regisss/math_qa huggingface dataset:
Problem: two dogsled teams raced across a 300 mile course in wyoming . team a finished the course in 3 fewer hours than team w . if team a ' s average speed was 5 mph greater than team w ' s , what was team w ' s average mph ?
Options: a ) 12 , b ) 15 , c ) 18 , d ) 20 , e ) 25
Rationale: "this is a very specific format that has appeared in a handful of real gmat questions , and you may wish to learn to recognize it : here we have a * fixed * distance , and we are given the difference between the times and speeds of two things that have traveled that distance . this is one of the very small number of question formats where backsolving is typically easier than solving directly , since the direct approach normally produces a quadratic equation . say team w ' s speed was s . then team w ' s time is 300 / s . team a ' s speed was then s + 5 , and team a ' s time was then 300 / ( s + 5 ) . we need to find an answer choice for s so that the time of team a is 3 less than the time of team w . that is , we need an answer choice so that 300 / ( s + 5 ) = ( 300 / s ) - 3 . you can now immediately use number properties to zero in on promising answer choices : the times in these questions will always work out to be integers , and we need to divide 300 by s , and by s + 5 . so we want an answer choice s which is a factor of 300 , and for which s + 5 is also a factor of 300 . so you can rule out answers a and c immediately , since s + 5 wo n ' t be a divisor of 300 in those cases ( sometimes using number properties you get to the correct answer without doing any other work , but unfortunately that ' s not the case here ) . testing the other answer choices , if you try answer d , you find the time for team w is 15 hours , and for team a is 12 hours , and since these differ by 3 , as desired , d is correct ."
Answer: d
Problem: if a ( a - 5 ) = 6 and b ( b - 5 ) = 6 where a ≠ b , then a + b =
Options: a ) − 48 , b ) − 2 , c ) 2 , d ) 9 , e ) 5
Rationale: "i . e . if a = - 1 then b = 6 or if a = 6 then b = - 1 but in each case a + b = - 1 + 6 = 5 answer : option e"
Answer: e
Problem: how many positive integers less than 100 have a remainder of 6 when divided by 13 ?
Options: a ) 2 , b ) 7 , c ) 6 , d ) 9 , e ) 10
Rationale: "we have to include 6 also . as 13 * 0 + 6 = 6 if somebody says to divide 6 by 13 , we will be telling we have 0 quotient and remainder as 6 . answer is c"
Answer: c
Problem: given f ( x ) = 3 x – 5 , for what value of x does 2 * [ f ( x ) ] – 1 = f ( 3 x – 6 )
Options: a ) 0 , b ) 4 , c ) 6 , d ) 7 , e ) 13
Rationale: "explanations we have the function f ( x ) = 3 x – 5 , and we want to some sophisticated algebra with it . let ’ s look at the two sides of the prompt equation separately . the left side says : 2 * [ f ( x ) ] – 1 — - this is saying : take f ( x ) , which is equal to its equation , and multiply that by 2 and then subtract 1 . 2 * [ f ( x ) ] – 1 = 2 * ( 3 x – 5 ) – 1 = 6 x – 10 – 1 = 6 x – 11 the right side says f ( 3 x – 6 ) — this means , take the algebraic expression ( 3 x – 6 ) and plug it into the function , as discussed above in the section “ how a mathematician things about a function . ” this algebraic expression , ( 3 x – 6 ) , must take the place of x on both sides of the function equation . f ( 3 x – 6 ) = 3 * [ 3 x – 6 ] – 5 = 9 x – 18 – 5 = 9 x – 23 now , set those two equal and solve for x : 9 x – 23 = 6 x – 11 9 x = 6 x – 11 + 23 9 x = 6 x + 12 9 x – 6 x = 12 3 x = 12 x = 4 answer = b"
Answer: b
Problem: in n is a positive integer less than 200 , and 18 n / 60 is an integer , then n has how many different positive prime factors ?
Options: a ) 2 , b ) 3 , c ) 5 , d ) 6 , e ) 8
Rationale: "( a ) . 18 n / 60 must be an integer . = > 3 n / 10 must be an integer . hence n must be a multiple of 2 * 5 . = > n has 2 different prime integers ."
Answer: a
Problem: the ratio of numbers is 3 : 4 and their h . c . f is 8 . their l . c . m is :
Options: a ) 12 , b ) 96 , c ) 24 , d ) 48 , e ) 98
Rationale: let the numbers be 3 x and 4 x . then their h . c . f = x . so , x = 8 . so , the numbers are 24 and 32 . l . c . m of 24 and 32 = 96 . answer : b
Answer: b
Problem: every year an amount increases by 1 / 8 th of itself . how much will it be after two years if its present value is rs . 59000 ?
Options: a ) 81000 , b ) 81007 , c ) 74671.875 , d ) 81066 , e ) 81022
Rationale: "59000 * 9 / 8 * 9 / 8 = 74671.875 answer : c"
Answer: c
Problem: a person buys an article at rs . 500 . at what price should he sell the article so as to make a profit of 30 % ?
Options: a ) 650 , b ) 882 , c ) 772 , d ) 652 , e ) 271
Rationale: "cost price = rs . 500 profit = 30 % of 500 = rs . 150 selling price = cost price + profit = 500 + 150 = 650 answer : a"
Answer: a
Problem: if the sum and difference of two numbers are 20 and 8 respectively , then the difference of their square is :
Options: a ) 12 , b ) 28 , c ) 160 , d ) 180 , e ) 18
Rationale: "let the numbers be x and y . then , x + y = 20 and x - y = 8 x 2 - y 2 = ( x + y ) ( x - y ) = 20 * 8 = 160 . answer : c"
Answer: c
Problem: raja complete a journey in 10 hours . he travels first half of the journey at the rate of 21 km / hr and second half at the rate of 24 km / hr . find the total journey in km .
Options: a ) 200 km , b ) 250 km , c ) 224 km , d ) 255 km , e ) 260 km
Rationale: consider x - - > ( 1 / 2 ) x / 21 + ( 1 / 2 ) x / 24 = 10 = = > x / 21 + x / 24 = 20 15 x = 168 * 20 = = > 224 km answer c
Answer: c
Problem: the percentage increase in the area of a rectangle , if each of its sides is increased by 20 % is :
Options: a ) 44 % , b ) 46 % , c ) 48 % , d ) 50 % , e ) 51 %
Rationale: "let original length = x metres and original breadth = y metres . original area = ( xy ) m 2 . new length = 120 x m = 6 x m . 100 5 new breadth = 120 y m = 6 y m . 100 5 new area = 6 x x 6 y m 2 = 36 xy m 2 . 5 5 25 the difference between the original area = xy and new - area 36 / 25 xy is = ( 36 / 25 ) xy - xy = xy ( 36 / 25 - 1 ) = xy ( 11 / 25 ) or ( 11 / 25 ) xy increase % = 11 xy x 1 x 100 % = 44 % . 25 xy a"
Answer: a
Problem: a person travels equal distances with speeds of 2 km / hr , 4 km / hr , 6 km / hr . and takes a total time of 11 minutes . find the total distance ?
Options: a ) 1 km , b ) 500 mts , c ) 600 mts , d ) 2 km , e ) 250 mts
Rationale: "let the each distance be x km total distance = 3 x then total time , ( x / 2 ) + ( x / 4 ) + ( x / 6 ) = 11 / 60 x = 0.2 total distance = 3 * 0.2 = 0.6 km = 600 meters correct option is c"
Answer: c
Problem: the ratio of the radius of two circles is 1 : 9 , and then the ratio of their areas is ?
