regisss/math_qa huggingface dataset:
Problem: in a certain parallelogram the degree measure of one angle exceeds that of the other by 50 what is the degree measure of the smaller angle ?
Options: a ) 65 , b ) 80 , c ) 85 , d ) 90 , e ) 95
Rationale: "in a parallelogram opposite angles are equal and the angles at each side are supplementary to each other ( supplementary angles are two angles that add up to 180 ° ) . given : x + ( x + 50 ) = 180 - - > x = 65 . answer : a ."
Answer: a
Problem: jim is able to sell a hand - carved statue for $ 550 which was a 35 % profit over his cost . how much did the statue originally cost him ?
Options: a ) $ 407.41 , b ) $ 412.40 , c ) $ 455.40 , d ) $ 474.90 , e ) $ 488.20
Rationale: "550 = 1.35 * x x = 550 / 1.35 = 407.407407 . . . which rounds to $ 407.41 , which is ( a ) ."
Answer: a
Problem: pipe b that can fill a tank in an hour and pipe a that can fill the tank in half an hour are opened simultaneously when the tank is empty . pipe a is shut 15 minutes before the tank overflows . when will the tank overflow ?
Options: a ) 32 mins , b ) 35 mins , c ) 40 mins , d ) 30 mins , e ) 36 mins
Rationale: the last 15 minutes only pipe b was open . since it needs 1 hour to fill the tank , then in 15 minutes it fills 1 / 4 th of the tank , thus 3 / 4 of the tank is filled with both pipes open . the combined rate of two pipes is 1 + 2 = 3 tanks / hour , therefore to fill 3 / 4 th of the tank they need ( time ) = ( work ) / ( rate ) = ( 3 / 4 ) / 3 = 1 / 4 hours = 15 minutes . total time = 15 + 15 = 30 minutes . answer : d
Answer: d
Problem: working together , tim and tom can type 12 pages in one hour . if they would be able to type 15 pages in one hour if tom increases his typing speed by 30 % , what is the ratio of tom ' s normal typing speed to that of tim ?
Options: a ) 1 / 5 , b ) 5 / 1 , c ) 4 / 1 , d ) 1 / 4 , e ) 1 / 3
Rationale: lets say tim types x pages an hour and tom types y pages an hour . we know that x + y = 12 tom increase speed by 30 % means he will type 1.3 y pages an hour . so we get x + 1.3 y = 15 we need to know the ratio of tom ' s speed to tim ' s speed . this is going to be proportional to the number of pages each can type in an hour , hence ( y / x ) . subtracting both : 0.3 y = 3 so y = 10 . . . so x = 2 ( y / x ) = 10 / 2 = 5 / 1 answer is ( b )
Answer: b
Problem: the interest on a certain deposit at 5 % per annum is rs . 101.20 in one year . how much will the additional interest in one year be on the same deposit at 6 % per annum ?
Options: a ) rs . 20.8 , b ) rs . 19.74 , c ) rs . 20.24 , d ) rs . 19.5 , e ) rs . 19.00
Rationale: explanation : principal , p = 100 × si / rt = 100 × 101.20 / 5 × 1 = 20 × 101.20 = rs . 2024 simple interest for rs . 2024 at 6 % per annum for 1 year , si = 2024 × 6 × 1100 = 121.44 additional interest = rs . 121.44 - rs . 101.20 = rs . 20.24 answer : option c
Answer: c
Problem: in an election , candidate a got 65 % of the total valid votes . if 15 % of the total votes were declared invalid and the total numbers of votes is 560000 , find the number of valid vote polled in favor of candidate .
Options: a ) 330000 , b ) 309400 , c ) 347000 , d ) 356000 , e ) 357000
Rationale: "total number of invalid votes = 15 % of 560000 = 15 / 100 × 560000 = 8400000 / 100 = 84000 total number of valid votes 560000 – 84000 = 476000 percentage of votes polled in favour of candidate a = 65 % therefore , the number of valid votes polled in favour of candidate a = 65 % of 476000 = 65 / 100 × 476000 = 30940000 / 100 = 309400 b )"
Answer: b
Problem: the profit obtained by selling an article for rs . 86 is the same as the loss obtained by selling it for rs . 42 . what is the cost price of the article ?
Options: a ) rs . 40 , b ) rs . 50 , c ) rs . 49 , d ) rs . 59 , e ) rs . 64
Rationale: "s . p 1 - c . p = c . p – s . p 2 86 - c . p = c . p - 42 2 c . p = 86 + 42 ; c . p = 128 / 2 = 64 answer : e"
Answer: e
Problem: a squirrel runs up a cylindrical post , in a perfect spiral path making one circuit for each rise of 4 feet . how many feet does the squirrel travels if the post is 16 feet tall and 3 feet in circumference ?
Options: a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16
Rationale: "total circuit = 16 / 4 = 4 total feet squirrel travels = 4 * 3 = 12 feet answer : a"
Answer: a
Problem: a batsman in his 12 th innings makes a score of 70 and thereby increases his average by 3 runs . what is his average after the 12 th innings if he had never been ‘ not out ’ ?
Options: a ) 42 , b ) 37 , c ) 44 , d ) 45 , e ) 46
Rationale: "let ‘ x ’ be the average score after 12 th innings ⇒ 12 x = 11 × ( x – 3 ) + 70 ∴ x = 37 answer b"
Answer: b
Problem: a train 125 m long passes a man , running at 2 km / hr in the same direction in which the train is going , in 10 seconds . the speed of the train is ?
Options: a ) 36 , b ) 50 , c ) 28 , d ) 47 , e ) 29
Rationale: "speed of the train relative to man = ( 125 / 10 ) m / sec = ( 25 / 2 ) m / sec . [ ( 25 / 2 ) * ( 18 / 5 ) ] km / hr = 45 km / hr . let the speed of the train be x km / hr . then , relative speed = ( x - 2 ) km / hr . x - 2 = 45 = = > x = 47 km / hr answer : d"
Answer: d
Problem: 50 persons like apple . 7 like orange and mango dislike apple . 10 like mango and apple and dislike orange . 4 like all . how many people like apple ?
Options: a ) 47 , b ) 46 , c ) 54 , d ) 57 , e ) 62
Rationale: "orange + mango - apple = 7 mango + apple - orange = 10 apple = 50 orange + mango + apple = 4 50 + 10 + 4 - 7 = 57 like apple answer : d"
Answer: d
Problem: 5 ^ 100 is divided by 18 . then what is the remainder ?
