regisss/math_qa huggingface dataset:
Problem: a sum of rs . 395 was divided among a , b , and c in such a way that b gets 25 % more than a and 20 % more than c . what is the share of a ?
Options: a ) rs . 195 , b ) rs . 180 , c ) rs . 98 , d ) rs . 120 , e ) rs . 130
Rationale: let each one ’ s share is a , b and c respectively , then b = 125 a / 100 = 120 c / 100 a = 100 b / 125 = 4 / 5 b , c = 100 b / 120 = 5 / 6 b 4 / 5 b + b + 5 / 6 b = 395 , 79 b / 30 = 395 , b = 395 * 30 / 79 = 150 a = 4 * 150 / 5 = 120 answer : d
Answer: d
Problem: the ratio 5 : 4 expressed as a percent equals
Options: a ) 12.5 % , b ) 40 % , c ) 80 % , d ) 125 % , e ) none
Rationale: "solution 5 : 4 = 5 / 4 = ( 5 / 4 x 100 ) % . = 125 % . answer d"
Answer: d
Problem: the current birth rate per certain number of people is 52 , whereas corresponding death rate is 16 per same number of people . if the net growth rate in terms of population increase is 1.2 percent , find number of persons . ( initally )
Options: a ) 4000 , b ) 2000 , c ) 3000 , d ) 5000 , e ) 1000
Rationale: "sol . net growth on x = ( 52 - 16 ) = 36 . net growth on 100 = ( 36 / x ã — 100 ) % = 1.2 % . then x = 3000 answer : c"
Answer: c
Problem: 14 , 28 , 20 , 40 , 32 , 64 , . . . ?
Options: a ) 10 , b ) 25 , c ) 56 , d ) 21 , e ) 36
Rationale: "first , multiply by 2 and then subtract 8 . 14 14 * 2 = 28 28 - 8 = 20 20 * 2 = 40 40 - 8 = 32 32 * 2 = 64 64 - 8 = 56 answer : c"
Answer: c
Problem: the average of runs of a cricket player of 20 innings was 32 . how many runs must he make in his next innings so as to increase his average of runs by 6 ?
Options: a ) 96 , b ) 106 , c ) 158 , d ) 116 , e ) 122
Rationale: "average = total runs / no . of innings = 32 so , total = average x no . of innings = 32 * 20 = 640 now increase in avg = 4 runs . so , new avg = 32 + 6 = 38 runs total runs = new avg x new no . of innings = 38 * 21 = 798 runs made in the 11 th inning = 798 - 640 = 158 answer : c"
Answer: c
Problem: a is half good a work man as b and together they finish a job in 26 days . in how many days working alone b finish the job ?
Options: a ) 98 days , b ) 21 days , c ) 17 days , d ) 39 days , e ) 19 days
Rationale: "wc = 1 : 2 2 x + x = 1 / 26 = > x = 1 / 78 2 x = 1 / 78 = > 39 days answer : d"
Answer: d
Problem: jane and ashley take 20 days and 10 days respectively to complete a project when they work on it alone . they thought if they worked on the project together , they would take fewer days to complete it . during the period that they were working together , jane took an eight day leave from work . this led to jane ' s working for four extra days on her own to complete the project . how long did it take to finish the project ?
Options: a ) 12 days , b ) 15 days , c ) 16 days , d ) 18 days , e ) 20 days
Rationale: "let us assume that the work is laying 40 bricks . jane = 2 bricks per day ashley = 4 brick per day together = 6 bricks per day let ' s say first 8 days ashley works alone , no of bricks = 32 last 4 days jane works alone , no . of bricks = 8 remaining bricks = 40 - 40 = 0 so together , they would take 0 / 6 = 0 total no . of days = 8 + 4 + 0 = 12 answer is a"
Answer: a
Problem: if john runs in the speed of 9 km / hr from his house , in what time will he reach the park which is 300 m long from his house ?
Options: a ) 2 , b ) 4 , c ) 5 , d ) 3 , e ) 6
Rationale: speed = 9 * 5 / 18 = 2.5 m / sec time taken = 300 / 2.5 = 120 sec ie . 2 mins . answer : a
Answer: a
Problem: a dishonest person wants to make a profit on the selling of milk . he would like to mix water ( costing nothing ) with milk costing 33 $ per litre so as to make a profit of 40 % on cost when he sells the resulting milk and water mixture for 36 $ . in what ratio should he mix the water and milk ?
Options: a ) 1 : 20 , b ) 1 : 10 , c ) 17 : 8 , d ) 17 : 4 , e ) 17 : 60
Rationale: first of all , let ' s consider 1 liter of the stuff he is going to sell - - - naive customers think it ' s pure milk , but we know it ' s some milk - water mixture . he is going to sell this liter of milk - water for $ 36 . this $ 36 should be a 40 % increase over cost . here , we need to think about percentage increases as multipliers . using multipliers ( cost ) * 1.40 = $ 36 cost = 36 / 1.4 = 360 / 12 = $ 25.71 if he wants a 40 % increase over cost on the sale of one liter of his milk - water , the cost has to be $ 25.71 . well , a liter of milk costs $ 33 , so if he is going to use just $ 30 of milk in his mixture , that ' s 25.71 / 33 = 60 / 77 of a liter . if milk is 60 / 77 of the liter , then water is 17 / 77 of the liter , and the ratio of water to milk is 17 : 60 . answer choice ( e )
Answer: e
Problem: if the sides of a triangle are 26 cm , 18 cm and 10 cm , what is its area ?
Options: a ) 90
b ) 110
c ) 130
d ) 140
e ) 150
Rationale: the triangle with sides 26 cm , 18 cm and 10 cm is right angled , where the hypotenuse is 26 cm . area of the triangle = 1 / 2 * 18 * 10 = 90 cm 2 answer : option a
Answer: a
Problem: if x is the sum of first 100 positive even integers and y is the sum of first 100 positive odd integers , what is the value of x - y ? please try to explain your answers
Options: a ) 0 , b ) 25 , c ) 50 , d ) 75 , e ) 100
Rationale: first even minus first odd = 2 - 1 = 1 ; the sum of first 2 even integers minus the sum of first 2 odd integers = ( 2 + 4 ) - ( 1 + 3 ) = 2 ; the sum of first 3 even integers minus the sum of first 3 odd integers = ( 2 + 4 + 6 ) - ( 1 + 3 + 5 ) = 3 ; we can see the patterns here , so the sum of first 100 positive even integers minus the sum of first 100 positive odd integers will be 100 . answer : e .
Answer: e
Problem: the ratio of the amount of the oil bill for the month of february to the amount of the oil bill for the month of january was 3 : 2 . if the oil bill for february had been $ 30 more , the corresponding ratio would have been 5 : 3 . how much was the oil bill for january ?
Options: a ) $ 120 , b ) $ 150 , c ) $ 180 , d ) $ 210 , e ) $ 240
Rationale: "3 : 2 = 9 : 6 and 5 : 3 = 10 : 6 . an increase in $ 30 increases the ratio by 1 : 6 . therefore , january ' s bill was 6 ( $ 30 ) = $ 180 . the answer is c ."
