regisss/math_qa huggingface dataset:
Problem: huey ' s hip pizza sells two sizes of square pizzas : a small pizza that measures 12 inches on a side and costs $ 10 , and a large pizza that measures 18 inches on a side and costs $ 20 . if two friends go to huey ' s with $ 30 apiece , how many more square inches of pizza can they buy if they pool their money than if they each purchase pizza alone ?
Options: a ) 5 square inches , b ) 36 square inches , c ) 15 square inches , d ) 25 square inches , e ) 350 square inches
Rationale: "in the first case each can buy one pizza of $ 10 and one pizza of $ 20 . in square inches that would be ( 12 * 12 = 144 ) for the small pizza and ( 18 * 18 = 324 ) for the large pizza . in total sq inches that would be ( 144 + 324 ) * 2 = 936 sq inches . in the second case if they pool their money together they can buy 3 large pizzas . in terms of square inches that would be 3 * 324 = 972 sq inches . hence , the difference is 36 square inches more ( 972 - 936 ) . the correct answer is b"
Answer: b
Problem: two goods trains each 75 m long are running in opposite directions on parallel tracks . their speeds are 45 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 ) 2.3 sec , b ) 4.2 sec , c ) 48 sec , d ) 7.2 sec , e ) 9 sec
Rationale: "relative speed = 45 + 30 = 75 km / hr . 75 * 5 / 18 = 125 / 6 m / sec . distance covered = 75 + 75 = 150 m . required time = 150 * 6 / 125 = 7.2 sec . answer : d"
Answer: d
Problem: if each participant of a chess tournament plays exactly one game with each of the remaining participants , then 153 games will be played during the tournament . find the number of participants .
Options: a ) 15 , b ) 16 , c ) 17 , d ) 18 , e ) 19
Rationale: "if the number of participants is 3 ( say a , b , c ) the number of games played will be 2 ( a plays against b and c ) + 1 ( b plays against c ) = 3 using the same logic , if the number of participants is n , the number of games played will be ( n - 1 ) + ( n - 2 ) + ( n - 3 ) + . . . 3 + 2 + 1 given that this sum = 153 = 1 + 2 + 3 + . . . ( n - 1 ) sum of first m positive integers is given by m ( m + 1 ) / 2 . so sum of first ( n - 1 ) positive integers is ( n - 1 ) * n / 2 153 = ( n - 1 ) * n / 2 ( n - 1 ) * n = 306 17 * 18 = 306 ( we know that 15 ^ 2 = 225 so the two consecutive numbers must be greater than 15 . also , 20 ^ 2 = 400 so the two numbers must be less than 20 . the pair of numbers in between 15 and 20 whose product ends with 6 is 17 and 18 ) so n = 18 answer ( d )"
Answer: d
Problem: find the ones digit of 73 ^ 340
Options: a ) 3 , b ) 5 , c ) 6 , d ) 7 , e ) 9
Rationale: "cyclicity of 3 is 3,9 , 7,1 after 4 multiplication again the cycle repeats . so divide 340 by 4 and we get 87 as quotient and 2 as remainder . so cycle will run for 87 times and then 2 times more . so pick up the 2 nd item from the cycle . hence answer a ."
Answer: a
Problem: if a lends rs . 2000 to b at 15 % per annum and b lends the same sum to c at 17 % per annum then the gain of b in a period of 4 years is ?
Options: a ) 155 , b ) 162 , c ) 157.5 , d ) 160 , e ) 157.12
Rationale: "( 2000 * 2 * 4 ) / 100 = > 160 answer : d"
Answer: d
Problem: how much time will a train of length 400 m moving at a speed of 72 kmph take to cross another train of length 300 m , moving at 36 kmph in the same direction ?
Options: a ) 40 sec , b ) 50 sec , c ) 60 sec , d ) 70 sec , e ) 80 sec
Rationale: "the distance to be covered = sum of their lengths = 400 + 300 = 700 m . relative speed = 72 - 36 = 36 kmph = 36 * 5 / 18 = 10 mps . time required = d / s = 700 / 10 = 70 sec . answer : d"
Answer: d
Problem: length of a rectangular plot is 26 mtr more than its breadth . if the cost of fencin gthe plot at 26.50 per meter is rs . 5300 , what is the length of the plot in mtr ?
