Cheukting/mathqa huggingface dataset:
Question (other): divide rs . 32000 in the ratio 3 : 5 ?
Options: a ) 12000 , 20000 , b ) 12000 , 200098 , c ) 12000 , 20007 , d ) 12000 , 20006 , e ) 12000 , 20001
Rationale: "3 / 8 * 32000 = 12000 5 / 8 * 32000 = 20000 answer : a"
Answer: a
Question (general): what is the hcf of 2 / 3 , 4 / 15 and 6 / 5
Options: a ) 7 / 45 , b ) 2 / 45 , c ) 4 / 15 , d ) 8 / 45 , e ) 2 / 15
Rationale: "explanation : hcf of fractions = hcf of numerators / lcm of denominators = ( hcf of 2 , 4 , 6 ) / ( lcm of 3 , 15 , 5 ) = 2 / 15 answer : option e"
Answer: e
Question (physics): n a race of 1000 m , a can beat by 100 m , in a race of 800 m , b can beat c by 100 m . by how many meters will a beat c in a race of 600 m ?
Options: a ) 127.6 , b ) 127.5 , c ) 127.0 , d ) 127.2 , e ) 127.3
Rationale: when a runs 1000 m , b runs 900 m and when b runs 800 m , c runs 700 m . when b runs 900 m , distance that c runs = ( 900 * 700 ) / 800 = 6300 / 8 = 787.5 m . in a race of 1000 m , a beats c by ( 1000 - 787.5 ) = 212.5 m to c . in a race of 600 m , the number of meters by which a beats c = ( 600 * 212.5 ) / 1000 = 127.5 m . answer : ob
Answer: b
Question (general): 3 , 14,39 , _ ?
Options: a ) 81 , b ) 82 , c ) 83 , d ) 84 , e ) 85
Rationale: "n ^ 3 + n ^ 2 + n soln : 1 ^ 3 + 1 ^ 2 + 1 = 3 2 ^ 3 + 2 ^ 2 + 2 = 8 + 4 + 2 = 14 3 ^ 3 + 3 ^ 2 + 3 = 27 + 9 + 3 = 39 4 ^ 3 + 4 ^ 2 + 4 = 64 + 16 + 4 = 84 answer : d"
Answer: d
Question (general): if x : y = 3 : 5 , find the value of ( 2 x + 4 y ) : ( 4 x – y )
Options: a ) 29 : 7 , b ) 22 : 7 , c ) 26 : 7 , d ) 20 : 7 , e ) 26 : 5
Rationale: "explanation : given : a / b = 3 / 5 ( 2 * 3 + 4 * 5 ) : ( 4 * 3 – 5 ) = 26 : 7 answer : c"
Answer: c
Question (physics): nd the area of trapezium whose parallel sides are 20 cm and 18 cm long , and the distance between them is 14 cm ?
Options: a ) 235 cm 2 , b ) 260 cm 2 , c ) 266 cm 2 , d ) 270 cm 2 , e ) 280 cm 2
Rationale: "area of a trapezium = 1 / 2 ( sum of parallel sides ) * ( perpendicular distance between them ) = 1 / 2 ( 20 + 18 ) * ( 14 ) = 266 cm 2 answer : c"
Answer: c
Question (general): a “ palindromic integer ” is an integer that remains the same when its digits are reversed . so , for example , 43334 and 516615 are both examples of palindromic integers . how many 6 - digit palindromic integers are both even and greater than 600,000 ?
Options: a ) 150 , b ) 200 , c ) 240 , d ) 300 , e ) 480
Rationale: "the first digit and last digit are the same so the 2 possibilities are 6 or 8 . the second and third digits can be any number from 0 to 9 . the total number of palindromic integers is 2 * 10 * 10 = 200 the answer is b ."
Answer: b
Question (gain): a reduction of 20 % in the price of salt enables a lady to obtain 4 kgs more for rs . 100 , find the original price per kg ?
Options: a ) 6.16 , b ) 6.21 , c ) 6.25 , d ) 2.4 , e ) 2.7
Rationale: "100 * ( 20 / 100 ) = 20 - - - 4 ? - - - 1 = > rs . 5 100 - - - 80 ? - - - 5 = > rs . 6.25 answer : c"
Answer: c
Question (general): kyle , david , and catherine each try independently to solve a problem . if their individual probabilities for success are 1 / 8 , 1 / 4 and 3 / 5 , respectively , what is the probability no one will solve the problem ?
