regisss/math_qa huggingface dataset:
Problem: a glass was filled with 40 ounces of water , and 0.01 ounce of the water evaporated each day during a 20 - day period . what percent of the original amount of water evaporated during this period ?
Options: a ) 0.005 % , b ) 0.02 % , c ) 0.5 % , d ) 5 % , e ) 20 %
Rationale: "we are given that 0.01 ounces of water evaporated each day . furthermore , we know that this process happened over a 20 - day period . to calculate the total amount of water that evaporated during this time frame we need to multiply 0.01 by 20 . this gives us : 0.01 x 20 = 0.2 ounces finally , we are asked for “ what percent ” of the original amount of water evaporated during this period . to determine this percentage , we have to make sure we translate the expression correctly . we can translate it to : ( amount evaporated / original amount ) x 100 % ( 0.2 / 40 ) x 100 % = 0.5 % answer c"
Answer: c
Problem: a family pays $ 800 per year for an insurance plan that pays 60 percent of the first $ 1,000 in expenses and 100 percent of all medical expenses thereafter . in any given year , the total amount paid by the family will equal the amount paid by the plan when the family ' s medical expenses total how much ?
Options: a ) $ 1,000 , b ) $ 1,200 , c ) $ 1,400 , d ) $ 1,600 , e ) $ 2,000
Rationale: assuming the medical expenses are $ 1000 or more , the family pays $ 800 + $ 400 = $ 1200 . the total amount paid by insurance plan for the first $ 1000 of expenses is $ 600 . the insurance will pay another $ 600 when the medical expenses are $ 1600 . the answer is d .
Answer: d
Problem: mike and his friend are going on a road trip and hoping to miss traffic . if they are driving at a rate of 6 miles per minute , what is their speed in kilometers per hour ? [ 1 km = 0.6 miles ]
Options: a ) 60 , b ) 30 , c ) 300 , d ) 600 , e ) none of the above
Rationale: to calculate the equivalent of kilometres in a mile 6 miles = 6 * ( 0.6 ) ^ - 1 = 10 kilometres in 1 hour there are 60 minutes speed in kmph = 10 * 60 = 600 correct answer - d
Answer: d
Problem: the amount of an investment will double in approximately 70 / p years , where p is the percent interest , compounded annually . if thelma invests $ 30,000 in a long - term cd that pays 5 percent interest , compounded annually , what will be the approximate total value of the investment when thelma is ready to retire 42 years later ?
Options: a ) $ 240,000 , b ) $ 320,000 , c ) $ 360,000 , d ) $ 450,000 , e ) $ 540,000
Rationale: "the amount of an investment will double in approximately 70 / p years , where p is the percent interest , compounded annually . if thelma invests $ 30,000 in a long - term cd that pays 5 percent interest , compounded annually , what will be the approximate total value of the investment when thelma is ready to retire 42 years later ? the investment gets doubled in 70 / p years . therefore , the investment gets doubled in 70 / 5 = every 14 years . after 42 years , the investment will get doubled 42 / 14 = 3 times . so the amount invested will get doubled thrice . so , 30000 * 2 ^ 3 = 240000 hence , the answer is a ."
Answer: a
Problem: the average weight of 10 students decreases by 6 kg when one of them weighing 120 kg is replaced by a new student . the weight of the student is
Options: a ) 62 kg , b ) 60 kg , c ) 70 kg , d ) 72 kg , e ) none of these
Rationale: "explanation : let the weight of student be x kg . given , difference in average weight = 6 kg = > ( 120 - x ) / 10 = 6 = > x = 60 answer : b"
Answer: b
Problem: the length of a rectangular landscape is 4 times its breadth . there is a playground in it whose area is 1200 square mtr & which is 1 / 3 rd of the total landscape . what is the length of the landscape ?
Options: a ) 90
b ) 100
c ) 120
d ) 130
e ) 140
Rationale: sol . x * 4 x = 3 * 1200 x = 30 length = 4 * 30 = 120 c
Answer: c
Problem: each week , harry is paid x dollars per hour for the first 30 hours and 2 x dollars for each additional hour worked that week . each week , james is paid x dollars per per hour for the first 40 hours and 2 x dollars for each additional hour worked that week . last week james worked a total of 41 hours if harry and james were paid the same amount last week , how many hours did harry work last week ?
Options: a ) 35 , b ) 36 , c ) 37 , d ) 38 , e ) 39
Rationale: "james worked for 41 hours hence he earned 40 * x + 1 * 2 x = 42 x dollars ; we know that harry also earned the same 42 x dollars , out of which he earned 30 x dollars for thefirst 30 hoursplus 12 x additional dollars . since for each additional hour he gets 2 x dollars then he worked for 12 x / 2 x = 6 additional hours , so harry worked for total of 30 + 6 = 36 hours . answer : b ."
Answer: b
Problem: the sum of 3 numbers is 98 . the ratio of the first to the second is 2 / 3 , and the ratio of the second to the third is 5 / 8 . the second number is :
Options: a ) 20 , b ) 30 , c ) 60 , d ) 70 , e ) 10
Rationale: b 30 let the three numbers be x , y and z . sum of the numbers is 98 . x + y + z = 98 … … … … … … ( i ) the ratio of the first to the second is 2 / 3 . x / y = 2 / 3 . x = 2 / 3 × y . x = 2 y / 3 . the ratio of the second to the third is 5 / 8 . y / z = 5 / 8 . z / y = 8 / 5 . z = 8 / 5 × y . z = 8 y / 5 . put the value of x = 2 y / 3 and z = 8 y / 5 in ( i ) . 2 y / 3 + y + 8 y / 5 = 98 49 y / 15 = 98 . 49 y = 98 × 15 . 49 y = 1470 . y = 1470 / 49 . y = 30 . therefore , the second number is 30 .
Answer: b
Problem: a trader sold an article on a certain price with 20 % profit . if he sold double of previous selling price then find its profit %
Options: a ) 140 % , b ) 120 % , c ) 100 % , d ) 90 % , e ) 80 %
Rationale: let cost price = 100 % selling price = 120 % new s . p . = 240 % p % = 240 - 100 = 140 % answer is a
Answer: a
Problem: if a and b get profits of rs . 6000 and rs . 4000 respectively at the end of year the ratio of their investments are ?
Options: a ) 1 : 4 , b ) 3 : 2 , c ) 2 : 3 , d ) 2 : 5 , e ) none of these
Rationale: "profit = investment * time so , 6000 = i 1 * 1 = 6000 4000 = i 2 * 1 = 4000 i 1 / i 2 = 6000 / 4000 = 3 / 2 answer : b"
Answer: b
Problem: the time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream . if the speed of the boat in still water is 57 kmph , find the speed of the stream ?
Options: a ) 15 , b ) 17 , c ) 19 , d ) 18 , e ) 16
Rationale: "the ratio of the times taken is 2 : 1 . the ratio of the speed of the boat in still water to the speed of the stream = ( 2 + 1 ) / ( 2 - 1 ) = 3 / 1 = 3 : 1 speed of the stream = 57 / 3 = 19 kmph . answer : c"
Answer: c
Problem: a dishonest dealer professes to sell goods at the cost price but uses a weight of 650 grams per kg , what is his percent ?
