7 take French, 9 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? options: A)7 B)6 C)9 D)4 E)8 SOLUTION:E 8 Add 7 + 9 + 4 to get 20. Then subtract 21 from the total students ⇒ 28 – 20 = 8. Answer is E #### E QUESTION:A man walked diagonally across a square lot. Approximately, what was the percent saved by not walking along the edges? options: A)30 B)39 C)87 D)27 E)91 SOLUTION:Let the side of the square(ABCD) be x meters. Then, AB + BC = 2x metres. AC = = (1.41x) m. Saving on 2x metres = (0.59x) m. Saving % = = 30% (approx) Answer:A #### A QUESTION:A certain list of 300 test scores has an arithmetic mean of 74 and a standard deviation of d, where d is positive. Which of the following two test scores, when added to the list, must result in a list of 302 test scores with a standard deviation less than d? options: A) 75 and 80 B) 80 and 85 C) 74 and 74 D) 75 and 75 E) 70 and 80 SOLUTION:Ans: C Deviation means spreading of the numbers from one median point value.. as the set is already established and we need to add only two numbers, this means we can only add numbers which are closer to the median to reduce the deviation. so 74 and 74 are the most close numbers and they will increase the number of elements in the set without changing the median value. C #### C QUESTION:At a supermarket, John spent 1/2 of his money on fresh fruits and vegetables, 1/3 on meat products, and 1/10 on bakery products. If he spent the remaining $8 on candy, how much did John spend at the supermarket? options: A) $60 B) $80 C) $90 D) $120 E) $180 SOLUTION:Let's let T = total number of dollars spent at the supermarket. With this variable we can set up an equation and determine T. We are given that John spent 1/2 of his money on fresh fruits and vegetables, or (1/2)T, 1/3 on meat products, or (1/3)T, and 1/10 on bakery products, or (1/10)T. We are also given that he spent the remaining $8 on candy. Since we know where all his money was allocated, we can sum these values together and set the sum to T. So we have: (1/2)T + (1/3)T + (1/10)T + 8 = T To get rid of the fractions we can multiply the entire equation by 30, and we obtain: 15T + 10T + 3T + 240 = 30T 28T + 240 = 30T 240 = 2T T = 120 John spent $90 at the supermarket. Answer: D #### D QUESTION:If p^2 – 6p + 8 = q, and p is a positive integer between 1 and 10, inclusive, what is the probability that q < 0? options: A)1/5 B)1/10 C)2/5 D)3/5 E)3/10 SOLUTION:(p-2)(p-4) = q p = 3 for this to be true, so 1/10 Ans :B #### B QUESTION:The average of three consecutive odd numbers is 12 more than one third of the first of these numbers. What is the last of the three numbers? options: A)15 B)17 C)19 D)21 E)23 SOLUTION:x,x+2,x+4 are three odd numbers (x+x+2+x+4)/3=12+(x/3) x=15 last no.=x+4=19 ANSWER:C #### C QUESTION:If 0.75: x :: 5:12, then x is equal to: options: A)1.12 B)1.16 C)1.8 D)1.3 E)None of these SOLUTION:Explanation: (x * 5) = (0.75 *12) X=9/5 = 1.80 Answer: C #### C QUESTION:Adding 30% of x to x is equivalent to multiplying x by which of the following? options: A)12.5 B)1.05 C)1.15 D)1.3 E)1.25 SOLUTION:130x/100= 1.3*x ANSWER:D #### D QUESTION:What is the value 201st term of a sequence if the first term of the sequence is 2 and each successive term is 3 more the term immediately preceding it? options: A)600 B)602 C)604 D)606 E)608 SOLUTION:The nth term is 2+3*(n-1). The 201st term is 2 + 3(200) = 602 The answer is B. #### B QUESTION:Two cars cover the same distance at the speed of 50 and 64 kmps respectively. Find the distance traveled by them if the slower car takes 1 hour more than the faster car. options: A)212 km B)214 km C)224 km D)216 km E)204 km SOLUTION:50(x + 1) = 64x X = 3.57 60 * 3.57 = 214 km ANSWER:B #### B QUESTION:Two concentric circles form a ring. The inner and outer circumferences of ring are (352/7) m and (518/7) m respectively. Find the width of the ring. options: A)2 B)4 C)6 D)8 E)None of them SOLUTION:Let the inner and outer radii be r and R meters. Then 2(22/7)r = (352/7) = r =((352/7) X (7/22) X (1/2))=8m. 2(22/7)R=(528/7) = R=((528/7) X (7/22) X (1/2))= 12m. Therefore, Width of the ring = (R - r) = (12 - 8) m = 4 m. Answer is B. #### B QUESTION:A man cheats while buying as well as while selling. While buying he takes 11% more than what he pays for and while selling he gives 20% less than what he claims to. Find the profit percent, if he sells at 9.09% below the cost price of the claimed weight. options: A)19.81% B)20% C)37.5% D)25% E)42.86% SOLUTION:There is a one step calculation method too. It requires more thought but is faster. The man takes 11% more than what he pays for. So if he claims to take 100 pounds, he pays $100 but he actually takes 111 pounds for which he will take from the customer $111. Hence, in effect, there is a 11% mark up. While selling, he sells 30% less. This means, he claims to sell 100 pounds and gets $100 but actually sells only 70 pounds and should have got only $70 for it. So this is again a mark up of $30 on $70. But he also sells at 9.09% less i.e. gives a discount of 1/11. (1 + m1%)(1 + m2%)(1 - d%) = (1 + p%) 11/10 * 10/7 * 10/11 = (1 + p%) profit % = 42.86%E #### E QUESTION:Two 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: options: A)11:5 B)3 : 2 C)1:2 D)3:5 E)7:8 SOLUTION:Answer: Option B Let 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) = 23 ==> 27 x + 17 y = 23 x + 23 y ==> 4 x = 6 y ==> x/y = 3/2. #### B QUESTION:Find the average marks of all the students in 2 separate classes, if the average marks of students in the first class of 55 students is 60 and that of another class of 48 students is 58 options: A)55.1 B)51.1 C)53.1 D)52.1 E)59.1 SOLUTION:Sum of the marks for the class of 55 students = 55 * 60 = 3300 Sum of the marks for the class of 48 students = 48 * 58 = 2784 Sum of the marks for the class of 103 students = 3300 + 2784 = 6084 Average marks of all the students = 6084/103 = 59.1 Answer:E #### E QUESTION:Max scored 6 marks more than what he did in the previous examination in which he scored 30. Maria scored 30 marks more than she did in the previous examination in which she scored 60. Who showed less improvement? options: A)58% B)50% C)80% D)20% E)55% SOLUTION:Max percentage improvement in the first exam = (6/30 × 100) % = (600/30) % = 20 % Maria percentage improvement in the first exam = (30/60 × 100) % = (3000/60) % = 50 % Hence, 20 % < 50 % Therefore, Max showed less improvement. Answer:B #### B QUESTION:12 men complete a work in 9 days. After they have worked for 6 days, 6 more men joined them. How many days will they take to complete the remaining work? options: A)3days B)4days C)2days D)8days E)5days SOLUTION:1 man's 1 day work = 1/108 12 men's 6 days work = 6/9 = 2/3 remaining work = 1 – 2/3 = 1/3 18 men's 1 days work = 18/108 = 1/6 1/6 work is done by them in 1 day therefore, 1/3 work is done by them in 6/3 = 2 days. ANSWER C 2days #### C QUESTION:A 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. options: A)24 B)36 C)48 D)60 E)64 SOLUTION:The number of ways to choose three cities is 4C3=4. The number of itineraries for each group of 3 cities is 3!. So the number of itineraries to three cities is 4*3!=24. The number of ways to choose four cities is 4C4=1. The number of itineraries for the group of 4 cities is 4!. So the number of itineraries to four cities is 4!=24. The total number of itineraries is 24+24=48. The answer is C. #### C QUESTION:Jack 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? options: A)3/14 B)1/7 C)0 D)1/2 E)12/21 SOLUTION:METHOD-1 Probability that the number on first die is 7 = 0 Probability that the number on Second die is 7 = 1/7 [Because 1 out of 7 faces is 7] Probability that Both Dice result in odd numbers = (0)*(1/7) = 0 Answer: Option C #### C QUESTION:Two trains are running in opposite directions with the same speed. If the length of each train is 120 metres and they cross each other in 12 seconds, then the speed of each train (in km/hr) is: options: A)18 km/hr B)26 km/hr C)36 km/hr D)42 km/hr E)52 km/hr SOLUTION:Let the speed of each train be x m/sec. Then, relative speed of the two trains = 2x m/sec. So, 2x = (120 + 120)/12 --> 2x = 20 --> x = 10. --> Speed of each train = 10 m/sec = 10 x 18/5 km/hr = 36 km/hr. Answer : C. #### C QUESTION:The speed of a boat in still water is 50kmph and the speed of the current is 20kmph. Find the speed downstream and upstream? options: A)40, 68 kmph B)40, 30 kmph C)70, 30 kmph D)40, 60 kmph E)20, 60 kmph SOLUTION:Speed downstream = 50 + 20 = 70 kmph Speed upstream = 50 - 20 = 30 kmph Answer: C #### C QUESTION:One train is traveling 45 kmph and other is at 10 meters a second. Ratio of the speed of the two trains is? options: A)5:4 B)9:4 C)5:6 D)5:0 E)2:4 SOLUTION:Explanation: 45 * 5/18 = 10 25:20 => 5:4 Answer: Option A #### A QUESTION:The radius of a circular wheel is 1.75 m, how many revolutions will it make in traveling 1 km? options: A)1000 B)817 C)278 D)268 E)280 SOLUTION:2 * 22/7 * 1.75 * x = 11000 x = 1000 Answer: A #### A QUESTION:What least no. must be subtracted from 5026 so that remaining no.is divisible by 5? options: A)3 B)4 C)5 D)6 E)1 SOLUTION:Explanation: On dividing 5026 by 5 we get the remainder 1, so 1 should be subtracted Option E #### E QUESTION:The 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 options: A)34 B)35 C)56 D)67 E)23.57 SOLUTION:Let the side of the square be a cm. Parameter of the rectangle = 2(16 + 14) = 60 cm Parameter of the square = 60 cm i.e. 4a = 60 A = 15 Diameter of the semicircle = 15 cm Circimference of the semicircle = 1/2(∏)(15) = 1/2(22/7)(15) = 330/14 = 23.57 cm to two decimal places Answer: Option E #### E QUESTION:If x is to be chosen at random from the set {5,6,7,8} and y is to be chosen at random from the set {7,8,9}, what`s the probability that xy will be even? options: A)1/6 B)1/3 C)1/2 D)5/6 E)2/3 SOLUTION:The product to be even either one or both must be even, so: P(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; Or: 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. Answer: E. #### E QUESTION:Solve below question 2x + 1 = -17 options: A)-8 B)-9 C)9 D)8 E)-7 SOLUTION:1. Subtract 1 from both sides: 2x + 1 - 1 = -17 - 1 2. Simplify both sides: 2x = -18 3. Divide both sides by 2: 4. Simplify both sides: x = -9 B #### B QUESTION:If n = 3p, where p is a prime number greater than 2, how many different positiveevendivisors does n have, including n ? options: A) Two B) Three C) Four D) Six E) Eight SOLUTION:This 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: n = 4 x 3 n = 12 Next we have to determine all the factors, or divisors, of P. Remember the term factor is synonymous with the term divisor. 1, 12, 6, 2, 4, 3 From this we see that we have 4 even divisors: 12, 6, 2, and 4. If you are concerned that trying just one value of p might not substantiate the answer, try another value for p. Let’s say p = 5, so n = 4 x 5 n = 20 The 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. No matter what the value of p, as long as it is a prime number greater than 2, n will always have 4 even divisors. The answer is B. #### B QUESTION:Find 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.15of money? options: A)1500 B)1992 C)9921 D)2798 E)2789 SOLUTION:P = 15(100/10)2 => P = 1500 Answer: A #### A QUESTION:Two spherical balls lie on the ground touching. If one of the balls has a radius of 6 cm, and the point of contact is 8 cm above the ground, what is the radius of the other ball? options: A)12 cm B)16 cm C)18 cm D)20 cm E)none of the these SOLUTION:similar triangle properties.. 2/r+6 = 6/r-6 giving r = 12. Answer: A #### A QUESTION:If x, y, and z are consecutive positive integers greater than 1, not necessarily in that order, then which of the following is (are) true? I. x > z II. 4x+ 4y > 4z III. yz > xz IV. xy > y + z options: A) I only B) II only C) II and III only D) II and IV only E) III and IV only SOLUTION:we do not know the values or the relative values but that the three are consecutive.. so the max difference in any two number is 2 and min 1.. lets see the choices.. I. x > z... we do not know the values or the relative values... need not be true.. II. 4x+ 4y > 4z or x+ y > z we take the worst case that z is teh largest and x and y are lowest possible..... so 2+3>4.. 5>4.. always true III. yz > xz we do not know the values or the relative values between x and y..need not be true IV. xy > y + z xy-y>z or y(x-1)>z... again lets take the worst scenario.. we 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 only ii is true ans B #### B QUESTION:Based on this year's costs, an orcharde grower budgets P dollars for planing N new trees next year. If the average cost of planting each tree were to increase 50% from this year's cost, then the greatest number of trees that the orchard grower could plant next year using P dollars would be options: A)33% less than N B)25% less than N C)equal to N D)20% greater than N E)25% greater than SOLUTION:Correct answer is (A). This year, the price of a tree is price1=P/N. If this price increases by 50% it becomes price2=P/N*1.50 Then with P dollars, you can grow P/price2 tress i.e. P/(P/N*1.50) i.e. N/1.5 i.e. .67% less* A #### A <<<Examples ends QUESTION:A man can row with a speed of 20 kmph in still water. If the stream flows at 5 kmph, then the speed in downstream is? options: A)22 B)28 C)25 D)82 E)34 SOLUTION:M = 20 S = 5 DS = 20 + 5 = 20.Answer:C #### C

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:Bob bikes to school every day at a steady rate of e 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? options: A)(x + y) / t B)2(e + t) / ey C)2eyt / (e + y) D)2(e + y + t) / ey E)x(y + t) + y(x + t) SOLUTION:If we choose for d (distance): 10 miles, for e 10 and for y 5. t would be 90 minutes or 1,5 hours. If I try this for answer choice C it fits. #### C QUESTION:A train 120 m long running at 72 kmph crosses a platform in 25 sec. What is the length of the platform? options: A)443 m B)354 m C)450 m D)380 m E)250 m SOLUTION:D 350 D = 72 * 5/18 = 25 = 500 – 120 = 380 #### D QUESTION:A 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 50 hrs and a machine of type S does the same job in 20 hours. If the company used the same number of each type of machine to do the job in 5 hours, how many machines of type R were used? options: A)18/7 B)16/7 C)15/7 D)22/7 E)20/7 SOLUTION:Rate of machine R =1/50 Rate of machine S =1/20 since same no of machines used for R and S to do the same work in 5 hrs So collective rate needed to finish the work in 5 hrs= 1/5 Let the no of machine be x So, x/50 +x/20 =1/5 (2x+5x)/100=1/5 7x=20 x=20/7 So no of machine R is 20/7 Answer E #### E QUESTION:In 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 W percentage of those asked favoured more than one of the 3 proposals. options: A) 10 B) 12 C) 17 D) 22 E) 30 SOLUTION:Bunuel, my answer for exactly 2 people was 17 and this was my approach: 100%=(A+B+C)-(AnB+AnC+BnC)-5%+22% which leads me to W=100%=(50+30+20)-(at least 2 people)-5%+22%.C #### C QUESTION:Excluding stoppages, the speed of a train is 45 kmph and including stoppages it is 30 kmph. Of how many minutes does the train stop per hour? options: A)A)5 B)B)10 C)C)20 D)D)30 E)E)40 SOLUTION:Explanation: T = 15/45 * 60 = 20 Answer: Option C #### C QUESTION:In what time will a train 80 m long cross an electric pole, it its speed be 144 km/hr? options: A)2.0 sec B)2.8 sec C)7.5 sec D)2.3 sec E)1.5 sec SOLUTION:Speed = 144 * 5/18 = 40 m/sec Time taken = 80/40 = 2.0 sec. Answer:A #### A QUESTION:(128.5 x 32) + (13.8 x 30) = ? x 25 options: A)524.48 B)556.02 C)574.36 D)181.04 E)595.46 SOLUTION:Explanation : ? = (128.5 x 32) + (13.8 x 30)/25 = 4112 + 414/25 = 181.04 Answer : Option D #### D QUESTION:A desalination process is able to remove 2/3 of salt in each cycle. If we have 1 liter of sea water that has 5% salt (i.e. 5 g in a liter), how much salt would have been removed from the liter of water after 3 cycles of the desalination process? options: A)4.15 B)4.21 C)4.52 D)4.81 E)4.93 SOLUTION:X is the initial quantity of salt in the water. After a cycle of desalination the quantity of salt left would be X1=X-2/3X i.e. X1=1/3X Same thing for X2, X3 respectively representing the quantity of salt left after 2, 3 cycles of desalination. So we have: X1=1/3 X X2=1/3 X1 X3=1/3 X2 By multiplying both ends of the equations we get: X1*X2*X3 = (1/3)^3 X*X1*X2 Simplification leaves us with: X3 = (1/3)^3 X X3 is the quantity of salt left after three cycles. So the cumulative quantity of salt (Q3) which has been removed after 3 cycles is: Q3= X-X3=X-(1/3)^3 X i.e. Q3 = X (1-(1/3)^3) In this case, given X was: X=5 g So we have Q3=5 * (1-1/27) = 5 * 26/27 = 4.814 g rounded Q3=4.81 Answer: D #### D QUESTION:Two pipes can fill a tank in 14 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 ? options: A)5.5 Hours B)7.5 Hours C)8.5 Hours D)9.5 Hours E)6.5 Hours SOLUTION:In 1 hour it fill 1/14 + 1/12 - 1/20 = 2/19 So fill tank fill up in 19/2= 9.5 Hours ANSWER:D #### D QUESTION:Find the circumference and area of radius 13 cm. options: A)124 cm² B)531 cm² C)354 cm² D)584 cm² E)594 cm² SOLUTION:Area of circle = πr² = 22/7 × 13 × 13 cm² = 531 cm² ANSWER:B #### B QUESTION:A work could be completed in 100days by x workers. However, due to the absence of 10workers, it was completed in 110days. The original no.of workers was: options: A)90 B)100 C)110 D)130 E)140 SOLUTION:sax Letlheo g alnumberofworkers hex x workers can do the wor - 100 days (x — 10) workers can do the work in 110 days 4 100x 1u1x— 10) 1100 Q x 110 C #### C QUESTION:At a dinner party, 5 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 W of different possible seating arrangements for the group? options: A)5 B)10 C)24 D)32 E)120 SOLUTION:Circular arrangements= (n-1)! Hence (4!) = 24=W Answer is C #### C QUESTION:If 4,5qD + 8,737 = 13,qD3, where q and D are distinct digits, what is the value of D – q? options: A)6 B)4 C)3 D)2 E)1 SOLUTION:4500+10q+d+8737=13003+100q+10d 13237+10 q+d=13003+100q+10d 234=90q+9d 26=10 q+d d=6 ^ q=2 ==> d-q= 4 ANSWER B #### B QUESTION:Three bottles whose capacities are as 5 : 3 : 2 are completely filled with milk mixed with water. The ratio of milk to water in the mixture of bottles are as 3 : 2, 2 : 1 and 3 : 1 respectively. Find the percentage of water in the new mixture obtained when 1/3rd of first, 1/2 of second and 2/3rd of the third bottle is taken out and mixed together options: A)66.66% B)50% C)16.66% D)33.33% E)36.33% SOLUTION:Let the percentage of water be X The quantity of new mixture = (5X/3) + (3X/2 )+ (4X/3) = 27X/6 = 9X/2. Percentage of milk = (5X/3) x (3/5) + (3X/2) x (2/3) + (4X/3) x (3/4) = 3X Percentage of water = (5X/3) x (2/5) + (3X/2) x (1/3) + (X/2) x (2/3) = 3X/2 Percentage of water = (3X/2)/(9X/2) x 100 = 100/3 = 33 (1/3)% ANSWER:D #### D QUESTION:If 4 men and 1 boy working together, can do two 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? options: A)3:2 B)2:1 C)3:3 D)1:2 E)6:1 SOLUTION:4M + 1B =2(1M + 1B) 4M + 1B = 2M + 2B 2M = 1B The required ratio of work done by a man and a boy = 1:2 D #### D QUESTION:If 0.5% of A =85 paise, then the value of A is ? options: A)Rs. 170 B)Rs. 17 C)Rs. 1.70 D)Rs. 4.25 E)None SOLUTION:Answer ∵ 0.5/100 of A = 85/100 ∴ A = Rs. (85 / 0.5) = Rs. 170 Correct Option: A #### A QUESTION:The product of the squares of two positive integers is 900. How many pairs of positive integers satisfy this condition? options: A)0 B)1 C)2 D)3 E)4 SOLUTION:Ans: E - 4 pairs (xˆ2)(yˆ2) = 900 [square root both sides] xy = 30 20 = 1x30, 3x10, 6x5, 5x6, 10x3, 30x1, 15x2, 2x15 Cancel the repeats This leaves us with exactly 4 options. Hence, E #### E QUESTION:(3 x 10^2) + (2 x 10) + 4 = options: A)302400 B)32400 C)30240 D)3240 E)324 SOLUTION:When you multiply a number by 10 you just add a zero => 3 x 10^2 => add 2 zeros => 3 x 10^2 = 300 =>2 x 10 = 20 => 4 = 4 =>3 x 10^2 + 2 x 10 + 4 = 300 + 20 + 4 = 324 => answer is E ( 324) #### E QUESTION:Two numbers are respectively 20% and 50% more than a third number. The ratio of the two numbers is: options: A)4:5 B)3:5 C)6:8 D)3:5 E)5:4 SOLUTION:third number be x. first no = 120% of x = 6x/5 second no = 150% of x = 3x/2 ratio in first two nos = (6x/5:3x/2)=> 4:5 ANSWER A #### A QUESTION:A toy RC car goes 3 feet per second. A boy wants to add an updated part to his RC that will allow the RC car to travel at 6 feet per second. How far will the upgraded car travel in 1 minute? Round to the nearest hundredth. options: A)200 feet B)250 feet C)300 feet D)360 feet E)400 feet SOLUTION:6 feet per sec x 60= 360 feet Answer D #### D QUESTION:Mr. Das decided to walk down the escalator of a mall. He found that if he walks down 26 steps, he requires 30seconds to reach the bottom. However, if he steps down 34 stair she would only require 18 seconds to get to the bottom. If the time is measured from the moment the top step begins to descend to the time he steps off the last step at the bottom, find out the height of the stair way insteps? options: A)5 B)6 C)7 D)8 E)9 SOLUTION:here when he step down 26 steps he has 30 seconds for remaining steps. if he step down 34 stairs he has only 18 sec. 30-18=12 12 secs for 8 steps.. 18 secs for 12 steps. 12+34=46 so ans is 46.. ANSWER:B #### B QUESTION:Three walls have wallpaper covering a combined area of 280 square meters. By overlapping the wallpaper to cover a wall with an area of 180 square meters, the area that is covered by exactly two layers of wallpaper is 36 square meters. What is the area that is covered with three layers of wallpaper? options: A)5 Square Meters B)32 Square Meters C)42 Square Meters D)83.3 Square Meters E)120 Square Meters SOLUTION:280 - 180 = 100 sq m of the wallpaper overlaps (in either two layers or three layers) If 36 sq m has two layers, 100 - 36 = 64 sq m of the wallpaper overlaps in three layers. 64 sq m makes two extra layers hence the area over which it makes two extra layers is 32 sq m. Answer (B). #### B QUESTION:76^77 /7 remainder is ? options: A)5 B)6 C)7 D)8 E)9 SOLUTION:as, 4^3/3=64/3 remainder=1 and also 4/3=1 and 5^3/3 remainder=2 and also 5/3=2 so it does not matter on the power value so the answer will be 76/7 remainder=6 ANSWER:B #### B QUESTION:If 50 percent of the members of a certain organization are women and 5/8 of the members of the organization are married men, which of the following statements concerning the membership must be true? I. The number of women in the organization is greater than the number of married men in the organization. II. The number of women in the organization is greater than the number of unmarried men in the organization. III. The number of married men in the organization is greater than the number of unmarried men in the organization. options: A)I B)II C)III D)I,II & III E)I,II SOLUTION:5/10 (50%) of the members are women and 5/8 of the members are married men. Let the total numbers of members is 80 (the LCM of 10 and 8). Then there are: 5/10*80 = 40 women; 80 - 40 = 40 men; 5/8*40 = 25 married men; 40 - 25 = 15 unmarried men. So, option I,II is true. Answer: E #### E QUESTION:A car traveled 448 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? options: A)14 B)18 C)21 D)22 E)27 SOLUTION:Let the speed in highway be h mpg and in city be c mpg. h = c+6 h miles are covered in 1 gallon 462 miles will be covered in 462/h. Similarly c miles are covered in 1 gallon 336 miles will be covered in 336/c. Both should be same (as car's fuel capacity does not change with speed) => 336/c = 448/h => 336/c = 448/(c+6) => 336c+336*6=448c =>c=336*6/112=18 Answer B. #### B QUESTION:The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 10 and 12. The larger of the two numbers is: options: A)276 B)295 C)322 D)345 E)354 SOLUTION:Clearly, the numbers are (23 x 10) and (23 x 12). Larger number = (23 x 12) = 276. Answer: Option A #### A QUESTION:If A and B are two prime numbers bigger than 2, which of the following can't be true? (1) A + B is an even number. (2) A - B is also a Even number. (3) A^B is also a prime number. options: A)1 only. B)2 only. C)3 only. D)2 and 3 only. E)1, 2 and 3. SOLUTION:Answer is D : 2 and 3 only (1) A + B is an even number. : All primes beyond 2 are odd, so odd+odd = even, so true (2) A - B is also a Even number. : True (3) A^B is also a prime number. : Beats the property of primes, so false Ans : C #### C QUESTION:If (x-13)(x-3) < 0, which of the following must be true? options: A)x^2 + 5x + 6 < 0 B)x^2 + 5x + 6 > 0 C)5 - x < 0 D)x - 5 < 0 E)13 - x > 0 SOLUTION:(x-13)(x-3)<0 can be written as (13-x)(x-3)>0 So,to inequality hold true multiple of (13-x) and (x-3) must be positive and if I let both elements positive/negative then the range becomes 3<x<13 Answer Choice E matched which says 13-x>0 or x<13,which must be true (I started to look from E to A for making easy decision first) Correct Answer E #### E QUESTION:The average salary of all the workers in a workshop is Rs. 8000. The average salary of 7 technicians is Rs. 16000 and the average salary of the rest is Rs. 6000. The total number of workers in the workshop is options: A)20 B)21 C)22 D)35 E)NONE SOLUTION:Sol. Let the total number of workers be x. Then, 8000x = (16000 × 7) + 6000 ( x – 7) ‹=› 2000x = 70000 ‹=› x = 35. Answer D #### D QUESTION:Sreenivas 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. 2178? options: A)2277 B)2669 C)2200 D)2766 E)2998 SOLUTION:Let the cost price of table for Sreenivas be Rs. x and given that, cost price of table for Mahesh = Rs. 2178. => (90%) of (110%) of x = Rs. 2178. => (90/100)(110/100)x = 2178 => x = (2178 * 100)/(9 * 11) => x = Rs. 2200 Answer: C #### C QUESTION:The mean of 50 observations was 36. It was found later that an observation 48 was wrongly taken as 23. The corrected new mean is? options: A)36.7 B)36.1 C)36.5 D)36.9 E)36.3 SOLUTION:Correct sum = (36 * 50 + 48 - 23) = 1825. Correct mean = 1825/50 = 36.5 Answer:C #### C QUESTION:Katie has 9 employees that she must assign to 3 different projects. If 3 employees are assigned to each project and no one is assigned to multiple projects, how many different combinations X of project assignments are possible? options: A)252 B)1,680 C)2,340 D)362,880 E)592,704 SOLUTION:The ways to select three employees out of 9 for first project = 9C3 The ways to select three employees out of Remaining 6 for Second project = 6C3 Third Project already has the group of three to be assigned to it so need to select that So total ways to assign 3 employees to each of 3 projects X= 9C3 * 6C3 * 1 = 1,680 Answer: Option B #### B QUESTION:A man can swim in still water at 7.5 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is? options: A)1.7 B)1.4 C)1.1 D)1.5 E)2.5 SOLUTION:M = 7.5 S = x DS = 7.5 + x US = 7.5 + x 7.5 + x = (7.5 - x)2 7.5 + x = 15 -2x 3x = 7.5 x = 2.5 Answer:E #### E QUESTION:In a certain company, a third of the workers do not have a retirement plan. 40% of the workers who do not have a retirement plan are women, and 40% of the workers who do have a retirement plan are men. If 120 of the workers of that company are men, how many of the workers are women? options: A)80 B)95 C)105 D)120 E)137 SOLUTION:Set up equation: x = total number of workers 120 = 0,4 * 2/3 * x + 0,6 * 1/3 * x 120 = 14/30 x x = 257 257 - 120 = 137 Answer E #### E QUESTION:A train ,135 meters long travels at a speed of 45 km/hr crosses a bridge in 30 seconds. The length of the bridge is options: A)270 m B)245 m C)235 m D)220 m E)240 m SOLUTION:Explanation: Assume the length of the bridge = x meter Total distance covered = 135+x meter total time taken = 30s speed = Total distance covered /total time taken = (135+x)/30 m/s => 45 × (10/36) = (135+x)/30 => 45 × 10 × 30 /36 = 135+x => 45 × 10 × 10 / 12 = 135+x => 15 × 10 × 10 / 4 = 135+x => 15 × 25 = 135+x = 375 => x = 375-135 =240 Answer: Option E #### E QUESTION:How 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? options: A)5040 B)40 C)400 D)5000 E)6000 SOLUTION:LOGARITHM => 10 diff letters req no of words = No of arrangements of 10 letters taking 4 at a time => 10P4 = (10*9*8*7) ==> 5040 ANSWER A #### A QUESTION:From the set of numbers x, y, t, z, p, q and w, how many different combinations can we have without the t and w in them? Ex:. (x,y), (x), (p,q,z,y,x), etc and (x,y)=(y,x) options: A)10 B)14 C)15 D)16 E)30 SOLUTION:Another way: Any letter (x, y, z, p, q) can be included or not. So, we have 2^5 combinations - 2 empty combinations = 30 combinations E #### E QUESTION:Equal weights of two alloys containing tin, copper and lead in the ratio 6:8:7 and 1:2:4 are melted and mixed together. What is the ratio of tin, copper and lead in the resultant alloy? options: A)11:8:3 B)3:1:8 C)17:28:27 D)9:4: 11 E)9:14: 11 SOLUTION:Let the weight of the two alloys be w each Required ratio = (6w/21+1w/7): (8w/21+2w/7 ): (7w/21+4w/7) = 9w/21 : 14w/21 : 11w/21 = 9:14: 11 ANSWER:E #### E QUESTION:A horse is tethered to one corner of a rectangular grassy field 36 m by 20 m with a rope 12 m long. Over how much area of the field can it graze? options: A)154 cm2 B)113 m2 C)123 m2 D)115 m2 E)None of these SOLUTION:Area of the shaded portion = 1⁄4 × π × (12)2 = 113 m2 Answer B #### B QUESTION:A certain ski shop sells pairs of gloves in 11 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? options: A)1/144 B)1/143 C)1/21 D)1/23 E)1/12 SOLUTION:there are 11 different colours sothere are 11 pairs of gloves dropped.. first can be any of 22..so 22/22.. second has to be its pair, which will be just one out of remaining 21.. 1/21.. overall prob=22/22*1/21= 1/21.. C #### C QUESTION:There are 200 cats in Cat-City. Out of the 200, 70 are street cats and the rest are domestic cats. 110 cats are gray, 25 out of the gray cats are NOT domestic ones. How many domestic cats are there which are not gray in Cat-City? options: A)90. B)45. C)50. D)40. E)25. SOLUTION:STREET-CAT DOMESTIC-Cat 70 130 (25gray+45other) 85gray+45other Answer:B #### B QUESTION:What is the sum of all remainders obtained when the first 120 natural numbers are divided by 9? options: A)397 B)401 C)403 D)405 E)399 SOLUTION:A positive integer can give only the following 9 remainders when divided by 9: 1, 2, 3, 4, 5, 6, 7, 8, and 0. 1 divided by 9 gives the remainder of 1; 2 divided by 9 gives the remainder of 2; ... 8 divided by 9 gives the remainder of 8; 9 divided by 9 gives the remainder of 0. We'll have 11 such blocks, since 99/9=11. The last will be: 91 divided by 9 gives the remainder of 1; 92 divided by 9 gives the remainder of 2; ... 98 divided by 9 gives the remainder of 8; 99 divided by 9 gives the remainder of 0. The last number, 100, gives the remainder of 1 when divided by 9, thus the sum of all remainders will be: 11(1+2+3+4+5+6+7+8+0)+1=405. Answer: D. #### D QUESTION:The ratio 3 : 5 expressed as a percent equals options: A)60% B)40% C)80% D)125% E)None SOLUTION:Solution 3 : 5 = 3/ 5 = (3 / 5 x 100)%. = 60 %. Answer A #### A QUESTION:A group of people,dogs, and birds has seventy legs, thirty heads, and twenty tails. How many cats are among this group? (Assume all birds have two legs and a tail.) options: A)0 B)5 C)13 D)15 E)20 SOLUTION:Write P, C, and B for the number of people, dogs, and birds respectively, so that we have 2P + 4C + 2B = 70, P + C + B = 30,C + B = 20: Comparing the last two equations we obtain P = 10, and the first equation simplifies to 4C + 2B = 50, or 2C + B = 25. Therefore, C = (2C + B) -(C + B) = 25- 5 = 5 correct answer B #### B QUESTION:2. The value of x + x(xx) when x = 2 is: options: A)5 B)10 C)8 D)15 E)20 SOLUTION:x + x(xx) Put the value of x = 2 in the above expression we get, 2 + 2(22) = 2 + 2(2 × 2) = 2 + 2(4) = 2 + 8 = 10 Answer : B #### B QUESTION:A 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: options: A)45 km/hr B)50 km/hr C)54 km/hr D)55 km/hr E)58 km/hr SOLUTION:Speed of the train relative to man = 125/10 m/sec = 25/2 m/sec. 2 = 25/2 x 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. Option B #### B QUESTION:A 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? options: A)230 B)288 C)267 D)256 E)298 SOLUTION:Relative speed = 120 + 80 = 200 km/hr. = 200 * 5/18 = 500/9 m/sec. Let the length of the other train be x m. Then, (x + 270)/9 = 500/9 => x = 230. Answer: A #### A QUESTION:The number of arrangements that can be made with the letters of the word MEADOWS so that the vowels occupy the even places? options: A)1178 B)144 C)66 D)8 E)55 SOLUTION:The word MEADOWS has 7 letters of which 3 are vowels. -V-V-V- As 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. Hence the total ways are 24 * 6 = 144. Answer: B #### B QUESTION:How many seconds will a 500 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? options: A)200 B)300 C)500 D)600 E)700 SOLUTION:Let length of tunnel is x meter Distance = 800+x meter Time = 1 minute = 60 seconds Speed = 78 km/hr = 78*5/18 m/s = 65/3 m/s Distance = Speed*Time 800+x = (65/3) * 60 800+x = 20 * 65 = 1300 x = 1300 - 800 = 500 meters Answer: Option C #### C QUESTION:The number of arrangements that can be made with the letters of the word LUCK so that the vowels occupy the even places? options: A)5 B)3 C)6 D)1 E)2 SOLUTION:The word MEADOWS has 7 letters of which 3 are vowels. -V-V-V- As the vowels have to occupy even places, they can be arranged in the 1 even places in 1! i.e., 1 ways. While the consonants can be arranged among themselves in the remaining 3 places in 3! i.e., 6 ways. Hence the total ways are 1 * 6 = 6. Answer:C #### C QUESTION:The number of students in 3 classes is in the ratio 2:3:4. If 12 students are increased in each class this ratio changes to 8:11:14. The total number of students in the three classes in the beginning was options: A)162 B)108 C)96 D)54 E)None SOLUTION:Solution: Let the number of students in the classes be 2x, 3x and 4x respectively; Total students = 2x+3x+4x = 9x. According to the question, (2x+12)/(3x+12) = 8/11 24x+96 = 22x+132 Or, 2x = 132-96 Or, x = 36/2 = 18 Hence, Original number of students, 9x = 9*18 = 162. Answer: Option A #### A QUESTION:A triangle and a parallelogram are constructed on the same base such that their areas are equal. If the altitude of the parallelogram is 100 m , then the altitude of the triangle is options: A)10√2 m B)100 m C)100√2 m D)200 m E)None SOLUTION:Solution Let the altitude of the triangle be hïand base of each be b. Then , (½ ×b× h1) where h2 = 100 m. = h1 = 2h2 = ( 2 x 100) m = 200 m. Answer D #### D QUESTION:The speeds of three motor bikes are in the ratio 12 : 4 : 2. The ratio between the time taken by them to travel the same distance is : options: A)1 : 3 : 4 B)1 : 3 : 6 C)1 : 2 : 6 D)1 : 3 : 5 E)1 : 4 : 6 SOLUTION:Ratio of time taken : 1/12 :1/4 : 1/2 = 1 : 3 : 6 ANSWER:B #### B QUESTION:A and B invest in a business in the ratio 3: 2. Assume that 5% of the total profit goes to charity. If A's share is Rs. 855, what is the total profit? options: A)1500 B)2000 C)3000 D)3500 E)2500 SOLUTION:Profit as x since 5% and 95% of x will be divided b/w A and B ration 3:2 =>profit 95x/100 * 3/5 given that A's share is Rs 855 => 95x/100 * 3/5 = 855 hence x = 1500 ANSWER A #### A QUESTION:There are cats got together and decided to kill the mice of 999919. Each cat kills equal number of mice and each cat kills more number of mice than cats there were. Then what are the number of cats? options: A)941,1009 B)991,1001 C)991,1009 D)791,1009 E)931,1009 SOLUTION:999919 can be written as 1000000 – 81 = 10002 – 92 ie of the form a2-b2=(a+b)(a-b) =(1000+9)*(1000-9) = (1009)*(991) Given that number of cats is less than number if mice. So number of cats is 991 and number of mice were 1009 Answer C #### C QUESTION:A mixture contains milk and water in the ratio 6:3. On adding 10 litters of water, the ratio of milk to water becomes 6:5. The quantity of milk in the original mixture is? options: A)90 B)45 C)110 D)40 E)50 SOLUTION:Explanation: milk:water = 6:3 6x : 3x + 10 = 6 : 5 5[6x] = 6[3x + 10] 30x = 18x + 60 30x - 18x = 60 12x = 60 x = 5 The quantity of milk in the original mixture is = 6 : 3 = 6 + 3 = 9 9x = 45 Short cut method - 2 : for Only milk problems milk : water 6 : 3 6 : 5 milk ratio same but water ratio 2 part incress per 10 liters 2 part of ratio -------> 10 liters 9part of ratio -------> 45 liters Answer: Option B #### B QUESTION: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 6%. What was its profit on the items sold in February? options: A)27.5% B)30% C)35% D)37.5% E)41% SOLUTION:Assume the total price = 100x Price after 20% markup = 120x Price after 25%further markup = 1.25*120x = 150x Price after the discount = 0.94*150x = 141x Hence total profit = 41% Option E #### E QUESTION:what is the sum of all 5 digits numbers which can be formed with the digits 0,1,2,3,4 without repetition options: A)2599980 B)2699980 C)2799980 D)2509980 E)2499980 SOLUTION:There is a simplest formula for solving these type of questions when we are using numbers along with 0 for finding sum. i,e........(sum of numbers)*{(n-1)!*(111...........n times)-(n-2)!*(111..........(n-1)times) } so,here by putting the values as, (0+1+2+3+4){(5-1)!*(11111)-(5-2)!*1111} = 10{(4!*11111)-(3!*1111)} = 10{266664-6666} = 2599980 ANSWER:A #### A QUESTION:If f(x) = 6x − √x and g(x) = x^2, what is f(g(4))? options: A)-4 B)8 C)16 D)32 E)92 SOLUTION:g(x) = x² g(4) = 4² = 16 So, f(g(4)) = f(16) f(x) = 6x − √x So, f(16) = 6(16) − √16 = 96 - 4 = 92 = E #### E QUESTION:In a game of 90 points, A can give B 5 points and C 15 points. then how many points B can give C in a game of 60? options: A)2.82 B)7.82 C)5.82 D)12.82 E)8.82 SOLUTION:In a game of 90 points,A give B 5 points and c 25 points means B=85,C=65 In 85 points B give 15 since 80-65=15 In 50 points B gives=50*15/85=8.82 ANSWER:E #### E QUESTION:In 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 $841,000 invested in preferred stocks, what is the total amount of money invested in the fund? options: A)$1,974,000 B)$2,538,000 C)$3,264,000 D)$3,826,000 E)$4,205,000 SOLUTION:Portion invested in preferred stock = 3/5 * 1/3 = 1/5 1/5 of fund = 841--- Fund = 5 * 841--- Here, we can avoid the math and simply look at 5 * 1 -> 5. Only option E has 5 in it. Answer (E). #### E QUESTION:Find the value of 1/(3+1/(3+1/(3-1/3))) options: A)21/89 B)89/27 C)27/89 D)1/14 E)1/56 SOLUTION:1/[3 + (1/(3+1/(3 - 1/3)))] => 1/[3 + 1/(3 + 1/(8/3))] => 1/[3 + 1/(3 + 3/8)] => 1/[3 + 8/27] => 1/(89/27) => 27/89 C #### C QUESTION:The largest 4 digit number exactly divisible by 44 is? options: A)9988 B)9939 C)9944 D)9954 E)9960 SOLUTION:Largest 4-digit number = 9999 44) 9999 (227 9988 Largest number : 9988 Answer : A #### A QUESTION:9823 + x = 13200, then x is ? options: A)3327 B)3237 C)3337 D)3377 E)None of these SOLUTION:Answer x = 13200 - 9823 = 3377 Option: D #### D <<<Examples ends QUESTION:Two 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? options: A)Rs. 13.50 B)Rs. 16.54 C)Rs. 16.80 D)Rs. 16.50 E)Rs. 16.00 SOLUTION:Explanation: Let the quantities of A and B mixed be 3x kg and 7x kg. Cost of 3x kg of A = 9(3x) = Rs. 27x Cost of 7x kg of B = 15(7x) = Rs. 105x Cost of 10x kg of the mixture = 27x + 105x = Rs. 132x Cost of 5 kg of the mixture = 132x/10x (5) = Rs. 66 Profit made in selling 5 kg of the mixture = 25/100 (cost of 5 kg of the mixture) = 25/100 * 66 = Rs. 16.50 Answer: Option D #### D

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:2+2^2+2^+......+2^9=? options: A)2044 B)1022 C)1056 D)1065 E)None of them SOLUTION:This is a G.P. in which a=2, r=2^2/2=2 and n=9 S^n=a(r^n -1)/(r-1) =2x(2^9-1)/(2-1) =2x(512-1)=2x511 =1022 Answer is B #### B QUESTION:A number whose fifth part increased by 4 is equal to its fourth part diminished by 4 is ? options: A)160 B)180 C)200 D)220 E)None SOLUTION:Answer Let the number be N. Then, (N/5) + 4 = (N/4) - 4 ⇒ (N/4) - (N/5) = 8 ⇒ (5N - 4N)/20 = 8 ∴ N = 160 Option: A #### A QUESTION:The average of 35 students in a class is 17 years. The average age of 25 students is 15. What is the average age of remaining 10 students? options: A)26 years B)27 years C)28 years D)29 years E)30 years SOLUTION:Sum of the ages of 14 students = (17 * 35) - (15 * 21) = 595 - 315 = 280 Required average = (280/10) = 28 years. Answer:C #### C QUESTION:In power plant, If 36 men can do a piece of work in 25 hours, in how many hours will 15 men do it ? options: A)40 hours B)50 hours C)60 hours D)70 hours E)None of these SOLUTION:Explanation : Let the required number of hours be x. Then, Less men, More hours (Indirect Proportion) 15 : 36 : : 25 : x => (15 * x) = (36 * 25) x=(36 x 25)/15 = 60 Hence, 15 men can do it in 60 hours. Answer : C #### C QUESTION:In order to fulfill a local school’s request for x cakes, B parents agreed to each bake an equal number of cakes. If p of the parents did not bake any cakes, which of the following represents the additional number of cakes that each of the other parents had to bake in order for the school’s request for x cakes to be fulfilled? options: A)px/B B)px/(B(B - P)) C)x/(B - P) D)p/(B - Px) E)p/(B(B - p)) SOLUTION:No of cakes each parent has to bake : x/B No of parents did not bake cake = p No of cakes that were not baked by p parents = p*x/B No of parents has to bake additional cakes = B-p additional number of cakes that each of the other parents had to bake in order for the school’s request for x cakes = px/(B(B - P)) Answer B #### B QUESTION:A carpenter makes 4 bunk beds every day. A military school needs to organize a place to sleep for 143 soldiers. If there are 5 carpenters working on the job, how many whole days in advance should they receive the order and start working in order to finish the right number of beds assuming that each bunk- bed is used by two soldiers? options: A)3. B)4. C)5. D)6. E)7. SOLUTION:I believe it is C because if 1C makes 3 beds in 1 day then: 1C's rate = 3/1 So 5c's = 3/1 * 5 = 15/1 = 15 beds in a day. Since we have 173 soldiers who need beds and bunk beds come in pairs, 72 is the least amount of beds needed. Time = Amount / Rate Time = 72 / (15/1) = 72/15, simplifying we get 72/15 = 24/5 = 4.7 So, in order for the carpenters to be able to finish they need 5 whole days. At first I made the mistake of thinking how many whole days it took them to finish (as in ignore the partial day) but the prompt clarifiesdays in advance, meaning how many days would they need to finish so even if they finish early, theyusedthat day. C #### C QUESTION:A 20 litre mixture of milk and water contains milk and water in the ratio 3 : 2. 10 litres of the mixture is removed and replaced with pure milk and the operation is repeated once more. At the end of the two removal and replacement, what is the ratio E of milk and water in the resultant mixture? options: A)17 : 3 B)9 : 1 C)3 : 17 D)5 : 3 E)11: 2 SOLUTION:he 20 litre mixture contains milk and water in the ratio of 3 : 2. Therefore, there will be 12 litres of milk in the mixture and 8 litres of water in the mixture. Step 1. When 10 litres of the mixture is removed, 6 litres of milk is removed and 4 litres of water is removed. Therefore, there will be 6 litres of milk and 4 litres of water left in the container. It is then replaced with pure milk of 10 litres. Now the container will have 16 litres of milk and 4 litres of water. Step 2. When 10 litres of the new mixture is removed, 8 litres of milk and 2 litres of water is removed. The container will have 8 litres of milk and 2 litres of water in it. Now 10 litres of pure milk is added. Therefore, the container will have 18 litres of milk and 2 litres of water in it at the end of the second step. Therefore, the ratio of milk and water is 18 : 2 or 9 : 1. Shortcut. We are essentially replacing water in the mixture with pure milk. Let W_o be the amount of water in the mixture originally = 8 litres. Let W_r be the amount of water in the mixture after the replacements have taken place. Then,{W_r}/{W_o}= (1-R/M)^n where R is the amount of the mixture replaced by milk in each of the steps, M is the total volume of the mixture and n is the number of times the cycle is repeated. Hence, {W_r}/{W_o} =(1/2)^2  =1/4 Therefore E,W_r ={W_o}/4= 8/4 = 2 litres.B #### B QUESTION:Find the value of (2 − 1/3) (1 − 1/4)(1 − 1/5)……… (1 − 1/99)(1 − 1/100) options: A)1/15 B)1/17 C)1/20 D)1/21 E)3/25 SOLUTION:Option 'C' (2 − 1/3) (1 − 1/4)(1 − 1/5)..... (1 − 1/99)(1 − 1/100) 5/3 × 3/4 × 4/5 × ....... 98/99 × 99/100 = 5/100 = 1/20 #### C QUESTION:If 13 = 13w/(1-w) ,then (4w)2 = options: A)1/4 B)1/2 C)1 D)2 E)4 SOLUTION:13-13w=13w 26w=13 w=1/2 4w=2 4w*2=2*2=4 ANSWER:E #### E QUESTION:Vijay bought 160 shirts at the rate of Rs. 255 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%? options: A)Rs. 321 B)Rs. 270 C)Rs. 277.5 D)Rs. 285 E)None of these SOLUTION:Total CP per shirt = 255 + 1400/160 + 1.75 + 320/160 = Rs. 267.5 SP = CP[(100 + profit%)/100] = 267.5 * [(100 + 20)/100] = Rs. 321. ANSWER:A #### A QUESTION:Mahesh marks an article 15% above the cost price of Rs. 540. What must be his discount percentage if he sells it at Rs. 496.80? options: A)18% B)21% C)20% D)19% E)None of these SOLUTION:CP = Rs. 540, MP = 540 + 15% of 540 = Rs. 621 SP = Rs. 496.80, Discount = 621 - 496.80 = 124.20 Discount % = 124.2/621 * 100 = 20% ANSWER:C #### C QUESTION:Out of four consonants and three vowels, how many words can be made so that each word contains two consonants and three vowels? options: A)480 B)540 C)600 D)720 E)900 SOLUTION:4C2 x 3C3 x 5! = 720 The answer is D. #### D QUESTION:A 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? options: A)615 m B)240 m C)168 m D)197 m E)691 m SOLUTION:Speed = 54 * 5/18 = 15 m/sec. Length of the train = 15 * 20 = 300 m. Let the length of the platform be x m . Then, (x + 300)/36 = 15 => x = 240 m Answer: B #### B QUESTION:As they say, beggars can't be choosers, in fact begger take what they can get. A begger on the street can make one cigarette out of every 6 cigarette butts he finds. After one whole day of searching and checking public ashtrays the begger finds a total of 72 cigarette butts. How many cigarettes can he make and smoke from the butts he found? options: A)14 B)18 C)15 D)10 E)20 SOLUTION:E 20 If the beggar can make a whole cigarette from 6 butts then he can make 12 cigarettes from the 72 he found. Once he smokes those, he then will have another 12 butts, which gives him enough to make another 2 cigarettes. A total of 14. #### A QUESTION:In measuring the sides of a rectangle, one side is taken 16% in excess and other 5% in deficit. Find the error percentage in the area calculated from these measurements. options: A)3.5% B)2.4% C)10.2% D)5% E)2.6% SOLUTION:Say both sides of the rectangle are equal to 100 (so consider that we have a square). In this case the area is 100*100=10,000. Now, the area obtained with wrong measurements would be 116*95=11,020, which is 10.2% greater than the actual area. Answer: C. #### C QUESTION:In 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? options: A)1, 2, 5 B)3, 4, 5 C)4, 5, 6 D)7, 8, 9 E)5, 2, 4 SOLUTION:XY=3 YZ=1+XY = 4 XZ=1+YZ=5 B is the correct option. #### B QUESTION:A rainstorm increased the amount of water stored in State J reservoirs from 160 billion gallons to 200 billion gallons. If the storm increased the amount of water in the reservoirs to 50 percent of total capacity, approximately how many billion gallons of water were the reservoirs short of total capacity prior to the storm? options: A)240 B)250 C)260 D)270 E)300 SOLUTION:Let total capacity be x we know 200 = 0.50x x = 200/0.50 = 400 Prior to storm, we had 160 bn gallons 400-160 = 240 Answer : A #### A QUESTION:A 180 meter long train crosses a man standing on the platform in 9 sec. What is the speed of the train? options: A)72 B)108 C)1266 D)188 E)211 SOLUTION:S = 180/9 * 18/5 = 72 kmph Answer: A #### A QUESTION:The average of a batsman for 40 innings is 50 runs. His highest score exceeds his lowest score by 172 runs. If these two innings are excluded, his average drops by 2 runs. Find his highest score. options: A)172 B)173 C)174 D)175 E)None of the above SOLUTION:Total runs = 40 × 50 = 2000 Let his highest score be = x Then his lowest score = x – 172 Now 200−x−(x−172)/38=48 ⇒ 2x = 2172 – 1824 ⇒ x = 174 Answer C #### C QUESTION:If 0.75: x :: 5:9, then x is equal to: options: A)1.12 B)1.16 C)1.2 D)1.35 E)None of these SOLUTION:Explanation: (x * 5) = (0.75 *9) X=6.75/5 = 1.35 Answer: D #### D QUESTION:The length of the bridge, which a train 130 meters long and travelling at 45 km/hr can cross in 30 seconds, is? options: A)265 m B)755 m C)245 m D)127 m E)156 m SOLUTION:Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time = 30 sec. Let the length of bridge be x meters. Then, (130 + X)/30 = 25/2 ==> 2(130 + X) = 750 ==> X = 245 m. Answer:C #### C QUESTION:If sequence T is defined for all positive integers n such that t(n +1) = t(n) + n, and t 3 = 14, what is t 24? options: A)101 B)187 C)191 D)201 E)287 SOLUTION:here is my way of solving this : tn +1 = tn + n, t 3 = 14 so: t 4 = t 3 + 3 t 5 = t 4 + 4, so we replace t 4 with the previous result : t 5 = (t 3 + 3 ) + 4 .... so we get t 24 = t 3 + 3 + 4 + 5 + 6....+ 23 the 3 + 4 + 5 + ... + 23 sequence is equal the sequence 1 + 2 + ... + 23, minus 1 + 2 at the beginning (so, minus 3) and the 1 + 2 ... + 23 sequence is equal to n*(n+1)/2 with n being 23, so equal to 23 * 24 / 2 = 276 so : t 20 = t 3 + 276 - 3 t 20 = 14 + 276 - 3 = 276 + 11 = 287, hence answer E #### E QUESTION:A and B together do a work in 20 days.B and C together in 15 days and C and A in 12 days.so A,B and C together finish same work in how many days? options: A)12 B)15 C)8 D)10 E)11 SOLUTION:(A+B) work in 1 day= 1/20,(B+C) work in 1 days = 1/15.,(C+A) work in 1 days=1/12 (1) adding=2[A+B+C] in 1 day work = [1/20+1/15+1/12]=1/5 (A+B+C) work in 1 day= 1/10 So,all three together finish work in 10 days Answer D #### D QUESTION:If a is Negative integers and b is positive integers and a ≠ 0 which of the following equal 0 ? options: A)a-b B)a^2+b^2 C)a*b D)a/b E)a^2-b^2 SOLUTION:All options Except E gives Non-zero answer. a should be negative integers and b should be an positive integers. (E)a^2-b^2 If b=0,a^2-b^2=a^2. a is negative integers. Any square of the negative integers gives us a positive numbers. So The option E is answer #### E QUESTION:A large box contains 19 small boxes and each small box contains 25 chocolate bars. How many chocolate bars are in the large box? options: A)475 B)350 C)450 D)550 E)650 SOLUTION:The number of chocolate bars is equal to 19 * 25 = 475 correct answer A #### A QUESTION:A sum of 11,500 amounts to 13,500 in 5 years at the rate of simple interest. What is the rate of interest? options: A)2% B)3% C)6% D)5% E)8% SOLUTION:B 3% S.I. = (13500 - 11500) = 2000. Rate = (100 x 2000)/(11500x5)% = 3% #### B QUESTION:In a tree, 3/7 of the birds are parrots while the rest are toucans. If 2/3 of the parrots are female and 7/10 of the toucans are female, what fraction of the birds in the tree are male? options: A)3/7 B)11/35 C)16/35 D)31/70 E)37/70 SOLUTION:Let x be the number of birds in the tree. The fraction of birds that are male parrots is (1/3)(3/7)=1/7. The fraction of birds that are male toucans is (3/10)(4/7)=6/35. The total fraction of male birds is 1/7 + 6/35 = 11/35. The answer is B. #### B QUESTION:A 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? options: A)19 cm2 B)30 cm2 C)17 cm2 D)18 cm2 E)12 cm2 SOLUTION:The circumference of the circle is equal to the permeter of the rectangle. Let l = 6x and b = 5x 2(6x + 5x) = 2 * 22/7 * 3.5 => x = 1 Therefore l = 6 cm and b = 5 cm Area of the rectangle = 6 * 5 = 30 cm2 Answer:B #### B QUESTION:The H.C.F of two numbers is 8. Which of the following can never be their L.C.M? options: A)55 B)44 C)66 D)60 E)12 SOLUTION:H.C.F of two numbers divides their L.C.M exactly. Clearly, 8 is not a factor of 60. Answer:D #### D QUESTION:If it takes a machine 1⁄3 minute to produce one item, how many items will it produce in 2 hours? options: A)1⁄3 B)4⁄3 C)80 D)120 E)360 SOLUTION:1 item takes 1/3 min so it takes 120 min to produce x x/3=120 the x=360 Answer:E #### E QUESTION:A paint store mixes 3/4 pint of red paint and 2/3 pint of white paint to make a new paint color called Perfect Pink. How many pints of red paint would be needed to make 40 pints of Perfect Pink paint? options: A)9 B)16 C)21 D)25 1/3 E)28 1/2 SOLUTION:3/4 pint is required to make 3/4 + 2/3 = 17/12 pint of perfect pink so 17/12 pint requires 3/4 pint of red.. 1 pint will require 3/4 * 12/17=9/17.. 40 pints will require 9/17 * 40= 21 pints.. C #### C QUESTION:A train 120 m long running at 60 kmph crosses a platform in 20 sec. What is the length of the platform? options: A)213 B)298 C)350 D)726 E)267 SOLUTION:D = 60 * 5/18 = 20 = 333 – 120 = 213 Answer: A #### A QUESTION:If 5a + 7b = n, where a and b are positive integers, what is the largest possible value of n for which exactly one pair of integers (a, b) makes the equation true? options: A)35 B)48 C)69 D)70 E)74 SOLUTION:5*a1 + 7*b1 = n 5*a2 + 7*b2 = n 5*(a1 - a2) = 7*(b2 - b1) since we are dealing with integers we can assume that a1 - a2 = 7*q and b2 - b1 = 5*q where q is integer, so whenever we get a pair for (a;b) we can find another one by simply adding 7 to a and subtracting 5 from b or vice versa, subtracting 7 from a and adding 5 to b. Lets check how it works for our numbers, starting from the largest: E)74 = 5*12 + 7*2 (a1 = 12, b1 = 2), subtract 7 fromaand add 5 tobrespectively, so a2 = 5 and b2 = 7, second pair - bad D)70 = 5*7 + 7*5 (a1 = 7, b1 = 5), if we add 7 to a we will have to subtract 5 from b but b can't be 0, so - no pair, if we subtract 7 from a, we'll get a = 0 which also isn't allowed - no pair, thus this is the only pair for (a;b) that works,good!, thus D is the answer #### D QUESTION:The basic one-way air fare for a child aged between 3 and 10 years costs half the regular fare for an adult plus a reservation charge that is the same on the child's ticket as on the adult's ticket. One reserved ticket for an adult costs $216 and the cost of a reserved ticket for an adult and a child (aged between 3 and 10) costs $327. What is the basic fare for the journey for an adult? options: A)$111 B)$52.5 C)$210 D)$58.5 E)$6 SOLUTION:Explanatory Answer Step 1: Assign variables and frame equations Let the basic fare for the child be $X. Basic one-way air fare of a child costs half the regular fare for an adult Therefore, the basic fare for an adult = 2(basic one-way airfare for a child) = $2X. Reservation charge is the same on the child's ticket as on the adult's ticket. Let the reservation charge per ticket be $Y Hence, an adult ticket will cost (Basic fare + Reservation charges) = 2X + Y = $216 ..... (1) And ticket for an adult and a child will cost (2X + Y) + (X + Y) = 3X + 2Y = $327 .... (2) Step 2: Solve the equations and determine basic fare for an adult Multiply equation (1) by 2: 4X + 2Y = 432 .... (3) Subtract equation (2) from equation (3): (4X + 2Y = 432) - (3X + 2Y = 327) ∴ X = $105. The basic fare of an adult ticket = 2X = 2*105 = $210 Answer C #### C QUESTION:A 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? options: A)12 days B)18 days C)15 days D)21 days E)22 days SOLUTION:Explanation: A and B can do work 1/6 in 1 day A alone can do 1/10 work in 1 day B alone can do (1/6 -1/10) =1/15 work in 1 day => complete work can be done in 15 days by B Answer: Option C #### C QUESTION:If Z = 52 and ACT = 48, then BAT will be equal to options: A)33 B)88 C)77 D)46 E)99 SOLUTION:Explanation: In the given code, A = 2, B = 4, C = 6,.... , Z = 52. So, ACT = 2 + 6 + 40 = 48 and BAT = 4 + 2 + 40 = 46 Answer: D) 46 #### D QUESTION:The population of a town is 8100. It decreases annually at the rate of 10% p.a. What was its population 2 years ago? options: A)9000 B)8000 C)8500 D)9500 E)10000 SOLUTION:Formula : ( After =100 denominator Ago = 100 numerator) 8100 × 100/90 × 100/90 = 10000 E) #### E QUESTION:A 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? options: A)0.07 B)0.049 C)0.7 D)0.49 E)4.9 SOLUTION:The volume of oil pumped to the tank = The volume of oil taken away from stationary cylinder. pi*49*10 = pi*h*100*100 (h is distance that the oil level dropped) h = 490/10,000 = 49/1000 = 0.049 ft The answer is B. #### B QUESTION:The average of 5 quantities is 12. The average of 3 of them is 4. What is the average of remaining 2 numbers? options: A)24 B)10 C)8 D)9.5 E)None of these SOLUTION:ANSWER: A (5x12-3x4)/2=24 #### A QUESTION:If f(x) = 3x^4 - 4x^3 - 2x^2 + 5x , then f(-1) = options: A)-4 B)-2 C)0 D)2 E)4 SOLUTION:f(-1) = 3(-1)^4 - 4(-1)^3 - 2(-1)^2 + 5(-1) = 3+4-2-5 = 0 The answer is C. #### C QUESTION:517 + 5.017 + 0.517 + 5.0017 = ? options: A)558.3657 B)527.5357 C)229.6357 D)629.5637 E)629.6753 SOLUTION:517 5.017 0.517 + 5.0017 -------- 527.5357 --------- Answer is B. #### B QUESTION:The expression (5x+2)/(x+3) is equivalent to which of the following? options: A)(5-2)/3 B)5 – (2/3) C)5 – (x)/(x+3) D)5 – (13)/(x+3) E)5 + (17)/(x+3) SOLUTION:Easiest way is to pick any number and put in (5x+2)/(x+3). Then check the options with the same number. I took x=1 and got D as the answer. #### D QUESTION:A 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? options: A)276 m B)279 m C)240 m D)207 m E)285 m SOLUTION:Speed = [54 * 5/18] m/sec = 15 m/sec. Length of the train = (15 * 20) m = 300 m. Let the length of the platform be x meters. Then, x + 300 / 39 = 15 x + 300 = 585 x =285m. Answer: E #### E QUESTION:In 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 favour of candidate? options: A)358000 B)368000 C)357000 D)358000 E)367000 SOLUTION:Total number of invalid votes = 15 % of 560000 = 15/100 × 560000 = 8400000/100 = 84000 Total number of valid votes 560000 – 84000 = 476000 Percentage of votes polled in favour of candidate A = 75 % Therefore, the number of valid votes polled in favour of candidate A = 75 % of 476000 = 75/100 × 476000 = 35700000/100 = 357000 Answer:C #### C QUESTION:In a class of 100 students, there are 50 who play soccer, 45 who play basketball, and 50 who play volleyball. Only 15 of these students play all three sports. Everyone plays at least one of these sports. How many of the students play exactly two of these sports? options: A)15 B)20 C)25 D)30 E)35 SOLUTION:Let S1 be the number of students who play exactly one of the three sports; S2 - the number of students who play exactly two of the three sports; and let S3 be the number of students who play all three sports. We know that S3 = 15 and S1 + S2 + S3 = 100 (the total number of students). Also in the sum 50+45+50 (soccer players + basketball players + volleyball players), each student who plays exactly one sport is counted once, the ones who play exactly two sports are counted twice, and those who play all three sports are counted three times. Thus, 50 + 45 + 50 = S1 + 2S2 + 3S3. Note that S2 = (S1 + 2S2 + 3S3) − (S1 + S2 + S3) − 2S3 = 15 correct answer A #### A QUESTION:The greatest possible length which can be used to measure exactly the length 7 m, 3 m 85 cm, 12 m 95 cm is : options: A)15 cm B)25 cm C)35 cm D)42 cm E)62 cm SOLUTION:Solution Required length = H.C.F. of 700 cm, 385 cm and 1295 cm = 35 cm. Answer C #### C QUESTION:The ages of Rahul and Madhan differ by 16 years. Six years ago, Madhan’s age was thrice as that of Rahul’s,find their present ages options: A)14 years, 30 years B)12 years, 28 years C)16 years, 34 years D)18 years, 38 years E)none of these SOLUTION:Let Rahul’s age = x years So, Madhan’s age = ( x + 16 )years Also, 3(x - 6) = x + 16 - 6 or, x = 14 Rahul’s age = 14 years And, Madhan’s age 14 + 16 = 30 years ANSWER:A #### A QUESTION:If x^2 - 1 = 0 and x < 0, which of the following must be equal to 0 ? options: A) x^2 - 9x B) x^2 - 9x + 20 C) x^2 - 2x + 3 D) x^2 + 2x + 1 E) x^2 + 5x + 6 SOLUTION:x^2-1 = 0 x= +1 or x = -1 if we substitute x= -1 in the equation x^2 +2x+1 = 1-2+1 = 0 D is also the answer #### D QUESTION:A 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? options: A)2 cm B)7 cm C)1 cm D)4 cm E)9 cm SOLUTION:Explanation: Volume of the wire (in Cylindrical shape) is equal to the volume of the sphere. π(16)2 * h = (4/3)π (12)3 => h = 9 cm Answer: Option E #### E QUESTION:The difference of the squares of two consecutive even integers is divisible by which of the following integers ? options: A)6 B)4 C)2 D)5 E)1 SOLUTION:Let the two consecutive even integers be 2n and (2n + 2). Then, (2n + 2)^2 = (2n + 2 + 2n)(2n + 2 - 2n) = 2(4n + 2) = 4(2n + 1), which is divisible by 4. ANSWER B #### B QUESTION:If $600 is deposited into a savings account at an annual interest rate of 4% that compounds monthly, what is the value of the investment after 7 years? options: A)$750.00 B)$823.50 C)$973.25 D)$100.25 E)$793.49 SOLUTION:Using CI Formula: A=P(1+r/n)^n*t A=600(1+4/7)^4*7 A=793.49 Option: E #### E QUESTION:Anne, Markov, Peter line up at a ticket window. In how many ways can they arrange themselves so that Peter is first in line from the window? options: A)a 24 B)b 12 C)c 9 D)d 2 E)e 3 SOLUTION:D Peter's position is fixed. Now we need to arrange all others around Peter. There are 2x1= 2 ways to arrange two people. #### D QUESTION:A mixture contains alcohol and water in the ratio 4 : 3. If 9 litres of water is added to the mixture, the ratio becomes 4: 5. Find the quantity of alcohol in the given mixture options: A)15 litres B)10 litres C)30 litres D)22 litres E)18 litres SOLUTION:Let the quantity of alcohol and water be 4x litres and 3x litres respectively 4x/(3x+9)=4/5 20x=4(3x+9) 8x=36 x=4.5 Quantity of alcohol = (4 x 4.5) litres = 18 litres. Answer is E #### E QUESTION:The 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. 16000, then find the annual income of A? options: A)Rs. 537600 B)Rs. 180000 C)Rs. 201600 D)Rs. 504000 E)None of these SOLUTION:B's monthly income = 16000 * 112/100 = Rs. 17920 B's monthly income = 2 parts ----> Rs. 17920 A's monthly income = 5 parts = 5/2 * 17920 = Rs. 44800 A's annual income = Rs. 44800 * 12 = Rs. 537600 ANSWER:A #### A QUESTION:If (x-13)(x-3) < 0, which of the following must be true? options: A)x^2 + 5x + 6 < 0 B)x^2 + 5x + 6 > 0 C)5 - x < 0 D)x - 5 < 0 E)13 - x > 0 SOLUTION:(x-13)(x-3)<0 can be written as (13-x)(x-3)>0 So,to inequality hold true multiple of (13-x) and (x-3) must be positive and if I let both elements positive/negative then the range becomes 3<x<13 Answer Choice E matched which says 13-x>0 or x<13,which must be true (I started to look from E to A for making easy decision first) Correct Answer E #### E QUESTION:If 3log(4*5^2) = x, find x options: A)5 B)6 C)7 D)8 E)9 SOLUTION:3(log2^2*5^2)=x 3log(5*2)^2=x 3*2log(5*2)=x 6log10=x log10 base 10=1 so 6*1=x x=6 ANSWER:B #### B QUESTION:Length 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? options: A)70 m B)60 m C)80 m D)90 m E)100 m SOLUTION:Let breadth = x metres. Then, length = (x + 20) metres. Perimeter = 5300 m = 200 m. 26.50 2[(x + 20) + x] = 200 2x + 20 = 100 2x = 80 x = 40. Hence, length = x + 20 = 60 m B #### B QUESTION:Find the median of the data 25, 37, 47, 18, 19, 26, 36. options: A)22 B)23 C)24 D)25 E)26 SOLUTION:Arranging the data in ascending order, we get 18, 19, 25, 26, 36, 37, 47 Here, the number of observations is odd, i.e., 7. Therefore, median = (n + 1/2)th observation. = (7 + 1/2)th observation. = (8/2)th observation = 4th observation. 4th observation is 26. Therefore, median of the data is 26. ANSWER :E #### E QUESTION:The average age of a husband and his wife was 23 years at the time of their marriage.After 5 years they have a one year old child.The average of the family is now? options: A)18 years B)23 years C)29 years D)26 years E)19 years SOLUTION:sum of the present age of husband, wife and child =(23*2+5*2)+1 = 57 years required average = 57/3 = 19 years. Answer :E #### E QUESTION:I. a^2 - 9a + 20 = 0, II. 2b^2 - 5b - 12 = 0 to solve both the equations to find the values of a and b? options: A)If a < b B)If a ≤ b C)If the relationship between a and b cannot be established D)If a > b E)If a ≥ b SOLUTION:I. (a - 5)(a - 4) = 0 => a = 5, 4 II. (2b + 3)(b - 4) = 0 => b = 4, -3/2 => a ≥ b Option E #### E QUESTION:Jim and Renee will play one game of Rock, Paper, Scissors. In this game, each will select and show a hand sign for one of the three items. Rock beats Scissors, Scissors beat Paper, and Paper beats Rock. Assuming that both Jim and Renee have an equal chance of choosing any one of the hand signs, what is the probability of a tie? options: A)5/6 B)2/3 C)1/2 D)5/12 E)3/9 SOLUTION:There are 3*3=9 combinations (cases) possible. In 3 cases there will be a tie (rock-rock, scissors/scissors, paper/paper). Now, out of 6 cases left Jim and Renee have equal chances of winning, so in 3 cases Jim will win and in other 3 Renee will win. So the probability of a tie is (favorable outcomes) / (total # of outcomes) = 3/9 Answer: E #### E QUESTION:Which of the following equations has a root in common with x^2−4x+3=0 ? options: A)x^2-4x-4=0 B)x^2-2x+1=0 C)x^2-x-1=0 D)x^2-10x-1=0 E)x^2+1=0 SOLUTION:If we carefully look at the given equation we can arrange it in the following manner: (x-1)(x-3) = 0 so the two roots are 1 and 3. Now put 1 and 3 in given equations. The equation in which one of them gives value 0, that will be our answer. (A) putting 1: we get -7; Putting 3 we get -7. Reject this option. (B) putting 1: we get 0. This is the equation. We are lucky. No need to check other options. B is the answer. #### B QUESTION:log3 N+log5 N what is 3 digit number N that will be whole number options: A)629 B)729 C)829 D)125 E)727 SOLUTION:No of values N can take is 1 5^3=125 ANSWER:D #### D QUESTION:The 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? options: A) 24 B) 26 C) 30 D) 46 E) 50 SOLUTION:carrrots = (carrrots + kiwi + x)*0.3 24 = (30 + 24 + x)*0.3 x = 26. Answer: B. #### B <<<Examples ends QUESTION:If YWVSQ is 25 - 24 - 21 - 19 - 17, Then MLIGF options: A)13 - 11 - 9 - 7 - 8 B)13 - 11 - 9 - 7 - 6 C)13 - 11 - 9 - 7 - 7 D)13 - 11 - 9 - 7 - 3 E)13 - 11 - 9 - 7 - 1 SOLUTION:MLIGF = 13 - 11 - 9 - 7 - 8 Note: this is a dummy question. Dont answer these questions Answer:A #### A

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:There 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. When 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. So 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 – one diamond was still left. Finally, they woke up the 7th thief and this time the diamonds were divided equally. How many diamonds did they steal in total? options: A)1101 B)1141 C)1120 D)1130 E)None SOLUTION:We 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. Answer B #### B QUESTION:The population of a town is 176400. If it increase at the rate of 5% per annum. What was its population 5 years ago? options: A)152460 B)214560 C)138214 D)210000 E)200000 SOLUTION:population 2 years ago = 176400/(1 + 5/100)^5 Answer is C #### C QUESTION:A new home buyer pays 4% annual interest on her first mortgage and 9% annual interest on her second mortgage. If she borrowed a total of $335,000, 80% of which was in the first mortgage, what is her approximate monthly interest payment? options: A)$1,395 B)$1,733 C)$3,466 D)$13,333 E)$20,796 SOLUTION:0.04x + 0.09y = 335000 [1] 0.04x = 0.80 * 335000 = 268000 [2] 268000 + 0.09y = 320000 --> 0.09y = 67000 [3] 268000 / 12 = 22333.3333 [4] 67000 / 12 = 5583.333 [5] Adding [4,5] we get: 27916 [6] Dividing [6] / 2 to get an average we get 1.395,ANS A #### A QUESTION:Jane makes toy bears. When she works with an assistant, she makes 53 percent more bears per week and works 10 percent fewer hours each week. Having an assistant increases Jane’s output of toy bears per hour by what percent? options: A)20% B)70% C)100% D)180% E)200% SOLUTION:Let's assume just Jane 40 bears per 40/hrs a week, so that is 1 bear/hr. With an assistant she makes 61.2 bears per 36 hours a week or 1.7 bears/hr ([40 bears * 1.53] / [40 hrs * .90]). [(1.7 - 1)/1] * 100% = 70% ANSWER:B #### B QUESTION:If n is a positive integer, what is the remainder when (6^(4n+3))(6^n) is divided by 10? options: A)7 B)2 C)4 D)6 E)8 SOLUTION:This one took me bout 3 1/2 min. Just testin numbers and what not. First notice that n is positive. Save time by noticing thatI worked out one solution where n=0 only to find that thats not an option :p. 1-7 stands for ^1 thru 6 1: 7*1=7 2: 7*7=9 3: 7*9=3 4: 7*3=1 5: 7*1=7 6: 7*7=9 7: 7*9=3 Pattern repeats every @ 5. Notice every ^4 or multiple of 4 is always going to be 1. This is just for future notice for similar problems. so 7^4n+3 ---> if n=1 then its ((7^7)*6))/10 which can say is going to be 3*8--> 18/10 --> R=8 Now from here if id double check just to make sure. 7^4(2)+3*6^2 ---> 7^11*36 or we can just say again 7^11*6 (b/c we are only interested in the units digit). Since ^12 is going to be 1 that means ^11 is going to be 3 (as taken from our pattern) so again 3*6=18/10 ---> R =7. A or J in this problem. #### A QUESTION:What is the perimeter of a triangle with sides 7 and 4 that has the maximum possible area? options: A)11 + √5 B)11 + √6 C)11 + 4√7 D)11 + √65 E)11 + 3√17 SOLUTION:We can maximize the area of the triangle by making these two sides the base and the height of a right angle triangle. Then the third side is the hypotenuse with a length of √(49+16) = √65 The perimeter is 11 + √65 The answer is D. #### D QUESTION:Can you deduce the pattern and find the next number in the series? 3, 24,81, 192, __? options: A)276 B)277 C)278 D)279 E)375 SOLUTION:Solution: 375 Explanation: 3 = 1^1^1 + 1^1^1 + 1^1^1 24 = 2^2^2 + 2^2^2 + 2^2^2 81 = 3^3^3 + 3^3^3 + 3^3^3 192 = 4^4^4 + 4^4^4 + 4^4^4 Thus the next number will be 375 =5^5^5 + 5^5^5 + 5^5^5 Answer E #### E QUESTION:The greatest possible length which can be used to measure exactly the length 7 m, 3 m 85 cm, 12 m 95 cm is : options: A)15 cm B)25 cm C)35 cm D)42 cm E)62 cm SOLUTION:Solution Required length = H.C.F. of 700 cm, 385 cm and 1295 cm = 35 cm. Answer C #### C QUESTION:Three unbiased coins are tossed. What is the probability of getting at most two heads? options: A)3/4 B)1/4 C)3/8 D)7/8 E)None of these SOLUTION:Explanation: Here S = {TTT, TTH, THT, HTT, THH, HTH, HHT, HHH} Let E = event of getting at most two heads. Then E = {TTT, TTH, THT, HTT, THH, HTH, HHT}. P(E) = n(E) / n(S) =7/8. ANSWER IS D #### D QUESTION:The length of a train and that of a platform are equal. If with a speed of 72 k/hr, the train crosses the platform in one minute, then the length of the train (in meters) is? options: A)227 B)299 C)276 D)600 E)211 SOLUTION:Speed = [72 * 5/18] m/sec = 20 m/sec; Time = 1 min. = 60 sec. Let the length of the train and that of the platform be x meters. Then, 2x/60 = 20 è x = 20 * 60 / 2 = 600 Answer: D #### D QUESTION:A man's speed with the current is 12 km / hr and the speed of the current is 2 km / hr. The man's speed against the current i options: A)8 km / hr B)9 km / hr C)10 km / hr D)12.5 km / hr E)None SOLUTION:Sol. Man's rate in still in water = (12- 2) km / hr = 10km / hr. Man's rate against the current = (10 - 2) km / hr = 8 km / hr. Answer A #### A QUESTION:A pineapple costs Rs 7 each and a watermelon costs Rs. 5 each. If I spend Rs 38 on total what is the number of pineapple I purchased? options: A)7 B)6 C)5 D)2 pineapples E)3 SOLUTION:Explanation: The equation for this problem can be made as: 5x + 7y =38 Where x is the number of watermelons and y is the number of pineapples. Now test for 2, 3 and 4: For y = 2 5x + 14 =38 x is not an integer For y = 3 5x = 17 X not an integer For y =4 X = 2 So 4 pineapples and 2 watermelons can be bought by 38 Rs. ANSWER:D #### D QUESTION:Arjun started a business with Rs. 20,000 and is joined afterwards by Anoop with Rs.80, 000. After how many months did Anoop join if the profits at the end of the year are divided equally? options: A)3 B)9 C)5 D)6 E)7 SOLUTION:Suppose Anoop joined after 3 months. Then, 20000 * 12 = 80000 * (12 – x) => x = 9. ANSWER:B #### B QUESTION:How many six-digit numbers are there such that all six digits are different and the first digit is not zero? options: A)472392 B)648421 C)720756 D)729951 E)810364 SOLUTION:All six digits are different and first digit is not zero. So first digit can be filled in 9 ways. And, second digit can be filled in 9 ways. And, third digit can be filled in 9 ways. And, fourth digit can be filled in 9 ways. And, fifth digit can be filled in 9 ways. And, sixth digit can be filled in 8 ways. Total ways = 9*9*9*9*9*8 = 472392 Hence option (A). #### A QUESTION:A paint store mixes 3/4 pint of red paint and 2/3 pint of white paint to make a new paint color called Perfect Pink. How many pints of red paint would be needed to make 35 pints of Perfect Pink paint? options: A)9 B)16 C)19 D)25 1/3 E)28 1/2 SOLUTION:3/4 pint is required to make 3/4 + 2/3 = 17/12 pint of perfect pink so 17/12 pint requires 3/4 pint of red.. 1 pint will require 3/4 * 12/17=9/17.. 35 pints will require 9/17 * 35= 19 pints.. C #### C QUESTION:20 beavers, working together in a constant pace, can build a dam in 3 hours. How many hours X will it take 12 beavers that work at the same pace, to build the same dam? options: A)2. B)4. C)X=5. D)X=6. E)8. SOLUTION:C. 5 hrs If there were 10 beavers it qould have taken double X = 6hrs.. so closest to that option is 5. #### C QUESTION:Gold 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? options: A)2 : 3 B)3 : 2 C)1 : 3 D)2 : 1 E)None of these SOLUTION:? Required ratio = 6?4 = 3 : 2 Answer B #### B QUESTION:What 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 ? options: A)1288 B)2797 C)3944 D)1299 E)1082 SOLUTION:Let the side of the square plot be 'a' ft. Given area of the plot (a x a) = 289 => a = 17 Length of the fence = Perimeter of the plot = 4a = 68 ft. Cost of building the fence = 68 x 58 = Rs. 3944. Answer: C #### C QUESTION:The 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. 26,000 is made? options: A)Rs. 1,10,000 B)Rs. 1,20,000 C)Rs. 1,22,000 D)Rs. 1,21,000 E)None of these SOLUTION:The value of the machine after two years = 0.8 * 0.8 * 1,50,000 = Rs. 96,000 SP such that a profit of Rs. 24,000 is made = 96,000 + 26,000 = Rs. 1,22,000 ANSWER:C #### C QUESTION:Last year Manfred received 26 paychecks. Each of his first 6 paychecks was $750; each of his remaining paychecks was $20 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? options: A) $752 B) $755 C) $765 D) $773 E) $775 SOLUTION:= (750*6+ 770 *20)/26 = 765 Answer is C. Posted from my mobile device #### C QUESTION:In a recent election, Ms. Robinson received 8000 voters 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 40 percent of the votes cast were cast by independent voters, which of the following represents the number of votes that Mrs. Robbins received? options: A) 0.06N+3200 B) 0.1N+7200 C) 0.4N+7200 D) 0.12N+8000 E) 0.06N+8000 SOLUTION:40% of N are independent voters, hence 60% of N are not independent voters. From this group she received 20% votes so, 0.2*0.6*N plus 8,000 votes from independents: total=0.2*0.6*N+8,000=0.12*N+8,000. Answer: D. #### D QUESTION:In a function they are distributing noble prize. In how many ways can 3 prizes be distributed among 4 boys when a boy gets any no. of prizes? options: A)25 B)43 C)64 D)78 E)98 SOLUTION:Ans.(C) Sol. In this case, repetitions are allowed, so all the three prizes can be given in 4 ways, i.e. (4 x 4 x 4) ways = 43 ways = 64 ways Or nr ways = 43 ways = 64 ways #### C QUESTION:w,x,y,z is an arithmetic sequence, which of the following options also qualifies as an arithmetiv sequence? I. w-6,x-6,y-6,z-6 II. 5w,2x,3y,5z III. 5w,5x,5y,5z options: A)II and III B)III only C)I and III D)I and II E)II only SOLUTION:lets look at the three choices... I. w-6,x-6,y-6,z-6 since the difference is constant, it is an arithmetic sequence... II. 5w,2x,3y,5z since the difference is not constant, it is not an arithmetic sequence III. 5w,5x,5y,5z since the difference is constant it is an arithmetic sequence... Answer is A) #### A QUESTION:What is the units digit of 3333^(333)*3333^(222)? options: A)0 B)2 C)4 D)6 E)8 SOLUTION:Each of the other explanations to this question has properly explained that you need to break down the calculation into pieces and figure out the repeatingpatternof the units digits. Here's another way to organize the information. We're given [(2222)^333][(3333)^222] We can 'combine' some of the pieces and rewrite this product as.... ([(2222)(3333)]^222) [(2222)^111] (2222)(3333) = a big number that ends in a 6 Taking a number that ends in a 6 and raising it to a power creates a nice pattern: 6^1 = 6 6^2 = 36 6^3 = 216 Etc. Thus, we know that ([(2222)(3333)]^222) will be a gigantic number that ends in a 6. 2^111 requires us to figure out thecycleof the units digit... 2^1 = 2 2^2 = 4 2^3 = 8 2^4 = 16 2^5 = 32 2^6 = 64 2^7 = 128 2^8 = 256 So, every 4powers, the pattern of the units digits repeats (2, 4, 8, 6.....2, 4, 8, 6....). 111 = 27 sets of 4 with a remainder of 3.... This means that 2^111 = a big number that ends in an 8 So we have to multiply a big number that ends in a 6 and a big number that ends in an 8. (6)(8) = 48, so the final product will be a gigantic number that ends in an 6. Final Answer: D #### D QUESTION:Sonalika goes 12 km towards North from a fixed point and then she goes 8 km towards South from there. In the end she goes 3 km towards east. How far and in what direction is she from her starting point? options: A)5km north east B)4km north east C)5km north west D)6km north east E)6km north west SOLUTION:she is currently at 5km north east from the starting point ANSWER:A #### A QUESTION:If 20m − n = p, then which of the following represents the average (arithmetic mean) of m, n, and p, in terms of m? options: A)2m −1 B)4m C)6m D)7m E)6m/5 SOLUTION:20m - n = p Add n to both sides: 20m = n + p Add m to both sides: 21m = n + p + m Now, divide both sides by 3 7m = (n + p + m)/3 = the average of n, p, and m D #### D QUESTION:Four hundred multiples of seven are chosen at random, and 100 multiples of eight are chosen at random. Approximately what percentage of the 500 selected numbers are odd? options: A)20% B)25% C)40% D)50% E)80% SOLUTION:About half the multiples of seven will be odd while all the multiples of eight are even. The percentage of odd numbers is about (1/2)(400) / 500 = 40% The answer is C. #### C QUESTION:Three 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? options: A) 8 B) 2 C) 6 D) 0 E) 12 SOLUTION:If B admitted 15 are overlapping with A admission of 17 But C does not overlap with anybody. Then no student will get nod from all the 3. Hence 0 student will get admission. Answer : D #### D QUESTION:The cost price of a radio is Rs.4800 and it was sold for Rs.4400, find the loss %? options: A)8 B)9 C)7 D)6 E)4 SOLUTION:4800 ---- 400 100 ---- ? => 8% Answer: A #### A QUESTION:The ratio 2 : 3 expressed as a percent equals options: A)12.5% B)40% C)67% D)125% E)None SOLUTION:Solution 2 : 3 = 2/ 3 = (2 / 3 x 100)%. = 66.6 %. Answer C #### C QUESTION:How 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. options: A)1875 B)2000 C)2375 D)2500 E)3875 SOLUTION:Number of combo with 4 as first digit + Number of combos with 4 as second digit = 1*4*5*5*5 + 3*5*5*5 = 2375 ANSWER:C #### C QUESTION:A is twice as good as workman as B and together they finish a piece of work in 18 days. In how many days will B alone finish the work. options: A)27 days B)54 days C)56 days D)68 days E)78 days SOLUTION:Explanation: As per question, A do twice the work as done by B. So A:B = 2:1 Also (A+B) one day work = 1/18 To get days in which B will finish the work, lets calculate work done by B in 1 day = =(1/18∗1/3)=1/54 [Please note we multiplied by 1/3 as per B share and total of ratio is 1/3] So B will finish the work in 54 days Option B #### B QUESTION:What is the smallest number which when increased by 3 is divisible by 27, 35, 25, & 21 ? options: A)4722 B)4725 C)4728 D)4731 E)4733 SOLUTION:Here smallest number means LCM Hence LCM of 27,35,25,21 = 3^3 x 5^2 x 7 = 4725 Therefore required number is 4725 - 3 =4722 Ans - A #### A QUESTION:Alice and Bob will throw three dice each. The score is the sum of points on all three dice. If Alice scores 17 in her attempt what is the probability that Bob will outscore Alice in his attempt? options: A)1/216 B)5/216 C)7/216 D)1/36 E)5/36 SOLUTION:The total number of ways the dice can land is 6*6*6=216. Bob must get a score of 18=6+6+6. There is only 1 way to do this. P(Bob wins)=1/216 The answer is A. #### A QUESTION:One hour after Yolanda started walking from X to Y, a distance of 80 miles, Bob started walking along the same road from Y to X. If Yolandaâs walking rate was 8 miles per hour and Bobâs was 9 miles per hour, how many miles had Bob walked when they met? options: A)38.07 B)40 C)42 D)39 E)40.07 SOLUTION:Let 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 8(t + 1) miles. These distances must sum to 80 miles, so 9t + 8(t + 1) = 80, which may be solved for t as follows 9t + 8(t + 1) = 80 9t + 8t + 8 = 80 17t = 72 T = 4.23 (hours) Therefore, Bob had walked 9t = 9(4.23) = 38.07 miles when they met. The best answer is A. #### A QUESTION:If 6^w is a factor of (10!)^2, What is the greatest possible value of w ? options: A)2 B)4 C)6 D)8 E)10 SOLUTION:w 10!= 10*9*8*7*6*5*4*3*2*1 = 2*5*3*3*2*2*2*7*2*3*5*2*2*3*2 = 2^8*3^4*5^2*7 6= 2*3 Therefore only the exponents of 2 and 3 are relevant, 2^8 or 3^4 -> higher number counts = 8 -> Answer Choice D #### D QUESTION:David invested certain amount in three different schemes. A, B and C with the rate of interest 10% p.a., 12% p.a. and 15% p.a. respectively. If the total interest accrued in one year was Rs. 3200 and the amount invested in scheme C was 150% of the amount invested in scheme A and 240% of the amount invested in scheme B, what was the amount invested in scheme B? options: A)5000 B)2787 C)2679 D)2790 E)2712 SOLUTION:Let x, y and z be the amount invested in schemes A, B and C respectively. Then, (x * 10 * 1)/100 + (y * 12 * 1)/100 + (z * 15 * 1)/100 = 3200 10x + 12y + 15z = 320000 Now, z = 240% of y = 12/5 y And, z = 150% of x = 3/2 x x = 2/3 z = ( 2/3 * 12/5) y = 8/5 y 16y + 12y + 36y = 320000 y = 5000 Sum invested in scheme B = Rs. 5000.Answer: A #### A QUESTION:In a market, a dozen eggs cost as much as a pound of rice, and a half-liter of kerosene costs as much as 8 eggs. If the cost of each pound of rice is $0.33, then how many E cents does a liter of kerosene cost? [One dollar has 100 cents.] options: A) 0.33 B) 0.44 C) 0.55 D) 44 E) 55 SOLUTION:Main thing to remember is answer is asked in cents, however when we calculate, it comes up as 0.44 $ Just multiply by 100, Answer E= 44.D #### D QUESTION:On a race track a maximum of 5 horses can race together at a time. There are a total of 25 horses. There is no way of timing the races. What is the minimum number Q of races we need to conduct to get the top 3 fastest horses? options: A)5 B)7 C)8 D)10 E)11 SOLUTION:Q=7 is the correct answer. Good solution Buneul.B #### B QUESTION:If five chimpanzee can eat five mangoes in five minutes. How many minutes would it take for four chimpanzee to eat four mangoes ? options: A)5 minutes B)10 minutes C)8 minutes D)14 minutes E)20 minutes SOLUTION:A 5 minutes #### A QUESTION:If 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 72? options: A)24 B)36 C)12 D)18 E)16 SOLUTION:The greatest common divisor of n and 16 is 4 --> n is a multiple of 4 but not a multiple of 8. The greatest common divisor of n and 15 is 3 --> n is a multiple of 3 but not a multiple of 5. 72=2*3*3*2*2 is divisible by 12. therefore the greatest common divisor is 12 C #### C QUESTION:Ayush was born two years after his father's marriage. His mother is five years younger than his father but 25 years older than Ayush who is 10 years old. At what age did the father get married ? options: A)28years B)29years C)30years D)31years E)32years SOLUTION:Explanation: Ayush's present age = 10 years. His mother's present age = (10 + 25) years = 35 years. Ayush's father's present age = (35+ 5) years = 40 years. Ayush's father's age at the time of Ayush's birth = (40 - 10) years = 30 years. Therefore Ayush's father's age at the time of marriage = (30 - 2) years = 28 years. Answer: A) 28 year #### A QUESTION:Two trains each 170m in length each, are running on two parallel lines in opposite directions. If one goes at the speed of 55km/h while the other travels at 50km/h. how long will it take for them to pass each other completely. options: A)15 sec B)11.6 sec C)31.6 sec D)12.6 sec E)23 sec SOLUTION:Explanation: D = 170 m + 170 m = 340 m RS = 55 + 50 = 105 * 5/18 = 146/5 T = 340 * 5/146 = 11.6 sec Answer: Option B #### B QUESTION:9, 35, 91, 189, 341, ? options: A)502 B)521 C)559 D)611 E)712 SOLUTION:Explanation : 13 + 23 = 9 23 + 33 = 35 33 + 43 = 91 43 + 53 = 189 53 + 63 = 341 63 + 73 = 559 Answer : Option C #### C QUESTION:Simple interest on a certain sum of money for 3 years at 8% per annum is half the compound interest on Rs. 4000 for 2 years at 10% per annum. The sum placed on simple interest is options: A)Rs.1550 B)Rs.1650 C)Rs.1750 D)Rs.2000 E)None SOLUTION:Solution C.I. =Rs[4000x(1+10/100)²-4000] Rs.(4000x11/10x11/10-4000) = Rs.940. Sum =Rs. [420x100 /3x8] = Rs.1750. Answer C #### C QUESTION:A certain rectangular window is four times as long as it is wide. If its perimeter is 50 feet, what are its dimensions in terms of length by width? options: A)12 by 2 B)11 by 3 C)20 by 5 D)10 by 4 E)9 by 3 SOLUTION:2x+2y=50 x+y=25 x+4x=25 5x=25 x=5 Answer C #### C QUESTION:A bag contains an equal number of one rupee, 50 paise and 25 paise coins respectively. If the total value is 35, how many coins of each type are there? options: A)20 coin B)30 coins C)28 coins D)25 coins E)None of these SOLUTION:Let number of each type of coin = x. Then, 1 × x + .50 × x + .25x = 35 ⇒ 1.75x = 35 ⇒ x = 20 coin Answer A #### A QUESTION:calendar=52097083 november=538=8651 march=2*308 blue=7154 december=? options: A)9535&153 B)9585&153 C)9525&153 D)9525&*53 E)9525&*54 SOLUTION:from above in formation d=9 e=5 c=2 e=5 m=3 b=1 e=5 r=8 95253158( Order doesnot matter i guess!) another thing is &=8 for mathcing above ans ANSWER:C #### C QUESTION:If a - b =6 and a2+b2=48 , find the value of ab. options: A)6 B)8 C)10 D)12 E)2 SOLUTION:Explanation: We know 2ab=(a2+b2)−(a−b)2 2ab=48−36=12 =>ab=6 Option E #### E QUESTION:At the beginning of year 1, an investor puts pp dollars into an investment whose value increases at a variable rate of xnxn per year, where nn is an integer ranging from 1 to 3 indicating the year. If 85<xn<11085<xn<110 for all nn between 1 and 3, inclusive, then at the end of 3 years, the value of the investment must be between? options: A)$p and $2p B)$2pand $5p C)$5p and $10p D)$10p and $ 25p E)$25p and $75p SOLUTION:Since the min rate of interest is 86% the min value of investment will be (1+0.86)^3*p = (1.86^3)*p. Similarly max value will be (2.1)^3*p. 2.1^3 is 9.5 or you can guess little over 8 so 10p may be good estimate. 1.86^3 is trickier to estimate. I knew root(3) = 1.73. So 1.86^2 is close to 3 and 3*1.8 is 5.4. So 5p is a close lower bound. So range is 5p to 10p. Answer C. #### C QUESTION:The average age of a group of 10 persons was decreased by 3 years when one person, whose age was 45 years, was replaced by a new person. Find the age of the new person? options: A)12 B)15 C)18 D)21 E)25 SOLUTION:Initial average age of the 10 persons be P. Age of the new person Q. Sum of the ages of the initial 10 persons = 10P New average = (P-3) 10(P-3) = 10P - 45 + Q => Q = 15 ANSWER:B #### B QUESTION:A problem is given to three students whose chances of solving it are 1/2, 1/3 and 1/4 respectively. What is the probability that the problem will be solved? options: A)2/4 B)3/4 C)4/5 D)5/6 E)6/7 SOLUTION:consider A,B,C events and AA,BB,CC not solving the problems now P(1)=1/2, P(B)=2/3 and P(C)=1/4 Not solving events =1/2*2/3*3/4 ==>1-1/4= 3/4 ANSWER B #### B QUESTION:A girl has to make pizza with different toppings. There are 8 different toppings. In how many ways can she make pizzas with 2 different toppings? options: A)16 B)56 C)112 D)28 E)38 SOLUTION:In 8 different toppings, selecting 2 diff toppings = 8c2 formula is n!/(n-c)! n = total number of toppings C = number chosen in a grouping. n=8 and c=2 so we get 8!/(8-2)! = (8*7*6*5*4*3*2*1)/(6*5*4*3*2*1) = 8*7 =56 ANSWER:B #### B QUESTION:In how many different ways can the letters of the word 'SOFTWARE' be arranged in such a way that the vowels always come together? options: A)120 B)360 C)1440 D)13440 E)4320 SOLUTION:The word 'SOFTWARE' contains 8 different letters. when the vowels OAE are always together, they can be supposed to form one letter. Thus, we have to arrange the letters SFTWR (OAE) Now, 5 letters can be arranged in 6!=720 ways. The vowels (OAE) can be arranged among themselves in 3!=6 ways. Required number of ways =(720*6)=4320. Answer is E #### E QUESTION:A semicircle has a radius of 9. What is the approximate perimeter of the semicircle? options: A)16 B)25 C)33 D)46 E)58 SOLUTION:The perimeter of a circle is 2*pi*r. The perimeter of a semicircle is 2*pi*r/2 + 2r = pi*r + 2r The perimeter is pi*9 + 2*9 which is about 46. The answer is D. #### D QUESTION:The lunch menu at a certain restaurant contains 4 different entrees and 5 different side dishes. If a meal consists of 1 entree and 2 different side dishes, how many different meal combinations Q could be chosen from this menu? options: A)10 B)20 C)40 D)80 E)100 SOLUTION:Q=4C1 * 5C2 = 4 * (5*4*3!)/(3!2!) = 4 * 10 = 40 Answer - C #### C QUESTION:There are cats got together and decided to kill the mice of 999919. Each cat kills equal number of mice and each cat kills more number of mice than cats there were. Then what are the number of cats? options: A)941,1009 B)991,1001 C)991,1009 D)791,1009 E)931,1009 SOLUTION:999919 can be written as 1000000 – 81 = 10002 – 92 ie of the form a2-b2=(a+b)(a-b) =(1000+9)*(1000-9) = (1009)*(991) Given that number of cats is less than number if mice. So number of cats is 991 and number of mice were 1009 Answer C #### C QUESTION:The 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? options: A)Rs. 120,002 B)Rs. 1,20,000 C)Rs. 1,20,00 D)Rs. 1,20,028 E)Rs. 1,20,011 SOLUTION:Explanation: The value of the machine after two years = 0.8 * 0.8 * 1,50,000 = Rs. 96,000 SP such that a profit of Rs. 24,000 is made = 96,000 + 24,000 = Rs. 1,20,000 Answer: B #### B QUESTION:Johnny bought six peanut butter cans at an average price (arithmetic mean) of 37.5¢. If Johnny returned two cans to the retailer, and the average price of the remaining cans was 31¢, then what is the average price, in cents, of the two returned peanut butter cans? options: A)5.5 B)11 C)47.5 D)50.5 E)67.5 SOLUTION:Total price of six cans = 6*37.5 = 225 Total price of 4 cans = 4*31 = 124 Total rice of two cans = 225 - 124 = 101 Average price of two cans = 101/2 = 50.5 c Another way to do it is this: Assume that the four leftover cans were of 31c each. The avg was 37.5c initially because the two cans were 36.5c each and were providing another 6.5c of cost to other 4 cans. So cost of the two cans = 2*37.5 + 4*6.5 = 101 Avg cost of the two cans = 101/2 = 50.5c Answer (D) #### D QUESTION:If the length of an edge of cube M is thrice the length of an edge of cube N, what is the ratio of the volume of cube N to the volume of cube M? options: A)2/13 B)1/27 C)1/5 D)1/9 E)1/8 SOLUTION:The length of cube N = 1; The length of cube M = 3; The ratio of the volume of cube N to the volume of cube M = 1^3/3^3 = 1/27 Answer : B #### B QUESTION:If a number is formed by writing integers 1 to 150 one after another, like 12345...150. How many W digits does this integer consists of? options: A)150 B)339 C)342 D)359 E)362 SOLUTION:Number of single digit integers = 9 Number of 2 digit integers = 99 - 10 + 1 = 90 Number of 3 digit integers = 150 - 100 + 1 = 51 Number of digits in the integer W= 1*9 + 2*90 + 3*51 = 9 + 180 + 153 = 342 Answer: C #### C QUESTION:A coin is tossed live times. What is the probability that there is at the least one tail? options: A)1/15 B)31/32 C)1/10 D)30/32 E)25/27 SOLUTION:Probability of getting least one tail at the coin tossed five times. = There is not even a single tail. = 1/32 ; P(T) = 1 - 1/32 = 31/32 ANSWER B #### B QUESTION:Two 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? options: A)29 B)29 C)60 D)19 E)12 SOLUTION:Let the speed of the slower train be x m/sec. Then, speed of the train = 2x m/sec. Relative speed = ( x + 2x) = 3x m/sec. (100 + 100)/8 = 3x => x = 25/3. So, speed of the faster train = 50/3 = 50/3 * 18/5 = 60 km/hr. Answer:C #### C QUESTION:Claire 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? options: A)39 B)50 C)66 D)57 E)60 SOLUTION:G+H =90 ...1 ; G/4 +H/3 =25 ....2 OR 3G +4H =25*12 =300 G =90-H OR 3(90-H) +4H =300 H = 300-270 =30 THEN G= 96-30 =66 C #### C <<<Examples ends QUESTION:By the how much is two-fifth of 300 greater than three -fifths of 125? options: A)15 B)3 C)5 D)45 E)None of these SOLUTION:Reqd no. = 2⁄5 × 300 - 3⁄5 × 125 = 120 - 75 = 45 Answer D #### D

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:A train 160m long is running at 30kmph. In how much time will it pass a platform 120m long? options: A)15.89 seconds B)24.36 seconds C)15.96 seconds D)14.93 seconds E)22.23 seconds SOLUTION:Distance travelled = 160 + 120m = 280m Speed = 30 * 5/8 = 75/4m Time = 280 * 4/75 = 14.93 Seconds Answer : D. #### D QUESTION:If 0 < n < 1, what is the median of the values n, n^-1, n^2, n^1/2 and n^3? options: A)n B)n^-1 C)n^2 D)n^1/2 E)n^3 SOLUTION:A. To make the problem less confusing, I picked a number between 0 and 1 such as n = 1/4 and calculate: n = 1/4 n^-1 = 4 n^2 = 1/16 n^(1/2) = 1/2 n^3 = 1/8. From this, rearrange the number and the median is 1/4, which is n. Answer A #### A QUESTION:A man sells a horse for Rs.920 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? options: A)287 B)279 C)267 D)860 E)940 SOLUTION:CP = SP + 1CP = SP - g 920 + x = 980 - 2x 3x = 60 => x =20 CP = 920 + 20 = 940 Answer:E #### E QUESTION:Today is Tuesday. 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? options: A)Saturday B)MONDAY C)TUESDAY D)WEDNESDAY E)FRIDAY SOLUTION:Today is Tuesday after three days--->Friday now, (Friday)after before day--->Thursday then, (Thursday)day after tomorrow--->Saturday ANSWER:A #### A QUESTION:The ratio of number of boys and girls in a school is 3:5. If there are 320 students in the school, find the number of girls in the school? options: A)150 B)250 C)300 D)200 E)280 SOLUTION:Let the number of boys and girls be 3x and 5x Total students = 320 Number of girls in the school = 5*320/8 = 200 Answer is D #### D QUESTION:((-1.9)(0.6) – (2.6)(1.2))/2.0 = ? options: A)-0.71 B)1.0 C)1.07 D)1.71 E)-2.13 SOLUTION:Dove straight into calculation but quickly realized that the sum of two negatives is a negative so there is only one option. -2.13 Answer E #### E QUESTION:(x —1)(x + 3) > 0 (x +5)(x—4) < 0 Which of the following values of x satisfy both inequalities shown? I. -6 II. -4 III. 2 IV. 3 options: A)I and II only B)I and III only C)II and III only D)II and IV only E)II, III, and IV SOLUTION:(x - 1)(x + 3) > 0 --> x<-3 or x>1. (x + 5)(x - 4) < 0 --> -5<x<4. Among choices only -4 and 2 satisfy both inequalities. Answer: E. #### E QUESTION:The R students in a class agree to contribute equally to buy their teacher a birthday present that costs y dollars. If q of the students later fail to contribute their share, which of the following represents the additional number of dollars that each of the remaining students must contribute in order to pay for the present? options: A) y/R B) y/(R-x) C) xy/(R-x) D) qy/(R(R-q)) E) y/(R(R-x)) SOLUTION:y/(R-q)- y/R if we simplify this we get choice D, which is the correct answer. #### D 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 T is in the same quadrant as the fourth vertex of the square? options: A)(-5, -3) B)(-5, 3) C)(5, -3) D)(3, -5) E)(3, 5) SOLUTION:The 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 T is in the same quadrant as the fourth vertex of the square? I marked the tricky part in red. It seems c is anegativenumber and d is a positive number. This means Vertex #1 = (c, d) is in QII (that is, negative x and positive y) Vertex #2 = (c, -d) is in QIII (that is, both xy negative) Vertex #3 = (-c, -d) is in QIV (that is y is negative, but x is positive) That means the last vertex should be in the first quadrant --- the only first quadrant point is (5, 3), answer =E. #### E QUESTION:If x is the smallest positive integer such that 4,536 multiplied by x is the square of an integer, then x must be options: A)12 B)21 C)16 D)17 E)14 SOLUTION:4536= 6*6*3*3*7*3, so we need one 7 and one 3 to make it a square of a number. so 7*3= 21 Ans: B #### B QUESTION:What will come in place of the x in the following Number series? 1, 2, 12, 7, 23, 12, 34, x options: A)14 B)15 C)16 D)17 E)18 SOLUTION:There are two series here 1, 12, 23, 34, ... (Increase by 11) 2, 7, 12, ... (Increase by 5) Hence, next term is 12 + 5 = 17 Correct Answer Choice is D #### D QUESTION:If sequence T is defined for all positive integers n such that t(n +1) = t(n) + n, and t 3 = 14, what is t 24? options: A)101 B)187 C)191 D)201 E)287 SOLUTION:here is my way of solving this : tn +1 = tn + n, t 3 = 14 so: t 4 = t 3 + 3 t 5 = t 4 + 4, so we replace t 4 with the previous result : t 5 = (t 3 + 3 ) + 4 .... so we get t 24 = t 3 + 3 + 4 + 5 + 6....+ 23 the 3 + 4 + 5 + ... + 23 sequence is equal the sequence 1 + 2 + ... + 23, minus 1 + 2 at the beginning (so, minus 3) and the 1 + 2 ... + 23 sequence is equal to n*(n+1)/2 with n being 23, so equal to 23 * 24 / 2 = 276 so : t 20 = t 3 + 276 - 3 t 20 = 14 + 276 - 3 = 276 + 11 = 287, hence answer E #### E QUESTION:If f(x)= 5x^3- 4x+8 and g(y)= 6y-4, then g(f(x)) = options: A)11x^2+4x+4 B)11x^2-12x+44 C)30x^3-24x+44 D)30x^3+4x+4 E)30x^3-12x+44 SOLUTION:g(f(x)) = 6(f(x)) -4 = 6(5x^3- 4x+8) - 4 = 30x^3-24x+44 =>C #### C QUESTION:The 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? options: A)33 B)88 C)66 D)12 E)99 SOLUTION:Speed of the boat downstream = 15 + 3 = 18 kmph = 18 * 5/18 = 5 m/s Hence time taken to cover 60 m = 60/5 = 12 seconds. Answer: D #### D QUESTION:The 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? options: A)18/35 B)18/38 C)18/34 D)18/31 E)18/30 SOLUTION:If both agree stating the same fact, either both of them speak truth of both speak false. Probability = 3/5 * 4/7 + 2/5 * 3/7 = 12/35 + 6/35 = 18/35. Answer:A #### A QUESTION:If BAT = 58 HAT = 52 CAT = 57 then whats RAT = ? options: A)42 B)45 C)34 D)76 E)25 SOLUTION:A 42 #### A QUESTION:There 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? options: A)980 B)1150 C)1360 D)1540 E)1720 SOLUTION:The number of ways to choose two teams is 17C2 = 17*16/2 = 136 The total number of games in the season is 10*136 = 1360. The answer is C. #### C QUESTION:The soldiers in two armies when they met in a battle were in the ratio of 10 : 3. Their respective losses were as 20 : 3 and the survivors as 40 : 13. If the number of survivors in the larger army be 24,000, find the original number of soldiers in each army ? options: A)28000, 8400 B)25000, 7500 C)29000, 2750 D)26000, 7800 E)27000, 7800 SOLUTION:Let the soldiers in the two armies be 10X, 3X and losses be 20Y, 3Y, Then we have, 10X - 20Y = 24000 ...(i) And 3X - 3Y = 24000 x 13/40 = 7800 Solving, we have 10X = 28000, 3X = 8400 ANSWER:A #### A QUESTION:In how many ways can the letters of the word ARRANGED be arranged in a row so that the vowels appear in alphabetic order? options: A)6720 B)5280 C)6240 D)5202 E)4020 SOLUTION:three letters can be arranged in 3! ways. only one combination AEI is required. 8 letters can be arranged in 8! ways. thus 8!/ 3! * 1 = 6720. A #### A QUESTION:P and Q can complete a work in 10 days and 6 days respectively. P alone started the work and Q joined him after 2 days till the completion of the work. How long did the work last? options: A)5 days B)10 days C)14 days D)22 days E)26 days SOLUTION:Explanation : Work done by P in 1 day = 1/10 Work done by Q in 1 day = 1/6 Work done by P in 2 days = 2 × (1/10) = 1/5 Remaining work = 1 – 1/5 = 4/5 Work done by P and Q in 1 day = 1/10 + 1/6 = 4/15 Number of days P and Q take to complete the remaining work = (4/5) / (4/15) = 3 Total days = 2 + 3 = 5 Answer : Option A #### A QUESTION:Anderson has a phone plan that charges a monthly rate of $50 for the first 1,000 minutes plus $0.25 for each additional minute. Which of the following functions models Anderson’s plan for all m > 1,000, with m as the number of minutes per month and f(m) as the monthly charge? options: A)f(m) = 0.25m B)f(m) = 0.25m + 50 C)f(m) = 0.25m – 200 D)f(m) = 0.25m – 950 E)f(m) = 0.25m + 1,000 SOLUTION:For m > 1,000 — that is, beyond 1,000 minutes of usage — the plan charges a usage fee based on the number of minutes used plus a flat rate of $50. With this information, you can create the following function: f(m) = Usage fee + 50 The usage fee is $0.25 per minute; however, the first 1,000 minutes are already paid for. So the usage fee is 0.25(m – 1,000). Plug this value into the preceding function and simplify: f(m) = 0.25(m – 1,000) + 50 f(m) = 0.25m – 250 + 50 f(m) = 0.25m – 200 correct answer C)f(m) = 0.25m – 200 #### C QUESTION:simplify : 3x - 5 + 23x - 9 options: A)2(14x-9) B)2(13x-7) C)(14-5x) D)2(10-7x) E)2x(14-7) SOLUTION:3x -5 +23x-9 , = 3x+23x - 5 - 9 = 26x - 14, = 2(13x - 7). correct answer : (B) #### B QUESTION:Depreciation applicable to an equipment is 20%.The value of the equipment 3 years from now will be less by options: A)48.8% B)47.8% C)46.8% D)49.8% E)45.8% SOLUTION:Value after 3 years will be 0.8^3 = 0.512 times the present value. so it will be less by 48.8%. ANSWER:A #### A QUESTION:One-sixth of the light switches produced by a certain factory are defective. Four-fifths of the defective switches are rejected and 1/20 of the non defective switches are rejected by mistake. If all the switches not rejected are sold, what percent of the switches sold by the factory are defective? options: A)4% B)5% C)6% D)11% E)16% SOLUTION:1/6 of the switches are defective. The defective switches that are not rejected are 1/5*1/6 = 1/30 = 4/120 of all switches. The non defective switches that are sold are 5/6*19/20 = 95/120 of all switches. The percent of switches sold that are defective is 4/99 which is about 4%. The answer is A. #### A QUESTION:After decreasing 50% in the price of an article costs Rs.620. Find the actual cost of an article? options: A)2777 B)2987 C)1200 D)1240 E)1671 SOLUTION:CP* (50/100) = 620 CP= 12.4 * 100 => CP = 1240 Answer: D #### D QUESTION:At the end of three years what will be the compound interest at the rate of 10% p.a. on an amount of Rs.25000? options: A)8275 B)1879 C)2779 D)2672 E)2782 SOLUTION:A = 25000(11/10)^3 = 33275 = 25000 ---------- 8275 Answer: A #### A QUESTION:A large box contains 21 small boxes and each small box contains 25 chocolate bars. How many chocolate bars are in the large box? options: A)250 B)350 C)450 D)550 E)525 SOLUTION:The number of chocolate bars is equal to 21 * 25 = 525 correct answer E #### E QUESTION:The average of 10 members is 15665. If 2 members have 20000 then what is the average of remaining? options: A)12581.25 B)13581.25 C)14581.25 D)15581.25 E)16581.25 SOLUTION:20000*2+8*x=15665*10 8x=156650-40000 x=116650/8 x=14581.25 ANSWER:C #### C QUESTION:If 5^10 x 2^10 = 10^n what is the value of n? options: A)16 B)14 C)12 D)10 E)18 SOLUTION:5^10*2^10 = 10^n or 10^10 =10^n n=10 D #### D QUESTION:There are 9 books on a shelf that consist of 3 paperback books and 6 hardback books. If 4 books are selected at random without replacement, how many different combinations are there which include at least one paperback book? options: A)95 B)103 C)111 D)119 E)127 SOLUTION:The total number of ways to select 4 books is 9C4 = 126 The number of ways which do not include any paperbacks is 6C4 = 15 The number of combinations with at least one paperback is 126-15 = 111 The answer is C. #### C QUESTION:When I add 4 times my age 4 years from now to 5 times my age 5 years from now, I get 10 times my current age. How old will I be 3 years from now? options: A)42 years B)41 years C)43 years D)40 years E)45 years SOLUTION:Let x= current age 4(x+4)+5(x+5)=10x ;so x=R 41 years Answer C #### C QUESTION:If a, b, and c are consecutive positive even integers and a > b > c, which of the following could be equal to a - b - c ? options: A)6 B)2 C)-1 D)-3 E)-4 SOLUTION:a = 2n (n>=3), b = 2n - 2, c = 2n - 4 a -b -c = 2n - (2n-2) - (2n-4) = 6 - 2n <= 0 since n >=3 , even -> E ANSWER:E #### E QUESTION:Sides of a rectangular park are in the ratio 3: 2 and its area is 3750 sq m, the cost of fencing it at 50 ps per meter is? options: A)277 B)299 C)125 D)99 E)22 SOLUTION:3x * 2x = 3750 => x = 25 2(75 + 50) = 250 m 250 * 1/2 = Rs.125 Answer:C #### C QUESTION:Three coworkers P , W , R meet for Dinner. P had 5 sandwiches, W had 3 and R had none. Both PW share their sandwiches with R such that each one got the same amount. If R paid $ 8 to PW, how much of $ 8 should P get? Assume both sandwiches and Dollars can be split. options: A)a) 5$ B)b) 3 $ C)c) 7 $ D)d) 4 $ E)e) 5.5 $ SOLUTION:we got total 8 sandwiches ....we are dividing equally in 3 people. per person: 8/3 initially p:8 W:3 r:0 now since r ate 8/3 so he is paying 8 dollars for 8/3 sandwiches. now p also ate 8/3 of his 5 sandwiches = so he gave 5-8/3 to r ==>7/3 to r ok we have 8 dollars for 8/3 sandwich therefore for 7/3 sandwich we will get 7 dollars. hence p should get 7 dollars. hence C #### C QUESTION:39 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? options: A)9 B)12 C)10 D)13 E)15 SOLUTION:Explanation: Let the required number of days be x More persons, less days (indirect proportion) More hours, less days (indirect proportion) Hence we can write as (persons)39:30 (hours) 5:6}:: x:12 ⇒39×5×12=30 × 6 × x ⇒39×5×2=30 × x ⇒39=3×x ⇒x=13 Answer: Option D #### D QUESTION:9.8 , 9.8 , 9.9 , 9.9 , 10.0 , 10.0 , 10.1 , 10.5 The mean and the standard deviation of the 8 numbers shown above is 10 and 0.212 respectively. What percent of the 8 numbers are within 1 standard deviation of the mean? options: A)90.5% B)87.5% C)80.5% D)77.5% E)70.5% SOLUTION:Within 1 standard deviation of the mean- means in the range {mean-1*sd; mean+1*sd} = {10-1*0.212; 10+0.3} = {9.788; 10.212}. From the 8 listed numbers, 7 are within this range so 6/8=87.5%. Answer: B. #### B QUESTION:If the perimeter of ΔACD is 9+3√3, what is the perimeter of equilateral triangle ΔABC? options: A)9 B)18−3√3 C)18 D)18+3√3 E)27 SOLUTION:The altitude of an equilateral triangle is side*√3/2. As perimeter of triangle ACD is 9+3√3, AC + CD + AD = (side+side/2+side*√3/2) = 9 + 3√3 or side =6. Perimeter of equilateral triangle, ABC is 3(side) or 18. Answer:(OptionC) #### C QUESTION:What distance will be covered by a bus moving at 126 kmph in 10 seconds? options: A)287 B)600 C)350 D)276 E)207 SOLUTION:126 kmph = 126 * 5/18 = 35 mps D = Speed * time = 35 * 10 = 350 m. Answer:C #### C QUESTION:The 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? options: A)5 kmph B)1 kmph C)6 kmph D)2 kmph E)3 kmph SOLUTION:The current of a stream = 1 The speed of the motor boat in still water= x Speed downstream = x + 1 Speed upstream = x - 1 since distance = speed × time, we have 35/(x + 1) + 35/(x - 1) = 12 kmph=6 kmph Answer : Option C #### C QUESTION:A 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 1 buckles is how many times that of 5 buckles and 6 buttons? options: A)7/15. B)2/5. C)6/11. D)5/9. E)8/15. SOLUTION:2buttons + 2buckles = 1/3(11buckles + 3buttons) 6buttons + 6buckles = 11buckles + 3buttons 3buttons = 5buckles Weight of 3buttons and 1buckles = 5buckles + 1buckles = 6buckles Weight of 6buttons and 5buckles = 10buckles + 5buckles = 15buckles (3buttons and 2buckles) = x * (6buttons and 5buckles) 6 = x*15 x = 6/15=2/5 Answer: B #### B QUESTION:man is 20 years older than his son. In two years, his age will be twice the age of his son. The present age of his son is: options: A)14years B)26 years C)17 years D)18 years E)22 years SOLUTION:Let the son's present age be x years. Then, man's present age = (x + 20) years. (x + 20) + 2 = 2(x + 2) x + 22 = 2x + 4 x = 18. answer :D #### D QUESTION:In expressing a length of 25.461 km as nearly as possible with the three significant digits, find the percentage error options: A)0.353% B)0.153% C)0.035% D)0.015% E)None of these SOLUTION:Explanation: Error = (25.5 - 25.461) = 0.039 Required percentage = 0.039/ 25.461×100=0.153 Option B #### B QUESTION:The positive integers p and q leave remainders of 2 and 3, respectively, when divided by 6. p > q. What is the remainder when p – q is divided by 6? options: A)5 B)4 C)3 D)2 E)1 SOLUTION:Let's test out some values of p and q that satisfy the given information. p leaves are remainder of 2 when divided by 6 So, p COULD equal 8 q leaves are remainder of 3 when divided by 6 So, q COULD equal 3 What is the remainder when p – q is divided by 6? So, p - q = 8 - 3 = 5, and when we divide 5 by 6, we get 0 with remainder 5 Answer: A #### A QUESTION:How 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? options: A)12 sec B)30 sec C)36 sec D)16 sec E)18 sec SOLUTION:Speed of train relative to man = 63 - 3 = 60 km/hr. = 60 * 5/18 = 50/3 m/sec. Time taken to pass the man = 600 * 3/50 = 36 sec. Answer: C #### C QUESTION:On a weekend, 3 friends went skiing and evenly split the cost of their cabin. If the amount paid by each person was an integer, which of the following could not have been the cost of the cabin? options: A)$110 B)$150 C)$225 D)$54 E)$75 SOLUTION:Each of the seven persons evenly splitting the cost is an integer amount, therefore check the divisibility by 3 for all answer choices. 110/3 = 36.67 150/3 = 50 225/3 = 75 54/3 = 18 75/3 = 25 A is not an integer amount. Answer:A #### A QUESTION:The average age of 8 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 options: A)22 B)30 C)99 D)28 E)17 SOLUTION:Explanation: Total age increased = (8 * 2) years = 16 years. Sum of ages of two new men = (21 + 23 + 16) years = 60 years Average age of two new men = (60/2) years = 30 years Answer: B #### B QUESTION:There are 36 students in a certain geometry class. If one third of the students are boys and three fourths of the boys are under six feet tall, how many boys in the class are under six feet tall? options: A)9 B)12 C)18 D)24 E)27 SOLUTION:Total Students = 36 One third of the students are boys = 1/3*36 = 12 Three fourths of the boys are under six feet tall = 3/4*12 = 9 ... Therefore Number of boys in the class under six feet tall = 9 ... Answer A.... Alternatively... Number of boys in the class under six feet tall = 3/4 of 1/3 of Total Students = 3/4*1/3*36 = 9... Answer A #### A QUESTION:The average of 6 no.'s is 3.95. The average of 2of them is 3.4, while the average of theother 2 is 3.85. What is the average of the remaining 2 no's? options: A)3.5 B)3.9 C)4.2 D)4.3 E)4.6 SOLUTION:Sum of the remaining two numbers = (3.95 * 6) - [(3.4 * 2) + (3.85 * 2)] = 23.70 - (6.8 + 7.7) = 23.70 - 14.5 = 9.20. Required average = (9.2 / 2) = 4.6. E #### E QUESTION:If 7 is 10 percent of 50 percent of a certain number, what is the number? options: A)150 B)217 C)100 D)90 E)140 SOLUTION:Using elimination method to pick the correct option it will be discovered that option E i.e 140 is the correct option because 50% of 140 is 70 and 10% of 70 is 7. ANSWER:E #### E QUESTION:A can complete a work in 15 days and B can do the same work in 9days. If A after doing 5days, leaves the work, find in how many days B will do the remaining work? options: A)2days B)4days C)6days D)7days E)10days SOLUTION:The required answer = (15-5)*9 / 15 = 40/10 = 6days Answer is C #### C QUESTION:If x is negative and y is positive, which of the following cannot be positive? options: A)x/y B)-x*y C)-x/y D)x^2+y E)x^6+y SOLUTION:- /+ = - x/y is negative. Answer : A #### A QUESTION:What is the unit’s digit of 7^5 options: A)1 B)3 C)5 D)7 E)9 SOLUTION:7^1=7 7^2=49 7^3=343 7^4=1(last digit) 7^5=7(last digit) and the cycle repeats after every 4 powers Therefore, last digit of 7^5=7 Answer D #### D QUESTION:If x and y are prime numbers such that x > y > 3, then x^2 − y^2 must be divisible by which one of the following numbers? options: A) 3 B) 7 C) 5 D) 9 E) 12 SOLUTION:If x=6 and y=4, then x^2-y^2=20and 20 is divisible only by 5 from the options, thus it must be correct. Answer: C. #### C QUESTION:Which one of the following numbers is exactly divisible by 12? options: A)A)12 B)B)13 C)C)14 D)D)15 E)E)16 SOLUTION:12/12=1 answer is A #### A QUESTION:The list price of a watch is 160. A retailer bought the same watch 122.40. He got two successive discounts one at 10% and the other at a rate which was not legible. What is the second discount rate? options: A)12% B)14% C)15% D)18% E)None of these SOLUTION:Retailer price = list price (1−d1/100)(1−d2/100) ⇒ 122.40 = 160(1−10/100)(1−d2/100) ⇒ 1−d2/100=122.40×100/160×90=0.85 ⇒ d2 = (1 - 0.85) × 100 = 15% Answer C #### C QUESTION:Andy solves problems 78 to 125 inclusive in a Math exercise. How many problems does he solve? options: A)53 B)52 C)51 D)50 E)48 SOLUTION:125-78+1= 48 'E' is the answer #### E QUESTION:Of all the students in a certain dormitory, 1/2 are first-year students and the rest are second-year students. If 4/5 of the first-year students have not declared a major and if the fraction of second-year students who have declared a major is 4 times the fraction of first-year students who have declared a major, what fraction of all the students in the dormitory are second-year students who have not declared a major? options: A)1/15 B)4/5 C)4/15 D)1/5 E)2/5 SOLUTION:tot students=x 1st year student=x/2----> non majaor=4/5(x/2)-----> maj=1/5(x/2) 2nd year student=x/2---->maj=4(1/5(x/2))=2/5(x)--->non major=x/2-2/5(x)=1/5(x) hence 1/5 D #### D QUESTION:The greatest possible length which can be used to measure exactly the length 7 m, 3 m 85 cm, 12 m 95 cm is : options: A)15 cm B)25 cm C)35 cm D)42 cm E)62 cm SOLUTION:Solution Required length = H.C.F. of 700 cm, 385 cm and 1295 cm = 35 cm. Answer C #### C QUESTION:What is the greatest prime factor of (11!10!) + (11!12!)? options: A)11 B)17 C)19 D)23 E)29 SOLUTION:11!10! + 11!12! = 11!10! (1+11*12) = 12!11!(133) = 12!11!(7*19) The greatest prime factor is 19. The answer is C. #### C QUESTION:Combine terms: 15a + 26b -4b – 16a. options: A)4a + 22b B)-28a + 30b C)-a + 22b D)28a + 30b E)5a + 30b SOLUTION:Solution: 15a + 26b -4b – 16a. = 15a – 16a + 26b – 4b. = -a + 22b. Answer: (C) #### C QUESTION:A man is 40 years older than his son. In six years, his age will be twice the age of his son. The present age of this son is options: A)31 years B)32 years C)33 years D)34 years E)35 years SOLUTION:Explanation: Let's Son age is x, then Father age is x+40. => 2(x+6) = (x+40+6) => 2x+12 = x+46 => x = 34 years Answer: Option D #### D QUESTION:The arithmetic mean of the scores of a group of students in a test was 52. 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: options: A)45 B)50 C)51.4 approx. D)54.6 approx. E)54 SOLUTION:Let the required means score be x. Then, 20 * 80 + 25 * 31 + 55 * x = 52 * 100 = 1600 + 775 + 55x = 5200 = 55x = 2825 = x = 565/11 = 51.4. ANSWER:C #### C QUESTION:A sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 878 in 4 years. The sum is: options: A)500 B)698 C)626 D)910 E)None SOLUTION:Sol. S.I. for 1 year = Rs. (878 - 815) = Rs. 63. S.I. for 3 years = Rs. (63 * 3) = Rs. 189. ∴ Principal = Rs. (815 - 189) = Rs. 626 Answer C #### C QUESTION:A train is 410 meter long is running at a speed of 45 km/hour. In what time will it pass a bridge of 140 meter length? options: A)76 seconds B)18 seconds C)40 seconds D)19 seconds E)44 seconds SOLUTION:Speed = 45 Km/hr = 45*(5/18) m/sec = 25/2 m/sec Total distance = 410+140 = 550 meter Time = Distance/speed = 550 * (2/25) = 44 seconds Answer: E #### E <<<Examples ends QUESTION:Each child has 2 pencils and 13 Skittles. If there are 6 children, how many pencils are there in total? options: A)16 B)12 C)18 D)22 E)08 SOLUTION:2*6=12.Answer is B. #### B

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:An air-conditioning unit costs $470. On December there was a discount for Christmas of 16%. Six months later, the holiday season was over so the company raised the price of the air-conditioning by 18%. How much will an air-conditioning unit cost in November? options: A)$466 B)$470 C)$472 D)$484 E)$491 SOLUTION:if its prevoius november (before discount) then price is $470. but if its November of next year then 16% discount on $470=470(1-16/100)=$394.8 again a corrected raised price of 18% over $394.8=394.8(1+18/100)=465.86~$466 Ans A #### A QUESTION:Aaron had $ 2100 left after spending 30 % of the money he took for shopping. How much money did he take along with him? options: A)2000 B)3000 C)4000 D)1000 E)5000 SOLUTION:Let the money he took for shopping be m. Money he spent = 30 % of m = 30/100 × m = 3/10 m Money left with him = m – 3/10 m = (10m – 3m)/10 = 7m/10 But money left with him = $ 2100 Therefore 7m/10 = $ 2100 m = $ 2100× 10/7 m = $ 21000/7 m = $ 3000 Therefore, the money he took for shopping is $ 3000. Answer:B #### B QUESTION:If a is an odd integer and b is an even integer which of the following must be an integer : options: A)a/b B)ab C)2a+b D)2(a+b) E)option B C and D SOLUTION:a= odd = e.g 3 b=even = e.g 6 A. odd/even for example 3/6 = 0.5 no even no odd B. odd * even = 3 * 6 = 18 even C. 2*odd + even = even + even even D. 2(even + odd) = 2(odd) even Hence E it is. #### E QUESTION:A student got twice as many sums wrong as he got right. If he attempted 27 sums in all, how many did he solve correctly ? options: A)12 B)16 C)18 D)9 E)12 SOLUTION:Explanation: Suppose the boy got x sums right and 2x sums wrong. Then, x + 2x = 27 3x = 27 x = 9. Answer:D #### D QUESTION:A boat can move upstream at 15 kmph and downstream at 35 kmph, then the speed of the current is? options: A)5 B)6 C)10 D)8 E)9 SOLUTION:US = 15 DS = 35 M = (35 - 15)/2 = 10 Answer: C #### C QUESTION:If x is divisible by 2, 14, and 11, which of the following must be the least multiple of x? options: A)308 B)154 C)70 D)44 E)0 SOLUTION:We are looking for the LCM (which is not 0) of 2, 11, 14: 2 * 11 * 7 = 154 ANSWER:B #### B QUESTION:A garrison of 1850 men has provisions for 28 days. At the end of 12 days, a reinforcement arrives, and it is now found that the provisions will last only for 10 days more. What is the reinforcement? options: A)1850 B)2960 C)3000 D)1110 E)1712 SOLUTION:1850 ---- 28 1850 ---- 16 x ----- 10 x*10 = 1850*16 x = 2960 1850 ------- 1110 Answer: D #### D QUESTION:The lowest number which should be added to 8247 so that the sum is exactly divisible by 5, 6, 7, 8 and 9 is: options: A)1833 B)1853 C)1733 D)1233 E)1832 SOLUTION:L.C.M. of 5, 6, 7, 8 and 9 = 2520. On dividing 8247 by 2520, the remainder is 687. Number to be added = (2520 - 687) = 1833. Answer: Option 'A' #### A QUESTION:The present population of a town is 4032. Population increase rate is 20% p.a. Find the population of town before 2 years? options: A)2500 B)2800 C)3500 D)3600 E)2050 SOLUTION:P = 4032 R = 20% Required population of town = P/(1 + R/100)^T = 4032/(1 + 20/100)^2 = 4032/(6/5)^2 = 2800(approximately) Answer is B #### B QUESTION:At a certain health club, 30 percent of the members use both the pool and sauna, but 50 percent of the members who use the pool do not use the sauna. What percent of the members of the health club use the pool? options: A)33 1/3% B)46 2/3% C)50% D)62 1/2% E)75% SOLUTION:P = pool S = sauna given P+S = 30 then let only S be x and only P will be 100 - (30+x) = 70 -x 50% of (70-x) = x => 35 - 0.5x = x => x = 23 1/3% so only P = 70 -23 1/3 = 46 2/3% Answer B #### B QUESTION:Harkamal purchased 8kg of grapes at the rate of 75 per kg and 9 kg of mangoes at the rate of 55 per kg. How much amount did he pay to the shopkeeper? options: A)A)1000 B)B)1055 C)C)1065 D)D)1075 E)E)1095 SOLUTION:Cost of 8 kg grapes = 75 × 8 = 600. Cost of 9 kg of mangoes = 55 × 9 = 495. Total cost he has to pay = 600 + 495 = 1095. E) #### E QUESTION:Which of the following is closer to (3!+2!)+(3!-2!)? options: A)8 B)22 C)10 D)14 E)12 SOLUTION:(3!+2!)+(3!-12!)=6+2+6-2 = 12 Answer: E #### E QUESTION:The number of positive integer solutions for the equation x +y +z + t = 18 is options: A)640 B)780 C)380 D)540 E)680 SOLUTION:The number of positive integer solutions for the equatio fx1+x2+⋯+xn=k (k-1)C(n-1)- where k is the number and n is number of variable in the equation. 18-1 C 4-1 = 17C3 = 680 Answer : E #### E QUESTION:A sock drawer contains 5 socks, each one a different solid color. The colors of the socks are yellow, green, blue, indigo, and violet. If a person reaches into the drawer and pulls out two socks, how many different color combinations are possible in the selected pair of socks? options: A)10 B)15 C)21 D)36 E)42 SOLUTION:Since the order in which we select the socks does not matter, we can use combinations. We can select 2 socks from 5 socks in 5C2 ways. 5C2 = 10 Answer : A #### A QUESTION:How many even multiples of 45 are there between 449 and 901? options: A)5 B)6 C)9 D)10 E)11 SOLUTION:450 = 10*45 900 = 20*45 The even multiples are 45 multiplied by 10, 12, 14, 16, 18, and 20 for a total of 6. The answer is B. #### B QUESTION:Out of the total 390 students studying in a college of Arts and Science, boys and girls are in the ratio of 7 : 6 respectively and the number of students studying Arts and Science are in the ratio of 3 : 7 respectively. The boys and girls studying Arts are in the ratio of 4 : 5 respectively. How many boys are studying science? options: A)52 B)65 C)115 D)158 E)168 SOLUTION:Given, boys and girls are in the ratio of 7 : 6, So, Number of boys = 7/13 x 390 = 210 Number of girls = 390 - 210 = 180 Students studying Arts and Science are in the ratio of 3 : 7, Number of students studying Arts = 3/10 x 390 = 117 Number of students studying Science = 390 - 117 = 273 Also boys and girls studying Arts are in the ratio of 4 : 5, Number of boys studying arts = 4/9 x 117 = 52 Number of boys studying science = 210 - 52 = 158 ANSWER:D #### D QUESTION:Four hundred multiples of seven are chosen at random, and 100 multiples of eight are chosen at random. Approximately what percentage of the 500 selected numbers are odd? options: A)20% B)25% C)40% D)50% E)80% SOLUTION:About half the multiples of seven will be odd while all the multiples of eight are even. The percentage of odd numbers is about (1/2)(400) / 500 = 40% The answer is C. #### C QUESTION:Tom and Linda stand at point A. Linda begins to walk in a straight line away from Tom at a constant rate of 4 miles per hour. One hour later, Tom begins to jog in a straight line in the exact opposite direction at a constant rate of 9 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? options: A)60 B)72 C)84 D)90 E)216 SOLUTION:E is the answer.... D = TS where D=distance, T=Time and S=Speed To travel half distance, (2+4T) = 9T ==> T = 2/5 ==> 24 minutes To travel double distance, 2(2+4T) = 9T ==> 4 ==> 240 minutes Difference, 216 minutes E #### E QUESTION:A 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? options: A)1350 B)8837 C)2377 D)3772 E)3881 SOLUTION:Area = (l + b +2d) 2d = (75 + 55 +2.5 * 2) 2*2.5 => 675 675 * 2 = Rs.1350 Answer: A #### A QUESTION:A 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 45min will be. options: A)60 km/h B)53 km/h C)40 km/h D)70 km/h E)65 km/h SOLUTION:Time=50/60 hr=5/6hr Speed=48mph distance=S*T=48*5/6=40km time=45/60hr=3/4hr New speed = 40* 4/3 kmph= 53kmph Answer : B #### B QUESTION:A reduction of 40% in the price of bananas would enable a man to obtain 64 more for Rs.40, what is reduced price per dozen? options: A)1 B)7 C)3 D)8 E)5 SOLUTION:40*(40/100) = 16 --- 64 ? --- 12 => Rs.3 Answer: D #### D QUESTION:A teacher grades students’ tests by subtracting twice the number of incorrect responses from the number of correct responses. If Student A answers each of the 100 questions on her test and receives a score of 79, how many questions did Student A answer correctly? options: A)55 B)60 C)93 D)82 E)91 SOLUTION:let the number of correct responses be x then the number of incorrect responses =100-x according to question x-2(100-x)=79 (subtracting twice of incorrect from correct) 3x=279 x=93 ANSWER:C #### C QUESTION:Cereal 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? options: A)2:5 B)1:3 C)2:7 D)3:4 E)1:5 SOLUTION:2% is 2%-points below 4% and 11% is 7%-points above 4%. The ratio of A:B should be 2:7. The answer is C. #### C QUESTION:How much 60% of 50 is greater than 40% of 30? options: A)18 B)28 C)26 D)27 E)23 SOLUTION:(60/100) * 50 – (40/100) * 30 30 - 12 = 18 Answer:A #### A QUESTION:If two numbers are in the ratio 2:3. If 10 is subtracted from both of the numbers then the ratio becomes 2:4 then find the biggest number? options: A)20 B)22 C)27 D)28 E)30 SOLUTION:Given Ratio => 2:3 2x - 10 : 3x - 10 = 2 : 4 4[2x - 10] = 2[3x - 10] 8x - 40 = 6x - 20 8x - 6x = 40 - 20 x = 10 Then biggest number is = 3x 3x = 30 Ans = E #### E QUESTION:50% of a number is added to 120, the result is the same number. Find the number? options: A)240 B)288 C)1687 D)997 E)121 SOLUTION:(50/100) * X + 120 = X X = 240 Answer:A #### A QUESTION:The average of 10 numbers is calculated as 16. It is discovered later on that while calculating the average, one number namely 36 was wrongly read as 26. The correct average is? options: A)A)17 B)B)18 C)C)19 D)D)22 E)E)24 SOLUTION:Explanation: 10 * 16 + 36 – 26=170 => 170/10 = 17 A) #### A QUESTION:If 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 5 days. If he works at reduced efficiency, he can work without break and finish that same job in 5 days. Dale's output at reduced efficiency is what fraction of his output at full efficiency? options: A)5/2 B)4/1 C)9/5 D)4/5 E)2/5 SOLUTION:We're told that there are 2 ways for Dale to complete a job: 1) Full Efficiency: 2 days of work followed by 1 dayofffor a total of 5 days. 2) Reduced Efficiency: 5 straight days with no days off. Working at Full Efficiency creates the following pattern: 2 days on, 1 day OFF, 2 days on, 1 day OFF, 2 days on, 1 day OFF, 2 days on = 2+1+2= 5 days Totals: 4 days on, 1 days off Reduced Efficiency means that Dale will do 6 days of work in 5 days, thus those Reduceddaysare 4/1 of Full Efficiency. Answer : B #### B QUESTION:Find the average of all the numbers between 6 and 34 which are divisible by 5 options: A)18 B)20 C)24 D)30 E)40 SOLUTION:Exp. Multiples of 5 between 6 and 34 are 10,15,20,25,30 Average = (10+15+20+25+30)/5 =5(10+30)/2*5 = 40/2 =20 Answer:B #### B QUESTION:Mr. Das decided to walk down the escalator of a mall. He found that if he walks down 26 steps, he requires 30seconds to reach the bottom. However, if he steps down 34 stair she would only require 18 seconds to get to the bottom. If the time is measured from the moment the top step begins to descend to the time he steps off the last step at the bottom, find out the height of the stair way insteps? options: A)5 B)6 C)7 D)8 E)9 SOLUTION:here when he step down 26 steps he has 30 seconds for remaining steps. if he step down 34 stairs he has only 18 sec. 30-18=12 12 secs for 8 steps.. 18 secs for 12 steps. 12+34=46 so ans is 46.. ANSWER:B #### B QUESTION:How many of the integers between 25 and 45 are even ? options: A)21 B)20 C)11 D)10 E)9 SOLUTION:Number start between 25 to 45 is 20 numbers half of them is even..which is 10 ANSWER:D #### D QUESTION:If a, b, c, d, e and f are integers and (ab + cdef) < 0, then what is the maximum number S of integers that can be negative? options: A)2 B)3 C)4 D)5 E)6 SOLUTION:Minimuum should be 1 Maximum should be 4: 1 out of a or b to make the multiplication negative 3 out of c, d, e or f to make the multiplication negative. Negative+Negative<0 Answer:C maximum will be 5.. you dont require both the multiplicatin to be negative for entire equation to be negative... any one a or b can be negative to make ab negative and it can still be more(away from 0) than the multiplication of 4 other -ve numbers... actually by writing minimum required as 1 out of 6,you are actually meaning S= 5 out of 6 also possible as you will see 5 or 1 will give you same equation.. ans D #### D QUESTION:A cistern 9 m long and 6 m wide contains water up to a breadth of 2 m 25 cm. Find the total area of the wet surface. options: A)142 m sqaure B)122 m sqaure C)135 m sqaure D)188 m sqaure E)None of these SOLUTION:Explanation: Area of the wet surface = 2[lb+bh+hl] - lb = 2 [bh+hl] + lb = 2[(6*2.25+9*2.25)]+9*6 = 122 m square Option B #### B QUESTION:The side of a cube is 8 m, Find the voiume? options: A)515 B)509 C)502 D)508 E)512 SOLUTION:Cube Volume = a(power)3 a(power)3 = 8(power)3 = 512 m(power)3. Answer is E. #### E QUESTION:5.005/4.004 = options: A)1.05 B)1.50015 C)1.501 D)1.5015 E)1.25 SOLUTION:5.005/4.004 = 5005/4004 = 5(1001)/4(1001) = 5/4 = 1.25 The answer is E. #### E QUESTION:If n divided by 7 has a remainder of 2, what is the remainder when 5 times n is divided by 7? options: A)1 B)2 C)3 D)5 E)6 SOLUTION:As per question => N=7P+2 for some integer p hence 5N => 35Q + 10 => remainder =>10 for some integer Q Alternatively => N=2 > 5N=> 10 => 10 divided by 7 will leave a remainder 3 hence C #### C QUESTION:Linda and Angela contract to paint a neighbor's house. Even though Linda spends 20% more time painting the house than Angela, each receives a payment of m dollars when the work is completed. If Angela decides to pay Linda n dollars so that they would have received the same compensation per hour worked, what is n in terms of m? options: A)A)(1/2)m B)B)(1/3)m C)C)(1/4)m D)D)(1/5)m E)E)(1/11)m SOLUTION:let angela work for 10hrs and get 1100 rs. (m =1100) According to question, linda works 20% more time and gets the same amount. so let linda work 12 hrs and get 1100 rs. so they do a total of 12 +10 =22 hrs of work and get 2200 rs together . The question basically asks to equalise their payment. so a total of 2200 rs is received by them and they do 20 hrs work together. average rate will be 2200/22 = 100 rs per hr. so linda should get 12*100 =1200 rs. But she got only 1100. so angela should give 100 rs to linda. answer = 100/1100 =1/11 answer E #### E QUESTION:A train 200 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? options: A)5 sec B)9 sec C)12 sec D)15 sec E)18 sec SOLUTION:Speed of the train relative to man = (68 - 8) kmph = (60* 5/18) m/sec = (50/3)m/sec Time taken by the train to cross the man = Time taken by It to cover 200 m at 50/3 m / sec = 200 *3/ 50 sec = 12sec Answer : C #### C QUESTION:If 2x = 3y = 10, then 9xy = ? options: A) 1,200 B) 200 C) 150 D) 40 E) 20 SOLUTION:2x = 10;x=5 3y = 10;y=10/3 Multiply: 9xy=9*5*10/3=150 Answer: C. #### C QUESTION:A photo-mat shop charges $0.50 for the first photo inside a film, and 40% cents less for each additional photo. How many photos can we develop with $24 if each film contains 36 photos? options: A)2 films and 6 photos B)5 films and 6 photos C)5 films and 14 photos D)6 films and 4 photos E)6 films and 28 photos SOLUTION:1st photo = 0.50 Subsequent = 0.50*0.6=0.3 Price of 1 full film=0.50+0.3*35=11 Price of 2 full film = 11*2=22 24-22=2 2=0.5+0.3x x=5 24--->2 full films and 1+5=6 photos Answer: A #### A QUESTION:If p and q are two different prime numbers, which of the following cannot be true? options: A)pq is odd. B)p + q is even. C)p + q is odd. D)pq is even. E)p/q is an integer SOLUTION:A 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 (p/q=integer means that p is a multiple of q). Answer: E. All other options are possible: A. pq is odd --> p=3 and q=5; B. p + q is even --> p=3 and q=5; C. p + q is odd --> p=2 and q=3; D. pq is even --> p=2 and q=3; E #### E QUESTION:If p and r are positive integers such that p > r > 1, what is the remainder when 92p × 5p+r + 11r × 6pr is divided by 10? options: A)A.0 B)B.1 C)C.3 D)D.4 E)E.5 SOLUTION:92p × 5p+r + 11r × 6pr--1=B #### B QUESTION:21 goats eat as much as 15 cows. How many goats eat as much as 35 cows? options: A)49 B)32 C)36 D)41 E)45 SOLUTION:Explanation: 15 cows ≡ 21 goats 1 cow ≡ 21/15 goats 35 cows ≡ 21×35/15 goats ≡ 21×7/3 goats ≡ 7 × 7 goats ≡ 49 goats Answer: Option A #### A QUESTION:4,25,121,289,? options: A)345 B)445 C)515 D)529 E)645 SOLUTION:Prime numbers- 2,3,5,7,11,13,17,19,23..... Series - 2^2,5^2,11^2,17^2,23^2 Series- 4, 25, 121, 289, 529. So next term in series is- 529. ANSWER:D #### D QUESTION:The average of 35 numbers is 25. If each number is multiplied by 5, find the new average? options: A)125 B)772 C)821 D)912 E)121 SOLUTION:Sum of the 35 numbers = 35 * 25 = 875 If each number is multiplied by 5, the sum also gets multiplied by 5 and the average also gets multiplied by 5. Thus, the new average = 25 * 5 = 125. Answer:A #### A QUESTION:If 15 men, working 9 hours a day, can reap a field in 16 days, in how many days will 18 men reap the field, working 8 hours a day? options: A)10 B)15 C)20 D)25 E)None of them SOLUTION:Let the required number of days be x. More men, Less days (indirect proportion) Less hours per day, More days (indirect proportion) Men 18 : 15 Hours per day 8: 9 } : :16 : x (18 x 8 x x)=(15 x 9 x 16)= x=(44 x 15)144 = 15 Hence, required number of days = 15. Answer is B. #### B QUESTION:One half of the people at the game wore the team colors. Two thirds of those people wore team hats as well. One fourth of those with team colors and team hats had banners to wave. Twenty five people had team colors and banners, but no hats. One hundred people had only banners. If there were 1824 people at the game, how many had banners? options: A)177 B)277 C)377 D)477 E)577 SOLUTION:1/2 x 1824 = 912 with team colors 2/3 x 912 = 608 with hats and colors 1/4 x 608 = 152 with hats, colors, and banners 152 + 100 + 25 = 277 with banners correct answer B #### B QUESTION:A day-trader plans to invest a total of $23,300 into 15 separate investments. If each investment requires a minimum deposit of $1,400, then which of the following is the maximum amount that she could put into any one investment? options: A)$2,800 B)$3,000 C)$3,700 D)$3,800 E)$3,900 SOLUTION:We can also just keep track of the HUNDREDS DIGITS(since the hundreds digit is different for each answer choice). Total of 14 minimized investments = (14)(1400) = $???600 The 15th investment + $???600 = $23,300 So, the HUNDREDS DIGITS of the 15th investment must be 7 Answer: C #### C QUESTION:According to a survey, at least 60% of people like apples, at least 75% like bananas and at least 80% like cherries. What is the minimum percentage of people who like all three? options: A)15% B)20% C)25% D)0% E)35% SOLUTION:It seems that something is wrong with your answer options. 1) minimum applesbananas: [XXXXXXXXXXXXXX------] - apples [-----XXXXXXXXXXXXXXX] - bananas mimimum ab = 60 - (100-75) = 35% 2) minimum (applesbananas)cherries: [XXXXXXXXX-----------] - applesbananas [----XXXXXXXXXXXXXXXX] - cherries mimimum ab = 35 - (100-80) =15% A #### A QUESTION:Which of the following is equal to 10^-(-2)^3? options: A)1/(10^8) B)1/(10^9) C)1/(10^5) D)1/(10^4) E)1/(10^3) SOLUTION:10^-(-2)^3 => 10^-(-2^3) => 10^-(8) = 1/(10^8) Answer : A #### A QUESTION:40, 45, 50, 55, 60, 75, 75, 90, 100, 100. The list above shows the scores of 10 schoolchildren on a certain test. If the standard deviation of the 10 scores is 21.2, rounded to the nearest tenth, how many of the scores are more than 1 standard deviation below the mean of the 10 scores? options: A)1 B)2 C)3 D)4 E)5 SOLUTION:The average of {40, 45, 50, 55, 60, 75, 75, 90, 100, 100} is 69. 1 standard deviation below the mean is 69 - 21.2 = 47.8. Hence there are two scores (40 and 45) more than 1 standard deviation below the mean. Answer B. #### B QUESTION:The forth proportional to 1,2,3 is? options: A)2 B)4 C)8 D)9 E)6 SOLUTION:Let the fourth proportional to 1,2,3 be x then 1:2::3:x 1x = 2*3 x = 6 Answer is E #### E QUESTION:If 9^y = 3^12, what is y? options: A)2 B)3 C)4 D)5 E)6 SOLUTION:3^2y = 3^12 2y=12, therefore y=6 E #### E QUESTION:One-fifth of the cost price, one-seventh of the marked price and one-sixth of the selling price are all equal. What is the gain or loss to the trader? options: A)120 % B)140 % C)162/3 % D)20 % E)None SOLUTION:Sol. CP/5 = SP/6 ⇒ SP/CP = 1.2 ⇒ 20% gain. Answer D #### D QUESTION:What is the sum of the numbers between 1 and 20, inclusive? options: A)310 B)200 C)215 D)285 E)210 SOLUTION:Sol. 1+2+3...17+18+19+20 answer. E #### E QUESTION:Two 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? options: A)270 B)277 C)200 D)257 E)271 SOLUTION:Relative speed = (72 - 36) * 5/18 = 2 * 5 = 10 mps. Distance covered in 27 sec = 20 * 10 = 200 m. The length of the faster train = 200 m. Answer: C #### C QUESTION:Salad dressing P is made up of 30% vinegar and 70% oil, and salad dressing Q contains 10% vinegar and 90% oil. If the two dressings are combined to produce a salad dressing that is 12% vinegar, dressing P comprises what percentage of the new dressing? options: A)50% B)40% C)30% D)20% E)10% SOLUTION:Let x be the percentage of dressing P in the new dressing. 0.3x + 0.1(1-x) = 0.12 0.2x = 0.02 x = 0.1 = 10% The answer is E. #### E QUESTION:The H.C.F. and L.C.M. of two numbers are 14 and 5040 respectively If one of the numbers is 144, find the other number options: A)400 B)256 C)120 D)490 E)None of these SOLUTION:Explanation: Solve this question by using below formula. Product of 2 numbers = product of their HCF and LCM 144 * x = 14 * 5040 x = (14*5040)/144 = 490 Option D #### D QUESTION:The average age of a husband, wife and their child 12 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? options: A)19.01 years B)5.25 years C)16 years D)15 years E)4.75 years SOLUTION:Sum of the present ages of husband, wife and child = (23 * 2 + 5 * 2) = 57 years. Required average = 57/12 = 4.75 years. Answer:E #### E QUESTION:Find the one which does not belong to that group ? options: A)41 B)43 C)53 D)47 E)57 SOLUTION:Explanation: 41, 43, 47 and 53 are prime numbers, but not 57. ANSWER IS E #### E QUESTION:Two trains are moving in opposite directions at 60 km/hr and 90 km/hr. Their lengths are 1.75 km and 1.25 km respectively. The time taken by the slower train to cross the faster train in seconds is? options: A)12 B)72 C)48 D)99 E)11 SOLUTION:Relative speed = 60 + 90 = 150 km/hr. = 150 * 5/18 = 125/3 m/sec. Distance covered = 1.75 + 1.25 = 3 km = 3000 m. Required time = 3000 * 3/125 = 72 sec. Answer: B #### B QUESTION:How 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? options: A)482 B)226 C)276 D)266 E)181 SOLUTION:Explanation: 20000(11/10)4 - 20000(6/5)2 = 482 Answer: A #### A QUESTION:A certain elevator has a safe weight limit of 1950 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 190 pounds and the average weight of the others being 200 pounds? options: A)7 B)8 C)9 D)10 E)11 SOLUTION:Lets assume there are 2X people. Half of them have average weight of 190 and other half has 200. Maximum Weight is = 1950 So 190*X + 200*X = 1950 => 390X = 1950 => X is approximately equal to 5. So total people is 2*5 = 10 Answer D. #### D QUESTION:A work could be completed in 100days by x workers. However, due to the absence of 10workers, it was completed in 110days. The original no.of workers was: options: A)90 B)106 C)110 D)120 E)130 SOLUTION:sax Letlheo g alnumberofworkers hex x workers can do the wor - 100 days (x — 10) workers can do the work in 110 days 4 100x 1u1x— 10) 1100 Q x 110 C #### C <<<Examples ends QUESTION:A collection of 20 coins, each with a face value of either 10 cents or 35 cents, has a total face value of $2.5. How many of the coins have a face value of 10 cents? options: A)24 B)18 C)32 D)16 E)20 SOLUTION:0.10(x)+0.35(20-x)=2.5 0.10x+7-0.35x=2.5 so x=18 ans is B #### B

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:The LCM and HCF of two numbers are 8 and 48 respectively. If one of them is 24, Find the other ? options: A)12 B)14 C)15 D)16 E)20 SOLUTION:HCF x LCM = Product of Numbers 8 x 48 = 24 x the other number other number = (8 x 48) / 24 other number = 16 ANSWER : D #### D QUESTION:How many kilograms of sugar costing Rs.9 per kg must be mixed with 27 kg of sugar costing Rs.7 per Kg so that there may be a gain of 10% by selling the mixture at Rs.9.24 per Kg? options: A)36 Kg B)42 Kg C)54 Kg D)63 Kg E)None of these SOLUTION:Solution Ratio of quantities of 1st and 2nd kind = 14 : 6 = 7 : 3. Let x kg of sugar of 1st kind be mixed with 27 kg of 2nd kind. Then, 7 : 3 = x : 27 or x = (7 x 27 / 3) = 63 kg Answer D #### D QUESTION:The sum of 55 consecutive integers is 5555. What is the greatest integer in the set? options: A)126 B)128 C)130 D)132 E)134 SOLUTION:Let x be the first integer in the set, then x+54 is the largest integer. The sum is: x+(x+1)+(x+2)+...+(x+54) = 55x + 54*55/2 = 55(x+27) Then x+27=101 x=74 The largest integer in the set is 74+54=128 The answer is B. #### B QUESTION:A man in train notice that he can count 51 telephone posts in 1 minute. If they are known to be 5 meters apart,then at what speed is the train traveling? options: A)100km/hr B)110km/hr C)50km/hr D)150km/hr E)200km/hr SOLUTION:Number of gaps between 51 telephone posts = 50 Distance traveled in 1 minute = 50*50 = 2500m = 2.5km Speed = 60*2.5=150km/hr Answer is D #### D QUESTION:If p, q and r are positive integers and satisfy x = (p + q -r)/r = (p - q + r)/q = (q + r - p)/p, then the value of x is? options: A)1/2 B)1 C)-1/2 D)-1 E)0 SOLUTION:When two or more ratios are equal, each of the ratios are equal to sum of the numerators divided by the sum of the denominators, provided sum of the denominators is non-zero. Hence, x = (p + q -r)/r = (p - q + r)/q = (q + r - p)/p => x = (p + q - r + p - q + r + q + r - p) / (r + q + p) => x = (r + q + p) / (r + q + p) = 1 p + q + r is non-zero. ANSWER:B #### B QUESTION:Which of the following is closest to (8!-7!)/(8!+7!)? options: A)0.01 B)0.8 C)0.2 D)1 E)10 SOLUTION:(8!-7!)/(8!+7!) 7! (8-1)/7! (8+1) 7/9 = 0.8 (approximately) B is the answer #### B QUESTION:Two trains of length 100 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? options: A)10 sec B)32 sec C)82 sec D)20 sec E)19 sec SOLUTION:Relative speed = (42 + 30) * 5/18 = 4 * 5 = 20 mps. Distance covered in passing each other = 100 + 280 = 380m. The time required = d/s = 380/20 = 19 sec. Answer:E #### E QUESTION:An aptitude test contains 4 questions from verbal reasoning, 5 questions from simple mathematics and 6 questions testing knowledge of English. Three questions are selected at random from the list of questions. The probability that all of them are from simple mathematics section, is: options: A)2/91 B)1/22 C)3/22 D)2/77 E)None of these SOLUTION:Explanation : Let S be the sample space. Then, n(S) = number of ways of selecting 3 questions out of 15= 15C3= (15 x 14 x 13)/(3 x 2 x 1)= 455 Let E = event of getting all the 3 questions from simple mathematics section. n(E) = 5C3 = 5C2 = (5 x 4)/(2 x 1) = 10 P(E) = n(E)/n(S) = 10/455 = 2/91 . Answer : A #### A QUESTION:Special 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? options: A)2(26)^3 B)26(26)^2 C)27(26)^2 D)26(26)^3 E)27(26)^3 SOLUTION:26^2+26^3 = 26^2(1+26)=27*26^2 The answer is C. #### C QUESTION:A person purchased a TV set for Rs. 16000 and a DVD player for Rs. 1800. He sold both the items together for Rs. 31150. What percentage of profit did he make? options: A)30% B)75% C)40% D)70% E)None of these SOLUTION:The total CP = Rs. 16000 + Rs. 1800 = Rs. 17800 and SP = Rs. 31150 Profit(%) = (31150 - 17800)/17800* 100 = 75% ANSWER:B #### B QUESTION:Find the sum of all odd numbers upto 100. options: A)200 B)1000 C)2500 D)3140 E)3200 SOLUTION:Sol. The given numbers are 1, 3, 5, 7, ..., 99. This is an A.P. with a = 1 and d = 2. Let it contain n terms. Then, 1 + (n - 1) x 2 = 99 or n = 50. Required sum = (n/2) (first term + last term) = 50(1 + 99)/2 = 2500. ANSWER C 2500 #### C QUESTION:Jerry wrote down all the positive integers that have at most 7 digits and contain only the digits 0 and 1. How many times did he write down the digit 1 ? options: A)128 B)224 C)288 D)448 E)512 SOLUTION:Jerry wrote down a total of 27 − 1 = 127 numbers (0 is missing). Add 0 to the numbers Jerry wrote. We divide the resulting 128 numbers in pairs. If x is one of the numbers Jerry wrote then we put it in pair with 1111111 − x (whose digits are also 0s and 1s). For example 1100101 is paired with 11010. In this way, we divide the numbers into 64 distinct pairs so that each number appears exactly once. Note that there are exactly 7 digits 1 in each pair. So, Jerry wrote the digit 1 exactly 64 × 7 = 448 times. correct answer D #### D QUESTION:Consider a sequence of numbers given by the expression 7 + (q - 1) * 5, where n runs from 1 to 80.What is the sum of this series ? options: A)409 B)1636 C)16360 D)16000 E)15360 SOLUTION:terms in this sequence are 7,12,17----402 now since this is an a.p. with a common difference of 5. therefore its sum can be given as q(a+l)/2----------------1) q= total no. of terms =80 a= first term=7 l= last term=402 subsituting values in the expression 1 we have 80(7+402)/2 = 40(409) =16360=C #### C QUESTION:A car is traveling 72 kilometers per hour. How many meters does the car travel in one minute? options: A)1,200 meters / minute B)1,300 meters / minute C)1,450 meters / minute D)1,550 meters / minute E)1,650 meters / minute SOLUTION:Convert hour into minutes ( 1 hour = 60 minutes) and kilometers into meters (1 km = 1000 m) and simplify 72 kilometers per hour = 72 km/hr = (72 * 1000 meters) / (60 minutes) = 1,200 meters / minute correct answer A #### A QUESTION:A 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? options: A)10 B)20 C)50 D)30 E)40 SOLUTION:Man's speed with the current = 15 km/hr => speed of the man + speed of the current = 15 km/hr speed of the current is 2.5 km/hr Hence, speed of the man = 15 - 2.5 = 12.5 km/hr man's speed against the current = speed of the man - speed of the current = 12.5 - 2.5 = 10 km/hr Answer is A. #### A QUESTION:Six 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 5, what is the probability that one of the two cards drawn is numbered 3 ? options: A)1/3 B)1/2 C)1/4 D)1/5 E)1/6 SOLUTION:(3,2) (2,3) (4,1) (1,4) – only 4 possible scenarios for sum to be 5. One from this 4 has already happened. From this four cases, only in two we have 3. So, the probability is 2 chances out of 4 that the one that occurred had 3: P=2/4.=1/2 Answer: B. #### B QUESTION:The average marks obtained by 120 cndidates in a certainexaminationis 35.if the average marks of passed candidate is 39 and that of the failedcandidates is 15,what is the number of candidates who passed the examination options: A)14 years B)14 years 5 month C)14 years 8 month D)15 years E)15 years 5 month SOLUTION:(d) Let No. of passed candidates are x So, x * 39 + (120 – x) 15= 120 * 35 x = 100 2.(a) Total increase = 8 * 2 = 16 years So, total age of two women = 35 + 45 +16= 96 Average age of two women=96/2=48 years 3(d) Total decrease = 20 * 2 = 40 month = 3 years 4 month So, age of new boy = 18 years – 3 years 4 month = 14 years 8 month C #### C QUESTION:A 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? options: A)12 B)17 C)15 D)19 E)26 SOLUTION:Let the average after the 16th inning be P. So, the average after the 15th inning will be (P-3) Hence, 15(P-30) + 64 = 16P => P = 19 Answer:D #### D QUESTION:Sum of 3 consecutive even no.'s is 26 more than the 1st no. of the series. Find the middle no.? options: A)10 B)12 C)16 D)18 E)21 SOLUTION:Let the numbers be x, x+2 and x+4 then x + x+2 + x+4 = x+26 3x + 6 = x + 26 2x = 20 \inline \therefore x = 10 \inline \therefore Middle number = x + 2 = 10+2 = 12 B #### B QUESTION:A, 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? options: A)2399 B)2889 C)2830 D)2878 E)3000 SOLUTION:Explanation: 60*5:36*6:75*3 100: 72: 75 100/247 * 7410 = 3000 Answer: E #### E QUESTION:In a sports club with 27 members, 17 play badminton and 19 play tennis and 2 do not play either. How many members play both badminton and tennis? options: A)7 B)8 C)9 D)10 E)11 SOLUTION:Let x play both badminton and tennis so 17-x play only badminton and 19-x play only tennis. 2 play none and there are total 30 students. hence, (17-x)+(19-x)+x+2=27 38-2x+x=27 38-x=27 x=11 So 8 members play both badminton and tennis. E #### E QUESTION:A train overtakes two persons walking along a railway track. The first person walks at 4.5 km/hr and the other walks at 5.4 km/hr. The train needs 8.4 and 8.5 seconds respectively to overtake them. What is the speed of the train if both the persons are walking in the same direction as the train? options: A)80 km/hr B)81 km/hr C)85 km/hr D)84 km/hr E)83 km/hr SOLUTION:Let x is the length of the train in meter and y is its speed in kmph x/8.4 = (y-4.5)(10/36) ---(1) x/8.5 = (y-5.4)(10/36) ---(2) Dividing 1 by 2 8.5/8.4 = (y-4.5)/ (y-5.4) => 8.4y - 8.4 × 4.5 = 8.5y - 8.5×5.4 .1y = 8.5×5.4 - 8.4×4.5 => .1y = 45.9-37.8 = 8.1 => y = 81 km/hr Answer is B. #### B QUESTION:If P(A) = 5/7 and P (B) = 2/5, find P (A n B) if A and B are independent events. options: A)7/25 B)3/25 C)8/25 D)2/7 E)3/17 SOLUTION:P (A n B) = P(A) . P(B) P (A n B) = 5/7 . 2/5 P (A n B) = 2/7. D #### D QUESTION:1100 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 ? options: A)A)63.3% B)B)52.4% C)C)81.2% D)D)75.4% E)E)72.11% SOLUTION:Total number of students = 1100+700 = 1800 Number of students passed = (31% of 1100+23% of 700) = 341+161 = 502 number of failures = 1298*100/1800= 72.11% Answer is E #### E QUESTION:HOW 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 10% options: A)36 B)40 C)32 D)42 E)45 SOLUTION:Let the weight of tea(25 per kg) to be used - X The total cost of the blend - total cost of 25 RS tea + total cost of 30 RS tea - 25X + 900 ( as the total weight of 30 RS tea is already given i.e 30) total weight of the blend = X + 30 ( which should be sold per 30 RS and result in 10% profit) The equation follows like this 25X + 900 + (10 % of (25X + 900)) = 30( X + 30) 25X + 900 +2.5 X + 90 = 30 X + 900 27.5 X + 990 = 30 X + 900 2.5 X = 90 X= 90/2.5 = 36 ANSWER:A #### A QUESTION:Two 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 options: A)1/3. B)1/2. C)3. D)2. E)6. SOLUTION:Difference = Average H - L = (H + L)/2, Solving for H/L gives 3. A quick check, H be 9 and L be 3, 9 - 3 = (9 + 3 )/2 C #### C QUESTION:(X)+1789+9011-7819=90510. Calculate the value of X options: A)87501 B)87599 C)87529 D)87520 E)87521 SOLUTION:x+1789+9011-7819=90510 =x+1789+9011=90510+7819 =x+10800=98329 =x=98329-10800 =87529 Answer is C #### C QUESTION:What is the smallest integer that, when increased by seven, is divisible by 14, 25, 36, and 81? options: A)1020600 B)1020593 C)56693 D)28343 E)18900 SOLUTION:14 = 2 * 7 25 = 5 * 5 36 = 2 * 2 * 3 * 3 81 = 3 * 3 * 3 * 3 So our answer is (2 * 2 * 3 * 3 * 3 * 3 * 5 * 5 * 7) - 7 = 56693, which is option C. #### C QUESTION:12 men take 18 days to complete a job whereas 12 women in 18 days can complete 1/3 of the same job. How many days will 10 men and 8 women together take to complete the same job? options: A)6 B)13 1⁄2 C)17 D)Data inadequate E)None of these SOLUTION:12 M × 18 = 12 W × 18 × 3/1 \ w = 1/3 M 10M + 8W = 10M + 8 × 1/3M = 12 2/3 M \12 2/3 men can complete the same work in 12×18/12 2/3=17days Answer C #### C QUESTION:A bus starts from city X. The number of women in the bus is half of the number of men. In city Y, 16 men leave the bus and eight women enter. Now, number of men and women is equal. In the beginning, how many passengers entered the bus ? options: A)15 B)30 C)36 D)72 E)46 SOLUTION:Explanation: Originally, let number of women = x. Then, number of men = 2x. So, in city Y, we have : (2x - 16) = (x + 8) or x = 24. Therefore Total number of passengers in the beginning = (x + 2x) = 3x = 72. Answer: D #### D QUESTION:A number x is multiplied with itself and then added to the product of 4 and x. If the result of these two operations is -8, what is the value of x? options: A)-4 B)-2 C)2 D)4 E)Cannot be determined. SOLUTION:A number x is multiplied with itself --> X^2 added to the product of 4 and x --> X^2+4X If the result of these two operations is -4 --> X^2+4X=-8 i.e X^2+4X+8=0 is the Quadratic equation which needs to be solved. no solution IMO E #### E QUESTION:The maximum numbers of students among them 671 Note books and 610 pencils can be distributed in such a way that each student gets the same number of note books and same number of pencils is options: A)91 B)910 C)61 D)1911 E)None SOLUTION:olution Required number of students. = H.C.F of 671 and 610. ‹=› 61. Answer C #### C QUESTION:In 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 W of her bushes have only yellow roses? options: A)20 B)30 C)50 D)70 E)80 SOLUTION:let, the number of bushes with only yellow flowers be x so, number of bushes with only yellow flowers will be 1.5x if total number of bushes of flowers= T then total number of bushes with yellow flowers= 0.8T we can say that total number of bushes with yellow flowers+ bushes with only white flowers= total number of bushes with flowers so, W=0.8T+x=T x=0.2T so, 1.5x=0.3T 30% flowers are yellow flowers OA B #### B QUESTION:A tank can supply water to a village for 30 days. If a leak at the bottom of the tank drains out 15 liters per day, the supply lasts for 20 days only. For how many days will the supply last if the leak drains out 20 liters per day? options: A)12 B)14 C)15 D)16 E)18 SOLUTION:Losing 15 liters per day results in a loss of 300 liters in 20 days. So, those 300 liters were for 10 days, making daily consumption of the village 30 liters per day. Thus the capacity of the tank is 30*30 = 900 liters. Losing 20 liters plus 30 liters gives 50 liters per day. At this rate the supply will last 900/50 = 18 days. The answer is E. #### E QUESTION:Convert 2/5 to a decimal options: A)0.1 B)0.2 C)0.3 D)0.4 E)0.5 SOLUTION:Divide 2 by 5: 2 / 5 = 0.4 Answer: 2/5 = 0.4 (D) #### D QUESTION:If six persons sit in a row, then the probability that three particular persons are always together is ? options: A)1/3 B)1/9 C)1/5 D)1/7 E)1/1 SOLUTION:Six 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 #### C QUESTION:Which expression is the greatest? options: A)3252/3257 B)3456/3461 C)3591/3596 D)3346/3351 E)3453/3458 SOLUTION:Let 3252/3257 be the original fraction. Notice that it is a positive Proper fraction. Hence adding the same constant to both the numerator and the denominator will increase the fraction as the fraction will move closer to one. Hence we just have to pick the number that adds the greatest value to both the numerator and the denominator. Options can be re-written as (x-5)x => 1-(5/x) A) 1- (5/3257) B) 1- (5/3461) C) 1- (5/3596) D) 1- (5/3351) E) 1- (5/3458) ANSWER:C #### C QUESTION:The area of a rectangle is 15 square centimeters and the perimeter is 16 square centimeters. What are the dimensions of the rectangle? options: A)2&4 B)3&5 C)4&6 D)5&7 E)6&8 SOLUTION:Let 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. 15 = x y and 16 = 2 x + 2 y Solve the second equation for x x = 8 - y Substitute x in the equation 15 = x y by 8 - y to rewrite the equation as 15 = (8 - y) y Solve for y to find y = 3 and y = 5 Use x = 8 - y to find x when y = 3 , x = 5 and when y = 5 , x = 3. The dimensions of the rectangle are 3 and 5. correct answer B #### B QUESTION:If all the 6 are replaced by 9, then the algebraic sum of all the numbers from 1 to 100(both inclusive) varies by options: A)330 B)340 C)350 D)360 E)370 SOLUTION:1 11 21 .......91 2 12 22........92 3 13 23........93 . . . .. . .. . . . . .. .. . .. . . . .. . . .. . ... there are total 20 occurrence of 6. once place at 6 th row in every column and tens place in 6 th column and diff of 6 and 9 is 3 so 3*1*10+3*10*10 = 330 ANSWER:A #### A QUESTION:A batsman in his 11th inning makes a score of 69 and their by increasing his average by 1. What is his average after the 11th inning? options: A)58 B)59 C)68 D)69 E)78 SOLUTION:10x + 69 = 11(x + 1) x = 58 + 1 = 59 Answer:B #### B QUESTION:A man bought 20 shares of Rs. 50 at 5 discount, the rate of dividend being 13. The rate of interest obtained is: options: A)27% B)87% C)15% D)66% E)88% SOLUTION:Investment = Rs. [20 x (50 - 5)] = Rs. 900. Face value = Rs. (50 x 20) = Rs. 1000. Dividend = Rs. 27 x 1000 = Rs. 135. 2 100 Interest obtained = 135 x 100 % = 15% 900 View Answer Discuss in Forum Answer: C #### C QUESTION:The price of a coat in a certain store is $500. If the price of the coat is to be reduced by $350, by what percent is the price to be reduced? options: A)70% B)15% C)20% D)25% E)30% SOLUTION:price of a coat in a certain store = $500 the price of the coat is to be reduced by $350 % change = (Final Value - Initial Value)*100 / Initial Value % Reduction= (Reduction in Price)*100 / Initial Value i.e. % Reduction= (350)*100 / 500 = 70% Answer: Option A #### A QUESTION:The cost of 2 chairs and 3 tables is Rs.1300. The cost of 3 chairs and 2 tables is Rs.1200. The cost of each table is more than that of each chair by? options: A)Rs.70 B)Rs.75 C)Rs.50 D)Rs.60 E)None of these SOLUTION:2C + 3T = 1300 --- (1) 3C + 3T = 1200 --- (2) Subtracting 2nd from 1st, we get -C + T = 100 => T - C = 100 ANSWER:E #### E QUESTION:Consider two statements Statement 1 => If R is an integer and R=2p+1 where p is not an integer. Statement 2 => If S is an integer and S=2q where q is not an integer Which of the following correctly specifies the Even/Odd nature of R and S respectively options: A)1) Odd,Even B)2) Odd,Odd C)3) Even,Odd D)4) Even,Even E)5) Cannot be determined SOLUTION:answer will be E R = integer R = 2p+1 = integer here p can be any n/2 and n can be even or odd , matters alot 2 get cancelled out if n were even R would odd if n odd R would be even ANSWER IS E #### E QUESTION:If 6^w is a factor of (10!)^2, What is the greatest possible value of w ? options: A)2 B)4 C)6 D)8 E)10 SOLUTION:w 10!= 10*9*8*7*6*5*4*3*2*1 = 2*5*3*3*2*2*2*7*2*3*5*2*2*3*2 = 2^8*3^4*5^2*7 6= 2*3 Therefore only the exponents of 2 and 3 are relevant, 2^8 or 3^4 -> higher number counts = 8 -> Answer Choice D #### D QUESTION:3,9,27,81,.... options: A)583 B)604 C)616 D)243 E)636 SOLUTION:1*3=3 3*3=9 9*3=27 27*3=81 81*3=243 ANSWER:D #### D QUESTION:There 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? options: A)90. B)80. C)50. D)40. E)25. SOLUTION:STREET-CAT DOMESTIC-Cat 70 130 (20gray+50other) 90gray+40other Answer:D #### D QUESTION:There 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. options: A)1 B)2 C)3 D)4 E)9 SOLUTION:145 divided by 12 = 12x12+1. That is, 1 banana will be extra after distributing 12 bananas to each candidate (12 in number). Answer A. #### A QUESTION:The sum of two consecutive number is 109. Which is the larger number? options: A)42 B)43 C)44 D)45 E)55 SOLUTION:Let consecutive number be x, x+1 Therefore sum of the consecutive number is x + x+1=109 2x+1=109 2x=108 x=54 Therefore larger number is x+1=55 ANSWER:E #### E QUESTION:A started a bussiness with a sum of Rs. 14000. After 4 months, B entered with an amount of Rs. 12000 and A added another 2,000 in the business. After 6 months, C entered with Rs. 20000 and 'B' withdrew Rs. 2000 from the business. What will be C's share of profit out of a total profit of Rs. 94000 at the end of 2 years. options: A)Rs. 376000 B)Rs. 204000 C)Rs. 36000 D)Rs. 18000 E)Rs. 260000 SOLUTION:Investments-- A=14000x4+16000x20=376000 B=12000x2+10000x18=204000 C=20000x18=360000 So C's Share = 94000xC/(A+B+C)=36000 ANSWER:C #### C QUESTION:A 2member committee comprising of one male & one female member is to be constitute out of 5 males and 3females. Among st the females. Ms.A refuses to be a member of the committee in which Mr.B is taken as the member. In how many different ways can the committee be constituted ? options: A)10 B)14 C)16 D)18 E)21 SOLUTION:5C1 * 3C1 -1 = 15-1 = 14 B #### B QUESTION:Rice weighing 3power3/4 pounds was divided equally and placed in 4 containers. how many ounces of rice were in each? options: A)15 ounces B)25 ounces C)12 ounces D)22 ounces E)35 ounces SOLUTION:3power3/4 / 4 pounds, = (4x3+3)/4 ponds. = (15/4) /4 ponds. = (15/4) / (1/4) ponds. = 15/16 pounds. 1 pound = 16 ounces. therefore, 15/16 pounds = 15/16*16 ounces = 15 ounces. Correct answer : (A) #### A QUESTION:A car covers a distance of 520 km in 4 hours. Find its speed? options: A)104 B)130 C)298 D)269 E)213 SOLUTION:520/4 = 130 kmph Answer:B #### B QUESTION:Sreenivas 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. 2178? options: A)2277 B)2669 C)2200 D)2766 E)2998 SOLUTION:Let the cost price of table for Sreenivas be Rs. x and given that, cost price of table for Mahesh = Rs. 2178. => (90%) of (110%) of x = Rs. 2178. => (90/100)(110/100)x = 2178 => x = (2178 * 100)/(9 * 11) => x = Rs. 2200 Answer: C #### C QUESTION:A car is traveling 68 kilometers per hour. How many meters does the car travel in one minute? options: A)1250m/min B)1133.33m/min C)2560m/min D)1670m/min E)1890m/min SOLUTION:Convert hour into minutes ( 1 hour = 60 minutes) and kilometers into meters (1 km = 1000 m) and simplify 68 kilometers per hour = 68 km/hr = (68 × 1000 meters) / (60 minutes) = 1,133.33 meters / minute correct answer is B)1133.33m/min #### B QUESTION:If x is a positive integer, then the least value of x for which x! is divisible by 10,000 is? Can someone please explain intuitively what the question is asking? options: A)5 B)9 C)12 D)15 E)20 SOLUTION:In 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. 5! = 120 has 1 trailing zeros. 10! will have 2 trailing zeros. 15! will have 3 trailing zeros. 20! will have 5 trailing zeros. Answer: E. #### E QUESTION:Stacy has a 63 page history paper due in 3 days. How many pages per day would she have to write to finish on time? options: A)9 B)8 C)10 D)8.5 E)21 SOLUTION:63/3=21 Answer : E #### E QUESTION:If n=3*4*p where p is a prime number greater than 3,how many different positive non-prime divisors does n have, excluding 1 and n? options: A)Six B)Seven C)Eight D)Nine E)Ten SOLUTION:n=3∗2^2∗p Number of divisors = 2 * 3 * 2 = 12 The 12 divisors includes 1, n, 3, 2 and p Number of different non prime divisors excluding 1 and n = 12 - 5 = 7 Answer: B #### B QUESTION:A 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? options: A)10 min past 7pm on wednesday B)20 min past 7pm on wednesday C)20 min past 9pm on wednesday D)26 min past 7pm on wednesday E)20 min past 4pm on wednesday SOLUTION:This 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 (7×24)+12 = 180 hours. To show the correct time, it has to gain 5 min. So the correct time will be shown on wednesday at 7:20 PM Answer: B #### B QUESTION:Find the smallest number which should be multiplied with 13225 to make it a perfect square. options: A)25 B)5 C)1 D)23 E)6 SOLUTION:13225 = 5*5*23*23 Required smallest number = 1 1 is the smallest number which should be multiplied with 13225 to make it a perfect square. ANSWER:C #### C QUESTION:1401 x 1401 = ? options: A)1962800 B)1962801 C)1960000 D)1951611 E)1951613 SOLUTION:1401 x 1401 = (1401)2 = (1400+1)2 = (1400)2 + (1)2 + (2 x 1400 x 1) = 1960000 + 1 + 2800 = 1960001+ 2800 = 1962801. B) #### B QUESTION:Fox 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? options: A)9% B)56.6% C)11% D)12% E)15% SOLUTION:You 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 3(15) = 45 - Fox 2(18) = 36 - Pony The total discount discount is $3 and you are asked to find the percent discount of pony jeans, so 45(18 - X)/100 + 36(X)/100 = 3 or 45*18 -45*x + 36*x =3*100 or 9x = -3*100 +45*18 x= 510/9 = 56.6% B #### B QUESTION:What is the range of all the roots of |x^2 - 5| = x ? options: A)4 B)3 C)2 D)1 E)0 SOLUTION:we get 2 quadratic equations here .. 1) x^2-x-5=0 ....... roots 2 , -1 2) x^2+x-5=0 ........ roots -2, 1 Inserting each root in given equation , it can be seen that -1 and -2 do not satisfy the equations . So value of x for given equation .... x=5 or x=1 I guess range is 5-1 =4 A #### A QUESTION:If grapes are 92% water and raisins are 20% water, then how much did a quantity of raisins, which currently weighs 10 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.) options: A)25 pounds B)46 pounds C)92 pounds D)100 pounds E)146 pounds SOLUTION:Since 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*10 --> x = 100. Answer: D. #### D <<<Examples ends QUESTION:John weighs twice as much as Susan. Susan's weight is 60% of Sam's weight. Mark weighs 50% of Lynn's weight. Lynn weighs 160% of John's weight. Which of these 5 people weighs the least? options: A)John B)Susan C)Sam D)Mark E)Lynn SOLUTION:John weighs twice as much as Susan --> J=2S --> John cannot weigh the least; Susan's weight is 60% of Sam's weight --> S=0.6*Sam --> Sam cannot weigh the least; Mark weighs 50% of Lynn's weight --> M=0.5*L --> Lynn cannot weigh the least; Lynn weighs 160% of John's weight --> L=1.9*J --> John cannot weigh the least (we already know that); As 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*(1.6*J)=0.8*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. Answer: B. #### B