Answer: c
Problem: if x - y - z = 03 x + 4 y + 3 z = 45 x + 2 y + 7 z = 22 , what is the value of z ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 2 , e ) 1
Rationale: explanation : 4 x + 2 y - 5 z = - 21 â € “ - - - - - - - i 2 x - 2 y + z = 7 â € “ - - - - - - ii 4 x + 3 y - z = - 1 - - - - - - - - iii solve the first equation for x . x - y - z = 0 x = y + z substitute the solution for x into the second and third equations . ii - - - > 3 * ( y + z ) + 4 y + 3 z = 4 3 y + 3 z + 4 y + 3 z = 4 7 y + 6 z = 4 iii - - - - > 5 * ( y + z ) + 2 y + 7 z = 22 5 y + 5 z + 2 y + 7 z = 22 7 y + 12 z = 22 subtract the new second equation from the new third equation and solve for z . 7 y + 12 z = 22 - ( 7 y + 6 z = 4 ) 6 z = 18 z = 3 answer is a
Answer: a
Problem: a call center has two teams . each member of team a was able to process 1 / 5 calls as compared to each member of team b . if team a has 5 / 8 as many number of call center agents as team b , what fraction of the total calls was processed by team b ?
Options: a ) 3 / 2 , b ) 3 / 4 , c ) 8 / 9 , d ) 1 / 2 , e ) 1 / 5
Rationale: "let team b has 8 agents , so team a has 5 agents let each agent of team b picked up 5 calls , so total calls by team b = 40 so , each agent in team a picked up 1 calls , so total calls for team a = 5 fraction for team b = 40 / ( 40 + 5 ) = 8 / 9 = answer = c"
Answer: c
Problem: how much space , in cubic units , is left vacant when maximum number of 3 x 3 x 3 cubes are fitted in a rectangular box measuring 6 x 9 x 11 ?
Options: a ) 112 , b ) 111 , c ) 110 , d ) 109 , e ) 108
Rationale: "no of cubes that can be accommodated in box = ( 6 * 9 * 11 ) / ( 3 * 3 * 3 ) 6 * 9 in numerator can be perfectly divided by 3 * 3 in denominator . side with length 11 ca n ' t be perfectly divided by 3 and hence is the limiting factor . closet multiple of 3 less that 11 is 9 . so vacant area in cube = = 6 * 9 * ( 11 - 9 ) = 6 * 9 * 2 = 108 ans - e"
Answer: e
Problem: the jogging track in a sports complex is 1000 meters in circumference . deepak and his wife start from the same point and walk in opposite directions at 20 km / hr and 17 km / hr respectively . they will meet for the first time in ?
Options: a ) 50 min , b ) 40 min , c ) 35 min , d ) 37 min , e ) 20 min
Rationale: "clearly , the two will meet when they are 1000 m apart to be 20 + 17 = 37 km apart , they take 1 hour to be 1000 m apart , they take 37 * 1000 / 1000 = 37 min . answer is d"
Answer: d
Problem: if the sum of two numbers is 18 and the sum of their squares is 180 , then the product of the numbers is
Options: a ) 72 , b ) 44 , c ) 80 , d ) 88 , e ) 48
Rationale: "according to the given conditions x + y = 18 and x ^ 2 + y ^ 2 = 180 now ( x + y ) ^ 2 = x ^ 2 + y ^ 2 + 2 xy so 18 ^ 2 = 180 + 2 xy so xy = 144 / 2 = 72 answer : a"
Answer: a
Problem: sam invested rs . 15000 @ 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 ) rs . 16,500 , b ) rs . 16 , 525.50 , c ) rs . 16 , 537.50 , d ) rs . 18,150 , e ) rs . 19,150
Rationale: "p = rs . 15000 ; r = 10 % p . a . = 5 % per half - year ; t = 1 year = 2 half - year amount = [ 15000 * ( 1 + 5 / 100 ) 2 ] = ( 15000 * 21 / 20 * 21 / 20 ) = rs . 16537.50 answer : c"
Answer: c
Problem: if the area of a square with sides of length 3 centimeters is equal to the area of a rectangle with a width of 3 centimeters , what is the length of the rectangle , in centimeters ?
Options: a ) 3 , b ) 8 , c ) 12 , d ) 16 , e ) 18
Rationale: "let length of rectangle = l 3 ^ 2 = l * 3 = > l = 9 / 3 = 3 answer a"
Answer: a
Problem: a is 1.5 times as fast as b . a alone can do the work in 30 days . if a and b work on alternative days , beginning with a , in how many days will the work be completed ?
Options: a ) 23 , b ) 22 , c ) 21 , d ) 36 , e ) 25
Rationale: "a can finish 1 work in 30 days b can finish 1 / 1.5 work in 30 days - since a is 1.5 faster than b this means b can finish 1 work in 30 * 1.5 days = 45 days now using the awesome gmat formula when two machines work together they can finish the job in = ab / ( a + b ) = 45 * 30 / ( 45 + 30 ) = 20 * 30 / 50 = 18 days since they alternate on days , it will take them double this time so total time = 18 * 2 = 36 days so answer is d"
Answer: d
Problem: 5355 x 51 = ?
Options: a ) 273105 , b ) 273243 , c ) 273247 , d ) 273250 , e ) 273258
Rationale: "5355 x 51 = 5355 x ( 50 + 1 ) = 5355 x 50 + 5355 x 1 = 267750 + 5355 = 273105 a"
Answer: a
Problem: he ratio between the sale price and the cost price of an article is 3 : 1 . what is the ratio between the profit and the cost price of that article ?
Options: a ) 2 : 1 , b ) 2 : 9 , c ) 2 : 4 , d ) 2 : 1 , e ) 2 : 5
Rationale: "let c . p . = rs . x and s . p . = rs . 3 x . then , gain = rs . 2 x required ratio = 2 x : x = 2 : 1 . answer : a"
Answer: a
Problem: p and q started a business investing rs . 85,000 and rs . 45,000 respectively . in what ratio the profit earned after 2 years be divided between p and q respectively ?
Options: a ) 17 : 6 , b ) 17 : 0 , c ) 17 : 4 , d ) 17 : 9 , e ) 17 : 3
Rationale: "p : q = 85000 : 45000 = 17 : 9 . answer : d"
Answer: d
Problem: there are a total of 100 jars on the shelf . small jars hold 3 liters and large jars hold 5 liters . the jars can hold a total of 376 liters . how many small jars are on the shelf ?
Options: a ) 49 , b ) 53 , c ) 56 , d ) 59 , e ) 62
Rationale: let s be the number of small jars and let l be the number of large jars . s + l = 100 . l = 100 - s . 3 s + 5 l = 376 . 3 s + 5 ( 100 - s ) = 376 . - 2 s + 500 = 376 . 2 s = 124 . s = 62 . the answer is e .
Answer: e
Problem: trapezoid jklm in the x - y plane has coordinates j = ( – 2 , – 5 ) , k = ( – 2 , 1 ) , l = ( 6 , 7 ) , and m = ( 6 , – 5 ) . what is its perimeter ?
