Cheukting/mathqa huggingface dataset:
Question (geometry): a rectangular swimming pool is 20 feet by 22 feet . a deck that has uniform width surrounds the pool . the total area of the pool and deck is 728 square feet . what is the width of the deck ?
Options: a ) 2
b ) 4
c ) 3
d ) 5
e ) 6
Rationale: let the width = w total area of the pool and deck = ( 2 w + 20 ) ( 2 w + 22 ) we can test the answer choices along with unit digit method a ) 2 feet . . . . . . . . . . . 24 * 26 has unit digit 8 . . . . . . . . . . eliminate b ) 2.5 feet . . . . . . . . . 25 * 33 has unit digit 5 . . . . . . . . . . eliminate c ) 3 feet . . . . . . . . . . . . 26 * 28 has unit digit 4 . . . . . . . . . . . hold d ) 4 feet . . . . . . . . . . . . 28 * 30 has unit digit 0 . . . . . . . . . . . eliminate e ) 5 feet . . . . . . . . . . . . 30 * 32 has unit digit 0 . . . . . . . . . . . eliminate answer : c w = 3
Answer: c
Question (other): three numbers are in the ratio 3 : 4 : 5 and their l . c . m . is 240 . their h . c . f is ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "let the numbers be 3 x , 4 x and 5 x their l . c . m . = 60 x 60 x = 240 x = 4 the numbers are 3 * 4 , 4 * 4 , 5 * 4 hence required h . c . f . = 4 answer is c"
Answer: c
Question (physics): a cistern is normally filled in 14 hours but takes two hours longer to fill because of a leak in its bottom . if the cistern is full , the leak will empty it in ?
Options: a ) 33 , b ) 88 , c ) 40 , d ) 99 , e ) 112
Rationale: "1 / 14 - 1 / x = 1 / 16 x = 112 answer : e"
Answer: e
Question (general): the overall age of x and y is 15 year greater than the overall age of y and z . z is how many decades younger that x ?
Options: a ) 11 , b ) 15 , c ) 12 , d ) 17 , e ) 19
Rationale: b 15 ( x + y ) â € “ ( y + z ) = 15 x â € “ z = 15
Answer: b
Question (other): sachin is younger than rahul by 5 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 ) 15.5
Rationale: "if rahul age is x , then sachin age is x - 5 , so ( x - 5 ) / x = 7 / 9 = > 9 x - 45 = 7 x = > 2 x = 45 = > x = 22.5 so sachin age is 22.5 - 7 = 15.5 answer : e"
Answer: e
Question (physics): two goods trains each 500 m long are running in opposite directions on parallel tracks . their speeds are 42 km / hr and 30 km / hr respectively . find the time taken by the slower train to pass the driver of the faster one ?
Options: a ) 22 , b ) 27 , c ) 50 , d ) 99 , e ) 12
Rationale: "relative speed = 42 + 30 = 72 km / hr . 72 * 5 / 18 = 20 m / sec . distance covered = 500 + 500 = 1000 m . required time = 1000 / 20 = 50 sec . answer : c"
Answer: c
Question (gain): julie put half of her savings in a savings account that pays an annual simple interest and half in a savings account that pays an annual compound interest . after two years she earned $ 128 and $ 140 from the simple interest account and the compound interest account respectively . if the interest rates for both accounts were the same , what was the amount of julie ' s initial savings ?
Options: a ) 640 , b ) 720 , c ) 1080 , d ) 1200 , e ) 1440
Rationale: "$ 128 for 2 years = $ 64 per year . extra $ 12 yearned with the compound interest is the percent yearned on percent . so , $ 12 is yearned on $ 64 , which means that the interest = 5 % . this on the other hand means that half of the savings = 64 * 5 = $ 320 . twice of that = $ 640 . answer : a ."
Answer: a
Question (general): every student in a room is either a junior or a senior . there is at least one junior and at least one senior in the room . if 2 / 5 of the juniors is equal to 1 / 3 of the seniors , what fraction of the students in the room are juniors ?