Options: a ) 3 / 80 , b ) 21 / 80 , c ) 5 / 16 , d ) 25 / 76 , e ) 9 / 80
Rationale: "p ( kyle will not solve ) = 1 - 1 / 8 = 7 / 8 p ( david will not solve ) = 1 - 1 / 4 = 3 / 4 p ( catherine will not solve ) = 1 - 3 / 5 = 2 / 5 p = ( 7 / 8 ) * ( 3 / 4 ) * ( 2 / 5 ) = 42 / 160 = 21 / 80 answer : b"
Answer: b
Question (general): if p and q are prime numbers , how many divisors does the product p ^ 6 * q ^ 7 have ?
Options: a ) 40 , b ) 56 , c ) 60 , d ) 62 , e ) 70
Rationale: "when a number n = a ^ x * b ^ y , where a and b are prime numbers , and x , y are positive integers , the number of divisors of n = ( x + 1 ) ( y + 1 ) therefore , the answer is b . 7 * 8 = 56"
Answer: b
Question (general): if there is an equal probability of a child being born a boy or a girl , what is the probability that a couple who have 4 children have two children of the same sex and one of the opposite sex ?
Options: a ) 1 / 3 , b ) 2 / 3 , c ) 1 / 4 , d ) 1 / 2 , e ) 3 / 5
Rationale: no of ways of selecting a gender - 2 c 1 no of ways of selecting any 2 children out of 4 = 4 c 2 total possible outcomes - 2 ^ 4 ( each child can be either a girl or a boy ) probability = 2 c 1 * 4 c 2 / 2 ^ 4 = 2 * 4 / 2 * 2 * 2 * 2 = 8 / 16 = 1 / 2 ans = d
Answer: d
Question (geometry): the measurement of a rectangular box with lid is 25 cmx 12 cmx 18 cm . find the volume of the largest sphere that can be inscribed in the box ( in terms of π cm 3 ) . ( hint : the lowest measure of rectangular box represents the diameter of the largest sphere )
Options: a ) 288 , b ) 48 , c ) 72 , d ) 864 , e ) 964
Rationale: "d = 12 , r = 6 ; volume of the largest sphere = 4 / 3 π r 3 = 4 / 3 * π * 6 * 6 * 6 = 288 π cm 3 answer : a"
Answer: a
Question (general): when a certain number x is divided by 72 , the remainder is 19 . what is the remainder when x is divided by 8 ?
Options: a ) 3 , b ) 2 , c ) 4 , d ) 1 , e ) 5
Rationale: "let possible value of x is 91 least possible value of x / 8 is 91 / 8 = > 11 quotient with remainder 3 thus answer is ( a ) 3"
Answer: a
Question (general): in a tournament prize of 1 st , 2 nd , and 3 rd is given in same interval . if total amount of prize rs 4800 and prize of 1 st is rs 2000 , find the interval ? ?
Options: a ) 600 , b ) 450 , c ) 350 , d ) 550 , e ) 400
Rationale: let the interval is x . prize of 2 nd and 3 rd is 2000 - x and 2000 - 2 x 2000 + 2000 - x + 2000 - 2 x = 4800 x = 400 answer : e
Answer: e
Question (general): if n = 8 ^ 11 – 1 , what is the units digit of n ?
Options: a ) 3 , b ) 1 , c ) 0 , d ) 6 , e ) 4
Rationale: "8 ^ 11 - 8 = 8 ( 8 ^ 10 - 1 ) = = > 8 ( 2 ^ 30 - 1 ) last digit of 2 ^ 30 is 4 based on what explanation livestronger is saying . 2 ^ 30 - 1 yields 4 - 1 = 3 as the unit digit . now on multiply this with 1 , we get unit digit as 3 . answer : a"
Answer: a
Question (gain): $ 600 will become $ 720 in 4 years find the rate of interest ?
Options: a ) 10 % , b ) 15 % , c ) 5 % , d ) 7 % , e ) 20 %
Rationale: "si = simple interest = a - p = 720 - 600 = $ 120 r = 100 si / pt = 100 * 120 / 600 * 4 = 5 % answer is c"
Answer: c
Question (geometry): the area of a circle is increased by 300 % . by what percent has the diameter of the circle increased ?
