Cheukting/mathqa huggingface dataset:
Question (geometry): a pyramid has a square base of 6 cm , and the four lateral faces are four congruent equilateral triangles . what is the total surface area of the pyramid in square cm ?
Options: a ) 36 + 18 * sqrt ( 3 )
b ) 36 + 36 * sqrt ( 3 )
c ) 72
d ) 72 + 36 * sqrt ( 3 )
e ) 72 + 72 * sqrt ( 3 )
Rationale: first of all , of course , the base has an area of 36 . for the lateral surfaces , it would be helpful to remember the formula for the area of an equilateral triangle . the area of one equilateral triangle is a = ( s ^ 2 * sqrt { 3 } ) / 4 . we know the side of the equilateral triangle must be the same as the square : s = 6 . thus , one of these equilateral triangles has an area of a = ( 6 ^ 2 * sqrt { 3 } ) / 4 = 9 * sqrt { 3 } . there are four identical triangles , so their combined area is a = 36 * sqrt { 3 } . now , add the square base , for a total surface area of a = 36 + 36 * sqrt { 3 } . answer = b
Answer: b
Question (gain): sonika deposited rs . 8000 which amounted to rs . 9200 after 3 years at simple interest . had the interest been 1.5 % more . she would get how much ?
Options: a ) 9560 , b ) 96288 , c ) 26667 , d ) 1662 , e ) 2882
Rationale: ( 8000 * 3 * 1.5 ) / 100 = 360 9200 - - - - - - - - 9560 answer : a
Answer: a
Question (geometry): a horse is tethered to one corner of a rectangular grassy field 36 m by 20 m with a rope 12 m long . over how much area of the field can it graze ?
Options: a ) 154 cm 2 , b ) 113 m 2 , c ) 123 m 2 , d ) 115 m 2 , e ) none of these
Rationale: "area of the shaded portion = 1 ⁄ 4 × π × ( 12 ) 2 = 113 m 2 answer b"
Answer: b
Question (general): there are 6 people in the elevator . their average weight is 170 lbs . another person enters the elevator , and increases the average weight to 151 lbs . what is the weight of the 7 th person .
Options: a ) 37 , b ) 168 , c ) 189 , d ) 190 , e ) 200
Rationale: "solution average of 7 people after the last one enters = 151 . â ˆ ´ required weight = ( 7 x 151 ) - ( 6 x 170 ) = 1057 - 1020 = 37 . 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 27 seconds . find the length of the faster train ?
Options: a ) 270 m , b ) 189 m , c ) 278 m , d ) 279 m , e ) 917 m
Rationale: "relative speed = ( 72 - 36 ) * 5 / 18 = 2 * 5 = 10 mps . distance covered in 27 sec = 27 * 10 = 270 m . the length of the faster train = 270 m . answer : a"
Answer: a
Question (general): find the smallest number in gp whose sum is 38 and product is 1728
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "let x , y , z be the numbers in geometric progression ? y ^ 2 = xz x + y + z = 38 xyz = 1728 xyz = xzy = y ^ 2 y = y ^ 3 = 1728 y = 12 y ^ 2 = xz = 144 z = 144 / x x + y + z = x + 12 + 144 / x = 38 x ^ 2 + 12 x + 144 = 38 x x ^ 2 - 26 x + 144 = 0 ( x - 18 ) ( x - 8 ) = 0 x = 8,18 if x = 8 , z = 38 - 8 - 12 = 18 the numbers are 8,12 , 18 their sum is 38 their product is 1,728 the smallest number is 8 answer : d"
Answer: d
Question (probability): a fair coin is tossed 4 times . what is the probability of getting at least 2 tails ?