Options: a ) 3 / 20 , b ) 1 / 3 , c ) 5 / 12 , d ) 12 / 17 , e ) 5 / 11
Rationale: "let total number of juniors = j total number of seniors = s ( 2 / 5 ) j = ( 1 / 3 ) s = > s = 6 / 5 j total number of students = j + s = ( 11 / 5 ) j fraction of the students in the room are juniors = j / ( j + s ) = j / [ ( 11 / 5 ) j ] = 5 / 11 answer e"
Answer: e
Question (general): dominos charges $ 6.25 for a veg pizza of std size that costs a total of $ 2.85 to make . pizza hut charges $ 5.80 for a similar pizza that costs $ 1.80 to make . if dominos sells 2000 pizzas , how many must pizza hut sell to make at least as much in total gross profit as its competitor does ?
Options: a ) 858 , b ) 1875 , c ) 14667 , d ) 63840 , e ) 146667
Rationale: dominos : profit / pizza = 6.25 - 2.85 = 3.75 : no of pizza = 2000 : gross profit = 2000 * 3.75 = 7500 pizza hut : profit / pizza = 4 : gross profit = 7500 : no of cups = 7500 / 4 = 1875 answer b
Answer: b
Question (gain): a certain company reported that the revenue on sales increased 20 % from 2000 to 2003 , and increased 40 % from 2000 to 2005 . what was the approximate percent increase in revenue for this store from 2003 to 2005 ?
Options: a ) 50 % , b ) 40 % , c ) 35 % , d ) 32 % , e ) 17 %
Rationale: "assume the revenue in 2000 to be 100 . then in 2003 it would be 120 and and in 2005 140 , so from 2003 to 2005 it increased by ( 140 - 120 ) / 120 = 20 / 120 = 17 % answer : e ."
Answer: e
Question (general): the average height of 30 students in a class was calculated as 175 cm . it has later found that the height of one of the students in the class was incorrectly written as 151 cm whereas the actual height was 136 cm . what was the actual average height of the students in the class ?
Options: a ) 174.5 , b ) 173.5 , c ) 172.5 , d ) 171.5 , e ) 170.5
Rationale: "the total height was 15 cm too much . the average height should be reduced by 15 cm / 30 = 0.5 cm the answer is a ."
Answer: a
Question (general): how many integers are between 2 and 57 / 7 , inclusive ?
Options: a ) 5 , b ) 7 , c ) 9 , d ) 10 , e ) 12
Rationale: "57 / 7 = 8 . xx we are not concerned about the exact value of 57 / 7 as we just need the integers . the different integers between 2 and 57 / 7 would be 2,3 , 4 , 5 , 6 , 7 , 8 . total number of integers = 7 option b"
Answer: b
Question (gain): mr . john used to purchase certain number of mangoes for $ 360 since the price of mangoes is reduced by 10 % he got 12 more mangoes today . find the original price of 130 mangoes .
Options: a ) 360 , b ) 380 , c ) 400 , d ) 406 , e ) 433
Rationale: "mr . john used to purchase certain number of mangoes for $ 360 since the price of mangoes is reduced by 10 % he got 12 more mangoes today . find the original price of 120 mangoes . method 1 : let price per mango = x . let number of mangoes be n . then , nx = 360 . now price = 0.9 x ; number of mangoes = n + 12 . total amount = 0.9 x * ( n + 12 ) = 360 . nx = 0.9 nx + 10.8 x = > 0.1 nx = 10.8 x = > n = 108 = > x = 360 / 108 = 3.33 original price of 130 mangoes = 130 * 3.33 = 433 . answer e"
Answer: e
Question (general): if 3 a – 2 b – 2 c = 32 and √ 3 a - √ ( 2 b + 2 c ) = 5 , what is the value of a + b + c ?
