Cheukting/mathqa huggingface dataset:
Question (physics): a train crosses a bridge of length 200 m in 10 seconds and a lamp post on the bridge in 5 seconds . what is the length of the train in metres ?
Options: a ) 375 m , b ) 750 m , c ) 200 m , d ) 800 m , e ) 300 m
Rationale: "let length of train = l case - 1 : distance = 200 + l ( while crossing the bridge ) time = 10 seconds i . e . speed = distance / time = ( 200 + l ) / 10 case - 2 : distance = l ( while passing the lamp post ) time = 5 seconds i . e . speed = distance / time = ( l ) / 5 but since speed has to be same in both cases so ( 200 + l ) / 10 = ( l ) / 5 i . e . 2 l = l + 200 i . e . l = 200 answer : option c"
Answer: c
Question (general): 10 ^ ( 600 ) ã · 10 ^ ( 580 ) = ?
Options: a ) 10 ^ 10 , b ) 10 ^ 20 , c ) 10 ^ 22 , d ) 10 ^ 23 , e ) 10 ^ 24
Rationale: 10 ^ ( 600 ) ã · 10 ^ ( 580 ) = 10 ^ ( 600 - 580 ) = 10 ^ 20 answer : b
Answer: b
Question (physics): the l . c . m of two numbers is 2310 and their h . c . f is 30 . if one number is 385 the other is
Options: a ) 180 , b ) 300 , c ) 270 , d ) 250 , e ) 350
Rationale: the other number = l . c . m * h . c . f / given number = 2310 * 30 / 385 = 180 answer is a .
Answer: a
Question (general): if n is a positive integer and the product of all integers from 1 to n , inclusive , is a multiple of 440 , what is the least possible value of n ?
Options: a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14
Rationale: "is it 11 ? 440 = 2 * 2 * 2 * 5 * 11 so the least value forncan be 11 . b"
Answer: b
Question (general): mary and mike enter into a partnership by investing $ 550 and $ 450 respectively . at the end of one year , they divided their profits such that a third of the profit is divided equally for the efforts they have put into the business and the remaining amount of profit is divided in the ratio of the investments they made in the business . if mary received $ 1000 more than mike did , what was the profit made by their business in that year ?
Options: a ) $ 8000 , b ) $ 10000 , c ) $ 15000 , d ) $ 12000 , e ) $ 12500
Rationale: "explanatory answer let the profit made during the year be $ 3 x therefore , $ x would have been shared equally and the remaining $ 2 x would have been shared in the ratio 5.5 : 4.5 i . e . , 55 % of 2 x would go to mary and 45 % of 2 x would go to mike . hence , mary would get ( 55 - 45 ) % of 2 x more than mike or 10 % of 2 x = $ 1000 i . e . , ( 60 / 100 ) * 2 x = 1000 or 2 x = 10000 . hence , the profit made by the company during the year $ 3 x = $ 15000 . answer : c"
Answer: c
Question (physics): a goods train runs at the speed of 72 kmph and crosses a 250 m long platform in 24 seconds . what is the length of the goods train ?
Options: a ) 230 m , b ) 240 m , c ) 260 m , d ) 270 m , e ) none of these
Rationale: "explanation : speed = [ 72 x ( 5 / 18 ) ] m / sec = 20 m / sec . time = 24 sec . let the length of the train be x metres . then , [ ( x + 250 ) / 24 ] = 20 = > x + 250 = 480 = > x = 230 . answer : a"
Answer: a
Question (physics): 20 men can dig a tunnel in 30 days . if after 10 days , 20 more men are deployed to dig the tunnel , how many more days it will take to dig the whole tunnel ?
Options: a ) 10 , b ) 15 , c ) 20 , d ) 25 , e ) 30
Rationale: a remaining work can be completed by 20 men in 30 - 10 = 20 days . if 20 men can do x work in 20 days , and let us say 40 men take n days to do the same work . now , more men , less number of days ( inversely proportion ) 20 : 40 : : n : 20 n = 20 x 20 / 40 = 10 days .