Options: a ) 1 / 16 , b ) 1 / 2 , c ) 3 / 16 , d ) 11 / 16 , e ) 3 / 8
Rationale: "let ' s find the probability of the opposite event and subtract this value from 1 . the opposite event would be getting zero tails ( so all heads ) or 1 tail . p ( hhhh ) = ( 12 ) 4 = 116 p ( hhhh ) = ( 12 ) 4 = 116 . p ( thhh ) = 4 ! 3 ! ∗ ( 12 ) 4 = 416 p ( thhh ) = 4 ! 3 ! ∗ ( 12 ) 4 = 416 , we are multiplying by 4 ! 3 ! 4 ! 3 ! since thhh scenario can occur in number of ways : thhh , hthh , hhth , or hhht ( notice that 4 ! 3 ! 4 ! 3 ! basically gives number of arrangements of 4 letters thhh out of which 3 h ' s are identcal ) . p ( t ≥ 2 ) = 1 − ( 116 + 416 ) = 1116 p ( t ≥ 2 ) = 1 − ( 116 + 416 ) = 1116 . answer : d ."
Answer: d
Question (physics): find the area of trapezium whose parallel sides are 30 cm and 18 cm long , and the distance between them is 15 cm .
Options: a ) 227 , b ) 299 , c ) 360 , d ) 161 , e ) 212
Rationale: "area of a trapezium = 1 / 2 ( sum of parallel sides ) * ( perpendicular distance between them ) = 1 / 2 ( 30 + 18 ) * ( 15 ) = 360 cm 2 answer : c"
Answer: c
Question (general): the mean of 50 observations is 100 . but later he found that there is decrements of 13 from each observations . what is the the updated mean is ?
Options: a ) 87 , b ) 97 , c ) 67 , d ) 57 , e ) 46
Rationale: "87 answer is a"
Answer: a
Question (general): if x and y are integers such that x ^ 2 = y and xy = 27 , then x – y = ?
Options: a ) - 30 , b ) - 20 , c ) - 6 , d ) 5 , e ) 20
Rationale: here x and y are integers . x ^ 2 = y xy = 27 . substitute x ^ 2 = y in xy = > x ^ 3 = 27 . here x 3 is positive , x is also positive . x = 3 then y = 9 . x - y = - 6 so option c is correct
Answer: c
Question (general): a pupil ' s marks were wrongly entered as 83 instead of 63 . due to the average marks for the class got increased by half . the number of pupils in the class is ?
Options: a ) 13 , b ) 18 , c ) 40 , d ) 82 , e ) 43
Rationale: "let there be x pupils in the class . total increase in marks = ( x * 1 / 2 ) = x / 2 x / 2 = ( 83 - 63 ) = > x / 2 = 20 = > x = 40 answer : c"
Answer: c
Question (physics): a trader sells 23 meters of cloth for rs . 529 at the profit of rs . 5 per metre of cloth . what is the cost price of one metre of cloth ?
Options: a ) 26 , b ) 88 , c ) 90 , d ) 42 , e ) 18
Rationale: "sp of 1 m of cloth = 529 / 23 = rs . 23 cp of 1 m of cloth = sp of 1 m of cloth - profit on 1 m of cloth = rs . 23 - rs . 5 = rs . 18 answer : e"
Answer: e
Question (gain): if an article is sold at 18 % profit instead of 9 % profit , then the profit would be $ 54 more . what is the cost price ?
Options: a ) $ 500 , b ) $ 600 , c ) $ 700 , d ) $ 800 , e ) $ 900
Rationale: 9 % * cost price = $ 54 1 % * cost price = $ 54 / 9 = $ 6 the cost price is $ 600 . the answer is b .
Answer: b
Question (physics): if 8 cats can kill 8 rats in 8 minutes , how long will it take 100 cats to kill 100 rats ?
Options: a ) 6 minutes , b ) 7 minutes , c ) 8 minutes , d ) 9 minutes , e ) 10 minutes
Rationale: it will take 8 minutes for 100 cats to kill 100 rats . 1 cat can kill 1 rat in 8 minutes , so 100 cats can kill 100 rats in 8 minutes answer c
Answer: c
Question (gain): peter invested a certain sum of money in a simple interest bond whose value grew to $ 400 at the end of 3 years and to $ 600 at the end of another 2 years . what was the rate of interest in which he invested his sum ?
