Cheukting/mathqa huggingface dataset:
Question (gain): if 40 % of a certain number is 160 , then what is 60 % of that number ?
Options: a ) 270 , b ) 380 , c ) 260 , d ) 360 , e ) 240
Rationale: "explanation : 40 % = 40 * 4 = 160 60 % = 60 * 4 = 240 answer : option e"
Answer: e
Question (general): if 22 percent of the students at a certain school went to a camping trip and took more than $ 100 , and 75 percent of the students who went to the camping trip did not take more than $ 100 , what percentage of the students at the school went to the camping trip ?
Options: a ) 95 , b ) 90 , c ) 88 , d ) 80 , e ) 75
Rationale: "let x be the number of students in the school . 0.22 x students went to the trip and took more than 100 $ . they compose ( 100 - 75 ) = 25 % of all students who went to the trip . therefore the toal of 0.22 x / 0.25 = 0.88 x students went to the camping which is 88 % . the answer is c"
Answer: c
Question (general): if a : b : c = 3 : 4 : 7 , then the ratio ( a + b + c ) : c is equal to
Options: a ) 2 : 1 , b ) 14 : 3 , c ) 7 : 2 , d ) 1 : 2 , e ) none
Rationale: solution : ( a + b + c ) = 3 + 4 + 7 = 14 and c = 7 then , ( a + b + c ) : c = 2 : 1 . answer : option a
Answer: a
Question (general): a certain library assesses fines for overdue books as follows . on the first day that a book is overdue , the total fine is $ 0.05 . for each additional day that the book is overdue , the total fine is either increased by $ 0.30 or doubled , whichever results in the lesser amount . what is the total for a book on the fifth day it is overdue ?
Options: a ) $ 0.60 , b ) $ 0.70 , c ) $ 0.80 , d ) $ 0.90 , e ) $ 1.00
Rationale: 1 st day fine - 0.05 2 nd day fine - 0.05 * 2 = 0.1 ( as doubling gives lower value ) 3 rd day fine - 0.1 * 2 = 0.2 ( as doubling gives lower value ) 4 th day fine - 0.2 * 2 = 0.4 ( as doubling gives lower value we add 0.3 this time ) 5 th day fine - 0.4 + 0.3 = 0.7 ( as doubling gives higher value we add 0.3 this time ) answer : b .
Answer: b
Question (general): linda spent 3 / 4 of her savings on furniture and the rest on a tv . if the tv cost her $ 230 , what were her original savings ?
Options: a ) $ 900 , b ) $ 800 , c ) $ 1000 , d ) $ 920 , e ) $ 1500
Rationale: "if linda spent 3 / 4 of her savings on furnitute , the rest 4 / 4 - 3 / 4 = 1 / 4 on a tv but the tv cost her $ 230 . so 1 / 4 of her savings is $ 230 . so her original savings are 4 times $ 230 = $ 920 correct answer d"
Answer: d
Question (general): 45 x ? = 10 % of 900
Options: a ) 2 , b ) 4 , c ) 5 , d ) 500 , e ) none
Rationale: answer let 45 x a = ( 10 x 900 ) / 100 ∴ a = ( 10 x 9 ) / 45 = 2 correct option : a
Answer: a
Question (geometry): a circle graph shows how the budget of a certain company was spent : 20 percent for transportation , 9 percent for research and development , 5 percent for utilities , 4 percent for equipment , 2 percent for supplies , and the remainder for salaries . if the area of each sector of the graph is proportional to the percent of the budget it represents , how many degrees of the circle are used to represent salaries ?
Options: a ) 90 °
b ) 135 °
c ) 216 °
d ) 240 °
e ) 270 °
Rationale: the percent of the budget for salaries is 100 - ( 20 + 9 + 5 + 4 + 2 ) = 60 % 100 % of the circle is 360 degrees . then ( 60 % / 100 % ) * 360 = 216 degrees the answer is c .
Answer: c
Question (gain): sales price is $ 44 , gross profit is 120 % of cost , what is the value of gross profit ?
