Cheukting/mathqa huggingface dataset:
Question (geometry): a certain rectangular window is three times as long as it is wide . if its perimeter is 32 feet , what are its dimensions in terms of length by width ?
Options: a ) 12 by 2
b ) 11 by 3
c ) 10.5 by 3.5
d ) 12 by 4
e ) 9 by 3
Rationale: 2 x + 2 y = 32 x + y = 16 x + 3 x = 16 4 x = 16 x = 4 answer d
Answer: d
Question (general): a car averages 50 mph for the first 4 hours of a trip and averages 80 mph for each additional hour . the average speed for the entire trip was 65 mph . how many hours long is the trip ?
Options: a ) 8 , b ) 7 , c ) 6 , d ) 5 , e ) 4
Rationale: let the time for which car averages 80 mph = t 65 * ( t + 4 ) = 50 * 4 + 80 t = > 15 t = 60 = > t = 4 total duration of the trip = 4 + 4 = 8 answer a
Answer: a
Question (gain): a sum of rs . 1000 at simple interest amounts to rs . 1192 in 4 years . the s . i . for 1 year is :
Options: a ) rs . 45 , b ) rs . 70 , c ) rs . 39 , d ) rs . 72 , e ) rs . 48
Rationale: s . i . for 4 years = rs . ( 1192 - 1000 ) = rs . 192 . s . i . for 1 year = rs . 192 / 4 = rs . 48 . answer : option e
Answer: e
Question (gain): a shopkeeper sells his goods at cost price but uses a faulty meter that weighs 900 grams . find the profit percent .
Options: a ) 12.11 , b ) 11.11 , c ) 13.11 , d ) 14.11 , e ) 15.11
Rationale: "explanation : ( 100 + g ) / ( 100 + x ) = true measure / faulty measure x = 0 true measure = 1000 faulty measure = 900 100 + g / 100 + 0 = 1000 / 900 100 + g = 10 / 9 * 100 g = 11.11 answer : b"
Answer: b
Question (gain): if 0.5 % of a = 75 paise , then the value of a is ?
Options: a ) rs . 150 , b ) rs . 17 , c ) rs . 1.70 , d ) rs . 4.25 , e ) none
Rationale: "answer ∵ 0.5 / 100 of a = 75 / 100 ∴ a = rs . ( 75 / 0.5 ) = rs . 150 correct option : a"
Answer: a
Question (general): if | 4 x + 6 | = 46 , what is the sum of all the possible values of x ?
Options: a ) 2 , b ) - 2 , c ) 4 , d ) - 5 , e ) 6
Rationale: "there will be two cases 4 x + 6 = 46 or 4 x + 6 = - 46 = > x = 10 or x = - 12 sum of both the values will be - 12 + 10 = - 2 answer is b"
Answer: b
Question (general): ( √ 27 + √ 192 ) / √ 54 = ?
Options: a ) 2 √ 2 , b ) 2 √ 3 , c ) 3 √ 2 , d ) 11 / ( 3 * √ 2 ) , e ) √ 2
Rationale: "( √ 27 + √ 192 ) / √ 54 = ( 3 √ 3 + 8 √ 3 ) / 3 √ 3 * 2 = 11 √ 3 / 3 √ 3 * 2 = 11 / ( 3 * √ 2 ) = 11 / ( 3 * √ 2 ) . hence , the correct answer is d ."
Answer: d
Question (general): 60 % of x is greater than 1 / 3 rd of x by 110 . what is x ?
Options: a ) 100.5 , b ) 200.5 , c ) 300.5 , d ) 350.5 , e ) 412.5
Rationale: "6 x / 10 - x / 3 = 110 4 x / 15 = 110 x = 412.5 answer : e"
Answer: e
Question (physics): a train traveling at 72 kmph crosses a platform in 32 seconds and a man standing on the platform in 18 seconds . what is the length of the platform in meters ?
Options: a ) 280 meters , b ) 360 meters , c ) 420 meters , d ) 600 meters , e ) can not be determined
Rationale: "speed of train = 72 * ( 5 / 18 ) = 20 m / s lets consider the man as a stationery point on the platform . crossing the point gives us the length of the train . lt = 20 * 18 = 360 m . crossing the platform gives us the length of trainlength of platform . l ( t + p ) = 20 * 32 = 640 m . so , length of platform = 640 - 360 = 280 m imo , answer a"
Answer: a
Question (gain): a man buys a cycle for rs . 1400 and sells it at a loss of 5 % . what is the selling price of the cycle ?