Options: a ) 400 %
b ) 200 %
c ) 300 %
d ) 100 %
e ) 800 %
Rationale: the area of the circle is increased by 300 % , thus the area is increased 4 times . the area of a circle it proportional to the square of the diameter ( area = π d ^ 2 / 4 ) , therefore the diameter must increase 2 times ( diameter increase 2 times = area increase 4 times ) , which is increase by 100 % . answer : d .
Answer: d
Question (physics): 18 men take 21 days of 8 hours each to do a piece of work . how many days of 6 hours each would 21 women take to do the same . if 3 women do as much work as 2 men ?
Options: a ) 32 , b ) 87 , c ) 36 , d ) 99 , e ) 77
Rationale: "3 w = 2 m 18 m - - - - - - 21 * 8 hours 21 w - - - - - - x * 6 hours 14 m - - - - - - x * 6 18 * 21 * 8 = 14 * x * 6 x = 36 answer : c"
Answer: c
Question (gain): find the simple interest on rs 7000 at 50 / 3 % for 9 months
Options: a ) rs . 1075 , b ) rs . 975 , c ) rs . 875 , d ) rs . 775 , e ) none of these
Rationale: "explanation : s . i . = p × r × t 100 so , by pu ƫ ing the values in the above formula , our result will be . required result = 7000 × 50 × 93 × 12 × 100 = 875 [ please note that we have divided by 12 as we converted 9 months in a year format ] answer : c"
Answer: c
Question (geometry): what is the area of a square with perimeter 4 p ?
Options: a ) p ^ 2 , b ) 4 p , c ) p ^ 2 / 4 , d ) p / 16 , e ) p ^ 2 / 16
Rationale: "each side is p a = ( p ) ^ 2 answer a"
Answer: a
Question (general): a school has 9 english 7 history and 6 geography teachers each teacher can teach 2 subjects max what is he minimum number of teachers required
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: total subjects = 9 + 7 + 6 = 22 max subjects by 1 teacher = 2 so , min of teachers required = 22 / 2 = 11 answer : e
Answer: e
Question (general): if in a certain code ` ` range ' ' is coded as 12345 and ` ` random ' ' is coded as 123678 . then the code for the word ` ` rand ' ' would be
Options: a ) 1236 , b ) 1365 , c ) 1200 , d ) 1526 , e ) 1325
Rationale: r - 1 a - 2 n - 3 d - 6 so for mango the code is 1236 answer : a
Answer: a
Question (physics): a goods train runs at the speed of 72 kmph and crosses a 230 m long platform in 26 seconds . what is the length of the goods train ?
Options: a ) 230 m , b ) 270 m , c ) 643 m , d ) 832 m , e ) 290 m
Rationale: "speed = ( 72 x 5 / 18 ) m / sec = 20 m / sec . time = 26 sec . let the length of the train be x metres . then , x + 230 / 26 = 20 x + 230 = 520 x = 290 . answer : e"
Answer: e
Question (physics): it takes joey the postman 1 hours to run a 2 mile long route every day . he delivers packages and then returns to the post office along the same path . if the average speed of the round trip is 6 mile / hour , what is the speed with which joey returns ?
Options: a ) 9 , b ) 12 , c ) 13 , d ) 14 , e ) 15
Rationale: "let his speed for one half of the journey be 3 miles an hour let the other half be x miles an hour now , avg speed = 5 mile an hour 2 * 2 * x / 3 + x = 6 4 x = 6 x + 18 = > 2 x = 18 x = 9 a"
Answer: a
Question (general): the distance from the x - axis to point p is half the distance from the y - axis to point p . if the coordinates of p are ( x , - 9 ) , how many units is p from the y - axis ?
Options: a ) 18 , b ) 12 , c ) 9 , d ) 4.5 , e ) 3
Rationale: "the x - axis is 9 units from the point p . thus the y - axis is 18 units from the point p . the answer is a ."
Answer: a
Question (general): if a ' s height is 45 % less than that of b , how much percent b ' s height is more than that of a ?
Options: a ) 66.66 % , b ) 81.81 % , c ) 66.766 % , d ) 86.66 % , e ) 66.65 %
Rationale: "excess of b ' s height over a ' s = [ ( 45 / ( 100 - 45 ) ] x 100 % = 81.81 % answer : b )"
Answer: b
Question (general): in an apartment building that has 490 units , 4 out of every 7 units are currently rented , including 1 / 4 of the one - bedroom units . if , of the rented apartments , there is a 6 : 1 ratio of two - bedroom units to one - bedroom units , and the building only consists of two - bedroom and one - bedroom units , how many two - bedroom units are not rented ?
