Cheukting/mathqa huggingface dataset:
Question (other): 45 pupil , out of them 12 in debate only and 22 in singing only . then how many in both ?
Options: a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 13
Rationale: the intersection for two = 45 - 12 - 22 = 11 play both games . answer : c
Answer: c
Question (other): of the 75 cars on a car lot , 45 have air - conditioning , 35 have power steering , and 12 have both air - conditioning and power steering . how many of the cars on the lot have neither air - conditioning nor power steering ?
Options: a ) 7 , b ) 8 , c ) 10 , d ) 15 , e ) 18
Rationale: "total - neither = all air conditioning + all power steering - both or 75 - neither = 45 + 35 - 12 = 68 . = > neither = 7 , hence a . answer : a"
Answer: a
Question (general): a corporation 5 times its annual bonus to 10 of its employees . what percent of the employees ’ new bonus is the increase ?
Options: a ) 12 % , b ) 18 % , c ) 80 % , d ) 20 % , e ) 15 %
Rationale: let the annual bonus be x . a corporation triples its annual bonus . so new bonus = 5 x . increase = 5 x - x = 4 x the increase is what percent of the employees ’ new bonus = ( 4 x / 5 x ) * 100 = 80 % hence c .
Answer: c
Question (general): the sum of ages of 5 children born at the intervals of 3 years each is 50 years . what is the age of the youngest child ?
Options: a ) 4 years , b ) 8 years , c ) 10 years , d ) none of these , e ) can not be determined
Rationale: "explanation let the ages of children be x , ( x + 3 ) , ( x + 6 ) , ( x + 9 ) and ( x + 12 ) years . then , x + ( x + 3 ) + ( x + 6 ) + ( x + 9 ) + ( x + 12 ) = 50 5 x = 20 x = 4 . age of the youngest child = x = 4 years . answer a"
Answer: a
Question (general): 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
Rationale: 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
Answer: a
Question (general): mr . evans will states that each of his children will receive an equal share of his estate and that his grandchildren will split a portion of the estate that is equal to the share received by each of his children . if mr . evans has 4 children and 5 grandchildren , then approximately what percentage of mr . evans estate will each grandchild receive ?
Options: a ) 20 % , b ) 17 % , c ) 4.0 % , d ) 3.3 % , e ) 2.8 %
Rationale: "20 / 5 = 4 answer : c"
Answer: c
Question (gain): if the selling price of 50 articles is equal to the cost price of 20 articles , then the loss or gain percent is :
Options: a ) 45 % , b ) 23 % , c ) 20 % , d ) 60 % , e ) 56 %
Rationale: "c . p . of each article be re . 1 . then , c . p . of 50 articles = rs . 50 ; s . p . of 50 articles = rs . 20 . loss % = 30 / 50 * 100 = 60 % answer d"
Answer: d
Question (general): the mean of 50 observations was 40 . it was found later that an observation 48 was wrongly taken as 23 . the corrected new mean is
Options: a ) 40.46 , b ) 36.1 , c ) 36.5 , d ) 39.1 , e ) none
Rationale: "sol . therefore correct sum = ( 40 × 50 + 48 – 23 ) = 2023 . therefore correct mean = 2023 / 50 = 40.46 . answer a"
Answer: a
Question (general): a certain tests consists 8 sections with 25 questions , numbered from 1 to 25 , in each section . if a student answered all of the even - numbered questions correctly and 3 / 4 of the odd - numbered questions correctly , what was the total number of questions he answered correctly ? a . 150 b . 172 c . 174 d . 175 e . 176
Options: a ) 174 , b ) 150 , c ) 180 , d ) 175 , e ) 190
Rationale: each set has 12 even and 13 odd numbered questions leading to total 96 even and 104 odd questions . 96 + 3 / 4 â ˆ — 104 = 96 + 78 = 17496 + 3 / 4 â ˆ — 104 = 96 + 78 = 174 answer : a
Answer: a
Question (physics): 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
Rationale: "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"
Answer: a
Question (general): when greenville state university decided to move its fine arts collection to a new library , it had to package the collection in 20 - inch by 20 - inch by 15 - inch boxes . if the university pays $ 0.60 for every box , and if the university needs 3.06 million cubic inches to package the collection , what is the minimum amount the university must spend on boxes ?
