Cheukting/mathqa huggingface dataset:
Question (general): if n is a prime number greater than 3 , what is the remainder when n ^ 2 is divided by 13 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 13 , e ) 5
Rationale: "there are several algebraic ways to solve this question including the one under the spoiler . but the easiest way is as follows : since we can not have two correct answersjust pick a prime greater than 3 , square it and see what would be the remainder upon division of it by 13 . n = 5 - - > n ^ 2 = 25 - - > remainder upon division 25 by 13 is 12 . answer : d ."
Answer: d
Question (general): having received his weekly allowance , john spent 3 / 5 of his allowance at the arcade . the next day he spent one third of his remaining allowance at the toy store , and then spent his last $ 0.60 at the candy store . what is john ’ s weekly allowance ?
Options: a ) $ 2.25 , b ) $ 3.00 , c ) $ 3.25 , d ) $ 3.65 , e ) $ 4.80
Rationale: "x = 3 x / 5 + 1 / 3 * 2 x / 5 + 60 4 x / 15 = 60 x = 225 = $ 2.25 the answer is a ."
Answer: a
Question (other): a certain university will select 1 of 7 candidates eligible to fill a position in the mathematics department and 2 of 11 candidates eligible to fill 2 identical positions in the computer science department . if none of the candidates is eligible for a position in both departments , how many different sets of 3 candidates are there to fill the 3 positions ?
Options: a ) 42 , b ) 70 , c ) 140 , d ) 165 , e ) 385
Rationale: "ans : 385 7 c 1 * 11 c 2 answer e )"
Answer: e
Question (other): in the year 1990 there are 5000 men 3000 women 2000 boys . in 1994 men are increased by 20 % women are increased by ratio of boys and women ?
Options: a ) 11000 , b ) 12000 , c ) 13000 , d ) 14000 , e ) 15000
Rationale: total population in year 1990 = 5000 + 3000 + 2000 = 10000 total population in year 1994 = ( ( 5000 * 120 / 100 ) + ( 3000 + ( 3000 * 2 / 3 ) ) + ( 2000 ) ) = 13000 answer : c
Answer: c
Question (general): a is two years older than b who is twice as old as c . if the total of the ages of a , b and c be 27 , the how old is b
Options: a ) 10 , b ) 8 , c ) 6 , d ) 5 , e ) 7
Rationale: "let c ' s age be x years . then , b ' s age = 2 x years . a ' s age = ( 2 x + 2 ) years . ( 2 x + 2 ) + 2 x + x = 27 5 x = 25 x = 5 . hence , b ' s age = 2 x = 10 years answer : a"
Answer: a
Question (general): what is the sum of the multiples of 4 between 13 and 125 inclusive ?
Options: a ) 1,890 , b ) 1,960 , c ) 2,200 , d ) 3,780 , e ) 4,400
Rationale: "the first multiple of 12 between 13 and 125 is 16 while the last is 124 total number of terms is given by 124 = 16 + ( n - 1 ) 4 4 n - 4 = 108 n = 112 / 4 = 28 or , ( 124 - 16 ) / 4 + 1 = 28 so , we have 28 multiples of 12 between 13 and 125 sum = 14 ( 2 * 16 + ( 27 ) 4 ) = 14 ( 140 ) = 1960 answer : b"
Answer: b
Question (geometry): the volume of a rectangular swimming pool is 840 cubic meters and water is flowing into the swimming pool . if the surface level of the water is rising at the rate of 0.5 meters per minute , what is the rate s , in cubic meters per minutes , at which the water is flowing into the swimming pool ?
