Cheukting/mathqa huggingface dataset:
Question (physics): how many paying stones , each measuring 2 m * 2 m are required to pave a rectangular court yard 30 m long and 18 m board ?
Options: a ) 99 , b ) 18 , c ) 135 , d ) 17 , e ) 12
Rationale: "30 * 18 = 2 * 2 * x = > x = 135 answer : c"
Answer: c
Question (general): a jogger running at 9 km / hr along side a railway track is 250 m ahead of the engine of a 100 m long train running at 99 km / hr in the same direction . in how much time will the train pass the jogger ?
Options: a ) 14 sec , b ) 67 sec , c ) 98 sec , d ) 36 sec , e ) 23 sec
Rationale: "speed of train relative to jogger = 99 - 9 = 90 km / hr . = 90 * 5 / 18 = 25 m / sec . distance to be covered = 250 + 100 = 350 m . time taken = 350 / 25 = 14 sec . answer : a"
Answer: a
Question (physics): a train 200 m long passes a man , running at 5 km / hr in the same direction in which the train is going , in 20 seconds . the speed of the train is ?
Options: a ) 36 , b ) 50 , c ) 88 , d ) 66 , e ) 23
Rationale: "speed of the train relative to man = ( 200 / 20 ) m / sec = 5 m / sec . [ 5 * ( 18 / 5 ) ] km / hr = 18 km / hr . let the speed of the train be x km / hr . then , relative speed = ( x - 5 ) km / hr . x - 5 = 18 = = > x = 23 km / hr . answer : e"
Answer: e
Question (general): a pupil ' s marks were wrongly entered as 73 instead of 65 . due to the average marks for the class got increased by half . the number of pupils in the class is ?
Options: a ) 18 , b ) 82 , c ) 16 , d ) 27 , e ) 29
Rationale: "let there be x pupils in the class . total increase in marks = ( x * 1 / 2 ) = x / 2 x / 2 = ( 73 - 65 ) = > x / 2 = 8 = > x = 16 . answer : c"
Answer: c
Question (general): the average salary of 16 people in the shipping department at a certain firm is $ 20,000 . the salary of 5 of the employees is $ 25,000 each and the salary of 4 of the employees is $ 16,000 each . what is the average salary of the remaining employees ?
Options: a ) $ 18,714 , b ) $ 18,500 , c ) $ 18,000 , d ) $ 15,850 , e ) $ 12,300
Rationale: total salary . . . 16 * 20 k = 320 k 5 emp @ 25 k = 125 k 4 emp @ 16 k = 64 k remaing 7 emp sal = 320 k - 125 k - 64 k = 131 k average = 131 k / 7 = 18714 ans : a
Answer: a
Question (gain): a shopkeeper sold an article at $ 100 with 30 % profit . then find its cost price ?
Options: a ) $ 120 , b ) $ 100 , c ) $ 91 , d ) $ 77 , e ) $ 69
Rationale: "cost price = selling price * 100 / ( 100 + profit ) c . p . = 100 * 100 / 130 = $ 77 ( approximately ) answer is d"
Answer: d
Question (gain): in an election between two candidates , the first candidate got 80 % of the votes and the second candidate got 480 votes . what was the total number of votes ?
Options: a ) 1600 , b ) 1800 , c ) 2000 , d ) 2200 , e ) 2400
Rationale: "let v be the total number of votes . 0.2 v = 480 v = 2400 the answer is e ."
Answer: e
Question (gain): peter invested a certain sum of money in a simple interest bond whose value grew to $ 400 at the end of 4 years and to $ 500 at the end of another 2 years . what was the rate of interest in which he invested his sum ?
Options: a ) 12 % , b ) 12.5 % , c ) 67 % , d ) 25 % , e ) 33 %
Rationale: "lets assume the principal amount ( initial amount invested ) to be p rate of interest to berand time as t . we need to find r now after a time of 4 years the principal p amounts to $ 400 and after a time of 6 years ( question says after another 6 years so 4 + 2 ) p becomes $ 500 . formulating the above data amount ( a 1 ) at end of 4 years a 1 = p ( 1 + 4 r / 100 ) = 400 amount ( a 2 ) at end of 6 years a 2 = p ( 1 + 2 r / 100 ) = 500 dividing a 2 by a 1 we get ( 1 + 4 r / 100 ) / ( 1 + 2 r / 100 ) = 5 / 4 after cross multiplication we are left with 4 r = 100 which gives r = 25 % option : d"
Answer: d
Question (geometry): twenty - one dots are evenly spaced on the circumference of a circle . how many combinations of three dots can we make from these 21 dots that do not form an equilateral triangle ?
