regisss/math_qa huggingface dataset:
Problem: a certain junior class has 1,200 students and a certain senior class has 800 students . among these students , there are 60 siblings pairs , each consisting of 1 junior and 1 senior . if 1 student is to be selected at random from each class , what is the probability that the 2 students selected at will be a sibling pair ?
Options: a ) 3 / 40,000 , b ) 1 / 3,600 , c ) 9 / 2,000 , d ) 1 / 60 , e ) 1 / 16,000
Rationale: "total number of ways of choosing one student from each group is = 800 * 1200 number of cases in which a sibling pair will be got is = 60 thus the probability that the 2 students selected will be a sibling pair is = 60 / ( 800 * 1200 ) = 1 / 16,000 e"
Answer: e
Problem: two trains are moving in opposite directions at 60 km / hr and 90 km / hr . their lengths are 1.10 km and 0.65 km respectively . the time taken by the slower train to cross the faster train in seconds is ?
Options: a ) 42 , b ) 77 , c ) 48 , d ) 99 , e ) 11
Rationale: relative speed = 60 + 90 = 150 km / hr . = 150 * 5 / 18 = 125 / 3 m / sec . distance covered = 1.10 + 0.65 = 1.75 km = 1750 m . required time = 1750 * 3 / 125 = 42 sec . answer : a
Answer: a
Problem: the sum of the fourth and twelfth term of an arithmetic progression is 20 . what is the sum of the first 10 terms of the arithmetic progression ?
Options: a ) 300 , b ) 100 , c ) 150 , d ) 170 , e ) 270
Rationale: n th term of a . p . is given by a + ( n - 1 ) d 4 th term = a + 3 d 12 th term = a + 11 d given a + 3 d + a + 11 d = 20 - - > 2 a + 14 d = 20 - - > a + 7 d = 10 sum of n term of a . p = n / 2 [ 2 a + ( n - 1 ) d ] subsitiuing n = 10 . . . we get 10 / 2 [ 2 a + 14 d ] = 10 [ a + 7 d ] = 10 * 10 = 100 . . . answer is b . . .
Answer: b
Problem: a salt manufacturing company produced a total of 3000 tonnes of salt in january of a particular year . starting from february its production increased by 100 tonnes every month over the previous months until the end of the year . find its ave 66 rage daily production for that year ?
Options: a ) 119 , b ) 185 , c ) 190 , d ) 116 , e ) 200
Rationale: "total production of salt by the company in that year = 3000 + 3100 + 3200 + . . . . + 4100 = 42600 . average monthly production of salt for that year = 42600 / 365 â ‰ ˆ 116 answer : d"
Answer: d
Problem: set x consists of the integers from 10 to 15 , inclusive , while set y consists of the integers from 5 to 10 , inclusive . how many distinct integers do belong to the both sets at the same time ?
Options: a ) 5 , b ) 8 , c ) 4 , d ) 1 , e ) 9
Rationale: "x = { 10 , 11 , 12,13 , 14,15 } y = { 5,6 , 7 , 8 , 9 , 10 } common elements = { 10 } = 1 element answer : option d ."
Answer: d
Problem: in a class of boys and girls vikas ' s rank is 9 th and tanvi ' s rank is 17 th . vikas ' s rank among the boys in that class is 4 th from the top and 18 th from the bottom and tanvi ' s rank among the girls is 8 th from top and 21 st from bottom . in the order of rank , how many girls are there between tanvi and vikas ?
Options: a ) 29 , b ) 8 , c ) 2 , d ) 4 , e ) 6
Rationale: explanation : vikas ' s rank in the class is 9 . so there are 8 people before him . his rank among boys is 4 . so 3 boys are before him . so there are 8 – 3 = 5 girls before him . tanvi ' s rank among the girls is 8 . so there are 7 girls before her . so number of girls between vikas and tanvi is 7 – 5 = 2 answer : c
Answer: c
Problem: arjun started a business with rs . 5,000 and is joined afterwards by anoop with rs . 10 , 000 . after how many months did anoop join if the profits at the end of the year are divided equally ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "suppose anoop joined after 3 months . then , 5000 * 12 = 10000 * ( 12 – x ) = > x = 6 . answer : d"
Answer: d
Problem: tom purchased 8 kg of apples at the rate of 70 per kg and 910 kg of mangoes at the rate of 55 per kg . how much amount did he pay to the shopkeeper ?
Options: a ) a ) 1110 , b ) b ) 1045 , c ) c ) 1055 , d ) d ) 1060 , e ) e ) 1075
Rationale: "cost of 8 kg apples = 70 × 8 = 560 . cost of 10 kg of mangoes = 55 × 10 = 550 . total cost he has to pay = 560 + 550 = 1110 . a )"
Answer: a
Problem: what is the value of √ 16 % ?
Options: a ) 20 % , b ) 30 % , c ) 40 % , d ) 50 % , e ) 60 %
Rationale: "explanation : br > √ 16 % = √ 14 / √ 100 = 4 / 10 = 40 / 100 = 40 % correct answer is c ) 40 %"
Answer: c
Problem: a certain company that sells only cars and trucks reported that revenues from car sales in 1997 were down 11 percent from 1996 and revenues from truck sales were up 7 percent from 1996 . if total revenues from car sales and truck sales in 1997 were up 1 percent from 1996 , what is the ratio q of revenue from car sales in 1996 to revenue from truck sales in 1996 ?
Options: a ) 1 : 2 , b ) 4 : 5 , c ) 1 : 1 , d ) 3 : 2 , e ) 5 : 3
Rationale: a . . i have probably solved this question 3 - 4 times by now . . remember the answer . . 1 : 2
Answer: a
Problem: a , b , k start from the same place and travel in the same direction at speeds of 30 km / hr , 40 km / hr , 50 km / hr respectively . b starts two hours after a . if b and k overtake a at the same instant , how many hours after a did k start ?
Options: a ) 2.4 , b ) 3.2 , c ) 4.0 , d ) 4.8 , e ) 5.6
Rationale: "in 2 hours , a travels 60 km . b can catch a at a rate of 10 km / hr , so b catches a 6 hours after b starts . so a and b both travel a distance of 240 km . c needs 4.8 hours to travel 240 km , so c leaves 3.2 hours after a . the answer is b ."
Answer: b
Problem: a certain shade of gray paint is obtained by mixing 3 parts of white paint with 5 parts of black paint . if 2 gallons of the mixture is needed and the individual colors can be purchased only in one gallon or half gallon cans , what is the least amount of paint r , in gallons , that must be purchased in order to measure out the portions needed for the mixture ?
