regisss/math_qa huggingface dataset:
Problem: in an election between two candidates , the winner has a margin of 10 % of the votes polled . if 1500 people change their mind and vote for the loser , the loser would have won by a margin of 10 % of the votes polled . find the total number of votes polled in the election ?
Options: a ) 30,000 , b ) 15,450 , c ) 45,000 , d ) 60,000 , e ) 15,000
Rationale: "total # of votes cast = 100 x , out of these , let the # of votes won by the winner = w , and for the loser ( l ) = 100 x - w . given that w - ( 100 x - w ) = 10 % of total votes cast = 10 x thus , 2 w - 100 x = 10 x → → w = 55 x and l = 100 x - 55 x = 45 x . according to the new condition , if the loser had won 45 x + 1500 votes , then , ( 45 x + 1500 ) - ( 55 x - 1500 ) = 10 % of total votes cast = 10 x thus , 3000 = 20 x and 100 x = 15000 answer : e"
Answer: e
Problem: in a certain game of dice , the player ’ s score is determined as a sum of three throws of a single die . the player with the highest score wins the round . if more than one player has the highest score , the winnings of the round are divided equally among these players . if john plays this game against 22 other players , what is the probability of the minimum score that will guarantee john some monetary payoff ?
Options: a ) 41 / 50 , b ) 1 / 216 , c ) 1 / 221 , d ) 1 / 84 , e ) 1 / 42
Rationale: "to guarantee that john will get some monetary payoff he must score the maximum score of 6 + 6 + 6 = 18 , because if he gets even one less than that so 17 , someone can get 18 and john will get nothing . p ( 18 ) = 1 / 6 ^ 3 = 1 / 216 . answer : b ."
Answer: b
Problem: line m lies in the xy - plane . the y - intercept of line m is - 2 , and line m passes through the midpoint of the line segment whose endpoints are ( 2 , 8 ) and ( 8 , - 2 ) . what is the slope of line m ?
Options: a ) - 2 , b ) - 1 , c ) 0 , d ) 1 , e ) 2
Rationale: "the midpoint of ( 2,8 ) and ( 8 , - 2 ) is ( 5,3 ) . the slope of a line through ( 0 , - 2 ) and ( 5,3 ) is ( 3 - ( - 2 ) ) / ( 5 - 0 ) = 5 / 5 = 1 the answer is d ."
Answer: d
Problem: the sale price sarees listed for rs . 340 after successive discount is 20 % and 15 % is ?
Options: a ) 298 , b ) 231 , c ) 342 , d ) 876 , e ) 291
Rationale: "340 * ( 80 / 100 ) * ( 85 / 100 ) = 231 answer : b"
Answer: b
Problem: what is 5 + 7
Options: a ) 2 , b ) 4 , c ) 10 , d ) 12 , e ) 11
Rationale: d
Answer: d
Problem: a train crosses a platform of 100 m in 15 sec , same train crosses another platform of length 250 m in 20 sec . then find the length of the train ?
Options: a ) 150 , b ) 88 , c ) 77 , d ) 62 , e ) 350
Rationale: "length of the train be â € ˜ x â € ™ x + 100 / 15 = x + 250 / 20 4 x + 400 = 3 x + 750 x = 350 m answer : e"
Answer: e
Problem: if 0.75 : x : : 5 : 9 , then x is equal to :
Options: a ) 1.12 , b ) 1.16 , c ) 1.2 , d ) 1.35 , e ) none of these
Rationale: "explanation : ( x * 5 ) = ( 0.75 * 9 ) x = 6.75 / 5 = 1.35 answer : d"
Answer: d
Problem: in the xy - plane , the point ( 3 , 1 ) is the center of a circle . the point ( 3 , - 2 ) lies inside the circle and the point ( - 2 , 1 ) lies outside the circle . if the radius r of the circle is an integer , then r =
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "an easy way to solve this question will be just to mark the points on the coordinate plane . you ' ll see that the distance between the center ( 3 , 1 ) and the point inside the circle ( 3 , - 2 ) is 3 units ( both points are on x = 3 line so the distance will simply be 1 - ( - 2 ) = 3 ) so the radius must be more than 3 units . the distance between the center ( 3,1 ) and the point outside the circle ( - 2,1 ) is 5 units ( both points are on y = 1 line so the distance will simply be 3 - ( - 2 ) = 5 ) so the radius must be less than 5 units , which implies 3 < r < 5 , thus as r is an integer then r = 4 . answer : c ."
Answer: c
Problem: s ( n ) is a n - digit number formed by attaching the first n perfect squares , in order , into one integer . for example , s ( 1 ) = 1 , s ( 2 ) = 14 , s ( 3 ) = 149 , s ( 4 ) = 14916 , s ( 5 ) = 1491625 , etc . how many digits t are in s ( 99 ) ?
Options: a ) t = 350 , b ) t = 353 , c ) t = 354 , d ) t = 356 , e ) 357
Rationale: "focus on the points where the number of digits in squares change : 1 , 2 , 3 - single digit squares . first 2 digit number is 10 . 4 , 5 , . . . 9 - two digit squares . to get 9 , the last number with two digit square , think that first 3 digit number is 100 which is 10 ^ 2 . so 9 ^ 2 must be the last 2 digit square . 10 , 11 , 12 , . . . 31 - three digit squares . to get 31 , think of 1000 - the first 4 digit number . it is not a perfect square but 900 is 30 ^ 2 . 32 ^ 2 = 2 ^ 10 = 1024 , the first 4 digit square . 32 - 99 - four digit squares . to get 99 , think of 10,000 - the first 5 digit number which is 100 ^ 2 . so number of digits in s ( 99 ) = 3 * 1 + 6 * 2 + 22 * 3 + 68 * 4 = 3 + 12 + 66 + 272 = 353 . b"
Answer: b
Problem: you have been given a physical balance and 7 weights of 57 , 55 , 45 , 44 , 43 , 41 and 85 kgs . keeping weights on one pan and object on the other , what is the maximum you can weigh less than 199 kgs .
Options: a ) 198 , b ) 195 , c ) 196 , d ) 197 , e ) 200
Rationale: "85 + 55 + 57 = 197 answer : d"
Answer: d
Problem: the average age of 7 men increases by 4 years when two women are included in place of two men of ages 26 and 30 years . find the average age of the women ?
Options: a ) 42 , b ) 40 , c ) 30 , d ) 18 , e ) 11
Rationale: "explanation : 26 + 30 + 7 * 4 = 84 / 2 = 42 answer : a"
Answer: a
Problem: what is the area of the square with the following coordinates : ( x , y ) , ( 20 , 20 ) , ( 20 , 9 ) , ( x , 9 ) ?
Options: a ) 121
b ) 132
c ) 144
d ) 156
e ) 169
Rationale: to find the area of a square , knowing the length of one side is sufficient . from the coordinates given , we can see that one side equals 11 . the area is 11 * 11 = 121 . the answer is a .
Answer: a
Problem: 450.271 + 369.422 ÷ 0.03 - 108.612 x 2.001 = ?
