regisss/math_qa huggingface dataset:
Problem: 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 12 , and the difference between the total number of strawberries and the total number of blueberries would increase by 76 . each blue box contains how many blueberries ?
Options: a ) 26 , b ) 28 , c ) 30 , d ) 32 , e ) 34
Rationale: "let x be the number of blueberries in each blue box . then there are x + 12 strawberries in each red box . x + ( x + 12 ) = 76 x = 32 the answer is d ."
Answer: d
Problem: 15 men take 20 days of 8 hours each to do a piece of work . how many days of 6 hours each would 21 women take to do the same . if 3 women do as much work as 2 men ?
Options: a ) 27.57 , b ) 28.57 , c ) 29.57 , d ) 30.57 , e ) 32
Rationale: 3 w = 2 m 15 m - - - - - - 20 * 8 hours 21 w - - - - - - x * 6 hours 14 m - - - - - - x * 6 15 * 20 * 8 = 14 * x * 6 x = 28.57 answer : b
Answer: b
Problem: an association of mathematics teachers has 1,500 members . only 525 of these members cast votes in the election for president of the association . what percent of the total membership voted for the winning candidate if the winning candidate received 36 percent of the votes cast ?
Options: a ) 7.5 % , b ) 5.8 % , c ) 4.2 % , d ) 34.5 % , e ) 12.6 %
Rationale: "total umber of members = 1500 number of members that cast votes = 525 since , winning candidate received 36 percent of the votes cast number of votes for winning candidate = ( 36 / 100 ) * 525 = 189 percent of total membership that voted for winning candidate = ( 189 / 1260 ) * 100 = 12.6 % answer e"
Answer: e
Problem: how many multiples of 10 are there between 81 and 358 ?
Options: a ) 24 , b ) 25 , c ) 26 , d ) 27 , e ) 28
Rationale: "10 * 9 = 90 10 * 35 = 350 total no of multiples = ( 35 - 9 ) + 1 = 27 answer d"
Answer: d
Problem: in a competitive examination in state a , 6 % candidates got selected from the total appeared candidates . states b had an equal number of candidates appeared and 7 % candidates got selected with 80 more candidates got selected than a . what was the number of candidates appeared from each state ?
Options: a ) 7600 , b ) 8000 , c ) 8400 , d ) data inadequate , e ) none of these
Rationale: "solution let the number of candidates appeared from each state be x . then , 7 % of x - 6 % of x = 80 ⇔ 1 % of x = 80 ⇔ x = 80 × 100 = 8000 . answer b"
Answer: b
Problem: a train leaves mumabai at 9 am at a speed of 45 kmph . after one hour , another train leaves mumbai in the same direction as that of the first train at a speed of 90 kmph . when and at what distance from mumbai do the two trains meet ?
Options: a ) 287 , b ) 279 , c ) 90 , d ) 278 , e ) 379
Rationale: "when the second train leaves mumbai the first train covers 45 * 1 = 45 km so , the distance between first train and second train is 45 km at 10.00 am time taken by the trains to meet = distance / relative speed = 45 / ( 90 - 45 ) = 1 hours so , the two trains meet at 2 p . m . the two trains meet 1 * 90 = 90 km away from mumbai . answer : c"
Answer: c
Problem: in 1990 the budgets for projects q and v were $ 660,000 and $ 860,000 , respectively . in each of the next 10 years , the budget for q was increased by $ 30,000 and the budget for v was decreased by $ 10,000 . in which year was the budget for q equal to the budget for v ?
Options: a ) 1992 , b ) 1993 , c ) 1994 , d ) 1995 , e ) 1996
Rationale: "let the no of years it takes is x . 660 + 30 x = 860 - 10 x - - > 40 x = 200 and x = 5 . thus , it happens in 1995 . d ."
Answer: d
Problem: a train 100 m long crosses a platform 200 m long in 15 sec ; find the speed of the train ?
Options: a ) 94 kmph , b ) 58 kmph , c ) 72 kmph , d ) 94 kmph , e ) 59 kmph
Rationale: "d = 100 + 200 = 300 t = 15 s = 300 / 15 * 18 / 5 = 72 kmph answer : c"
Answer: c
Problem: the average salary of 15 people in the shipping department at a certain firm is $ 20,000 . the salary of 5 of the employees is $ 25,000 each and the salary of 4 of the employees is $ 20,000 each . what is the average salary of the remaining employees ?
Options: a ) $ 19,250 , b ) $ 15,800 , c ) $ 18,000 , d ) $ 15,850 , e ) $ 12,300
Rationale: "total salary . . . 15 * 20 k = 300 k 5 emp @ 25 k = 125 k 4 emp @ 20 k = 80 k remaing 6 emp sal = 300 k - 125 k - 80 k = 95 k average = 95 k / 6 = 15800 ans : b"
Answer: b
Problem: if 0.10 of a number is equal to 0.070 of another number , the ratio of the numbers is :
Options: a ) 2 : 3 , b ) 3 : 4 , c ) 7 : 10 , d ) 20 : 3 , e ) 30 : 7
Rationale: "0.10 a = 0.070 b - > a / b = 0.07 / 0.10 = 7 / 10 : . a : b = 7 : 10 answer : c"
Answer: c
Problem: a person spends 1 / 3 rd of the money with him on clothes , 1 / 5 th of the remaining on food and 1 / 4 th of the remaining on travel . now , he is left with rs 600 . how much did he have with him in the beginning ?
Options: a ) s 200 , b ) s 1500 , c ) s 300 , d ) s 450 , e ) s 550
Rationale: "suppose the amount in the beginning was rs ’ x ’ money spent on clothes = rs 1 x / 3 balance = rs 2 x / 3 money spent on food = 1 / 5 of 2 x / 3 = rs 2 x / 15 balance = 2 x / 3 - 2 x / 15 = rs 8 x / 15 money spent on travel = 1 / 4 of 8 x / 15 = rs 2 x / 15 = 8 x / 15 - 2 x / 15 = 6 x / 15 = rs 2 x / 5 therefore 2 x / 5 = 100 = 1500 answer : b"
Answer: b
Problem: a fruit drink is made of orange , watermelon , and grape juice , where 15 percent of the drink is orange juice and 60 percent is watermelon juice . if the drink is made with 30 ounces of grape juice , how many ounces is the drink total ?
Options: a ) 120 , b ) 160 , c ) 190 , d ) 200 , e ) 400
Rationale: let the total number of ounces in the drink be x . % of orange = 15 % % of watermelon = 60 % % of grape = 100 % - 75 % = 25 % 0.25 x = 30 x = 120 therefore there are a total of 120 ounces in the drink . the answer is a .
Answer: a
Problem: sam invested rs . 3000 @ 10 % per annum for one year . if the interest is compounded half - yearly , then the amount received by sam at the end of the year will be ?
