Cheukting/mathqa huggingface dataset:
Question (general): | x + 3 | – | 4 - x | = | 8 + x | how many s solutions will this equation have ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "| x | = x when x > = 0 ( x is either positive or 0 ) | x | = - x when x < 0 ( note here that you can put the equal to sign here as well x < = 0 because if x = 0 , | 0 | = 0 = - 0 ( all are the same ) so the ' = ' sign can be put with x > 0 or with x < 0 . we usually put it with ' x > 0 ' for consistency . a"
Answer: a
Question (physics): in a games hour 4 different types of players came to the ground ? cricket 11 , hokey 15 , football 21 , softball 15 . how many players are present in the ground ?
Options: a ) 70 , b ) 52 , c ) 62 , d ) 49 , e ) 50
Rationale: "total number of players = 11 + 15 + 21 + 15 = 62 answer is c"
Answer: c
Question (physics): how long does a train 120 m long traveling at 60 kmph takes to cross a bridge of 170 m in length ?
Options: a ) sec , b ) sec , c ) sec , d ) sec , e ) sec
Rationale: "d = 120 + 170 = 290 m s = 60 * 5 / 18 = 50 / 3 t = 290 * 3 / 50 = 17.4 sec answer : d"
Answer: d
Question (general): what is the ratio of 6 / 7 to the product 3 * ( 7 / 3 ) ?
Options: a ) 3 : 7 , b ) 1 : 3 , c ) 3 : 21 , d ) 6 : 49 , e ) 3 : 49
Rationale: "6 / 7 / 21 / 3 = 6 / 49 . . . imo option d ."
Answer: d
Question (general): a caterer ordered 125 ice - cream bars and 125 sundaes . if the total price was $ 275.00 and the price of each ice - cream bar was $ 0.60 , what was the price of each sundae ?
Options: a ) $ 0.60 , b ) $ 0.80 , c ) $ 1.00 , d ) $ 1.20 , e ) $ 1.60
Rationale: "let price of a sundae = s price of ice cream bar = . 6 $ 125 * . 6 + 125 * s = 275 = > 125 * s = 200 = > s = 1.6 answer e"
Answer: e
Question (general): a batsman makes a score of 50 runs in the 6 th inning and thus increases his average by 2 . find his average after 6 th inning .
Options: a ) 40 , b ) 50 , c ) 60 , d ) 70 , e ) 80
Rationale: "let the average after 6 th inning = x then , average after 5 th inning = x - 2 5 ( x - 2 ) + 50 = 6 x x = 10 - 50 = 40 answer is a"
Answer: a
Question (general): 49 ã — 49 ã — 49 = 7 ^ ?
Options: a ) 4 , b ) 7 , c ) 8 , d ) 6 , e ) none of these
Rationale: "49 ã — 49 ã — 49 = 7 ? or , 7 ( 2 ) ã — 7 ( 2 ) ã — 7 ( 2 ) = 7 ? or 7 ( 6 ) = 7 ? or , ? = 6 answer d"
Answer: d
Question (geometry): a circle in the coordinate plane passes through points ( - 3 , - 2 ) and ( 1 , - 4 ) . what is the smallest possible area of that circle ?
Options: a ) 13 π , b ) 26 π , c ) 262 √ π , d ) 5 π , e ) 64 π
Rationale: "the distance between the two points is sqrt ( 20 ) . radius = sqrt ( 20 ) / 2 area = pi * ( sqrt ( 20 ) / 2 ) ^ 2 d . 5 π"
Answer: d
Question (general): the sum of the present ages of two persons a and b is 90 . if the age of a is twice that of b , find the sum of their ages 5 years hence ?
Options: a ) 50 , b ) 60 , c ) 70 , d ) 80 , e ) 100
Rationale: "a + b = 90 , a = 2 b 2 b + b = 90 = > b = 30 then a = 60 . 5 years , their ages will be 65 and 35 . sum of their ages = 65 + 35 = 100 . answer : e"
Answer: e
Question (physics): the distance between two cities a and b is 330 km . a train starts from a at 8 a . m . and travels towards b at 60 km / hr . another train starts from b at 9 a . m . and travels towards a at 75 km / hr . at what time do they meet ?