Options: a ) 100 % , b ) 12.5 % , c ) 67 % , d ) 25 % , e ) 33 %
Rationale: "lets assume the principal amount ( initial amount invested ) to be p rate of interest to berand time as t . we need to find r now after a time of 3 years the principal p amounts to $ 400 and after a time of 5 years ( question says after another 5 years so 3 + 2 ) p becomes $ 600 . formulating the above data amount ( a 1 ) at end of 3 years a 1 = p ( 1 + 3 r / 100 ) = 400 amount ( a 2 ) at end of 8 years a 2 = p ( 1 + 5 r / 100 ) = 600 dividing a 2 by a 1 we get ( 1 + 5 r / 100 ) / ( 1 + 3 r / 100 ) = 6 / 8 after cross multiplication we are left with r = 100 option : a"
Answer: a
Question (general): 3 / 4 of 1 / 2 of 2 / 5 of 5080 = ?
Options: a ) 392 , b ) 229 , c ) 753 , d ) 493 , e ) 762
Rationale: "e 762 ? = 5080 * ( 2 / 5 ) * ( 1 / 2 ) * ( 3 / 4 ) = 762"
Answer: e
Question (general): how many integers k greater than 100 and less than 800 are there such that if the hundreds and the unit digits of k are reversed , the resulting integer is k + 99 ?
Options: a ) 50 , b ) 60 , c ) 70 , d ) 80 , e ) 90
Rationale: "not sure if this is the shortest . . but this is how i did this there are 6 sets of integers with hundreds and units digits exchanged that satisfies k + 99 . 1 . 102 | 201 ( satisfies k + 99 , where k = 102 ) 2 . 203 | 302 ( satisfies k + 99 , where k = 203 ) 3 . . . . 4 . . . . 5 . . . . 6 . 607 | 708 each set has 10 such numbers . 1 . 102 | 201 ( still k + 99 holds good ) 2 . 112 | 211 3 . 122 | 221 4 . 132 | 231 5 . . . . 6 . . . . 7 . . . . 8 . . . . 9 . 182 | 281 10 . 192 | 291 therefore , 6 sets with 10 such number in each set will give 6 x 10 = 60 integers . b"
Answer: b
Question (gain): √ 4 percent of 4 √ 4 =
Options: a ) 0.16 , b ) 0.17 , c ) 0.18 , d ) 0.2 , e ) 0.19
Rationale: √ 4 = 2 so , √ 4 percent of 4 √ 4 = 2 percent of ( 4 ) ( 2 ) = ( 2 / 100 ) ( 8 ) = 16 / 100 = 0.16 answer : a
Answer: a
Question (general): a palindrome is a number that reads the same forward and backward , such as 616 . how many even , 4 - digit numbers are palindromes ?
Options: a ) 40 , b ) 45 , c ) 50 , d ) 90 , e ) 2500
Rationale: "first recognize you only need to consider the first two digits ( because the second two are just the first two flipped ) there are 90 possibilities for the first two digits of a 4 digit number , 10 - 99 inclusive . everything starting with a 2,4 , 6,8 will be odd , which is 4 / 9 ths of the combinations . 4 / 9 * 90 = 40 answer : a"
Answer: a
Question (physics): 12 men work 8 hours per day to complete the work in 10 days . to complete the same work in 8 days , working 12 hours a day , the number of men required ?
Options: a ) 11 days , b ) 12 days , c ) 9 days , d ) 8 days , e ) 10 days
Rationale: "that is , 1 work done = 12 × 8 × 10 then , 12 8 × 10 = ? × 12 × 8 ? ( i . e . no . of men required ) = 12 × 8 × 10 / 12 × 8 = 8 days e )"
Answer: e
Question (general): 8 people decided to split the restaurant bill evenly . if the bill was $ 214.15 dollars , how much money did they 1 cent is the smallest unit ?