Options: a ) 2554.0 , b ) 3387.0 , c ) 2503.0 , d ) 3307.5 , e ) 16537.11
Rationale: "p = rs . 3000 ; r = 10 % p . a . = 5 % per half - year ; t = 1 year = 2 half - year amount = [ 3000 * ( 1 + 5 / 100 ) 2 ] = ( 3000 * 21 / 20 * 21 / 20 ) = rs . 3307.50 answer : d"
Answer: d
Problem: the parameter of a square is equal to the perimeter of a rectangle of length 7.5 cm and breadth 6.5 cm . find the circumference of a semicircle whose diameter is equal to the side of the square . ( round off your answer to two decimal places ) ?
Options: a ) 10.2 , b ) 10.27 , c ) 10.23 , d ) 10.21 , e ) 10.25
Rationale: "let the side of the square be a cm . parameter of the rectangle = 2 ( 7.5 + 5.5 ) = 26 cm parameter of the square = 26 cm i . e . 4 a = 26 a = 6.5 diameter of the semicircle = 6.5 cm circimference of the semicircle = 1 / 2 ( â ˆ  ) ( 6.5 ) = 1 / 2 ( 22 / 7 ) ( 6.5 ) = 143 / 14 = 10.21 cm to two decimal places answer : d"
Answer: d
Problem: a space shuttle orbits the earth at about 12 kilometers per second . this speed is equal to how many kilometers per hour ?
Options: a ) 480 , b ) 2,880 , c ) 4,800 , d ) 28,800 , e ) 43,200
Rationale: "seconds in 1 hours : 60 s in 1 min 60 min in 1 hr 60 * 60 = 3600 sec in 1 hr 12 * 3600 = 43,200 answer : e"
Answer: e
Problem: a collection of books went on sale , and 2 / 3 of them were sold for $ 1.50 each . if none of the 36 remaining books were sold , what was the total amount received for the books that were sold ?
Options: a ) $ 180 , b ) $ 135 , c ) $ 108 , d ) $ 60 , e ) $ 54
Rationale: since 2 / 3 of the books in the collection were sold , 1 / 3 were not sold . the 36 unsold books represent 1 / 3 of the total number of books in the collection , and 2 / 3 of the total number of books equals 2 ( 36 ) or 72 . the total proceeds of the sale was 72 ( $ 1.50 ) or $ 108 . the best answer is therefore c .
Answer: c
Problem: if 213 × 16 = 3408 , then 0.16 × 2.13 is equal to :
Options: a ) 0.3408 , b ) 3.408 , c ) 34.08 , d ) 340.8 , e ) none of these
Rationale: "solution 0.16 × 2.13 = ( 16 / 100 x 213 / 100 ) = ( 16 x 213 / 10000 ) = 3408 / 10000 = 0.3408 . answer a"
Answer: a
Problem: what is the smallest positive integer x such that 80 - x is the cube of a positive integer
Options: a ) 16 , b ) 12 , c ) 47 , d ) 9 , e ) 12
Rationale: "given 80 - x is a perfect cube so we will take 64 = 4 * 4 * 4 80 - x = 64 x = 80 - 64 = 16 correct option is a"
Answer: a
Problem: the l . c . m of two numbers is 495 and their h . c . f is 5 . if the sum of the numbers is 10 , then their difference is :
Options: a ) 10 , b ) 46 , c ) 70 , d ) 90 , e ) 100
Rationale: "let the numbers be x and ( 100 - x ) . then , x ( 100 - x ) = 5 * 495 x 2 - 100 x + 2475 = 0 ( x - 55 ) ( x - 45 ) = 0 x = 55 or 45 the numbers are 45 and 55 . required difference = 55 - 45 = 10 . answer : a"
Answer: a
Problem: if two dice are thrown together , the probability of getting a square number on both the dice is
Options: a ) 5 / 12 , b ) 1 / 3 , c ) 1 / 4 , d ) 1 / 12 , e ) 2 / 3
Rationale: the number of exhaustive outcomes is 36 . let e be the event of getting a sqaure number on both the dice . p ( e ) = 3 / 36 = 1 / 12 . d )
Answer: d
Problem: what is the area of a square field whose diagonal of length 28 m ?
Options: a ) 288 , b ) 289 , c ) 200 , d ) 112 , e ) 392
Rationale: "d 2 / 2 = ( 28 * 28 ) / 2 = 392 answer : e"
Answer: e
Problem: in 1982 and 1983 , company b ’ s operating expenses were $ 12.0 million and $ 13.0 million , respectively , and its revenues were $ 15.6 million and $ 18.8 million , respectively . what was the percent increase in company b ’ s profit ( revenues minus operating expenses ) from 1982 to 1983 ?
Options: a ) 3 % , b ) 61 1 / 9 % , c ) 25 % , d ) 33 1 / 3 % , e ) 60 %
Rationale: "profit in 1982 = 15.6 - 12 = 3.6 million $ profit in 1983 = 18.8 - 13 = 5.8 million $ percentage increase in profit = ( 5.8 - 3.6 ) / 3.6 * 100 % = 61 1 / 9 % answer b"
Answer: b
Problem: 16 machines can do a work in 10 days . how many machines are needed to complete the work in 40 days ?
Options: a ) 10 , b ) 6 , c ) 4 , d ) 7 , e ) 5
Rationale: "required number of machines = 16 * 10 / 40 = 4 answer is c"
Answer: c
Problem: the salary of a , b , c , d , e is rs . 8000 , rs . 5000 , rs . 15000 , rs . 7000 , rs . 9000 per month respectively , then the average salary of a , b , c , d , and e per month is
Options: a ) rs . 7000 , b ) rs . 8000 , c ) rs . 8800 , d ) rs . 9000 , e ) none
Rationale: "answer average salary = 8000 + 5000 + 15000 + 7000 + 9000 / 5 = rs . 8800 correct option : c"
Answer: c
Problem: if n is a prime number greater than 19 , what is the remainder when n ^ 2 is divided by 12 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 5
Rationale: "there are several algebraic ways to solve this question , but the easiest way is as follows : since we can not have two correct answers just pick a prime greater than 19 , square it and see what would be the remainder upon division of it by 12 . n = 23 - - > n ^ 2 = 529 - - > remainder upon division 529 by 12 is 1 . answer : b ."
Answer: b
Problem: total number of 4 digit number do not having the digit 3 or 6 .
Options: a ) 22 , b ) 28 , c ) 27 , d ) 19 , e ) 11
Rationale: answer : d
Answer: d
Problem: the average weight of a , b and c is 43 kg . if the average weight of a and b be 40 kg and that of b and c be 43 kg , then the weight of b is :
Options: a ) 33 kg , b ) 31 kg , c ) 32 kg , d ) 36 kg , e ) 37 kg
Rationale: "let a , b , c represent their respective weights . then , we have : a + b + c = ( 45 x 3 ) = 129 . . . . ( i ) a + b = ( 40 x 2 ) = 80 . . . . ( ii ) b + c = ( 43 x 2 ) = 86 . . . . ( iii ) adding ( ii ) and ( iii ) , we get : a + 2 b + c = 166 . . . . ( iv ) subtracting ( i ) from ( iv ) , we get : b = 37 . b ' s weight = 37 kg . e"
Answer: e
Problem: the length of rectangle is thrice its breadth and its perimeter is 80 m , find the area of the rectangle ?