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:What is the tens digit of 7^1415? options: A)0 B)1 C)2 D)3 E)4 SOLUTION:7^1 = 7 7^2 = 49 7^3 = 343 7^4 = 2401 7^5 = 16807 7^6 = 117649 We 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 ) 0 , 4 , 4 , 0 . 1415= 4*353 + 3 The ten's digit will be 4 . Answer E #### E QUESTION:The average age 9 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? options: A)14 years B)17 years C)18 years D)12 years E)11 years SOLUTION:9 * 2 = 181 Answer:C #### C QUESTION:How many of the positive factors of 42 , 104 and how many common factors are there in numbers? options: A)4 B)2 C)3 D)5 E)1 SOLUTION:factors of 42 - 1,2,3,6,7,14,21,42 factors of 104 - 1,2,4,8,13,26,52,104 Comparing both, we have two common factors of 40 and 104- 1,2, Answer(B) #### B QUESTION:In Rwanda, the chance for rain on any given day is 1/2. What is the probability that it rains on 4 out of 6 consecutive days in Rwanda? options: A)4/7 B)3/7 C)15/64 D)4/28 E)28/135 SOLUTION:using Binomial. theorem nCr (p)^r (q)^n-r 6C4 (1/2)^4 (1/2)^r which is 15/64 Answer is C. #### C QUESTION:A, 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? options: A)388 B)299 C)266 D)400 E)2871 SOLUTION:2*12 : 3*12 : 4*24 1: 3: 4 1/8 * 3200 = 400.Answer: D #### D QUESTION:Eddy 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 540 kms and City A and City C is 300 kms. What is the ratio of their average speed of travel? (Eddy: Freddy) options: A)8/3 B)3/8 C)8/5 D)12/5 E)5/3 SOLUTION:Distance traveled by Eddy = 540 km Time taken by Eddy = 3 hours Average speed of Eddy = 540/3 = 180 km/hour Distance traveled by Freddy = 300 km Time taken by Freddy = 4 hours Average speed of Freddy = 300/4 = 75 km/hour Ratio of average speed of Eddy to Freddy = 180/75 = 12/5 Answer D #### D QUESTION:The average weight of a group of 30 friends increases by 2 kg when the weight of their football coach was removed. If average weight of the group after removing the weight of the football coach is 28 kg, what is the weight of their football coach? options: A)31 kg B)60 kg C)61 kg D)62 kg E)88 kg SOLUTION:let c=coach's weight original total weight=(30 friends)(30 kg avge)=900kg (900-c)/(30-1)=28 kg avge c=88 kg Answer - E #### E QUESTION:At an elementary school, 70% of the faculty members are women and 40% of the faculty members are married. If 1⁄3 of the men are single, what fraction of the women are married? options: A)5⁄7 B)7⁄10 C)2/7 D)7⁄30 E)5⁄70 SOLUTION:--------------------M------W--------Total Marrried----------20-----20---------40 Not married-----10-----50---------60 Total-------------30-----70--------100 need married woman/total woman, so 20/70=2/7 C #### C QUESTION:If 6 (A's capital) = 8 (B's capital) = 10 (C's capital). Then the ratio of their capitals is? options: A)20:15:15 B)20:15:10 C)20:15:12 D)20:15:11 E)20:15:13 SOLUTION:6A = 8B = 10 C A:B:C = 1/6:1/8:1/10 = 20:15:12.Answer: C #### C QUESTION:the banker's discount on a bill due 4 months hence at 15% is Rs.420. what is the true discount? options: A)41 B)400 C)390 D)380 E)480 SOLUTION:TD= (BD * 100)/(100+TR)= (420 * 100)/100+((4/12)*15)= (420 * 100)/100+((1/3)*15) =(420 * 100)/100+5= (84 * 100)/21 = 4*100=400 correct answer: (B) #### B QUESTION:Difference between a two-digit number and the number obtained by interchanging the two digits is 36, what is the difference between two numbers options: A)2 B)4 C)8 D)12 E)14 SOLUTION:Explanation: Let the ten digit be x, unit digit is y. Then (10x + y) - (10y + x) = 36 => 9x - 9y = 36 => x - y = 4. Option B #### B QUESTION:Rs.1210 were divided among 3 person P, Q, R so that P:Q=5:4 and Q: R=9:10. Then R gets the amount. options: A)Rs. 300 B)Rs. 400 C)Rs. 480 D)Rs. 490 E)Rs. 500 SOLUTION:P : Q = 5 : 4, Q : R = 9 : 10 = ( 9 x 4 / 9 ) : ( 10 x 4 / 9 ) = 4 : 40 / 9. So, P : Q : R = 5 : 4 : 40 /9 = 45 : 36 : 40 Sum of ratio terms is = ( 45 + 36 + 40 ) =121. R share of amount is Rs (1210 x 40 / 121) = Rs. 400. B #### B QUESTION:The population of a town is 10000. It increases annually at the rate of 10% p.a. What will be its population after 2 years? options: A)12300 B)12350 C)12100 D)12500 E)12600 SOLUTION:Formula : ( After =100 denominator Ago = 100 numerator) 10000 × 110/100 × 110/100 = 12100 C #### C QUESTION:If an amount of Rs 41,910 is distributed equally amongst 22 persons, how much amount would each person get? options: A)Rs 1905 B)Rs 2000 C)Rs 745 D)Rs 765 E)None SOLUTION:Required amount =41910/22 = Rs 1905 Answer A #### A QUESTION:Two concentric circles form a ring. The inner and outer circumferences of ring are (352/7) m and (518/7) m respectively. Find the width of the ring. options: A)2 B)4 C)6 D)8 E)None of them SOLUTION:Let the inner and outer radii be r and R meters. Then 2(22/7)r = (352/7) = r =((352/7) X (7/22) X (1/2))=8m. 2(22/7)R=(528/7) = R=((528/7) X (7/22) X (1/2))= 12m. Therefore, Width of the ring = (R - r) = (12 - 8) m = 4 m. Answer is B. #### B QUESTION:What is the minimum value of |x-4| + |x+8| + |x-5| ? options: A)-13 B)13 C)5 D)7 E)8 SOLUTION:A cannot be the answer as all the three terms are in modulus and hence the answer will be non negative. |x-4| >= 0 --> Minimum occurs at x = 4 |x+8| >= 0 --> Minimum occurs at x = -8 |x-5| >= 0 --> Minimum occurs at x = 5 x = -8 --> Result = 12 + 0 + 13 = 25. Also any negative value will push the combined value of |x-4| + |x-5| to a value > 9. x = 4 --> Result = 0 + 12 + 1 = 13 x = 5 --> Result = 1 + 13 + 0 = 14 x = 8 --> Result = 4 + 16 + 3 = 23 So minimum value of the expression occurs at x = 4 and the resultant value = 13 Answer: B #### B QUESTION:In a market, a dozen eggs cost as much as a pound of rice, and a half-liter of kerosene costs as much as 6 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.] options: A) 0.33 B) 0.44 C) 33 D) 44 E) 55 SOLUTION:A dozen eggs cost as much as a pound of rice --> 12 eggs = 1 pound of rice = 33 cents; A half-liter of kerosene costs as much as 6 eggs --> 6 eggs = 1/2 liters of kerosene. How many cents does a liter of kerosene cost --> 1 liter of kerosene = 12 eggs = 12/12*33 = 33 cents. Answer: C. #### C QUESTION:A ranch has both horses and ponies. Exactly 3/10 of the ponies have horseshoes, and exactly 5/8 of the ponies with horseshoes are from Iceland. If there are 4 more horses than ponies, what is the minimum possible combined number of horses and ponies on the ranch? options: A)116 B)132 C)148 D)164 E)180 SOLUTION:3/10*P are ponies with horseshoes, so P is a multiple of 10. 5/8*3/10*P = 3/16*P are Icelandic ponies with horseshoes, so P is a multiple of 16. The minimum value of P is 80. Then H = P+4 = 84. The minimum number of horses and ponies is 164. The answer is D. #### D QUESTION:A train running at the speed of 60 km/hr crosses a pole in 6 seconds. Find the length of the train. options: A)150 m B)145 m C)100 m D)135 m E)155 m SOLUTION:Speed = 60*(5/18) m/sec = 50/3 m/sec Length of Train (Distance) = Speed * Time (50/3) * 6 = 100 meter ANSWER: C #### C QUESTION:If Susan takes 10 seconds to run y yards, how many minutes will it take her to run x yards at the same rate? options: A)xy/10 B)10x/(60y) C)60xy/10 D)xy/540 E)540x/y SOLUTION:The answer is B. She runs x yards in 10x/y seconds =10x/60y minutes. #### B QUESTION:The function g(p) is defined for integers p such that if p is even, g(p) = p/2 and if p is odd, g(p) = p + 5. Given that g(g(g(g(g(p))))) = 19, how many possible values for p would satisfy this equation? options: A)1 B)5 C)7 D)8 E)11 SOLUTION:Let me define terms: in g(p) = R p is argument, R is result, g() is function, in g(g(g(g(g(p))))), g1 is inner most, g5 is outermost for identification. From definition of function g, we can deduce that: If Result is even then two possibilities for argument = 1 Even 1 Odd If Result is odd then one possibility for argument = 1 Even Since final result = 19 = Odd Possibilities: g1:1 Even g2: 1*(Even,Odd ) =1 Even 1 Odd g3: 1*(Even,Odd) + 1 Even =2 Even 1 Odd g4: 2*(Even, Odd) + 1 Even =3 Even 2 Odd g5: 3*(Even, Odd) + 2 Even =5 Even 3 Odd = Total 8 Ans D it is! #### D QUESTION:In how many ways can 5 different rings be worn in four particular fingers? (Some fingers may get more than one ring and some may get no rings.) Can somebody explain? options: A)6720 B)7720 C)7820 D)7950 E)8120 SOLUTION:First ring can be worn in 4 ways (on any of the four fingers); Second ring can be worn in 5 ways (as it can go on any of four fingers - 4 ways; plus it can go below the first one - 1); Third ring can be worn in 6 ways (the same logic as for the second ring); Fourth ring can be worn in 7 ways; Fifth ring can be worn in 8 ways; Total: 4*5*6*7*8=6720. ANS:A #### A QUESTION:The average weight of 19 students is 15kg. by the admission of a new student the average weight is reduced to 14.8 kg. the weight of the new student is ? options: A)10.6 kg B)10.8 kg C)11 kg D)14.9 kg E)None SOLUTION:Answer Weight of new student = Total weight of all 20 students - Total weight of initial 19 students = (20 x 14.8 - 19 x 15) kg = 11 kg. Correct Option: C #### C QUESTION:When 242 is divided by a certain divisor the remainder obtained is 15. When 698 is divided by the same divisor the remainder obtained is 27. 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? options: A)11 B)17 C)13 D)23 E)37 SOLUTION:let that divisor be x since remainder is 15 or 27 it means divisor is greater than 27. now 242-15=227 =kx (k is an integer and 234 is divisble by x) similarly 698-27=671 = lx (l is an integer and 689 is divisible by x) adding both 698 and 242 = (227+671)+15+27 =x(k+l) + 42 when we divide this number by x then remainder will be equal to remainder of (42 divided by x) = 5 hence x = 42-5 = 37 hence E #### E QUESTION:The 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? options: A)13 B)12 C)11 D)15 E)10 SOLUTION:Let the present ages of Paul and Ben be 5x years and 2x years respectively 4x+4 = 28 4x = 24 x = 6 Ben's age = 2x = 12 years Answer is B #### B QUESTION:An 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? options: A)4.04 B)4.02 C)4.01 D)4.05 E)4.06 SOLUTION:Formula for Calculation of Percentage error is: =(x−y−(xy)/100)% =(2+2+(2×2)/100)%=4.04% Answer is A. #### A QUESTION:Ratio between Rahul and Deepak is 4:3, After 6 Years Rahul age will be 26 years. What is Deepak present age. options: A)14 B)15 C)20 D)22 E)24 SOLUTION:Explanation: Present age is 4x and 3x, => 4x + 6 = 26 => x = 5 So Deepak age is = 3(5) = 15 Option B #### B QUESTION:A train 100 m long passes a man, running at 15 km/hr in the same direction in which the train is going, in 20 seconds. The speed of the train is: options: A)16 km/hr. B)33 km/hr. C)21 km/hr. D)49 km/hr. E)76 km/hr. SOLUTION:Speed of the train relative to man =100/20m/sec=5 m/sec. =5 x 18/5 km/hr = 18 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 15) km/hr. x - 15 = 18 x = 33 km/hr. ANSWER:B #### B QUESTION:Find the value of y from (12)^3 x 6^4 ÷ 432 = y? options: A)3452 B)2343 C)2435 D)2578 E)5184 SOLUTION:Given Exp. = (12)3 x 64 = (12)3 x 64 = (12)2 x 62 = (72)2 = 5184 432 12 x 62 E #### E QUESTION:In a certain game there are 8 steps, referred to as step 1, step 2, and so on with the final step being step 8. The steps are played one after the other. In each step a score of 1, 2, 3, or 4 is obtained. Angel played the game, getting at least one score of each of 1, 2, 3, and 4, and never getting the same score in consecutive steps. What is the greatest possible score that Angel could have gotten? options: A)15 B)18 C)21 D)23 E)29 SOLUTION:There are two conditions: 1. Angel got at least one score of each of 1, 2, 3, and 4. 2. She never got the same score in consecutive steps. Taking that into account, the greatest possible score that Angel could have gotten is 4 + 1 + 4 + 2 + 4 + 3 = 18. Answer: B. #### B QUESTION:If equation |x/2| + |y/2| = 2 encloses a certain region on the coordinate plane, what is the area of this region? options: A)20 B)32 C)100 D)200 E)400 SOLUTION:The equation can be reduced to intercept form as |x/4| + |y/4| = 1, so these are lines in four quadrants with x and y intercept as 14, so it is a rhombus with diagonals of 8 each and hence area = 1/2*d1*d2 = 1/2*8*8 = 32. Answer B. #### B QUESTION:If in a triangle, the area is numerically equal to the perimeter, then the radius of the inscribed circle of the triangle is options: A)1 B)2 C)3 D)4 E)5 SOLUTION:Solution Radius = Area / Semi perimeter = [Area x 2 / Area] = 2. Answer B #### B QUESTION:A, 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? options: A)3:6:7 B)3:4:7 C)9:4:7 D)3:4:6 E)3:5:7 SOLUTION:A:B:C = (40000 * 36) : (80000 * 12 + 40000 * 24) : (120000 * 24 + 40000 * 12) = 144:192:336 = 3:4:7 Answer: B #### B QUESTION:On planet korba, a solar blast has melted the ice caps on its equator. 9 years after the ice melts, tiny planetoids called echina start growing on the rocks. Echina grows in the form of circle, and the relationship between the diameter of this circle and the age of echina is given by the formula d = 4*[sqrt(t-9)] for t>9, where d represents the diameter in mm and t the number of years since the solar blast. Jagan recorded the radius of some echina at a particular spot as 7mm. How many years back did the solar blast occur? options: A)17 B)21.25 C)12.25 D)14.05 E)18 SOLUTION:radius=7mm. So dia= 14mm. putting D=14 in equation we can easily calculate t=21.25 ANSWER:B #### B QUESTION:What is the units digit of (12^3)(15^4)(31^7)? options: A)0 B)2 C)4 D)6 E)8 SOLUTION:The units digit of 12^3 is the units digit of 2^3 which is 8. The units digit of 15^4 is the units digit of 5^4 which is 5. The units digit of 31^7 is the units digit of 1^7 which is 1. The units digit of 8*5*1 is 0. The answer is A. #### A QUESTION:In a hotel, 60% had vegetarian lunch while 30% had non-vegetarian lunch and 15% had both type of lunch. If 96 people were present, how many did not eat either type of lunch ? options: A)27 B)26 C)25 D)24 E)20 SOLUTION:Explanation: n(A)=(60/100∗96)=288/5 n(B)=(30/100∗96)=144/5 n(A∩B)=(15100∗96)=72/5 People who have either or both lunch n(A∪B)=288/5+144/5−72/5 =360/5=72 So People who do no have either lunch were = 96 -72 = 24 ANSWER IS D #### D QUESTION:Anil does a work in 90 days, Bittu in 40 days and Chintu in 12 days. They work one after another for a day each, starting with Anil followed by Bittu and then by Chintu. If the total wages received are Rs 360 and Anil, Bittu, Chintu share them in the ratio of the work done, find their respective individual wages. options: A)Rs 40, Rs 60 and Rs 260 B)Rs 36, Rs 81 and Rs 243 C)Rs 42, Rs 86 and Rs 232 D)Rs 38, Rs 88 and Rs 234 E)none of these SOLUTION:Let the total work done be 360 units. Therefore, work done by Anil, Bittu and Chintu in single day are 4 units, 9 units and 30 units respectively. Each of them working for 9 days Anil and Bittu will be able to complete 4 units and 9 units of their work on the 9th day but Chintu will be doing remaining 3 units of work. Hence, individual work done by them to complete the whole work is 36 units, 81 units and 243 units till the end of 9th day for each of them. Thus, respective wages on the basis of work done is Rs 36, Rs 81 and Rs 243 respectively for Anil, Bittu and Chintu. ANSWER:B #### B QUESTION:When the positive integer y is divided by 9, the remainder is 5. What is the remainder when 3y is divided by 9? options: A)0 B)1 C)3 D)4 E)6 SOLUTION:Lets take the number as y when y is divided by 9 the remainder is 5 hence y can be written as y=9k +5 Multiplying by 3 will give 3y = 27k + 15 we can also write 3y = 27k + 9 + 6 Now 27k and 9 are divisible by 9 leaving the remainder as 6 hence E is the answer. #### E QUESTION:Two 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? options: A)16 km/hr B)17 km/hr C)60 km/hr D)15 km/hr E)19 km/hr SOLUTION:Let the speed of the slower train be x m/sec. Then, speed of the train = 2x m/sec. Relative speed = ( x + 2x) = 3x m/sec. (100 + 100)/8 = 3x => x = 25/3. So, speed of the faster train = 50/3 = 50/3 * 18/5 = 60 km/hr. Answer: C #### C QUESTION:The length of a rectangle is twice its breadth. If its length is decreased by 4 cm and breadth is increased by 5 cm, the area of the rectangle is increased by 75 sq. cm. Find the length of the rectangle. options: A)10/3cm B)20/3cm C)20cm D)16cm E)14cm SOLUTION:Explanation: Let breadth = x. Then, length = 2x. Then, (2x - 4) (x + 5) - 2x * x = 75 => 6x - 25 = 75 => x =20/3. Length of the rectangle = 20/3 cm. Answer: Option B #### B QUESTION:A no. x when divided by 221 gives a remainder 43, what remainder will beobtained by dividingthe same no.17? options: A)1 B)4 C)9 D)11 E)13 SOLUTION:221 + 43 = 264/17 = 9 (Remainder) C #### C QUESTION:Three hoses work to fill a tub at at different rate. Hose Q and B, working together, can fill the tub in 6/5 of an hour. Hoses Q and C can fill it in 3/2 an hour. Houses B and C can fill it in 2 hours. How long does it take all 3 hoses, working together, to fill the tub? Edited for accurate solution options: A)3/10 B)2/5 C)1/2 D)1 E)6/5 SOLUTION:Convert the given time to rate and you will be able to add it up. Total Rate of Q and B = Rate of Q + Rate of B = 1/(6/5) = 5/6 Total Rate of Q and C = Rate of Q + Rate of C = 1/(3/2) = 2/3 Total Rate of B and C = Rate of B + Rate of C = 1/2 Adding all three, 2(Rate of Q + Rate of B + Rate of C) = 5/6 + 2/3 + 1/2 = 2 Rate of Q + Rate of B + Rate of C = 1 tub/hour Time taken by all three together to fill up the tub is 1 hour=D #### D QUESTION:Each 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 45 hours If Harry and James were paid the same amount last week, how many hours did Harry work last week ? options: A)35 B)36 C)37 D)43 E)39 SOLUTION:James worked for 41 hours hence he earned 40*x+5*2x=50x dollars; We know that Harry also earned the same 50x dollars, out of which he earned 30x dollars for thefirst 30 hoursplus 20x additional dollars. Since for each additional hour he gets 1.5x dollars then he worked for 20x/1.5x=13 additional hours, so Harry worked for total of 30+13=43 hours. Answer: D. #### D QUESTION:In a certain school, 20% of students are below 8 years of age. The number of students above 8 years of age is 2/3 of the number of students of 8 years of age which is 48. What is the total number of students in the school? options: A)200 B)300 C)600 D)700 E)100 SOLUTION:E 100 Let the number of students be x. Then, Number of students above 8 years of age = (100 - 20)% of x = 80% of x. 80% of x = 48 + 2/3 of 48 80/100x = 80 x = 100. #### E QUESTION:The average age of 20 men in the class is 15.6 years. Five new men join and the new average becomes 15.56 years. What was the average age of five new men? options: A)15.5 B)15.4 C)15.25 D)15.3 E)15.6 SOLUTION:Total age of 20 men = 15.6 x 20 = 312 Now, total age of 25 men = 389. Total age of five men added later = 389 - 312 = 77. Hence, the total average of five men = 77/5 = 15.4 ANSWER:B #### B QUESTION:The sub-duplicate ratio of 25:49 is options: A)4:3 B)5:7 C)6:4 D)1:4 E)2:3 SOLUTION:root(25):root(49)=5:7 ANSWER:B #### B QUESTION:The 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 ? options: A)4 B)8 C)6 D)2 E)1 SOLUTION:Let the number off boys in the group originally be x. Total weight of the boys = 30x After the boy weighing 35 kg joins the group, total weight of boys = 30x + 35 So 30x + 35 + 31(x + 1) = > x = 4. Answer:A #### A QUESTION:A train crosses a platform of 150 m in 10 sec, same train crosses another platform of length 250 m in 15 sec. then find the length of the train? options: A)150m B)180m C)159m D)250m E)50 m SOLUTION:Length of the train be ‘X’ X + 150/10= X + 250/15 3X + 450 = 2X + 500 X = 50m Answer:E #### E QUESTION:On flipping 3 coins together what is the outcomes for exactly one head and one tail? options: A){HHH, HTH, THH, TTH, THT, HTT} B){HHT, HTH, THH, TTH, THT, TTT} C){HHT, HTH, THH, TTH, THT, HTT} D){HHT, HTH, THH, TTH, THT, TTT} E)None SOLUTION:Sample space, S = {HHH, HHT, HTH, THH, TTH, THT, HTT, TTT} Favorable outcomes for at least two heads = favorable outcomes for one head and one tail and favorable outcomes for more than one head and one tail. = {HHT, HTH, THH, TTH, THT, HTT} C #### C QUESTION:In a garment industry, 12 men working 8 hours per day complete a piece of work in 10 days. To complete the same work in 12 days, working 16 hours a day, the number of men required is: options: A)4 B)5 C)6 D)8 E)9 SOLUTION:Explanation : Let the required number of men be x. Less days, More men (Indirect Proportion) More working hrs per day, Less men (Indirect Proportion) Days 8 : 10 Working Hrs 16: 8 :: 12 : x => 12 x 16 x x = 10 x 8 x 12 => x = 10 x 8 x 12 / (12 x 16) => x = 5 Answer : B #### B QUESTION:The 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 açai berry juice, which cost $262.85 per litre and $3104.35 per litre, respectively. The manager has already opened 32 litres of the mixed fruit juice. How many litres of the açai berry juice does he need to add? options: A)17 litres B)21.3 litres C)11 litres D)07 litres E)38 litres SOLUTION:262.85(32)+3,104.35x = 1,399.45(32 + x) Solve the equation. 262.85(32)+3,104.35x = 1,399.45(32 + x) 8,411.2 + 3,104.35x = 44,782.4 + 1,399.45x 8,411.2 + 1,704.9x = 44,782.4 1,704.9x = 36,371.2 x ≈ 21.3 Answer is B. #### B QUESTION:A 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? options: A)12 B)17 C)15 D)19 E)26 SOLUTION:Let the average after the 16th inning be P. So, the average after the 15th inning will be (P-3) Hence, 15(P-30) + 64 = 16P => P = 19 Answer:D #### D QUESTION:The 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? options: A)8m. B)6m. C)4m. D)2m. E)5m. SOLUTION:Explanation: Let the sides of the rectangle be l and b respectively. From the given data, (√l2 + b2) = (1 + 108 1/3 %)lb => l2 + b2 = (1 + 325/3 * 1/100)lb = (1 + 13/12)lb = 25/12 lb => (l2 + b2)/lb = 25/12 12(l2 + b2) = 25lb Adding 24lb on both sides 12l2 + 12b2 + 24lb = 49lb 12(l2 + b2 + 2lb) = 49lb but 2(l + b) = 28 => l + b = 14 12(l + b)2 = 49lb => 12(14)2 = 49lb => lb = 48 Since l + b = 14, l = 8 and b = 6 l - b = 8 - 6 = 2m. Answer: Option D #### D QUESTION:On day one, a store sold 125 bags. On each of the next d days, the company sold 83 bags. If the average daily sales of bags over this time period (including day one) is 90 bags, what is the value of d? options: A)4 B)5 C)6 D)7 E)8 SOLUTION:125 + 83d = 90(d+1). 7d = 35. d = 5. The answer is B. #### B QUESTION:If xy ≠ 0 and x^2y^2 − 2xy = 24, which of the following could be y in terms of x? I. 6/x II. -4/x III. 1/x options: A)I only B)II only C)I and II only D)I and III E)II and III SOLUTION:(x^2)(y^2) –2xy - 24 = 0 (xy – 6)(xy + 4) = 0 xy – 6 = 0 or xy + 4 = 0 xy = 6 or xy = -4 Since we need y in terms of x, we can isolate y in both of our equations. y = 6/x or y = -4/x Answer: C #### C QUESTION:A person starting with Rs.64 and making 6 bets, wins 3times 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? options: A)Rs.37 B)Rs.45 C)Rs.47 D)Rs.53 E)Rs.59 SOLUTION:As 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). The overall resultant will remain same. So final amount with the person will be (in all cases): =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 Hence the final result is: 64−27=3764−27=37: A loss of Rs.37 A #### A QUESTION:On dividing 12401 by a certain number, we get 76 as quotient and 13 as remainder. What is the divisor? options: A)163 B)785 C)852 D)456 E)852 SOLUTION:Divisor *quotient+remainder=dividend divisor=(dividend)-(remainder)/quotient (12401-13)/76=163 Answer(A) #### A QUESTION:If two letters are chosen at random (without replacement) from the word COMPUTER, what is the probability that none of the letters are vowels? options: A)2/7 B)3/7 C)3/14 D)5/14 E)11/28 SOLUTION:The number of ways to choose two letters is 8C2 = 28 The number of ways to choose two consonants is 5C2 = 10. P(no vowels) = 10/28 = 5/14 The answer is D. #### D QUESTION:Today is Monday. After 61 days, it will be: options: A)SUNDAY B)SATURSDAY C)FRIDAY D)THURSDAY E)MONDAY SOLUTION:Each day of the week is repeated after 7 days. So, after 63 days, it will be Monday. After 61 days, it will be Saturday. Answer: Option B #### B QUESTION:A gardener sells 100 metres of fencing for Rs. 7500 at a loss of Rs. 3 per metre. Find his cost price for one metre of fencing? options: A)54 B)67 C)62 D)78 E)72 SOLUTION:SP per metre = 7500/100 = Rs. 75 Loss per metre = Rs. 3 CP per metre = 75 + 3 = Rs. 78 Answer: D #### D QUESTION:On dividing 122 by a number, the quotient is 6 and the remainder is 2. Find the divisor? options: A)14 B)16 C)18 D)20 E)22 SOLUTION:d = (D-R)/Q = (122 - 2)/6 = 122/6 = 20 D) #### D QUESTION:What is the maximum number of points that 10 circles of different radii intersect? options: A)24 B)26 C)33 D)90 E)100 SOLUTION:the maximum number of points that two circles intersect is two. therefore, each of these 10 circles intersect two point with each of the other 9 circles. as a consequence, the number of these points is equal to two times the number of combination of the 10 circles. 2∗(10!)/(2!∗10!)=90 Answer: D #### D QUESTION:36 people {a1, a2… a36} meet and shake hands in a circular fashion. In other words, there are totally 36 handshakes involving the pairs, {a1, a2}, {a2, a3}, …, {a35, a36}, {a36, a1}. Then size of the smallest set of people such that the rest have shaken hands with at least one person in the set is options: A)76 B)55 C)44 D)12 E)91 SOLUTION:Ans: {a1, a2}, {a2, a3},{a3, a4}, {a4, a5},{a5, a6}, {a6, a7} …, {a35, a36}, {a36, a1} From the above arrangement, If we separate a3, a6, a9, .....a36. Total 12 persons the reamining persons must have shaked hand with atleast one person. So answer is 12. Answer:D #### D QUESTION:What is the greatest prime factor of 4^16 - 2^30? options: A)2 B)3 C)5 D)7 E)11 SOLUTION:4^16 - 2^30 =(2^2)^16 - 2^30 = 2^32 - 2^30 = 2^30 (2^2 -1) = 2^30 * (4-1) = 2^30 * 3 The greatest prime factor is 3. The answer is B. #### B <<<Examples ends QUESTION:If integers w and b are distinct factors of 30, which of the following CANNOT be a factor of 30? I. wb + b^2 II. (w+ b)^2 III. w + b options: A)I only B)II only C)III only D)I and II only E)I, II, and III SOLUTION:Factors of 30 are: 1, 2, 3, 5, 6, 10, 15, and 30. I. wb + b^2 --> if w=1 and b=2 then wb + b^2=6, which is a factor of 30. OK; II. (w + b)^2 --> (w + b)^2 is a perfect square, no perfect square (but 1) is a factor of 30. DISCARD; III. w + b --> if w=1 and b=2 then w + b=3, which is a factor of 30. OK. Answer: B. #### B

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:The 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 options: A)153550 m^2 B)153600 m^2 C)153700 m^2 D)153800 m^2 E)153900 m^2 SOLUTION:Explanation: Perimeter = Distance covered in 8 min. = 12000 x 8 m = 1600 m. 60 Let length = 3x metres and breadth = 2x metres. Then, 2(3x + 2x) = 1600 or x = 160. Length = 480 m and Breadth = 320 m. Area = (480 x 320) m2 = 153600 m^2. Option B #### B QUESTION:In what time will a train 100 m long cross an electric pole, it its speed be 144 km/hr? options: A)2.5 sec B)1.3 sec C)7.6 sec D)10 sec E)3.6 sec SOLUTION:Answer: Option A Speed = 144 * 5/18 = 40 m/sec Time taken = 100/40 = 2.5 sec. #### A QUESTION:A 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 3 rounds per hour respectively. How many times shall they cross each other before 8.30 a.m. ? options: A)7 B)2 C)9 D)2 E)8 SOLUTION:B 2 Relative speed = 2 + 3 = 5 rounds per hour. So, they cross each other 5 times in an hour and 2 times in half an hour. Hence, they cross each other 2 times before 8.30 a.m. #### B QUESTION:A train 410 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long? options: A)40 sec B)50 sec C)44 sec D)49 sec E)60 sec SOLUTION:Speed = 45 * 5/18 = 25/2 m/sec Total distance covered = 410 + 140 = 550 m Required time = 550 * 2/25 = 44 sec Answer:C #### C QUESTION:For every integer n ≥ 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(99) – g(97)? options: A)98 B)100 C)0 D)99 E)97 SOLUTION:g(99) = 1*3*5*7*9*...*99 g(97) = 1*3*5*7*9*...*97 g(99) - g(97) = 1*3*5*7*9*...*99 - 1*3*5*7*9*...*97 = 1*3*5*7*9*...*97*(99 - 1) = 1*3*5*7*9*...*97*98 hence:A. #### A QUESTION:A 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 options: A)8.95km/hr B)26.7km/hr C)27.8km/hr D)28.5km/hr E)8.45km/hr SOLUTION:average speed = (2*50*20)/50+20 km/hr =28.5 km/hr Answer (D) #### D QUESTION:he average of 30 numbers is zero. Of them, at the most, how many may be greater than zero? options: A)29 B)1 C)10 D)30 E)8 SOLUTION:Average of 30 numbers = 0. Sum of 30 numbers (0 x 30) = 0. It is quite possible that 29 of these numbers may be positive and if their sum is a the 30th number is (-a). Answer: Option A #### A QUESTION:Find (7x + 8y ) / (x-2y) if x/2y = 3/2 ? options: A)24 B)25 C)26 D)27 E)29 SOLUTION:x/2y=3/2 =>x=6y/2=3y =>(7x+8y)/(x-2y)=((7*(3y))+8y)/(3y-2y) =>29y/y=29 ANSWER:E #### E QUESTION:Sum of 3 consecutive even no.'s is 26 more than the 1st no. of the series. Find the middle no.? options: A)8 B)twelve (12) C)14 D)16 E)18 SOLUTION:Let the numbers be x, x+2 and x+4 then x + x+2 + x+4 = x+26 3x + 6 = x + 26 2x = 20 \inline \therefore x = 10 \inline \therefore Middle number = x + 2 = 10+2 = 12 B #### B QUESTION:If c = 9/25, w = 15/32, and m + w + c = 1, which of the following gives the values of m, w, and c in increasing order? options: A)c, m, w B)c, w, m C)m, w, c D)m, c, w E)w, m, c SOLUTION:Answer D - m, c, w c ~ 1/3 w ~ 1/2 and m+w+c = 1 hence m ~ 1/6 Hence increasing order would be m -> c -> w Aswer D #### D QUESTION:In a particular course, only two grades are given all semester: the midterm exam, which counts for 25% of the semester grade, and the final exam, which counts for the remainder. Lindsey's semester grade was 88%. If the highest possible score on either exam is 100%, what is the lowest possible A score that Lindsey could have received on her midterm exam? options: A)52% B)64% C)72% D)76% E)80% SOLUTION:If the midterm counts for 25% of the total grade, then the final exam must count for the remaining 75%, meaning that in this weighted average problem the final is weighted 3 times as much as the midterm. Using the weighted average mapping strategy, then, and maximizing her final exam score so that you minimize her midterm score, you have: 100-------------88----------------------------x And you know that the ratio is 3:1. Since the final exam score of 100 is weighted heavier, then the difference of 12 between 100 and 88 is the1part of the ratio, meaning that 3(12) is the 3 portion. That equals 36, so the midterm score (x) is 36 less than the weighted average of 88. 88 - 36 = 52, sothe correct answer is 52%. #### A QUESTION:A 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.5 per sq m? options: A)6500 B)2779 C)2779 D)3900 E)2781 SOLUTION:Area = (l + b – d) d (80 + 60 – 10)10 => 1300 m2 1300 * 5 = Rs.6500 Answer:A #### A QUESTION:In how many different number of ways a Committee of 2person of can be selected from 2boys and 2girls such that at least 1 girl is included in the committe options: A)3 B)4 C)2 D)5 E)9 SOLUTION:1G 1B 2G = (2C1*2C1)+2C2 = (2*2)+1 = 5 Total 2M 2W 4C2=6 2C2=1 At least one girl = total - with out girl At least one girl = 6-1=5 D) #### D QUESTION:If 63 percent of a class answered the first question on a certain test correctly, 49 percent answered the second question on the test correctly, and 20 percent answered neither of the questions correctly, what percent answered both correctly? options: A)22% B)24% C)26% D)28% E)32% SOLUTION:63% answered the first question correctly and 20% answered neither correctly. Then 17% missed the first question but answered the second question correctly. Then the percent who answered both correctly is 49% - 17% = 32%. The answer is E. #### E QUESTION:If q is a positive integer and q^2 is divisible by 12, then the largest positive integer that must divide q ^3 is options: A) 2^3 B) 2^6 C) 3^3 D) 6^3 E) 12^2 SOLUTION:Since 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)) q^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 So, q will have a 2 and a 3. Or q will be a multiple of 6 So, largest possible integer than should divide q^3 is 6^3 So, Answer will be D #### D QUESTION:The ratio between a two-digit number and the sum of the digits of that number is 4 : 1.If the digit in the unit's place is 3 more than the digit in the ten’s place, what is the number? options: A)47 B)36 C)58 D)25 E)14 SOLUTION:Let the ten's digit be x. Then, unit's digit = (x + 3). Sum of the digits = x + (x + 3) = 2x + 3. Number = l0x + (x + 3) = llx + 3. 11x+3 / 2x + 3 = 4 / 1 => 11x + 3 = 4 (2x + 3) => 3x = 9 => x = 3. Hence, required number = 11x + 3 = 36. Answer is B. #### B QUESTION:What 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? options: A)Rs.3944 B)Rs.3948 C)Rs.3988 D)Rs.3949 E)Rs.3923 SOLUTION:Let the side of the square plot be a ft. a2 = 289 => a = 17 Length of the fence = Perimeter of the plot = 4a = 68 ft. Cost of building the fence = 68 * 58 = Rs.3944. Answer: A #### A QUESTION:Six persons A,B,C,D,E &F went to soldier cinema. There are six consecutive seats. A sits in the first seat followed by B, followed by C and so on. If A taken on of the six seats, then B should sit adjacent to A. C should sit adjacent to A or B. D should sit adjacent to A, B or C and so on. How many possibilities are there ? options: A)30 B)32 C)34 D)36 E)38 SOLUTION:First we have to arrange A, there is 1 method for it, for second person B, there are 2 methods one left and one right, for third 2 methods are there same as for B similarly for others, so total number of methods = 1*2*2*2*2*2 = 32 ANSWER:B #### B QUESTION:The sum of the squares of three number is 138,while the sum of their products taken two at a time is 131. their sum is : options: A)20 B)30 C)40 D)None of these E)Cannot be determined SOLUTION:Solution Let the numbers be a,b and c then, a 2 + b 2+ c 2 = 138 and (ab + b c + ac) = 131. (a + b+ c)2 = a 2 + b 2 + c 2 + 2(ab + b c + ca) = 138 + 2 * 131 = 400 . ⇒ (a + b + c) = 400/20= 20 Answer A #### A QUESTION:A walks around a circular field at the rate of one round per hour while B runs around it at the rate of eleven 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? options: A)6 min B)12 min C)10 min D)15 min E)16 min SOLUTION:Since 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. Relative speed of A and B = 11 - 1 = 10 rounds per hour. Time taken to complete one round at this speed = 1/10 hr = 6 min. A #### A QUESTION:In 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 W of her bushes have only yellow roses? options: A)20 B)30 C)50 D)70 E)80 SOLUTION:let, the number of bushes with only yellow flowers be x so, number of bushes with only yellow flowers will be 1.5x if total number of bushes of flowers= T then total number of bushes with yellow flowers= 0.8T we can say that total number of bushes with yellow flowers+ bushes with only white flowers= total number of bushes with flowers so, W=0.8T+x=T x=0.2T so, 1.5x=0.3T 30% flowers are yellow flowers OA B #### B QUESTION:For each 6-month period during a light bulb's life span, the odds of it not burning out from over-use are half what they were in the previous 6-month period. If the odds of a light bulb burning out during the first 6-month period following its purchase are 2/7, what are the odds of it burning out during the period from 6months to 1 year following its purchase? options: A)5/27 B)2/9 C)1/2 D)4/9 E)2/3 SOLUTION:P(of not burning out in a six mnth period)=1/2 of P(of not burning out in prev 6 mnth period) P(of burning out in 1st 6 mnth)= 2/7 --->P( of not burning out in 1st 6 mnth)=1-2/7=5/7 ---->P(of not burning out in a six mnth period)=1/2 *5/7=1/3 --->P(of burning out in a six mnth period)=1-1/3=2/3 now P( of burning out in 2nd six mnth period)=P( of not burning out in 1st six mnth)*P(of burning out in a six mnth) =5/7 * 2/3=1/2 Ans C #### C QUESTION:If p and q are two different prime numbers, which of the following cannot be true? options: A)pq is odd. B)p + q is even. C)p + q is odd. D)pq is even. E)p/q is an integer SOLUTION:A 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 (p/q=integer means that p is a multiple of q). Answer: E. All other options are possible: A. pq is odd --> p=3 and q=5; B. p + q is even --> p=3 and q=5; C. p + q is odd --> p=2 and q=3; D. pq is even --> p=2 and q=3; E #### E QUESTION:In 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? options: A)7000 B)7200 C)7400 D)7600 E)8000 SOLUTION:State A and State B had an equal number of candidates appeared. In state A, 6% candidates got selected from the total appeared candidates In state B, 7% candidates got selected from the total appeared candidates But in State B, 80 more candidates got selected than State A From these, it is clear that 1% of the total appeared candidates in State B = 80 => total appeared candidates in State B = 80 x 100 = 8000 => total appeared candidates in State A = total appeared candidates in State B = 8000 E) #### E QUESTION:A person saved $10 in buying an item on sale. If he spent $100 for the item, approximately how much percent he saved in the transaction? options: A)8% B)10% C)2% D)5% E)6% SOLUTION:Actual price = 100+10 = $110 Saving = 10/110 * 100 = 100/11 =10% approximately Answer is B #### B QUESTION:If n is an integer and 102n^2 is less than or equal to 8100, what is the greatest possible value of n? options: A)7 B)8 C)9 D)10 E)11 SOLUTION:102 * n^2 <=8100 n^2 <=8100/102 which will be less than 81 since 8100/100 = 81 which is the square of 9 Next closest value of n where n^2<=81 is 8 Ans B #### B QUESTION:Rajan borrowed Rs.4000 at 5% p.a compound interest. After 2 years, he repaid Rs.2210 and after 2 more year, the balance with interest. What was the total amount that he paid as interest? options: A)675.5 B)635.5 C)635.28 D)635.98 E)635.03 SOLUTION:4000 200 ---- I 200 10 ---- II --------------- 4410 2210 -------- 2000 110 ---- III 110 5.50 ---- IV ----------- 2425.50 2210 ----------- 4635.50 4000 ---------- 635.50 Answer:B #### B QUESTION:If the integer w is rounded to the nearest hundred, the result represents a 66 2/3 % increase over the value obtained when w is rounded to the nearest ten. which of the following is a possible value of w? options: A)64 B)67 C)99 D)133 E)147 SOLUTION:We have to check options 1 by 1. 64 rounded to nearest hundred = 100 64 rounded to nearest ten = 60 now difference = 40 the result represents a 66 2/3 % increase over the value obtained when x is rounded to the nearest ten. therefore 40/60)*100 = 66 2/3 ==>this is the answer. 99 rounded to nearest ten = 100 133 rounded to nearest ten = 130 133 rounded to nearest hundred w= 100=A #### A QUESTION:The sector of a circle has radius of 35 cm and central angle 135o. Find its perimeter? options: A)91.5 cm B)11.5 cm C)91.8 cm D)92.5 cm E)152.5 cm SOLUTION:Perimeter of the sector = length of the arc + 2(radius) = (135/360 * 2 * 22/7 * 35) + 2(35) = 49.5 + 70 = 152.5 cm Answer:E #### E QUESTION:When the positive integer k is divided by the positive integer n , the remainder is 13. If k/n = 81.2 , what is the value of n? options: A)9 B)20 C)55 D)70 E)81 SOLUTION:Here's an approach that's based on Number Properties and a bit ofbrute forcemath: We're told that K and N are both INTEGERS. Since K/N = 81.2, we can say that K = 81.2(N) N has tomultiply outthe .2 so that K becomes an INTEGER. With the answers that we have to work with, N has to be a multiple of 5. Eliminate A and E. With the remaining answers, we can TEST THE ANSWERS and find the one that fits the rest of the info (K/N = 81.2 and K/N has a remainder of 11) Answer B: If N = 20, then K = 1624; 1624/20 has a remainder of 4 NOT A MATCH Answer C: If N = 55, then K = 4466; 4466/55 has a remainder of 11 MATCH. Final Answer: B #### B QUESTION:A man sells a horse for Rs. 620 and loses something, if he had sold it for Rs.860 , his gain would have been double the former loss. Find the cost price of the horse? options: A)27 B)98 C)27 D)80 E)71 SOLUTION:CP = SP + 1CP = SP - g 620 + x = 860 - 2x 3x = 240 => x = 80 Answer:D #### D QUESTION:The value of (34.5*0.473*1.567)/(0.0673*23.25*7.57) is close to options: A)2 B)1.15 C)2.05 D)2.16 E)2.35 SOLUTION:(34.5*0.473*1.567)/(0.0673*23.25*7.57) = 25.5710895/11.845 = 2.16 ANSWER:D #### D QUESTION:If n is a positive integer and the product of all the integers from 1 to n, inclusive, is a multiple of 123, what is the least possible value of n? options: A)37 B)123 C)41 D)52 E)87 SOLUTION:123 is 3 * 41, so n needs to be at least 41, so the answer is C. #### C QUESTION:How many 0's are there in the binary form of 6*1024 + 4*64 + 2 options: A)6 B)7 C)8 D)10 E)9 SOLUTION:6*1024 + 4*64 + 2 = 6144+256 +2 = 6402 in binary code 6402 base 10 = 11001 000000 10 in base 2. so 9 zeros are there. ANSWER:E #### E QUESTION:The 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? options: A)9.33% B)9.44% C)9.45% D)9.56% E)9.67% SOLUTION:69*(90/100)*((100-x)/100) = 56.16 x = 9.56% ANSWER:D #### D QUESTION:In expressing a length of 81.472 km as nearly as possible with the three significant digits, find the percentage error options: A)0.35% B)0.34% C)0.034% D)0.035% E)None of these SOLUTION:Explanation: Error = (81.5 - 81.472) = 0.028 Required percentage = 0.028/ 81.472×100=0.034 Option C #### C QUESTION:Large, medium and small ships are used to bring water. 4 large ships carry as much water as 7 small ships; 3 medium ships carry as much water as 2 large ships and 1 small ship. If 15 large, 7 medium and 14 small ships, each made 36 journeys to bring a certain quantity of water, then in how many journeys will 12 large, 14 medium and 21 small ships bring the same quantity of water? options: A)29 B)30 C)20 D)50 E)55 SOLUTION:Explanation : Here, Large, Medium and Small ships are denoted by the symbol L, M and S. Now, according to the question, 4L = 7S. ------(i) 3M = 2L + S. ------(ii) Using above equations, the ratios of the capacity of the Large, Medium and Small ships are :- 7: 6 : 4. Let, the number of journeys required be x. Since, quantity of water remains the same, so :- =((15×7+7×6+14×4)36) = x (12×7+14×6+21×4). =>((15×7+7×6+14×4)36) / (12×7+14×6+21×4)= x =>x=7308/252 =>x=29. Answer : A #### A QUESTION:If x and y are integers and x + y = 5, which of the following must be true? options: A)x and y are consecutive integers. B)If x < 0, then y > 0. C)If x > 0, then y < 0. D)Both x and y are even. E)Both x and y are less than 5. SOLUTION:Notice that the question asks which of the following MUST be true, not COULD be true. Given: x + y = 5 A. x and y are consecutive integers: not necessarily true, for example x=1 and y=4; B. 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; C. If x > 0, then y < 0: not necessarily true, for example x=1 and y=4; D. 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; E. Both x and y are less than 5: not necessarily true, for example x=6 and y=-1; Answer: B. #### B QUESTION:The ratio of pens to pencils is 5 to 6. There are 5 more pencils than pens. How many pencils are there? options: A)24 B)30 C)36 D)42 E)48 SOLUTION:Let the number of pens be 5x and the number of pencils be 6x. 6x - 5x = 5 x = 5 The number of pencils is 30. The answer is B. #### B QUESTION:A basketball coach is choosing her starting lineup from a team of 11 girls. 7 of the girls are post players and 4 are guards. If she chooses 3 post players and 2 guards, how many different lineups can be made? options: A)210 B)220 C)240 D)260 E)270 SOLUTION:(7c3)*(4c2) [7!/(3!*4!)]*[4!/(2!*2!)] 35*6 210 A #### A QUESTION:By selling 150 mangoes, a fruit-seller gains the selling price of 30 mangoes. Find the gain percent? options: A)27% B)25% C)21% D)85% E)24% SOLUTION:SP = CP + g 150 SP = 150 CP + 30 SP 120 SP = 150 CP 120 --- 30 CP 100 --- ? => 25% Answer:B #### B QUESTION:You roll N (N > 1) number of M (M > 1) sided dice at once. What is the probability they will all land on the same number? options: A)N/(M^N) B)M/(N^M) C)1/(M^(N-1)) D)1/(N^(M-1)) E)1/(M-1)^N SOLUTION:The correct rolls are any M-ples: 11...1, 22...2, ..., MM...M. This is makes M possibilities. The N dice can roll M*M*...*M (M^N) number of ways. Thus the probability of landing on the same number is M/(M^N) = 1/(M^(N-1)). Answer: C. #### C QUESTION:Thefactor countof an integer n greater than 1 is the number of distinct prime factors of n. For example, the factor count of 36 is 2, since 2 and 3 are the distinct prime factors of 36 = 2 x 2 x 3 x 3. For which of the following integers is the factor count greatest W? options: A) 60 B) 61 C) 62 D) 63 E) 64 SOLUTION:60 = 2*2*3*5 factor count =3 61= prime number 62 = 2*31 factor count=2 63=3*3*7 factor count=2 64=2*2*2*2*2*2 factor count=1=W answer is A. #### A QUESTION:JERRY has 13 ten-dollar bills, 11 five-dollar bills, and 17 one-dollar bills. If JERRY needs to pay exactly $128, what is the least number of bills he will need to use? options: A)16 B)35 C)46 D)577 E)576 SOLUTION:128 is the total sum of money. as we have 13 10 dollar bills so the closest we can get to 128 using the 10 dollar bills is by using 12 * 10 dollar bils 128-120 = 8 so now we need to get 8 from either 5 dollar bills or 1 dollar bills 8 - 5 (use only 1 5 dollar bill) = 3 so we can get 3 from using 3 $1 bills. Hence 16 ( 12+1+3 ) ANSWER IS A #### A QUESTION:A 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. What is the total distance traveled by the man? options: A)5.79 B)5.73 C)5.76 D)5.75 E)5.71 SOLUTION:M = 6 S = 1.2 DS = 7.2 US = 4.8 x/7.2 + x/4.8 = 1 x = 2.88 D = 2.88 * 2 = 5.76 \Answer:C #### C QUESTION:Four of the five parts numbered (a),(b),(c),(d) and (e) in the following equation are exactly equal. Which of the parts is not equal to the other four? The number of that part is the answer. options: A)45 × 120 + 5(2) × 10 B)113 × 25 × 2 C)27 × 25 × 8 + 15 × 6 + 4 × 40 D)226 × 5 + 113 × 45 = E)50(2) × 2 + 13 × 50 SOLUTION:Others equal 5650. Answer D #### D QUESTION:If x, y, and z are all factors of 35, which of the following must be true? options: A)The product xyz > 35 B)Either x = y, y = z, or x = z C)x – y – z = even D)The product xyz is odd E)yz/x is an integer SOLUTION:All the factors of 35 are odd numbers. The product of odd numbers is odd. The answer is D. #### D QUESTION:A man buys a cycle for Rs.1200 and sells it at a loss of 15%. What is the selling price of the cycle? options: A)Rs.1090 B)Rs.1020 C)Rs.1190 D)Rs.1202 E)NONE SOLUTION:Solution S.P = 85% of Rs.1200 = Rs.(85/100×1200) Rs.1020. Answer B #### B QUESTION:If the price of a certain bond on May 1st was 2/3 the price of the bond on June 1st and the price of the bond on July 1st was 25% greater than the price of the bond on May 1st. then the price of the bond on June 1st st was what percent of the average (arithmetic mean) price of the bond on May 1st and July 1st? options: A)50% B)75% C)120% D)133 1/3% E)150% SOLUTION:The price on June 1st = 12 (assume); The price on May 1st = 2/3*12 = 8; The price on July 1st = 8*1.25 = 10. The average price of the bond on May 1st and July 1st = (8+10)/2 = 9. The price of the bond on June 1st (12) is 4/3 times (134%) the average price of the bond on May 1st and July 1st. Answer: D. #### D QUESTION:A certain university will select 1 of 3 candidates eligible to fill a position in the mathematics department and 2 of 10 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? options: A)42 B)70 C)140 D)135 E)315 SOLUTION:1 of 3 will be chosen for the math 2 of 10 will be chosen for the computer None of the 3 chosen people can be in more than one departments. We can choose any of the 3 candidates for the math dep., which gives as 3 selections. We can choose 2 of the 10 candidates for the computer dep., which gives us 2 selections and 8 rejections. So, the way to find how many different selections of 2 candidates we can have for the computer dep., we do: 10! /2!*8!= (9*10) / 2 = 90 / 2 = 45. We are multiplying our individual selections: 3*45 = 135 In the bolded part, we don't have to multiply all of the numbers, as those in 8! are included in 10!, so we simplify instead. Ans D #### D QUESTION:A $84.95 lawn chair was sold for $59.95 at a special sale. By approximately what percent was the price decreased? options: A)15% B)20% C)25% D)29% E)80% SOLUTION:Listed selling price of chair = 84.95 $ Discounted selling price of chair = 59.95 $ Discount = 84.95 - 59.95 = 25 $ % decrease in price of chair = (25/84.95) * 100% = 29 % approx Answer D #### D QUESTION:A machine manufactures notebooks in a series of five colors: red, blue, black, white, and yellow. After producing a notebook of one color from that series, it produces a notebook of the next color. Once five are produced, the machine repeats the same pattern. If the machine began a day producing a red notebook and completed the day by producing a black notebook, how many notebooks could have been produced that day? options: A)27 B)34 C)50 D)61 E)78 SOLUTION:A machine manufactures notebooks in a series of five colors: red, blue, black, white, and yellow. Machine starts manufacturing Red and ended on Black. This means that either machine has manufactured 3, 8, 13, 18, 23, 28, 33, 38, 43, 48, 53, 58, 63, 68, 73, 78 Only 78 is given in the options. So answer = 78 ANSWER:E #### E QUESTION:Jen has a jar of jam, and she ate 1/3 of the jam for lunch. If Jen ate 1/7 of the remaining jam for dinner, what fraction of the jam was left after dinner? options: A)2/7 B)3/7 C)4/7 D)9/14 E)11/14 SOLUTION:Let x be the amount of jam at the beginning. After lunch, the remaining jam was (2/3)x. After dinner, the remaining jam was (6/7)(2/3)x = (4/7)x. The answer is C. #### C QUESTION:A 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? options: A)615 m B)240 m C)168 m D)197 m E)691 m SOLUTION:Speed = 54 * 5/18 = 15 m/sec. Length of the train = 15 * 20 = 300 m. Let the length of the platform be x m . Then, (x + 300)/36 = 15 => x = 240 m Answer: B #### B QUESTION:Of the science books in a certain supply room, 40 are on botany, 45 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 area science? options: A)186 B)225 C)294 D)302 E)314 SOLUTION:The worst case scenario is to remove all the books on botany, zoology, and geology. Also we can remove 79 books each from physics and chemistry. The total is 40 + 45 + 50 + 79 + 79 = 293. The next book removed must either be physics or chemistry, ensuring 80 books in that subject. The answer is C. #### C QUESTION:A reduction of 5% in the price of sugar enables a lady to obtain 5kgs more for Rs.500, find the original price per kg? options: A)5.26 B)5.0 C)5.52 D)6.2 E)5.8 SOLUTION:Answer: 500*(5/100) = 25 --- 5 ? --- 1 => Rs.5 500 --- 475 ? --- 5 => Rs.5.26.Answer: A #### A QUESTION:Convert 2/5 to a decimal options: A)0.1 B)0.2 C)0.3 D)0.4 E)0.5 SOLUTION:Divide 2 by 5: 2 / 5 = 0.4 Answer: 2/5 = 0.4 (D) #### D QUESTION:What is the greatest possible length that can be used to measure exactly the following Lengths 7m, 3m 85cm, 12m 95cm? options: A)25 cms B)30 cms C)35 cms D)38 cms E)45 cms SOLUTION:HCF of 7m, 3m 85cm, 12m 95cm is 35 cms. ANSWER:C #### C QUESTION:In 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? options: A)75 B)78 C)80 D)82 E)86 SOLUTION:Divisor = (6 * 3) + 2 = 20 5 * Quotient = 20 Quotient = 4. Dividend = (Divisor * Quotient) + Remainder Dividend = (20 * 4) + 6 = 86 E) #### E QUESTION:A 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. What is the total distance traveled by the man? options: A)5.78 B)5.79 C)5.76 D)5.74 E)5.721 SOLUTION:M = 6 S = 1.2 DS = 7.2 US = 4.8 x/7.2 + x/4.8 = 1 x = 2.88 D = 2.88 * 2 = 5.76.Answer: C #### C QUESTION:12. What is the dividend. divisor 17, the quotient is 9 and the remainder is 7. options: A)150 B)152 C)154 D)158 E)160 SOLUTION:D = d * Q + R D = 17 * 9 + 7 D = 153 + 7 D = 160 ANSWER E #### E QUESTION:The current birth rate per thousand is 32, where as corresponding death rate is 10 per thousand. The net growth rate in terms of population increase in percent is given by? options: A)2.0% B)3.2% C)3.9% D)4% E)5.1% SOLUTION:Net growth on 1000 = 32-10 = 20 Net growth on 100 = 20*100/1000 = 2.0% Answer is A #### A QUESTION:If f(x) = (x^2 - 1)/(x), what is f(1/x) in terms of f(x)? options: A)-1*f(x) B)f(x) C)1/f(x) D)-1/f(x) E)2*f(x) SOLUTION:f(1/x) = ((1/x)2 - 1) / ((1/x)) = ((1/x^2) - 1) / (1/x) = ((1-x^2)/(x^2)) / (1/x = (1-x^2)/(x^2) = - ( (x^4) -1) / (x) = -1* f(x) Answer is A. #### A QUESTION:Out of the total 390 students studying in a college of Arts and Science, boys and girls are in the ratio of 7 : 6 respectively and the number of students studying Arts and Science are in the ratio of 3 : 7 respectively. The boys and girls studying Arts are in the ratio of 4 : 5 respectively. How many boys are studying science? options: A)52 B)65 C)115 D)158 E)168 SOLUTION:Given, boys and girls are in the ratio of 7 : 6, So, Number of boys = 7/13 x 390 = 210 Number of girls = 390 - 210 = 180 Students studying Arts and Science are in the ratio of 3 : 7, Number of students studying Arts = 3/10 x 390 = 117 Number of students studying Science = 390 - 117 = 273 Also boys and girls studying Arts are in the ratio of 4 : 5, Number of boys studying arts = 4/9 x 117 = 52 Number of boys studying science = 210 - 52 = 158 ANSWER:D #### D <<<Examples ends QUESTION:If n is a positive integer, then n(n+1)(n+2) is +ve and options: A)divisible by 4 whenever n is even B)divisible by 3 only when n is odd C)odd whenever n is odd D)even only when n is odd E)even only when n is even SOLUTION:n*(n+1)*(n+2)= +ve even integer divisible by 4 ( e.g 3,4,&5) A #### A

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:The 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: options: A)5:2 B)7:3 C)9:2 D)13:4 E)3:4 SOLUTION:Let the age of father and son 10 years ago be 3x and x years respectively. Then, (3x + 10) + 10 = 2[(x + 10) + 10] 3x + 20 = 2x + 40 => x = 20. Required ratio = (3x + 10):(x + 10) = 70:30 = 7:3 ANSWER:B #### B QUESTION:The ratio between the length and the breadth of a rectangular park is 1 : 4. If a man cycling along the boundary 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? options: A)124545 m B)134561 m C)156787 m D)15450 m E)102400 m SOLUTION:Perimeter = Distance covered in 8 min. = 12000 x 8 m = 1600 m. 60 Let length = 1x metres and breadth = 4x metres. Then, 2(1x + 4x) = 1600 or x =160. Length = 160 m and Breadth = 640 m. Area = (160 x 640) m2 = 102400 m E #### E QUESTION:The area of sector of a circle whose radius is 12 metro and whose angle at the center is 42° is? options: A)52.7 m2 B)57.8 m2 C)52.8 m2 D)72.8 m2 E)52.8 m2 SOLUTION:42/360 * 22/7 * 12 * 12 = 52.8 m2 Answer: C #### C QUESTION:A train running at the speed of 60 km/hr crosses a pole in 6 seconds. Find the length of the train. options: A)150 m B)145 m C)100 m D)135 m E)155 m SOLUTION:Speed = 60*(5/18) m/sec = 50/3 m/sec Length of Train (Distance) = Speed * Time (50/3) * 6 = 100 meter ANSWER: C #### C QUESTION:The 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? options: A)20 years B)21 years C)22 years D)23 years E)24 years SOLUTION:Explanation: Let the average age of the whole team by x years. 11x – (24 + 27) = 9(x -1) 11x – 9x = 42 2x = 42 x = 21. So, average age of the team is 21 years. Answer B #### B QUESTION:A basketball is dropped from a height of 40 feet. If it bounces back up to a height that is exactly half of its previous height, and it stops bouncing after hitting the ground for the fourth time, then how many total feet will the ball have traveled after 3 full bounces. options: A)50 B)55 C)110 D)75 E)80 SOLUTION:Initial distance = 40 feet first bounce = 20 feet up + 20 feet down = 40 feet second bouche = 10 feet up + 10 feet down = 20 feet third bounce = 5 feet up and 5 feet down= 10 feet total distance covered = 40+40+20+10= 110 ANSWER IS C #### C QUESTION:Average of five numbers is 26. If one number is excluded the average becomes 28. The excluded number is options: A)10 B)12 C)16 D)20 E)18 SOLUTION:Explanation: Number is (5*26) - (4*28) = 130-112 = 18 Answer: Option E #### E QUESTION:A certain quantity of 40% concentration solution is replaced with 25% concentration solution such that the concentration of the combined amount is 35%. What's the ratio of the amount of solution that was replaced to the amount of solution that was not replaced? options: A)1:3 B)1:2 C)2:3 D)2:1 E)3:1 SOLUTION:From the wording in the prompt, we're essentially mixing two liquids: Liquid X is 40% concentrate Liquid Y is 25% concentrate We're supposed to mix some of each and end up with a solution that is 35% concentrate. The prompt doesn't give us specific amounts of liquids to work with and the question itself asks for the ratio of the two liquids, so we could even TEST VALUES if doing it that way made it easier for you. For now though, here's the Algebra: X = # of ounces of liquid X Y = # of ounces of liquid Y (.4X + .25Y) / (X + Y) = .35 .4X + .25Y = .35X + .35Y .05X = .1Y 5X = 10Y From here, you have to be CAREFUL to answer the question that is ASKED. 5X = 10Y Y/X = 5/10 = 1/2 ANSWER:B #### B QUESTION:I sold a book at a profit of 10%. Had I sold it for $120 more, 15% would have been gained. Find the cost price? options: A)$2000 B)$2500 C)$2400 D)$3120 E)$1540 SOLUTION:115% of cost - 110% of cost = $120 5% of cost = $120 cost = 120*100/5 = $2400 Answer is C #### C QUESTION:Harriet planned to complete a certain task on Wednesday, January 1, but because of illness the completion date was postponed 45 days. On which day of the week in February was the task completed? options: A)Tuesday B)Wednesday C)Saturday D)Sunday E)Monday SOLUTION:This type of story problem is essentially just about a repeating pattern and a 'remainder.' We're told that Harriet planned to complete a certain task on WEDNESDAY, January 1, but because of illness the completion date was postponed 45 DAYS. We're asked on what day of the week the task was actually completed on. Since the task was supposed to be completed on a Wednesday.... A 1 day postponement would be Thursday A 2 day postponement would be Friday A 3 day postponement would be Saturday A 4 day postponement would be Sunday A 5 day postponement would be Monday A 6 day postponement would be Tuesday A 7 day postponement would be Wednesday A 8 day postponement would be Thursday Etc. So this question is ultimately asking how many 'groups of 7' are there, and how many 'leftover days' are there, when you postpone 45 days. 45/7 = 6 remainder 3 This means that there are 6 full weeks AND 3 extra days after a Wednesday....Thus, the task was completed on a Saturday. C #### C QUESTION:Find the average of all prime numbers between 10 and 30. options: A)30 B)33.6 C)39.8 D)18.6 E)None SOLUTION:Sol. There are six prime numbers between 10 and 30. They are 11, 13, 17, 19, 23, 29 ∴ Required average = [11+ 13+ 17+19+ 23+ 29 / 6] = 112/ 6 = 18.6 Answer D #### D QUESTION:A jogger running at 9 km/hr along side a railway track is 240 m ahead of the engine of a 140 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger? options: A)19 sec B)38 sec C)36 sec D)16 sec E)11 sec SOLUTION:Speed of train relative to jogger = 45 - 9 = 36 km/hr. = 36 * 5/18 = 10 m/sec. Distance to be covered = 240 + 140 = 360 m. Time taken = 380/10 = 38 sec. Answer: B #### B QUESTION:If a person walks at 16 km/hr instead of 12 km/hr, he would have walked 20 km more. The actual distance traveled by him is? options: A)50 B)65 C)70 D)61 E)60 SOLUTION:Let the actual distance traveled be x km. Then, x/12 = (x + 20)/16 x - 60 =>x = 60km. Answer: E #### E QUESTION:A and B invest money in the ratio 6:7 and they has loss of Rs.7800 at the end of year. what is the share of loss of B? options: A)Rs.4200 B)Rs.4300 C)Rs.4400 D)Rs.4500 E)None of the above SOLUTION:et ratio of A and B be 6x & 7x so net loss = 6x+7x= 7800 x=600 A=6x=6(600)=3600 B= 7x=7(600)=4200 so, B= 4200 ANSWER:A #### A QUESTION:Find the compound interest on $1000 in 2years at 4% per annum, the interest being compounded half-yearly? options: A)$645.56 B)$82.43 C)$954.26 D)$745.69 E)$1020.45 SOLUTION:Principle = $10000 Rate = 2% half yearly = 4 half years Amount = 1000*(1 + 2/100)^4 = 1000 * 51/50 * 51/50 * 51/50 * 51/50 = $1082.43 C.I. = 1082.43-1000 = $82.43 Answer is B #### B QUESTION:The owner of a cell phone shop charges his customer 23% more than the cost price. If a customer paid Rs.8,517 for a cell phone, then what was the cost price of the cell phone? options: A)Rs.5,845 B)Rs.6,750 C)Rs.5,700 D)Rs.6,925 E)None of these SOLUTION:Explanation: 123% of CP =SP Therefore, CP = Rs.8,517x100/123 = Rs.6925 Answer: Option D #### D QUESTION:A 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? options: A)Rs. 375 B)Rs. 400 C)Rs. 600 D)Rs. 800 E)Rs. 850 SOLUTION:C's 1 day's work = 1/3 - (1/6 + 1/8) = 1/3 - 7/24 = 1/24 A's wages : B's wages : C's wages = 1/6 : 1/8 : 1/24 = 4: 3 : 1 C's share (for 3 days) = Rs. (3 * 1/24 * 3200) =Rs.400 Answer = B #### B QUESTION:The G.C.D. of 1.08, 0.36 and 0.8 is: options: A)0.04 B)0.9 C)0.18 D)0.108 E)0.118 SOLUTION:Given numbers are 1.08, 0.36 and 0.80. H.C.F. of 108, 36 and 80 is 18, H.C.F. of given numbers = 0.04. Answer: Option A #### A QUESTION:If 0.003^5 is represented in its shortest possible decimal form, how many 0’s to the right of the decimal point does it contain? options: A)9 B)10 C)11 D)12 E)13 SOLUTION:0.003^5= (3*10^-3)^5 = 243*10^-15 = 0.243*10^-12 which would have 12 zeros to the right of the decimal point. The answer is D. #### D QUESTION:A store reduced the price of all items in the store by 9% 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? options: A)80.0 B)80.9 C)81.0 D)81.1 E)81.9 SOLUTION:consider price of the all items as $100 after a initial reduction of 9% price becomes = 0.91 *100 = $ 91 after the final reduction of 10% price becomes = 0.9* 91 = $ 81.9 price of all items on second day is 81.9% of price on first day correct answer option E #### E QUESTION:A 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? options: A)22.7 kmph B)12.7 kmph C)27.6 kmph D)12.5 kmph E)22.1 kmph SOLUTION:Let the speed of the man in still water be a kmph and let the speed of the stream be b kmph. Now 30/(a + b) + 20/(a - b) = 4 and 45/(a + b) + 40/(a - b) = 7 Solving the equation, the speed of man in still water is 12.5 kmph.Answer: D #### D QUESTION:What sum of money put at C.I amounts in 2 years to Rs.8840 and in 3 years to Rs.9261? options: A)8054 B)8877 C)2877 D)2678 E)1011 SOLUTION:8840 ---- 421 100 ---- ? => 4.76% x *104.76/100 * 104.76/100 = 8840 x*1.0975=8840 x=8840/1.0975 => 8054.54 Answer: A #### A QUESTION:There is a 10% chance that Tigers will not win at all during the whole season. There is a 30% 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? options: A)A)55% B)B)60% C)C)80% D)D)72% E)E)70% SOLUTION:There is a 10% chance that Tigers will not win at all during the whole season We can infer that there is 90% chance Tigers will win . Similarly There is a 30% chance that Federer will not play at all in the whole season We can also infer that there is 70% chance that Federer will play. Answer E #### E QUESTION:One student to pass the subject as probability 1/4. another man to get driving licence and student passed subject probability 1/6. find the probability man get driving licence. options: A)1/3 B)2/3 C)4/3 D)5/3 E)1/4 SOLUTION:Let the probability of the man get driving licence is x. so, 1/4 * x = 1/6 x = 2/3. ANSWER:B #### B QUESTION:The distance light travels in one year is approximately 5,870,000,000,000 miles. The distance light travels in 100 years is: options: A)587 × 10<10>(exponent) miles B)587 × 10<-12> (exponent) miles C)587 × 10<-10>(exponent) miles D)587 × 10<12>(exponent) miles E)587 × 10<8>(exponent) miles SOLUTION:The distance of the light travels in 100 years is: 5,870,000,000,000 × 100 miles. = 587,000,000,000,000 miles. = 587 ×10<12>(exponent) miles #### D QUESTION:Calculate the ratio between x and y if 30% of x equal to 50% of y? options: A)4 : 5 B)3 : 5 C)3 : 7 D)3 : 2 E)4 : 5 SOLUTION:Explanation: 30 x = 50 y x: y = 30: 50 = 3 : 5 Answer:B #### B QUESTION:There r 3 boys & 4 girls; Howmany ways they r arranged such that boys should be always together ? options: A)120ways B)220ways C)420ways D)720ways E)520ways SOLUTION:By kept 3boys together(1) and arranging 4 girls with them 5! = 5*4*3*2*1 = 120ways. (i.e., 4+1 =5) Possible arrangements of 3 boys in following ways 3! = 3*2*1 = 6ways Now, arrange all with the boys together 120*6 = 720ways ANSWER:D #### D QUESTION:A and B start from Opladen and Cologne respectively at the same time and travel towards each other at constant speeds along the same route. After meeting at a point between Opladen and Cologne, A and B proceed to their destinations of Cologne and Opladen respectively. A reaches Cologne 40 minutes after the two meet and B reaches Opladen 60 minutes after their meeting. How long did A take to cover the distance between Opladen and Cologne? options: A)1 hour B)1 hour 20 minutes C)2 hours 30 minutes D)1 hour 40 minutes E)2 hours 10 minutes SOLUTION:v1 and V2 are speeds. v1.t /60 = v2 v2.t/40 = v1 v1/v2 = 3/2 which train A would 60. 2/3 mins to cover the same distance 40 + 40 = 80 mins (ANS B) #### B QUESTION:In 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: options: A)4 B)5 C)6 D)7 E)9 SOLUTION:Explanation : Let the required number of men be x. Less days, More men (Indirect Proportion) More working hrs per day, Less men (Indirect Proportion) Days 8 : 10 Working Hrs 15 : 9 :: 12 : x => 12 x 15 x x = 10 x 8 x 12 => x = 10 x 9 x 12 / (12 x 15) => x = 7 Answer : D #### D QUESTION:Louie takes out a three-month loan of $2000. 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? options: A)A)333 B)B)383 C)C)402 D)D)433 E)E)804 SOLUTION:Here's the calculation for that case, assume monthly payment is X. After 1st month: (2000)(1.1)-X = 2200-X After 2nd month: (2200-X)(1.1)-X = 2420-2.21X After 3rd month: (2420-2.21X)(1.1)-X = 2662-3.31X Now, the amount after the last payment in 3rd month must bring the total to 0. Hence: 2662-3.31X = 0 X = 2662/3.31 = 804 Answer E #### E QUESTION:A train running at the speed of 60 km/hr crosses a pole in 9 seconds. Find the length of the train? options: A)150 meter B)876 meter C)167 meter D)719 meter E)169 meter SOLUTION:Speed = 60*(5/18) m/sec = 50/3 m/sec Length of Train (Distance) = Speed * Time (50/3) * 9 = 150 meter Answer: A #### A QUESTION:An 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? options: A)40: 20 B)42: 21 C)50: 100 D)15: 25 E)It cannot be determined by the information given. SOLUTION:While you can figure out most of this question, there is not enough information to completely tell. the answer is E. #### E QUESTION:If x,p,q, and r are positive integers and (p)×(q)×(r)=x^2, which of the following could be the values of p,q, and r? options: A)3, 16, 25 B)9, 25, 24 C)2,16, 32 D)2, 9, 16 E)8, 16, 36 SOLUTION:This is one of those questions where using the given options is fastest way to get the solution. We need to find a set where 3 numbers can be paired into 2 pairs of some numbers because we need a product which is a square number. C fits the bill. 2*16*32 = 2*4*4*8*4 =4*4*8*8 ans C #### C QUESTION:A bag contains 6 white and 4 black balls .2 balls are drawn at random. find the probability that they are of same colour. options: A)15/7 B)4/17 C)7/18 D)19/6 E)7/15 SOLUTION:Let S be the sample space Then n(S)=no of ways of drawing 2 balls out of (6+4)=10c2=(10*9)/(2*1)=45 Let E=event of getting both balls of same colour Then n(E)=no of ways(2 balls out of six) or(2 balls out of 4) =(6c2+4c2)=(6*5)/(2*1)+(4*3)/(2*1)=15+6=21 P(E)=n(E)/n(S)=21/45=7/15 Option E #### E QUESTION:How many four letter words are formed using the letters of the word POLICE? options: A)280 B)321 C)330 D)360 E)370 SOLUTION:The number of letters in the given word is four. The number of three letter words that can be formed using these four letters is 6P4 = 6 * 5 * 4 * 3 = 360. Answer: D #### D QUESTION:The volume of a cube is 3375 cc. Find its surface. options: A)1350 B)1150 C)1456 D)1254 E)1489 SOLUTION:a3 = 3375 => a = 15 6a2 = 6 * 15 * 15 = 1350 Answer: A #### A QUESTION:The expression (11.98 x 11.98 + 11.98 x x + 0.02 x 0.02) will be a perfect square for x equal to: options: A)0.04 B)0.004 C)0.4 D)0.0004 E)None of them SOLUTION:Given expression = (11.98)(power 2) + (0.02)(power 2) + 11.98 x x. For the given expression to be a perfect square, we must have 11.98 x (x) = 2 x 11.98 x 0.02 or x = 0.04 Answer is A #### A QUESTION:Working alone at their respective constant rates, A can complete a task in ‘a’ days and B in ‘b’ days. They take turns in doing the task with each working 2 days at a time. If A starts they finish the task in exact 8 days. If B starts, they take a day more. How long does it take to complete the task if they both work together? options: A)6 B)7 C)8 D)4 E)2 SOLUTION:Work done by AB in a day = xy respectively. When A starts: No. of days when A works = 4No. of days when B works = 4 → 4x + 4y = 1 When B starts: No. of days when A works = 5No. of days when B works = 3 → 5x + 3y = 1 Solving the above two equations for xy x = 1/8 y = 1/8 → Total work done by AB in a day = 1/8 + 1/8 = 1/4 → No. of days to complete the work when both work together = 4 Answer: D #### D QUESTION:What is the next number in the given series 4,18,100,294,....? options: A)1210 B)1220 C)1230 D)1240 E)1250 SOLUTION:The given series is difference of cubes and squares of consecutive prime numbers. 2*2*2-2*2=4, 3*3*3-3*3=18, 5*5*5-5*5=100, 7*7*7-7*7=294, 11*11*11-11*11=1210 ANSWER:A #### A QUESTION:It is required to seat 4 boys and 3 girls in a row so that the girls occupy the even places. How many such arrangements are possible? options: A)142 B)144 C)3680 D)3280 E)3680 SOLUTION:Total number of candidates = 4 + 3 = 7. In the row of 7 positions, the even places are 2nd, 4th, 6th . Now, number of even places = 3. Number of girls to occupy the even places = 3. Even places can be filled = P (3, 3) ways. Number of boys = 4. The remaining 4 places can be filled by 4 boys = P (4, 4) ways By the fundamental principle of counting: The required number of seating arrangements P(3, 3) x P(4, 4) = 3! x 4! = 6 x 24 = 144 ANSWER:B #### B QUESTION:What is x if x + 5y = 24 and y = 2? options: A)1 B)3 C)5 D)7 E)14 SOLUTION:Substitute y by 2 in x + 5y = 24 x + 5(2) = 24 x + 10 = 24 If we substitute x by 14 in x + 10 = 24, we have 14 + 10 = 24. Hence x = 14 correct answer E #### E QUESTION:A, 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 ? options: A)Rs. 832 B)Rs. 830 C)Rs. 822 D)Rs. 812 E)Rs. 810 SOLUTION:Let the total amount in the partnership be 'x'. Then A's share = x/3 B's share = x/4 C's share = x/5 D's share = x - (x/3 + x/4 +x/5) = 13x/60 A : B : C : D = x/3 : x/4 : x/5 : 13x/60 = 20 : 15 : 12 : 13 A's share in the profit of Rs. 2490 = 20 (2490/60) = Rs. 830. Answer: B #### B QUESTION:A 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: options: A)5% B)8% C)10% D)12% E)6% SOLUTION:C.P. of 56 kg rice = Rs. (26 x 20 + 30 x 36) = Rs. (520 + 1080) = Rs. 1600. S.P. of 56 kg rice = Rs. (56 x 30) = Rs. 1680. Gain =(80/1600x 100)% = 5%. Answer is A. #### A QUESTION:A certain kind of necklace is made from 9 gold, 6 blue, and 3 white beads. What is the maximum number of these necklaces that can be made from 36 beads of each color ? options: A)8 B)4 C)6 D)5 E)4 SOLUTION:Atleast 9 gold breads are needed to make a necklace, so irrespective of the combinations of blue and white beads, the number of necklaces that can be formed will be 36/9 =4 Answer:- E #### E QUESTION:If x is to be chosen at random from the set {5,6,7,8} and y is to be chosen at random from the set {1,2,3}, what`s the probability that xy will be even? options: A)1/6 B)1/3 C)2/3 D)1/2 E)5/6 SOLUTION:The product to be even either one or both must be even, so: P(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; Or: 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. Answer: C. #### C QUESTION:The ratio between the perimeter and the width of a rectangle is 5:1. If the area of the rectangle is 54 square centimeters, what is the length of the rectangle in centimeters? options: A)6 B)7 C)8 D)9 E)10 SOLUTION:Perimeter = 2(W+L) = 5W 3W = 2L W = 2L/3 WL = 54 2L^2/3 = 54 L^2 = 81 L = 9 cm The answer is D. #### D QUESTION:J is faster than P. J and P each walk 24 km. Sum of the speeds of J and P is 7 kmph. Sum of time taken by them is 14 hours. Then J speed is equal to options: A)22 B)14 C)6 D)8 E)16 SOLUTION:Given J > P J + P = 7, only options are (6, 1), (5, 2), (4, 3) From the given options, If J = 4 the P = 3. Times taken by them = 244+243=14 Answer:B #### B QUESTION:Three business people wish to invest in a new company. Each person is willing to pay one third of the total investment. After careful calculations, they realize that each of them would pay $8,200 less if they could find two more equal investors. How much is the total investment in the new business? options: A)$61,500 B)$54,000 C)$21,000 D)$ 5,400 E)$ 3,600 SOLUTION:Total Investment between 5: (x/5) Total investment including 8200 less between 3 people(x-(8200*3))/3 Set both eq. equal to each other. 61,500 Answer A) #### A QUESTION:On increasing the price of T.V. sets by 40%, their sale decreases by 20%. What is the effect on the revenue receipts of the shop ? options: A)4 B)5 C)56 D)12 E)7 SOLUTION:Explanation: Let the price be = Rs.100, and number of units sold = 100 Then, sale value = Rs.(100 × 100) = Rs.10000 New sale value = Rs.(140 × 80) = Rs.11200 Increase% = 1200/10000 × 100 = 12% Answer: D #### D QUESTION:Two finite sets have m and n elements respectively. The total number of subsets of first set is 56 more than the total number of subsets of the second set. The values of m and n respectively are: options: A)7, 6 B)5, 1 C)6, 3 D)8, 7 E)None of these SOLUTION:Explanation : Let A and B be such sets, i.e., n (A) = m, n (B) = n So, n (P(A)) = 2m and n (P(B)) = 2n Thus n (P(A)) – n (P(B)) = 56, i.e. 2m – 2n = 56 ⇒ 2n (2m-n - 1) = 23 x 7 ⇒ n = 3 , 2m-n – 1 = 7 ⇒ m = 6 Answer : C #### C QUESTION:How 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 ? options: A)48 B)36 C)26 D)11 E)18 SOLUTION:Explanation: Here distance d = 600 mts speed s = 63 - 3 = 60 kmph = 60 x 5/18 m/s time t = = 36 sec. Answer: B #### B QUESTION:A horse chases a pony 8 hours after the pony runs. Horse takes 12 hours to reach the pony. If the average speed of the horse is 320 kmph, what s the average speed of the pony? options: A)182kmph B)192kmph C)193kmph D)196kmph E)190kmph SOLUTION:pony take 20 hours and horse take 12 hours...then Distance chased by them is 320*12.so speed of pony is (320*12)/20=192kmph. ANSWER IS B #### B QUESTION:Sonika bought a V.C.R. at the list price of 18,900. If the rate of sales tax was 8%, find the amount she had to pay for purchasing the V.C.R. options: A)20,412 B)19,780 C)19,680 D)19,380 E)None of these SOLUTION:Sol. List price of V.C.R. =18,900 Rate of sales tax = 8% ∴ Sales tax = 8% of 18,900 = 8⁄100 × 18500 = 1512 So, total amount which Sonika had to pay for purchasing the V.C.R. = 18,900 + 1512 = 20,412. Answer A #### A QUESTION:200 is what percent of 40? . options: A)0.2% B)2% C)5% D)20% E)500% SOLUTION:200= x*40/100 x = 500% Ans; E #### E QUESTION:A small family consisting of 4 ( father , mother , son , daughter ) goes to a photo studio . Father says to the photographer , " I need all the possible photographs of our family " . how many pictures can he take , such that at least one person should be there in the photo options: A)61 B)62 C)63 D)64 E)65 SOLUTION:4C1+4C2+4C3+4C4=15. If their positions also takes into consideration then the ans will be 64 ANSWER:D #### D QUESTION:Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 3 or 5? options: A)5/20 B)9/25 C)8/20 D)9/20 E)6/20 SOLUTION:Explanation: Here, S = {1, 2, 3, 4, ...., 19, 20}. Let E = event of getting a multiple of 3 or 5 = {3, 6 , 9, 12, 15, 18, 5, 10, 20} answer 9/20 Answer D #### D QUESTION:Two cards are drawn together from a pack of 52 cards. The probability that one is a spade and one is a heart, is: options: A)13/109 B)13/162 C)13/111 D)13/102 E)13/112 SOLUTION:Let S be the sample space. Then, n(S) = \inline {\color{Black}52C_{2} }=(52 x 51)/(2 x 1) = 1326. Let E = event of getting 1 spade and 1 heart. n(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. P(E) = n(E)/n(S) = 169/1326 = 13/102. Answer: D) 13/102 #### D QUESTION:a milkman makes a profit of 20% on the sale of milk. If he were to add 10% water to the milk, by what % would his profit increase? options: A)50 % B)60 % C)70 % D)80 % E)40 % SOLUTION:let he sells 100 lit of milk @ 120 rs. means his cost price must b 100 to gain 20% profit. Nw he adds 10% milk ie total milk z 110 lit. Now he will get 132 rs. by selling 110 lit f milk (120*110/100) total profit = 32 rs increased profit =12 rs %age increase= 12/20= 60 % ANSWER:B #### B QUESTION:The ratio between the perimeter and the breadth of a rectangle is 5 : 1. If the area of the rectangle is 216 sq. cm, what is the length of the rectangle? options: A)16cm B)18cm C)24cm D)Data inadequate E)None of these SOLUTION:Explanation: 2(l+b)/b=5/1 2l + 2b = 5b 3b = 2l b = 2/3 l Then, Area = 216 cm2 l x b = 216 l x (2/3)l = 216 l2 = 324. l = 18 cm. Answer: B #### B QUESTION:Mr. loyd wants to fence his Square shaped land of 150Sqft each side.If a pole is laid every 30ft how many poles do he need? options: A)20 B)30 C)40 D)50 E)60 SOLUTION:If each side is 120 feet..then total perimeter is 150*4=600 poles every 20 feet hence no of poles= 600/20=30 ANSWER:B #### B QUESTION:A painting crew painted 80 houses. They painted the first y houses at a rate of x houses per week. Then more painters arrived and everyone worked together to paint the remaining houses at a rate of 3.25x houses per week. How many weeks did it take to paint all 80 houses, in terms of x and y? options: A)(320 - y)/(5x) B)(y +220)/(5x) C)5(80 - y)/(4x) D)(y + 400)/(4x) E)(4y + 320)/(5x) SOLUTION:Ans B Plug some numbers Let y = 40 houses and x = 20 then they painted 20 houses per week as painters were added to the group , the rate of the group increased to 3.25 x => 3.25 * 20 = 65 houses per week total time they took = (40/20) + (40/65) = 2.6 weeks Putting the values of x and y in equation B (y +220)/(5x) = (40+220)/5*20 = 260/100 = 2.6 #### B QUESTION:When positive integer x is divided by positive integer y, the result is 59.32. What is the sum W of all possible 2-digit remainders for x/y? options: A)560 B)616 C)672 D)728 E)784 SOLUTION:ans B 616... remainders = .32=32/100=8/25=16/50 and so on.. so two digit remainders are 16+24+32+....+96.. W=8(2+3+4....+12)=616 #### B QUESTION:The 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 options: A)20 B)21 C)22 D)23 E)24 SOLUTION:Solution Let the toatl number of workers be x. Then 8000x=(12000 x 7) + 6000 (x -7) 2000x =42000 x= 21. Answer B #### B QUESTION:A 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? options: A)7 cm B)6 cm C)4 cm D)3 cm E)9 cm SOLUTION:Volume of the wire (in Cylindrical shape) is equal to the volume of the sphere. π(16)2 * h = (4/3)π (12)3 => h = 9 cm Answer: E #### E <<<Examples ends QUESTION:In a jar there are 15 white balls, 25 red balls, 10 blue balls and 20 green balls. How many balls must be taken out in order to make sure we took out 8 of the same color? options: A)a) 8 B)b) 23 C)c) 29 D)d) 32 E)e) 53 SOLUTION:Thats 29 in C. #### C

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:The 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? options: A)277 B)268 C)287 D)480 E)281 SOLUTION:Let the side of the square be a cm. Let the length and the breadth of the rectangle be l cm and b cm respectively. 4a = 2(l + b) 2a = l + b l . b = 480 We cannot find ( l + b) only with the help of l . b. Therefore a cannot be found . Area of the square cannot be found. Answer:D #### D QUESTION:3x^2 + 5x - 2 = options: A)(3x-1)(x+2) B)(3x-4)(x+2) C)(3x-4)(x-2) D)(3x-2)(x+4) E)none of above SOLUTION:3x^2 + 5x - 2 = 3x^2 + 6x - x - 2 = 3x (x + 2) - (x+2) = (3x-1) (x+2) Option A #### A QUESTION:An order was placed for the supply of a carper whose length and breadth were in the ratio of 3 : 2. Subsequently, the dimensions of the carpet were altered such that its length and breadth were in the ratio 7 : 3 but were was no change in its parameter. Find the ratio of the areas of the carpets in both the cases. options: A)8:9 B)8:7 C)8:1 D)8:2 E)8:8 SOLUTION:Let the length and breadth of the carpet in the first case be 3x units and 2x units respectively. Let the dimensions of the carpet in the second case be 7y, 3y units respectively. From the data,. 2(3x + 2x) = 2(7y + 3y) => 5x = 10y => x = 2y Required ratio of the areas of the carpet in both the cases = 3x * 2x : 7y : 3y = 6x2 : 21y2 = 6 * (2y)2 : 21y2 = 6 * 4y2 : 21y2 = 8 : 7 Answer:B #### B QUESTION:Which one the following fractions has the biggest value? options: A)211/711 B)201/711 C)191/711 D)221/711 E)181/711 SOLUTION:All options have the same denominator 711. If denominator is same, the fraction with the biggest value will be the one with the biggest numerator. Answer (D). #### D QUESTION:A 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? options: A)4/8 B)9/2 C)7/6 D)9 E)2/21 SOLUTION:Explanation: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles. Probability that both marbles are blue = ³Câ‚‚/¹⁵Câ‚‚ = (3 * 2)/(15 * 14) = 1/35 Probability that both are yellow = ²Câ‚‚/¹⁵Câ‚‚ = (2 * 1)/(15 * 14) = 1/105 Probability that one blue and other is yellow = (³C₁ * ²C₁)/¹⁵Câ‚‚ = (2 * 3 * 2)/(15 * 14) = 2/35 Required probability = 1/35 + 1/105 + 2/35 = 3/35 + 1/105 = 1/35(3 + 1/3) = 10/(3 * 35) = 2/21 Answer: E #### E QUESTION:The average of 35 numbers is 25. If each number is multiplied by 5, find the new average? options: A)125 B)772 C)821 D)912 E)121 SOLUTION:Sum of the 35 numbers = 35 * 25 = 875 If each number is multiplied by 5, the sum also gets multiplied by 5 and the average also gets multiplied by 5. Thus, the new average = 25 * 5 = 125. Answer:A #### A QUESTION:If p^2 – 6p + 8 = q, and p is a positive integer between 1 and 10, inclusive, what is the probability that q < 0? options: A)1/5 B)1/10 C)2/5 D)3/5 E)3/10 SOLUTION:(p-2)(p-4) = q p = 3 for this to be true, so 1/10 Ans :B #### B QUESTION:The sum of two numbers is 18. Their difference is 4. What are the numbers? options: A)8,6 B)9,9 C)11,7 D)15,3 E)13,9 SOLUTION:Let two numbers be x and y. Equation (i): x + y = 18 Equation (ii): x - y = 4 Solve system of equations: 2x=22 x=11 y=7 Answer C is correct. #### C QUESTION:50 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 4m3 , then the rise in the water level in the tank will be: options: A)20 cm B)25 cm C)35 cm D)50 cm E)None of these SOLUTION:Explanation: Total volume of water displaced =(4 x 50) m3 = 200 m3 Rise in water level = 200/40×20= 0.25m = 25cm Answer: B #### B QUESTION:A 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 G will the work get over? options: A)60 B)70 C)G=75 D)G=80 E)100 SOLUTION:We can also use the concept of man-days here 100 days -->10men so the job includes 100*10=1000 man-days After 20 days 1/4 of Job is completed so 1/4 X 1000 man-days=250 man-days Job is done Now the Balance Job=1000-250=750 man-days worth of Job Since 2 men are fired so B/L men=8 Therefore Total no. of days of Job=750 man-day/8 days = 375/4=94 days (approx.) Now since this is total and Ques. is asking for additional no. of days, So 94-20=74 days The nearest approx. to answer is 75 Ans: C (75 days) #### C QUESTION:By walking at 3/4th of his usual speed, a man reaches office 16 minutes later than usual. What is his usual time? options: A)48min B)50min C)65min D)60min E)70min SOLUTION:let T be the usual time. time spent=4T/3 therefore, 4T/3=T+16 4T=3T+48...therefor T=48min ANSWER:A #### A QUESTION:Find the length of the wire required to go 12 times round a square field containing 104976 m2. options: A)15840 B)3388 C)2667 D)8766 E)15552 SOLUTION:a2 = 104976 => a = 324 4a = 1296 1296 * 12 = 15552 Answer: E #### E QUESTION:In 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 favour of candidate? options: A)358000 B)368000 C)357000 D)358000 E)367000 SOLUTION:Total number of invalid votes = 15 % of 560000 = 15/100 × 560000 = 8400000/100 = 84000 Total number of valid votes 560000 – 84000 = 476000 Percentage of votes polled in favour of candidate A = 75 % Therefore, the number of valid votes polled in favour of candidate A = 75 % of 476000 = 75/100 × 476000 = 35700000/100 = 357000 Answer:C #### C QUESTION:Ratio between Rahul and Deepak is 4:3, After 6 Years Rahul age will be 26 years. What is Deepak present age. options: A)14 B)15 C)20 D)22 E)24 SOLUTION:Explanation: Present age is 4x and 3x, => 4x + 6 = 26 => x = 5 So Deepak age is = 3(5) = 15 Option B #### B QUESTION:A 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? options: A)13 8/3 days B)13 1/3 days C)13 6/3 days D)63 1/3 days E)13 5/3 days SOLUTION:5/30 + 20/x = 1 x = 24 1/30 + 1/24 = 3/40 40/3 = 13 1/3 days Answer:B #### B QUESTION:Murali 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? options: A)12 B)50 C)87 D)26 E)12 SOLUTION:Let the distances between city A to B and B to C be 2x km and 3x km respectively. Total time taken to cover from A to C = (2x)/40 + (3x)/60 = (6x + 6x)/120 = 12x/120 = x/10 Average speed = (2x + 3x)/(x/10) = 50 kmph. Answer: B #### B QUESTION:The average salary of all the workers in a workshop is Rs. 8000. The average salary of 7 technicians is Rs. 16000 and the average salary of the rest is Rs. 6000. The total number of workers in the workshop is options: A)20 B)21 C)22 D)35 E)NONE SOLUTION:Sol. Let the total number of workers be x. Then, 8000x = (16000 × 7) + 6000 ( x – 7) ‹=› 2000x = 70000 ‹=› x = 35. Answer D #### D QUESTION:Two taps can separately fill a cistern 5 minutes and 15 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? options: A)A)7 B)B)6 C)C)8 D)D)9 E)E)4.74 SOLUTION:1/5 + 1/15 - 1/x = 1/18 x = 4.74 Answer:E #### E QUESTION:A retailer buys 100 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 % ? options: A)110 B)175 C)212 D)218 E)220 SOLUTION:let the market price of each pen be $1 then, Cost Price of 100 pens = $ 36 Selling Price of 100 pens =99% of $100=$ 99 profit %=((63*100)/36) %=175% Answer B #### B QUESTION:A, B and C enter into a partnership. They invest Rs. 70,000, 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? options: A)21 : 32 : 4 B)21 : 26 : 4 C)21: 12 : 1 D)21: 16 : 28 E)none SOLUTION:Sol. A : B : C = (40000 * 36) : (80000 * 12 + 40000 * 24) : (120000 * 24 + 40000 * 12) =252 : 192 : 336 = 21: 16 : 28 Answer D #### D QUESTION:On a map the distance between two mountains is 310 inches. The actual distance between the mountains is 136 km. Ram is camped at a location that on the map is 34 inch from the base of the mountain. How many km is he from the base of the mountain? options: A)14.83 B)14.81 C)14.91 D)14.82 E)14.12 SOLUTION:Explanation: Since 310 inch = 136 km So 1 inch = 136/310 km So 34 inch = (136 × 34)/ 310 = 14.91 km Answer: C #### C QUESTION:If x is 20 percent greater than 98, then x = options: A)68 B)70.4 C)86 D)105.6 E)117.6 SOLUTION:x=98*1.2=117.6 So the answer is E. #### E QUESTION:Find the largest number of four digits which is exactly divisible by 27,18,16,15 options: A)8600 B)8610 C)8620 D)8630 E)8640 SOLUTION:Explanation: LCM of 27-18-16-15 is 2160. After dividing 9999 by 2160 we get 1359 remainder. So answer will be 9999-1359 = 8640 Option E #### E QUESTION:A family X went for a vacation. Unfortunately it rained for 13 days when they were there. But whenever it rained in the mornings, they had clear afternoons and vice versa. In all they enjoyed 11 mornings and 12 afternoons. How many days did they stay there totally? options: A)16 B)18 C)20 D)13 E)14 SOLUTION:Explanation : Clearly 11 mornings and 12 afternoons = 23 half days => Since 13 days raining means 13 half days. => So 23-13 =10 halfdays ( not effecetd by rain ) => So 10 halfdays =5 fulldays Hence , Total no. of days = 13+5 =18 days Answer : B #### B QUESTION:Sally has a gold credit card with a certain spending limit, and a platinum card with twice the spending limit of the gold card. Currently, she has a balance on her gold card that is 1/3 of the spending limit on that card, and she has a balance on her platinum card that is 1/4 of the spending limit on that card. If Sally transfers the entire balance on her gold card to her platinum card, what portion of her limit on the platinum card will remain unspent? options: A)7/12 B)29/60 C)17/30 D)19/30 E)11/15 SOLUTION:Let s assume the platinum card spending limit =x Gold card spending limit will be =x/2 balance on gold card is =x/2*1/3=x/6 Platinum card unspent limit is= x-1/4x=3/4x So if gold card balance is transferred then the rest unspent will be 3/4x-x/6=7/12x So the ans is A #### A QUESTION:A group of college friends plan to rent a house together for x dollars per month, which is to be shared equally among them. If four, rather than five people rent the house together, how many more dollars, in terms of x, will each person have to pay for rent per month? options: A)x/4 B)x/5 C)x/9 D)x/20 E)4x/9 SOLUTION:If 5 people share the rent, each person would pay x/5. If 4 people share the rent, each person will pay x/4. The extra amount each person pays is x/4 - x/5 = 5x/20 - 4x/20 = x/20 The answer is D. #### D QUESTION:How many quarters are equal to 7 dollars? options: A)1 B)28 C)12 D)9 E)7 SOLUTION:7 * 4 = 28 quarters Answer : B #### B QUESTION:In a game of 80 points; A can give B 5 points and C 15 points. Then how many points B can give C in a game of 60 ? options: A)B can give C 1 points B)B can give C 4 points C)B can give C 2 points D)B can give C 6 points E)B can give C 8 points SOLUTION:A: B = 80 : 75, A : C = 80 : 65. B/C = ( B/ A * A/C) = (75 / 80 * 80 / 65) = 15/13 = 60 /52 = 60: 5 Therfore ,In a game of 60, B can give C 8 points. Answer is E. #### E QUESTION:A sum of money invested at compound interest to Rs. 800 in 3 years and to Rs 880 in 4 years. The rate on interest per annum is. options: A)4% B)5% C)6% D)7% E)10% SOLUTION:Explanation: S.I. on Rs 800 for 1 year = 80 Rate = (100*80)/(800*1) = 10% Answer: E #### E QUESTION:A retail appliance store priced a video recorder at 20 percent above the wholesale cost of $200. If a store employee applied the 15 percent employee discount to the retail price to buy the recorder, how much did the employee pay for the recorder? options: A) $204 B) $216 C) $220 D) $230 E) $240 SOLUTION:Wholesale cost of video recorder = 200 $ Video recorder was priced at 20 percent above 200 = 240 $ % discount given by store employee = 15 Emlpoyee paid = .85 * 240 = 204 $ Answer A #### A QUESTION:Two numbers are in the ratio 3 : 4. If the sum of numbers is 63, find the numbers. options: A)26,37 B)25,38 C)27,36 D)28,35 E)29,34 SOLUTION:Sum of the terms of the ratio = 3 + 4 = 7 Sum of numbers = 63 Therefore, first number = 3/7 × 63 = 27 Second number = 4/7 × 63 = 36 Therefore, the two numbers are 27 and 36. Answer:C #### C QUESTION:The present ratio of students to teachers at a certain school is 35 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? options: A)5 B)8 C)10 D)12 E)15 SOLUTION:We are given that the ratio of students to teacher is 35 to 1. We can rewrite this using variable multipliers. students : teachers = 35x : x We 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: Students/Teachers  25/1 = (35x + 50)/(x + 5) If we cross multiply we have: 25(x + 5) = 35x + 50 25x + 125 = 35x + 50 7.5 = x x~8 Since x is the present number of teachers, currently there are 8 teachers. Answer B. #### B QUESTION:If 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? options: A)2:5 B)1:3 C)5:8 D)6:1 E)7:2 SOLUTION:9M + 2B =8(1M + 1B) 9M + 2B = 8M + 8B 1M = 6B The required ratio of work done by a man and a boy =6:1 Answer:D #### D QUESTION:A boat takes 90 minutes less to travel 36 miles downstream than to travel the same distance upstream. If the speed of the boat in still water is 10 mph, the speed of the stream is: options: A)4 mph B)2.5 mph C)3 mph D)2 mph E)None of these SOLUTION:Explanation : Speed of the boat in still water = 10 mph Let speed of the stream be x mph Then, speed downstream = (10+x) mph speed upstream = (10-x) mph Time taken to travel 36 miles upstream - Time taken to travel 36 miles downstream = 90/60 hours =>36/(10−x) − 36/(10+x) = 3/2 =>12/(10−x) − 12/(10+x) = 1/2 =>24(10 + x) − 24(10 − x) = (10 + x)(10 − x) =>240 + 24x − 240 + 24x = (100−x2) =>48x = 100 − x2 =>x2 + 48x − 100 =0 =>(x+50)(x−2)=0 => x = -50 or 2. Answer : Option D #### D QUESTION:Plane leaves from Chelsea every 35 minutes from West Ham airport. Air hostess told Frank Lampard that the plane had left 25 minutes ago and the next plane for Chelsea will leave at 7:00 p.m. At what time air hostess convey this information to Frank Lampard? options: A)5:35 p.m B)6:50 p.m C)7:35 p.m D)8:35 p.m E)9:35 p.m SOLUTION:Explanation: Time of Frank Lampard last missed plane = 7:00 p.m - 35 min = 6:25 p.m As this information has been given to Frank Lampard 25 minutes after the plane has already left, the air hostess gave the information at 6:25 p.m + 25 min = 6:50 p.m Answer B #### B QUESTION:A 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 63 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? options: A)14 B)45 C)54 D)65 E)81 SOLUTION:Just check the answers and reverse the numbers until you get 63. 81 - 18 = 63 Answer E #### E QUESTION:A 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? options: A)4 B)5 C)6 D)7 E)8 SOLUTION:If n is a perfect square and a perfect cube, then n = a^6 for some integer a. The numbers are 1^6=1, 2^6=64, 3^6= 729, 4^6=4096, 5^6=15,625. The answer is B. #### B QUESTION:If six persons sit in a row, then the probability that three particular persons are always together is? options: A)1/9 B)1/3 C)1/5 D)1/1 E)1/2 SOLUTION:Six 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 #### C QUESTION:man is 36 years older than his son. In two years, his age will be twice the age of his son. The present age of his son is: options: A)14years B)26 years C)17 years D)34 years E)22 years SOLUTION:Let the son's present age be x years. Then, man's present age = (x + 20) years. (x + 36) + 2 = 2(x + 2) x + 38 = 2x + 4 x = 34. answer :D #### D QUESTION:Jane and Ashley take 10 days and 40 days respectively to complete a project when they work on it alone. They thought if they worked on the project together, they would take fewer days to complete it. During the period that they were working together, Jane took an eight day leave from work. This led to Jane's working for four extra days on her own to complete the project. How long did it take to finish the project ? options: A)10.2 Days B)15.2 Days C)16.2 Days D)18 Days E)20 Days SOLUTION:Let us assume that the work is laying 40 bricks. Jane = 4 bricks per day Ashley = 1 brick per day Together = 5 bricks per day Let's say first 8 days Ashley works alone, No of bricks = 8 Last 4 days Jane works alone, No. of bricks = 16 Remaining bricks = 40 - 24= 16 So together, they would take 16/5 = 3.2 Total no. of days = 8 + 4 + 3.2 = 15.2 Answer is B #### B QUESTION:Which is greater than 16 options: A)1.6 B)66 C)6 D)-6 E)6.1 SOLUTION:66 greater than 16. Answer: B #### B QUESTION:If we have 12 people in a meeting, in how many ways they can sit around a table? options: A)11*10! B)9*8! C)8*7! D)7*6! E)6*5! SOLUTION:If there arenpeople sitting around a table, there are(n-1)!possible arrangements: Here, n=12 (n-1)!=11!=11*10! Ans:A #### A QUESTION:The product of the squares of two positive integers is 900. How many pairs of positive integers satisfy this condition? options: A)0 B)1 C)2 D)3 E)4 SOLUTION:Ans: E - 4 pairs (xˆ2)(yˆ2) = 900 [square root both sides] xy = 30 20 = 1x30, 3x10, 6x5, 5x6, 10x3, 30x1, 15x2, 2x15 Cancel the repeats This leaves us with exactly 4 options. Hence, E #### E QUESTION:Ravi can do a piece of work in 30 days while Prakash can do it in 40 days. In how many days will they finish it together? options: A)17 1/7 B)17 1/9 C)17 1/2 D)17 1/7 E)17 1/5 SOLUTION:1/30 + 1/40 = 7/120 120/7 = 17 1/7 days Answer: A #### A QUESTION:Find 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.15of money? options: A)1500 B)2999 C)2772 D)2987 E)2661 SOLUTION:P = 15(100/10)2 => P = 1500.Answer:A #### A QUESTION:How many of the following numbers are divisible by 132 ? 264, 396, 462, 792, 968, 2178, 5184, 6336 options: A)3 B)4 C)5 D)6 E)7 SOLUTION:B 4 By using your calculator you can calculate that the following numbers are divisible by 132 : 264, 396, 792 and 6336. Required number of number = 4. #### B QUESTION:40 is subtracted from 60% of a number, the result is 50. Find the number? options: A)150 B)140 C)130 D)120 E)110 SOLUTION:(60/100) * X – 40 = 50 6X = 900 X = 150 ANSWER:A #### A QUESTION:A 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? options: A)400 B)991 C)881 D)771 E)551 SOLUTION:2000 ---- 50 2000 ---- 40 x ----- 50 x*50 = 2000*40 x=1600 2000 ------- 400 Answer: A #### A QUESTION:A research team that must consists of 3 members is to be formed from a pool of 6 scientists. How many different teams are possible? options: A)17 B)10 C)40 D)26 E)20 SOLUTION:Note that the team must consist of 3 members, not at least 3 members. Hence, all you have to do is 6C3 = 20 Answer (E) #### E QUESTION:A person can swim in still water at 8 km/h. If the speed of water 4 km/h, how many hours will the man take to swim back against the current for 8km? options: A)2 B)4 C)5 D)6 E)7 SOLUTION:M = 8 S = 4 US = 8 - 4 = 4 D = 4 T = 8/4 = 2 Answer:A #### A QUESTION:Cheese, bologna, and peanut butter sandwiches were made for a picnic in a ratio of 5 to 7 to 8. If a total of 140 sandwiches were made, how many bologna sandwiches were made? options: A)15 B)30 C)38 D)42 E)49 SOLUTION:For deciding such task we should calculate all parts 5 + 7 + 8 = 20 parts and we should calculate how many sandwiches holds 1 part: 140 / 20 = 7 sandwiches in one part For bologna we have 7 parts so: 7 * 7 = 49 Answer is E #### E QUESTION:A boat goes 100 km downstream in 10 hours, and 200 Km upstream in 25 hours. The speed of the stream is? options: A)1 B)22 1/7 C)2 D)22 1/2 E)3 SOLUTION:100 --- 10 DS = 10 ? ---- 1 200 ---- 30 US = 8 ? ----- 1 S = (10 - 8)/2 = 1 kmph. Answer:A #### A QUESTION:The average of twelve numbers is 7. The average of first nine numbers is 6 and the average of last two numbers is 10. What is the middle number? options: A)A)9 B)B)10 C)C)12 D)D)7 E)E)13 SOLUTION:The total of twelve numbers = 12X7 = 84 The total of first 9 and last 2 numbers is = 9 X 6+2 X 10 = 74 So, the middle number is (84 - 74 ) = 10 B #### B QUESTION:If Teena is driving at 55 miles per hour and is currently 7.5 miles behind Yoe, who is driving at 40 miles per hour in the same direction then in how many minutes will Teena be 15 miles ahead of Yoe? options: A)15 B)60 C)75 D)90 E)105 SOLUTION:This 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. Teena covers 55 miles in 60 mins. Yoe covers 40 miles in 60 mins So teena gains 15 miles every 60 mins Teena need to cover 7.5 +15 miles. Teena can cover 7.5 miles in 30 mins Teena will cover 15 miles in 60 mins So answer 30+60= 90 mins.D #### D QUESTION:Walking 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? options: A)60% B)50% C)25% D)20% E)10% SOLUTION:{Total} = {finance} + {marketing} - {both} + {neither} 100 = 25 + 55 - {both} + 40 {both} = 20%. Answer: D. #### D QUESTION:The total cost of 100 paper plates and 200 paper cups is $7.50 At the same rates what is the total cost of 20 of the plates and 40 of the cups? options: A)$.90 B)$1.00 C)$1.20 D)$1.50 E)$1.60 SOLUTION:U dont need to go through all this What u have with u is 100 P + 200 C = $7.50 Just divide the equation by 5 and you will get what u are looking for 20P + 40 C = $1.50 Therefore OA is D #### D QUESTION:Two 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? options: A)8 B)10 C)12 D)11 E)15 SOLUTION:Speed = 120/10 = 12 m/sec speed of the second train = 120/5 = 8 m/sec relative speed = 12+8 = 20 m/sec Req time = 120+120/20 = 12 sec ANSWER C #### C QUESTION:If the number 653ab is divisible by 90, then (a + b) = ? options: A)2 B)3 C)4 D)6 E)8 SOLUTION:90 = 10 x 9 Clearly, 653ab is divisible by 10, so b = 0 Now, 653a0 is divisible by 9. So, (6 + 5 + 3 + a + 0) = (14 + a) is divisible by 9. So, a = 4. Hence, (a + b) = (4 + 0) = 4. ANSWER:C #### C QUESTION:You need to climb 10 stairs. At each support, you can walk one stair or you can jump two stairs. In what number alternative ways you'll climb ten stairs? options: A)99 B)79 C)55 D)89 E)66 SOLUTION:D #### D QUESTION:jhon has 10 choclates, jennifer has 5 choclates. Totally how many choclates they have in all? options: A)5 B)10 C)15 D)20 E)14 SOLUTION:10+5=15. Answer is C #### C QUESTION:Sandy bought 65 books for $1480 from one shop and 55 books for $920 from another shop. What is the average price that Sandy paid per book? options: A)$38 B)$18 C)$99 D)$27 E)$20 SOLUTION:average price per book = (1480 + 920) / (65 + 55) = 2400 / 120 = $20 The answer is E. #### E QUESTION:Which of the number is odd one out ? options: A)84129 B)32418 C)47632 D)36119 E)67626 SOLUTION:C 47632 as 32*32 !=476 #### C QUESTION:A tank is filled in 10 hours by three pipes A, B and C. 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? options: A)70 hours B)30 hours C)35 hours D)50 hours E)40 hours SOLUTION:Efficiency of pipes A,B,C =1:2:4 Therefore, in 10 hours, part of the tank filled by A =17 Therefore, pipe A alone requires 10×7=70 hours to fill the tank. Answer: Option A #### A QUESTION:6x − 12 = 6y 5y + 5x = 10 Which of the following is the number of solutions to the system of equations shown above? options: A)More than three B)Exactly three C)Exactly two D)Exactly one E)None SOLUTION:6x − 12 = 6y => 6x - 6y = 12 => x- y =2 -- 1 5y + 5x = 10 =>x + y = 2 -- 2 From equation 1 and 2 , we get 2x = 4 => x=2 y=0 Therefore , the given system will have Exactly one solution D #### D <<<Examples ends QUESTION:A train 400 m long can cross an electric pole in 20 sec and then find the speed of the train? options: A)72 Kmph B)28 Kmph C)29 Kmph D)65 Kmph E)25 Kmph SOLUTION:Length = Speed * time Speed = L/T S = 400/20 S = 20 M/Sec Speed= 20*18/5 (To convert M/Sec in to Kmph multiply by 18/5) Speed = 72 Kmph Answer:A #### A

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:What approximate value should come in place of question mark (?) in the following equation 287.532 + 1894.029 – 657.48 = 743.095 + ? options: A)870 B)790 C)780 D)770 E)890 SOLUTION:? = 285 + 1895 – 655 – 745 or, ? = 780 Answer C #### C QUESTION:A certain elevator has a safe weight limit of 1950 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 190 pounds and the average weight of the others being 200 pounds? options: A)7 B)8 C)9 D)10 E)11 SOLUTION:Lets assume there are 2X people. Half of them have average weight of 190 and other half has 200. Maximum Weight is = 1950 So 190*X + 200*X = 1950 => 390X = 1950 => X is approximately equal to 5. So total people is 2*5 = 10 Answer D. #### D QUESTION:10 men working 6 hrs per day manufacture 200 shoes in 18 days. How many hours a day must 15 men work to manufacture the same 200 shoes in 12 days? options: A)6 B)10 C)12 D)15 E)18 SOLUTION:Let the required number of hours be x. More men, less hours per day (Indirect proportion) Less days, more working hours per day (Indirect proportion) men 15 : 10 } : : 6 : x days 12 : 18 .'. 15*12*x = 10*18*6 = x = 10*18*6/(15*12) = x = 6 ANSWER : A #### A QUESTION:Jim drove 768 miles of a 1200 miles journey. How many more miles does he need to drive to finish his journey? options: A)432 miles B)651 miles C)387 miles D)954 miles E)556 miles SOLUTION:The number of miles to drive to finish his journey is given by 1200 - 768 = 432 miles correct answer A #### A QUESTION:If a commission of 10% is given on the marked price of a book, the publisher gains 20%. If the commission is increased to 15%, the gain is: options: A)16(2/3)% B)13(1/3)% C)15 (1/6)% D)15% E)None of these SOLUTION:Let C.P.=Rs. 100. First S.P.=Rs. 120 Now, S.P. =Rs. 120, commission=10% Therefore, Marked Price=[(100/90)X120]=Rs. 400/3. No, marked price=400/3, commission=15% Therefore, S.P.=85% of 400/3=[(85/100)X(400/3)]=340/3. Therefore, Gain%=[(340/3)-100]=40/3=13(1/3)%. ANSWER:B #### B QUESTION:What is the probability of flipping a fair coin five times and the coin landing on heads on at least two flips? options: A)5/8 B)7/8 C)11/16 D)13/16 E)27/32 SOLUTION:The number of possible outcomes is 2^5=32. 0 heads: There is 1 way to have all tails. 1 head: There are 5 ways to have one head. P(0 or 1 head)=6/32=3/16 P(at least 2 heads)=1 - 3/16 = 13/16 The answer is D. #### D QUESTION:The ratio of two numbers is 4 : 7 and their H.C.F. is 4. Their L.C.M. is options: A)112 B)22 C)56 D)27 E)35 SOLUTION:Explanation: Let the numbers be 4x and 7x. Then, their H.C.F. = x. So, x = 4. So, the numbers 16 and 28. L.C.M. of 16 and 28 = 112. Answer: Option A #### A QUESTION:In a division sum, the remainder is 6 and the divisor is 5 times the quotient and is obtained by adding 7 to the thrice of the remainder. The dividend is options: A)74 B)78 C)86 D)92 E)106 SOLUTION:Divisor = (6 * 3) + 7 = 25 5 * Quotient = 25 Quotient = 5. Dividend = (Divisor * Quotient) + Remainder Dividend = (20 * 5) + 6 = 106. E) #### E QUESTION:A pineapple costs Rs 7 each and a watermelon costs Rs. 5 each. If I spend Rs 38 on total what is the number of pineapple I purchased? options: A)7 B)6 C)5 D)2 pineapples E)3 SOLUTION:Explanation: The equation for this problem can be made as: 5x + 7y =38 Where x is the number of watermelons and y is the number of pineapples. Now test for 2, 3 and 4: For y = 2 5x + 14 =38 x is not an integer For y = 3 5x = 17 X not an integer For y =4 X = 2 So 4 pineapples and 2 watermelons can be bought by 38 Rs. ANSWER:D #### D QUESTION:The 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? options: A)2^9 B)2^14 C)2^18 D)2^40 E)2^48 SOLUTION:26 letters in the alphabet, 26*2 = 52 letters, since the password is case-sensitive. Accounting for possibilities of the other special characters we have; 26+26+10+1+1 = 64, or 2^6 possibilities per character of the password. Total number of possible combinations: (2^6)^8 = 2^48 ANSWER:E #### E QUESTION:The average of twelve numbers is 7. The average of first nine numbers is 6 and the average of last two numbers is 10. What is the middle number? options: A)A)9 B)B)10 C)C)12 D)D)7 E)E)13 SOLUTION:The total of twelve numbers = 12X7 = 84 The total of first 9 and last 2 numbers is = 9 X 6+2 X 10 = 74 So, the middle number is (84 - 74 ) = 10 B #### B QUESTION:Find the number of different prime factors of 6440 options: A)4 B)2 C)3 D)5 E)6 SOLUTION:Explanation: L.C.M of 6440 = 2 x 2 x 2 x 5 x 7 x 23 2, 5,7,23 Number of different prime factors is 4. Answer: Option A #### A QUESTION:In a garment industry, 12 men working 8 hours per day complete a piece of work in 10 days. To complete the same work in 12 days, working 16 hours a day, the number of men required is: options: A)4 B)5 C)6 D)8 E)9 SOLUTION:Explanation : Let the required number of men be x. Less days, More men (Indirect Proportion) More working hrs per day, Less men (Indirect Proportion) Days 8 : 10 Working Hrs 16: 8 :: 12 : x => 12 x 16 x x = 10 x 8 x 12 => x = 10 x 8 x 12 / (12 x 16) => x = 5 Answer : B #### B QUESTION:A certain club has 10 members, including Tarry. 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 Tarry will be either the member chose to be secretary or the member chose to be treasurer? options: A)1/720 B)1/80 C)1/10 D)1/9 E)1/5 SOLUTION:In 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 Probability to become a secretary = (9/10 * 1/9) = 1/10 Similar concept for treasurer. Probability of not president = 9/10, Probability of not secretary = 8/9, probability of treasurer 1/8 probability to become a treasurer = (9/10 * 8/9 * 1/8) = 1/10 Since, the problem is saying Tarry secretary OR Treasurer it is addition: 1/10 + 1/10 = 1/5=E #### E QUESTION:A took 15 seconds to cross a rectangular field diagonally walking at the rate of 52 m/min and B took the same time to cross the same field along its sides walking at the rate of 68m/min. The area of the field is? options: A)33 B)60 C)88 D)27 E)26 SOLUTION:Explanation: length of the diagonal = 52*(15/60) =13m sum of length and breadth = 68*(15/60) = 17m \inline {\color{Black}\sqrt{l^{2}+b^{2}}=13 \; or\; l+b=17 } area =lb = 1/2[(2lb)] = 1/2[(l+b)² - (l²+b²)] = 1/2[17² -169] =1/2*120 = 60 sq meter Answer: B) 60 #### B QUESTION:Two 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 5 seconds.What is the length of the fast trian? options: A)23 m B)23 2/9 m C)27m D)27 7/9m E)29 7/9m SOLUTION:relative speed=20kmph=50/9m/sec length of the train=50/9*5=250/9=27 7/9m ANSWER:D #### D QUESTION:Find the third proportional to 63 and 29.9? options: A)14.09 B)14.29 C)14.19 D)14.16 E)None of these SOLUTION:Explanation: Formula = Third proportional = (b × b)/a A = 63 and B = 29.9 (29.9 × 29.9)/ 63 = 894.01/63 = 14.19 Answer: Option C #### C QUESTION:If Jenee earns a raise of between 5% and 10%, non-inclusive, by what fraction could her salary have increased? options: A)1/4 B)1/5 C)1/10 D)3/50 E)1/20 SOLUTION:Perhaps it is also easy to just translate the % into fractions: 6%: 6/100 = 3/50 7%: 7/100 8%: 8/100 = 4/50 =2/25 9%: 9/100 Only 3/50 exists in the answer choices, so ANS D #### D QUESTION:What is the rate percent when the simple interest on Rs.800 amount to Rs.160 in 4 Years? options: A)5 B)6 C)7 D)1 E)2 SOLUTION:160 = (180*4*R)/100 R = 5% Answer: A #### A QUESTION:When positive integer A is divided by positive integer B, the result is 9.44. Which of the following could be the integer B is ? options: A)11 B)44 C)24 D)25 E)22 SOLUTION:the remainder will be obtained from the decimal part when A is divided by B i.e. 0.44 0.44 = 44/100 = 11/25 so possible remainders are 11,22,33,44. Only option A-11 satisfies this for remainder 11, A=236 and B=25 Ans - D #### D QUESTION:By selling a bicycle for Rs. 2,850, a shopkeeper gains 14%. If the profit is reduced to 8%, then the selling price will be: options: A)Rs. 2,600 B)Rs. 2,700 C)Rs. 2,800 D)Rs. 3000 E)NOne SOLUTION:Solution: Let Cost Price was X. X + 14% of X = 2850 X + 14X/100 = 2850 X + 0.14X = 2850 1.14X = 2850 X = 2500. So, Cost Price = Rs. 2500. Now, Selling Price When profit remains at 8%, = 2500 + 8% of 2500 = Rs. 2700. Short-Cut CP of bicycle = 100/114*2850 = Rs. 2500; SP for a profit of 8% = 108/100*2500 = Rs. 2700. Answer: Option B #### B QUESTION:The angle between the minute hand and the hour hand of a clock when the time is 4.20, is: options: A)10º B)75º C)90º D)130º E)180º SOLUTION:Angle traced by hour hand in 13/3 hrs = (360/12 x 13/3)º = 130º. Angle traced by min. hand in 20 min. = (360/60 x 20)º = 120º. Required angle = (130 - 120)º = 10º. Answer A #### A QUESTION:A, B and C enter into a partnership. They invest Rs. 70,000, 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? options: A)21 : 32 : 4 B)21 : 26 : 4 C)21: 12 : 1 D)21: 16 : 28 E)none SOLUTION:Sol. A : B : C = (40000 * 36) : (80000 * 12 + 40000 * 24) : (120000 * 24 + 40000 * 12) =252 : 192 : 336 = 21: 16 : 28 Answer D #### D QUESTION:In a division sum, the divisor is ten times the quotient and five times the remainder. If the remainder is 42, the dividend is? options: A)4452 B)4445 C)4330 D)4334 E)4336 SOLUTION:Divisor = (5 * 42) = 210 = 10 * Quotient = Divisor => Quotient = 210/10 = 21 Dividend = (Divisor * Quotient) + Remainder Dividend = (210 * 21) + 42 = 4452 A #### A QUESTION:If 22 lines are drawn in a plane such that no two of them are parallel and no three are concurrent, then in how many points do they intersect? options: A)125 B)187 C)231 D)375 E)460 SOLUTION:If two lines are not parallel, then they will intersect in exactly one point. Lines can be extended infinitely on both ends so somewhere they will intersect with each other if they are not parallel. We are also given that no three lines are concurrent. This means that no three lines intersect at the same point. So every pair of two lines we select will have a unique point of intersection which they will not share with any third line. The number of ways to select 2 lines from 22 lines is 22C2 = 231 The answer is C. #### C QUESTION:What is x if x + 5y = 24 and y = 2? options: A)1 B)3 C)5 D)7 E)14 SOLUTION:Substitute y by 2 in x + 5y = 24 x + 5(2) = 24 x + 10 = 24 If we substitute x by 14 in x + 10 = 24, we have 14 + 10 = 24. Hence x = 14 correct answer E #### E QUESTION:The true discount on a bill of Rs. 2560 is Rs. 360. What is the banker's discount? options: A)Rs. 432 B)Rs. 422 C)Rs. 419 D)Rs. 442 E)None of these SOLUTION:Explanation : F = Rs. 2560 TD = Rs. 360 PW = F - TD = 2560 - 360 = Rs. 2200 True Discount is the Simple Interest on the present value for unexpired time =>Simple Interest on Rs. 2200 for unexpired time = Rs. 360 Banker's Discount is the Simple Interest on the face value of the bill for unexpired time = Simple Interest on Rs. 2160 for unexpired time =360/2200 × 2560 = 0.16 × 2560 = Rs. 419 Answer : Option C #### C QUESTION:The population of a town is 7500. It decreases annually at the rate of 10% p.a. What was its population 2 years ago? options: A)9300 B)8000 C)8500 D)9500 E)10000 SOLUTION:Formula : ( After =100 denominator Ago = 100 numerator) 7500 × 100/90 × 100/90 = 9259 A) #### A QUESTION:One card is drawn from a pack of 52 cards. What is the probability that the card drawn is not a face card? options: A)4/15 B)5/17 C)9/13 D)3/13 E)7/15 SOLUTION:Out of 52 cards there will be 16 face cards are there. probability of getting not a face card = 36/52 = 9/13 Answer is C #### C QUESTION:The cash difference between the selling prices of an article at a profit of 4% and 8% is Rs 3. The ratio of two selling prices is options: A)51:52 B)52:54 C)53:54 D)54:55 E)None of these SOLUTION:Explanation: Let the Cost price of article is Rs. x Required ratio = (104% of x) / (108% of x) =104/108 =52/54 = 52:54. Answer: B #### B QUESTION:If 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 options: A)1 B)3 C)5 D)7 E)9 SOLUTION:P ÷ 44 = 432 => P = 432 * 44 = 19008 P / 31 = 19008 / 31 = 613, remainder = 5 C #### C QUESTION:The average weight of 8 person’s 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? options: A)76 kg B)76.5 kg C)85 kg D)Data inadequate E)None of these SOLUTION:EXPLANATION Total weight increased = (8 x 2.5) kg = 20 kg. Weight of new person = (65 + 20) kg = 85 kg. Answer C #### C QUESTION:A number when divided by 779 gives a remainder 47. By dividing the same number by 19, what would be the remainder? options: A)9 B)8 C)7 D)6 E)5 SOLUTION:Number = ( 779 x a) + 47, where "a" is the quotient = (19 x 41 x a) + (19 x 2) + 9 = 19 x (41a + 2) + 9 = 19 x (New quotient) + 9 \inline \fn_jvn \therefore Required remainder = 9 Answer:A #### A QUESTION:A card is randomly drawn from a deck of 52 cards. What is the probability getting either a King or a Diamond? options: A)5/43 B)8/32 C)6/26 D)4/13 E)2/31 SOLUTION:Total number of cards = 52 Total Number of King Cards = 4 P(King) = 4/52 P(Diamond) = 13/52 P(King and Diamond) = 1/52 P(King or a Diamond) = P(King) + P(Diamond) – P(King and Diamond) =4/52+13/52–1/52=16/52=4/13 Answer D #### D QUESTION:Due to 10% decrease in the price of sugar and John can buy 5kg more sugar in Rs100 , then find the CP of sugar? options: A)Rs. 1(2/9) B)Rs. 2(2/9) C)Rs. 2(1/9) D)Rs. 4(2/9) E)Rs. 3(1/9) SOLUTION:Here r = 10 % ,x = 100 and A = 5 kg Actual price of sugar = 10*100/((100-10 )*5) = Rs. 2(2/9) B #### B QUESTION:Pipe 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? options: A)1.5 B)2 C)2.5 D)3 E)3.5 SOLUTION:The part filled by A + B + C in 1 hour = 1/6 + 1/4 + 1/12 = 12/24 = 1/2 All the three pipes together will fill the tank in 2 hours. The answer is B. #### B QUESTION:If n=3*4*p where p is a prime number greater than 3,how many different positive non-prime divisors does n have, excluding 1 and n? options: A)Six B)Seven C)Eight D)Nine E)Ten SOLUTION:n=3∗2^2∗p Number of divisors = 2 * 3 * 2 = 12 The 12 divisors includes 1, n, 3, 2 and p Number of different non prime divisors excluding 1 and n = 12 - 5 = 7 Answer: B #### B QUESTION:Two 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? options: A)10 B)12 C)15 D)20 E)25 SOLUTION:Speed of the first train = 120/10 = 12 m/sec. Speed of the second train = 120/5 = 8 m/sec. Relative speed = 12 + 8 = 20 m/sec. Required time = (120 + 120)/20 = 12 sec. ANSWER:B #### B QUESTION:A board 7ft. 9 inches long is divided into 3 equal parts . What is the length of each part? options: A)2ft. 7 inches B)4ft. 7 inches C)1ft. 7 inches D)3ft. 7 inches E)None of them SOLUTION:Length of board=7ft. 9 inches=(7*12+9)inches=93 inches. Therefore, Length of each part = (93/3) inches = 31 inches = 2ft. 7 inches Answer is A. #### A QUESTION:In how many different ways can the letters of the word ‘ARMOUM’ be arranged? options: A)230 B)250 C)260 D)300 E)360 SOLUTION:ARMOUR = 6 letter whereas R repeated twice 6! 6xSx4x3x2x1 => 360 E #### E QUESTION:12 times a number gives 156. The number is options: A)11 B)12 C)13 D)None E)Cannot be determined SOLUTION:Explanation: Let the number be 'N' 12×N=156⇒N=13 Correct Option: C #### C QUESTION:A factory that employs 1000 assembly line workers pays each of these workers $5 per hour for the first 40 hours worked during a week and 1½ times that rate for hours worked in excess of 40. What was the total payroll for the assembly-line workers for a week in which 30 percent of them worked 25 hours, 50 percent worked 40 hours, and the rest worked 50 hours? options: A) $180,000 B) $185,000 C) $180,000 D) $200,000 E) $192,500 SOLUTION:30% of 1000 = 300 worked for 20 hours Payment @ 5/hr Total Payment = 300*25*5 = 37500 50 % of 1000 = 500 worked for 40 hours Payment @ 5/hr Total payment = 500*40*5 = 100000 Remaining 200 worked for 50 Hours Payment for first 40 Hours @ 5 /hr Payment = 200*40*5 = 40000 Payment for next 10 hr @ 7.5/hr Payment = 200 * 10 * 7.5 = 15000 Total Payment = 37500+100000 + 40000 +15000 = 192500 Hence , answer is E #### E QUESTION:The perimeters of two squares are 80 cm and 64 cm. Find the perimeter of a third square whose area is equal to the difference of the areas of the two squares. options: A)42cm B)44cm C)46cm D)48cm E)49cm SOLUTION:Explanation: Side of first square = (80/4) = 20 cm; Side of second square = (64/4)cm = 16 cm. Area of third square = [(20)2 - (16)2] cm2 = (400 - 256) cm2 = 144 cm2. Side of third square = (144)(1/2) cm = 12 cm. Required perimeter = (12 x 4) cm = 48 cm. Answer: Option D #### D QUESTION:There 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? options: A)2 B)3 C)14 D)16 E)20 SOLUTION:60% of 30 = 18. So, there are 18 red socks and there are 12 blue socks. Check out this possible cases once we have selected TWO socks: case a: 2 red socks, in which case we have a pair of matching socks. DONE! case b: 2 blue socks, in which case we have a pair of matching socks. DONE! case c: 1 red sock and 1 blue sock. No matching socks, so we're not done yet. Since 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. If 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. In both cases, we are guaranteed to have a pair of matching socks. So, selecting 3 socks guarantees that we have a pair of matching socks. ANSWER:B #### B QUESTION:If the price has fallen by 20% what percent of its consumption be: increased so that the expenditure may be the same as before? options: A)A)11% B)B)10% C)1/9 % D)1/11 % E)1/4% SOLUTION:100 – 20 = 80 80------20 100------? => 1/4% ANSWER:E #### E QUESTION:In an animal behavior experiment, 25 tagged white pigeons and 250 tagged gray pigeons were released from a laboratory. Within one week, 88 percent of the white pigeons and 80.5 percent of the gray pigeons had returned to the laboratory. What percent of the total number of pigeons returned to the laboratory? options: A)80.5 B)82 C)81.5 D)85 E)81.25 SOLUTION:Weighted mix method is best here.... Ratio is 1:10 for 88:80.5... So the answer required = 80.5+ (88-80.5)*1/10=80.5+7.5*1/10 80.5+0.75=81.25 E #### E QUESTION:At 12.00 hours, J starts to walk from his house at 6 kmph. At 13.30, P follows him from J's house on his bicycle at 8 kmph. When will J be 3 km behind P? options: A)19.39 B)19.3 C)19.32 D)19.33 E)19.36 SOLUTION:By the time P starts J is 1.5 hr x 6 = 9 km away from his house. J is 3 km behind when P is 3 km ahead of him. ie., P has to cover 12 km. So he takes 12 / (8 - 6) = 6 hrs after 13.30. So the required time is 19.30Hrs Answer:B #### B QUESTION:Jaclyn buys $60 000 worth of debentures in a company. She earns 9.5% p.a. simple interest, paid to her quarterly (that is, every 3 months). If the agreed period of the debenture was 18 months: calculate the amount of interest Jaclyn will earn for each quarter options: A)1187.5 B)1234 C)1289 D)1425 E)None of these SOLUTION:Explanation: I=(p x r x t)/100 = 60000*9.5/100*(18/12)^1/6 = 1425 Answer: D #### D QUESTION:A sum of money lent out at S.I. amounts to a total of $480 after 2 years and to $680 after a further period of 5 years. What was the initial sum of money that was invested? options: A)$360 B)$380 C)$400 D)$420 E)$440 SOLUTION:S.I for 5 years = $680 - $480 = $200 The S.I. is $40/year S.I. for 2 years = $80 Principal = $480 - $80 = $400 The answer is C. #### C QUESTION:What number has a 3:4 ratio to the number 400? options: A)130 B)100 C)200 D)300 E)120 SOLUTION:3:4 = x: 200 4x = 3*400 x=300 ANSWER:D #### D QUESTION:A picnic attracts 200 persons. There are 20 more men than women, and 20 more adults than children. How many men are at this picnic? options: A)240 B)65 C)110 D)130 E)200 SOLUTION:Adult + Children = 200 Let, Children = y then, Adult = y+20 i.e. y+(y+20) = 200 i.e. y = 900 i.e. Adult = 90+20 = 110 Adults include only Men and Women i.e. Men + Women = 110 Let women, W = x then Men, M = x+20 i.e. x+(x+20) = 2x+20 = 110 i.e. x = 45 i.e. Men, M = 45+20 = 65 Answer: Option B #### B QUESTION:In 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? options: A)1 B)40 C)20 D)26 E)30 SOLUTION:Explanation : One bag of husk = 20 cows per day ⇒ 20 × 1 × 20 = 1 × 20 × x For one cow = 20 days Answer : C #### C QUESTION:In a class, the average age of 28 boys is 12 years and the average of 20 girls is 8 years. what is the average age of the whole class? options: A)10.3 Years B)12.3 Years C)12.6 Years D)13 Years E)15 Years SOLUTION:Total age of 48 students (28X 12+20 X 8) = 496 Average = 496/48 = 10.3 Years A #### A QUESTION:A straight pipe 5 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? options: A) 1/6 and 1/4 only B) 1/4 and 1/3 only C) 1/6, 1/4, and 1/3 D) 1/12, 1/6 and 1/4 E) 1/12, 1/6, and 1/3 SOLUTION:Since 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. In 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). Distinct lengths would be: 3=3/12=1/4, 6-4=2=2/12=1/6meters long pieces. Answer: A. #### A QUESTION:How many of the positive factors of 42 , 104 and how many common factors are there in numbers? options: A)4 B)2 C)3 D)5 E)1 SOLUTION:factors of 42 - 1,2,3,6,7,14,21,42 factors of 104 - 1,2,4,8,13,26,52,104 Comparing both, we have two common factors of 40 and 104- 1,2, Answer(B) #### B QUESTION:For 2consecutive yrs, my incomes are in the ratio of 4:7 and expenses in the ratio of 3:5. If my income in the 2nd yr is Rs. 42000 & my expenses in the first yr in Rs.21000, my total savings for the two-year is options: A)Rs. 8000 B)Rs. 9000 C)Rs. 9900 D)Rs. 98900 E)Rs. 10000 SOLUTION:Sol. Income in first year = * x 42000 = Rs. 24000 Expenses in second year = \ x 21000 = Rs. 35000 Total savings = Total income - Total expenses = (42000 + 24000)- (21000 + 35000) = 66000 - S6000 = Rs. 10000 E #### E QUESTION:How 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? options: A)24 sec B)30 sec C)27 sec D)28 sec E)29 sec SOLUTION:Speed of train relative to man = 63 - 3 = 60 km/hr. = 60 * 5/18 = 50/3 m/sec. Time taken to pass the man = 400 * 3/50 = 24 sec. Answer:A #### A QUESTION:A 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? options: A)40 B)50 C)60 D)70 E)80 SOLUTION:Speed of the train relative to man = 125/10 = 25/2 m/sec. = 25/2 * 18/5 = 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. Answer: Option B #### B QUESTION:The 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? options: A)6 B)7 C)8 D)9 E)10 SOLUTION:To get 45 points as end of season we need another 35 points or more from remaining 15 matches: Option A= 6*3+9*1=27 Option B=7*3 + 8*1=29 Option C=8*3+7*1=31 Option D=9*3+6*1=33 Option E=10*3+5*1=35 hence option E-10 #### E QUESTION:A 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 1997. She ended on her options: A)a) thumb B)b) the index finger C)c) the middle finger D)d) the ring finger E)e) the little finger SOLUTION:Notice the pattern. The thumb lansd up at numbers 1,9,17,25,33,... so every 8th number By this patter the thumb is also at number 1993 (multiple of 8 + 1) Hence 1997 has to be the ring finger Answer is (D) #### D QUESTION:Three number are in the ratio of 3 : 4 : 5 and their L.C.M. is 600. What is their H.C.F.? options: A)10 B)20 C)30 D)40 E)50 SOLUTION:Let the numbers be 3x, 4x and 5x. Then, their L.C.M. = 60x 60x = 600 x = 10 The numbers are (3 x 10), (4 x 10) and (5 x 10). The H.C.F. is 10. The answer is A. #### A QUESTION:On Sunday morning, Pugsley and Wednesday are trading pet spiders. If Pugsley were to give Wednesday four of his spiders, Wednesday would then have four times as many spiders as Pugsley does. But, if Wednesday were to give Pugsley five of her spiders, Pugsley would now have five fewer spiders than Wednesday had before they traded. How many pet spiders does Pugsley have before the trading game commences? options: A)6 B)7 C)8 D)10 E)12 SOLUTION:If Pugsley were to give Wednesday four of his spiders, Wednesday would then have five times as many spiders as Pugsley does: (w + 4) = 4(p - 4) If Wednesday were to give Pugsley five of her spiders, Pugsley would now have five fewer spiders than Wednesday had before they traded: p + 5 = w - 5 Solving gives p = 10 and w = 20. Answer: D. #### D QUESTION:A train overtakes two persons walking along a railway track. The first person walks at 4.5 km/hr and the other walks at 5.4 km/hr. The train needs 8.4 and 8.5 seconds respectively to overtake them. What is the speed of the train if both the persons are walking in the same direction as the train? options: A)80 km/hr B)81 km/hr C)85 km/hr D)84 km/hr E)83 km/hr SOLUTION:Let x is the length of the train in meter and y is its speed in kmph x/8.4 = (y-4.5)(10/36) ---(1) x/8.5 = (y-5.4)(10/36) ---(2) Dividing 1 by 2 8.5/8.4 = (y-4.5)/ (y-5.4) => 8.4y - 8.4 × 4.5 = 8.5y - 8.5×5.4 .1y = 8.5×5.4 - 8.4×4.5 => .1y = 45.9-37.8 = 8.1 => y = 81 km/hr Answer is B. #### B QUESTION:Solution 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 65 percent carbonated water, what percent of the volume of the mixture is P? options: A)20% B)40% C)50% D)60% E)80% SOLUTION:65% is 15%-points below 80% and 10%-points above 55%. So the ratio of solution P to solution Q is 2:3. Mixture P is 2/5 = 40% of the volume of mixture PQ. The answer is B. #### B <<<Examples ends QUESTION:The average age of three boys is 40 years and their ages are in proportion 6:10:8. What is the age in years of the youngest boy? options: A)8 B)10 C)7 D)6 E)5 SOLUTION:6x + 10x + 8x = 40 x =1.6 6x = 10 Answer:B #### B

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:Of 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 ? options: A)200 B)160 C)112 D)80 E)600 SOLUTION:The # oflong-termemployees is 90%*800=720. After y of them retire new # oflong-termemployees would become 720-y. Total # of employees would become 800-y. We want 720-y to be 60% of 800-y --> 720-y=(800 -y)*60% --> y = 600. Answer: E. #### E QUESTION:If a number is formed by writing integers 1 to 150 one after another, like 12345...150. How many W digits does this integer consists of? options: A)150 B)339 C)342 D)359 E)362 SOLUTION:Number of single digit integers = 9 Number of 2 digit integers = 99 - 10 + 1 = 90 Number of 3 digit integers = 150 - 100 + 1 = 51 Number of digits in the integer W= 1*9 + 2*90 + 3*51 = 9 + 180 + 153 = 342 Answer: C #### C QUESTION:The length of the longest tape in cm which can be used to measure exactly, the length 100cm; 2m25cm; and 7m80cm is: options: A)30 B)5 C)10 D)36 E)25 SOLUTION:The three lengths in cm are 100, 225 &780. HCF of 100, 225 &780 is 5. Hence, the answer is 5 cm. ANSWER:B #### B QUESTION:Due to construction, the speed limit along an 9-mile section of highway is reduced from 45 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 ? options: A)A) 5.61 B)B) 3.42 C)C) 10 D)D) 15 E)E) 24 SOLUTION:Old time in minutes to cross 9 miles stretch = 9*60/45 = 9*4/3 = 12 New time in minutes to cross 9 miles stretch = 9*60/35 = 9*12/7 = 15.42 Time difference = 3.42 Ans:B #### B QUESTION:Of the 11 temporary employees in a certain company, 4 will be hired as permanent employees. If 5 of the 11 temporary employees are women, how many of the possible groups of 4 employees consist of 3 women and one man? options: A)22 B)35 C)60 D)70 E)105 SOLUTION:another approach : one scenario : [WWWM] now we have 5 ways for the first women , 4 ways for the 2nd women and , 3 ways for the third women. and 6 ways to select one man so 5*4*3*6 = 360 now the three women are same so combinations with win them are irrelevant the 3 women can we arranged in 3! ways hence 360/3!= 360/6= 60 C #### C QUESTION:What is the sum of all the multiples of 10 between 0 and 75? options: A)500 B)620 C)450 D)340 E)280 SOLUTION:The multiples of 10 between 0 and 99 are 10, 20, 30, 40, 50, 60, 70. If these are all added together, the result is 280. Final Answer: E #### E QUESTION:What annual payment will discharge a debt of Rs. 1030 due in 2 years at the rate of 5% compound interest? options: A)553.94 B)551.25 C)534.33 D)543.33 E)646.33 SOLUTION:Explanation: Let each installment be Rs. x. Then, x/(1 + 5/100) + x/(1 + 5/100)2 = 1030 820x + 1030 * 441 x = 553.94 So, value of each installment = Rs. 553.94 Answer: Option A #### A QUESTION:Carol is four times Alice’s age but only twice as old as Betty. Alice is thirty-six years younger than Carol. How old is Betty? options: A)36 B)39 C)42 D)48 E)24 SOLUTION:Beyond the obvious Algebra approach to this question, it can also be solved by TESTing THE ANSWERS. We're told 3 facts about the relative ages of 3 people: 1) Carol's age is 4 times Alice's age 2) Carol's age is 2 times Betty's age 3) Carol is 36 years older than Alice We're asked for BETTY'S age. Since Carol is TWICE Betty's age, Betty is clearly younger than Carol, so we'll TEST smaller answer first. IF.... Betty = 24 Then Carol = 2(24) = 48 Then Alice = 48 - 36 = 12 AND 48/4 =12 All of these values mesh perfectly with the facts and with one another, so Betty MUST be 24 E #### E QUESTION:Seats for Maths, Physics and Biology are in the ratio of 4 : 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? options: A)2 : 3 : 4 B)6 : 7 : 8 C)8 : 15 : 20 D)Cannot be determined E)None of these SOLUTION:Reqd ratio 4 × 140⁄100 : 7 × 150⁄100 : 8 × 175⁄100 = 4 × 140 : 7 × 150 : 8 × 175 = 8 : 15 : 20 Answer C #### C QUESTION:There are 6 red shoes, 4 green shoes. If one draw randomly a shoe what is the probability of getting a red shoe options: A)1/9 B)2/9 C)3/5 D)4/9 E)2/3 SOLUTION:total 10 from take one. 10c1=10 red 6 from one 6c1=6 6/10= 3/5 ANSWER:C #### C QUESTION:walking at ¾ of his usual speed ,a man is late by 2 ½ hr. the usual time is. options: A)7 B)8 ½ C)7 ½ D)7 ¾ E)9 ½ SOLUTION:Usual speed = S Usual time = T Distance = D New Speed is ¾ S New time is 4/3 T 4/3 T – T = 5/2 T=15/2 = 7 ½ Answer is C. #### C QUESTION:If 2x = 3y = 10, then 9xy = ? options: A) 1,200 B) 200 C) 150 D) 40 E) 20 SOLUTION:2x = 10;x=5 3y = 10;y=10/3 Multiply: 9xy=9*5*10/3=150 Answer: C. #### C QUESTION:A 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? options: A)300 B)320 C)350 D)345 E)568 SOLUTION:Speed = [300 / 18] m/sec = 50/3 m/sec. Let the length of the platform be x meters. Then, x + 300 / 39 = 50/3 3(x + 300) = 1950 è x = 350 Answer: Option C #### C QUESTION:In how many ways can six members be selected from a group of ten members? options: A)10C6 B)10C8 C)10C4 D)10C3 E)10C1 SOLUTION:Six members can be selected from ten members in 10C6 = 10C4 ways. Answer: B #### B QUESTION:A man can place 6 large boxes or 9 boxes inside a carton. Can you calculate in how many cartons can he place 66 boxes ? options: A)9 B)10 C)11 D)12 E)13 SOLUTION:A 5 cartons for large boxes = 5 * 6 = 30 boxes 4 cartons for small boxes = 4 * 9 = 36 boxes He will need 9 cartons to place 66 boxes. #### A QUESTION:There are three departments having students 64,58,24 .In an exam they have to be seated in rooms such that each room has equal number of students and each room has students of one type only (No mixing of departments). Find the minimum number of rooms required? options: A)73 B)74 C)75 D)76 E)77 SOLUTION:WE NEED TO TAKE GCD WHICH IS 2 THUS ALL THE ROOMS WILL HAVE 2 STUDENTS OF THE SAME DEPT 1) 64/2 = 32 2) 58/2 = 29 3) 24/2 = 12 TOTAL NO. OF MIN ROOMS REQD = 32+12+29 = 73 ANSWER:A #### A QUESTION:1397 x 1397 = ? options: A)1951609 B)1951601 C)1951602 D)1951603 E)1951604 SOLUTION:1397 x 1397 = (1397)2 = (1400 - 3)2 = (1400)2 + (3)2 - (2 x 1400 x 3) = 1960000 + 9 - 8400 = 1960009 - 8400 = 1951609. Answer:A #### A QUESTION:Four 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? options: A)120 B)80 C)48 D)192 E)40 SOLUTION:Four 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. But we are told that one of these individual works is 15hrs. hence, possible scenarios, if (1)2x =15 => 16x = 120 (2) 3x =15 => 16x = 80 (3) 5x =15 => 16x = 48 (4) 6x =15 => 16x = 40 Hence Answer is D 192 which can not be any of these. #### D QUESTION:The smallest 2 digit prime number is? options: A)A)11 B)B)13 C)C)19 D)D)113 E)E)None SOLUTION:The smallest 3-digit number is 10, which is divisible by 2. 10 is not a prime number. 11 is a prime number. Hence 11 is the smallest 2-digit prime number. A) #### A QUESTION:Anand and Deepak started a business investing Rs. 1000 and Rs. 5000 respectively. Out of a total profit of Rs. 2000, Deepak's share is: options: A)3776 B)1284.2 C)8400 D)1666.6 E)1671.8 SOLUTION:Ratio of their shares = 1000: 5000= 1:5 Deepak's share = 2000 * 5/6 = Rs. 1666.6. Answer: D #### D QUESTION:If x is an even integer and y = 5x + 1, which of the following CANNOT be a divisor of y? options: A)11 B)31 C)21 D)41 E)30 SOLUTION:x takes even values as 2,4,6,8., y=5x+1 x is an even term so 5x must be an even term when it adds with 1 so it must be a odd integer 30 didn't follows this condition ans is E #### E QUESTION:A guy was asked to specify his age in years. He said, “Take my age 6 years hence, multiply it by six and subtract six of my age 6 years ago and you will know my age.” What was the age of that guy? options: A)18 B)35 C)53 D)69 E)72 SOLUTION:Current age of the guy = A years. Then, 6 (A + 6) – 6 (A – 6) = A (6A + 36) – (6A – 36) = A A = 72 E #### E QUESTION:The 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? options: A)18/35 B)18/18 C)18/19 D)18/17 E)18/12 SOLUTION:If both agree stating the same fact, either both of them speak truth of both speak false. Probability = 3/5 * 4/7 + 2/5 * 3/7 = 12/35 + 6/35 = 18/35 Answer:A #### A QUESTION:What percent of 120 are 90? options: A)33 B)66 C)75 D)44 E)31 SOLUTION:(?% /100) * 120 = 90 ? = 75% Answer: C #### C QUESTION:A 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 options: A)45 min B)60 min C)55 min D)70 min E)80 min SOLUTION:Time = 50/60 hr = 5/6hr Speed = 48mph distance = S*T = 48 * 5/6 = 40km time = 40/60hr = 2/3hr New speed = 40* 3/2 kmph = 60kmph Answer : B. #### B QUESTION:A coin is weighted so that the probability of heads on any flip is 0.1, while the probability of tails is 0.9. If the coin is flipped 5 times independently, which of the following represents the probability that tails will appear no more than twice? options: A)(0.1)^5 + 5(0.1)^4(0.9) + 10(0.1)^3(0.9)^2 B)(0.1)^5 + 4(0.1)^4(0.9) + 6(0.1)^3(0.9)^2 C)(0.6)^5 + 3(0.6)^4(0.4) + 2(0.6)^3(0.4)^2 D)(0.6)^5 + 2(0.6)^4(0.4) + (0.6)^3(0.4)^2 E)(0.6)^5 + (0.6)^4(0.4) + (0.6)^3(0.4)^2 SOLUTION:Probability of Head, P(H) = 0.1 Probability of Tail, P(T) = 0.9 Tail will appear NO more than twice i.e. favourable cases 2 Tails and 3 Heads, Probability = 5C2*(0.1)^3*(0.9)^2 1 Tail and 4 Heads, Probability = 5C1*(0.1)^4*(0.9)^2 0 Tail and 5 Heads, Probability = (0.1)^5 Required Probability = Sum of all Favourable cases = (0.1)^5 + 5(0.1)^4(0.9) + 10(0.1)^3(0.9)^2 Answer: option A #### A QUESTION:What is the sum of all the even numbers between 31 and 99, inclusive? options: A)3,000 B)2,562 C)2,500 D)2,180 E)2,766 SOLUTION:To figure this problem out, you just have to add all the even numbers, starting with 32. 32+34+36+38 and so on, all the way up to 98. You'll get 2,180, so Final Answer: D #### D QUESTION:A store reduced the price of all items in the store by 12% 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? options: A)80.0 B)79.2 C)81.0 D)81.1 E)81.9 SOLUTION:consider price of the all items as $100 after a initial reduction of 12% price becomes = 0.88 *100 = $ 88 after the final reduction of 10% price becomes = 0.9* 88 = $ 79.2 price of all items on second day is 79.2% of price on first day correct answer option B #### B QUESTION:how many prime no. are there from 0 to 50? options: A)14 B)15 C)16 D)17 E)19 SOLUTION:we calculate it manually.we know the definition of prime no.prime no. should only have two distinct​ natural no. divisor 1 and itself. note:1 is not a prime no. 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47 total no.=15 answer B #### B QUESTION:Calculate the circumference of a circular field whose radius is 10 centimeters. options: A)20 π cm B)19 π cm C)28 π cm D)25 π cm E)30 π cm SOLUTION:Circumference C is given by C = 2πr = 2π*10 = 20 π cm Answer: A #### A QUESTION:In a garden, there are 10 rows and 16 columns of mango trees. The distance between the two trees is 2 metres and a distance of one metre is left from all sides of the boundary of the garden. The length of the garden is options: A)32 m B)22 m C)24 m D)26 m E)28 m SOLUTION:Explanation: Each row contains 16 plants. There are 15 gapes between the two corner trees (15 x 2) metres and 1 metre on each side is left. Therefore Length = (30 + 2) m = 32 m. Answer: A #### A QUESTION:From a pack of cards two cards are drawn one after the other, with replacement. The probability that the first card is a spade and the second card is a jack is? options: A)1/50 B)1/13 C)1/26 D)1/52 E)1/4 SOLUTION:Probability of a spade = 13/52 = 1/4 Probability of a jack = 4/52 = 1/13 Probability of both = P1*P2 = 1/(4*13) = 1/52 Answer is D. #### D QUESTION:A square, with perimeter 40, is inscribed in a circle. What is the area of the circle? options: A)50π B)40π C)30π D)25π E)35π SOLUTION:Area of circuscribed circle = pi/2*area of square Area of square = (40/4)^2 = 10^2= 100 Area of circle = pi/2*100=50pi Answer : A #### A QUESTION:There are 5 different letters and 5 letter boxes of same size shape and colors. How many method are possible to post the letters? options: A)50 B)51 C)52 D)53 E)54 SOLUTION:50000 ->1 41000 ->5 31100 ->10 32000 ->10 21110 ->10 22100 ->15 11111 ->1 1+5+10+10+10+30+1=52 ANSWER:C #### C QUESTION:A total of $20,000 was invested in two certificates of deposit at simple annual interest rates of 3 percent and 6 percent, respectively. If the total interest on the two certificates was $1,440 at the end of one year, what fractional part of the $20.000 was invested at the higher rate? options: A) 3/8 B) 21/25 C) 1/2 D) 3/5 E) 3/4 SOLUTION:x * 3/100 * 1 + (20000 - x) * 8/100 * 1 = 1440 3x - 8x = 144000 - 160000 => -5x = -16000 => x = 32000 So 16800/20000 = 21/25 Answer - B #### B QUESTION:A train running at the speed of 60 km/hr crosses a pole in 12 seconds. What is the length of the train? options: A)120 metres B)180 metres C)324 metres D)200 metres E)180 metres SOLUTION:Speed=(60 x 5/18)/m/sec = 50/3 m/sec. Length of the train = (Speed x Time). Length of the train = 50 x 12/3 m = 200 m. ANSWER : OPTION D #### D QUESTION:The average (arithmetic mean) of the 5 positive integers k, m, r, s, and t is 10, and k < m < r < s < t. If t is 20, what is the greatest possible value of the median of the 5 integers? options: A)16 B)18 C)13 D)20 E)22 SOLUTION:We need to find the median which is the third value when the numbers are in increasing order. Since k<m<r<s<t, the median would be r. The average of the positive integers is 10 which means that in effect, all numbers are equal to 10. If the largest number is 20, it is 10 more than 20. We need r to be maximum so k and m should be as small as possible to get the average of 10. Since all the numbers are positive integers, k and m cannot be less than 1 and 2 respectively. 1 is 9 less than 10 and 2 is 8 less than 10 which means k and m combined are 17 less than the average. 20 is already 10 more than 10 and hence we only have 17 - 10 = 7 extra to distribute between r and s. Since s must be greater than r, r can be 10+3 = 13 and s can be 10+4 = 14. So r is 13. Answer (C) #### C QUESTION:If the area of a square with sides of length 6 centimeters is equal to the area of a rectangle with a width of 4 centimeters, what is the length of the rectangle, in centimeters? options: A)4 B)8 C)12 D)9 E)18 SOLUTION:Let length of rectangle = L 6^2 = L*4 => L = 36/4 = 9 Answer D #### D QUESTION:On dividing 144 by a number, the quotient is 13 and the remainder is 1. Find the divisor. options: A)A)11 B)B)14 C)C)16 D)D)18 E)E)22 SOLUTION:d = (D-R)/Q = (144 - 1)/13 = 143/13 = 11 A) #### A QUESTION:Machine P and Machine Q are each used to manufacture 880 sprockets. It takes Machine P 10 hours longer to produce 880 sprockets than Machine Q. Machine Q produces 10% more sprockets per hour than Machine A. How many sprockets per hour does Machine A produce? options: A)2 B)4 C)6 D)8 E)10 SOLUTION:P makes x sprockets per hour. Then Q makes 1.1x sprockets per hour. 880/x = 880/1.1x + 10 1.1(880) = 880 + 11x 11x = 88 x = 8 The answer is D. #### D QUESTION:Tanks A and B are each in the shape of a right circular cylinder. The interior of tank A has a height of 9 meters and a circumference of 8 meters, and the interior of tank B 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 B? options: A)72% B)80% C)100% D)120% E)125% SOLUTION:For A, r=8/2pi. Its capacity = (4pi)^2 * 9= 144pi For B, r=10/pi. Its capacity = (5pi)^2 *8 = 200pi A/B = 144pi/200pi = 0.72 A #### A QUESTION:A desalination process is able to remove 2/3 of salt in each cycle. If we have 1 liter of sea water that has 5% salt (i.e. 5 g in a liter), how much salt would have been removed from the liter of water after 3 cycles of the desalination process? options: A)4.15 B)4.21 C)4.52 D)4.81 E)4.93 SOLUTION:X is the initial quantity of salt in the water. After a cycle of desalination the quantity of salt left would be X1=X-2/3X i.e. X1=1/3X Same thing for X2, X3 respectively representing the quantity of salt left after 2, 3 cycles of desalination. So we have: X1=1/3 X X2=1/3 X1 X3=1/3 X2 By multiplying both ends of the equations we get: X1*X2*X3 = (1/3)^3 X*X1*X2 Simplification leaves us with: X3 = (1/3)^3 X X3 is the quantity of salt left after three cycles. So the cumulative quantity of salt (Q3) which has been removed after 3 cycles is: Q3= X-X3=X-(1/3)^3 X i.e. Q3 = X (1-(1/3)^3) In this case, given X was: X=5 g So we have Q3=5 * (1-1/27) = 5 * 26/27 = 4.814 g rounded Q3=4.81 Answer: D #### D QUESTION:How 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% ? options: A)25 liters B)27 liters C)30 liters D)32 liters E)35 liters SOLUTION:Let x ltr water to be added 2ltr alcohol to be represented as (20(1-3/4(new soln.=15+x))) 2=5%*(15+x)-------->x=25 Ans A #### A QUESTION:If a man buys 10 lollipops for $90 and sold them for $6 dollars determine his loss. options: A)50 B)60 C)70 D)20 E)90 SOLUTION:Cost of 10 lollipops = $80 Sold each lollipop for $6 So he sold 10 lollipops for $(10 × 6) = $60 Loss = $(80 – 60) = $20 answer :D Therefore, loss = $ 20. #### D QUESTION:A man's speed with the current is 20 kmph and speed of the current is 5 kmph. The Man's speed against the current will be options: A)11 kmph B)10 kmph C)14 kmph D)17 kmph E)None of these SOLUTION:Explanation: Speed with current is 20, speed of the man + It is speed of the current Speed in sƟll water = 20 - 5 = 15 Now speed against the current will be speed of the man - speed of the current = 15 - 5 = 10 kmph Answer: B #### B QUESTION:The LCM and HCF of two numbers are 100 and 10 respectively. Find the larger of the two numbers if their sum is 110. options: A)100 B)12 C)35 D)466 E)56 SOLUTION:There are 2 approaches in solving this. Methode 1. HCF * LCM = The Actual Number. 100* 10= 1000 So the answer which we are looking for has to be a factor of 1000. So among the options shortlist the answers by eliminating those numbers which is not divisible by 1000. and then take the highest number as the answer as the question asks abt the highest number. answer is A #### A QUESTION:385, 462, 572, 396, 429, 671, 264 options: A)385 B)429 C)671 D)264 E)None of these SOLUTION:Solution In each number except 429,the middle digit is the sum of the other two. Answer B #### B QUESTION:The compound and the simple interests on a certain sum at the same rate of interest for two years are Rs.11730 and Rs.10200 respectively. Find the sum. options: A)33498 B)17000 C)2665 D)28876 E)313 SOLUTION:The simple interest for the first year is 10200/2 is Rs.5100 and compound interest for first year also is Rs.5100. The compound interest for second year on Rs.5100 for one year So rate of the interest = (100 * 1530)/ (5100 * 1) = 30% p.a. So P = (100 * 10200)/ (30 * 2) = Rs.17000 Answer:B #### B QUESTION:385, 462, 572, 396, 424, 671, 264 options: A)385 B)424 C)671 D)264 E)None of these SOLUTION:Solution In each number except 424,the middle digit is the sum of the other two. Answer B #### B QUESTION:Subtracting 10% from X is the same as multiplying X by what number? options: A)80% B)90% C)10% D)50% E)60% SOLUTION:Explanation: X - (10/100) X = X * ? ? = 90% ANSWER IS B #### B QUESTION:In a college, 1 percent of students hate math, 2 percent of students hate English, 1 percent hate French and 4 percent hate German. Can you find out the percentage of students who hate all 4 subjects ? options: A)8% B)5% C)7% D)12% E)19% SOLUTION:A 8% of student hate all four subjects. #### A QUESTION:A can do a job in 18 days and B can do it in 30 days. A and B working together will finish twice the amount of work in ------- days? options: A)22 1/8 B)22 1/2 C)22 1/1 D)22 1/5 E)22 1/9 SOLUTION:1/18 + 1/30 = 8/90 = 4/45 45/4 = 11 ¼ *2 = 22 1/2 days Answer:B #### B QUESTION:What is the units digit of (3^5)(4^13)? options: A)2 B)4 C)6 D)7 E)8 SOLUTION:-> The ones place of (~3)^n repeats after 4 times like 39713. The ones place of (~4)^n repeats after 2 times like 464. Then, 3^5=3^4*1+13^1., 4^13=4^2*6+1=4^1=~4 which is (3^5)(4^13) (3^1)(~4)=(~3)(~4)=~2. Therefore, the answer is A. #### A QUESTION:If 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)? options: A)35 B)45 C)55 D)65 E)75 SOLUTION:(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) Therefore, the product should have factors with a difference of 2. 35 = 5*7, so this is a possible value for the original expression. The answer is A. #### A QUESTION:The speed of a train is 90 kmph. What is the distance covered by it in 10 minutes? options: A)15 B)66 C)77 D)52 E)42 SOLUTION:90 * 10/60 = 15 kmph Answer:A #### A QUESTION:A 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? options: A)40 B)50 C)60 D)70 E)80 SOLUTION:Speed of the train relative to man = 125/10 = 25/2 m/sec. = 25/2 * 18/5 = 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. Answer: Option B #### B QUESTION:In the graph below, no axes or origin is shown. If point B's coordinates are (10,4), which of the following coordinates would most likely be A's? options: A)(17, -2) B)(10, 6) C)(6, 8) D)(-10, 3) E)(-2, -17) SOLUTION:wherever be the axis as per question y coordinate of point A will be greater than 3 and X coordinate will be lower than 10. B rules.. #### B QUESTION:If the numerator of a fraction W is tripled, and the denominator of a fraction is doubled, the resulting fraction will reflect an increase of what percent? options: A)16 1⁄6% B)25% C)33 1⁄3% D)50% E)66 2⁄3% SOLUTION:This question can be dealt with conceptually or by TESTing VALUES. We're told that the numerator of a fraction W is tripled and the denominator of that same fraction is doubled. We're asked for the resulting increase, in percentage terms, of that fraction. Let's TEST 2/1 If we triple the numerator and double the denominator, we end up with.... (2x3)/(1x2) = 6/2 = 3 Since we're increasing 2 to 3, we're increasing that fraction by (3-2)/2 = 1/2 of itself = 50% D #### D QUESTION:A 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? options: A)9 B)8 C)7 D)6 E)5 SOLUTION:Volume of the wire (in Cylindrical shape) is equal to the volume of the sphere. π(16)2 * h = (4/3)π (12)3 => h = 9 cm Answer:A #### A QUESTION:Six 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 5, what is the probability that one of the two cards drawn is numbered 3 ? options: A)1/3 B)1/2 C)1/4 D)1/5 E)1/6 SOLUTION:(3,2) (2,3) (4,1) (1,4) – only 4 possible scenarios for sum to be 5. One from this 4 has already happened. From this four cases, only in two we have 3. So, the probability is 2 chances out of 4 that the one that occurred had 3: P=2/4.=1/2 Answer: B. #### B QUESTION:If 1 > 1 - ab > 0, which of the following must be true? I. a/b > 0 II. ab < 1 III. a/b < 2 options: A)I only B)II only C)III only D)I and II only E)I and III only SOLUTION:MANHATTAN GMATOFFICIAL SOLUTION: You can manipulate the original compound inequality as follows, making sure to perform each manipulation on every term: 1 > 1 - ab > 0 0 > -a b > -1 Subtract 1 from all three terms. 0 < ab < 1 Multiply all three terms by -1 and flip the inequality signs. Therefore 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. Therefore, the correct answer is (D). #### D QUESTION:A, B and C rents a pasture for Rs.638. 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? options: A)270 B)198 C)676 D)156 E)122 SOLUTION:12*8 :16*9 = 18*6 8: 12: 9 9/29 * 638= 198 Answer: B #### B QUESTION:A 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? options: A)(0.2)^5 + 5(0.2)^4(0.8) + 10(0.2)^3(0.8)^2 B)(0.3)^5 + 4(0.3)^4(0.8) + 6(0.3)^3(0.8)^2 C)(0.3)^5 + 3(0.3)^4(0.8) + 2(0.3)^3(0.8)^2 D)(0.3)^5 + 2(0.3)^4(0.8) + (0.3)^3(0.8)^2 E)(0.6)^5 + (0.6)^4(0.4) + (0.6)^3(0.4)^2 SOLUTION:Probability of Head, P(H) = 0.2 Probability of Tail, P(T) = 0.8 Tail will appear NO more than twice i.e. favourable cases 2 Tails and 3 Heads, Probability = 5C2*(0.2)^3*(0.8)^2 1 Tail and 4 Heads, Probability = 5C1*(0.2)^4*(0.8)^2 0 Tail and 5 Heads, Probability = (0.2)^5 Required Probability = Sum of all Favourable cases = (0.2)^5 + 5(0.2)^4(0.8) + 10(0.2)^3(0.8)^2 Answer: option A #### A QUESTION:P beats Q by 250 meter in a kilometer race. Find Q's speed if P's speed is 16 meter/sec. options: A)21 meter/sec B)7 meter/sec C)12 meter/sec D)18 meter/sec E)28 meter/sec SOLUTION:P's speed = 16m/s P's distance = 1000m (as it is a km race) t = 1000/16 = 62.5 sec Q's distance = 1000-250= 750m Q's time to complete this distance is also 62.5 sec. Q's speed = dist/time = 750/62.5 = 12 m/s Hence C is the answer. #### C <<<Examples ends QUESTION:When positive integer F is divided by positive integer B, the result is 4.35. Which of the following could be the reminder when F is divided by B? options: A) 13 B) 14 C) 15 D) 16 E) 17 SOLUTION:the remainder will be obtained from the decimal part when F is divided by B i.e. 0.35 0.35 = 35/100 = 7/20 so possible remainders are 7,14,21,28. Only option B-14 satisfies this PS: for B-14 F=174 and B=40 #### B

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:Karen places a bet with Tom that she will beat Tom in a car race by 4 miles even if Karen starts 4 minutes late. Assuming that Karen drives at an average speed of 60 mph and Tom drives at an average speed of 45 mph, how many Y miles will Tom drive before Karen wins the bet? options: A)15 B)18 C)21 D)24 E)27 SOLUTION:Let K and T be the speeds of Karen and Tom respectively. t be the time that Karen will travel ----> t+4/60 will be the total time Tom will travel by the time the distance between Karen and Tom is 4 miles. Thus, per the question , K(t) - T(t+4/60) = 4 ---> t = 7/15 hours Thus the distance traveled by Tom when Karen is 4 miles ahead of him Y: T*(t+4/60) = 45 (7/15+4/60) = 24 miles. D is the correct answer. #### D QUESTION:How many factors of 2475 are odd numbers greater than 1? options: A)3 B)4 C)17 D)6 E)7 SOLUTION:prime factors of 330 are 2^1,3^2,5^2 and 11^1 total divisors = (power if a prime factor+1) total no. of odd factors(3,5,11) = (2+1)(2+1)(1+1) =18 since we need odd divisors other than 1 =>18-1 = 17 odd divisors C is the answer #### C QUESTION:What will come in place of the x in the following Number series? 12, 38, 116, 350, 1052, x options: A)2450 B)2560 C)3200 D)3400 E)3158 SOLUTION:12 12 × 3 + 2 = 38 38 × 3 + 2 = 116 116 × 3 + 2 = 350 350 × 3 + 2 = 1052 1052 × 3 + 2 = 3158 E #### E QUESTION:Convert the 11/36 m/s into kilometers per hour? options: A)2.9 kmph B)1.1 kmph C)1.3 kmph D)1.2 kmph E)5.7 kmph SOLUTION:11/36 m/s = 11/36 * 18/5 = 11/10 = 1.1 kmph. Answer: B #### B QUESTION:The 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) options: A)Rs.20043.94 B)Rs.20043.97 C)Rs.20043.96 D)Rs.20043.16 E)Rs.20043.17 SOLUTION:Let the rate of interest be R% p.a. (49500)(3)(R)/100 = 17820 495R = 5940 R = 12 CI on Rs.49500 at 12% p.a. for three years = 49500{[1 + 12/100]3 - 1} = 69543.936 - 49500 = Rs.20043.94 when rounded off to two decimal places. Answer:A #### A QUESTION:In 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, what was the number of valid votes that the other candidate got? options: A)2800 B)2700 C)2100 D)2500 E)3000 SOLUTION:Total no of votes = 7500 20 % invalid =>80% valid tot valid votes = 7500*80/100 =>valid for 2nd candidate got 7500*80/100*45/100 =2700 ANSWER B #### B QUESTION:On dividing 12401 by a certain number, we get 76 as quotient and 13 as remainder. What is the divisor? options: A)163 B)785 C)852 D)456 E)852 SOLUTION:Divisor *quotient+remainder=dividend divisor=(dividend)-(remainder)/quotient (12401-13)/76=163 Answer(A) #### A QUESTION:The distance light travels in one year is approximately 5,870,000,000,000 miles. The distance light travels in 100 years is: options: A)587 × 10<10>(exponent) miles B)587 × 10<-12> (exponent) miles C)587 × 10<-10>(exponent) miles D)587 × 10<12>(exponent) miles E)587 × 10<8>(exponent) miles SOLUTION:The distance of the light travels in 100 years is: 5,870,000,000,000 × 100 miles. = 587,000,000,000,000 miles. = 587 ×10<12>(exponent) miles #### D QUESTION:Bullock likes to keep a spare tyre in his car every time. On a certain day, he travels 1, 00,000 km and just to make the most of all the tyres, he changes the tyres between his journey such that each tyre runs the same distance. What is the distance traveled by each tyre? options: A)75000 B)80000 C)90000 D)67800 E)50000 SOLUTION:B 80,000. The distance traveled by each tyre: 4/5 * 1, 00, 000km = 80,000 km. #### B QUESTION:One day a car rental agency rented 3/4 of its cars, including 4/5 of its cars with CD players. If 3/5 of its cars have CD players, what percent of the cars that were not rented had CD players? options: A)23/40 B)17/30 C)12/25 D)7/15 E)3/10 SOLUTION:The cars with CD players which were not rented is (1/5)(3/5) = 3/25 of all the cars. The cars which were not rented is 1/4 of all the cars. The percent of non-rented cars which had CD players is (3/25) / (1/4) = 12/25 The answer is C. #### C QUESTION:A car covers a distance of 829 km in 7 hours. Find its speed? options: A)104 kmph B)289 kmph C)118 kmph D)277 kmph E)177 kmph SOLUTION:829/7 = 118 kmph Answer: C #### C QUESTION:The banker's gain on a sum due 6 years hence at 12% per annum is Rs. 684. What is the banker's discount? options: A)1240 B)1120 C)1190 D)1634 E)None of these SOLUTION:Explanation : TD = (BG ×100)/TR = (684×100)/(6×12) = Rs. 950 BG = BD – TD => 684= BD - 950 => BD = 684 + 950 = 1634 Answer : Option D #### D QUESTION:The number of defects in the first five cars to come through a new production line are 9, 7, 10, 4, and 8, respectively. If the sixth car through the production line has either 3, 7, or 12 defects, for which of theses values does the mean number of defects per car for the first six cars equal the median? I. 3 II. 7 III. 12 options: A)I only B)II only C)III only D)I and III only E)I, II, and III SOLUTION:C for 7 we will have mean as 7.16(approx) and median as 7 but for 3 we will have mean and median = 6.5 and for 12 we will have median and mean =8 #### C QUESTION:What is the probability of drawing a queen from a deck of 52 cards? options: A)4/13 B)1/13 C)4 D)1 E)2/13 SOLUTION:Total number of cards,n(s)=52 Total number of queen cards,n(e)=4 p(e)=n(e)/n(s)=4/52=1/13 Option B is answer #### B QUESTION:What is the greatest power that 7 can be raised to so that the resulting number is a factor of 21!? options: A)2 B)3 C)4 D)5 E)6 SOLUTION:the number of 7s in 21!= 21/7=3.. ans B #### B QUESTION:Hari and Giri started a business by investing Rs.45000 and Rs.54000 respectively. What is the share of Giri out of annual profit of Rs.13200 ? options: A)6000 B)5400 C)6200 D)7200 E)8200 SOLUTION:Investment Ratio = Profit Sharing Ratio. Ratio of Investments Hari : Giri = Rs.45000 : 54000 => 5 : 6. Giri share = 13200 × 6 / 11 = Rs.7200 Hari share = 13200 × 5 / 11 = Rs.6000 Option A #### A QUESTION:present ages of sameer and anand are in the ratio of 5:4 respectively. three years hence, the ratio of their ages will become 11:9 respectively . what anand's present age in years options: A)27 B)24 C)40 D)32 E)35 SOLUTION:sameer and anand be 5x years and 4x years respectively (5x+3)/(4x+3)=11/9 9(5x+3)= 11(4x+3), 45x+27=44x+33 45x-44x=33-27 x=6, therefore anand's present age : 4x=24 years correct answer(B) #### B QUESTION:Mr. 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 options: A)$145 B)$250 C)$300 D)$175 E)$150 SOLUTION:Let the 1st paycheck be x(integer).Mr. Rodger got a weekly raise of $145. so after completing the 1st week she will get $ (x+145).similarly after completing the 2nd week she will get $(x+145)+$145.=$(x+145+145=$(x+290). so in this way end of every week her salary will increase by $145. correct answer will be (A) #### A QUESTION:A fruit seller had some oranges. He sells 20% oranges and still has 380 oranges. How many oranges he had originally? options: A)475 B)700 C)220 D)400 E)None of these SOLUTION:Explanation : He sells 20% of oranges and still there are 380 oranges remaining => 80% of oranges = 380 ⇒ (80 × Total Oranges)/100 = 380 ⇒ Total Oranges/100 = 4.75 ⇒ Total Oranges = 4.75 × 100 = 475 Answer : Option A #### A QUESTION:In how many ways can 5 different rings be worn in four particular fingers? (Some fingers may get more than one ring and some may get no rings.) Can somebody explain? options: A)6720 B)7720 C)7820 D)7950 E)8120 SOLUTION:First ring can be worn in 4 ways (on any of the four fingers); Second ring can be worn in 5 ways (as it can go on any of four fingers - 4 ways; plus it can go below the first one - 1); Third ring can be worn in 6 ways (the same logic as for the second ring); Fourth ring can be worn in 7 ways; Fifth ring can be worn in 8 ways; Total: 4*5*6*7*8=6720. ANS:A #### A QUESTION:x and y are positive integers of h. If 1/x + 1/y < 2, which of the following must be true? options: A) x + y > 4 B) xy>1 C) x/y + y/x < 1 D) (x - y)^2 > 0 E) None of the above SOLUTION:Answer is B: 1/X + 1/Y < 2 The maximum value of 1/X is 1 because if X equals any other number greater than one it will be a fraction. The same is true with 1/Y. So 1/X and 1/Y will always be less than 2 as long as both X and Y are not both equal to one at the same time. Another way of putting it is: X*Y>1.B #### B QUESTION:How long will a train 100m long travelling at 72kmph take to overtake another train 200m long travelling at 54kmph ? options: A)60 sec B)70 sec C)80 sec D)50 sec E)90 sec SOLUTION:72 kmph=72*5/18 mps=20mps. 54 kmph=54*5/18 mps=15 mps. The train has to travel (200+100)m=300m to overtake the other one. Resultant velocity=(20-15)mps=5 mps time it takes to travel 300m at a velocity of 5 mps is 60 sec.. Ans 60 sec. ANSWER:A #### A QUESTION:x, y, a, and b are positive integers. When x is divided by y, the remainder is 6. When a is divided by b, the remainder is 14. Which of the following is NOT a possible value for y + b? options: A)24 B)21 C)20 D)17 E)15 SOLUTION:Important note: remainder is ALWAYS less than divisor, thus y>6 and b>14 --> y+b>20. Answer: C. #### C QUESTION:A train 360 m long runs with a speed of 45 km/hr. What time will it take to pass a platform of 140 m long? options: A)38 sec B)35 sec C)44 sec D)40 sec E)50 sec SOLUTION:Explanation: Speed = 45 km/hr = 45×(10/36) m/s = 150/12 = 50/4 = 25/2 m/s Total distance = length of the train + length of the platform = 360 + 140 = 500 meter Time taken to cross the platform = 500/(25/2) = 500×2/25 = 40 seconds Answer: Option D #### D QUESTION:If 50 apprentices can finish a job in 4 hours, and 30 journeymen can finish the same job in 7 hours, how much of the job should be completed by 10 apprentices and 15 journeymen in one hour? options: A)17/140 B)29/180 C)26/143 D)1/5 E)39/121 SOLUTION:50 apprentices can finish the job in 4 hours,thus: 10 apprentices can finish the job in 4*5 = 20 hours; In 1 hour 10 apprentices can finish 1/20 of the job. 30 journeymen can finish the same job in 4,5 hours,thus: 15 journeymen can finish the job in 7*2 = 14 hours; In 1 hour 15 journeymen can finish 1/14 of the job. Therefore, in 1 hour 10 apprentices and 15 journeymen can finish 1/20+1/14=17/140 of the job. Answer: A #### A QUESTION:A heap of coconuts is divided into groups of 2, 3 and 5 and each time one coconut is left over. The least number of Coconuts in the heap is? options: A)31 B)41 C)51 D)61 E)65 SOLUTION:LCM = 30 => 30 + 1 = 31 ANSWER:A #### A QUESTION:Which of the following describes all values of x for which 4–x^2 >= 0? options: A) x >= 1 B) x <= –1 C) 0 <= x <= 1 D) x <= –1 or x >= 1 E) –2 <= x <= 2 SOLUTION:4 - x^2 >=0 means x^2 - 4 <=0 => (x-2)(x+2) <= 0 => -2 <= x <= 2 Answer - E #### E QUESTION:A bag contains 50 black balls and 10 white balls. One ball is drawn at random. What is the probability that the ball is white? options: A)1 B)1/6 C)1/3 D)1/2 E)None of these SOLUTION:Explanation: Total cases = 50 + 10 = 60 Favourable cases = 10 So probability = 10/60 = 1/6 Answer: B #### B QUESTION:A train 120 m long running at 72 kmph crosses a platform in 25 sec. What is the length of the platform? options: A)443 m B)354 m C)450 m D)380 m E)250 m SOLUTION:D 350 D = 72 * 5/18 = 25 = 500 – 120 = 380 #### D QUESTION:Suppose x is a positive even number, all of whose digits are either 3 or 4. If x is also divisible by both 3 and 4, how many digits are in the smallest possible value of x? options: A)Three B)Four C)Five D)Six E)Seven SOLUTION:Since the number is positive and even and contains only 3 and 4 as digits, then its numbers digit is 4 and is fixed. As there are not many possibilities for x, I found the most simple method to just start plug in numbers starting from the first and least value of x, which is answer key A. three If x would have 3 digits, then we have 4 possibilities (since 4 is always the number digit for an even number): 334: is divisible by 4 but not by 3 344: is divisible by 4 but not by 3 434: is not divisible by 4 nor by 3 444: is divisible by 4 AND by 3 - then CORRECT ANSWER A #### A QUESTION:How 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? options: A)482 B)226 C)276 D)266 E)181 SOLUTION:Explanation: 20000(11/10)4 - 20000(6/5)2 = 482 Answer: A #### A QUESTION:For each positive integer,the quantitySn is defined such thatSn+2=(Sn)^2 -S(n+2).in addition ,S2=1.then which of the following must be true. options: A)a)S4 +S3 +1=0 B)b)(S1)^2 +S4 +2=0 C)c) ifS1=-1thenS4 is also equal to-1. D)d) ifS4 =-7thenS1=-2. E)e) ifS1 =-3thenS4=-7 SOLUTION:Since all the answers include S4, let's start from there. S4=S2^2-S3 S3=S1^2-S2 Substituting S3 into the first equation we get: S4=S2^2-(S1^2-S2) Since S2=1 S4=1-(S1^2-1) S4=2-S1^2 We need S1^2 in order to calculate S4. E) provides S1 and from there we can calculate S4: S4=2-(-3)^2 S4=-7 Correct. As a side note, I would be very careful with answers in the formif S4=x then S1=y(such as option D ), as we are dealing with S1^2 (not S1), S1 can have two different values and it can not be determined for sure which root is the right answer. For example: If S4=-7 then S1=3 : if we substitute S4 with - 7 we get: -7=2-S1^2 S1^2=9 now S1 can be +/-3 !! E #### E QUESTION:If w<0, which of the following must be true? options: A)–100 < w < 100 B)w ≤ –1 C)w ≤ 1 D)w^2 ≥ 1/4 E)–100 < w < 0 SOLUTION:w is a negative number. A. –100 < w < 100w can be a negative number less than -100 B. w ≤ –1w can be a fraction, in which case it would be greater than -1 C. w ≤ 1must be true since 1 is positive and w is negative D. w^2 ≥ 1/4not true if w is a negative fraction like -1/5 E. –100 < w < 0w can be a negative number less than -100=C #### C QUESTION:By selling 50 meters of cloth. I gain the selling price of 15 meters. Find the gain percent? options: A)72 6/7% B)82 6/7% C)22 6/7% D)42 6/7% E)82 2/7% SOLUTION:Explanation: SP = CP + g 50 SP = 50 CP + 15 SP 35 SP = 50 CP 35 --- 15 CP gain 100 --- ? => 42 6/7% Answer: D #### D QUESTION:The length of a train and that of a platform are equal. If with a speed of 216 k/hr, the train crosses the platform in one minute, then the length of the train (in meters) is? options: A)1752 B)1799 C)1719 D)1750 E)1800 SOLUTION:Speed = [216 * 5/18] m/sec = 60 m/sec; Time = 1 min. = 60 sec. Let the length of the train and that of the platform be x meters. Then, 2x/60 = 60 è x = 60 * 60 / 2 = 1800 Answer: E #### E QUESTION:A jogger jogs at 1/6 of his usual speed. how much % he has to increase speed to reach normal pace of walking options: A)100 B)200 C)300 D)400 E)500 SOLUTION:suppose usual speed is x, then current speed is x/6. to gain normal speed, he has to gain 5x/6 % increase = 100*(5x/6)/(x/6) = 500% ANSWER:E #### E QUESTION:If the two hands in a clock are 11 minutes divisions apart,then the angle between them is options: A)66° B)18° C)24° D)60° E)None of these SOLUTION:In a clock, each minute makes 6° ∴ 11 minutes will make 6 × 11 = 66° Answer A #### A QUESTION:A person walking at 4 Kmph reaches his office 8 minutes late. If he walks at 6 Kmph, he reaches there 8 minutes earlier. How far is the office from his house? options: A)3 1/5 Km B)2 1/5 Km C)4 Km D)4 1/5 Km E)3 3/5 Km SOLUTION:Formula = S1*S2/S2-S1 * T1+T2/60 = 4*6/2 * 16/6 = 24/2 * 16/60 = 8 * 2/5 = 16/5 = 3 1/5 Km A #### A QUESTION:If julie rows 32 km upstream and 72 km down steam taking 4 hours each, then the speed of the stream options: A)1.5kmph B)0.5kmph C)0.4kmph D)1.6kmph E)2.5kmph SOLUTION:Speed upstream = 32/4 = 8 kmph Speed down stream = 72/8 = 9 kmph Speed of stream = ½ (9-8) = 0.5kmph ANSWER:B #### B QUESTION:In a game, one player throws two fair, six-sided die at the same time. If the player receives at least a four or a one on either die, that player wins. What is the probability that a player wins after playing the game once? options: A)1/3 B)4/9 C)5/9 D)2/3 E)3/4 SOLUTION:We're looking for the number of outcomes that include AT LEAST a 1 or a 4. #getting a one in 1st die = {(1,1), (1,2), ...(1,6) }= 6 #getting a one in 2nd die {(2,1), ...(5,1),(6,1) } = 4 [exclude 1,1 and 4,1] since it will be counted twice #getting a three in 1st die {(3,1), (3,2), ...(3,6) }= 6 #getting a three in 1st die {(2,4), (3,4), ...(6,4) } = 4 [exclude 1,4 and 4,4] since it will be counted twice Total possibities = 20 Probability of rolling at least a 1 or a 4 on two dice: 20/36 = 5/9 C #### C QUESTION:How many positive integers r less than 30 have no common prime factor with 30? options: A)5 B)6 C)7 D)8 E)9 SOLUTION:r=30=2*3*5. So, the number must be less than 30 and not have primes 2, 3, or 5. This means that the number could be: 1, 7, 11, 13, 17, 19, 23, or 29. Total of 8 numbers. Answer: D. #### D QUESTION:Computer completes the first iteration in 10 seconds and then the following iterations are completed in 7 seconds as constants are already loaded. What is the maximum number of completed iterations under 5 minutes? options: A)41 B)42 C)43 D)44 E)45 SOLUTION:b must be an integer as it is the number of completed iterations at a rate of 7sec/iteration 10 + 7b =5*60 7b = 290 b= 41 The total number of iterations --> 41+1 = 42 and 43rd iteration will be completed at 304seconds which is above 5 minutes ANSWER: B #### B QUESTION:A 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? options: A)200 B)220 C)240 D)250 E)260 SOLUTION:Speed = [54 * 5/18] m/sec = 15 m/sec. Length of the train = (15 * 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: Option C #### C QUESTION:If the sum of a set of 5 different positive prime numbers is 94, what is the difference between largest and smallest prime numbers between them? options: A)53 B)51 C)47 D)41 E)31 SOLUTION:All prime numbers apart from 2 are odd. Even + Even = Even Odd + Even = Odd Odd + Odd = Even We are given 5 different prime numbers, whose sum is 94 i.e even If we include 2, we will have 4 odd prime numbers and one even. This sum would be odd If we exclude 2, we will have 5 odd numbers. This sum would be even Hence 2 is included. The possible 5 no. are = 11+7+2+43+31 = 94 the difference between largest and smallest prime numbers between them = 43 - 2 = 41 Ans - D #### D QUESTION:Find the principle on a certain sum of money at 5% per annum for 2 2/5 years if the amount being Rs.1120? options: A)1000 B)289 C)209 D)280 E)892 SOLUTION:1120 = P [1 + (5*12/5)/100] P= 1000 Answer: A #### A QUESTION:Machine X takes 10 hours longer than machine Y to produce 1080 Widgets. Machine Y produces 20 percent more widgets in an hour than machine x does in an hour. How many widgets per hour does machine X produce options: A)100 B)65 C)25 D)11 E)18 SOLUTION:Machine Y produces 20 percent more widgets in an hour than machine x does in an hour. So if machine X produces 100 widgets, then machine Y produces 120 widgets. Ratio of 120/100 = 6/5. This is their speed of work (Y:X). i.e. speed of their work (X:Y) = 5/6 Now, time is inversely proportional to speed. Hence the ratio of the time spent (X:Y)= 6/5 Let us assume that they spend 6x and 5x hours. Given that 6x-5x = 10 So, x = 10. Hence 6x = 6*10 = 60 hours. Hence X takes 120 hours to produce 1080 widgets. So, in 1 hour, it can produce (1 * 1080)/60 = 18 Hence option (E). #### E QUESTION:(A% of 2B + B% of A) is equal to ? options: A)A% of B B)B% of A C)3% of AB D)AB% of 3 E)None SOLUTION:Answer A% of 2B + B% of A =2AB/100 + AB/100 = 23AB/100 = 3% of AB Correct Option: C #### C QUESTION:The speed of a boat in still water in 20 km/hr and the rate of current is 6 km/hr. The distance travelled downstream in 12 minutes is: options: A)10.6 B)5.2 C)10.8 D)5.4 E)5.0 SOLUTION:Speed downstream = (20 + 6) = 26 kmph Time = 24 minutes =12/60 hour = 1/5 hour Distance travelled = Time × speed =1/5×26 = 5.20 km Answer is B. #### B QUESTION:What least number should be added to 1056, so that the sum is completely divisible by 23? options: A)4 B)3 C)2 D)1 E)0 SOLUTION:Explanation : 1056 ÷ 23 = 45 with remainder = 21 Remainder = 21. 21 + 2 = 23. Hence 2 should be added to 1056 so that the sum will be divisible by 23. Answer : Option C #### C QUESTION:If Raj shares all of his amount equally among his five friends then each of his friend's amount increased by $10 then Raj had how much? options: A)$10 B)$20 C)$30 D)$40 E)$50 SOLUTION:Five friends amount increased by $10 and Raj shared equally so amount = 5 * 10 = 50 Answer:E #### E QUESTION:If n = 7p, where p is a prime number greater than 2, how many different positiveevendivisors does n have, including n ? options: A) Two B) Three C) Four D) Six E) Eight SOLUTION:This 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: n = 4 x 3 n = 12 Next we have to determine all the factors, or divisors, of P. Remember the term factor is synonymous with the term divisor. 1, 12, 6, 2, 4, 3 From this we see that we have 4 even divisors: 12, 6, 2, and 4. If you are concerned that trying just one value of p might not substantiate the answer, try another value for p. Let’s say p = 5, so n = 4 x 5 n = 20 The 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. No matter what the value of p, as long as it is a prime number greater than 2, n will always have 4 even divisors. The answer is E #### E QUESTION:3+33+333+33.33=? options: A)362.33 B)372.33 C)402.33 D)702 E)None of them SOLUTION:3 33 333 33.33 ---------- 402.33 ---------- Answer is C #### C QUESTION:Five 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 50 years. The age of E is? options: A)50 B)47 C)48 D)49 E)46 SOLUTION:Solution 5 years ago average age of A,B,C,D = 45 years => 5 years ago total age of A, B, C, D = 45 x 4 = 180 years => Total present age of A, B, C, D = 180 + 5x4 = 200 years If E's present age is x years = 200+x/5= 50 x=50 years. Answer A #### A QUESTION:The length of the bridge, which a train 130 meters long and travelling at 45 km/hr can cross in 30 seconds, is? options: A)766 m B)156 m C)245 m D)156 m E)156 m SOLUTION:Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time = 30 sec. Let the length of bridge be x meters. Then, (130 + X)/30 = 25/2 ==> 2(130 + X) = 750 ==> X = 245 m. Answer: C #### C QUESTION:A 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. options: A)2/7 B)3/11 C)4/15 D)5/21 E)6/25 SOLUTION:The total number of ways to sell 6 bottles from 10 is 10C6 = 210. The number of ways to sell 4 bottles of apple juice is 5C4*5C2 = 5*10 = 50 P(selling 4 bottles of apple juice) = 50/210 = 5/21 The answer is D. #### D QUESTION:A certain number of men can finish a piece of work in 10 days. However, if there were 10 less men it will take 10 days more for the work to be finished. How many men were there originally? options: A)10 men B)30 men C)40 men D)20 men E)none of these SOLUTION:Let x be the number of men originally Thus, 10x=(10+10)(x-10) 10x=20(x-10) x=2(x-10) x = 20 ANSWER:D #### D QUESTION:A 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? options: A)76 seconds B)17 seconds C)40 seconds D)16 seconds E)14 seconds SOLUTION:Speed = 45 Km/hr = 45*(5/18) m/sec = 25/2 m/sec Total distance = 360+140 = 500 meter Time = Distance/speed = 500 * (2/25) = 40 seconds Answer:C #### C QUESTION:In 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 8,000 have been vaccinated against both, how many have been vaccinated only against rubella? options: A)2,5000 B)7,500 C)10,000 D)15,000 E)16,000 SOLUTION:Use a single variable as far as possible. Number vaccinated only against mumps = x Number vaccinated against both = 2x = 8000 (so x = 4000) Then, number vaccinated against mumps (including both) = x + 2x = 3x Number vaccinated against rubella = 2*3x = 6x Then, number vaccinated against only rubella = 6x - 2x = 4x = 4*4000 = 16,000 Answer (E) #### E QUESTION:Of 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: options: A)18 B)19 C)20 D)21 E)22 SOLUTION:Explanation: Let first number be x. So,2nd no. = 4x & 3rd no.=8x. So,x+4x+8x=78 × 3 = 234. 13x = 234 x = 234/13 Hence,smallest Number x=18. Answer: A #### A QUESTION:In how much time will a train of length 100 m, moving at 36 kmph cross an electric pole? options: A)16 sec B)18 sec C)19 sec D)10 sec E)17 sec SOLUTION:Convert kmph to mps. 36 kmph = 36 * 5/18 = 10 mps. The distance to be covered is equal to the length of the train. Required time t = d/s = 100/10 = 10 sec. Answer: D #### D QUESTION:597**6 is divisible by both 3 and 11. The non-zero digits in the Hundred’s and ten’s places are respectively: options: A)3 and 6 B)7 and 9 C)2 and 6 D)4 and 7 E)None SOLUTION:Solution : Let the given number be 597xy6. Then (5+9+7+x+y+6)=(27+x+y) must be divisible by 3 And, (6+x+9)-(y+7+5)=(x-y+3) must be either 0 or divisible by 11. x-y+3=0 => y=x+3 27+x+y) =>(27+x+x+3) =>(30+2x) => x = 3 and y = 6. Answer A #### A QUESTION:A number when divided by 779 gives a remainder 47. By dividing the same number by 19, what would be the remainder? options: A)9 B)8 C)7 D)6 E)5 SOLUTION:Number = ( 779 x a) + 47, where "a" is the quotient = (19 x 41 x a) + (19 x 2) + 9 = 19 x (41a + 2) + 9 = 19 x (New quotient) + 9 \inline \fn_jvn \therefore Required remainder = 9 Answer:A #### A QUESTION:What is the remainder when 3^29 is divided by 5? options: A)0 B)1 C)2 D)3 E)4 SOLUTION:The units digit of powers of 3 follow a repeating cycle of four: {3, 9, 7, 1} 29 has the form 4k+1, so the units digit of 3^29 is 3. The remainder when dividing by 5 is 3. The answer is D. #### D QUESTION:A ball is bought for Rs.400 and sold at a gain of 20% find its selling price? options: A)Rs.480/- B)Rs.490/- C)Rs.500/- D)Rs.520/- E)Rs.540/- SOLUTION:100 % ------> 400 (100 * 4 = 400) 120 % ------> 480 (120 * 4 = 480) Selling price = Rs.480/- A #### A <<<Examples ends QUESTION:The 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: options: A)3 months B)4 months C)5 months D)6 months E)7 months SOLUTION:S.I. on Rs. 1600 = T.D. on Rs. 1680. Rs. 1600 is the P.W. of Rs. 1680, i.e., Rs. 80 is on Rs. 1600 at 15%. Time = (100x80)/(1600x15)= 1/3 year = 4 months answer : B #### B