Options: a ) 15 % , b ) 25 % , c ) 65 % , d ) 53.8 % , e ) 35 %
Rationale: "explanation : 650 - - - 350 100 - - - ? = > 53.8 % answer : d"
Answer: d
Problem: the slant height of a cone is 12 cm and radius of the base is 4 cm , find the curved surface of the cone .
Options: a ) 33 , b ) 88 , c ) 48 , d ) 77 , e ) 27
Rationale: "π * 12 * 4 = 48 answer : c"
Answer: c
Problem: what is the remainder when ( 55 ) ( 57 ) is divided by 7 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 5 , e ) 6
Rationale: "( 55 ) ( 57 ) = ( 56 - 1 ) ( 56 + 1 ) = 56 ^ 2 - 1 which is 1 less than a multiple of 7 . then the remainder will be 6 . the answer is e ."
Answer: e
Problem: the sum of ages of 4 children born 2 years different each is 40 yrs . what is the age of the elder child ?
Options: a ) 13 , b ) 9 , c ) 16 , d ) 17 , e ) 18
Rationale: "let the ages of children be x , ( x + 2 ) , ( x + 4 ) , ( x + 6 ) years . then , x + ( x + 2 ) + ( x + 4 ) + ( x + 6 ) = 40 4 x + 12 = 40 = > 4 x = 28 x = 7 x + 6 = 7 + 6 = 13 answer : a"
Answer: a
Problem: the ratio , by volume , of bleach to detergent to water in a certain solution is 2 : 40 : 100 . the solution will be altered so that the ratio of bleach to detergent is tripled while the ratio of detergent to water is halved . if the altered solution will contain 200 liters of water , how many liters of detergent will it contain ?
Options: a ) 60 , b ) 55 , c ) 50 , d ) 45 , e ) 40
Rationale: "b : d : w = 2 : 40 : 100 bnew / dnew = ( 1 / 3 ) * ( 2 / 40 ) = ( 1 / 60 ) dnew / wnew = ( 1 / 2 ) * ( 40 / 100 ) = ( 1 / 5 ) wnew = 200 dnew = wnew / 5 = 200 / 5 = 40 so , answer will be e"
Answer: e
Problem: a tank is 25 m long 12 m wide and 6 m deep . the cost of plastering its walls and bottom at 75 paise per sq m is
Options: a ) rs . 258 , b ) rs . 358 , c ) rs . 458 , d ) rs . 558 , e ) none of these
Rationale: "explanation : area to be plastered = [ 2 ( l + b ) × h ] + ( l × b ) = [ 2 ( 25 + 12 ) × 6 ] + ( 25 × 12 ) = 744 sq m cost of plastering = 744 × ( 75 / 100 ) = rs . 558 answer : d"
Answer: d
Problem: it takes printer a 4 more minutes more than printer b to print 40 pages . working together , the two printers can print 50 pages in 6 minutes . how long will it take printer a to print 140 pages ?
Options: a ) 12 , b ) 18 , c ) 20 , d ) 42 , e ) 30
Rationale: "if it takes 4 more minutes for a to print 40 pages than it takes b , it takes 5 more minutes for a to print 50 pages than it takes b . thus if b is the number of minutes than b takes to print 50 pages , we can write : 1 / b + 1 / ( b + 5 ) = 1 / 6 ( since in 1 minute , they print 1 / 6 th of the 50 page job ) 6 ( 2 b + 5 ) = b ( b + 5 ) b ^ 2 - 7 b - 30 = 0 ( b - 10 ) ( b + 3 ) = 0 b = 10 thus it takes a 15 minutes to print 50 pages and 15 * 140 / 50 = 42 minutes to print 140 pages ( answer d )"
Answer: d
Problem: there is a total of 100 marbles in a box , each of which is red , green , blue , or white . if one marble is drawn from the box at random , the probability that it will be white is 1 / 4 and the probability that it will be green is 1 / 5 . what is the probability that the marble will be either red or blue ?
Options: a ) 2 / 3 , b ) 3 / 5 , c ) 7 / 10 , d ) 9 / 20 , e ) 11 / 20
Rationale: "p ( red or blue ) = 1 - p ( white ) - p ( green ) = 20 / 20 - 5 / 20 - 4 / 20 = 11 / 20 the answer is e ."
Answer: e
Problem: you and your friend spent a total of $ 11 for lunch . your friend spent $ 3 more than you . how much did your friend spend on their lunch ?
Options: a ) $ 9 , b ) $ 3 , c ) $ 7 , d ) $ 6 , e ) $ 5
Rationale: "my lunch = l , my friends lunch = l + 1 ( l ) + ( l + 3 ) = 11 l + l + 3 - 3 = 11 - 3 2 l = 8 l = 4 my friends lunch l + 3 = 4 + 3 = $ 7 , the answer is c"
Answer: c
Problem: what is the square root of 9 ?
Options: a ) 1 , b ) 3 , c ) 2 , d ) 4 , e ) 9
Rationale: "3 x 3 = 9 answer b"
Answer: b
Problem: 3 business people wish to invest in a new company . each person is willing to pay one third of the total investment . after careful calculations , they realize that each of them would pay $ 2200 less if they could find two more equal investors . how much is the total investment in the new business ?
Options: a ) $ 11,000 , b ) $ 50,000 , c ) $ 16,500 , d ) $ 6,600 , e ) $ 3,600
Rationale: total investment between 5 : ( x / 5 ) total investment including 2200 less between 3 people ( x - ( 2200 * 3 ) ) / 3 set both eq . equal to each other . 16,500 answer c )
Answer: c
Problem: haresh went to buy fruits . she bought 1 apple , 3 bananas , 5 oranges and paid 21 rupees . another person bought 7 apple , 5 bananas , 3 oranges and paid 51 rupees . if i want to buy 1 apple , 1 banana , 1 orange then how much i have to pay ?
Options: a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 7
Rationale: there can be multiple possible rates of apple , banana and orange to satisfy given conditions , but cost of 1 apple , 1 banana , 1 orange will be rs 9 . 1 x + 3 y + 5 z = 21 . . . . . . . . ( 1 ) 7 x + 5 y + 3 z = 51 . . . . . . . . ( 2 ) adding ( 1 ) and ( 2 ) , we get 8 x + 8 y + 8 z = 72 8 * ( x + y + z ) = 72 x + y + z = 9 answer : b
Answer: b
Problem: 5 cylinders are built successively , the first is 4 meters tall and the following cylinders are each 4 meters taller than the previous . if the perimeter is 10 pi m , what is the total surface area of the 5 cylinders , excluding the bases of each cylinder ?
