Cheukting/mathqa huggingface dataset:
Question (general): 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
Rationale: "explanation : let ' s son age is x , then father age is x + 40 . = > 2 ( x + 6 ) = ( x + 40 + 6 ) = > 2 x + 12 = x + 46 = > x = 34 years answer : option d"
Answer: d
Question (physics): the perimeter of a semi circle is 198 cm then the radius is ?
Options: a ) 22 , b ) 28 , c ) 98 , d ) 38.5 , e ) 13
Rationale: "36 / 7 r = 198 = > r = 38.5 answer : d"
Answer: d
Question (general): for any number z , z * is defined as the greatest positive even integer less than or equal to y . what is the value of 6.35 – 6.35 * ?
Options: a ) 0.35 , b ) 0.5 , c ) 6.25 , d ) 0.25 , e ) 6.0
Rationale: "since z * is defined as the greatest positive even integer less than or equal to z , then 6.35 * = 6 ( the greatest positive even integer less than or equal to 6.35 is 6 ) . hence , 6.35 – 6.35 * = 6.35 - 6 = 0.35 answer : a ."
Answer: a
Question (physics): joe drives 360 miles at 60 miles per hour , and then he drives the next 120 miles at 40 miles per hour . what is his average speed for the entire trip in miles per hour ?
Options: a ) 42 , b ) 53 , c ) 50 , d ) 54 , e ) 56
Rationale: t 1 = 360 / 60 = 6 hours t 2 = 120 / 40 = 3 hours t = t 1 + t 2 = 9 hours avg speed = total distance / t = 480 / 9 = 53 mph = b
Answer: b
Question (general): 12 . what is the dividend . divisor 17 , the quotient is 9 and the remainder is 8 .
Options: a ) 161 , b ) 152 , c ) 154 , d ) 158 , e ) 144
Rationale: "d = d * q + r d = 17 * 9 + 8 d = 153 + 8 d = 161 answer a"
Answer: a
Question (physics): car a runs at the speed of 55 km / hr and reaches its destination in 8 hours . car b runs at the speed of 70 km / h and reaches its destination in 4 hours . what is the ratio of distances covered by car a and car b ?
Options: a ) 3 : 7 , b ) 4 : 9 , c ) 11 : 7 , d ) 5 : 7 , e ) 6 : 11
Rationale: "car a travels 55 × 8 = 440 km car b travels 70 × 4 = 280 km the ratio is 440 : 280 = 44 : 28 = 11 : 7 the answer is c ."
Answer: c
Question (physics): a train running at the speed of 70 km / hr crosses a pole in 36 seconds . what is the length of the train ?
Options: a ) 700 , b ) 770 , c ) 707 , d ) 710 , e ) 720
Rationale: "speed = ( 70 * 5 / 18 ) m / sec = ( 175 / 9 ) m / sec length of the train = ( speed x time ) = ( 175 / 9 * 36 ) m = 700 m . answer : a"
Answer: a
Question (physics): a jeep takes 3 hours to cover a distance of 440 km . how much should the speed in kmph be maintained to cover the same direction in 1 / 2 th of the previous time ?
Options: a ) 48 kmph , b ) 252 kmph , c ) 293 kmph , d ) 263 kmph , e ) 265 kmph
Rationale: "time = 3 distance = 340 1 / 2 of 3 hours = 6 * 1 / 2 = 1.5 hours required speed = 440 / 1.5 = 293 kmph c )"
Answer: c
Question (general): what is the sum of all possible 3 - digit numbers that can be constructed using the digits 2 , 4 , and 5 if each digit can be used only once in each number ?
Options: a ) 2442 , b ) 2552 , c ) 2662 , d ) 2772 , e ) 2882
Rationale: "there are 6 possible arrangements of the three numbers . then each number will be in the hundreds , tens , and ones place two times each . the sum is 2 ( 222 ) + 2 ( 444 ) + 2 ( 555 ) = 2442 the answer is a ."
Answer: a
Question (physics): 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
Rationale: perimeter = distance covered in 8 min . = 12000 x 8 m = 1600 m . 60 let length = 1 x metres and breadth = 4 x metres . then , 2 ( 1 x + 4 x ) = 1600 or x = 160 . length = 160 m and breadth = 640 m . area = ( 160 x 640 ) m 2 = 102400 m e
Answer: e
Question (general): the difference between the ages of two persons is 20 years . fifteen years ago , the elder one was twice as old as the younger one . the present age of the younger person is ?