Options: a ) 2 , b ) 2 1 / 2 , c ) 3 , d ) 3 1 / 2 , e ) 4
Rationale: given w : b = 3 : 5 that means say 3 gallons of white paint + 5 gallons of black paint = 8 gallons of paint mixture . but we want least amount of whiteblack paints for minimum of 2 gallons of mixture , so lets reduce keeping same ratio , 1.5 : 2.5 gives 1.5 + 2.5 = 4 gallons of mixture , but we want only 2 gallons , lets further reduce 0.75 : 1.25 gives 1 + 1.5 = 2.5 gallons of mixture . this looks ok , but lets reduce further just to be sure 0.375 : 0.625 gives 0.5 + 1 = 1.5 gallons of mixture , thats less than 2 gallons of mixture , so not acceptable . so correct ans is 2.5 gallons . b
Answer: b
Problem: what least number must be subtracted from 652543 so that remaining no . is divisible by 12
Options: a ) 3 , b ) 5 , c ) 7 , d ) 8 , e ) 9
Rationale: "explanation : on dividing 652543 by 12 we get the remainder 7 , so 7 should be subtracted option c"
Answer: c
Problem: if 20 men can build a wall 112 metres long in 6 days , what length of a similar wall can be built by 25 men in 3 days ?
Options: a ) 65 mtr . , b ) 52 mtr , c ) 70 mtr . , d ) 78 mtr . , e ) 17 mtr .
Rationale: "20 men is 6 days can build 112 metres 25 men in 3 days can build = 112 * ( 25 / 20 ) x ( 3 / 6 ) = 70 meters answer : c ."
Answer: c
Problem: if the sides of a triangle are 26 cm , 24 cm and 12 cm , what is its area ?
Options: a ) 144 , b ) 772 , c ) 288 , d ) 266 , e ) 2848
Rationale: "the triangle with sides 26 cm , 24 cm and 12 cm is right angled , where the hypotenuse is 26 cm . area of the triangle = 1 / 2 * 24 * 12 = 144 cm 2 answer : a"
Answer: a
Problem: in a certain candy store , 22 % of the customers are caught sampling the candy and are charged a small fine , but 10 % of the customers who sample the candy are not caught . what is the total percent of all customers who sample candy ?
Options: a ) 22 % , b ) 23 % , c ) 24.4 % , d ) 25 % , e ) 34 %
Rationale: "since 10 % of the customers who sample the candyare notcaught , then 90 % of the customers who sample the candyarecaught : { % of customers who sample candy } * 0.90 = 0.22 ; { % of customers who sample candy } = 0.25 . answer : c ."
Answer: c
Problem: carl can wash all the windows of his house in 7 hours . his wife maggie can wash all the windows in 4 hours . how many hours will it take for both of them working together to wash all the windows ?
Options: a ) 2 , b ) 2 1 / 4 , c ) 11 6 / 2 , d ) 4 1 / 2 , e ) 5
Rationale: work hrs = ab / ( a + b ) = 28 / 11 = 11 6 / 2 answer is c
Answer: c
Problem: each month , after jill pays for rent , utilities , food , and other necessary expenses , she has one fifth of her net monthly salary left as discretionary income . of this discretionary income , she puts 30 % into a vacation fund , 20 % into savings , and spends 35 % on eating out and socializing . this leaves her with $ 108 dollar , which she typically uses for gifts and charitable causes . what is jill ’ s net monthly salary ?
Options: a ) $ 2400 , b ) $ 3200 , c ) $ 6000 , d ) $ 3600 , e ) $ 9600
Rationale: "let x be the monthly salary 15 % of 1 / 5 * x = 108 x = 3600 answer d"
Answer: d
Problem: if a certain toy store ' s revenue in november was 2 / 3 of its revenue in december and its revenue in january was 1 / 3 of its revenue in november , then the store ' s revenue in december was how many times the average ( arithmetic mean ) of its revenues in november and january ?
Options: a ) 1 / 4 , b ) 1 / 2 , c ) 2 / 3 , d ) 2 , e ) 3
Rationale: "let dec rev = 100 then nov rev is 2 / 3 ( 100 ) = > 67 therefore jan rev = 1 / 3 ( nov rev ) = 1 / 3 ( 67 ) = > 23 hence dec rev = x * ( nov rev + jan rev ) / 2 100 = x * ( 67 + 23 ) / 2 x = 100 / 45 = > 2.22 = 3 ans ) e"
Answer: e
Problem: the largest two digit number which is a perfect cube , is :
Options: a ) 25 , b ) 36 , c ) 49 , d ) 64 , e ) 81
Rationale: "explanation : 4 * 4 * 4 = 64 answer : d"
Answer: d
Problem: a , b , c and d enter into partnership . a subscribes 1 / 3 of the capital b 1 / 4 , c 1 / 5 and d the rest . how much share did a get in a profit of rs . 2475 ?
Options: a ) s . 800 , b ) s . 810 , c ) s . 825 , d ) s . 900 , e ) s . 920
Rationale: "2475 * 1 / 3 = 825 option c"
Answer: c
Problem: a rectangular tank measuring 5 m × 4.5 m × 2.1 m is dug in the centre of the field measuring 13.5 m × 2.5 . the earth dug out is spread evenly over the remaining portion of a field . how much is the level of the field raised ?
Options: a ) 4.0 m , b ) 4.1 m , c ) 4.2 m , d ) 4.3 m , e ) none of these
Rationale: area of the field = 13.5 × 2.5 = 33.75 m 2 area covered by the rectangular tank = 5 × 4.5 = 22.50 m 2 area of the field on which the earth dug out is to be spread = 33.75 – 22.50 = 11.25 m 2 let the required height be h . then , 11.25 × h = 5 × 4.5 × 2.1 or h = 4.2 m answer c
Answer: c
Problem: a batsman makes a score of 80 runs in the 11 th inning and thus increases his average by 5 . find his average after 11 th inning .
Options: a ) 40 , b ) 50 , c ) 62 , d ) 30 , e ) 56
Rationale: "let the average after 11 th inning = x then , average after 10 th inning = x - 5 10 ( x - 5 ) + 80 = 11 x x = 80 - 50 = 30 answer is d"
Answer: d
Problem: paul has to secure 50 % marks to clear his exam of class 7 th . he got 50 marks and failed by 10 marks . what is the maximum marks ?
Options: a ) 100 , b ) 110 , c ) 120 , d ) 210 , e ) 200
Rationale: c 120 to pass the exam ravish needs 50 + 10 = 60 marks . = > ( 60 / 50 ) * 100 = 120
Answer: c
Problem: on a two - dimensional coordinate plane , the line s = x ^ 2 - x ^ 3 touches the x - axis in how many places ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "apparently it ' s s = x ^ 2 - x ^ 3 instead of s = x ^ 2 - s ^ 3 . in this case : the x - intercept is the value ( s ) of x for s = 0 . 0 = x ^ 2 - x ^ 3 ; 0 = x ^ 2 ( 1 - x ) ; x = 0 or x = 1 . answer : c ."
Answer: c
Problem: two vertical ladders length of 6 m and 11 m are kept vertically at a distance of 12 m . find the top distance of both ladders ?