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:David obtained 76, 65, 82, 67 and 85 marks (out in 100) in English, Mathematics, Physics, Chemistry and Biology. What are his average marks? options: A)65 B)69 C)72 D)75 E)None of these SOLUTION:Solution Average = (76+65+82+67+85 / 5) =(375 / 5) = 75. Answer D #### D QUESTION:In 1970 there were 8,902 women stockbrokers in the United States. By 1978 the number had increased to 24,947. Approximately what was the percent increase? options: A) 45% B) 125% C) 145% D) 150% E) 180% SOLUTION:The percent increase is (24947-8902)/8902=16045/8902=1.80 So the approximate answer is E #### E QUESTION:Average temperature of first 4 days of a week is 6°C and that of the last 4 days is 40.3°C. If the average temperature of the week be 39.1°C, the temperature on 4th day is? options: A)36.7°C B)38.6°C C)39.8°C D)41.9°C E)51.9°C SOLUTION:Let temperature on 4th day be X°C Therefore, 4 x 38.6 + 4 x 40.3 - X = 7 x 39.1 => X = 41.9 Therefore, temperature on 4th day = 41.9°C. ANSWER:D #### D QUESTION:An 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? options: A)23777 B)35000 C)29977 D)26777 E)19871 SOLUTION:Let the sum invested at 9% be Rs. x and that invested at 11% be Rs. (100000 - x). Then, (x * 9 * 1)/100 + [(100000 - x) * 11 * 1]/100 = (100000 * 29/3 * 1/100) (9x + 1100000 - 11x)/100 = 29000/3 = 9700 (9x + 1100000 - 11x) = 970000 x = 65000 Sum invested at 9% = Rs. 65000 Sum invested at 11% = Rs. (100000 - 65000) = Rs. 35000. Answer: B #### B QUESTION:The circumferences of two circles are 264 meters and 352 meters. Find the difference between the areas of the larger and the smaller circles? options: A)4329 B)2799 C)4312 D)2799 E)2712 SOLUTION:Let the radii of the smaller and the larger circles be s m and l m respectively. 2∏s = 264 and 2∏l = 352 s = 264/2∏ and l = 352/2∏ Difference between the areas = ∏l2 - ∏s2 = ∏{1762/∏2 - 1322/∏2} = 1762/∏ - 1322/∏ = (176 - 132)(176 + 132)/∏ = (44)(308)/(22/7) = (2)(308)(7) = 4312 sq m Answer: C #### C QUESTION:In 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? options: A)4/M B)4M C)900M D)M/900 E)M/4 SOLUTION:The time it takes to wash 15P pots is 15M minutes which is 15M / 60 = M/4 hours. The answer is E. #### E QUESTION:The successive discounts 20% and 15% are equal to a single discount of? options: A)43% B)72% C)32% D)44% E)29% SOLUTION:C 32% Let the CP of an article be Rs. 100 Given that successive discounts are 20% and 15%. SP = 85% of 80% of 100 = (85/100)(80/100)(100) => SP = Rs. 68 Clearly, single discount is 32%. #### C QUESTION:A boat can move upstream at 25 kmph and downstream at 35 kmph, then the speed of the current is? options: A)5 B)9 C)4 D)1 E)3 SOLUTION:US = 25 DS = 35 M = (35 - 25)/2 = 5 Answer: A #### A QUESTION:A student divided a number by 2/3 when he required to multiply by 3/2. Calculate the percentage of error in his result. options: A)0 B)16 C)18 D)1 E)120 SOLUTION:suppose the no is 100 first condition if it mistakenly divided the no by 2/3 ==>100/(2/3)==>150 second condition the no should multiply by 3/2 ==> 100*3/2 ==> 150 hence output should be 150 and mistakenly the output is 150 so pecentage error is zero ANSWER:A #### A QUESTION:In a LAB experiment, a 100 ml compound of element X and element Y needs to be increased to 150 ml by adding some quantity of element X, and some quantity of element Y. If the original compound contains 30% of element X, how much (in ml) of element Y must be added so that element X will be exactly one third of the resulting mixture ? options: A)40 ml B)100/3 ml C)30 ml D)20/3 ml E)10 ml SOLUTION:There are 0.3*100=30 ml of element X in the initial solution. We need X to be 1/3rd of 150 ml in the resulting solution, so 50 ml. Thus out of 50 ml of solution added, 20 must be X (in order it to become 50 ml) ans the remaining 30 must be Y. Answer: C #### C QUESTION:William earned $3,200 per month as a teacher for the ten months from September to June. Then he took a job as a barista at a local café, where he earned $2,000 per month during July and August. What was his average monthly pay for the 12 months? options: A)$2,400 B)$2,800 C)$2,600 D)$3,000 E)$2,500 SOLUTION:E. William earned $3,200 × 10 = $32,000 as a teacher, and he earned $2,000 × 2 = $4,000 as a barista. So he earned $32,000 + $4,000 = $36,000 over the 12 months. Plug these values into the formula for the mean: mean=sum of values/number of values=>36.000/12=3.000 correct answer D)$3.000 #### D QUESTION:Rs.800 amounts to Rs.920 in 3 years at simple interest. If the interest is increased by 3%, it would amount to how much? options: A)226 B)Rs.992 C)665 D)771 E)211 SOLUTION:(800*3*3)/ 100 = 72 920 + 72 = 992 Answer: B #### B QUESTION:If f(x) = -2x2 + 8x - 4, which of the follwoing is true? options: A)The maximum value of f(x) is -4. B)The graph of f opens upward. C)The graph of f has no x-intercept D)f is not a one to one function. E)The maximum value of f(x) is 4. SOLUTION:f(x) is a quadratic function and its graph is a parabola that may be intercepted by horizontal lines at two points and therefore is not a one to one function. The answer is D correct answer D #### D QUESTION:In a series of six consecutive even numbers, the sum of the third and sixth numbers is 30. What are the third and sixth number respectively? options: A)10,16 B)8,14 C)16,22 D)14,20 E)12, 18 SOLUTION:Let the numbers be x, x + 2, x + 4, x + 6, x + 8 and x + 10. Given (x + 4) + (x + 10) = 30 => 2x + 14 = 30 => x = 8 The third number = x + 4 = 8 + 4 = 12. The sixth number = x + 10 = 8 + 10 = 18. Answer: E #### E QUESTION:The five sides of a pentagon have lengths of 2, 3, 4, 5 and 6 inches. Four 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 ? options: A) 5 B) 12 C) 24 D) 32 E) 120 SOLUTION:CONCEPT: The number of ways to arrange n elements around a circular Manner is (n-1)!. But 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. The 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. Answer: option A #### A QUESTION:How many ways are there for 4 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? options: A)48 B)12 C)72 D)100 E)720 SOLUTION:So 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 4 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 4! different ways, so total 2*4!=48. Answer A. #### A QUESTION:What is the are of an equilateral triangle of side 4 cm? options: A)2√3 B)3√3 C)5√3 D)4√3 E)8√3 SOLUTION:Area of an equilateral triangle = √3/4 S2 If S = 4, Area of triangle = √3/4 * 4 * 4 = 4√3 cm2; Answer:D #### D QUESTION:Look at this series: 14, 28, 20, 40, 32, 64, ... What number should come next? options: A)52 B)56 C)96 D)128 E)None SOLUTION:Explanation: This is an alternating multiplication and subtracting series: First, multiply by 2 and then subtract 8. Answer: Option B #### B QUESTION:A 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? options: A)276 Marks B)200 Marks C)186 Marks D)187 Marks E)167 Marks SOLUTION:30% ------------ 50 45% ------------ 25 ---------------------- 15% ------------- 75 30% -------------- ? 150 + 50 = 200 Marks Answer: B #### B QUESTION:For a finite sequence of non zero numbers, the number of variations in 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 3, -3, 2, 5, -4, -6 ? options: A)1 B)2 C)3 D)4 E)5 SOLUTION:Given sequence: {1, -3, 2, 5, -4, -6} The questions basically asks: how manypairs of consecutive termsare there in the sequence such that the product of these consecutive terms is negative. 1*(-3)=-3=negative; -3*2=-6=negative; 2*5=10=positive; 5*(-4)=-20=negative; (-4)*(-6)=24=positive. So there are 3 pairs of consecutive terms of the sequence for which the product is negative. Answer: A. #### A QUESTION:The difference between a number and its two-fifth is 510. What is 10% of that number ? options: A)33 B)85 C)37 D)27 E)28 SOLUTION:Explanation: Let the number be x. Then, . 10 % 0f 850 = 85. Answer: B) 85 #### B QUESTION:if 8^25 divided by 7 then what is reminder options: A)25 B)1 C)0 D)2 E)3 SOLUTION:8^25/7 8 can be written as 7*1+1 (7*1+1)^25/7 (ax+1)^n/a always gives the remainder 1 here a=7,x=1,n=25 Hence remainder is 1 ANSWER:B #### B QUESTION:What is the value of √36% ? options: A)10% B)20% C)30% D)60% E)40% SOLUTION:Explanation: br>√16% =√36/√100 =6/10 =60/100=60% correct answer is D)60% #### D QUESTION:Difference 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? options: A)2500 m^2 B)2510 m^2 C)2520 m^2 D)2540 m^2 E)2590 m^2 SOLUTION:Solving the two equations, we get: l = 63 and b = 40. Area = (l x b) = (63 x 40) m2 = 2520 m^2 C #### C QUESTION:Karen places a bet with Tom that she will beat Tom in a car race by 4 miles even if Karen starts 4 minutes late. Assuming that Karen drives at an average speed of 60 mph and Tom drives at an average speed of 45 mph, how many Y miles will Tom drive before Karen wins the bet? options: A)15 B)18 C)21 D)24 E)27 SOLUTION:Let K and T be the speeds of Karen and Tom respectively. t be the time that Karen will travel ----> t+4/60 will be the total time Tom will travel by the time the distance between Karen and Tom is 4 miles. Thus, per the question , K(t) - T(t+4/60) = 4 ---> t = 7/15 hours Thus the distance traveled by Tom when Karen is 4 miles ahead of him Y: T*(t+4/60) = 45 (7/15+4/60) = 24 miles. D is the correct answer. #### D QUESTION:The tailor has a 10 meter long piece of fabric for which to sew a ball room dress. She has to cuts this fabric into strips of 200 centimeters each. How long will it take the tailor to complete this tasks if each 200 centimeter took 5 minutes to cut ? options: A)150 B)200 C)188 D)245 E)123 SOLUTION:The tailors would need to cut the fabric 49 times thus the total amount spent would be 245 minutes. The answer is D #### D QUESTION:The velocity of a falling object in a vacuum is directly proportional to the amount of time the object has been falling. If after 5 seconds an object is falling at a speed of 90 miles per hour, how fast will it be falling after 18 seconds? options: A)18 miles per hour B)90 miles per hour C)216 miles per hour D)324 miles per hour E)5400 miles per hour SOLUTION:Since Velocity is proportional to Time Velocity =k*Timewhere k is the constant of proportionality Time= 5 seconds Velocity = 5k = 90 miles per Hour i.e. k = 18 i.e. The relation between Velocity and Time becomes Velocity =18*Time Time= 18 seconds Velocity = 18*18 = 324 miles per hour Answer: Option D #### D QUESTION:A pool which was 1/5 full to begin with, was filled at a constant rate for 6/5 hours until it was until it was 8/9 full. At this rate, how much time would it take to completely fill this pool if it was empty to begin with? options: A)8 hrs 45 mins. B)9 hrs. C)9 hrs 30 mins. D)1 hrs 45 mins. E)15 hrs 30 mins SOLUTION:The pool was 1/5 full initially. In 6/5 hrs, it was filled to 8/9 of its capacity. Therefore, in 6/5 hrs, 8/9 - 1/5 was the amount of volume filled. So, 6/5 hrs = 8/9 - 1/5 = 31/45 Therefore, for filling the vessel from empty to full, you would require 6/5 * 45/31 = 1 Hrs 45 Mins. Hence D #### D QUESTION:In a college, 95 percent of students Passed in math, 97 percent of students Passed in English, 99 percent Passed in French and 92 percent Passed in German. Can you find out the percentage of students who Passed in all 4 subjects ? options: A)92% B)90% C)96% D)83% E)89% SOLUTION:D 83% of student Passed in all four subjects. #### D QUESTION:Every Monday, Marina eats one croissant and every Tuesday she eats two croissants. On each subsequent day of the week, she eats a number of croissants equal to the sum of the croissants eaten on the two previous days, with the exception that if she eats more than four croissants on any particular day, the next day she will eat only one croissant. At the end of the week (which runs from Monday through Sunday), the cycle resets, and Marina goes back to eating one croissant on Monday, two on Tuesday, and so forth. If a particular month begins on a Tuesday, how many croissants will Marina eat on the 24th of that month? options: A)1 B)2 C)3 D)5 E)6 SOLUTION:She eat as follow Mon - 1 Tue - 2 Wed - 3 Thr - 5 Fri - 1(since she had more than 4 previous day) sat - 6 sunday - 1 (since she had more than 4 previous day) so 24th day of month she will have 5. Answer is D #### D QUESTION:All of the stocks on the over-the-counter market are designated by either a 4-letter or a 5-letter code 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? a. b. c. d. e. options: A)2(26^5) B)26(26^4) C)27(26^4) D)26(26^5) E)27(26^5) SOLUTION:no of different stocks for 4-letter code = 26^4 no of different stocks for 4-letter code = 26^5 total = 26^4 + 26^5 = 26^4(26+1) = 27(26^4) ANS:C #### C QUESTION:What is the least integer that is a sum of four different prime numbers each greater than 50? options: A)232 B)234 C)236 D)238 E)240 SOLUTION:The sum of the four smallest primes greater than 53+59+61+67=240. The answer is E. #### E QUESTION:If the diagonal of a rectangle is 17 cm long and its perimeter is 46 cm, find the area of the rectangle. options: A)127 cm^2 B)125 cm^2 C)120 cm^2 D)102 cm^2 E)None of them SOLUTION:Let length = x and breadth = y. Then, 2 (x + y) = 46 or x + y = 23 and x^2 + y^2 = (17)^2 = 289. Now, (x + y)^2 = (23)^2 <=> (x^2 + y^2) + 2xy = 529 <=> 289 + 2xy = 529 =xy=120 Area = xy = 120 cm^2 Answer is C. #### C QUESTION:Pipe A runs 10 liters of water per minute into a tank that has a total volume of 1,200 liters. Pipe B fills an half the tank in 1 hours. Working together how long will it take both pipes to fill the tank ? options: A)2 hours and 36 minutes B)1.5 hours C)9 hours and 12 minutes D)15 hours E)1 hour and 12 minutes. SOLUTION:Pipe A has a rate of 10 liters per minute which equals a rate of 600 liters per hour. Pipe B has a rate of 400 liters per hour. 400 + 600 (A+B) = Together they have a rate of 1000 liters per hour. 1200 (The tank ) / 1000 = 6/5 = 1 hour and 12 minutes Answer -E #### E QUESTION:A trader has 50 kg of pulses, part of which he sells at 8 per cent profit and the rest at 18 per cent profii. He gains 14 per cent on the whole. What is the quantity sold at 18 per cent profit? options: A)30 kg B)25 kg C)20 kg D)40 kg E)none of these SOLUTION:Ratio of quantities sold at 8% profit and 18% profit =>4:6 = 2:3 Therefore,the quantity sold at 18% profit =>50/(2 + 3) x 3 =>30 kg ANSWER:A #### A QUESTION:A set of numbers has the property that for any number t in the set, t + 2 is in the set. If -1 is in the set, which of the following must also be in the set? I. 1 II. -4 III. 5 options: A)I only B)II only C)I and III only D)II and III only E)I, II, and III SOLUTION:The question is which of the following must be in the set, not could be in the set. If -1 is in the set so must be -1+2=1, as 1 is in the set so must be 1+2=3, as 3 is in the set so must be 3+2=5 and so on. So basically knowing that -1 is in the set we can say that ALL odd numbers more than -1 are also in the set. Answer: C. #### C QUESTION:If r and s are positive integers and r-s=6, which of the following has the greatest value J? options: A)2r B)2s C)r +s D)2r-s E)2s-r SOLUTION:You can answer this question by using Number Properties and logic or by TESTing VALUES. We'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. IF.... R = 8 S = 2 Answer A: 2R = 2(8) = 16 Answer B: 2S = 2(2) = 4 Answer C: R+S = 8+2 = 10 Answer D: 2R-S = 2(8) - 2 = 14 Answer E: 2S-R = 2(2) - 8 = -4 Final Answer: A #### A QUESTION:Find the highest common factor of 36 and 84. options: A)4 B)6 C)12 D)18 E)19 SOLUTION:36 = 22 x 32 84 = 22 x 3 x 7 H.C.F. = 22 x 3 = 12. Answer: Option C #### C QUESTION:A man can row upstream at 10kmph and downstream at 18 kmph. The speed of the stream is options: A)2.5 km/hr B)4 km/hr C)5 km/hr D)10.5 km/hr E)None SOLUTION:Sol. Speed of stream = 1/2(18 -10) kmph = 4 kmph. Answer B #### B QUESTION:CONVERT 2.5 hectares in ares options: A)130 ares. B)160 ares. C)180 ares. D)230 ares. E)250 ares. SOLUTION:2.5 hectares in ares 1 hectare = 100 ares Therefore, 2.5 hectares = 2.5 × 100 ares = 250 ares. ANSWER- E #### E QUESTION:How many digits are required to number a book containing 250 pages? options: A)756 B)642 C)492 D)372 E)250 SOLUTION:9 pages from 1 to 9 will require 9 digits. 90 pages from 10 to 99 will require 90*2=180 digits. 250-(90+9)=151 pages will require 151*3=453 digits. The total number of digits is 9+180+453=642. The answer is B. #### B QUESTION:Two 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? options: A)50 B)88 C)77 D)55 E)23 SOLUTION:Let the length of each train be x m. Then, distance covered = 2x m. Relative speed = 46 - 36 = 10 km/hr. = 10 * 5/18 = 25/9 m/sec. 2x/36 = 25/9 => x = 50. Answer: A #### A QUESTION:In a fuel station the service costs $1.65 per car, every liter of fuel costs 0.65$. 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? options: A)320$ B)380$ C)420$ D)448.8$ E)480$ SOLUTION:Total Cost = ( 1.65*12 ) + ( 0.65 * 12 * 55 ) = 19.8 + 429 => 448.8 Hence answer will be (D) #### D QUESTION:3,10,29,66,__ options: A)125 B)165 C)145 D)127 E)112 SOLUTION:3=1*1*1+2 10=2*2*2+2 29=3*3*3+2 66=4*4*4+2 Similarly 5*5*5+2=127 ANSWER:D #### D QUESTION:hat should come in place of question mark (?) in the following equation ? 197 × ? + 16(2) = 2620 options: A)22 B)12 C)14 D)16 E)None of these SOLUTION:? = 2620−256 /197=12 Answer B #### B QUESTION:A car moves at 80 km/hr. What is the speed of the car in meters per second ? options: A)20 2/9m sec B)22 2/9m sec C)24 2/9m sec D)26 2/9m sec E)28 2/9m sec SOLUTION:Explanation: Speed=(80∗5/18)m/sec =200/9m/sec =22 2/9msec Option B #### B QUESTION:A 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 52 years now, the son's age five years back was? options: A)16 years B)14 years C)18 years D)21 years E)15 years SOLUTION:Let the son's present age be x years. Then, (52 - x) = x 2x = 52 => x = 26 Son's age 5 years back = (26 - 5) = 21 years. Answer: D #### D QUESTION:In each term of a sequence, 3 is added to get the next term. If the first term is 6, what is the 64th term? options: A) 192 B) 154 C) 134 D) 174 E) 120 SOLUTION:1rst term + 63 terms = 6 + 3+3+3+3+3+3+3+...+3 (63 times) 6 + (3 x 63) = 3 + 189 = 192 Answer A #### A QUESTION:Divide Rs. 1300 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? options: A)346 B)368 C)375 D)337 E)325 SOLUTION:A+B+C = 1300 A = 1/3(B+C); B = 2/3(A+C) A/(B+C) = 1/3 A = 1/4 * 1300 => 325 Answer:E #### E QUESTION:In how many different ways can the letters of the word ‘ARMOUM’ be arranged? options: A)230 B)250 C)260 D)300 E)360 SOLUTION:ARMOUR = 6 letter whereas R repeated twice 6! 6xSx4x3x2x1 => 360 E #### E QUESTION:Ten cards numbered 1 to 10 are placed in a box and then one card is drawn randomly. If it is known that the number on the drawn card is more than 5, what is the probability that it is an even number? options: A)1/2 B)2/5 C)3/5 D)2/7 E)3/10 SOLUTION:There are 5 numbers higher than 5 and 3 of them are even. The probability is 3/5. The answer is C. #### C QUESTION:Varma can read a book in k minutes. What part of the book can he read in 8 minutes?(k>8) options: A)6/k B)8/k C)83k D)2/k E)1/k SOLUTION:Part of the book he can read in 1 minute = 1/k Part of the book he can read in 8 minutes =8/k. Answer: B #### B QUESTION:A teacher will pick a group of 9 students from a group of 14 students that includes Bart and Lisa. If one of all the possible 9-student groups is picked at random, what is the probability of picking a group that includes both Bart and Lisa? options: A)11/70 B)36/91 C)21/47 D)121/390 E)3/71 SOLUTION:Probability = Favorable Outcomes / Total Outcomes Total Outcomes= Total No. of ways of Picking Group of 9 out of 14 = 14C9 = 14! / (9! * 5!) = 2002 Favorable Outcomes= Total No. of ways of Picking Group of 9 out of 14 such that B and L are always in the group (i.e. we only have to pick remaining two out of remaining 12 as B and L must be there is group) = 12C7 = 792 Hence,Probability=792/2002=36/91 Answer: Option B #### B QUESTION:Ten years ago, a mother was four times older than her daughter. After ten years, the mother will be twice older than daughter. The present age of the daughter is options: A)22 B)21 C)24 D)20 E)19 SOLUTION:Let the mother’s present age be ’x’ Let the daughter’s age be ’y’; 10 years ago; (x - 10) = 4(y - 10) or x - 4y = - 30.. (1) 10 years later; (x + 10) = 2(y + 10) or x - 2y = 10.. (2) Solving (1) & (2) y = 20 ANSWER:D #### D QUESTION:During a recent track meet, Peter ran x meters of the 100 meter dash in 9 seconds; running at the same rate, how many seconds will it take Peter to run z meters of the 200 meter dash? options: A)9/xz B)9zx C)9x/z D)9z/x E)xz/9 SOLUTION:Speed of Peter = x/9 meters per second Time needed to run z meters = DISTANCE/SPEED = z / (x/9) =9z/x Option D The values 100m and 200m have no role to play here and are just given to confuse you. #### D QUESTION:If t= 4p, where p is a prime number greater than 2, how many different positive even divisors does t have, including t ? options: A) Two B) Three C) Four D) Six E) Eight SOLUTION:t=4p since t = 4p thenevendivisors are: 4p/4p= 1 4p/2p= 2 4p/4= p 4p/2= 2p so the answer is (C) #### C QUESTION:Consider 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. 6300 interest only for the period. The principal amount borrowed by her was options: A)Rs. 2000 B)Rs. 17500 C)Rs. 15000 D)Rs. 20000 E)None of these SOLUTION:Explanation : Principal = Rs. (100×6300 / 12×3) => Rs. 17500. Answer : B #### B QUESTION:Two 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 7 days? options: A)2/5 B)7/18 C)1/4 D)1/9 E)2/6 SOLUTION:A's one day's work = 1/30 B's one day's work = 1/45 (A + B)'s one day's work = 1/30 + 1/45 = 1/18 The part of the work completed in 7 days = 7 (1/18) = 7/18. ANSWER B #### B QUESTION:Tom 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 ? options: A)1/2 B)2/5 C)2/3 D)3/7 E)3/11 SOLUTION:Ashwini hits the target definitely, hence required probability that atleast 2 shots hit the target is given by Karan hits tha target and Raja not hit the target. or Karan does not hit the target and Raja hits the target. or. Karan hits the target and Raja hits the target = 2/6 x 3/6 + 4/6 x 3/6 + 2/6 x 3/6 = 24/36 = 2/3 C #### C QUESTION:As part of a promotion designed to attract visitors, an amusement park gives out 24,600 free tickets per year. Usually, the number of tickets given away each month is constant. Due to an employee error, only 10,000 tickets were given out in the first four months of the year. How many tickets should the amusement park give out in the fifth month so that it will begin the sixth month back on its regular giveaway schedule? options: A)205 B)207 C)220 D)225 E)250 SOLUTION:24600/12=2050 2050*5=10250 10250-10000=250 Answer E #### E QUESTION:If a card is randomly drawn from a well shuffled pack of cards, what is the probability of drawing a black card or a king? options: A)6/13 B)7/10 C)4/11 D)7/13 E)5/26 SOLUTION:There are 26 black cards and 2 red kings. P(black card or king) = 28/52 = 7/13 The answer is D. #### D QUESTION:What is the greatest of 3 consecutive integers whose sum is 30 ? options: A)11 B)7 C)8 D)9 E)5 SOLUTION:The sum of three consecutive integers can be written as n + (n + 1) + (n + 2) = 3n + 3 If the sum is 24, we need to solve the equation 3n + 3 = 30; => 3n = 27; => n = 9 The greatest of the three numbers is therefore 9 + 2 = 11 Answer: A #### A QUESTION:Which of the following is closest to (-6/7)^199？ options: A)-1 B)-1/2 C)0 D)1 E)2 SOLUTION:(-6/7)^4 = 1296/2401 which is already close to 1/2. For larger exponents, the expression will get closer and closer to zero. The answer is C. #### C QUESTION:6% of customers that enter a store on any given day must not pay tax. If 1000 people shop every day, how many people pay taxes in the store every week options: A)6500 B)6580 C)7200 D)7120 E)6800 SOLUTION:6% of customers do not pay taxes. 6/100 * 1000 customers do not pay taxes. 6/100 * 1000 = 60 Therefore 1000 - 60 customers do pay taxes. 1000 - 60 = 940 940 * 7 days per week = 6580 B) #### B <<<Examples ends QUESTION:Salesperson 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? options: A)$21,000 B)$18,000 C)$15,000 D)$ 14,500 E)$4,000 SOLUTION:sometime, setting up an equation is an easy way to go with: 350 + 0.06 (x - 1000) = 0.08 x x = 14,500 Ans : D #### D

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:After successive discounts of 20%, 10% and 5% a certain good is sold for Rs. 6400. Find the actual price of the good. options: A)s. 6000 B)s. 9000 C)s. 10800 D)s. 9357 E)s. 9980 SOLUTION:Let actual price was 100. After three successive discount this will become, 100 ==20% discount => 80 ==10% discount => 72 ==5% discount = 68.4 Now Compare, 68.4 = 6400 1 = 6400/68.4 100 = (6400*100)/68.4 = Rs. 9357. Answer: Option D #### D QUESTION:If k is the sum of the digits of integer m, and m=12n, where n is an integer, which of the following must be true? options: A)k is not divisible by 9 B)The sum of the digits of k is divisible by 3 C)m is a multiple of 2k D)k is a multiple of 9 E)k is a multiple of 6 SOLUTION:m= 12n i.e n =1,2,3 ,4 etc or -1,-2.-3 ,-4 then m =12,24,36,48 or -12 ,-24 ,-36 ,-48 then k 3,6 9,12 or -(1+2) , -(4+2) , -(3+6) ,-(4+8) . ans B #### B QUESTION:Can you find next number in tricky mathematical series below? 111 , 113 , 117 , 119 , 123 , 137 ? options: A)151 B)161 C)171 D)131 E)121 SOLUTION:Solution: 151 (131+20) Explanation: 1st 7 prime numbers post 100 are 101 , 103 , 107 , 109 , 113 , 127 , 131 ...Adding 20 to numbers 121 , 123 , 127 , 129 , 133 , 147 , 151 Answer A #### A QUESTION:I. a^2 - 9a + 20 = 0, II. 2b^2 - 5b - 12 = 0 to solve both the equations to find the values of a and b? options: A)If a < b B)If a ≤ b C)If the relationship between a and b cannot be established D)If a > b E)If a ≥ b SOLUTION:I. (a - 5)(a - 4) = 0 => a = 5, 4 II. (2b + 3)(b - 4) = 0 => b = 4, -3/2 => a ≥ b Option E #### E QUESTION:A 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? options: A)200 B)300 C)400 D)500 E)None of them SOLUTION:Let the share of each nephews be Rs.x. Then,share of each daughter=rs4x;share of each son=Rs.5x; So,5*5x+4*4x+2*x=8600 25x+16x+2x=8600 =43x=8600 x=200; Answer is A. #### A QUESTION:in 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? options: A)11101 B)11110 C)10111 D)11011 E)11010 SOLUTION:4+3=7 since base is 7 so it will become 0 giving 1 carry to next digits(so 4+7=0) 3+4 + 1 carry from above step= 1 and 1 carry to next digit 2+5 + 1 carry to next digit= 1 and 1 carry 1+6= 11 so ans=11110 ANSWER:B #### B QUESTION:present ages of sameer and anand are in the ratio of 5:4 respectively. three years hence, the ratio of their ages will become 11:9 respectively . what anand's present age in years options: A)27 B)24 C)40 D)32 E)35 SOLUTION:sameer and anand be 5x years and 4x years respectively (5x+3)/(4x+3)=11/9 9(5x+3)= 11(4x+3), 45x+27=44x+33 45x-44x=33-27 x=6, therefore anand's present age : 4x=24 years correct answer(B) #### B QUESTION:By walking at 3/4th of his usual speed, a man reaches office 16 minutes later than usual. What is his usual time? options: A)48min B)50min C)65min D)60min E)70min SOLUTION:let T be the usual time. time spent=4T/3 therefore, 4T/3=T+16 4T=3T+48...therefor T=48min ANSWER:A #### A QUESTION:Free notebooks were distributed equally among children of a class. The number of notebooks each child got was one-eighth of the number of children. Had the number of children been half, each child would have got 16 notebooks. Total how many notebooks were distributed ? options: A)689 B)569 C)123 D)512 E)456 SOLUTION:Explanation: Let total number of children be x Then, x x1/8X=x/2*16,x=64 Number of notebooks =1/8x^2=(1/8*64*64)=512 Answer:D #### D QUESTION:What is the sum of all 3 digit numbers that leave a remainder of '2' when divided by 6? options: A)82,650 B)64,850 C)64,749 D)49,700 E)56,720 SOLUTION:Find the number , Upon Sum of 3 Digits of a number Gives a Reminder 2 when it is Divided by 6 Seeing the Options After Dividing an Finding the Reminder of 2 My Answer was A #### A QUESTION:A man can swim in still water at 4.5 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is? options: A)1.7 B)1.4 C)1.1 D)1.5 E)1.9 SOLUTION:M = 4.5 S = x DS = 4.5 + x US = 4.5 + x 4.5 + x = (4.5 - x)2 4.5 + x = 9 -2x 3x = 4.5 x = 1.5 Answer:D #### D QUESTION:How many seconds will a 300 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? options: A)11 sec B)18 sec C)77 sec D)14 sec E)12 SOLUTION:Speed of train relative to man = 63 - 3 = 60 km/hr. = 60 * 5/18 = 50/3 m/sec. Time taken to pass the man = 300 * 3/50 = 18 sec. Answer: B #### B QUESTION:The 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: options: A)Rs. 3500 B)Rs. 3750 C)Rs. 3840 D)Rs. 3900 E)None SOLUTION:EXPLANATION Let the cost of a chair and that of a table be Rs. x and Rs. y respectively. Then, 10x = 4y or y = 5b/2 x 15x + 2y = 4000 15x + 2 x 5/2 x= 4000 20x = 4000 x = 200. So, y = 172 = 500. Hence, the cost of 12 chairs and 3 tables = 12x + 3y = Rs. (2400 + 1500) = Rs. 3900. Answer D #### D QUESTION:5.005/4.004 = options: A)1.05 B)1.50015 C)1.501 D)1.5015 E)1.25 SOLUTION:5.005/4.004 = 5005/4004 = 5(1001)/4(1001) = 5/4 = 1.25 The answer is E. #### E QUESTION:The 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 6 minutes, then the area of the park (in sq. m) is: options: A)153601 B)153600 C)86400 D)153603 E)153604 SOLUTION:Perimeter = Distance covered in 6 min. =(12000/60) x 6m = 1200 m. Let length = 3x metres and breadth = 2x metres. Then, 2(3x + 2x) = 1200 or x = 120. Length = 360 m and Breadth = 240 m. Area = (360 x 240) m2 = 86400 m2. Answer: C #### C QUESTION:Shekhar 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’s share in the profit of Rs. 1,50,000 earned at the end of 3 years from the start of the business in 1999?. options: A)Rs. 10000 B)Rs. 20000 C)Rs. 30000 D)Rs. 40000 E)Rs. 50000 SOLUTION:Shekhar : Rajeev : Jatin = (25000 X 12 + 35000 X 12 + 45000 X 12) : (35000 X 24) : (35000 X 12) = 1260000 : 840000 : 420000 = 3 : 2 : 1. Rajeev’s share = Rs.(150000×2/6) = Rs. 50000 Answer E #### E QUESTION:Annika 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 51 minutes. If Annika continues east, then turns around and retraces her path to reach the start of the trail in exactly 51 minutes, for how many kilometers total did she hike east? options: A)3.625 B)3 C)4.5 D)4 E)3.5 SOLUTION:Set up two R x T =D cases. 1. 1/12 km/ min x T = 2.75 from which T= 33 mins. We know total journey time now is 51 +33 =84. The rate is the same ie 1/12km/min. set up second R x T =D case. 1/12 km/min x 84 = 7 km Now the total journey would be halved as distance would be same in each direction. 7/2 =3.5 E. #### E QUESTION:4 dice are thrown simultaneously on the board. Find the probability show the same face. options: A)1/213 B)1/215 C)1/216 D)2/113 E)3/114 SOLUTION:The total number of elementary events associated to the random experiments of throwing four dice simultaneously is: =6×6×6×6=64=6×6×6×6=64 n(S)=64n(S)=64 Let XX be the event that all dice show the same face. 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)}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)} n(X)=6n(X)=6 Hence required probability, =n(X)n(S)=664=n(X)n(S)=664 =1/216 C #### C QUESTION:If a light flashes every 6 seconds, how many times will it flash in 2/5 of an hour? options: A)181 B)211 C)241 D)271 E)301 SOLUTION:In 2/5 of an hour there are 24*60 = 1440 seconds The number of 6-second intervals = 1440/6 = 240 After the first flash, there will be 240 more flashes for a total of 241. The answer is C. #### C QUESTION:What approximate value should come in place of question mark (?) in the following equation? 33 1⁄3% of 768.9 + 25% of 161.2 – 66.12 = ? options: A)230 B)225 C)232 D)220 E)240 SOLUTION:? = 33 1⁄3% of 768.9 + 25% of 161.2 – 66.12 = 1⁄3 of 768.9 + 1⁄4 of 161.2 – 66.12 = 256.3 + 40.3 – 66.12 ≈ 232 Answer C #### C QUESTION:How many 7-letter words can be formed using the letters of the English alphabet that contain 2 different vowels and 5 different consonants? options: A)4!*5c2 *21c2 B)4!*5c3 *21c2 C)5!*5c2 *21c2 D)7!*5c2 *21c5 E)6!*5c2 *21c2 SOLUTION:combination for 2 vowels out of 5 = 5c2 ways combination for 5 consonants of 21 = 21c5 ways Additionally the arrangement can be = 7! total arrangements =7!*5c2 *21c5 D #### D QUESTION:Sum of the local value and the face value of 4 in the numeral 153489216 is options: A)40004 B)4004 C)4000004 D)400004 E)44 SOLUTION:(Local value of 4) + (Face value of 4) = (400000 + 4) = 400004 D #### D QUESTION:Two friends want to buy a snack. They combine their money and find they have $3.80, consisting of quarters, dimes, and nickels. If they have 34 coins and the number of quarters is half the number of nickels, how many quarters do they have? options: A)7 B)8 C)9 D)10 E)11 SOLUTION:Let x be the number of quarters. Then 2x is the number of nickels. (1) 25x + 10x + 10D = 380. Then 7x + 2D = 76 (2) 3x + D = 34. Then 6x + 2D = 68 Let's subtract equation (2) from equation (1). x = 8 The answer is B. #### B QUESTION:How many necklace of 12 beads each can be made from 18 beads of different colours? options: A)18!(6 x 29) B)18!(6 x 21) C)18!(6 x 24) D)18!(6 x 22) E)18!(6 x 44) SOLUTION:Explanation: Here clock-wise and anti-clockwise arrangements are same. Hence total number of circular–permutations: \inline {\color{Black} \frac{18P_{12}}{2\times 12}} = \inline {\color{Black} \frac{18!}{6\times 24}} Answer: C) 18!(6 x 24) #### C QUESTION:Tom purchased 8kg of apples at the rate of 70 per kg and 9 kg of mangoes at the rate of 70 per kg. How much amount did he pay to the shopkeeper? options: A)A)1040 B)B)1045 C)C)1055 D)D)1190 E)E)1075 SOLUTION:Cost of 8 kg apples= 70 × 8 = 560. Cost of 9 kg of mangoes = 70 × 9 = 630. Total cost he has to pay = 560 + 630 = 1190. D) #### D QUESTION:If f(x) = 6x − √x and g(x) = x^2, what is f(g(4))? options: A)-4 B)8 C)16 D)32 E)92 SOLUTION:g(x) = x² g(4) = 4² = 16 So, f(g(4)) = f(16) f(x) = 6x − √x So, f(16) = 6(16) − √16 = 96 - 4 = 92 = E #### E QUESTION:In a race of 1000 meters, A can beat B by 100 meters, in a race of 800 meters, B can beat C by 100 meters. By how many meters will A beat C in a race of 600 meters? options: A)125.5 meters B)126.5 meters C)127.5 meters D)128.5 meters E)None of these SOLUTION:Explanation: When A runs 1000 meters, B runs 900 meters and when B runs 800 meters, C runs 700 meters. Therefore, when B runs 900 meters, the distance that C runs = (900 x 700)/800 = 6300/8 = 787.5 meters. So, in a race of 1000 meters, A beats C by (1000 - 787.5) = 212.5 meters to C. So, in a race of 600 meters, the number of meters by Which A beats C = (600 x 212.5)/1000 = 127.5 meters. Answer: C #### C QUESTION:A right triangle has sides of a, b, and 7, respectively, where a and b are both integers. What is the value of (a + b)? options: A)40 B)42 C)46 D)48 E)49 SOLUTION:LET a= hypotenuse , b =base ,7 = perpendicular . therefore a^2 -b^2 =7^2 or (a+b)(a-b) = 49 a+b =49/a-b ' a-b cannot be zero ..therefore a+ b =49 where a-b is equal to 1 E #### E QUESTION:A man took a loan at rate of 12% per annum simple interest. After 3 years he had to pay 3600 interest. The principal amount borrowed by him was. options: A)Rs 10000 B)Rs 15000 C)Rs 16000 D)Rs 17000 E)None of these SOLUTION:Explanation: S.I.=P∗R∗T/100 =>P=S.I.∗100/R∗T =>P=3600∗100/12∗3=Rs10000 Option A #### A QUESTION:There are 3 teams each with 8 basket players. How many combinations are there if we were to pick 2 players from the 3 teams such that no team was picked twice? options: A)50 B)23 C)192 D)28 E)45 SOLUTION:There are altogether three arrangements, which are we can select two members each from team A and B, each from team A and C, and each from team B and C. For each arrangement, there are altogether 64 possibilities (8*8) since each team has 8 players. So there are a total of 192 possibilities (64*3). I hope this method is easier for you to understand. #### C QUESTION:An even and an odd integer are multiplied together. Which of the following numbers could not be the square of their product? options: A)4 B)16 C)25 D)36 E)100 SOLUTION:25 = 5^2 so it can not be the square of an even number multiplied by an odd number. The answer is C. #### C QUESTION:How many 3-digit even numbers are possible such that if one of the digits is 4, the next/succeeding digit to it should be 7? options: A)305 B)5 C)365 D)405 E)495 SOLUTION:470, 472, 474, 476, and 478, so total 5. Hence Option B. #### B QUESTION:Danny 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 192, what is the area of the side face of the box? options: A)13 B)16 C)18 D)29 E)32 SOLUTION:Lets suppose length= l, breadth= b, depth= d Front face area= l*w = 1/2 w*d (l=1/2 d or d=2l) top face area= w*d side face area= w*d = 1.5 d*l (w=1.5l) Volume = l*w*d= 192 l*1.5l*2l= 192 l=4 Side face area= l*d= l*2l= 4*2*4 =32 E is the answer #### E QUESTION:A, B and C shared the profit in a business in the ratio 5 : 7 : 8. They had partnered for 14 months, 2 months and 7 months respectively. What was the ratio of their investments? options: A)10:12:14 B)12:24:28 C)20:22:12 D)5:49:16 E)None of these SOLUTION:Explanation : Ratio in which A,B and C shared the profit = 5 : 7 : 8 Assume that the ratio of their investment = a:b:c Then 14a : 2b : 7c = 5 : 7 : 8 Good to go, we got the equation. Now it's a matter of time to find a, b and c 14a/2b = 5/7 => 98a = 10b => b = 98a/10 = 49a/5 ---(1) 14a/7c =5/8 => 2a/c =5/8 => 16a = 5c => c = 16a/5 ---(2) a : b : c = a : 49a/5 : 16a/5 = 1 : 49/20 : 16/5 = 5 : 49 : 16. Answer : Option D #### D QUESTION:If square-root of 15 is 3.87. Then find the value of square-root of (5/3) options: A)1.29 B)1.39 C)1.49 D)1.59 E)1.69 SOLUTION:=> root 5/ root 3 = (root 5/ root 3)*(root 3/ root 3) = root 15/ root 9 = 3.87/3 = 1.29 ANSWER:A #### A QUESTION:Two pens and three pencils cost Rs 86. four Pens and a pencil cost Rs. 112. find the cost of a pen and that of a pencil. options: A)12 B)10 C)15 D)19 E)20 SOLUTION:Let the cost of a pen ands a pencil be Rs. X and Rs. Y respectively. Then, 2x + 3y = 86 ….(i) and 4x + y =112. Solving (i) and (ii), we get: x = 25 and y = 12. Cost of a pen =Rs. 25 and the cost of a pencil =Rs. 12. Answer is A. #### A QUESTION:A Card marked 1 and 2 on its two faces. Two colors, white and black are used to paint the two faces of the card. If the card is painted with the different colors, in how many ways can the card be painted? options: A)3 B)6 C)2 D)12 E)27 SOLUTION:If the base of the card is white, then in order the card to be painted with the different colors, the top must be white.Another side can be painted in Black. But we can have the base painted in either of the two colors, thus the total number of ways to paint the card is 2*1=2. Answer: C. #### C QUESTION:If a = -1, what is the value of –(a^2 + a^3 + a^4 + a^5+a^6)? options: A)-14 B)-4 C)-1 D)4 E)14 SOLUTION:if a = -1, then putting values in equation = -[ (-1)^2 + (-1)^3 + (-1^4) + (-1^5)+(-1^6) ] = -[ 1 - 1 + 1 - 1 + 1] = -1 Answer = C = -1 #### C QUESTION:How many positive integers less than 300 can be formed using the numbers 1, 2, 3 and 5 for the digits? options: A) 48 B) 52 C) 66 D) 68 E) 84 SOLUTION:Notice that we can find the number of 2 and 3 digit numbers by just assuming the first digit can also be zero: 0 1 1 1 2 2 2 3 3 2 5 5 Number of possibilities = 3*4*4 = 48. Then, just add up the number of 1 digits numbers = 4, so total is 48+4 = 52. Answer: B #### B QUESTION:What is the smallest positive integer x, such that 1944x is a perfect cube? options: A)4 B)3 C)8 D)12 E)18 SOLUTION:Take out the factors of 1944 that will come 2^3*3^3 *3^2. for perfect cube you need every no. raise to the power 3. for 1944 to be a perfect cube, need 1 3 that means =3 B is the answer. #### B QUESTION:Two brothers Ram and Ravi appeared for an exam. The probability of selection of Ram is 5/7 and that of Ravi is 1/5. Find the probability that both of them are selected. options: A)2/35 B)2/3 C)7/35 D)1/7 E)7/5 SOLUTION:Let A be the event that Ram is selected and B is the event that Ravi is selected. P(A) = 5/7 P(B) = 1/5 Let C be the event that both are selected. P(C) = P(A) x P(B) as A and B are independent events: = 5/7 x 1/5 = 1/7 ANSWER:D #### D QUESTION:If 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 options: A)48 km B)50 km C)40 km D)22 km E)70 km SOLUTION:B 50 km. Let the actual distance travelled be x km. Then x/10=(x+20)/14 --> 14x = 10x + 200 --> 4x = 200 --> x = 50 km. #### B QUESTION:The 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. 28,000 is made? options: A)Rs. 1,10,000 B)Rs. 1,20,000 C)Rs. 1,24,000 D)Rs. 1,21,000 E)None of these SOLUTION:The value of the machine after two years = 0.8 * 0.8 * 1,50,000 = Rs. 96,000 SP such that a profit of Rs. 24,000 is made = 96,000 + 28,000 = Rs. 1,24,000 ANSWER:C #### C QUESTION:Amy has two decks of 54 cards each: Deck 1 and Deck 2. She takes 8 black cards from Deck 2 and adds them to Deck 1 and shuffles it thoroughly. She now picks a card from the newly formed pack of cards. If the probability of either picking a red ace or a king from the newly formed pack is greater than 1/8, what is the probability that Amy picks a black king or a red Jack from the new pack? options: A)1/6 B)1/8 C)1/9 D)1/10 E)1/12 SOLUTION:Your solution is correct answer should be 1/12. E #### E QUESTION:There are 6 identical pens and 9 identical books. In how many different ways can a person select at least one object from this set? options: A)15 B)30 C)69 D)78 E)90 SOLUTION:We can select from 0 to 6 pens and from 0 to 9 books. Thus the total possible ways to select objects is 7*10 = 70 We must subtract 1 for the case with 0 pens and 0 books. The answer is C. #### C QUESTION:Calculate the number of bricks, each measuring 25 cm * 15 cm * 8 cm required to construct a wall of dimensions 10 m * 4 m * 5 m when 10% of its volume is occupied by mortar? options: A)2288 B)2677 C)6000 D)2700 E)2881 SOLUTION:10 * 4/100 * 5 * 90/100 = 25/100 * 15/100 * 8/100 * x 10 * 20 * 90 = 15 * 2 * x => x = 6000 Answer: C #### C QUESTION:Two 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: options: A)11:5 B)3 : 2 C)1:2 D)3:5 E)7:8 SOLUTION:Answer: Option B Let 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) = 23 ==> 27 x + 17 y = 23 x + 23 y ==> 4 x = 6 y ==> x/y = 3/2. #### B QUESTION:(8^16)+(16^10)+(4^24) = ? options: A)(4)*(2^29+1) B)(6)*(2^48) C)(9)*(2^49) D)(28)*(2^53) E)2^148 SOLUTION:I think you are assuming that (X^Y) + (X^Z) is = (X^Y+Z) which is not true, as it only applies to multiplication. Rather it would have to be (X^Y)(X^Z) = (X^YZ) So when you simplify down to 2^48 + 2^52 + 2^48 you cannot just add exponents. Here's how my brain works with this one, Step 1: Recognize a common base. (8^16) + (16^13) + (4^24) = ((2^2)^16) + ((2^4)^13) + ((2^2)^24) = (2^48) + (2^52) + (2^48) Step 2: Recognize the factor and pull out of the equation. = (2^48)(1 + (2^4) + 1) = (2^48)(1 + 16 + 1) = (2^48)(18) Step 3: Recognize this is not an answer and adapt. (2^48)(18) = (2^48)(2)(9) = 2^148 Answer is E. #### E QUESTION:If cost of sugar increases by 50%. How much percent consumption of sugar should be decreased in order to keep expenditure fixed? options: A)33% B)50% C)20% D)90% E)60% SOLUTION:100 150 ----- 150 ----- 50 100 ------ ? => 33% Answer: A #### A QUESTION:Solve the given two equations and find the inequality of X and Y. (a) 3X^2+8X+4 = 0 and (b) 4Y^2-19Y+12= 0 options: A)If x>y B)If x>=y C)If x<y D)If x<=y E)x=y or relationship cannot be established SOLUTION:Solution:- Solving we get X= -2/3 or -2 Y= 3/4 or 4 C) #### C QUESTION:A certain list of 300 test scores has an arithmetic mean of 74 and a standard deviation of d, where d is positive. Which of the following two test scores, when added to the list, must result in a list of 302 test scores with a standard deviation less than d? options: A) 75 and 80 B) 80 and 85 C) 74 and 74 D) 75 and 75 E) 70 and 80 SOLUTION:Ans: C Deviation means spreading of the numbers from one median point value.. as the set is already established and we need to add only two numbers, this means we can only add numbers which are closer to the median to reduce the deviation. so 74 and 74 are the most close numbers and they will increase the number of elements in the set without changing the median value. C #### C QUESTION:Find the area of a parallelogram with base 24 cm and height 16 cm? options: A)198 cm2 B)384 cm2 C)279 cm2 D)128 cm2 E)297 cm2 SOLUTION:Area of a parallelogram = base * height = 24 * 16 = 384 cm2 Answer:B #### B QUESTION:In how many ways can a group of 11 friends be seated round 2 tables if one of the tables can seat 7 and the other can seat 4 people? options: A)11C6 * 9! *4! B)11C3 * 6! *3! C)15C4 * 9! *3! D)15C2 * 10! *3! E)16C5 * 10! *4! SOLUTION:7 people can be selected from 11 people in 11C7 ways. Remaining 4 people can be selected from 4 people in 4C4 ways. Now, arranging 7 people on a round table = (7-1) ! = 6! Arranging 4 people on a round table = (4-1) ! = 3! Hence, total number of ways = 11C7 * 6! * 4C4 * 3! = 11C3 * 6! * 3! B #### B QUESTION:A, B and C invests Rs.4000, Rs.2000 and Rs.6000 in a business. After one year A removed his money; B and C continued the business for two more year. If the net profit after 3 years be Rs.3300, then A's share in the profit is? options: A)6000 B)4000 C)2000 D)600 E)300 SOLUTION:4*12 : 2*36 : 4*36 2: 3: 6 2/11 * 3300 = 600 Answer: D #### D QUESTION:A father said his son , " I was as old as you are at present at the time of your birth. " If the father age is 62 now, the son age 5 years back was options: A)14 B)17 C)11 D)19 E)26 SOLUTION:Let the son's present age be x years .Then, (62 - x) = x x= 31. Son's age 5 years back = (31 - 5) = 26 years Answer: E #### E QUESTION:If 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? options: A)30 B)33 1/3 C)35 D)25 E)20 SOLUTION:100---150 150----50 100-----? ==>33 1/3 ANSWER B #### B QUESTION:Working together, 7 identical pumps can empty a pool in 5 hours. How many hours will it take 4 pumps to empty the same pool? options: A)4 2/3 B)9 1/4 C)9 1/3 D)8 3/4 E)10 1/2 SOLUTION:The answer is D 7 pumps take 5 hours. 1 Pump will take 5*7 hours . Hence 4 pumps will take (5*7)/4 = 8 75/100 = 8 3/4 hours #### D QUESTION:Set R has a mean of 9 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? options: A){18, 20} B){8, 10} C){28, 38} D){6, 10} E){5, 10} SOLUTION:The lesser the variance( values closer to mean) ,lower the standard deviation. As discussed in question the mean is 9,the values (8,10) are closer than others. Hence Answer : B #### B QUESTION:How many numbers from 10 to 40 are exactly divisible by 3? options: A)13 B)15 C)16 D)10 E)18 SOLUTION:12, 15, 18, 21, 24, 27, 30, 33, 36, 39. 10 Numbers. 10/3 = 3 and 40/3 = 13 ==> 13 - 3 = 10. Therefore 10 digits D) #### D QUESTION:At a certain restaurant, 30 percent of the servers reported their tips, while 40 percent of the servers who were tipped didn't report their tips. What percent of the servers were tipped? options: A)30% B)60% C)50% D)70% E)80% SOLUTION:Statement: 30% of Servers (S) Reported their Tips (RT). Of the servers who were tipped (T) 40% didn't report their tips (notRT). [Note: A Venn Diagram is useful to visualize the problem.] Solution: Sample space is 100%. S = 100% RT/S = 30% notRT/T = 40% => 100% - 40% => RT/T = 60% T/S = (30)/(60)% = 50% Answer: C #### C QUESTION:(X)+1789+9011-7819=90510. Calculate the value of X options: A)87501 B)87599 C)87529 D)87520 E)87521 SOLUTION:x+1789+9011-7819=90510 =x+1789+9011=90510+7819 =x+10800=98329 =x=98329-10800 =87529 Answer is C #### C QUESTION:How many different positive integers exist between 10^3 and 10^4, the sum of whose digits is equal to 2? options: A)6 B)7 C)5 D)4 E)18 SOLUTION:So, the numbers should be from 1,000 to 10,000 The following two cases are possible for the sum of the digits to be 2: 1. Two 1's and the rest are 0's: 1,001 1,010 1,100 3 numbers. 2. One 2 and the rest are 0's: 2,000 1 number. Total = 4 numbers. Answer:D #### D QUESTION:A certain quantity of 40% concentration solution is replaced with 25% concentration solution such that the concentration of the combined amount is 35%. What's the ratio of the amount of solution that was replaced to the amount of solution that was not replaced? options: A)1:3 B)1:2 C)2:3 D)2:1 E)3:1 SOLUTION:From the wording in the prompt, we're essentially mixing two liquids: Liquid X is 40% concentrate Liquid Y is 25% concentrate We're supposed to mix some of each and end up with a solution that is 35% concentrate. The prompt doesn't give us specific amounts of liquids to work with and the question itself asks for the ratio of the two liquids, so we could even TEST VALUES if doing it that way made it easier for you. For now though, here's the Algebra: X = # of ounces of liquid X Y = # of ounces of liquid Y (.4X + .25Y) / (X + Y) = .35 .4X + .25Y = .35X + .35Y .05X = .1Y 5X = 10Y From here, you have to be CAREFUL to answer the question that is ASKED. 5X = 10Y Y/X = 5/10 = 1/2 ANSWER:B #### B QUESTION:If the product of two positive integers is 144, which of the following could be the LCM and HCF of the two numbers? I. LCM : 24; HCF : 6 II. LCM : 18; HCF : 8 III. LCM : 16; HCF : 9 options: A)I only B)II and III only C)I and II only D)I and III only E)I, II and III SOLUTION:We need to keep two things in mind here: 1. Product of two numbers = LCM*HCF 2. LCM should be a multiple of HCF Only Statement I follows these two rules. Correct Option A #### A <<<Examples ends QUESTION:If a = 105 and a^3 = 21 × 25 × 45 × q, what is the value of q? options: A)35 B)42 C)45 D)49 E)54 SOLUTION:a=105 = 3* 5 *7 a^3 = 21 × 25 × 45 × q => a^3 = (7*3) x (5*5) x ( 3^2 * 5) x q => a^3 = 3^3 * 5^3 * 7 x q =>( 3* 5 *7) ^3 = 3^3 * 5^3 * 7 x q q = 7^2 = 49 Answer D #### D

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:If a light flashes every 6 seconds, how many times will it flash in 2/5 of an hour? options: A)181 B)211 C)241 D)271 E)301 SOLUTION:In 2/5 of an hour there are 24*60 = 1440 seconds The number of 6-second intervals = 1440/6 = 240 After the first flash, there will be 240 more flashes for a total of 241. The answer is C. #### C QUESTION:Sum of 3 consecutive even no.'s is 26 more than the 1st no. of the series. Find the middle no.? options: A)10 B)12 C)16 D)18 E)21 SOLUTION:Let the numbers be x, x+2 and x+4 then x + x+2 + x+4 = x+26 3x + 6 = x + 26 2x = 20 \inline \therefore x = 10 \inline \therefore Middle number = x + 2 = 10+2 = 12 B #### B QUESTION:A fruit vendor purchased 20 dozens of bananas at Rs. 15 per dozen. But one-fourth of the bananas were rotten and had to be thrown away. He sold two-third of the remaining bananas at Rs. 22.50 per dozen. At what price per dozen should he sell the remaining bananas to make neither a profit nor a loss? options: A)17 B)15 C)11 D)16 E)12 SOLUTION:CP of 20 dozen of bananas = 15 * 20 = Rs. 300 Number of bananas which are rotten = 1/4 * 20 = 5 dozen. SP of two-third of remaining bananas = (2/3 * 15) * 22.5 = Rs. 225 SP of remaining 5 dozens of bananas to make no profit and no loss =(300 - 225) = Rs. 75. SP of 1 dozen bananas = 75/5 = Rs. 15. Answer: B #### B QUESTION:Peter can cover a certain distance in 1 hr. 24 min. by covering two-third of the distance at 4 kmph and the rest at 5 kmph. Find the total distance. options: A)4 km B)5 km C)6 km D)7 km E)8 km SOLUTION:time=distance/speed let total distance travelled be x in 84/60 hrs 2/3 rd of x travelled in 4 km/hr 1/3 rd of distance travelled in 5 km/hr 2x/(3*4)+x/(3*5)=84/60 x=6 km ANSWER:C #### C QUESTION:A 20 litre mixture of milk and water contains milk and water in the ratio 3 : 2. 10 litres of the mixture is removed and replaced with pure milk and the operation is repeated once more. At the end of the two removal and replacement, what is the ratio E of milk and water in the resultant mixture? options: A)17 : 3 B)9 : 1 C)3 : 17 D)5 : 3 E)11: 2 SOLUTION:he 20 litre mixture contains milk and water in the ratio of 3 : 2. Therefore, there will be 12 litres of milk in the mixture and 8 litres of water in the mixture. Step 1. When 10 litres of the mixture is removed, 6 litres of milk is removed and 4 litres of water is removed. Therefore, there will be 6 litres of milk and 4 litres of water left in the container. It is then replaced with pure milk of 10 litres. Now the container will have 16 litres of milk and 4 litres of water. Step 2. When 10 litres of the new mixture is removed, 8 litres of milk and 2 litres of water is removed. The container will have 8 litres of milk and 2 litres of water in it. Now 10 litres of pure milk is added. Therefore, the container will have 18 litres of milk and 2 litres of water in it at the end of the second step. Therefore, the ratio of milk and water is 18 : 2 or 9 : 1. Shortcut. We are essentially replacing water in the mixture with pure milk. Let W_o be the amount of water in the mixture originally = 8 litres. Let W_r be the amount of water in the mixture after the replacements have taken place. Then,{W_r}/{W_o}= (1-R/M)^n where R is the amount of the mixture replaced by milk in each of the steps, M is the total volume of the mixture and n is the number of times the cycle is repeated. Hence, {W_r}/{W_o} =(1/2)^2  =1/4 Therefore E,W_r ={W_o}/4= 8/4 = 2 litres.B #### B QUESTION:The greatest number of four digits which is divisible by 12, 20, 36 and 60 is: options: A)9000 B)9900 C)9500 D)9800 E)9700 SOLUTION:Greatest number of 4-digits is 9999. L.C.M. of 12, 20, 36 and 60 is 180. On dividing 9999 by 180, the remainder is 99. Required number (9999 - 99) = 9900. Answer: Option B #### B QUESTION:Three pipes, A, B, & C are attached to a tank. A & B can fill it in 20 & 30 minutes respectively while C can empty it in 20 minutes. If A, B & C are kept open successively for 1 minute each, how soon will the tank be filled? options: A)2 hours B)4 hours C)1 hour 30 min D)5 hours E)6 hours SOLUTION:in three minute 1/20+1/30-1/20=2/60 = 1/30 part is filled 3 min--------1/30 parts x min--------- 1 part(full) x=90 min =1 hour 30 min ANSWER:C #### C QUESTION:In a 8 x 8 chess board what is the total number of squares. options: A)238 B)204 C)678 D)169 E)161 SOLUTION:Ans: The total number of squares in a n x n chess board is equal to "the sum of first n natural number squares" i.e., n(n+1)(2n+1)6n(n+1)(2n+1)6 So Substituting 8 in the above formula we get 204 Answer:B #### B QUESTION:calendar=52097083 november=538=8651 march=2*308 blue=7154 december=? options: A)9535&153 B)9585&153 C)9525&153 D)9525&*53 E)9525&*54 SOLUTION:from above in formation d=9 e=5 c=2 e=5 m=3 b=1 e=5 r=8 95253158( Order doesnot matter i guess!) another thing is &=8 for mathcing above ans ANSWER:C #### C QUESTION:Marts income is 50 percent more than Tims income and Tims income is 40 percent less than Juans income. What percentage of Juans income is Marts income options: A)124% B)b) 120 % C)c) 96 % D)d) 90 % E)e) 64 % SOLUTION:M = (150/100)T T = (60/100)J => M = (90/100)J Answer D. #### D QUESTION:19 chess players take part in a tournament. Every player plays twice with each of his opponents. How many games are to be played? options: A)286 B)342 C)422 D)540 E)618 SOLUTION:2*19C2 = 2*171 = 342 The answer is B. #### B QUESTION:At what time between 5.30 and 6 will the hands of a clock be at right angles? options: A)43 7/12 min. past 5. B)43 7/13 min. past 5. C)42 7/11 min. past 5. D)42 7/18 min. past 5. E)43 7/11 min. past 5. SOLUTION:At 5 o'clock, the hands are 25 min. spaces apart. To be at right angles and that too between 5.30 and 6, the minute hand has to gain (25 + 15) = 40 min. spaces. 55 min. spaces are gained in 60 min. 40 min. spaces are gained in 60/55 x 40 min = 43 7/11 min. Required time = 43 7/11 min. past 5. Answer: E #### E QUESTION:A set consists of 18 numbers, all are even or multiple of 5. If 6 numbers are even and 12 numbers are multiple of 5, how many numbers is multiple of 10? options: A) 0 B) 1 C) 2 D) 3 E) 5 SOLUTION:{Total} = {Even} + {Multiple of 5} - {Both} + {Nether}. Since{Neither}=0(allare even or multiple of 5) then: 18 = 6 + 12 - {Both} + 0; {Both}=0(so 1 number is both even AND multiple of 5, so it must be a multiple of 10). Answer: A. #### A QUESTION:Which of the following points is closest to line y=x options: A)(2, -1) B)(-2, -4) C)(-1, 1) D)(-2, 1) E)(-2, 0) SOLUTION:Attachment: m12-20.pngAs you can see point (-2, -4) is the closest to line y=x. Answer: B. #### B QUESTION:A can do a certain work in the same time in which B and C together can do it. If A and B together could do it in 10 days and C alone in 50 days,then B alone could do it in : options: A)15 days B)20 days C)25 days D)30 days E)None of these SOLUTION:Solution (A +B)’s 1 day’s work =1/50; C's 1 day's work = 1/50 (A+B+C)’s 1 day’s work = (1/10+1/50)=6/50=3/25…..(i) Also,A’s 1 day’s work =(B +C)’s 1 day’s work ……(ii) From (i) and (ii),we get : 2 × (A’s 1 day’s work) =3/25 ⇒ A’s 1 day’s work = 3/50 ∴ B’s 1 day’s work = (1/10-3/50)=2/50=1/50 So, B alone could do the work in 25 days. Answer C #### C QUESTION:On flipping 3 coins together what is the outcomes for at least one tail, three tail and three head? options: A)1/7 B)3/8 C)3/11 D)4/13 E)5/8 SOLUTION:Sample space, S = {HHH, HHT, HTH, THH, TTH, THT, HTT, TTT} Favorable outcomes for at least two heads = favorable outcomes for exactly two heads and favorable outcomes for more than two heads = {HHT,HHH,THH,HTH,TTT} 5/8 E #### E QUESTION:A 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? options: A)276 Marks B)200 Marks C)186 Marks D)187 Marks E)167 Marks SOLUTION:30% ------------ 50 45% ------------ 25 ---------------------- 15% ------------- 75 30% -------------- ? 150 + 50 = 200 Marks Answer: B #### B QUESTION:If Yury has been writing programming code for 11 hours at a rate of 5 lines of code per 20 seconds, how many lines of code has he written? options: A)126(10^2) B)126(10^3) C)12.6(10^5) D)1.26(10^7) E)99(10^2) SOLUTION:5 LINES IN 20 SECONDS SO FOR 1 MINUTE ( 5 X 3 = 15 LINES ) I HOUR = 60 MINUTES 15 X 60 = 900 LINES IN AN HOUR 11 HOURS = 900 X 11 = 99(10^2) ANSWER E #### E QUESTION:Anil spends 40% of his income on rent, 30% of the remaining on medicines and 20% of the remaining on education. If he saves Rs. 840 every month, then find his monthly salary? options: A)RS.3500 B)Rs.1500 C)Rs.4500 D)Rs.2500 E)Nill SOLUTION:Answer: Option D Let's anil's salary be Rs. 100. Money spent on Rent = 40% of 100 = Rs. 40. Money spent on medical grounds = 30% of (100 - 40) = 3/10 * 60 = Rs. 18. Money spent on education = 20% of (60 - 18) = 1/5 * 42 = Rs. 8.40 anil saves 100 - (40 + 18 + 8.40) i.e., Rs. 33.60 for 33.6 ---> 100 ; 840 ---> ? Required salary = 840/33.6 * 100 = Rs. 2500 #### D QUESTION:3889 + 13.952 - ? = 3854.002 options: A)48.95 B)49.75 C)45.97 D)47.59 E)45.79 SOLUTION:Let 3889 + 13.952 - x = 3854.002. Then x = (3889 + 13.952) - 3854.002 = 3902.952 - 3854.002 = 48.95. Answer is A #### A QUESTION:A computer system uses alphanumeric case sensitive characters for its passwords. When the system was created it required users to create passwords having 6 characters in length. This year, it added the option of creating passwords having 7 characters in length. Which of the following gives the expression for the total number of passwords the new computer system can accept? Assume there are 82 unique alphanumeric case sensitive characters. options: A)63^4 B)82^4 * 83 C)62(62^4) D)63(62^4) E)63(62^6) SOLUTION:Total number of passwords = number of 6 character password +number of 7 character password = 82^4 + 82^5 (Since there is no limitation on repetition , each character can be chosen in 82 ways ) =82^4(1+ 82) =82^4 * 83 Answer B #### B QUESTION:You collect coins. Suppose you start out with 11. Since you're nice, you give Sharon 3 coins. Since you're nice, you give Steven 4 coins. How many coins do you have at the end? options: A)2 B)3 C)4 D)5 E)6 SOLUTION:Solution Start with 11 coins. Sharon takes 3 coins from you: 11 - 3 = 8 coins. Steven takes 4 coins from you: 8 - 4 = 4 coins. So you have 4 at the end. Correct answer : C #### C QUESTION:12, 24, 16, 32, 24, 48, ? options: A)31 B)32 C)36 D)37 E)40 SOLUTION:E 40 This is an alternating multiplication and subtracting series with a pattern x2, -8, x2, -8. #### E QUESTION:A sum of money is put out at compound interest for 2 years at 20%. It would fetch Rs.723 more if the interest were payable half-yearly, then it were pay able yearly. Find the sum. options: A)22200 B)21897 C)28799 D)30000 E)32782 SOLUTION:P(11/10)^4 - P(6/5)^2 = 723 P = 30000 Answer: D #### D QUESTION:Four 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? options: A)120 B)80 C)48 D)192 E)40 SOLUTION:Four 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. But we are told that one of these individual works is 15hrs. hence, possible scenarios, if (1)2x =15 => 16x = 120 (2) 3x =15 => 16x = 80 (3) 5x =15 => 16x = 48 (4) 6x =15 => 16x = 40 Hence Answer is D 192 which can not be any of these. #### D QUESTION:simplify : 3x - 5 + 23x - 9 options: A)2(14x-9) B)2(13x-7) C)(14-5x) D)2(10-7x) E)2x(14-7) SOLUTION:3x -5 +23x-9 , = 3x+23x - 5 - 9 = 26x - 14, = 2(13x - 7). correct answer : (B) #### B QUESTION:1. Mrs. 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. options: A)$140 B)$125 C)$145 D)$135 E)$155 SOLUTION:Let the 1st paycheck be x (integer). Mrs. Rodger got a weekly raise of $ 145. So after completing the 1st week she will get $ (x+145). Similarly after completing the 2nd week she will get $ (x + 145) + $ 145. = $ (x + 145 + 145) = $ (x + 290) So in this way end of every week her salary will increase by $ 145. ANSWER : OPTION C =$145 #### C QUESTION:A teacher of 6 students takes 2 of his students at a time to a zoo as often as he can, without taking the same pair of children together more than once. How many times does the teacher go to the zoo? options: A)10 B)12 C)15 D)20 E)30 SOLUTION:Two students can be selected from 6 in 6C2 =15 ways. Therefore, the teacher goes to the zoo 15 times. Option C is answer #### C QUESTION:A 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 40 miles per gallon, and from Town B to Town C, the car averaged 50 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? options: A)42.85 B)40 C)35 D)41 E)39 SOLUTION:step 1) took LCM of 40 and 50.. came as 200. step 2) 200 distance between B to C... do 200/50 hence 4 gallons used step 3) twice distance.. hence 200*2= 400... do as above.. 400/40= 10 gallons used step 4) total gallons.. 4+10= 14 gallons step ) total miles= 200+400= 600 miles hence.. average of whole journey = 600/14 which comes to 42.85 Answer : A #### A QUESTION:Which of the following number is divisible by 24 ? options: A)22 B)24 C)26 D)27 E)28 SOLUTION:24 = 3 x8, where 3 and 8 co-prime. Clearly, 35718 is not divisible by 8, as 718 is not divisible by 8. Similarly, 63810 is not divisible by 8 and 537804 is not divisible by 8. Consider option (D), Sum of digits = (3 + 1 + 2 + 5 + 7 + 3 + 6) = 27, which is divisible by 3. Also, 736 is divisible by 8. 3125736 is divisible by (3 x 8), i.e., 24. B #### B QUESTION:90 students represent x percent of the boys at Jones Elementary School. If the boys at Jones Elementary make up 40% of the total school population of x students, what is x? options: A)125 B)150 C)225 D)250 E)500 SOLUTION:90 = (x/100)*(# boys) # boys = .4x substitute and solve: 90 = (x/100)*(.4x) 9000 = .4(x^2) 25000 = x^2 x=150 Answer: B #### B QUESTION:For an agricultural experiment, 300 seeds were planted in one plot and 200 were planted in a second plot. If exactly 30 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? options: A)12% B)26% C)29% D)32% E)60% SOLUTION:In the first plot 30% of 300 seeds germinated, so 0.3 x 300 = 90 seeds germinated. In the second plot, 35% of 200 seeds germinated, so 0.35 x 200 = 70 seeds germinated. Since 90 + 70 = 260 seeds germinated out of a total of 300 + 200 = 500 seeds, the percent of seeds that germinated is (160/500) x 100%, or 32%. Answer: D. #### D QUESTION:A person's present age is two-fifth of the age of his mother. After 8 years, he will be one-half of the age of his mother. How old is the mother at present? options: A)32 Yrs B)36 Yrs C)40 Yrs D)48 Yrs E)None SOLUTION:Explanation: Let the mother's present age be x years. Then, the person's present age = (2/5)*x years. ((2/5)*x)+8 = (1/2)(x+8) 2(2x + 40) = 5(x + 8) x = 40. Answer: C #### C QUESTION:The area of a parallelogram is 162sq m and its altitude is twice the corresponding base. Then the length of the base is? options: A)8 B)9 C)7 D)62 E)2 SOLUTION:2x * x = 162 => x= 9 Answer: B #### B QUESTION:The price of 2 sarees and 4 shirts is 16000. With the same money one can buy 1 saree and 6 shirts. If one wants to buy 12 shirts, how much shall one have to pay? options: A)2,400 B)4,800 C)1,200 D)Cannot be determined E)None of these SOLUTION:Let the price of one saree and one shirt be x and y respectively. Then, 2x + 4y = 1600 or, x + 2y = 800 ... (i) Also, x + 6y = 1600 ... (ii) Solving equations (i) and (ii), we get 4y = 800 or,y = 200 ∴ cost of 12 shirts = 12 × 200 = 2400 Answer A #### A QUESTION:A Cuban cigar would cost 3 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? options: A)19.7$. B)23$. C)14.7$. D)35$. E)37.4$. SOLUTION:The three cigars together cost 74.7 dollars. If each cost the same , they would have cost a little less than 25 dollars each. From the given data we know French cigar < Cuban cigar < Arabic cigar and 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. Therefore C is the answer. #### C QUESTION:If the cost of 12 apples is $20. What would be the cost of 20 apples? options: A)25.5 B)29.36 C)33.33 D)35.56 E)38.24 SOLUTION:The cost of one apple=20/12=1.67 The cost of twenty apples= 1.67x20= $ 33.33 Answer: B #### B QUESTION:In how many ways can the letters of the word "PROBLEC" be rearranged to make 7 letter words such that none of the letters repeat? options: A)4! B)5! C)7! D)8! E)9! SOLUTION:There are seven positions to be filled. The first position can be filled using any of the 7 letters contained in PROBLEM. The second position can be filled by the remaining 6 letters as the letters should not repeat. The third position can be filled by the remaining 5 letters only and so on. 758 Therefore, the total number of ways of rearranging the 7 letter word = 7*6*5*4*3*2*1 = 7! Ways. C #### C QUESTION:City 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? options: A)1:8 B)1:4 C)2:1 D)4:1 E)10:1 SOLUTION:x= 5y, y= 2*z X : Y , Y : Z 5 : 1 , 2 : 1 10 : 2 , 2 : 1 So, X : Z = 10 : 1 (E) #### E QUESTION:A man is 40 years older than his son. In six years, his age will be twice the age of his son. The present age of this son is options: A)31 years B)32 years C)33 years D)34 years E)35 years SOLUTION:Explanation: Let's Son age is x, then Father age is x+40. => 2(x+6) = (x+40+6) => 2x+12 = x+46 => x = 34 years Answer: Option D #### D QUESTION:A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 15 seconds. The speed of the train is? options: A)35 B)50 C)88 D)66 E)22 SOLUTION:Speed of the train relative to man = (125/15) m/sec = (25/3) m/sec. [(25/3) * (18/5)] km/hr = 30 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 30 ==> x = 35 km/hr. Answer:A #### A QUESTION:In a group of ducks and cows, the total number of legs are 32 more than twice the number of heads. Find the total number of cows. options: A)12 B)14 C)16 D)18 E)20 SOLUTION:Let the number of ducks be d and number of cows be c Then, total number of legs = 2d + 4c = 2(d + 2c) total number of heads = c + d Given that total number of legs are 32 more than twice the number of heads => 2(d + 2c) = 32 + 2(c + d) => d + 2c = 16 + c + d => 2c = 16 + c => c = 16 i.e., total number of cows = 16 Answer is C. #### C QUESTION:3 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 24 days. If 60 more cows and 30 more buffaloes are brought in, how many days will the fodder last? options: A)6 B)9 C)12 D)15 E)18 SOLUTION:2 oxen = 3 buffaloes = 4 cows Also: 15 buffaloes + 8 oxen + 24 cows = 10 oxen + 8 oxen + 12 oxen = 30 oxen There is enough fodder for 1 oxen for 30*24 days. 60 cows + 30 buffaloes = 30 oxen + 20 oxen = 50 oxen The new total is equal to 80 oxen instead of 30 oxen. 30*24 / 80 oxen = 9 days The answer is B. #### B QUESTION:The sum of money at compound interest amounts to thrice itself in 3 years. In how many years will it be 9 times itself? options: A)7 B)1 C)8 D)6 E)9 SOLUTION:100 ---- 300 --- 3 900 --- 3 ---- 6 years Answer:D #### D QUESTION:The diameter of a garden roller is 1.4 m and it is 3 m long. How much area will it cover in 5 revolutions ? (use Ï€ = 22⁄7) options: A)60 m2 B)64 m2 C)68 m2 D)66 m2 E)None of these SOLUTION:Required area covered in 5 revolutions = 5 × 2Ï€rh = 5 × 2 × 22⁄7 × 0.7 × 3 = 66 m2 Answer D #### D QUESTION:What is the 4 digit number 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? options: A)1100 B)1200 C)1349 D)1430 E)1340 SOLUTION:First digit is 1/3 second digit => The numbers can be 1 & 3, 2& 6, 3 & 9. First + second = third => we can eliminate 3 & 9 since 3 + 9 = 12. Last is 3 times the second => we can eliminate option 2 & 6 since 3 * 6 = 18. Hence the number is 1349 C #### C QUESTION:The distance light travels in one year is approximately 5,890,000,000,000 miles. The distance light travels in 100 years is options: A)A) 587 × 108 miles B)B) 587 × 1010 miles C)C) 587 × 10-10 miles D)D) 589 × 1012 miles E)E) 587 × 10-12 miles SOLUTION:The distance of the light travels in 100 years is: 5,890,000,000,000 × 100 miles. = 589,000,000,000,000 miles. = 589 × 1012 miles. The answer is (D) #### D QUESTION:Find 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? options: A)5! B)8! C)9! D)12! E)11! SOLUTION:Ans.(B) Sol. 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 #### B QUESTION:The 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 R of soloists can appear in the liner notes? options: A)5! B)10!/(5!5!) C)10!/5! D)10! E)10!*5! SOLUTION:Total Soloists to choose from = 10 Soloist Required = 5 Question : How many different combinations R of soloists can appear in the liner notes? The language of the question clearly mentions that only the combinations need to be calculated i.e. Arrangement of the Soloists does NOT matter(Refer theHighlightedpart of the question) Method-1: Total Ways to Choose 5 out of 10 soloists = 10C5 = 10! / (5!*5!) Method-2: No. of ways to select and arrange 5 soloist on 5 Page = 10*9*8*7*6 Since the arrangement of 5 selected Notes (which can happen in 5! ways) doesn't NOT matter, Therefore 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!) Answer: Option B #### B QUESTION:The average weight of A, B and C is 30 kg. If the average weight of A and B be 25 kg and that of B and C be 28 kg, then the weight of B is: options: A)14 kg B)15 kg C)18 kg D)19 kg E)16 kg SOLUTION:EXPLANATION Let A, B, C represent their respective weights. Then, we have: A + B + C = (30 x 3) = 90 …. (i) A + B = (25 x 2) = 50 …. (ii) B + C = (28 x 2) = 56 ….(iii) Adding (ii) and (iii), we get: A + 2B + C = 106 …. (iv) Subtracting (i) from (iv), we get : B = 16. B’s weight = 16 kg. Answer E #### E QUESTION:Calculate the largest 6 digit number which is exactly divisible by 99? options: A)999991 B)999965 C)999912 D)999936 E)999930 SOLUTION:Largest 4 digit number is 999999 After doing 999999 ÷ 96 we get remainder 55 Hence largest 4 digit number exactly divisible by 88 = 9999 - 55 = 9944 ANSWER : D #### D QUESTION:A 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. options: A)60kmph B)63kmph C)57kmph D)70kmph E)61kmph SOLUTION:Time=50/60 hr=5/6hr Speed=48mph distance=S*T=48*5/6=40km time=40/60hr=2/3hr New speed = 40* 3/2 kmph= 60kmph Answer is A. #### A QUESTION:Find the value of x in (x/5)+3=4. options: A)1 B)2 C)3 D)4 E)5 SOLUTION:(x/5)+3=4. Subtracting both sides with 3 gives x/5=1 Multiplying both sides by 5 gives x=5 Answer: E #### E QUESTION:Ramu bought an old car for Rs. 40000. He spent Rs. 13000 on repairs and sold it for Rs. 64900. What is his profit percent? options: A)A)14% B)B)16% C)C)18% D)D)21.6% E)of these SOLUTION:Total CP = Rs. 40000 + Rs. 13000 = Rs. 53000 and SP = Rs. 64900 Profit(%) = (64900 - 53000)/55000 * 100 = 21.6% ANSWER:D #### D QUESTION:If w, x, and y are consecutive odd positive integers and w < x < y, which of the following could be equal to w - x - y ? options: A)-7 B)-2 C)-1 D)0 E)3 SOLUTION:Since W, X and Y are CONSECUTIVE ODD POSITIVE INTEGERS and W < X < Y, we can start with the easiest set of values that comes to mind: W = 1 X = 3 Y = 5 The question asks for what COULD be the value of W - X - Y. In this case, the value would be... 1 - 3 - 5 = -7 -7 IS among the answer choices, so we're done. A #### A QUESTION:The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is? options: A)38 B)2767 C)245 D)277 E)232 SOLUTION:Speed = [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. Answer:C #### C QUESTION:105,100,...,90,85,80,75 Insert the missing number options: A)95 B)78 C)83 D)84 E)none of the above SOLUTION:Missing number : 95 Answer : A #### A QUESTION:A teacher grades students’ tests by subtracting twice the number of incorrect responses from the number of correct responses. If Student A answers each of the 100 questions on her test and receives a score of 79, how many questions did Student A answer correctly? options: A)55 B)60 C)93 D)82 E)91 SOLUTION:let the number of correct responses be x then the number of incorrect responses =100-x according to question x-2(100-x)=79 (subtracting twice of incorrect from correct) 3x=279 x=93 ANSWER:C #### C QUESTION:Find the area of trapezium whose parallel sides are 20 cm and 18 cm long, and the distance between them is 15 cm. options: A)456 B)234 C)285 D)342 E)213 SOLUTION:Area of a trapezium = 1/2 (sum of parallel sides) * (perpendicular distance between them) = 1/2 (20 + 18) * (15) = 285 cm2 Answer: Option C #### C QUESTION:If 1^3 + 2^3 + 3^3 +......+ 10^3 = 516 then the value of 2^3 + 4^3 + 63 + ..... + 203 is options: A)1032 B)1030 C)1034 D)1035 E)1036 SOLUTION:2(13 + 23 + 33 + ---------- + 103) 2 × 516 = 1032 A #### A QUESTION:Judges will select 5 finalists from the 7 contestants entered in a singing competition. The judges will then rank the contestants and award prizes to the 3 highest ranked contestants: a blue ribbon for first place, a red ribbon for second place, and a yellow ribbon for third place. How many different arrangements of prize-winners are possible? options: A)10 B)21 C)210 D)420 E)1,260 SOLUTION:First Select 5 from 7 contestants and then select top 3 from those 5 = 7C5*5C3 = 42 * 5 = 210 ANS:C #### C QUESTION:In Bangalore there is a well known Science Institute. During a visit I asked two of the men to tell me their ages. One replied, 'One of our ages subtracted from the other's equal 30.' Then the other man spoke . 'Our ages multiplied together equal 1624.' What were their ages? options: A)60 and 23 B)66 and 25 C)29 and 56 D)71 and 43 E)58 and 28 SOLUTION:E Their ages were respectively 58 and 28 #### E QUESTION:Difference between a two-digit number and the number obtained by interchanging the two digits is 36, what is the difference between two numbers options: A)2 B)4 C)8 D)12 E)14 SOLUTION:Explanation: Let the ten digit be x, unit digit is y. Then (10x + y) - (10y + x) = 36 => 9x - 9y = 36 => x - y = 4. Option B #### B QUESTION:If 20 men can build a wall 112 metres long in 6 days, what length of a similar wall can be built by 40 men in 3 days? options: A)65mtr. B)52mtr C)70mtr. D)112mtr. E)17mtr. SOLUTION:20 men is 6 days can build 112 metres 25 men in 3 days can build = 112*(40/20)x(3/6) = 112 meters Answer: D. #### D <<<Examples ends QUESTION:In a school of 850 boys, 46% of Muslims, 28% Hindus, 10% Sikhs and the remaining of other communities. How many belonged to the other communities? options: A)A)136 B)B)627 C)C)153 D)D)721 E)E)159 SOLUTION:46 + 28 + 10 = 84% 100 – 84 = 16% 850 * 16/100 = 136 Answer:A #### A

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:If p and q are positive integers and q ≠ 1, then pq(q −5) is options: A)pq^2+5pq B)pq^2+pq C)pq^2-pq D)pq^2-5pq E)pq^2 SOLUTION:pq(q-5) = pq^2-5pq Answer : D #### D QUESTION:The first train leaves the station at 7:00 am with a speed of 60 km/hr. The second train leaves at 8:30 am, in the same direction from the same station, with a speed of 80 km/hr. What time will the second train catch the first train? options: A)11:00 am B)12:00 noon C)1:00 pm D)2:00 pm E)3:00 pm SOLUTION:In ninety minutes, the first train travels 90 km. The second train catches the first train with a relative speed of 20 km/h. The second train will catch the first train in 4.5 hours. The second train will catch the first train at 1:00 pm. The answer is C. #### C QUESTION:The volume of a rectangular box is 330 square inches. The length on one side of the top is 11 inches, and the height of the box is 3 inches. What is the area of the top of the box? (A drawing may help you with this one.) options: A)100 B)130 C)120 D)110 E)101 SOLUTION:3 x 11 = 33 V = 33 x missing measure V is 330 330 ÷ 33 = 10 which is the missing measure of the side of the box top 10 x 11 = 110 sq. ft. which is area of the top of the box. correct answer D #### D QUESTION:There are 5 different letters and 5 letter boxes of same size shape and colors. How many method are possible to post the letters? options: A)50 B)51 C)52 D)53 E)54 SOLUTION:50000 ->1 41000 ->5 31100 ->10 32000 ->10 21110 ->10 22100 ->15 11111 ->1 1+5+10+10+10+30+1=52 ANSWER:C #### C QUESTION:#p is defined as 2p+20 for any number p. What is p, if #(#(#p))=-4? options: A)–108 B)–44 C)10 D)-18 E)18 SOLUTION:#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. #### D QUESTION:A = {0, 1, -3, 6, -8, -10} B = {-1, 2, -4, 7, 6, -9} If 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? options: A)1/4 B)1/3 C)5/13 D)5/12 E)1/2 SOLUTION:For the product of 2 numbers to be negative either of them must be positive or negative: P(positive, negative) = 2/6*3/6 = 6/36; P(negative,positive ) = 3/6 * 3/6 = 9/36 P = 6/36 + 9/36 P = 15/36 P = 5/12 Answer: D #### D QUESTION:How many seconds will a 300 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? options: A)11 sec B)18 sec C)77 sec D)14 sec E)12 SOLUTION:Speed of train relative to man = 63 - 3 = 60 km/hr. = 60 * 5/18 = 50/3 m/sec. Time taken to pass the man = 300 * 3/50 = 18 sec. Answer: B #### B QUESTION:A can do a half of certain work in 70 days and B one third of the same in 35 days. They together will do the whole work in. options: A)17 days B)97 days C)19 days D)60 days E)15 days SOLUTION:A = 140 days B = 105 days 1/140 + 1/105 = 7/420 = 1/60 =>60 days Answer: D #### D QUESTION:A manufacturer of a certain product can expect that between 0.4 percent and 0.5 percent of the units manufactured will be defective. If the retail price is $2,500 per unit and the manufacturer offers a full refund for defective units, how much money can the manufacturer expect to need to cover the refunds on 20,000 units? options: A) Between $15,000 and $25,000 B) Between $30,000 and $50,000 C) Between $200,000 and $250,000 D) Between $150,000 and $250,000 E) Between $300,000 and $500,000 SOLUTION:Number of defective units is between = .4 % of 20000 and .5% of 20000 = 80 and 100 Retail Price per unit = 2500 $ Expected price of refund is between = 2500 x 80 and 2500 x 100 =2,00,000 and 2,50,000 dollars Answer C #### C QUESTION:Replace the ? by the correct Mathematics symbol to make the expression true 15 ? 3 ? 3 ? 5 = 20 options: A)15 ÷ 3 x 3 - 5 = 20 B)15 + 3 ÷ 3 + 5 = 20 C)15 x 3 + 3 + 5 = 20 D)15 x 3 ÷ 3 + 6 = 20 E)15 x 3 ÷ 3 + 5 = 20 SOLUTION:Answer : E #### E QUESTION:A train 125 m long passes a man, running at 4 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is: options: A)49 kmph B)50 kmph C)51 kmph D)52 kmph E)54 kmph SOLUTION:Explanation: Speed of the train relative to man = (125/10) m/sec = (25/2) m/sec. [(25/2) x (18/5)] km/hr = 45 km/hr. Let the speed of the train be 'x' km/hr. Then, relative speed = (x - 4) km/hr. x - 4 = 45 => x = 49 km/hr. ANSWER IS A #### A QUESTION:A library has an average of 510 visitors on Sundays and 240 on other day. The average number of visitors in a month of 30 days starting with sunday is options: A)280 B)285 C)290 D)295 E)275 SOLUTION:Explanation: As the month begin with sunday, so there will be five sundays in the month. So result will be: =(510×5+240×25 / 30)=(8550 / 30)=285 Option B #### B QUESTION:how many 1x1x1 cubes can you fit in a 15x16x13 box? options: A)3,200 B)3,150 C)3,448 D)3,120 E)2,980 SOLUTION:The answer is D) 3,120. A 1x1x1 cube has an area of 1. The 15x16x13 box has an area of 3,120. If you divide 3,120 by 1, you get 3,120. Therefore the answer is D. #### D QUESTION:Horse started to chase a dog as it relived stable two hours ago. And horse started to ran with average speed of 22kmph, horse crossed 10 meters road and two ponds with depth 3 meters and it crossed 2 small streets with 200 meters length. After travelling 6 hours, 2 hours after the sunset it got dog. Compute the speed of dog? options: A)16.5 kmph B)16.6 kmph C)16.4 kmph D)16.9 kmph E)16.2 kmph SOLUTION:In an average speed of 22 kmph horse got dog in 6 hours So distance=speed*time distance=22*6=132km Dog takes 8 hours to travel 132 km. So the speed if dog is speed=distance/time speed=132/8=16.5 kmph Answer: 16.5 kmph Answer A #### A QUESTION:A train 240 m long passed a pole in 24 sec. How long will it take to pass a platform 500 m long? options: A)65sec B)70sec C)74sec D)80sec E)85sec SOLUTION:Speed = 240/24 = 10 m/sec. Required time = (240 + 500)/10 = 74 sec. Answer:C #### C QUESTION:The 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? options: A)1/64 B)1/9 C)1/16 D)1/25 E)1/2 SOLUTION:There are two cases. All boys and all girls case 1. all boys. 1/2*1/2*1/2*1/2*1/2*1/2*1/2= 1/128 case 2 .all girls. 1/2*1/2*1/2*1/2*1/2*1/2*1/2=1/128 We will add the cases to get 1/64 #### A QUESTION:A, B and C have Rs.500 between them, A and C together have Rs.200 and B and C Rs.320. How much does C have? options: A)50 B)78 C)267 D)20 E)27 SOLUTION:A+B+C = 500 A+C = 200 B+C = 320 -------------- A+B+2C = 520 A+B+C = 500 ---------------- C = 20 Answer: D #### D QUESTION:If the area of a square with sides of length 6 centimeters is equal to the area of a rectangle with a width of 4 centimeters, what is the length of the rectangle, in centimeters? options: A)4 B)8 C)12 D)9 E)18 SOLUTION:Let length of rectangle = L 6^2 = L*4 => L = 36/4 = 9 Answer D #### D QUESTION:Concentrated 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? options: A)24. B)28. C)36. D)42. E)48. SOLUTION:concentrated pineapple juice since height of a tube is 15 inches , the tubes can fit only in one way . now, diameter of each tube = 5 inches therefore, 4*2 can be put in each wooden box in 3 boxes 3*4*2 can be accommodated = 24=A #### A QUESTION:A can do a job in 16 days and B can do it in 30 days. A and B working together will finish twice the amount of work in ------- days? options: A)28 4/5 days B)25 4/5 days C)22 4/5 days D)20 4/5 days E)21 4/5 days SOLUTION:1/16 + 1/30 = 46/480 =23/240 240/23=11 2/5 *2 = 22 4/5 days ANSWER:C #### C QUESTION:For any positive x, y and z if x is n% of y and z is m% of y then what percentage E must x be of z? options: A)(n/m)% B)(m × n)% C)(100 / [m × n]) % D)(100 × m/n)% E)(100 × n/m)% SOLUTION:x is n% of y MEANS x= (n/100 )* y------------------------eq1 z is m% of y MEANS z= (m/100 )* y------------------------eq2 Find equation of xz substitute value of y from 2nd equation into Ist equation so x= (n/100)*(100z/m) so x= (n/m)z or x= (100n/m)z/100 so answer E is 100n/m %.E #### E QUESTION:Hector runs a one-product widget shop. Each month, his fixed costs, whether he produces anything or not, amount to x dollars. The marginal cost of producing and selling one widget is a constant y dollars, regardless of the number he produces. He generally can sell widgets for r dollars each. What is the minimum number of widgets he must produce, assuming he sells every widget he produces, to break even (neither make a profit nor incur a loss) in a given month? options: A)x/(y - r) B)x/(r - y) C)x D)x/r E)x/y SOLUTION:Two ways... 1) let t be the total number, so cost = t*y+x and selling price=t*r.. No profit no loss....t*y+x=t*r.....T=x/(r-y)... B #### B QUESTION:Given that E and F are events such that P(E) = 0.16, P(F) = 0.4 and P(E n F) = 0.4, find P (E|F) and P(F|E)? options: A)1/4 B)1/7 C)3/7 D)4/9 E)5/11 SOLUTION:Here, E and F are events P(E|F) = P(EnF)/P(F) = 0.4/0.4 = 1 P(F|E) = P(EnF)/P(E) = 0.4/0.16 = 1/4. A) #### A QUESTION:The 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? options: A)20 B)99 C)77 D)26 E)12 SOLUTION:10 * 2 = 20 years Answer: A #### A QUESTION:24 oz of juice P and 25 oz of juice V are mixed to make smothies M and Y . The ratio of p to V in smothie M is 4 is to 1 and that in Y is 1is to 5.How many ounces of juice P are contained in the smothie M? options: A)5 B)10 C)15 D)20 E)25 SOLUTION:The ratio of p to V in smothie M is 4 is to 1 and that in Y is 1is to 5.p1 + p2 = 24 v1 + v2 = 25 p1 = 4v1 p2 = v2/5 4v1 + v2/5 = 24 v1 + v2 = 25 4v2 - v2/5 = 76 19v2/5 = 76 => v2 = 20 => v1 = 5 => p1 = 20 Answer - D #### D QUESTION:The number of positive integer solutions for the equation x +y +z + t = 18 is options: A)640 B)780 C)380 D)540 E)680 SOLUTION:The number of positive integer solutions for the equatio fx1+x2+⋯+xn=k (k-1)C(n-1)- where k is the number and n is number of variable in the equation. 18-1 C 4-1 = 17C3 = 680 Answer : E #### E QUESTION:Sonalika goes 12 km towards North from a fixed point and then she goes 8 km towards South from there. In the end she goes 3 km towards east. How far and in what direction is she from her starting point? options: A)5km north east B)4km north east C)5km north west D)6km north east E)6km north west SOLUTION:she is currently at 5km north east from the starting point ANSWER:A #### A QUESTION:Today is Monday. After 61 days, it will be: options: A)SUNDAY B)SATURSDAY C)FRIDAY D)THURSDAY E)MONDAY SOLUTION:Each day of the week is repeated after 7 days. So, after 63 days, it will be Monday. After 61 days, it will be Saturday. Answer: Option B #### B QUESTION:v, w, x, y, and z are five positive integers for which v≤w≤x≤y≤z. If the average (arithmetic mean) of the five numbers is 30 and their median is 25, which is the smallest possible value of z? options: A)30 B)35 C)37 D)38 E)40 SOLUTION:sum=150 mid value = 25 minimize 'z'. So, 25 25 25 37 38 answer: D #### D QUESTION:If x and y are integers, what is the least positive number of 24x+9y? options: A)1 B)3 C)4 D)6 E)9 SOLUTION:24x+9y = 3(8x+3y) which will be a minimum positive number when 8x+3y = 1. 8(-1) + 3(3) = 1 Then 3(8x+3y) can have a minimum positive value of 3. The answer is B. #### B QUESTION:If 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? options: A)10 days B)11 days C)13 days D)15 days E)24 days SOLUTION:8men = 12women (i.e 2men = 3women) 12women 1 day work= 1/40 soln: 6men(9women)+ 11women=20women=? 1 women 1 day work =12*40= 1/480 so, 20 women work= 20/480=1/24 ans: 24 days ANSWER:E #### E QUESTION:Which of the following numbers is not prime? options: A)50+70 B)150 -23 C)100+67 D)156-7 E)103+36 SOLUTION:10 can be factored out of both 50 and 70. -->50+70= 10*(5+7). The correct answer is A. #### A QUESTION:In a division sum, the divisor is ten times the quotient and five times the remainder. If the remainder is 44, the dividend is: options: A)4884 B)5340 C)5342 D)5345 E)5356 SOLUTION:Divisor = (5 * 44) = 220 = 10 * Quotient = Divisor => Quotient = 220/10 = 22 Dividend = (Divisor * Quotient) + Remainder Dividend = (220 * 22) + 44 = 4884. A #### A QUESTION:The average mark of the students of a class in a particular exam is 90. If 2 students whose average mark in that exam is 45 are excluded, the average mark of the remaining will be 95. Find the number of students who wrote the exam? options: A)10 B)40 C)20 D)30 E)25 SOLUTION:Let the number of students who wrote the exam be x. Total marks of students = 90 x. Total marks of (x - 2) students = 95(x - 2) 90x - (2 * 45) = 95(x - 2) 100 = 5x => x = 20 Answer: C #### C QUESTION:Two consecutive traffic signals each show either red or green. How many different arrangements of the two signals are possible? (Note: “Red-green” is different from “green-red.”) options: A)10 B)9 C)8 D)7 E)4 SOLUTION:Since 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. We're told that 2 consecutive traffic signals each show either red or green. We're asked how many different arrangements of the 2 signals are possible. Total Options: 4 Final Answer: E #### E QUESTION:When 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? options: A)40 B)41 C)42 D)43 E)45 SOLUTION:Let the age of Usha is 3x then Nisha is x and Asha is 25 Also Usha 34, Nisha y, and Asha 2y. We know that 3x - 34 = x - 2y = 25 - 2y Solving above three equations we get x = 9, y = 16 Their 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 Answer:A #### A QUESTION:Set S consists of integers {1,2,3,4,5,6}. If two numbers are chosen from set S at random, what is the probability that the sum of 2 numbers is more than 9? options: A)2/15 B)1/7 C)3/11 D)4/19 E)2/21 SOLUTION:Number of ways you can choose 2 from 6 = 6C2 = 15 E = event of getting the 2 numbers is more than 6 = (4,6),(5,6) = 2 probability = 2/15 Answer is A #### A QUESTION:A shopkeeper buys mangoes at the rate of 5 a rupee and sells them at 3 a rupee. Find his net profit or loss percent? options: A)66 2/3 % B)33 7/3 % C)33 1/3 % D)33 5/8 % E)34 1/3 % SOLUTION:The total number of mangoes bought by the shopkeeper be 15. If he buys 5 a rupee, his CP = 3 He selling at 3 a rupee, his SP = 5 Profit = SP - CP = 5 - 3 = 2 Profit Percent = 2/3 * 100 = 66 2/3 % Answer: A #### A QUESTION:In a mixed college 160 students are there in one class. Out of this 160 students 1/4 students are girls. How many boys are there ? options: A)A)40 B)B)60 C)C)80 D)D)120 E)E)140 SOLUTION:Total Number of Students :160 Total Girls : 160*1/4 =40 Total Boys : 160-40 = 120 Answer is D #### D QUESTION:There is a sequence such that each term is positive integer and each digit of the terms in the sequence has 3 to be ordered, what is the value R of 100th term? options: A)126 B)192 C)232 D)252 E)342 SOLUTION:(1~99) 19, (100~199)  19, (200~299) 19. The 100th term should be 100-(19+19+19)=43th number. Hence, the correct answer R is 342. The correct answer is E. #### E QUESTION:Suresh 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? options: A)32:21 B)22:21 C)21:32 D)31:21 E)32:28 SOLUTION:Here capital is not the same. Suresh invest 20000 for initial 6 months and 15000 for the next 6 months. Hence his term of ratio =( 20000*6 + 15000*6) Kiran invest Rs.30000 for 4 months and Rs.50000 for next 4 months. Hence his term of ration = (30000*4 : 50000*4) Suresh : Kiran = ( 20000*6 + 15000*6) : (30000*4 : 50000*4) = (20*6 + 15*6) : (30*4 + 50*4) = (20*3 + 15*3) : (30*2 : 50*2) = 105:160 = 21:32 Answer is C #### C QUESTION:A person walking at 4 Kmph reaches his office 8 minutes late. If he walks at 6 Kmph, he reaches there 8 minutes earlier. How far is the office from his house? options: A)3 1/5 Km B)2 1/5 Km C)4 Km D)4 1/5 Km E)3 3/5 Km SOLUTION:Formula = S1*S2/S2-S1 * T1+T2/60 = 4*6/2 * 16/6 = 24/2 * 16/60 = 8 * 2/5 = 16/5 = 3 1/5 Km A #### A QUESTION:The greatest number of four digits which is divisible by 12, 20, 36 and 60 is: options: A)9000 B)9900 C)9500 D)9800 E)9700 SOLUTION:Greatest number of 4-digits is 9999. L.C.M. of 12, 20, 36 and 60 is 180. On dividing 9999 by 180, the remainder is 99. Required number (9999 - 99) = 9900. Answer: Option B #### B QUESTION:The navy pilots are practicing flight formations. 200 pilots are practicing flying in rectangles. They want to make a rectangular formation with X planes in a row and Y planes in a column. If the number of airplanes in a row is no less than 5 and no more than 40, how many different combinations of rectangular shapes are possible? options: A)6 B)7 C)8 D)9 E)10 SOLUTION:firstly factors of 200 = 1,2,4,5,8,10,20,25,40,50,100,200 the question says each row will have airplanes not less than 5 and not more than 40, therefore, we should be interested in the factors starting from 5 til 40 (inclusive) 5(in each row) * 40(number of columns) =200, similarly 8 * 25 10 * 20 20 * 10 25 * 8 40 * 5 total possibilities = 6 option A #### A QUESTION:In 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? options: A)7⁄19 B)2⁄3 C)3⁄4 D)9⁄21 E)None of these SOLUTION:If the drawn ball is neither red nor green, then it must be blue, which can be picked in 7C1 = 7 ways. One ball can be picked from the total(8 + 7 + 6 = 21) in 21C1 = 21 ways. ∴ Reqd probability = 7⁄21 = 1⁄3 Answer E #### E QUESTION:Find a a prime number the options below. options: A)78 B)80 C)81 D)82 E)83 SOLUTION:Clearly, 83 is a prime number. E #### E QUESTION:Two 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 2:3 and 3:1 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. options: A)99:61 B)99:160 C)61:160 D)61:99 E)99:160 SOLUTION:Vessel A = 300 gallons --> milk = 120, water = 180; Vessel B = 500 gallons --> milk = 375, water = 125; Vessel A + B = 800 gallons --> milk = 495, water 305. The ratio = 495/305 --> reduce by 5 = 99/61. Answer: A. #### A QUESTION:If 1+2+3+...+n=n (n+1), then 3 (1+3+5+....+99)=? options: A)7000 B)7250 C)7500 D)7750 E)6750 SOLUTION:Explanation : To solve this use the formula of AP, Sn= (n/2)(a+l) ................(1) To find n, use => Tn= a+(n-1)d => 99=1+(n-1)2 => n=50 Use value of n in (1) then, Sn = (50/2)(1+99) = 2500 Ans:- 3(Sn) = 7500 Answer : C #### C QUESTION:Set #1 = {A, B} Set #2 = {K, L, M, N, O, P} There 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? options: A)1/6 B)1/3 C)7/12 D)2/3 E)5/6 SOLUTION:So Not a vowel in Set-1 : 1/2 And not a vowel in Ser-2:5/6 Now, 1/2∗5/6=5/12 This is for not a vowel. Then for at least one vowel will be = 1−5/12=7/12 Answer will be C. #### C QUESTION:A trader sells two brands of petrol; one is Extra Premium and other one is speed. He mixes 12 litres Extra Premium with 3 litres of speed and by selling this mixture at the price of Extra Premium he gets the profit of 9.09. If the price of Extra Premium Rs. 48 per litre, then the price of Speed is: options: A)Rs. 38 per litre B)Rs. 42 per litre C)Rs. 28 per litre D)Rs. 28 per litre E)None of These SOLUTION:Solution: Selling price mix EP, = (CP + 9.09% of CP) 48 = 12/11 of CP CP = 44 No, using Alligation method, MCQ Aptitude Profit and Loss11 4:1 Thus, X = 44 Thus, the price of speed brand is Rs. 28/litre. Answer: Option C #### C QUESTION:Two of his favorite buildings are Chicago’s Sears (Willis) Tower and Dubai’s Burj Khalifa. If Burj Khalifa stands at 830 meters high and Sears stands at 527 meters high, how much higher is Burj Khalifa than Sears? options: A)300 B)250 C)130 D)303 E)111 SOLUTION:830-527=303. Answer is D. #### D QUESTION:A 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? options: A)Rs.24028 B)Rs.24000 C)Rs.24003 D)Rs.24029 E)Rs.24029 SOLUTION:Ratio of investments of A and B is (70000 * 12) : (120000 * 6) = 7 : 6 Total profit = Rs. 52000 Share of B = 6/13 (52000) = Rs.24000 Answer: B #### B QUESTION:The sum of the first 40 positive even integers is 1,640. What is the sum of the first 40 odd integers? options: A)1500 B)1600 C)1400 D)1200 E)1000 SOLUTION:Sum of first n even numbers = n(n+1) =1640 Sum of first n odd numbers = n^2 = 40*40 = 1600 (here n=40) Answer : B #### B QUESTION:In May Mrs Lee's earnings were 50 percent of the Lee family's total income. In June Mrs Lee earned 20 percent more than in May. If the rest of the family's income was the same both months, then, in June, Mrs Lee's earnings were approximately what percent of the Lee family's total income ? options: A)55 B)56 C)34 D)78 E)23 SOLUTION:Lets say the Family Income is 100 In May, lee earned 50Family income is 50 In june, Lee earned 20% more than May, so it is (50+20*50/100 = 60) Family Income is same 50 In June Lee's Income percent is 60*100/110 ~ 55 Ans is A #### A QUESTION:If HARD is coded as 1357 and SOFT is coded as 2468 what will 21448 stand for? options: A)SHOOR B)SHOOA C)SHOOT D)SHEOT E)SWOOT SOLUTION:HARD = 1357 => 1=H, 3=A , 5=R , 7=D SOFT = 2468 => 2=S, 4=O , 6=F , 8=T so, 21448 = SHOOT ANSWER:C #### C QUESTION:A person says that their speed while going to a city was 10mph however while returning as there is no much traffic they came with a speed of 15mph. what is their average speed? options: A)12 B)13 C)14 D)15 E)16 SOLUTION:Avg speed= 2xy/x+y Hence Ans: 12 ANSWER:A #### A QUESTION:For all positive integers n and m, the function A(n) equals the following product: (1 + 1/2 + 1/2^2)(1 + 1/3 + 3^2)(1 + 1/8 + 8^2)…(1 + 1/p_n + 1/p_n^2), where p_n is the nth smallest prime number, while B(m) equals the sum of the reciprocals of all the positive integers from 1 through m, inclusive. The largest reciprocal of an integer in the sum that B(25) represents that is NOT present in the distributed expansion of A(5) is options: A)1/3 B)1/5 C)1/6 D)1/7 E)1/8 SOLUTION:For all positive integers n and m, A(n) = (1 + 1/2 + 1/2^2)(1 + 1/3 + 3^2)(1 + 1/5 + 5^2)…(1 + 1/p_n + 1/p_n^2), where p_n is the nth smallest prime number, note:i think there's a typo in the above function, A(n) could be (1 + 1/2 + 1/2^2)(1 + 1/3 +1/3^2)(1 + 1/5 +1/5^2)…(1 + 1/p_n + 1/p_n^2) B(m) = sum of the reciprocals of all the positive integers from 1 through m, inclusive. A(5), here 5 represents the 5th smallest prime number; the 5th smallest prime number is 11 {2, 3, 5, 7, 11, ...} A(5) = (1 + 1/2 + 1/2^2)(1 + 1/3 + 3^2)(1 + 1/5 + 5^2)(1 + 1/7 + 1/7^2)(1 + 1/11 + 11^2) The distributed expansion of A(5) = 1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 +1/7 + 1/9+ 1/10 + 1/11 +1/12 + 1/14+ ... missing numbers are 1/8, 1/13, 1/16, .... B(25) = (1 + 1/2 + 1/3 + 1/4 + ... + 1/16 + 1/17 + ... + 1/25) here the largest reciprocal is 1 and the reciprocals are arranged in descending order based on their values The largest reciprocal that present in B(25) but not in A(5) is 1/3 Answer A #### A 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? options: A)(-5, -3) B)(-5, 3) C)(5, -3) D)(3, -5) E)(3, 5) SOLUTION:The 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? I marked the tricky part in red. It seems c is anegativenumber and d is a positive number. This means Vertex #1 = (c, d) is in QII (that is, negative x and positive y) Vertex #2 = (c, -d) is in QIII (that is, both xy negative) Vertex #3 = (-c, -d) is in QIV (that is y is negative, but x is positive) That means the last vertex should be in the first quadrant --- the only first quadrant point is (5, 3), answer =E. #### E QUESTION:The functions f and g are defined for all the positive integers n by the following rule: f(n) is the number of perfect squares less than n and g(n) is the number of primes numbers less than n. If f(x) + g(x) = 16, then x is in the range: options: A)30 < x < 36 B)30 < x < 37 C)31 < x < 37 D)31 < x < 38 E)32 < x < 38 SOLUTION:f(n) = number of perfect squares less than n 1,4,9,16,25,36 f(25) = 4 f(26)=f(27)=...=f(35)=f(36) = 5 f(37) = 6 g(n) = number of prime numbers less than n 2,3,5,7,11,13,17,19,23,29,31,37 g(31)=10 g(32)=g(33)=...=g(36)=g(37) = 11 g(38)=12 f(x)+g(x)=16 implies that f(x)=5 and g(x)=11. So, x = 32,33,34,35,or36. Answer C, 31 < x < 37. #### C QUESTION:Sam, Suresh and Sanket run a race of 1400 meters. Sam runs twice as fast as Suresh while Suresh runs thrice as fast as Sanket. If Sanket finishes the race by clocking 15 minutes, how far was Suresh from the finish line when Sam must have finished the race? options: A)450 m B)680 m C)700 m D)900 m E)1000 m SOLUTION:Explanation: When Sanket finishes the race in 15 minutes, Suresh & Sam would finish the same race in 5 minutes and 2.5 minutes respectively. Thus, when Sam reaches the ”finish” mark, Suresh must be “half-way” through i.e. 700 meters behind the “finish” line when “Sam” must have finished the race ANSWER C #### C QUESTION:On a summer camp, 25% of the campers paid $110 each, 35% paid $80 each and the rest paid $65 each. What percentage of the total amount paid came from the campers who paid $80? options: A)18% B)21% C)33.35 D)33.3% E)37.5% SOLUTION:let the total no of campers be 100 total amount = (25*110)+(35*80)+(40*65) = 2750+2800+2600= $8150 required percentage = (2800/8150)*100=33.35% C #### C QUESTION:The amount of water (in ml) that should be added to reduce 9 ml. Lotion, containing 50% alcohol, to a lotion containing 45% alcohol, is? options: A)1 B)4 C)5 D)6 E)7 SOLUTION:4.5 4.5 45% 55% 45% ----- 4.5 55% ------? => 5.5 - 4.5 = 1 ml ANSWER:A #### A QUESTION:A single discount equivalent to the discount series of 20%, 15% and 8% is? options: A)37.4 B)31.8 C)31.6 D)31.3 E)31.1 SOLUTION:100*(80/100)*(85/100)*(92/100) = 62.6 100 - 62.6 = 37.4 Answer:A #### A QUESTION:In a rectangular coordinate system, what is the area of a rectangle whose vertices have the coordinates (-9, 1), (1, 1), (1, -8) and (-9, -8)? options: A)72 B)180 C)70 D)90 E)140 SOLUTION:Length of side 1= 9+1=10 Length of side 2= 8+1= 9 Area of rectangle= 10*9= 90 D is the answer #### D <<<Examples ends QUESTION:What is the value of: -9^7 + 9^9 ? options: A) 9^2 B) -18^16 C) 63(9^7) D) -80(9^7) E) 80(9^7) SOLUTION:-9^7 + 9^9 = 9^7 (-1 + 9^2) = 9^7 (-1 + 81) = 80 (9^7), Answer E. #### E

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:In Rwanda, the chance for rain on any given day is 1/2. What is the probability that it rains on 4 out of 6 consecutive days in Rwanda? options: A)4/7 B)3/7 C)15/64 D)4/28 E)28/135 SOLUTION:using Binomial. theorem nCr (p)^r (q)^n-r 6C4 (1/2)^4 (1/2)^r which is 15/64 Answer is C. #### C QUESTION:The average weight of 8 person's 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? options: A)80 kg B)85 kg C)90 kg D)100 kg E)110 kg SOLUTION:Total weight increased = (8 x 2.5) kg = 20 kg. Weight of new person = (65 + 20) kg = 85 kg. B) #### B QUESTION:A 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? options: A)1 B)6 C)7 D)9 E)3 SOLUTION:Speed of train relative to man = 60 + 6 = 66 km/hr. = 66 * 5/18 = 55/3 m/sec. Time taken to pass the men = 110 * 3/55 = 6 sec. Answer: B #### B QUESTION:What is the sum of odd integers from 35 to 55, inclusive? options: A)495 B)1,500 C)1,240 D)1,120 E)1,100 SOLUTION:Number of odd integers = (55-35)/2 + 1 = 20/2 + 1 = 11 Sum of odd integers = (35+55)/2 * 11 = 495 Answer A #### A QUESTION:A jogger jogs at 1/6 of his usual speed. how much % he has to increase speed to reach normal pace of walking options: A)100 B)200 C)300 D)400 E)500 SOLUTION:suppose usual speed is x, then current speed is x/6. to gain normal speed, he has to gain 5x/6 % increase = 100*(5x/6)/(x/6) = 500% ANSWER:E #### E QUESTION:If 1 = 6 2 = 12 3 = 18 4 = 24 5 = 30 Then 6 = ? Hint: Its a logic Riddle not a mathematical riddle options: A)1 B)2 C)3 D)4 E)5 SOLUTION:A 1 As stated 1=6 => 6=1 #### A QUESTION:If December 3rd, 1999 is a Friday, what day is January 7th, 2000? options: A)Wednesday B)Thursday C)Friday D)Saturday E)Sunday SOLUTION:There is difference of 35 days from Dec. 3rd 1999 to Jan. 7th 2000. 35/7 has a remainder of 0. Jan. 7th is: Friday + 0 days = Friday The answer is C. #### C QUESTION:If f(a)=5b, what is the value of (f(a)-f(6b)) ? options: A)32b B)25b C)6a-6b D)3a+2b E)52a SOLUTION:f(a)=5b f(6b) = 30b (f(6b)-f(a)) = 30b-5b = 25b Answer is B #### B QUESTION:A milk man has 30 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: options: A)20% B)25% C)33.33% D)35% E)None of these SOLUTION:Explanation: when 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 30 liters of milk. Therefore, profit percentage = 35 %. Answer: D #### D QUESTION:A merchant sells an item at a 20% discount, but still makes a gross profit of 25 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? options: A)20% B)40% C)56.25% D)60% E)75% SOLUTION:original SP = X Cost =C current selling price = .8x ( 20% discount) .8x = 1.5C (25% profit) x= 1.25/.8 *C x= 12.5/8 C Original selling price is 1.5625C which is 56.25% profit Answer C #### C QUESTION:If a positive integer n is divisible by both 2 and 3, then n must also be divisible by which of the following? I. 6 II. 5 III. 18 options: A)None B)I only C)II only D)I and II E)II and III SOLUTION:A multiple of 2 and 3 is also a multiple of 6, but not necessarily a multiple of 5 or 18. The answer is B. #### B QUESTION:Ayesha's father was 29 years of age when she was born while her mother was 23 years old when her brother three years younger to her was born. What is the difference between the ages of her parents? options: A)2 years B)4 years C)6 years D)8 years E)9 years SOLUTION:Mother's age when Ayesha's brother was born = 23 years. Father's age when Ayesha's brother was born = (29 + 3) years = 32 years. Required difference = (32 - 23) years = 9 years. Answer: Option E #### E QUESTION:If the average of a sequence of consecutive multiple of 18 is 153, and the greatest term is 270, how many terms R in the sequence are smaller than the average options: A)5 B)6 C)7 D)8 E)9 SOLUTION:Let the sequence have N terms starting 18*K --> 18K, 18(K+1), 18(K+2), .... , 18(K+N-1) is the sequence. The sum of the sequence is ---> 18K + 18(K+1) + 18(K+2) + .... + 18(K+N-1) =18*(K+(K+1)+...+(K+N-1)) = 18*(N*(2K+N-1)/2). So the average is 153=[18*(N*(2K+N-1)/2)]/N = 18*(2K+N-1)/2 = 9 *(2K+N-1) ---> by cancelling 9 we get 2K+N-1=17 --> 2K+N=18 ---*). On the other hand, since the greatest term is 270, 18(K+N-1)=270 --> by cancelling 18 we get K+N-1=15 --> K+N=16 ---**). By *), **) we have K=2, N=14. Since 153/18 = 8.5, 18*8<153<18*9. So the number of terms R which are smaller than the average is 18*2, 18*3, ..... ,18*8 ---> 7. The answer is C. #### C QUESTION:If n is an integer, what is the greatest possible value for n that would still make the following statement true: 11*10^n < 1/10 ? options: A)–4 B)–3 C)–2 D)–1 E)0 SOLUTION:Just putting values, the LHS becomes n=0 --> 11 n=-1 --> 11/10 n=-2 --> 11/100 n=-3 --> 11/1000 Anything lower will be smaller than 11/1000. n=-2, equality doesnt hold but it does for n=-3. Answer is B. #### B QUESTION:The area of a square is 4489 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. options: A)5:28 B)5:19 C)5:12 D)5:13 E)43:134 SOLUTION:Let the length and the breadth of the rectangle be l cm and b cm respectively. Let the side of the square be a cm. a2 = 4489 a = 67 L = 2a and b = a - 24 b : l = a - 24 : 2a = 43 : 134 Answer:E #### E QUESTION:The average speed of a car is 1 4/5 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? options: A)300 km B)320 km C)360 km D)390 km E)400 km SOLUTION:Sol. Average speed of a tractor = 25 km / h The speed of a bus in an hour = 25 × 2 = 50 km The speed of a car in an hour = 9/5 * 50 = 90 km So, the distance covered by car in 4 h is 90 × 4 = 360 km Ans.(C) #### C QUESTION:Look at this series: 5.2, 4.8, 4.4, 4, ... What number should come next? options: A)3 B)3.3 C)3.5 D)3.6 E)None SOLUTION:Explanation: In this simple subtraction series, each number decreases by 0.4. Answer: Option D #### D QUESTION:Simple interest on a sum at 4% per annum for 2 years is Rs.80. The C.I. on the same sum for the same period is? options: A)Rs.81.60 B)Rs.160 C)Rs.172 D)Rs.727 E)Rs.728 SOLUTION:SI = 40 + 40 CI = 40 + 40 + 1.6 = 81.6 Answer:A #### A QUESTION:Carmen made a sculpture from small pieces of wood. The sculpture is 2 feet 10 inches tall.Carmen places her sculpture on a base that is 2 inches tall. How tall are the sculpture andbase together? options: A)3.1 feet B)3.2 feet C)3.3 feet D)3.0 feet E)3.5 feet SOLUTION:we know 1 feet =12 inch then 2 feet =24 inch 24+10=34 then 34+2=36 36/12=3.0 feet ANSWER:D #### D QUESTION:There are 4 copies of 5 different pencils. In how many ways can they be arranged on a shelf? options: A)20!/4! B)20!/5(4!) C)20!/(4!)^5 D)20! E)5! SOLUTION:There are 4 copies of 5 different pencils.20!/((4!)^5) Answer - C #### C QUESTION:The 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? options: A)289 cm B)800 cm C)829 cm D)288 cm E)289 cm SOLUTION:Area of the square = s * s = 5(125 * 64) => s = 25 * 8 = 200 cm Perimeter of the square = 4 * 200 = 800 cm. Answer: B #### B QUESTION:The price of pulses has fallen by 18%. How many quintals can be bought for the same amount which was sufficient to buy 16 quintals at the higher price? options: A)20.5 B)22.5 C)19.5 D)18.4 E)32.5 SOLUTION:80% of original price can buy = 16 quintals. Therefore, he can buy ( 16 x 100 )/ 82 = 19.5 quintals at the lower price. ANSWER:C #### C QUESTION:The smallest 2 digit prime number is? options: A)A)11 B)B)13 C)C)19 D)D)113 E)E)None SOLUTION:The smallest 3-digit number is 10, which is divisible by 2. 10 is not a prime number. 11 is a prime number. Hence 11 is the smallest 2-digit prime number. A) #### A QUESTION:In order to obtain an income of Rs. 580 from 15% stock at Rs. 100, one must make an investment of options: A)5363 B)6240 C)8700 D)5600 E)2732 SOLUTION:To obtain Rs. 10, investment = Rs. 100. To obtain Rs. 580, investment = = Rs. 8700. Answer: C #### C QUESTION:The population of a village is 7800. It increases annually at the rate of 18% p.a. What will be its population after 2 years? options: A)10000 B)12000 C)13000 D)10860 E)14400 SOLUTION:Formula : ( After =100 denominator Ago = 100 numerator) 7800 × 118/100 × 118/100 = 10860 D #### D QUESTION:If Leo gains 10 pounds, he will weigh 50% more than his sister Kendra. Currently their combined weight is 160 pounds. What is Leo's current weight? options: A)80 B)86 C)92 D)98 E)104 SOLUTION:L+K = 160 and so K = 160-L L+10 = 1.5K = 1.5(160-L) 2.5L = 230 L = 92 The answer is C. #### C QUESTION:14. The sum and the product of two numbers are 25 and 144 respectively, the difference of the number is? options: A)7 B)9 C)8 D)5 E)4 SOLUTION:x + y = 25 xy = 144 (x- y)2 = (x + y)2 – 4xy (x- y)2 = 625 – 576 => (x – y) = 7 ANSWER: A #### A QUESTION:The length of the bridge, which a train 140 meters long and travelling at 45 km/hr can cross in 30 seconds, is: options: A)230 B)244 C)245 D)238 E)235 SOLUTION:Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time = 30 sec. Let the length of bridge be x meters. Then, (140 + X)/30 = 25/2 ==> 2(140 + X) = 750 ==> X = 235 m. Answer: Option E #### E QUESTION:According 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 6 - ounce cans of the concentrate are required to prepare 200 6-ounce servings of orange juice? options: A)25 B)34 C)50 D)67 E)50 SOLUTION:Orange juice concentrate: water::1:3 total quantity of orange juice = 200*6 = 1200 oz so Orange juice concentrate: water :: 300 oz:900 oz no. of 6 oz can = 300 oz/6 oz = 50 Answer E, 50 cans #### E QUESTION:Exactly four sides of a certain 10-sided die are red. What is the probability that Kumar rolls the die 3 times and the die lands with a red side up for the first time on the third roll? options: A)0.3 B)0.2 C)0.01 D)0.148 E)0.144 SOLUTION:Total no. of sides = 10 Sides that are red = 4 Probability that the die lands with red side up = 4/10 Therefore, Probability that the die does not land with red side up = 1 - 4/10 = 6/10 Probability that Kumar rolls the die 3 times and the die lands with a red side up for the first time on the third roll = (1st roll - non red face) X (2nd roll - non red face) X (3rd roll - red face) = (6/10) X (6/10) X (4/10) = 144/1000 = 0.144 E #### E QUESTION:What distance will be covered by a bus moving at 36 kmph in 30 seconds? options: A)287 B)600 C)289 D)300 E)207 SOLUTION:36 kmph = 36 * 5/18 = 10 mps D = Speed * time = 10 * 30 = 300 m. Answer:D #### D QUESTION:The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is: options: A)247 m B)256 m C)245 m D)527 m E)725 m SOLUTION:Speed = [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. Answer:C #### C QUESTION:In a college, the ratio of the number of boys to girls is 8 : 5. If there are 300 girls, the total number of students in the college is options: A)420 B)520 C)620 D)780 E)820 SOLUTION:Explanation: Let the boy are 8x and Girls are 5x => 5x = 300 => x = 60 Total students = 8x+5x = 13x = 13(60) = 780 Option D #### D QUESTION:A 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? options: A)18:11 B)18:18 C)18:22 D)18:39 E)18:39 SOLUTION:Explanation: A 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. A : B 8000*18 : (8000*4) + (4000*14) 14400 : 88000 A:B = 18:11 Answer:A #### A QUESTION:72 hens cost Rs. __ 96.7__. Then what does each hen cost, where two digits in place of ‘__’ are not visible or are written in illegible hand? options: A)Rs. 3.23 B)Rs. 5.11 C)Rs. 5.51 D)Rs. 7.22 E)None SOLUTION:Explanation : The best way to solve this question is to multiply the alternatives by 72 and find which one gives the middle three digits 96.7. To cut time, you can choose to multiply 72 by integer values only, e.g. 72 × 3 = 216, 72 × 5 = 360 and 72 × 7 = 504. It must be remembered that the decimal part of the answer will be multiplied by 72 and the actual answer will increase . Let us now roughly multiply the decimal values of the options also by 72, e.g. 72 x 0.2 = 14.4, 72 × 0.1 = 7.2 and 72 × 0.5 = 36. So, option (1) will yield (216 + 14) = 230 (approximately), option(2) will yield (360 + 7) = 367 (approximately), option(3) will yield (360 + 36) = 396 (approximately), and option(4) will yield (504 + 14) = 528 (approximately). Of these only option (3) satisfies our requirement of 2nd and 3rd digits being 96. Answer : C #### C QUESTION:If points A and B are (8-3) units apart, which of the following can have only one possible value? I. The area of a square region with side AB II. The circumference of a circle passing through points A and B III. The area of a rectangular region with diagonal AB options: A)I only B)II only C)III only D)I and II only E)I and III only SOLUTION:I. The area of a square region with side AB --> side=AB=(8-3) or 5 --> the area of a square is 5^2=25, so only one possible value; II. The circumference of a circle passing through points A and B --> circle is not defined by only two points, hence the circumference of a circle passing through points A and B can take infinitely many values. For example consider when AB=diameter and when points A and B are not the endpoints of the diameter; III. The area of a rectangular region with diagonal AB --> consider the case when AB is the diagonal of a square (the area is 25/2) and the case when AB is the diagonal of a rectangle with the sides equal to 3 and 4 (the area 12). Answer: A. #### A QUESTION:How many seconds will a 500 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? options: A)299 meters B)278 meters C)500 meters D)276 meters E)299 meters SOLUTION:Let length of tunnel is x meter Distance = 800+x meter Time = 1 minute = 60 seconds Speed = 78 km/hr = 78*5/18 m/s = 65/3 m/s Distance = Speed*Time 800+x = (65/3) * 60 800+x = 20 * 65 = 1300 x = 1300 - 800 = 500 meters Answer: C #### C QUESTION:If X gets 25% more than Y and Y gets 20% more than Z, the share of Z out of Rs. 740 will be: options: A)Rs. 300 B)Rs. 200 C)Rs. 240 D)Rs. 350 E)None of these SOLUTION:Z share = Z, Y = 1.2Z X = 1.25×1.2Z, X+Y+Z =740 (1.25× 1.2+1.2+1)Z=74 3.7Z=740, Z=200 Answer: . B. #### B QUESTION:What is the sum of all three digit integers formed using the digits 1, 2, and 3 (repetition is allowed) options: A)4443 B)5980 C)5992 D)5990 E)5994 SOLUTION:n = 3*3*3 = 27 <x> = (333 + 111) / 2 = 222 Sum = number of integers x average value n * <x> = 27 * 222 = 5994 answer = E #### E QUESTION:A and B invests Rs.8000 and Rs.9000 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? options: A)32 : 48 B)32 : 42 C)32 : 45 D)32 : 41 E)42 : 45 SOLUTION:Explanation: A : B (8000*4)+(4000*8) : (9000*6)+(6000*6) 64000 : 90000 32 : 45 Answer:C #### C QUESTION:A 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? options: A)288 B)266 C)120 D)287 E)212 SOLUTION:Speed = (12/10 * 60) km/hr = (72 * 5/18) m/sec = 20 m/sec. Length of the train = 20 * 6 = 120 m. Answer: C #### C QUESTION:At what rate p.a a sum of Rs. 2400 will become Rs. 3600/- in 5 years. options: A)10% B)15% C)20% D)12% E)23% SOLUTION:Explanation: principal P = 2400/- Rate of interest R = ? Time T = 5 years Accumulated Amount A = Rs.10400/- A = P + I A = P + PTR/100 A = P(1+ TR/100) 2400[ 1 + (5 x R)/100] = 3600 2[(20 + R)/20] = 3 20 + R = 30 R = 10% Answer: Option A #### A QUESTION:A man can row upstream at 25 kmph and downstream at 39 kmph, and then find the speed of the man in still water? options: A)22 B)37 C)32 D)27 E)18 SOLUTION:US = 25 DS = 39 M = (39 + 25)/2 = 32 Answer:C #### C QUESTION:A 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? options: A)1.5 B)2 C)2.5 D)3 E)3.5 SOLUTION:10 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 #### A QUESTION:Seven children — A, B, C, D, E, F, and G — 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 R are there for the children? options: A)240 B)480 C)720 D)1440 E)3600 SOLUTION:MAGOOSHOFFICIAL SOLUTION: First, we will consider the restricted elements — children ABG have to be in three seats in a row. How many “three in a row” seats are there in a row of seven seats? X X X _ _ _ _ _ X X X _ _ _ _ _ X X X _ _ _ _ _ X X X _ _ _ _ _ X X X There are five different “three in a row” 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 — just those two orders. This means the total number of configurations for these three children is 5*2 = 10. Now, 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 — that’s a permutation of the 4 items —- 4P4 = 4! = 24. For any single configuration of ABG, there are 24 ways that the other children could be seated in the remaining seats. Finally, we’ll combine with the Fundamental Counting Principle. We have 10 ways for the first three, and 24 ways for the remaining four. That’s a total number of configurations R of 24*10 = 240. Answer = A #### A QUESTION:4 professors and 6 students are being considered for membership on a supervisory committee which must consist of 3 people. If the committee has to include at least 2 professor, how many ways can this committee be formed? options: A)36 B)64 C)72 D)80 E)100 SOLUTION:you count up combinations twice. 4*9*8... and let me name 6 with students A,B,C,..,F after choosing a professor, when you choose Student A and B, you can choose A first, then B. Or B first, then A. Both combination are same. I don't think that's the only mistake. 64 is a factor of = 2^2*4^2 144 is a factor of = 2^4*3^2. These are very different numbers and you cannot divide 144 with something to get to 64. #### B QUESTION:The first republic day of the India was celebrated on 26th January,1950. It was options: A)221 B)28 C)276 D)20 E)22 SOLUTION:1-1-1 AD fall on Monday. We calculate the number of odd days till 24th december, 1995. Number of odd days till 1600 years = 0 1601 to 1700 = 5 1701 to 1800 = 5 1801 to 1900 = 5 49 years contains = 37 normal + 12 leap years =12 × 2 + 37 = 61 odd days = 61/7 = 5 odd days 25th January 1950 = 25/7 = 4 odd days Total odd days =15 + 5 + 4 = 24/7 = 3 odd days So 26th January,1950 is Thursday Answer:B #### B QUESTION:If 15% of 40 is greater than 25% of a number by 2, the number is options: A)14 B)16 C)18 D)20 E)22 SOLUTION:Explanation: 15/100 * 40 - 25/100 * x = 2 or x/4 = 4 so x = 16 Option B #### B QUESTION:For how many integer values of n will the value of the expression 4n + 7 be an integer greater than 1 and less than 60? options: A)10 B)15 C)8 D)12 E)20 SOLUTION:4n+7 > 1 4n> -6 n > -(3/2) n> -1.5 (n = -1, 0, 1 ,2 3........ upto infinity) From second constraint 4n+7 < 60 4n< 53 n < 13. 25 n = (-infinity, .......-3, -2, -1, 0, 1, 2, .........upto 13) Combining the two -1.5 < n<13.25 n = 1 to 13 (48 integers) and n = -1 and 0 so 15 integers. B #### B QUESTION:For 1rs 4p interest wat will be for 5000rs? options: A)350Rs B)450Rs C)200Rs D)30Rs E)448Rs SOLUTION:For 1rs , 4p interest for 5000rs, x x= 5000/1 * 4p ==> 20000 paise To express in rs, 20000/100 = 200rs ANSWER:C #### C QUESTION:If n is the product of the integers from 1 to 20 inclusive, what is the greatest integer k for which 2k2k is a factor of n? options: A)10 B)12 C)15 D)18 E)20 SOLUTION:There are 10 numbers divisible by 2 There are 5 numbers divisible by 4 There are 2 numbers divisible by 8 There is 1 number divisible by 16. Hence the total number of 2’s in 20! are 10+5+2+1=18 ANSWER:D #### D QUESTION:Four hundred multiples of seven are chosen at random, and 100 multiples of eight are chosen at random. Approximately what percentage of the 500 selected numbers are odd? options: A)20% B)25% C)40% D)50% E)80% SOLUTION:About half the multiples of seven will be odd while all the multiples of eight are even. The percentage of odd numbers is about (1/2)(400) / 500 = 40% The answer is C. #### C QUESTION:The compound ratio of 2/3, 6/7, 1/3 and 1/8 is given by? options: A)1/48 B)1/42 C)1/40 D)1/41 E)1/43 SOLUTION:2/3 * 6/7 * 1/3 * 1/8 = 1/42 Answer: B #### B QUESTION:A 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 : options: A)13 1/3 days B)16 days C)15 days D)20 days E)30 days SOLUTION:C alone can finish the work in 80 days. (A + B)can do it in 20 days (A + B)s 1 days wok = 1/20. As 1 days work : Bs 1 days Work = 1/2 : 1 = 1:2. A’s 1 day’s 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 (A+B+c)S 1 day’s work = (1/60) + (1/30) + (1/80) = 1/16 All the three together will finish it in 16 days. ANSWER:B #### B QUESTION: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? options: A)187 B)180 C)289 D)216 E)279 SOLUTION:Length of the train be ‘X’ X + 120/15 = X + 180/18 6X + 720 = 5X + 900 X = 180m Answer:B #### B QUESTION:Today is Monday. After 61 days, it will be: options: A)SUNDAY B)SATURSDAY C)FRIDAY D)THURSDAY E)MONDAY SOLUTION:Each day of the week is repeated after 7 days. So, after 63 days, it will be Monday. After 61 days, it will be Saturday. Answer: Option B #### B QUESTION:The areas, in kilometers squared, of some countries are given below. USA: 9,629,091, Russia: 19,098,242, China: 9,598,094, Canada: 9,984,670, the UK: 242,400 and India: 3,287,263. What is the difference between the areas of Russia and China? options: A)5,476,811 kilometers squared B)9,500,148 kilometers squared C)9,843,123 kilometers squared D)1,878,965 kilometers squared E)4,787,900 kilometers squared SOLUTION:he difference between the areas of Russia and China is given by 19,098,242 - 9,598,094 = 9,500,148 kilometers squared correct answer B #### B QUESTION:There are 5 men and 11 women. In how many ways one can select a group of 6 with at-least 3 men? options: A)1932 B)1933 C)1934 D)1935 E)1936 SOLUTION:(5c3*11c3)+(5c4*11c2)+(5c5*11c1) 1936 ANSWER:E #### E QUESTION:At the end of a business conference the ten people present all shake hands with each other once. How many handshakes will there be altogether ? options: A)20 B)45 C)55 D)90 E)85 SOLUTION:Explanation: Clearly, total number of handshakes = (9+ 8 + 7 + 6 + 5 + 4 + 3 + 2+1) = 45. Answer: B #### B QUESTION:When 732 is subtracted form the square of a number, the answer that is obtained is 5280. What is the number? options: A)228 B)103 C)286 D)122 E)102 SOLUTION:Explanation: Let the number be x x2 - 732 = 5280 x2 = 5280 + (70+3)2 = 5280 + 4900 + 420 + 9 = 10609 = 10000 + 2(100)(3) + 32 = (100 + 3)2 x = 100 + 3 = 103. Answer: B #### B QUESTION:For 2consecutive yrs, my incomes are in the ratio of 4:7 and expenses in the ratio of 3:5. If my income in the 2nd yr is Rs. 42000 & my expenses in the first yr in Rs.21000, my total savings for the two-year is options: A)Rs. 8000 B)Rs. 9000 C)Rs. 9900 D)Rs. 98900 E)Rs. 10000 SOLUTION:Sol. Income in first year = * x 42000 = Rs. 24000 Expenses in second year = \ x 21000 = Rs. 35000 Total savings = Total income - Total expenses = (42000 + 24000)- (21000 + 35000) = 66000 - S6000 = Rs. 10000 E #### E QUESTION:A 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? options: A)$500 B)$1000 C)$2000 D)$3000 E)5000 dollar SOLUTION:Explanation: In scientific notation 240 million is 2.4x10^8. So the per capita expenditure was: ($1.2x10^12)/(2.4x10^8)=($1.2)/(2.4)x10^12-8=$0.5x10^4=$5000 Answer: Option E #### E QUESTION:Klaudia can choose any two of four different candles and any 8 of 9 different flowers for a centerpiece arrangement. Given these choices, how many candle + flower groupings can she select? options: A)54 B)72 C)96 D)144 E)432 SOLUTION:Klaudia can choose any two of four different candles and any 8 of 9 different flowers for a centerpiece arrangement.2 candles from 4 candles: 4C2: 6 8 flowers from 9 flowers: 9C8 : 9 So total grouping 9*6= 54. Answer is A. #### A QUESTION:A number x is 4 times another number y. The percentage that y is less than x is options: A)12.5% B)75% C)80% D)11% E)1% SOLUTION:Say y=1 and x=4. Then y=1 is less than x=4 by (4-1)/4*100=3/4*100=75%. Answer: B. #### B <<<Examples ends QUESTION:During 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‟s total per-gallon discount is what percent of Kim‟s total per-gallon discount? options: A)80% B)107% C)116.7% D)120% E)140% SOLUTION:Kim 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%. Isabella purchased 25 gallons of gas. She paid for 5 + 0.9*20 = 23 gallons, so the overall discount she got was .5/25 = 8%. 8 is 8/7.5*100 = 107% of 7.5. Answer: B. #### B

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:Jerry’s average (arithmetic mean) score on the first 3 of 4 tests is 81. If Jerry wants to raise his average by 2 points, what score must he earn on the fourth test? options: A)87 B)89 C)90 D)93 E)95 SOLUTION:Total score on 3 tests = 81*3 = 243 Jerry wants the average to be = 83 Hence total score on 4 tests should be = 83*4 = 332 Score required on the fourth test = 332 - 243 = 89 Option B #### B QUESTION:Find a a prime number the options below. options: A)78 B)80 C)81 D)82 E)83 SOLUTION:Clearly, 83 is a prime number. E #### E QUESTION:A bicyclist travels uphill from town A to town B for 2 hours at an average speed of 5 miles per hour and returns along the same road at an average speed of 6 miles per hour. What is the bicyclist’s average speed for the round trip, in miles per hour? options: A)(a) 60/11 B)(b) 5 C)(c) 26/5 D)(d) 27/5 E)(e) 28/5 SOLUTION:from the uphill we can find out the distance = 5*2 = 10 average speed = total distance/total time = 20/ (2+ (10/6)) = 60/11 Answer is A. #### A QUESTION:A shopping mall give 40% sale on T-shirts and increase 25% price of pants. The cost price of pants and T-shirts are 1500 and 400 respectively. Overall they makes a? options: A)200 B)250 C)300 D)215 E)180 SOLUTION:Let the SP of the pants and T-shirts be Rs. p and Rs. t respectively. p = 1500(1 + 25/100) = 1500 + 375 t = 400(1 - 40/100) = 400 - 160 Total SP - Total CP = p + t - (1500 + 400) = 375 - 160 = Rs. 215 As this is positive, an overall profit of Rs. 500 was made. Answer: D #### D QUESTION:When the positive integer c is divided by 11, the quotient is d and the remainder 3. When c is divided by 19, the remainder is also 3. What is the remainder when d is divided by 19? options: A)4 B)3 C)2 D)1 E)0 SOLUTION:Any Number which when divided by divisor d1,d2, etc. leaving same remainderrtakes the form ofK+r where k = LCM (d1,d2) In this case the divisors are 1119 and remainder is 3. so LCM (11,19) = 209 So N= 209+3 = 212 Also c=d1q+3 ; which means d1q=209d1=11 therefore q=19 And ( d divided by 19)19/19 leaves remainder 0. Answer is E #### E QUESTION:Tom and Bob have a total of 49 toys. If Bob has 5 more toys than Tom, how many toys does each one have? options: A)27 B)32 C)43 D)54 E)77 SOLUTION:If 5 toys are taken out of 49 toys and the remaining ones distributed to Tom and Bob, they will both have equal numbers of toys 49 - 5 = 44 for Tom and Bob If distributed equally, each one will have 44 / 2 = 22 toys Bob has 5 more toys than Tom, so Bob has 22 + 5 = 27 toys correct answer A #### A QUESTION:The 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? options: A)9 B)4 C)8 D)5 E)3 SOLUTION:S = 4 M = x DS = x + 4 US = x - 4 6/(x + 4) + 6/(x - 4) = 2 x = 8 Answer:C #### C QUESTION:In an exam, a candidate secured 504 marks our of the maximum mark of M. If the maximum mark M is converted into 800 marks, he would have secured 384 marks. What is the value of M? options: A)278 B)2890 C)270 D)2702 E)1050 SOLUTION:504/M = 384/800 (504 * 800) / 384 = M M = 1050 Answer:E #### E QUESTION:The average temperature for Wednesday, Thursday and Friday was 40oC. The average for Thursday, Friday and Saturday was 41oC. If temperature on Saturday was 42oC, what was the temperature on Wednesday? options: A)39oC B)44oC C)38oC D)41oC E)None SOLUTION:Solution: Average temperature for Wednesday, Thursday and Friday = 40oC Total temperature = 3*40 = 120oC Average temperature for Thursday, Friday and Saturday = 41oC Total temperature = 41*3 = 123oC Temperature on Saturday = 42oC Now, (Thursday + Friday + Saturday) - (Wednesday + Thursday + Friday) = 123-120; Saturday - Wednesday = 3 Wednesday = 42-3 = 39oC. Answer: Option A #### A QUESTION:If grapes are 92% water and raisins are 20% water, then how much did a quantity of raisins, which currently weighs 15 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.) options: A)25 pounds B)46 pounds C)150 pounds D)100 pounds E)146 pounds SOLUTION:Since 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*15 --> x = 150. Answer: C. #### C QUESTION:The sum of two numbers is 16. The difference is 4. What are the two numbers?Let x be the first number. Ley y be the second number x + y = 16 x - y = 4 options: A)10 and 6 B)10 and 5 C)10 and 4 D)10 and 3 E)10 and 2 SOLUTION:Solution Let x be the first number. Ley y be the second number x + y = 16 x - y = 4 Solve the system of equations by elimination Adding the left sides and the right sides gives: x + x + y + -y = 16 + 4 2x = 20 x = 10 Since x + y = 16, 10 + y = 16 10 + y = 16 10 - 10 + y = 16 - 10 y = 6 The numbers are 10 and 6 Answer A #### A QUESTION:If y ≠ 3 and 2a/y is a prime integer greater than 2, which of the following must be true? I. xa= y II. y = 1 III. a and y are prime integers. options: A) None B) I only C) II only D) III only E) I and II SOLUTION:Note that we are asked which of the following MUST be true, not COULD be true. For such kind of questions if you can prove that a statement is NOT true for one particular set of numbers, it will mean that this statement is not always true and hence not a correct answer. So we should try to make the listed statements not true for some x and y (which satisfy y≠3 and 2x/y=prime>2). I. a = y --> not necessarily true: a=3 and y=2 (2a/y=3=prime>2); II. y=1 --> not necessarily true: a=3 and y=2 (2a/y=3=prime>2); III. a and y are prime integers --> not necessarily true: a=10 and y=4 (2a/y=5=prime>2). Answer: A. #### A QUESTION: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 85. Find the third number? options: A)A)37 B)B)85 C)C)48 D)D)43 E)E)84 SOLUTION:Let the numbers be 5x, 6x, 7x. Largest number = 7x. Smallest number = 5x. Third number = 6x. 7x + 5x = 6x + 85 6x = 85 => third number is 85. Answer: Option B #### B QUESTION:How many words can be formed by using all letters of the word ‘DESK’ ? options: A)16 B)20 C)24 D)28 E)32 SOLUTION:The word contains 4 different letters. The number of permutations is 4! = 24 The answer is C. #### C QUESTION:If 2994 ÷ 14.5 = 179, then 29.94 ÷ 1.45 = ? options: A)17.1 B)17.3 C)17.5 D)17.7 E)17.9 SOLUTION:29.94/ 1.45 = 299.4/14.5 = (2994/14.5) x 1/10) [ Here, Substitute 179 in the place of 2994/14.5 ] = 179/10 = 17.9 Answer is E. #### E QUESTION:A circular 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? options: A)Rs.45 B)Rs.48 C)Rs.44 D)Rs.43 E)Rs.41 SOLUTION:π (152 - 132) = 176 176 * 1/4 = Rs.44 Answer:C #### C QUESTION:Two 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 6 sec. What is the length of the fast train? options: A)27 7/6 B)27 7/5 C)277/2 D)300/9 E)27 7/1 SOLUTION:Relative speed = (40 - 20) = 20 km/hr. = 20 * 5/ 18 = 50/9 m/sec. Length of faster train = 50/9 * 6 = 300/9 = 300/9 m. Answer:D #### D QUESTION:The 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? options: A)18/35 B)18/18 C)18/19 D)18/17 E)18/12 SOLUTION:If both agree stating the same fact, either both of them speak truth of both speak false. Probability = 3/5 * 4/7 + 2/5 * 3/7 = 12/35 + 6/35 = 18/35 Answer:A #### A QUESTION:In a hotel, 60% had vegetarian lunch while 30% had non-vegetarian lunch and 15% had both type of lunch. If 96 people were present, how many did not eat either type of lunch ? options: A)27 B)26 C)25 D)24 E)20 SOLUTION:Explanation: n(A)=(60/100∗96)=288/5 n(B)=(30/100∗96)=144/5 n(A∩B)=(15100∗96)=72/5 People who have either or both lunch n(A∪B)=288/5+144/5−72/5 =360/5=72 So People who do no have either lunch were = 96 -72 = 24 ANSWER IS D #### D QUESTION:Seed mixture X is 40 percent ryegrass and 60 percent bluegrass by weight; seed mixture Y is 25 percent ryegrass and 75 percent fescue. If a mixture of X and Y contains 32 percent ryegrass, what percent of the weight of this mixture is X ? options: A) 10% B) 33.33 % C) 46.66% D) 50% E) 66.66 % SOLUTION:---------------->Ryegrass X--------------> 40% Y--------------> 25% M(mixture)---->32% 0.4X + (M-X)0.25 = 0.32M 0.15X = 0.07M X = 0.4666M X = 46.66% of M C #### C QUESTION:Let f(x) = x^2 + bx + c. If f(4) = 0 and f(-3) = 0, then b + c = options: A)18 B)15 C)-13 D)-21 E)-24 SOLUTION:f(x) = x^2 + bx + c. If f(4) = 0 and f(-3) = 0, then b + c = f(4) = 0= 16+4b+c--- Taking 16 to the other side -> 4b+c= -16 f(-3) = 0= 9-3b+c --- taking -3b+c to the other side -> 3b-c=9 When we add these 2 equations, we get 7b= -7---> b= -1 And while substituting b= -1 we get c= -12. b+c= -13--- Answer C #### C QUESTION:When 1/10 percent of 3,000 is subtracted from 1/10 of 3,000, the difference is options: A)2970 B)297 C)2997 D)300 E)30 SOLUTION:(1/10)*3000 - (1/10)%*3000 = 300 - (1/1000)*3000 = 300 - 3 = 297 The answer is B. #### B QUESTION:The 19th of September 1987 was a Saturday. If 1988 was a leap-year, what day of the week was the 26th of September 1990? options: A)Monday B)Tuesday C)Wednesday D)Thursday E)Friday SOLUTION:19th September 1987: Saturday 1988: Monday (due to leap year) 1989: Tuesday 1990: Wednesday Hence 26th September was a Wednesday. The answer is C. #### C QUESTION:If f(c)=c^2 and c is a positive integer, which of the following CANNOT be the value of f(f(c))? options: A)81 B)16 C)300 D)256 E)625 SOLUTION:f(c)=c^2 f(f(c)) = (c^2)^2 = c^4 Therefore f(f(c)) will be numbers that are 4th power of other numbers. Checking the options: 81 = 3^4 16 = 2^4 300. This cannot be written as the 4th power of any number 256 = 4^4 625 = 5^4 Answer: C #### C QUESTION:If n is an integer greater than 8, which of the following must be divisible by 8 ? options: A)n(n + 5)(n – 6) B)n(n + 2)(n – 1) C)n(n + 1)(n – 4) D)n(n + 3)(n – 5) E)n(n + 5)(n – 6) SOLUTION:If n= 9 , then (n-1) is divisible by 8 . B #### B QUESTION:A student completes a 3 part exam as follows. The student completes sections A in 6 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? options: A)7:1 B)9:2 C)8:3 D)5:2 E)6:1 SOLUTION:The time spent on section B and section C is 27 minutes each. The ratio of C to A is 27:6 = 9:2 The answer is B. #### B QUESTION:A sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 854 in 4 years. The sum is : options: A)700 B)690 C)650 D)698 E)728 SOLUTION:Explanation : Simple Interest (SI) for 1 year = 854-815 = 39 Simple Interest (SI) for 3 years = 39 × 3 = 117 Principal = 815 - 117 = Rs.698 Answer : Option D #### D QUESTION:A sum of money is put out at compound interest for 2 years at 20%. It would fetch Rs.482 more if the interest were payable half-yearly, then it were pay able yearly. Find the sum. options: A)2200 B)1897 C)8799 D)2000 E)2782 SOLUTION:P(11/10)4 - P(6/5)2 = 482 P = 2000 Answer: D #### D QUESTION:There are two inlets and one outlet to a cistern. One of the inlets takes 4 hours to fill up the cistern and the other inlet takes twice as much time to fill up the same cistern. Both of the inlets are turned on at 8:30 AM with the cistern completely empty, and at 10:30AM, the outlet is turned on and it takes 1 more hour to fill the cistern completely. How much time does the outlet working alone takes to empty the cistern when the cistern is full? options: A)2 hours B)2.5 hours C)3 hours D)3.5 hours E)8 hours SOLUTION:The combined inflow rate of the two inlets is 1/4 + 1/8 = 3/8 cistern/hour. Thus, working together, it takes 8/3 hours (time is reciprocal of rate) to fill the cistern. From 8:30 AM to 10:30 AM, so in 2 hours, the inlet pipes will fill (time)*(rate) =2*3/8 = 3/4 th of the cistern . Then the outlet is turned on and the remaining 1/4 th of the cistern is filled in 1 hour. Letting x to be the rate of the outlet, we would have: 3/8 - x = 1/4 --> x = 1/8 cistern/hour, which means that it takes 8 hours the outlet working alone to empty the cistern. Answer: E. #### E QUESTION:A 45° -45° - 90° right triangle has hypotenuse of length h. What is the area of the triangle E in terms of h? options: A)h/ √2 B)h/2 C)h/4 D)(h)^2 E)(h)^2/4 SOLUTION:IF...each of the two shorter sides = 3, then the hypotenuse = H = 3(root2). The AREA E= (1/2)(Base)(Height) = (1/2)(3)(3) = 9/2. So we're looking for an answer that = 9/2 when H = 3(root2). There's only one answer that matches... E #### E QUESTION:Which one of the following numbers is exactly divisible by 12? options: A)A)12 B)B)13 C)C)14 D)D)15 E)E)16 SOLUTION:12/12=1 answer is A #### A QUESTION:If 4x + y = 8 and −2x + y = 13, then what is the value of 2x + 2y? options: A)1/7 B)3 C)15 D)21 E)60/7 SOLUTION:4x + y = 8 −2x + y = 13 Adding both the equations --> 2x + 2y = 21 Answer: D #### D QUESTION:A start walking from a place at a uniform speed of 5 kmph in a particular direction. After half an hour, B starts from the same place and walks in the same direction as A at a uniform speed and overtakes A after 1 hour 48 minutes. Find the speed of B. options: A)4.7 kmph B)5.6 kmph C)4 kmph D)7 kmph E)5.3 kmph SOLUTION:Distance covered by A in 30 min = 1 Km B covers extra 1km in 1 hour 48 minutes (9/5 hr) i.e. Relative speed of B over A = 1/(9/5) = 5/9 So the speed of B = Speed of A + 5/9 = 5 + 5/9 = 5.55 Answer B #### B QUESTION:217 + 2.017 + 0.217 + 2.0017 = ? options: A)229.3657 B)229.7563 C)229.6357 D)229.5637 E)221.2357 SOLUTION:217 2.017 0.217 + 2.0017 -------- 221.2357 --------- Answer is E. #### E QUESTION:A runner runs the 40 miles from Marathon to Athens at a constant speed. Halfway through the run she injures her foot, and continues to run at half her previous speed. If the second half takes her 11 hours longer than the first half, how many hours did it take the runner to run the second half? options: A)14 B)15 C)18 D)22 E)33 SOLUTION:The runner runs the first 20 miles at speed v and the second 20 miles at speed v/2. The time T2 to run the second half must be twice the time T1 to run the first half. T2 = 2*T1 = T1+11 T1 = 11 and so T2 = 22. The answer is D. #### D QUESTION:If Tim had lunch at $60.50 and he gave 20% tip, how much did he spend? options: A)$30.60 B)$72.60 C)$70.60 D)$40.60 E)$50.60 SOLUTION:The tip is 20% of what he paid for lunch. Hence tip = 20% of 60.50 = (20/100)*60.50 = $12.1 Total spent 60.50 + 12.1 = $72.6 correct answer B #### B QUESTION:If s,u, and v are positive integers and 2s=2u+2v, which of the following must be true? i. s=0 ii. u is not equal to v iii.u > v options: A)None B)I only C)II only D)III only E)II and III SOLUTION:Notice 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. Given: 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. . Answer: A #### A QUESTION:A constructor estimates that 8 people can paint Mr khans house in 3 days. If he uses 4 people instead of 8,how long will they take to complete the job? options: A)6 B)8 C)3 D)4 E)0 SOLUTION:Explanation: Use formula For a work Members × days = constant 8 × 3 = 4 × a a = 6 so answer is 6 days Answer: A #### A QUESTION:On the number line, if x is halfway between -8 and 4, and if y is halfway between -4 and 6, what number is halfway between x and y? options: A)-1.5 B)-0.5 C)0.5 D)1.5 E)2.5 SOLUTION:x= -2 and y = 1. The answer is B. #### B QUESTION:Rs.2600 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? options: A)s.1200 B)s.1542 C)s.1528 D)s.1540 E)s.1549 SOLUTION:A+B+C = 2600 4A = 3B = 2C = x A:B:C = 1/4:1/3:1/2 = 3:4:6 6/13 * 2600 = Rs.1200 Answer: A #### A QUESTION:In a group of 28 junior high school students, 7 take French, 9 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? options: A)7 B)6 C)9 D)4 E)8 SOLUTION:E 8 Add 7 + 9 + 4 to get 20. Then subtract 21 from the total students ⇒ 28 – 20 = 8. Answer is E #### E QUESTION:A man whose speed is 6.5 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 2.5 kmph, find his average speed for the total journey ? options: A)1 kmph B)5 kmph C)5.5 kmph D)4 kmph E)7 kmph SOLUTION:Explanation: Speed of Man = 6.5 kmph Speed of stream = 2.5 kmph Speed in DownStream = 9 kmph Speed in UpStream = 4 kmph Average Speed = (2 x 9 x 4)/13 = 5.5 kmph. Answer: C #### C QUESTION:A 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 1.5 km long? options: A)1 mins B)3 mins C)8 mins D)6 mins E)4 mins SOLUTION:D = 25 * 60 + 1500 = 3000 m T = 3000/60 * 18/5 = 180 sec = 3 mins Answer: B #### B QUESTION:31 of the scientists that attended a certain workshop were Wolf Prize laureates, and 12 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? options: A)A)11 B)B)23 C)C)24 D)D)29 E)D)36 SOLUTION:lets solve by creating equation.. W = 31.. Total = 50.. Not W = 50 -31= 19.. Now let people who were neither be x, so out of 19 who won Nobel = x+3.. so x+x+3=19 or x=8.. so who won Nobel but not Wolf = x+3 = 11.. But people who won BOTH W and N = 12.. so total who won N = 11+12 = 23.. B #### B QUESTION:The diagonal of a rhombus are 25 m and 50 m. Its area is: options: A)900 B)800 C)700 D)625 E)650 SOLUTION:Area of the rhombus = 1/2 d1d2 = ( 1/2 × 25 × 50 ) Cm(power)2 = 25 × 25 = 625 Cm(power)2 Answer is D. #### D QUESTION:Set R has a mean of 15 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? options: A){11,26} B){18,19} C){16,18} D){16,16} E){14,16} SOLUTION:The lesser the variance( values closer to mean) ,lower the standard deviation. As discussed in question the mean is 15,the values (14,16) are closer than others. Hence Answer : E #### E QUESTION:The price of 10 bat is equal to that of 4 balls. The price of 15 balls and 2 bats together is Rs. 4000. The total price of 12 chairs and 3 balls is: options: A)Rs. 3200 B)Rs. 3500 C)Rs. 3700 D)Rs. 3900 E)Rs. 4000 SOLUTION:Let the cost of a chair and that of a table be Rs. x and Rs. y respectively. Then, 10x = 4y or y = 5 x. 2 15x + 2y = 4000 15x + 2 x 5 x = 4000 2 20x = 4000 x = 200. So, y = 5 x 200 = 500. 2 Hence, the cost of 12 chairs and 3 tables = 12x + 3y = Rs. (2400 + 1500) = Rs. 3900. D) #### D QUESTION:A certain computer manufacturing firm last year produced 80 percent of its computers using parts made by its subsidiary company. If the remaining 10,000 computers were produced using parts purchased from another parts manufacturer, how many computers were produced by the computer manufacturing firm altogether? options: A)60000 B)60100 C)60500 D)50000 E)70000 SOLUTION:80% parts used of subsidary company, so 20% parts used of other companies. Now, 20% parts = 10,000 computers So, 1% parts = 10,000/20 Or, 100% parts = 50,000 computers. Hence answer is (D) #### D QUESTION:The average of four consecutive odd numbers is 24. Find the largest number. options: A)25 B)27 C)29 D)31 E)32 SOLUTION:Explanation: Let the numbers are x, x+2, x+4, x+6, then =>x+(x+2)+(x+4)+(x+6)4=24 =>4x+12)4=24 =>x+3=24=>x=21 So largest number is 21 + 6 = 27 Answer: Option B #### B QUESTION:If the price of an article went up by 20%, then by what percent should it be brought down to bring it back to its original price? options: A)16 2/3% B)16 4/3% C)16 7/3% D)16 6/3% E)16 2/3% SOLUTION:Let the price of the article be Rs. 100. 20% of 100 = 20. New price = 100 + 20 = Rs. 120 Required percentage = (120 - 100)/120 * 100 = 20/120 * 100 = 50/3 = 16 2/3%. Answer:A #### A QUESTION:Three number are in the ratio of 3 : 4 : 5 and their L.C.M. is 600. What is their H.C.F.? options: A)10 B)20 C)30 D)40 E)50 SOLUTION:Let the numbers be 3x, 4x and 5x. Then, their L.C.M. = 60x 60x = 600 x = 10 The numbers are (3 x 10), (4 x 10) and (5 x 10). The H.C.F. is 10. The answer is A. #### A QUESTION:If 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? options: A) (x + 100)/18 B) x/18 C) (100 − x)/18 D) (x − 100)/18 E) 100x/18 SOLUTION:CPI in end of 1967 = 100 CPI in end of 1985 = x Number of years = 18 Average annual increase in CPI R= (x-100)/18 Answer D #### D QUESTION:A 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.5 per sq m? options: A)6500 B)2779 C)2779 D)3900 E)2781 SOLUTION:Area = (l + b – d) d (80 + 60 – 10)10 => 1300 m2 1300 * 5 = Rs.6500 Answer:A #### A QUESTION:Excepting ‘seldom’ which means – rarely, infrequently and not often, is the antonym. options: A)22 B)278 C)267 D)176 E)971 SOLUTION:Answer:D #### D QUESTION:If it is true that x > -3 and x < 7, which of the following must be true? options: A)x > 3 B)x < -7 C)x < 3 D)-3 < x < 7 E)none of the above. SOLUTION:the range is -3 < x < 7 A. x > 3 - no because x can be between -3 < x < 3 B. x < -7 - no because the values of x are always >-7 C. x < 3 - no because x can be between 3 < x < 7 D. -3 < x < 7 - true because x can be between -3 < x < 7 E. none of the above. Answer: D #### D QUESTION:Four of the five parts numbered (a) ,(b) ,(c) (d) and (e) in the following equation are exactly equal. Which of the parts is not equal to the other four? The number of that part is the answer. options: A)2a2 – ab + 3b2 B)(a – b)(2a – 3b) + 4ab C)(a – b)2 + (a2 + ab + 2b2) D)(a + b)2 + (a2 + 2b2 – 3ab) E)(a + b)(a – b) + (2a2 – ab + 4b2) SOLUTION:The other parts are equal to 34. Answer E #### E QUESTION:If Re.1 amounts to Rs.9 over a period of 20 years. What is the rate of simple interest? options: A)49% B)90% C)60% D)40% E)41% SOLUTION:8 = (1*20*R)/100 R = 40% Answer:D #### D QUESTION:10 chess players take part in a tournament. Every player plays twice with each of his opponents. How many games are to be played? options: A)90 B)98 C)35 D)99 E)80 SOLUTION:Though 2*(10C2) 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. The first guy has to play 2 matches with the rest of 9, so he'll play 18 matches. Similarly, second guy has to play with the rest of 8 as his 2 games with the first guy are already played. So he plays 16 matches. This continues like this and the total matches are 18+16+14...+2 18+16+...+2 = 2(9+8+...+1) = 2((9*10)/2) = 9*10 = 90. ANSWER:A #### A QUESTION:How many seconds will a train 100 meters long take to cross a bridge 150 meters long if the speed of the train is 36 kmph? options: A)65 sec B)88 sec C)25 sec D)88 sec E)55 sec SOLUTION:D = 100 + 150 = 250 S = 36 * 5/18 = 10 mps T = 250/10 = 25 sec Answer: C #### C QUESTION:The 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: options: A)Rs. 3500 B)Rs. 3600 C)Rs. 3900 D)Rs. 4000 E)Rs. 4100 SOLUTION:Let the cost of a chair and that of a table be Rs. x and Rs. y respectively. Then, 10x = 4y or y = 5 x. 2 15x + 2y = 4000 15x + 2 x 5 x = 4000 2 20x = 4000 x = 200. So, y = 5 x 200 = 500. 2 Hence, the cost of 12 chairs and 3 tables = 12x + 3y = Rs. (2400 + 1500) = Rs. 3900. C #### C QUESTION:What is the average of xx,2x2x,and 66? options: A)x+2 B)x+2x C)x+2x+2 D)2x+2 E)x+2x-2 SOLUTION:By the definition of an average, we get: x+2x+63=3x+63x+2x+63=3x+63 =3(x+2)3=x+2.=3(x+2)3=x+2. Hence, the answer is x+2x+2 or Option C #### C QUESTION:Cheese, bologna, and peanut butter sandwiches were made for a picnic in a ratio of 4 to 5 to 11. If a total of 120 sandwiches were made, how many bologna sandwiches were made? options: A)15 B)30 C)38 D)42 E)48 SOLUTION:For deciding such task we should calculate all parts 4 + 5 + 11 = 20 parts and we should calculate how many sandwiches holds 1 part: 120 / 20 = 6 sandwiches in one part For bologna we have 7 parts so: 5* 6 = 30 Answer is B #### B QUESTION:When x is even, [x] = x/2 + 1, when x is odd [x] = 2x + 1 then [7]*[8] = ? options: A)[22] B)[44] C)[75] D)[88] E)[90] SOLUTION:[7]*[8]=(7*2+1)(8/2+1) =[75]. Ans -C #### C QUESTION:Ram 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? options: A)2000 B)2879 C)2700 D)2797 E)2761 SOLUTION:(10*10)/100 = 1%loss 100 --- 99 ? --- 1980 => Rs.2000 Answer:A #### A <<<Examples ends QUESTION:What is the units digit of 3333^(333)*3333^(222)? options: A)0 B)2 C)4 D)6 E)8 SOLUTION:Each of the other explanations to this question has properly explained that you need to break down the calculation into pieces and figure out the repeatingpatternof the units digits. Here's another way to organize the information. We're given [(2222)^333][(3333)^222] We can 'combine' some of the pieces and rewrite this product as.... ([(2222)(3333)]^222) [(2222)^111] (2222)(3333) = a big number that ends in a 6 Taking a number that ends in a 6 and raising it to a power creates a nice pattern: 6^1 = 6 6^2 = 36 6^3 = 216 Etc. Thus, we know that ([(2222)(3333)]^222) will be a gigantic number that ends in a 6. 2^111 requires us to figure out thecycleof the units digit... 2^1 = 2 2^2 = 4 2^3 = 8 2^4 = 16 2^5 = 32 2^6 = 64 2^7 = 128 2^8 = 256 So, every 4powers, the pattern of the units digits repeats (2, 4, 8, 6.....2, 4, 8, 6....). 111 = 27 sets of 4 with a remainder of 3.... This means that 2^111 = a big number that ends in an 8 So we have to multiply a big number that ends in a 6 and a big number that ends in an 8. (6)(8) = 48, so the final product will be a gigantic number that ends in an 6. Final Answer: D #### D