Options: a ) 0.125 , b ) 0.25 , c ) 0.5 , d ) 0.75 , e ) not enough information to determine the rate
Rationale: "the correct answer is e . there are not enough info to answer the question . a 840 cubic meters rectangle is built from : height * length * width . from the question we know the volume of the pool and the filling rate . a pool can have a height of 10 * width 8.4 * length 10 and have a volume of 840 cubic meters , and it can have a height of 1 meter , width of 100 meters and length of 8.4 . in both cases the pool will fill up in a different rate = e"
Answer: e
Question (geometry): four horses are tethered at 4 corners of a square field of side 70 metres so that they just can not reach one another . the area left ungrazed by the horses is :
Options: a ) 1050 sq . m
b ) 3850 sq . m
c ) 950 sq . m
d ) 1075 sq . m
e ) 1065 sq . m
Rationale: area ungrazed is given by total area - 4 * area grazed by each horse = 70 * 70 - 4 * ( 90 / 360 ) * pi * ( 70 / 2 ) ^ 2 as the angle made by the horse is 90 degree , so applying the area of the sector , = theta / 360 * pi * radius ^ 2 above = 70 * 70 - pi * ( 70 / 2 ) * ( 70 / 2 ) = 70 * 70 { 1 - pi / 4 } = 70 * 70 { 6 / ( 7 * 4 ) } , expanding pi = 22 / 7 = ( 70 * 70 * 6 ) / ( 7 * 4 ) = 1050 sq m answer : a
Answer: a
Question (gain): a dealer purchases 15 articles for rs . 25 and sells 12 articles for rs . 38 . find the profit percentage ?
Options: a ) 80 % , b ) 90 % , c ) 59 % , d ) 40 % , e ) 53 %
Rationale: l . c . m of 15 and 12 = 60 cp of 60 articles = rs . 100 ( 25 * 4 ) sp of 60 articles = rs . 190 ( 30 * 5 ) profit percentage = ( 190 - 100 ) / 100 * 100 = 90 % answer : b
Answer: b
Question (gain): redo ’ s manufacturing costs for sets of horseshoes include a $ 10000 initial outlay , and $ 20 per set . they can sell the sets $ 50 . if profit is revenue from sales minus manufacturing costs , and the company producessells 500 sets of horseshoes , what was their profit ?
Options: a ) $ 4500 , b ) $ 3500 , c ) $ 5500 , d ) $ 5000 , e ) $ 6300
Rationale: total manufacturing cost = 10000 + 500 * 20 = 20000 total selling cost = 500 * 50 = 25000 profit = 25000 - 20000 = 5000 answer : d
Answer: d
Question (general): from below option 50 is divisible by which one ?
Options: a ) 3 , b ) 2 , c ) 7 , d ) 8 , e ) 9
Rationale: "50 / 2 = 25 b"
Answer: b
Question (general): in n is a positive integer less than 200 , and 24 n / 60 is an integer , then n has how many different positive prime factors ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 6 , e ) 8
Rationale: "( a ) . 24 n / 60 must be an integer . = > 2 n / 5 must be an integer . hence n must be a multiple of 5 . = > n has 1 different prime integers ."
Answer: a
Question (general): on rainy mornings , mo drinks exactly n cups of hot chocolate ( assume that n is an integer ) . on mornings that are not rainy , mo drinks exactly 4 cups of tea . last week mo drank a total of 42 cups of tea and hot chocolate together . if during that week mo drank 14 more tea cups than hot chocolate cups , then how many rainy days were there last week ?
Options: a ) 0 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "t = the number of cups of tea c = the number of cups of hot chocolate t + c = 42 t - c = 14 - > t = 28 . c = 14 . mo drinks 4 cups of tea a day then number of days that are not rainy = 28 / 4 = 7 so number of rainy days = 7 - 7 = 0 a is the answer ."
Answer: a
Question (general): 469157 * 9999
Options: a ) 1691100843 , b ) 4591100843 , c ) 4691100843 , d ) 3691100843 , e ) none of these
Rationale: "explanation : 469157 * ( 10000 - 1 ) = 4691570000 - 469157 = 4691100843 option c"
Answer: c
Question (general): what is the largest 4 digit number exactly divisible by 72 ?
Options: a ) 4676 , b ) 4678 , c ) 8888 , d ) 9504 , e ) 9936
Rationale: "largest 4 digit number = 9999 9999 ÷ 72 = 138 , remainder = 63 hence largest 4 digit number exactly divisible by 88 = 9999 - 63 = 9936 answer : e"
Answer: e
Question (other): apple costs l rupees per kilogram for first 30 kgs and q rupees per kilogram for each additional kilogram . if the price of 33 kilograms is 360 and for 36 kgs of apples is 420 then the cost of first 25 kgs of apples is
Options: a ) 100 , b ) 250 , c ) 125 , d ) 110 , e ) 115
Rationale: "ans : by framing equations we get 30 l + 3 q = 360 30 l + 6 q = 420 eliminate q by multiplying the first equation by 2 and subtracting second equation from the first then we get l = 10 cost of 10 kgs of apples = 25 x 10 = 250 answer : b"
Answer: b
Question (general): if x = 3 ^ 27 and x ^ x = 3 ^ k , what is k ?