Options: a ) 10 , b ) 11 , c ) 13 , d ) 15 , e ) 16
Rationale: "here n = 18 = 2 × 32 ϕ ( 18 ) = 18 ( 1 − 12 ) ( 1 − 13 ) = 6 so 56 when divided by 18 , remainder is 1 . so we can write the given expression 5100 = ( 56 ) 16 × 54 = ( 1 ) 16 × 54 = 52 × 52 = 7 × 7 = 49 now 49 when divided by 18 , remainder is 13 . c"
Answer: c
Problem: a corporation that had $ 120 billion in profits for the year paid out $ 200 million in employee benefits . approximately what percent of the profits were the employee benefits ? ( note : 1 billion = 10 ^ 9 )
Options: a ) 50 % , b ) 20 % , c ) 5 % , d ) 4 % , e ) 0.17 %
Rationale: "required answer = [ employee benefit / profit ] * 100 = [ ( 200 million ) / ( 120 billion ) ] * 100 = [ ( 200 * 10 ^ 6 ) / ( 120 * 10 ^ 9 ) ] * 100 = ( 1.7 / 1000 ) * 100 = 0.17 % so answer is ( e )"
Answer: e
Problem: a , b and c have rs . 900 between them , a and c together have rs . 400 and b and c rs . 750 . how much does c have ?
Options: a ) 100 , b ) 150 , c ) 200 , d ) 250 , e ) 350
Rationale: "a + b + c = 900 a + c = 400 b + c = 750 - - - - - - - - - - - - - - a + b + 2 c = 1150 a + b + c = 900 - - - - - - - - - - - - - - - - c = 250 answer : d"
Answer: d
Problem: dividing by 3 ⁄ 8 and then multiplying by 5 ⁄ 8 is the same as dividing by what number ?
Options: a ) 31 ⁄ 5 , b ) 16 ⁄ 5 , c ) 20 ⁄ 9 , d ) 9 ⁄ 20 , e ) 5 ⁄ 3
Rationale: "say x / 3 / 8 * 5 / 8 = x * 8 / 3 * 5 / 8 = x * 5 / 3 e"
Answer: e
Problem: there are 84 supermarkets in the fgh chain . all of them are either in the us or canada . if there are 10 more fgh supermarkets in the us than in canada , how many fgh supermarkets are there in the us ?
Options: a ) 20 , b ) 31 , c ) 42 , d ) 47 , e ) 64
Rationale: "x + ( x - 10 ) = 84 - - > x = 47 . answer : d ."
Answer: d
Problem: a positive integer , which when added to 1000 , gives a sum which is greater than when it is multiplied by 1000 . this positive integer is
Options: a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9
Rationale: solution ( 1000 + n ) > ( 1000 n ) clearly , n = 1 . answer a
Answer: a
Problem: the average of 11 numbers is 22 . average of the first 6 of them is 19 and that of the last 6 is 27 . find the 6 th number ?
Options: a ) 12 , b ) 25 , c ) 34 , d ) 29 , e ) 27
Rationale: sum of all the 11 numbers = 11 * 22 = 242 sum of the first 6 of them = 6 * 19 = 114 sum of the last 6 of them = 6 * 27 = 162 so , the 8 th number = 242 + 114 - 162 = 34 . answer : c
Answer: c
Problem: 10 men , working 6 hours a day can complete a work in 18 days . how many hours a day must 15 men work to complete the same work in 12 days ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "solution let the required number of hours per day be x . more men , less hours per day ( indirect proportion ) less days , more hours per day ( indirect proportion ) ∴ 15 × 12 × x = 10 × 18 × 6 ⇔ x = 10 x 18 x 6 / 15 x 12 = x = 6 . answer a"
Answer: a
Problem: 15 men can complete a piece of work in 30 days . in how many days can 10 men complete that piece of work ?
Options: a ) 45 , b ) 50 , c ) 34 , d ) 27 , e ) 11
Rationale: "15 * 30 = 10 * x = > x = 45 days answer : a"
Answer: a
Problem: 6 bells commence tolling together and toll at intervals of 2 , 4 , 6 , 8 10 and 12 seconds respectively . in 30 minutes , how many times do they toll together ?
Options: a ) 4 , b ) 10 , c ) 15 , d ) 16 , e ) none
Rationale: l . c . m . of 2 , 4 , 6 , 8 , 10 , 12 is 120 . so , the bells will toll together after every 120 seconds ( 2 minutes ) . in 30 minutes , they will toll together 30 / 2 + 1 = 16 times answer d
Answer: d
Problem: the ratio between the length and the breadth of a rectangular park is 3 : 2 . if a man cycling along theboundary of the park at the speed of 12 km / hr completes one round in 8 min , then the area of the park ( in sq . m ) is ?
Options: a ) 143530 m , b ) 145600 m , c ) 153600 m , d ) 134500 m , e ) 155600 m
Rationale: "perimeter = distance covered in 8 min . = 12000 x 8 m = 1600 m . 60 let length = 3 x metres and breadth = 2 x metres . then , 2 ( 3 x + 2 x ) = 1600 or x = 160 . length = 480 m and breadth = 320 m . area = ( 480 x 320 ) m 2 = 153600 m c"
Answer: c
Problem: a sporting goods store sold 64 frisbees in one week , some for $ 3 and the rest for $ 4 each . if receipts from frisbee sales for the week totaled $ 200 , what is the fewest number of $ 4 frisbees that could have been sold ?
Options: a ) 24 , b ) 8 , c ) 12 , d ) 4 , e ) 2
Rationale: "in this question however , because we are told that exactly 64 frisbees have been sold and revenue was exactly $ 204 , there is only one possible solution for the number of $ 3 and $ 4 frisbees sold . to solve , we have 2 equations and 2 unknowns let x = number of $ 3 frisbees sold let y = number of $ 4 frisbees sold x + y = 64 3 x + 4 y = 200 x = 64 - y 3 ( 64 - y ) + 4 y = 200 192 - 3 y + 4 y = 200 y = 8 answer : b"
Answer: b
Problem: when average age of 24 members are 0 , how many members greater than 0 ?
Options: a ) 17 , b ) 23 , c ) 21 , d ) 24 , e ) 25
Rationale: "average of 24 numbers = 0 . sum of 24 numbers ( 0 x 24 ) = 0 . it is quite possible that 23 of these numbers may be positive and if their sum is a then 24 th number is ( - a ) answer is 23 ( b )"
Answer: b
Problem: a shopkeeper sold an article at $ 100 with 15 % profit . then find its cost price ?
Options: a ) $ 120 , b ) $ 100 , c ) $ 91 , d ) $ 87 , e ) $ 69
Rationale: "cost price = selling price * 100 / ( 100 + profit ) c . p . = 100 * 100 / 115 = $ 87 ( approximately ) answer is d"
Answer: d
Problem: marcella has 26 pairs of shoes . if she loses 9 individual shoes , what is the greatest number of matching pairs she could have left ?
Options: a ) 21 , b ) 20 , c ) 19 , d ) 16 , e ) 15
Rationale: "marcella has 26 pairs of shoes and loses 9 shoes . to minimize the loss of identical pairs of shoes we want marcella to lose as many identical pairs as possible . this would yield 4 identical pairs and 1 additional shoe ( destroying 5 pairs of shoes ) . the 26 pairs of shoes minus the 5 ' destroyed ' pairs yields 21 pairs that still fulfill the requirements . answer : a"
Answer: a
Problem: eight identical machines can produce 360 aluminum cans per hour . if all of the machines work at the same constant rate , how many cans could 5 such machines produce in 4 hours ?