Options: a ) 360 , b ) 376 , c ) 299 , d ) 276 , e ) 111
Rationale: "2 ( 3 x + x ) = 80 l = 36 b = 10 lb = 36 * 10 = 360 a"
Answer: a
Problem: a dog breeder currently has 9 breeding dogs . 6 of the dogs have exactly 1 littermate , and 3 of the dogs have exactly 2 littermates . if 2 dogs are selected at random , what is the probability r that both selected dogs are not littermates ?
Options: a ) 1 / 6 , b ) 2 / 9 , c ) 5 / 6 , d ) 7 / 9 , e ) 8 / 9
Rationale: "we have three pairs of dogs for the 6 with exactly one littermate , and one triplet , with each having exactly two littermates . so , in fact there are two types of dogs : those with one littermate - say a , and the others with two littermates - b . work with probabilities : choosing two dogs , we can have either one dog of type b or none ( we can not have two dogs both of type b ) . the probability of choosing one dog of type b and one of type a is 3 / 9 * 6 / 8 * 2 = 1 / 2 ( the factor of 2 for the two possibilities ba and ab ) . the probability r of choosing two dogs of type a which are not littermates is 6 / 9 * 4 / 8 = 1 / 3 ( choose one a , then another a which is n ' t the previous one ' s littermate ) . the required probability is 1 / 2 + 1 / 3 = 5 / 6 . find the probability for the complementary event : choose aa or bb . probability of choosing two dogs of type a who are littermates is 6 / 9 * 1 / 8 = 1 / 12 . probability of choosing two dogs of type b ( who necessarily are littermates ) is 3 / 9 * 2 / 8 = 1 / 12 . again , we obtain 1 - ( 1 / 12 + 1 / 12 ) = 5 / 6 . answer : c"
Answer: c
Problem: a train running at the speed of 60 km / hr crosses a pole in 21 seconds . what is the length of the train ?
Options: a ) 350 m , b ) 278 m , c ) 876 m , d ) 150 m , e ) 267 m
Rationale: "speed = ( 60 * 5 / 18 ) m / sec = ( 50 / 3 ) m / sec length of the train = ( speed x time ) = ( 50 / 3 * 21 ) m = 350 m . answer : a"
Answer: a
Problem: a number when divided by 214 gives a remainder 35 , what remainder will be obtained by dividing the same number 14 ?
Options: a ) 7 , b ) 10 , c ) 11 , d ) 2 , e ) 3
Rationale: "explanation : 214 + 35 = 249 / 14 = 11 ( remainder ) answer : c"
Answer: c
Problem: a number whose fifth part increased by 3 is equal to its fourth part diminished by 3 is ?
Options: a ) 120 , b ) 180 , c ) 200 , d ) 220 , e ) none
Rationale: "answer let the number be n . then , ( n / 5 ) + 3 = ( n / 4 ) - 3 â ‡ ’ ( n / 4 ) - ( n / 5 ) = 6 â ‡ ’ ( 5 n - 4 n ) / 20 = 6 â ˆ ´ n = 120 option : a"
Answer: a
Problem: a military camp has a food reserve for 250 personnel for 40 days . if after 15 days 50 more personnel are added to the camp , find the number of days the reserve will last for ?
Options: a ) 25 , b ) 67 , c ) 26 , d ) 29 , e ) 18
Rationale: explanation : as the camp has a reserve for 250 personnel that can last for 40 days , after 10 days the reserve left for 250 personnel is for 30 days . now 50 more personnel are added in the camp . hence , the food reserve for 300 personnel will last for : 250 : 300 : : x : 30 … … . . ( it is an indirect proportion as less men means more days ) x = ( 250 * 30 ) / 300 x = 25 days answer : a
Answer: a
Problem: what is x if x + 2 y = 12 and y = 3 ?
Options: a ) a ) 10 , b ) b ) 8 , c ) c ) 6 , d ) d ) 4 , e ) e ) 2
Rationale: "x = 12 - 2 y x = 12 - 6 . x = 6 answer : c"
Answer: c
Problem: in how many years rs 200 will produce the same interest at 10 % as rs . 1000 produce in 2 years at 12 %
Options: a ) 13 , b ) 9 , c ) 11 , d ) 12 , e ) 10
Rationale: explanation : clue : firstly we need to calculate the si with prinical 1000 , time 2 years and rate 12 % , it will be rs . 240 then we can get the time as time = ( 100 * 240 ) / ( 200 * 10 ) = 12 option d
Answer: d
Problem: a store ’ s selling price of $ 2240 for a certain computer would yield a profit of 40 percent of the store ’ s cost for the computer . what selling price would yield a profit of 60 percent of the computer ’ s cost ?
Options: a ) $ 2400 , b ) $ 2464 , c ) $ 2560 , d ) $ 2732 , e ) $ 2800
Rationale: "1.4 x = 2240 x = 2240 / 1.4 so , 1.6 x = 2240 * 1.6 / 1.4 = 2560 answer : - c"
Answer: c
Problem: a person buys 18 local tickets for rs 110 . each first class ticket costs rs 10 and each second class ticket costs rs 3 . what will another lot of 18 tickets in which the numbers of first class and second class tickets are interchanged cost ?
Options: a ) 112 , b ) 118 , c ) 121 , d ) 124 , e ) none of these
Rationale: explanation : let , there are x first class ticket and ( 18 - x ) second class tickets . then , 110 = 10 x + 3 ( 18 − x ) . = > 110 = 10 x + 54 − 3 x . = > 7 x = 56 . = > x = 8 . if the number of the first class and second class tickets are interchanged , then the total cost would be 10 × 10 + 3 × 8 = 124 . answer : d
Answer: d
Problem: for all numbers a and b , the operationis defined by ab = ( a + 2 ) ( b – 3 ) . if 3 y = – 30 , then y =
Options: a ) – 15 , b ) – 6 , c ) - 3 , d ) 6 , e ) 15
Rationale: ( 3 + 2 ) ( y - 3 ) = - 30 . . x - 3 = - 6 . . x = - 3 c
Answer: c
Problem: a train 250 m long running at 72 kmph crosses a platform in 40 sec . what is the length of the platform ?
Options: a ) 450 m , b ) 200 m , c ) 250 m , d ) 270 m , e ) 300 m
Rationale: "d = 72 * 5 / 18 = 40 = 800 â € “ 250 = 450 m answer : a"
Answer: a
Problem: out of 3 given numbers , the first one is twice the second and 3 times the third . if the average of these numbers is 88 , then the difference between first and third is .
Options: a ) 92 , b ) 39 , c ) 87 , d ) 96 , e ) none
Rationale: sum of three number is = 88 * 3 = 264 let three numbers are a , b , c and a is the highest and c is the lowest then , 2 b = a so b = a / 2 and 3 c = a so c = a / 3 we can write , a + b + c = 264 a + a / 2 + a / 3 = 264 11 a / 6 = 264 a = 144 so , c = 144 / 3 = 48 so there difference is = 144 - 48 = 96 answer d
Answer: d
Problem: an item is being sold for $ 10 each . however , if a customer will “ buy at least 3 ” they have a promo discount of 32 % . also , if a customer will “ buy at least 10 ” items they will deduct an additional 8 % to their “ buy at least 3 ” promo price . if sam buys 10 pcs of that item how much should he pay ?
