regisss/math_qa huggingface dataset:
Problem: working alone at its constant rate , machine a produces x boxes in 5 minutes and working alone at its constant rate , machine b produces 2 x boxes in 10 minutes . how many minutes does it take machines a and b , working simultaneously at their respective constant rates , to produce 3 x boxes ?
Options: a ) 3 minutes , b ) 7.5 minutes , c ) 5 minutes , d ) 6 minutes , e ) 12 minutes
Rationale: "rate = work / time given rate of machine a = 2 x / 10 min machine b produces 2 x boxes in 10 min hence , machine b produces 2 x boxes in 10 min . rate of machine b = 2 x / 10 we need tofind the combined time that machines a and b , working simultaneouslytakeat their respective constant rates let ' s first find the combined rate of machine a and b rate of machine a = 2 x / 10 min + rate of machine b = 2 x / 10 = 4 x / 10 now combine time = combine work needs to be done / combine rate = 3 x / 4 x * 10 = 7.5 min ans : b"
Answer: b
Problem: a factory that employs 1000 assembly line workers pays each of these workers $ 5 per hour for the first 40 hours worked during a week and 1 ½ times that rate for hours worked in excess of 40 . what was the total payroll for the assembly - line workers for a week in which 30 percent of them worked 35 hours , 50 percent worked 40 hours , and the rest worked 50 hours ?
Options: a ) $ 180,000 , b ) $ 185,000 , c ) $ 190,000 , d ) $ 207,500 , e ) $ 205,000
Rationale: "30 % of 1000 = 300 worked for 20 hours payment @ 5 / hr total payment = 300 * 35 * 5 = 52500 50 % of 1000 = 500 worked for 40 hours payment @ 5 / hr total payment = 500 * 40 * 5 = 100000 remaining 200 worked for 50 hours payment for first 40 hours @ 5 / hr payment = 200 * 40 * 5 = 40000 payment for next 10 hr @ 7.5 / hr payment = 200 * 10 * 7.5 = 15000 total payment = 52500 + 100000 + 40000 + 15000 = 207500 hence , answer is d"
Answer: d
Problem: solution a is 20 % sugar and solution b is 80 % sugar . if you have 30 ounces of solution a and 60 ounces of solution b , in what ratio could you mix solution a with solution b to produce 50 ounces of a 50 % sugar solution ?
Options: a ) 6 : 4 , b ) 6 : 14 , c ) 4 : 4 , d ) 4 : 6 , e ) 3 : 7
Rationale: forget the volumes for the time being . you have to mix 20 % and 80 % solutions to get 50 % . this is very straight forward since 50 is int he middle of 20 and 80 so we need both solutions in equal quantities . if this does n ' t strike , use w 1 / w 2 = ( a 2 - aavg ) / ( aavg - a 1 ) w 1 / w 2 = ( 80 - 50 ) / ( 50 - 20 ) = 1 / 1 so the volume of the two solutions will be equal . answer has to be 4 : 4 = c
Answer: c
Problem: 12 different biology books and 8 different chemistry books lie on a shelf . in how many ways can a student pick 2 books of each type ?
Options: a ) 80 , b ) 160 , c ) 720 , d ) 1600 , e ) 1848
Rationale: no . of ways of picking 2 biology books ( from 12 books ) = 12 c 2 = ( 12 * 11 ) / 2 = 66 no . of ways of picking 2 chemistry books ( from 8 books ) = 8 c 2 = ( 8 * 7 ) / 2 = 28 total ways of picking 2 books of each type = 66 * 28 = 1848 ( option e )
Answer: e
Problem: the total price of a basic computer and printer are $ 2,500 . if the same printer had been purchased with an enhanced computer whose price was $ 500 more than the price of the basic computer , then the price of the printer would have been 1 / 3 of that total . what was the price of the basic computer ?
Options: a ) 1500 , b ) 1600 , c ) 1750 , d ) 1900 , e ) 2000
Rationale: "let the price of basic computer be c and the price of the printer be p : c + p = $ 2,500 . the price of the enhanced computer will be c + 500 and total price for that computer and the printer will be 2,500 + 500 = $ 3,000 . now , we are told that the price of the printer is 1 / 3 of that new total price : p = 1 / 3 * $ 3,000 = $ 1000 plug this value in the first equation : c + 1000 = $ 2,500 - - > c = $ 1,500 . answer : a ."
Answer: a
Problem: a baseball card decreased in value 20 % in its first year and 20 % in its second year . what was the total percent decrease of the card ' s value over the two years ?
Options: a ) 28 % , b ) 30 % , c ) 32 % , d ) 36 % , e ) 72 %
Rationale: "consider the initial value of the baseball card as $ 100 after first year price = 100 * 0.8 = 80 after second year price = 80 * 0.8 = 64 final decrease = [ ( 100 - 64 ) / 100 ] * 100 = 36 % correct answer - d"
Answer: d
Problem: 2 is what percent of 50
Options: a ) 2 % , b ) 4 % , c ) 6 % , d ) 8 % , e ) none of these
Rationale: "explanation : 2 / 50 * 100 = 1 / 25 * 100 = 4 % option b"
Answer: b
Problem: the contents of a certain box consist of 14 apples and 26 oranges . how many oranges must be removed from the box so that 70 percent of the pieces of fruit in the box will be apples ?
Options: a ) 3 , b ) 6 , c ) 14 , d ) 17 , e ) 20
Rationale: "the objective here is that 70 % of the fruit in the box should be apples . now , there are 14 apples at start and there is no talk of removing any apples , so number of apples should remain 14 and they should constitute 70 % of total fruit , so total fruit = 14 / 0.7 = 20 so we should have 20 - 14 = 6 oranges . right now , there are 26 oranges , so to get to 6 oranges , we should remove 26 - 6 = 20 oranges . answer e"
Answer: e
Problem: light glows for every 20 seconds . how many max . times did it glow between 1 : 57 : 58 and 3 : 20 : 47 am .
Options: a ) 380 times , b ) 381 times , c ) 382 times , d ) 248 times , e ) 482 times
Rationale: "time difference is 1 hr , 22 min , 49 sec = 4969 sec . so , light glows floor ( 4969 / 20 ) = 248 times . answer : d"
Answer: d
Problem: each week , harry is paid x dollars per hour for the first 18 hours and 1.5 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 ) 34 , b ) 36 , c ) 37 , d ) 38 , e ) 39
Rationale: "42 x = 18 x + 1.5 x ( h - 18 ) = = > 42 = 18 + 1.5 ( h - 18 ) = = > h - 18 = 24 / 1.5 = 16 = = > h = 34 answer is a"
Answer: a
Problem: the average of first five multiples of 2 is ?
Options: a ) 6 , b ) 8 , c ) 9 , d ) 5 , e ) 7
Rationale: "average = 2 ( 1 + 2 + 3 + 4 + 5 ) / 5 = 30 / 5 = 6 . answer : a"
Answer: a
Problem: in an intercollegiate competition that lasted for 3 days , 157 students took part on day 1 , 111 on day 2 and 98 on day 3 . if 89 took part on day 1 and day 2 and 56 took part on day 2 and day 3 and 32 took part on all three days , how many students took part only on day 1 ?
