Cheukting/mathqa huggingface dataset:
Question (gain): in a graduate physics course , 70 percent of the students are male and 30 percent of the students are married . if two - sevenths of the male students are married , what fraction of the female students is married ?
Options: a ) 2 / 7 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 5 / 7
Rationale: "let assume there are 100 students of which 70 are male and 30 are females if 30 are married then 70 will be single . now its given that two - sevenths of the male students are married that means 2 / 7 of 70 = 20 males are married if 30 is the total number of students who are married and out of that 20 are males then the remaining 10 will be females who are married . total females = 30 married females = 10 then single females = 30 - 10 = 20 we need to find the fraction of female students who are single i . e single female students / total female student = 10 / 30 = 1 / 3 [ b ]"
Answer: b
Question (geometry): the area of a rectangle is 63 sq m . the width is two meters shorter than the length . what is the width ?
Options: a ) 9
b ) 7
c ) - 9
d ) 11
e ) 6
Rationale: a = l x w w = l - 2 l = w + 2 a = ( w + 2 ) x w a = w ^ 2 + 2 x w 63 = w ^ 2 + 2 w 0 = w ^ 2 + 2 w - 63 0 = ( w + 9 ) ( w - 7 ) w = - 9 and w = 7 , width can not be negative so w = 7 answer is b
Answer: b
Question (general): when the positive integer x is divided by 9 , the remainder is 5 . what is the remainder when 8 x is divided by 9 ?
Options: a ) 0 , b ) 1 , c ) 3 , d ) 4 , e ) 6
Rationale: "i tried plugging in numbers x = 9 q + 5 x = 14 8 x = 112 8 x / 9 = 9 * 12 + 4 remainder is 4 . answer is d ."
Answer: d
Question (physics): a man can row upstream at 25 kmph and downstream at 65 kmph , and then find the speed of the man in still water ?
Options: a ) 45 , b ) 86 , c ) 30 , d ) 78 , e ) 38
Rationale: "us = 25 ds = 65 m = ( 65 + 25 ) / 2 = 45 answer : a"
Answer: a
Question (physics): a train crosses a bridge of length 150 m in 7.5 seconds and a lamp post on the bridge in 2.5 seconds . what is the length of the train in metres ?
Options: a ) 37.5 m , b ) 75 m , c ) 25 m , d ) 80 m , e ) 30 m
Rationale: let length of train = l case - 1 : distance = 150 + l ( while crossing the bridge ) time = 7.5 seconds i . e . speed = distance / time = ( 150 + l ) / 7.5 case - 2 : distance = l ( while passing the lamp post ) time = 2.5 seconds i . e . speed = distance / time = ( l ) / 2.5 but since speed has to be same in both cases so ( 150 + l ) / 7.50 = ( l ) / 2.5 i . e . 3 l = l + 150 i . e . 2 l = 150 i . e . l = 75 answer : option b
Answer: b
Question (gain): at a special sale , 12 tickets can be purchased for the price of 3 tickets . if 12 tickets are purchased at the sale , the amount saved will be what percent of the original price of the 12 tickets ?
Options: a ) 20 % , b ) 33.3 % , c ) 40 % , d ) 50 % , e ) 75 %
Rationale: "let the price of a ticket be rs . 100 , so 3 tickets cost 300 & 12 tickets cost 1200 12 tickets purchased at price of 3 tickets ie . , for 300 , so amount saved s rs . 900 , % of 5 tickets = ( 900 / 1200 ) * 100 = 75 % answer : e"
Answer: e
Question (general): if x > 0 , x / 40 + x / 20 is what percent of x ?