Options: a ) 1 : 8 , b ) 1 : 6 , c ) 1 : 9 , d ) 1 : 3 , e ) 1 : 81
Rationale: "r 1 : r 2 = 1 : 9 π r 12 : π r 22 r 12 : r 22 = 1 : 81 answer : e"
Answer: e
Problem: the average salary of all the workers in a workshop is rs . 9000 . the average salary of 6 technicians is rs . 12000 and the average salary of the rest is rs . 6000 . the total number of workers in the workshop is ?
Options: a ) a ) 23 , b ) b ) 21 , c ) c ) 52 , d ) d ) 56 , e ) e ) 12
Rationale: "let the total number of workers be x . then , 9000 x = ( 12000 * 6 ) + 6000 ( x - 6 ) = > 3000 x = 36000 = x = 12 . answer : e"
Answer: e
Problem: the first flight out of phoenix airport had a late departure . if the next 3 flights departed on - time , how many subsequent flights need to depart from phoenix on - time , for the airport ' s on - time departure rate to be higher than 60 % ? i will see what is the quickest way to solve it then i will provide the explanation
Options: a ) 6 , b ) 7 , c ) 9 , d ) 4 , e ) 11
Rationale: the following approach might be the easiest one and less error prone . we need on - time departure rate to be higher than 6 / 10 , so it should be at least 7 / 11 , which means that 7 out of 11 flights must depart on time . since for now 3 out of 4 flights departed on time then 7 - 3 = 4 subsequent flights need to depart on - time . answer : d
Answer: d
Problem: 6 ) a marketing firm determined that , of 300 households surveyed , 80 used neither brand a nor brand b soap . 60 used only brand a soap and for every household that used both brands of soap , 3 used only brand b soap . how many of the 200 household surveyed used both brands of soap ?
Options: a ) a ) 15 , b ) b ) 20 , c ) c ) 30 , d ) d ) 40 , e ) e ) 45
Rationale: "220 = at least one of soap a or b both brands = x brand b = 3 x = > 60 + x + 3 x = 220 = > 4 x = 160 = > x = 40 answer - d"
Answer: d
Problem: tom , working alone , can paint a room in 6 hours . peter and john , working independently , can paint the same room in 3 hours and 8 hours , respectively . tom starts painting the room and works on his own for one hour . he is then joined by peter and they work together for an hour . finally , john joins them and the three of them work together to finish the room , each one working at his respective rate . what fraction of the whole job was done by peter ?
Options: a ) 7 / 15 , b ) 11 / 25 , c ) 17 / 35 , d ) 23 / 45 , e ) 27 / 55
Rationale: "tom paints 1 / 6 of the room in the first hour . tom and peter paint 1 / 6 + 1 / 3 = 1 / 2 of the room in the next hour for a total of 4 / 6 . the three people then paint the remaining 2 / 6 in a time of ( 2 / 6 ) / ( 15 / 24 ) = 8 / 15 hours peter worked for 23 / 15 hours so he painted 23 / 15 * 1 / 3 = 23 / 45 of the room . the answer is d ."
Answer: d
Problem: a perfect square is defined as the square of an integer and a perfect cube is defined as the cube of an integer . how many positive integers n are there such that n is less than 50,000 and at the same time n is a perfect square and a perfect cube ?
Options: a ) 3
b ) 4
c ) 5
d ) 6
e ) 7
Rationale: if n is a perfect square and a perfect cube , then n = a ^ 6 for some integer a . the numbers are 1 ^ 6 = 1 , 2 ^ 6 = 64 , 3 ^ 6 = 729 , 4 ^ 6 = 4096 , 5 ^ 6 = 15,625 , 6 ^ = 46,656 . the answer is d .
Answer: d
Problem: at joel ’ s bookstore , the current inventory is 40 % historical fiction . of the historical fiction books , 40 % are new releases , while 40 % of the other books are new releases . what fraction of all new releases are the historical fiction new releases ?
Options: a ) 4 / 25 , b ) 8 / 23 , c ) 2 / 5 , d ) 8 / 15 , e ) 2 / 5
Rationale: "let there be 100 books in all historic fiction books = 40 % of total = 40 other books = 60 new historic fiction = 40 % of 40 = 16 other new books = 40 % of 60 = 24 total new books = 24 + 16 = 40 fraction = 16 / 40 = 2 / 5 ans : e"
Answer: e
Problem: the price of lunch for 15 people was $ 209.00 , including a 15 percent gratuity for service . what was the average price per person , excluding the gratuity ?
Options: a ) $ 11.73 , b ) $ 12.66 , c ) $ 13.80 , d ) $ 14.00 , e ) $ 15.87
Rationale: "take the initial price before the gratuity is 100 the gratuity is calculated on the final price , so as we assumed the final bill before adding gratuity is 100 so gratuity is 15 % of 100 is 15 so the total price of meals is 115 so the given amount i . e 209 is for 115 then we have to calculate for 100 for 115 209 for 100 x so by cross multiplication we get 115 x = 100 * 209 = > x = 100 * 209 / 110 by simplifying we get x as 190 which is the price of lunch before gratuity so the gratuity is 19 so as the question ask the average price person excluding gratuity is 190 / 15 = 12.66 so our answer is b )"
Answer: b
Problem: the average of 50 numbers id 44 . if two numbers , namely 45 and 55 are discarded , the average of the remaining numbers is :
Options: a ) 22.35 , b ) 33.25 , c ) 22.25 , d ) 11.35 , e ) 43.75
Rationale: "explanation : total of 50 numbers = ( 50 × 44 ) = 2200 total of 48 numbers = ( 2200 - ( 45 + 55 ) ] = 2100 required average = 2100 / 48 = 43.75 answer : e"
Answer: e
Problem: mike earns $ 14 per hour and phil earns $ 12 per hour . approximately how much less , as a percentage , does phil earn than mike per hour ?
Options: a ) 25 % , b ) 32.5 % , c ) 14 % , d ) 37.5 % , e ) 40 %
Rationale: "what % less of 14 is 12 let it be x % less , then = 14 ( 1 - x / 100 ) = 12 1 - x / 100 = 12 / 14 x = 100 / 7 x = 14 % ans c"
Answer: c
Problem: what is the remainder when 45 * 49 is divided by 8 ?
Options: a ) 1 , b ) 3 , c ) 4 , d ) 5 , e ) 7
Rationale: "we can make use of the rule : remainder of { ( a * b ) / n } } = remainder of ( a / n ) * remainder of ( b / n ) here remainder of { 45 * 49 ) / 8 } } = remainder of ( 45 / 8 ) * remainder of ( 49 / 8 ) = 5 * 1 = 7 answer : d"
Answer: d
Problem: 6 persons in an organization including a and b were to be divided in two groups of 3 members each . the total number of groups containing both a and b is what fraction of the total number of groups which can be formed ?
Options: a ) 3 / 10 , b ) 1 / 70 , c ) 3 / 14 , d ) 1 / 10 , e ) 11 / 14
Rationale: the fraction is nothing but the probability . . number to choose 3 out of 6 = 6 c 3 number to choose a and b and 2 from remaining 4 = 4 c 2 . . prob of a and b choosen = 4 c 2 / 6 c 3 = 3 / 10 answer : a
Answer: a
Problem: solution x is 80 % chemical a and 20 % chemical b by volume . solution y is 50 % chemical a and 50 % chemical b by volume . if a mixture of x and y is 68 % chemical a , what percent of the mixture is solution x ?