Options: a ) 3 ^ 9 , b ) 3 ^ 12 , c ) 3 ^ 27 , d ) 3 ^ 30 , e ) 3 ^ 33
Rationale: "solution : we know that x = 3 ^ 27 which implies x ^ x = ( 3 ^ 27 ) ^ ( 3 ^ 27 ) = 3 ^ ( 27 * 3 ^ 27 ) [ because ( x ^ y ) ^ z = x ^ ( y * z ) ) ] so 3 ^ ( 3 ^ 3 * 3 ^ 27 ) = 3 ^ ( 3 ^ ( 3 + 27 ) ) [ because x ^ a * x ^ b = x ^ ( a + b ) ] therefore x ^ x = 3 ^ ( 3 ^ 30 ) given that x ^ x = 3 ^ k so 3 ^ ( 3 ^ 30 ) = 3 ^ k since the base is same the exponent will also be same therefore k = 3 ^ 30 answer : d"
Answer: d
Question (general): find the least number which when divided by 5,6 , 7,8 leaves a remainder 3 but when divided by 9 leaves no remainder
Options: a ) 9632 , b ) 7896 , c ) 8741 , d ) 1683 , e ) 8523
Rationale: "l . c . m of 5,6 , 7,8 = 840 required number is of the form of 840 k + 3 least value of k for which ( 840 k + 3 ) is divided by 9 is k = 2 required number = ( 840 * 2 + 3 ) = 1683 answer ( d )"
Answer: d
Question (geometry): the ratio of the radius of two circles is 3 : 4 , and then the ratio of their areas is ?
Options: a ) 1 : 7 , b ) 9 : 16 , c ) 1 : 9 , d ) 3 : 7 , e ) 3 : 4
Rationale: "r 1 : r 2 = 3 : 4 î r 1 ^ 2 : î r 2 ^ 2 r 1 ^ 2 : r 2 ^ 2 = 9 : 16 answer : b"
Answer: b
Question (general): evaluate : 30 - | - x + 6 | for x = 10
Options: a ) 16 , b ) 26 , c ) 36 , d ) 46 , e ) 56
Rationale: substitute x by 10 in the given expression and evaluate 30 - | - ( 10 ) + 6 | = 30 - | - 10 + 6 | = 30 - | - 4 | = 30 - 4 = 26 correct answer b ) 26
Answer: b
Question (gain): in a partnership , a invests 1 ⁄ 6 of the capital for 1 ⁄ 6 of the time , b invests 1 ⁄ 3 of the capital for 1 ⁄ 3 of the time and c , the rest of the capital for whole time . find a ’ s share of the total profit of 2300
Options: a ) 100 , b ) 200 , c ) 300 , d ) 400 , e ) none of these
Rationale: remaining capital = 1 - ( 1 ⁄ 6 + 1 ⁄ 3 ) = 1 ⁄ 2 ratio of their profit = 1 ⁄ 6 × [ 1 ⁄ 6 × 12 ] : 1 ⁄ 3 × [ 1 ⁄ 3 × 12 ] : 1 ⁄ 2 × 12 = 1 ⁄ 3 : 4 ⁄ 3 : 6 = 1 : 4 : 18 ∴ a ' s share = 1 / 1 + 4 + 18 × 2300 = 100 answer a
Answer: a
Question (gain): a shopkeeper has 280 kg of apples . he sells 40 % of these at 20 % profit and remaining 50 % at 30 % profit . find his % profit on total .
Options: a ) 23 % , b ) 25 % , c ) 26 % , d ) 28 % , e ) 35 %
Rationale: "if the total quantity was 100 then 40 x 20 % + 50 x 30 % = 23 this profit will remain same for any total quantity unless the % of products remains the same . hence ' a ' is the answer"
Answer: a
Question (physics): car x began traveling at an average speed of 35 miles per hour . after 48 minutes , car y began traveling at an average speed of 39 miles per hour . when both cars had traveled the same distance , both cars stopped . how many miles did car x travel from the time car y began traveling until both cars stopped ?
