| { |
| "dataset_name": "Math_QA", |
| "group_index": 6, |
| "source_file": "/hkfs/work/workspace/scratch/tum_fmp0582-dndworkspace/自己训练lora/prepare/data/math/Math_QA.json", |
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| "total_records": 10000, |
| "sample_count": 100, |
| "generated_at": "2025-11-05T12:58:28Z", |
| "seed": 760231939, |
| "samples": [ |
| { |
| "prompt": "vinoth can complete a painting work in 20 days . prakash can do the same work in 25 days . they start the work together but vinoth quit after 3 days of work . how many days are required to complete the remaining painting work by prakash .\na ) 15.25 days , b ) 16.25 days , c ) 17.25 days , d ) 18.25 days , e ) 19.25 days", |
| "response": "vinoth can complete the painting work in one day is 1 / 20 prakash can complete the same work in one day is 1 / 25 both of them can complete the work in 1 / 20 + days = 9 / 100 ( 1 / 20 + 1 / 25 ) they must have completed in three days = 9 / 100 * 3 = 27 / 100 remaining work to be done is by prakash = 1 - 27 / 100 = 73 / 100 for one work , prakash can do in 25 days for 73 / 100 work , he can do in 73 / 100 * 25 = 73 / 4 days or 18.25 days answer : d", |
| "system": "" |
| }, |
| { |
| "prompt": "a certain college ' s enrollment at the beginning of 1992 was 20 percent greater than it was at the beginning of 1991 , and its enrollment at the beginning of 1993 was 5 percent greater than it was at the beginning of 1992 . the college ' s enrollment at the beginning of 1993 was what percent greater than its enrollment at the beginning of 1991 ?\na ) 17.5 % , b ) 26 % , c ) 30 % , d ) 35 % , e ) 38 %", |
| "response": "\"suppose enrollment in 1991 was 100 then enrollment in 1992 will be 120 and enrollment in 1993 will be 120 * 1.05 = 126 increase in 1993 from 1991 = 126 - 100 = 26 answer : b\"", |
| "system": "" |
| }, |
| { |
| "prompt": "in a certain town , the ratio of ny yankees fans to ny mets fans is 3 : 2 , and the ratio of ny mets fans to boston red sox fans is 4 : 5 . if there are 330 baseball fans in the town , each of whom is a fan of exactly one of those three teams , how many ny mets fans are there in this town ?\na ) 72 , b ) 88 , c ) 95 , d ) 120 , e ) 135", |
| "response": "\"the ratio of yankees : mets : red sox = 6 : 4 : 5 the mets fans are 4 / 15 of the population . ( 4 / 15 ) * 330 = 88 the answer is b .\"", |
| "system": "" |
| }, |
| { |
| "prompt": "a trader mixes 80 kg of tea at 15 per kg with 20 kg of tea at cost price of 20 per kg . in order to earn a profit of 35 % , what should be the sale price of the mixed tea ?\na ) 23.75 , b ) 21.6 , c ) 20 , d ) 19.2 , e ) none of these", |
| "response": "\"c . p . of mixture = 80 × 15 + 20 × 20 / 80 + 20 = 16 ∴ s . p . = ( 100 + 35 ) / 100 × 16 = 21.6 answer b\"", |
| "system": "" |
| }, |
| { |
| "prompt": "a couple married in 1980 had two children , one in 1982 and the other in 1984 . their combined ages will equal the years of the marriage in ?\na ) 1986 , b ) 1985 , c ) 1987 , d ) 1988 , e ) 1989", |
| "response": "sum of year = 1 + 9 + 8 + 0 = ( 18 ) 1 + 8 = 9 1 + 9 + 8 + 2 = ( 20 ) 2 + 0 = 2 1 + 9 + 8 + 4 = ( 13 ) 1 + 3 = 4 now 9 + 2 + 4 = ( 15 ) 1 + 5 = 6 nd option a 1 + 9 + 8 + 6 = 24 ( 2 + 4 ) = 6 answer : a", |
| "system": "" |
| }, |
| { |
| "prompt": "after 10 % of the inhabitants of a village disappeared , a panic set in during which 25 % of the remaining inhabitants left the village . at that time , the population was reduced to 4725 . what was the number of original inhabitants ?\na ) 5000 , b ) 7000 , c ) 4000 , d ) 8000 , e ) 9000", |
| "response": "\"let the total number of original inhabitants be x . ( 75 / 100 ) * ( 90 / 100 ) * x = 4725 ( 27 / 40 ) * x = 4725 x = 4725 * 40 / 27 = 7000 the answer is b .\"", |
| "system": "" |
| }, |
| { |
| "prompt": "jacob is 39 years old . he is 3 times as old as his brother . how old will jacob be when he is twice as old ?\na ) 63 , b ) 64 , c ) 65 , d ) 76 , e ) 67", |
| "response": "\"j = 39 ; j = 3 b ; b = 39 / 3 = 13 ; twice as old so b = 13 ( now ) + ( 13 ) = 26 ; jacob is 39 + 26 = 65 answer : c\"", |
| "system": "" |
| }, |
| { |
| "prompt": "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 ?\na ) 145 , b ) 180 , c ) 181 , d ) 184 , e ) 150", |
| "response": "\"length of the train be ‘ x ’ x + 120 / 15 = x + 180 / 18 6 x + 720 = 5 x + 900 x = 180 m answer : option b\"", |
| "system": "" |
| }, |
| { |
| "prompt": "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\na ) 22 , b ) 30 , c ) 99 , d ) 38 , e ) 27", |
| "response": "\"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\"", |
| "system": "" |
| }, |
| { |
| "prompt": "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 ?\na ) 4 / 11 , b ) 1 / 2 , c ) 15 / 22 , d ) 144 / 17 , e ) 11 / 4", |
| "response": "\"p 1 takes 12 hrs rate for p 2 p 3 together = 1 / 16 + 1 / 18 = 17 / 144 therefore they take 144 / 17 ratio = 144 / 17 = d\"", |
| "system": "" |
| }, |
| { |
| "prompt": "a rectangular box 60 m long and 40 m wide has two concrete crossroads running in the middle of the box and rest of the box has been used as a lawn . the area of the lawn is 2109 sq . m . what is the width of the road ?\n['a ) 3 m', 'b ) 4 m', 'c ) 5 m', 'd ) 6 m', 'e ) 2 m']", |
| "response": "total area of cross roads = 60 x + 40 x − x 2 but total area of the cross roads = 291 m 2 hence , 60 x + 40 x − x 2 = 291 ⇒ 100 x − x 2 = 291 ⇒ x 2 − 100 x + 291 = 0 ⇒ ( x − 97 ) ( x − 3 ) = 0 ⇒ x = 3 answer : a", |
| "system": "" |
| }, |
| { |
| "prompt": "1 ltr of water is added with 3 ltr of a solution containing 33 % of alcohol in the water . the % of alcohol in the new mixture is ?\na ) 22 % , b ) 23 % , c ) 24.5 % , d ) 24.75 % , e ) 30 %", |
