Cheukting/mathqa huggingface dataset:
Question (general): in the hillside summer camp there are 50 children . 80 % of the children are boys and the rest are girls . the camp administrator decided to make the number of girls only 10 % of the total number of children in the camp . how many more boys must she bring to make that happen ?
Options: a ) 55 , b ) 50 , c ) 40 . , d ) 30 . , e ) 25 .
Rationale: "given there are 50 students , 80 % of 50 = 40 boys and remaining 10 girls . now here 80 % are boys and 20 % are girls . now question is asking about how many boys do we need to add , to make the girls percentage to 20 or 20 % . . if we add 50 to existing 40 then the count will be 90 and the girls number will be 10 as it . now boys are 90 % and girls are 10 % . ( out of 100 students = 90 boys + 10 girls ) . imo option b is correct ."
Answer: b
Question (gain): a man invests rs . 8,000 at the rate of 5 % per annum . how much more should he invest at the rate of 8 % , so that he can earn a total of 6 % per annum ?
Options: a ) rs . 1200 , b ) rs . 1300 , c ) rs . 1500 , d ) rs . 4000 , e ) none of these
Rationale: explanation : interest on rs . 8000 at 5 % per annum = ( 8000 × 5 × 1 ) / 100 = rs . 400 let his additional investment at 8 % = x interest on rs . x at 8 % per annum = ( x × 8 × 1 ) / 100 = 2 x / 25 . to earn 6 % per annum for the total , interest = ( 8000 + x ) × 6 × 1 / 100 . = > 400 + 2 x / 25 = ( 8000 + x ) × 6 × 1 / 100 . = > 40000 + 8 x = ( 8000 + x ) × 6 . = > 40000 + 8 x = 48000 + 6 x . = > 2 x = 8000 . = > x = 4000 . answer : d
Answer: d
Question (general): how many 3 digit odd numbers do not use any digit more than once
Options: a ) 1720 , b ) 216 , c ) 224 , d ) 2460 , e ) 280
Rationale: "the way i solved it is a b c ( hundreds , tens , units ) c can be 1 3 5 7 9 ( any of the 5 digits ) a can be anything except ( d or 0 ) so 8 possibilitie b can be anything execpt ( a d c ) so 7 possibilities total ways are 7 * 8 * 5 = 280 ans : e"
Answer: e
Question (physics): a sum of 25 was paid for a work which a can do in 32 days , b in 20 days , b and c in 12 days and d in 24 days . how much did c receive if all the 4 work together ?
Options: a ) 14 ⁄ 3 , b ) 16 ⁄ 3 , c ) 15 ⁄ 3 , d ) 17 ⁄ 3 , e ) none of these
Rationale: a ' s one day ' s work = 1 ⁄ 32 b ' s one day ' s work = 1 ⁄ 20 ( b + c ) ' s one day ' s work = 1 ⁄ 12 ∴ c ' s one day ' s work = 1 ⁄ 12 - 1 ⁄ 20 = 1 ⁄ 30 d ' s one day ' s work = 1 ⁄ 24 ∴ ( a + b + c + d ) ' s one day ' s work 1 / 32 + 1 / 20 + 1 / 30 + 1 / 24 = 75 + 120 + 80 + 100 / 2400 = 375 ⁄ 2400 = 15 ⁄ 96 = 5 ⁄ 32 ∴ out of 5 ⁄ 32 of work done 1 ⁄ 30 of the work is done by c . ⇒ out of 25 paid for the work , c will receive 1 / 30 / 5 / 32 × 25 , i . e , 1 ⁄ 30 × 32 ⁄ 5 × 25 , i . e , 16 ⁄ 3 answer b
Answer: b
Question (physics): a room 13 m 47 cm long and 7 m 77 cm broad is to be paved with square tiles . find the least number of square tiles required to cover the floor .