Options: a ) 12 , b ) 10 , c ) 11 , d ) 09 , e ) 03
Rationale: "suppose they meet x hrs after 8 a . m . then , ( distance moved by first in x hrs ) + [ distance moved by second in ( x - 1 ) hrs ] = 330 60 x + 75 ( x - 1 ) = 330 = > x = 3 so , they meet at ( 8 + 3 ) i . e . , 11 a . m . answer : c"
Answer: c
Question (general): a high school has 360 students 1 / 2 attend the arithmetic club , 5 / 8 attend the biology club and 3 / 4 attend the chemistry club . 3 / 8 attend all 3 clubs . if every student attends at least one club how many students attend exactly 2 clubs .
Options: a ) 45 , b ) 40 , c ) 35 , d ) 50 , e ) 55
Rationale: "basically , this question is asking you to figure out how many students are being double - counted . a - club has 180 members ( 1 / 2 of 360 ) b - club has 225 members ( 5 / 8 of 360 ) c - club has 270 members ( 3 / 4 of 360 ) we can create an equation to solve this : 180 + 225 + 270 = n + x + 2 y where n is the number of students , x is the number of students in two clubs , and y is the number of students in three clubs . the question provides y for us ( 135 ) . 180 + 225 + 270 = 360 + x + 270 x = 405 - 360 = 45 a"
Answer: a
Question (gain): the cash difference between the selling prices of an article at a profit of 8 % and 6 % is rs . 3 . the ratio of the two selling prices is ?
Options: a ) 52 : 56 , b ) 52 : 53 , c ) 52 : 50 , d ) 54 : 53 , e ) 52 : 51
Rationale: "let c . p . of the article be rs . x . then , required ratio = 108 % of x / 106 % of x = 108 / 106 = 54 / 53 = 54 : 53 answer : d"
Answer: d
Question (gain): reena took a loan of $ . 1200 with simple interest for as many years as the rate of interest . if she paid $ 588 as interest at the end of the loan period , what was the rate of interest ?
Options: a ) 3.6 , b ) 7 , c ) 18 , d ) can not be determined , e ) none of these
Rationale: "let rate = r % and time = r years . then , 1200 x r x r / 100 = 588 12 r 2 = 588 r 2 = 49 r = 7 . answer : b"
Answer: b
Question (general): what is x if x + 5 y = 24 and y = 2 ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 14
Rationale: "substitute y by 2 in x + 5 y = 24 x + 5 ( 2 ) = 24 x + 10 = 24 if we substitute x by 14 in x + 10 = 24 , we have 14 + 10 = 24 . hence x = 14 correct answer e"
Answer: e
Question (general): the wages earned by robin is 20 % more than that earned by erica . the wages earned by charles is 60 % more than that earned by erica . how much percent is the wages earned by charles more than that earned by robin ?
Options: a ) 18.75 % , b ) 33 % , c ) 30 % , d ) 50 % , e ) 100 %
Rationale: "let wage of erica = 10 wage of robin = 1.2 * 10 = 12 wage of charles = 1.6 * 10 = 16 percentage by which wage earned by charles is more than that earned by robin = ( 16 - 12 ) / 12 * 100 % = 4 / 12 * 100 % = 33 % answer b"
Answer: b
Question (general): there are two numbers . if 10 % of the first number is added to the second number , then the second number increases to its 6 - fifth . what is the ratio of the first number to the second number ?
Options: a ) 3 : 2 , b ) 4 : 3 , c ) 8 : 7 , d ) 5 : 8 , e ) 2 : 1
Rationale: let the two numbers be x and y . ( 1 / 10 ) * x + y = ( 6 / 5 ) * y ( 1 / 10 ) * x = ( 1 / 5 ) * y x / y = 2 / 1 = 2 / 1 the answer is e .