Options: a ) 3 , b ) 9 , c ) 10 , d ) 12 , e ) 14
Rationale: "when we look at the two equations , we can relize some similarity , so lets work on it . . 3 a – 2 b – 2 c = 32 can be written as √ 3 a ^ 2 - √ ( 2 b + 2 c ) ^ 2 = 32 { √ 3 a - √ ( 2 b + 2 c ) } { √ 3 a + √ ( 2 b + 2 c ) } = 32 . . or 4 * √ 3 a + √ ( 2 b + 2 c ) = 32 . . or √ 3 a + √ ( 2 b + 2 c ) = 8 . . now lets work on these two equations 1 ) √ 3 a - √ ( 2 b + 2 c ) = 4 . . 2 ) √ 3 a + √ ( 2 b + 2 c ) = 8 . . a ) add the two eq . . √ 3 a + √ ( 2 b + 2 c ) + √ 3 a - √ ( 2 b + 2 c ) = 12 . . 2 √ 3 a = 12 . . or √ 3 a = 6 . . 3 a = 36 . . a = 12 . b ) subtract 1 from 2 . . √ 3 a + √ ( 2 b + 2 c ) - √ 3 a + √ ( 2 b + 2 c ) = 4 . . 2 √ ( 2 b + 2 c ) = 4 . . √ ( 2 b + 2 c ) = 2 . . 2 b + 2 c = 4 . . or b + c = 2 . . from a and b a + b + c = 12 + 2 = 14 . . b"
Answer: b
Question (general): if n is a positive integer and the product of all the integers from 1 to n , inclusive , is a multiple of 1000 , what is the least possible value of n ?
Options: a ) 12 , b ) 11 , c ) 14 , d ) 13 , e ) 15
Rationale: 1000 = 2 * 2 * 2 * 5 * 5 * 5 , so we need 3 factors of 2 and 3 factors of 5 . therefore , the smallest value of n is 15 , so the answer is e .
Answer: e
Question (general): in the first m games of a team ' s season , the ratio of the team ' s wins to its losses was 1 : 2 . in the subsequent n games , the ratio of the team ´ s wins to losses was 1 : 4 . if m : n = 4 : 5 , what was the ratio of the team ' s wins to its losses for all m + n games ?
Options: a ) 7 : 20 , b ) 9 : 23 , c ) 11 : 27 , d ) 23 : 54 , e ) 31 : 77
Rationale: "m = 4 / 9 of total games n = 5 / 9 of total games wins = 1 / 3 * 4 / 9 + 1 / 5 * 5 / 9 = 4 / 27 + 3 / 27 = 7 / 27 losses = 1 - 7 / 27 = 20 / 27 the ratio of wins to losses is 7 : 20 . the answer is a ."
Answer: a
Question (general): in an it company , there are a total of 120 employees including 50 programmers . the number of male employees is 80 , including 35 male programmers . how many employees must be selected to guaranty that we have 3 programmers of the same sex ?
Options: a ) 10 , b ) 50 , c ) 55 , d ) 35 , e ) 75
Rationale: "you could pick 70 non - programmers , 2 male programmers , and 2 female programmers , and still not have 3 programmers of the same sex . but if you pick one more person , you must either pick a male or a female programmer , so the answer is 75 . e"
Answer: e
Question (physics): a and b can do a piece of work in 6 days , b and c in 8 days , c and a in 12 days . how long will c take to do it ?
Options: a ) 48 days , b ) 55 days , c ) 24 days , d ) 33 days , e ) 40 days
Rationale: "2 c = 1 / 8 + 1 / 12 – 1 / 6 = 1 / 24 c = 1 / 48 = > 48 days answer : a"
Answer: a
Question (physics): john can row at 5 kmph and still water . he takes 5 hours to row from a to b and back . what is the distance between a and b if the speed of the stream is 1 kmph ?
Options: a ) 28 km , b ) 12 km , c ) 16 km , d ) 30 km , e ) 20 km
Rationale: let the distance between a and b be x km . total time = x / ( 5 + 1 ) + x / ( 5 - 1 ) = 5 = > x / 6 + x / 4 = 4 = > ( 2 x + 3 x ) / 12 = 5 = > x = 12 km . answer : b
Answer: b
Question (geometry): a semicircle has a radius of 12 . what is the approximate perimeter of the semicircle ?
