regisss/math_qa huggingface dataset:
Problem: if a is an integer greater than 2 but less than 11 and b is an integer greater than 11 but less than 21 , what is the range of a / b ?
Options: a ) 52 / 45 , b ) 23 / 47 , c ) 60 / 41 , d ) 51 / 42 , e ) 41 / 60
Rationale: "the way to approach this problem is 2 < a < 11 and 11 < b < 21 minimum possible value of a is 3 and maximum is 10 minimum possible value of b is 12 and maximum is 20 range = max a / min b - min a / max b ( highest - lowest ) 10 / 12 - 3 / 20 = 41 / 60 hence e"
Answer: e
Problem: at what price must an article costing rs . 100 be marked in order that after deducting 5 % from the list price . it may be sold at a profit of 25 % on the cost price ?
Options: a ) 131.58 , b ) 62.0 , c ) 62.6 , d ) 62.1 , e ) 62.2
Rationale: "cp = 100 sp = 100 * ( 125 / 100 ) = 125 mp * ( 95 / 100 ) = 125 mp = 131.58 answer : a"
Answer: a
Problem: how long does a train 110 m long running at a speed of 72 kmph take to cross a bridge 132 m in length ?
Options: a ) 9.8 sec , b ) 12.1 sec , c ) 12.42 sec , d ) 14.3 sec , e ) 24.3 sec
Rationale: "72 km / hr = 72 * 5 / 18 m / sec = 20 m / sec time = d / s = 110 + 132 / 20 = 242 / 20 = 12.1 sec answer : b"
Answer: b
Problem: a train 110 meters long is running with a speed of 60 kmph . in what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going ?
Options: a ) 7 sec , b ) 6 sec , c ) 8 sec , d ) 4 sec , e ) 2 sec
Rationale: "speed of train relative to man = ( 60 + 6 ) km / hr = 66 km / hr [ 66 * 5 / 18 ] m / sec = [ 55 / 3 ] m / sec . time taken to pass the man = [ 110 * 3 / 55 ] sec = 6 sec answer : b"
Answer: b
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 6 km ?
Options: a ) 3 , b ) 5 , c ) 6 , d ) 67 , e ) 7
Rationale: "m = 4 s = 2 us = 4 - 2 = 2 d = 6 t = 6 / 2 = 3 answer : a"
Answer: a
Problem: in an election , candidate x got 75 % of the total valid votes . if 15 % of the total votes were declared invalid and the total numbers of votes is 560000 , find the number of valid vote polled in favour of candidate ?
Options: a ) 280000 , b ) 300000 , c ) 355000 , d ) 356000 , e ) 357000
Rationale: total number of invalid votes = 15 % of 560000 = 15 / 100 × 560000 = 8400000 / 100 = 84000 total number of valid votes 560000 – 84000 = 476000 percentage of votes polled in favour of candidate x = 75 % therefore , the number of valid votes polled in favour of candidate x = 75 % of 476000 = 75 / 100 × 476000 = 35700000 / 100 = 357000 e )
Answer: e
Problem: the average of first 15 natural numbers is ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: "sum of 15 natural no . = 240 / 2 = 120 average = 120 / 15 = 8 answer : b"
Answer: b
Problem: at 6 ′ o a clock ticks 6 times . the time between first and last ticks is 35 seconds . how long does it tick at 12 ′ o clock
Options: a ) 77 , b ) 76 , c ) 28 , d ) 66 , e ) 11
Rationale: "explanation : for ticking 6 times , there are 5 intervals . each interval has time duration of 35 / 5 = 7 secs at 12 o ' clock , there are 11 intervals , so total time for 11 intervals = 11 × 7 = 77 secs . answer : a"
Answer: a
Problem: a no . when divided by the sum of 555 and 445 gives 2 times their difference as quotient & 20 as remainder . find the no . is ?
Options: a ) 122456 , b ) 220020 , c ) 220022 , d ) 235467 , e ) 220026
Rationale: "( 555 + 445 ) * 2 * 110 + 20 = 220000 + 20 = 220020 b"
Answer: b
Problem: a case contains c cartons . each carton contains b boxes , and each box contains 300 paper clips . how many paper clips are contained in 2 cases ?
Options: a ) 300 bc , b ) 300 b / c , c ) 600 bc , d ) 600 b / c , e ) 600 / bc
Rationale: "2 cases * c cartons / case * b boxes / carton * 300 clips / box = 600 bc paper clips the answer is c ."
Answer: c
Problem: solve the equation for x : 2 x - 21 + 3 x = 4 + 9 - x
Options: a ) 4 , b ) 5 , c ) 5.6 , d ) 9.2 , e ) 3.1
Rationale: "c 5.6 5 x + x = 13 + 21 6 x = 34 = > x = 5.6"
Answer: c
Problem: how many positive integers less than 5,000 are evenly divisible by neither 15 nor 20 ?
Options: a ) 4,514 , b ) 4,477 , c ) 4,521 , d ) 4,428 , e ) 4,349
Rationale: "integers less than 5000 divisible by 15 5000 / 15 = 333 . something , so 333 integers less than 5000 divisible by 20 5000 / 20 = 238 . # # , so 238 we have double counted some , so take lcm of 15 and 20 = 105 and divide by 5000 , we get 47 . so all numbers divisible by 15 and 20 = 333 + 238 - 47 = 524 now subtract that from 4999 . 4999 - 524 = 4477 answer b ."
Answer: b
Problem: the cost price of an article is 70 % of the marked price . calculate the gain percent after allowing a discount of 10 % .
Options: a ) 13.6 % , b ) 28.6 % , c ) 35.6 % , d ) 42.3 % , e ) none
Rationale: "sol . let marked price = rs . 100 . then , c . p . = rs . 70 . s . p = rs . 90 . â ˆ ´ gain % = [ 20 / 70 * 100 ] % = 28.6 % . answer b"
Answer: b
Problem: lola rolls a die 3 times . what is the probability that she gets a 4 on the last one of the 3 rolls ?
Options: a ) 215 / 216 , b ) 216 , c ) 1 / 216 , d ) none , e ) 2
Rationale: the die has 6 sides and it was rolle 3 times , then 6 * 6 * 6 = 216 the number of ways to get 4 is 1 then 1 / 216 the probability would be 1 - 1 / 216 = 215 / 216 answer a
Answer: a
Problem: the contents of a certain box consist of 48 apples and 30 kiwis . how many kiwis must be added to the box so that exactly 30 % of the pieces of fruit in the box will be apples ?
Options: a ) 90 , b ) 72 , c ) 82 , d ) 54 , e ) 65
Rationale: "apple = ( apple + kiwi + x ) * 0.3 48 = ( 30 + 48 + x ) * 0.3 x = 82 answer : c"
Answer: c
Problem: a rectangular park 60 m long and 40 m wide has two concrete crossroads running in the middle of the park and rest of the park has been used as a lawn . if the area of the lawn is 2109 sq . m , then what is the width of the road ?
