regisss/math_qa huggingface dataset:
Problem: eddy and freddy start simultaneously from city a and they travel to city b and city c respectively . eddy takes 3 hours and freddy takes 4 hours to complete the journey . if the distance between city a and city b is 510 kms and city a and city c is 300 kms . what is the ratio of their average speed of travel ? ( eddy : freddy )
Options: a ) 8 / 3 , b ) 3 / 8 , c ) 8 / 5 , d ) 5 / 8 , e ) 34 / 15
Rationale: distance traveled by eddy = 510 km time taken by eddy = 3 hours average speed of eddy = 510 / 3 = 170 km / hour distance traveled by freddy = 300 km time taken by freddy = 4 hours average speed of freddy = 300 / 4 = 75 km / hour ratio of average speed of eddy to freddy = 170 / 75 = 34 / 15 answer e
Answer: e
Problem: two brothers ram and ravi appeared for an exam . the probability of selection of ram is 4 / 7 and that of ravi is 1 / 5 . find the probability that both of them are selected .
Options: a ) 4 / 35 , b ) 2 / 3 , c ) 7 / 35 , d ) 5 / 7 , e ) 7 / 5
Rationale: let a be the event that ram is selected and b is the event that ravi is selected . p ( a ) = 4 / 7 p ( b ) = 1 / 5 let c be the event that both are selected . p ( c ) = p ( a ) x p ( b ) as a and b are independent events : = 4 / 7 x 1 / 5 = 4 / 35 answer : a
Answer: a
Problem: the cross - section of a cannel is a trapezium in shape . if the cannel is 12 m wide at the top and 2 m wide at the bottom and the area of cross - section is 4200 sq m , the depth of cannel is ?
Options: a ) 500 , b ) 600 , c ) 700 , d ) 800 , e ) 900
Rationale: "1 / 2 * d ( 12 + 2 ) = 4200 d = 600 answer : b"
Answer: b
Problem: 120 kg of an alloy a is mixed with 180 kg of alloy b . if alloy a has lead and tin in the ratio 2 : 3 and alloy b has tin and copper in the ratio 3 : 5 , then the amount of tin in the new alloy is ?
Options: a ) 100.6 kg , b ) 120.3 kg , c ) 139.5 kg , d ) 140.8 kg , e ) 114.5 kg
Rationale: "quantity of tin in 120 kg of a = 120 * 3 / 5 = 72 kg quantity of tin in 180 kg of b = 180 * 3 / 8 = 67.5 kg quantity of tin in the new alloy = 72 + 67.5 = 139.5 kg answer is c"
Answer: c
Problem: how many seconds will a train 120 meters long take to cross a bridge 150 meters long if the speed of the train is 36 kmph ?
Options: a ) 17 sec , b ) 21 sec , c ) 25 sec , d ) 27 sec , e ) 29 sec
Rationale: "d = 120 + 150 = 270 s = 36 * 5 / 18 = 10 mps t = 270 / 10 = 27 sec"
Answer: d
Problem: 3 / 4 of a number is 19 less than the original number . the number is ?
Options: a ) 84 , b ) 64 , c ) 76 , d ) 72 , e ) none
Rationale: answer let the original number be n . so from question n - 3 n / 4 = 19 ⇒ 4 n - 3 n = 76 ∴ n = 76 option : c
Answer: c
Problem: the cost price of 40 articles is the same as the selling price of x articles . if the profit is 25 % , what is x ?
Options: a ) 26 , b ) 28 , c ) 30 , d ) 32 , e ) 34
Rationale: "let the cost price = y the cost price of 40 articles = 40 y the selling price of x articles = 1.25 y * x 1.25 y * x = 40 y x = 40 / 1.25 = 32 the answer is d ."
Answer: d
Problem: a man can row 6 kmph in still water . when the river is running at 3 kmph , it takes him 1 hour to row to a place and black . what is the total distance traveled by the man ?
Options: a ) 5.75 , b ) 4.5 , c ) 5.76 , d ) 5.74 , e ) 5.71
Rationale: "m = 6 s = 3 ds = 9 us = 3 x / 9 + x / 3 = 1 x = 2.25 d = 2.25 * 2 = 4.5 answer : b"
Answer: b
Problem: the interest on a certain deposit at 4.5 % p . a . is rs . 202.50 in one year . how much will the additional interest in one year be on the same deposit at 5 % p . a ?
Options: a ) rs . 20.25 , b ) rs . 22.50 , c ) rs . 25 , d ) rs . 42.75 , e ) none
Rationale: "solution s . i = rs . 202.50 , r = 4.5 % , t = 1 year principal = rs ( 100 * 202.50 / 4.5 * 1 ) = rs . 4500 now p = rs . 4500 , r = 5 % , t = 1 year s . i = ( 4500 * 5 * 1 / 100 ) = rs . 225 different in interest = rs . ( 225 - 202.50 ) = rs . 22.50 answer b"
Answer: b
Problem: ( ( - 1.9 ) ( 0.6 ) – ( 2.6 ) ( 1.2 ) ) / 5.0 = ?
Options: a ) - 0.852 , b ) 1.0 , c ) 1.07 , d ) 1.71 , e ) 2.71
Rationale: "dove straight into calculation but quickly realized that the sum of two negatives is a negative so there is only one option . - 0.852 answer a"
Answer: a
Problem: what is the remainder when 12987 ^ ( 65987036 ) is divided by 5 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "we need to find the units digit of the number . the units digit of powers of seven repeats 7 , 9 , 3 , and 1 cyclically . since 65987036 has the form 4 a , the units digit is 1 . then the remainder when dividing by 5 is 1 . the answer is b ."
Answer: b
Problem: if the wheel is 12 cm then the number of revolutions to cover a distance of 1056 cm is ?
Options: a ) 18 , b ) 26 , c ) 14 , d ) 12 , e ) 91
Rationale: "2 * 22 / 7 * 12 * x = 1056 = > x = 14 answer : c"
Answer: c
Problem: if the length and breadth of a rectangular room are each increased by 1 m , then the area of floor is increased by 21 sq . m . if the length is creased by 1 m and breadth is decreased by 1 m , then the area is decreased by 5 sq . m . the perimeter of the floor is :
Options: a ) 27
b ) 35
c ) 40
d ) 49
e ) 38
Rationale: let length = x meters and breadth = y meters . then , ( x + 1 ) ( y + 1 ) - xy = 21 x + y = 20 ã ¢ â ‚ ¬ â ¦ ã ¢ â ‚ ¬ â ¦ ã ¢ â ‚ ¬ â ¦ ã ¢ â ‚ ¬ â ¦ ã ¢ â ‚ ¬ â ¦ ã ¢ â ‚ ¬ â ¦ 1 and , xy - [ ( x + 1 ) ( y - 1 ) ] = 5 x - y = 6 ã ¢ â ‚ ¬ â ¦ ã ¢ â ‚ ¬ â ¦ ã ¢ â ‚ ¬ â ¦ ã ¢ â ‚ ¬ â ¦ ã ¢ â ‚ ¬ â ¦ ã ¢ â ‚ ¬ â ¦ . . 2 solving ( i ) and ( ii ) , we get : x = 13 and y = 7 so , length = 13 m and breadth = 7 m . perimeter = [ 2 ( 13 + 7 ) ] m = 40 m . answer : c
Answer: c
Problem: a car is 15 minutes late by running at a speed of 4 / 5 th of its actual speed . the actual time taken by the car to cover that distance is :
Options: a ) 30 minutes , b ) 1 hour , c ) 2 hours , d ) 3 hours , e ) none of these
Rationale: explanation : new speed = 4 / 5 th of its actual speed new time = 5 / 4 th of its actual time = > 5 / 4 t - t = 15 / 60 = 1 / 4 = > 1 / 4 t = 1 / 4 = > t = 1 hour answer : b
Answer: b
Problem: the average runs scored by a batsman in 20 matches is 40 . in the next 10 matches the batsman scored an average of 30 runs . find his average in all the 30 matches ?