Options: a ) 24 , b ) 33 , c ) 39 , d ) 40 , e ) 42
Rationale: cost + profit = sales cost + ( 120 / 100 ) cost = 44 cost = 20 profit = 44 - 20 = 24 answer ( a )
Answer: a
Question (gain): seed mixture x is 40 % ryegrass and 60 % bluegrass by weight ; seed mixture y is 25 % ryegrass and 75 % fescue . if a mixture of x and y contains 30 % ryegrass , what percent of the weight of the mixture is x ?
Options: a ) 10 % , b ) 33.33 % , c ) 40 % , d ) 50 % , e ) 66.67 %
Rationale: "x - wt of mix x added y - wt of mix y added 0.4 x + 0.25 y = 0.3 ( x + y ) 0.1 x = 0.05 y x / y = 5 / 10 = 1 / 2 y / x = 2 ( y + x ) / x = 3 = > x / ( y + x ) * 100 = 100 / 3 = 33.33 % answer : b"
Answer: b
Question (general): a circular road runs around a circular garden . if the sum of the circumferences of the inner and outer circles is 88 metres and the radius of the inner circle is one - third of the outer circle , then the width of the road is :
Options: a ) 4 metres , b ) 5 metres , c ) 7 metres , d ) 6 metres , e ) 8 metres
Rationale: let radius of inner circle = r 1 radius of outer circle = r 2 also r 1 = 1 / 3 * r 2 3 * r 1 = r 2 circumference of inner circle = 2 * pi * r 1 circumference of outer circle = 2 * pi * r 2 = 6 * pi * r 1 ( since r 2 = 3 * r 1 ) 2 * pi * r 1 + 6 * pi * r 1 = 88 ( as per question ) r 1 = 3.5 m r 2 = 3 * 3.5 = 10.5 m width of road = 10.5 - 3.5 = 7 m ans . answer : c
Answer: c
Question (general): in a multiple choice test comprising 5 questions , each with 4 choices , what is the probability of a student getting 3 or more questions correct ? each question has only one correct answer and the student is equally likely to choose any of the 4 choices .
Options: a ) 24 / 256 , b ) 53 / 512 , c ) 105 / 512 , d ) 459 / 512 , e ) 47 / 256
Rationale: probability for choosing correct answer is 1 / 4 and incorrect answer is 3 / 4 for 3 correct answers , c ( 5,3 ) * ( 1 / 4 ) ^ 3 * ( 3 / 4 ) ^ 2 = 90 / ( 4 ^ 5 ) for 4 correct answers , c ( 5,4 ) * ( 1 / 4 ) ^ 4 * ( 3 / 4 ) ^ 1 = 15 / ( 4 ^ 5 ) for 5 correct answers , c ( 5,5 ) * ( 1 / 4 ) ^ 5 * ( 3 / 4 ) ^ 0 = 1 / ( 4 ^ 5 ) so total probability = 106 / 1024 = 53 / 512 ans b
Answer: b
Question (physics): p and q together can do a work in 6 days . if p alone can do it in 15 days . in how many days can q alone do it ?
Options: a ) 5 , b ) 4 , c ) 10 , d ) 11 , e ) 12
Rationale: 1 / 6 - 1 / 15 = = > 1 / 10 = = > 10 answer c
Answer: c
Question (other): in a certain animal shelter , the ratio of the number of catsto the number of dogs is 15 to 7 . if 12 additional dogs were to be taken in by the shelter , the ratio of the number of cats to the number of dogs would be 15 to 11 . how many cats are in the shelter ?