Options: a ) 53 m , b ) 63 m , c ) 73 m , d ) 83 m , e ) 93 m
Rationale: "let breadth = x metres . then , length = ( x + 26 ) metres . perimeter = 5300 m = 200 m . 26.50 2 [ ( x + 26 ) + x ] = 200 2 x + 26 = 100 2 x = 74 x = 37 hence , length = x + 26 = 63 m b"
Answer: b
Problem: on a map the distance between two mountains is 312 inches . the actual distance between the mountains is 136 km . ram is camped at a location that on the map is 34 inch from the base of the mountain . how many km is he from the base of the mountain ?
Options: a ) 14.83
b ) 14.81
c ) 14.8
d ) 14.82
e ) 14.12
Rationale: explanation : since 312 inch = 136 km so 1 inch = 136 / 312 km so 34 inch = ( 136 × 34 ) / 312 = 14.82 km answer : d
Answer: d
Problem: the sum of the present ages of a father and his son is 42 years . 6 years ago , father ' s age was 4 times the age of the son . after 6 years , son ' s age will be :
Options: a ) 14 , b ) 16 , c ) 18 , d ) 20 , e ) 22
Rationale: let the present ages of son and father be x and ( 42 - x ) years respectively . then , ( 42 - x ) - 6 = 4 ( x - 6 ) 36 - x = 4 x - 24 x = 12 the son ' s age after 6 years will be 18 . the answer is c .
Answer: c
Problem: two trains a and b starting from two points and travelling in opposite directions , reach their destinations 9 hours and 16 hours respectively after meeting each other . if the train a travels at 80 kmph , find the rate at which the train b runs .
Options: a ) 40 , b ) 160 , c ) 120 , d ) 80 , e ) 100
Rationale: "if two objects a and b start simultaneously from opposite points and , after meeting , reach their destinations in ‘ a ’ and ‘ b ’ hours respectively ( i . e . a takes ‘ a hrs ’ to travel from the meeting point to his destination and b takes ‘ b hrs ’ to travel from the meeting point to his destination ) , then the ratio of their speeds is given by : sa / sb = √ ( b / a ) i . e . ratio of speeds is given by the square root of the inverse ratio of time taken . sa / sb = √ ( 4 / 16 ) = 2 / 4 = 1 / 2 this gives us that the ratio of the speed of a : speed of b as 1 : 2 . since speed of a is 80 kmph , speed of b must be 80 * ( 2 / 1 ) = 160 kmph b"
Answer: b
Problem: a recipe requires 2 1 / 2 ( mixed number ) cups of flour 2 3 / 4 ( mixed number ) cups of sugar and 1 1 / 3 ( mixed number ) cups of milk to make one cake . victor has 15 cups if flour , 16 cups of sugar and 8 cups of milk . what is the greatest number of cakes tom can make using this recipe ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: less work up front : go through each item and see what the greatest number of cakes you can make with each . the lowest of these will be the right answer . flour : 15 cups , we need 2.5 cups each . just keep going up the line to see how many cakes we can make : that means i can make 2 cakes with 5 cups , so 6 cakes overall with 15 cups . i ' ve already got the answer narrowed to either a or b . sugar : 16 cups , we need 2.75 cups each . same principle . i can make 2 cups with 5.5 cups , so to make 6 cakes i ' d need 16.5 cups . i do n ' t have that much sugar , so we ' re limited to 5 cakes . no need to even do milk because we ' re already at 5 . sugar will be the limiting factor . answer is a
Answer: a
Problem: the c . p of 10 pens is equal to the s . p of 5 pens . find his gain % or loss % ?
Options: a ) 50 % , b ) 40 % , c ) 30 % , d ) 60 % , e ) 20 %
Rationale: 10 cp = 5 sp 10 - - - 5 cp gain 100 - - - ? = > 50 % ( gain ) answer : a
Answer: a
Problem: the average of 6 no . ' s is 3.95 . the average of 2 of them is 4.2 , while the average of theother 2 is 3.85 . what is the average of the remaining 2 no ' s ?