Options: a ) 2
b ) 3.5
c ) 3
d ) 4
e ) 5
Rationale: area of the park = ( 60 x 40 ) m 2 = 2400 m 2 . area of the lawn = 2109 m 2 . area of the crossroads = ( 2400 - 2109 ) m 2 = 291 m 2 . let the width of the road be x metres . then , 60 x + 40 x - x 2 = 291 x 2 - 100 x + 291 = 0 ( x - 97 ) ( x - 3 ) = 0 x = 3 . c )
Answer: c
Problem: a group of people participate in some curriculum , 35 of them practice yoga , 20 study cooking , 15 study weaving , 7 of them study cooking only , 5 of them study both the cooking and yoga , 3 of them participate all curriculums . how many people study both cooking and weaving ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "both cooking and weaving = 20 - ( 7 + 5 + 3 ) = 5 so , the correct answer is e ."
Answer: e
Problem: a can finish a work in 48 days , b in 9 days and c in 2 days , b and c start the work but are forced to leave after 3 days . the remaining work was done by a in ?
Options: a ) 10 days , b ) 12 days , c ) 6 days , d ) 20 days , e ) 8 days
Rationale: "b + c 1 day work = 1 / 9 + 1 / 12 = 7 / 36 work done by b and c in 3 days = 7 / 36 * 3 = 7 / 12 remaining work = 1 - 7 / 12 = 5 / 12 1 / 48 work is done by a in 1 day 5 / 12 work is done by a in 48 * 5 / 12 = 20 days answer is d"
Answer: d
Problem: the length of the bridge , which a train 140 metres long and travelling at 45 km / hr can cross in 30 seconds , is :
Options: a ) 200 m , b ) 235 m , c ) 245 m , d ) 250 m , e ) 270 m
Rationale: "let the length of the bridge : l the equation now is l + 140 / 12.5 m / s ( 45 km / hr or 12.5 m / s ) = 30 solving , l = 235 m answer : b"
Answer: b
Problem: in a certain animal shelter , the ratio of the number of catsto the number of dogs is 15 to 7 . if 16 additional dogs were to be taken in by the shelter , the ratio of the number of cats to the number of dogs would be 15 to 11 . how many cats are in the shelter ?
Options: a ) 15 , b ) 25 , c ) 30 , d ) 45 , e ) 60
Rationale: "this ratio question can be solved in a couple of different ways . here ' s an algebraic approach . . . we ' re told that the ratio of the number of cats to the number of dogs is 15 : 7 . we ' re then told that 16 more dogs are added to this group and the ratio becomes 15 : 11 . we ' re asked for the number of cats . algebraically , since the number of cats is a multiple of 15 and the number of dogs is a multiple of 7 , we can write this initial relationship as . . . 15 x / 7 x when we add the 16 cats and factor in the ' ending ratio ' , we have an equation . . . . 15 x / ( 7 x + 16 ) = 15 / 11 here we have 1 variable and 1 equation , so we can solve for x . . . . ( 15 x ) ( 11 ) = ( 7 x + 16 ) ( 15 ) ( x ) ( 11 ) = ( 7 x + 16 ) ( 1 ) 11 x = 7 x + 16 4 x = 16 x = 4 with this x , we can figure out the initial number of dogs and cats . . . initial dogs = 15 x = 15 ( 4 ) = 60 final answer : d"
Answer: d
Problem: for the positive integers x , x + 2 , x + 4 , x + 7 , and x + 32 , the mean is how much greater than the median ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 4 , e ) 5
Rationale: "mean = ( x + x + 2 + x + 4 + x + 7 + x + 32 ) / 5 = ( 5 x + 45 ) / 5 = x + 9 median = x + 4 thus mean - median = x + 9 - ( x + 4 ) = 5 answer = e"
Answer: e
Problem: the ratio of the volumes of two cubes is 27 : 64 . what is the ratio of their total surface areas ?
Options: a ) 18 : 21
b ) 81 : 13
c ) 8 : 15
d ) 16 : 21
e ) 1 : 13
Rationale: ratio of the sides = ³ √ 27 : ³ √ 64 = 3 : 4 ratio of surface areas = 32 : 42 = 16 : 21 answer : d
Answer: d
Problem: a driver would have reduced the time it took to drive from home to the store by 1 / 3 if the average speed had been increased by 18 miles per hour . what was the actual average speed , in miles per hour , when the driver drove from home to the store ?
Options: a ) 36 , b ) 40 , c ) 44 , d ) 48 , e ) 52
Rationale: "let r be the original speed and let t be the original time . since the distance remains the same ( we ' re just changing the rate and time ) , any increase in rate or time is met with a decrease in the other term . decreasing the time by 1 / 3 would give us : d = ( r ) ( t ) = ( 2 t / 3 ) ( x * r ) x = 3 / 2 since ( 2 t / 3 ) ( 3 r / 2 ) = ( r ) ( t ) = d 3 r / 2 = r + 18 r / 2 = 18 r = 36 the answer is a ."
Answer: a
Problem: what is the probability q of randomly selecting an arrangement of the letters of the wordmediterraneanin which the first letter is e and the last letter is r ?
Options: a ) 1 / 13 , b ) 1 / 20 , c ) 1 / 26 , d ) 1 / 50 , e ) 1 / 100
Rationale: why do you calculate the total combinations and everything , it is much easier to calculate as follows : 3 / 13 * 1 * 1 * 1 * 1 . . . . . * 2 / 12 = 6 / 156 = 1 / 26 this is because 3 / 13 = probability that first letter will be e and 2 / 12 = probability that thefirstletter will be r . between everything else cuts down to 1 * 1 * 1 . . . e . g . probability q of the second letter is 11 / 11 = 1 , > we do not care what ' s in between . c
Answer: c
Problem: the speed of a train is 90 kmph . what is the distance covered by it in 20 minutes ?
Options: a ) 15 , b ) 66 , c ) 77 , d ) 30 , e ) 42
Rationale: "90 * 20 / 60 = 30 kmph answer : d"
Answer: d
Problem: a man can row downstream at the rate of 45 kmph and upstream at 23 kmph . find the man ’ s rate in still water and rate of current ?
Options: a ) 8.5 , b ) 10.0 , c ) 12.5 , d ) 11.0 , e ) 8.25
Rationale: rate of still water = 1 / 2 ( down stream + upstream ) = 1 / 2 ( 45 + 23 ) = 34 kmph rate of current = 1 / 2 ( down stream - upstream ) = 1 / 2 ( 45 - 23 ) = 1 / 2 ( 22 ) = 11 kmph answer is d .
Answer: d
Problem: how many numbers from 9 to 79 are exactly divisible by 11 ?
Options: a ) 5 , b ) 7 , c ) 9 , d ) 11 , e ) 12
Rationale: "9 / 11 = 0 and 79 / 11 = 7 = = > 7 - 0 = 7 numbers answer : b"
Answer: b
Problem: the speed of a car is 20 km in the first hour and 60 km in the second hour . what is the average speed of the car ?