Options: a ) 31 , b ) 36.67 , c ) 88 , d ) 13 , e ) 12
Rationale: "total score of the batsman in 20 matches = 800 . total score of the batsman in the next 10 matches = 300 . total score of the batsman in the 30 matches = 1100 . average score of the batsman = 1100 / 30 = 36.67 . answer : b"
Answer: b
Problem: the maitre ' d at an expensive manhattan restaurant has noticed that 60 % of the couples order dessert and coffee . however , 20 % of the couples who order dessert do n ' t order coffee . what is the probability t that the next couple the maitre ' d seats will not order dessert ?
Options: a ) 20 % , b ) 25 % , c ) 40 % , d ) 60 % , e ) 75 %
Rationale: "could you use a venn diagram and just go with the number 100 . 60 people order dessert and coffee . . . which is the union of d and c . t = 2 / 10 of d are n ' t in d u c = so 8 / 10 of d are in duc which means = 60 = 8 / 10 d . so d in total = 75 , and 15 d ' s are n ' t in d union c . which means 25 people are in c only + neither . b 25 %"
Answer: b
Problem: anne bought doughnuts for a class breakfast party . she bought 6 chocolate doughnuts , 8 coconut doughnuts , and 8 jam - filled doughnuts . how many doughnuts did anne buy in all ?
Options: a ) 22 , b ) 36 , c ) 39 , d ) 21 , e ) 11
Rationale: "add the numbers of doughnuts . 6 + 8 + 8 = 22 . answer is a ."
Answer: a
Problem: i sold a book at a profit of 10 % . had i sold it for $ 110 more , 15 % would have been gained . find the cost price ?
Options: a ) $ 2000 , b ) $ 2200 , c ) $ 3000 , d ) $ 3120 , e ) $ 1540
Rationale: 115 % of cost - 110 % of cost = $ 110 5 % of cost = $ 110 cost = 110 * 100 / 5 = $ 2200 answer is b
Answer: b
Problem: find the perimeter and area of the rectangle of length 19 cm and breadth 13 cm .
Options: a ) 71 cm 2 , b ) 121 cm 2 , c ) 141 cm 2 , d ) 171 cm 2 , e ) 247 cm 2
Rationale: "length = 19 cm , breadth = 13 cm perimeter of rectangle = 2 ( length + breadth ) = 2 ( 19 + 13 ) cm = 2 × 32 cm = 64 cm we know that the area of rectangle = length × breadth = ( 19 × 13 ) cm 22 = 247 cm 2 answer : e"
Answer: e
Problem: 90 % of the population of a village is 36000 . the total population of the village is ?
Options: a ) 26799 , b ) 24000 , c ) 26682 , d ) 29973 , e ) 40000
Rationale: "x * ( 90 / 100 ) = 36000 x = 400 * 100 x = 40000 answer : e"
Answer: e
Problem: ( ( - 1.9 ) ( 0.6 ) – ( 2.6 ) ( 1.2 ) ) / 2.0 = ?
Options: a ) - 0.71 , b ) - 2.13 , c ) 1.07 , d ) 1.71 , e ) 2.71
Rationale: "dove straight into calculation ( ( - 1.9 ) ( 0.6 ) – ( 2.6 ) ( 1.2 ) ) / 2.0 = - 2.13 answer b"
Answer: b
Problem: the probability that a number selected at random from the first 50 natural numbers is a composite number is
Options: a ) 17 / 26 , b ) 17 / 25 , c ) 17 / 20 , d ) 17 / 22 , e ) 17 / 21
Rationale: the number of exhaustive events = ⁵ ⁰ c ₁ = 50 . we have 15 primes from 1 to 50 . number of favourable cases are 34 . required probability = 34 / 50 = 17 / 25 . nswer : b
Answer: b
Problem: a retailer buys 80 pens at the market price of 36 pens from a wholesaler , if he sells these pens giving a discount of 1 % , what is the profit % ?
Options: a ) 110 , b ) 115 , c ) 112 , d ) 118 , e ) 120
Rationale: "let the market price of each pen be $ 1 then , cost price of 80 pens = $ 36 selling price of 80 pens = 99 % of $ 80 = $ 79.20 profit % = ( ( 43.20 * 100 ) / 36 ) % = 120 % answer e ) 120"
Answer: e
Problem: if there are only 2 wheelers and 4 wheelers parked in a school located at the heart of the city , find the number of 4 wheelers parked there if the total number of wheels is 66 ?
Options: a ) 11 , b ) 12 , c ) 13 , d ) 16 , e ) 17
Rationale: "four wheeler = 16 * 4 = 64 ( max ) 2 wheel = 1 so no of 4 wheeler = 16 answer : d"
Answer: d
Problem: a train running at the speed of 27 km / hr crosses a post in 20 seconds . what is the length of the train ?
Options: a ) 200 , b ) 150 , c ) 300 , d ) 175 , e ) 250
Rationale: "speed = ( 27 x 5 / 18 ) = 7.5 m / sec . length of the train = ( speed x time ) . length of the train = 7.5 x 20 m = 150 m . answer : b"
Answer: b
Problem: what is the rate percent when the simple interest on rs . 800 amount to rs . 128 in 4 years ?
Options: a ) 5 % , b ) 3 % , c ) 4 % , d ) 9 % , e ) 1 %
Rationale: "128 = ( 800 * 4 * r ) / 100 r = 4 % answer : c"
Answer: c
Problem: a restaurant spends one quarter of its monthly budget for rent and half of the rest for food and beverages . what percentage of the budget does the restaurant spend for food and beverages ?
Options: a ) 23.5 % , b ) 32.5 % , c ) 35 % , d ) 37.5 % , e ) 75 %
Rationale: "let the total budget be 100 as per the question , restaurant spends one quarter of its monthly budget for rent = 25 half of the rest for food and beverages = 75 / 2 = 37.5 therefore , percentage spent on food and beverage = 37.5 answer : d"
Answer: d
Problem: if a is a positive integer , and if the units digit of a ^ 2 is 4 and the units digit of ( a + 1 ) ^ 2 is 1 , what is the units digit of ( a + 2 ) ^ 2 ?
Options: a ) 0 , b ) 2 , c ) 4 , d ) 6 , e ) 8
Rationale: if the units digit of a ^ 2 is 4 , then the units digit of a is either 2 or 8 . if the units digit of ( a + 1 ) ^ 2 is 1 , then the units digit of a + 1 is either 1 or 9 . to satisfy both conditions , the units digit of a must be 8 . then a + 2 has the units digit of 0 , thus the units digit of ( a + 2 ) ^ 2 will be 0 . the answer is a .