Options: a ) $ 306 , b ) $ 275 , c ) $ 510 , d ) $ 1,250 , e ) $ 2,550
Rationale: "total no . of boxes = 3060000 / ( 20 × 20 × 15 ) = 510 total cost = 510 × $ 0.6 = $ 306 answer a"
Answer: a
Question (general): if 2 x + y = 7 and x + 2 y = 5 , then 10 xy / 3 = ?
Options: a ) a ) 10 , b ) b ) 2 , c ) c ) 17 / 5 , d ) d ) 18 / 5 , e ) e ) 4
Rationale: "2 * ( x + 2 y = 5 ) equals 2 x + 4 y = 10 2 x + 4 y = 10 - 2 x + y = 7 = 3 y = 3 therefore y = 1 plug and solve . . . 2 x + 1 = 7 2 x = 6 x = 3 ( 10 * 3 * 1 ) / 3 = 30 / 3 = 10 a"
Answer: a
Question (general): the sum of ages of 5 children born at the intervals of 3 years each is 80 years . what is the age of the youngest child ?
Options: a ) 3 years , b ) 4 years , c ) 6 years , d ) 7 years , e ) 10 years
Rationale: "let the ages of children be x , ( x + 3 ) , ( x + 6 ) , ( x + 9 ) and ( x + 12 ) years . then , x + ( x + 3 ) + ( x + 6 ) + ( x + 9 ) + ( x + 12 ) = 80 5 x = 50 x = 10 . age of the youngest child = x = 10 years . e )"
Answer: e
Question (gain): 2 is what percent of 40 ?
Options: a ) 0.2 % , b ) 2 % , c ) 5 % , d ) 20 % , e ) 500 %
Rationale: "2 = x * 40 / 100 x = 5 % ans ; c"
Answer: c
Question (general): a no . when divided by 221 gives a remainder 43 , what remainder will beobtained by dividing the same number 19 ?
Options: a ) 3 , b ) 6 , c ) 9 , d ) 11 , e ) 15
Rationale: "221 + 43 = 264 / 17 = 9 ( remainder ) c"
Answer: c
Question (other): tea worth rs . 126 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
Options: a ) 175.59 , b ) 175.5 , c ) 175.57 , d ) 175.52 , e ) 175.11
Rationale: "explanation : since first second varieties are mixed in equal proportions , so their average price = rs . ( 126 + 135 / 2 ) = rs . 130.50 so , 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 . cost of 1 kg tea of 1 st kind cost of 1 kg tea of 2 nd kind x - 153 / 22.50 = 1 = > x - 153 = 22.50 = > x = 175.50 . hence , price of the third variety = rs . 175.50 per kg . answer : c ) rs . 175.50"
Answer: c
Question (physics): in an examination , a student scores 4 marks for every correct answer and loses 1 mark for every wrong answer . if he attempts all 80 questions and secures 120 marks , the number of questions he attempts correctly , is :
Options: a ) 35 , b ) 46 , c ) 42 , d ) 30 , e ) 40
Rationale: "let the number of correct answers be x . number of incorrect answers = ( 80 â € “ x ) . 4 x â € “ 1 ( 80 â € “ x ) = 120 or 5 x = 200 or x = 40 . answer : e"
Answer: e
Question (other): find the compound ratio of ( 2 : 3 ) , ( 6 : 11 ) and ( 11 : 4 ) is
Options: a ) 3 : 2 , b ) 2 : 1 , c ) 1 : 1 , d ) 4 : 5 , e ) 2 : 3
Rationale: "required ratio = 2 / 3 * 6 / 11 * 11 / 4 = 2 / 1 = 1 : 1 answer is c"
Answer: c
Question (general): a no . when divided by the sum of 555 and 445 gives 2 times their difference as quotient & 10 as remainder . find the no . is ?
