Cheukting/mathqa huggingface dataset:
Question (general): a parking garage rents parking spaces for $ 10 per week or $ 24 per month . how much does a person save in a year by renting by the month rather than by the week ?
Options: a ) $ 140 , b ) $ 160 , c ) $ 220 , d ) $ 232 , e ) $ 260
Rationale: "10 $ per week ! an year has 52 weeks . annual charges per year = 52 * 10 = 520 $ 30 $ per month ! an year has 12 months . annual charges per year = 12 * 24 = 288 $ 520 - 288 = 232 ans d"
Answer: d
Question (physics): a boat running downstream covers a distance of 12 km in 2 hours while for covering the same distance upstream , it takes 3 hours . what is the speed of the boat in still water ?
Options: a ) 8 kmph , b ) 5 kmph , c ) 4 kmph , d ) 6 kmph , e ) 7 kmph
Rationale: "speed downstream = 12 / 2 = 6 kmph speed upstream = 12 / 3 = 4 kmph speed of the boat in still water = 6 + 4 / 2 = 5 kmph answer : b"
Answer: b
Question (geometry): what is the area of a square field whose diagonal of length 20 m ?
Options: a ) 288
b ) 289
c ) 200
d ) 112
e ) 178
Rationale: d 2 / 2 = ( 20 * 20 ) / 2 = 200 answer : c
Answer: c
Question (gain): a sum of rs . 12,500 amounts to rs . 15,500 in 4 years at the rate of simple interest . what is the rate of interest ?
Options: a ) 3 % , b ) 4 % , c ) 5 % , d ) 6 % , e ) 7 %
Rationale: s . i . = rs . ( 15500 - 12500 ) = rs . 3000 . rate = ( 100 x 3000 ) / ( 12500 x 4 ) % = 6 % answer : d
Answer: d
Question (gain): ravi purchased a refrigerator and a mobile phone for rs . 15000 and rs . 8000 respectively . he sold the refrigerator at a loss of 4 percent and the mobile phone at a profit of 10 percent . overall he make a .
Options: a ) loss of rs . 200 , b ) loss of rs . 100 , c ) profit of rs . 100 , d ) profit of rs . 200 , e ) none of these
Rationale: "let the sp of the refrigerator and the mobile phone be rs . r and rs . m respectively . r = 15000 ( 1 - 4 / 100 ) = 15000 - 600 m = 8000 ( 1 + 10 / 100 ) = 8000 + 800 total sp - total cp = r + m - ( 15000 + 8000 ) = - 600 + 800 = rs . 200 as this is positive , an overall profit of rs . 200 was made . answer : d"
Answer: d
Question (physics): tim came second in math . when his mother asked him how much he had scored , he answered that he got the sum of the first 8 even numbers . his mother immediately worked out the answer . how much had he scored in math ?
Options: a ) 80 , b ) 90 , c ) 30 , d ) 72 , e ) 60
Rationale: d 72 sum = ( n x n ) + n hence , 8 x 8 = 64 + 8 = 72
Answer: d
Question (physics): a and b can do a work in 5 days , b and c in 15 days and c and a in 25 days . in how many days will the work be completed , if all three of them work together ?
Options: a ) 26 / 18 , b ) 42 / 15 , c ) 48 / 63 , d ) 12 / 36 , e ) 150 / 23
Rationale: "one day work of a and b = 1 / 5 one day work of b and c = 1 / 15 one day work of c and a = 1 / 25 2 ( a + b + c ) = 1 / 5 + 1 / 15 + 1 / 25 2 ( a + b + c ) = 23 / 75 ( a + b + c ) = 23 / 150 number of days required = 150 / 23 days . answer : e"
Answer: e
Question (gain): 22 percent of 300
Options: a ) 50 , b ) 55 , c ) 62 , d ) 77 , e ) 66
Rationale: 1 % of 300 = 3 22 % of 300 = 22 * 3 = 66 answer : e
Answer: e
Question (physics): working individually , allison can sew dresses for 9 hours and al can sew dresses in 12 hours . if allison and al work together but independently at the task for 3 hours , at which point al leaves , how many remaining hours will it take allison to complete the task alone ?