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:The HCF and LCM of two numbers m and n are respectively 6 and 210. If m + n = 72, then 1/m + 1/n is equal to options: A)1/35 B)3/35 C)5/37 D)2/35 E)None SOLUTION:Answer We have, m x n = 6 x 210 = 1260 ∴ 1/m + 1/n = (m + n)/mn = 72/1260 = 4/70 = 2/35 Correct Option: D #### D QUESTION:Which of the following must be true? 1) Every prime number greater than 5 can be written as either as 8n+1 or 8n-1 2) Every prime number greater than 5 can be written as 4n+1 or 4n-1 3) Every number greater than 5 of the form 8n+1 or 8n-1 is a prime number. options: A)1,2,3 B)2,3 C)1,2 D)only 1 E)only 2 SOLUTION:Every prime number greater than 3 can be written in the form of 8n+1 or 8n-1 where n is an integer. So 1 can be possible. 3. This is not possible as 2 and 3 are being prime , we can't write then in the form of 8n+1 or 8n-1. C #### C QUESTION:Let x be a positive integer, what is the remainder when 2^(3x+3)+3 is divided by 3? options: A)0 B)1 C)2 D)3 E)4 SOLUTION:For: (2^(3x+3)+3)/3 Let n = 3x + 3 2^n 2^1 = 2 2^2 = 4 2^3 = 8 2^4 = 16 2^5 = 32, last digit pattern repeats 2, 4, 8, 6, 2, .... Rule: x^(m+n) = (x^m)(x^n) (2^(3x))(2^3) Rule: x^(mn) = (x^m)^n ((2^3)^x)(8) => Now, (8)(8) + 3 = (64) + 3 => and, 4 + 2 + 1 => Finally, (6 + 1)/3, and remainder is 1. Answer: B #### B QUESTION:15 + sqrt(- 6 + 8×5÷4) =? options: A)31 B)32 C)33 D)34 E)35 SOLUTION:According to order of operations, inner brackets first where 8x5÷4 is first calculated since it has a multiplication and a division. 8x5÷4 = 40÷4 = 10 Hence 15 + sqrt(- 6 + 8×5÷4) = 15+ sqrt(- 6 + 10) = 15 + sqrt(4) = 15 + 16 = 31 correct answer A)31 #### A QUESTION:If the number 517 * 324 is completely divisible by 3, then the smallest whole number in the place of * will be: options: A)0 B)1 C)2 D)None of these E)Cannot be determined SOLUTION:Explanation: Sum of digits = (5 + 1 + 7 + x + 3 + 2 + 4) = (22 + x), which must be divisible by 3. x = 2. Answer: Option C #### C QUESTION:Two 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? options: A)11 B)60 C)77 D)55 E)12 SOLUTION:Let the speed of the slower train be x m/sec. Then, speed of the train = 2x m/sec. Relative speed = ( x + 2x) = 3x m/sec. (100 + 100)/8 = 3x => x = 25/3. So, speed of the faster train = 50/3 = 50/3 * 18/5 = 60 km/hr. Answer: C #### C QUESTION:Danny 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 192, what is the area of the side face of the box? options: A)13 B)16 C)18 D)29 E)32 SOLUTION:Lets suppose length= l, breadth= b, depth= d Front face area= l*w = 1/2 w*d (l=1/2 d or d=2l) top face area= w*d side face area= w*d = 1.5 d*l (w=1.5l) Volume = l*w*d= 192 l*1.5l*2l= 192 l=4 Side face area= l*d= l*2l= 4*2*4 =32 E is the answer #### E QUESTION:A merchant purchased a jacket for $180 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’s gross profit on this sale? options: A)$0 B)$3 C)$4 D)$12 E)$15 SOLUTION:Let selling price = x So, x = 180 + 25x/100 Calculating above, x = 240 Selling price =240 20% Discount on Selling price = 192 So, profit = 192-180 = 12 Answer = D #### D QUESTION:What should come in place of the question mark (?) in the following equation? 5978 + 6134 + 7014 = ? options: A)19226 B)16226 C)19216 D)19126 E)None of these SOLUTION:? = 5978 + 6134 + 7014 = 19126 Answer D #### D QUESTION:A 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 ? options: A)34 B)40 C)68 D)88 E)None of these SOLUTION:Solution We have : l = 20 ft and lb = 680 sq. ft. So, b = 34 ft. ∴ Length of fencing = (l + 2b) = (20 + 68) ft = 88 ft. Answer D #### D QUESTION:Sonalika goes 12 km towards North from a fixed point and then she goes 8 km towards South from there. In the end she goes 3 km towards east. How far and in what direction is she from her starting point? options: A)5km north east B)4km north east C)5km north west D)6km north east E)6km north west SOLUTION:she is currently at 5km north east from the starting point ANSWER:A #### A QUESTION:Jolene entered an 18-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? options: A)$506.00 B)$726.24 C)$900.00 D)$920.24 E)$926.24 SOLUTION:If 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. Interest earned after the first time interval: $10,000*2%=$200; Interest earned after the second time interval: ($10,000+$200)*3%=$300+$6=$306; Interest earned after the third time interval: ($10,000+$200+$306)*4%=$400+$8+(~$12)=~$420; Total: 200+306+(~420)=~$926. Answer: E. #### E QUESTION:James took a 3-hour bike ride. In the second hour he traveled 6 miles, which was 20 percent farther than he traveled the first hour. If he traveled 25 percent farther in the third hour than he did in the second hour, how many miles did jose travel during the entire ride? options: A)54.0 B)54.9 C)18.5 D)57.0 E)63.0 SOLUTION:Let the distance travelled in the first hour be x. Thus, 1.2x = 6, x = 5. Now, the distance travelled in the 3rd hour = 6+1/4∗6=7.5 The only option ending with a 0.5 in the decimal place is C. ANSWER:C #### C QUESTION:The ages of Rahul and Madhan differ by 16 years. Six years ago, Madhan’s age was thrice as that of Rahul’s,find their present ages options: A)14 years, 30 years B)12 years, 28 years C)16 years, 34 years D)18 years, 38 years E)none of these SOLUTION:Let Rahul’s age = x years So, Madhan’s age = ( x + 16 )years Also, 3(x - 6) = x + 16 - 6 or, x = 14 Rahul’s age = 14 years And, Madhan’s age 14 + 16 = 30 years ANSWER:A #### A QUESTION:There are two taps, which are used to fill the tank and one tap to empty the tank. First tap fill the tank in 10 min., while the second takes quarter of an hour to fill the tank if both are operated independently.Third tap is capable of emptying the tank in seven and a half minutes. If all the taps are opened simultaneously how long (if ever) will it take for the tank to get filled completely? options: A)10 minutes B)20 minutes C)30 minutes D)40 minutes E)50 minutes SOLUTION:Pipe A fills the tank in 10 min Pipe B fills the tank in 15 min Pipe C empties the tank in 15/2 min If all the three opened simultaneously then in 1 min 1/10 + 1/15 - 2/15 of the tank will be filled that means 1/30 th of the tank will be filled in 1 min So it will take 30 minutes to fill the tank completely if all three pipes opened ANSWER:C #### C QUESTION:A ship sails 4 degrees north, then 14 S. then 17 N. then 19 S. and has finally 11 degrees of south latitude. What was her latitude at starting ? options: A)0 B)1 C)2 D)3 E)None of these SOLUTION:Let x = the latitude sought. Then marking the northings +, and the southings -; By the statement x + 4 - 14 + 17 - 19 = -11 And x = 1. Answer B #### B QUESTION:After harvest, out of a total of N apples from an orchard, if 1/4 of those tested had infection A and, of those with infection A, 1/2 also had infection B, how many apples did not have both infection A and B? options: A)N/15 B)7N/8 C)14N/15 D)N/5 E)4N/5 SOLUTION:1/4 of tested had infection A, thus N/4 had infection A; Of those with infection A, 1/2 also had infection B, thus 1/2*N/4 = N/8 had both infections A and B. Therefore, N - N/8 = 7N/8 did not have both infection A and B. Answer: B. #### B QUESTION:What is the difference between the greatest and the smallest five digit numbers formed using the digits 7, 0, 3, 4 and 2 without repeating the digits? options: A)53978 B)53916 C)53961 D)56781 E)None of these SOLUTION:Explanation: The greatest 5 digit number that can be formed using the given digits = 74320 The smallest 5 digit number that can be formed using the given digits = 20342 .: The required difference = 74320 - 20342 = 53978 Answer: Option A #### A QUESTION:A bucket full of nuts was discovered by the crow living in the basement. The crow eats a sixth of the total number of nuts in 4 hours. How many hours i total will it take the crow to finish a quarter of the nuts? options: A)6 B)8 C)10 D)12 E)14 SOLUTION:In one hour, the crow eats 1/24 of the nuts. (1/4) / (1/24) = 6 hours The answer is A. #### A QUESTION:A started a business with 4500 and another person B joined after some period with 3000. Determine this period after B joined the business if the profit at the end of the year is divided in the ratio 2 : 1 options: A)After 3 months B)After 4 months C)After 6 months D)After 2 1⁄2 months E)None of these SOLUTION:Let B joined after x months. Then, 4500 × 12 : 3000 (12 – x) = 2 : 1 Ratio of their investments 4500×12/3000(12−x)=2/1 ⇒ x = 3 Answer A #### A QUESTION:The total of the ages of Amar, Akbar and Anthony is 40 years. What was the total of their ages two years ago ? options: A)71 B)44 C)36 D)16 E)18 SOLUTION:Explanation: Required sum = (40 - 3 x 2) years = (40 - 6) years = 36 years. Answer: C #### C QUESTION:If 2m + n = 7 and m + 2n = 5, then (2m + n)/2 = options: A) 1 B) 7/2 C) 17/5 D) 18/5 E) 4 SOLUTION:2*(m+2m = 5) equals 2m+4n=10 2m+4n=10 - 2m + n= 7 = 3n=3 Therefore n = 1 Plug and solve... 2m + 1 = 7 2m=6 m=3 (6+1)/2= 7/2 B #### B QUESTION:If a number between 0 and 1/2 is selected at random, which of the following will the number most likely be between? options: A)0 and 3/20 B)3/20 and 1/5 C)1/5 and 1/4 D)1/4 and 3/10 E)3/10 and 1/2 SOLUTION:A. 0 and 3/20 - covers 0 to 3/20 but leaves out 3/20 to 10/20. So in essence, covers only 3 parts out of 10 parts B. 3/20 and 1/5 - covers 3/20 to 4/20 (= 1/5). So in essence, covers only 1 part out of 10 parts C. 1/5 and 1/4 - covers 4/20 to 5/20. So in essence, covers only 1 part out of 10 parts D. 1/4 and 3/10 - covers 5/20 to 6/20. So in essence, covers only 1 part out of 10 parts E. 3/10 and 1/2 - covers 6/20 to 10/20. So in essence, covers 4 parts out of 10 parts. Since this range is the widest, so the probability of the number lying in this range is the highest. Answer (E) #### E QUESTION:Running at the same constant rate, 16 identical machines can produce a total of 32 shirt per minute. At this rate, how many shirt could 8 such machines produce in 10 minutes? options: A) 911 B) 100 C) 101 D) 160 E) 785 SOLUTION:Let's take the approach that uses the answer choices to eliminate wasted time. 32/16 = 2 shirt per minute per machine. 8 machines = 16 per minute. 10 minutes worth = 160 shirt. Looking at the answers it is clear...we can only choose (D) THE CORRECT ANSWER IS D. #### D QUESTION:A cycle is bought for Rs.450 and sold for Rs.520, find the gain percent? options: A)18 B)14 C)20 D)15 E)15.55 SOLUTION:450 ---- 70 100 ---- ? => 15.55% Answer: E #### E QUESTION:The present age of a father is 3 years more than three times the age of his son. Five years hence, father's age will be 10 years more than twice the age of the son. Find the present age of the father. options: A)33 B)38 C)27 D)40 E)48 SOLUTION:if the present age be x years. father's will be (3x+3)years.. so, (3x+3+5)=2(x+3)+10 or, x=8 so the fathers present age =(3x+3)=(3*8+3)years =27 years.. ANSWER : OPTION C #### C QUESTION:If a person throw 2 dice simultaneously then find the probability of the sum of dots is 3 multiply ? options: A)1/2 B)1/3 C)2/5 D)7/9 E)1/4 SOLUTION:If 2 dies are thrown E = event of getting a prime number = 12 total number of possible out comes = 36 probability = 12/36 = 1/3 Answer is B #### B QUESTION:365:90::623:? options: A)36 B)45 C)123 D)63 E)none of these SOLUTION:365---3*6*5....90 623---6*2*3....36 answer A #### A QUESTION:When a merchant imported a certain item, he 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 $94.50, what was the total value of the item? options: A)$2,350 B)$2,850 C)$3,250 D)$3,400 E)$3,750 SOLUTION:Let x be the value in excess of $1,000. 0.07x = 94.5 x = $1,350 The total value was $1,350 + $1,000 = $2,350. The answer is A. #### A QUESTION:Which of the following can be expressed as a terminating decimal? options: A)1/25 + 1/35 B)1/225 + 1/1,250 C)1/11,000 + 1/13,000 D)1/75 + 1/35 E)1/125 + 1/8 SOLUTION:In such questions, it is always easier to find an answer instead of eliminating choices. Let us start with the simplest ones first. A. 1/25 + 1/35 = 12/175 = 12/25*1/7 1/7 does is not a terminating decimal. E. 1/125 + 1/8 = 8 + 125/ 1000 = 133/1000 This is a terminating decimal and our answer. Correct Option: E #### E QUESTION:A train 125 m long passes a man, running at 15 km/hr in the same direction in which the train is going, in 10 sec. The speed of the train is? options: A)60 km/hr B)50 km/hr C)36 km/hr D)26 km/hr E)87 km/hr SOLUTION:Speed of the train relative to man = 125/10 = 25/2 m/sec. = 25/2 * 18/5 = 45 km/hr Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 15 = 45 => x = 60 km/hr. Answer:A #### A QUESTION:The 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? options: A)12a.m B)10a.m C)19a.m D)76a.m E)37a.m SOLUTION:D = 110 – 20 = 90 RS = 20 + 25 = 45 T = 90/45 = 2 hours 8 a.m. + 2 = 10 a.m. Answer: B #### B QUESTION:Ratio between Rahul and Deepak is 4:3, After 2 Years Rahul age will be 26 years. What is Deepak present age. options: A)14 B)18 C)20 D)22 E)24 SOLUTION:Explanation: Present age is 4x and 3x, => 4x + 2 = 26 => x = 6 So Deepak age is = 3(6) = 18 Option B #### B QUESTION:Every year an amount increases by 1/8th of itself. How much will it be after two years if its present value is Rs.64000? options: A)81000 B)81027 C)81089 D)81027 E)28939 SOLUTION:64000* 9/8 * 9/8 = 81000 Answer: A #### A QUESTION:One day a car rental agency rented 3/4 of its cars, including 4/5 of its cars with CD players. If 3/5 of its cars have CD players, what percent of the cars that were not rented had CD players? options: A)23/40 B)17/30 C)12/25 D)7/15 E)3/10 SOLUTION:The cars with CD players which were not rented is (1/5)(3/5) = 3/25 of all the cars. The cars which were not rented is 1/4 of all the cars. The percent of non-rented cars which had CD players is (3/25) / (1/4) = 12/25 The answer is C. #### C QUESTION:Jane and Ashley take 10 days and 40 days respectively to complete a project when they work on it alone. They thought if they worked on the project together, they would take fewer days to complete it. During the period that they were working together, Jane took an eight day leave from work. This led to Jane's working for four extra days on her own to complete the project. How long did it take to finish the project ? options: A)10.2 Days B)15.2 Days C)16.2 Days D)18 Days E)20 Days SOLUTION:Let us assume that the work is laying 40 bricks. Jane = 4 bricks per day Ashley = 1 brick per day Together = 5 bricks per day Let's say first 8 days Ashley works alone, No of bricks = 8 Last 4 days Jane works alone, No. of bricks = 16 Remaining bricks = 40 - 24= 16 So together, they would take 16/5 = 3.2 Total no. of days = 8 + 4 + 3.2 = 15.2 Answer is B #### B QUESTION:How many minutes does the minute hand gain in every one hour? options: A)55 B)60 C)65 D)No gain E)None of these SOLUTION:55 ANSWER:A #### A QUESTION:Find the average marks of all the students in 2 separate classes, if the average marks of students in the first class of 55 students is 60 and that of another class of 48 students is 58 options: A)55.1 B)51.1 C)53.1 D)52.1 E)59.1 SOLUTION:Sum of the marks for the class of 55 students = 55 * 60 = 3300 Sum of the marks for the class of 48 students = 48 * 58 = 2784 Sum of the marks for the class of 103 students = 3300 + 2784 = 6084 Average marks of all the students = 6084/103 = 59.1 Answer:E #### E QUESTION:A, 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 1/3rd 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? options: A)1/3 B)2/9 C)9/46 D)7/19 E)1/6 SOLUTION:The first thing to notice is that A is faster than B and B is faster than C. Since 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. If A works for 2 days, B works for 1 day and C works for only 2/3 of the day. Therefore total work done = (2*2) + (1*1) + (1/3*1/3) = 46/9 Proportion of work done by B = (1*1) / (46/9) = 9/46 Hence Answer C. #### C QUESTION:Two 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 ? options: A)3 B)2 C)1/2 D)1/3 E)There isn't enough data to answer the question. SOLUTION:M - N = (M + N)/2 Solving for N/M = 1/3 D #### D QUESTION:If x and y are positive integers greater than 1 such that x – y and x/y are both even integers, which of the following numbers must be non-prime integers? I. x II. x + y III. y/x options: A)I only B)II only C)III only D)I and II E)I ,II and III SOLUTION:Ans: from the conditions given to us we get x>y and the min value of y can be 2 , therefore x will be a multiple of 4 so both I and ii will always be non-prime but iii will not be an integer. Answer (D). #### D QUESTION:If xy > 0, which of the following must be negative? options: A)-x/-y B)x/y C)-x/y D)2xy E)x+y SOLUTION:- / + = - Answer : C #### C QUESTION:If 63 percent of a class answered the first question on a certain test correctly, 49 percent answered the second question on the test correctly, and 20 percent answered neither of the questions correctly, what percent answered both correctly? options: A)22% B)24% C)26% D)28% E)32% SOLUTION:63% answered the first question correctly and 20% answered neither correctly. Then 17% missed the first question but answered the second question correctly. Then the percent who answered both correctly is 49% - 17% = 32%. The answer is E. #### E QUESTION:If a point (x,y) is randomly selected within the square shown in the figure above, (the vertices are on 1,1 1,-1, -1,1 -1,-1) what are the W odds that x^2+y^2>1? options: A)1. pi/4 B)2. W=pi/16 C)3. W=1-pi/4 D)4. W=1-pi/16 E)5.4-pi SOLUTION:area of the square will be 4, and the area of circle with center (0,0) and radius 1 will be pi. then succesful outcomes = 4 - pi (the area where x2+y2 will be greater than 1) total outcomes = 4 therefore probability = (4-pi)/4 C #### C QUESTION:How many diagonals does a 62-sided convex polygon have? options: A)1829 B)2356 C)3458 D)3843 E)4820 SOLUTION:A 62-sided convex polygon has 62 vertices. If 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. If 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 However, we must recognize that we have counted every diagonal twice. To account for counting each diagonal twice, we must divide 3658 by 2 to get 1829. The answer is A. #### A QUESTION:Find out the wrong number in the given sequence of numbers. 1, 2, 6, 15, 31, 55 options: A)55 B)6 C)15 D)31 E)91 SOLUTION:1(result) + (1*1) = 2. 2(result) + (2*2) = 6. 6(result) + (3*3) = 15. 15(result) + (4*4) = 31. 31(result) + (5*5) = 56. Now we are getting 56 not 55.. So 55 is the wrong number of the given. answer : A #### A QUESTION:The 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? options: A)1/64 B)1/9 C)1/16 D)1/25 E)1/2 SOLUTION:There are two cases. All boys and all girls case 1. all boys. 1/2*1/2*1/2*1/2*1/2*1/2*1/2= 1/128 case 2 .all girls. 1/2*1/2*1/2*1/2*1/2*1/2*1/2=1/128 We will add the cases to get 1/64 #### A QUESTION:Seats for Maths, Physics and Biology are in the ratio of 4 : 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? options: A)2 : 3 : 4 B)6 : 7 : 8 C)8 : 15 : 20 D)Cannot be determined E)None of these SOLUTION:Reqd ratio 4 × 140⁄100 : 7 × 150⁄100 : 8 × 175⁄100 = 4 × 140 : 7 × 150 : 8 × 175 = 8 : 15 : 20 Answer C #### C QUESTION:If c and d are prime numbers, which of the following CANNOT be the sum of c and d? options: A)5 B)9 C)13 D)23 E)33 SOLUTION:All answer choices but D are odd. In order odd number to be the sum of two prime numbers one must be even, so 2, and another odd. Now, 23=2+21. Since 21 is not a prime then 23 cannot be written as the sum of two prime numbers. Answer: D #### D QUESTION:A box contains 4 chocobars and 4 ice creams. Tom eats 3 of them, by randomly choosing. What is the probability of choosing 2 chocobars and 1 icecream? options: A)9/3 B)1/7 C)2/8 D)2/7 E)4/7 SOLUTION:Probability of choosing 1 chocobar = 4/8 = 1/2 After taking out 1 chocobar, the total number is 7. Probability of choosing 2nd chocobar = 3/7 Probability of choosing 1 icecream out of a total of 6 = 4/6 = 2/3 So the final probability of choosing 2 chocobars and 1 icecream = 1/2 * 3/7 * 2/3 = 1/7 B #### B QUESTION:If taxi fares were Rs 1.00 for the first 1/5 mile and Rs 0.20 for each 1/5 miles thereafter. The taxi fare for a 3-mile ride was options: A)Rs 1.56 B)Rs 2.40 C)RS 3.00 D)Rs 3.80 E)Rs 4.20 SOLUTION:first 1/5 mile costs = 1.00 remaining miles to be covered = 3-1/5 =14/5, =1/5 +1/5+1/5+.... until 14, hence 14*0.20=2.80 total fare = 2.80 + 1.00 =3.80 ANSWER:D #### D QUESTION:A cistern 9 m long and 6 m wide contains water up to a breadth of 2 m 25 cm. Find the total area of the wet surface. options: A)142 m sqaure B)122 m sqaure C)135 m sqaure D)188 m sqaure E)None of these SOLUTION:Explanation: Area of the wet surface = 2[lb+bh+hl] - lb = 2 [bh+hl] + lb = 2[(6*2.25+9*2.25)]+9*6 = 122 m square Option B #### B QUESTION:Several people are sitting around a round table playing a card game with a deck of 67 cards. Each person is dealt one card per deal, and the cards are dealt in a clockwise fashion. If Martin is dealt both the first card of the deck and the last card of the deck, which of the following could be the total number of people sitting at the table? options: A)4 B)5 C)7 D)11 E)13 SOLUTION:Let n be the number of people at the table. If Martin gets the first and the last card, it means Martin got one more card than the others. Thus 67/n has a remainder of 1 and so 67-1 = 66 is a multiple of n. The answer is D. #### D QUESTION:A 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? options: A)150 m B)200 m C)240 m D)400 m E)150 m SOLUTION:Answer: Option C Speed = [54 * 5/18] m/sec = 15 m/sec. Length of the train = (15 * 20) m = 300 m. Let the length of the platform be x meters. Then, x + 300 / 36 = 15 x + 300 = 540 x = 240 m. #### C QUESTION:Two 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? options: A)22 B)66 C)48 D)77 E)21 SOLUTION:Relative speed = 45 + 30 = 75 km/hr. 75 * 5/18 = 125/6 m/sec. Distance covered = 500 + 500 = 1000 m. Required time = 1000 * 6/125 = 48 sec. Answer:C #### C QUESTION:A shopkeeper sold an article for 240 after giving 20% discount on the labelled price and made 20% profit on the cost price. What would have been the percentage profit,had he not given the discount’? options: A)25% B)50% C)23% D)28% E)None of these SOLUTION:Cost price = 240×100/120= 200 S.P. at no discount = 240×100/80 = 300 ∴ % profit = 100×100/200 = 50 % Answer B #### B QUESTION:In the new budget, the price of rice rose by 20%. By how much percent must a common man reduce his consumption so that his expenditure on it does not increase? options: A)16.66% B)17% C)15.8% D)12% E)None of these SOLUTION:Explanation : Solution: reduction in consumption = [r/(100+r) * 100]% = (20/120 * 100) = 16.66% Answer : A #### A QUESTION:A car runs at the speed of 60 km per hour when not serviced and runs at 80 kmph when serviced. After servicing the car covers a certain distance in 4 hours. How much time will the car take to cover the same distance when not serviced? options: A)6 hours 12 minutes B)5 hours 33 minutes C)8 hours 15 minutes D)7 hours 12 minutes E)None SOLUTION:Explanation : Time = 80*4 / 60 = 5 hours 33 mins Answer – B #### B QUESTION:If grapes are 90% water and raisins are 15% water, then how many kilograms did a quantity of raisins, which currently weighs 12 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.) options: A)96 B)98 C)100 D)102 E)104 SOLUTION:Let x be the original weight of the grapes. The weight of the grape pulp was 0.1x. Since the grape pulp is 85% of the raisins, 0.1x = 0.85(12 kg). Then x = 8.5*12 = 102 kg. The answer is D. #### D QUESTION:A ball is bought for Rs.400 and sold at a gain of 40% find its selling price? options: A)A)Rs.560/- B)B)Rs.490/- C)C)Rs.500/- D)D)Rs.520/- E)E)Rs.540/- SOLUTION:100 % ------> 400 (100 * 4 = 400) 140 % ------> 560 (140 * 4 = 560) Selling price = Rs.560/- A #### A QUESTION:If n divided by 7 has a remainder of 2, what is the remainder when 5 times n is divided by 7? options: A)1 B)2 C)3 D)5 E)6 SOLUTION:As per question => N=7P+2 for some integer p hence 5N => 35Q + 10 => remainder =>10 for some integer Q Alternatively => N=2 > 5N=> 10 => 10 divided by 7 will leave a remainder 3 hence C #### C QUESTION:Joan and Karl each bought a stove and the sum of their purchases was $700. If twice of what Joan paid was $80 more than what Karl paid, what did Joan pay for her stove? options: A)$240 B)$260 C)$280 D)$300 E)$320 SOLUTION:J+K=700 so K=700-J 2J=K+80 2J=(700-J)+80 3J=780 J=260 The answer is B. #### B QUESTION:A certain no. when divided by 50 leaves a remainder 25, what is the remainder if the same no.be divided by 15? options: A)3 B)4 C)5 D)8 E)9 SOLUTION:Explanation: 50 + 25 = 75/15 = 5 (Remainder) C #### C QUESTION:R is the set of positive even integers less than 101, and S is the set of the squares of the integers in R. How many elements does the intersection of R and S contain ? options: A) None B) Two C) Four D) Five E) Seven SOLUTION:R is the set of positive even integers less than 101, and S is the set of the squares of the integers in R. How many elements does the intersection of R and S contain? R=2,4,6,8,10,12... S=4,16,36,64... Numbers: 4, 16, 36, 64, and 100 are even integers (less than 101) that are in both sets. Solution: Five Answer: D #### D <<<Examples ends QUESTION:A person saved $10 in buying an item on sale. If he spent $100 for the item, approximately how much percent he saved in the transaction? options: A)8% B)10% C)2% D)5% E)6% SOLUTION:Actual price = 100+10 = $110 Saving = 10/110 * 100 = 100/11 =10% approximately Answer is B #### B

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:The 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? options: A)1267 B)1201 C)1200 D)1209 E)1216 SOLUTION:P --- 10 ---- 600 P --- 5 ----- 300 3P --- 5 ----- 900 ------ => 1200 Answer: C #### C QUESTION:The number of stamps that P and Q had were in the ratio of 7:2 respectively. After P gave Q 15 stamps, the ratio of the number of P's stamps to the number of Q's stamps was 2:1. As a result of the gift, P had how many more stamps than Q? options: A)25 B)35 C)45 D)55 E)65 SOLUTION:P started with 7k stamps and Q started with 2k stamps. (7k-15)/(2k+15) = 2/1 3k = 45 k = 15 P has 7(15) - 15 = 90 stamps and Q has 2(15)+15 = 45 stamps. The answer is C. #### C QUESTION:if a person cover 3/5 part of his journey by train,7/20 part of his journey by bus and rest 6.5 km. by walk.what is total distance of his journey? options: A)65 km B)100 km C)120 km D)130 km E)75 km SOLUTION:let total distance be=x km.then, 3x/5+7x/20+6.5=x;12x+7x+130=20x;x=130 hence total distance=130 km. answer D #### D QUESTION:By selling an article for $180, a person gains $30. What is the gain %? options: A)25% B)30% C)50% D)20% E)10% SOLUTION:S.P. = $180 Gain = $30 C.P. = 180-30 = 150 Gain% = 30/150 * 100 = 20% Answer is D #### D QUESTION:The forth proportional to 2,4,6 is? options: A)8 B)12 C)15 D)18 E)22 SOLUTION:Let the fourth proportional to 2,4,6 be x then 2:4::6:x 2x = 4*6 x = 12 Answer is B #### B QUESTION:In 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 ? options: A)8 B)14 C)18 D)24 E)26 SOLUTION:Explanation: Let the number of boys be x. Then, (3/4)x = 21 or x = 21 x(4/3) = 28. If total number of students is y, then (2/3) y = 28 or y = 28 x (3/2) = 42. Therefore Number of girls in the class = (42 - 28) = 14. Answer: B #### B QUESTION:At a certain restaurant, 30 percent of the servers reported their tips, while 40 percent of the servers who were tipped didn't report their tips. What percent of the servers were tipped? options: A)30% B)60% C)50% D)70% E)80% SOLUTION:Statement: 30% of Servers (S) Reported their Tips (RT). Of the servers who were tipped (T) 40% didn't report their tips (notRT). [Note: A Venn Diagram is useful to visualize the problem.] Solution: Sample space is 100%. S = 100% RT/S = 30% notRT/T = 40% => 100% - 40% => RT/T = 60% T/S = (30)/(60)% = 50% Answer: C #### C QUESTION:In how many ways letters of the word LEADER be arranged? options: A)5 B)78 C)69 D)58 E)120 SOLUTION:LEADER has 6 letters, out of which E repeated 2 times. Hence total ways = 6! / (2!) = 120 ways E #### E QUESTION:If a man rows at the rate of 5 kmph in still water and his rate against the current is 3.5 kmph,then the man’s rate along the current is : options: A)4.25 kmph B)6 kmph C)6.5 kmph D)8.5 kmph E)None of these SOLUTION:Solution Let the rate along the current be x kmph.Then,1/2(x + 3.5) = 5 or x = 6.5 kmph. Answer C #### C QUESTION:Tough and Tricky questions: Coordinate Geometry. Line L contains the points (2,3) and (p,c). If c = 2, which of the following could be the equation of line m, which is perpendicular to line L? options: A) 2x + y = px + 7 B) 2x + y = –px C) x + 2y = px + 7 D) y – 7 = x ÷ (p – 2) E) 2x + y = 7 – px SOLUTION:So we need m=p-2, so we should get y=mx+b form in answer choices (A) 2x+y=px+7 => y=px-2x+7 => y=x(p-2)+7. It is what we need (B) 2x + y = –px => y=-px-2x => y=x(-p-2). Wrong (C) x + 2y = px + 7 => y=x(p-1/2)+7/2. Wrong (D) y – 7 = x ÷ (p – 2) => y=(1/p-2)x+7. Wrong (E) 2x + y = 7 – px => y=-px-2x+7 => y=x(-p-2)+7. Wrong A #### A QUESTION:The product of all the prime numbers less than 10 is closest to which of the following powers of 10 ? options: A) 10^9 B) 10^8 C) 10^2 D) 10^6 E) 10^5 SOLUTION:P = 2*3*5*7 ~ 10^ 2 Answer : C #### C QUESTION:Three people candidates contested an election and they received 1136, 7636 and 11628 votes respectively. What is the percentage of the total votes did the winning candidate get? options: A)40% B)45% C)57% D)58% E)60% SOLUTION:tot no of votes = (1136+7636+11628) = 20400 req = > (11628/20400 * 100) = > 57% ANSWER C #### C QUESTION:A 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? options: A)5 m B)6 m C)4 m D)7 m E)8 m SOLUTION:Let radius of the outer circle be R and radius of the inner circle be r. Circumference of the outer circle = Circumference of the inner circle = But, or, R - r = Thus, width of the road = 7 m D #### D QUESTION:The average speed of a car is 1 4/5 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? options: A)300 km B)320 km C)360 km D)390 km E)400 km SOLUTION:Sol. Average speed of a tractor = 25 km / h The speed of a bus in an hour = 25 × 2 = 50 km The speed of a car in an hour = 9/5 * 50 = 90 km So, the distance covered by car in 4 h is 90 × 4 = 360 km Ans.(C) #### C QUESTION:William earned $3,200 per month as a teacher for the ten months from September to June. Then he took a job as a barista at a local café, where he earned $2,000 per month during July and August. What was his average monthly pay for the 12 months? options: A)$2,400 B)$2,800 C)$2,600 D)$3,000 E)$2,500 SOLUTION:E. William earned $3,200 × 10 = $32,000 as a teacher, and he earned $2,000 × 2 = $4,000 as a barista. So he earned $32,000 + $4,000 = $36,000 over the 12 months. Plug these values into the formula for the mean: mean=sum of values/number of values=>36.000/12=3.000 correct answer D)$3.000 #### D QUESTION:If r, s, and t are three different positive integers whose sum is prime, which of the following statements could be true? options: A)Each of r + s, r + t, and s + t is prime. B)Each of r + 3, s + 3, and t + 3 is prime. C)Each of r, s, and t is prime. D)The average (arithmetic mean) of r, s, and t is prime. E)r + s = t SOLUTION:the question asks could be!!!! this means that if at least one option works, it is the answer. 3, 7, 19 satisfies the condition, since 29 is a prime number. Since the question asks for a could be - we know automatically that C is the answer. #### C QUESTION:A man took loan from a bank at the rate of 12% p.a. S.I. After 3 years he had to pay Rs. 5400 interest only for the period. The principal amount borrowed by him was? options: A)15002 B)15001 C)15000 D)15007 E)15009 SOLUTION:Principal = (100 * 5400) / (12 * 3) = Rs. 15000.Answer:C #### C QUESTION:Find the compound interest and the amount on Rs.8000 at 5% per annum for 3 years when C.I is reckoned yearly? options: A)Rs.1261 B)Rs.1440 C)Rs.1185 D)Rs.1346 E)Rs.1446 SOLUTION:A = 8000(21/20)3 = 9261 = 8000 --------- 1261 ANSWER:A #### A QUESTION:If the average of a sequence of consecutive multiple of 18 is 153, and the greatest term is 270, how many terms R in the sequence are smaller than the average options: A)5 B)6 C)7 D)8 E)9 SOLUTION:Let the sequence have N terms starting 18*K --> 18K, 18(K+1), 18(K+2), .... , 18(K+N-1) is the sequence. The sum of the sequence is ---> 18K + 18(K+1) + 18(K+2) + .... + 18(K+N-1) =18*(K+(K+1)+...+(K+N-1)) = 18*(N*(2K+N-1)/2). So the average is 153=[18*(N*(2K+N-1)/2)]/N = 18*(2K+N-1)/2 = 9 *(2K+N-1) ---> by cancelling 9 we get 2K+N-1=17 --> 2K+N=18 ---*). On the other hand, since the greatest term is 270, 18(K+N-1)=270 --> by cancelling 18 we get K+N-1=15 --> K+N=16 ---**). By *), **) we have K=2, N=14. Since 153/18 = 8.5, 18*8<153<18*9. So the number of terms R which are smaller than the average is 18*2, 18*3, ..... ,18*8 ---> 7. The answer is C. #### C QUESTION:A 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? options: A)287 sec B)288 sec C)48 sec D)16 sec E)17 sec SOLUTION:D = 540 + 180 = 720 S = 54 * 5/18 = 15 mps T = 720/15 = 48 sec Answer: C #### C QUESTION:How many 4-letter word with or without meaning can be formed out of the letters of the word 'LOGARITHMS' if repetition of letters is not allowed options: A)5040 B)1254 C)4510 D)1203 E)4510 SOLUTION:'LOGARITHMS' contains 10 different letters Required number of words = Number of arrangements of 100 letters taking 4 at a time = 10P4 = 10 * 9 * 8 * 7 = 5040 Ans: A #### A QUESTION:A new home buyer pays 4% annual interest on her first mortgage and 9% annual interest on her second mortgage. If she borrowed a total of $335,000, 80% of which was in the first mortgage, what is her approximate monthly interest payment? options: A)$1,395 B)$1,733 C)$3,466 D)$13,333 E)$20,796 SOLUTION:0.04x + 0.09y = 335000 [1] 0.04x = 0.80 * 335000 = 268000 [2] 268000 + 0.09y = 320000 --> 0.09y = 67000 [3] 268000 / 12 = 22333.3333 [4] 67000 / 12 = 5583.333 [5] Adding [4,5] we get: 27916 [6] Dividing [6] / 2 to get an average we get 1.395,ANS A #### A QUESTION:A 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? options: A)246 m B)240 m C)257 m D)577 m E)567 m SOLUTION:Speed = (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 #### B QUESTION:In 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 W percentage of those asked favoured more than one of the 3 proposals. options: A) 10 B) 12 C) 17 D) 22 E) 30 SOLUTION:Bunuel, my answer for exactly 2 people was 17 and this was my approach: 100%=(A+B+C)-(AnB+AnC+BnC)-5%+22% which leads me to W=100%=(50+30+20)-(at least 2 people)-5%+22%.C #### C QUESTION:Distance 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? options: A)67.0 km /hr B)67.2 km /hr C)69.0 km /hr D)69.2 km /hr E)None SOLUTION:Solution Required average speed =(2xy / x+y)km/hr = 2 x 84 x 56 /(84 + 56) = (2 x 84 x 85 /140) = 67.2 km/hr. Answer B #### B QUESTION:The area of a rectangle is 15 square centimeters and the perimeter is 16 square centimeters. What are the dimensions of the rectangle? options: A)3 and 5 B)3 and 6 C)3 and 7 D)3 and 8 E)3 and 9 SOLUTION:Let 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. 15 = x y and 16 = 2 x + 2 y Solve the second equation for x x = 8 - y Substitute x in the equation 15 = x y by 8 - y to rewrite the equation as 15 = (8 - y) y Solve for y to find y = 3 and y = 5 Use x = 8 - y to find x when y = 3 , x = 5 and when y = 5 , x = 3. The dimensions of the rectangle are 3 and 5. As an exercise, check that the perimeter of this rectangle is 16 and its area is 15. Answer A #### A QUESTION:In a recent election, James received 5 percent of the 2,000 votes cast. To win the election, a candidate needed to receive more than 50 percent of the vote. How many additional votes would James have needed to win the election? options: A)901 B)989 C)990 D)991 E)1,001 SOLUTION:James = (5/100)*2000 = 100 Votes to win = (50/100)*Total Votes +1 = (50/100)*2000 +1 = 1001 Remaining Voted needed to win election = 1001 - 100 = 901 Answer: option A #### A QUESTION:When N is divided by T, the quotient is S and the remainder is M. Which of the following expressions is equal to N? options: A)ST B)S + V C)ST + M D)T(S+V) E)T(S – V) SOLUTION:Using the rule dividend = Quotient * divisor + remainder =>ST + M C is correct #### C QUESTION:A boy has nine trousers and 12 shirts. In how many different ways can he select a trouser and a shirt? options: A)109 ways B)908 ways C)128 ways D)108 ways E)104 ways SOLUTION:The boy can select one trouser in nine ways. The boy can select one shirt in 12 ways. The number of ways in which he can select one trouser and one shirt is 9 * 12 = 108 ways. Answer:D #### D QUESTION:If 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? options: A)22 B)40 C)28 D)21 E)27 SOLUTION:A.M. of 75 numbers = 35 Sum of 75 numbers = 75 * 35 = 2625 Total increase = 75 * 5 = 375 Increased sum = 2625 + 375 = 3000 Increased average = 3000/75 = 40. Answer: B #### B QUESTION:Mukesh weight 56.7 kg. If he reduces his weight in the ratio 7:6. New weight of Mukesh is ? options: A)47.6 B)48.6 C)49.6 D)50.6 E)51.6 SOLUTION:Given ratio is 7:6; let weight before and after reduction be 7x and 6x respectively. A/Q 7x=56.7 => x=56.7/7 => x= 8.1 Reduced weight= 6x= 6*8.1= 48.6; hence reduced weight= 48.6 ANSWER:B #### B QUESTION:If six persons sit in a row, then the probability that three particular persons are always together is -. options: A)1/5 B)1/7 C)1/9 D)1/2 E)2/7 SOLUTION:3!4! Required probability = 3!4!/6! = 1/5 ANSWER A #### A QUESTION:Share Rs.4200 among John, Jose & Binoy in the ration 2 : 4 : 6.Find the amount received by John? options: A)900 B)1000 C)1254 D)1795 E)1400 SOLUTION:Amount received by sanjay. 4 / 12 X 4200 = 1400= ( related ratio / sum of ratio ) x Total amount So, the Amount received by sanjay is 1400. E #### E QUESTION:A 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. 6900? options: A)s. 4991 B)s. 5991 C)s. 6001 D)s. 6991 E)s. 7391 SOLUTION:total fr 5 mnths=(6435+6927+6855+7230+6562)=Rs34009. Reqd.sale=Rs.[(6900*6)-34009] = Rs.(41400-34009) = Rs.7391. ANSWER:E #### E QUESTION:If x percent of 400 is 20 percent of 700, then x = options: A)200 B)350 C)700 D)400 E)1,400 SOLUTION:x/100(400) = 2/10(700) x = 400. Option D. #### D QUESTION:(A% of 5B + B% of A) is equal to ? options: A)A% of B B)B% of A C)6% of AB D)AB% of 3 E)None SOLUTION:Answer A% of 5B + B% of A =5AB/100 + AB/100 = 6AB/100 = 6% of AB Correct Option: C #### C QUESTION:A meal cost $ 35.50 adn there was no tax. If the tip was more than 5 pc but less than 8pc of the price, then the total amount paid should be: options: A)40-42 B)39-41 C)38-40 D)37-38 E)36-37 SOLUTION:5%(35.5) = 1.775 8%(35.5) = 2.84 total amount could have been 35.5+1.775 and 35.5+2.84 => could have been between 37.275 and 38.34 => approximately between 37 and 38 Answer is B.D #### D QUESTION:(+15) + (-11) - (+5) - (-7) options: A)8 B)2 C)6 D)5 E)3 SOLUTION:= 15-11-57 22-16, [adding all integers with plus (+) sign together and with minus (-) sign respectively together = +6 or simply 6. correct answer (C) #### C QUESTION:A man’s speed with the current is 17 km/hr and the speed of the current is 2.5 km/hr. the man’s speed against the current is : options: A)8.5 km/hr B)12 km/hr C)10 km/hr D)12.5 km/hr E)None of these SOLUTION:Solution Man's rate in still water = (17-2.5) km/hr = 14.5 km/hr. Man's rate against the current = (14.5-2.5) km/hr = 12 km/hr Answer B #### B QUESTION:To furnish a room in a model home an interior decorator is to select 2 chairs and 2 tables from the collection of chairs and tables in a warehouse that are all different from each other. If there are 5 chairs in the warehouse and if 150 different combinations are possible, how many tables w are there in the warehouse? options: A)6 B)8 C)10 D)15 E)30 SOLUTION:Total number of ways to choose 2 chairs from 5 w= 5C2=10 Total number of combination=150 That means we need get 15 combinations from the selection of tables.... Screening through the answers.... 6C2=15..... 15*10=150 Answer is 6... A #### A QUESTION:Expenditures of a Company (in Lakh Rupees) per Annum Over the given Years. Year Item of Expenditure Salary Fuel and Transport Bonus Interest on Loans Taxes 1998 288 98 3.00 23.4 83 1999 342 112 2.52 32.5 108 2000 324 101 3.84 41.6 74 2001 336 133 3.68 36.4 88 2002 420 142 3.96 49.4 98 Total expenditure on all these items in 1998 was approximately what percent of the total expenditure in 2002? options: A)62% B)69.45% C)70% D)71% E)72% SOLUTION:Required percentage = [ (288 + 98 + 3.00 + 23.4 + 83) x 100 ] % (420 + 142 + 3.96 + 49.4 + 98) = [ 495.4 x 100 ] % 713.36 ~= 69.45%. B) #### B QUESTION:By 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%? options: A)228 B)480 C)267 D)288 E)276 SOLUTION:SP = 800 Profit = 25% CP = (SP)*[100/(100+P)] = 800 * [100/125] = 640 Loss = 25% = 25% of 640 = Rs.160 SP = CP - Loss = 640 - 160 = Rs.480 Answer: B #### B QUESTION:Pipe 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? options: A)1.5 B)2 C)2.5 D)3 E)3.5 SOLUTION:The part filled by A + B + C in 1 hour = 1/6 + 1/4 + 1/12 = 12/24 = 1/2 All the three pipes together will fill the tank in 2 hours. The answer is B. #### B QUESTION:A, 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? options: A)14700 B)14500 C)14900 D)14300 E)14000 SOLUTION:Total amount invested = 50000 Assume that investment of C =x. Then investment of B =5000+x, Investment of A =4000+5000+x=9000+x x+5000+x+9000+x=50000 ⇒3x+14000=50000 ⇒3x=50000–14000=36000 ⇒x=36000/3=12000 Investment of C =x=12000 Investment of B =5000+x=17000 Investment of A =9000+x=21000 Ratio of the investment of A, B and C =21000:17000:12000 =21:17:12 Share of A = Total profit ×21/50 =35000×21/50=700×21=14700 Answer is A. #### A QUESTION:Two 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 ? options: A)3 B)2 C)1/2 D)1/3 E)There isn't enough data to answer the question. SOLUTION:M - N = (M + N)/2 Solving for N/M = 1/3 D #### D QUESTION:If each side of the square is increased by 25% find the percentage change in its area? options: A)89.45% B)56.25% C)89.98% D)54.48% E)45.0% SOLUTION:let each side of the square be a. then area =a^2 new side=125a/100=5a/4 new area=(5a/4)^2=25a^2/16 increase in area=(25a^2/16-a^2)=9a^2/16 increased %=(9a^2/16*1/a^2*100)=56.25% Answer is(B) #### B QUESTION:A set consist of 2k-1 element. What is the number of subsets of this set which contain at most k-1 elements? options: A)2^(2k-2) B)2^(2k) - 2 C)2^(2k) -1 D)2^(2k) E)2^(2k-1) SOLUTION:I used k=3, so then we have 5!/2!3! + 5!/4!1! + 5!/0!5! 10 + 5 + 1 = 16 So our target is 16 Now replace in answer choices A gives us 2^4 = 16 Hence A is the correct option Read 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 Avoid 2 since you will get 1 arrangement (k-1) and may be risky since 1 is a number with certain unique properties #### A QUESTION:If (a-3)(b-2) =0, which of the following must be true ? I. a=3 and b=2 II. if a is not = 3, then b=2 III. if a=3, then b is not=2 options: A)I only B)II only C)III only D)I and II E)II and III SOLUTION:(a-3)(b-2)=0 So either a=3 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. The answer is B. #### B QUESTION:Three friends X, Y, Z rented a auto for Rs.520. A used it for 6 hours, B used it for 9 hours and C used it for 11 hours. What is the hire charges paid by Y: options: A)Rs 140 B)Rs 160 C)Rs 180 D)Rs 200 E)None SOLUTION:X : Y : Z = 7 : 8 : 11. Hire charges paid by Y = Rs(520×9/26) = Rs.180. Answer C #### C QUESTION:A, 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? options: A)3630 B)3637 C)3630 D)3631 E)3635 SOLUTION:6300:4200:10500 3:2:5 3/10 * 12100 = 3630 Answer: A #### A QUESTION:A train speeds past a pole in 15 sec and a platform 100 m long in 25 sec, its length is? options: A)158 m B)150 m C)110 m D)130 m E)157 m SOLUTION:Let the length of the train be x m and its speed be y m/sec. Then, x/y = 15 => y = x/15 (x + 100)/25 = x/15 => x = 150 m. Answer: B #### B QUESTION:The 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? options: A)7 B)4 C)6 D)9 E)3 SOLUTION:65*(90/100)*((100-x)/100) = 56.16 x = 4% Answer: B #### B QUESTION:total dinning bill of 3 people was $139.00 and 10% tip divided the bill evenly ?what is the bill amount each person shared . options: A)21.84 B)50.96 C)53.84 D)24.84 E)50.26 SOLUTION:dinner bill of 3 person = 139 + 10% tip so, 10% of 139 = (139*10)/100 = 13.9 So, the actual total amount = 139+13.9 = $ 152.9 so per head bill = 152.9/3 = $ 50.96 ANSWER:B #### B QUESTION:A group of five girls and three boys have tickets for seven adjacent seats in one row of a theater. If the three boys will not sit in three adjacent seats, how many possible different seating arrangements are there for these 8 theatre-goers? options: A)8! – 2!3!2! B)8! – 6!3! C)8 × 2!3!2! D)8! – 5!3! E)2!3!2! SOLUTION:There are 3 boys and 4 girls , we want to calculate the seating arrangements if three boys do not sit together, like MMM. Let's calculate the # of arrangements when they SIT together and subtract from total # of arrangements of these 8 persons without restriction. Thus we'll get the # of arrangements asked in the question. 1. Total # of arrangements of 8 is 8!. 2. # of arrangements when 3 boys are seated together, like MMM; Among themselves these 3 boys can sit in 3! # of ways, Now consider these 3 boys as one unit like this {MMM}. We'll have total of 6 units: {MMM}{W}{W}{W}{W}{W}. The # of arrangements of these 5 units is 5!. Hence total # of arrangements when 3 men sit together is: 3!6!. # of arrangements when 3 boys do not sit together would be: 8!-3!6!. Answer: B). #### B QUESTION:The variables a and b are non-zero integers W. If a = 2b^3/c, what happens to c when a is halved and b is doubled? options: A)c is not changed. B)c is halved. C)c is doubled. D)c is multiplied by 4. E)c is multiplied by 16. SOLUTION:a=2b^3/c c=2b^3/a when a is halved and b is doubled c=2(2b)^3/(a/2) c=16*2b^3/a Ans. E c is multiplied by 16. #### E QUESTION:The average weight of 19 students is 15kg. by the admission of a new student the average weight is reduced to 14.9 kg. the weight of the new student is ? options: A)10.6 kg B)10.8 kg C)11 kg D)13 kg E)None SOLUTION:Answer Weight of new student = Total weight of all 20 students - Total weight of initial 19 students = (20 x 14.9 - 19 x 15) kg = 13 kg. Correct Option: D #### D QUESTION:A 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 $1,000. If the price of the car in 1996 was $22,000, what is the car's price in 2002? options: A)$18,400 B)$19,700 C)$20,200 D)$20,400 E)$21,100 SOLUTION:Price in 96 = 22000 Price decrease each year = 2.5/100*22000 = 550 Price in 97 = 22000 - 550 Price in 98 = 22000 - 2*550 Price in 99 = 22000 - 3*550 Price in 00 = 22000 - 4*550 Price in 01 = 22000 - 5*550 Price in 02 = 22000 - 6*550 = 18700 Investment in the car = 1000 Net price of the car in 02 = 18700 + 1000 = $19700 Correct Option: B #### B QUESTION:If 20 men can build a wall 112 metres long in 6 days, what length of a similar wall can be built by 40 men in 3 days? options: A)65mtr. B)52mtr C)70mtr. D)112mtr. E)17mtr. SOLUTION:20 men is 6 days can build 112 metres 25 men in 3 days can build = 112*(40/20)x(3/6) = 112 meters Answer: D. #### D QUESTION:The ratio, by volume, of soap to alcohol to water in a certain solution is 20:50:80. 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 100 cubic centimeters of alcohol, how many cubic centimeters of water will it contain? options: A)520 B)640 C)700 D)750 E)800 SOLUTION:soap:alcohol Initial ratio soap:alcohol: water --> 20:50:80 Initial soap:alcohol = 20/50 =20:50 after doubled soap:alcohol =2* 20/50 = 40:50 Initial soap:water = 20/80=20:80 after halved soap:water: 1/2 * 20/80 = 10/80 = 10:80 After soap: alcohol:water --> 40:50:320-->4:5:32 given alcohol 100 cubic centimeter. ratio is 80:100:640(4:5:32) For 100 cubic centimeter of Alcohol --- 640cubic cm water is required. Answer-B #### B QUESTION:The total marks obtained by a student in Mathematics and Physics is 50 and his score in Chemistry is 20 marks more than that in Physics. Find the average marks scored in Mathamatics and Chemistry together. options: A)15 B)25 C)35 D)45 E)55 SOLUTION:Let the marks obtained by the student in Mathematics, Physics and Chemistry be M, P and C respectively. Given , M + C = 50 and C - P = 20 M + C / 2 = [(M + P) + (C - P)] / 2 = (50 + 20) / 2 = 35. ANSWER:C #### C QUESTION:Look at this series: 5.2, 4.8, 4.4, 4, ... What number should come next? options: A)3 B)3.3 C)3.5 D)3.6 E)None SOLUTION:Explanation: In this simple subtraction series, each number decreases by 0.4. Answer: Option D #### D QUESTION:A tank is filled in SIX 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? options: A)56 hours B)28 hours C)55 hours D)66 hours E)21 hours SOLUTION:1/A + 1/B + 1/C = 1/6 (Given) Also given that A = 2B and B = 2C => 1/2B + 1/B + 2/B = 1/6 => (1 + 2 + 4)/2B = 1/6 => 2B/7 = 6 => B = 21 hours. Answer: E #### E QUESTION:John want to buy a $100 Trouser at the store, but he think it’s too expensive. Finally, it goes on sale for $10. What is the percent decrease? options: A)90% B)30% C)40% D)70% E)80% SOLUTION:The is always the difference between our starting and ending points. In this case, it’s 100 – 10 = 90. The “original” is our starting point; in this case, it’s 100. (90/100)*100 = (0.9)*100 = 90%. A #### A QUESTION:A, 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.2430 ? options: A)s. 832 B)s. 830 C)s. 822 D)s. 812 E)s. 810 SOLUTION:Let the total amount in the partnership be 'x'. Then A's share = x/3 B's share = x/4 C's share = x/5 D's share = x - (x/3 + x/4 +x/5) = 13x/60 A : B : C : D = x/3 : x/4 : x/5 : 13x/60 = 20 : 15 : 12 : 13 A's share in the profit of Rs. 2430 = 20 (2430/60) = Rs. 810. Answer: E #### E <<<Examples ends QUESTION:What should be added to 4750 so that it may become a perfect square? options: A)11 B)15 C)16 D)17 E)18 SOLUTION:69x69=4761 4761-4750 = 11 If added to 11 get perfect square answer =A #### A

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:Which of the following are orthogonal pairs? a. 3i+2j b. i+j c. 2i-3j d. -7i+j ??? options: A)a,b B)a,c C)b,c D)a,d E)b,d SOLUTION:a. 3i+2j and c. 2i-3j are orthogonal pair. as the dot product of two vectors is zero;so they are orthogonal. ANSWER:B #### B QUESTION:If x is divisible by 2, 14, and 11, which of the following must be the least multiple of x? options: A)308 B)154 C)70 D)44 E)0 SOLUTION:We are looking for the LCM (which is not 0) of 2, 11, 14: 2 * 11 * 7 = 154 ANSWER:B #### B QUESTION:What is the difference between local value & face value of 9 in the numeral 65793? options: A)8453 B)8956 C)8991 D)9890 E)10000 SOLUTION:(Local value of 9) - (Face value of 9) = (9000 - 9) = 8991 C #### C QUESTION:A dealer purchased an article at 3/4 of its list price and sold 50% more than the list price. Find his gain percent? options: A)109% B)160% C)100% D)600% E)108% SOLUTION:MP = 100 CP = 75 SP = 150 ------ 75 ---- 75 100 ---- ? => 100% Answer:C #### C QUESTION:Dany bought a total of 20 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? options: A)4 B)10 C)7 D)8 E)12 SOLUTION:Let 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 20. Hence X + Y = 20 If X is the number of cards at $0.25, then the X cards cost 0.25 X If Y is the number of cards at $0.15, then the Y cards cost 0.15 Y The total cost of the X cards and the the Y cards is known to be $4.2 and also given by 0.25 X + 0.15 Y = 4.2 We now need to solve the system of equations X + Y = 20 0.25 X + 0.15 Y = 4.2 The first equation gives Y = 20 - X. Substitute y by 20 - x in the second equation and solve 0.25 X + 0.15 (20 - X) = 4.2 X(0.25 - 0.15) + 3 = 4.2 0.1 X = 1.2 X = 12 and Y = 20 - 12 = 8 correct answer D #### D QUESTION:The 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 options: A)20 B)21 C)22 D)28 E)NONE SOLUTION:Sol. Let the total number of workers be x. Then, 8000x = (14000 × 7) + 6000 ( x – 7) ‹=› 2000x = 56000 ‹=› x = 28. Answer D #### D QUESTION:Ten years ago, a mother was four times older than her daughter. After ten years, the mother will be twice older than daughter. The present age of the daughter is options: A)22 B)21 C)24 D)20 E)19 SOLUTION:Let the mother’s present age be ’x’ Let the daughter’s age be ’y’; 10 years ago; (x - 10) = 4(y - 10) or x - 4y = - 30.. (1) 10 years later; (x + 10) = 2(y + 10) or x - 2y = 10.. (2) Solving (1) & (2) y = 20 ANSWER:D #### D QUESTION:A certain protective additive increases from 20 days to 25 days the time between required maintenance checks on an industrial vehicle. By what percent is the time between maintenance checks increased by using the additive? options: A)25% B)33 1/3% C)50% D)66 2/3% E)75% SOLUTION:General formula for percent increase or decrease, (percent change): percent=Change/Original∗100 So, the time between maintenance checks increased by 25−20/20∗100=25 Answer: A. #### A QUESTION:The area of a triangle is with base 5.5m and height 6m? options: A)11 m2 B)16.5 m2 C)18.5 m2 D)19.5 m2 E)12 m2 SOLUTION:1/2 * 5.5* 6 = 16.5 m2 Answer: B #### B QUESTION:A leak in the bottom of a tank can empty the full tank in 6 hours. An inlet pipe fills water at the rate of 2.5 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? options: A)5729 B)5760 C)2889 D)3600 E)2799 SOLUTION:1/x - 1/6 = -1/8 x = 24 hrs 24 * 60 * 2.5 = 3600.Answer: D #### D QUESTION:Out of 40 applicants to a law school, 15 majored in political science, 20 had a grade point average higher than 3.0, and 10 did not major in political science and had a GPA equal to or lower than 3.0. How many T applicants majored in political science and had a GPA higher than 3.0? options: A)5 B)10 C)15 D)25 E)35 SOLUTION:Total applicants = 40 Political science = 15 and Non political science = 40 - 15 = 25 GPA > 3.0 = 20 and GPA <= 3.0 = 20 10 Non political science students had GPA <= 3.0 --> 15 Non political science students had GPA > 3.0 GPA > 3.0 in political science = Total - (GPA > 3.0 in non political science) T= 20 - 15 = 5 Answer: A #### A QUESTION:A 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? options: A)276 m B)279 m C)240 m D)207 m E)285 m SOLUTION:Speed = [54 * 5/18] m/sec = 15 m/sec. Length of the train = (15 * 20) m = 300 m. Let the length of the platform be x meters. Then, x + 300 / 39 = 15 x + 300 = 585 x =285m. Answer: E #### E QUESTION:The population of a town is 10000. It increases annually at the rate of 10% p.a. What will be its population after 2 years? options: A)12300 B)12350 C)12100 D)12500 E)12600 SOLUTION:Formula : ( After =100 denominator Ago = 100 numerator) 10000 × 110/100 × 110/100 = 12100 C #### C QUESTION:The 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? options: A)3 dm B)4 dm C)5 dm D)6 dm E)7 dm SOLUTION:33 + 43 + 53 = a3 => a = 6 ANSWER:D #### D QUESTION:The principal that amounts to Rs. 4913 in 3 years at 6 1/4 % per annum C.I. compounded annually, is? options: A)288 B)267 C)200 D)4096 E)2771 SOLUTION:Principal = [4913 / (1 + 25/(4 * 100))3] = 4913 * 16/17 * 16/17 * 16/17 = Rs. 4096. Answer: D #### D QUESTION:If population of certain city increases at the rate of 5%. If population in 1981 was 185220, then population in 1978 was? options: A)160000 B)228788 C)266891 D)267689 E)127791 SOLUTION:X * (105/100) * (105/100) * (105/100) = 185220 X = 185220/1.157625 X = 160000 Answer:A #### A QUESTION:How many quarters are equal to 4 dollars? options: A)16 B)8 C)12 D)9 E)7 SOLUTION:4*4 = 16 quarters Answer : A #### A QUESTION:A person starts walking at a speed of 5km/hr through half the distance, rest of the distance he covers with aspeed 4km/hr. Total time of travel is 36 hours. What is the maximum distance he can cover? options: A)20km B)40km C)60km D)80km E)160km SOLUTION:t=d/s, so 36=x/2*1/5+x/2*1/4(because half distance with 5 km/ph, and remaining half with 4km/hr) 36=x(18/80) x=160km ANSWER:E #### E QUESTION:In 10 years, A will be twice as old5as B was 10 years ago. If A is now 7 years older than B, the present age of B is options: A)35 B)37 C)39 D)41 E)42 SOLUTION:Explanation: Let B's age = x years. Then, As age = (x+ 7) years. (x+7+10)=2(x—10) hence x=37. Present age of B = 37 years Answer: Option B #### B QUESTION:Due to 10% decrease in the price of sugar and John can buy 5kg more sugar in Rs100 , then find the CP of sugar? options: A)Rs. 1(2/7) B)Rs. 2(1/9) C)Rs. 3(2/11) D)Rs. 2(2/13) E)Rs. 2(2/7) SOLUTION:Here r = 10 % ,x = 100 and A = 5 kg Actual price of sugar = 10*100/((100-10 )*5) = Rs. 2(2/9) B #### B QUESTION:A 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: options: A)35.55 km/hr B)36 km/hr C)71 km/hr D)71.11 km/hr E)70 km/hr SOLUTION:Total time taken =((160/64)+(160/80))hrs=9/2hrs. Average speed =(320 x2/9)km/hr= 71.11 km/hr. ANSWER D #### D QUESTION:In a college, 1 percent of students hate math, 2 percent of students hate English, 1 percent hate French and 4 percent hate German. Can you find out the percentage of students who hate all 4 subjects ? options: A)8% B)5% C)7% D)12% E)19% SOLUTION:A 8% of student hate all four subjects. #### A QUESTION:250 men work for 16 days and finish a work. How many men would do a job 3 times the previous one in 20 days? options: A)700 B)666 C)600 D)400 E)800 SOLUTION:Number of men needed to finish the required work (variation, proportion method ) =3*16*250/20 =600 Answer : C #### C QUESTION:The reflex angle between the hands of a clock at 10.25 is: options: A)180º B)192 1/2 º C)195º D)197 1/2 º E)197 º SOLUTION:Angle traced by hour hand in 125/12 hrs ={(360/12)x(125/2)}º = 312 1/2 º . Angle traced by minute hand in 25 min =(360/60)x 25 º= 150º. Reflex angle = 360º -(312 1/2- 150º )= 360º - 162 1/2º= 197 1/2º . Answer: D #### D QUESTION:If a randomly selected non-negative single digit integer is added to {2, 3, 4, 9}. What is the probability that the median of the set will increase but the range still remains the same? options: A)0.2 B)0.3 C)0.4 D)0.5 E)0.6 SOLUTION:We are selecting from non-negative single digit integers, so from {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}. These 10 digits represent the total number of outcomes. Hence, the total number of outcomes is 10. We need to find the probability that the median of the set will increase but the range still remains the same. The median of the set is (3 + 4)/2 = 3.5, thus the number selected must be 4 or greater. For the range to remain the same, the number must be between 2 and 9 inclusive. To satisfy both conditions, the number selected must be 4, 5, 6, 7, 8, or 9. The probability is 6/10 = 0.6 The answer is E. #### E QUESTION:The cash difference between the selling prices of an article at a profit of 4% and 8% is Rs 3. The ratio of two selling prices is options: A)51:52 B)52:54 C)53:54 D)54:55 E)None of these SOLUTION:Explanation: Let the Cost price of article is Rs. x Required ratio = (104% of x) / (108% of x) =104/108 =52/54 = 52:54. Answer: B #### B QUESTION:In a two digit number, the digit in the units place is two times the digit in ten's place and sum of the digits is equal to 6. What is the number? options: A)24 B)28 C)32 D)36 E)38 SOLUTION:Solution Let the ten digits be x. Then,units digit=2x Therefore x + 2x = 6 ‹=›3x = 6 ‹=›x= 2. So, ten's digit = 2, unit's digit = 4. Hence, the required number is 24. Answer A #### A QUESTION:In 2010, Arman’s birthday was on a Thursday. What day of the week was it 64 days after his birthday? options: A)Thursday B)Friday C)Saturday D)Sunday E)Monday SOLUTION:Day of week after 64 days after Arman's birthday = 7*9 + 1 Saturday as the period will have 9 weeks and 1 days . The 1 days in the end will be Friday . Answer B #### B QUESTION:Find the odd man out. 1, 3, 9, 12, 19, 29 options: A)12 B)9 C)1 D)3 E)29 SOLUTION:12 is an even number. All other given numbers are odd Answer is A #### A QUESTION:What is the perimeter of a regular polygon with sides of length 15 cm and internal angles measuring 145° each? options: A)96 cm B)108 cm C)120 cm D)132 cm E)154.28 cm SOLUTION:Sum of all interior angles is given by: 180(n-2) = n is number of sides 180(n-2) = 145*n from here n = 10.28 So perimeter becomes 15*10.28= 154.28 Answer: E #### E QUESTION:A basket has 5 apples and 5 oranges. Three fruits are picked at random. What is the probability that at least 2 apples are picked? options: A)1/2 B)3/5 C)3/8 D)4/9 E)7/10 SOLUTION:The total possible choices are 10C3 = 120 The ways to choose 3 apples: 5C3 = 10 The ways to choose 2 apples: 5C2 * 5C1 = 50 P(at least 2 apples) = 60/120 = 1/2 The answer is A. #### A QUESTION:January 1, 2007 was Monday. What day of the week lies on Jan. 1, 2008? options: A)Monday B)Tuesday C)Wednesday D)Friday E)Sunday SOLUTION:The year 2007 is an ordinary year. So, it has 1 odd day. day of the year 2007 was Monday day of the year 2008 will be 1 day beyond Monday Hence, It will be Tuesday. answer : B #### B QUESTION:In a certain lottery drawing, two balls are selected at random from a container with 10 balls, numbered from 1 to 10, 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? options: A)$9 x 10^4 B)$9.90 x 10^6 C)$1.00 x 10^7 D)$1.05 x 10^7 E)$9.90 x 10^7 SOLUTION:The max product of any two balls can be 9 * 10 = 9900 = 9 * 10 If we multiply it by $1000 the max amount will be 9 * 10^4. A #### A QUESTION:Four machines, each working at the same constant rate, together can complete a certain job in 20 days. How many additional machines, each working at the same constant rate, will be needed to complete the job in 10 days? options: A)5 B)3 C)4 D)6 E)1 SOLUTION:Rate of one machine = 1 job / (20*4) days let X = number of machines needed to complete the job in 10 days 1/(4*20) * 10 * X = 1 job X = 8 8-4= 4 ANSWER: C #### C QUESTION:If (x + 1)^2 = 144, which of the following could be the value of 2x? options: A)–26 B)–13 C)–10 D)12 E)-21 SOLUTION:You can also get to the answer by backsolving using answer choices Starting with choice B = -13 (x + 1)^2 = 144 (-13 + 1)^2 = 144 =====> (-12)^2 = 144 Bingo, Clearly, among the answer choices only -13 will result in 144 in the equation so x must be -11, Then 2x = 2 * -13 = -26 Answer: A #### A QUESTION:A rectangular paper when folded into two congruent parts had a perimeter of 34cm foer each part folded along one set of sides and the same is 38cm. When folded along the other set of sides. What is the area of the paper? options: A)140 B)388 C)238 D)119 E)112 SOLUTION:when folded along the breadth we have 2(l/2 +b) = 34 or l+2b = 34...........(1) when folded along the length, we have 2(l+b/2)=38 or 2l+b =38.....(2) from 1 &2 we get l=14 and b=10 Area of the paper = 14*10 = 140 sq cmV Answer: A #### A QUESTION:Four bells commence tolling together and toll at intervals of 2, 4, 6, 8 seconds respectively. In 18 minutes, how many times do they toll together ? options: A)43 B)44 C)45 D)46 E)47 SOLUTION:LCM of 2, 4, 6, 8 is 24. So, after each 24 seconds, they would toll together. Hence, in 18 minutes, they would toll 18*60 seconds / 24 seconds = 45 times But then the question says they commence tolling together. So, they basically also toll at thebeginning(0second). So, total tolls together = 45+1 = 46 Answer C #### C QUESTION:How many days will there be from 26th January,1996 to 15th May,1996(both days included)? options: A)102 B)103 C)111 D)120 E)None of these SOLUTION:Explanation : Number of days from 26-Jan-1996 to 15-May-1996 (both days included) = 6(Jan) + 29(Feb) + 31 (Mar) + 30(Apr)+ 15(May) = 111.. Answer : Option C #### C QUESTION:Which of the following is not a prime number ? options: A)502 B)503 C)509 D)521 E)523 SOLUTION:Clearly, 502 is not a prime number. Answer : A #### A QUESTION:Carol spends 1/4 of her savings on a stereo and 1/2 less than she spent on the stereo for a television. What fraction of her savings did she spend on the stereo and television? options: A)1/4 B)2/7 C)5/12 D)3/8 E)7/12 SOLUTION:Total Savings = S Amount spent on stereo = (1/4)S Amount spent on television = (1-1/2)(1/4)S = (1/2)*(1/4)*S = (1/8)S (Stereo + TV)/Total Savings = S(1/4 + 1/8)/S = 3/8 Answer: D #### D QUESTION:In a box of 8 pens, a total of 3 are defective. If a customer buys 2 pens selected at random from the box, what is the probability that neither pen will be defective? options: A)2/10 B)3/11 C)4/13 D)5/14 E)6/17 SOLUTION:P(neither pen is defective) = 5/8*4/7 = 5/14 The answer is D. #### D QUESTION:Three pipes of same capacity can fill a tank in 8 hours. If there are only two pipes of same capacity, the tank can be filled in? options: A)15 hours B)12 hours C)76 hours D)16 hours E)81 hours SOLUTION:The part of the tank filled by three pipes in one hour = 1/8 => The part of the tank filled by two pipes in 1 hour = 2/3 * 1/8 = 1/12. The tank can be filled in 12 hours. Answer: B #### B QUESTION:A certain sum of money doubles itself in 10 years in how much many years will it trible itself at the same rate? options: A)7 1/2 years B)20 years C)15 years D)38 years E)30 years SOLUTION:100 ---- 100 --- 10 100 --- 10 -------------------- 300 ---- 20 years ANSWER:B #### B QUESTION:The number of cars present at a particular time was measured at 4,999 different locations on Tuesday and on Wednesday. The number of locations that had more cars on Wednesday was 20% higher than the number of locations that had more cars on Tuesday. How many of the locations had more cars on Tuesday? options: A)1,159 B)1,333 C)1,860 D)2,160 E)2,272 SOLUTION:The question states that all these 4,999 locations were measured twice, once on each day. It also breaks the 4,999 into two groups, the higher-on-Tuesday locations and the higher-on-Wednesday locations, which we can call T and W. Therefore, we can write two equations: For each of the first and second day count of locations, T + W = 4999 But, for the second day count, W = 1.20 T i.e. for Second day count, T + 1.20T = 4999 i.e. 2.20 T = 4999 i.e. T = 2272 E #### E QUESTION:In a jar there are balls in different colors: blue, red, green and yellow. The probability of drawing a blue ball is 1/4. The probability of drawing a red ball is 1/5. The probability of drawing a green ball is 1/10. If a jar cannot contain more than 50 balls, how many yellow balls are in the Jar? options: A)5. B)7. C)9. D)10. E)17. SOLUTION:We need to get some number which is less than 50 and exactly divisible by 4,5 and 10 Lets take LCM of three balls 4,5 and 10 =20. The 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. The 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. The 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. Then out of 20 - ( 5 + 4 + 2 ) = 9 YELLOW balls. IMO option C is correct. #### C QUESTION:In what time will a train 200 m long cross an electric pole, it its speed be 144 km/hr? options: A)2.5 sec B)2.9 sec C)3.5 sec D)7.5 sec E)5 sec SOLUTION:Speed = 144 * 5/18 = 40 m/sec Time taken = 200/40 = 5 sec. Answer: E #### E QUESTION:What is 30% of 210? options: A)61 B)63 C)65 D)67 E)69 SOLUTION:X/210 = 30/100 100X = 210X30 X =(210X30)/100 X =6300/100 = 63 ANSWER = B = 63 #### B QUESTION:If p^2 – 6p + 8 = q, and p is a positive integer between 1 and 10, inclusive, what is the probability that q < 0? options: A)1/5 B)1/10 C)2/5 D)3/5 E)3/10 SOLUTION:(p-2)(p-4) = q p = 3 for this to be true, so 1/10 Ans :B #### B QUESTION:P is 30% more efficient than Q. P can complete a work in 23 days. If P and Q work together, how much time will it take to complete the same work? options: A)11 B)12 C)13 D)14 E)15 SOLUTION:Work done by P in 1 day = 1/23 Let work done by Q in 1 day = q q × (130/100) = 1/23 => q = 100/(23×130) = 10/(23×13) Work done by P and Q in 1 day = 1/23 + 10/(23×13) = 23/(23×13)= 1/13 => P and Q together can do the work in 13 days Answer is C. #### C QUESTION:A dealer purchases 15 articles for Rs. 25 and sells 12 articles for Rs. 35. Find the profit percentage? options: A)80% B)50% C)75% D)40% E)53% SOLUTION:L.C.M of 15 and 12 = 60 CP of 60 articles = Rs. 100 (25 * 4) SP of 60 articles = Rs. 175 (35 * 5) Profit percentage = (175 - 100)/100 * 100 = 75% Answer: C #### C QUESTION:The 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? options: A)8 B)2 C)9 D)4 E)6 SOLUTION:Explanation: [15000 * (1 + R/100)2 - 15000] - (15000 * R * 2)/100 = 96 15000[(1 + R/100)2 - 1 - 2R/100] = 96 15000[(100 + R)2 - 10000 - 200R]/10000 = 96 R2 = (96 * 2)/3 = 64 => R = 8 Rate = 8% Answer: Option A #### A QUESTION:If the sum of the interior angles of a regular polygon measures up to 1080 degrees, then how many sides does the polygon have? options: A)10 B)16 C)8 D)11 E)14 SOLUTION:one of the interior angle = 180 - 360/n sum of the interior angles is = n (180 - 360/n) given n(180 - 360/n)=1080 180n - 360 = 1080 180n = 1440 n = 1440/180 = 8 ANSWER:C #### C QUESTION:20 people are there, they are shaking hands together, how many hand shakes possible, if they are in pair of cyclic sequence. options: A)21 B)20 C)40 D)42 E)19 SOLUTION:n for cyclic hand shake and n-1 for linear handshake. so here no of hand shake is 20. ANSWER:B #### B QUESTION:4 Women & 6 men have to be seated in a row given that no two women can sit together. How many different arrangements are there. options: A)6! x 7P4 B)6! x 9P4 C)6! x 5P4 D)6! x 3P4 E)6! x 2P4 SOLUTION:Let us first sit all the 6 men in 6 positions in 6! ways. Now there are 7 gaps between them in which 4 women can sit in 7P47P4 ways. So total ways are 6! x 7P4 Answer:A #### A QUESTION:16.02 × 0.1 = ? options: A)0.1602 B)0.001602 C)1.6021 D)0.01602 E)None of these SOLUTION:16.02 × 0.1 = 1.602 The answer is C. #### C QUESTION:If 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? options: A)44 B)48 C)45 D)47 E)49 SOLUTION:Let the required length be x meters More men, More length built (Direct proportion) Less days, Less length built (Direct Proportion) Men 20:35 and Days 6:3::56:x Therefore (20 x 6 x (X))=(35 x 3 x 56) x=(35x3x56)/120=49 Hence, the required length is 49 m. Answer is E. #### E QUESTION:The H.C.F of two numbers is 8. Which of the following can never be their L.C.M? options: A)55 B)44 C)66 D)60 E)12 SOLUTION:H.C.F of two numbers divides their L.C.M exactly. Clearly, 8 is not a factor of 60. Answer:D #### D QUESTION:There 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. options: A)460 B)490 C)493 D)455 E)424 SOLUTION:Ways to pick 4 cans so that at least one red and at least one blue cans to remain the refrigerator = total 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 12C4−8C4−4C4=495−70−1=424 ANSWER:E #### E QUESTION:At Joes Steakhouse the hourly wage for a chef is 20% 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 $6.50 per hour, how much less than a manager does a chef earn each hour? options: A)$2.6 B)$2.40 C)$3.40 D)$4.40 E)$5.40 SOLUTION:Manager wages per hour = $6.50 Dishwasher wages per hour = half of manager's wages. = 1/2($6.50) ==> $3.25 Chef wages per hour = 20% greater than Dishwasher wages --> 20% of $3.25 = (20*($3.25)) /100 --> ($65)/100 --> $0.65 Therefore, Chef wages per hour = $3.25 + $0.65 ==> $3.9 Difference of wages between manager and chef = $6.50 - $3.9 ==> $2.6 ANSWER:A #### A QUESTION:If x and y are positive numbers and z = xy^2, a 50 percent increase in x and a 30 percent decrease in y would result in which of the following changes in z? options: A)decrease of 7.5% B)decrease of 26.5% C)increase of 16.5% D)increase of 24.5% E)increase of 32.5% SOLUTION:After the changes, z = 1.5x*(0.7y)^2 = (1.5*0.49)xy^2 = 0.735*z The answer is B. #### B QUESTION:A cube of side one meter length is cut into small cubes of side 5 cm each. How many such small cubes can be obtained? options: A)2878 B)8000 C)1000 D)2997 E)2701 SOLUTION:Along one edge, the number of small cubes that can be cut = 100/5 = 20 Along each edge 5 cubes can be cut. (Along length, breadth and height). Total number of small cubes that can be cut = 20 * 20 * 20 = 8000 Answer: B #### B QUESTION:The length of a rectangular floor is more than its breadth by 200%. If Rs. 324 is required to paint the floor at the rate of Rs. 3 per sq m, then what would be the length of the floor? options: A)65 B)44 C)18 D)16 E)14 SOLUTION:Let the length and the breadth of the floor be l m and b m respectively. l = b + 200% of b = l + 2b = 3b Area of the floor = 324/3 = 108 sq m l b = 108 i.e., l * l/3 = 108 l2 = 324 => l = 18. Answer:C #### C QUESTION:How long does a train 110 m long traveling at 60 kmph takes to cross a bridge of 390 m in length? options: A)18.9 sec B)88.9 sec C)22.9 sec D)30.00 sec E)72.0 sec SOLUTION:D = 110 + 390 = 500 m S = 60 * 5/18 = 50/3 T = 500 * 3/50 = 30 sec Answer: D #### D QUESTION:When 1/10 percent of 3,000 is subtracted from 1/10 of 3,000, the difference is options: A)2970 B)297 C)2997 D)300 E)30 SOLUTION:(1/10)*3000 - (1/10)%*3000 = 300 - (1/1000)*3000 = 300 - 3 = 297 The answer is B. #### B <<<Examples ends QUESTION:A 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 : options: A)16000 B)18000 C)20000 D)30000 E)None of these SOLUTION:Explanation: Number of bricks =Courtyard area /1 brick area =(1800×1200 /12×6)=30000 Option D #### D

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:An art gallery owner is hanging paintings for a new show. Of the five paintings she has to choose from, she can only hang three on the main wall of the gallery. Assuming that she hangs as many as possible on that wall, in how many ways can she arrange the paintings? options: A)18 B)30 C)60 D)120 E)216 SOLUTION:Arrangment means permutations questions.. 5P3 = 5!/3! = 60. IMO option C is correct answer.. #### C QUESTION:The 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? options: A)38 B)27 C)75 D)28 E)21 SOLUTION:Explanation: The 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. Answer: C #### C QUESTION:A can do a work in 8 days. B can do the same work in 24 days. If both A & B are working together in how many days they will finish the work? options: A)3 B)5 C)4 D)2 E)6 SOLUTION:A rate = 1/8 B rate = 1/24 (A+B) rate = (1/8)+(1/24) = 1/6 A & B finish the work in 6days correct option is E #### E QUESTION:If 2994 ÷ 14.5 = 171, then 29.94 ÷ 1.45 = ? options: A)17.1 B)17.3 C)17.5 D)17.7 E)17.2 SOLUTION:29.94/ 1.45 = 299.4/14.5 = (2994/14.5) x 1/10) [ Here, Substitute 171 in the place of 2994/14.5 ] = 171/10 = 17.1 Answer is A. #### A QUESTION:A person can row at 10 kmph in still water. If the velocity of the current is 2 kmph and it takes him 5 hour to row to a place and come back, how far is the place? options: A)24km B)30km C)48km D)12km E)15km SOLUTION:Speed of down stream = 10+2 = 12kmph speed of upstream = 10-2 = 8kmph Let the required distance be xkm x/12 + x/8 = 5 2x+3x = 120 x = 24 km Answer is A #### A QUESTION:During a certain two-week period, 75 percent of the movies rented from a video store were comedies, and of the remaining movies rented, there were 2/3 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? options: A)5 A B)10 A C)15 A D)18 A E)25 A SOLUTION:Movies: 75 % comedies. 25 % remaining genre. Now in this 25 %, there are only 2 categories. Action movies and Drama Movies. If Action = x; Drama movies = 2x/3. Total 5x/3. 5x/3 = 25; x = 15 Action movies: 15 % Drama movies: 10 % we can say that out of 100 z,: comedies: 75 z action: 15 z drama: 10 z Now action movies were A This means: A = 15 z. z = A/ 15 Comedies: 75 z = 75 * (A/15) 5 A A is the answer. #### A QUESTION:curie bakes 5 cookies for 5 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? options: A)1 B)2 C)3 D)4 E)5 SOLUTION:curie made 5*5 cookies = 25 cookies. 2 friends eat 3 cookies, leaving 9 remaining for 2 friends. 9 is not divisible by 2. The 2 friends ate a cumulative number of cookies less than 9 that must be divisible by 2, because the number is the same. The nearest multiple of 2 is 8. 9-8=1 A is the correct answer #### A QUESTION:A 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: options: A)45 km/hr B)50 km/hr C)54 km/hr D)55 km/hr E)58 km/hr SOLUTION:Speed of the train relative to man = 125/10 m/sec = 25/2 m/sec. 2 = 25/2 x 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. Option B #### B QUESTION:A candidate got 35% of the votes and lost to the rival by 1350 votes. How many votes were cast? options: A)4000 B)4500 C)5000 D)5500 E)6000 SOLUTION:35%-----------L 65%-----------W ------------------ 30% = 1350 10% = 450 100% of the votes = 4500 Answer: B #### B QUESTION:Which of the following can be expressed as a terminating decimal? options: A)1/25 + 1/35 B)1/225 + 1/1,250 C)1/11,000 + 1/13,000 D)1/75 + 1/35 E)1/125 + 1/8 SOLUTION:In such questions, it is always easier to find an answer instead of eliminating choices. Let us start with the simplest ones first. A. 1/25 + 1/35 = 12/175 = 12/25*1/7 1/7 does is not a terminating decimal. E. 1/125 + 1/8 = 8 + 125/ 1000 = 133/1000 This is a terminating decimal and our answer. Correct Option: E #### E QUESTION:In a box, there are 4 green, 5 black and 7 red pencils. One pen is picked up randomly. What is the probability that it is neither black nor red? options: A)2/5 B)1/5 C)1/2 D)1/3 E)1/4 SOLUTION:Explanation : Neither black nor red means the pencils drawn is green. Total number of outcomes = (4+5+7) = 16. Number of Favourable outcomes = 4 = Number of green pencils. Hence, Probability of the event = 4/16 = 1/4. Answer : E #### E QUESTION:The greatest number of four digits which is divisible by 12, 20, 36 and 60 is: options: A)9000 B)9900 C)9500 D)9800 E)9700 SOLUTION:Greatest number of 4-digits is 9999. L.C.M. of 12, 20, 36 and 60 is 180. On dividing 9999 by 180, the remainder is 99. Required number (9999 - 99) = 9900. Answer: Option B #### B QUESTION:A man swims downstream 72 km and upstream 45 km taking 9 hours each time; what is the speed of the current? options: A)1.7 B)1.5 C)1.2 D)1.1 E)1.9 SOLUTION:72 --- 9 DS = 8 ? ---- 1 45 ---- 9 US = 5 ? ---- 1 S = ? S = (8 - 5)/2 = 1.5 Answer: B #### B QUESTION:On a certain day, Tim invested $600 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’s investment in the first 2 years was how much greater than the total amount of interest earned by Lana’s investment in the first 2 years? options: A)$5 B)$15 C)$44 D)$100 E)$105 SOLUTION:Compounded 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. With respect to the problem at hand, at the end of two years, Tim would have 600(1.10)^2 = 600(1.21) = 726 and Lana would have 800(1.05)^2 = 800(1.1025) = 882 Thus, Tim earned 126 dollars, while Lana earned 82 dollars The difference is $44 and the answer is C. #### C QUESTION:Rohit spent 30 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 Rohit have left over? options: A)29% B)35% C)46% D)47% E)52% SOLUTION:SayRohit's earning last month was $100. Rohit spent 30 percent of his earning last month on rent --> $30 on rent; 20 percent less than what he spent on rent to purchase a new dishwasher --> $30*0.8=$24 on the dishwasher. Left over amount 100 - (30 + 24) = $46 Answer: C #### C QUESTION:Calculate the speed of a boat in still water (in km/hr) if in one hour, the boat goes 13 km/hr downstream and 10 km/hr upstream. options: A)3 kmph B)9 kmph C)4 kmph D)8 kmph E)6 kmph SOLUTION:Speed in still water = (13 + 5)1/2 kmph = 9 kmph. answer :B #### B QUESTION:If x and y are positive integers, and 1 is the greatest common divisor of x and y, what is the greatest common divisor S of 2x and 3y? options: A)1 B)S=Cannot be determined C)S=2 D)5 E)6 SOLUTION:My explanation: from question stem we know that nothing is common between X and Y , X and Y are two prime numbers eg: X=2, Y=3 and their GCD(2,3) =1 and so 2X and 3Y will have a GCD(2X,3Y) = 1 . what if either X or Y was 1, eg: X=1,Y=4 then GCD(1,4) =1 , but GCD(2,12) = 2. and hence answer B #### B QUESTION:A 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? options: A)70 minutes B)72 minutes C)80 minutes D)76 minutes E)77 minutes SOLUTION:Time taken to reach = 2400/30= 80 minutes ANSWER:C #### C QUESTION:If n is an integer greater than 8, which of the following must be divisible by 3? options: A)1. n (n+1) (n-4) B)2. n (n+2) (n-1) C)3. n (n+3) (n-5) D)4. n (n+4) (n-2) E)5. n (n+5) (n-6) SOLUTION:We need to find out the number which is divisible by three, In every 3 consecutive integers, there must contain 1 multiple of 3. So n+4 and n+1 are same if we need to find out the 3's multiple. replace all the numbers which are more than or equal to three 1. n (n+1) (n-4) = > n(n+1)(n-1) = > (n-1)n(n+1) 2. n (n+2) (n-1) = > n(n+2)(n-1) = > (n-1)n(n+1) 3. n (n+3) (n-5) = > n(n+0)(n-2) = > (n-2)n(n) 4. n (n+4) (n-2) = > n(n+1)(n-2) = > (n-2)n(n+1) 5. n (n+5) (n-6) = > n(n+2)(n-0) = > (n)n(n+2) from the above onlyoption Ais product of consecutive three numbers. C #### C QUESTION:A company has 2 directors and 5 managers. How many different committees with 5 people can be chosen having at least 1 director? options: A)500 B)720 C)4500 D)20 E)55 SOLUTION:atleast one means exactly one and more than one. different committees with 5 people can be chosen having at least 1 director is (2c1*5c4) + (2c2*5c3) = 20; Hence D. #### D QUESTION:Working at their respective constant rates, Paul, Abdul and Adam alone can finish a certain work in 3, 4, and 5 hours respectively. If all three work together to finish the work, what fraction R of the work will be done by Adam? options: A) 1/4 B) 12/47 C) 1/3 D) 5/12 E) 20/47 SOLUTION:Let the total work be 60 units. Pual does 60/3 =20 units of work per hr. abdul does 15 units per hr and adam does 12 units per hr. If all work together they do (20 + 15 + 12) units per hr = 47 units per hr. So the time taken to finish the work = 60/47 hrs. adam will do 60/47 * 12 units of work in 60/47 hr . fraction of work adam does =work done by adam / total work R>( 60/47 *12)/60 =12/47 Answer B #### B QUESTION:A tank is filled in 10 hours by three pipes A, B and C. 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? options: A)70 hours B)30 hours C)35 hours D)50 hours E)40 hours SOLUTION:Efficiency of pipes A,B,C =1:2:4 Therefore, in 10 hours, part of the tank filled by A =17 Therefore, pipe A alone requires 10×7=70 hours to fill the tank. Answer: Option A #### A QUESTION:Rs. 1400 is divided into three parts A, B and C. How much A is more than C if their ratio is 1/3:1/3:1/6? options: A)300 B)992 C)772 D)552 E)280 SOLUTION:1/3:1/3:1/6 = 2:2:1 1/5*1400 = 280 560-280 = 280 Answer: E #### E QUESTION:A school has received 60% of the amount it needs for a new building by receiving a donation of $500 each from people already solicited. People already solicited represent 50% 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? options: A)$200 B)$333.33 C)$100.25 D)$277.78 E)$377.00 SOLUTION:Let us suppose there are 100 people. 50% of them donated $25000 ( 500 * 50 ) $25000 is 60% of total amount. So total amount = 25000 * 100/60 Remaining amount is 40% of total amount. 40% of total amount = 25000 * (100/60) * (40/100) = 50000/3 This amount has to be divided by 50( remaining people are 50 ) So per head amount is 50000/3 / 50 = 32000/180 = 333.33; ANSWER:B #### B QUESTION:Four different objects 1,2,3,4 are distributed at random in four places marked 1,2,3,4. What is the probability that none of the objects occupy the place corresponding to its number? options: A)17/24 B)3/8 C)1/2 D)5/8 E)5/3 SOLUTION:Explanation : Let a particular number (say) number 2 occupies position 1. Then all possible arrangement are given as: =>(2,1,3,4), (2,1,4,3), (2,3,4,1), (2,4,1,4), (2,4,1,3), (2,4,3,1). Out of these six, three (2,1,3,4), (2,3,1,4), (2,4,3,1) are not acceptable because numbers 3 and 4 occupy the correct positions. Hence, the required probability = 3/6 = 1/2. Answer : C #### C QUESTION:Sandy had $231 left after spending 30% of the money she took for shopping. How much money did Sandy take along with her? options: A)$270 B)$290 C)$310 D)$330 E)$350 SOLUTION:Let the money Sandy took for shopping be x. 0.7x = 231 x = 330 The answer is D. #### D QUESTION:Ram purchased a TV and a DVD Player for Rs. 25000 and Rs. 5000 respectively. He sold the DVD Player at a loss of 4 percent and TV at a profit of 10 percent. Overall he make a.? options: A)2200 B)2500 C)2800 D)2300 E)2000 SOLUTION:Let the SP of the TV and the DVD Player be Rs. r and Rs. m respectively. r = 25000(1 + 10/100) = 25000 + 2500 m = 5000(1 - 4/100) = 5000 - 200 Total SP - Total CP = r + m - (25000 + 5000) = 2500 - 200 = Rs. 2300 As this is positive, an overall profit of Rs. 2300 was made. Answer: D #### D QUESTION:Mr. 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 options: A)$145 B)$250 C)$300 D)$175 E)$150 SOLUTION:Let the 1st paycheck be x(integer).Mr. Rodger got a weekly raise of $145. so after completing the 1st week she will get $ (x+145).similarly after completing the 2nd week she will get $(x+145)+$145.=$(x+145+145=$(x+290). so in this way end of every week her salary will increase by $145. correct answer will be (A) #### A QUESTION:A 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? options: A)50 B)80 C)100 D)125 E)21 SOLUTION:Let old diameter be 4 , so radius is 2 Old area = 4π New diameter is 4.4 , so radius is 2.2 New area = 4.84π Increase in area is 0.84π % increase in area = 0.84/4*100 So, % increase is 21% Answer will be (E) #### E QUESTION:Mr. Jones sold two pens at $1 each. Based on the cost, his profit one was 50% and his loss on the other was 40%. On the sale of the pipes. Find the amount of his profit or loss? options: A)lost 10 cents B)lost 4 cents C)broke even D)gained 4 cents E)gained 40 cents SOLUTION:50 % profit on $ 1 = $ 50/100 × 1 = $ 0.50× 1 = $ 0.50 Similarly, 40 % loss on $ 1 = $ 40/100 × 1 = $ 0.40× 1 = $ 0.40 Therefore, in one pen his profit is $ 0.50 and in the other pipe his loss is $ 0.40 So profit by amount $0.40. Answer is E. #### E QUESTION:If the discount on Rs. 498 at 5% simple interest is Rs.18, when is the sum due? options: A)8 months B)11 months C)10 months D)9 months E)12 months SOLUTION:Explanation : F = Rs. 498 TD = Rs. 18 PW = F - TD = 498 - 18 = Rs. 480 R = 5% TD = (PW × TR)/100 ⇒ 18 = (480 × T × 5)/100 ⇒ 18 = 24 × T ⇒ T = 18/24 = 3/4 years = (12×3)/4 months = 9 months Answer : Option D #### D QUESTION:In a college 1/5th of the girls and 1/8th of the boys took part in a social camp. What of the total number of student in the college took part in the camp ? options: A)13/40 B)13/80 C)2/13 D)Data inadequate E)None SOLUTION:Answer Out of the 5 girls, 1 took part in the camp. Out of the 8 boys, 1 took part in the camp. ∴ 2/13 of total number of students took part in the camp. Correct Option: C #### C QUESTION:Find the average of all the numbers between 6 and 34 which are divisible by 5 options: A)18 B)20 C)24 D)30 E)40 SOLUTION:Exp. Multiples of 5 between 6 and 34 are 10,15,20,25,30 Average = (10+15+20+25+30)/5 =5(10+30)/2*5 = 40/2 =20 Answer:B #### B QUESTION:If 5 machines can produce 20 units in 10 hours, how long would it take 20 machines to produce 200 units? options: A)50 hours B)40 hours C)25 hours D)12 hours E)8 hours SOLUTION:Here, we're told that 5 machines can produce 20 units in 10 hours.... That 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. 20 units/5 machines = 4 units are made by each machine every 10 hours Now that we know how long it takes each machine to make 4 units, we can break THIS down further if we choose to... 10 hours/4 units = 2.5 hours per unit when 1 machine is working. The prompt asks us how long would it take 20 machines to produce 200 units. If 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. (2.5 hours)(10 times) = 25 hours Final Answer: [Reveal]Spoiler: C #### C QUESTION:In 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? options: A)80% B)20% C)40% D)50% E)None of these SOLUTION:Number of students passed = 60% of 140 = 60/100 * 140 = 84 Number of students failed = 140 - 84 = 56. Required percentage = 28/56 * 100 = 50%. ANSWER:D #### D QUESTION:A certain music store stocks 800 cellos and 600 violas. Of these instruments, there are 100 cello-viola pairs, such that a cello and a viola were both made with wood from the same tree (each tree can make at most one viola and one cello, so there are no pairs other than these 90). If one viola and one cello are chosen at random, what is the probability that the two instruments are made with wood from the same tree? options: A)3/16,000 B)1/4,800 C)3/1,600 D)1/90 E)2/45 SOLUTION:Solution provided by stanford2012 is correct: 100/800 choosing one of the cellos which has a pair viola, 1/600 choosing the viola which is the pair of chosen cello --> P=100/800*1/600=1/4,800. Answer: B. #### B QUESTION:1+ 1+ 1+ 2 × 1^2 + 2 × 1^1+ 2 × 1^4 + 2 × 1^5 + 2 × 1^6 + 2 × 1^7 = options: A) 1^7 B) 1^8 C) 1^14 D) 1^28 E) 3^30 SOLUTION:We have the sum of 9 terms. Now, if all terms were equal to the largest term 2*1^7 we would have: sum=9*(2*1^7)=2*1^9=~1^10, so the actual sum is less than 1^10 and more than 1^7 (option A) as the last term is already more than that. So the answer is clearly B. Answer: B. #### B QUESTION:Find the area of right angled triangle whose hypotenuse is 15 cm and one of the sides is 12 cm. options: A)34 cm² B)38 cm² C)54 cm² D)56 cm² E)64 cm² SOLUTION:AB² = AC² - BC² = 15² - 12² = 225 - 144 = 81 Therefore, AB = 9 Therefore, area of the triangle = ¹/₂ × base × height = ¹/₂ × 12 × 9 = 54 cm² ANSWER : C #### C QUESTION:How many two digit numbers of distinct digits can be formed by using digits 1, 2, 3, 4, 5, 6 and 7 such that the numbers are divisible by 3? options: A)9 B)10 C)11 D)12 E)14 SOLUTION:A number will be divisible by 3 if sum of all the digits of the number is divisible by 3 Here the Possible sum of the two distinct digits can be 3, 6, 9 and 12 only in order to satisfy the given condition If sum of Digits = 3, No. = 12, 21 --- 2 Cases If sum of Digits = 6, No. = 15, 24, 42, 51 --- 4 Cases If sum of Digits = 9, No. = 27, 36, 45, 54, 63, 72 --- 6 Cases If sum of Digits = 12, No. = 57, 75 --- 2 Cases Total Cases = 2+4+6+2 = 14 cases Answer: option E #### E QUESTION:In 1990 a total of c earthquakes occurred worldwide, some but not all of which occurred in Asia. If e 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? options: A)c/e B)e/c C)e/(c-e) D)c/(c-e) E)1- (e/c) SOLUTION:We're given a couple of facts to work with: 1) There were a total of c earthquakes 2) Of those earthquakes, e of them occurred in Asia We'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. Let's TEST VALUES c = 5 total earthquakes e = 2 occurred in Asia Thus, there were 3 earthquakes that DID NOT occur in Asia.... The answer to the question is 2:3 We just need to plug in the values for c and e and find the match... Answer A: c/e = 5/2 NOT a match Answer B: e/c = 2/5 NOT a match Answer C: e/(c-e) = 2/(5-2) = 2/3 This IS a match Answer D: c/(c-e) = 5/(5-2) = 5/3 NOT a match Answer E: 1 - (e/c) = 1-2/5 = 3/5 NOT a match C #### C QUESTION:If x < y < z and y - x > 5, where x is an even integer and y and z are odd integers, what is the least possible value Q of z - x? options: A)6 B)7 C)8 D)9 E)10 SOLUTION:x<y<z To find the least possible value for z-x; we need to find the values for z and x that can be closest to each other. If x is some even number, then what could be minimum possible odd z. If x is some even number y-x>5; y>x+5; minimum value for y=x+5+2=x+7[Note: x+5 is as even+odd=odd and nearest odd greater than x+5 is x+5+2] Minimum value for z=y+2=x+7+2=x+9 [Note: z=y+2 because both z and y are odd. Difference between two odd numbers is 2] Q=z-x = x+9-x= 9 Ans:D #### D QUESTION:If 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? options: A)44 B)48 C)45 D)47 E)49 SOLUTION:Let the required length be x meters More men, More length built (Direct proportion) Less days, Less length built (Direct Proportion) Men 20:35 and Days 6:3::56:x Therefore (20 x 6 x (X))=(35 x 3 x 56) x=(35x3x56)/120=49 Hence, the required length is 49 m. Answer is E. #### E QUESTION:There are some students in a school.The 1/2 of number of students is a whole number. The 1/6 of number of students is a whole number. The 1/5 of number of students is a whole number. The 1/7 of number of students is a whole number.Find the number of students. options: A)200 B)210 C)220 D)230 E)240 SOLUTION:210 ANSWER:B #### B QUESTION:Simple interest on a sum at 4% per annum for 2 years is Rs.80. The C.I. on the same sum for the same period is? options: A)Rs.81.60 B)Rs.160 C)Rs.172 D)Rs.727 E)Rs.728 SOLUTION:SI = 40 + 40 CI = 40 + 40 + 1.6 = 81.6 Answer:A #### A QUESTION:The 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 options: A)11 B)15 C)6 D)8 E)76 SOLUTION:Explanation: Age of the 15th student = [15 * 15 - (14 * 5 + 16 * 9)] = (225-214) = 11 years. Answer: A) 11 #### A QUESTION:A football field is 9600 square yards. If 1200 pounds of fertilizer are spread evenly across the entire field, how many pounds of fertilizer were spread over an area of the field totaling 5600 square yards? options: A)450 B)600 C)700 D)2400 E)3200 SOLUTION:Answer C) 9600 yards need 1200 lbs 1 Yard will need 1200/9600 = 1/8 lbs 3600 Yards will need 1/8* 5600 Yards = 700lbs #### C QUESTION:Two 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 6 sec. What is the length of the fast train? options: A)27 7/6 B)27 7/5 C)277/2 D)300/9 E)27 7/1 SOLUTION:Relative speed = (40 - 20) = 20 km/hr. = 20 * 5/ 18 = 50/9 m/sec. Length of faster train = 50/9 * 6 = 300/9 = 300/9 m. Answer:D #### D QUESTION:8 chess players take part in a tournament. Every player plays twice with each of his opponents. How many games are to be played? options: A)66 B)52 C)58 D)55 E)56 SOLUTION:Though 2*(8C2) 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. The first guy has to play 2 matches with the rest of 7, so he'll play 14 matches. Similarly, second guy has to play with the rest of 6 as his 2 games with the first guy are already played. So he plays 12 matches. This continues like this and the total matches are 14+12+10...+2 14+12+...+2 = 2(7+6+...+1) = 2((7*8)/2) = 7*8 =56. ANSWER:E #### E QUESTION:There are four prime numbers written in ascending order. The product of first three is 385 and that of last three is 1001. The last number is: options: A)9 B)13 C)15 D)12 E)19 SOLUTION:Explanation: abc/bcd=385/1001=>a/d=5/13 So d = 13 Option B #### B QUESTION:If “*” is called “+”, “/” is called “*”, “-” is called “/”, “+” is called “-”. 240*80 / 60 + 40 / 10 = ? options: A)-2305 B)-2407 C)2509 D)-2101 E)None of these SOLUTION:Explanation: Given : 240*80 / 60 + 40 / 10 = ? Substituting the coded symbols for mathematical operations, we get, 240 / 80 - 60 * 40 - 10 = ? 3 - 2400 - 10 = -2407 ANSWER : B #### B QUESTION:A car covers a distance of 624 km in 6 ½ hours. Find its speed? options: A)104 B)140 C)200 D)150 E)250 SOLUTION:624/6 = 104 kmph ANSWER A #### A QUESTION:10, 20, 12, 24, 16, 32, ? options: A)20 B)21 C)22 D)23 E)24 SOLUTION:E 24 This is an alternating multiplication and subtracting series with a pattern x2, -8, x2, -8. #### E QUESTION:What is the sum of all remainders obtained when the first 100 natural numbers are divided by 7? options: A)397 B)401 C)403 D)405 E)364 SOLUTION:A positive integer can give only the following 9 remainders when divided by 9: 1, 2, 3, 4, 5, 6, 7, 8, and 0. 1 divided by 9 gives the remainder of 1; 2 divided by 9 gives the remainder of 2; ... 8 divided by 9 gives the remainder of 8; 9 divided by 9 gives the remainder of 0. We'll have 11 such blocks, since 99/9=11. The last will be: 91 divided by 9 gives the remainder of 1; 92 divided by 9 gives the remainder of 2; ... 98 divided by 9 gives the remainder of 8; 99 divided by 9 gives the remainder of 0. The last number, 100, gives the remainder of 1 when divided by 9, thus the sum of all remainders will be: 11(1+2+3+4+5+6+7+8+0)+1=364. Answer: E. #### E QUESTION:The average age of a class is 15.8 years. The average age of boys in the class is 16.4 years while that of girls is 15.4 years. What is the ratio of boys to girls in the class? options: A)1:2 B)3:4 C)3:5 D)2:3 E)None of these SOLUTION:let x = number of girls y = number of boys sum of girls ages / x = 15.4 sum of boys ages / y = 16.4 The sum of the girls' ages is 15.4x, and boys' sum is 16.4y (sum of girls ages + sum of boys ages) / (x+y)= 15.8 (15.4x + 16.4y) / (x+y) = 15.8 15.4x + 16.4y = 15.8(x+y) 15.4x + 16.4y = 15.8x + 15.8y 0.6y = 0.4x 0.6y/x = 0.4 y/x = 0.4/0.6 y/x = 2/3 which is the ratio of boys to girls ANSWER:D #### D QUESTION:If 5^10 x 2^10 = 10^n what is the value of n? options: A)16 B)14 C)12 D)10 E)18 SOLUTION:5^10*2^10 = 10^n or 10^10 =10^n n=10 D #### D QUESTION:The speed at which a man can row a boat in still water is 14 kmph. If he rows downstream, where the speed of current is 2 kmph, what time will he take to cover 40 metres? options: A)16 seconds B)34 seconds C)9 seconds D)12 seconds E)15 seconds SOLUTION:Speed of the boat downstream = 14 + 2 = 16 kmph = 16 * 5/18 = 40/9 m/s Hence time taken to cover 40 m = 40*9/40 = 9 seconds. Answer: C #### C QUESTION:If x is an integer, then x(x – 1)(x – k) must be evenly divisible by six when k is any of the following values EXCEPT options: A)-4 B)-2 C)-1 D)2 E)5 SOLUTION:We have the product of 3 integers: (x-1)x(x-k). Note that the product of 3 integers is divisible by 6 if at least one multiple is divisible by 6. Now, to guarantee that at least one integer out of x, (x – 1), and (x – k) is divisible by 6 these numbers must have different remainders upon division by 3, meaning that one of them should have remainder of 1, another reminder of 2 and the last one remainder of 0, so be divisible by 6. Next, if k=2 then we'll have (x-1)x(x-2)=(x-1)x(x-2) --> which means that (x-1) and (x-2) will have the same remainder upon division by 6. Thus for k=2 we won't be sure whether (x-1)x(x-k) is divisible by 6. Answer: D. #### D QUESTION:AB +BA ___ 101 In the addition problem above, A and B represent digits in two different two-digit numbers. What is the sum of A and B? options: A)6 B)8 C)10 D)11 E)14 SOLUTION:two ways to do it.. 1) straight logic.. we can see that ones digit is 1 when units digit B and A are added.. only 10 fits in.. C #### C QUESTION:In a hotel, 60% had vegetarian lunch while 30% had non-vegetarian lunch and 15% had both type of lunch. If 96 people were present, how many did not eat either type of lunch ? options: A)27 B)26 C)25 D)24 E)20 SOLUTION:Explanation: n(A)=(60/100∗96)=288/5 n(B)=(30/100∗96)=144/5 n(A∩B)=(15100∗96)=72/5 People who have either or both lunch n(A∪B)=288/5+144/5−72/5 =360/5=72 So People who do no have either lunch were = 96 -72 = 24 ANSWER IS D #### D QUESTION:Find the principle on a certain sum of money at 5% per annum for 3 1/5 years if the amount being Rs.870? options: A)Rs.700 B)Rs.780 C)Rs.750 D)Rs.1000 E)None of these SOLUTION:Explanation: 870 = P [1 + (5*16/5)/100] P= 750 Answer: Option C #### C QUESTION:At what rate p.a a sum of Rs. 2400 will become Rs. 3600/- in 5 years. options: A)10% B)15% C)20% D)12% E)23% SOLUTION:Explanation: principal P = 2400/- Rate of interest R = ? Time T = 5 years Accumulated Amount A = Rs.10400/- A = P + I A = P + PTR/100 A = P(1+ TR/100) 2400[ 1 + (5 x R)/100] = 3600 2[(20 + R)/20] = 3 20 + R = 30 R = 10% Answer: Option A #### A QUESTION:(+15) + (-11) - (+5) - (-7) options: A)8 B)2 C)6 D)5 E)3 SOLUTION:= 15-11-57 22-16, [adding all integers with plus (+) sign together and with minus (-) sign respectively together = +6 or simply 6. correct answer (C) #### C QUESTION:From a pack of 52 cards, 1 card is drawn at random. Find the probability of a face card drawn options: A)4/13 B)1/52 C)1/4 D)1/5 E)None of above SOLUTION:Explanation: Total number of cases = 52 Total face cards = 16 [favourable cases] So probability = 16/52 = 4/13 Answer: A #### A QUESTION:A park square in shape has a 3 metre wide road inside it running along its sides. The area occupied by the road is 1764 square metres. What is the perimeter along the outer edge of the road? options: A)576 metres B)589 metres C)600 metres D)700 metres E)None SOLUTION:Solution Let the length of the outer edges be x metres. Then, length of the inner edge = ( x - 6)m. ∴ x2 - (x-6)2 = 1764 ‹=› x2-(x2-12x+36)= 1764 ‹=›12x = 1800 ‹=›x = 150. ∴ Required perimeter = (4x)m ‹=› (4 x 150)m = 600m. Answer C #### C <<<Examples ends QUESTION:If Susan takes 10 seconds to run y yards, how many minutes will it take her to run x yards at the same rate? options: A)xy/10 B)10x/(60y) C)60xy/10 D)xy/540 E)540x/y SOLUTION:The answer is B. She runs x yards in 10x/y seconds =10x/60y minutes. #### B

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:The average of 20 results is 65 and the average of other 65 results is 20 . what is the average of all the results? options: A)30 B)25 C)48 D)50 E)None SOLUTION:Answer Sum of 85 result = sum of 20 result + sum of 65 result. = 20 x 65 + 65 x 20 = 2600 Correct Option: A #### A QUESTION:A 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 80 km downstream? options: A)2 hours B)3 hours C)4 hours D)5 hours E)None SOLUTION:Solution Speed Downstream = (13 + 4) km/hr = 17 km/hr. Time taken to travel 80 km downstream =(80 / 17)hrs = 4 hrs 42 minutes. Answer E #### E QUESTION:Calculate the largest 3 digit number which is exactly divisible by 89? options: A)911 B)969 C)979 D)977 E)971 SOLUTION:Largest 4 digit number is 999 After doing 999 ÷ 89 we get remainder 20 Hence largest 3 digit number exactly divisible by 89 = 999 - 20 = 979 C #### C QUESTION:Anitha had 80 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. 4000. How much amount (in Rs) did she have in the denomination of Rs 45? options: A)3500 B)72 C)2000 D)3000 E)4000 SOLUTION:Let the number of 45-rupee notes = x Then, the number of 95-rupee notes = (80 – x) 45x + 95(80 – x) = 4000 or x + 2(80 – x) = 95 or x = 72. ANSWER:B #### B QUESTION:Zoey 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? options: A)$3 B)$2 C)$9 D)$1 E)$4 SOLUTION:Zoey 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. #### D QUESTION:If 0 < M < Y, M is an odd number and Y is a prime number, which of the following can be the value of M + Y ? options: A)11. B)13. C)17. D)10. E)7. SOLUTION:If m is odd ,implies m(odd)+y(odd/even prime)=(Even/Odd) If Y is even, the 2 is the even prime , therefore y=2m=1 since 0<M<Y therefore M+Y =3. But 3 is not an option which implies y is odd, Now M(odd)+Y(odd)=Even 10 is the only option that is even=D #### D QUESTION:x, y, and z are three positive integers whose average is 10. If x≤y≤z and z-x=3, which of the following could be the median W of x, y, and z? I. 9 II. 10 III. 11 options: A)I only B)II only C)III only D)I and II only E)I and III only SOLUTION:Average gives us an idea that 3 nos. are close to 10. so 10, 10, 10 is an unacceptable option because (z-x =3), but it helps in getting other combinations. Let us see options. If 9 has to be median W. 1st term has to less than 9 or equal to 9. (also maintain z-x = 3) 9 9 12 --> satisfies all conditions so 9 can be a median value. If 11 has to be a median 3rd term has to be 11 or more than 11. (also maintain z-x = 3) 8 11 11 -->satisfies all conditions so 9 can be a median value. Now for 10 to be median. z+ x = 20 and z-x = 3, we wont have integer values of z. 10 cannot be a median E is the answer. #### E QUESTION:Two numbers are in the ratio of 5:7. If 25 be subtracted from each, they are in the ratio of 35:59. Find the numbers? options: A)60,87 B)60,81 C)60,88 D)60,84 E)60,89 SOLUTION:(5x-25):(7x-25) = 35:59 x = 12 => 60,84 Answer:D #### D QUESTION:14. The sum and the product of two numbers are 25 and 144 respectively, the difference of the number is? options: A)7 B)9 C)8 D)5 E)4 SOLUTION:x + y = 25 xy = 144 (x- y)2 = (x + y)2 – 4xy (x- y)2 = 625 – 576 => (x – y) = 7 ANSWER: A #### A QUESTION:A and B can do a piece of work in 11 days. With the help of C they finish the work in 5 days. C alone can do that piece of work in? options: A)15.5 days B)19.5 days C)17.5 days D)9.2 days E)18.5 days SOLUTION:C = 1/5 – 1/11 = 6/55 => 9.2 days ANSWER:D #### D QUESTION:If 1 = 6 2 = 12 3 = 18 4 = 24 5 = 30 6 = 36 Then 24 = ? Hint: Its a logic Riddle not a mathematical riddle options: A)1 B)2 C)4 D)6 E)8 SOLUTION:C 24 As stated 4=24 => 24=4 Answer is C #### C QUESTION:Find the value of x. (47% of 1442 - 36% of 1412) + 66 = x? options: A)1 B)2 C)3 D)6 E)5 SOLUTION:D) 6 #### D QUESTION:A 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? options: A)287 sec B)288 sec C)48 sec D)16 sec E)17 sec SOLUTION:D = 540 + 180 = 720 S = 54 * 5/18 = 15 mps T = 720/15 = 48 sec Answer: C #### C QUESTION:The difference between the value of a number increased by 25% and the value of the original number decreased by 30% is 22. What is the original number? options: A)40 B)50 C)65 D)70 E)90 SOLUTION:Let the original # be x then 1.25x−0.7x=22 --> x=40 Answer: A. #### A QUESTION:If x = 4 and y = −2, what is the value of (x − 2y)^y? options: A)−100 B)0.015 C)0.25 D)4 E)8 SOLUTION:Quickly we can spot that answer is neither integer nor negative. Eliminate A, DE by inversing and squaring 0.015 Answer: B #### B QUESTION:√7 percent of 7√7 = options: A)0.55 B)0.96 C)0.1 D)0.45 E)0.6 SOLUTION:The other solutions are great, but here's one more approach. First, we scan the answer choices to see that they are quite spread apart. This means we can also use someAPPROXIMATION All test-takers must memorize the following approximations: √2 ≈ 1.4 √3 ≈ 1.7 √5 ≈ 2.2 √6 ≈ 2.4 √7 ≈ 2.6 So, √7 percent of 7√7 ≈ 2.6 percent of (7)(2.6) ≈ (2.6/100)(18.2) ≈ 47.32/100 ≈ 0.47 Check the answer choices to see that D is the only answer that's close. Answer: D #### D QUESTION:A dishonest dealer professes to sell goods at the cost price but uses a weight of 850 grams per kg, what is his percent? options: A)28% B)25% C)55% D)17.6% E)55% SOLUTION:850 --- 150 100 --- ? => 17.6% Answer: D #### D QUESTION:An electric pump can fill a tank in 5 hours. Because of a leak in the tank, it took 10hours to fill the tank. If the tank is full, how much time will the leak take to empty it? options: A)10hours B)12hours C)8hours D)5hours E)15hours SOLUTION:Work done by the leak in 1 hour = 1/5 - 1/10 = 1/10 The leak will empty the tank in 10hours Answer is A #### A QUESTION:If p is the product of the integers from 1 to 38, inclusive, what is the greatest integer k for which 3^k is a factor of p? options: A)13 B)15 C)17 D)19 E)21 SOLUTION:38! has 3, 6, 9,....30, 33, 36 as factors, which are 12 multiples of 3. We need to add 5 more to these 12 because of 9, 18, 27, and 36. The greatest integer of k is 17. The answer is C. #### C QUESTION:A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 215 m long? options: A)40 B)46 C)88 D)77 E)21 SOLUTION:: Speed = 45 * 5/18 = 25/2 m/sec Total distance covered = 360 + 215 = 575 m Required time = 575 * 2/25 = 46 sec Answer:B #### B QUESTION:The distance from City A to City B is 150 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? options: A)42.85 B)44 C)46 D)48 E)50 SOLUTION:The time it takes Cara to drive to City B is 150 / 30 = 5 hours. Dan needs to take less than 3.5 hours for the trip. Dan needs to exceed a constant speed of 150 / 3.5 = 42.85 miles per hour. The answer is A. #### A QUESTION:If two integers x,y (x>y) are selected from -5 to 6 (inclusive), how many cases are there? options: A)62 B)66 C)70 D)74 E)78 SOLUTION:There are 12 integers from -5 to 6 inclusive. 12C2 = 66. The answer is B. #### B QUESTION:A number x is multiplied with itself and then added to the product of 4 and x. If the result of these two operations is 5, what is the value of x? options: A)-4 B)-2 C)2 D)1 and -5 E)Cannot be determined. SOLUTION:A number x is multiplied with itself --> X^2 added to the product of 4 and x --> X^2+4X If the result of these two operations is -4 --> X^2+4X=5 i.e X^2+4X-5=0 is the Quadratic equation which needs to be solved. (X-1)(X+5) = 0 Hence X=1. C=-5 IMO D #### D QUESTION:A 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? options: A)Rs.18000 B)Rs.15000 C)Rs.17000 D)Rs.14000 E)NONE SOLUTION:25*12: 30*12: 35*8 15:18:14 14/47 * 47000 = 14000 ANSWER:D #### D QUESTION:It takes 30 days to fill a laboratory dish with bacteria. If the size of the bacteria doubles each day, how long did it take for the bacteria to fill 1/64 of the dish? options: A)20 B)22 C)24 D)26 E)28 SOLUTION:The bacteria doubles each day, so after 29 days, the dish was half full. After 28 days, the dish was one quarter full. After 27 days, the dish was one eighth full. After 26 days, the dish was one sixteenth full. After 25 days, the dish was 1/32 full. After 24 days, the dish was 1/64 full. The answer is C. #### C QUESTION:Three-fifth of a two digit number exceeds its one fifth by 6. What is the sum of the digits of the number? options: A)6 B)9 C)11 D)12 E)15 SOLUTION:Explanation: 3x/5 – x/5 = 6 => x =15 1 + 5 = 6 A) #### A QUESTION:Vijay's salary is Rs. 21,600 per month. In the first month of the year, he spends 30% of his income on clothing, 20% of the remaining on entertainment and some percentage of the remaining on food. He saves of the amount he spends. Find the percentage of spending on food as a percentage of saving. options: A)180% B)124% C)160% D)154% E)140% SOLUTION:Let monthly income be = x on clothing =.3x on entertainment = .2(.7x) =.14x on food = (.16x)k saving =( .3x .14x .16xk)*13 solving we get k =.31.16 putting the value and we get ...... on the food =.31x ,and saving =.25x %on food / %on saving = .06x/.25x =24% correct answer - B #### B QUESTION:Rahul take a loan of sum Rs.550.This is to be repaid in two equal annual installments. If the rate of interest be 20% compounded annually,then find the value of each installment? options: A)360 B)420 C)230 D)540 E)610 SOLUTION:Let the value of each installment be Rs.x [x/(1+(20/100))]+[x/(1+(20/100))2]=550 (100x/120)+(10000x/14400)=550 (5x/6)+(25x/36)=550 x=360 Option A #### A QUESTION:Molly 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? options: A)6 B)7 C)7.5 D)8 E)9 SOLUTION:Each day, Molly can do 1/15 of the task. Each day, Sandy can do 1/10 of the task. Each day, they can do 1/15 + 1/10 = 1/6 of the task. The task will be completed in 6 days. The answer is A. #### A QUESTION:20 people are there, they are shaking hands together, how many hand shakes possible,if they are in pair of cyclic sequence. options: A)19 B)20 C)21 D)22 E)23 SOLUTION:in case of cycle no of handshakes = no of persons hence ans = 20 ANSWER:B #### B QUESTION:Last year Manfred received 26 paychecks. Each of his first 6 paychecks was $750; each of his remaining paychecks was $20 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? options: A) $752 B) $755 C) $765 D) $773 E) $775 SOLUTION:= (750*6+ 770 *20)/26 = 765 Answer is C. Posted from my mobile device #### C QUESTION:Vicky's salary is 75% more than Ashu's. Vicky got a raise of 40% on his salary while Ashu got a raise of 25% on his salary. By what percent is Vicky's salary more than Ashu's? options: A)96% B)51.1% C)90% D)52.1% E)None of these SOLUTION:Solution: Let Ashu's salary = 100; Ashu's salary after rise = 125. Then Vicky's salary = 175. Vicky's salary after rise of 40% = 245. [As 10% of Vicky's salary is 17.5 then 40% = 17.5*4 = 70] . Difference between Vicky's salary and Ashu's salary = 245-125 = 120; . % more Vicky's salary than Ashu's = 120*100/125 = 96%. Answer: Option A #### A QUESTION:Given two fair dice, what is the probability E that the sum of their numbers is 4 if exactly one die shows a 3? options: A)a) 2/11 B)b) 1/18 C)c) 3/11 D)d) 2/39 E)e) 1/5 SOLUTION:If exactly one die shows 3, there are 10 such combinations (given that we have 2 fair dice). 1:3, 2:3, 4:3, 5:3, 6:3, 3:1, 3:2, 3:4, 3:5, 3:6 The sum of numbers would be 4 for two events: 1:3, 3:1. E=2/11 would be the answer if 'at least one of the die shows a 3'.A #### A QUESTION:A garrison of 1850 men has provisions for 28 days. At the end of 12 days, a reinforcement arrives, and it is now found that the provisions will last only for 10 days more. What is the reinforcement? options: A)1850 B)2960 C)3000 D)1110 E)1712 SOLUTION:1850 ---- 28 1850 ---- 16 x ----- 10 x*10 = 1850*16 x = 2960 1850 ------- 1110 Answer: D #### D QUESTION:A man buys Rs. 60 shares paying 9% dividend. The man wants to have an interest of 12% on his money. The market value of each share is: options: A)s. 12 B)s. 15 C)s. 18 D)s. 21 E)s. 45 SOLUTION:Dividend on Rs. 60 = Rs. 9/100 x 60 =Rs. 5.4 . Rs. 12 is an income on Rs. 100. Rs. 5.4 is an income on Rs.100/12 x 5.4 = Rs. 45. Answer: Option E #### E QUESTION:What is the smallest number which when increased by 3 is divisible by 18, 70, 25 and 21? options: A)2327 B)2757 C)3147 D)3587 E)3997 SOLUTION:When increased by 3, the number must include at least 2*3^2*5^2*7 = 3150 The answer is C. #### C QUESTION:Jake, Lena, Fred, John and Inna need to drive home from a corporate reception in an SUV that can seat 7 people. If only Inna or Jake can drive, how many seat allocations are possible? options: A)30 B)42 C)120 D)360 E)720 SOLUTION:5 people ,7 seats, only 2 can drive if inna is in one seat remaining, 4 people can be arranged in 4p4 i.e 4! =24 ways since any one can drive total ways = 24 *2= 48 ways 4 seats can be chosen out of remaining 6 seats in 6c4 ways = 6!/(4!*2!)= 15 ways 48*15=720 ANSWER:E #### E QUESTION:At what time between 7 and 8 o'clock will the hands of a clock be in the same straight line but, not together? options: A)5 min. past 7 B)5(2/11) min. past 7 C)5(3/11) min. past 7 D)5(5/11) min. past 7 E)5(5/11) min. past 8 SOLUTION:When the hands of the clock are in the same straight line but not together, they are 30 minute spaces apart. At 7 o'clock, they are 25 min. spaces apart. Minute hand will have to gain only 5 min. spaces. 55 min. spaces are gained in 60 min. 5 min. spaces are gained in 5(5/11) min. ANSWER:D #### D QUESTION:Find the average marks of all the students in 2 separate classes, if the average marks of students in the first class of 55 students is 60 and that of another class of 48 students is 58 options: A)55.1 B)51.1 C)53.1 D)52.1 E)59.1 SOLUTION:Sum of the marks for the class of 55 students = 55 * 60 = 3300 Sum of the marks for the class of 48 students = 48 * 58 = 2784 Sum of the marks for the class of 103 students = 3300 + 2784 = 6084 Average marks of all the students = 6084/103 = 59.1 Answer:E #### E QUESTION:If 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? options: A)10 days B)11 days C)13 days D)15 days E)24 days SOLUTION:8men = 12women (i.e 2men = 3women) 12women 1 day work= 1/40 soln: 6men(9women)+ 11women=20women=? 1 women 1 day work =12*40= 1/480 so, 20 women work= 20/480=1/24 ans: 24 days ANSWER:E #### E QUESTION:Two numbers are in the ratio 3:5. If 9 be subtracted from each, they are in the ratio of 3:2. The first number is: options: A)A)3 B)B)98 C)C)34 D)D)35 E)E)62 SOLUTION:(3x-9):(5x-9) = 3:2 x = 1 => 3x = 3 Answer:A #### A QUESTION:Two 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? options: A)95 minutes B)90 minutes C)88 minutes D)95 minutes E)None of these SOLUTION:Explanation : Let us consider that speed of train , first man and second man are respectively t, f and s. According to first given condition goods train crossed the first person moving in same direction in 20 sec. So length of the will be 20(t-f) Similarly train crossed the second man in 18 sec. So length of the train will be 18(t+s) on comparing these two equations, we get 20(t-f) = 18(t+s) => 2t = 20f + 18s => t = 10f + 9s Now it is given that After 10 min the train crossed the other person who is coming in opposite direction. So,If we consider this way of train as L then the next equation will be L = 600t (here 600 is used for 10 minutes) Finally as asked in the question the time required to meet the two man after the train has passed will be given by Time = (L-600 f)/(f+s) {here 600f is used for the distance traveled by first man in 10 minutes} => = (600t-600f) / (f+s) => = [600(10f+9s)-600f] / (f+s) => = 600(10f+9s-f) / (f+s) = 600 * 9(f+s) / (f+s) => =600*9 seconds => = 600*9/60min => = 90 minutes Hence (B) is the correct answer. Answer : B #### B QUESTION:A 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? options: A)15 kmph B)10 kmph C)12 kmph D)12.5 kmph E)None of these SOLUTION:Let the speed of the man in still water be a kmph and let the speed of the stream be b kmph. Now 30/(a + b) + 20/(a - b) = 4 and 45/(a + b) + 40/(a - b) = 7 Solving the equation, the speed of man in still water is 12.5 kmph. ANSWER:D #### D QUESTION:The function f(Z) represents the number of ways that prime numbers can be uniquely summed to form a certain number Z such that Z = a + b + c + d… where those summed variables are each prime and a ≤ b ≤ c ≤ d ... For instance f(8) = 3 and the unique ways are 2 + 2 + 2 + 2 and 2 + 3 + 3 and 3 + 5. What is f(12)? options: A)4 B)5 C)6 D)9 E)7 SOLUTION:Its better to start with 2 and check whether sum of two primes is primes is even. 1) 2(6 times) 2) 2(3 times) + 3(2 times) 3) 2(2 times) + 3 + 5 4) 2 + 3 + 7 5) 2 + 5 + 5 6) 3(4 times) 7) 5 + 7 Answer: E #### E QUESTION:If 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? options: A)1 B)2 C)5 D)7 E)14 SOLUTION:Try with the options - A. If BC = 1 , both B and C must be 1 B. 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 C. 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 D. If BC = 6 , then we can have the following possibilities i. 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 ii. 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 E. 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 Thus answer is (D) #### D QUESTION:Which of the following CANNOT be a value of 8/(x–8)? options: A)-1 B)-1/2 C)0 D)2 E)8 SOLUTION:The question doesn't ask for the value of x here, but for the possible results of the equation. If 8/(x-8) = 0, then the numerator must be 0. But since the numerator is 8, the fraction can not be equal to 0. The answer is C. #### C QUESTION:What inequality represents the condition 1<x<13? options: A)|x|<3 B)|x+5|<4 C)|x-7|<6 D)|-5+x|<4 E)|3+x|<5 SOLUTION:1<x<13 represents segment with length: 13-1 = 12 center: (13+1)/2 = 7 For any |x-a|<b a is a center and b is a half of length. So, |x-7|<12/2 represents our inequality (answer C) #### C QUESTION:If KING is coded as 17 and MASS is coded as 29 Then DON is coded as options: A)12 B)16 C)18 D)None E)cannot be determined SOLUTION:Explanation : KING = 11+9+14+7=41 i.e (4*4)+(1*1)=17 MASS = 13+1+19+19=52 i.e (5*5)+(2*2)=29 DON = 4+14+15=33 i.e(3*3)+(3*3)=18 Hence (C) is correct Answer : C #### C QUESTION:There were r red balls and y yellow balls in a bag. Three red balls and four yellow ones were added to the bag. What is the probability that a yellow ball and then a red ball will be selected if Jerry pulls out two balls at random, and puts the first ball back before pulling the second ball? options: A)(y+4)/(y+r+7)*(r+3)/(y+r+7) B)(y+3)/(y+r+7) + (r+4)/(y+r+6) C)(y+3)/(y+r+7)*(r+4)/(y+r+6) D)(y+3)/(y+r+7)*(r+3)/(y+r+7) E)(y+3)/(y+r+7) + (r+3)/(y+r+6) SOLUTION:Currently we have r red and y yellow balls. After adding new balls, we have red = r + 3 Yellow = y + 4. Total = r + y + 7 Now question says we are taking one ball first putting it back and then taking another ball. So, it means both the times, the number of ways of selecting one ball will be Total C 1 or (r+y+7)C1 So, Probability of selecting 1st as yellow and then 2nd as red = [(y+4)C1 / (r+y+7)C1] * [(r +3)C1 / (r+y+7)C1] Answer : option A. #### A QUESTION:In a stack of cards, 11 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 5/6 . What is the number of cards in the stack? options: A)10 B)11 C)12 D)15 E)18 SOLUTION:This question can be solved by TESTing THE ANSWERS. Answer C: 12 total cards With 12 total cards, and 11 blue cards, the probability of pulling two blue cards is... (11/12)(10/11) = 110/132 ~= 5/6 This is an exact MATCH for what we were told, so this MUST be the answer. Final Answer: C #### C QUESTION:How many even multiples of 55 are there between 549 and 1101? options: A)5 B)6 C)9 D)10 E)11 SOLUTION:550 = 10*55 1100 = 20*55 The even multiples are 55 multiplied by 10, 12, 14, 16, 18, and 20 for a total of 6. The answer is B. #### B QUESTION:A 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? options: A)2 B)3 C)4 D)5 E)6 SOLUTION:Given: 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<x^6<10^3 --> 0<x^2<10 --> x can be 1, 2 or 3 hence nn can be 1^6, 2^6 or 3^6. Answer: B. #### B QUESTION:If y ≠ 3 and 2h/y is a prime integer greater than 2, which of the following must be true? I. h = y II. y = 1 III. h and y are prime integers. options: A) None B) I only C) II only D) III only E) I and II SOLUTION:Note that we are asked which of the following MUST be true, not COULD be true. For such kind of questions if you can prove that a statement is NOT true for one particular set of numbers, it will mean that this statement is not always true and hence not a correct answer. So we should try to make the listed statements not true for some h and y (which satisfy y≠3 and 2h/y=prime>2). I. h = y --> not necessarily true: h=3 and y=2 (2h/y=3=prime>2); II. y=1 --> not necessarily true: h=3 and y=2 (2h/y=3=prime>2); III. h and y are prime integers --> not necessarily true: h=10 and y=4 (2h/y=5=prime>2). Answer: A. #### A QUESTION:If the average (arithmetic mean) of 5 positive temperatures is z degrees Fahrenheit, then the sum of the 3 greatest of these temperatures, in degrees Fahrenheit, could be: options: A)6z B)4z C)5z/3 D)3z/2 E)3z/5 SOLUTION:The sum of three greatest should be more than sum of two lowest. The total sum is; 5z A. 6z; 6z is more than 5z. Not possible. B. 4z; 5z-4z=z(Possible) C. 5z/3; 10z/3; 10z/3 > 5z/3. Not possible D. 3z/2; 7z/2; 7z/2 > 3z/2. Not possible E. 3z/5; 22z/5; 22z/5 > 3z/5. Not possible. Ans:B #### B QUESTION:The area of square ABCD above is 18. The shaded region is the intersection of the square and a circular region centered at C. What is the area of the shaded region? options: A)18−9/4∗π B)18−9/2∗π C)9+9/4∗π D)9+9/2∗π E)9/2−9/4∗π SOLUTION:=Square - Quarter circle =18- pi*18/4 =18- pi*9/2 ANSWER:B #### B QUESTION:A seller mixed 4 dozen bananas costing Rs.12 per dozen with 6 dozen bananas at Rs.8 per dozen then what is the cost price of mixed bananas per dozen? options: A)Rs.6.40 B)Rs.10 C)Rs.9.6 D)Rs.10.2 E)None of the above SOLUTION:4 dozens of bananas cost is rs12 then 4*12=48 6 dozens of bananas cost is rs8 then 6*8=48 48+48/4+6=96/10=9.6 ANSWER:C #### C QUESTION:A rectangular box of volume x has width, depth and height in the ratio of 5:1:2 (in that order). What is the width as a function of x? options: A)(4x/12)^(1/2) B)(10x/4)^(1/2) C)(5x)^(1/2) D)(2x/5)^(1/2) E)(4x/3)^(1/2) SOLUTION:We are given width = 5, depth = 1, height = 2 Then Volume x = Width x Depth x Height = 5*1*2 = 10 i.e. x = 10 i.e. The correct option should result in 5 (the width) on substituting the value of x=10 Checking options with x=10 A) (4x/12)^(1/2) = (4*10/12)^(1/2) = (40/12)^(1/2) INCORRECT ANSWER B) (10x/4)^(1/2) = (10*10/4)^(1/2) = 25^(1/2) = 5 CORRECT ANSWER C) (5x)^(1/2) = (5*10)^(1/2) = 50^(1/2) INCORRECT ANSWER D) (2x/5)^(1/2) = (2*10/5)^(1/2) = 4^(1/2) = 2 INCORRECT ANSWER E) (4x/3)^(1/2) = (4*10/3)^(1/2) = 40/3^(1/2) INCORRECT ANSWER Answer: Option B #### B QUESTION:A can do a piece of work in 80 days. He works at it for 10 days & then B alone finishes the remaining work in 42 days. In how much time will A and B, working together, finish the work? options: A)30 days B)20 days C)25 days D)35 days E)45 days SOLUTION:Work done by A in 10 days = 10/80 = 1/8 Remaining work = (1 - (1/8)) = 7/8 Now, work will be done by B in 42 days. Whole work will be done by B in (42 x 8/7) = 48 days Therefore, A’s one day’s work = 1/80 B’s one day’s work = 1/48 (A+B)’s one day’s work = 1/80 + 1/48 = 8/240 = 1/30 Hence, both will finish the work in 30 days. ANSWER:A #### A QUESTION:Two pipes can fill the cistern in 10hr and 12 hr respectively, while the third empty it in 20hr. If all pipes are opened simultaneously, then the cistern will be filled in options: A)7.5 hr B)8 hr C)8.5 hr D)10 hr E)None of these SOLUTION:Solution: Work done by all the tanks working together in 1 hour. 1/10+1/12−1/20=2/15 Hence, tank will be filled in 15/2=7.5 hour Option(A) #### A QUESTION:A city with a population of 160,080 is to be divided into 8 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? options: A)18,200 B)18,300 C)18,400 D)18,500 E)18,600 SOLUTION:The minimum possible population occurs when all the other districts have a population that is 10% greater than the least populated district. Let p be the population of the least populated district. Then 160,080 = p + 7(1.1)p 8.7p=160,080 p = 18,400 The answer is C. #### C QUESTION:If p/q = 5/4 , then 2p+q= ? options: A)12 B)14 C)13 D)15 E)16 SOLUTION:let p=5, q=4 then 2*5+4=14 so 2p+q=14. ANSWER:B #### B QUESTION:Out of 6 consonants and 3 vowels, how many words of 4 consonants and 2 vowels can be formed? options: A)1050 B)25200 C)32400 D)5800 E)6800 SOLUTION:Number of ways of selecting (4 consonants out of 6) and (2 vowels out of 3) = 6C4 * 3C2 = 6C2 * 3C1 = 6*5 *3 2*1 = 15*3= 45 Number of groups, each having 4 consonants and 2 vowels= 45. Each group consists of 6 letters. Number of ways of arranging 6 letters among themselves = 6! = (6*5*4*3*2*1)= 720 Therefore, Required number of words= 45*720= 32400 ANSWER:C #### C QUESTION:A person purchased a TV set for Rs. 16000 and a DVD player for Rs. 1800. He sold both the items together for Rs. 31150. What percentage of profit did he make? options: A)30% B)75% C)40% D)70% E)None of these SOLUTION:The total CP = Rs. 16000 + Rs. 1800 = Rs. 17800 and SP = Rs. 31150 Profit(%) = (31150 - 17800)/17800* 100 = 75% ANSWER:B #### B QUESTION:The 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? options: A)1000 B)1500 C)2000 D)3000 E)4000 SOLUTION:Let monthly income of A = a monthly income of B = b monthly income of C = c a + b = 2 × 5050 .... (Equation 1) b + c = 2 × 6250 .... (Equation 2) a + c = 2 × 5200 .... (Equation 3) (Equation 1) + (Equation 3) - (Equation 2) => a + b + a + c - (b + c) = (2 × 5050) + (2 × 5200) - (2 × 6250) => 2a = 2(5050 + 5200 - 6250) => a = 4000 i.e., Monthly income of A = 4000 Answer is E. #### E <<<Examples ends QUESTION:A 200 meter long train crosses a platform in 50 seconds while it crosses a signal pole in 42 seconds. What is the length of the platform? options: A)39.9 B)37.88 C)35 D)38.88 E)38.09 SOLUTION:Speed = [200 / 42] m/sec = 100/21 m/sec. Let the length of the platform be x meters. Then, x + 200 / 50 = 100/21 21(x + 200) = 5000 è x = 38.09 m. Answer: E #### E

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:Two men started from the same place walk at the rate of 10kmph and 12kmph respectively. What time will they take to be 20 km apart, if they walk in the same direction? options: A)5hours B)10hours C)8hours D)10hours E)12hours SOLUTION:To be 2km apart they take 1 hour To be 10km apart they take = 1/2 * 20 =10 hours Answer is B #### B QUESTION:John has 75 pencils, he distribute 20 pencils to his friends in his class. Then how many pencils are remaining to him? options: A)10 B)67 C)32 D)44 E)55 SOLUTION:75-20=55. Answer is E #### E QUESTION:A 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 1 buckles is how many times that of 5 buckles and 6 buttons? options: A)7/15. B)2/5. C)6/11. D)5/9. E)8/15. SOLUTION:2buttons + 2buckles = 1/3(11buckles + 3buttons) 6buttons + 6buckles = 11buckles + 3buttons 3buttons = 5buckles Weight of 3buttons and 1buckles = 5buckles + 1buckles = 6buckles Weight of 6buttons and 5buckles = 10buckles + 5buckles = 15buckles (3buttons and 2buckles) = x * (6buttons and 5buckles) 6 = x*15 x = 6/15=2/5 Answer: B #### B QUESTION:Find the unit's digit in the product 2467 153 * 34172? options: A)1 B)3 C)2 D)5 E)7 SOLUTION:Unit's digit in the given product=Unit's digit in 7 153 * 172 Now 7 4 gives unit digit 1 7 152 gives unit digit 1 7 153 gives 1*7=7.Also 172 gives 1 Hence unit's digit in the product =7*1=7. Option A #### A QUESTION:There are 3 teams each with 6 basket players. How many combinations are there if we were to pick 2 players from the 3 teams such that no team was picked twice? options: A)50 B)23 C)108 D)28 E)45 SOLUTION:There are altogether three arrangements, which are we can select two members each from team A and B, each from team A and C, and each from team B and C. For each arrangement, there are altogether 36 possibilities (6*6) since each team has 6 players. So there are a total of 108 possibilities (36*3). I hope this method is easier for you to understand. #### C QUESTION:There are 9 people and 9 chairs. In how many different ways people can occupy the chairs? options: A)362880 B)340009 C)250909 D)345008 E)1000 SOLUTION:number of ways =9! = 362880 Answer is A #### A QUESTION:The average (arithmetic man) of three integers a, b, and c is exactly once the median. If a < b < c and a = 0, what is the value of c/b? options: A)2 B)3 C)4 D)5 E)Cannot be determined from the information given. SOLUTION:The average of three integers a, b, and c is exactly twice the median --> (a+b+c)/3=b --> since a=0, then (0+b+c)/3=b --> c=2b --> c/b=2. Answer: A. #### A QUESTION:Tickets numbered 1 to 10 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn bears a number which is a multiple of 2? options: A)1/3 B)2/5 C)1/2 D)2/3 E)1/4 SOLUTION:Here, S = {1,2,3,......,9,10} E= event getting a multiple of 3 = {2,4,6,8,10} probability = 5/10 = 1/2 correct option is C #### C QUESTION:Of the families in City X in 1956, 25 percent owned a personal computer. The number of families in City X owning a computer in 1960 was 15 percent greater than it was in 1956, and the total number of families in City X was 5 percent greater in 1956 than it was in 1960. what percent of the families in City X owned a personal computer in 1960? options: A)50% B)51.22% C)5.26% D)7.20% E)27.38% SOLUTION:Say a 100 families existed in 1956 then the number of families owning a computer in 1956 - 25 Number of families owning computer in 1960 = 25 * 115/100 = 28.75 Number of families in 1960 = 105 The percentage = 28.75/105 * 100 = 27.38%. Option: E #### E QUESTION:40 liters of a mixture is created by mixing Liquid P and Liquid Q in the ratio 5:3. How many liters of Liquid Q must be added to make the ratio 5:6? options: A)5 B)8 C)10 D)12 E)15 SOLUTION:Let x be the amount of liquid Q to be added. (3/8)*40 + x = (6/11)*(40+x) 1320 + 88x = 1920 + 48x 40x = 600 x = 15 The answer is E. #### E QUESTION:The basic one-way air fare for a child aged between 3 and 10 years costs half the regular fare for an adult plus a reservation charge that is the same on the child's ticket as on the adult's ticket. One reserved ticket for an adult costs $216 and the cost of a reserved ticket for an adult and a child (aged between 3 and 10) costs $327. What is the basic fare for the journey for an adult? options: A)$111 B)$52.5 C)$210 D)$58.5 E)$6 SOLUTION:Explanatory Answer Step 1: Assign variables and frame equations Let the basic fare for the child be $X. Basic one-way air fare of a child costs half the regular fare for an adult Therefore, the basic fare for an adult = 2(basic one-way airfare for a child) = $2X. Reservation charge is the same on the child's ticket as on the adult's ticket. Let the reservation charge per ticket be $Y Hence, an adult ticket will cost (Basic fare + Reservation charges) = 2X + Y = $216 ..... (1) And ticket for an adult and a child will cost (2X + Y) + (X + Y) = 3X + 2Y = $327 .... (2) Step 2: Solve the equations and determine basic fare for an adult Multiply equation (1) by 2: 4X + 2Y = 432 .... (3) Subtract equation (2) from equation (3): (4X + 2Y = 432) - (3X + 2Y = 327) ∴ X = $105. The basic fare of an adult ticket = 2X = 2*105 = $210 Answer C #### C QUESTION:In a class, the average age of 30 boys is 13 years and the average of 20 girls is 12 years. what is the average age of the whole class? options: A)12 Years B)12.6 Years C)13.6 Years D)14 Years E)14.5 Years SOLUTION:Total age of 50 students (30X 13+20 X 12) = 630 Average = 630/50 = 12.6 Years \ B #### B QUESTION:Two brothers take the same route to school on their bicycles, one gets to school in 25 minutes and the second one gets to school in 36 minutes. The ratio of their speeds is options: A)4 : 5 B)1 : 2 C)6 : 7 D)5 : 6 E)None SOLUTION:Solution Let us name the brothers as A and B. = (A'S speed) : (B's speed) =√b : √a = √25 : √36 = 5 : 6 Answer D #### D QUESTION:Of the 4 distinguishable wires that lead into an apartment, 2 are for cable television service, and 4 are for telephone service. Using these wires, how many distinct combinations of 3 wires are there such that at least 1 of the wires is for cable television? options: A)6 B)7 C)8 D)9 E)10 SOLUTION:Given: Total number of wires = 5 Number of cable wires = 2 Number of telephone wires = 3 To find: Number of combination which has at least one cable wires Solution: No of ways of selecting'at least'1 cable wire means, we can select more than one as well. The minimum we can select is one and the maximum we can select, given the constraints that 3 wires need to be selected in total and there are 2 cable wires, is 2 Since it is a combination of wires, the arrangement is not important Approach 1: Number of ways of selecting at least one cable wire in a selection of 3 wires from 5 wires =Selection 1(Number of ways of selecting one cable wire and two telephone wires )+Selection 2(Number of ways of selecting two cable wires and 1 telephone wire) Selection 1 Number of ways of selecting one cable wire = 2C1 = 2 Number of ways of selecting 2 telephone wires = 3C2 = 3 Total = 2C1 * 3C2 = 6 ( m ways of doing something and n ways of doing something else together give m*n ways of doing - the holy grail rule in Combinatorics) Selection 2 Number of ways of selecting one cable wire = 2C2 = 1 Number of ways of selecting 2 telephone wires = 3C1 = 3 Total = 2C2 * 3C1 = 3 ( m ways of doing something and n ways of doing something else together give m*n ways of doing - the holy grail rule in Combinatorics) Selection 1 + Selection 2 = 9 ways of selecting 3 wires out of 5 such that at least one is a cable wire Approach 2 Number of ways of selecting 3 wires out of 5 such that at least one is a cable wire =Selection X(Total number of ways of selecting 3 wires from the 5) -Selection Y(total ways of selecting 3 wires such that none is a cable i.e all the three are telephone wires) Total number of ways of selecting 3 wires out of 5 = 5C2 = 10 Number ways of selecting 3 wires such that none is a cable i.e all the three are telephone wires = 3C3 ( 3 telephone wires and we are selecting all the three at once) = 1 Selection X - Selection Y = 6 Answer is Option A #### A QUESTION:In a series of six consecutive odd numbers, the sum of the second and fifth numbers is 28. What is the third number? options: A)9 B)11 C)17 D)13 E)15 SOLUTION:Let the numbers be x, x + 1, x + 3, x + 5 and x + 7. Given (x + 1) + (x + 7) = 28 => 2x + 8 = 28 => x = 10 The third number = x + 3 = 10 + 3 = 13. Answer: D #### D QUESTION:In 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? options: A)6 B)8 C)10 D)12 E)14 SOLUTION:Let the number of buffaloes be x and the number of ducks be y. Then 4x+2y=2(x+y)+24 =>x=12 ANSWER D 12 #### D QUESTION:A and B together invested Rs. 20,000 in a business. At the end of the year, out of total profit is Rs. 5,000 B's share was Rs. 2000. A's investment was options: A)s. 4,500 B)s. 8,250 C)s. 10,500 D)s. 11,250 E)s. 12,000 SOLUTION:A+B=20000 total profit=5000 5000-2000=3000 3000;2000=3:2 then 3*20000/5=12000 ANSWER:E #### E QUESTION:A 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? options: A)4 days B)2 days C)6 days D)8 days E)9 days SOLUTION:C 6 days 4/10 + 9/x = 1 => x = 15 1/10 + 1/15 = 1/6 => 6 days #### C QUESTION:The smallest number which when divided by 20, 25, 35 and 40 leaves a remainder of 14, 19, 29 and 34 respectively is? options: A)1994 B)1494 C)1349 D)1496 E)1500 SOLUTION:LCM = 1400 1400 - 6 = 1394 ANSWER:C #### C QUESTION:A man has Rs.10350 in the form of Rs.50 notes and Rs.500 notes. The total number of notes are 36.Find the number of notes of Rs.50 denomination. options: A)15 B)21 C)17 D)19 E)21 SOLUTION:Total Money = Rs. 10350. Let 50 rupees note was X. Then 500 rupees note = 36 - X Now, 50*X + 500 * (36 - X) = 10350 50X + 18000 - 500X = 10350 - 450X = - 7650 X = 17. No. of 50 rupees note = 17. Answer: Option C #### C QUESTION:An order was placed for the supply of a carpet whose breadth was 6 m and length was 1.44 times the breadth. What be the cost of a carpet whose length and breadth are 40% more and 25% more respectively than the first carpet. Given that the ratio of carpet is Rs. 45 per sq m? options: A)Rs.4082.67 B)Rs.4082.49 C)Rs.4082.48 D)Rs.4082.40 E)Rs.4082.13 SOLUTION:Length of the first carpet = (1.44)(6) = 8.64 cm Area of the second carpet = 8.64(1 + 40/100) 6 (1 + 25/100) = 51.84(1.4)(5/4) sq m = (12.96)(7) sq m Cost of the second carpet = (45)(12.96 * 7) = 315 (13 - 0.04) = 4095 - 12.6 = Rs.4082.40 Answer: D #### D QUESTION:What is the value of √36% ? options: A)10% B)20% C)30% D)60% E)40% SOLUTION:Explanation: br>√16% =√36/√100 =6/10 =60/100=60% correct answer is D)60% #### D QUESTION:If x and y are integers and x + y = 3, which of the following must be true? options: A)If x < 0, then y > 0. B)x and y are consecutive integers. C)If x > 0, then y < 0. D)Both x and y are even. E)Both x and y are less than 5. SOLUTION:In option C if x > 0,then y<0 means x is +ve and y is -ve In option B if x < 0, then y>0 means y is +ve and x is -ve, both are same and satisfying x+y = 5. How option A is right could you explain #### A QUESTION:Which of the following is not divisible by 6? options: A)10032 B)21192 C)47816 D)91232 E)72031 SOLUTION:Divisibility rule of 6: Number must be divisible by both 2 and 3 Option A: 10032, Divisible by 2. Hence divisible by 6 Option B: 21192, Divisible by 2 & 3. Hence divisible by 6 Option C: 47816, Divisible by 2. Hence divisible by 6 Option D: 91232, Divisible by 2. Hence divisible by 6 Option E: 72031, Not divisible by 2 or 3. Hence 72031 is not divisible by 6 #### E QUESTION:On a weekend, 3 friends went skiing and evenly split the cost of their cabin. If the amount paid by each person was an integer, which of the following could not have been the cost of the cabin? options: A)$110 B)$150 C)$225 D)$54 E)$75 SOLUTION:Each of the seven persons evenly splitting the cost is an integer amount, therefore check the divisibility by 3 for all answer choices. 110/3 = 36.67 150/3 = 50 225/3 = 75 54/3 = 18 75/3 = 25 A is not an integer amount. Answer:A #### A QUESTION:A 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? options: A)227 B)350 C)881 D)277 E)271 SOLUTION:Speed = 300/18 = 50/3 m/sec. Let the length of the platform be x meters. Then, (x + 300)/39 = 50/3 3x + 900 = 1950 => x = 350 m. Answer: B #### B QUESTION:((-1.9)(0.6) – (2.6)(1.2))/2.0 = ? options: A)-0.71 B)1.0 C)1.07 D)1.71 E)-2.13 SOLUTION:Dove straight into calculation but quickly realized that the sum of two negatives is a negative so there is only one option. -2.13 Answer E #### E QUESTION:If x/y = 5 and (4a - x)/(b - y) = 5, then the value of a/b is? options: A) –3 B) -2 C) 1 D) 5/4 E) 3 SOLUTION:x = 5y 4a - 5y = 5(b - y) 4a - 5y = 5b - 5y 4a = 5b a/b = 5/4 Answer: D #### D QUESTION:A boat goes 100 km downstream in 10 hours, and 200 Km upstream in 25 hours. The speed of the stream is? options: A)1 B)22 1/7 C)2 D)22 1/2 E)3 SOLUTION:100 --- 10 DS = 10 ? ---- 1 200 ---- 30 US = 8 ? ----- 1 S = (10 - 8)/2 = 1 kmph. Answer:A #### A QUESTION:A and B invest in a business in the ratio 3: 2. Assume that 5% of the total profit goes to charity. If A's share is Rs. 855, what is the total profit? options: A)1500 B)2000 C)3000 D)3500 E)2500 SOLUTION:Profit as x since 5% and 95% of x will be divided b/w A and B ration 3:2 =>profit 95x/100 * 3/5 given that A's share is Rs 855 => 95x/100 * 3/5 = 855 hence x = 1500 ANSWER A #### A QUESTION:One of the following numbers can be marked out as the odd one out. can you find which one? 1) 680986879 2) 716089780 3) 820670987 4) 932967879 options: A)The odd number is 680986879 B)The odd number is 820670987 C)The odd number is 716089780 D)The odd number is 932967879 E)None SOLUTION:Correct Answer : B if you add up the first three digits of all the numbers, it adds up to 14 except for second option 820670987 #### B QUESTION:The area of a square is equal to five times the area of a rectangle of dimensions 27 cm * 16 cm. What is the perimeter of the square? options: A)140 B)240 C)340 D)144 E)122 SOLUTION:Area of the square = s * s = 3(27 * 16) => s = 9 * 4 = 36 cm Perimeter of the square = 4 * 36 = 144 cm. Answer: D #### D QUESTION:A popular website requires users to create a password consisting of the digits {1,2,3,4,5,6,7}. If no digit may be repeated and each password must be at least 6 digits long, how many passwords are possible? options: A)6! + 7! B)2 x 7! C)6! x 7! D)13! E)14! SOLUTION:If we choose the 7 different digits then they can be arranged in 7! ways. The number of possible 6-digit passwords is 7*6*5*4*3*2 = 7! The total number of passwords is 7! + 7! = 2*7! The answer is B. #### B QUESTION:Three 6 faced dice are thrown together. The probability that exactly two dice show the same number on them is options: A)5/18 B)5/12 C)5/15 D)5/14 E)5/11 SOLUTION:Using question number 11 and 12, we get the probability as 1 - (1/36 + 5/9) = 5/12.Answer:B #### B QUESTION:A is older than B by 5years. Seven years hence, thrice A's age shall be equal to four times that of B. Find their present ages. options: A)14, 7 B)10, 5 C)13, 8 D)12, 8 E)8, 12 SOLUTION:Explanation: Let the present ages of A and B be 'a' and 'b' respectively. 3(a + 7)= 4( (b +7 ) --- (1) =>3a-4b=7 -------(1) a-b = 5 -------(2) Solving (1) and (2) we get b=8 Substituting b = 8 in second equation, we get a= 13. Answer : C => 2a = 32 => a = 16. Answer: C #### C QUESTION:The ages of two persons differ by 24 years. If 5 years ago, the elder one be 5 times as old as the younger one, their present ages (in years) are respectively options: A)20,20 B)20,10 C)25,15 D)35,11 E)None of these SOLUTION:Explanation: Let their ages be x and (x + 24) years. 5 (x - 5) = (x + 24 - 5) or 4x = 44 or x = 11. Their present ages are 35 years and 11 years Option D #### D QUESTION:What is the leastvalue of x. So that 23x57 is divisible by 3? options: A)3 B)4 C)1 D)5 E)6 SOLUTION:The sum of the digits of the number is divisible by 3, then the number is divisible by3. 2 + 3 + x + 5 + 7 = 17 + x Least value of x may be 1 Therefore 17 + 1 = 18 is divisible by 3. C #### C QUESTION:A 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 18 km/hr. What is the length of the platform? options: A)80 B)240 C)288 D)277 E)221 SOLUTION:Speed = 18 * 5/18 = 5 m/sec. Length of the train =5 * 20 = 100 m. Let the length of the platform be x m . Then, (x + 100)/36 = 5 => x = 80 m. Answer: A #### A QUESTION:Janet has to pay back her bank loan over 10 months following the below sequence. $50, $55, $65, $80, $85, $95, $110, $115, $125, ? How much will she pay back on the tenth month? options: A)$155 B)$140 C)$135 D)$125 E)$130 SOLUTION:The sequence progresses +5, +10, +15 repeated; The amount to pay back on the 10th Month is $140 Ans B #### B QUESTION:Pipe A can fill a tank in 2 hr, pipe B in 4hr and pipe C in 8hr. If all the pipes are open in how many hours will tank be filled? options: A)1hr 27min B)2hr 19min C)3hr 14min D)3hr E)5hr 45min SOLUTION:Part filled by (A+B+C) in 1hour = 1/2 + 1/4 + 1/8 = 7/8 All the 3 pipes together will fill the tank in 1hour 27min Answer is A #### A QUESTION:The 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? options: A)600 cm B)800 cm C)400 cm D)1000 cm E)None of these SOLUTION:Area of the square = s * s = 5(125 * 64) => s = 25 * 8 = 200 cm Perimeter of the square = 4 * 200 = 800 cm. ANSWER:B #### B QUESTION:We bought a total of 90 books at the store. Math books cost $4 and history books cost $5. The total price was $390. How many math books did we buy? options: A)57 B)60 C)63 D)66 E)69 SOLUTION:M + H = 90 H = 90 - M 4M + 5H = 390 4M + 5*(90 - M) = 390 M = 60 The answer is B. #### B QUESTION:A survey was sent to 90 customers, 7 of whom responded. Then the survey was redesigned and sent to another 63 customers, 9 of whom responded. By approximately what percent did the response rate increase from the original survey to the redesigned survey? options: A)2% B)6% C)14% D)28% E)63% SOLUTION:case 1: (7/90)=x/100 x=8% case 2: (9/63)=y/100 y=14% So percent increase is =(y-x)=(14-8)%=6% Answer is B #### B QUESTION:A 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? options: A)72 B)27 C)40 D)28 E)20 SOLUTION:800*(25/100) = 200 ---- 5 ? ---- 1 => Rs.40 Answer:C #### C QUESTION:The Guests at a football banquet consumed a total of 411 pounds of food. if no individual guest consumed more than 2.5 pounds of food, What is the minimum number of guests that could have attended the banquet? options: A)165 B)161 C)162 D)163 E)164 SOLUTION:To minimize one quantity maximize other. 164*2.5 (max possible amount of food a guest could consume) = 410 pounds, so there must be more than 164 guests, next integer is 165. Answer: A. #### A QUESTION:The students of a particular class were given two tests for evaluation. Twenty Five percent of the class cleared both the tests and forty five percent of the students were able to clear the first test. You have to calculate the percentage of those students who passed the first test and were also able to pass the second test. How will you do it? options: A)48% B)55% C)60% D)71% E)80% SOLUTION:C 60% In all such cases where you have to find out the probability of anything with an already given situation, you have to use the formula for conditional probability. In this case, you have to find out the probability that the second test was passed by a student given that he passed the first test already. Therefore, P(Second/First) = P (First and Second)/ P (First) = 0.25/0.42 =0.60 =60 % #### C QUESTION:A grocer has a sale of Rs. 5420, Rs. 5660, Rs. 6200, Rs. 6350 and Rs. 6500 for 5 consecutive months. Find the sale he should have in the sixth month, so that he gets an average sale of Rs. 6500? options: A)Rs. 5870 B)Rs. 5991 C)Rs. 8870 D)Rs. 6850 E)None of these SOLUTION:Explanation: Total sale for 5 months = Rs. (5420 + 5660 + 6200 + 6350 + 6500) = Rs. 30,130 Therefore, required sale = Rs. [(6500 * 6) – 30,130] = Rs. (39000 – 30,130) = Rs. 8870 ANSWER C #### C QUESTION:In the class of 50 students, 30 speak Tamil and 30 speak Telugu. What is the lowest possible number of students who speak both the languages? options: A)A)8 B)B)10 C)C)20 D)D)30 E)E)32 SOLUTION:let the student who speaks tamil-x let the student who speaks telugu-y as (xuy)-(xny)=total 30+30-(xny)=50 =10 B) #### B QUESTION:What percent is 2 gm of 1 kg? options: A)0.5 % B)0.2% C)1.5% D)2% E)3% SOLUTION:1 kg = 1000 gm 2/1000 × 100 = 200/1000 =1/5 = 0.2 % B) #### B QUESTION:A day-trader plans to invest a total of $23,300 into 15 separate investments. If each investment requires a minimum deposit of $1,400, then which of the following is the maximum amount that she could put into any one investment? options: A)$2,800 B)$3,000 C)$3,700 D)$3,800 E)$3,900 SOLUTION:We can also just keep track of the HUNDREDS DIGITS(since the hundreds digit is different for each answer choice). Total of 14 minimized investments = (14)(1400) = $???600 The 15th investment + $???600 = $23,300 So, the HUNDREDS DIGITS of the 15th investment must be 7 Answer: C #### C QUESTION:864.942 - ? + 45.76 = 547.905 options: A)A)899.015 B)B)752.804 C)C)714.642 D)D)362.797 E)of these SOLUTION:Explanation: 362.797 Answer: Option D #### D QUESTION:Robert ate 7 chocolates, Nickel ate 5 chocolates. How many more chocolates did Robert ate than nickel? options: A)A)4 B)B)7 C)C)9 D)D)5 E)E)2 SOLUTION:7-5=2. Answer is E #### E QUESTION:Marla starts running around a circular track at the same time Nick starts walking around the same circular track. Marla completes 20 laps around the track per hour and Nick completes 10 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? options: A)5 B)8 C)24 D)15 E)20 SOLUTION:Maria's rate - 20 laps per hour --> 20/60 laps/min Nick's rate - 10 laps per hour --> 10/60 laps/min lets set equations: 20/60*t=4 (since Maria had to run 4 laps before Nick would start) 10/60*t=0 (Hick has just started and hasn't run any lap yet) (20/60-10/60)*t=4-0 (since Nick was chasing Maria) t=24 min needed Maria to run 4 laps Answer : C #### C QUESTION:If the LCM and HCF of 8 and another number is 24 and 4 respectively. Find the other number ? options: A)11 B)12 C)14 D)15 E)16 SOLUTION:HCF x LCM = Product of Numbers 4 x 24 = 8 x the other number other number = (4 x 24) / 8 other number = 12 ANSWER : B #### B QUESTION:A train 400 m long can cross an electric pole in 20 sec and then find the speed of the train? options: A)72 Kmph B)28 Kmph C)29 Kmph D)65 Kmph E)25 Kmph SOLUTION:Length = Speed * time Speed = L/T S = 400/20 S = 20 M/Sec Speed= 20*18/5 (To convert M/Sec in to Kmph multiply by 18/5) Speed = 72 Kmph Answer:A #### A QUESTION:What percent is 4 gm of 1 kg? options: A)1.5 % B)0.4 % C)2.5 % D)3.5 % E)4 % SOLUTION:1 kg = 1000 gm 4/1000 × 100 = 400/1000 =2/5 = 0.4 % B) #### B QUESTION:Myra drove at an average speed of 30 miles per hour for some time and then at an average speed of 60 miles/hr for the rest of the journey. If she made no stops during the trip and her average speed for the entire journey was 50 miles per hour, for what fraction of the total time did she drive at 30 miles/hour? options: A)The average speed is 1/5 miles per hour. B)The average speed is 1/3 miles per hour. C)The average speed is 2/5 miles per hour. D)The average speed is 2/3 miles per hour. E)The average speed is 3/5 miles per hour. SOLUTION:We know the average speed and must find the fraction of time taken at a particular speed. t1/t2 = (A2 – Aavg)/(Aavg – A1) t1/t2 = (60 – 50)/(50 – 30) = 1/2 So out of a total of 3 parts of the journey time, she drove at 30 mph for 1 part and at 60 mph for 2 parts of the time. Fraction of the total time for which she drove at 30 mph is 1/3. ANSWER (B) #### B QUESTION:The speed of a boat in still water is 50kmph and the speed of the current is 20kmph. Find the speed downstream and upstream? options: A)40, 68 kmph B)40, 30 kmph C)70, 30 kmph D)40, 60 kmph E)20, 60 kmph SOLUTION:Speed downstream = 50 + 20 = 70 kmph Speed upstream = 50 - 20 = 30 kmph Answer: C #### C QUESTION:A bag contains 7 green and 8 white balls. If two balls are drawn simultaneously, the probability that both are of the same colour is -. options: A)7/18 B)7/19 C)7/11 D)7/12 E)7/15 SOLUTION:Drawing two balls of same color from seven green balls can be done in ⁷C₂ ways. Similarly from eight white balls two can be drawn in ways. 7/15 Answer: E #### E QUESTION:In an examination, a pupil's average marks were 63 per paper. If he had obtained 20 more marks for his Geography paper and 2 more marks for his History paper, his average per paper would have been 65. How many papers were there in the examination ? options: A)12 B)27 C)26 D)11 E)22 SOLUTION:Let the number of papers be x. Then, 63x + 20 + 2 = 65x or 2x = 22 or x = 11. Answer: D #### D QUESTION:A will states that the estate would be divided among six sons with the remainder donated to charity. One stipulation in the will is that no one among the sons can receive an amount within 12% of another's amount. If one of the beneficiaries received $30,000, what is the smallest possible range between the highest and lowest amounts (rounded to the nearest dollar) among the six sons? options: A)$4096 B)$14043 C)$7892 D)$17736 E)$15336 SOLUTION:1st - 30,000. 2nd - 0.88*30,000 = 26,400 3rd - 0.88*26,400 = 23,232 4th - 0.88*23,232 = 20,444.16 5th - 0.88*20,444.16 = ~17,990.86 6th - 0.88*17,990.86 = ~15,831.96 Range = 30,000 - 15,831 = 14,168 Answer: B. #### B QUESTION:If n is a natural number, then 6n^2 + 6n is always divisible by? options: A)6 only B)6 and 12 C)12 only D)18 only E)20 only SOLUTION:6n^2 + 6n = 6n(n+1), which is always divisible by 6 and 12 both, since n(n+1) is always even. Answer is B #### B QUESTION:In a class, there are 20 boys whose average age is decreased by 2 months, when one boy aged 17 years replaced by a new boy. The age of the new boy is? options: A)14 years 8 months B)15 years C)13 years 8 months D)17 years 10 months E)17 years SOLUTION:Total decrease = (20 x 2) months = 3 years 4 months Age of the new boy = 17 years - 3 years 4 months. = 13 years 8 months. ANSWER:C #### C QUESTION:A 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? options: A)6 min B)8 min C)7 min D)9 min E)1 min SOLUTION:The combined rate of filling/emptying the tank = 1/10 - 1/6 = -1/15 Since the rate is negative, the tank will be emptied. A full tank would take 15 minutes to empty. Since the tank is only three-fifths full, the time is (3/5) * 15 = 9 minutes The answer is D. #### D <<<Examples ends QUESTION:A photo-mat shop charges $0.50 for the first photo inside a film, and 40% cents less for each additional photo. How many photos can we develop with $24 if each film contains 36 photos? options: A)2 films and 6 photos B)5 films and 6 photos C)5 films and 14 photos D)6 films and 4 photos E)6 films and 28 photos SOLUTION:1st photo = 0.50 Subsequent = 0.50*0.6=0.3 Price of 1 full film=0.50+0.3*35=11 Price of 2 full film = 11*2=22 24-22=2 2=0.5+0.3x x=5 24--->2 full films and 1+5=6 photos Answer: A #### A

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:The 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? options: A)7:9 B)7:3 C)7:2 D)7:9 E)7:1 SOLUTION:Let the age of father and son 10 years ago be 3x and x years respectively. Then, (3x + 10) + 10 = 2[(x + 10) + 10] 3x + 20 = 2x + 40 => x = 20. Required ratio = (3x + 10):(x + 10) = 70:30 = 7:3 Answer:B #### B QUESTION:The length of a rectangle is halved, while its breadth is tripled. What is the % change in area? options: A)30% B)40% C)50% D)60% E)65% SOLUTION:Let original length = x and original breadth = y. Original area = xy. New length = x . 2 New breadth = 3y. New area = x x 3y = 3 xy. 2 2 Increase % = 1 xy x 1 x 100 % = 50%. 2 xy C #### C QUESTION:A semicircle has a radius of 9. What is the approximate perimeter of the semicircle? options: A)16 B)25 C)33 D)46 E)58 SOLUTION:The perimeter of a circle is 2*pi*r. The perimeter of a semicircle is 2*pi*r/2 + 2r = pi*r + 2r The perimeter is pi*9 + 2*9 which is about 46. The answer is D. #### D QUESTION:On dividing 144 by a number, the quotient is 13 and the remainder is 1. Find the divisor. options: A)A)11 B)B)14 C)C)16 D)D)18 E)E)22 SOLUTION:d = (D-R)/Q = (144 - 1)/13 = 143/13 = 11 A) #### A QUESTION:10, 20, 12, 24, 16, 32, ? options: A)20 B)21 C)22 D)23 E)24 SOLUTION:E 24 This is an alternating multiplication and subtracting series with a pattern x2, -8, x2, -8. #### E QUESTION:The greatest number that divides 60 and 190 leaving remainder 6 and 10 respectively is: options: A)15 B)18 C)19 D)22 E)23 SOLUTION:explanation: 60-6= 54 ,190-10= 180 Highest number that divides 54 and 180 is HCF of numbers HCF of 54 nad 180= 18 Answer:B #### B QUESTION:A, B and C, each working alone can complete a job in 6, 8 and 12 days respectively. If all three of them work together to complete a job and earn $ 1170, what will be B's share of the earnings? options: A)$390 B)$520 C)$1080 D)$1170 E)$630 SOLUTION:Explanatory Answer A, B and C will share the amount of $1170 in the ratio of the amounts of work done by them. As A takes 6 days to complete the job, if A works alone, A will be able to complete 1/6 th of the work in a day. Similarly, B will complete 1/8th and C will complete 1/12th of the work. So, the ratio of the work done by A : B : C when they work together will be equal to 1/6 : 1/8 : 1/12 Multiplying the numerator of all 3 fractions by 24, the LCM of 6, 8 and 12 will not change the relative values of the three values. We get 24/6 : 24/8 : 24/12 = 4 : 3 : 2. i.e., the ratio in which A : B : C will share $1170 will be 4 : 3 : 2. Hence, B's share will be 3*1170/9 = 390. correct choice is (A) #### A QUESTION:A car starts from X and moves towards Y. At the same time another car starts from Y and moves towards X. Both travel at a constant speed and meet after 5 hours. During that time, the faster car traveled 2/3 of the distance XY. How long would it take the slower car to travel the distance XY? options: A)6 hours B)8 hours C)10 hours D)12 hours E)15 hours SOLUTION:If one car travelled 2/3, then the other car must have travelled only 1/3, as they are meeting after 5 hours in a certain point. So: (1/3)XY= 4*y --> It took the car 5 hours to travel 1/3 of the distance at a constant speed y. So if we solve this last equation: XY= 3*5*y= 15*y --> It will take this car 15 hours in total to reach its final destination. Answer: E #### E QUESTION:Let x be a positive integer, what is the remainder when 4^(2x+5)+3 is divided by 5? options: A)2 B)3 C)4 D)1 E)5 SOLUTION:For: (4^(2x+5)+3)/5 Let n = 2x + 5 4^n 4^1 = 4 4^2 = 16 4^3 = 64 4^4 = 256, last digit pattern repeats 4, 6, 4, 6, .... Rule: x^(m+n) = (x^m)(x^n) (4^(2x))(4^5) Rule: x^(mn) = (x^m)^n (4^2)(4^x)(4^5) => Now, (6)(4)(4) + 3 = (6) + 3 => Finally, 9/5 and remainder is 4. Answer: C #### C QUESTION:Suresh 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? options: A)32:21 B)22:21 C)21:32 D)31:21 E)32:28 SOLUTION:Here capital is not the same. Suresh invest 20000 for initial 6 months and 15000 for the next 6 months. Hence his term of ratio =( 20000*6 + 15000*6) Kiran invest Rs.30000 for 4 months and Rs.50000 for next 4 months. Hence his term of ration = (30000*4 : 50000*4) Suresh : Kiran = ( 20000*6 + 15000*6) : (30000*4 : 50000*4) = (20*6 + 15*6) : (30*4 + 50*4) = (20*3 + 15*3) : (30*2 : 50*2) = 105:160 = 21:32 Answer is C #### C QUESTION:A and B invests Rs.3000 and Rs.6500 respectively in a business. If A doubles his capital after 6 months. In what ratio should A and B divide that year's profit? options: A)8:8 B)9:8 C)9:6 D)9:5 E)9:13 SOLUTION:(3*6 + 6*6): (6.5*12) 54:78 => 9:13 Answer: E #### E QUESTION:The membership of a committee consists of 3 English teachers, 4 Mathematics teachers, and 2 Social Studies teachers. If 2 committee members are to be selected at random to write the committee’s report, what is the probability that the two members selected will both be social teachers? options: A)2/3 B)1/12 C)2/9 D)1/2 E)1/24 SOLUTION:Probability of first member an English teacher = 3/9 Probability of second member an English teacher = 2/8 Probability of both being english teacher = 3/9 x 2/8 =1/12 (B) #### B QUESTION:A train 160m long is running at 30kmph. In how much time will it pass a platform 120m long? options: A)15.89 seconds B)24.36 seconds C)15.96 seconds D)14.93 seconds E)22.23 seconds SOLUTION:Distance travelled = 160 + 120m = 280m Speed = 30 * 5/8 = 75/4m Time = 280 * 4/75 = 14.93 Seconds Answer : D. #### D QUESTION:If the sides of a triangle are 26 cm, 24 cm and 20 cm, what is its area? options: A)120 B)772 C)288 D)266 E)240 SOLUTION:The triangle with sides 26 cm, 24 cm and 20 cm is right angled, where the hypotenuse is 26 cm. Area of the triangle = 1/2 * 24 * 20 = 240 cm2 Answer: E #### E QUESTION:If the sides of a triangle are 39 cm, 36 cm and 15 cm, what is its area? options: A)230 cm^2 B)240 cm^2 C)250 cm^2 D)260 cm^2 E)270 cm^2 SOLUTION:The triangle with sides 39 cm, 36 cm and 15 cm is right angled, where the hypotenuse is 39 cm. Area of the triangle = 1/2 * 36 * 15 = 270 cm^2 Answer: E #### E QUESTION:A can do a piece of work 20 days. B can do work in 35 days. In how many days they will complete the work together? options: A)15 days B)16.32 days C)12.72 days D)17 days E)18 days SOLUTION:LCM = 140, Ratio= 20:35=4:7 No of days= 140/(4+7) = 90/5 = 12.72 days ANSWER:C #### C QUESTION:1397 x 1397 = ? options: A)1961609 B)1851609 C)1951619 D)1951609 E)1851619 SOLUTION:1397 x 1397 = (1397)^2 = (1400 - 3)^2 = (1400)^2 + (3)^2 - (2 x 1400 x 3) = 1960000 + 9 - 8400 = 1960009 - 8400 = 1951609. Answer is D. #### D QUESTION:45 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? options: A)80 litres B)90 litres C)120 litres D)170 litres E)None of these SOLUTION:Explanatory Answer To cover a distance of 800 kms using a 800 cc engine, the amount of diesel required = 800/600*45 = 60 litres. However, the vehicle uses a 1200 cc engine and the question states that the amount of diesel required varies directly as the engine capacity. i.e., for instance, if the capacity of engine doubles, the diesel requirement will double too. Therefore, with a 1200 cc engine, quantity of diesel required = 1200/800*60 = 90 litres. Answer B #### B QUESTION:A string of 15 light bulbs is wired in such a way that if any individual light bulb fails, the entire string fails. If for each individual light bulb the probability of failing during time period T is 0.06, what is the probability that the string of light bulbs will fail during the time period T? options: A)1 - (0.94)^15 B)(0.06)^15 C)1 - (0.06)^15 D)(0.94)^15 E)0.06^150 SOLUTION:The string of light bulbs will fail if at least one light bulb fails. So, let's find the probability of the opposite event and subtract that value from 1. The opposite event is when none of the 15 light bulbs fails, since the probability of each light bulb not to fail is 1-0.06=0.94 the probability that none of the 15 light bulbs fails is 0.94^15. Hence, the probability that at least one light bulb fails is 1-0.94^15. Answer: A. Now, you should have spotted that your reasoning was not right because of one simple thing, consider the case when we have 100 light bulbs instead of 15, then according to your logic the probability that the string of light bulbs will fail would be 100*0.06=6, which is not possible since the probability of an event cannot be more than 1 (100%). #### A QUESTION:Of 70 players on a football team, 46 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? options: A)54 B)59 C)63 D)71 E)62 SOLUTION:Total = 70 Thrower = 46 Rest = 70 - 46 = 24 Left Handed = 24/3 = 8 Right handed = 16 If all Thrower are right handed then total right handed is 46 + 16 = 62 so E. 62 is the right answer #### E QUESTION:For what values of k will the pair of equations 3(3x + 4y) = 36 and kx + 12y = 30 does not have a unique solution? options: A)12 B)9 C)3 D)7.5 E)2.5 SOLUTION:we have 2 equations 1. 3(3x + 4y) = 36 --> 3x + 4y = 12 -- > 9x + 12y = 36 2. kx + 12y = 30 substract 1-2, we get (9-K)x = 6 i.e. x = 6/(9-k) then, 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 #### B QUESTION:Two brothers take the same route to school on their bicycles, one gets to school in 25 minutes and the second one gets to school in 36 minutes. The ratio of their speeds is options: A)4 : 5 B)1 : 2 C)6 : 7 D)5 : 6 E)None SOLUTION:Solution Let us name the brothers as A and B. = (A'S speed) : (B's speed) =√b : √a = √25 : √36 = 5 : 6 Answer D #### D QUESTION:At a certain supplier, a machine of type A costs $23,000 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? options: A)$5,280 B)$11,200 C)$12,000 D)$12,800 E)$13,200 SOLUTION:Total Cost of 2 Machines of Type A = 20% of (Cost of 2 machine A) + remainder + 40 % remainder = 20% of 46000 + (46000 - 20% of 46000) + 40% of (46000 - 20% of 46000) = 60720 Total Cost of 1 Machine of Type B = 20% of (Cost of 1 machine B) + remainder + 40 % remainder = 20% of 50000 + (50000 - 20% of 50000) + 40% of (50000 - 20% of 50000) = 66000 Diff = 66000 - 60720 = 5280 Hence, A. #### A QUESTION:2 men catch 2 fish in 2 minutes. At this rate, how many men could catch 500 fish in 500 minutes? options: A)2 B)4 C)6 D)500 E)0 SOLUTION:2 men.....there are no other!!!! #### A QUESTION:If 2994 ÷ 14.5 = 179, then 29.94 ÷ 1.45 = ? options: A)17.1 B)17.3 C)17.5 D)17.7 E)17.9 SOLUTION:29.94/ 1.45 = 299.4/14.5 = (2994/14.5) x 1/10) [ Here, Substitute 179 in the place of 2994/14.5 ] = 179/10 = 17.9 Answer is E. #### E QUESTION:Souju's age is 115% of what it was 10 years ago, but 83 1/3% of what it will be after 10 years. What is her present age? options: A)56 years B)72 years C)56 years D)66 years E)76 years SOLUTION:Let the age before 10 years =x. Then, 115x/100=x+10 ⇒115x=100x+1000 ⇒x=1000/15=66 Present age =x+10=66+10=76 ANSWER:E #### E QUESTION:If a quality control check is made inspecting a sample of 2 light bulbs from a box of 12 lighbulbs, how many different samples can be chosen? options: A)6 B)24 C)36 D)66 E)72 SOLUTION:Try using the formula for combinations: n!/r!(n-r)! 12!/2!(12-2)! 12!/2!*10! 12*11/2*1 =66 ANSWER:D #### D QUESTION:A man can row upstream at 22 kmph and downstream at 42 kmph, and then find the speed of the man in still water? options: A)29 B)92 C)30 D)32 E)23 SOLUTION:US = 22 DS = 42 M = (42 + 22)/2 = 32 Answer:D #### D QUESTION:A 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 70% total profit if he has already sold one of the four cars at Rs. 1.2 lakh? options: A)1.8 lakh B)1.3 lakh C)1.9 lakh D)8.1 lakh E)6.1 lakh SOLUTION:Explanation: Total cost of 4 cars = 1+2 = 3 lakh Total SP of 4 cars = 3 x 1.7 = 5.1 lakh SP of 1 car = 1.2 lakh SP of rest 3 cars = 5.1 - 1.2 = 3.9 lakh Average SP of all the 3 cars = 1.3 lakh Answer: B) #### B QUESTION:In a simultaneous throw of 2 dice what is the probability of getting a total of 4? options: A)1/2 B)1/4 C)2/9 D)1/12 E)3/13 SOLUTION:n(S) = 6*6 = 36 E = {(1,3),(2,2),(3,1)} Probability = 3/36 = 1/12 Answer is D #### D QUESTION:A question paper consists of five problems, each problem having three internal choices. In how many ways can a candidate attempt one or more problems? options: A)676 B)833 C)1023 D)839 E)1035 SOLUTION:Given that, the question paper consists of five problems. For each problem, one or two or three or none of the choices can be attempted. Hence, the required number of ways = 45 - 1. = 210 - 1 = 1024 - 1 = 1023 Answer:C #### C QUESTION:If r is a positive integer and r^2 is divisible by 12, then the largest positive integer that must divide r ^3 is options: A) 2^3 B) 2^6 C) 3^3 D) 6^3 E) 12^2 SOLUTION:Since r is an integer so r 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 r^2 as a multiple of 12)) r^2 is divisible by 12 (12 = 2*2*3), So, r should have at least one 2 and one 3 so that r^2 has a 2^2 and two 3 So, r will have a 2 and a 3. Or r will be a multiple of 6 So, largest possible integer than should divide r^3 is 6^3 So, Answer will be D #### D QUESTION:Three friends A, Band C started a business by investing a sum of money in the ratio of 5 : 7 : 6. After 6 months C withdraws half of his capital. If the sum invested by ‘A’ is 40,000, out of a total annual profit of 33,000, C’s share will be options: A)9,000 B)12,000 C)11,000 D)10,000 E)None of these SOLUTION:Sum invested by A, B and C is 5 × 12 : 7 × 12 : 6 × 6 + 3 × 6 or, 60 : 84 : 54 or, 10 : 14 : 9 \Share of C = 9⁄33 × 33,000 = 9,000 Answer A #### A QUESTION:Raffle 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? options: A)2/5 B)2/7 C)33/83 D)51/250 E)100/249 SOLUTION:SOLUTION The 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. Answer: D #### D QUESTION:Becky, Merry and John want to share a chocolate bar evenly. What part of the bar will each of them take? What part of the bar will Becky and Merry have together? options: A)1/3 B)2/3 C)2/4 D)None of these E)Cannot be determined SOLUTION:Solution The children need to divide the bar into three pieces. So everyone will take 1/3 of the chocolate bar. Two girls together will have two pieces, hence, mathematically speaking, they will have 2/3 of the bar Answer B #### B QUESTION:What is the dividend. divisor 17, the quotient is 9 and the remainder is 5 options: A)134 B)136 C)140 D)158 E)160 SOLUTION:D = d * Q + R D = 17 * 9 + 5 D = 153 + 5 D = 158 #### D QUESTION:How many seconds will a train 100 meters long take to cross a bridge 150 meters long if the speed of the train is 72 kmph? options: A)22 sec B)77 sec C)25 sec D)18 sec E)12.5 sec SOLUTION:D = 100 + 150 = 250 S = 72 * 5/18 = 20 mps T = 250/20 = 12.5 sec Answer:E #### E QUESTION:A girl has to make pizza with different toppings. There are 8 different toppings. In how many ways can she make pizzas with 2 different toppings? options: A)16 B)56 C)112 D)28 E)38 SOLUTION:In 8 different toppings, selecting 2 diff toppings = 8c2 formula is n!/(n-c)! n = total number of toppings C = number chosen in a grouping. n=8 and c=2 so we get 8!/(8-2)! = (8*7*6*5*4*3*2*1)/(6*5*4*3*2*1) = 8*7 =56 ANSWER:B #### B QUESTION:In Cliff’s impressive rock collection, there are half as many igneous rocks as sedimentary rocks. Of the igneous rocks, 2/3 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? options: A)180 B)45 C)60 D)90 E)135 SOLUTION:We can start with the known quantity and then go on to find the others. Shiny igneous ricks are 40. These are (2/3) of total igneous rocks. (2/3)*Total igneous rocks = 40 Total igneous rocks = 40 * (3/2) = 60 Total sedimentary rocks = 2*Total igneous rocks = 2*60 = 120 Total number of rocks = 60 + 120 = 180 Answer (A) #### A QUESTION:Using all the letters of the word "FRIDAY", how many different words can be formed? options: A)A)7 B)B)8! C)C)8 D)D)7! E)E)5! SOLUTION:Explanation: Total number of letters = 5 Using these letters the number of 5 letters words formed is 5!. Answer: Option E #### E QUESTION:In 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 Q in the class? options: A)A)10 B)B)12 C)C)15 D)D)20 E)E)25 SOLUTION:the difference between the highest and lowest salaries is $100,000. So there are at least 2 people - say one with salary 0 and the other with 100k. No salary will be outside this range. Median = 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. Mean = 20k more than median so in our example, mean salary = 70k On the number line, 0........50k (median)........100k Mean = 70k So 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: 0....50k.....100k, 100k, 100k But 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: 0, ... 50k, 50k, 50k, 50k, ... 100k, 100k, 100k, 100k, 100k the median is not at 50k yet. Add another 3 people at 50k and another 2 at 100k to get 0, 50k, 50k, 50k, 50k, 50k, 50k, 50k, 100k, 100k, 100k, 100k, 100k, 100k, 100k Now the median is 50k and mean is 70k. Total number of people is 15. Answer (C) #### C QUESTION:If equation |x/2| + |y/2| = 2 encloses a certain region on the coordinate plane, what is the area of this region? options: A)20 B)32 C)100 D)200 E)400 SOLUTION:The equation can be reduced to intercept form as |x/4| + |y/4| = 1, so these are lines in four quadrants with x and y intercept as 14, so it is a rhombus with diagonals of 8 each and hence area = 1/2*d1*d2 = 1/2*8*8 = 32. Answer B. #### B QUESTION:What approximate value should come in plce of question mark (?) in the following equations ? 728.038 x 54.978 - 72.016 x 85.250 = ? options: A)31400 B)32700 C)33900 D)34400 E)32400 SOLUTION:Explanation : ? = 728 x 55 - 72 x 85.25 = 40040 - 6138 = 339900 Answer : Option C #### C QUESTION:A garrison of 1850 men has provisions for 28 days. At the end of 12 days, a reinforcement arrives, and it is now found that the provisions will last only for 10 days more. What is the reinforcement? options: A)1850 B)2960 C)3000 D)1110 E)1712 SOLUTION:1850 ---- 28 1850 ---- 16 x ----- 10 x*10 = 1850*16 x = 2960 1850 ------- 1110 Answer: D #### D QUESTION:if Juan takes 10 seconds to run y yards, how many seconds will it take him to run x yards at the same rate? options: A)11x/y B)10x/y C)x/11y D)11/xy E)xy/11 SOLUTION:Answer is B. The rate of running hards: 10 minutes per y hards. Thus the time for running x hards = x hards * 10 minutes/y hards = 10x/y #### B QUESTION:The present age of a father is 3 years more than three times the age of his son. Five years hence, father's age will be 10 years more than twice the age of the son. Find the present age of the father. options: A)33 B)38 C)27 D)40 E)48 SOLUTION:if the present age be x years. father's will be (3x+3)years.. so, (3x+3+5)=2(x+3)+10 or, x=8 so the fathers present age =(3x+3)=(3*8+3)years =27 years.. ANSWER : OPTION C #### C QUESTION:Today is Sunday. The day after 59 days will be options: A)Monday B)Wednesday C)Saturday D)Sunday E)None of these SOLUTION:Explanation : 59 days = 8 weeks 3 days = 3 odd days Hence if today is Sunday, After 59 days, it will be = (Sunday + 3 odd days) = Wednesday. Answer : Option B #### B QUESTION:If a - b =6 and a2+b2=48 , find the value of ab. options: A)6 B)8 C)10 D)12 E)2 SOLUTION:Explanation: We know 2ab=(a2+b2)−(a−b)2 2ab=48−36=12 =>ab=6 Option E #### E QUESTION:A and B start a business jointly. A invests Rs.16000 for 8 months and B remains in the business for 4 months. Out of the total profit B claims 2/7th share. How much money is contributed by B? options: A)128228 B)12800 C)12819 D)12818 E)12812 SOLUTION:16*8: x*4 = 5:2 x = 12.8 => Rs.12800 Answer: B #### B QUESTION:A 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 $1,500. If the price of the car in 1996 was $22,000, what is the car's price in 2002? options: A)$18,400 B)$19,500 C)$20,200 D)$20,400 E)$21,100 SOLUTION:Important point to notice- 2.5% decrease from the original price 2.5% of 22,000= 550 Total reduction in 6 years= 550*6= 3300 Final price= 22,000 +1500 - 3300= 20,200 C is the answer #### C QUESTION:On a weekend, 3 friends went skiing and evenly split the cost of their cabin. If the amount paid by each person was an integer, which of the following could not have been the cost of the cabin? options: A)$110 B)$150 C)$225 D)$54 E)$75 SOLUTION:Each of the seven persons evenly splitting the cost is an integer amount, therefore check the divisibility by 3 for all answer choices. 110/3 = 36.67 150/3 = 50 225/3 = 75 54/3 = 18 75/3 = 25 A is not an integer amount. Answer:A #### A QUESTION:A and B can do a work in 10 days and 15 days respectively. A starts the work and B joins him after 2 days. In how many days can they complete the remaining work? options: A)6 days B)2 days C)4 4/5 days D)3 days E)9 days SOLUTION:Work done by A in 2 days = 2/10 = 1/5 Remaining work = 4/5 Work done by both A and B in one day = 1/10 + 1/15 = 5/30 = 1/6 Remaining work = 4/5 * 6/1 = 24/5 = 4 4/5 days. Answer: C #### C QUESTION:The volumes of two cones are in the ratio 1 : 12 and the radii of the cones are in the ratio of 1 : 4. What is the ratio of their heights? options: A)A)2:5 B)B)2:7 C)C)2:2 D)D)2:1 E)E)4:3 SOLUTION:The volume of the cone = (1/3)πr2h Only radius (r) and height (h) are varying. Hence, (1/3)π may be ignored. V1/V2 = r12h1/r22h2 => 1/12 = (1)2h1/(4)2h2 => h1/h2 = 4/3 i.e. h1 : h2 = 4 : 3 Answer: E #### E QUESTION:A student is ranked 12th from right and 6th from left. How many students are there in totality ? options: A)17 B)19 C)20 D)21 E)22 SOLUTION:From right 12 , From left 6 Total = 12+6-1 = 17 ANSWER:B #### B QUESTION:In a kilometer race, A beats B by 16 meters or 10 seconds. What time does A take to complete the race? options: A)167 sec B)190 sec C)176 sec D)716 sec E)615 sec SOLUTION:Time taken by B run 1000 meters = (1000 * 10)/16 = 625 sec. Time taken by A = 625 - 10 = 615 sec. Answer:E #### E QUESTION:During a trip, joe traveled x percent of the total distance at an average speed of 30 miles per hour and the rest of the distance at an average speed of 40 miles per hour. In terms of x, what was Francine's average speed for the entire trip? options: A)(180-x)/2 B)(x+60)/4 C)(300-x)/5 D)600/(115-x) E)12000/x+300 SOLUTION:total distance =100 ;total time = T t1 = x/30 t2 = 100-x /40 T =t1+t2 = x/30 + 100-x/40 = (40x + 3000- 30x)/1200 = (10x+3000)/1200 = x+300/120 av speed = 100*120/x+300 = 12000/x+300 E #### E QUESTION:If p and w are positive integers such that p > w > 1, what is the remainder when 92p × 5p+w + 11w × 6pw is divided by 10? options: A)A.0 B)B.1 C)C.3 D)D.4 E)E.5 SOLUTION:92p × 5p+w + 11w × 6pw--1=B #### B QUESTION:If x/y =4/3, then (x-y)/x? options: A)-1/2 B)-1/4 C)1/3 D)1/2 E)1/4 SOLUTION:we have this law of fraction: a/b=c/d= (a-c)/(b-d) x/y=4/3 ---> x/4=y/3= (x-y)/(4-3)=(x-y)/(1) ---> (x-y)/x= 1/4 Answer: E #### E QUESTION:There are 7000 people in the particular village , among them 30% are educated and out of these 28% are doing agriculture and out of them 50% are woman's. Then find out the number of woman's who are educated and doing agriculture? options: A)294 B)235 C)350 D)288 E)580 SOLUTION:Total number of people in the village = 7000; out of them 30% educated = 2100; out of them 28% doing agriculture = 588; out of them 50% are woman's = 294. #### A QUESTION:A train passes a station platform in 34 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? options: A)248 m B)210 m C)277 m D)765 m E)176 m SOLUTION:Speed = (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)/34 = 15 ==> x + 300 = 510 ==> x = 210 m. Answer: B #### B QUESTION:The present worth of Rs.676 due in 2 years at 4% per annum compound interest is options: A)Rs.150.50 B)Rs.154.75 C)Rs.156.25 D)Rs.625 E)None SOLUTION:Solution Present Worth = Rs.[676/(1+4/100)²] = Rs.(676x25/26x25/26) = Rs.625 Answer D #### D QUESTION:Four bells commence tolling together and toll at intervals of 2, 4, 6, 8 seconds respectively. In 18 minutes, how many times do they toll together ? options: A)43 B)44 C)45 D)46 E)47 SOLUTION:LCM of 2, 4, 6, 8 is 24. So, after each 24 seconds, they would toll together. Hence, in 18 minutes, they would toll 18*60 seconds / 24 seconds = 45 times But then the question says they commence tolling together. So, they basically also toll at thebeginning(0second). So, total tolls together = 45+1 = 46 Answer C #### C QUESTION:The simple form of the ratio 4/5:8/9 is? options: A)5:8 B)4:9 C)5:9 D)5:3 E)9:10 SOLUTION:4/5 : 8/9 = 9:10 Answer: E #### E QUESTION:There 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? options: A)980 B)1150 C)1360 D)1540 E)1720 SOLUTION:The number of ways to choose two teams is 17C2 = 17*16/2 = 136 The total number of games in the season is 10*136 = 1360. The answer is C. #### C <<<Examples ends QUESTION:If six persons sit in a row, then the probability that three particular persons are always together is -. options: A)1/5 B)1/7 C)1/9 D)1/2 E)2/7 SOLUTION:3!4! Required probability = 3!4!/6! = 1/5 ANSWER A #### A