Options: a ) s . 1090 , b ) s . 1160 , c ) s . 1190 , d ) s . 1202 , e ) s . 1330
Rationale: "since , c . p = 1400 loss % = ( c . p - s . p ) / c . p * 100 5 = ( 1400 - s . p ) / 1400 * 100 so , after solving answer = 1330 . answer : e"
Answer: e
Question (physics): the population of a bacteria colony doubles every day . if it was started 5 days ago with 2 bacteria and each bacteria lives for 12 days , how large is the colony today ?
Options: a ) 512 , b ) 768 , c ) 64 , d ) 2048 , e ) 4096
Rationale: "2 ^ 5 ( 2 ) = 2 ^ 6 = 64 the answer is c"
Answer: c
Question (physics): a goods train runs at the speed of 72 kmph and crosses a 250 m long platform in 36 seconds . what is the length of the goods train ?
Options: a ) 470 m , b ) 240 m , c ) 260 m , d ) 270 m , e ) none of these
Rationale: "explanation : speed = [ 72 x ( 5 / 18 ) ] m / sec = 20 m / sec . time = 36 sec . let the length of the train be x metres . then , [ ( x + 250 ) / 36 ] = 20 = > x + 250 = 720 = > x = 470 . answer : a"
Answer: a
Question (general): if an integer n is to be selected at random from 1 to 900 , inclusive , what is probability n ( n + 1 ) will be divisible by 9 ?
Options: a ) 1 / 9 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 9 , e ) 2 / 3
Rationale: for n ( n + 1 ) to be a multiple of 9 , either n or n + 1 has to be a multiple of 9 . thus n must be of the form 9 k or 9 k - 1 . the probability is 2 / 9 . the answer is d .
Answer: d
Question (general): find the sum the difference between the compound and s . i . on a certain sum of money for 2 years at 10 % per annum is rs . 100 of money ?
Options: a ) 1500 , b ) 6000 , c ) 2500 , d ) 1400 , e ) 2000
Rationale: "p = 100 ( 100 / 10 ) 2 = > p = 2000 answer : e"
Answer: e
Question (physics): 45 workers work 8 hours to dig a hole 30 meters deep . how many extra workers should be hired to dig another hole 45 meters deep by working for 6 hours ?
Options: a ) 25 , b ) 35 , c ) 45 , d ) 55 , e ) 65
Rationale: "45 workers * 8 hours / 30 meters = x * 6 / 45 x = 90 total workers 90 - 45 = 45 new workers the answer is c ."
Answer: c
Question (general): if p / q = 4 / 5 , then the value of 4 / 7 + { ( 2 q - p ) / ( 2 q + p ) } is ?
Options: a ) 3 / 7 , b ) 34 , c ) 1 , d ) 2 , e ) 3
Rationale: "answer given exp . = 4 / 7 + { ( 2 q - p ) / ( 2 q + p ) } dividing numerator as well as denominator by q , exp = 4 / 7 + { 2 - p / q ) / ( 2 + p / q ) } = 4 / 7 + { ( 2 - 4 / 5 ) / ( 2 + 4 / 5 ) } = 4 / 7 + 6 / 14 = 4 / 7 + 3 / 7 = 7 / 7 = 1 . correct option : c"
Answer: c
Question (general): patrick purchased 70 pencils and sold them at a loss equal to the selling price of 20 pencils . the cost of 70 pencils is how many times the selling price of 70 pencils ?
Options: a ) 0.75 , b ) 0.8 , c ) 1 , d ) 1.28 , e ) 1.35
Rationale: "say the cost price of 70 pencils was $ 70 ( $ 1 per pencil ) and the selling price of 1 pencil was p . selling at a loss : 70 - 70 p = 20 p - - > p = 7 / 9 . ( cost price ) / ( selling price ) = 1 / ( 7 / 9 ) = 9 / 7 = 1.28 . answer : d ."
Answer: d
Question (physics): 3 men and 8 women complete a task in same time as 6 men and 2 women do . how much fraction of work will be finished in same time if 4 men and 5 women will do that task .