Options: a ) 220010 , b ) 145778 , c ) 220110 , d ) 235467 , e ) 220001
Rationale: "( 555 + 445 ) * 2 * 110 + 10 = 220000 + 10 = 220010 a"
Answer: a
Question (other): in a sports club with 55 members , 23 play badminton and 29 play tennis and 7 do not play either . how many members play both badminton and tennis ?
Options: a ) 3 , b ) 5 , c ) 4 , d ) 7 , e ) 8
Rationale: "23 + 29 = 52 but where as total number is 55 - 7 = 48 therefore answer is 52 - 48 = 4 hence answer is c"
Answer: c
Question (physics): a garrison of 500 men has provisions for 20 days . at the end of 14 days , a reinforcement arrives , and it is now found that the provisions will last only for 3 days more . what is the reinforcement ?
Options: a ) 500 , b ) 1000 , c ) 1500 , d ) 3000 , e ) 2000
Rationale: "500 - - - - 20 500 - - - - 6 x - - - - - 3 x * 3 = 500 * 6 x = 1000 500 - - - - - - - 500 answer : a"
Answer: a
Question (physics): how long does a train 165 meters long running at the rate of 54 kmph take to cross a bridge 660 meters in length ?
Options: a ) 55 sec , b ) 40 sec , c ) 45 sec , d ) 30 sec , e ) 35 sec
Rationale: "t = ( 660 + 165 ) / 54 * 18 / 5 t = 55 answer a"
Answer: a
Question (physics): in covering a distance of 54 km , abhay takes 2 hours more than sameer . if abhay doubles his speed , then he would take 1 hour less than sameer . abhay ' s speed is :
Options: a ) 5 kmph , b ) 6 kmph , c ) 6.25 kmph , d ) 7.5 kmph , e ) 9 kmph
Rationale: "let abhay ' s speed be x km / hr . then , 54 / x - 54 / 2 x = 3 6 x = 54 x = 9 km / hr . answer : option e"
Answer: e
Question (physics): the length of minute hand of a clock is 5.6 cm . what is the area covered by this in 10 minutes
Options: a ) 15.27 , b ) 16.27 , c ) 17.27 , d ) 16.41 , e ) 19.27
Rationale: area of circle is pi * r ^ 2 but in 10 minutes area covered is ( 10 / 60 ) * 360 = 60 degree so formula is pi * r ^ 2 * ( angle / 360 ) = 3.14 * ( 5.6 ^ 2 ) * ( 60 / 360 ) = 16.41 cm ^ 2 answer : d
Answer: d
Question (general): john has $ 1600 at the beginning of his trip , after spending money , he still has exactly $ 600 less than he spent on the trip . how much money does john still have ?
Options: a ) $ 200 , b ) $ 400 , c ) $ 600 , d ) $ 800 , e ) $ 500
Rationale: suppose total money spent = x not spend ( money he still has ) = x - 600 x + x - 600 = 1600 x = 1100 money not spend = 1100 - 600 = 500 answer : e
Answer: e
Question (physics): a train 1000 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 ) 1000 m , d ) 278 m , e ) 287 m
Rationale: "speed = 78 * 5 / 18 = 65 / 3 m / sec . time = 1 min = 60 sec . let the length of the train be x meters . then , ( 1000 + x ) / 60 = 65 / 3 x = 300 m . answer : c"
Answer: c
Question (general): students at a school were on average 180 cm tall . the average female height was 170 cm , and the average male height was 181 cms . what was the ratio of men to women ?