Options: a ) 34 , b ) 35 , c ) 38 , d ) 40 , e ) ( f ) 42
Rationale: "jk = 6 lm = 11 kl = using distance formula 10 jm = using distance formula 8 sum of all is 35 b"
Answer: b
Problem: find large no . from below question the difference of two numbers is 1365 . on dividing the larger number by the smaller , we get 6 as quotient and the 10 as remainder
Options: a ) 1235 , b ) 1456 , c ) 1567 , d ) 1636 , e ) 1635
Rationale: "let the smaller number be x . then larger number = ( x + 1365 ) . x + 1365 = 6 x + 10 5 x = 1355 x = 271 large number = 271 + 1365 = 1636 d"
Answer: d
Problem: 1 , 0.2 , 0.08 , 0.48 , 0.0384 , ____
Options: a ) 0.0584 , b ) 0.0484 , c ) 0.0434 , d ) 0.0384 , e ) none
Rationale: "1 , 0.2 , 0.08 , 0.48 , 0.0384 , . . . . . 1 * 0.2 = 0.2 0.2 * 0.4 = 0.08 0.08 * 0.6 = 0.048 0.048 * 0.8 = 0.0384 so 0.0384 * 1 = 0.0384 answer : d"
Answer: d
Problem: a certain number when divided by 45 leaves a remainder 31 , what is the remainder if the same number be divided by 15 ?
Options: a ) 2 , b ) 7 , c ) 6 , d ) 1 , e ) 9
Rationale: "explanation : 45 + 31 = 76 / 15 = 1 ( remainder ) answer : d"
Answer: d
Problem: a person is saving money to purchase a car . he earns â £ 4000 per month and saves â £ 500 to buy the car . if he needs â £ 45000 to buy his dream car . how much money he will earn , before he saves enough money to buy the car ?
Options: a ) a - 352000 , b ) b - 356000 , c ) c - 360000 , d ) d - 348000 , e ) e - 340000
Rationale: he is saving â £ 500 per month . he needs â £ 45000 and it takes â £ 45000 / â £ 500 = 90 months to save the money . in 90 months , he earns 90 * â £ 4000 = â £ 36000 . answer : c
Answer: c
Problem: by investing rs . 1800 in 9 % stock , syam earns rs . 120 . the stock is then quoted at
Options: a ) rs . 135 , b ) rs . 96 , c ) rs . 85 , d ) rs . 122 , e ) rs . 142
Rationale: "explanation : assume that face value = rs . 100 . dividend per share = rs . 9 ( as it is a 9 % stock ) by investing rs . 1800 , he earns rs . 120 investment needed to earn rs . 9 = 1800 × 9 / 120 = rs . 135 ie , stock is then quoted ( then market value ) = rs . 135 answer : option a"
Answer: a
Problem: the rowing athletes in a rowing conference voted for coach of the year . each rower who voted chose exactly 3 coaches to vote for among the 36 coaches in the conference . if each of the 36 coaches received exactly 5 votes ( a 36 way tie ) , how many rowers voted for coach of the year ?
Options: a ) 60 , b ) 70 , c ) 75 , d ) 84 , e ) 90
Rationale: there were 36 * 5 = 180 total votes made . if each voter picked 3 coaches , there were 180 / 3 = 60 voters . a
Answer: a
Problem: i . x + 2 y + 3 z = 2 ii . x + y - z = 0 iii . 2 x + 2 y - z = 1 what is the value of y in the system above ?
Options: a ) - 2 , b ) - 1 , c ) 0 , d ) 1 , e ) 2
Rationale: 1 . from the given system of equations i can make equation ii . to be x + y = z 2 . now put that in iii . : 2 x + 2 y - ( x + y ) = 1 = 2 x + 2 y - x - y = 1 = x + y = 1 that gives usz = 1 ! 3 . put z = 1 in i . and solve : x + 2 y + 3 = 2 ; calculate minus 3 = x + 2 y = - 1 ; calculate minus x = 2 y = - 1 - x ; 4 . now put 2 y = - 1 - x in iii . and solve : 2 x + ( - 1 - x ) - 1 = 1 = x - 2 = 1 ; calculate plus 2 that gives usx = 3 5 . now solve for y with x = 3 and z = 1 : x + y = 1 = 3 + y = 1 ; calculate minus 3 that gives y = - 2 , and hence answer ( a ) - 2
Answer: a
Problem: if grapes are 90 % water and raisins are 15 % water , then how many kilograms did a quantity of raisins , which currently weighs 12 kilograms , weigh when all the raisins were grapes ? ( assume that the only difference between their raisin - weight and their grape - weight is water that evaporated during their transformation . )
Options: a ) 96 , b ) 98 , c ) 100 , d ) 102 , e ) 104
Rationale: "let x be the original weight of the grapes . the weight of the grape pulp was 0.1 x . since the grape pulp is 85 % of the raisins , 0.1 x = 0.85 ( 12 kg ) . then x = 8.5 * 12 = 102 kg . the answer is d ."
Answer: d
Problem: salesperson a ' s compensation for any week is $ 210 plus 6 percent of the portion of a ' s total sales above $ 1,000 for that week . salesperson b ' s compensation for any week is 8 percent of b ' s total sales for that week . for what amount of total weekly sales would both salespeople earn the same compensation ?
Options: a ) $ 3500 , b ) $ 5500 , c ) $ 7500 , d ) $ 9500 , e ) $ 11,500
Rationale: "210 + 0.06 ( x - 1000 ) = 0.08 x 0.02 x = 150 x = $ 7,500 the answer is c ."
Answer: c
Problem: a car travels uphill at 30 km / hr and downhill at 50 km / hr . it goes 100 km uphill and 50 km downhill . find the average speed of the car ?
Options: a ) 32 kmph , b ) 33 kmph , c ) 34 kmph , d ) 35 kmph , e ) 36 kmph
Rationale: "avg speed = total distance / total time . total distance traveled = 100 + 50 = 150 km ; time taken for uphill journey = 100 / 30 = 10 / 3 ; time taken for down hill journey = 50 / 50 = 5 / 5 ; avg speed = 150 / ( 10 / 3 + 5 / 5 ) = 35 kmph answer : d"
Answer: d
Problem: if [ [ x ] ] = x ^ 2 + 2 x + 4 , what is the value of [ [ 7 ] ] ?
Options: a ) 3 , b ) 9 , c ) 15 , d ) 67 , e ) 25
Rationale: "these functions questions might look intimidating , but they just test your knowledge about how well you can substitute values [ [ x ] ] = x ^ 2 + 2 x + 4 [ [ 7 ] ] = 7 ^ 2 + 2 * 7 + 4 = 67 . option d"
Answer: d
Problem: a fruit seller had some oranges . he sells 40 % oranges and still has 540 oranges . how many oranges he had originally ?
Options: a ) 700 , b ) 900 , c ) 720 , d ) 730 , e ) 740
Rationale: "60 % of oranges = 540 100 % of oranges = ( 540 × 100 ) / 6 = 900 total oranges = 900 answer : b"
Answer: b
Problem: if | 5 x - 15 | = 100 , then find the sum of the values of x ?
Options: a ) 1 , b ) - 2 , c ) 6 , d ) - 3 , e ) 4
Rationale: "| 5 x - 15 | = 100 5 x - 15 = 100 or 5 x - 15 = - 100 5 x = 115 or 5 x = - 85 x = 23 or x = - 17 sum = 23 - 17 = 6 answer is c"
Answer: c
Problem: the speed of a boat in still water is 25 kmph . if it can travel 10 km upstream in 1 hr , what time it would take to travel the same distance downstream ?
