regisss/math_qa huggingface dataset:
Problem: if 9 a - b = 10 b + 50 = - 12 b - 2 a , what is the value of 11 a + 11 b ?
Options: a ) - 4 , b ) - 2 , c ) 0 , d ) 2 , e ) 4
Rationale: this implies 9 a - b = 10 b + 50 , 9 a - b = - 12 b - 2 a , 10 b + 50 = - 12 b - 2 a manipulating the second equation gives us 9 a - b = - 12 b - 2 a = = > 11 a + 11 b = 0 answer is c
Answer: c
Problem: the current of a stream runs at the rate of 4 kmph . a boat goes 6 km and back to the starting point in 2 hours , then find the speed of the boat in still water ?
Options: a ) 5 , b ) 6 , c ) 8 , d ) 4 , e ) 1
Rationale: s = 4 m = x ds = x + 4 us = x - 4 6 / ( x + 4 ) + 6 / ( x - 4 ) = 2 x = 8 answer : c
Answer: c
Problem: cathy and jim begin running at the same time and they start at the same place on a straight path . cathy runs at 10 miles per hour , and jim runs at 6 miles per hour . after 18 minutes , cathy stops to stretch . if it takes cathy 27 minutes to stretch and jim continues to run during this time , how many minutes will it take cathy to catch up to jim ?
Options: a ) 20.5 , b ) 21.5 , c ) 22.5 , d ) 23.5 , e ) 24.5
Rationale: in 18 minutes , cathy runs 3 miles . in 45 minutes , jim runs 4.5 miles . cathy can catch jim at a rate of 4 miles per hour . since jim is ahead by 1.5 miles , it will take cathy 1.5 / 4 hours = 22.5 minutes to catch jim . the answer is c .
Answer: c
Problem: the speed of a car is 65 km in the first hour and 45 km in the second hour . what is the average speed of the car ?
Options: a ) 72 kmph , b ) 55 kmph , c ) 50 kmph , d ) 80 kmph , e ) 82 kmph
Rationale: "s = ( 65 + 45 ) / 2 = 55 kmph answer : b"
Answer: b
Problem: set x consists of all two - digit primes and set y consists of all positive multiples of 4 less than 100 . if the two sets are combined into one , what will be the range of the new set ?
Options: a ) 84 , b ) 93 , c ) 90 , d ) 92 , e ) 95
Rationale: "set x = { 11 , 13 , 17 , . . . . . . . . . . . . . , 83 , 89 , 97 } set y = { 4 , 8 , 12 , . . . . . . . . . . . . . . . , 88 , 92 , 96 } combining two sets , say set z set z = { 4,8 , 11 , 12,13 , 17 , . . . . . . . . . . . . . . . . . . . , 83 , 88 , 89 , 92 , 96 , 97 } range = max value - min value range ( z ) = 97 - 4 = 93 oa b is the answer ."
Answer: b
Problem: car z travels 50 miles per gallon of gasoline when driven at a constant rate of 45 miles per hour , but travels 20 percent fewer miles per gallon of gasoline when driven at a constant rate of 60 miles per hour . how many miles does car z travel on 10 gallons of gasoline when driven at a constant rate of 60 miles per hour ?
Options: a ) 320 , b ) 375.2 , c ) 400 , d ) 408.3 , e ) 440
Rationale: "the question stem asks us for the distance possible with 10 gallons of fuel at a constant speed of 60 miles per hour . we therefore first calculate the fuel efficiency at that speed . the stem tells us that at 50 miles / hour , the car will run 40 miles / gallon and at 60 miles / hour , that distance decreases by 20 % . we can therefore conclude that the car will travel 40 miles / gallon at a constant speed of 60 miles / gallon . with 10 gallons of fuel , the car can therefore travel 40 miles / gallon * 10 gallons = 400 miles . answer c ."
Answer: c
Problem: 30 % of employees are women with fair hair . 40 % of fair - haired employees are women . what percent of employees have fair hair ?
Options: a ) 25 , b ) 30 , c ) 50 , d ) 55 , e ) 75
Rationale: "i came up with ( e ) 75 think of 100 people total : from the first fact , 30 of these are women with fair hair . from the second fact , these 20 women make up 40 % of the total fair haired population . we can then make a ratio of 60 : 40 fair haired men to fair haired women . this means that ( 60 / 40 ) * 30 equals the number of fair haired men , which is 45 men with fair hair . add this 45 to the 30 women and get 75 fair haired men and women out of 100 total men and women . 75 % e"
Answer: e
Problem: the mean daily profit made by a shopkeeper in a month of 30 days was rs . 350 . if the mean profit for the first fifteen days was rs . 255 , then the mean profit for the last 15 days would be
Options: a ) rs . 200 , b ) rs . 445 , c ) rs . 275 , d ) rs . 425 , e ) none of these
Rationale: "average would be : 350 = ( 255 + x ) / 2 on solving , x = 445 . answer : b"
Answer: b
Problem: a rectangle the length of which is 8 inches and the width of which is 6 inches is made up 48 1 inch by 1 inch squares . through how many of the squares does a diagonal of the rectangle pass ?
Options: a ) 6
b ) 8
c ) 10
d ) 12
e ) 16
Rationale: 1 ) if the two sides are co - prime , sum of sides - 1 . . 2 ) and if not co - prime , sum of sides - hcf of sides . . the difference is related to the diagonal passing through a vertex of squares at some place . . here 6 and 8 are not co - primes , so ans = 6 + 8 − hcf ( 6,8 ) = 14 − 2 = 12 answer : d
Answer: d
Problem: if x + y = 3 and x 2 y 3 + y 2 x 3 = 27 , what is the value of xy ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "xy = 3 as x + y = 3 x 2 y 3 + y 2 x 3 = 27 x 2 y 2 ( y + x ) = 27 substituting x + y x 2 y 2 = 9 xy = 3 answer : c"
Answer: c
Problem: the balance of a trader weighs 10 % less than it should . still the trader marks up his goods to get an overall profit of 20 % . what is the mark up on the cost price ?
Options: a ) 40 % , b ) 8 % , c ) 25 % , d ) 16.66 % , e ) 9 %
Rationale: "original cost before weight adjustment : x cost after 90 % weight adjustment : 9 / 10 x 20 % profit on 9 / 10 x : ( 120 / 100 ) ( 9 / 10 ) ( x ) or 108 x / 100 mark up on original cost of x : ( 108 x / 100 ) / x - 1 = 8 / 100 answer : b"
Answer: b
Problem: water is leaking out from a cylinder container at the rate of 0.31 m ^ 3 per minute . after 10 minutes , the water level decreases 16 meters . what is value of the radius in meters ?
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 1 / 6 , e ) 1 / 8
Rationale: "10 * 0.31 = 3.1 = pi * r ^ 2 * h r ^ 2 = 3.1 / ( pi * 16 ) which is about 1 / 16 r = 1 / 4 the answer is c ."