Options: a ) 40 , b ) 44 , c ) 35 , d ) 49 , e ) 38
Rationale: "day 1 & 2 = 89 ; only day 1 & 2 ( 89 - 32 ) = 57 , day 2 & 3 = 56 ; only day 2 & 3 ( 56 - 32 ) = 24 , only day 1 = 157 - ( 57 + 24 + 32 ) = 44 answer : b"
Answer: b
Problem: a student committee on academic integrity has 72 ways to select a president and vice president from a group of candidates . the same person can not be both president and vice president . how many candidates are there ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: "xc 1 * ( x - 1 ) c 1 = 72 x ^ 2 - x - 72 = 0 ( x - 9 ) ( x + 8 ) = 0 x = 9 , - 8 - 8 ca n ' t possible . c"
Answer: c
Problem: a metallic sheet is of rectangular shape with dimensions 48 m x 36 m . from each of its corners , a square is cut off so as to make an open box . if the length of the square is 3 m , the volume of the box ( in m 3 ) is :
Options: a ) 3780 , b ) 5120 , c ) 6420 , d ) 8960 , e ) 7960
Rationale: "clearly , l = ( 48 - 6 ) m = 42 m , b = ( 36 - 6 ) m = 30 m , h = 8 m . volume of the box = ( 42 x 30 x 3 ) m 3 = 3780 m 3 . answer : option a"
Answer: a
Problem: find the numbers which are in the ratio 3 : 2 : 4 such that the sum of the first and the second added to the difference of the third and the second is 21 ?
Options: a ) 4 , 3,22 , b ) 4 , 4,22 , c ) 9 , 3,32 , d ) 9 , 6,12 , e ) 9 , 2,23
Rationale: let the numbers be a , b and c . a : b : c = 3 : 2 : 4 given , ( a + b ) + ( c - b ) = 21 = > a + c = 21 = > 3 x + 4 x = 21 = > x = 3 a , b , c are 3 x , 2 x , 4 x a , b , c are 9 , 6 , 12 . answer : d
Answer: d
Problem: in a certain village , 20 litres of water are required per household per month . at this rate , if there are 10 households in the village , how long ( in months ) will 2000 litres of water last ?
Options: a ) 5 , b ) 2 , c ) 10 , d ) 1 , e ) 12
Rationale: i find it much easier to understand with real numbers , so choose ( almost ) any numbers to replace m , n and p : in a certain village , m 20 litres of water are required per household per month . at this rate , if there aren 10 households in the village , how long ( in months ) willp 2000 litres of water last ? water required is 20 * 10 = 200 ( m * n ) water available is 2000 ( p ) it will last 10 months ( p / m * n ) ans : c
Answer: c
Problem: if x + | x | + y = 5 and x + | y | - y = 6 what is x + y = ?
Options: a ) 1 , b ) - 1 , c ) 3 , d ) 12 , e ) 13
Rationale: if x < 0 and y < 0 , then we ' ll have x - x + y = 7 and x - y - y = 6 . from the first equation y = 7 , so we can discard this case since y is not less than 0 . if x > = 0 and y < 0 , then we ' ll have x + x + y = 7 and x - y - y = 6 . solving gives x = 4 > 0 and y = - 1 < 0 - - > x + y = 3 . since in ps questions only one answer choice can be correct , then the answer is c ( so , we can stop here and not even consider other two cases ) . answer : c . adding both eqn we get 2 x + ixi + iyi = 13 now considering x < 0 and y > 0 2 x - x + y = 13 we get x + y = 12 hence answer should be d
Answer: d
Problem: a certain clock rings two notes at quarter past the hour , 4 notes at half past , and 6 notes at 3 - quarters past . on the hour , it rings 8 notes plus an additional number of notes equal to whatever hour it is . how many notes will the clock ring from 1 : 00 p . m . through 5 : 00 p . m . , including the rings at 1 : 00 and 5 : 00 ?
Options: a ) 87 , b ) 95 , c ) 102 , d ) 103 , e ) 115
Rationale: form 1 pm to 5 pm . excluding the actual hour chime we have 20 ( 1 pm ) + 20 ( 2 pm ) + 20 ( 3 pm ) + 20 ( 4 pm ) + 8 ( 5 pm ) = 88 now the hour chimes are 1 + 2 + 3 + 4 + 5 = 15 total = 88 + 15 = 103 answer d .
Answer: d
Problem: on an order of 9 dozen boxes of a consumer product , a retailer receives an extra dozen free . this is equivalent to allowing him a discount of :
Options: a ) 10 % , b ) 15 % , c ) 20 % , d ) 25 % , e ) 30 %
Rationale: "clearly , the retailer gets 1 dozen out of 10 dozens free . equivalent discount = 1 / 10 * 100 = 10 % . answer a ) 10 %"
Answer: a
Problem: the total age of a and b is 13 years more than the total age of b and c . c is how many years younger than a ?
Options: a ) 13 , b ) 24 , c ) c is elder than a , d ) data inadequate , e ) none
Rationale: "solution [ ( a + b ) - ( b + c ) ] = 13 â € ¹ = â € º a - c = 13 . answer a"
Answer: a
Problem: rs . 1200 is divided so that 5 times the first share , 10 times the 2 nd share and fifteen times third share amount to the same . what is the value of the second share ?
Options: a ) s 525 , b ) s 527 , c ) s 598 , d ) s 400 , e ) s 500
Rationale: "a + b + c = 1200 5 a = 10 b = 15 c = x a : b : c = 1 / 5 : 1 / 10 : 1 / 15 = 3 : 2 : 1 2 / 6 * 1200 = rs 400 answer : d"
Answer: d
Problem: jackie has two solutions that are 4 percent sulfuric acid and 12 percent sulfuric acid by volume , respectively . if these solutions are mixed in appropriate quantities to produce 60 liters of a solution that is 5 percent sulfuric acid , approximately how many liters of the 4 percent solution will be required ?
Options: a ) 18 , b ) 20 , c ) 24 , d ) 36 , e ) 26.25
Rationale: "let a = amount of 4 % acid and b = amount of 12 % acid . now , the equation translates to , 0.04 a + . 12 b = . 05 ( a + b ) but a + b = 60 therefore . 04 a + . 12 b = . 05 ( 60 ) = > 4 a + 12 b = 300 but b = 60 - a therefore 4 a + 12 ( 60 - a ) = 300 = > 16 a = 420 hence a = 26.25 . answer : e"
Answer: e
Problem: if the product of 6 integers is negative , at most how many of the integers can be negative ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "product of even number of - ve numbers is positive so it cant be 6 . answer : d"
Answer: d
Problem: there is a 50 % chance jen will visit chile this year , while there is a 50 % chance that she will visit madagascar this year . what is the probability that jen will visit either chile or madagascar this year , but not both ?
Options: a ) 25.0 % , b ) 50.0 % , c ) 62.5 % , d ) 75.0 % , e ) 80.0 %
Rationale: "p ( chile and not madagascar ) = 0.5 * 0.5 = 0.25 p ( madagascar and not chile ) = 0.5 * 0.5 = 0.25 total probability = 0.25 + 0.25 = 0.5 = 50 % the answer is b ."