| "response": "\"we have a 3 litre solution containing 33 % of alcohol in the water . = > quantity of alcohol in the solution = 3 ã — 33 / 100 now 1 litre of water is added to the solution . = > total quantity of the new solution = 3 + 1 = 4 percentage of alcohol in the new solution = 3 ã — 33 / 100 4 ã — 100 = 3 ã — 331004 ã — 100 = 3 ã — 8.25 / 100 = 24.75 % d\"", |
| "system": "" |
| }, |
| { |
| "prompt": "a soft drink company had 6000 small and 10000 big bottles in storage . if 12 % of small 15 % of big bottles have been sold , then the total bottles remaining in storage is\na ) 15360 , b ) 13780 , c ) 15060 , d ) 14930 , e ) 16075", |
| "response": "\"6000 + 10000 - ( 0.12 * 6000 + 0.15 * 10000 ) = 13780 . answer : b .\"", |
| "system": "" |
| }, |
| { |
| "prompt": "a man performs 1 / 2 of the total journey by rail , 1 / 3 by bus and the remaining 2 km on foot . his total journey is\na ) 16 km , b ) 10 km , c ) 12 km , d ) 24 km , e ) 25 km", |
| "response": "\"explanation : let the journey be x km then , 1 x / 2 + 1 x / 3 + 2 = x 5 x + 12 = 6 x x = 12 km answer : option c\"", |
| "system": "" |
| }, |
| { |
| "prompt": "if the numbers 1 to 97 are written on 97 pieces of paper , ( one on each ) and one piece is picked at random , then what is the probability that the number drawn is neither prime nor composite ?\na ) 1 / 50 , b ) 1 / 25 , c ) 1 / 97 , d ) 1 , e ) 2", |
| "response": "\"there are 25 primes , 71 composite numbers from 1 to 97 . the number which is neither prime nor composite is 1 . therefore , required probability = 1 / 97 . answer : c\"", |
| "system": "" |
| }, |
| { |
| "prompt": "there are 600 employees in a room . 99 % are managers . how many managers must leave the room to bring down the percentage of managers to 98 % ?\na ) 100 , b ) 200 , c ) 250 , d ) 300 , e ) 400", |
| "response": "\"there are 594 managers and 6 others . the 6 others would compose 2 % of the total number of people if there were 300 people in the room . thus 300 managers must leave . the answer is d .\"", |
| "system": "" |
| }, |
| { |
| "prompt": "two friends decide to get together ; so they start riding bikes towards each other . they plan to meet halfway . each is riding at 6 mph . they live 36 miles apart . one of them has a pet carrier pigeon and it starts flying the instant the friends start traveling . the pigeon flies back and forth at 19 mph between the 2 friends until the friends meet . how many miles does the pigeon travel ?\na ) 54 , b ) 57 , c ) 60 , d ) 36 , e ) 96", |
| "response": "\"b 57 it takes 3 hours for the friends to meet ; so the pigeon flies for 3 hours at 19 mph = 57 miles\"", |
| "system": "" |
| }, |
| { |
| "prompt": "the average ( arithmetic mean ) of 16 students first quiz scores in a difficult english class is 62.5 . when one student dropped the class , the average of the remaining scores increased to 62.0 . what is the quiz score of the student who dropped the class ?\na ) a ) 10 , b ) b ) 25 , c ) c ) 40 , d ) d ) 55 , e ) e ) 70", |
| "response": "\"total score of 16 students is 16 * 62.50 = 1000 total score of 15 students is 15 * 62 = 930 so , the score of the person who left is 70 ( 1000 - 930 ) answer will be ( e )\"", |
| "system": "" |
| }, |
| { |
| "prompt": "what is the decimal equivalent of ( 1 / 6 ) ^ 2 ?\na ) 0.0016 , b ) 0.0625 , c ) 0.16 , d ) 0.278 , e ) 0.5", |
| "response": "\"( 1 / 6 ) ² = ( 1 / 6 ) ( 1 / 6 ) = 1 / 36 approach # 1 : use long division to divide 36 into 1 to get 1 / 36 = 0.0278 d\"", |
| "system": "" |
| }, |
| { |
| "prompt": "a , b , c , d and e are ve consecutive odd numbers the sum of a and c is 146 . what is the value of e ?\na ) 75 , b ) 81 , c ) 71 , d ) 79 , e ) none of these", |
| "response": "a + c = 146 ⇒ a + a + 4 = 146 ⇒ a = 146 - 4 / 2 = 71 ∴ e = a + 8 = 71 + 8 = 79 answer d", |
| "system": "" |
| }, |
| { |
| "prompt": "75 is what percent of 125 ?\na ) 60 % , b ) 40 % , c ) 45 % , d ) 50 % , e ) 55 %", |
| "response": "75 / 125 × 100 = 50 % answer : a", |
| "system": "" |
| }, |
| { |
| "prompt": "in an office , totally there are 800 employees and 25 % of the total employees are males . 40 % of the males in the office are at - least 50 years old . find the number of males aged below 50 years ?\na ) 120 , b ) 160 , c ) 132 , d ) 130 , e ) none of these", |
| "response": "\"number of male employees = 800 * 25 / 100 = 200 required number of male employees who are less than 50 years old = 200 * ( 100 - 40 ) % = 200 * 60 / 100 = 120 . answer : a\"", |
| "system": "" |
| }, |
| { |
| "prompt": "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 q at the restaurant ? ( assume that all boxes are filled to capacity . )\na ) 96 , b ) 240 , c ) q = 256 , d ) q = 384 , e ) q = 480", |
| "response": "\"most test takers would recognize the system of equations in this prompt and just do algebra to get to the solution ( and that ' s fine ) . the wording of the prompt and the ' spread ' of the answer choices actually provide an interesting ' brute force ' shortcut that you can take advantage of to eliminate the 4 wrong answers . . . . 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 28 suntil 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\"", |
| "system": "" |
| }, |
| { |
| "prompt": "today joelle opened an interest - bearing savings account and deposited $ 6000 . if the annual interest rate is 5 percent compounded interest , and she neither deposits nor withdraws money for exactly 2 years , how much money will she have in the account ?\na ) $ 6715 , b ) $ 5615 , c ) $ 6415 , d ) $ 6615 , e ) $ 6315", |
| "response": "interest for 1 st year = 6000 * 5 / 100 = 300 interest for 2 nd year = 6300 * 5 / 100 = 315 total = 6000 + 300 + 315 = 6615 answer : d", |
| "system": "" |
| }, |
| { |
| "prompt": "what is the greatest prime factor of 4 ^ 6 - 1 ?\na ) 13 , b ) 17 , c ) 19 , d ) 23 , e ) 29", |
| "response": "\"4 ^ 6 - 1 = ( 4 ^ 3 - 1 ) ( 4 ^ 3 + 1 ) = 63 * 65 = 7 * 9 * 5 * 13 the answer is a .\"", |