Options: a ) 12980 , b ) 12532 , c ) 12610 , d ) 12430 , e ) 12560
Rationale: "explanation : ? = 450.271 + ( 369.422 ÷ 0.03 ) - ( 108.612 x 2.001 ) ≈ 450 + 369 / 0.03 - ( 109 x 2 ) ≈ 450 + 12300 - 218 ≈ 12532 answer : option b"
Answer: b
Problem: how many 3 - digit numerals begin with a digit that represents a prime number ?
Options: a ) 16 , b ) 80 , c ) 400 , d ) 180 , e ) 240
Rationale: prime digits 2 , 35 and 7 . three digit numbers _ _ _ 1 st place can be filled in 4 ways 2 nd place can be filled in 10 ways 3 rd place can be filled in 10 ways total = 4 * 10 * 10 = 400 ans : c
Answer: c
Problem: if leo gains 10 pounds , he will weigh 50 % more than his sister kendra . currently their combined weight is 150 pounds . what is leo ' s current weight ?
Options: a ) 80 , b ) 86 , c ) 92 , d ) 98 , e ) 104
Rationale: "l + k = 150 and so k = 150 - l l + 10 = 1.5 k = 1.5 ( 150 - l ) 2.5 l = 215 l = 86 the answer is b ."
Answer: b
Problem: a group of workers had agreed on a very strange payment schedule . each of them would get $ 100 for every day that they had worked , but for every day they did not work will have to return $ 25 . after 30 days they realised they did not earn any money . how many days the workers did not work ?
Options: a ) 15 , b ) 24 , c ) 30 , d ) 20 , e ) 10
Rationale: the workers earn 4 times more than they have to return per day for not working . so the number of days they did not work is 4 times the number of days they worked . that means 24 days of not working in 30 days . correct answer b
Answer: b
Problem: a pump can fill a tank with a water in 2 hours . because of a leak , it took 2 x 1 / 3 hours to fill the tank . the leak can drain all the water of the tank in
Options: a ) 5 hrs , b ) 7 hrs , c ) 12 hrs , d ) 14 hrs , e ) none
Rationale: "sol . work done by the leak in 1 hour = ( 1 / 2 - 3 / 7 ) = 1 / 14 . ∴ leak will empty the tank in 14 hrs . answer d"
Answer: d
Problem: if 2 x + y = 7 and x + 2 y = 5 , then ( 2 x + 2 y ) / 3 =
Options: a ) 3 , b ) 4 / 3 , c ) 17 / 5 , d ) 18 / 5 , e ) 4
Rationale: "2 * ( x + 2 y = 5 ) equals 2 x + 4 y = 10 2 x + 4 y = 10 - 2 x + y = 7 = 3 y = 3 therefore y = 1 plug and solve . . . 2 x + 1 = 7 2 x = 6 x = 3 ( 2 * 3 + 2 * 1 ) / 3 = ( 6 + 3 ) / 3 = 9 / 3 = 3 a"
Answer: a
Problem: johnny travels a total of one hour to and from school . on the way there he jogs at 5 miles per hour and on the return trip he gets picked up by the bus and returns home at 25 miles per hour . how far is it to the school ?
Options: a ) 2 miles , b ) 4 miles , c ) 6.6 miles , d ) 8 miles , e ) 10 miles
Rationale: answer : c ) 6.6 miles . average speed for round trip = 2 * a * b / ( a + b ) , where a , b are speeds so , average speed was = 2 * 5 * 25 / ( 5 + 25 ) = 6.6 m / hr the distance between schoolhome should be half of that . ie . 6.6 miles answer c
Answer: c
Problem: what is the units digit of ( 12 ^ 3 ) ( 15 ^ 4 ) ( 31 ^ 7 ) ?
Options: a ) 0 , b ) 2 , c ) 4 , d ) 6 , e ) 8
Rationale: "the units digit of 12 ^ 3 is the units digit of 2 ^ 3 which is 8 . the units digit of 15 ^ 4 is the units digit of 5 ^ 4 which is 5 . the units digit of 31 ^ 7 is the units digit of 1 ^ 7 which is 1 . the units digit of 8 * 5 * 1 is 0 . the answer is a ."
Answer: a
Problem: the cost price of an article is 64 % of the marked price . calculate the gain percent after allowing a discount of 12 % ?
Options: a ) 37.5 % , b ) 37.6 % , c ) 38.5 % , d ) 17.5 % , e ) 37.2 %
Rationale: "let marked price = rs . 100 . then , c . p . = rs . 64 , s . p . = rs . 88 gain % = 24 / 64 * 100 = 37.5 % . answer : a"
Answer: a
Problem: the average of 25 results is 18 . the average of first 12 of those is 14 and the average of last 12 is 17 . what is the 13 th result ?
Options: a ) 74 , b ) 75 , c ) 69 , d ) 78 , e ) 45
Rationale: "solution : sum of 1 st 12 results = 12 * 14 sum of last 12 results = 12 * 17 13 th result = x ( let ) now , 12 * 14 + 12 * 17 + x = 25 * 18 or , x = 78 . answer : option d"
Answer: d
Problem: an woman sitting in a train which is travelling at 20 kmph observes that a goods train travelling in a opposite direction , takes 15 seconds to pass him . if the goods train is 300 m long , find its speed .
Options: a ) 52 , b ) 54 , c ) 56 , d ) 58 , e ) 60
Rationale: relative speed = ( 300 / 15 ) m / s = ( 300 / 15 ) * ( 18 / 5 ) = 72 kmph speed of goods train = 72 - 20 = 52 kmph answer is a
Answer: a
Problem: a number consists of 3 digits whose sum is 10 . the middle digit is equal to the sum of the other two and the number will be increased by 99 if its digits are reversed . the number is
Options: a ) 145 , b ) 185 , c ) 253 , d ) 370 , e ) none
Rationale: solution let the number be x . then 2 x = 10 or x = 5 . so , the number is either 253 or 352 . since the number increases on reversing the digits , so the hundred ' s digit is smaller than the units digit . hence , required number = 253 . answer c
Answer: c
Problem: what least number must be subtracted from 7538 so that remaining no . is divisible by 14
Options: a ) 3 , b ) 5 , c ) 6 , d ) 8 , e ) 9
Rationale: "explanation : on dividing 7538 by 14 we get the remainder 6 , so 6 should be subtracted option c"
Answer: c
Problem: in a survey of parents , exactly 5 / 6 of the mothers and 3 / 4 of the fathers held full - time jobs . if 60 percent of the parents surveyed were women , what percent of the parents did not hold full - time jobs ?
Options: a ) 12 % , b ) 15 % , c ) 18 % , d ) 20 % , e ) 25 %
Rationale: "fathers without full - time jobs are 1 / 4 * 2 / 5 = 2 / 20 of all the parents surveyed . mothers without full - time jobs are 1 / 6 * 3 / 5 = 1 / 10 of all the parents surveyed . the percent of parents without full - time jobs is 2 / 20 + 1 / 10 = 1 / 5 = 20 % the answer is d ."