Options: a ) 675 , b ) 900 , c ) 1,800 , d ) 5,900 , e ) 7,500
Rationale: "8 machines / 360 cans = 5 machines / x cans 8 x = 1800 x = 225 ( 225 ) ( 4 hours ) = 900 cans . the answer is b ."
Answer: b
Problem: how many different ways can 2 students be seated in a row of 8 desks , so that there is always at least one empty desk between the students ?
Options: a ) 50 , b ) 42 , c ) 24 , d ) 20 , e ) 12
Rationale: "21 ways to seat the students : with two empty seats between 1 empty w / one student on the left most 1 empty . . . . right most two students can be interchanged 21 x 2 = 42 b"
Answer: b
Problem: the probability that event a occurs is 0.4 , and the probability that event b occurs is 0.45 . if the probability that either event a or event b occurs is 0.6 , what is the probability that event b and event b will occur ?
Options: a ) 0.25 , b ) 0.15 , c ) 0.45 , d ) 0.5 , e ) 0.55
Rationale: "p ( a or b ) = p ( a ) + p ( b ) - p ( a n b ) 0.6 = 0.4 + p ( a n b ) + 0.45 p ( b ) = 0.25 ans : a"
Answer: a
Problem: 60 is increased by 50 % . find the final number .
Options: a ) 100 , b ) 110 , c ) 90 , d ) 30 , e ) 160
Rationale: "final number = initial number + 50 % ( original number ) = 60 + 50 % ( 60 ) = 60 + 30 = 90 . answer c"
Answer: c
Problem: in a certain company , a third of the workers do not have a retirement plan . 20 % of the workers who do not have a retirement plan are women , and 30 % of the workers who do have a retirement plan are men . if 120 of the workers of that company are men , how many of the workers are women ?
Options: a ) 80 , b ) 95 , c ) 105 , d ) 120 , e ) 210
Rationale: "20 % of the workerswithoutretirement plan are women , this means 80 % of the workerswithoutretirement plan are men right ? makes 100 % = no retirement plan . then 40 % of those wo have a retirement plan are men , which means 60 % of those who have a retirement plan are women . these percentages are always refering to the subgroupsretirement plan = yesandno retirement plan . make the total workers equal x and work from there and it should be fine > x / 3 have no retirement plan at all . i struggled with the question a lot , it was hard for me although usually i have no problems with sets questions like this . i believe it must be a 700 + question . yes , you are right . i read the question incorrectly ! i glazed overnotfor some reason . if 20 % of the workers who do not have a retirement plan are women , 80 % who do not have retirement plan are men . also 40 % who do have retirement plan are men . since 1 / 3 do not have retirement plan and 2 / 3 do have , it becomes a simple weighted average question . cavg = ( 70 * 1 + 40 * 2 ) / 3 = 50 % are men total = 120 * 100 / 50 = 240 no . of women = 240 - 120 = 120 d"
Answer: d
Problem: a retailer bought a machine at a wholesale price of $ 90 and later on sold it after a 10 % discount of the retail price . if the retailer made a profit equivalent to 20 % of the whole price , what is the retail price q of the machine ?
Options: a ) 81 , b ) 100 , c ) 120 , d ) 135 , e ) 160
Rationale: "since the wholesale price was $ 90 and the profit was 20 % of the wholesale price ( [ . 2 ] [ 90 ] = $ 18 ) , the retail price would have to be above $ 108 , but not that much greater than that . let ' s start by testing answer c : $ 120 . . . . if . . . . . retail price q = $ 120 10 % discount off = $ 120 - ( . 1 ) ( 120 ) = 120 - 12 = 108 20 % profit on wholesale price = 90 + ( . 2 ) ( 90 ) = 90 + 18 = 108 these two numbers match , so this must be the answer ! final answer : [ reveal ] spoiler : c"
Answer: c
Problem: what is the 28 th digit to the right of the decimal point in the decimal form of 5 / 11 ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "5 / 11 = 0.45454545 . . . the even numbered positions in the decimal expansion are all 5 . the answer is c ."
Answer: c
Problem: a large box contains 16 small boxes and each small box contains 25 chocolate bars . how many chocolate bars are in the large box ?
Options: a ) 250 , b ) 350 , c ) 450 , d ) 400 , e ) 650
Rationale: "the number of chocolate bars is equal to 16 * 25 = 400 correct answer d"
Answer: d
Problem: the sum of 4 consecutive even numbers is 52 , find the third number ?
Options: a ) 14 , b ) 10 , c ) 12 , d ) 16 , e ) 20
Rationale: let the first number be n let the second number be n + 2 let the third number be n + 4 let the third number be n + 6 n + n + 2 + n + 4 + n + 6 = 52 combine like terms : 4 n + 12 = 52 4 n + 12 = 52 4 n = 52 - 12 4 n = 40 n = 10 n + 2 = 12 n + 4 = 14 n + 6 = 16 the third number is 14 answer : a
Answer: a
Problem: a rectangular parking space is marked out by painting three of its sides . if the length of the unpainted side is 99 feet , and the sum of the lengths of the painted sides is 37 feet , find out the area of the parking space in square feet ?
Options: a ) 126 sq . ft
b ) 64 sq . ft
c ) 100 sq . ft
d ) 120 sq . ft
e ) 140 sq . ft
Rationale: explanation : solution 1 length = 9 feet breadth = 37 − 9 / 2 = 14 feet area = 9 × 14 = 126 square feet answer : option a
Answer: a
Problem: the ratio between the presents of the a and b is 6 : 7 . if b is 4 years older than a , what will be the ratio of the ages of a and b after 4 years ?
Options: a ) 1 : 2 , b ) 9 : 11 , c ) 7 : 8 , d ) 6 : 7 , e ) 3 : 4
Rationale: let a and b ages will be 6 x and 7 x 7 x - 6 x = 4 x = 4 required ratio = 6 x + 4 : 7 x + 4 = 28 : 32 = 7 : 8 answer is c
Answer: c
Problem: in an election between two candidates , one got 55 % of the total valid votes , 20 % of the votes were invalid . if the total number of votes was 8000 , the number of valid votes that the other candidate got , was :
Options: a ) 3500 , b ) 3600 , c ) 3270 , d ) 3700 , e ) 4000
Rationale: "number of valid votes = 80 % of 8000 = 6400 . valid votes polled by other candidate = 45 % of 8000 = ( 45 / 100 ) x 8000 = 3600 answer = b"
Answer: b
Problem: a certain city with a population of 72,000 is to be divided into 11 voting districts , and no district is to have a population that is more than 10 percent greater than the population of any other district what is the minimum possible population that the least populated district could have ?
Options: a ) a ) 6,000 , b ) b ) 10,800 , c ) c ) 10,900 , d ) d ) 11,000 , e ) e ) 11,100
Rationale: "let x = number of people in smallest district x * 1.1 = number of people in largest district x will be minimised when the number of people in largest district is maximised 10 * x * 1.1 = 11 x = total number of people in other districts so we have 11 x + x = 72 k x = 6,000 answer : a"
Answer: a
Problem: joe drives 420 miles at 60 miles per hour , and then he drives the next 120 miles at 40 miles per hour . what is his average speed for the entire trip in miles per hour ?