Answer: e
Question (general): each child has 2 pencils and 13 skittles . if there are 6 children , how many pencils are there in total ?
Options: a ) 16 , b ) 12 , c ) 18 , d ) 22 , e ) 08
Rationale: 2 * 6 = 12 . answer is b .
Answer: b
Question (gain): a reduction of 40 % in the price of bananas would enable a man to obtain 60 more for rs . 40 , what is reduced price per dozen ?
Options: a ) 1.2 , b ) 2.2 , c ) 3.2 , d ) 4.2 , e ) 5
Rationale: "40 * ( 40 / 100 ) = 16 - - - 60 ? - - - 12 = > rs . 3.2 answer : c"
Answer: c
Question (general): in a fuel station the service costs $ 2.05 per car , every liter of fuel costs 0.6 $ . assuming that you fill up 3 mini - vans and 2 trucks , how much money will the fuel cost to all the cars owners total , if a mini - van ' s tank is 70 liters and a truck ' s tank is 120 % bigger and they are all empty - ?
Options: a ) 312.6 $ , b ) 321.05 $ , c ) 343.7 $ , d ) 398.85 $ , e ) 412.12 $
Rationale: "service cost of 3 van and 2 truck = 2.05 * ( 3 + 2 ) = 10.5 fuel in 3 van = 3 * 70 = 210 litre fuel in 2 trucks = 2 * 70 ( 1 + 120 / 100 ) = 308 total fuel ( van + truck ) = 518 litre total fuel cost = 518 * 0.6 = 310.8 total cost = fuel + service = 310.8 + 10.25 = 321.05 answer is b"
Answer: b
Question (gain): a man two flats for $ 675958 each . on one he gains 16 % while on the other he loses 16 % . how much does he gain or lose in the whole transaction ?
Options: a ) 2 % , b ) 2.56 % , c ) 3.12 % , d ) 4.65 % , e ) 5.12 %
Rationale: "in such a case there is always a loss loss % = ( 16 / 10 ) ^ 2 = 64 / 25 = 2.56 % answer is b"
Answer: b
Question (gain): in an office , 60 percent of the workers have at least 5 years of service , and a total of 16 workers have at least 10 years of service . if 90 percent of the workers have fewer than 10 years of service , how many of the workers have at least 5 but fewer than 10 years of service ?
Options: a ) 96 , b ) 64 , c ) 50 , d ) 144 , e ) 160
Rationale: "( 10 / 100 ) workers = 16 = > number of workers = 160 ( 60 / 100 ) * workers = x + 16 = > x = 96 answer a"
Answer: a
Question (geometry): a rectangular lawn of dimensions 120 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 . 3 per sq m ?
Options: a ) s . 5100 , b ) s . 3900 , c ) s . 3228 , d ) s . 3922 , e ) s . 3928
Rationale: "area = ( l + b – d ) d ( 120 + 60 – 10 ) 10 = > 1700 m 2 1700 * 3 = rs . 5100 answer : 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 502 to 600 inclusive ?
Options: a ) 23,550 , b ) 27,550 , c ) 31,550 , d ) 35,550 , e ) 39,550
Rationale: "2 + 4 + 6 + 8 + . . . + 100 = 2550 502 + 504 + . . . + 600 = 50 ( 500 ) + ( 2 + 4 + . . . + 100 ) = 25,000 + 2550 = 27,550 the answer is b ."
Answer: b
Question (other): if n is the greatest positive integer for which 2 ^ n is a factor of 8 ! , then n = ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10
Rationale: "8 ! = 40320 e . 2 ^ 10 = 512 ( 40320 / 512 ) - this is not a factor of 8 ! d . 2 ^ 8 = 256 ( 40320 / 256 ) - this is not a factor of 8 ! c . 2 ^ 6 = 64 ( 720 / 64 ) - this is a factor of 8 ! c is answer"
Answer: c
Question (general): when x is multiplied by 3 , the result is 18 more than the result of subtracting x from 70 . what is the value of x ?