Options: a ) 725 pi sq m
b ) 1025 pi sq m
c ) 600 pi sq m
d ) 125 pi sq m
e ) 850 pi sq m
Rationale: s . a . = h x p + 2 x a we need to excude the bottom area , so the formula becomes : s . a . = h x p + a p = 2 pi x r , so 10 pi = 2 pi x r r = 5 since we have 5 cylinders with different heights the equation becomes s . a . = ( 4 + 8 + 12 + 16 + 20 ) x 10 pi + 5 x pi x r ^ 2 60 x 10 pi + 5 pi x 5 ^ 2 600 pi + 125 pi = 725 pi sq . m . answer is a
Answer: a
Problem: mahesh can do a piece of work in 60 days . he works at it for 20 days and then rajesh finished it in 30 days . how long will y take to complete the work ?
Options: a ) 45 , b ) 25 , c ) 37 , d ) 41 , e ) 30
Rationale: "work done by mahesh in 60 days = 20 * 1 / 60 = 1 / 3 remaining work = 1 - 1 / 3 = 2 / 3 2 / 3 work is done by rajesh in 30 days whole work will be done by rajesh is 30 * 3 / 2 = 45 days answer is a"
Answer: a
Problem: a land owner needs to fence his semicircular land leaving an opening of length of 3 m for access . the radius of the semicircular plot is 7 m . how long would be the fence in meters ?
Options: a ) 22 , b ) 33 , c ) 36 , d ) 44 , e ) 51
Rationale: perimeter of the semicircle = ï € xd / 2 + d = ï € x 7 + 14 = 22 + 14 = 36 m length of the fence = 36 - 3 = 33 m answer : b
Answer: b
Problem: two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 16 kmph and 21 kmph respectively . when they meet , it is found that one train has travelled 60 km more than the other one . the distance between the two stations is ?
Options: a ) 222 km , b ) 333 km , c ) 555 km , d ) 444 km , e ) 666 km
Rationale: d 444 km 1 h - - - - - 5 ? - - - - - - 60 12 h rs = 16 + 21 = 37 t = 12 d = 37 * 12 = 444
Answer: d
Problem: a contest will consist of n questions , each of which is to be answered eithertrueorfalse . anyone who answers all n questions correctly will be a winner . what is the least value of n for which the probability is less than 1 / 10000 that a person who randomly guesses the answer to each question will be a winner ?
Options: a ) 5 , b ) 10 , c ) 50 , d ) 100 , e ) 1000
Rationale: "a contest will consist of n questions , each of which is to be answered eithertrueorfalse . anyone who answers all n questions correctly will be a winner . what is the least value of n for which the probability is less than 1 / 1000 that a person who randomly guesses the answer to each question will be a winner ? a . 5 b . 10 c . 50 d . 100 e . 1000 soln : ans is b probability that one question is answered right is 1 / 2 . now for minimum number of questions needed to take probability less than 1 / 1000 is = > ( 1 / 2 ) ^ n < 1 / 10000 n = 100 satisfies this . d"
Answer: d
Problem: if a = 105 and a ^ 3 = 21 × 25 × 45 × q , what is the value of q ?
Options: a ) 35 , b ) 42 , c ) 45 , d ) 49 , e ) 54
Rationale: "a = 105 = 3 * 5 * 7 a ^ 3 = 21 × 25 × 45 × q = > a ^ 3 = ( 7 * 3 ) x ( 5 * 5 ) x ( 3 ^ 2 * 5 ) x q = > a ^ 3 = 3 ^ 3 * 5 ^ 3 * 7 x q = > ( 3 * 5 * 7 ) ^ 3 = 3 ^ 3 * 5 ^ 3 * 7 x q q = 7 ^ 2 = 49 answer d"
Answer: d
Problem: what number should replace the question mark ? 5 , 24 , 11 , 20 , 17 , 16 , - - - ?
Options: a ) 20 , b ) 23 , c ) 22 , d ) 21 , e ) 26
Rationale: "answer : b 5 , 24 , 11 , 20 , 17 , 16 , 23 ? there are two alternate sequences : + 6 and - 4 ."
Answer: b
Problem: the average ( arithmetic mean ) of 4 different integers is 72 . if the largest integer is 90 , what is the least possible value of the smallest integer ?
Options: a ) 1 , b ) 19 , c ) 21 , d ) 30 , e ) 33
Rationale: total of integers = 72 * 4 = 288 lowest of the least possible integer is when the middle 2 intergers are at the maximum or equal to the highest possible integer . but all integers are distinct . so if the largest integer is 90 , then the middle 2 will be 88 and 89 lowest of least possible integer = 288 - ( 90 + 89 + 88 ) = 288 - 267 = 21 answer : c
Answer: c
Problem: stacy has a 66 page history paper due in 6 days . how many pages per day would she have to write to finish on time ?
Options: a ) 9 , b ) 8 , c ) 11 , d ) 8.5 , e ) 6
Rationale: 66 / 6 = 11 answer : c
Answer: c
Problem: jane makes toy bears . when she works with an assistant , she makes 80 percent more bears per week and works 10 percent fewer hours each week . having an assistant increases jane ’ s output of toy bears per hour by what percent w ?
Options: a ) 20 % , b ) 80 % , c ) 100 % , d ) 180 % , e ) 200 %
Rationale: c . let ' s assume just jane 40 bears per 40 / hrs a week , so that is 1 bear / hr . with an assistant she makes 72 bears per 36 hours a week or 2 bears / hr ( [ 40 bears * 1.8 ] / [ 40 hrs * . 90 ] ) . w = [ ( 2 - 1 ) / 1 ] * 100 % = 100 %
Answer: c
Problem: diana took out a charge account at the general store and agreed to pay 7 % simple annual interest . if she charges $ 75 on her account in january , how much will she owe a year later , assuming she does not make any additional charges or payments ?
Options: a ) $ 79.25 , b ) $ 79.50 , c ) $ 79.75 , d ) $ 80.00 , e ) $ 80.25
Rationale: 1.07 * $ 75 = $ 80.25 the answer is e .
Answer: e
Problem: a rower whose speed is 9 km / hr in still water rows to a certain point upstream and back to the starting point in a river which flows at 3 km / hr . what is the rower ' s average speed ( in km / hr ) for the total journey ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: "time upstream = d / 6 time downstream = d / 12 total time = d / 6 + d / 12 = d / 4 average speed = 2 d / ( d / 4 ) = 8 km / hr the answer is b ."
Answer: b
Problem: a man completes of a job in 10 days . at this rate , how many more days will it takes him to finish the job ?
Options: a ) 6 , b ) 12 , c ) 7 , d ) 15 , e ) 5
Rationale: work done = 5 / 8 balance work = ( 1 - 5 / 8 ) = 3 / 8 let the required number of days be x . then , ( 5 / 8 ) : ( 3 / 8 ) = : : 10 : x ( 5 / 8 ) * x = ( 3 / 8 ) * 10 x = ( 3 / 8 ) * 10 * ( 8 / 5 ) x = 6 . answer is a .
Answer: a
Problem: in a sample of 800 high school students in which all students are either freshmen , sophomores , juniors , or seniors , 22 percent are juniors and 74 percent are not sophomores . if there are 160 seniors , how many more freshmen than sophomores are there among the sample of students ?