Options: a ) 58 , b ) 62 , c ) 66 , d ) 70 , e ) 74
Rationale: "the perimeter of a circle is 2 * pi * r . the perimeter of a semicircle is 2 * pi * r / 2 + 2 r = pi * r + 2 r the perimeter is pi * 12 + 2 * 12 which is about 62 . the answer is b ."
Answer: b
Question (general): a certain sum of money is divided among a , b and c so that for each rs . a has , b has 65 paisa and c 40 paisa . if c ' s share is rs . 64 , find the sum of money ?
Options: a ) 328 , b ) 262 , c ) 72 , d ) 205 , e ) 267
Rationale: a : b : c = 100 : 65 : 40 = 20 : 13 : 8 8 - - - - 64 41 - - - - ? = > rs . 328 answer : a
Answer: a
Question (gain): sonika bought a v . c . r . at the list price of 18,400 . if the rate of sales tax was 8 % , find the amount she had to pay for purchasing the v . c . r .
Options: a ) 19,872 , b ) 19,780 , c ) 19,680 , d ) 19,380 , e ) none of these
Rationale: "sol . list price of v . c . r . = 18,400 rate of sales tax = 8 % ∴ sales tax = 8 % of 18,400 = 8 ⁄ 100 × 18400 = 1472 so , total amount which sonika had to pay for purchasing the v . c . r . = 18,400 + 1472 = 19,872 . answer a"
Answer: a
Question (general): if x is equal to the sum of the integers from 60 to 80 , inclusive , and y is the number of even integers from 60 to 80 , inclusive , what is the value of x + y ?
Options: a ) 1361 , b ) 1481 , c ) 1601 , d ) 1721 , e ) 1841
Rationale: "x = 60 + 61 + . . . + 80 = 21 ( 70 ) = 1470 y = 11 x + y = 1481 the answer is b ."
Answer: b
Question (general): a mixture contains alcohol and water in the ratio 2 : 5 . if 10 liters of water is added to the mixture , the ratio becomes 2 : 7 . find the quality of alcohol in the given mixture .
Options: a ) 5 , b ) 10 , c ) 15 , d ) 20 , e ) 25
Rationale: let the quantity of alcohol and water be 2 x and 5 x 2 x / ( 5 x + 10 ) = 2 / 7 20 x = 4 ( 3 x + 5 ) x = 5 quantity of alcohol = 2 * 5 = 10 liters . answer is b
Answer: b
Question (general): in the biology lab of ` ` jefferson ' ' high school there are 5.4 * 10 ^ 6 germs , equally divided among 10800 petri dishes . how many germs live happily in a single dish ?
Options: a ) 100 , b ) 200 , c ) 500 , d ) 1000 , e ) 5000
Rationale: 5.4 * 10 ^ 6 / 10800 = = > 54 * 10 ^ 3 / 108 = = > 54000 / 108 = 500 answer : c
Answer: c
Question (general): if x is 11 percent greater than 80 , then x =
Options: a ) 88.8 , b ) 91.0 , c ) 88.0 , d ) 70.9 , e ) 71.2
Rationale: "11 % of 80 = ( 80 * 0.11 ) = 8.8 11 % greater than 80 = 80 + 8.8 = 88.8 answer is clearly a ."
Answer: a
Question (physics): a , b and c completed a piece of work , a worked for 6 days , b for 9 days and c for 4 days . their daily wages were in the ratio of 3 : 4 : 5 . find the daily wages of c , if their total earning was rs . 1628 ?
Options: a ) s . 109 , b ) s . 108 , c ) s . 110 , d ) s . 103 , e ) s . 102
Rationale: "3 x 4 x 5 x 6 9 4 18 x + 36 x + 20 x = 1628 74 x = 1628 = > x = 22 5 x = 110 rs . answer : c"
Answer: c
Question (general): 8 people decided to split the restaurant bill evenly . if the bill was $ 314.12 dollars , how much money did they 1 cent is the smallest unit ?