Options: a ) 50 , b ) 90 , c ) 100 , d ) 105 , e ) 140
Rationale: "rented = 4 / 7 * 490 = 280 . rented two - bedroom = 6 / 7 * 280 = 240 ; rented one - bedroom = 1 / 7 * 280 = 40 ( or 280 - 240 = 40 ) . rented one - bedroom units are 1 / 4 of all one - bedroom : 1 / 4 * { all one bedroom } = 40 - - > { all one - bedroom } = 160 { all two - bedroom } = 490 - 160 = 330 two - bedroom not rented = 330 - 240 = 90 b"
Answer: b
Question (probability): in how many ways 6 boys and 6 girls can be seated in a row so that boys and girls are alternate ?
Options: a ) 1063800 , b ) 1083600 , c ) 1036800 , d ) 1053800 , e ) 1073600
Rationale: "number of ways = 2 * 6 ! * 6 ! = 1036800 answer is c"
Answer: c
Question (gain): the cost price of 12 articles is equal to the selling price of 10 articles . what is the profit percent ?
Options: a ) 10 % , b ) 20 % , c ) 30 % , d ) 40 % , e ) 50 %
Rationale: "10 * sp = 12 * cp sp = 1.2 * cp the profit percent is 20 % . the answer is b ."
Answer: b
Question (physics): a man rows his boat 65 km downstream and 45 km upstream , taking 2 1 / 2 hours each time . find the speed of the stream ?
Options: a ) 5 kmph , b ) 4 kmph , c ) 9 kmph , d ) 8 kmph , e ) 1 kmph
Rationale: "speed downstream = d / t = 65 / ( 2 1 / 2 ) = 26 kmph speed upstream = d / t = 45 / ( 2 1 / 2 ) = 18 kmph the speed of the stream = ( 26 - 18 ) / 2 = 4 kmph answer : b"
Answer: b
Question (general): arnold and danny are two twin brothers that are celebrating their birthday . the product of their ages today is smaller by 9 from the product of their ages a year from today . what is their age today ?
Options: a ) 2 . , b ) 4 . , c ) 5 . , d ) 7 , e ) 9 .
Rationale: "ad = ( a + 1 ) ( d + 1 ) - 9 0 = a + d - 8 a + d = 8 a = d ( as they are twin brothers ) a = d = 4 b is the answer"
Answer: b
Question (general): 27 * 27 * 27 * 27 = 3 ^ ?
Options: a ) 7 , b ) 12 , c ) 5 , d ) 6 , e ) 8
Rationale: "3 ^ 3 * 3 ^ 3 * 3 ^ 3 * 3 ^ 3 = 3 ^ ( 3 + 3 + 3 + 3 ) = 3 ^ 12 answer : 12 option : b"
Answer: b
Question (gain): there were two candidates in an election . winner candidate received 60 % of votes and won the election by 240 votes . find the number of votes casted to the winning candidate ?
Options: a ) 228 , b ) 720 , c ) 255 , d ) 199 , e ) 231
Rationale: "w = 60 % l = 40 % 60 % - 40 % = 20 % 20 % - - - - - - - - 240 60 % - - - - - - - - ? = > 720 answer : b"
Answer: b
Question (general): a factory producing tennis balls stores them in either big boxes , 25 balls per box , or small boxes , 20 balls per box . if 153 freshly manufactured balls are to be stored , what is the least number of balls that can be left unboxed ?
Options: a ) 2 , b ) 1 , c ) 3 , d ) 5 , e ) 4
Rationale: "we have to work with multiples of 20 and 25 . first , we must know the limits of this multiples , so : 152 / 25 = 6 . . . . so the max is 6 152 / 20 = 7 . . . so the max is 7 153 - 150 = 3 ( 6 big box ) answer : c"
Answer: c
Question (general): what least number should be subtracted from 997 so that the remainder when divided by 5 , 9 , and 11 will leave in each case the same remainder 3 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: the lcm of 5,9 and 11 is 495 . the next multiple is 2 * 495 = 990 . 990 + { remainder } = 990 + 3 = 993 , which is 4 less than 997 . answer : d .