Options: a ) 45 / 12 , b ) 23 / 12 , c ) 40 / 33 , d ) 34 / 12 , e ) 43 / 5
Rationale: in first 3 hrs al will finish 3 / 12 = 1 / 4 of work and allison will finish 3 / 9 = 1 / 3 work so total 1 / 4 + 1 / 3 = 7 / 12 work is finished and 1 - 7 / 12 = 5 / 12 work remaining . now allison will take ( 5 / 12 ) * 9 = 45 / 12 hrs to finish it . so answer is a .
Answer: a
Question (general): 3 friends are planning to attend a concert . if another friend also goes with them , they will get a group discount on their tickets . if the new total price of the tickets with the group discount is the same as the original total price of the tickets without the group discount , how much is the discount ?
Options: a ) 5 % , b ) 10 % , c ) 20 % , d ) 25 % , e ) 33 %
Rationale: let x be the original price of one ticket . the total original cost is 3 x . the new cost is 4 y , where y is the discounted price of one ticket . 3 x = 4 y y = 3 x / 4 = 0.75 x which is a discount of 25 % . the answer is d .
Answer: d
Question (gain): the true discount on a bill of rs . 540 is rs . 90 . the banker ' s discount is :
Options: a ) rs . 60 , b ) rs . 108 , c ) rs . 110 , d ) rs . 112 , e ) rs . 122
Rationale: "p . w . = rs . ( 540 - 90 ) = rs . 450 . s . i . on rs . 450 = rs . 90 . s . i . on rs . 540 = rs . ( 90 / 450 ) x 540 = rs . 108 . b . d . = rs . 108 . answer : b"
Answer: b
Question (general): when positive integer x is divided by positive integer y , the remainder is 3 . if x / y = 96.15 , what is the value of y ?
Options: a ) 96 , b ) 75 , c ) 48 , d ) 25 , e ) 20
Rationale: by the definition of a remainder , the remainder here is equal to 3 / y . the remainder in decimal form is given as . 15 therefore , 3 / y = . 15 solve for y and get 20 . e
Answer: e
Question (gain): fetched a total simple interest of rs . 4216.25 at the rate of 9 p . c . p . a . in 5 years . what is the sum ?
Options: a ) rs . 8928 , b ) rs . 89228 , c ) rs . 8911 , d ) rs . 8925 , e ) rs . 8922
Rationale: explanation : principal = rs . = rs . = rs . 8925 answer : d
Answer: d
Question (general): the average of 10 numbers is calculated as 15 . it is discovered later on that while calculating the average , one number namely 36 was wrongly read as 26 . the correct average is ?
Options: a ) 16 , b ) 18 , c ) 19 , d ) 22 , e ) 24
Rationale: "explanation : 10 * 15 + 36 – 26 = 160 / 10 = 16 a )"
Answer: a
Question (general): if x is 20 percent greater than 98 , then x =
Options: a ) 68 , b ) 70.4 , c ) 86 , d ) 105.6 , e ) 117.6
Rationale: "x = 98 * 1.2 = 117.6 so the answer is e ."
Answer: e
Question (general): 30 pens and 75 pencils were purchased for 450 . if the average price of a pencil was 2.00 , find the average price of a pen .
Options: a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14
Rationale: since average price of a pencil = 2 ∴ price of 75 pencils = 150 ∴ price of 30 pens = ( 450 – 150 ) = 300 ∴ average price of a pen = 360 ⁄ 60 = 10 answer a
Answer: a
Question (physics): a person is traveling at 100 km / hr and reached his destiny in 5 then find the distance ?
Options: a ) 250 km , b ) 300 km , c ) 500 km , d ) 450 km , e ) 350 km
Rationale: "t = 5 hr s = 100 km / hr d = t * s = 100 * 5 = 500 km answer is c"
Answer: c
Question (general): if jake loses 29 pounds , he will weigh twice as much as his sister . together they now weigh 99 pounds . what is jake ' s present weight , in pounds ?