Answer: b
Problem: a pipe takes a hours to fill the tank . but because of a leakage it took 7 times of its original time . find the time taken by the leakage to empty the tank
Options: a ) 50 min , b ) 60 min , c ) 90 min , d ) 80 min , e ) 70 min
Rationale: pipe a can do a work 60 min . lets leakage time is x ; then 1 / 60 - 1 / x = 1 / 420 x = 70 min answer : e
Answer: e
Problem: at chennai it rained as much on tuesday as on all the others days of the week combined . if the average rainfall for the whole week was 3 cm . how much did it rain on tuesday ?
Options: a ) 2.625 cm , b ) 3 cm , c ) 10.5 cm , d ) 15 cm , e ) none of these
Rationale: total rainfall = 3 x 7 = 21 cm hence , rainfall received on tuesday = 21 / 2 ( as it rained as much on tuesday as on all the others days of the week combined ) = 10.5 cm . answer : c
Answer: c
Problem: a shopkeeper buys mangoes at the rate of 4 a rupee and sells them at 2 a rupee . find his net profit or loss percent ?
Options: a ) 100 % , b ) 200 % , c ) 250 % , d ) 300 % , e ) 50 %
Rationale: "the total number of mangoes bought by the shopkeeper be 12 . if he buys 4 a rupee , his cp = 3 he selling at 2 a rupee , his sp = 4 profit = sp - cp = 4 - 2 = 2 profit percent = 2 / 2 * 100 = 100 % answer : a"
Answer: a
Problem: ( 3 * 10 ^ 2 ) * ( 4 * 10 ^ - 2 ) = ?
Options: a ) 14 , b ) 12 , c ) 1200 , d ) 1.2 , e ) 14.11
Rationale: 3 * 10 ^ 2 = 300 4 * 10 ^ - 2 = 0.04 ( 3 * 10 ^ 2 ) * ( 4 * 10 ^ - 2 ) = 300 * 0.04 = 12.00 the answer is option b
Answer: b
Problem: the ratio of three numbers is 1 : 2 : 3 and their sum is 60 . the second number of the three numbers is ?
Options: a ) 24 , b ) 26 , c ) 20 , d ) 29 , e ) 30
Rationale: "1 : 2 : 3 total parts = 6 6 parts - - > 60 1 part - - - - > 10 the second number of the three numbers is = 2 * 10 = 20 answer : c"
Answer: c
Problem: natasha climbs up a hill , and descends along the same way she went up . it takes her 3 hours to reach the top and 2 hours to come back down . if her average speed along the whole journey is 3 kilometers per hour , what was her average speed ( in kilometers per hour ) while climbing to the top ?
Options: a ) 1.5 , b ) 2.5 , c ) 3.75 , d ) 5 , e ) 7.5
Rationale: "lets assume distance to top as x , so the total distance travelled by natasha = 2 x total time taken = 3 + 2 = 5 hrs avg speed = total dist / total time taken = 2 x / 5 avg speed of complete journey is given as = 3 hrs 2 x / 5 = 3 x = 7.5 miles avg speed while climbing = distance / time = 7.5 / 3 = 2.5 option b"
Answer: b
Problem: the annual birth and death rate in a country per 1000 are 39.4 and 19.4 respectively . the number of years k in which the population would be doubled assuming there is no emigration or immigration is
Options: a ) 20 , b ) k = 25 , c ) 30 , d ) k = 35 , e ) 40
Rationale: "suppose the population of the country in current year is 1000 . so annual increase is 1000 + 39.4 - 19.4 = 1020 hence every year there is an increase of 2 % . 2000 = 1000 ( 1 + ( 2 / 100 ) ) ^ n n = 35 answer is d ."
Answer: d
Problem: susan made a block with small cubes of 8 cubic cm volume to make a block , 3 small cubes long , 9 small cubes wide and 5 small cubes deep . she realizes that she has used more small cubes than she really needed . she realized that she could have glued a fewer number of cubes together to lock like a block with same dimensions , if it were made hollow . what is the minimum number of cubes that she needs to make the block ?
Options: a ) 113
b ) 114
c ) 115
d ) 116
e ) 117
Rationale: the total volume ( in terms of number of cubes ) of the solid = 3 * 9 * 5 = 135 the total volume ( in terms of number of cubes ) of the hollow = ( 3 - 2 ) * ( 9 - 2 ) * ( 5 - 2 ) = 21 so number of cubes required = 135 - 21 = 114 answer : b
Answer: b
Problem: a pupil ' s marks were wrongly entered as 83 instead of 63 . due to that the average marks for the class got increased by half ( 1 / 2 ) . the number of pupils in the class is :
Options: a ) 32 , b ) 50 , c ) 40 , d ) 20 , e ) 10
Rationale: "let there be x pupils in the class . total increase in marks = x x 1 / 2 = x / 2 x / 2 = ( 83 - 63 ) x / 2 = 20 x = 40 . answer : c"
Answer: c
Problem: in how many ways can 21 books on english and 19 books on french be placed in a row on a shelf so that two books on french may not be together ?
Options: a ) 3990 , b ) 1540 , c ) 1995 , d ) 3672 , e ) none of these
Rationale: "in order that two books on french are never together , we must place all books as under x e x e x e x e x e . . . . . x e x where e denotes the position of an english book and x that of a french book . since there are 21 books on english , the number of places marked x are therefore , 22 . now , 19 places out of 22 can be chosen in 22 c 19 = 22 c 3 = ( 22 x 21 x 20 ) / ( 3 x 2 x 1 ) = 1540 ways answer b ."
Answer: b
Problem: 120 is what percent of 40 ?
Options: a ) 5 % , b ) 20 % , c ) 50 % , d ) 300 % , e ) 500 %
Rationale: "40 * x = 120 - - > x = 3 - - > 3 expressed as percent is 300 % . answer : d ."
Answer: d
Problem: an alloy of copper and zinc contains copper and zinc in the ratio 9 : 6 . another alloy of copper and zinc contains copper and zinc in the ratio 6 : 9 . in what ratio should the two alloys be mixed so that the resultant alloy contains equal proportions of copper and zinc ?
Options: a ) 1 : 5 , b ) 1 : 4 , c ) 1 : 3 , d ) 1 : 1 , e ) 1 : 2
Rationale: "let alloy _ 1 be x units , and let alloy _ 2 be y units . so , fraction of copper in alloy _ 1 = 9 x / 15 , and fraction of zinc in alloy _ 1 = 6 x / 15 similarly , fraction of copper in alloy _ 2 = 6 y / 15 , and fraction of zinc in alloy _ 2 = 9 y / 15 . mixing them , we get copper = 9 x / 15 + 6 y / 15 ; zinc = 6 x / 15 + 9 y / 15 so , 9 x + 6 y = 6 x + 9 y - > 3 x = 3 y - > x / y = 3 / 3 = 1 / 1 so , they must be mixed in the ratio 1 : 1 answer : d"
Answer: d
Problem: a searchlight on top of the watchtower makes 4 revolutions per minute . what is the probability that a man appearing near the tower will stay in the dark for at least 12 seconds ?