Options: a ) 22 , b ) 27 , c ) 13 , d ) 19 , e ) 17
Rationale: so distance between the top points = ad = 122 + 52 − − − − − − − √ = 13122 + 52 = 13 so in paper b he did well . answer : c
Answer: c
Problem: the volume of a certain substance is always directly proportional to its weight . if 48 cubic inches of the substance weigh 112 ounces , what is the volume , in cubic inches , of 84 ounces of this substance ?
Options: a ) 27
b ) 36
c ) 42
d ) 64
e ) 147
Rationale: 112 ounces of a substance has a volume of 48 cubic inches 84 ounces of a substance has a volume of ( 48 / 112 ) * 84 = 36 cubic inches answer b
Answer: b
Problem: a batsman makes a score of 95 runs in the 11 th inning and thus increases his average by 5 . find his average after 11 th inning .
Options: a ) 40 , b ) 50 , c ) 62 , d ) 45 , e ) 56
Rationale: "let the average after 11 th inning = x then , average after 10 th inning = x - 5 10 ( x - 5 ) + 95 = 11 x x = 95 - 50 = 45 answer is d"
Answer: d
Problem: the largest six digit number which is a perfect cube , is :
Options: a ) 970299 , b ) 907289 , c ) 992289 , d ) 900279 , e ) 999999
Rationale: "explanation : 99 * 99 * 99 = 970299 answer : a"
Answer: a
Problem: of the three - digit positive integers that have no digits equal to zero , how many have two digits that are equal to each other and the remaining digit different from the other two ?
Options: a ) 24 , b ) 36 , c ) 72 , d ) 1 , e ) 216
Rationale: "assume : a , b , c is the digit and a , b , c not = 0 thus a , b , c could be 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , and 9 count the possible way to get three digit number abc . a = b , and c must be different from a , b thus , there are 3 possible ways of digit arrangement : aac , aca , caa case i : aac = > ( digit 1 st ) x ( digit 2 nd ) x ( digit 3 rd ) = > 9 x 1 x 8 { pick any number from group = 9 possible ways } x { pick number the same as the first pick = 1 way } x { pick any number from the rest = 8 possible ways } = 9 x 1 x 8 = 72 possible ways case ii : aca = > same as case i you have 72 possible ways case iii : caa = > same as case i you have 72 possible ways total of this set of number = 72 + 72 + 72 = 216 e ) is the answer"
Answer: e
Problem: a cistern can be filled by a tap in 7 hours while it can be emptied by another tap in 9 hours . if both the taps are opened simultaneously , then after how much time will the cistern get filled ?
Options: a ) 4.5 hrs , b ) 5 hrs , c ) 6.5 hrs , d ) 17.2 hrs , e ) 31.5 hrs
Rationale: "net part filled in 1 hour = 1 / 7 - 1 / 9 = 2 / 63 therefore the cistern will be filled in 63 / 2 hours or 31.5 hours . answer : e"
Answer: e
Problem: 16.036 divided by 0.04 gives :
Options: a ) 40.09 , b ) 4.06 , c ) 40.06 , d ) 400.9 , e ) 400.6
Rationale: = 16.036 / 0.04 = 1603.6 / 4 = 400.9 answer is d .
Answer: d
Problem: a canoe has two oars , left and right . each oar either works or breaks . the failure or non - failure of each oar is independent of the failure or non - failure of the other . you can still row the canoe with one oar . the probability that the left oar works is 3 / 5 . the probability that the right oar works is also 3 / 5 . what is the probability r that you can still row the canoe ?
Options: a ) 9 / 25 , b ) 10 / 25 , c ) 6 / 10 , d ) 2 / 3 , e ) 21 / 25
Rationale: "simply look at the question from the other side . what is the probability that you can ’ t row the canoe ? this would be 2 / 5 x 2 / 5 = 4 / 25 . using the idea that the probability of something happening is 1 – the probability that it doesn ’ t happen , you can use the following equation to reach the right answer r : 1 – 4 / 25 = 21 / 25 . answer choice e ."
Answer: e
Problem: a is the average ( arithmetic mean ) of the first 7 positive multiples of 8 and b is the median of the first 3 positive multiples of positive integer n . if the value of a ^ 2 – b ^ 2 is zero , what is the value of n ?
Options: a ) 10 , b ) 12 , c ) 16 , d ) 24 , e ) 32
Rationale: "if a ^ 2 - b ^ 2 = 0 , then let ' s assume that a = b . a must equal the 4 th positive multiple of 4 , thus a = 32 , which also equals b . b is the second positive multiple of n , thus n = 32 / 2 = 16 . the answer is c ."
Answer: c
Problem: the population of a bacteria culture doubles every 3 minutes . approximately how many minutes will it take for the population to grow from 1,000 to 500,000 bacteria
Options: a ) 27 , b ) 12 , c ) 14 , d ) 16 , e ) 18
Rationale: this one ' s easy . 1000 * 2 ^ t = 500,000 2 ^ t = 500 now gauging , since 2 ^ 8 = 256 , then 2 ^ 9 = 512 so t = 9 but be careful , ' t ' is in time intervals of 3 minutes so answer is 9 * 3 = 27 minutes answer ( a )
Answer: a
Problem: shopkeeper rise price by 36 % and gives successive discount of 10 % and 15 % . what is overall % gain or loss ?
Options: a ) 5.04 % , b ) 4.04 % , c ) 3.04 % , d ) 6.04 % , e ) 7.04 %
Rationale: "let d initial price be 100 36 % rise now price = 136 / 100 * 100 = 136 10 % discount then price = 136 * 90 / 100 = 122.4 15 % discount then price = 122.4 * 85 / 100 = 104.04 so gain = 104.04 - 100 = 4.04 gain % = gain * 100 / cp = = > 4.04 * 100 / 100 = 4.04 % answer : b"
Answer: b
Problem: set j consists of 18 consecutive even numbers . if the smallest term in the set is - 22 , what is the range of the positive integers in set j ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10
Rationale: "since there are only 18 integers , another approach is the just list all 18 . we get : - 22 , - 20 , - 18 , - 16 , - 14 , - 12 , - 10 , - 8 , - 6 , - 4 , - 2 , 0 , 2 , 4 , 6 , 8 , 10 , 12 range of positive integers = 12 - 2 = 10 answer : e"
Answer: e
Problem: suresh and ramesh started a business investing rs . 24,000 and rs . 40,000 respectively . out of total profit of rs . 18,000 , what is suresh ' s share ?
Options: a ) s . 6750 , b ) s . 7750 , c ) s . 8750 , d ) s . 9372 , e ) s . 9750
Rationale: explanation : ratio of suresh and ramesh ' s share = 24,000 : 40,000 = 3 : 5 suresh ' s share = rs . ( 18000 x 3 / 8 ) = rs . 6750 answer : a
Answer: a
Problem: what is the square root of 36 , divided by 6 ?
Options: a ) 9 , b ) 36 , c ) 122 , d ) 6 , e ) 1
Rationale: "square root is a number times itself square root of 36 = 6 , 6 / 6 = 1 ( e ) 1"
Answer: e
Problem: a man swims downstream 32 km and upstream 24 km taking 4 hours each time , what is the speed of the man in still water ?