Answer: d
Problem: on a scale of map , 0.4 cm represents 5.3 km . if the distance between the points on the map is 64 cm , the actual distance between these points is :
Options: a ) 9 km , b ) 72.5 km , c ) 190.75 km , d ) 848 km , e ) none of these
Rationale: explanation : let the actual distance be x km . then , more distance on the map , more is the actual distance ( direct proportion ) = > 0.4 : 64 : : 5.3 : x = > 0.4 x = 64 x 5.3 = > x = 64 x 5.3 / 0.4 = > x = 848 answer : d
Answer: d
Problem: the ratio w , by volume of soap to alcohol to water in a 76 litre solution is 2 : 50 : 100 . the solution is then altered by adding more soap , alcohol and water . after this alteration the ratio , by volume of soap to water in the solution doubles whereas the ratio , by volume of soap to water remains the same as before . what could be the resulting volume .
Options: a ) 79 litres , b ) 78 litres , c ) 77 litres , d ) 152 liters , e ) 304 litres
Rationale: i guess it should be the ratio w , by volume ofsoaptowaterin the solutiondoubleswhereas the ratio , by volume ofalocoholtowaterremains thesameas before 2 : 50 : 100 = > 1 : 25 : 50 . if we add all the parts , we get 76 liters so we have 1 liters of soap , 25 liters of alcohol and 50 liters of water . now as per the question , soap : water doubles but alcohol to water remains the same . so soap becomes 2 liters , alcohol remains 25 liters and water remains at 50 liters . hence 77 liters - option c )
Answer: c
Problem: the sum of the numbers is 98 . if the ratio between the first and the second be 2 : 3 and that between the second and third be 5 : 8 , then find the second number ?
Options: a ) 24 , b ) 30 , c ) 36 , d ) 42 , e ) 50
Rationale: given ratios 2 : 3 5 : 8 10 : 15 : 24 the second number = 98 / ( 10 + 15 + 24 ) * 15 = 30 answer is b
Answer: b
Problem: jaime earned enough money by selling seashells at 35 cents each to buy several used paperback books at 55 cents each . if he spent all of the money he earned selling seashells to buy the books , what is the least number of seashells he could have sold ?
Options: a ) 5 , b ) 11 , c ) 17 , d ) 22 , e ) 30
Rationale: let ' s test answer d : 22 seashells . . . . with 22 seashells , jamie would have 22 ( 35 ) = 770 cents . this would allow him to buy 14 books for 770 cents total , with no money left over . this is an exact match for what we were told , so this must be the answer . final answer : [ reveal ] spoiler : d
Answer: d
Problem: a manufacturer produces a certain men ' s athletic shoe in integer sizes from 8 to 17 . for this particular shoe , each unit increase in size corresponds to a 1 / 5 - inch increase in the length of the shoe . if the largest size of this shoe is 40 % longer than the smallest size , how long , in inches , is the shoe in size 15 ?
Options: a ) 5.4 , b ) 5.9 , c ) 6.3 , d ) 6.7 , e ) 7.5
Rationale: let x be the length of the size 8 shoe . then 0.4 x = 9 / 5 x = 4.5 inches the size 15 shoe has a length of 4.5 + 7 / 5 = 5.9 inches the answer is b .
Answer: b
Problem: the average salary / head of allthe workers in a workshop is rs . 850 , if the average salary / head of 7 technician is rs . 1000 and the average salary / head of the rest is rs . 780 , the total no . of workers in the work - shop is ?
Options: a ) 18 , b ) 20 , c ) 22 , d ) 24 , e ) 26
Rationale: "let the total number of workers be y . so sum of salary for all workers = sum of salary of 7 technician + sum of salary for other y - 7 workers . 7 x 1000 + 780 ( y - 7 ) = 850 y ⇒ 7000 + 780 y - 5460 = 850 y ⇒ 70 y = 1540 ∴ y = 22 so total number of workers = 22 c"
Answer: c
Problem: a man buys a cycle for rs . 1600 and sells it at a loss of 20 % . what is the selling price of the cycle ?
Options: a ) 1410 , b ) 1420 , c ) 1430 , d ) 1440 , e ) 1280
Rationale: "s . p . = 80 % of rs . 1600 = 80 / 100 x 1600 = rs . 1280 answer : e"
Answer: e
Problem: 15 people went to a hotel for combine dinner party 10 of them spent rs . 50 each on their dinner and rest spent 4 more than the average expenditure of all the 15 . what was the total money spent by them .
Options: a ) 1628.4 , b ) 1534 , c ) 780 , d ) 1496 , e ) none of these
Rationale: "solution : let average expenditure of 15 people be x . then , 15 x = 10 * 50 + 5 * ( x + 4 ) ; or , 15 x = 10 * 50 + 5 x + 20 ; or , x = 52 ; so , total money spent = 52 * 15 = rs . 780 . answer : option c"
Answer: c
Problem: what is the maximum number of pieces of birthday cake of size 5 ” by 5 ” that can be cut from a cake 15 ” by 15 ” ?
Options: a ) 5 , b ) 10 , c ) 16 , d ) 20 , e ) 9
Rationale: "the prompt is essentially asking for the maximum number of 5 x 5 squares that can be cut from a larger 15 by 15 square . since each ' row ' and each ' column ' of the larger square can be sub - divided into 3 ' pieces ' each , we have ( 3 ) ( 3 ) = 9 total smaller squares ( at maximum ) . e"
Answer: e
Problem: the width of a rectangular hall is ½ of its length . if the area of the hall is 450 sq . m , what is the difference between its length and breadth ?
Options: a ) 8 m , b ) 10 m , c ) 12 m , d ) 15 m , e ) 17 m
Rationale: "let the length of the hall be x m breadth of the hall = 1 x / 2 m area of the hall = length * breadth 450 = x * 1 x / 2 x ² = 900 x = 30 difference between the length and breadth of the hall = x - 1 x / 2 = x / 2 = 30 / 2 = 15 m answer : d"
Answer: d
Problem: if p / q = 4 / 5 , then the value of 1 / 7 + { ( 2 q - p ) / ( 2 q + p ) } is ?
Options: a ) 4 / 7 , b ) 34 , c ) 1 , d ) 2 , e ) 3
Rationale: "answer given exp . = 4 / 7 + { ( 2 q - p ) / ( 2 q + p ) } dividing numerator as well as denominator by q , exp = 1 / 7 + { 2 - p / q ) / ( 2 + p / q ) } = 1 / 7 + { ( 2 - 4 / 5 ) / ( 2 + 4 / 5 ) } = 1 / 7 + 6 / 14 = 1 / 7 + 3 / 7 = 4 / 7 correct option : a"
Answer: a
Problem: when a natural number n is successively divided by 1020 , 3040 . the remainders are 5060 , 7080 . what will be the sum of the remainders if the order of the division is reversed ?
Options: a ) 16 , b ) 14 , c ) 28 , d ) 11 , e ) 9
Rationale: 10 20 30 40 50 60 70 80 leave the top right - most number 8 start with bottom right - most number 5 80 * 30 + 70 = 2470 2470 * 20 + 60 = 49460 49460 * 10 + 50 = 494650 this is the number required now , do the successive division in the reverse order the sum of the remainders is 28 hence , the correct option is c
Answer: c
Problem: in the land of oz only one or two - letter words are used . the local language has 68 different letters . the parliament decided to forbid the use of the seventh letter . how many words have the people of oz lost because of the prohibition ?