Answer: c
Problem: working together , wayne and his son can shovel the entire driveway in three hours . if wayne can shovel six times as fast as his son can , how many hours would it take for his son to shovel the entire driveway on his own ?
Options: a ) 4 , b ) 6 , c ) 8 , d ) 7 , e ) 12
Rationale: "w : the time for wyane to do the job s : the time for his son to do the job we have 1 / w + 1 / s = 1 / 6 and w = 6 s then we have 1 / ( 6 * s ) + 1 / s = 1 / 6 < = > 7 / ( 6 * s ) = 1 / 6 < = > s = 7 ans : d"
Answer: d
Problem: a 600 meter long train crosses a signal post in 40 seconds . how long will it take to cross a 7.2 kilometer long bridge , at the same speed ?
Options: a ) 4 min , b ) 2 min , c ) 8 min , d ) 9 min , e ) 3 min
Rationale: "s = 600 / 40 = 15 mps s = 7200 / 15 = 480 sec = 8 min . answer : c"
Answer: c
Problem: a bag contains 6 black and 7 white balls . one ball is drawn at random . what is the probability that the ball drawn is white ?
Options: a ) 4 , b ) 4 / 3 , c ) 4 / 5 , d ) 4 / 9 , e ) 7 / 13
Rationale: "let number of balls = ( 6 + 7 ) = 13 . number of white balls = 7 . p ( drawing a white ball ) = 7 / 13 hence answer is e"
Answer: e
Problem: a car traveling at a certain constant speed takes 2 seconds longer to travel 1 kilometer than it would take to travel 1 kilometer at 100 kilometers per hour . at what speed , in kilometers per hour , is the car traveling ?
Options: a ) 71.5 , b ) 72 , c ) 72.5 , d ) 73 , e ) 94.7
Rationale: "many approaches are possible , one of them : let the distance be 1 kilometer . time to cover this distance at 100 kilometers per hour is 1 / 100 hours = 3,600 / 100 seconds = 36 seconds ; time to cover this distance at regular speed is 36 + 2 = 38 seconds = 38 / 3,600 hours = 4 / 379 hours ; so , we get that to cover 1 kilometer 1 / ( 4 / 379 ) hours is needed - - > regular speed 94.7 kilometers per hour ( rate is a reciprocal of time or rate = distance / time ) . answer : e ."
Answer: e
Problem: how many multiples of 4 are there between 4 and 64 ?
Options: a ) 12 , b ) 64 , c ) 14 , d ) 16 , e ) 60
Rationale: "it should be mentioned whether 4 and 64 are inclusive . if 4 and 64 are inclusive , then the answer is ( 64 - 4 ) / 4 + 1 = 16 . if 4 and 64 are not inclusive , then the answer is ( 60 - 8 ) / 4 + 1 = 14 . since oa is c , then we have not inclusive case ."
Answer: c
Problem: points a , b , c , and d , in that order , lie on a line . if ab = 3 cm , ac = 4 cm , and bd = 8 cm , what is cd , in centimeters ?
Options: a ) 7 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "putting a value to each point , lets use the following : a - 0 b - 3 ( ab = 3 ) c - 4 ( ac = 4 ) d - 11 ( bd = 8 ) cd is 11 - 4 = 7 . ans a"
Answer: a
Problem: a can do a piece of work in 5 hours ; b and c together can do it in 3 hours , while a and c together can do it in 2 hours . how long will b alone take to do it ?
Options: a ) 30 , b ) 20 , c ) 10 , d ) 6 , e ) 5
Rationale: "a ' s 1 hour ' s work = 1 / 5 ; ( b + c ) ' s 1 hour ' s work = 1 / 3 ; ( a + c ) ' s 1 hour ' s work = 1 / 2 . ( a + b + c ) ' s 1 hour ' s work = ( 1 / 5 + 1 / 3 ) = 8 / 15 . b ' s 1 hour ' s work = ( 8 / 15 - 1 / 2 ) = 1 / 30 . therefore a alone will take 30 hours to do the work . a"
Answer: a
Problem: there is a 10 % chance that tigers will not win at all during the whole season . there is a 20 % chance that federer will not play at all in the whole season . what is the greatest possible probability that the tigers will win and federer will play during the season ?
Options: a ) 55 % , b ) 60 % , c ) 70 % , d ) 72 % , e ) 80 %
Rationale: "there is a 10 % chance that tigers will not win at all during the whole season we can infer that there is 90 % chance tigers will win . similarly there is a 20 % chance that federer will not play at all in the whole season we can also infer that there is 80 % chance that federer will play . answer e"
Answer: e
Problem: lally ' s internet provider offers unlimited traffic which costs $ 0.5 per day charged off at 12 a . m . the service is discontinued when client ' s debt exceeds $ 5 . if today in the morning lally makes a payment of $ 7 , for how many days , including today , will she be connected to the internet without any additional payments , given her initial balance was $ 0 ?
Options: a ) 15 , b ) 24 , c ) 25 , d ) 26 , e ) 13
Rationale: day 0 - payment of $ 7 is made in the morning ( after 12 am midnight ) day 1 onwards ( after 12 am midnight ) internet service will begin and will run for 7 * 2 = 14 days i . e . at the end of day 15 balance will be zero . now lally can still use the internet till her debt reaches $ 5 which means total of 5 * 2 = 10 days . now the question states for how many days , including today , will she be connected to the internet without any additional payments i . e . we will have to include day 0 also in our final answer . therefore total no . of days = 1 + 14 + 10 = 25 = c
Answer: c
Problem: a retailer bought a machine at a wholesale price of $ 108 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 of the machine ?
Options: a ) 81 , b ) 100 , c ) 120 , d ) 135 , e ) 144
Rationale: "my solution : wholesale price = 108 retail price , be = x he provides 10 % discount on retail price = x - 10 x / 100 this retail price = 20 % profit on wholesale price x - 10 x / 100 = 108 + 1 / 5 ( 108 ) x = 144 ; answer : e"
Answer: e
Problem: if n is the smallest integer such that 72 times n is the square of an integer , what is the value of n ?
Options: a ) 2 , b ) 3 , c ) 6 , d ) 12 , e ) 24
Rationale: "72 can written as = 2 * 2 * 2 * 3 * 3 - - > 2 ^ 3 * 3 ^ 2 - - - ( 1 ) so for 72 * n to be a square of an integer , the integer should have even powers to the prime numbers it composed of . here 2 already has even power - > so n has to be 3 to make the power of 2 in ( 1 ) even option a is correct"
Answer: a
Problem: in one day , juan sends keith 8 times as many messages as he sends laurence , and laurence sends missy 4.5 times as many messages as he receives from juan . if missy received 18 messages from laurence , how many messages does keith receive from juan ?