Options: a ) 1 / 2 , b ) 2 / 3 , c ) 1 / 3 , d ) 1 / 4 , e ) 1 / 5
Rationale: "the searchlight completes one revolution every 15 seconds . the probability that the man ' s area will be lit up is 12 / 15 = 4 / 5 . the probability that he will stay in the dark is 1 - 4 / 5 = 1 / 5 the answer is e ."
Answer: e
Problem: which is the smallest no which divides 2880 and gives a perfect square ?
Options: a ) 4
b ) 9
c ) 3
d ) 5
e ) 7
Rationale: 2880 = 20 * 144 ( because w . k . t 144 is perfect square ) = 2 * 10 * 144 = 2 * 2 * 5 * 144 = 4 * 5 * 144 ( here 4 and 144 are perfect square ) so the smallest number is 5 answer : d
Answer: d
Problem: 4.036 divided by 0.02 gives :
Options: a ) 10.09 , b ) 1.06 , c ) 10.06 , d ) 201.8 , e ) 100.9
Rationale: "= 4.036 / 0.02 = 403.6 / 2 = 201.8 answer is d ."
Answer: d
Problem: stacy and heather are 5 miles apart and walk towards each other along the same route . stacy walks at constant rate that is 1 mile per hour fast than heather ' s constant rate of 5 miles / hour . if heather starts her journey 24 minutes after stacy , how far from the original destination has heather walked when the two meet ? .
Options: a ) 2.5 mile , b ) 1.9 mile , c ) 1.7 mile , d ) 1.5 mile , e ) 1.18 mile
Rationale: "ss - stacy ' s speed = 6 m / hr sh - heather ' s speed = 5 m / hr in 24 minutes stacy will cover = ( 24 / 60 ) * 6 = 2.4 miles now since both are walking in opposite directions , add their speeds - 6 + 5 = 11 m / hr and distance to cover is 5 - 2.4 = 2.6 time taken = distance / speed = 2.6 / 11 = 0.23 hrs heather will cover = 5 * 0.23 = 1.18 miles . answer e"
Answer: e
Problem: a train travels from albany to syracuse , a distance of 120 miles , at the average rate of 50 miles per hour . the train then travels back to albany from syracuse . the total travelling time of the train is 5 hours and 30 minutes . what was the average rate of speed of the train on the return trip to albany ?
Options: a ) 31 , b ) 38.7 , c ) 35 , d ) 36 , e ) 39
Rationale: 50 * t = 120 therefore t = 120 / 50 = 2.4 on return speed * ( 5.5 - 2.4 ) = 120 therefore t = 120 / 3.1 = 38.70 b
Answer: b
Problem: a train crosses a platform of 180 m in 15 sec , same train crosses another platform of length 250 m in 20 sec . then find the length of the train ?
Options: a ) 30 , b ) 887 , c ) 167 , d ) 197 , e ) 161
Rationale: "length of the train be ‘ x ’ x + 180 / 15 = x + 250 / 20 20 x + 3600 = 15 x + 3750 5 x = 150 x = 30 m answer : a"
Answer: a
Problem: 2 + 2 + 2 ² + 2 ³ . . . + 2 ^ 7
Options: a ) 2 ^ 9 , b ) 2 ^ 10 , c ) 2 ^ 16 , d ) 2 ^ 35 , e ) 2 ^ 8
Rationale: "2 + 2 = 2 ^ 2 2 ^ 2 + 2 ^ 2 = ( 2 ^ 2 ) * ( 1 + 1 ) = 2 ^ 3 2 ^ 3 + 2 ^ 3 = ( 2 ^ 3 ) * ( 1 + 1 ) = 2 ^ 4 so you can notice the pattern . . . in the end you will have 2 ^ 7 + 2 ^ 7 , which will give you 2 ^ 8 answer e"
Answer: e
Problem: what will be the difference between simple interest and compound interest @ 10 % per annum on a sum of rs . 1000 after 4 years ?
Options: a ) rs . 31 , b ) rs . 32.10 , c ) rs . 40.40 , d ) rs . 64.10 , e ) none
Rationale: solution s . i . = rs ( 1000 x 10 x 4 / 100 ) = rs . 400 . c . i . = rs . [ 1000 x ( 1 x 10 / 100 ) 4 - 1000 ] = rs . 464.10 ∴ difference = rs . ( 464.10 - 400 ) = rs . 64.10 answer d
Answer: d
Problem: two men start together to walk a certain distance , one at 4 kmph and another at 3 kmph . the former arrives half an hour before the latter . find the distance .
Options: a ) 6 km , b ) 7 km , c ) 8 km , d ) 9 km , e ) none of these
Rationale: let the distance be x km . then , x / 3 - x / 4 = 1 / 2 ( 4 x - 3 x ) / 12 = 1 / 2 x = 6 km answer : a
Answer: a
Problem: cubes with each side one inch long are glued together to form a larger cube . the larger cube ' s face is painted with red color and the entire assembly is taken apart . 25 small cubes are found with no paints on them . how many of unit cubes have at least one face that is painted red ?
Options: a ) 64 , b ) 72 , c ) 86 , d ) 98 , e ) 100
Rationale: "use the options . the options which after getting added to 25 shows a cube of a number could be right . here 64 + 25 = 89 72 + 25 = 97 86 + 25 = 111 98 + 25 = 123 100 + 25 = 125 - - - ( 5 * 5 * 5 ) so we have 100 as the answer ! e"
Answer: e
Problem: there are 35 kids in a play school . 26 kids play with white color balls and some kids play with yellow color balls and 19 kids play with both color balls . how many kids use yellow color balls ?
Options: a ) 12 , b ) 32 , c ) 5 , d ) 28 , e ) 35
Rationale: explanation : n ( aub ) = n ( a ) + n ( b ) - n ( anb ) . . . . ( 1 ) n ( a ) = number of kids playing with white color balls = 26 n ( aub ) = total number of kids in the play school = 35 n ( anb ) = number of kids playing with both white and yellow color balls = 19 we have to find , n ( b ) = number of kids playing with yellow color balls from ( 1 ) , 35 = 26 + n ( b ) - 19 n ( b ) = 35 + 19 - 26 = 28 hence , answer is 28 kids play with yellow color balls . answer : d
Answer: d
Problem: in the rectangular coordinate system , what is the x - intercept of a line passing through ( 10 , 3 ) and ( − 8 , − 6 ) ?
Options: a ) 4 , b ) 2 , c ) 0 , d ) − 2 , e ) − 4
Rationale: "slope = rise / run = 9 / 18 = 1 / 2 the equation of the line is y = ( 1 / 2 ) x + b 3 = ( 1 / 2 ) ( 10 ) + b b = - 2 the equation of the line is y = ( 1 / 2 ) x - 2 to find the x - intercept , let y = 0 : 0 = ( 1 / 2 ) x - 2 x = 4 the answer is a ."
Answer: a
Problem: in a certain boys camp , 20 % of the total boys are from school a and 30 % of those study science . if there are 21 boys in the camp that are from school a but do not study science then what is the total number of boys in the camp ?