| "system": "" |
| }, |
| { |
| "prompt": "for any integer n greater than 1 , # n denotes the product of all the integers from 1 to n , inclusive . how many prime numbers are there between # 6 + 2 and # 6 + 6 , inclusive ?\na ) none , b ) one , c ) two , d ) three , e ) four", |
| "response": "\"given that n * denotes the product of all the integers from 1 to n , inclusive so , 6 * + 2 = 6 ! + 2 and 6 * + 6 = 6 ! + 6 . now , notice that we can factor out 2 our of 6 ! + 2 so it can not be a prime number , we can factor out 3 our of 6 ! + 3 so it can not be a prime number , we can factor out 4 our of 6 ! + 4 so it can not be a prime number , . . . the same way for all numbers between 6 * + 2 = 6 ! + 2 and 6 * + 6 = 6 ! + 6 , inclusive . which means that there are no primes in this range . answer : a .\"", |
| "system": "" |
| }, |
| { |
| "prompt": "integer m has 4 different prime factors and n has 3 different prime factors . if m and n has the greatest common factor of 15 , how many different prime factors does mn have ?\na ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8", |
| "response": "as m and n has gcf of 15 , 3 * 5 should be common factor for both m and n . m = 3 * 5 * p 1 * p 2 n = 3 * 5 * p 3 mn = 3 ^ 2 * 5 ^ 2 * p 1 * p 2 * p 3 mn has prime numbers of 3,5 , p 1 , p 2 p 3 b", |
| "system": "" |
| }, |
| { |
| "prompt": "solution for 4.75 + . 303 + . 432\na ) 2.91 , b ) 5.911 , c ) 5.485 , d ) 5.986 , e ) 2.999", |
| "response": "\"4.75 + . 303 + . 432 = 0 0 = 0 - 4.75 - 0.303 - 0.432 0 = - 5.485 answer : c\"", |
| "system": "" |
| }, |
| { |
| "prompt": "the difference between simple and compound interests compounded annually on a certain sum of money for 2 years at 4 % per annum is rs 1 . find the sum\na ) rs 600 , b ) rs 625 , c ) rs 650 , d ) rs 675 , e ) none of these", |
| "response": "explanation : let the sum be p s . i . = p ∗ 4 ∗ 2 / 100 = 2 p / 25 c . i . = p ( 1 + 4 / 100 ) 2 − p = 676 p / 625 − p = 51 p / 625 as , c . i . - s . i = 1 = > 51 p / 625 − 2 p / 25 = 1 = > 51 p − 50 p / 625 = 1 p = 625 option b", |
| "system": "" |
| }, |
| { |
| "prompt": "find the sum of all odd number upto 250 .\na ) 15345 , b ) 15645 , c ) 15625 , d ) 15342 , e ) 15683", |
| "response": "\"explanation : number of odd numbers upto 250 = n / 2 = 250 / 2 = 125 sum of first 125 odd numbers = ( 125 ) 2 = 15625 answer : option c\"", |
| "system": "" |
| }, |
| { |
| "prompt": "the smallest number which when diminished by 4 , is divisible by 12 , 16 , 18 , 21 and 28 is\na ) 1008 , b ) 1012 , c ) 1022 , d ) 1032 , e ) 1043", |
| "response": "\"required number = ( l . c . m of 12 , 16 , 18 , 21,28 ) + 4 = 1008 + 4 = 1012 answer : b\"", |
| "system": "" |
| }, |
| { |
| "prompt": "on an order of 99 dozen boxes of a consumer product , a retailer receives an extra dozen free . this is equivalent to allowing him a discount of :\na ) 0.1 % , b ) 0.5 % , c ) 1 % , d ) 5 % , e ) 10 %", |
| "response": "\"clearly , the retailer gets 1 dozen out of 100 dozens free . equivalent discount = 1 / 100 * 100 = 1 % . answer c ) 1 %\"", |
| "system": "" |
| }, |
| { |
| "prompt": "a candidate got 25 % of the votes polled and he lost to his rival by 4000 votes . how many votes were cast ?\na ) 7500 , b ) 2028 , c ) 2775 , d ) 5496 , e ) 8000", |
| "response": "\"25 % - - - - - - - - - - - l 75 % - - - - - - - - - - - w - - - - - - - - - - - - - - - - - - 50 % - - - - - - - - - - 4000 100 % - - - - - - - - - ? = > 8000 answer : e\"", |
| "system": "" |
| }, |
| { |
| "prompt": "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 ?\na ) 10 , b ) 20 , c ) 25 , d ) 30 , e ) 37.5", |
| "response": "total distance = 100 miles ( easier to work with % ) 75 % of the distance = 75 miles 25 % of the distance = 25 miles 1 st part of the trip → 75 / 60 = 1.25 2 nd 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 2 nd part of the trip formula : 25 / s = 1.25 » s = 20 ans b", |
| "system": "" |
| }, |
| { |
| "prompt": "one fourth of a solution that was 12 % salt by weight was replaced by a second solution resulting in a solution that was 16 percent sugar by weight . the second solution was what percent salt by weight ?\na ) 28 % , b ) 34 % , c ) 22 % , d ) 18 % , e ) 8.5 %", |
| "response": "consider total solution to be 100 liters and in this case you ' ll have : 75 * 0.12 + 25 * x = 100 * 0.16 - - > x = 0.28 . answer : a .", |
| "system": "" |
| }, |
| { |
| "prompt": "there are 50 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 ?\na ) 1000 , b ) 3000 , c ) 1225 , d ) 6000 , e ) 9000", |
| "response": "\"50 players are there . two players play one game with one another . so 50 c 2 = 50 * 49 / 2 = 1225 so option c is correct\"", |
| "system": "" |
| }, |
| { |
| "prompt": "if x and y are integers such that x ^ 2 = 3 y and xy = 36 , then x – y = ?\na ) - 30 , b ) - 20 , c ) - 5 , d ) 5 , e ) 0", |
| "response": "here x and y are integers . x ^ 2 = 3 y , xy = 36 . substitute ( x ^ 2 ) / 3 = y in xy = > x ^ 3 = 36 * 3 = > x ^ 3 = 108 . here x ^ 3 is positive , x is also positive . x = 6 then y = 6 . x - y = 0 so option e is correct", |
| "system": "" |
| }, |
| { |
| "prompt": "the radius of a semi circle is 4.8 cm then its perimeter is ?\na ) 32.51 , b ) 32.4 , c ) 32.1 , d ) 32.92 , e ) 24.69", |
| "response": "\"36 / 7 r = 4.8 = 24.69 answer : e\"", |
| "system": "" |
| }, |
| { |
| "prompt": "find the 25 th term of an arithmetic progression whose first term is 5 and the common difference is 7 .\na ) 145 , b ) 38 , c ) 173 , d ) 156 , e ) 189", |
| "response": "n th term of a . p = a + ( n - 1 ) * d = 5 + ( 25 - 1 ) * 7 , = 5 + 168 = 173 . answer : c", |
| "system": "" |
| }, |
| { |
| "prompt": "along a yard 434 metres long , 32 trees are palnted at equal distances , one tree being at each end of the yard . what is the distance between two consecutive trees\na ) 14 , b ) 16 , c ) 10 , d ) 11 , e ) 12", |
