Cheukting/mathqa huggingface dataset:
Question (physics): a and b can do a piece of work in 12 days . with the help of c they finish the work in 3 days . c alone can do that piece of work in ?
Options: a ) 40 days , b ) 2 days , c ) 4 days , d ) 8 days , e ) 40 days
Rationale: "c 30 days c = 1 / 3 – 1 / 12 = 1 / 4 = > 4 days"
Answer: c
Question (general): the average of 11 numbers is 9.9 . if the average of the first 6 numbers is 10.5 and that of the last 6 numbers is 11.4 , then the middle number is
Options: a ) 71.5 , b ) 11.5 , c ) 81.5 , d ) 11.5 , e ) 22.5
Rationale: explanation : middle numbers = [ ( 10.5 x 6 + 11.4 x 6 ) - 9.9 x 11 ] = 22.5 . answer : e
Answer: e
Question (general): in how many ways can an answer key for a quiz be written if the quiz contains 3 true - false questions followed by 3 multiple - choice questions with 4 answer choices each , if the correct answers to all true - false questions can not be the same ?
Options: a ) 164 , b ) 224 , c ) 280 , d ) 384 , e ) 476
Rationale: "there are 2 ^ 3 = 8 possibilities for the true - false answers . however we need to remove two cases for ttt and fff . there are 4 * 4 * 4 = 64 possibilities for the multiple choice questions . the total number of possibilities is 6 * 64 = 384 . the answer is d ."
Answer: d
Question (general): if 2 ^ 5 , 3 ^ 3 , and 12 ^ 2 are all factors of the product of 936 and w where w is a positive integer , what is the smallest possible value of w ?
Options: a ) 26 , b ) 39 , c ) 42 , d ) 144 , e ) 156
Rationale: "here 156 has three two ' s two three ' s and one 13 rest of them must be in w so w = 12 * 3 * 4 = 144 smash d"
Answer: d
Question (other): the ratio of 3 numbers is 5 : 1 : 4 and their sum is 1000 . the last number of the 3 numbers is ?
Options: a ) 24 , b ) 26 , c ) 27 , d ) 400 , e ) 30
Rationale: 5 : 1 : 4 total parts = 10 10 parts - - > 1000 1 part - - - - > 100 the last number of the three numbers is = 4 * 100 = 400 answer : d
Answer: d
Question (general): when average age of 21 members are 0 , how many members greater than 0 ?
Options: a ) 17 , b ) 20 , c ) 21 , d ) 24 , e ) 25
Rationale: "average of 21 numbers = 0 . sum of 21 numbers ( 0 x 21 ) = 0 . it is quite possible that 20 of these numbers may be positive and if their sum is a then 21 st number is ( - a ) answer is 20 ( b )"
Answer: b
Question (geometry): the length of the rectangular field is double its width . inside the field there is square shaped pond 8 m long . if the area of the pond is 1 / 72 of the area of the field . what is the length of the field ?
Options: a ) 73 , b ) 32 , c ) 34 , d ) 43 , e ) 96
Rationale: "explanation : a / 72 = 8 * 8 = > a = 8 * 8 * 72 x * 2 x = 8 * 8 * 72 x = 48 = > 2 x = 96 answer : option e"
Answer: e
Question (general): for any positive number x , the function [ x ] denotes the greatest integer less than or equal to x . for example , [ 1 ] = 1 , [ 1.367 ] = 1 and [ 1.899 ] = 1 . if k is a positive integer such that k ^ 2 is divisible by 45 and 80 , what is the units digit of k ^ 3 / 4000 ?
Options: a ) 0 , b ) 1 , c ) 27 , d ) 54 , e ) 0
Rationale: "k = [ lcm of 80 and 45 ] * ( any integer ) however minimum value of k is sq . rt of 3 ^ 2 * 4 ^ 2 * 5 ^ 2 = 60 * any integer for value of k ( 60 ) * any integer unit value will be always zero . e"
Answer: e
Question (general): how many times digit 6 is used while writing numbers from 80 to 1000 ?