Options: a ) 13 / 14 , b ) 13 / 10 , c ) 13 / 18 , d ) 13 / 16 , e ) 13 / 11
Rationale: 3 m + 8 w = 6 m + 2 w 3 m = 6 w 1 m = 2 w therefore 3 m + 8 w = 14 w 4 m + 5 w = 13 w answer is 13 / 14 answer : a
Answer: a
Question (general): 40 % of x is greater than 1 / 3 rd of x by 110 . what is x ?
Options: a ) 1100 , b ) 2100 , c ) 1300 , d ) 1650 , e ) 1400
Rationale: "4 x / 10 - x / 3 = 110 1 x / 15 = 110 x = 1650 answer : d"
Answer: d
Question (other): the ratio of boarders to day students at a school was originally 5 to 12 . however , after a number of new boarders join the initial 330 boarders , the ratio changed to 1 to 2 . if no boarders became day students and vice versa , and no students left the school , how many new boarders joined the school ?
Options: a ) 48 , b ) 66 , c ) 72 , d ) 80 , e ) 84
Rationale: let x be the number of new boarders . the ratio changed from 5 : 12 up to 1 : 2 = 6 : 12 . 330 / ( 330 + x ) = 5 / 6 x = 66 the answer is b .
Answer: b
Question (physics): a flagpole 18 meters high casts a shadow of length 45 meters . if a building under similar conditions casts a shadow of length 70 meters , what is the height of the building ( in meters ) ?
Options: a ) 20 , b ) 24 , c ) 28 , d ) 32 , e ) 36
Rationale: "the height : length ratio will be equal in both cases . 18 / 45 = x / 70 x = 28 the answer is c ."
Answer: c
Question (general): the average weight of a group of boys is 20 kg . after a boy of weight 33 kg joins the group , the average weight of the group goes up by 1 kg . find the number of boys in the group originally ?
Options: a ) 12 , b ) 14 , c ) 18 , d ) 24 , e ) 10
Rationale: "let the number off boys in the group originally be x . total weight of the boys = 20 x after the boy weighing 33 kg joins the group , total weight of boys = 20 x + 33 so 20 x + 33 = 21 ( x + 1 ) = > x = 12 . answer : a"
Answer: a
Question (other): presently the ratio between the ages of dan and james is 6 : 5 . after 4 years dan will be 28 . what is the present age of james ?
Options: a ) 20 , b ) 19 , c ) 21 , d ) 18 , e ) 22
Rationale: let the present ages dan and james be 6 x years and 5 x years respectively 6 x + 4 = 28 6 x = 24 x = 4 kim ' s age = 5 x = 20 years answer is a
Answer: a
Question (general): the sum of two numbers is 62 , and one of them is 12 more than the other . what are the two numbers ?
Options: a ) 36 - 48 , b ) 50 - 34 , c ) 60 - 24 , d ) 42 - 42 , e ) 25 - 37
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 62 : word problem = 62 the line over x + 12 is a grouping symbol called a vinculum . it saves us writing parentheses . we have : 2 x = 62 â ˆ ’ 12 = 50 . x = 50 / 2 = 25 . this is the first number . therefore the other number is x + 12 = 25 + 12 = 37 . the sum of 25 + 37 is 62 . e"
Answer: e
Question (physics): a tank is filled by 3 pipes a , b , c in 5 hours . pipe c is twice as fast as b and b is twice as fast as a . how much will pipe a alone take to fill the tank ?
Options: a ) 25 hr , b ) 35 hr , c ) 40 hr , d ) 20 hr , e ) 50 hr
Rationale: "suppose pipe a alone take x hours to fill the tank then pipe b and c will take x / 2 and x / 4 hours respectively to fill the tank . 1 / x + 2 / x + 4 / x = 1 / 5 7 / x = 1 / 5 x = 35 hours answer is b"
Answer: b
Question (physics): if 12 men and 16 boys can do a piece of work in 5 days ; 13 men and 24 boys can do it in 4 days , then the ratio of the daily work done by a man to that of a boy is ?