Answer: d
Question (general): a garden center sells a certain grass seed in 5 - pound bags at $ 13.82 per bag , 10 - pound bags at $ 20.43 per bag , and 25 - pound bags $ 32.25 per bag . if a customer is to buy at least 65 pounds of the grass seed , but no more than 80 pounds , what is the least possible cost of the grass seed that the customer will buy ?
Options: a ) $ 94.03 , b ) $ 96.75 , c ) $ 98.75 , d ) $ 102.07 , e ) $ 105.3
Rationale: "there can be 2 cases 1 ) 25 + 25 + 10 + 5 = $ 98.75 or 2 ) 25 + 25 + 25 = $ 96.75 c"
Answer: c
Question (general): in a group of cows and chickens , the number of legs was 14 more than twice the number of heads . the number of cows was :
Options: a ) 3 , b ) 5 , c ) 9 , d ) 7 , e ) 8
Rationale: d 7 let the number of cows be x and their legs be 4 x . let the number of chicken be y and their legs be 2 x . total number of legs = 4 x + 2 y . total number of heads = x + y . the number of legs was 14 more than twice the number of heads . therefore , 2 × ( x + y ) + 14 = 4 x + 2 y . or , 2 x + 2 y + 14 = 4 x + 2 y . or , 2 x + 14 = 4 x [ subtracting 2 y from both sides ] . or , 14 = 4 x – 2 x [ subtracting 2 x from both sides ] . or , 14 = 2 x . or , x = 7 [ dividing by 2 on both sides ] . therefore , the number of cows = 7 .
Answer: d
Question (general): what least number should be subtracted from 13604 such that the remainder is divisible by 87 ?
Options: a ) 32 , b ) 29 , c ) 28 , d ) 30 , e ) 31
Rationale: "13604 ÷ 87 = 156 , remainder = 32 hence 32 is the least number which can be subtracted from 13604 such that the remainder is divisible by 87 answer is a"
Answer: a
Question (other): water consists of hydrogen and oxygen , and the approximate ratio , by mass , of hydrogen to oxygen is 2 : 16 . approximately how many grams of oxygen are there in 153 grams of water ?
Options: a ) 16 , b ) 72 , c ) 112 , d ) 136 , e ) 142
Rationale: "since the ratio , by mass , of hydrogen to oxygen is 2 : 16 , then oxygen is 16 / ( 2 + 16 ) = 8 / 9 of mass of water . therefore there are 153 * 8 / 9 = 136 grams of oxygen in 153 grams of water . answer : d ."
Answer: d
Question (general): how many zeros does 135 ^ 19 x 42 ^ 17 end with ?
Options: a ) 0 , b ) 2 , c ) 5 , d ) 13 , e ) 17
Rationale: "to know the zeros we need to know how many 10 ' s are there for this need to find number of 2 s and 5 s ( 2 * 5 = 10 ) 135 = ( 5 x 3 ^ 3 ) ^ 19 so number of 5 s are = 19 42 = ( 2 x 7 x 3 ) ^ 17 so number of 2 s = 17 so tot number of 10 s in this number is ( 17 - > 2 s x 17 - > 5 s ) so answer is 17 answer : e"
Answer: e
Question (physics): due to construction , the speed limit along an 5 - mile section of highway is reduced from 40 miles per hour to 22 miles per hour . approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ?
Options: a ) a ) 3.12 , b ) b ) 8 , c ) c ) 10 , d ) d ) 15 , e ) e ) 6.13
Rationale: "old time in minutes to cross 5 miles stretch = 5 * 60 / 40 = 5 * 3 / 2 = 7.5 new time in minutes to cross 5 miles stretch = 5 * 60 / 22 = 5 * 30 / 11 = 13.63 time difference = 6.13 ans : e"
Answer: e
Question (general): 2 : 5 = 4 / 3 : x . the value of x is ?
Options: a ) 10 / 3 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: x * 2 = 5 * 4 / 3 x * 2 = 20 / 3 x = 10 / 3 answer : a
Answer: a
Question (general): how many even integers n , such that 20 < = n < = 200 are of the form 3 k + 4 , where k is any natural number ?
Options: a ) 26 , b ) 30 , c ) 34 , d ) 38 , e ) 42
Rationale: "the first number is 22 = 16 + 6 ( 1 ) . we can continue adding 6 to make a list : 22 , 28 , 34 , . . . the last number is 196 = 16 + 6 ( 30 ) there are 30 numbers in the list . the answer is b ."