Options: a ) 105 , b ) 140 , c ) 175 , d ) 210 , e ) 245
Rationale: "in 48 minutes , car x travels 28 miles . car y gains 4 miles each hour , so it takes 7 hours to catch car x . in 7 hours , car x travels 245 miles . the answer is e ."
Answer: e
Question (general): how many 4 - digit positive integers are there in which all 4 digits are even ?
Options: a ) 625 , b ) 600 , c ) 500 , d ) 400 , e ) 256
Rationale: "positive integers - 2 , 4,6 , 8,0 let the integers of a four digit positive number be abcd a can take four values ( 2,4 , 6,8 ) b can take five values ( 0 , 2,4 , 6,8 ) c can take five values ( 0 , 2,4 , 6,8 ) d can take five values ( 0 , 2,4 , 6,8 ) the total is 5 * 5 * 5 * 4 the answer according to me is 500 answer : c"
Answer: c
Question (general): benny goes to the market for buying some apples to be distributed between her 9 kids equally . she takes 360 dollars with her . the cost of each apple is 4 dollars . how many apples does she buy to share them equally between her eighteen kids ?
Options: a ) 8 , b ) 9 , c ) 5 , d ) 7 , e ) 10
Rationale: cost of each apple = 4 dollars apples that benny can buy with the amount she has = 360 / 4 = 90 . apples that each kid gets evenly = 90 / 18 = 5 apples . so the answer is c = 5
Answer: c
Question (physics): it takes nine minutes to load a certain video on a cellphone , and fifteen seconds to load that same video on a laptop . if the two devices were connected so that they operated in concert at their respective rates , how many seconds would it take them to load the video , rounded to the nearest hundredth ?
Options: a ) 13.58 , b ) 13.87 , c ) 14.24 , d ) 14.59 , e ) 14.85
Rationale: the laptop can load the video at a rate of 1 / 15 of the video per second . the phone can load the video at a rate of 1 / ( 60 * 9 ) = 1 / 540 of the video per second . the combined rate is 1 / 15 + 1 / 540 = 37 / 540 of the video per second . the time required to load the video is 540 / 37 = 14.59 seconds . the answer is d .
Answer: d
Question (gain): a sum of money invested at compound interest to rs . 800 in 3 years and to rs 820 in 4 years . the rate on interest per annum is .
Options: a ) 0.4 % , b ) 5.0 % , c ) 2.5 % , d ) 7 % , e ) 8 %
Rationale: explanation : s . i . on rs 800 for 1 year = 20 rate = ( 100 * 20 ) / ( 800 * 1 ) = 2.5 % answer : c
Answer: c
Question (general): if two positive numbers are in the ratio 1 / 9 : 1 / 7 , then by what percent is the second number more than the first ?
Options: a ) 67 % . , b ) 70 % . , c ) 60 % . , d ) 28.6 % . , e ) 80 % .
Rationale: "given ratio = 1 / 9 : 1 / 7 = 7 : 9 let first number be 7 x and the second number be 9 x . the second number is more than first number by 2 x . required percentage = 2 x / 7 x * 100 = 28.6 % . answer : d"
Answer: d
Question (gain): find compound interest on rs . 7500 at 4 % per annum for 2 years , compounded annually
Options: a ) rs 312 , b ) rs 412 , c ) rs 512 , d ) rs 612 , e ) none of these
Rationale: explanation : please apply the formula amount = p ( 1 + r 100 ) nc . i . = amount - p answer : d
Answer: d
Question (geometry): the front wheels of a wagon are 2 π feet in circumference and the rear wheels are 3 π feet in circumference . when the front wheels have made 10 more revolutions than the rear wheels , how many feet has the wagon travelled ?