Options: a ) 26 minutes , b ) 23 minutes , c ) 15 minutes , d ) 19 minutes , e ) 28 minutes
Rationale: speed of boat in still water = 25 km / hr speed upstream = 10 ⁄ 1 = 10 km / hr speed of the stream = ( 25 - 10 ) = 15 km / hr speed downstream = ( 25 + 15 ) = 40 km / hr time taken to travel 10 km downstream = 10 / 40 hours = ( 10 × 60 ) / 40 = 15 minutes answer is c
Answer: c
Problem: a train 125 m long passes a man , running at 10 km / hr in the same direction in which the train is going , in 10 seconds . the speed of the train is ?
Options: a ) 36 , b ) 50 , c ) 55 , d ) 26 , e ) 29
Rationale: "speed of the train relative to man = ( 125 / 10 ) m / sec = ( 25 / 2 ) m / sec . [ ( 25 / 2 ) * ( 18 / 5 ) ] km / hr = 45 km / hr . let the speed of the train be x km / hr . then , relative speed = ( x - 10 ) km / hr . x - 10 = 45 = = > x = 55 km / hr answer : c"
Answer: c
Problem: on an order of 5 dozen boxes of a consumer product , a retailer receives an extra dozen free . this is equivalent to allowing him a discount of :
Options: a ) 15 % , b ) 16 1 / 6 % , c ) 16 2 / 3 % , d ) 20 % , e ) 30 %
Rationale: "clearly , the retailer gets 1 dozen out of 6 dozens free . equivalent discount = 1 / 6 * 100 = 16 2 / 3 % . answer : c"
Answer: c
Problem: seller selling an apple for rs . 17 , a seller loses 1 / 6 th of what it costs him . the cp of the apple is ?
Options: a ) 10 , b ) 12 , c ) 18 , d ) 19 , e ) 20
Rationale: "sp = 17 loss = cp 18 loss = cp − sp = cp − 17 ⇒ cp 18 = cp − 17 ⇒ 17 cp 18 = 17 ⇒ cp 18 = 1 ⇒ cp = 18 c"
Answer: c
Problem: there are two positive numbers in the ratio 7 : 11 . if the larger number exceeds the smaller by 16 , then find the smaller number ?
Options: a ) 25 , b ) 26 , c ) 30 , d ) 24 , e ) 28
Rationale: let the two positive numbers be 7 x and 11 x respectively . 11 x - 7 x = 16 4 x = 16 = > x = 4 = > smaller number = 7 x = 28 . answer : e
Answer: e
Problem: what is rate of interest if principal . amount be 400 , simple interest 120 and time 2 year .
Options: a ) 10 , b ) 12.5 , c ) 25 , d ) 12 , e ) 15
Rationale: "s . i = ( p * r * t ) / 100 120 = 800 r / 100 r = 120 / 8 = 15 % answer e"
Answer: e
Problem: a fair coin is tossed 15 times . what is the probability of getting more heads than tails in 15 tosses ?
Options: a ) 1 / 2 , b ) 63 / 128 , c ) 4 / 7 , d ) 61 / 256 , e ) 63 / 64
Rationale: "on each toss , the probability of getting a head is 1 / 2 and the probability of getting a tail is 1 / 2 . there is no way to get the same number of heads and tails on an odd number of tosses . there will either be more heads or more tails . then there must be more heads on half of the possible outcomes and more tails on half of the possible outcomes . p ( more heads ) = 1 / 2 the answer is a ."
Answer: a
Problem: a bowler can take max . 3 wickets in a over . if he bowls 6 overs in an innings , how many maximum wickets can he take ?
Options: a ) 8 , b ) 9 , c ) 11 , d ) 7 , e ) 10
Rationale: 10 because after 10 wickets , the innings is complete . answer : e
Answer: e
Problem: if the personal income tax rate is lowered from 42 % to 32 % , what is the differential savings for a tax payer having an annual income before tax to the tune of $ 42400 ?
Options: a ) $ 3500 , b ) $ 5000 , c ) $ 4240 , d ) $ 7000 , e ) $ 10000
Rationale: "saving = ( 42 - 32 ) % of 42400 = 4240 . answer : c"
Answer: c
Problem: ( 5568 / 87 ) 1 / 3 + ( 72 x 2 ) 1 / 2 = ( ? ) 1 / 2 ?
Options: a ) 256 , b ) 4 , c ) √ 2 , d ) 16 , e ) none
Rationale: answer ? ) 1 / 2 = ( 5568 / 87 ) 1 / 3 + ( 72 x 2 ) 1 / 2 = ( 64 ) 1 / 3 + ( 144 ) 1 / 2 ∴ ? = ( 4 + 12 ) 2 = 256 correct option : a
Answer: a
Problem: at the end of the first quarter , the share price of a certain mutual fund was 20 percent higher than it was at the beginning of the year . at the end of the second quarter , the share price was 50 percent higher than it was at the beginning of the year . what was the percent increase in the share price from the end of the first quarter to the end of the second quarter ?
Options: a ) 20 % , b ) 25 % , c ) 30 % , d ) 33 % , e ) 40 %
Rationale: say price at the beginning of year = 100 end of 1 st quarter = 100 + 20 = 120 end of 2 nd quarter = 100 + 50 = 150 percentage increase between 1 st & 2 nd quarter = 150 − 120 / 120 ∗ 100 = 25 answer = b
Answer: b
Problem: find the 25 % of rs . 800 .
Options: a ) s . 50 , b ) s . 200 , c ) s . 100 , d ) s . 80 , e ) s . 60
Rationale: "explanation : 25 % of 800 = > 25 / 100 * 800 = rs . 200 answer : b"
Answer: b
Problem: what is the 50 th digit to the right of the decimal point in the decimal form of 48 / 88 ?
Options: a ) 6 , b ) 7 , c ) 9 , d ) 11 , e ) 4
Rationale: "we have to use some long division . this long division allows us to get 48 / 88 in decimal form , which is 0.545454 … where “ 54 ” is repeating . we can see that the 1 st , 3 rd , 5 th digit to the right of the decimal point is a 5 and that the 2 nd , 4 th , 6 th digit to the right of the decimal point is a 4 . in other words , each odd - positioned digit is a 5 , and each even - positioned digit is a 4 . then about the 50 digit to the right of the decimal point and we see that 50 is even , we know that the 50 th digit is a 4 . answer e ."
Answer: e
Problem: a crate measures 5 feet by 8 feet by 12 feet on the inside . a stone pillar in the shape of a right circular cylinder must fit into the crate for shipping so that it rests upright when the crate sits on at least one of its six sides . what is the radius , in feet , of the pillar with the largest volume that could still fit in the crate ?
Options: a ) 2 , b ) 4 , c ) 5 , d ) 8 , e ) 12
Rationale: "we can find the radius of all the three cases of cylinders . the only crux to find the answer faster is that : voulme is pi * r ^ 2 * h . the volume is a function of r ^ 2 . so r has to be the highest to find the largest volume . so r = 5 for the surface 8 * 12 face . volume = 125 pi answer c"
Answer: c
Problem: a pharmaceutical company received $ 4 million in royalties on the first $ 50 million in sales of and then $ 12 million in royalties on the next $ 170 million in sales . by approximately what percentage did the ratio of royalties to sales decrease from the first $ 50 million in sales to the next $ 170 million in sales ?