Options: a ) 70 , b ) 245 , c ) 150 , d ) 35 , e ) 350
Rationale: "since 30 % of the boys from school a study science , then 70 % of the boys from school a do not study science and since 20 % of the total number of boys are from school a , then 0.2 * 0.7 = 0.14 , or 14 % of the boys in the camp are from school a and do not study science . we are told that this number equals to 21 , so 0.14 * { total } = 21 - - > { total } = 150 . answer : c ."
Answer: c
Problem: a train 110 m long is running with a speed of 80 km / hr . in what time will it pass a man who is running at 8 km / hr in the direction opposite to that in which the train is going ?
Options: a ) 5 , b ) 6 , c ) 4.5 , d ) 8 , e ) 9
Rationale: "speed of train relative to man = 80 + 8 = 88 km / hr . = 88 * 5 / 18 = 220 / 9 m / sec . time taken to pass the men = 110 * 9 / 220 = 4.5 sec . answer : option c"
Answer: c
Problem: tickets numbered 1 to 10 are mixed up and then a ticket is drawn at random . what is the probability that the ticket drawn bears a number which is a multiple of 2 ?
Options: a ) 1 / 3 , b ) 2 / 5 , c ) 1 / 2 , d ) 2 / 3 , e ) 1 / 4
Rationale: "here , s = { 1 , 2,3 , . . . . . . , 9,10 } e = event getting a multiple of 3 = { 2 , 4,6 , 8,10 } probability = 5 / 10 = 1 / 2 correct option is c"
Answer: c
Problem: set a contains all the even numbers between 6 and 50 inclusive . set b contains all the even numbers between 106 and 150 inclusive . what is the difference between the sum of elements of set b and the sum of the elements of set a ?
Options: a ) 2300 , b ) 2550 , c ) 5050 , d ) 6275 , e ) 11325
Rationale: "set a contains 6 , 8 , . . . 50 set b contains 102 , 104 , 106 . . . 150 number of terms in each set = 23 difference between corresponding terms in set a and b = 100 difference between sum of set b and set a = 100 * 23 = 2300 answer a"
Answer: a
Problem: david completes a piece of work in 5 days , john completes the same work in 9 days . if both of them work together , then the number of days required to complete the work is ?
Options: a ) 3.2 days , b ) 8 days , c ) 10 days , d ) 12 days , e ) 14 days
Rationale: ifa can complete a work in x days and b can complete the same work in y days , then , both of them together can complete the work in x y / x + y days . that is , the required no . of days = 5 × 9 / 14 = 3.2 days answer : a
Answer: a
Problem: what is the unit digit in 8 ^ 100 ?
Options: a ) 0 , b ) 1 , c ) 6 , d ) 3 , e ) 5
Rationale: unit digit in 8 ^ 100 = unit digit in [ ( 8 ^ 4 ) ^ 25 ] but unit digit in 8 ^ 4 = 6 unit digit 8 ^ 100 = 6 answer is c
Answer: c
Problem: the citizens of planet nigiet are 8 fingered and have thus developed their decimal system in base 8 . a certain street in nigiet contains 1000 buildings numbered 1 to 1000 in base 8 . how many 3 s are used in numbering these buildings ? express your answer in base 10
Options: a ) 192 , b ) 200 , c ) 196 , d ) 198 , e ) none
Rationale: "explanation : number 3 in 1 - 100 comes 20 times . 101 - 200 - > 20 times 201 - 300 - > 20 times 301 - 400 - > 120 times 401 - 500 - > 20 times 501 - 600 - > 20 times 601 - 700 - > 20 times 701 - 800 - > 20 times 801 - 900 - > 20 times 901 - 1000 - > 20 times total times : 300 times ( any no . from 1 to 9 except 0 will occur 300 times ) 8 based planet . . then 3 * 8 ( 2 ) + 0 * 8 ( 1 ) + 0 * 8 ( 0 ) = 192 answer : a"
Answer: a
Problem: mixture a is 30 percent alcohol , and mixture b is 60 percent alcohol . if the two are poured together to create a 4 - gallon mixture that contains 40 percent alcohol , approximately how many gallons of mixture a are in the mixture ?
Options: a ) 0.8 , b ) 0.7 , c ) 0.6 , d ) 0.5 , e ) 0.4
Rationale: "( 60 - 50 ) / ( 50 - 30 ) = qa / qb 10 / 20 = qa / qb 1 / 2 = qa / qb qa = ( 1 / 6 ) * 4 = 4 / 6 = 1 / 2 = 0.50 answer : d"
Answer: d
Problem: 12 men work 8 hours per day to complete the work in 10 days . to complete the same work in 4 days , working 15 hours a day , the number of men required ?
Options: a ) 15 days , b ) 12 days , c ) 16 days , d ) 18 days , e ) 20 days
Rationale: that is , 1 work done = 12 × 8 × 10 then , 12 8 × 10 = ? × 15 × 6 ? ( i . e . no . of men required ) = 12 × 8 × 10 / 15 × 6 = 16 days c )
Answer: c
Problem: due to construction , the speed limit along an 4 - mile section of highway is reduced from 55 miles per hour to 35 miles per hour . approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ?
Options: a ) 5 , b ) 8 , c ) 10 , d ) 15 , e ) 2
Rationale: "4 / 35 - 4 / 55 = 4 / 5 * ( 11 - 7 ) / 77 = 4 / 5 * 4 / 77 * 60 min = 4 * 12 * 4 / 77 = 192 / 77 ~ 2.4 answer - e"
Answer: e
Problem: if k ^ 3 is divisible by 162 , what is the least possible value of integer k ?
Options: a ) 12 , b ) 15 , c ) 18 , d ) 24 , e ) 36
Rationale: "k ^ 3 = 162 * x = 2 * 3 ^ 4 * x the factors of k must at minimum include 2 * 3 ^ 2 = 18 . the answer is c ."
Answer: c
Problem: when positive integer x is divided by 11 , the quotient is y and the remainder is 4 . when 2 x is divided by 8 , the quotient is 3 y and the remainder is 3 . what is the value of 13 y – x ?
Options: a ) 1 , b ) 0 , c ) - 1 , d ) - 2 , e ) - 4
Rationale: "( 1 ) x = 11 y + 4 ( 2 ) 2 x = 24 y + 3 let ' s subtract equation ( 1 ) from equation ( 2 ) . 13 y - 1 = x 13 y - x = 1 the answer is a ."
Answer: a
Problem: a company has two types of machines , type r and type s . operating at a constant rate a machine of r does a certain job in 36 hours and a machine of type s does the job in 12 hours . if the company used the same number of each type of machine to do job in 12 hours , how many machine r were used ?
Options: a ) 3 , b ) 4 , c ) 6 , d ) 9 / 2 , e ) 12
Rationale: "yes there is a typo in the question , i got the same ques on my gmat prep last week , and the questions goes as : a company has two types of machines , type r and type s . operating at a constant rate a machine of r does a certain job in 36 hours and a machine of type s does the job in 12 hours . if the company used the same number of each type of machine to do job in 2 hours , how many machine r were used ? so for a job to be done in 2 hours r = 1 / 2 r _ a ( rate of machine r ) = 1 / 36 r _ s ( rate of machine s ) = 1 / 12 lets say x machines are used to attain the desired rate , thus x / 36 + x / 12 = 1 / 2 ( desired r = 1 / 2 i . e . to complete the job in 2 hours ) ( x + 3 x ) / 36 = 1 / 2 4 x / 36 = 1 / 2 x = 9 / 2 . qa = 9 / 2 ( answer d )"
Answer: d
Problem: a can do a piece of work in 20 days ; b can do the same in 30 days . a started alone but left the work after 10 days , then b worked at it for 10 days . c finished the remaining work in 10 days . c alone can do the whole work in ?