Options: a ) 30 π , b ) 45 π , c ) 60 π , d ) 90 π , e ) none
Rationale: solution let the rear wheel make x revolutions . then , the front wheel makes ( x + 10 ) revolutions . ( x + 10 ) x 3 π = x × 2 π ‹ = › 3 x + 30 = 2 x ‹ = › x = 30 . distance travelled by the wagon = ( 2 π x 30 ) ft ‹ = › ( 60 π ) ft . answer c
Answer: c
Question (physics): lcm of two numbers is 7700 and hcf is 11 . if one number is 308 then other number is
Options: a ) 269 , b ) 285 , c ) 300 , d ) 275 , e ) none of these
Rationale: option d
Answer: d
Question (physics): a car is running at a speed of 80 kmph . what distance will it cover in 20 sec ?
Options: a ) 100 m , b ) 440 m , c ) 180 m , d ) 200 m , e ) 250 m
Rationale: speed = 80 kmph = 80 * 5 / 18 = 22 m / s distance covered in 20 sec = 22 * 10 = 440 m answer is b
Answer: b
Question (general): a , b , c subscribe rs . 50,000 for a business . a subscribes rs . 4000 more than b and b rs . 5000 more than c . out of a total profit of rs . 35,000 , a receives
Options: a ) rs . 8400 , b ) rs . 11,900 , c ) rs . 13,600 , d ) rs . 14,700 , e ) none
Rationale: "solution : let c = x . then , b = x + 5000 and a = x + 5000 + 4000 = x + 9000 . so , x + x + 5000 + x + 9000 = 50000 . = > 3 x = 36000 . = > x = 12000 . a : b : c = 21000 : 17000 : 12000 = 21 : 17 : 12 . so a ' s share = rs . ( 35000 x 21 / 50 ) = rs . 14,700 . answer : option d"
Answer: d
Question (geometry): the radius of a cylindrical vessel is 7 cm and height is 2 cm . find the whole surface of the cylinder ?
Options: a ) 281 , b ) 396 , c ) 440 , d ) 767 , e ) 1981
Rationale: "r = 7 h = 2 2 π r ( h + r ) = 2 * 22 / 7 * 7 ( 9 ) = 396 answer : b"
Answer: b
Question (general): a charitable association sold an average of 66 raffle tickets per member . among the female members , the average was 70 raffle tickets . the male to female ratio of the association is 1 : 2 . what was the average number r of tickets sold by the male members of the association
Options: a ) 50 , b ) 56 , c ) 58 , d ) 62 , e ) 66
Rationale: "given that , total average r sold is 66 , male / female = 1 / 2 and female average is 70 . average of male members isx . ( 70 * f + x * m ) / ( m + f ) = 66 - > solving this equation after substituting 2 m = f , x = 58 . ans c ."
Answer: c
Question (physics): a train 880 m long is running at a speed of 78 km / hr . if it crosses a tunnel in 1 min , then the length of the tunnel is ?
Options: a ) 510 , b ) 540 , c ) 500 , d ) 420 , e ) 589
Rationale: "speed = 78 * 5 / 18 = 65 / 3 m / sec . time = 1 min = 60 sec . let the length of the train be x meters . then , ( 880 + x ) / 60 = 65 / 3 x = 420 m . answer : option d"
Answer: d
Question (general): if x is less than y by 50 % then y exceed x by :
Options: a ) 33.33 % , b ) 100 % , c ) 75 % , d ) 66.66 % , e ) none of these
Rationale: "using formula ( x / ( 100 - x ) * 100 ) where x is percentage decrease ( here it is 25 % ) = > 50 ( 100 - 50 ) * 100 = 100 % answer : b"
Answer: b
Question (gain): arun purchased 30 kg of wheat at the rate of rs . 11.50 per kg and 20 kg of wheat at the rate of 14.25 per kg . he mixed the two and sold the mixture . approximately what price per kg should be sell the mixture to make 30 % profit ?
Options: a ) 66.3 , b ) 76.3 , c ) 86.3 , d ) 16.3 , e ) 36.3
Rationale: "explanation : c . p . of 50 kg wheat = ( 30 * 11.50 + 20 * 14.25 ) = rs . 630 . s . p . of 50 kg wheat = 130 % of rs . 630 = 130 / 100 * 630 = rs . 819 . s . p . per kg = 819 / 50 = rs . 16.38 = 16.30 . answer : d"
Answer: d
Question (gain): what was the principal , if at 5 % per annum the interest after 10 years amounted to rs . 3100 less than the sum lent ?