Options: a ) 6 % , b ) 25 % , c ) 37 1 / 2 % , d ) 60 % , e ) 75 %
Rationale: "just plug and chug . since the question asks for percents , pick 100 . ( but any number will do . ) 100 / 40 + 100 / 20 = 2.5 + 5 = 7.5 7.5 is 75 % of 100 = e"
Answer: e
Question (general): the average age of students of a class is 15.8 years . the average age of boys in the class is 16.6 years and that of the girls is 15.4 years . the ration of the number of boys to the number of girls in the class is :
Options: a ) 1 : 2 , b ) 2 : 3 , c ) 2 : 4 , d ) 2 : 1 , e ) 2 : 9
Rationale: "let the ratio be k : 1 . then , k * 16.6 + 1 * 15.4 = ( k + 1 ) * 15.8 = ( 16.6 - 15.8 ) k = ( 15.8 - 15.4 ) = k = 0.4 / 0.6 = 1 / 2 required ratio = 1 / 1 : 1 = 1 : 2 . answer : a"
Answer: a
Question (other): solution a is 20 % salt and solution b is 60 % salt . if you have 30 ounces of solution a and 60 ounces of solution b , in what ratio could you mix solution a with solution b to produce 50 ounces of a 50 % salt solution ?
Options: a ) 6 : 4 , b ) 6 : 14 , c ) 4 : 4 , d ) 4 : 6 , e ) 1 : 3
Rationale: "forget the volumes for the time being . you have to mix 20 % and 80 % solutions to get 50 % . this is very straight forward since 50 is int he middle of 20 and 80 so we need both solutions in equal quantities . if this does n ' t strike , use w 1 / w 2 = ( a 2 - aavg ) / ( aavg - a 1 ) w 1 / w 2 = ( 60 - 50 ) / ( 50 - 20 ) = 1 / 3 so the volume of the two solutions will be equal . answer has to be 1 : 3 e ."
Answer: e
Question (physics): if 11.25 m of a uniform steel rod weighs 42.75 kg . what will be the weight of 8 m of the same rod ?
Options: a ) 22.8 kg , b ) 25.6 kg , c ) 28 kg , d ) 30.4 kg , e ) none of these
Rationale: explanation : let the required weight be x kg . then , less length , less weight ( direct proportion ) = > 11.25 : 8 : : 42.75 : x = > 11.25 x x = 8 x 42.75 = > x = ( 8 x 42.75 ) / 11.25 = > x = 30.4 answer : d
Answer: d
Question (physics): the radius of the wheel of a bus is 250 cms and the speed of the bus is 66 km / h , then the r . p . m . ( revolutions per minutes ) of the wheel is
Options: a ) 70 , b ) 125 , c ) 300 , d ) 500 , e ) none of these
Rationale: "radius of the wheel of bus = 250 cm . then , circumference of wheel = 2 ï € r = 500 ï € = 1571.43440 cm distance covered by bus in 1 minute = 66 â  „ 60 ã — 1000 ã — 100 cms distance covered by one revolution of wheel = circumference of wheel = 1571.45 cm â ˆ ´ revolutions per minute = 6600000 / 60 ã — 1571.43 = 70 answer a"
Answer: a
Question (physics): 1000 men have provisions for 21 days . if 800 more men join them , for how many days will the provisions last now ?
Options: a ) 12.9 , b ) 12.5 , c ) 12.6 , d ) 11.6 , e ) 12.1
Rationale: "1000 * 21 = 1800 * x x = 11.6 answer : d"
Answer: d
Question (geometry): a rectangular wall is covered entirely with two kinds of decorative tiles : regular and jumbo . 1 / 3 of the tiles are jumbo tiles , which have a length three times that of regular tiles and have the same ratio of length to width as the regular tiles . if regular tiles cover 40 square feet of the wall , and no tiles overlap , what is the area of the entire wall ?
Options: a ) 160 , b ) 220 , c ) 360 , d ) 440 , e ) 560
Rationale: "the number of jumbo tiles = x . the number of regular tiles = 2 x . assume the ratio of the dimensions of a regular tile is a : a - - > area = a ^ 2 . the dimensions of a jumbo tile is 3 a : 3 a - - > area = 9 a ^ 2 . the area of regular tiles = 2 x * a ^ 2 = 40 . the area of jumbo tiles = x * 9 a ^ 2 = 4.5 ( 2 x * a ^ 2 ) = 4.5 * 40 = 180 . total area = 40 + 180 = 220 . answer : b ."