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:X percents of the rooms are suits, Y percent of the rooms are painted light blue. Which of the following best represents the least percentage of the light blue painted suits? options: A)X-Y B)Y-X +100 C)100X-Y D)X+Y-100 E)100-XY SOLUTION:Using the simple formula 100 = X + Y - BOTH - > Here X = % of Suits , Y = % of light blue painted rooms and BOTH = % of suits painted in light blue colour So now, BOTH = X+Y -100 and now you can manipulate the value of X and Y to get the max and minimum values. Hence Answer D #### D QUESTION:If f(x) = (x^2 - 1)/(x), what is f(1/x) in terms of f(x)? options: A)-1*f(x) B)f(x) C)1/f(x) D)-1/f(x) E)2*f(x) SOLUTION:f(1/x) = ((1/x)2 - 1) / ((1/x)) = ((1/x^2) - 1) / (1/x) = ((1-x^2)/(x^2)) / (1/x = (1-x^2)/(x^2) = - ( (x^4) -1) / (x) = -1* f(x) Answer is A. #### A QUESTION:At 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? options: A)20 B)15 C)25 D)18 E)12 SOLUTION:Let the present ages of Arun and Deepak be 4x and 3x years respectively. Then, 4x + 6 = 26 => x = 5 Deepak's age = 3x = 15 years. ANSWER B #### B QUESTION:Tanks P and B are each in the shape of a right circular cylinder. The interior of tank P has a height of 10 meters and a circumference of 8 meters, and the interior of tank B has a height of 8 meters and a circumference of 10 meters. The capacity of tank P is what percent of the capacity of tank B? options: A)75% B)80% C)100% D)120% E)125% SOLUTION:B. For P, r=8/2pi. Its capacity = (4pi)^2 * 10= 160pi For B, r=10/pi. Its capacity = (5pi)^2 *8 = 200pi P/B = 160pi/200pi = 0.8 #### B QUESTION:A merchant has 1000 kg of sugar part of which he sells at 8% profit and the rest at 18% profit. He gains 14% on the whole. The Quantity sold at 18% profit is options: A)400 kg B)560 kg C)600 kg D)640 kg E)None SOLUTION:Solution ratio of 1st and 2nd parts = 4 : 6 = 2 : 3. Quantity of 2nd kind = (3/5 x 1000)kg = 600 kg. Answer C #### C QUESTION:A is four times as fast as B. If B alone can do a piece of work in 60 days, in what time can A and B together complete the work? options: A)10 B)12 C)22 D)28 E)20 SOLUTION:A can do the work in 60/4 i.e., 15 days. A and B's one day's work = 1/15 + 1/60 = (4 + 1)/60 = 1/12 So A and B together can do the work in 12 days. Answer: B #### B QUESTION:The value of 0.1 x 0.1 x 0.1 + 0.02 x 0.02 x 0.02 is: 0.2 x 0.2 x 0.2 + 0.04 x 0.04 x 0.04 options: A)0.0125 B)0.125 C)0.25 D)0.5 E)None of these SOLUTION:Explanation: Given expression = (0.1)3 + (0.02)3=1= 0.125 23 [(0.1)3 + (0.02)3] =8 Answer- B #### B QUESTION:A 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? options: A)4/8 B)9/2 C)7/6 D)9 E)2/21 SOLUTION:Explanation: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles. Probability that both marbles are blue = ³Câ‚‚/¹⁵Câ‚‚ = (3 * 2)/(15 * 14) = 1/35 Probability that both are yellow = ²Câ‚‚/¹⁵Câ‚‚ = (2 * 1)/(15 * 14) = 1/105 Probability that one blue and other is yellow = (³C₁ * ²C₁)/¹⁵Câ‚‚ = (2 * 3 * 2)/(15 * 14) = 2/35 Required probability = 1/35 + 1/105 + 2/35 = 3/35 + 1/105 = 1/35(3 + 1/3) = 10/(3 * 35) = 2/21 Answer: E #### E QUESTION:The 40 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? options: A)4 B)6 C)8 D)9 E)10 SOLUTION:The formula is Total = A+B+C - sum of exactly two + 2*all three + neither 21+18+19-x-2*5=40 solving for x you get 8 Answer C #### C QUESTION:The size of the wooden block is 5 x 10 x 20 cm .How many such blocks will be required to construct a solid wooden cube of minimum size? options: A)6 B)8 C)12 D)16 E)18 SOLUTION:Explanation: Side of smallest cube = L.C.M of 5,10,20 = 20cm Volume of the cube = (20 x 20 x 20)cm3 = 8000 cm3 Volume of the block= (5 x 10 x 20) cm3 = 1000 cm3 Number of blocks = (8000/1000) = 8 Answer: B #### B QUESTION:The length of a rectangular floor is more than its breadth by 200%. If Rs. 240 is required to paint the floor at the rate of Rs. 3 per sq m, then what would be the length of the floor? options: A)65 B)44 C)18 D)15.49 E)14 SOLUTION:Let the length and the breadth of the floor be l m and b m respectively. l = b + 200% of b = l + 2b = 3b Area of the floor = 240/3 = 80 sq m l b = 80 i.e., l * l/3 = 240 l2 = 240 => l =15.49 Answer:D #### D QUESTION:The 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: options: A)279 B)283 C)308 D)318 E)342 SOLUTION:Other number = (11 x 7700)/275 = 308. Answer: Option C #### C QUESTION:A man invested an amount of Rs.8000 in a fixed deposit scheme for 2 years at compound interest of 5% per annum. How much amount will Albert get on maturity of the fixed deposit ? options: A)Rs.8600 B)Rs.8620 C)Rs.8820 D)Rs. 8840 E)Rs. 8940 SOLUTION:Amount = 8000 *1+(5/100)2 = 8000 *21/20 * 21/20 = Rs.8820 ANSWER:C #### C QUESTION:When running a mile during a recent track meet, Nuria was initially credited with a final time of 5 minutes, 42 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? options: A)5 minutes, 17.6 seconds B)5 minutes, 21.8 seconds C)5 minutes, 43.56 seconds D)5 minutes, 44.44 seconds E)6 minutes, 10.4 seconds SOLUTION:One approach: The watch starts to work after Nuria began his running. It means the time should be greater than credited 5 minutes, 42 seconds. The only number is 6 minutes, 10.4 seconds. Another approach: 11/25 close to 30 second when added to the 5 minutes, 44 seconds, it means it passes 6 minute. Answer: E #### E QUESTION:2 pipes can separately fill a tank in 20hrs and 30hrs respectively. Both the pipes are opened tofill the tank, a leak develops in the tank through which one-third of water supplied by both the pipes goes out. What is the total time taken to fill the tank? options: A)12 hrs B)14 hrs C)16 hrs D)18 hrs E)20 hrs SOLUTION:1/20 + 1/30 = 1/12 1 + 1/3 = 4/3 1 --- 12 4/3 --- ? 4/3 * 12 = 16 hrs C #### C QUESTION:The value of ((x – y)³ + (y - z)³ + (z – x)³)/(21 (x – y) (y – z) (z – x)) is equal to : options: A)0 B)1/12 C)1/7 D)1/4 E)1/3 SOLUTION:Since (x – y) + (y – z) + (z – x) = 0, so (x – y)³ + (y – z)³ + (z – x)³= 3 (x – y) (y – z) (z – x). (3 (x – y) (y – z) (z – x))/(21(x – y) (y – z) (z – x)) = 1/7. ANSWER:C #### C QUESTION:35 binders can bind 1400 books in 21 days. How many binders will be required to bind 1600 books in 20 days? options: A)87 B)18 C)42 D)16 E)10 SOLUTION:Binders Books Days 35 1400 21 x 1600 20 x/35 = (1600/1400) * (21/20) => x = 42 Answer:C #### C QUESTION:Kiran 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? options: A)10 B)88 C)267 D)28 E)21 SOLUTION:Let the time taken to cover from A to B in car and cycle be x hours and y hours respectively. x + y = 7 --- (1) ; 2x = 4 --- (2) solving both the equations, we get y = 5 So, time taken to cover both ways by cycle = 2y hours = 10 hours. Answer: A #### A QUESTION:Pencils, Pens and Exercise books in a shop are in the ratio of 14: 4 : 3. If there are 140 pencils, the number of exercise books in the shop is: options: A)30 B)27 C)35 D)33 E)37 SOLUTION:Explanation : Let Pencils = 14x, Pens = 4x & Exercise books = 3x. Now, 14x = 140 hence x = 10 Number of exercise books = 3x = 30 Answer : A #### A QUESTION:The 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? options: A)11 am B)10 am C)9 am D)12 pm E)11.30 am SOLUTION:meet x hrs after 8 a.m. (Distance moved by first in x hrs) + [Distance moved by second in (x-1) hrs] = 330 ==>60x+75(x-1) = 330 x=3. So,they meet at (8+3). i.e 11a.m. ANSWER A #### A QUESTION:A, 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? options: A)299 B)267 C)269 D)400 E)276 SOLUTION:2*12 : 3*12 : 4*24 1: 3: 4 1/8 * 3200 = 400 Answer: D #### D QUESTION:The size of a flat-screen television is given as the length of the screen’s diagonal. How many square inches greater is the screen of a square 34-inch flat-screen television than a square 27-inch flat-screen television? options: A)106.75 B)213.5 C)427 D)729 E)1,156 SOLUTION:Diagonal of a square =√2*side of square => side =Diagonal/(√2) Area of square =s*s =(diagonal^2)/2 Difference of both tv's =(34^2-27^2)/2 =427 ANSWER:C #### C QUESTION:If x, y, and z are consecutive positive integers greater than 1, not necessarily in that order, then which of the following is (are) true? I. x > z II. 4x+ 4y > 4z III. yz > xz IV. xy > y + z options: A) I only B) II only C) II and III only D) II and IV only E) III and IV only SOLUTION:we do not know the values or the relative values but that the three are consecutive.. so the max difference in any two number is 2 and min 1.. lets see the choices.. I. x > z... we do not know the values or the relative values... need not be true.. II. 4x+ 4y > 4z or x+ y > z we take the worst case that z is teh largest and x and y are lowest possible..... so 2+3>4.. 5>4.. always true III. yz > xz we do not know the values or the relative values between x and y..need not be true IV. xy > y + z xy-y>z or y(x-1)>z... again lets take the worst scenario.. we 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 only ii is true ans B #### B QUESTION:A and B together can do a piece of work in 6 days and A alone can do it in 13 days. In how many days can B alone can do it? options: A)12 days B)15 days C)78/7 days D)21 days E)22/7 days SOLUTION:Explanation: A and B can do work 1/6 in 1 day A alone can do 1/13 work in 1 day B alone can do (1/6 -1/13) =7/78 work in 1 day => complete work can be done in 78/7 days by B Answer: Option C #### C QUESTION:If x = 3 and y = 2, what is the value of 5(x-y)^2 - xy ? options: A)-8 B)-7 C)-1 D)-2 E)-5 SOLUTION:x = 3 and y = 2 x-y = 3 - 2 = 1 x*y = 3 * 2 = 6 Now we apply it in the equation 5(x-y)^2 - xy =5 (1)^2-6 ==>5*1 -6 = 5-6 =-1 Answer : C #### C QUESTION:The product Z of two prime numbers is between 15 and 36. If one of the prime numbers is greater than 2 but less than 6 and the other prime number is greater than 8 but less than 24, then what is Z? options: A)35 B)33 C)28 D)21 E)15 SOLUTION:The smallest possible product is 33 which is 3*11. All other products are too big. The answer is B. #### B QUESTION:Walking at 8KMPH From Point E to Point railway station, mike will miss the train by 5 minutes. If he walks at 10KMPH he will reach the station by 5 minutes early.What is the distance between Point E to Railway station? options: A)A)9KM B)B)6.66KM C)C)7.25KM D)D)12.40KM E)E)13KM SOLUTION:Since time differences given are in minutes so let's convert speed in Km per minute 8 kmph = 8/60 km per minute = (2/15) km per minute 10 kmph = 10/60 km per minute = (1/6) km per minute Let, Time of train to depart from station = t minutes Distance between Point E and Railway Station = Speed*Time = (2/15)*(t+5) Distance between Point E and Railway Station = Speed*Time = (1/6)*(t-5) i.e. (2/15)*(t+5) = (1/6)*(t-5) i.e. 12t+60 = 15t - 75 i.e. 3t = 135 i.e. t = 45 minutes i.e. Distance = (1/6)*(t-5) = (1/6)*(45-5) = 40/6 = 20/3 Km = 6.66 Km Answer: Option B #### B QUESTION:The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is: options: A)247 m B)256 m C)245 m D)527 m E)725 m SOLUTION:Speed = [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. Answer:C #### C QUESTION:A mixture of 150 liters of wine and water contains 15% water. How much more water should be added so that water becomes 25% of the new mixture? options: A)10 B)30 C)20 D)15 E)17 SOLUTION:Number of liters of water in150 liters of the mixture = 15% of 150 = 15/100 * 150 = 22.5 liters. P liters of water added to the mixture to make water 25% of the new mixture. Total amount of water becomes (22.5 + P) and total volume of mixture is (150 + P). (22.5 + P) = 25/100 * (150 + P) 90+4P = 150+P P = 20 liters. Answer: C #### C QUESTION:in 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? options: A)11101 B)11110 C)10111 D)11011 E)11010 SOLUTION:4+3=7 since base is 7 so it will become 0 giving 1 carry to next digits(so 4+7=0) 3+4 + 1 carry from above step= 1 and 1 carry to next digit 2+5 + 1 carry to next digit= 1 and 1 carry 1+6= 11 so ans=11110 ANSWER:B #### B QUESTION:If x = y^2, and x and y are positive integers, which of the following numbers could be the value of x? options: A)10,573 B)11,908 C)12,322 D)13,924 E)14,537 SOLUTION:The square of an integer can have a units digit of 0, 1, 4, 5, 6, or 9. The answer is D. #### D QUESTION:The cross-section of a cannel is a trapezium in shape. If the cannel is 12 m wide at the top and 8 m wide at the bottom and the area of cross-section is 690 sq m, the depth of cannel is? options: A)39 B)28 C)27 D)69 E)71 SOLUTION:1/2 * d (12 + 8) = 690 d = 69 Answer: D #### D QUESTION:If w<0, which of the following must be true? options: A)–100 < w < 100 B)w ≤ –1 C)w ≤ 1 D)w^2 ≥ 1/4 E)–100 < w < 0 SOLUTION:w is a negative number. A. –100 < w < 100w can be a negative number less than -100 B. w ≤ –1w can be a fraction, in which case it would be greater than -1 C. w ≤ 1must be true since 1 is positive and w is negative D. w^2 ≥ 1/4not true if w is a negative fraction like -1/5 E. –100 < w < 0w can be a negative number less than -100=C #### C QUESTION:One computer can upload 100 megabytes worth of data in 4 seconds. Two computers, including this one, working together, can upload 1300 megabytes worth of data in 20 seconds. How long would it take for the second computer, working on its own, to upload 100 megabytes of data? options: A) 6 B) 2.5 C) 9 D) 11 E) 13 SOLUTION:Since the first computer can upload 100 megabytes worth of data in 4 seconds then in 4*5=20 seconds it can upload 5*100=500 megabytes worth of data, hence the second computer in 20 seconds uploads 1300-500=800 megabytes worth of data. The second computer can upload 100 megabytes of data in 2.5 seconds. Answer: B. #### B QUESTION:A bag contains 50 P, 25 P and 10 P coins in the ratio 5: 9: 4, amounting to Rs. 206. Find the number of coins of each type respectively. options: A)200, 360,162 B)200, 460,160 C)200, 360,160 D)200, 360,138 E)200, 360,129 SOLUTION:Explanation: let ratio be x. Hence no. of coins be 5x ,9x , 4x respectively Now given total amount = Rs.206 => (.50)(5x) + (.25)(9x) + (.10)(4x) = 206 we get x = 40 => No. of 50p coins = 200 => No. of 25p coins = 360 => No. of 10p coins = 160 Answer: C) #### C QUESTION:If ‘+’ means ‘×’, ‘-‘ means ‘+’, ‘×’ means ‘÷’ and ‘÷’ means ‘-‘ then find the value of; 6 – 9 + 8 × 3 ÷ 15 = options: A)6 B)10 C)12 D)-2 E)15 SOLUTION:E 15 #### E QUESTION:The sale price sarees listed for Rs.528 after successive discount is 20% and 10% is? options: A)288 B)277 C)380 D)290 E)262 SOLUTION:528*(80/100)*(90/100) = 380 Answer: C #### C QUESTION:[1/(1.2.3)] + [1/(2.3.4)] + [1/(3.4.5)] + [1/(4.5.6)] is equal to options: A)7 / 30 B)11 / 30 C)13 / 30 D)17 / 30 E)None SOLUTION:Answer Given Exp. = [(4 x 5 x 6) + (5 x 6) + (2 x 6) + (2 x 3)] / [(2 x 3 x 4 x 5 x 6)] = 168 / (24 x 30) = 7 / 30 Correct Option: A #### A QUESTION:If 20% of a number = 1000, then 120% of that number will be? options: A)20 B)120 C)360 D)6000 E)820 SOLUTION:Let the number x. Then, 20% of x = 1000 x = (1000 * 100)/20 = 5000 120% of x = (120/100 * 5000) = 6000. ANSWER:D #### D QUESTION:A 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? options: A)50 B)80 C)100 D)125 E)21 SOLUTION:Let old diameter be 4 , so radius is 2 Old area = 4π New diameter is 4.4 , so radius is 2.2 New area = 4.84π Increase in area is 0.84π % increase in area = 0.84/4*100 So, % increase is 21% Answer will be (E) #### E QUESTION:How many factors does 35^2 have? options: A)2 B)8 C)24 D)25 E)26 SOLUTION:36^2 = 6*6*6*6 = 2^4*3^4 Total factors = (4+1)*(4+1) = 6*4 = 24 Answer C. #### C QUESTION:The probability that Alex will solve a problem is 1/5. What is the probability that he solves at least one problem out of 4 problems? options: A)64/125 B)256/625 C)64/625 D)369/625 E)359/625 SOLUTION:The probability that Alex will not solve a problem = 4/5. The probability that Alex will not solve 10 problems = (4/5)4 = 256/625. Hence, the probability that Alex will solve at least one problem = 1 - 256/625 = 369/625. ANSWER:D #### D QUESTION:An amount of money is to be distributed among Faruk, Vasim and Ranjith in the ratio 3 : 5 : 8. If Vasims share is Rs. 1500, what is the difference between Faruk's and Ranjith's shares? options: A)s 1200 B)s 1500 C)s 1600 D)s 1900 E)s 1700 SOLUTION:Explanation : Let P = Faruk, Q = Vasim, R = Ranjith Let P = 3x, Q = 5x and R = 8x. Then, 5x = 1500 ? x = 300. P=900,Q=1500 and R = 2400. Hence, (R - p) = (2400 - 900) = 1500 Answer : B #### B QUESTION:Two trains are moving in opposite directions at 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.9 km respectively. The time taken by the slower train to cross the faster train in seconds is? options: A)22 B)287 C)48 D)277 E)21 SOLUTION:Relative speed = 60 + 90 = 150 km/hr. = 150 * 5/18 = 125/3 m/sec. Distance covered = 1.10 + 0.9 = 2 km = 2000 m. Required time = 2000 * 3/125 = 48 sec. Answer: C #### C QUESTION:An investor receives a total combined return of 7% on his two different investments. On his $40,000 investment he receives a return of 6%. What is the return on his $20,000 investment? options: A)7.25% B)7.5% C)8% D)8.5% E)9% SOLUTION:0.06 * 40000 + 20000x = 0.07(60000) solving for x give x = 9% option E #### E QUESTION:A 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 1.2 km long? options: A)2 mins 14 sec B)2 mins 34 sec C)162 sec D)244 sec E)2 mins 44 sec SOLUTION:D = 25 * 60 + 1200 = 2700 m T = 2700/60 * 18/5 = 162 sec ANSWER:C #### C QUESTION:A 270m long train running at the speed of 120kmph crosses another train running in opposite direction at the speed of 80kmph in 9 second. What is the length of the other train? options: A)150m B)230m C)290m D)310m E)420m SOLUTION:Relative speed = 120+80 = 200*5/18 = 500/9 m/s Let the length of the other train be x meters x+270/9 = 500/9 x = 230m Answer is B #### B QUESTION:What is the sum of the numbers between 1 and 20, inclusive? options: A)310 B)200 C)215 D)285 E)210 SOLUTION:Sol. 1+2+3...17+18+19+20 answer. E #### E QUESTION:On dividing 122 by a number, the quotient is 6 and the remainder is 2. Find the divisor? options: A)14 B)16 C)18 D)20 E)22 SOLUTION:d = (D-R)/Q = (122 - 2)/6 = 122/6 = 20 D) #### D QUESTION:On dividing 12401 by a certain number, we get 76 as quotient and 13 as remainder. What is the divisor? options: A)163 B)785 C)852 D)456 E)852 SOLUTION:Divisor *quotient+remainder=dividend divisor=(dividend)-(remainder)/quotient (12401-13)/76=163 Answer(A) #### A QUESTION:On a map the distance between two mountains is 310 inches. The actual distance between the mountains is 136 km. Ram is camped at a location that on the map is 34 inch from the base of the mountain. How many km is he from the base of the mountain? options: A)14.83 B)14.81 C)14.91 D)14.82 E)14.12 SOLUTION:Explanation: Since 310 inch = 136 km So 1 inch = 136/310 km So 34 inch = (136 × 34)/ 310 = 14.91 km Answer: C #### C QUESTION:walking at ¾ of his usual speed ,a man is late by 2 ½ hr. the usual time is. options: A)7 B)8 ½ C)7 ½ D)7 ¾ E)9 ½ SOLUTION:Usual speed = S Usual time = T Distance = D New Speed is ¾ S New time is 4/3 T 4/3 T – T = 5/2 T=15/2 = 7 ½ Answer is C. #### C QUESTION:A gardener sells 100 metres of fencing for Rs. 7500 at a loss of Rs. 3 per metre. Find his cost price for one metre of fencing? options: A)54 B)67 C)62 D)78 E)72 SOLUTION:SP per metre = 7500/100 = Rs. 75 Loss per metre = Rs. 3 CP per metre = 75 + 3 = Rs. 78 Answer: D #### D QUESTION:If A got 80 marks and B got 60 marks, then what percent of A's mark is B's mark? options: A)60% B)80% C)65% D)75% E)None of these SOLUTION:A's marks = 80 ; B's marks = 60. Let x% of A = B => x/100 * 80 = 60 => x = (60 * 100)/80 = 75 B's marks is 75% of A's marks. ANSWER:D #### D QUESTION:A shop owner professes to sell his articles at certain cost price but he uses false weights with which he cheats by 14% while buying and by 20% while selling. What is his percentage profit? options: A)10.22% B)20.22% C)21.22% D)42.5% E)Can't be calculated SOLUTION:The owner buys 100 kg but actually gets 114kg; The owner sells 100 kg but actually gives 80kg; Profit: (114-80)/80*100=~42.5% Answer: D. #### D QUESTION:Rs.900 amounts to Rs.920 in 3 years at simple interest. If the interest is increased by 3%, it would amount to how much? options: A)Rs.1056 B)Rs.1001 C)Rs.2056 D)Rs.1026 E)Rs.1856 SOLUTION:(900*3*3)/100 = 81 920 + 81 = 1001 ANSWER:B #### B QUESTION:Klaudia can choose any two of four different candles and any 8 of 9 different flowers for a centerpiece arrangement. Given these choices, how many candle + flower groupings can she select? options: A)54 B)72 C)96 D)144 E)432 SOLUTION:Klaudia can choose any two of four different candles and any 8 of 9 different flowers for a centerpiece arrangement.2 candles from 4 candles: 4C2: 6 8 flowers from 9 flowers: 9C8 : 9 So total grouping 9*6= 54. Answer is A. #### A QUESTION:Excluding stoppages,the speed of the bus is 54kmph and including stoppages,it is 27kmph. For how many minutes does the bus stop per hr options: A)12 min B)11 min C)13 min D)20 min E)30 min SOLUTION:Due to stoppages,it covers 27km less. time taken to cover 27 km is [27/54 *60] min = 30min Answer is E. #### E QUESTION:The points A(0, 0), B(0, 4a - 2) and C(2a + 1, 2a + 6) form a triangle. If angle ABC = 90, what is the area of triangle ABC? options: A)58 B)70 C)63 D)65 E)72 SOLUTION:1/2bh=1/2(2a+1)(2a+6) Now 4a-2=2a+6 2a=8 . a=4 Therefore, A(0,0); B(0,14); C(9,14) 1/2*9*14=63 Answer: C #### C QUESTION:Consider the sets Tn = {n, n + 1, n + 2, n + 3, n + 4}, where n = 1, 2, 3,...., 66. How many of these sets contain 6 or any integral multiple thereof (i.e., any one of the numbers 6, 12, 18, ...)? options: A)(a) 80 B)(b) 55 C)(c) 82 D)(d) 83 E)(e) 84 SOLUTION:T1: 1,2,3,4,5 T2: 2,3,4,5,6 T3: 3,4,5,6,7 etc. means that every multiple of 6 will be involved in 5 sets. We have (66-6)/6+1=11 such multiples. So, final number of sets is 11*5=55 Answer : B #### B QUESTION:Karthikeyan arranged a party to celebrate his birth day.20 of his close friends were invited. One friend left before the cake was cut due to an urgent phone call.The big cake was drawing the attention of the party visitors. This cake is to be divided among friends and of course Karthikeyan will get his share. A man eats 3 pieces, a woman eats two pieces and a child eats half a piece of cake. Including Karthikeyan count the number of men,women and children in the party. There are 20 pieces of cake in all. options: A)6 women, 2 men and 12 children B)7 women, 1 men and 12 children C)5 women, 1 men and 14 children D)4 women, 2 men and 14 children E)None of these SOLUTION:Let the number of men be m, number of women be w and number of children be c Total number of pieces = Pieces ate by men + Pieces ate by women + Pieces ate by children There are 20 total pieces. Also a man eats 3 pieces, a woman eats 2 and children half. Therefore above equation becomes. 20 = 3m + 2w + 1/2c In the above equation, you have to substitute the values given in options to find which one satisfies the equation. Option c with m = 1, c = 14 and w = 5 perfectly satisfies the equation as follows 20 = 3(1) + 2(5) + (1/2)(14) 20 = 20 i,e our equation is satisfied perfectly by option c ANSWER:C #### C QUESTION:In 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 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 Ms. Robbins received? options: A)0.06N + 3,200 B)0.1N + 7,200 C)0.4N + 7,200 D)0.1N + 8,000 E)0.06N + 7,000 SOLUTION:total vote = N vote cast by independent voters = 0.4 N vote cast by registered voters = 0.6 N vote received by Ms. Robbins = 7000 + 10% of vote be registered voters = 7000 + 0.06 N Answer choice E #### E QUESTION:The 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. 26,000 is made? options: A)Rs. 1,10,000 B)Rs. 1,20,000 C)Rs. 1,22,000 D)Rs. 1,21,000 E)None of these SOLUTION:The value of the machine after two years = 0.8 * 0.8 * 1,50,000 = Rs. 96,000 SP such that a profit of Rs. 24,000 is made = 96,000 + 26,000 = Rs. 1,22,000 ANSWER:C #### C QUESTION:The number of defects in the first five cars to come through a new production line are 9, 7, 10, 4, and 8, respectively. If the sixth car through the production line has either 3, 7, or 12 defects, for which of theses values does the mean number of defects per car for the first six cars equal the median? I. 3 II. 7 III. 12 options: A)I only B)II only C)III only D)I and III only E)I, II, and III SOLUTION:C for 7 we will have mean as 7.16(approx) and median as 7 but for 3 we will have mean and median = 6.5 and for 12 we will have median and mean =8 #### C <<<Examples ends QUESTION:In an examination 60% failed in Math and 40% failed in French. If 10% failed in both. What % of students passed in both. options: A)25% B)15% C)20% D)30% E)10% SOLUTION:Passed in Math = 100 - 60 = 40% Passed in French = 100 - 40 = 60% Students who passed Math or French = 100 -10 = 90% Students passed in Math and French = (Passed in Math) + (Passed in French) - (Students who passed Math or French) = 60+40-90 =10% ANSWER:E #### E

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:A 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? options: A)4 yr 10 month B)6 yr 10 month C)7 yr 11 month D)7 yr 10 month E)8 yr 10 month SOLUTION:When C is 4yr 6 month i.e. 54 months old A is 79 month old.. B is 15 month older than A When A is 79 months old then, B is 94 months old i.e. 7yr 10 month ANSWER:D #### D QUESTION:In 24 minutes, the hour hand of a clock moves through an angle of: options: A)60° B)24° C)12° D)5° E)None SOLUTION:12 hour = 360˚, 1 hr. = 360/12 = 30˚ 60 min = 30˚, 1 min 30/60 = .5˚ 24 min. = 1/2 ×24 = 12˚ Answer: C #### C QUESTION:The dimensions of a field are 10 m by 10 m. A pit 5 m long, 5 m wide and 3 m deep is dug in one corner of the field and the earth removed has been evenly spread over the remaining area of the field. What will be the rise in the height of field as a result of this operation ? options: A)2m B)2.5m C)1.5m D)1.25m E)1m SOLUTION:The volume of the earth removed is 5*5*3 = 75 m^3. The remaining area of the field is 10*10 - 5*5 = 75 m^2. 75 m^3 of the earth evenly spread over the area of 75 m^2 will rise the height by (height) = (volume)/(area) = 75/75 = 1 m. Answer: E #### E QUESTION:If x is a positive integer, which of the following must be odd? options: A)x+1 B)x^2+x C)x^2+x+7 D)x^2−1 E)3x^2−3 SOLUTION:A. X+1 = can be odd or even. Since O + O =E or E + O = O B. X^2 + X = X(X+1). Since from the above derivation we already know the term X+1 can be Odd or Even, directly substitute here. X(ODD) = Even (When X is Even) or X(EVEN) = EVEN [When X is ODD] C. Here's the answer. Since we know the term x^2 + X can always take a EVEN number, EVEN + 7 = ODD Hence C. #### C QUESTION:How 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? options: A)5040 B)40 C)400 D)5000 E)6000 SOLUTION:LOGARITHM => 10 diff letters req no of words = No of arrangements of 10 letters taking 4 at a time => 10P4 = (10*9*8*7) ==> 5040 ANSWER A #### A QUESTION:In an encryption code 'PLAYS' is written as '{:SUD' when encoded and 'SLEEP' is written as 'D:RR{' when encoded. How is ''SLAPPY" written in that encryption code? options: A)D:S{{U B)SLAPPY C){RUDD: D){:SUU{ E)U{{S:D SOLUTION:D = S : = L S = A P = { P = { Y = U Correct Answer: A #### A QUESTION:A group of 11 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? options: A) E/(12 - n) B) (12 - n)/E C) E/[12(12-n)] D) nE / [11(11-n)] E) (12-n)E/(12n) SOLUTION:total cost =E no of people willing to participate initially =11 initial cost for each =E/11 when n people decided not to participate Cost for each =E/11-n D #### D QUESTION:If MAPLE is coded as VOKZN then how will CAMEL be coded? options: A)OVNZF B)OUNZX C)OVNZX D)XZNVO E)XZNVV SOLUTION: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 Z Y X W V U T S R Q P O N M L K J I H G F E D C B A So each alphabet is replaced by the above rule and also whole word is reversed i.e MAPLE - after just replacing each alphabet (by above rule) we get NZKOV,then we reverse this word again and we get VOKZN. so this way CAMEL becomes OVNZX ANSWER:C #### C QUESTION:Pavan travelled for 15 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. options: A)408 km B)409 km C)410 km D)412 km E)419 km SOLUTION:Let the distance travelled be x km. Total time = (x/2)/30 + (x/2)/25 = 15 => x/60 + x/50 = 15 => (5x + 6x)/300 = 15 => x = 409 km ANSWER:B #### B QUESTION:if price of t.v set is reduced by 25%, then its sale increases by 75%, find net effect on sale value options: A)31 B)32 C)46 D)47 E)48 SOLUTION:- a + b + ((-a)(b)/100) = -25+75+(-25*75)/100 = -25+75-19 =31 ANSWER:A #### A QUESTION:At a game of billiards,A can give B 15 points in 60 and A can give C 20 points in 60.How many points can B give C in a game of 90 ? options: A)30 points B)20 points C)10 points D)12 points E)None of these SOLUTION:Solution A : B = 60 : 45 and A : C = 60 : 40. ∴ B/C =( B/A x A/C) = (45/60 x 60/40) = 45/40 =90/80= 90 : 80 ∴ B can give C 10 points in a game of 90. Answer C #### C QUESTION:Express 50 mps in kmph? options: A)172 B)160 C)150 D)180 E)120 SOLUTION:25 * 18/5 = 180 kmph Answer:D #### D QUESTION:By selling 12 pencils for a rupee a man loses 20%. How many for a rupee should he sell in order to gain 20%? options: A)9 B)4 C)8 D)7 E)65 SOLUTION:80% --- 12 120% --- ? 80/120 * 12 = 8 Answer: A #### A QUESTION:Bruce and Anne can clean their house in 4 hours working together at their respective constant rates. If Anne’s speed were doubled, they could clean their house in 3 hours working at their respective rates. How many hours does it currently take Anne to clean the house on her own? options: A)6 B)7 C)8 D)12 E)14 SOLUTION:Lets suppose Anne and Bruce take A and B hrs working separately So in 1 hour they can together finish 1/A + 1/B portion of the work which equals 1/4 (As the work is completed in 4 hours) After anne doubles her rate of work the portion completed by the both is 1/A +2/B which is equal to 1/3 (As the work is completed in 3 hours) Solving these 2 equations we can find B as 12 ANSWER:D #### D QUESTION:What is x if x + 5y = 24 and y = 2? options: A)1 B)3 C)5 D)7 E)14 SOLUTION:Substitute y by 2 in x + 5y = 24 x + 5(2) = 24 x + 10 = 24 If we substitute x by 14 in x + 10 = 24, we have 14 + 10 = 24. Hence x = 14 correct answer E #### E QUESTION:The 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 32 ? options: A)440 B)512 C)550 D)620 E)750 SOLUTION:Large numbers are made in two ways: Either by taking small prime numbers and raising them to higher powers or taking large prime numbers in the first place. 31*2 = 62 (large prime number) 2^6 = 64 (many small prime numbers) To get a sum as large as 32 or more, you would need some large prime numbers. So options such as 512, 700 and 750 which have small prime numbers as factors should be ignored first. 440 also splits into 11, 4( which is 2*2), 2, 5 - relatively small prime numbers. You are left with 620 which is 31*2*2*5 (sum greater than 32) Answer D #### D QUESTION:The present ages of three persons in proportions 4 : 7 : 9. Eight years ago, the sum of their ages was 56. Find their present ages (in years). options: A)8, 20, 28 B)16, 28, 36 C)20, 35, 45 D)18, 24, 32 E)None of these SOLUTION:Explanation: Let their present ages be 4x, 7x and 9x years respectively. Then, (4x - 8) + (7x - 8) + (9x - 8) = 56 20x = 80 x = 4. Their present ages are 4x = 16 years, 7x = 28 years and 9x = 36 years respectively. Answer: B #### B QUESTION:Which of the following is closest to (8!-7!)/(8!+7!)? options: A)0.01 B)0.8 C)0.2 D)1 E)10 SOLUTION:(8!-7!)/(8!+7!) 7! (8-1)/7! (8+1) 7/9 = 0.8 (approximately) B is the answer #### B QUESTION:A man sitting in a train which is travelling at 64 kmph observes that a goods train travelling in a opposite direction, takes 18seconds to pass him. If the goods train is 420 m long, find its speed. options: A)32 B)15 C)18 D)20 E)25 SOLUTION:Relative speed = (420/18)m/s = (420/18)*(18/5) = 84 kmph speed of goods train = 84-64 = 20 kmph Answer is D #### D QUESTION:Zayn, Mark, David ,Peter, Harry and Paula line up at a ticket window. In how many ways can they arrange themselves so that David is second in line from the window? options: A)a 100 B)b 112 C)c 90 D)d 120 E)e 30 SOLUTION:D David's position is fixed. Now we need to arrange all others around David. There are 5x4x3x2x1= 120 ways to arrange five people. #### D QUESTION:George can do 3/5 of work in 9days.He then calls in pauls and they completed the work in 4days.How long paul would take long to complete the work? options: A)32 B)28 C)35 D)30 E)22 SOLUTION:George work is (5/3)*9 =15; 1 day work of george is 1/15 ; remaining is 2/5th; paul & george work is 5/2*4=10 ; their 1 day work is 1/10; and only paul work is (1/10)-(1/15)=30 ANSWER:D #### D QUESTION:A cistern has a leak which would empty the cistern in 20 minutes. A tap is turned on which admits 6 liters a minute into the cistern, and it is emptied in 24 minutes. How many liters does the cistern hold? options: A)480 B)487 C)720 D)729 E)268 SOLUTION:1/x - 1/20 = -1/24 x = 120 120 * 6 = 720 Answer:C #### C QUESTION:A person travels first 100km at 40km/hr and the next 100km at 60km/hr. The average speed for the first 200km of the tour is? options: A)36km/hr B)50km/hr C)48km/hr D)60km/hr E)55km/hr SOLUTION:Total time taken = 100/40 + 100/60 = 25/6 hrs Average speed = 200*6/25 = 48km/hr Answer is C #### C QUESTION:Find compound interest on $ 8000 at 15% per annum for 2 years 4 months, compounded annually. options: A)3109 B)3209 C)3108 D)3107 E)3100 SOLUTION:Time = 2 years 4 months = 2(4/12) years = 2(1/3) years. Amount = $ [8000 X (1+­(15/100))2 X (1+((1/3)*15)/100)] =$ [8000 * (23/20) * (23/20) * (21/20)] = $ 11109. . :. C.I. = Rs. (11109 - 8000) = $ 3109. Answer A. #### A QUESTION:How many pieces of 0.85 metres can be cut from a rod 42.5 metres long? options: A)30 B)40 C)50 D)60 E)70 SOLUTION:Number of pieces = 42.5/0.85 = 42.50/0.85 = 4250/85 = 50. ANSWER:C #### C QUESTION:A certain university will select 1 of 3 candidates eligible to fill a position in the mathematics department and 2 of 10 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? options: A)42 B)70 C)140 D)135 E)315 SOLUTION:1 of 3 will be chosen for the math 2 of 10 will be chosen for the computer None of the 3 chosen people can be in more than one departments. We can choose any of the 3 candidates for the math dep., which gives as 3 selections. We can choose 2 of the 10 candidates for the computer dep., which gives us 2 selections and 8 rejections. So, the way to find how many different selections of 2 candidates we can have for the computer dep., we do: 10! /2!*8!= (9*10) / 2 = 90 / 2 = 45. We are multiplying our individual selections: 3*45 = 135 In the bolded part, we don't have to multiply all of the numbers, as those in 8! are included in 10!, so we simplify instead. Ans D #### D QUESTION:Jill works as a waitress at the local diner where she earns an hourly wage of $7.00 per hour and a standard tip rate of 5% of the cost of the orders she serves. If she worked four 12-hour shifts this week and averaged $40 in orders per hour, how much did Jill earn this week? options: A)280 B)300 C)320 D)432 E)400 SOLUTION:Jill earns 7 dollars/hour and the hourly tip is (1/20)*40. Jill thus earns 7*12+12*2 per day(or 7(12)+2(12)=9(12)=108). Jill has worked for 4 days -> 108*4=432. This matches answer choice D. #### D QUESTION:Two cars cover the same distance at the speed of 60 and 64 kmps respectively. Find the distance traveled by them if the slower car takes 1 hour more than the faster car options: A)960 km B)950 m C)906 km D)906 m E)950 m SOLUTION:60(x + 1) = 64x X = 15 60 * 16 = 960 km ANSWER A #### A QUESTION:Gary had an average score of 70 on his first four quizzes. He had an average score of 75 on his first five quizzes. What score did he receive on his fifth quiz? options: A)90 B)95 C)65 D)42 E)43 SOLUTION:The sum of Gary's first 4 scores is 4 · 70 and the sum of his first 5 scores is 5 · 75, so he received 5 · 75 − 4 · 70 on his 5th quiz. You can do the arithmetic or note that the answer ends in a 5 and eliminate answer C because it is lower than the average. The correct answer is B. #### B QUESTION:A & 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 4000 as profit , what is their total profit? options: A)28000 B)30000 C)32000 D)34000 E)None of these SOLUTION:Explanation : Suppose B's investment = x. Then A's investment= 3x Suppose Bs period of investment = y, then A's period of investment = 2y A : B = 3x * 2y : xy = 6 : 1 Total profit * 1/7 = 4000 => Total profit = 4000*7 = 28000. Answer : Option A #### A QUESTION:One train is traveling 36 kmph and other is at 12.5 meters a second. Ratio of the speed of the two trains is? options: A)5:4 B)5:6 C)5:0 D)5:4 E)4:5 SOLUTION:36 * 5/18 = 12.5 20:25 => 4:5 Answer: E #### E QUESTION:At a certain supplier, a machine of type A costs $23,000 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? options: A)$5,280 B)$11,200 C)$12,000 D)$12,800 E)$13,200 SOLUTION:Total Cost of 2 Machines of Type A = 20% of (Cost of 2 machine A) + remainder + 40 % remainder = 20% of 46000 + (46000 - 20% of 46000) + 40% of (46000 - 20% of 46000) = 60720 Total Cost of 1 Machine of Type B = 20% of (Cost of 1 machine B) + remainder + 40 % remainder = 20% of 50000 + (50000 - 20% of 50000) + 40% of (50000 - 20% of 50000) = 66000 Diff = 66000 - 60720 = 5280 Hence, A. #### A QUESTION:N is one of the numbers below. N is such that when multiplied by 0.75 gives 1. Which number is equal to N? options: A)3/2 B)5/3 C)1+1/3 D)1 1/2 E)1 1/3 SOLUTION:N is such that when multiplied by 0.75 gives 1" is written mathematically as N * 0.75 = 1 Solve for N N = 1/0.75 = 100/75 = (75 + 25) / 75 = 75/75 + 25/75 = 1+1/3 correct answer C #### C QUESTION:When the price of an article was reduced by 35% its sale increased by 80%. What was the net effect on the sale? options: A)17% increase B)44% decrease C)60% increase D)66% increase E)66% decrease SOLUTION:if n items are sold for $p each, revenue is $np. If we reduce the price by 35%, the new price is 0.65p. If we increase the number sold by 80%, the new number sold is 1.8n. So the new revenue is (0.65p)(1.8n) = 1.17np, which is 1.17 times the old revenue, so is 17% greater. ANSWER:A #### A QUESTION:A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long? options: A)40 sec B)65 sec C)18 sec D)16 sec E)17 sec SOLUTION:Speed = 45 * 5/18 = 25/2 m/sec Total distance covered = 360 + 140 = 500 m Required time = 500 * 2/25 = 40 sec Answer:A #### A QUESTION:Which of the following integers is NOT a divisor of x if x = (21)(3^7) – (7)? options: A)2 B)4 C)7 D)9 E)10 SOLUTION:(21)(3^7) is divisible by 3 but 7 is not divisible by 3. Therefore (21)(3^7) - 7 is not divisible by 3 and thus not divisible by 9. The answer is D. #### D QUESTION:By selling an article at Rs.600, a profit of 25% is made. Find its cost price? options: A)228 B)200 C)279 D)480 E)221 SOLUTION:SP = 600 CP = (SP)*[100/(100+P)] = 600 * [100/(100+25)] = 600 * [100/125] = Rs.480.Answer:D #### D QUESTION:A manufacturer of a certain product can expect that between 0.4 percent and 0.5 percent of the units manufactured will be defective. If the retail price is $2,500 per unit and the manufacturer offers a full refund for defective units, how much money can the manufacturer expect to need to cover the refunds on 20,000 units? options: A) Between $15,000 and $25,000 B) Between $30,000 and $50,000 C) Between $200,000 and $250,000 D) Between $150,000 and $250,000 E) Between $300,000 and $500,000 SOLUTION:Number of defective units is between = .4 % of 20000 and .5% of 20000 = 80 and 100 Retail Price per unit = 2500 $ Expected price of refund is between = 2500 x 80 and 2500 x 100 =2,00,000 and 2,50,000 dollars Answer C #### C QUESTION:If |x| = 4x - 1, then x = ? options: A)3 B)1/2 C)1 and 1/2 D)-1/2 E)-1 SOLUTION:Answer: A Approach: Substituted option A i.e x=1. Inequality satisfied. #### A QUESTION:A 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? options: A)600,400 B)500,500 C)300,700 D)800,1200 E)550,1450 SOLUTION:Ratio of their works A:B = 6:4 Ratio of their wages A:B = 2:3 A's share = (2/5)2000 = 800 B's share = (3/5)2000 = 1200 correct option is D #### D QUESTION:A bike covers a certain distance at the speed of 68km/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? options: A)85 km/h B)85.34 km/h C)87.67 km/h D)90.66 km/h E)90.64 km/h SOLUTION:Ans.(D) Sol. Total distance = 68 × 8 = 544 km Now speed = 544/6 = 90.66 km/h #### D QUESTION:If n is a positive integer and n^2 is divisible by 72, then the largest positive integer V that must divide n is? options: A)6 B)12 C)24 D)36 E)48 SOLUTION:Q: If n is a positive integer and n^2 is divisible by 72, then the largest positive integer V that must divide n is: A 6, B 12, C 24, D 36, E 48 n^2 is divisible by 72, but it must also be greater than 72. If n is an integer, then n^2 must be a perfect square. The factorization of 72 is (8)(9), so if it is multiplied by 2, it will be (2)(8)(9) = (16)(9) = 144, a perfect square. So n^2 must be at least 144 or a multiple of 144, which means that n must be 12 or a multiple of 12.B #### B QUESTION:A man can row a boat at 10 kmph in still water. If the speed of the stream is 6 kmph, what is the time taken to row a distance of 60 km downstream? options: A)30/18 B)30/21 C)30/11 D)30/7 E)30/8 SOLUTION:Speed downstream = 10 + 6 = 26 kmph. Time required to cover 60 km downstream = d/s = 60/16 = 30/8 hours. Answer:E #### E QUESTION:Two cars cover the same distance at the speed of 50 and 64 kmps respectively. Find the distance traveled by them if the slower car takes 1 hour more than the faster car. options: A)212 km B)214 km C)224 km D)216 km E)204 km SOLUTION:50(x + 1) = 64x X = 3.57 60 * 3.57 = 214 km ANSWER:B #### B QUESTION:The value of ((x – y)³ + (y - z)³ + (z – x)³)/(21 (x – y) (y – z) (z – x)) is equal to : options: A)0 B)1/12 C)1/7 D)1/4 E)1/3 SOLUTION:Since (x – y) + (y – z) + (z – x) = 0, so (x – y)³ + (y – z)³ + (z – x)³= 3 (x – y) (y – z) (z – x). (3 (x – y) (y – z) (z – x))/(21(x – y) (y – z) (z – x)) = 1/7. ANSWER:C #### C QUESTION:How many different values of positive integer x, for which |x+7|<x, are there? options: A)0 B)2 C)3 D)8 E)16 SOLUTION:Answer A I opted to put the random value option. i used 0 , 7 , -7 and the the extreme of 30 and -30.. i was able to solve it in 1:09 B #### B QUESTION:One of the longest sides of the triangle is 20 m,the other side is 10 m.Area of the triangle is 80m^2.What is the another side of the triangle? options: A)2sqrt(61) B)2sqrt(62) C)2sqrt(63) D)2sqrt(64) E)2sqrt(65) SOLUTION:base of triangle is 20 and area is 80 therefore height=2*80/20=8. now one side of triangle is of 10. so we can get the point were the base is divided by applying Pythagoras therm so division pt =sqrt(10^2-8^2)=sqrt(36)=6 threfore other half is 14. now second side=sqrt(14^2+8^2)=sqrt(260)=2sqrt(65) ANSWER:E #### E QUESTION:If x/y =4/3, then (x-y)/x? options: A)-1/2 B)-1/4 C)1/3 D)1/2 E)1/4 SOLUTION:we have this law of fraction: a/b=c/d= (a-c)/(b-d) x/y=4/3 ---> x/4=y/3= (x-y)/(4-3)=(x-y)/(1) ---> (x-y)/x= 1/4 Answer: E #### E QUESTION:What is the ratio of y to x if (x + 3y) / ( x - y) = 5/4? options: A)-15/4 B)-5/3 C)1/17 D)3/5 E)15/1 SOLUTION:Solving for y/x gives, 1/17 (C) #### C QUESTION:Which one the following fractions has the biggest value? options: A)211/711 B)201/711 C)191/711 D)221/711 E)181/711 SOLUTION:All options have the same denominator 711. If denominator is same, the fraction with the biggest value will be the one with the biggest numerator. Answer (D). #### D QUESTION:A man cycling along the road noticed that every 18 minutes a bus overtakes him and every 6 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? options: A)5 minutes B)6 minutes C)8 minutes D)9 minutes E)10 minutes SOLUTION:Let's say the distance between the buses is d. We want to determine Interval=\frac{d}{b}, where b is the speed of bus. Let the speed of cyclist be c. Every 18 minutes a bus overtakes cyclist: \frac{d}{b-c}=18, d=18b-18c; Every 6 minutes cyclist meets an oncoming bus: \frac{d}{b+c}=6, d=6b+6c; d=18b-18c=6b+6c, --> b=2c, --> d=18b-9b=9b. Interval=\frac{d}{b}=\frac{9b}{b}=9 Answer: D (9 minutes). #### D QUESTION:The true discount on a bill of Rs.4320 is Rs.720.The banker's discount is options: A)862 B)864 C)866 D)868 E)None of these SOLUTION:Solution P.W = Rs.(4320 - 720) = Rs. 3600 S.I on Rs. 4320 =Rs.(720/3600 x 4320) = Rs. 864. Answer B #### B QUESTION:What is the perimeter of a square field whose diagonal is 8√2? options: A)82 m B)32 m C)27 m D)26 m E)76 m SOLUTION:4a = 32 m Answer: B #### B QUESTION:What is the HCF of 2/3, 5/9 and 6/5 options: A)1/45 B)2/45 C)4/15 D)8/45 E)9/45 SOLUTION:Explanation: HCF of Fractions = HCF of Numerators/LCM of Denominators = (HCF of 2, 5, 6)/(LCM of 3, 9, 5) = 1/45 Answer: Option A #### A QUESTION:What percent of a day is 15 hours? options: A)37×1/2% B)16×1/2% C)18×2/3% D)22×1/2% E)None SOLUTION:Solution Required percentage = (15/24×100)% = (75 / 2)%. = 37×1/2%. Answer A #### A QUESTION:Let x be a positive integer, what is the remainder when 4^(2x+5)+3 is divided by 5? options: A)2 B)3 C)4 D)1 E)5 SOLUTION:For: (4^(2x+5)+3)/5 Let n = 2x + 5 4^n 4^1 = 4 4^2 = 16 4^3 = 64 4^4 = 256, last digit pattern repeats 4, 6, 4, 6, .... Rule: x^(m+n) = (x^m)(x^n) (4^(2x))(4^5) Rule: x^(mn) = (x^m)^n (4^2)(4^x)(4^5) => Now, (6)(4)(4) + 3 = (6) + 3 => Finally, 9/5 and remainder is 4. Answer: C #### C QUESTION:Can you deduce the pattern and find the next number in the series? 3, 24,81, 192, __? options: A)276 B)277 C)278 D)279 E)375 SOLUTION:Solution: 375 Explanation: 3 = 1^1^1 + 1^1^1 + 1^1^1 24 = 2^2^2 + 2^2^2 + 2^2^2 81 = 3^3^3 + 3^3^3 + 3^3^3 192 = 4^4^4 + 4^4^4 + 4^4^4 Thus the next number will be 375 =5^5^5 + 5^5^5 + 5^5^5 Answer E #### E QUESTION:In a partnership between A, B and C. A's capital is Rs.5000. If his share of a profit of Rs.800 is Rs.300 and C's share is Rs.130, what is B's capital? options: A)19878 B)12798 C)6166 D)11750 E)22073 SOLUTION:300 + 130 = 430 800 - 430 = 370 300 ---- 5000 370 ---- ? => 6166 Answer: C #### C QUESTION:In a class,10 students like to play Basketball and 8 like to play Cricket. 4 students like to play on both Basketball and Cricket. How many students like to play Basketball or Cricket or both? options: A)12 B)15 C)16 D)18 E)14 SOLUTION:Draw a Venn Diagram yourself ! B + C - BC = Number of students that play either Basketball or Cricket 10 +8 - 4 = 14 E) #### E QUESTION:If $x is invested at a constant annually compound interest rate of k percent, what is the ratio of the total amount including interest after 7n years to that after 3n years? options: A)(1+k/100)^n B)(1+k)^n C)(1+kn/100) D)(1+k/100)^4n E)(1+kn) SOLUTION:Amount after 7n years will be = x ( 1 + k/100)^4n Amount after 3n years will be = x ( 1 + k/100)^3n So, required ratio will be - { x ( 1 + k/100)^7n } / {x ( 1 + k/100)^3n } = (1+k/100)^4n Hence answer will be a. (1+k/100)^4n D #### D QUESTION:The speed of a boat in still water is 50kmph and the speed of the current is 20kmph. Find the speed downstream and upstream? options: A)40, 68 kmph B)40, 30 kmph C)70, 30 kmph D)40, 60 kmph E)20, 60 kmph SOLUTION:Speed downstream = 50 + 20 = 70 kmph Speed upstream = 50 - 20 = 30 kmph Answer: C #### C QUESTION:Two trains are running in opposite directions with the same speed. If the length of each train is 120 metres and they cross each other in 12 seconds, then the speed of each train (in km/hr) is: options: A)18 km/hr B)26 km/hr C)36 km/hr D)42 km/hr E)52 km/hr SOLUTION:Let the speed of each train be x m/sec. Then, relative speed of the two trains = 2x m/sec. So, 2x = (120 + 120)/12 --> 2x = 20 --> x = 10. --> Speed of each train = 10 m/sec = 10 x 18/5 km/hr = 36 km/hr. Answer : C. #### C QUESTION:A babysitter is paid a regular rate of $16 per hour for any number of hours that does not exceed 30 hours per week. For any overtime hours worked in excess of 30 hours per week, the babysitter is paid a rate that is 75% higher than his regular rate. If last week the babysitter earned $760, how many total hours did she work that week? options: A)40 B)30 C)35 D)25 E)45 SOLUTION:For 30 hrs = 30*16=480 Excess = 760-480=280 For extra hours =.75(16)=12 in addition to $16. Thus, 12+16=28 Number of extra hrs =280/28=10 Total hrs =30+10=40 Answer A 40 #### A QUESTION:The average marks of a class of 30 students is 50 and that of another class of 50 students is 60. Find the average marks of all the students? options: A)56.25 B)52.9 C)52.1 D)52.3 E)42.5 SOLUTION:Sum of the marks for the class of 30 students = 30 * 50 = 1500 Sum of the marks for the class of 50 students = 50 * 60 = 3000 Sum of the marks for the class of 80 students = 1500 + 3000 = 4500 Average marks of all the students = 4500/80 = 56.25 Answer:A #### A <<<Examples ends QUESTION:A 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 W 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? options: A) 0.8(80 – y) B) 0.8 + 0.0025y C) 80/y – 1.25 D) 80/1.25y E) 80 – 0.25y SOLUTION:This may be a case of bad numberpicking but it worked for me. 80 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. 80-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. Which means finishing all houses at normal rate W=> 2*4 = 8 weeks. Faster rate = 4+3,2 = 7,2 weeks. 7,2/8 = 9/10 = 0,9. Insert y=40 in equations and it is clear that only (B) gives us 0,9. #### B

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:Average temperature of first 4 days of a week is 6°C and that of the last 4 days is 40.3°C. If the average temperature of the week be 39.1°C, the temperature on 4th day is? options: A)36.7°C B)38.6°C C)39.8°C D)41.9°C E)51.9°C SOLUTION:Let temperature on 4th day be X°C Therefore, 4 x 38.6 + 4 x 40.3 - X = 7 x 39.1 => X = 41.9 Therefore, temperature on 4th day = 41.9°C. ANSWER:D #### D QUESTION:In 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? options: A)1:4 B)1:3 C)2:3 D)3:4 E)None of these SOLUTION:Explanation: 33.33% 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 #### B QUESTION:Balls of equal size are arranged in rows to form an equilateral triangle. the top most row consists of one ball, the 2nd row of two balls and so on. If 253 balls are added, then all the balls can be arranged in the shape of square and each of the sides of the square contain 8 balls less than the each side of the triangle did. How many balls made up the triangle? options: A)903 B)2209 C)2878 D)1210 E)1560 SOLUTION:As expected, this question boils down to 2 equation, Consider total number of Balls in Triangle = T and number of balls in last row = x. 1+2+3+...+x = T x(x+1)/2 = T ----(a) As mentioned in the question, side of a square will be (x-8) and total number of Balls in square will be (T+253) (x-8)^2 = T+253 -----(b) Now the hardest part of the question will be to solve these 2 equations and this looks like time consuming BUT the easy way will be plug and play. Also, we've to find a value of T (from 5 optiosn given below) which can make a square of a a number. One we know this, it will be a cake walk. We can see that option A fits this criteria in eq (b). Add - 903+253 = 1156 = 34^2 = (x-8)^2 Hence, x = 42. Cross check by putting in eq (a) = x(x+1)/2 = T = > 42*43/2=903 Hence, answer is A. #### A QUESTION:A man can row upstream at 25 kmph and downstream at 35 kmph, and then find the speed of the man in still water? options: A)37 B)38 C)30 D)77 E)27 SOLUTION:US = 25 DS = 35 M = (35 + 25)/2 = 30 Answer:C #### C QUESTION:Pipe A that can fill a tank in an hour and pipe B that can fill the tank in half an hour are opened simultaneously when the tank is empty. Pipe B is shut 10 minutes before the tank overflows. When will the tank overflow? options: A)37 mins B)35 mins C)40 mins D)32 mins E)36 mins SOLUTION:The last 10 minutes only pipe A was open. Since it needs 1 hour to fill the tank, then in 10 minutes it fills 1/5th of the tank, thus 5/6 of the tank is filled with both pipes open. The combined rate of two pipes is 1 + 2 = 3 tanks/hour, therefore to fill 5/6th of the tank they need (time) = (work)/(rate) = (5/6)/3 = 5/18 hours = 27 minutes. Total time = 10+ 27= 37 minutes. Answer: A. #### A QUESTION:The ratio of investments of A, B and C is 5:6:7. If they share the profit in the ratio of 5:9:21, then find the ratio of their periods of investments. options: A)2:3:6 B)3:5:6 C)3:2:4 D)2:4:3 E)2:5:3 SOLUTION:The ratio of investments of A, B and C is 5:6:7. The ratio of shares of A, B and C is 5:9:21. Therefore, Ratio of their periods of investments is (5/5) : (9/6) : (21/7) = 1:3/2:3 = 2:3:6. ANSWER:A #### A QUESTION:An investor bought two shares of stock, which he sold for $36 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: options: A)a profit of $5 B)a profit of $3 C)a loss of $3 D)a loss of $5 E)neither a profit nor a loss SOLUTION:The cost of the first stock was 36/1.2=30, so the profit from it is 6. The cost of the second stock was 36/0.8=45, so loss from it is 9. Overall the loss is $3. The answer is C. #### C QUESTION:A train running at a speed of 36 kmph crosses an electric pole in 12 seconds. In how much time will it cross a 350 m long platform? options: A)87 min B)82 min C)86 min D)47 min E)72 min SOLUTION:Let the length of the train be x m. When a train crosses an electric pole, the distance covered is its own length. So, x = 12 * 36 * 5 /18 m = 120 m. Time taken to cross the platform = (120 +350)/ 36 * 5/18 = 47 min. Answer:D #### D QUESTION:A number when divided by 128 gives a remainder 34, what remainder will be obtained by dividing the same number 19? options: A)7 B)6 C)9 D)10 E)3 SOLUTION:Explanation: 128 + 34 = 162/19 = 10 (Remainder) Answer: D #### D QUESTION:A die is tossed. Find the probability of getting a multiple of 2 ? options: A)1/5 B)2/3 C)1/6 D)1/3 E)1/2 SOLUTION:S = {1,2,3,4,5,6} E= event of getting a multiple of 2 = {2,4,6} P(E) = 3/6 = 1/2 Answer is E #### E QUESTION:A 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. options: A)125/128 B)115/122 C)125/126 D)125/122 E)125/112 SOLUTION:Required probability = 1 - 1/126 = 125/126 Answer:C #### C QUESTION:Of the science books in a certain supply room, 50 are on botany, 60 are on zoology, 90 are on physics. 40 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? options: A)81 B)159 C)309 D)285 E)324 SOLUTION:First, you can take all 50 Botany books, all 60 zoology books and all 40 geology books because you're sure to never pick 80 of them. There are still 90 on physics and 110 on chemistry The worst case could be that we pick 79 physics and 79 chemistry. So that the next book picked will necessary complete 80 books picked, either in physics or chemistry. Minimum number of books picked to reach 80 in the same science should be : 50 + 60 + 40 + 79 +79 + 1 = 309 C #### C QUESTION:How many positive integers will divide evenly into 440? options: A)8 B)12 C)16 D)18 E)20 SOLUTION:520 = 10*13*4 = 8*5*13 = 2^3*5*13 We need to positive integers will divide evenly into 520 or simply the factors of 520 If a number is of the form 2^a*3^b*5^c, Total factors = (a+1)(b+1)(c+1) Therefore, number of factors of 520 = (3+1)*(1+1)*(1+1) = 4*2*2 = 18 Option D #### D QUESTION:On final examination a student's average (arithmetic mean) score on 4 subjects is 90. What must be his score on a 5th subject for his average score on the 5 subjects to be 92? options: A)60 B)70 C)80 D)90 E)100 SOLUTION:(4*90+x)/5=92 x=(5*92)-(4*90) x= 460 - 360 total score required 460 - 360=100 Correct answer is E #### E QUESTION:Evaluate combination 100C100 options: A)10000 B)1000 C)10 D)1 E)0 SOLUTION:Explanation: nCn=1 100C100=1 Option D #### D QUESTION:Income and expenditure of a person are in the ratio 5 : 4. If the income of the person is Rs. 15000, then find his savings? options: A)3600 B)3607 C)3608 D)3602 E)3000 SOLUTION:Let the income and the expenditure of the person be Rs. 5x and Rs. 4x respectively. Income, 5x = 15000 => x = 3000 Savings = Income - expenditure = 5x - 4x = x So, savings = Rs. 3000. Answer:E #### E QUESTION:A man's age is 125% of what it was 10 years ago, but 83 X 1/3% of what it will be after 10years. What is his present age? options: A)20 B)60 C)50 D)70 E)80 SOLUTION:C 50 Let the age before 10 years =x Then, 125x/100=x+10 ⇒125x=100x+1000 ⇒x=1000/25=40 Present age =x+10=40+10=50 #### C QUESTION:105,100,...,90,85,80,75 Insert the missing number options: A)95 B)78 C)83 D)84 E)none of the above SOLUTION:Missing number : 95 Answer : A #### A QUESTION:A number x is 4 times another number y. The percentage that y is less than x is options: A)12.5% B)75% C)80% D)11% E)1% SOLUTION:Say y=1 and x=4. Then y=1 is less than x=4 by (4-1)/4*100=3/4*100=75%. Answer: B. #### B QUESTION:In 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, what was the number of valid votes that the other candidate got? options: A)2800 B)2700 C)2100 D)2500 E)3000 SOLUTION:Total no of votes = 7500 20 % invalid =>80% valid tot valid votes = 7500*80/100 =>valid for 2nd candidate got 7500*80/100*45/100 =2700 ANSWER B #### B QUESTION:Solution X is 30% chemical A and 70% chemical B by volume. Solution Y is 40% chemical A and 60% chemical B by volume. If a mixture of X and Y is 36% chemical A, what percent of the mixture is Solution X? options: A)30% B)35% C)40% D)45% E)50% SOLUTION:The volume of the mixture be X+Y. 0.3X +0.4Y=0.36(X+Y) X=2Y/3 X/(X+Y)=(2Y/3) / (5Y/3)=2/5=40%. The answer is C. #### C QUESTION:Five years ago, John’s age was half of the age he will be in 4 years. How old is he now? options: A)14years B)15years C)16years D)17years E)18years SOLUTION:Let John=j,j-5=(j+4)/2,then j=14years ANSWER:A #### A QUESTION:If P gets 25% more than Q, then by what percent does Q get less than P? options: A)60% B)22% C)12% D)20% E)13% SOLUTION:Let Q get 1 unit. 25% of 1 unit = 1/4 = 0.25 P gets (1 + 0.25) i.e., 1.25 units. Difference = (1.25 - 1) = 0.25 Required percentage = 0.25/1.25 * 100 = 1/5 * 100 = 20% Answer: C #### C QUESTION:An bus covers a certain distance at a speed of 100 kmph in 5 hours. To cover the samedistance in 1hr, it must travel at a speed of? options: A)500 km/hr B)640 km/hr C)656 km/hr D)731 km/hr E)720 km/hr SOLUTION:Distance = (100 x 5) = 500 km. Required speed = 500 km/hr. A #### A QUESTION:What will come in place of the x in the following Number series? 5,28,57,88,125 options: A)123 B)143 C)166 D)190 E)210 SOLUTION:28=23+5 57=29+28 88=31+57 125=37+88 166=41+125 =166 C #### C QUESTION:At 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? options: A)16 B)17 C)10 D)18 E)15 SOLUTION:Let the present ages of Arun and Deepak be 4x and 3x years respectively. Then, 4x + 2 = 26 => x = 8 Deepak's age = 3x = 18 years. Answer: D #### D QUESTION:In a friendship gang Aravind has 2 gang, in how many ways can he invite one or more of the gang to his house? options: A)25 B)49 C)3 D)87 E)36 SOLUTION:Aravind can select one or more than one of his 8 gang. => Required number of ways = 2^2 – 1= 3. C #### C QUESTION:Tough and Tricky questions: Combinations. Three students - 2 boys and 1 girls - are to sit side by side for a makeup exam. How many ways could they arrange themselves given that no two boys and no two girls can sit next to one another? options: A)2 B)4 C)72 D)240 E)720 SOLUTION:2!*1!*2 = 2*1*2 = 4 ways. Ans. B) 4 #### B QUESTION:The average salary of all the workers in a workshop is $1000. The average salary of 5 technicians is $5000 and the average salary of the rest is $500. The total number of workers in the shop is? options: A)25 B)20 C)15 D)30 E)18 SOLUTION:Let the total number of workers be x 1000x = 5000*5 + 500(x-5) x = 25 Answer is A #### A QUESTION:A 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? options: A)200 B)300 C)400 D)500 E)None of them SOLUTION:Let the share of each nephews be Rs.x. Then,share of each daughter=rs4x;share of each son=Rs.5x; So,5*5x+4*4x+2*x=8600 25x+16x+2x=8600 =43x=8600 x=200; Answer is A. #### A QUESTION:A, 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? options: A)299 B)267 C)269 D)400 E)276 SOLUTION:2*12 : 3*12 : 4*24 1: 3: 4 1/8 * 3200 = 400 Answer: D #### D QUESTION:Large, medium and small ships are used to bring water. 4 large ships carry as much water as 7 small ships; 3 medium ships carry as much water as 2 large ships and 1 small ship. If 15 large, 7 medium and 14 small ships, each made 36 journeys to bring a certain quantity of water, then in how many journeys will 12 large, 14 medium and 21 small ships bring the same quantity of water? options: A)29 B)30 C)20 D)50 E)55 SOLUTION:Explanation : Here, Large, Medium and Small ships are denoted by the symbol L, M and S. Now, according to the question, 4L = 7S. ------(i) 3M = 2L + S. ------(ii) Using above equations, the ratios of the capacity of the Large, Medium and Small ships are :- 7: 6 : 4. Let, the number of journeys required be x. Since, quantity of water remains the same, so :- =((15×7+7×6+14×4)36) = x (12×7+14×6+21×4). =>((15×7+7×6+14×4)36) / (12×7+14×6+21×4)= x =>x=7308/252 =>x=29. Answer : A #### A QUESTION:The number of arrangements that can be made with the letters of the word PETER so that the vowels occupy the even places? options: A)18 B)20 C)40 D)12 E)14 SOLUTION:The word MEADOWS has 7 letters of which 3 are vowels. -V-V-V- As the vowels have to occupy even places, they can be arranged in the 2 even places in 2! i.e., 2 ways. While the consonants can be arranged among themselves in the remaining 4 places in 3! i.e., 24 ways. Hence the total ways are 2 * 6 = 12. Answer:D #### D QUESTION:A single letter is selected at random from the word 'SIMS'. The probability that it is a vowel is..?? options: A)1/4 B)3/11 C)4/11 D)3/7 E)1/2 SOLUTION:total vowels = 1, total number of letters = 4 so probability = 1/4 ANSWER:A #### A QUESTION:2 hours after train A leaves Lucknow a train B leaves the same stationtraveling in the same direction at an average speed of 20 km/hr. After traveling 6 hrsthe train B overtakes the train A. What is the average speed of the train A? options: A)15 km/hr B)16 km/hr C)17 km/hr D)18 km/hr E)None of these SOLUTION:Explanation : Total distance covered by B=20*6=120kmTotal time taken by A to cover same distance=2+6=8 hrsaverage speed of A=120/8=15 km/hr Answer : A #### A QUESTION:Three photographers, Lisa, Mike and Norm, take photos of a wedding. The total of Lisa and Mikes photos is 40 less than the sum of Mike's and Norms. If Norms photos number 10 more than twice the number of Lisa's photos, then how many photos did Norm Take? options: A)40 B)50 C)70 D)80 E)90 SOLUTION:L+M=M+N-40 / N=2L+10 40=M+N-L-M 40=N-L 40=2L+10-L 30=L 2(30)+10=70 C #### C QUESTION:A man saves Rs 500 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. options: A)Rs 662 B)Rs 1665.01 C)Rs 1662.02 D)Rs 1655.06 E)None of these SOLUTION:Explanation: =[500(21/20×21/20×21/20)+500(21/20×21/20)+500(21/20)]=1655.06 Answer: D #### D QUESTION:Rahul 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? options: A)Rs 15 B)Rs 12.10 C)Rs 21.70 D)Rs 16.80 E)None of these SOLUTION:Explanation : Let the cost of the tax items = x Given that tax rate = 6% Cost of tax items, x*(6/100) = 30/100 x = 5 rs Now non taxable item = total cost - cost for taxable item - tax = 27 - 5 - 0.30 =21.70 Answer : C #### C QUESTION:Difference between two numbers is 5, six times of the smaller lacks by 6 from the four times of the greater. Find the numbers? options: A)12, 9 B)10, 5 C)12, 7 D)11, 6 E)12, 6 SOLUTION:x – y = 5 4x – 6y = 6 x = 12 y = 7 ANSWER:C #### C QUESTION:If 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? options: A)2 B)3 C)4 D)5 E)6 SOLUTION:We 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. 2(60+p+60+q)= 240 + 2(p + q). 2(p+q) can range from 0 up to a maximum value of 36 when p=q=9. Then the tens and ones digits of 2(x+y) can range from 40 up to 76. There can be 4 possibilities for the tens digit. The answer is C. #### C QUESTION: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? options: A)20/67 B)20/63 C)20/19 D)20/18 E)20/28 SOLUTION:Required probability = (⁵C₃ . ⁴C₁)/⁹C₄ = (10 * 4)/126 = 20/63 Answer: B #### B QUESTION:10 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? options: A)2 B)1 C)7 D)6 E)4 SOLUTION:1 women's 1 day work = 1/70 1 child's 1 day work = 1/140 (5 women + 10 children)'s 1 day work = (5/10 + 10/140) = (1/14 + 1/14) = 1/7 5 women and 10 children will complete the work in 7 days. Answer:C #### C QUESTION:A class average mark in an exam is 70. The average of students who scored below 60 is 50. The average of students who scored 60 or more is 75. If the total number of students in this class is 20, how many students scored below 60? options: A)5 B)10 C)15 D)20 E)25 SOLUTION:Let n the number of students who scored below 60 and N the number of students who scored 60 or more. Xi the grades below 60 and Yi the grades 60 or above. [sum(Xi) + sum(Yi)] / 20 = 70 : class average sum(Xi) / n = 50 : average for less that 60 sum(Yi) / N = 75 : average for 60 or more 50n + 75N = 1400 : combine the above equations n + N = 20 : total number of students n = 4 and N = 16 : solve the above system correct answer D #### D QUESTION:The ratio between the number of sheep and the number of horses at the Stewart farm is 1 to 7, If each horse is fed 230 ounces of horse food per day and the farm needs a total 12,880 ounces of horse food per day, what is the number of sheep in the farm? options: A)18 B)28 C)32 D)56 E)8 SOLUTION:Let the number of sheeps and horses be 1x and 7x. Now total number of horses = total consumption of horse food/consumption per horse = 12880/230 = 56, which is equal to 7x. => x = 8 Sheeps = 1x = 1*8 = 8. Hence E #### E QUESTION:A pump can fill a tank with water in 2 hours. Because of a leak, it took 2 1/3 hours to fill the tank. The leak can drain all the water of the tank in? options: A)17 hr B)19 hr C)10 hr D)14 hr E)16 hr SOLUTION:Work done by the tank in 1 hour = (1/2 - 1/3) = 1/14 Leak will empty the tank in 14 hrs. Answer:D #### D QUESTION:The sum of the first 50 positive even integers is 2,000. What is the sum of the odd integers from 101 to 200, inclusive? options: A) 5,050 B) 7,500 C) 8,050 D) 15,000 E) 19,600 SOLUTION:101+103+.......199 If we remove 100 from each of these it will be sum of 1st 100 odd numbers. so 101+103+.......199 = 50 * 100 + (1+3+5+7+......) sum of 1st 100 natural numbers = (100 * 101) / 2 = 5050 Sum of 1st 50 positive even integers = 2000 sum of 1st 100 odd numbers = 5050 - 2000 = 3050 so 101+103+.......199 = 50 * 100 + (1+3+5+7+......) = 5000 + 3050 =8050 C is the answer. #### C QUESTION: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: options: A)3:5 B)2:1 C)16:15 D)4:5 E)None of these SOLUTION:Explanation: For an income of Re. 1 in 9% stock at 96, investment = Rs. 96/9 = Rs.32/3 For an income Re. 1 in 12% stock at 120, investment = Rs. 120/12 = Rs. 10. Ratio of investments =(32/3) : 10 = 32 : 30 = 16 : 15. Answer: C #### C QUESTION:There 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. When 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. So 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 – one diamond was still left. Finally, they woke up the 7th thief and this time the diamonds were divided equally. How many diamonds did they steal in total? options: A)2397 B)2401 C)2411 D)2423 E)None of the above SOLUTION:We 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. Answer B #### B QUESTION:If a company gains 10 %, the wholesale dealer 15 % and the retailer 25 %, then find the cost of production of a table if the retail price was Rs 1265 options: A)800 B)700 C)750 D)850 E)900 SOLUTION:cost P = 125/100 * 115/100 * 110/100 = 1265 253/160p=1265==> p =800 ANSWER A #### A QUESTION:Linda and Angela contract to paint a neighbor's house. Even though Linda spends 20% more time painting the house than Angela, each receives a payment of m dollars when the work is completed. If Angela decides to pay Linda n dollars so that they would have received the same compensation per hour worked, what is n in terms of m? options: A)A)(1/2)m B)B)(1/3)m C)C)(1/4)m D)D)(1/5)m E)E)(1/11)m SOLUTION:let angela work for 10hrs and get 1100 rs. (m =1100) According to question, linda works 20% more time and gets the same amount. so let linda work 12 hrs and get 1100 rs. so they do a total of 12 +10 =22 hrs of work and get 2200 rs together . The question basically asks to equalise their payment. so a total of 2200 rs is received by them and they do 20 hrs work together. average rate will be 2200/22 = 100 rs per hr. so linda should get 12*100 =1200 rs. But she got only 1100. so angela should give 100 rs to linda. answer = 100/1100 =1/11 answer E #### E QUESTION:If x and y are prime numbers such that x > y > 3, then x^2 − y^2 must be divisible by which one of the following numbers? options: A) 3 B) 4 C) 5 D) 9 E) 12 SOLUTION:If x=8 and y=6, then x^2-y^2=28 and 28 is divisible only by 4 from the options, thus it must be correct. Answer: B. #### B QUESTION:A photographer is to take group photographs of a class of students for the school magazine such that each photograph should have five students. If there are four girls and four boys in the class and each photograph must not have two girls or two boys standing together, how many different photographs can the photographer take? options: A)80 B)288 C)4^4 D)576 E)288^2 SOLUTION:The condition that TWO boys or TWO girls cannot be together means they should be alternate.. Total five means 3 of one and 2 of other.. 1) choose 3 girls and arrange them... 4C3*3! = 4!= 24 2 boys can be choosen in 4C2 and arrange them in 2! Ways... 4C2*2!= 12 Total ways = 24*12 = 288.. 2) same as above.. 2 girls and 3 boys.. 288 Total 288*2=576 ANS:D #### D QUESTION:In Orange County, one eighth 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? options: A)200 B)210 C)216 D)224 E)235 SOLUTION:The number must be a multiple of both 8 and 7 so the answer is 224. The answer is D. #### D QUESTION:A die is thrown twice and the sum of the numbers appearing is observed to be 6. find the conditional probability that the number 4 has appeared at least once? options: A)2/5 B)3/5 C)3/11 D)3/13 E)3/17 SOLUTION:Let E be the event that ‘number 4 appears at least once’ and F be the event that ‘the sum of the numbers appearing is 6’. Then, E = {(4,1), (4,2), (4,3), (4,4), (4,5), (4,6), (1,4), (2,4), (3,4), (5,4), (6,4)} and F = {(1,5), (2,4), (3,3), (4,2), (5,1)} We have P(E) = 11/36 and P (F) = 5/36 Also EnF = {(2,4), (4,2)} Therefore P(EnF) = 2/36 the required probability P(E|F) = P(EnF)/P(F) = (2/36)/(5/36) = 2/5. A) #### A QUESTION:What is the area of a square field whose diagonal of length 24 m? options: A)256 B)289 C)200 D)288 E)178 SOLUTION:d2/2 = (24 * 24)/2 = 288 Answer: D #### D QUESTION:If n divided by 3 has a remainder of 2, what is the remainder when 2 times n is divided by 3? options: A)1 B)2 C)3 D)5 E)0 SOLUTION:As per question => N=3P+2 for some integer p hence 2N => 6Q + 4 => remainder => 1 for some integer Q hence A #### A QUESTION:A is half good a work man as B and together they finish a job in 32 days. In how many days working alone B finish the job? options: A)98 days B)21 days C)48 days D)18 days E)19 days SOLUTION:WC = 1:2 2x + x = 1/32 => x = 1/96 2x = 1/96 => 48 days Answer:C #### C QUESTION:What is the difference between the C.I. on Rs. 9000 for 1 1/2 years at 4% per annum compounded yearly and half-yearly? options: A)s.2.04 B)s.2.08 C)s.3.67 D)s.2.83 E)s.2.42 SOLUTION:C.I. when interest is compounded yearly = [9000 * (1 + 4/100) * (1 + (1/2 * 4)/100] = 9000 * 26/25 * 51/50 = Rs. 9547.2 C.I. when interest is compounded half-yearly = [9000 * (1 + 2/100)2] = (9000 * 51/50 * 51/50 * 51/50) = Rs. 9550.87 Difference = (9550.87 - 9547.2) = Rs.3.67. Answer: C #### C QUESTION:Rajan borrowed Rs.4000 at 5% p.a compound interest. After 2 years, he repaid Rs.2210 and after 2 more year, the balance with interest. What was the total amount that he paid as interest? options: A)635.50 B)635.53 C)635.57 D)635.52 E)635.51 SOLUTION:4000 200 ---- I 200 10 ---- II --------------- 4410 2210 -------- 2000 110 ---- III 110 5.50 ---- IV ----------- 2425.50 2210 ----------- 4635.50 4000 ---------- 635.50 Answer: A #### A QUESTION:Katherine invested a certain sum of money in a bank that paid simple interest. The amount grew to $350 at the end of 2 years. She waited for another 3 years and got a final amount of $425. What was the principal amount that she invested at the beginning? options: A)$360 B)$380 C)$300 D)$280 E)$275 SOLUTION:What shall be the rate of interest.? Does that is not required for the calculation? Not really! Keep in mind that the interest earned each year will be the same in Simple Interest. At the end of 2 years, Amount = $350 At the end of 5 years, Amount = $425 This means she earned an interest of $75 in 3 years. Or $25 in each year. We know that the interest earned each year will be the same. Therefore she must have earned $50 in 2 years. Hence Principal Amount = $350 - $50 = $300 Option C #### C QUESTION:A 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? options: A)1 B)6 C)7 D)9 E)3 SOLUTION:Speed of train relative to man = 60 + 6 = 66 km/hr. = 66 * 5/18 = 55/3 m/sec. Time taken to pass the men = 110 * 3/55 = 6 sec. Answer: B #### B QUESTION:The sum of two numbers is 16. The difference is 4. What are the two numbers?Let x be the first number. Ley y be the second number x + y = 16 x - y = 4 options: A)10 and 6 B)10 and 5 C)10 and 4 D)10 and 3 E)10 and 2 SOLUTION:Solution Let x be the first number. Ley y be the second number x + y = 16 x - y = 4 Solve the system of equations by elimination Adding the left sides and the right sides gives: x + x + y + -y = 16 + 4 2x = 20 x = 10 Since x + y = 16, 10 + y = 16 10 + y = 16 10 - 10 + y = 16 - 10 y = 6 The numbers are 10 and 6 Answer A #### A QUESTION:21 ball numbered 1 to 21. A ballis drawn and then another ball is drawn without replacement. options: A)7/41 B)3/41 C)9/42 D)4/51 E)5/13 SOLUTION:The probability that first toy shows the even number, =1021=1021 Since, the toy is not replaced there are now 9 even numbered toys and total 20 toys left. Hence, probability that second toy shows the even number, =920=920 Required probability, =(1021)×(920)=(1021)×(920) =9/42 C #### C QUESTION:Find the value of x in (x/5)+3=4. options: A)1 B)2 C)3 D)4 E)5 SOLUTION:(x/5)+3=4. Subtracting both sides with 3 gives x/5=1 Multiplying both sides by 5 gives x=5 Answer: E #### E <<<Examples ends QUESTION:A bag contains an equal number of one rupee, 50 paise and 25 paise coins respectively. If the total value is 175, how many coins of each type are there? options: A)20 coins B)30 coins C)50 coins D)100 coins E)None of these SOLUTION:Let number of each type of coin = x. Then, 1 × x + .50 × x + .25x = 175 ⇒ 1.75x = 175 ⇒ x = 100 coins Answer D #### D

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:Sakshi 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: options: A)15 B)16 C)18 D)25 E)None of these SOLUTION:EXPLANATION Ratio of times taken by Sakshi and Tanya = 125 : 100 = 5 : 4. Suppose Tanya takes x days to do the work. 5 : 4 :: 20 : x => x =(4x20/5) x = 16 days. Hence, Tanya takes 16 days to complete the work. Answer B #### B QUESTION:what is the least number. which should be added to 221 to make it a perfect square? options: A)5 B)8 C)4 D)6 E)7 SOLUTION:221+4=225 15^2 ANSWER:C #### C QUESTION:A reduction of 46% in the price of bananas would enable a man to obtain 64 more for Rs.40, what is reduced price per dozen? options: A)2.45 B)8.45 C)7.45 D)3.45 E)1.45 SOLUTION:Explanation: 40*(46/100) = 18.4 --- 64 ? --- 12 => Rs.3.45 Answer: D #### D QUESTION:The capacity of a tank of dimensions (8m x 6m x 2.5m)is options: A)120 litres B)1200 litres C)12000 litres D)120000 litres E)None of these SOLUTION:Explanation: capacity of atank =volume of tank = (8 x 100 x 6 x 100 x 2.5 x 100)/1000 litres = 120000 litres Answer: D #### D QUESTION:Find the expenditure on digging a well 14m deep and of 3m diameter at Rs.15 per cubic meter? options: A)Rs.1185 B)Rs.1285 C)Rs.1385 D)Rs.1485 E)Rs.1495 SOLUTION:22/7 * 14 * 3/2 * 3/2 = 99 m2 99 * 15 = 1485 ANSWER:D #### D QUESTION:There are 200 cats in Cat-City. Out of the 200, 70 are street cats and the rest are domestic cats. 110 cats are gray, 25 out of the gray cats are NOT domestic ones. How many domestic cats are there which are not gray in Cat-City? options: A)90. B)45. C)50. D)40. E)25. SOLUTION:STREET-CAT DOMESTIC-Cat 70 130 (25gray+45other) 85gray+45other Answer:B #### B QUESTION:A starts business with Rs.3500 and after 5 months, B joins with A as his partner. After a year, the profit is divided in the ratio 2 : 3. What is B’s contribution in the Capital ? options: A)24887 B)20778 C)23788 D)9000 E)2811 SOLUTION:Explanation: A invested Rs.3500 for 12 months. Let B joined with investment x. And he invested for 12 - 5 = 7 months. So there profit ratio = (3500 × 12) : (7x) = 2 : 3 ⇒ x = 9000 Answer: D #### D QUESTION:Two 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? options: A)36 B)76 C)98 D)27 E)24 SOLUTION:(3x-9):(5x-9) = 9:17 x = 12 => 3x = 36 Answer:A #### A QUESTION:SCORE INTERVAL----------------NUMBER OF SCORES 50-59-------------------------- 2 60-69--------------------------10 70-79--------------------------16 80-89--------------------------5 90-99--------------------------2 The table above shows the distribution of test scores for a group of management trainees. Which score interval contains the median of the 35 scores? options: A)16th B)20th C)22th D)24th E)18th(70-79) SOLUTION:Total scores= 2+10+16+5+2 = 35, which is odd, therefore the median is the Floor(35/2)+1 = 18th score. And the 18th score is in the 70-79 range, because 50-69 only reference 12 scores. E #### E QUESTION:Virat buys an old car for Rs. 50000 and spends Rs. 6000 on its repairs. If he sells the scooter for Rs. 70000, his gain percent is: options: A)25% B)11 (1/9) % C)12 (2/3) % D)12% E)None of these SOLUTION:Explanation: C.P. = Rs. (50000 + 6000) = Rs. 56000 S.P. = Rs. 70000. Gain% = ( (14000 / 56000) * 100 ) % = 25% ANSWER A #### A QUESTION:A 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? options: A)14 liters B)76 liters C)10 liters D)11 liters E)12 liters SOLUTION:Number of liters of water in150 liters of the mixture = 20% of 150 = 20/100 * 150 = 30 liters. P liters of water added to the mixture to make water 25% of the new mixture. Total amount of water becomes (30 + P) and total volume of mixture is (150 + P). (30 + P) = 25/100 * (150 + P) 120 + 4P = 150 + P => P =10 liters. Answer: C #### C QUESTION:A shopkeeper buys mangoes at the rate of 5 a rupee and sells them at 3 a rupee. Find his net profit or loss percent? options: A)66 2/3 % B)33 7/3 % C)33 1/3 % D)33 5/8 % E)34 1/3 % SOLUTION:The total number of mangoes bought by the shopkeeper be 15. If he buys 5 a rupee, his CP = 3 He selling at 3 a rupee, his SP = 5 Profit = SP - CP = 5 - 3 = 2 Profit Percent = 2/3 * 100 = 66 2/3 % Answer: A #### A QUESTION:A trader has 50 kg of pulses, part of which he sells at 8 per cent profit and the rest at 18 per cent profii. He gains 14 per cent on the whole. What is the quantity sold at 18 per cent profit? options: A)30 kg B)25 kg C)20 kg D)40 kg E)none of these SOLUTION:Ratio of quantities sold at 8% profit and 18% profit =>4:6 = 2:3 Therefore,the quantity sold at 18% profit =>50/(2 + 3) x 3 =>30 kg ANSWER:A #### A QUESTION:76^77 /7 remainder is ? options: A)5 B)6 C)7 D)8 E)9 SOLUTION:as, 4^3/3=64/3 remainder=1 and also 4/3=1 and 5^3/3 remainder=2 and also 5/3=2 so it does not matter on the power value so the answer will be 76/7 remainder=6 ANSWER:B #### B QUESTION:The length of the bridge, which a train 130 meters long and travelling at 45 km/hr can cross in 30 seconds, is? options: A)766 m B)156 m C)245 m D)156 m E)156 m SOLUTION:Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time = 30 sec. Let the length of bridge be x meters. Then, (130 + X)/30 = 25/2 ==> 2(130 + X) = 750 ==> X = 245 m. Answer: C #### C QUESTION:The area of a circle is increased by 1500%. By what percent has the diameter of the circle increased? options: A) 100% B) 500% C) 300% D) 600% E) 800% SOLUTION:The area of the circle is increased by 1500%, thus the area is increased 16 times. The area of a circle it proportional to the square of the diameter (area=πd^2/4), therefore the diameter must increase 4 times (diameter increase 4 times = area increase 16 times), which is increase by 500%. Answer: B. #### B QUESTION:Thomas 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? options: A)10 B)14 C)19 D)21 E)25 SOLUTION:The cost of buying a single computer= Rs(500000/11)=Rs. 45454.5 The cost of selling a selling computer=Rs(550000/11)=Rs. 50000.0 Profit per computer=Rs.(50000-45454.5)=Rs. 4545.5 The % of profit in selling a single computer=(4545.5/45454.5)*100=10% Answer:A #### A QUESTION:The C.P of 15 books is equal to the S.P of 18 books. Find his gain% or loss%? options: A)16 2/3% loss B)11 2/3% loss C)66 2/3% loss D)12 2/3% loss E)17 2/3% loss SOLUTION:Explanation: 15 CP = 18 SP 18 --- 3 CP loss 100 --- ? => 16 2/3% loss Answer: A #### A QUESTION:If 7a = 2b = 15, then 42ab = options: A)75 B)125 C)675 D)1100 E)1250 SOLUTION:7a * 2b = 15 * 15 = 225 14 ab = 225 i.e. 42 ab = 675 Answer: Option C #### C QUESTION:A car covers a distance of 630 km in 6 hours. Find its speed? options: A)105 B)7778 C)266 D)288 E)121 SOLUTION:624/6 = 105 kmph Answer:A #### A QUESTION:The tailor has a 10 meter long piece of fabric for which to sew a ball room dress. She has to cuts this fabric into strips of 200 centimeters each. How long will it take the tailor to complete this tasks if each 200 centimeter took 5 minutes to cut ? options: A)150 B)200 C)188 D)245 E)123 SOLUTION:The tailors would need to cut the fabric 49 times thus the total amount spent would be 245 minutes. The answer is D #### D QUESTION:A 8000 liter tank, half-full of water is being filled from a pipe with a flow rate of 1 kiloliter every 2 minutes. At the same time, the tank is losing water from two drains at a rate of 1 kiloliter every 4 minutes and every 6 minutes. How many minutes does it take to fill the tank completely? options: A)8 B)12 C)18 D)24 E)48 SOLUTION:In: we have: 1,000/2min = 500 litres per minute Out: we have: 1,000/4 + 1,000/6 Then do: IN - OUT to figure out the net inflow per minute (you get 83.3). Then divide the total number of litres you need (4,000 by that net inflow to get the minutes) - 48 min. Answer E. #### E QUESTION:The equation (M )/84 = (p – 7)/21 relates two temperature scales, where M is the number of degrees on one scale and P is the number of degrees on the other scale. Which of the following equations can be used to convert temperatures from the P scale to the M scale? options: A)(P-7)*6 B)(P-7)*5 C)(P-7)*2 D)(P-7)*3 E)(P-7)*4 SOLUTION:M/84 =(P-7)/21 M = (P-7)*84/21 =(P-7)*4 E #### E QUESTION:By selling an article at Rs.600, a profit of 25% is made. Find its cost price? options: A)Rs.486 B)Rs.455 C)Rs.487 D)Rs.480 E)Rs.489 SOLUTION:SP = 600 CP = (SP)*[100/(100+P)] = 600 * [100/(100+25)] = 600 * [100/125] = Rs.480 Answer: D #### D QUESTION:From a theatre troupe of eight members, including Lou, one person will be randomly chosen to play Abel, another person will be randomly chosen to play Barry, and a third person will be randomly chosen to play Caine. What is the probability that Lou will NOT be chosen to play either Abel or Caine? options: A)1/168 B)1/8 C)1/4 D)1/3 E)3/4 SOLUTION:"one person will be randomly chosen to play Abel, another person will be randomly chosen to play Barry, and a third person will be randomly chosen to play Caine" The above statement is NOT clear Still a solution: For 8 students we have 3 posts one post can be occupied by only one member no two posts can be occupied by the same member probability(P) for a member getting selected for particular 2 of the 3 posts= probable outcomes=1(Caine)+1(Abel)=2 total outcomes=1(Caine)+1(Abel)+1(Barry)+5(non post positions)=8 =2/8=1/4 Probability required for the given case= 1-P=1-1/4=3/4 Answer: E #### E QUESTION:In what ratio should a variety of rice costing $6 per kg be mixed with another variety of rice costing $8.75 per kg to obtain a mixture costing $7.50 per kg? options: A)4/7 B)5/6 C)5/9 D)4/8 E)3/8 SOLUTION:B 5/6 Let us say the ratio of the quantities of cheaper and dearer varieties = x : y By the rule of allegation, x/y = (87.5 - 7.50) / (7.50 - 6) = 5/6 #### B QUESTION:Adding 30% of x to x is equivalent to multiplying x by which of the following? options: A)12.5 B)1.05 C)1.15 D)1.3 E)1.25 SOLUTION:130x/100= 1.3*x ANSWER:D #### D QUESTION:A certain sum of money doubles itself in 10 years in how much many years will it trible itself at the same rate? options: A)20 years B)28 years C)24 years D)27 years E)57 years SOLUTION:100 ---- 100 --- 10 100 --- 10 -------------------- 300 ---- 20 years Answer:A #### A QUESTION:In how many ways a committee consisting of 5 men and 6 women can be formed from 8 men and 10 women? options: A)266 B)86400 C)11760 D)5040 E)None of these SOLUTION:Here, 5 men out of 8 men and 6 women out of 10 women can be chosen in 8C5 × 10C6 ways, i.e., 11760 ways. Answer C #### C QUESTION:A woman begins bicycling with a pace of 8 kmph and she increases her pace every two hours by 2 kmph. She does not increase her pace as soon as her pace reaches her maximum speed of 12 kmph. How many hours did she bicycle if she traveled 64 kms? options: A)6 1⁄7 hours B)6 2⁄7 hours C)8 2⁄7 hours D)Cannot be determined E)None of these SOLUTION:Distance covered in first two hours = 8 × 2 = 16 km Distance covered in next two hours = 10 × 2 = 20 km Distance covered in next two hours = 12 × 2 = 24 km Distance covered in first six hours 16 + 20 + 24 = 60 km Remaining distance = 64 – 60 = 4 km. Now, this distance will be covered at the speed of 12 km/hr. ∴ Time taken = 4⁄12 = 1⁄3 hour. Total time= 6 + 1⁄3 = 6 1⁄3 hour Answer E #### E QUESTION:The present average age of a family of five members is 24 years. If the present age of the youngest member in the family is ten years, then what was the average age of the family at the time of the birth of the youngest member ? (Assume no death occurred in the family since the birth of the youngest) options: A)27.5 years B)17 years C)17.5 years D)16.5 years E)15.5 years SOLUTION:Present total age of the members = 24(5) = 120 years. Present age of the youngest member = 10 years Present total age of the remaining four members = 120 -10 = 110 years Their average age at the time of the birth of the youngest member = [110 - (4 * 10)] / 4 = 17.5 years ANSWER:C #### C QUESTION:A train 410 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long? options: A)40 sec B)50 sec C)44 sec D)49 sec E)60 sec SOLUTION:Speed = 45 * 5/18 = 25/2 m/sec Total distance covered = 410 + 140 = 550 m Required time = 550 * 2/25 = 44 sec Answer:C #### C QUESTION:Salesperson 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? options: A)$21,000 B)$18,000 C)$15,000 D)$ 14,500 E)$4,000 SOLUTION:sometime, setting up an equation is an easy way to go with: 350 + 0.06 (x - 1000) = 0.08 x x = 14,500 Ans : D #### D QUESTION:If the speed of X meters per second is equivalent to the speed of Y kilometers per minute, what is Y in terms of X? (1 kilometer=1000 meters) options: A)0.06x B)6x/5 C)18x/5 D)60x E)3600000x SOLUTION:x=1000y/60 y = 0.06x Answer : A #### A QUESTION:The radius of a semi circle is 6.3 cm then its perimeter is? options: A)35.4 cm B)32.4 cm C)32 cm D)30 cm E)35 cm SOLUTION:Explanation: 36/7 r = 6.3 = 32.4 ANSWER IS B #### B QUESTION:597**6 is divisible by both 3 and 11. The non-zero digits in the Hundred’s and ten’s places are respectively: options: A)3 and 6 B)7 and 9 C)2 and 6 D)4 and 7 E)None SOLUTION:Solution : Let the given number be 597xy6. Then (5+9+7+x+y+6)=(27+x+y) must be divisible by 3 And, (6+x+9)-(y+7+5)=(x-y+3) must be either 0 or divisible by 11. x-y+3=0 => y=x+3 27+x+y) =>(27+x+x+3) =>(30+2x) => x = 3 and y = 6. Answer A #### A QUESTION:Mohan 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? options: A)A)Rs.520 B)B)Rs.594 C)C)Rs.596 D)D)Rs.595 E)None of these SOLUTION:Explanation: Price of 10 kgs of rice at Rs.26/kg = 10x26 = Rs.260 Price of 8 kgs of pulses at Rs.26/kg = 10x26 = Rs.260 Therefore, Total amount = Rs.260+Rs.260 = Rs.520. Answer: Option A #### A QUESTION:A 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 $752 in total compensation, how many total hours did he work that week? options: A)36 B)40 C)44 D)48 E)52 SOLUTION:For 40 hrs = 40*16=640 Excess = 752-640=112 For extra hours =.75(16)=12+16=28 Number of extra hrs =112/28=28/7=4 Total hrs =40+4=44 Answer C 44 #### C QUESTION:What is the Value given by the equation (-2+a)^2=(a-2)^2? options: A)Indefinite B)Two C)Three D)One E)None SOLUTION:(-2+a)^2=(a-2)^2 Both the equations in RHS and LHS are equal So it give the Value One Option D is answer #### D QUESTION:There are 7 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? options: A)21 B)30 C)45 D)60 E)90 SOLUTION:7 players are there. two players play one game with one another. so 7C2=7*6/2 =21 SO OPTION A is correct #### A QUESTION:The area of a rectangle is 15 square centimeters and the perimeter is 16 square centimeters. What are the dimensions of the rectangle? options: A)2&4 B)3&5 C)4&6 D)5&7 E)6&8 SOLUTION:Let 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. 15 = x y and 16 = 2 x + 2 y Solve the second equation for x x = 8 - y Substitute x in the equation 15 = x y by 8 - y to rewrite the equation as 15 = (8 - y) y Solve for y to find y = 3 and y = 5 Use x = 8 - y to find x when y = 3 , x = 5 and when y = 5 , x = 3. The dimensions of the rectangle are 3 and 5. correct answer B #### B QUESTION:From 6 positive numbers and 6 negative numbers, how many groups F of 4 numbers, yielding a positive product, can be formed? options: A)720 B)625 C)30 D)960 E)255 SOLUTION:Potential combinations of 4 numbers that will yield positive product ++++ 4C6 ---- 4C6 ++-- 2C6*2C6 4C6 + 4C6 + 2C6*2C6 F=15 +15 + 15*15 = 255=E #### E QUESTION:x =3 4 5 y= 27 36 9 then what is the relation between x and y options: A)1*X)^2 B)1*X)^3 C)1*X)^4 D)1*X)^5 E)1*X)^6 SOLUTION:Y=(1*X)^2 9=(1*3)^2 9=9 ANSWER:A #### A QUESTION:A can finish a work in 18 days and B can do the same work in 15 days. B worked for 10 days and left the job. In how many days, A alone can finish the remaining work? options: A)6 B)5 C)5.5 D)7 E)8 SOLUTION:B's 10 day's work = ( 1 x 10 ) = 2 . 15 3 Remaining work = ( 1 - 2 ) = 1 . 3 3 Now, 1 work is done by A in 1 day. 18 Therefore 1 work is done by A in ( 18 x 1 ) = 6 days. #### A QUESTION:At Joes Steakhouse the hourly wage for a chef is 20% 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 $6.50 per hour, how much less than a manager does a chef earn each hour? options: A)$2.6 B)$2.40 C)$3.40 D)$4.40 E)$5.40 SOLUTION:Manager wages per hour = $6.50 Dishwasher wages per hour = half of manager's wages. = 1/2($6.50) ==> $3.25 Chef wages per hour = 20% greater than Dishwasher wages --> 20% of $3.25 = (20*($3.25)) /100 --> ($65)/100 --> $0.65 Therefore, Chef wages per hour = $3.25 + $0.65 ==> $3.9 Difference of wages between manager and chef = $6.50 - $3.9 ==> $2.6 ANSWER:A #### A QUESTION:A 200 meter long train crosses a platform in 50 seconds while it crosses a signal pole in 42 seconds. What is the length of the platform? options: A)39.9 B)37.88 C)35 D)38.88 E)38.09 SOLUTION:Speed = [200 / 42] m/sec = 100/21 m/sec. Let the length of the platform be x meters. Then, x + 200 / 50 = 100/21 21(x + 200) = 5000 è x = 38.09 m. Answer: E #### E QUESTION:A 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? options: A)5/6 km/hr B)25 km/hr C)79.2 km/hr D)15 km/hr E)38 km/hr SOLUTION:Explanation: Let the length of the train be x m and its speed be y m/sec. Then, x/y = 8 => x = 8y (x + 264)/20 = y y = 22 Speed = 22 m/sec = 22 * 18/5 = 79.2 km/hr Answer:C #### C QUESTION:In a sequence of 40 numbers, each term, except for the first one, is 7 less than the previous term. If the greatest term in the sequence is 282, what is the smallest term in the sequence? options: A)2 B)-2 C)0 D)8 E)9 SOLUTION:Which term is the greatest? The first or the last? It is given to you that every term is 7 less than the previous term. Hence as you go on, your terms keep becoming smaller and smaller. The first term is the greatest term. An = 282 + (40 - 1)*(-7) An = 282 - 273 = 9 E #### E QUESTION:The 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? options: A)38 B)27 C)75 D)28 E)21 SOLUTION:Explanation: The 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. Answer: C #### C QUESTION:Exactly four sides of a certain 10-sided die are red. What is the probability that Kumar rolls the die 3 times and the die lands with a red side up for the first time on the third roll? options: A)0.3 B)0.2 C)0.01 D)0.148 E)0.144 SOLUTION:Total no. of sides = 10 Sides that are red = 4 Probability that the die lands with red side up = 4/10 Therefore, Probability that the die does not land with red side up = 1 - 4/10 = 6/10 Probability that Kumar rolls the die 3 times and the die lands with a red side up for the first time on the third roll = (1st roll - non red face) X (2nd roll - non red face) X (3rd roll - red face) = (6/10) X (6/10) X (4/10) = 144/1000 = 0.144 E #### E QUESTION:Sebastian bought a meal at a restaurant and left a 15% tip. With the tip, he paid exactly $35.42. How much did the meal cost without the tip? options: A)$28.98 B)$29.91 C)$30.15 D)$30.60 E)$30.80 SOLUTION:The tip is a percent increase of 15%, which is 115%. Let x equal the price before the tip. Thus, 115% of this price equals $35.42: 1.15x = 35.42 Divide both sides by 1.15:=>x=35.42/1.15=30.80 correct answer E)$30.80 #### E QUESTION:A took 15 seconds to cross a rectangular field diagonally walking at the rate of 52 m/min and B took the same time to cross the same field along its sides walking at the rate of 68m/min. The area of the field is? options: A)33 B)60 C)88 D)27 E)26 SOLUTION:Explanation: length of the diagonal = 52*(15/60) =13m sum of length and breadth = 68*(15/60) = 17m \inline {\color{Black}\sqrt{l^{2}+b^{2}}=13 \; or\; l+b=17 } area =lb = 1/2[(2lb)] = 1/2[(l+b)² - (l²+b²)] = 1/2[17² -169] =1/2*120 = 60 sq meter Answer: B) 60 #### B QUESTION:Here 10 programmers, type 10 lines within 10 minutes then 60 lines can type within 60 minutes. How many programmers are needed? options: A)16 B)10 C)6 D)60 E)50 SOLUTION:10 10 programmer 10 line 10 mins. 10 programmer 20 line 20 mins. . . . .10 programmer 60 line 60 mins. ANSWER:D #### D QUESTION:In how many different ways can the letters of the word 'CAREER' be arranged? options: A)10 ways B)20 ways C)180 ways D)60 ways E)40 ways SOLUTION:Totally there are 6 letters on the word CAREER. it contains 1C,1A,2R,2E. The no of ways is 6!/2!2!=180 ways. ANSWER:C #### C QUESTION:A 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? options: A)150 m B)200 m C)240 m D)400 m E)150 m SOLUTION:Answer: Option C Speed = [54 * 5/18] m/sec = 15 m/sec. Length of the train = (15 * 20) m = 300 m. Let the length of the platform be x meters. Then, x + 300 / 36 = 15 x + 300 = 540 x = 240 m. #### C QUESTION:18 business executives and 7 chairmen meet at a conference. If each business executive shakes the hand of every other business executive and every chairman once, and each chairman shakes the hand of each of the business executives but not the other chairmen, how many handshakes would take place? options: A)144 B)131 C)279 D)90 E)45 SOLUTION:there are 18 business exec and in each handshake 2 business execs are involved. hence 18C2=153 Also, each of 18 exec will shake hand with every 7 other chairmen for total of 126 handshake. total=153+126=279 ANS: C #### C QUESTION:If 5x + 3 = 10x – 17, what is the value of x? options: A)1 B)2 C)3 D)4 E)5 SOLUTION:solve for x: 5x+3=10x-17 20=5x 4=x correct answer D)4 #### D QUESTION:A 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 40 years now, the son's age 10 years back was: options: A)10 years B)19 years C)33 years D)38 years E)39years SOLUTION:Let the son's present age be x years. Then, (40 - x) = x 2x = 40. x = 20 Son's age 5 years back (20 - 10) = 10 years. Answer:A #### A QUESTION:A rectangle the length of which is 8 inches and the width of which is 6 inches is made up 48 1 inch by 1 inch squares. Through how many of the squares does a diagonal of the rectangle pass? options: A)6 B)8 C)10 D)12 E)16 SOLUTION:1)If the two sides are co-prime, SUM of sides -1.. 2)and if not co-prime , Sum of sides - HCF of sides.. the difference is related to the diagonal passing through a vertex of squares at some place.. here 6 and 8 are NOT co-primes, so ans =6+8−HCF(6,8)=14−2=12 ANSWER:D #### D QUESTION:If x is an integer, then x(x – 1)(x – k) must be evenly divisible by six when k is any of the following values EXCEPT options: A)-4 B)-2 C)-1 D)2 E)5 SOLUTION:We have the product of 3 integers: (x-1)x(x-k). Note that the product of 3 integers is divisible by 6 if at least one multiple is divisible by 6. Now, to guarantee that at least one integer out of x, (x – 1), and (x – k) is divisible by 6 these numbers must have different remainders upon division by 3, meaning that one of them should have remainder of 1, another reminder of 2 and the last one remainder of 0, so be divisible by 6. Next, if k=2 then we'll have (x-1)x(x-2)=(x-1)x(x-2) --> which means that (x-1) and (x-2) will have the same remainder upon division by 6. Thus for k=2 we won't be sure whether (x-1)x(x-k) is divisible by 6. Answer: D. #### D QUESTION:If a card is drawn from a well shuffled pack of cards, the probability of drawing a spade or a king is options: A)4/17 B)4/16 C)4/15 D)4/13 E)4/12 SOLUTION:P(SᴜK) = P(S) + P(K) - P(S∩K), where S denotes spade and K denotes king. P(SᴜK) = 13/52 + 4/52 - 1/52 = 4/13 Answer:D #### D QUESTION:A set of numbers has the property that for any number t in the set,t+4 is in the set. If -3 is in the set, which of the following must also be in the set? I. 9 II. 2 III. 4 options: A)II,III only B)I only C)I,III only D)II only E)III only SOLUTION:question is asking for must be there elements. According to the question if t is there t+4 must be there. if -3 is the starting element the sequence is as follows. S ={-3,1,5,9....} if -3 is not the starting element the sequence is as follows S = {...-7,-3,1,5,9...} By observing the above two sequences we can say that 9 must be there in set S. Answer : B #### B QUESTION:The total of the ages of Amar, Akbar and Anthony is 30 years. What was the total of their ages three years ago ? options: A)20 years B)28 years C)71 years D)21 years E)31 years SOLUTION:Explanation: Required sum = (30 - 3 x 3) years = (30 - 9) years = 21 years. Answer: Option D #### D QUESTION:A car covers a distance of 520 km in 4 hours. Find its speed? options: A)104 B)130 C)298 D)269 E)213 SOLUTION:520/4 = 130 kmph Answer:B #### B <<<Examples ends QUESTION:Out of 15 consecutive numbers, 2 are chosen at random. The probability that they are both odds or both primes is? options: A)1/1 B)1/7 C)1/8 D)1/3 E)1/2 SOLUTION:A leap year has 52 weeks and two days Total number of cases = 7 Number of favourable cases = 1 i.e., {Saturday, Sunday} Required Probability = 1/7 Answer:B #### B

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:John bought 2 shares and sold them for $98 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 options: A) a profit of $10 B) a profit of $8 C) a loss of $4 D) a loss of $10 E) neither a profit nor a loss SOLUTION:$ Profit of the share sold at 20% profit = 120-98 20-? $18 profit on the sale of 1 share. $ Loss of the share sold at 20% loss= 80-98 20-? $22 loss on the sale of 1 share. 18-22=Loss of $4 Answer: C #### C QUESTION:A train 160m long is running at 30kmph. In how much time will it pass a platform 120m long? options: A)15.89 seconds B)24.36 seconds C)15.96 seconds D)14.93 seconds E)22.23 seconds SOLUTION:Distance travelled = 160 + 120m = 280m Speed = 30 * 5/8 = 75/4m Time = 280 * 4/75 = 14.93 Seconds Answer : D. #### D QUESTION:If 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 − a? options: A)25 B)70 C)90 D)140 E)It cannot be determined from the information given SOLUTION:the arithmetic mean of a and b =(a+b)/2=45 -- a+b=90 --1 similarly for b+c=160 --2 subtracting 1 from 2 we have c-a=70; ANSWER:B #### B QUESTION:What is the cost of leveling the field in the form of parallelogram at the rate of Rs.50/10 sq.metre, whose base & perpendicular distance from the other side being 54m & 24m respectively? options: A)Rs. 6000 B)Rs. 6300 C)Rs. 6400 D)Rs. 6480 E)Rs. 7000 SOLUTION:Area of the parallelogram = Length of the base * Perpendicular height = 54 * 24 = 1296 m. Total cost of levelling = Rs. 6480 D #### D QUESTION:A tank contains 10,000 gallons of a solution that is 5 percent sodium chloride by volume. If 5,500 gallons of water evaporate from the tank, the remaining solution will be approximately what percent sodium chloride? options: A) 1.25% B) 3.75% C) 6.25% D) 6.67% E) 11.11% SOLUTION:The 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 10,000-5,500=4,500 gallons and sodium chloride is 500 gallons (5% of initial solution of 10,000 gallons) then sodium chloride is 500/4,500*100=~11.11% of the remaining solution of 4,500 gallons. Answer: E. #### E QUESTION:$378 is divided among A, B, and C so that A receives half as much as B, and B receives half as much as C. How much money is C's share? options: A)$200 B)$208 C)$216 D)$224 E)$232 SOLUTION:Let the shares for A, B, and C be x, 2x, and 4x respectively. 7x = 378 x = 54 4x = 216 The answer is C. #### C QUESTION:A man’s speed with the current is 17 km/hr and the speed of the current is 2.5 km/hr. the man’s speed against the current is : options: A)8.5 km/hr B)12 km/hr C)10 km/hr D)12.5 km/hr E)None of these SOLUTION:Solution Man's rate in still water = (17-2.5) km/hr = 14.5 km/hr. Man's rate against the current = (14.5-2.5) km/hr = 12 km/hr Answer B #### B QUESTION:Consider 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. 5400 interest only for the period. The principal amount borrowed by her was options: A)Rs. 2000 B)Rs. 10000 C)Rs. 15000 D)Rs. 20000 E)None of these SOLUTION:Explanation : Principal = Rs. (100×5400 / 12×3) => Rs. 15,000. Answer : C #### C QUESTION:There are 100 men in town. Out of which 85% were married, 70% have a phone, 75% own a car, 80% own a house. What is the maximum number of people who are married, own a phone, own a car and own a house? options: A)20 B)15 C)10 D)5 E)None of these SOLUTION:% of married = 85% % of phone = 70% % of car = 75% % of house = 80. Therefore, % of not married = 15% % of not having phone = 30% % of not owning car = 25% % of not having house = 20% So, % of not having any of these things = 15 +25+ 30 + 20 = 90% So, % of people having all = 100 -90 = 10% Thus, people = 10. ANSWER -OPTION C #### C QUESTION:The difference between a two-digit number obtained by interchanging the positions of its digits is 36. What is the difference between the two digits of that number? options: A)4 B)9 C)3 D)Cannot be determined E)None of theses SOLUTION:Let the two-digit number be 10x + y. Then, (10x + y) – (10y + x) = 36 or x – y = 4 Answer A #### A QUESTION:Which of the following is a pair of co–primes? options: A)(16, 62) B)(18, 25) C)(21, 35) D)(23, 92) E)none SOLUTION:Solution H.C.F. of 18 and 25 is 1. So, they are co-primes. Answer B #### B QUESTION:Nil and Ethan are brothers. They left their home at the same time and drove to the same beach. Nil drove at a speed of 30 miles per hour. Ethan drove at a speed of 20 miles per hour. Nil arrived at the beach 0.5 hour earlier than Ethan. What is the distance between their home and the beach? options: A)20 miles B)30 miles C)40 miles D)50 miles E)60 miles SOLUTION:Every hour, Nil gets ahead of Ethan 30 - 20 = 10 miles. When Nil arrived at the beach, Ethan is only 20 × 0.5 = 10 miles behind. That tells us they only drove 1 hour when Nil arrived at the beach. The distance between their home and the beach is Nil’s speed × Nil’s time = 30 × 1 = 30 miles. correct answer B #### B QUESTION:A, B and C have Rs.500 between them, A and C together have Rs.200 and B and C Rs.320. How much does C have? options: A)50 B)78 C)267 D)20 E)27 SOLUTION:A+B+C = 500 A+C = 200 B+C = 320 -------------- A+B+2C = 520 A+B+C = 500 ---------------- C = 20 Answer: D #### D QUESTION:Tough and Tricky questions: Distance/Rate. On a reconnaissance mission, a state-of-the-art nuclear powered submarine traveled 200 miles to reposition itself in the proximity of an aircraft carrier. This journey would have taken 1 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? options: A)20 B)40 C)50 D)80 E)100 SOLUTION:Say, if speed is 40, 200/40 = 5 hrs and 200/50 = 4 hrs (a reduction of 1 hr -> Correct answer) Answer (B) #### B QUESTION:What number should replace the question mark? 11, 15, 16, 12, 21, 9, ---? options: A)21 B)29 C)28 D)27 E)26 SOLUTION:Answer: E 11, 15, 16, 12, 21, 9, ---? There are two alternate sequences: +5 and -3. #### E QUESTION:A man can place 6 large boxes or 9 boxes inside a carton. Can you calculate in how many cartons can he place 66 boxes ? options: A)9 B)10 C)11 D)12 E)13 SOLUTION:A 5 cartons for large boxes = 5 * 6 = 30 boxes 4 cartons for small boxes = 4 * 9 = 36 boxes He will need 9 cartons to place 66 boxes. #### A QUESTION:2/5 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? options: A)3/20 B)7/30 C)5/16 D)1/3 E)2/5 SOLUTION:Straight method.... 1/4 of 2/5 + 1/5 of 1/4 = 2/20 +1/20 =3/20 ANSWER:A #### A QUESTION:Company 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 $12.00 each, what was Company C’s gross profit? options: A) $2,250 B) $2,500 C) $4,100 D) $3,250 E) $4,500 SOLUTION:Cost of 500 trucks: (100 * 5 ) + (400 * 3.5) = 500 + 1400 =$ 1900 Revenue : 500 * 12 = $6000 Profit: 6000 - 1900 = $ 4100 Option C is correct #### C QUESTION:If 7 spiders make 7 webs in 7 days, then 1 spider will make 1 web in how many days? options: A)7 B)6 C)5 D)4 E)3 SOLUTION:Let the required number days be x. Less spiders, More days (Indirect Proportion) Less webs, Less days (Direct Proportion) spiders 1:7 Webs 7:1 1 x 7 x x = 7 x 1 x 7 => x= 7 Answer is 7 #### A QUESTION:The income derived from a Rs. 100, 13% stock at Rs. 105, is : options: A)Rs. 5 B)Rs. 8 C)Rs. 13 D)Rs. 18 E)Rs. 19 SOLUTION:Solution Income on Rs. 100 stock = Rs. 13. Answer C #### C QUESTION:A 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 $752 in total compensation, how many total hours did he work that week? options: A)36 B)40 C)44 D)48 E)52 SOLUTION:For 40 hrs = 40*16=640 Excess = 752-640=112 For extra hours =.75(16)=12+16=28 Number of extra hrs =112/28=28/7=4 Total hrs =40+4=44 Answer C 44 #### C QUESTION:12, 24, 16, 32, 24, 48, ? options: A)31 B)32 C)36 D)37 E)40 SOLUTION:E 40 This is an alternating multiplication and subtracting series with a pattern x2, -8, x2, -8. #### E QUESTION:A cistern 10 m long and 8 m wide contains water up to a depth of 1 m 50 cm. The total area of the wet surface is: options: A)120 m2 B)136 m2 C)128 m2 D)130 m2 E)134 m2 SOLUTION:Area of the wet surface = [2(lb + bh + lh) - lb] = 2(bh + lh) + lb = [2 (8 x 1.50 + 10 x 1.50) + 8 x 10] m2 = 134 m2. answer :E #### E QUESTION:A cube is painted red on all faces. It is then cut into 27 equal smaller cubes. How many cubes are painted on only 2 faces? options: A)12 B)8 C)6 D)10 E)16 SOLUTION:The mini-cubes with 2 painted sides are ALL on the edge of the cube, in the "middle" of the edge. There are 4 in front, 4 in back and 4 more on the "strip" that runs around the left/top/right/bottom of the cube. 4 + 4 + 4 = 12. Answer A #### A QUESTION:The ratio of the ages of Mini and Minakshi is 4 : 3. The sum of their ages is 28 years. The ratio of their ages after 6 years will be options: A)2 : 3 B)7 : 11 C)5 : 4 D)4 : 5 E)11 : 9 SOLUTION:Let Mini’s age = 4x and Minakshi’s age = 3x Then 4x + 3x = 28 x = 4 Mini’s age = 16 years And Minakshi’s age = 12 years Ratio of their ages after 8 years = (16 + 6) : (12 + 6) = 22 : 18 = 11 : 9 ANSWER:E #### E QUESTION:If 5^29 * 4^15 = 2 * 10^n, what is the value of n? options: A)11 B)21 C)22 D)29 E)32 SOLUTION:My attempt: 5^(29) * 4^(15) = 2*10^p 5^(29) * 2 ^ (30) = 2 * (2*5)^p 5^(29) * 2 ^ (30) = 2 * 2^(p) * 5^(p) 5^(29) * 2 ^ (30) = 2^(p+1) * 5^(p) => (p+1) = 30 => p = 29 Answer: 29 (D) #### D QUESTION:If q is a positive integer and q^2 is divisible by 12, then the largest positive integer that must divide q ^3 is options: A) 2^3 B) 2^6 C) 3^3 D) 6^3 E) 12^2 SOLUTION:Since 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)) q^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 So, q will have a 2 and a 3. Or q will be a multiple of 6 So, largest possible integer than should divide q^3 is 6^3 So, Answer will be D #### D QUESTION:How 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 ? options: A)3.5 years B)4 years C)4.5 years D)5 years E)None of these SOLUTION:Solution Time =(100*81/450*4.5) years =4 years Answer B #### B QUESTION:A thief is noticed by a policeman from a distance of 200 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? options: A)100 m B)150 m C)190 m D)200 m E)220 m SOLUTION:Explanation: Relative speed of the thief and policeman = (11 – 10) km/hr = 1 km/hr Distance covered in 6 minutes =1/60X6km=1/10km=100m Distance between the thief and policeman = (200 – 100) m = 100 m. ANSWER IS A #### A QUESTION:If a certain coin is flipped, the probability that the coin will land heads is 1/2. If the coin is flipped 6 times, what is the probability that it will land heads up on the first 4 flips but not on the last 2 flips? options: A)1/8 B)1/16 C)1/32 D)1/64 E)1/128 SOLUTION:P(HHHHTT) = 1/2*1/2*1/2*1/2*1/2*1/2 = 1/64 The answer is D. #### D QUESTION:A 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? options: A)40 B)50 C)60 D)70 E)80 SOLUTION:Speed of the train relative to man = 125/10 = 25/2 m/sec. = 25/2 * 18/5 = 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. Answer: Option B #### B QUESTION:If f(x)= 5x^2- 2x+6 and g(y)= 3y-8, then g(f(x)) options: A)82x^2-9x+38 B)15x^2-6x+10 C)58x^2-4x+58 D)87x^2-5x+96 E)98x^2-7x+94 SOLUTION:g(f(x))=3(5x^2-2x+6)-8 =15x^2-6x+18-8 =15x^2-6x+10 the answer is B #### B QUESTION:A batsman in his 15th inning makes a score of 75 and their by increasing his average by 3. What is his average after the 15th inning? options: A)31 B)32 C)33 D)34 E)35 SOLUTION:14x + 75 = 15(x + 3) x = 30 + 3 = 33 Answer:C #### C QUESTION:Raffle 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? options: A)2/5 B)2/7 C)33/83 D)51/250 E)100/249 SOLUTION:SOLUTION The 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. Answer: D #### D QUESTION:In what time will a train 80 m long cross an electric pole, it its speed be 144 km/hr? options: A)2.0 sec B)2.8 sec C)7.5 sec D)2.3 sec E)1.5 sec SOLUTION:Speed = 144 * 5/18 = 40 m/sec Time taken = 80/40 = 2.0 sec. Answer:A #### A QUESTION:At a certain supplier, a machine of type A costs $23,000 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? options: A)$5,280 B)$11,200 C)$12,000 D)$12,800 E)$13,200 SOLUTION:Total Cost of 2 Machines of Type A = 20% of (Cost of 2 machine A) + remainder + 40 % remainder = 20% of 46000 + (46000 - 20% of 46000) + 40% of (46000 - 20% of 46000) = 60720 Total Cost of 1 Machine of Type B = 20% of (Cost of 1 machine B) + remainder + 40 % remainder = 20% of 50000 + (50000 - 20% of 50000) + 40% of (50000 - 20% of 50000) = 66000 Diff = 66000 - 60720 = 5280 Hence, A. #### A QUESTION:Which of the following must be divisible by 4, given that y is a positive integer? options: A)(y−1)*y*(y+3) B)y^2*(y−3) C)y(y^2−2) D)y(y+2)^3 E)(y−2)·(y+1)·(y+3) SOLUTION:option A) (y−1)*y*(y+3)- assume y any positive integer e.g 5, plug it into the various options and check if the result . hence answer should be A #### A QUESTION:A 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? options: A)days B)days C)days D)1/2 days E)days SOLUTION:Explanation: 10/40 + 10/30 + 10/x = 1 x = 24 days Answer: A #### A QUESTION:jhon has 10 choclates, jennifer has 5 choclates. Totally how many choclates they have in all? options: A)5 B)10 C)15 D)20 E)14 SOLUTION:10+5=15. Answer is C #### C QUESTION:12 litres of water are poured into an aquarium of dimensions 50cm length, 30cm breadth, and 40cm height. How high (in cm) will the water rise? (1 litre = 1000cm³) options: A)6 B)8 C)10 D)20 E)40 SOLUTION:we have 1 litre = 1000cm³ (thanks Bunuel) =>12 litres = 12*1000 = 12000cm³ Let call the height of the water is x the breadth and length of the water will equal the aquarium The volume of the water: 50 * 30 * x = 12000cm³ => x = 12000/(50*30) = 8 cm Answer is B #### B QUESTION:A store’s selling price of $2500 for a certain printer would yield a profit of 40 percent of the store’s cost for the printer. What selling price would yield a profit of 50 percent of the printer’s cost? options: A) $2400 B) $2464 C) $2650 D) $2478 E) $2800 SOLUTION:1.4x = 2500 x=2500/1.4 so, 1.5X = 2500*1.5/1.4= 2478 Answer:- D #### D QUESTION:A man can row upstream at 8kmph and downstream at 13 kmph. The speed of the stream is options: A)2.5 km/hr B)4.2 km/hr C)5 km/hr D)10.5 km/hr E)None SOLUTION:Sol. Speed of stream = 1/2(13 -8) kmph = 2.5 kmph. Answer A #### A QUESTION:Pumping 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? options: A)3.25 B)3.6 C)4.2 D)4.4 E)5.14 SOLUTION:Time taken by First tank Fill 1/2 the tank = 6 hours i.e. Time taken by First tank to Fill 1 complete the tank =12 hours Time taken by Second tank Fill 2/3 the tank = 6 hours i.e. Time taken by First tank to Fill 1 complete the tank = (3/2)*6 = 9 hours in 1 Hour, Both tanks together Fill the tank = (1/12)+(1/9) = 7/36 tank i.e. Time taken by Both tank to Fill 1 complete the tank = 36/7 hours = 5.14 hours Answer: option E #### E QUESTION:Consider a sequence of numbers given by the expression 7 + (a - 1) * 5, where n runs from 1 to 80.What is the sum of this series ? options: A)409 B)1636 C)16360 D)16000 E)15360 SOLUTION:terms in this sequence are 7,12,17----402 now since this is an a.p. with a common difference of 5. therefore its sum can be given as a(f+l)/2----------------1) a= total no. of terms =80 f= first term=7 l= last term=402 subsituting values in the expression 1 we have 80(7+402)/2 = 40(409) =16360=C #### C QUESTION:On a ferry, there are 32 cars and 8 trucks. The cars have an average mass of 900 kg and the trucks have an average mass of 3000 kg. What is the average mass of all 40 vehicles on the ferry? options: A)1200 B)1240 C)1280 D)1320 E)1360 SOLUTION:The total mass of the vehicles is 32*900+8*3000=52800 The average mass is 52800/40=1320 The answer is D. #### D QUESTION:The radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 500 resolutions? options: A)754 m B)704 m C)708 m D)706 m E)204 m SOLUTION:In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 500 resolutions. = 500 * 2 * 22/7 * 22.4 = 70400 cm = 704 m Answer:B #### B QUESTION:In an examination 60% failed in Math and 40% failed in French. If 10% failed in both. What % of students passed in both. options: A)25% B)15% C)20% D)30% E)10% SOLUTION:Passed in Math = 100 - 60 = 40% Passed in French = 100 - 40 = 60% Students who passed Math or French = 100 -10 = 90% Students passed in Math and French = (Passed in Math) + (Passed in French) - (Students who passed Math or French) = 60+40-90 =10% ANSWER:E #### E QUESTION:A train 240 m long passes a pole in 24 seconds. How long will it take to pass a platform 650 m long? options: A)65 sec B)89 sec C)100 sec D)150 sec E)160 sec SOLUTION:Explanation: Speed =240/24 m/sec = 10 m/sec Required time =(240+650 /10)sec=89sec ANSWER IS B #### B QUESTION:a and b are positive integers less than or equal to 9 and multiple of 4. If a and b are assembled into the seven-digit number abaabab, which of the following must be a factor of abaabab? options: A)3 B)4 C)5 D)7 E)8 SOLUTION:The last two digit of the number are ab. Both a and b are multiple of 4,thus the last two digits are divisible by 4, which makes the number abaabab divisible by 4. Thus 4 is always a factor of abaabab. Answer: B #### B QUESTION:The 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? options: A)7:6 B)7:3 C)7:4 D)7:2 E)7:1 SOLUTION:Let the age of father and son 10 years ago be 3x and x years respectively. Then, (3x + 10) + 10 = 2[(x + 10) + 10] 3x + 20 = 2x + 40 => x = 20. Required ratio = (3x + 10):(x + 10) = 70:30 = 7:3 Answer: B #### B QUESTION:Arun has certain number of books. It is not less than 15 and not more than 30. If he wants to give these books equally to 2 of his friends, then 1 book will remain. If he wants to give these books equally to 3 of his friends, then 2 books will remain. If he wants to give these books equally to 4 of his friends, then 3 books will remain. What is the number of books he had? options: A)23 B)24 C)25 D)26 E)27 SOLUTION:Explanation : If he wants to give these books equally to 2 of his friends, then 1 book will remain, it means possible number of books = 15,17,19,21,23,25,27,29 If he wants to give these books equally to 3 of his friends, then 2 books will remain, it means possible number of books = 17,20,23,26,29 If he wants to give these books equally to 4 of his friends, then 3 book will remain, it means possible number of books = 15,19,23,27 Hence ,the common number is only 23 so it will be answer. Answer : A #### A QUESTION:A 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? options: A)Rs.400 B)Rs.450 C)Rs.550 D)Rs.500 E)Rs.650 SOLUTION:Explanation: P - 340 = (P*4*8)/100 P = 500 ANSWER IS D #### D QUESTION:28% of employees are women with fair hair. 40% of fair-haired employees are women. What percent of employees have fair hair? options: A)25 B)30 C)50 D)55 E)70 SOLUTION:I came up with (E) 70 Think of 100 people total: From the first fact, 28 of these are women with fair hair. From the second fact, these 20 women make up 40% of the total fair haired population. We can then make a ratio of 60:40 fair haired men to fair haired women. This means that (60/40)*28 equals the number of fair haired men, which is 42 men with fair hair. Add this 42 to the 28 women and get 70 fair haired men and women out of 100 total men and women. 70%E #### E QUESTION:If the digits 35 in the decimal 0.00035 repeat indefinitely, what is the value of (10^5-10^3)(0.00035)? options: A)37 B)41 C)3.5e-05 D)35 E)3.5e-07 SOLUTION:99*0.35=34.65 approx. 35 Answer : B #### B QUESTION:A family made a down payment of $20 and borrowed the balance on a set of encyclopedias that cost $120. The balance with interest was paid in 7 monthly payments of $15.2 each and a final payment of $7. The amount of interest paid was what percent of the amount borrowed? options: A) 6% B) 12% C) 13.4% D) 16% E) 20% SOLUTION:interest paid = 15.2*7+7 - 100 = 13.4 % off the balance = (13.4/100) * 100 = 13.4 % Answer is C. #### C QUESTION:The average age of the mother and her six children is 9 years which is reduced by 5 years if the age of the mother is excluded. How old is the mother? options: A)39 B)41 C)42 D)43 E)44 SOLUTION:Total age of mother and 6 children = avg x n = 9 x (6+1)= 63 If mother is excluded new average is (9 - 5) = 4 so for 6 children = 6 x 4 =24 so mother's age is 63 - 24 =39 Answer: Option A #### A QUESTION:Out 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? options: A)17/65 B)17/29 C)17/21 D)P(EᴜP) =17/20 E)17/212 SOLUTION:n(S) = 20 n(Even no) = 10 = n(E) n(Prime no) = 8 = n(P) P(EᴜP) = 10/20 + 8/20 - 1/20 = 17/20.Answer:D #### D QUESTION:The factorial expression 10!/2! is not divisible by which of the following integers? options: A)3 B)5 C)6 D)7 E)None of these SOLUTION:10!/2! => 10 x 9 x 8 x7 x 6 x 5 x 4x3 (A) 3 Can divide 12 or 9 (B) 5 Can divide 10 (C) 6 Can divide 12 (D) 7 can divide 7,21,28 Hence answer will be (E) #### E QUESTION:A toy store regularly sells all stock at a discount of 10 percent. If an additional 10 percent were deducted from the discount price during a special sale, what would be the lowest possible price of a toy costing $10 before any discount? options: A) $7.20 B) $8.00 C) $8.10 D) $8.27 E) $9.00 SOLUTION:sale price = (original price - 10% decrease) - 10% decrease price = [10 * (90/100)] * (90/100) = 10 * (.90) * (.90) = 9 * .90 = 8.10 The answer is C. #### C QUESTION:Walking with 4/5 of my usual speed, I arrive at the bus stop 8 minutes later than normal. How many minutes does it take to walk to the bus stop at my usual speed? options: A)20 B)24 C)28 D)32 E)36 SOLUTION:Let t = usual time = distance / usual speed t + 8 = distance / (4* usual speed/5) = (5 * distance) / (4 * usual speed) = 5t/4 t = 32 The answer is D. #### D QUESTION:On dividing 144 by a number, the quotient is 13 and the remainder is 1. Find the divisor. options: A)A)11 B)B)14 C)C)16 D)D)18 E)E)22 SOLUTION:d = (D-R)/Q = (144 - 1)/13 = 143/13 = 11 A) #### A QUESTION:Let S be the set of values which can be written as the sum of 5 consecutive perfect squares. What is the smallest element of S which is divisible by 17? options: A)255 B)355 C)522 D)355 E)664 SOLUTION:Each element of S can be written in the form (x- 2)2 + (x - 1)2 + x2 + (x + 1)2 + (x + 2)2 = x2 + 2x2 + 2 + 2x2 + 8 = 5x2 + 10 = 5(x2 + 2) where x is some positive integer with x 3. By iterating over values of x, we observe that when x = 7, x2 + 2 = 51 = 3 * 17; no smaller value of x exists which satisfies the problem statement. Hence, the solution is 5(x2 + 2) = 5 *51 = 255 correct answer A #### A QUESTION:On a race track a maximum of 5 horses can race together at a time. There are a total of 25 horses. There is no way of timing the races. What is the minimum number Q of races we need to conduct to get the top 3 fastest horses? options: A)5 B)7 C)8 D)10 E)11 SOLUTION:Q=7 is the correct answer. Good solution Buneul.B #### B QUESTION:man is 20 years older than his son. In two years, his age will be twice the age of his son. The present age of his son is: options: A)14years B)26 years C)17 years D)18 years E)22 years SOLUTION:Let the son's present age be x years. Then, man's present age = (x + 20) years. (x + 20) + 2 = 2(x + 2) x + 22 = 2x + 4 x = 18. answer :D #### D <<<Examples ends QUESTION:(0.5)(power 3) - (0.1)(power 3)/ (0.5)(power 2) + 0.05 + (0.1)(power 2) is: options: A)0.8 B)0.4 C)0.96 D)0.69 E)0.76 SOLUTION:Given expression = (0.5) (power 3) - (0.1)(power 3) / (0.5)(power 2) + (0.5 x 0.1) + (0.1)(power 2) = a (power 3) - b(power 3) / a(power 2) + ab + b(power 2) = (a - b) = (0.5 - 0.1) = 0.4 Answer is B #### B

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:In how much time will a train of length 100 m, moving at 36 kmph cross an electric pole? options: A)16 sec B)18 sec C)19 sec D)10 sec E)17 sec SOLUTION:Convert kmph to mps. 36 kmph = 36 * 5/18 = 10 mps. The distance to be covered is equal to the length of the train. Required time t = d/s = 100/10 = 10 sec. Answer: D #### D QUESTION:A prize pool for a competition is divided up so that the first place winner receives 50%, the second place 30%, and third place receives 20%. If the third place competitor receives 100 000 dollars, how much is the total prize pool in dollars? options: A)500 000 B)1 000 000 C)2 000 000 D)5 000 000 E)250 000 SOLUTION:The ratio is 5:3:2. Since third place received 100 000 dollars, a part-to-whole ratio can be set up to figure out how much the total prize pool is. 5+3+2 = 10 10/2 = X/100 000 5*100 000 = X 500 000 = X Answer: A) #### A QUESTION:In the equation x^2+kx+1=0, x is a variable and k is a constant. If the quadratic equation has two distinct real roots, which of the following could be true? I) k=0 II) k=−1 III) k=−3 options: A)I only B)III only C)I and II only D)II and III only E)I and III only SOLUTION:Please format the question properly. Per the question, x^2+kx+1=0 with k=constant. For a quadratic equation (ax2+bx+c=0) to have 2 distinct roots ---> D=b2−4ac>0 ---> k^2−4>0 --->k<−2or k>2 . Only III falls in these ranges. B is the correct answer. #### B QUESTION:Two 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? options: A)28 B)10 C)28 D)27 E)13 SOLUTION:4/12 + x/15 = 1 x = 10 Answer:B #### B QUESTION:JOHN and ANDREW can finish the work 9 days if they work together. They worked together for 6 days and then ANDREW left. JOHN finished the remaining work in another 6 days. In how many days JOHN alone can finish the work? options: A)30 days B)60 days C)18 days D)80 days E)90 days SOLUTION:Amount of work done by JOHN and ANDREW in 1 day = 1/9 Amount of work done by JOHN and ANDREW in 6 days = 6 × (1/9) = 2/3 Remaining work – 1 – 2/3 = 1/3 JOHN completes 1/3 work in 6 days Amount of work JOHN can do in 1 day = (1/3)/6 = 1/18 => JOHN can complete the work in 18 days Answer : C #### C QUESTION:m:n = 5: 8 , n: p = 6 : 7 , m:n:p = ? options: A)30 : 48 : 54 B)30 : 48 : 56 C)30 : 48 : 50 D)30 : 48 : 52 E)30 : 48 : 58 SOLUTION:m:n = 5: 8 n: p = 6 : 7 m:n:p =30 : 48 : 56 Answer : B #### B QUESTION:At a dinner party, 7 people are to be seated around a circular table. Two seating arrangement 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? options: A)5 B)10 C)720 D)32 E)120 SOLUTION:Has to be C. Simple formula: There are (n - 1)! ways to arrange n distinct objects in a circle hence (7-1)! = 6!= 720 #### C QUESTION:In how many different number of ways 5 boys and 4 girls can sit on a bench? options: A)700 B)710 C)720 D)362880 E)740 SOLUTION:npn = n! 9p9 = 9 X 8 X 7 X 6 × 5 × 4 × 3 × 2 × 1 = 362880 D #### D QUESTION:How many integers n are there such that 1< 5n +5 < 40? options: A)2 B)3 C)4 D)5 E)7 SOLUTION:Solution: 1< 5n + 5 < 40 is a compound inequality. Compound inequalities often need to be manipulated, and we can use the rules of algebra that we already know, to do this. Just as with equations, whatever we do to one part of a compound inequality, we must do to all parts of the compound inequality. Let’s first isolate n within the inequality. 1< 5n + 5 < 40 We first subtract 5 from all three parts of the inequality, and we obtain: -4 < 5n < 35 Next, we divide both sides of the inequality by 5 and we get: -4/5 < n < 7 The integers that are greater than -4/5 and less than 4 are 0, 1, 2, and 3. Thus, there are 4 integers that satisfy the inequality 1 < 5n + 5 < 40. The answer is E #### E QUESTION:The 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? options: A)1 B)2 C)8 D)7 E)0 SOLUTION:S = 4 M = x DS = x + 4 US = x - 4 6/(x + 4) + 6/(x - 4) = 2 x = 8 Answer: C #### C QUESTION:A three digit number divisible by 7 becomes divisible by 3 when 7 is added to it. The largest such number is : options: A)891 B)896 C)882 D)867 E)864 SOLUTION:Out of all the 5 options, only 896 is NOT divisible by 3. All others are divisible So Answer = B(No further calculation required) Addition of any two non-divisible numbers by 3 gives the resultant divisible by 3 7 is non-divisible by 3; we are adding a number to that so that the resultant becomes divisible by 3 Applying the above rule,It means that the number which we are going to add should be non-divisible by 3 So comes the answer = 896 Answer : B #### B QUESTION:The average of a batsman for 40 innings is 50 runs. His highest score exceeds his lowest score by 172 runs. If these two innings are excluded, his average drops by 2 runs. Find his highest score. options: A)172 B)173 C)174 D)175 E)None of the above SOLUTION:Total runs = 40 × 50 = 2000 Let his highest score be = x Then his lowest score = x – 172 Now 200−x−(x−172)/38=48 ⇒ 2x = 2172 – 1824 ⇒ x = 174 Answer C #### C QUESTION:On dividing 12401 by a certain number, we get 76 as quotient and 13 as remainder. What is the divisor? options: A)163 B)785 C)852 D)456 E)852 SOLUTION:Divisor *quotient+remainder=dividend divisor=(dividend)-(remainder)/quotient (12401-13)/76=163 Answer(A) #### A QUESTION:How many integers between 5000 and 6000 that have distinct digits and increase from left to right ? options: A)10 B)48 C)60 D)20 E)600 SOLUTION:Since the numbers must be distinct and increasing from left to right, The only arrangements we could come-up with are: 545_ --> 4 546_ --> 3 547_ --> 2 548_ --> 1 556_ --> 3 557_ --> 2 558_ --> 1 567_ --> 2 568_ --> 1 578_ --> 1 Number of integers =20 D #### D QUESTION:If the average (arithmetic mean) of five consecutive negative integers is 2k – 1, what is the difference W between the greatest and least of the five integers? options: A)4K B)4k^2 -4k C)4-4k D)4 E)4k+4 SOLUTION:(n-2 + n - 1 + n + n + 1 + n + 2)/5 = 2k - 1 => n = 10k - 5 Greatest = n + 2 = 10k - 5 + 2 = 10k - 3 Least = n - 2 = 10k - 5 - 2 => Difference W= 10k - 3 - (10k - 7) = 4 Answer - D #### D QUESTION:A and B together do a work in 20 days.B and C together in 15 days and C and A in 12 days.so A,B and C together finish same work in how many days? options: A)12 B)15 C)8 D)10 E)11 SOLUTION:(A+B) work in 1 day= 1/20,(B+C) work in 1 days = 1/15.,(C+A) work in 1 days=1/12 (1) adding=2[A+B+C] in 1 day work = [1/20+1/15+1/12]=1/5 (A+B+C) work in 1 day= 1/10 So,all three together finish work in 10 days Answer D #### D QUESTION:A goods train runs at the speed of 72 km/hr and crosses a 280 m long platform in 26 sec. What is the length of the goods train? options: A)278 B)166 C)151 D)240 E)109 SOLUTION:Speed = 72 * 5/18 = 20 m/sec. Time = 26 sec. Let the length of the train be x meters. Then, (x + 280)/26 = 20 x = 240 m. Answer:D #### D QUESTION:Mohan 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? options: A)A)Rs.520 B)B)Rs.594 C)C)Rs.596 D)D)Rs.595 E)None of these SOLUTION:Explanation: Price of 10 kgs of rice at Rs.26/kg = 10x26 = Rs.260 Price of 8 kgs of pulses at Rs.26/kg = 10x26 = Rs.260 Therefore, Total amount = Rs.260+Rs.260 = Rs.520. Answer: Option A #### A QUESTION:Find the compound interest on $30000 in 2years at 4% per annum, the interest being compounded half-yearly? options: A)$645.56 B)$824.32 C)$954.26 D)$2472.96 E)$1020.45 SOLUTION:Principle = $10000 Rate = 2% half yearly = 4 half years Amount = 30000*(1 + 2/100)^4 = 30000 * 51/50 * 51/50 * 51/50 * 51/50 = $32472.96 C.I. = 32472.96-10000 = $2472.96 Answer is D #### D QUESTION:If 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? options: A)4/5 km B)4/6 km C)4/9 km D)4/1 km E)4/3 km SOLUTION:x/3 – x/4 = 4/60 x = 4/5 km Answer: A #### A QUESTION:If 0.75: x :: 5:12, then x is equal to: options: A)1.12 B)1.16 C)1.8 D)1.3 E)None of these SOLUTION:Explanation: (x * 5) = (0.75 *12) X=9/5 = 1.80 Answer: C #### C QUESTION:Kamal obtained 66, 65, 77, 62 and 75 marks(out of 100) in English, Mathematics, Physics, Chemistry and Biology. What are his average marks? options: A)65 B)69 C)72 D)75 E)NOne SOLUTION:Sol. Average = 66 + 65 + 77 + 62 + 75 / 5) = (345 / 5) = 69. Answer B #### B QUESTION:If 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? options: A)331/8% B)26.67% C)28.5% D)332/3% E)131/3% SOLUTION:100 140 ------ 140-------40 100-------? => 28.5% Answer:C #### C QUESTION:If x is three times larger than n , and if 2n+3 is 20% of 25, what is the value of ? options: A)1 B)2 C)3 D)6 E)12 SOLUTION:Then the wordings of question are misleading. Moreover, it'd also be a bad way to convey x=4n, if it really wanted to convey so. From other questions that I have seen, proper wordings could be: If x is three times as large as n OR simply, If x is three times n.C #### C QUESTION:What is the perimeter of a triangle with sides 7 and 4 that has the maximum possible area? options: A)11 + √5 B)11 + √6 C)11 + 4√7 D)11 + √65 E)11 + 3√17 SOLUTION:We can maximize the area of the triangle by making these two sides the base and the height of a right angle triangle. Then the third side is the hypotenuse with a length of √(49+16) = √65 The perimeter is 11 + √65 The answer is D. #### D QUESTION:A discount of 10 percent on an order of goods followed by a discount of 20 percent amounts to options: A)the same as one 45 percent discount B)the same as one 38 percent discount C)the same as one 36 percent discount D)the same as one 30 percent discount E)the same as one 28 percent discount SOLUTION:0.9*0.8*x=0.72x from initial value, meaning 0.28 or 36% discount E #### E QUESTION:What will $2500 amount to in three years if it is invested at 20% per year compound interest, with the interest being compounded annually? options: A)$3760 B)$3980 C)$4210 D)$4320 E)$4760 SOLUTION:After one year: 1.2 * $2500 After two years: (1.2)^2 * $2500 After three years: (1.2)^3 * $2500 = $4320 The answer is D. #### D QUESTION:w,x,y,z is an arithmetic sequence, which of the following options also qualifies as an arithmetiv sequence? I. w-6,x-6,y-6,z-6 II. 5w,2x,3y,5z III. 5w,5x,5y,5z options: A)II and III B)III only C)I and III D)I and II E)II only SOLUTION:lets look at the three choices... I. w-6,x-6,y-6,z-6 since the difference is constant, it is an arithmetic sequence... II. 5w,2x,3y,5z since the difference is not constant, it is not an arithmetic sequence III. 5w,5x,5y,5z since the difference is constant it is an arithmetic sequence... Answer is A) #### A QUESTION:A trader expects a gain of 15 % on his cost price. If in a week his sale is of Rs. 580, then what is his profit? options: A)75.65 B)73.26 C)72.5 D)70.78 E)71.62 SOLUTION:Explanation: We are given selling price = Rs. 580 and expected profit of 15 % Therefore, we can easily solve this numerical, considering basic formulae of profit and loss. Let cost price = x Selling price = C.P. + Profit S.P. = C.P. + (15% of C.P.) ---------- (We know that profit is gained on cost price) 580 = x + (0.15 x) 580 = 1.15 x Therefore, x = 504.347 Cost Price = Rs. 504.35 Now, we have the cost price and hence, Profit = S. P. – C.P. = 580 – 504.35 = Rs. 75.65 The trader gets a profit of Rs. 75.65 ANSWER IS A #### A QUESTION:A train passes a station platform in 36 seconds and a man standing on the platform in 24 seconds. If the speed of the train is 54 km/hr, what is the length of the platform? options: A)180 B)240 C)288 D)267 E)211 SOLUTION:Speed = (54 * 5/18) m/sec = 15 m/sec. Length of the train = (15 x 24)m = 360 m. Let the length of the platform be x meters. Then, (x + 360)/36 = 15 ==> x + 360 = 540 ==> x = 180 m.Answer: A #### A QUESTION:A cistern 4 m long and 8 m wide contains water up to a depth of 1 m 25 cm. The total area of the wet surface is: options: A)49 m2 B)50 m2 C)52 m2 D)62 m2 E)55 m2 SOLUTION:Area of the wet surface = [2(lb + bh + lh) - lb] = 2(bh + lh) + lb = [2 (8 x 1.25 + 4 x 1.25) + 8 x 4] m2 = 62 m2. answer :D #### D QUESTION:If six persons sit in a row, then the probability that three particular persons are always together is ? options: A)1/5 B)1/7 C)1/2 D)1/1 E)1/9 SOLUTION:Six 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 #### C QUESTION:The sale price shirts listed for Rs.1000 after successive discount is 15% and 2% is? options: A)338 B)823 C)833 D)337 E)733 SOLUTION:1000*(85/100)*(98/100) = 833 Answer: C #### C QUESTION:A 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. He was afraid of forgetting his PIN. He wrote down the number 125 in his diary to remember his PIN. He also wrote out the way to calculate 125 : "Multiply the card number by PIN. Divide the product by 997. The remainder is 125". Once, Prafull saw his diary in which Pinaki wrote this number 125. Prafull did a lot of purchasing, as he now knows Pinaki's PIN. What is Pinaki's PIN? options: A)874 B)872 C)876 D)875 E)879 SOLUTION:Explanation : Let, the PIN is x. According to the question, The card number =996 and Remainder =125. Thus, (996 × x)/997=125. =>x= 872. Answer : B #### B QUESTION:How many positive integers less than 250 are multiple of 4 but NOT multiples of 6? options: A)20 B)31 C)42 D)53 E)64 SOLUTION:Multiples of 4 less than 250 = {4,8,12,......248} = 62 numbers Multiples of 4 which are multiples of 3 too ={12,24,36.....240} = 20 numbers So required number= 62-20 = 42 Choice C #### C QUESTION:Rs.1210 were divided among 3 person P, Q, R so that P:Q=5:4 and Q: R=9:10. Then R gets the amount. options: A)Rs. 300 B)Rs. 400 C)Rs. 480 D)Rs. 490 E)Rs. 500 SOLUTION:P : Q = 5 : 4, Q : R = 9 : 10 = ( 9 x 4 / 9 ) : ( 10 x 4 / 9 ) = 4 : 40 / 9. So, P : Q : R = 5 : 4 : 40 /9 = 45 : 36 : 40 Sum of ratio terms is = ( 45 + 36 + 40 ) =121. R share of amount is Rs (1210 x 40 / 121) = Rs. 400. B #### B QUESTION:A bus started its journey from Mumbai and reached Pune in 44min with its average speed of 50 km/hr. If the average speed of the bus is increased by 5km/hr, how much time will it take to cover the same distance? options: A)20 B)30 C)35 D)40 E)50 SOLUTION:Sol. Distance between Ramgarh and Devgarh =(50*44)/60=110/3 Average speed of the bus is increased by 5 km/hr then the speed of the bus = 55 km/hr Required time = 110/3*60/55 = 40 min D #### D QUESTION:For how many integers n is 1^n+2 = (n+2)^1? options: A)0 B)1 C)2 D)None of these E)3 SOLUTION:If n=0 1^0+2 = (0+2)^1 1^2 = 1 ; 2^1 =2 not ok If n=1 1^1+2 =1 ; (1+2)^1=3^1=3 not OK So, Answer : D #### D QUESTION:There are three different hoses used to fill a pool: hose U, hose y, and hose z. Hose U can fill the pool in a days, hose y in b days, and hose z in c days, where a > b > c. When all three hoses are used together to fill a pool, it takes d days to fill the pool. Which of the following must be true? I. d<c II. d>b III. c/3<d<a/3 options: A)I B)II C)III D)II &III E)I &II SOLUTION:Name T = full pool U fills a pool in a days ==> 1 day U fills: T/a Y fills a pool in b days ==> 1 day Y fills: T/b Z fills a pool in c days ==> 1 day Z fills: T/c 1 day (U+Y+Z) together fill: T(1/a + 1/b + 1/c) d days (U+Y+Z) together fill: T ==> d = T1 / T(1/a+1/b+1/c) = abc/(ab+bc+ca) ==>d = abc/(ab+bc+ca) d cannot be greater than c ; d is greater than b ; d is greater than c/3 but not less than a/3 B #### B QUESTION:In a college, the ratio of the number of boys to girls is 8 : 5. If there are 300 girls, the total number of students in the college is options: A)420 B)520 C)620 D)780 E)820 SOLUTION:Explanation: Let the boy are 8x and Girls are 5x => 5x = 300 => x = 60 Total students = 8x+5x = 13x = 13(60) = 780 Option D #### D QUESTION:How many factors of 2475 are odd numbers greater than 1? options: A)3 B)4 C)17 D)6 E)7 SOLUTION:prime factors of 330 are 2^1,3^2,5^2 and 11^1 total divisors = (power if a prime factor+1) total no. of odd factors(3,5,11) = (2+1)(2+1)(1+1) =18 since we need odd divisors other than 1 =>18-1 = 17 odd divisors C is the answer #### C QUESTION:Three numbers are in the ratio 1:3:5 and their H.C.F is 5. The numbers are? options: A)5, 15, 35 B)5, 15, 30 C)5, 15, 25 D)5, 15, 40 E)5, 15, 20 SOLUTION:Let the required numbers be x, 3x and 5x. Then, their H.C.F = x. So, x = 5. The numbers are 5, 15, 25. Answer: C #### C QUESTION:A train 250 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: options: A)95 km/hr B)50 km/hr C)54 km/hr D)55 km/hr E)56 km/hr SOLUTION:Speed of the train relative to man = (250/10) m/sec = 25 m/sec. [(25 * (18/5)] km/hr = 90km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 90 ==> x = 95 km/hr. ANSWER: A #### A QUESTION:There are 2 red chips and 2 blue ones. When arranged in a row, they form a certain color pattern, for example RBRRB. How many color patterns? options: A)A)10 B)B)12 C)C)24 D)D)60 E)E)100 SOLUTION:Using anagram method: 4_3_2_1 R_R_B_B so.. 4!/Number of repeated letters (2!)(2!) = 6 ANS:D #### D QUESTION:If x = 3 and y = 2, what is the value of 5(x-y)^2 - xy ? options: A)-8 B)-7 C)-1 D)-2 E)-5 SOLUTION:x = 3 and y = 2 x-y = 3 - 2 = 1 x*y = 3 * 2 = 6 Now we apply it in the equation 5(x-y)^2 - xy =5 (1)^2-6 ==>5*1 -6 = 5-6 =-1 Answer : C #### C QUESTION:What is the sum of all even numbers from 1 to 401? options: A)122821 B)281228 C)281199 D)122850 E)40200 SOLUTION:Explanation: 400/2 = 200 200 * 201 = 40200 Answer: E #### E QUESTION:An article is bought for Rs.700 and sold for Rs.900, find the gain percent? options: A)33 1/8% B)33 8/3% C)28 4/7% D)35 1/3% E)32 1/3% SOLUTION:700 ---- 200 100 ---- ? => 28 4/7% Answer: C #### C QUESTION:what is the smallest integer that is multiple of 7, 12 and 20 options: A)141 B)180 C)130 D)122 E)420 SOLUTION:Correct Answer :E It is the lcm of 7, 12 and 20 which is 420 #### E QUESTION:If 12 ounces of a strong vinegar solution are diluted with 50 ounces of water to form a eight-percent vinegar solution, what was the concentration of the original solution? options: A)9.3% B)17.3% C)26.67% D)35.5% E)41.3% SOLUTION:Let X be the quantity of non-vinegar in the strong vinegar solution Thus vinegar quantity will be 12 - X When 50 ounces of water were added the percentage of vinegar becomes 8%, thus (12 - X)/62 = 8/100 From this equation X = 7.04 Answer (12-7.04)/12 = 41.3% ANSWER:E #### E QUESTION:The third proportional to 2 and 6 is? options: A)18 B)17 C)14 D)15 E)13 SOLUTION:(6*6)/2 = 18 Answer:A #### A QUESTION:A flagpole 18 meters high casts a shadow of length 45 meters. If a building under similar conditions casts a shadow of length 50 meters, what is the height of the building (in meters)? options: A)16 B)20 C)24 D)28 E)32 SOLUTION:The height:length ratio will be equal in both cases. 18 / 45 = x / 50 x = 20 The answer is B. #### B QUESTION:Every 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? options: A)36/125 B)36/120 C)30/125 D)30/140 E)36/140 SOLUTION:Probability of basket = 3/5 Probability of no basket = 2/5 Required probability=3* 3/5*2/5*2/5 =36/125 A is the answer . #### A QUESTION:Bruce 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? options: A)1040 B)1050 C)1055 D)1065 E)1075 SOLUTION:Cost of 8 kg grapes = 70 × 8 = 560. Cost of 9 kg of mangoes = 55 × 9 = 490. Total cost he has to pay = 560 + 490 = 1055 C #### C QUESTION:Ganesh is one year more than twice Kumar's age. The sum of their age is 7. How old each? options: A)6, 4 B)5, 2 C)2, 5 D)7, 3 E)3, 7 SOLUTION:Explanation: Let the present ages of Anand and Bala be 'a' and 'b' respectively. Given a - 2b = 1 --- (1) a+b = 7----(2) =>b =7-a Substituting b = 7-a in first equation, 3a-14 = 1 => a = 5 => b = 2 Answer: B #### B QUESTION:Cara picked a number of pears, each of which she sold, canned, or poached. If she canned 40 percent more than she poached, and she poached 80 percent less than she sold. If there were a total of 111 pears, then how many pears did she sell? options: A)69 B)72 C)75 D)78 E)81 SOLUTION:Let x be the amount of pears that she sold. Then she poached 0.2x. Then she canned 1.4*0.2x=0.28x. The total amount of pears is x+0.2x+0.28x=1.48x The fraction of pears that she sold is 1/1.48=100/148=25/37. The number of pears she sold is (25/37)*111=75. The answer is C. #### C QUESTION:A, 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.2430? options: A)s.800 B)s.810 C)s.820 D)s.900 E)s.920 SOLUTION:2430 * 1/3 = 810 Option B #### B QUESTION:The average age of 30 students in a class is 14 years. If the age of teacher is also included, the average becomes 15 years, find the age of the teacher. options: A)43 B)44 C)45 D)47 E)48 SOLUTION:Explanation: If teacher's age is 14 years, there is no change in the average. But teacher has contributed 1 year to all the students along with maintaining his age at 15. Age of teacher = Average age of all + Total increase in age = 15 + (1 x 30 ) = 45 years Answer:C #### C QUESTION:A candidate got 35% of the votes polled and he lost to his rival by 2250 votes. How many votes were cast? options: A)7500 B)7508 C)7528 D)7527 E)7232 SOLUTION:35%-----------L 65%-----------W ------------------ 30%----------2250 100%---------? => 7500 Answer:A #### A QUESTION:Statement: Concerns have risen about air pollution in Indian cities. A recent report by the World Health Organization (WHO) states that of the 20 most polluted cities in the world, 13 are in India. Action: I. Pollution committee should immediately take certain measures to control the pollution levels in India. II. Licenses of polluting industries should be cancelled and owners should be put behind the bars. options: A)Only I follows B)Only II follows C)Either I or II follows D)Neither I nor II follows E)Both I and II follow SOLUTION:Explanation: Only one follows. The given statement describes the problem and the actions mention the solutions for the same. Second option is to be avoided because it is a negative and harsh approach. As listed in tips and tricks section also Options which are negative in nature and provide harsh solutions should be avoided. ANSWER IS A #### A QUESTION:The maximum number of students among them 100 pens and 50 pencils can be distributed in such a way that each student get the same number of pens and same number of pencils? options: A)50 B)75 C)69 D)79 E)82 SOLUTION:number of pens = 100 number of pencils = 50 Required number of students = H.C.F. of 100 and 50 = 50 Answer is A #### A QUESTION:Four of the five parts numbered (a),(b),(c),(d) and (e) in the following equation are exactly equal. Which of the parts is not equal to the other four? The number of that part is the answer. options: A)45 × 120 + 5(2) × 10 B)113 × 25 × 2 C)27 × 25 × 8 + 15 × 6 + 4 × 40 D)226 × 5 + 113 × 45 = E)50(2) × 2 + 13 × 50 SOLUTION:Others equal 5650. Answer D #### D QUESTION:A batsman scored 120 runs whichincluded 3 boundaries and 8sixes. What % of his total score did he make by running between the wickets options: A)40 % B)50 % C)60 % D)70 % E)80 % SOLUTION:Number of runs made by running = 110 - (3 x 4 + 8 x 6) = 120 - (60) = 60 Now, we need to calculate 60 is what percent of 120. => 60/120 * 100 = 50 % B #### B QUESTION:In how many different ways can the letters of the word ‘ARMOUM’ be arranged? options: A)230 B)250 C)260 D)300 E)360 SOLUTION:ARMOUR = 6 letter whereas R repeated twice 6! 6xSx4x3x2x1 => 360 E #### E QUESTION:The sum of the first 40 positive even integers is 1,640. What is the sum of the first 40 odd integers? options: A)1500 B)1600 C)1400 D)1200 E)1000 SOLUTION:Sum of first n even numbers = n(n+1) =1640 Sum of first n odd numbers = n^2 = 40*40 = 1600 (here n=40) Answer : B #### B <<<Examples ends QUESTION:In a certain school, 20% of students are below 8 years of age. The number of students above 8 years of age is 2/3 of the number of students of 8 years of age which is 48. What is the total number of students in the school? options: A)200 B)300 C)600 D)700 E)100 SOLUTION:E 100 Let the number of students be x. Then, Number of students above 8 years of age = (100 - 20)% of x = 80% of x. 80% of x = 48 + 2/3 of 48 80/100x = 80 x = 100. #### E