Options: a ) 15 , b ) 45 , c ) 30 , d ) 45 , e ) 60
Rationale: this ratio question can be solved in a couple of different ways . here ' s an algebraic approach . . . we ' re told that the ratio of the number of cats to the number of dogs is 15 : 7 . we ' re then told that 12 more dogs are added to this group and the ratio becomes 15 : 11 . we ' re asked for the number of cats . algebraically , since the number of cats is a multiple of 15 and the number of dogs is a multiple of 7 , we can write this initial relationship as . . . 15 x / 7 x when we add the 12 cats and factor in the ' ending ratio ' , we have an equation . . . . 15 x / ( 7 x + 12 ) = 15 / 11 here we have 1 variable and 1 equation , so we can solve for x . . . . ( 15 x ) ( 11 ) = ( 7 x + 12 ) ( 15 ) ( x ) ( 11 ) = ( 7 x + 12 ) ( 1 ) 11 x = 7 x + 12 4 x = 12 x = 3 with this x , we can figure out the initial number of dogs and cats . . . initial dogs = 15 x = 15 ( 3 ) = 45 final answer : b
Answer: b
Question (other): the ratio between the sale price and the cost price of an article is 9 : 5 . what is the ratio between the profit and the cost price of that article ?
Options: a ) 23 , b ) 1 : 2 , c ) 4 : 5 , d ) 3 : 5 , e ) 25
Rationale: "c . p . = rs . 5 x and s . p . = rs . 9 x . then , gain = rs . 4 x required ratio = 4 x : 5 x = 4 : 5 c"
Answer: c
Question (gain): a reduction of 20 % in the price of salt enables a lady to obtain 10 kgs more for rs . 300 , find the original price per kg ?
Options: a ) s . 7.7 , b ) s . 7.4 , c ) s . 7.5 , d ) s . 7.1 , e ) s . 7.9
Rationale: "100 * ( 20 / 100 ) = 20 - - - 10 ? - - - 1 = > rs . 2 300 - - - 80 ? - - - 2 = > rs . 7.5 answer : c"
Answer: c
Question (general): 8 is 6 % of a , and 6 is 8 % of b . c equals b / a . what is the value of c ?
Options: a ) 3 / 8 , b ) 8 / 15 , c ) 9 / 16 , d ) 12 / 25 , e ) 16 / 27
Rationale: "6 a / 100 = 8 a = 400 / 3 8 b / 100 = 6 b = 75 c = b / a = 75 * 3 / 400 = 9 / 16 the answer is c ."
Answer: c
Question (other): of the 65 house in a development , 50 have a two - car garage , 40 have an in - the - ground swimming pool , and 35 have both a two - car garage and an in - the - ground swimming pool . how many houses in the development have neither a two - car garage nor an in - the - ground swimming pool ?
Options: a ) 10 , b ) 15 , c ) 20 , d ) 25 , e ) 30
Rationale: neither car nor garage = total - garage - ( swim - common ) = 65 - 50 - ( 40 - 35 ) = 65 - 55 = 10 answer a
Answer: a
Question (general): exactly 3 / 8 of the people in the room are under the age of 21 , and exactly 5 / 12 of the people in the room are over the age of 65 . if the total number of the people in the room is greater than 50 and less than 100 , how many people in the room are under the age of 21 ?
Options: a ) 21 , b ) 36 , c ) 39 , d ) 60 , e ) 65
Rationale: "the total number of the people in the room must be a multiple of both 8 and 12 ( in order 3 / 7 and 5 / 13 of the number to be an integer ) , thus the total number of the people must be a multiple of lcm of 8 and 12 , which is 96 . since , the total number of the people in the room is greater than 50 and less than 100 , then there are 96 people in the room . therefore there are 3 / 8 * 96 = 36 people in the room under the age of 21 . answer : b ."
Answer: b
Question (general): we have boxes colored either red or blue . in each blue box there is a fixed number of blueberries . in each red box there is a fixed number of strawberries . if we dispose of one blue box for one additional red box , the total number of berries would increase by 10 , and the difference between the total number of strawberries and the total number of blueberries would increase by 50 . each blue box contains how many blueberries ?
Options: a ) 10 , b ) 15 , c ) 20 , d ) 25 , e ) 30
Rationale: "let x be the number of blueberries in each blue box . then there are x + 10 strawberries in each red box . x + ( x + 10 ) = 50 x = 20 the answer is c ."
Answer: c
Question (general): if x / y = 3 and ( 2 a - x ) / ( 3 b - y ) = 3 , then the value of a / b is ?
