Cheukting/mathqa huggingface dataset:
Question (general): in arun ' s opinion , his weight is greater than 61 kg but leas than 72 kg . his brother does not agree with arun and he thinks that arun ' s weight is greater than 60 kg but less than 70 kg . his mother ' s view is that his weight can not be greater than 64 kg . if all of them are correct in their estimation , what is the average of diferent probable weights of arun ?
Options: a ) 86.5 kg , b ) 62.5 kg , c ) 46.5 kg , d ) 26.5 kg , e ) 16.5 kg
Rationale: let arun ' s weight be x kg . according to arun , 61 < x < 72 . according to arun ' s brother , 60 < x < 70 . according to arun ' s mother , x < 64 . the values satisfying all the above conditions are 62 and 63 . required average = ( 62 + 63 ) / 2 = 62.5 kg answer : b
Answer: b
Question (general): a and b together have $ 1210 . if of a ' s amount is equal to of b ' s amount , how much amount does b have ?
Options: a ) $ 400 , b ) $ 489 , c ) $ 484 , d ) $ 365 , e ) % 342
Rationale: ( 4 / 15 ) a = ( 2 / 5 ) b = > a = ( ( 2 / 5 ) * ( 15 / 4 ) ) b = > a = ( 3 / 2 ) b = > a / b = 3 / 2 a : b = 3 : 2 b ' s share = rs . ( 1210 * ( 2 / 5 ) ) = $ 484 option c
Answer: c
Question (gain): what profit percent is made by selling an article at a certain price , if by selling at 2 / 3 rd of that price , there would be a loss of 20 % ?
Options: a ) 20 % , b ) 28 % , c ) 60 % , d ) 26 % , e ) 30 %
Rationale: "sp 2 = 2 / 3 sp 1 cp = 100 sp 2 = 80 2 / 3 sp 1 = 80 sp 1 = 120 100 - - - 20 = > 20 % answer : a"
Answer: a
Question (general): what is the minimum value of | x - 4 | + | x + 6 | + | x - 5 | ?
Options: a ) - 3 , b ) 3 , c ) 5 , d ) 7 , e ) 11
Rationale: a can not be the answer as all the three terms are in modulus and hence the answer will be non negative . | x - 4 | > = 0 - - > minimum occurs at x = 4 | x + 6 | > = 0 - - > minimum occurs at x = - 6 | x - 5 | > = 0 - - > minimum occurs at x = 5 x = - 6 - - > result = 10 + 0 + 11 = 21 . also any negative value will push the combined value of | x - 4 | + | x - 5 | to a value > 9 . x = 4 - - > result = 0 + 10 + 1 = 11 x = 5 - - > result = 1 + 11 + 0 = 12 x = 6 - - > result = 2 + 12 + 1 = 15 so minimum value of the expression occurs at x = 4 and the resultant value = 11 answer : e
Answer: e
Question (general): how many five - digit numbers that do not contain the digits 4 or 7 are there ?
Options: a ) 44648 , b ) 27844 , c ) 28642 , d ) 16864 , e ) 32458
Rationale: "we can have 7 digits ( 1 , 2,3 , 5,6 , 8,9 ) for the first place ( ten thousand ' s place ) . and similarly 8 digits for thousand ' s , hundred ' s , tenth ' s and unit digit . ( 0,1 , 2,3 , 5,6 , 8,9 ) so in total 7 * 8 * 8 * 8 * 8 = 28672 hence c"
Answer: c
Question (geometry): the larger interior angle of a parallelogram is 90 ° more than its smaller interior angle . what is the measure of the smaller interior angle of the parallelogram ?
Options: a ) 90 ° , b ) 75 ° , c ) 60 ° , d ) 45 ° , e ) 30 °
Rationale: let smaller be x , larger becomes x + 90 . . . total of all angles = 360 so 4 x + 180 = 360 and x = 45 answer : d
Answer: d
Question (physics): a train is 400 meter long is running at a speed of 60 km / hour . in what time will it pass a bridge of 800 meter length ?