Options: a ) 5 : 2 , b ) 5 : 1 , c ) 4 : 3 , d ) 4 : 1 , e ) 10 : 1
Rationale: we ' re given a few facts to work with : 1 ) the average height of the females is 170 cm 2 ) the average height of the males is 181 cm 3 ) the average of the group is 180 cm we ' re asked for the ratio of men to women . w = number of women m = number of men ( 170 w + 181 m ) / ( w + m ) = 180 170 w + 181 m = 180 w + 180 m 1 m = 10 w m / w = 10 / 1 the ratio of men to women is 10 to 1 . e
Answer: e
Question (geometry): if the length of the longest chord of a certain circle is 18 , what is the radius of that certain circle ?
Options: a ) 2.5 , b ) 9 , c ) 10 , d ) 15 , e ) 20
Rationale: "longest chord of a circle is the diameter of the circle diameter = 2 * radius if diameter of the circle is given as 18 = 2 * 9 so radius of the circle = 9 correct answer - b"
Answer: b
Question (physics): a cistern 10 meters long and 4 meters wide contains water up to a depth of 1 meter 25 cm . what is the total area of the wet surface ?
Options: a ) 45 , b ) 55 , c ) 65 , d ) 75 , e ) 85
Rationale: area of the wet surface = [ 2 ( lb + bh + lh ) - lb ] = 2 ( bh + lh ) + lb = [ 2 ( 4 x 1.25 + 10 x 1.25 ) + 10 x 4 ] = 75 the answer is d .
Answer: d
Question (probability): a certain junior class has 1,000 students and a certain senior class has 800 students . among these students , there are 20 siblings pairs , each consisting of 1 junior and 1 senior . if 1 student is to be selected at random from each class , what is the probability that the 2 students selected at will be a sibling pair ?
Options: a ) 3 / 40,000 , b ) 1 / 3,600 , c ) 9 / 2,000 , d ) 1 / 40,000 , e ) 1 / 15
Rationale: "total number of ways of choosing one student from each group is = 800 * 1000 number of cases in which a sibling pair will be got is = 60 thus the probability that the 2 students selected will be a sibling pair is = 20 / ( 800 * 1000 ) = 1 / 40,000 d"
Answer: d
Question (general): if 50 % of ( x - y ) = 30 % of ( x + y ) then what percent of x is y ?
Options: a ) 2.5 % , b ) 10 % , c ) 5 % , d ) 15 % , e ) 25 %
Rationale: "50 % of ( x - y ) = 30 % of ( x + y ) ( 50 / 100 ) ( x - y ) = ( 30 / 100 ) ( x + y ) 5 ( x - y ) = 3 ( x + y ) 2 x = 8 y x = 4 y therefore required percentage = ( ( y / x ) x 100 ) % = ( ( y / 4 y ) x 100 ) = 25 % answer is e ."
Answer: e
Question (physics): how many seconds does sandy take to cover a distance of 600 meters , if sandy runs at a speed of 18 km / hr ?
Options: a ) 100 , b ) 120 , c ) 140 , d ) 160 , e ) 180
Rationale: 18 km / hr = 18000 m / 3600 s = 5 m / s time = 600 / 5 = 120 seconds the answer is b .
Answer: b
Question (physics): calculate how many days it will take for 10 boys to paint a 80 m long wall if 6 boys can paint a 70 m long wall in 8 days ,
Options: a ) 9.48 days , b ) 3.48 days , c ) 7.48 days , d ) 5.48 days , e ) 6.48 days
Rationale: "the length of wall painted by one boy in one day = 70 / 6 * 1 / 8 = 1.46 m no . of days required to paint 50 m cloth by 8 boys = 80 / 10 * 1 / 1.46 = 5.48 days . d"
Answer: d
Question (general): a no . when divided by the sum of 555 and 445 gives 2 times their difference as quotient & 60 as remainder . find the no . is ?