Answer: a
Question (general): if the product of 10 integers is negative , at most how many of the integers can be negative ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 9 , e ) 6
Rationale: "the product of 10 integers is negative thus an odd number of integers need to be negative to have a negative product we are asked at most how many are required . so , the highest odd integer before 6 , i . e . 9 correct option : d"
Answer: d
Question (physics): two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds . the ratio of their speeds is :
Options: a ) 3 / 7 , b ) 3 / 2 . , c ) 3 / 88 , d ) 3 / 8 . , e ) 2 / 2 .
Rationale: "let the speeds of the two trains be x m / sec and y m / sec respectively . then , length of the first train = 27 x meters , and length of the second train = 17 y meters . ( 27 x + 17 y ) / ( x + y ) = 23 = = > 27 x + 17 y = 23 x + 23 y = = > 4 x = 6 y = = > x / y = 3 / 2 . answer : b"
Answer: b
Question (gain): the difference between the compound interest compounded annually and simple interest for 2 years at 20 % per annum is rs . 72 . find the principal ?
Options: a ) 2277 , b ) 2667 , c ) 3600 , d ) 2766 , e ) 1800
Rationale: "p = 72 ( 100 / 5 ) ^ 2 = > p = 1800 answer : e"
Answer: e
Question (general): in a division , a student took 63 as divisor instead of 36 . his answer was 24 . the correct answer is -
Options: a ) 42 , b ) 32 , c ) 48 , d ) 28 , e ) 38
Rationale: "x / 63 = 24 . x = 24 * 63 . so correct answer would be , ( 24 * 63 ) / 36 = 42 . answer : a"
Answer: a
Question (general): the sum of the numbers is 550 . if the first number be twice the second and third number be one - third of the first , then the second number is :
Options: a ) 48 , b ) 150 , c ) 72 , d ) 84 , e ) 27
Rationale: "let the second number be x . then , first number = 2 x and third number = 2 x / 3 . 2 x + x + 2 x / 3 = 550 11 x / 3 = 550 x = 150 answer : b"
Answer: b
Question (general): what is 121 times 11 ?
Options: a ) 1331 , b ) 1313 , c ) 1133 , d ) 3131 , e ) 3311
Rationale: a 1331
Answer: a
Question (general): if ( 1 – 1.25 ) n = 4 , then n =
Options: a ) − 400 , b ) − 16 , c ) − 4 , d ) 4 , e ) 400
Rationale: "( 1 – 1.25 ) n = 4 simplify to get : - 0.25 n = 4 rewrite as ( - 1 / 4 ) n = 4 multiply both sides by - 4 to get : n = - 16 answer : b"
Answer: b
Question (probability): four 6 faced dice are thrown together . the probability that all the three show the same number on them is ?
Options: a ) 1 / 32 , b ) 1 / 216 , c ) 1 / 33 , d ) 1 / 38 , e ) 1 / 34
Rationale: "the three dice can fall in 6 * 6 * 6 * 6 = 1296 ways . hence the probability is 6 / 1296 = 1 / 216 answer : b"
Answer: b
Question (general): the average age of 25 students in a class is 12 years . if teacher ' s age is also included then average increases 1 year then find the teacher ' s age ?
Options: a ) 40 , b ) 35 , c ) 29 , d ) 38 , e ) 42
Rationale: "total age of 25 students = 25 * 12 = 300 total age of 26 persons = 26 * 13 = 338 age of teacher = 338 - 300 = 38 years answer is d"
Answer: d
Question (general): 7 , 26 , 63 , 124 , 215 , 342 , ( . . . . )
Options: a ) 481 , b ) 391 , c ) 511 , d ) 421 , e ) 452
Rationale: "explanation : the series is ( 2 ^ 3 - 1 ) , ( 3 ^ 3 - 1 ) , ( 4 ^ 3 - 1 ) , ( 5 ^ 3 - 1 ) , ( 6 ^ 3 - 1 ) , ( 7 ^ 3 - 1 ) , . . . hence , next number is ( 8 ^ 3 - 1 ) = 511 answer : option c"
Answer: c
Question (physics): a team p of 20 engineers can complete work or task in 32 days . another team q of 16 engineers can complete same task in 30 days . then the ratio of working capacity of 1 member of p to the 1 member of q is a . 3 : 2
Options: a ) 22 , b ) 34 , c ) 77 , d ) 29 , e ) 21
Rationale: explanation : let the capacity of an engineer in p = x units , and in q = y units . working capacity of p = x × 32 × 20 working capacity of q = y × 16 × 30 as the total work is same , we equate the above equations . ⇒ x × 32 × 20 = y × 16 × 30 ⇒ xy = 16 × 3032 × 20 = 34 answer : b
Answer: b
Question (general): a certain kind of necklace is made from 9 green , 6 white , and 3 orange beads . what is the maximum number of these necklaces that can be made from 45 beads of each color ?