Options: a ) $ 314.16 , b ) $ 314.17 , c ) $ 314.18 , d ) $ 314.19 , e ) $ 314.20
Rationale: "if the last three digits of a whole number are divisible by 8 , then the entire number is divisible by 8 the last 3 digit 412 not divisible by a hence , we need to add 4 to this number for it to be divisible by 8 correct option : a"
Answer: a
Question (general): the average ( arithmetic mean ) monthly income of 4 workers is $ 1000 . after one worker ’ s income increases by 50 percent the new average income is $ 1200 . what was the original income of the worker whose monthly income increased ?
Options: a ) $ 1,800 , b ) $ 1,500 , c ) $ 1,300 , d ) $ 1,600 , e ) $ 1,100
Rationale: increase in total income was 200 * 4 = $ 800 , we know that this increase was 50 % ( 1 / 2 ) of the workers original income , thus his / her original income was 800 * 2 = $ 1,600 . answer : d
Answer: d
Question (general): if the numerator of a fraction be increased by 15 % and its denominator be diminished by 8 % , the value of the fraction is 15 / 16 . find the original fraction .
Options: a ) 3 / 4 , b ) 1 / 4 , c ) 1 / 2 , d ) 1 , e ) none of them
Rationale: "let the original fraction be x / y . then ( 115 % of x ) / ( 92 % of y ) = 15 / 16 = > ( 115 x / 92 y ) = 15 / 16 = ( ( 15 / 16 ) * ( 92 / 115 ) ) = 3 / 4 answer is a ."
Answer: a
Question (gain): in town x , 72 percent of the population are employed , and 36 percent of the population are employed males . what percent of the employed people in town x are females ?
Options: a ) 16 % , b ) 25 % , c ) 32 % , d ) 40 % , e ) 50 %
Rationale: "total employed people 72 % , out of which 36 are employed males , hence 36 % are employed females . ( employed females ) / ( total employed people ) = 36 / 72 = 1 / 2 = 50 % answer : e ."
Answer: e
Question (physics): the radius of a wheel is 22.4 cm . what is the distance covered by the wheel in making 100 resolutions .
Options: a ) 140 m , b ) 141 m , c ) 142 m , d ) 143 m , e ) 144 m
Rationale: "in one resolution , the distance covered by the wheel is its own circumference . distance covered in 100 resolutions . = 100 * 2 * 22 / 7 * 22.4 = 14100 cm = 141 m answer : b"
Answer: b
Question (physics): speed of a boat in standing water is 9 kmph and the speed of the stream is 6 kmph . a man rows to place at a distance of 210 km and comes back to the starting point . the total time taken by him is :
Options: a ) 92 hours , b ) 24 hours , c ) 84 hours , d ) 48 hours , e ) none
Rationale: "sol . speed upstream = 3 kmph ; speed downstream = 9 kmph . ∴ total time taken = [ 210 / 3 + 210 / 9 ] hours = 84 hours . answer c"
Answer: c
Question (physics): a cistern 9 m long and 4 m wide contains water up to a depth of 1 m 25 cm . the total area of the wet surface is :
Options: a ) 49 m 2 , b ) 50 m 2 , c ) 53.5 m 2 , d ) 68.5 m 2 , e ) 57 m 2
Rationale: "area of the wet surface = [ 2 ( lb + bh + lh ) - lb ] = 2 ( bh + lh ) + lb = [ 2 ( 4 x 1.25 + 9 x 1.25 ) + 9 x 4 ] m 2 = 68.5 m 2 . answer : option d"
Answer: d
Question (general): at a contest with 2,500 participants , 1 / 2 of the people are aged 10 to 12 . next year , the number of people aged 10 to 12 will increase by 1 / 5 . after this change , what percentage of the total 2,500 people will the 10 - to 12 - year - olds represent ?
Options: a ) 55 % , b ) 60 % , c ) 50 % , d ) 45 % , e ) 66 %
Rationale: "i just wanted to mention a couple of things here : * this is a pure ratio question ; the number 2,500 is completely irrelevant , and you can ignore it if you like . when we increase something by 1 / 5 , we are multiplying it by 1 + 1 / 5 = 6 / 5 , so the answer here must be ( 1 / 2 ) * ( 6 / 5 ) = 3 / 5 = 60 % . 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 140 km downstream
Options: a ) 3 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 = 140 km time taken = distance / speed = 140 / 28 = 5 hours answer : option c"
Answer: c
Question (probability): there are 10 pairs of socks and 2 socks are worn from that such that the pair of socks worn are not of the same pair . what is the number of pair that can be formed .