Options: a ) 42 , b ) 48 , c ) 56 , d ) 208 , e ) 256
Rationale: "sophomores = 26 % juniors = 22 % seniors = 160 / 800 = 20 % total : 68 % 1 - 68 % = 32 % ( freshmen ) 0,32 * 800 - 0,26 * 800 = 256 - 208 = 48 . answer choice b"
Answer: b
Problem: a student needs 60 % of the marks on a test to pass the test . if the student gets 80 marks and fails the test by 100 marks , find the maximum marks set for the test .
Options: a ) 250 , b ) 300 , c ) 350 , d ) 400 , e ) 450
Rationale: "60 % = 180 marks 1 % = 3 marks 100 % = 300 marks the answer is b ."
Answer: b
Problem: a football player scores 2 goals in his fifth match thus increasing his average goals score by 0.1 . the total number of goals in his 5 matches would be
Options: a ) 4 , b ) 6 , c ) 8 , d ) 10 , e ) 12
Rationale: "while this question can be solved with a rather straight - forward algebra approach ( as the other posters have noted ) , it can also be solved by testing the answers . one of those numbers must be the total number of goals . . . from a tactical standpoint , it ' s best to test either answer b or answer d , so if the answer is not correct , then you would have a gauge for whether you should gohigherorlowerwith your next test . here , i ' ll start with answer c = 8 goals if . . . . total goals = 8 goals 5 th game = 2 goals 1 st 4 games = 6 goals avg . for 1 st 4 games = 6 / 4 = 1.5 goal / game avg . for all 5 games = 8 / 5 = 1.6 goals / game this is an exact match for what we ' re told in the prompt , so answer c must be the answer ."
Answer: c
Problem: if the weight of 12 meters long rod is 14 kg . what is the weight of 6 meters long rod ?
Options: a ) 8 kg . , b ) 10.8 kg . , c ) 7 kg . , d ) 18.0 kg , e ) none
Rationale: "answer ∵ weight of 12 m long rod = 14 kg ∴ weight of 1 m long rod = 14 / 12 kg ∴ weight of 6 m long rod = 14 x 6 / 12 = 7 kg option : c"
Answer: c
Problem: a man can row downstream at 18 kmph and upstream at 16 kmph . find the speed of the man in still water and the speed of stream respectively ?
Options: a ) 13 , 3 , b ) 12 , 6 , c ) 15 , 3 , d ) 14 , 4 , e ) 17 , 1
Rationale: "explanation : let the speed of the man in still water and speed of stream be x kmph and y kmph respectively . given x + y = 18 - - - ( 1 ) and x - y = 16 - - - ( 2 ) from ( 1 ) & ( 2 ) 2 x = 34 = > x = 17 , y = 1 . answer : option e"
Answer: e
Problem: after giving a discount of rs . 45 the shopkeeper still gets a profit of 20 % , if the cost price is rs . 180 . find the markup % ?
Options: a ) 0.4 , b ) 0.55 , c ) 0.45 , d ) 0.48 , e ) 0.58
Rationale: cost price = 180 s . p = 180 * 120 / 100 = 216 disc = 45 so . . . mark price = 216 + 45 = 261 . . . . . . mark up % = 261 - 180 / 180 = 81 / 180 = . 45 or 45 % answer : c
Answer: c
Problem: if x , y , and z are positive integers and 3 x = 2 y = 4 z , then the least possible value of x + y + z is
Options: a ) 15 , b ) 25 , c ) 30 , d ) 42 , e ) 13
Rationale: "given 3 x = 2 y = 4 z x + y + z in terms of x = x + ( 3 x / 2 ) + ( 3 x / 4 ) = 26 x / 8 = 13 x / 4 now checking with each of the answers and see which value gives a minimum integer value . a x = 4 / 13 * 15 , not an integer b , c , e can be ruled out similarly . d is minimum value as x = 13 * 4 / 13 = 4 answer is e"
Answer: e
Problem: a train travelling 80 kmph to pass through a tunnel of 70 km at 5 : 12 am . the train leaves the tunnel at 5 : 18 am . find the length of train ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: distance = speed * time let x is length of train 5 : 18 - 5 : 12 = 6 minutes = 6 / 60 hr = 1 / 10 hr now d = ( x + 7 ) = 80 kmph * 1 / 10 x = 1 km answer : a
Answer: a
Problem: if x is equal to the sum of the integers from 30 to 50 , inclusive , and y is the number of even integers from 30 to 50 , inclusive , what is the value of x + y ?
Options: a ) 810 , b ) 811 , c ) 830 , d ) 850 , e ) 851
Rationale: since the integers from 30 - 50 are consecutive we can use the ` ` median x # of terms formula ' ' to determine x . there are 21 terms and the median is 40 . this gives a total of 21 x 40 = 840 . there are 11 even integers from 30 - 50 = y . therefore , x + y = 851 . answer : e
Answer: e
Problem: of the 100 people in a room , 2 / 5 are women . if 1 / 4 of the people are married , what is the maximum number of women in the room who could be unmarried ?
Options: a ) 32 , b ) 34 , c ) 36 , d ) 38 , e ) 40
Rationale: women = 2 / 5 * 100 = 40 married = 1 / 4 * 100 = 25 unmarried = 75 max ( un - married women ) = 40 answer e
Answer: e
Problem: the length of the bridge , which a train 160 meters long and travelling at 45 km / hr can cross in 30 seconds , is :
Options: a ) 230 , b ) 244 , c ) 245 , d ) 215 , e ) 236
Rationale: "speed = ( 45 * 5 / 18 ) m / sec = ( 25 / 2 ) m / sec . time = 30 sec . let the length of bridge be x meters . then , ( 160 + x ) / 30 = 25 / 2 = = > 2 ( 160 + x ) = 750 = = > x = 215 m . answer : option d"
Answer: d
Problem: yesterday ' s closing prices of 1,760 different stocks listed on a certain stock exchange were all different from today ' s closing prices . the number of stocks that closed at a higher price today than yesterday was 20 percent greater than the number that closed at a lower price . how many of the stocks closed at a higher price today than yesterday ?
Options: a ) 960 , b ) 726 , c ) 1,100 , d ) 1,320 , e ) 1,694
Rationale: "lets consider the below - the number of stocks that closed at a higher price = h the number of stocks that closed at a lower price = l we understand from first statement - > h + l = 1760 - - - - ( 1 ) we understand from second statement - > h = ( 120 / 100 ) l = > h = 1.2 l - - - - ( 2 ) solve eq ( 1 ) ( 2 ) to get h = 960 . a is my answer ."
Answer: a
Problem: if a certain toy store ' s revenue in november was 2 / 5 of its revenue in december and its revenue in january was 1 / 5 of its revenue in november , then the store ' s revenue in december was how many times the average ( arithmetic mean ) of its revenues in november and january ?
Options: a ) 5 / 2 , b ) 10 / 3 , c ) 15 / 4 , d ) 25 / 3 , e ) 25 / 6
Rationale: "n = 2 d / 5 j = n / 5 = 2 d / 25 the average of november and january is ( n + j ) / 2 = 12 d / 25 / 2 = 6 d / 25 d is 25 / 6 times the average of november and january . the answer is e ."
Answer: e
Problem: john was thrice as old as tom 6 years ago . john will be 3 / 2 times as old as tom in 6 years . how old is tom today ?