Options: a ) 13 , b ) 26 , c ) 32 , d ) 48 , e ) 56
Rationale: juan - - > laurence = x messages ; juan - - > keith = 8 x messages ( juan sends keith eight times as many messages as he sends laurence ) ; laurence - - > missy = 4.5 x = 18 ( laurence sends missy 4.5 times as many messages as he receives from juan ) . 4.5 x = 18 - - > x = 4 - - > 8 x = 32 . answer : c .
Answer: c
Problem: the area of a triangle will be when a = 1 m , b = 2 m , c = 3 m , a , b , c being lengths of respective sides .
Options: a ) 0 sq m
b ) 7 sq m
c ) 2 sq m
d ) 3 sq m
e ) 6 sq m
Rationale: s = ( 1 + 2 + 3 ) / 2 = 3 = > no triangle exists answer : a
Answer: a
Problem: edward earns $ 7.00 per hour for the first 40 hours he works per week , and twice this rate for overtime . if michael earned $ 210 last week , how many hours did he work ?
Options: a ) 43 , b ) 44 , c ) 45 , d ) 46 , e ) 47
Rationale: $ 7 * 40 + $ 12 * x = $ 210 - - > x = 5 hours . total working hours = 40 + 5 = 45 answer : c .
Answer: c
Problem: i bought two books ; for rs . 470 . i sold one at a loss of 15 % and other at a gain of 19 % and then i found each book was sold at the same price . find the cost of the book sold at a loss ?
Options: a ) 274.17 , b ) 280.17 , c ) 299.17 , d ) 266.17 , e ) 279.17
Rationale: "x * ( 85 / 100 ) = ( 470 - x ) 119 / 100 x = 274.17 answer : a"
Answer: a
Problem: 18 women can complete a work in 7 days and 10 children take 14 days to complete the work . how many days will 5 women and 10 children take to complete the work ?
Options: a ) 8 days , b ) 6 days , c ) 7 days , d ) 9 days , e ) 1 days
Rationale: "1 women ' s 1 day work = 1 / 126 1 child ' s 1 day work = 1 / 140 ( 5 women + 10 children ) ' s 1 day work = ( 5 / 126 + 10 / 140 ) = 1 / 9 5 women and 10 children will complete the work in 9 days . answer : d"
Answer: d
Problem: when positive integer x is divided by positive integer y , the remainder is 9 . if x / y = 96.45 , what is the value of y ?
Options: a ) 96 , b ) 75 , c ) 48 , d ) 20 , e ) 12
Rationale: "guys , one more simple funda . 5 / 2 = 2.5 now . 5 x 2 = 1 is the remainder 25 / 4 = 6.25 now . 25 x 4 = 1 is the remainder 32 / 5 = 6.4 now . 4 x 5 = 2 is the remainder given x / y = 96.45 and remainder is 9 so . 45 x y = 9 hence y = 20 ans d"
Answer: d
Problem: an employee ’ s annual salary was increased $ 5000 . if her new annual salary now equals $ 25000 what was the percent increase ?
Options: a ) 15 % , b ) 80 % , c ) 20 % , d ) 22 % , e ) 24 %
Rationale: new annual salary = $ 25000 salary increase = $ 5000 . original salary = $ 25000 - $ 5000 . = $ 20000 % increase = ( $ 15000 / $ 75000 ) * 100 = 80 % hence b .
Answer: b
Problem: it takes avery 3 hours to build a brick wall while tom can do it in 4 hours . if the two start working together and after an hour avery leaves , how much time will it take tom to complete the wall on his own ?
Options: a ) 25 minutes . , b ) 55 minutes . , c ) 1 hour and 41 minutes , d ) 1 hour and 35 minutes , e ) 1 hour and 20 minutes
Rationale: "avery ' s efficiency is 100 / 3 = 33 % tom ' s = 100 / 4 = 25 % they worked together for 1 hour and finished 58 % of the job remaining = 42 % tom will complete 25 % in 60 minutes , and 17 % in 60 * 17 / 25 minutes = 40.8 minutes time taken by tom to finish the remaining on his own = 60 + 40.8 = 100.8 minutes ( adjusting for 0.2 ) ~ 101 minutes answer : c"
Answer: c
Problem: of the 200 employees in a certain company , 30 percent will be relocated to city x and the remaining 70 percent will be relocated to city y . however , 40 percent of the employees prefer city y and 60 percent prefer city x . what is the highest possible number of employees who will be relocated to the city they prefer ?
Options: a ) 115 , b ) 120 , c ) 140 , d ) 152 , e ) 165
Rationale: 120 prefer x ( group 1 ) ; 80 prefer y ( group 2 ) . city y needs 140 people : letall 80 who prefer y ( entire group 2 ) be relocated there , the rest 60 will be those who prefer x from group 1 ; city x needs 60 people : 120 - 60 = 60 from group 1 will be relocated to x , which they prefer . so , the highest possible number of employees who will be relocated to the city they prefer is 80 + 60 = 140 . answer : c .
Answer: c
Problem: the arithmetic mean and standard deviation of a certain normal distribution are 14.5 and 1.7 , respectively . what value is exactly 2 standard deviations less than the mean ?
Options: a ) 10.5 , b ) 11 , c ) 11.1 , d ) 12 , e ) 12.5
Rationale: "mean = 14.5 two standard deviations is 1.7 + 1.7 = 3.4 there could be two calues for this . mean + two standard deviations = 17.9 mean - two standard deviations = 11.1 answer choice has 11.1 and so c is the answer ."
Answer: c
Problem: divide rs . 1700 among a , b and c so that a receives 1 / 3 as much as b and c together and b receives 2 / 3 as a and c together . a ' s share is ?
Options: a ) 346 , b ) 425 , c ) 375 , d ) 337 , e ) 639
Rationale: "a + b + c = 1700 a = 1 / 3 ( b + c ) ; b = 2 / 3 ( a + c ) a / ( b + c ) = 1 / 3 a = 1 / 4 * 1700 = > 425 answer : b"
Answer: b
Problem: the sector of a circle has radius of 24 cm and central angle 135 o . find its perimeter ?
Options: a ) 91.5 cm , b ) 11.5 cm , c ) 104.6 cm , d ) 92.5 cm , e ) 99.5 cm
Rationale: "perimeter of the sector = length of the arc + 2 ( radius ) = ( 135 / 360 * 2 * 22 / 7 * 24 ) + 2 ( 24 ) = 56.6 + 48 = 104.6 cm answer : c"
Answer: c
Problem: what is the x - intercept of a line that passes through the point ( 3 , 4 ) and has a slope of 2 ?