Options: a ) 72 seconds , b ) 27 seconds , c ) 40 seconds , d ) 128 seconds , e ) 18 seconds
Rationale: "speed = 60 km / hr = 60 * ( 5 / 18 ) m / sec = 150 / 9 m / sec total distance = 400 + 800 = 1200 meter time = distance / speed = 1200 * ( 9 / 150 ) = 72 seconds answer : a"
Answer: a
Question (general): a man saves 20 % of his monthly salary . if an account of dearness of things he is to increase his monthly expenses by 20 % , he is only able to save rs . 200 per month . what is his monthly salary ?
Options: a ) rs . 5000 , b ) rs . 25000 , c ) rs . 7500 , d ) rs . 8500 , e ) rs . 9500
Rationale: "income = rs . 100 expenditure = rs . 80 savings = rs . 20 present expenditure 80 * ( 20 / 100 ) = rs . 96 present savings = 100 – 96 = rs . 4 100 - - - - - - 4 ? - - - - - - - - - 200 = > 5000 answer : a"
Answer: a
Question (general): the average height of 20 students is 20 cm and the average height of 11 students is 20 cm . what is the average height of the 31 students ?
Options: a ) 40 cm , b ) 20 cm , c ) 30 cm , d ) 25 cm , e ) 35 cm
Rationale: the total height of the 31 students = ( 20 * 20 ) + ( 11 * 20 ) = 400 + 220 = 620 cm the required average height = 620 / 31 = 20 cm answer : b
Answer: b
Question (general): a certain ball team has an equal number of right - and left - handed players . on a certain day , two - thirds of the players were absent from practice . of the players at practice that day , two - third were left handed . what is the ratio of the number of right - handed players who were not at practice that day to the number of lefthanded players who were not at practice ?
Options: a ) 1 / 3 , b ) 2 / 3 , c ) 5 / 7 , d ) 7 / 5 , e ) 3 / 2
Rationale: say the total number of players is 18 , 9 right - handed and 9 left - handed . on a certain day , two - thirds of the players were absent from practice - - > 12 absent and 6 present . of the players at practice that day , one - third were left - handed - - > 6 * 2 / 3 = 4 were left - handed and 2 right - handed . the number of right - handed players who were not at practice that day is 9 - 2 = 7 . the number of left - handed players who were not at practice that days is 9 - 4 = 5 . the ratio = 7 / 5 . answer : d
Answer: d
Question (physics): excluding the stoppages , the speed of a bus is 64 km / hr and including the stoppages the speed o the bus is 48 km / hr . for how many minutes does the bus stop per hour ?
Options: a ) 22 , b ) 15 , c ) 77 , d ) 28 , e ) 91
Rationale: answer : b ) 15 minutes
Answer: b
Question (gain): what amount does an investor receive if the investor invests $ 3000 at 10 % p . a . compound interest for two years , compounding done annually ?
Options: a ) $ 3420 , b ) $ 3630 , c ) $ 3870 , d ) $ 4040 , e ) $ 4220
Rationale: "a = ( 1 + r / 100 ) ^ n * p ( 1.1 ) ^ 2 * 5000 = 1.21 * 5000 = 3630 the answer is b ."
Answer: b
Question (gain): a fruit seller sells mangoes at the rate of rs . 12 per kg and thereby loses 15 % . at what price per kg , he should have sold them to make a profit of 5 %
Options: a ) rs 8.82 , b ) rs 9.82 , c ) rs 10.82 , d ) rs 14.82 , e ) none of these
Rationale: "explanation : 85 : 12 = 105 : x x = ( 12 × 105 / 85 ) = rs 14.82 option d"
Answer: d
Question (gain): a sells a bicycle to b and makes a profit of 35 % . b sells the same bicycle to c at a profit of 45 % . if the final s . p . of the bicycle was rs . 225 , find out the cost price of the bicycle for a .
Options: a ) 237 , b ) 126 , c ) 971 , d ) 611 , e ) 115
Rationale: "explanation : let cp be 100 a sells at 35 % profit so sp = 135 b sells at 45 % profit = 135 x ( 1 + 45 / 100 ) = 195.75 cp sp 100 - - - 195.75 x - - - 225 cp = 225 x 100 / 195.75 = 114.94 answer : e"
Answer: e
Question (other): how many zeros does 10 ! end with ?