Options: a ) 12 % , b ) 15 % , c ) 45 % , d ) 52 % , e ) 56 %
Rationale: "( 12 / 170 ) / ( 4 / 50 ) = 15 / 17 = 88 % it means that 12 / 170 represents only 88 % . therefore a decrease of 12 % . answer a"
Answer: a
Problem: what is the minimum number of square tiles required to tile a floor of length 5 metres 78 cm and width 3 metres 74 cm ?
Options: a ) 187 , b ) 180 , c ) 190 , d ) 195 , e ) 197
Rationale: length = width = = > square = 5 m 78 cm and 3 m 74 5 m 78 cm = 578 cm and 3 m 74 cm = 374 cm hcf of 578 and 374 = 34 square is 34 = 578 * 374 / 34 * 34 = = 17 * 11 = 187 answer a
Answer: a
Problem: three rugs have a combined area of 204 square meters . by overlapping the rugs to cover floor area of 140 square meters , the area that is covered by exactly two layers of rug is 24 square meters . what is the area that is covered with three layers of rug ?
Options: a ) 18 square meters , b ) 20 square meters , c ) 24 square meters , d ) 28 square meters , e ) 30 square meters
Rationale: "total = rug 1 + rug 2 + rug 3 - { overlap of exactly 2 rugs } - 2 * { overlap of exactly 3 rugs } 140 = 204 - 24 - 2 * { overlap of exactly 2 rugs } - - > { overlap of exactly 3 rugs } = 20 . answer : b ."
Answer: b
Problem: there is a train and car . the ratio between the speed of a train & a car is 24 : 19 respectively . also , a bus covered a distance of 320 km in 5 hours . the speed of the bus is 2 / 3 rd of the speed of the train . how many kilometers will the car cover in 4 hours ?
Options: a ) 276 , b ) 290 , c ) 304 , d ) 318 , e ) 332
Rationale: "the speed of the bus is 320 / 5 = 64 km / hr the speed of the train is ( 64 * 3 ) / 2 = 96 km / hr the speed of the car is 96 / 24 * 19 = 76 km / hr the distance covered by the car in 4 hours is 76 × 4 = 304 km the answer is c ."
Answer: c
Problem: in a group of 100 cars , 37 cars do not have air conditioning . if at least 41 cars have racing stripes , what is the greatest number of cars that could have air conditioning but not racing stripes ?
Options: a ) 45 , b ) 47 , c ) 59 , d ) 51 , e ) 53
Rationale: "lets assume ac = 63 ( includesonly ac carsandcars with ac and racing stripes ) lets assume rs ( racing stripes ) > = 41 ( includescars with ac and racing stripesandonly racing stripes ) . now since we want to maximize ( only ac ) we have to see to it thatcars with ac and racing stripesis minimal ( assume 0 ) but since rs > = 41 . . we have to assign atleast 4 tocars with ac and racing stripes . hence ac = 63 - 4 = 59 . the answer is"
Answer: c
Problem: a man goes downstream at 12 kmph , and upstream 8 kmph . the speed of the stream is
Options: a ) 2 kmph , b ) 4 kmph , c ) 16 kmph , d ) 2.5 kmph , e ) 26 kmph
Rationale: "speed of the stream = 1 / 2 ( 12 - 8 ) kmph = 2 kmph . correct option a"
Answer: a
Problem: micheal and adam can do together a piece of work in 20 days . after they have worked together for 18 days micheal stops and adam completes the remaining work in 10 days . in how many days micheal complete the work separately .
Options: a ) 25 days , b ) 100 days , c ) 120 days , d ) 110 days , e ) 90 days
Rationale: "rate of both = 1 / 20 together they do = 1 / 20 * 18 = 9 / 10 left work = 1 - 9 / 10 = 1 / 10 adam completes 1 / 10 work in 10 day so he took 10 * 10 = 100 days to complete the left work alone . thus the rate of adam is 1 / 100 rate of micheal = 1 / 20 - 1 / 100 = 1 / 25 thus micheal takes 25 days to complete the whole work . ans . a ."
Answer: a
Problem: sides of a rectangular park are in the ratio 3 : 2 and its area is 3750 sq m , the cost of fencing it at 30 ps per meter is ?
Options: a ) s . 122 , b ) s . 105 , c ) s . 125 , d ) s . 120 , e ) s . 121
Rationale: "3 x * 2 x = 3750 = > x = 25 2 ( 75 + 30 ) = 210 m 210 * 1 / 2 = rs . 105 answer : b"
Answer: b
Problem: how many 7 in between 1 to 80 ?
Options: a ) 18 , b ) 20 , c ) 22 , d ) 23 , e ) 24
Rationale: "7 , 17,27 , 37,47 , 57,67 , 70,71 , 72,73 , 74,75 , 76,77 ( two 7 ' s ) , 78,79 18 7 ' s between 1 to 80 answer : a"
Answer: a
Problem: a batsman in his 12 th innings makes a score of 115 and thereby increases his average by 3 runs . what is his average after the 12 th innings if he had never been ‘ not out ’ ?
Options: a ) 42 , b ) 43 , c ) 44 , d ) 82 , e ) 46
Rationale: "let ‘ x ’ be the average score after 12 th innings ⇒ 12 x = 11 × ( x – 4 ) + 115 ∴ x = 82 answer d"
Answer: d
Problem: the ratio 3 : 5 expressed as a percent equals
Options: a ) 60 % , b ) 40 % , c ) 80 % , d ) 125 % , e ) none
Rationale: "solution 3 : 5 = 3 / 5 = ( 3 / 5 x 100 ) % . = 60 % . answer a"
Answer: a
Problem: when positive integer n is divided by positive integer j , the remainder is 28 . if n / j = 142.07 , what is value of j ?
Options: a ) 300 , b ) 375 , c ) 400 , d ) 460 , e ) 500
Rationale: when a number is divided by another number , we can represent it as : dividend = quotient * divisor + remainder so , dividend / divisor = quotient + remainder / divisor given that n / j = 142.07 here 142 is the quotient . given that remainder = 28 so , 142.07 = 142 + 28 / j so , j = 400 answer - c
Answer: c
Problem: find the annual dividend received by nishita from 1200 preferred shares and 3000 common shares both of par value rs . 50 each if the dividend paid on preferred shares is 10 % and semi - annual dividend of 3 ½ % is declared on common shares .
Options: a ) 16000 , b ) 16500 , c ) 17000 , d ) 17500 , e ) 18000
Rationale: total number of preferred shares = 1200 face value = rs . 50 dividend paid on preferred shares is 10 % dividend per share = 50 × 10 / 100 = rs . 5 total dividend = 1200 × 5 = 6000 total number of common shares = 3000 face value = rs . 50 semi - annual dividend of 3 ½ % is declared on common shares . semi - annual dividend per share = 50 × 7 / 2 × 100 = rs . 74 total semi - annual dividend = 7 / 4 × 3000 = rs . 5250 annual dividend = rs . 5250 × 2 = rs . 10500 total dividend on all all shares ( preferred and common ) = 6000 + 10500 = rs . 16500 answer is b .