Options: a ) 1299
b ) 1305
c ) 1311
d ) 1317
e ) 1323
Rationale: the total number of ways we can choose three dots is 21 c 3 = 1330 . we can form seven equilateral triangles from these twenty - one dots . there are 1330 - 7 = 1323 combinations which do not form an equilateral triangle . the answer is e .
Answer: e
Question (geometry): if the area of circle is 616 sq cm then its circumference ?
Options: a ) 76
b ) 55
c ) 88
d ) 21
e ) 11
Rationale: the area of circle = pie * r ^ 2 = 616 = > r = 14 2 * 22 / 7 * 14 = 88 answer : c
Answer: c
Question (other): the ratio of boarders to day scholars at a school is 7 to 16 . however , after a few new students join the initial 560 boarders , the ratio changed to 1 to 2 , respectively . if no boarders became day scholars and vice versa , and no students left the school , how many boarders joined the school ?
Options: a ) 48 , b ) 64 , c ) 70 , d ) 80 , e ) 84
Rationale: let day scholars be ds and boarders be b given b / ds = 7 / 16 - - - > eq 1 initially b = 560 and x be new boarders joined then from eq 1 , we get ds = 16 / 7 * 560 = 1280 now , new ration is 560 + x / ds = 1 / 2 560 + x / 1280 = 1 / 2 = > 1120 + 2 x = 1280 = > 2 x = 160 = > x = 80 ans option d
Answer: d
Question (general): when positive integer n is divided by positive integer p , the quotient is 18 , with a remainder of 6 . when n is divided by ( p + 2 ) , the quotient is 15 and the remainder is 3 . what is the value of n ?
Options: a ) 151 , b ) 331 , c ) 168 , d ) 691 , e ) 871
Rationale: n / p = 18 6 / p = 18 p + 6 n / ( p + 2 ) = 15 2 / ( p + 2 ) = 15 p + 30 + 3 solving these two equations we get p = 9 n = 168 answer is c .
Answer: c
Question (general): in an examination , 25 % of total students failed in hindi , 35 % failed in english and 40 % in both . the percentage of these who passed in both the subjects is :
Options: a ) 10 % , b ) 20 % , c ) 60 % , d ) 80 % , e ) 50 %
Rationale: "pass percentage = 100 - ( 25 + 35 - 40 ) = 100 - 20 = 80 answer : d"
Answer: d
Question (gain): population of a city in 20004 was 1400000 . if in 2005 there isan increment of 15 % , in 2006 there is a decrements of 35 % and in 2007 there is an increment of 45 % , then find the population of city at the end of the year 2007
Options: a ) 354354 , b ) 545454 , c ) 465785 , d ) 456573 , e ) 2818075 / 2
Rationale: "required population = p ( 1 + r 1 / 100 ) ( 1 - r 2 / 100 ) ( 1 + r 3 / 100 ) = p ( 1 + 15 / 100 ) ( 1 - 35 / 100 ) ( 1 + 45 / 100 ) = 2818075 / 2 e"
Answer: e
Question (geometry): the slant height of a cone is 15 cm and radius of the base is 3 cm , find the curved surface of the cone ?
Options: a ) 26 , b ) 134 , c ) 141 , d ) 190 , e ) 28
Rationale: "π * 15 * 3 = 141 answer : c"
Answer: c
Question (physics): a train 360 m long is running at a speed of 45 km / hr . in what time will it pass a bridge 340 m long ?
Options: a ) 56 sec , b ) 42 sec , c ) 45 sec , d ) 48 sec , e ) 50 sec
Rationale: "speed = 45 * 5 / 18 = 25 / 2 m / sec total distance covered = 360 + 340 = 700 m required time = 700 * 2 / 25 = 56 sec answer : a"
Answer: a
Question (general): if ( 55 ^ 55 + 55 ) is divided by 56 , then the remainder is : ?