Options: a ) 42 , b ) 54 , c ) 50 , d ) 54 , e ) 56
Rationale: "t 1 = 420 / 60 = 7 hours t 2 = 120 / 40 = 3 hours t = t 1 + t 2 = 10 hours avg speed = total distance / t = 540 / 10 = 54 mph = b"
Answer: b
Problem: in a caravan , in addition to 60 hens , there are 35 goats and 6 camels with some keepers . if the total number of feet be 193 more than the number of heads in the caravan , the number of keepers is
Options: a ) 5 , b ) 10 , c ) 15 , d ) 20 , e ) 25
Rationale: explanation : let number of keepers be x . then , total number of feet = 2 x 60 + 4 x 35 + 4 x 6 + 2 x = 2 x + 284 . total number of heads = 60 + 35 + 6 + x = 101 + x . therefore ( 2 x + 284 ) = ( 101 + x ) + 193 or x = 10 . answer : b
Answer: b
Problem: 100 liter solution of cool - drink is made from 10 % jasmine water . if 5 liters of jasmine and 10 liters of water were added to the solution , what percent of the solution is jasmine ?
Options: a ) 1 / 13 , b ) 2 / 23 , c ) 3 / 31 , d ) 4 / 15 , e ) 2 / 3
Rationale: denominator 100 + 5 + 10 115 numerator 100 * 0.1 = 10 - - - > jasmine water 10 + 5 = 15 - - - > new content of jasmine water in new solution ratio 3 / 23 answer is b
Answer: b
Problem: a box contain red , blue and green colored balls . the number of red balls is 80 and the number of blue balls is 60 . the number of green balls subtracted from the number of red balls is the same as the number of green balls added with the number of blue balls . then the number of green balls is ?
Options: a ) 80 , b ) green balls = 70 , c ) 60 , d ) 85 , e ) 140
Rationale: answer let the number of green balls be x . then , x - 60 = 80 - x â ‡ ’ 2 x = 80 + 60 = 140 â ‡ ’ 2 x = 140 â ˆ ´ x = 70 correct option : b
Answer: b
Problem: two kinds of vodka are mixed in the ratio 1 : 2 and 2 : 1 and they are sold fetching the profit 25 % and 20 % respectively . if the vodkas are mixed in equal ratio and the individual profit percent on them are increased by 4 / 3 and 5 / 3 times respectively , then the mixture will fetch the profit of
Options: a ) 18 % , b ) 20 % , c ) 21 % , d ) 25 % , e ) can not be determined
Rationale: answer : d .
Answer: d
Problem: a car traveled 75 % of the way from town a to town b at an average speed of 80 miles per hour . the car travels at an average speed of s miles per hour for the remaining part of the trip . the average speed for the entire trip was 40 miles per hour . what is s ?
Options: a ) 16 , b ) 20 , c ) 25 , d ) 30 , e ) 37.5
Rationale: "total distance = 100 miles ( easier to work with % ) 75 % of the distance = 75 miles 25 % of the distance = 25 miles 1 st part of the trip → 75 / 80 = 0.9375 2 nd part of the trip → 25 / s = t total trip → ( 75 + 25 ) / 40 = 0.9375 + t » 100 / 40 = 0.9375 + t » 2.5 = 0.9375 + t » t = 1.5625 back to 2 nd part of the trip formula : 25 / s = 1.5625 » s = 16 ans a"
Answer: a
Problem: in a division , divident is 725 , divisior is 36 and quotient is 20 . find the remainder .
Options: a ) a ) 4 , b ) b ) 3 , c ) c ) 2 , d ) d ) 5 , e ) e ) 6
Rationale: "explanation : 725 = 36 x 20 + r 725 = 720 + r r = 725 - 720 = 5 answer : option d"
Answer: d
Problem: a number is selected at random from the first 30 natural numbers . what is the probability that the number is a multiple of either 4 or 15 ?
Options: a ) 17 / 30 , b ) 2 / 5 , c ) 3 / 10 , d ) 4 / 15 , e ) 11 / 30
Rationale: number of multiples of 4 from 1 through 30 = 30 / 4 = 7 number of multiples of 15 from 1 through 30 = 30 / 15 = 2 number of multiples of 4 and 15 both from 1 through 30 = number of multiples of 15 * 4 ( = 60 ) = 0 total favourable cases = 7 + 2 - 0 = 9 probability = 9 / 30 = 3 / 10 answer : option c
Answer: c
Problem: a car gets 28 miles to the gallon . if it is modified to use a solar panel , it will use only 80 percent as much fuel as it does now . if the fuel tank holds 15 gallons , how many more miles will the car be able to travel , per full tank of fuel , after it has been modified ?
Options: a ) 85 , b ) 90 , c ) 95 , d ) 100 , e ) 105
Rationale: "originally , the distance the car could go on a full tank was 15 * 28 = 420 miles . after it has been modified , the car can go 28 / 0.8 = 35 miles per gallon . on a full tank , the car can go 15 * 35 = 525 miles , thus 105 miles more . the answer is e ."
Answer: e
Problem: how many of the positive factors of 63 , 84 and how many common factors are there in numbers ?
Options: a ) 2 , b ) 4 , c ) 3 , d ) 5 , e ) 1
Rationale: "factors of 63 - 1,3 , 7,9 , 21,63 factors of 84 - 1,2 , 3,4 , 6,7 , 12,14 , 21,28 , 42,84 comparing both , we have three common factors of 63 and 84 - 1,3 , 7,21 answer ( b )"
Answer: b
Problem: a cistern 10 m long and 8 m wide contains water up to a depth of 1 m 50 cm . the total area of the wet surface is :
Options: a ) 120 m 2 , b ) 136 m 2 , c ) 128 m 2 , d ) 130 m 2 , e ) 134 m 2
Rationale: "area of the wet surface = [ 2 ( lb + bh + lh ) - lb ] = 2 ( bh + lh ) + lb = [ 2 ( 8 x 1.50 + 10 x 1.50 ) + 8 x 10 ] m 2 = 134 m 2 . answer : e"
Answer: e
Problem: jim and cara begin running at the same time and they start at the same place on a straight path . jim runs at 6 miles per hour , and cara runs at 5 miles per hour . after 30 minutes , jim stops to stretch . if it takes jim 18 minutes to stretch and cara continues to run during this time , how many minutes will it take jim to catch up to cara ?
Options: a ) 40 , b ) 50 , c ) 60 , d ) 70 , e ) 80
Rationale: in 30 minutes , jim runs 3 miles . in 48 minutes , cara runs 4 miles . jim can catch cara at a rate of 1 mile per hour . since cara is ahead by 1 mile , it will take jim 1 hour = 60 minutes to catch cara . the answer is c .