Answer: a
Problem: the ratio of the volumes of two cubes is 125 : 512 . what is the ratio of their total surface areas ?
Options: a ) 81 : 121 , b ) 25 : 64 , c ) 729 : 1331 , d ) 27 : 121 , e ) none of these
Rationale: "ratio of the sides = â ³ â ˆ š 125 : â ³ â ˆ š 512 = 5 : 8 ratio of surface areas = 5 ^ 2 : 8 ^ 2 = 25 : 64 answer : b"
Answer: b
Problem: an error 1 % in excess is made while measuring the side of a square . the percentage of error in the calculated area of the square is :
Options: a ) 2.01 , b ) 30.1 , c ) 3.01 , d ) 25.01 , e ) 4.05
Rationale: "explanation : 100 cm is read as 101 cm . a 1 = ( 100 × 100 ) cm 2 = 10000 and a 2 = ( 101 × 101 ) cm 2 = 10609 ( a 2 - a 1 ) = 10201 - 10000 = 201 = > 201 / 10000 * 100 = 2.01 answer : a"
Answer: a
Problem: george went to a fruit market with certain amount of money . with this money he can buy either 40 oranges or 40 mangoes . he retains 10 % of the money for taxi fare and buys 20 mangoes . how many oranges can he buy ?
Options: a ) 25 , b ) 30 , c ) 20 , d ) 16 , e ) 12
Rationale: "let the amount of money be 200 let cost of 1 orange be 4 let cost of 1 mango be 4 he decides to retain 10 % of 200 = 20 for taxi fare , so he is left with 180 he buys 20 mangoes ( @ 4 ) so he spends 80 money left is 100 ( 180 - 80 ) no of oranges he can buy = 100 / 4 = > 25 so , george can buy 25 oranges . a"
Answer: a
Problem: the average mark of the students of a class in a particular exam is 80 . if 5 students whose average mark in that exam is 60 are excluded , the average mark of the remaining will be 90 . find the number of students who wrote the exam .
Options: a ) 22 , b ) 27 , c ) 15 , d ) 99 , e ) 21
Rationale: "let the number of students who wrote the exam be x . total marks of students = 80 x . total marks of ( x - 5 ) students = 90 ( x - 5 ) 80 x - ( 5 * 60 ) = 90 ( x - 5 ) 150 = 10 x = > x = 15 . answer : c"
Answer: c
Problem: ann and bob drive separately to a meeting . ann ' s average driving speed is greater than bob ' s avergae driving speed by one - third of bob ' s average driving speed , and ann drives twice as many miles as bob . what is the ratio w of the number of hours ann spends driving to the meeting to the number of hours bob spends driving to the meeting ?
Options: a ) 8 : 3 , b ) 3 : 2 , c ) 4 : 3 , d ) 2 : 3 , e ) 3 : 8
Rationale: "say the rate of bob is 3 mph and he covers 6 miles then he needs 6 / 3 = 2 hours to do that . now , in this case the rate of ann would be 3 + 3 * 1 / 3 = 4 mph and the distance she covers would be 6 * 2 = 12 miles , so she needs 12 / 4 = 3 hours for that . the ratio w of ann ' s time to bob ' s time is 3 : 2 . answer : b ."
Answer: b
Problem: if a is a positive integer , and if the units digit of a ^ 2 is 9 and the units digit of ( a + 1 ) ^ 2 is 4 , what is the units u digit of ( a + 2 ) ^ 2 ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 6 , e ) c . 14
Rationale: "i also got a . by punching in numers : u . . . 7 ^ 2 = . . . 9 . . . 8 ^ 2 = . . . 4 . . . 9 ^ 2 = . . . 1 . a"
Answer: a
Problem: find the value of 72515 x 9999 = m ?
Options: a ) 345434667 , b ) 246465757 , c ) 465767867 , d ) 725077485 , e ) 645354643
Rationale: "72515 x 9999 = 72515 x ( 10000 - 1 ) = 72515 x 10000 - 72515 x 1 = 725150000 - 72515 = 725077485 d"
Answer: d
Problem: a can give b 50 meters start and c 200 meters start in a kilometer race . how much start can b give c in a kilometer race ?
Options: a ) 157.89 , b ) 157.13 , c ) 157.22 , d ) 111.0 , e ) 111.12
Rationale: "a runs 1000 m while b runs 950 m and c runs 800 m . the number of meters that c runs when b runs 1000 m , = ( 1000 * 800 ) / 950 = 842.10 m . b can give c = 1000 - 842.10 = 157.89 m . answer : a"
Answer: a
Problem: the present population of a town is 1240 . population increase rate is 4 % p . a . find the population of town after 1 years ?
Options: a ) 990 , b ) 1215 , c ) 1345 , d ) 1142 , e ) 1290
Rationale: "p = 1240 r = 4 % required population of town = p * ( 1 + r / 100 ) ^ t = 1240 * ( 1 + 4 / 100 ) = 1240 * ( 26 / 25 ) = 1290 ( approximately ) answer is e"
Answer: e
Problem: sandy bought 65 books for $ 1080 from one shop and 55 books for $ 840 from another shop . what is the average price that sandy paid per book ?
Options: a ) $ 14 , b ) $ 16 , c ) $ 18 , d ) $ 20 , e ) $ 22
Rationale: "average price per book = ( 1080 + 840 ) / ( 65 + 55 ) = 1920 / 120 = $ 16 the answer is b ."
Answer: b
Problem: a merchant marks goods up by 80 % and then offers a discount on the marked price . the profit that the merchant makes after offering the discount is 35 % . what % discount did the merchant offer ?
Options: a ) 20 % , b ) 25 % , c ) 30 % , d ) 35 % , e ) 40 %
Rationale: "let p be the original price of the goods and let x be the rate after the markup . ( 1.8 p ) * x = 1.35 p x = 1.35 / 1.8 = 0.75 which is a discount of 25 % . the answer is b ."
Answer: b
Problem: the average height of 20 students in a class was calculated as 175 cm . it has later found that the height of one of the students in the class was incorrectly written as 151 cm whereas the actual height was 136 cm . what was the actual average height of the students in the class ?
Options: a ) 174.75 cm , b ) 174.25 cm , c ) 173.75 cm , d ) 173.25 cm , e ) 172.75 cm
Rationale: the total height was 15 cm too much . the average height should be reduced by 15 cm / 20 = 0.75 cm the answer is b .
Answer: b
Problem: the cost price of a radio is rs . 3300 and it was sold for rs . 1230 , find the loss % ?
Options: a ) 62.7 % , b ) 65 % , c ) 88 % , d ) 65 % , e ) 62 %
Rationale: "3300 - - - - 2070 100 - - - - ? = > 62.7 % answer : a"
Answer: a
Problem: at what rate percent per annum will the simple interest on a sum of money be 3 / 5 of the amount in 10 years ?