Options: a ) $ 92.00 , b ) $ 88.00 , c ) $ 87.04 , d ) $ 80.96 , e ) $ 70.00
Rationale: "without any discount sam should pay 10 * 10 = $ 100 . now , the overall discount would be slightly less than 40 % , thus he must pay slightly more than $ 60 . only answer choice e fits . answer : e ."
Answer: e
Problem: r is the set of positive odd integers less than 200 , and s is the set of the squares of the integers in r . how many elements does the intersection of r and s contain ?
Options: a ) none , b ) two , c ) four , d ) five , e ) seven
Rationale: "r is the set of positive odd integers less than 200 , and s is the set of the squares of the integers in r . how many elements does the intersection of r and s contain ? r = 1,3 , 5,7 , 9,11 , 13,15 . . . s = 1 , 9,25 , 49,81 . . . numbers : 1 , 9 , 25 , 49 , 81 , 121 , and 169 are odd integers ( less than 200 ) that are in both sets . solution : seven answer : e"
Answer: e
Problem: the cost to park a car in a certain parking garage is $ 9.00 for up to 2 hours of parking and $ 1.75 for each hour in excess of 2 hours . what is the average ( arithmetic mean ) cost per hour to park a car in the parking garage for 9 hours ?
Options: a ) $ 1.09 , b ) $ 1.67 , c ) $ 2.25 , d ) $ 2.36 , e ) $ 2.50
Rationale: "total cost of parking for 9 hours = 9 $ for the first 2 hours and then 1.75 for ( 9 - 2 ) hours = 9 + 7 * 1.75 = 21.25 thus the average parking price = 21.25 / 9 = 2.36 $ d is the correct answer ."
Answer: d
Problem: find the compound interest on $ 30000 in 2 years at 4 % per annum , the interest being compounded half - yearly ?
Options: a ) $ 645.56 , b ) $ 824.32 , c ) $ 954.26 , d ) $ 2472.96 , e ) $ 1020.45
Rationale: "principle = $ 10000 rate = 2 % half yearly = 4 half years amount = 30000 * ( 1 + 2 / 100 ) ^ 4 = 30000 * 51 / 50 * 51 / 50 * 51 / 50 * 51 / 50 = $ 32472.96 c . i . = 32472.96 - 10000 = $ 2472.96 answer is d"
Answer: d
Problem: the average waight of a , b , c is 45 kg . the avg wgt of a & b be 40 kg & that of b , c be 43 kg . find the wgt of b .
Options: a ) 34 kg , b ) 40 kg , c ) 42 kg , d ) 41 kg , e ) 31 kg
Rationale: ". let a , b , c represent their individual wgts . then , a + b + c = ( 45 * 3 ) kg = 135 kg a + b = ( 40 * 2 ) kg = 80 kg & b + c = ( 43 * 2 ) kg = 86 kg b = ( a + b ) + ( b + c ) - ( a + b + c ) = ( 80 + 86 - 135 ) kg = 31 kg . answer is e ."
Answer: e
Problem: of the 600 residents of clermontville , 35 % watch the television show island survival , 40 % watch lovelost lawyers and 50 % watch medical emergency . if all residents watch at least one of these 3 shows and 18 % watch exactly 2 of these shows , then how many clermontville residents z watch all of the shows ?
Options: a ) 150 , b ) 108 , c ) 42 , d ) 21 , e ) - 21
Rationale: oa is d . 100 = a + b + c - ab - ac - bc + abc , which is the same as the following formula 100 = a + b + c + ( - ab - ac - bc + abc + abc + abc ) - 2 abc . the term between parantheses value 18 % so the equation to resolve is 100 = 35 + 40 + 50 - 18 - 2 abc therefore the value of abc is z = 3.5 % of 600 , is 21 . d is the correct answer
Answer: d
Problem: john ' s marks wrongly entered as 82 instead of 62 . due to that the average marks for the class got increased by half ( 1 / 2 ) . the number of john in the class is ?
Options: a ) 70 , b ) 78 , c ) 80 , d ) 84 , e ) 90
Rationale: otal increase in marks = x x 1 = x 2 2 x / 2 = ( 82 - 62 ) x / 2 = 40 x = 80 . c
Answer: c
Problem: a train running at the speed of 90 km / hr crosses a pole in 10 seconds . find the length of the train .
Options: a ) 150 , b ) 180 , c ) 250 , d ) 200 , e ) 225
Rationale: "speed = 90 * ( 5 / 18 ) m / sec = 25 m / sec length of train ( distance ) = speed * time 25 * 10 = 250 meter answer : c"
Answer: c
Problem: milk is poured from a full rectangular container with dimensions 4 inches by 9 inches by 10 inches into a cylindrical container with a diameter of 6 inches . if the milk does not overflow , how many inches high will the milk reach ?
Options: a ) 60 / π
b ) 24
c ) 40 / π
d ) 10
e ) 3 π
Rationale: let the height of level of milk in the cylinder = h since , volume of milk is constant . therefore 4 * 9 * 10 = π π * 3 ^ 2 * h = > π * h = 40 = > h = 40 / ( π ) answer c
Answer: c
Problem: if 65 % of a number is greater than 5 % of 60 by 23 , what is the number ?
Options: a ) 65 , b ) 40 , c ) 55 , d ) 30 , e ) 60
Rationale: "explanation : 65 / 100 * x - 5 / 100 * 60 = 23 65 / 100 * x - 3 = 23 65 / 100 * x = 26 x = 26 * 100 / 65 x = 40 answer : option b"
Answer: b
Problem: 8 men and 2 boys working together can do 4 times as much work as a man and a boy . working capacity of man and boy is in the ratio
Options: a ) 1 : 2 , b ) 1 : 3 , c ) 2 : 1 , d ) 2 : 3 , e ) none of these
Rationale: explanation : let 1 man 1 day work = x 1 boy 1 day work = y then 8 x + 2 y = 4 ( x + y ) = > 4 x = 2 y = > x / y = 2 / 4 = > x : y = 1 : 2 option a
Answer: a
Problem: the difference between the place value and the face value of 7 in the numeral 856973 is
Options: a ) 63 , b ) 6973 , c ) 5994 , d ) 6084 , e ) none of these
Rationale: ( place value of 7 ) - ( face value of 7 ) = ( 70 - 7 ) = 63 answer : option a
Answer: a
Problem: if a person walks at 15 km / hr instead of 5 km / hr , he would have walked 20 km more . the actual distance traveled by him is ?
Options: a ) 50 km , b ) 76 km , c ) 18 km , d ) 10 km , e ) 97 km
Rationale: "let the actual distance traveled be x km . then , x / 5 = ( x + 20 ) / 15 10 x - 100 = > x = 10 km . answer : d"
Answer: d
Problem: the diameter of a cylindrical tin is 4 cm and height is 5 cm . find the volume of the cylinder ?