Options: a ) $ 214.16 , b ) $ 214.17 , c ) $ 214.18 , d ) $ 214.19 , e ) $ 214.20
Rationale: "if the last three digits of a whole number are divisible by 8 , then the entire number is divisible by 8 the last 3 digit 415 not divisible by a hence , we need to add 1 to this number for it to be divisible by 8 correct option : a"
Answer: a
Question (general): in a fuel station the service costs $ 1.50 per car , every liter of fuel costs 0.35 $ . assuming that you own 3 limos and 2 fleet vans and all fuel tanks are empty . how much will it cost to fuel all cars together if a limo tank is 32 liters and an fleet van tank is 75 % bigger ?
Options: a ) $ 78.80 , b ) $ 79.80 , c ) $ 78.90 , d ) $ 79.90 , e ) $ 77.80
Rationale: "lots of calculations . 1.50 * 4 + 3 * . 35 * 32 + 2 * ( 7 / 4 ) * 32 * . 35 answer = $ 78.80 the correct option is a"
Answer: a
Question (general): a soccer store typically sells replica jerseys at a discount of 30 percent to 50 percent off list price . during the annual summer sale , everything in the store is an additional 20 percent off the original list price . if a replica jersey ' s list price is $ 80 , approximately what y percent of the list price is the lowest possible sale price ?
Options: a ) 20 , b ) 25 , c ) 30 , d ) 40 , e ) 50
Rationale: "let the list price be 2 x for min sale price , the first discount given should be 50 % , 2 x becomes x here now , during summer sale additional 20 % off is given ie sale price becomes 0.8 x it is given lise price is $ 80 = > 2 x = 80 = > x = 40 and 0.8 x = 32 so lowest sale price is 32 , which y is 40 % of 80 hence , d is the answer"
Answer: d
Question (general): each year for 4 years , a farmer increased the number of trees in a certain orchard by 1 / 4 of the number of trees in the orchard of the preceding year . if all of the trees thrived and there were 12500 trees in the orchard at the end of 4 year period , how many trees were in the orchard at the beginning of the 4 year period .
Options: a ) 5113 , b ) 5117 , c ) 5120 , d ) 8119 , e ) 10115
Rationale: "trees increase by 1 / 4 the number of trees in preceding year . hence , correct answer must be divisible by 4 . based on divisibility rules , if last 2 digits are divisible by 4 then the number is divisible by 4 . thus , we can eliminate a , b , d , e the answer to be c again , trees increase by 1 / 4 the number of trees in preceding year . hence , the number of trees increase by 5 / 4 times the number of trees the preceding year . if x = initial number of trees = 5120 year 1 = 5 / 4 x year 2 = ( 5 / 4 ) ( 5 / 4 ) x year 3 = ( 5 / 4 ) ( 5 / 4 ) ( 5 / 4 ) x year 4 = ( 5 / 4 ) ( 5 / 4 ) ( 5 / 4 ) ( 5 / 4 ) x only for answer d : ( 5 / 4 ) ( 5 / 4 ) ( 5 / 4 ) ( 5 / 4 ) 5120 = 12500 hence , correct answer = c"
Answer: c
Question (gain): a and b began business with rs . 3000 and rs . 4000 after 8 months , a withdraws rs . 1000 and b advances rs . 1000.00001 more . at the end of the year , their profits amounted to rs . 714 find the share of a .
Options: a ) 240 , b ) 272 , c ) 379 , d ) 277 , e ) 122
Rationale: explanation : ( 3 * 8 + 2 * 4 ) : ( 4 * 8 + 5 * 4 ) 8 : 13 8 / 21 * 714 = 272 answer : b
Answer: b
Question (physics): a train 120 m long running at 60 kmph crosses a platform in 35 sec . what is the length of the platform ?
Options: a ) 338 , b ) 277 , c ) 463 , d ) 456 , e ) 271
Rationale: "d = 60 * 5 / 18 = 35 = 583 – 120 = 463 answer : c"
Answer: c
Question (gain): jar a has 6 % more marbles than jar b . what percent of marbles from jar a need to be moved into jar b so that both jars have equal marbles ?
