regisss/math_qa huggingface dataset:
Problem: a movie buff owns movies on dvd and on blu - ray in a ratio of 7 : 2 . if she buys 4 more blu - ray movies , that ratio would change to 13 : 4 . if she owns movies on no other medium , what was the original number of movies in her library before the extra purchase ?
Options: a ) 22 , b ) 28 , c ) 77 , d ) 99 , e ) 234
Rationale: "if u can just keep an eye on the options 99 is the only multiple of 9 in options given . . so you can mark it wid in seconds . now coming to the process m ( d ) = 7 x and b ( d ) = 2 x now from the next line the new eqn becomes 7 x / ( 2 x + 6 ) = 11 / 4 solving it 28 x = 26 x + 52 x = 11 which means m ( d ) = 182 and b ( d ) = 52 so total initially is m ( d ) + b ( d ) = 234 e"
Answer: e
Problem: there are 25 balls in a jar . you take out 5 blue balls without putting them back inside , and now the probability of pulling out a blue ball is 1 / 5 . how many blue balls were there in the beginning ?
Options: a ) 12 . , b ) 9 . , c ) 8 . , d ) 7 . , e ) 6 .
Rationale: "9 = 5 blue balls + 20 / 5 answer : b"
Answer: b
Problem: a circular well with a diameter of 4 metres , is dug to a depth of 24 metres . what is the volume of the earth dug out ?
Options: a ) 32 m 3 , b ) 36 m 3 , c ) 40 m 3 , d ) 44 m 3 , e ) 301.6
Rationale: "solution volume = π r 2 h ‹ = › ( 22 / 7 × 2 × 2 × 24 ) m 3 ‹ = › 301.6 m 3 . answer e"
Answer: e
Problem: priya and her father differ in their ages by 31 years . after 8 years . if the sum of their ages will be 69 , their present ages are
Options: a ) 11 , 42 , b ) 12 , 24 , c ) 15 , 42 , d ) 16 , 19 , e ) 33 , 44
Rationale: a 11 , 42 let the age of priya = x years then , the age of her father = ( x + 31 ) years atq , ( x + 8 ) + ( x + 31 + 8 ) = 69 2 x + 47 = 69 2 x = 69 – 47 = 22 x = 11 the age of priya = 11 years the age of her father = 11 + 31 = 42 years
Answer: a
Problem: if 7 spiders make 7 webs in 7 days , then how many days are needed for 1 spider to make 1 web ?
Options: a ) 1 , b ) 7 , c ) 3 , d ) 14 , e ) 16
Rationale: "explanation : let , 1 spider make 1 web in x days . more spiders , less days ( indirect proportion ) more webs , more days ( direct proportion ) hence we can write as ( spiders ) 7 : 1 ( webs ) 1 : 7 } : : x : 7 ⇒ 7 × 1 × 7 = 1 × 7 × x ⇒ x = 7 answer : option b"
Answer: b
Problem: the price of lunch for 13 people was $ 207 including a 15 % gratuity for service . what was the average price per person , excluding the gratuity ?
Options: a ) 11.73 , b ) 12 , c ) 13.85 , d ) 14 , e ) 15.87
Rationale: "clearly c is the answer i used poe here lets consider option ( c ) 13 * 13.85 = 180 now 180 ( 115 / 100 ) = 207 = > possible answer imo c"
Answer: c
Problem: a shopkeeper sold an article at $ 1800 with 20 % profit . then find its cost price ?
Options: a ) $ 1000 , b ) $ 1500 , c ) $ 1850 , d ) $ 1600 , e ) $ 2000
Rationale: "cost price = selling price * 100 / ( 100 + profit ) c . p . = 1800 * 100 / 120 = $ 1500 answer is b"
Answer: b
Problem: find the principle on a certain sum of money at 5 % per annum for 2 years if the amount being rs . 1120 ?
Options: a ) 1018 , b ) 1067 , c ) 1977 , d ) 1056 , e ) 1097
Rationale: "1120 = p [ 1 + ( 5 * 2 ) / 100 ] p = 1018 answer : a"
Answer: a
Problem: a man swims downstream 24 km and upstream 16 km taking 4 hours each time , what is the speed of the man in still water ?
Options: a ) 8 , b ) 5 , c ) 24 , d ) 12 , e ) 36
Rationale: "24 - - - 4 ds = 6 ? - - - - 1 16 - - - - 4 us = 4 ? - - - - 1 m = ? m = ( 6 + 4 ) / 2 = 5 answer : b"
Answer: b
Problem: when positive integer k is divided by 5 , the remainder is 2 . when k is divided by 6 , the remainder is 5 . if k is less than 38 , what is the remainder when k is divided by 7 ?