Options: a ) 6 , b ) 8 , c ) 10 , d ) 12 , e ) 14
Rationale: "j - 6 = 3 ( t - 6 ) , so j = 3 t - 12 j + 6 = 3 / 2 * ( t + 6 ) 2 j + 12 = 3 t + 18 2 ( 3 t - 12 ) + 12 = 3 t + 18 3 t = 30 t = 10 the answer is c ."
Answer: c
Problem: a rainstorm increased the amount of water stored in state j reservoirs from 130 billion gallons to 160 billion gallons . if the storm increased the amount of water in the reservoirs to 60 percent of total capacity , approximately how many billion gallons of water were the reservoirs short of total capacity prior to the storm ?
Options: a ) 92 , b ) 85 , c ) 136.67 , d ) 140.67 , e ) 150
Rationale: "let total capacity be x we know 160 = 0.60 x x = 160 / 0.60 = 266.67 prior to storm , we had 130 bn gallons 266.67 - 130 = 136.67 answer : c"
Answer: c
Problem: what is the 8 th digit to the right of the decimal point in the decimal equivalent of 73 / 11 ?
Options: a ) 1 , b ) 3 , c ) 4 , d ) 5 , e ) 2
Rationale: "73 / 11 = 6.6363 . . . . 63 is non - terminating repeating decimal . the 8 th digit to the right of decimal point will be 3 . answer b"
Answer: b
Problem: if rs . 510 be divided among a , b , c in such a way that a gets 2 / 3 of what b gets and b gets 1 / 4 of what c gets , then their shares are respectively ?
Options: a ) rs . 300 , b ) rs . 360 , c ) rs . 389 , d ) rs . 368 , e ) rs . 323
Rationale: "( a = 2 / 3 b and b = 1 / 4 c ) = a / b = 2 / 3 and b / c = 1 / 4 a : b = 2 : 3 and b : c = 1 : 4 = 3 : 12 a : b : c = 2 : 3 : 12 a ; s share = 510 * 2 / 17 = rs . 60 b ' s share = 510 * 3 / 17 = rs . 90 c ' s share = 510 * 12 / 17 = rs . 360 . answer : b"
Answer: b
Problem: if p # q denotes the least common multiple of p and q , then p = ( ( 12 # 16 ) # ( 18 # 24 ) ) = ?
Options: a ) 216 , b ) 180 , c ) 144 , d ) 108 , e ) 72
Rationale: "there are several ways to find the least common multiple of two numbers . in this case , the most efficient method is to use the greatest common factor : ( a * b ) / ( gcf ab ) = lcm ab the greatest common factor of 12 and 16 is 4 . so , 12 # 16 = 12 * 16 / 4 = 48 . the greatest common factor of 18 and 24 is 6 . so , 18 # 24 = 18 * 24 / 6 = 72 finally , the greatest common factor of 48 and 72 is 24 . so , p = ( ( 12 # 16 ) # ( 18 # 24 ) ) = 48 # 72 = ( 48 * 72 ) / 24 = 2 * 72 = 144 the correct answer is c ."
Answer: c
Problem: if ( 18 ^ a ) * 9 ^ ( 3 a – 1 ) = ( 2 ^ 6 ) ( 3 ^ b ) and a and b are positive integers , what is the value of a ?
Options: a ) 22 , b ) 11 , c ) 9 , d ) 6 , e ) 3
Rationale: "( 18 ^ a ) * 9 ^ ( 3 a – 1 ) = ( 2 ^ 6 ) ( 3 ^ b ) = 2 ^ a . 9 ^ a . 9 ^ ( 3 a – 1 ) = ( 2 ^ 6 ) ( 3 ^ b ) just compare powers of 2 from both sides answer = 6 = d"
Answer: d
Problem: there are 8 teams in a certain league and each team plays each of the other teams exactly twice . if each game is played by 2 teams , what is the total number of games played ?
Options: a ) 15 , b ) 16 , c ) 28 , d ) 56 , e ) 64
Rationale: "every team plays with 7 teams . . . so total no of matches = 8 x 7 = 56 . now , each match is played twice = > 56 x 2 but 2 teams play a match = > 56 x 2 / 2 = 56 . ans : d"
Answer: d
Problem: a shopkeeper buys mangoes at the rate of 4 a rupee and sells them at 3.5 a rupee . find his net profit or loss percent ?
Options: a ) 13.2 % , b ) 15.2 % , c ) 14.28 % , d ) 32 1 / 3 % , e ) 33 1 / 2 %
Rationale: "the total number of mangoes bought by the shopkeeper be 12 . if he buys 4 a rupee , his cp = 3.5 he selling at 3.5 a rupee , his sp = 4 profit = sp - cp = 4 - 3.5 = 0.5 profit percent = 0.5 / 3.5 * 100 = 14.28 % answer : c"
Answer: c
Problem: solution a is made up of alcohol and water mixed in the ratio of 21 : 4 by volume ; solution b is made up of alcohol and water mixed in the ratio of 2 : 3 by volume . if solution a and solution b are mixed in the ratio of 5 : 6 by volume , what percent of the resultant mixture is alcohol ?
Options: a ) 32.5 % , b ) 40 % , c ) 60 % , d ) 65 % , e ) can not be determined
Rationale: let mixture after mixing a and b is 110 ml ( number assumed for calculation because of 5 : 6 ) now solution a is 50 ml and solu b is 60 ml further in a 100 ml a contains 84 ml alch so 50 ml contain 42 ml in mix b 100 ml solution contain 40 ml alc , 60 ml of b , it will be 24 ml alcohol . so 42 + 24 = 66 in 110 ml solution which is 60 % answer : c
Answer: c
Problem: at veridux corporation , there are 180 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 135 male associates , how many female managers are there ?
Options: a ) 95 , b ) 20 , c ) 85 , d ) 75 , e ) 35
Rationale: "well , first let â € ™ s take care of the â € œ totals â €  . the numbers in the â € œ totals â €  row must add up . if 90 are females , the other 180 â € “ 90 = 90 must be males . similarly , the numbers in the â € œ totals â €  column must add up . if 40 are managers , then the other 180 â € “ 40 = 140 must be associates . now , in the â € œ associate â €  row , 135 + e = 140 , which means e = 5 â € ” the other 5 associates must be female . now , to find b , which is what the question is asking , we need only look at the sum in the â € œ female â €  column : b + 5 = 90 , which means b = 85 . there are fifteen female managers in this company . thus , the answer = ( c ) ."
Answer: c
Problem: keats library purchases a number of new books , all in the category of biography , and the library does not acquire any other books . with the addition of the new biographies , the biography collection of the library amounts to 55 % of the total number of books in the library . if prior to the purchase , only 20 % of the books in keats library were biographies , by what percent has the number of biographies in the library increased ?
Options: a ) 270 % , b ) 310 % , c ) 350 % , d ) 390 % , e ) 430 %
Rationale: "let x be the number of new biographies added to the library . let b be the original number of biographies , so the original number of books was 5 b . 0.55 ( 5 b + x ) = b + x 1.75 b = 0.45 x x = 3.9 b the answer is d ."
