Cheukting/mathqa huggingface dataset:
Question (gain): exactly 18 % of the reporters for a certain wire service cover local politics in country x . if 40 % of the reporters who cover politics for the wire service do not cover local politics in country x , what percent of the reporters for the wire service do not cover politics ?
Options: a ) 20 % , b ) 42 % , c ) 44 % , d ) 70 % , e ) 84 %
Rationale: "let ' s assume there are 100 reporters - - > 18 reporters cover local politics . now , as 40 % of the reporters who cover all politics do not cover local politics then the rest 60 % of the reporters who cover politics do cover local politics , so if there are x reporters who cover politics then 60 % of them equal to 18 ( # of reporters who cover local politics ) : 0.6 x = 18 - - > x = 30 , hence 30 reporters cover politics and the rest 100 - 30 = 70 reporters do not cover politics at all . answer : d ."
Answer: d
Question (general): when 200 is divided by positive integer x , the remainder is 5 . what is the remainder when 395 is divided by x ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 6 , e ) 5
Rationale: "if 200 / x leaves a reminder 5 then ( 200 - 5 ) i . e . 195 is divisible by x so ( 200 + 195 ) / x leaves a reminder rem ( 200 / x ) + rem ( 195 / x ) = > 5 + 0 = 5 answer : e"
Answer: e
Question (general): xy = 1 then what is ( 7 ^ ( x + y ) ^ 2 ) / ( 7 ^ ( x - y ) ^ 2 )
Options: a ) 2401 , b ) 4 , c ) 8 , d ) 16 , e ) 32
Rationale: "( x + y ) ^ 2 - ( x - y ) ^ 2 ( x + y + x - y ) ( x + y - x + y ) ( 2 x ) ( 2 y ) 4 xy 4 7 ^ 4 = 2401 answer a"
Answer: a
Question (general): if a ( a + 2 ) = 80 and b ( b + 2 ) = 80 , where a ≠ b , then a + b =
Options: a ) - 3 , b ) - 4 , c ) - 6 , d ) - 8 , e ) - 2
Rationale: i . e . if a = 8 then b = - 10 or if a = - 10 then b = 8 but in each case a + b = - 10 + 8 = - 2 answer : e
Answer: e
Question (physics): a man sitting in a train which is traveling at 40 kmph observes that a goods train , traveling in opposite direction , takes 9 seconds to pass him . if the goods train is 280 m long , find its speed . ?
Options: a ) 50 kmph , b ) 58 kmph , c ) 62 kmph , d ) 65 kmph , e ) 72 kmph
Rationale: "relative speed = 280 / 9 m / sec = ( ( 280 / 9 ) * ( 18 / 5 ) ) kmph = 112 kmph . speed of goods train = ( 112 - 40 ) kmph = 72 kmph . answer : e"
Answer: e
Question (general): evaluate : 45 - 12 * 3 * 2 = ?
Options: a ) 62 , b ) 52 , c ) 37 , d ) 12 , e ) 22
Rationale: "according to order of operations , 12 ? 3 ? 2 ( division and multiplication ) is done first from left to right 12 * * 2 = 4 * 2 = 8 hence 45 - 12 * 3 * 2 = 45 - 8 = 37 correct answer c"
Answer: c
Question (physics): a tank is 25 m long 12 m wide and 6 m deep . the cost of plastering its walls and bottom at 55 paise per sq m is
Options: a ) rs . 209.20 , b ) rs . 309.20 , c ) rs . 409.20 , d ) rs . 509.20 , e ) none of these
Rationale: explanation : area to be plastered = [ 2 ( l + b ) ã — h ] + ( l ã — b ) = [ 2 ( 25 + 12 ) ã — 6 ] + ( 25 ã — 12 ) = 744 sq m cost of plastering = 744 ã — ( 55 / 100 ) = rs . 409.20 answer : c
Answer: c
Question (general): let p be a prime number greater than 2 and let n = 14 p . how many even numbers divide n ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: answer : a . there is exactly one . the prime factorization of 14 is 14 = 2 * 7 , so n = 2 * 7 * p = 7 * 2 * p = 7 * 2 p , so 2 p is the only even number that divides n .