Options: a ) 65 , b ) 66 , c ) 67 , d ) 131 , e ) 136
Rationale: "the answer to the question is indeed e . the problem with above solutions is that they do not consider words like aa , bb , . . . the number of 1 letter words ( x ) that can be made from 68 letters is 68 ; the number of 2 letter words ( xx ) that can be made from 68 letters is 68 * 68 , since each x can take 68 values . total : 68 + 68 * 68 . similarly : the number of 1 letter words ( x ) that can be made from 67 letters is 67 ; the number of 2 letter words ( xx ) that can be made from 67 letters is 67 * 67 , since each x can take 67 values . total : 67 + 67 * 67 . the difference is ( 68 + 68 * 68 ) - ( 67 + 67 * 67 ) = 136 . answer : e ."
Answer: e
Problem: if the sales tax be reduced from 4 ( 1 / 3 ) % to 2 ( 1 / 2 ) % , then what difference does it make to a person who purchases a bag with marked price of rs . 8000 ?
Options: a ) 146.69 , b ) 146.66 , c ) 146.62 , d ) 146.61 , e ) 146.6
Rationale: "explanation : required difference = ( 4 ( 1 / 3 ) of rs . 8000 ) - ( 2 ( 1 / 2 ) of rs . 8000 ) = ( 13 / 3 – 5 / 2 ) % of rs . 8000 = ( 11 / 6 ) x ( 1 / 100 ) x 8000 = rs . 146.66 answer : b"
Answer: b
Problem: how many positive 3 - digit integers are divisible by both 3 and 7 ?
Options: a ) 43 , b ) 45 , c ) 47 , d ) 50 , e ) 52
Rationale: a number to be divisible by both 3 and 7 should be divisible by the least common multiple of 3 and 7 so by 21 . multiples of 21 between 100 and 999 , inclusive is ( last - first ) / multiple + 1 = ( 987 - 105 ) / 21 + 1 = 42 + 1 = 43 answer : a .
Answer: a
Problem: the average of 50 numbers id 62 . if two numbers , namely 45 and 55 are discarded , the average of the remaining numbers is :
Options: a ) 22.3 , b ) 33.2 , c ) 22.2 , d ) 51.3 , e ) 62.5
Rationale: "explanation : total of 50 numbers = ( 50 × 62 ) = 3100 total of 48 numbers = ( 3100 - ( 45 + 55 ) ] = 3000 required average = 3000 / 48 = 62.5 answer : e"
Answer: e
Problem: in what time will a train 100 meters long cross an electric pole , if its speed is 144 km / hr
Options: a ) 8.5 seconds , b ) 2.8 seconds , c ) 3.5 seconds , d ) 2.5 seconds , e ) 2.6 seconds
Rationale: "first convert speed into m / sec speed = 144 * ( 5 / 18 ) = 40 m / sec time = distance / speed = 100 / 40 = 2.5 seconds answer : d"
Answer: d
Problem: what is the unit digit of ( 6 ! * 6 ! / 6 ! * 3 ! ) ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: ( 6 ! * 6 ! / 6 ! * 3 ! ) = ( 6 ! / 3 ! ) = 720 / 6 = 120 units digit of the above product will be equal to 0 answer a
Answer: a
Problem: two vessels contains equal number of mixtures milk and water in the ratio 5 : 3 and 6 : 2 . both the mixtures are now mixed thoroughly . find the ratio of milk to water in the new mixture so obtained ?
Options: a ) 11 : 5 , b ) 9 : 13 , c ) 5 : 11 , d ) 11 : 3 , e ) 15 : 4
Rationale: "the ratio of milk and water in the new vessel is = ( 5 / 8 + 6 / 8 ) : ( 3 / 8 + 2 / 8 ) = 11 / 8 : 5 / 8 = 11 : 5 answer is a"
Answer: a
Problem: mona and donald fly to rome for the weekend . they take cash only in notes of $ 10 and notes of € 10 . mona carries 3 times the amount of euros donald carries . she also carries as many dollars as donald carries . the number of € 10 notes they take is double the number of $ 10 notes they take . if donald carries a total of 39 notes ( of either $ 10 or € 10 , ) then what is the total number of notes ( of either $ 10 or € 10 , ) they take ?
Options: a ) 130 , b ) 80 , c ) 100 , d ) 120 , e ) 150
Rationale: let e 10 = x no . d 10 = y no . donald is having x + y notes mona carries 3 x + y again x = 2 y or donald x + y = 39 or 3 y = 39 y = 13 ; x = 26 , total notes they carry = 104 + 26 = 130 a
Answer: a
Problem: in a lake , there is a patch of lily pads . every day , the patch doubles in size . it takes 34 days for the patch to cover the entire lake , how many days would it take the patch to cover half of the lake ?
Options: a ) 33 , b ) 2 ^ 4 * 3 , c ) 24 , d ) 38 , e ) 47
Rationale: "working backward from the day it ' s covered : day 34 : fully covered day 33 : half covered so 33 days answer : a"
Answer: a
Problem: the water level in a reservoir has been dropping at the rate of 14 inches per day . exactly 5 days ago , the water level was at h inches . what will be the water level exactly 4 days from now if the rate at which the level is dropping remains the same ?
Options: a ) h − 12 , b ) h − 56 , c ) h − 14 , d ) h + 14 , e ) h - 126
Rationale: "drop = 14 inches / day 5 days ago = h , means now it ' s equal h - 70 and in 4 days = h - 70 - 56 = h - 126 answer e"
Answer: e
Problem: how long does a train 165 meters long running at the rate of 54 kmph take to cross a bridge 850 meters in length ?
Options: a ) 28 , b ) 27 , c ) 55 , d ) 18 , e ) 67.7
Rationale: "t = ( 850 + 165 ) / 54 * 18 / 5 t = 67.7 answer : e"
Answer: e
Problem: in the faculty of reverse - engineering , 350 second year students study numeric methods , 250 second year students study automatic control of airborne vehicles and 100 second year students study them both . how many students are there in the faculty if the second year students are approximately 25 % of the total ?
Options: a ) 1800 , b ) 1900 , c ) 2100 , d ) 2000 , e ) 2200
Rationale: "total number of students studying both are 350 + 250 - 100 = 500 ( subtracting the 100 since they were included in the both the other numbers already ) . so 25 % of total is 500 , so 100 % is 2000 answer is d"
Answer: d
Problem: how many numbers from 39 to 79 are exactly divisible by 11 ?
Options: a ) 5 , b ) 7 , c ) 4 , d ) 11 , e ) 12
Rationale: 39 / 11 = 1 and 79 / 11 = 7 = = > 7 - 3 = 4 numbers answer : c
Answer: c
Problem: in the coordinate plane , points ( x , 1 ) and ( 12 , y ) are on line k . if line k passes through the origin and has slope 1 / 2 , then x + y =
Options: a ) 4.5 , b ) 7 , c ) 8 , d ) 11 , e ) 12
Rationale: "line k passes through the origin and has slope 1 / 2 means that its equation is y = 1 / 2 * x . thus : ( x , 1 ) = ( 2 , 1 ) and ( 12 , y ) = ( 12,6 ) - - > x + y = 2 + 6 = 8 . answer : c ."