Options: a ) 2 , b ) 4 , c ) 3 , d ) 5 , e ) 6
Rationale: "cant think of a straight approach but here is how i solved it : k is divided by 5 and remainder is 2 . this means k = 5 n + 2 ( n is an integer ) so the possible values of k = { 2 , 7 , 12 , 17 , 22 , 27 , 32 , 37 } ( less than 38 ) secondly , if k is divided by 6 , the remainder is 5 = > k = 6 m + 5 so the possible value set for k = { 5 , 11 , 17 , 23 , 29,35 } ( less than 38 ) 17 is the only common number in both the sets . hence k = 17 answer : c"
Answer: c
Problem: a alone can do a piece of work in 6 days and b alone in 8 days . a and b undertook to do it for rs . 6000 . with the help of c , they completed the work in 3 days . how much is to be paid to c ?
Options: a ) s . 375 , b ) s . 400 , c ) s . 600 , d ) s . 750 , e ) s . 850
Rationale: "c ' s 1 day ' s work = 1 / 3 - ( 1 / 6 + 1 / 8 ) = 1 / 3 - 7 / 24 = 1 / 24 a ' s wages : b ' s wages : c ' s wages = 1 / 6 : 1 / 8 : 1 / 24 = 4 : 3 : 1 c ' s share ( for 3 days ) = rs . ( 3 * 1 / 24 * 6000 ) = rs . 750 answer = d"
Answer: d
Problem: a can do a job in 9 days and b can do it in 27 days . a and b working together will finish twice the amount of work in - - - - - - - days ?
Options: a ) 22 days , b ) 18 days , c ) 22 6 / 2 days , d ) 27 days , e ) 9 days
Rationale: "1 / 9 + 1 / 27 = 3 / 27 = 1 / 9 9 / 1 = 9 * 2 = 18 days answer : b"
Answer: b
Problem: what will be the remainder when 13 ^ 36 is divided by 2196 ?
Options: a ) 0 , b ) 1 , c ) 12 , d ) 2195 , e ) 5
Rationale: "in such qs , best is to get the dividend and divisor in some friendly figures . . 13 ^ 36 = ( 13 ^ 3 ) ^ 12 = 2197 ^ 12 = ( 2196 + 1 ) ^ 12 when ( 2196 + 1 ) ^ 12 is divided by 2196 , all terms in the expansion are divisible by 2196 except 1 ^ 12 , so the remainder will be 1 answer : b"
Answer: b
Problem: for what value of x , is | x – 5 | + | x + 5 | + | x | = 27 ?
Options: a ) 0 , b ) 3 , c ) - 3 , d ) 9 , e ) - 9
Rationale: "for what value of x , is | x – 5 | + | x + 5 | + | x | = 27 ? it ' s easiest just to plug in answer choices : ( d ) : 9 | x – 5 | + | x + 5 | + | x | = 27 ? | 9 - 5 | + | 9 + 5 | + | 9 | = 27 ? | 4 | + | 14 | + | 9 | = 27 ( d )"
Answer: d
Problem: if an organization were to sell n tickets for a theater production , the total revenue from ticket sales would be 20 percent greater than the total costs of the production . if the organization actually sold all but 5 percent of the n tickets , the total revenue from ticket sales was what percent greater than the total costs of the production ?
Options: a ) 4 % , b ) 10 % , c ) 14 % , d ) 15 % , e ) 18 %
Rationale: let cost of prod for 1 ticket = 1 so cop for n tickets = n so for selling n tickets , sp = 1.2 * n = 1.2 n so sp of 1 ticket = 1.2 sp of 95 % tickets = 1.2 * 0.95 n so profit % = ( 1.2 * 0.95 n - n ) / n * 100 = 0.14 * 100 = 14 % answer - c
Answer: c
Problem: virginia , adrienne , and dennis have taught history for a combined total of 96 years . if virginia has taught for 9 more years than adrienne and for 12 fewer years than dennis , for how many years has dennis taught ?
Options: a ) 23 , b ) 32 , c ) 35 , d ) 41 , e ) 42
Rationale: let number of years taught by virginia = v number of years taught by adrienne = a number of years taught by dennis = d v + a + d = 96 v = a + 9 = > a = v - 9 v = d - 12 = > a = ( d - 12 ) - 9 = d - 21 d - 9 + d - 21 + d = 96 = > 3 d = 96 + 30 = 126 = > d = 42 answer e
Answer: e
Problem: the average salary of 20 people in the shipping department at a certain firm is $ 1000 . the salary of 10 of the employees is $ 600 each and the salary of 6 of the employees is $ 200 each . what is the average salary of the remaining employees ?