Options: a ) 116636 , b ) 116406 , c ) 116647 , d ) 116291 , e ) 116675
Rationale: "explanation : area of the room = ( 1347 x 777 ) cm 2 . size of largest square tile = h . c . f . of 1347 cm and 777 cm = 3 cm . area of 1 tile = ( 3 x 3 ) cm 2 . number of tiles required = ( 1347 × 777 ) / ( 3 × 3 ) = 116291 answer : option d"
Answer: d
Question (general): if a number p is prime , and 2 p + 3 = q , where q is also prime , then the decimal expansion of 1 / q will produce a decimal with q - 1 digits . if this method produces a decimal with 166 digits , what is the units digit of the product of p and q ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9
Rationale: "1 / 5 = 0.2 . . ( a repeating pattern one digit long ) a"
Answer: a
Question (geometry): what will be the percentage increase in the area of the cube ' s surface if each of the cube ' s edges grows by 60 % ?
Options: a ) 150 % , b ) 160 % , c ) 156 % , d ) 158 % , e ) 162 %
Rationale: "the question is very easy . my logic is the following : a surface = 6 * a ^ 2 after 60 % increase a surface = 6 * ( ( 1.6 a ) ^ 2 ) = 6 * 2.56 * a ^ 2 the increase in the surface area = ( 6 * 2.56 * a ^ 2 - 6 * a ^ 2 ) / 6 * a ^ 2 = ( 6 * a ^ 2 ( 2.56 - 1 ) ) / ( 6 * a ^ 2 ) = 2.56 - 1 = 1.56 = 156 % answer : c"
Answer: c
Question (gain): the workforce of company x is 60 % female . the company hired 20 additional male workers , and as a result , the percent of female workers dropped to 55 % . how many employees did the company have after hiring the additional male workers ?
Options: a ) 160 , b ) 220 , c ) 240 , d ) 360 , e ) 420
Rationale: let ' s xx be total quantity of employees 0.6 x = females before adding men 0.55 ( x + 20 ) = females after adding men as quantity of women does n ' t change we can make an equation : 0.6 x = 0.55 ( x + 20 ) 0.05 x = 11 x = 220 - this is quantity of employees before adding 2020 men so after adding it will be 240 answer is c
Answer: c
Question (general): if | 20 x - 10 | = 90 , then find the product of the values of x ?
Options: a ) - 45 , b ) 50 , c ) - 62 , d ) 35 , e ) - 20
Rationale: "| 20 x - 10 | = 90 20 x - 10 = 90 or 20 x - 10 = - 90 20 x = 100 or 20 x = - 80 x = 5 or x = - 4 product = - 4 * 5 = - 20 answer is e"
Answer: e
Question (general): two brothers took the gmat exam , the higher score is x and the lower one is y . if the difference between the two scores is 1 / 3 , what is the value of x / y ?
Options: a ) 3 . , b ) 2 . , c ) 1 / 2 . , d ) 4 , e ) there is n ' t enough data to answer the question .
Rationale: answer is d : 4 x - y = ( x + y ) / 2 solving for x / y = 4
Answer: d
Question (physics): let a be the event that a randomly selected two digit number is divisible by 2 and let b be the event that a randomly selected two digit number is divisible by 10 . what is p ( a and b ) ?
Options: a ) 1 / 20 , b ) 1 / 15 , c ) 1 / 12 , d ) 1 / 8 , e ) 1 / 2
Rationale: "p ( a and b ) = 1 / 2 * 1 / 10 = 1 / 20 the answer is a ."
Answer: a
Question (general): in a flight of 600 km , an aircraft was slowed down due to bad weather . its average speed for the trip was reduced by 200 km / hr and the time of flight increased by 30 minutes . the duration of the flight is :
Options: a ) 1 hour , b ) 2 hour , c ) 3 hour , d ) 4 hour , e ) 5 hour
Rationale: "let the duration of the flight be x hours then 600 / x - 600 / x ( 1 / 2 ) = 200 = 600 / x - 1200 / 2 x + 1 = 200 = x ( 2 x + 1 ) = 3 = 2 xsquare + x - 3 = 0 = ( 2 x + 3 ) ( x - 1 ) = 0 = x = 1 hr ( neglecting the - ve value of x ) answer : option a"
Answer: a
Question (physics): a person travels equal distances with speeds of 50 km / hr , 100 km / hr and 120 km / hr and takes a total time of 23 minutes . the total distance is ?