Options: a ) 20 % , b ) 25 % , c ) 30 % , d ) 35 % , e ) 40 %
Rationale: "the volume of the mixture be x + y . 0.8 x + 0.5 y = 0.68 ( x + y ) 0.12 x = 0.18 y x = 3 y / 2 x / ( x + y ) = ( 3 y / 2 ) / ( 5 y / 2 ) = 3 / 5 = 40 % . the answer is e ."
Answer: e
Problem: what number has a 5 : 1 ratio to the number 11 ?
Options: a ) 22 , b ) 50 , c ) 55 , d ) 52 , e ) 12
Rationale: "5 : 1 = x : 10 x = 55 answer : c"
Answer: c
Problem: in a class , if 50 % of the boys were girls , then there would be 50 % more girls than boys . what percentage of the overall class is girls ?
Options: a ) 25 % , b ) 33.33 % , c ) 40 % , d ) 20 % , e ) 10 %
Rationale: detailed solution for questions of this type , it is best to go from the final step . in the final state , the number of girls should be 1.5 * the number of boys . when 50 % of the boys are taken as girls , let the number of boys = x number of girls = 1.5 x total number of students = 2.5 x original number of boys = 2 x ( 50 % of boys = x ) original number of girls = 0.5 x girls form 20 % of the overall class . correct answer d .
Answer: d
Problem: a man can row downstream at the rate of 30 kmph and upstream at 10 kmph . find the man ’ s rate in still water and rate of current ?
Options: a ) 10 , b ) 8.0 , c ) 9.5 , d ) 9.0 , e ) 8.25
Rationale: "rate of still water = 1 / 2 ( down stream + upstream ) = 1 / 2 ( 30 + 10 ) = 20 kmph rate of current = 1 / 2 ( down stream - upstream ) = 1 / 2 ( 30 - 10 ) = 1 / 2 ( 20 ) = 10 kmph answer is a ."
Answer: a
Problem: the cost of a one - family home was $ 120,000 in 1980 . in 1988 , the price had increased to $ 192,000 . what was the percent increase in the cost of the home ?
Options: a ) 60 % , b ) 50 % , c ) 55 % , d ) 40 % , e ) 33.3 %
Rationale: increase = 192000 - 120000 = 72000 % increase = 72000 * 100 / 120000 = 60 % answer : option a
Answer: a
Problem: a dishonest dealer professes to sell goods at the cost price but uses a weight of 900 grams per kg , what is his percent ?
Options: a ) 11.11 % , b ) 25 % , c ) 22 % , d ) 29 % , e ) 45 %
Rationale: "900 - - - 100 100 - - - ? = > 11.11 % answer : a"
Answer: a
Problem: in the standard formulation of a flavored drink the ratio by volume of flavoring to corn syrup to water is 1 : 12 : 30 . in the sport formulation , the ratio of flavoring to corn syrup is three times as great as in the standard formulation , and the ratio of flavoring to water is half that of the standard formulation . if a large bottle of the sport formulation contains 5 ounces of corn syrup , how many ounces of water does it contain ?
Options: a ) 45 , b ) 50 , c ) 55 , d ) 60 , e ) 75
Rationale: "f : c : w 1 : 12 : 30 sport version : f : c 3 : 12 f : w 1 : 60 or 3 : 180 so c : f : w = 12 : 3 : 180 c / w = 12 / 180 = 3 ounces / x ounces x = 5 * 180 / 12 = 75 ounces of water e"
Answer: e
Problem: what is the value of x ^ 2 yz − xyz ^ 2 , if x = - 1 , y = 1 , and z = 3 ?
Options: a ) 20 , b ) 24 , c ) 30 , d ) 12 , e ) 48
Rationale: "1 * 1 * 3 - ( - 1 * 1 * 9 ) = 3 + 9 = 12 ans : d"
Answer: d
Problem: a batsman in his 19 th inning makes a score of 100 and their by increasing his average by 2 . what is his average after the 19 th inning ?
Options: a ) 58 , b ) 60 , c ) 62 , d ) 64 , e ) 66
Rationale: "18 x + 100 = 19 ( x + 2 ) x = 62 + 2 = 64 answer : d"
Answer: d
Problem: b takes 12 more days than a to finish a task . b and a start this task and a leaves the task 12 days before the task is finished . b completes 60 % of the overall task . how long would b have taken to finish the task if he had worked independently ?
Options: a ) 48 days , b ) 36 days , c ) 28 days , d ) 32 days , e ) 22 days
Rationale: detailed solution let us say a and b split their share of the task and started doing their respective shares simultaneously . let ’ s say a takes a days to finish the task . therefore , b takes a + 12 days to finish the entire task . a has to finish 40 % of the task , since b is doing the rest . so a will only take 2 a / 5 number of days . b only has to finish 60 % of the task , so b will take ( 3 ( a + 12 ) / 5 ) number of days . but as we know , b starts working along with a and finishes 12 days after a stops working . so , ( 3 ( a + 12 ) / 5 ) = ( ( 2 a ) / 5 + 12 ) 3 a + 36 = 2 a + 60 a = 24 ; b = 36 days . answer choice b
Answer: b
Problem: a train 100 m long is running with a speed of 68 kmph . in what time will it pass a man who is running at 8 kmph in the same direction in which the train is going ?
Options: a ) 6 sec . , b ) 7 sec . , c ) 9 sec . , d ) 11 sec . , e ) none
Rationale: "solution speed of the train relative to man = ( 68 - 8 ) = 60 kmph = 60 x 5 / 18 = 50 / 3 m / sec . time taken by it to cover 100 m at ( 50 / 3 ) m / sec = ( 100 x 3 / 50 ) sec = 6 sec . answer a"
Answer: a
Problem: with a uniform speed a car covers the distance in 8 hours . had the speed been increased by 4 km / hr , the same distance could have been covered in 7 1 / 2 hours . what is the distance covered ?
Options: a ) 347 , b ) 480 , c ) 288 , d ) 278 , e ) 131
Rationale: "let the distance be x km . then , x / ( 7 1 / 2 ) - x / 8 = 4 2 x / 15 - x / 8 = 4 = > x = 480 km . answer : b"
Answer: b
Problem: an error 19 % in excess is made while measuring the side of a square . now what is the percentage of error in the calculated area of the square ?
Options: a ) 6.64 % , b ) 41.61 % , c ) 45.64 % , d ) 46.64 % , e ) 10.64 %
Rationale: "percentage error in calculated area = ( 19 + 19 + ( 19 ã — 19 ) / 100 ) % = 41.61 % answer : b"
Answer: b
Problem: in the first 20 overs of a cricket game , the run rate was only 4.2 . what should be the run rate in the remaining 30 overs to reach the target of 324 runs ?
Options: a ) 7.25 , b ) 8.5 , c ) 8 , d ) 9.15 , e ) 10
Rationale: "explanation : required run rate = ( 324 - 4.2 20 ) = 240 / 30 = 8 . answer : c"
Answer: c
Problem: x and y are integers . a + b < 11 , and a > 6 . what is the smallest possible value of a - b ?