Options: a ) 24 days , b ) 60 days , c ) 86 days , d ) 45 days , e ) 17 days
Rationale: "10 / 20 + 10 / 30 + 10 / x = 1 x = 60 days answer : b"
Answer: b
Problem: a money lender lent rs . 800 at 3 % per year and rs . 1400 at 5 % per year . the amount should be returned to him when the total interest comes to rs . 350 . find the number of years .
Options: a ) 3.5 , b ) 3.72 , c ) 4 , d ) 4.25 , e ) 4.5
Rationale: ( 800 xtx 3 / 100 ) + ( 1400 xtx 5 / 100 ) = 350 â † ’ t = 3.72 answer b
Answer: b
Problem: two watches are set for an alarm at 10 0 ' clock in the night . one watch gains 2 minutes per hour . when the faster watch shows 4 : 12 in the morning when the alarm rings what does the correct watch show ?
Options: a ) 5 : 00 , b ) 4 : 00 , c ) 4 : 10 , d ) 5 : 20 , e ) 6 : 00
Rationale: the faster watch gains 2 minutes per hour the two watches show 10 : 00 at 10 0 ' clock at 11 0 ' clock - the correct watch is at 11 : 00 the faster watch is at 11 : 02 ( 1 hour + gains 2 minutes per hour ) at 12 midnight - the correct watch is at 12 : 00 the faster watch is at 12 : 04 ( 2 hours + gains 4 minutes per 2 hours ) in 6 hours the faster watch gains 6 * 2 = 12 minutes and is at 4 : 12 and the correct watch is at 4 : 00 answer is b
Answer: b
Problem: if 3 x – 5 y = 5 and x / x + y = 5 / 7 , then what is the value of x – y ?
Options: a ) 9 , b ) 6 , c ) 4 , d ) 3 , e ) none of these
Rationale: 3 x – 5 y = 5 . . . ( i ) and xx + y = 57 xx + y = 57 ⇒ 7 x = 5 x + 5 y ⇒ 2 x = 5 y . . . ( ii ) from ( i ) and ( ii ) , x = 5 and y = 2 ∴ x – y = 3 answer d
Answer: d
Problem: a , b and c are partners . a receives 2 / 3 of profits , b and c dividing the remainder equally . a ' s income is increased by rs . 300 when the rate to profit rises from 5 to 7 percent . find the capital of b ?
Options: a ) 3750 , b ) 7799 , c ) 2500 , d ) 2772 , e ) 2912
Rationale: "a : b : c = 2 / 3 : 1 / 6 : 1 / 6 = 4 : 1 : 1 x * 2 / 100 * 2 / 3 = 300 b capital = 22500 * 1 / 6 = 3750 . answer : a"
Answer: a
Problem: john borrowed 3 soccer boots from jake , and forgot them on the field , if peter came across a total of 15 boots on the field jake ' s boots inclusive , and he took 4 boots at random , what is the probability that jake ' s boots were not amongst the 4 taken ? .
Options: a ) 12 / 91 , b ) 3 / 15 , c ) 12 / 15 , d ) 33 / 91 , e ) 3 / 91
Rationale: since jake owns 3 of the boots , the subset from which the 4 boots should be chosen are the 12 boots not owned by jake from the universe of 15 . the first boot can be one of the 12 from the 15 with probability 12 / 15 . the second boot can be one of the 11 from the 14 remaining with probability 11 / 14 . the third boot can be one of the 10 from the 13 remaining with probability 10 / 13 . the fourth boot can be one of the 9 from the 12 remaining with probability 9 / 12 . the total probability will be 12 / 15 × 11 / 14 × 10 / 13 × 9 / 12 . on cancellation , this comes to 33 / 91 . thus , the answer is d - 33 / 91
Answer: d
Problem: a student needs 30 % of the marks on a test to pass the test . if the student gets 80 marks and fails the test by 40 marks , find the maximum marks set for the test .
Options: a ) 400 , b ) 500 , c ) 600 , d ) 700 , e ) 800
Rationale: 30 % = 120 marks 1 % = 4 marks 100 % = 400 marks the answer is a .
Answer: a
Problem: set a consists of the integers from 5 to 10 , inclusive , while set b consists of the integers from 1 to 8 , inclusive . how many distinct integers do belong to the both sets at the same time ?
Options: a ) 5 , b ) 10 , c ) 8 , d ) 2 , e ) 4
Rationale: "a = { 5,6 , 7 , 8 , 9 , 10 } b = { 1,2 , 3,4 , 5,6 , 7,8 } common elements = { 5,6 , 7 , 8 } = 4 elements answer : option e ."
Answer: e
Problem: he average weight of 8 persons increases by 2.5 kg when a new person comes in place of one of them weighing 75 kg . what might be the weight of the new person ?
Options: a ) 75 kg , b ) 95 kg , c ) 45 kg , d ) 85 kg , e ) 25 kg
Rationale: "explanation : total weight increased = ( 8 x 2.5 ) kg = 20 kg . weight of new person = ( 75 + 20 ) kg = 95 kg . answer : b"
Answer: b
Problem: a rectangle a has an area of 30 square centimeters . square b has a perimeter of 16 centimeters . if square b is placed within square a and a random point is chosen within square a , what is the probability the point is not within square b ?
Options: a ) 9 / 30
b ) 14 / 30
c ) 4 / 9
d ) 3 / 5
e ) 6 / 25
Rationale: i guess it ' s mean that square b is placed within rectangle a entirely . since , the perimeter of b is 16 , then its side is 16 / 4 = 4 and the area is 4 ^ 2 = 16 ; empty space between the squares is 30 - 16 = 14 square centimeters , so if a random point is in this area then it wo n ' t be within square b : p = favorable / total = 14 / 30 . answer : b .
Answer: b
Problem: a garden center sells a certain grass seed in 5 - pound bags at $ 13.85 per bag , 10 - pound bags at $ 20.40 per bag , and 25 - pound bags $ 32.25 per bag . if a customer is to buy at least 65 pounds of the grass seed , but no more than 80 pounds , what is the least possible cost of the grass seed that the customer will buy ?