Options: a ) - 2 , b ) - 1 , c ) 0 , d ) 1 , e ) 2
Rationale: first , plot the point ( 3 , 4 ) on a graph . a slope of 2 means “ up 2 , over 1 , ” so plot this point on a graph , too . here ’ s the resulting graph : y over 1 up 2 ( 1 , 0 ) ( 2 , 2 ) ( 3 , 4 ) ( 4 , 6 ) x the line passes through the x - axis at 1 , making the correct answer d ) 1
Answer: d
Problem: raja spends 35 % of his monthly income on household items , 20 % of his monthly income on buying cloths , 5 % of his monthly income on medicines and saves the remaining amount which is rs . 15000 . find his monthly income .
Options: a ) rs . 40000 , b ) rs . 36000 , c ) rs . 37500 , d ) rs . 45000 , e ) none of these
Rationale: savings 40 % - 15000 expenditure 60 % - 22500 total - 37500 answer : c
Answer: c
Problem: what least number should be subtracted from 13600 such that the remainder is divisible by 87 ?
Options: a ) 27 , b ) 29 , c ) 28 , d ) 30 , e ) 31
Rationale: "13600 ÷ 87 = 156 , remainder = 28 hence 28 is the least number which can be subtracted from 13600 such that the remainder is divisible by 87 answer is c"
Answer: c
Problem: four bells commence tolling together and toll at intervals of 2 , 4 , 6 , 8 seconds respectively . in 18 minutes , how many times do they toll together ?
Options: a ) 43 , b ) 44 , c ) 45 , d ) 46 , e ) 47
Rationale: "lcm of 2 , 4 , 6 , 8 is 24 . so , after each 24 seconds , they would toll together . hence , in 18 minutes , they would toll 18 * 60 seconds / 24 seconds = 45 times but then the question says they commence tolling together . so , they basically also toll at thebeginning ( 0 second ) . so , total tolls together = 45 + 1 = 46 answer c"
Answer: c
Problem: what percent of 150 is 40 ?
Options: a ) 0.25 % , b ) 26.67 % , c ) 25 % , d ) 40 % , e ) 250 %
Rationale: "150 * x / 100 = 40 x = 2 * 40 / 3 x = 26.67 ans : b"
Answer: b
Problem: list k consists of 12 consecutive integers . if - 5 is the least integer in list k , what is the range of the positive integers in list k ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 11 , e ) 12
Rationale: "answer = a = 5 if least = - 5 , then largest = 6 range = 6 - 1 = 5"
Answer: a
Problem: a dishonest dealer professes to sell goods at the cost price but uses a weight of 920 grams per kg , what is his percent ?
Options: a ) 22 % , b ) 25 % , c ) 77 % , d ) 99 % , e ) 8.7 %
Rationale: "920 - - - 80 100 - - - ? = > 8.7 % answer : e"
Answer: e
Problem: a man cheats while buying as well as while selling . while buying he takes 10 % more than what he pays for and while selling he gives 20 % less than what he claims to . find the profit percent , if he sells at 10 % below the cost price of the claimed weight .
Options: a ) 19.81 % , b ) 20 % , c ) 37.5 % , d ) 23.75 % , e ) 37.5 %
Rationale: "there is a one step calculation method too . it requires more thought but is faster . the man takes 10 % more than what he pays for . so if he claims to take 100 pounds , he pays $ 100 but he actually takes 110 pounds for which he will take from the customer $ 110 . hence , in effect , there is a 10 % mark up . while selling , he sells 20 % less . this means , he claims to sell 100 pounds and gets $ 100 but actually sells only 80 pounds and should have got only $ 80 for it . so this is again a mark up of $ 20 on $ 80 which is 25 % . but he also sells at 10 % less ( 1 + m 1 % ) ( 1 + m 2 % ) ( 1 - d % ) = ( 1 + p % ) 11 / 10 * 5 / 4 * 9 / 10 = ( 1 + p % ) profit % = 23.75 % d"
Answer: d
Problem: a case contains c cartons . each carton contains b boxes , and each box contains 600 paper clips . how many paper clips are contained in 2 cases ?
Options: a ) 600 bc , b ) 600 b / c , c ) 1200 bc , d ) 1200 b / c , e ) 1200 / bc
Rationale: 2 cases * c cartons / case * b boxes / carton * 600 clips / box = 1200 bc paper clips the answer is c .
Answer: c
Problem: an army ’ s recruitment process included n rounds of selection tasks . for the first a rounds , the rejection percentage was 60 percent per round . for the next b rounds , the rejection percentage was 50 percent per round and for the remaining rounds , the selection percentage was 70 percent per round . if there were 10000 people who applied for the army and 350 were finally selected , what was the value of n ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 9 , e ) 8
Rationale: "fastly i reduce 60 % till it gets closer to our required 2000 candidates step ( 1 ) 40000 accepted . step ( 2 ) another 40 % of 40000 = 16000 accepted . here it is quiet observable that if we further deduct candidate by 60 % it would change our probablity of easy going 2000 candidate . so i would get to second stage of recruitment where 50 % is accepted step ( 3 ) 50 % of 16000 = 8000 step ( 4 ) 50 % of 8000 = 4000 step ( 5 ) 50 % of 4000 = 2000 step ( 6 ) 50 % of 2000 = 1000 step ( 7 ) 50 % of 1000 = 500 last step of accepting 70 % of 500 = 350 ( our target ) total 8 steps required . ans d"
Answer: d
Problem: the number 133 is equal to the sum of the cubes of two integers . what is the product of those integers ?
Options: a ) 8 , b ) 15 , c ) 21 , d ) 27 , e ) 10
Rationale: "2 ^ 3 + 5 ^ 3 = 133 the number is 2 * 5 = 10 e"
Answer: e
Problem: a ladder 30 feet long is leaning against a wall that is perpendicular to level ground . the bottom of the ladder is 10 feet from the base of the wall . if the top of the ladder slips down 5 feet , how many feet will the bottom of the ladder slip ?
Options: a ) 14 , b ) 15 , c ) 18.92 , d ) 19 , e ) 25
Rationale: 30 ^ 2 - 10 ^ 2 = 800 it means that the height is equal to 28.28 . since the top of the ladder slips down 5 feet , then the height of the wall = 28.28 - 5 = 23.28 the bottom = sqrt ( 30 ^ 2 - 23.28 ^ 2 ) = sqrt ( 900 - 541.95 ) = 18.92 ans is c
Answer: c
Problem: if 3 workers collect 48 kg of cotton in 4 days , how many kg of cotton will 9 workers collect in 2 days ?