Options: a ) 54 , b ) 55 , c ) 53 , d ) 56 , e ) 57
Rationale: solution : ( x ^ n + 1 ) is divisible by ( x + 1 ) , when n is odd . . ' . ( 55 ^ 55 + 1 ) is divisible by ( 55 + 1 ) = 56 . when ( 55 ^ 55 + 1 ) + 54 is divided by 56 , the remainder is 54 . answer a
Answer: a
Question (general): g ( x ) is defined as the product of all even integers k such that 0 < k ≤ x . for example , g ( 14 ) = 2 × 4 × 6 × 8 × 10 × 12 × 14 . if g ( a ) is divisible by 4 ^ 11 , what is the smallest possible value for a ?
Options: a ) 22 , b ) 24 , c ) 28 , d ) 32 , e ) 44
Rationale: "g ( a ) = 4 ^ 11 = 2 ^ 22 . so we have to find a product with atleast 22 2 ' s in it . in option 1 22 the total no of 2 ' s = [ 22 / 2 ] + [ 22 / 4 ] + [ 22 / 8 ] + [ 22 / 16 ] = 11 + 5 + 2 + 1 = 19 in option 2 24 the total no of 2 ' s = [ 24 / 2 ] + [ 24 / 4 ] + [ 24 / 8 ] + [ 24 / 16 ] = 12 + 6 + 3 + 1 = 22 . hence b"
Answer: b
Question (general): the least common multiple of positive integer m and 3 - digit integer n is 690 . if n is not divisible by 3 and m is not divisible by 2 , what is the value of n ?
Options: a ) 115 , b ) 230 , c ) 460 , d ) 575 , e ) 690
Rationale: the lcm of n and m is 690 = 2 * 3 * 5 * 23 . m is not divisible by 2 , thus 2 goes to n n is not divisible by 3 , thus 3 goes to m . from above : n must be divisible by 2 and not divisible by 3 : n = 2 * . . . in order n to be a 3 - digit number it must take all other primes too : n = 2 * 5 * 23 = 230 . answer : b .
Answer: b
Question (gain): if 5 % more is gained by selling an article for rs . 350 than by selling it for rs . 340 , the cost of the article is :
Options: a ) rs . 50 , b ) rs . 160 , c ) rs . 200 , d ) rs . 225 , e ) rs . 325
Rationale: "let c . p . be rs . x . then , 5 % of x = 350 - 340 = 10 x / 20 = 10 = > x = 200 answer : c"
Answer: c
Question (general): a certain characteristic in a large population has a distribution that is symmetric about the mean m . if 68 percent of the distribution lies within one standard deviation d of the mean , what percent f of the distribution is less than m + d ?
Options: a ) 16 % , b ) 32 % , c ) 48 % , d ) 84 % , e ) 92 %
Rationale: "d the prompt says that 68 % of the population lies between m - d and m + d . thus , 32 % of the population is less than m - d or greater than m + d . since the population is symmetric , half of this 32 % is less than m - d and half is greater than m + d . thus , f = ( 68 + 16 ) % or ( 100 - 16 ) % of the population is less than m + d . d"
Answer: d
Question (general): the difference between the local value and the face value of 9 in the numeral 62975148 is
Options: a ) 899999 , b ) 899991 , c ) 899891 , d ) 899981 , e ) 899000
Rationale: "explanation : ( local value of 9 ) - ( face value of 9 ) = ( 900000 - 9 ) = 899991 b )"
Answer: b
Question (physics): a man complete a journey in 10 hours . he travels first half of the journey at the rate of 21 km / hr and second half at the rate of 24 km / hr . find the total journey in km .
Options: a ) 220 km , b ) 224 km , c ) 230 km , d ) 234 km , e ) 255 km
Rationale: "( 1 / 2 ) x / 21 + ( 1 / 2 ) x / 24 = 10 x / 21 + x / 24 = 20 15 x = 168 x 20 x = [ 168 x 20 / 15 ] = 224 km answer is b"
Answer: b
Question (other): the compound ratio of 3 : 4 , 3 : 2 and 4 : 5 ?