Options: a ) 1 , b ) 2 , c ) 4 , d ) - 2 , e ) - 4
Rationale: focus on the transition points and plug in the values . a > 6 so a could be 7 , 8 , 9 , 10 , 11 etc look at a = 7 7 + b < 11 b < 4 b could be 3 , 2 , 1 , 0 , - 1 etc when b is 3 , we get a - b = 4 this must be the smallest value because as a increases , b reduces so a - b increases . take another example . a = 11 so b < 0 . a - b will give a value greater than 11 . answer ( c ) .
Answer: c
Problem: a mobile battery in 1 hour charges to 20 percent . how much time ( in minute ) will it require more to charge to 65 percent .
Options: a ) 145 , b ) 150 , c ) 195 , d ) 160 , e ) 130
Rationale: 1 hr = 20 percent . thus 15 min = 5 percent . now to charge 65 percent 195 min . answer : c
Answer: c
Problem: if x is the product of the positive integers from 1 to 8 , inclusive , and if i , k , m , and p are positive integers such that x = 2 ^ i * 3 ^ k * 5 ^ m * 7 ^ p , then i + k + m + p =
Options: a ) 4 , b ) 7 , c ) 8 , d ) 11 , e ) 12
Rationale: given that x = 8 ! = 2 ^ 7 ∗ 3 ^ 2 ∗ 5 ∗ 7 x . hence , x = 2 ^ 7 ∗ 3 ^ 2 ∗ 5 ^ 1 ∗ 7 ^ 1 = 2 ^ i ∗ 3 ^ k ∗ 5 ^ m ∗ 7 p , since i , k , m , and p are positive integers , then we can equate the exponents , so we have that i = 7 , k = 2 , m = 1 , and p = 1 therefore , i + k + m + p = 7 + 2 + 1 + 1 = 11 answer : d .
Answer: d
Problem: find the base k of the number system , if ( 524 ) 8 = ( 664 ) k ?
Options: a ) 4
b ) 5
c ) 6
d ) 7
e ) 8
Rationale: 5 * 8 ^ 2 + 2 * 8 ^ 1 + 4 * 8 ^ 0 = 6 * k ^ 2 + 6 * k ^ 1 + 4 * k ^ 0 320 + 16 + 4 = 6 ( k ^ 2 ) + 6 k + 4 340 = 6 ( k ^ 2 ) + 6 k + 4 6 ( k ^ 2 ) + 6 k + 4 - 340 = 0 6 ( k ^ 2 ) + 6 k - 336 = 0 dividing by 6 ; ( k ^ 2 ) + k - 56 = 0 solving this quadratic equation we get , k = 7 and k = - 8 thus k = 7 answer : d
Answer: d
Problem: if n is the greatest number that will divide 1305 , 4665 and 6905 , leaving the same remainder in each case . what is the sum of the digits of n ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 5 , e ) 4
Rationale: n = h . c . f . of ( 4665 - 1305 ) , ( 6905 - 4665 ) and ( 6905 - 1305 ) = h . c . f . of 3360 , 2240 and 5600 = 1120 . sum of digits in n = ( 1 + 1 + 2 + 0 ) = 4 answer : e
Answer: e
Problem: an area of a circularplace is 17 hectares . find the cost of fencing it at the rate of rs . 3 permeter approximately .
Options: a ) rs . 4000
b ) rs . 4450
c ) rs . 4457
d ) rs . 4560
e ) rs . 5457
Rationale: area = ( 17.56 x 10000 ) m 2 = 175600 m 2 . π r 2 = 175600 ⇔ ( r ) 2 = ( 175600 x ( 7 / 22 ) ) ⇔ r = 236.37 m . circumference = 2 π r = ( 2 x ( 22 / 7 ) x 236.37 ) m = 1485.78 m . cost of fencing = rs . ( 1485.78 x 3 ) = rs . 4457 . c
Answer: c
Problem: having received his weekly allowance , john spent 3 / 5 of his allowance at the arcade . the next day he spent one third of his remaining allowance at the toy store , and then spent his last $ 0.90 at the candy store . what is john ’ s weekly allowance ?
Options: a ) $ 2.40 , b ) $ 3.00 , c ) $ 3.40 , d ) $ 3.60 , e ) $ 4.80
Rationale: "total allowance = x amount spent at the arcade = 3 / 5 x amount remaining = 2 / 5 x amount spent at the toy store = 2 / 5 * 1 / 3 x = 2 / 15 x amount remaining = 2 / 5 x - 2 / 15 x = 4 / 15 x now , 4 / 15 x = $ 0.9 therefore , x = $ 3.40 . answer c"
Answer: c
Problem: if a tire rotates at 400 revolutions per minute when the car is traveling 96 km / h , what is the circumference of the tire ?
Options: a ) 7 meters , b ) 9 meters , c ) 4 meters , d ) 5 meters , e ) 3 meters
Rationale: "400 rev / minute = 400 * 60 rev / 60 minutes = 24,000 rev / hour 24,000 * c = 96,000 m : c is the circumference c = 4 meters correct answer c"
Answer: c
Problem: a certain characteristic in a large population has a distribution that is symmetric about the mean m . if 68 % of the distribution lies one standard deviation f of the mean , what percent of the distribution is less than m + f ?
Options: a ) 16 % , b ) 32 % , c ) 48 % , d ) 84 % , e ) 92 %
Rationale: "16 % ________________________________________________ m + f 34 % ________________________________________________ m 34 % ________________________________________________ m - f 16 % since 68 % lies one standard deviation from mean m , = > 50 % of 68 % lies on either side as it is symmetric about m . thus 16 % lie below m - f and 16 % lie above m + f now below m + f = 16 + 34 + 34 = 84 % hence d"
Answer: d
Problem: the result when a number subtracted from 100 is the same as the number added to 40 . what is the number ?
Options: a ) 70 , b ) 65 , c ) 80 , d ) 140 , e ) 60
Rationale: "answer let the number be x . then , x - 40 = 100 - x â ‡ ’ 2 x = 100 + 40 = 140 â ‡ ’ 2 x = 140 â ˆ ´ x = 70 correct option : a"
Answer: a
Problem: if a / b = 6 / 5 , then ( 5 a + 4 b ) / ( 5 a - 4 b ) = ?
Options: a ) 4 , b ) 7 , c ) 5 , d ) 3 , e ) 6
Rationale: "answer dividing numerator as well as denominator by b , we get given exp . = ( 5 a + 4 b ) / ( 5 a - 4 b ) = ( 5 a / b + 4 ) / ( 5 a / b - 4 ) since a / b = 6 / 5 this implies that = [ ( 5 * 6 ) / 5 + 4 ] / [ ( 5 * 6 ) / 5 - 4 ) ] = ( 6 + 4 ) / ( 6 - 4 ) = 5 option : c"
Answer: c
Problem: running at their respective constant rate , machine x takes 2 days longer to produce w widgets than machines y . at these rates , if the two machines together produce 5 w / 4 widgets in 3 days , how many days would it take machine x alone to produce 1 w widgets .
