regisss/math_qa huggingface dataset:
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: for all real numbers v , an operation is defined by the equation v * = v - v / 3 . if ( v * ) * = 24 , then v =
Options: a ) 45 , b ) 48 , c ) 51 , d ) 54 , e ) 57
Rationale: "( v * ) * = ( v - v / 3 ) - ( v - v / 3 ) / 3 24 = 2 v / 3 - 2 v / 9 = 4 v / 9 v = 54 the answer is d ."
Answer: d
Problem: the least perfect square , which is divisible by each of 21,36 and 66 is
Options: a ) 213444
b ) 214344
c ) 214434
d ) 213443
e ) none of these
Rationale: l . c . m . of 21 , 36 , 66 = 2772 . now , 2772 = 2 x 2 x 3 x 3 x 7 x 11 to make it a perfect square , it must be multiplied by 7 x 11 . so , required number = 22 x 32 x 72 x 112 = 213444 answer a
Answer: a
Problem: what is the greatest prime factor of 2 ^ 10 - 1 ?
Options: a ) 17 , b ) 19 , c ) 23 , d ) 29 , e ) 31
Rationale: "2 ^ 10 - 1 = ( 2 ^ 5 - 1 ) ( 2 ^ 5 + 1 ) = 31 * 33 the answer is e ."
Answer: e
Problem: a wholesaler wishes to sell 100 pounds of mixed nuts at $ 2.50 a pound . she mixes peanuts worth $ 1.50 a pound with cashews worth $ 5.00 a pound . how many pounds of cashews must she use ?
Options: a ) 40 , b ) 45 , c ) 50 , d ) 55 , e ) 60
Rationale: "from the question stem we know that we need a mixture of 100 pounds of peanuts and cashews . if we represent peanuts as x and cashews as y , we get x + y = 100 . since the wholesaler wants to sell the mixture of 100 pounds @ $ 2.50 , we can write this as : $ 2.5 * ( x + y ) = $ 1.5 x + $ 4 y from the equation x + y = 100 , we can rewrite y as y = 100 - x and substitute this into our equation to get : $ 2.5 * ( x + 100 - x ) = $ 1.5 x + $ 4 ( 100 - x ) if you solve for x , you will get x = 60 , and therefore y = 40 . so the wholesaler must use 40 pounds of cashews . you can substitute into the original equation to see that : $ 250 = $ 1.5 ( 60 ) + $ 4 ( 40 ) answer is b"
Answer: b
Problem: 4 years ago , paula was 4 times as old as karl . in 12 years , paula will be twice as old as karl . what is the sum of their ages now ?
Options: a ) 36 , b ) 40 , c ) 44 , d ) 48 , e ) 52
Rationale: "p - 4 = 4 ( k - 4 ) and so p = 4 k - 12 p + 12 = 2 ( k + 12 ) ( 4 k - 12 ) + 12 = 2 k + 24 k = 12 p = 36 p + k = 48 the answer is d ."
Answer: d
Problem: there are 15 teams in a certain league and each team plays each of the other teams exactly twice . if each game is played by 2 teams , what is the total number of games played ?
Options: a ) 15 , b ) 16 , c ) 28 , d ) 56 , e ) 210
Rationale: "every team plays with 14 teams . . . so total no of matches = 15 x 14 = 210 . now , each match is played twice = > 210 x 2 but 2 teams play a match = > 210 x 2 / 2 = 210 . answer : e"
Answer: e
Problem: if w / x = 2 / 3 and w / y = 6 / 15 , then ( x + y ) / y =
Options: a ) 4 / 5 , b ) 6 / 5 , c ) 7 / 5 , d ) 8 / 5 , e ) 9 / 5
Rationale: w / x = 2 / 3 = > x = 3 / 2 w and w / y = 6 / 15 = > y = 15 / 6 w ( x + y ) / y = ( 3 / 2 w + 15 / 6 w ) / 15 / 6 w = 4 w / ( 15 / 6 w ) = 8 / 5 correct option : d
Answer: d
Problem: a “ palindromic integer ” is an integer that remains the same when its digits are reversed . so , for example , 43334 and 516615 are both examples of palindromic integers . how many 6 - digit palindromic integers are both even and greater than 500,000 ?
Options: a ) 160 , b ) 200 , c ) 240 , d ) 300 , e ) 480
Rationale: the first digit and last digit are the same so the 2 possibilities are 6 or 8 . the second and third digits can be any number from 0 to 9 . the total number of palindromic integers is 2 * 10 * 10 = 200 the answer is b .