Options: a ) 145646 , b ) 236578 , c ) 645353 , d ) 456546 , e ) 220060
Rationale: "( 555 + 445 ) * 2 * 110 + 60 = 220000 + 60 = 220060 e"
Answer: e
Question (physics): a monkey start climbing up a tree 18 ft tall . each hour it hops 3 ft and slips back 2 ft . how much time would it take the monkey to reach the top .
Options: a ) 15 hrs , b ) 18 hrs , c ) 19 hrs , d ) 17 hrs , e ) 16 hrs
Rationale: "if monkey hops 3 ft and slips back 2 ft in a hour , it means the monkey hops ( 3 ft - 2 ft ) = 1 ft / hr . similarly in 15 hrs it wil be 15 ft . bt since the height of the tree is 18 ft , so if the monkey hops up the tree in the next hr i . e 16 th hr then it reaches at the top of the tree . hence it takes 16 hrs for monkey to reach at the top answer : e"
Answer: e
Question (physics): jane and ashley take 8 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 ) 14 days , b ) 15 days , c ) 16 days , d ) 18 days , e ) 20 days
Rationale: "let us assume that the work is laying 40 bricks . jane = 5 bricks per day ashley = 1 brick per day together = 6 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 = 20 remaining bricks = 40 - 28 = 12 so together , they would take 12 / 6 = 2 total no . of days = 8 + 4 + 2 = 14 answer is a"
Answer: a
Question (general): if an integer n is to be selected at random from 1 to 100 , inclusive , what is probability n ( n + 1 ) will be divisible by 32 ?
Options: a ) 2 / 7 , b ) 3 / 7 , c ) 1 / 16 , d ) 1 / 14 , e ) 1 / 12
Rationale: "because n ( n + 1 ) is always an even product of even * odd or odd * even factors , there is a probability of 1 that that it will be divisible by 2 , and , thus , a probability of 1 / 2 that it will be divisible by 4 and , thus , a probability of 1 / 4 that it will be divisible by 8 and , thus , a probability of 1 / 8 that it will be divisible by 16 and , thus , a probability of 1 / 16 that it will be divisible by 32 1 * 1 / 16 = 1 / 16 answer : c"
Answer: c
Question (general): today jim is twice as old as fred , and sam is 4 years younger than fred . 4 years ago jim was 8 times as old as sam . how old is jim now ?
Options: a ) 8 , b ) 12 , c ) 16 , d ) 20 , e ) 24
Rationale: 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 4 years younger than fred 3 ) four years ago , jim was 8 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 6 years old 4 years ago , jim was 16 and sam was 2 , so jim was 8 times sam ' s age . this is an exact match for what we were told , so this must be the answer . d
Answer: d
Question (physics): a bullet train 150 m long is running with a speed of 30 kmph . in what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the bullet train is going ?
Options: a ) 23 sec , b ) 15 sec , c ) 12 sec , d ) 11 sec , e ) 15 sec
Rationale: e 15 sec speed of the bullet train relative to man = ( 30 + 6 ) kmph = 36 * 5 / 18 m / sec = 30 / 3 m / sec . time taken by the bullet train to cross the man = time taken by it to cover 150 m at ( 30 / 3 ) m / sec = ( 150 * 3 / 30 ) sec = 15 sec
Answer: e
Question (general): the sum of all the integers k such that – 21 < k < 24 is
Options: a ) 0 , b ) - 2 , c ) - 25 , d ) - 39 , e ) - 51
Rationale: "- 20 - - - - - - - - - - - - - - - - - - 0 - - - - - - - - - - - - - - - - - 23 values upto + 23 cancels outwe are left with only - 20 - 19 sum of which is - 39 . hence option d . d"
Answer: d
Question (gain): a dealer purchases 15 articles for rs . 25 and sells 12 articles for rs . 30 . find the profit percentage ?