Options: a ) 30 , b ) 35 , c ) 25 , d ) 28 , e ) 32
Rationale: let their ages be x years and ( x + 20 ) years then , ( x + 20 ) - 15 = 2 ( x - 15 ) x + 5 = 2 x - 30 x = 35 answer is b
Answer: b
Question (general): if 70 percent of 600 is 40 percent of x , then x = ?
Options: a ) 105 , b ) 168 , c ) 342 , d ) 660 , e ) 1050
Rationale: "given : 0.7 * 600 = 0.4 x - - > 420 = 4 / 10 * x - - > x = 1,050 . answer : e ."
Answer: e
Question (geometry): find the sum of divisors of 544 which are perfect squares
Options: a ) 21
b ) 22
c ) 23
d ) 24
e ) 25
Rationale: perfect squares divisiors are 1 , 2 ^ 2 & 2 ^ 4 only sum of divisors of 544 which are perfect squares = 1 + 2 ^ 2 + 2 ^ 4 = 21 answer : a
Answer: a
Question (gain): find compound interest on $ 6000 at 15 % per annum for 2 years 4 months , compounded annually .
Options: a ) 2331.75 , b ) 2209.75 , c ) 2108.75 , d ) 2107.75 , e ) 2100.75
Rationale: "time = 2 years 4 months = 2 ( 4 / 12 ) years = 2 ( 1 / 3 ) years . amount = $ [ 6000 x ( 1 + ­ ( 15 / 100 ) ) 2 x ( 1 + ( ( 1 / 3 ) * 15 ) / 100 ) ] = $ [ 6000 * ( 23 / 20 ) * ( 23 / 20 ) * ( 21 / 20 ) ] = $ 8331.75 . : . c . i . = rs . ( 8331.75 - 6000 ) = $ 2331.75 answer a ."
Answer: a
Question (gain): a towel , when bleached , lost 30 % of its length and 40 % of its breadth . what is the percentage decrease in area ?
Options: a ) 24 % , b ) 30 % , c ) 44 % , d ) 58 % , e ) 64 %
Rationale: "percentage change in area = ( − 30 − 40 + ( 30 × 40 ) / 100 ) % = − 58 % i . e . , area is decreased by 58 % answer : d"
Answer: d
Question (gain): in order to obtain an income of rs . 3800 from 70 % stock at rs . 280 , one must make an investment of
Options: a ) rs . 16000 , b ) rs . 15000 , c ) rs . 15250 , d ) rs . 15200 , e ) rs . 15300
Rationale: "explanation : market value = rs . 280 required income = rs . 3800 . here face value is not given . take face value as rs . 100 if it is not given in the question to obtain rs . 70 ( ie , 70 % of the face value 100 ) , investment = rs . 280 to obtain rs . 3800 , investment = 280 / 70 ã — 3800 = rs . 15200 answer : option d"
Answer: d
Question (physics): a train 300 m long can cross an electric pole in 15 sec and then find the speed of the train ?
Options: a ) 65 kmph , b ) 70 kmph , c ) 72 kmph , d ) 75 kmph , e ) 78 kmph
Rationale: "length = speed * time speed = l / t s = 300 / 15 s = 20 m / sec speed = 20 * 18 / 5 ( to convert m / sec in to kmph multiply by 18 / 5 ) speed = 72 kmph answer : c"
Answer: c
Question (physics): a pipe can empty 2 / 3 rd of a cistern in 12 mins . in 5 mins , what part of the cistern will be empty ?
Options: a ) 2 / 3 , b ) 5 / 18 , c ) 4 / 9 , d ) 3 / 8 , e ) 4 / 7
Rationale: 2 / 3 - - - - 12 ? - - - - - 5 = = > 5 / 18 b
Answer: b
Question (probability): jane and thomas are among the 8 people from which a committee of 3 people is to be selected . how many different possible committees of 3 people can be selected from these 8 people if at least one of either jane or thomas is to be selected ?
Options: a ) 24 , b ) 28 , c ) 32 , d ) 36 , e ) 40
Rationale: "the total number of ways to choose 3 people from 8 is 8 c 3 = 56 . the number of committees without jane or thomas is 6 c 3 = 20 . there are 56 - 20 = 36 possible committees which include jane and / or thomas . the answer is d ."