Options: a ) 6 % , b ) 7 % , c ) 9 % , d ) 3 % , e ) 1 %
Rationale: "let sum = x . then , s . i . = 2 x / 5 , time = 10 years . rate = ( 100 * 3 x ) / ( x * 5 * 10 ) = 6 % answer : a"
Answer: a
Problem: ( 3220 + 6160 ) / 28
Options: a ) 380 , b ) 350 , c ) 335 , d ) 310 , e ) none of these
Rationale: "explanation : as per bodmas rule , first we will solve the equation in bracket then we will go for division = ( 9380 ) / 28 = 335 option c"
Answer: c
Problem: working simultaneously and independently at an identical constant rate , 5 machines of a certain type can produce a total of x units of product p in 4 days . how many of these machines , working simultaneously and independently at this constant rate , can produce a total of 2 x units of product p in 2 days ?
Options: a ) 11 , b ) 13 , c ) 15 , d ) 18 , e ) 20
Rationale: "the rate of 5 machines is rate = job / time = x / 4 units per day - - > the rate of 1 machine 1 / 5 * ( x / 4 ) = x / 20 units per day ; now , again as { time } * { combined rate } = { job done } then 2 * ( m * x / 20 ) = 2 x - - > m = 20 . answer : e ."
Answer: e
Problem: heinz produces tomato puree by boiling tomato juice . the tomato puree has only 20 % water while the tomato juice has 90 % water . how many litres of tomato puree will be obtained from 20 litres of tomato juice ?
Options: a ) 2 litres , b ) 2.4 litres , c ) 2.5 litres , d ) 6 litres , e ) 4 litres
Rationale: "tomato juice has 90 % water and 10 % tomato tomato puree has 20 % water and 80 % tomato so 20 liter of tomato juice has 20 * 90 / 100 = 18 liters of water and 2 liters of tomato . as tomato puree has 80 % content of tomato , so 2 liters of tomato from 20 liter juice corresponds to 80 % so tomato purees that can be obtained = 100 * 2 / 80 = 2.5 answer : c"
Answer: c
Problem: if a speaks the truth 40 % of the times , b speaks the truth 80 % of the times . what is the probability that at least one will tell the truth
Options: a ) 0.18 , b ) 0.12 , c ) 1.02 , d ) 1.2 , e ) 1.3
Rationale: "probability of a speaks truth p ( a ) = 4 / 10 ; false = 6 / 10 probability of b speaks truth p ( b ) = 8 / 10 ; false = 2 / 10 . for given qtn ans = 1 - ( neither of them tell truth ) . because a & b are independent events = 1 - [ ( 6 / 10 ) * ( 2 / 10 ) ] = 1 - 12 / 100 = 1 - 0.88 = 0.12 answer : b"
Answer: b
Problem: a seller of used cars has 12 cars to sell and each of his clients selected 4 cars that he liked most . if each car was selected exactly thrice , how many clients visited the garage ?
Options: a ) 9 , b ) 10 , c ) 12 , d ) 14 , e ) 16
Rationale: "ifno caris selected more than once then the number of clients = 12 / 4 = 3 but since every car is being selected three times so no . of clients must be thrice as well = 3 * 3 = 9 answer : option a"
Answer: a
Problem: the length of a rectangular landscape is 3 times its breadth . there is a playground in it whose area is 1600 square mtr & which is 1 / 3 rd of the total landscape . what is the length of the landscape ?
Options: a ) 90 , b ) 160 , c ) 150 , d ) 120 , e ) 140
Rationale: "sol . x * 3 x = 3 * 2500 x = 50 length = 3 * 50 = 150 c"
Answer: c
Problem: set a contains all the even numbers between 2 and 50 inclusive . set b contains all the even numbers between 62 and 110 inclusive . what is the difference between the sum of elements of set b and the sum of the elements of set a ?
Options: a ) 1500 , b ) 3100 , c ) 4400 , d ) 6200 , e ) 7400
Rationale: "each term in set b is 60 more than the corresponding term in set a . the difference of the sums = 25 * 60 = 1500 . the answer is a ."
Answer: a
Problem: the cost price of 20 articles is the same as the selling price of x articles . if the profit is 25 % , then the value of x is :
Options: a ) 15 , b ) 16 , c ) 18 , d ) 25 , e ) 27
Rationale: "explanation : let the cost price of 1 article be z . so , the cost price of 20 article = 20 z - - - - - - - - - - - - - - - - - - - - - - - - - ( 1 ) selling price of 20 articles = 20 z + 25 % of 20 z = 25 z = > selling price of 1 article = 25 z / 20 = ( 5 / 4 ) * z = > selling price of x articles = ( 5 / 4 ) * z * x - - - - - - - - - - - - - - - - - - - - - - - - - ( 2 ) given that selling price ( s . p . ) of x articles = cost price ( c . p . ) of 20 articles = > ( 5 / 4 ) * z * x = 20 z = > x = 16 answer : b"
Answer: b
Problem: the ratio of male to female in a class is 2 : 3 . the career preference of the students in the class are to be represented in a circle graph . if the area of the graph allocated to each career preference is to be proportional to the number of students who have that career preference , how many degrees of the circle should be used to represent a career that is preferred by one fourth of the males and 3 / 4 th of the females in the class ?
Options: a ) a ) 160 degree
b ) b ) 198 degree
c ) c ) 191 degree
d ) d ) 192 degree
e ) e ) 204 degree
Rationale: let the common ratio be x . . so m = 2 x and f = 3 x and total = 5 x 1 / 4 of m = 2 x / 4 and 3 / 4 of f = 9 / 4 x . . total preferring that carrer = x / 2 + 9 x / 4 = 11 x / 4 now 5 x = 360 , so x = 360 / 5 = 72 . . so 72 * 11 / 4 = 198 ans 198 b
Answer: b
Problem: at what price must an article costing rs . 47.50 be marked in order that after deducting 20 % from the list price . it may be sold at a profit of 25 % on the cost price ?
Options: a ) 62.5 , b ) 62.3 , c ) 62.7 , d ) 74.2 , e ) 62.9
Rationale: cp = 47.50 sp = 47.50 * ( 125 / 100 ) = 59.375 mp * ( 80 / 100 ) = 59.375 mp = 74.2 answer : d
Answer: d
Problem: a mail handler needs 3 hours to sort the mail . his assistant takes 6 hours to sort the mail . how many hours will it take for both of them working together to sort the mail ?
Options: a ) 3 , b ) 2 , c ) 1 , d ) 2 1 / 2 , e ) 1 1 / 5
Rationale: work hrs = ab / ( a + b ) = 18 / 9 = 2 answer is b
Answer: b
Problem: a bag contains 7 black and 8 white balls . if two balls are drawn simultaneously , what is the probability that both are of the same color is ?
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 2 / 3 , d ) 3 / 5 , e ) 7 / 15
Rationale: drawing two balls of same color from seven black balls can be done in ⁷ c ₂ ways . similarly from eight white balls two can be drawn in ⁸ c ₂ ways . p = ⁷ c ₂ / ¹ ⁵ c ₂ + ⁸ c ₂ / ¹ ⁵ c ₂ = 7 / 15 answer is e
Answer: e
Problem: if it is assumed that 60 percent of those who receive a questionnaire by mail will respond and 240 responses are needed , what is the minimum number of questionnaires that should be mailed ?
Options: a ) 400 , b ) 500 , c ) 600 , d ) 700 , e ) 800
Rationale: "let x be the minimum number of questionnaires to be mailed . 0.6 x = 240 x = 400 the answer is a ."