Answer: b
Question (general): how many positive integers less than 10,000 are such that the product of their digits is 210 ?
Options: a ) 24 , b ) 30 , c ) 48 , d ) 54 , e ) 72
Rationale: "210 = 2 x 5 x 3 x 7 = 5 x 6 x 7 x 1 = 5 x 6 x 7 those are the only sets of digits we can use to for the numbers ( any other combination of factors will have two digit factors ) . numbers using 2,5 , 3,7 = 4 ! numbers using 5,6 , 7,1 = 4 ! numbers using 5 , 6,7 ( 3 - digit numbers ) = 3 ! answer = 24 + 24 + 6 = 54 answer is ( d )"
Answer: d
Question (general): find the last term of a g . p whose first term is 9 and common ratio is ( 1 / 3 ) if the sum of the terms of the g . p is ( 40 / 3 )
Options: a ) 1 / 3 , b ) 2 / 5 , c ) 1 / 4 , d ) 2 / 3 , e ) 4 / 5
Rationale: sum of the g . p . = ( first term - r * last term ) / 1 – r 40 / 3 = 9 – 1 / 3 ( last term ) / 2 / 3 last term = ( - 40 / 3 * 2 / 3 + 9 ) * 3 = - 80 / 3 + 27 = 1 / 3 answer : a
Answer: a
Question (general): the average of marks obtained by 120 boys was 36 . if the average of marks of passed boys was 39 and that of failed boys was 15 , the number of boys who passed the examination is ?
Options: a ) 105 , b ) 110 , c ) 120 , d ) 130 , e ) 140
Rationale: "let the number of boys who passed = x . then , 39 x x + 15 x ( 120 - x ) = 120 x 36 24 x = 4320 - 1800 = > x = 2520 / 24 x = 105 . hence , the number of boys passed = 105 . answer : a"
Answer: a
Question (general): shekar scored 76 , 65 , 82 , 62 and 85 marks in mathematics , science , social studies , english and biology respectively . what are his average marks ?
Options: a ) 74 , b ) 69 , c ) 75 , d ) 85 , e ) 90
Rationale: "explanation : average = ( 76 + 65 + 82 + 62 + 85 ) / 5 = 370 / 5 = 74 hence average = 74 answer : a"
Answer: a
Question (physics): a rectangular plot measuring 10 meters by 50 meters is to be enclosed by wire fencing . if the poles of the fence are kept 5 meters apart . how many poles will be needed ?
Options: a ) 46 m , b ) 66 m , c ) 26 m , d ) 24 m , e ) 25 m
Rationale: "perimeter of the plot = 2 ( 10 + 50 ) = 120 m no of poles = 120 / 5 = 24 m answer : d"
Answer: d
Question (physics): x can finish a work in 21 days . y can finish the same work in 15 days . y worked for 5 days and left the job . how many days does x alone need to finish the remaining work ?
Options: a ) 12 , b ) 13 , c ) 16 , d ) 14 , e ) 18
Rationale: "work done by x in 1 day = 1 / 21 work done by y in 1 day = 1 / 15 work done by y in 5 days = 5 / 15 = 1 / 3 remaining work = 1 – 1 / 3 = 2 / 3 number of days in which x can finish the remaining work = ( 2 / 3 ) / ( 1 / 21 ) = 14 d"
Answer: d
Question (general): country c imposes a two - tiered tax on imported cars : the first tier imposes a tax of 16 % of the car ' s price up to a certain price level . if the car ' s price is higher than the first tier ' s level , the tax on the portion of the price that exceeds this value is 8 % . if ron imported a $ 14,000 imported car and ended up paying $ 1440 in taxes , what is the first tier ' s price level ?
Options: a ) $ 1600 , b ) $ 6000 , c ) $ 6050 , d ) $ 7050 , e ) $ 4000
Rationale: "let t be the tier price , p be total price = 14000 per the given conditions : 0.16 t + 0.08 ( p - t ) = 1440 - - - - > t = 8000 . e is the correct answer ."