Options: a ) 10 , b ) 4 , c ) 4 , d ) 3 , e ) 2
Rationale: "according to above 10 ! has 10 / 5 = 2 = 2 trailing zeros . answer : e"
Answer: e
Question (general): find the value of y from ( 12 ) ^ 2 x 6 ^ 4 ÷ 432 = y ?
Options: a ) 2134 , b ) 2234 , c ) 2540 , d ) 2560 , e ) 432
Rationale: 432 e
Answer: e
Question (gain): find the simple interest on rs . 5000 at 6 % per annum for the period from 5 th feb to 19 th april , 2015 .
Options: a ) rs . 40 , b ) rs . 50 , c ) rs . 60 , d ) rs . 70 , e ) none of these
Rationale: "explanation : given : 1 ) principal = rs . 5000 2 ) rate of interest = 6 % 3 ) time = 5 th feb to 19 th april , 2015 first find the time period 5 th feb to 19 th april , 2015 feb = 28 – 5 = 23 days march = 31 days april = 19 days total days = 23 + 31 + 19 = 73 days convert days into years , by dividing it by 365 time = 73 / 365 = 1 / 5 simple interest = ( p × r × t ) / 100 = [ 5000 × 6 × ( 1 / 5 ) ] / 100 = rs . 60 simple interest = rs . 60 answer is c"
Answer: c
Question (physics): a train passes a station platform in 36 sec and a man standing on the platform in 20 sec . if the speed of the train is 36 km / hr . what is the length of the platform ?
Options: a ) 160 , b ) 240 , c ) 288 , d ) 277 , e ) 221
Rationale: "speed = 36 * 5 / 18 = 10 m / sec . length of the train = 10 * 20 = 200 m . let the length of the platform be x m . then , ( x + 200 ) / 36 = 10 = > x = 160 m . answer : a"
Answer: a
Question (physics): car a runs at the speed of 42 km / hr & reaches its destination in 6 hr . car b runs at the speed of 52 km / h & reaches its destination in 9 h . what is the respective ratio of distances covered by car a & car b ?
Options: a ) 11 : 6 , b ) 7 : 13 , c ) 13 : 7 , d ) 15 : 6 , e ) 13 : 6
Rationale: "sol . distance travelled by car a = 42 × 6 = 252 km distance travelled by car b = 52 × 9 = 468 km ratio = 252 / 468 = 7 : 13 b"
Answer: b
Question (physics): the speed of a car is 90 km in the first hour and 55 km in the second hour . what is the average speed of the car ?
Options: a ) 72.5 kmph , b ) 75 kmph , c ) 87 kmph , d ) 56 kmph , e ) 86 kmph
Rationale: "s = ( 90 + 55 ) / 2 = 72.5 kmph answer : a"
Answer: a
Question (gain): by selling 15 pencils for a rupee a man loses 25 % . how many for a rupee should he sell in order to gain 25 % ?
Options: a ) 8 , b ) 9 , c ) 7 , d ) 6 , e ) 5
Rationale: "75 % - - - 15 125 % - - - ? 75 / 125 * 15 = 9 answer : b"
Answer: b
Question (general): find the remainder of the division ( 3 ^ 14 ) / 4 .
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "find the pattern of the remainders after each power : ( 3 ^ 1 ) / 4 remainder 3 ( 3 ^ 2 ) / 4 remainder 1 - - > this is where the cycle ends ( 3 ^ 3 ) / 4 remainder 3 - - > this is where the cycle begins again ( 3 ^ 4 ) / 4 remainder 1 continuing the pattern to ( 3 ^ 14 ) / 4 gives us a remainder of 1 final answer : a ) 1"
Answer: a
Question (physics): a certain machine produces 850 units of product p per hour . working continuously at this constant rate , this machine will produce how many units of product p in 7 days ?