Answer: a
Problem: the average of first five multiples of 7 is :
Options: a ) 9 , b ) 16 , c ) 15 , d ) 8 , e ) 21
Rationale: "explanation : ( 7 ( 1 + 2 + 3 + 4 + 5 ) / 5 = 7 x 15 / 5 = 21 answer : e"
Answer: e
Problem: a does half as much work as b in 3 - fourth of the time . if together they take 18 days to complete the work , how much time shall b take to do it ?
Options: a ) 30 days , b ) 35 days , c ) 40 days , d ) 45 days , e ) 50 days
Rationale: explanation : let ‘ x ’ be the number of days taken by b alone to finish the whole work then , a alone will finish the whole work in 3 x / 4 × 2 days = 3 x / 2 days . then , working together , 3 x / 2 × x / 3 x / 2 + x = 18 days 3 x × x / 5 x = 18 3 x / 5 = 18 therefore , the number of days taken by b = x = 18 × 5 / 3 = 30 days . answer : option a
Answer: a
Problem: a certain sum of money is divided among a , b and c so that for each rs . a has , b has 65 paisa and c 40 paisa . if c ' s share is rs . 56 , find the sum of money ?
Options: a ) 288 , b ) 287 , c ) 72 , d ) 205 , e ) 267
Rationale: "a : b : c = 100 : 65 : 40 = 20 : 13 : 8 8 - - - - 56 41 - - - - ? = > rs . 287 answer : b"
Answer: b
Problem: in what time will a train 80 m long cross an electric pole , it its speed be 144 km / hr ?
Options: a ) 2.0 sec , b ) 2.8 sec , c ) 7.5 sec , d ) 2.3 sec , e ) 1.5 sec
Rationale: "speed = 144 * 5 / 18 = 40 m / sec time taken = 80 / 40 = 2.0 sec . answer : a"
Answer: a
Problem: john purchased 1375 large bottles at $ 1.75 per bottle and 690 small bottles at $ 1.35 per bottle . what was the approximate average price paid per bottle ?
Options: a ) $ 1.62 , b ) $ 1.64 , c ) $ 1.68 , d ) $ 1.72 , e ) $ 1.76
Rationale: "( 1375 * 1.75 + 690 * 1.35 ) / ( 1375 + 690 ) = ~ 1.62 option ( a )"
Answer: a
Problem: an investor deposited $ 5,000 to open a new savings account that earned 8 percent annual interest , compounded quarterly . if there were no other transactions in the account , what was the amount of money in the account 6 months after the account was opened ?
Options: a ) $ 5050 , b ) $ 5101 , c ) $ 5202 , d ) $ 5303 , e ) $ 5404
Rationale: "the amount in the account after 6 months is 1.02 * 1.02 ( $ 5,000 ) = $ 5202 the answer is c ."
Answer: c
Problem: 1 , 8 , 27 , 64 , . . .
Options: a ) 25 , b ) 48 , c ) 59 , d ) 63 , e ) 125
Rationale: "explanation : numbers are 1 ^ 3 = 1 2 ^ 3 = 8 3 ^ 3 = 27 4 ^ 3 = 17 5 ^ 3 = 125 answer : e"
Answer: e
Problem: a pet store holds cats and dogs . if the difference between the number of cats and the number of dogs is 11 . what could be the ratio of cats to dogs in the pet store ?
Options: a ) 1 : 3 , b ) 1 : 4 , c ) 1 : 5 , d ) 44 : 55 , e ) 4 : 6
Rationale: say theratioof cats to dogs is a / b . then thenumberof cats would be ax and thenumberof dogs bx , for some positive integer x . we are told that ax - bx = 11 - - > x ( a - b ) = 11 . since 11 is a prime number it could be broken into the product of two positive multiples only in one way : x ( a - b ) = 1 * 11 . the above implies that either x = 1 and ( a - b ) = 11 or x = 11 and ( a - b ) = 1 . therefore the correct answer should have the difference between numerator and denominator equal to 1 or 11 . for the original question only option which fits is e , 4 : 5 . cats = 11 * 4 = 44 and dogs = 11 * 5 = 55 . answer : d .
Answer: d
Problem: john makes $ 60 a week from his job . he earns a raise and now makes $ 90 a week . what is the % increase ?
Options: a ) 16 % , b ) 50 % , c ) 17 % , d ) 17.61 % , e ) 17.56 %
Rationale: "increase = ( 30 / 60 ) * 100 = ( 3 / 6 ) * 100 = 50 % . b"
Answer: b
Problem: a rope of which a calf is tied is increased from 12 m to 23 m , how much additional grassy ground shall it graze ?
Options: a ) 2989 , b ) 2789 , c ) 1210 , d ) 1288 , e ) 1211
Rationale: "π ( 232 – 122 ) = 1210 answer : c"
Answer: c
Problem: x can finish a work in 21 days . y can finish the same work in 15 days . yworked for 10 days and left the job . how many days does x alone need to finish the remaining work ?
Options: a ) 3 , b ) 5 , c ) 7 , d ) 8 , e ) 9
Rationale: "work done by x in 1 day = 1 / 21 work done by y in 1 day = 1 / 15 work done by y in 10 days = 10 / 15 = 2 / 3 remaining work = 1 – 2 / 3 = 1 / 3 number of days in which x can finish the remaining work = ( 1 / 3 ) / ( 1 / 21 ) = 7 c"
Answer: c
Problem: a sells a bicycle to b and makes a profit of 25 % . b sells the same bicycle to c at a profit of 50 % . if the final s . p . of the bicycle was rs . 225 , find out the cost price of the bicycle for a .
Options: a ) 237 , b ) 126 , c ) 971 , d ) 611 , e ) 120
Rationale: explanation : let cp be 100 a sells at 25 % profit so sp = 125 b sells at 50 % profit = 125 x ( 1 + 50 / 100 ) = 187.5 cp - - - sp 100 - - - 187.5 x - - - 225 cp = 225 x 100 / 187.5 = 120 answer : e
Answer: e
Problem: two trains of equal are running on parallel lines in the same direction at 18 km / hr and 36 km / hr . the faster train passes the slower train in 36 sec . the length of each train is ?
Options: a ) 25 , b ) 26 , c ) 27 , d ) 28 , e ) 21
Rationale: "let the length of each train be x m . then , distance covered = 2 x m . relative speed = 46 - 36 = 10 km / hr . = 10 * 5 / 18 = 25 / 9 m / sec . 2 x / 18 = 25 / 9 = > x = 25 . answer : a"
Answer: a
Problem: the average marks of a class of 12 students is 40 and that of another class of 28 students is 60 . find the average marks of all the students ?
Options: a ) 52.2 , b ) 59.5 , c ) 52.8 , d ) 52.5 , e ) 54.0
Rationale: "sum of the marks for the class of 12 students = 12 * 40 = 480 sum of the marks for the class of 28 students = 28 * 60 = 1680 sum of the marks for the class of 40 students = 480 + 1680 = 2160 average marks of all the students = 2160 / 40 = 54 answer : e"
Answer: e
Problem: if 10 gallons of grape juice are added to 40 gallons of a mixture , which contains 20 percent grape juice then what percent of the resulting mixture is grape juice ?