Options: a ) 25 % , b ) 50 % , c ) 20 % , d ) 5 % , e ) none of these
Rationale: "l . c . m of 15 and 12 = 60 cp of 60 articles = rs . 100 ( 25 * 4 ) sp of 60 articles = rs . 150 ( 30 * 5 ) profit percentage = ( 150 - 100 ) / 100 * 100 = 50 % answer : b"
Answer: b
Question (general): the digital sum of a number is the sum of its digits . for how many of the positive integers 24 - 130 inclusive is the digital sum a multiple of 7 ?
Options: a ) 7 , b ) 8 , c ) 14 , d ) 16 , e ) 20
Rationale: "is there other way than just listing ? 25 34 43 52 59 61 68 70 77 86 95 106 115 124 14 ways . . c"
Answer: c
Question (physics): a worker ' s daily wage is increased by 50 % and the new wage is $ 30 per day . what was the worker ' s daily wage before the increase ?
Options: a ) $ 15 , b ) $ 18 , c ) $ 20 , d ) $ 22 , e ) $ 25
Rationale: let x be the daily wage before the increase . 1.5 x = $ 30 x = $ 20 the answer is c .
Answer: c
Question (gain): what is 120 % of 13 / 24 of 600 ?
Options: a ) 320 , b ) 390 , c ) 440 , d ) 480 , e ) 510
Rationale: "120 % * 13 / 24 * 360 = 1.2 * 13 * 25 = 390 the answer is b ."
Answer: b
Question (physics): if the weight of 12 meters long rod is 13.4 kg . what is the weight of 6 meters long rod ?
Options: a ) 6.7 kg . , b ) 10.8 kg . , c ) 12.4 kg . , d ) 18.0 kg , e ) none
Rationale: "answer ∵ weight of 12 m long rod = 13.4 kg ∴ weight of 1 m long rod = 13.4 / 12 kg ∴ weight of 6 m long rod = 13.4 x 6 / 12 = 6.7 kg option : a"
Answer: a
Question (general): evaluate : 60 - 12 * 3 * 2 = ?
Options: a ) 42 , b ) 52 , c ) 62 , d ) 72 , e ) 82
Rationale: "according to order of operations , 12 ? 3 ? 2 ( division and multiplication ) is done first from left to right 12 * * 2 = 4 * 2 = 8 hence 60 - 12 * 3 * 2 = 60 - 8 = 52 correct answer b"
Answer: b
Question (geometry): a rectangular photograph is surrounded by a border that is 1 inch wide on each side . the total area of the photograph and the border is m square inches . if the border had been 4 inches wide on each side , the total area would have been ( m + 108 ) square inches . what is the perimeter of the photograph , in inches ?
Options: a ) 34 , b ) 36 , c ) 16 , d ) 40 , e ) 42
Rationale: "let length and breadth of photograph be l and b respectively . perimeter is given by 2 * ( l + b ) - - - - - ( 1 ) according to the question : ( l + 2 ) ( b + 2 ) = m - - - - ( 2 ) and ( l + 8 ) ( b + 8 ) = m + 108 - - - - - - - - - > ( l + 8 ) ( b + 8 ) - 108 = m - - - - - - ( 3 ) equating ( 2 ) and ( 3 ) ( l + 2 ) ( b + 2 ) = ( l + 8 ) ( b + 8 ) - 108 lb + 2 l + 2 b + 4 = lb + 8 l + 8 b + 64 - 108 simplify 6 l + 6 b = 48 - - - - - - > 2 ( l + b ) = 16 ( check eq ( 1 ) ) answer is c"
Answer: c
Question (general): a store sells 2 kinds of jelly beans mixes ( a and b ) both made up of red and yellow beans . if b contains 20 % more red beans than a but 10 % fewer yellow beans . and jar a contains twice as many red beans as yellow by what percent is the number of beans in jar b larger than the number in jar a
Options: a ) 5 , b ) 6 , c ) 8 , d ) 9 , e ) 10
Rationale: a has 10 yellows 20 reds total = 30 so b has 1.2 x 20 = 24 reds 0.9 x 10 = 9 yellows total = 33 difference = 3 / 30 = 10 % answer : e
Answer: e
Question (other): find the greatest common factor ( gfc ) of 24 , 40 and 60 .