Options: a ) 9 , b ) 8 , c ) 6 , d ) 7 , e ) 2
Rationale: "32 - - - 4 ds = 8 ? - - - - 1 24 - - - - 4 us = 6 ? - - - - 1 m = ? m = ( 8 + 6 ) / 2 = 7 answer : d"
Answer: d
Problem: during a sale , the price of a pair of shoes is marked down 15 % from the regular price . after the sale ends , the price goes back to the original price . what is the percent of increase to the nearest percent from the sale price back to the regular price for the shoes ?
Options: a ) 9 % , b ) 10 % , c ) 11 % , d ) 18 % , e ) 90 %
Rationale: assume the price = 100 price during sale = 85 price after sale = 100 percent increase = 15 / 85 * 100 = 18 % approx . correct option : d
Answer: d
Problem: a and b can do a piece of work in 18 and 9 days respectively . a does the work for a few days and left , then b continued for 6 days . how many days did a and b work together ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: a and b work together for 2 days . a 1 day work 1 / 18 b 1 day work 1 / 9 let a work x days . then equation form is ( x / 18 ) + ( ( x + 6 ) / 9 ) = 1 from this equation x value is 2 . answer : b
Answer: b
Problem: a and b can finish a work in 10 days while a alone can do the same work in 20 days . in how many days b alone will complete the work ?
Options: a ) 20 days , b ) 48 days , c ) 98 days , d ) 31 days , e ) 22 days
Rationale: "b = 1 / 10 – 1 / 20 = 1 / 20 = > 20 days answer : a"
Answer: a
Problem: a combustion reaction forms carbon dioxide . a carbon dioxide molecule contains one carbon and two oxygen atoms . if , over a period of 12 minutes , a combustion reaction creates 12,000 molecules of carbon dioxide then approximately how many more atoms of oxygen than carbon are created on average per minute ?
Options: a ) 20 , b ) 60 , c ) 600 , d ) 1,000 , e ) 1,200
Rationale: "solution : 12,000 carbon dioxide molecules are created over a period of 12 minutes . therefore 12,000 / 12 = 1,000 carbon dioxide molecules are created on average per minute each carbon dioxide molecule contains one carbon atom and two oxygen atoms . so 1,000 carbon dioxide molecules contain 1 × 1,000 = 1,000 carbon atoms and 2 × 1,000 = 2,000 oxygen atoms . the difference is 2,000 – 1,000 = 1,000 . the correct answer is d ."
Answer: d
Problem: 8 ! / ( 8 - 2 ) ! = ?
Options: a ) 36 , b ) 46 , c ) 56 , d ) 66 , e ) 96
Rationale: 8 ! / ( 8 - 2 ) ! = 8 ! / 6 ! = 8 * 7 = 56 . hence , the correct answer is c .
Answer: c
Problem: sally , mark , sarah , steve and jim are inheriting the money from their grandmother . she left them $ 527500 to split equally between all of them . if the money is split equally , how much money will each person receive ?
Options: a ) $ 135875 , b ) $ 52700 , c ) $ 127900 , d ) $ 105500 , e ) $ 105000
Rationale: there are 5 people inheriting the money . we have to take the total of the inheritance and divide it by 5 for each person receiving money . $ 527500 / 5 = $ 105500 . therefore the correct answer is d .
Answer: d
Problem: if the cost price of 165 chocolates is equal to the selling price of 150 chocolates , the gain percent is
Options: a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12
Rationale: "let c . p . of each chocolate be re . 1 . then , c . p . of 150 chocolates = rs . 150 ; s . p . of 150 chocolates = rs . 165 . gain % = 15 / 150 * 100 = 10 % answer : c"
Answer: c
Problem: on a trip covering 450 km , a bicyclist travels the first 300 km at 20 km per hour and the remainder of the distance at 15 km per hour . what is the average speed , in km per hour , for the entire trip ?
Options: a ) 16.5 , b ) 17.0 , c ) 17.5 , d ) 18.0 , e ) 18.5
Rationale: "time 1 = 300 / 20 = 15 hours time 2 = 150 / 15 = 10 hours total time = 25 hours average speed = 450 / 25 = 18 km / hr the answer is d ."
Answer: d
Problem: jack and jill work at a hospital with 2 other workers . for an internal review , 2 of the 4 workers will be randomly chosen to be interviewed . what is the probability that jack and jill will both be chosen ?
Options: a ) 1 / 3 , b ) 1 / 6 , c ) 1 / 15 , d ) 3 / 8 , e ) 2 / 3
Rationale: "1 / 4 c 2 = 1 / 6 . answer : b ."
Answer: b
Problem: if 15 % of 30 % of 50 % of a number is 126 , then what is the number ?
Options: a ) 5000 , b ) 5600 , c ) 5400 , d ) 4500 , e ) none of these
Rationale: "let the number be a given , 15 / 100 * 30 / 100 * 50 / 100 * a = 126 = > 3 / 20 * 3 / 10 * 1 / 2 * a = 126 = > a = 10 * 20 * 10 * 2 = 5600 . answer : b"
Answer: b
Problem: a full stationary oil tank that is a right circular cylinder has a radius of 100 feet and a height of 25 feet . oil is pumped from the stationary tank to an oil truck that has a tank that is a right circular cylinder until the truck ' s tank is completely filled . if the truck ' s tank has a radius of 5 feet and a height of 12 feet , how far ( in feet ) did the oil level drop in the stationary tank ?
Options: a ) 2.5 , b ) 0.025 , c ) 0.05 , d ) 0.03 , e ) 3
Rationale: "the volume of oil pumped to the tank = the volume of oil taken away from stationary cylinder . pi * 25 * 12 = pi * h * 100 * 100 ( h is distance that the oil level dropped ) h = 300 / 10,000 = 3 / 100 = 0.03 ft the answer is d ."
Answer: d
Problem: company x provides bottled water to its employees in 5 liter bottles , $ 2 each . at least how many 5 l bottles must company x buy monthly , so that new contract with $ 100 fixed monthly rate and $ 1 for 10 l bottle each paid off ? ( assume that no other costs apply )
Options: a ) 121 , b ) 125 , c ) 132 , d ) 134 , e ) 138
Rationale: let the no . of 5 liter bottles be x , so the no . of 10 l bottles will be x / 2 ( to equate the vol . ) since the total cost will be equal , 2 x = 100 + x / 2 so x = 133.33 or 134 . answer is ( d ) .
Answer: d
Problem: when the price of an article was reduced by 35 % its sale increased by 80 % . what was the net effect on the sale ?