Options: a ) – 3 , b ) 9 / 2 , c ) 1 , d ) 2 , e ) 3
Rationale: x = 3 y 2 a - 3 y = 3 ( 3 b - y ) 2 a - 3 y = 9 b - 3 y 2 a = 9 b a / b = 9 / 2 answer : b
Answer: b
Question (general): if z is a multiple of 9702 , what is the remainder when z ^ 2 is divided by 4 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) it depends on z .
Rationale: "2 is a factor of 9702 , so 2 is a factor of z . then 2 ^ 2 = 4 is a factor of z ^ 2 . then the remainder when z ^ 2 is divided by 4 is 0 . the answer is a ."
Answer: a
Question (gain): a man buys a cycle for rs . 1400 and sells it at a loss of 15 % . what is the selling price of the cycle ?
Options: a ) rs . 1200 , b ) rs . 890 , c ) rs . 600 , d ) rs . 1190 , e ) rs . 450
Rationale: "explanation : s . p . = 85 % of rs . 1400 = rs . ( 85 / 100 * 1400 ) = rs . 1190 answer : d"
Answer: d
Question (physics): a and b can finish a work in 12 days while a alone can do the same work in 24 days . in how many days b alone will complete the work ?
Options: a ) 76 days , b ) 48 days , c ) 98 days , d ) 31 days , e ) 24 days
Rationale: "b = 1 / 12 – 1 / 24 = 1 / 24 = > 24 days answer : e"
Answer: e
Question (general): when n is divided by 5 the remainder is 3 . what is the remainder when ( n + 2 ) ^ 2 is divided by 5 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "n = 5 x + 3 , for some integer x ( n + 2 ) ^ 2 = ( 5 x + 5 ) ^ 2 = 5 y , for some integer y when we divide this by 5 , the remainder is 0 . the answer is a ."
Answer: a
Question (general): if an average hard drive had a capacity of 0.3 tb in 2000 , and average hard drive capacities double every 5 years , what will be the average hard drive capacity in 2050 ?
Options: a ) 3072 , b ) 512 , c ) 768 , d ) 1024 , e ) 1536
Rationale: "0.3 * 2 ^ 10 = 0.3 * 1024 = 307.2 the answer is a ."
Answer: a
Question (physics): the radius of a wheel is 22.4 cm . what is the distance covered by the wheel in making 250 resolutions ?
Options: a ) 277 m , b ) 704 m , c ) 352 m , d ) 288 m , e ) 378 m
Rationale: "in one resolution , the distance covered by the wheel is its own circumference . distance covered in 250 resolutions . = 250 * 2 * 22 / 7 * 22.4 = 35200 cm = 352 m answer : c"
Answer: c
Question (general): if grapes are 93 % water and raisins are 16 % water , then how many kilograms did a quantity of raisins , which currently weighs 8 kilograms , weigh when all the raisins were grapes ? ( assume that the only difference between their raisin - weight and their grape - weight is water that evaporated during their transformation . )
Options: a ) 92 , b ) 96 , c ) 100 , d ) 104 , e ) 108
Rationale: let x be the original weight . the weight of the grape pulp was 0.07 x . since the grape pulp is 84 % of the raisins , 0.07 x = 0.84 ( 8 ) . then x = 12 * 8 = 96 kg . the answer is b .
Answer: b
Question (general): find the slope of the line perpendicular to the line y = x - 7
Options: a ) 1 , b ) 2 , c ) - 1 , d ) 4 , e ) 5
Rationale: two lines are perpendicular if the product of their slopes is equal to - 1 . the slope of the given line is equal to 1 . if m is the slope of the line perpendicular to the given line , then m × 1 = - 1 solve for m m = - 1 correct answer c ) - 1
Answer: c
Question (general): set a consists of all the prime numbers between 10 and 25 . what is the range of set a ?
Options: a ) 12 , b ) 13 , c ) 16.6 , d ) 17 , e ) 23
Rationale: "the range of a set of data is the difference between the highest and lowest values in the set in this set , highest number = 23 lowest number = 11 range = highest - lowest = 23 - 11 = 12 option a"
Answer: a
Question (physics): a train running at a speed of 36 kmph crosses an electric pole in 12 seconds . in how much time will it cross a 370 m long platform ?