Answer: b
Problem: a trader sold an article on a certain price with 40 % profit . if he sold double of previous selling price then find its profit %
Options: a ) 140 % , b ) 180 % , c ) 120 % , d ) 100 % , e ) 150 %
Rationale: "let cost price = 100 % selling price = 140 % new s . p . = 280 % p % = 280 - 100 = 180 % answer is b"
Answer: b
Problem: the average price of an decoration piece increases over the years . if from 1990 to 1996 , the price of the decoration piece increased by 13 % and from 1996 to 2001 it increased by 20 % , what is the price of the decoration piece in 2001 if the price in 1990 was $ 11500 ?
Options: a ) $ 15594 . , b ) $ 15322 . , c ) $ 14786 . , d ) $ 14543 . , e ) $ 12988 .
Rationale: whenever you have a question in which a value is increased by x % and then increased by y % then the overall effective increase = ( x + y + xy / 100 ) % the effective increase = 13 + 20 + ( 13 × 20 / 100 ) = 35.6 % this is a little more 33 % or 1 / 3 the original value . the quickest way to solve this question is to use approximation . 11500 + 1 / 3 ( 12000 ) = 15500 therefore option a is the answer . i selected 12000 because it ' s value is a little more 11500 and it ' s easier to divide by 3 ( ie to calculate 1 / 3 or 33 % ) .
Answer: a
Problem: how many 2 - inch by 3 - inch rectangular tiles are required to tile this shaded region ?
Options: a ) less than 10
b ) 10 — 100
c ) 101 — 1,000
d ) 1,001 — 1,500
e ) 1,500 +
Rationale: convert all feet into inches as we are looking into tiles which are in inches so total area of garden = 6 * 12 * 12 * 12 shaded region = 12 * 12 ( 6 * 12 - 2 * 3 ) = 12 * 12 * 2 * 3 ( 12 - 1 ) no of 2 ' ' * 3 ' ' tiles required = 12 ∗ 12 ∗ 12 ∗ 2 ∗ 3 ∗ 11 / 2 ∗ 3 = 12 ∗ 12 ∗ 11 = 1584 > 1500 so ans is 1500 + answer : e
Answer: e
Problem: a cube is painted red on all faces . it is then cut into 27 equal smaller cubes . how many h cubes are painted on only 2 faces ?
Options: a ) 12 , b ) 8 , c ) 6 , d ) 10 , e ) 16
Rationale: "1 ) draw a simple cube 2 ) draw 9 squares on each face of the cube ( so that it looks like a rubik ' s cube ) - this is what the cube will look like when it ' s cut into 27 equal smaller cubes . 3 ) remember that the outside of the cube is the part that ' s painted . . . . the mini - cubes with 2 painted sides are all on the edge of the cube , in themiddleof the edge . there are 4 in front , 4 in back and 4 more on thestripthat runs around the left / top / right / bottom of the cube . h = 4 + 4 + 4 = 12 . answer a"
Answer: a
Problem: the length of a rectangle is increased by 15 % and its breadth is decreased by 20 % . what is the effect on its area ?
Options: a ) 1288 , b ) 1299 , c ) 1000 , d ) 10000 , e ) 9200
Rationale: "100 * 100 = 10000 115 * 80 = 9200 answer : e"
Answer: e
Problem: solve the quickfire maths brain teaser â ˆ š 16 % = ?
Options: a ) 30 % , b ) 40 % , c ) 85 % , d ) 19 % , e ) 29 %
Rationale: "â ˆ š 16 % = > â ˆ š 16 / â ˆ š 100 = > 4 / 10 = > 40 / 100 = > 40 % b"
Answer: b
Problem: how many seconds will a train 150 meters long take to cross a bridge 150 meters long if the speed of the train is 36 kmph ?
Options: a ) 28 sec , b ) 23 sec , c ) 29 sec , d ) 30 sec , e ) 36 sec
Rationale: "d d = 150 + 150 = 300 s = 36 * 5 / 18 = 10 mps t = 300 / 10 = 30 sec"
Answer: d
Problem: the price of a bushel of corn is currently $ 3.20 , and the price of a peck of wheat is $ 8.80 . the price of corn is increasing at a constant rate of 5 x cents per day while the price of wheat is decreasing at a constant rate of x ( 2 ^ 1 / 2 ) - x cents per day . what is the approximate price when a bushel of corn costs the same amount as a peck of wheat ?
Options: a ) $ 8.40 , b ) $ 5.10 , c ) $ 5.30 , d ) $ 5.50 , e ) $ 5.60
Rationale: "i tried using time / rate approach : - initial price difference = 8.80 - 3.20 = 5.60 price of corn increasing by 5 x price of wheat decreasing by x ( 1.4 ) - x = . 4 x since both the quantities are moving towards reducing the price gap hence : - relative increase = 5 x + . 4 x let t be the time by which gap is filled so , 5.6 = t ( 5.4 x ) - > t = ( 5.6 ) / 5.4 x final price = 3.20 + 5 x * t - > 3.20 + 5 * 5.6 / 5.4 = 8.4 answer a ."