Options: a ) 7 , b ) 8 , c ) 5 , d ) 6 , e ) 2
Rationale: atleast 9 green breads are needed to make a necklace , so irrespective of the combinations of white and orange beads , the number of necklaces that can be formed will be 45 / 9 = 5 answer : - c
Answer: c
Question (general): for 2 consecutive yrs , my incomes are in the ratio of 4 : 7 and expenses in the ratio of 3 : 5 . if my income in the 2 nd yr is rs . 42000 & my expenses in the first yr in rs . 22000 , my total savings for the two - year is
Options: a ) s . 8000 , b ) s . 9000 , c ) s . 9900 , d ) s . 9990 , e ) s . 10000
Rationale: "sol . income in first year = * x 42000 = rs . 24000 expenses in second year = \ x 21000 = rs . 35000 total savings = total income - total expenses = ( 42000 + 24000 ) - ( 22000 + 35000 ) = 66000 - 57000 = rs . 9000 b"
Answer: b
Question (general): the average of 45 results is 25 and the average of other 25 results is 45 . what is the average of all the results ?
Options: a ) 24 , b ) 32 , c ) 48 , d ) 50 , e ) none
Rationale: "answer sum of 70 result = sum of 45 result + sum of 25 result . = 45 x 25 + 25 x 45 = 2250 / 70 correct option : b"
Answer: b
Question (gain): a , b and c invests rs . 2000 , rs . 3000 and rs . 4000 in a business . after two year a removed his money ; b and c continued the business for one more year . if the net profit after 3 years be rs . 4800 , then a ' s share in the profit is ?
Options: a ) 600 , b ) 400 , c ) 678 , d ) 867 , e ) 768
Rationale: "2 * 24 : 3 * 36 : 4 * 36 4 : 9 : 12 4 / 25 * 4800 = 768 answer : e"
Answer: e
Question (general): 10 friends meet for movie 20 for picnic and 5 for games 4 for movie & picnic 2 for movie & games , 0 for picnic & games , 2 for all , how many are students are there in all ?
Options: a ) 30 , b ) 31 , c ) 32 , d ) 33 , e ) 34
Rationale: n ( a u b u c ) = n ( a ) + n ( b ) + n ( c ) - n ( a intersection b ) - n ( a intersection c ) - n ( c intersection b ) + n ( a intersection b - intersection c ) hence , total no . of students = 10 + 20 + 5 - 4 - 0 - 2 + 2 = 31 . answer : b
Answer: b
Question (physics): the angle between the minute hand and the hour hand of a clock when the time is 9.30 , is
Options: a ) 35 ° , b ) 65 ° , c ) 45 ° , d ) 105 ° , e ) 95 °
Rationale: "angle between hands of a clock when the minute hand is behind the hour hand , the angle between the two hands at m minutes past h ' o clock = 30 ( h − m / 5 ) + m / 2 degree when the minute hand is ahead of the hour hand , the angle between the two hands at m minutes past h ' o clock = 30 ( m / 5 − h ) − m / 2 degree here h = 9 , m = 30 and minute hand is behind the hour hand . hence the angle = 30 ( h − m / 5 ) + m / 2 = 30 ( 9 − 30 / 5 ) + 30 / 2 = 30 ( 9 − 6 ) + 15 = 30 × 3 + 15 = 105 ° answer is d ."