Options: a ) 79 kmph , b ) 40 kmph , c ) 34 kmph , d ) 23 kmph , e ) 14 kmph
Rationale: "s = ( 20 + 60 ) / 2 = 40 kmph answer : b"
Answer: b
Problem: what least number should be added to 1053 , so that the sum is completely divisible by 23
Options: a ) a ) 4 , b ) b ) 1 , c ) c ) 2 , d ) d ) 3 , e ) e ) 5
Rationale: "explanation : ( 1053 / 23 ) gives remainder 18 18 + 5 = 23 , so we need to add 5 answer : option e"
Answer: e
Problem: an error 5 % in excess is made while measuring the side of a square . the percentage of error in the calculated area of the square is
Options: a ) 10.4 % , b ) 10.25 % , c ) 10.23 % , d ) 10.26 % , e ) 10.5 %
Rationale: "100 cm is read as 102 cm . a 1 = ( 100 x 100 ) cm 2 and a 2 ( 105 x 105 ) cm 2 . ( a 2 - a 1 ) = [ ( 105 ) 2 - ( 100 ) 2 ] = ( 105 + 100 ) x ( 105 - 100 ) = 1025 cm 2 . percentage error = 10.25 b"
Answer: b
Problem: the average weight of 6 person ' s increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg . what might be the weight of the new person ?
Options: a ) 76 kg , b ) 80 kg , c ) 85 kg , d ) data inadequate , e ) none of these
Rationale: "explanation : total weight increased = ( 6 x 2.5 ) kg = 15 kg . weight of new person = ( 65 + 15 ) kg = 80 kg . answer : b"
Answer: b
Problem: which greatest possible length can be used to measure exactly 10 meter 40 cm , 14 meter 10 cm and 7 meter 90 cm
Options: a ) 45 cm , b ) 25 cm , c ) 24 cm , d ) 15 cm , e ) 10 cm
Rationale: "explanation : convert first all terms into cm . i . e . 1040 cm , 1410 cm , 790 cm . now whenever we need to calculate this type of question , we need to find the hcf . hcf of above terms is 10 . option e"
Answer: e
Problem: a shopkeeper sells 200 metres of cloth for rs . 12000 at a loss of rs . 6 per metre . find his cost price for one metre of cloth ?
Options: a ) s . 59 , b ) s . 58 , c ) s . 09 , d ) s . 50 , e ) s . 66
Rationale: "sp per metre = 12000 / 200 = rs . 60 loss per metre = rs . 6 cp per metre = 60 + 6 = rs . 66 answer : e"
Answer: e
Problem: in what ratio must rice at $ 9.30 / kg be mixed with rice at $ 10.80 / kg so that the mixture is worth $ 10 / kg ?
Options: a ) 1 : 3 , b ) 9 : 4 , c ) 8 : 7 , d ) 11 : 9 , e ) 11 : 7
Rationale: 9.30 x + 10.80 y = 10 ( x + y ) . 80 y = . 70 x x / y = 8 / 7 c is the answer
Answer: c
Problem: a can contains a mixture of liquids a and b is the ratio 7 : 5 . when 9 litres of mixture are drawn off and the can is filled with b , the ratio of a and b becomes 7 : 9 . how many liter q of liquid a was contained by the can initially ?
Options: a ) 10 , b ) 20 , c ) 21 , d ) 25 , e ) 27
Rationale: "as a : b : : 7 : 5 - - - > only option c is a multiple of 7 and hence it is a good place to start . also a : b : : 7 : 5 means that , a = ( 712 ) * total and b = ( 5 / 12 ) * total if a = 21 , b = 15 - - - > remove 9 litres - - - > you remove ( 7 / 12 ) * 9 of a - - - > a remaining = 21 - ( 7 / 12 ) * 9 = 63 / 4 similarly , for b , you remove ( 5 / 12 ) * 9 - - - > b remaining = 15 - ( 5 / 12 ) * 9 = 45 / 4 and then add 9 more litres of b - - - > 9 + 45 / 4 = 81 / 4 thus a / b ( final ratio ) = ( 45 / 4 ) / ( 81 / 4 ) = 7 : 9 , the same as the final ratio mentioned in the question . hence c is the correct answer . a / b = 7 / 9 = ( 7 x - ( 7 / 12 ) * 9 ) / ( 5 x - ( 5 / 12 ) * 9 + 9 ) , where 7 x and 5 x are initial quantities of a and b respectively . thus , 7 / 9 = ( 7 x - ( 7 / 12 ) * 9 ) / ( 5 x - ( 5 / 12 ) * 9 + 9 ) - - - > giving you x = 3 . thus a ( original ) q = 7 * 3 = 21 . c"
Answer: c
Problem: a sum of money at simple interest amounts to rs . 855 in 3 years and to rs . 854 in 4 years . the sum is :
Options: a ) s . 650 , b ) s . 690 , c ) s . 738 , d ) s . 700 , e ) s . 718
Rationale: "s . i . for 1 year = rs . ( 854 - 815 ) = rs . 39 . s . i . for 3 years = rs . ( 39 x 3 ) = rs . 117 . principal = rs . ( 855 - 117 ) = rs . 738 . answer : option c"
Answer: c
Problem: a salesperson received a commission of 3 percent of the sale price for each of the first 100 machines that she sold and 4 percent of the sale price for each machine that she sold after the first 100 . if the sale price of each machine was $ 10,000 and the salesperson received a $ 42,000 commission , how many machines did she sell ?
Options: a ) 90 , b ) 103 , c ) 130 , d ) 115 , e ) 120
Rationale: first 100 machines = 3 % commission = 0.03 * 100 * 10000 = 30000 commission from sale of next machines = 42000 - 30000 = 12000 so 30 more machines . . total = 130 machines imo c . . .
Answer: c
Problem: in a class of students , 1 / 2 of the number of girls is equal to 1 / 6 of the total number of students . what is the ratio of boys to girls in the class ?
Options: a ) 1 / 2 , b ) 2 / 3 , c ) 2 / 1 , d ) 3 / 2 , e ) 4 / 3
Rationale: "( 1 / 2 ) g = ( 1 / 6 ) ( b + g ) 6 g = 2 b + 2 g 4 g = 2 b b / g = 2 / 1 . the answer is c ."
Answer: c
Problem: if x is less than y by 45 % then y exceed x by :
Options: a ) 33.33 % , b ) 25 % , c ) 81.81 % , d ) 66.66 % , e ) none of these
Rationale: "using formula ( x / ( 100 - x ) * 100 ) where x is percentage decrease ( here it is 25 % ) = > 45 / ( 100 - 45 ) * 100 = 81.81 % answer : c"
Answer: c
Problem: if the least common multiple of two prime numbers x and y is 77 , where x > y , then the value of 2 x + y is
Options: a ) 11 , b ) 17 , c ) 21 , d ) 29 , e ) 33
Rationale: "lcm ( x , y ) = 77 and both x an y are prime . the only values of x and y can be 11 and 7 ( x = 11 and y = 7 ) 2 x + y = 2 * 11 + 7 = 29 correct option : d"
Answer: d
Problem: convert 0.35 in to a vulgar fraction ?
Options: a ) 18 / 50 , b ) 16 / 50 , c ) 7 / 20 , d ) 19 / 50 , e ) none
Rationale: "answer 0.35 = 35 / 100 = 7 / 20 correct option : c"
Answer: c
Problem: how many multiples of 10 are there between 10 and 1000 , exclusive ?
Options: a ) 98 , b ) 99 , c ) 100 , d ) 101 , e ) 97
Rationale: "98 multiples of 5 between 1 and 36 exclusive . from 10 * 2 upto 10 * 99 , ( 2 , 3,4 , . . . , 99 ) . hence , 98 multiples ! correct option is a"
Answer: a
Problem: find the average of all the numbers between 6 and 29 which are divisible by 5 ?