Options: a ) 15 km , b ) 30 km , c ) 45 km , d ) 50 km , e ) 60 km
Rationale: "let the total distance be 3 x km x / 50 + x / 100 + x / 120 = 23 / 60 23 x / 600 = 23 / 60 23 x = 230 x = 10 km total distance = 3 x = 30 km answer is b"
Answer: b
Question (physics): two pipes can fill the cistern in 10 hr and 12 hr respectively , while the third empty it in 25 hr . if all pipes are opened simultaneously , then the cistern will be filled in
Options: a ) 7.5 hr , b ) 6.98 hr , c ) 8.5 hr , d ) 10 hr , e ) none of these
Rationale: "solution : work done by all the tanks working together in 1 hour . 1 / 10 + 1 / 12 − 1 / 25 = 1 / 7 hence , tank will be filled in 6.98 hour option ( b )"
Answer: b
Question (general): if 5 + 3 + 2 = 151022 , 9 + 2 + 4 = 183652 , then 7 + 2 + 5 = ?
Options: a ) 223888 , b ) 143547 , c ) 2607778 , d ) 126997 , e ) 127811
Rationale: if the given number is a + b + c then a . b | a . c | a . b + a . c - b ⇒ ⇒ 5 + 3 + 2 = 5.3 | 5.2 | 5.3 + 5.2 - 3 = 151022 ⇒ ⇒ 9 + 2 + 4 = 9.2 | 9.4 | 9.2 + 9.4 - 2 = 183652 7 + 2 + 5 = 7.2 | 7.5 | 7.2 + 7.5 - 2 = 143547 answer : b
Answer: b
Question (physics): the inner circumference of a circle race track 18 m wide is 880 m . find the radius of the outer circle .
Options: a ) 120 m
b ) 145 m
c ) 130 m
d ) 140 m
e ) 122 m
Rationale: let inner radius be r metres then 2 π r = 640 2 × 22 / 7 r = 880 44 / 7 r = 880 r = 880 × 7 / 44 = 140 m answer is d .
Answer: d
Question (gain): 4 mat - weavers can weave 4 mats in 4 days . at the same rate , how many mats would be woven by 14 mat - weavers in 14 days ?
Options: a ) 25 , b ) 19 , c ) 39 , d ) 61 , e ) 49
Rationale: "let the required number of bottles be x . more weavers , more mats ( direct proportion ) more days , more mats ( direct proportion ) wavers 4 : 14 : : 4 : x days 4 : 14 4 * 4 * x = 14 * 14 * 4 x = ( 14 * 14 * 4 ) / ( 4 x 4 ) x = 49 . answer is e ."
Answer: e
Question (general): find √ ? / 15 = 4 ?
Options: a ) 76 , b ) 5776 , c ) 304 , d ) 3600 , e ) none
Rationale: "answer let √ n / 15 = 4 then √ n = 15 x 4 = 60 ∴ n = 60 x 60 = 3600 . correct option : d"
Answer: d
Question (general): if a ( a - 1 ) = 20 and b ( b - 1 ) = 20 , where a ≠ b , then a + b =
Options: a ) − 48 , b ) − 1 , c ) 2 , d ) 46 , e ) 67
Rationale: "i . e . if a = 5 then b = - 4 or if a = - 4 then b = 5 but in each case a + b = - 5 + 4 = - 1 answer : option b"
Answer: b
Question (general): 10 % people of a village in sri lanka died by bombardment , 20 % of the remainder left the village on account of fear . if now the population is reduced to 3240 , how much was it in the beginning ?
Options: a ) a ) 3800 , b ) b ) 4200 , c ) c ) 4400 , d ) d ) 4500 , e ) e ) 4600
Rationale: "x * ( 90 / 100 ) * ( 80 / 100 ) = 3240 x = 4500 answer : d"
Answer: d
Question (physics): the length of the bridge , which a train 130 meters long and travelling at 45 km / hr can cross in 30 seconds , is ?