Options: a ) 14 % , b ) 25 % , c ) 28 % , d ) 36 % , e ) 50 %
Rationale: official solution : if we start with 40 gallons of a mixture that is 10 % grape juice , then we have : 40 × 0.20 = 8 gallons of grape juice . 40 × 0.80 = 32 gallons of other components . if we add 10 gallons of grape juice , we will end up with 18 gallons of grape juice and 32 gallons of other components , and we will have a total of 50 gallons of the mixture . so 18 / 50 of the new mixture is grape juice . now we convert this to a percent : percent grape juice = 18 / 50 = 36 / 100 = 36 % . the correct answer is choice ( d )
Answer: d
Problem: a shopkeeper has 280 kg of apples . he sells 85 % of these at 20 % profit and remaining 60 % at 30 % profit . find his % profit on total .
Options: a ) 24 % , b ) 25 % , c ) 26 % , d ) 28 % , e ) 35 %
Rationale: "if the total quantity was 100 then 85 x 20 % + 60 x 30 % = 85 this profit will remain same for any total quantity unless the % of products remains the same . hence ' e ' is the answer"
Answer: e
Problem: 15 men take 21 days of 8 hrs . each to do a piece of work . how many days of 5 hrs . each would it take for 21 women if 3 women do as much work as 2 men ?
Options: a ) 30 , b ) 20 , c ) 16 , d ) 26 , e ) 36
Rationale: "let 1 man does 1 unit / hr of work 15 m in 21 days of 8 hrs will do ( 15 * 21 * 8 ) units 3 w = 2 m 1 w = ( 2 / 3 ) units / hr 21 w with 6 hrs a day will take ( 15 * 21 * 8 ) / ( 21 * 5 * ( 2 / 3 ) ) days = > 36 days answer : e"
Answer: e
Problem: ann and bob drive separately to a meeting . ann ' s average driving speed is greater than bob ' s avergae driving speed by one - third of bob ' s average driving speed , and ann drives twice as many miles as bob . what is the ratio e of the number of hours ann spends driving to the meeting to the number of hours bob spends driving to the meeting ?
Options: a ) 8 : 3 , b ) 3 : 2 , c ) 4 : 3 , d ) 2 : 3 , e ) 3 : 8
Rationale: "say the rate of bob is 3 mph and he covers 6 miles then he needs 6 / 3 = 2 hours to do that . now , in this case the rate of ann would be 3 + 3 * 1 / 3 = 4 mph and the distance she covers would be 6 * 2 = 12 miles , so she needs 12 / 4 = 3 hours for that . the ratio e of ann ' s time to bob ' s time is 3 : 2 . answer : b ."
Answer: b
Problem: as a treat for her two crying children , a mother runs to the freezer in which she has 4 cherry ice pops , 3 orange ice pops , and 4 lemon - lime ice pops . if she chooses two at random to bring outside to the children , but realizes as she runs out the door that she can not bring them different flavors without one invariably being jealous of the other and getting even more upset , what is the probability that she has to return to the freezer to make sure that they each receive the same flavor ?
Options: a ) 1 / 99 , b ) 1 / 6 , c ) 5 / 18 , d ) 13 / 18 , e ) 5 / 6
Rationale: probability of not getting the same flavor - > fouvarable - > cherry - orange [ 4 c 1 * 3 c 1 [ or simply 4 * 3 ] or cherry - lemon [ 4 * 4 ] or orange - lemon [ 3 * 4 ] prob = ( 4 * 3 + 4 * 4 + 3 * 4 ) / 9 c 2 = 40 / 3960 = 1 / 99 answer - > a
Answer: a
Problem: a and b together can complete a work in 12 days . a alone complete it in 20 days . if b does the work only for half a day daily , then in how many days a and b together will complete the work ?
Options: a ) 110 days , b ) 11 days , c ) 15 days , d ) 20 days , e ) 17 days
Rationale: b ' s one day work = ( 1 / 12 - 1 / 20 ) = 1 / 30 . now , ( a + b ) ' s one day work = ( 1 / 20 + 1 / 60 ) = 1 / 15 . [ ∵ b work for half day only ] . so , a and b together will complete the work in 15 days . correct answer : ` ` c ' ' .
Answer: c
Problem: in a fuel station the service costs $ 1.65 per car , every liter of fuel costs 0.65 $ . assuming that a company owns 12 cars and that every fuel tank contains 55 liters and they are all empty , how much money total will it cost to fuel all cars ?
Options: a ) 320 $ , b ) 380 $ , c ) 420 $ , d ) 448.8 $ , e ) 480 $
Rationale: "total cost = ( 1.65 * 12 ) + ( 0.65 * 12 * 55 ) = 19.8 + 429 = > 448.8 hence answer will be ( d )"
Answer: d
Problem: a certain rectangular crate measures 6 feet by 8 feet by 10 feet . a cylindrical gas tank is to be made for shipment in the crate and will stand upright when the crate is placed on one of its six faces . what should the radius of the tank be if it is to be of the largest possible volume ?
Options: a ) 4 , b ) 4 , c ) 6 , d ) 8 , e ) 10
Rationale: "ans is ` ` b ' ' . for max volume of cylinder ( pi * r ^ 2 * h ) we need to max out r ^ 2 * h . we do n ' t know what the dimensions of the crate refer to . . therefore for max vol base should be 8 x 10 i . e . of radius 8 / 2 = 4 b"
Answer: b
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 . 950 per sq . metre .
Options: a ) s . 20,550 , b ) s . 15,600 , c ) s . 20,900 , d ) s . 17,600 , e ) s . 17,900
Rationale: "area of the floor = ( 5.5 ã — 4 ) m 2 = 22 m 2 . cost of paving = rs . ( 950 ã — 22 ) = rs . 20900 answer : option c"
Answer: c
Problem: the function f ( n ) is defined as the product of all the consecutive positive integers between 3 and n ^ 2 , inclusive , whereas the function g ( n ) is defined as the product of the squares of all the consecutive positive integers between 1 and n , inclusive . the exponent on 2 in the prime factorization of f ( 3 ) / g ( 3 ) is
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "f ( 3 ) / g ( 3 ) = product ( 1 to 3 ^ 2 ) / 1.2 ^ 2.3 ^ 2 = 1 . 2.3 . 4.5 . 6.7 . 8.9 / 1 . 4.9 = 1 . 2.3 . ( 2 ^ 2 ) . 5 . ( 2.3 ) . 7 . ( 2 ^ 3 ) . 9 / 1 . ( 2 ^ 2 ) . 9 = 1 . ( 2 ^ 7 ) . 3.5 . 7.9 / 1 . ( 2 ^ 2 ) . 9 loof for 2 ^ 7 / 2 ^ 2 = 2 ^ 5 - - - - exponent 3 answer : c"
Answer: c
Problem: how long does a train 110 m long running at the speed of 72 km / hr takes to cross a bridge 136 m length ?
Options: a ) 82.1 sec . , b ) 12.3 sec , c ) 19.1 sec . , d ) 17.1 sec . , e ) 42.1 sec .
Rationale: "speed = 72 * 5 / 18 = 20 m / sec total distance covered = 110 + 136 = 246 m . required time = 246 / 20 = 12.3 sec . answer : b"
Answer: b
Problem: by approximately what percent is x greater than 5 / 11 if ( 4 / 11 ) ( x ) = 1 ?