Answer: a
Question (gain): compound interest of rs . 5000 at 10 % per annum for 1 1 / 2 years will be ( interest compounded half yearly ) .
Options: a ) rs . 473 , b ) rs . 374 , c ) rs . 495 , d ) rs . 788 , e ) none of the above
Rationale: "10 % interest per annum will be 5 % interest half yearly for 3 terms ( 1 1 / 2 years ) so compound interest = 5000 [ 1 + ( 5 / 100 ) ] ^ 3 - 5000 = 5000 [ ( 21 / 20 ) ^ 3 - 1 ] = 5000 ( 9261 - 8000 ) / 8000 = 5 * 1261 / 8 = 788 answer : d"
Answer: d
Question (general): a train starts full of passengers . at the first station , it drops one - third of the passengers and takes 280 more . at the second station , it drops one - half of the new total and takes 12 more . on arriving at the third station , it is found to have 248 passengers . find the number of passengers in the beginning .
Options: a ) 240 , b ) 248 , c ) 280 , d ) 288 , e ) 290
Rationale: let x be no . of passengers at beginning at , 1 st station is drops 1 / 3 rd so remaining 2 / 3 rd are in train only plus 280 i . e . , 2 x / 3 + 280 at 2 nd stop 1 / 2 of new total and 12 more i . e . , ( 2 x / 3 + 280 ) / 2 + 12 = 248 on solving above equation we get x as 288 answer : d
Answer: d
Question (gain): the credit card and a global payment processing companies have been suffering losses for some time now . a well known company recently announced its quarterly results . according to the results , the revenue fell to $ 52.0 billion from $ 69.0 billion , a year ago . by what percent did the revenue fall ?
Options: a ) 20.8 , b ) 24.6 , c ) 31.8 , d ) 32.5 , e ) 33.8
Rationale: "$ 69 - $ 52 = 17 $ ( 17 / 69 ) * 100 = 24.6 % answer : b"
Answer: b
Question (gain): what will be the compound interest on rs . 35000 after 3 years at the rate of 12 % per annum
Options: a ) rs 13123.20 , b ) rs 14103.48 , c ) rs 12172.48 , d ) rs 14172.48 , e ) none of these
Rationale: "explanation : ( 35000 × ( 1 + 12 / 100 ) 3 ) = > 35000 × 28 / 25 × 28 / 25 × 28 / 25 = > 49172.48 so compound interest will be 49172.48 - 35000 = rs 14172.48 option d"
Answer: d
Question (other): in what ratio must wheat at rs . 3.20 pe rkg be mixed with wheat at rs . 2.90 per kg so that the mixture be worth rs . 3.08 per kg
Options: a ) 3 : 4 , b ) 3 : 2 , c ) 3 : 5 , d ) 3 : 7 , e ) 2 : 3
Rationale: if 2 ingredients are mixed , then the required ratio is given by , the rule of allegation c . p of a unit quantity of cheaper ( c ) c . p . of a unit quantity of dearer ( d ) mean price ( m ) d - m m - c  required ratio is cheaper quantity : dearer quantity = ( d - m ) : ( m - c ) answer with explanation : given i . c . p of a unit quantity of i kind ( p ) = 3.20 ii . c . p of a unit quantity of ii kind ( p ) = 2.90 iii . mean price ( p ) = 3.08 iv . d – m = 3.08 – 2.90 = 0.18 v . m – c = 3.20 – 3.08 = 0.12  required ratio = 0.18 : 0.12 = 3 : 2 answer : b
Answer: b
Question (physics): a , b and c can do a piece of work in 24 days , 30 days and 40 days respectively . they began the work together but c left 10 days before the completion of the work . in how many days was the work completed ?