Answer: d
Question (geometry): find the surface area of a 10 cm x 4 cm x 3 cm brick
Options: a ) 84 , b ) 124 , c ) 164 , d ) 180 , e ) 120
Rationale: "explanation : surface area = [ 2 ( 10 x 4 + 4 x 3 + 10 x 3 ) ] cm 2 = 164 cm 2 answer : c"
Answer: c
Question (general): 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
Rationale: "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"
Answer: a
Question (general): what is the least value of x . so that 30 x 55 is divisible by 3 ?
Options: a ) 4 , b ) 5 , c ) 1 , d ) 2 , e ) 7
Rationale: "the sum of the digits of the number is divisible by 3 , then the number is divisible by 3 . 3 + 0 + x + 5 + 5 = 13 + x least value of x may be 2 therefore 13 + 2 = 15 is divisible by 3 . d"
Answer: d
Question (physics): if a motorist had driven 1 hour longer on a certain day and at an average rate of 4 miles per hour faster , he would have covered 70 more miles than he actually did . how many more miles would he have covered than he actually did if he had driven 2 hours longer and at an average rate of 10 miles per hour faster on that day ?
Options: a ) 100 , b ) 120 , c ) 140 , d ) 150 , e ) 160
Rationale: "case 1 : let rate = r , time = t , and distance = d so d = rt case 2 : ( d + 70 ) = ( r + 4 ) ( t + 1 ) case 3 : ( d + x ) = ( r + 10 ) ( t + 2 ) x = 140 ans c"
Answer: c
Question (general): 2 ^ ( 2 x / 3 ) = 2 ^ ( x / 2 ) what is the value of x ?
Options: a ) 2 , b ) 2 / 3 , c ) 1 , d ) 0 , e ) - 2
Rationale: 2 x / 3 = x / 2 4 x = 3 x 4 x - 3 x = 0 ; x = 0 ans : d
Answer: d
Question (geometry): a box measuring 35 inches long by 20 inches wide by 10 inches deep is to be filled entirely with identical cubes . no space is to be left unfilled . what is the smallest number of cubes that can accomplish this objective ?
Options: a ) 17 , b ) 18 , c ) 54 , d ) 56 , e ) 864
Rationale: "least number of cubes will be required when the cubes that could fit in are biggest . 5 is the biggest number that could divide all three , 35 , 20 and 10 . thus side of cube must be 5 , and total number of cubes = 35 / 5 * 20 / 5 * 10 / 5 = 56 ans d it is ."
Answer: d
Question (other): how many prime numbers between 1 and 100 are factors of 1771 ?
Options: a ) 2 , b ) 6 , c ) 5 , d ) 4 , e ) 3
Rationale: "factor of 1771 = 7 * 11 * 23 - - - 3 prime numbers e"
Answer: e
Question (general): what is the sum of all possible solutions to | x - 4 | ^ 2 + | x - 4 | = 20 ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 3
Rationale: "denote | x - 4 | as y : y ^ 2 + y = 20 - - > y = - 5 or y = 4 . discard the first solution since y = | x - 4 | , so it ' s an absolute value and thus can not be negative . y = | x - 4 | = 4 - - > x = 8 or x = - 1 . the sum = 7 . answer : d ."
Answer: d
Question (general): if p represents the product of the first 14 positive integers , then p is not a multiple of :
Options: a ) a ) 99 , b ) b ) 84 , c ) c ) 51 , d ) d ) 65 , e ) e ) 57
Rationale: a ) 99 = 9 * 11 b ) 84 = 4 * 7 * 3 c ) 51 = 17 * 3 d ) 65 = 5 * 13 e ) 57 = 19 * 3 since 17 is not there in first 15 positive numbers it is the only possibility c
Answer: c
Question (general): the average weight of 10 girls increases by 5 kg when a new girl comes in place of one of them weighing 50 kg . what might be the weight of the new girl ?
Options: a ) 90 kg , b ) 100 kg , c ) 95 kg , d ) 85 kg , e ) 92 kg
Rationale: "total weight increased = 10 x 5 kg = 50 kg . weight of new person = 50 + 50 kg = 100 kg answer : b"
Answer: b
Question (general): 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
Rationale: "d = ( d - r ) / q = ( 144 - 1 ) / 13 = 143 / 13 = 11 a )"
Answer: a
Question (general): a shop produces sarongs . the daily average production is given by 5 n + 20 , where n is the number of workers aside from the owner . in the first k days , 500 units are produced , and then 5 workers are added to the team . after another k days , the cumulative total is 1100 . how many workers were part of the latter production run ?