Options: a ) 2 : 1 , b ) 2 : 8 , c ) 2 : 9 , d ) 2 : 5 , e ) 2 : 2
Rationale: "let 1 man ' s 1 day work = x and 1 boy ' s 1 day work = y . then , 12 x + 16 y = 1 / 5 and 13 x + 24 y = 1 / 4 solving these two equations , we get : x = 1 / 100 and y = 1 / 200 required ratio = x : y = 1 / 100 : 1 / 200 = 2 : 1 . answer : a"
Answer: a
Question (gain): a certain company ’ s profit in 1996 was 20 percent greater than its profit in 1995 , and its profit in 1997 was 20 percent greater than its profit in 1996 . the company ’ s profit in 1997 was what percent greater than its profit in 1995 ?
Options: a ) 5 % , b ) 18 % , c ) 33 % , d ) 44 % , e ) 38 %
Rationale: "profit in 1995 - 100 profit in 1996 - 120 % increae profit in 1997 in comparison to 1995 = 20 + 120 * 20 % = 44 correct option : d"
Answer: d
Question (gain): a cycle is bought for rs . 670 and sold for rs . 880 , find the gain percent ?
Options: a ) 31 % , b ) 35 % , c ) 54 % , d ) 38 % , e ) 80 %
Rationale: "explanation : 670 - - - - 210 100 - - - - ? = > 31 % answer : a"
Answer: a
Question (general): a certain no . when divided by 20 leaves a remainder 25 , what is the remainder if the same no . be divided by 15 ?
Options: a ) 3 , b ) 4 , c ) 6 , d ) 8 , e ) 9
Rationale: "explanation : 20 + 25 = 45 / 15 = 3 ( remainder ) a"
Answer: a
Question (gain): the s . i . on a certain sum of money for 6 years at 14 % per annum is half the c . i . on rs . 7000 for 2 years at 7 % per annum . the sum placed on s . i . is ?
Options: a ) 603.75 , b ) 555.75 , c ) 569.55 , d ) 256.25 , e ) 563.23
Rationale: c . i . = [ 7000 * ( 1 + 7 / 100 ) 2 - 7000 ] = ( 7000 * 11 / 10 * 11 / 10 - 7000 ) = rs . 1014.3 . sum = ( 507.15 * 100 ) / ( 6 * 14 ) = rs . 603.75 answer : a
Answer: a
Question (gain): selling an kite for rs . 30 , a shop keeper gains 20 % . during a clearance sale , the shopkeeper allows a discount of 10 % on the marked price . his gain percent during the sale is ?
Options: a ) 8 % , b ) 10 % , c ) 11 % , d ) 15 % , e ) 20 %
Rationale: explanation : marked price = rs . 30 c . p . = 100 / 120 * 30 = rs . 25 sale price = 90 % of rs . 30 = rs . 27 required gain % = 0.2 / 25 * 100 = 8 % . answer : a
Answer: a
Question (gain): a fruit seller sells mangoes at the rate of rs . 10 per kg and thereby loses 15 % . at what price per kg , he should have sold them to make a profit of 5 %
Options: a ) rs 8.81 , b ) rs 9.35 , c ) rs 10.35 , d ) rs 12.35 , e ) none of these
Rationale: "explanation : 85 : 10 = 105 : x x = ( 10 × 105 / 85 ) = rs 12.35 option d"
Answer: d
Question (general): a certain galaxy is known to comprise approximately 3 x 10 ^ 11 stars . of every 50 million of these stars , one is larger in mass than our sun . approximately how many stars in this galaxy are larger than the sun ?
Options: a ) 800 , b ) 6,000 , c ) 8,000 , d ) 12,000 , e ) 80,000
Rationale: "total no . of stars on galaxy = 3 * 10 ^ 11 of every 50 million stars , 1 is larger than sun . 1 million = 10 ^ 6 therofore , 50 million = 50 * 10 ^ 6 total no . of stars larger than sun = 3 * 10 ^ 11 / 50 * 10 ^ 6 = 30 * 10 ^ 3 / 5 = 6000 therefore answer is b"
Answer: b
Question (gain): a hostel had provisions for 250 men for 32 days . if 50 men left the hostel , how long will the food last at the same rate ?