Options: a ) 19 , b ) 27 , c ) 29 , d ) 47 , e ) 49
Rationale: let the length of the train be x m . when a train crosses an electric pole , the distance covered is its own length . so , x = 12 * 36 * 5 / 18 m = 120 m . time taken to cross the platform = ( 120 + 370 ) / 36 * 5 / 18 = 49 min . answer : e
Answer: e
Question (physics): a train of 25 carriages , each of 60 meters length , when an engine also of 60 meters length is running at a speed of 60 kmph . in what time will the train cross a bridge 2.5 km long ?
Options: a ) 4 , b ) 3 , c ) 5 , d ) 7 , e ) 9
Rationale: "d = 25 * 60 + 2500 = 4000 m t = 4000 / 60 * 18 / 5 = 240 sec = 4 mins answer : a"
Answer: a
Question (geometry): the length of a rectangle is halved , while its breadth is tripled . what is the % change in area ?
Options: a ) 30 % , b ) 40 % , c ) 50 % , d ) 60 % , e ) 65 %
Rationale: "let original length = x and original breadth = y . original area = xy . new length = x . 2 new breadth = 3 y . new area = x x 3 y = 3 xy . 2 2 increase % = 1 xy x 1 x 100 % = 50 % . 2 xy c"
Answer: c
Question (gain): there were two candidates in an election . winner candidate received 60 % of votes and won the election by 288 votes . find the number of votes casted to the winning candidate ?
Options: a ) 776 , b ) 864 , c ) 299 , d ) 257 , e ) 125
Rationale: "w = 60 % l = 40 % 60 % - 40 % = 20 % 20 % - - - - - - - - 288 60 % - - - - - - - - ? = > 864 answer : b"
Answer: b
Question (general): in the rectangular coordinate system , what is the x - intercept of a line passing through ( 10 , 3 ) and ( − 2 , − 3 ) ?
Options: a ) 4 , b ) 2 , c ) 0 , d ) − 2 , e ) − 4
Rationale: "slope = rise / run = 6 / 12 = 1 / 2 the equation of the line is y = ( 1 / 2 ) x + b 3 = ( 1 / 2 ) ( 10 ) + b b = - 2 the equation of the line is y = ( 1 / 2 ) x - 2 to find the x - intercept , let y = 0 : 0 = ( 1 / 2 ) x - 2 x = 4 the answer is a ."
Answer: a
Question (other): the h . c . f . of two numbers is 23 and the other two factors of their l . c . m . are 13 and 14 . the larger of the two numbers is :
Options: a ) 276 , b ) 299 , c ) 322 , d ) 345 , e ) 355
Rationale: "clearly , the numbers are ( 23 x 13 ) and ( 23 x 14 ) . larger number = ( 23 x 14 ) = 322 . answer : option c"
Answer: c
Question (physics): a and b undertake to do a piece of work for rs . 600 . a alone can do it in 6 days while b alone can do it in 8 days . with the help of c , they finish it in 3 days . ! find the share of b .
Options: a ) 225 , b ) 500 , c ) 75 , d ) 800 , e ) none 0 of them
Rationale: "c ' s 1 day ' s work = 1 / 3 - ( 1 / 6 + 1 / 8 ) = 24 a : b : c = ratio of their 1 day ' s work = 1 / 6 : 1 / 8 : 1 / 24 = 4 : 3 : 1 . a ’ s share = rs . ( 600 * 4 / 8 ) = rs . 300 , b ' s share = rs . ( 600 * 3 / 8 ) = rs . 225 . c ' s share = rs . [ 600 - ( 300 + 225 » ) = rs . 75 . answer is a"
Answer: a
Question (physics): the radius of a wheel is 22.4 cm . what is the distance covered by the wheel in making 500 resolutions
Options: a ) 700 , b ) 704 , c ) 704 , d ) 706 , e ) 707
Rationale: "in one resolution , the distance covered by the wheel is its own circumference . distance covered in 500 resolutions . = 500 * 2 * 22 / 7 * 22.4 = 70400 cm = 704 m answer : option b"
Answer: b
Question (physics): a 220 m long train running at the speed of 120 km / hr crosses another train running in opposite direction at the speed of 80 km / hr in 9 sec . what is the length of the other train ?