Options: a ) 17 % increase , b ) 44 % decrease , c ) 60 % increase , d ) 66 % increase , e ) 66 % decrease
Rationale: "if n items are sold for $ p each , revenue is $ np . if we reduce the price by 35 % , the new price is 0.65 p . if we increase the number sold by 80 % , the new number sold is 1.8 n . so the new revenue is ( 0.65 p ) ( 1.8 n ) = 1.17 np , which is 1.17 times the old revenue , so is 17 % greater . answer : a"
Answer: a
Problem: two trains travel in opposite directions at 36 kmph and 45 kmph and a man sitting in slower train passes the faster train in 10 seconds . the length of the faster train is
Options: a ) 225 m , b ) 100 m , c ) 120 m , d ) 180 m , e ) none
Rationale: "solution relative speed = ( 36 + 45 ) km / hr = ( 81 x 5 / 18 ) m / sec = ( 45 / 2 ) m / sec length of the train = ( 45 / 2 x 10 ) m = 225 m . answer a"
Answer: a
Problem: s ( n ) is a n - digit number formed by attaching the first n perfect squares , in order , into one integer . for example , s ( 1 ) = 1 , s ( 2 ) = 14 , s ( 3 ) = 149 , s ( 4 ) = 14916 , s ( 5 ) = 1491625 , etc . how many digits r are in s ( 99 ) ?
Options: a ) r = 350 , b ) r = 353 , c ) r = 354 , d ) r = 356 , e ) 357
Rationale: "focus on the points where the number of digits in squares change : 1 , 2 , 3 - single digit squares . first 2 digit number is 10 . 4 , 5 , . . . 9 - two digit squares . to get 9 , the last number with two digit square , think that first 3 digit number is 100 which is 10 ^ 2 . so 9 ^ 2 must be the last 2 digit square . 10 , 11 , 12 , . . . 31 - three digit squares . to get 31 , think of 1000 - the first 4 digit number . it is not a perfect square but 900 is 30 ^ 2 . 32 ^ 2 = 2 ^ 10 = 1024 , the first 4 digit square . 32 - 99 - four digit squares . to get 99 , think of 10,000 - the first 5 digit number which is 100 ^ 2 . so number of digits in s ( 99 ) = 3 * 1 + 6 * 2 + 22 * 3 + 68 * 4 = 3 + 12 + 66 + 272 = r = 353 . b"
Answer: b
Problem: with a uniform speed a car covers the distance in 8 hours . had the speed been increased by 6 km / hr , the same distance could have been covered in 7 1 / 2 hours . what is the distance covered ?
Options: a ) 187 km , b ) 480 km , c ) 720 km , d ) 297 km , e ) 671 km
Rationale: "let the distance be x km . then , x / ( 7 1 / 2 ) - x / 8 = 6 2 x / 15 - x / 8 = 6 = > x = 720 km . answer : c"
Answer: c
Problem: if a and b are positive integers and ( 2 ^ a ) ^ b = 2 ^ 2 , what is the value of 2 ^ a * 2 ^ b ?
Options: a ) 8 , b ) 4 , c ) 16 , d ) 32 , e ) 64
Rationale: "2 ^ ab = 2 ^ 2 therefore ab = 2 either a = 1 or 2 or b = 2 or 1 therefore 2 ^ a * 2 ^ b = 2 ^ ( a + b ) = 2 ^ 3 = 8 a"
Answer: a
Problem: when 242 is divided by a certain divisor the remainder obtained is 4 . when 698 is divided by the same divisor the remainder obtained is 8 . however , when the sum of the two numbers 242 and 698 is divided by the divisor , the remainder obtained is 7 . what is the value of the divisor ?
Options: a ) 5 , b ) 17 , c ) 13 , d ) 23 , e ) none of these
Rationale: "let that divisor be x since remainder is 4 or 8 it means divisor is greater than 8 . now 242 - 4 = 238 = kx ( k is an integer and 234 is divisble by x ) similarly 698 - 8 = 690 = lx ( l is an integer and 689 is divisible by x ) adding both 698 and 242 = ( 238 + 690 ) + 4 + 8 = x ( k + l ) + 12 when we divide this number by x then remainder will be equal to remainder of ( 12 divided by x ) = 7 hence x = 12 - 7 = 5 hence a"
Answer: a
Problem: in a college , the ratio of the number of boys to girls is 6 : 5 . if there are 200 girls , the total number of students in the college is
Options: a ) 440 , b ) 520 , c ) 620 , d ) 720 , e ) 820
Rationale: "explanation : let the boy are 6 x and girls are 5 x = > 5 x = 200 = > x = 40 total students = 6 x + 5 x = 11 x = 11 ( 40 ) = 440 option a"
Answer: a
Problem: what is the greater of the two numbers whose product is 1280 , given that the sum of the two numbers exceeds their difference by 32 ?
Options: a ) a ) 90 , b ) b ) 100 , c ) c ) 110 , d ) d ) 70 , e ) 80
Rationale: "let the greater and the smaller number be g and s respectively . g * s = 1288 g + s exceeds g - s by 32 i . e . , g + s - ( g - s ) = 32 i . e . , 2 s = 32 = > s = 16 . g = 1280 / s = 80 . answer : e"
Answer: e
Problem: p , q and r have rs . 8000 among themselves . r has two - thirds of the total amount with p and q . find the amount with r ?
Options: a ) rs . 3200 , b ) rs . 3600 , c ) rs . 2400 , d ) rs . 4000 , e ) none of these
Rationale: "let the amount with r be rs . r r = 2 / 3 ( total amount with p and q ) r = 2 / 3 ( 8000 - r ) = > 3 r = 16000 - 2 r = > 5 r = 16000 = > r = 3200 . answer : a"
Answer: a
Problem: an error 2 % 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 ) 4.04 % , b ) 4.00 % , c ) 4.14 % , d ) 5.04 % , e ) none
Rationale: "100 cm is read as 102 cm . a 1 = ( 100 x 100 ) cm 2 and a 2 ( 102 x 102 ) cm 2 . ( a 2 - a 1 ) = [ ( 102 ) 2 - ( 100 ) 2 ] = ( 102 + 100 ) x ( 102 - 100 ) = 404 cm 2 . percentage error = 404 x 100 % = 4.04 % 100 x 100 a"
Answer: a
Problem: in 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 1000 m ?
Options: a ) 122.9 m , b ) 127.5 m . , c ) 122.2 m , d ) 222.9 m , e ) 212.5 m
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 1000 m , the number of meters by which a beats c = ( 1000 * 212.5 ) / 1000 = 212.5 m . answer : e
Answer: e
Problem: how many positive integers between 1 and 300 are there such that they are multiples of 9 ?
Options: a ) 31 , b ) 33 , c ) 35 , d ) 36 , e ) 23
Rationale: "multiples of 9 = 9 , 18,27 , - - - - - 297 number of multiples of 15 = > 9 * 33 = 297 answer is b"
Answer: b
Problem: a squirrel runs up a cylindrical post , in a perfect spiral path making one circuit for each rise of 5 feet . how many feet does the squirrel travels if the post is 25 feet tall and 3 feet in circumference ?