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:An order was placed for the supply of a carper whose length and breadth were in the ratio of 3 : 2. Subsequently, the dimensions of the carpet were altered such that its length and breadth were in the ratio 7 : 3 but were was no change in its parameter. Find the ratio of the areas of the carpets in both the cases. options: A)8:6 B)8:7 C)8:9 D)8:1 E)8:2 SOLUTION:Let the length and breadth of the carpet in the first case be 3x units and 2x units respectively. Let the dimensions of the carpet in the second case be 7y, 3y units respectively. From the data,. 2(3x + 2x) = 2(7y + 3y) => 5x = 10y => x = 2y Required ratio of the areas of the carpet in both the cases = 3x * 2x : 7y : 3y = 6x2 : 21y2 = 6 * (2y)2 : 21y2 = 6 * 4y2 : 21y2 = 8:7 Answer: B #### B QUESTION:If w,x,y,z are consecutive positive integers ; then which of the following is always odd? [1] w*x+(y+2)^2*z [2] w^x + z^y [3] 13x^2 options: A)1 B)2 C)3 D)1 and 2 E)2 and 3 SOLUTION:Plug in some numbers w = 1 x = 2 y = 3 z = 4 Check the options - [1] w*x+(y+2)^2*z = 1*2 + (3+2)^2 * 4 => 2 + 25*4 = 102{ Not an odd Number } [2] w^x + z^y = 1^2 + 4^3 => 1 + 64 = 65{ Odd number } [3] 13x^2 = 13*4 =52 even [2] B #### B QUESTION:A cycle is bought for Rs.450 and sold for Rs.520, find the gain percent? options: A)18 B)14 C)20 D)15 E)15.55 SOLUTION:450 ---- 70 100 ---- ? => 15.55% Answer: E #### E QUESTION:Solve below question 2x + 1 = -17 options: A)-8 B)-9 C)9 D)8 E)-7 SOLUTION:1. Subtract 1 from both sides: 2x + 1 - 1 = -17 - 1 2. Simplify both sides: 2x = -18 3. Divide both sides by 2: 4. Simplify both sides: x = -9 B #### B QUESTION:The variables a and b are non-zero integers W. If a = 2b^3/c, what happens to c when a is halved and b is doubled? options: A)c is not changed. B)c is halved. C)c is doubled. D)c is multiplied by 4. E)c is multiplied by 16. SOLUTION:a=2b^3/c c=2b^3/a when a is halved and b is doubled c=2(2b)^3/(a/2) c=16*2b^3/a Ans. E c is multiplied by 16. #### E QUESTION:A four-digit code can consist of the digits 0 ~ 9 except that it does not contain the digits 1, 2, 4, and 6 at all. If repeated digits are allowed, what is the probability that it has at least one even digit? options: A)23/24 B)31/36 C)55/64 D)65/81 E)75/121 SOLUTION:P(no even digits) = 2/3*2/3*2/3*2/3 = 16/81 P(at least one even digit) = 1 - 16/81 = 65/81 The answer is D. #### D QUESTION:A basketball is dropped from a height of 40 feet. If it bounces back up to a height that is exactly half of its previous height, and it stops bouncing after hitting the ground for the fourth time, then how many total feet will the ball have traveled after 3 full bounces. options: A)50 B)55 C)110 D)75 E)80 SOLUTION:Initial distance = 40 feet first bounce = 20 feet up + 20 feet down = 40 feet second bouche = 10 feet up + 10 feet down = 20 feet third bounce = 5 feet up and 5 feet down= 10 feet total distance covered = 40+40+20+10= 110 ANSWER IS C #### C QUESTION:Tough and Tricky questions: Number Properties. If (z + 3)/6 is an integer, what is remainder when z is divided by 6? options: A)2 B)3 C)4 D)5 E)6 SOLUTION:6/6=1 Ans B #### B QUESTION:If x and y are integers and x + y = 5, which of the following must be true? options: A)x and y are consecutive integers. B)If x < 0, then y > 0. C)If x > 0, then y < 0. D)Both x and y are even. E)Both x and y are less than 5. SOLUTION:Notice that the question asks which of the following MUST be true, not COULD be true. Given: x + y = 5 A. x and y are consecutive integers: not necessarily true, for example x=1 and y=4; B. 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; C. If x > 0, then y < 0: not necessarily true, for example x=1 and y=4; D. 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; E. Both x and y are less than 5: not necessarily true, for example x=6 and y=-1; Answer: B. #### B QUESTION:What is the median from the below series 90, 93, 93, 88, 95, 88, 97, 87, and 98 options: A)80 B)85 C)93 D)97 E)100 SOLUTION:Ordering the data from least to greatest, we get: 87, 88, 88, 90, 93, 93, 95, 96, 98 The median quiz score was 93. (Four quiz scores were higher than 93 and four were lower.) C #### C QUESTION:A retailer buys 140 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 % ? options: A)105 B)155 C)125 D)185 E)285 SOLUTION:let the market price of each pen be $1 then, Cost Price of 140 pens = $ 36 Selling Price of 140 pens =99% of $140=$ 138.60 profit %=((102.60*100)/36) %=285% Answer E #### E QUESTION:The 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 younger child insists of standing by his dog? options: A)12 B)24 C)30 D)48 E)120 SOLUTION:We need to find the number of arrangements of Father, Mother, Child-1, Child-2, and a Dog, so that C2 and D are always together. Consider F and M to be one unit, then we would have total of four units: {F}, {M}, {C1}, {C2D}. The number of arrangements of these four units is 4!, but C2 and D within their unit can be arranged in 2 ways: {C2D} or {DC2}, so total number of arrangements is 4!*2=48. Answer: D #### D QUESTION:The population of a bacteria colony doubles every day. If it was started 6 days ago with 2 bacteria and each bacteria lives for 12 days, how large is the colony today? options: A)512 B)768 C)1024 D)2048 E)128 SOLUTION:2^6(2) = 2^7 = 128 The answer is E. #### E QUESTION:Two 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? options: A)270 B)277 C)200 D)257 E)271 SOLUTION:Relative speed = (72 - 36) * 5/18 = 2 * 5 = 10 mps. Distance covered in 27 sec = 20 * 10 = 200 m. The length of the faster train = 200 m. Answer: C #### C QUESTION:By travelling at 60 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? options: A)30 kmph B)28 kmph C)26 kmph D)24 kmph E)22 kmph SOLUTION:Let the time taken to reach the destination be 3x hours. Total distance = 60 * 3x = 180x km He covered 2/3 * 180x = 120x km in 1/3 * 3x = x hours So, the remaining 60x km, he has to cover in 2x hours. Required speed = 60x/2x =30 kmph. Answer: A #### A QUESTION:At a monthly meeting, 2/3 of the attendees were males and 3/4 of the male attendees arrived on time. If 5/6 of the female attendees arrived on time, what fraction of the attendees at the monthly meeting did not arrive on time? options: A)1/3 B)1/4 C)3/8 D)2/9 E)5/18 SOLUTION:Males who did not arrive on time are 1/4*2/3 = 1/6 of the attendees. Females who did not arrive on time are 1/6*1/3 = 1/18 of the attendees. The fraction of all attendees who did not arrive on time is 1/6 + 1/18 = 2/9 The answer is D. #### D QUESTION:In a exam there are 26 number of question. For one write question add 8 marks and for one wrong 5 marks subtract. One candidate answered all questions. His marks is 0. How many answers was correct? options: A)9 B)10 C)11 D)12 E)13 SOLUTION:let no. of right ques be x, then no. of wrong ques will be= 26 - x now, according to ques 8x - (26-x)5 = 0, hence x=10...no. of right ques is 10 ANSWER:B #### B QUESTION:Which of the following options is an appropriate approximate value in the following equation’? 3 4/3 of 155.83+22% of 1547= ? - 504.7 options: A)1855.94 B)1557.94 C)1257.94 D)1837.94 E)1857.94 SOLUTION:3 4/3 of 155.83+22% of 1547= ? - 504.7 1012.9+340.34= ? - 504.7 1012.9+340.34 +504.7= ? ≈ 1857.94 Answer E #### E QUESTION:A bus starts from city X. The number of women in the bus is half of the number of men. In city Y, 14 men leave the bus and seven women enter. Now, number of men and women is equal. In the beginning, how many passengers entered the bus ? options: A)63 B)30 C)36 D)45 E)46 SOLUTION:Explanation: Originally, let number of women = x. Then, number of men = 2x. So, in city Y, we have : (2x - 14) = (x + 7) or x = 21. Therefore Total number of passengers in the beginning = (x + 2x) = 3x = 63. Answer: A #### A QUESTION:If the price of petrol increases by 44, by how much must a user cut down his consumption so that his expenditure on petrol remains constant? options: A)25% B)20% C)16.67% D)33.33% E)None of these SOLUTION:Explanation : let us assume before increase the petrol will be Rs. 100. After increase it will be Rs (100+44) i.e 144. Now, his consumption should be reduced to :- =(144−100)/144 ∗ 100. Hence, the consumption should be reduced to 30.6%. Answer : E #### E QUESTION:Find the largest number of four digits which is exactly divisible by 27,18,16,15 options: A)8600 B)8610 C)8620 D)8630 E)8640 SOLUTION:Explanation: LCM of 27-18-16-15 is 2160. After dividing 9999 by 2160 we get 1359 remainder. So answer will be 9999-1359 = 8640 Option E #### E QUESTION:A 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 : options: A)Rs.80 B)Rs.115.20 C)Rs.120 D)Rs.125.40 E)None of these SOLUTION:Explanation: For an income of Rs. 10, investment = Rs. 96. For an income of Rs. 12, investment = (96/10x12) =115.20 Answer: B #### B QUESTION:A 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? options: A)200 B)992 C)772 D)662 E)552 SOLUTION:Profit on first article = 20% of 1000 = 200. This is equal to the loss he makes on the second article. That, is he makes neither profit nor loss. Answer: A #### A QUESTION:Two 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’s amount. At the end of the year 25% profit was earned which was equal to 98,000. What was the amount invested by R? options: A)2,10,000 B)1,05,000 C)1,75,000 D)84,000 E)None of these SOLUTION:Ratio for amount invested by P, Q & R = 5x × 12 : 6x × 12 : 6x × 6 = 60x : 72x : 36x = 5x : 6x : 3x Profit = 98000 = 25% of T where, T = Total amount T = 392000 Amount received by R = 3x /3x+6x+5x(392000) = 84000 Answer D #### D QUESTION:If y ≠ 3 and 2a/y is a prime integer greater than 2, which of the following must be true? I. xa= y II. y = 1 III. a and y are prime integers. options: A) None B) I only C) II only D) III only E) I and II SOLUTION:Note that we are asked which of the following MUST be true, not COULD be true. For such kind of questions if you can prove that a statement is NOT true for one particular set of numbers, it will mean that this statement is not always true and hence not a correct answer. So we should try to make the listed statements not true for some x and y (which satisfy y≠3 and 2x/y=prime>2). I. a = y --> not necessarily true: a=3 and y=2 (2a/y=3=prime>2); II. y=1 --> not necessarily true: a=3 and y=2 (2a/y=3=prime>2); III. a and y are prime integers --> not necessarily true: a=10 and y=4 (2a/y=5=prime>2). Answer: A. #### A QUESTION:4 bells first begin to toll together with an intervals of 5, 10, 15 & 20 sec. How many times does they toll together in an hr? options: A)50 B)60 C)70 D)80 E)90 SOLUTION:5|5, 10, 15, 20 2|1, 2, 3, 4 |1, 1, 3, 2 L.C.M of 5, 10, 15, 20 is 60 60 times B #### B QUESTION:Zoey 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? options: A)$3 B)$2 C)$9 D)$1 E)$4 SOLUTION:Zoey 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. #### D QUESTION:The price of a laptop . 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? options: A)A)19009 B)B)19074 C)C)19008 D)D)19000 E)E)19002 SOLUTION:Explanation: Money paid in cash = R . 1000 Balance payment = (20000 - 1000) = Rs. 19000 Answer: Option D #### D QUESTION:The area of a parallelogram is 128sq m and its altitude is twice the corresponding base. Then the length of the base is? options: A)8 B)9 C)7 D)6 E)5 SOLUTION:2x * x = 128 => x= 8 Answer: A #### A QUESTION:A family X went for a vacation. Unfortunately it rained for 13 days when they were there. But whenever it rained in the mornings, they had clear afternoons and vice versa. In all they enjoyed 11 mornings and 12 afternoons. How many days did they stay there totally? options: A)16 B)18 C)20 D)13 E)14 SOLUTION:Explanation : Clearly 11 mornings and 12 afternoons = 23 half days => Since 13 days raining means 13 half days. => So 23-13 =10 halfdays ( not effecetd by rain ) => So 10 halfdays =5 fulldays Hence , Total no. of days = 13+5 =18 days Answer : B #### B QUESTION:The total of the ages of Amar, Akbar and Anthony is 40 years. What was the total of their ages two years ago ? options: A)71 B)44 C)36 D)16 E)18 SOLUTION:Explanation: Required sum = (40 - 3 x 2) years = (40 - 6) years = 36 years. Answer: C #### C QUESTION:The difference between the compound interest compounded annually and simple interest for 2 years at 20% per annum is Rs.144. Find the principal? options: A)3377 B)2997 C)3600 D)2799 E)7719 SOLUTION:P = 144(100/5)2 => P = 3600 Answer:C #### C QUESTION:Y and Z started a business investing Rs. 70,000 and Rs. 30,000 respectively. In what ratio the profit earned after 5 years be divided between Y and Z respectively? options: A)6:3 B)3:7 C)7:3 D)3:6 E)None of these SOLUTION:Y:Z = 70000 : 30000 = 7:3. ANSWER:C #### C QUESTION:For any non-zero a and b that satisfy |ab| = -ab and |a| = -a, |b-4| + |ab-b| = options: A)ab-4 B)2b-ab-4 C)ab+4 D)ab-2b+4 E)4-ab SOLUTION:Given: |ab| = -ab and |a| = -a Question: |b-4| + |ab-b| = ? **** Looking at |ab| = -ab tells us that either one of a or b is negative. **** Looking at |a| = -a tells us that a must be negative **** Combine two observations: b is positive Let a=-1 and b=1 |b-4| + |ab-b| = |1-4| + |-1-1| = 5 Test a) |ab-4| = |(1)(-1)-4| = |-5|=5 Test b) 2b-ab-4 = (2)(1) - (-1) - 4 = -1 Test c) ab+4 = -1 + 4 = 3 Test d) ab-2b+4 = -1-2(1)+4=1 test e) 4-1=3 ANSWER=A #### A QUESTION:If an amount of Rs 41,910 is distributed equally amongst 22 persons, how much amount would each person get? options: A)Rs 1905 B)Rs 2000 C)Rs 745 D)Rs 765 E)None SOLUTION:Required amount =41910/22 = Rs 1905 Answer A #### A QUESTION:Anand and Deepak started a business investing Rs. 4,500 and Rs. 6,000 respectively. Out of a total profit of Rs. 420. Deepak's share is? options: A)s. 280 B)s. 310 C)s. 240 D)s. 840 E)s. 400 SOLUTION:Ratio of their shares = 4500 : 6000 = 3 : 4 Deepak's share = Rs. (420 * 4/7) = Rs. 240 ANSWER "C #### C QUESTION:Of 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? options: A)81 B)159 C)166 D)285 E)304 SOLUTION:I solve it using the tough luck technique: According 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. 80 books of the same science subjects is possible only for two subjects: Physics=90>80 OR Chemistry=100>80 Now, we need to be certain that out of the books we picked, there are either at least 80 physics books or 80 chemistry books What if we pick the first 80 books and none of them is either Physics or Chemistry. Possible. Thus, we first count all our negatives. We picked: 50 Botany Books 65 Zoology Books 30 Geology Books Now, 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!! Thus, in order to make sure that we have 80 books of either of these 2 subjects, we must pick 79*2+1 books Because, we could have picked the books in following order; 1st book picked: Physics 2nd book picked: Chemistry 3rd book picked: Physics Thus, Total= 50+65+30+79*2+1=145+1+158=304 Ans:E #### E QUESTION:The diagonal of a rhombus are 40 m and 30 m. Its area is: options: A)600 B)450 C)350 D)500 E)620 SOLUTION:Area of the rhombus = 1/2 d1d2 = ( 1/2 × 40 × 30) Cm(power)2 = 40 × 15 = 600 Cm(power)2 Answer is A. #### A QUESTION:For how many integer values of n will the value of the expression 4n + 7 be an integer greater than 1 and less than 60? options: A)10 B)15 C)8 D)12 E)20 SOLUTION:4n+7 > 1 4n> -6 n > -(3/2) n> -1.5 (n = -1, 0, 1 ,2 3........ upto infinity) From second constraint 4n+7 < 60 4n< 53 n < 13. 25 n = (-infinity, .......-3, -2, -1, 0, 1, 2, .........upto 13) Combining the two -1.5 < n<13.25 n = 1 to 13 (48 integers) and n = -1 and 0 so 15 integers. B #### B QUESTION:The ratio of the volumes of two cubes is 729 : 1331. What is the ratio of their total surface areas? options: A)81 : 121 B)81 : 127 C)81 : 191 D)81 : 161 E)81 : 182 SOLUTION:Explanation: Ratio of the sides = ³√729 : ³√1331 = 9 : 11 Ratio of surface areas = 92 : 112 = 81 : 121 Answer: Option A #### A QUESTION:Each student at a certain university is given a four-character identification code, the rest two characters of which are digits between 0 and 9, inclusive, and the last two characters of which are selected from the 26 letters of the alphabet. If characters may be repeated and the same characters used in a different order constitute a different code, how many different identification codes can be generated following these rules? options: A)135,200 B)67,600 C)64,000 D)60,840 E)58,500 SOLUTION:First two parts for the code, are digits between 0-9, therefore, 10 options for the first part of the code, and as characters may be repeated, 10 options for the second part as well Therefore, we have 10 X 10 possibilities for the first and second part of the code Last two parts of the code, are characters selected from the 26 letters of the alphabet, therefore, 26 options for the third part of the code, and as characters may be repeated, 26 options for the fourth part as well Therefore, we have 26 X 26 possibilities for the third and fourth part of the code so, in all total no. of different identification codes generated following these rules = 10 X 10 X 26 X 26 = 67600 Answer B #### B QUESTION:Meena bought a watch with 25% discount on the selling price. If the watch cost her Rs.1545. What is the original selling price of the watch? options: A)Rs.2050 B)Rs.2040 C)Rs.2030 D)Rs.2060 E)None of these SOLUTION:Explanation: CP of Meenal is 75% of the Original SP. :. Original SP = 1545x100/75 = Rs.2060. Answer: Option D #### D QUESTION:A certain list of 300 test scores has an arithmetic mean of 74 and a standard deviation of d, where d is positive. Which of the following two test scores, when added to the list, must result in a list of 302 test scores with a standard deviation less than d? options: A) 75 and 80 B) 80 and 85 C) 74 and 74 D) 75 and 75 E) 70 and 80 SOLUTION:Ans: C Deviation means spreading of the numbers from one median point value.. as the set is already established and we need to add only two numbers, this means we can only add numbers which are closer to the median to reduce the deviation. so 74 and 74 are the most close numbers and they will increase the number of elements in the set without changing the median value. C #### C QUESTION:The overall age of X and Y is 19 year greater than the overall age of Y and Z. Z is how many decades younger that X? options: A)11 B)15 C)12 D)19 E)20 SOLUTION:D 19 (X + Y) – (Y + Z) = 19 X – Z = 19 #### D QUESTION:If the simple interest on a sum of money for 2 years at 5% per annum is Rs. 52, what is the compound interest on the same sum at the rate and for the same time? options: A)s. 53.30 B)s. 53.22 C)s. 51.219 D)s. 53.18 E)s. 51.10 SOLUTION:Explanation: Sum = (52 * 100) / (2 * 5) = Rs. 520 Amount = [520 * (1 + 5/100)2] = Rs. 573.3 C.I. = (573.3 - 520) = Rs. 53.30. Answer:A #### A QUESTION:By selling 50 meters of cloth. I gain the selling price of 15 meters. Find the gain percent? options: A)42 8/7% B)42 6/4% C)42 6/7% D)42 3/7% E)42 6/9% SOLUTION:SP = CP + g 50 SP = 50 CP + 15 SP 35 SP = 50 CP 35 --- 15 CP gain 100 --- ? => 42 6/7% Answer: D #### D QUESTION:A certain list consists of 21 different numbers. If n is in the list and n is 5 times the average (arithmetic mean) of the other 20 numbers in the list, then n is what fraction of the sum of the 21 numbers in the list? options: A)1/20 B)1/6 C)1/5 D)4/21 E)5/21 SOLUTION:series : a1, a2....a20,n sum of a1+a2+...+a20 = 20*x (x = average) so, n = 5*x Hence, a1+a2+..+a20+n = 25x So, the fraction asked = 5x/25x = 1/5 Answer C #### C QUESTION:The perimeter of a rectangular yard is completely surrounded by a fence that measures 36 meters. What is the length of the yard if the area of the yard is 40 meters squared? options: A)12 B)10 C)8 D)14 E)16 SOLUTION:Perimeter of rectangular yard = 2(l + b) = 36 --> l + b = 18 Area = l * b = 40 b = 18 - l l(18 - l) = 40 18l - l^2 = 40 l^2 - 18l + 40 = 0 Upon simplifying we get l = 5 or 8. Only 8 is there in the answer choice. Answer: C #### C QUESTION:12 litres of water are poured into an aquarium of dimensions 50cm length, 30cm breadth, and 40cm height. How high (in cm) will the water rise? (1 litre = 1000cm³) options: A)6 B)8 C)10 D)20 E)40 SOLUTION:we have 1 litre = 1000cm³ (thanks Bunuel) =>12 litres = 12*1000 = 12000cm³ Let call the height of the water is x the breadth and length of the water will equal the aquarium The volume of the water: 50 * 30 * x = 12000cm³ => x = 12000/(50*30) = 8 cm Answer is B #### B QUESTION:Find the number which is nearest to 3105 and is exactly divisible by 21 options: A)1208 B)3108 C)241 D)217 E)3147 SOLUTION:On dividing 3105 by 21, we get 18 as remainder. Number to be added to 3105 = (21 - 18) - 3. Hence, required number = 3105 + 3 = 3108. ANSWER B 3108 #### B QUESTION:Tom 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 ? options: A)1/2 B)2/5 C)2/3 D)3/7 E)3/11 SOLUTION:Ashwini hits the target definitely, hence required probability that atleast 2 shots hit the target is given by Karan hits tha target and Raja not hit the target. or Karan does not hit the target and Raja hits the target. or. Karan hits the target and Raja hits the target = 2/6 x 3/6 + 4/6 x 3/6 + 2/6 x 3/6 = 24/36 = 2/3 C #### C QUESTION:If x^2 - 1 = 0 and x < 0, which of the following must be equal to 0 ? options: A) x^2 - 9x B) x^2 - 9x + 20 C) x^2 - 2x + 3 D) x^2 + 2x + 1 E) x^2 + 5x + 6 SOLUTION:x^2-1 = 0 x= +1 or x = -1 if we substitute x= -1 in the equation x^2 +2x+1 = 1-2+1 = 0 D is also the answer #### D QUESTION:Find the one which does not belong to that group ? options: A)3 B)4 C)5 D)9 E)7 SOLUTION:Explanation: 3, 5, 9 and 7 are odd numbers, but not 4. ANSWER IS B #### B QUESTION:Find the length of the wire required to go 12 times round a square field containing 104976 m2. options: A)15840 B)3388 C)2667 D)8766 E)15552 SOLUTION:a2 = 104976 => a = 324 4a = 1296 1296 * 12 = 15552 Answer: E #### E QUESTION:Albert buys 4 horses and 9 cows for Rs. 13,400. If he sells the horses at 10% profit and the cows at 20% profit, then he earns a total profit of Rs. 1880. The cost of a horse is: options: A)Rs. 1000 B)Rs. 2000 C)Rs. 2500 D)Rs. 3000 E)Rs. 3500 SOLUTION:Let C.P. of each horse be Rs. x and C.P. of each cow be Rs. y. Then, 4x + 9y = 13400 -- (i) And, 10% of 4x + 20% of 9y = 1880 2/5 x + 9/5 y = 1880 => 2x + 9y = 9400 -- (ii) Solving (i) and (ii), we get : x = 2000 and y = 600. Cost price of each horse = Rs. 2000. ANSWER:B #### B QUESTION:If a wagon wheel had 10 more spokes, the angle between them would decrease by 6 degrees. Can you identify the number of spokes in the wheel? options: A)20 spokes B)10 spokes C)30 spokes D)15 spokes E)25 spokes SOLUTION:A 20 spokes 360/S = A 360/(S +10) = A – 6 Thus there are 20 spokes in the wheel. #### A QUESTION:Two pipes A and B can fill a tank in 50hour and 75 hours respectively. If both the pipes are opened simultaneously, how much time will be taken to fill the tank? options: A)15hrs B)20hrs C)25hrs D)30hrs E)32hrs SOLUTION:Part filled by A in 1 hour = 1/50 part filled by B in 1 hour = 1/75 Part filled by A+B in 1 hour = 1/50 + 1/75 = 1/30 Both the pipes will together will fill the tank in 30 hours. Answer is D #### D QUESTION:If KING is coded as 17 and MASS is coded as 29 Then DON is coded as options: A)12 B)16 C)18 D)None E)cannot be determined SOLUTION:Explanation : KING = 11+9+14+7=41 i.e (4*4)+(1*1)=17 MASS = 13+1+19+19=52 i.e (5*5)+(2*2)=29 DON = 4+14+15=33 i.e(3*3)+(3*3)=18 Hence (C) is correct Answer : C #### C QUESTION:The volume of a cube is 3375 cc. Find its surface. options: A)1350 B)1150 C)1456 D)1254 E)1489 SOLUTION:a3 = 3375 => a = 15 6a2 = 6 * 15 * 15 = 1350 Answer: A #### A QUESTION:If a number between 0 and 1/2 is selected at random, which of the following will the number most likely be between? options: A)0 and 3/20 B)3/20 and 1/5 C)1/5 and 1/4 D)1/4 and 3/10 E)3/10 and 1/2 SOLUTION:A. 0 and 3/20 - covers 0 to 3/20 but leaves out 3/20 to 10/20. So in essence, covers only 3 parts out of 10 parts B. 3/20 and 1/5 - covers 3/20 to 4/20 (= 1/5). So in essence, covers only 1 part out of 10 parts C. 1/5 and 1/4 - covers 4/20 to 5/20. So in essence, covers only 1 part out of 10 parts D. 1/4 and 3/10 - covers 5/20 to 6/20. So in essence, covers only 1 part out of 10 parts E. 3/10 and 1/2 - covers 6/20 to 10/20. So in essence, covers 4 parts out of 10 parts. Since this range is the widest, so the probability of the number lying in this range is the highest. Answer (E) #### E QUESTION:The price of a certain painting increased by 30% during the first year and decreased by 20% during the second year. The price of the painting at the end of the 2-year period was what percent of the original price? options: A)102% B)105% C)120% D)135% E)104% SOLUTION:Easiest thing to do: Assume that price is 100 Price at the end of yr 1: 100+ 30 = 130 Price at the end of year 2 = 130 - 130*0.20 = 130*0.80 = 104 Hence required answer = (104/100)*100% = 104% Answer is E. #### E QUESTION:36 men can complete a piece of work in 18 days. In how many days will 27 men complete the same work? options: A)12 B)18 C)22 D)24 E)none of these SOLUTION:Let the required number of days be x. Less men, More days (Indirect Proportion) 27 : 36 :: 18 : x 27 * x = 36 * 18 x = (36 * 18)/27 x = 24. Answer is D. #### D QUESTION:A 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. options: A)310 meter B)335 meter C)345 meter D)350 meter E)375 meter SOLUTION:Explanation: Speed = Distance/time = 300/18 = 50/3 m/sec Let the length of the platform be x meters then Distance=Speed∗Timex+300=50/3 X 39 =>3(x+300)=1950=>x=350 meters ANSWER IS D #### D QUESTION:If 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? options: A)22 B)40 C)28 D)21 E)27 SOLUTION:A.M. of 75 numbers = 35 Sum of 75 numbers = 75 * 35 = 2625 Total increase = 75 * 5 = 375 Increased sum = 2625 + 375 = 3000 Increased average = 3000/75 = 40. Answer: B #### B <<<Examples ends QUESTION:A boat having a length 7 m and breadth 3 m is floating on a lake. The boat sinks by 1 cm when a man gets on it. The mass of the man is: options: A)100 kg B)120 kg C)89 Kg D)80 Kg E)210 Kg SOLUTION:Volume of water displaced = (7 x 3 x 0.01) m3 = 0.21 m3. Mass of man = Volume of water displaced x Density of water = (0.21 x 1000) kg = 210 kg. Answer: E #### E

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:A and B invests Rs.4000 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? options: A)3:5 B)3:8 C)3:2 D)9:9 E)3:1 SOLUTION:(4*6 + 8*6): (4*12) 72:48 => 3:2 Answer:C #### C QUESTION:In a division sum, the divisor is ten times the quotient and five times the remainder. If the remainder is 44, the dividend is: options: A)4884 B)5340 C)5342 D)5345 E)5356 SOLUTION:Divisor = (5 * 44) = 220 = 10 * Quotient = Divisor => Quotient = 220/10 = 22 Dividend = (Divisor * Quotient) + Remainder Dividend = (220 * 22) + 44 = 4884. A #### A QUESTION:If 7 spiders make 7 webs in 7 days, then 1 spider will make 1 web in how many days? options: A)7 B)6 C)5 D)4 E)3 SOLUTION:Let the required number days be x. Less spiders, More days (Indirect Proportion) Less webs, Less days (Direct Proportion) spiders 1:7 Webs 7:1 1 x 7 x x = 7 x 1 x 7 => x= 7 Answer is 7 #### A QUESTION:For every positive even integer n, the function h(n) is defined to be the product of all the even integers from 2 to n, inclusive. If p is the smallest prime factor of h(100) +1, then p is? options: A)between 2 and 20 B)between 10 and 20 C)between 20 and 30 D)between 30 and 40 E)greater than 40 SOLUTION:SOL: Lets consider h(100): => 2*4*6*8.........*98*100 => (2*1) * (2 * 2) * (2 * 3) * (2 * 4)............ * (2 * 49) * (2 * 50) => (2^50) * (1*2*3*4........*49*50) => h(100) = (2^50) * (50!) We can thus conclude that h(100) is divisible by every number from 1 to 50. Thus all the prime numbers between 1 and 50 are prime factors of h(100). But when 1 is added [h(100) + 1] is no more divisible by any of these prime numbers. Thus the smallest prime factor of [h(100) + 1] would have to be a number greater than 50; ANSWER:E #### E QUESTION:How many days will there be from 26th January,1996 to 15th May,1996(both days included)? options: A)102 B)103 C)111 D)120 E)201 SOLUTION:Explanation : Number of days from 26-Jan-1996 to 15-May-1996 (both days included) = 6(Jan) + 29(Feb) + 31 (Mar) + 30(Apr)+ 15(May) = 111 Answer : Option C #### C QUESTION:You can collect as many rubies and emeralds as you can. Each ruby is worth Rs. 4 crore and each emerald is worth Rs. 5 crore. Each ruby weighs 0.3 kg. And each emerald weighs 0.4 kg. Your bag can carry at the most 12 kg. What should you collect to get the maximum wealth? options: A)20 rubies and 15 emeralds B)40 rubies C)28 rubies and 9 emeralds D)None of these E)Cannot be determined SOLUTION:Explanation : The limits our wealth is the capacity of bag which is 12 Kg. So we should make each unit of weight to worth the max. Rubee: 0.3 Kg worth 4 Crore, so 1 Kg of Rubee is worth 4/(0.3) = 40/3 = 13.33 Crore. Emerald: 0.4 Kg worth 5 crore so 1 Kg of Emerald is worth 5/(0.4) = 50/4 = 12.5 Crore. As value per kilogram is more for Rubee we should pick max rubees for max wealth. Here we can accomadate the whole 12Kg with 40 rubees which is worth 160 Crore. Answer : B #### B QUESTION:The 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? options: A)1 B)2 C)8 D)7 E)0 SOLUTION:S = 4 M = x DS = x + 4 US = x - 4 6/(x + 4) + 6/(x - 4) = 2 x = 8 Answer: C #### C QUESTION:A cycle is bought for Rs.900 and sold for Rs.1125, find the gain percent? options: A)27% B)20% C)80% D)30% E)25% SOLUTION:900 ---- 225 100 ---- ? => 25% Answer: E #### E QUESTION:A certain university will select 1 of 7 candidates eligible to fill a position in the mathematics department and 3 of 10 candidates eligible to fill 3 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 4 candidates are there to fill the 4 positions? options: A)420 B)770 C)840 D)165 E)315 SOLUTION:1 of 7 will be chosen for the math 3 of 10 will be chosen for the computer None of the 4 chosen people can be in more than one departments. We can choose any of the 7 candidates for the math dep., which gives as 7 selections. We can choose 3 of the 10 candidates for the computer dep., which gives us 3 selections and 7 rejections. So, the way to find how many different selections of 2 candidates we can have for the computer dep., we do: 10! /3!*7!= 120 We are multiplying our individual selections: 7*120 = 840 In the bolded part, we don't have to multiply all of the numbers, as those in 8! are included in 10!, so we simplify instead. Ans C #### C QUESTION:A tank has both an inlet pipe and an outlet pipe. Working alone, the inlet pipe can fill up the tank in 4 hours. Working alone, the outlet pipe can empty out the tank in 10 hours. If it is desired that the tank should be filled, from empty, exactly 6 hours after the inlet pipe is turned on at 9:30am, then at what time should the outlet pipe be opened ? options: A)8:30am B)9:30am C)10:00am D)10:30am E)11:30am SOLUTION:In 6 hours the inlet pipe will pump in water equal to 6*1/4 = 6/4 of the pool. So, 2/4 more than necessary, which should be compensated by the outlet pipe. To pump out 2/4 of the water the outlet pipe needs 20/4 = 5 hours. Therefore, the outlet pipe should be opened at 9:30am + 6 hours - 5 hours = 10:30am. Answer: D #### D QUESTION:12 men take 18 days to complete a job whereas 12 women in 18 days can complete 1/3 of the same job. How many days will 10 men and 8 women together take to complete the same job? options: A)6 B)13 1⁄2 C)17 D)Data inadequate E)None of these SOLUTION:12 M × 18 = 12 W × 18 × 3/1 \ w = 1/3 M 10M + 8W = 10M + 8 × 1/3M = 12 2/3 M \12 2/3 men can complete the same work in 12×18/12 2/3=17days Answer C #### C QUESTION:An express traveled at an average speed of 100 km/hr, stopping for 3 min after every 75 kn. How long did it take to reach its destination 600 km from the starting point? options: A)6 hrs 21 min B)6 hrs 91 min C)6 hrs 01 min D)6 hrs 23 min E)3 hrs 21 min SOLUTION:Time taken to cover 600 km = 600/100 = 6 hrs. Number of stoppages = 600/75 - 1 = 7 Total time of stoppages = 3 * 7 = 21 min Hence, total time taken = 6 hrs 21 min. Answer:A #### A QUESTION:Ben is driving on the highway at x miles per hour. (One mile equals 5,280 feet.) Ben's tires have a circumference of t feet. Which of the following expressions gives the number of revolutions each wheel turns in one hour? options: A)5,280(x/t) B)5,280(y/x) C)5,280(xy) D)5,280/(xy) E)(xy)/5,280 SOLUTION:In one hour, at the rate of x miles per hour, Ben covers x miles, so 5,280x feet. The number of revolutions = distance/circumference = 5,280x/t. Answer: A. #### A QUESTION:Enrollment in City College in 1980 was 83 1/3 percent of enrollment in 1990. What was the percent increase in the college’s enrollment from 1980 to 1990? options: A)10% B)16 2/3 % C)20% D)25% E)183 1/3% SOLUTION:Let 100 is the enrollment in 1990. Enrollment in 1980= 83.3 % increase= (Increase from 1980 to 1990)/Enrollment in 1983 =>16.7*100/83.3 =20% ANSWER:C #### C QUESTION:Income and expenditure of a person are in the ratio 5 : 4. If the income of the person is Rs. 15000, then find his savings? options: A)3600 B)3607 C)3608 D)3602 E)3000 SOLUTION:Let the income and the expenditure of the person be Rs. 5x and Rs. 4x respectively. Income, 5x = 15000 => x = 3000 Savings = Income - expenditure = 5x - 4x = x So, savings = Rs. 3000. Answer:E #### E QUESTION:Two consecutive traffic signals each show either red or green. How many different arrangements of the two signals are possible? (Note: “Red-green” is different from “green-red.”) options: A)10 B)9 C)8 D)7 E)4 SOLUTION:Since 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. We're told that 2 consecutive traffic signals each show either red or green. We're asked how many different arrangements of the 2 signals are possible. Total Options: 4 Final Answer: E #### E QUESTION:30% of all fishermen in Piscataquis County are also hunters while only 20% of all hunters are fishermen. If there are 1500 hunters in Piscataquis County then how many fishermen are there? options: A)800 B)1000 C)1200 D)1500 E)1800 SOLUTION:800score Official Solution: People who do both hunting and fishing make 30% of fishermen and 20% of hunters. There are 1500 hunters so 1500 × 20% = 300 pers. do both hunting and fishing. Same people make 30% of all fishermen.30% of fishermen = 300 pers. Fishermen = (300 / 30) × 100 pers. = 1000 pers. The correct answer is choice (B). #### B QUESTION:How many different positive integers exist between 10^3 and 10^4, the sum of whose digits is equal to 2? options: A)6 B)7 C)5 D)4 E)18 SOLUTION:So, the numbers should be from 1,000 to 10,000 The following two cases are possible for the sum of the digits to be 2: 1. Two 1's and the rest are 0's: 1,001 1,010 1,100 3 numbers. 2. One 2 and the rest are 0's: 2,000 1 number. Total = 4 numbers. Answer:D #### D QUESTION:A mixture of 85 kg contains milk and water in the ratio 27 : 7. How much more water is to be added to get a new mixture containing milk and water in the ratio 3:1? options: A)5 kg B)6.5 kg C)7.5 kg D)8 kg E)9 kg SOLUTION:Milk in 85 kg of mix = 85* (27/34) = 135/2 kg. Water in it = 85-135/2 = 35/2 kg. Let x kg of water be added to it. Then, (135/2)/(35/2 + x) = 3/1; 135/(35 +2x) = 3/1; 105 + 6x = 135 ; 6x = 30; x = 5 The quantity of water to be added = 5 kg ANSWER:A #### A QUESTION:I have a three digit number in my mind. In that number, the tens digit is seven more than the ones digit and the hundreds digit is six less than the tens digit. What is the number? options: A)281 B)239 C)254 D)276 E)277 SOLUTION:A 281 #### A QUESTION:A alone can complete a work in 16 days and B alone can complete in 12 days. Starting with A they work on alternate days. The total work will be completed in? options: A)12 B)13 C)13 5/7 D)13 ¾ E)None of these SOLUTION:Explanation: (A+B)’s 2 day work = 1/16 + 1/12 = 7/18 work done in 6 pairs of days=7/48 x 6 = 7/8 remaining work = 1/8 work done by A on 13th day =1/16 remaining work = 1/16 on 14th day its B turn 1/12 work is done by B in 1 day 1/16 work is done by B in 12 x 1/16 = 3/4 day total time taken =13 ¾ days Answer: Option D #### D QUESTION:factor: 3y (x-3)-2(x-3) options: A)(x-3)-2(x-3) B)(x-3)power2 C)(x-3)(3y-2) D)3y(x-3) E)x-3 SOLUTION:3y(x-3)-2(x-3), = (x-3)(3y-2). Answer: (C) #### C QUESTION:Set P consists of integers {3, -8, Y, 19, -6} and set B consists of integers {k, -3, 0, 16, -5, 9}. Number L represents the median of set P, number M represents mode of set B and number Z = L^M. If Y is an integer greater than 21, for what value of k will Z be a divisor of 26? options: A)-2 B)-1 C)0 D)1 E)2 SOLUTION:P = {3,-8,Y,19,-6} B = {k,-3,0,16,-5,9} Y > 21 So L = Median of P = 3 M = Mode of Set B Z = (3)^M If Z is a divisor of 26, (3)^M = 1 because 26 does not have 3 as a factor => M = 0 Hence k = 0, as M is mode and 0 will be the most frequently occuring number in set B. Answer - C #### C QUESTION:The difference between a number and its three-fifths is 50.What is the number? options: A)75 B)100 C)125 D)Cannot be determined E)None of these SOLUTION:Suppose the number is N. Then N - 3⁄5N = 50 ⇒ 2N⁄5 = 50 ∴ N=50×52=125 Answer.C #### C QUESTION:The average weight of 5 person's increases by 4 kg when a new person comes in place of one of them weighing 50kg. What is the weight of the new person? options: A)70 B)86.5 C)80 D)88.5 E)75 SOLUTION:Total increase in weight =5 × 4=20 If x is the weight of the new person, total increase in weight = x−50 => 20= x - 50 => x = 20+50= 70 ANSWER:A #### A QUESTION:What least no. must be subtracted from 5026 so that remaining no.is divisible by 5? options: A)3 B)4 C)5 D)6 E)1 SOLUTION:Explanation: On dividing 5026 by 5 we get the remainder 1, so 1 should be subtracted Option E #### E QUESTION:A 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. options: A)73.41 B)74.31 C)72.43 D)73.43 E)73.82 SOLUTION:Total marks = 35 x 72 =2520 Corrected total marks = 2520 - 35 + 99 =2584 Correct Average = 2584/35 = 73.82 Answer : E #### E QUESTION:Monica 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 4 muffins remained. How many guests did Monica plan on? options: A)3. B)4. C)5. D)6. E)7. SOLUTION:Let x be the number of guests. Number of muffins prepared = 5x + 2 Number of muffins eaten + Number of muffins remaining = Number of muffins prepared 6(x - 1) + 4 = 5x + 2 6x - 4 = 5x + 2 x = 6 Answer: D #### D QUESTION:If there is exactly one root of the equation x^2 + ax - b, where a and b are positive constants, what is b in terms of a? options: A)a/2 B)a C)-a^2/4 D)a^2/2 E)a^2/4 SOLUTION:one root for a quadratic equation ax^2+bx+c is possible only when b^2 = 4ac ---1 Here b = a c= b a = 1 substituting these values in 1, we have a^2 = -4b => b =-a^2/4 Answer is C. #### C QUESTION:8500 + (1600 ÷ ?) of 1/5 = 8501 options: A)310 B)312 C)320 D)325 E)345 SOLUTION:Explanation: => 8500 + (1600/?) × 1/5 = 8501 => 1600/? × 1/5 = 8501 - 8500 = 1 => ? = 1600/5 = 320 Answer: Option C #### C QUESTION:A painting at an art gallery is framed such that the area of the square frame is 1/2 the area of the painting itself. If the diagonal line connecting corners of the frame has a length of 6, what is the area of the painting inside the frame? options: A)12 B)20 C)30 D)40 E)50 SOLUTION:Suppose side of the painting(which is a square) is a and side of the outer square(painting+frame) is b Area of painting = a^2 and we know that the area of the frame is (1/2) of that of the painting so Area of frame = (1/2) * a^2 Area of Frame + Painting = a^2 + (1/2)*a^2 = (3/2)*a^2 which is equal to b^2 Line connecting the corners of the frame is the diagonal of the outer square which is equal to b*sqrt2 so, b * sqrt2 = 6 so, b = 3 * sqrt2 b^2 = 18 we know that b^2 = (3/2)*a^2 so, a^2 = (2/3)*b^2 = (2/3)*18 = 12 And area of painting = a^2 = 12 So, answer will be A. #### A QUESTION:A copy machine, working at a constant rate, makes 35 copies per minute. A second copy machine, working at a constant rate, makes 75 copies per minute. Working together at their respective rates, how many copies do the two machines make in half an hour ? options: A)90 B)2,700 C)3,300 D)5,400 E)324,000 SOLUTION:Together the two machines make 35+75=110 copies per minute. So, in half an hour they will make 110*30=3,300 copies. Answer: C. #### C QUESTION:In how many different ways can the letters of the word 'OPTICAL' be arranged so that the vowels always come together? options: A)610 B)720 C)825 D)920 E)650 SOLUTION:Explanation: The word 'OPTICAL' has 7 letters. It has the vowels 'O','I','A' in it and these 3 vowels should always come together. Hence these three vowels can be grouped and considered as a single letter. That is, PTCL(OIA). Hence we can assume total letters as 5 and all these letters are different. Number of ways to arrange these letters =5!=5×4×3×2×1=120=5!=5×4×3×2×1=120 All the 3 vowels (OIA) are different Number of ways to arrange these vowels among themselves =3!=3×2×1=6=3!=3×2×1=6 Hence, required number of ways =120×6=720 ANSWER IS B #### B QUESTION:If w persons take y days to complete z similar jobs, how long does it take y persons to complete 1 such job? options: A)z B)x C)x/y D)z/x E)y/z SOLUTION:the Q doesn't seem to be having the any correct answer as a choice.. since we are looking for days, lets keep days in end and work out a solution.. w person can do z jobs in y days.. so w person can do 1 job in y/z days.. and 1 person can do 1 job in y^2/z days.. so y person can complete 1 job in y^2/zy=y/z.. so the answer should be y/z=E #### E QUESTION:A man can do a piece of work in 5days, but with the help of his son, he can finish it in 4days. In what time can the son do it alone? options: A)5 B)5 1/2 C)7 1/2 D)6 E)20 SOLUTION:Son's 1day work = 1/4 - 1/5 = 1/20 Son alone can do the work in 20days = 20 days Answer is E #### E QUESTION:A man buys an item at Rs. 750 and sells it at the loss of 20 percent. Then what is the selling price of that item options: A)Rs. 660 B)Rs. 760 C)Rs. 600 D)Rs. 960 E)None of these SOLUTION:Explanation: Here always remember, when ever x% loss, it means S.P. = (100 - x)% of C.P when ever x% profit, it means S.P. = (100 + x)% of C.P So here will be (100 - x)% of C.P. = 80% of 750 = 80/100 * 750 = 600 Option C #### C QUESTION:When a merchant imported a certain item, he 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 $94.50, what was the total value of the item? options: A)$2,350 B)$2,850 C)$3,250 D)$3,400 E)$3,750 SOLUTION:Let x be the value in excess of $1,000. 0.07x = 94.5 x = $1,350 The total value was $1,350 + $1,000 = $2,350. The answer is A. #### A QUESTION:When 3 fair coins are tossed simultaneously, in how many outcomes will the first and the last coin turn up heads? options: A)1 B)2 C)8 D)31 E)30 SOLUTION:Total outcome is 2^3 = 8 Favourable cases = H_ H The second place can be occupied by either H or T There are 2^1 =2 ways that can be done. Hence, the correct option is B #### B QUESTION:On a map the distance between two mountains is 310 inches. The actual distance between the mountains is 136 km. Ram is camped at a location that on the map is 34 inch from the base of the mountain. How many km is he from the base of the mountain? options: A)14.83 B)14.81 C)14.91 D)14.82 E)14.12 SOLUTION:Explanation: Since 310 inch = 136 km So 1 inch = 136/310 km So 34 inch = (136 × 34)/ 310 = 14.91 km Answer: C #### C QUESTION:The speed at which a man can row a boat in still water is 14 kmph. If he rows downstream, where the speed of current is 2 kmph, what time will he take to cover 40 metres? options: A)16 seconds B)34 seconds C)9 seconds D)12 seconds E)15 seconds SOLUTION:Speed of the boat downstream = 14 + 2 = 16 kmph = 16 * 5/18 = 40/9 m/s Hence time taken to cover 40 m = 40*9/40 = 9 seconds. Answer: C #### C QUESTION:A train running at the speed of 60 km/hr crosses a pole in 30 seconds. What is the length of the train? options: A)500 m B)620 m C)872 m D)150 m E)765 m SOLUTION:Speed=(60 * 5/18) m/sec = (50/3) m/sec Length of the train = (Speed x Time) = (50/3 * 30) m = 500 m. Answer: A #### A QUESTION:If an integer n is to be chosen at random from the integers 1 to 94, inclusive, what is the probability that n(n + 1)(n + 2) will be divisible by 8? options: A)1/4 B)3/8 C)1/2 D)5/8 E)59/94 SOLUTION:n(n+1)(n+2) will be divisible by 8 when n is a multiple of 2 or when (n+1) is a multiple of 8. Thus when n is even, this whole expression will be divisible by 8. from 1 to 96, there are 47 even integers. Now when (n+1) is multiple by 8, we have 12 such values for (n+1) probability that n(n+1)(n+2) will be divisible by 8 = (47 + 12)/94 = 59/94 = 5/8 Ans is E #### E QUESTION:In how many ways can the letters of the word ARRANGED be arranged in a row so that the vowels appear in alphabetic order? options: A)6720 B)5280 C)6240 D)5202 E)4020 SOLUTION:three letters can be arranged in 3! ways. only one combination AEI is required. 8 letters can be arranged in 8! ways. thus 8!/ 3! * 1 = 6720. A #### A QUESTION:A 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 60 kmph. When and at what distance from Mumbai do the two trains meet? options: A)187 B)279 C)120 D)278 E)379 SOLUTION:When the second train leaves Mumbai the first train covers 40 * 1 = 40 km So, the distance between first train and second train is 40 km at 10.00am Time taken by the trains to meet = Distance / relative speed = 40 / (60 -40) = 2 hours So, the two trains meet at 12 a.m. The two trains meet 2 * 60 = 120 km away from Mumbai. Answer:C #### C QUESTION:The price of lunch for 10 people was $207 including a 15% gratuity for service. What was the average price per person, EXCLUDING the gratuity? options: A)11.73 B)12 C)13.8 D)14 E)18 SOLUTION:Clearly E is the answer I used POE here Lets consider option (E) 10*18= 180 now 180(115/100)=207 => possible ANSWER IMO E #### E QUESTION:What is the greatest of 3 consecutive integers whose sum is 27 ? options: A)6 B)7 C)8 D)9 E)11 SOLUTION:The sum of three consecutive integers can be written as n + (n + 1) + (n + 2) = 3n + 3 If the sum is 24, we need to solve the equation 3n + 3 = 27; => 3n = 27; => n = 9 The greatest of the three numbers is therefore 9 + 2 = 11 Answer: E #### E QUESTION:There are 1000 students in a school and among them 25 % of them attends chess class. 50% of the students who are in the chess class are also enrolled for swimming. No other students are interested in swimming so how many will attend the swimming class if all enrolled attends? options: A)1 B)10 C)125 D)50 E)20 SOLUTION:25% of 1000 gives 250. so 250 attends chess and 50% of 250 gives 125 so 125 enrolled for swimming Answer: C #### C QUESTION:Lottery 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? options: A)9/100 B)1/10 C)11/100 D)19/100 E)1/5 SOLUTION:Probability = No of balls with exactly one 1 / total number of balls = {1,10,12 to 19, 21,31,41,51,61,71,81,91,100}/100 = 19/100 Answer is D #### D QUESTION:Two 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? options: A)26 km/hr B)17 km/hr C)60 km/hr D)77 km/hr E)46 km/hr SOLUTION:Let the speed of the slower train be x m/sec. Then, speed of the train = 2x m/sec. Relative speed = ( x + 2x) = 3x m/sec. (100 + 100)/8 = 3x => x = 25/3. So, speed of the faster train = 50/3 = 50/3 * 18/5 = 60 km/hr. Answer:C #### C QUESTION:Three candidates contested an election and received 1130, 7530 and 11620 votes respectively. What percentage of the total votes did the winning candidate get? options: A)57% B)57.3% C)65% D)90% E)80% SOLUTION:total votes are 20280 ( sum of votes obtained by 3 candidates) percentage of the total votes recd by the winning candidate = 100*11620/20280 = 57.3% ANSWER:B #### B QUESTION:575.104 x 15.98 ÷ 9.001 + 21.25 = ? options: A)983.578 B)1043.65 C)1033.65 D)656.112 E)456.512 SOLUTION:Explanation: ? = 575.104 x 15.98 ÷ 9.001 + 21.25 ≈ (575.104 x 16/9) + 21.25 ≈ 1022.40 + 21.25 ≈ 1043.65 Answer: Option B #### B QUESTION:In the new budget the price of Petrol rose by 20%. By how much percent must a person reduce his consumption so that his expenditure on it does not increase? options: A)16.67% B)25% C)20.45% D)31.56% E)40% SOLUTION:Reduce in consumption = R/(100+R) *100% = 20/120 *100 = 16.67% Answer is A #### A QUESTION:A cube is painted red on all faces. It is then cut into 27 equal smaller cubes. How many J cubes are painted on only 2 faces? options: A)12 B)8 C)6 D)10 E)16 SOLUTION:1) Draw a simple cube 2) 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. 3) Remember that the OUTSIDE of the cube is the part that's painted.... The 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. J=4 + 4 + 4 = 12. Answer A #### A QUESTION:Let x be a positive integer, what is the remainder when 2^(3x+3)+3 is divided by 3? options: A)0 B)1 C)2 D)3 E)4 SOLUTION:For: (2^(3x+3)+3)/3 Let n = 3x + 3 2^n 2^1 = 2 2^2 = 4 2^3 = 8 2^4 = 16 2^5 = 32, last digit pattern repeats 2, 4, 8, 6, 2, .... Rule: x^(m+n) = (x^m)(x^n) (2^(3x))(2^3) Rule: x^(mn) = (x^m)^n ((2^3)^x)(8) => Now, (8)(8) + 3 = (64) + 3 => and, 4 + 2 + 1 => Finally, (6 + 1)/3, and remainder is 1. Answer: B #### B QUESTION:Three unbiased coins are tossed. What is the probability of getting at most two heads? options: A)3/4 B)7/8 C)3/8 D)5/6 E)9/11 SOLUTION:Here S = {TTT, TTH, THT, HTT, THH, HTH, HHT, HHH} Let E = event of getting at most two heads. Then E = {TTT, TTH, THT, HTT, THH, HTH, HHT}. P(E)=n(E)/n(S) =7/8 The answer should be B #### B QUESTION:man is 36 years older than his son. In two years, his age will be twice the age of his son. The present age of his son is: options: A)14years B)26 years C)17 years D)34 years E)22 years SOLUTION:Let the son's present age be x years. Then, man's present age = (x + 20) years. (x + 36) + 2 = 2(x + 2) x + 38 = 2x + 4 x = 34. answer :D #### D QUESTION:In how many K 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? options: A)720 B)864 C)900 D)936 E)1,296 SOLUTION:Total number of four letter passwords = 6*6*6*6= 1296 ------(1) Total number of passwords in which no letter repeats = 6C4*4!= 15*24=360------(2) therefore required value K= (1)-(2)= 1296-360=936.D #### D QUESTION:In an examination, 25% of total students failed in Hindi, 50% failed in English and 25% in both. The percentage of these who passed in both the subjects is : options: A)23 B)37 C)28 D)40 E)50 SOLUTION:Explanation: Formula n(a∪b) = n(a) + n(b) − n(a∩b) Fail in Hindi or English = 25 + 50 – 25 = 50 Therefore students who passed = 100 – 50 = 50. Answer: E #### E QUESTION:What least number should be added to 1056, so that the sum is completely divisible by 23? options: A)4 B)3 C)2 D)1 E)0 SOLUTION:Explanation : 1056 ÷ 23 = 45 with remainder = 21 Remainder = 21. 21 + 2 = 23. Hence 2 should be added to 1056 so that the sum will be divisible by 23. Answer : Option C #### C QUESTION:How many of the integers between 25 and 45 are even ? options: A)21 B)20 C)11 D)10 E)9 SOLUTION:Number start between 25 to 45 is 20 numbers half of them is even..which is 10 ANSWER:D #### D QUESTION:One young and one old man reach a same distance in 20min and 30min respectively. If old starts at 10.00am and youngman starts at 10.05am. When they meet. Pls provide solution options: A)12m B)14m C)15m D)16m E)17m SOLUTION:The real ans is 10:15am Let the dis be 30 m Old man travel 1m/min Young travel 1.5m/min At 10:05 old man = 5m young = 0m At 10:10 old man = 10m young = 7.5m At 10:15 old man= 15m young = 15m ANSWER:C #### C QUESTION:How many 3 – digit number can be formed from the digit 2, 3, 5, 6, 7 and 9, which are divisible by 5 and none of the digits is repeated? options: A)5 B)10 C)15 D)20 E)25 SOLUTION:Solution Since each desired number is divisible by 5, so we must have 5 at the unit place. So, there is 1 way of doing it. Tens place can be filled by any of the remaining 5 numbers. So, there are 5 ways of filling the tens place. The hundreds place can now be filled by any of the reaming 4 digits. so, there are 4 ways of filling it. So, Required number of numbers = (1 × 5 × 4) = 20 . Answer D #### D QUESTION:Find large number from below question The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 asquotient and the 15 as remainder? options: A)1245 B)1567 C)1678 D)1335 E)1635 SOLUTION:Let the smaller number be x. Then larger number = (x + 1365). x + 1365 = 6x + 15 5x = 1350 x = 270 Large number = 270+1365 = 1635 E #### E QUESTION:Jim and Reneey will play one game of Rock, Paper, Scissors. In this game, each will select and show a hand sign for one of the three items. Rock beats Scissors, Scissors beat Paper, and Paper beats Rock. Assuming that both Jim and Reneey have an equal chance of choosing any one of the hand signs, what is the probability that Jim will win? options: A)5/6 B)2/3 C)1/2 D)5/12 E)1/3 SOLUTION:1/3 probability of jim winning is basically the sum of three probabilities: probability of jim picking rock and reneey picking scissors = 1/3*1/3 = 1/9 probability of jim picking scissors and reneey picking paper = 1/3*1/3=1/9 probability of jim picking paper and reneey picking rock = 1/3*1/3=1/9 1/9 + 1/9 + 1/9 = 3/9 = 1/3=E #### E <<<Examples ends QUESTION:The area of a triangle will be when a = 3m, b = 5m, c = 10m, a, b, c being lengths of respective sides? options: A)3 B)6 C)4 D)9 E)1 SOLUTION:S = (3 + 5 + 10)/2 = 9 Answer:D #### D

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:John and Jacob set out together on bicycle traveling at 12 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 12 miles per hour? (consider John's deceleration/acceleration before/after the flat to be negligible) options: A)3 B)2 1/3 C)3 1/2 D)4 E)4 1/2 SOLUTION:John's speed - 12 miles/hr Jacob's speed - 9 miles/hr After 40min (i.e 2/3hr), distance covered by John = 12x2/3 = 8 miles. Jacob 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. Now, when John starts riding back, the distance between them is 7 miles. Jacob and John are moving in the same direction.For John to catch Jacob, the effective relative speed will be 12-9 = 3 miles/hr. Thus, to cover 7 miles at 3 miles/hr, John will take 7/3 = 2 1/3 hours Answer B #### B QUESTION:To 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. options: A)530 B)675 C)330 D)987 E)854 SOLUTION:Let x e 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: 3⋅25+(x−3)⋅30=75+30(x−3) Therefore: 25x=75+30(x−3)−100 25x=75+30x−90−100 190−75=30x−25 115=5x x=23 So the company worked 23 days and they made 23⋅25+100=675 pieces. #### B QUESTION:A man can row downstream at 20 kmph and upstream at 10 kmph. Find the speed of the man in still water and the speed of stream respectively? options: A)15,2 B)15, 4 C)15, 8 D)15, 5 E)15,7 SOLUTION:Let the speed of the man in still water and speed of stream be x kmph and y kmph respectively. Given x + y = 20 --- (1) and x - y = 10 --- (2) From (1) & (2) 2x = 30 => x = 15, y = 5. Answer:D #### D QUESTION:Two trains of length 350 m and 250 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 36 kmph and 36 kmph. After how much time will the trains meet? options: A)27/7 sec B)20/7 sec C)5 sec D)21/7 sec E)32/7 sec SOLUTION:They are moving in opposite directions, relative speed is equal to the sum of their speeds. Relative speed = (36 + 36)*5/18 = 4*5 = 20 mps. The time required = d/s = 100/20 = 5 sec. Answer : C #### C QUESTION:Which of the following is closest to (8!-7!)/(8!+7!)? options: A)0.01 B)0.8 C)0.2 D)1 E)10 SOLUTION:(8!-7!)/(8!+7!) 7! (8-1)/7! (8+1) 7/9 = 0.8 (approximately) B is the answer #### B QUESTION:How many seconds will a train 100 meters long take to cross a bridge 150 meters long if the speed of the train is 42 kmph? options: A)21.4 sec B)77 sec C)25 sec D)18 sec E)17 sec SOLUTION:D = 100 + 150 = 250 S = 42 * 5/18 = 11.7 mps T = 250/11.7 = 21.4 sec Answer:A #### A QUESTION:If all the 6 are replaced by 9, then the algebraic sum of all the numbers from 1 to 100(both inclusive) varies by options: A)330 B)340 C)350 D)360 E)370 SOLUTION:1 11 21 .......91 2 12 22........92 3 13 23........93 . . . .. . .. . . . . .. .. . .. . . . .. . . .. . ... there are total 20 occurrence of 6. once place at 6 th row in every column and tens place in 6 th column and diff of 6 and 9 is 3 so 3*1*10+3*10*10 = 330 ANSWER:A #### A QUESTION:The Simple Interest on Rs. 7300 from 11 May, 1987 to 10 September 1987 ( Both day Include ) at 5% per annum is : options: A)120 B)123 C)125 D)128 E)130 SOLUTION:Time from 11 May to 10 September, 1987 =21+30+31+31+10 = 123 days Time : 123 days = 123/365 year S.I =(7300x123x5)/(365x100)=Rs.123 answer :B #### B QUESTION:In a recent head-to-head run-off election, 12,000 absentee ballets were cast. 1/6 of the absentee ballets were thrown out and 3/5 of the remaining absentee ballets were cast for Candidate A. How many absentee votes did Candidate B receive? options: A)2,000 B)3,000 C)4,000 D)8,000 E)9,000 SOLUTION:5/6 * 2/5 (total absentee votes) = 1/3 (total votes)=1/3*12000=4000 Answer is C #### C QUESTION:Molly 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? options: A)6 B)7 C)7.5 D)8 E)9 SOLUTION:Each day, Molly can do 1/15 of the task. Each day, Sandy can do 1/10 of the task. Each day, they can do 1/15 + 1/10 = 1/6 of the task. The task will be completed in 6 days. The answer is A. #### A QUESTION:If a particular player is always chosen, in how many ways can a cricket-be chosen out of 15 players? options: A)1236 B)1345 C)1358 D)1321 E)1365 SOLUTION:A particular player is always chosen, it means that 10 players are selected out of the remaining 14 players. =. Required number of ways = 14C10 = 14C4 = 14!/4!x19! = 1365 E #### E QUESTION:D is the set of all the multiples of 5 between 20 and 100. E is the set of all the factors of 999. Set D and Set E have how many numbers in common? options: A)2 B)1 C)3 D)0 E)12 SOLUTION:D is a set of multiples of 5. 999 is NOT a multiple of 5, hence none of its factors is a multiple of 5. Therefore, those two sets won't have any overlap. Answer: D #### D QUESTION:The average salary of all the workers in a workshop is Rs. 8000. The average salary of 7 technicians is Rs. 16000 and the average salary of the rest is Rs. 6000. The total number of workers in the workshop is options: A)20 B)21 C)22 D)35 E)NONE SOLUTION:Sol. Let the total number of workers be x. Then, 8000x = (16000 × 7) + 6000 ( x – 7) ‹=› 2000x = 70000 ‹=› x = 35. Answer D #### D QUESTION:A train 360 m long is running at a speed of 45 kmph.In what time will it pass a bridge 140 m long? options: A)40 sec B)42 sec C)45 sec D)48 sec E)49 sec SOLUTION:speed of the train 45* 5/18 = 25/2 m/sec time = (360+140)/25/2 = 500*2/25 =40sec ANSWER:A #### A QUESTION:The navy pilots are practicing flight formations. 200 pilots are practicing flying in rectangles. They want to make a rectangular formation with X planes in a row and Y planes in a column. If the number of airplanes in a row is no less than 5 and no more than 40, how many different combinations of rectangular shapes are possible? options: A)6 B)7 C)8 D)9 E)10 SOLUTION:firstly factors of 200 = 1,2,4,5,8,10,20,25,40,50,100,200 the question says each row will have airplanes not less than 5 and not more than 40, therefore, we should be interested in the factors starting from 5 til 40 (inclusive) 5(in each row) * 40(number of columns) =200, similarly 8 * 25 10 * 20 20 * 10 25 * 8 40 * 5 total possibilities = 6 option A #### A QUESTION:The entire contents of a full sack of flour can be used to make 15 cupcakes and 10 pizzas. The same full sack of flour can be used to make 7 cupcakes and 14 pizzas. If a full sack of flour is used to make only pizzas, how many pizzas can be made? options: A)10 B)21 1/2 C)18 3/4 D)19 E)19 1/4 SOLUTION:15x+10y=7x+14y x=1/2y. Answer B #### B QUESTION:A train running at the speed of 30 km/hr crosses a pole in 6 sec. What is the length of the train? options: A)20 m B)70 m C)50 m D)Cannot be determined E)None of these SOLUTION:Speed = 30 * 5/18 = 25/3 m/sec Length of the train = speed * time = 25/3 * 6 = 50 m ANSWER:C #### C QUESTION:In how much time will a train of length 100 m, moving at 36 kmph cross an electric pole? options: A)16 sec B)18 sec C)19 sec D)10 sec E)17 sec SOLUTION:Convert kmph to mps. 36 kmph = 36 * 5/18 = 10 mps. The distance to be covered is equal to the length of the train. Required time t = d/s = 100/10 = 10 sec. Answer: D #### D QUESTION:Efrida and Frazer who live 13 miles apart, meet at a restaurant that is directly north of Efrida's home and directly east of Frazer's home. If the restaurant is two miles closer to Efrida's home, than to Frazer's home, how many miles is the restaurant from Frazer's home? options: A)6 B)7 C)8 D)10 E)11 SOLUTION:It's a simple geometry problem. Look at the diagram below: Answer: E. #### E QUESTION:A 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? options: A)96 km B)100 km C)106 km D)116 km E)126 km SOLUTION:Distance covered in first two hours = 10 × 2 = 20 km Distance covered in next two hours = 12 × 2 = 24 km Distance covered in next two hours = 14 × 2 = 48 km Distance covered in first six hours 20 + 24 + 48 = 92 km Remaining distance = 8 km 92 + 8 = 100 km Answer B #### B QUESTION:A man buys s cycle for $100 and sells it at a loss of 30%. What is the selling price of the cycle? options: A)$50 B)$60 C)$70 D)$80 E)$90 SOLUTION:S.P. = 70% of the $100 = 70/100 * 100 = $70 Answer is C #### C QUESTION:Consider 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, ...)? options: A)(a) 80 B)(b) 81 C)(c) 82 D)(d) 65 E)(e) 84 SOLUTION:T1: 1,2,3,4,5 T2: 2,3,4,5,6 T3: 3,4,5,6,7 etc. means that every multiple of 6 will be involved in 5 sets. We have (78-6)/6+1=13 such multiples. So, final number of sets is 13*5=65 Answer: D #### D QUESTION:If three sides of the triangle are 8 , 15 and A respectively then the how many values can A ? options: A)[A] 6 B)[B] 7 C)[C] 8 D)[D]9 E)[E] infinite number of values SOLUTION:Needed: How many Values can A take Concept: Sum of any two sides of a triangle is greater then the third side. Case 1: 8+5 > A => A<13 Case 2: 5+A > 8 => A >3 Case 3: 8+A > 5 => A > -3 (Always true since A is one side of a Triangle) Finally, 3 < A < 13. So, we can have infinite number of sides between 3 and 13. Answer = E PS: If question said A can take only integer value, the A = 9. Answer choice D. #### D QUESTION:The area of a rectangle is 15 square centimeters and the perimeter is 16 square centimeters. What are the dimensions of the rectangle? options: A)3 and 5 B)3 and 6 C)3 and 7 D)3 and 8 E)3 and 9 SOLUTION:Let 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. 15 = x y and 16 = 2 x + 2 y Solve the second equation for x x = 8 - y Substitute x in the equation 15 = x y by 8 - y to rewrite the equation as 15 = (8 - y) y Solve for y to find y = 3 and y = 5 Use x = 8 - y to find x when y = 3 , x = 5 and when y = 5 , x = 3. The dimensions of the rectangle are 3 and 5. As an exercise, check that the perimeter of this rectangle is 16 and its area is 15. Answer A #### A QUESTION:A beauty pageant is being held with 50 competitors (one from each state in the USA). Each competitor has an equal chance of winning the competition. Four competitors will be chosen, and each will win either 1st, 2nd, 3rd, or 4th place. What is the probability California, Florida, and Hawaii will win three of the four places? options: A)3/100 B)3/5 C)1/100 D)1/4,900 E)1/5 SOLUTION:Combination Formula: nCr = n!/(r!(n - r)!), where n is the population/set, and r is the sample/subset. Total number possible = 50C4 - 50!/(4!(50 - 4)!) = 230,300 Number CA possible = 1C1 = 1 Number FL possible = 1C1 = 1 Number HI possible = 1C1 = 1 Number other possible = 47C1 = 47 Probability Formula: P(A) = (Number Favorable Outcomes)/(Total Number Possible Outcomes) P(CA, FL, HI) = (1C1)(1C1)(1C1)(47C1)/50C4 = 47/230,300 = 1/4,900 Answer: D #### D QUESTION:What is the greatest of 3 consecutive integers whose sum is 30 ? options: A)11 B)7 C)8 D)9 E)5 SOLUTION:The sum of three consecutive integers can be written as n + (n + 1) + (n + 2) = 3n + 3 If the sum is 24, we need to solve the equation 3n + 3 = 30; => 3n = 27; => n = 9 The greatest of the three numbers is therefore 9 + 2 = 11 Answer: A #### A QUESTION:January 1, 2007 was Monday. What day of the week lies on Jan. 1, 2008? options: A)Monday B)Tuesday C)Wednesday D)Friday E)Sunday SOLUTION:The year 2007 is an ordinary year. So, it has 1 odd day. day of the year 2007 was Monday day of the year 2008 will be 1 day beyond Monday Hence, It will be Tuesday. answer : B #### B QUESTION:A trader sells 85 meters of cloth for $8925 at the profit of $15 per metre of cloth. What is the cost price of one metre of cloth? options: A)$69 B)$78 C)$90 D)$86 E)$77 SOLUTION:C $90 SP of 1m of cloth = 8925/85 = $105 CP of 1m of cloth = SP of 1m of cloth - profit on 1m of cloth = $105 - $15 = $90. #### C QUESTION:A reduction in the price of petrol by 10% enables a motorist to buy 5 gallons more for $280. Find the original price of petrol? options: A)$11 B)$5 C)$45 D)$400 E)$6.2 SOLUTION:Price decreased by 10%, so 9/10 times, which means that original gallons bought increased 10/9 times. Since this increase equals to 5 gallons then 45 gallons were bought originally (45*10/9=50 --> increase 5 gallons). Hence original price was 280/45=$6.2 Answer: E. #### E QUESTION:There are two bridges running parallel over river Kauvery, and they are 1 KM apart. A man started rowing the boat upstream under first bridge, his hat fell into river while he was exactly under second bridge. He realized that after 15 mts, and started rowing in opposite direction, he eventually caught his hat under First Bridge. What is the speed of river Kauvery? options: A)5km/h B)4km/h C)3km/h D)1km/h E)2km/h SOLUTION:Let the upstream velocity=xkm/h so he goes first 1 km then 15 min with this velocity so total goes=x*15/60+1 km=x+4/4 km and now he in downstream cover this distance in 15 min so his downstream velocity=x+4/4*15=x+4/60 now speed of river=1/2[downstream speed-upstream speed] =1/2[x+4/60-x/60]km/min =2km/h ANSWER:E #### E QUESTION:Which of the following is(are) true for a@b=b@a? I. a@b=b+ba II. a@b=(a+b)(a-b) III. a@b=(a/b)+(b/a) options: A)only Ⅰ B)only Ⅱ C)only Ⅲ D)only ⅠⅢ E)only ⅡⅢ SOLUTION:-> If I. a@b=ab+ba, a@b=ab+ba=ba+ab=b@a (X). If II. a@b=(a+b)(a-b), a@b=(a+b)(a-b)≠(b+a)/(b-a)=b@a (O). If III.a@b=(a/b)+(b/a), a@b=(a/b)+(b/a)=(b/a)+(a/b)=b@a (O). Thus, ⅠⅢ are the answers. Therefore, A is the answer. #### A QUESTION:Peter rolls two dice at the same time. What is the probability that total sum of the numbers on the dices is 4? options: A)a) 1/12 B)b) 1/36 C)c) 1/6 D)d) 5/12 E)e) 1/3 SOLUTION:We can have 6 different outcomes on a dice. Total outcomes on two dices = 6*6 We need only the cases where total sum of the numbers on the dices is 4 They can be {1, 3}, {2, 2}, {3, 1} A total of 3 outcomes Probability = favorable outcomes/ total outcomes = 3/36 = 1/12. Option A #### A QUESTION:A train 280 m long, running with a speed of 63 km/hr will pass a tree in? options: A)18 sec B)16 sec C)19 sec D)11 sec E)12 sec SOLUTION:: Speed = 63 * 5/18 = 35/2 m/sec Time taken = 280 * 2/35 = 16 sec Answer: B #### B QUESTION:A train 360 m long runs with a speed of 45 km/hr. What time will it take to pass a platform of 140 m long? options: A)38 sec B)35 sec C)44 sec D)40 sec E)50 sec SOLUTION:Explanation: Speed = 45 km/hr = 45×(10/36) m/s = 150/12 = 50/4 = 25/2 m/s Total distance = length of the train + length of the platform = 360 + 140 = 500 meter Time taken to cross the platform = 500/(25/2) = 500×2/25 = 40 seconds Answer: Option D #### D QUESTION:An 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? options: A)520 km/hr B)640 km/hr C)656 km/hr D)731 km/hr E)720 km/hr SOLUTION:Distance = (240 x 5) = 1200 km. Speed = Distance/Time Speed = 1200/(5/3) km/hr. [We can write 1 hours as 5/3 hours] Required speed = 1200 x 3 km/hr = 720 km/hr. 5 E #### E QUESTION:Among all sales staff at Listco Corporation, college graduates and those without college degrees are equally represented . Each sales staff member is either a level-1 or level-2 employee. Level-1 college graduates account for 15% of Listco's sales staff. Listco employs 90 level-1 employees, 30 of whom are college graduates. How many sales staff members without college degrees are level-2 employees ? options: A)46 B)42 C)56 D)32 E)40 SOLUTION:I'm going in on this one. So let's say that we have the following So we know that L1 = 90 and that C and L1 = 0.15X , we should set up a double set matrix btw but anyways, I'm just explaining the point with this problem. Now we are told that 0.15x = 30, therefore the grand total is 200. Now we know that L2 is 200 - 90 = 110. We also learn that C and No C are equally represented thus 100 each. Therefore No C and No L2 will be 100 - 60 = 40. Thus E is the correct answer choice #### E QUESTION:In Rwanda, the chance for rain on any given day is 1/2. What is the probability that it rains on 4 out of 6 consecutive days in Rwanda? options: A)4/7 B)3/7 C)15/64 D)4/28 E)28/135 SOLUTION:using Binomial. theorem nCr (p)^r (q)^n-r 6C4 (1/2)^4 (1/2)^r which is 15/64 Answer is C. #### C QUESTION:The average weight of A, B and C is 30 kg. If the average weight of A and B be 25 kg and that of B and C be 28 kg, then the weight of B is: options: A)14 kg B)15 kg C)18 kg D)19 kg E)16 kg SOLUTION:EXPLANATION Let A, B, C represent their respective weights. Then, we have: A + B + C = (30 x 3) = 90 …. (i) A + B = (25 x 2) = 50 …. (ii) B + C = (28 x 2) = 56 ….(iii) Adding (ii) and (iii), we get: A + 2B + C = 106 …. (iv) Subtracting (i) from (iv), we get : B = 16. B’s weight = 16 kg. Answer E #### E QUESTION:Tea 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: options: A)175.5 B)170 C)169.5 D)180 E)190 SOLUTION:Since first and second varieties are mixed in equal proportions. average price = 126+135/2 = 130.50 o, 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. x - 153 = 22.50 x = 175.50 ANSWER A #### A QUESTION:What is the greatest prime factor of (11!10!) + (11!12!)? options: A)11 B)17 C)19 D)23 E)29 SOLUTION:11!10! + 11!12! = 11!10! (1+11*12) = 12!11!(133) = 12!11!(7*19) The greatest prime factor is 19. The answer is C. #### C QUESTION:If 5^29 * 4^15 = 2 * 10^n, what is the value of n? options: A)11 B)21 C)22 D)29 E)32 SOLUTION:My attempt: 5^(29) * 4^(15) = 2*10^p 5^(29) * 2 ^ (30) = 2 * (2*5)^p 5^(29) * 2 ^ (30) = 2 * 2^(p) * 5^(p) 5^(29) * 2 ^ (30) = 2^(p+1) * 5^(p) => (p+1) = 30 => p = 29 Answer: 29 (D) #### D QUESTION:If set A={2,2,2,....,n times} , set B={3,3,3,3....m times} and set C={13,13,13...k time} , then in terms of m,n and k , how many possible subsets from sets A,B, and C can be created ? options: A)a) k(n+m+mn)+ k B)b) (1+n+m+mn)(k+1) C)c) k^2(mn+n/m) D)d) kmn(k+m+n) E)e) None of the above. SOLUTION:a) how many 2's are included? b) how many 3's are included? and c) how many 11's are included? For 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. NOTICE 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. The 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: (mn + m + n + 1)(k + 1). Mike B #### B QUESTION:If a particular player is never chosen, in how many ways can 11 cricket players be chosen out of 14 players? options: A)45 B)56 C)64 D)78 E)90 SOLUTION:A particular players is never chosen, it means that 11 players are selected out of 13 players. => Required number of ways = 13C11 = 78 D #### D QUESTION:A father said his son , " I was as old as you are at present at the time of your birth. " If the father age is 62 now, the son age 5 years back was options: A)14 B)17 C)11 D)19 E)26 SOLUTION:Let the son's present age be x years .Then, (62 - x) = x x= 31. Son's age 5 years back = (31 - 5) = 26 years Answer: E #### E QUESTION:Tharak covers a part of the journey at 20 kmph and the balance at 70 kmph taking total of 8 hours to cover the distance of 400 km. How many hours has been driving at 20 kmph? options: A)3 hours 12 minute B)2 hours C)4 hours 40 minutes D)3 hours 20 minutes E)3 hours 18 minute SOLUTION:Let x be no. Of hours, and he travelled at 20kmph. And balance distance (8-x)hr at 70kmph. Total distance=20x+(8-x)hr =400 20x+(8-x)70=400 20x+560-70x=400 20x-70x=400-560 -50x=-160 x=3.2 =3 hr 12minutes ANSWER:A #### A QUESTION:The remainder obtained when a prime number greater than 4 is divided by 4 is options: A)a) 1 or 3 B)b) 1 or 5 C)c) 3 or 5 D)d) 4 or 5 E)e) 5 SOLUTION:The easiest way to answer this question is probably to pick numbers. Use the next two prime numbers greater than 4, i.e. 7 and 5: 7/4 = 1 + remainder of 3 5 / 4 = 1 + remainder of 1 This is already sufficient to see that answer choice a) is correct. A #### A QUESTION:In how many ways the word "KIT" can be arranged? options: A)6 B)8 C)18 D)21 E)24 SOLUTION:Explanation : The required number of ways = 3! = 6 Answer : A #### A QUESTION:During a behavioral experiment in a psychology class, each student is asked to compute his or her lucky number by raising 7 to the power of the student's favorite day of the week (numbered 1 through 7 for Monday through Sunday respectively), multiplying the result by 3, and adding this to the doubled age of the student in years, rounded to the nearest year. If a class consists of 28 students, what is the probability that the median lucky number in the class will be a non-integer? options: A)0% B)10% C)20% D)30% E)40% SOLUTION:Student's age is integral value. In question, we are multiplying student's age by 2 and adding some 3* 7^x something over there. It means Even (2* age of students) + Odd (3) * 7 ^x (where x is day of week). We know that 7^x is always odd. (e.g. 7, 49, 243, 1701, and repeat). => 3* odd is again odd. 2 * age of students is always even. So final equation is even +odd = odd. Avg of any number of odd digits or any number of even digits can never be non integral value. So 0% is the answer A. #### A QUESTION:If y ≠ 3 and 2h/y is a prime integer greater than 2, which of the following must be true? I. h = y II. y = 1 III. h and y are prime integers. options: A) None B) I only C) II only D) III only E) I and II SOLUTION:Note that we are asked which of the following MUST be true, not COULD be true. For such kind of questions if you can prove that a statement is NOT true for one particular set of numbers, it will mean that this statement is not always true and hence not a correct answer. So we should try to make the listed statements not true for some h and y (which satisfy y≠3 and 2h/y=prime>2). I. h = y --> not necessarily true: h=3 and y=2 (2h/y=3=prime>2); II. y=1 --> not necessarily true: h=3 and y=2 (2h/y=3=prime>2); III. h and y are prime integers --> not necessarily true: h=10 and y=4 (2h/y=5=prime>2). Answer: A. #### A QUESTION:A car traveling at a certain constant speed takes 2 seconds longer to travel 1 kilometer than it would take to travel 1 kilometer at 900 kilometers per hour. At what speed, in kilometers per hour, is the car traveling? options: A)671.5 B)600 C)672.5 D)673 E)773.5 SOLUTION:Many approaches are possible, one of them: Let the distance be 1 kilometer. Time to cover this distance at 900 kilometers per hour is 1/900 hours = 3,600/900 seconds = 4 seconds; Time to cover this distance at regular speed is 900+2=902 seconds = 902/3,600 hours = 1/600 hours; So, we get that to cover 1 kilometer 1/600 hours is needed --> regular speed 600 kilometers per hour (rate is a reciprocal of time or rate=distance/time). Answer: B. #### B QUESTION:Two 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? options: A)26 km/hr B)17 km/hr C)60 km/hr D)42 km/hr E)46 km/hr SOLUTION:Let the speed of the slower train be x m/sec. Then, speed of the train = 2x m/sec. Relative speed = ( x + 2x) = 3x m/sec. (100 + 100)/5 = 3x => x = 20/3. So, speed of the faster train = 40/3 = 40/3 * 18/5 = 42 km/hr. Answer:D #### D QUESTION:If n is an integer, which of the following CANNOT be a factor of 3n+4? options: A)4 B)5 C)6 D)7 E)8 SOLUTION:3n+4=3(n+1)+1 cannot be a multiple of 3, it's 1 more than multiple of 3: ... 4, 7, 10, 13, 16, ... Hence it cannot be a multiple of 2*3=6 as well. Answer: C. #### C QUESTION:A class average mark in an exam is 70. The average of students who scored below 60 is 50. The average of students who scored 60 or more is 75. If the total number of students in this class is 20, how many students scored below 60? options: A)5 B)10 C)15 D)20 E)25 SOLUTION:Let n the number of students who scored below 60 and N the number of students who scored 60 or more. Xi the grades below 60 and Yi the grades 60 or above. [sum(Xi) + sum(Yi)] / 20 = 70 : class average sum(Xi) / n = 50 : average for less that 60 sum(Yi) / N = 75 : average for 60 or more 50n + 75N = 1400 : combine the above equations n + N = 20 : total number of students n = 4 and N = 16 : solve the above system correct answer D #### D QUESTION:The first year, two cows produced 8100 litres of milk. The second year their production increased by 15% and 10% respectively, and the total amount of milk increased to 9100 litres a year. How many litres were milked from one cow? options: A)2178 lt B)3697 lt C)6583 lt D)4370 lt E)5548 lt SOLUTION:Let x be the amount of milk the first cow produced during the first year. Then the second cow produced (8100−x) litres of milk that year. The second year, each cow produced the same amount of milk as they did the first year plus the increase of 15%15% or 10% So 8100+15100⋅x+10100⋅(8100−x)=9100 Therefore 8100+320x+110(8100−x)=9100 120x=190 x=3800 Therefore, the cows produced 3800 and 4300 litres of milk the first year, and 4370 and 4730 litres of milk the second year, => one cow produced 4370 litres correct answer is D)4370 lt #### D QUESTION:The ratio, by volume, of soap to alcohol to water in a certain solution is 20:50:80. 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 100 cubic centimeters of alcohol, how many cubic centimeters of water will it contain? options: A)520 B)640 C)700 D)750 E)800 SOLUTION:soap:alcohol Initial ratio soap:alcohol: water --> 20:50:80 Initial soap:alcohol = 20/50 =20:50 after doubled soap:alcohol =2* 20/50 = 40:50 Initial soap:water = 20/80=20:80 after halved soap:water: 1/2 * 20/80 = 10/80 = 10:80 After soap: alcohol:water --> 40:50:320-->4:5:32 given alcohol 100 cubic centimeter. ratio is 80:100:640(4:5:32) For 100 cubic centimeter of Alcohol --- 640cubic cm water is required. Answer-B #### B QUESTION:There 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. options: A)460 B)490 C)493 D)455 E)424 SOLUTION:Ways to pick 4 cans so that at least one red and at least one blue cans to remain the refrigerator = total 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 12C4−8C4−4C4=495−70−1=424 ANSWER:E #### E QUESTION:A 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.672 find the share of A. options: A)256 B)388 C)379 D)277 E)122 SOLUTION:Explanation: (3*8 + 2*4):(4*8 + 5*4) 8:13 8/21 * 672 = 256 Answer: A #### A QUESTION:A man's basic pay for a 40 hour week is Rs.20. Overtime is paid for at 25% above the basic rate. In a certain week he worked overtime and his total wage was Rs.25. He therefore worked for a total of : options: A)45 hours B)47 hours C)48 hours D)50 hours E)None SOLUTION:Explanation: Basic rate per hour = Rs.(20/40)= Rs.1/2 Overtime per hour = 125% of Rs.1/2=125/100×1/2=Rs.5/8 Suppose he worked x hours overtime. Then,20+5/8x=25 or 5/8x=5 x=5×8/5=8 hours So he worked in all for (40+8) hours = 48 hours. Correct Option: C #### C QUESTION:If a^2+b^2=177and ab=54 then find the value of a+b/a-b? options: A)1 B)3 C)5 D)7 E)9 SOLUTION:(a+b)^2=a^2+b^2+2ab=117+2*24=225 a+b=15 (a-b)^2=a^2+b^2-2ab=117-2*54 a-b=3 a+b/a-b=15/3=5 Answer is C. #### C QUESTION:Which of the following is an integer? I. 9! / 6! II. 9! / 8! III. 9! / 7!5! options: A)I only B)II only C)III only D)I and II only E)I, II, and III SOLUTION:9!/6! = 9*8*7 which is an integer. 9!/8! = 9 which is an integer. 9!/7!5! = 9*8 / 5*4*3*2 = 3/5 which is not an integer. The answer is D. #### D QUESTION:A man buys $50 shares in a company which pays 10% dividend. If the man gerts 12.5% on his investment, at what price did he buy the shares? options: A)37.5 B)40 C)50 D)48 E)52 SOLUTION:Dividend on 1 share = $(10/100*50) =$5 $12.5 is an income on an investment of $100 $5 is an income on an investment of $(100*2/25*5)=40 Thus, cost of 1 share =$40 ANSWER B #### B QUESTION:A bullock-cart travels 24 kilometers in 3 hours and an another bullock-cart travels 120 kilometers in 2 hours. What will be the ratio of their speeds? options: A)2 : 15 B)1 : 5 C)2 : 3 D)3 : 2 E)None of these SOLUTION:First cart speed will be 24/3=8 Second cart speed is 120/2=60 So, ratio is 8/60=2/15 ANSWER:A #### A QUESTION:A bat is bought for Rs.400 and sold at a gain of 20% find its selling price options: A)Rs.480/- B)Rs.500/- C)Rs.520/- D)Rs.540/- E)Rs.560/- SOLUTION:100 % ------> 400 (100 * 4 = 400) 120 % ------> 480 (120 * 4 = 480) Selling price = Rs.480/- A #### A QUESTION:On a race track a maximum of 5 horses can race together at a time. There are a total of 25 horses. There is no way of timing the races. What is the minimum number Q of races we need to conduct to get the top 3 fastest horses? options: A)5 B)7 C)8 D)10 E)11 SOLUTION:Q=7 is the correct answer. Good solution Buneul.B #### B <<<Examples ends QUESTION:If 6 (A's capital) = 8 (B's capital) = 16 (C's capital). Then the ratio of their capitals is? options: A)8:15:16 B)8:15:68 C)8:6:3 D)20:15:11 E)20:15:19 SOLUTION:6A = 8B = 16 C A:B:C = 1/6:1/8:1/16 = 8:6:3 Answer: C #### C

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:Calculate how many seconds it will take for 4 bells to toll together again, given that they begin to toll together respectively at the intervals of 9, 12, 15 and 18 seconds? options: A)186 B)130 C)180 D)181 E)120 SOLUTION:LCM of 9, 12, 15 and 18 is 180 LCM=180 ANSWER:C #### C QUESTION:A sells his goods 50% cheaper than B but 50% dearer than C. The cheapest is? options: A)A B)B C)C D)all alike E)None of these SOLUTION:Let B = 100 A = 50 C * (150/100) = 50 3C = 100 C = 33.3 then 'C' Cheapest ANSWER:C #### C QUESTION:It is given that 2^32 + 1 is exactly divisible by a certain number. Which one of the following is also divisible by the same number X? options: A)a. 2^96 + 1 B)b. 2^16 - 1 C)c. 2^16 + 1 D)d. 7 * 2^33 E)e. 2^64 + 1 SOLUTION:a³ + b³ =(a+b)(a² -ab +b²) Now, let (2^32 + 1) be (a+b) a³ + b³ = (2^96 + 1) Now, as mentioned in formula above, a³ + b³ is always divisible by (a+b) So any factor of X=(a+b) is a factor of (a³ + b³) Henca A #### A QUESTION:At what rate percent on simple interest will Rs.750 amount to Rs.900 in 5 years? options: A)5% B)3 1/2% C)4% D)5 1/2 % E)6% SOLUTION:150 = (750*5*R)/100 R = 4% Answer :C #### C QUESTION:Shopkeeper rise price by 32% and gives successive discount of 10% and 15%. What is overall % gain or loss? options: A)0.98% B)4.98% C)3.95% D)6.98% E)7.98% SOLUTION:Let d initial price be 100 32 % rise now price = 132/100*100 = 132 10% discount Then price = 132 * 90/100 = 118.8 15 % discount Then price = 118.8 * 85/100 = 100.98 So Gain = 100.98 - 100 = 0.98 Gain % = Gain * 100 /CP ==> 0.98* 100 /100 = 0.98% ANSWER:A #### A QUESTION:A student got twice as many sums wrong as he got right. If he attempted 27 sums in all, how many did he solve correctly ? options: A)12 B)16 C)18 D)9 E)12 SOLUTION:Explanation: Suppose the boy got x sums right and 2x sums wrong. Then, x + 2x = 27 3x = 27 x = 9. Answer:D #### D QUESTION:The variables a and b are non-zero integers W. If a = 2b^3/c, what happens to c when a is halved and b is doubled? options: A)c is not changed. B)c is halved. C)c is doubled. D)c is multiplied by 4. E)c is multiplied by 16. SOLUTION:a=2b^3/c c=2b^3/a when a is halved and b is doubled c=2(2b)^3/(a/2) c=16*2b^3/a Ans. E c is multiplied by 16. #### E QUESTION:A 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? options: A)112 B)50 C)77 D)14 E)12 SOLUTION:Speed 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. Answer: B #### B QUESTION:A train 310 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? options: A)4 B)6 C)5 D)17 E)13 SOLUTION:Speed of train relative to man = (60 + 6) km/hr = 66 km/hr [66 * 5/18] m/sec = [55/3] m/sec. Time taken to pass the man = [310 * 3/55] sec = 17 sec ANSWER:D #### D QUESTION:After an ice began to melt out from the freezer, in the first hour lost 3/4, in the second hour lost 3/4 of its remaining. If after two hours, the volume is 0.3 cubic inches, what is the original volume of the cubic ice, in cubic inches? options: A)2.5 B)3.0 C)4.8 D)6.5 E)8.0 SOLUTION:Let initial volume of ice be = x Ice Remaining after 1 hour = x - 0.75x = 0.25x Ice Remaining after 2 hour = (1/4)x - (3/4 * 1/4 * x) = (1/16)x (1/16)x = 0.3 x = 4.8 Alternate solution: Try to backsolve. Initial volume = 4.8 After one hour --> (1/4)4.8 = 1.2 After two hours --> (1/4)1.2 = 0.3 Answer: C #### C QUESTION:A train running at the speed of 60 km/hr crosses a pole in 9 seconds. Find the length of the train? options: A)150 meter B)876 meter C)167 meter D)719 meter E)169 meter SOLUTION:Speed = 60*(5/18) m/sec = 50/3 m/sec Length of Train (Distance) = Speed * Time (50/3) * 9 = 150 meter Answer: A #### A QUESTION:On 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’s investment in the first 2 years was how much greater than the total amount of interest earned by Lana’s investment in the first 2 years? options: A)$5 B)$15 C)$50 D)$100 E)$105 SOLUTION:Compounded 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. With respect to the problem at hand, at the end of two years, Tim would have 1,000(1.10)^2 = 1,000(1.21) = 1,210 and Lana would have 2,000(1.05)^2 = 2,000(1.1025) = 2,205 Thus, Tim earned 210 dollars, while Lana earned 205 dollars The difference is $5 and the answer is A. #### A QUESTION:If the President and Vice President must sit next to each other in a row with 2 other members of the Board, how many different seating arrangements are possible? options: A)10 B)16 C)18 D)12 E)18 SOLUTION:We need to take President and VP as one unit. Therefore we have 3 people to arrange=3! ways Also, we both President and VP can be arranged in 2 ! ways. Reqd no of ways=3!*2!=12 ways Answer D #### D QUESTION:The avg weight of A,B & C is 70 kg. If D joins the group, the avg weight of the group becomes 70 kg.If another man E who weights is 3 kg more than D Replaces A, Then the avgof B,C,D&E becomes 68 kg. What is the weight of A? options: A)81 B)65 C)75 D)89 E)90 SOLUTION:A + B + C = 3 *70 = 210 A + B + C + D = 4 * 70 = 280 ---- (i) So, D = 70& E = 70 + 3 = 73 B + C + D +E =68 * 4 = 272 --- (ii) From Eq. (i) & (ii) A-E = 280 –272 = 8 A = E +8 = 73 + 8 = 81 Answer : A #### A QUESTION:A shopkeeper sells some toys at Rs. 250 each. What percent profit does he make? To find the answer, which of the following information given in Statements I and II is/are necessary? I. Number of toys sold. II. Cost price of each toy. options: A)Only I is necessary B)Only II is necessary C)Both I and II are necessary D)Either I or II ins necessary E)None of these SOLUTION:EXPLANATION S.P. = Rs. 250 each. To find gain percent, we must know the C.P. of each. answer is (B). #### B QUESTION:In 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? options: A)30% B)70% C)100% D)250% E)300% SOLUTION:cp = 100 profit = 320 ans SP = 420 new CP = 125% of RS 100 = Rs 125 New SP = 420 profit = (420-125) = 295 req % (295/420*100)% = 1475/21% = 70% ANSWER B #### B QUESTION:#p is defined as 2p-20 for any number p. What is p, if #(#(#p))=6? options: A)–108 B)–44 C)10 D)16 E)18.25 SOLUTION:#p = 2p-20 --->#(#p) = 2(2p-20)-20 = 4p-60 and thus #(4p-60) = 2(4p-60)-20 = 8p-140 = 6 ---> 8p= 146 ---> p = 18.25, E is the correct answer. #### E QUESTION:3x^2 + 5x - 2 = options: A)(3x-1)(x+2) B)(3x-4)(x+2) C)(3x-4)(x-2) D)(3x-2)(x+4) E)none of above SOLUTION:3x^2 + 5x - 2 = 3x^2 + 6x - x - 2 = 3x (x + 2) - (x+2) = (3x-1) (x+2) Option A #### A QUESTION:Rajan and Rakesh started a business and invested Rs. 20,000 and Rs. 25,000 respectively. After 4 months Rakesh left and Mukesh joined by investing Rs. 15,000. At the end of the year there was a profit of Rs. 4,600. What is the share of Rajan? options: A)2000 B)2100 C)2200 D)2300 E)2400 SOLUTION:Ratio of share of Rajan, Rakesh nd Mukesh => 20000:25000:15000 =>4:5:3 =>4*12 : 5*4 : 3*8 [Since Rakesh left after 4 months nd Mukesh joined after 4 months...] => 12:5:6 Share of Rajan => 4600*12/23 = 2400 ANSWER:E #### E QUESTION:A committee of 3 persons is to be formed from 3 company secretaries, 4 economists and 1 chartered accountant. What is the probability that each of the three professions is represented in the committee? options: A)1/28 B)3/28 C)1/14 D)4/28 E)3/14 SOLUTION:3/8*4/7*1/6*3! = 3/14. We are multiplying by 3! because we can choose secretary, economist, and accountant is several way: SEA, SAE, ESA, EAS, ASE, AES. Answer: E. #### E QUESTION:In May Mrs Lee's earnings were 50 percent of the Lee family's total income. In June Mrs Lee earned 20 percent more than in May. If the rest of the family's income was the same both months, then, in June, Mrs Lee's earnings were approximately what percent of the Lee family's total income ? options: A)55 B)56 C)34 D)78 E)23 SOLUTION:Lets say the Family Income is 100 In May, lee earned 50Family income is 50 In june, Lee earned 20% more than May, so it is (50+20*50/100 = 60) Family Income is same 50 In June Lee's Income percent is 60*100/110 ~ 55 Ans is A #### A QUESTION:A 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? options: A)Rs.18000 B)Rs.15000 C)Rs.17000 D)Rs.14000 E)NONE SOLUTION:25*12: 30*12: 35*8 15:18:14 14/47 * 47000 = 14000 ANSWER:D #### D QUESTION:For an agricultural experiment, 300 seeds were planted in one plot and 200 were planted in a second plot. If exactly 30 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? options: A)12% B)26% C)29% D)32% E)60% SOLUTION:In the first plot 30% of 300 seeds germinated, so 0.3 x 300 = 90 seeds germinated. In the second plot, 35% of 200 seeds germinated, so 0.35 x 200 = 70 seeds germinated. Since 90 + 70 = 260 seeds germinated out of a total of 300 + 200 = 500 seeds, the percent of seeds that germinated is (160/500) x 100%, or 32%. Answer: D. #### D QUESTION:A sock drawer contains 5 socks, each one a different solid color. The colors of the socks are yellow, green, blue, indigo, and violet. If a person reaches into the drawer and pulls out two socks, how many different color combinations are possible in the selected pair of socks? options: A)10 B)15 C)21 D)36 E)42 SOLUTION:Since the order in which we select the socks does not matter, we can use combinations. We can select 2 socks from 5 socks in 5C2 ways. 5C2 = 10 Answer : A #### A QUESTION:The area of a triangle is with base 12m and height 5m? options: A)88 m2 B)30 m2 C)66 m2 D)77 m2 E)31 m2 SOLUTION:1/2 * 12 * 5 = 30 m2 Answer: B #### B QUESTION:Dawson got a weekly raise of $160. If he gets paid every other week, write an integer describing how the raise will affect his paycheck. options: A)150 B)160 C)170 D)180 E)190 SOLUTION:Let the 1st paycheck be x (integer). Dawson got a weekly raise of $ 160. So after completing the 1st week she will get $ (x+160). Similarly after completing the 2nd week she will get $ (x + 160) + $ 160. = $ (x + 160 + 160) = $ (x + 320) So in this way end of every week her salary will increase by (B)$ 160. #### B QUESTION:A stock trader originally bought 300 shares of stock from a company at a total cost of m dollars. If each share was sold at 60% above the original cost per share of stock, then interns of m for how many dollars was each share sold? options: A)a) 2m/300 B)b) m/300 C)c) 5m/900 D)d) m/300 + 50 E)e) 350/m SOLUTION:Let Cost of 300 shares be $ 3000 So, Cost of 1 shares be $ 10 =>m/300 Selling price per share = (100+60)/100 * m/300 Or, Selling price per share = 5/3 * m/300 => 5m/900 Hence answer will be (C) #### C 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 T is in the same quadrant as the fourth vertex of the square? options: A)(-5, -3) B)(-5, 3) C)(5, -3) D)(3, -5) E)(3, 5) SOLUTION:The 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 T is in the same quadrant as the fourth vertex of the square? I marked the tricky part in red. It seems c is anegativenumber and d is a positive number. This means Vertex #1 = (c, d) is in QII (that is, negative x and positive y) Vertex #2 = (c, -d) is in QIII (that is, both xy negative) Vertex #3 = (-c, -d) is in QIV (that is y is negative, but x is positive) That means the last vertex should be in the first quadrant --- the only first quadrant point is (5, 3), answer =E. #### E QUESTION:Present ages of X and Y are in the ratio 5:6 respectively. Seven years hence this ratio will become 6:7 respectively. What is X's present age in years? options: A)35 years B)77 years C)55 years D)44 years E)33 years SOLUTION:Let the present ages of X and Y be 5x and 6x years respectively. Then, (5x + 7)/(6x + 7) = 6/7 7(5x + 7) = 6(6x + 7) => x = 7 X's present age = 5x = 35 years.Answer: A #### A QUESTION:The average of 10 members is 15665. If 2 members have 20000 then what is the average of remaining? options: A)12581.25 B)13581.25 C)14581.25 D)15581.25 E)16581.25 SOLUTION:20000*2+8*x=15665*10 8x=156650-40000 x=116650/8 x=14581.25 ANSWER:C #### C QUESTION:Mrs. 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. options: A)$140 B)$141 C)$142 D)$147 E)$145 SOLUTION:Let the 1st paycheck be x (integer). Mrs. Rodger got a weekly raise of $ 147. So after completing the 1st week she will get $ (x+147). Similarly after completing the 2nd week she will get $ (x + 147) + $ 147. = $ (x + 147 + 147) = $ (x + 294) So in this way end of every week her salary will increase by $ 147. correct answer D)$147 #### D QUESTION:A retailer buys a radio for Rs 225. His overhead expenses are Rs 30. He sellis the radio for Rs 300. The profit percent of the retailer is options: A)10% B)50% C)25% D)17.6% E)None of these SOLUTION:Explanation: cost price = (225 + 30) = 255 sell price = 300 gain = (45/255)*100 = 17.6%. Answer: D #### D QUESTION:In 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? options: A)1140 B)1160 C)1180 D)1200 E)1040 SOLUTION:Number of sweets each child got = 15% of 80 = 15/100 * 80 = 12. Number of sweets 80 children got = 70 * 12 = 840. Number of sweets each youngster got = 25% of 80 = 25/100 * 80 = 20. Number of sweets 10 youngsters got = 10 * 20 = 200. Total number of sweets = 840 + 200 = 1040. E) #### E QUESTION:If p ≠ 1 and if qp/(q - p) = 1, what is the value of q in terms of p? options: A)(p+1)/p B)(p - 1)/p C)p/(p + 1) D)p/(1-p) E)(1 - p)/p SOLUTION:This 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. Here, 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. Final Answer: D #### D QUESTION:M 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: options: A)35000 B)40000 C)50000 D)60000 E)None SOLUTION:Suppose N invested Rs. x. Then, 40000/x = 4/5 or y = [40000 x 5/ 4] = 50000. Answer C #### C QUESTION:Ratio between Rahul and Deepak is 4:3, After 2 Years Rahul age will be 26 years. What is Deepak present age. options: A)14 B)18 C)20 D)22 E)24 SOLUTION:Explanation: Present age is 4x and 3x, => 4x + 2 = 26 => x = 6 So Deepak age is = 3(6) = 18 Option B #### B QUESTION:For any non-zero a and b that satisfy |ab| = -ab and |a| = -a, |b-4| + |ab-b| = options: A)ab-4 B)2b-ab-4 C)ab+4 D)ab-2b+4 E)4-ab SOLUTION:Given: |ab| = -ab and |a| = -a Question: |b-4| + |ab-b| = ? **** Looking at |ab| = -ab tells us that either one of a or b is negative. **** Looking at |a| = -a tells us that a must be negative **** Combine two observations: b is positive Let a=-1 and b=1 |b-4| + |ab-b| = |1-4| + |-1-1| = 5 Test a) |ab-4| = |(1)(-1)-4| = |-5|=5 Test b) 2b-ab-4 = (2)(1) - (-1) - 4 = -1 Test c) ab+4 = -1 + 4 = 3 Test d) ab-2b+4 = -1-2(1)+4=1 test e) 4-1=3 ANSWER=A #### A QUESTION:21 goats eat as much as 15 cows. How many goats eat as much as 35 cows? options: A)49 B)32 C)36 D)41 E)45 SOLUTION:Explanation: 15 cows ≡ 21 goats 1 cow ≡ 21/15 goats 35 cows ≡ 21×35/15 goats ≡ 21×7/3 goats ≡ 7 × 7 goats ≡ 49 goats Answer: Option A #### A QUESTION:How many different positive integers are factors of 196 ? options: A) 1 B) 2 C) 3 D) 49 E) 36 SOLUTION:15, 14×15, 14=7^2 × 2^2 So total factors = (6+1)(6+1) = 49 Answer: D #### D QUESTION:In a can, there is a mixture of milk and water in the ratio 5:3. If the can is filled with an additional 20 liters of milk, the can would be full and the ratio of milk and water would become 3:1. Find the capacity of the can? options: A)52 B)56 C)60 D)64 E)68 SOLUTION:Let C be the capacity of the can. (5/8)*(C-20)+20=(3/4)*C 5C-100+160=6C C=60 The answer is C. #### C QUESTION:In how many different ways can the letter of the word 'BOTTLE ' be arranged in such a way that the vowels occupy the odd positions? options: A)63 B)48 C)85 D)52 E)47 SOLUTION:In the given word there 6 letters in that there are 2 vowels and 4 consonants no of ways of arranging the vowels=2p2=2 no of ways of arranging the consonants=4p4=24 total number of ways 24*2=48 Answer(B) #### B QUESTION:A 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 27m/h. what is the speedof the person while he was going to his office? options: A)8km/h B)10km/h C)12km/h D)13km/h E)18km/h SOLUTION:u = k , v= 3k \inline \therefore \frac{2uv}{u+v}\: \: \Rightarrow \frac{2\times k\times 3k}{(k+3k)}=27 \inline \Rightarrow 1.5k = 27 \inline \Rightarrow k=18km/h E #### E QUESTION:If BAT = 58 HAT = 52 CAT = 57 then whats RAT = ? options: A)42 B)45 C)34 D)76 E)25 SOLUTION:A 42 #### A QUESTION:A train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds. Its length is? options: A)176 m B)198 m C)197 m D)150 m E)168 m SOLUTION:Let the length of the train be x meters and its speed be y m/sec. They, x / y = 15 => y = x/15 x + 100 / 25 = x / 15 x = 150 m. Answer:D #### D QUESTION:If Re.1 amounts to Rs.9 over a period of 20 years. What is the rate of simple interest? options: A)49% B)90% C)60% D)40% E)41% SOLUTION:8 = (1*20*R)/100 R = 40% Answer:D #### D QUESTION:The average of three consecutive odd numbers is 12 more than one third of the first of these numbers. What is the last of the three numbers? options: A)15 B)17 C)19 D)21 E)23 SOLUTION:x,x+2,x+4 are three odd numbers (x+x+2+x+4)/3=12+(x/3) x=15 last no.=x+4=19 ANSWER:C #### C QUESTION:A family X went for a vacation. Unfortunately it rained for 13 days when they were there. But whenever it rained in the mornings, they had clear afternoons and vice versa. In all they enjoyed 11 mornings and 12 afternoons. How many days did they stay there totally? options: A)16 B)18 C)20 D)13 E)14 SOLUTION:Explanation : Clearly 11 mornings and 12 afternoons = 23 half days => Since 13 days raining means 13 half days. => So 23-13 =10 halfdays ( not effecetd by rain ) => So 10 halfdays =5 fulldays Hence , Total no. of days = 13+5 =18 days Answer : B #### B QUESTION:In 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? options: A)15 B)20 C)25 D)30 E)35 SOLUTION:55 + 40 + 20 = 115 This number includes some people counted twice and some people counted three times. 115 - 88 = 27, and this number represents people counted twice or three times. 7% of the people are counted two extra times. The percentage of people counted one extra time is 27 - 7(2) = 13. The percentage of people who liked more than one product is 7% + 13% = 20%. The answer is B. #### B QUESTION:Three people are playing cards. What is the probability that a card drawn from a pack of 52 cards will be a diamond or a king? options: A)1/13 B)2/15 C)4/13 D)3/17 E)1/19 SOLUTION:Here, n(S) = 52 There are 13 cards that are diamond (including one king) and there are 3 more kings. Let E = event of getting a diamond or a king. Then, n(E) = (13 + 3) = 16 P (E) = 16 / 52 = 4/13 C #### C QUESTION:Mr. Ram is on tour and he has Rs 360 for his expenses. If he exceeds his tour by 4 days he must cut down daily expenses by Rs 3. The number of days of Mr. Ram's tour programme is options: A)28 Days B)24 Days C)22 Days D)20 Days E)None of these SOLUTION:Solution: Let Ram under takes a tour of x days. Then, expenses for each day = 360/x 360/x+4=360/x−3 x=20x=20 and −24−24 Hence, x= 20 days. Option(D) #### D QUESTION:12 buckets of water fill a tank when the capacity of each tank is 13.5 litres. How many buckets will be needed to fill the same tank, if the capacity of each bucket is 9 litres? options: A)15 bukets B)17 bukets C)18 bukets D)19 bukets E)None of these SOLUTION:Explanation: Capacity of the tank = (12*13.5) litres = 162 litres Capacity of each bucket = 9 litres. So we can get answer by dividing total capacity of tank by total capacity of bucket. Number of buckets needed = (162/9) = 18 buckets Option C #### C QUESTION:A two-digit number is such that the product of the digits is 8. When 18 is added to the number, then the digits are reversed. The number is: options: A)18 B)24 C)42 D)81 E)28 SOLUTION:Let the ten's and unit's digit be x and 8/x respectively. Then, (10x + 8/x) + 18 = 10 * 8/x + x 9x2 + 18x - 72 = 0 x2 + 2x - 8 = 0 (x + 4)(x - 2) = 0 x = 2 So, ten's digit = 2 and unit's digit = 4. Hence, required number = 24. ANSWER:B #### B QUESTION:A 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? options: A)$500 B)$1000 C)$2000 D)$3000 E)5000 dollar SOLUTION:Explanation: In scientific notation 240 million is 2.4x10^8. So the per capita expenditure was: ($1.2x10^12)/(2.4x10^8)=($1.2)/(2.4)x10^12-8=$0.5x10^4=$5000 Answer: Option E #### E QUESTION:In a joint business, the capital of A, B and C were Rs. 45000, Rs. 30000 and Rs. 22500 respectively. A withdrew half of his capital after 4 months. After 9 months of this withdrawal, there was a total profit of Rs. 28400. Find the A share of profit? options: A)10600 B)10400 C)10200 D)12200 E)14200 SOLUTION:Given A=45000 B=30000 C=22500 A:B:C= 450:300:225 As A withdrew its half of capital after 4 months,it can withdraw 22500 rupees But before 4 months, it is 45000 only and the profit is calculated after withdrwal it is almost 9+4=13 months.For that 9 months, the capital for A is half of its original capital, So A= 450*4+ 225*9= 1800+2025= 3825 Similarly, B= 300*13=3900 Similarly,C= 225*13= 2925 Therefore, ratio of A:B:C= 3825: 3900 : 2925= 51:52:39 A's share=51/142(28400)=10200 ANSWER:C #### C QUESTION:The difference of the squares of two consecutive even integers is divisible by which of the following numbers? options: A)4 B)3 C)7 D)6 E)9 SOLUTION:Let the consecutive even integers are n and (n + 2) difference of the squares = (n + 2)^2 - n^2 = (n^2 + 4n + 4) - n^2 = 4n + 4 = 4(n + 1) which is divisible by 4 Answer is A #### A QUESTION:A train 320 m long passed a pole in 28 sec. How long will it take to pass a platform 700 m long? options: A)12 sec B)59 sec C)93 sec D)89 sec E)46 sec SOLUTION:Speed = 320/28 = 11 m/sec. Required time = (320 + 700)/11 = 92.7 sec. Answer: C #### C QUESTION:Evaluate : (2.39)(power 2) - (1.61) (power 2) / 2.39 - 1.61 options: A)4 B)6 C)8 D)2 E)10 SOLUTION:Given Expression = a(power 2) - b(power 2) / a-b = (a + b)(a - b) / (a-b) = (a + b) = (2.39 + 1.61) = 4. Answer is A. #### A QUESTION:What is the greatest prime factor of 4^16 - 2^30? options: A)2 B)3 C)5 D)7 E)11 SOLUTION:4^16 - 2^30 =(2^2)^16 - 2^30 = 2^32 - 2^30 = 2^30 (2^2 -1) = 2^30 * (4-1) = 2^30 * 3 The greatest prime factor is 3. The answer is B. #### B QUESTION:The volume of a sphere with radius r is (4/3)*pi*r^3 and the surface area is 4*pi*r^3. If a sperical balloon has a volume of 4500 pi cubic centimeters, what is hte surface area of the balloon in square centimeters? options: A)a. 40 B)b. 100 C)c. 400 D)d. 1,000 E)e. 2,000 SOLUTION:The surface area is 4.pi.r^2 (its area remember not volume) as 4/3.pi.r^3=4500pi r=15 so area = 4.pi.r^2= 900.pi= 900 x 3.14 = 2000 (approx) E #### E QUESTION:A Card marked 1 and 2 on its two faces. Two colors, white and black are used to paint the two faces of the card. If the card is painted with the different colors, in how many ways can the card be painted? options: A)3 B)6 C)2 D)12 E)27 SOLUTION:If the base of the card is white, then in order the card to be painted with the different colors, the top must be white.Another side can be painted in Black. But we can have the base painted in either of the two colors, thus the total number of ways to paint the card is 2*1=2. Answer: C. #### C QUESTION:A, B and C can do a piece of work in 7 days, 14 days and 28 days respectively. How long will they taken, if all the three work together? options: A)6 days B)4 days C)8 days D)5 days E)1 days SOLUTION:1/7 + 1/14 + 1/28 = 7/28 = 1/4 => 4 days Answer: B #### B QUESTION:If the speed of the boat in still water is 12km/hr and the speed of the stream is 5km/hr. Find the time taken to travel 34kms down stream. options: A)4 hrs. B)1 hrs. C)3 hrs. D)2 hrs. E)5 hrs. SOLUTION:DS =speed of the boat + speed of the stream 5+12 =17km/hr. Time taken to cover 34km down stream =34/17 =2hrs. Answer : D #### D QUESTION:A man can row upstream at 45 kmph and downstream at 55 kmph, and then find the speed of the man in still water? options: A)32 kmph B)34 kmph C)30 kmph D)50 kmph E)65 kmph SOLUTION:US = 45 DS = 55 M = (45 + 55)/2 = 50 Answer:D #### D QUESTION:Given that p is a positive even integer with a positive units digit, if the units digit of p^3 minus the units digit of p^2 is equal to 0, what is the units digit of p +2? options: A)7 B)8 C)9 D)10 E)11 SOLUTION:p is a positiveeveninteger with apositive units digit--> the units digit of p can be 2, 4, 6, or 8 --> In order the units digit of p^3 - p^2 to be 0, the units digit of p^3 and p^2 must be the same. Thus the units digit of p can be 0, 1, 5 or 6. Intersection of values is 6, thus the units digit of p + 2 is 6 + 2 = 8. Answer: B. #### B <<<Examples ends QUESTION:A is twice as good a workman as B and together they complete a work in 12 days. In how many days A alone can do the work? options: A)32 B)33 C)34 D)35 E)36 SOLUTION:A’s one day’s work : B’s one day’s work= 2:1 (A+B)’s one day’s work= 1/12 B’s one day’s work= 1/12 *1/3 = 1/36 B alone can do the work in 36 days ANSWER:E #### E

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:Two numbers are in the ratio 3 : 4. If the sum of numbers is 63, find the numbers. options: A)26,37 B)25,38 C)27,36 D)28,35 E)29,34 SOLUTION:Sum of the terms of the ratio = 3 + 4 = 7 Sum of numbers = 63 Therefore, first number = 3/7 × 63 = 27 Second number = 4/7 × 63 = 36 Therefore, the two numbers are 27 and 36. Answer:C #### C QUESTION:A monkey ascends a greased pole 12 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 ? options: A)21st B)22nd C)23rd D)24th E)None of these SOLUTION:In 2 minutes, he ascends = 1 metre ∴ 10 metres, he ascends in 20 minutes. ∴ He reaches the top in 21st minute. Answer B #### B QUESTION:A reduction of 25% in the price of oil enables a house wife to obtain 5kgs more for Rs.1000, what is the reduced price for kg? options: A)s.50 B)s.46 C)s.49 D)s.41 E)s.42 SOLUTION:1000*(25/100) = 250 ---- 5 ? ---- 1 => Rs.50 Answer: A #### A QUESTION:For a certain exam,a score of 86 was 5 standard deviations above mean and a score of 67 was 2.5 standard deviations above mean.What was the mean score for the exam? options: A)50 B)55 C)48 D)42 E)49 SOLUTION:Mean+5SD=86 Mean+2.5SD=67 By solving above equations we get, SD (absolute value)=7.6 Mean=48 ANS. C #### C QUESTION:The difference between simple and compound interest on Rs. 1600 for one year at 10% per annum reckoned half-yearly is? options: A)8 B)3 C)9 D)4 E)2 SOLUTION:S.I. = (1600 * 10 * 1)/100 = Rs. 160 C.I. = [1600 * (1 + 5/100)2 - 1600] = Rs. 164 Difference = (164 - 160) = Rs.4. Answer:D #### D QUESTION:A toy store regularly sells all stock at a discount of 10 percent. If an additional 10 percent were deducted from the discount price during a special sale, what would be the lowest possible price of a toy costing $10 before any discount? options: A) $7.20 B) $8.00 C) $8.10 D) $8.27 E) $9.00 SOLUTION:sale price = (original price - 10% decrease) - 10% decrease price = [10 * (90/100)] * (90/100) = 10 * (.90) * (.90) = 9 * .90 = 8.10 The answer is C. #### C QUESTION:A can complete a project in 20 days and B can complete the same project in 20 days. If A and B start working on the project together and A quits 10 days before the project is completed, in how many days will the project be completed? options: A)18 days B)27 days C)26.67 days D)16 days E)15 days SOLUTION:Let X = the number of days taken to complete the project. The amount of work done by A is (x-10) * (1/20). The amount of work done by B is (x) * (1/30). (1/20)*(x-10) + (1/20)*(x) = 1 (x/20) + (x/20) - (10/20) = 1 x/10 = 3/2 x = 15 Therefore, the answer is E: 15. #### E QUESTION:Three positive integers a, b, and c are such that their average is 20 and a ≤ b ≤ c. If the median is (a + 11), what is the least possible value of c? options: A)23 B)21 C)25 D)26 E)24 SOLUTION:Solution Given Data 3 positive integers Average of a, b, and c = 20. So, a+b+c3a+b+c3 = 20 or a + b + c = 60 a ≤ b ≤ c Median = (a + 11) Median of these 3 numbers a, b, and c is ‘b’ because a ≤ b ≤ c Therefore, b = a + 11 Objective To find the least value of 'c' Theoretically, the least value of c is when c = b. Therefore, a + (a + 11) + (a + 11) = 60 (b and c are equal and b, the median, is a + 11) Or 3a = 38 or a = 12.66 So, b = c = 12.66 + 11 = 23.66 However, we know that these numbers are all integers. Therefore, a, b, and c cannot take these values. So, the least value for c with this constraint is NOT likely to be when c = b Let us increment c by 1. Let c = (b + 1) In this scenario, a + (a + 11) + (a + 12) = 60 Or 3a = 37. The value of the numbers is not an integer in this scenario as well. Let us increment c again by 1. i.e., c = b + 2 Now, a + (a + 11) + (a + 13) = 60 Or 3a = 36 or a = 12. If a = 12, b = 23 and c = 25. The least value for c that satisfies all these conditions is 25. Correct answer is choice C. #### C QUESTION:A word is defined as a sequence of five dots arranged in a row. Each dot is colored either red, yellow, or blue. How many distinct words can be formed? options: A)124 B)150 C)212 D)243 E)316 SOLUTION:3^5 = 243 The answer is D. #### D QUESTION:What is the smallest possible common multiple of three integers, all larger than 53? options: A)27. B)54. C)846. D)19,656. E)21,924. SOLUTION:The Least common positive multiple would be for the immediate least number(s) after 53 i.e 54. Since nowhere is it stated that the three integers must be different, the integers could be 54,54 and 54... leading to least possible positive common multiple to be 54. Answer B. #### B QUESTION:When 30 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? options: A)3 : 4 B)4 : 3 C)3 : 2 D)Data inadequate E)None of these SOLUTION:Let the first and the second numbers be x and y respect then y + 30% of x = 140% of y or, y + 0.3x = 1.4y or, 0.3x = 0.4y ∴ x : y = 0.4 : 0.3 = 4 : 3 Answer B #### B QUESTION:The sector of a circle has radius of 20 cm and central angle 135o. Find its perimeter? options: A)91.5 B)87.1 C)91.7 D)91.3 E)91.1 SOLUTION:Perimeter of the sector = length of the arc + 2(radius) = (135/360 * 2 * 22/7 * 20) + 2(20) = 47.1 + 40 = 87.1 cm Answer:B #### B QUESTION:Mice can multiply very fast. Adult mice can give birth once every month, and baby mice grow into adult mice in just two months after they are born. If you would buy a baby mouse just after it was born, how many mice would you have in 10 months? options: A)1 B)2 C)3 D)4 E)5 SOLUTION:One. You cannot have more mice if you start with one! Answer A #### A QUESTION:The ratio of two numbers is 4 : 7 and their H.C.F. is 4. Their L.C.M. is options: A)112 B)22 C)56 D)27 E)35 SOLUTION:Explanation: Let the numbers be 4x and 7x. Then, their H.C.F. = x. So, x = 4. So, the numbers 16 and 28. L.C.M. of 16 and 28 = 112. Answer: Option A #### A QUESTION:What annual payment dischargea debit of Rs.12900, due in 4yrs.At 5% rate? options: A)2000 B)2200 C)3000 D)3400 E)3500 SOLUTION:A.P.=(200X12900)/[4(200+5X3)]=3000 Ans Alternative 100+105+110+115=12900 430=12900 100=12900/(430)X100=3000 C #### C QUESTION:The reflex angle between the hands of a clock at 10.25 is: options: A)180º B)192 1/2 º C)195º D)197 1/2 º E)197 º SOLUTION:Angle traced by hour hand in 125/12 hrs ={(360/12)x(125/2)}º = 312 1/2 º . Angle traced by minute hand in 25 min =(360/60)x 25 º= 150º. Reflex angle = 360º -(312 1/2- 150º )= 360º - 162 1/2º= 197 1/2º . Answer: D #### D QUESTION:Each 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 45 hours If Harry and James were paid the same amount last week, how many hours did Harry work last week ? options: A)35 B)36 C)37 D)43 E)39 SOLUTION:James worked for 41 hours hence he earned 40*x+5*2x=50x dollars; We know that Harry also earned the same 50x dollars, out of which he earned 30x dollars for thefirst 30 hoursplus 20x additional dollars. Since for each additional hour he gets 1.5x dollars then he worked for 20x/1.5x=13 additional hours, so Harry worked for total of 30+13=43 hours. Answer: D. #### D QUESTION:Of 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? options: A)2443200 B)3643200 C)5443200 D)1443200 E)2163200 SOLUTION:Of 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? A. 24 B. 36 C. 72 D. 144 E. 216 Choosing the digit for p - 9 ways; Choosing the digit for q - 8 ways; Choosing the digit for r - 7ways; Choosing the digit for s - 6ways; Choosing the digit for t - 5ways; # of permutations of 3 digits in ppqrst - 6!/2! Total: 9*8*7*6*5*6!/2!=5443200. Answer: C. #### C QUESTION:The average successfull Search time for sequential search on n items is options: A)n/2 B)(n-1)/2 C)(n+1)/2 D)log(n)+1 E)(n)+1 SOLUTION:To understand this think as there is an array and now you are searching for an element which is a[0] element in that arrary...so for this you need to do 1 comparison. Now similarly for sequential searching suppose your are looking for an element which is present at 2nd position i.e a[1] position of that array then you will get answer within 2 comparisons. Now similarly if you have n elements and your desired element is the nth element then you will have to do n comparisons. so we can write total search time will be: (1+2+3+........+n) average search time will be (1+2+3+........+n)/n NOW we know sum of n natural numbers i.e 1+2+3+.....n= {n(n+1)}/2 ANSWER: C #### C QUESTION:P and Q can complete a work in 10 days and 6 days respectively. P alone started the work and Q joined him after 2 days till the completion of the work. How long did the work last? options: A)5 days B)10 days C)14 days D)22 days E)26 days SOLUTION:Explanation : Work done by P in 1 day = 1/10 Work done by Q in 1 day = 1/6 Work done by P in 2 days = 2 × (1/10) = 1/5 Remaining work = 1 – 1/5 = 4/5 Work done by P and Q in 1 day = 1/10 + 1/6 = 4/15 Number of days P and Q take to complete the remaining work = (4/5) / (4/15) = 3 Total days = 2 + 3 = 5 Answer : Option A #### A QUESTION:The mean of 50 observations is 200. But later he found that there is decrements of 15 from each observations. what is the the updated mean is ? options: A)170 B)185 C)190 D)198 E)200 SOLUTION:185 Answer is B #### B QUESTION:The average age of 29 students in a group is 15 years. when teacher's age is included to it, the average increases by one.What is the teacher's age in years? options: A)31 B)36 C)29 D)53 E)57 SOLUTION:age of the teacher=(29*16-29*15) =29 years. ANSWER:C #### C QUESTION:The speed of a boat in still water is 50kmph and the speed of the current is 20kmph. Find the speed downstream and upstream? options: A)40, 68 kmph B)40, 30 kmph C)70, 30 kmph D)40, 60 kmph E)20, 60 kmph SOLUTION:Speed downstream = 50 + 20 = 70 kmph Speed upstream = 50 - 20 = 30 kmph Answer: C #### C QUESTION:Express of the following as a fraction: 25% options: A)1/4 B)1/8 C)2/9 D)3/6 E)None of them SOLUTION:25% = 25/100= 1/4. Answer is A. #### A QUESTION:In a simultaneous throw of 2 dice what is the probability of getting a total of 6? options: A)1/4 B)5/36 C)2/11 D)3/13 E)1/5 SOLUTION:n(S) = 6*6 = 36 E = {(1,5),(2,4),(3,3),(4,2),(5,1)} Probability = 5/36 Answer is B #### B QUESTION:A man can row upstream 10 kmph and downstream 30 kmph. Find the rate of the stream and man rate in still water. options: A)15,20 B)30,20 C)1,20 D)20,20 E)10,20 SOLUTION:Explanation: Please remember, If a is rate downstream and b is rate upstream Rate of current = 1/2(a-b) Rate in still water = 1/2(a+b) => Rate of current = 1/2(30-10) = 10 kmph => Rate in still water = 1/2(30+10) = 20 kmph Option E #### E QUESTION:The speed at which a man can row a boat in still water is 9 kmph. If he rows downstream, where the speed of current is 3 kmph, what time will he take to cover 60 metres? options: A)16 seconds B)34 seconds C)14 seconds D)18 seconds E)15 seconds SOLUTION:Speed of the boat downstream = 9 + 3 = 12 kmph = 12 * 5/18 = 10/3 m/s Hence time taken to cover 60 m = 60*3/10 = 18 seconds. Answer: D #### D QUESTION:The average age of a husband and his wife was 23 years at the time of their marriage.After 5 years they have a one year old child.The average of the family is now? options: A)18 years B)23 years C)29 years D)26 years E)19 years SOLUTION:sum of the present age of husband, wife and child =(23*2+5*2)+1 = 57 years required average = 57/3 = 19 years. Answer :E #### E QUESTION:A dishonest dealer professes to sell goods at the cost price but uses a false weight and gains 25%. Find his false weight age? options: A)2288 B)277 C)800 D)2878 E)211 SOLUTION:25 = E/(1000 - E) * 100 1000 - E = 4E 1000 = 5E => E = 200 1000 - 200 = 800.Answer: C #### C QUESTION:A grocer has a sale of Rs. 5420, Rs. 5660, Rs. 6200, Rs. 6350 and Rs. 6500 for 5 consecutive months. Find the sale he should have in the sixth month, so that he gets an average sale of Rs. 6500? options: A)Rs. 5870 B)Rs. 5991 C)Rs. 8870 D)Rs. 6850 E)None of these SOLUTION:Explanation: Total sale for 5 months = Rs. (5420 + 5660 + 6200 + 6350 + 6500) = Rs. 30,130 Therefore, required sale = Rs. [(6500 * 6) – 30,130] = Rs. (39000 – 30,130) = Rs. 8870 ANSWER C #### C QUESTION:The only contents of a container are 4 blue disks and 8 green disks. If 3 disks are selected one after the other, and at random and without replacement from the container, what is the probability that 1 of the disks selected is blue, and 2 of the disks selected are green? options: A)21/55 B)28/55 C)34/55 D)5/8 E)139/220 SOLUTION:Prob of selecting one blue and two green is (4*8*7/12*11*10) one blue and two green can be arranged in 3!/2! ways hence the prob becomes 3*4*8*7/12*11*10=28/55 Correct answer is B #### B QUESTION:log3 N+log12 N what is 3 digit number N that will be whole number options: A)6291 B)7292 C)1728 D)1929 E)1727 SOLUTION:No of values N can take is 1 12^3=1728 ANSWER:C #### C QUESTION:Evaluate: |4 - 8(3 - 12)| - |5 - 11| = options: A)49 B)55 C)69 D)70 E)82 SOLUTION:According to order of operations, inner brackets first. Hence |4 - 8(3 - 12)| - |5 - 11| = |4 - 8*(-9)| - |5 - 11| According to order of operations, multiplication within absolute value signs (which may be considered as brackets when it comes to order of operations) next. Hence = |4 + 72| - |5 - 11| = |76| - |-6| = 76 - 6 = 70 correct answer D)70 #### D QUESTION:he average weight of 8 persons increases by 2.5 kg when a new person comes in place of one of them weighing 60 kg. What might be the weight of the new person ? options: A)75 kg B)55 kg C)80 kg D)85 kg E)25 kg SOLUTION:Explanation: Total weight increased = (8 x 2.5) kg = 20 kg. Weight of new person = (60 + 20) kg = 80 kg. Answer: C #### C QUESTION:If x and y are integers such that (x+1)^2 is less than or equal to 16 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? options: A) -16 B) -10 C) 0 D) 14 E) 16 SOLUTION:(x+1)^2 <= 16 x <= 3 x >= -5 (y-1)^2< 64 y < 9 y > -7 Max possible value of xy is -5 × -6 = 30 minimum possible value of xy is -5 × 8 = -40 -40 + 30 = -10 Answer : B #### B QUESTION:The average height of 35 boys in a class was calculated as 182cm. 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).? options: A)180.27 cm B)180.29 cm C)978.29 cm D)178.89 cm E)176.29 cm SOLUTION:Calculated average height of 35 boys = 182 cm. Wrong total height of 35 boys = 182 * 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 = 182cm - (166 cm - 106 cm)/35 = 182 cm - 60 /35 cm = 182 cm - 1.71 cm = 180.29 cm. Answer: B #### B QUESTION:16 welders work at a constant rate they complete an order in 8 days. If after the first day, 9 welders start to work on the other project, how many more days the remaining welders will need to complete the rest of the order? options: A)5 B)2 C)8 D)4 E)16 SOLUTION:1. We need to find out the time taken by 7 workers after day 1. 2. total no.of wokers * total time taken = time taken by 1 worker 3. Time taken by 1 worker = 16*8 = 128 days 4. But on day 1 sixteen workers had already worked finishing 1/8 of the job. So 7 workers have to finish only 7/8 of the job. 5. Total time taken by 7 workers can be got from formula used at (2). i.e., 7* total time taken = 128. Total time taken by 7 workers to finish the complete job is 128/7 = 18.286 days. 6. Time taken by 7 workers to finish 7/8 of the job is 7/8 * 18.286 = 16 days. The answer is choice E #### E QUESTION:Ram 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. options: A)12 , 18 B)8 , 10 C)18 , 20 D)20 , 25 E)None of these SOLUTION:Explanation : Let speed of ram and shakil be x and y resp. Case 1 : Ram gives a start of 200m and beats Shakil by 1 minute. 2000/x - 1800/y= -60 2000/x= 1800/y -60---------------------(1) Case2: Ram gives Shakil a start of 6 min and is beaten by 1000 meters distance travelled by shakil in 6 minutes= (6*60*y) meters = 360y meters 1000/x = (2000- 360y)/y------------------(2) Solve equation 1 and 2 to obtain x and y Answer is x = 8 minutes, y = 10 minutes Hence (B) is the corret answer. Answer : B #### B QUESTION:If y is an integer, then the least possible value of |23 - 4y| is options: A)1 B)2 C)3 D)4 E)5 SOLUTION:We know that 4y is a multiple of 4, so let’s first look at the multiples of 4 closest to 23. We have “20” and “24”. Let’s subtract both of these from 23 and see which one produces the smallest result. When 4y = 20, y is 5 and when 4y = 24, y is 5. Let’s start with letting y = 4. |23-4(5)| |23-20| |3| = 3 Next, let’s let y equal 5. |23-4(6)| |23-24| |-1| = 1 We see that the smallest possible value of |23-4y| is 1. Answer A. #### A QUESTION:A 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? options: A)227 B)268 C)240 D)889 E)232 SOLUTION:Speed = [54 * 5/18] m/sec = 15 m/sec. Length of the train = (15 * 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:C #### C QUESTION:The 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? options: A)1320 sq.metres B)4260 sq.metres C)6870 sq.metres D)7875 sq.metres E)None of these SOLUTION:Let the length and breadth be 7x and 5x respectively. Then, P = 2(7x + 5x) = 360 ⇒ x = 15 Area = 7 × 15 × 5 × 15 = 7875 sq.m. Answer D #### D QUESTION:Two 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? options: A)9:36 B)9:31 C)9:35 D)9:37 E)9:32 SOLUTION:1/4 : 3/4 = (1:3)5 = 5:15 1/5 : 4/5 = (1:4)4 = 4:16 ------ 9:31 Answer: B #### B QUESTION:The average weight of a group of persons increased from 48 kg to 51 kg, when two persons weighing 78 kg and 93 kg join the group. Find the initial number of members in the group? options: A)87 B)67 C)23 D)75 E)25 SOLUTION:Let the initial number of members in the group be n. Initial total weight of all the members in the group = n(48) From the data, 48n + 78 + 93 = 51(n + 2) => 51n - 48n = 69 => n = 23 Therefore there were 23 members in the group initially. Answer: C #### C QUESTION:Which number should replace both the asterisks in (* /18) x (*/162) = 1 ? options: A)27 B)36 C)54 D)72 E)90 SOLUTION:Let (y/18) x (y/162) = 1 y^2 = 18 x 162 = 18 x 18 x 9 y = (18 x 3) = 54 The answer is C. #### C QUESTION:Out of 40 applicants to a law school, 15 majored in political science, 20 had a grade point average higher than 3.0, and 10 did not major in political science and had a GPA equal to or lower than 3.0. How many T applicants majored in political science and had a GPA higher than 3.0? options: A)5 B)10 C)15 D)25 E)35 SOLUTION:Total applicants = 40 Political science = 15 and Non political science = 40 - 15 = 25 GPA > 3.0 = 20 and GPA <= 3.0 = 20 10 Non political science students had GPA <= 3.0 --> 15 Non political science students had GPA > 3.0 GPA > 3.0 in political science = Total - (GPA > 3.0 in non political science) T= 20 - 15 = 5 Answer: A #### A QUESTION:The total marks obtained by a student in Mathematics and Physics is 50 and his score in Chemistry is 20 marks more than that in Physics. Find the average marks scored in Mathamatics and Chemistry together. options: A)15 B)25 C)35 D)45 E)55 SOLUTION:Let the marks obtained by the student in Mathematics, Physics and Chemistry be M, P and C respectively. Given , M + C = 50 and C - P = 20 M + C / 2 = [(M + P) + (C - P)] / 2 = (50 + 20) / 2 = 35. ANSWER:C #### C QUESTION:A man cheats while buying as well as while selling. While buying he takes 11% more than what he pays for and while selling he gives 20% less than what he claims to. Find the profit percent, if he sells at 9.09% below the cost price of the claimed weight. options: A)19.81% B)20% C)37.5% D)25% E)42.86% SOLUTION:There is a one step calculation method too. It requires more thought but is faster. The man takes 11% more than what he pays for. So if he claims to take 100 pounds, he pays $100 but he actually takes 111 pounds for which he will take from the customer $111. Hence, in effect, there is a 11% mark up. While selling, he sells 30% less. This means, he claims to sell 100 pounds and gets $100 but actually sells only 70 pounds and should have got only $70 for it. So this is again a mark up of $30 on $70. But he also sells at 9.09% less i.e. gives a discount of 1/11. (1 + m1%)(1 + m2%)(1 - d%) = (1 + p%) 11/10 * 10/7 * 10/11 = (1 + p%) profit % = 42.86%E #### E QUESTION:If A and B are two prime numbers bigger than 2, which of the following can't be true? (1) A + B is an even number. (2) A - B is also a Even number. (3) A^B is also a prime number. options: A)1 only. B)2 only. C)3 only. D)2 and 3 only. E)1, 2 and 3. SOLUTION:Answer is D : 2 and 3 only (1) A + B is an even number. : All primes beyond 2 are odd, so odd+odd = even, so true (2) A - B is also a Even number. : True (3) A^B is also a prime number. : Beats the property of primes, so false Ans : C #### C QUESTION:Jemma takes 2 hours to swim the 4 miles from buoy A to buoy B. Tired from her swim, she then continues to buoy C at half her previous speed. If buoy C is 6 miles away from buoy B, how many more hours will pass before Jemma reaches Buoy C? options: A)4 B)5 C)6 D)7 E)8 SOLUTION:Time taken for Jemma to reach buoy B is 2 hours. The distance between the buoys is 4 miles. Distance travelled/time taken = Average speed Hence the average speed to travel the distance is 2m/hr Now, she would have to travel 6 miles . However as she is tired the speed is half or 1m/hr Hence, it will take her 6 hours (Option C) #### C QUESTION:A train, 800 meter long is running with a speed of 78 km/hr. It crosses a tunnel in 1 minute. What is the length of the tunnel ? options: A)650 meter B)555 meter C)500 meter D)458 meter E)None of these SOLUTION:Explanation: Let length of tunnel is x meter Distance = 800+x meter Time = 1 minute = 60 seconds Speed = 78 km/hr = 78*5/18 m/s = 65/3 m/s Distance = Speed*Time =>800+x=65/3∗60 =>800+x=20∗65=1300 =>x=1300−800=500 So the length of the tunnel is 500 meters. Option C #### C QUESTION:One young and one old man reach a same distance in 20min and 30min respectively. If old starts at 10.00am and youngman starts at 10.05am. When they meet. Pls provide solution options: A)12m B)14m C)15m D)16m E)17m SOLUTION:The real ans is 10:15am Let the dis be 30 m Old man travel 1m/min Young travel 1.5m/min At 10:05 old man = 5m young = 0m At 10:10 old man = 10m young = 7.5m At 10:15 old man= 15m young = 15m ANSWER:C #### C QUESTION:It takes 3 workers a total of 15 hours to build a giant machine with each worker working at the same rate. If 5 workers start to build the machine at 11:00 AM, and one extra worker per hour is added beginning at 1:00 PM, at what time will the machine be complete? options: A)4:30 B)4:45 C)5:00 D)5:15 E)5:30 SOLUTION:3 workers build 1/15 of a machine in one hour. 1 worker builds 1/45 of a machine in one hour. In the first 2 hours, 5 workers build 5*(1/45)*2=10/45 of a machine. From 1:00 to 2:00, 6 workers build another 6/45. The total is 16/45. From 2:00 to 3:00, 7 workers build another 7/45. The total is 23/45. From 3:00 to 4:00, 8 workers build another 8/45. The total is 31/45. From 4:00 to 5:00, 9 workers build another 9/45. The total is 40/45. To build another 5/45, 10 workers need (5/10)*60 minutes which is 30 minutes. The machine is complete at 5:30. The answer is E. #### E QUESTION:An optometrist charges $150 per pair for soft contact lenses and $85 per pair for hard contact lenses. Last week she sold 5 more pairs of soft lenses than hard lenses. If her total sales for pairs of contact lenses last week were $2,160, what was the total number of pairs of contact lenses that she sold? options: A) 11 B) 13 C) 15 D) 17 E) 19 SOLUTION:(x+5)*150 +x*85=2160 =>x=6 total lens=6+(6+5)= 17 Answer D #### D QUESTION:A man can do a piece of work in 5days, but with the help of his son, he can finish it in 4days. In what time can the son do it alone? options: A)5 B)5 1/2 C)7 1/2 D)6 E)20 SOLUTION:Son's 1day work = 1/4 - 1/5 = 1/20 Son alone can do the work in 20days = 20 days Answer is E #### E QUESTION:The fourth proportional to 5, 8, 15 is options: A)18 B)19 C)20 D)24 E)None SOLUTION:Sol. Let the fourth proportional to 5, 8, 15 be x. Then, 5 : 8 : : 15 : x ⇔ 5x = (8x15) ⇔ x = (8x15) / 5 = 24. Answer D #### D QUESTION:The G.C.D of 1.08, 0.42 and 0.9 is options: A)0.19 B)0.1 C)0.06 D)0.11 E)0.12 SOLUTION:Explanation: Given numbers are 1.08 , 0.42 and 0.90 H.C.F of 108, 42 and 90 is 6 [because G.C.D is nothing but H.C.F] therefore H.C.F of given numbers = 0.06 Answer: C) #### C QUESTION:On dividinng 109 by a number, the quotient is 9 and the remainder is 1. Find the divisor. options: A)12 B)14 C)15 D)16 E)17 SOLUTION:d = (D-R)/Q = (109 - 1)/9 = 108/9 = 18 A #### A QUESTION:What is the sum of the different positive prime factors of 960? options: A)5 B)10 C)15 D)17 E)21 SOLUTION:Prime factorization of 960 =96 * 10 =16*6 * 10 =4*4 * 2*3 * 2*5 =2*2 * 2*2 * 2* 3 * 2*5 =2^6 * 3 * 5 Sum of the different positive prime factors of 960 = 2+3+5 =10 Answer B #### B QUESTION:In 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? options: A)39yr B)42yr C)45yr D)32yr E)50yr SOLUTION:Let B's present age = x years Then A's present age = x+9 years x+9+10 = 2(x-10) x + 19 = 2x - 20 x = 39years Answer is A #### A QUESTION:The 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 options: A)1,000 B)2,000 C)2,100 D)2,250 E)2,540 SOLUTION:Explanation: I1 = (P x 3 x 11)/100 = P/3 I2 = (P x 4 x 4)/100 = 4P/25 I3 = (P x 1 x 5)/100 = P/20 P/3 + 4P/25 + P/20 = 540 27P/50 = 540 P = 1000 Answer: Option A #### A QUESTION:A shopkeeper sells some toys at Rs. 250 each. What percent profit does he make? To find the answer, which of the following information given in Statements I and II is/are necessary? I. Number of toys sold. II. Cost price of each toy. options: A)Only I is necessary B)Only II is necessary C)Both I and II are necessary D)Either I or II ins necessary E)None of these SOLUTION:EXPLANATION S.P. = Rs. 250 each. To find gain percent, we must know the C.P. of each. answer is (B). #### B QUESTION:A and B can do a piece of work in 18 days; Band C can do it in 24 days A and C can do it in 36 days. In how many days will A, Band C finish it together? options: A)16 days B)12 days C)3 days D)5 days E)9 days SOLUTION:Sol. (A + B)'s 1 day's work = (1/18) (B + C)'s 1 day's work = (1/24) and (A + C)'s 1 day's work = (1/36) Adding, we get: 2 (A + B + C)'s 1 day's work =¬(1/18 + 1/24 + 1/36) =9/72 =1/8 (A +B + C)'s 1 day's work =1/16 Thus, A, Band C together can finish the work in 16 days. Ans: A #### A QUESTION:The average age of a family of 5 members is 20 years. If the age of the youngest member be 10 years then what was the average age of the family at the time of the birth of the youngest member? options: A)13.5 B)14 C)15 D)12.5 E)None SOLUTION:Solution: At present the total age of the family = 5*20 =100. The total age of the family at the time of the birth of the youngest member, =[100−10−(10*4)]=50. Therefore, average age of the family at the time of birth of the youngest member, = 50/4 = 12.5. Answer: Option D #### D QUESTION:If, 1 * 3 * 5 = 16 3 * 5 * 7 = 38 Then find, 15 * 17 * 19 =? options: A)89 B)49 C)68 D)38 E)338 SOLUTION:E 338 (19 * 17) + 15 = 338 #### E <<<Examples ends QUESTION:The dimensions of each book in an encyclopedia set measures 8 in x 4 in x 12 in. (l x w x h). Each shelf (i.e. each divider) has a surface area of 848 sq in., where the thickness is 1 in and the width is 16 in. Assuming there is enough space in between shelves, how many shelves are needed to fit all of the books? options: A)7 B)12 C)13 D)5 E)26 SOLUTION:Surface area of each shelf= 2ab + 2ac + 2bc 848 = 2 x 1 x 16 + 2 x 1 x c + 2 x 16 x c 848 = 32 + 2c + 32c 816 = 34c c = 24 in. (i.e. the length of each shelf) Each book is 4 in thick 24/4 = 6 books per shelf 26/6 = 4.333=5 shelves Answer is D #### D

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:Three hundred multiples of seven are chosen at random, and 700 multiples of eight are chosen at random. Approximately what percentage of the 1000 selected numbers are odd? options: A)15% B)25% C)35% D)50% E)80% SOLUTION:About half the multiples of seven will be odd while all the multiples of eight are even. The percentage of odd numbers is about (1/2)(300) / 1000 = 15% The answer is A. #### A QUESTION:It 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 car is? options: A)3:9 B)3:3 C)3:4 D)3:1 E)3:2 SOLUTION:Let the speed of the train be x km/hr and that of the car be y km/hr. Then, 120/x + 480/y = 8 or 1/x + 4/y = 1/15 --- (i) And, 200/x + 400/y = 25/3 or 1/x + 2/y = 1/24 --- (ii) Solving (i) and (ii), we get x = 60 and y = 80 Ratio of speeds = 60:80 = 3:4 Answer: C #### C QUESTION:Three (rather lazy) men A, B and C working together can do a work in 5 days. They start the work together and A works for 1 day and takes rest on the second day, B works for 2 days and takes rest on the next two days and C works for 2 days and takes rest on the next three days. In how many days will the work be completed ? (A, B, C work at the same rate) options: A)7 days B)8 days C)9 days D)10 days E)11 days SOLUTION:Total work is 3*5 = 15 units. A does 1 day of work every 2 days. B does 2 days of work every 4 days. C does 2 days of work every 5 days. Test the options. In 7 days: A will do 1*3 + 1 = 4 units (3 complete cycles and 1 day of work). B will do 2*1+ 2= 4 units (1 complete cycle, 2 days of work, and 1 day of rest). C will do 2*1 + 2 =4 units (1 complete cycle and 2 days of work). Total = 4 + 4 + 4 = 12 units. In 8 days: A will do 1*4 = 4 units (4 complete cycles). B will do 2*2= 4 units (2 complete cycles). C will do 2*1 + 2 =4 units (1 complete cycle, 2 days of work, and 1 day of rest). Total = 4 + 4 + 4 = 12 units. In 9 days: A will do 1*4 + 1 = 5 units (4 complete cycles and 1 day of work). B will do 2*2+ 1 = 4 units (2 complete cycles and 1 day of work). C will do 2*1 + 2 = 4 units (1 complete cycle, 2 days of work, and two days of rest). Total = 5 + 5 + 4 = 14 units. In 10 days: A will do 1*5 = 5 units (5 complete cycles). B will do 2*2+ 2= 6 units (2 complete cycle and 2 days of work). C will do 2*2 =4 units (2 complete cycles). Total = 5 + 6 + 4 = 15 units. Therefore, the answer is D. #### D QUESTION:When I add 4 times my age 4 years from now to 5 times my age 5 years from now, I get 10 times my current age. How old will I be 3 years from now? options: A)42 years B)41 years C)43 years D)40 years E)45 years SOLUTION:Let x= current age 4(x+4)+5(x+5)=10x ;so x=R 41 years Answer C #### C QUESTION:A bat is bought for Rs.400 and sold at a gain of 30% find its selling price? options: A)s.460/- B)s.480/- C)s.500/- D)s.520/- E)s.540/- SOLUTION:100 % ------> 400 (100 * 4 = 400) 130 % ------> 520 (130 * 4 = 520) Selling price = Rs.520/- Option 'D' #### D QUESTION:What distance (in meters) will be covered by a bus moving at 54 km/hr in 15 seconds? options: A)175 B)200 C)225 D)250 E)275 SOLUTION:54 km/hr = 54 * 5/18 = 15 m/s distance = 15 * 15 = 225 meters The answer is C. #### C QUESTION:The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is: options: A)288 B)2609 C)245 D)298 E)221 SOLUTION:Speed = [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.Answer:C #### C QUESTION:A certain number of workers can do a work in 25 days. If there were 10 workers more it could be finished in 10 days less. How many workers are there? options: A)15 B)30 C)28 D)24 E)32 SOLUTION:number of workers = 10* (25-10)/10 = 15 Answer is A #### A QUESTION:In how many different ways can the letters of the word ‘ARMOUM’ be arranged? options: A)230 B)250 C)260 D)300 E)360 SOLUTION:ARMOUR = 6 letter whereas R repeated twice 6! 6xSx4x3x2x1 => 360 E #### E QUESTION:Find all integers x NOT EQUAL TO 3 such that X-3|X^3-3 options: A)1,2,3,4,5 B)-21,-9,-5,-3,-1,0,1,2,4,5,6,7,9,11,15,27 C)1 D)6 E)-1,0,1 SOLUTION:Let x-3=t. Thus, t is an integer not equal to such'that t|(t+3)^2-3, which is equivalent to the condition t|3^3-3, or t|24. Therefore, it is necessary and sufficient for t to be an integer divisor of 24, hence t must be equal to one of the numbers +or-1, +or-2, +or-3, +or-4, +or-6, +or-8, +or-12, +or-24. For x = t+3 we obtain the values -21, -9, -5, -3, -1,0,1,2,4,5,6,7, 9, 11, 15, and 27. Correct Answer B -21,-9,-5,-3,-1,0,1,2,4,5,6,7,9,11,15,27 #### B QUESTION:How many factors of 2475 are odd numbers greater than 1? options: A)3 B)4 C)17 D)6 E)7 SOLUTION:prime factors of 330 are 2^1,3^2,5^2 and 11^1 total divisors = (power if a prime factor+1) total no. of odd factors(3,5,11) = (2+1)(2+1)(1+1) =18 since we need odd divisors other than 1 =>18-1 = 17 odd divisors C is the answer #### C QUESTION:Darcy lives 1.5 miles from work. She can walk to work at a constant rate of 3 miles per hour, or she can ride the train to work at a constant rate of 20 miles per hour. If she rides the train, there is an additional x minutes spent walking to the nearest train station, waiting for the train, and walking from the final train station to her work. If it takes Darcy a total of 10 more minutes to commute to work by walking than it takes her to commute to work by riding the train, what is the value of x? options: A)10.5 B)15 C)15.5 D)30 E)60 SOLUTION:The time it takes Darcy to walk to work is (1.5/3)*60 = 30 minutes The time it takes Darcy to take the train is (1.5/20)*60 + x = 4.5 + x minutes It takes 15 minutes longer to walk, so 30 = 4.5 + x + 10 x=15.5 minutes Answer: C #### C QUESTION:A 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: options: A)14 B)17 C)19 D)22 E)24 SOLUTION:Let the son's present age be x years. Then, (38 - x) = x 2x = 38. x = 19. Son's age 5 years back (19 - 5) = 14 years. Answer : A #### A QUESTION:What is the smallest positive integer x, such that 1944x is a perfect cube? options: A)4 B)3 C)8 D)12 E)18 SOLUTION:Take out the factors of 1944 that will come 2^3*3^3 *3^2. for perfect cube you need every no. raise to the power 3. for 1944 to be a perfect cube, need 1 3 that means =3 B is the answer. #### B QUESTION:Find the smallest number which when divided by 13 and 16 leaves respective remainders of 2 and 5. options: A)128 B)197 C)127 D)182 E)091 SOLUTION:Explanation: Let 'N' is the smallest number which divided by 13 and 16 leaves respective remainders of 2 and 5. Required number = (LCM of 13 and 16) - (common difference of divisors and remainders) = (208) - (11) = 197. Answer:B #### B QUESTION:If 11.25 m of a uniform steel rod weighs 42.75 kg. what will be the weight of 7 m of the same rod? options: A)22.8 kg B)26.6 kg C)28 kg D)26.5 kg E)None of these SOLUTION:Explanation : Let the required weight be x kg. Then, Less length, Less weight (Direct Proportion) => 11.25 : 7 :: 42.75 : x => 11.25 x x = 7 x 42.75 => x = (7 x 42.75) / 11.25 => x = 26.6 Answer : B #### B QUESTION:Jar X is 1/4 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? options: A)2/5 B)1/4 C)1/3 D)1/2 E)2/3 SOLUTION:Let P be the capacity of Jar X. The amount of water in Jar Y is 1/2*P/2=P/4 Then the total amount in Jar X is P/4+P/4=P/2 The answer is D. #### D QUESTION:A man can hit a target once in 4 shots. If he fires 4 shots in succession, what is the probability that he will hit his target? options: A)175/256 B)451/365 C)312/456 D)156/754 E)164/784 SOLUTION:The man will hit the target if he hits it once or twice or thrice or all four times in the four shots that he takes. So, the only possibility when the man will not hit the target is when he fails to hit the target in even one of the four shots that he takes. The event of not hitting the target even once is the complement of the event of hitting the target at least once. The probability that he will not hit the target in any given shot = 1 – 1/4 = ¾ Therefore, the probability that he will not hit the target in any of the four shots =3/4*3/4*3/4*3/4=81/256 The probability that he will hit the target at least in one of the four shots=1-81/256 =175/256 Ans:A #### A QUESTION:If there are four distinct pairs of brothers and sisters, then in how many ways can a committee of 3 be formed and NOT have siblings in it? options: A)8 B)24 C)32 D)56 E)192 SOLUTION:let AABBCCDD is the group with same letter representing a sibling pair. total # ways to select 3 from 8 is 8C3=56 Qtn: committee of 3 NOT having siblings in it = Total (56) - committee of 3 with siblings in it committee of 3 with siblings = select 2As and one from rem. 6. This can be done in 4 ways as 4 different letters A,B,C and D = 4 * (2C2*6C1) = 24 Hence Answer = 56-24 = 32 ANS:C #### C QUESTION:The C.P of 10 pens is equal to the S.P of 15 pens. Find his gain % or loss%? options: A)loss 16 2/8% B)loss 16 6/3% C)loss 16 2/3% D)loss 18 2/3% E)loss 33.33% SOLUTION:10 CP = 15 SP 15 --- 5 100 --- ? => 33.33% (Loss) Answer:E #### E QUESTION:On a weekend, 3 friends went skiing and evenly split the cost of their cabin. If the amount paid by each person was an integer, which of the following could not have been the cost of the cabin? options: A)$110 B)$150 C)$225 D)$54 E)$75 SOLUTION:Each of the seven persons evenly splitting the cost is an integer amount, therefore check the divisibility by 3 for all answer choices. 110/3 = 36.67 150/3 = 50 225/3 = 75 54/3 = 18 75/3 = 25 A is not an integer amount. Answer:A #### A QUESTION:If 1 = 6 2 = 12 3 = 18 4 = 24 5 = 30 6 = 36 Then 24 = ? Hint: Its a logic Riddle not a mathematical riddle options: A)1 B)2 C)4 D)6 E)8 SOLUTION:C 24 As stated 4=24 => 24=4 Answer is C #### C QUESTION:The sale price sarees listed for Rs.150 after successive discount is 20% and 10% is? options: A)187 B)120 C)108 D)178 E)175 SOLUTION:150*(80/100)*(90/100) = 108 Answer:C #### C QUESTION:What is the area of the square with the following coordinates: (x, y), (20, 20), (20, 6), (x, 6)? options: A)64 B)81 C)125 D)196 E)225 SOLUTION:To find the area of a square, knowing the length of one side is sufficient. From the coordinates given, we can see that one side equals 14. The area is 14*14 = 196. The answer is D. #### D QUESTION:A took 15 seconds to cross a rectangular field diagonally walking at the rate of 52 m/min and B took the same time to cross the same field along its sides walking at the rate of 68m/min. The area of the field is? options: A)33 B)60 C)88 D)27 E)26 SOLUTION:Explanation: length of the diagonal = 52*(15/60) =13m sum of length and breadth = 68*(15/60) = 17m \inline {\color{Black}\sqrt{l^{2}+b^{2}}=13 \; or\; l+b=17 } area =lb = 1/2[(2lb)] = 1/2[(l+b)² - (l²+b²)] = 1/2[17² -169] =1/2*120 = 60 sq meter Answer: B) 60 #### B QUESTION:John professes to sell his goods at the cost price but he made use of 800 grams instead of a kg, what is the gain percent? options: A)12 1/3% B)12 1/4% C)12 2/3% D)12 2/1% E)12 1/2% SOLUTION:800 --- 100 100 --- ? => 12 1/2% Answer:E #### E QUESTION:What is the probability that a leap year has 53 Sundays and 52 Mondays? options: A)1/9 B)1/8 C)1/3 D)1/7 E)1/2 SOLUTION:A leap year has 52 weeks and two days Total number of cases = 7 Number of favourable cases = 1 i.e., {Saturday, Sunday} Required Probability = 1/7 Answer:D #### D QUESTION:A bank offers 3% compound interest calculated on quarter-yearly basis. A customer deposits $ 15000 each in 1st month. At the end of the year, the amount he would have gained by way of interest is? options: A)200 B)150 C)455 D)300 E)600 SOLUTION:Amount = (15000)* (1 + (3/4*100))^4 Amount = 15000 * (1+ 0.0075)^4 = 15455 ------(for investment in 1st month) Interest = 15455-15000 = 455.............. Ans -C #### C QUESTION:The 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. options: A)20 years. B)30 years. C)40 years. D)50 years. E)60 years. SOLUTION:Sol. Let the age of the younger person be x years. Then, age of the elder perosn = (x + 16) years. ∴ 3(x - 6) = (x + 16 - 6) ⇔ 3x - 18 = x + 10 ⇔ 2x = 28 ⇔ x = 14 Hence, their present ages are 14 years and 30 years. Answer B #### B QUESTION:A certain sum amount to $1400 in 2 yrs and $2000 in five years on certain fixed simple interest. In how many yrs would the amount be $1840 had it been put at the rate of interest compounded annually? options: A)4.5 B)3.5 C)3 D)2 E)1 SOLUTION:We can form equations as following: Initial amount = P, Total amount after interest = T, Interest per year = I T = P+I Given T1 = P+2I = 1400 T2 = P+ 5I = 2000 From this we get, P = 1000I = 200 $ Now we know that simple interest is<Compound interest ( CI = SI only after 1st year if CI is compounded annually) consider simple interest - after 1st yer it is 200$ , after 2nd years it is 400$ and after 3rd year it is 600$. To get a 440 $ compound interest the duration have to be > 1 year and < 3 years. Only option fitting : Option D. #### D QUESTION:TOM traveled the entire 60 miles trip. If he did the first 12 miles of at a constant rate 24 miles per hour and the remaining trip of at a constant rate 48 miles per hour, what is the his average speed, in miles per hour? options: A)20mph B)24mph C)30mph D)40mph E)42mph SOLUTION:avg speed = total distance/ total time = (d1+d2)/(t1+t2) = (12+48) / ((12/24)+(48/48)) = 60*2/3 = 40mph D #### D QUESTION:For a certain set of numbers, if x is in the set, then x - 4 is also in the set. If the number 1 is in the set , which of the following must also be in the set ? a) 4 b) -3 c) -6 options: A)a only, B)b only, C)c only, D)a and b only E)b and c only SOLUTION:Notice that the question asks which of the following MUST be in the set, not COULD be in the set. Since 1 is in the set, then so must be 1-4=-3. Similarly, since -3 is in the set, then so must be -3-3=-6. Could 4 and -1 be in the set? Certainly, but we don't know that for sure. Answer: E. Regarding your question: we don't know which is the source integer in the set, if it's 1, then 4 won't be in the set but if the source integer is say 7, then 4 will be in the set. So, 4 may or may not be in the set. #### E QUESTION:Given two fair dice, what is the probability G that the sum of their numbers is 4 if exactly one die shows a 3? options: A)a) 2/11 B)b) 1/18 C)c) 3/11 D)d) 2/39 E)e) 1/5 SOLUTION:If exactly one die shows 3, there are 10 such combinations (given that we have 2 fair dice). 1:3, 2:3, 4:3, 5:3, 6:3, 3:1, 3:2, 3:4, 3:5, 3:6 The sum of numbers would be 4 for two events: 1:3, 3:1. G=2/11 would be the answer if 'at least one of the die shows a 3'.A #### A QUESTION:How many integers between 2000 and 3000 that have distinct digits and increase from left to right ? options: A)10 B)20 C)60 D)120 E)600 SOLUTION:Since the numbers must be distinct and increasing from left to right, The only arrangements we could come-up with are: 245_ --> 4 246_ --> 3 247_ --> 2 248_ --> 1 256_ --> 3 257_ --> 2 258_ --> 1 267_ --> 2 268_ --> 1 Number of integers =20 B #### B QUESTION:Ten years ago, a mother was four times older than her daughter. After ten years, the mother will be twice older than daughter. The present age of the daughter is options: A)22 B)21 C)24 D)20 E)19 SOLUTION:Let the mother’s present age be ’x’ Let the daughter’s age be ’y’; 10 years ago; (x - 10) = 4(y - 10) or x - 4y = - 30.. (1) 10 years later; (x + 10) = 2(y + 10) or x - 2y = 10.. (2) Solving (1) & (2) y = 20 ANSWER:D #### D QUESTION:A political candidate collected $1,749 from a fund raising dinner. If each supporter contributed at least $50, what is the greatest possible number of contributors at the dinner? options: A)33 B)34 C)35 D)36 E)37 SOLUTION:Nearest to 1749≈1750 175/50=35 (Caution: Collection is 1750 - 1 = 1749) Counting 1 less = 50*34 = 1700 >> 49 remains which will be adjusted with the 34 members 51* 34 = 1734 >> 15 remains which will be adjusted with 15 members 52 * 15 + 51 * 19 = 780 + 969 = 1749 Answer = B #### B QUESTION:Two trains running in opposite directions cross a man standing on the platform in 20 seconds and 18 seconds respectively and they cross each other in 19 seconds. The ratio of their speeds is: options: A)1 : 1 B)3 : 2 C)3 : 8 D)3 : 25 E)3 : 4 SOLUTION:Let the speeds of the two trains be x m/sec and y m/sec respectively. Then, length of the first train = 20 x meters, and length of the second train = 18 y meters. (20 x + 15 y) / (x + y) = 19 ==> 20 x + 18 y = 19 x + 19 y ==> x = y ==> x/y = 1/1 Answer: Option A #### A QUESTION:Which of the number is odd one out ? options: A)84129 B)32418 C)47632 D)36119 E)67626 SOLUTION:C 47632 as 32*32 !=476 #### C QUESTION:John 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? options: A)17 B)18 C)19.7 D)21 E)27 SOLUTION:Total cost of the items he purchased = Rs.25 Given that out of this Rs.25, 30 Paise is given as tax => Total tax incurred = 30 Paise = Rs.30/100 Let the cost of the tax free items = x Given that tax rate = 6% ∴ (25−30/100−x)6/100 = 30/100 ⇒ 6(25 −0.3 −x) = 30 ⇒ (25 − 0.3 − x) = 5 ⇒ x = 25 − 0.3 − 5 = 19.7 C) #### C QUESTION:From a total of 5 boys and 6 girls, how many 4-person committees can be selected if the committee must have exactly 2 boys and 2 girls? options: A)16 B)24 C)60 D)120 E)150 SOLUTION:Answer=E=150 No of 4 person committees that can be formed=5C2*6C2=150 Answer E #### E QUESTION:Find the common ratio of three numbers in G.P whose product is 216 and the sum of the products taken in pairs is 114. options: A)2 or ½ B)2/3 or 3/2 C)¾ or 4/3 D)4 or ¼ E)5 or 1/5 SOLUTION:Let the terms be a/r, a , ar a/r *a * ar = a 3 =216, a =6 (a/r*a )+ (a*ar) + (ar*a/r ) =114, a 2/r + a 2 r + a 2 =114 a 2 ( 1/r + r +1 ) = 114, 36[( 1+ r 2 +r )/r] =114 6 [( 1 +r 2+ r )/r ]= 19, 6 r 2 -13 r + 6 = 0, On solving, r = 2/3 or 3/2 ANSWER:B #### B QUESTION:There are three different hoses used to fill a pool: hose U, hose y, and hose z. Hose U can fill the pool in a days, hose y in b days, and hose z in c days, where a > b > c. When all three hoses are used together to fill a pool, it takes d days to fill the pool. Which of the following must be true? I. d<c II. d>b III. c/3<d<a/3 options: A)I B)II C)III D)II &III E)I &II SOLUTION:Name T = full pool U fills a pool in a days ==> 1 day U fills: T/a Y fills a pool in b days ==> 1 day Y fills: T/b Z fills a pool in c days ==> 1 day Z fills: T/c 1 day (U+Y+Z) together fill: T(1/a + 1/b + 1/c) d days (U+Y+Z) together fill: T ==> d = T1 / T(1/a+1/b+1/c) = abc/(ab+bc+ca) ==>d = abc/(ab+bc+ca) d cannot be greater than c ; d is greater than b ; d is greater than c/3 but not less than a/3 B #### B QUESTION:Which number is the odd one out? 159 248 951 357 122 582 options: A)951 B)246 C)325 D)147 E)852 SOLUTION:A 951 In the rest there is the same difference between each digit, eg: 9(–4) 5 (–4)1 #### A QUESTION:Ratio between Rahul and Deepak is 4:3, After 2 Years Rahul age will be 26 years. What is Deepak present age. options: A)14 B)18 C)20 D)22 E)24 SOLUTION:Explanation: Present age is 4x and 3x, => 4x + 2 = 26 => x = 6 So Deepak age is = 3(6) = 18 Option B #### B QUESTION:A new home buyer pays 4% annual interest on her first mortgage and 9% annual interest on her second mortgage. If she borrowed a total of $335,000, 80% of which was in the first mortgage, what is her approximate monthly interest payment? options: A)$1,395 B)$1,733 C)$3,466 D)$13,333 E)$20,796 SOLUTION:0.04x + 0.09y = 335000 [1] 0.04x = 0.80 * 335000 = 268000 [2] 268000 + 0.09y = 320000 --> 0.09y = 67000 [3] 268000 / 12 = 22333.3333 [4] 67000 / 12 = 5583.333 [5] Adding [4,5] we get: 27916 [6] Dividing [6] / 2 to get an average we get 1.395,ANS A #### A QUESTION:An 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.2400, what will be the difference between Q and R's share? options: A)8877 B)3000 C)7787 D)1799 E)1711 SOLUTION:4 --- 2000 5 --- ? => 3000 Answer: B #### B QUESTION:A number x is 8 times another number y. The percentage that y is less than x is options: A)12.5% B)87.5% C)80% D)11% E)1% SOLUTION:Say y=1 and x=8. Then y=1 is less than x=8 by (8-1)/8*100=7/8*100=87.5%. Answer: B. #### B QUESTION:Thomas 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? options: A)10 B)14 C)19 D)21 E)25 SOLUTION:The cost of buying a single computer= Rs(500000/11)=Rs. 45454.5 The cost of selling a selling computer=Rs(550000/11)=Rs. 50000.0 Profit per computer=Rs.(50000-45454.5)=Rs. 4545.5 The % of profit in selling a single computer=(4545.5/45454.5)*100=10% Answer:A #### A QUESTION:A sum of Rs. 12500 amounts to Rs. 15500 in 4 years at the rate of simple interest. What is the rate of interest? options: A)4% B)5% C)6% D)8% E)14% SOLUTION:S.I. = (15500 - 12500) = Rs. 3000/- Rate = (100 * 3000) / (12500 * 4) = 6% ANSWER:C #### C QUESTION:A train running at the speed of 60 km/hr crosses a pole in 9 seconds. Find the length of the train? options: A)150 meter B)299 meter C)666 meter D)155 meter E)144 meter SOLUTION:Speed = 60*(5/18) m/sec = 50/3 m/sec Length of Train (Distance) = Speed * Time (50/3) * 9 = 150 meter Answer: A #### A QUESTION:If a quarter kg of onions costs 80 paise, how many paise will 100 gm cost? options: A)32 paise B)65 paise C)56 paise D)87 paise E)15 paise SOLUTION:Explanation: Let the required cost be x paise. Less weight, Less cost (Direct proportion) 250 : 100 : : 80 : x 250 * x = (100 * 80) x = (100 * 80) / 250 x = 32 ANSWER: A #### A QUESTION:One pipe can fill a tank four 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: options: A)180 min B)160 min C)280 min D)18 min E)190 min SOLUTION:Let the slower pipe alone can fill the tank in x minutes Then the faster pipe can fill the tank in x/4 minutes Part filled by the slower pipe in 1 minute = 1/x Part filled by the faster pipe in 1 minute = 4/x Part filled by both the pipes in 1 minute = (1/x)+(4/x) Answer is A It is given that both the pipes together can fill the tank in 36 minutes ⇒ Part filled by both the pipes in 1 minute = 1/36 (1/x)+(4/x)=1/36 5/x=1/36 x=5×36=180 i.e.,the slower pipe alone fill the tank in 180 minutes #### A QUESTION:A cab driver 5days income was $45, $50, $60, $65 , $90. Then his average income is? options: A)A)$58 B)B)$42 C)C)$65 D)D)$48 E)E)$62 SOLUTION:avg = sum of observations/number of observations avg income=(45+50+60+65+90)/5 = 62 Answer is E #### E QUESTION:If 4a = 16b and 8b = 13c, Find a:b:c? options: A)52:13:8 B)13:7:52 C)7:13:52 D)7:13:54 E)None of these SOLUTION:Explanation: (4a = 16b ==> a/b = 16/4) and (8b = 13c ==> b/c = 13/8) ==> a:b = 16:4 and b:c = 13:8 a:b:c = 52:13:8 Answer: Option A #### A QUESTION:On dividinng 109 by a number, the quotient is 9 and the remainder is 1. Find the divisor. options: A)12 B)14 C)15 D)16 E)17 SOLUTION:d = (D-R)/Q = (109 - 1)/9 = 108/9 = 18 A #### A QUESTION:How many of the positive factors of 19 are not factors of 29? options: A)0 B)1 C)2 D)3 E)4 SOLUTION:Factors of 19 - 1, 19 factors of 29- 1, 29 Comparing both, we have three factors of 19 which are not factors of 29- 19, The answer is B #### B QUESTION:4 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? options: A)4 days B)6 days C)7 days D)9 days E)1 days SOLUTION:1 women's 1 day work = 1/28 1 child's 1 day work = 1/140 (5 women + 10 children)'s 1 day work = (5/28 + 10/140) = 1/4 5 women and 10 children will complete the work in 4 days. Answer: A #### A QUESTION:Peter can cover a certain distance in 1 hr. 24 min. by covering two-third of the distance at 4 kmph and the rest at 5 kmph. Find the total distance. options: A)4 km B)5 km C)6 km D)7 km E)8 km SOLUTION:time=distance/speed let total distance travelled be x in 84/60 hrs 2/3 rd of x travelled in 4 km/hr 1/3 rd of distance travelled in 5 km/hr 2x/(3*4)+x/(3*5)=84/60 x=6 km ANSWER:C #### C QUESTION:Find the odd man out. 1, 3, 9, 12, 19, 29 options: A)12 B)9 C)1 D)3 E)29 SOLUTION:12 is an even number. All other given numbers are odd Answer is A #### A QUESTION:If two-third of a bucket is filled in 100 seconds then the time taken to fill the bucket completely will be . options: A)90 seconds B)150 seconds C)60 seconds D)100 seconds E)120 seconds SOLUTION:2/3 filled in 100 seconds 1/3 filled in 50 secs then 2/3+1/3=100 + 50 seconds = 150 seconds ANSWER: B #### B QUESTION:From an island, it is possible to reach the mainland by either Ferry P or Ferry Q. Ferry P travels for 3 hours at 6 kilometers per hour, while Ferry Q takes a route that is three times longer. If Ferry P is slower than Ferry Q by 3 kilometers per hour, how many hours longer is the journey of Ferry Q compared with the journey of Ferry P? options: A)1 B)2 C)3 D)4 E)5 SOLUTION:The distance traveled by Ferry P is 18 km. Then the distance traveled by Ferry Q is 54 km. Ferry Q travels at a speed of 9 kph. The time of the journey for Ferry Q is 54/9 = 6 hours, which is 3 hours more than Ferry P. The answer is C. #### C QUESTION:The percentage profit earned by selling an article for $1920 is equal to the percentage loss incurred by selling the same article for $1280. At what price should the article be sold to make 25% profit? options: A)$3000 B)$1000 C)$2000 D)$5000 E)$6000 SOLUTION:C $2000 Let C.P. be $x. Then, (1920 - x)/x * 100 = (x - 1280)/x * 100 1920 - x = x - 1280 2x = 3200 => x = 1600 Required S.P. = 125 % of $1600 = 125/100 * 1600 = $2000. #### C QUESTION:The C.P of 10 pens is equal to the S.P of 12 pens. Find his gain % or loss%? options: A)16 2/7% B)16 2/6% C)16 2/3% D)16 7/3% E)12 2/3% SOLUTION:10 CP = 12 SP 12 --- 2 CP loss 100 --- ? => 16 2/3% Answer: C #### C QUESTION:A 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 secretary or the member chosen to be the president? options: A) 1/720 B) 1/5 C) 1/10 D) 1/9 E) 1/6 SOLUTION:This question is much easier than it appears. Each 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 and the probability that Harry will be selected to be the president is also 1/10. So, the probability that Harry will be selected to be either the secretary or the the president is 1/10+1/10=2/10. Answer: B #### B <<<Examples ends QUESTION:If x^2 + 1/x^2 = 3,what is the value of x^4 + 1/x^4 ? options: A)7 B)12 C)14 D)16 E)18 SOLUTION:IMPORTANT: I notice that if we SQUARE x², we get x⁴, and if we SQUARE 1/x², we get 1/x⁴, so let's see what happens if we take the equation x² + 1/x² = 3 andSQUAREboth sides: (x² + 1/x²)²= 9 So, (x² + 1/x²)(x² + 1/x²) = 9 Expand to get: x⁴ + 1 + 1 + 1/x⁴ = 9 Simplify: x⁴ + 1/x⁴ = 7 Answer: A #### A

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:The area of a rectangular field is equal to 750 square meters. Its perimeter is equal to 110 meters. Find the width of this rectangle. options: A)5 B)10 C)15 D)20 E)25 SOLUTION:L * W = 750 : area , L is the length and W is the width. 2 L + 2 W = 110 : perimeter L = 55 - w : solve for L (55 - W) * W = 750 : substitute in the area equation W = 25 and L = 30 correct answer E #### E QUESTION:If 5% more is gained by selling an book for $ 350 than by selling it for $ 340, the cost of the book is: options: A)160 B)210 C)200 D)227 E)220 SOLUTION:C 200 Let C.P. be $ x. Then, 5% of x = 350 - 340 = 10 x/20 = 10 => x = 200 #### C QUESTION:Narendra started a business, investing 30000. Six months later, Chandan joined him with 15000. If they make a profit of 10000 at the end of the year, what should be the share of Narendra? options: A)Rs.7000 B)Rs.8000 C)Rs.8500 D)Rs.8600 E)Rs.8700 SOLUTION:The ratio of their investments = 30000 × 12 : 15000 × 6 = 4 : 1. :. Narendra’s share on profit of Rs.10000 = 10000 × 4/5 = Rs.8000. B) #### B QUESTION:10 people went to a hotel for combine dinner party 5 of them spent Rs. 20 each on their dinner and rest spent 4 more than the average expenditure of all the 10. What was the total money spent by them. options: A)1628.4 B)1534 C)1492 D)240 E)None of these SOLUTION:Solution: Let average expenditure of 10 people be x. then, 10x = 20*5+5*(x+4); Or, 10x = 20*5+5x+20; Or, x = 24; So, total money spent = 24*10 = Rs. 240. Answer: Option D #### D QUESTION:In an entrance exam, 3 marks is awarded for every correct answer and (-1) for every wrong answer. If a student gets 38 marks after attempting all questions, find the number of questions answered correctly if the total questions were 70. options: A)27 B)88 C)26 D)29 E)71 SOLUTION:Explanation: Let x be the number of questions answered correctly. Hence, number of questions whose answer were wrong = (70 – x) 3*x + (70 – x)*(-1) = 38 4x = 38 + 70 = 108 x = 27 ANSWER:A #### A QUESTION:A data set with a mean of 60 has a standard deviation of 1.5. Which of the following is the smallest number that falls within one standard deviation of the mean? options: A)53 B)56 C)58 D)63.5 E)65 SOLUTION:One standard deviation of the mean is from{mean}-{deviation}=60-1.5=58.5 to{mean}+{deviation}=60+1.5=61.5. The smallest number within this range from the options is 58. Answer: C. Hope this helps. #### C QUESTION:(A% of 5B + B% of A) is equal to ? options: A)A% of B B)B% of A C)6% of AB D)AB% of 3 E)None SOLUTION:Answer A% of 5B + B% of A =5AB/100 + AB/100 = 6AB/100 = 6% of AB Correct Option: C #### C QUESTION:A is twice as good a work man as B and together they finish the work in 14 days. In how many days A alone can finish the work? options: A)5 days B)21 days C)15 days D)25 days E)30 days SOLUTION:Explanation: WC = 2:1 2x + x = 1/14 => x = 1/42 2x = 1/21 A can do the work in 21 days. Answer: B #### B QUESTION:Working alone, A can complete a certain kind of job in 6 hours. A and D, working together at their respective rates, can complete one of these jobs in 4 hours. In how many hours can D, working alone, complete one of these jobs? options: A) 8 B) 10 C) 12 D) 14 E) 16 SOLUTION:Let total time taken by D to complete the job = D total time taken by A to complete the job = 6 Work done by A in an hour 1/A = 1/6 Working together A and D can complete the job in 4 hours 1/A + 1/D = 1/4 =>1/D = 1/4 - 1/A = 1/4 - 1/6 = 1/12 => D = 12 hours Answer C #### C QUESTION:A 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 ? options: A)90 B)70 C)50 D)80 E)60 SOLUTION:Let number of notes of each denomination be x. Then x + 5x + 10x = 480 16x = 480 x = 30. Hence, total number of notes = 3x = 90. Answer is A. #### A QUESTION:Exactly 3/8 of the people in the room are under the age of 21, and exactly 5/12 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? options: A)21 B)36 C)39 D)60 E)65 SOLUTION:The total number of the people in the room must be a multiple of both 8 and 12 (in order 3/7 and 5/13 of the number to be an integer), thus the total number of the people must be a multiple of LCM of 8 and 12, which is 96. Since, the total number of the people in the room is greater than 50 and less than 100, then there are 96 people in the room. Therefore there are 3/8*96=36 people in the room under the age of 21. Answer: B. #### B QUESTION:Pure milk costs 3.60 per litre. A milkman adds water to 25 litres of pure milk and sells the mixture at 3 per litre. How many litres of water does he add? options: A)2 litres B)5 litres C)7 litres D)11 litres E)None of these SOLUTION:In mixture, Quantity of pure milk /Quantity of water=3−0/3.6−3=3/0.6=5/1 Since in every 5 litres of milk, he adds 1 litre of water. ∴ In every 25 litres of milk, he adds 5 litres of water. Answer B #### B QUESTION:Two trains are moving in opposite directions at 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.9 km respectively. The time taken by the slower train to cross the faster train in seconds is? options: A)99 B)277 C)48 D)99 E)22 SOLUTION:Relative speed = 60 + 90 = 150 km/hr. = 150 * 5/18 = 125/3 m/sec. Distance covered = 1.10 + 0.9 = 2 km = 2000 m. Required time = 2000 * 3/125 = 48 sec. Answer:C #### C QUESTION:There is a rectangular prism made of 1 in cubes that has been covered in tin foil. There are exactly 128 cubes that are not touching any tin foil on any of their sides. If the width of the figure created by these 128 cubes is twice the length and twice the height, what is the measure y in inches of the width of the foil covered prism? options: A)4 B)6 C)8 D)9 E)10 SOLUTION:If the width is w, then length and height would be w/2. So, w*w/2*w/2 = 128 => w^3 = (2^3)*64 = (2^3) * (4^3) => w = 2*4 = 8 in. Along the width of the cuboid, 8 cubes don't touch the tin foil. So the actual width will be non-touching cubes + touching cubes = 8 +2 =y=10 Ans E. #### E QUESTION:There are 100 men in town. Out of which 85% were married, 70% have a phone, 75% own a car, 80% own a house. What is the maximum number of people who are married, own a phone, own a car and own a house? options: A)20 B)15 C)10 D)5 E)None of these SOLUTION:% of married = 85% % of phone = 70% % of car = 75% % of house = 80. Therefore, % of not married = 15% % of not having phone = 30% % of not owning car = 25% % of not having house = 20% So, % of not having any of these things = 15 +25+ 30 + 20 = 90% So, % of people having all = 100 -90 = 10% Thus, people = 10. ANSWER -OPTION C #### C QUESTION:36 men can complete a piece of work in 18 days. In how many days will 72 men complete the same work ? options: A)24 B)17 C)18 D)9 E)11 SOLUTION:Explanation: Less Men, means more Days {Indirect Proportion} Let the number of days be x then, 72 : 36 :: 18 : x x = 9 Answer: D) 9 days #### D QUESTION:The 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? I. c > a II. c = a III. c < a options: A)I only B)II only C)III only D)I and II only E)II and III only SOLUTION:Let q = 10% then l = 100/11 % let b = 100 then a = 110 after increasing a by l and decreasing b yq we get c= 108 therefore c<a C it is answer #### C QUESTION:Maths, Physics and chemistry books are stored on a library shelf that can accommodate 25 books. Currently, 20% of the shelf spots remain empty. There are twice as many maths books as physics books and the number of physics books is 4 greater than that of chemistry books. Among all the books, 12 books are soft cover and the remaining are hard-cover. If there are a total of 7 hard-cover books among the maths and physics books. What is the probability Q, that a book selected at random is either a hard cover book or a chemistry book? options: A)1/10 B)3/20 C)1/5 D)1/4 E)9/20 SOLUTION:First phase of this problem requires you to determine how many mathematics and chemistry books are even on the shelf. To do so, you have the equations: m + p + c = 20 (since 4/5 of the 25 spots are full of books) m = 2p p = 4 + c From that, you can use Substitution to get everything down to one variable. c = p - 4 m = 2p p = p Then (p - 4) + 2p + p = 20, so 4p = 24 and p = 6. That means that there are 12 math, 6 physics, and 2 chemistry books on the shelf. With those numbers, you also know that there are 8 total hardcovers, 1 of which is chemistry. So if your goal is to get either a hardcover or a chemistry, there are 9 ways towin- either one of the 7 hardcovers that aren't chemistry or the two chemistry books. So out of the 20 total, Q=9 provide the desired outcome, making the answer E. #### E QUESTION:Find the total number of divisors of 1728(including 1 and 1728) options: A)28 B)29 C)30 D)31 E)32 SOLUTION:1728=2^6*3^3 no. of divisors = (6+1)*(3+1)=28 ANSWER:A #### A QUESTION:The length of a room is 5.5 m and width is 3.75 m. What is the cost of paying the floor by slabs at the rate of $400 per sq. metre. options: A)$8250 B)$8350 C)$8650 D)$8450 E)$8500 SOLUTION:Area =5.5×3.75 sq. metre. Cost for 1 sq. metre. = $400 Hence, total cost =5.5×3.75×400= $8250 A #### A QUESTION:The edges of a cuboid are respectively 3cm, 4cm and 12 cm. Find the length of the diagonal of cuboid. options: A)9: 8 B)9: 5 C)9: 1 D)9: 2 E)9: 4 SOLUTION:a1 : a2 = 3 : 1 6 a12 : 6 a22 = 9: 1 Answer:C #### C QUESTION:A chair is bought for Rs.200/- and sold at Rs.310/- find gain or loss percentage options: A)15% loss B)20% gain C)25% gain D)30% gain E)55% gain SOLUTION:Formula = (Selling price ~ Cost price)/Cost price * 100 = (310- 200)/200= 55% gain E #### E QUESTION:A 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 A. The store sold the first 150 copies in the first week at 80% more than A, and then over the next month, sold a 100 more at 20% more than A. Finally, to clear shelf space, the store sold the remaining copies to a bargain retailer at 40% less than A. What was the bookstore’s net percent profit or loss on the entire lot of 400 books? options: A) 30% loss B) 10% loss C) 10% profit D) 20% profit E) 60% profit SOLUTION:[[A(150)(1.8)+A(100)(1.2)+A(150)(0.6)]/400A] - 1 [50[(3)(1.8) + (2)(1.2) + (3)(0.6)] / (50)(8)] - 1 [(5.4 + 2.4 + 1.8)/8] - [8/8] +1.6/8 +20% answer is D #### D QUESTION:Mohan 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? options: A)A)Rs.520 B)B)Rs.594 C)C)Rs.596 D)D)Rs.595 E)None of these SOLUTION:Explanation: Price of 10 kgs of rice at Rs.26/kg = 10x26 = Rs.260 Price of 8 kgs of pulses at Rs.26/kg = 10x26 = Rs.260 Therefore, Total amount = Rs.260+Rs.260 = Rs.520. Answer: Option A #### A QUESTION:There are 36 students in a certain geometry class. If one third of the students are boys and three fourths of the boys are under six feet tall, how many boys in the class are under six feet tall? options: A)9 B)12 C)18 D)24 E)27 SOLUTION:Total Students = 36 One third of the students are boys = 1/3*36 = 12 Three fourths of the boys are under six feet tall = 3/4*12 = 9 ... Therefore Number of boys in the class under six feet tall = 9 ... Answer A.... Alternatively... Number of boys in the class under six feet tall = 3/4 of 1/3 of Total Students = 3/4*1/3*36 = 9... Answer A #### A QUESTION:Ramu bought an old car for Rs. 36000. He spent Rs. 15000 on repairs and sold it for Rs. 62900. What is his profit percent? options: A)16% B)17% C)18% D)58% E)23% SOLUTION:Total CP = Rs. 36000 + Rs. 15000 = Rs. 51000 and SP = Rs. 62900 Profit(%) = (62900 - 51000)/51000 * 100 = 23% Answer: E #### E QUESTION:What is the 4 digit number 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? options: A)1244 B)1532 C)1349 D)1423 E)1543 SOLUTION:First digit is 1/3 second digit => The numbers can be 1 & 3, 2& 6, 3 & 9. First + second = third => we can eliminate 3 & 9 since 3 + 9 = 12. Last is 3 times the second => we can eliminate option 2 & 6 since 3 * 6 = 18. Hence the number is 1349 C #### C QUESTION:The length of a rectangular floor is more than its breadth by 200%. If Rs. 240 is required to paint the floor at the rate of Rs. 3 per sq m, then what would be the length of the floor? options: A)65 B)44 C)18 D)15.49 E)14 SOLUTION:Let the length and the breadth of the floor be l m and b m respectively. l = b + 200% of b = l + 2b = 3b Area of the floor = 240/3 = 80 sq m l b = 80 i.e., l * l/3 = 240 l2 = 240 => l =15.49 Answer:D #### D QUESTION:A right circular cylinder has a height of 25 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? options: A)500(π – 3) B)500(π – 2.5) C)500(π – 2) D)500(π – 1) E)625(π – 1.5) SOLUTION:[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? The square base has sides of sqrt(50) due to the 45-45-90 triangle 25*25*pi - 15*sqrt(50)^2 =625(π – 1.5) E. 500(π – 1.5) #### E QUESTION:The average value of property of Mittal, Ambani and Singhania is Rs.11111 crore. The property of Singhania is as less than the property of Mittal is greater than the average property of both the Singhania and Mittal. The value of property of Ambani is? options: A)Rs. 17111 crore B)Rs. 11121 crore C)Rs. 11111 crore D)Rs. 12111 crore E)Rs. 11611 crore SOLUTION:Explanation: {M+A+S}{3}=11111 {S+M}{2}=11111 (\inline \because M - 11111 = 11111 - S) Rightarrow A = 11111 Answer: C #### C QUESTION:A man buys a cycle for Rs.1400 and sells it at a loss of 18%. What is the selling price of the cycle? options: A)Rs.1148 B)Rs.1160 C)Rs.1190 D)Rs.1202 E)NONE SOLUTION:Solution S.P = 82% of Rs.1400 = Rs.(82/100×1400) Rs.1148. Answer A #### A QUESTION:Given a circular wheel of 3.62 m radius how many revolutions will the will make to travel a distance of 1 km? options: A)22754.3 B)22254.2 C)25754.2 D)22753.2 E)22254.2 SOLUTION:2 * 22/7 * 3.62 * x = 22754.3 x = 1000 Answer: A #### A QUESTION:Solve x^2 – 7x = 0 options: A)(0,7) B)(0,3) C)(0,2) D)(0,5) E)(0,6) SOLUTION:This quadratic factors easily: Copyright © Elizabeth Stapel 2002-2011 All Rights Reserved x^2 – 7x = 0 x(x – 7) = 0 x = 0 or x – 7 = 0 x = 0 or x = 7 The solution is x = 0, 7 Ans: A #### A QUESTION:Four children have small toys. The first child has 1/10 of the toys, the second child has 12 more toys than the first, the third child has one more toy of what the first child has and the fourth child has double the third child. How many toys are there? options: A)20 toys B)30 toys C)40 toys D)60 toys E)50 toys SOLUTION:x : the total number of toys x/10 : the number of toys for first child x/10 + 12 : the number of toys for second child x/10 + 1 : the number of toys for the third child 2(x/10 + 1) : the number of toys for the fourth child x/10 + x/10 + 12 + x/10 + 1 + 2(x/10 + 1) = x x = 30 toys : solve for x correct answer B #### B QUESTION:In 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? options: A)23000 B)22000 C)20000 D)25000 E)30000 SOLUTION:Winner - Looser 55% - 45% If 3000 people change their mind and vote for the loser: Winner - Looser 45% - 55% Thus 3,000 people compose 10% of all voters, which means that the total number of votes is 30,000. Answer: E. #### E QUESTION:The first three terms of an infinite sequence are 2, 7, and 22. After the first term, each consecutive term can be obtained by multiplying the previous term by 3 and then adding 1. What is the sum of the tens digit and the units digit of the 51st term in the sequence? options: A)9 B)8 C)7 D)6 E)4 SOLUTION:Following the rule of Infinite sequence we obtain the terms of the sequence as mentioned below 02,07,22,67, 202, 607, 1822, 5467... Observe the last two digits of the sequence which have the cyclicity of4and the last two digits repeat in the order {02, 07, 22, 67} Also 51st Term =6*8 +3 i.e. 51th Terms will have same Last two digits as 3rd term of the sequence = 22 i.e. Sum of lat two digits of 35th Term = 2+2 = 4 E #### E QUESTION:It 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 car is? options: A)3:9 B)3:3 C)3:4 D)3:1 E)3:2 SOLUTION:Let the speed of the train be x km/hr and that of the car be y km/hr. Then, 120/x + 480/y = 8 or 1/x + 4/y = 1/15 --- (i) And, 200/x + 400/y = 25/3 or 1/x + 2/y = 1/24 --- (ii) Solving (i) and (ii), we get x = 60 and y = 80 Ratio of speeds = 60:80 = 3:4 Answer: C #### C QUESTION:If a town of 65,000 people is growing at a rate of approx. 1% per year, the population of the town in 5 years will be closest to? options: A)a.66000 B)b.67000 C)c.68000 D)d.69000 E)e.70000 SOLUTION:1% is quite small and hence the answer is A) #### A QUESTION:A 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? options: A)14 minutes B)12 minutes C)15 minutes D)18 minutes E)None of these SOLUTION:Explanation: As the squirrel climbs 5 m in one minute and slips 2 metres in the next minute, it climbs 3 metres in 2 minute To climb 26 metres, the time required is: The squirrel will climb (26 – 5) = 21 metres = 7 * 3 metres in 7 * 2 = 14 minutes Also, the last 5 metres it climbs in another 1 minute Hence, total time required = 14 + 1 = 15 minutes ANSWER C #### C QUESTION:The average monthly salary of 20 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 ? options: A)3700 B)3890 C)88798 D)2789 E)2891 SOLUTION:Explanation: Manager's monthly salary Rs. (1700 * 21 - 1600 * 20) = Rs. 3700. Answer: A) 3700 #### A QUESTION:A 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. options: A)2/7 B)3/11 C)4/15 D)5/21 E)6/25 SOLUTION:The total number of ways to sell 6 bottles from 10 is 10C6 = 210. The number of ways to sell 4 bottles of apple juice is 5C4*5C2 = 5*10 = 50 P(selling 4 bottles of apple juice) = 50/210 = 5/21 The answer is D. #### D QUESTION:In a group of 28 junior high school students, 7 take French, 9 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? options: A)7 B)6 C)9 D)4 E)8 SOLUTION:E 8 Add 7 + 9 + 4 to get 20. Then subtract 21 from the total students ⇒ 28 – 20 = 8. Answer is E #### E QUESTION:Let 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. How many matches were played? options: A)99 matches. B)88 matches. C)77 matches. D)66 matches. E)119 matches. SOLUTION:Solution: 119 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 119 matches were played. Answer E #### E QUESTION:A man can do a piece of work in 6 days, but with the help of his son he can do it in 3 days. In what time can the son do it alone ? options: A)7 days B)6 days C)5 days D)4 days E)None of these SOLUTION:Explanation: In this type of question, where we have one person work and together work done. Then we can easily get the other person work just by subtracting them. As Son's one day work = (1/3−1/6)=(6−3)/18=1/6 So son will do whole work in 6 days Answer: B #### B QUESTION:Before a salary increase, the weekly salary of a worker for 44 hours in a week was as much as the worker is paid now for 40 hours of work in a week. What is the percent increase in the worker's salary per hour? options: A)4 B)6 C)8 D)10 E)12 SOLUTION:Let x be the original salary per hour. Let y be the salary per hour after the increase. 40y=44x y=(44/40)x=1.1x The salary increased 10%. The answer is D. #### D QUESTION:At what rate of interest is an amount doubled in two years, when compounded annually? options: A)41.4% B)43.4% C)31.4% D)30% E)21.4% SOLUTION:Let the rate of interest be r. The amount gets doubled in two years => P(1 + r/100)2 = 2p => 1 + r/100 = √2 => r/100 = √2 - 1 = 0.414 => r = 100(0.414) = 41.4% ANSWER:A #### A QUESTION:The average weight of 10 person's increases by 2.5 kg when a new person comes in place of one of them weighing 50 kg. What might be the weight of the new person? options: A)76 kg B)76.5 kg C)75 kg D)Data inadequate E)None of these SOLUTION:Explanation: Total weight increased = (10 x 2.5) kg = 25 kg. Weight of new person = (50 + 25) kg = 75 kg. Answer: C #### C QUESTION:A trader marks his books 20% more than the cost price. If he allows 30% discount, then find his gain or loss percent? options: A)2% profit B)2% loss C)16% loss D)No profit No loss E)None of these SOLUTION:Let CP of an book = 100 MP of an book = 120 Discount 30 % on 120 = 36 SP of the book = 120 - 36 = 84 loss = 16% Answer : C #### C QUESTION:In an election between two candidates, 10% of votes are were declares invalid. First candidate got 5400 votes which were 60% of the total valid votes . The total number of votes enrolled in that election was: options: A)9000 B)98000 C)30000 D)11000 E)12000 SOLUTION:100 % - 10 % = 90 % 54%-36%=18% 18% ------> 5400 ( 18 × 300 = 5400) 100% -------> 30000 votes (100 × 300 = 30000) C #### C QUESTION:If |x^2 − 12| = x, which of the following could be the value of x? options: A)-4 B)-3 C)1 D)2 E)3 SOLUTION:|x2−12|=x|x2−12|=x |x2−12||x2−12|cannot be negative; anything that comes out of mod is always positive so |x2−12|>0|x2−12|>0 Out of our options A= -4 B= -3 cannot be the right answer because none of them are greater than 0 Now only Option C=1 or D=2 or E=3 are contenders for right answers. A quick Cursory crude calculation will tell you that E is the right choice |−32−12|=3|−32−12|=3 |9−12|=3|9−12|=3 |−3|=3|−3|=3 3=33=3 ANSWER IS E #### E QUESTION:At what rate of annual simple interest,a certain sum will amount to four times in 15 year? options: A)15% B)17.5% C)20% D)25% E)35% SOLUTION:r=? t=15 yrs SI=p*r*t/100 Amount = SI+p = 4p (p*r*15/100)+p = 4p p(15r/100 + 1) = 4p 15r + 100 = 400 15r = 300 r = 20% ANSWER:C #### C QUESTION:Which of the following is closest to (8!-7!)/(8!+7!)? options: A)0.01 B)0.8 C)0.2 D)1 E)10 SOLUTION:(8!-7!)/(8!+7!) 7! (8-1)/7! (8+1) 7/9 = 0.8 (approximately) B is the answer #### B QUESTION:At 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.) options: A)96 B)240 C)E=256 D)E=384 E)E=480 SOLUTION:Most 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.... We'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. This means, at the minimum, we have... 1 small box and 17 large boxes = 1(12) + 17(16) = 12 + 272 = 284 glasses at the MINIMUM Since the question asks for the total number of glasses, we can now eliminate Answers A, B and C.... The difference in the number of boxes MUST be 16 though, so we could have.... 2 small boxes and 18 large boxes 3 small boxes and 19 large boxes etc. With 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.... 284+28 = 312 312+28 = 340 340+28 = 368 368+28 = 396 At this point, we've 'gone past' Answer D, so the correct answer MUST be Answer E.....But here's the proof.... 396+28 = 424 424+28 = 452 452+28 = 480 Final Answer: E #### E QUESTION:A certain meter records voltage between 0 and 10 volts inclusive. If the average value of 3 recordings on the meter was 9 volts, what was the smallest possible recording in volts? options: A)2 B)3 C)4 D)5 E)7 SOLUTION:if average of 3 is 9 so sum of 3 should be 27 3 recording can be from 0-10 inclusive to find one smallest other two should be highest so, lets assume three var are a,b,c say a is smallest and give b and c greatest readings say 10 and 10 so a has to be 7 E #### E QUESTION:A 2-year certificate of deposit is purchased for R 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? options: A)k(1.06)^2 B)k(1.06)^8 C)k(1.015)^2 D)R(1.015)^8 E)k(1.03)^4 SOLUTION:Annual Rate of interest= 6% Quaterly rate of interest= 6/4% = 1.5% Now, periods of compounding in 2 years= 8 (8 quarters) Thus R(1.015)^8 Answer: D #### D QUESTION:The ratio of the number of boys and girls in a college is 7 : 8. If the percentage increase in the number of boys and girls be 20% and 10% respectively, what will be the new ratio? options: A)8 : 9 B)21 : 22 C)17 : 18 D)12 : 20 E)Cannot be determined SOLUTION:Originally, let the number of boys and girls in the college be 7x and 8x respectively. Their increased number is (120% of 7x) and (110% of 8x). (120/100 x 7x) and (110/100 x 8x) 42x/5 and 44x/5 The required ratio = (42x/5 : 44x/5)= 21 : 22. ANSWER B #### B QUESTION:On a race track a maximum of 5 horses can race together at a time. There are a total of 25 horses. There is no way of timing the races. What is the minimum number Q of races we need to conduct to get the top 3 fastest horses? options: A)5 B)7 C)8 D)10 E)11 SOLUTION:Q=7 is the correct answer. Good solution Buneul.B #### B QUESTION:If the population of a certain country increases at the rate of 1 person every 60 seconds, by how many persons does the population increase in 2 Hours? options: A)120 B)80 C)100 D)150 E)140 SOLUTION:Answer = 1 * 120(2 hour = 120 minutes)= 120 Answer = A #### A QUESTION:A sum of money becomes 7/6 of itself in 6 years at a certain rate of simple interest. The rate per annum is? options: A)50/9 B)50/13 C)50/17 D)25/9 E)5 5/1 SOLUTION:Let sum = x. Then, amount = 7x/6 S.I. = 7x/6 - x = x/6; Time = 6 years. Rate = (100 * x) / (x * 6 * 6) = 25/9 %. Answer:D #### D QUESTION:There are 30 people in a party. If everyone is to shake hands with one another, how many hand shakes are possible? options: A)435 B)367 C)361 D)297 E)261 SOLUTION:Explanation: Total number of persons = n = 30 Shakehands involve only 2 persons = r = 2 Number of shakehands = nCr = 30C2 30C2 = (30 * 29) /(2 * 1) = 435 nCr = (n!) / r! (n – r)! = 30! / 2! 28! = 435 ANSWER:A #### A QUESTION:If 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? options: A)30 B)33 1/3 C)35 D)25 E)20 SOLUTION:100---150 150----50 100-----? ==>33 1/3 ANSWER B #### B QUESTION:A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train? options: A)120 metres B)180 metres C)324 metres D)150 metres E)180 metres SOLUTION:Speed=(60 x 5/18)/m/sec = 50/3 m/sec. Length of the train = (Speed x Time). Length of the train = 50 x 9/3 m = 150 m. ANSWER : OPTION D #### D QUESTION:If c = 9/25, w = 15/32, and m + w + c = 1, which of the following gives the values of m, w, and c in increasing order? options: A)c, m, w B)c, w, m C)m, w, c D)m, c, w E)w, m, c SOLUTION:Answer D - m, c, w c ~ 1/3 w ~ 1/2 and m+w+c = 1 hence m ~ 1/6 Hence increasing order would be m -> c -> w Aswer D #### D QUESTION:The 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? options: A)1 B)17 C)88 D)12 E)15 SOLUTION:Let the breadth of the plot be b m. Length of the plot = 3 b m (3b)(b) = 867 3b2 = 867 b2 = 289 = 172 (b > 0) b = 17 m. Answer: B #### B <<<Examples ends QUESTION:If f(x)= 5x^2- 2x+6 and g(y)= 3y-8, then g(f(x)) options: A)82x^2-9x+38 B)15x^2-6x+10 C)58x^2-4x+58 D)87x^2-5x+96 E)98x^2-7x+94 SOLUTION:g(f(x))=3(5x^2-2x+6)-8 =15x^2-6x+18-8 =15x^2-6x+10 the answer is B #### B