Options: a ) 280 , b ) 270 , c ) 260 , d ) 250 , e ) 240
Rationale: "relative speed = 120 + 80 = 200 km / hr . = 200 * 5 / 18 = 500 / 9 m / sec . let the length of the other train be x m . then , ( x + 220 ) / 9 = 500 / 9 = > x = 280 . answer : option a"
Answer: a
Question (general): the sum of the first 50 positive even integers is 2550 . what is the sum of the even integers from 402 to 500 inclusive ?
Options: a ) 14,550 , b ) 18,550 , c ) 22,550 , d ) 26,550 , e ) 30,550
Rationale: "2 + 4 + 6 + 8 + . . . + 100 = 2550 402 + 404 + . . . + 500 = 50 ( 400 ) + ( 2 + 4 + . . . + 100 ) = 20,000 + 2550 = 22,550 the answer is c ."
Answer: c
Question (general): we run a business that rents out canoes and kayaks . a canoe rental costs $ 9 per day , and a kayak rental costs $ 12 dollars per day . one day , our business rents out 4 canoes for every 3 kayaks and receives a total of $ 432 in revenue . how many more canoes than kayaks were rented out ?
Options: a ) 10 , b ) 9 , c ) 8 , d ) 7 , e ) 6
Rationale: "let x be the number of canoes . then 3 x / 4 is the number of kayaks . 9 x + ( 3 x / 4 ) * 12 = 432 9 x + 9 x = 432 18 x = 432 x = 24 ( canoes ) 3 x / 4 = 18 ( kayaks ) there were 24 - 18 = 6 more canoes rented out . the answer is e ."
Answer: e
Question (gain): ramu bought an old car for rs . 48000 . he spent rs . 14000 on repairs and sold it for rs . 72900 . what is his profit percent ?
Options: a ) 16 % , b ) 17.5 % , c ) 18.2 % , d ) 58.5 % , e ) 13 %
Rationale: "total cp = rs . 48000 + rs . 14000 = rs . 62000 and sp = rs . 72900 profit ( % ) = ( 72900 - 62000 ) / 62000 * 100 = 17.5 % answer : b"
Answer: b
Question (gain): rs . 2600 is divided into two parts such that if one part be put out at 5 % simple interest and the other at 6 % , the yearly annual income may be rs . 140 . how much was lent at 5 % ?
Options: a ) 1600 , b ) 1700 , c ) 1800 , d ) 1900 , e ) 2000
Rationale: "( x * 5 * 1 ) / 100 + [ ( 2600 - x ) * 6 * 1 ] / 100 = 140 x = 1600 answer : a"
Answer: a
Question (probability): a bag contains 6 white marbles and 6 black marbles . if each of 6 girls and 6 boys randomly selects and keeps a marble , what is the probability that all of the girls select the same colored marble ?
Options: a ) 1 / 35 , b ) 1 / 10 , c ) 1 / 3 , d ) 1 / 462 , e ) 1 / 252
Rationale: "first , total ways to select for all boys and girls , i . e 12 ! / ( 6 ! * 6 ! ) = 12 * 11 * 10 * 9 * 8 * 7 / 6 * 5 * 4 * 3 * 2 = 924 then there are one two way girls can have all same colors , either white or black . the number of ways in which 6 girls can select 6 white balls = 6 c 6 = 1 the number of ways in which 6 girls can select 6 black balls = 6 c 6 = 1 therefore , total favorable outcomes / total outcomes = 2 / 924 = 1 / 462 d"
Answer: d
Question (general): the average weight of 7 person ' s increases by 3.5 kg when a new person comes in place of one of them weighing 75 kg . what might be the weight of the new person ?