Options: a ) 648 , b ) 300 , c ) 252 , d ) 225 , e ) 26
Rationale: there are 100 numbers which begin with 600 next , in every 10 numbers such as 100 to 110 , 110 to 120 , 120 to 130 6 comes at least once . number of such intervals = end limit - first no . / interval . our range of numbers is 100 - 1000 1000 - 100 = 900 / 10 = 90 number of 10 s interval in this is 90 . so 90 ' 6 s ' so far we have calculated 190 . the total now comes to 280 . the nearest to which is 225 . hence d .
Answer: d
Question (gain): p and q invested in a business . they earned some profit which they divided in the ratio of 2 : 3 . if p invested rs . 60 , 000 , the amount invested by q is :
Options: a ) rs . 65,000 , b ) rs . 70,000 , c ) rs . 80,000 , d ) rs . 90,000 , e ) rs . 60,000
Rationale: "suppose q invested rs . y . then , y = 60,000 / y = 2 / 3 or y = 60000 / 2 * 3 = 90,000 . answer : d"
Answer: d
Question (physics): if m = | | n – 3 | – 2 | , for how many values of n is m = 5 ?
Options: a ) 5 , b ) 4 , c ) 2 , d ) 3 , e ) 1
Rationale: m = | | n – 3 | – 2 | can be 4 only and only when n - 3 = + / - 7 . so there are 2 values of n answer : c
Answer: c
Question (general): the average of 30 results is 20 and the average of other 20 results is 30 . what is the average of all the results ?
Options: a ) 24 , b ) 25 , c ) 48 , d ) 50 , e ) none
Rationale: "answer sum of 50 result = sum of 30 result + sum of 20 result . = 30 x 20 + 20 x 30 = 1200 correct option : a"
Answer: a
Question (general): when an amount was distributed among 14 boys , each of them got $ 80 more than the amount received by each boy when the same amount is distributed equally among 18 boys . what was the amount ?
Options: a ) 5050 , b ) 5020 , c ) 5040 , d ) 5030 , e ) 5075
Rationale: "let the total amount be rs . x the , x / 14 - x / 18 = 80 = = > 2 x / 126 = 80 = = > x / 63 = 63 x 80 = 5040 . hence the total amount is 5040 . answer c ."
Answer: c
Question (general): if 5 % of a number is equal to one - third of another number , what is the ratio of first number to the second number ?
Options: a ) 2 : 5 , b ) 20 : 3 , c ) 3 : 7 , d ) 6 : 11 , e ) 2 : 3
Rationale: "let 5 % of a = 1 / 3 b then 5 a / 100 = 1 b / 3 a / 20 = b / 3 a / b = 20 / 3 a : b = 20 : 3 answer is b"
Answer: b
Question (gain): a baseball card decreased in value 50 % in its first year and 10 % in its second year . what was the total percent decrease of the card ' s value over the two years ?
Options: a ) 28 % , b ) 55 % , c ) 32 % , d ) 36 % , e ) 72 %
Rationale: "let the initial value of baseball card = 100 after first year , value of baseball card = ( 1 - 50 / 100 ) * 100 = 50 after second year , value of baseball card = ( 1 - 10 / 100 ) * 50 = 45 total percent decrease of the card ' s value over the two years = ( 100 - 45 ) / 100 * 100 % = 55 % answer b"
Answer: b
Question (general): 2 ^ 35 ^ 26 ^ 1 find largest value ?
Options: a ) 2 , b ) 3 , c ) 1 , d ) 10 , e ) 25
Rationale: explanation : 2 ^ 3 = 2 * 2 * 2 = 8 5 ^ 2 = 5 * 5 = 25 6 ^ 1 = 6 * 1 = 6 hence 5 ^ 2 is the largest one answer : e
Answer: e
Question (gain): what is 35 % of 4 / 13 of 585 ?
Options: a ) 52 , b ) 63 , c ) 74 , d ) 85 , e ) 96
Rationale: "this problem can be solved easily if we just use approximation : 35 % is a little over 1 / 3 , while 4 / 13 is a little less than 4 / 12 , which is 1 / 3 . thus , the answer is about 1 / 3 of 1 / 3 of 585 , or 1 / 9 of 585 . since the first 1 / 3 is a slight underestimate and the second 1 / 3 is a slight overestimate , the errors will partially cancel each other out . our estimate will be relatively accurate . the number 585 is between 540 and 630 , so ( 1 / 9 ) * 585 will be about 65 . keeping track not only of your current estimate , but also of the degree to which you have overestimated or underestimated , can help you pinpoint the correct answer more confidently . the closest answer is 63 , so this is the answer to choose . the answer is b ."