Options: a ) 69 , b ) 135 , c ) 139 , d ) 147 , e ) 188
Rationale: "j = jake ’ s current weight , in pounds s = sister ’ s current weight , in pounds we are told that “ if jake loses 8 pounds , he will weigh twice as much as his sister . we put this into an equation : j – 29 = 2 s j = 2 s + 29 ( equation 1 ) next , we are told that “ together they now weigh 89 pounds . ” we can also put this into an equation . j + s = 89 ( equation 2 ) to solve this equation , we can substitute 2 s + 8 from equation 1 for the variable j in equation 2 : 2 s + 29 = 89 - s 3 s = 60 s = 20 j + 20 = 89 j = 69 answer : a"
Answer: a
Question (gain): a man can row downstream at the rate of 18 kmph and upstream at 6 kmph . find the man ’ s rate in still water and rate of current ?
Options: a ) 8.5 , b ) 6.0 , c ) 9.5 , d ) 9.0 , e ) 8.25
Rationale: "rate of still water = 1 / 2 ( down stream + upstream ) = 1 / 2 ( 18 + 6 ) = 12 kmph rate of current = 1 / 2 ( down stream - upstream ) = 1 / 2 ( 18 - 6 ) = 1 / 2 ( 12 ) = 6 kmph answer is b ."
Answer: b
Question (general): the average ( arithmetic mean ) of the even integers from 0 to 40 inclusive is how much greater than the average ( arithmetic mean ) of the even integers from 0 to 20 inclusive ?
Options: a ) 5 , b ) 8 , c ) 10 , d ) 15 , e ) 20
Rationale: "the sum of even numbers from 0 to n is 2 + 4 + . . . + n = 2 ( 1 + 2 + . . . + n / 2 ) = 2 ( n / 2 ) ( n / 2 + 1 ) / 2 = ( n / 2 ) ( n / 2 + 1 ) the average is ( n / 2 ) ( n / 2 + 1 ) / ( n / 2 + 1 ) = n / 2 the average of the even numbers from 0 to 40 is 40 / 2 = 20 the average of the even numbers from 0 to 20 is 20 / 2 = 10 the answer is c ."
Answer: c
Question (general): what is the smallest number h which when increased by 5 is completely divisible by 8 , 11 and 24 ?
Options: a ) 264 , b ) 259 , c ) 269 , d ) 270 , e ) 282
Rationale: this question includes a number of great number property shortcuts that you can take advantage of : 1 ) the question asks for the smallest number that , when increased by 5 is divisible by 8 , 11 and 24 . since the answers are numbers , we can test the answers . 2 ) any number that is divisible by 24 is also divisible by 8 , so we really just need to consider the 11 and the 24 . 3 ) to be divisible by 24 , the end number must be even . since we ' re adding 5 to get to that end number , the starting number must be odd . the last shortcut allows us to eliminate answers a , d and e . between answers b and c , testing b first will prove that , when increased by 5 , the end sum is divisible by both 11 and 24 . final answer : b
Answer: b
Question (gain): the cost price of a radio is rs . 1500 and it was sold for rs . 1290 , find the loss % ?
Options: a ) 14 % , b ) 16 % , c ) 17 % , d ) 78 % , e ) 28 %
Rationale: "1500 - - - - 210 100 - - - - ? = > 14 % answer : a"
Answer: a
Question (gain): in an election a candidate who gets 60 % of the votes is elected by a majority of 900 votes . what is the total number of votes polled ?
Options: a ) a ) 4500 , b ) b ) 5200 , c ) c ) 6900 , d ) d ) 7520 , e ) e ) 6000
Rationale: "let the total number of votes polled be x then , votes polled by other candidate = ( 100 - 60 ) % of x = 40 % of x 60 % of x - 40 % of x = 900 20 x / 100 = 900 x = 900 * 100 / 20 = 4500 answer is a"
Answer: a
Question (general): ( 17 ) 3.75 x ( 17 ) ? = 178
Options: a ) 2.29 , b ) 2.75 , c ) 4.25 , d ) 4.5 , e ) none of these
Rationale: "solution let ( 17 ) 3.75 * ( 17 ) x = 178 . then , ( 17 ) 3.5 + x = ( 17 ) 8 . ∴ 3.75 + x = 8 ⇔ x = ( 8 - 3.75 ) ⇔ x = 4.25 answer c"
Answer: c
Question (physics): the speed of a boat in still water in 15 km / hr and the rate of current is 3 km / hr . the distance travelled downstream in 12 minutes is :
Options: a ) 1.2 km , b ) 2.4 km , c ) 3.2 km , d ) 3.6 km , e ) 4.6 km
Rationale: "speed downstream = ( 15 + 3 ) kmph = 18 kmph . distance travelled = 18 x 12 / 60 km = 3.6 km . answer : d"
Answer: d
Question (general): if 1000 microns = 1 decimeter , and 1 , 000,000 angstroms = 1 decimeter , how many angstroms equal 1 micron ?