| "response": "\"explanation : 32 trees have 31 gaps between them , required distance ( 434 / 31 ) = 14 option a\"", |
| "system": "" |
| }, |
| { |
| "prompt": "a reduction of 50 % in the price of oil enables a house wife to obtain 5 kgs more for rs . 800 , what is the reduced price for kg ?\na ) s . 42 , b ) s . 46 , c ) s . 40 , d ) s . 80 , e ) s . 34", |
| "response": "\"800 * ( 50 / 100 ) = 400 - - - - 5 ? - - - - 1 = > rs . 80 answer : d\"", |
| "system": "" |
| }, |
| { |
| "prompt": "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 ?\na ) 67 , b ) 55 , c ) 62 , d ) 47 , e ) 57", |
| "response": "\"x : y : z = 100 : 50 : 40 10 : 5 : 4 10 - - - 30 19 - - - ? = > 57 answer : e\"", |
| "system": "" |
| }, |
| { |
| "prompt": "some of 40 % - intensity red paint is replaced with 20 % solution of red paint such that the new paint intensity is 20 % . what fraction of the original paint was replaced ?\na ) 2 / 5 , b ) 2 / 3 , c ) 1 / 3 , d ) 1 / 2 , e ) 1 / 1", |
| "response": "\"let total paint = 1 let amount replaced = x 40 ( 1 - x ) + 20 x = 20 x = 1 / 1 answer : e\"", |
| "system": "" |
| }, |
| { |
| "prompt": "the price of an item is discounted 10 percent on day 1 of a sale . on day 2 , the item is discounted another 10 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 ?\na ) 28 % , b ) 40 % , c ) 64.8 % , d ) 70 % , e ) 72 %", |
| "response": "\"let initial price be 1000 price in day 1 after 10 % discount = 900 price in day 2 after 10 % discount = 810 price in day 3 after 20 % discount = 648 so , price in day 3 as percentage of the sale price on day 1 will be = 648 / 900 * 100 = > 72 % answer will definitely be ( e )\"", |
| "system": "" |
| }, |
| { |
| "prompt": "a car traveling at a certain constant speed takes 5 seconds longer to travel 1 km than it would take to travel 1 km at 90 km / hour . at what speed , in km / hr , is the car traveling ?\na ) 70 , b ) 80 , c ) 74 , d ) 75 , e ) 78", |
| "response": "\"time to cover 1 kilometer at 80 kilometers per hour is 1 / 90 hours = 3,600 / 90 seconds = 40 seconds ; time to cover 1 kilometer at regular speed is 40 + 5 = 45 seconds = 45 / 3,600 hours = 1 / 80 hours ; so , we get that to cover 1 kilometer 1 / 80 hours is needed - - > regular speed 80 kilometers per hour ( rate is a reciprocal of time or rate = distance / time ) . answer : b .\"", |
| "system": "" |
| }, |
| { |
| "prompt": "the percentage increase in the area of rectangle , if each of its side is increased by 20 % is ?\na ) 30 % , b ) 44 % , c ) 50 % , d ) 55 % , e ) 60 %", |
| "response": "\"let original length = x meters original breadth = y meters original area = xy m ^ 2 new length = 120 x / 100 new breadth = 120 y / 100 = 6 y / 5 new area = 6 x / 5 * 6 y / 5 = 36 xy / 25 m ^ 2 increase percent = 11 xy / 25 * 1 / xy * 100 = 44 % answer is b\"", |
| "system": "" |
| }, |
| { |
| "prompt": "if 2 ^ 4 , 3 ^ 3 , and 10 ^ 3 are factors of the product of 1,452 and w , where w is a positive integer , what is the smallest possible value of w ?\na ) 198 , b ) 288 , c ) 363 , d ) 360 , e ) 484", |
| "response": "i will go with d ( pending elements to match is 2 ^ 2 * 3 ^ 2 * 10 ^ 1 = 360", |
| "system": "" |
| }, |
| { |
| "prompt": "in a survey of 335 employees , 104 of them are uninsured , 54 work part time , and 12.5 percent of employees who are uninsured work part time . if a person is to be randomly selected from those surveyed , what is the probability that the person will neither work part time nor be uninsured ?\na ) 38 / 67 , b ) 8 / 41 , c ) 9 / 348 , d ) 1 / 8 , e ) 41 / 91", |
| "response": "\"- - - - - - - - - ui - - - - - - - - - - - - - - - - nui - - - - - - - total pt - - - - ( 12.5 / 100 ) * 104 = 13 - - - - - - - - - - - - - 54 npt - - - 104 - 13 - - - - - - - - - - - - - - x - - - - - - - - 281 total - - 104 - - - - - - - - - - - - - - - - - - - - - - - - - - - - 335 we have to find not part time and not uninsured . in other words not part time and insured = x / 335 = ( 281 - 104 + 13 ) / 335 = 38 / 67 answer is a .\"", |
| "system": "" |
| }, |
| { |
| "prompt": "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 36 miles per hour . how many miles from the station was train a overtaken by train b ?\na ) 320 , b ) 360 , c ) 400 , d ) 440 , e ) 480", |
| "response": "\"after two hours , train a is ahead by 60 miles . train b can catch up at a rate of 6 miles per hour . the time to catch up is 60 / 6 = 10 hours . in 10 hours , train a travels another 30 * 10 = 300 miles for a total of 360 miles . the answer is b .\"", |
| "system": "" |
| }, |
| { |
| "prompt": "david and andrew can finish the work 12 days if they work together . they worked together for 8 days and then andrew left . david finished the remaining work in another 8 days . in how many days david alone can finish the work ?\na ) 30 days , b ) 60 days , c ) 70 days , d ) 80 days , e ) 24 days", |
| "response": "amount of work done by david and andrew in 1 day = 1 / 12 amount of work done by david and andrew in 8 days = 8 ã — ( 1 / 12 ) = 2 / 3 remaining work â € “ 1 â € “ 2 / 3 = 1 / 3 david completes 1 / 3 work in 8 days amount of work david can do in 1 day = ( 1 / 3 ) / 8 = 1 / 24 = > david can complete the work in 24 days answer : e", |
| "system": "" |
| }, |
| { |
| "prompt": "4 / 6 of the population of the country of venezia lives in montague province , while the rest lives in capulet province . in the upcoming election , 80 % of montague residents support romeo , while 70 % of capulet residents support juliet ; each resident of venezia supports exactly one of these two candidates . rounded if necessary to the nearest percent , the probability that a juliet supporter chosen at random resides in capulet is\na ) 28 % , b ) 41 % , c ) 45 % , d ) 64 % , e ) 78 %", |