Options: a ) 4.2 , b ) 4.4 , c ) 4.6 , d ) 3.8 , e ) 5.7
Rationale: "sum of the remaining two numbers = ( 3.95 * 6 ) - [ ( 4.2 * 2 ) + ( 3.85 * 2 ) ] = 7.60 . required average = ( 7.6 / 2 ) = 3.8 . d"
Answer: d
Problem: 20 one identical machines , running continuously at the same constant rate , take 9 days to complete a shipment . how many additional machines , each running at the same constant rate , would be needed to reduce the time required to complete a shipment by two days ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 6 , e ) 9
Rationale: from the question you know that 21 r = 1 / 9 . the question asks you ( partially ) to make the rate from 1 / 9 to 1 / 7 ( drop from 9 day to 7 ) . so the only thing that you need to do is to find the magic number than can convert 1 / 9 to 1 / 7 . so 1 / 9 * x = 1 / 7 ( 1 equation with one unknown ) . so by solving this you get x = 9 / 7 . thats it then ! take the magic number 9 / 7 and multiply both sides of the original equation and you have : 21 * ( 9 / 7 ) * r = ( 9 / 7 ) * 1 / 9 27 * r = 1 / 7 , hence 27 r = 1 / 7 , therefore 6 more machines ! d
Answer: d
Problem: a furniture dealer purchased a desk for $ 150 and then set the selling price equal to the purchase price plus a markup that was 40 % of the selling price . if the dealer sold the desk at the selling price , what was the amount of the dealer ' s gross profit from the purchase and the sale of the desk ?
Options: a ) $ 40 , b ) $ 60 , c ) $ 80 , d ) $ 90 , e ) $ 100
Rationale: "purchase price = 150 selling price = x 150 + 0.4 * x = x 0.6 * x = 150 x = 250 profit = 250 - 150 = 100 answer : e"
Answer: e
Problem: the number of sailors on a ship is 78 % more than the number of officers . the ratio of sailors to officers would be
Options: a ) 33 : 25 , b ) 47 : 20 , c ) 47 : 25 , d ) 89 : 50 , e ) 97 : 50
Rationale: sailor = 1.78 * officer sailor / officer = 1.78 / 1 = 178 / 100 = 89 / 50 answer will be d
Answer: d
Problem: three 7 faced dice are thrown together . the probability that all the three show the same number on them is ?
Options: a ) 1 / 38 , b ) 1 / 49 , c ) 1 / 39 , d ) 1 / 42 , e ) 1 / 29
Rationale: "it all 3 numbers have to be same basically we want triplets . 111 , 222 , 333 , 444 , 555 , 666 and 777 . those are seven in number . further the three dice can fall in 7 * 7 * 7 = 343 ways . hence the probability is 7 / 343 = 1 / 49 answer : b"
Answer: b
Problem: how much more would rs . 10000 fetch , after two years , if it is put at 20 % p . a . compound interest payable half yearly than if is put at 20 % p . a . compound interest payable yearly ?
Options: a ) 241 , b ) 725 , c ) 992 , d ) 837 , e ) 923
Rationale: "10000 ( 11 / 10 ) 4 - 10000 ( 6 / 5 ) 2 = 241 answer : a"
Answer: a
Problem: what is the decimal equivalent of ( 1 / 4 ) ^ 2 ?
Options: a ) 0.0016 , b ) 0.0625 , c ) 0.16 , d ) 0.25 , e ) 0.5
Rationale: "1 / 4 = 25 / 100 = > ( 25 / 100 ) ^ 2 = 625 / 10000 = 0.0625 answer : b"
Answer: b
Problem: a paint store mixes 3 / 4 pint of red paint and 2 / 3 pint of white paint to make a new paint color called perfect pink . how many pints of red paint would be needed to make 33 pints of perfect pink paint ?