Answer: b
Question (other): if both 5 ^ 2 and 3 ^ 3 are factors of n x ( 2 ^ 5 ) x ( 12 ^ 2 ) x ( 7 ^ 3 ) x ( 10 ) , what is the smallest possible positive value of n ?
Options: a ) 15 , b ) 45 , c ) 75 , d ) 125 , e ) 150
Rationale: "( 2 ^ 5 ) x ( 12 ^ 2 ) x ( 7 ^ 3 ) x ( 10 ) has two appearances of 3 ( in 12 ^ 2 ) and one appearance of 5 ( in the 10 ) . thus n must include at least 3 * 5 = 15 the answer is a ."
Answer: a
Question (gain): at a small company , 64 percent of the employees are women , and 60 percent of the employees are married . if 2 / 3 of the men are single , what fraction of the women are married ?
Options: a ) 5 / 16 , b ) 3 / 4 , c ) 9 / 20 , d ) 7 / 10 , e ) 5 / 7
Rationale: "lets take total employees are 100 . given that , total women = 64 and total married = 60 . total men = 100 - 64 = 36 and single men = 2 / 3 * 36 = 24 . married men = total men - single men = 36 - 24 = 12 . married women = total married - married men = 60 - 12 = 48 . fraction of women are married = married women / total women = 48 / 64 = 3 / 4 . ans b"
Answer: b
Question (gain): if annual decrease in the population of a town is 10 % and the present number of people is 500 what will the population be in 1 year ?
Options: a ) 450 , b ) 310 , c ) 250 , d ) 410 , e ) 390
Rationale: "population in 1 year = 500 ( 1 - 10 / 100 ) = 500 * 90 / 100 = 450 answer is a"
Answer: a
Question (general): if | x | = 7 x - 5 , then x = ?
Options: a ) 1 , b ) 1 / 2 , c ) 1 and 1 / 2 , d ) 2 , e ) - 1
Rationale: "answer : a approach : substituted option a i . e x = 1 . inequality satisfied . d"
Answer: d
Question (general): the sum of two numbers is 56 , and one of them is 12 more than the other . what are the two numbers ?
Options: a ) 36 - 48 , b ) 22 - 34 , c ) 60 - 24 , d ) 42 - 42 , e ) 21 - 63
Rationale: "in this problem , we are asked to find two numbers . therefore , we must let x be one of them . let x , then , be the first number . we are told that the other number is 12 more , x + 12 . the problem states that their sum is 56 : word problem = 56 the line over x + 12 is a grouping symbol called a vinculum . it saves us writing parentheses . we have : 2 x = 56 â ˆ ’ 12 = 44 . x = 44 / 2 = 22 . this is the first number . therefore the other number is x + 12 = 22 + 12 = 34 . the sum of 22 + 34 is 56 . b"
Answer: b
Question (geometry): a horse is tethered to one corner of a rectangular grassy field 46 m by 20 m with a rope 17 m long . over how much area of the field can it graze ?
Options: a ) 154 cm 2 , b ) 308 m 2 , c ) 227 m 2 , d ) 407 m 2 , e ) none of these
Rationale: "area of the shaded portion = 1 ⁄ 4 × π × ( 17 ) 2 = 227 m 2 answer c"
Answer: c
Question (gain): a person incurs 5 % loss by selling a watch for $ 1140 . at what price should the watch be sold to earn 5 % profit ?