Options: a ) 730 % , b ) 560 % , c ) 410 % , d ) 505 % , e ) 209 %
Rationale: "what percent is x greater than 5 / 11 if ( 4 / 11 ) ( x ) = 1 ? = > x = 11 / 4 % change = [ ( 11 / 4 - 5 / 11 ) / ( 5 / 11 ) ] * 100 = 505 % ans , d"
Answer: d
Problem: two mba admissions committees are to be formed randomly from 6 second year mbas with 3 members each . what is the probability that jane will be on the same committee as albert ?
Options: a ) 12 % , b ) 20 % , c ) 33 % , d ) 40 % , e ) 50 %
Rationale: total number of ways to choose 3 member committee - 6 c 3 = ( 6 ! / 3 ! 3 ! ) = 20 no . of ways albert n jane are in same committee : - ( 4 c 1 * 2 ) = 8 probability = ( 8 / 20 ) * 100 = 40 % . ans : : d
Answer: d
Problem: a group of 7 teenagers recently visited the japanese restaurant . the total bill for the meal , including 20 % gratuity , came to $ 840 . on average , how much did the meal of each individual cost before gratuity ?
Options: a ) $ 160 , b ) $ 96 , c ) $ 90 , d ) $ 10 , e ) $ 55
Rationale: 7 teenagers - so total 7 people the bill $ 840 includes 20 % gratuity . . . so the actual cost of dinner was $ 700 now , the cost per person will be $ 700 / 7 which is $ 10 option d
Answer: d
Problem: a particular library has 75 books in a special collection , all of which were in the library at the beginning of the month . these book are occasionally loaned out through an inter - library program . if , by the end of the month , 65 percent of books that were loaned out are returned and there are 68 books in the special collection at that time , how many books of the special collection were loaned out during that month ?
Options: a ) 20 , b ) 30 , c ) 35 , d ) 40 , e ) 55
Rationale: "total = 75 books . 65 % of books that were loaned out are returned - - > 100 % - 65 % = 35 % of books that were loaned out are not returned . now , there are 68 books , thus 76 - 68 = 7 books are not returned . { loaned out } * 0.35 = 7 - - > { loaned out } = 20 . answer : a ."
Answer: a
Problem: a shopkeeper forced to sell at cost price , uses a 950 grams weight for a kilogram . what is his gain percent ?
Options: a ) 10 % , b ) 9 % , c ) 11.11 % , d ) 5.26 % , e ) none of these
Rationale: "shopkeeper sells 950 g instead of 1000 g . so , his gain = 1000 - 950 = 50 g . thus , % gain = ( 50 * 100 ) / 950 = 5.26 % . answer : option d"
Answer: d
Problem: if 7 ^ q is a factor of the product of the integers from 1 to 100 , inclusive , what is the largest value of q ?
Options: a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16
Rationale: so the question just means that we have to find all the multiples q of 7 between 1 to 100 so there are 14 multiples of 7 ( 7 - 98 ) but 49 and 98 contain two 7 ' s as factors so we have to add 14 + 2 = 16 e
Answer: e
Problem: susan drove an average speed of 30 miles per hour for the first 60 miles of a tripthen at a average speed of 60 miles / hr for the remaining 30 miles of the trip if she made no stops during the trip what was susan ' s avg speed in miles / hr for the entire trip
Options: a ) 35 , b ) 36 , c ) 45 , d ) 50 , e ) 55
Rationale: "avg . speed = total distance / total time total distance = 90 miles total time = 60 / 30 + 30 / 60 = 5 / 2 avg . speed = 36 answer - b"
Answer: b
Problem: a 415 m long train is running at 63 km / hr . in how much time will it cross a tunnel 285 m long ?
Options: a ) 25 , b ) 35 , c ) 45 , d ) 60 , e ) 40
Rationale: "speed of the train = ( 63 * 5 / 18 ) m / sec = 35 / 2 m / sec . distance travelled = ( speed x time ) time = ( distance travelled / speed ) distance travelled = length of the train + length of the tunnel = 415 + 285 = 700 m time = ( 700 / 35 / 2 ) = 40 sec answer : e"
Answer: e
Problem: the bankers discount of a certain sum of money is rs . 288 and the true discount on the same sum for the same time is rs . 240 . the sum due is :
Options: a ) 1400 , b ) 1420 , c ) 1440 , d ) 1460 , e ) 1480
Rationale: "sum = ( b . d * t . d ) / ( b . d - t . d ) ( 288 * 240 ) / 288 - 240 ; 1440 answer : c"
Answer: c
Problem: a shopkeeper sold an article offering a discount of 4 % and earned a profit of 32 % . what would have been the percentage of profit earned if no discount was offered ?
Options: a ) 24.5 , b ) 28.5 , c ) 30.5 , d ) 32.5 , e ) 37.5
Rationale: let c . p . be rs . 100 . then , s . p . = rs . 132 let marked price be rs . x . then , 96 / 100 x = 132 x = 13200 / 96 = rs . 137.5 now , s . p . = rs . 137.5 , c . p . = rs . 100 profit % = 37.5 % . answer : e
Answer: e
Problem: the volume of the sphere qq is ( dfrac { 37 } { 64 } % ) less than the volume of sphere pp and the volume of sphere rr is ( dfrac { 19 } { 27 } % ) less than that of sphere qq . by what is the surface areaof sphere rr less than the surfacearea of sphere pp ?
Options: a ) 50 %
b ) 60 %
c ) 75 %
d ) 80 %
e ) 89 %
Rationale: let the volume of sphere pp be 64 parts . therefore volume of sphere qq = 64 − 3764 % = 64 − 3764 % of 6464 = 64 − 37 = 27 = 64 − 37 = 27 parts . the volume of rr = 27 − 1927 × 27 = 27 − 1927 × 27 = 27 − 19 = 8 = 27 − 19 = 8 parts . volume ratio : = p : q : r = 64 : 27 : 8 = p : q : r = 64 : 27 : 8 radius ratio : = p : q : r = 4 : 3 : 2 = p : q : r = 4 : 3 : 2 the surface area will be 16 : 9 : 516 : 9 : 5 surface area of rr is less than the surface area of sphere pp 16 k − 4 k = 12 k 16 k − 4 k = 12 k now , = 12 k 16 k × 100 = 12 k 16 k × 100 = 75 % = 75 % thus surface area of sphere rr is less than the surface area of sphere p by 75 % c
Answer: c
Problem: what will be the cost of gardening 1 meter boundary around a rectangular plot having perimeter of 340 meters at the rate of rs . 10 per square meter ?
Options: a ) rs . 3430
b ) rs . 3440
c ) rs . 3450
d ) rs . 3460
e ) rs . 3490
Rationale: explanation : in this question , we are having perimeter . we know perimeter = 2 ( l + b ) , right so , 2 ( l + b ) = 340 as we have to make 1 meter boundary around this , so area of boundary = ( ( l + 2 ) + ( b + 2 ) - lb ) = 2 ( l + b ) + 4 = 340 + 4 = 344 so required cost will be = 344 * 10 = 3440 answer : option b
Answer: b
Problem: a can do a piece of work in 15 days . a does the work for 5 days only and leaves the job . b does the remaining work in 18 days . in how many days b alone can do the work ?