Options: a ) 17 , b ) 20 , c ) 25 , d ) 30 , e ) 15
Rationale: average = ( 10 + 15 + 20 + 25 ) 4 = 70 / 4 = 17 answer is a
Answer: a
Problem: train a leaves the station traveling at 30 miles per hour . two hours later train в leaves the same station traveling in the same direction at 36 miles per hour . how many miles from the station was train a overtaken by train b ?
Options: a ) 320 , b ) 360 , c ) 400 , d ) 440 , e ) 480
Rationale: "after two hours , train a is ahead by 60 miles . train b can catch up at a rate of 6 miles per hour . the time to catch up is 60 / 6 = 10 hours . in 10 hours , train a travels another 30 * 10 = 300 miles for a total of 360 miles . the answer is b ."
Answer: b
Problem: in a flight of 600 km , an aircraft was slowed down due to bad weather . its average speed for the trip was reduced by 200 km / hr and the time of flight increased by 30 minutes . the duration of the flight is ?
Options: a ) 1 hr , b ) 2 hr , c ) 6 hr , d ) 8 hr , e ) 7 hr
Rationale: let the duration of the flight be x hours . then , 600 / x - 600 / ( x + 1 / 2 ) = 200 x ( 2 x + 1 ) = 3 2 x 2 + x - 3 = 0 ( 2 x + 3 ) ( x - 1 ) = 0 x = 1 hr . answer : a
Answer: a
Problem: solve the quickfire maths brain teaser √ 9 % = ?
Options: a ) 30 % , b ) 40 % , c ) 85 % , d ) 19 % , e ) 29 %
Rationale: "a 30 % √ 9 % = > √ 9 / √ 100 = > 3 / 10 = > 30 / 100 = > 30 %"
Answer: a
Problem: balls of equal size are arranged in rows to form an equilateral triangle . the top most row consists of one ball , the 2 nd row of two balls and so on . if 789 balls are added , then all the balls can be arranged in the shape of square and each of the sides of the square contain 8 balls less than the each side of the triangle did . how many balls made up the triangle ?
Options: a ) 1711 , b ) 2209 , c ) 2878 , d ) 1210 , e ) 1560
Rationale: "as expected , this question boils down to 2 equation , consider total number of balls in triangle = t and number of balls in last row = x . 1 + 2 + 3 + . . . + x = t x ( x + 1 ) / 2 = t - - - - ( a ) as mentioned in the question , side of a square will be ( x - 8 ) and total number of balls in square will be ( t + 789 ) ( x - 8 ) ^ 2 = t + 789 - - - - - ( b ) now the hardest part of the question will be to solve these 2 equations and this looks like time consuming but the easy way will be plug and play . also , we ' ve to find a value of t ( from 5 optiosn given below ) which can make a square of a a number . one we know this , it will be a cake walk . we can see that option a fits this criteria in eq ( b ) . add - 1711 + 789 = 2500 = 50 ^ 2 = ( x - 8 ) ^ 2 hence , x = 58 . cross check by putting in eq ( a ) = x ( x + 1 ) / 2 = t = > 58 * 59 / 2 = 1711 hence , answer is a ."
Answer: a
Problem: the average of 20 numbers is calculated as 30 . it is discovered later on that while calculating the average , one number namely 36 was wrongly read as 26 . the correct average is ?
Options: a ) 40 , b ) 26 , c ) 60 , d ) 97 , e ) 12
Rationale: "20 * 30 + 36 – 26 = 160 / 10 = 60 answer : 60 answer is c"
Answer: c
Problem: when n is divided by 12 , the remainder is 2 . what is the remainder when 4 n is divided by 5 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "let n = 2 ( leaves a remainder of 2 when divided by 15 ) 4 n = 4 ( 2 ) = 8 , which leaves a remainder of 3 when divided by 5 . answer c"
Answer: c
Problem: s is a set of 64 consecutive multiples of 4 . if the smallest number in s is 68 , then the greatest number in s is
Options: a ) 198 , b ) 297 , c ) 320 , d ) 402 , e ) 405
Rationale: last term = first term + ( total no . of terms - 1 ) consecutive difference s is a set of 64 consecutive multiples of 4 . if the smallest number in s is 68 , then the greatest number in s is first term = 68 ; total terms = 64 ; difference = 4 68 + ( 63 ) 4 = 320 ans c
Answer: c
Problem: the “ s - number ” of a number x is defined as the ones digit of 2 ^ x . antony rolls a die with 6 sides labeled with the integers from 1 to 6 , each of which has an equal probability of landing face - up . he then takes 3 ^ s , where s is the s - number of the result of his die roll , and plots 3 ^ s on a number line as the point a . finally , he repeats this entire process , this time plotting the result as the point b . what is the probability that the distance between a and b is greater than the value of b ?
Options: a ) 3 / 8 , b ) 13 / 36 , c ) 17 / 36 , d ) 19 / 36 , e ) 23 / 36
Rationale: if you calculate 3 ^ s for 1 st roll , all 6 results will be 9 , 81 , 6561 , 729 , 9 , 81 . this result is the same for 2 nd roll . 9 , 81 , 6561 , 729 , 9 , 81 . about distance : if the first result is 9 and the second is also 9 , the distance is 9 - 9 = 0 which is smaller than 9 . if the first result is 9 and the second is 81 , the distance is 81 - 9 = 72 which is also smaller than b which has the value of 81 . if the first result is 81 and the second is 9 , the distance will be greater than b . distance 81 - 9 = 72 > 9 . on the first roll , the probability of getting result 9 is 2 / 6 . in this case no other alternative values for second roll which would make the distance greater than b . so probability is 0 . so next estimations are : probability of getting 81 on the first roll ( 2 / 6 ) * probability of getting 9 on the second roll ( 2 / 6 ) = 1 / 9 probability of getting 729 on the first roll ( 1 / 6 ) * probability of getting 9 , 81 on the second roll ( 4 / 6 ) = 1 / 9 probability of getting 6561 on the first roll ( 1 / 6 ) * probability of getting 9 , 81 , 729 on the first roll ( 5 / 6 ) = 5 / 36 all together : 1 / 9 + 1 / 9 + 5 / 36 = 13 / 36 = b
Answer: b
Problem: two numbers are respectively 20 % and 50 % more than a third number . what percentage is the first of the second ?
Options: a ) 25 % , b ) 60 % , c ) 80 % , d ) 55 % , e ) 74 %
Rationale: "required answer = ( 100 + x ) / ( 100 + y ) * 100 = 120 * 100 / 150 = 80 % answer is c"
Answer: c
Problem: calculate how much time could be saved if the train would run at its usual speed , given that it ran at 3 / 4 of its own speed and got to its destination in 10 hours ?
Options: a ) 1.5 hrs , b ) 2.5 hrs , c ) 3.5 hrs , d ) 1.2 hrs , e ) 2.9 hrs
Rationale: "new speed = 3 / 4 of usual speed new time = 3 / 4 of usual time 3 / 4 of usual time = 10 hrs usual time = 10 * 3 / 4 = 7.5 hrs time saved = 10 - 7.5 = 2.5 hrs answer is b"
Answer: b
Problem: angelina walked 1200 meters from her home to the grocery at a constant speed . she then walked 480 meters to the gym at double the speed . she spent 40 seconds less on her way from the grocery to the gym than on her way from home to the grocery . what was angelina ' s speed , in meters per second , from the grocery to the gym ?