Options: a ) 10 , b ) 1000 , c ) 100 , d ) 0.01 , e ) 0.0001
Rationale: "1000 microns = 1 decimeter , and 1 , 000,000 angstroms = 1 decimeter 1000 microns = 1 , 000,000 angstroms 1 micron = 1 , 000,000 / 1,000 = 1,000 answer : b"
Answer: b
Question (physics): 10 men , working 7 hours a day can complete a work in 18 days . how many hours a day must 15 men work to complete the same work in 12 days ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: the number of hours required to complete the work is 10 * 7 * 18 = 1260 15 × 12 × ( x ) = 1260 x = 7 the answer is b .
Answer: b
Question (general): calculate the value of n from the below equation : y ^ 4 â ˆ ’ 20 y + 1 = 22
Options: a ) 5 , b ) 3 , c ) 6 , d ) 2 , e ) 1
Rationale: use elimination method to find the correct option . you find that of all the options 3 is the correct value for y answer : b
Answer: b
Question (general): the average of first five prime numbers greater than 37 is ?
Options: a ) 32.2 , b ) 32.98 , c ) 42.3 , d ) 48.6 , e ) 32.4
Rationale: "41 + 43 + 47 + 53 + 59 = 243 / 5 = 48.6 answer : d"
Answer: d
Question (probability): a bag contains 6 black and 6 white balls . one ball is drawn at random . what is the probability that the ball drawn is white ?
Options: a ) 3 / 4 , b ) 1 / 2 , c ) 1 / 7 , d ) 1 / 8 , e ) 4 / 3
Rationale: "let number of balls = ( 6 + 6 ) = 12 . number of white balls = 6 . p ( drawing a white ball ) = 6 / 12 = 1 / 2 . option b ."
Answer: b
Question (gain): the list price of an article is rs . 67 . 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 ) 3.86 % , b ) 4.86 % , c ) 5.86 % , d ) 6.86 % , e ) 7.86 %
Rationale: 67 * ( 90 / 100 ) * ( ( 100 - x ) / 100 ) = 56.16 x = 6.86 % answer : d
Answer: d
Question (physics): karen places a bet with tom that she will beat tom in a car race by 4 miles even if karen starts 4 minutes late . assuming that karen drives at an average speed of 60 mph and tom drives at an average speed of 45 mph , how many w miles will tom drive before karen wins the bet ?
Options: a ) 15 , b ) 18 , c ) 21 , d ) 24 , e ) 27
Rationale: "let k and t be the speeds of karen and tom respectively . t be the time that karen will travel - - - - > t + 4 / 60 will be the total time tom will travel by the time the distance between karen and tom is 4 miles . thus , per the question , k ( t ) - t ( t + 4 / 60 ) = 4 - - - > t = 7 / 15 hours thus the distance traveled by tom when karen is 4 miles ahead of him w : t * ( t + 4 / 60 ) = 45 ( 7 / 15 + 4 / 60 ) = 24 miles . d is the correct answer ."
Answer: d
Question (geometry): rectangle a has sides a and b , and rectangle b has sides c and d . if a / c = b / d = 2 / 3 , what is the ratio of rectangle a ’ s area to rectangle b ’ s area ?
Options: a ) 4 / 9 , b ) 2 / 3 , c ) 3 / 2 , d ) 9 / 2 , e ) 9 / 4
Rationale: "the area of rectangle a is ab . c = 3 a / 2 and d = 3 b / 2 . the area of rectangle b is cd = 9 ab / 4 . the ratio of rectangle a ' s area to rectangle b ' s area is ab / ( 9 ab / 4 ) = 4 / 9 . the answer is a ."