Options: a ) 6200 , b ) 3000 , c ) 3000 , d ) 2000 , e ) 1000
Rationale: "p - 2336 = ( p * 10 * 5 ) / 100 p = 6200 answer : a"
Answer: a
Question (gain): the list price of an article is rs . 68 . a customer pays rs . 56.16 for it . he was given two successive discounts , one of them being 10 % . the other discount is ?
Options: a ) 3.23 % , b ) 4.23 % , c ) 5.23 % , d ) 7.23 % , e ) 8.23 %
Rationale: "68 * ( 90 / 100 ) * ( ( 100 - x ) / 100 ) = 56.16 x = 8.23 % answer : e"
Answer: e
Question (geometry): the cost of the paint is rs . 36.50 per kg . if 1 kg of paint covers 16 square feet , how much will it cost to paint outside of a cube having 8 feet each side .
Options: a ) rs . 850 , b ) rs . 860 , c ) rs . 876 , d ) rs . 886 , e ) none of these
Rationale: "explanation : we will first calculate the surface area of cube , then we will calculate the quantity of paint required to get answer . here we go , surface area = 6 a 2 = 6 ∗ 8 ( 2 ) = 384 sq feet quantity required = 38416 = 24 kg cost of painting = 36.50 ∗ 24 = rs . 876 option c"
Answer: c
Question (physics): two consultants can type up a report in 12.5 hours and edit it in 7.5 hours . if mary needs 30 hours to type the report and jim needs 12 hours to edit it alone , how many w hours will it take if jim types the report and mary edits it immediately after he is done ?
Options: a ) 41.4 , b ) 34.1 , c ) 13.4 , d ) 12.4 , e ) 10.8
Rationale: "break down the problem into two pieces : typing and editing . mary needs 30 hours to type the report - - > mary ' s typing rate = 1 / 30 ( rate reciprocal of time ) ( point 1 in theory below ) ; mary and jim can type up a report in 12.5 and - - > 1 / 30 + 1 / x = 1 / 12.5 = 2 / 25 ( where x is the time needed for jim to type the report alone ) ( point 23 in theory below ) - - > x = 150 / 7 ; jim needs 12 hours to edit the report - - > jim ' s editing rate = 1 / 12 ; mary and jim can edit a report in 7.5 and - - > 1 / y + 1 / 12 = 1 / 7.5 = 2 / 15 ( where y is the time needed for mary to edit the report alone ) - - > y = 20 ; how many w hours will it take if jim types the report and mary edits it immediately after he is done - - > x + y = 150 / 7 + 20 = ~ 41.4 answer : a ."
Answer: a
Question (gain): a scuba diver descends at a rate of 35 feet per minute . a diver dive from a ship to search for a lost ship at the depth of 3500 feet below the sea level . . how long will he take to reach the ship ?
Options: a ) 160 minutes , b ) 120 minutes , c ) 100 minutes , d ) 76 minutes , e ) 77 minutes
Rationale: "time taken to reach = 3500 / 35 = 100 minutes answer : c"
Answer: c
Question (physics): a snail , climbing a 42 feet high wall , climbs up 4 feet on the first day but slides down 2 feet on the second . it climbs 4 feet on the third day and slides down again 2 feet on the fourth day . if this pattern continues , how many days will it take the snail to reach the top of the wall ?
Options: a ) 20 , b ) 26 , c ) 32 , d ) 39 , e ) 51
Rationale: "total transaction in two days = 4 - 2 = 2 feet in 38 days it will climb 38 feet on the 39 th day , the snail will climb 4 feet , thus reaching the top therefore , total no of days required = 39 d"
Answer: d
Question (gain): at what rate percent on simple interest will rs . 900 amount to rs . 950 in 5 years ?