Options: a ) 33 , b ) 45 , c ) 20 , d ) 77 , e ) 21
Rationale: "r = 2 h = 5 π * 2 * 2 * 5 = 20 π cc answer : c"
Answer: c
Problem: the sum of 3 consecutive numbers is definitely
Options: a ) positive . , b ) divisible by 2 . , c ) divisible by 4 . , d ) divisible by 3 . , e ) divisible by 5 .
Rationale: "if 1 st term is x : x + ( x + 1 ) + ( x + 2 ) = 3 x + 3 - - - > always divisible by 3 if 2 nd term is x : ( x - 1 ) + x + ( x + 1 ) = 3 x - - - > always divisible by 3 if 3 rd term is x : ( x - 2 ) + ( x - 1 ) + x = 3 x - 3 - - - > always divisible by 3 answer : d"
Answer: d
Problem: for all even integers n , h ( n ) is defined to be the sum of the even integers between 6 and n , inclusive . what is the value of h ( 18 ) / h ( 10 ) ?
Options: a ) 1.8 , b ) 4 , c ) 6 , d ) 18 , e ) 60
Rationale: "concept : when terms are in arithmetic progression ( a . p . ) i . e . terms are equally spaced then mean = median = ( first + last ) / 2 and sum = mean * number of terms h ( 18 ) = [ ( 6 + 18 ) / 2 ] * 7 = 84 h ( 10 ) = ( 6 + 10 ) / 2 ] * 3 = 24 h ( 18 ) / h ( 10 ) = ( 84 ) / ( 24 ) ~ 4 answer : b"
Answer: b
Problem: 20 % of a 6 litre solution and 60 % of 4 litre solution are mixed . what percentage of the mixture of solution
Options: a ) 36 % , b ) 35 % , c ) 34 % , d ) 33 % , e ) 32 %
Rationale: 20 % of 6 litre is ( 6 * 20 / 100 ) = 1.2 litre 60 % of 4 litre is ( 60 * 4 / 100 ) = 2.4 litre the mixture is 3.6 litre so the percentage is ( 3.6 * 100 / 10 ) = 36 % answer : a
Answer: a
Problem: population of a city decreases by 10 % at the end of first year and increases by 10 % at the end of second year and again decreases by 10 % at the end of third year . if the population of the city at the end of third year is 4455 , then what was the population of the city at the beginning of the first year ?
Options: a ) 5000 , b ) 4500 , c ) 4950 , d ) 1000 , e ) 2000
Rationale: m . f = 90 / 100 * 110 * 100 * 90 / 100 = 81 * 11 / 1000 population before 3 yrs = i . q / m . f = 4455 * 1000 / 81 * 11 = 5000 answer : a
Answer: a
Problem: a contractor is engaged for 30 days on the condition thathe receives rs . 25 for each day he works & is fined rs . 7.50 for each day is absent . he gets rs . 425 in all . for how many days was he absent ?
Options: a ) 8 , b ) 10 , c ) 15 , d ) 17 , e ) 19
Rationale: 30 * 25 = 750 425 - - - - - - - - - - - 325 25 + 7.50 = 32.5 325 / 32.5 = 10 b
Answer: b
Problem: stalin and heather are 20 miles apart and walk towards each other along the same route . stalin walks at constant rate that is 1 mile per hour faster than heather ' s constant rate of 5 miles / hour . if heather starts her journey 20 minutes after stalin , how far from the original destination has heather walked when the two meet ?
Options: a ) 4 miles , b ) 6 miles , c ) 9 miles , d ) 10 miles , e ) 12 mile
Rationale: original distance between s and h = 20 miles . speed of s = 5 + 1 = 6 mph , speed of h = 5 mph . time traveled by h = t hours - - - > time traveled by s = t + 20 / 60 = t + 2 / 6 hours . now , the total distances traveled by s and h = 20 miles - - - > 6 * ( t + 2 / 6 ) + 5 * t = 20 - - - > t = 8 / 11 hours . thus h has traveled for 8 / 11 hours giving you a total distance for h = 5 * 8 / 11 ~ 4 miles . a is thus the correct answer . p . s . : based on the wording of the question , you should calculatehow far from theoriginal destination has heather walkedwhen the two meet . ' original destination ' for h does not make any sense . original destination for h was situated at a distance of 20 miles .
Answer: a
Problem: what is the square root of 16 ?
Options: a ) 8 , b ) 4 , c ) 35 , d ) 42 , e ) 86
Rationale: "4 x 4 = 16 answer b"
Answer: b
Problem: a bag marked at $ 240 is sold for $ 120 . the rate of discount is ?
Options: a ) 10 % , b ) 25 % , c ) 20 % , d ) 50 % , e ) 45 %
Rationale: "rate of discount = 120 / 240 * 100 = 50 % answer is d"
Answer: d
Problem: the average weight of 8 person ' s increases by 2 kg when a new person comes in place of one of them weighing 65 kg . what might be the weight of the new person ?
Options: a ) 70 kg , b ) 80 kg , c ) 81 kg , d ) 90 kg , e ) 91 kg
Rationale: "total weight increased = ( 8 x 2 ) kg = 16 kg . weight of new person = ( 65 + 16 ) kg = 81 kg . c )"
Answer: c
Problem: the mean proportional between 4 and 9 is ?
Options: a ) 33 , b ) 77 , c ) 35 , d ) 88 , e ) 29
Rationale: "7 / 20 * 100 = 35 answer : b"
Answer: b
Problem: a man buy a book in rs 50 & sale it rs 100 . what is the rate of profit ? ? ?
Options: a ) 10 % , b ) 100 % , c ) 30 % , d ) 25 % , e ) 28 %
Rationale: "cp = 50 sp = 100 profit = 100 - 50 = 50 % = 50 / 50 * 100 = 100 % answer : b"
Answer: b
Problem: a cistern has a leak which would empty the cistern in 20 minutes . a tap is turned on which admits 6 liters a minute into the cistern , and it is emptied in 24 minutes . how many liters does the cistern hold ?
Options: a ) 480 , b ) 287 , c ) 720 , d ) 270 , e ) 927
Rationale: "1 / x - 1 / 20 = - 1 / 24 x = 120 120 * 6 = 720 answer : c"
Answer: c
Problem: a group of students was interviewed for that if it was asked whether or not they speak french and / or english . among those who speak french , 20 speak english well , while 60 of them do not speak english . if 60 % of students do not speak french , how many students were surveyed ?