Answer: a
Problem: find the area of the quadrilateral of one of its diagonals is 28 cm and its off sets 9 cm and 6 cm ?
Options: a ) 210 cm 2 , b ) 150 cm 2 , c ) 168 cm 2 , d ) 198 cm 2 , e ) 987 cm 2
Rationale: "1 / 2 * 28 ( 9 + 6 ) = 210 cm 2 answer : a"
Answer: a
Problem: the largest one digit number which is a perfect cube , is :
Options: a ) 7 , b ) 8 , c ) 9 , d ) 1 , e ) 0
Rationale: "explanation : 2 * 2 * 2 = 8 answer : b"
Answer: b
Problem: when the price of a product was decreased by 20 % , the number sold increased by 60 % . what was the effect on the total revenue ?
Options: a ) 28 % , b ) 32 % , c ) 35 % , d ) 45 % , e ) 52 %
Rationale: let the price of the product be $ 100 and let original sale be 100 pieces then , total revenue = 100 * 100 = $ 10000 new revenue = 80 * 160 = $ 12800 increase in revenue = 2800 * 100 / 10000 = 28 % answer is a
Answer: a
Problem: in a rare coin collection , all coins are either pure gold or pure silver , and there is initially one gold coin for every 3 silver coins . with the addition of 15 more gold coins to the collection , the ratio of gold coins to silver coins is 1 to 2 . based on this information , how many total coins are there now in this collection ( after the acquisition ) ?
Options: a ) 124 , b ) 135 , c ) 146 , d ) 157 , e ) 168
Rationale: initially the number of gold coins and silver coins is 2 k and 6 k . after adding gold coins , the number of coins is 3 k and 6 k . thus k = 15 and the total number of coins is 9 k = 135 . the answer is b .
Answer: b
Problem: positive integer y is 50 percent of 50 percent of positive integer x , and y percent of x equals 100 . what is the value of y ?
Options: a ) 50 , b ) 100 , c ) 200 , d ) 1,000 , e ) 2,000
Rationale: "y = 50 % of 50 % 0 f x = x / 4 and y / 100 of x = 100 y / 100 * 4 y = 100 y = 50 answer - a"
Answer: a
Problem: after giving a discount of rs . 45 the shopkeeper gets a loss of 10 % , if the cost price is rs . 180 . find the markup % ?
Options: a ) 0.21 , b ) 0.2 , c ) 0.17 , d ) 0.21 , e ) 0.15
Rationale: "cost price = 180 s . p = 180 * 90 / 100 = 162 disc = 45 so . . . mark price = 162 + 45 = 207 . . . . . . mark up % = 207 - 180 / 180 = 81 / 180 = . 15 or 15 % answer : e"
Answer: e
Problem: a student has to obtain 35 % of the total marks to pass . he got 100 marks and failed by 40 marks . the maximum marks are ?
Options: a ) 280 , b ) 400 , c ) 420 , d ) 480 , e ) 520
Rationale: "let the maximum marks be x then , 35 % of x = 100 + 40 35 x / 100 = 140 35 x = 140 * 100 = 14000 x = 400 answer is b"
Answer: b
Problem: if a : b = 3 : 4 , b : c = 7 : 9 , c : d = 5 : 7 , find a : d ?
Options: a ) 5 / 12 , b ) 5 / 15 , c ) 5 / 10 , d ) 5 / 11 , e ) 5 / 13
Rationale: "a / d = ( 3 / 4 ) * ( 7 / 9 ) * ( 5 / 7 ) = > 5 / 12 answer : a"
Answer: a
Problem: the average age of an adult class is 40 years . 12 new students with an avg age of 32 years join the class . therefore decreasing the average by 4 year . find what was theoriginal strength of class ?
Options: a ) 8 , b ) 12 , c ) 15 , d ) 17 , e ) 18
Rationale: "let original strength = y then , 40 y + 12 x 32 = ( y + 12 ) x 36 ⇒ 40 y + 384 = 36 y + 432 ⇒ 4 y = 48 ∴ y = 12 b"
Answer: b
Problem: a , b and c can do a piece of work in 24 days , 30 days and 40 days respectively . they began the work together but c left 12 days before the completion of the work . in how many days was the work completed ?