Options: a ) 2.8 % , b ) 3.0 % , c ) 3.2 % , d ) 3.4 % , e ) 3.6 %
Rationale: "an easy way to solve this question is by number plugging . assume there are 100 marbles in jar b then in jar a there will be 106 marbles . now , for both jars to have equal marbles we should move 3 marbles from a to b , which is 3 / 106 = ~ 2.8 % of a . answer : a ."
Answer: a
Question (general): for any integer n greater than 1 , n * denotes the product of all the integers from 1 to n , inclusive . how many prime numbers t are there between 6 * + 2 and 6 * + 6 , inclusive ?
Options: a ) none , b ) one , c ) two , d ) three , e ) four
Rationale: "given that n * denotes the product of all the integers from 1 to n , inclusive so , 6 * + 2 = 6 ! + 2 and 6 * + 6 = 6 ! + 6 . now , notice that we can factor out 2 our of 6 ! + 2 so it can not be a prime number , we can factor out 3 our of 6 ! + 3 so it can not be a prime number , we can factor out 4 our of 6 ! + 4 so it can not be a prime number , . . . the same way for all numbers between 6 * + 2 = 6 ! + 2 and 6 * + 6 = 6 ! + 6 , inclusive . which means that there are no primes t in this range . answer : a ."
Answer: a
Question (gain): shawn invested one half of his savings in a bond that paid simple interest for 2 years and received $ 400 as interest . he invested the remaining in a bond that paid compound interest , interest being compounded annually , for the same 2 years at the same rate of interest and received $ 605 as interest . what was the value of his total savings before investing in these two bonds ?
Options: a ) 3000 , b ) 5000 , c ) 2000 , d ) 4000 , e ) 6000
Rationale: "so , we know that shawn received 20 % of the amount he invested in a year . we also know that in one year shawn received $ 200 , thus 0.2 x = $ 200 - - > x = $ 1,000 . since , he invested equal sums in his 2 bonds , then his total savings before investing was 2 * $ 1,000 = $ 2,000 . answer : c"
Answer: c
Question (gain): a tank is filled to one quarter of its capacity with a mixture consisting of water and sodium chloride . the proportion of sodium chloride in the tank is 40 % by volume and the capacity of the tank is 24 gallons . if the water evaporates from the tank at the rate of 0.5 gallons per hour , and the amount of sodium chloride stays the same , what will be the concentration of water in the mixture in 4 hours ?
Options: a ) 40 % , b ) 44 % , c ) 48 % , d ) 52 % , e ) 56 %
Rationale: "the number of gallons in the tank is ( 1 / 4 ) 24 = 6 gallons the amount of sodium chloride is 0.4 ( 6 ) = 2.4 gallons at the start , the amount of water is 0.6 ( 6 ) = 3.6 gallons after 4 hours , the amount of water is 3.6 - 0.5 ( 4 ) = 1.6 gallons the concentration of water is 1.6 / ( 2.4 + 1.6 ) = 40 % the answer is a ."
Answer: a
Question (other): what number has a 5 : 1 ratio to the number 10 ?
Options: a ) 74 , b ) 50 , c ) 94 , d ) 59 , e ) 48
Rationale: "answer : option b explanation : 5 : 1 = x : 10 x = 50 answer : option b"
Answer: b
Question (physics): a 125 meter long train crosses a man standing on the platform in 5 sec . what is the speed of the train ?
Options: a ) 229 , b ) 108 , c ) 278 , d ) 126 , e ) 90
Rationale: "s = 125 / 5 * 18 / 5 = 90 kmph answer : e"
Answer: e
Question (physics): excluding stoppages , the speed of a bus is 80 km / hr and including stoppages , it is 70 km / hr . for how many minutes does the bus stop per hour ?
Options: a ) 11 min , b ) 10 min , c ) 8 min , d ) 6 min , e ) 5 min
Rationale: "due to stoppages , it covers 10 km less . time taken to cover 10 km = 10 / 80 * 60 = 8 min . answer : c"
Answer: c
Question (physics): a , b and c can do a piece of work in 7 days , 14 days and 28 days respectively . how long will they take to finish the work , if all the three work together ?