Answer: a
Question (other): the probability that event a occurs is 0.4 , and the probability that events a and b both occur is 0.25 . if the probability that either event a or event b occurs is 0.8 , what is the probability that event b will occur ?
Options: a ) 0.05 , b ) 0.15 , c ) 0.45 , d ) 0.5 , e ) 0.65
Rationale: "p ( a or b ) = p ( a ) + p ( b ) - p ( a n b ) 0.8 = 0.4 + p ( b ) - 0.25 p ( b ) = 0.65 ans : e"
Answer: e
Question (general): a lemonade stand sold only small and large cups of lemonade on tuesday . 1 / 5 of the cups sold were small and the rest were large . if the large cups were sold for 7 / 6 as much as the small cups , what fraction of tuesday ' s total revenue was from the sale of large cups ?
Options: a ) 7 / 16 , b ) 7 / 15 , c ) 10 / 21 , d ) 14 / 17 , e ) 1 / 2
Rationale: let the total # of cups be 10 . # of small cups sold 1 / 5 * 10 = 2 ; # of large cups sold 10 - 2 = 8 ; let the price of small cup be $ 6 , then the price of larges cup would be 7 / 6 * 6 = $ 7 ; revenue from small cups : 2 * $ 6 = $ 12 ; revenue from large cups cups : 8 * $ 7 = $ 56 ; fraction of total revenue from large cups : 56 / ( 56 + 12 ) = 14 / 17 . answer : d .
Answer: d
Question (general): if money is invested at r percent interest , compounded annually , the amount of the investment will double in approximately 50 / r years . if luke ' s parents invested $ 14,500 in a long term bond that pays 12 percent interest compounded annually , what will be the approximate total amount of the investment 12 years later , when luke is ready for college ?
Options: a ) 62,000 , b ) 85,500 , c ) 95,500 , d ) 120,500 , e ) 100,000
Rationale: answer equals d in 48 years . i thought by 50 th year it would reach 120,500 . options should have been separated more widely for clarity .
Answer: d
Question (general): 12 is 4 % of a , and 4 is 12 % of b . c equals b / a . what is the value of c ?
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 6 , d ) 1 / 9 , e ) 1 / 12
Rationale: "4 a / 100 = 12 a = 300 12 b / 100 = 4 b = 100 / 3 c = b / a = 100 / ( 3 * 300 ) = 1 / 9 the answer is d ."
Answer: d
Question (physics): a contractor undertook to make 15 km of roadway in 40 weeks . in 10 weeks , 3 km was complete by 180 men working 8 hours a day . the men then agreed to work 1 hour a day overtime , and some boys were engaged to assist them , the work was finished in the stipulated time ( 40 weeks ) . how many boys were employed , if the work of 3 boys is equal to that of 2 men ?
Options: a ) 48 , b ) 50 , c ) 22 , d ) 27 , e ) 221
Rationale: explanation : let the capacity of man = 3 units , and boy = 2 units per hour . now total work = 3 × 180 × 8 × 7 × 10 = 3 km . - - - - - - - ( 1 ) let k boys were recruited . now total work = ( 3 × 180 + 2 × k ) × 9 × 7 × 30 = 12 km . - - - - - - ( 2 ) by dividing 2 nd equation by 1 st , ⇒ ( 540 + 2 k ) × 9 × 7 × 303 × 180 × 8 × 7 × 10 = 4 ( 540 + 2 k ) × 9 × 7 × 303 × 180 × 8 × 7 × 10 = 4 ⇒ k = 50 answer : b
Answer: b
Question (physics): a man can row 7 kmph in still water . when the river is running at 1.2 kmph , it takes him 1 hour to row to a place and black . how far is the place ?