Options: a ) 13 days , b ) 16 days , c ) 18 days , d ) 11 days , e ) 38 days
Rationale: "one day work of a , b and c = 1 / 24 + 1 / 30 + 1 / 40 = 1 / 10 work done by a and b together in the last 12 days = 12 * ( 1 / 24 + 1 / 30 ) = 9 / 10 remaining work = 1 / 10 the number of days required for this initial work = 1 days . the total number of days required = 12 + 1 = 13 days . answer : a"
Answer: a
Problem: a parking garage rents parking spaces for $ 10 per week or $ 25 per month . how much does a person save in a year by renting by the month rather than by the week ?
Options: a ) $ 120 , b ) $ 160 , c ) $ 220 , d ) $ 240 , e ) $ 260
Rationale: "10 $ per week ! an year has 52 weeks . annual charges per year = 52 * 10 = 520 $ 30 $ per month ! an year has 12 months . annual charges per year = 12 * 25 = 300 $ 520 - 300 = 120 ans a"
Answer: a
Problem: if n is a positive integer and the product of all integers from 1 to n , inclusive , is a multiple of 630 , what is the least possible value of n ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "630 = 2 * 3 * 3 * 5 * 7 , so n must be at least 7 . the answer is c ."
Answer: c
Problem: the total marks obtained by a student in mathematics and physics is 30 and his score in chemistry is 20 marks more than that in physics . find the average marks scored in mathamatics and chemistry together .
Options: a ) 40 , b ) 30 , c ) 25 , d ) data inadequate , e ) none of these .
Rationale: "let the marks obtained by the student in mathematics , physics and chemistry be m , p and c respectively . given , m + c = 30 and c - p = 20 m + c / 2 = [ ( m + p ) + ( c - p ) ] / 2 = ( 30 + 20 ) / 2 = 25 . answer : c"
Answer: c
Problem: a lent rs . 5000 to b for 2 years and rs . 3000 to c for 4 years on simple interest at the same rate of interest and received rs . 1540 in all from both of them as interest . the rate of interest per annum is ?
Options: a ) 7 % , b ) 12 % , c ) 74 % , d ) 10 % , e ) 45 %
Rationale: "let the rate be r % p . a . then , ( 5000 * r * 2 ) / 100 + ( 3000 * r * 4 ) / 100 = 1540 100 r + 120 r = 1540 r = 7 % answer : a"
Answer: a
Problem: solve for x and check : 25 x = 675
Options: a ) 675 , b ) 725 , c ) 895 , d ) 1025 , e ) none of these
Rationale: "solution : dividing each side by 25 , we obtain ( 25 x / 675 ) = ( 675 / 25 ) therefore : x = 27 check : 25 x = 675 ( 25 * 27 ) = 675 675 = 675 answer : a"
Answer: a
Problem: given that x and y are events such that z ( x ) = 0.02 z ( y ) = 0.10 z ( xny ) = 0.10 z ( x | y ) = find z ( x | y ) and z ( x | y )
Options: a ) 1 / 5 , b ) 1 / 6 , c ) 1 / 6 , d ) 1 / 4 , e ) 1 / 2
Rationale: here , x and y are events z ( x | y ) = z ( xny ) / z ( y ) = 0.10 / 0.10 = 1 q ( g | h ) = z ( xny ) / z ( x ) = 0.4 / 0.02 = 1 / 5 answer is a
Answer: a
Problem: a jar contains a mixture of ab in the ratio 4 : 1 . when 40 l of mixture is replaced with liquid b , ratio becomes 2 : 3 . how many liters of liquid a was present in mixture initially .
Options: a ) 12 , b ) 15 , c ) 16 , d ) 64 , e ) 25
Rationale: 40 litres of mixture that is replaced will contain 32 litres of a and 8 litres of b ( as a : b = 4 : 1 ) let the initial volume of the mixture be 4 k + 1 k = 5 k so by condition , [ 4 k - 32 ] / [ k - 8 + 40 ] = 2 / 3 = > 12 k - 96 = 2 k - 16 + 80 = > 10 k = 160 solve for k which is k = 16 so initial volume of liquid a = 4 k = 64 litres answer : d
Answer: d
Problem: the length of a rectangle is 3 times its width . if the width of the rectangle is 6 inches , what is the rectangle ' s area , in square inches ?
Options: a ) 30 square inches , b ) 108 square inches , c ) 68 square inches , d ) 89 square inches , e ) 92 square inches
Rationale: "if the width is 6 in and the length is 3 times the width , then the length is 3 * 6 = 18 in the area is given by 6 * 18 = 108 square inches correct answer b"
Answer: b
Problem: a , b and c started a business with capitals of rs . 8000 , rs . 10000 and rs . 12000 respectively . at the end of the year , the profit share of b is rs . 2500 . the difference between the profit shares of a and c is ?