Answer: c
Problem: in a rectangular coordinate system , what is the area of a rhombus whose vertices have the coordinates ( 0 , 3.5 ) , ( 8 , 0 ) , ( 0 , - 3.5 ) , ( - 8 , 0 ) ?
Options: a ) 56 , b ) 88 , c ) 112 , d ) 116 , e ) 120
Rationale: "area of rhombus = 1 / 2 * d 1 * d 2 length of 1 st diagonal = 8 + 8 = 16 length of 2 nd diagonal = 3.5 + 3.5 = 7 area = 1 / 2 * 16 * 7 = 56 a is the answer"
Answer: a
Problem: when a number is divided by 6 & then multiply by 12 the answer is 8 what is the no . ?
Options: a ) 4.5 , b ) 5 , c ) 5.5 , d ) 5.8 , e ) 4
Rationale: "if $ x $ is the number , x / 6 * 12 = 8 = > 2 x = 8 = > x = 4.0 e"
Answer: e
Problem: in one year , the population , of a village increased by 30 % and in the next year , it decreased by 30 % . if at the end of 2 nd year , the population was 13650 , what was it in the beginning ?
Options: a ) 7787 , b ) 8000 , c ) 15000 , d ) 1277 , e ) 2081
Rationale: "x * 130 / 100 * 70 / 100 = 13650 x * 0.91 = 13650 x = 13650 / 0.91 = > 15000 answer : c"
Answer: c
Problem: three table runners have a combined area of 208 square inches . by overlapping the runners to cover 80 % of a table of area 175 square inches , the area that is covered by exactly two layers of runner is 24 square inches . what is the area of the table that is covered with three layers of runner ?
Options: a ) 22 square inches
b ) 20 square inches
c ) 24 square inches
d ) 28 square inches
e ) 30 square inches
Rationale: total = a + b + c - ( sum of exactly 2 - group overlaps ) - 2 * ( all three ) + neither 80 % * 175 = 208 - 24 - 2 * ( all three ) + 0 2 * ( all three ) = 208 - 24 - 140 all three = 22 answer : a
Answer: a
Problem: calculate the amount that an investor needs to be invest to earn $ 460 in interest in 12 months if the investor plans to invest x dollars in a savings account that pays interest at an annual rate of 9 % compounded semi - annually ?
Options: a ) 7,000 , b ) 4,000 , c ) 6,000 , d ) 5,000 , e ) 8,000
Rationale: "the approach is substitution , our interest requirement is 460 after 12 months , 2 compounding period . calculate the compound interest on each option and find out the one that yields 460 in 12 months 5,000 yielded $ 460 using the formula a = p ( 1 + r / n ) nt hence answer is d"
Answer: d
Problem: the least number , which when divided by 48,60 , 72,108 and 140 leaves 38,50 , 62,98 and 130 as remainder respectively , is :
Options: a ) 11115 , b ) 15110 , c ) 15120 , d ) 15210 , e ) 12510
Rationale: "solution here ( 48 - 38 ) = 10 , ( 60 - 50 ) = 10 , ( 72 - 62 ) = 10 , ( 108 - 98 ) = 10 & ( 140 - 130 ) = 10 . so , required number = ( l . c . m . of 48 , 60,72 , 108,140 ) - 10 = 15120 - 10 = 15110 . answer b"
Answer: b
Problem: company c sells a line of 25 products with an average retail price of $ 1,200 . if none of these products sells for less than $ 400 , and exactly 12 of the products sell for less than $ 1,000 , what is the greatest possible selling price of the most expensive product ?
Options: a ) 10,000 , b ) 11.0 , c ) 12,000 , d ) 13,200 , e ) 14,000
Rationale: "the average price of 25 products is $ 1,200 means that the total price of 25 products is 25 * 1,200 = $ 30,000 . next , since exactly 12 of the products sell for less than $ 1,000 , then let ' s make these 12 items to be at $ 400 each ( min possible ) . now , the remaining 12 items can not be priced less than $ 1,000 , thus the minimum possible price of each of these 12 items is $ 1,000 . thus the minimum possible value of 24 products is 12 * 400 + 12 * 1,000 = $ 16,800 . therefore , the greatest possible selling price of the most expensive product is $ 30,000 - $ 16,800 = $ 13,200 . answer : d ."
Answer: d
Problem: how many bricks , each measuring 80 cm x 11.25 cm x 6 cm , will be needed to build a wall of 8 m x 6 m x 22.5 cm ?
Options: a ) 6400 , b ) 2000 , c ) 5500 , d ) 7400 , e ) 3000
Rationale: "number of bricks = volume of the wall / volume of 1 brick = ( 800 x 600 x 22.5 ) / ( 80 x 11.25 x 6 ) = 2000 answer : b"
Answer: b
Problem: a man goes downstream at 13 kmph , and upstream 8 kmph . the speed of the stream is
Options: a ) 0 kmph , b ) 4 kmph , c ) 16 kmph , d ) 2.5 kmph , e ) 26 kmph
Rationale: "speed of the stream = 1 / 2 ( 13 - 8 ) kmph = 2.5 kmph . correct option : d"
Answer: d
Problem: drum x is 1 / 2 full of oil and drum y , which has twice the capacity of drum x , is 1 / 2 full of oil . if all of the oil in drum x is poured into drum y , then drum y will be filled to what capacity ?
Options: a ) 2 / 3 , b ) 3 / 4 , c ) 4 / 5 , d ) 5 / 6 , e ) 7 / 8
Rationale: "( 1 / 2 ) x = ( 1 / 4 ) y ( 1 / 4 ) y + ( 1 / 2 ) y = ( 3 / 4 ) y the answer is b ."
Answer: b
Problem: the average weight of 8 people increases by 2.5 kg when a new person comes in place of one of them weighing 45 kg . what is the weight of the new person ?
Options: a ) 75 kg , b ) 85 kg , c ) 95 kg , d ) 65 kg , e ) 55 kg
Rationale: the total weight increase = ( 8 x 2.5 ) kg = 20 kg weight of new person = ( 45 + 20 ) kg = 65 kg the answer is d .
Answer: d
Problem: average of 10 matches is 32 , how many runs one should should score to increase his average by 3 runs .
Options: a ) a ) 65 , b ) b ) 76 , c ) c ) 78 , d ) d ) 80 , e ) e ) 88
Rationale: "explanation : average after 11 innings should be 35 so , required score = ( 11 * 35 ) - ( 10 * 32 ) = 385 - 320 = 65 answer : option a"
Answer: a
Problem: how many internal diagonals does a hexagon ( six sided polygon ) have ?
Options: a ) 5 , b ) 6 , c ) 8 , d ) 9 , e ) 10
Rationale: "number of diagonals in any polygon can be found using this formula : n ( n - 3 ) / 2 here n = 6 no . of diagonals = 6 ( 6 - 3 ) / 2 = 9 ans d"
Answer: d
Problem: running at their respective constant rate , machine x takes 2 days longer to produce w widgets than machines y . at these rates , if the two machines together produce 5 w / 4 widgets in 3 days , how many days would it take machine x alone to produce 3 w widgets .