Options: a ) 30 , b ) 40 , c ) 50 , d ) 60 , e ) 65
Rationale: "a hostel had provisions for 250 men for 32 days if 50 men leaves the hostel , remaining men = 250 - 50 = 200 we need to find out how long the food will last for these 200 men . let the required number of days = x days more men , less days ( indirect proportion ) ( men ) 250 : 200 : : x : 32 250 × 32 = 200 x 5 × 32 = 4 x x = 5 × 8 = 40 answer b"
Answer: b
Question (geometry): a cube has a volume of 216 cubic feet . if a similar cube is twice as long , twice as wide , and twice as high , then the volume , in cubic feet of such cube is ?
Options: a ) 24 , b ) 1728 , c ) 64 , d ) 80 , e ) 100
Rationale: "volume = 216 = side ^ 3 i . e . side of cube = 6 new cube has dimensions 12 , 12 , and 12 as all sides are twice of teh side of first cube volume = 12 * 12 * 12 = 1728 square feet answer : option b"
Answer: b
Question (general): how many different values of positive integer x , for which | x + 5 | < x , are there ?
Options: a ) 0 , b ) 2 , c ) 3 , d ) 8 , e ) 16
Rationale: "answer e i opted to put the random value option . i used 0 , 5 , - 5 and the the extreme of 40 and - 40 . . i was able to solve it in 1 : 09 e"
Answer: e
Question (gain): if a speaks the truth 80 % of the times , b speaks the truth 60 % of the times . what is the probability that they tell the truth at the same time
Options: a ) 0.49 , b ) 0.48 , c ) 0.41 , d ) 0.482 , e ) 0.411
Rationale: explanation : probability that a speaks truth is 80 / 100 = 0.8 probability that b speaks truth is 60 / 100 = 0.6 since both a and b are independent of each other so probability of a intersection b is p ( a ) × p ( b ) = 0.8 × 0.6 = 0.48 answer : b
Answer: b
Question (general): tickets numbered from 1 to 27 are mixed and then a ticket is selected randomly . what is the probability that the selected ticket bears a number which is a multiple of 3 ?
Options: a ) 1 / 3 , b ) 2 / 5 , c ) 3 / 10 , d ) 3 / 7 , e ) 1 / 7
Rationale: "here , s = [ 1 , 2 , 3 , 4 , … . , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 ] let e = event of getting a multiple of 3 = [ 3 , 6 , 9 , 12 , 15 , 18 , 21 , 24 , 27 ] p ( e ) = n ( e ) / n ( s ) = 9 / 27 = 1 / 3 the answer is a ."
Answer: a
Question (gain): a man can row downstream at the rate of 12 km / hr and upstream at 6 km / hr . find man ' s rate in still water and the rate of current ?
Options: a ) 9,6 , b ) 6,3 , c ) 9,3 , d ) 6,6 , e ) none of these
Rationale: "explanation : rate of still water = 1 / 2 ( 12 + 6 ) = 9 km / hr rate of current = 1 / 2 ( 12 - 6 ) = 3 km / hr answer : option c"
Answer: c
Question (general): if a is an integer greater than 7 but less than 25 and b is an integer greater than 34 but less than 44 , what is the range of a / b ?
Options: a ) 21 / 34 , b ) 1 / 12 , c ) 15 / 64 , d ) 17 / 35 , e ) 7 / 6
Rationale: "the way to approach this problem is 7 < a < 25 and 34 < b < 41 minimum possible value of a is 8 and maximum is 24 minimum possible value of b is 35 and maximum is 40 range = max a / min b - min a / max b ( highest - lowest ) 24 / 35 - 8 / 40 = 17 / 35 hence d"
Answer: d
Question (gain): if the simple interest on a sum of money for 2 years at 5 % per annum is rs . 55 , what is the compound interest on the same sum at the rate and for the same time ?
Options: a ) s . 56.37 , b ) s . 53.22 , c ) s . 56.219 , d ) s . 51.18 , e ) s . 51.11
Rationale: "explanation : sum = ( 55 * 100 ) / ( 2 * 5 ) = rs . 550 amount = [ 550 * ( 1 + 5 / 100 ) 2 ] = rs . 606.375 c . i . = ( 606.375 - 550 ) = rs . 56.37 answer : a"
Answer: a
Question (general): if 2 ^ ( 2 w ) = 8 ^ ( w − 4 ) , what is the value of w ?