Options: a ) 1 : 9 , b ) 1 : 7 , c ) 1 : 2 , d ) 9 : 10 , e ) 1 : 4
Rationale: "3 / 4 * 3 / 2 * 4 / 5 = 9 / 10 = 9 : 10 answer : d"
Answer: d
Question (gain): the true discount on a bill of rs . 2460 is rs . 360 . what is the banker ' s discount ?
Options: a ) rs . 432 , b ) rs . 422 , c ) rs . 412 , d ) rs . 442 , e ) none of these
Rationale: "explanation : f = rs . 2460 td = rs . 360 pw = f - td = 2460 - 360 = rs . 2100 true discount is the simple interest on the present value for unexpired time = > simple interest on rs . 2100 for unexpired time = rs . 360 banker ' s discount is the simple interest on the face value of the bill for unexpired time = simple interest on rs . 2460 for unexpired time = 360 / 2100 × 2460 = 0.17 × 2460 = rs . 422 answer : option b"
Answer: b
Question (general): a number is doubled and 5 is added . if the resultant is trebled , it becomes 111 . what is that number ?
Options: a ) 12 , b ) 29 , c ) 27 , d ) 16 , e ) 99
Rationale: "explanation : let the number be x . therefore , 3 ( 2 x + 5 ) = 111 6 x + 15 = 111 6 x = 96 x = 16 answer : d"
Answer: d
Question (general): a sum of money is to be distributed among a , b , c , d in the proportion of 5 : 2 : 4 : 3 . if c gets rs . 700 more than d , what is b ' s share ?
Options: a ) rs . 500 , b ) rs . 1400 , c ) rs . 2000 , d ) rs . 2500 , e ) none of the above
Rationale: "let the shares of a , b , c and d be rs . 5 x , rs . 2 x , rs . 4 x and rs . 3 x respectively . then , 4 x - 3 x = 700 x = 700 . b ' s share = rs . 2 x = rs . ( 2 x 700 ) = rs . 1400 . answer = b"
Answer: b
Question (gain): if the simple interest on a sum of money for 5 years at 9 % per annum is rs . 800 , what is the compound interest on the same sum at the rate and for the same time ?
Options: a ) rs . 947.55 , b ) rs . 957.55 , c ) rs . 857.55 , d ) rs . 657.55 , e ) rs . 357.55
Rationale: "sum = ( 800 * 100 ) / ( 5 * 9 ) = rs . 1 , 777.78 c . i . on rs . rs . 1 , 777.78 for 5 years at 9 % = rs . 2 , 735.33 . = rs . 2 , 735.33 - 1 , 777.78 = rs . 957.55 answer : b"
Answer: b
Question (general): find the difference between c . i and s . i on a sum of money rs . 2000 for 2 years . at 4 % p . a
Options: a ) rs . 2.20 , b ) rs . 3.20 , c ) rs . 4.20 , d ) rs . 5.20 , e ) rs . 3.25
Rationale: p 9 r / 100 ) ^ 2 = 2000 ( 4 / 100 ) ^ 2 = rs . 3.20 answer : b
Answer: b
Question (physics): if 5 machines can produce 20 units in 10 hours , how long would it take 10 machines to produce 100 units ?
Options: a ) 25 , b ) 30 , c ) 35 , d ) 24 , e ) 96
Rationale: "5 machines would produce 100 units in 50 hours . increasing the amount of machines by 2 would mean dividing 50 hours by 2 . 50 / 2 = 25 answer : a"
Answer: a
Question (physics): a , b and c , each working alone can complete a job in 6 , 8 and 12 days respectively . if all three of them work together to complete a job and earn $ 2340 , what will be a ' s share of the earnings ?