Options: a ) 7,000 , b ) 24,000 , c ) 40,000 , d ) 142,800 , e ) 168,000
Rationale: "since 7 days consist of 24 * 7 hours the total hours of a week is 168 hours . since every hour the machine produces 850 units of product p the total product during 168 hours is 850 * 168 = 142,800 . correct option : d"
Answer: d
Question (geometry): the area of a circular field is 17.56 hectares . find the cost of fencing it at the rate of rs . 5 per metre approximately
Options: a ) 4457 , b ) 4567 , c ) 4235 , d ) 4547 , e ) 7429
Rationale: "explanation : area = ( 17.56 x 10000 ) m 2 = 175600 m 2 . π r 2 = 175600 ⇔ ( r ) 2 = ( 175600 x ( 7 / 22 ) ) ⇔ r = 236.37 m . circumference = 2 π r = ( 2 x ( 22 / 7 ) x 236.37 ) m = 1485.78 m . cost of fencing = rs . ( 1485.78 x 5 ) = rs . 7429 . answer : option e"
Answer: e
Question (physics): a contractor undertakes to built a walls in 50 days . he employs 70 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 ) 105 , b ) 30 , c ) 35 , d ) 20 , e ) none of these
Rationale: "70 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 , 70 × 25 × 0.6 = m 2 × 25 × 0.4 or m 2 = 70 × 25 × 0.6 / 25 × 0.4 = 105 men answera"
Answer: a
Question (other): a number is said to be prime saturated if the product of all the different positive prime factors of n is less than the square root of n . what is the greatest two digit prime saturated integer ?
Options: a ) 99 , b ) 98 , c ) 97 , d ) 96 answer , e ) 95
Rationale: "the square roots of all numbers from answer choices are between 9 and 10 , so the product of primes of the number we are looking should be less then 9 , so this number should have only 2 - s , only 3 - s , only 5 - s , or only 2 - s and 3 - s as its primes . only 96 satisfies this . answer : d ."
Answer: d
Question (general): in how many no . between 10 and 40 exactly two of the digits is 4 ?
Options: a ) 10 , b ) 15 , c ) 35 , d ) 1 , e ) 45
Rationale: "it ' s simple can be solved by elimination of answer choices . option b and c are too large , not possible . even ae are large to have correct choice . ans : d"
Answer: d
Question (general): 10 people went to a hotel for combine dinner party 8 of them spent rs . 10 each on their dinner and rest spent 4 more than the average expenditure of all the 10 . what was the total money spent by them .
Options: a ) 1628.4 , b ) 110 , c ) 1492 , d ) 1496 , e ) none of these
Rationale: "solution : let average expenditure of 10 people be x . then , 10 x = 8 * 10 + 2 * ( x + 4 ) ; or , 10 x = 10 * 10 + 2 x + 8 ; or , x = 11 ; so , total money spent = 11 * 10 = rs . 110 . answer : option b"
Answer: b
Question (physics): a carpenter worked alone for 1 day on a job that would take him 6 more days to finish . he and another carpenter completed the job in 5 more days . how many days would it have taken the second carpenter to do the complete job working alone ?
Options: a ) 4.5 , b ) 7.5 , c ) 9.5 , d ) 17.5 , e ) 24.5
Rationale: a carpenter worked only 1 day on something that takes him 6 more days . means ; carpenter finishes his work in 7 days . let his buddy finish the same task in x days . respective rates per day : 1 / 7 and 1 / x to complete 1 work : first guy worked for 5 days @ rate = 1 / 7 per day . second one worked for 5 days @ rate = 1 / x per day expression : days * rate = work 5 * 1 / 7 + 5 * 1 / x = 1 5 x + 35 = 7 x 2 x = 35 x = 17.5 days . ans : d
Answer: d
Question (general): find the least number of five digits which is exactly divisible by 12 and 18 ?
Options: a ) a ) 1080 , b ) b ) 10080 , c ) c ) 10025 , d ) d ) 11080 , e ) e ) 12080
Rationale: "the smallest five digit numbers are 10025 , 10080,11080 10025 is not divisible by 12 10080 is divisible by both 12 and 18 answer : b"
Answer: b
Question (general): how many odd prime numbers are there less than 75 ?