Options: a ) 4 , b ) 9 , c ) 2 , d ) 11 , e ) none
Rationale: "1 / 7 + 1 / 14 + 1 / 28 = 7 / 28 = 1 / 4 all three can finish the work in 4 days answer : a"
Answer: a
Question (general): in the youth summer village there are 200 people , 100 of them are not working , 75 of them have families and 125 of them like to sing in the shower . what is the largest possible number of people in the village , which are working , that do n ' t have families and that are singing in the shower ?
Options: a ) 125 , b ) 150 , c ) 100 , d ) 130 , e ) 140
Rationale: total = 200 not working = 100 having family = 75 like to sing in shower = 125 working = 200 - 100 = 100 not having family = 200 - 75 = 125 like to sing in shower = 125 largest possible number is the lowest possible among the above thus 100 c
Answer: c
Question (other): nitin ranks 18 th in a class of 49 students . what is rank from the last ?
Options: a ) 33 , b ) 38 , c ) 32 , d ) 28 , e ) 19
Rationale: "explanation : number students behind the nitin in rank = ( 49 - 18 ) = 31 nitin is 32 nd from the last answer : c ) 32"
Answer: c
Question (physics): lamp a flashes every 6 seconds , lamp b flashes every 8 seconds , lamp c flashes every 10 seconds . at a certain instant of time all 3 lamps flash simultaneously . during the period of 6 minutes after that how many times will exactly two lamps flash ? ( please include any flash of exactly two lights which occurs at the 6 minute mark . )
Options: a ) 24 , b ) 25 , c ) 26 , d ) 27 , e ) 28
Rationale: 6 minutes is 360 seconds . lamp a and lamp b will flash together every 24 seconds . 360 / 24 = 15 . in the time period , lamp a and lamp b will flash together 15 times . lamp a and lamp c will flash together every 30 seconds . 360 / 30 = 12 . in the time period , lamp a and lamp c will flash together 12 times . lamp b and lamp c will flash together every 40 seconds . 360 / 40 = 9 . in the time period , lamp b and lamp c will flash together 9 times . all three lights will flash together every 2 * 2 * 2 * 3 * 5 = 120 seconds . 360 / 120 = 3 . we have counted these triple flashes three times , so we need to subtract three times the number of times that all three lights flash together . the number of times that exactly two lights flash together is 15 + 12 + 9 - 9 = 27 times . the answer is d .
Answer: d
Question (general): when positive integer x is divided by positive integer y , the result is 59.32 . what is the sum q of all possible 2 - digit remainders for x / y ?
Options: a ) 560 , b ) 616 , c ) 672 , d ) 728 , e ) 784
Rationale: "ans b 616 . . . remainders = . 32 = 32 / 100 = 8 / 25 = 16 / 50 and so on . . so two digit remainders are 16 + 24 + 32 + . . . . + 96 . . q = 8 ( 2 + 3 + 4 . . . . + 12 ) = 616"
Answer: b
Question (gain): a man walking at a rate of 10 km / hr crosses a bridge in 12 minutes . the length of the bridge is ?
Options: a ) 2000 , b ) 1492 , c ) 1667 , d ) 1254 , e ) 1112
Rationale: speed = 10 * 5 / 18 = 50 / 18 m / sec distance covered in 10 minutes = 50 / 18 * 12 * 60 = 2000 m answer is a
Answer: a
Question (gain): there are 1000 students in a school and among them 30 % of them attends chess class . 10 % of the students who are in the chess class are also enrolled for swimming . no other students are interested in swimming so how many will attend the swimming class if all enrolled attends ?
Options: a ) 1 , b ) 10 , c ) 100 , d ) 30 , e ) 20
Rationale: 30 % of 1000 gives 300 . so 300 attends chess and 10 % of 300 gives 30 . so 30 enrolled for swimming answer : d
Answer: d
Question (gain): a computer store offers employees a 10 % discount off the retail price . if the store purchased a computer from the manufacturer for $ 800 dollars and marked up the price 10 % to the final retail price , how much would an employee save if he purchased the computer at the employee discount ( 10 % off retail price ) as opposed to the final retail price .