Options: a ) 288 , b ) 266 , c ) 245 , d ) 277 , e ) 211
Rationale: speed = ( 45 * 5 / 18 ) m / sec = ( 25 / 2 ) m / sec . time = 30 sec . let the length of bridge be x meters . then , ( 130 + x ) / 30 = 25 / 2 = = > 2 ( 130 + x ) = 750 = = > x = 245 m . answer : c
Answer: c
Question (gain): a sum of rs . 2743 is lent into two parts so that the interest on the first part for 8 years at 3 % per annum may be equal to the interest on the second part for 3 years at 5 % per annum . find the second sum ?
Options: a ) 1642 , b ) 1640 , c ) 1632 , d ) 1688 , e ) 6386
Rationale: "( x * 8 * 3 ) / 100 = ( ( 2743 - x ) * 3 * 5 ) / 100 24 x / 100 = 41145 / 100 - 15 x / 100 39 x = 41145 = > x = 1055 second sum = 2743 – 1055 = 1688 answer : d"
Answer: d
Question (physics): tom and john traveled in the same direction along the equal route at their constant speed rates of 15 km per hour and 10 km per hour , respectively . after 15 minutes tom passed john , tom reaches a certain gas station , how many t minutes it takes john to reach the station ?
Options: a ) 5 min , b ) 6 min , c ) 7 and 1 / 2 min , d ) 8 min , e ) 10 min
Rationale: since the question states “ after 15 minutes ” , we can say tom traveled 15 / 4 km for 15 minutes as he can travel 15 km per hour . hence , using the same logic , we can say john traveled 10 / 4 km as he travels 10 km per hour . so , john has to travel ( 15 / 4 ) - ( 10 / 4 ) km = 5 / 4 km more . since john ’ s speed is 10 km / hour , which means 1 km / 6 minutes . as he has to travel 5 / 4 km more , it is going to take him 6 ( 5 / 4 ) minutes . hence , t = 6 ( 5 / 4 ) = 15 / 2 minutes . the correct answer is c .
Answer: c
Question (general): when positive integer n is divided by positive integer j , the remainder is 18 . if n / j = 134.08 , what is value of j ?
Options: a ) 22 , b ) 56 , c ) 78 , d ) 112 , e ) 225
Rationale: "when a number is divided by another number , we can represent it as : dividend = quotient * divisor + remainder so , dividend / divisor = quotient + remainder / divisor given that n / j = 134.08 here 134 is the quotient . given that remainder = 18 so , 134.08 = 134 + 18 / j so , j = 225 ans e"
Answer: e
Question (physics): a can finish a work in 18 days and b can do the same work in 15 days . b worked for 10 days and left the job . in how many days , a alone can finish the remaining work ?
Options: a ) 5 , b ) 5 1 / 2 , c ) 6 , d ) 8 , e ) none of these
Rationale: b ' s 10 day ' s work = ( 1 / 15 * 10 ) = 2 / 3 remaining work = ( 1 - 2 / 3 ) = 1 / 3 now , 1 / 18 work is done by a in 1 day 1 / 3 work is done by a in ( 18 * 1 / 3 ) = 6 days . correct option : c
Answer: c
Question (general): the difference of two numbers is 1375 . on dividing the larger number by the smaller , we get 6 as quotient and the 15 as remainder . what is the smaller number ?
Options: a ) 240 , b ) 272 , c ) 295 , d ) 360 , e ) 252
Rationale: "let the smaller number be x . then larger number = ( x + 1375 ) . x + 1375 = 6 x + 15 5 x = 1360 x = 272 smaller number = 270 . answer b"
Answer: b
Question (gain): the population of a town is 7600 . it decreases annually at the rate of 10 % p . a . what was its population 2 years ago ?
Options: a ) 9400 , b ) 8000 , c ) 8500 , d ) 9500 , e ) 10000
Rationale: "formula : ( after = 100 denominator ago = 100 numerator ) 7600 ã — 100 / 90 ã — 100 / 90 = 9382 a )"
Answer: a
Question (general): the average of first 10 prime numbers which are odd is ?
Options: a ) 22.2 , b ) 22.1 , c ) 15.3 , d ) 15.8 , e ) 14.6
Rationale: explanation : sum of first 10 prime no . which are odd = 158 average = 158 / 10 = 15.8 answer : d
Answer: d
Question (gain): on increasing the price of t . v . sets by 60 % , their sale decreases by 20 % . what is the effect on the revenue receipts of the shop ?