Answer: d
Problem: after decreasing 24 % in the price of an article costs rs . 836 . find the actual cost of an article ?
Options: a ) 1667 , b ) 6789 , c ) 1200 , d ) 1100 , e ) 1421
Rationale: cp * ( 76 / 100 ) = 836 cp = 11 * 100 = > cp = 1100 answer : d
Answer: d
Problem: two isosceles triangles have equal vertical angles and their areas are in the ratio 16 : 36 . find the ratio of their corresponding heights .
Options: a ) 4 / 6 , b ) 5 / 4 , c ) 3 / 2 , d ) 5 / 7 , e ) 2 / 3
Rationale: "we are basically given that the triangles are similar . in two similar triangles , the ratio of their areas is the square of the ratio of their sides and also , the square of the ratio of their corresponding heights . therefore , area / area = height ^ 2 / height ^ 2 = 16 / 36 - - > height / height = 4 / 6 . answer : a ."
Answer: a
Problem: in a weight - lifting competition , the total weight of joe ' s two lifts was 1500 pounds . if twice the weight of his first lift was 300 pounds more than the weight of his second lift , what was the weight , in pounds , of his first lift ?
Options: a ) 225 , b ) 275 , c ) 325 , d ) 350 , e ) 600
Rationale: "this problem is a general word translation . we first define variables and then set up equations . we can define the following variables : f = the weight of the first lift s = the weight of the second lift we are given that the total weight of joe ' s two lifts was 1500 pounds . we sum the two variables to obtain : f + s = 1500 we are also given that twice the weight of his first lift was 300 pounds more than the weight of his second lift . we express this as : 2 f = 300 + s 2 f – 300 = s we can now plug in ( 2 f – 300 ) for s into the first equation , so we have : f + 2 f – 300 = 1500 3 f = 1,800 f = 600 answer is e ."
Answer: e
Problem: the cash realised on selling a 14 % stock is rs . 109.25 , brokerage being 1 / 4 % is
Options: a ) 123 , b ) 109 , c ) 100 , d ) 156 , e ) 240
Rationale: "explanation : cash realised = rs . ( 109.25 - 0.25 ) = rs . 109 . answer : b"
Answer: b
Problem: if 47.5 % of the 880 students at a certain college are enrolled in biology classes , how many students at the college are not enrolled in a biology class ?
Options: a ) 110 , b ) 330 , c ) 550 , d ) 462 , e ) 880
Rationale: "students enrolled in biology are 47.5 % and therefore not enrolled are 52.5 % . so of 880 is 880 * . 525 = 462 answer is d 462"
Answer: d
Problem: two ships are sailing in the sea on the two sides of a lighthouse . the angle of elevation of the top of the lighthouse is observed from the ships are 30 ° and 45 ° respectively . if the lighthouse is 100 m high , the distance between the two ships is :
Options: a ) 173 m , b ) 200 m , c ) 273 m , d ) 300 m , e ) 373 m
Rationale: let ab be the lighthouse and c and d be the positions of the ships . then , ab = 100 m , acb = 30 ° and adb = 45 ° . ab = tan 30 ° = 1 ac = ab x 3 = 1003 m . ac 3 ab = tan 45 ° = 1 ad = ab = 100 m . ad cd = ( ac + ad ) = ( 1003 + 100 ) m = 100 ( 3 + 1 ) = ( 100 x 2.73 ) m = 273 m . answer = c
Answer: c
Problem: a tank can supply water to a village for 80 days . if a leak at the bottom of the tank drains out 10 liters per day , the supply lasts for 60 days only . for how many days will the supply last if the leak drains out 20 liters per day ?
Options: a ) 42 , b ) 45 , c ) 48 , d ) 50 , e ) 55
Rationale: "losing 10 liters per day results in a loss of 600 liters in 60 days . so , those 600 liters were for 20 days , making daily consumption of the village 30 liters per day . thus the capacity of the tank is 30 * 80 = 2400 liters . losing 20 liters plus 30 liters gives 50 liters per day . at this rate the supply will last 2400 / 50 = 48 days . the answer is c ."
Answer: c
Problem: a can do a work in 25 days and b can do it in 10 days . in how many days a and b can do the work ?
Options: a ) 20 days , b ) 10 days , c ) 6 8 / 7 days , d ) 8 days , e ) 7 days
Rationale: "explanation : a ' s 1 day ' s work = 1 / 25 b ' s 1 day ' s work = 1 / 10 they work together = 1 / 25 + 1 / 10 = 7 / 50 = 50 / 7 = 6 8 / 7 days answer : option c"
Answer: c
Problem: a ' and ' b ' are positive integers such that their lcm is 20 and their hcf is 1 . what is the difference between the maximum and minimum possible values of ' a - b ' ?
Options: a ) 28 , b ) 29 , c ) 34 , d ) 38 , e ) 36
Rationale: possible values of a and b can be 54 ; 45 and 120 ; 201 maximum possible value for a - b is 20 - 1 = 19 minimum possible value for a - b is 1 - 20 = - 19 19 - ( - 19 ) = 38 ans is d
Answer: d
Problem: the size of a television screen is given as the length of the screen ' s diagonal . if the screens were flat , then the area of a square 18 - inch screen would be how many square inches greater than the area of a square 16 - inch screen ?
Options: a ) 2
b ) 4
c ) 34
d ) 38
e ) 40
Rationale: pythogoras will help here ! let the sides be x and diagonal be d then d ^ 2 = 2 x ^ 2 and area = x ^ 2 now plug in the given diagonal values to find x values and then subtract the areas ans will be 18 ^ 2 / 2 - 16 ^ 2 / 2 = 68 / 2 = 34 ans c .
Answer: c
Problem: an alloy weighing 24 ounces is 70 percent gold . how many ounces of pure gold must be added to create an alloy that is 80 percent gold ?
Options: a ) 6 , b ) 9 , c ) 12 , d ) 24 , e ) 48
Rationale: "in 24 ounces , gold is 24 * ( 70 / 100 ) = 16.8 ounces . now we add x ounces of pure gold to make it 90 % gold . so 16.8 + x = ( 24 + x ) * 80 / 100 = > x = 12 . answer is c ."
Answer: c
Problem: find the principle on a certain sum of money at 5 % per annum for 2 2 / 5 years if the amount being rs . 1456 ?
Options: a ) 1000 , b ) 2217 , c ) 2889 , d ) 2777 , e ) 1300
Rationale: "1456 = p [ 1 + ( 5 * 12 / 5 ) / 100 ] p = 1300 answer : e"
Answer: e
Problem: what is the 4 digit no . in which the 1 st digit is 1 / 3 of the second , the 3 rd is the sum of the 1 st and 2 nd , and the last is 3 times the second ?
Options: a ) 1123 , b ) 1234 , c ) 1349 , d ) 1455 , e ) 1567
Rationale: first digit is 1 / 3 second digit = > the numbers can be 1 & 3 , 2 & 6 , 3 & 9 . first + second = third = > we can eliminate 3 & 9 since 3 + 9 = 12 . last is 3 times the second = > we can eliminate option 2 & 6 since 3 * 6 = 18 . hence the number is 1349 c
Answer: c
Problem: what number is 76 more than one - fourth of itself ?