Answer: b
Question (general): find a sum for 1 st 4 prime number ' s ?
Options: a ) 25 , b ) 17 , c ) 30 , d ) 34 , e ) 36
Rationale: "required sum = ( 2 + 3 + 5 + 7 ) = 17 note : 1 is not a prime number option b"
Answer: b
Question (other): two vessels having volumes in the ratio 3 : 5 are filled with water and milk solutions . the ratio of milk and water in the two vessels are 5 : 1 and 6 : 4 respectively . if the contents of both the vessel are empties into a larger vessel , find the ratio of milk and water in the larger vessel .
Options: a ) 12 : 5 , b ) 11 : 5 , c ) 13 : 5 , d ) 14 : 5 , e ) 9 : 5
Rationale: "vessel a = 300 gallons - - > milk = 250 , water = 50 ; vessel b = 500 gallons - - > milk = 300 , water = 200 ; vessel a + b = 800 gallons - - > milk = 550 , water 250 the ratio = 550 / 250 - - > 11 : 5 answer : b"
Answer: b
Question (physics): how many seconds will a 750 meter long train moving with a speed of 63 km / hr take to cross a man walking with a speed of 3 km / hr in the direction of the train ?
Options: a ) 48 , b ) 36 , c ) 26 , d ) 11 , e ) 45
Rationale: "explanation : here distance d = 750 mts speed s = 63 - 3 = 60 kmph = 60 x 5 / 18 m / s time t = = 45 sec . answer : e"
Answer: e
Question (general): a certain country had a total annual expenditure of $ 7.2 x 10 ^ 11 last year . if the population of the country was 240 million last year , what was the per capita expenditure ?
Options: a ) $ 500 , b ) $ 1,000 , c ) $ 2,000 , d ) $ 3,000 , e ) $ 5,000
Rationale: "total expenditure / population = per capita expenditure hence , ( 7,2 x 10 ^ 11 ) / 240 000 000 = ( 7,2 x 10 ^ 11 ) / ( 2,4 x 10 ^ 8 ) = 3 x 10 ^ ( 11 - 8 ) = 3 x 10 ^ 3 = 3000 . answer is d ."
Answer: d
Question (general): a certain manufacturer produces items for which the production costs consist of annual fixed costs totaling $ 130,000 and variables costs averaging $ 5 per item . if the manufacturer ’ s selling price per item is $ 15 , how many items the manufacturer produce and sell to earn an annual profit of $ 150,000 ?
Options: a ) 2,858 , b ) 18,667 , c ) 28,000 , d ) 35,000 , e ) 40,000
Rationale: "let the items manufactured or sold bex 130000 + 5 x = 15 x - 150000 10 x = 280000 x = 28000 ans : c"
Answer: c
Question (geometry): what should be added to 4529 so that it may become a perfect square ?
Options: a ) 94 , b ) 95 , c ) 96 , d ) 97 , e ) 98
Rationale: "68 x 68 = 4624 4624 - 4529 = 95 if added to 95 get perfect square answer = b"
Answer: b
Question (general): barbata invests $ 2400 in the national bank at 5 % . how much additional money must she invest at 8 % so that the total annual income will be equal to 8 % of her entire investment ?
Options: a ) 1200 , b ) 3000 , c ) 1000 , d ) 3600 , e ) 2400
Rationale: "let the additional invested amount for 8 % interest be x ; equation will be ; 2400 + 0.05 * 2400 + x + 0.08 x = 2400 + x + 0.08 ( 2400 + x ) 0.05 * 2400 + 0.08 x = 0.06 x + 0.08 * 2400 0.02 x = 2400 ( 0.08 - 0.05 ) x = 2400 * 0.03 / 0.02 = 3600 ans : d"
Answer: d
Question (general): if x : y = 3 : 4 , find ( 4 x + 5 y ) : ( 5 x - 2 y ) .