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:At an international conference, “Yellow” world countries and “Blue” world countries are the only participants. The ratio of “Yellow” world participants to “Blue” world participants is 3:2. If one-third of “Yellow” world participants are left-handed and two-thirds of “Blue” world participants are left-handed, then what is the fraction of the participants who are left-handed? options: A)7 B)7/15 C)5/8 D)9/2 E)4/6 SOLUTION:Yellow: Blue = 3:2 Let Yellow = 3x and Blue = 2x 1/3 of Yellow are left handed => 1/3 * 3x = 3x/3 Yellow left handed 2/3 of Blue are left handed => 2/3 *2x = 4x/3 blue left handed fraction of participants who are left handed = total left handed/ total participants = (yellow left handed + blue left handed)/total participants = (3x/3 + 4x/3)/(3x+2x) = (7x/15x) = 7/15 Answer : B #### B QUESTION:Yearly subscription to professional magazines cost a company $940.00. To Make a 25% cut in the magazine budget, how much less must be spent? options: A)705 B)655 C)656 D)657 E)658 SOLUTION:total cost 940 940*25/100=235 so the cut in amount is 235 the less amount to be spend is 940-235=705 ANSWER:A #### A QUESTION:A man can row upstream at 10kmph and downstream at 24 kmph. The speed of the stream is options: A)2.5 km/hr B)4.2 km/hr C)7 km/hr D)10.5 km/hr E)None SOLUTION:Sol. Speed of stream = 1/2(24 -10) kmph = 7 kmph. Answer C #### C QUESTION:A man swims downstream 30 km and upstream 18 km taking 3 hours each time, what is the speed of the man in still water? options: A)2 kmph B)8 kmph C)16 kmph D)4 kmph E)6 kmph SOLUTION:30 --- 3 DS = 10 ? ---- 1 18 ---- 3 US = 6 ? ---- 1 M = ? M = (10 + 6)/2 = 8 ANSWER:B #### B QUESTION:What number should replace the question mark? 11, 15, 16, 12, 21, 9, ---? options: A)21 B)29 C)28 D)27 E)26 SOLUTION:Answer: E 11, 15, 16, 12, 21, 9, ---? There are two alternate sequences: +5 and -3. #### E QUESTION:3, 5, 7, 11, 13, 17, 19, ____ options: A)25 B)36 C)23 D)49 E)27 SOLUTION:The sequence is a series of prime numbers, 3, 5, 7, 11, 13, 17, 19, 23.... Answer : C. #### C QUESTION:If the sum of the interior angles of a regular polygon measures 1440o, how many sides does the polygon have? options: A)10 sides B)8 sides C)12 sides D)9 sides E)None of these SOLUTION:Explanatory Answer Step 1: Compute sum of all interior and exterior angles The sum of an exterior angle and an interior angle of a polygon = 180o. The sum of all the exterior angles of a polygon = 360o. From the question stem: sum of all interior angles of the given polygon = 1440o. Therefore, sum of all the interior and all exterior angles of the polygon = 1440 + 360 = 1800o. Step 2: Compute number of sides If there are 'n' sides to this polygon, then the sum of all the exterior and interior angles = 180 * n = 1800o. Therefore, n = 10. Alternative Approach : Using formula Sum of all interior angles of a convex polygon = (n - 2)* 180 So, (n - 2) * 180 = 1440 n - 2 = 8 n = 10 Choice A #### A QUESTION:If there are three sum of money P, Q and R so that P is the simple interest on Q and Q is the simple interest of R, rate % and time are same in each case, then the relation of P, Q and R is given by options: A)P2 = QR B)Q2 = PR C)R2 = PQ D)PQR = 100 E)None of these SOLUTION:P = Q×r×t/100 and Q = R×r×t/100 ⇒ P/Q=Q/R=r×t/100 ∴ Q2 = PR. Answer B #### B QUESTION:If a wagon wheel had 10 more spokes, the angle between them would decrease by 6 degrees. Can you identify the number of spokes in the wheel? options: A)20 spokes B)10 spokes C)30 spokes D)15 spokes E)25 spokes SOLUTION:A 20 spokes 360/S = A 360/(S +10) = A – 6 Thus there are 20 spokes in the wheel. #### A QUESTION:A school has received 30% of the amount it needs for a new building by receiving a donation of $500 each from people already solicited. People already solicited represent 60% 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? options: A)$200 B)$250 C)$100 D)$350 E)$875 SOLUTION:Let us suppose there are 100 people. 60% of them donated $30000 ( 500 * 60 ) $30000 is 30% of total amount. So total amount = 30000 * 100/60 Remaining amount is 70% of total amount. 70% of total amount = 30000 * (100/60) * (70/100) = 35000 This amount has to be divided by 40 ( remaining people are 40 ) So per head amount is 35000/40 = $875; ANSWER:E #### E QUESTION:A reduction of 20% in the price of salt enables a lady to obtain 10kgs more for Rs.300, find the original price per kg? options: A)s.7.7 B)s.7.4 C)s.7.5 D)s.7.1 E)s.7.9 SOLUTION:100*(20/100) = 20 --- 10 ? --- 1 => Rs.2 300 --- 80 ? --- 2 => Rs.7.5 Answer:C #### C QUESTION:Beth received 3/5 of the votes cast in a certain election. What fraction of the other votes cast would she have needed in order to have received 3/4 of the votes cast? options: A)1/5 B)2/7 C)3/8 D)7/20 E)1/2 SOLUTION:Let the total votes be 100. Beth received 60 votes, other votes 100-60=40. In order to have received 1/2 of the votes she needed 75 votes so 15 more, which is 15/40 = 3/8 of the other votes. Answer: C. #### C QUESTION:A 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? options: A)22772 B)24000 C)23877 D)23789 E)28222 SOLUTION:Explanation: Ratio of investments of A and B is (70000 * 12) : (120000 * 6) = 7 : 6 Total profit = Rs. 52000 Share of B = 6/13 (52000) = Rs. 24000 Answer: B #### B QUESTION:After a mathematics exam, 20 percent of the students reported that they didn't study, while 20 percent of the students who didn't study refused to admit they hadn't studied. What percent of the students didn't study? options: A)15% B)50% C)35% D)20% E)25% SOLUTION:Statement: 20% of Students (S) Reported they Didn't Study (RDS). Of the students who didn't study (DS) 20% refused to admit they didn't study (notRDT). [Note: A Venn Diagram is useful to visualize the problem.] Solution: Sample space is 100%. S = 100% RDS/S = 20% notRDS/DS = 20% => 100% - 20% => RDS/DS = 80% DS/S = (20)/(80)% = 25% Answer: E #### E QUESTION:If x ≠ 1 and if yx/(y - x) = 1, what is the value of y in terms of x? options: A)(1-x)/x B)(x - 1)/x C)x/(x + 1) D)(x + 1)/x E)x/(1-x) SOLUTION:This 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. Here, 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. Final Answer: E #### E QUESTION:What is the units digit of (3^5)(4^13)? options: A)2 B)4 C)6 D)7 E)8 SOLUTION:-> The ones place of (~3)^n repeats after 4 times like 39713. The ones place of (~4)^n repeats after 2 times like 464. Then, 3^5=3^4*1+13^1., 4^13=4^2*6+1=4^1=~4 which is (3^5)(4^13) (3^1)(~4)=(~3)(~4)=~2. Therefore, the answer is A. #### A QUESTION:List I: 3, 6, 14, 19 List II: x, 3, 14, 8, 19 options: A) 6 B) 7 C) 8 D) 9 E) 10 SOLUTION:We start by calculating the median of the numbers of list I: 3, 6, 14, 19. We see that the numbers in the list are in order already and, since we have an even number of numbers, the median is the average of the two middle numbers. median = (6 + 14)/2 median = 20/2 median = 10 The median of list I is 7. Looking at list II: x, 3, 6, 14, 19, we see that we have an odd number of terms. Thus, when the list is ordered from least to greatest the median must be the middle term. Since the medians of the two lists must be equal, we know that the median of list II must be 10 and therefore x is 10. The answer is E. #### E QUESTION:There are six leopards and one sheep. Leopard can eat sheep but since as the land is magical, the leopards who eats the sheep , turns into sheep and then can be eaten by the remaining leopard(s). If we leave them for some time then how many sheep and leopard will be there , when we come back ? options: A)4 leopard and one sheep B)5 leopard and one sheep C)6 leopard and one sheep D)7 leopard and one sheep E)None SOLUTION:Solution: 5 leopard and one sheep since all animal are rational , once 1st leopard eats the sheep all the rest of leopard would know about this. Answer B #### B QUESTION:What is the probability that a two digit number selected at random is a multiple of 3 and not a multiple of 5 ? options: A)1/15 B)2/15 C)4/15 D)7/15 E)None of these SOLUTION:Explanation : Since every third number starting from 10 will be divisible by 3, so total number of numbers divisible by 3 are 90/3 = 30 Numbers which are divisible by 3 and 5 both are numbers which are multiple of 15. For the range 10 to 99, 15 is the first number divisible by 15 and 90 is the last number. So total number of numbers divisible by 15 are: (90-15)/15 + 1 = 5 + 1 = 6 Number of numbers which are divisible by 3 are 30 and number of numbers which are divisible by 3 and 5 both are 6. So number of numbers divisible by 3 and not by 5 are: 30-6=24 So total probability = 24/90 = 4/15 Answer : C #### C QUESTION:Three 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? options: A)56% B)64% C)62.2% D)68% E)61% SOLUTION:If initial cost is Rs 100, then Final cost will be 100*0.7*0.6*0.9 = Rs. 37.8 savings = 100-37.8=62.2 so 62.2% ANSWER:C #### C QUESTION:A wooden box of dimensions 4 m x 2 m x 4 m is to carry rectangularboxes of dimensions 4 cm x 2 cm x 2 cm. The maximum number ofboxes that can be carried in the wooden box, is options: A)9800000 B)2000000 C)7500000 D)1200000 E)None of these SOLUTION:Explanation: Number = (400*200*400)/4*2*2 = 2000000 Answer: B #### B QUESTION:Suppose you work for a manufacturing plant that pays you $12.50 an hour plus $0.16 for each widget you make. How many widgets must you produce in a 40 hour week to earn $620 (before payroll deductions)? options: A)670 B)710 C)750 D)790 E)830 SOLUTION:total pay = 40*$12.50 + $0.16*x = 620 x = 120 / 0.16 = 750 The answer is C. #### C QUESTION:John had a stock of 700 books in his bookshop. He sold 50 on Monday, 82 on Tuesday, 60 on Wednesday, 48 on Thursday and 40 on Friday. What percentage of the books were not sold? options: A)26.5% B)50% C)46.5% D)56.5% E)60% SOLUTION:Let N be the total number of books sold. Hence N = 50 + 82 + 64 + 78 + 135 = 280 Let M be the books NOT sold M = 700 - N = 700 - 280 = 420 Percentage Books not sold / total number of books = 420/700= 0.60 = 60% correct answer E #### E QUESTION:Yearly subscription to professional magazines cost a company $840.00. To Make a 30% cut in the magazine budget, how much less must be spent? options: A)654 B)655 C)656 D)588 E)658 SOLUTION:total cost 840 840*30/100=252 so the cut in amount is 252 the less amount to be spend is 840-252=588 ANSWER:D #### D QUESTION:If 18 is 15 percent of 25 percent of a certain number, what is the number? options: A)9 B)36 C)480 D)81 E)400 SOLUTION:Let the certain number be x. => (15/100)*(25/100)*x = 18; => x=480; Ans is (C). #### C QUESTION:A car covers a distance of 624 km in 6 ½ hours. Find its speed? options: A)104 B)190 C)109 D)278 E)211 SOLUTION:Explanation: 624/6 = 104 kmph Answer:C #### C QUESTION:For Consecutive integers x, y and z, where x > y > z, which of the following CANNOT be the value of (x2−y2)∗(y2−z2)(x^2−y^2)∗(y^2−z^2) ? options: A)63 B)99 C)195 D)276 E)323 SOLUTION:2 ways: 1) x-odd y-even z-odd (odd^2−even^2)(even^2−odd^2)=even 2) x-even y-odd z-even (even^2−odd^2)(odd^2−even^2)=even The only even answer we have is D) 276 #### D QUESTION:If x^2 > x^3 > x^1, which of the following could NOT be the value of x? options: A)-0.5 B)-1.2 C)-1/5 D)-2/3 E)-0.1 SOLUTION:x^2 > x^3 > x^1 1)Here we have an even power of a variable (x) that is greater than both a larger odd power of the variable x and a smaller odd power of the variable x. This can be possible only if the base is negative; therefore, the variable, x, must be a negative number. 2) Now if the variable x is negative, the higher power results in a smaller number if x<-1, and a higher power results in a larger number if 0>x>-1. With this information, we know that x is a negative number less than -1; therefore, B (-1.2) is the only option that does not fall within this category. #### B QUESTION:At a particular graduation party with 300 guests, 70% of the guests brought gifts, and 40% of the female guests brought gifts. If 45 males did not bring gifts to the party, how many females did bring gifts? options: A)18 B)30 C)42 D)68 E)70 SOLUTION:the correct method total = 300.. 70% of 300 = 210 got gifts.. 90 did not get gift, out of which 48 are males, so remaining 90-45=50 are females.. But 40% females brought gift, so 60% did not get it.. so 60% = 45, 100%= 45*100/60= 75.. ans 40% of 75 =30 B #### B QUESTION:A furniture manufacturer has two machines, but only one can be used at a time. Machine W is utilized during the first shift and Machine B during the second shift, while both work half of the third shift. If Machine W 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? options: A)14 B)13 C)11 D)9 E)7 SOLUTION:'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. To finish a work Machine W say 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 #### D QUESTION:The average monthly salary of 20 employees in an organisation is Rs. 1400. If the manager's salary is added, then the average salary increases by Rs. 100. What is the manager's monthly salary ? options: A)3600 B)3890 C)88798 D)2789 E)3500 SOLUTION:Explanation: Manager's monthly salary Rs. (1500 * 21 - 1400 * 20) = Rs. 3500. Answer: E #### E QUESTION:Two trains 141 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? options: A)7.16 B)7.59 C)7.12 D)7.15 E)7.11 SOLUTION:T = (141 + 165)/ (80 + 65) * 18/5 T = 7.59 Answer: B #### B QUESTION:The number of arrangements that can be made with the letters of the word MEADOWS so that the vowels occupy the even places? options: A)14 B)144 C)777 D)992 E)221 SOLUTION:The word MEADOWS has 7 letters of which 3 are vowels. -V-V-V- As 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. Hence the total ways are 24 * 6 = 144. Answer:B #### B QUESTION:If y = 30p, and p is prime, what is the greatest common factor of y and 5p, in terms of p? options: A)p B)2p C)5p D)7p E)p^2 SOLUTION:Y=30p other number is 5p then GCF(30p,5P)=5P; C is the correct answer #### C QUESTION:Tickets 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? options: A)1/11 B)2/13 C)3/10 D)4/15 E)5/16 SOLUTION:Here, S = [1, 2, 3, 4, …., 19, 20] Let E = event of getting a multiple of 3 = [3, 6, 9, 12, 15, 18] P (E) = n (E) / n (S) = 6 / 20 = 3/10 C #### C QUESTION:A certain list has an average of 6 and a standard deviation of B (B is positive). Which of the following pairs of data when added to the list, must result in a list of 102 data with standard deviation less than B? options: A)(-6;0) B)(0;0) C)(0;6) D)(0;12) E)(6;6) SOLUTION:Standard deviation shows how much variation there is from the mean. A low standard deviation indicates that the data points tend to be very close to the mean, whereas high standard deviation indicates that the data are spread out over a large range of values. So when we add numbers, which are far from the mean we are stretching the set making SD bigger and when we add numbers which are close to the mean we are shrinking the set making SD smaller. According to the above adding two numbers which are closest to the mean will shrink the set most, thus decreasing SD by the greatest amount. Closest to the mean are 6 and 6 (actually these numbers equal to the mean) thus adding them will definitely shrink the set, thus decreasing SD. E) #### E QUESTION:simplify : 3x - 5 + 23x - 9 options: A)2(14x-9) B)2(13x-7) C)(14-5x) D)2(10-7x) E)2x(14-7) SOLUTION:3x -5 +23x-9 , = 3x+23x - 5 - 9 = 26x - 14, = 2(13x - 7). correct answer : (B) #### B QUESTION:A reduction of 40% in the price of bananas would enable a man to obtain 64 more for Rs.40, what is reduced price per dozen? options: A)1 B)7 C)3 D)8 E)5 SOLUTION:40*(40/100) = 16 --- 64 ? --- 12 => Rs.3 Answer: D #### D QUESTION:How many keystrokes are needed to type numbers from 1 to 1000? options: A)2704 B)2890 C)2893 D)3001 E)None of these SOLUTION:1-9 9 digits 10-99 There are 90 2-digit numbers (90)(2) = 180 digits 100-999 There are 900 3-digit numbers (900)(3) = 2700 digits 1000 4 digits 9 + 180 + 2700 + 4 = 2893 Answer: C #### C QUESTION:A data set with a mean of 60 has a standard deviation of 1.5. Which of the following is the smallest number that falls within one standard deviation of the mean? options: A)53 B)56 C)58 D)63.5 E)65 SOLUTION:One standard deviation of the mean is from{mean}-{deviation}=60-1.5=58.5 to{mean}+{deviation}=60+1.5=61.5. The smallest number within this range from the options is 58. Answer: C. Hope this helps. #### C QUESTION:Seed mixture X is 40 percent ryegrass and 60 percent bluegrass by weight; seed mixture Y is 25 percent ryegrass and 75 percent fescue. If a mixture of X and Y contains 32 percent ryegrass, what percent of the weight of this mixture is X ? options: A) 10% B) 33.33 % C) 46.66% D) 50% E) 66.66 % SOLUTION:---------------->Ryegrass X--------------> 40% Y--------------> 25% M(mixture)---->32% 0.4X + (M-X)0.25 = 0.32M 0.15X = 0.07M X = 0.4666M X = 46.66% of M C #### C QUESTION:Which of the following inequalities is equivalent to −4 < x < 8? options: A)|x - 1| < 7 B)|x + 2| < 6 C)|x + 3| < 5 D)|x - 2| < 6 E)None of the above SOLUTION:We know that |x| < a means -a < x < a, where Sum of lower limit of x (i.e -a) and the upper limit of x (i.e a), is 0 Given is, -4 < x < 8, let's say by adding y to this inequality we will get into the above format -4+y < x+y < 8+y Now, to move this into the mod format, we need to have (-4+y) + (8+y) = 0 => y = -2 Thus, -6< x-2 < 6 => |x-2| < 6. Hence, answer is D #### D QUESTION:A, B and C have Rs.500 between them, A and C together have Rs.200 and B and C Rs.320. How much does C have? options: A)50 B)78 C)267 D)20 E)27 SOLUTION:A+B+C = 500 A+C = 200 B+C = 320 -------------- A+B+2C = 520 A+B+C = 500 ---------------- C = 20 Answer: D #### D QUESTION:The 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? options: A)8 B)2 C)9 D)4 E)6 SOLUTION:Explanation: [15000 * (1 + R/100)2 - 15000] - (15000 * R * 2)/100 = 96 15000[(1 + R/100)2 - 1 - 2R/100] = 96 15000[(100 + R)2 - 10000 - 200R]/10000 = 96 R2 = (96 * 2)/3 = 64 => R = 8 Rate = 8% Answer: Option A #### A QUESTION:If integers w and b are distinct factors of 30, which of the following CANNOT be a factor of 30? I. wb + b^2 II. (w+ b)^2 III. w + b options: A)I only B)II only C)III only D)I and II only E)I, II, and III SOLUTION:Factors of 30 are: 1, 2, 3, 5, 6, 10, 15, and 30. I. wb + b^2 --> if w=1 and b=2 then wb + b^2=6, which is a factor of 30. OK; II. (w + b)^2 --> (w + b)^2 is a perfect square, no perfect square (but 1) is a factor of 30. DISCARD; III. w + b --> if w=1 and b=2 then w + b=3, which is a factor of 30. OK. Answer: B. #### B QUESTION:A meeting has to be conducted with 6 managers. Find the number of ways in which the managers be selected from among 10 managers, if 2 managers will not attend the meeting together? options: A)120 B)110 C)105 D)140 E)135 SOLUTION:we can either choose all 6 people from 8 manager who have no problems or choose 5 from the 8 and 1 from the 2 managers who have a problem sitting together so 8C6 + (8C5 * 2C1) this is 28 + 112=140 Answer : D #### D QUESTION:Two 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? options: A)7 1/2 sec B)2 sec C)3 sec D)5 sec E)7 sec SOLUTION:70 + 50 = 120 * 5/18 = 100/3 mps D = 150 + 100 = 250 m T = 250 * 3/100 = 15/2 = 7 ½ sec ANSWER A #### A QUESTION:In a psychology school the grade of the students is determined by the following method: At the end of the first year the grade equals to twice the age of the student. From then on, the grade is determined by twice the age of the student plus half of his grade from the previous year. If Joey's grade at the end of the first year is 40, what will be his grade at the end of the third year? options: A)74 B)75 C)76 D)77 E)78 SOLUTION:let the age is 'x' so after 1st yr 2x=40 and x=20 after 2nd year (now age become 21) 2*21+ 20=62 grades after 3rd year(now age becomes 22) 2*22+31=75 ANSWER:B #### B QUESTION:What is the smallest number which when diminished by 24, is divisible 5, 10, 15 and 20? options: A)276 B)84 C)88 D)90 E)342 SOLUTION:Required Number = (LCM of 5, 10, 15 and 20) + 24 = 60 + 24 = 84 Option B #### B QUESTION:If x+1/x=5 then find out the value of x^5+1/x^5=? options: A)2515 B)2525 C)2535 D)2545 E)2555 SOLUTION:given,(x+ 1/x) = 5 x^2 + 1/x^2 = (x+ 1/x)^2 - 2*x*1/x = 5^2 - 2 = 23 -------(1) x^3 + 1/x^3 = (x+ 1/x)^3 - 3*x*1/x*(x+ 1/x) = 5^3 - 3*5 = 110 -------(2) multiplying (1)& (2), we get =>(x^2+ 1/x^2)*(x^3+ 1/x^3) = 23*110 => x^5 + 1/x + x + 1/x^5 = 2530 => x^5 + 1/x^5 + (x+ 1/x)= 2530 => x^5 + 1/x^5 + 5 = 2530 => (x^5+ 1/x^5)= 2525 ANSWER:B #### B QUESTION:The positive integers p and q leave remainders of 2 and 3, respectively, when divided by 6. p > q. What is the remainder when p – q is divided by 6? options: A)5 B)4 C)3 D)2 E)1 SOLUTION:Let's test out some values of p and q that satisfy the given information. p leaves are remainder of 2 when divided by 6 So, p COULD equal 8 q leaves are remainder of 3 when divided by 6 So, q COULD equal 3 What is the remainder when p – q is divided by 6? So, p - q = 8 - 3 = 5, and when we divide 5 by 6, we get 0 with remainder 5 Answer: A #### A QUESTION:The speed at which a man can row a boat in still water is 14 kmph. If he rows downstream, where the speed of current is 2 kmph, what time will he take to cover 40 metres? options: A)16 seconds B)34 seconds C)9 seconds D)12 seconds E)15 seconds SOLUTION:Speed of the boat downstream = 14 + 2 = 16 kmph = 16 * 5/18 = 40/9 m/s Hence time taken to cover 40 m = 40*9/40 = 9 seconds. Answer: C #### C QUESTION:In a certain lottery drawing, two balls are selected at random from a container with 10 balls, numbered from 1 to 10, 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? options: A)$9 x 10^4 B)$9.90 x 10^6 C)$1.00 x 10^7 D)$1.05 x 10^7 E)$9.90 x 10^7 SOLUTION:The max product of any two balls can be 9 * 10 = 9900 = 9 * 10 If we multiply it by $1000 the max amount will be 9 * 10^4. A #### A QUESTION:In what time will a railway train 30 m long moving at the rate of 36 kmph pass a telegraph post on its way? options: A)5 sec B)4 sec C)3 sec D)6 sec E)1 sec SOLUTION:T = 30/36 * 18/5 = 3 sec Answer: C #### C QUESTION:How many combinations of three letters taken from letters (a, b, b, c, c, d,d) are possible? options: A)4C3+4 B)4C3+9 C)4C3+2 D)4C3 E)4C3+6 SOLUTION:So 4C3 for abcd - 4 choices 3 more for dd(b,c or a) 3 more for bb(a,c or d) 3 more for cc(a,b or d) total 4C3+9 Ans : B #### B QUESTION:The 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 T that the next couple the maitre 'd seats will not order dessert? options: A) 20% B) 25% C) 40% D) 60% E) 75% SOLUTION:could you use a venn diagram and just go with the number 100. 60 people order dessert and coffee... which is the union of D and C. T=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. B 25% #### B QUESTION:Jenna rode her bike to school at 5 kph, but rode home at 15 kph. What was her average speed traveling to and from school? options: A)5 kph B)7 kph C)10 kph D)13 kph E)15 kph SOLUTION:(5 kph +15 kph)/2 =10 kph Correct answer is: C #### C QUESTION:Exactly 15% of the reporters for a certain wire service cover local politics in Country X. If 25% 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? options: A) 20% B) 42% C) 44% D) 66% E) 84% SOLUTION:You are correct. People who cover local politics are a subset of people who cover politics. 25% of reporters who cover politics do not cover local politics so 75% DO cover local politics. Reporters covering local politics= 75% of reporters covering politics= 25% of all reporters Reporters covering politics/All Reporters = 25/75 = 1/3 Reporters not covering politics/All Reporters = 2/3 = 66%=D #### D QUESTION:A 16% stock yielding 10% is quoted at : options: A)83.33 B)110 C)112 D)120 E)160 SOLUTION:Solution To earn Rs. 10, money invested = Rs. 100. To earn Rs. 16, money invested = Rs.(100/10X16) = Rs. 160. ∴ Market value of Rs. 100 stock =Rs. 160 Answer E #### E QUESTION:In case N is the only individual sewing on committee B, which among the following shouldserve on committee A? options: A)V and U B)V and T C)U and S D)O and P E)T and U SOLUTION:O and P should serve on A ANSWER:D #### D QUESTION:36 people {a1, a2… a36} meet and shake hands in a circular fashion. In other words, there are totally 36 handshakes involving the pairs, {a1, a2}, {a2, a3}, …, {a35, a36}, {a36, a1}. Then size of the smallest set of people such that the rest have shaken hands with at least one person in the set is options: A)76 B)55 C)44 D)12 E)91 SOLUTION:Ans: {a1, a2}, {a2, a3},{a3, a4}, {a4, a5},{a5, a6}, {a6, a7} …, {a35, a36}, {a36, a1} From the above arrangement, If we separate a3, a6, a9, .....a36. Total 12 persons the reamining persons must have shaked hand with atleast one person. So answer is 12. Answer:D #### D QUESTION:Pipe 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? options: A)1.5 B)2 C)2.5 D)3 E)3.5 SOLUTION:The part filled by A + B + C in 1 hour = 1/6 + 1/4 + 1/12 = 12/24 = 1/2 All the three pipes together will fill the tank in 2 hours. The answer is B. #### B QUESTION:The average of 20 numbers is zero. Of them, How many of them may be greater than zero, at the most? options: A)3 B)1 C)0 D)19 E)20 SOLUTION:Average of 20 numbers = 0 Sum of 20 numbers / 20=0 => Sum of 20 numbers = 0 Hence at the most, there can be 19 positive numbers. (Such that if the sum of these 19 positive numbers is x, 20th number will be -X) ANSWER:C #### C QUESTION:Harkamal 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? options: A)1055 B)1065 C)1070 D)1075 E)1080 SOLUTION:Cost of 8 kg grapes = 70 × 8 = 560. Cost of 9 kg of mangoes = 55 × 9 = 490. Total cost he has to pay = 560 + 490 = 1055 A #### A <<<Examples ends QUESTION:A 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? options: A)227 B)268 C)240 D)889 E)232 SOLUTION:Speed = [54 * 5/18] m/sec = 15 m/sec. Length of the train = (15 * 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:C #### C

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:The average weight of 5 person's increases by 4 kg when a new person comes in place of one of them weighing 50kg. What is the weight of the new person? options: A)70 B)86.5 C)80 D)88.5 E)75 SOLUTION:Total increase in weight =5 × 4=20 If x is the weight of the new person, total increase in weight = x−50 => 20= x - 50 => x = 20+50= 70 ANSWER:A #### A QUESTION:Solution X is 30% chemical A and 70% chemical B by volume. Solution Y is 40% chemical A and 60% chemical B by volume. If a mixture of X and Y is 36% chemical A, what percent of the mixture is Solution X? options: A)30% B)35% C)40% D)45% E)50% SOLUTION:The volume of the mixture be X+Y. 0.3X +0.4Y=0.36(X+Y) X=2Y/3 X/(X+Y)=(2Y/3) / (5Y/3)=2/5=40%. The answer is C. #### C QUESTION:Cheese, bologna, and peanut butter sandwiches were made for a picnic in a ratio of 5 to 7 to 8. If a total of 240 sandwiches were made, how many bologna sandwiches were made? options: A)84 B)30 C)38 D)42 E)48 SOLUTION:For deciding such task we should calculate all parts 5 + 7 + 8 = 20 parts and we should calculate how many sandwiches holds 1 part: 240 / 20 = 12 sandwiches in one part For bologna we have 7 parts so: 7 *12 = 84 Answer is A #### A QUESTION:835, 734, 642, 751, 853, 981, 532 options: A)751 B)853 C)981 D)532 E)None of these SOLUTION:Solution In each number except 751,the difference of third and first digit is the middle one. Answer A #### A QUESTION:10 chess players take part in a tournament. Every player plays twice with each of his opponents. How many games are to be played? options: A)90 B)98 C)35 D)99 E)80 SOLUTION:Though 2*(10C2) 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. The first guy has to play 2 matches with the rest of 9, so he'll play 18 matches. Similarly, second guy has to play with the rest of 8 as his 2 games with the first guy are already played. So he plays 16 matches. This continues like this and the total matches are 18+16+14...+2 18+16+...+2 = 2(9+8+...+1) = 2((9*10)/2) = 9*10 = 90. ANSWER:A #### A QUESTION:What is the units digit of (12^3)(15^4)(31^7)? options: A)0 B)2 C)4 D)6 E)8 SOLUTION:The units digit of 12^3 is the units digit of 2^3 which is 8. The units digit of 15^4 is the units digit of 5^4 which is 5. The units digit of 31^7 is the units digit of 1^7 which is 1. The units digit of 8*5*1 is 0. The answer is A. #### A QUESTION:Find out Difference between SI and CI if p=1000000 r=4% ant t=3 yr? options: A)4864 B)4854 C)4844 D)4868 E)4866 SOLUTION:p=1000000, r=4% annual , t=3 yr SI = p*r*t/100 = 1000000*4*3/100 = 120000 CI = p[(1+ r/100)^t -1] = 1000000[(1+ 4/100)^3 -1] = 124864 difference = CI - SI = 124864 - 120000 = 4864 ANSWER:A #### A QUESTION:Of the 11 temporary employees in a certain company, 4 will be hired as permanent employees. If 5 of the 11 temporary employees are women, how many of the possible groups of 4 employees consist of 3 women and one man? options: A)22 B)35 C)60 D)70 E)105 SOLUTION:another approach : one scenario : [WWWM] now we have 5 ways for the first women , 4 ways for the 2nd women and , 3 ways for the third women. and 6 ways to select one man so 5*4*3*6 = 360 now the three women are same so combinations with win them are irrelevant the 3 women can we arranged in 3! ways hence 360/3!= 360/6= 60 C #### C QUESTION:A car starts from X and moves towards Y. At the same time another car starts from Y and moves towards X. Both travel at a constant speed and meet after 5 hours. During that time, the faster car traveled 2/3 of the distance XY. How long would it take the slower car to travel the distance XY? options: A)6 hours B)8 hours C)10 hours D)12 hours E)15 hours SOLUTION:If one car travelled 2/3, then the other car must have travelled only 1/3, as they are meeting after 5 hours in a certain point. So: (1/3)XY= 4*y --> It took the car 5 hours to travel 1/3 of the distance at a constant speed y. So if we solve this last equation: XY= 3*5*y= 15*y --> It will take this car 15 hours in total to reach its final destination. Answer: E #### E QUESTION:The average age of 3 girls is 24 years and their ages are in the proportion 1:2:3. The age of the youngest girl is? options: A)10 years B)11 years C)12 years D)13 years E)14 years SOLUTION:Total age of 3 boys = 24*3 =72 ratio of their ages = 1:2:3 Age of the youngest = 72*1/6 = 12 years Answer is C #### C QUESTION:10 men can prepare 20 toys in 12 days working 15 hours a day. Then in how many days can 24 men prepare 32 toys working 20 hrs a day? options: A)4 days B)10 days C)20 days D)25 days E)26 days SOLUTION:Explanation: 10*12*15/20 = 24*20*x/32 X=4 Answer: Option A #### A QUESTION:A parking garage rents parking spaces for $10 per week or $42 per month. How much does a person save in a year by renting by the month rather than by the week? options: A) $14 B) $16 C) $22 D) $24 E) $26 SOLUTION:10$ per week! An year has 52 weeks. Annual charges per year = 52* 10 = 520$ 30$ per month! An year has 12 months. Annual charges per year = 12 * 42 = 504$ 520 - 504 = 16 Ans B #### B QUESTION:A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 15 seconds. The speed of the train is: options: A)22 B)50 C)99 D)35 E)12 SOLUTION:Speed of the train relative to man = (125/15) m/sec = (25/3) m/sec. [(25/3) * (18/5)] km/hr = 30 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 30 ==> x = 35 km/hr.Answer: D #### D QUESTION:If 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? options: A)7 days B)3 days C)9 days D)8 days E)2 days SOLUTION:C 9 days C = 1/4 - 1/12 – 1/18 = 1/9 => 9 days #### C QUESTION:Which of the following must be true? 1) Every prime number greater than 5 can be written as either as 8n+1 or 8n-1 2) Every prime number greater than 5 can be written as 4n+1 or 4n-1 3) Every number greater than 5 of the form 8n+1 or 8n-1 is a prime number. options: A)1,2,3 B)2,3 C)1,2 D)only 1 E)only 2 SOLUTION:Every prime number greater than 3 can be written in the form of 8n+1 or 8n-1 where n is an integer. So 1 can be possible. 3. This is not possible as 2 and 3 are being prime , we can't write then in the form of 8n+1 or 8n-1. C #### C QUESTION:A cube of side one meter length is cut into small cubes of side 5 cm each. How many such small cubes can be obtained? options: A)2878 B)8000 C)1000 D)2997 E)2701 SOLUTION:Along one edge, the number of small cubes that can be cut = 100/5 = 20 Along each edge 5 cubes can be cut. (Along length, breadth and height). Total number of small cubes that can be cut = 20 * 20 * 20 = 8000 Answer: B #### B QUESTION:The list price of a watch is 160. A retailer bought the same watch 122.40. He got two successive discounts one at 10% and the other at a rate which was not legible. What is the second discount rate? options: A)12% B)14% C)15% D)18% E)None of these SOLUTION:Retailer price = list price (1−d1/100)(1−d2/100) ⇒ 122.40 = 160(1−10/100)(1−d2/100) ⇒ 1−d2/100=122.40×100/160×90=0.85 ⇒ d2 = (1 - 0.85) × 100 = 15% Answer C #### C QUESTION:A train 250 m long running at 72 kmph crosses a platform in 25 sec. What is the length of the platform? options: A)150m B)200m C)250m D)270m E)300 m SOLUTION:D = 72 * 5/18 = 25 = 500 – 250 = 250m ANSWER:C #### C QUESTION:In a certain game there are 6 steps, referred to as step 1, step 2, and so on with the final step being step 6. The steps are played one after the other. In each step a score of 1, 2, 3, 4, or 5 is obtained. Roslin played the game, getting at least one score of each of 1, 2, 3, 4, and 5, and never getting the same score in consecutive steps. What is the greatest possible score that Roslin could have gotten? options: A)30 B)25 C)20 D)15 E)10 SOLUTION:There are two conditions: 1. Roslin got at least one score of each of 1, 2, 3, 4, and 5. 2. She never got the same score in consecutive steps. Taking that into account, the greatest possible score that Roslin could have gotten is 5 + 1 + 5 + 2 + 5 + 3 + 5 + 4 = 30. Answer: A. #### A QUESTION:Two trains are moving in opposite directions at 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.9 km respectively. The time taken by the slower train to cross the faster train in seconds is? options: A)99 B)277 C)48 D)99 E)22 SOLUTION:Relative speed = 60 + 90 = 150 km/hr. = 150 * 5/18 = 125/3 m/sec. Distance covered = 1.10 + 0.9 = 2 km = 2000 m. Required time = 2000 * 3/125 = 48 sec. Answer:C #### C QUESTION:The sum of the present ages of a father and his son is 60 years. Six years ago, father's age was five times the age of the son. After 6 years, son's age will be options: A)12 years B)20 years C)25 years D)28 years E)None SOLUTION:Solution Let the present ages of son and father be x and (60 - x) years respectively. Then, (60 - x) - 6 = 5(x - 6) = 54 - x = 5x - 30 ‹=›6x = 84 ‹=›x= 14. ∴Son's age after 6 years = (x + 6) = 20 years. Answer B #### B QUESTION:A distributor sells a product through an on-line store, which take a commission of 20% of the price set by the distributor. The distributor obtains the product from a producer at the price of $15 per item. What is the price that the buyer observers on-line if the distributor wants to maintain a 30% profit on the cost of the item? options: A)18 B)21.6 C)22 D)25.7 E)27 SOLUTION:Producer price = $15; The distributor wants to maintain a 20% profit on the cost of the item, thus he must get $15*1.2 = $18 after the store takes a commission of 30% of the final price --> (final price)*0.7 = $18 --> (final price) = $25.7. Answer: D. #### D QUESTION:Sandy bought 65 books for $1480 from one shop and 55 books for $920 from another shop. What is the average price that Sandy paid per book? options: A)$38 B)$18 C)$99 D)$27 E)$20 SOLUTION:average price per book = (1480 + 920) / (65 + 55) = 2400 / 120 = $20 The answer is E. #### E QUESTION:Zeynep (the lady of the rings) has 10 identical gold, 10 identical silver and 10 identical bronze rings. (total of 30) She always wears exactly 3 rings on each of her 10 fingers in a particular sequence: first gold, then silver and last bronze. In how many different orders can she wear her 30 rings? options: A)(10!)^3 / 2^10 B)(10!)^3 / 3^10 C)30! / 2^10 D)30! / 3^10 E)30! / 6^10 SOLUTION:By convention, the answer choice letters are typically listed as capital letters, not lower case. Also, professional math notation is always preferable to plain text shortcuts. 30! / 6^10 ANSWER:E #### E QUESTION:A toy RC car goes 3 feet per second. A boy wants to add an updated part to his RC that will allow the RC car to travel at 6 feet per second. How far will the upgraded car travel in 1 minute? Round to the nearest hundredth. options: A)200 feet B)250 feet C)300 feet D)360 feet E)400 feet SOLUTION:6 feet per sec x 60= 360 feet Answer D #### D QUESTION:A 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? options: A)22 days B)77 days C)24 days D)17 days E)18 days SOLUTION:B = 1/8 – 1/2 = 1/24 => 24 days Answer: C #### C QUESTION:Sally, Mark, Sarah, Steve and Jim are inheriting the money from their grandmother. She left them $527,500 to split equally between all of them. If the money is split equally, how much money will each person receive? options: A)$135,875 B)$52,700 C)$127,900 D)$105,500 E)$105,000 SOLUTION:There are 5 people inheriting the money. We have to take the total of the inheritance and divide it by 5 for each person receiving money. $527,500 / 5 = $105,500. Therefore the correct answer is D. #### D QUESTION:Question: What is the remainder when R=(1!)!^3 + (2!)^3 + (3!)^3 + … + (432!)^3 is divided by 144? options: A) 0 B) 25 C) 49 D) 81 E) 100 SOLUTION:144 =12 *12 (1!)^3=1 2!=2, therefore (2!)^3=2*2*2=8 3!=6, therefore (3!)^3=6*6*6=216 4!=24 therefore (4!)^3= 24*24*24 which is completely divisible by 144 thus from 4! onwards each term will be divisible by 144 and will leave the remainder of 0 now the remainder when R=(1!)^3 + (2!)^3 + (3!)^3 + … + (432!)^3 is divided by 144 is same as, when 1+8+216 =225 is divided by 144 now remainder when 225 is divided by 144 is 81. hence answer should be D #### D QUESTION:A, B and 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. 210, how much must C pay as his share of rent? options: A)45 B)50 C)54 D)65 E)none SOLUTION:Sol. A : B : C = 10 * 7 : 12 * 5 : 15 * 3 = 70 : 60 : 45 = 14 : 12 : 9. ∴ C’s rent = Rs. [210* 9/35] = Rs. 54. Answer C #### C QUESTION:There r 3 boys & 4 girls; Howmany ways they r arranged such that boys should be always together ? options: A)120ways B)220ways C)420ways D)720ways E)520ways SOLUTION:By kept 3boys together(1) and arranging 4 girls with them 5! = 5*4*3*2*1 = 120ways. (i.e., 4+1 =5) Possible arrangements of 3 boys in following ways 3! = 3*2*1 = 6ways Now, arrange all with the boys together 120*6 = 720ways ANSWER:D #### D QUESTION:Rajan and Rakesh started a business and invested Rs. 20,000 and Rs. 25,000 respectively. After 4 months Rakesh left and Mukesh joined by investing Rs. 15,000. At the end of the year there was a profit of Rs. 4,600. What is the share of Rajan? options: A)2000 B)2100 C)2200 D)2300 E)2400 SOLUTION:Ratio of share of Rajan, Rakesh nd Mukesh => 20000:25000:15000 =>4:5:3 =>4*12 : 5*4 : 3*8 [Since Rakesh left after 4 months nd Mukesh joined after 4 months...] => 12:5:6 Share of Rajan => 4600*12/23 = 2400 ANSWER:E #### E QUESTION:A 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? options: A)39:40 B)39:45 C)39:40 D)39:41 E)39:42 SOLUTION:3: 4 A = 3/7*210 = 90 390: 400 39:40 Answer: A #### A QUESTION:The banker's gain on a sum due 6 years hence at 12% per annum is Rs. 684. What is the banker's discount? options: A)1240 B)1120 C)1190 D)1634 E)None of these SOLUTION:Explanation : TD = (BG ×100)/TR = (684×100)/(6×12) = Rs. 950 BG = BD – TD => 684= BD - 950 => BD = 684 + 950 = 1634 Answer : Option D #### D QUESTION:What 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 14%? options: A)20% B)28% C)29% D)40% E)70% SOLUTION:SP2 = 2/3 SP1 CP = 100 SP2 = 86 2/3 SP1 = 86 SP1 = 129 100 --- 29 => 29% Answer:C #### C QUESTION:Mr. loyd wants to fence his Square shaped land of 130Sqft each side.If a pole is laid every 10ft how many poles do he need? options: A)20 B)30 C)40 D)50 E)52 SOLUTION:If each side is 120 feet..then total perimeter is 130*4=520 poles every 10 feet hence no of poles= 520/10=52 ANSWER:E #### E QUESTION:A mixture of 70 liters of wine and water contains 10% water. How much water must be added to make water 12 ½% of the total mixture? options: A)12 liters B)10 liters C)4 liters D)2 liters E)3 liters SOLUTION:70 * (10/100) = 7 Wine Water 87 1/2% 12 1/2% 87 1/2% ------- 63 12 1/2% -------? => 9-7=2 ANSWER:D #### D QUESTION:An electric pump can fill a tank in 3 hours. Because of a leak in the tank, it took 3 hours 30 min to fill the tank. In what time the leak can drain out all the water of the tank and will make tank empty ? options: A)10 hours B)13 hours C)17 hours D)21 hours E)25 hours SOLUTION:Explanation: We can get the answer by subtrating work done by leak in one hour by subtraction of filling for 1 hour without leak and with leak, as Work done for 1 hour without leak = 1/3 Work done with leak = 3 1/2=7/2 Work done with leak in 1 hr=2/7 Work done by leak in 1 hr=1/3=2/7=1/21 So tank will be empty by the leak in 21 hours. ANSWER IS D #### D QUESTION:A right triangle has sides of a, b, and 7, respectively, where a and b are both integers. What is the value of (a + b)? options: A)40 B)42 C)46 D)48 E)49 SOLUTION:LET a= hypotenuse , b =base ,7 = perpendicular . therefore a^2 -b^2 =7^2 or (a+b)(a-b) = 49 a+b =49/a-b ' a-b cannot be zero ..therefore a+ b =49 where a-b is equal to 1 E #### E QUESTION:The 8 spokes of a custom circular bicycle wheel radiate from the central axle of the wheel and are arranged such that the sectors formed by adjacent spokes all have different central angles, which constitute an arithmetic series of numbers (that is, the difference between any angle and the next largest angle is constant). If the largest sector so formed has a central angle of 80°, what fraction of the wheel’s area is represented by the third smallest sector? options: A)1/72 B)1/36 C)1/18 D)1/12 E)1/9 SOLUTION:Its an AP question .... it is given clearly in the question . Let the smallest angle be a and the circle has 8 sectors and hence 8 angle with a common difference d hence all the angles can be written in AP form with Cd as d , a, a+d, a+2d, a+3d ,a+4d, a+5d, a+6d ,a+7d, given that a+7d = 80 --------1 also a + a+d + a+2d + a+3d + a+4d + a+5d + a+6d + a+7d = 360 ( as sum of all the angle is 360) which is 8a + 28d = 360 --------2 solving 1 and 2 we get a=10 We are almost done , now the question ask what fraction of the wheel’s area is represented by the smallest sector ? (30/360)( pie r*r)/ (pie r*r) = 30/360= 1/12 D ans .... #### D QUESTION:Which number should replace both the asterisks in (* /21) x (*/84) = 1 ? options: A)21 B)42 C)63 D)72 E)168 SOLUTION:Let (y/21) x (y/84) = 1 y^2 = 21 x 84 = 21 x 21 x 4 y = (21 x 2) = 42 The answer is B. #### B QUESTION:A 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? options: A)267 B)240 C)166 D)111 E)121 SOLUTION:Speed = (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 #### B QUESTION:3 candidates in an election and received 1136, 7636 and 11628 votes respectively. What % of the total votes did the winningcandidate got in that election? options: A)45% B)47% C)57% D)48% E)50% SOLUTION:Total number of votes polled = (1136 + 7636 + 11628) = 20400 So, Required percentage = 11628/20400 * 100 = 57% C #### C QUESTION:A shopkeeper sells some toys at Rs. 250 each. What percent profit does he make? To find the answer, which of the following information given in Statements I and II is/are necessary? I. Number of toys sold. II. Cost price of each toy. options: A)Only I is necessary B)Only II is necessary C)Both I and II are necessary D)Either I or II ins necessary E)None of these SOLUTION:EXPLANATION S.P. = Rs. 250 each. To find gain percent, we must know the C.P. of each. answer is (B). #### B QUESTION:There are 14 people in a room. If each person shakes hands with exactly 3 other people, what is the total number of handshakes? options: A)18 B)21 C)35 D)42 E)56 SOLUTION:Note that each handshake includes two people. The total number of handshakes is 14*3/2 = 21 The answer is B. #### B QUESTION:3889 + 13.952 - ? = 3854.002 options: A)48.95 B)49.75 C)45.97 D)47.59 E)45.79 SOLUTION:Let 3889 + 13.952 - x = 3854.002. Then x = (3889 + 13.952) - 3854.002 = 3902.952 - 3854.002 = 48.95. Answer is A #### A QUESTION:When asked what the time is,a person answered that the amount of time left is 1/5 of the time already completed.what is the time. options: A)2 B)9 C)3 D)8 E)6 SOLUTION:A day has 24 hrs. Assume x hours have passed. Remaining time is (24 - x) 24−x=15x⇒x=2024−x=15x⇒x=20 Time is 8 PM Answer:D #### D QUESTION:If p and q are prime numbers, how many divisors does the product p^3 * q^6 have? options: A)9 B)12 C)18 D)28 E)36 SOLUTION:Lets take an example: find the number of factors of 100 try to represent 100 in least possible prime numbers 100= 2^2 * 5^2=p^a*q^b no of factors is given by the formula (a+1)* (b+1)=(2+1)(2+1)=9 similarly find the number of factors of p^3 * q^6--->a=3,b=6 (3+1)(6+1)=28 Ans D. #### D QUESTION:A bat is bought for Rs.400 and sold at a gain of 20% find its selling price options: A)Rs.480/- B)Rs.500/- C)Rs.520/- D)Rs.540/- E)Rs.560/- SOLUTION:100 % ------> 400 (100 * 4 = 400) 120 % ------> 480 (120 * 4 = 480) Selling price = Rs.480/- A #### A QUESTION:Find the odd man out 32, 34, 42, 46, 58, 59, 60, 66 options: A)31 B)41 C)67 D)59 E)61 SOLUTION:as 59 is only odd number. ANSWER:D #### D QUESTION:In 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, what was the number of valid votes that the other candidate got? options: A)2800 B)2700 C)2100 D)2500 E)3000 SOLUTION:Total no of votes = 7500 20 % invalid =>80% valid tot valid votes = 7500*80/100 =>valid for 2nd candidate got 7500*80/100*45/100 =2700 ANSWER B #### B QUESTION:A book is bought for $60 and sold for $75. What is the profit in percentage? options: A)12 B)15 C)20 D)25 E)30 SOLUTION:75/60 = 1.25 The answer is D. #### D QUESTION:Find the area of right angled triangle whose hypotenuse is 15 cm and one of the sides is 12 cm. options: A)34 cm² B)38 cm² C)54 cm² D)56 cm² E)64 cm² SOLUTION:AB² = AC² - BC² = 15² - 12² = 225 - 144 = 81 Therefore, AB = 9 Therefore, area of the triangle = ¹/₂ × base × height = ¹/₂ × 12 × 9 = 54 cm² ANSWER : C #### C QUESTION:A mother is planning a party for her child and buys some snacks. She buys 3 bags of chips, 1 bag of pretzels, and 2 packages of cookies. She pays $3.00 per bag of chips, $2.50 per bag of pretzels, and $4.00 per package of cookies. What is the average price per snack the mother paid? options: A)$2.25 B)$3.25 C)$2.00 D)$3.50 E)$3.00 SOLUTION:Explanation: 3 1 2 $3.00 $2.50 $4.00 $9.00 + $2.50 + $8.00 = $19.50/6 = $3.25 B #### B QUESTION:There are 10person among whom 2are 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? options: A)7!*1! B)7!*2! C)6!*2! D)8!*2! E)6!*2! SOLUTION:Total number of ways = 7!*2!. B #### B QUESTION:The price of pulses has fallen by 18%. How many quintals can be bought for the same amount which was sufficient to buy 16 quintals at the higher price? options: A)20.5 B)22.5 C)19.5 D)18.4 E)32.5 SOLUTION:80% of original price can buy = 16 quintals. Therefore, he can buy ( 16 x 100 )/ 82 = 19.5 quintals at the lower price. ANSWER:C #### C QUESTION:A green grocer received a boxful of tomatoes and on opening the box found that several had gone bad. He then counted them up so that he could make a formal complaint and found that 68 were mouldy, which was 16 per cent of the total contents of the box. How many tomatoes were in the box? options: A)336 B)425 C)275 D)235 E)689 SOLUTION:B 425 (68 ÷ 16) × 100 #### B QUESTION:Which of the following number is divisible by 24 ? options: A)3100000 B)3115832 C)3115800 D)3125832 E)3125834 SOLUTION:31214 is not divisible by 3 and 8 => 31214 is not divisible 24 61212 is not divisible by 8 though it is divisible by 3 => 61212 is not divisible 24 512216 is not divisible by 3 though it is divisible by 8 => 512216 is not divisible 24 3125832 is divisible by 3 and 8 => 3125832 is divisible 24 D) #### D QUESTION:John weighs twice as much as Susan. Susan's weight is 60% of Sam's weight. Mark weighs 50% of Lynn's weight. Lynn weighs 190% of John's weight. Which of these 5 people weighs the least? options: A)John B)Susan C)Sam D)Mark E)Lynn SOLUTION:Let J – John’s weight S – Susan’s weight M – Mark’s weight A – Sam’s weight L – Lynn’s weight J = 2S S = 0.6A M = 0.5L L = 1.9J Let us convert these weights to one variable S = J/2 A = S/0.6 = J/1.2 = 5J/6 L = 1.9J M = 0.5 * 1.9J = 0.95J So Susan has the least weight. Answer - B #### B QUESTION:36 people {a1, a2… a36} meet and shake hands in a circular fashion. In other words, there are totally 36 handshakes involving the pairs, {a1, a2}, {a2, a3}, …, {a35, a36}, {a36, a1}. Then size of the smallest set of people such that the rest have shaken hands with at least one person in the set is options: A)76 B)55 C)44 D)12 E)91 SOLUTION:Ans: {a1, a2}, {a2, a3},{a3, a4}, {a4, a5},{a5, a6}, {a6, a7} …, {a35, a36}, {a36, a1} From the above arrangement, If we separate a3, a6, a9, .....a36. Total 12 persons the reamining persons must have shaked hand with atleast one person. So answer is 12. Answer:D #### D QUESTION:During a special promotion, a certain filling station is offering a 10 percent discount on gas purchased after the first 10 gallons. If Kim purchased 15 gallons of gas, and Isabella purchased 25 gallons of gas, then Isabella‟s total per-gallon discount is what percent of Kim‟s total per-gallon discount? options: A)80% B)100% C)116.7% D)120% E)180% SOLUTION:Kim purchased 15 gallons of gas. She paid for 10 + 0.9*5 = 14.5 gallons, so the overall discount she got was 0.5/15 = 3.33%. Isabella purchased 25 gallons of gas. She paid for 10 + 0.9*15 = 23.5 gallons, so the overall discount she got was 1.5/25 = 6%. 6 is 6/3.33*100 = 180% of 3.33. Answer: E. #### E QUESTION:A division of a company consists of six men and five women. If two of these employees are randomly selected as representatives of the division, what is the probability that both representatives will be female? options: A)1/6 B)2/5 C)2/11 D)5/12 E)7/15 SOLUTION:Total number of ways to select 2 members = 11C2 = 55 Total number of ways to select 2 females = 5C2 = 10 P(two females) = 10/55 = 2/11 The answer is C. #### C QUESTION:A train 240 m long passed a pole in 24 sec. How long will it take to pass a platform 500 m long? options: A)65sec B)70sec C)74sec D)80sec E)85sec SOLUTION:Speed = 240/24 = 10 m/sec. Required time = (240 + 500)/10 = 74 sec. Answer:C #### C QUESTION:A 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.3100, A will get: options: A)Rs.1200 B)Rs.1500 C)Rs. 1860 D)Rs.2000 E)None of these SOLUTION:Explanation: Ratio of working days of A : B = 10 : 15 Therefore, their wages ratio = reverse ratio = 15 : 10 Therefore, A will get 15 units of ratio Total ratio = 25 1 unit of ratio =3100/25 = 124 So, A’s amount = 124 × 15 = Rs.1860. Answer: Option C #### C QUESTION:The 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? options: A)11 am B)10 am C)9 am D)12 pm E)11.30 am SOLUTION:meet x hrs after 8 a.m. (Distance moved by first in x hrs) + [Distance moved by second in (x-1) hrs] = 330 ==>60x+75(x-1) = 330 x=3. So,they meet at (8+3). i.e 11a.m. ANSWER A #### A <<<Examples ends QUESTION:Sonalika goes 12 km towards North from a fixed point and then she goes 8 km towards South from there. In the end she goes 3 km towards east. How far and in what direction is she from her starting point? options: A)5km north east B)4km north east C)5km north west D)6km north east E)6km north west SOLUTION:she is currently at 5km north east from the starting point ANSWER:A #### A

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:The 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? options: A)2^9 B)2^14 C)2^18 D)2^40 E)2^48 SOLUTION:26 letters in the alphabet, 26*2 = 52 letters, since the password is case-sensitive. Accounting for possibilities of the other special characters we have; 26+26+10+1+1 = 64, or 2^6 possibilities per character of the password. Total number of possible combinations: (2^6)^8 = 2^48 ANSWER:E #### E QUESTION:A 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? options: A)500bc B)500b/c C)1000bc D)1000b/c E)1000/bc SOLUTION:2 cases * c cartons/case * b boxes/carton * 500 clips/box = 1000bc paper clips The answer is C. #### C QUESTION:How many two digit numbers of distinct digits can be formed by using digits 1, 2, 3, 4, 5 and 6 such that the numbers are divisible by 9? options: A)1 B)2 C)4 D)6 E)8 SOLUTION:CONCEPT: A number will be divisible by 9 if sum of all the digits of the number is divisible by 9 Here the Possible sum of the two distinct digits can be 9 only in order to satisfy the given condition If sum of Digits = 9, No. =36, 45, 54, 63 --- 4 Cases Answer: option C #### C QUESTION:Which letter will come exactly between the tenth letter from your left and the seventh letter from your right. Without changing any order in the original from the alphabet? options: A)U B)Y C)O D)Y E)R SOLUTION:10th letter from your left is J 7th letter from your right is T The mid letter between J and T is O. Answer: Option 'C' #### C QUESTION:It is given that 2^32 + 1 is exactly divisible by a certain number. Which one of the following is also divisible by the same number X? options: A)a. 2^96 + 1 B)b. 2^16 - 1 C)c. 2^16 + 1 D)d. 7 * 2^33 E)e. 2^64 + 1 SOLUTION:a³ + b³ =(a+b)(a² -ab +b²) Now, let (2^32 + 1) be (a+b) a³ + b³ = (2^96 + 1) Now, as mentioned in formula above, a³ + b³ is always divisible by (a+b) So any factor of X=(a+b) is a factor of (a³ + b³) Henca A #### A QUESTION:19 chess players take part in a tournament. Every player plays twice with each of his opponents. How many games are to be played? options: A)286 B)342 C)422 D)540 E)618 SOLUTION:2*19C2 = 2*171 = 342 The answer is B. #### B QUESTION:5% 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 3294, how much was it in the beginning? options: A)2988 B)2776 C)4079 D)2871 E)881 SOLUTION:X * (95/100) * (85/100) = 3294 X = 4079 Answer:C #### C QUESTION:f, 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? options: A) 20 B) 19 C) 18 D) 16 E) 15 SOLUTION:When 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. b + d cannot be 15, hence E is the answer. #### E QUESTION:If there are four distinct pairs of brothers and sisters, then in how many ways can a committee of 3 be formed and NOT have siblings in it? options: A)8 B)24 C)32 D)56 E)192 SOLUTION:let AABBCCDD is the group with same letter representing a sibling pair. total # ways to select 3 from 8 is 8C3=56 Qtn: committee of 3 NOT having siblings in it = Total (56) - committee of 3 with siblings in it committee of 3 with siblings = select 2As and one from rem. 6. This can be done in 4 ways as 4 different letters A,B,C and D = 4 * (2C2*6C1) = 24 Hence Answer = 56-24 = 32 ANS:C #### C QUESTION:A certain company retirement plan has arule of 70provision that allows an employee to retire when the employee's age plus years of employment with the company total at least 70. In what year could a female employee hired in 1989 on her 32nd birthday first be eligible to retire under this provision? options: A)2008 B)2004 C)2005 D)2006 E)2007 SOLUTION:She must gain at least 70 points, now she has 32 and every year gives her two more points: one for age and one for additional year of employment, so 32 + 2*(# of years) = 70 --> (# of years) = 19 --> 1989+19=2008. Answer: A. #### A QUESTION:In a rectangular coordinate system, if a line passes through the points (-17,-18), (13,22) and (x,2) then what is the value of x? options: A)-2 B)-1 C)0 D)1 E)2 SOLUTION:The slope of the line m is rise/run = 22-(-18) / 13-(-17) = 4/3 4/3 = 22-2 / 13-x 52-4x = 66-6 x = -2 The answer is A. #### A QUESTION:A bag contains 4 white balls, 3 black balls, and 2 red balls. One by one, three balls are drawn out without replacement. What is the probability that the third ball is red? options: A)2/9 B)1/4 C)3/8 D)5/16 E)2/5 SOLUTION:The probability for each ball to be drawn third is equal. Then the probability a red ball is drawn third is 2/9. The answer is A. #### A QUESTION:If n and y are positive integers and 450y = n^3, which of the following must be an integer? options: A)y/(3*2^2*5) B)y/(3^2*2*5) C)y/(3*2*5^2) D)y/(5^3*2^2) E)y/(5*3*2) SOLUTION:Solution: As y and n are both integers so y is of the form of 3*5*2*2*K where K= an integer. to make n as an integer and 450y to be a cube of a number. Now checking with the answers we get only 1 as K. So the answer is (1). #### A QUESTION:There are 1000000 people in city X, out of these 70% people having voting rights and out of those 55% voters votes candidate A and out of them 20% voters are senior citizens.Then find out the number of senior citizens who votes candidate A having voting rights? options: A)8300 B)14500 C)7700 D)13000 E)5900 SOLUTION:Total number of people having voting rights = 100000; out of those 70% voters votes candidate A = 70000; out of them 55% voters votes candidate A = 38500; out of them 20% voters are senior citizens = 7700 #### C QUESTION:A man saves Rs 500 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. options: A)Rs 662 B)Rs 1665.01 C)Rs 1662.02 D)Rs 1655.06 E)None of these SOLUTION:Explanation: =[500(21/20×21/20×21/20)+500(21/20×21/20)+500(21/20)]=1655.06 Answer: D #### D QUESTION:Kiran 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? options: A)10 hours B)17 hours C)19 hours D)16 hours E)27 hours SOLUTION:Let the time taken to cover from A to B in car and cycle be x hours and y hours respectively. x + y = 7 --- (1) ; 2x = 4 --- (2) solving both the equations, we get y = 5 So, time taken to cover both ways by cycle = 2y hours = 10 hours. Answer: A #### A QUESTION:How many kilograms of sugar costing Rs.9 per kg must be mixed with 27 kg of sugar costing Rs.7 per Kg so that there may be a gain of 10% by selling the mixture at Rs.9.24 per Kg? options: A)36 Kg B)42 Kg C)54 Kg D)63 Kg E)None of these SOLUTION:Solution Ratio of quantities of 1st and 2nd kind = 14 : 6 = 7 : 3. Let x kg of sugar of 1st kind be mixed with 27 kg of 2nd kind. Then, 7 : 3 = x : 27 or x = (7 x 27 / 3) = 63 kg Answer D #### D QUESTION:In a village the average age of n people is 42 years. But after the verification it was found that the age of a person had been considered 20 years less than the actual age, so the new average, after the correction,increased by 1. The value of n is? options: A)11 B)20 C)28 D)17 E)13 SOLUTION:Explanation: It is the same as a person with 20 years more age replaces an existing person of the group ( or village) Since the total age of the village having n persons, is being increased by 20 years and the average age of village is being increased by 1 year, hence there are total 20 people in the village. Alternatively : ( n x 42 ) + 20 = ( n x 43 ) => n=20 Answer: B #### B QUESTION:A 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 60 kmph. When and at what distance from Mumbai do the two trains meet? options: A)187 B)279 C)120 D)278 E)379 SOLUTION:When the second train leaves Mumbai the first train covers 40 * 1 = 40 km So, the distance between first train and second train is 40 km at 10.00am Time taken by the trains to meet = Distance / relative speed = 40 / (60 -40) = 2 hours So, the two trains meet at 12 a.m. The two trains meet 2 * 60 = 120 km away from Mumbai. Answer:C #### C QUESTION:The sum of two numbers is 40 and their product is 300. What will be the sum of their reciprocals? options: A)1/40 B)8/75 C)75/4 D)2/15 E)75/6 SOLUTION:(1/a)+(1/b)=(a+b)/ab=40/300=2/15 ANSWER:D #### D QUESTION:In the city of San Durango, 40 people own cats, dogs, or rabbits. If 20 people owned cats, 30 owned dogs, 10 owned rabbits, and 10 owned exactly two of the three types of pet, how many people owned all three? options: A)5 B)7 C)9 D)11 E)13 SOLUTION:Total = C + D + R - (CD + DR + CR) - 2CDR 40 = 20 + 30 + 10 - (10) - 2x x = 5 So, answer will be A #### A QUESTION:Three houses of the same type were advertised to be let in a locality. four men made separate applications for a house. What is the probability that each of them applied for the same house. options: A)1/4 B)1/6 C)1/8 D)1/9 E)3/256 SOLUTION:Since 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 Let us consider case where all 4 men choose House no 1 So for First men it will be 1/4,second men 1/4 , third men also 1/4 and fourth man 1/4 So probability of selecting house no 1 is 1/4*1/4*1/4*1/4= 1/256 And since there are 3 such house so probability that each men select the same house is 3*1/256 Ans is E #### E QUESTION:If n divided by 3 has a remainder of 2, what is the remainder when 2 times n is divided by 3? options: A)1 B)2 C)3 D)5 E)0 SOLUTION:As per question => N=3P+2 for some integer p hence 2N => 6Q + 4 => remainder => 1 for some integer Q hence A #### A QUESTION:A train running at the speed of 60 km/hr crosses a pole in 6 seconds. Find the length of the train. options: A)150 m B)145 m C)100 m D)135 m E)155 m SOLUTION:Speed = 60*(5/18) m/sec = 50/3 m/sec Length of Train (Distance) = Speed * Time (50/3) * 6 = 100 meter ANSWER: C #### C QUESTION:If x is divisible by 2, 14, and 11, which of the following must be the least multiple of x? options: A)308 B)154 C)70 D)44 E)0 SOLUTION:We are looking for the LCM (which is not 0) of 2, 11, 14: 2 * 11 * 7 = 154 ANSWER:B #### B QUESTION:What 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 ? options: A)1288 B)2797 C)3944 D)1299 E)1082 SOLUTION:Let the side of the square plot be 'a' ft. Given area of the plot (a x a) = 289 => a = 17 Length of the fence = Perimeter of the plot = 4a = 68 ft. Cost of building the fence = 68 x 58 = Rs. 3944. Answer: C #### C QUESTION:A man on tour travels first 120 km at 60 km/hr and the next 160 km at 80 km/hr. Find the average speed for first 280 km of tour. options: A)70.00 km/hr B)71.11 km/hr C)72.11 km/hr D)73.11 km/hr E)None of these SOLUTION:Explanation: We know Time = Distance/speed So total time taken = (120/60+160/80)=4hours Time taken for 280 Km = 280/4=70.km/hr Option A #### A QUESTION:If x is Negative integer ,y is positive integer, and 7x+3y=14 , which of the following could be the value of x ? options: A)-1 B)-5 C)-2 D)-3 E)-4 SOLUTION:Use answer options to solve this problem - x is negative integer (-1,-2,-3......) put x=-1 7x+3y=14 7(-1)+3y=14 -7+3y=14 3y=14+7 3y=21 y=7 Answer will be (A) #### A QUESTION:John throws a coin until a series of six consecutive heads or three consecutive tails appears. What is the probability that the game will end after the seventh throw? options: A)1/64 B)2/16 C)3/16 D)7/16 E)9/16 SOLUTION:Let's consider the routes that would lead to ending the game on the fourth toss. In order to be a win at that point, tosses #2#3#4 would all have to be the same, either H or T, and in order for the game NOT to end on the third toss, the first toss would have to be different from the other four. Thus, the only two possible sequences are H-T-T-T-T-T ----> P = (1/2)^7= 1/128 T-H-H-H-H-H ----> P = (1/2)^7= 1/128 Either one of these would satisfy the condition, so we could have one or the other. OR means add in probability. 1/128 + 1/128 = 2/128 = 1/64 Answer(A). #### A QUESTION:A 3 by 4 rectangle is inscribed in circle. What is the circumference of the circle? options: A)2.5π B)3π C)5π D)4π E)10π SOLUTION:If a rectangle is inscribed in a circle, then the diagonal of the rectangle = diameter of the circle. In this case, diagonal = (9 + 16)^(1/2) = 5 Hence the radius = 2.5 Circumference = 2πr = 2π*2.5 = 5π Correct Option: C #### C QUESTION:If ty > 0 and yz < 0, which of the following must be negative: options: A)tyz B)ty(z^2) C)t(y^2)z D)t(y^2)(z^2) E)(x^2)(y^2)(z^2) SOLUTION:ty > 0 means that ty is positive. yz < 0 means that yz is negative. t(y^2)z = (ty)(yz) = positive*negative = negative. Thus option C is always negative. #### C QUESTION:A 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 18 km/hr. What is the length of the platform? options: A)80 B)240 C)288 D)277 E)221 SOLUTION:Speed = 18 * 5/18 = 5 m/sec. Length of the train =5 * 20 = 100 m. Let the length of the platform be x m . Then, (x + 100)/36 = 5 => x = 80 m. Answer: A #### A QUESTION:15 + sqrt(- 6 + 8×5÷4) =? options: A)31 B)32 C)33 D)34 E)35 SOLUTION:According to order of operations, inner brackets first where 8x5÷4 is first calculated since it has a multiplication and a division. 8x5÷4 = 40÷4 = 10 Hence 15 + sqrt(- 6 + 8×5÷4) = 15+ sqrt(- 6 + 10) = 15 + sqrt(4) = 15 + 16 = 31 correct answer A)31 #### A QUESTION:In the city of San Durango, 50 people own cats, dogs, or rabbits. If 20 people owned cats, 30 owned dogs, 30 owned rabbits, and 20 owned exactly two of the three types of pet, how many people owned all three? options: A)2 B)4 C)8 D)5 E)12 SOLUTION:Total = C + D + R - (CD + DR + CR) - 2CDR 50 = 20 + 30 + 30 - (20) - 2x x = 5 So, answer will be D #### D QUESTION:Darcy lives 1.5 miles from work. She can walk to work at a constant rate of 3 miles per hour, or she can ride the train to work at a constant rate of 20 miles per hour. If she rides the train, there is an additional x minutes spent walking to the nearest train station, waiting for the train, and walking from the final train station to her work. If it takes Darcy a total of 10 more minutes to commute to work by walking than it takes her to commute to work by riding the train, what is the value of x? options: A)10.5 B)15 C)15.5 D)30 E)60 SOLUTION:The time it takes Darcy to walk to work is (1.5/3)*60 = 30 minutes The time it takes Darcy to take the train is (1.5/20)*60 + x = 4.5 + x minutes It takes 15 minutes longer to walk, so 30 = 4.5 + x + 10 x=15.5 minutes Answer: C #### C QUESTION:Two trains of equal are running on parallel lines in the same direction at 48 km/hr and 36 km/hr. The faster train passes the slower train in 36 sec. The length of each train is? options: A)60 m B)72 m C)80 m D)82 m E)84 m SOLUTION:Let the length of each train be x m. Then, distance covered = 2x m. Relative speed = 48 - 36 = 12 km/hr. = 12 * 5/18 = 10/3 m/sec. 2x/36 = 10/3=> x = 60. ANSWER:A #### A QUESTION:Sebastian bought a meal at a restaurant and left a 15% tip. With the tip, he paid exactly $35.42. How much did the meal cost without the tip? options: A)$28.98 B)$29.91 C)$30.15 D)$30.60 E)$30.80 SOLUTION:The tip is a percent increase of 15%, which is 115%. Let x equal the price before the tip. Thus, 115% of this price equals $35.42: 1.15x = 35.42 Divide both sides by 1.15:=>x=35.42/1.15=30.80 correct answer E)$30.80 #### E QUESTION:#88 A necklace is made by stringing C individual beads together in the repeating pattern red bead, green bead, white bead, blue bead, and yellow bead. If the necklace design begins with a red bead and ends with a white bead, then C could equal options: A)16 B)32 C)41 D)54 E)58 SOLUTION:You can just write out the pattern and count: RGWBYRGWBYRGWBY... But to save time a good test taker will just look for a pattern. Min # is 3, because W is the third one. Then every 5 beads another white comes, so it must be 3+5+5+5.. and so on... 3+5 = 8 3+5+5 = 13 3+5+5+5=18 3+5+5+5+5=23 So you see it ends in either 8 or 3. 58 IS THE NO. E #### E QUESTION:The average of first 20 natural numbers is? options: A)5.6 B)10.5 C)10.1 D)5.8 E)5.2 SOLUTION:Sum of 20 natural no. = 420/2 = 210 Average = 210/20 = 10.5 Answer:B #### B QUESTION:P, Q and R can complete a work in 24, 6 and 12 days respectively. The work will be completed in --- days if all of them are working together. options: A)2 B)3 3⁄7 C)4 ¼ D)5 E)5 ¼ SOLUTION:Explanation : Work done by P in 1 day = 1/24 Work done by Q in 1 day = 1/6 Work done by R in 1 day = 1/12 Work done by P,Q and R in 1 day = 1/24 + 1/6 + 1/12 = 7/24 => Working together, they will complete the work in 24/7 days = 3 3⁄7 days Answer : Option B #### B QUESTION:A retailer sold an appliance for $100. If the retailer's gross profit on the appliance was 25 percent of the retailer's cost for the appliance, how many dollars was the retailer's gross profit? options: A)$10 B)$16 C)$20 D)$24 E)$25 SOLUTION:Let P be the original price paid by the retailer. 1.25*P = 100 P = 80 The profit is $20. The answer is C. #### C QUESTION:A 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? options: A)123 B)166 C)240 D)157 E)198 SOLUTION:Speed = [54 * 5/18] m/sec = 15 m/sec. Length of the train = (15 * 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: C #### C QUESTION:A toy store regularly sells all stock at a discount of 10 percent. If an additional 10 percent were deducted from the discount price during a special sale, what would be the lowest possible price of a toy costing $10 before any discount? options: A) $7.20 B) $8.00 C) $8.10 D) $8.27 E) $9.00 SOLUTION:sale price = (original price - 10% decrease) - 10% decrease price = [10 * (90/100)] * (90/100) = 10 * (.90) * (.90) = 9 * .90 = 8.10 The answer is C. #### C QUESTION:?% of 360 = 126 options: A)277 B)35 C)64 D)72 E)None of these SOLUTION:?% of 360 = 126 or, ? = 126×100/360=35 Answer B #### B QUESTION:A 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 4 buckles is how many times that of 5 buckles and 6 buttons? options: A)7/15. B)4/9. C)6/11. D)3/5. E)8/15. SOLUTION:2buttons + 2buckles = 1/3(11buckles + 3buttons) 6buttons + 6buckles = 11buckles + 3buttons 3buttons = 5buckles Weight of 3buttons and 4buckles = 5buckles + 4buckles = 9buckles Weight of 6buttons and 5buckles = 10buckles + 5buckles = 15buckles (3buttons and 2buckles) = x * (6buttons and 5buckles) 9 = x*15 x = 9/15=3/5 Answer: D #### D QUESTION:7^1+7^2+7^3+...........+7^2015 find out how many numbers present which unit place contain 3 ? options: A)502 B)503 C)504 D)505 E)506 SOLUTION:7^3,7^7,7^11,7^15,7^19.........7^2015 contains last digit=3. Now,we see 3,7,11,15....2015 are in AP tn=a+(n-1)d 2015=3+(n-1)4 2015=3+4n-4 4n=2016 n=504 ANSWER:C #### C QUESTION:A corporation ten times its annual bonus to 25 of its employees. What percent of the employees’ new bonus is the increase? options: A)25% B)44% C)38% D)9% E)90% SOLUTION:Let the annual bonus be X. A corporation triples its annual bonus. So new bonus = 10X. Increase = 10X-X =9X The increase is what percent of the employees’ new bonus = (9X/10X)*100 = 90% Hence E. #### E QUESTION:A 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 21 months? options: A)18:11 B)18:15 C)21:11 D)18:121 E)18:112 SOLUTION:A invests Rs.8000 for 21 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. A : B 8000*21 : (8000*4) + (4000*14) 168000 : 88000 A:B = 21:11.Answer:C #### C QUESTION:A natural number has exactly 10 divisors including 1 and itself.how many distint prime factors this natural number will have? options: A)37 B)29 C)27 D)99 E)11 SOLUTION:Answer:D #### D QUESTION:If a and b are the roots of the equation x2 - 9x + 20 = 0, find the value of a2 + b2 + ab? options: A)10 B)25 C)36 D)61 E)87 SOLUTION:Explanation: a2 + b2 + ab = a2 + b2 + 2ab - ab i.e., (a + b)2 - ab from x2 - 9x + 20 = 0, we have a + b = 9 and ab = 20. Hence the value of required expression (9)2 - 20 = 61. Answer D #### D QUESTION:Rahul went to a shop and bought things worth Rs. 45, 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? options: A)A)19.7 B)B)19.9 C)C)20.9 D)D)21.9 E)E)39.7 SOLUTION:Total cost of the items he purchased = Rs.45 Given that out of this Rs.45, 30 Paise is given as tax => Total tax incurred = 30 Paise = Rs.30/100 Let the cost of the tax free items = x Given that tax rate = 6% ∴ (45−30/100−x)6/100 = 30/100 ⇒ 6(45 −0.3 −x) = 30 ⇒ (45 − 0.3 − x) = 5 ⇒ x = 45 − 0.3 − 5 = 39.7 E) #### E QUESTION:If A:B:C = 2:3:4, then find AB:BC:CA options: A)5:9:24 B)6:9:24 C)7:9:24 D)8:9:24 E)None of these SOLUTION:Explanation: Let A = 2x, B = 3x, C = 4x, then, AB=2x3x=23BC=3x4x=34CA=4x2x=21=>AB:BC:CA=23:34:21=8:9:24 Answer: D #### D QUESTION:2^2*3^3*2^2*3^6 = options: A)3^5*2^5 B)2^9*3^4 C)2^4*3^9 D)5^8 E)6^10 SOLUTION:2^2*3^3*2^2*3^6 = A) 3^5*2^5 B) 2^9*3^4 C) 2^4*3^9 D) 5^8 E) 6^10 If the base is same, powers are added so that follows C) 2^4*3^9. Hence the answer is C #### C QUESTION:One day, Raviraj left home and cycled 20 Km southwards, turned right and cycled 10 km and turned right and cycled 20 Km and turned left and cycled 20 Km. How many kilometres will he have to cycle to reach his home straight ? options: A)50 B)30 C)40 D)60 E)80 SOLUTION:Raviraj starts from home at A, moves 20 Km in south upto B. Then he turns right and moves 10 Km upto C, then he turns right and moves 20 Km upto D, then he turns lefts and moves 20 Km upto E. So from image it is clear that, if he moves straight then he will have to move AD+DE, AD = BC = 10 Km So, he will have to move 10 + 20 = 30 Km ANSWER B #### B QUESTION:A boat having a length 8 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: options: A)12 kg B)60 kg C)72 kg D)160 kg E)None of these SOLUTION:Explanation: Volume of water displaced = (8 x 2 x 0.01) m3 = 0.16 m3. ∴ Mass of man = Volume of Water displaced x Density of water = (0.16 x 1000)kg = 160 kg. Answer: D #### D QUESTION:A car dealership has 40 cars on the lot, 15% of which are silver. If the dealership receives a new shipment of 80 cars, 30% of which are not silver, what percentage of total number of cars are silver? options: A)20% B)25% C)30% D)35% E)40% SOLUTION:The number of silver cars is 0.15*40 + 0.3*80 = 30 The percentage of cars which are silver is 30/120 = 25% The answer is B. #### B QUESTION:If n + 14 is a positive odd integer, which of the following must be true about the sum of the next four integers? options: A)It is a multiple of 3 B)It is a multiple of 4 C)It is a multiple of 2 D)It is a multiple of 5 E)It is a prime number SOLUTION:n+14 is a positive odd integer. This means n will be an odd integer The next 4 integers would be: n + 14, n + 15, n + 16, n + 17 Sum = 4n + 62 This sum will always be even. Option C #### C QUESTION:Which of the following is not a prime number ? options: A)502 B)503 C)509 D)521 E)523 SOLUTION:Clearly, 502 is not a prime number. Answer : A #### A QUESTION:Two trains are moving in opposite directions at 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.9 km respectively. The time taken by the slower train to cross the faster train in seconds is? options: A)40 B)41 C)48 D)67 E)45 SOLUTION:Relative speed = 60 + 90 = 150 km/hr. = 150 * 5/18 = 125/3 m/sec. Distance covered = 1.10 + 0.9 = 2 km = 2000 m. Required time = 2000 * 3/125 = 48 sec. Answer: Option C #### C QUESTION:If 0 < a < b and k = (6a + 7b)/b , which of the following must be true? options: A)k < 2 B)k < 7 C)k < 9 D)k > 15 E)k < 11 SOLUTION:Please 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. As for your question, it is very simple and straightforward with number plug in. Assume a=1 and b=2 as a < b, you get k = (6+14)/2 = 10. This eliminates all but option E, making it the correct answer. #### E QUESTION:Set A = {1, 2, 3, 4, 5, 6, q} Which of the following possible values for q would cause Set A to have the smallest standard deviation? options: A) 1 B) 2.5 C) 3 D) 3.5 E) 7 SOLUTION:I agree. The mean of the set q =1,2,3,4,5,6 is 3.5 . Now if we add one extra number to the set, in order for the standard deviation to be minimum, that number must be as close as possible to the original set (1,2,3,4,5,6). Therefore we have to choose the number closest to 3,5 from the options we have, leaving D as the best choice. Answer D. #### D QUESTION:28% of employees are women with fair hair. 40% of fair-haired employees are women. What percent of employees have fair hair? options: A)25 B)30 C)50 D)55 E)70 SOLUTION:I came up with (E) 70 Think of 100 people total: From the first fact, 28 of these are women with fair hair. From the second fact, these 20 women make up 40% of the total fair haired population. We can then make a ratio of 60:40 fair haired men to fair haired women. This means that (60/40)*28 equals the number of fair haired men, which is 42 men with fair hair. Add this 42 to the 28 women and get 70 fair haired men and women out of 100 total men and women. 70%E #### E QUESTION:The ratio between v and y is 7/9; v and y are increased by 4, what is the ratio between the new values of v and y? options: A)7/9 B)14/9 C)7/18 D)11/13 E)It Cannot Be Determined SOLUTION:Ratio = 7k/9k = 7/9, 14/18, etc. v and y are increased by 4 --> (7k + 4)/(9k + 4) New ratio can be 11/13, 18/22, etc. Answer: E #### E QUESTION:A 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? options: A)22 days B)4 days C)13 days D)6 days E)9 days SOLUTION:(A + B)'s 1 day's work = (1/4). A's 1 day's work = (1/12). B's 1 day's work =((1/4)-(1/12))=(1/6) Hence, B alone can complete the work in 6 days. Answer is D. #### D <<<Examples ends QUESTION:In the new budget the price of Petrol rose by 20%. By how much percent must a person reduce his consumption so that his expenditure on it does not increase? options: A)16.67% B)25% C)20.45% D)31.56% E)40% SOLUTION:Reduce in consumption = R/(100+R) *100% = 20/120 *100 = 16.67% Answer is A #### A

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:Favid has d books, which is 3 times as many as Jeff and 1/2 as many as Paula. How many books do the three of them have altogether, in terms of d? options: A) 5/6*d B) 7/3*d C) 10/3*d D) 7/2*d E) 9/2*d SOLUTION:Favid has d books; Jeff has d/3 books; Paula has 2d books; Total = d+d/3+2d=10d/3. Answer: C. #### C QUESTION:Insert the missing number 100,91,....,76,70 options: A)82 B)83 C)84 D)81 E)80 SOLUTION:Missing number: 83 Answer: B #### B QUESTION:How many liters of pure alcohol must be added to a 100-liter solution that is 20 percent alcohol in order to produce a solution that is 32 percent alcohol? options: A) 7/2 B) 5 C) 20/3 D) 8 E) 300/17 SOLUTION:20% Alcohol solution means; in the 100 liter solution, 20 liters of solution is alcohol and 80 liters other solvents. If we addxliters of alcohol to the solution, the solution becomes100+xliters and alcohol, which was 20 liters, becomes 20+x liters. According to the statement; 20+x = 32% of (100+x) OR 20+x=(100+x)8/25 500+25x=800+8x 17x=300 x=300/17 Ans:E #### E QUESTION:A batsman makes a score of 100 runs in the 11th inning and thus increases his average by 5. Find his average after 11th inning. options: A)40 B)50 C)62 D)45 E)56 SOLUTION:Let the average after 11th inning = x Then, average after 10th inning = x-5 10(x-5)+100 = 11x x = 100-50 = 50 Answer is B #### B QUESTION:From the set of numbers x, y, t, z, p, q and w, how many different combinations can we have without the t and w in them? Ex:. (x,y), (x), (p,q,z,y,x), etc and (x,y)=(y,x) options: A)10 B)14 C)15 D)16 E)30 SOLUTION:Another way: Any letter (x, y, z, p, q) can be included or not. So, we have 2^5 combinations - 2 empty combinations = 30 combinations E #### E QUESTION:Of the 25 cupcakes in the bakery, 20 percent are chocolate. How many vanilla cupcakes must be sold in order to bring the number of chocolate cupcakes up to 50 percent of the cupcakes in the bakery? options: A)1 B)5 C)10 D)15 E)20 SOLUTION:Now, there are 5 chocolate cupcakes (20% of 25) and 25-5=20 vanilla cupcakes at the bakery. We need there to be 5 chocolate and 5 vanilla cupcakes, in this case there will be 50% chocolate and 50% vanilla. Therefore 20-5=15 vanilla cupcakes must be sold. Answer: D. #### D QUESTION:For the set { 3, 3, 4, 4, 5, 5, x}, which of the following values of x will most increase the standard deviation? options: A)(-3)^2 B)2 C)3 D)4 E)5 SOLUTION:Standard Deviation Step 1, as pointed out by others, is to find out the mean = 4 Step 2, For each number: subtract the Mean and square the result = (1-4)^2=(-3)^2 (2-4)^2=(-2)^2 (3-4)^2 =(-1)^2 (4-4)^2=(.0)^2 (5-4)^2=(1)^2 Clearly (1-4)^2=(-3)^2 will give you the greatest value among all the other options. Hence A #### A QUESTION:If 6 (A's capital) = 8 (B's capital) = 8 (C's capital). Then the ratio of their capitals is? options: A)4:15:16 B)4:15:68 C)4:3:3 D)20:15:11 E)20:15:19 SOLUTION:6A = 8B = 8 C A:B:C = 1/6:1/8:1/8 = 4:3:3 Answer: C #### C QUESTION:Find the odd man out. 14,35,49,60,70 options: A)14 B)35 C)49 D)60 E)70 SOLUTION:All except 60 are multiples of 7 Answer is D #### D QUESTION:Albert invested amount of 8000 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 options: A)Rs. 8510 B)Rs. 8620 C)Rs. 8730 D)Rs. 8820 E)None of these SOLUTION:Explanation: =>(8000×(1+5/100)2) =>8000×21/20×21/20 =>8820 Option D #### D QUESTION:If the sum of the interior angles of a regular polygon measures up to 1080 degrees, then how many sides does the polygon have? options: A)10 B)16 C)8 D)11 E)14 SOLUTION:one of the interior angle = 180 - 360/n sum of the interior angles is = n (180 - 360/n) given n(180 - 360/n)=1080 180n - 360 = 1080 180n = 1440 n = 1440/180 = 8 ANSWER:C #### C QUESTION:Patrick purchased 90 pencils and sold them at a loss equal to the selling price of 40 pencils. The cost of 90 pencils is how many times the selling price of 90 pencils? options: A) 0.75 B) 0.8 C) 1 D) 1.2 E) 1.44 SOLUTION:Say the cost price of 90 pencils was $90 ($1 per pencil) and the selling price of 1 pencil was p. Selling at a loss: 90 - 90p = 40p --> p = 9/13. (cost price)/(selling price) = 1/(9/13) = 13/9 = 1.44. Answer: E. #### E QUESTION:Set S consists of integers {7, 8, 10, 12, 13}. If integer n is included in the set, the average (arithmetic mean) of set S will increase by 10%. What is the value of integer n? options: A)10 B)12 C)16 D)22 E)24 SOLUTION:The average of the numbers in set S is 10. If we increase the mean by 10%, the new mean is 11. Thus, on average, 5 numbers increase by 1. Therefore n = 11+5 = 16 The answer is C. #### C QUESTION:In 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: options: A)Both reach at the same time B)P wins by 100 m C)Q wins by 50 m D)Q wins by 100 m E)None of these SOLUTION:Explanation : When P starts running for 300 m and Q for 500 m then, the ratio of speeds of P and Q is 3 : 5. According 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. Thus, Both reach at the same time. Answer : A #### A QUESTION:36 men can complete a piece of work in 18 days. In how many days will 27 men complete the same work? options: A)12 B)18 C)22 D)24 E)none of these SOLUTION:Let the required number of days be x. Less men, More days (Indirect Proportion) 27 : 36 :: 18 : x 27 * x = 36 * 18 x = (36 * 18)/27 x = 24. Answer is D. #### D QUESTION:A buffet costs rs300. owner reduced the price 20% less. he got profit of 25% on its revenue. what is the percentage increase in number of customers? options: A)56% B)57% C)58% D)45% E)35% SOLUTION:let assume he sells 1 buffet daily, now then 300*1 = revenue (eq -1) if he reduced his price by 20% then , 240*(customer) = 125/100*revenue customer = 1.25*300/240 = 1.56 means 56 % increase in customer. ANSWER:A #### A QUESTION:The area of a triangle is with base 3m and height 4m? options: A)4 m2 B)6 m2 C)18 m2 D)19 m2 E)12 m2 SOLUTION:1/2 * 3 * 4 = 6 m2 Answer: B #### B QUESTION:Lorna invests $6000, 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? options: A)$160 B)$1,600 C)$2,200 D)$4,400 E)$5,840 SOLUTION:11+6=17%, therefore 17/100*6000= 1020, now add 1020 + 580= 1600. (B) #### B QUESTION:Buses 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 A on which the buses leave at the same time. options: A)A=Tuesday B)Wednesday C)Thursday D)Sunday E)A=The busses will never leave at the same time SOLUTION:The answer is E. I 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. Alternatively, 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 #### E QUESTION:The average age of 3 girls is 24 years and their ages are in the proportion 1:2:3. The age of the youngest girl is? options: A)10 years B)11 years C)12 years D)13 years E)14 years SOLUTION:Total age of 3 boys = 24*3 =72 ratio of their ages = 1:2:3 Age of the youngest = 72*1/6 = 12 years Answer is C #### C QUESTION:A 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? options: A)200 B)300 C)400 D)500 E)None of them SOLUTION:Let the share of each nephews be Rs.x. Then,share of each daughter=rs4x;share of each son=Rs.5x; So,5*5x+4*4x+2*x=8600 25x+16x+2x=8600 =43x=8600 x=200; Answer is A. #### A QUESTION:A shop owner sells 100 lemons and gains SP of 40 lemons. Find the gain %? options: A)62 2/3% B)64 2/3% C)66 2/3% D)66 5/3% E)68 2/3% SOLUTION:Gain=40 lemons Total 100 lemons CP 100-40=60 (40/60)*100 =66 2/3% Ans C #### C QUESTION:Find the length of the longest pole that can be placed in a room 12 m long 8m broad and 9m high. options: A)13 B)14 C)15 D)16 E)17 SOLUTION:Length of longest pole = Length of the diagonal of the room = sqrt(12^2+8^2+9^2= sqrt(289)= 17 m. Answer is E. #### E QUESTION:In how many ways can the letters of the word CAVERN be arranged in a row so that the vowels appear in alphabetic order? options: A)360 B)720 C)620 D)180 E)36 SOLUTION:Two letters can be arranged in 2! ways. only one combination EIU is required. 6 letters can be arranged in 6! ways. thus 6!/ 2! * 1 = 360. A #### A QUESTION:A train 250 m long is running at a speed of 58 kmph. How long does it take to pass a man who is running at 8 kmph in the same direction as the train? options: A)5 sec B)9 sec C)12 sec D)18 sec E)15 sec SOLUTION:Answer : D. Speed of the train relative to man = (58 - 8) kmph = (50* 5/18) m/sec = (125/9)m/sec Time taken by the train to cross the man = Time taken by It to cover 250 m at 125/9 m / sec = 250 *9/ 125 sec = 18sec #### D QUESTION:Mr. Jones sold two pens at $1 each. Based on the cost, his profit one was 50% and his loss on the other was 40%. On the sale of the pipes. Find the amount of his profit or loss? options: A)lost 10 cents B)lost 4 cents C)broke even D)gained 4 cents E)gained 40 cents SOLUTION:50 % profit on $ 1 = $ 50/100 × 1 = $ 0.50× 1 = $ 0.50 Similarly, 40 % loss on $ 1 = $ 40/100 × 1 = $ 0.40× 1 = $ 0.40 Therefore, in one pen his profit is $ 0.50 and in the other pipe his loss is $ 0.40 So profit by amount $0.40. Answer is E. #### E QUESTION:A 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. options: A)310 meter B)335 meter C)345 meter D)350 meter E)375 meter SOLUTION:Explanation: Speed = Distance/time = 300/18 = 50/3 m/sec Let the length of the platform be x meters then Distance=Speed∗Timex+300=50/3 X 39 =>3(x+300)=1950=>x=350 meters ANSWER IS D #### D QUESTION:A boat can move upstream at 25 kmph and downstream at 35 kmph, then the speed of the current is? options: A)5 B)6 C)7 D)82 E)43 SOLUTION:US = 25 DS = 35 M = (35 - 25)/2 = 5 Answer: A #### A QUESTION:Out 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 ? options: A)124 B)144 C)134 D)142 E)143 SOLUTION:The 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 #### B QUESTION:The lowest number which should be added to 8247 so that the sum is exactly divisible by 5, 6, 7, 8 and 9 is: options: A)1833 B)1853 C)1733 D)1233 E)1832 SOLUTION:L.C.M. of 5, 6, 7, 8 and 9 = 2520. On dividing 8247 by 2520, the remainder is 687. Number to be added = (2520 - 687) = 1833. Answer: Option 'A' #### A QUESTION:William earned $3,200 per month as a teacher for the ten months from September to June. Then he took a job as a barista at a local café, where he earned $2,000 per month during July and August. What was his average monthly pay for the 12 months? options: A)$2,400 B)$2,800 C)$2,600 D)$3,000 E)$2,500 SOLUTION:E. William earned $3,200 × 10 = $32,000 as a teacher, and he earned $2,000 × 2 = $4,000 as a barista. So he earned $32,000 + $4,000 = $36,000 over the 12 months. Plug these values into the formula for the mean: mean=sum of values/number of values=>36.000/12=3.000 correct answer D)$3.000 #### D QUESTION:How many of the positive factors of 19 are not factors of 29? options: A)0 B)1 C)2 D)3 E)4 SOLUTION:Factors of 19 - 1, 19 factors of 29- 1, 29 Comparing both, we have three factors of 19 which are not factors of 29- 19, The answer is B #### B QUESTION:How many positive integers less than 100 have a remainder of 3 when divided by 13? options: A)6 B)7 C)8 D)9 E)3 SOLUTION:We have to include 3 also.As 13*0 + 3 =3 If somebody says to divide 3 by 13 ,we will be telling we have 0 quotient and remainder as 3. Answer is E #### E QUESTION:There are 136 employees in Company X. If the number of employees who birth in June is the greatest, what is the least possible number of the employees in the company who birth in June? options: A)15 B)11 C)12 D)13 E)14 SOLUTION:IMO 15 Take each answer choice and substract it from 136 and the divided this with 11. A #### A QUESTION:The closest approximation of F(69.28 × 0.004)/0.03 is options: A)0.092 B)0.92 C)9.2 D)92 E)920 SOLUTION:F(69.28 × 0.004)/0.03 1. 0.004 = 4 × 10^(-3) 2. 0.03 = 3 × 10^(-2) 3. (a × b)/c = a × (b/c) 4. 0.004/0.03 = 4 × 10^(-3)/ (3 × 10^(-2)) = 4 × 10^( -3 - (-2))/3 = 4 × 10^(-1) / 3 = (4/3) × 10^(-1) = 1.333 × 10^(-1) Therefore, (69.28 × 0.004)/0.03 = 69.28 × (0.004/0.03) = 69.28 × 1.33 × 10^(-1) = 69.28 × 1.33/10 = 6.928*1.33 Now, 7 × 2 = 14 7 × 1 = 7 or better: 6.9 × 1 = 6.9 6.9 × 2 = 13.8 hence, 6.9 <6.928 × 1.33 < 13.8 9.2 is the only answer that satisfies this condition.C #### C QUESTION:Fathers age is 5 times his son’s age. 4 years back the father was 9 times older than son.Find the fathers’ present age. options: A)40 years B)33 years C)22 years D)33 years E)44 years SOLUTION:Ans. 40 years #### A QUESTION:A boy has eight trousers and 10 shirts. In how many different ways can he select a trouser and a shirt? options: A)80 ways B)86 ways C)88 ways D)108 ways E)89 ways SOLUTION:The boy can select one trouser in eight ways. The boy can select one shirt in 10 ways. The number of ways in which he can select one trouser and one shirt is 8 * 10 = 80 ways. Answer:A #### A QUESTION:What is the greatest possible length that can be used to measure exactly the following Lengths 7m, 3m 85cm, 12m 95cm? options: A)25 cms B)30 cms C)35 cms D)38 cms E)45 cms SOLUTION:HCF of 7m, 3m 85cm, 12m 95cm is 35 cms. ANSWER:C #### C QUESTION:The average salary/head of allthe workers in a workshop is Rs.750, if the average salary/head of 5 technician is Rs.900 and the average salary/head of the rest is Rs.700, the total no. of workers in the work-shop is ? options: A)18 B)20 C)22 D)24 E)26 SOLUTION:Let the total number of workers be y. So sum of salary for all workers = sum of salary of 5 technician + sum of salary for other y -5 workers. 5 x 900 + 700(y -5) = 750 y ⇒ 4500 + 700y - 3500 = 750y ⇒ 50y = 1000 ∴ y = 20 So total number of workers = 20 B #### B QUESTION:If 4x = 8^y, which of the following expresses x in terms of y? options: A)2^(y-2) B)2^(y-1) C)2^(3y-2) D)2^(2y-3) E)2^y SOLUTION:By exponential simplification. 4 = 2^2 and 8=2^3 therefore (2^2)x=(2^3)^y gives x=(2^3y)/(2^2) further simplified to x=(2^3y)(2^-2) which gives x=2^(3y-2) (because exponential is additive in multiplication. i.e. a^b*a^c=a^(b+c). Answer: C #### C QUESTION:At what time between 4 & 5 will the hands of a watch point in opposite directions? options: A)50 min past 4 B)42 5/11 min past 4 C)43 min past 4 D)40 min past 4 E)50 4/11 min past 4 SOLUTION:At 4 o'clock, the hands of the watch are 20 min. spaces apart. To be in opposite directions, they must be 30min. spaces apart. Minute hand will have to gain 5 min. spaces. 55min spaces are gained in 60 min. 5 min. spaces are gained in (60/55 * 50) min. or 54 6/11 min. Required time = 54 6/11 min. past 4. Answer is E #### E QUESTION:If you add all the numbers on your mobile phone except 8 and 2, what is the answer? options: A)55 B)25 C)85 D)45 E)35 SOLUTION:We have to add 0,1,3,4,5,6,7 & 9 to find the answer. Therefore 0+1+3+4+5+6+7+9=35 Answer is E #### E QUESTION:If xy > 0, which of the following must be negative? options: A)-x/-y B)x/y C)-x/y D)2xy E)x+y SOLUTION:- / + = - Answer : C #### C QUESTION:x men working x hours per day can do x units of a work in xx days. How much work can be completed by y men working y hours per day in y days? options: A)x2/y2 units B)y3/x2 units C)x3/y2 units D)y2/x2 units E)None SOLUTION:Explanation: Let amount of work completed by y men working y hours per in y days = w units More men, more work(direct proportion) More hours, more work(direct proportion) More days, more work(direct proportion) Hence we can write as (men)x:y (hours)x:y (days)x:y }::x:w ⇒x^3w=y^3x ⇒w=y^3x/x^3 =y^3/x^2 Answer: Option B #### B QUESTION:A and B start a business with Rs.6000 and Rs.8000 respectively. Hoe should they share their profits at the end of one year? options: A)3:3 B)3:4 C)3:8 D)3:1 E)3:2 SOLUTION:They should share the profits in the ratio of their investments. The ratio of the investments made by A and B = 6000 : 8000 => 3:4.Answer: B #### B QUESTION:A cube of edge 7 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: options: A)1:25 B)1:49 C)1:52 D)1:522 E)None SOLUTION:Sol. Required ratio = 6 * 1 * 1 / 6 * 7 * 7 = 1/49 = 1:49. Answer B #### B QUESTION:1 + 9 + 8 = ? considering, 28 + 8 + 92 = 10 what is....? options: A)7 B)8 C)9 D)6 E)10 SOLUTION:Equation 28 + 8 + 92 = 10 can be derived from twenty eight(t) + eight(e) + ninetytwo (n) = ten => 10 Similarly for equation, 1 + 9 + 8 One (o) + nine (n) + eight (e) => one (1) correct answer is E)10 #### E QUESTION:How many 6-digits number are Palindromic numbers? A Palindromic number reads the same forward and backward, example options: A)100 B)610 C)729 D)900 E)1000 SOLUTION:The 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, 9∗10∗10∗1∗1∗1=9009∗10∗10∗1∗1∗1=900 Answer D #### D QUESTION:A reduction of 30% in the price of apples would enable a man to obtain 54 more for Rs.30, what is reduced price per dozen? options: A)1 B)2 C)6 D)7 E)10 SOLUTION:B 30*(30/100) = 9 --- 54 ? --- 12 => Rs.2 #### B QUESTION:What is the value of √36% ? options: A)10% B)20% C)30% D)60% E)40% SOLUTION:Explanation: br>√16% =√36/√100 =6/10 =60/100=60% correct answer is D)60% #### D QUESTION:Arjun started a business with Rs. 20,000 and is joined afterwards by Anoop with Rs.80, 000. After how many months did Anoop join if the profits at the end of the year are divided equally? options: A)3 B)9 C)5 D)6 E)7 SOLUTION:Suppose Anoop joined after 3 months. Then, 20000 * 12 = 80000 * (12 – x) => x = 9. ANSWER:B #### B QUESTION:A father said his son , " I was as old as you are at present at the time of your birth. " If the father age is 62 now, the son age 5 years back was options: A)14 B)17 C)11 D)19 E)26 SOLUTION:Let the son's present age be x years .Then, (62 - x) = x x= 31. Son's age 5 years back = (31 - 5) = 26 years Answer: E #### E QUESTION:4 dice are thrown simultaneously on the board. Find the probability show the same face. options: A)1/213 B)1/215 C)1/216 D)2/113 E)3/114 SOLUTION:The total number of elementary events associated to the random experiments of throwing four dice simultaneously is: =6×6×6×6=64=6×6×6×6=64 n(S)=64n(S)=64 Let XX be the event that all dice show the same face. 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)}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)} n(X)=6n(X)=6 Hence required probability, =n(X)n(S)=664=n(X)n(S)=664 =1/216 C #### C QUESTION:The timing of a college is from 12 p.m to 5.00 p.m. Five lectures are held in the given duration and a break of 5 minutes after each lecture is given to the students. Find the duration of each lecture. options: A)56 minutes B)45 minutes C)30 minutes D)48 minutes E)44 minutes SOLUTION:Explanation: Total time a student spends in college = 5 hours 00 minutes = 300 minutes As there are 5 lectures, the number of breaks between lectures is 4. Total time of the break = 20 minutes Hence, the duration of each lecture is = (300 – 20)/5 = 56 minutes ANSWER A #### A QUESTION:A student is ranked 12th from right and 6th from left. How many students are there in totality ? options: A)17 B)19 C)20 D)21 E)22 SOLUTION:From right 12 , From left 6 Total = 12+6-1 = 17 ANSWER:B #### B QUESTION:A cubical block of metal weighs 6 pounds. How much will another cube of the same metal weigh if its sides are twice as long? options: A)48 B)99 C)266 D)28 E)17 SOLUTION:Explanation: If you double the sides of a cube, the ratio of the surface areas of the old and new cubes will be 1: 4. The ratio of the volumes of the old and new cubes will be 1: 8. Weight is proportional to volume. So, If the first weighs 6 pounds, the second weighs 6x8 pounds =48. Answer: A) 48 #### A QUESTION:We run a business that rents out canoes and kayaks. A canoe rental costs $11 per day, and a kayak rental costs $16 dollars per day. One day, our business rents out 4 canoes for every 3 kayaks and receives a total of $460 in revenue. How many more canoes than kayaks were rented out? options: A)8 B)7 C)6 D)5 E)4 SOLUTION:Let x be the number of canoes. Then 3x/4 is the number of kayaks. 11x+(3x/4)*16=460 11x+12x=460 23x=460 x=20 (canoes) 3x/4=15 (kayaks) There were 20-15 = 5 more canoes rented out. The answer is D. #### D QUESTION:The population of a town is 10000. It increases annually at the rate of 10% p.a. What will be its population after 2 years? options: A)12300 B)12350 C)12100 D)12500 E)12600 SOLUTION:Formula : ( After =100 denominator Ago = 100 numerator) 10000 × 110/100 × 110/100 = 12100 C #### C QUESTION:If x is a positive integer, then the least value of x for which x! is divisible by 10,000 is? Can someone please explain intuitively what the question is asking? options: A)5 B)9 C)12 D)15 E)20 SOLUTION:In 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. 5! = 120 has 1 trailing zeros. 10! will have 2 trailing zeros. 15! will have 3 trailing zeros. 20! will have 5 trailing zeros. Answer: E. #### E QUESTION:If 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? options: A)15 B)45 C)75 D)125 E)150 SOLUTION:(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). Thus n must include at least 3 * 5 = 15 The answer is A. #### A QUESTION:there are two cubes with ratio between volume is 125:64. then what is the value of length of each cube? options: A)25:16 B)16:25 C)4:5 D)5:4 E)150:96 SOLUTION:given 6a12:a22=150:96 then a12:a22=25:16 a1:a2=5:4 so the answer is D #### D QUESTION:Listed below are the mean temperatures measured in the Tokharian desert in a certain month. What is the median temperature E in that particular month? Mean Temp (C°) No. of days 29 --------------------> 5 30 --------------------> 11 31 --------------------> 8 32 --------------------> 6 options: A)29 B)30 C)30.5 D)31 E)32 SOLUTION:to find out median===>they must be arranged in ascending order. 29 29 29...(5 times)30 30 30 30.....(11 times)31 31 31.....(8 times)32 32 32 .....(6 times) total days=5+11+8+6=30 therefore 30 numbers ...median E will be==>mean of 15 and 16 th place temperature===>(30+30)/2=30 hence B #### B QUESTION:If 5x + 3 = 10x – 17, what is the value of x? options: A)1 B)2 C)3 D)4 E)5 SOLUTION:solve for x: 5x+3=10x-17 20=5x 4=x correct answer D)4 #### D QUESTION:The arithmetic mean of set P is zero. If Q = {-2.22; -1.96; -1.68; 1.62; 1.94; 2.16} is the subset of P consisting of all those elements in P which are more than two but less than three standard deviations away from the arithmetic mean of P, what could be equal to the standard deviation of P? options: A)0.54 B)0.77 C)0.82 D)0.97 E)1.62 SOLUTION:This is a fairly straightforward question that can be solved quickly by just applying the options We are provided with Mean, m= 0 and Q = {-2.22; -1.96; -1.68; 1.62; 1.94; 2.16} is the subset of P Q consists of all those elements in P that are more than 2 but less than 3 SDs away from the arithmetic mean of P If an element is 1 PD away from the mean, we can write it as either m + PD or m - PD Similarly, if an element is 2 PDs away from the mean, we can write it as either m + 2*PD or m - 2*PD So, if these elements lie within 2 and 3 PDs of mean, m=0 we can find which one of these values of PD satisfies each value within Q Only PD = 0.77 does Answer : B #### B <<<Examples ends QUESTION:Eddy 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 540 kms and City A and City C is 300 kms. What is the ratio of their average speed of travel? (Eddy: Freddy) options: A)8/3 B)3/8 C)8/5 D)12/5 E)5/3 SOLUTION:Distance traveled by Eddy = 540 km Time taken by Eddy = 3 hours Average speed of Eddy = 540/3 = 180 km/hour Distance traveled by Freddy = 300 km Time taken by Freddy = 4 hours Average speed of Freddy = 300/4 = 75 km/hour Ratio of average speed of Eddy to Freddy = 180/75 = 12/5 Answer D #### D

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:How many positive integers less than 250 are there such that they are multiples of 15 or multiples of 14? options: A)30 B)31 C)32 D)33 E)34 SOLUTION:250/15 = 16 (plus remainder) so there are 16 multiples of 15 250/14 = 17 (plus remainder) so there are 17 multiples of 14 We need to subtract 1 because 15*14 is a multiple of both so it was counted twice. The total is 16+17-1 = 32 The answer is C. #### C QUESTION:An aptitude test contains 4 questions from verbal reasoning, 5 questions from simple mathematics and 6 questions testing knowledge of English. Three questions are selected at random from the list of questions. The probability that all of them are from simple mathematics section, is: options: A)2/91 B)1/22 C)3/22 D)2/77 E)None of these SOLUTION:Explanation : Let S be the sample space. Then, n(S) = number of ways of selecting 3 questions out of 15= 15C3= (15 x 14 x 13)/(3 x 2 x 1)= 455 Let E = event of getting all the 3 questions from simple mathematics section. n(E) = 5C3 = 5C2 = (5 x 4)/(2 x 1) = 10 P(E) = n(E)/n(S) = 10/455 = 2/91 . Answer : A #### A QUESTION:y = x^2 + bx + 512 cuts the x axis at (h, 0) and (k, 0). If h and k are integers, what is the least value of b? options: A)-512 B)-257 C)-256 D)-513 E)128 SOLUTION:As the curve cuts the x-axis at (h,0) and (k,0). Therefore h,k are the roots of the quadratic equation. For the quadratic equation is in the form of ax^2+bx+c=0, The product of the roots =c/a= 512/1=256 and the sum of the roots =-b/a=-b 512 can be expressed as product of two numbers in the following ways: 1 * 512 2 * 256 4 * 128 8 * 64 16 *32 The sum of the roots is maximum when the roots are 1 and 256 and the maximum sum is 1 + 512 = 513. The least value possible for b is therefore -513. D #### D QUESTION:0.9*0.007= ­­­­­­­­­­_________ options: A)0.063 B)0.0063 C)0.63 D)0.00063 E)63 SOLUTION:9*7=63 Sum of decimal places= 4 So, 0.9*0.007= 0.0063 ANSWER:B #### B QUESTION:What will be the product of (50-1)*(50-2)*(50-3)*..............*(50-79)*(50-80)? options: A)less than -100,000 B)-2500 C)0 D)2500 E)more than 100,000 SOLUTION:One of the terms is (50-50) so the product is 0. The answer is C. #### C QUESTION:A standard Veggiematik machine can chop 36 carrots in 4 minutes. How many carrots can 6 standard Veggiematik machines chop in 5 minutes? options: A)36 B)54 C)108 D)270 E)324 SOLUTION:ONE Veggiematik machine can chop 36 carrots in 4 minutes So, ONE Veggiematik machine can chop (1.5)(36) carrots in (1.5)(4) minutes In other words, ONE Veggiematik machine can chop 54 carrots in5minutes So,SIXVeggiematik machines can chop (5)(54) carrots in5minutes In other words, SIX Veggiematik machines can chop 270 carrots in5minutes Answer D #### D QUESTION:Tickets 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? options: A)1/11 B)2/13 C)3/10 D)4/15 E)5/16 SOLUTION:Here, S = [1, 2, 3, 4, …., 19, 20] Let E = event of getting a multiple of 3 = [3, 6, 9, 12, 15, 18] P (E) = n (E) / n (S) = 6 / 20 = 3/10 C #### C QUESTION:A certain university will select 1 of 7 candidates eligible to fill a position in the mathematics department and 3 of 10 candidates eligible to fill 3 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 4 candidates are there to fill the 4 positions? options: A)420 B)770 C)840 D)165 E)315 SOLUTION:1 of 7 will be chosen for the math 3 of 10 will be chosen for the computer None of the 4 chosen people can be in more than one departments. We can choose any of the 7 candidates for the math dep., which gives as 7 selections. We can choose 3 of the 10 candidates for the computer dep., which gives us 3 selections and 7 rejections. So, the way to find how many different selections of 2 candidates we can have for the computer dep., we do: 10! /3!*7!= 120 We are multiplying our individual selections: 7*120 = 840 In the bolded part, we don't have to multiply all of the numbers, as those in 8! are included in 10!, so we simplify instead. Ans C #### C QUESTION:Together, 15 type A machines and 7 type B machines can complete a certain job in 4 hours. Together 8 type B machines and 15 type C machines can complete the same job in 11 hours. How many W hours would it take one type A machine, one type B machine, and one type C machine working together to complete the job (assuming constant rates for each machine)? options: A) 22 hours B) 30 hours C) 44 hours D) 60 hours E) It cannot be determined from the information above. SOLUTION:Say the rates of machines A, B and C are a, b, and c, respectively. Together 15 type A machines and 7 type B machines can complete a certain job in 4 hours --> 15a + 7b = 1/4; Together 8 type B machines and 15 type C machines can complete the same job in 11 hours --> 8b + 15c = 1/11. Sum the above: 15a + 15b + 15c = 1/4 + 1/11 = 15/44 --> reduce by 15: a + b + c = 1/44 --> so, the combined rate of the three machines is 1/44 job/hour --> time is reciprocal of the rate, thus machines A, B and C can do the job W in 44 hours. Answer: C. #### C QUESTION:If a - b =6 and a2+b2=48 , find the value of ab. options: A)6 B)8 C)10 D)12 E)2 SOLUTION:Explanation: We know 2ab=(a2+b2)−(a−b)2 2ab=48−36=12 =>ab=6 Option E #### E QUESTION:How many 3 – digit number can be formed from the digit 2, 3, 5, 6, 7 and 9, which are divisible by 5 and none of the digits is repeated? options: A)5 B)10 C)15 D)20 E)25 SOLUTION:Solution Since each desired number is divisible by 5, so we must have 5 at the unit place. So, there is 1 way of doing it. Tens place can be filled by any of the remaining 5 numbers. So, there are 5 ways of filling the tens place. The hundreds place can now be filled by any of the reaming 4 digits. so, there are 4 ways of filling it. So, Required number of numbers = (1 × 5 × 4) = 20 . Answer D #### D QUESTION:Eesha bought two varities of rice costing 50Rs per kg and 60 Rs per kg and mixed them in some ratio.Then she sold that mixture at 70 Rs per kg making a profit of 20 % What was the ratio of the micxture? options: A)1 : 9 B)1 by 5 C)1 : 7 D)1 : 3 E)1 : 1 SOLUTION:Selling price of the mixture = 70 and profit = 20% Cost price of the mixture = 70×100120=70×5670×100120=70×56 By applying alligation rule: So ratio = 60−1753:1753−5060−1753:1753−50 = 1 : 5 Answer:B #### B QUESTION:If x^2 > x^3 > x^1, which of the following could NOT be the value of x? options: A)-0.5 B)-1.2 C)-1/5 D)-2/3 E)-0.1 SOLUTION:x^2 > x^3 > x^1 1)Here we have an even power of a variable (x) that is greater than both a larger odd power of the variable x and a smaller odd power of the variable x. This can be possible only if the base is negative; therefore, the variable, x, must be a negative number. 2) Now if the variable x is negative, the higher power results in a smaller number if x<-1, and a higher power results in a larger number if 0>x>-1. With this information, we know that x is a negative number less than -1; therefore, B (-1.2) is the only option that does not fall within this category. #### B QUESTION:If an amount of Rs 41,910 is distributed equally amongst 22 persons, how much amount would each person get? options: A)Rs 1905 B)Rs 2000 C)Rs 745 D)Rs 765 E)None SOLUTION:Required amount =41910/22 = Rs 1905 Answer A #### A QUESTION:A 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? options: A)210m B)240m C)963m D)874m E)578m SOLUTION:Explanation: Speed = (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)240m #### B QUESTION:The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along theoundary 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? options: A)124545 m B)134561 m C)156787 m D)15450 m E)153600 m SOLUTION:Perimeter = Distance covered in 8 min. = 12000 x 8 m = 1600 m. 60 Let length = 3x metres and breadth = 2x metres. Then, 2(3x + 2x) = 1600 or x = 160. Length = 480 m and Breadth = 320 m. Area = (480 x 320) m2 = 153600 m E #### E QUESTION:A, 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? options: A)11 B)18 C)99 D)77 E)51 SOLUTION:A:B = 2:3 B:C = 2:5 A:B:C = 4:6:15 6/25 * 75 = 18 Answer: B #### B QUESTION:Six consecutive traffic signals each show either red or green. How many different arrangements of the six signals are possible? options: A)90 B)79 C)64 D)57 E)36 SOLUTION:Since 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. We're told that 6 consecutive traffic signals each show either red or green. We're asked how many different arrangements of the 6 signals are possible. Total Options: 64 Final Answer: C #### C QUESTION:What is the decimal equivalent of (1/2)^2? options: A)0.0016 B)0.0625 C)0.16 D)0.25 E)0.5 SOLUTION:(1/2)² = (1/2)(1/2)= 1/4 APPROACH #1: use long division to divide 4 into 1 to get 1/4 = 0.25 D #### D QUESTION:What will come in place of the x in the following Number series? 18, 22, 30, 46 ,78, X options: A)35 B)56 C)142 D)87 E)98 SOLUTION:(C) The pattern is +4, +8, +16, +32, +64 So the missing term is = 142 #### C QUESTION:A rectangular field has area equal to 150 sq m and perimeter 50 m. Its length and breadth must be? options: A)15 m, 12 m B)15 m, 11 m C)15 m, 20 m D)15 m, 10 m E)15 m, 11 m SOLUTION:lb = 150 2(l + b) = 50 => l + b = 25 l – b = 5 l = 15 b = 10 D #### D QUESTION:in a certain flower shop, which stocks four types of flowers, there are 1/2 as many violets as carnations, and 1/2 as many tulips as violets. If there are equal numbers of roses and tulips, what percent of the flowers in the shop are carnations? options: A)50 B)55 C)60 D)45 E)40 SOLUTION:Given :- Violets - C/2 Carnations - C Tulip - C/4 Rose - C/4 Total flowers in terms of C = C/2+C+C/4+C/4 = 2C Percentage of Carnations = C/2C *100 =50% Answer A #### A QUESTION:A and B start a business with Rs.6000 and Rs.8000 respectively. Hoe should they share their profits at the end of one year? options: A)3:3 B)3:4 C)3:8 D)3:1 E)3:2 SOLUTION:They should share the profits in the ratio of their investments. The ratio of the investments made by A and B = 6000 : 8000 => 3:4.Answer: B #### B QUESTION:When n is divided by 24, the remainder is 6. What is the remainder when 3n is divided by 8? options: A)3 B)4 C)5 D)6 E)2 SOLUTION:Let n=6 (leaves a remainder of 6 when divided by 24) 3n = 3(6) =18, which leaves a remainder of 2 when divided by 8. Answer E #### E QUESTION:Marla starts running around a circular track at the same time Nick starts walking around the same circular track. Marla completes 20 laps around the track per hour and Nick completes 10 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? options: A)5 B)8 C)24 D)15 E)20 SOLUTION:Maria's rate - 20 laps per hour --> 20/60 laps/min Nick's rate - 10 laps per hour --> 10/60 laps/min lets set equations: 20/60*t=4 (since Maria had to run 4 laps before Nick would start) 10/60*t=0 (Hick has just started and hasn't run any lap yet) (20/60-10/60)*t=4-0 (since Nick was chasing Maria) t=24 min needed Maria to run 4 laps Answer : C #### C QUESTION:If the price of a certain bond on May 1st was 1/2 the price of the bond on June 1st and the price of the bond on July 1st was 50% greater than the price of the bond on May 1st. then the price of the bond on June 1st st was what percent of the average (arithmetic mean) price of the bond on May 1st and July 1st? options: A)50% B)75% C)120% D)133 1/3% E)160% SOLUTION:The price on June 1st = 12 (assume); The price on May 1st = 1/2*12 = 6; The price on July 1st = 6*1.5 = 9. The average price of the bond on May 1st and July 1st = (6+9)/2 = 7.5. The price of the bond on June 1st (12) is 8/5 times (160%) the average price of the bond on May 1st and July 1st. Answer: E. #### E QUESTION:A merchant mixes three varieties of rice costing Rs.20/kg, Rs.24/kg and Rs.30/kg and sells the mixture at a profit of 20% at Rs.30 / kg. How many kgs of the second variety will be in the mixture if 2 kgs of the third variety is there in the mixture? options: A)1 kgs B)3 kgs C)5 kgs D)6 kgs E)None of these SOLUTION:Explanation : If the selling price of mixture is Rs.30/kg and the merchant makes a profit of 20%, then the cost price of the mixture = 30/1.2 = Rs.25/kg. We need to find out the ratio in which the three varieties are mixed to obtain a mixture costing Rs.25 /kg. Let variety A cost Rs.20/kg, variety B cost Rs.24 / kg and variety C cost Rs.30/kg. The mean desired price falls between B and C. Step 1: Find out the ratio Qa:Qc using alligation rule. Qa/Qc=(30−25)/(25−20)=1/1. Step 2: Find out the ratio Qb:Qc using alligation rule. Qb/Qc=30−25/(25−24)=5/1. Step 3: Qc is found by adding the value of Qc in step 1 and step 2 =1+1=2. Therefore, the required ratio =1:5:2. If there are 2 kgs of the third variety in the mixture, then there will be 5 kgs of the second variety in the mixture. Answer : C #### C QUESTION:Insert the missing number 100,91,....,76,70 options: A)82 B)83 C)84 D)81 E)80 SOLUTION:Missing number: 83 Answer: B #### B QUESTION:A 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? options: A)6/25 B)5/16 C)4/9 D)3/7 E)2/5 SOLUTION:Let x be the fraction of her take-home pay that the worker saved. Let P be the monthly pay. 12xP = 8(1-x)P 12xP = 8P - 8xP 20xP = 8P x = 2/5 The answer is E. #### E QUESTION:The first train leaves the station at 6:00 am with a speed of 60 km/hr. The second train leaves at 7:00 am, in the same direction from the same station, with a speed of 80 km/hr. What time will the second train catch the first train? options: A)9:00 am B)10:00 am C)11:00 am D)12:00 noon E)1:00 pm SOLUTION:In one hour, the first train travels 60 km. The second train catches the first train with a relative speed of 20 km/h. The second train will catch the first train at 10:00 am. The answer is B. #### B QUESTION:A 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? options: A)1/190 B)1/20 C)1/9 D)1/10 E)1/92 SOLUTION:The 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 Answer: C. #### C QUESTION:Each child has 2 pencils and 13 Skittles. If there are 6 children, how many pencils are there in total? options: A)16 B)12 C)18 D)22 E)08 SOLUTION:2*6=12.Answer is B. #### B QUESTION:A “Sophie Germain” 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 9 is options: A)3 B)7 C)21 D)189 E)267 SOLUTION:In that case, the Sophie prime numbers greater than 9 are 11,23,47,59, .. which yields units digit as 1,3,7 and 9 Product would be 1 x 3 x 7x9 =189 Answer should be D #### D QUESTION:In a recent election, Ms. Robbins received 8,000 votes cast by independent voters, that is, voters not registered with a specific political party. She also received 5 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 Ms. Robbins received? options: A)0.06N + 3,200 B)0.1N + 7,200 C)0.4N + 7,200 D)0.1N + 8,000 E)0.03N + 8,000 SOLUTION:I will go with option E According to question 40 percent of total votes (N) cas were cast by independent voters. This implies 60 percent of N are voters that belong to political party. And she received 8000 votes from independent voters and 5 percent from registered voters (i.e 0.05 * 0.6 * N = 0.03N). Hence total votes = 8000 + 0.03N ....option E #### E QUESTION:Find the number of different prime factors of 6440 options: A)4 B)2 C)3 D)5 E)6 SOLUTION:Explanation: L.C.M of 6440 = 2 x 2 x 2 x 5 x 7 x 23 2, 5,7,23 Number of different prime factors is 4. Answer: Option A #### A QUESTION:If s,u, and v are positive integers and 2s=2u+2v, which of the following must be true? i. s=u ii. u is not equal to v iii. s > v options: A)None B)I only C)II only D)III only E)II and III SOLUTION:Given: 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 III must be true. Answer: D. #### D QUESTION:Sam, Suresh and Sanket run a race of 1400 meters. Sam runs twice as fast as Suresh while Suresh runs thrice as fast as Sanket. If Sanket finishes the race by clocking 15 minutes, how far was Suresh from the finish line when Sam must have finished the race? options: A)450 m B)680 m C)700 m D)900 m E)1000 m SOLUTION:Explanation: When Sanket finishes the race in 15 minutes, Suresh & Sam would finish the same race in 5 minutes and 2.5 minutes respectively. Thus, when Sam reaches the ”finish” mark, Suresh must be “half-way” through i.e. 700 meters behind the “finish” line when “Sam” must have finished the race ANSWER C #### C QUESTION:Average of five numbers is 27. If one number is excluded the average becomes 25. The excluded number is options: A)35 B)45 C)55 D)65 E)67 SOLUTION:Explanation: Number is (5*27) - (4*25) = 135-100 = 35 Answer: Option A #### A QUESTION:A train 120 m in length crosses a telegraph post in 6 seconds. The speed of the train is? options: A)72 kmph B)88 kmph C)54 kmph D)18 kmph E)19 kmph SOLUTION:S = 120/6 * 18/5 = 72 kmph Answer: A #### A QUESTION:Kamal will complete work in 20 days. If Suresh is 25% more efficient than Kamal, he can complete the work in --- days. options: A)11 B)12 C)13 D)15 E)16 SOLUTION:Work done by Kamal in 1 day = 1/20 Work done by Suresh in 1 day = (1/20) × (125/100) = 5/80 = 1/16 => Suresh can complete the work in 16 days Answer is E. #### E QUESTION:A bag contains an equal number of one rupee, 50 paise and 25 paise coins respectively. If the total value is 70, how many coins of each type are there? options: A)20 coins B)30 coins C)40 coins D)25 coins E)None of these SOLUTION:Let number of each type of coin = x. Then, 1 × x + .50 × x + .25x = 70 ⇒ 1.75x = 70 ⇒ x = 40 coins Answer C #### C QUESTION:Replace X with the appropriate number in 2 , 4 , 6 , 30 , 32 , 34 , X options: A)38 B)8 C)5 D)36 E)37 SOLUTION:D list of consecutive numbers that does not contain a 'e' in the spelling #### D QUESTION:What is the difference between the place value of 2 in the numeral 7229? options: A)150 B)160 C)180 D)190 E)200 SOLUTION:Option 'C' 200 - 20 = 180 #### C QUESTION:Kurt, 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: The paint will be namedBrun Yif it contains 2 jars of brown paint and no yellow. The paint will be namedBrun Xif the paint contains 3 jars of brown paint. The paint will be namedJaune Xif the paint contains at least 2 jars of yellow. The paint will be namedJaune Yif the paint contains exactly 1 jar of yellow. What is the probability W that the new color will be one of theJaunecolors? options: A)5/42 B)37/42 C)1/21 D)4/9 E)5/9 SOLUTION:I get B. Jaune Y = (4 choose 1)*(5 choose 2) = 4*10 = 40 Jaune X = (4 choose 2)*(5 choose 1) + (4 choose 3) = 6*5 + 4 = 34 Total combinations = 9 choose 3 = 84 Probability of Jaune W= (40 + 34)/84 = 37/42 #### B QUESTION:Calculate the speed of a boat in still water (in km/hr) if in one hour, the boat goes 13 km/hr downstream and 10 km/hr upstream. options: A)3 kmph B)9 kmph C)4 kmph D)8 kmph E)6 kmph SOLUTION:Speed in still water = (13 + 5)1/2 kmph = 9 kmph. answer :B #### B QUESTION:Two cars cover the same distance at the speed of 60 and 64 kmps respectively. Find the distance traveled by them if the slower car takes 1 hour more than the faster car options: A)960 km B)950 m C)906 km D)906 m E)950 m SOLUTION:60(x + 1) = 64x X = 15 60 * 16 = 960 km ANSWER A #### A QUESTION:P is three times as old as Q. In 10 years, P will be twice as old as Q. How old was P three years ago? options: A)27 B)30 C)33 D)36 E)39 SOLUTION:P = 3Q so Q = P/3 P+10 = 2(Q+10) = 2(P/3+10) P/3 = 10 P = 30 Three years ago, P was 27. The answer is A. #### A QUESTION:A shopkeeper buys two articles for Rs.1000 each and then sells them, making 10% profit on the first article and 10% loss on second article. Find the net profit or loss percent? options: A)200 B)100 C)276 D)280 E)279 SOLUTION:Profit on first article = 10% of 1000 = 100. This is equal to the loss he makes on the second article. That, is he makes neither profit nor loss. Answer: B #### B QUESTION:The sum of two numbers is 16. The difference is 4. What are the two numbers? options: A)10-6 B)8-8 C)9-7 D)11-5 E)13-3 SOLUTION:Let x be the first number. Ley y be the second number x + y = 16 x - y = 4 Solve the system of equations by elimination Adding the left sides and the right sides gives: x + x + y + -y = 16 + 4 2x = 20 x = 10 Since x + y = 16, 10 + y = 16 10 + y = 16 10 - 10 + y = 16 - 10 y = 6 The numbers are 10 and 6 correct answer is A)10-6 #### A QUESTION:Look at this series: 3, 4, 7, 8, 11, 12, ... What number should come next? options: A)7 B)10 C)14 D)15 E)16 SOLUTION:Explanation: This alternating addition series begins with 3; then 1 is added to give 4; then 3 is added to give 7; then 1 is added, and so on. Answer: Option D #### D QUESTION:Anil spends 40% of his income on rent, 30% of the remaining on medicines and 20% of the remaining on education. If he saves Rs. 840 every month, then find his monthly salary? options: A)RS.3500 B)Rs.1500 C)Rs.4500 D)Rs.2500 E)Nill SOLUTION:Answer: Option D Let's anil's salary be Rs. 100. Money spent on Rent = 40% of 100 = Rs. 40. Money spent on medical grounds = 30% of (100 - 40) = 3/10 * 60 = Rs. 18. Money spent on education = 20% of (60 - 18) = 1/5 * 42 = Rs. 8.40 anil saves 100 - (40 + 18 + 8.40) i.e., Rs. 33.60 for 33.6 ---> 100 ; 840 ---> ? Required salary = 840/33.6 * 100 = Rs. 2500 #### D QUESTION:Ramu bought an old car for Rs. 40000. He spent Rs. 13000 on repairs and sold it for Rs. 64900. What is his profit percent? options: A)17% B)22.4% C)18% D)14% E)16% SOLUTION:Total CP = Rs. 40000 + Rs. 13000 = Rs. 53000 and SP = Rs. 64900 Profit(%) = (64900 - 53000)/53000 * 100 = 22.4% Answer: B #### B QUESTION:How many odd integers X between 200 and 600 are there such that their tens digit is even? options: A)20 B)25 C)100 D)150 E)200 SOLUTION:The hundreds digit can take 4 values: 2, 3, 4 and 5; The tens digit can take 5 values: 0, 2, 4, 6 and 8; The units digit can take 5 values: 1, 3, 5, 7 and 9; Total X: 4*5*5=100. Answer: C. #### C QUESTION:Pavan travelled for 15 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. options: A)408 km B)409 km C)410 km D)412 km E)419 km SOLUTION:Let the distance travelled be x km. Total time = (x/2)/30 + (x/2)/25 = 15 => x/60 + x/50 = 15 => (5x + 6x)/300 = 15 => x = 409 km ANSWER:B #### B QUESTION:Each of the 20 boxes in a certain shipment weighs either 10 pounds or 20 pounds, and the average (arithmetic mean) weight of the boxes in the shipment is 18 pounds. If the average weight of the boxes in the shipment is to be reduced to 15 pounds by removing some of the 20-pound boxes, how many 20-pound boxes must be removed? options: A)10 B)12 C)14 D)16 E)18 SOLUTION:If the average of 10-pound and 20-pound boxes is 18, the ratio of 10-pound boxes:20-pound boxes is 1:4. So out of 20 boxes, 4 are 10-pound boxes and 16 are 20-pound boxes. If the average of 10 and 20-pound boxes is to be 15, the ratio of 10-pound boxes:20-pound boxes should be 1:1. The number of 10 pound boxes remains the same so we still have 4 of them. To get a ratio of 1:1, the number of 20-pound boxes must be 4. We need to remove 12 of the 20-pound boxes. The answer is B. #### B QUESTION:Large, medium and small ships are used to bring water. 4 large ships carry as much water as 7 small ships; 3 medium ships carry as much water as 2 large ships and 1 small ship. If 15 large, 7 medium and 14 small ships, each made 36 journeys to bring a certain quantity of water, then in how many journeys will 12 large, 14 medium and 21 small ships bring the same quantity of water? options: A)29 B)30 C)20 D)50 E)55 SOLUTION:Explanation : Here, Large, Medium and Small ships are denoted by the symbol L, M and S. Now, according to the question, 4L = 7S. ------(i) 3M = 2L + S. ------(ii) Using above equations, the ratios of the capacity of the Large, Medium and Small ships are :- 7: 6 : 4. Let, the number of journeys required be x. Since, quantity of water remains the same, so :- =((15×7+7×6+14×4)36) = x (12×7+14×6+21×4). =>((15×7+7×6+14×4)36) / (12×7+14×6+21×4)= x =>x=7308/252 =>x=29. Answer : A #### A QUESTION:How many four digit even numbers can be formed using the digits {2, 3, 5, 1, 7, 9} options: A)20 B)40 C)80 D)140 E)60 SOLUTION:Explanation: The given digits are 1, 2, 3, 5, 7, 9 A number is even when its units digit is even. Of the given digits, two is the only even digit. Units place is filled with only '2' and the remaining three places can be filled in ⁵P₃ ways. Number of even numbers = ⁵P₃ = 60. Answer:E #### E QUESTION:present ages of sameer and anand are in the ratio of 5:4 respectively. three years hence, the ratio of their ages will become 11:9 respectively . what anand's present age in years options: A)27 B)24 C)40 D)32 E)35 SOLUTION:sameer and anand be 5x years and 4x years respectively (5x+3)/(4x+3)=11/9 9(5x+3)= 11(4x+3), 45x+27=44x+33 45x-44x=33-27 x=6, therefore anand's present age : 4x=24 years correct answer(B) #### B QUESTION:At Joes Steakhouse the hourly wage for a chef is 20% 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 $6.50 per hour, how much less than a manager does a chef earn each hour? options: A)$2.6 B)$2.40 C)$3.40 D)$4.40 E)$5.40 SOLUTION:Manager wages per hour = $6.50 Dishwasher wages per hour = half of manager's wages. = 1/2($6.50) ==> $3.25 Chef wages per hour = 20% greater than Dishwasher wages --> 20% of $3.25 = (20*($3.25)) /100 --> ($65)/100 --> $0.65 Therefore, Chef wages per hour = $3.25 + $0.65 ==> $3.9 Difference of wages between manager and chef = $6.50 - $3.9 ==> $2.6 ANSWER:A #### A QUESTION:There are 6 identical pens and 9 identical books. In how many different ways can a person select at least one object from this set? options: A)15 B)30 C)69 D)78 E)90 SOLUTION:We can select from 0 to 6 pens and from 0 to 9 books. Thus the total possible ways to select objects is 7*10 = 70 We must subtract 1 for the case with 0 pens and 0 books. The answer is C. #### C QUESTION:Two different solutions of alcohol with respective proportions of alcohol to water of 3:1 and 2:3 were combined. What is the concentration of alcohol in the new solution if the first solution was 4.6 times the amount of the second solution? options: A)62.0 B)65.25 C)68.75 D)70.15 E)72.35 SOLUTION:SOL: Lets assume that 46L of sol1 was mixed with 10L of sol2. Alcohol in Sol1: 46*3/4 = 34.5L Alcohol in Sol2: 10*2/5 = 4L Total Alcohol in the mixed solution of 56L = 34.5 + 4 = 38.5L Alcohol concentration in the new sol: (38.5/56)*100 = 68.75% ANSWER:C #### C QUESTION:Sagar was riding bike towards north,turned left road 1 km turnes towrds left &road 2km found himself 1km west of starting how far did he road north? options: A)2km in north. B)2km in south. C)2km in east. D)2km in west. E)4km in north. SOLUTION:He travelled total distance of 3km. From which he travelled 1km in west. Hence in all he travelled total 2km in north. ANSWER:A #### A QUESTION:Find the expenditure on digging a well 14m deep and of 3m diameter at Rs.15 per cubic meter? options: A)Rs.1185 B)Rs.1285 C)Rs.1385 D)Rs.1485 E)Rs.1495 SOLUTION:22/7 * 14 * 3/2 * 3/2 = 99 m2 99 * 15 = 1485 ANSWER:D #### D QUESTION:The sale price sarees listed for Rs.390 after successive discount is 15% and 25% is? options: A)298 B)237 C)248 D)876 E)291 SOLUTION:390*(85/100)*(75/100) = 248 Answer: C #### C <<<Examples ends QUESTION:A garrison of 1850 men has provisions for 28 days. At the end of 12 days, a reinforcement arrives, and it is now found that the provisions will last only for 10 days more. What is the reinforcement? options: A)1850 B)2960 C)3000 D)1110 E)1712 SOLUTION:1850 ---- 28 1850 ---- 16 x ----- 10 x*10 = 1850*16 x = 2960 1850 ------- 1110 Answer: D #### D

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:A flagpole 18 meters high casts a shadow of length 45 meters. If a building under similar conditions casts a shadow of length 50 meters, what is the height of the building (in meters)? options: A)16 B)20 C)24 D)28 E)32 SOLUTION:The height:length ratio will be equal in both cases. 18 / 45 = x / 50 x = 20 The answer is B. #### B QUESTION:A family has two children. find the probability that both the children are girls given that at least one of them is a girl? options: A)1/3 B)1/5 C)1/7 D)1/9 E)2/3 SOLUTION:Let b stand for boy and g for girl. The sample space of the experiment is S = {(g, g), (g, b), (b, g), (b, b)} Let E and F denote the following events : E : ‘both the children are girls’ F : ‘at least one of the child is a girl’ Then E = {(g,g)} and F = {(g,g), (g,b), (b,g)} Now E n F = {(g,g)} Thus P(F) = 3/4 and P (E n F )= 1/4 Therefore P(E|F) = P(E ∩ F)/P(F) = (1/4)/(3/4) = 1/3 A) #### A QUESTION:If a sum of money at simple interest doubles in 6 years, it will become 4 times in options: A)15years B)16years C)11years D)18years E)12years SOLUTION:Explanation: let sum =x . s.i.=x rate =(100*x)/(x*6)=50/3% now ,sum =x, s.i= 3x, rate =50/3% time =(100*3x)/(x*50/3) = 18 years Answer: D #### D QUESTION:Today is Monday. After 61 days, it will be: options: A)SUNDAY B)SATURSDAY C)FRIDAY D)THURSDAY E)MONDAY SOLUTION:Each day of the week is repeated after 7 days. So, after 63 days, it will be Monday. After 61 days, it will be Saturday. Answer: Option B #### B QUESTION:In what time will a railway train 75 m long moving at the rate of 50 kmph pass a telegraph post on its way? options: A)3 B)5.4 C)4.3 D)6.5 E)7 SOLUTION:T = 75/50 * 18/5 = 5.4 sec Answer:B #### B QUESTION:The number of new words that can be formed by rearranging the letters of the word 'TOO' is options: A)5 B)10 C)11 D)2 E)3 SOLUTION:Explanation: Number of words which can be formed = 3! - 1 = 6 - 1 = 5. Answer: A #### A QUESTION:On a race track a maximum of 5 horses can race together at a time. There are a total of 25 horses. There is no way of timing the races. What is the minimum number Q of races we need to conduct to get the top 3 fastest horses? options: A)5 B)7 C)8 D)10 E)11 SOLUTION:Q=7 is the correct answer. Good solution Buneul.B #### B QUESTION:On a shelf, 2 books of Geology, 2 books of Sociology and 5 of Economics are to be arranged in such a way that the books of any subject are to be together. Find in how many ways can this be done? options: A)2880 B)2778 C)2682 D)8222 E)6282 SOLUTION:Explanation: There are books of 3 subjects (Geology, Sociology and Economics), hence they can be arranged in 3! (3 * 2 * 1) = 6 ways. Further, in each category (subject), books are to be arranged in different order, we get, Required number of ways: 3! * [2! * 2! * 5!] = 2880 ANSWER: A #### A QUESTION:In 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? options: A)1140 B)1160 C)1180 D)1200 E)1040 SOLUTION:Number of sweets each child got = 15% of 80 = 15/100 * 80 = 12. Number of sweets 80 children got = 70 * 12 = 840. Number of sweets each youngster got = 25% of 80 = 25/100 * 80 = 20. Number of sweets 10 youngsters got = 10 * 20 = 200. Total number of sweets = 840 + 200 = 1040. E) #### E QUESTION:in a certain flower shop, which stocks four types of flowers, there are 1/2 as many violets as carnations, and 1/2 as many tulips as violets. If there are equal numbers of roses and tulips, what percent of the flowers in the shop are carnations? options: A)50 B)55 C)60 D)45 E)40 SOLUTION:Given :- Violets - C/2 Carnations - C Tulip - C/4 Rose - C/4 Total flowers in terms of C = C/2+C+C/4+C/4 = 2C Percentage of Carnations = C/2C *100 =50% Answer A #### A QUESTION:When a 192 meters long rod is cut down into small pieces of length 3.2 meters each. Then how many pieces are available ? options: A)52 B)68 C)62 D)67 E)69 SOLUTION:Answer No. of pieces = Total length / Length of each piece = 192/3.2 = 60 Option: D #### D QUESTION:While calculating the edge of a square, a worker makes an error of 2% in excess. What % error does he make in calculating area? (%) options: A)4.09 B)4.0 C)4.04 D)4.02 E)4.01 SOLUTION:Explanation: Given Error = 2% while measuring the side of a square. If the correct value of the side of square is 100, the measured value: => 100 + 2% *100 = 100+2=102 The area of square with edge 100 = side*side => 100*100 => 10000 The area of square with side 102 = 102*102= 10404 Error in area calculation = 10404-1000 = 404 % error= (404/10000)*100 = 4.04% ANSWER: C #### C QUESTION:A, B and C enter into a partnership. A initially invests Rs. 25 lakhs and adds another Rs. 10 lakhs after one year. B initially invests Rs. 35 lakhs and withdraws Rs. 10 lakhs after 2 years and C invests Rs. 30 lakhs. In what ratio should the profits be divided at the end of 3 years ? options: A)11:10:15 B)20:17:23 C)19:19:18 D)5:4:9 E)None of these SOLUTION:Explanation: A:B:CA:B:C =(25 lakhs××1)+(35 lakhs××2) :(35 lakhs××2+25 lakhs××1) :(30 lakhs××3) = 95 lakhs : 95 lakhs : 90 lakhs =19:19:18=19:19:18. ANSWER IS C #### C QUESTION:A 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 4 buckles is how many times that of 5 buckles and 6 buttons? options: A)7/15. B)4/9. C)6/11. D)3/5. E)8/15. SOLUTION:2buttons + 2buckles = 1/3(11buckles + 3buttons) 6buttons + 6buckles = 11buckles + 3buttons 3buttons = 5buckles Weight of 3buttons and 4buckles = 5buckles + 4buckles = 9buckles Weight of 6buttons and 5buckles = 10buckles + 5buckles = 15buckles (3buttons and 2buckles) = x * (6buttons and 5buckles) 9 = x*15 x = 9/15=3/5 Answer: D #### D QUESTION:An 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? options: A)23777 B)35000 C)29977 D)26777 E)19871 SOLUTION:Let the sum invested at 9% be Rs. x and that invested at 11% be Rs. (100000 - x). Then, (x * 9 * 1)/100 + [(100000 - x) * 11 * 1]/100 = (100000 * 29/3 * 1/100) (9x + 1100000 - 11x)/100 = 29000/3 = 9700 (9x + 1100000 - 11x) = 970000 x = 65000 Sum invested at 9% = Rs. 65000 Sum invested at 11% = Rs. (100000 - 65000) = Rs. 35000. Answer: B #### B QUESTION:In a two-digit number, the digit in the unit’s place is four times the digit in ten’s place and sum of the digits is equal to 10. What is the number? options: A)14 B)41 C)41 D)None of these E)Cannot be determined SOLUTION:Solution Let the ten's digits be x. Then, unit's digit = 4x. ∴ x + 4x = 10 ⇔ 5x = 10 ⇔ x = 2. So, ten's digit = 2, unit's digit = 8. Hence, the required number is 28. Answer D #### D QUESTION:Consider the word RMTMR. 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. options: A)14355 B)15432 C)17576 D)18543 E)16878 SOLUTION:The 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 chosen in 26 x 26 = 676 ways Having chosen the first two letters, the third letter can be chosen in 26 ways. All the three letters can be chosen in 676 x 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. C #### C QUESTION:A student needed 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 is the value of x? options: A)7 B)8 C)9 D)6 E)5 SOLUTION:(3+11+7+9+15+13+8+19+17+21+14+x)/12 =12 ⇒(137+x)/12=12 ⇒137+x=144 ⇒x=144−137=7 Answer is A. #### A QUESTION:A fruit seller sells mangoes at the rate of Rs.16 per kg and thereby loses 12%. At what price per kg, he should have sold them to make a profit of 20%? options: A)Rs.21.81 B)Rs.12 C)Rs.12.25 D)Rs.12.31 E)None SOLUTION:Solution 88 : 16 = 120 : x x= (16×120/88) = Rs.21.81 Hence, S.p per Kg = Rs.21.81 Answer A #### A QUESTION:What is 35% of 4/13 of 585? options: A)52 B)63 C)74 D)85 E)96 SOLUTION:This 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. The number 585 is between 540 and 630, so (1/9)*585 will be about 65. Keeping 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. The closest answer is 63, so this is the answer to choose. The answer is B. #### B QUESTION:(a/2)/(b/c) In the expression above, a, b, and c are different numbers and each is one of the numbers 1, 2, or 4. What is the largest possible value of the expression? options: A)8/2 B)2/4 C)1/8 D)2/4 E)4/6 SOLUTION:(a/2)/(b/c) = (a*c)/2b The expression will have the largest value when numerator (a*c) is the largest. = (2*4)/2*1 =8/2 Answer A #### A QUESTION:The tax on a commodity is diminished by 20% and its consumption increased by 15%. The effect on revenue is? options: A)7% decrease B)8% decrease C)9% decrease D)6% decrease E)4% decrease SOLUTION:100 * 100 = 10000 80 * 115 = 9200 ----------- 10000-----------800 100-----------? => 8% decrease Answer: B #### B QUESTION:The distance from City A to City B is 150 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? options: A)42.85 B)44 C)46 D)48 E)50 SOLUTION:The time it takes Cara to drive to City B is 150 / 30 = 5 hours. Dan needs to take less than 3.5 hours for the trip. Dan needs to exceed a constant speed of 150 / 3.5 = 42.85 miles per hour. The answer is A. #### A QUESTION:1000 men have provisions for 15 days. If 200 more men join them, for how many days will the provisions last now? options: A)10.5 B)12.5 C)13.5 D)11.5 E)11 SOLUTION:1000*15 = 1200*x x = 12.5 ANSWER B #### B QUESTION:Terry is having lunch at a salad bar. There are two types of lettuce to choose from, as well as three types of tomatoes, and four types of olives. He must also choose whether or not to have one of the two types of soup on the side. If Terry has decided to have the salad and soup combo and he picks one type of lettuce, one type of tomato, and one type of olive for his salad, how many total options does he have for his lunch combo? options: A)9 B)11 C)24 D)48 E)54 SOLUTION:Terry can pick one lunch salad bar....we can choose lettuce 2c1 , tomatoes - 3c1 and olives - 4c1... Two types of soups , if he picks one then 2c1 ways. Terry decided to have the combo : Soup + salad...Hmmm... Using the above information, we get ( 2c1 * 2c1* 3c1 * 4c1 ) = 48.. ANS option D is correct answer.. #### D QUESTION:A, B and C have Rs.500 between them, A and C together have Rs.200 and B and C Rs.320. How much does C have? options: A)50 B)78 C)267 D)20 E)27 SOLUTION:A+B+C = 500 A+C = 200 B+C = 320 -------------- A+B+2C = 520 A+B+C = 500 ---------------- C = 20 Answer: D #### D QUESTION:Find the odd man out. 187, 264, 386, 473, 682, 781 options: A)386 B)187 C)781 D)682 E)564 SOLUTION:Explanation : In all numbers except 386, the middle digit is the sum of other two digits. Answer : Option A #### A QUESTION:An art gallery owner is hanging paintings for a new show. Of the five paintings she has to choose from, she can only hang three on the main wall of the gallery. Assuming that she hangs as many as possible on that wall, in how many ways can she arrange the paintings? options: A)18 B)30 C)60 D)120 E)216 SOLUTION:Arrangment means permutations questions.. 5P3 = 5!/3! = 60. IMO option C is correct answer.. #### C QUESTION:In a game of 90 points, A can give B 5 points and C 15 points. then how many points B can give C in a game of 60? options: A)2.82 B)7.82 C)5.82 D)12.82 E)8.82 SOLUTION:In a game of 90 points,A give B 5 points and c 25 points means B=85,C=65 In 85 points B give 15 since 80-65=15 In 50 points B gives=50*15/85=8.82 ANSWER:E #### E QUESTION:If Rs.7500 are borrowed at C.I at the rate of 4% per annum, then after 2 years the amount to be paid is? options: A)1227 B)2088 C)26788 D)8112 E)1871 SOLUTION:A = 7500(26/25)2 = 8112 Answer: D #### D QUESTION:Mr Katial buys a house for Rs 1,00,000 and rents it. He puts 12.5% of each month’s 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? options: A)Rs 634.76 B)Rs 554.76 C)Rs 654.76 D)Rs 664.76 E)none of these SOLUTION:Let the monthly rent be Rs X. We have, 5.5% of 100000 = 12 (X - 12.5% of X) - 325 5500/12 = X - (X/8) - 325/12 5500/12 + 325/12 = 7/8 x X X = 5825/12 x 8/7 Rs 554.76 per month ANSWER:B #### B QUESTION:The average age of 20 men in the class is 15.6 years. Five new men join and the new average becomes 15.56 years. What was the average age of five new men? options: A)15.5 B)15.4 C)15.25 D)15.3 E)15.6 SOLUTION:Total age of 20 men = 15.6 x 20 = 312 Now, total age of 25 men = 389. Total age of five men added later = 389 - 312 = 77. Hence, the total average of five men = 77/5 = 15.4 ANSWER:B #### B QUESTION:Diana picked a number of pears, each of which she sold, canned, or poached. If she canned 60 percent more than she poached, and she poached 50 percent less than she sold. If there were a total of 115 pears, then how many pears did she sell? options: A)41 B)44 C)47 D)50 E)53 SOLUTION:Let x be the amount of pears that she sold. Then she poached 0.5x. Then she canned 1.6*0.5x=0.8x. The total amount of pears is x+0.5x+0.8x=2.3x The fraction of pears that she sold is 1/2.3=10/23. The number of pears she sold is (10/23)*115=50. The answer is D. #### D QUESTION:Set R has a mean of 12 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? options: A){15, 16} B){3, 4} C){6, 7} D){5, 6} E){11, 13} SOLUTION:The lesser the variance( values closer to mean) ,lower the standard deviation. As discussed in question the mean is 12,the values (11,13) are closer than others. Hence Answer : E #### E QUESTION:The least number which when increased by 4 each divisible by each one of 22, 32, 36 and 54 is : options: A)427 B)859 C)860 D)4320 E)None of these SOLUTION:Solution Required number = (L.C.M. of 24, 32, 36, 54) - 4 = 864 - 4 = 860. Answer C #### C QUESTION:After an ice began to melt out from the freezer, in the first hour lost 3/4, in the second hour lost 3/4 of its remaining. If after two hours, the volume is 0.2 cubic inches, what is the original volume of the cubic ice, in cubic inches? options: A)2.5 B)3.2 C)4.0 D)6.5 E)8.0 SOLUTION:Let initial volume of ice be = x Ice Remaining after 1 hour = x - 0.75x = 0.25x Ice Remaining after 2 hour = (1/4)x - (3/4 * 1/4 * x) = (1/16)x (1/16)x = 0.2 x = 3.2 Alternate solution: Try to backsolve. Initial volume = 3.2 After one hour --> (1/4)3.2 = 0.8 After two hours --> (1/4)0.8 = 0.2 Answer: B #### B QUESTION:Find out the next word in the series below... FAG, GAF, HAI, IAH, ...? options: A)GAK B)JAK C)HGF D)JAH E)KHG SOLUTION:In first FAG it was reodering the first and last letters and these are the continuous alphabets ANSWER:B #### B QUESTION:At a certain college, 60 percent of the total number of students are freshmen. If 40 percent of the fresh-men are enrolled in the school of liberal arts and, of these, 20 percent are psychology majors, what percent of the students at the college are freshmen psychology majors enrolled in the school of liberal arts? options: A)4% B)8% C)4.2% D)4.8% E)5% SOLUTION:Let's say there is a TOTAL of100students at this college. 60 percent of the total number of students are freshmen. # of freshmen = 60% of 100 =60 40 percent of the fresh-men are enrolled in the school of liberal arts... Number of liberal arts freshmen = 40% of 60 =24 ...and, of these, 20 percent are psychology majors... Number of liberal arts freshmen who are psychology majors = 20% of 24=4.8 What percent of the students at the college are freshmen psychology majors enrolled in the school of liberal arts? 4.8/100= 4.8% Answer:D #### D QUESTION:A and B starts a business with Rs.8000 each, and after 8 months, B withdraws half of his capital . How should they share the profits at the end of the 18 months? options: A)18:11 B)18:13 C)23:12 D)11:9 E)11:10 SOLUTION:A invests Rs.8000 for 18 months, but B invests Rs.8000 for the first 8 months and then withdraws Rs.4000. So, the investment of B for remaining 10 months is Rs.4000 only. A : B 8000*18 : (8000*8) + (4000*10) 144000 : 104000 A:B = 18:13 ANSWER:B #### B QUESTION:Pipe A can fill a tank in 8 hours, pipe B in 4 hours and pipe C in 24 hours. If all the pipes are open, in how many hours will the tank be filled? options: A)1.9 hour B)2.1 hour C)4.7 hour D)2.4 hour E)3.2 hour SOLUTION:Part filled by pipe A in 1 hour =1/8 Part filled by pipe B in 1 hour =1/4 Part filled by pipe C in 1 hour =1/24 Part filled by pipes A,B,C together in 1 hour=1/8+1/4+1/24=10/24 i.e, pipes A,B,C together can fill the tank in = 24/10 hr =2.4 hour. ANSWER:D #### D QUESTION:Exactly 3/8 of the people in the room are under the age of 21, and exactly 5/12 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? options: A)21 B)36 C)39 D)60 E)65 SOLUTION:The total number of the people in the room must be a multiple of both 8 and 12 (in order 3/7 and 5/13 of the number to be an integer), thus the total number of the people must be a multiple of LCM of 8 and 12, which is 96. Since, the total number of the people in the room is greater than 50 and less than 100, then there are 96 people in the room. Therefore there are 3/8*96=36 people in the room under the age of 21. Answer: B. #### B QUESTION:Ganesh is one year more than twice Kumar's age. The sum of their age is 7. How old each? options: A)6, 4 B)5, 2 C)2, 5 D)7, 3 E)3, 7 SOLUTION:Explanation: Let the present ages of Anand and Bala be 'a' and 'b' respectively. Given a - 2b = 1 --- (1) a+b = 7----(2) =>b =7-a Substituting b = 7-a in first equation, 3a-14 = 1 => a = 5 => b = 2 Answer: B #### B QUESTION:Jerry, an electrician, worked 5 months out of the year. What percent of the year did he work? (round answer to the nearest hundredth) What percent 12 is 5? 12 months = 1 year options: A)58.33% B)68.33% C)78.33% D)88.33% E)41.66% SOLUTION:1. Multiply the opposites 5 x 100 = 500 100=5/12 Divide by the remaining number 41.66% (rounded to hundredth) correct answer E #### E QUESTION:The 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. 28,000 is made? options: A)Rs. 1,10,000 B)Rs. 1,20,000 C)Rs. 1,24,000 D)Rs. 1,21,000 E)None of these SOLUTION:The value of the machine after two years = 0.8 * 0.8 * 1,50,000 = Rs. 96,000 SP such that a profit of Rs. 24,000 is made = 96,000 + 28,000 = Rs. 1,24,000 ANSWER:C #### C QUESTION:An order was placed for the supply of a carpet whose breadth was 6 m and length was 1.44 times the breadth. What be the cost of a carpet whose length and breadth are 40% more and 25% more respectively than the first carpet. Given that the ratio of carpet is Rs. 45 per sq m? options: A)Rs.4082.67 B)Rs.4082.99 C)Rs.4082.29 D)Rs.4082.40 E)Rs.4082.12 SOLUTION:Length of the first carpet = (1.44)(6) = 8.64 cm Area of the second carpet = 8.64(1 + 40/100) 6 (1 + 25/100) = 51.84(1.4)(5/4) sq m = (12.96)(7) sq m Cost of the second carpet = (45)(12.96 * 7) = 315 (13 - 0.04) = 4095 - 12.6 = Rs.4082.40 Answer:D #### D QUESTION:If 18 is 15 percent of 25 percent of a certain number, what is the number? options: A)9 B)36 C)480 D)81 E)400 SOLUTION:Let the certain number be x. => (15/100)*(25/100)*x = 18; => x=480; Ans is (C). #### C QUESTION:Diana is painting statues. She has 7/8 of a gallon of paint remaining. Each statue requires 1/8 gallon of paint. How many statues can she paint? options: A)7 B)20 C)28 D)14 E)19 SOLUTION:number of statues=all the paint÷amount used per statue =7/8 ÷ 1/8 =7/8*8/1 =7/1 =7 Answer is A. #### A QUESTION:A 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? options: A)5 m B)6 m C)4 m D)7 m E)8 m SOLUTION:Let radius of the outer circle be R and radius of the inner circle be r. Circumference of the outer circle = Circumference of the inner circle = But, or, R - r = Thus, width of the road = 7 m D #### D QUESTION:Mr. Sane invested a total amount of 16,500 for two years in two schemes A and B with rate of simple interest 10 p.c.p.a. and 12 p.c.p.a. respectively. If the total amount of interest earned was 3,620, what was the amount invested in scheme B? options: A)8,000 B)8,600 C)8,150 D)Data inadequate E)None of these SOLUTION:% interest on total amount per annum = 3620×100/16500×2=362/33% Now, use Alligation method. Hence, ratio of amount invested in schemes A and B = (12 - 362⁄33) : (362⁄33 - 10) = 17 : 16 Hence, amount invested in B = 16×16500/(17+16)=8000 Answer A #### A QUESTION:The value of a 10.5% stock, in which an income of Rs.756 is derived by investing Rs.9000, brokerage being% is : options: A)Rs. 113.5 B)Rs. 119.7 C)Rs. 124.75 D)Rs. 130.75 E)Rs. 134.45 SOLUTION:For an income of Rs.756, investment = Rs.9000 For an income of Rs., investment = = Rs.125 For a Rs.100 stock, investment = Rs.125. Market value of Rs. 100 stock = = Rs. 124.75 C #### C QUESTION:A shopkeeper sold an article at $100 with 30% profit. Then find its cost price? options: A)$120 B)$100 C)$91 D)$77 E)$69 SOLUTION:cost price = selling price *100/(100+profit) C.P. = 100*100/130 = $77(approximately) Answer is D #### D QUESTION:The first train leaves the station at 6:00 am with a speed of 60 km/hr. The second train leaves at 7:00 am, in the same direction from the same station, with a speed of 80 km/hr. What time will the second train catch the first train? options: A)9:00 am B)10:00 am C)11:00 am D)12:00 noon E)1:00 pm SOLUTION:In one hour, the first train travels 60 km. The second train catches the first train with a relative speed of 20 km/h. The second train will catch the first train at 10:00 am. The answer is B. #### B QUESTION:A trader bought a car at 20% discount on its original price. He sold it at a 40% increase on the price he bought it. What percent of profit did he make on the original price? options: A)18% B)22% C)12% D)92% E)14% SOLUTION:Original price = 100 CP = 80 S = 80*(140/100) = 112 100 - 112 = 12% Answer: C #### C QUESTION:The area of a parallelogram is 162sq m and its altitude is twice the corresponding base. Then the length of the base is? options: A)8 B)9 C)7 D)62 E)2 SOLUTION:2x * x = 162 => x= 9 Answer: B #### B QUESTION:The largest natural number by which the product of three consecutive even natural numbers is always divisible, is options: A)16 B)24 C)48 D)96 E)78 SOLUTION:Solution Required number = (2×4×6) = 48. Answer C #### C QUESTION:A box contains 8 pairs of shoes (16 shoes in total). If two shoes are selected at random, what it is the probability that they are matching shoes? options: A)1/190 B)1/20 C)1/19 D)1/10 E)1/15 SOLUTION:The problem with your solution is that we don't choose 1 shoe from 16, 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*1/15(as after taking one at random there are 15 shoes left and only one is the pair of the first one)=1/15 Answer: E. #### E QUESTION:A sum of money is sufficient to pay B's wages for 12 days and C's wages for 24 days. The same money is sufficient to pay the wages of both for? options: A)6 B)7 C)8 D)9 E)10 SOLUTION:Let the total money be $x B's 1day work = $ x/12 C's 1day work = $ x/24 A+B 1day work = $ x/8 Money is sufficient to pay the wages of both for 8days Answer is C #### C QUESTION:Three 6 faced dice are thrown together. The probability that exactly two dice show the same number on them is options: A)5/9 B)5/12 C)1/36 D)7/12 E)4/9 SOLUTION:Using question number 11 and 12, we get the probability as 1 - (1/36 + 5/9) = 5/12 ANSWER:B #### B QUESTION:John tossed a fair coin 2 times. What is the probability that the coin landed heads up exactly twice? options: A)0.5 B)0.55 C)0.6 D)0.65 E)0.7 SOLUTION:The probability is exactly same as the cion landed tail up once. That is 2*(1/2)^2 = 2/4 =0.5. The answer is, therefore, (A). #### A QUESTION:A girl has 10 jeans and 12 shirts. In how many different ways can she select a jeans and a shirts? options: A)A)100 B)B)102 C)C)108 D)D)110 E)E)120 SOLUTION:The girl can select one jeans in 10 ways. The girl can select one shirt in 12 ways. The number of ways in which he can select one jeans and one shirt is 10 * 12 = 120 ways. E #### E QUESTION:How many seconds will a 900 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? options: A)22 B)54 C)99 D)77 E)12 SOLUTION:Speed of train relative to man = 63 - 3 = 60 km/hr. = 60 * 5/18 = 50/3 m/sec. Time taken to pass the man = 900 * 3/50 = 54 sec. Answer: B #### B QUESTION:If circles x and y have the same area and circle x has a circumference of 14π, half of the radius of circle y is: options: A)16 B)8 C)4 D)3.5 E)1 SOLUTION:x be radius of circle x y be radius of circle y given: pi*x^2 = pi*y^2 also, 2*pi*x = 14*pi x =7 thus y =7 y/2 = 3.5 Ans: D #### D QUESTION:A reduction of 10% in the price of tea enables a dealer to purchase 25 kg more tea for Rs. 22500. What is the reduced price per kg of tea? options: A)Rs. 70 B)Rs. 80 C)Rs. 90 D)Rs. 100 E)None SOLUTION:Solution: 1st Method: Let the original price of tea be Rs. x/kg. After reduction the price becomes = x -10% of x = 9x/10 per kg. Now, (22500/(9x/10))-22500/x = 25 Or, 22500[10/9x- 1/x] = 25 Or, 25*9x = 22500; Or, x = (22500/2589) = Rs. 100. Hence, new price = 90 per kg. Thought process Method: Let the original price be Rs. 100 per kg, he get tea = 22500/100 = 225 kg. After reduction the price becomes = 90 per kg, he get tea = 22500/90 = 250 kg. So, reduction price is Rs. 90 per kg as it enables him to buy 25 kg of more tea. Answer: Option C #### C QUESTION:An optometrist charges $150 per pair for soft contact lenses and $85 per pair for hard contact lenses. Last week she sold 5 more pairs of soft lenses than hard lenses. If her total sales for pairs of contact lenses last week were $2,160, what was the total number of pairs of contact lenses that she sold? options: A) 11 B) 13 C) 15 D) 17 E) 19 SOLUTION:(x+5)*150 +x*85=2160 =>x=6 total lens=6+(6+5)= 17 Answer D #### D <<<Examples ends QUESTION:The sum of money will be double itself in 30years and simple interest find rate of interest? options: A)A)2.33% B)B)3.33% C)C)4.33% D)D)5.33% E)E)6.33% SOLUTION:T = 30 years P= principle amount = x A = total amount = 2x SI = simple interest = A-P = 2x-x = x R = 100SI/PT = 100x/30x =3.33% Answer is B #### B