Options: a ) 20 , b ) 1 , c ) 2 , d ) 16 , e ) 17
Rationale: "odd prime number less than 75 : 3 , 5 , 7 , 11 , 13 , 17 , 19 , 23 , 29 , 31 , 37 , 41 , 43 , 47 , 53 , 59 , 61 , 67 , 71 , 73 there is 20 the odd prime number answer is a"
Answer: a
Question (physics): a is twice as good a workman as b and they took 7 days together to do the work b alone can do it in .
Options: a ) 23 days , b ) 25 days , c ) 21 days , d ) 26 days , e ) 29 days
Rationale: "c 21 days wc = 2 : 1 2 x + x = 1 / 7 x = 1 / 21 = > 21 days"
Answer: c
Question (general): if x is a positive integer with fewer than 3 digits , what is the probability that c x * ( x + 1 ) is a multiple of either 4 or 5 ?
Options: a ) 4 / 99 , b ) 2 / 25 , c ) 8 / 99 , d ) 49 / 100 , e ) 86 / 99
Rationale: "interesting question ! also one that we should be able to answer very quickly be keeping an eye on our best friends , the answer choices . we know that x belongs to the set { 1 , 2 , 3 , . . . , 99 } . we want to know the probability c that x ( x + 1 ) is a multiple of either 4 or 5 . when will this happen ? if either x or ( x + 1 ) is a multiple of 4 or 5 . since 4 * 5 is 20 , let ' s look at the first 20 numbers to get a rough idea of how often this happens . out of the numbers from 1 to 20 : 4 , 5 , 6 , 8 , 9 , 10 , 11 , 12 , 13 , 15 , 16 , 17 , 20 so , 14 out of the first 20 numbers match our criteria . since : probability = ( # of desired outcomes ) / ( total # of possibilities ) , we guesstimate the answer to be 14 / 20 . since ( e ) is the only answer greater than 1 / 2 , we go with ( e ) ."
Answer: e
Question (gain): if the cost price of 65 chocolates is equal to the selling price of 50 chocolates , the gain percent is :
Options: a ) 35 % , b ) 10 % , c ) 20 % , d ) 30 % , e ) 33 %
Rationale: "explanation : solution : let c . p . of each chocolate be re . 1 . then , c . p . of 50 chocolates = rs . 50 ; s . p . of 50 chocolates = rs . 65 . . ' . gain % = 15 * 100 / 50 = 30 % answer : d"
Answer: d
Question (physics): a train , 155 meters long travels at a speed of 45 km / hr crosses a bridge in 30 seconds . the length of the bridge is
Options: a ) 270 m , b ) 245 m , c ) 235 m , d ) 220 m , e ) 240 m
Rationale: "explanation : assume the length of the bridge = x meter total distance covered = 155 + x meter total time taken = 30 s speed = total distance covered / total time taken = ( 155 + x ) / 30 m / s = > 45 ã — ( 10 / 36 ) = ( 155 + x ) / 30 = > 45 ã — 10 ã — 30 / 36 = 155 + x = > 45 ã — 10 ã — 10 / 12 = 155 + x = > 15 ã — 10 ã — 10 / 4 = 155 + x = > 15 ã — 25 = 155 + x = 375 = > x = 375 - 155 = 220 answer : option d"
Answer: d
Question (other): sachin is younger than rahul by 7 years . if the ratio of their ages is 7 : 9 , find the age of sachin
Options: a ) 24.58 , b ) 24.5 , c ) 24.3 , d ) 24.9 , e ) 24.1
Rationale: "if rahul age is x , then sachin age is x - 7 , so ( x - 7 ) / x = 7 / 9 = > 9 x - 63 = 7 x = > 2 x = 63 = > x = 31.5 so sachin age is 31.5 - 7 = 24.5 answer : b"
Answer: b
Question (gain): the present population of a town is 500 . population increase rate is 10 % p . a . find the population of town before 2 years ?