Options: a ) 12.5 days , b ) 16 days , c ) 18 days , d ) 11 days , e ) 38 days
Rationale: "one day work of a , b and c = 1 / 24 + 1 / 30 + 1 / 40 = 1 / 10 work done by a and b together in the last 10 days = 10 * ( 1 / 24 + 1 / 30 ) = 3 / 4 remaining work = 1 / 4 the number of days required for this initial work = 2.5 days . the total number of days required = 10 + 2.5 = 12.5 days . answer : a"
Answer: a
Question (general): if a 2 + b 2 + c 2 = 213 and ab + bc + ca = 6 , then a + b + c is
Options: a ) 14 , b ) 20 , c ) 15 , d ) 32 , e ) 64
Rationale: "by formula , ( a + b + c ) ^ 2 = a ^ 2 + b ^ 2 + c ^ 2 + 2 ( ab + bc + ca ) , since , a ^ 2 + b ^ 2 + c ^ 2 = 213 and ab + bc + ca = 6 , ( a + b + c ) ^ 2 = 213 + 2 ( 6 ) = 225 = 15 ^ 2 therefore : a + b + c = 15 answer : c"
Answer: c
Question (general): if a - b = 6 and a 2 + b 2 = 48 , find the value of ab .
Options: a ) 8 , b ) 10 , c ) 12 , d ) 6 , e ) 19
Rationale: "2 ab = ( a 2 + b 2 ) - ( a - b ) 2 = 48 - 36 = 12 ab = 6 . answer : d"
Answer: d
Question (gain): a certain article of clothing was discounted during a special sale to 2 / 5 of its original retail price . when the clothing did n ' t sell , it was discounted even further to 1 / 2 of its original retail price during a second sale . by what percent did the price of this article of clothing decrease from the first sale to the second sale ?
Options: a ) 50 % , b ) 33.33 % , c ) 25 % , d ) 16.66 % , e ) 12.5 %
Rationale: "say the original retail price of the item was $ 200 . the price after the first sale = 3 / 5 * $ 200 = $ 120 . the price after the second sale = 1 / 2 * $ 200 = $ 100 . the percent change from the first sale to the second = ( 120 - 100 ) / 120 = 1 / 3 = 16.66 % . answer : d ."
Answer: d
Question (general): a committee is reviewing a total of 30 x black - and - white films and 6 y color films for a festival . if the committee selects y / x % of the black - and - white films and all of the color films , what fraction of the selected films are in color ?
Options: a ) 22 / 21 , b ) 20 / 21 , c ) 23 / 21 , d ) 25 / 21 , e ) 28 / 21
Rationale: "say x = y = 10 . in this case we would have : 30 x = 300 black - and - white films ; 6 y = 60 color films . y / x % = 10 / 10 % = 1 % of the black - and - white films , so 3 black - and - white films and all 60 color films , thus total of 63 films were selected . color films thus compose 60 / 63 = 20 / 21 of the selected films . answer : b"
Answer: b
Question (gain): after paying a 10 percent tax on all income over $ 3000 , a person had a net income of $ 12000 . what was the income before taxes ?
Options: a ) $ 13300 , b ) $ 13000 , c ) $ 12900 , d ) $ 10000 , e ) $ 9000
Rationale: let x be the income over 3000 then ( x - x / 10 ) + 3000 = 12000 = > x = 10000 therefore income before taxes = 10000 + 3000 = 13000 option ( b )
Answer: b
Question (gain): sam invested rs . 8000 @ 10 % per annum for one year . if the interest is compounded half - yearly , then the amount received by sam at the end of the year will be ?
Options: a ) 3200.0 , b ) 11520.0 , c ) 8820.0 , d ) 7354.0 , e ) 16537.11
Rationale: "p = rs . 8000 ; r = 10 % p . a . = 5 % per half - year ; t = 1 year = 2 half - year amount = [ 8000 * ( 1 + 5 / 100 ) 2 ] = ( 8000 * 21 / 20 * 21 / 20 ) = rs . 8820.00 answer : c"
Answer: c
Question (general): half a number plus 5 is 11 . what is the number ?
Options: a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14
Rationale: "solution let x be the number . always replace ` ` is ' ' with an equal sign ( 1 / 2 ) x + 5 = 11 ( 1 / 2 ) x + 5 - 5 = 11 - 5 ( 1 / 2 ) x = 6 2 × ( 1 / 2 ) x = 6 × 2 x = 12 answer c"
Answer: c
Question (gain): a can complete a certain job in 19 days . b is 90 % more efficient than a . in how many days can b complete the same job ?