Options: a ) $ 2500 , b ) $ 3200 , c ) $ 4500 , d ) $ 5000 , e ) $ 5200
Rationale: "total salary . . . 20 * 1000 = 20000 10 emp @ 600 = 6000 6 emp @ 200 = 1200 remaing 4 emp salary = 20000 - 6000 - 1200 = 12800 average = 12800 / 4 = 3200 answer is b"
Answer: b
Problem: an aeroplane covers a certain distance of 670 kmph in 6 hours . to cover the same distance in 6 1 / 4 hours , it must travel at a speed of
Options: a ) 440 , b ) 540 , c ) 643 , d ) 740 , e ) 250
Rationale: "speed of aeroplane = 670 kmph distance travelled in 6 hours = 670 * 6 = 4020 km speed of aeroplane to acver 4020 km in 25 / 4 = 4020 * 4 / 25 = 643 km answer c ."
Answer: c
Problem: a cube is divided into 216 identical cubelets . each cut is made parallel to some surface of the cube . but before doing that , the cube is painted with green on one set of opposite faces , red on another set of opposite faces , and blue on the third set of opposite faces . how many cubelets are painted with exactly one colour ?
Options: a ) 72
b ) 84
c ) 96
d ) 108
e ) 120
Rationale: each side of the cube has 6 x 6 = 36 cubelets . only the interior cubelets are painted one colour . on each side , 4 x 4 = 16 cubelets are painted one colour . since the cube has six sides , the number of cubes with one colour is 6 * 16 = 96 the answer is c .
Answer: c
Problem: a sum fetched a total simple interest of $ 4061.25 at the rate of 9 p . c . p . a . in 5 years . what is the sum ?
Options: a ) $ 8829 , b ) $ 2840 , c ) $ 6578 , d ) $ 7782 , e ) $ 8926
Rationale: "e 8926 principal = $ 100 x 4016.25 / 9 x 5 = $ 406125 / 45 = $ 8926 ."
Answer: e
Problem: the average of 5 consecutive odd numbers is 55 . what is the difference between the highest and lowest numbers ?
Options: a ) 2 , b ) 5 , c ) 8 , d ) 9 , e ) 10
Rationale: explanation : let the numbers be x , x + 2 , x + 4 , x + 6 and x + 8 . then , ( x + ( x + 2 ) + ( x + 4 ) + ( x + 6 ) + ( x + 8 ) ) / 5 = 55 5 x + 20 = 275 x = 255 / 5 = 51 . so , required difference = ( 51 + 8 ) 51 = 8 answer : c
Answer: c
Problem: in a class of 25 students in an examination in maths 3 students scored 95 marks each , 5 get zero each and the average of the rest was 45 . what is the average of the whole class ?
Options: a ) a ) 47 , b ) b ) 45.6 , c ) c ) 42 , d ) d ) 48 , e ) e ) 49
Rationale: "explanation : total marks obtained by a class of 25 students = 3 * 95 + 5 * 0 + 17 * 45 = 1050 average marks of whole class = 1050 / 25 = 42 answer : option c"
Answer: c
Problem: 18.05 ã — 0.001 = ?
Options: a ) 0.1805 , b ) 0.01805 , c ) 1.805 , d ) 0.001805 , e ) none of these
Rationale: "18.05 ã — 0.001 = ? or , ? = 0.01805 answer b"
Answer: b
Problem: a school has 4 section of chemistry in class x having 40 , 35 , 45 and 42 students . the mean marks obtained in chemistry test are 50 , 60 , 55 and 45 respectively for the 4 sections . determine the overall average of marks per student .
Options: a ) 50.25 , b ) 52.25 , c ) 51.25 , d ) 53.25 , e ) none of the above
Rationale: "required average marks = 40 × 50 + 35 × 60 + 45 × 55 + 42 × 45 / 40 + 35 + 45 + 42 = 2000 + 2100 + 2475 + 1890 / 162 = 8465 ⁄ 162 = 52.25 answer b"
Answer: b
Problem: ajay can walk 7 km in 1 hour . in how many hours he can walk 80 km ?