Options: a ) $ 1260 , b ) $ 1150 , c ) $ 1542 , d ) $ 1000 , e ) $ 1292
Rationale: let the new selling price be $ x ( 100 - loss % ) : ( 1 st s . p . ) = ( 100 + gain % ) : ( 2 nd s . p . ) ( 100 - 5 ) / 1140 = ( 100 + 5 ) / x x = 105 * 1140 / 95 = 1260 answer is a
Answer: a
Question (general): if the average of 10 consecutive integers is 22.5 then the 10 th integer is : -
Options: a ) 15 , b ) 20 , c ) 23 , d ) 27 , e ) 25
Rationale: "the average falls between the 5 th and 6 th integers , integer 5 = 22 , integer 6 = 23 . counting up to the tenth integer we get 27 . answer : d"
Answer: d
Question (geometry): find the area of a parallelogram with base 32 cm and height 22 cm ?
Options: a ) 281 , b ) 284 , c ) 704 , d ) 640 , e ) 920
Rationale: "area of a parallelogram = base * height = 32 * 22 = 704 cm 2 answer : c"
Answer: c
Question (gain): sarah operated her lemonade stand monday through friday over a two week period and made a total profit of 350 dollars . on hot days she sold cups of lemonade for a price that was 25 percent higher than the regular days . each cup she sold had a total cost of 75 cents and sarah did not incur any other costs . if every day she sold exactly 32 cups and 4 of the days were hot , then what was the price of 1 cup on a hot day ?
Options: a ) $ 1.50 , b ) $ 1.88 , c ) $ 2.09 , d ) $ 2.50 , e ) $ 3.25
Rationale: "6 regular days - - > sales = 6 * 32 * x = 192 x ; 4 hot days - - > sales = 4 * 32 * ( 1.25 x ) = 160 x ; total sales = 192 x + 160 x = 352 x . total cost = 10 * 32 * 0.75 = 240 . profit = 352 x - 240 = 350 - - > x = 1.676 . 1.25 x = ~ 2.09 . answer : c ."
Answer: c
Question (other): if 1 = 6 2 = 12 3 = 18 4 = 24 5 = 30 6 = 36 then 12 = ? hint : its a logic riddle not a mathematical riddle
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: b 2 as stated 2 = 12 = > 12 = 2 answer is b
Answer: b
Question (other): what is the number of integers from 1 to 900 ( inclusive ) that are divisible by neither 11 nor by 35 ?
Options: a ) 884 , b ) 890 , c ) 892 , d ) 910 , e ) 945
Rationale: "normally , i would use the method used by bunuel . it ' s the most accurate . but if you are looking for a speedy solution , you can use another method which will sometimes give you an estimate . looking at the options ( most of them are spread out ) , i wont mind trying it . ( mind you , the method is accurate here since the numbers start from 1 . ) in 1000 consecutive numbers , number of multiples of 11 = 1000 / 11 = 90 ( ignore decimals ) in 1000 consecutive numbers , number of multiples of 35 = 1000 / 35 = 28 number of multiples of 11 * 35 i . e . 385 = 1000 / 385 = 2 number of integers from 1 to 1000 that are divisible by neither 11 nor by 35 = 1000 - ( 90 + 28 - 2 ) { using the concept of sets here ) = 892 think : why did i say the method is approximate in some cases ? think what happens if the given range is 11 to 1010 both inclusive ( again 1000 numbers ) what is the number of multiples in this case ? c"
Answer: c
Question (general): 217 + 2.017 + 0.217 + 2.0017 = ?
Options: a ) 229.3657 , b ) 229.7563 , c ) 229.6357 , d ) 229.5637 , e ) 221.2357
Rationale: 217 2.017 0.217 + 2.0017 - - - - - - - - 221.2357 - - - - - - - - - answer is e .
Answer: e
Question (general): two men amar and bhuvan have the ratio of their monthly incomes as 6 : 5 . the ratio of their monthly expenditures is 3 : 2 . if bhuvan saves one - fourth of his income , find the ratio of their monthly savings ? a . 3 : 5
Options: a ) 3 : 9 , b ) 3 : 10 , c ) 3 : 21 , d ) 3 : 12 , e ) 3 : 14
Rationale: let the monthly incomes of amar and bhuvan be 6 x and 5 x respectively . let the monthly expenditure of amar and bhuvan be 3 y and 2 y respectively . savings of bhuvan every month = 1 / 4 ( 5 x ) = ( his income ) - ( his expenditure ) = 5 x - 2 y . = > 5 x = 20 x - 8 y = > y = 15 x / 8 . ratio of savings of amar and bhuvan = 6 x - 3 y : 1 / 4 ( 5 x ) = 6 x - 3 ( 15 x / 8 ) : 5 x / 4 = 3 x / 8 : 5 x / 4 = 3 : 10 . answer : option b
Answer: b
Question (physics): if 3 cm of a pencil is purple , 2 cm of the remaining is black and the remaining 1 cm is blue , what is the total length of the pencil ?