Answer: e
Question (general): what is the remainder when the number r = 14 ^ 2 * 15 ^ 8 is divided by 5 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 4 , e ) 5
Rationale: "14 ^ 2 has units digit 6 15 ^ 8 has units digit 5 thus r = 14 ^ 2 * 15 ^ 8 has units digit 0 and will be divisible by 5 . the remainder will be zero answer : ( a )"
Answer: a
Question (physics): p is able to do a piece of work in 20 days and q can do the same work in 10 days . if they can work together for 2 days , what is the fraction of work left ?
Options: a ) 5 / 10 , b ) 9 / 10 , c ) 7 / 10 , d ) 6 / 10 , e ) 4 / 10
Rationale: "explanation : amount of work p can do in 1 day = 1 / 20 amount of work q can do in 1 day = 1 / 10 amount of work p and q can do in 1 day = 1 / 20 + 1 / 10 = 3 / 20 amount of work p and q can together do in 2 days = 2 × ( 3 / 20 ) = 3 / 10 fraction of work left = 1 – 3 / 10 = 7 / 10 answer : option c"
Answer: c
Question (general): carina has 70 ounces of coffee divided into 5 - and 10 - ounce packages . if she has 2 more 5 - ounce packages than 10 - ounce packages , how many 10 - ounce packages does she have ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "lets say 5 and 10 ounce packages be x and y respectively . given that , 5 x + 10 y = 70 and x = y + 2 . what is the value of y . substituting the x in first equation , 5 y + 10 + 10 y = 70 - > y = 60 / 15 . = 4 c"
Answer: c
Question (general): the average weight of a , b and c is 45 kg . if the average weight of a and b be 42 kg and that of b and c be 43 kg , then the weight of b is :
Options: a ) 33 kg , b ) 31 kg , c ) 32 kg , d ) 36 kg , e ) 35 kg
Rationale: "let a , b , c represent their respective weights . then , we have : a + b + c = ( 45 x 3 ) = 135 . . . . ( i ) a + b = ( 42 x 2 ) = 84 . . . . ( ii ) b + c = ( 43 x 2 ) = 86 . . . . ( iii ) adding ( ii ) and ( iii ) , we get : a + 2 b + c = 170 . . . . ( iv ) subtracting ( i ) from ( iv ) , we get : b = 35 b ' s weight = 35 kg . e"
Answer: e
Question (general): john found that the average of 15 numbers is 40 . if 11 is added to each number then the mean of number is ?
Options: a ) 51 , b ) 45 , c ) 65 , d ) 78 , e ) 64
Rationale: "( x + x 1 + . . . x 14 ) / 15 = 40 51 option a"
Answer: a
Question (physics): a boat goes 100 km downstream in 8 hours , and 75 km upstream in 15 hours . the speed of the stream is ?
Options: a ) 3 , b ) 6.5 , c ) 5.5 , d ) 4 , e ) 3.75
Rationale: "100 - - - 10 ds = 12.5 ? - - - - 1 75 - - - - 15 us = 5 ? - - - - - 1 s = ( 12.5 - 5 ) / 2 = 3.75 kmph . answer : e"
Answer: e
Question (other): what is the number of integers from 1 to 1000 ( inclusive ) that are divisible by neither 11 nor by 30 ?
Options: a ) 884 , b ) 890 , c ) 892 , d ) 910 , e ) 945
Rationale: "normally , i would use the method used by bunuel . it ' s the most accurate . but if you are looking for a speedy solution , you can use another method which will sometimes give you an estimate . looking at the options ( most of them are spread out ) , i wont mind trying it . ( mind you , the method is accurate here since the numbers start from 1 . ) in 1000 consecutive numbers , number of multiples of 11 = 1000 / 11 = 90 ( ignore decimals ) in 1000 consecutive numbers , number of multiples of 35 = 1000 / 35 = 28 number of multiples of 11 * 35 i . e . 385 = 1000 / 385 = 2 number of integers from 1 to 1000 that are divisible by neither 11 nor by 35 = 1000 - ( 90 + 28 - 2 ) { using the concept of sets here ) = 884 think : why did i say the method is approximate in some cases ? think what happens if the given range is 11 to 1010 both inclusive ( again 1000 numbers ) what is the number of multiples in this case ? a"
Answer: a
Question (physics): two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 26 kmph and 21 kmph respectively . when they meet , it is found that one train has traveled 60 km more than the other one . the distance between the two stations is ?