Options: a ) 10 feet
b ) 12 feet
c ) 13 feet
d ) 15 feet
e ) 18 feet
Rationale: total circuit = 25 / 5 = 5 total feet squirrel travels = 5 * 3 = 15 feet answer : d
Answer: d
Problem: a man swims downstream 48 km and upstream 42 km taking 6 hours each time ; what is the speed of the current ?
Options: a ) 3 kmph , b ) 0.5 kmph , c ) 13 kmph , d ) 6.5 kmph , e ) 7 : 3 kmph
Rationale: "explanation : 48 - - - 6 ds = 8 ? - - - - 1 42 - - - - 6 us = 7 ? - - - - 1 s = ? s = ( 8 - 7 ) / 2 = 0.5 answer : option b"
Answer: b
Problem: the average weight of 16 girls in a class is 50.25 kg and that of the remaining 8 girls is 45.15 kg . find the average weights of all the girls in the class .
Options: a ) a ) 48.55 , b ) b ) 49 , c ) c ) 51 , d ) d ) 61 , e ) e ) 62
Rationale: required average = ( 50.25 x 16 + 45.15 x 8 ) / ( 16 + 8 ) = ( 804 + 361.20 ) / 24 = 1165.20 / 24 = 48.55 kg answer is a
Answer: a
Problem: if rs . 782 is divided into 3 parts , proportional to 1 / 2 : 2 / 3 : 3 / 4 find the first part .
Options: a ) 190 , b ) 204 , c ) 220 , d ) 230 , e ) none of these
Rationale: explanation : 1 / 2 : 2 / 3 : 3 / 4 = 6 : 8 : 9 first part = 782 ∗ 6 / 23 = 204 option b
Answer: b
Problem: the hcf of two numbers is 50 and the other two factors of their lcm are 11 and 12 . what is the largest number .
Options: a ) 462 , b ) 450 , c ) 480 , d ) 504 , e ) 600
Rationale: "explanation : hcf of the two numbers = 50 hcf will be always a factor of lcm 50 is factor of lcm other two factors are 11 & 12 then the numbers are ( 50 * 11 ) and ( 50 x 12 ) = 550 and 600 answer : option e"
Answer: e
Problem: find the value for m ? 21 ( m + n ) + 21 = 21 ( - m + n ) + 21
Options: a ) 0 , b ) - 1 , c ) 1 , d ) 2 , e ) 3
Rationale: 21 m + 21 n - 21 = - 21 m + 21 n + 21 42 m = 42 = > m = 1 c
Answer: c
Problem: find 40 % of 320
Options: a ) 96 , b ) 94 , c ) 128 , d ) 74 , e ) 110
Rationale: "we know that r % of m is equal to r / 100 × m . so , we have 40 % of 320 40 / 100 × 320 = 128 answer : c"
Answer: c
Problem: at 1 : 00 pm , a truck left city p and headed toward city q at a constant speed of 50 km / h . one hour later , a car left city q and headed toward city p along the same road at a constant speed of 40 km / h . if the distance between city p and city q is 230 km , at what time will the truck and the car meet each other ?
Options: a ) 4 : 00 , b ) 4 : 30 , c ) 5 : 00 , d ) 5 : 30 , e ) 6 : 00
Rationale: "at 2 : 00 pm , the truck and the car are 180 km apart . the truck and the car complete a distance of 90 km each hour . the time it takes to meet is 180 / 90 = 2 hours . they will meet at 4 : 00 pm . the answer is a ."
Answer: a
Problem: a certain telescope increases the visual range at a particular location from 50 kilometers to 150 kilometers . by what percent is the visual range increased by using the telescope ?
Options: a ) 30 % , b ) 33 1 / 2 % , c ) 40 % , d ) 60 % , e ) 200 %
Rationale: original visual range = 50 km new visual range = 150 km percent increase in the visual range by using the telescope = ( 150 - 50 ) / 50 * 100 % = 2 * 100 % = 200 % answer e
Answer: e
Problem: the ratio between the length and the breadth of a rectangular park is 3 : 2 . if a man cycling along the boundary 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 ) 153200 , b ) 153400 , c ) 153600 , d ) 154000 , e ) 154200
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 2 . c"
Answer: c
Problem: a contractor undertakes to built a walls in 50 days . he employs 60 peoples for the same . however after 25 days he finds that only 40 % of the work is complete . how many more man need to be employed to complete the work in time ?
Options: a ) 25 , b ) 90 , c ) 35 , d ) 20 , e ) none of these
Rationale: "60 men complete 0.4 work in 25 days . applying the work rule , m 1 × d 1 × w 2 = m 2 × d 2 × w 1 we have , 60 × 25 × 0.6 = m 2 × 25 × 0.4 or m 2 = 60 × 25 × 0.6 / 25 × 0.4 = 90 men answerb"
Answer: b
Problem: excluding stoppages , the average speed of a bus is 50 km / hr and including stoppages , the average speed of the bus is 40 km / hr . for how many minutes does the bus stop per hour ?
Options: a ) 12 min , b ) 18 min , c ) 16 min , d ) 20 min , e ) 26 min
Rationale: "in 1 hr , the bus covers 50 km without stoppages and 40 km with stoppages . stoppage time = time take to travel ( 50 - 40 ) km i . e 10 km at 50 km / hr . stoppage time = 10 / 50 hrs = 12 min answer : a"
Answer: a
Problem: the largest prime number is ?
Options: a ) 11 , b ) 13 , c ) 5 , d ) 7 , e ) 9
Rationale: "the largest prime number is 13 . b )"
Answer: b
Problem: the total marks obtained by a student in mathematics and physics is 20 and his score in chemistry is 20 marks more than that in physics . find the average marks scored in mathamatics and chemistry together .
Options: a ) 40 , b ) 26 , c ) 20 , d ) 28 , e ) 22
Rationale: "let the marks obtained by the student in mathematics , physics and chemistry be m , p and c respectively . given , m + c = 20 and c - p = 20 m + c / 2 = [ ( m + p ) + ( c - p ) ] / 2 = ( 20 + 20 ) / 2 = 20 . answer : c"
Answer: c
Problem: how many numbers from 10 to 10000 are exactly divisible by 9 ?
Options: a ) 900 , b ) 1000 , c ) 1110 , d ) 1200 , e ) 1400
Rationale: "10 / 9 = 1 and 10000 / 9 = 1111 = = > 1111 - 1 = 1110 . therefore 1110 answer : c"
Answer: c
Problem: the average age of 36 students in a group is 14 years . when teacher ' s age is included to it , the average increases by one . what is the teacher ' s age in years ?
Options: a ) 21 years , b ) 71 years , c ) 51 years , d ) 91 years , e ) 11 years
Rationale: "explanation : age of the teacher = ( 37 * 15 - 36 * 14 ) years = 51 years . answer : c"
Answer: c
Problem: find the principle on a certain sum of money at 5 % per annum for 4 years if the amount being rs . 1120 ?