Options: a ) 6 , b ) 6.25 , c ) 7 , d ) 7.5 , e ) 10
Rationale: "let , total work unit = 190 units a can finish in 19 days = 190 unit work i . e . a can finish in 1 days = 10 unit work i . e . b can finish in 1 days = 10 + ( 90 / 100 ) * 10 = 19 unit work days in which b will complete the work alone = 190 / 19 = 10 days answer : option e"
Answer: e
Question (physics): if 20 men can build a water fountain 56 metres long in 7 days , what length of a similar water fountain can be built by 35 men in 3 days ?
Options: a ) 40 m , b ) 42 m , c ) 47 m , d ) 49 m , e ) 50 m
Rationale: "explanation : let the required length be x metres more men , more length built ( direct proportion ) less days , less length built ( direct proportion ) men 20 : 35 days 7 : 3 : : 56 : x therefore ( 20 x 7 x x ) = ( 35 x 3 x 56 ) x = ( 35 x 3 x 56 ) / 140 = 42 hence , the required length is 42 m . answer : b"
Answer: b
Question (general): jaime earned enough money by selling seashells at 20 cents each to buy several used paperback books at 55 cents each . if he spent all of the money he earned selling seashells to buy the books , what is the least number of seashells he could have sold ?
Options: a ) 5 , b ) 10 , c ) 22 , d ) 25 , e ) 30
Rationale: "let ' s test answer c : 22 seashells . . . with 22 seashells , jamie would have 22 ( 20 ) = 440 cents . this would allow him to buy 8 books for 440 cents total , so this is the correct answer . c"
Answer: c
Question (general): how many positive integers less than 248 are multiple of 4 but not multiples of 6 ?
Options: a ) 20 , b ) 41 , c ) 42 , d ) 53 , e ) 64
Rationale: "244 / 4 = 61 multiples of 4 which are a multiple of 6 will be of the form 2 * 2 * 3 = 12 n where n > 0 240 / 12 = 20 61 - 20 = 41 answer : b"
Answer: b
Question (geometry): a rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered . if the area of the field is 210 sq . feet , how many feet of fencing will be required ?
Options: a ) 34 , b ) 41 , c ) 68 , d ) 88 , e ) none
Rationale: "explanation we have : l = 20 ft and lb = 210 sq . ft . so , b = 10.5 ft . length of fencing = ( l + 2 b ) = ( 20 + 21 ) ft = 41 ft . answer b"
Answer: b
Question (general): in the coordinate plane a slope of the line k is 4 times the x - intercept of the line k . what is the y - intercept of the line k ?
Options: a ) - 4 , b ) 4 , c ) - 1 / 4 , d ) 1 / 4 , e ) 2
Rationale: as 4 y = mx + c , from 4 y = 0 m + m we get y = 1 / 4 . hence , the correct answer choice is d .
Answer: d
Question (general): find the smallest four - digit number which is a multiple of 112 .
Options: a ) 896 , b ) 1008 , c ) 1120 , d ) 1024 , e ) none of these
Rationale: "the smallest four digit number is 1000 . if 1000 is divided by 112 , the remainder is 104 . 112 - 104 = 8 , if 8 is added to 1000 , it will become the smallest four digit number and a multiple of 112 . answer : b"
Answer: b
Question (general): the difference between the place values of two sevens in the numerical 69758472 is
Options: a ) 0 , b ) 6993 , c ) 699930 , d ) 996330 , e ) none of them
Rationale: "required difference = ( 700000 - 70 ) = 699930 . answer is c"
Answer: c
Question (general): a set s = { x , - 8 , - 5 , - 3 , 3 , 6 , 9 , y } with elements arranged in increasing order . if the median and the mean of the set are the same , what is the value of | x | - | y | ?
Options: a ) 2 , b ) 0 , c ) - 1 , d ) can not be determined , e ) 1
Rationale: "median of the set = ( - 3 + 3 ) / 2 = 0 as per statement , mean of the set = 0 mean of the set | y | - | x | + 18 - 16 = 0 ( where x is negative n y is positive ) | y | - | x | = - 2 so the absolute difference between two numbers is 2 answer a"
Answer: a
Question (gain): the market value of a certain machine decreased by 30 percent of its purchase price each year . if the machine was purchased in 1982 for its market value of $ 10,000 , what was its market value two years later ?