Options: a ) 6 , b ) 3 , c ) 1 , d ) 4 , e ) 2
Rationale: answer is a ) 6
Answer: a
Question (physics): a car covers a distance of 624 km in 2 2 / 5 hours . find its speed ?
Options: a ) 104 kmph , b ) 194 kmph , c ) 109 kmph , d ) 260 kmph , e ) 271 kmph
Rationale: "624 / 2 2 / 5 = 260 kmph answer : d"
Answer: d
Question (physics): find the perimetri of trapezium with sides 4 , 6,12 and distance between two parallel side is 3 .
Options: a ) 27
b ) 26
c ) 28
d ) 25
e ) 24
Rationale: 1 / 2 * ( 6 + 12 ) * 3 = 27 answer : a
Answer: a
Question (general): the average of first five prime numbers greater than 20 is ?
Options: a ) 32.2 , b ) 32.98 , c ) 32.3 , d ) 32.8 , e ) 32.4
Rationale: "23 + 29 + 31 + 37 + 41 = 161 / 5 = 32.2 answer : a"
Answer: a
Question (other): a certain telephone company offers two plans , a and b . under plan a , the company charges a total of $ 0.60 for the first 6 minutes of each call and $ 0.06 per minute thereafter . under plan b , the company charges $ 0.08 per minute of each call . what is the duration of a call , in minutes , for which the company charges the same amount under plan a and under plan b ?
Options: a ) 12 , b ) 9 , c ) 15 , d ) 21 , e ) 30
Rationale: "let the duration , in minutes , for which the company charges the same under plan a and plan b be t minutes . then under plan a the cost would be $ 0.6 + 0.06 ( t - 6 ) and under plan b the cost would be $ 0.08 t . we want these amount to be equal : 0.6 + 0.06 ( t - 6 ) = 0.08 t - - > 60 + 6 ( t - 6 ) = 8 t - - > t = 12 . answer : a ."
Answer: a
Question (gain): solution x is 10 % chemical a and 90 % chemical b by volume . solution y is 20 % chemical a and 80 % chemical b by volume . if a mixture of x and y is 12 % chemical a , what percent of the mixture is solution x ?
Options: a ) 80 % , b ) 75 % , c ) 70 % , d ) 65 % , e ) 60 %
Rationale: "the volume of the mixture be x + y . 0.1 x + 0.2 y = 0.12 ( x + y ) x = 4 y x / ( x + y ) = 4 / 5 = 80 % . the answer is a ."
Answer: a
Question (other): the flowerman sale , all of the prices of the flowers sold were different . if the price of a radio sold at the flowerman sale was both the 17 th highest price and the 42 th lowest price among the prices of the slowers sold , how many flowers were sold at the flowerman sale ?
Options: a ) 38 , b ) 34 , c ) 58 , d ) 63 , e ) 73
Rationale: 16 + 41 + 1 = 58 answer : c
Answer: c
Question (gain): milk contains 5 % water . what quantity of pure milk should be added to 10 litres of milk to reduce this 2 % ?
Options: a ) 15 litres , b ) 16 litres , c ) 17 litres , d ) 25 litres , e ) 35 litres
Rationale: present ration of milk to water is 95 : 5 amount of milk is 10 litres hence , pure milk content is 9.5 litre and water content is 0.5 litres now , we should not disturb the water content so , 0.5 litres of water is equivalent to 2 % so 100 % mixture is : ( 0.5 / 2 ) * 100 = 25 litre thus , milk should be added = 25 - 10 = 15 litres of pure milk answer : a
Answer: a
Question (general): in the set of positive integers from 1 to 80 , what is the sum of all the odd multiples of 5 ?