Options: a ) 4 , b ) 6 , c ) 8 , d ) 10 , e ) 12
Rationale: "i am getting 12 . e . hope havent done any calculation errors . . approach . . let y = no . of days taken by y to do w widgets . then x will take y + 2 days . 1 / ( y + 2 ) + 1 / y = 5 / 12 ( 5 / 12 is because ( 5 / 4 ) w widgets are done in 3 days . so , x widgets will be done in 12 / 5 days or 5 / 12 th of a widget in a day ) solving , we have y = 4 = > x takes 6 days to doing x widgets . answer : b"
Answer: b
Problem: if the number 761 * 829 is completely divisible by 9 , then the smallest whole number in place of * will b
Options: a ) 4 , b ) 5 , c ) 3 , d ) 8 , e ) 9
Rationale: sum of digits = ( 7 + 6 + 1 + x + 8 + 2 + 9 ) = ( 33 + x ) , which must be divisible by 9 . x = 3 . c )
Answer: c
Problem: teas worth rs . 126 per kg and rs . 135 per kg are mixed with a third variety in the ratio 1 : 1 : 2 . if the mixture is worth rs 157 per kg , the price of the third variety per kg will be ?
Options: a ) rs . 147.50 , b ) rs . 785.50 , c ) rs . 179.50 , d ) rs . 258.50 , e ) none of these
Rationale: explanation : since first and second varieties are mixed in equal proportions . so , their average price = rs . ( 126 + 135 ) / 2 . = > rs . 130.50 . so , the mixture is formed by mixing two varieties , one at rs . 130.50 per kg and the other at say , rs . x per kg in the ratio 2 : 2 , i . e . , 1 : 1 . we have to find x . by the rule of alligation , we have : cost of 1 kg cost of 1 kg of 1 st kind of 2 nd kind ( rs . 130.50 ) ( rs . x ) \ / mean price ( rs . 157 ) / \ x â ˆ ’ 157 22.50 = > x â ˆ ’ ( 157 / 22.50 ) = 1 . = > x â ˆ ’ 157 = 22.50 . = > x = 179.50 rs . answer : c
Answer: c
Problem: the sub - duplicate ratio of 9 : 25 is
Options: a ) 4 : 3 , b ) 1 : 2 , c ) 3 : 5 , d ) 1 : 4 , e ) 2 : 3
Rationale: root ( 9 ) : root ( 25 ) = 3 : 5 answer : c
Answer: c
Problem: sushil got thrice as many marks in english as in science . his total marks in english , science and maths are 162 . if the ratio of his marks in english and maths is 3 : 5 , find his marks in science ?
Options: a ) 18 , b ) 68 , c ) 67 , d ) 55 , e ) 56
Rationale: "s : e = 1 : 3 e : m = 3 : 5 - - - - - - - - - - - - s : e : m = 3 : 9 : 15 3 / 27 * 162 = 18 answer : a"
Answer: a
Problem: a train moves past a post and a platform 264 m long in 8 seconds and 20 seconds respectively . what is the speed of the train ?
Options: a ) 79.2 km / hr , b ) 69 km / hr , c ) 74 km / hr , d ) 61 km / hr , e ) none of these
Rationale: let x is the length of the train and v is the speed time taken to move the post = 8 s = > x / v = 8 = > x = 8 v - - - ( 1 ) time taken to cross the platform 264 m long = 20 s ( x + 264 ) / v = 20 = > x + 264 = 20 v - - - ( 2 ) substituting equation 1 in equation 2 , we get 8 v + 264 = 20 v = > v = 264 / 12 = 22 m / s = 22 × 36 / 10 km / hr = 79.2 km / hr answer : b
Answer: b
Problem: of 120 applicants for a job , 56 had at least 4 years ' experience , 72 had degrees , and 12 had less than 4 years ' experience and did not have a degree . how many of the applicants had at least 4 years ' experience and a degree ?
Options: a ) 10 , b ) 15 , c ) 22 , d ) 20 , e ) 24
Rationale: "120 - 12 = 108 108 - 56 - 72 = - 20 then 20 are in the intersection between 4 years experience and degree . answer : d"
Answer: d
Problem: a started a business with an investment of rs . 70000 and after 6 months b joined him investing rs . 120000 . if the profit at the end of a year is rs . 39000 , then the share of b is ?
Options: a ) a ) 34500 , b ) b ) 24000 , c ) c ) 24098 , d ) d ) 19007 , e ) e ) 18000
Rationale: "ratio of investments of a and b is ( 70000 * 12 ) : ( 120000 * 6 ) = 7 : 6 total profit = rs . 39000 share of b = 6 / 13 ( 39000 ) = rs . 18000 answer : e"
Answer: e
Problem: divide rs . 32000 in the ratio 3 : 5 ?
Options: a ) 12000 , 20000 , b ) 12000 , 200098 , c ) 12000 , 20007 , d ) 12000 , 20006 , e ) 12000 , 20001
Rationale: "3 / 8 * 32000 = 12000 5 / 8 * 32000 = 20000 answer : a"
Answer: a
Problem: what is the hcf of 2 / 3 , 4 / 15 and 6 / 5
Options: a ) 7 / 45 , b ) 2 / 45 , c ) 4 / 15 , d ) 8 / 45 , e ) 2 / 15
Rationale: "explanation : hcf of fractions = hcf of numerators / lcm of denominators = ( hcf of 2 , 4 , 6 ) / ( lcm of 3 , 15 , 5 ) = 2 / 15 answer : option e"
Answer: e
Problem: n a race of 1000 m , a can beat by 100 m , in a race of 800 m , b can beat c by 100 m . by how many meters will a beat c in a race of 600 m ?
Options: a ) 127.6 , b ) 127.5 , c ) 127.0 , d ) 127.2 , e ) 127.3
Rationale: when a runs 1000 m , b runs 900 m and when b runs 800 m , c runs 700 m . when b runs 900 m , distance that c runs = ( 900 * 700 ) / 800 = 6300 / 8 = 787.5 m . in a race of 1000 m , a beats c by ( 1000 - 787.5 ) = 212.5 m to c . in a race of 600 m , the number of meters by which a beats c = ( 600 * 212.5 ) / 1000 = 127.5 m . answer : ob
Answer: b
Problem: 3 , 14,39 , _ ?
Options: a ) 81 , b ) 82 , c ) 83 , d ) 84 , e ) 85
Rationale: "n ^ 3 + n ^ 2 + n soln : 1 ^ 3 + 1 ^ 2 + 1 = 3 2 ^ 3 + 2 ^ 2 + 2 = 8 + 4 + 2 = 14 3 ^ 3 + 3 ^ 2 + 3 = 27 + 9 + 3 = 39 4 ^ 3 + 4 ^ 2 + 4 = 64 + 16 + 4 = 84 answer : d"
Answer: d
Problem: if x : y = 3 : 5 , find the value of ( 2 x + 4 y ) : ( 4 x – y )
Options: a ) 29 : 7 , b ) 22 : 7 , c ) 26 : 7 , d ) 20 : 7 , e ) 26 : 5
Rationale: "explanation : given : a / b = 3 / 5 ( 2 * 3 + 4 * 5 ) : ( 4 * 3 – 5 ) = 26 : 7 answer : c"
Answer: c
Problem: nd the area of trapezium whose parallel sides are 20 cm and 18 cm long , and the distance between them is 14 cm ?
Options: a ) 235 cm 2 , b ) 260 cm 2 , c ) 266 cm 2 , d ) 270 cm 2 , e ) 280 cm 2
Rationale: "area of a trapezium = 1 / 2 ( sum of parallel sides ) * ( perpendicular distance between them ) = 1 / 2 ( 20 + 18 ) * ( 14 ) = 266 cm 2 answer : c"
Answer: c
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 600,000 ?