Answer: d
Question (physics): two pipes a and b can separately fill a tank in 12 and 15 minutes respectively . a third pipe c can drain off 36 liters of water per minute . if all the pipes are opened , the tank can be filled in 15 minutes . what is the capacity of the tank ?
Options: a ) 542 , b ) 540 , c ) 514 , d ) 829 , e ) 432
Rationale: "1 / 12 + 1 / 15 - 1 / x = 1 / 15 x = 12 12 * 36 = 432 answer : e"
Answer: e
Question (general): how many integerskgreater than 100 and less than 700 are there such that if the hundreds and the units digits ofkare reversed , the resulting integer is k + 99 ?
Options: a ) 50 , b ) 60 , c ) 70 , d ) 80 , e ) 90
Rationale: "numbers will be like 102 = > 201 = 102 + 99 203 = > 302 = 103 + 99 so the hundereth digit and units digit are consecutive where unit digit is bigger than hundred digit . there will be five pairs of such numbers for every pair there will 10 numbers like for 12 = > 102 , 112,132 , 142,152 , 162,172 , 182,192 . total = 5 * 10 = 50 hence a ."
Answer: a
Question (physics): a can give b 100 meters start and c 200 meters start in a kilometer race . how much start can b give c in a kilometer race ?
Options: a ) 111.12 m , b ) 221.12 m , c ) 271.12 m , d ) 611.12 m , e ) 191.12 m
Rationale: "explanation : a runs 1000 m while b runs 900 m and c runs 800 m . the number of meters that c runs when b runs 1000 m , = ( 1000 * 800 ) / 900 = 8000 / 9 = 888.88 m . b can give c = 1000 - 888.88 = 111.12 m . answer : a"
Answer: a
Question (general): the product x of two prime numbers is between 17 and 60 . if one of the prime numbers is greater than 2 but less than 6 and the other is greater than 13 but less than 25 , then x =
Options: a ) 18 , b ) 29 , c ) 37 , d ) 44 , e ) 57
Rationale: "option bc can be ruled out as they themselves are prime numbers 18 = 2 * 9 = 3 * 6 > > ignore 44 = 2 * 22 = 4 * 11 > > ignore 57 = 3 * 19 > > answer answer = e"
Answer: e
Question (general): alok ordered 16 chapatis , 5 plates of rice , 7 plates of mixed vegetable and 6 ice - cream cups . the cost of each chapati is rs . 6 , that of each plate of rice is rs . 45 and that of mixed vegetable is rs . 70 . the amount that alok paid the cashier was rs . 961 . find the cost of each ice - cream cup ?
Options: a ) rs . 25 , b ) rs . 22.50 , c ) rs . 20 , d ) rs . 17.50 , e ) none of these
Rationale: "let the cost of each ice - cream cup be rs . x 16 ( 6 ) + 5 ( 45 ) + 7 ( 70 ) + 6 ( x ) = 961 96 + 225 + 490 + 6 x = 961 6 x = 150 = > x = 25 . answer : a"
Answer: a
Question (geometry): a diagonal of a polygon is an segment between two non - adjacent vertices of the polygon . how many diagonals does a regular 20 - sided polygon have ?
Options: a ) 875
b ) 170
c ) 1425
d ) 2025
e ) 2500
Rationale: there ' s a direct formula for this . number of diagonals in a regular polygon = [ n * ( n - 3 ) ] / 2 , n = number of sides of the regular polygon . here , n = 20 . plugging it in , we get 170 diagonals ! answer ( b ) .
Answer: b
Question (general): if 70 % of a number is equal to two - third of another number , what is the ratio of first number to the second number ?
Options: a ) 5 : 7 , b ) 18 : 23 , c ) 17 : 19 , d ) 20 : 21 , e ) 2 : 3
Rationale: "let 70 % of a = 2 / 3 b . then , 70 a / 100 = 2 b / 3 = > 7 a / 10 = 2 b / 3 a / b = ( 2 / 3 * 10 / 7 ) = 20 / 21 a : b = 20 : 21 . answer : d"
Answer: d
Question (other): a number is said to be prime saturated if the product of all the different positive prime factors of z is less than the square root of z . what is the greatest two digit prime saturated integer ?