Options: a ) 4 , b ) 5 , c ) 56 , d ) 28 , e ) 7
Rationale: explanation : let the price be = rs . 100 , and number of units sold = 100 then , sale value = rs . ( 100 × 100 ) = rs . 10000 new sale value = rs . ( 160 × 80 ) = rs . 12800 increase % = 2800 / 10000 × 100 = 28 % answer : d
Answer: d
Question (general): a meal cost $ 35.50 adn there was no tax . if the tip was more than 2 pc but less than 12 pc of the price , then the total amount paid should be :
Options: a ) 40 - 43 , b ) 39 - 42 , c ) 39 - 42 , d ) 38 - 41 , e ) 36 - 40
Rationale: "2 % ( 35.5 ) = 0.71 12 % ( 35.5 ) = 4.26 total amount could have been 35.5 + 0.71 and 35.5 + 4.26 = > could have been between 36.21 and 39.76 = > approximately between 36 and 40 answer is e ."
Answer: e
Question (gain): in an office in singapore there are 60 % female employees . 50 % of all the male employees are computer literate . if there are total 62 % employees computer literate out of total 1200 employees , then the no . of female employees who are computer literate ?
Options: a ) 504 , b ) 674 , c ) 672 , d ) 960 , e ) none
Rationale: solution : total employees , = 1200 female employees , 60 % of 1200 . = ( 60 * 1200 ) / 100 = 720 . then male employees , = 480 50 % of male are computer literate , = 240 male computer literate . 62 % of total employees are computer literate , = ( 62 * 1200 ) / 100 = 744 computer literate . thus , female computer literate = 744 - 240 = 504 . answer : option a
Answer: a
Question (general): a paint store mixes 3 / 4 pint of red paint and 2 / 3 pint of white paint to make a new paint color called perfect pink . how many pints of red paint would be needed to make 40 pints of perfect pink paint ?
Options: a ) 9 , b ) 16 , c ) 21 , d ) 25 1 / 3 , e ) 28 1 / 2
Rationale: "3 / 4 pint is required to make 3 / 4 + 2 / 3 = 17 / 12 pint of perfect pink so 17 / 12 pint requires 3 / 4 pint of red . . 1 pint will require 3 / 4 * 12 / 17 = 9 / 17 . . 40 pints will require 9 / 17 * 40 = 21 pints . . c"
Answer: c
Question (physics): two trains of length 100 m and 200 m are 100 m apart . they start moving towards each other on parallel tracks , at speeds 72 kmph and 90 kmph . in how much time will the trains cross each other ?
Options: a ) 80 / 8 , b ) 80 / 9 , c ) 80 / 5 , d ) 80 / 3 , e ) 80 / 1
Rationale: "relative speed = ( 72 + 90 ) * 5 / 18 = 9 * 5 = 45 mps . the time required = d / s = ( 100 + 100 + 200 ) / 45 = 400 / 45 = 80 / 9 sec . answer : b"
Answer: b
Question (gain): a fruit seller sells mangoes at the rate of rs . 13 per kg and thereby loses 25 % . at what price per kg , he should have sold them to make a profit of 15 % ?
Options: a ) rs . 11.81 , b ) rs . 19.93 , c ) rs . 12.25 , d ) rs . 12.31 , e ) none
Rationale: "solution 75 : 13 = 115 : x x = ( 13 ã — 115 / 75 ) = rs . 19.93 hence , s . p per kg = rs . 19.93 answer b"
Answer: b
Question (physics): mahesh can do a piece of work in 40 days . he works at it for 20 days and then rajesh finished it in 30 days . how long will y take to complete the work ?
Options: a ) 45 , b ) 25 , c ) 37 , d ) 41 , e ) 60
Rationale: "work done by mahesh in 60 days = 20 * 1 / 40 = 1 / 2 remaining work = 1 - 1 / 2 = 1 / 2 1 / 2 work is done by rajesh in 30 days whole work will be done by rajesh is 30 * 2 = 60 days answer is e"
Answer: e
Question (gain): a store ’ s selling price of $ 2240 for a certain printer would yield a profit of 40 percent of the store ’ s cost for the printer . what selling price would yield a profit of 50 percent of the printer ’ s cost ?