| "response": "\"total population = 60 ( assume ) . 4 / 6 * 60 = 40 people from montague . 2 / 6 * 60 = 20 people from capulet . 0.2 * 40 = 8 people from montague support juliet . 0.7 * 20 = 14 people from capulet support juliet . the probability that a juliet supporter chosen at random resides in capulet is 14 / ( 8 + 14 ) = ~ 64 . answer : d\"", |
| "system": "" |
| }, |
| { |
| "prompt": "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 12 gallons of gasoline left in its tank at the end , then what percent of the tank was used to travel 80 miles at 60 mph ?\na ) 15 % , b ) 20 % , c ) 25 % , d ) 30 % , e ) 14 %", |
| "response": "\"total time for travelling 80 miles @ 60 mph = 80 / 60 = 4 / 3 hour = 80 minutes . given , the car uses 1 gallon for every 40 minutes of driving @ 60 mph . thus in 80 minutes it will use = 2 gallons . thus , full tank = 2 + 12 = 14 gallons - - - > 2 / 14 = 14 % of the fuel used . e is the correct answer .\"", |
| "system": "" |
| }, |
| { |
| "prompt": "f ( x ) is a function such that f ( x ) + 3 f ( 8 - x ) = x for all real numbers x . find the value of f ( 2 )\na ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4", |
| "response": "\"f ( x ) + 3 f ( 8 - x ) = f ( 2 ) + 3 f ( 6 ) = 2 : x = 2 above f ( 6 ) + 3 f ( 2 ) = 6 : x = 6 above f ( 6 ) = 6 - 3 f ( 2 ) : solve equation c for f ( 6 ) f ( 2 ) + 3 ( 6 - 3 f ( 2 ) ) = 2 : substitute f ( 2 ) = 2 : solve above equation correct answer c\"", |
| "system": "" |
| }, |
| { |
| "prompt": "due to construction , the speed limit along an 10 - mile section of highway is reduced from 55 miles per hour to 30 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 ?\na ) a ) 6.24 , b ) b ) 8 , c ) c ) 10 , d ) d ) 9.1 , e ) e ) 24", |
| "response": "\"old time in minutes to cross 10 miles stretch = 10 * 60 / 55 = 10 * 12 / 11 = 10.9 new time in minutes to cross 10 miles stretch = 10 * 60 / 30 = 10 * 2 = 20 time difference = 9.1 ans : d\"", |
| "system": "" |
| }, |
| { |
| "prompt": "40 percent of the members of a study group are women , and 20 percent of those women are lawyers . if one member of the study group is to be selected at random , what is the probability that the member selected is a woman lawyer ?\na ) 0.2 , b ) 0.08 , c ) 0.16 , d ) 0.14 , e ) 0.15", |
| "response": "\"say there are 100 people in that group , then there would be 0.4 * 0.20 * 100 = 8 women lawyers , which means that the probability that the member selected is a woman lawyer is favorable / total = 8 / 100 . answer : b\"", |
| "system": "" |
| }, |
| { |
| "prompt": "find the compound ratio of ( 2 : 3 ) , ( 5 : 11 ) and ( 11 : 2 ) is\na ) 3 : 2 , b ) 2 : 1 , c ) 1 : 2 , d ) 4 : 5 , e ) 5 : 3", |
| "response": "\"required ratio = 2 / 3 * 5 / 11 * 11 / 2 = 2 / 1 = 5 : 3 answer is e\"", |
| "system": "" |
| }, |
| { |
| "prompt": "if x and y are both odd prime numbers and x < y , how many distinct positive integer factors does 2 xy have ?\na ) 3 , b ) 4 , c ) 6 , d ) 8 , e ) 12", |
| "response": "the solution should be the same for all numbers that fulfill the condition above . as x and y are odd prime numbers , they must be > 2 . also , they must be distinct as x < y . i choose x = 3 and y = 5 : how many factors does 2 x 3 x 5 = 30 have : 1 , 2 , 3 , 5 , 6 , 10 , 15 , 30 = 8 distinct positive integer factors . hence , the correct answer is d .", |
| "system": "" |
| }, |
| { |
| "prompt": "a question paper has 2 parts , a & b , each containing 5 questions . if a student has to choose 3 from part a & 4 from part b , in how many ways can he choose the questions ?\na ) 50 , b ) 100 , c ) 152 , d ) 150 , e ) 55", |
| "response": "\"there 3 questions in part a out of which 4 question can be chosen as = 5 c 3 . similarly , 5 questions can be chosen from 10 questions of part b as = 5 c 4 . hence , total number of ways , = 5 c 3 * 5 c 4 = [ 5 ! / ( 2 ! 3 ! ) ] * [ 5 ! / ( 4 ! * 1 ) ] = { 10 } * { 5 * 4 ! / ( 4 ! ) } = 10 * 5 = 50 . a\"", |
| "system": "" |
| }, |
| { |
| "prompt": "if the charge of staying in a student youth hostel $ 18.00 / day for the first week , and $ 12.00 / day for each additional week , how much does it cost to stay for 23 days ?\na ) $ 318 , b ) $ 289 , c ) $ 282 , d ) $ 274 , e ) $ 286", |
| "response": "total number of days of stay = 23 charge of staying in first week = 18 * 7 = 126 $ charge of staying for additional days = ( 23 - 7 ) * 12 = 16 * 12 = 192 $ total charge = 126 + 192 = 318 $ answer a", |
| "system": "" |
| }, |
| { |
| "prompt": "a meeting has to be conducted with 5 managers . find the number of ways in which the managers be selected from among 8 managers , if 2 managers will not attend the meeting together ?\na ) 40 , b ) 36 , c ) 42 , d ) 45 , e ) 47", |
| "response": "\"we can either choose all 5 people from 6 manager who have no problems or choose 4 from the 6 and 1 from the 2 managers who have a problem sitting together so 6 c 5 + ( 6 c 4 * 2 c 1 ) this is 6 + 30 = 36 answer : b\"", |
| "system": "" |
| }, |
| { |
| "prompt": "5 n - 3 > 12 and 7 n - 5 < 44 ; n must be between which numbers ?\na ) 1 and 8 , b ) 2 and 6 , c ) 0 and 9 , d ) 3 and 7 , e ) 2 and 9", |
| "response": "5 n - 3 > 12 5 n > 15 n > 3 7 n - 5 < 44 7 n < 49 n < 7 so n must be between 3 and 7 3 < n < 7 correct answer d", |
| "system": "" |
| }, |
| { |
| "prompt": "if the sum and difference of two numbers are 15 and 10 respectively , then the difference of their square is :\na ) 12 , b ) 150 , c ) 160 , d ) 180 , e ) 18", |
| "response": "\"let the numbers be x and y . then , x + y = 15 and x - y = 10 x 2 - y 2 = ( x + y ) ( x - y ) = 15 * 10 = 150 . answer : b\"", |
| "system": "" |
| }, |
| { |
| "prompt": "ram , who is half as efficient as krish , will take 24 days to complete a task if he worked alone . if ram and krish worked together , how long will they take to complete the task ?\na ) 16 days , b ) 12 days , c ) 8 days , d ) 6 days , e ) 18 days", |