Options: a ) 1.11 % , b ) 5.93 % , c ) 4.33 % , d ) 5.33 % , e ) 6.33 %
Rationale: "50 = ( 900 * 5 * r ) / 100 r = 1.11 % answer : a"
Answer: a
Question (general): if the price of sugar rises from rs . 10 per kg to rs . 12 per kg , a person , to have no increase in the expenditure on sugar , will have to reduce his consumption of sugar by
Options: a ) 17 % , b ) 20 % , c ) 25 % , d ) 30 % , e ) none
Rationale: "sol . let the original consumption = 100 kg and new consumption = x kg . so , 100 x 10 = x × 12 = x = 83 kg . ∴ reduction in consumption = 17 % . answer a"
Answer: a
Question (other): initially , the men and women in a room were in the ratio of 4 : 5 . then , 2 men entered the room and 3 women left the room . then , the number of women doubled . now there are 14 men in the room . how many e women are currently in the room ?
Options: a ) 12 , b ) 14 , c ) 15 , d ) 24 , e ) 36
Rationale: "the number of women doubled means that they have become 24 from 12 . . and we have to tell the current strength so 24 is the answer . . let the number be 4 x and 5 x . . given 4 x + 2 = 14 . . so x = 3 . . women number = 5 * 3 - 3 = 12 , then doubled = 24 . . ans d"
Answer: d
Question (other): find the compound ratio of ( 2 : 3 ) , ( 3 : 4 ) and ( 1 : 4 ) is
Options: a ) 1 : 2 , b ) 2 : 3 , c ) 1 : 8 , d ) 4 : 5 , e ) 3 : 2
Rationale: "required ratio = 2 / 3 * 3 / 4 * 1 / 4 = 1 / 8 = 1 : 8 answer is c"
Answer: c
Question (other): in a neighborhood having 90 households , 11 did not have either a car or a bike . if 16 households had a both a car and a bike and 44 had a car , how many had bike only ?
Options: a ) 30 , b ) 35 , c ) 20 , d ) 18 , e ) 10
Rationale: "{ total } = { car } + { bike } - { both } + { neither } - - > 90 = 44 + { bike } - 16 + 11 - - > { bike } = 51 - - > # those who have bike only is { bike } - { both } = 51 - 16 = 35 . answer : b ."
Answer: b
Question (gain): a bag marked at $ 150 is sold for $ 120 . the rate of discount is ?
Options: a ) 10 % , b ) 25 % , c ) 20 % , d ) 50 % , e ) 45 %
Rationale: "rate of discount = 30 / 150 * 100 = 20 % answer is c"
Answer: c
Question (physics): a man swims downstream 70 km and upstream 30 km taking 10 hours each time ; what is the speed of the current ?
Options: a ) 1 , b ) 4 , c ) 2 , d ) 6 , e ) 8
Rationale: "70 - - - 10 ds = 7 ? - - - - 1 30 - - - - 10 us = 3 ? - - - - 1 s = ? s = ( 7 - 3 ) / 2 = 2 answer : c"
Answer: c
Question (other): a certain university will select 1 of 7 candidates eligible to fill a position in the mathematics department and 2 of 8 candidates eligible to fill 2 identical positions in the computer science department . if none of the candidates is eligible for a position in both departments , how many different sets of 3 candidates are there to fill the 3 positions ?
Options: a ) 42 , b ) 70 , c ) 140 , d ) 196 , e ) 315
Rationale: "ans : 196 7 c 1 * 8 c 2 answer d )"
Answer: d
Question (general): a certain store sells all maps at one price and all books at another price . on monday the store sold 12 maps and 10 books for a total of $ 38.00 , and on tuesday the store sold 12 maps and 9 books for a total of $ 30.00 . at this store , how much less does a map sell for than a book ?
Options: a ) $ 0.25 , b ) $ 0.50 , c ) $ 0.75 , d ) $ 1.00 , e ) $ 4.5
Rationale: "12 x + 10 y = 38 12 x + 9 y = 30 subtracting 1 from 2 y = 8 therefore x = 3.5 difference in price = 4.5 e"
Answer: e
Question (physics): if an object travels at three feet per second , how many feet does it travel in one hour ?
Options: a ) 3488 , b ) 10800 , c ) 12788 , d ) 1800 , e ) 2881
Rationale: explanation : if an object travels at 2 feet per second it covers 3 x 60 feet in one minute , and 3 x 60 x 60 feet in one hour . answer = 10800 answer : b ) 10800
Answer: b