Options: a ) 101 , b ) 225 , c ) 304 , d ) 324 , e ) 336
Rationale: "1 / 4 x + 76 = x that means 76 = 3 / 4 x x = ( 76 * 4 ) / 3 = 304 / 3 = 101 a is the answer"
Answer: a
Problem: a certain shade of gray paint is obtained by mixing 3 parts of white paint with 5 parts of black paint . if 2 gallons of the mixture is needed and the individual colors can be purchased only in one gallon or half gallon cans , what is the least amount of paint w , in gallons , that must be purchased in order to measure out the portions needed for the mixture ?
Options: a ) 2 , b ) 2 1 / 2 , c ) 3 , d ) 3 1 / 2 , e ) 4
Rationale: "given w : b = 3 : 5 that means say 3 gallons of white paint + 5 gallons of black paint = 8 gallons of paint mixture . but we want least amount of whiteblack paints for minimum of 2 gallons of mixture , so lets reduce keeping same ratio , 1.5 : 2.5 gives 1.5 + 2.5 = 4 gallons of mixture , but we want only 2 gallons , lets further reduce 0.75 : 1.25 gives 1 + 1.5 = 2.5 gallons of mixture . this looks ok , but lets reduce further just to be sure 0.375 : 0.625 gives 0.5 + 1 = 1.5 gallons of mixture , thats less than 2 gallons of mixture , so not acceptable . so correct ans is 2.5 gallons . b"
Answer: b
Problem: someone on a skateboard is traveling 15 miles per hour . how many feet does she travel in 30 seconds ? ( 1 mile = 5280 feet )
Options: a ) 600 ft , b ) 660 ft , c ) 670 ft , d ) 680 ft , e ) 700 ft
Rationale: "per second = > 15 * 5280 ft / 60 * 60 = 22 ft 30 seconds = > 22 * 30 = 660 ft answer : b"
Answer: b
Problem: a company produces 72000 bottles of water everyday . if a case can hold 10 bottles of water . how many cases are required by the company to hold its one day production
Options: a ) 2000 , b ) 4500 , c ) 5000 , d ) 7200 , e ) 9000
Rationale: "number of bottles that can be held in a case = 10 number of cases required to hold 72000 bottles = 72000 / 10 = 7200 cases . so the answer is d = 7200"
Answer: d
Problem: the sum of 99 consecutive integers is 9999 . what is the greatest integer in the set ?
Options: a ) 100 , b ) 120 , c ) 149 , d ) 150 , e ) 151
Rationale: "sum of n numbers = ( n ( 2 a + ( n - 1 ) d ) ) / 2 where n = no of terms a = 1 st term , d - difference between two terms ( ie d = a 2 - a 1 ) here sum = 9999 , n = 99 d = 1 ( since consecutive numbers ) 9999 = ( 99 / 2 ) * ( 2 a + ( 99 - 1 ) 1 ) from this ' a ' ( ie the 1 st term ) = 52 nth term in a sequence : nth term = a + ( n - 1 ) d here a = 52 , n = 99 , d = 1 so nth term = 52 + ( 99 - 1 ) * 1 therefore nth term = 150 answer : d"
Answer: d
Problem: a train of 24 carriages , each of 60 meters length , when an engine also of 60 meters length is running at a speed of 60 kmph . in what time will the train cross a bridge 3.5 km long ?
Options: a ) 4 , b ) 3 , c ) 5 , d ) 7 , e ) 9
Rationale: "d = 25 * 60 + 3500 = 5000 m t = 5000 / 60 * 18 / 5 = 300 sec = 5 mins answer : c"
Answer: c
Problem: the tax on a commodity is diminished by 20 % and its consumption increased by 15 % . the effect on revenue is ?
Options: a ) 9 % decrease , b ) 8 % decrease , c ) 6 % decrease , d ) 1 % decrease , e ) 2 % decrease
Rationale: "100 * 100 = 10000 80 * 115 = 9200 - - - - - - - - - - - 10000 - - - - - - - - - - - 800 100 - - - - - - - - - - - ? = > 8 % decrease answer : b"
Answer: b
Problem: the length of a rectangular floor is more than its breadth by 200 % . if rs . 484 is required to paint the floor at the rate of rs . 3 / sq m , what would be the length of the floor ?
Options: a ) 12 , b ) 18 , c ) 20 , d ) 22 , e ) 24
Rationale: "let the length and the breadth of the floor be l m and b m respectively . l = b + 200 % of b = l + 2 b = 3 b area of the floor = 484 / 3 = 161.33 sq m l b = 161.33 i . e . , l * l / 3 = 161.33 l ^ 2 = 484 = > l = 22 . d"
Answer: d
Problem: a train running at the speed of 50 km / hr crosses a pole in 9 seconds . find the length of the train ?
Options: a ) 125 , b ) 272 , c ) 278 , d ) 277 , e ) 112
Rationale: "speed = 50 * ( 5 / 18 ) m / sec = 125 / 9 m / sec length of train ( distance ) = speed * time ( 125 / 9 ) * 9 = 125 meter answer : a"
Answer: a
Problem: the expression x # y denotes the product of the consecutive multiples of 3 between x and y , inclusive . what is the sum of the exponents in the prime factorization of 21 # 33 ?
Options: a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16
Rationale: "first , let ' s translate the expression 21 # 33 , using the definition given : 21 # 33 = 21 × 24 × 27 × 30 × 33 we need the prime factorization of this product . let ' s factor out 3 from each multiple . 21 # 33 = 3 ^ 6 ( 7 × 8 × 9 × 10 × 11 ) now let ' s replace each consecutive integer with its prime factorization : 21 # 33 = 3 ^ 5 ( 7 × 2 ^ 3 × 3 ^ 2 × ( 2 × 5 ) × 11 ) let ' s group the prime bases : 21 # 33 = 2 ^ 4 × 3 ^ 7 × 5 × 7 × 11 the sum of the exponents is 4 + 7 + 1 + 1 + 1 = 14 the answer is c ."
Answer: c
Problem: after decreasing 20 % in the price of an article costs rs . 620 . find the actual cost of an article ?
Options: a ) 775 , b ) 620 , c ) 750 , d ) 800 , e ) 720
Rationale: "cp * ( 80 / 100 ) = 620 cp = 7.75 * 100 = > cp = 775 answer : a"
Answer: a
Problem: 90 % of the population of a village is 23040 . the total population of the village is ?
Options: a ) 32256 , b ) 24000 , c ) 24936 , d ) 25600 , e ) none
Rationale: "answer ∵ 90 % of p = 23040 ∴ p = ( 23040 x 100 ) / 90 = 25600 correct option : d"
Answer: d
Problem: if y is the smallest positive integer such that 8,820 multiplied by y is the square of an integer , then y must be
Options: a ) 2 , b ) 5 , c ) 6 , d ) 7 , e ) 14
Rationale: "i just tried plugging in the numbers and found out that 5 * 8820 = 44 , 100 , which is a square of 210 b"
Answer: b
Problem: a train 100 m long crosses a platform 125 m long in 40 sec ; find the speed of the train ?