Options: a ) 4 , b ) 6 , c ) 18 , d ) 10 , e ) 12
Rationale: "i am getting 12 . e . hope havent done any calculation errors . . approach . . let y = no . of days taken by y to do w widgets . then x will take y + 2 days . 1 / ( y + 2 ) + 1 / y = 5 / 12 ( 5 / 12 is because ( 5 / 4 ) w widgets are done in 3 days . so , x widgets will be done in 12 / 5 days or 5 / 12 th of a widget in a day ) solving , we have y = 4 = > x takes 6 days to doing x widgets . so , he will take 18 days to doing 3 w widgets . answer : c"
Answer: c
Problem: find a sum for 1 st 7 prime number ' s ?
Options: a ) 25 , b ) 28 , c ) 58 , d ) 34 , e ) 36
Rationale: "required sum = ( 2 + 3 + 5 + 7 + 11 + 13 + 17 ) = 58 note : 1 is not a prime number option c"
Answer: c
Problem: a and b can do a piece of work in 9 days . with the help of c they finish the work in 6 days . c alone can do that piece of work in ?
Options: a ) 33 , b ) 878 , c ) 18 , d ) 88 , e ) 11
Rationale: "c = 1 / 6 â € “ 1 / 9 = 1 / 18 = > 18 days answer : c"
Answer: c
Problem: the length of a rectangular garden is three times its width . if the area of the rectangular garden is 507 square meters , then what is the width of the rectangular garden ?
Options: a ) 10
b ) 11
c ) 12
d ) 13
e ) 14
Rationale: let x be the width of the garden . 3 x ^ 2 = 507 x ^ 2 = 169 x = 13 the answer is d .
Answer: d
Problem: due to construction , the speed limit along an 9 - mile section of highway is reduced from 55 miles per hour to 30 miles per hour . approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ?
Options: a ) a ) 5.61 , b ) b ) 8 , c ) c ) 10 , d ) d ) 15 , e ) e ) 8.19
Rationale: "old time in minutes to cross 9 miles stretch = 9 * 60 / 55 = 9 * 12 / 11 = 9.81 new time in minutes to cross 9 miles stretch = 9 * 60 / 30 = 9 * 2 / 1 = 18 time difference = 8.19 ans : e"
Answer: e
Problem: 220 % of a number x is 44 . what is 44 % of x .
Options: a ) 8.8 , b ) 8.9 , c ) 6.6 , d ) 7.7 , e ) none
Rationale: solution : given , 220 % of x = 44 or , x = 20 . thus , 44 % of 20 = ( 44 * 20 ) / 100 = 8.8 answer : option a
Answer: a
Problem: what is the smallest of 6 consecutive odd integers whose average ( arithmetic mean ) is b + 2 ?
Options: a ) b - 3 , b ) b - 6 , c ) b - 1 , d ) b , e ) b + 1
Rationale: since the numbers are consecutive odd integers , mean = median = 3 rd integer + 4 th integer / 2 and 1 st integer = 3 rd integer - 4 let ' s say 3 rd integer = n and 4 th integer = n + 2 2 n + 2 / 2 = b + 2 n = b + 1 1 st integer = b + 1 - 4 = b - 3 a is the answer
Answer: a
Problem: a motorcyclist goes from bombay to pune , a distance of 180 kms at an average of 20 kmph speed . another man starts from bombay by car 2 â ½ hours after the first , and reaches pune â ½ hour earlier . what is the ratio of the speed of the motorcycle and the car ?
Options: a ) 1 : 2 , b ) 2 : 3 , c ) 1 : 9 , d ) 1 : 5 , e ) 1 : 1
Rationale: "t = 180 / 20 = 9 h t = 9 - 3 = 6 time ratio = 9 : 6 = 3 : 2 speed ratio = 2 : 3 answer : b"
Answer: b
Problem: on thursday mabel handled 90 transactions . anthony handled 10 % more transactions than mabel , cal handled 2 / 3 rds of the transactions that anthony handled , and jade handled 19 more transactions than cal . how much transactions did jade handled ?
Options: a ) 80 , b ) 81 , c ) 82 , d ) 83 , e ) 85
Rationale: "solution : mabel handled 90 transactions anthony handled 10 % more transactions than mabel anthony = 90 + 90 × 10 % = 90 + 90 × 0.10 = 90 + 9 = 99 cal handled 2 / 3 rds of the transactions than anthony handled cal = 2 / 3 × 99 = 66 jade handled 19 more transactions than cal . jade = 66 + 19 = 85 jade handled = 85 transactions . answer : e"
Answer: e
Problem: in a garden , there are 10 rows and 12 columns of mango trees . the distance between the two trees is 2 metres and a distance of six metres is left from all sides of the boundary of the garden . what is the length of the garden ?
Options: a ) 32 , b ) 34 , c ) 26 , d ) 28 , e ) 30
Rationale: "between the 12 mango trees , there are 11 gaps and each gap has 2 meter length also , 6 meter is left from all sides of the boundary of the garden . hence , length of the garden = ( 11 ã — 2 ) + 6 + 6 = 34 meter answer is b ."
Answer: b
Problem: a garrison of 150 men has provisions for 31 days . at the end of 16 days , a reinforcement arrives , and it is now found that the provisions will last only for 5 days more . what is the reinforcement ?
Options: a ) 150 , b ) 450 , c ) 400 , d ) 600 , e ) 300
Rationale: "150 - - - - 31 150 - - - - 15 x - - - - - 5 x * 5 = 150 * 15 x = 450 150 - - - - - - - 300 answer : e"
Answer: e
Problem: the lenght of a room is 5.5 m and width is 4 m . find the cost of paving the floor by slabs at the rate of rs . 800 per sq . metre .
Options: a ) rs . 15,550 , b ) rs . 15,600 , c ) rs . 16,500 , d ) rs . 17,600 , e ) rs . 17,900
Rationale: area of the floor = ( 5.5 × 4 ) m 2 = 22 m 2 . cost of paving = rs . ( 800 × 22 ) = rs . 17600 . answer : option d
Answer: d
Problem: employees of a certain company are each to receive a unique 8 - digit identification code consisting of the digits 0 , 1 , 2 , 3 , 4 , 5 , 6 , and 7 such that no digit is used more than once in any given code . in valid codes , the second digit in the code is exactly twice the first digit . how many valid codes are there ?
Options: a ) 1220 , b ) 1840 , c ) 2160 , d ) 2480 , e ) 2760
Rationale: "there are 6 ! ways to make codes starting with 12 . there are 6 ! ways to make codes starting with 24 . there are 6 ! ways to make codes starting with 36 . the number of codes is 3 * 6 ! = 2160 . the answer is c ."
Answer: c
Problem: if x is 13 percent greater than 80 , then x =
Options: a ) 88.8 , b ) 90.4 , c ) 88.0 , d ) 70.9 , e ) 71.2
Rationale: "13 % of 80 = ( 80 * 0.13 ) = 10.4 11 % greater than 80 = 80 + 10.4 = 90.4 answer is clearly b ."