Options: a ) $ 2800 , b ) $ 2464 , c ) $ 2650 , d ) $ 2732 , e ) $ 2400
Rationale: "1.4 x = 2240 x = 2240 / 1.4 so , 1.5 x = 2240 * 1.5 / 1.4 = 2400 answer : - e"
Answer: e
Question (physics): a contractor undertakes to built a walls in 50 days . he employs 50 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 ) 30 , c ) 35 , d ) 20 , e ) none of these
Rationale: "50 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 , 50 × 25 × 0.6 = m 2 × 25 × 0.4 or m 2 = 50 × 25 × 0.6 / 25 × 0.4 = 75 men answera"
Answer: a
Question (physics): convert 500 miles into meters ?
Options: a ) 784596 , b ) 845796 , c ) 804670 , d ) 784596 , e ) 864520
Rationale: "1 mile = 1609.34 meters 500 mile = 500 * 1609.34 = 804670 meters answer is c"
Answer: c
Question (general): the average ( arithmetic mean ) of the 5 positive integers k , m , r , s , and t is 12 , and k < m < r < s < t . if t is 20 , what is the greatest possible value of the median of the 5 integers ?
Options: a ) 16 , b ) 18 , c ) 19 , d ) 20 , e ) 22
Rationale: "we need to find the median which is the third value when the numbers are in increasing order . since k < m < r < s < t , the median would be r . the average of the positive integers is 12 which means that in effect , all numbers are equal to 12 . if the largest number is 20 , it is 8 more than 12 . we need r to be maximum so k and m should be as small as possible to get the average of 12 . since all the numbers are positive integers , k and m can not be less than 1 and 2 respectively . 1 is 11 less than 12 and 2 is 10 less than 12 which means k and m combined are 21 less than the average . 20 is already 8 more than 12 and hence we only have 21 - 8 = 13 extra to distribute between r and s . since s must be greater than r , r can be 12 + 6 = 18 and s can be 12 + 7 = 19 . so r is 18 . answer ( d )"
Answer: d
Question (physics): a work as fast as b . if b can complete a work in 36 days independently , the number of days in which a and b can together finish the work in ?
Options: a ) 12 days , b ) 3 days , c ) 4 days , d ) 5 days , e ) 6 days
Rationale: "ratio of rates of working of a and b = 2 : 1 ratio of times taken = 1 : 2 a ' s 1 day work = 1 / 18 b ' s 1 day work = 1 / 36 a + b 1 day work = 1 / 18 + 1 / 36 = 3 / 36 = 1 / 12 a and b can finish the work in 12 days answer is a"
Answer: a
Question (physics): a car covers a distance of 200 km in 2 hours 40 minutes , whereas a jeep covers the same distance in 2 hours . what is the ratio of t
Options: a ) 3 : 4 , b ) 4 : 3 , c ) 4 : 5 , d ) 5 : 4 , e ) 8 : 7
Rationale: a 3 : 4
Answer: a
Question (general): the average of 13 numbers is 60 . average of the first 7 of them is 54 and that of the last 7 is 61 . find the 8 th number ?
Options: a ) 25 , b ) 83 , c ) 45 , d ) 53 , e ) 64
Rationale: "sum of all the 13 numbers = 13 * 60 = 780 sum of the first 7 of them = 7 * 54 = 378 sum of the last 7 of them = 7 * 61 = 427 so , the 8 th number = 427 + 378 - 780 = 25 . answer : a"
Answer: a
Question (general): a man is 22 years older than his son . in three years , his age will be thrice the age of his son . the present age of this son is
Options: a ) 8 years , b ) 2 years , c ) 7 years , d ) 8 years , e ) 5 years
Rationale: "let ' s son age is x , then father age is x + 22 . = > 3 ( x + 3 ) = ( x + 22 + 3 ) = > 3 x + 9 = x + 25 = > 2 x = 16 years = 8 years answer : d"
Answer: d
Question (general): for each color copy , print shop x charges $ 1.20 and print shop y charges $ 1.70 . how much greater is the charge for 70 color copies at print shop y than at print shop x ?