Options: a ) 12 , b ) 23 , c ) 34 , d ) 48 , e ) 52
Rationale: "let the speed be x . . . so time taken from home to grocery = 1200 / x . . the speed to gym = 2 x . . so time taken = 480 / 2 x = 240 / x . . its given 1200 / x - 240 / x = 40 . . 960 / x = 40 . . x = 24 m / secs . . so grocery to gym = 2 * 24 = 48 m / s . . . d"
Answer: d
Problem: a waiter ' s salary consists of his salary and tips . during one week his tips were 5 / 2 of his salary . what fraction of his income came from tips ?
Options: a ) 4 / 9 , b ) 5 / 4 , c ) 5 / 8 , d ) 5 / 7 , e ) 6 / 9
Rationale: income = salary ( s ) + tips = s + s * 5 / 2 = s * 7 / 2 tips = s * 7 / 2 fraction of his income came from tips = ( s * 5 / 2 ) / ( s * 7 / 2 ) = 5 / 7 answer : d
Answer: d
Problem: if a certain number x is divided by 82 , the reminder is 5 . what is the reminder when x + 7 is divided by 41 ?
Options: a ) 12 , b ) 5 , c ) 6 , d ) 16 , e ) 18
Rationale: "x can be written as 82 k + 5 or x = 5 , 87,169 , etc . when k = 0 , 1,2 etc x + 7 = 82 k + 5 + 7 = 82 k + 12 or x + 7 = 12,94 , 176 etc . k = 0 , 1,2 when divided by 41 , we will get the remainder 12 . a"
Answer: a
Problem: a reduction of 50 % in the price of apples would enable a man to obtain 80 more for rs . 55 , what is reduced price per dozen ?
Options: a ) 1 , b ) 3 , c ) 4 , d ) 7 , e ) 10
Rationale: c 55 * ( 50 / 100 ) = 28 - - - 64 ? - - - 12 = > rs . 4
Answer: c
Problem: what is the next number : 3 , 18 , 258 , __
Options: a ) 2928 , b ) 3638 , c ) 4098 , d ) 4418 , e ) 5378
Rationale: "4 ^ 0 + 2 = 3 4 ^ 2 + 2 = 18 4 ^ 4 + 2 = 258 4 ^ 6 + 2 = 4098 the answer is c ."
Answer: c
Problem: cindy has her eye on a sundress but thinks it is too expensive . it goes on sale for 15 % less than the original price . before cindy can buy the dress , however , the store raises the new price by 25 % . if the dress cost $ 85 after it went on sale for 15 % off , what is the difference between the original price and the final price ?
Options: a ) $ 0.00 , b ) $ 1.00 , c ) $ 3.40 , d ) $ 5.00 , e ) $ 6.25
Rationale: "0.85 * { original price } = $ 85 - - > { original price } = $ 100 . { final price } = $ 85 * 1.25 = $ 106.25 . the difference = $ 106.25 - $ 100 = $ 6.25 . answer : e ."
Answer: e
Problem: how many books each of volume 200 meter cube can be packed into a crate of volume 4000 meter cube ?
Options: a ) 20 , b ) 40 , c ) 60 , d ) 80 , e ) can not be determined
Rationale: "gud question with a simple concept . in geo if we want to insert one shape into another we need to know the dimensions of the two shapes . in above with volume given , we can come up with different shapes , so we cant know the answer for ex : 4000 m 3 can be 400 * 10 or 40 * 100 or just 4000 * 1 we do n ' t know , so we cant calculate answer : e"
Answer: e
Problem: a committee is reviewing a total of 20 x black - and - white films and 6 y color films for a festival . if the committee selects y / x % of the black - and - white films and all of the color films , what fraction q of the selected films are in color ?
Options: a ) 1 / 130 , b ) 1 / 5 , c ) 3 / 13 , d ) 10 / 13 , e ) 30 / 31
Rationale: it ' s y / xpercentnot y / x . if x = 20 and y = 10 . then : 20 x = 400 black - and - white films ; 6 y = 60 color films . y / x % = 10 / 20 % = 0.5 % of the black - and - white films , so 2 black - and - white films and all 60 color films , thus total of 62 films were selected . color films thus compose q = 60 / 62 = 30 / 31 of the selected films . answer : e .
Answer: e
Problem: a train travels 125 km in 2.5 hours and 270 km in 3 hours . find the average speed of train .
Options: a ) 80 kmph , b ) 60 kmph , c ) 72 kmph , d ) 90 kmph , e ) none of these
Rationale: "as we know that speed = distance / time for average speed = total distance / total time taken thus , total distance = 125 + 270 = 395 km thus , total speed = 5.5 hrs or , average speed = 5 = 395 / 5.5 or , 72 kmph . answer : c"
Answer: c
Problem: if 4 x = 6 y = z , what is x + y , in terms of z ?
Options: a ) z / 2 , b ) 5 z / 12 , c ) z / 3 , d ) 3 z / 5 , e ) z / 9
Rationale: "4 x = 6 y = z x = z / 4 and y = z / 6 x + y = z / 4 + z / 6 = 5 z / 12 answer is b"
Answer: b
Problem: when x is even , [ x ] = x / 2 + 1 , when x is odd [ x ] = 2 x + 1 then [ 7 ] * [ 8 ] = ?
Options: a ) [ 22 ] , b ) [ 44 ] , c ) [ 75 ] , d ) [ 88 ] , e ) [ 90 ]
Rationale: "[ 7 ] * [ 8 ] = ( 7 * 2 + 1 ) ( 8 / 2 + 1 ) = [ 75 ] . ans - c"
Answer: c
Problem: the price of a car is marked at $ 12,000 . if the car has successive discounts of 20 % , 15 % and 5 % , then at what price does a customer buy the car ?
Options: a ) $ 7524 , b ) $ 7752 , c ) $ 7880 , d ) $ 8196 , e ) $ 8324
Rationale: 0.95 * 0.85 * 0.8 * 12000 = $ 7752 the answer is b .
Answer: b
Problem: a dealer offers a cash discount of 10 % and still makes a profit of 20 % when he further allows 45 articles to be sold at the cost price of 40 articles to a particular sticky bargainer . how much percent above the cost price were his articles listed ?
Options: a ) 40 % , b ) 50 % , c ) 55 % , d ) 80 % , e ) 90 %
Rationale: "given cash discount - 10 % profit - 20 % items sold - 45 price sold at = list price of 40 assume list price = $ 10 total invoice = $ 400 - 10 % cash discount = $ 360 let cost price of 45 items be x so total cost = 45 * x given the shopkeeper had a profit of 20 % 45 * x * 120 / 100 = 360 or x = $ 20 / 3 = $ 6 + ( 2 / 3 ) which means his products were listed at $ 10 which is a 50 % markup over $ 6 + ( 2 / 3 ) answer b"
Answer: b
Problem: at the end of year x , automobile installment credit accounted for 20 % of all outstanding consumer installment credit . at that time automobile finance companies extended $ 57 billion of credit , or 1 / 3 of the automobile installment credit . how many billion dollars of consumer installment credit was outstanding at that time ?