Options: a ) 3.3 , b ) 3.4 , c ) 3.5 , d ) 3.6 , e ) 3.7
Rationale: "m = 7 s = 1.2 ds = 7 + 1.2 = 8.2 us = 7 - 1.2 = 5.8 x / 8.2 + x / 5.8 = 1 x = 3.40 . answer : b"
Answer: b
Question (general): find the least number of complete years in which a sum of money put out at 33.3 % compound interest will be more than double of itself ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "3 years answer : a"
Answer: a
Question (general): the sum of the squares of three numbers is 138 , while the sum of their products taken two at a time is 131 . their sum is
Options: a ) 15 , b ) 20 , c ) 25 , d ) 35 , e ) 45
Rationale: "explanation : let the numbers be a , b and c . then , a 2 + b 2 + c 2 = 138 and ( ab + bc + ca ) = 131 ( a + b + c ) 2 = a 2 + b 2 + c 2 + 2 ( ab + bc + ca ) = 138 + 2 x 131 = 400 = > ( a + b + c ) = 400 − − − √ = 20 . option b"
Answer: b
Question (gain): by selling a book for 290 , 20 % profit was earned . what is the cost price of the book ?
Options: a ) a ) 215 , b ) b ) 241 , c ) c ) 230 , d ) d ) 235 , e ) e ) 240
Rationale: "sp = 120 % of cp ; : . cp = 290 × 100 / 120 = 241 option ' b '"
Answer: b
Question (general): if a number n is chosen at random from the set of two - digit integers whose digits are both prime numbers , what is the probability w that n is divisible by 3 ?
Options: a ) 1 / 3 , b ) ¼ , c ) 9 / 25 , d ) 5 / 16 , e ) 0
Rationale: prime digits are : 2 , 3 , 5 , 7 total number of 2 digit # s with both digits prime are : 4 * 4 = 16 out of these numbers divisible by 3 = 33 , 27 , 57 , 72 and 75 . i had to find the numbers manually using the 4 numbers above . = > prob = 5 / 16 . ans d . took me 3 : 20 mins .
Answer: d
Question (general): a women purchased 3 towels @ rs . 100 each , 5 towels @ rs . 150 each and two towels at a certain rate which is now slipped off from his memory . but she remembers that the average price of the towels was rs . 170 . find the unknown rate of two towels ?
Options: a ) a ) 400 , b ) b ) 650 , c ) c ) 500 , d ) d ) 550 , e ) e ) 600
Rationale: "10 * 170 = 1700 3 * 100 + 5 * 150 = 1050 1700 – 1050 = 650 b"
Answer: b
Question (general): a grocer has a sale of rs . 5266 , rs . 5768 , rs . 5922 , rs . 5678 and rs . 6029 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 5600 ?
Options: a ) 4637 , b ) 4737 , c ) 4937 , d ) 5937 , e ) 5978
Rationale: "total sale for 5 months = rs . ( 5266 + 5768 + 5922 + 5678 + 6029 ) = rs . 28663 . required sale = rs . [ ( 5600 x 6 ) - 28663 ] = rs . ( 33600 - 28663 ) = rs . 4937 . answer : c"
Answer: c
Question (gain): in a certain pond , 40 fish were caught , tagged , and returned to the pond . a few days later , 40 fish were caught again , of which 2 were found to have been tagged . if the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond , what ` s the approximate number of fish in the pond ?
Options: a ) 400 , b ) 800 , c ) 1250 , d ) 2500 , e ) 10 000
Rationale: "the percent of tagged fish in the second catch is 2 / 40 * 100 = 5 % . we are told that 5 % approximates the percent of tagged fish in the pond . since there are 40 tagged fish , then we have 0.05 x = 40 - - > x = 800 . answer : b ."
Answer: b
Question (general): the guests at a football banquet consumed a total of 327 pounds of food . if no individual guest consumed more than 2 pounds of food , what is the minimum number of guests that could have attended the banquet ?
Options: a ) 160 , b ) 161 , c ) 162 , d ) 163 , e ) 164
Rationale: to minimize one quantity maximize other . 163 * 2 ( max possible amount of food a guest could consume ) = 326 pounds , so there must be more than 163 guests , next integer is 164 . answer : e .