Options: a ) $ 1100 , b ) $ 520 , c ) $ 1040 , d ) $ 1170 , e ) $ 630
Rationale: "explanatory answer a , b and c will share the amount of $ 2340 in the ratio of the amounts of work done by them . as a takes 6 days to complete the job , if a works alone , a will be able to complete 1 / 6 th of the work in a day . similarly , b will complete 1 / 8 th and c will complete 1 / 12 th of the work . so , the ratio of the work done by a : b : c when they work together will be equal to 1 / 6 : 1 / 8 : 1 / 12 multiplying the numerator of all 3 fractions by 24 , the lcm of 6 , 8 and 12 will not change the relative values of the three values . we get 24 / 6 : 24 / 8 : 24 / 12 = 4 : 3 : 2 . i . e . , the ratio in which a : b : c will share $ 2340 will be 4 : 3 : 2 . hence , a ' s share will be 4 * 2340 / 9 = 1040 correct choice is ( c )"
Answer: c
Question (physics): the area of a square field 3136 sq m , if the length of cost of drawing barbed wire 3 m around the field at the rate of rs . 1.00 per meter . two gates of 1 m width each are to be left for entrance . what is the total cost ?
Options: a ) s . 666 , b ) s . 1140 , c ) s . 999 , d ) s . 1085 , e ) s . 1020
Rationale: "a 2 = 3136 = > a = 56 56 * 4 * 3 = 672 – 6 = 666 * 1.0 = 666 answer : a"
Answer: a
Question (physics): the pinedale bus line travels at an average speed of 60 km / h , and has stops every 5 minutes along its route . yahya wants to go from his house to the pinedale mall , which is 5 stops away . how far away , in kilometers , is pinedale mall away from yahya ' s house ?
Options: a ) 25 km , b ) 30 km , c ) 40 km , d ) 50 km , e ) 60 km
Rationale: "number of stops in an hour : 60 / 5 = 12 distance between stops : 60 / 12 = 5 km distance between yahya ' s house and pinedale mall : 5 x 5 = 25 km imo , correct answer is ` ` a . ' '"
Answer: a
Question (general): a positive number x is multiplied by 10 , and this product is then divided by 3 . if the positive square root of the result of these two operations equals x , what is the value of x ?
Options: a ) 9 / 4 , b ) 3 / 2 , c ) 4 / 3 , d ) 2 / 3 , e ) 10 / 3
Rationale: "sq rt ( 10 x / 3 ) = x = > 10 x / 3 = x ^ 2 = > x = 10 / 3 ans - e"
Answer: e
Question (gain): if 90 % of a = 30 % of b and b = c % of a , then the value of c is ?
Options: a ) 900 , b ) 800 , c ) 600 , d ) 300 , e ) none
Rationale: "answer ∵ 90 a / 100 = 30 b / 100 = ( 30 / 100 ) x ac / 100 ∴ c = 100 x ( 100 / 30 ) x ( 90 / 100 ) = 300 correct option : d"
Answer: d
Question (general): in a group of dogs and people , the number of legs was 28 more than twice the number of heads . how many dogs were there ? [ assume none of the people or dogs is missing a leg . ]
Options: a ) 4 , b ) 7 , c ) 12 , d ) 14 , e ) 28
Rationale: if there were only people , there would be exactly twice the number of legs as heads . each dog contributes two extra legs over and above this number . so 28 extra legs means 14 dogs . correct answer d
Answer: d
Question (gain): in a company , 50 percent of the employees are men . if 60 percent of the employees are unionized and 70 percent of these are men , what percent of the non - union employees are women ?
Options: a ) 85 % , b ) 80 % , c ) 75 % , d ) 70 % , e ) 65 %
Rationale: "the percent of employees who are unionized and men is 0.7 * 0.6 = 42 % the percent of employees who are unionized and women is 60 - 42 = 18 % 50 % of all employees are women , so non - union women are 50 % - 18 % = 32 % 40 % of all employees are non - union . the percent of non - union employees who are women is 32 % / 40 % = 80 % the answer is b ."
Answer: b
Question (other): 9 log 9 ( 4 ) = ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "exponential and log functions are inverse of each other . hence aloga ( x ) = x , for all x real and positive . and therefore 9 log 9 ( 4 ) = 4 correct answer d"
Answer: d
Question (general): the average of runs of a cricket player of 20 innings was 32 . how many runs must he make in his next innings so as to increase his average of runs by 5 ?