Options: a ) 9 , b ) 16 , c ) 17 , d ) 25 1 / 3 , e ) 28 1 / 2
Rationale: "3 / 4 pint is required to make 3 / 4 + 2 / 3 = 17 / 12 pint of perfect pink so 17 / 12 pint requires 3 / 4 pint of red . . 1 pint will require 3 / 4 * 12 / 17 = 9 / 17 . . 33 pints will require 9 / 17 * 33 = 17 pints . . c"
Answer: c
Problem: a rectangular field has area equal to 150 sq m and perimeter 50 m . its length and breadth must be ?
Options: a ) 15 m , 15 m
b ) 15 m , 90 m
c ) 16 m , 10 m
d ) 15 m , 10 m
e ) 15 m , 30 m
Rationale: lb = 150 2 ( l + b ) = 50 = > l + b = 25 l – b = 5 l = 15 b = 10 answer : d
Answer: d
Problem: if 5 + 7 / x = 6 - 5 / x , then x =
Options: a ) 7 , b ) 14 , c ) 12 , d ) 6 / 7 , e ) 5
Rationale: we ' re given the equation 5 + 7 / x = 6 - 5 / x . we ' re asked for the value of x . the common - denominator of these 4 numbers is x , so we need to multiply both sides of the equation by x , giving us . . . 5 x + 7 x / x = 6 x - 5 x / x we can then eliminate that denominator , which gives us . . . . 5 x + 7 = 6 x - 5 12 = x c
Answer: c
Problem: the average of 15 numbers is calculated as 30 . 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 ) 12 , b ) 26 , c ) 16 , d ) 45 , e ) 12
Rationale: "15 * 30 + 36 – 26 = 450 / 10 = 45 answer : d"
Answer: d
Problem: kelly has had 3 pay cuts in her salary in the past 6 months . if the first pay cut was 8 % , the second pay cut was 14 % and the third was 18 % . what will be the percentage decrease , if the salary is decreased in a single shot ?
Options: a ) 35.9 % , b ) 34.12 % , c ) 32.12 % , d ) 35.12 % , e ) 31.12 %
Rationale: let rs . 100 be initial salary . salary after 1 st decrease , 8 % = 92 salary after 2 nd decrease , 14 % = 79.12 i . e . reduced by 14 percent of 92 salary after 3 rd decrease , 18 % = 64.88 i . e . reduced by 18 percent of 79.12 so if its decreased in single shot = i = ( ( b - a ) / b ) * 100 = 35.12 % answer : d
Answer: d
Problem: a , b and c are partners . a receives 2 / 3 of profits , b and c dividing the remainder equally . a ' s income is increased by rs . 400 when the rate to profit rises from 5 to 7 percent . find the capital of c ?
Options: a ) 3377 , b ) 2899 , c ) 5000 , d ) 2778 , e ) 1991
Rationale: "a : b : c = 2 / 3 : 1 / 6 : 1 / 6 = 4 : 1 : 1 x * 2 / 100 * 2 / 3 = 400 c ' s capital = 30000 * 1 / 6 = 5000 answer : c"
Answer: c
Problem: how many distinct integer values of n satisfy the inequality | | n - 3 | + 4 | ≤ 11 ?
Options: a ) 15 , b ) 16 , c ) 17 , d ) 8 , e ) 19
Rationale: "so i can write this as in - 3 i + 4 < = 11 or in - 3 i < = 7 so n can have - 4 to 10 = 8 true values . . . . d"
Answer: d
Problem: in the coordinate plane , a circle centered on point ( - 3 , - 4 ) passes through point ( 1 , 2 ) . what is the area of the circle ?
Options: a ) 9 π , b ) 18 π , c ) 25 π , d ) 37 π , e ) 52 π
Rationale: "r ^ 2 = ( - 3 - 1 ) ^ 2 + ( - 4 - 2 ) ^ 2 = 16 + 36 = 52 area of circle = π r ^ 2 = 52 π answer : e"
Answer: e
Problem: a and b began business with rs . 3000 and rs . 4000 after 8 months , a withdraws rs . 1000 and b advances rs . 1000 more . at the end of the year , their profits amounted to rs . 630 find the share of a ?