Options: a ) 621 , b ) 276 , c ) 236 , d ) 1000 , e ) 211
Rationale: "explanation : ratio of investments of a , b and c is 8000 : 10000 : 12000 = 4 : 5 : 6 and also given that , profit share of b is rs . 2500 = > 5 parts out of 15 parts is rs . 2500 now , required difference is 6 - 4 = 2 parts required difference = 2 / 5 ( 2500 ) = rs . 1000 answer : d"
Answer: d
Problem: a truck drives 80 miles on local roads at 30 mph , and 50 miles on the highway at 60 mph , the truck also take a hour lunch break . what is the average speed of the entire trip ?
Options: a ) 30 mph , b ) 29 mph , c ) 28 mph , d ) 31 mph , e ) 23 mph
Rationale: so the answer is plainly a . . . . we have a general relation for speed , time and distance : v ( velocity ) * t ( time ) = d ( distance ) for first part we have d = 80 miles , and v = 30 mph so we can obtain time : 30 * t = 80 or t = 80 / 30 = 2.6 hours the needed time to cover 80 miles in the same way we should divide 50 to 60 to find the needed time to cover 50 miles , so t = 0.8 hours so the total time for covering total distance would be 2.6 + 0.8 + 1 ( lunch time ) = 4.4 hours and total distance is 80 + 50 = 130 miles final stage : average speed is total distance divide to total time : 130 / 4.4 = 29.5 miles per hour rounding up to 30 . . . .
Answer: a
Problem: carrey rented a car for rs . 20 plus rs . 0.25 per kilometer driven . samuel rented a car for rs . 24 plus rs . 0.16 per kilometer driven . if each drove d km . and each was charged exactly the same amount for the rental , then d equals ?
Options: a ) 44.4 , b ) 44.8 , c ) 1 , d ) 19 , e ) 44.11
Rationale: explanation : 20 + 0.25 × d = 24 + 0.16 d solving we get d = 44.4 answer : a
Answer: a
Problem: the first doughnut is priced at $ 1 and then if you purchase additional doughnuts as dozens then the price is $ 6 / dozen . what is the total number of doughnuts purchased if you paid $ 24 ?
Options: a ) 44 , b ) 46 , c ) 48 , d ) 50 , e ) 52
Rationale: $ 24 = 4 * $ 6 the number of doughnuts is 4 * 12 = 48 the answer is c .
Answer: c
Problem: the speed of the boat in still water in 12 kmph . it can travel downstream through 48 kms in 3 hrs . in what time would it cover the same distance upstream ?
Options: a ) 8 hours , b ) 6 hours , c ) 4 hours , d ) 5 hours , e ) 6 hours
Rationale: "still water = 12 km / hr downstream = 48 / 3 = 16 km / hr upstream = > > still water = ( u + v / 2 ) = > > 12 = u + 16 / 2 = 8 km / hr so time taken in upstream = 48 / 8 = 6 hrs answer : e"
Answer: e
Problem: on a sum of money , the simple interest for 2 years is rs . 326 , while the compound interest is rs . 340 , the rate of interest being the same in both the cases . the rate of interest is
Options: a ) 15 % , b ) 14.25 % , c ) 8.58 % , d ) 10.5 % , e ) 11.5 %
Rationale: "explanation : the difference between compound interest and simple interest on rs . p for 2 years at r % per annum = ( r ã — si ) / ( 2 ã — 100 ) difference between the compound interest and simple interest = 340 - 326 = 14 ( r ã — si ) / ( 2 ã — 100 ) = 14 ( r ã — 326 ) / ( 2 ã — 100 ) = 14 r = 8.58 % answer : option c"
Answer: c
Problem: in a certain supermarket , a triangular display of cans is arranged in 9 rows , numbered 1 through 9 from top to bottom . each successively numbered row contains 3 more cans than the row immediately above it . if there are fewer than 120 cans in the entire display , how many cans are in the seventh row ?
Options: a ) 13 , b ) 15 , c ) 17 , d ) 19 , e ) 21
Rationale: "let x be the number of cans in row 1 . the total number of cans is x + ( x + 3 ) + . . . + ( x + 24 ) = 9 x + 3 ( 1 + 2 + . . . + 8 ) = 9 x + 3 ( 8 ) ( 9 ) / 2 = 9 x + 108 since the total is less than 120 , x must equal 1 . the number of cans in the 7 th row is 1 + 3 ( 6 ) = 19 the answer is d ."
Answer: d
Problem: the length of a rectangle is 3 times its width . if the width of the rectangle is 4 inches , what is the rectangle ' s area , in square inches ?