Options: a ) 74 kg , b ) 78.5 kg , c ) 99.5 kg , d ) data inadequate , e ) none of these
Rationale: "total weight increased = ( 7 x 3.5 ) kg = 24.5 kg . weight of new person = ( 75 + 24.5 ) kg = 99.5 kg . answer : option c"
Answer: c
Question (other): in a group of people , if 30 people were made to stand in each column , 16 columns could be formed . if 32 people were made to stand in a column , how many columns could be formed ?
Options: a ) 15 , b ) 20 , c ) 25 , d ) 30 , e ) 35
Rationale: "16 * 30 = 32 * n n = 15 the answer is a ."
Answer: a
Question (general): what least number must be subtracted from 427398 so that remaining no . is divisible by 10
Options: a ) 3 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: "explanation : on dividing 427398 by 10 we get the remainder 8 , so 8 should be subtracted answer : option e"
Answer: e
Question (general): the average age of applicants for a new job is 10 , with a standard deviation of 8 . the hiring manager is only willing to accept applicants whose age is within one standard deviation of the average age . assuming that all applicants ' ages are integers and that the endpoints of the range are included , what is the maximum number of different ages of the applicants ?
Options: a ) 8 , b ) 16 , c ) 17 , d ) 18 , e ) 34
Rationale: minimum age = average - 1 standard deviation = 10 - 8 = 2 maximum age = average + 1 standard deviation = 10 + 8 = 18 maximum number of different ages of the applicants = 18 - 2 + 1 = 17 answer c
Answer: c
Question (physics): ajay can ride 50 km in 1 hour . in how many hours he can ride 900 km ?
Options: a ) 10 hrs , b ) 15 hrs , c ) 20 hrs , d ) 25 hrs , e ) 18 hrs
Rationale: 1 hour he ride 50 km he ride 900 km in = 900 / 50 * 1 = 18 hours answer is e
Answer: e
Question (gain): a and b invests rs . 6000 and rs . 12000 in a business . after 4 months , a withdraws half of his capital and 2 months later , b withdraws one - third of his capital . in what ratio should they share the profits at the end of the year ?
Options: a ) 32 : 99 , b ) 8 : 21 , c ) 32 : 45 , d ) 34 : 89 , e ) 35 : 21
Rationale: "a : b ( 6000 * 4 ) + ( 3000 * 8 ) : ( 12000 * 6 ) + ( 9000 * 6 ) 48000 : 126000 8 : 21 answer : b"
Answer: b
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 7 even numbers . his mother immediately worked out the answer . how much had he scored in math ?
Options: a ) 80 , b ) 90 , c ) 56 , d ) 70 , e ) 60
Rationale: "c 56 sum = ( n x n ) + n hence , 7 x 7 = 49 + 7 = 56"
Answer: c
Question (physics): the speed at which a man can row a boat in still water is 15 kmph . if he rows downstream , where the speed of current is 3 kmph , what time will he take to cover 80 metres ?
Options: a ) 16 seconds , b ) 76 seconds , c ) 26 seconds , d ) 12 seconds , e ) 18 seconds
Rationale: "speed of the boat downstream = 15 + 3 = 18 kmph = 18 * 5 / 18 = 5 m / s hence time taken to cover 80 m = 80 / 5 = 16 seconds . answer : a"
Answer: a
Question (general): a certain clock marks every hour by striking a number of times equal to the hour , and the time required for a stroke is exactly equal to the time interval between strokes . at 6 : 00 the time lapse between the beginning of the first stroke and the end of the last stroke is 44 seconds . at 12 : 00 , how many seconds elapse between the beginning of the first stroke and the end of the last stroke ?
Options: a ) a . 72 , b ) b . 50 , c ) c . 92 , d ) d . 46 , e ) e . 44
Rationale: at 6 : 00 it ' ll chime 6 times . if we assume that the time taken to chime is x , then time between chimes is also x . so you have 6 chimes , which is 6 x and 5 time intervals between chimes . this means that 11 x = 44 seconds . thus x = 4 seconds . by a similar logic , at 12 : 00 , there are 12 chimes and 11 intervals so the total time is ( 12 + 11 ) x = 23 x = 92 seconds . answer c
Answer: c