| "response": "\"answer ram takes 24 days to complete the task , if he works alone . krish is twice as efficient as ram is . so , working alone , krish will take half the time to complete the task . i . e . , 12 days . ram will complete 1 / 24 th of the task in a day . krish will complete 1 / 12 th of the task in a day . when they work together , they will complete 1 / 24 + 1 / 12 = 1 / 8 th of the task in a day . therefore , when they work together they will complete the task in 8 days . choice c\"", |
| "system": "" |
| }, |
| { |
| "prompt": "a jar contains only red , yellow , and orange marbles . if there are 3 red , 3 yellow , and 4 orange marbles , and 3 marbles are chosen from the jar at random without replacing any of them , what is the probability that 2 yellow , 1 red , and no orange marbles will be chosen ?\na ) 1 / 60 , b ) 1 / 45 , c ) 2 / 45 , d ) 3 / 22 , e ) 5 / 22", |
| "response": "\"i started by finding the 2 probabilities , without calculation , like this : p ( yyr ) p ( yry ) p ( ryy ) i calculated the first one and ended in 1 / 22 . i looked at the answer choices at this point and saw answer d : 3 / 22 . this helped me realise that for the 3 possible orderings the probabbility is the same . so , it should be ( 1 / 45 ) * ( 2 ) , which indeed is 2 / 45 . c\"", |
| "system": "" |
| }, |
| { |
| "prompt": "express a speed of 60 kmph in meters per second ?\na ) 10 mps , b ) 16.67 mps , c ) 97.67 mps , d ) 17.67 mps , e ) 18 mps", |
| "response": "\"60 * 5 / 18 = 16.67 mps answer : b\"", |
| "system": "" |
| }, |
| { |
| "prompt": "the length of a rectangular floor is more than its breadth by 500 % . if rs . 324 is required to paint the floor at the rate of rs . 6 per sq m , then what would be the length of the floor ?\na ) 24.6 m . , b ) 23.4 m . , c ) 22.5 m . , d ) 23.8 m . , e ) 25.5 m .", |
| "response": "\"let the length and the breadth of the floor be l m and b m respectively . l = b + 500 % of b = l + 5 b = 6 b area of the floor = 324 / 6 = 54 sq m l b = 54 i . e . , l * l / 6 = 108 l 2 = 648 = > l = 25.5 m . answer : e\"", |
| "system": "" |
| }, |
| { |
| "prompt": "a trader sold an article on a certain price with 20 % profit . if he sold double of previous selling price then find its profit %\na ) 140 % , b ) 120 % , c ) 100 % , d ) 90 % , e ) 80 %", |
| "response": "let cost price = 100 % selling price = 120 % new s . p . = 240 % p % = 240 - 100 = 140 % answer is a", |
| "system": "" |
| }, |
| { |
| "prompt": "what is the 8 th digit to the right of the decimal point in the decimal equivalent of 73 / 11 ?\na ) 1 , b ) 3 , c ) 4 , d ) 5 , e ) 2", |
| "response": "\"73 / 11 = 6.6363 . . . . 63 is non - terminating repeating decimal . the 8 th digit to the right of decimal point will be 3 . answer b\"", |
| "system": "" |
| }, |
| { |
| "prompt": "the tax on a commodity is diminished by 20 % and its consumption increased by 15 % . the effect on revenue is ?\na ) 9 % decrease , b ) 8 % decrease , c ) 6 % decrease , d ) 1 % decrease , e ) 2 % decrease", |
| "response": "\"100 * 100 = 10000 80 * 115 = 9200 - - - - - - - - - - - 10000 - - - - - - - - - - - 800 100 - - - - - - - - - - - ? = > 8 % decrease answer : b\"", |
| "system": "" |
| }, |
| { |
| "prompt": "a and b start a business , with a investing the total capital of rs . 5000 , on the condition that b pays a interest @ 10 % per annum on his half of the capital . a is a working partner and receives rs . 500 per month from the total profit and any profit remaining is equally shared by both of them . at the end of the year , it was found that the income of a is twice that of b . find the total profit for the year ?\na ) a ) 2500 , b ) b ) 3500 , c ) c ) 5000 , d ) d ) 6000 , e ) e ) 8000", |
| "response": "interest received by a from b = 10 % of half of rs . 5000 = 10 % * 2500 = 250 . amount received by a per annum for being a working partner = 500 * 12 = rs . 1000 . let ' p ' be the part of the remaining profit that a receives as his share . total income of a = ( 250 + 1000 + p ) total income of b = only his share from the remaining profit = ' p ' , as a and b share the remaining profit equally . income of a = twice the income of b ( 250 + 1000 + p ) = 2 ( p ) p = 1250 total profit = 2 p + 1000 = 2 * 1250 + 1000 = 3500 answer : b", |
| "system": "" |
| }, |
| { |
| "prompt": "find the l . c . m . of 72 , 108 and 2100 .\na ) 37800 , b ) 37600 , c ) 37200 , d ) 37500 , e ) none of them", |
| "response": "72 = 2 ^ 3 x 3 ^ 2 , 108 = 3 ^ 3 x 2 ^ 2 , 2100 = 2 ^ 2 x 5 ^ 2 x 3 x 7 . l . c . m . = 2 ^ 3 x 3 ^ 3 x 5 ^ 2 x 7 = 37800 . answer is a .", |
| "system": "" |
| }, |
| { |
| "prompt": "on a map , 1.5 inches represent 24 miles . how many miles approximately is the distance if you measured 46 centimeters assuming that 1 - inch is 2.54 centimeters ?\na ) 174.2 , b ) 212 , c ) 288.1 , d ) 290 , e ) 282.4", |
| "response": "\"1.5 inch = 2.54 * 1.5 cm . so , 2.54 * 1.5 represents 24 miles . so for 46 cm . : 46 / ( 2.54 * 1.5 ) = x / 24 - - - > x = 24 * 46 / ( 3.81 ) = 290 answer will be d .\"", |
| "system": "" |
| }, |
| { |
| "prompt": "ifaequals the sum of the even integers from 2 to 20 , inclusive , andbequals the sum of the odd integers from 1 to 19 , inclusive , what is the value of ( a - b ) / 2 ?\na ) 1 , b ) 10 , c ) 19 , d ) 5 , e ) 2", |
| "response": "\"answer is 10 yes ! there is really a faster way to solve it . sum of consecutive odd or even integers = ( no . of odd or even ints ) * ( first int + last int ) / 2 here a = sum of even ints from 2 to 20 , inclusive number of even ints = 10 , first int + last int = 2 + 20 = 22 a = 10 * 22 / 2 = 110 b = sum of odd ints from 1 to 19 , inclusive number of odd ints = 10 , first int + last int = 1 + 19 = 20 a = 10 * 20 / 2 = 100 ( a - b ) / 2 = 110 - 100 = 10 / 2 = 5 ans : d\"", |