Options: a ) 26 , b ) b ) 10 , c ) c ) 11 , d ) d ) 15 , e ) e ) 23.5
Rationale: the daily average production is given by 5 n + 20 - given in the first k days , 500 units are produced = ( 5 n + 20 ) k = 500 k = 500 / 5 n + 20 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 5 workers were added = 5 ( n + 5 ) + 20 = 5 n + 45 cumulative is 1100 . . thus for the current period = 1100 - 500 = 600 ( 5 n + 45 ) k = 600 k = 600 / 5 n + 45 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 equate 1 and 2 500 / 5 n + 20 = 600 / 5 n + 45 500 ( 5 n + 45 ) = 600 ( 5 n + 20 ) 2500 n + 22500 = 3000 n + 12000 - 500 n = - 10500 n = 21 thus n + 5 = 26 hence a
Answer: a
Question (geometry): find the area of a parallelogram with base 24 cm and height 16 cm ?
Options: a ) 298 cm 2 , b ) 384 cm 2 , c ) 279 cm 2 , d ) 297 cm 2 , e ) 278 cm 2
Rationale: "area of a parallelogram = base * height = 24 * 16 = 384 cm 2 answer : b"
Answer: b
Question (gain): the principal that amounts to rs . 4893 in 3 years at 6 1 / 4 % per annum c . i . compounded annually , is ?
Options: a ) s . 3096 , b ) s . 4076 , c ) s . 4085 , d ) s . 4096 , e ) s . 5096
Rationale: principal = [ 4913 / ( 1 + 25 / ( 4 * 100 ) ) 3 ] = 4893 * 16 / 17 * 16 / 17 * 16 / 17 = rs . 4085 . answer : c
Answer: c
Question (general): what is the remainder when 46 * 49 is divided by 8 ?
Options: a ) 1 , b ) 3 , c ) 4 , d ) 6 , e ) 7
Rationale: "we can make use of the rule : remainder of { ( a * b ) / n } } = remainder of ( a / n ) * remainder of ( b / n ) here remainder of { 46 * 49 ) / 8 } } = remainder of ( 46 / 8 ) * remainder of ( 49 / 8 ) = 6 * 1 = 6 answer : d"
Answer: d
Question (general): an old man distributed all the gold coins he had to his two sons into two different numbers such that the difference between the squares of the two numbers is 25 times the difference between the two numbers . how many coins did the old man have ?
Options: a ) 24 , b ) 26 , c ) 30 , d ) 25 , e ) 40
Rationale: "let the number of coins one son got be x and the number of coins another got be y . total = x + y . x ^ 2 - y ^ 2 = 25 ( x - y ) - - > x + y = 25 . answer : d ."
Answer: d
Question (physics): 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 15 kilometers by car . what is the distance , in kilometers , from the dormitory to the city ?
Options: a ) 67 , b ) 45 , c ) 60 , d ) 90 , e ) 120
Rationale: "i believe there is a better way to do it . basically one of the options should satisfy the given criteria . 60 did 1 / 5 * 60 = 12 2 / 3 * 60 = 40 so total distance 52 + remaining 15 = 67"
Answer: c
Question (general): if 18 ! / 3 ^ x is an integer , what is the greatest possible value of x ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 8
Rationale: "18 - 3 * 3 * 2 15 - 5 * 3 12 - 4 * 3 9 - 3 * 3 6 - 2 * 3 3 - 1 * 3 hence max of 3 ^ 8 is allowed . imo e ."
Answer: e
Question (other): the ratio of 2 numbers is 3 : 7 and their h . c . f . is 10 . their l . c . m . is ?
Options: a ) 220 , b ) 210 , c ) 252 , d ) 236 , e ) 260
Rationale: "let the numbers be 3 x and 7 x their h . c . f . = 10 so the numbers are 3 * 10 , 7 * 10 = 30,70 l . c . m . = 210 answer is b"
Answer: b
Question (physics): two trains are moving in opposite directions @ 100 kmph and 120 kmph . their length are 500 m and 700 m . the time taken by the slower train to cross faster train in second is ?
Options: a ) 15 sec , b ) 18.3 sec , c ) 19.6 sec , d ) 20.4 sec , e ) 22.5 sec
Rationale: relative speed = 100 + 120 = 220 * 5 / 18 = 550 / 9 m / s distance covered = 500 + 700 = 1200 m required time = 1200 * 9 / 550 = 19.6 sec answer is c
Answer: c
Question (general): if two positive numbers are in the ratio 1 / 8 : 1 / 5 , then by what percent is the second number more than the first ?