Options: a ) 96 , b ) 106 , c ) 128 , d ) 137 , e ) 122
Rationale: "average = total runs / no . of innings = 32 so , total = average x no . of innings = 32 * 20 = 640 now increase in avg = 4 runs . so , new avg = 32 + 5 = 37 runs total runs = new avg x new no . of innings = 37 * 21 = 777 runs made in the 11 th inning = 777 - 640 = 137 answer : d"
Answer: d
Question (general): yearly subscription to professional magazines cost a company $ 840.00 . to make a 30 % cut in the magazine budget , how much less must be spent ?
Options: a ) 654 , b ) 655 , c ) 656 , d ) 588 , e ) 658
Rationale: "total cost 840 840 * 30 / 100 = 252 so the cut in amount is 252 the less amount to be spend is 840 - 252 = 588 answer : d"
Answer: d
Question (geometry): the area of a square is 4900 sq cm . find the ratio of the breadth and the length of a rectangle whose length is same the side of the square and breadth is 20 cm less than the side of the square ?
Options: a ) 5 : 8 , b ) 5 : 10 , c ) 5 : 13 , d ) 5 : 7 , e ) 5 : 16
Rationale: "let the length and the breadth of the rectangle be l cm and b cm respectively . let the side of the square be a cm . a 2 = 4900 a = ( 4900 ) ^ 1 / 2 = 70 l = a and b = a - 20 b : l = a - 20 : a = 50 : 70 = 5 : 7 answer : d"
Answer: d
Question (gain): a man walking at a rate of 10 km / hr crosses a bridge in 18 minutes . the length of the bridge is ?
Options: a ) 1521 , b ) 3000 , c ) 1667 , d ) 1254 , e ) 1112
Rationale: "speed = 10 * 5 / 18 = 50 / 18 m / sec distance covered in 10 minutes = 50 / 18 * 18 * 60 = 3000 m answer is b"
Answer: b
Question (physics): the inner circumference of a circular race track , 14 m wide , is 440 m . find radius of the outer circle .
Options: a ) 84
b ) 86
c ) 82
d ) 80
e ) none of them
Rationale: let inner radius be r metres . then , 2 ( 22 / 7 ) r = 440 = r = ( 440 x ( 7 / 44 ) ) = 70 m . radius of outer circle = ( 70 + 14 ) m = 84 m . answer is a
Answer: a
Question (physics): r is the set of positive even integers less than 20 , and s is the set of the squares of the integers in r . how many elements does the intersection of r and s contain ?
Options: a ) none
b ) two
c ) three
d ) five
e ) seven
Rationale: squares < 20 { 1,4 , 9,16 } s = { 1,4 , 9,16 } r = { 2 , . . . . . 18 } hence c .
Answer: c
Question (general): elena ’ s bread recipe calls for 3 ounces of butter for each 4 cups of flour used . she needs to make 7 times the original recipe . if 12 ounces of butter is used , then how many cups of flour are needed ?
Options: a ) 1 , b ) 4 , c ) 9 , d ) 13 , e ) 28
Rationale: "solving through algebra route : 3 b + 4 f = x amount if we multiply this equation with 7 we get : 21 b + 28 f = 7 x therefore , we got 21 ounces of butter and 7 x amount of quantity when we use 28 ounces of floor . ans : e"
Answer: e
Question (physics): find the area , diameter = 13 m .
Options: a ) 132.00 square meter , b ) 132.04 square meter , c ) 132.78 square meter , d ) 132.24 square meter , e ) 113.43 square meter
Rationale: "diameter = 13 meter . radius = diameter / 2 . = 13 / 2 . = 6.5 meter . area of a circle = ï € r 2 . here , pi ( ï € ) = 3.14 meter , radius ( r ) = 6.5 area of a circle = 3.14 ã — 6.5 ã — 6.5 . = 3.14 ã — 42.25 . = 132.78 square meter answer : 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 45 , find the other ?
Options: a ) 100 , b ) 160 , c ) 120 , d ) 200 , e ) 150
Rationale: "other number = 12 * 600 / 45 = 160 answer is b"
Answer: b
Question (general): in a can , there is a mixture of milk and water in the ratio 4 : 3 . if the can is filled with an additional 8 liters of milk , the can would be full and the ratio of milk and water would become 2 : 1 . find the capacity of the can ?