| "system": "" |
| }, |
| { |
| "prompt": "a motorcyclist goes from bombay to pune , a distance of 224 kms at an average of 32 kmph speed . another man starts from bombay by car 2 ½ hours after the first , and reaches pune ½ hour earlier . what is the ratio of the speed of the motorcycle and the car ?\na ) 1 : 2 , b ) 1 : 5 , c ) 4 : 7 , d ) 1 : 1 , e ) 1 : 8", |
| "response": "\"t = 224 / 32 = 7 h t = 7 - 3 = 4 time ratio = 7 : 4 speed ratio = 4 : 7 answer : c\"", |
| "system": "" |
| }, |
| { |
| "prompt": "if a is an integer greater than 9 but less than 26 and b is an integer greater than 14 but less than 31 , what is the range of a / b ?\na ) 1 , b ) 1 / 2 , c ) 5 / 6 , d ) 2 / 3 , e ) 4 / 3", |
| "response": "\"range of a / b = max ( a / b ) - min ( a / b ) to get max ( a / b ) = > max ( a ) / min ( b ) = 25 / 15 to get min ( a / b ) = > min ( a ) / max ( b ) = 10 / 30 range = 25 / 15 - 10 / 30 = 4 / 3\"", |
| "system": "" |
| }, |
| { |
| "prompt": "if a and b are positive integers and ( 5 ^ a ) ^ b = 5 ^ 2 , what is the value of 2 ^ a * 2 ^ b ?\na ) 3125 , b ) 625 , c ) 5 , d ) 25 , e ) 125", |
| "response": "\"5 ^ ab = 5 ^ 2 therefore ab = 2 either a = 1 or 2 or b = 2 or 1 therefore 5 ^ a * 5 ^ b = 5 ^ ( a + b ) = 5 ^ 3 = 125 e\"", |
| "system": "" |
| }, |
| { |
| "prompt": "a tank with a volume of 30 cubic feet has one inlet pipe and 2 outlet pipes . the inlet pipe fills water into the tank at the rate of 3 cubic inches / min and the 2 outlet pipes empty it out at the rates of 12 cubic inches / min and 6 cubic inches / min respectively . if all 3 pipes are opened when the tank is full , how many minutes does it take to empty the tank ? ( 1 foot = 12 inches )\n['a ) 2345', 'b ) 3456', 'c ) 4567', 'd ) 5678', 'e ) 6789']", |
| "response": "the tank is emptied at this rate : 12 + 6 - 3 = 15 cubic inches / min the tank has a volume of 30 * 12 * 12 * 12 = 51840 cubic inches . the time it takes to empty the tank is 51840 / 15 = 3456 minutes . the answer is b .", |
| "system": "" |
| }, |
| { |
| "prompt": "the expression x # y denotes the product of the consecutive multiples of 3 between x and y , inclusive . what is the sum of the exponents in the prime factorization of 21 # 30 ?\na ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14", |
| "response": "\"first , let ' s translate the expression 21 # 30 , using the definition given : 21 # 30 = 21 × 24 × 27 × 30 we need the prime factorization of this product . let ' s factor out 3 from each multiple . 21 # 30 = 3 ^ 4 ( 7 × 8 × 9 × 10 ) now let ' s replace each consecutive integer with its prime factorization : 21 # 30 = 3 ^ 4 ( 7 × 2 ^ 3 × 3 ^ 2 × ( 2 × 5 ) ) let ' s group the prime bases : 21 # 30 = 2 ^ 4 × 3 ^ 6 × 5 × 7 the sum of the exponents is 4 + 6 + 1 + 1 = 12 the answer is c .\"", |
| "system": "" |
| }, |
| { |
| "prompt": "the sum of the first 80 positive even integers is 2,550 . what is the sum of the odd integers from 101 to 200 , inclusive ?\na ) 5,050 , b ) 7,500 , c ) 10,500 , d ) 15,000 , e ) 19,600", |
| "response": "\"101 + 103 + . . . . . . . 199 if we remove 100 from each of these it will be sum of 1 st 100 odd numbers . so 101 + 103 + . . . . . . . 199 = 80 * 100 + ( 1 + 3 + 5 + 7 + . . . . . . ) sum of 1 st 100 natural numbers = ( 100 * 101 ) / 2 = 5050 sum of 1 st 80 positive even integers = 2550 sum of 1 st 100 odd numbers = 5050 - 2550 = 2500 so 101 + 103 + . . . . . . . 199 = 80 * 100 + ( 1 + 3 + 5 + 7 + . . . . . . ) = 8000 + 2500 = 10500 c is the answer .\"", |
| "system": "" |
| }, |
| { |
| "prompt": "in assembling a bluetooth device , a factory uses one of two kinds of modules . one module costs $ 10 and the other one , that is cheaper , costs $ 3.5 . the factory holds a $ 45 worth stock of 11 modules . how many of the modules in the stock are of the cheaper kind ?\na ) 30 , b ) 28 , c ) 25 , d ) 20 , e ) 10", |
| "response": "so the number of $ 3.50 modules must be 10 so that the leftover 1 modules are of $ 10 which will give a total value $ 45 . 10 * 3.50 + 1 * 10 = 35 + 10 = 45 answer : e", |
| "system": "" |
| }, |
| { |
| "prompt": "what will be the fraction of 5 %\na ) 1 / 20 , b ) 1 / 50 , c ) 1 / 75 , d ) 1 / 25 , e ) none of these", |
| "response": "\"explanation : 5 * 1 / 100 = 1 / 20 . option a\"", |
| "system": "" |
| }, |
| { |
| "prompt": "if a certain number is divided by 11 , the quotient , dividend , and divisor , added together , will amount to 71 . what is the number ?\na ) 18 , b ) 28 , c ) 48 , d ) 38 , e ) 55", |
| "response": "\"let x = the number sought . then x / 11 + x + 11 = 71 and x = 55 . e\"", |
| "system": "" |
| }, |
| { |
| "prompt": "when you multiply a number by 4 and then subtract 3 , the result is the same as if you first subtracted 7 from the same number and then multiplied by 9 . what is the number ?\na ) a ) 23 , b ) b ) 13 , c ) c ) 19 , d ) d ) 12 , e ) e ) 10", |
| "response": "let x equal the number and then change the words into an equation and solve for x : 4 x – 3 = 9 ( x – 7 ) 4 x – 3 = 9 x – 63 60 = 5 x 12 = x correct answer d ) 12", |
| "system": "" |
| }, |
| { |
| "prompt": "if a takes x days to do a work then b takes 2 x days to do the same work then with in how many day ' s a will alone complete this work ?\na ) 27 , b ) 23 , c ) 24 , d ) 25 , e ) 26", |
| "response": "1 / x + 1 / 2 x = 1 / 18 = > 3 / 2 x = 1 / 18 = > x = 27 days . hence , a alone can finish the work in 27 days . answer : a", |
| "system": "" |
| }, |
| { |
| "prompt": "rectangular tile each of size 80 cm by 40 cm must be laid horizontally on a rectangular floor of size 130 cm by 230 cm , such that the tiles do not overlap and they are placed with edges jutting against each other on all edges . a tile can be placed in any orientation so long as its edges are parallel to the edges of floor . no tile should overshoot any edge of the floor . the maximum number of tiles that can be accommodated on the floor is :\na ) 6 , b ) 2 , c ) 8 , d ) 9 , e ) 7", |