Options: a ) 150 , 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 reduction of 20 % in the price of salt enables a lady to obtain 4 kgs more for rs . 100 , find the original price per kg ?
Options: a ) 6.16 , b ) 6.21 , c ) 6.25 , d ) 2.4 , e ) 2.7
Rationale: "100 * ( 20 / 100 ) = 20 - - - 4 ? - - - 1 = > rs . 5 100 - - - 80 ? - - - 5 = > rs . 6.25 answer : c"
Answer: c
Problem: kyle , david , and catherine each try independently to solve a problem . if their individual probabilities for success are 1 / 8 , 1 / 4 and 3 / 5 , respectively , what is the probability no one will solve the problem ?
Options: a ) 3 / 80 , b ) 21 / 80 , c ) 5 / 16 , d ) 25 / 76 , e ) 9 / 80
Rationale: "p ( kyle will not solve ) = 1 - 1 / 8 = 7 / 8 p ( david will not solve ) = 1 - 1 / 4 = 3 / 4 p ( catherine will not solve ) = 1 - 3 / 5 = 2 / 5 p = ( 7 / 8 ) * ( 3 / 4 ) * ( 2 / 5 ) = 42 / 160 = 21 / 80 answer : b"
Answer: b
Problem: if p and q are prime numbers , how many divisors does the product p ^ 6 * q ^ 7 have ?
Options: a ) 40 , b ) 56 , c ) 60 , d ) 62 , e ) 70
Rationale: "when a number n = a ^ x * b ^ y , where a and b are prime numbers , and x , y are positive integers , the number of divisors of n = ( x + 1 ) ( y + 1 ) therefore , the answer is b . 7 * 8 = 56"
Answer: b
Problem: if there is an equal probability of a child being born a boy or a girl , what is the probability that a couple who have 4 children have two children of the same sex and one of the opposite sex ?
Options: a ) 1 / 3 , b ) 2 / 3 , c ) 1 / 4 , d ) 1 / 2 , e ) 3 / 5
Rationale: no of ways of selecting a gender - 2 c 1 no of ways of selecting any 2 children out of 4 = 4 c 2 total possible outcomes - 2 ^ 4 ( each child can be either a girl or a boy ) probability = 2 c 1 * 4 c 2 / 2 ^ 4 = 2 * 4 / 2 * 2 * 2 * 2 = 8 / 16 = 1 / 2 ans = d
Answer: d
Problem: the measurement of a rectangular box with lid is 25 cmx 12 cmx 18 cm . find the volume of the largest sphere that can be inscribed in the box ( in terms of π cm 3 ) . ( hint : the lowest measure of rectangular box represents the diameter of the largest sphere )
Options: a ) 288 , b ) 48 , c ) 72 , d ) 864 , e ) 964
Rationale: "d = 12 , r = 6 ; volume of the largest sphere = 4 / 3 π r 3 = 4 / 3 * π * 6 * 6 * 6 = 288 π cm 3 answer : a"
Answer: a
Problem: when a certain number x is divided by 72 , the remainder is 19 . what is the remainder when x is divided by 8 ?
Options: a ) 3 , b ) 2 , c ) 4 , d ) 1 , e ) 5
Rationale: "let possible value of x is 91 least possible value of x / 8 is 91 / 8 = > 11 quotient with remainder 3 thus answer is ( a ) 3"
Answer: a
Problem: in a tournament prize of 1 st , 2 nd , and 3 rd is given in same interval . if total amount of prize rs 4800 and prize of 1 st is rs 2000 , find the interval ? ?
Options: a ) 600 , b ) 450 , c ) 350 , d ) 550 , e ) 400
Rationale: let the interval is x . prize of 2 nd and 3 rd is 2000 - x and 2000 - 2 x 2000 + 2000 - x + 2000 - 2 x = 4800 x = 400 answer : e
Answer: e
Problem: if n = 8 ^ 11 – 1 , what is the units digit of n ?
Options: a ) 3 , b ) 1 , c ) 0 , d ) 6 , e ) 4
Rationale: "8 ^ 11 - 8 = 8 ( 8 ^ 10 - 1 ) = = > 8 ( 2 ^ 30 - 1 ) last digit of 2 ^ 30 is 4 based on what explanation livestronger is saying . 2 ^ 30 - 1 yields 4 - 1 = 3 as the unit digit . now on multiply this with 1 , we get unit digit as 3 . answer : a"
Answer: a
Problem: $ 600 will become $ 720 in 4 years find the rate of interest ?
Options: a ) 10 % , b ) 15 % , c ) 5 % , d ) 7 % , e ) 20 %
Rationale: "si = simple interest = a - p = 720 - 600 = $ 120 r = 100 si / pt = 100 * 120 / 600 * 4 = 5 % answer is c"
Answer: c
Problem: the area of a circle is increased by 300 % . by what percent has the diameter of the circle increased ?
Options: a ) 400 %
b ) 200 %
c ) 300 %
d ) 100 %
e ) 800 %
Rationale: the area of the circle is increased by 300 % , thus the area is increased 4 times . the area of a circle it proportional to the square of the diameter ( area = π d ^ 2 / 4 ) , therefore the diameter must increase 2 times ( diameter increase 2 times = area increase 4 times ) , which is increase by 100 % . answer : d .
Answer: d
Problem: 18 men take 21 days of 8 hours each to do a piece of work . how many days of 6 hours each would 21 women take to do the same . if 3 women do as much work as 2 men ?
Options: a ) 32 , b ) 87 , c ) 36 , d ) 99 , e ) 77
Rationale: "3 w = 2 m 18 m - - - - - - 21 * 8 hours 21 w - - - - - - x * 6 hours 14 m - - - - - - x * 6 18 * 21 * 8 = 14 * x * 6 x = 36 answer : c"
Answer: c
Problem: find the simple interest on rs 7000 at 50 / 3 % for 9 months
Options: a ) rs . 1075 , b ) rs . 975 , c ) rs . 875 , d ) rs . 775 , e ) none of these
Rationale: "explanation : s . i . = p × r × t 100 so , by pu ƫ ing the values in the above formula , our result will be . required result = 7000 × 50 × 93 × 12 × 100 = 875 [ please note that we have divided by 12 as we converted 9 months in a year format ] answer : c"
Answer: c
Problem: what is the area of a square with perimeter 4 p ?
Options: a ) p ^ 2 , b ) 4 p , c ) p ^ 2 / 4 , d ) p / 16 , e ) p ^ 2 / 16
Rationale: "each side is p a = ( p ) ^ 2 answer a"
Answer: a
Problem: a school has 9 english 7 history and 6 geography teachers each teacher can teach 2 subjects max what is he minimum number of teachers required
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: total subjects = 9 + 7 + 6 = 22 max subjects by 1 teacher = 2 so , min of teachers required = 22 / 2 = 11 answer : e
Answer: e
Problem: if in a certain code ` ` range ' ' is coded as 12345 and ` ` random ' ' is coded as 123678 . then the code for the word ` ` rand ' ' would be
Options: a ) 1236 , b ) 1365 , c ) 1200 , d ) 1526 , e ) 1325
Rationale: r - 1 a - 2 n - 3 d - 6 so for mango the code is 1236 answer : a
Answer: a
Problem: a goods train runs at the speed of 72 kmph and crosses a 230 m long platform in 26 seconds . what is the length of the goods train ?