Options: a ) 88 kg , b ) 65 kg , c ) 72 kg , d ) 44 kg , e ) 55 kg
Rationale: ( 3 * 4 ) / 48 = ( 9 * 2 ) / x x = 72 kg answer : c
Answer: c
Problem: a number divided by 34 leaves remainder 37 what is the remainder when same number divided by 9
Options: a ) 7 , b ) 8 , c ) 9 , d ) 0 , e ) 1
Rationale: "add 34 + 37 = 72 now 72 divided by 9 so we get 0 as reaminder answer : d"
Answer: d
Problem: a certain article of clothing was discounted during a special sale to 3 / 4 of its original retail price . when the clothing did n ' t sell , it was discounted even further to 1 / 3 of its original retail price during a second sale . by what percent did the price of this article of clothing decrease from the first sale to the second sale ?
Options: a ) 50 % , b ) 33.33 % , c ) 25 % , d ) 55.55 % , e ) 12.5 %
Rationale: "say the original retail price of the item was $ 200 . the price after the first sale = 3 / 4 * $ 200 = $ 150 . the price after the second sale = 1 / 3 * $ 200 = $ 200 / 3 . the percent change from the first sale to the second = ( 150 - 200 / 3 ) / 150 = 1 / 3 = 55.55 % . answer : d ."
Answer: d
Problem: what is the least number which should be added to 2597 so that the sum is exactly divisible by 5 , 6 , 4 , and 3 ?
Options: a ) 17 , b ) 23 , c ) 26 , d ) 35 , e ) 43
Rationale: "l . c . m . of 5 , 6 , 4 and 3 = 60 . when dividing 2597 by 60 , the remainder is 17 . the number to be added = 60 - 17 = 43 . the answer is e ."
Answer: e
Problem: find the greatest number which leaves the same remainder when it divides 16 , 46 and 82 .
Options: a ) 18 , b ) 8 , c ) 12 , d ) 16 , e ) none of these
Rationale: "82 - 46 = 36 46 - 16 = 20 82 - 16 = 66 the h . c . f of 20 , 36 and 66 is 2 . answer : e"
Answer: e
Problem: evaluate : | 8 - 8 ( 3 - 12 ) | - | 5 - 11 | = ?
Options: a ) 40 , b ) 74 , c ) 60 , d ) 70 , e ) 80
Rationale: "according to order of operations , inner brackets first . hence | 8 - 8 ( 3 - 12 ) | - | 5 - 11 | = | 8 - 8 * ( - 9 ) | - | 5 - 11 | according to order of operations , multiplication within absolute value signs ( which may be considered as brackets when it comes to order of operations ) next . hence = | 8 + 72 | - | 5 - 11 | = | 80 | - | - 6 | = 80 - 6 = 74 correct answer b ) 74"
Answer: b
Problem: heinz produces tomato puree by boiling tomato juice . the tomato puree has only 20 % water while the tomato juice has 90 % water . how many liters of tomato puree will be obtained from 25 litres of tomato juice ?
Options: a ) 2.8 liters . , b ) 3.125 liters . , c ) 8.5 liters . , d ) 2.6 liters . , e ) 2.1 liters .
Rationale: answer : explanation : in each of the solutions , there is a pure tomato component and some water . so while boiling , water evaporates but tomato not . so we equate tomato part in the both equations . â ‡ ’ â ‡ ’ 10 % ( 25 ) = 80 % ( x ) â ‡ ’ â ‡ ’ x = 3.125 liters . answer : b
Answer: b
Problem: triathlete dan runs along a 4 - mile stretch of river and then swims back along the same route . if dan runs at a rate of 10 miles per hour and swims at a rate of 6 miles per hour , what is his average rate for the entire trip in miles per minute ?
Options: a ) 1 / 8 , b ) 2 / 15 , c ) 3 / 15 , d ) 1 / 4 , e ) 3 / 8
Rationale: "dan travels 8 miles round trip . running part : ( 4 / 10 * 60 = 24 minutes ) swimming part : ( 4 / 6 * 60 = 40 minutes ) 8 miles in ( 24 + 40 ) minutes 8 / 64 = 1 / 8 mile per minute answer : 1 / 8 mile per minute"
Answer: a
Problem: at a small company , 58 percent of the employees are women , and 60 percent of the employees are married . if 2 / 3 of the men are single , what fraction of the women are married ?
Options: a ) 5 / 16 , b ) 1 / 3 , c ) 23 / 29 , d ) 7 / 10 , e ) 5 / 7
Rationale: lets take total employees are 100 . given that , total women = 58 and total married = 60 . total men = 100 - 58 = 42 and single men = 2 / 3 * 42 = 28 . married men = total men - single men = 42 - 28 = 14 . married women = total married - married men = 60 - 14 = 46 . fraction of women are married = married women / total women = 46 / 58 = 23 / 29 . ans c
Answer: c
Problem: if a function f is defined by f ( x ) = - 1 / x for all non zero numbers x . if f ( a ) = - 1 / 3 and f ( ab ) = 1 / 6 then b = ?
Options: a ) 2 , b ) 1 / 2 , c ) - 1 / 2 , d ) - 2 , e ) - 12
Rationale: f ( a ) = - 1 / 3 = - 1 / a , and thus a = 3 f ( ab ) = 1 / 6 , and thus ab = - 6 3 b = - 6 b = - 2 the answer is d .
Answer: d
Problem: if 10 men can reap 80 hectares in 24 days , then how many hectares can 36 men reap in 30 days ?
Options: a ) 127 , b ) 237 , c ) 360 , d ) 450 , e ) 281
Rationale: "explanation : let the required no of hectares be x . then men - - - hectares - - - days 10 - - - - - - - - - 80 - - - - - - - - - 24 36 - - - - - - - - - x - - - - - - - - - 30 more men , more hectares ( direct proportion ) more days , more hectares ( direct proportion ) x = 36 / 10 * 30 / 24 * 80 x = 360 answer : c"
Answer: c
Problem: a man can row a distance of 5 km in 60 min with the help of the tide . the direction of the tide reverses with the same speed . now he travels a further 20 km in 10 hours . how much time he would have saved if the direction of tide has not changed ?
Options: a ) 2 , b ) 8 , c ) 1 , d ) 6 , e ) 5
Rationale: "explanation : he covered 5 km in 1 hour , so he might cover 20 km in 4 hours . but he took 10 hours . he would have saved 10 – 4 = 6 hours . answer : d"
Answer: d
Problem: a certain fraction is equivalent to 2 / 5 . if the numerator of the fraction is increased by 4 and the denominator is doubled , the new fraction is equivalent to 1 / 4 . what is the difference of the numerator and denominator of the original fraction ?
Options: a ) 49 , b ) 35 , c ) 28 , d ) 24 , e ) 21
Rationale: "x / y = 2 / 5 - > 1 ( x + 4 ) / 2 y = 1 / 4 - > 2 divide 1 by 2 : = > 2 x / ( x + 4 ) = 8 / 5 = > 5 x = 4 x + 16 = > x = 16 = > y = 5 / 2 * 16 = 40 so x - y = 24 the answer is d"
Answer: d
Problem: a couple who own an appliance store discover that if they advertise a sales discount of 10 % on every item in the store , at the end of one month the number of total items sold increases 15 % . their gross income from sales for one month increases by what percent ?