Options: a ) 250 , b ) 225 , c ) 175 , d ) 195 , e ) 200
Rationale: "number of students who speak french are 60 + 20 = 80 of total students , the percentage of students who do not speak french was 60 % - - > percentage of who do is 40 % 80 - - - - - - - 40 % x - - - - - - - 100 % x = 80 * 100 / 40 = 200 = number of all students answer is e"
Answer: e
Problem: the average weight of 29 students is 28 kg . by the admission of a new student , the average weight is reduced to 27.2 kg . the weight of the new student is
Options: a ) 4 kg , b ) 21.6 kg , c ) 22.4 kg , d ) 21 kg , e ) none of these
Rationale: "exp . the total weight of 29 students = 29 * 28 the total weight of 30 students = 30 * 27.2 weight of the new student = ( 30 * 27.2 – 29 * 28 ) = 816 - 812 = 4 answer : a"
Answer: a
Problem: the average expenditure of a labourer for 6 months was 80 and he fell into debt . in the next 4 months by reducing his monthly expenses to 60 he not only cleared off his debt but also saved 30 . his monthly income i
Options: a ) 70 , b ) 72 , c ) 75 , d ) 78 , e ) 80
Rationale: "income of 6 months = ( 6 × 80 ) – debt = 480 – debt income of the man for next 4 months = 4 × 60 + debt + 30 = 270 + debt ∴ income of 10 months = 750 average monthly income = 750 ÷ 10 = 75 answer c"
Answer: c
Problem: the length of a rectangle is halved , whileits breadth is tripled . wat is the % change in area ?
Options: a ) 40 % , b ) 45 % , c ) 50 % , d ) 65 % , e ) 70 %
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
Problem: a man saves 25 % of his monthly salary . if an account of dearness of things he is to increase his monthly expenses by 10 % , he is only able to save rs . 175 per month . what is his monthly salary ?
Options: a ) rs . 1000 , b ) rs . 2000 , c ) rs . 1500 , d ) rs . 3000 , e ) rs . 3100
Rationale: "income = rs . 100 expenditure = rs . 75 savings = rs . 25 present expenditure 75 + 75 * ( 10 / 100 ) = rs . 82.5 present savings = 100 – 82.50 = rs . 17.50 if savings is rs . 17.50 , salary = rs . 100 if savings is rs . 175 , salary = 100 / 17.5 * 175 = 1000 answer : a"
Answer: a
Problem: a 15 % stock yielding 12 % is quoted at :
Options: a ) s . 83.33 , b ) s . 110 , c ) s . 112 , d ) s . 125 , e ) s . 140
Rationale: "income of rs 12 on investment of rs 100 income of rs 15 on investment of ? = ( 15 * 100 ) / 12 = 125 answer : d"
Answer: d
Problem: on june 1 a bicycle dealer noted that the number of bicycles in stock had decreased by 2 for each of the past 5 months . if the stock continues to decrease at the same rate for the rest of the year , how many fewer bicycles will be in stock on september 1 than were in stock on january 1 ?
Options: a ) 18 , b ) 12 , c ) 20 , d ) 32 , e ) 36
Rationale: "jan 1 = c feb 1 = c - 2 march 1 = c - 4 april 1 = c - 8 may 1 = c - 10 june 1 = c - 12 july 1 = c - 14 aug 1 = c - 16 sept 1 = c - 18 difference between stock on september 1 than were in stock on january 1 will be - c - ( c - 18 ) = 18 hence answer will be ( a )"
Answer: a
Problem: having received his weekly allowance , john spent 3 / 5 of his allowance at the arcade . the next day he spent one third of his remaining allowance at the toy store , and then spent his last $ 0.92 at the candy store . what is john ’ s weekly allowance ?
Options: a ) $ 2.55 , b ) $ 2.85 , c ) $ 3.15 , d ) $ 3.45 , e ) $ 3.75
Rationale: "x = 3 x / 5 + 1 / 3 * 2 x / 5 + 92 4 x / 15 = 92 x = 345 = $ 3.45 the answer is d ."
Answer: d
Problem: a salesman ’ s terms were changed from a flat commission of 5 % on all his sales to a fixed salary of rs . 1300 plus 2.5 % commission on all sales exceeding rs . 4000 . if his remuneration as per new scheme was rs . 600 more than that by the previous schema , his sales were worth ?
Options: a ) 12028 , b ) 12000 , c ) 12019 , d ) 12197 , e ) 18000
Rationale: [ 1300 + ( x - 4000 ) * ( 2.5 / 100 ) ] - x * ( 5 / 100 ) = 600 x = 18000 answer : c
Answer: c
Problem: a sum fetched a total simple interest of 4020.75 at the rate of 9 % . p . a . in 5 years . what is the sum ?
Options: a ) 5768 , b ) 8925 , c ) 2345 , d ) 6474 , e ) 8935
Rationale: "principal = ( 100 x 4020.75 ) / ( 9 x 5 ) = 402075 / 45 = 8935 . answer e"
Answer: e
Problem: two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 28 kmph and 21 kmph respectively . when they meet , it is found that one train has traveled 60 km more than the other one . the distance between the two stations is ?
Options: a ) 457 km , b ) 444 km , c ) 547 km , d ) 588 km , e ) 653 km
Rationale: "1 h - - - - - 5 ? - - - - - - 60 12 h rs = 28 + 21 = 49 t = 12 d = 49 * 12 = 588 answer : d"
Answer: d
Problem: exactly 3 / 7 of the people in the room are under the age of 21 , and exactly 5 / 11 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 ) 35 , c ) 33 , d ) 60 , e ) 65
Rationale: the total number of the people in the room must be a multiple of both 7 and 11 ( in order 3 / 7 and 5 / 11 of the number to be an integer ) , thus the total number of the people must be a multiple of lcm of 7 and 11 , which is 77 . since , the total number of the people in the room is greater than 50 and less than 100 , then there are 77 people in the room . therefore there are 3 / 7 * 77 = 33 people in the room under the age of 21 . answer : c .
Answer: c
Problem: one night 15 percent of the female officers on a police force were on duty . if 300 officers were on duty that night and half of these were female officers , how many female officers were on the police force ?
Options: a ) 90 , b ) 180 , c ) 270 , d ) 500 , e ) 1,000
Rationale: "let total number of female officers in the police force = f total number of officers on duty on that night = 300 number of female officers on duty on that night = 300 / 2 = 150 ( 15 / 100 ) * f = 150 = > f = 1000 answer e"
Answer: e
Problem: with # andeach representing different digits in the problem below , the difference between # and # # is 801 . what is the value of ? # - # # ____ 812
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: 100 x - ( 10 x + x ) - - - - - - - - - - - 89 x = 801 x = 9 c
Answer: c
Problem: a cat leaps 5 leaps for every 4 leaps of a dog , but 3 leaps of the dog are equal to 4 leaps of the cat . what is the ratio of the speed of the cat to that of the dog ?
Options: a ) 11 : 15 , b ) 15 : 11 , c ) 16 : 15 , d ) 15 : 16 , e ) 11 : 16
Rationale: "solution : given ; 3 dog = 4 cat ; or , dog / cat = 4 / 3 ; let cat ' s 1 leap = 3 meter and dogs 1 leap = 4 meter . then , ratio of speed of cat and dog = 3 * 5 / 4 * 4 = 15 : 16 . ' ' answer : option d"
Answer: d
Problem: ( √ 97 + √ 486 ) / √ 54 = ?
Options: a ) 2 √ 2 , b ) 2 √ 3 , c ) 3 √ 2 , d ) 3 √ 3 , e ) 13 / 3
Rationale: "( √ 96 + √ 486 ) / √ 54 = ( 4 √ 6 + 9 √ 6 ) / 3 √ 6 = 13 √ 6 / 3 √ 6 = 13 / 3 hence , the correct answer is e ."