Options: a ) 5 days , b ) 7 days , c ) 27 days , d ) 9 days , e ) 10 days
Rationale: "explanation : a ’ s 5 day work = 5 * 1 / 15 = 1 / 3 remaining work = 1 - 1 / 3 = 2 / 3 b completes 2 / 3 work in 6 days b alone can do in x days 2 / 3 * x = 18 x = 27 days answer : option c"
Answer: c
Problem: the h . c . f . of two numbers is 30 and the other two factors of their l . c . m . are 25 and 24 . the larger of the two numbers is
Options: a ) 276 , b ) 799 , c ) 712 , d ) 750 , e ) none
Rationale: "solution clearly , the numbers are ( 30 x 25 ) and ( 30 x 24 ) . larger number = ( 30 x 25 ) = 750 . answer d"
Answer: d
Problem: by investing in 1623 % stock at 64 , one earns rs . 1800 . the investment made is
Options: a ) s . 6500 , b ) s . 7500 , c ) s . 5640 , d ) s . 5760 , e ) s . 6912
Rationale: "explanation : market value = rs . 64 face value is not given and hence take it as rs . 100 16 2 / 3 % of the face value = 50 / 3 ie , to earn 50 / 3 , investment = rs . 64 hence , to earn rs . 1800 , investment needed = 64 × 3 × 1800 / 50 = 6912 answer : option e"
Answer: e
Problem: arun purchased 30 kg of wheat at the rate of rs . 11.50 per kg and 20 kg of wheat at the rate of 14.25 per kg . he mixed the two and sold the mixture . approximately what price per kg should be sell the mixture to make 15 % profit ?
Options: a ) 14.49 , b ) 16.33 , c ) 16.35 , d ) 16.3 , e ) 16.32
Rationale: "c . p . of 50 kg wheat = ( 30 * 11.50 + 20 * 14.25 ) = rs . 630 . s . p . of 50 kg wheat = 115 % of rs . 630 = 115 / 100 * 630 = rs . 724.5 s . p . per kg = 724.5 / 50 = 14.49 a"
Answer: a
Problem: one pipe can fill a tank four times as fast as another pipe . if together the two pipes can fill the tank in 36 minutes , then the slower pipe alone will be able to fill the tank in :
Options: a ) 180 min , b ) 144 min . , c ) 126 min , d ) 114 min , e ) 124 min
Rationale: explanation : let time taken by the faster pipe to fill the tank = x minutes . then , time taken by the slower pipe to fill the tank = 4 x minutes . time taken by both pipes together to fill the tank = x x 4 x / x + 4 x = 4 x / 5 4 x / 5 = 36 ⇒ x = 45 time taken by the slower pipe to fill the tank = 4 x = 180 minutes . answer : option a
Answer: a
Problem: carl is facing very difficult financial times and can only pay the interest on a $ 10,000 loan he has taken . the bank charges him a quarterly compound rate of 8 % . what is the approximate interest he pays annually ?
Options: a ) 1500 , b ) 1750 , c ) 2000 , d ) 3500 , e ) 2500
Rationale: "an easy way too attempt this is by approximation : for the first quarter , he pays 8 % of 10,000 which is $ 800 . so for the four quarters in the year , he will approximately play 800 * 4 = 3200 over the entire year . because of compound interest it will be more than 3200 . approx . option d is correct . answer : d"
Answer: d
Problem: a patient is given exactly 750 milliliters of a mixture of two medications daily . medication a contains 40 % pain killer and medication b contains 20 % pain killer . if the patient receives exactly 215 milliliters of pain killer daily , how many milliliters of medication b are in the mixture ?
Options: a ) 150 , b ) 225 , c ) 325 , d ) 425 , e ) 550
Rationale: let there be a milliliters of medication a and b milliliters of medication b a + b = 750 - - 1 medication a contains 40 % pain killer and medication b contains 20 % pain killer . ( 40 / 100 ) * a + ( 20 / 100 ) * b = 215 = > ( 2 / 5 ) * a + ( 1 / 5 ) * b = 215 multiplying by 5 , we get 2 a + b = 1075 - - 2 equation 2 - equation 1 , we get a = 325 b = 425 answer d
Answer: d
Problem: a train passes a platform in 18 seconds . the same train passes a man standing on the platform in 20 seconds . if the speed of the train is 54 km / hr , the length of the platform is
Options: a ) 120 , b ) 250 , c ) 260 , d ) 230 , e ) 220
Rationale: "speed of the train = 54 km / hr = ( 54 × 10 ) / 36 m / s = 15 m / s length of the train = speed × time taken to cross the man = 15 × 20 = 300 m let the length of the platform = l time taken to cross the platform = ( 300 + l ) / 15 = > ( 300 + l ) / 15 = 18 = > 300 + l = 15 × 18 = 270 = > l = 390 - 270 = 120 meter answer is a ."
Answer: a
Problem: let s is a set of all natural numbers less than 120 such that hcf of any element in s and 120 is 1 . find the sum of all elements in s ?
Options: a ) 1584 , b ) 7640 , c ) 5640 , d ) 7240 , e ) 6780
Rationale: s is a set of all natural numbers less than 120 such that hcf of any element in s and 120 is 1 . such numbers are , s = { 1 , 7 , 11 , 13 , 17 , 19 , 23 , 29 , 31 , 37 , 41 , 43 , 47 , 53 , 59 , 61 , 67 , 71 , 73 , 79 , 83 , 89 , 97 , 101 , 103 , 107 , 109 , 113 } sum of s = 1584 . answer : a
Answer: a
Problem: a swimmer can swim in still water at 4 km / h . if the speed of the water current is 2 km / h , how many hours will the swimmer take to swim against the current for 5 km ?
Options: a ) 2.0 , b ) 2.5 , c ) 3.0 , d ) 3.5 , e ) 4.0
Rationale: "the swimmer can swim against the current at a speed of 4 - 2 = 2 km / h . the time it will take is 5 / 2 = 2.5 hours . the answer is b ."
Answer: b
Problem: if a tire rotates at 400 revolutions per minute when the car is traveling 48 km / h , what is the circumference of the tire ?
Options: a ) 7 meters , b ) 9 meters , c ) 8 meters , d ) 2 meters , e ) 3 meters
Rationale: "400 rev / minute = 400 * 60 rev / 60 minutes = 24,000 rev / hour 24,000 * c = 48,000 m : c is the circumference c = 2 meters correct answer d"
Answer: d
Problem: a snooker tournament charges $ 45.00 for vip seats and $ 20.00 for general admission ( “ regular ” seats ) . on a certain night , a total of 320 tickets were sold , for a total cost of $ 7500 . how many fewer tickets were sold that night for vip seats than for general admission seats ?
Options: a ) 200 , b ) 276 , c ) 230 , d ) 240 , e ) 250
Rationale: let no of sits in vip enclosure is x then x * 45 + 20 ( 320 - x ) = 7500 or 25 x = 7500 - 6400 , x = 1100 / 25 = 44 vip = 44 general 320 - 44 = 276 b
Answer: b
Problem: find the principle on a certain sum of money at 5 % per annum for 3 1 / 5 years if the amount being rs . 1160 ?
Options: a ) rs . 1000 , b ) rs . 1100 , c ) rs . 1010 , d ) rs . 10000 , e ) none of these
Rationale: "explanation : 1160 = p [ 1 + ( 5 * 16 / 5 ) / 100 ] p = 1000 answer : option a"
Answer: a