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: we first write the prime factorization of each given number 24 = 2 × 2 × 2 × 3 = 23 * cubic * × 3 40 = 2 × 2 × 2 × 5 = 23 * cubic * × 5 60 = 2 × 2 × 3 × 5 = 22 * square * × 3 × 5 gfc = 22 * square * = 4 corect answer is d ) 4
Answer: d
Question (general): when 242 is divided by a certain divisor the remainder obtained is 12 . when 698 is divided by the same divisor the remainder obtained is 16 . however , when the sum of the two numbers 242 and 698 is divided by the divisor , the remainder obtained is 10 . what is the value of the divisor ?
Options: a ) 11 , b ) 18 , c ) 13 , d ) 23 , e ) none of these
Rationale: "let that divisor be x since remainder is 12 or 16 it means divisor is greater than 16 . now 242 - 12 = 230 = kx ( k is an integer and 234 is divisble by x ) similarly 698 - 16 = 682 = lx ( l is an integer and 689 is divisible by x ) adding both 698 and 242 = ( 230 + 682 ) + 12 + 16 = x ( k + l ) + 28 when we divide this number by x then remainder will be equal to remainder of ( 28 divided by x ) = 10 hence x = 28 - 10 = 18 hence b"
Answer: b
Question (gain): the cost price of an article is 64 % of the marked price . calculate the gain percent after allowing a discount of 20 % ?
Options: a ) 37.5 % , b ) 48 % , c ) 50.5 % , d ) 52 % , e ) 25 %
Rationale: "explanation : let marked price = rs . 100 . then , c . p . = rs . 64 , s . p . = rs . 80 gain % = 16 / 64 * 100 = 25 % . answer : option e"
Answer: e
Question (gain): by selling 22 pens for a rupee a woman loses 10 % . how many for a rupee should he sell in order to gain 50 % ?
Options: a ) 12 , b ) 14 , c ) 45 , d ) 13 , e ) 65
Rationale: "d 90 % - - - 22 150 % - - - ? 90 / 150 * 22 = 13"
Answer: d
Question (general): 1394 x 1394
Options: a ) 1943236 , b ) 1981709 , c ) 18362619 , d ) 2031719 , e ) none of these
Rationale: "1394 x 1394 = ( 1394 ) 2 = ( 1400 - 2 ) 2 = ( 1400 ) 2 + ( 6 ) 2 - ( 6 x 1400 x 6 ) = 1943236 . answer : option a"
Answer: a
Question (general): a and b start a business jointly . a invests rs 16000 for 8 month and b remains in the business for 4 months . out of total profit , b claims 2 / 7 of the profit . how much money was contributed by b ?
Options: a ) 12800 , b ) 13000 , c ) 11500 , d ) 12500 , e ) 12000
Rationale: b claims 2 / 7 of the profit a claims remaining 5 / 7 of the profit = > a : b = 5 / 7 : 2 / 7 = 5 : 2 let the money contributed by b = b then a : b = 16000 × 8 : b × 4 therefore , 16000 × 8 : b × 4 = 5 : 2 16000 × 8 × 2 = b × 4 × 5 16000 × 2 × 2 = b × 5 3200 × 2 × 2 = b b = 12800 answer is a .
Answer: a
Question (general): the second of two numbers is two less than 3 times the first . find the numbers if there sum is 82 .
Options: a ) 7 - 19 , b ) 8 - 20 , c ) 10 - 16 , d ) 15 - 9 , e ) 21 - 61
Rationale: we are looking for two numbers . # 1 - x # 2 - 3 x â € “ 2 the sum is 82 . # 1 + # 2 = 82 substituting x + 3 x â € “ 2 = 82 4 x â € “ 2 = 82 4 x = 84 x = 21 the first number is 21 , the second number is two less than three times 21 or 61 . correct answer e
Answer: e