Answer: c
Problem: what is the value of 4 ^ 4 + 4 ^ 6 ?
Options: a ) 4 ^ 12 , b ) 4 ^ 35 , c ) 17 ( 4 ^ 5 ) , d ) 8 ^ 12 , e ) 17 ( 4 ^ 4 )
Rationale: "4 ^ 4 + 4 ^ 6 = 4 ^ 4 ( 1 + 4 ^ 2 ) = 4 ^ 4 * 17 answer e"
Answer: e
Problem: if xerox paper costs 5 cents a sheet and a buyer gets 10 % discount on all xerox paper one buys after the first 2000 papers and 20 % discount after first 10000 papers , how much will it cost to buy 35000 sheets of xerox paper ?
Options: a ) $ 1250 , b ) $ 1060 , c ) $ 1450 , d ) $ 900 , e ) $ 1000
Rationale: "30 sec approach - solve it using approximation 35000 sheet at full price , 5 cent = 1750 35000 sheet at max discount price , 4 cent = 1400 your ans got to be between these two . ans c it is ."
Answer: c
Problem: a rectangular floor that measures 6 meters by 8 meters is to be covered with carpet squares that each measure 2 meters by 2 meters . if the carpet squares cost $ 12 apiece , what is the total cost for the number of carpet squares needed to cover the floor ?
Options: a ) $ 200 , b ) $ 240 , c ) $ 480 , d ) $ 960 , e ) $ 144
Rationale: "the width of the rectangular floor ( 6 m ) is a multiple of one side of the square ( 2 m ) , and the length of the floor ( 8 m ) is also a multiple of the side of the square . so the number of carpets to cover the floor is ( 6 / 2 ) * ( 8 / 2 ) = 12 . the total cost is 12 * 12 = $ 144 the answer is , therefore , e ."
Answer: e
Problem: in a public show 50 % of the seats were filled . if there were 600 seats in the hall , how many seats were vacant ?
Options: a ) 100 , b ) 110 , c ) 120 , d ) 300 , e ) 150
Rationale: "50 % of 600 = 50 / 100 × 600 = 300 therefore , the number of vacant seats = 600 - 300 = 300 . answer : d"
Answer: d
Problem: how many even number in the range between 10 to 100 inclusive are not divisible by 3
Options: a ) 15 , b ) 30 , c ) 31 , d ) 33 , e ) 46
Rationale: "we have to find the number of terms that are divisible by 2 but not by 6 ( as the question asks for the even numbers only which are not divisible by 3 ) for 2 , 10 , 12,14 . . . 100 using ap formula , we can say 100 = 10 + ( n - 1 ) * 2 or n = 46 . for 6 , 12,18 , . . . 96 using ap formula , we can say 96 = 12 + ( n - 1 ) * 6 or n = 15 . hence , only divisible by 2 but not 3 = 46 - 15 = 31 . hence , answer c"
Answer: c
Problem: a and b are partners in a business . a contributes 1 / 4 of the capital for 15 months and b received 2 / 3 of the profit . for how long b ’ s money was used ?
Options: a ) 4 months , b ) 6 months , c ) 8 months , d ) 10 months , e ) none
Rationale: "sol . let the total profit be rs . z . then , b ’ share = rs . 2 z / 3 , a ’ s share = rs . [ z - 2 z / 3 ] = rs . z / 3 ∴ a : b = z / 3 : 2 z / 3 = 1 : 2 . let the total capital be rs . x and suppose b ’ s money was used for x months . then , [ 1 / 4 x * 15 ] / [ 3 / 4 x * y ] = 1 / 2 ⇔ y = [ 15 * 2 / 3 ] = 10 . thus , b ’ s money was used for 10 months . answer d"
Answer: d
Problem: a man buys rs . 52 shares paying 9 % dividend . the man wants to have an interest of 12 % on his money . the market value of each share is :
Options: a ) s . 12 , b ) s . 15 , c ) s . 18 , d ) s . 21 , e ) s . 39
Rationale: "dividend on rs . 52 = rs . 9 / 100 x 52 = rs . 4.68 . rs . 12 is an income on rs . 100 . rs . 4.68 is an income on rs . 100 / 12 x 4.68 = rs . 39 . answer : option e"
Answer: e
Problem: at deluxe paint store , fuchsia paint is made by mixing 5 parts of red paint with 3 parts of blue paint . mauve paint is made by mixing 4 parts of red paint with 5 parts blue paint . how many liters of blue paint must be added to 32 liters of fuchsia to change it to mauve paint ?
Options: a ) 9 , b ) 13 , c ) 15 , d ) 16 , e ) 18
Rationale: "in 32 liters , red = 5 / 8 * 32 = 20 and blue = 12 so , 20 / ( 12 + x ) = 4 / 5 or , x = 13 ( answer b )"
Answer: b
Problem: if 5 / w + 5 / x = 5 / y and wx = y , then the average ( arithmetic mean ) of w and x is
Options: a ) 1 / 2 , b ) 1 , c ) 2 , d ) 4 , e ) 8
Rationale: "given : 5 / w + 5 / x = 5 / ywx = y find : ( w + x ) / 2 = ? 5 ( 1 / w + 1 / x ) = 5 ( 1 / y ) - divide both sides by 5 ( 1 / w + 1 / x ) = 1 / y ( x + w ) / wx = 1 / wx - sub ' d in y = wx x + w - 1 = 0 x + w = 1 therefore ( w + x ) / 2 = 1 / 2 ans : a"
Answer: a
Problem: on a certain day , orangeade was made by mixing a certain amount of orange juice with an equal amount of water . on the next day , orangeade was made by mixing the same amount of orange juice with twice the amount of water . on both days , all the orangeade that was made was sold . if the revenue from selling the orangeade was the same for both days and if the orangeade was sold at $ 0.60 per glass on the first day , what was the price e per glass on the second day ?
Options: a ) $ 015 , b ) $ 0.20 , c ) $ 0.30 , d ) $ 0.40 , e ) $ 0.45
Rationale: "on the first day 1 unit of orange juice and 1 unit of water was used to make 2 units of orangeade ; on the second day 1 unit of orange juice and 2 units of water was used to make 3 units of orangeade ; so , the ratio of the amount of orangeade made on the first day to the amount of orangeade made on the second day is 2 to 3 . naturally the ratio of the # of glasses of orangeade made on the first day to the # of glasses of orangeade made on the second day is 2 to 3 . we are told thatthe revenue from selling the orangeade was the same for both daysso the revenue from 2 glasses on the first day equals to the revenue from 3 glasses on the second day . say the price of the glass of the orangeade on the second day was $ x then 2 * 0.6 = 3 * x - - > x = $ 0.4 . answer : d ."
Answer: d
Problem: jerry went to a shop and bought things worth rs . 45 , out of which 30 % went on sales tax on taxable purchases . if the tax rate was 6 % , then what was the cost of the tax free items ?