Options: a ) 90 , b ) 85 , c ) 75 , d ) 95 , e ) 82
Rationale: first of all you should remember that there is a difference in left and right sock . now no . of way to select any of the sock = 10 and for second = 9 so total methods = 10 * 9 = 90 answer : a
Answer: a
Question (general): a large box contains 17 small boxes and each small box contains 26 chocolate bars . how many chocolate bars are in the large box ?
Options: a ) a ) 442 , b ) b ) 490 , c ) c ) 380 , d ) d ) 450 , e ) e ) 690
Rationale: the only thing you have to do is a simple multiply we have : 17 * 26 = 442 correct answer is : a ) 442
Answer: a
Question (other): find out the ratio of milk to that of water , if a mixture is formed after mixing milk and water of 3 different vessels containning the mixture of milk to that of water in the proportion 3 : 2 , 7 : 3 , 9 : 2 respectively .
Options: a ) 233 : 97 , b ) 235 : 98 , c ) 236 : 97 , d ) 265 : 98 , e ) 234 : 97
Rationale: 3 + 2 = 57 + 3 = 109 + 2 = 11 now , 3 / 5 + 7 / 10 + 9 / 11 : 2 / 5 + 3 / 10 + 2 / 11 = > 233 / 110 : 97 / 110 = > 233 : 97 answer : a
Answer: a
Question (general): a student scored an average of 85 marks in 3 subjects : physics , chemistry and mathematics . if the average marks in physics and mathematics is 90 and that in physics and chemistry is 70 , what are the marks in physics ?
Options: a ) 86 , b ) 16 , c ) 76 , d ) 65 , e ) 26
Rationale: given m + p + c = 85 * 3 = 255 - - - ( 1 ) m + p = 90 * 2 = 180 - - - ( 2 ) p + c = 70 * 2 = 140 - - - ( 3 ) where m , p and c are marks obtained by the student in mathematics , physics and chemistry . p = ( 2 ) + ( 3 ) - ( 1 ) = 180 + 140 - 255 = 65 answer : d
Answer: d
Question (general): if you write down all the numbers from 1 to 100 , then how many times do you write 2 ?
Options: a ) a ) 11 , b ) b ) 18 , c ) c ) 20 , d ) d ) 21 , e ) e ) 22
Rationale: "explanation : clearly , from 1 to 100 , there are ten numbers with 2 as the unit ' s digit - 2 , 12 , 22 , 32 , 42 , 52 , 62 , 72 , 82 , 92 ; and ten numbers with 2 as the ten ' s digit - 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 . so , required number = 10 + 10 = 20 . answer : c"
Answer: c
Question (geometry): abce is an isosceles trapezoid and acde is a rectangle . ab = 10 and ec = 20 . what is the length of ae .
Options: a ) 5 , b ) 10 , c ) 12 , d ) 15 , e ) 20
Rationale: as abce is an isosceles trapezoid and ec is twice times ab , we can consider the given trapezoid as half of a regular hexagon ( as length of diagonal in regular hexagon is always double the side ) . thus , sides ab = ae = bc . = > ae = 10 . answer : b
Answer: b
Question (general): evaluate 24.39 + 562.093 + 35.96
Options: a ) 631.344 , b ) 622.443 , c ) 623.434 , d ) 632.423 , e ) 632.443
Rationale: "24.39 + 562.093 + 35.96 = 622.443 option b"
Answer: b
Question (gain): rs 3400 is divided into two parts such that one part is put out at 3 % and the other at 5 % . if the annual interest earned from both the investments be rs 144 , find the first part .