Options: a ) 30 square inches , b ) 75 square inches , c ) 68 square inches , d ) 48 square inches , e ) 92 square inches
Rationale: "if the width is 4 in and the length is 3 times the width , then the length is 3 * 4 = 12 in the area is given by 4 * 12 = 48 square inches correct answer d"
Answer: d
Problem: the average age of students of a class is 15.8 years . the average age of boys in the class is 16.4 years and that of the girls is 15.7 years . the ration of the number of boys to the number of girls in the class is ?
Options: a ) 1 : 6 , b ) 2 : 3 , c ) 2 : 5 , d ) 2 : 1 , e ) 2 : 4
Rationale: "let the ratio be k : 1 . then , k * 16.4 + 1 * 15.7 = ( k + 1 ) * 15.8 = ( 16.4 - 15.8 ) k = ( 15.8 - 15.7 ) = k = 0.1 / 0.6 = 1 / 6 required ratio = 1 / 6 : 1 = 1 : 6 . answer : a"
Answer: a
Problem: a man walking at a rate of 5 km / hr crosses a bridge in 15 minutes . the length of the bridge is ?
Options: a ) 1250 m , b ) 1310 m , c ) 1500 m , d ) 1000 m , e ) 1195 m
Rationale: "speed = 5 * 5 / 18 = 25 / 18 m / sec distance covered in 15 minutes = 25 / 18 * 15 * 60 = 1250 m answer is a"
Answer: a
Problem: a train traveling at 108 kmph crosses a platform in 30 seconds and a man standing on the platform in 12 seconds . what is the length of the platform in meters ?
Options: a ) 240 meters , b ) 360 meters , c ) 420 meters , d ) 600 meters , e ) can not be determined
Rationale: "answer distance covered by the train when crossing a man and when crossing a platform when a train crosses a man standing on a platform , the distance covered by the train is equal to the length of the train . however , when the same train crosses a platform , the distance covered by the train is equal to the length of the train plus the length of the platform . the extra time that the train takes when crossing the platform is on account of the extra distance that it has to cover . i . e . , length of the platform . compute length of platform length of the platform = speed of train * extra time taken to cross the platform . length of platform = 108 kmph * 12 seconds convert 108 kmph into m / sec 1 kmph = 5 / 18 m / s ( this can be easily derived . but if you can remember this conversion , it saves a good 30 seconds ) . ∴ 108 kmph = 5 / 18 ∗ 108 = 30 m / sec therefore , length of the platform = 30 m / s * 12 sec = 360 meters . choice b"
Answer: b
Problem: the ratio of investments of two partners p and q is 7 : 5 and the ratio of their profits is 7 : 11 . if p invested the money for 5 months , find for how much time did q invest the money ?
Options: a ) 19 , b ) 17 , c ) 13 , d ) 11 , e ) 12
Rationale: "7 * 5 : 5 * x = 7 : 11 x = 11 answer : d"
Answer: d
Problem: a fair price shopkeeper takes 10 % profit on his goods . he lost 30 % goods during theft . his loss percent is :
Options: a ) 23 % , b ) 42 % , c ) 32 % , d ) 12 % , e ) 22 %
Rationale: "explanation : suppose he has 100 items . let c . p . of each item be re . 1 . total cost = rs . 100 . number of items left after theft = 70 . s . p . of each item = rs . 1.10 total sale = 1.10 * 70 = rs . 77 hence , loss % = 23 / 100 * 100 = 23 % answer : a"
Answer: a
Problem: some people are standing square . from them 32 are removed and then form a small square and then 8 more removed . now we can not form the square . so how many people are there at the beginning ?
Options: a ) 31 , b ) 32 , c ) 33 , d ) 34 , e ) ca n ' t be determined
Rationale: we should find the two square numbers whose difference is 32 . starting from 9,16 , 25,36 , 49,64 , 81,100 , . . . . we observe 81 - 49 = 32 & 49 - 8 = 41 which is not a square . answer : e
Answer: e
Problem: how many seconds will a 500 m long train take to cross a man walking with a speed of 3 km / hr in the direction of the moving train if the speed of the train is 63 km / hr ?
Options: a ) 22 , b ) 30 , c ) 88 , d ) 26 , e ) 12
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 = 500 * 3 / 50 = 30 sec . answer : b"
Answer: b
Problem: the ages of 2 persons differ by 32 years . if 12 years ago the elder one be 6 times as old as the younger one , find the present age of elder person .