Options: a ) 19 , b ) 19.7 , c ) 21.3 , d ) 29.5 , e ) 39.7
Rationale: "total cost of the items he purchased = rs . 45 given that out of this rs . 45 , 30 % is given as tax = > total tax incurred = 30 % = rs . 30 / 100 let the cost of the tax free items = x given that tax rate = 6 % ∴ ( 45 − 30 / 100 − x ) 6 / 100 = 30 / 100 ⇒ 6 ( 45 − 0.3 − x ) = 30 ⇒ ( 45 − 0.3 − x ) = 5 ⇒ x = 45 − 0.3 − 5 = 39.7 e )"
Answer: e
Problem: in an examination , 25 % of total students failed in hindi , 48 % failed in english and 27 % in both . the percentage of these who passed in both the subjects is :
Options: a ) 23 , b ) 54 , c ) 28 , d ) 40 , e ) 81
Rationale: "explanation : formula n ( a â ˆ ª b ) = n ( a ) + n ( b ) â ˆ ’ n ( a â ˆ © b ) fail in hindi or english = 25 + 48 â € “ 27 = 46 therefore students who passed = 100 â € “ 46 = 54 . answer : b"
Answer: b
Problem: if john makes a contribution to a charity fund at school , the average contribution size will increase by 50 % reaching $ 75 per person . if there were 2 other contributions made before john ' s , what is the size of his donation ?
Options: a ) $ 125 , b ) $ 150 , c ) $ 200 , d ) $ 250 , e ) $ 450
Rationale: "cavg = average contribution before john cavg * 1.5 = 75 , therefore the average cont is $ 50 before john . if he needs to increase the average contribution by $ 25 , he must put in $ 25 for each of the 2 people . so $ 50 . but , he also has to put in the average for himself ( the threeth person ) , so add $ 75 . so $ 125 is your answer . answer a"
Answer: a
Problem: if 20 % of a number = 100 , then 120 % of that number will be ?
Options: a ) 20 , b ) 120 , c ) 360 , d ) 600 , e ) 820
Rationale: let the number x . then , 20 % of x = 100 x = ( 100 * 100 ) / 20 = 500 120 % of x = ( 120 / 100 * 500 ) = 600 . answer : d
Answer: d
Problem: in what ratio should a variety of rice costing rs . 20 per kg be mixed with another variety of rice costing rs . 31.50 per kg to obtain a mixture costing rs . 23.75 per kg ?
Options: a ) 16 : 30 , b ) 30 : 14 , c ) 16 : 31 , d ) 31 : 15 , e ) 15 : 31
Rationale: "let us say the ratio of the quantities of cheaper and dearer varieties = x : y by the rule of allegation , x / y = ( 31.50 - 23.75 ) / ( 23.75 - 20 ) = 31 / 15 answer : d"
Answer: d
Problem: n and m are each 3 - digit integers . each of the numbers 2 , 34 , 6 , 7 , and 8 is a digit of either n or m . what is the smallest possible positive difference between n and m ?
Options: a ) 39 , b ) 49 , c ) 58 , d ) 113 , e ) 131
Rationale: you have 6 digits : 2 , 3 , 4 , 6 , 7 , 8 each digit needs to be used to make two 3 digit numbers . this means that we will use each of the digits only once and in only one of the numbers . the numbers need to be as close to each other as possible . the numbers can not be equal so the greater number needs to be as small as possible and the smaller number needs to be as large as possible to be close to each other . the first digit ( hundreds digit ) of both numbers should be consecutive integers now let ' s think about the next digit ( the tens digit ) . to minimize the difference between the numbers , the tens digit of the greater number should be as small as possible and the tens digit of the smaller number should be as large as possible . so let ' s not use 2 and 8 in the hundreds places and reserve them for the tens places . now what are the options ? try and make a pair with ( 3 * * and 4 * * ) . make the 3 * * number as large as possible and make the 4 * * number as small as possible . 387 and 426 ( difference is 39 ) or try and make a pair with ( 6 * * and 7 * * ) . make the 6 * * number as large as possible and make the 7 * * number as small as possible . we get 684 and 723 ( difference is 39 ) a
Answer: a
Problem: if three painters can complete three rooms in two hours , how many hours 5 painters would it take to do 20 rooms ?
Options: a ) 6 , b ) 9 , c ) 7 , d ) 8 , e ) 5
Rationale: "explanation : three painters can complete three rooms in two hours . so 20 rooms can be painted in 8 hrs by 5 painters answer : e ) 5 painters"
Answer: e
Problem: if anangletis defined as 1 percent of 1 degree , then how many anglets are there in a fifth circle ?
Options: a ) 0.36 , b ) 7200 , c ) 360 , d ) 3,600 , e ) 36,000
Rationale: "1 degree * 1 / 100 = 1 anglet so 1 degree = 100 anglets = > 72 degrees = 7200 anglets answer - b"
Answer: b
Problem: worker a takes 5 hours to do a job . worker b takes 10 hours to do the same job . how long it take both a & b , working together but independently , to do the same job ?
Options: a ) 20 / 9 , b ) 40 / 9 , c ) 50 / 9 , d ) 60 / 9 , e ) 10 / 3
Rationale: "one day work of a = 1 / 5 one day work of b = 1 / 10 so one day work of a and b together = 1 / 5 + 1 / 10 = 3 / 10 so total days required = 10 / 3 answer : e"
Answer: e
Problem: every day , the value of a stock rises by exactly two dollars in the morning , and then falls by exactly one dollar in the afternoon . if the stock ' s value at the start of the first day is $ 100 , on what day will the stock ' s value first reach $ 200 ?
Options: a ) 50 , b ) 99 , c ) 100 , d ) 101 , e ) 200
Rationale: note that each day the stock is worth $ 1 more than on the previous day , and that on the first day it rises to $ 102 and then falls to $ 101 . therefore , on the nth day , the stock ' s value rises to n + 101 dollars in the morning and falls to n + 100 dollars in the afternoon . the solution is therefore the smallest n for which n + 101 = 200 , or n = 99 . in particular , the stock will be $ 200 in the middle of day 99 , although not at the end of this day . correct answer b
Answer: b
Problem: how many pieces of 75 cm can be cut from a rope 52.5 meters long ?
Options: a ) 30 , b ) 40 , c ) 60 , d ) none , e ) can not be determined
Rationale: "explanation : total pieces of 75 cm that can be cut from a rope of 52.5 meters long is = ( 52.5 meters ) / ( 75 cm ) = ( 52.5 meters ) / ( 0.75 meters ) = 70 answer : d"
Answer: d
Problem: bruce purchased 8 kg of grapes at the rate of 70 per kg and 10 kg of mangoes at the rate of 55 per kg . how much amount did he pay to the shopkeeper ?
Options: a ) a ) 1040 , b ) b ) 1050 , c ) c ) 1055 , d ) d ) 1110 , e ) e ) 1075
Rationale: "cost of 8 kg grapes = 70 × 8 = 560 . cost of 10 kg of mangoes = 55 × 10 = 550 . total cost he has to pay = 560 + 550 = 1110 d"
Answer: d
Problem: for a certain exam , a score of 86 was 5 standard deviations above mean and a score of 67 was 2.5 standard deviations above mean . what was the mean score for the exam ?