Options: a ) $ 94.03 , b ) $ 96.75 , c ) $ 98.75 , d ) $ 102.07 , e ) $ 105.3
Rationale: "there can be 2 cases 1 ) 25 + 25 + 10 + 5 = $ 98.75 or 2 ) 25 + 25 + 25 = $ 96.75 c"
Answer: c
Problem: the difference between compound interest and simple interest on a certain amount of money at 5 % per annum for 2 years is 20 . find the sum :
Options: a ) 4500 , b ) 7500 , c ) 5000 , d ) 8000 , e ) none of these
Rationale: "sol . ( d ) let the sum be 100 . therefore , si = 100 × 5 × 2100 = 10100 × 5 × 2100 = 10 and ci = 100 ( 1 + 5100 ) 2 − 100100 ( 1 + 5100 ) 2 − 100 ∴ = 100 × 21 × 2120 × 20 − 100 = 414 = 100 × 21 × 2120 × 20 − 100 = 414 difference of ci and si = 41 ⁄ 4 - 10 = 1 ⁄ 4 if the difference is 1 ⁄ 4 , the sum = 100 = > if the difference is 20 , the sum = 400 × 20 = 8000 answer d"
Answer: d
Problem: if the sales tax reduced from 3 1 / 2 % to 3 1 / 3 % , then what difference does it make to a person who purchases an article with market price of rs . 8400 ?
Options: a ) rs . 12 , b ) rs . 16 , c ) rs . 14 , d ) rs . 10 , e ) rs . 18
Rationale: "required difference = [ 3 ½ % of rs . 8400 ] – [ 3 1 / 3 % of rs . 8400 ] = [ ( 7 / 20 - ( 10 / 3 ) ] % of rs . 8400 = 1 / 6 % of rs . 8400 = rs . [ ( 1 / 6 ) 8 ( 1 / 100 ) * 8400 ] = rs . 14 . answer is c ."
Answer: c
Problem: how many two - digit whole numbers yield a remainder of 2 when divided by 12 and also yield a remainder of 2 when divided by 6 ?
Options: a ) none , b ) five , c ) six , d ) seven , e ) eight
Rationale: "the possible number n can be written as follow : n = multiple of lcm ( 12,6 ) + 1 st such number n = 12 x + 2 possible values = 2 , 26,38 , 50,62 , 86,98 answer : 6 such 2 digit number . c ."
Answer: c
Problem: find ( 7 x + 8 y ) / ( x - 2 y ) if x / 2 y = 3 / 2 ?
Options: a ) 24 , b ) 25 , c ) 26 , d ) 27 , e ) 29
Rationale: x / 2 y = 3 / 2 = > x = 6 y / 2 = 3 y = > ( 7 x + 8 y ) / ( x - 2 y ) = ( ( 7 * ( 3 y ) ) + 8 y ) / ( 3 y - 2 y ) = > 29 y / y = 29 answer : e
Answer: e
Problem: kramer can pack 10 boxes of cigarettes per minute . if there are 5 boxes of cigarettes in one case , how many cases can kramer pack in 2 hours ?
Options: a ) 100 , b ) 120 , c ) 240 , d ) 150 , e ) 200
Rationale: kramer can pack 10 boxes per min . therefore in 2 hrs ( 120 mins ) he can pack 120 * 10 = 1200 boxes . if there are 5 boxes in one case then then the total number of cases packed by kramer = 1200 / 5 = 240 answer is c
Answer: c
Problem: what number should replace the question mark ? 11 , 15 , 16 , 12 , 21 , 9 , - - - ?
Options: a ) 21 , b ) 29 , c ) 28 , d ) 27 , e ) 26
Rationale: "answer : e 11 , 15 , 16 , 12 , 21 , 9 , - - - ? there are two alternate sequences : + 5 and - 3 ."
Answer: e
Problem: list d consists of 12 consecutive integers . if - 4 is the least integer in list d , what is the range of positive integers in list d ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 11 , e ) 12
Rationale: since - 4 is the least integer in list d , then 7 is the largest integer in that list . thus the range of the positive integers in the list is 7 - 1 = 6 . answer : b .
Answer: b
Problem: a train 125 m long passes a man , running at 15 km / hr in the same direction in which the train is going , in 10 sec . the speed of the train is ?
Options: a ) 40 , b ) 50 , c ) 60 , d ) 79 , e ) 80
Rationale: "speed of the train relative to man = 125 / 10 = 25 / 2 m / sec . = 25 / 2 * 18 / 5 = 45 km / hr let the speed of the train be x km / hr . then , relative speed = ( x - 15 ) km / hr . x - 15 = 45 = > x = 60 km / hr . answer : option c"
Answer: c
Problem: the ratio of the volumes of two cubes is 729 : 1000 . what is the ratio of their total surface areas ?
Options: a ) 1 : 12 , b ) 81 : 13 , c ) 46 : 51 , d ) 86 : 16 , e ) 56 : 13
Rationale: "ratio of the sides = ³ √ 729 : ³ √ 1000 = 9 : 10 ratio of surface areas = 92 : 102 = 46 : 51 answer : c"
Answer: c
Problem: the average weight of 9 person ' s increases by 5.5 kg when a new person comes in place of one of them weighing 86 kg . what might be the weight of the new person ?
Options: a ) 72 kg , b ) 77.5 kg , c ) 135.5 kg , d ) data inadequate , e ) none of these
Rationale: "total weight increased = ( 9 x 5.5 ) kg = 49.5 kg . weight of new person = ( 86 + 49.5 ) kg = 135.5 kg . answer : option c"
Answer: c
Problem: in a maths test , students were asked to find 5 / 16 of a certain number . one of the students by mistake found 5 / 6 th of that number and his answer was 50 more than the correct answer . find the number .
Options: a ) 96 , b ) 280 , c ) 384 , d ) 400 , e ) 500
Rationale: "explanation : let the number be x . 5 * x / 6 = 5 * x / 16 + 50 25 * x / 48 = 50 x = 96 answer a"
Answer: a
Problem: a rectangle having length 150 cm and width 40 cm . if the length of the rectangle is increased by fifteen percent then how much percent the breadth should be decreased so as to maintain the same area .
Options: a ) 25 % , b ) 9.09 % , c ) 40 % , d ) 75 % , e ) none of these
Rationale: "explanation : solution : ( 15 / ( 150 + 15 ) * 100 ) % = 9.09 % answer : b"
Answer: b
Problem: two numbers n and 12 have lcm = 42 and gcf = 6 . find n .
Options: a ) 35 , b ) 56 , c ) 21 , d ) 87 , e ) 24
Rationale: "the product of two integers is equal to the product of their lcm and gcf . hence . 12 * n = 42 * 6 n = 42 * 6 / 12 = 21 correct answer c"
Answer: c
Problem: ajay spends 45 % of his monthly income on household items , 25 % of his monthly income on buying cloths , 7.5 % of his monthly income on medicines and saves the remaining amount which is rs . 9000 . find his monthly income .
Options: a ) rs . 40000 , b ) rs . 36000 , c ) rs . 50000 , d ) rs . 45000 , e ) none of these
Rationale: "let the monthly income of ajay be rs . x savings of ajay = x - ( 45 + 25 + 7.5 ) / 100 * x = 22.5 / 100 x 22.5 / 100 x = 9000 x = 40000 . answer : a"
Answer: a
Problem: the average of numbers 0.44204 , 0.44203 , 0.44202 and 0.44201 is ?