Options: a ) 230 m , b ) 270 m , c ) 643 m , d ) 832 m , e ) 290 m
Rationale: "speed = ( 72 x 5 / 18 ) m / sec = 20 m / sec . time = 26 sec . let the length of the train be x metres . then , x + 230 / 26 = 20 x + 230 = 520 x = 290 . answer : e"
Answer: e
Problem: it takes joey the postman 1 hours to run a 2 mile long route every day . he delivers packages and then returns to the post office along the same path . if the average speed of the round trip is 6 mile / hour , what is the speed with which joey returns ?
Options: a ) 9 , b ) 12 , c ) 13 , d ) 14 , e ) 15
Rationale: "let his speed for one half of the journey be 3 miles an hour let the other half be x miles an hour now , avg speed = 5 mile an hour 2 * 2 * x / 3 + x = 6 4 x = 6 x + 18 = > 2 x = 18 x = 9 a"
Answer: a
Problem: the distance from the x - axis to point p is half the distance from the y - axis to point p . if the coordinates of p are ( x , - 9 ) , how many units is p from the y - axis ?
Options: a ) 18 , b ) 12 , c ) 9 , d ) 4.5 , e ) 3
Rationale: "the x - axis is 9 units from the point p . thus the y - axis is 18 units from the point p . the answer is a ."
Answer: a
Problem: if a ' s height is 45 % less than that of b , how much percent b ' s height is more than that of a ?
Options: a ) 66.66 % , b ) 81.81 % , c ) 66.766 % , d ) 86.66 % , e ) 66.65 %
Rationale: "excess of b ' s height over a ' s = [ ( 45 / ( 100 - 45 ) ] x 100 % = 81.81 % answer : b )"
Answer: b
Problem: in an apartment building that has 490 units , 4 out of every 7 units are currently rented , including 1 / 4 of the one - bedroom units . if , of the rented apartments , there is a 6 : 1 ratio of two - bedroom units to one - bedroom units , and the building only consists of two - bedroom and one - bedroom units , how many two - bedroom units are not rented ?
Options: a ) 50 , b ) 90 , c ) 100 , d ) 105 , e ) 140
Rationale: "rented = 4 / 7 * 490 = 280 . rented two - bedroom = 6 / 7 * 280 = 240 ; rented one - bedroom = 1 / 7 * 280 = 40 ( or 280 - 240 = 40 ) . rented one - bedroom units are 1 / 4 of all one - bedroom : 1 / 4 * { all one bedroom } = 40 - - > { all one - bedroom } = 160 { all two - bedroom } = 490 - 160 = 330 two - bedroom not rented = 330 - 240 = 90 b"
Answer: b
Problem: in how many ways 6 boys and 6 girls can be seated in a row so that boys and girls are alternate ?
Options: a ) 1063800 , b ) 1083600 , c ) 1036800 , d ) 1053800 , e ) 1073600
Rationale: "number of ways = 2 * 6 ! * 6 ! = 1036800 answer is c"
Answer: c
Problem: the cost price of 12 articles is equal to the selling price of 10 articles . what is the profit percent ?
Options: a ) 10 % , b ) 20 % , c ) 30 % , d ) 40 % , e ) 50 %
Rationale: "10 * sp = 12 * cp sp = 1.2 * cp the profit percent is 20 % . the answer is b ."
Answer: b
Problem: a man rows his boat 65 km downstream and 45 km upstream , taking 2 1 / 2 hours each time . find the speed of the stream ?
Options: a ) 5 kmph , b ) 4 kmph , c ) 9 kmph , d ) 8 kmph , e ) 1 kmph
Rationale: "speed downstream = d / t = 65 / ( 2 1 / 2 ) = 26 kmph speed upstream = d / t = 45 / ( 2 1 / 2 ) = 18 kmph the speed of the stream = ( 26 - 18 ) / 2 = 4 kmph answer : b"
Answer: b
Problem: arnold and danny are two twin brothers that are celebrating their birthday . the product of their ages today is smaller by 9 from the product of their ages a year from today . what is their age today ?
Options: a ) 2 . , b ) 4 . , c ) 5 . , d ) 7 , e ) 9 .
Rationale: "ad = ( a + 1 ) ( d + 1 ) - 9 0 = a + d - 8 a + d = 8 a = d ( as they are twin brothers ) a = d = 4 b is the answer"
Answer: b
Problem: 27 * 27 * 27 * 27 = 3 ^ ?
Options: a ) 7 , b ) 12 , c ) 5 , d ) 6 , e ) 8
Rationale: "3 ^ 3 * 3 ^ 3 * 3 ^ 3 * 3 ^ 3 = 3 ^ ( 3 + 3 + 3 + 3 ) = 3 ^ 12 answer : 12 option : b"
Answer: b
Problem: there were two candidates in an election . winner candidate received 60 % of votes and won the election by 240 votes . find the number of votes casted to the winning candidate ?
Options: a ) 228 , b ) 720 , c ) 255 , d ) 199 , e ) 231
Rationale: "w = 60 % l = 40 % 60 % - 40 % = 20 % 20 % - - - - - - - - 240 60 % - - - - - - - - ? = > 720 answer : b"
Answer: b
Problem: a factory producing tennis balls stores them in either big boxes , 25 balls per box , or small boxes , 20 balls per box . if 153 freshly manufactured balls are to be stored , what is the least number of balls that can be left unboxed ?
Options: a ) 2 , b ) 1 , c ) 3 , d ) 5 , e ) 4
Rationale: "we have to work with multiples of 20 and 25 . first , we must know the limits of this multiples , so : 152 / 25 = 6 . . . . so the max is 6 152 / 20 = 7 . . . so the max is 7 153 - 150 = 3 ( 6 big box ) answer : c"
Answer: c
Problem: what least number should be subtracted from 997 so that the remainder when divided by 5 , 9 , and 11 will leave in each case the same remainder 3 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: the lcm of 5,9 and 11 is 495 . the next multiple is 2 * 495 = 990 . 990 + { remainder } = 990 + 3 = 993 , which is 4 less than 997 . answer : d .
Answer: d
Problem: a garden center sells a certain grass seed in 5 - pound bags at $ 13.82 per bag , 10 - pound bags at $ 20.43 per bag , and 25 - pound bags $ 32.25 per bag . if a customer is to buy at least 65 pounds of the grass seed , but no more than 80 pounds , what is the least possible cost of the grass seed that the customer will buy ?
Options: a ) $ 94.03 , b ) $ 96.75 , c ) $ 98.75 , d ) $ 102.07 , e ) $ 105.3
Rationale: "there can be 2 cases 1 ) 25 + 25 + 10 + 5 = $ 98.75 or 2 ) 25 + 25 + 25 = $ 96.75 c"
Answer: c
Problem: in a group of cows and chickens , the number of legs was 14 more than twice the number of heads . the number of cows was :
Options: a ) 3 , b ) 5 , c ) 9 , d ) 7 , e ) 8
Rationale: d 7 let the number of cows be x and their legs be 4 x . let the number of chicken be y and their legs be 2 x . total number of legs = 4 x + 2 y . total number of heads = x + y . the number of legs was 14 more than twice the number of heads . therefore , 2 × ( x + y ) + 14 = 4 x + 2 y . or , 2 x + 2 y + 14 = 4 x + 2 y . or , 2 x + 14 = 4 x [ subtracting 2 y from both sides ] . or , 14 = 4 x – 2 x [ subtracting 2 x from both sides ] . or , 14 = 2 x . or , x = 7 [ dividing by 2 on both sides ] . therefore , the number of cows = 7 .