Options: a ) 1.5 % , b ) 2.5 % , c ) 3.5 % , d ) 4.5 % , e ) 5.5 %
Rationale: "let p be the original price and let x be the number of items sold originally . the original income is p * x . after the changes , the income is 0.9 p * 1.15 x = 1.035 * ( p * x ) , an increase of 3.5 % . the answer is c ."
Answer: c
Problem: if a man lost 8 % by selling oranges at the rate of 25 a rupee at how many a rupee must he sell them to gain 25 % ?
Options: a ) 20 , b ) 15 , c ) 18.4 , d ) 20 , e ) 12.8
Rationale: "92 % - - - - 25 125 % - - - - ? 92 / 125 * 25 = 18.4 answer : c"
Answer: c
Problem: how many positive integers less than 100 are there such that they are multiples of 13 or multiples of 12 but not both ?
Options: a ) 15 , b ) 16 , c ) 17 , d ) 18 , e ) 19
Rationale: "for 13 : 13 . . . 91 = 13 * 7 = 7 for 12 : 12 . . . 96 = 12 * 8 = 8 but there is no integer 13 * 12 . so n = ( 7 ) + ( 8 ) = 15 a"
Answer: a
Problem: a certain experimental mathematics program was tried out in 2 classes in each of 38 elementary schools and involved 44 teachers . each of the classes had 1 teacher and each of the teachers taught at least 1 , but not more than 3 , of the classes . if the number of teachers who taught 3 classes is n , then the least and greatest possible values of n , respectively , are
Options: a ) 0 and 13 , b ) 0 and 14 , c ) 0 and 16 , d ) 1 and 9 , e ) 2 and 8
Rationale: "one may notice that greatest possible values differ in each answer choice in contrast to the least values , which repeat . to find out the greatest value you should count the total classes ( 38 * 2 = 76 ) , then subtract the total # of teachers since we know from the question that each teacher taught at least one class ( 76 - 44 = 32 ) . thus we get a number of the available extra - classes for teachers , and all that we need is just to count how many teachers could take 2 more classes , which is 32 / 2 = 16 . so the greatest possible value of the # of teachers who had 3 classes is 16 . only answer c has this option ."
Answer: c
Problem: if y exceeds x by 20 % , then x is less than y by ?
Options: a ) 16 2 / 8 % , b ) 16 8 / 3 % , c ) 16 2 / 3 % , d ) 76 2 / 3 % , e ) 17 2 / 3 %
Rationale: x = 100 y = 120 120 - - - - - - 20 100 - - - - - - - ? = > 16 2 / 3 % answer : c
Answer: c
Problem: express a speed of 90 kmph in meters per second ?
Options: a ) 10 mps , b ) 76 mps , c ) 26 mps , d ) 97 mps , e ) 25 mps
Rationale: "90 * 5 / 18 = 25 mps answer : e"
Answer: e
Problem: together , 15 type a machines and 7 type b machines can complete a certain job in 4 hours . together 8 type b machines and 15 type c machines can complete the same job in 11 hours . how many w hours would it take one type a machine , one type b machine , and one type c machine working together to complete the job ( assuming constant rates for each machine ) ?
Options: a ) 22 hours , b ) 30 hours , c ) 44 hours , d ) 60 hours , e ) it can not be determined from the information above .
Rationale: "say the rates of machines a , b and c are a , b , and c , respectively . together 15 type a machines and 7 type b machines can complete a certain job in 4 hours - - > 15 a + 7 b = 1 / 4 ; together 8 type b machines and 15 type c machines can complete the same job in 11 hours - - > 8 b + 15 c = 1 / 11 . sum the above : 15 a + 15 b + 15 c = 1 / 4 + 1 / 11 = 15 / 44 - - > reduce by 15 : a + b + c = 1 / 44 - - > so , the combined rate of the three machines is 1 / 44 job / hour - - > time is reciprocal of the rate , thus machines a , b and c can do the job w in 44 hours . answer : c ."
Answer: c
Problem: the smallest value of n , for which n + 2 is not a prime number , is
Options: a ) 1,2 , b ) 4,6 , c ) 2,4 , d ) 8,12 , e ) 9,6
Rationale: ( 1 + 2 ) = 3 . ( 2 + 2 ) = 4 . ( 3 + 2 ) = 5 . ( 4 + 2 ) = 6 . which is not prime , n = 2,4 . answer : c
Answer: c
Problem: a man traveled from the village to the post - office at the rate of 25 kmph and walked back at the rate of 4 kmph . if the whole journey took 5 hours 48 minutes , find the distance of the post - office from the village ?
Options: a ) 70 m , b ) 80 km , c ) 20 km , d ) 10 km , e ) 73 km
Rationale: explanation : average speed = , here a = 25 b = 4 = 2 x 25 x 4 / ( 25 + 4 ) = 200 / 29 km / hr . distance covered in 5 hours 48 minutes = speed x time = ( 200 / 29 ) x ( 29 / 5 ) distance covered in 5 hours 48 minutes = 40 kms . distance of the post office from the village = ( 40 / 2 ) = 20 km . answer : c
Answer: c
Problem: a bag contains 21 toys numbered 1 to 21 . a toy is drawn and then another toy is drawn without replacement . find the probability that both toys will show even numbers .
Options: a ) 5 / 21 , b ) 9 / 42 , c ) 6 / 22 , d ) 4 / 21 , e ) 3 / 21
Rationale: since there are 10 even numbers in the given range , the probability that the first toy shows an even number = 10 / 21 since the toy is not replaced , there are now 9 even numbered toys and total 20 toys left . hence , probability that the second toy shows an even number = 9 / 20 . required probability = 10 / 21 x 9 / 20 = 9 / 42 . answer : b
Answer: b
Problem: trapezoid jklm in the x - y plane has coordinates j = ( – 2 , – 4 ) , k = ( – 2 , 1 ) , l = ( 6 , 7 ) , and m = ( 6 , – 4 ) . what is its perimeter ?