Options: a ) 50 , b ) 55 , c ) 48 , d ) 42 , e ) 49
Rationale: "mean + 5 sd = 86 mean + 2.5 sd = 67 by solving above equations we get , sd ( absolute value ) = 7.6 mean = 48 ans . c"
Answer: c
Problem: rebecca ' s annual income is $ 20 , and jimmy ' s annual income is $ 10 , . by how much must rebecca ' s annual income increase so that it constitutes 55 % of rebecca and jimmy ' s combined income ?
Options: a ) 8 , b ) 9 , c ) 7.77 , d ) 10 , e ) 11
Rationale: total rebecca = x + 20 ; total = x + 20 + 10 x + 20 / x + 30 = 55 / 100 therefore x = 7.77 c
Answer: c
Problem: 162 students represent x percent of the boys at a school . if the boys at the school make up 50 % of the total school population of x students , what is x ?
Options: a ) 120 , b ) 150 , c ) 180 , d ) 250 , e ) 440
Rationale: "let b be the number of boys in the school . 162 = xb / 100 b = 0.5 x 16200 = 0.5 x ^ 2 x ^ 2 = 32400 x = 180 the answer is c ."
Answer: c
Problem: if x , y , and z are positive integers , and 4 x = 5 y = 6 z , then the least possible value of x + y + z is
Options: a ) 15 , b ) 28 , c ) 37 , d ) 42 , e ) 60
Rationale: take lcm of 4,5 and 6 = 60 now 4 x = 60 = > x = 15 5 y = 60 = > y = 12 6 z = 60 = > z = 10 115 + 12 + 10 = 37 . option c .
Answer: c
Problem: what is the remainder when 3 ^ 30 is divided by 5 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "the units digit of powers of 3 follow a repeating cycle of four : { 3 , 9 , 7 , 1 } 30 has the form 4 k + 2 , so the units digit of 3 ^ 30 is 9 . the remainder when dividing by 5 is 4 . the answer is e ."
Answer: e
Problem: if two painters can complete four rooms in two hours , how many painters would it take to do 24 rooms in 8 hours ?
Options: a ) 7 , b ) 8 , c ) 4 , d ) 6 , e ) 1
Rationale: "explanation : two painters can complete four rooms in two hours . so 24 rooms can be painted in 8 hrs by 4 painters answer : c ) 4 painters"
Answer: c
Problem: a tank is filled by 3 pipes with uniform flow . the first two pipes operating simultaneously fill the tan in the same time during which the tank is filled by the third pipe alone . the 2 nd pipe fills the tank 5 hours faster than first pipe and 4 hours slower than third pipe . the time required by first pipe is
Options: a ) 13 hours , b ) 45 hours , c ) 15 hours , d ) 12 hours , e ) 11 hours
Rationale: if first pipe fills tank in x hrs , then second pipe fills tank in x - 5 hrs and 3 rd pipe fills tank in x - 9 hrs , then as per given condition 1 / x + 1 / ( x - 5 ) = 1 / ( x - 9 ) solving it , we get x = 15 hrs answer : c
Answer: c
Problem: a train 210 m in length crosses a telegraph post in 13 seconds . the speed of the train is ?
Options: a ) 77 kmph , b ) 55 kmph , c ) 54 kmph , d ) 58 kmph , e ) 76 kmph
Rationale: s = 210 / 13 * 18 / 5 = 58 kmph answer : d
Answer: d
Problem: a sum was put at simple interest at certain rate for 3 years . had it been put at 1 % higher rate it would have fetched rs . 75 more . the sum is : a . rs . 2,400 b . rs . 2,100 c . rs . 2,200 d . rs . 2,480
Options: a ) 2500 , b ) 2100 , c ) 2200 , d ) 2300 , e ) 2400
Rationale: "1 percent for 3 years = 75 1 percent for 1 year = 25 = > 100 percent = 2500 answer : a"
Answer: a
Problem: alex takes a loan of $ 5,000 to buy a used truck at the rate of 2 % simple interest . calculate the annual interest to be paid for the loan amount .
Options: a ) 100 , b ) 150 , c ) 720 , d ) 200 , e ) 750
Rationale: "from the details given in the problem principle = p = $ 5,000 and r = 2 % or 0.02 expressed as a decimal . as the annual interest is to be calculated , the time period t = 1 . plugging these values in the simple interest formula , i = p x t x r = 5,000 x 1 x 0.02 = 100.00 annual interest to be paid = $ 100 answer : a"
Answer: a
Problem: during the first two weeks of january , the total rainfall in springdale was 40 inches . if the rainfall during the second week was 1.5 times the rainfall during the first week , what was the rainfall during the second week of january ?
Options: a ) 5 inches , b ) 6 inches , c ) 9 inches , d ) 10 inches , e ) 24 inches
Rationale: "total rainfall in 2 weeks = 40 inches . assume the rainfall in second week = 1 . x rainfall in first week = x total rainfall = 2.5 x = 40 inches x = 16 and 1.5 x = 24 rainfall during second week = 24 inches option e"
Answer: e
Problem: tom , working alone , can paint a room in 20 hours . peter and john , working independently , can paint the same room in 10 hours and 5 hours , respectively . tom starts painting the room and works on his own for two hour . he is then joined by peter and they work together for two hour . finally , john joins them and the three of them work together to finish the room , each one working at his respective rate . what fraction of the whole job was done by peter ?
Options: a ) 5 / 7 , b ) 7 / 8 , c ) 2 / 5 , d ) 3 / 5 , e ) 1 / 5
Rationale: "let the time when all three were working together be t hours . then : tom worked for t + 4 hour and has done 1 / 20 * ( t + 4 ) part of the job ; peter worked for t + 2 hour and has done 1 / 10 * ( t + 2 ) part of the job ; john worked for t hours and has done 1 / 5 * t part of the job : 1 / 20 * ( t + 4 ) + 1 / 10 * ( t + 2 ) + 1 / 5 * t = 1 - - > multiply by 20 - - > ( t + 4 ) + ( 2 t + 2 ) + 4 t = 20 - - > t = 2 ; hence peter has done 1 / 10 * ( 2 + 2 ) = 4 / 10 = 2 / 5 answer : c"
Answer: c
Problem: a van takes 5 hours to cover a distance of 450 km . what speed in kph should the van maintain to cover the same distance in 3 / 2 of the previous time ?
Options: a ) 56 , b ) 60 , c ) 64 , d ) 68 , e ) 72
Rationale: "( 3 / 2 ) * 5 = 7.5 hours 450 / 7.5 = 60 kph the answer is b ."
Answer: b
Problem: what is the compound interest paid on a sum of rs . 4500 for the period of 2 years at 10 % per annum .