Answer: e
Question (gain): a report consists of 20 sheets each of 55 lines and each such line consist of 65 characters . this report is retyped into sheets each of 65 lines such that each line consists of 70 characters . the percentage reduction in number of sheets is closest to
Options: a ) 20 , b ) 5 , c ) 30 , d ) 35 , e ) 67
Rationale: explanation : total no of characters = 20 * 55 * 65 . from the problem it is clear that 20 * 55 * 65 = x * 65 * 70 . we get x = 15.6 ∼ 16 because these are sheets . therefore 4 less sheets . hencde , there is 20 % decrease in number of sheets . answer : a
Answer: a
Question (general): students at a school were on average 180 cm tall . the average female height was 170 cm , and the average male height was 184 cms . what was the ratio q of men to women ?
Options: a ) 5 : 2 , b ) 5 : 1 , c ) 4 : 3 , d ) 4 : 1 , e ) 3 : 1
Rationale: ( a ) q = 184 x 5 + 170 x 2 = 1260 . a
Answer: a
Question (general): 8 / 4 / 2 = ?
Options: a ) 0 , b ) 2 , c ) 5 , d ) 4 , e ) 1
Rationale: "8 / 4 / 2 = ( 8 / 4 ) / 2 = 2 / 2 = 1 answer is e ."
Answer: e
Question (general): a wholesaler wishes to sell 100 pounds of mixed nuts at $ 2.00 a pound . she mixes peanuts worth $ 1.50 a pound with cashews worth $ 4.00 a pound . how many pounds of cashews must she use ?
Options: a ) 40 , b ) 45 , c ) 50 , d ) 55 , e ) 60
Rationale: "from the question stem we know that we need a mixture of 100 pounds of peanuts and cashews . if we represent peanuts as x and cashews as y , we get x + y = 100 . since the wholesaler wants to sell the mixture of 100 pounds @ $ 2.50 , we can write this as : $ 2.5 * ( x + y ) = $ 1.5 x + $ 4 y from the equation x + y = 100 , we can rewrite y as y = 100 - x and substitute this into our equation to get : $ 2.5 * ( x + 100 - x ) = $ 1.5 x + $ 4 ( 100 - x ) if you solve for x , you will get x = 60 , and therefore y = 40 . so the wholesaler must use 40 pounds of cashews . you can substitute into the original equation to see that : $ 250 = $ 1.5 ( 60 ) + $ 4 ( 40 ) answer is c ."
Answer: c
Question (gain): by weight , liquid x makes up 0.7 percent of solution p and 1.2 percent of solution q . if 200 grams of solution p are mixed with 800 grams of solution q , then liquid x accounts for what percent of the weight of the resulting solution ?
Options: a ) 1.2 % , b ) 1.1 % , c ) 1.0 % , d ) 0.9 % , e ) 0.8 %
Rationale: "the number of grams of liquid x is 0.7 ( 200 ) / 100 + 1.2 ( 800 ) / 100 = 1.4 + 9.6 = 11 grams . 11 / 1000 = 1.1 % the answer is b ."
Answer: b
Question (physics): a courtyard is 20 meter long and 16 meter board is to be paved with bricks of dimensions 20 cm by 10 cm . the total number of bricks required is ?
Options: a ) 16000 , b ) 27778 , c ) 20000 , d ) 27999 , e ) 17799
Rationale: "number of bricks = courtyard area / 1 brick area = ( 2000 × 1600 / 20 × 10 ) = 16000 answer : a"
Answer: a
Question (physics): a car takes 4 hours to cover a distance of 540 km . how much should the speed in kmph be maintained to cover the same direction in 3 / 2 th of the previous time ?
Options: a ) 92 kmph , b ) 98 kmph , c ) 90 kmph , d ) 80 kmph , e ) 82 kmph
Rationale: "time = 4 distence = 540 3 / 2 of 4 hours = 4 * 3 / 2 = 6 hours required speed = 540 / 6 = 90 kmph c )"
Answer: c
Question (general): 3 / 8 of 168 * 15 / 5 + x = 549 / 9 + 275
Options: a ) 107 , b ) 147 , c ) 10 , d ) 296 , e ) none of these
Rationale: "explanation : let 3 / 8 of 168 * 15 / 5 + x = 549 / 9 + 275 then , 63 * 15 / 5 + x = 61 + 275 63 * 3 + x = 336 189 + x = 336 x = 147 answer b"
Answer: b