Options: a ) 180 , b ) 245 , c ) 320 , d ) 260 , e ) 270
Rationale: "reduce to 1 - 80 5 - 15 - 25 - 35 - 45 - - 55 - - 65 - - 75 are valid multiples . add them - - > 320 c"
Answer: c
Question (general): dan ' s age after 18 years will be 8 times his age 3 years ago . what is the present age of dan ?
Options: a ) 4 , b ) 6 , c ) 8 , d ) 10 , e ) 12
Rationale: "let dan ' s present age be x . x + 18 = 8 ( x - 3 ) 7 x = 42 x = 6 the answer is b ."
Answer: b
Question (general): the wages earned by robin is 44 % more than that earned by erica . the wages earned by charles is 60 % more than that earned by erica . how much % is the wages earned by charles more than that earned by robin ?
Options: a ) 23 % , b ) 18.75 % , c ) 30 % , d ) 30.55 % , e ) 100 %
Rationale: "explanatory answer let the wages earned by erica be $ 100 then , wages earned by robin and charles will be $ 144 and $ 160 respectively . charles earns $ 44 more than robin who earns $ 144 . therefore , charles ' wage is 44 / 144 * 100 = 30.55 % . the correct choice is ( d )"
Answer: d
Question (gain): solution p is 20 percent lemonade and 80 percent carbonated water by volume ; solution q is 45 percent lemonade and 55 percent carbonated water by volume . if a mixture of pq contains 67.5 % percent carbonated water , what percent of the volume of the mixture is p ?
Options: a ) 25 % , b ) 40 % , c ) 50 % , d ) 60 % , e ) 75 %
Rationale: "67.5 % is 12.5 % - points below 80 % and 12.5 % - points above 55 % . so the ratio of solution p to solution q is 1 : 1 . mixture p is 1 / 2 = 50 % of the volume of mixture pq . the answer is c ."
Answer: c
Question (general): the average age of a family of 6 members is 40 years . if the age of the youngest member is 7 years , what was the average age of the family at the birth of the youngest member ?
Options: a ) 33 , b ) 18 , c ) 21 , d ) 12 , e ) 19
Rationale: "present age of total members = 6 x 40 = 240 7 yrs back their ages were = 6 x 7 = 42 ages at the birth of youngest member = 240 - 42 = 198 therefore , avg age at the birth of youngest member = 198 / 6 = 33 . answer : a"
Answer: a
Question (physics): a man rows his boat 80 km downstream and 38 km upstream , taking 3 hours each time . find the speed of the stream ?
Options: a ) 6 , b ) 9 , c ) 7 , d ) 8 , e ) 2
Rationale: "speed downstream = d / t = 80 / ( 3 ) = 27 kmph speed upstream = d / t = 38 / ( 3 ) = 9 kmph the speed of the stream = ( 27 - 9 ) / 2 = 9 kmph answer : b"
Answer: b
Question (general): if x ⁄ 2 + 5 ⁄ 4 = 5 ⁄ 4 , what is the value of x ?
Options: a ) – 2 , b ) – 1 , c ) 0 , d ) 1 , e ) 2
Rationale: x ⁄ 2 + 5 ⁄ 4 = 5 ⁄ 4 let ' s multiply both sides by 4 . 2 x + 5 = 5 2 x = 0 x = 0 the answer is c .
Answer: c
Question (gain): at what rate percent per annum will a sum of money double in 7 years .
Options: a ) 12.5 % , b ) 13.5 % , c ) 14.2 % , d ) 14.5 % , e ) 21.5 %
Rationale: "let principal = p , then , s . i . = p and time = 8 years rate = [ ( 100 x p ) / ( p x 8 ) ] % = 14.2 % per annum . answer : c"
Answer: c
Question (general): sum of the squares of 3 no . ' s is 99 and the sum of their products taken two at a time is 131 . find the sum ?
Options: a ) 20 , b ) 24 , c ) 19 , d ) 28 , e ) 30
Rationale: "( a + b + c ) 2 = a 2 + b 2 + c 2 + 2 ( ab + bc + ca ) = 99 + 2 * 131 a + b + c = √ 361 = 19 c"
Answer: c
Question (geometry): a rectangular lawn of dimensions 80 m * 60 m has two roads each 10 m wide running in the middle of the lawn , one parallel to the length and the other parallel to the breadth . what is the cost of traveling the two roads at rs . 2 per sq m ?