Answer: e
Problem: a secret can be told only 2 persons in 5 minutes . the same person tells to 2 more persons and so on . how long will take to tell it to 768 persons ?
Options: a ) 25 min , b ) 32 min , c ) 33 min , d ) 34 min , e ) 35 min
Rationale: at start one person will tell to 2 persons , it will take 5 min , now that 1 + 2 = 3 persons will tell this to next 6 persons , then 1 + 2 + 6 = 9 persons will tell to next 18 persons , then 1 + 2 + 6 + 18 = 27 persons to 54 similarly 1 + 2 + 6 + 18 + 54 = 81 persons will tell this to 162 persons similarly 1 + 2 + 6 + 18 + 54 + 162 = 243 persons will tell this to 486 persons , upto this step total persons who have listened this secret = 2 + 6 + 18 + 54 + 162 + 486 = 728 , and total time taken upto this step = 5 * 6 = 30 min , now next 5 min will be sufficient to tell this message to next 40 persons so total time taken = 35 min answer : e
Answer: e
Problem: in what time will a train 110 m long cross an electric pole , it its speed be 144 km / hr ?
Options: a ) 2.35 sec , b ) 2.85 sec , c ) 7.5 sec , d ) 2.75 sec , e ) 1.5 sec
Rationale: "speed = 144 * 5 / 18 = 40 m / sec time taken = 110 / 40 = 2.75 sec . answer : d"
Answer: d
Problem: 9 . on level farmland , two runners leave at the same time from the intersection of two country roads . one runner jogs due north at a constant rate of 6 miles per hour while the second runner jogs due east at a constant rate that is 2 miles per hour faster than the first runner ' s rate . how far apart , to the nearest mile , will they be after 1 / 2 hour ?
Options: a ) 6 , b ) 7 , c ) 5 , d ) 12 , e ) 14
Rationale: "if runner 1 is going north and runner 2 is going east they are like two sides of a 90 degree triangle . side 1 = 6 m / h - - > 3 m in 1 / 2 hr side 2 = 8 m / h - - > 4 m in 1 / 2 hr to complete this right angle triangle d ^ 2 = 4 ^ 2 + 3 ^ 2 d ^ 2 = 25 = 5 answer option c"
Answer: c
Problem: find the smallest number which when divided by 13 and 15 leaves respective remainders of 2 and 4
Options: a ) 187 , b ) 197 , c ) 184 , d ) 219 , e ) 227
Rationale: let ' n ' is the smallest number which divided by 13 and 15 leaves respective remainders of 2 and 4 . required number = ( lcm of 13 and 15 ) - ( common difference of divisors and remainders ) = ( 195 ) - ( 11 ) = 184 . answer : c
Answer: c
Problem: if sharon ' s weekly salary increased by 16 percent , she would earn $ 406 per week . if instead , her weekly salary were to increase by 20 percent , how much would she earn per week ?
Options: a ) $ 420 , b ) $ 382 , c ) $ 385 , d ) $ 392 , e ) $ 399
Rationale: "( 406 / 116 ) 120 = 420 in this case long division does not take much time . ( 406 / 116 ) = 3.5 35 * 12 = 420 ( 350 + 70 ) answer a"
Answer: a
Problem: two tains are running in opposite directions with the same speed . if the length of each train is 120 metres and they cross each other in 12 seconds , then the speed of each train ( in km / hr ) is :
Options: a ) 12 , b ) 24 , c ) 36 , d ) 48 , e ) 38
Rationale: sol . let the speed of each train be x m / sec . then , relative speed of the two trains = 2 x m / sec . so , 2 x = ( 120 + 120 ) / 12 ⇔ 2 x = 20 ⇔ x = 10 . ∴ speed of each train = 10 m / sec = [ 10 * 18 / 5 ] km / hr = 36 km / hr . answer c
Answer: c
Problem: a taxi company charges $ 2.5 for the first quarter of a mile and fifteen cents for each additional quarter of a mile . what is the maximum distance someone could travel with $ 4.90 ?
Options: a ) 4 miles , b ) 4 1 / 4 miles , c ) 4 3 / 4 miles , d ) 5 1 / 2 miles , e ) 6 1 / 4 miles
Rationale: "if we start out with $ 4.90 and have to spend $ 2.5 for the first quarter - mile , we will have $ 2.40 left to spend on quarter - mile intervals . since $ 2.40 / $ 0.15 = 16 , we can buy 16 more quarter - miles , and will travel 17 quarter miles in all : 17 × 1 / 4 = 4 1 / 4 miles . the correct answer is choice ( b ) ."
Answer: b
Problem: a student has to obtain 60 % of the total marks to pass . he got 160 marks and failed by 20 marks . the maximum marks are ?
Options: a ) 210 , b ) 280 , c ) 300 , d ) 320 , e ) 340
Rationale: "let the maximum marks be x then , 60 % of x = 160 + 20 60 x / 100 = 180 60 x = 180 * 100 = 18000 x = 300 answer is c"
Answer: c
Problem: in a renowned city , the average birth rate is 7 people every two seconds and the death rate is 2 people every two seconds . estimate the size of the population net increase that occurs in one day .
Options: a ) 215,000 , b ) 216,000 , c ) 217,000 , d ) 218,000 , e ) 219,000
Rationale: this question can be modified so that the birth rate is given every m seconds and the death rate is given every n seconds . for this particular question : increase in the population every 2 seconds = 7 - 2 = 5 people . total 2 second interval in a day = 24 * 60 * 60 / 2 = 43,200 population increase = 43,200 * 5 = 216,000 . hence b .
Answer: b
Problem: two trains of equal are running on parallel lines in the same direction at 46 km / hr and 36 km / hr . the faster train passes the slower train in 36.00001 sec . the length of each train is ?
Options: a ) 50 , b ) 99 , c ) 77 , d ) 26 , e ) 23
Rationale: "let the length of each train be x m . then , distance covered = 2 x m . relative speed = 46 - 36 = 10 km / hr . = 10 * 5 / 18 = 25 / 9 m / sec . 2 x / 36 = 25 / 9 = > x = 50 . answer : a"
Answer: a
Problem: two numbers n and 14 have lcm = 56 and gcf = 10 . find n .
Options: a ) 24 , b ) 40 , c ) 44 , d ) 54 , e ) 64
Rationale: "the product of two integers is equal to the product of their lcm and gcf . hence . 14 × n = 56 × 10 n = 56 × 10 / 14 = 40 correct answer b"
Answer: b
Problem: how many liters of water must be evaporated from 50 liters of a 2 percent sugar solution to get a 4 percent sugar solution ?
Options: a ) 20 , b ) 25 , c ) 30 , d ) 35 , e ) 40
Rationale: "let x be the amount that needs to be evaporated . 0.02 ( 50 ) = 0.04 ( 50 - x ) 0.04 x = 2 - 1 x = 1 / 0.04 = 25 liters the answer is b ."
Answer: b
Problem: a batsman scored 60 runs which included 2 boundaries and 2 sixes . what percent of his total score did he make by running between the wickets .