Options: a ) 34 , b ) 36 , c ) 38 , d ) 40 , e ) 42
Rationale: "this one may look challenging initially , but all kinds of simplifying tricks . first of all , j & k have the same x - coordinate , so that ’ s a vertical segment , and the length is jk = 1 – ( – 4 ) = 5 . l & m also have the same x - coordinate , so that ’ s also a vertical segment , and the length is lm = 7 – ( – 4 ) = 11 . j & m have the same y - coordinate , so that ’ s also a horizontal segment , and the length is jm = 6 – ( – 2 ) = 8 . right there , we have the lengths of three of the four sides . the last side to find is kl . from k = ( – 2 , 1 ) , we have to go over 8 and up 6 to get to l = ( 6 , 7 ) , so 6 and 8 the legs of the right triangle , and kl is the hypotenuse . we recognize another common pythagorean triplet — ( 6 , 8 , 10 ) , which is a multiple of the ( 3 , 4 , 5 ) triplet . thus , without further calculations , we immediately know kl = 10 . perimeter = jk + kl + lm + jm = 5 + 10 + 11 + 8 = 34 answer = a"
Answer: a
Problem: a tradesman by means of his false balance defrauds to the extent of 20 % ? in buying goods as well as by selling the goods . what percent does he gain on his outlay ? a . 20 % b . 45 %
Options: a ) 77 , b ) 66 , c ) 44 , d ) 99 , e ) 11
Rationale: g % = 20 + 20 + ( 20 * 20 ) / 100 = 44 % answer : c
Answer: c
Problem: a numberais squared and then multiplied by negative 3 . the result of this operation r is equal to 3 times the sum of 3 timesaand two . what is one possible value ofa ?
Options: a ) - 3 , b ) - 2 , c ) 1 , d ) 2 , e ) 3
Rationale: r = - 3 * a ^ 2 = 3 ( 3 a + 2 ) a = - 2 or - 1 a = - 2 = b
Answer: b
Problem: a bag contains 10 red jellybeans and 10 blue jellybeans . if 3 jellybeans are removed one at a time , at random and are not replaced , what is the probability e that all 3 jellybeans removed from the bag are blue ?
Options: a ) 9 / 100 , b ) 2 / 19 , c ) 1 / 8 , d ) 3 / 20 , e ) 3 / 10
Rationale: "method - 1 10 red jellybeans and 10 blue jellybeans total outcomes = no . of ways to choose 3 jelly bean at random out of a total 20 jellybeans = 20 c 3 = 1140 favourable outcomes = no . of ways to choose 3 jelly bean such that they are all blue out of 10 blue = 10 c 3 = 120 probability = favourable outcomes / total outcomes = 10 c 3 / 20 c 3 probability e = 120 / 1140 = 2 / 19 answer : option b method - 2 probability of first jelly bean to be blue = 10 / 20 [ total 10 blue out of total 20 jellybeans ] probability of second jelly bean to be blue = 9 / 19 [ total 9 blue remaining out of total 19 jellybeans remaining ] probability of third jelly bean to be blue = 8 / 18 [ total 8 blue remaining out of total 18 jellybeans remaining ] required probability = ( 10 / 20 ) * ( 9 / 19 ) * ( 8 / 18 ) = 2 / 19 answer : option b"
Answer: b
Problem: a train 50 m long takes 6 sec to cross a man walking at 5 kmph in a direction opposite to that of the train . find the speed of the train ?
Options: a ) 15 kmph , b ) 25 kmph , c ) 35 kmph , d ) 45 kmph , e ) 55 kmph
Rationale: "let the speed of the train be x kmph speed of the train relative to man = x + 5 = ( x + 5 ) * 5 / 18 m / sec 50 / [ ( x + 5 ) * 5 / 18 ] = 6 30 ( x + 5 ) = 900 x = 25 kmph answer is b"
Answer: b
Problem: for any integer n greater than 1 , n * denotes the product of all the integers from 1 to n , inclusive . how many prime numbers are there between 6 * + 2 and 6 * + 6 , inclusive ?
Options: a ) none , b ) one , c ) two , d ) three , e ) four
Rationale: "given that n * denotes the product of all the integers from 1 to n , inclusive so , 6 * + 2 = 6 ! + 2 and 6 * + 6 = 6 ! + 6 . now , notice that we can factor out 2 our of 6 ! + 2 so it can not be a prime number , we can factor out 3 our of 6 ! + 3 so it can not be a prime number , we can factor out 4 our of 6 ! + 4 so it can not be a prime number , . . . the same way for all numbers between 6 * + 2 = 6 ! + 2 and 6 * + 6 = 6 ! + 6 , inclusive . which means that there are no primes in this range . answer : a ."
Answer: a
Problem: what is the area of an equilateral triangle whose one side length is 50 ?
Options: a ) 225 √ 3 , b ) 325 √ 3 , c ) 425 √ 3 , d ) 525 √ 3 , e ) 625 √ 3
Rationale: - > - > the area of an equilateral triangle with one side length of a is √ 3 a 2 / 4 . thus , √ 3 ( 50 ^ 2 ) / 4 = 625 √ 3 and the answer is e .
Answer: e
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 5 times 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 $ 0.80 per glass on the first day , what was the price per glass on the second day ?
Options: a ) $ 015 , b ) $ 0.27 , 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 5 units of water was used to make 6 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 6 . 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 6 . 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 6 glasses on the second day . say the price of the glass of the orangeade on the second day was $ x then 2 * 0.8 = 6 * x - - > x = $ 0.27 . answer : b .
Answer: b
Problem: if 2 men or 3 women can reap a field in 10 days how long will 4 men and 5 women take to reap it ?
Options: a ) 2 / 25 , b ) 11 / 30 , c ) 3 / 60 , d ) 5 / 42 , e ) 7 / 12
Rationale: "explanation : 2 men reap 1 / 10 field in 1 day 1 man reap 1 / ( 2 x 10 ) 3 women reap 1 / 10 field in 1 day 1 woman reap 1 / ( 10 x 3 ) 4 men and 5 women reap 4 / ( 2 x 10 ) + 5 / ( 3 x 10 ) ) = 11 / 30 in 1 day 4 men and 5 women will reap the field in 11 / 30 days answer : option b"
Answer: b
Problem: the average of 11 10 prime numbers which are odd is ?
Options: a ) 17.72 , b ) 18.52 , c ) 19.63 , d ) 16.53 , e ) 15.63
Rationale: explanation : sum of first 11 prime no . which are odd = 195 average = 195 / 11 = 17.72 answer : a
Answer: a
Problem: the first doughnut is priced at $ 1 and then if you purchase additional doughnuts as dozens then the price is $ 6 / dozen . what is the total number of doughnuts purchased if you paid $ 25 ?
Options: a ) 45 , b ) 49 , c ) 53 , d ) 57 , e ) 61
Rationale: "$ 25 = 4 * $ 6 + $ 1 the number of doughnuts is 4 * 12 + 1 = 49 the answer is b ."
Answer: b
Problem: during the first two weeks of january , the total rainfall in springdale was 25 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 ) 15 inches
Rationale: "total rainfall in 2 weeks = 25 inches . assume the rainfall in second week = 1 . x rainfall in first week = x total rainfall = 2.5 x = 25 inches x = 10 and 1.5 x = 15 rainfall during second week = 9 inches option e"
Answer: e
Problem: a train crosses a bridge of length 200 m in 10 seconds and a lamp post on the bridge in 5 seconds . what is the length of the train in metres ?