Options: a ) 171 , b ) 855 , c ) 870 , d ) 788 , e ) 684
Rationale: "system of equations a = ( 20 / 100 ) c ( 1 / 3 ) a = 57 - - > a = 171 substitution 171 = ( 20100 ) c c = ( 100 / 20 ) 171 - calculate 171 / 20 * 100 the correct answer b . the answer is 855 ."
Answer: b
Problem: a man can row upstream at 32 kmph and downstream at 48 kmph , and then find the speed of the man in still water ?
Options: a ) 22 , b ) 37 , c ) 30 , d ) 27 , e ) 40
Rationale: "us = 32 ds = 48 m = ( 48 + 32 ) / 2 = 40 answer : e"
Answer: e
Problem: the ratio between the length and the breadth of a rectangular park is 3 : 2 . if a man cycling alongthe oundary of the park at the speed of 12 km / hr completes one round in 8 minutes , then the area of the park ( in sq . m ) is
Options: a ) 124345 m , b ) 233234 m , c ) 153600 m , d ) 123567 m , e ) 168999 m
Rationale: "perimeter = distance covered in 8 min . = 12000 x 8 m = 1600 m . 60 let length = 3 x metres and breadth = 2 x metres . then , 2 ( 3 x + 2 x ) = 1600 or x = 160 . length = 480 m and breadth = 320 m . area = ( 480 x 320 ) m 2 = 153600 m c"
Answer: c
Problem: the radius of the two circular fields is in the ratio 3 : 10 the area of the first field is what percent less than the area of the second ?
Options: a ) 71 % , b ) 51 % , c ) 91 % , d ) 81 % , e ) 61 %
Rationale: "r = 3 ï € r 2 = 9 r = 10 ï € r 2 = 100 100 ï € â € “ 9 ï € = 91 100 - - - - ? = > 91 % . answer : c"
Answer: c
Problem: 3 buffaloes eat as much as 4 cows or 2 oxen . at a farm , there are 15 buffaloes , 8 oxen , and 24 cows . the fodder for these cattle is available for 24 days . if 60 more cows and 30 more buffaloes are brought in , how many days will the fodder last ?
Options: a ) 6 , b ) 9 , c ) 12 , d ) 15 , e ) 18
Rationale: "2 oxen = 3 buffaloes = 4 cows also : 15 buffaloes + 8 oxen + 24 cows = 10 oxen + 8 oxen + 12 oxen = 30 oxen there is enough fodder for 1 oxen for 30 * 24 days . 60 cows + 30 buffaloes = 30 oxen + 20 oxen = 50 oxen the new total is equal to 80 oxen instead of 30 oxen . 30 * 24 / 80 oxen = 9 days the answer is b ."
Answer: b
Problem: an woman swims downstream 64 km and upstream 24 km taking 8 hours each time ; what is the speed of the current ?
Options: a ) 1.6 , b ) 1.8 , c ) 3.5 , d ) 1.5 , e ) 2.5
Rationale: "64 - - - 8 ds = 8 ? - - - - 1 24 - - - - 8 us = 3 ? - - - - 1 s = ? s = ( 8 - 3 ) / 2 = 2.5 answer : e"
Answer: e
Problem: what is 30 % of 210 ?
Options: a ) 61 , b ) 63 , c ) 65 , d ) 67 , e ) 69
Rationale: "x / 210 = 30 / 100 100 x = 210 x 30 x = ( 210 x 30 ) / 100 x = 6300 / 100 = 63 answer = b = 63"
Answer: b
Problem: company x provides bottled water to its employees in 1 liter bottles , $ 2 each . at least how many 1 l bottles must company x buy monthly , so that new contract with $ 50 fixed monthly rate and $ 1 for 10 l bottle each paid off ? ( assume that no other costs apply )
Options: a ) 28 , b ) 29 , c ) 30 , d ) 31 , e ) 27
Rationale: let the no . of 1 liter bottles be x , so the no . of 10 l bottles will be x / 10 ( to equate the vol . ) since the total cost will be equal , 2 x = 50 + x / 10 so x = 26.31 or 27 . answer is ( e ) .
Answer: e
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 15.3 years , the ratio of the number of boys to the number of girls in the class is
Options: a ) 7 : 3 , b ) 2 : 3 , c ) 9 : 3 , d ) 6 : 3 , e ) 5 : 6
Rationale: "explanation : let the ratio be k : 1 . then , k * 16.4 + 1 * 15.3 = ( k + 1 ) * 15.8 < = > ( 16.4 - 15.8 ) k = ( 15.8 - 15.3 ) < = > k = 0.5 / 0.6 = 5 / 6 . required ratio = 5 / 6 : 1 = 5 : 6 . answer : e"
Answer: e
Problem: a train can travel 50 % faster than a car . both start from point a at the same time and reach point b 75 kms away from a at the same time . on the way , however , the train lost about 12.5 minutes while stopping at the stations . what is the speed of the car ?
Options: a ) 22 , b ) 28 , c ) 120 , d ) 287 , e ) 278
Rationale: let speed of the car = x kmphthen speed of the train = ( 100 + 50 ) 100 x = 150100 x = 32 x kmphtime taken by the car to travel from a to b = 75 x hourstime taken by the train to travel from a to b = 75 ( 32 x ) + 12.560 hourssince both start from a at the same time and reach point b at the same time 75 x = 75 ( 32 x ) + 12.56025 x = 12.560 x = 25 × 6012.5 = 2 × 60 = 120 answer : c
Answer: c
Problem: if the sides of a triangle are 39 cm , 32 cm and 10 cm , what is its area ?
Options: a ) 120 , b ) 772 , c ) 288 , d ) 160 , e ) 2848
Rationale: "the triangle with sides 39 cm , 32 cm and 10 cm is right angled , where the hypotenuse is 39 cm . area of the triangle = 1 / 2 * 32 * 10 = 160 cm 2 answer : d"
Answer: d
Problem: the remainder when q = 1 + 3 + 3 ^ 2 + 3 ^ 3 + . . . . . . . . . . + 3 ^ 200 is divided 13 .
Options: a ) 12 , b ) 7 , c ) 0 , d ) 5 , e ) 3
Rationale: q = 1 + 3 + 3 ^ 2 + 3 ^ 3 + . . . . . . . . . . . . . . . . . . + 3 ^ 200 is a geometric progression having common ratio as ' 3 ' and number of terms as ' 201 ' . since sum to n terms in gp = a ( r ^ n - 1 ) / ( r - 1 ) where a = first term and r = common ration hence , 1 * ( 3 ^ 201 - 1 ) / ( 3 - 1 ) rem of ( 3 ^ 201 - 1 ) / 2 divided by 13 3 ^ 201 - 1 / 26 wkt , 3 ^ 3 = 27 = 26 + 1 { ( 26 + 1 ) ^ 67 - 1 } / 26 { 1 - 1 } / 26 = > 0 . c
Answer: c
Problem: p and q invested in a shop . the profits were divided in the ratio of 5 : 2 respectively . if p invested rs . 5600 , the amount invested by q is :
Options: a ) 3500 , b ) 5600 , c ) 2200 , d ) 2400 , e ) none
Rationale: suppose q invested rs . y . then , 5600 / y = 5 / 2 or y = [ 5600 x 2 / 5 ] = 2240 answer e
Answer: e
Problem: a car gets 20 kilometers per gallon of gasoline . how many gallons of gasoline would the car need to travel 120 kilometers ?