Options: a ) - 4 , b ) - 2 , c ) 11 , d ) 13 , e ) 22
Rationale: "the equation that can be formed is : 3 x - 18 = 70 - x or , 4 x = 88 or , x = 22 . e answer ."
Answer: e
Question (general): what is the average of xx , 2 x 2 x , and 66 ?
Options: a ) x + 2 , b ) x + 2 x , c ) x + 2 x + 2 , d ) 2 x + 2 , e ) x + 2 x - 2
Rationale: "by the definition of an average , we get : x + 2 x + 63 = 3 x + 63 x + 2 x + 63 = 3 x + 63 = 3 ( x + 2 ) 3 = x + 2 . = 3 ( x + 2 ) 3 = x + 2 . hence , the answer is x + 2 x + 2 or option c"
Answer: c
Question (physics): 10 men can complete a work in 7 days . but 10 women need 14 days to complete the same work . how many days will 5 men and 10 women need to complete the work ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 10
Rationale: work done by 10 men in 1 day = 1 / 7 work done by 1 man in 1 day = ( 1 / 7 ) / 10 = 1 / 70 work done by 10 women in 1 day = 1 / 14 work done by 1 woman in 1 day = 1 / 140 work done by 5 men and 10 women in 1 day = 5 × ( 1 / 70 ) + 10 × ( 1 / 140 ) = 5 / 70 + 10 / 140 = 1 / 7 = 5 men and 10 women can complete the work in 7 days answer : option c
Answer: c
Question (gain): vijay sells a cupboard at 10 % below cost price . had he got rs . 1500 more , he would have made a profit of 10 % . what is the cost price of the cupboard ?
Options: a ) 7450 , b ) 7500 , c ) 7400 , d ) 7500 , e ) none of these
Rationale: "explanation : cost price = 1500 / ( 0.10 + 0.10 ) = 1500 / 0.20 = rs . 7500 answer b"
Answer: b
Question (general): there has been successive increases of 20 % and then 10 % in the price of gas from the previous month . by what percentage should a driver reduce gas consumption so that the expenditure does not change ?
Options: a ) 16 % , b ) 20 % , c ) 24 % , d ) 28 % , e ) 32 %
Rationale: "let p be the original price per unit of gas . let x be the original gas consumption . let y be the reduced gas consumption . y * 1.1 * 1.2 * p = x * p y = x / ( 1.1 * 1.2 ) which is about 0.76 x which is a decrease of about 24 % . the answer is c ."
Answer: c
Question (geometry): the length of a rectangle is increased by 35 % and its breadth is decreased by 20 % . what is the effect on its area ?
Options: a ) 10800 , b ) 1299 , c ) 1000 , d ) 10000 , e ) 2887
Rationale: "100 * 100 = 10000 135 * 80 = 10800 answer : a"
Answer: a
Question (physics): express 25 mps in kmph ?
Options: a ) 23 , b ) 88 , c ) 90 , d ) 27 , e ) 21
Rationale: "25 * 18 / 5 = 90 kmph answer : c"
Answer: c
Question (physics): a can finish a work in 24 days and b can do the same work in 15 days . b worked for 10 days and left the job . in how many days , a alone can finish the remaining work ?
Options: a ) 6 , b ) 5 , c ) 5.5 , d ) 7 , e ) 8
Rationale: "b ' s 10 day ' s work = ( 1 x 10 ) = 2 . 15 3 remaining work = ( 1 - 2 ) = 1 . 3 3 now , 1 work is done by a in 1 day . 24 therefore 1 work is done by a in ( 24 x 1 ) = 8 days . e"
Answer: e
Question (general): a satellite is composed of 30 modular units , each of which is equipped with a set of sensors , some of which have been upgraded . each unit contains the same number of non - upgraded sensors . if the number of non - upgraded sensors on one unit is 1 / 6 the total number of upgraded sensors on the entire satellite , what fraction of the sensors on the satellite have been upgraded ?