Options: a ) 30 % , b ) 33.33 % , c ) 40 % , d ) 60 % , e ) 50 %
Rationale: "explanation : number of runs made by running = 60 - ( 2 x 4 + 2 x 6 ) = 60 - ( 20 ) = 20 now , we need to calculate 20 is what percent of 60 . = > 20 / 60 * 100 = 33.33 % option b"
Answer: b
Problem: if 3 people can do 3 times of a particular work in 3 days , then how many days would it take 5 people to do 5 times of that particular work ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 5 , e ) 8
Rationale: 3 people can do the work one time in one day . 1 person can do 1 / 3 of the work in one day . 5 people can do 5 / 3 of the work in one day . 5 people can do 5 times the work in 3 days . the answer is c .
Answer: c
Problem: what is the value of â ˆ š 64 % ?
Options: a ) 80 % , b ) 20 % , c ) 40 % , d ) 90 % , e ) 26 %
Rationale: "explanation : br > â ˆ š 64 % = â ˆ š 64 / â ˆ š 100 = 8 / 10 = 80 / 100 = 80 % correct answer is a ) 80 %"
Answer: a
Problem: tom opened a shop investing rs . 500 . jose joined him 2 months later , investing rs . 350 . they earned a profit of rs . 1720 after completion of one year . what will be jose ' s share of profit ?
Options: a ) 80 , b ) 20 , c ) 30 , d ) 41 , e ) 15
Rationale: "sol = ~ s - so anju ’ s share = [ 5 / 9 ] x 1720 = 80 a"
Answer: a
Problem: the sides of a rectangular field are in the ratio 3 : 4 . if the area of the field is 8748 sq . m , the cost of fencing the field @ 25 paise per metre is
Options: a ) rs . 55.50 , b ) rs . 67.50 , c ) rs . 86.50 , d ) rs . 94.50 , e ) none of these
Rationale: "solution let length = ( 3 x ) metres and breadth = ( 4 x ) metres . then , 3 x × 4 x = 8748 ⇔ 12 x 2 = 8748 ⇔ x 2 = 729 ⇔ x = 27 . so , length = 81 m and breadth = 108 m . perimeter = [ 2 ( 81 + 108 ) ] m = 378 m . ∴ cost of fencing = rs . ( 0.25 × 378 ) = rs . 94.50 . answer d"
Answer: d
Problem: the angle between the minute hand and the hour hand of a clock when the time is 4.20 , is :
Options: a ) 10 d , b ) 0 d , c ) 15 d , d ) 5 d , e ) 20 d
Rationale: "angle traced hr 13 / 3 = ( 360 / 12 * 13 / 3 ) = 130 traced by min hand 20 min = ( 360 / 60 * 20 ) = 120 req = ( 130 - 120 ) = 10 d answer a"
Answer: a
Problem: the positive numbers w , x , y , and z are such that x is 40 percent greater than y , y is 20 percent greater than z , and w is 20 percent less than x . what percent greater than z is w ?
Options: a ) 15.2 % , b ) 16.0 % , c ) 20.0 % , d ) 23.2 % , e ) 24.8 %
Rationale: "my strategy is same as thedobermanbut instead take z = 100 , which makes life a bit easy . as : z = 100 y = 120 ( 20 % greater than z ) z = 144 ( 20 % greater than y ) now calculate w 20 % less than z = 144 * 80 / 100 = 115.2 now by just looking , relation between w and z : w - z / z * 100 = 23.2 - answer d"
Answer: d
Problem: if 10 men do a work in 80 days , in how many days will 20 men do it ?
Options: a ) 18 days , b ) 38 days , c ) 40 days , d ) 48 days , e ) 50 days
Rationale: "10 * 80 = 20 * x x = 40 days answer : c"
Answer: c
Problem: a trader sells 60 meters of cloth for rs . 8400 at the profit of rs . 12 per metre of cloth . what is the cost price of one metre of cloth ?
Options: a ) 128 , b ) 140 , c ) 123 , d ) 110 , e ) 150
Rationale: "sp of 1 m of cloth = 8400 / 60 = rs . 140 cp of 1 m of cloth = sp of 1 m of cloth - profit on 1 m of cloth = rs . 140 - rs . 12 = rs . 128 . answer : a"
Answer: a
Problem: 48 is divided into two parts in such a way that seventh part of first and ninth part of second are equal . find the smallest part ?
Options: a ) 66 , b ) 26 , c ) 42 , d ) 27 , e ) 21
Rationale: "x / 7 = y / 9 = > x : y = 7 : 9 7 / 16 * 48 = 21 answer : e"
Answer: e
Problem: a car covers a distance of 624 km in 6 â ½ hours . find its speed ?
Options: a ) 104 , b ) 190 , c ) 109 , d ) 278 , e ) 211
Rationale: explanation : 624 / 6 = 104 kmph answer : c
Answer: c
Problem: when average age of 23 members are 0 , how many members greater than 0 ?
Options: a ) 17 , b ) 22 , c ) 21 , d ) 24 , e ) 25
Rationale: "average of 23 numbers = 0 . sum of 23 numbers ( 0 x 23 ) = 0 . it is quite possible that 22 of these numbers may be positive and if their sum is a then 23 rd number is ( - a ) answer is 22 ( b )"
Answer: b
Problem: if 2 : 9 : : x : 18 , then find the value of x
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "explanation : treat 2 : 9 as 2 / 9 and x : 18 as x / 18 , treat : : as = so we get 2 / 9 = x / 18 = > 9 x = 36 = > x = 4 option c"
Answer: c
Problem: during the first two weeks of january , the total rainfall in springdale was 35 inches . if the rainfall during the second week was 1.5 times the rainfall during the first week , what was the rainfall during the second week of january ?
Options: a ) 5 inches , b ) 6 inches , c ) 9 inches , d ) 10 inches , e ) 21 inches
Rationale: total rainfall in 2 weeks = 35 inches . assume the rainfall in second week = 1 . x rainfall in first week = x total rainfall = 2.5 x = 35 inches x = 14 and 1.5 x = 21 rainfall during second week = 21 inches option e
Answer: e
Problem: if you roll one fair 6 - sided die , what is the probability that the number is even or less than 3 ?
Options: a ) 2 / 3 , b ) 1 / 2 , c ) 3 / 4 , d ) 5 / 6 , e ) 1 / 3
Rationale: the numbers which satisfy the conditions are 1 , 2 , 4 , and 6 . the probability is 4 / 6 = 2 / 3 the answer is a .
Answer: a
Problem: a fifth of arun â € ™ s marks in mathematics exceed a third of his marks in english by 20 . if he got 260 marks in two subjects together how many marks did he got in english ?
Options: a ) 12080 , b ) 18060 , c ) 20060 , d ) 20040 , e ) none of them
Rationale: let arun â € ™ s marks in mathematics and english be x and y then ( 1 / 5 ) x - ( 1 / 3 ) y = 20 3 x - 5 y = 300 â € ¦ â € ¦ > ( 1 ) x + y = 260 â € ¦ â € ¦ . > ( 2 ) solving ( 1 ) and ( 2 ) x = 200 and y = 60 answer is c .
Answer: c