Answer: b
Problem: length of a rectangular plot is 32 mtr more than its breadth . if the cost of fencin gthe plot at 26.50 per meter is rs . 5300 , what is the length of the plot in mtr ?
Options: a ) 56 m , b ) 66 m , c ) 76 m , d ) 86 m , e ) 96 m
Rationale: "let breadth = x metres . then , length = ( x + 32 ) metres . perimeter = 5300 m = 200 m . 26.50 2 [ ( x + 32 ) + x ] = 200 2 x + 32 = 100 2 x = 68 x = 34 . hence , length = x + 32 = 66 m b"
Answer: b
Problem: the distance from city a to city b is 120 miles . while driving from city a to city b , bob drives at a constant speed of 40 miles per hour . alice leaves city a 30 minutes after bob . what is the minimum constant speed in miles per hour that alice must exceed in order to arrive in city b before bob ?
Options: a ) 45 , b ) 48 , c ) 50 , d ) 52 , e ) 54
Rationale: the time it takes bob to drive to city b is 120 / 40 = 3 hours . alice needs to take less than 2.5 hours for the trip . alice needs to exceed a constant speed of 120 / 2.5 = 48 miles per hour . the answer is b .
Answer: b
Problem: solve : 12.05 * 5.4 + 0.6
Options: a ) 108.45 , b ) 110.45 , c ) 106.45 , d ) 109.45 , e ) none of them
Rationale: = 12.05 * ( 5.4 / 0.6 ) = ( 12.05 * 9 ) = 108.45 answer is a .
Answer: a
Problem: an investment yields an interest payment of $ 225 each month . if the simple annual interest rate is 9 % , what is the amount of the investment ?
Options: a ) $ 30,000 , b ) $ 30,400 , c ) $ 31,300 , d ) $ 32,500 , e ) $ 35,100
Rationale: "let the principal amount = p simple annual interest = 9 % simple monthly interest = ( 9 / 12 ) = ( 3 / 4 ) % ( 3 / 4 ) * ( p / 100 ) = 225 = > p = ( 225 * 4 * 10 ^ 2 ) / 3 = 75 * 4 * 10 ^ 2 = 300 * 10 ^ 2 = 30000 answer a"
Answer: a
Problem: list i : { y , 2 , 4 , 7 , 10 , 11 } list ii : { 3 , 3 , 4 , 6 , 7 , 10 } if the median q of list i is equal to the sum of the median of list ii and the mode of list ii , then y equals
Options: a ) 5 , b ) 7 , c ) 8 , d ) q = 9 , e ) 10
Rationale: mode of list ii = 3 median q of list ii = 4 + 6 / 2 = 5 sum of mode + mean = 3 + 5 = 8 now to make 8 as the median we need to find a value of y such that if the no . of terms in list 1 are odd then y = 8 else if even then 7 + y / 2 = 8 here its even so 7 + y / 2 = 8 from this y = 9 ( d )
Answer: d
Problem: in a college the ratio of the numbers of boys to the girls is 8 : 5 . if there are 135 girls , the total number of students in the college is ?
Options: a ) 562 , b ) 351 , c ) 452 , d ) 416 , e ) 512
Rationale: "let the number of boys and girls be 8 x and 5 x then , 5 x = 135 x = 27 total number of students = 13 x = 13 * 27 = 351 answer is b"
Answer: b
Problem: an agent , gets a commission of 2.5 % on the sales of cloth . if on a certain day , he gets rs . 18 as commission , the cloth sold through him on that day is worth
Options: a ) 333 , b ) 500 , c ) 887 , d ) 720 , e ) 132
Rationale: "explanation : let the total sale be rs . x . then , 2.5 % . of x = 18 < = > ( 25 / 10 * 1 / 100 * x ) = 18 < = > x = 720 . answer : d"
Answer: d
Problem: if 45 - [ 28 - { 37 - ( 15 - * ) } ] = 58 , then * is equal to :
Options: a ) - 29 , b ) - 19 , c ) 19 , d ) 29 , e ) 39
Rationale: "45 - [ 28 - { 37 - ( 15 - * ) } ] = 58 = > 45 - [ 28 - { 37 - 15 + * } ] = 58 45 - [ 28 - 37 + 15 - * ] = 58 = > 45 [ 43 - 37 - * ] = 58 45 - [ 6 - * ] = 58 = > 45 - 6 + * = 58 39 + * = 58 = > * = 58 - 39 = 19 answer : c"
Answer: c
Problem: if the wheel is 14 cm then the number of revolutions to cover a distance of 1056 cm is ?
Options: a ) 17 , b ) 19 , c ) 17 , d ) 12 , e ) 91
Rationale: "2 * 22 / 7 * 14 * x = 1056 = > x = 12 answer : d"
Answer: d
Problem: a man walked a certain distance south and then the same distance plus 7 km due west . he is now 13 km from his starting point . what are the distances south and west that he walked ?
Options: a ) 512 , b ) 612 , c ) 712 , d ) 513 , e ) 613
Rationale: if a man walked distance ( in km ) ' x ' towards south & then ' x + 7 ' towards west . distance from starting point = hypotenuse of a right triangle with sides x & ( x + 7 ) so 13 ^ 2 = x ^ 2 + ( x + 7 ) ^ 2 x ^ 2 + 7 x - 60 = 0 or ( x + 12 ) ( x - 5 ) = 0 , so x = 5 distance towards west = x + 7 = 5 + 7 = 12 km . answer : a
Answer: a
Problem: out of 40 applicants to a law school , 15 majored in political science , 20 had a grade point average higher than 3.0 , and 10 did not major in political science and had a gpa equal to or lower than 3.0 . how many r applicants majored in political science and had a gpa higher than 3.0 ?
Options: a ) 5 , b ) 10 , c ) 15 , d ) 25 , e ) 35
Rationale: "total applicants = 40 political science = 15 and non political science = 40 - 15 = 25 gpa > 3.0 = 20 and gpa < = 3.0 = 20 10 non political science students had gpa < = 3.0 - - > 15 non political science students had gpa > 3.0 gpa > 3.0 in political science = total - ( gpa > 3.0 in non political science ) r = 20 - 15 = 5 answer : a"
Answer: a
Problem: a grocer is storing soap boxes in cartons that measure 25 inches by 42 inches by 60 inches . if the measurement of each soap box is 7 inches by 12 inches by 5 inches , then what is the maximum number of soap boxes that can be placed in each carton ?
Options: a ) 210 , b ) 150 , c ) 280 , d ) 300 , e ) 420
Rationale: "however the process of dividing the volume of box by the volume of a soap seems flawed but it does work in this case due to the numbers dimensions of the box = 25 * 42 * 60 dimensions of the soap = 5 * 12 * 7 placing the 7 inch side along 42 inch side we get 6 soaps in a line and in a similar way 5 along 25 and 6 along 60 we get = 5 x 6 x 5 = 150 so the question is why this particular arrangement , in order to maximize number of soaps we need to minimize the space wasted and this is the only config where we dont waste any space so we can expect the maximum number the answer is ( b )"
Answer: b
Problem: if 25 % of x is 15 less than 15 % of 1600 , then x is ?