Options: a ) $ 8,000 , b ) $ 4,000 , c ) $ 3,200 , d ) $ 2,400 , e ) $ 800
Rationale: "b . market value in 1982 = $ 10000 market value in 1983 = $ 10000 - ( $ 10000 x 30 / 100 ) = 10000 - 3000 = $ 7000 market value in 1984 = market value in 1983 - ( 30 % of $ 10000 ) = 7000 - 3000 = $ 4000"
Answer: b
Question (other): the value of log 2 16 is
Options: a ) 1 / 8 , b ) 4 , c ) 8 , d ) 16 , e ) 17
Rationale: "solution let log 216 = n . then , 2 n = 16 = 24 ‹ = › n = 4 . answer b"
Answer: b
Question (general): dividing by 3 ⁄ 7 and then multiplying by 5 ⁄ 6 is the same as dividing by what number ?
Options: a ) 35 ⁄ 18 , b ) 16 ⁄ 5 , c ) 20 ⁄ 9 , d ) 9 ⁄ 20 , e ) 5 ⁄ 16
Rationale: "say x / 3 / 7 * 5 / 6 = x * 7 / 3 * 5 / 6 = x * 35 / 18 a"
Answer: a
Question (gain): the ratio of investments of two partners p and q is 7 : 5 and the ratio of their profits is 7 : 13 . if p invested the money for 5 months , find for how much time did q invest the money ?
Options: a ) 19 , b ) 17 , c ) 13 , d ) 10 , e ) 12
Rationale: "7 * 5 : 5 * x = 7 : 13 x = 13 answer : c"
Answer: c
Question (physics): excluding stoppages , the speed of a bus is 50 kmph and including stoppages , it is 45 kmph . for how many minutes does the bus stop per hour ?
Options: a ) 7 min , b ) 6 min , c ) 9 min , d ) 10 min , e ) 11 min
Rationale: "due to stoppages , it covers 5 km less . time taken to cover 5 km = ( 5 / 50 ) x 60 = 6 min answer : b"
Answer: b
Question (gain): by selling 16 pencils for a rupee a man loses 20 % . how many for a rupee should he sell in order to gain 20 % ?
Options: a ) 28 , b ) 25 , c ) 24 , d ) 23 , e ) 21
Rationale: "80 % - - - 16 120 % - - - ? 80 / 120 * 16 = 24 answer : c"
Answer: c
Question (other): the ratio of spinsters to cats is 2 to 9 . if there are 42 more cats than spinsters , how many spinsters are there ?
Options: a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 13
Rationale: "let 2 x be the number of spinsters . then 9 x is the number of cats . 9 x - 2 x = 42 x = 6 and the number of spinsters is 2 ( 6 ) = 12 . the answer is d ."
Answer: d
Question (general): find the smallest number in a gp whose sum is 38 and product 1728
Options: a ) 12 , b ) 20 , c ) 8 , d ) all of these , e ) none of these
Rationale: "in gp : - a / r + a + ar . . . . = 38 a ( 1 + r + r ^ 2 ) = 38 r . . . . . . eq 1 product a ^ 3 = 1728 a = 12 now put this value in eq 1 12 ( 1 + r + r ^ 2 ) = 38 r r = 2 / 3 and 3 / 2 . . so sallest number is 8 answer : c"
Answer: c
Question (general): what no . should be subtracted from x ^ 3 + 4 x 2 − 7 x + 12 x ^ 3 + 4 x ^ 2 − 7 x + 12 , if it is to be perfectly divisible by x + 3 x + 3 ?