Options: a ) 5 / 6 , b ) 1 / 5 , c ) 1 / 6 , d ) 1 / 7 , e ) 1 / 24
Rationale: "let x be the number of upgraded sensors on the satellite . the number of non - upgraded sensors per unit is x / 6 . the number of non - upgraded sensors on the whole satellite is 30 ( x / 6 ) = 5 x . the fraction of sensors which have been upgraded is x / ( x + 5 x ) = x / 6 x = 1 / 6 the answer is c ."
Answer: c
Question (general): a certain class of students is being divided into teams . the class can either be divided into 16 teams with an equal number of players on each team or 24 teams with an equal number of players on each team . what is the lowest possible number of students in the class ?
Options: a ) 6 , b ) 36 , c ) 48 , d ) 60 , e ) 72
Rationale: "let total no of students in the class be n so , we are told that n is divisible by both 16 24 so , lets find the least common multiple of 16 24 , ie 48 so our answer is ( c ) 48"
Answer: c
Question (gain): if 5 % more is gained by selling an article for rs . 350 than by selling it for rs . 320 , the cost of the article is
Options: a ) 289 , b ) 231 , c ) 200 , d ) 288 , e ) 600
Rationale: "explanation : let c . p . be rs . x . then , 5 % of x = 350 - 320 = 30 x / 20 = 30 = > x = 600 answer : e"
Answer: e
Question (physics): a hall 36 m long and 15 m broad is to be paved with stones , each measuring 5 dm by 5 dm . the number of stones required is :
Options: a ) 180 , b ) 1800 , c ) 18 , d ) 2160 , e ) 1.8
Rationale: "area of the hall = 3600 * 1500 area of each stone = ( 50 * 50 ) therefore , number of stones = ( 3600 * 1500 / 50 * 50 ) = 2160 answer : d"
Answer: d
Question (general): on the number line , the number p is twice as many units from - 2 as - 2 is from 3 . if p is less than – 2 , what is the value of p ?
Options: a ) – 12 , b ) – 10 , c ) – 6 , d ) 10 , e ) 14
Rationale: "distance between - 2 and 3 = 5 since number p is twice as many units from - 2 as - 2 is from 3 , therefore p can be - 12 since , p is less than - 2 , the value of p = - 12 answer a"
Answer: a
Question (physics): before leaving home for the town of madison , pete checks a map which shows that madison is 6 inches from his current location , gardensquare . pete arrives in madison 2.5 hours later and drove at an average speed of 60 miles per hour . at what scale , in inches per mile , is the map drawn ?
Options: a ) 1 / 25 , b ) 1 / 30 , c ) 1 / 10 , d ) 2 , e ) 30
Rationale: "pete covered 2.5 * 60 = 150 miles which correspond to 6 inches on the map - - > scale in inches per mile is 6 / 150 = 1 / 25 . answer : a ."
Answer: a
Question (gain): a person lent a certain sum of money at 5 % per annum at simple interest and in 8 years the interest amounted to $ 480 less than the sum lent . what was the sum lent ?
Options: a ) 700 , b ) 800 , c ) 900 , d ) 1000 , e ) 1100
Rationale: "p - 480 = ( p * 5 * 8 ) / 100 p = 800 the answer is b ."
Answer: b
Question (other): all numbers from 1 to 200 ( in decimal system ) are written in base 6 and base 7 systems . how many of the numbers will have a non - zero units digit in both base 6 and base 7 notations ?
Options: a ) 143
b ) 200
c ) 157
d ) 122
e ) 132
Rationale: detailed solution if a number written in base 6 ends with a zero , it should be a multiple of 6 . in other words , the question wants us to find all numbers from 1 to 200 that are not multiples of 6 or 7 . there are 33 multiples of 6 less than 201 . there are 28 multiples of 7 less than 201 . there are 4 multiples of 6 & 7 ( or multiple of 42 ) from 1 to 200 . so , total multiples of 6 or 7 less than 201 = 33 + 28 - 4 = 57 . number of numbers with non - zero units digit = 200 - 57 = 143 . correct answer : a
Answer: a
Question (physics): two trains are moving in the same direction at 72 kmph and 36 kmph . the faster train crosses a man in the slower train in 25 seconds . find the length of the faster train ?