Options: a ) 99 , b ) 98 , c ) 97 , d ) 96 , e ) 95
Rationale: "clearly d a number is said to be prime saturated if the product of all the different positive prime factors of z is less than the square root of z . 96 has more number of smaller prime factor thats the clue ! ! = d"
Answer: d
Question (general): the average monthly income of p and q is rs . 2050 . the average monthly income of q and r is rs . 5250 and the average monthly income of p and r is rs . 6200 . the monthly income of r is :
Options: a ) 5100 , b ) 4900 , c ) 9400 , d ) 1500 , e ) 3200
Rationale: "explanation : let p , q and r represent their respective monthly incomes . then , we have : p + q = ( 2050 x 2 ) = 4100 . . . . ( i ) q + r = ( 5250 x 2 ) = 10500 . . . . ( ii ) p + r = ( 6200 x 2 ) = 12400 . . . . ( iii ) adding ( i ) , ( ii ) and ( iii ) , we get : 2 ( p + q + r ) = 27000 or p + q + r = 13500 . . . . ( iv ) subtracting ( i ) from ( iv ) , we get p = 9400 . p ' s monthly income = rs . 9400 . answer : c"
Answer: c
Question (general): find large number from below question the difference of two numbers is 1311 . on dividing the larger number by the smaller , we get 11 as quotient and the 11 as remainder
Options: a ) 1209 , b ) 1324 , c ) 1441 , d ) 1300 , e ) 1635
Rationale: "let the smaller number be x . then larger number = ( x + 1311 ) . x + 1311 = 11 x + 11 10 x = 1300 x = 130 large number = 130 + 1311 = 1441 answer : c"
Answer: c
Question (other): 1 blue dice and 2 red dice are thrown . . . . what is the probability that the no . appeared on blue dice is always greater than both the no . appeared on the 2 red dice . .
Options: a ) 55 / 216 , b ) 56 / 216 , c ) 57 / 216 , d ) 54 / 216 , e ) 53 / 216
Rationale: if the no . on blue dice is 2 then 2 red dice can take ( 1,1 ) value = 1 ^ 2 if the no . on blue dice is 3 then 2 red dice can take ( 1,1 ) ( 1,2 ) ( 2,1 ) ( 2,2 ) = 2 ^ 2 if the no . on blue dice is 4 then 2 red dice can take ( 1,1 ) ( 1,2 ) ( 2,1 ) ( 2,2 ) ( 1,3 ) ( 2,3 ) ( 3,2 ) ( 3,1 ) ( 3,3 ) = 3 ^ 2 similarly , if the no . on blue dice is 5 then 2 red dice can take = 4 ^ 2 and if the no . on blue dice is 6 then 2 red dice can take = 5 ^ 2 therefor , probability = total no . of favourable outcome / total no . of possible outcome = 1 ^ 2 + 2 ^ 2 + 3 ^ 2 + 4 ^ 2 + 5 ^ 2 / 216 = 55 / 216 answer : a
Answer: a
Question (other): a certain university will select 1 of 6 candidates eligible to fill a position in the mathematics department and 2 of 9 candidates eligible to fill 2 identical positions in the computer science department . if none of the candidates is eligible for a position in both departments , how many different sets of 3 candidates are there to fill the 3 positions ?
Options: a ) 216 , b ) 212 , c ) 214 , d ) 210 , e ) 120
Rationale: "1 c 6 * 2 c 9 = 6 * 36 = 216 the answer is ( a )"
Answer: a
Question (physics): excluding stoppages , the speed of the bus is 54 kmph and including stoppages , it is 36 kmph . for how many minutes does the bus stop per hr
Options: a ) 12 min , b ) 11 min , c ) 13 min , d ) 19 min , e ) 20 min
Rationale: due to stoppages , it covers 18 km less . time taken to cover 18 km is [ 18 / 54 * 60 ] min = 20 min answer is e .
Answer: e
Question (general): a person ' s present age is two - fifth of the age of his mother . after 4 years , he will be one - half of the age of his mother . how old is the mother at present ?