Options: a ) 512 , b ) 615 , c ) 810 , d ) 413 , e ) 123
Rationale: "p = 500 r = 10 % required population of town = p / ( 1 + r / 100 ) ^ t = 500 / ( 1 + 10 / 100 ) ^ 2 = 500 / ( 11 / 10 ) ^ 2 = 413 ( approximately ) answer is d"
Answer: d
Question (geometry): a perfect square is defined as the square of an integer and a perfect cube is defined as the cube of an integer . how many positive integers n are there such that n is less than 5,000 and at the same time n is a perfect square and a perfect cube ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "if n is a perfect square and a perfect cube , then n = a ^ 6 for some integer a . the numbers are 1 ^ 6 = 1 , 2 ^ 6 = 64 , 3 ^ 6 = 729 , 4 ^ 6 = 4096 . the answer is c ."
Answer: c
Question (general): the price of commodity x increases by 30 cents every year , while the price of commodity y increases by 20 cents every year . if in 2001 , the price of commodity x was $ 4.20 and the price of commodity y was $ 4.40 , in which year will commodity x cost 90 cents more than the commodity y ?
Options: a ) 2010 , b ) 2011 , c ) 2012 , d ) 2013 , e ) 2014
Rationale: the cost of commodity x increases by 10 cents per year relative to commodity y . the price of x must gain 20 + 90 = $ 1.10 cents on commodity y , which will take 11 years . the answer is c .
Answer: c
Question (gain): shawn invested one half of his savings in a bond that paid simple interest for 2 years and received $ 650 as interest . he invested the remaining in a bond that paid compound interest , interest being compounded annually , for the same 2 years at the same rate of interest and received $ 725 as interest . what was the value of his total savings before investing in these two bonds ?
Options: a ) 1000 , b ) 1,250 , c ) 2,250 , d ) 3,250 , e ) 4,250
Rationale: so , we know that shawn received 20 % of the amount he invested in a year . we also know that in one year shawn received $ 325 , thus 0.2 x = $ 325 - - > x = $ 1625 since , he invested equal sums in his 2 bonds , then his total savings before investing was 2 * $ 1,625 = $ 3,250 answer d
Answer: d
Question (gain): at joel ’ s bookstore , the current inventory is 40 % historical fiction . of the historical fiction books , 40 % are new releases , while 70 % of the other books are new releases . what fraction of all new releases are the historical fiction new releases ?
Options: a ) 4 / 25 , b ) 8 / 29 , c ) 2 / 5 , d ) 8 / 15 , e ) 2 / 3
Rationale: "let there be 100 books in all historic fiction books = 40 % of total = 40 other books = 60 new historic fiction = 40 % of 40 = 16 other new books = 70 % of 60 = 42 total new books = 58 fraction = 16 / 58 = 8 / 29 ans : b"
Answer: b
Question (general): 10 years ago , the age of anand was one - third the age of bala at that time . the present age of bala is 10 years more than the present age of anand . find the present age of anand ?
Options: a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16
Rationale: let the present ages of anand and bala be ' a ' and ' b ' respectively . a - 10 = 1 / 3 ( b - 10 ) - - - ( 1 ) b = a + 10 substituting b = a + 12 in first equation , a - 10 = 1 / 3 ( a + 0 ) = > 3 a - 30 = a = > 2 a = 30 = > a = 15 . answer : d
Answer: d
Question (general): the average of 10 numbers is 40.2 . later it is found that two numbers have been wrongly copied . the first is 17 greater than the actual number and the second number added is 13 instead of 31 . find the correct average .
Options: a ) 40.3 , b ) 40.4 , c ) 40.6 , d ) 40.8 , e ) none of the above
Rationale: "sum of 10 numbers = 402 corrected sum of 10 numbers = 402 – 13 + 31 – 17 = 403 hence , new average = 403 ⁄ 10 = 40.3 answer a"
Answer: a
Question (general): nails and screws are manufactured at a uniform weight per nail and a uniform weight per screw . if the total weight of one screw and one nail is half that of 6 screws and one nail , then the total weight of 3 screws , and 3 nails is how many times that of 4 screws and 2 nails ?