Options: a ) 288 , b ) 564 , c ) 877 , d ) 278 , e ) 178
Rationale: "1 h - - - - - 5 ? - - - - - - 60 12 h rs = 26 + 21 = 47 t = 12 d = 47 * 12 = 564 answer : b"
Answer: b
Question (general): what is the smallest no . which must be added to 25268 so as to obtain a sum which is divisible by 11 ?
Options: a ) 5 , b ) 10 , c ) 11 , d ) 20 , e ) 30
Rationale: "for divisibility by 11 , the difference of sums of digits at even and odd places must be either zero or divisible by 11 . for 25268 , difference = ( 2 + 2 + 8 ) - ( 5 + 6 ) = 12 - 11 = 1 . the units digit is at odd place . so we add 10 to the number = > 25268 + 10 = 25278 now , ( 2 + 2 + 8 ) - ( 5 + 7 ) = 12 - 12 = 0 = > 25268 is also divisible by 11 b"
Answer: b
Question (physics): a train 455 m long , running with a speed of 63 km / hr will pass a tree in ?
Options: a ) 22 sec , b ) 16 sec , c ) 17 sec , d ) 39 sec , e ) 12 sec
Rationale: "speed = 63 * 5 / 18 = 35 / 2 m / sec time taken = 455 * 2 / 35 = 39 sec answer : d"
Answer: d
Question (gain): the price of an item is discounted 10 percent on day 1 of a sale . on day 2 , the item is discounted another 10 percent , and on day 3 , it is discounted an additional 15 percent . the price of the item on day 3 is what percentage of the sale price on day 1 ?
Options: a ) 28 % , b ) 40 % , c ) 64.8 % , d ) 76.5 % , e ) 72 %
Rationale: "original price = 100 day 1 discount = 10 % , price = 100 - 10 = 90 day 2 discount = 10 % , price = 90 - 9 = 81 day 3 discount = 15 % , price = 81 - 12.15 = 68.85 which is 68.85 / 90 * 100 of the sale price on day 1 = ~ 76.5 % answer d"
Answer: d
Question (physics): an aeroplane covers a certain distance at a speed of 120 kmph in 4 hours . to cover the same distance in 1 2 / 3 hours , it must travel at a speed of :
Options: a ) 520 , b ) 288 , c ) 820 , d ) 740 , e ) 720
Rationale: "distance = ( 240 x 5 ) = 480 km . speed = distance / time speed = 480 / ( 5 / 3 ) km / hr . [ we can write 1 2 / 3 hours as 5 / 3 hours ] required speed = ( 480 x 3 / 5 ) km / hr = 288 km / hr answer b ) 288 km / hr"
Answer: b
Question (general): the present age of a father is 3 years more than 3 times the age of his son . 5 years hence , father ' s age will be 10 years more than twice the age of the son . find the present age of the father .
Options: a ) 33 , b ) 38 , c ) 27 , d ) 40 , e ) 48
Rationale: if the present age be x years . father ' s will be ( 3 x + 3 ) years . . so , ( 3 x + 3 + 5 ) = 2 ( x + 3 ) + 10 or , x = 8 so the fathers present age = ( 3 x + 3 ) = ( 3 * 8 + 3 ) years = 27 years . . answer : option c
Answer: c
Question (physics): the h . c . f . of two numbers is 12 and their l . c . m . is 600 . if one of the number is 20 , find the other ?