Options: a ) 270 , b ) 250 , c ) 187 , d ) 257 , e ) 271
Rationale: "relative speed = ( 72 - 36 ) * 5 / 18 = 2 * 5 = 10 mps . distance covered in 25 sec = 25 * 10 = 250 m . the length of the faster train = 250 m . answer : b"
Answer: b
Question (other): an urn contains 6 red , 5 blue and 2 green marbles . if 2 marbles are picked at random , what is the probability that both are red ?
Options: a ) 6 / 13 , b ) 5 / 26 , c ) 6 / 26 , d ) 9 / 26 , e ) 10 / 27
Rationale: option ( b ) is correct p ( both are red ) , 6 c 2 / 13 c 2 = 5 / 26 answer b
Answer: b
Question (gain): if 125 % of j is equal to 25 % of k , 150 % of k is equal to 50 % of l , and 175 % of l is equal to 75 % of m , then 30 % of m is equal to what percent of 200 % of j ?
Options: a ) 0.35 , b ) 3.5 , c ) 525 , d ) 350 , e ) 3500
Rationale: "imo answer should be 350 . . . consider j = 10 , then k = 50 , l = 150 and m = 350 . . . . 30 % of 350 , comes out to be 105 . . . . 200 % of 10 is 20 . . . . ( 105 * 100 ) / 20 = 525 . . . . ans : c"
Answer: c
Question (general): solve below question 2 x + 1 = - 15
Options: a ) - 8 , b ) - 9 , c ) 9 , d ) 8 , e ) - 7
Rationale: "2 x + 1 = - 15 x = - 8 a"
Answer: a
Question (general): a salesman ' s income consists of a commission and a base salary of $ 350 per week . over the past 5 weeks , his weekly income totals have been $ 556 , $ 413 , $ 420 , $ 436 and $ 395 . what must his average ( arithmetic mean ) commission be per week over the next two weeks so that his average weekly income is $ 500 over the 7 - week period ?
Options: a ) $ 150 , b ) $ 290 , c ) $ 365 , d ) $ 715 , e ) $ 730
Rationale: "total weekly income over 5 weeks = $ 556 + $ 413 + $ 420 + $ 436 + $ 395 = $ 2220 for avg weekly income to be $ 500 over 7 weeks , we need total weekly income over 7 weeks = $ 3500 now , $ 3500 - $ 2220 = $ 1280 from this , we subtract base salary for 2 weeks i . e $ 350 * 2 = $ 700 therefore , commission = $ 1280 - $ 700 = $ 580 for 2 weeks avg weekly commission = $ 290 answer b"
Answer: b
Question (general): a man can row 4.8 km / hr in still water . it takes him twice as long to row upstream as to row downstream . what is the rate of the current ?
Options: a ) 1.9 , b ) 1.7 , c ) 1.2 , d ) 1.5 , e ) 1.6
Rationale: "speed of boat in still water ( b ) = 4.8 km / hr . speed of boat with stream ( down stream ) , d = b + u speed of boat against stream ( up stream ) , u = b – u it is given upstream time is twice to that of down stream . ⇒ downstream speed is twice to that of upstream . so b + u = 2 ( b – u ) ⇒ u = b / 3 = 1.6 km / hr . answer : e"
Answer: e
Question (general): 125 liters of a mixture of milk and water contains in the ratio 3 : 2 . how much water should now be added so that the ratio of milk and water becomes 3 : 4 ?