Options: a ) 8.5 gallons , b ) 5 gallons , c ) 7 gallons , d ) 5.5 gallons , e ) 6 gallons
Rationale: "each 20 kilometers , 1 gallon is needed . we need to know how many 20 kilometers are there in 120 kilometers ? 120 / 20 = 4.5 * 1 gallon = 6 gallons correct answer e"
Answer: e
Problem: a cuboidal block 6 cm x 9 cm x 12 cm is cut up into an exact number of equal cubes . the least possible number of equal cubes will be
Options: a ) 6 , b ) 9 , c ) 24 , d ) 30 , e ) 35
Rationale: explanation : volume of block = ( 6 x 9 x 12 ) cm 3 = 648 cm 3 side of largest cube = h . c . f of 6 , 912 = 3 cm volume of the cube = ( 3 x 3 x 3 ) = 27 cm 3 number of cubes = ( 648 / 27 ) = 24 answer : c
Answer: c
Problem: in a class of 25 students , 2 students did not borrow any books from the library , 12 students each borrowed 1 book , 4 students each borrowed 2 books , and the rest borrowed at least 3 books . if the average number of books per student was 2 , what is the maximum number of books any single student could have borrowed ?
Options: a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12
Rationale: "the total number of books the students borrowed is 25 * 2 = 50 . the students who borrowed zero , one , or two books borrowed 12 * 1 + 4 * 2 = 20 books . the 7 students who borrowed at least three books borrowed 50 - 20 = 30 books . if 6 of these students borrowed exactly 3 books , then the maximum that one student could have borrowed is 30 - 18 = 12 books . the answer is e ."
Answer: e
Problem: the sector of a circle has radius of 21 cm and central angle 180 o . find its perimeter ?
Options: a ) 91.5 , b ) 92 , c ) 108 , d ) 94 , e ) 95
Rationale: "perimeter of the sector = length of the arc + 2 ( radius ) = ( 135 / 360 * 2 * 22 / 7 * 21 ) + 2 ( 21 ) = 108 cm answer : option c"
Answer: c
Problem: beginning in town a , biker bob rides his bike 30 miles west , 6 miles north , 15 miles east , and then 18 miles north , to town b . how far apart are town a and town b ? ( ignore the curvature of the earth . )
Options: a ) 27 miles , b ) 25 miles , c ) 24 miles , d ) 28.3 miles , e ) 23 miles
Rationale: "using pythagoras we have one side i , e total distance traveled in north direction = 18 + 6 = 24 m other being the base ie distance traveled west - distance traveled eat = 30 - 15 = 15 m now this third side or the distance between town a and town b = 24 ^ 2 + 15 ^ 2 = sq root 801 = 28.3 m answer : d"
Answer: d
Problem: a bowl of nuts is prepared for a party . brand p mixed nuts are 20 % almonds and brand q ' s deluxe nuts are 25 % almonds . if a bowl contains a total of 68 ounces of nuts , representing a mixture of both brands , and 15 ounces of the mixture are almonds , how many ounces of brand q ' s deluxe mixed nuts are used ?
Options: a ) 16 , b ) 28 , c ) 32 , d ) 44 , e ) 48
Rationale: "lets say x ounces of p is mixed with q . = > 68 - x ounces of q is present in the mixture ( as the total = 68 ounces ) given total almond weight = 15 ounces ( 20 x / 100 ) + ( 25 / 100 ) ( 68 - x ) = 15 = > x = 40 = > 68 - 40 = 28 ounces of q is present in the mixture . answer is b ."
Answer: b
Problem: two trains 200 m and 300 m long run at the speed of 70 kmph and 50 kmph in opposite directions in parallel tracks . the time which they take to cross each other is ?
Options: a ) 10 sec , b ) 15 sec , c ) 18 sec , d ) 20 sec , e ) 22 sec
Rationale: "relative speed = 70 + 50 = 120 kmph * 5 / 18 = 100 / 3 m / s distance covered in crossing each other = 200 + 300 = 500 m required time = 500 * 3 / 100 = 15 sec answer is b"
Answer: b
Problem: find the area of a parallelogram with base 12 cm and height 10 cm ?
Options: a ) 297 cm 2 , b ) 384 cm 2 , c ) 120 cm 2 , d ) 267 cm 2 , e ) 186 cm 2
Rationale: "area of a parallelogram = base * height = 12 * 10 = 120 cm 2 answer : c"
Answer: c
Problem: 6 lights begin to flash together at 12 : 00 noon and flash respectively at intervals of 3 , 4 , 5 , 6 , 7 , and 8 seconds . not including the flash at 12 : 00 noon , how many more times will all 6 lights flash together before 1 : 00 pm ( i . e . one hour later ) ?
Options: a ) 4 , b ) 6 , c ) 8 , d ) 10 , e ) 12
Rationale: the least common multiple is 2 * 2 * 2 * 3 * 5 * 7 = 840 . 3600 seconds / 840 = 4 + remainder . the answer is a .
Answer: a
Problem: a is the hundreds digit of the 3 digit integer x , b is the tens digit of x , and c is the units digit of x . 2 a = b = 4 c , and a > 0 . what is the difference between the two greatest possible values of x ? tip : dont stop till you have exhausted all answer choices to arrive at the correct one .
Options: a ) 124 , b ) 241 , c ) 394 , d ) 421 , e ) 842
Rationale: ratio of a : b : c = 2 : 4 : 1 two possible greatest single digit values for b are 8 and 4 if b is 8 , then x = 482 if b is 4 , then x = 241 difference = 482 - 241 = 241 b is the answer
Answer: b
Problem: find the slope of the line perpendicular to the line y = ( 1 / 2 ) x - 7
Options: a ) 1 , b ) 2 , c ) - 2 , d ) 4 , e ) 5
Rationale: "two lines are perpendicular if the product of their slopes is equal to - 1 . the slope of the given line is equal to 1 / 2 . if m is the slope of the line perpendicular to the given line , then m × ( 1 / 2 ) = - 1 solve for m m = - 2 correct answer c ) - 2"
Answer: c
Problem: the sale price of an article including the sales tax is rs . 616 . the rate of sales tax is 10 % . if the shopkeeper has made a profit of 25 % , then the cost price of the article is :
Options: a ) 500 , b ) 277 , c ) 222 , d ) 448 , e ) 111
Rationale: "explanation : 110 % of s . p . = 616 s . p . = ( 616 * 100 ) / 110 = rs . 560 c . p = ( 100 * 560 ) / 125 = rs . 448 answer : d"
Answer: d
Problem: the triplicate ratio of 1 : 2 is ?
Options: a ) 1 : 7 , b ) 1 : 8 , c ) 1 : 3 , d ) 1 : 1 , e ) 1 : 2
Rationale: "13 : 23 = 1 : 8 answer : b"
Answer: b
Problem: a number with an interesting property : when i divide it by 2 , the remainder is 1 . when i divide it by 3 , the remainder is 2 . when i divide it by 4 , the remainder is 3 . when i divide it by 5 , the remainder is 4 . when i divide it by 6 , the remainder is 5 . when i divide it by 7 , the remainder is 6 . when i divide it by 8 , the remainder is 7 . when i divide it by 9 , the remainder is 8 . when i divide it by 10 , the remainder is 9 . it ' s not a small number , but it ' s not really big , either . when i looked for a smaller number with this property i could n ' t find one . can you find it ?