Options: a ) 945 , b ) 620 , c ) 610 , d ) 600 , e ) none of these
Rationale: "solution = interest % for 1 st year = 10 interest % for 2 nd year = 10 + 10 % of 10 = 10 + 10 * 10 / 100 = 11 total % of interest = 10 + 11 = 21 total interest = 21 % 4500 = 4500 * ( 21 / 100 ) = 945 answer a"
Answer: a
Problem: at veridux corporation , there are 250 employees . of these , 90 are female , and the rest are males . there are a total of 40 managers , and the rest of the employees are associates . if there are a total of 145 male associates , how many female managers are there ?
Options: a ) 15 , b ) 20 , c ) 25 , d ) 30 , e ) 35
Rationale: "250 employees : 90 male , 160 female 40 managers , 210 associates 145 male associates implies 65 female associates which means the remaining 25 females must be managers c . 25"
Answer: c
Problem: if 10 parallel lines in a plane is intersected by a family of another 8 parallel lines , how many parallelograms are there in the network thus formed ?
Options: a ) 80 , b ) 63 , c ) 120 , d ) 160 , e ) 1260
Rationale: "parallelogram can formed by 2 horizontal and 2 vertical lines for horizontal 10 c 2 for vertical 8 c 2 total parallelogram is 10 c 2 * 8 c 2 = 45 * 28 = 1260 answer : e"
Answer: e
Problem: on rainy mornings , mo drinks exactly n cups of hot chocolate ( assume that n is an integer ) . on mornings that are not rainy , mo drinks exactly 5 cups of tea . last week mo drank a total of 22 cups of tea and hot chocolate together . if during that week mo drank 8 more tea cups than hot chocolate cups , then how many rainy days were there last week ?
Options: a ) 2 , b ) 4 , c ) 3 , d ) 5 , e ) 6
Rationale: "t = the number of cups of tea c = the number of cups of hot chocolate t + c = 22 t - c = 8 - > t = 15 . c = 7 . mo drinks 5 cups of tea a day then number of days that are not rainy = 15 / 5 = 3 so number of rainy days = 7 - 3 = 4 b is the answer ."
Answer: b
Problem: two cars a and b start from boston and new york respectively simultaneously and travel towards each other at constant speeds along the same route . after meeting at a point between boston and new york the two cars a and b proceed to their respective destinations of new york and boston . car a reaches new york 10 minutes after the two cars have met and car b reaches boston 90 minutes after they have met . how long did car a take to cover the distance between boston and new york ?
Options: a ) 1 hour , b ) 1 hour 10 minutes , c ) 2 hours 30 minutes , d ) 50 minutes , e ) 2 hours 10 minutes
Rationale: "both cars leave at the same time both cars travel at constant speed stealing a useful piece of information from paragkan : if two objects a and b start from opposite points and , after having met en route , reach their respective destinations in a and b mins ( or any other measure of time ) respectively , then the ratio of their speeds ratio of speed : ( a / b ) = sq . rt ( b / a ) sq . rt ( b / a ) sq . rt ( 90 / 10 ) sq . rt ( 3 / 2 ) so , for every three units of distance a travels , b travels two . because we know the ratio of speed and the time it took b to travel the distance a has n ' t yet covered , we can find the time it took a to cover the distance b did in 90 minutes . 90 * ( 2 / 3 ) where 2 / 3 represents the lesser amount of time it took a to travel the distance b did in 90 minutes . = 60 minutes . therefore , a took 10 minutes to travel the first portion then 60 minutes to travel the distance b did in 90 minutes . a spent ( 10 + 60 ) = 50 minutes on the road . d . 50 minutes"
Answer: d
Problem: 70 % of a number is added to 120 , the result is the same number . find the number ?
Options: a ) 300 , b ) 400 , c ) 1687 , d ) 997 , e ) 121
Rationale: "( 70 / 100 ) * x + 120 = x 2 x = 800 x = 400 answer : b"
Answer: b
Problem: two spherical balls lie on the ground touching . if one of the balls has a radius of 4 cm , and the point of contact is 6 cm above the ground , what is the radius of the other ball ?
Options: a ) 10 cm , b ) 12 cm , c ) 14 cm , d ) 16 cm , e ) 18 cm
Rationale: similar triangle properties . . 2 / r + 4 = 4 / r - 4 giving r = 14 . answer : c
Answer: c
Problem: 1370 , 1320 , 1070 , - 180 ?
Options: a ) - 6430 , b ) - 6530 , c ) - 6630 , d ) - 6730 , e ) - 6830
Rationale: 1370 , 13201070 , - 180 , ? 1370 - 50 * ( 5 ^ 0 ) = 1320 1320 - 50 * ( 5 ^ 1 ) = 1070 1070 - 50 * ( 5 ^ 2 ) = - 180 - 180 - 50 * ( 5 ^ 3 ) = - 6430 answer : a .
Answer: a
Problem: mary and mike enter into a partnership by investing $ 650 and $ 350 respectively . at the end of one year , they divided their profits such that a third of the profit is divided equally for the efforts they have put into the business and the remaining amount of profit is divided in the ratio of the investments they made in the business . if mary received $ 600 more than mike did , what was the profit made by their business in that year ?
Options: a ) $ 3000 , b ) $ 3200 , c ) $ 3300 , d ) $ 3400 , e ) $ 4000
Rationale: "explanatory answer let the profit made during the year be $ 3 x therefore , $ x would have been shared equally and the remaining $ 2 x would have been shared in the ratio 6.5 : 3.5 i . e . , 65 % of 2 x would go to mary and 35 % of 2 x would go to mike . hence , mary would get ( 65 - 35 ) % of 2 x more than mike or 30 % of 2 x = $ 600 i . e . , ( 30 / 100 ) * 2 x = 600 or 2 x = 2000 . hence , the profit made by the company during the year $ 3 x = $ 3000 . answer : a"
Answer: a
Problem: a train 150 meters long takes 6 seconds to cross a man walking at 5 kmph in the direction opposite to that of the train . find the speed of the train .
Options: a ) 45 kmph , b ) 50 kmph , c ) 85 kmph , d ) 60 kmph , e ) 70 kmph
Rationale: "explanation : let the speed of the train be x kmph . speed of the train relative to man = ( x + 5 ) kmph = ( x + 5 ) × 5 / 18 m / sec . therefore 150 / ( ( x + 5 ) × 5 / 18 ) = 6 < = > 30 ( x + 5 ) = 2700 < = > x = 85 speed of the train is 85 kmph . answer : option c"
Answer: c
Problem: a , b and c start a business each investing 20,000 . after 5 months a withdrew 10000 , b withdrew 15000 and c invests 5000 more . at the end of the year , a total profit of 58000 was recorded . find the share of b .
Options: a ) 20,000 , b ) 21,200 , c ) 28,200 , d ) 13,500 , e ) none of these
Rationale: ratio of the capitals of a , b and c = 20000 ã — 5 + 10000 ã — 7 : 20000 ã — 5 + 5000 ã — 7 : 20000 ã — 5 + 25000 ã — 7 = 170000 : 135000 : 275000 = 170 : 135 : 275 . b â € ™ s share = ( 58000 ã — 135 â  „ 580 ) = 13500 answer d
Answer: d