Options: a ) $ 27 , b ) $ 29 , c ) $ 31 , d ) $ 33 , e ) $ 35
Rationale: the difference in the two prices is $ 1.70 - $ 1.20 = $ 0.50 for each color copy . each color copy will cost an extra $ 0.50 at print shop y . 70 * $ 0.50 = $ 35 the answer is e .
Answer: e
Question (physics): pipe a fills a tank of capacity 850 liters at the rate of 40 liters a minute . another pipe b fills the same tank at the rate of 30 liters a minute . a pipe at the bottom of the tank drains the tank at the rate of 20 liters a minute . if pipe a is kept open for a minute and then closed and pipe b is open for a minute and then closed and then pipe c is open for a minute and then closed and the cycle is repeated , when will the tank be full ?
Options: a ) 42 minutes , b ) 51 minutes , c ) 39 minutes , d ) 40 minutes 20 seconds , e ) none of these
Rationale: "in one cycle they fill 40 + 30 - 20 = 50 liters 850 = 50 * n = > n = 17 here n = number of cycles . total time = 17 * 3 = 51 as in one cycle there are 3 minutes . thus 51 minutes answer : b"
Answer: b
Question (general): a picnic attracts 240 persons . there are 80 more men than women , and 80 more adults than children . how many men are at this picnic ?
Options: a ) 240 , b ) 75 , c ) 110 , d ) 120 , e ) 200
Rationale: "adult + children = 240 let , children = y then , adult = y + 80 i . e . y + ( y + 80 ) = 240 i . e . y = 80 i . e . adult = 80 + 80 = 160 adults include only men and women i . e . men + women = 160 let women , w = x then men , m = x + 80 i . e . x + ( x + 20 ) = 2 x + 80 = 160 i . e . x = 40 i . e . men , m = 40 + 80 = 120 answer : option d"
Answer: d
Question (physics): tap a runs 3 liters of water per minute into a bucket that has a total volume of 36 liters . tap b fills a third of the bucket in 20 mins . working together how long will it take both taps to fill the bucket ?
Options: a ) 10 minutes , b ) 1.5 hours , c ) 9 hours and 12 minutes , d ) 15 hours , e ) 1 hour and 48 minutes .
Rationale: pipe a has a rate of 3 liters per minute which equals a rate of 180 liters per hour . pipe b has a rate of 36 liters per hour . 180 + 36 ( a + b ) = together they have a rate of 2000 liters per hour . 36 ( the bucket ) / 216 = 1 / 6 = 10 minutes answer - a
Answer: a
Question (general): what is the smallest integer that is multiple of 5 , 7,11
Options: a ) a ) 70 , b ) b ) 35 , c ) c ) 385 , d ) d ) 280 , e ) e ) 140
Rationale: "it is the lcm of 5 , 7 and 11 which is 385 . the answer is c ."
Answer: c
Question (gain): a , b and c enter into a partnership . a invests 3 times as much as b invests and 2 / 3 of what c invests . at the end of the year , the profit earned is rs . 22000 . what is the share of c ?
Options: a ) rs . 2250 , b ) rs . 3375 , c ) rs . 6000 , d ) rs . 5625 , e ) none of these
Rationale: "explanation : let the investment of c be rs . x . the inverstment of b = rs . ( 2 x / 3 ) the inverstment of a = rs . ( 3 × ( 2 / 3 ) x ) = rs . ( 2 x ) ratio of capitals of a , b and c = 2 x : 2 x / 3 : x = 6 : 2 : 3 c ' s share = rs . [ ( 3 / 11 ) × 22000 ] = rs . 6000 answer : option c"
Answer: c
Question (geometry): if the radius of a circle is decreased 40 % , what happens to the area ?
Options: a ) 10 % decrease , b ) 20 % decrease , c ) 36 % decrease , d ) 40 % decrease , e ) 64 % decrease
Rationale: "area of square = pi * radius ^ 2 new radius = 0.6 * old radius so new area = ( 0.6 ) ^ 2 old area = > 4 / 25 of old area = > 36 % old area ans : e"
Answer: e