Answer: b
Problem: an integer n between 1 and 99 , inclusive , is to be chosen at random . what is the probability that n ( n + 1 ) will be divisible by 3 ?
Options: a ) 1 / 9 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 5 / 6
Rationale: "n ( n + 1 ) to be divisible by 3 either n or n + 1 must be a multiples of 3 . in each following group of numbers : { 1 , 2 , 3 } , { 4 , 5 , 6 } , { 7 , 8 , 9 } , . . . , { 97 , 98 , 99 } there are exactly 2 numbers out of 3 satisfying the above condition . for example in { 1 , 2 , 3 } n can be : 2 , or 3 . thus , the overall probability is 2 / 3 . answer : d ."
Answer: d
Problem: in a throw of a coin probability of getting a head .
Options: a ) 1 / 3 , b ) 2 / 3 , c ) 1 / 4 , d ) 2 / 5 , e ) 1 / 2
Rationale: "s = { h , t } e = { h } probability = n ( e ) / n ( s ) = 1 / 2 correct option is e"
Answer: e
Problem: how many numbers from 10 to 40 are exactly divisible by 3 ?
Options: a ) 13 , b ) 15 , c ) 16 , d ) 10 , e ) 18
Rationale: "12 , 15 , 18 , 21 , 24 , 27 , 30 , 33 , 36 , 39 . 10 numbers . 10 / 3 = 3 and 40 / 3 = 13 = = > 13 - 3 = 10 . therefore 10 digits d )"
Answer: d
Problem: in a dairy farm , 45 cows eat 45 bags of husk in 45 days . in how many days one cow will eat one bag of husk ?
Options: a ) 34 days , b ) 45 days , c ) 46 days , d ) 50 days , e ) none of these
Rationale: "explanation : less cows , more days ( indirect proportion ) less bags , less days ( direct proportion ) [ cows 1 45 bags 45 1 ] : : 45 : x = > x ∗ 45 ∗ 1 = 45 ∗ 1 ∗ 45 = > x = 45 option b"
Answer: b
Problem: how many pieces of 85 cm length can be cut from a rod of 17 meters long ?
Options: a ) 50 , b ) 40 , c ) 30 , d ) 20 , e ) 10
Rationale: number of pieces = 1700 / 85 = 20 the answer is d .
Answer: d
Problem: in the land of oz only one or two - letter words are used . the local language has 64 different letters . the parliament decided to forbid the use of the seventh letter . how many words have the people of oz lost because of the prohibition ?
Options: a ) 65 , b ) 66 , c ) 67 , d ) 131 , e ) 128
Rationale: "the answer to the question is indeed e . the problem with above solutions is that they do not consider words like aa , bb , . . . the number of 1 letter words ( x ) that can be made from 64 letters is 64 ; the number of 2 letter words ( xx ) that can be made from 64 letters is 64 * 64 , since each x can take 64 values . total : 64 + 64 * 64 . similarly : the number of 1 letter words ( x ) that can be made from 63 letters is 63 ; the number of 2 letter words ( xx ) that can be made from 63 letters is 63 * 63 , since each x can take 63 values . total : 63 + 63 * 63 . the difference is ( 64 + 64 * 64 ) - ( 63 + 63 * 63 ) = 128 . answer : e ."
Answer: e
Problem: while working alone at their constant rates , computer x can process 240 files in 8 hours , and computer y can process 240 files in 6 hours . if all files processed by these computers are the same size , how many hours would it take the two computers , working at the same time at their respective constant rates , to process a total of 240 files ?
Options: a ) 3 , b ) 3.4 , c ) 3.8 , d ) 4 , e ) 4.5
Rationale: "both computers together process files at a rate of 240 / 8 + 240 / 6 = 30 + 40 = 70 files per hour . the time required to process 240 files is 240 / 70 which is about 3.4 hours the answer is b ."
Answer: b
Problem: the average of 6 no . ' s is 3.95 . the average of 2 of them is 4.4 , while the average of theother 2 is 3.85 . what is the average of the remaining 2 no ' s ?
Options: a ) 4.2 , b ) 4.4 , c ) 3.6 , d ) 5.6 , e ) 5.7
Rationale: "sum of the remaining two numbers = ( 3.95 * 6 ) - [ ( 4.4 * 2 ) + ( 3.85 * 2 ) ] = 7.20 . required average = ( 7.2 / 2 ) = 3.6 . c"
Answer: c
Problem: two tains of equal lengths take 10 seconds and 20 seconds respectively to cross a telegraph post . if the length of each train be 120 metres , in what time ( in seconds ) will they cross each other travelling in opposite direction ?
Options: a ) 12 , b ) 14 , c ) 16 , d ) 20 , e ) 13.3
Rationale: "sol . speed of the first train = [ 120 / 10 ] m / sec = 12 m / sec . speed of the second train = [ 120 / 20 ] m / sec = 6 m / sec . relative speed = ( 12 + 6 ) = m / sec = 18 m / sec . ∴ required time = ( 120 + 120 ) / 18 secc = 13.3 sec . answer e"
Answer: e
Problem: the speed of a train including stoppages is 90 kmph and excluding stoppages is 120 kmph . of how many minutes does the train stop per hour ?
Options: a ) 9 , b ) 10 , c ) 12 , d ) 14 , e ) 15
Rationale: explanation : t = 30 / 120 * 60 = 15 answer : option e
Answer: e
Problem: the price of a cycle is reduced by 25 per cent . the new price is reduced by a further 30 per cent . the two reductions together are equal to a single reduction of
Options: a ) 45 % , b ) 47.5 % , c ) 35 % , d ) 32.5 % , e ) 30 %
Rationale: price = p initially price reduced by 25 % which means new price is 3 / 4 p now on this new price further 30 percent is reduced which means the new price is merely 70 percent of 3 / 4 p = = > ( 3 / 4 ) x ( 7 / 10 ) p = 21 / 40 p is the new price after both deduction which is 52.5 percent of the original value p . this implies this entire series of deduction is worth having discounted 47.5 % of p . so answer is b = 47.5 %
Answer: b
Problem: a certain industrial loom weaves 0.128 meters of cloth every second . approximately how many seconds will it take for the loom to weave 15 meters of cloth ?
Options: a ) 114 , b ) 115 , c ) 116 , d ) 117 , e ) 118
Rationale: let the required number of seconds be x more cloth , more time , ( direct proportion ) hence we can write as ( cloth ) 0.128 : 15 : : 1 : x = > 0.128 * x = 15 = > x = 15 / 0.128 = > x = 117 answer : d
Answer: d
Problem: # p is defined as 2 p + 20 for any number p . what is p , if # ( # ( # p ) ) = 12 ?
Options: a ) – 16 , b ) – 44 , c ) 10 , d ) 16 , e ) 18
Rationale: # p = 2 p + 20 - - - > # ( # p ) = 2 ( 2 p + 20 ) + 20 = 4 p + 60 and thus # ( 4 p + 60 ) = 2 ( 4 p + 60 ) + 20 = 8 p + 140 = 12 - - - > 8 p = - 128 - - - > p = - 16 , a is the correct answer .