Options: a ) a ) 25 , b ) b ) 40 , c ) c ) 20 , d ) d ) 45 , e ) e ) 28
Rationale: "let the mother ' s present age be x years then the person ' s present age = 2 x / 5 ( 2 x / 5 ) + 4 = 1 / 2 ( x + 4 ) 2 ( 2 x + 20 ) = 5 ( x + 4 ) x = 20 answer is c"
Answer: c
Question (physics): a 150 m long train crosses a platform in 39 sec while it crosses a signal pole in 18 sec . what is the length of the platform ?
Options: a ) 300 , b ) 175 , c ) 360 , d ) 370 , e ) 380
Rationale: "speed = 150 / 18 = 25 / 3 m / sec . let the length of the platform be x meters . then , ( x + 150 ) / 39 = 25 / 3 = > x = 325 m . l = 325 - 150 = 175 m answer : option b"
Answer: b
Question (general): a bag contains an equal number of one rupee , 50 paise and 25 paise coins respectively . if the total value is 35 , how many coins of each type are there ?
Options: a ) 20 coins , b ) 30 coins , c ) 28 coins , d ) 25 coins , e ) none of these
Rationale: "let number of each type of coin = x . then , 1 × x + . 50 × x + . 25 x = 35 ⇒ 1.75 x = 35 ⇒ x = 20 coins answer a"
Answer: a
Question (other): a girl scout was selling boxes of cookies . in a month , she sold both boxes of chocolate chip cookies ( $ 1.25 each ) and boxes of plain cookies ( $ 0.75 each ) . altogether , she sold 1,585 boxes for a combined value of $ 1 , 588.25 . how many boxes of plain cookies did she sell ?
Options: a ) 0 , b ) 233 , c ) 500 , d ) 695 , e ) 786
Rationale: "let # plain cookies sold be x then # chocolate cookies = ( total cookies - x ) equating for x ( 0.75 ) * x + ( 1.25 ) * ( 1585 - x ) = 1588.25 = > x = 786 first get the difference of the revenue to the number of boxes . 1588.25 - 1585 = 3.25 now you know that the difference between plain cookies boxes and chocolate cookies boxes is small . we now divide the revenue by two . 1588.25 / 2 = ~ 794 because the difference between the possible answers is big , this leaves us with choice e ."
Answer: e
Question (general): how many positive even integers less than 100 contain digits 5 or 7 ?
Options: a ) 10 , b ) 17 , c ) 18 , d ) 19 , e ) 20
Rationale: "two digit numbers : 5 at tens place : 50 , 52,54 , 56,58 7 at tens place : 70 , 72,74 , 76,78 if 5 and 7 is at units place , the number cant be even total : 5 + 5 = 10 answer a"
Answer: a
Question (physics): a person can swim in still water at 4 km / h . if the speed of water 2 km / h , how many hours will the man take to swim back against the current for 10 km ?
Options: a ) 3 , b ) 5 , c ) 8 , d ) 9 , e ) 6
Rationale: "m = 4 s = 2 us = 4 - 2 = 2 d = 10 t = 10 / 2 = 5 answer : b"
Answer: b
Question (general): the price of a certain painting increased by 25 % during the first year and decreased by 15 % during the second year . the price of the painting at the end of the 2 - year period was what percent of the original price ?
Options: a ) 109 % , b ) 106.25 % , c ) 120 % , d ) 115 % , e ) 110 %
Rationale: "easiest thing to do : assume that price is 100 price at the end of yr 1 : 100 + 25 = 125 price at the end of year 2 = 125 - 125 * 0.15 = 125 * 0.85 = 106.25 hence required answer = ( 106.25 / 100 ) * 100 % = 106.25 % answer is b ."
Answer: b
Question (physics): a car runs at the speed of 25 km per hour when not serviced and runs at 75 kmph when serviced . after servicing the car covers a certain distance in 5 hours . how much time will the car take to cover the same distance when not serviced ?