Options: a ) 3 , b ) 6 , c ) 9 , d ) 12 , e ) 15
Rationale: 2 ^ ( 2 w ) = 8 ^ ( w − 4 ) 2 ^ ( 2 w ) = 2 ^ ( 3 * ( w − 4 ) ) 2 ^ ( 2 w ) = 2 ^ ( 3 w - 12 ) let ' s equate the exponents as the bases are equal . 2 w = 3 w - 12 w = 12 the answer is d .
Answer: d
Question (physics): a is twice as good as b . and together they finish a piece of work in 18 days . in how many days will a alone finish the work
Options: a ) 25 , b ) 27 , c ) 15 , d ) 18 , e ) 21
Rationale: ( a ' s 1 day work ) : ( b ' s 1 day work ) = 2 : 1 a + b 1 day work = 1 / 18 a ' s 1 day work = ( 1 / 18 ) * ( 2 / 3 ) = 1 / 27 a alone can finish the work in 27 days answer is b
Answer: b
Question (general): what is the local value of 7 in the difference of 100889 and local value of 3 in 28943712 ?
Options: a ) 7000 , b ) 700 , c ) 70000 , d ) 70 , e ) 7
Rationale: "100889 - ( local value of 3 ) = 100889 - 3000 = 97889 local value of 7 in 97889 = 7000 a"
Answer: a
Question (general): everyone shakes hands with everyone else in a room . total number of handshakes is 55 . number of persons = ?
Options: a ) 14 , b ) 12 , c ) 11 , d ) 15 , e ) 16
Rationale: "in a room of n people , the number of possible handshakes is c ( n , 2 ) or n ( n - 1 ) / 2 so n ( n - 1 ) / 2 = 55 or n ( n - 1 ) = 110 or n = 11 answer is ( c )"
Answer: c
Question (gain): what will be the fraction of 4 %
Options: a ) 1 / 20 , b ) 1 / 50 , c ) 1 / 75 , d ) 1 / 25 , e ) none of these
Rationale: "explanation : 4 * 1 / 100 = 1 / 25 . friends i know it is quite simple , but trust me while solving percentage questions in hurry we use to do these types of mistake only . so i recommend you to have a bit practise of this option d"
Answer: d
Question (general): the least number which must be subtracted from 670 to make it exactly divisible by 9 is :
Options: a ) a ) 2 , b ) b ) 3 , c ) c ) 4 , d ) d ) 5 , e ) e ) 6
Rationale: "on dividing 670 by 9 , we get remainder = 4 therefore , required number to be subtracted = 4 answer : c"
Answer: c
Question (probability): three unbiased coins are tossed . what is the probability of getting 2 heads and 2 tail ?
Options: a ) 5 / 8 , b ) 1 / 4 , c ) 3 / 8 , d ) 7 / 8 , e ) 1 / 8
Rationale: "let , h - - > head , t - - > tail here s = { ttt , tth , tht , htt , thh , hth , hht , hhh } let e = event of getting 3 heads then e = { thh , hth , hht , tht , tth } p ( e ) = n ( e ) / n ( s ) = 5 / 8 answer is a"
Answer: a
Question (gain): in an election a candidate who gets 84 % of the votes is elected by a majority of 476 votes . what is the total number of votes polled ?
Options: a ) 630 , b ) 700 , c ) 535 , d ) 450 , e ) 815
Rationale: "let the total number of votes polled be x then , votes polled by other candidate = ( 100 - 84 ) % of x = 16 % of x 84 % of x - 16 % of x = 476 68 x / 100 = 476 x = 476 * 100 / 68 = 700 answer is b"
Answer: b
Question (general): 3 numbers are in the ratio 5 : 6 : 8 . the sum of its longest and smallest numbers equals the sum of the third number and 49 . find the third number ?
Options: a ) a ) 54 , b ) b ) 75 , c ) c ) 48 , d ) d ) 42 , e ) e ) 63
Rationale: let the numbers be 5 x , 6 x , 8 x . largest number = 8 x . smallest number = 5 x . third number = 6 x . 8 x + 5 x = 6 x + 49 7 x = 49 = > x = 7 6 x = 42 = > third number is 42 . answer : d
Answer: d
Question (gain): the price of an item changed from $ 120 to $ 100 . then later the price decreased again from $ 100 to $ 80 . which of the two decreases was larger in percentage term ?