Options: a ) 872 , b ) 738 , c ) 900 , d ) 840 , e ) 83
Rationale: "25 % of x = x / 4 ; 15 % of 1600 = 15 / 100 * 1600 = 240 given that , x / 4 = 240 - 15 = > x / 4 = 225 = > x = 900 . answer : c"
Answer: c
Problem: 30 ladies and 60 gentlemen are present at a party . there are 23 couples among them . if a lady and a gentleman is selected at random , what is the probability that they will be a couple ?
Options: a ) 1 / 200 , b ) 1 / 100 , c ) 1 / 50 , d ) 1 / 40 , e ) 23 / 1800
Rationale: in how many ways we can select a woman and a man from 30 women and 60 men ? in 30 * 60 = 1800 ways . we have a total of 23 couples so , the probability of selecting a couple is 23 / 1800 = 23 / 1800 . ans - e
Answer: e
Problem: in a class , 30 % of the students speaks truth , 20 % speaks lie and 10 % speaks both . if a student is selected at random , what is the probability that he has speak truth or lie ?
Options: a ) 1 / 4 , b ) 2 / 3 , c ) 3 / 5 , d ) 2 / 5 , e ) 2 / 7
Rationale: d ) 2 / 5
Answer: d
Problem: the milk level in a rectangular box measuring 50 feet by 25 feet is to be lowered by 6 inches . how many gallons of milk must be removed ? ( 1 cu ft = 7.5 gallons )
Options: a ) 100 , b ) 250 , c ) 750 , d ) 4687.5 , e ) 5635.5
Rationale: "6 inches = 1 / 2 feet ( there are 12 inches in a foot . ) , so 50 * 25 * 1 / 2 = 625 feet ^ 3 of milk must be removed , which equals to 625 * 7.5 = 4687.5 gallons . answer : d ."
Answer: d
Problem: in the new budget , the price of kerosene oil rose by 25 % . by how much percent must a person reduce his consumption so that his expenditure on it does not increase ?
Options: a ) 10 , b ) 20 , c ) 30 , d ) 40 , e ) none of them
Rationale: reduction in consumption = [ ( ( r / ( 100 + r ) ) * 100 ] % = [ ( 25 / 125 ) * 100 ] % = 20 % . answer is b .
Answer: b
Problem: the length of minute hand of a clock is 5.2 cm . what is the area covered by this in 10 minutes
Options: a ) 15.27 , b ) 14.15 , c ) 17.27 , d ) 18.27 , e ) 19.27
Rationale: "area of circle is pi * r ^ 2 but in 10 minutes area covered is ( 10 / 60 ) * 360 = 60 degree so formula is pi * r ^ 2 * ( angle / 360 ) = 3.14 * ( 5.2 ^ 2 ) * ( 60 / 360 ) = 14.15 cm ^ 2 answer : b"
Answer: b
Problem: the lcm of two numbers is 2310 and hcf is 26 . if one of the numbers is 210 . then what is the other number ?
Options: a ) 715 , b ) 825 , c ) 286 , d ) 582 , e ) 465
Rationale: "first number * second number = lcm * hcf other number = 2310 * 26 / 210 = 11 * 26 = 286 answer : c"
Answer: c
Problem: find the compound interest accrued on an amount of rs . 14,800 at 13.5 % p . a at the end of two years . ( round off your answer to nearest integer )
Options: a ) 3337 , b ) 2782 , c ) 2788 , d ) 4266 , e ) 2321
Rationale: ci = 14800 { [ 1 + 13.5 / 100 ] 2 - 1 } = 14800 { [ 1 + 27 / 200 ] 2 - 1 = 14800 { 2 + 27 / 200 } { 27 / 200 } = ( 74 ) [ 2 + 27 / 200 ] ( 27 ) = 1998 [ 2 + 27 / 200 ] = 3996 + 269.73 = rs . 4266 answer : d
Answer: d
Problem: if all of the telephone extensions in a certain company must be even numbers , and if each of the extensions uses all 4 of the digits 1 , 2 , 3 , and 8 , what is the greatest number of 4 - digit extensions that the company can have ?
Options: a ) 4 , b ) 6 , c ) 12 , d ) 16 , e ) 24
Rationale: since the phone number must be even , the unit ' s digit can be either 2 or 8 . when the unit ' s digit is 2 - - > number of possibilities is 3 ! = 6 when the unit ' s digit is 8 - - > number of possibilities is 3 ! = 6 largest number of extensions = 6 + 6 = 12 answer : c
Answer: c
Problem: a rectangular grass field is 75 m * 55 m , it has a path of 2.5 m wide all round it on the outside . find the area of the path and the cost of constructing it at rs . 7 per sq m ?
Options: a ) 4350 , b ) 4725 , c ) 4328 , d ) 4329 , e ) 4829
Rationale: "area = ( l + b + 2 d ) 2 d = ( 75 + 55 + 2.5 * 2 ) 2 * 2.5 = > 675 675 * 7 = rs . 4725 answer : b"
Answer: b
Problem: of 40 applicants for a job , 24 had at least 4 years ' experience , 15 had degrees , and 4 had less than 4 years ' experience and did not have a degree . how many of the applicants had at least 4 years ' experience and a degree ?
Options: a ) 14 , b ) 3 , c ) 9 , d ) 7 , e ) 5
Rationale: "set a : people with more than 4 years exp set b : people with degree aub = total - ( less than 4 exp and no degree ) aub = 40 - 4 = 36 aub = a + b - aib aib = 15 + 24 - 36 = 3 answer b"
Answer: b
Problem: what is the sum of all the multiples of 3 between 30 and 80 ?
Options: a ) 2103 , b ) 2106 , c ) 1053 , d ) 1252 , e ) 1535
Rationale: "you first have to know all the multiples of 3 between 30 and 80 . they are 3 , 6,9 , 12,15 , 18,21 , 24,27 , 30,33 , 36,39 , 42,45 , 48,51 , 54,57 , 60,63 , 66,69 , 72,75 , and 78 . if you add all these numbers together , you get 1053 . final answer : c"
Answer: c
Problem: the first half of the 20 th century , the population of a particular country increased by 200 percent . in the second half of the century , the population increased by 300 percent . what was the percent increase for the 20 th century as a whole ?
Options: a ) 500 % , b ) 600 % , c ) 800 % , d ) 1100 % , e ) 1200 %
Rationale: say initially population was 100 . what is 200 % of 100 ? it is 200 / 100 * 100 = 200 . an increase of 200 % means the new population became 100 + 200 = 300 what is 300 % of 300 ? it is 300 / 100 * 300 = 900 an increase of 300 % means the new population now is 300 + 900 = 1200 so from 100 , the population increased to 1200 i . e . an increase of 1100 . 1100 is what percent of 100 ? 1100 = x / 100 * 100 i . e . it is 1100 % d
Answer: d
Problem: at a certain restaurant , the average ( arithmetic mean ) number of customers served for the past x days was 60 . if the restaurant serves 120 customers today , raising the average to 70 customers per day , what is the value of x ?