Options: a ) 8 hours , b ) 16 hours , c ) 15 hours , d ) 7 hours , e ) none
Rationale: "explanation : time = 75 * 5 / 25 = 15 hours answer â € “ d"
Answer: d
Question (general): rs . 1010 / - distributed among a , b and c such that on decreasing their shares by rs . 25 , rs . 10 and rs . 15 respectively , the balance money would be divided among them in the ratio 3 : 2 : 5 . then , c ’ s share is : ?
Options: a ) rs . 485 , b ) rs . 495 / - , c ) rs . 575 , d ) rs . 685 , e ) rs . 592
Rationale: a : b : c = 3 : 2 : 5 total parts = 10 c ' s share is = 5 parts 10 - - - - - > rs . 960 / - 3 - - - - - > rs . 480 / - a ' s total = 480 + 15 = rs . 495 / - b )
Answer: b
Question (physics): a is twice as good a work man as b and together they finish a piece of work in 36 days . the number of days taken by b alone to finish the work is :
Options: a ) 100 days . , b ) 108 days . , c ) 98 days . , d ) 47 days . , e ) 103 days .
Rationale: solution ( a ’ s 1 day ’ s work ) : ( b ’ s 1 day ’ s work ) = 2 : 1 . ( a + b ) ' s 1 day ’ s work = 1 / 36 divide 1 / 36 in the ratio 2 : 1 . ∴ b ’ s 1 day ’ s work = ( 1 / 36 x 1 / 3 ) = 1 / 108 hence , b alone can finish the work in 108 days . answer b
Answer: b
Question (gain): 5 % of ( 25 % of $ 1600 ) is ?
Options: a ) $ 20 , b ) $ 30 , c ) $ 45 , d ) $ 15 , e ) $ 60
Rationale: 5 % of ( 25 % of $ 1600 ) = 5 / 100 ( 25 / 100 * 1600 ) = $ 20 answer is a
Answer: a
Question (probability): what is the smallest number by which 2880 must be divided in order to make it into a perfect square ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "880 / 3 = 960 is not a perfect square 2880 / 4 = 720 is not a perfect square 2880 / 5 = 576 which is perfect square of 24 answer : c"
Answer: c
Question (general): how many diagonals does a 60 - sided convex polygon have ?
Options: a ) 960 , b ) 1280 , c ) 1710 , d ) 2560 , e ) 3420
Rationale: "a 60 - sided convex polygon has 60 vertices . if we examine a single vertex , we can see that we can connect it with 57 other vertices to create a diagonal . note that we ca n ' t connect the vertex to itself and we ca n ' t connect it to its adjacent vertices , since this would not create a diagonal . if each of the 60 vertices can be connected with 57 vertices to create a diagonal then the total number of diagonals would be ( 60 ) ( 57 ) = 3420 however , we must recognize that we have counted every diagonal twice . to account for counting each diagonal twice , we must divide 3420 by 2 to get 1710 . the answer is c ."
Answer: c
Question (general): rs . 1210 were divided among 3 person p , q , r so that p : q = 5 : 4 and q : r = 9 : 10 . then r gets the amount ?
Options: a ) rs . 300 , b ) rs . 400 , c ) rs . 480 , d ) rs . 500 , e ) rs . 520
Rationale: p : q = 5 : 4 , q : r = 9 : 10 = ( 9 x 4 / 9 ) : ( 10 x 4 / 9 ) = 4 : 40 / 9 . so , p : q : r = 5 : 4 : 40 / 9 = 45 : 36 : 40 sum of ratio terms is = ( 45 + 36 + 40 ) = 121 . r share of amount is rs ( 1210 x 40 / 121 ) = rs . 400 . b
Answer: b
Question (general): a fruit drink is made of orange , watermelon , and grape juice , where 35 percent of the drink is orange juice and 35 percent is watermelon juice . if the drink is made with 45 ounces of grape juice , how many ounces is the drink total ?
Options: a ) 120 , b ) 140 , c ) 150 , d ) 180 , e ) 200
Rationale: "let the total number of ounces in the drink be x . % of orange = 35 % % of watermelon = 35 % % of grape = 100 % - 70 % = 30 % 0.30 x = 45 x = 150 therefore there are a total of 150 ounces in the drink . the answer is c ."
Answer: c