Options: a ) 70 % , b ) 90 % , c ) 60 % , d ) 50 % , e ) 65 %
Rationale: "given ratio = 1 / 8 : 1 / 5 = 5 : 8 let first number be 5 x and the second number be 8 x . the second number is more than first number by 3 x . required percentage = 3 x / 5 x * 100 = 60 % . answer : c"
Answer: c
Question (general): if the price of a certain bond on may 1 st was 1 / 4 the price of the bond on june 1 st and the price of the bond on july 1 st was 25 % greater than the price of the bond on may 1 st . then the price of the bond on june 1 st st was what percent of the average ( arithmetic mean ) price of the bond on may 1 st and july 1 st ?
Options: a ) 100 % , b ) 150 % , c ) 155 % , d ) 300 % , e ) 355 %
Rationale: "the price on june 1 st = 12 ( assume ) ; the price on may 1 st = 1 / 4 * 12 = 3 ; the price on july 1 st = 3 * 1.25 = 3.75 . the average price of the bond on may 1 st and july 1 st = ( 3 + 3.75 ) / 2 = 3.375 . the price of the bond on june 1 st ( 12 ) is 32 / 9 times ( 355.55 % ) the average price of the bond on may 1 st and july 1 st . answer : e ."
Answer: e
Question (general): what is the remainder when 1003 * 1005 * 1007 is divided by 15
Options: a ) 3 , b ) 17 , c ) 14 , d ) 0 , e ) 7
Rationale: "1003 / 15 = = > remainder = 13 1005 / 15 = = > remainder = 0 1007 / 15 = = > remainder = 2 13 * 0 * 2 = 0 / 15 = = > remainder = 0 answer : d"
Answer: d
Question (physics): how many seconds will a 250 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 , b ) 30 , c ) 40 , d ) 15 , e ) 60
Rationale: "speed of train relative to man = 63 - 3 = 60 km / hr . = 60 * 5 / 18 = 50 / 3 m / sec . time taken to pass the man = 250 * 3 / 50 = 15 sec . answer : option d"
Answer: d
Question (general): the last two - digits in the multiplication 122 × 123 × 125 × 127 × 129 will be
Options: a ) 20 , b ) 50 , c ) 30 , d ) 40 , e ) 10
Rationale: solution the answer will be 50 since , ( 125 × 122 ) will give 50 as the last two digits . answer b
Answer: b
Question (physics): riya and priya set on a journey . riya moves eastward at a speed of 20 kmph and priya moves westward at a speed of 30 kmph . how far will be priya from riya after 30 minutes
Options: a ) 25 kms , b ) 10 kms , c ) 50 kms , d ) 30 kms , e ) 40 kms
Rationale: "total eastward distance = 20 kmph * 1 / 2 hr = 10 km total westward distance = 30 kmph * 1 / 2 hr = 15 km total distn betn them = 10 + 15 = 25 km ans 25 km answer : a"
Answer: a
Question (physics): a 300 m long train crosses a platform in 39 sec while it crosses a signal pole in 10 sec . what is the length of the platform ?
Options: a ) 187 m , b ) 350 m , c ) 267 m , d ) 287 m , e ) 870 m
Rationale: "speed = 300 / 10 = 30 m / sec . let the length of the platform be x meters . then , ( x + 300 ) / 39 = 30 = > x = 870 m . answer : e"
Answer: e
Question (general): how many digits are in the number 50 ^ 8 × 8 ^ 3 × 11 ^ 2 x 10 ^ 2 ?
Options: a ) 22 , b ) 20 , c ) 21 , d ) 18 , e ) 17
Rationale: "whenever you are asked to find the number of digits , try to bring the number in multiples of 10 . this way , we can wasily calculate the umber of 0 ' s through the powers of 10 50 ^ 8 × 8 ^ 3 × 11 ^ 2 x 10 ^ 2 = ( 5 ^ 2 * 2 ) ^ 8 * 2 ^ 9 * 11 ^ 2 x 10 ^ 2 = 5 ^ 16 * 2 ^ 17 * 11 ^ 2 x 10 ^ 2 = 2 * 11 ^ 2 * 10 ^ 16 x 10 ^ 2 = 242 * 10 ^ 18 hence we would have 16 trailing 0 ' s and the three digits from 242 total digits = 3 + 18 = 21 correct option : c"
Answer: c
Question (other): 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 ) 7 : 9
Rationale: "mixture a has a total of 5 + 3 = 8 parts . if in the final mixture this represents 4 parts , then the total number of parts in mixture b should be ( 8 / 4 ) * 3 = 6 . so , we should take of mixture b a quantity with 2 and 4 parts , respectively . this will give us in the final mixture ( 5 + 2 ) : ( 3 + 4 ) , which means 7 : 7 , or 1 : 1 . answer a ."