Options: a ) 2 , b ) 5 , c ) 9 , d ) 15 , e ) 30
Rationale: "withoutusing the formula , we can see that today the restaurant served 50 customers above the average . the total amount above the average must equal total amount below the average . this additional 50 customers must offset the “ deficit ” below the average of 70 created on the x days the restaurant served only 60 customers per day . 50 / 10 = 5 days . choice ( a ) . withthe formula , we can set up the following : 70 = ( 60 x + 120 ) / ( x + 1 ) 70 x + 70 = 60 x + 120 10 x = 50 x = 5 answer choice ( b )"
Answer: b
Problem: 100 students appeared in 2 tests . 60 students passed 1 st test . 40 students passed in the 2 nd test . 20 students passed in both 1 and 2 tests . what is the probability of the students who failed in both tests ?
Options: a ) 10 % , b ) 15 % , c ) 20 % , d ) 25 % , e ) 30 %
Rationale: 20 student passed both two test 40 student passed only 1 st test 20 student passed only 2 nd test so 100 - ( 20 + 40 + 20 ) = 20 student failed in both sub so ans is 20 % answer : c
Answer: c
Problem: how many 3 - digit even numbers are possible such that if one of the digits is 5 , the next / succeeding digit to it should be 6
Options: a ) 5 , b ) 305 , c ) 365 , d ) 405 , e ) 495
Rationale: 560 , 562 , 564 , 566 , and 568 , so total 5 . hence option a .
Answer: a
Problem: there has been successive increases of 30 % and then 20 % in the price of gas from the previous month . by what percentage should a driver reduce gas consumption so that the expenditure does not change ?
Options: a ) 20 % , b ) 24 % , c ) 28 % , d ) 32 % , e ) 36 %
Rationale: "let p be the original price per unit of gas . let x be the original gas consumption . let y be the reduced gas consumption . y * 1.2 * 1.3 * p = x * p y = x / ( 1.2 * 1.3 ) which is about 0.64 x which is a decrease of about 36 % . the answer is e ."
Answer: e
Problem: a train speeds past a pole in 50 seconds and a platform 500 m long in 100 seconds . its length is :
Options: a ) 550 m . , b ) 300 m . , c ) 600 m . , d ) 400 m . , e ) 500 m .
Rationale: "let the length of the train be x meters and its speed be y m / sec . they , x / y = 50 = > y = x / 50 x + 500 / 100 = x / 50 x = 500 m . answer : option e"
Answer: e
Problem: if m is an integer such that ( - 2 ) ^ 2 m = 2 ^ ( 24 - m ) then m = ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: "2 m = 24 - m 3 m = 24 m = 8 the answer is b ."
Answer: b
Problem: a seller of used cars has 16 cars to sell and each of his clients selected 2 cars that he liked most . if each car was selected exactly thrice , how many clients visited the garage ?
Options: a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 24
Rationale: ifno caris selected more than once then the number of clients = 16 / 2 = 8 but since every car is being selected three times so no . of clients must be thrice as well = 8 * 3 = 24 answer : option e
Answer: e
Problem: two numbers are in the ratio 3 : 5 . if 9 be subtracted from each , they are in the ratio of 9 : 17 . the first number is ?
Options: a ) 36 , b ) 76 , c ) 98 , d ) 27 , e ) 24
Rationale: "( 3 x - 9 ) : ( 5 x - 9 ) = 9 : 17 x = 12 = > 3 x = 36 answer : a"
Answer: a
Problem: the smallest fraction , which each of 6 / 7 , 5 / 14 , 10 / 21 will divide exactly is ?
Options: a ) 30 / 7 , b ) 30 / 9 , c ) 30 / 2 , d ) 30 / 3 , e ) 30 / 6
Rationale: "required fraction = l . c . m of 6 / 7 , 5 / 14 , 10 / 21 = ( l . c . m of 6 , 5 , 10 ) / ( h . c . f of 7 , 14 , 21 ) = 30 / 7 answer : a"
Answer: a
Problem: a solution contains 8 parts of water for every 7 parts of lemonade syrup . how many parts of the solution should be removed and replaced with water so that the solution will now contain 40 % lemonade syrup ?
Options: a ) 1.5 , b ) 1.75 , c ) 2.14 , d ) 2.34 , e ) 2.64
Rationale: "let the total solution is 150 l with 80 l water & 70 l syrup . to make 40 % syrup solution , the result solution must have 90 l syrup and 60 l syrup . therefore we are taking 10 l of syrup from initial solution and replacing with water . using urinary method : 70 l syrup in 150 l solution 10 l syrup in 21.4 l solution we started by multiplying 10 now to get to the result we need to divide by 10 = > amount of solution to be replaced with water = ( 21.4 / 10 ) = 2.14 . correct option : c"
Answer: c
Problem: the length of a rectangular floor is more than its breadth by 200 % . if rs . 640 is required to paint the floor at the rate of rs . 5 per sq m , then what would be the length of the floor ?
Options: a ) 19.6 m . , b ) 20.0 m . , c ) 19.3 m . , d ) 18.5 m . , e ) 18.9 m .
Rationale: "let the length and the breadth of the floor be l m and b m respectively . l = b + 200 % of b = l + 3 b = 3 b area of the floor = 640 / 5 = 128 sq m l b = 128 i . e . , l * l / 3 = 128 l 2 = 384 = > l = 19.6 m . answer : a"
Answer: a
Problem: a reduction of 15 % in the price of wheat enables a house wife to obtain 3 kgs more for rs . 500 , what is the reduced price for kg ?
Options: a ) rs . 10 , b ) rs . 15 , c ) rs . 20 , d ) rs . 25 , e ) rs . 30
Rationale: explanation : 500 * ( 15 / 100 ) = 75 - - - - 3 ? - - - - 1 = > rs . 25 answer : d
Answer: d
Problem: in a certain corporation , there are 300 male employees and 150 female employees . it is known that 20 % of the male employees have advanced degrees and 40 % of the females have advanced degrees . if one of the 450 employees is chosen at random , what is the probability this employee has an advanced degree or is female ?
Options: a ) 7 / 15 , b ) 3 / 10 , c ) 3 / 5 , d ) 2 / 5 , e ) 3 / 4
Rationale: "p ( female ) = 150 / 450 = 1 / 3 p ( male with advanced degree ) = 0.2 * 300 / 450 = 60 / 450 = 2 / 15 the sum of the probabilities is 7 / 15 the answer is a ."
Answer: a
Problem: the ration of the father ’ s age to his son ’ s age is 7 : 3 . the product of their ages is 756 . the ratio of their ages after 6 years will be :
Options: a ) 5 : 2 , b ) 2 : 1 , c ) 11 : 7 , d ) 13 : 9 , e ) none of these
Rationale: solution let the present ages of the father and son be 7 x and 3 x years respectively . then , 7 x 3 x = 756 ⇔ 21 x 2 = 756 ⇔ x 2 = 36 ⇔ x = 6 . ∴ required ratio = ( 7 x + 6 ) : ( 3 x + 6 ) = 48 : 24 = 2 : 1 . answer b
Answer: b
Problem: at a certain university , 68 % of the professors are women , and 70 % of the professors are tenured . if 90 % of the professors are women , tenured , or both , then what percent of the men are tenured ?
Options: a ) 25 , b ) 37.5 , c ) 55 , d ) 62.5 , e ) 75
Rationale: total women = 68 % total men = 40 % total tenured = 70 % ( both men and women ) therefore , women tenured + women professors + men tenured = 90 % men tenured = 22 % but question wants to know the percent of men that are tenured 22 % / 40 % = 55 % c
Answer: c