Options: a ) 38 , b ) 42 , c ) 46 , d ) 49 , e ) 62
Rationale: according to remainder theorem when dfracf ( x ) x + adfracf ( x ) x + a , then the remainder is f ( − a ) f ( − a ) . in this case , as x + 3 x + 3 divides x 3 + 4 x 2 − 7 x + 12 – kx 3 + 4 x 2 − 7 x + 12 – k perfectly ( kk being the number to be subtracted ) , the remainder is 0 when the value of xx is substituted by - 3 . i . e . , ( − 3 ) 3 + 4 ( − 3 ) 2 − 7 ( − 3 ) + 12 − k = 0 ( − 3 ) 3 + 4 ( − 3 ) 2 − 7 ( − 3 ) + 12 − k = 0 or − 27 + 36 + 21 + 12 = k − 27 + 36 + 21 + 12 = k or k = k = 42 b
Answer: b
Question (general): 76 is divided into two parts in such a way that seventh part of first and ninth part of second are equal . find the smallest part ?
Options: a ) 13.25 , b ) 38.25 , c ) 33.25 , d ) 34.25 , e ) 31.25
Rationale: "x / 7 = y / 9 = > x : y = 7 : 9 7 / 16 * 76 = 33.25 answer : c"
Answer: c
Question (general): in a division sum , the quotient is 40 , the divisor 72 and the remainder 64 , find the dividend ?
Options: a ) 2674 , b ) 2944 , c ) 2464 , d ) 2924 , e ) 2994
Rationale: explanation : 40 * 72 + 64 = 2944 answer : b
Answer: b
Question (gain): a store sells chairs and tables . if the price of 3 chairs and 1 table is 60 % of the price of 1 chair and 3 tables , and the price of 1 table and 1 chair is $ 80 , what is the price , in dollars , of 1 table ? ( assume that every chair has the same price and every table has the same price . )
Options: a ) 68 , b ) 84 , c ) 72 , d ) 60 , e ) 64
Rationale: "let c = chair ; t = table 3 c + 1 t = 0.6 ( 1 c + 3 t ) or c ( 3 - 0.6 ) = 1.8 t - 1 t or 2.4 c = 0.8 t therefore c = 0.8 / 2.4 t = 1 / 3 t ic + 1 t = 80 or 1 / 3 t + 1 t = 80 therefore t = 80 * 3 / 4 = 60 d"
Answer: d
Question (general): the probability that a man will be alive for 10 more yrs is 1 / 4 & the probability that his wife will alive for 10 more yrs is 1 / 3 . the probability that none of them will be alive for 10 more yrs , is
Options: a ) 1 / 2 , b ) 1 , c ) 2 / 3 , d ) 3 / 5 , e ) 3 / 8
Rationale: sol . required probability = pg . ) x p ( b ) = ( 1 — d x ( 1 — i ) = : x 1 = 1 / 2 ans . ( a )
Answer: a
Question (general): how many positive even integers less than 100 contain digits 4 or 7 ?
Options: a ) 16 , b ) 17 , c ) 18 , d ) 19 , e ) 20
Rationale: "one digit numbers : 4 two digit numbers : 4 at tens place : 40 , 42,44 , 46,48 7 at tens place : 70 , 72,74 , 76,78 4 at units place : 14 , 24,34 , 54,64 , 84,94 ( duplicates removed ) if 7 is at units place , the number cant be even total : 1 + 5 + 5 + 7 = 18 answer c"
Answer: c
Question (physics): a car traveled from san diego to san francisco at an average speed of 48 miles per hour . if the journey back took twice as long , what was the average speed of the trip ?
Options: a ) 24 . , b ) 32 . , c ) 36 , d ) 42 . , e ) 44 .
Rationale: "let the time taken be = x one way distance = 48 x total distance traveled = 2 * 48 x = 96 x total time taken = x + 2 x = 3 x average speed = 96 x / 3 x = 32 answer : b"
Answer: b
Question (general): amount of bacteria present time amount 1 : 00 p . m . 8.0 grams 4 : 00 p . m . x grams 7 : 00 p . m . 12.4 grams data for a certain biology experiment are given in the table above . if the amount of bacteria present increased by the same fraction during each of the two 3 - hour periods shown , how many grams of bacteria were present at 4 : 00 p . m . ?