Options: a ) 2288 , b ) 2779 , c ) 2779 , d ) 3900 , e ) 2600
Rationale: "area = ( l + b â € “ d ) d ( 80 + 60 â € “ 10 ) 10 = > 1300 m 2 1300 * 2 = rs . 2600 answer : e"
Answer: e
Question (general): the ratio of ducks and frogs in a pond is 37 : 39 respectively . the average number of ducks and frogs in the pond is 150 . what is the number of frogs in the pond ?
Options: a ) 148 , b ) 154 , c ) 156 , d ) 144 , e ) none
Rationale: "solution : ratio of ducks and frogs in pond , = 37 : 39 . average of ducks and frogs in pond , = 150 . so , total number of ducks and frogs in the pond , = 2 * 150 = 300 . therefore , number of frogs , = ( 300 * 39 ) / 76 = 154 . answer : option b"
Answer: b
Question (other): the monthly incomes of a and b are in the ratio 5 : 2 . b ' s monthly income is 12 % more than c ' s monthly income . if c ' s monthly income is rs . 14000 , then find the annual income of a ?
Options: a ) rs . 420000 , b ) rs . 180000 , c ) rs . 201600 , d ) rs . 470400 , e ) none of these
Rationale: "b ' s monthly income = 14000 * 112 / 100 = rs . 15680 b ' s monthly income = 2 parts - - - - > rs . 15680 a ' s monthly income = 5 parts = 5 / 2 * 15680 = rs . 39200 a ' s annual income = rs . 39200 * 12 = rs . 470400 answer : d"
Answer: d
Question (geometry): in the rectangular coordinate system , points ( 2 , 0 ) and ( – 2 , 0 ) both lie on circle c . what is the maximum possible value of the radius of c ?
Options: a ) 2 , b ) 4 , c ) 8 , d ) 16 , e ) none of the above
Rationale: "the answer is a it takes 3 distinct points to define a circle . only 2 are given here . the two points essentially identify a single chord of the circle c . since no other information is provided , however , the radius of the circle can essentially be anything . all this information tell us is that the radius isgreater 2"
Answer: a
Question (physics): if ram and gohul can do a job in 10 days and 15 days independently , how many days would they take to complete the same job working simultaneously ?
Options: a ) 10 , b ) 5 , c ) 8 , d ) 6 , e ) 13
Rationale: if total work is x . ram working rate = x / 10 per day . working rate of gohul = x / 15 per day . rate of work = ( x / 10 ) + ( x + 15 ) = 30 x / 5 x = 6 days the answer is option d
Answer: d
Question (physics): trapezoid jklm in the x - y plane has coordinates j = ( – 2 , – 4 ) , k = ( – 2 , 2 ) , l = ( 6 , 8 ) , and m = ( 6 , – 4 ) . what is its perimeter ?
Options: a ) 34 , b ) 36 , c ) 38 , d ) 40 , e ) ( f ) 42
Rationale: "jk = 6 lm = 12 kl = using distance formula 10 jm = using distance formula 8 sum of all is 36 b"
Answer: b
Question (general): a box contains 7 purple , 5 blue and 11 yellow balls . what is the minimum number of tries required to get one blue and one yellow ball ?
Options: a ) 16 , b ) 17 , c ) 18 , d ) 19 , e ) 20
Rationale: 11 yellow + 7 purple + after that we have only one option that is to be blue so answer is 19 answer : d
Answer: d
Question (gain): the length of a rectangular floor is more than its breadth by 200 % . if rs . 361 is required to paint the floor at the rate of rs . 3.00001 / sq m , what would be the length of the floor ?
Options: a ) 18 , b ) 19 , c ) 20 , d ) 22 , e ) 24
Rationale: "let the length and the breadth of the floor be l m and b m respectively . l = b + 200 % of b = l + 2 b = 3 b area of the floor = 361 / 3 = 120.33 sq m l b = 120.33 i . e . , l * l / 3 = 120.33 l ^ 2 = 361 = > l = 19 . b"
Answer: b