Options: a ) 10 % , b ) 20 % , c ) 30 % , d ) 40 % , e ) 50 %
Rationale: first decrease in percent part / whole = ( 120 - 100 ) / 120 = 0.17 = 17 % second decrease in percent part / whole = ( 100 - 80 ) / 100 = 0.20 = 20 % the second decrease was larger in percent term . the part were the same in both cases but the whole was smaller in the second decrease . answer b
Answer: b
Question (general): what is the next number : 3 , 11 , 83 , __
Options: a ) 631 , b ) 731 , c ) 831 , d ) 849 , e ) 901
Rationale: "3 ^ 0 + 2 = 3 3 ^ 2 + 2 = 11 3 ^ 4 + 2 = 83 3 ^ 6 + 2 = 731 the answer is b ."
Answer: b
Question (gain): a man sells a car to his friend at 14 % loss . if the friend sells it for rs . 54000 and gains 20 % , the original c . p . of the car was :
Options: a ) rs . 22325.58 , b ) rs . 32325.58 , c ) rs . 52325.58 , d ) rs . 62325.58 , e ) none of these
Rationale: "explanation : s . p = rs . 54,000 . gain earned = 20 % c . p = rs . [ 100 / 120 ã — 54000 ] = rs . 45000 this is the price the first person sold to the second at at loss of 14 % . now s . p = rs . 45000 and loss = 14 % c . p . rs . [ 100 / 86 ã — 45000 ] = rs . 52325.58 . correct option : c"
Answer: c
Question (gain): a dishonest shopkeeper professes to sell pulses at the cost price , but he uses a false weight of 960 gm . for a kg . his gain is … % .
Options: a ) 4.16 % , b ) 5.36 % , c ) 4.26 % , d ) 6.26 % , e ) 7.26 %
Rationale: "his percentage gain is 100 * 40 / 960 as he is gaining 40 units for his purchase of 960 units . so 4.16 % . answer : a"
Answer: a
Question (geometry): if two sides of a triangle have lengths 3 and 8 , which of the following could be the perimeter of the triangle ? i . 9 ii . 15 iii . 19
Options: a ) none
b ) i only
c ) ii only
d ) iii only
e ) i , ii , and iii
Rationale: the length of any side of a triangle must be larger than the positive difference of the other two sides , but smaller than the sum of the other two sides . therefore : ( 8 - 3 ) < { third side } < ( 8 + 3 ) . 5 < { third side } < 11 . perimeter = { third side } + 8 + 3 = { third side } + 11 . 16 < { perimeter } < 22 . answer d
Answer: d
Question (gain): increasing the original price of an article by 10 percent and then increasing the new price by 10 percent is equivalent to increasing the original price by
Options: a ) 20 % , b ) 20.5 % , c ) 20.8 % , d ) 21 % , e ) 21.8 %
Rationale: "1.1 * 1.1 * x = 1.21 * x the answer is d ."
Answer: d
Question (physics): a can run 1.5 km distance in 2 min 20 seconds , while b can run this distance in 2 min 30 sec . by how much distance can a beat b ?
Options: a ) 90 m , b ) 100 m , c ) 120 m , d ) 180 m , e ) 190 m
Rationale: "a takes time 2.20 minutes = 140 sec b takes time 2.30 minutes = 150 sec diffrence = 150 - 140 = 10 sec now we are to find distance covered in 10 sec by b 150 sec = 1500 m 1 sec = 10 m 10 sec = 10 x 10 = 100 m answer : b"
Answer: b
Question (gain): a 6 % stock yields 8 % . the market value of the stock is ?
Options: a ) rs . 11 , b ) rs . 75 , c ) rs . 17 , d ) rs . 16 , e ) rs . 22
Rationale: "for an income of rs . 8 , investment = rs . 100 . for an income of rs 6 , investment = rs . \ inline \ left ( \ frac { 100 } { 8 } \ times 6 \ right ) = rs . 75 market value of rs . 100 stock = rs . 75 . answer : b"
Answer: b
Question (geometry): if y is the smallest positive integer such that 6300 multiplied by y is the square of an integer , then y must be
Options: a ) 5 , b ) 7 , c ) 15 , d ) 35 , e ) 45
Rationale: "6300 = 2 ^ 2 * 3 ^ 2 * 5 ^ 2 * 7 to be perfect square , we need to multiply by at least 7 . the answer is b ."
Answer: b