Answer: a
Question (gain): running at the same constant rate , 15 identical machines can produce a total of 45 bags per minute . at this rate , how many bags could 150 such machines produce in 8 minutes ?
Options: a ) 9,00 , b ) 1,800 , c ) 2,700 , d ) 3,600 , e ) 4,800
Rationale: "let ' s take the approach that uses the answer choices to eliminate wasted time . 45 / 15 = 3 bags per minute per machine . 150 machines = 450 per minute . 8 minutes worth = 3600 bags . looking at the answers it is clear . . . we can only choose ( d ) . the correct answer is d ."
Answer: d
Question (general): what is the remainder when 1031 * 1047 * 1050 * 1053 is divided by 33 ?
Options: a ) 3 , b ) 24 , c ) 30 , d ) 21 , e ) 18
Rationale: "take the remainder from each of 1031 / 33 , 1047 / 33 and so on . . 1031 / 33 gives remainder = 8 1047 / 33 gives remainder = 24 1050 / 33 gives remainder = 27 1053 / 33 gives remainder = 30 the net remainder is the product of above individual remainders . i . e = 8 * 24 * 27 * 30 break them into pairs 8 * 24 / 33 gives remainder 27 and 27 * 30 / 33 gives remainder 18 so 27 * 18 / 33 gives remainder 24 . b"
Answer: b
Question (physics): a train 700 m long can cross an electric pole in 40 sec and then find the speed of the train ?
Options: a ) 987 , b ) 271 , c ) 72 , d ) 27 , e ) 63
Rationale: "length = speed * time speed = l / t s = 700 / 40 s = 17.5 m / sec speed = 17.5 * 18 / 5 ( to convert m / sec in to kmph multiply by 18 / 5 ) speed = 63 kmph answer : e"
Answer: e
Question (physics): a is twice as good a work man as b and together they finish the work in 12 days . in how many days a alone can finish the work ?
Options: a ) 12 days , b ) 14 days , c ) 28 days , d ) 18 days , e ) 16 days
Rationale: "wc = 2 : 1 2 x + x = 1 / 12 = > x = 1 / 36 2 x = 1 / 18 a can do the work in 18 days . answer : d"
Answer: d
Question (other): 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
Rationale: solution provided by stanford 2012 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 .
Answer: b
Question (general): total 85 matches are conducted in knockout match type . how many players will be participated in that tournament ?
Options: a ) 85 , b ) 81 , c ) 53 , d ) 82 , e ) 84
Rationale: 84 players answer : e
Answer: e
Question (other): if log 27 = 1.431 , then the value of log 9 is : 0.934 b . 0.945 c . 0.954 d . 0.958
Options: a ) 0.954 , b ) 0.93 , c ) 0.933 , d ) 0.96 , e ) 0.974
Rationale: "if log 27 = 1.431 , then the value of log 9 is : a . 0.934 b . 0.945 c . 0.954 d . 0.958 answer : option c explanation : log 27 = 1.431 log ( 33 ) = 1.431 3 log 3 = 1.431 log 3 = 0.477 log 9 = log ( 32 ) = 2 log 3 = ( 2 x 0.477 ) = 0.954 . answer a"
Answer: a
Question (gain): a sum fetched a total simple interest of rs . 4016.25 at the rate of 8 % p . a . in 5 years . what is the sum ?
Options: a ) rs . 10060.625 , b ) rs . 10040.62 , c ) rs . 12040.62 , d ) rs . 20040.625 , e ) rs . 10030.625
Rationale: "principal = ( 100 * 4016.25 ) / ( 8 * 5 ) = rs . 10040.625 . answer : b"
Answer: b
Question (general): the population of a bacteria culture doubles every 5 minutes . approximately how many minutes will it take for the population to grow from 1,000 to 500,000 bacteria
Options: a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 45
Rationale: "this one ' s easy . 1000 * 2 ^ t = 500,000 2 ^ t = 500 now gauging , since 2 ^ 8 = 256 , then 2 ^ 9 = 512 so t = 9 but be careful , ' t ' is in time intervals of 5 minutes so answer is 9 * 5 = 45 minutes answer ( e )"
Answer: e