Options: a ) 30 , b ) 48.5 , c ) 50.4 , d ) 62.6 , e ) 47.9
Rationale: "age of the younger person = x age of the elder person = x + 32 6 ( x - 12 ) = x + 32 - 12 x = 18.4 age of elder person = 18.4 + 32 = 50.4 answer is c"
Answer: c
Problem: on a certain date , pat invested $ 8,000 at x percent annual interest , compounded annually . if the total value of the investment plus interest at the end of 10 years will be $ 32,000 , in how many years total will the total value of the investment plus interest increase to $ 64,000 ?
Options: a ) 15 , b ) 16 , c ) 18 , d ) 20 , e ) 24
Rationale: "32,000 = 8,000 ( 1 + x ) ^ 10 4 = ( 1 + x ) ^ 10 = 2 ^ 2 ( 1 + x ) ^ 10 = ( ( 1 + x ) ^ 5 ) ^ 2 = 2 ^ 2 therefore , ( 1 + x ) ^ 5 = 2 64,000 = 8,000 ( 1 + x ) ^ n ( 1 + x ) ^ n = 8 ( 1 + x ) ^ n = 2 ^ 3 ( 1 + x ) ^ n = ( ( 1 + x ) ^ 5 ) ^ 3 = ( 1 + x ) ^ 15 therefore , n = 15 . the answer is a ."
Answer: a
Problem: the average age of 10 men is increased by years when two of them whose ages are 21 years and 23 years are replaced by two new men . the average age of the two new men is
Options: a ) 22 , b ) 30 , c ) 99 , d ) 38 , e ) 32
Rationale: "total age increased = ( 10 * 2 ) years = 20 years . sum of ages of two new men = ( 21 + 23 + 20 ) years = 64 years average age of two new men = ( 64 / 2 ) years = 32 years . answer : e"
Answer: e
Problem: if 64 ( 8 ^ x ) = 1 then x =
Options: a ) 2 , b ) – 1 , c ) 0 , d ) 1 , e ) - 2
Rationale: "8 ^ x = 1 / 64 8 ^ x = 1 / 8 ^ 2 8 ^ x = 8 ^ - 2 x = - 2 e"
Answer: e
Problem: a rectangle having length 105 cm and width 40 cm . if the length of the rectangle is increased by twenty five percent then how much percent the breadth should be decreased so as to maintain the same area .
Options: a ) 25 % , b ) 19.23 % , c ) 40 % , d ) 75 % , e ) none of these
Rationale: "explanation : solution : ( 25 / ( 105 + 25 ) * 100 ) % = 19.23 % answer : b"
Answer: b
Problem: a tailor trims 6 feet from opposite edges of a square piece of cloth , and 5 feet from the other two edges . if 80 square feet of cloth remain , what was the length of a side of the original piece of cloth ?
Options: a ) 16 , b ) 18 , c ) 20 , d ) 24 , e ) 32
Rationale: "let the original side of the square be x . ( x - 12 ) * ( x - 10 ) = 80 = 8 * 10 x = 20 the answer is c ."
Answer: c
Problem: the base and height of a parallelogram are 12 m and 6 m respectively . then its area is = = = = = = ?
Options: a ) 27 sq . m
b ) 126 sq . m
c ) 84 sq . m
d ) 18 sq . m
e ) 72 sq . m
Rationale: a = b * h = > a = 12 * 6 = 72 sq . m . answer : ( e )
Answer: e
Problem: how many prime numbers are between 76 / 8 and 124 / 5 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "76 / 8 = 38 / 4 = 19 / 2 = 10 - 124 / 5 = 25 - prime numbers between 10 and 29 are 11 , 13 , 17 , 19 , and 23 - sign signifies that the number is marginally less . answer e"
Answer: e
Problem: evaluate : 40 - 12 * 3 * 2 = ?
Options: a ) 62 , b ) 52 , c ) 32 , d ) 12 , e ) 22
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 40 - 12 * 3 * 2 = 40 - 8 = 32 correct answer c"
Answer: c
Problem: pipe a can fill a tank in 6 minutes and pipe b cam empty it in 24 minutes . if both the pipes are opened together after how many minutes should pipe b be closed , so that the tank is filled in 30 minutes ?
Options: a ) 18 , b ) 27 , c ) 96 , d ) 27 , e ) 21
Rationale: "let the pipe b be closed after x minutes . 30 / 6 - x / 24 = 1 = > x / 24 = 30 / 6 - 1 = 4 = > x = 4 * 24 = 96 . answer : c"
Answer: c
Problem: what is the compound interest on rs : 40,000 for 4 months at the rate of 5 % per annum
Options: a ) 670.85 , b ) 671.85 , c ) 672.85 , d ) 673.85 , e ) 674.85
Rationale: "it is monthly compound rate = 5 / 12 % per month 40000 * ( 1 + 5 / 1200 ) ^ 4 - 40000 = 670.85 answer : a"
Answer: a
Problem: mark and ann together were allocated n boxes of cookies to sell for a club project . mark sold 6 boxes less than n and ann sold 2 boxes less than n . if mark and ann have each sold at least one box of cookies , but together they have sold less than n boxes , what is the value of n ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "if n = 7 mark sold 1 box and ann sold 5 boxes total 6 < 7 answer : e"
Answer: e
Problem: the number of diagonals of a polygon of n sides is given by the formula q = n ( n - 3 ) / 2 . if a polygon has twice as many diagonals as sides , how many sides does it have ?