Options: a ) 86 , b ) 88 , c ) 90 , d ) 92 , e ) 94
Rationale: "cost price = 800 profit = 10 % = 10 % of 800 = 80 selling price = cp + profit sp = 880 a discount of 10 % to employees means 10 % off on 880 so 10 % of 880 = 88 ans b"
Answer: b
Question (gain): exactly 15 % of the reporters for a certain wire service cover local politics in country x . if 25 % of the reporters who cover politics for the wire service do not cover local politics in country x , what percent of the reporters for the wire service do not cover politics ?
Options: a ) 20 % , b ) 42 % , c ) 44 % , d ) 80 % , e ) 84 %
Rationale: "let ' s assume there are 100 reporters - - > 15 reporters cover local politics . now , as 25 % of the reporters who cover all politics do not cover local politics then the rest 75 % of the reporters who cover politics do cover local politics , so if there are x reporters who cover politics then 75 % of them equal to 15 ( # of reporters who cover local politics ) : 0.75 x = 15 - - > x = 20 , hence 20 reporters cover politics and the rest 100 - 20 = 80 reporters do not cover politics at all . answer : d ."
Answer: d
Question (gain): two numbers are respectively 50 % and 20 % more than a third number . the percentage that is first of the second is ?
Options: a ) 125 % , b ) 97 % , c ) 118 % , d ) 52 % , e ) 83 %
Rationale: "i ii iii 150 120 100 120 - - - - - - - - - - 150 100 - - - - - - - - - - - ? = > 125 % answer : a"
Answer: a
Question (general): of 70 players on a football team , 43 are throwers . the rest of the team is divided so one third are left - handed and the rest are right handed . assuming that all throwers are right handed , how many right - handed players are there total ?
Options: a ) 54 , b ) 59 , c ) 61 , d ) 71 , e ) 92
Rationale: "total = 70 thrower = 43 rest = 70 - 43 = 27 left handed = 27 / 3 = 9 right handed = 18 if all thrower are right handed then total right handed is 43 + 18 = 61 so c . 61 is the right answer"
Answer: c
Question (physics): in how many seconds will a train 100 meters long pass an oak tree , if the speed of the train is 36 km / hr ?
Options: a ) 6 , b ) 8 , c ) 10 , d ) 12 , e ) 14
Rationale: "speed = 36 * 5 / 18 = 10 m / s time = 100 / 10 = 10 seconds the answer is c ."
Answer: c
Question (gain): a pair of articles was bought for $ 1000 at a discount of 10 % . what must be the marked price of each of the article ?
Options: a ) $ 555.55 , b ) $ 500 , c ) $ 350 , d ) $ 400 , e ) $ 600
Rationale: "s . p . of each of the article = 1000 / 2 = $ 500 let m . p = $ x 90 % of x = 500 x = 500 * 100 / 90 = $ 555.55 answer is a"
Answer: a
Question (gain): what is 15 % of 2 / 3 of 0.5 ?
Options: a ) 0.05 , b ) 0.9 , c ) 9 , d ) 90 , e ) none of the above
Rationale: "the best way to solve these questions is to convert every term into fraction ( 15 / 100 ) * ( 2 / 3 ) * ( 5 / 10 ) = 150 / 3000 = 0.05 option a"
Answer: a
Question (general): the bus fare for two persons for travelling between agra and aligarh id 4 - thirds the train fare between the same places for one person . the total fare paid by 6 persons travelling by bus and 8 persons travelling by train between the two places is rs . 1512 . find the train fare between the two places for one person ?
Options: a ) rs . 126 , b ) rs . 132 , c ) rs . 120 , d ) rs . 114 , e ) none of these
Rationale: let the train fare between the two places for one person be rs . t bus fare between the two places for two persons rs . 4 / 3 t = > 6 / 2 ( 4 / 3 t ) + 8 ( t ) = 1512 = > 12 t = 1512 = > t = 126 . answer : a
Answer: a