| "response": "\"area of tile = 80 * 40 = 3200 area of floor = 130 * 230 = 29900 no of tiles = 29900 / 3200 = 9.34 so , the no of tile = 9 answer : d\"", |
| "system": "" |
| }, |
| { |
| "prompt": "100 is increased by 50 % . find the final number .\na ) 100 , b ) 110 , c ) 150 , d ) 155 , e ) 160", |
| "response": "\"final number = initial number + 50 % ( original number ) = 100 + 50 % ( 100 ) = 100 + 50 = 150 . answer c\"", |
| "system": "" |
| }, |
| { |
| "prompt": "at a certain zoo , the ratio of sea horse to penguins is 5 to 11 . if there are 85 more penguins than sea horses at the zoo , how many sea horses are there ?\na ) 24 , b ) 36 , c ) 48 , d ) 70 , e ) 132", |
| "response": "5 / 11 = x / x + 85 5 * 85 = 6 x x = 70 d . 70", |
| "system": "" |
| }, |
| { |
| "prompt": "0.03 x 0.5 = ?\na ) 0.0001 , b ) 0.001 , c ) 0.015 , d ) 0.1 , e ) none of these", |
| "response": "\"explanation : 3 x 5 = 15 . sum of decimal places = 3 0.02 x 0.5 = 0.015 answer - c\"", |
| "system": "" |
| }, |
| { |
| "prompt": "each child has 4 pencils and 13 skittles . if there are 8 children , how many pencils are there in total ?\na ) 16 , b ) 12 , c ) 18 , d ) 22 , e ) 32", |
| "response": "4 * 8 = 32 . answer is e .", |
| "system": "" |
| }, |
| { |
| "prompt": "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 u apples did each person get before 45 people joined the feast ?\na ) 20 . , b ) 21 . , c ) 22 . , d ) 23 . , e ) 24 .", |
| "response": "\"before solving it algebraically , let us prime factorize 1430 = 2 * 5 * 11 * 13 . since number of apples per person * total persons u = 1430 , the answer should be a factor of 1430 . only c is . and that ' s your answer . c\"", |
| "system": "" |
| }, |
| { |
| "prompt": "if the numerator of a fraction is increased by 50 % and denominator by 20 % , the fraction become 9 / 15 . what was the original fraction ?\na ) 12 / 25 , b ) 13 / 25 , c ) 3 / 5 , d ) 6 / 7 , e ) 7 / 8", |
| "response": "\"explanation : let the fraction be x / y we have 150 x / 120 y = 9 / 15 = x / y = 12 / 25 answer : option a\"", |
| "system": "" |
| }, |
| { |
| "prompt": "what is the rate percent when the simple interest on rs . 910 amount to rs . 260 in 4 years ?\na ) 7.14 , b ) 6.14 , c ) 5.14 , d ) 3.14 , e ) 2.14", |
| "response": "\"260 = ( 910 * 4 * r ) / 100 r = 7.14 % answer : a\"", |
| "system": "" |
| }, |
| { |
| "prompt": "in 1979 approximately 1 / 3 of the 37.3 million airline passengers traveling to or from the united states used kennedy airport . if the number of such passengers that used miami airport was 1 / 4 the number that used kennedy airport and 3 times the number that used logan airport , approximately how many millions of these passengers used logan airport that year ?\na ) 18.6 , b ) 9.3 , c ) 6.2 , d ) 3.1 , e ) 1.03", |
| "response": "\"number of passengers using kennedy airport = 37 / 3 = ~ 12.43 passengers using miami airport = 12.43 / 4 = ~ 3.1 passengers using logan airport = 3.1 / 3 = ~ 1.03 so e\"", |
| "system": "" |
| }, |
| { |
| "prompt": "convert the 12 / 36 m / s into kilometers per hour ?\na ) 3.5 kmph . , b ) 2.5 kmph . , c ) 1.2 kmph . , d ) 1.5 kmph . , e ) 1.9 kmph .", |
| "response": "\"15 / 36 m / s = 12 / 36 * 18 / 5 = 1 ( 1 / 5 ) = 1.2 kmph . answer : c\"", |
| "system": "" |
| }, |
| { |
| "prompt": "how many kg of pure salt must be added to 100 kg of 10 % solution of salt and water to increase it to a 25 % solution ?\na ) a ) 6.7 , b ) b ) 1.3 , c ) c ) 9.6 , d ) d ) 20 , e ) e ) 7.9", |
| "response": "\"amount salt in 100 kg solution = 10 * 100 / 100 = 10 kg let x kg of pure salt be added then ( 10 + x ) / ( 100 + x ) = 25 / 100 40 + 4 x = 100 + x 3 x = 60 x = 20 answer is d\"", |
| "system": "" |
| }, |
| { |
| "prompt": "a train running at the speed of 72 km / hr crosses a pole in 9 seconds . what is the length of the train ?\na ) 286 , b ) 278 , c ) 255 , d ) 180 , e ) 287", |
| "response": "\"speed = ( 72 * 5 / 18 ) m / sec = ( 20 ) m / sec length of the train = ( speed x time ) = ( 20 * 9 ) m = 180 m . answer : d\"", |
| "system": "" |
| }, |
| { |
| "prompt": "let q represent a set of 7 distinct prime numbers . if the sum of the numbers in q is even and x is a member of q , then what is the least possible value that x can be ?\na ) 1 , b ) 2 , c ) 3 , d ) 5 , e ) 7", |
| "response": "q = p 1 + p 2 + p 3 + p 4 + p 5 + p 6 + p 7 = even ( and all primes are distinct ) if the least prime is 2 then we have sum of q = even . ans . c . 3", |
| "system": "" |
| }, |
| { |
| "prompt": "evaluate : 11 + sqrt ( - 4 + 6 × 4 ÷ 3 ) = . . . .\na ) 3 , b ) 33 , c ) 43 , d ) 23 , e ) 13", |
| "response": "according to order of operations , inner brackets first where 6 × 4 ÷ 3 is first calculated since it has a multiplication and a division . 6 × 4 ÷ 3 = 24 ÷ 3 = 8 hence 11 + sqrt ( - 4 + 6 × 4 ÷ 3 ) = 11 + sqrt ( - 4 + 8 ) = 11 + sqrt ( 4 ) = 11 + 2 = 13 correct answer is e ) 13", |
| "system": "" |
| }, |
| { |
| "prompt": "a trader sold an item at a loss of 18 % . if he had increased the price by $ 25 he would have made a gain of 5 % . what is the cost price of the item ?\na ) $ 414.78 , b ) $ 424.78 , c ) $ 534.78 , d ) $ 434.78 , e ) $ 435.78", |
| "response": "let c . p . be $ x then 105 % of x - 82 % of x = 100 23 % of x = 100 23 / 100 * x = 100 23 x = 10000 x = 434.78 answer is d", |
| "system": "" |
| }, |
| { |
| "prompt": "5 x 1.6 - 2 x 1.4 / 1.3 = ?\na ) 3 , b ) 0 , c ) 5 , d ) 4 , e ) 2", |
| "response": "\"given expression = ( 8 - 2.8 ) / 1.3 = 5.2 / 1.3 = 52 / 1.3 = 4 . answer is d .\"", |
| "system": "" |
| } |
| ] |
| } |