Options: a ) 12 liters , b ) 32 liters , c ) 41 liters , d ) 50 liters , e ) 34 liters
Rationale: "milk = 3 / 5 * 125 = 75 liters water = 50 liters 75 : ( 50 + p ) = 3 : 4 150 + 3 p = 400 = > p = 50 50 liters of water are to be added for the ratio become 3 : 4 . answer : d"
Answer: d
Question (general): a pupil ' s marks were wrongly entered as 35 instead of 23 . due to that the average marks for the class got increased by half . the number of pupils in the class is :
Options: a ) 30 , b ) 80 , c ) 20 , d ) 25 , e ) 24
Rationale: let there be x pupils in the class . total increase in marks = ( x * 1 / 2 ) = x / 2 . x / 2 = ( 35 - 23 ) = > x / 2 = 12 = > x = 24 . answer : e
Answer: e
Question (general): there are 6 baskets numbered from 1 to 6 and filled with apples . 10 children are asked to pick apples one by one from each basket such that the number of apples picked by each child from each basket is equal to the number marked on the basket . if there were 1000 apples in total and the baskets were filled in such a way that none of the basket became empty in the process , how many apples were left in the end ?
Options: a ) 90 , b ) 91 , c ) 210 , d ) 790 , e ) 910
Rationale: "total number of apples in the basket initially = 1000 each child picks up = 1 + 2 + 3 + 4 + 5 + 6 = 6 * 7 / 2 = 21 total number of apples picked up by 10 children = 21 * 10 = 210 number of apples left in the end = 1000 - 210 = 790 answer is d"
Answer: d
Question (probability): in a lottery there are 100 prizes and 300 blanks . a lottery is drawn at random . what is the probability of getting a prize ?
Options: a ) 1 / 2 , b ) 5 / 400 , c ) 1 / 5 , d ) 1 / 3 , e ) 1 / 4
Rationale: "total draws = prizes + blanks = 100 + 300 = 400 probability of getting a prize = 100 / 400 = 1 / 4 correct option is e"
Answer: e
Question (physics): the radius of a wheel is 22.4 cm . what is the distance covered by the wheel in making 400 resolutions ?
Options: a ) 708 m , b ) 704 m , c ) 774 m , d ) 714 m , e ) 563.2 m
Rationale: "in one resolution , the distance covered by the wheel is its own circumference . distance covered in 500 resolutions . = 400 * 2 * 22 / 7 * 22.4 = 56320 cm = 563.2 m answer : e"
Answer: e
Question (general): q is as much younger than r as he is older than t . if the sum of the ages of r and t is 50 years , what is definitely the difference between r and q ' s age ?
Options: a ) 23 , b ) 28 , c ) 25 , d ) 19 , e ) 11
Rationale: explanation : given r – q = q – t and r + t = 50 which gives q = 25 as the difference between r & q and q & t is same so answer is 25 years answer : c
Answer: c
Question (general): if x and y are integers , what is the least positive number of 24 x + 21 y ?
Options: a ) 3 , b ) 5 , c ) 6 , d ) 8 , e ) 9
Rationale: "24 x + 21 y = 3 ( 8 x + 7 y ) which will be a minimum positive number when 8 x + 7 y = 1 . 8 ( 1 ) + 7 ( - 1 ) = 1 then 3 ( 8 x + 7 y ) can have a minimum positive value of 3 . the answer is a ."
Answer: a
Question (general): the average of runs of a cricket player of 20 innings was 32 . how many runs must he make in his next innings so as to increase his average of runs by 3 ?
Options: a ) 95 , b ) 106 , c ) 122 , d ) 116 , e ) 122
Rationale: "average = total runs / no . of innings = 32 so , total = average x no . of innings = 32 * 20 = 640 now increase in avg = 4 runs . so , new avg = 32 + 3 = 35 runs total runs = new avg x new no . of innings = 35 * 21 = 735 runs made in the 11 th inning = 735 - 640 = 95 answer : a"
Answer: a
Question (gain): a sum of money deposited at c . i . amounts to rs . 500 in 3 years and to rs . 650 in 4 years . find the rate percent ?
Options: a ) 25 % , b ) 30 % , c ) 35 % , d ) 40 % , e ) 45 %
Rationale: "500 - - - 150 100 - - - ? = > 30 % answer : b"
Answer: b