Options: a ) 40 , b ) 36 , c ) 32 , d ) 28 , e ) 24
Rationale: "let c be the capacity of the can . ( 4 / 7 ) * ( c - 8 ) + 8 = ( 2 / 3 ) * c 12 c - 96 + 168 = 14 c 2 c = 72 c = 36 the answer is b ."
Answer: b
Question (general): according to the directions on the can of frozen orange juice concentrate , 1 can of concentrate is to be mixed with 3 cans of water to make orange juice . how many 12 ounces cans of the concentrate are required to prepare 272 6 ounces servings of orange juice ?
Options: a ) a ) 25 , b ) b ) 34 , c ) c ) 50 , d ) d ) 67 , e ) e ) 100
Rationale: "its b . total juice rquired = 272 * 6 = 1632 ounce 12 ounce concentate makes = 12 * 4 = 48 ounce juice total cans required = 1632 / 48 = 34 . answer b"
Answer: b
Question (gain): to produce an annual income of rs . 1200 from a 12 % stock at 90 , the amount of stock needed is :
Options: a ) rs . 10,000 , b ) rs . 10,800 , c ) rs . 14,400 , d ) rs . 16,000 , e ) none of these
Rationale: solution for an income of rs . 12 , stock needed = rs . 100 . for an income of rs . 1200 , stock needed = rs . 100 / 12 x 1200 = 10000 answer a
Answer: a
Question (general): if the least common addition of two prime numbers x and y is 10 , where x > y , then the value of 2 x + y is
Options: a ) 7 , b ) 9 , c ) 14 , d ) 17 , e ) 21
Rationale: "( x + y ) = 10 and both x an y are prime . the only values of x and y can be 7 and 3 ( x = 7 and y = 3 ) 2 x + y = 2 * 7 + 3 = 17 correct option : d"
Answer: d
Question (physics): what is the length of a bridge ( in meters ) , which a train 156 meters long and travelling at 45 km / h can cross in 40 seconds ?
Options: a ) 308 , b ) 320 , c ) 332 , d ) 344 , e ) 356
Rationale: "speed = 45 km / h = 45000 m / 3600 s = 25 / 2 m / s in 40 seconds , the train can travel 25 / 2 * 40 = 500 meters 500 = length of train + length of bridge length of bridge = 500 - 156 = 344 meters the answer is d ."
Answer: d
Question (probability): a store has 10 bottles of juice , including 6 bottles of apple juice . in the evening , 6 bottles of juice are sold one by one . what is the probability of selling 3 bottles of apple juice among the 6 bottles ? assume that every bottle has an equal chance of being bought .
Options: a ) 2 / 11 , b ) 4 / 15 , c ) 6 / 17 , d ) 8 / 21 , e ) 10 / 25
Rationale: "the total number of ways to sell 6 bottles from 10 is 10 c 6 = 210 . the number of ways to sell 3 bottles of apple juice is 6 c 3 * 4 c 3 = 20 * 4 = 80 p ( selling 3 bottles of apple juice ) = 80 / 210 = 8 / 21 the answer is d ."
Answer: d
Question (physics): if 10 men can reap 120 acres of land in 15 days , how many acres of land can 20 men reap in 30 days ?
Options: a ) 120 , b ) 240 , c ) 360 , d ) 1200 , e ) 480
Rationale: "10 men 120 acres 15 days 20 men ? 30 days 120 * 20 / 10 * 30 / 15 120 * 2 * 2 120 * 4 = 480 answer : e"
Answer: e
Question (gain): the profit earned by selling an article for 852 is equal to the loss incurred when the same article is sold for 448 . what should be the sale price of the article for making 50 per cent profit ?
Options: a ) 960 , b ) 975 , c ) 1,200 , d ) 920 , e ) none of these
Rationale: "let the profit or loss be x and 852 – x = 448 + x or , x = 404 ⁄ 2 = 202 \ cost price of the article = 852 – x = 448 + x = 650 \ sp of the article = 650 × 150 ⁄ 100 = 975 answer b"
Answer: b