Options: a ) 933 , b ) 1067 , c ) 1977 , d ) 1056 , e ) 1097
Rationale: "1120 = p [ 1 + ( 5 * 4 ) / 100 ] p = 933 answer : a"
Answer: a
Problem: out of 10 students in a class , 4 are from maharashtra , 3 are from karnataka , and 3 are from goa . four students are to be selected at random . what are the chances that at least one is from karnataka ?
Options: a ) 1 / 3 , b ) 4 / 9 , c ) 5 / 6 , d ) 3 / 7 , e ) 1 / 4
Rationale: "total possible ways of selecting 4 students out of 10 = 10 c 4 = ( 10 * 9 * 8 * 7 ) / ( 4 * 3 * 2 * 1 ) = 210 the number of ways of selecting a 4 students in which no student belongs to karnataka = 7 c 4 number of ways of selecting atleast one student from karnataka = 15 c 4 - 7 c 4 = 175 probability = 175 / 210 = 5 / 6 answer is c"
Answer: c
Problem: a sum was put at simple interest at a certain rate for 3 years had it been put at 3 % higher rate , it would have fetched 81 more . find the sum .
Options: a ) 500 , b ) 600 , c ) 700 , d ) 800 , e ) 900
Rationale: "difference in s . i . = p × t / 100 ( r 1 − r 2 ) ⇒ 81 = p × 3 x 3 / 100 ( ∵ r 1 - r 2 = 2 ) ⇒ p = 81 × 100 / 3 x 3 = 900 answer e"
Answer: e
Problem: the least whole number which when subtracted from both the terms of the ratio 6 : 7 to give a ratio less than 16 : 21 , is
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "explanation : let x is subtracted . then , ( 6 − x ) / ( 7 − x ) < 16 / 21 21 ( 6 — x ) < 16 ( 7 — x ) = > 5 x > 14 = x > 2.8 least such number is 3 option a"
Answer: a
Problem: the total cost of 100 paper plates and 200 paper cups is $ 6.00 at the same rates what is the total cost of 20 of the plates and 40 of the cups ?
Options: a ) $ . 90 , b ) $ 1.00 , c ) $ 1.20 , d ) $ 1.50 , e ) $ 1.60
Rationale: u dont need to go through all this what u have with u is 100 p + 200 c = $ 6.00 just divide the equation by 5 and you will get what u are looking for 20 p + 40 c = $ 1.20 therefore oa is c
Answer: c
Problem: if the price of sugar rises from rs . 3 per kg to rs . 5 per kg , a person , to have no increase in the expenditure on sugar , will have to reduce his consumption of sugar by
Options: a ) 15 % , b ) 20 % , c ) 25 % , d ) 30 % , e ) 40 %
Rationale: sol . let the original consumption = 100 kg and new consumption = x kg . so , 100 x 3 = x × 5 = x = 60 kg . ∴ reduction in consumption = 40 % . answer e
Answer: e
Problem: a 1200 m long train crosses a tree in 120 sec , how much time will i take to pass a platform 300 m long ?
Options: a ) 176 sec , b ) 190 sec , c ) 178 sec , d ) 150 sec , e ) 276 sec
Rationale: "l = s * t s = 1200 / 120 s = 10 m / sec . total length ( d ) = 1500 m t = d / s t = 1500 / 10 t = 150 sec answer : d"
Answer: d
Problem: find the average of all prime numbers between 30 and 50 .
Options: a ) 30 , b ) 33.6 , c ) 39.8 , d ) 44.9 , e ) none
Rationale: "sol . there are five prime numbers between 30 and 50 . they are 31 , 37 , 41 , 43 and 47 ∴ required average = [ 31 + 37 + 41 + 43 + 47 / 5 ] = 199 / 5 = 39.8 answer c"
Answer: c
Problem: there are 2 available positions and 50 candidates , one half of whom are democrats and another half are republicans . if it was decided that the positions would be filled at random , then what is the probability w that the both positions will be taken by members of just one party ?
Options: a ) 1 / 25 , b ) 12 / 49 , c ) 1 / 4 , d ) 24 / 49 , e ) 1 / 2
Rationale: "w probability of one party having both spots : ( 1 / 2 ) * ( 24 / 49 ) = 12 / 49 ( 1 / 2 ) or ( 25 / 50 ) because it does not matter which party or which person gets the first spot . ( 24 / 49 ) because after one person from a particular party is chosen , there are 24 members of the same party left out of 49 total candidates . since this result can happen for both parties , ( 12 / 49 ) + ( 12 / 49 ) = ( 24 / 49 ) answer : d"
Answer: d
Problem: a gambler bought $ 3,000 worth of chips at a casino in denominations of $ 30 and $ 100 . that evening , the gambler lost 16 chips , and then cashed in the remainder . if the number of $ 30 chips lost was 2 more or 2 less than the number of $ 100 chips lost , what is the largest amount of money that the gambler could have received back ?
Options: a ) $ 2,040 , b ) $ 2,120 , c ) $ 1,960 , d ) $ 1,920 , e ) $ 2,030
Rationale: "in order to maximize the amount of money that the gambler kept , we should maximize # of $ 30 chips lost and minimize # of $ 100 chips lost , which means that # of $ 30 chips lost must be 2 more than # of $ 100 chips lost . so , if # of $ 30 chips lost is x then # of $ 100 chips lost should be x - 2 . now , given that total # of chips lost is 16 : x + x - 2 = 16 - - > x = 9 : 9 $ 30 chips were lost and 9 - 2 = 7 $ 100 chips were lost . total worth of chips lost is 9 * 30 + 7 * 100 = $ 970 , so the gambler kept $ 3,000 - $ 970 = $ 2,030 . answer : e"
Answer: e
Problem: an association of mathematics teachers has 1,260 members . only 445 of these members cast votes in the election for president of the association . what percent of the total membership voted for the winning candidate if the winning candidate received 60 percent of the votes cast ?
Options: a ) 75 % , b ) 58 % , c ) 42 % , d ) 34 % , e ) 22 %
Rationale: "total umber of members = 1260 number of members that cast votes = 445 since , winning candidate received 60 percent of the votes cast number of votes for winning candidate = ( 60 / 100 ) * 445 = 267 percent of total membership that voted for winning candidate = ( 267 / 1260 ) * 100 = 21.19 % answer e"
Answer: e
Problem: what is the smallest positive integer x , such that 5000 x is a perfect cube ?
Options: a ) 4 , b ) 6 , c ) 8 , d ) 25 , e ) 18
Rationale: "take out the factors of 5000 that will come 10 ^ 3 * 5 . for perfect cube you need every no . raise to the power 3 . for 5000 x to be a perfect cube , you need two 5 that means 25 . d is the answer ."
Answer: d
Problem: a leak in the bottom of a tank can empty the full tank in 6 hours . an inlet pipe fills water at the rate of 6 litres a minute . when the tank is full , the inlet is opened and due to the leak , the tank is empty in 12 hours . how many litres does the cistern hold ?