Options: a ) 100 , b ) 360 , c ) 120 , d ) 200 , e ) 150
Rationale: "other number = 12 * 600 / 20 = 360 answer is b"
Answer: b
Question (general): what is the next no . 4 12 84
Options: a ) 632 , b ) 732 , c ) 832 , d ) 850 , e ) 902
Rationale: "3 ^ 0 + 3 = 4 3 ^ 2 + 3 = 12 3 ^ 4 + 3 = 84 3 ^ 6 + 3 = 732 answer : b"
Answer: b
Question (general): x and y are positive integers . when x is divided by 9 , the remainder is 2 , and when x is divided by 7 , the remainder is 4 . when y is divided by 11 , the remainder is 3 , and when y is divided by 13 , the remainder is 12 . what is the least possible value of y - x ?
Options: a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16
Rationale: "when x is divided by 9 , the remainder is 2 : so , the possible values of x are : 2 , 11 , 21 , 29 , etc . when x is divided by 7 , the remainder is 4 : so , the possible values of x are : 4 , 11,18 , . . . stop . since both lists include 11 , the smallest possible value of x is 11 . when y is divided by 11 , the remainder is 3 : so , the possible values of y are : 3 , 14 , 25 , etc . when y is divided by 13 , the remainder is 12 : so , the possible values of y are : 12 , 25 , . . . stop . since both lists include 25 , the smallest possible value of y is 25 since the smallest possible values of x and y are 11 and 25 respectively , the smallest possible value of y - x is 14 . so , c is the correct answer to the original question ."
Answer: c
Question (general): at joes steakhouse the hourly wage for a chef is 22 % greater than that of a dishwasher , and the hourly wage of a dishwasher is half as much as the hourly wage of a manager . if a managers wage is $ 8.50 per hour , how much less than a manager does a chef earn each hour ?
Options: a ) $ 1.40 , b ) $ 2.40 , c ) $ 3.315 , d ) $ 4.40 , e ) $ 5.40
Rationale: "manager wages per hour = $ 8.50 dishwasher wages per hour = half of manager ' s wages . = 1 / 2 ( $ 8.50 ) = = > $ 4.25 chef wages per hour = 22 % greater than dishwasher wages - - > 22 % of $ 4.25 = ( 22 * ( $ 4.25 ) ) / 100 - - > ( $ 93.5 ) / 100 - - > $ 0.935 therefore , chef wages per hour = $ 4.25 + $ 0.935 = = > $ 5.185 difference of wages between manager and chef = $ 8.50 - $ 5.185 = = > $ 3.315 answer : c"
Answer: c
Question (gain): if xerox paper costs 5 cents a sheet and a buyer gets 10 % discount on all xerox paper one buys after the first 2000 papers and 20 % discount after first 10000 papers , how much will it cost to buy 15000 sheets of xerox paper ?
Options: a ) $ 1250 , b ) $ 700 , c ) $ 1350 , d ) $ 900 , e ) $ 1000
Rationale: 30 sec approach - solve it using approximation 15000 sheet at full price , 5 cent = 750 15000 sheet at max discount price , 4 cent = 600 your ans got to be between these two . ans b it is .
Answer: b
Question (general): if the sum of two positive integers is 18 and the difference of their squares is 36 , what is the product of the two integers ?
Options: a ) 108 , b ) 80 , c ) 128 , d ) 135 , e ) 143
Rationale: "let the 2 positive numbers x and y x + y = 18 - - 1 x ^ 2 - y ^ 2 = 36 = > ( x + y ) ( x - y ) = 36 - - 2 using equation 1 in 2 , we get = > x - y = 2 - - 3 solving equation 1 and 3 , we get x = 10 y = 8 product = 10 * 8 = 80 answer b"
Answer: b
Question (general): a certain number when divided by 80 leaves a remainder 25 , what is the remainder if the same no . be divided by 15 ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 9
Rationale: "explanation : 80 + 25 = 105 / 15 = 7 ( remainder ) d"
Answer: d
Question (geometry): a rectangular circuit board is designed to have a width of w inches , a length of l inches , a perimeter of p inches , and an area of c square inches . which of the following equations must be true ?