Options: a ) 0.44202 , b ) 0.44204 , c ) 0.442022 , d ) 0.442025 , e ) none
Rationale: "answer average = ( 0.44204 + 0.44203 + 0.44202 + 0.44201 ) / 4 = 1.7681 / 4 = 0.442025 correct option : d"
Answer: d
Problem: the length of the bridge , which a train 145 metres long and travelling at 45 km / hr can cross in 30 seconds , is :
Options: a ) 200 m , b ) 230 m , c ) 245 m , d ) 250 m , e ) 270 m
Rationale: "let the length of the bridge : l the equation now is l + 145 / 12.5 m / s ( 45 km / hr or 12.5 m / s ) = 30 solving , l = 230 m answer : b"
Answer: b
Problem: how many diagonals does a polygon with 19 sides have , if one of its vertices does not connect to any diagonal ?
Options: a ) 135 , b ) 125 , c ) 120 , d ) 110 , e ) 140
Rationale: "if i calculate it using the formulae , # diagonals = n ( n - 3 ) / 2 each vertex sends of n - 3 diagonals n = 19 - 1 then 18 * ( 18 - 3 ) / 2 = 135 correct option : a"
Answer: a
Problem: sachin is younger than rahul by 7 years . if their ages are in the respective ratio of 7 : 9 , how old is sachin ?
Options: a ) 22.5 years , b ) 24.5 years , c ) 12.5 years , d ) 28.5 years , e ) 29.5 years
Rationale: "let rahul ' s age be x years . then , sachin ' s age = ( x - 7 ) years . therefore ( x - 7 ) / x = 7 / 9 9 x - 63 = 7 x 2 x = 63 x = 31.5 hence , sachin ' s age = ( x - 7 ) = 24.5 years . answer : b"
Answer: b
Problem: a train running at the speed of 72 km / hr crosses a pole in 9 sec . what is the length of the train ?
Options: a ) 288 , b ) 279 , c ) 277 , d ) 272 , e ) 180
Rationale: "speed = 72 * 5 / 18 = 20 m / sec length of the train = speed * time = 20 * 9 = 180 m answer : e"
Answer: e
Problem: find the 12 th term of an arithmetic progression whose first term is 2 and the common difference is 8 .
Options: a ) 45 , b ) 38 , c ) 44 , d ) 90 , e ) 96
Rationale: "n th term of a . p = a + ( n - 1 ) * d = 2 + ( 12 - 1 ) * 8 , = 2 + 88 = 90 . answer : d"
Answer: d
Problem: a set consists of 20 numbers , all are even or multiple of 5 . if 9 numbers are even and 12 numbers are multiple of 5 , how many numbers is multiple of 10 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 5
Rationale: "{ total } = { even } + { multiple of 5 } - { both } + { nether } . since { neither } = 0 ( allare even or multiple of 5 ) then : 20 = 9 + 12 - { both } + 0 ; { both } = 1 ( so 1 number is both even and multiple of 5 , so it must be a multiple of 10 ) . answer : b ."
Answer: b
Problem: united telephone charges a base rate of $ 6.00 for service , plus an additional charge of $ 0.25 per minute . atlantic call charges a base rate of $ 12.00 for service , plus an additional charge of $ 0.20 per minute . for what number of minutes would the bills for each telephone company be the same ?
Options: a ) 20 minutes , b ) 110 minutes , c ) 120 minutes , d ) 140 minutes , e ) 160 minutes
Rationale: "lets take number of minutesx . given that , 6 + 0.25 x = 12 + 0.2 x - > 0.05 x = 2 - > x = 120 minutes ans c"
Answer: c
Problem: the ratio of three numbers is 1 : 3 : 4 and the sum of their squares is 2600 . the sum of the numbers is ?
Options: a ) a ) 10 , b ) b ) 12 , c ) c ) 15 , d ) d ) 14 , e ) e ) 9
Rationale: "let the numbers be x , 3 x , 4 x then , x ^ 2 + 9 x ^ 2 + 16 x ^ 2 = 2600 26 x ^ 2 = 2600 x ^ 2 = 100 x = 10 answer is a"
Answer: a
Problem: a , b and c enter into partnership . a invests some money at the beginning , b invests double the amount after 6 months , and c invests thrice the amount after 8 months . if the annual gain be rs . 18000 . a ' s share is ?
Options: a ) rs . 7500 , b ) rs . 7200 , c ) rs . 6000 , d ) rs . 5750 , e ) rs . 6750
Rationale: "x * 12 : 2 x * 6 : 3 x * 4 1 : 1 : 1 1 / 3 * 18000 = 6000 answer : c"
Answer: c
Problem: the difference of two numbers is 1365 . on dividing the larger number by the smaller , we get 6 as quotient and 15 as remainder . what is the smaller number ?
Options: a ) 240 , b ) 270 , c ) 295 , d ) 360 , e ) 365
Rationale: "let the smallest number be x . then larger number = ( x + 1365 ) x + 1365 = 6 x + 15 = 5 x = 1350 x = 270 smaller number = 270 . answer : b"
Answer: b
Problem: in a 100 m race , sam beats john by 4 seconds . on the contrary , if sam allowed john to start 24 m ahead of sam , then sam and john reach the finishing point at the same time . how long does sam take to run the 100 m race ?
Options: a ) 4 seconds , b ) 25 seconds , c ) 19 seconds , d ) 21 seconds , e ) 6.25 seconds
Rationale: "their difference is 4 second but this difference is 0 if john allows sam to start the race from 24 m ahead . that means jhon was 24 m away from finishing line when they started together . so he will cover 24 m in 4 seconds . so his speed = 24 / 4 = 6 metre / second . so time taken = 100 / 4 = 25 seconds . so sam took = 19 seconds . correct answer = c"
Answer: c
Problem: the contents of a certain box consist of 14 apples and 20 oranges . how many oranges must be removed from the box so that 70 percent of the pieces of fruit in the box will be apples ?
Options: a ) 3 , b ) 6 , c ) 14 , d ) 17 , e ) 20
Rationale: the objective here is that 70 % of the fruit in the box should be apples . now , there are 14 apples at start and there is no talk of removing any apples , so number of apples should remain 14 and they should constitute 70 % of total fruit , so total fruit = 14 / 0.7 = 20 so we should have 20 - 14 = 6 oranges . right now , there are 20 oranges , so to get to 6 oranges , we should remove 20 - 6 = 14 oranges . answer c
Answer: c
Problem: a reduction of 25 % in the price of oil enables a house wife to obtain 5 kgs more for rs . 500 , what is the reduced price for kg ?
Options: a ) 25 , b ) 60 , c ) 70 , d ) 80 , e ) 20
Rationale: "a 500 * ( 25 / 100 ) = 125 - - - - 5 ? - - - - 1 = > rs . 25"
Answer: a
Problem: there are two concentric circles with radii 8 and 6 . if the radius of the outer circle is increased by 25 % and the radius of the inner circle decreased by 50 % , by what percent does the area between the circles increase ?
Options: a ) 225 , b ) 250 , c ) 275 , d ) 300 , e ) 325
Rationale: "the area of a circle is pir ^ 2 , where r is the radius . the area of the big circle is 64 pi . the area of the small circle is 36 pi . the area a 1 between the circles is 28 pi . when the big circle ' s radius increases , the new area is 100 pi . when the small circle ' s radius decreases , the new area is 9 pi . the area a 2 between the circles is 91 pi . the ratio of a 2 / a 1 is 91 / 28 = 3.25 which is an increase of 225 % . the answer is a ."
Answer: a