Options: a ) 36.21 , b ) 77.11 , c ) 54.12 , d ) 33.0 , e ) 20.25
Rationale: "d = 100 + 125 = 225 t = 40 s = 225 / 40 * 18 / 5 = 20.25 kmph answer : e"
Answer: e
Problem: a group of men decided to do a work in 15 days , but 8 of them became absent . if the rest of the group did the work in 18 days , find the original number of men ?
Options: a ) 15 , b ) 48 , c ) 54 , d ) 33 , e ) 45
Rationale: "original number of men = 8 * 18 / ( 18 - 15 ) = 48 answer is b"
Answer: b
Problem: x , y , and z are all unique numbers . if x is chosen randomly from the set { 5 , 6 , 7 , 8 , 9 , 10 , 11 } and y and z are chosen randomly from the set { 20 , 21 , 22 , 23 } , what is the probability that x and y are prime and z is not ?
Options: a ) 1 / 5 , b ) 3 / 20 , c ) 1 / 7 , d ) 2 / 15 , e ) 3 / 28
Rationale: "p ( x is prime ) = 3 / 7 p ( y is prime ) = 1 / 4 if y is prime , then z is not prime since y and z are unique . then the probability is 3 / 7 * 1 / 4 = 3 / 28 the answer is e ."
Answer: e
Problem: a and b can do a piece of work in 2 days , b and c in 3 days , c and a in 4 days . how long will c take to do it ?
Options: a ) 14 days , b ) 20 days , c ) 22 days , d ) 24 days , e ) 26 days
Rationale: "2 c = 1 / 3 + 1 / 4 – 1 / 2 = 1 / 12 c = 1 / 24 = > 24 days answer : d"
Answer: d
Problem: a tourist does not have to pay tax on the first $ 600 of goods he purchases in country b , but does have to pay a 12 percent tax on the portion of the total value that is in excess of $ 600 . what tax must be paid by a tourist if he buys goods with a total value of $ 1720 ?
Options: a ) $ 54.00 , b ) $ 64.80 , c ) $ 90.00 , d ) $ 100.80 , e ) $ 134.40
Rationale: "correct answer : e the tourist must pay tax on $ 1720 - $ 600 = $ 1120 . thus , the amount of tax he has to pay is 0.12 ( $ 1120 ) = $ 134.40 . the correct answer is e ."
Answer: e
Problem: the area of one square is x ^ 2 + 10 x + 25 and the area of another square is 4 x ^ 2 − 20 x + 25 . if the sum of the perimeters of both squares is 36 , what is the value of x ?
Options: a ) 3 , b ) 5 , c ) 7 , d ) 9 , e ) 11
Rationale: "the areas are ( x + 5 ) ^ 2 and ( 2 x - 5 ) ^ 2 . the lengths of the sides are x + 5 and 2 x - 5 . if we add the two perimeters : 4 ( x + 5 ) + 4 ( 2 x - 5 ) = 36 12 x = 36 x = 3 the answer is a ."
Answer: a
Problem: when magnified 1000 times by an electron microscope , the image of a certain circular piece of tissue has a diameter of 0.3 centimeter . the actual diameter of the tissue , in centimeters , is
Options: a ) 0.005 , b ) 0.002 , c ) 0.001 , d ) 0.0003 , e ) 0.0002
Rationale: it is very easy if x is the diameter , then the magnified length is 1000 x . ince 1000 x = 0.3 then x = 0.3 / 1000 = 0.0003 . the answer is d
Answer: d
Problem: a group of n students can be divided into equal groups of 4 with 3 student left over or equal groups of 5 with 3 students left over . what is the sum of the two smallest possible values of n ?
Options: a ) 66 , b ) 46 , c ) 49 , d ) 53 , e ) 86
Rationale: "4 x + 3 = 5 y + 3 . . . . . . . . . . . ie : 4 x - 5 y = 0 x , y must be > 1 and y is even ie ( 2 , 4,6 , . . etc ) if y = 2 thus x = fraction ( not possible ) if y = 4 thus x = 5 n = 23 if y = 6 thus x = not possible fraction if y = 8 thus x = 10 n = 43 23 + 43 = 66 . . . . . a"
Answer: a
Problem: a 600 meter long train crosses a signal post in 40 seconds . how long will it take to cross a 9 kilometer long bridge , at the same speed ?
Options: a ) 4 min , b ) 2 min , c ) 10 min , d ) 9 min , e ) 3 min
Rationale: "s = 600 / 40 = 15 mps s = 9000 / 15 = 600 sec = 10 min . answer : c"
Answer: c
Problem: q - 1 : how many two digit numbers of distinct digits can be formed by using digits 1 , 2 , 3 , 4 , 5 , 6 and 7 such that the numbers are divisible by 5 ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "6 two digit numbers divisible by 5 must end in either 0 or 5 . since there is no 0 , all correct answers are a combination of the other digits and 5 . there are six other numbers plus the 5 so there are 6 correct answers . correct answer is d ."
Answer: d
Problem: a car travels at a speed of 65 miles per hour . how far will it travel in 9 hours ?
Options: a ) 125 miles , b ) 225 miles , c ) 585 miles , d ) 425 miles , e ) 525 miles
Rationale: "during each hour , the car travels 65 miles . for 9 hours it will travel 65 + 65 + 65 + 65 + 65 + 65 + 65 + 65 + 65 = 9 × 65 = 585 miles correct answer is c ) 585 miles"
Answer: c
Problem: how many of the integers between 45 and 105 are even ?
Options: a ) 21 , b ) 30 , c ) 11 , d ) 10 , e ) 9
Rationale: "number start between 45 to 105 is 60 numbers half of them is even . . which is 30 answer : b"
Answer: b
Problem: yearly subscription to professional magazines cost a company $ 940.00 . to make a 50 % cut in the magazine budget , how much less must be spent ?
Options: a ) 654 , b ) 655 , c ) 656 , d ) 657 , e ) 470
Rationale: "total cost 940 940 * 50 / 100 = 470 so the cut in amount is 470 the less amount to be spend is 940 - 470 = 470 answer : e"
Answer: e
Problem: price of a book increases 15 % successively ( 2 times ) what is the new price of the book more compared to that of the old price :
Options: a ) 32.25 % , b ) 23.34 % , c ) 36 % , d ) 39 % , e ) 29 %
Rationale: new price is 1.15 * 1.15 * old price = 1.3225 * old price increase in price = 0.3225 * old price % increase = 100 * 0.3225 * old price / old price = 32.25 % answer : a
Answer: a
Problem: there are 7 fictions and 6 non - fictions . how many cases are there such that 2 fictions and 2 non - fictions are selected from them ?
Options: a ) 90 , b ) 120 , c ) 315 , d ) 180 , e ) 200
Rationale: "number of ways of selecting 2 fiction books = 7 c 2 number of ways of selecting 2 non fiction books = 6 c 2 7 c 2 * 6 c 2 = 21 * 15 = 315 answer : c"
Answer: c