Options: a ) s 4000 , b ) s 1800 , c ) s 800 , d ) s 500 , e ) s 1300
Rationale: "explanation : average rate = ( 144 / 3400 ) * 100 = 4.24 ratio = 7.65 : 12.35 so , first part = ( 7.65 / 20 ) * 3400 = rs 1300 . answer : e"
Answer: e
Question (general): at a certain college , 40 percent of the total number of students are freshmen . if 50 percent of the fresh - men are enrolled in the school of liberal arts and , of these , 50 percent are psychology majors , what percent of the students at the college are freshmen psychology majors enrolled in the school of liberal arts ?
Options: a ) 10 % , b ) 12 % , c ) 14 % , d ) 16 % , e ) 18 %
Rationale: "let ' s say there is a total of 100 students at this college . 40 percent of the total number of students are freshmen . # of freshmen = 40 % of 100 = 40 50 percent of the fresh - men are enrolled in the school of liberal arts . . . number of liberal arts freshmen = 50 % of 40 = 20 . . . and , of these , 50 percent are psychology majors . . . number of liberal arts freshmen who are psychology majors = 50 % of 20 = 10 what percent of the students at the college are freshmen psychology majors enrolled in the school of liberal arts ? 10 / 100 = 10 % answer : a"
Answer: a
Question (gain): 90 students represent x percent of the boys at jones elementary school . if the boys at jones elementary make up 40 % of the total school population of x students , what is x ?
Options: a ) 125 , b ) 150 , c ) 225 , d ) 250 , e ) 500
Rationale: "90 = ( x / 100 ) * ( # boys ) # boys = . 4 x substitute and solve : 90 = ( x / 100 ) * ( . 4 x ) 9000 = . 4 ( x ^ 2 ) 25000 = x ^ 2 x = 150 answer : b"
Answer: b
Question (general): in x game of billiards , x can give y 20 points in 60 and he can give z 30 points in 60 . how many points can y give z in x game of 100 ?
Options: a ) 30 , b ) 20 , c ) 25 , d ) 40 , e ) 50
Rationale: "c 25 x scores 60 while y score 40 and z scores 30 . the number of points that z scores when y scores 100 = ( 100 * 30 ) / 40 = 25 * 3 = 75 . in x game of 100 points , y gives ( 100 - 75 ) = 25 points to c ."
Answer: c
Question (general): 3500 – ( 1000 ÷ 20.50 ) is equal to :
Options: a ) 3451.21 , b ) 3029.0 , c ) 2993.03 , d ) 2984.36 , e ) none of these
Rationale: explanation : given exp . = 3500 - ( ( 1000 ÷ 2050 ) * 100 ) = 3451.21 answer a
Answer: a
Question (physics): a man swims downstream 60 km and upstream 40 km taking 4 hours each time ; what is the speed of the current ?
Options: a ) 3 kmph , b ) 2.5 kmph , c ) 13 kmph , d ) 6.5 kmph , e ) 7 : 3 kmph
Rationale: "explanation : 60 - - - 4 ds = 15 ? - - - - 1 40 - - - - 4 us = 10 ? - - - - 1 s = ? s = ( 15 - 10 ) / 2 = 2.5 answer : option b"
Answer: b
Question (physics): two trains of equal length 120 metres move in the same direction . the faster train completely overtakes the slower one in 15 seconds . if the slower train were to move at half its speed , the over taking would take in 10 seconds . at what speeds are the 2 trains moving ( faster and slower respectively in m / s )
Options: a ) 24 , 22 , b ) 32 , 16 , c ) 30 , 18 , d ) 28 , 14 , e ) none of these
Rationale: the total distance covered for over taking = length of the two trains = 120 + 120 = 240 speed of faster train be x m / s and slower train be y m / s in the first case relative speed = x - y relative speed = distance / time taken = x - y = 240 / 15 = 16 m / s … … … ( 1 ) in the second case , the slower train moves at half its speed relative speed = x - 0.5 y = 240 / 10 = 24 m / s … … … … … … … . . ( 2 ) solving equation 1 & 2 we get x = 32 and y = 16 . : . the speed of the faster and slower trains are 32 m / s and 16 m / s respectively answer : b
Answer: b