Options: a ) 4 , b ) 5 / 2 , c ) 2 , d ) 3 / 2 , e ) 5 / 4
Rationale: "let the weight of nail be n and that of screw be s . . so s + w = 1 / 2 * ( 6 s + 1 n ) . . . or 1 n = 4 s . . lets see the weight of 3 s and 3 n = 3 s + 3 * 4 s = 15 s . . and weight of 4 s and 2 n = 4 s + 2 * 4 s = 12 s . . ratio = 15 s / 12 s = 15 / 12 = 5 / 4 answer : e"
Answer: e
Question (physics): the length of a room is 5.5 m and width is 3.75 m . find the cost of paving the floor by slabs at the rate of rs . 1200 per sq . metre .
Options: a ) rs . 15000 , b ) rs . 15550 , c ) rs . 24750 , d ) rs . 16500 , e ) none of these
Rationale: "solution area of the floor = ( 5.5 × 3.75 ) m 2 = 20.625 m 2 ∴ cost of paving = rs . ( 1200 × 20.625 ) = 24750 . answer c"
Answer: c
Question (physics): 15 men take 21 days of 8 hrs . each to do a piece of work . how many days of 6 hrs . each would it take for 21 women if 3 women do as much work as 2 men ?
Options: a ) 30 , b ) 20 , c ) 19 , d ) 29 , e ) 39
Rationale: let 1 man does 1 unit / hr of work 15 m in 21 days of 8 hrs will do ( 15 * 21 * 8 ) units 3 w = 2 m 1 w = ( 2 / 3 ) units / hr 21 w with 6 hrs a day will take ( 15 * 21 * 8 ) / ( 21 * 6 * ( 2 / 3 ) ) days = > 30 days answer : a
Answer: a
Question (general): 4 brothers adam , bill , charles and david together contributed certain amount of money and purchased a car . the contribution made by adam is half that of the total contribution made by the other 3 brothers , contribution made by bill is one - fourth of the total contribution made by the other 3 brothers and the contribution made by charles is two - third of the total contribution made by the other 3 brothers . if the total price of the car is $ 9750 , find the contribution made by david .
Options: a ) $ 540 , b ) $ 580 , c ) $ 600 , d ) $ 650 , e ) $ 680
Rationale: given that a : ( b + c + d ) = 1 : 2 . hence a contributed 1 / 3 rd of the total price . given b : ( a + c + d ) = 1 : 4 hence b contributed 1 / 5 th of the total price . given c : ( a + b + d ) = 2 : 3 hence c contributed 2 / 5 th of the total price . thus the contribution made by a , b and c = 1 / 3 + 1 / 5 + 2 / 5 = 14 / 15 so , the remaining 1 / 15 th of the price is contributed by david . hence david ' s contribution = 1 / 15 × 9750 = $ 650 . the answer is d .
Answer: d
Question (other): share rs . 6000 among john , jose & binoy in the ration 2 : 4 : 6 . find the amount received by john ?
Options: a ) 900 , b ) 980 , c ) 1200 , d ) 1240 , e ) 2000
Rationale: "amount received by sanjay . 4 / 12 x 6000 = 2000 = ( related ratio / sum of ratio ) x total amount so , the amount received by sanjay is 2000 . e"
Answer: e
Question (physics): a worker makes a toy in every 2 h . if he works for 120 h , then how many toys will he make ?
Options: a ) 40 , b ) 60 , c ) 45 , d ) 39 , e ) none
Rationale: "no . of toys = 120 / 2 = 60 answer : b"
Answer: b
Question (general): find the sum of all odd numbers up to 100 .
Options: a ) 2500 , b ) 2400 , c ) 2300 , d ) 2200 , e ) 2100
Rationale: "the given numbers are 1 , 3 , 5 , 7 , . . . , 99 . this is an a . p . with a = 1 and d = 2 . let it contain n terms . then , 1 + ( n - 1 ) x 2 = 99 or n = 50 . required sum = n / 2 ( first term + last term ) = 50 / 2 ( 1 + 99 ) = 2500 . answer is a ."
Answer: a