Options: a ) 3 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: "q = n ( n - 3 ) q = 2 * n 2 n = n ( n - 3 ) = > 2 = n - 3 = > n = 5 answer b"
Answer: b
Problem: a fair price shopkeeper takes 10 % profit on his goods . he lost 70 % goods during theft . his loss percent is :
Options: a ) 72 % , b ) 42 % , c ) 32 % , d ) 67 % , e ) 22 %
Rationale: "explanation : suppose he has 100 items . let c . p . of each item be re . 1 . total cost = rs . 100 . number of items left after theft = 30 . s . p . of each item = rs . 1.10 total sale = 1.10 * 30 = rs . 33 hence , loss % = 67 / 100 * 100 = 67 % answer : d"
Answer: d
Problem: the age of somu is one - third his father ' s . 8 years back he was one - fifth of his father ' s age . what is his persent age ?
Options: a ) 11 , b ) 13 , c ) 14 , d ) 16 , e ) 10
Rationale: "explanation : let somu ' s age be x and that of his father be 3 x . so , x - 8 = 3 x - 8 / 5 = x = 16 answer : option d"
Answer: d
Problem: 13 buckets of water fill a tank when the capacity of each bucket is 42 litres . how many buckets will be needed to fill the same tank , if the capacity of each bucket is 6 litres ?
Options: a ) 91 , b ) 80 , c ) 96 , d ) 98 , e ) 90
Rationale: "capacity of the tank = ( 13 ã — 42 ) litre number of buckets required of capacity of each bucket is 17 litre = 13 ã — 42 / 6 = 13 ã — 7 = 91 answer is a"
Answer: a
Problem: a car ferry can hold up to 70 tons of cargo . what is the greatest number of vehicles that the ferry can carry if half the vehicles are cars with an average ( arithmetic mean ) weight of 0.75 tons and half of the vehicles are trucks with an average ( arithmetic mean ) weight of 4 tons ?
Options: a ) 14 , b ) 20 , c ) 28 , d ) 32 , e ) 36
Rationale: "the weight of one car and one truck is 4.75 tons . 70 / 4.75 = 14 plus a remainder the ferry could carry 14 cars and 14 trucks for a total of 28 vehicles . the answer is c ."
Answer: c
Problem: 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 22 seconds . the ratio of their speeds is ?
Options: a ) 3 / 1 , b ) 3 / 1 , c ) 1 / 1 , d ) 3 / 5 , e ) 5 / 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 ) = 22 = = > 27 x + 17 y = 22 x + 22 y = = > 5 x = 5 y = = > x / y = 1 / 1 . answer : c"
Answer: c
Problem: exactly 3 / 7 of the people in the room are under the age of 21 , and exactly 5 / 9 of the people in the room are over the age of 65 . if the total number of the people in the room is greater than 50 and less than 100 , how many people in the room are under the age of 21 ?
Options: a ) 27 , b ) 35 , c ) 39 , d ) 60 , e ) 65
Rationale: "the total number of the people in the room must be a multiple of both 7 and 9 ( in order 3 / 7 and 5 / 9 of the number to be an integer ) , thus the total number of the people must be a multiple of lcm of 7 and 9 , which is 63 . since , the total number of the people in the room is greater than 50 and less than 100 , then there are 91 people in the room . therefore there are 3 / 7 * 63 = 27 people in the room under the age of 21 . answer : a ."
Answer: a
Problem: 4 , 12 , 48 , 240 , 1440 , 10080 , ( . . . )
Options: a ) 80640 , b ) 10080 , c ) 6200 , d ) 10020 , e ) 12500
Rationale: "explanation : go on multiplying the given numbers by 3 , 4 , 5 , 6 , 7,8 answer : option a"
Answer: a
Problem: the product of two successive numbers is 7832 . which is the smaller of the two numbers ?
Options: a ) 78 , b ) 68 , c ) 88 , d ) 97 , e ) 37
Rationale: "c 88 from the given alternatives , 88 × 89 = 7832 ∴ smaller number = 88"
Answer: c