Options: a ) 375 m , b ) 750 m , c ) 200 m , d ) 800 m , e ) 300 m
Rationale: "let length of train = l case - 1 : distance = 200 + l ( while crossing the bridge ) time = 10 seconds i . e . speed = distance / time = ( 200 + l ) / 10 case - 2 : distance = l ( while passing the lamp post ) time = 5 seconds i . e . speed = distance / time = ( l ) / 5 but since speed has to be same in both cases so ( 200 + l ) / 10 = ( l ) / 5 i . e . 2 l = l + 200 i . e . l = 200 answer : option c"
Answer: c
Problem: 10 ^ ( 600 ) ã · 10 ^ ( 580 ) = ?
Options: a ) 10 ^ 10 , b ) 10 ^ 20 , c ) 10 ^ 22 , d ) 10 ^ 23 , e ) 10 ^ 24
Rationale: 10 ^ ( 600 ) ã · 10 ^ ( 580 ) = 10 ^ ( 600 - 580 ) = 10 ^ 20 answer : b
Answer: b
Problem: the l . c . m of two numbers is 2310 and their h . c . f is 30 . if one number is 385 the other is
Options: a ) 180 , b ) 300 , c ) 270 , d ) 250 , e ) 350
Rationale: the other number = l . c . m * h . c . f / given number = 2310 * 30 / 385 = 180 answer is a .
Answer: a
Problem: if n is a positive integer and the product of all integers from 1 to n , inclusive , is a multiple of 440 , what is the least possible value of n ?
Options: a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14
Rationale: "is it 11 ? 440 = 2 * 2 * 2 * 5 * 11 so the least value forncan be 11 . b"
Answer: b
Problem: mary and mike enter into a partnership by investing $ 550 and $ 450 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 $ 1000 more than mike did , what was the profit made by their business in that year ?
Options: a ) $ 8000 , b ) $ 10000 , c ) $ 15000 , d ) $ 12000 , e ) $ 12500
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 5.5 : 4.5 i . e . , 55 % of 2 x would go to mary and 45 % of 2 x would go to mike . hence , mary would get ( 55 - 45 ) % of 2 x more than mike or 10 % of 2 x = $ 1000 i . e . , ( 60 / 100 ) * 2 x = 1000 or 2 x = 10000 . hence , the profit made by the company during the year $ 3 x = $ 15000 . answer : c"
Answer: c
Problem: a goods train runs at the speed of 72 kmph and crosses a 250 m long platform in 24 seconds . what is the length of the goods train ?
Options: a ) 230 m , b ) 240 m , c ) 260 m , d ) 270 m , e ) none of these
Rationale: "explanation : speed = [ 72 x ( 5 / 18 ) ] m / sec = 20 m / sec . time = 24 sec . let the length of the train be x metres . then , [ ( x + 250 ) / 24 ] = 20 = > x + 250 = 480 = > x = 230 . answer : a"
Answer: a
Problem: 20 men can dig a tunnel in 30 days . if after 10 days , 20 more men are deployed to dig the tunnel , how many more days it will take to dig the whole tunnel ?
Options: a ) 10 , b ) 15 , c ) 20 , d ) 25 , e ) 30
Rationale: a remaining work can be completed by 20 men in 30 - 10 = 20 days . if 20 men can do x work in 20 days , and let us say 40 men take n days to do the same work . now , more men , less number of days ( inversely proportion ) 20 : 40 : : n : 20 n = 20 x 20 / 40 = 10 days .
Answer: a
Problem: if the product of 10 integers is negative , at most how many of the integers can be negative ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 9 , e ) 6
Rationale: "the product of 10 integers is negative thus an odd number of integers need to be negative to have a negative product we are asked at most how many are required . so , the highest odd integer before 6 , i . e . 9 correct option : d"
Answer: d
Problem: two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds . the ratio of their speeds is :
Options: a ) 3 / 7 , b ) 3 / 2 . , c ) 3 / 88 , d ) 3 / 8 . , e ) 2 / 2 .
Rationale: "let the speeds of the two trains be x m / sec and y m / sec respectively . then , length of the first train = 27 x meters , and length of the second train = 17 y meters . ( 27 x + 17 y ) / ( x + y ) = 23 = = > 27 x + 17 y = 23 x + 23 y = = > 4 x = 6 y = = > x / y = 3 / 2 . answer : b"
Answer: b
Problem: the difference between the compound interest compounded annually and simple interest for 2 years at 20 % per annum is rs . 72 . find the principal ?
Options: a ) 2277 , b ) 2667 , c ) 3600 , d ) 2766 , e ) 1800
Rationale: "p = 72 ( 100 / 5 ) ^ 2 = > p = 1800 answer : e"
Answer: e
Problem: in a division , a student took 63 as divisor instead of 36 . his answer was 24 . the correct answer is -
Options: a ) 42 , b ) 32 , c ) 48 , d ) 28 , e ) 38
Rationale: "x / 63 = 24 . x = 24 * 63 . so correct answer would be , ( 24 * 63 ) / 36 = 42 . answer : a"
Answer: a
Problem: the sum of the numbers is 550 . if the first number be twice the second and third number be one - third of the first , then the second number is :
Options: a ) 48 , b ) 150 , c ) 72 , d ) 84 , e ) 27
Rationale: "let the second number be x . then , first number = 2 x and third number = 2 x / 3 . 2 x + x + 2 x / 3 = 550 11 x / 3 = 550 x = 150 answer : b"
Answer: b
Problem: what is 121 times 11 ?
Options: a ) 1331 , b ) 1313 , c ) 1133 , d ) 3131 , e ) 3311
Rationale: a 1331
Answer: a
Problem: if ( 1 – 1.25 ) n = 4 , then n =
Options: a ) − 400 , b ) − 16 , c ) − 4 , d ) 4 , e ) 400
Rationale: "( 1 – 1.25 ) n = 4 simplify to get : - 0.25 n = 4 rewrite as ( - 1 / 4 ) n = 4 multiply both sides by - 4 to get : n = - 16 answer : b"
Answer: b
Problem: four 6 faced dice are thrown together . the probability that all the three show the same number on them is ?
Options: a ) 1 / 32 , b ) 1 / 216 , c ) 1 / 33 , d ) 1 / 38 , e ) 1 / 34
Rationale: "the three dice can fall in 6 * 6 * 6 * 6 = 1296 ways . hence the probability is 6 / 1296 = 1 / 216 answer : b"
Answer: b
Problem: the average age of 25 students in a class is 12 years . if teacher ' s age is also included then average increases 1 year then find the teacher ' s age ?
Options: a ) 40 , b ) 35 , c ) 29 , d ) 38 , e ) 42
Rationale: "total age of 25 students = 25 * 12 = 300 total age of 26 persons = 26 * 13 = 338 age of teacher = 338 - 300 = 38 years answer is d"
Answer: d