Options: a ) 12.0 , b ) 12.1 , c ) 12.2 , d ) 10.0 , e ) 10.4
Rationale: the question says that bacteria increased by same fraction , not by same amount in 2 intervals of 3 hours . let x represent the amount of bacteria present at 4 : 00 pm . since the fractional increase must remain constant from 1 to 4 pm as it is from 4 pm to 7 pm : fractional increase from 1 pm to 4 pm = x / 8.0 fractional increase from 4 pm to 7 pm = 12.4 / x x \ 8 = 12.4 \ x x ^ 2 = 12.4 * 8 x = 10 answer : d
Answer: d
Question (other): find the ratio in which rice at rs . 7.20 a kg be mixed with rice at rs . 5.60 a kg to produce a mixture worth rs . 6.30 a kg ?
Options: a ) 1 : 3 , b ) 2 : 3 , c ) 3 : 4 , d ) 7 : 9 , e ) none of these
Rationale: "solution required ratio = 70 : 90 = 7 : 9 answer d"
Answer: d
Question (gain): i bought two books ; for rs . 300 . i sold one at a loss of 15 % and other at a gain of 19 % and then i found each book was sold at the same price . find the cost of the book sold at a loss ?
Options: a ) 175 , b ) 280 , c ) 189 , d ) 278 , e ) 268
Rationale: "x * ( 85 / 100 ) = ( 300 - x ) 119 / 100 x = 175 answer : a"
Answer: a
Question (physics): p works 25 % more efficiently than q and q works 50 % more efficiently than r . to complete a certain project , p alone takes 50 days less than q alone . if , in this project p alone works for 60 days and then q alone works for 130 days , in how many days can r alone complete the remaining work ?
Options: a ) 50 days , b ) 83.6 days , c ) 100 days , d ) 150 days , e ) 80 days
Rationale: "p works 25 % more efficiently than q : something that takes q 5 days , takes p 4 days q works 50 % more efficiently than r : something that takes r 7.5 days , takes q 5 days p alone takes 50 days less than q : for every 4 days p works , q has to work an extra day . hence p alone can do it in 200 days and q alone in 250 days and hence r alone in 380 days p works for 60 days - - > 60 / 200 work done = > 30 % q works for 130 days - - > 130 / 250 work done = > 52 % 22 % work left . . . r alone will take 22 % * 380 = 83.6 days answer is ( b )"
Answer: b
Question (general): a confectioner decides to sell all of his pastry due to the coming holiday . his pastry goods are equally divided among a group of 15 regular customers . if only 49 customers come to the bakery , each one will receive 6 less pastry goods . how much pastry does the confectioner needs to sell ?
Options: a ) 450 . , b ) 459 . , c ) 432 . , d ) 502 . , e ) 522 .
Rationale: "pastry is divided in 15 customers equally . so , total number of pastry must be a multiple of 15 only option a satisfies the condition , and hence is the answer"
Answer: a
Question (general): for any integer p , * p is equal to the product of all the integers between 1 and p , inclusive . how many prime numbers are there between * 8 + 3 and * 8 + 8 , inclusive ?
Options: a ) none , b ) one , c ) two , d ) three , e ) four
Rationale: "generally * p or p ! will be divisible by all numbers from 1 to p . therefore , * 8 would be divisible by all numbers from 1 to 8 . = > * 8 + 3 would give me a number which is a multiple of 3 and therefore divisible ( since * 8 is divisible by 3 ) in fact adding anyprimenumber between 1 to 8 to * 8 will definitely be divisible . so the answer is none ( a ) ! supposing if the question had asked for prime numbers between * 8 + 3 and * 8 + 11 then the answer would be 1 . for * 8 + 3 and * 8 + 13 , it is 2 and so on . . . a"
Answer: a
Question (geometry): the surface area of a sphere is same as the curved surface area of a right circular cylinder whose height and diameter are 12 cm each . the radius of the sphere is :
Options: a ) 4 cm , b ) 6 cm , c ) 8 cm , d ) 10 cm , e ) 9 cm
Rationale: "explanation : curved surface area of sphere = 4 / π r 2 surface area of cylinder = 2 π rh = > 4 / π r 2 = 2 π rh = > r 2 = 6 ∗ 12 / 2 = > r 2 = 36 = > r = 6 note : diameter of cylinder is 12 so radius is taken as 6 . option b"
Answer: b