Options: a ) 240 , b ) 278 , c ) 209 , d ) 267 , e ) 262
Rationale: "( 3 * 8 + 2 * 4 ) : ( 4 * 8 + 5 * 4 ) 8 : 13 8 / 21 * 630 = 240 answer : a"
Answer: a
Problem: what is the sum of the 1 st 5 prime numbers greater than 20 ?
Options: a ) 121 , b ) 151 , c ) 168 , d ) 164 , e ) 161
Rationale: "required sum = ( 23 + 29 + 31 + 37 + 41 ) = 161 note : 1 is not a prime number answer e"
Answer: e
Problem: the population of a bacteria culture doubles every 2 minutes . approximately how many minutes will it take for the population to grow from 1000 to 1000000 bacteria
Options: a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 20
Rationale: the question basically asks how many minutes it takes for a population to increase by factor 1000 ( 1000000 / 1000 = 1000 ) . now you know that every two minutes the population doubles , i . e . is multiplied by 2 . so the equation becomes : 2 ^ x > = 1000 , where x represents the number of times the population doubles . a lot of people remember that 2 ^ 10 = 1024 . i . e . the population has to double 10 times . since it takes the population 2 minutes to double once it takes 10 * 2 minutes = 20 minutes to double nine times . thus , solution e = 20 is correct .
Answer: e
Problem: a woman bought a pack of 36 eggs , but the seller told her that there were 3 rotten eggs in the pack . she forgot it and begun to prepare a recipe that needs 2 eggs . what is the probability that both choosen eggs will be rotten ?
Options: a ) 1 / 210 , b ) 2 / 210 , c ) 3 / 210 , d ) 1 / 119 , e ) 2 / 119
Rationale: there are 3 rotten eggs in a pack of 36 . thus the probability of picking 2 rotten eggs is : ( 3 / 36 ) ( 2 / 35 ) = 1 / 210 . the correct answer is a .
Answer: a
Problem: if a person walks at 20 km / hr instead of 10 km / hr , he would have walked 20 km more . the actual distance traveled by him is :
Options: a ) 20 km , b ) 56 km , c ) 60 km , d ) 70 km , e ) 80 km
Rationale: "let the actual distance travelled be x km . x / 10 = ( x + 20 ) / 14 20 x = 10 x + 200 10 x = 200 x = 20 km . answer : a"
Answer: a
Problem: 20 % of a number is more than 30 % of 120 by 80 . find the number ?
Options: a ) 520 , b ) 560 , c ) 580 , d ) 620 , e ) 610
Rationale: ( 20 / 100 ) * x – ( 30 / 100 ) * 120 = 80 1 / 5 x = 116 x = 580 answer : c
Answer: c
Problem: find the average of all prime numbers between 40 and 80 .
Options: a ) 59.4 , b ) 56 , c ) 39.8 , d ) 44.9 , e ) none
Rationale: "sol . there are five prime numbers between 40 and 80 . they are 41 , 43 , 47 , 53 , 59 , 61 , 67 , 71 , 73 , 79 â ˆ ´ required average = [ 41 + 43 + 47 + 53 + 59 + 61 + 67 + 71 + 73 + 79 / 10 ] = 594 / 10 = 59.4 answer a"
Answer: a
Problem: the population of a bacteria colony doubles every day . if it was started 9 days ago with 2 bacteria and each bacteria lives for 12 days , how large is the colony today ?
Options: a ) 512 , b ) 768 , c ) 1024 , d ) 2048 , e ) 4096
Rationale: "it started 9 days ago . so bacterias keep growing for 9 days + today = 10 days 2 ^ 10 = 1024 c is the answer"
Answer: c
Problem: in may , the groundskeeper at spring lake golf club built a circular green with an area of 65 π square feet . in august , the groundskeeper doubled the distance from the center of the green to the edge of the green . what is the total area of the renovated green ?
Options: a ) 105 π , b ) 130 π , c ) 200 π , d ) 260 π , e ) 320 π
Rationale: "area = π r ^ 2 , so doubling the radius results in an area that is 4 times the original area . 4 ( 65 π ) = 260 π the answer is d ."
Answer: d
Problem: on dividing 190 by a number , the quotient is 9 and the remainder is 1 . find the divisor ?