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:If the product of the integers from 1 to n is divisible by 378, what is the least possible value of n? options: A)7 B)8 C)9 D)10 E)11 SOLUTION:378 = 2 x 3 x 3 x 3 x 7 N must include at least 3, 2*3, and 3*3. The answer is C. #### C QUESTION:The 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? options: A)A)2/3 B)B)5/7 C)C)4/7 D)D)5/9 E)E)None of these SOLUTION:Let the numerator and denominator of the fraction be 'n' and 'd' respectively. d = 2n - 1 (n + 1)/(d + 1) = 4/5 5n + 5 = 4d + 4 5n + 5 = 4(2n - 1) + 4 => n = 5/3 d = 2n - 1 => d = 3/7 Hence the fraction is : 5/7 ANSWER:B #### B QUESTION:The difference between the length and breadth of a rectangle is 23 m. If its perimeter is 206 m, then its area is : options: A)1520 m2 B)2420 m2 C)2480 m2 D)2520 m2 E)None of these SOLUTION:Solution We have : (l - b) = 23 and 2 (l + b) = 206 or (l + b) = 103. Solving the two equations, we get, l = 63 and b = 40. ∴ Area = (l × b) = (63 × 40) m2 = 2520 m2. Answer D #### D QUESTION:0.40 represents what percent of 0.008? options: A)0.05% B)0.5% C)5% D)500% E)5000% SOLUTION:One more method 0.40 represents what percent of 0.008? Adjusting the decimal 400 represents what percent of 8? Divide by 8 50 represents what percent of 1? Answer = 50*100 = 5000% = E #### E QUESTION:What should be added to 4750 so that it may become a perfect square? options: A)11 B)15 C)16 D)17 E)18 SOLUTION:69x69=4761 4761-4750 = 11 If added to 11 get perfect square answer =A #### A QUESTION:A trader sells 85 meters of cloth for Rs. 8925 at the profit of Rs. 25 per metre of cloth. What is the cost price of one metre of cloth? options: A)80 B)28 C)90 D)26 E)11 SOLUTION:Explanation: SP of 1m of cloth = 8925/85 = Rs. 105 CP of 1m of cloth = SP of 1m of cloth - profit on 1m of cloth = Rs. 105 - Rs. 25 = Rs. 80. Answer: A #### A QUESTION:The average of the marks of 30 students in a class is 45. If the marks of each student are doubled, find the new average? options: A)85 B)77 C)33 D)90 E)75 SOLUTION:Sum of the marks for the 30 students = 30 * 45 = 1350. The marks of each student are doubled, the sum also will be doubled. The new sum = 1350 * 2 = 2700. So, the new average = 2700/30 = 90. Answer:D #### D QUESTION:2/5 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? options: A)3/20 B)7/30 C)5/16 D)1/3 E)2/5 SOLUTION:Straight method.... 1/4 of 2/5 + 1/5 of 1/4 = 2/20 +1/20 =3/20 ANSWER:A #### A QUESTION:We bought 85 hats at the store. Blue hats cost $6 and green hats cost $7. The total price was $600. How many green hats did we buy? options: A)A)36 B)B)90 C)C)40 D)D)42 E)E)44 SOLUTION:Let B be the number of blue hats and let G be the number of green hats. B+G=85. B=85-G. 6B+7G=600. 6(85-G)+7G=600. 510-6G+7G=600. G=600-510=90. The answer is B. #### B QUESTION:If the number 653ab is divisible by 90, then (a + b) = ? options: A)2 B)3 C)4 D)6 E)8 SOLUTION:90 = 10 x 9 Clearly, 653ab is divisible by 10, so b = 0 Now, 653a0 is divisible by 9. So, (6 + 5 + 3 + a + 0) = (14 + a) is divisible by 9. So, a = 4. Hence, (a + b) = (4 + 0) = 4. ANSWER:C #### C QUESTION:The greatest possible length which can be used to measure exactly the length 7m, 3m 85cm, 12 m 95 cm is options: A)15 cm B)25 cm C)35 cm D)42 cm E)43 cm SOLUTION:Explanation: Required Length = H.C.F of 700 cm, 385 cm and 1295 c = 35 cm. Answer: C #### C QUESTION:Terry is having lunch at a salad bar. There are two types of lettuce to choose from, as well as three types of tomatoes, and four types of olives. He must also choose whether or not to have one of the two types of soup on the side. If Terry has decided to have the salad and soup combo and he picks one type of lettuce, one type of tomato, and one type of olive for his salad, how many total options does he have for his lunch combo? options: A)9 B)11 C)24 D)48 E)54 SOLUTION:Terry can pick one lunch salad bar....we can choose lettuce 2c1 , tomatoes - 3c1 and olives - 4c1... Two types of soups , if he picks one then 2c1 ways. Terry decided to have the combo : Soup + salad...Hmmm... Using the above information, we get ( 2c1 * 2c1* 3c1 * 4c1 ) = 48.. ANS option D is correct answer.. #### D QUESTION:Machine X takes 10 hours longer than machine Y to produce 1080 Widgets. Machine Y produces 20 percent more widgets in an hour than machine x does in an hour. How many widgets per hour does machine X produce options: A)100 B)65 C)25 D)11 E)18 SOLUTION:Machine Y produces 20 percent more widgets in an hour than machine x does in an hour. So if machine X produces 100 widgets, then machine Y produces 120 widgets. Ratio of 120/100 = 6/5. This is their speed of work (Y:X). i.e. speed of their work (X:Y) = 5/6 Now, time is inversely proportional to speed. Hence the ratio of the time spent (X:Y)= 6/5 Let us assume that they spend 6x and 5x hours. Given that 6x-5x = 10 So, x = 10. Hence 6x = 6*10 = 60 hours. Hence X takes 120 hours to produce 1080 widgets. So, in 1 hour, it can produce (1 * 1080)/60 = 18 Hence option (E). #### E QUESTION:When Professor Wang looked at the rosters for this term's classes, she saw that the roster for her economics class (E) had 20 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 4 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? options: A)30 B)44 C)42 D)46 E)50 SOLUTION:Total # of students 20+28+18-(9+7+10)+4=44. Answer: B. #### B QUESTION:At what rate of annual simple interest,a certain sum will amount to four times in 15 year? options: A)15% B)17.5% C)20% D)25% E)35% SOLUTION:r=? t=15 yrs SI=p*r*t/100 Amount = SI+p = 4p (p*r*15/100)+p = 4p p(15r/100 + 1) = 4p 15r + 100 = 400 15r = 300 r = 20% ANSWER:C #### C QUESTION:Pumping alone at their respective constant rates, one inlet pipe fills an empty tank to 1/3 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? options: A)3.25 B)3.6 C)4.2 D)4.4 E)6 SOLUTION:Time taken by First tank Fill 1/3 the tank = 6 hours i.e. Time taken by First tank to Fill 1 complete the tank = 18 hours Time taken by Second tank Fill 2/3 the tank = 6 hours i.e. Time taken by First tank to Fill 1 complete the tank = (3/2)*6 = 9 hours in 1 Hour, Both tanks together Fill the tank = (1/18)+(1/9) = 1/6 tank i.e. Time taken by Both tank to Fill 1 complete the tank = 6 hours Answer: option E #### E QUESTION:An even and an odd integer are multiplied together. Which of the following numbers could not be the square of their product? options: A)4 B)16 C)25 D)36 E)100 SOLUTION:25 = 5^2 so it can not be the square of an even number multiplied by an odd number. The answer is C. #### C QUESTION:A and B invest in a business in the ratio 3: 2. Assume that 5% of the total profit goes to charity. If A's share is Rs. 855, what is the total profit? options: A)1500 B)2000 C)3000 D)3500 E)2500 SOLUTION:Profit as x since 5% and 95% of x will be divided b/w A and B ration 3:2 =>profit 95x/100 * 3/5 given that A's share is Rs 855 => 95x/100 * 3/5 = 855 hence x = 1500 ANSWER A #### A QUESTION:A 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? options: A)12.2 B)12.9 C)12.6 D)12.5 E)12.3 SOLUTION:Let the speed of the man in still water be a kmph and let the speed of the stream be b kmph. Now 30/(a + b) + 20/(a - b) = 4 and 45/(a + b) + 40/(a - b) = 7 Solving the equation, the speed of man in still water is 12.5 kmph. Answer: D #### D QUESTION:Harkamal 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? options: A)1055 B)1050 C)1057 D)1060 E)1070 SOLUTION:Cost of 8 kg grapes = 70 × 8 = 560. Cost of 9 kg of mangoes = 55 × 9 = 490. Total cost he has to pay = 560 + 490 = 1055. A #### A QUESTION:A rectangular paper when folded into two congruent parts had a perimeter of 34cm foer each part folded along one set of sides and the same is 38cm. When folded along the other set of sides. What is the area of the paper? options: A)140 B)388 C)238 D)119 E)112 SOLUTION:when folded along the breadth we have 2(l/2 +b) = 34 or l+2b = 34...........(1) when folded along the length, we have 2(l+b/2)=38 or 2l+b =38.....(2) from 1 &2 we get l=14 and b=10 Area of the paper = 14*10 = 140 sq cmV Answer: A #### A QUESTION:The fourth proportional to 12, 16 and 18 is? options: A)24 B)66 C)55 D)88 E)61 SOLUTION:(15*18)/12 = 24 Answer:A #### A QUESTION:Ayesha'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? options: A)6 B)40 C)50 D)10 E)20 SOLUTION:Mother's age when Ayesha's brother was born = 42 years. Father's age when Ayesha's brother was born = (58 + 4) years = 62 years. Required difference = (62 - 42) years = 20 years. Answer:E #### E QUESTION:In a bowl, the number of marbles gets doubled after every minute. If the bowl gets filled after two hours of such process, how long do you think it will take for it to be half filled. options: A)1 hour and 59 minutes B)2 hour and 59 minutes C)4 hour and 59 minutes D)4 hour and 59 minutes E)5 hour and 59 minutes SOLUTION:Solution: The correct way to solve this question is go backwards. If the number of marble gets doubled every minute and after two hours, it is filled completely, one minute ago it would be half. So, it will take 1 hour and 59 minutes for it to be filled half. Answer A #### A QUESTION:A 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? options: A)3 B)7.5 C)2.25 D)1.5 E)4 SOLUTION:M = 9 S = x DS = 9 + x US = 9 - x 9 + x = (9 - x)2 9 + x = 18 -2x 3x = 9 x = 3 ANSWER:A #### A QUESTION:Find the median of the data 25, 37, 47, 18, 19, 26, 36. options: A)22 B)23 C)24 D)25 E)26 SOLUTION:Arranging the data in ascending order, we get 18, 19, 25, 26, 36, 37, 47 Here, the number of observations is odd, i.e., 7. Therefore, median = (n + 1/2)th observation. = (7 + 1/2)th observation. = (8/2)th observation = 4th observation. 4th observation is 26. Therefore, median of the data is 26. ANSWER :E #### E QUESTION:If an average hard drive had a capacity of 0.4 TB in 2000, and average hard drive capacities double every 5 years, what will be the average hard drive capacity in 2050? options: A)256 B)512 C)4096 D)1024 E)1536 SOLUTION:0.4*2^10=0.4*1024=409.6 The answer is C. #### C QUESTION:there is four light.all light glow in blue,white,yellow and red. all glow together and take different color.every time each light change its color in given four of the color.but at same time no two light have same color then tell how many design will form? options: A)20 B)24 C)18 D)16 E)22 SOLUTION:it is so simple,it is just permutation of 4 item. 4P4=4!=24 answer B #### B QUESTION:Rs 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 7000 Find money given by 10%? options: A)30000 B)40000 C)50000 D)60000 E)70000 SOLUTION:let first parrt is x and second part is y then x+y=50000----------eq1 total profit=profit on x +profit on y 7000=(x*10*1)/100 + (y*20*1)/100 70000=x+2y-----------------------------------eq2 70000=50000+y so y=20000 then x =50000-20000=30000 first part =30000 ANSWER:A #### A QUESTION:If a - b =6 and a2+b2=48 , find the value of ab. options: A)6 B)8 C)10 D)12 E)2 SOLUTION:Explanation: We know 2ab=(a2+b2)−(a−b)2 2ab=48−36=12 =>ab=6 Option E #### E QUESTION:What is 2/5 of 5/9 of 1/2? options: A)1/4 B)1/9 C)9/16 D)5/8 E)16/9 SOLUTION:2/5 * 5/9 * 1/2= 1/9 Answer: B #### B QUESTION:calendar=52097083 november=538=8651 march=2*308 blue=7154 december=? options: A)9535&153 B)9585&153 C)9525&153 D)9525&*53 E)9525&*54 SOLUTION:from above in formation d=9 e=5 c=2 e=5 m=3 b=1 e=5 r=8 95253158( Order doesnot matter i guess!) another thing is &=8 for mathcing above ans ANSWER:C #### C QUESTION:The 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? options: A)1 : 9 B)1 : 3 C)1 : 2 D)1 : 1 E)3 : 3 SOLUTION:Suppose age of Laxmi is x years. The difference of their ages \inline \therefore Ratio of their ages after 3 years = = = 12 : 36 = 1 : 3 Answer:B #### B QUESTION:3,8,18,38,78,__ options: A)158 B)156 C)154 D)150 E)148 SOLUTION:8=3*2+2 18=8*2+2 38=18*2+2 78=38*2+2 158=78*2+2 ANSWER:A #### A QUESTION:The 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? options: A)5:6 B)25:27 C)15:16 D)20:21 E)It cannot be determined from the information given SOLUTION:The ratio cannot be straight way added any quantity... 1:2means 1X:2X... So when you add a quantity, it becomes 1x + 15 : 2x +15.. So value of x is must.. Ans E #### E QUESTION:There 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? options: A)21 B)25 C)16 D)22 E)20 SOLUTION:Two ball will be chosen. At least 1 blue ball Total ways = 8C2 = 28 Total without any blue ball = 4C2 = 6 Hence ways in which at least one blue will be present = 28 - 6 = 22 Correct option: D #### D QUESTION:What number should replace the question mark? 16, 23, 19, 19, 22, 15, 25, ? options: A)11 B)12 C)13 D)14 E)15 SOLUTION:A 11 There are two alternate sequences + 3 and - 4 #### A QUESTION:Evaluate 25% of 450 + 45% of 250 options: A)225 B)242 C)252 D)262 E)272 SOLUTION:Explanation: = (25/100) * 450 + (45/100) * 250 = 225 Option A #### A QUESTION:Jerry travels 8 miles at an average speed of 40 miles per hour, stops for 13 minutes, and then travels another 20 miles at an average speed of 60 miles per hour. What is Jerry’s average speed, in miles per hour, for this trip? options: A)48 B)42.5 C)44 D)50 E)52.5 SOLUTION:Total Time taken by jerry = (8/40)*60 Minutes + 13 Minutes + (20/60)*60 Minutes = 35 Minutes Average Speed = Total Distance / Total Time = (8+20) miles / (35/60)Hours = 28*60 / 35 = 48 Miles per hour Answer: option A #### A QUESTION:A train is moving at a speed of 50km/hr and its length is 500m. Find the time taken by it to pass a man standing near the railway line? options: A)30sec B)45sec C)36sec D)29sec E)52sec SOLUTION:Speed of the train = 50*5/18 = 250/18 m/sec Distance moved in passing the standing man = 500m Required time taken = 500/(250/18) = 500*18/250 = 36sec Answer is C #### C QUESTION:Rs.900 amounts to Rs.920 in 3 years at simple interest. If the interest is increased by 3%, it would amount to how much? options: A)Rs.1056 B)Rs.1001 C)Rs.2056 D)Rs.1026 E)Rs.1856 SOLUTION:(900*3*3)/100 = 81 920 + 81 = 1001 ANSWER:B #### B QUESTION:The average of a couple was 26Yrs when they were married 6Yrs ago.The avg age of the couple and a child, who was born during the interval, is 22Yrs now. How old is the child now ? options: A)2 Yrs B)4 Yrs C)3 Yrs D)1 Yrs E)None of these SOLUTION:(a+b-6-6)/2=26; a+b=64; a+b+c/3=22; solving both c=2 ANSWER:A #### A QUESTION:If 5x + 3 = 10x – 17, what is the value of x? options: A)1 B)2 C)3 D)4 E)5 SOLUTION:solve for x: 5x+3=10x-17 20=5x 4=x correct answer D)4 #### D QUESTION:A volunteer organization is recruiting new members. In the fall they manage to increase their number by 7%. By the spring however membership falls by 19%. What is the total change in percentage from fall to spring? options: A)16.16% B)15.55% C)14.44% D)13.33% E)12.22% SOLUTION:(100%+7%)*(100%-19%) = 1.07*.81 = 0.8667 1-0.8667 = 13.33% lost = -13.33% The Answer is D The organization has lost 13.33% of its total volunteers from fall to spring. #### D QUESTION:If 9^y = 3^12, what is y? options: A)2 B)3 C)4 D)5 E)6 SOLUTION:3^2y = 3^12 2y=12, therefore y=6 E #### E QUESTION:The integer K is positive, but less than 400. If 21K is a multiple of 180, how many unique prime factors does K have? options: A)1 B)2 C)3 D)4 E)5 SOLUTION:Also note here the relevance of 'K must be less than 400'. 21K is 180n (a multiple of 180). 180n = 2^2 * 3^2 * 5 * n = 3*7*K n must have a 7 at least. K must have two 2s, a 3 and a 5 at least. This means it must be at least 2*2*3*5 = 60. So 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. Answer (C) #### C QUESTION:In how many ways can a teacher write an answer key for a mini-quiz that contains 3 true-false questions followed by 2 multiples-choice questions with 4 answer choices each, if the correct answers to all true-false questions cannot be the same? options: A)88 B)90 C)96 D)98 E)102 SOLUTION:2 multiples-choice questions can be answered in = 4 x 4 = 16 ways 3 true-false questions can be answered in = 2x2x2 = 8 ways But out of the 8 ways, 2 ways [(True-True-True) (False-False-False)]will contain same answers Thus 3 true-false questions can be answered in = 2x2x2 = 6 ways Total ways to answer the quiz = 16 x 6 = 96 Answer C #### C QUESTION:A certain no. when divided by 50 leaves a remainder 25, what is the remainder if the same no.be divided by 15? options: A)3 B)4 C)5 D)8 E)9 SOLUTION:Explanation: 50 + 25 = 75/15 = 5 (Remainder) C #### C QUESTION:A farmer used 1,034 acres of land for beans, wheat, and corn in the ratio of 5 : 2 : 4, respectively. How many Y acres were used for corn? options: A) 188 B) 258 C) 376 D) 470 E) 517 SOLUTION:consider 5x acres of land used for bean consider 2x acres of land used for wheat consider 4x acres of land used for corn Total given is 1034 acres 11x =1034 x = 94 land used for corn Y= 4 * 94 = 376 correct option - C #### C QUESTION:Let 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: options: A)4 B)6 C)5 D)7 E)9 SOLUTION:N = H.C.F. of (4665 - 1305), (6905 - 4665) and (6905 - 1305) = H.C.F. of 3360, 2240 and 5600 = 1120. Sum of digits in N = ( 1 + 1 + 2 + 0 ) = 4 Answer: Option A #### A QUESTION:I. j; k; m; n; p II. j - 10; m; m; m; p + 15 III. j + 2; k + 1; m; n - 1; p - 2 If 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? options: A) I, III, II B) II, I, III C) II, III, I D) III, I, II E) III, II, I SOLUTION:Range of 1st Set = (p-j) Range of 2nd Set = P+15 - j +10 = (p-j) +25 Range of 3rd Set = P -2 - j - 2 = (p-j) - 4 R2 > R1 > R3 ==> SD2 > SD1 > SD3 Since,D= Higher the Range -> More Dispersion in the Set -> More Standard Deviation.B #### B QUESTION:A starts walking at 4 kmph and 4 hours after his start B starts cycling at 10 kmph. After how much distance will B catch up with A options: A)26.2 km B)25.7 km C)23.2 km D)26.67 km E)None of these SOLUTION:Explanation: Distance travelled by each of them is to be made equal. => Distance travelled walking = Distance covered cycling. Let after 4 hours of walking, A walk for x hours more before B catches up with him. => Distance = Speed * Time (4+x)4 = 10x x = 8/3 Therefore, It takes B 8/3 hours to catch up with A. Distance: 8/3 x 10 = 80/3 km = 26.67 ANSWER: D #### D QUESTION:What will come in place of the x in the following Number series? 18, 22, 30, x ,78, 142 options: A)23 B)25 C)46 D)49 E)50 SOLUTION:(C) The pattern is +4, +8, +16, +32, +64 So the missing term is = 30 + 16 = 46 . #### C QUESTION:Walking with 4/5 of my usual speed, I miss the bus by 5 minutes. What is my usual time? options: A)22 B)88 C)27 D)20 E)98 SOLUTION:Speed Ratio = 1:4/5 = 5:4Time Ratio = 4:51 -------- 5 4 --------- ? è 20.Answer: D #### D QUESTION:If x is less than y by 25% then y exceed x by: options: A)33.33% B)25% C)75% D)66.66% E)None of these SOLUTION:Using formula (x/(100-x)*100) where x is Percentage decrease (here it is 25%) => 25(100-25)*100 =33.33% ANSWER:A #### A QUESTION:Find the Missing Number 1, 2, 4, 10, 16, 40, 64 (Successive terms are related) options: A)100 B)200 C)300 D)90 E)80 SOLUTION:Well, the pattern looked REALLY familiar to me, like it's a binary progression. And it is...but with a twist. 2^0 = 1 2^1 = 2 2^2 = 4 2^3 = 8 2^4 = 16 2^5 = 32 2^6 = 64 You'll note that all the numbers up there match your sequence...except for 2^3 = 8 (10 in your sequence) and 2^5 = 32 (40 in your sequence). BUT, if you convert 8 to base 8, you get 10. And if you convert 32 to base 8, you get 40. Which indicates that every other number starting with the first one is expressed in base 10 and every other number starting with the second number is expressed in base 8. If this is true, then you next number would be: 2^7 = 128 That is the base 10 number. Since this number should be expressed in base 8 (following the pattern), it should be 200. ANSWER:A #### A QUESTION:In how many a committee of 5 members can be selected from 6men 5 ladies consisting of 3 men and 2 ladies options: A)231 B)150 C)200 D)450 E)451 SOLUTION:(3 men out of 6) and (2 ladies out of 5) are to be chosen Required number of ways =(6C3 * 5C2) = 200 Ans: C #### C QUESTION:Seats for Maths, Physics and Biology are in the ratio of 4 : 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? options: A)2 : 3 : 4 B)6 : 7 : 8 C)8 : 15 : 20 D)Cannot be determined E)None of these SOLUTION:Reqd ratio 4 × 140⁄100 : 7 × 150⁄100 : 8 × 175⁄100 = 4 × 140 : 7 × 150 : 8 × 175 = 8 : 15 : 20 Answer C #### C QUESTION:66 cubic centimetres of silver is drawn into a wire 1 mm in diameter. The length of the wire in metres will be : options: A)84 m B)88 m C)120 m D)137 m E)None SOLUTION:Sol. Let the length of the wire b h. Radius = 1/2 mm = 1/20 cm. Then, 22/7 * 1/20 * 1/20 * h = 66 ⇔ = [66 * 20 * 20 * 7 / 22] = 8400cm = 84 m. Answer A #### A QUESTION:Five 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 10 years? options: A)30 B)35 C)40 D)50 E)60 SOLUTION:Explanation : (A + B), five years ago = (15 * 2) = 30 years. (A+B), now = (30+5*2)years=40 years. (A + B + C), now = (20 x 3) years =60 years. C, now = (60 - 40) years = 20 years. C, after 10 years = (20 + 10) years =30 years. Answer : A #### A QUESTION:Worker A takes 12 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? options: A)40 days B)40/9 days C)39/9 days D)30/9 days E)20/3 days SOLUTION:A's one hour work = 1/12. B's one hour work = 1/15. (A+B)'s one hour work = 1/12+1/15 = 9/60 = 3/20. Both A & B can finish the work in 20/3 days E #### E QUESTION:What is the Compound Interest on Rs.7000 at 8.5% p.a. compounded half-yearly for 5 years. options: A)3616.5 B)3613.5 C)3313.5 D)3616.5 E)3113.5 SOLUTION:Compound interest : A = P(1 + r/n)nt A = 10,613.50 C.I. >> 10,613.50 - 7000 >> Rs. 3613.5 Answer:B #### B QUESTION:A car covers a distance of 624 km in 6 ½ hours. Find its speed? options: A)104 B)190 C)109 D)278 E)211 SOLUTION:Explanation: 624/6 = 104 kmph Answer:C #### C QUESTION:An industrial loom weaves 0.128 metres of cloth every second. Approximately, how many seconds will it take for the loom to weave 25 metre of cloth ? options: A)175 seconds B)195 seconds C)155 seconds D)115 seconds E)115 seconds SOLUTION:Explanation: Let the time required by x seconds. Then, More cloth means More time (Direct Proportion) So, 0.128 : 1 :: 25 : x => x = {\color{Blue} \frac{25\times 1}{0.128}} => x = 195.31 So time will be approx 195 seconds Answer: B #### B <<<Examples ends QUESTION:A group of five girls and three boys have tickets for seven adjacent seats in one row of a theater. If the three boys will not sit in three adjacent seats, how many possible different seating arrangements are there for these 8 theatre-goers? options: A)8! – 2!3!2! B)8! – 6!3! C)8 × 2!3!2! D)8! – 5!3! E)2!3!2! SOLUTION:There are 3 boys and 4 girls , we want to calculate the seating arrangements if three boys do not sit together, like MMM. Let's calculate the # of arrangements when they SIT together and subtract from total # of arrangements of these 8 persons without restriction. Thus we'll get the # of arrangements asked in the question. 1. Total # of arrangements of 8 is 8!. 2. # of arrangements when 3 boys are seated together, like MMM; Among themselves these 3 boys can sit in 3! # of ways, Now consider these 3 boys as one unit like this {MMM}. We'll have total of 6 units: {MMM}{W}{W}{W}{W}{W}. The # of arrangements of these 5 units is 5!. Hence total # of arrangements when 3 men sit together is: 3!6!. # of arrangements when 3 boys do not sit together would be: 8!-3!6!. Answer: B). #### B

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:What is the perimeter of a square with area 9p^2/25 ? options: A)3p/4 B)3p^2/4 C)12p/5 D)3p^2 E)4p/3 SOLUTION:Area of square, (side)^2 = (3p/5)^2 Therefore side of the square = 3p/5 Perimeter of square = 4*side = 4* (3p/5) = 12p/5 Answer is C. #### C QUESTION:Due to construction, the speed limit along an 5-mile section of highway is reduced from 60 miles per hour to 40 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 ? options: A)A) 3.12 B)B) 2.5 C)C) 10 D)D) 15 E)E) 24 SOLUTION:Old time in minutes to cross 5 miles stretch = 5*60/60 = 5*1/1 = 5 New time in minutes to cross 5 miles stretch = 5*60/40 = 5*3/2 = 7.5 Time difference = 2.5 Ans:B #### B QUESTION:A person purchased a TV set for Rs. 16000 and a DVD player for Rs. 1600. He sold both the items together for Rs. 31150. What percentage of profit did he make? options: A)70.00% B)86.98% C)76.99% D)45% E)None of these SOLUTION:The total CP = Rs. 16000 + Rs. 1600 = Rs. 17600 and SP = Rs. 31150 Profit(%) = (31150 - 17600)/17600* 100 = 76.99% ANSWER:C #### C QUESTION:Which of the following number will completely divide (49^15)-1? options: A)8 is the number B)6 C)22 D)12 E)14 SOLUTION:x^n - 1 will be divisible by x+1 only when n is even. 49^15 - 1 = (7^2)^15 - 1 = 7^30 - 1 which is divisible by 7+1 i.e. 8 Answer is A #### A QUESTION:What is the Compound Interest on Rs.7000 at 8.5% p.a. compounded half-yearly for 5 years. options: A)3616.5 B)3613.5 C)3313.5 D)3616.5 E)3113.5 SOLUTION:Compound interest : A = P(1 + r/n)nt A = 10,613.50 C.I. >> 10,613.50 - 7000 >> Rs. 3613.5 Answer:B #### B QUESTION:A fruit salad mixture consists of apples, peaches, and grapes. There are 3 times as many pounds of apples as grapes and 2.5 times as many pounds of peaches as grapes. If a mixture that has an average (arithmetic mean) of 39 pounds per fruit, how many more pounds of apples than grapes does the mixture have? options: A)5 B)12 C)19 D)36 E)50 SOLUTION:A+P+G= 39*3 A=3G P=2.5G 3G+2.5G+G= 39*3 G=39*3/6.5= 18 A= 6*3=54 Difference = 36 'D' is the answer #### D QUESTION:Each of the integers from 1 to 18 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 options: A)19 B)12 C)11 D)10 E)3 SOLUTION:Out of the 18 integers: 9 are odd and 9 are even. If 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: 1. we will end up picking odd numbers one by one, so we will pick all 9 odd numbers first 2. 10th number will be the first even number So we need to withdraw at least 10 numbers to make sure that we get one even number and the product of all the integers picked is even. So, answer will be 10. (D) #### D QUESTION:Souju's age is 115% of what it was 10 years ago, but 83 1/3% of what it will be after 10 years. What is her present age? options: A)56 years B)72 years C)56 years D)66 years E)76 years SOLUTION:Let the age before 10 years =x. Then, 115x/100=x+10 ⇒115x=100x+1000 ⇒x=1000/15=66 Present age =x+10=66+10=76 ANSWER:E #### E QUESTION:A bag contains 4 white balls, 3 black balls, and 2 red balls. One by one, three balls are drawn out without replacement. What is the probability that the third ball is red? options: A)2/9 B)1/4 C)3/8 D)5/16 E)2/5 SOLUTION:The probability for each ball to be drawn third is equal. Then the probability a red ball is drawn third is 2/9. The answer is A. #### A QUESTION:If the sides of a triangle are 26 cm, 24 cm and 10 cm, what is its area? options: A)120 cm2 B)187 cm2 C)178 cm2 D)189 cm2 E)176 cm2 SOLUTION:The triangle with sides 26 cm, 24 cm and 10 cm is right angled, where the hypotenuse is 26 cm. Area of the triangle = 1/2 * 24 * 10 = 120 cm2 Answer: A #### A QUESTION:The average of 6 no.'s is 3.95. The average of 2of them is 3.4, while the average of theother 2 is 3.85. What is the average of the remaining 2 no's? options: A)3.4 B)3.9 C)4.1 D)4.2 E)4.6 SOLUTION:Sum of the remaining two numbers = (3.95 * 6) - [(3.4 * 2) + (3.85 * 2)] = 23.70 - (6.8 + 7.7) = 23.70 - 14.5 = 9.20. Required average = (9.2 / 2) = 4.6. E #### E QUESTION:A car travels from P to Q at a constant speed. If its speed were increased by 20km/hr, it would have taken two hour lesser to cover the distance. It would have taken further 30 minutes lesser if the speed was further increased by 10 km/hr. The distance between the two cities options: A)100 km B)120 km C)150 km D)180 km E)None of these SOLUTION:Explanation : Let the distance between two cities = D, D = x*t (x = usual speed and t is the actual time) D = (X + 20)*(T -2) and D = (X +30)*(T – 2.5) Solve the above equation, u will get T = 5 and X = 30, so distance = 30*5 = 150 km Answer – C #### C QUESTION:How many two digit numbers of distinct digits can be formed by using digits 1, 2, 3, 4, 5 and 6 such that the numbers are divisible by 9? options: A)1 B)2 C)4 D)6 E)8 SOLUTION:CONCEPT: A number will be divisible by 9 if sum of all the digits of the number is divisible by 9 Here the Possible sum of the two distinct digits can be 9 only in order to satisfy the given condition If sum of Digits = 9, No. =36, 45, 54, 63 --- 4 Cases Answer: option C #### C QUESTION:If x^2 + 1/x^2 = 9, what is the value of x^4 + 1/x^4 ? options: A)10 B)72 C)79 D)16 E)18 SOLUTION:IMPORTANT: I notice that if we SQUARE x², we get x⁴, and if we SQUARE 1/x², we get 1/x⁴, so let's see what happens if we take the equation x² + 1/x² = 9 andSQUAREboth sides: (x² + 1/x²)²= 81 So, (x² + 1/x²)(x² + 1/x²) = 81 Expand to get: x⁴ + 1 + 1 + 1/x⁴ = 81 Simplify: x⁴ + 1/x⁴ = 79 Answer: C #### C QUESTION:There are 100 men in town. Out of which 85% were married, 70% have a phone, 75% own a car, 80% own a house. What is the maximum number of people who are married, own a phone, own a car and own a house? options: A)20 B)15 C)10 D)5 E)None of these SOLUTION:% of married = 85% % of phone = 70% % of car = 75% % of house = 80. Therefore, % of not married = 15% % of not having phone = 30% % of not owning car = 25% % of not having house = 20% So, % of not having any of these things = 15 +25+ 30 + 20 = 90% So, % of people having all = 100 -90 = 10% Thus, people = 10. ANSWER -OPTION C #### C QUESTION:Set A contains all the even numbers between 8 and 50 inclusive. Set B contains all the even numbers between 108 and 150 inclusive. What is the difference between the sum of elements of set B and the sum of the elements of set A? options: A)2200 B)2550 C)5050 D)6275 E)11325 SOLUTION:Set A contains 8, 10, 12... 50 Set B contains 108 , 110 , 112 ... 150 Number of terms in each set = 22 Difference between corresponding terms in set A and B = 100 Difference between Sum of set B and set A = 100*22 = 2200 Answer A #### A QUESTION:If HARD is coded as 1357 and SOFT is coded as 2468 what will 21448 stand for? options: A)SHOOR B)SHOOA C)SHOOT D)SHEOT E)SWOOT SOLUTION:HARD = 1357 => 1=H, 3=A , 5=R , 7=D SOFT = 2468 => 2=S, 4=O , 6=F , 8=T so, 21448 = SHOOT ANSWER:C #### C QUESTION:In what time will a train 100 m long cross an electric pole, it its speed be 144 km/hr? options: A)2.5 sec B)4.25 sec C)5 sec D)12.5 sec E)12 sec SOLUTION:Speed = 144 * 5/18 = 40 m/sec Time taken = 100/40 = 2.5 sec. ANSWER:A #### A QUESTION:Right 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 ≤ x ≤ 2 and 4 ≤ y ≤ 9 , then how many different triangles can be drawn that will meet these conditions? options: A)54 B)432 C)864 D)2,916 E)148,824 SOLUTION:We 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. Choose the (x,y) coordinates for vertex A: 9C1*4C1; Choose 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); Choose 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). 9C1*4C1*8C1*3C1=864. Answer: C. #### C QUESTION:On January 1, 2010, Dolly invests 30% of his retirement savings in Antarctic largecap stocks, 30% in Antarctic midcaps, and 40% in Antarctic smallcaps. In 2010, largecaps rise 10%, midcaps rise 20%, and smallcaps rise 15% in the Antarctic stock market; however, in 2011, largecaps fall 20% and midcaps fall 10%, while smallcaps rise x% in Antarctica. If, on January 1, 2012, Dolly has the same total amount of retirement savings as he did two years before, then x is between options: A)10 and 20 B)20 and 30 C)30 and 40 D)40 and 50 E)50 and 60 SOLUTION:Pick a smart number for the total retirement savings Dolly starts with—say, $10,000. (If you pick $100, you’ll wind up needing to track decimals, so give yourself more zeros to start with.) Here are the starting values: L = $3000 M = $3000 S = $4000 Apply the first year’s changes, so that you have these numbers on 1/1/2012: Newer L = $3000 + 10% = $3300 Newer M = $3000 + 20% = $3600 Newer S = $4000 + 15% = $4600 Now apply the second year’s changes to L and M: Newest L = $3300– 20% = $3300– $660 = $2640 Newest M = $3600– 10% = $3600– $360 = $3240 Add these to get $5880. So the newest S must be $10,000 (the target final total of Dolly’s retirement savings) minus $5880, $4120 The dollar change in S from 1/1/12 to 1/1/13 is $4600 – $480 = $4120. So the question is this: what percent change does $480 represent, from a starting point of $4600? Since $4600 is a nasty divisor, switch to benchmarks: 10% of $4600 = $460. So 20% is just double that, or $920. And so on. From this $480 lies between $460 and $920 The correct answer is A. #### A QUESTION:The HCF and LCM of two numbers m and n are respectively 6 and 210. If m + n = 72, then 1/m + 1/n is equal to options: A)1/35 B)3/35 C)5/37 D)2/35 E)None SOLUTION:Answer We have, m x n = 6 x 210 = 1260 ∴ 1/m + 1/n = (m + n)/mn = 72/1260 = 4/70 = 2/35 Correct Option: D #### D QUESTION:(128.5 x 32) + (13.8 x 30) = ? x 25 options: A)524.48 B)556.02 C)574.36 D)181.04 E)595.46 SOLUTION:Explanation : ? = (128.5 x 32) + (13.8 x 30)/25 = 4112 + 414/25 = 181.04 Answer : Option D #### D QUESTION:The roof of an apartment building is rectangular and its length is 4 times longer than its width. If the area of the roof is 900 feet squared, what is the difference between the length and the width of the roof? options: A)38. B)40. C)42. D)44. E)45. SOLUTION:Let the width= x x*4x=900 x^2= 225 x= 15 Length= 4*15= 60 difference= 60-15= 45 E is the answer #### E QUESTION:If x is the smallest positive integer such that 4,536 multiplied by x is the square of an integer, then x must be options: A)12 B)21 C)16 D)17 E)14 SOLUTION:4536= 6*6*3*3*7*3, so we need one 7 and one 3 to make it a square of a number. so 7*3= 21 Ans: B #### B QUESTION:Distances from you to Man united is written below. CHELSEA and ARSENAL are 700 kms away SPURS 1800 kms away WOLVES 200 kms away Based on the system , How far should it be to MANCITY ? options: A)1100 miles. B)3100 miles. C)2100 miles. D)5100 miles. E)4100 miles. SOLUTION:Solution: 2100 miles. Each vowel equivalent to 500 and each consonant equivalent to -200 Answer C #### C QUESTION:Which of the following options is an appropriate approximate value in the following equation’? 3 4/3 of 155.83+22% of 1547= ? - 504.7 options: A)1855.94 B)1557.94 C)1257.94 D)1837.94 E)1857.94 SOLUTION:3 4/3 of 155.83+22% of 1547= ? - 504.7 1012.9+340.34= ? - 504.7 1012.9+340.34 +504.7= ? ≈ 1857.94 Answer E #### E QUESTION:A person can swim in still water at 20 km/h. If the speed of water 12 km/h, how many hours will the man take to swim back against the current for 40km? options: A)3 B)4 C)5 D)6 E)7 SOLUTION:M = 20 S = 12 US = 20 - 12 = 8 D = 40 T = 40/8 = 5 Answer:C #### C QUESTION:A small family consisting of 4 ( father , mother , son , daughter ) goes to a photo studio . Father says to the photographer , " I need all the possible photographs of our family " . how many pictures can he take , such that at least one person should be there in the photo options: A)61 B)62 C)63 D)64 E)65 SOLUTION:4C1+4C2+4C3+4C4=15. If their positions also takes into consideration then the ans will be 64 ANSWER:D #### D QUESTION:The probability that Alex will solve a problem is 1/5. What is the probability that he solves at least one problem out of 4 problems? options: A)64/125 B)256/625 C)64/625 D)369/625 E)359/625 SOLUTION:The probability that Alex will not solve a problem = 4/5. The probability that Alex will not solve 10 problems = (4/5)4 = 256/625. Hence, the probability that Alex will solve at least one problem = 1 - 256/625 = 369/625. ANSWER:D #### D QUESTION:The ratio E, by volume of soap to alcohol to water in a 76 litre solution is 2: 50: 100 . The solution is then altered by adding more soap, alcohol and water.After this alteration the ratio, by volume of soap to water in the solution doubles whereas the ratio, by volume of soap to water remains the same as before. What COULD BE the resulting volume. options: A)79 litres B)78 litres C)77 litres D)152 liters E)304 litres SOLUTION:I guess it should be the ratio E, by volume ofsoaptowaterin the solutiondoubleswhereas the ratio, by volume ofalocoholtowaterremains thesameas before 2:50: 100 => 1 : 25 : 50. If we add all the parts, we get 76 liters So we have 1 liters of Soap, 25 liters of Alcohol and 50 liters of Water. Now as per the Question, Soap : Water doubles but alcohol to water remains the same. So Soap becomes 2 liters, Alcohol remains 25 liters and Water remains at 50 liters. Hence 77 liters - Option C) #### C QUESTION:The total cost of 100 paper plates and 200 paper cups is $7.50 At the same rates what is the total cost of 20 of the plates and 40 of the cups? options: A)$.90 B)$1.00 C)$1.20 D)$1.50 E)$1.60 SOLUTION:U dont need to go through all this What u have with u is 100 P + 200 C = $7.50 Just divide the equation by 5 and you will get what u are looking for 20P + 40 C = $1.50 Therefore OA is D #### D QUESTION:If x is divisible by 2 and 7, which of the following must divide evenly into x? I. 60 II. 32 III. 14 options: A)I,II only B)I,III only C)I only D)III only E)II only SOLUTION:If x is divisible by 2,7 means it will be = or > 14, 28,42 etc... That are not divisible by 60, 32. So, the answer is D #### D QUESTION:Two 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 seconds. What is the length of the fast train? options: A)23 m B)23 (2/9)m C)38 (8/9)m D)29 m E)28 m SOLUTION:Relative speed = (40 - 20) km/hr = (20 x(5/18))m/sec = (50/9)m/sec. Therefore Length of faster train = ((50/9) x 7) m = (350/9)m = 38 (8/9) m. C #### C QUESTION:A, B and C have Rs.400 between them, A and C together have Rs.200 and B and C Rs.350. How much does C have? options: A)A)150 B)B)140 C)C)130 D)D)120 E)E)110 SOLUTION:A+B+C = 400 A+C = 200 B+C = 350 -------------- A+B+2C = 550 A+B+C = 400 ---------------- C = 150 Answer:A #### A QUESTION:Running at their respective constant rates, machine X takes 6 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 2w widgets? options: A)8 B)6 C)4 D)10 E)12 SOLUTION:Together they make 5/4 w widgets in 3 days. So they make w widgets in 3*4/5 = 12/5 days. 1/(t+2) + 1/t = 5/12 Now, calculating this is really cumbersome so try to plug in options to get to the answer. If machine X takes 12 days to produce 2w widgets, it would take 6 days to make w widgets, t would be 4. 1/6 + 1/4 = 5/12 It works so t = 4. Answer : A #### A QUESTION:Solve the equation for x : 19(x + y) + 17 = 19(-x + y) - 21 options: A)1 B)-1 C)2 D)-2 E)3 SOLUTION:B -1 19x + 19y + 17 = -19x + 19y - 21 38x = -38 => x = -1 #### B QUESTION:Two dice are thrown simultaneously. What is the probability of getting two numbers whose product is even? options: A)5/5 B)5/9 C)3/4 D)5/7 E)5/2 SOLUTION:In a simultaneous throw of two dice, we have n(S) = (6 x 6) = 36. Then, E = {(1, 2), (1, 4), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 2), (3, 4), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 2), (5, 4), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}=27 The probability = 27/36 = 3/4. Answer: C #### C QUESTION:The total of a company's assets in 1994 was 100% greater than the total in 1993, which in turn was 400% 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? options: A)5N B)7N C)10N D)15N E)20N SOLUTION:In 1992, the company's assets were N. In 1993, the company's assets were N + 4N = 5N. In 1994, the company's assets were 5N + 5N = 10N. The answer is C. #### C QUESTION:The sum of two numbers is 40 and their product is 300. What will be the sum of their reciprocals? options: A)1/40 B)8/75 C)75/4 D)2/15 E)75/6 SOLUTION:(1/a)+(1/b)=(a+b)/ab=40/300=2/15 ANSWER:D #### D QUESTION:150 ml of 30% sulphuric acid was added to approximate 400 ml of 12% sulphuric acid solution. Find the approximate concentration C of the acid in the mixture? options: A)1/2 B)1/3 C)1/4 D)1/6 E)1/5 SOLUTION:Do not need any computation 30%-----------21%---------12% if volume of both sol. were equal the concentration C would be 21%=1/5, but 12% is more than 3 times only possibility is 1/6 D #### D QUESTION:A man has some hens and cows. If the number of heads be 44 and the number of feet equals 140, then the number of hens will be: options: A)22 B)23 C)18 D)26 E)28 SOLUTION:let hens be x and cows be y now, feet: x*2+y*4=140 heads: x*1+y*1=44 implies, 2x+4y=140 and x+y=44 solving these two equations, we get x=18 and y=26 Therefore, hens are 26. ANSWER:C #### C QUESTION:Bullock likes to keep a spare tyre in his car every time. On a certain day, he travels 1, 00,000 km and just to make the most of all the tyres, he changes the tyres between his journey such that each tyre runs the same distance. What is the distance traveled by each tyre? options: A)75000 B)80000 C)90000 D)67800 E)50000 SOLUTION:B 80,000. The distance traveled by each tyre: 4/5 * 1, 00, 000km = 80,000 km. #### B QUESTION:The 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? options: A)6 kmph B)7 kmph C)9 kmph D)4 kmph E)2 kmph SOLUTION:S = 1 M = x DS = x + 1 US = x - 1 35/(x + 1) + 35/(x - 1) = 12 x = 6 Answer: A #### A QUESTION:Concentrated 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? options: A)24. B)28. C)36. D)42. E)48. SOLUTION:concentrated pineapple juice since height of a tube is 15 inches , the tubes can fit only in one way . now, diameter of each tube = 5 inches therefore, 4*2 can be put in each wooden box in 3 boxes 3*4*2 can be accommodated = 24=A #### A QUESTION:What is the present worth of Rs. 132 due in 2 years at 5% simple interest per annum? options: A)288 B)266 C)120 D)277 E)6123 SOLUTION:Let the present worth be Rs. x. Then, S.I. = (132 - x) (x * 5 * 2) / 100 = (132 - x) 10x = 13200 - 100x 110x = 13200 => x = 120. Answer: C #### C QUESTION:What will $2500 amount to in three years if it is invested at 20% per year compound interest, with the interest being compounded annually? options: A)$3760 B)$3980 C)$4210 D)$4320 E)$4760 SOLUTION:After one year: 1.2 * $2500 After two years: (1.2)^2 * $2500 After three years: (1.2)^3 * $2500 = $4320 The answer is D. #### D QUESTION:A 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? options: A)1 B)6 C)7 D)9 E)3 SOLUTION:Speed of train relative to man = 60 + 6 = 66 km/hr. = 66 * 5/18 = 55/3 m/sec. Time taken to pass the men = 110 * 3/55 = 6 sec. Answer: B #### B QUESTION:If |x + 132| = 32 what is the sum of all the values of x. options: A)-264 B)200 C)-64 D)0 E)-328 SOLUTION:There will be two cases x+132 = 32 and x+132 = -32 Solve for x => x=32-132=> x=-100 or x= -32 - 132 => x= -164 The sum of both values will be -164 + -100 = -264 Answer is A #### A QUESTION:John purchased a fridge & 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. options: A)Rs. 100 B)Rs. 150 C)Rs. 200 D)Rs. 300 E)Rs. 350 SOLUTION:Let the SP of the refrigerator and the mobile phone be Rs. r and Rs. m respectively. r = 15000(1 - 4/100) = 15000 - 600 m = 8000(1 + 10/100) = 8000 + 800 Total SP - Total CP = r + m - (15000 + 8000) = -600 + 800 = Rs. 200 As this is positive, an overall profit of Rs. 200 was made. C #### C QUESTION:A woman begins bicycling with a pace of 8 kmph and she increases her pace every two hours by 2 kmph. She does not increase her pace as soon as her pace reaches her maximum speed of 12 kmph. How many hours did she bicycle if she traveled 64 kms? options: A)6 1⁄7 hours B)6 2⁄7 hours C)8 2⁄7 hours D)Cannot be determined E)None of these SOLUTION:Distance covered in first two hours = 8 × 2 = 16 km Distance covered in next two hours = 10 × 2 = 20 km Distance covered in next two hours = 12 × 2 = 24 km Distance covered in first six hours 16 + 20 + 24 = 60 km Remaining distance = 64 – 60 = 4 km. Now, this distance will be covered at the speed of 12 km/hr. ∴ Time taken = 4⁄12 = 1⁄3 hour. Total time= 6 + 1⁄3 = 6 1⁄3 hour Answer E #### E QUESTION:66 cubic centimetres of silver is drawn into a wire 1 mm in diameter. The length of the wire in metres will be : options: A)84 m B)88 m C)120 m D)137 m E)None SOLUTION:Sol. Let the length of the wire b h. Radius = 1/2 mm = 1/20 cm. Then, 22/7 * 1/20 * 1/20 * h = 66 ⇔ = [66 * 20 * 20 * 7 / 22] = 8400cm = 84 m. Answer A #### A QUESTION:The area of a rectangular plot is 460 square metres. If the length is 15% more than the breadth, what is the breadth of the plot? options: A)14 M B)20 M C)18 M D)12 M E)15 M SOLUTION:LB = 460 M2 LET BREATH = B L = B * (100 + 15)/100 = 115B/100 FROM THESE 115B/100 * B = 460 B2 = 46000/115 = 400 B = ROOT OF 400 = 20 M ANSWER B #### B QUESTION:Simple interest on a certain sum of money for 3 years at 8% per annum is half the compound interest on Rs. 4000 for 2 years at 10% per annum. The sum placed on simple interest is options: A)Rs.1550 B)Rs.1650 C)Rs.1750 D)Rs.2000 E)None SOLUTION:Solution C.I. =Rs[4000x(1+10/100)²-4000] Rs.(4000x11/10x11/10-4000) = Rs.940. Sum =Rs. [420x100 /3x8] = Rs.1750. Answer C #### C QUESTION:A certain shade of gray paint is obtained by mixing 3 parts of white paint with 5 parts of black paint. If 2 gallons of the mixture is needed and the individual colors can be purchased only in one gallon or half gallon cans, what is the least amount of paint W, in gallons, that must be purchased in order to measure out the portions needed for the mixture? options: A)2 B)2 1/2 C)3 D)3 1/2 E)4 SOLUTION:Given W:B = 3:5 That means say 3 gallons of white paint + 5 gallons of black paint = 8 gallons of paint mixture. But we want least amount of whiteblack paints for minimum of 2 gallons of mixture, so lets reduce keeping same ratio, 1.5 : 2.5 gives 1.5 + 2.5 = 4 gallons of mixture, but we want only 2 gallons, lets further reduce 0.75: 1.25 gives 1+1.5 =2.5 gallons of mixture. This looks ok, but lets reduce further just to be sure 0.375: 0.625 gives 0.5 + 1 = 1.5 gallons of mixture, thats less than 2 gallons of mixture, so not acceptable. So correct ans is 2.5 gallons. B #### B QUESTION:Find the total number of prime factors in the expression (4)^11 x (7)^5 x (11)^2. options: A)29 B)27 C)28 D)24 E)21 SOLUTION:(4)^11x (7)^5 x (11)^2 = (2 x 2)^11 x (7)^5 x (11)^2 = 2^11 x 2^11 x7^5x 11^2 = 2^22 x 7^5 x11^2 Total number of prime factors = (22 + 5 + 2) = 29. Answer is A. #### A QUESTION:How many diagonals does a 62-sided convex polygon have? options: A)1829 B)2356 C)3458 D)3843 E)4820 SOLUTION:A 62-sided convex polygon has 62 vertices. If 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. If 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 However, we must recognize that we have counted every diagonal twice. To account for counting each diagonal twice, we must divide 3658 by 2 to get 1829. The answer is A. #### A QUESTION:If n=3*4*p where p is a prime number greater than 3,how many different positive non-prime divisors does n have, excluding 1 and n? options: A)Six B)Seven C)Eight D)Nine E)Ten SOLUTION:n=3∗2^2∗p Number of divisors = 2 * 3 * 2 = 12 The 12 divisors includes 1, n, 3, 2 and p Number of different non prime divisors excluding 1 and n = 12 - 5 = 7 Answer: B #### B QUESTION:The 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 options: A)3 months B)4 months C)6 months D)8 months E)10 months SOLUTION:Solution S.I on Rs. 1600 = T.D on Rs. 1680. Rs.1600 is the P.W of Rs.1680. Rs.80 is S.I on Rs.1600 at 15%. Time = (100x80 / 600x15) = 1/3 year = 4 months. Answer B #### B QUESTION:In a Lake, there is a patch of lily pads. Every day, the patch doubles in size. It takes 39 days for the patch to cover the entire lake, how many days would it take the patch to cover half of the lake? options: A)36 B)2^4*3 C)24 D)38 E)47 SOLUTION:Working backward from the day it's covered: day 39: fully covered day 38: half covered So 38 days ANSWER:D #### D QUESTION:The volume of a sphere with radius r is (4/3)*pi*r^3 and the surface area is 4*pi*r^3. If a sperical balloon has a volume of 4500 pi cubic centimeters, what is hte surface area of the balloon in square centimeters? options: A)a. 40 B)b. 100 C)c. 400 D)d. 1,000 E)e. 2,000 SOLUTION:The surface area is 4.pi.r^2 (its area remember not volume) as 4/3.pi.r^3=4500pi r=15 so area = 4.pi.r^2= 900.pi= 900 x 3.14 = 2000 (approx) E #### E QUESTION:Let f(x) = x^2 + bx + c. If f(4) = 0 and f(-3) = 0, then b + c = options: A)18 B)15 C)-13 D)-21 E)-24 SOLUTION:f(x) = x^2 + bx + c. If f(4) = 0 and f(-3) = 0, then b + c = f(4) = 0= 16+4b+c--- Taking 16 to the other side -> 4b+c= -16 f(-3) = 0= 9-3b+c --- taking -3b+c to the other side -> 3b-c=9 When we add these 2 equations, we get 7b= -7---> b= -1 And while substituting b= -1 we get c= -12. b+c= -13--- Answer C #### C QUESTION:All of the stocks on the over-the-counter market are designated by either a 4-letter or a 5-letter code 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? a. b. c. d. e. options: A)2(26^5) B)26(26^4) C)27(26^4) D)26(26^5) E)27(26^5) SOLUTION:no of different stocks for 4-letter code = 26^4 no of different stocks for 4-letter code = 26^5 total = 26^4 + 26^5 = 26^4(26+1) = 27(26^4) ANS:C #### C QUESTION:A car covers a distance of 624 km in 3 hours. Find its speed? options: A)104 kmph B)194 kmph C)208 kmph D)174 kmph E)101 kmph SOLUTION:624/3 =208 kmph Answer:C #### C QUESTION:Find the average marks of all the students in 2 separate classes, if the average marks of students in the first class of 55 students is 60 and that of another class of 48 students is 58 options: A)55.1 B)51.1 C)53.1 D)52.1 E)59.1 SOLUTION:Sum of the marks for the class of 55 students = 55 * 60 = 3300 Sum of the marks for the class of 48 students = 48 * 58 = 2784 Sum of the marks for the class of 103 students = 3300 + 2784 = 6084 Average marks of all the students = 6084/103 = 59.1 Answer:E #### E <<<Examples ends QUESTION:Ifaequals the sum of the even integers from 2 to 60, inclusive, andbequals the sum of the odd integers from 1 to 59, inclusive, what is the value of a - b ? options: A)1 B)10 C)30 D)20 E)21 SOLUTION:This is a solution from Beatthegmat: even numbers: (60-2)/2 + 1 = 30 even integers. (60+2)/2 = 31 is the average of the even set. sum = avg*(#of elements) = 31*30 = 930 = a odd numbers: (59-1)/2 + 1 = 30 odd integers. (59+1)/2 = 30 is the average of the odd set. sum = avg*(#of elements) = 30*30 = 900 = b a-b = 930 - 900 = 30. Answer : C #### C

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:If Tim had lunch at $60.50 and he gave 20% tip, how much did he spend? options: A)$30.60 B)$72.60 C)$70.60 D)$40.60 E)$50.60 SOLUTION:The tip is 20% of what he paid for lunch. Hence tip = 20% of 60.50 = (20/100)*60.50 = $12.1 Total spent 60.50 + 12.1 = $72.6 correct answer B #### B QUESTION:A 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 1 buckles is how many times that of 5 buckles and 6 buttons? options: A)7/15. B)2/5. C)6/11. D)5/9. E)8/15. SOLUTION:2buttons + 2buckles = 1/3(11buckles + 3buttons) 6buttons + 6buckles = 11buckles + 3buttons 3buttons = 5buckles Weight of 3buttons and 1buckles = 5buckles + 1buckles = 6buckles Weight of 6buttons and 5buckles = 10buckles + 5buckles = 15buckles (3buttons and 2buckles) = x * (6buttons and 5buckles) 6 = x*15 x = 6/15=2/5 Answer: B #### B QUESTION:A 45° -45° - 90° right triangle has hypotenuse of length h. What is the area Q of the triangle in terms of h? options: A)h/ √2 B)h/2 C)h/4 D)(h)^2 E)(h)^2/4 SOLUTION:IF...each of the two shorter sides = 3, then the hypotenuse = H = 3(root2). The AREA Q= (1/2)(Base)(Height) = (1/2)(3)(3) = 9/2. So we're looking for an answer that = 9/2 when H = 3(root2). There's only one answer that matches... E #### E QUESTION:If x and y are positive integers, find which of the following CANNOT be the greatest common divisor of 25x and 20y? options: A)5 B)5(x-y) C)20x D)20y E)35x SOLUTION:We are looking for a choice that CANNOT be the greatest common divisor of 25x and 20y ...which means 35x and 20y when divided by the answer choice the quotient should not be a integer. lets check a. 5 25x/5 = 5x and 20y/5 = 4y both are integers so eliminate b. 5(x-y) when x = 2 and y = 1 it could be be the greatest common divisor ..so eliminate c. 20x when x = 1 its 20 and 20 cannot be the greatest common divisor of 25x and 20y ... or 25x/20x = 5/4 which is not a integer. so answer is C. #### C QUESTION:power windows: 60% anti-lock brakes: 25% CD player: 45% The table above shows the number of vehicles at Bill's car dealership that have certain features. No vehicle has all three features, but 10% have power windows and anti-lock brakes, 15% have anti-lock brakes and a CD player, and 22% have power windows and a CD player. What percent of the vehicles at Bill's car dealership have a CD player but no power windows or anti-lock brakes? options: A)25 B)8 C)11 D)3 E)0 SOLUTION:Answer: B Were looking for the number of cars with a CD player but no other features. We know that 40% of the cars have a CD player, 15% have a CD player and anti-lock brakes, while 22% have a CD player and power windows. Since no car has all three features, those account for all of the possibilities except for what were looking for. If a car has a CD player, it must either have anti-lock brakes, power windows, or no other features. Since the total of cars with a CD player is 45%, we can set up the following equation: 45=15+22+x x=8, choice B. #### B QUESTION:A 25% stock yielding 20% is quoted at: options: A)s. 83.33 B)s. 110 C)s. 112 D)s. 125 E)s. 140 SOLUTION:Income of Rs 20 on investment of Rs 100 Income of Rs 25 on investment of ? = (25*100)/20=125 ANSWER:D #### D QUESTION:To 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. options: A)530 B)675 C)330 D)987 E)854 SOLUTION:Let x e 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: 3⋅25+(x−3)⋅30=75+30(x−3) Therefore: 25x=75+30(x−3)−100 25x=75+30x−90−100 190−75=30x−25 115=5x x=23 So the company worked 23 days and they made 23⋅25+100=675 pieces. #### B QUESTION:The average salary of all the workers in a workshop is Rs. 8000. The average salary of 7 technicians is Rs. 16000 and the average salary of the rest is Rs. 6000. The total number of workers in the workshop is options: A)20 B)21 C)22 D)35 E)NONE SOLUTION:Sol. Let the total number of workers be x. Then, 8000x = (16000 × 7) + 6000 ( x – 7) ‹=› 2000x = 70000 ‹=› x = 35. Answer D #### D QUESTION:The ratio of the cost price and the selling price is 4:5. The profit percent is: options: A)233 B)37 C)25 D)27 E)11 SOLUTION:Explanation: Let C.P. = Rs. 4x. Then, S.P. = Rs. 5x Gain = (5x - 4x) = Rs. x Gain % = (x * 100)/ 4x = 25%. Answer: C #### C QUESTION:Dany bought a total of 20 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? options: A)4 B)10 C)7 D)8 E)12 SOLUTION:Let 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 20. Hence X + Y = 20 If X is the number of cards at $0.25, then the X cards cost 0.25 X If Y is the number of cards at $0.15, then the Y cards cost 0.15 Y The total cost of the X cards and the the Y cards is known to be $4.2 and also given by 0.25 X + 0.15 Y = 4.2 We now need to solve the system of equations X + Y = 20 0.25 X + 0.15 Y = 4.2 The first equation gives Y = 20 - X. Substitute y by 20 - x in the second equation and solve 0.25 X + 0.15 (20 - X) = 4.2 X(0.25 - 0.15) + 3 = 4.2 0.1 X = 1.2 X = 12 and Y = 20 - 12 = 8 correct answer D #### D QUESTION:A man invested an amount of Rs.8000 in a fixed deposit scheme for 2 years at compound interest of 5% per annum. How much amount will Albert get on maturity of the fixed deposit ? options: A)Rs.8600 B)Rs.8620 C)Rs.8820 D)Rs. 8840 E)Rs. 8940 SOLUTION:Amount = 8000 *1+(5/100)2 = 8000 *21/20 * 21/20 = Rs.8820 ANSWER:C #### C QUESTION:For 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 + [8.3] - 6.6? options: A)12.6. B)15.8. C)14.4. D)16.2. E)16.4. SOLUTION:[6.5] x [2/3] + [2] x 7.2 + [8.3] - 6.6 = 6*0 + 2*7.2 + 8 - 6.6 = 0 +14.4 +1.4 15.8 Answer B #### B QUESTION:If the simple interest on a sum of money for 2 years at 5% per annum is Rs. 50, what is the compound interest on the same sum at the rate and for the same time? options: A)Rs. 51.25 B)Rs. 51.22 C)Rs. 51.219 D)Rs. 51.18 E)Rs. 51.11 SOLUTION:Explanation: Sum = (50 * 100) / (2 * 5) = Rs. 500 Amount = [500 * (1 + 5/100)2] = Rs. 551.25 C.I. = (551.25 - 500) = Rs. 51.25. Answer:A #### A QUESTION:The roof of an apartment building is rectangular and its length is 4 times longer than its width. If the area of the roof is 900 feet squared, what is the difference between the length and the width of the roof? options: A)38. B)40. C)42. D)44. E)45. SOLUTION:Let the width= x x*4x=900 x^2= 225 x= 15 Length= 4*15= 60 difference= 60-15= 45 E is the answer #### E QUESTION:If a train, travelling at a speed of 180 kmph, crosses a pole in 5 sec, then the length of train is? options: A)250 m B)112 m C)117 m D)125 m E)123 m SOLUTION:A A = 180 * 5/18 * 5 = 250 m #### A QUESTION:Express of the following as a fraction: 25% options: A)1/4 B)1/8 C)2/9 D)3/6 E)None of them SOLUTION:25% = 25/100= 1/4. Answer is A. #### A QUESTION:In 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? options: A)6^6 ways B)8^9 ways C)7^8 ways D)8^7 ways E)8^6 ways SOLUTION:6 people can be prized with distinct prizes in 6^6 ways ANSWER:A #### A QUESTION:I have a three digit number in my mind. In that number, the tens digit is seven more than the ones digit and the hundreds digit is six less than the tens digit. What is the number? options: A)281 B)239 C)254 D)276 E)277 SOLUTION:A 281 #### A QUESTION:In what ratio P:Q should the Mixture P of milk and water in the ratio of 5:3 be mixed with another Mixture Q of milk and water in the ratio 1:3 so that the resultant mixture contains equal quantities of milk and water? options: A)5:2 B)4:3 C)3:2 D)2:1 E)4:1 SOLUTION:(5/8)*P +(1/4)*Q = (3/8)*P+(3/4)*Q 2P=4Q P/Q = 2/1 The answer is D. #### D QUESTION:A university cafeteria offers 1 flavors of pizza - pepperoni. 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 ? options: A)4 B)8 C)12 D)1 E)32 SOLUTION:1 flavours * 1 choices = 1C1*1C1 = 1*1=1=D #### D QUESTION:At what price must Kantilal sell a mixture of 80kg. Sugar at Rs.6.75 per kg. with 120 kg. at Rs.8 per kg. to gain 20% ? options: A)Rs.7.50 per kg B)Rs.8.20 per kg C)Rs.8.85 per kg D)Rs.9 per kg. E)None SOLUTION:Explanation: Total C.P of 200 kg of sugar = Rs.(80×6.75+120×8)=Rs.1500 C.P of 1 kg = Rs.[1500/200]=Rs.7.50 Gain required = 20% S.P of 1 kg = (120% of Rs.7.50) = Rs.[120/100×7.50]=Rs.9 per kg. Correct Option : D #### D QUESTION:40, 45, 50, 50, 60, 75, 75, 100, 100, 100. The list above shows the scores of 10 schoolchildren on a certain test. If the standard deviation of the 10 scores is 22.7, rounded to the nearest tenth, how many of the scores are more than 1 standard deviation below the mean of the 10 scores? options: A)1 B)2 C)3 D)4 E)5 SOLUTION:The average of {40, 45, 50, 50, 60, 75, 75, 100, 100, 100} is 69.5. 1 standard deviation below the mean is 69.5 - 22.7 = 46.8. Hence there are two scores (40 and 45) more than 1 standard deviation below the mean. Answer B. #### B QUESTION:Two trains of length 160 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? options: A)28 B)266 C)990 D)20 E)22 SOLUTION:Relative speed = (42 + 30) * 5/18 = 4 * 5 = 20 mps. Distance covered in passing each other = 160 + 280 = 440 m. The time required = d/s = 440/20 = 22 sec. Answer: E #### E QUESTION:Which of the following is a prime number ? options: A)27 B)45 C)97 D)98 E)100 SOLUTION:Clearly, 97 is a prime number. #### C QUESTION:A train is 485 meter long is running at a speed of 45 km/hour. In what time will it pass a bridge of 140 meter length options: A)20 seconds B)30 seconds C)40 seconds D)50 seconds E)None of these SOLUTION:Explanation: Speed = 45 Km/hr = 45*(5/18) m/sec = 25/2 m/sec Total distance = 485+140 = 625 meter Time = Distance/speed =625∗2/25=50seconds Option D #### D QUESTION:Find the value of x which satisfies the relation Log10 3+log10 (4x+1)=log10 (x+1)+1 options: A)2.5 B)3.5 C)3.2 D)6.8 E)9.8 SOLUTION:[log10a + log10b = log10 ab] and also 1 can be written as log10 10, so question can be rewritten as: log10 (3(4x+1))=log10(10(x+1)), this can be solved to get 12x+3=10x+10, that gives x=7/2=3.5 ANSWER:B #### B QUESTION:Length of a rectangular plot is 28 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? options: A)54 m B)64 m C)74 m D)84 m E)94 m SOLUTION:Let breadth = x metres. Then, length = (x + 28) metres. Perimeter = 5300 m = 200 m. 26.50 2[(x + 28) + x] = 200 2x + 28 = 100 2x = 72 x = 36. Hence, length = x + 28 = 64 m B #### B QUESTION:In a school of 700 students, 45% wear blue shirts, 23% wear red shirts, 15% wear green shirts, and the remaining students wear other colors. How many students wear other colors (not blue, not red, not green)? options: A)109 B)119 C)129 D)139 E)149 SOLUTION:45 + 23 + 15 = 83% 100 – 83 = 17% 700 * 17/100 = 119 The answer is B. #### B QUESTION:Out of 470 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 ? options: A)80 B)150 C)100 D)180 E)220 SOLUTION:n(A)=325,n(B)=175,n(AuB)=470-50=420. Required number = n(AnB)=n (A)+n (B)-n(AuB)=325+175-420=80. Answer is A #### A QUESTION:Bruce 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? options: A)1040 B)1050 C)1055 D)1065 E)1075 SOLUTION:Cost of 8 kg grapes = 70 × 8 = 560. Cost of 9 kg of mangoes = 55 × 9 = 490. Total cost he has to pay = 560 + 490 = 1055 C #### C QUESTION:150 candies are distributed to children with the same number of candies for each child. What can’t be the range which includes the number of children? options: A)1~10 B)10~20 C)20~30 D)45~55 E)55~65 SOLUTION:150 = 2*3*5^2 There are factors in each range except for 55~65 The answer is E. #### E QUESTION:Faiza has 4 purses, she gives 3 purse as gift. Now how many purse did she have ? options: A)2 B)5 C)1 D)9 E)4 SOLUTION:4-3=1. Answer is C #### C QUESTION:12,31,68,129,220,? options: A)129 B)220 C)387 D)347 E)520 SOLUTION:2*2*2 + 4 = 12 3*3*3 +4 = 31 4*4*4 + 4 = 68 5*5*5 + 4 = 129 6*6*6 + 4 = 220 7 *7 *7 + 4 = 347 ANSWER : D #### D QUESTION:Rice weighing 33/4 pounds was divided equally and placed in 4 containers. How many ounces of rice were in each container? (Note that 1 pound = 16 ounces) options: A)27 B)30 C)33 D)36 E)39 SOLUTION:33/4 ÷ 4 = 33/16 pounds in each container 33/16 pounds * 16 ounces / pound = 33 ounces in each container The answer is C. #### C QUESTION:What is the shortest distance between points (-2, 1) and (2,-2)? options: A)1 B)2 C)3 D)4 E)5 SOLUTION:The shortest distance between any two points is a line. Points are written in the (x,y) format, where x is the x-coordinate and y is the y-coordinate. Calculate the difference between the x and y values of each coordinate. Difference between y values = 1 - (-2) = 1 + 2 = 3 Difference between x values = (-2) - 2 = -4 If you start at (2, -2) and travel over -4 units (i.e., travel to the left) and then travel straight up 3 units, you will end up at (-2, 1). This sketches out a right triangle, where the hypotenuse is the length of the shortest distance between the two points (i.e., a straight line between the two points). Use the Pythagorean Theorem with a = -4 and b = 3 to solve for this distance between the two points. a2+ b2 = c2 (-4)2+ 32 = c2 Solve for c 16 + 9 = c2 25 = c2 c = 5 (Negative 5 cannot be a solution to a length so it is discarded) Answer is E #### E QUESTION:An investor invests in a new fund. The fund averages 20% growth annually for the first three years, but it loses 40% of its value in the fourth year. At the end of four years, the value of the fund is approximately what percent of the original amount? options: A)91.23% B)95.56% C)97.86% D)101.45% E)103.68% SOLUTION:0.6*1.2^3 = 1.0368 The answer is E. #### E QUESTION:P is three times as old as Q. In 11 years, P will be twice as old as Q. How old was P three years ago? options: A)21 B)24 C)27 D)30 E)33 SOLUTION:P = 3Q so Q = P/3 P+11 = 2(Q+11) = 2(P/3+11) P/3 = 11 P = 33 Three years ago, P was 30. The answer is D. #### D QUESTION:The ratio 25:50 expressed as percent equals to options: A)50 % B)85 % C)25 % D)75 % E)None of above SOLUTION:Explanation: Actually it means 25 is what percent of 50, which can be calculated as, (25/50)*100 = 25 * 2 = 50 Answer: Option A #### A QUESTION:The G.C.D. of 1.08, 0.33 and 0.9 is: options: A)0.03 B)0.9 C)0.18 D)0.108 E)None SOLUTION:EXPLANATION Given numbers are 1.08, 0.33 and 0.90. H.C.F. of 108, 33 and 90 is 3, H.C.F. of given numbers = 0.03. Answer A #### A QUESTION:What is the cost of leveling the field in the form of parallelogram at the rate of Rs.50/10 sq.metre, whose base & perpendicular distance from the other side being 54m & 24m respectively? options: A)Rs. 6000 B)Rs. 6300 C)Rs. 6400 D)Rs. 6480 E)Rs. 7000 SOLUTION:Area of the parallelogram = Length of the base * Perpendicular height = 54 * 24 = 1296 m. Total cost of levelling = Rs. 6480 D #### D QUESTION:At the beginning of year 1, an investor puts pp dollars into an investment whose value increases at a variable rate of xnxn per year, where nn is an integer ranging from 1 to 3 indicating the year. If 85<xn<11085<xn<110 for all nn between 1 and 3, inclusive, then at the end of 3 years, the value of the investment must be between? options: A)$p and $2p B)$2pand $5p C)$5p and $10p D)$10p and $ 25p E)$25p and $75p SOLUTION:Since the min rate of interest is 86% the min value of investment will be (1+0.86)^3*p = (1.86^3)*p. Similarly max value will be (2.1)^3*p. 2.1^3 is 9.5 or you can guess little over 8 so 10p may be good estimate. 1.86^3 is trickier to estimate. I knew root(3) = 1.73. So 1.86^2 is close to 3 and 3*1.8 is 5.4. So 5p is a close lower bound. So range is 5p to 10p. Answer C. #### C QUESTION:The mean of 50 observations is 200. But later he found that there is decrements of 15 from each observations. what is the the updated mean is ? options: A)170 B)185 C)190 D)196 E)200 SOLUTION:185 Answer is B #### B QUESTION:A shopping mall give 40% sale on T-shirts and increase 25% price of pants. The cost price of pants and T-shirts are 1500 and 400 respectively. Overall they makes a? options: A)200 B)250 C)300 D)215 E)180 SOLUTION:Let the SP of the pants and T-shirts be Rs. p and Rs. t respectively. p = 1500(1 + 25/100) = 1500 + 375 t = 400(1 - 40/100) = 400 - 160 Total SP - Total CP = p + t - (1500 + 400) = 375 - 160 = Rs. 215 As this is positive, an overall profit of Rs. 500 was made. Answer: D #### D QUESTION:A two digit number reversed and multiplied by 4 is 3 more than the original digit. what is the digit? options: A)61 B)62 C)63 D)64 E)66 SOLUTION:If no is xy , then 10x+y = 4*(10y+x)-3= 40y +4x-3 6x-39y +3 =0 2x-13y +1 =0 13 y =2x+1 when y=1, x=6 so number is 61. ANSWER:A #### A QUESTION:The sector of a circle has radius of 21 cm and central angle 130o. Find its perimeter? options: A)91.5 cm B)89.6 cm C)91.8 cm D)92.5 cm E)99.5 cm SOLUTION:Perimeter of the sector = length of the arc + 2(radius) = (130/360 * 2 * 22/7 * 21) + 2(21) = 47.6 + 42 = 89.6 cm Answer:B #### B QUESTION:Replace X with the appropriate number in 2 , 4 , 6 , 30 , 32 , 34 , X options: A)38 B)8 C)5 D)36 E)37 SOLUTION:D list of consecutive numbers that does not contain a 'e' in the spelling #### D QUESTION:The perimeter of one face of a cube is 48 cm. Its volume will be: options: A)125cm3 B)400cm3 C)250cm3 D)625cm3 E)None of these SOLUTION:Explanation: Edge of cude = 48/4 = 12 cm Volume = a*a*a = 12*12*12 = 1728 cm cube Option E #### E QUESTION:Concentrated orange 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 orange juice, at the most, can fit into 3 wooden boxes? options: A)24. B)28. C)36. D)42. E)48 SOLUTION:Diameter of tube= 5 inches Height of wooden tube= 15 inches Two tubes can stand in 31 inches height Two tubes can fit in 11 inches length Two tubes can fit in 10 inches width So, one box can hold 8 tubes Three boxes can hold= 8*3= 24 tubes A is the answer #### A QUESTION:If 0.75: x :: 5:9, then x is equal to: options: A)1.12 B)1.16 C)1.2 D)1.35 E)None of these SOLUTION:Explanation: (x * 5) = (0.75 *9) X=6.75/5 = 1.35 Answer: D #### D QUESTION:In how much time would the simple interest on a certain sum be 0.125 times the principal at 10% per annum? options: A)1 1/4 B)1 1/6 C)1 1/0 D)1 1/5 E)1 5/1 SOLUTION:Let sum = x. Then, S.I. = 0.125x = 1/8 x, R = 10% Time = (100 * x) / (x * 8 * 10) = 5/4 = 1 1/4 years.Answer: A #### A QUESTION:33 1/3% OF 330? options: A)80 B)90 C)110 D)120 E)130 SOLUTION:33 1/3 % = 1/3 1/3 × 330 = 110 C) #### C QUESTION:A person crosses a 600 m long street in 5 minutes. What is his speed in km per hour? options: A)7.1 B)7.2 C)7.5 D)7.4 E)7.3 SOLUTION:distance = 600 meter time = 5 minutes = 5 x 60 seconds = 300 seconds Speed = distance/time=600/300=2m/s=2×18/5 km/hr=36/5 km/hr=7.2 km/hr Answer is B. #### B QUESTION:In a river flowing at 2 km/hr, a boat travels 32 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. options: A)10 hours B)12 hours C)14 hours D)16 hours E)None of these SOLUTION:Explanation : speed of the boat = 6 km/hr Speed downstream = (6+2) = 8 km/hr Speed upstream = (6-2) = 4 km/hr Distance travelled downstream = Distance travelled upstream = 32 km Total time taken = Time taken downstream + Time taken upstream = (32/8) + (32/4) = (32/8) + (64/8) = (96/8) = 12 hr. Answer : Option B #### B QUESTION:The sum of the two numbers is 11 and their product is 24. What is the sum of the reciprocals of these numbers ? options: A)11/24 B)11/25 C)13 D)13/15 E)None SOLUTION:Let the numbers be x x and y y Then x + y = 11 x y = 24 x+y=11xy=24 Hence, x + y x y = 11 24 x+yxy=1124 ⇒ 1 y + 1 x = 11 24 Answer is A #### A QUESTION:Two pipes A&B can fill a tank in 24 min and 32 min respectively. If both the pipes are opened simultaneously, after how much time B should be closed so that the tank is full in 18 min. options: A)8 min B)3 min C)21 min D)23 min E)24 min SOLUTION:3/4 tank is filled by A in 18 mins. then balance 1/4 tank is filled by B in 32*1/4 = 8 mins. ANSWER:A #### A QUESTION:E = {2, 3, 4, 5} B = {4, 5, 6, 7, 8} Two integers will be randomly selected from the sets above, one integer from set E and one integer from set B. What is the probability that the sum of the two integers will equal 9 ? options: A) 0.15 B) 0.20 C) 0.25 D) 0.30 E) 0.33 SOLUTION:The total number of pairs E,B possible is 4*5=20. Out of these 20 pairs only 4 sum up to 9: (2, 7); (3, 6), (4, 5) and (5, 4). The probability thus is 4/20=0.2. Answer: B. #### B QUESTION:There were two candidates in an election. Winner candidate received 60% of votes and won the election by 288 votes. Find the number of votes casted to the winning candidate? options: A)776 B)864 C)299 D)257 E)125 SOLUTION:W = 60% L = 40% 60% - 40% = 20% 20% -------- 288 60% -------- ? => 864 Answer:B #### B QUESTION:The volume of a sphere with radius r is (4/3)*pi*r^3 and the surface area is 4*pi*r^3. If a sperical balloon has a volume of 4500 pi cubic centimeters, what is hte surface area of the balloon in square centimeters? options: A)a. 40 B)b. 100 C)c. 400 D)d. 1,000 E)e. 2,000 SOLUTION:The surface area is 4.pi.r^2 (its area remember not volume) as 4/3.pi.r^3=4500pi r=15 so area = 4.pi.r^2= 900.pi= 900 x 3.14 = 2000 (approx) E #### E QUESTION:Find the sum of all odd number upto 250. options: A)15345 B)15645 C)15625 D)15342 E)15683 SOLUTION:Explanation: Number of odd numbers upto 250 = n/2 = 250/2 = 125 Sum of first 125 odd numbers = (125)2 = 15625 Answer: Option C #### C QUESTION:The average of four positive integers is 67. 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? options: A)72 B)78 C)80 D)82 E)84 SOLUTION:Let the four integers be A, B, C and D where A > B > C > D. (A + B + C + D)/4 = 67 => A + B + C + D = 268 ---> (1) A = 93, D = 39 and B - C = 28 (1) => B + C = 268 - (A + D) = 268 - 132 = 136. B + B -28 = 136 B = (136 + 28)/2 = 82 ANSWER:D #### D QUESTION:If n is an integer and 5^n > 4,000,000, what is the least possible value of n? options: A)7 B)8 C)9 D)10 E)11 SOLUTION:When you separate the 4000000 into factors of 5 and 2 you get - > 10^6 x 2^2 = 5^6 x 2^8 2 to the ^ 8 = 256 so its 256 x 5^6 that means 5^6 x 5^x must be greater 5^x > 256 5^1=5 5^2=25 5^3= 125 5^4= 625 - > so x must be at least 4 5^(6+4)= 5^10 ANSWER:D #### D QUESTION:A retailer buys 80 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 % ? options: A)110 B)115 C)112 D)118 E)120 SOLUTION:let the market price of each pen be $1 then, Cost Price of 80 pens = $ 36 Selling Price of 80 pens =99% of $80=$ 79.20 profit %=((43.20*100)/36) %=120% Answer E)120 #### E QUESTION:It costs a man 75 dollars to buy the things that he needs to make hotdogs. The city allows him to sell his hotdog somewhere near the city hall. However, the city hall charges him 1 dollar for each hotdog sold Calculate the break even point if the price he charges for 1 hotdog is $1.50 options: A)140 B)150 C)160 D)170 E)180 SOLUTION:Let x be the number of hotdogs sold Let C be the cost of buying and selling x hotdogs Let R be the revenue made for selling x hotdogs R = selling price of 1 hotdog × number of hotdogs sold R = 1.50x C = fixed cost + variable cost variable cost = fee charged for 1 hotdog × number of hotdogs sold variable cost = 1x C = 75 + 1x R = C 1.50x = 75 + 1x 1.50x - 1x = 75 + 1x - 1x 0.5x = 75 x = 150 since 0.5 × 150 = 75 The break even point is to sell 150 hotdogs. Answer B #### B QUESTION:There is a 10% chance that Tigers will not win at all during the whole season. There is a 30% 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? options: A)A)55% B)B)60% C)C)80% D)D)72% E)E)70% SOLUTION:There is a 10% chance that Tigers will not win at all during the whole season We can infer that there is 90% chance Tigers will win . Similarly There is a 30% chance that Federer will not play at all in the whole season We can also infer that there is 70% chance that Federer will play. Answer E #### E <<<Examples ends QUESTION:Statements: In a one day cricket match, the total runs made by a team were 200. Out of these 160 runs were made by spinners. Conclusions: 1) 80% of the team consists of spinners. 2) The opening batsmen were spinners. options: A)Only conclusion I follows B)Only conclusion II follows C)Either I or II follows D)Neither I nor II follows E)Both I and II follow SOLUTION:According to the statement, 80% of the total runs were made by spinners. So, I does not follow. Nothing about the opening batsmen is mentioned in the statement. So, II also does not follow. D #### D

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:Excluding stoppages, the speed of a bus is 50 kmph and including stoppages, it is 43 kmph. For how many minutes does the bus stop per hour? options: A)70 min B)16 min C)20 min D)8.4 min E)40 min SOLUTION:D 8.4 min Due to stoppages, it covers 7 km less. Time taken to cover 9 km = (7/50 x 60) min = 8.4 min #### D QUESTION:If X is to be chosen at random from the integers between 1 to 6, inclusive, and Y is to be chosen at random from the integers between 7 and 11, inclusive, what is the probability that X + Y will be even? options: A)1/2 B)2/3 C)3/4 D)4/5 E)5/6 SOLUTION:X+Y will be even if X and Y are both even or both odd. P(X and Y are both even) = 3/6*2/5 = 1/5 P(X and Y are both odd) = 3/6*3/5 = 3/10 P(X+Y is even) = 1/5 + 3/10 = 1/2 The answer is A. #### A QUESTION:Working alone, A can complete a certain kind of job in 6 hours. A and D, working together at their respective rates, can complete one of these jobs in 4 hours. In how many hours can D, working alone, complete one of these jobs? options: A) 8 B) 10 C) 12 D) 14 E) 16 SOLUTION:Let total time taken by D to complete the job = D total time taken by A to complete the job = 6 Work done by A in an hour 1/A = 1/6 Working together A and D can complete the job in 4 hours 1/A + 1/D = 1/4 =>1/D = 1/4 - 1/A = 1/4 - 1/6 = 1/12 => D = 12 hours Answer C #### C QUESTION:In a Quiz the points in each round for the first,second and third were 1000,50,20 . No other points were given. Sam participated in several rounds in the competition and the product of his score was 50000. In How many rounds did he participate? options: A)Cannot be determined B)43 C)3 D)6 E)10 SOLUTION:Correct answer is A because we are given that there won't be any points awarded for rounds other than 1st three position. Thus, it may happen that he played 100 rounds out of only 7 rounds were there in which he was awarded some points. #### A QUESTION:When 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? options: A)40 B)41 C)42 D)43 E)45 SOLUTION:Let the age of Usha is 3x then Nisha is x and Asha is 25 Also Usha 34, Nisha y, and Asha 2y. We know that 3x - 34 = x - 2y = 25 - 2y Solving above three equations we get x = 9, y = 16 Their 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 Answer:A #### A QUESTION:X is an even number and Y is a positive odd number. Which of the following expressions cannot be even? options: A)(XY)^Y B)X^3Y^3 C)X^3 D)XY E)Y^2 SOLUTION:If x is even, let x = 0 and see what happens. A. [(0)(Y)]^Y = 0 (EVEN - ELIMINATE) B. 0³Y³ = 0 (EVEN - ELIMINATE) C. 0³ = 0 (EVEN - ELIMINATE) D. (0)Y = 0 (EVEN - ELIMINATE) E. Y² Answer:E #### E QUESTION:The price of a T.V. set worth Rs. 15000 is to be paid in 20 installments of Rs. 1500 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? options: A)29997 B)28088 C)13500 D)19000 E)2799 SOLUTION:Money paid in cash = Rs. 1500 Balance payment = (15000- 1500) = Rs. 13500 .Answer:C #### C QUESTION:400 students took a mock exam in Delhi, 60% of the boys and 80% of the girls cleared the cut off in the examination. If the total percentage of students qualifying is 65%, how many girls appeared in the examination? options: A)50 B)100 C)120 D)140 E)180 SOLUTION:60%*x+80%*(400-x)=65%*400 Ans=100 ANSWER:B #### B QUESTION:All the milk in container A which was filled to its brim was poured into two containers B and C. The quantity of milk in container B was 62.5% less than the capacity of container A. If 150 liters was now transferred from C to B, then both the containers would have equal quantities of milk. What was the initial quantity of milk in container A? options: A)1200 B)1723 C)1129 D)2613 E)1372 SOLUTION:A B has 62.5% or (5/8) of the milk in A. Therefore, let the quantity of milk in container A(initially) be 8k. Quantity of milk in B = 8k - 5k = 3k. Quantity of milk in container C = 8k - 3k = 5k Container: A B C Quantity of milk: 8k 3k 5k It is given that if 150 liters was transferred from container C to container B, then both the containers would have equal quantities of milk. 5k - 150= 3k + 150 => 2k = 300 => k = 150 The initial quantity of milk in A = 8k = 8 * 150= 1200 liters. #### A QUESTION:Two cars, Car1 and Car2 move towards each other from Z 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 Z starting from Y? options: A)15.5 sec B)8.4 sec C)33.6 sec D)31.11 sec E)16.8 sec SOLUTION:Z--------------------------------------|----------------------------Y Car A(20mps)------------------------->P<---------------Car B(15mps) Let 2 cars meet each other at point P in t seconds. Car1 covers distance= 20t. Car2 covers distance=15t. So, total distance ZY= 35t. From P, Car 1 reaches onto Y in 10 secs. So it covers 15t further. so, 15t/20 = 10 So t=40/3 sec and total distance = (35*40)/3 Hence Car2 will cover total distance in (35*40)/(3*15) = 31.11 sec approx. Answer D #### D QUESTION:A 140 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? options: A)35 B)20 C)47 D)36 E)40 SOLUTION:1: 2/5 = 5: 2 2/7 * 140 =40 Answer:E #### E QUESTION:From (1, 2, 3, 4, 5, 6), one number is picked out and replaced and one number is picked out again. If the sum of the 2 numbers is 7, what is the probability that the 2 numbers included the number 5? options: A)1/5 B)2/5 C)3/10 D)3/5 E)1/3 SOLUTION:We know that the sum of two numbers picked was 7. So, there could be the following cases: (1, 6); (6, 1); (2, 5); (5, 2); (3, 4); (4, 3); Total of 6 cases out of which 2 have 5, thus the probability is 2/6=1/3. Ans E #### E QUESTION:When asked what the time is,a person answered that the amount of time left is 4/8 of the time already completed.what is the time. options: A)2 PM B)9 PM C)4 PM D)8 PM E)6 PM SOLUTION:A day has 24 hrs. Assume x hours have passed. Remaining time is (24 - x) 24−x=4/8x⇒x=20 Time is 4 PM Answer:C #### C QUESTION:A shopkeeper buys two articles for Rs.1000 each and then sells them, making 10% profit on the first article and 10% loss on second article. Find the net profit or loss percent? options: A)200 B)100 C)276 D)280 E)279 SOLUTION:Profit on first article = 10% of 1000 = 100. This is equal to the loss he makes on the second article. That, is he makes neither profit nor loss. Answer: B #### B QUESTION:Seven 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: options: A)7/8 B)1/8 C)1/3 D)1/6 E)1/9 SOLUTION:Original share of 1 person =1/7 New share of 1 person =1/6 Increase =1/6 - 1/7 =1/42 Required fraction = (1/42)/(1/7)=1/6 Answer is D. #### D QUESTION:log(a(a(a)^1/4)^1/4)^1/4 here base is a. options: A)0 B)21/64 C)1 D)22/63 E)23/65 SOLUTION:log(a(a(a^1/4)^1/4)^1/4 => log(a(a^1+1/4)^1/4)^1/4 => log(a(a^5/4)^1/4)^1/4 =>log(a(a^5/16)^1/4 =>log(a^1+5/16)^1/4 =>log(a^21/16)^1/4 =>log(a^21/64) =>21/64 log(a) =>21/64 ANSWER:B #### B QUESTION:A sock drawer contains 5 socks, each one a different solid color. The colors of the socks are yellow, green, blue, indigo, and violet. If a person reaches into the drawer and pulls out two socks, how many different color combinations are possible in the selected pair of socks? options: A)10 B)15 C)21 D)36 E)42 SOLUTION:Since the order in which we select the socks does not matter, we can use combinations. We can select 2 socks from 5 socks in 5C2 ways. 5C2 = 10 Answer : A #### A QUESTION:If a company allocates 15 percent of its budget to advertising, 10 percent to capital improvements, and 60 percent to salaries, what fraction of its budget remains for other allocations? options: A)4/5 B)3/5 C)3/20 D)1/5 E)1/10 SOLUTION:15 + 10 + 60 = 85% 100 - 85 = 15% to all others C #### C QUESTION:Rahul 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? options: A)19 B)19.7 C)19.9 D)21.7 E)22.8 SOLUTION:Total cost of the items he purchased = Rs.25 Given that out of this Rs.25, 30 Paise is given as tax => Total tax incurred = 30 Paise = Rs.30/100 Let the cost of the tax free items = x Given that tax rate = 6% ∴ (25−30/100−x)6/100 = 30/100 ⇒ 6(25 −0.3 −x) = 30 ⇒ (25 − 0.3 − x) = 5 ⇒ x = 25 − 0.3 − 5 = 19.7 B) #### B QUESTION:Determine the value of 62/54 divided by 62/54 options: A)0 B)1 C)2 D)3 E)none SOLUTION:Solution: Each number divided by itself equals 1. Answer B #### B QUESTION:Barbara has 8 shirts and 9 pants. How many clothing combinations does Barbara have, if she doesn’t wear 3 specific shirts with 2 specific pants? options: A)66 B)51 C)36 D)70 E)56 SOLUTION:Total no of combinations available is= 8 shirts X 9 pants = 72 Eliminate the 3shirts X 2 pants combo = 6 which gives.......>> 72-6=66 ANSWER: A #### A QUESTION:In a class of 50 students, 20 play SNOOKER, 15 play Cricket and 11 play Football. 7 play both SNOOKER and Cricket, 4 play Cricket and Football and 5 play SNOOKER and football. If 18 students do not play any of these given sports, how many students play exactly two of these sports? options: A)10 B)12 C)34 D)45 E)566 SOLUTION:Notice that7 play both SNOOKER and Cricket does not mean that out of those 7, some does not play Football too. The same for Cricket/Football and SNOOKER/Football. [color=#ffff00]{Total}={SNOOKER}+{Cricket}+{Football}-{HC+CH+HF}+{All three}+{Neither}For more check ADVANCED OVERLAPPING SETS PROBLEMS [/color] 50=20+15+11-(7+4+5)+{All three}+18 --> {All three}=2; Those who play ONLY SNOOKER and Cricket are 7-2=5; Those who play ONLY Cricket and Football are 4-2=2; Those who play ONLY SNOOKER and Football are 5-2=3; Hence, 5+2+3=10 students play exactly two of these sports. Answer: A. #### A QUESTION:A train 280 m long, running with a speed of 63 km/hr will pass a tree in? options: A)18 sec B)16 sec C)19 sec D)11 sec E)12 sec SOLUTION:: Speed = 63 * 5/18 = 35/2 m/sec Time taken = 280 * 2/35 = 16 sec Answer: B #### B QUESTION:Which 2 digit number has its digits reversed when you double it and take 1? options: A)33 B)34 C)35 D)36 E)37 SOLUTION:reverse it and you get 73 which is 2*37-1. ANSWER:E #### E QUESTION:f a < b < c , which of the following must be true? (I) a < b^2 (II) b − a < c (III) a^2 < b^2 < c^2 options: A)None B)I only C)II only D)III only E)II and III SOLUTION:(I) a < b^2. Not necessarily true fractions: try a=1/3 and b=1/2. (II) b − a < c. Not necessarily true: try a=-1, b=0, and c=1. (III) a^2 < b^2 < c^2. Not necessarily true: try a=-1, b=0, and c=1. None of the options must be true. Answer: A. #### A QUESTION:The probability that A speaks truth is 15/23 and that of B speaking truth is 17/29. What is the probability that they agree in stating the same fact? options: A)182/395 B)129/289 C)197/353 D)479/667 E)None of these SOLUTION:If both agree stating the same fact, either both of them speak truth of both speak false. Probability = 15/23 * 17/29 + 14/23 * 16/29 = 255/667 + 224/667 = 479/667 ANSWER:D #### D QUESTION:Find value of x (11^2 + 12^2 + 13^2 + ... + 20^2) = x options: A)1200 B)1340 C)1234 D)1203 E)2485 SOLUTION:(11^2 + 12^2 + 13^2 + ... + 20^2) = (1^2 + 2^2 + 3^2 + ... + 20^2) - (1^2 + 2^2 + 3^2 + ... + 10^2) 6 = 20 x 21 x 41 - 10 x 11 x 21 6 6 = (2870 - 385) = 2485 E #### E QUESTION:How many positive integers W between 200 and 300 (both inclusive) are not divisible by 2, 3 or 5? options: A)3 B)16 C)75 D)24 E)26 SOLUTION:1) I figured there are 101 integers (300 - 200 + 1 = 101). Since the set begins with an even and ends with an even, there are 51 evens. 2) Question says integers are not divisible by 2, leaving all of the odds (101 - 51 = 50 integers). 3) Question says integers are not divisible by 5, removing all the integers ending in 5 (already took out those ending in 0). Take out 10 integers (2?5, ? = 0 to 9), leaving us with 40 integers. 4) Now the painstaking part. We have to remove the remaining numbers that are multiples of 3. Those are 201, 207, 213, 219, 231, 237, 243, 249, 261, 267, 273, 279, 291, and 297...a total of 14 numbers. 26 numbers left! 6) Answer choice E. #### E QUESTION:The measures of the 2 acute angles of a triangle are in the ratio of 3 : 6. What arethe measures of the 2 angles? options: A)20° B)70° C)60° D)120° E)140° SOLUTION:If the ratio of the two angles is 3:6, then the measures of two angles can be written as 3x and 6x. Also the two acute angles of a triangle is equal to 90°. Hence 3x + 6x = 90 9x = 90 x = 10 Measures of the two acute angles are 3x = 3 × 10 = 30° 6x = 6 × 10 = 60° C #### C QUESTION:A 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? options: A)15/56 B)41/56 C)13/28 D)15/28 E)5/14 SOLUTION:The 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. Ways to select 6 out of total 8 = 8C6 Ways to select 4 out of 5 white balls = 5C4 Ways to select 2 out of 3 blue balls = 3C2 Thus the required probability = (5C4*3C2)/8C6 = 15/28. D is thus the correct answer. #### D QUESTION:A 300 meter long train crosses a platform in 36 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform? options: A)300m B)278m C)350m D)228m E)282m SOLUTION:Speed = [300 / 18] m/sec = 50/3 m/sec. Let the length of the platform be x meters. Then, x + 300 / 36 = 50/3 3(x + 300) = 1800 è x = 300m. Answer:A #### A QUESTION:If x and y are positive integers such that (3x + 7y) is a multiple of 11, then which of the following will be divisible by 11 ? options: A)4x + 6y B)x + y + 4 C)4x - 9y D)9x + 4y E)x + y - 4 SOLUTION:By hit and trial, we put x = 5 and y = 1 so that (3x + 7y) = (3 x 5 + 7 x 1) = 22, which is divisible by 11. (4x + 6y) = ( 4 x 5 + 6 x 1) = 26, which is not divisible by 11; (x + y + 4 ) = (5 + 1 + 4) = 10, which is not divisible by 11; (9x + 4y) = (9 x 5 + 4 x 1) = 49, which is not divisible by 11; (4x - 9y) = (4 x 5 - 9 x 1) = 11, which is divisible by 11. correct answer C #### C QUESTION:A juice manufacturer organized taste-testing sessions featuring four brands of orange juice, A, B, C and D. All customers who participated told the organizer which variety they thought was the most similar to freshly-squeezed orange juice. 61% preferred brand A and exactly half as many preferred brand B. Only 55 chose brand C. Which of the following could be the number of customers who preferred brand D? options: A) 1 B) 8 C) 19 D) 20 E) 27 SOLUTION:I get D, but I'm not sure that my method is sound. You have A + B + C + D = total testers. Stating the variety they think is most similar to freshly squeezed orange juice means each person should get 1 vote. x = total number of testers A + B + C + D .61x + (.5)(.61x) + 65 + D = x .61x + .305x + 65 + D = x I took total testers = 1000 because that gives me nice numbers to deal with. Also, if I use 200 total testers, that gives me A = 122, B = 61, C = 65...that's over 200 without considering D. x = 400 A = 244, B = 122, C = 65..also over 400 x = 600 A = 366, B = 183 C = 65....also over 600 x = 800 A = 488, B = 244, C = 65...D = 3...not an option on the list. x = 1000 A = 610 B = 305 C = 65 D = 20....the first time I get an answer that is an option in the question. C #### C QUESTION:A boy has 9 trousers and 10 shirts. In how many different ways can he select a trouser and a shirt? options: A)100 B)102 C)104 D)108 E)90 SOLUTION:The boy can select one trouser in nine ways. The boy can select one shirt in 12 ways. The number of ways in which he can select one trouser and one shirt is 9 * 10 = 90 ways. E #### E QUESTION:A 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? options: A)12.6 kmph B)17.5 kmph C)12.8 kmph D)12.5 kmph E)14.5 kmph SOLUTION:Let the speed of the man in still water be a kmph and let the speed of the stream be b kmph. Now 30/(a + b) + 20/(a - b) = 4 and 45/(a + b) + 40/(a - b) = 7 Solving the equation, the speed of man in still water is 12.5 kmph. Answer: D #### D QUESTION:In 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? options: A)A)1:5 B)B)1:1 C)C)1:8 D)D)1:9 E)E)1:3 SOLUTION:Number of men in the colony = 5/7 * 70 = 50. Number of women in the colony = 2/7 * 70 = 20. Number educated women in the colony = 1/5 * 30 = 6. Number of uneducated women in the colony = 4/5 * 50 = 24. Number of educated persons in the colony = 8 /35 * 70 = 16. As 6 females are educated, remaining 10 educated persons must be men. Number of uneducated men in the colony = 50 - 10 = 40. Number of educated men and uneducated men are in the ratio 10 : 40 i.e., 1:4. Answer:A #### A QUESTION:Half of 2 percent written as decimal is options: A)5 B)0.01 C)0.05 D)0.005 E)None of these SOLUTION:Explanation: It will be 1/2(2%) = 1/2(2/100) = 2/200 = 0.01 Answer: Option B #### B QUESTION:What is the least number of squares tiles required to pave the floor of a room 15.17 m long and 9.02 m broad? options: A)814 B)266 C)287 D)999 E)661 SOLUTION:Explanation: Length of largest tile = H.C.F. of 1517 cm and 902 cm = 41 cm. Area of each tile = Required number of tiles = = 814 Answer: A) 814 #### A QUESTION:What is the smallest positive integer that can be multiplied by 605 to make it a perfect square? options: A)2 B)3 C)5 D)7 E)11 SOLUTION:605 is multiplied by 5 gives 3025 Its a square root of 55 Answer is 5 -Option C #### C QUESTION:Marla starts running around a circular track at the same time Nick starts walking around the same circular track. Marla completes 20 laps around the track per hour and Nick completes 10 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? options: A)5 B)8 C)24 D)15 E)20 SOLUTION:Maria's rate - 20 laps per hour --> 20/60 laps/min Nick's rate - 10 laps per hour --> 10/60 laps/min lets set equations: 20/60*t=4 (since Maria had to run 4 laps before Nick would start) 10/60*t=0 (Hick has just started and hasn't run any lap yet) (20/60-10/60)*t=4-0 (since Nick was chasing Maria) t=24 min needed Maria to run 4 laps Answer : C #### C QUESTION:For which of the following values of s is (40+s)/s an integer? options: A)3 B)4 C)9 D)11 E)40 SOLUTION:This problem has to be solved by checking the options (40 + s)/s For this entity to be an integer, 50 + s should be divisible by s Option A: 43/3 - Not an Integer Option B:44/4 - Not an Integer Option C: 49/9 - Not an integer Option D: 51/11 - Not an integer Option E - 80/40- Integer Correct Option: E #### E QUESTION:A bag contains 4 white balls, 3 black balls, and 2 red balls. One by one, three balls are drawn out without replacement. What is the probability that the third ball is red? options: A)2/9 B)1/4 C)3/8 D)5/16 E)2/5 SOLUTION:The probability for each ball to be drawn third is equal. Then the probability a red ball is drawn third is 2/9. The answer is A. #### A QUESTION:How many six-digit numbers are there such that all six digits are different and the first digit is not zero? options: A)472392 B)648421 C)720756 D)729951 E)810364 SOLUTION:All six digits are different and first digit is not zero. So first digit can be filled in 9 ways. And, second digit can be filled in 9 ways. And, third digit can be filled in 9 ways. And, fourth digit can be filled in 9 ways. And, fifth digit can be filled in 9 ways. And, sixth digit can be filled in 8 ways. Total ways = 9*9*9*9*9*8 = 472392 Hence option (A). #### A QUESTION:A car traveled 75% of the way from town A to town B at an average speed of 60 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 ? options: A)10 B)20 C)25 D)30 E)37.5 SOLUTION:Total distance = 100 miles (easier to work with %) 75% of the distance = 75 miles 25% of the distance = 25 miles 1st part of the trip → 75/60 = 1.25 2nd part of the trip → 25/S = t Total trip → (75+25)/40 = 1.25 + t » 100/40 = 1.25 + t » 2.5 = 1.25 + t » t = 1.25 Back to 2nd part of the trip formula: 25/S = 1.25 » S = 20 Ans B #### B QUESTION:In a game, one player throws two fair, six-sided die at the same time. If the player receives at least a four or a one on either die, that player wins. What is the probability that a player wins after playing the game once? options: A)1/3 B)4/9 C)5/9 D)2/3 E)3/4 SOLUTION:We're looking for the number of outcomes that include AT LEAST a 1 or a 4. #getting a one in 1st die = {(1,1), (1,2), ...(1,6) }= 6 #getting a one in 2nd die {(2,1), ...(5,1),(6,1) } = 4 [exclude 1,1 and 4,1] since it will be counted twice #getting a three in 1st die {(3,1), (3,2), ...(3,6) }= 6 #getting a three in 1st die {(2,4), (3,4), ...(6,4) } = 4 [exclude 1,4 and 4,4] since it will be counted twice Total possibities = 20 Probability of rolling at least a 1 or a 4 on two dice: 20/36 = 5/9 C #### C QUESTION:A set consists of 18 numbers, all are even or multiple of 5. If 6 numbers are even and 12 numbers are multiple of 5, how many numbers is multiple of 10? options: A) 0 B) 1 C) 2 D) 3 E) 5 SOLUTION:{Total} = {Even} + {Multiple of 5} - {Both} + {Nether}. Since{Neither}=0(allare even or multiple of 5) then: 18 = 6 + 12 - {Both} + 0; {Both}=0(so 1 number is both even AND multiple of 5, so it must be a multiple of 10). Answer: A. #### A QUESTION:The 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? options: A)14/33 B)7/33 C)2/7 D)13/73 E)12/27 SOLUTION:Combination Probability Formula: nCr = n!/[r!(n-r)!] Total possible, select 5 people from 12 people = 12C5 = 12!/[5!(12 - 5)!] = 792. To have 3 women there must be 2 men, select 2 men from 4 = 4C2 = 6. And, select 3 women from 8 = 8C3 = 56. 3 women and 2 men = (6)(56) = 336 Probability = (number outcomes favorable)/(total number outcomes) = 336/792 = 14/33 Answer: A #### A QUESTION:Three coworkers P , W , R meet for Dinner. P had 5 sandwiches, W had 3 and R had none. Both PW share their sandwiches with R such that each one got the same amount. If R paid $ 8 to PW, how much of $ 8 should P get? Assume both sandwiches and Dollars can be split. options: A)a) 5$ B)b) 3 $ C)c) 7 $ D)d) 4 $ E)e) 5.5 $ SOLUTION:we got total 8 sandwiches ....we are dividing equally in 3 people. per person: 8/3 initially p:8 W:3 r:0 now since r ate 8/3 so he is paying 8 dollars for 8/3 sandwiches. now p also ate 8/3 of his 5 sandwiches = so he gave 5-8/3 to r ==>7/3 to r ok we have 8 dollars for 8/3 sandwich therefore for 7/3 sandwich we will get 7 dollars. hence p should get 7 dollars. hence C #### C QUESTION:Find out the C.I on Rs.5000 at 4% p.a. compound half-yearly for 1 1/2 years. options: A)306.05 B)306.00 C)306.04 D)306.05 E)306.01 SOLUTION:A = 5000(51/50)3 = 5306.04 5000 ----------- 306.04 Answer: A #### A QUESTION:Sum 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? options: A)9 B)5 C)6 D)2 E)1 SOLUTION:Explanation: x + y = 15 2x – 3y = 5 x = 10 y = 5 Answer: B #### B QUESTION:If a quality control check is made inspecting a sample of 2 light bulbs from a box of 12 lighbulbs, how many different samples can be chosen? options: A)6 B)24 C)36 D)66 E)72 SOLUTION:Try using the formula for combinations: n!/r!(n-r)! 12!/2!(12-2)! 12!/2!*10! 12*11/2*1 =66 ANSWER:D #### D QUESTION:An 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.3600, what will be the difference between Q and R's share? options: A)2788 B)4500 C)7282 D)2782 E)2729 SOLUTION:4 --- 3600 5 --- ? => 4500 Answer:B #### B QUESTION:The largest 4 digit number exactly divisible by 44 is? options: A)9988 B)9939 C)9944 D)9954 E)9960 SOLUTION:Largest 4-digit number = 9999 44) 9999 (227 9988 Largest number : 9988 Answer : A #### A QUESTION:In what time will a train 120 m long cross an electric pole, it its speed be 144 km/hr? options: A)2.5 sec B)3 sec C)8.9 sec D)6.9 sec E)2.9 sec SOLUTION:Speed = 144 * 5/18 = 40 m/sec Time taken = 120/40 = 3 sec. Answer: B #### B QUESTION:What is the total cost of 2 sandwiches at $2.49 each and 4 sodas at $1.87 each? options: A)$3.36 B)$6.85 C)$8.46 D)$10.08 E)$12.46 SOLUTION:Answer = E 2 * 2.49 + 4 * 1.87 = 2 (2.50 - 0.01) + 4 (2.00 - 0.13) = 5 + 8 - 0.02 - 0.52 = 13 - 0.54 = 12.46 #### E QUESTION:The ratio between the present ages of P and Q is 6:7. If Q is 4 years old than P, what will be the ratio of the ages of P and Q after 4 years options: A)A)3:4 B)of these C)C)4:3 D)inadequate E)B)3:5 SOLUTION:Let P's age and Q's age be 6x and 7x years respectively. Then, 7x - 6x = 4 => x = 4 Required ratio = (6x + 4) : (7x + 4) 28 : 32 = 7:8 ANSWER:B #### B QUESTION:Two 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? options: A)22 sec B)77 sec C)76 sec D)20 sec E)24 sec SOLUTION:Relative speed = (42 + 30) * 5/18 = 4 * 5 = 20 mps. Distance covered in passing each other = 200 + 280 = 480 m. The time required = d/s = 480/20 = 24 sec. Answer:E #### E QUESTION:The length of the bridge, which a train 150 metres long and travelling at 45 km/hr can cross in 30 seconds, is? options: A)76 m B)178 m C)225 m D)187 m E)176 m SOLUTION:Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (150 + x)/30 = 25/2 => 2(150 + x)= 750 => x = 225 m. Answer: C #### C QUESTION:A cube is painted red on all faces. It is then cut into 27 equal smaller cubes. How many J cubes are painted on only 2 faces? options: A)12 B)8 C)6 D)10 E)16 SOLUTION:1) Draw a simple cube 2) 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. 3) Remember that the OUTSIDE of the cube is the part that's painted.... The 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. J=4 + 4 + 4 = 12. Answer A #### A QUESTION:Population of a city in 20004 was 1000000. If in 2005 there isan increment of 15% , in 2006 there is a decrements of 35 % and in 2007 there is an increment of 45%, then find the population of city atthe end of the year 2007 options: A)1056787 B)1076658 C)1079767 D)1079977 E)1083875 SOLUTION:Required population = P (1 + R1/100)(1 - R2/100)(1 + R3/100) = P (1 + 15/100)(1 - 35/100)(1 + 45/100) = 1083875 E #### E QUESTION:Sonika deposited Rs.6200 which amounted to Rs.7200 after 5 years at simple interest. Had the interest been 3% more. She would get how much? options: A)9680 B)8130 C)8134 D)8556 E)9808 SOLUTION:(6200*5*3)/100 = 930 7200 -------- 8130 Answer: B #### B QUESTION:If 15% of 40 is greater than 25% of a number by 2, the number is options: A)14 B)16 C)18 D)20 E)22 SOLUTION:Explanation: 15/100 * 40 - 25/100 * x = 2 or x/4 = 4 so x = 16 Option B #### B QUESTION:By selling an article at Rs.600, a profit of 25% is made. Find its cost price? options: A)Rs.486 B)Rs.455 C)Rs.487 D)Rs.480 E)Rs.489 SOLUTION:SP = 600 CP = (SP)*[100/(100+P)] = 600 * [100/(100+25)] = 600 * [100/125] = Rs.480 Answer: D #### D QUESTION:The price of 2 sarees and 4 shirts is 16000. With the same money one can buy 1 saree and 6 shirts. If one wants to buy 12 shirts, how much shall one have to pay? options: A)2,400 B)4,800 C)1,200 D)Cannot be determined E)None of these SOLUTION:Let the price of one saree and one shirt be x and y respectively. Then, 2x + 4y = 1600 or, x + 2y = 800 ... (i) Also, x + 6y = 1600 ... (ii) Solving equations (i) and (ii), we get 4y = 800 or,y = 200 ∴ cost of 12 shirts = 12 × 200 = 2400 Answer A #### A <<<Examples ends QUESTION:What annual payment will discharge a debt of Rs. 1025 due in 2 years at the rate of 5% compound interest? options: A)Rs. 560 B)Rs. 560.75 C)Rs. 551.25 D)Rs. 550 E)Rs. 560 SOLUTION:Explanation: Present worth of Rs. x due T years hence is given by Present Worth (PW) = x/(1+R/100)T Let x be the annual payment Then, present worth of x due 1 year hence + present worth of x due 2 year hence = 1025 x(1 + 5/100)1 + x(1 + 5/100)2 = 1025 x/(21/20) + x/(21/20)2 = 1025 20x/21 + 400x/441 = 1025 820x/441 = 1025 x = (1025 × 441)/820 = (205 × 441)/164 = Rs. 551.25 Answer: Option C #### C

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:The Guests at a football banquet consumed a total of 411 pounds of food. if no individual guest consumed more than 2.5 pounds of food, What is the minimum number of guests that could have attended the banquet? options: A)165 B)161 C)162 D)163 E)164 SOLUTION:To minimize one quantity maximize other. 164*2.5 (max possible amount of food a guest could consume) = 410 pounds, so there must be more than 164 guests, next integer is 165. Answer: A. #### A QUESTION:A candidate got 35% of the votes polled and he lost to his rival by 2250 votes. How many votes were cast? options: A)7500 B)7508 C)7528 D)7527 E)7232 SOLUTION:35%-----------L 65%-----------W ------------------ 30%----------2250 100%---------? => 7500 Answer:A #### A QUESTION:The amount of water (in ml) that should be added to reduce 9 ml. Lotion, containing 50% alcohol, to a lotion containing 45% alcohol, is? options: A)1 B)4 C)5 D)6 E)7 SOLUTION:4.5 4.5 45% 55% 45% ----- 4.5 55% ------? => 5.5 - 4.5 = 1 ml ANSWER:A #### A QUESTION:In how many ways letters of the word LEADER be arranged? options: A)5 B)78 C)69 D)58 E)120 SOLUTION:LEADER has 6 letters, out of which E repeated 2 times. Hence total ways = 6! / (2!) = 120 ways E #### E QUESTION:The sum of first nine prime numbers is? options: A)12 B)100 C)24 D)28 E)30 SOLUTION:Required sum = (2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23) = 100. Note: 1 is not a prime number. Definition: A prime number (or a prime) is a natural number that has exactly two distinct natural number divisors: 1 and itself. B #### B QUESTION:David obtained 70, 60, 78, 60 and 65 marks (out of 100) in English, Mathematics,Physics, Chemistry and Biology What are his average marks ? options: A)75 B)27.6 C)66.6 D)16.5 E)11 SOLUTION:Explanation: Average = (70+ 60+ 78+ 60+ 65 )/ 5 = 333/5 = 66.6. Answer:C #### C QUESTION:If 13 = 13w/(1-w) ,then (4w)2 = options: A)1/4 B)1/2 C)1 D)2 E)4 SOLUTION:13-13w=13w 26w=13 w=1/2 4w=2 4w*2=2*2=4 ANSWER:E #### E QUESTION:Ramu bought an old car for Rs. 42000. He spent Rs. 13000 on repairs and sold it for Rs. 66900. What is his profit percent? options: A)22 B)77 C)18 D)21.6 E)88 SOLUTION:Total CP = Rs. 42000 + Rs. 13000 = Rs. 55000 and SP = Rs. 66900 Profit(%) = (66900 - 55000)/55000 * 100 = 21.6% Answer: D #### D QUESTION:A 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? options: A)9 B)8 C)7 D)6 E)5 SOLUTION:Volume of the wire (in Cylindrical shape) is equal to the volume of the sphere. π(16)2 * h = (4/3)π (12)3 => h = 9 cm Answer:A #### A QUESTION:In a business school case competition, the top three teams receive cash prizes of $5,000, $3,000, and $2,000, respectively, while the remaining teams are not ranked and do not receive any prizes. There are 6 participating teams, named Team A, Team B, Team C, Team D, Team E, and Team F. If Team A wins one of the prizes, Team B will also win one of the prizes. How many outcomes S of the competition are possible? options: A)18 B)20 C)54 D)84 E)120 SOLUTION:the ways the three teams can be selected is.. i) A is selected, B is also selected, third can be any of the remaining 4.. so total ways 4.. they can be arranged in 4*3!=24 ways.. ii) A is not selected. threee teams can be selected from remaining 5 so total arrangements =5C3*3!=60 total S=84 outcomes D #### D QUESTION:When the positive integer y is divided by 9, the remainder is 5. What is the remainder when 3y is divided by 9? options: A)0 B)1 C)3 D)4 E)6 SOLUTION:Lets take the number as y when y is divided by 9 the remainder is 5 hence y can be written as y=9k +5 Multiplying by 3 will give 3y = 27k + 15 we can also write 3y = 27k + 9 + 6 Now 27k and 9 are divisible by 9 leaving the remainder as 6 hence E is the answer. #### E QUESTION:Two 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? A. 30 km/hr B. 45 km/hr options: A)11 B)78 C)60 D)28 E)81 SOLUTION:Let the speed of the slower train be x m/sec. Then, speed of the train = 2x m/sec. Relative speed = ( x + 2x) = 3x m/sec. (100 + 100)/8 = 3x => x = 25/3. So, speed of the faster train = 50/3 = 50/3 * 18/5 = 60 km/hr.Answer: C #### C QUESTION:If a = -1, what is the value of –(a^2 + a^3 + a^4 + a^5+a^6)? options: A)-14 B)-4 C)-1 D)4 E)14 SOLUTION:if a = -1, then putting values in equation = -[ (-1)^2 + (-1)^3 + (-1^4) + (-1^5)+(-1^6) ] = -[ 1 - 1 + 1 - 1 + 1] = -1 Answer = C = -1 #### C QUESTION:The length of the bridge, which a train 140 metres long and travelling at 45 km/hr can cross in 30 seconds, is? options: A)10 m B)16 m C)245 m D)19 m E)235 m SOLUTION:Speed = [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. Answer: E #### E QUESTION:4 dice are thrown simultaneously on the board. Find the probability show the same face. options: A)1/213 B)1/215 C)1/216 D)2/113 E)3/114 SOLUTION:The total number of elementary events associated to the random experiments of throwing four dice simultaneously is: =6×6×6×6=64=6×6×6×6=64 n(S)=64n(S)=64 Let XX be the event that all dice show the same face. 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)}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)} n(X)=6n(X)=6 Hence required probability, =n(X)n(S)=664=n(X)n(S)=664 =1/216 C #### C QUESTION:Two sides of a triangle have length 6 and 8. Which of the following are possible areas of the triangle? I. 4 II. 12 III. 24 options: A)I, II, and III B)I and II only C)II and III only D)I and III only E)II only SOLUTION:Answer = A. I, II, and III With dimensions of only 2 sides given (for a triangle), this becomes an open ended question Any area is possible out of the three #### A QUESTION:what no should be subtracted from 92555 to make it a perfect square ? options: A)128 B)158 C)178 D)139 E)140 SOLUTION:root 92555= 304.228 and 304^2=92416 92555-92416=139 should be subtracted from 92555 to make it a perfect square ANSWER:D #### D QUESTION:By selling 33 metres of cloth , one gains the selling price of 11 metres . Find the gain percent . options: A)20% B)30% C)40% D)50% E)60% SOLUTION:(SP of 33m)-(CP of 33m)=Gain=SP of 11m SP of 22m = CP of 33m Let CP of each metre be Re.1 , Then, CP of 22m= Rs.22,SP of 22m=Rs.33. Gain%=[(11/22)*100]%=50% ANSWER D #### D QUESTION:Which of the following inequalities is equivalent to −4 < x < 8? options: A)|x - 1| < 7 B)|x + 2| < 6 C)|x + 3| < 5 D)|x - 2| < 6 E)None of the above SOLUTION:We know that |x| < a means -a < x < a, where Sum of lower limit of x (i.e -a) and the upper limit of x (i.e a), is 0 Given is, -4 < x < 8, let's say by adding y to this inequality we will get into the above format -4+y < x+y < 8+y Now, to move this into the mod format, we need to have (-4+y) + (8+y) = 0 => y = -2 Thus, -6< x-2 < 6 => |x-2| < 6. Hence, answer is D #### D QUESTION:Solution X is 30% chemical A and 70% chemical B by volume. Solution Y is 40% chemical A and 60% chemical B by volume. If a mixture of X and Y is 36% chemical A, what percent of the mixture is Solution X? options: A)30% B)35% C)40% D)45% E)50% SOLUTION:The volume of the mixture be X+Y. 0.3X +0.4Y=0.36(X+Y) X=2Y/3 X/(X+Y)=(2Y/3) / (5Y/3)=2/5=40%. The answer is C. #### C QUESTION:How many liters of water must be evaporated from 50 liters of a 3-percent sugar solution to get a 20-percent solution? options: A)45 B)33 1/3 C)27 D)16 2/3 E)15 SOLUTION:How many liters of water must be evaporated from 50 liters of a 3-percent sugar solution to get a 20-percent solution? 3% of a 50 liter solution is 1.5L. So you are trying to determine how many liters must a solution be for the 1.5L to represent 20% of the solution. Set up an inequality and solve for x: 1.5/x = 1/20 x = 30 Since you need a 15L solution, you must evaporate 45 of the original 50L solution to get a 20% solution. Answer is A. #### A QUESTION:If i walk with 30 miles/hr i reach 1 hour before and if i walk with 20 miles/hr i reach 1 hour late.Find the distance between 2 points and the exact time of reaching destination is 11 am then find the speed with which it walks. options: A)120 MILES B)130 MILES C)140 MILES D)150 MILES E)160 MILES SOLUTION:LET ORIGINAL SPEED BE V AND TIME TAKEN BE T... AS DISTANCE BETWEEN TWO POINTS IS CONSTANT, 30*(T-1)=20*(T+1)=V*T HENCE, V=24MILE/HR T=5 HRS DISTANCE BETWEEN TWO POINTS IS 120 MILES ANSWER:A #### A QUESTION:Zachary is helping his younger brother, Sterling, learn his multiplication tables. For every question that Sterling answers correctly, Zachary gives him 3 pieces of candy. For every question that Sterling answers incorrectly, Zachary takes away two pieces of candy. After 6 questions, if Sterling had answered 2 more questions correctly, he would have earned 31 pieces of candy. How many of the 6 questions did Zachary answer correctly? options: A)6 B)7 C)8 D)9 E)10 SOLUTION:i got two equations: 3x-2y=25 x+y=6 3x-2(6-x)=25 3x-12+2x=25 5x=37 x=7.4 or between 7 and 8. (ANS B) #### B QUESTION:Excepting ‘seldom’ which means – rarely, infrequently and not often, is the antonym. options: A)22 B)278 C)267 D)176 E)971 SOLUTION:Answer:D #### D QUESTION:The average of 45 results is 10. The average of first 22 of them is 16 and that of last 22 is 20. Find the 23 result? options: A)600 B)480 C)538 D)650 E)560 SOLUTION:23th result = sum of 45results - sum of 44 results 10*45-16*22+20*22 = 450-352+440 = 538 Answer is C #### C QUESTION:Find the number of solutions for 3x+4y=60, if x and y are positive integers options: A)1 B)2 C)3 D)4 E)5 SOLUTION:3x+4y=60 =>x=(60-4y)/3 as x and y are positive integers, put y=1,2,3,... & find x y=3,x=16 y=6,x=12 y=9,x=8 y=12,x=4 (x,y)=(4,12),(8,9),(12,6),(16,3) only 4 solution ANSWER:D #### D QUESTION:A man buys s cycle for $100 and sells it at a loss of 10%. What is the selling price of the cycle? options: A)$50 B)$60 C)$70 D)$80 E)$90 SOLUTION:S.P. = 90% of the $100 = 90/100 * 100 = $90 Answer is E #### E QUESTION:Let S be the set of permutations of the sequence 2, 3, 4, 5, 6 for which the first term is not 2. A permutation is chosen randomly from S. The probability that the second term is 5 is given by a/b (in lowest terms). What is a+b? options: A)5 B)6 C)11 D)16 E)19 SOLUTION:The number of possible permutation without 2 in the first digit is 4X4X3X2X1=96 ways. The number of possible permutations with 5 in the second term is= 3X3X2X1=18 ways. 18c1/96c1 = 18/96= 3/16= > a+b=19. ANSWER:E #### E QUESTION:A work which could be finished in 12 days was finished 3 days earlier after 10 more men joined. The number of men employed was? options: A)22 B)20 C)88 D)71 E)10 SOLUTION:x ------- 12 (x + 10) ---- 6 x * 12 = (x + 10)6 x = 10 \Answer: E #### E QUESTION:What 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 ? options: A)1288 B)2797 C)3944 D)1299 E)1082 SOLUTION:Let the side of the square plot be 'a' ft. Given area of the plot (a x a) = 289 => a = 17 Length of the fence = Perimeter of the plot = 4a = 68 ft. Cost of building the fence = 68 x 58 = Rs. 3944. Answer: C #### C QUESTION:A team of eight entered for a shooting competition. The best marks man scored 82 points. If he had scored 92 points, the average scores for. The team would have been 83. How many points altogether did the team score? options: A)662 B)672 C)654 D)642 E)721 SOLUTION:8 * 83 = 664 – 10 = 654 ANSWER:C #### C QUESTION:The present ratio of students to teachers at a certain school is 35 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? options: A)5 B)8 C)10 D)12 E)15 SOLUTION:We are given that the ratio of students to teacher is 35 to 1. We can rewrite this using variable multipliers. students : teachers = 35x : x We 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: Students/Teachers  25/1 = (35x + 50)/(x + 5) If we cross multiply we have: 25(x + 5) = 35x + 50 25x + 125 = 35x + 50 7.5 = x x~8 Since x is the present number of teachers, currently there are 8 teachers. Answer B. #### B QUESTION:2, 4, 6, 8, 10, ? options: A)10 B)14 C)16 D)12 E)24 SOLUTION:The sequence is a series of even numbers, 2, 4, 6, 8, 10, 12.... Answer : D. #### D QUESTION:If x is Negative integer ,y is positive integer, and 7x+3y=14 , which of the following could be the value of x ? options: A)-1 B)-5 C)-2 D)-3 E)-4 SOLUTION:Use answer options to solve this problem - x is negative integer (-1,-2,-3......) put x=-1 7x+3y=14 7(-1)+3y=14 -7+3y=14 3y=14+7 3y=21 y=7 Answer will be (A) #### A QUESTION:A car covers a distance of 520 km in 4 hours. Find its speed? options: A)104 B)130 C)298 D)269 E)213 SOLUTION:520/4 = 130 kmph Answer:B #### B QUESTION:The 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: options: A)400 B)500 C)600 D)800 E)1000 SOLUTION:Let the sum be $. P. (P(1+10/100)^2-P)=525 P((11/10)^2-1)=2500 SUM = 2500 So SI = 500 ANSWER B #### B QUESTION:A 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. options: A)15 kmph B)36 kmph C)21 kmph D)17 kmph E)19 kmph SOLUTION:Let the speed of the goods train be x kmph. Distance covered by goods train in 10 hours= Distance covered by express train in 4 hours 10x = 4 x 90 or x =36. So, speed of goods train = 36kmph. Ans: B #### B QUESTION:A group of 11 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? options: A) E/(12 - n) B) (12 - n)/E C) E/[12(12-n)] D) nE / [11(11-n)] E) (12-n)E/(12n) SOLUTION:total cost =E no of people willing to participate initially =11 initial cost for each =E/11 when n people decided not to participate Cost for each =E/11-n D #### D QUESTION:The ratio between the present ages of P and Q is 6:8. If Q is 4 years old than P, what will be the ratio of the ages of P and Q after 4 years? options: A)A)8:9 B)B)3:5 C)C)4:3 D)inadequate E)of these SOLUTION:Let P's age and Q's age be 6x and 8x years respectively. Then, 8x - 6x = 4 => x =2 Required ratio = (6x + 4) : (7x + 4) 16 : 18 = 8:9 ANSWER:A #### A QUESTION:At what time between 4 & 5 will the hands of a watch point in opposite directions? options: A)50 min past 4 B)42 5/11 min past 4 C)43 min past 4 D)40 min past 4 E)50 4/11 min past 4 SOLUTION:At 4 o'clock, the hands of the watch are 20 min. spaces apart. To be in opposite directions, they must be 30min. spaces apart. Minute hand will have to gain 5 min. spaces. 55min spaces are gained in 60 min. 5 min. spaces are gained in (60/55 * 50) min. or 54 6/11 min. Required time = 54 6/11 min. past 4. Answer is E #### E QUESTION:A 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 ? options: A)A)1km B)B)300m C)C)650m D)D)750m E)E)800m SOLUTION:Relative speed of the policeman = 20-15 = 5 km/hr time taken by policeman to cover 100m = (100/1000)*(1/5) = 1/50 hr In 1/50 hr the thief covers a distance of 15/50 km = 3/10 km = 300m Answer is B #### B QUESTION:A 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? options: A) 7 B) 6 C) 5 D) 4 E) 3 SOLUTION:18 wins, 2 losses - total 20 games played. The team has played 2/3rd of all games so total number of games = 30 3/4th 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. Answer (C) #### C QUESTION:A 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? options: A)35 hours B)25 hours C)20 hours D)Cannot be determined E)None of these SOLUTION:Suppose the efficiencies of pipes C, B and A are 4K, 2K and K. Since, the tank is filled in 5 hours by the three pipes having combined efficiency equal to 7K, the time required to fill the tank by A alone = 7K×5 /K=35hours Answer A #### A QUESTION:In 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 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 Ms. Robbins received? options: A)0.06N + 3,200 B)0.1N + 7,200 C)0.4N + 7,200 D)0.1N + 8,000 E)0.06N + 7,000 SOLUTION:total vote = N vote cast by independent voters = 0.4 N vote cast by registered voters = 0.6 N vote received by Ms. Robbins = 7000 + 10% of vote be registered voters = 7000 + 0.06 N Answer choice E #### E QUESTION:Find the number that fits somewhere into the middle of the series. Some of the items involve both numbers and letters Look at this series: D12, H16, __, P24, T28, ... What number should fill the blank? options: A)H16 B)I17 C)J18 D)K19 E)L20 SOLUTION:E L20 In this series, the letters progress by 4, and the numbers increase by 4. #### E QUESTION:Out of 12 students in a class, 7 are wearing blue shirts, 3 are wearing green shirts, and 2 are wearing red shirts. Four students are to be selected at random. What is the probability that at least one is wearing a green shirt? options: A)25/33 B)31/44 C)41/55 D)53/66 E)65/77 SOLUTION:Total possible ways to choose 4 students out of 12 = 12C4 = 495 The number of ways to choose 4 students with no green shirts = 9C4 = 126 P(no green shirts) = 126/495 = 14/55 P(at least 1 green shirt) = 1 - 14/55 = 41/55 The answer is C. #### C QUESTION:A painting at an art gallery is framed such that the area of the square frame is 1/2 the area of the painting itself. If the diagonal line connecting corners of the frame has a length of 6, what is the area of the painting inside the frame? options: A)12 B)20 C)30 D)40 E)50 SOLUTION:Suppose side of the painting(which is a square) is a and side of the outer square(painting+frame) is b Area of painting = a^2 and we know that the area of the frame is (1/2) of that of the painting so Area of frame = (1/2) * a^2 Area of Frame + Painting = a^2 + (1/2)*a^2 = (3/2)*a^2 which is equal to b^2 Line connecting the corners of the frame is the diagonal of the outer square which is equal to b*sqrt2 so, b * sqrt2 = 6 so, b = 3 * sqrt2 b^2 = 18 we know that b^2 = (3/2)*a^2 so, a^2 = (2/3)*b^2 = (2/3)*18 = 12 And area of painting = a^2 = 12 So, answer will be A. #### A QUESTION:A reduction of 46% in the price of bananas would enable a man to obtain 64 more for Rs.40, what is reduced price per dozen? options: A)2.45 B)8.45 C)7.45 D)3.45 E)1.45 SOLUTION:Explanation: 40*(46/100) = 18.4 --- 64 ? --- 12 => Rs.3.45 Answer: D #### D QUESTION:A baker filled with a measuring cup with 1/3 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? options: A)1/8 cup B)3/8 cup C)11/24 cup D)1/2 cup E)7/8 cup SOLUTION:1/3 is the original water in cup .half in batter.So left is 1/6 out which 1/8 is spilled out.So again left with 1/24. so 50% more than what he started was = 1/3+1/2*(1/3)=1/2 Amount of water needed to add = 1/2 - 1/24=11/24 C #### C QUESTION:A license plate in the country Kerrania consists of four digits followed by two letters. The letters A, B, and C are used only by government vehicles while the letters D through Z are used by non-government vehicles. Kerrania's intelligence agency has recently captured a message from the country Gonzalia indicating that an electronic transmitter has been installed in a Kerrania government vehicle with a license plate starting with 79. If it takes the police 9 minutes to inspect each vehicle, what is the probability that the police will find the transmitter within three hours? options: A) 18/79 B) 1/6 C) 1/25 D) 19/900 E) 1/900 SOLUTION:Everything is correct except that you assumed the letters can't be repeated. It can be repeated. AA BB CC AB, AC, BC, BA, CA, CB. Thus; total government vehicles = (10)^2*(3)^2 = 100*9 = 900 Vehicles inspected within 3 hours = 60*3/9 = 19 P = 19/900 Ans:D #### D QUESTION:A basket contains 7 apples, of which 1 is spoiled and the rest are good. If we select 2 apples from the basket simultaneously and at random, what is the probability that the 2 apples selected will include the spoiled apple? options: A)1/5 B)2/7 C)2/9 D)3/5 E)4/11 SOLUTION:The total number of ways to choose 2 apples is 7C2 = 21 The number of ways that include the spoiled apple is 6C1 = 6 P(the spoiled apple is included) = 6/21 = 2/7 The answer is B. #### B QUESTION:A train running at the speed of 60 km/hr crosses a pole in 30 seconds. What is the length of the train? options: A)500 m B)620 m C)872 m D)150 m E)765 m SOLUTION:Speed=(60 * 5/18) m/sec = (50/3) m/sec Length of the train = (Speed x Time) = (50/3 * 30) m = 500 m. Answer: A #### A QUESTION:Today is Monday. After 61 days, it will be: options: A)SUNDAY B)SATURSDAY C)FRIDAY D)THURSDAY E)MONDAY SOLUTION:Each day of the week is repeated after 7 days. So, after 63 days, it will be Monday. After 61 days, it will be Saturday. Answer: Option B #### B QUESTION:Two trains are moving in opposite directions at 60 km/hr and 90 km/hr. Their lengths are 1.75 km and 1.25 km respectively. The time taken by the slower train to cross the faster train in seconds is? options: A)12 B)72 C)48 D)99 E)11 SOLUTION:Relative speed = 60 + 90 = 150 km/hr. = 150 * 5/18 = 125/3 m/sec. Distance covered = 1.75 + 1.25 = 3 km = 3000 m. Required time = 3000 * 3/125 = 72 sec. Answer: B #### B QUESTION:A man invests Rs. 5,000 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? options: A)Rs. 1200 B)Rs. 1300 C)Rs. 2500 D)Rs. 2000 E)None of these SOLUTION:Explanation : Interest on Rs.5000 at 5% per annum = ( 5000 × 5 × 1) / 100 = Rs. 250 Let his additional investment at 8% = x Interest on Rs.x at 8% per annum = ( x × 8 × 1 ) / 100 = 2x/25. To earn 6% per annum for the total, interest = (5000 + x) × 6 × 1/100. => 250 + 2x/25 = (5000 + x) × 6 × 1/100. => 25000 + 8x = (5000 + x) × 6. => 25000 + 8x = 30000 + 6x. => 2x=5000. => x=2500. Answer : C #### C QUESTION:There are 4 prime numbers in ascending order. The multiplication of 1st 3 is 385 and that of last 3is 1001. what is the last number is options: A)10 B)15 C)16 D)13 E)18 SOLUTION:Explanation: abcbcd=3851001=>ad=513 abcbcd=3851001=>ad=513 So d = 13 D #### D QUESTION:A 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 secretary or the member chosen to be the president? options: A) 1/720 B) 1/5 C) 1/10 D) 1/9 E) 1/6 SOLUTION:This question is much easier than it appears. Each 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 and the probability that Harry will be selected to be the president is also 1/10. So, the probability that Harry will be selected to be either the secretary or the the president is 1/10+1/10=2/10. Answer: B #### B QUESTION:How long does a train 110 m long running at the speed of 36 km/hr takes to cross a bridge 132 m length? options: A)12.9 sec B)12.1 sec C)24.2 sec D)16.8 sec E)14.9 sec SOLUTION:Speed = 36 * 5/18 = 10 m/sec Total distance covered = 110 + 132 = 242 m. Required time = 242/10 = 24.2 sec. Answer: C #### C QUESTION:hat should come in place of question mark (?) in the following equation ? 197 × ? + 16(2) = 2620 options: A)22 B)12 C)14 D)16 E)None of these SOLUTION:? = 2620−256 /197=12 Answer B #### B QUESTION:The function f is defined for all positive integers n by the following rule: f(n) is the product of the distinct prime factors of n. If f(n) < 75 and n is not prime, what is the greatest possible value of f(n)? options: A)72 B)69 C)65 D)60 E)58 SOLUTION:Since we need the largest value of f (n), we will start with the largest option. Option A: 2*2*2*2*2*2 = . This is not a product of distinct prime numbers. Hence incorrect Option B: 69 = 3*23. This is a product of distinct prime numbers. Rest all the options are smaller that 69. Correct Option: B #### B QUESTION:Meena bought a watch with 25% discount on the selling price. If the watch cost her Rs.1545. What is the original selling price of the watch? options: A)Rs.2050 B)Rs.2040 C)Rs.2030 D)Rs.2060 E)None of these SOLUTION:Explanation: CP of Meenal is 75% of the Original SP. :. Original SP = 1545x100/75 = Rs.2060. Answer: Option D #### D QUESTION:A person was going through train from Bombay to Pune. After every five minutes he finds a train coming from opposite direction. Velocity of trains are equal of either direction. If the person reached Pune in one hour then how many trains he saw in the journey ? options: A)9 B)10 C)11 D)12 E)13 SOLUTION:11 ANSWER:C #### C QUESTION:John is three times as old as Sam. If John will be twice as old as Sam in six years, how old was Sam four years ago? options: A)2 B)4 C)6 D)8 E)16 SOLUTION:j= 3s after 6 years j +6 = 2(s+6) j= 2s+6 2s +6 = 3s s= 6 four years ago s= 6-4= 2 A is the answer #### A QUESTION:One-third of Rahul’s savings in National Savings Certificate is equal to one-half of his savings in Public Provident Fund. If he has Rs. 3,50,000 as total savings, how much has he saved in Public Provident Fund ? options: A)Rs. 130,000 B)Rs. 150,000 C)Rs. 160,000 D)Rs. 140,000 E)None SOLUTION:EXPLANATION Let savings in N.S.C and P.P.F. be Rs. x and Rs. (350000 – x) respectively. Then, 1/3x=1/2(350000-x) => x/3 + x/2 = 175000 => 5x/6 = 175000 => x= 175000 x 6 /5= 210000 Savings in Public Provident Fund = Rs. (350000 – 210000) = Rs. 140000 Answer D #### D <<<Examples ends QUESTION:36 men can complete a piece of work in 18 days. In how many days will 27 men complete the same work? options: A)16 B)18 C)24 D)22 E)26 SOLUTION:C 24 Let the required number of days be x. Less men, More days (Indirect Proportion) 27 : 36 :: 18 : x <-> 27 x x = 36 x 18 x = (36 x 18)/27 x = 24 #### C

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:A train starts full of passengers at the first station it drops 1/3 of the passengers and takes 280 more at the second station it drops one half the new total and takes twelve more. On arriving at the third station it is found to have 244 passengers. Find the no of passengers in the beginning? options: A)292 B)180 C)276 D)144 E)168 SOLUTION:Let no of passengers in the beginning be X After first station no passengers=(X-X/3)+280=2X/3 +280 After second station no passengers =1/2(2X/3+280)+12 1/2(2X/3+280)+12=244 2X/3+280=2*232 = 464 - 280 = 184 2X/3=184 X=276. So the answer is option C) 276. #### C QUESTION:For Consecutive integers x, y and z, where x > y > z, which of the following CANNOT be the value of (x2−y2)∗(y2−z2)(x^2−y^2)∗(y^2−z^2) ? options: A)63 B)99 C)195 D)276 E)323 SOLUTION:2 ways: 1) x-odd y-even z-odd (odd^2−even^2)(even^2−odd^2)=even 2) x-even y-odd z-even (even^2−odd^2)(odd^2−even^2)=even The only even answer we have is D) 276 #### D QUESTION:A certain sum amount to $1400 in 2 yrs and $2000 in five years on certain fixed simple interest. In how many yrs would the amount be $1840 had it been put at the rate of interest compounded annually? options: A)4.5 B)3.5 C)3 D)2 E)1 SOLUTION:We can form equations as following: Initial amount = P, Total amount after interest = T, Interest per year = I T = P+I Given T1 = P+2I = 1400 T2 = P+ 5I = 2000 From this we get, P = 1000I = 200 $ Now we know that simple interest is<Compound interest ( CI = SI only after 1st year if CI is compounded annually) consider simple interest - after 1st yer it is 200$ , after 2nd years it is 400$ and after 3rd year it is 600$. To get a 440 $ compound interest the duration have to be > 1 year and < 3 years. Only option fitting : Option D. #### D QUESTION:A man took loan from a bank at the rate of 12% p.a. simple interest. After 3 years he had to pay Rs. 5400 interest only for the period. The principal amount borrowed by him was: options: A)Rs. 2000 B)Rs. 10,000 C)Rs. 15,000 D)Rs. 20,000 E)Rs. 26,000 SOLUTION:Principal = Rs.(100 x 5400)/(12x3) = Rs. 15000. Answer: Option C #### C QUESTION:Two 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? options: A)11 B)10 C)8 D)12 E)15 SOLUTION:Suppose they meet x hours after 8 a.m. Distance covered by A in x hours = 20x km. Distance covered by B in (x - 1) hours = 25(x - 1) km. Therefore 20x + 25(x - 1) = 110 45x = 135 x = 3. So, they meet at 11 a.m. Answer: A #### A QUESTION:How many points (x, y) lie on the line segment between (22, 12 2/3) and (16, 17 2/3) such that x and y are both integers? options: A)1 B)5 C)7 D)8 E)9 SOLUTION:slope = (17 2/3 - 12 2/3) / (16 - 22) = -5/6 y = mx + b => 12 2/3 = -22*5/6 + b => b = 31 y = -5x/6 + 31 Only integer values work, and the only multiples of 6 between 16 and 22 for x values is 18, thus 1 point. A #### A QUESTION:3^b + 3^b + 3^b = options: A)7^b B)7^(b + 1) C)7^(7b) D)3^(b + 1) E)49^B SOLUTION:Easy one. 3*3^b = 3^(b+1) Ans. D #### D QUESTION:In each term of a sequence, 3 is added to get the next term. If the first term is 6, what is the 64th term? options: A) 192 B) 154 C) 134 D) 174 E) 120 SOLUTION:1rst term + 63 terms = 6 + 3+3+3+3+3+3+3+...+3 (63 times) 6 + (3 x 63) = 3 + 189 = 192 Answer A #### A QUESTION:A 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 66 books in the special collection at that time, how many books of the special collection were loaned out during that month? options: A)20 B)30 C)35 D)45 E)55 SOLUTION:there are 9 books less(75-66) which represents 20% of the loaned books (100-80) So total loaned out books = 45 Answer D #### D QUESTION:1/2+[(2/3*3/8)+4]-7/16= options: A)29/16 B)19/16 C)69/16 D)9/13 E)0 SOLUTION:1/2+[(2/3*3/8)+4]-7/16= 1/2+[(1/4)+4]-7/16= 1/2+[17/4]-7/16= 8/16 + 68/16 - 7/16 = 69/16 C #### C QUESTION:The 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? options: A)18/35 B)18/18 C)18/19 D)18/17 E)18/12 SOLUTION:If both agree stating the same fact, either both of them speak truth of both speak false. Probability = 3/5 * 4/7 + 2/5 * 3/7 = 12/35 + 6/35 = 18/35 Answer:A #### A QUESTION:A password for a computer uses three digits from 0 to 9, inclusive. What is the probability that the digits of the password solely consist of prime numbers or zero? options: A)1/32 B)1/16 C)1/8 D)2/5 E)1/2 SOLUTION:To calculate all the possibilities, there are 10 choices for each digit. The number of possibilities for five digits is 10 × 10 × 10 = 1,000 possible combinations. Prime numbers constitute 2, 3 In addition to zero, this is 3 total possibility for each digit. So the number of satisfactory variants is 3× 3 × 3 . So the probability is 1/2 × 1/2 × 1/2 = 1/8. The right answer is choice (C). #### C QUESTION:If 3 persons can do 3 times of a particular work in 3 days, then, 7 persons can do 7 times of that work in options: A)6 days B)2 days C)3 days D)5 days E)4 days SOLUTION:That is, 1 person can do one time of the work in 3 days. Therefore, 7 persons can do 7 times work in the same 3 days itself. C #### C QUESTION:At the end of three years what will be the compound interest at the rate of 10% p.a. on an amount of Rs.25000? options: A)8275 B)1879 C)2779 D)2672 E)2782 SOLUTION:A = 25000(11/10)^3 = 33275 = 25000 ---------- 8275 Answer: A #### A QUESTION:Which of the following is closest to (8!-7!)/(8!+7!)? options: A)0.01 B)0.8 C)0.2 D)1 E)10 SOLUTION:(8!-7!)/(8!+7!) 7! (8-1)/7! (8+1) 7/9 = 0.8 (approximately) B is the answer #### B QUESTION:A retail appliance store priced a video recorder at 20 percent above the wholesale cost of $200. If a store employee applied the 15 percent employee discount to the retail price to buy the recorder, how much did the employee pay for the recorder? options: A) $204 B) $216 C) $220 D) $230 E) $240 SOLUTION:Wholesale cost of video recorder = 200 $ Video recorder was priced at 20 percent above 200 = 240 $ % discount given by store employee = 15 Emlpoyee paid = .85 * 240 = 204 $ Answer A #### A QUESTION:A tree of height 36m is on one edge of a road broke at a certain height. It fell in such a way that the top of the tree touches the other edge of the road. If the breadth of the road is 12m, then what is the height at which the tree broke? options: A)16 B)17 C)18 D)19 E)20 SOLUTION:Let the tree was broken at x meters height from the ground and 36 - x be the length of other part of the tree. From the diagram, (36−x)2=x2+122(36−x)2=x2+122 ⇒1296−72x+x2=x2+144⇒1296−72x+x2=x2+144 ⇒72x=1296−144⇒72x=1296−144 ⇒x=16 Answer:A #### A QUESTION:William earned $3,200 per month as a teacher for the ten months from September to June. Then he took a job as a barista at a local café, where he earned $2,000 per month during July and August. What was his average monthly pay for the 12 months? options: A)$2,400 B)$2,800 C)$2,600 D)$3,000 E)$2,500 SOLUTION:E. William earned $3,200 × 10 = $32,000 as a teacher, and he earned $2,000 × 2 = $4,000 as a barista. So he earned $32,000 + $4,000 = $36,000 over the 12 months. Plug these values into the formula for the mean: mean=sum of values/number of values=>36.000/12=3.000 correct answer D)$3.000 #### D QUESTION:There are three foam generators in the factory, each of the first two can generate 8 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? options: A)120. B)132. C)146. D)154. E)115 SOLUTION:Let the foam generators capacity be - A = 8 lit/hr B = 8 lit/hr C = 18 lit/hr Total foam generation in 1 hour will be 34 lit ( 8 + 8 + 18 ) ; since in 1 and 1/2 hr they will generate 34 + 17 => 51 litres... Now one of the first generators stops working ( Say A stops working ) , so we have - B = 8 lit/hr C = 18 lit/hr Total foam generation in 2 hour will be 52 litres {2 (8+18)} The third generator stops working and now only B works for the remaining time 1 and 1/2 ( 5 - 1 and 1/2 - 2 )... Foam generated by B will be 3/2 * 8 => 12 litres So, total foam generated will be 115 Litres ( 51 + 52 + 12 ) ; hence answer will be (E) #### E QUESTION:In 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 finance majors? options: A)3 B)5 C)8 D)11 E)17 SOLUTION:pqrs = 1365 = 3* 5 *7 * 13 Since 1< p < q < r < s, the number of students who are finance majors is q = 5. The answer is B. #### B QUESTION:The 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 $30,000? options: A)$38,796. B)$29,232. C)$38,976. D)$39,679. E)$36,796. SOLUTION:30,000 *1.16*.84= Unit and tens digit of the expression is 6 and 7 respectively. Only option B fulfills the condition and hence is the answer #### B QUESTION:At the end of three years what will be the compound interest at the rate of 10% p.a. on an amount of Rs.18000? options: A)6620 B)2888 C)2776 D)2997 E)5958 SOLUTION:A = 18000(11/10)^3 = 23958 = 18000 ---------- 5958 Answer: E #### E QUESTION:36 men can complete a piece of work in 18 days. In how many days will 72 men complete the same work ? options: A)24 B)17 C)18 D)9 E)11 SOLUTION:Explanation: Less Men, means more Days {Indirect Proportion} Let the number of days be x then, 72 : 36 :: 18 : x x = 9 Answer: D) 9 days #### D QUESTION:A 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 ? options: A)100 m B)120 m C)130 m D)150 m E)None of these SOLUTION:Explanation : Solution: Relative speed = (9 - 8) = 1 km/hr. Distance covered in 3 minutes = (1 * 3/60) km = 1/20 km = 50 m. .'. Distance between the criminal and policeman = (265 - 50) m = 215 m. Answer : E #### E QUESTION:How many 4 letter combinations can be made from the letters of the word VERMONT if the first letter has to be a vowel and the last letter has to be a consonant, and each letter can be used only once? options: A)21 B)42 C)120 D)600 E)200 SOLUTION:Vowel: E O Consonants: V R M N T First letter can be filled in 2 Ways ( As the question states thatfirst letter has to be a vowel) Fourth letter can be filled in 5 Ways ( As the question states thatthe last letter has to be a consonant) Now since each letter can be used only once, and 2 letters out of 7 letters are already used in First and fourth letter Second letter can be filled in 5 Ways Third letter can be filled in 4 Ways So, Total number of ways = 2 Ways x 5 Ways x 4 ways x 5 ways = 200 Answer E #### E QUESTION:There are cats got together and decided to kill the mice of 999919. Each cat kills equal number of mice and each cat kills more number of mice than cats there were. Then what are the number of cats? options: A)941,1009 B)991,1001 C)991,1009 D)791,1009 E)931,1009 SOLUTION:999919 can be written as 1000000 – 81 = 10002 – 92 ie of the form a2-b2=(a+b)(a-b) =(1000+9)*(1000-9) = (1009)*(991) Given that number of cats is less than number if mice. So number of cats is 991 and number of mice were 1009 Answer C #### C QUESTION:A is twice as good a workman as B and together they complete a work in 12 days. In how many days A alone can do the work? options: A)32 B)33 C)34 D)35 E)36 SOLUTION:A’s one day’s work : B’s one day’s work= 2:1 (A+B)’s one day’s work= 1/12 B’s one day’s work= 1/12 *1/3 = 1/36 B alone can do the work in 36 days ANSWER:E #### E QUESTION:A committee of 3 persons is to be formed from 3 company secretaries, 4 economists and 1 chartered accountant. What is the probability that each of the three professions is represented in the committee? options: A)1/28 B)3/28 C)1/14 D)4/28 E)3/14 SOLUTION:3/8*4/7*1/6*3! = 3/14. We are multiplying by 3! because we can choose secretary, economist, and accountant is several way: SEA, SAE, ESA, EAS, ASE, AES. Answer: E. #### E QUESTION:A 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? options: A)30/18 hours B)37/13 hours C)80/13 hours D)30/13 hours E)60/29 hours SOLUTION:Speed downstream = 20 + 9 = 29 kmph. Time required to cover 60 km downstream = d/s = 60/29 = 60/29 hours. Answer: E #### E QUESTION:A 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 W on this shipment? options: A)a) $100 B)b) $115 C)c) $125 D)d) $130 E)e) $135 SOLUTION:I recommend one should use fractions to solve this one rather than converting it into decimals Sol: 1500 heads -> $600 1 head -> $600/1500 1 head -> $(2/5) 25% more of (2/5) -> 125/100 * 2/5 = $(1/2) He sold 2/3*1500 = 1000 heads for $(1/2) per head Total revenue by selling 1000 heads = 1000 * 1/2 = $500 Heads left: 500 Cost per head: 90% of the previous price: 90/100 * 1/2 = $(9/20) Total revenue by selling 500 heads = 9/20 * 500 = 225 Total revenue after selling 1500 cabbage heads - 225+500 = $725 Money spent on the purchase: $600 Profit W= 725-600 = $125 Ans:C #### C QUESTION:If 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? I. 14.5 II. 15.3 III. 9.5 options: A)I only B)I and II only C)II only D)III only E)I and III only SOLUTION:Mean = 12 SD = 1.3 2 SD above mean = 12+2*1.3 = 14.6 2 SD below mean = 12-2*1.3 = 9.4 14.5 and 9.5 lies in the range of 2SD from mean Answer: Option C #### C QUESTION:What is the next number of the following sequence 7, 0, 1, 8, 5, 12, 9, 26, 3, 2, 23, ? options: A)28 B)29 C)30 D)31 E)32 SOLUTION:7,0,1,8,5,12,9,26,3,2,23,X (7,0,1,8),(5,12,9,26),(3,2,23,X) 7+0+1=8 5+12+9=26 3+2+23=X => X=28 ANSWER:A #### A QUESTION:After an ice began to melt out from the freezer, in the first hour lost 3/4, in the second hour lost 3/4 of its remaining. If after two hours, the volume is 0.3 cubic inches, what is the original volume of the cubic ice, in cubic inches? options: A)2.5 B)3.0 C)4.8 D)6.5 E)8.0 SOLUTION:Let initial volume of ice be = x Ice Remaining after 1 hour = x - 0.75x = 0.25x Ice Remaining after 2 hour = (1/4)x - (3/4 * 1/4 * x) = (1/16)x (1/16)x = 0.3 x = 4.8 Alternate solution: Try to backsolve. Initial volume = 4.8 After one hour --> (1/4)4.8 = 1.2 After two hours --> (1/4)1.2 = 0.3 Answer: C #### C QUESTION:Determine the value of 62/54 divided by 62/54 options: A)0 B)1 C)2 D)3 E)none SOLUTION:Solution: Each number divided by itself equals 1. Answer B #### B QUESTION:Three 6 faced dice are thrown together. The probability that exactly two dice show the same number on them is options: A)5/9 B)5/12 C)1/36 D)7/12 E)4/9 SOLUTION:Using question number 11 and 12, we get the probability as 1 - (1/36 + 5/9) = 5/12 ANSWER:B #### B QUESTION:A student is ranked 13th from right and 8th from left.how many are there? options: A)18 B)19 C)20 D)21 E)22 SOLUTION:13th from right means = x + 12 8th from left means = 7 + x Total = 12+7+1 = 20 ANSWER:C #### C QUESTION:A marble statue is being carved by a sculptor. In the first week 35% is cut away, in the second week 20% of the remainder is cut away and in the third week 25% of the remainder is cut away and polished to produce the final statue. The weight of the final statue is 48.75 lbs. What was the weight of the original piece of marble? options: A)134 B)167 C)125 D)113 E)111 SOLUTION:C lb : reverse the calculations: So 48.75 ÷ 0.75 = 65, 65 ÷ 0.8 = 81.25 and 81.25 ÷ 0.65 = 125. #### C QUESTION:A boat can move upstream at 20 kmph and downstream at 35 kmph, then the speed of the current is? options: A)5 kmph B)7.5 kmph C)8 kmph D)9 kmph E)4 kmph SOLUTION:US = 20 DS = 35 M = (35 - 20)/2 = 7.5 Answer:B #### B QUESTION:A 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? options: A)7 cm B)6 cm C)4 cm D)3 cm E)9 cm SOLUTION:Volume of the wire (in Cylindrical shape) is equal to the volume of the sphere. π(16)2 * h = (4/3)π (12)3 => h = 9 cm Answer: E #### E QUESTION:A single discount equivalent to the discount series of 10%, 10% and 5% is? options: A)23.05 B)31.95 C)21.65 D)23.45 E)23.15 SOLUTION:100*(90/100)*(90/100)*(95/100) = 76.95 100 - 76.95 = 23.05 Answer: A #### A QUESTION:There 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? options: A)8 B)10 C)12 D)14 E)15 SOLUTION:Number of ways in which one can travel from P to R =3×4=12 Answer: Option C #### C QUESTION:A can run 288 metre in 28 seconds and B in 32 seconds. By what distance A beat B? options: A)38 metre B)28 metre C)23 metre D)15 metre E)36 metre SOLUTION:Clearly, A beats B by 4 seconds Now find out how much B will run in these 4 seconds Speed of B = Distance/Time taken by B=288/32=9 m/s Distance covered by B in 4 seconds = Speed × time =9×4=36 metre i.e., A beat B by 36 metre Answer is E #### E QUESTION:A train 120 m long running at 72 kmph crosses a platform in 25 sec. What is the length of the platform? options: A)443 m B)354 m C)450 m D)380 m E)250 m SOLUTION:D 350 D = 72 * 5/18 = 25 = 500 – 120 = 380 #### D QUESTION:X, Y, and Z are consecutive numbers and X > Y > Z. Also, X + 3Y + 3Z = 5Y + 8. What is the value of Z? options: A)2 B)3 C)4 D)5 E)6 SOLUTION:If X, Y, and Z are consecutive numbers and X > Y > Z, then Y = Z+1 and X = Z+2. X + 3Y + 3Z = 5Y + 8 Z+2+3Z+3+3Z = 5Z+5+8 2Z = 8 Z = 4 The answer is C. #### C QUESTION:What is the 4 digit number in which the 1st digit is 1/3 of the second, the 3rd is the sum of the 1st and 2nd, & the last is three times the second? options: A)1234 B)1567 C)1349 D)1456 E)1356 SOLUTION:First digit is 1/3 second digit => The numbers can be 1 & 3, 2& 6, 3 & 9. First + second = third => we can eliminate 3 & 9 since 3 + 9 = 12. Last is 3 times the second => we can eliminate option 2 & 6 since 3 * 6 = 18. Hence the number is 1349 C #### C QUESTION:Tom and Bob have a total of 49 toys. If Bob has 5 more toys than Tom, how many toys does each one have? options: A)27 B)32 C)43 D)54 E)77 SOLUTION:If 5 toys are taken out of 49 toys and the remaining ones distributed to Tom and Bob, they will both have equal numbers of toys 49 - 5 = 44 for Tom and Bob If distributed equally, each one will have 44 / 2 = 22 toys Bob has 5 more toys than Tom, so Bob has 22 + 5 = 27 toys correct answer A #### A QUESTION:Murali 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? options: A)17 kmph B)50 kmph C)18 kmph D)17 kmph E)11 kmph SOLUTION:Let the distances between city A to B and B to C be 2x km and 3x km respectively. Total time taken to cover from A to C = (2x)/40 + (3x)/60 = (6x + 6x)/120 = 12x/120 = x/10 Average speed = (2x + 3x)/(x/10) = 50 kmph. Answer:B #### B QUESTION:if 8^25 divided by 7 then what is reminder options: A)25 B)1 C)0 D)2 E)3 SOLUTION:8^25/7 8 can be written as 7*1+1 (7*1+1)^25/7 (ax+1)^n/a always gives the remainder 1 here a=7,x=1,n=25 Hence remainder is 1 ANSWER:B #### B QUESTION:In the faculty of Reverse-Engineering, 100 second year students study numeric methods, 100 second year students study automatic control of airborne vehicles and 25 second year students study them both. How many students are there in the faculty if the second year students are approximately 50% of the total? options: A)340 B)335 C)370 D)360 E)350 SOLUTION:Total number of students studying both are 100 + 100 - 25 = 175 (Subtracting the 25 since they were included in the both the other numbers already). So 50% of total is 175, so 100% is 350 Answer is E #### E QUESTION:A 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? options: A)33/95 B)33/91 C)33/94 D)33/16 E)33/17 SOLUTION:Given 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 = ¹²C₄/¹⁵C₄ = (12 * 11 * 10 * 9)/(15 * 14 * 13 * 12) = 33/91 Answer:B #### B QUESTION:A 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? options: A)18% B)20% C)17% D)18% E)None of these SOLUTION:Explanation: Let the CP of the article = Rs.100. Then labeled price = Rs.130. SP = Rs.130- 10% of 130 = Rs.130-13 = Rs.117. Gain = Rs.117 – Rs.100 = Rs.17 Therefore, gain/profit percent = 17%. Answer: Option C #### C QUESTION:The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is? options: A)165 B)771 C)245 D)177 E)121 SOLUTION:Speed = [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. Answer: C #### C QUESTION:The 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. 28,000 is made? options: A)Rs. 1,10,000 B)Rs. 1,20,000 C)Rs. 1,24,000 D)Rs. 1,21,000 E)None of these SOLUTION:The value of the machine after two years = 0.8 * 0.8 * 1,50,000 = Rs. 96,000 SP such that a profit of Rs. 24,000 is made = 96,000 + 28,000 = Rs. 1,24,000 ANSWER:C #### C QUESTION:A company that ships boxes to a total of 12 distribution centers uses color coding to identify each center. If either a single color or a pair of two different colors is chosen to represent each center and if each center is uniquely represented by that choice of one or two colors, what is the minimum number of colors needed for the coding? (Assume that the order of the colors in a pair does not matter.) options: A)4 B)5 C)6 D)12 E)24 SOLUTION:Let's start with 4 minimum number of colors So single color code we can make 4 nos. Now if we need to make 2 color combination out of 4 we can do so in 4!/2!*2! or 4*3/2 or 6 So total we can make 4+6=10 color combinations but we have 12 boxes So let's look at 5 we get 5 single color codes and out 5 color choices, we can choose 2 in 5!/2!*3! ways or 10 ways. So total we can have 5+10=15 color combinations. So, minimum number we need will be 5 Ans is B....... #### B QUESTION:If x, y, and z are consecutive positive integers greater than 1, not necessarily in that order, then which of the following is (are) true? I. x > z II. 2x+ 2y > 2z III. yz > xz IV. xy > y + z options: A) I only B) II only C) II and III only D) II and IV only E) III and IV only SOLUTION:we do not know the values or the relative values but that the three are consecutive.. so the max difference in any two number is 2 and min 1.. lets see the choices.. I. x > z... we do not know the values or the relative values... need not be true.. II. 2x+ 2y > 2z or x+ y > z we take the worst case that z is teh largest and x and y are lowest possible..... so 2+3>4.. 5>4.. always true III. yz > xz we do not know the values or the relative values between x and y..need not be true IV. xy > y + z xy-y>z or y(x-1)>z... again lets take the worst scenario.. we 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 only ii is true ans B #### B QUESTION:Two trains 200m and 250m long run at the speed of 72kmph and 18kmph in opposite directions in parallel tracks. The time which they take to cross each other is? options: A)5.6sec B)8.9sec C)10.8sec D)12.6sec E)18 sec SOLUTION:Relative speed = 72+18 = 90 kmph * 5/18 = 25 m/s Distance covered in crossing each other = 200+250 = 450m Required time = 450*1/25 = 18 sec Answer is E #### E QUESTION:What is the smallest positive integer x, such that 1944x is a perfect cube? options: A)4 B)3 C)8 D)12 E)18 SOLUTION:Take out the factors of 1944 that will come 2^3*3^3 *3^2. for perfect cube you need every no. raise to the power 3. for 1944 to be a perfect cube, need 1 3 that means =3 B is the answer. #### B QUESTION:A bike covers a certain distance at the speed of 67km/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? options: A)89.33 km/h B)85.34 km/h C)87.67 km/h D)90.25 km/h E)90.64 km/h SOLUTION:Ans.(A) Sol. Total distance = 67 × 8 = 536 km Now speed = 536/6 = 89.33 km/h #### A QUESTION:√(36)^2 options: A)6 B)14 C)36 D)21 E)None of these SOLUTION:explanation √(36)^2 =? or, ? = 36 Answer C #### C QUESTION:What is the smallest number which when increased by 3 is divisible by 27, 35, 25, & 21 ? options: A)4722 B)4725 C)4728 D)4731 E)4733 SOLUTION:Here smallest number means LCM Hence LCM of 27,35,25,21 = 3^3 x 5^2 x 7 = 4725 Therefore required number is 4725 - 3 =4722 Ans - A #### A QUESTION:Excluding stoppages, the speed of a bus is 50 kmph and including stoppages, it is 43 kmph. For how many minutes does the bus stop per hour? options: A)70 min B)16 min C)20 min D)8.4 min E)40 min SOLUTION:D 8.4 min Due to stoppages, it covers 7 km less. Time taken to cover 9 km = (7/50 x 60) min = 8.4 min #### D QUESTION:A man can swim in still water at 7.5 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is? options: A)1.7 B)1.4 C)1.1 D)1.5 E)2.5 SOLUTION:M = 7.5 S = x DS = 7.5 + x US = 7.5 + x 7.5 + x = (7.5 - x)2 7.5 + x = 15 -2x 3x = 7.5 x = 2.5 Answer:E #### E QUESTION:How many integers between 2000 and 3000 that have distinct digits and increase from left to right ? options: A)10 B)20 C)60 D)120 E)600 SOLUTION:Since the numbers must be distinct and increasing from left to right, The only arrangements we could come-up with are: 245_ --> 4 246_ --> 3 247_ --> 2 248_ --> 1 256_ --> 3 257_ --> 2 258_ --> 1 267_ --> 2 268_ --> 1 Number of integers =20 B #### B QUESTION:The number of new words that can be formed by rearranging the letters of the word 'TOO' is options: A)5 B)10 C)11 D)2 E)3 SOLUTION:Explanation: Number of words which can be formed = 3! - 1 = 6 - 1 = 5. Answer: A #### A <<<Examples ends QUESTION:A 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? options: A)23/35 B)23/38 C)23/18 D)53/18 E)23/22 SOLUTION:Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles. Probability 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 = (⁶C₁ * ⁹C₁)/¹⁵C₂ + ⁶C₂/¹⁵C₂ = (6 * 9 * 2)/(15 * 14) + (6 * 5)/(15 * 14) = 36/70 + 1/7 = 46/70 = 23/35 Answer:A #### A

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:A train running at the speed of 36 km/hr crosses a pole in 9 seconds. What is the length of the train? options: A)286 B)278 C)90 D)150 E)287 SOLUTION:Speed=(36 * 5/18) m/sec = (10) m/sec Length of the train = (Speed x Time) = (10 * 9) m = 90 m. Answer:C #### C QUESTION:A train 400 m long can cross an electric pole in 20 sec and then find the speed of the train? options: A)17 Kmph B)78 Kmph C)72 Kmph D)18 Kmph E)19 Kmph SOLUTION:Length = Speed * time Speed = L/T S = 400/20 S = 20 M/Sec Speed= 20*18/5 (To convert M/Sec in to Kmph multiply by 18/5) Speed = 72 Kmph Answer: C #### C QUESTION:In a college, the ratio of the number of boys to girls is 8 : 5. If there are 300 girls, the total number of students in the college is options: A)420 B)520 C)620 D)780 E)820 SOLUTION:Explanation: Let the boy are 8x and Girls are 5x => 5x = 300 => x = 60 Total students = 8x+5x = 13x = 13(60) = 780 Option D #### D QUESTION:The average age of a husband, wife and their child 12 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? options: A)19.01 years B)5.25 years C)16 years D)15 years E)4.75 years SOLUTION:Sum of the present ages of husband, wife and child = (23 * 2 + 5 * 2) = 57 years. Required average = 57/12 = 4.75 years. Answer:E #### E QUESTION:If 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 ? options: A)x-2 B)x-4 C)x+4 D)x-3 E)x-1 SOLUTION:Original Digits=xy i.e. Number=10x+y After reversing the digits: Digits=yx i.e. Number=10y+x 10y+x is 36 more than 10x+y 10x+y+36=10y+x 10x-x+36=10y-y 9x+36=9y x+4=y OR y=x+4 Answer : C #### C QUESTION:A man’s speed with the current is 17 km/hr and the speed of the current is 2.5 km/hr. the man’s speed against the current is : options: A)8.5 km/hr B)12 km/hr C)10 km/hr D)12.5 km/hr E)None of these SOLUTION:Solution Man's rate in still water = (17-2.5) km/hr = 14.5 km/hr. Man's rate against the current = (14.5-2.5) km/hr = 12 km/hr Answer B #### B QUESTION:Express of the following as a fraction: 25% options: A)1/4 B)1/8 C)2/9 D)3/6 E)None of them SOLUTION:25% = 25/100= 1/4. Answer is A. #### A QUESTION:If we know that a positive integer is a multiple of 4, how many (distinct) possibilities are there for the last digit of the integer? options: A)3 B)4 C)5 D)6 E)7 SOLUTION:the last digit of the integer may be any of (0,2,4,6,8) so, 1/5 ANSWER:C #### C QUESTION:Sum of 3 consecutive even no.'s is 34 more than the 1st no. of the series. Find the middle no.? options: A)8 B)12 C)14 D)16 E)18 SOLUTION:Let the numbers be x, x+2 and x+4 then x + x+2 + x+4 = x+34 3x + 6 = x + 34 2x = 28 \inline \therefore x = 14 \inline \therefore Middle number = x + 2 = 14+2 = 16 D #### D QUESTION:Joshua is fifth from the bottom in a queue of 100 boys. What is the position of Joshua from the top of the queue? options: A)51 B)52 C)53 D)54 E)55 SOLUTION:Solution: 51 Explanation: The position of boys higher than Joshua in the queue is 100 - 50 = 50. Therefore, the position of Joshua from the top is 50 + 1 = 51. Answer A #### A QUESTION:In a rectangular coordinate system, if a line passes through the points (-17,-18), (13,22) and (x,2) then what is the value of x? options: A)-2 B)-1 C)0 D)1 E)2 SOLUTION:The slope of the line m is rise/run = 22-(-18) / 13-(-17) = 4/3 4/3 = 22-2 / 13-x 52-4x = 66-6 x = -2 The answer is A. #### A QUESTION:P and Q are both positive integers. When P is divided by Q, the remainder is some positive integer D, and when P is divided by (Q + 7), the remainder is also D. If P/Q = 1020.75 and P/(Q + 7) = 816.6, then which of the following gives the correct set of {D, Q}? options: A){6, 12} B){6, 15} C){21,28} D){9, 15} E){15, 24} SOLUTION:p/q= d=p/q+7 d= .75 q d= .6(q+7) we get d = 21 and q = 28. Answer = C. #### C QUESTION:30% of the men are more than 25 years old and 80% of the men are less than or equal to 50 years old. 20% of all men play football. If 20% of the men above the age of 50 play football, what percentage of the football players are less than or equal to 50 years? options: A)15% B)20% C)80% D)70% E)90% SOLUTION:Explanation : Let number of men = 100. Then, 80 men are less than or equal to 50 years old i.e 20 men are greater than 50 years of age. Now, the number of men above 50 years who play football = 20% of 20 = 4. 20% of all men play football i.e total no. of men who play football = 20, out of which 4 men are above 50 years old. So, 20 - 4 = 16 men are less than or equal to 50 years old. Therefore, percentage of football players less than or equal to 50 years = (16/20) x 100 = 80% . Answer : C #### C QUESTION:In 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? options: A)A)10 B)B)12 C)C)15 D)D)20 E)E)25 SOLUTION:the difference between the highest and lowest salaries is $100,000. So there are at least 2 people - say one with salary 0 and the other with 100k. No salary will be outside this range. Median = 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. Mean = 20k more than median so in our example, mean salary = 70k On the number line, 0........50k (median)........100k Mean = 70k So 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: 0....50k.....100k, 100k, 100k But 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: 0, ... 50k, 50k, 50k, 50k, ... 100k, 100k, 100k, 100k, 100k the median is not at 50k yet. Add another 3 people at 50k and another 2 at 100k to get 0, 50k, 50k, 50k, 50k, 50k, 50k, 50k, 100k, 100k, 100k, 100k, 100k, 100k, 100k Now the median is 50k and mean is 70k. Total number of people is 15. Answer (C) #### C QUESTION:There 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? options: A)120. B)132. C)141 D)154. E)166. SOLUTION:Let the foam generators capacity be - A = 12 lit/hr B = 12 lit/hr C = 18 lit/hr Total 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... Now one of the first generators stops working ( Say A stops working ) , so we have - B = 12 lit/hr C = 18 lit/hr Total foam generation in 2 hour will be 60 litres {2 (12+18)} The third generator stops working and now only B works for the remaining time 1 and 1/2 ( 5 - 1 and 1/2 - 2 )... Foam generated by B will be 3/2 * 12 => 18 litres So, total foam generated will be 141 Litres ( 63 + 60 + 18 ) ; hence answer will be (C) #### C QUESTION:Carolyn bought 16 gumballs, Lew bought 14 gumballs, and Carey bought X gumballs. The average (arithmetic mean) number of gumballs the three bought is between 19 and 25, inclusive. What is the difference between the greatest number and the smallest number of gumballs Carey could have bought? options: A)20 B)18 C)24 D)26 E)28 SOLUTION:Smallest gumballs = (19-16) + (19-14) +19= 27 Largest gumballs = (25-16) + (25-14) +25= 45 Difference = 45 - 27 = 18 B #### B QUESTION:By selling 150 mangoes, a fruit-seller gains the selling price of 30 mangoes. Find the gain percent? options: A)11 B)25 C)77 D)99 E)21 SOLUTION:SP = CP + g 150 SP = 150 CP + 30 SP 120 SP = 150 CP 120 --- 30 CP 100 --- ? => 25%.Answer:B #### B QUESTION:Meena bought a watch with 25% discount on the selling price. If the watch cost her Rs.1545. What is the original selling price of the watch? options: A)Rs.2050 B)Rs.2040 C)Rs.2030 D)Rs.2060 E)None of these SOLUTION:Explanation: CP of Meenal is 75% of the Original SP. :. Original SP = 1545x100/75 = Rs.2060. Answer: Option D #### D QUESTION:If x, y, and z are all factors of 35, which of the following must be true? options: A)The product xyz > 35 B)Either x = y, y = z, or x = z C)x – y – z = even D)The product xyz is odd E)yz/x is an integer SOLUTION:All the factors of 35 are odd numbers. The product of odd numbers is odd. The answer is D. #### D QUESTION:A teacher of 6 students takes 2 of his students at a time to a zoo as often as he can, without taking the same pair of children together more than once. How many times does the teacher go to the zoo? options: A)10 B)12 C)15 D)20 E)30 SOLUTION:Two students can be selected from 6 in 6C2 =15 ways. Therefore, the teacher goes to the zoo 15 times. Option C is answer #### C QUESTION:What is the remainder when 4^381 is divided by 5 ? options: A)0 B)1 C)2 D)3 E)4 SOLUTION:I also agree that the remainder is '4' (using the last digit of the powers of 7). Could we have the official answer please?E #### E QUESTION:Three workers have a productivity ratio of 3 to 5 to 6. 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 8th 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? options: A)12 to 1 B)6 to 1 C)5 to 1 D)20 to 7 E)1 to 5 SOLUTION:The fastest worker who does 6 units of job worked for all 10 hours, so he did 6*10=60 units of job; The slowest worker who does 3 unit of job worked for only 4+3=7 hours (first 4 hours and last 3 hours), so he did 3*7=21 The ratio thus is 60 to 21, or 20 to 7. Answer: D. #### D QUESTION:Six children — A, B, C, D, E and F— are going to sit in six chairs in a row. The children B & 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? options: A)240 B)720 C)1440 D)4320 E)4800 SOLUTION:for such questions , we can treat both as one then total person=5. these 5 can be arranged in 5! ways.. but within these 5 , one consists of two people who can be arranged in 2 ways BF or FB.. so ans =5!*2=240 ans A #### A QUESTION:If x and y are positive integers, find which of the following CANNOT be the greatest common divisor of 25x and 20y? options: A)5 B)5(x-y) C)20x D)20y E)35x SOLUTION:We are looking for a choice that CANNOT be the greatest common divisor of 25x and 20y ...which means 35x and 20y when divided by the answer choice the quotient should not be a integer. lets check a. 5 25x/5 = 5x and 20y/5 = 4y both are integers so eliminate b. 5(x-y) when x = 2 and y = 1 it could be be the greatest common divisor ..so eliminate c. 20x when x = 1 its 20 and 20 cannot be the greatest common divisor of 25x and 20y ... or 25x/20x = 5/4 which is not a integer. so answer is C. #### C QUESTION:A and B together have $1210. If 4/15 of A's amount is equal to 2/5 of B's amount, how much amount does B have? options: A)$310 B)$395 C)$484 D)$512 E)$542 SOLUTION:4/15 A = 2/5 B A = 2/5 * 15/4 B A = 3/2 B A/B = 3/2 A:B = 3:2 B's share = 1210*2/5 = $484 Answer is C #### C QUESTION:Out of four consonants and three vowels, how many words can be made so that each word contains two consonants and three vowels? options: A)480 B)540 C)600 D)720 E)900 SOLUTION:4C2 x 3C3 x 5! = 720 The answer is D. #### D QUESTION:Sides of a rectangular park are in the ratio 3: 2 and its area is 3750 sq m, the cost of fencing it at 50 ps per meter is? options: A)277 B)299 C)125 D)99 E)22 SOLUTION:3x * 2x = 3750 => x = 25 2(75 + 50) = 250 m 250 * 1/2 = Rs.125 Answer:C #### C QUESTION:Rs.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’s share? options: A)Rs.130 B)Rs.145 C)Rs.154 D)Rs.160 E)Rs.164 SOLUTION:Let Y gets Rs x. Then We can say X gets Rs (x + 20 ) and Y gets Rs ( x + 35) . x + 20 + x + x + 35 = 385 3x = 330 x = 110 . R’s share = Rs ( 110 + 35 ) = Rs.145 B #### B QUESTION:The vertex of a rectangle are (1, 0), (9, 0), (1, 2) and (9, 2) respectively. If line L passes through the origin and divided the rectangle into two identical quadrilaterals, what is the slope of line L? options: A)5 B)4 C)1/2 D)1/5 E)1/8 SOLUTION:If line L divides the rectangle into two identical quadrilaterals, then it must pass through the center (5, 1). The slope of a line passing through (0,0) and (5, 1) is 1/5. The answer is D. #### D QUESTION:A 200 meter long train crosses a platform in 50 seconds while it crosses a signal pole in 42 seconds. What is the length of the platform? options: A)39.9 B)37.88 C)35 D)38.88 E)38.09 SOLUTION:Speed = [200 / 42] m/sec = 100/21 m/sec. Let the length of the platform be x meters. Then, x + 200 / 50 = 100/21 21(x + 200) = 5000 è x = 38.09 m. Answer: E #### E QUESTION:In a business school case competition, the top three teams receive cash prizes of $5,000, $3,000, and $2,000, respectively, while the remaining teams are not ranked and do not receive any prizes. There are 6 participating teams, named Team A, Team B, Team C, Team D, Team E, and Team F. If Team A wins one of the prizes, Team B will also win one of the prizes. How many outcomes S of the competition are possible? options: A)18 B)20 C)54 D)84 E)120 SOLUTION:the ways the three teams can be selected is.. i) A is selected, B is also selected, third can be any of the remaining 4.. so total ways 4.. they can be arranged in 4*3!=24 ways.. ii) A is not selected. threee teams can be selected from remaining 5 so total arrangements =5C3*3!=60 total S=84 outcomes D #### D QUESTION:Two 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 18 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? options: A)565 B)444 C)676 D)767 E)408 SOLUTION:1h ----- 2 ? ------ 60 12 h RS = 16 + 18 = 34 T = 12 D = 34 * 12 =408 Answer: E #### E QUESTION:A 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 12 miles per gallon, and from Town B to Town C, the car averaged 14 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? options: A)13 B)13.5 C)14 D)14.5 E)15 SOLUTION:Ans is E Given d_ab = 2*d_bc let d_ab = d and d_bc = x so d=2x for average miles per gallon = (d+x)/((d/12)+(x/14)) = 15 (formula avg speed = total distance/ total time) #### E QUESTION:A 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 50 hrs and a machine of type S does the same job in 20 hours. If the company used the same number of each type of machine to do the job in 5 hours, how many machines of type R were used? options: A)18/7 B)16/7 C)15/7 D)22/7 E)20/7 SOLUTION:Rate of machine R =1/50 Rate of machine S =1/20 since same no of machines used for R and S to do the same work in 5 hrs So collective rate needed to finish the work in 5 hrs= 1/5 Let the no of machine be x So, x/50 +x/20 =1/5 (2x+5x)/100=1/5 7x=20 x=20/7 So no of machine R is 20/7 Answer E #### E QUESTION:The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is: options: A)247 m B)256 m C)245 m D)527 m E)725 m SOLUTION:Speed = [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. Answer:C #### C QUESTION:When an amount was distributed among 14 boys, each of them got $80 more than the amount received by each boy when the same amount is distributed equally among 18 boys. What was the amount? options: A)5050 B)5020 C)5040 D)5030 E)5075 SOLUTION:Let the total amount be Rs. X the, x/14 - x/18 = 80 ==> 2x/126 = 80 ==> x/63 = 63 x 80 = 5040. Hence the total amount is 5040. Answer C. #### C QUESTION:Brenda 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 100 meters past their first meeting point. Each girl runs at a constant speed. What is the length of the track in meters? options: A)250 B)300 C)350 D)400 E)500 SOLUTION:Nice problem. +1. First timetogetherthey run half of the circumference. Second timetogetherthey run full circumference. First time Brenda runs 100 meters, thus second time she runs 2*100 = 200 meters. Since second time (when they run full circumference) Brenda runs 200 meters and Sally runs 100 meters, thus the circumference is 200 + 100 = 300 meters. Answer: B. #### B QUESTION:Rs.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? options: A)10% B)16% C)70% D)80% E)20% SOLUTION:Let the rate of interest during the second year be R%. Given, 4500 * {(100 + 12)/100} * {(100 + R)/100} = 5544 R = 10% Answer:A #### A QUESTION:In an intercollegiate competition that lasted for 3 days, 175 students took part on day 1, 210 on day 2 and 150 on day 3. If 80 took part on day 1 and day 2 and 70 took part on day 2 and day 3 and 20 took part on all three days, how many students took part only on day 1? options: A)25 B)45 C)55 D)70 E)30 SOLUTION:Day 1&2 = 80; Only Day 1&2 (80-20) = 60, Day 2&3 = 70; Only Day 2&3 (70-20) = 50, Only Day 1 = 175 - (60+50+20) = 45 Answer:B #### B QUESTION:The ratio E, by volume of soap to alcohol to water in a 76 litre solution is 2: 50: 100 . The solution is then altered by adding more soap, alcohol and water.After this alteration the ratio, by volume of soap to water in the solution doubles whereas the ratio, by volume of soap to water remains the same as before. What COULD BE the resulting volume. options: A)79 litres B)78 litres C)77 litres D)152 liters E)304 litres SOLUTION:I guess it should be the ratio E, by volume ofsoaptowaterin the solutiondoubleswhereas the ratio, by volume ofalocoholtowaterremains thesameas before 2:50: 100 => 1 : 25 : 50. If we add all the parts, we get 76 liters So we have 1 liters of Soap, 25 liters of Alcohol and 50 liters of Water. Now as per the Question, Soap : Water doubles but alcohol to water remains the same. So Soap becomes 2 liters, Alcohol remains 25 liters and Water remains at 50 liters. Hence 77 liters - Option C) #### C QUESTION:If an average hard drive had a capacity of 0.4 TB in 2000, and average hard drive capacities double every 5 years, what will be the average hard drive capacity in 2050? options: A)256 B)512 C)4096 D)1024 E)1536 SOLUTION:0.4*2^10=0.4*1024=409.6 The answer is C. #### C QUESTION:To be considered grade AE, an egg must weigh between 75 and 90 grams, including the shell. Shells of grade AE eggs weigh between 3 and 5 grams. What is the smallest possible mass, in grams, of a 12-egg omelet, assuming that only grade AE eggs are used, the shells are all discarded, and no mass is lost in the cooking process? options: A)800 B)840 C)864 D)900 E)1,080 SOLUTION:We're asked for the smallest possible mass, so what could the lowest mass be per egg AE? A 75 gram egg, with a 5 gram shell, or 70 grams ofcookingmass. 12 x 70 = 840, so the answer is B. #### B QUESTION:If 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%? options: A)3 B)8 C)9 D)6 E)4 SOLUTION:96% ---- 12 144% ---- ? 96/144 * 12 = 8 Answer: B #### B QUESTION:If a sum on compound interest becomes three times in 4 years, then with the same interest rate, the sum will become 81 times in: options: A)12 years B)18 years C)16 years D)14 years E)19 years SOLUTION:Explanation: The sum P becomes 3P in 4 years on compound interest 3P = P(1+R/100)4 ⇒ 3 = (1+R/100)4 Let the sum P becomes 81P in n years 81P = P(1+R/100)n ⇒ 81 = (1+R/100)n ⇒ (3)4 = (1+R/100)n ⇒ ((1+R/100)4)4 = (1+R/100)n ⇒ (1+R/100)16 = (1+R/100)n n=16 i.e, the sum will become 81 times in 16 years ANSWER IS C #### C QUESTION:If 1 = 6 2 = 12 3 = 18 4 = 24 5 = 30 Then 6 = ? Hint: Its a logic Riddle not a mathematical riddle options: A)1 B)2 C)3 D)4 E)5 SOLUTION:A 1 As stated 1=6 => 6=1 #### A QUESTION:On return from a business trip Mr. Chidambaram was to be picked up from the railway station by his coachman. Someone he managed a train connection earlier and thus arrived two hours too early. Immediately on arrived he rang up home for the coach and was told that it had just left in order to be exactly in time for the train by which he was scheduled to come. To save the time he started walking homeward at 3kmph. On the way he met the coachman who brought him home an hour before schedule. How far is the Mr. Chidambaram’s house from the railway station? options: A)22 B)18 C)99 D)27 E)11 SOLUTION:Very good questions. Appeared in Puzzles book of Ravi Nirula. Let the train's correct time is 9.00 am. Now chidambaram reached the station at 7 am and he was informed that the coachman (car) left at 7 am. So car takes 2 hours to reach the station. This car expected to reach home at 11 am. But the car after picking up chidambaram, reached home 1 hour early. i.e., 10 am. So car has travelled 3 hours and 1.5 hours towards the station. So it picked him up at 8.30 am. Car saved distance equivalent to 30 minutes. but this distance is covered by Chidambaram by walk. He took 1.5 hours to cover this distance. So Car speed is 3 times that of his walking speed. Car speed = 3 × 3 = 9 km. We know that car takes 2 hours to reach station. So the distance = 9 × 2 = 18 km. Answer:B #### B QUESTION:A man wants to sell his scooter .There are two offers one at Rs12000 cash and other at a credit of Rs12880 to be paid after 8 months ,money being at 18% per annum which is better offer? options: A)Rs.12880 B)Rs.12000 C)Both are equally good D)None of the above E)Cannot be determined SOLUTION:Explanation: PW of Rs.12,880 due 8 months hence =Rs.[12880×100/100+(18×812)]=Rs.11500= Clearly 12000 in cash is a better offer. Answer: B #### B QUESTION:If a man rows at the rate of 5 kmph in still water and his rate against the current is 3.5 kmph,then the man’s rate along the current is : options: A)4.25 kmph B)6 kmph C)6.5 kmph D)8.5 kmph E)None of these SOLUTION:Solution Let the rate along the current be x kmph.Then,1/2(x + 3.5) = 5 or x = 6.5 kmph. Answer C #### C QUESTION:3 candidates in an election and received 5136, 7636 and 11628 votes respectively. What % of the total votes did the winningcandidate got in that election? options: A)45% B)48% C)57% D)59% E)61% SOLUTION:Total number of votes polled = (5136 + 7636 + 11628) = 24400 So, Required percentage = 11628/24400 * 100 = 48% B #### B QUESTION:On dividing 144 by a number, the quotient is 13 and the remainder is 1. Find the divisor. options: A)A)11 B)B)14 C)C)16 D)D)18 E)E)22 SOLUTION:d = (D-R)/Q = (144 - 1)/13 = 143/13 = 11 A) #### A QUESTION:A 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? options: A)Rs. 7500 B)Rs. 9000 C)Rs. 9500 D)Rs. 10,000 E)None of these SOLUTION:Explanation: A:B:C = (20000 * 24) : (15000 * 24) : (20000 * 18) = 4:3:3 B's share = 25000 * 3/10 = Rs. 7500. ANSWER IS A #### A QUESTION:The greatest possible length which can be used to measure exactly the length 7 m, 3 m 85 cm, 12 m 95 cm is : options: A)15 cm B)25 cm C)35 cm D)42 cm E)62 cm SOLUTION:Solution Required length = H.C.F. of 700 cm, 385 cm and 1295 cm = 35 cm. Answer C #### C QUESTION:70,76, 74,85,90,105,105,130,130,130 The 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. options: A)1 B)2 C)3 D)4 E)5 SOLUTION:How 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. We 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. Answer: C. #### C QUESTION:Let x be a positive integer, what is the remainder when 4^(2x+5)+3 is divided by 5? options: A)2 B)3 C)4 D)1 E)5 SOLUTION:For: (4^(2x+5)+3)/5 Let n = 2x + 5 4^n 4^1 = 4 4^2 = 16 4^3 = 64 4^4 = 256, last digit pattern repeats 4, 6, 4, 6, .... Rule: x^(m+n) = (x^m)(x^n) (4^(2x))(4^5) Rule: x^(mn) = (x^m)^n (4^2)(4^x)(4^5) => Now, (6)(4)(4) + 3 = (6) + 3 => Finally, 9/5 and remainder is 4. Answer: C #### C QUESTION: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? options: A)10 B)41 C)31 D)21 E)22 SOLUTION:Explanation: 1 man’s 1 day’s work = 1/3, ¼ day’s work = 1/3 × ¼ = 1/12 1 woman’s 1 day’s work = ¼, ¼ day’s work = ¼ × ¼ = 1/16 1 boy’s 1 day’s work = 1/12, ¼ day’s work = 1/12 × ¼ = 1/48 Let ‘x’ be the No. of boys required. Then, (1 man + 1 woman + x boy)’s ¼ day’s work 1/12 + 1/16 + x/48 = 1 = (4 + 3 + x)/48 = 1 i.e. 7 + x= 48 and x = 41. Answer: Option B #### B QUESTION:Sandy had $231 left after spending 30% of the money she took for shopping. How much money did Sandy take along with her? options: A)$270 B)$290 C)$310 D)$330 E)$350 SOLUTION:Let the money Sandy took for shopping be x. 0.7x = 231 x = 330 The answer is D. #### D QUESTION:what is the radius of a circle that has a circumference of 3.14 meters? options: A)0.5 mtr B)1.5 mtr C)2.3 mtr D)0.2 mtr E)1.2 mtr SOLUTION:circumference of a cirlce = 2nr, given circumference= 3.14 mtr. 2nr= 3.14, 2 x 3.14 x r= 3.14, = 6.28 x r=3.14, r= 3.14/6.28, = 0.5mtr. correct answer: (A) #### A QUESTION:Boy sells a book for Rs. 450 he gets a loss of 10 %, To gain 10 %, what should be the SP? options: A)Rs.320 B)Rs.450 C)Rs.550 D)Rs.640 E)Rs.680 SOLUTION:Find Selling Price to gain 10 %. Now, we are asked to find selling price to gain 10% profit. Hint: Selling Price = (100 + Gain%) × C.P. 100 Selling Price = (100 + 10) × 500 100 Selling Price = (110) × 500 100 Therefore, selling Price = Rs.550 C #### C QUESTION:A 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? options: A)150 m B)200 m C)240 m D)400 m E)150 m SOLUTION:Answer: Option C Speed = [54 * 5/18] m/sec = 15 m/sec. Length of the train = (15 * 20) m = 300 m. Let the length of the platform be x meters. Then, x + 300 / 36 = 15 x + 300 = 540 x = 240 m. #### C QUESTION:A room 5 m 44 cm long and 3 m 74 cm broad needs to be paved with square tiles. What will be the least number of square tiles required to cover the floor? options: A)176 B)124 C)224 D)186 E)190 SOLUTION:LENGTH = 5 M 44 CM = 544 CM BREADTH = 3 M 74 CM = 374 CM AREA = 544 * 374 HCF = 34 AREA OF SQUARE = 34 * 34 CM2 NO OF TILES REQ = 544* 374/34*34 = 16 * 11 =176 ANSWER A #### A QUESTION:A 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? options: A) 1:2 B) 4:5 C) 1:1 D) 3:2 E) 5:3 SOLUTION:A.. I have probably solved this question 3-4 times by now.. Remember the answer.. 1:2 #### A QUESTION:A train 360 m long is running at a speed of 54 km/hr. In what time will it pass a bridge 140 m long? options: A)40 sec B)11 sec C)88 sec D)33.33 sec E)10 sec SOLUTION:Speed = 54 * 5/18 = 15 m/sec Total distance covered = 360 + 140 = 500 m Required time = 500 * 1/15 = 33.33 sec Answer: D #### D QUESTION:The 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's present age is : options: A)50 years B)46 years C)20 years D)45 years E)30 years SOLUTION:Let the sum of present ages of the two sons be x years. then father's present age =3x years. (3x+5)=2(x+10) 3x+5=2x+20 x=15. Hence, father's present age =45 years. Answer is D #### D QUESTION:Two 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 90 kmph. After how much time will the trains meet? options: A)20/8 sec B)20/4 sec C)5/2 sec D)22/7 sec E)60/7 sec SOLUTION:They are moving in opposite directions, relative speed is equal to the sum of their speeds. Relative speed = (54 + 90)*5/18 = 8*5 = 40 mps. The time required = d/s = 100/40 = 5/2 sec.Answer:C #### C <<<Examples ends QUESTION:Find the Missing Number 1, 2, 4, 10, 16, 40, 64 (Successive terms are related) options: A)100 B)200 C)300 D)90 E)80 SOLUTION:Well, the pattern looked REALLY familiar to me, like it's a binary progression. And it is...but with a twist. 2^0 = 1 2^1 = 2 2^2 = 4 2^3 = 8 2^4 = 16 2^5 = 32 2^6 = 64 You'll note that all the numbers up there match your sequence...except for 2^3 = 8 (10 in your sequence) and 2^5 = 32 (40 in your sequence). BUT, if you convert 8 to base 8, you get 10. And if you convert 32 to base 8, you get 40. Which indicates that every other number starting with the first one is expressed in base 10 and every other number starting with the second number is expressed in base 8. If this is true, then you next number would be: 2^7 = 128 That is the base 10 number. Since this number should be expressed in base 8 (following the pattern), it should be 200. ANSWER:A #### A