Options: a ) 2588 , b ) 2474 , c ) 2254 , d ) 2519 , e ) 8725
Rationale: d 2519 the number has to end in 9 . looked brute force for small numbers . 59 and 119 were promising , but no cigar . then looked for agreement among 39 + multiples of 40 , 69 + multiples of 70 and 89 + multiples of 90 smallest one was 2519 .
Answer: d
Problem: 65 % of a number is 21 less than 4 / 5 th of that number . what is the number ?
Options: a ) 100 , b ) 120 , c ) 140 , d ) 130 , e ) 115
Rationale: let the number be x then , 4 x / 5 - ( 65 % of x ) = 21 4 x / 5 - 65 x / 100 = 21 x = 140 answer is c
Answer: c
Problem: what is the sum of the integers 45 through 175 inclusive ?
Options: a ) 12,295 , b ) 13,000 , c ) 14,300 , d ) 14,410 , e ) 28,820
Rationale: "sum of n consecutive positive integers = n ( n + 1 ) / 2 . . in one case n = 44 and other 175 . . . subtract the sum to get the answer sum of first 175 + ive numbers = 175 * 176 / 2 = 15400 . . sum of first 45 + i ' ve numbers = 45 * 44 / 2 = 990 . . answer = 15400 - 990 = 14410 answer : d"
Answer: d
Problem: the ratio of males to females in a class is 2 : 3 . the career preferences of the students in the class are represented in a circle graph . if the area of the graph allocated to each career preference is proportional to the number of students who have that career preference , how many degrees of the circle should be used to represent a career that is preferred by one - half of the males and one - fourth of the females in the class ?
Options: a ) 120 , b ) 126 , c ) 132 , d ) 138 , e ) 144
Rationale: "1 / 2 * 2 / 5 + 1 / 4 * 3 / 5 = 4 / 20 + 3 / 20 = 7 / 20 the number of degrees is 7 / 20 * 360 = 126 degrees the answer is b ."
Answer: b
Problem: a vendor sells 60 percent of the apples he had and throws away 40 percent of the remainder . the next day , the vendor sells 50 percent of the remaining apples and throws away the rest . in total , what percent of his apples does the vendor throw away ?
Options: a ) 24 , b ) 26 , c ) 28 , d ) 30 , e ) 32
Rationale: "let x be the original number of apples . on day one , the vendor throws away ( 0.4 ) ( 0.4 ) x = 0.16 x . the remaining apples are ( 0.6 ) ( 0.4 ) x = 0.24 x . on day two , the vendor throws away ( 0.5 ) ( 0.24 ) x = 0.12 x . the vendor throws away a total of 0.16 x + 0.12 x = 0.28 x . the vendor throws away 28 percent of the apples . the answer is c ."
Answer: c
Problem: a vendor sells 80 percent of the pears he had and throws away 50 percent of the remainder . the next day , the vendor sells 80 percent of the remaining pears and throws away the rest . in total , what percent of his pears does the vendor throw away ?
Options: a ) 6 , b ) 8 , c ) 10 , d ) 12 , e ) 14
Rationale: "let x be the original number of pears . on day one , the vendor throws away ( 0.5 ) ( 0.2 ) x = 0.1 x . the remaining pears are ( 0.5 ) ( 0.2 ) x = 0.1 x . on day two , the vendor throws away ( 0.2 ) ( 0.1 ) x = 0.02 x . the vendor throws away a total of 0.1 x + 0.02 x = 0.12 x . the vendor throws away 12 percent of the pears . the answer is d ."
Answer: d
Problem: a train 700 m long can cross an electric pole in 20 sec and then find the speed of the train ?
Options: a ) 117 kmph , b ) 178 kmph , c ) 126 kmph , d ) 118 kmph , e ) 119 kmph
Rationale: "length = speed * time speed = l / t s = 700 / 20 s = 35 m / sec speed = 35 * 18 / 5 ( to convert m / sec in to kmph multiply by 18 / 5 ) speed = 126 kmph answer : c"
Answer: c
Problem: the average weight of 8 persons increases by 3.5 kg when a new person comes in place of one of them weighing 65 kg . what might be the weight of the new person ?
Options: a ) 75 kg , b ) 65 kg , c ) 55 kg , d ) 85 kg , e ) 93 kg
Rationale: "total weight increased = ( 8 x 3.5 ) kg = 28 kg . weight of new person = ( 65 + 28 ) kg = 93 kg . answer : e"
Answer: e
Problem: an industrial loom weaves 1.14 meters of cloth every second . approximately , how much time will it take to weave 52 meters of cloth ?
Options: a ) 29.32 sec , b ) 42.51 sec , c ) 39.25 sec , d ) 45.61 sec , e ) none of these
Rationale: explanation : given loom weaves 1.14 mts of cloth in one second then 52 mts of cloth can be weaved by loom in , 1.14 - - - - - 1 52.0 - - - - - - ? = > 52 / 1.14 = 45.61 sec answer is d
Answer: d
Problem: one pipe can fill a tank three times as fast as another pipe . if together the two pipes can fill tank in 37 min , then the slower pipe alone will be able to fill the tank in ?
Options: a ) 229 , b ) 787 , c ) 144 , d ) 148 , e ) 121
Rationale: "let the slower pipe alone fill the tank in x min . then , faster pipe will fill it in x / 3 min . 1 / x + 3 / x = 1 / 37 4 / x = 1 / 37 = > x = 148 min . answer : d"
Answer: d
Problem: if 10 machines can produce 20 units in 10 hours , how long would it take 40 machines to produce 100 units ?
Options: a ) 9.5 , b ) 6.4 , c ) 2.3 , d ) 8.9 , e ) 12.5
Rationale: "10 machines would produce 100 units in 50 hours . increasing the amount of machines by 4 would mean dividing 50 hours by 4 . 50 / 4 = 12.5 answer : e"
Answer: e
Problem: when positive integer n is divided by positive integer j , the remainder is 14 . if n / j = 134.07 , what is value of j ?
Options: a ) 22 , b ) 56 , c ) 78 , d ) 200 , e ) 175
Rationale: "1 ) we know that decimal part of decimal quotient = { remainder / divisor } so 0.07 , the decimal part of the decimal quotient , must equal the remainder , 14 , divided by the divisor j . 0.07 = 14 / j 0.07 * j = 14 j = 14 / 0.07 = 1400 / 7 = 200 so j = 200 , answer = d ."
Answer: d
Problem: if m : n is 2 : 9 and n : p is 9 : 4 then m : p is equal to
Options: a ) 1 : 4 , b ) 1 : 3 , c ) 5 : 2 , d ) 3 : 2 , e ) 1 : 2
Rationale: the two ratios given are having the same number 9 for n in both the ratios . hence - m : n = 2 : 9 n : p = 9 : 4 = > m : p = 2 : 4 = > 1 : 2 answer e
Answer: e
Problem: the product of two numbers is 1320 and their h . c . f is 6 . the l . c . m of the numbers is
Options: a ) 220 , b ) 1314 , c ) 1326 , d ) 7920 , e ) none
Rationale: "solution l . c . m = product of numbers / h . c . f ‹ = › 1320 / 6 ‹ = › 220 . answer a"
Answer: a