Options: a ) 32 / 7 , b ) 13 / 7 , c ) 2 / 7 , d ) 32 / 17 , e ) 2 / 17
Rationale: ". x / y = 3 / 4  ( 4 x + 5 y ) / ( 5 x + 2 y ) = ( 4 ( x / y ) + 5 ) / ( 5 ( x / y ) - 2 ) = ( 4 ( 3 / 4 ) + 5 ) / ( 5 ( 3 / 4 ) - 2 ) = ( 3 + 5 ) / ( 7 / 4 ) = 32 / 7 answer a 32 / 7"
Answer: a
Question (general): find two integers , neither of which ends in a zero , and whose product is exactly 1 , 000,000
Options: a ) 64 and 15,625 , b ) 60 and 15,625 , c ) 64 and 15,620 , d ) 64 and 15,635 , e ) 64 and 16,625
Rationale: "1 , 000,000 = 10 ^ 6 = 10 x 10 x 10 x 10 x 10 x 10 = ( 2 x 5 ) x ( 2 x 5 ) x ( 2 x 5 ) x ( 2 x 5 ) x ( 2 x 5 ) x ( 2 x 5 ) = ( 2 ^ 6 ) x ( 5 ^ 6 ) = 64 x 15625 so the numbers are 64 and 15,625 answer : a"
Answer: a
Question (general): the average of 17 numbers is 59 . average of the first 9 of them is 56 and that of the last 9 is 63 . find the 9 th number ?
Options: a ) 64 , b ) 68 , c ) 65 , d ) 66 , e ) 67
Rationale: sum of all the 17 numbers = 17 * 59 = 1,003 sum of the first 9 of them = 9 * 56 = 504 sum of the last 9 of them = 9 * 63 = 567 so , the 8 th number = 504 + 567 - 1,003 = 68 . answer : b
Answer: b
Question (physics): a boat can travel with a speed of 24 km / hr in still water . if the speed of the stream is 4 km / hr , find the time taken by the boat to go 56 km downstream
Options: a ) 2 hours , b ) 4 hours , c ) 5 hours , d ) 6 hours , e ) 7 hours
Rationale: "explanation : speed of the boat in still water = 24 km / hr speed of the stream = 4 km / hr speed downstream = ( 22 + 5 ) = 28 km / hr distance travelled downstream = 56 km time taken = distance / speed = 56 / 28 = 2 hours answer : option a"
Answer: a
Question (gain): carl is facing very difficult financial times and can only pay the interest on a $ 10,000 loan he has taken . the bank charges him a quarterly compound rate of 7 % . what is the approximate interest he pays annually ?
Options: a ) 1000 , b ) 1500 , c ) 3000 , d ) 2500 , e ) 2400
Rationale: "an easy way too attempt this is by approximation : for the first quarter , he pays 7 % of 10,000 which is $ 700 . so for the four quarters in the year , he will approximately play 700 * 4 = 2800 over the entire year . because of compound interest it will be more than 2800 . approx . option c is correct . answer : c"
Answer: c
Question (physics): a alone can do a piece of work in 6 days and b alone in 8 days . a and b undertook to do it for rs . 3200 . with the help of c , they completed the work in 3 days . how much is to be paid to c ?
Options: a ) rs . 450 , b ) rs . 600 , c ) rs . 800 , d ) rs . 375 , e ) rs . 400
Rationale: "c ' s 1 day ' s work = 1 / 3 - ( 1 / 6 + 1 / 8 ) = 1 / 24 . a ' s wages : b ' s wages : c ' s wages = 1 / 6 : 1 / 8 : 1 / 24 = 4 : 3 : 1 . c ' s share ( for 3 days ) = rs . ( 3 x 1 / 24 x 3200 ) = rs . 400 . correct option ` ` e ' ' ."
Answer: e
Question (general): 1 / 2 - [ ( 2 / 5 * 5 / 32 ) + 1 ] + 9 / 16 =
Options: a ) 29 / 16 , b ) 19 / 16 , c ) 15 / 16 , d ) 9 / 13 , e ) 0
Rationale: "1 / 2 - [ ( 2 / 5 * 5 / 32 ) + 1 ] + 9 / 16 = 1 / 2 - [ ( 1 / 16 ) + 1 ] + 9 / 16 = 1 / 2 - [ 17 / 16 ] + 9 / 16 = 8 / 16 - 17 / 16 + 9 / 16 = 0 the answer is e ."
Answer: e
Question (physics): mariah has decided to hire three workers . to determine whom she will hire , she has selected a group of 20 candidates . she plans to have one working interview with 3 of the 20 candidates every day to see how well they work together . how many days will it take her to have working interviews with all the different combinations of job candidates ?
Options: a ) 520 , b ) 120 , c ) 300 , d ) 30 , e ) 333
Rationale: 520 . answer a
Answer: a