Answer: a
Problem: when positive integer n is divided by positive integer j , the remainder is 14 . if n / j = 134.08 , what is value of j ?
Options: a ) 22 , b ) 56 , c ) 78 , d ) 112 , e ) 175
Rationale: "1 ) we know that decimal part of decimal quotient = { remainder / divisor } so 0.08 , the decimal part of the decimal quotient , must equal the remainder , 14 , divided by the divisor j . 0.08 = 14 / j 0.08 * j = 14 j = 14 / 0.08 = 1400 / 8 = 700 / 4 = 350 / 2 = 175 so j = 175 , answer = e ."
Answer: e
Problem: a seller of used cars has 10 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 ) 15 , d ) 14 , e ) 16
Rationale: "ifno caris selected more than once then the number of clients = 10 / 2 = 5 but since every car is being selected three times so no . of clients must be thrice as well = 5 * 3 = 15 answer : option c"
Answer: c
Problem: two numbers are in respectively 10 % and 40 % more than a third number . the ratio of the two numbers is ?
Options: a ) 11 : 14 , b ) 7 : 9 , c ) 17 : 25 , d ) 15 : 26 , e ) 2 : 3
Rationale: let the 3 rd number be x then , first number = 110 % of x = 110 x / 100 = 11 x / 10 second number = 140 % of x = 140 x / 100 = 7 x / 5 ratio of first two numbers = 11 x / 10 : 7 x / 5 = 11 : 14 answer is a
Answer: a
Problem: find the number of shares that can be bought for rs . 8200 if the market value is rs . 20 each with brokerage being 2.8 % .
Options: a ) 237 , b ) 270 , c ) 398.8 , d ) 166 , e ) 111
Rationale: "explanation : cost of each share = ( 20 + 2.8 % of 20 ) = rs . 20.56 therefore , number of shares = 8200 / 20.56 = 398.8 answer : c"
Answer: c
Problem: a 300 meter long train crosses a platform in 27 seconds while it crosses a signal pole in 18 seconds . what is the length of the platform ?
Options: a ) 150 m , b ) 278 m , c ) 350 m , d ) 228 m , e ) 282 m
Rationale: "speed = [ 300 / 18 ] m / sec = 50 / 3 m / sec . let the length of the platform be x meters . then , x + 300 / 27 = 50 / 3 3 ( x + 300 ) = 1350 è x = 150 m . answer : a"
Answer: a
Problem: the average age of a family of 6 members is 34 years . if the age of the youngest member is 7 years , what was the average age of the family at the birth of the youngest member ?
Options: a ) 15 , b ) 18 , c ) 21 , d ) 12 , e ) 27
Rationale: "present age of total members = 6 x 34 = 204 7 yrs back their ages were = 6 x 7 = 42 ages at the birth of youngest member = 204 - 42 = 162 therefore , avg age at the birth of youngest member = 162 / 6 = 27 . answer : e"
Answer: e
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 $ 20,000 each and the salary of 4 of the employees is $ 16,000 each . what is the average salary of the remaining employees ?
Options: a ) $ 19,250 , b ) $ 18,500 , c ) $ 18,000 , d ) $ 15,850 , e ) $ 22,600
Rationale: "total salary . . . 15 * 20 k = 300 k 5 emp @ 20 k = 100 k 4 emp @ 16 k = 64 k remaing 6 emp sal = 300 k - 100 k - 64 k = 136 k average = 136 k / 6 = 22600 ans : e"
Answer: e
Problem: find the value of x in ( x / 5 ) + 3 = 4 .
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: ( x / 5 ) + 3 = 4 . subtracting both sides with 3 gives x / 5 = 1 multiplying both sides by 5 gives x = 5 answer : e
Answer: e
Problem: if a can do a work in 10 days and a and b can do a same piece of job in 5 days . in how days can do a work b alone ?
Options: a ) 10 , b ) 20 , c ) 5 , d ) 15 , e ) 9
Rationale: a ' s one day work = 1 / 10 a + b = 1 / 5 ( one day work ) b = ( 1 / 5 ) - a = ( 1 / 5 ) - ( 1 / 10 ) = 1 / 10 ( one day work ) b can done a work in 10 days . answer option a
Answer: a
Problem: pipe a and pipe b fill water into a tank of capacity 1000 litres , at a rate of 200 l / min and 50 l / min . pipe c drains at a rate of 25 l / min . pipe a is open for 1 min and closed , then pipe b is open for 2 min and closed . further the pipe c is opened and drained for another 2 min . this process is repeated until the tank is filled . how long will it take to fill the tank ?
Options: a ) 15 , b ) 17 , c ) 18 , d ) 56 , e ) 20
Rationale: "tank capacity : 1000 l , 1 st - 200 l / min for 1 min , volume filled : 200 l 2 nd - 100 l / min for 2 min , volume filled : 100 l 3 rd ( water draining ) : 25 l / min * 2 : 50 l total : ( 200 + 100 ) - 50 = 250 l filled for 1 cycle number of 250 in 1000 l tank : 1000 / 250 = 4 time taken to fill : 4 * total time = 4 * 5 = 20 ( option e )"
Answer: e
Problem: a car traveled 480 miles per tankful of gasoline on the highway and 336 miles per tankful of gasoline in the city . if the car traveled 6 fewer miles per gallon in the city than on the highway , how many miles per gallon did the car travel in the city ?
Options: a ) 14 , b ) 16 , c ) 21 , d ) 22 , e ) 27
Rationale: "let the speed in highway be h mpg and in city be c mpg . h = c + 6 h miles are covered in 1 gallon 462 miles will be covered in 462 / h . similarly c miles are covered in 1 gallon 336 miles will be covered in 336 / c . both should be same ( as car ' s fuel capacity does not change with speed ) = > 336 / c = 480 / h = > 336 / c = 480 / ( c + 6 ) = > 336 c + 336 * 6 = 480 c = > c = 336 * 6 / 144 = 14 answer a ."
Answer: a
Problem: what is the least number should be added to 1056 , so the sum of the number is completely divisible by 26 ?
Options: a ) 10 , b ) 20 , c ) 30 , d ) 40 , e ) 50
Rationale: "( 1056 / 26 ) gives remainder 16 10 + 16 = 26 , so we need to add 10 a"
Answer: a
Problem: what is the smallest number which , when increased by 5 , is divisible by 7 , 8 , and 24 ?
Options: a ) 148 , b ) 153 , c ) 158 , d ) 163 , e ) 168
Rationale: "lcm ( 7 , 8,24 ) = 24 x 7 = 168 so the least divisible number is 168 , and the number we are looking for is 168 - 5 = 163 . the answer is d ."
Answer: d
Problem: the length of a rectangle is reduced by 15 % . by what % would the width have to be increased to maintain the original area ?
Options: a ) 10 %
b ) 20 %
c ) 17.6 %
d ) 30 %
e ) 35 %
Rationale: sol . required change = ( 15 * 100 ) / ( 100 - 15 ) = 17.6 % c
Answer: c