Answer: d
Problem: what least number should be subtracted from 13604 such that the remainder is divisible by 87 ?
Options: a ) 32 , b ) 29 , c ) 28 , d ) 30 , e ) 31
Rationale: "13604 ÷ 87 = 156 , remainder = 32 hence 32 is the least number which can be subtracted from 13604 such that the remainder is divisible by 87 answer is a"
Answer: a
Problem: water consists of hydrogen and oxygen , and the approximate ratio , by mass , of hydrogen to oxygen is 2 : 16 . approximately how many grams of oxygen are there in 153 grams of water ?
Options: a ) 16 , b ) 72 , c ) 112 , d ) 136 , e ) 142
Rationale: "since the ratio , by mass , of hydrogen to oxygen is 2 : 16 , then oxygen is 16 / ( 2 + 16 ) = 8 / 9 of mass of water . therefore there are 153 * 8 / 9 = 136 grams of oxygen in 153 grams of water . answer : d ."
Answer: d
Problem: how many zeros does 135 ^ 19 x 42 ^ 17 end with ?
Options: a ) 0 , b ) 2 , c ) 5 , d ) 13 , e ) 17
Rationale: "to know the zeros we need to know how many 10 ' s are there for this need to find number of 2 s and 5 s ( 2 * 5 = 10 ) 135 = ( 5 x 3 ^ 3 ) ^ 19 so number of 5 s are = 19 42 = ( 2 x 7 x 3 ) ^ 17 so number of 2 s = 17 so tot number of 10 s in this number is ( 17 - > 2 s x 17 - > 5 s ) so answer is 17 answer : e"
Answer: e
Problem: due to construction , the speed limit along an 5 - mile section of highway is reduced from 40 miles per hour to 22 miles per hour . approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ?
Options: a ) a ) 3.12 , b ) b ) 8 , c ) c ) 10 , d ) d ) 15 , e ) e ) 6.13
Rationale: "old time in minutes to cross 5 miles stretch = 5 * 60 / 40 = 5 * 3 / 2 = 7.5 new time in minutes to cross 5 miles stretch = 5 * 60 / 22 = 5 * 30 / 11 = 13.63 time difference = 6.13 ans : e"
Answer: e
Problem: 2 : 5 = 4 / 3 : x . the value of x is ?
Options: a ) 10 / 3 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: x * 2 = 5 * 4 / 3 x * 2 = 20 / 3 x = 10 / 3 answer : a
Answer: a
Problem: how many even integers n , such that 20 < = n < = 200 are of the form 3 k + 4 , where k is any natural number ?
Options: a ) 26 , b ) 30 , c ) 34 , d ) 38 , e ) 42
Rationale: "the first number is 22 = 16 + 6 ( 1 ) . we can continue adding 6 to make a list : 22 , 28 , 34 , . . . the last number is 196 = 16 + 6 ( 30 ) there are 30 numbers in the list . the answer is b ."
Answer: b
Problem: find a sum for 1 st 4 prime number ' s ?
Options: a ) 25 , b ) 17 , c ) 30 , d ) 34 , e ) 36
Rationale: "required sum = ( 2 + 3 + 5 + 7 ) = 17 note : 1 is not a prime number option b"
Answer: b
Problem: two vessels having volumes in the ratio 3 : 5 are filled with water and milk solutions . the ratio of milk and water in the two vessels are 5 : 1 and 6 : 4 respectively . if the contents of both the vessel are empties into a larger vessel , find the ratio of milk and water in the larger vessel .
Options: a ) 12 : 5 , b ) 11 : 5 , c ) 13 : 5 , d ) 14 : 5 , e ) 9 : 5
Rationale: "vessel a = 300 gallons - - > milk = 250 , water = 50 ; vessel b = 500 gallons - - > milk = 300 , water = 200 ; vessel a + b = 800 gallons - - > milk = 550 , water 250 the ratio = 550 / 250 - - > 11 : 5 answer : b"
Answer: b
Problem: how many seconds will a 750 meter long train moving with a speed of 63 km / hr take to cross a man walking with a speed of 3 km / hr in the direction of the train ?
Options: a ) 48 , b ) 36 , c ) 26 , d ) 11 , e ) 45
Rationale: "explanation : here distance d = 750 mts speed s = 63 - 3 = 60 kmph = 60 x 5 / 18 m / s time t = = 45 sec . answer : e"
Answer: e
Problem: a certain country had a total annual expenditure of $ 7.2 x 10 ^ 11 last year . if the population of the country was 240 million last year , what was the per capita expenditure ?
Options: a ) $ 500 , b ) $ 1,000 , c ) $ 2,000 , d ) $ 3,000 , e ) $ 5,000
Rationale: "total expenditure / population = per capita expenditure hence , ( 7,2 x 10 ^ 11 ) / 240 000 000 = ( 7,2 x 10 ^ 11 ) / ( 2,4 x 10 ^ 8 ) = 3 x 10 ^ ( 11 - 8 ) = 3 x 10 ^ 3 = 3000 . answer is d ."
Answer: d
Problem: a certain manufacturer produces items for which the production costs consist of annual fixed costs totaling $ 130,000 and variables costs averaging $ 5 per item . if the manufacturer ’ s selling price per item is $ 15 , how many items the manufacturer produce and sell to earn an annual profit of $ 150,000 ?
Options: a ) 2,858 , b ) 18,667 , c ) 28,000 , d ) 35,000 , e ) 40,000
Rationale: "let the items manufactured or sold bex 130000 + 5 x = 15 x - 150000 10 x = 280000 x = 28000 ans : c"
Answer: c
Problem: what should be added to 4529 so that it may become a perfect square ?
Options: a ) 94 , b ) 95 , c ) 96 , d ) 97 , e ) 98
Rationale: "68 x 68 = 4624 4624 - 4529 = 95 if added to 95 get perfect square answer = b"
Answer: b
Problem: barbata invests $ 2400 in the national bank at 5 % . how much additional money must she invest at 8 % so that the total annual income will be equal to 8 % of her entire investment ?
Options: a ) 1200 , b ) 3000 , c ) 1000 , d ) 3600 , e ) 2400
Rationale: "let the additional invested amount for 8 % interest be x ; equation will be ; 2400 + 0.05 * 2400 + x + 0.08 x = 2400 + x + 0.08 ( 2400 + x ) 0.05 * 2400 + 0.08 x = 0.06 x + 0.08 * 2400 0.02 x = 2400 ( 0.08 - 0.05 ) x = 2400 * 0.03 / 0.02 = 3600 ans : d"
Answer: d
Problem: if x : y = 3 : 4 , find ( 4 x + 5 y ) : ( 5 x - 2 y ) .
Options: a ) 32 / 7 , b ) 13 / 7 , c ) 2 / 7 , d ) 32 / 17 , e ) 2 / 17
Rationale: ". x / y = 3 / 4  ( 4 x + 5 y ) / ( 5 x + 2 y ) = ( 4 ( x / y ) + 5 ) / ( 5 ( x / y ) - 2 ) = ( 4 ( 3 / 4 ) + 5 ) / ( 5 ( 3 / 4 ) - 2 ) = ( 3 + 5 ) / ( 7 / 4 ) = 32 / 7 answer a 32 / 7"
Answer: a