Options: a ) 2 w ^ 2 + pw + 2 c = 0
b ) 2 w ^ 2 − pw + 2 c = 0
c ) 2 w ^ 2 − pw − 2 c = 0
d ) w ^ 2 + pw + c = 0
e ) w ^ 2 − pw + 2 c = 0
Rationale: p = 2 ( l + w ) - - - - - - - - - - - - - - - - - 1 ) c = lw - - - - - - - - - - - - - - - - - - - - - - - - 2 ) option a is not possible why ? ? because all the terms are positive . lets try option b , put value of p and a from 1 and 2 we have , 2 w ^ 2 - 2 ( l + w ) w + 2 ( lw ) 2 w ^ 2 - 2 lw - 2 w ^ 2 + 2 lw = 0 . hence answer is b .
Answer: b
Question (gain): a candidate appearing for an examination has to secure 35 % marks to pass paper i . but he secured only 42 marks and failed by 23 marks . what is the maximum mark for paper i ?
Options: a ) 110 , b ) 120 , c ) 186 , d ) 140 , e ) 150
Rationale: "he secured 42 marks nd fail by 23 marks so total marks for pass the examinatn = 65 let toal marks x x * 35 / 100 = 65 x = 186 answer : c"
Answer: c
Question (other): how many odd integers from 1 to 50 ( both inclusive ) have odd number of factors ?
Options: a ) 13 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "integers having odd number of factors will be perfect squares . odd numbers will have odd perfect squares . thus , the possible values for the perfect squares are : 1,9 , 25,49 and the corresponding integers are 1,3 , 5,7 ( more than 3 ) . thus b is the correct answer ."
Answer: b
Question (physics): a rectangular plot measuring 90 metres by 40 metres is to be enclosed by wire fencing . if the poles of the fence are kept 5 metres apart , how many poles will be needed ?
Options: a ) 55 , b ) 56 , c ) 57 , d ) 52 , e ) none of these
Rationale: "solution perimeter of the plot = 2 ( 90 + 40 ) = 260 m . ∴ number of poles = [ 260 / 5 ] = 52 m answer d"
Answer: d
Question (general): find the value for x from below equation : x / 3 = - 2 ?
Options: a ) - 6 , b ) 1 , c ) - 2 , d ) - 3 , e ) 4
Rationale: 1 . multiply both sides by 3 : x * 3 / 3 = - 2 / 3 2 . simplify both sides : x = - 6 a
Answer: a
Question (physics): dan can do a job alone in 12 hours . annie , working alone , can do the same job in just 9 hours . if dan works alone for 4 hours and then stops , how many hours will it take annie , working alone , to complete the job ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10
Rationale: "dan can complete 1 / 12 of the job per hour . in 4 hours , dan completes 4 ( 1 / 12 ) = 1 / 3 of the job . annie can complete 1 / 9 of the job per hour . to complete the job , annie will take 2 / 3 / 1 / 9 = 6 hours . the answer is c ."
Answer: c
Question (geometry): the measurement of a rectangular box with lid is 25 cmx 18 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 ) 972 , e ) 964
Rationale: "d = 18 , r = 9 ; volume of the largest sphere = 4 / 3 π r 3 = 4 / 3 * π * 9 * 9 * 9 = 972 π cm 3 answer : d"
Answer: d
Question (other): the probability that a computer company will get a computer hardware contract is 3 / 4 and the probability that it will not get a software contract is 5 / 9 . if the probability of getting at least one contract is 4 / 5 , what is the probability that it will get both the contracts ?
Options: a ) 11 / 30 , b ) 31 / 60 , c ) 41 / 80 , d ) 51 / 120 , e ) 71 / 180
Rationale: "let , a ≡ event of getting hardware contract b ≡ event of getting software contract ab ≡ event of getting both hardware and software contract . p ( a ) = 3 / 4 , p ( ~ b ) = 5 / 9 = > p ( b ) = 1 - ( 5 / 9 ) = 4 / 9 . a and b are not mutually exclusive events but independent events . so , p ( at least one of a and b ) = p ( a ) + p ( b ) - p ( ab ) . = > 4 / 5 = ( 3 / 4 ) + ( 4 / 9 ) - p ( ab ) . = > p ( ab ) = 71 / 180 . hence , the required probability is 71 / 180 . the answer is e ."
Answer: e