Options: a ) 7580 , b ) 7960 , c ) 8290 , d ) 4320 , e ) none
Rationale: "solution work done by the inlet in 1 hour = ( 1 / 6 - 1 / 12 ) = 1 / 12 . work done by the inlet in 1 min . = ( 1 / 12 × 1 / 60 ) = 0.001389 volume of 0.001389 part = 6 litres . therefore , volume of whole = 1 / 0.001389 x 6 ‹ = › 4320 litres . answer d"
Answer: d
Problem: maxwell leaves his home and walks toward brad ' s house . one hour later , brad leaves his home and runs toward maxwell ' s house . if the distance between their homes is 24 kilometers , maxwell ' s walking speed is 4 km / h , and brad ' s running speed is 6 km / h . what is the total time it takes maxwell before he meets up with brad ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 8
Rationale: "total distance = 24 kms maxwell speed = 4 kms / hr maxwell travelled for 1 hour before brad started , therefore maxwell traveled for 4 kms in 1 hour . time taken = total distance / relative speed total distance after brad started = 20 kms relative speed ( opposite side ) ( as they are moving towards each other speed would be added ) = 6 + 4 = 10 kms / hr time taken to meet brad after brad started = 20 / 10 = 2 hrs distance traveled by maxwell = maxwell ' s speed * time taken = 4 * 2 = 8 + 4 = 12 kms . . . therefore total time taken by maxwell to meet brad = distance travelled by maxwell / maxwell ' s speed = 12 / 4 = 3 hrs . . . answer a"
Answer: a
Problem: one robot builds a robot in 1 hour , another one builds a robot in 2 hours . the 2 robots work together and when a new robot is complete , it joins the others , working at a constant rate of one robot in 2 hours . how much time will it take until there are 3 robots altogether , if the robots build only one robot at a time ?
Options: a ) 40 min , b ) 94 min , c ) 110 min , d ) 112 min , e ) 120 min
Rationale: "first the 2 robots work at the rate of 1 + 1 / 2 = 3 / 2 so they complete one robot in 2 / 3 rd of an hour = 40 minutes - ( 1 ) and now we have 3 robots in 40 minutes answer - a"
Answer: a
Problem: if 20 percent of the students at a certain school went to a camping trip and took more than $ 100 , and 75 percent of the students who went to the camping trip did not take more than $ 100 , what percentage of the students at the school went to the camping trip ?
Options: a ) 95 , b ) 90 , c ) 85 , d ) 80 , e ) 75
Rationale: "let x be the number of students in the school . 0.2 x students went to the trip and took more than 100 $ . they compose ( 100 - 75 ) = 25 % of all students who went to the trip . therefore the toal of 0.2 x / 0.25 = 0.8 x students went to the camping which is 80 % . the answer is d"
Answer: d
Problem: in a group of 400 readers who read science fiction or literacy works or both , 250 read science fiction and 230 read literacy works . how many read both science fiction and literacy works ?
Options: a ) 70 , b ) 80 , c ) 90 , d ) 100 , e ) 110
Rationale: "consider total number of reader n ( s u l ) = 400 people who read science fiction n ( s ) = 250 people who read literacy works n ( l ) = 230 both science fiction and literacy n ( s ∩ l ) = ? n ( s u l ) = n ( s ) + n ( l ) - n ( s ∩ l ) 400 = 250 + 230 - n ( s ∩ l ) n ( s ∩ l ) = 480 - 400 n ( s ∩ l ) = 80 so people read both science fiction and literacy works are 80 answer : b"
Answer: b
Problem: if 12 men and 16 boys can do a piece of work in 5 days and 13 men together will 24 boys can do it in 4 days . compare the daily work done by a man with that of a boy ?
Options: a ) 2 : 5 , b ) 2 : 9 , c ) 2 : 4 , d ) 2 : 1 , e ) 2 : 2
Rationale: 12 m + 16 b - - - - - 5 days 13 m + 24 b - - - - - - - 4 days 60 m + 80 b = 52 m + 96 b 8 m = 16 b = > 1 m = 2 b m : b = 2 : 1 answer : d
Answer: d
Problem: the pilot of a small aircraft with a 40 - gallon fuel tank wants to fly to cleveland , which is 480 miles away . the pilot recognizes that the current engine , which can fly only 10 miles per gallon , will not get him there . by how many miles per gallon must the aircraft ’ s fuel efficiency be improved to make the flight to cleveland possible ?
Options: a ) 2 , b ) 4 , c ) 12 , d ) 40 , e ) 160
Rationale: "actual miles / gallon is = 480 / 40 = 12 miles / gallon . current engine miles / gallon is 10 miles / gallon . additional 2 miles / gallon is required to match the actual mileage . imo option a ."
Answer: a
Problem: a certain bus driver is paid a regular rate of $ 12 per hour for any number of hours that does not exceed 40 hours per week . for any overtime hours worked in excess of 40 hours per week , the bus driver is paid a rate that is 75 % higher than his regular rate . if last week the bus driver earned $ 976 in total compensation , how many total hours did he work that week ?
Options: a ) 60 , b ) 68 , c ) 65 , d ) 64 , e ) 61
Rationale: "for 40 hrs = 40 * 12 = 480 excess = 976 - 480 = 496 for extra hours = . 75 ( 12 ) = 9 + 12 = 21 number of extra hrs = 496 / 21 = 23.62 total hrs = 40 + 23.62 = 63.62 = 64 approx . answer d 64"
Answer: d
Problem: three numbers are in the ratio 3 : 4 : 5 and their average is 36 . the largest number is :
Options: a ) 30 , b ) 98 , c ) 27 , d ) 21 , e ) 45
Rationale: "explanation : let the numbers be 3 x , 4 x and 5 x , then , ( 3 x + 4 x + 5 x ) / 3 = 36 = > 12 x = 36 * 3 = > x = 9 largest number 5 x = 5 * 9 = 45 answer : e"
Answer: e
Problem: 5 cats can catch 5 mice in 5 minutes . how many cats does it take to catch 100 mice in 100 minutes ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: let x be no . of cat 5 cat catch 5 mice in 5 min 5 cat catch 1 mice in ( 5 / 5 = 1 min ) 1 cat catch 1 mice in 1 * 5 = 5 min 1 cat catch 100 mice in 5 * 100 min x cat catch 100 mice in ( 5 * 100 ) / x min a / q ( 5 * 100 ) / x = 100 = > 5 * 100 = x * 100 = > x = 5 answer : e
Answer: e
Problem: the tax on a commodity is diminished by 19 % and its consumption increased by 15 % . the effect on revenue is ?
Options: a ) 2 % , b ) 8.85 % , c ) 5.85 % , d ) 6.85 % , e ) 1 %
Rationale: "100 * 100 = 10000 81 * 115 = 9315 - - - - - - - - - - - 10000 - - - - - - - - - - - 685 100 - - - - - - - - - - - ? = > 6.85 % decrease answer : d"
Answer: d