Options: a ) a ) 12 , b ) b ) 15 , c ) c ) 16 , d ) d ) 17 , e ) e ) 21
Rationale: "d = ( d - r ) / q = ( 190 - 1 ) / 9 = 189 / 9 = 21 e )"
Answer: e
Problem: let c be defined as the sum of all prime numbers between 0 and 32 . what is c / 3
Options: a ) 155 , b ) 129 , c ) 61 , d ) 47 , e ) 53.3
Rationale: "prime numbers between 0 and 30 - 2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 , 23 , 29 , 31 sum , c = 160 c / 3 = 53,3 answer e"
Answer: e
Problem: exactly 28 % of the reporters for a certain wire service cover local politics in country x . if 30 % of the reporters who cover politics for the wire service do not cover local politics in country x , what percent of the reporters for the wire service do not cover politics ?
Options: a ) 20 % , b ) 42 % , c ) 44 % , d ) 60 % , e ) 84 %
Rationale: "let ' s assume there are 100 reporters - - > 28 reporters cover local politics . now , as 30 % of the reporters who cover all politics do not cover local politics then the rest 70 % of the reporters who cover politics do cover local politics , so if there are x reporters who cover politics then 70 % of them equal to 28 ( # of reporters who cover local politics ) : 0.7 x = 28 - - > x = 40 , hence 40 reporters cover politics and the rest 100 - 40 = 60 reporters do not cover politics at all . answer : d ."
Answer: d
Problem: a group of students decided to collect as many paise from each member of group as is the number of members . if the total collection amounts to rs . 98.01 , the number of the member is the group is :
Options: a ) 57 , b ) 67 , c ) 77 , d ) 99 , e ) 97
Rationale: "money collected = ( 98.01 x 100 ) paise = 9801 paise . number of members = square root of 9801 = 99 . answer : option d"
Answer: d
Problem: the speed of a car is 60 km in the first hour and 30 km in the second hour . what is the average speed of the car ?
Options: a ) 45 kmph , b ) 65 kmph , c ) 75 kmph , d ) 85 kmph , e ) 90 kmph
Rationale: "explanation : s = ( 60 + 30 ) / 2 = 45 kmph a )"
Answer: a
Problem: how many figures are required for numbering the pages of a book containing 1000 pages ?
Options: a ) 2726 , b ) 2878 , c ) 2893 , d ) 2765 , e ) 1811
Rationale: "explanation : 1 to 9 = 9 * 1 = 9 10 to 99 = 90 * 2 = 180 100 to 999 = 900 * 3 = 2700 1000 = 4 - - - - - - - - - - - 2893 answer : c"
Answer: c
Problem: if the length of the longest chord of a certain circle is 10 , what is the radius of that certain circle ?
Options: a ) 2.5
b ) 5
c ) 10
d ) 15
e ) 20
Rationale: longest chord of a circle is the diameter of the circle diameter = 2 * radius if diameter of the circle is given as 10 = 2 * 5 so radius of the circle = 5 correct answer - b
Answer: b
Problem: in how many ways 2 boys and 2 girls can be seated in a row so that boys and girls are alternate ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: "number of ways = 2 * 2 ! * 2 ! = 8 answer is b"
Answer: b
Problem: for what value of x , is | x – 3 | + | x + 1 | + | x | = 8 ?
Options: a ) 0 , b ) 3 , c ) - 3 , d ) 4 , e ) - 2
Rationale: "for what value of x , is | x – 3 | + | x + 1 | + | x | = 8 ? it ' s easiest just to plug in answer choices : ( e ) : - 2 | x – 3 | + | x + 1 | + | x | = 8 ? | - 2 - 3 | + | - 2 + 1 | + | - 2 | = 8 ? | 1 | + | 5 | + | 4 | = 8 ( e )"
Answer: e
Problem: the ratio of number of boys and girls in a school is 3 : 2 . if there are 100 students in the school , find the number of girls in the school ?
Options: a ) 25 , b ) 30 , c ) 35 , d ) 40 , e ) 50
Rationale: "let the number of boys and girls be 3 x and 2 x total students = 100 number of girls in the school = 2 * 100 / 5 = 40 answer is d"
Answer: d