Options: a ) 5 hrs , b ) 11.4 hrs , c ) 15.5 hrs , d ) 20.4 hrs , e ) 30 hrs
Rationale: "1 hour he walk 8 km he walk 80 km in = 80 / 7 * 1 = 11.4 hours answer is b"
Answer: b
Problem: the percentage profit earned by selling an article for rs . 1320 is equal to the percentage loss incurred by selling the same article for rs . 1280 . at what price should the article be sold to make 25 % profit ?
Options: a ) 3000 , b ) 1230 , c ) 2000 , d ) 1625 , e ) 3400
Rationale: "c . p . be rs . x . then , ( 1320 - x ) / x * 100 = ( x - 1280 ) / x * 100 1320 - x = x - 1280 2 x = 2600 = > x = 1300 required s . p . = 125 % of rs . 1300 = 125 / 100 * 1300 = rs . 1625 . anser d"
Answer: d
Problem: the compound ratio of 5 : 1 , 3 : 1 and 2 : 5 ?
Options: a ) 6 : 1 , b ) 1 : 3 , c ) 1 : 5 , d ) 1 : 1 , e ) 1 : 6
Rationale: 5 / 1 * 3 / 1 * 2 / 5 = 30 / 5 6 : 1 answer : a
Answer: a
Problem: 130 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 ) 13 days
Rationale: "1 women ' s 1 day work = 1 / 910 1 child ' s 1 day work = 1 / 140 ( 5 women + 10 children ) ' s 1 day work = ( 5 / 910 + 10 / 140 ) = 1 / 13 5 women and 10 children will complete the work in 13 days . answer : e"
Answer: e
Problem: a grocer has a sale of rs . 3435 , rs . 3920 , rs . 3855 , rs . 4230 and rs . 3560 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 3500 ?
Options: a ) 500 , b ) 1000 , c ) 6000 , d ) 7000 , e ) 2000
Rationale: "total sale for 5 months = rs . ( 3435 + 3920 + 3855 + 4230 + 3560 ) = rs . 19000 . required sale = rs . [ ( 3500 x 6 ) - 19000 ] = rs . ( 21000 - 19000 ) = rs . 2000 answer : option e"
Answer: e
Problem: a number of 55 marbles is to be divided and contain with boxes . if each box is to contain 3 , 4 , or 5 marbles , what is the largest possible number of boxes ?
Options: a ) 10 , b ) 12 , c ) 15 , d ) 16 , e ) 19
Rationale: to maximize # of boxes we should minimize marbles per box : 17 * 3 + 1 * 4 + 1 * 5 = 50 - - > 17 + 1 + 1 = 19 . answer : e .
Answer: e
Problem: the length of a side of a hexagon is 7 inches . what is the perimeter ?
Options: a ) 48 , b ) 42 , c ) 44 , d ) 45 , e ) 40
Rationale: "hexagon . it means 6 equal sides . p = 6 ( 7 ) = 42 inches answer b"
Answer: b
Problem: working alone , printers x , y , and z can do a certain printing job , consisting of a large number of pages , in 12 , 25 , and 30 hours , respectively . what is the ratio of the time it takes printer x to do the job , working alone at its rate , to the time it takes printers y and z to do the job , working together at their individual rates ?
Options: a ) 4 / 11 , b ) 1 / 2 , c ) 15 / 22 , d ) 150 / 11 , e ) 11 / 4
Rationale: "p 1 takes 12 hrs rate for p 2 p 3 together = 1 / 25 + 1 / 30 = 11 / 150 therefore they take 150 / 11 ratio = 150 / 11 = d"
Answer: d
Problem: how many numbers from 45 to 110 are exactly divisible by 12 ?
Options: a ) 5 , b ) 7 , c ) 6 , d ) 11 , e ) 12
Rationale: "option ' c ' 45 / 12 = 3 and 110 / 12 = 9 = = > 9 - 3 = 6 numbers"
Answer: c
Problem: 40 is subtracted from 60 % of a number , the result is 50 . find the number ?
Options: a ) 150 , b ) 330 , c ) 277 , d ) 279 , e ) 712
Rationale: "( 60 / 100 ) * x – 40 = 50 6 x = 900 x = 150 answer : a"
Answer: a
Problem: a man has rs . 10350 in the form of rs . 50 notes and rs . 500 notes . the total number of notes are 108 . find the number of notes of rs . 50 denomination .
Options: a ) 15 , b ) 21 , c ) 17 , d ) 19 , e ) 97
Rationale: "total money = rs . 10350 . let 50 rupees note was x . then 500 rupees note = 108 - x now , 50 * x + 500 * ( 108 - x ) = 10350 50 x + 54000 - 500 x = 10350 - 450 x = - 43650 x = 97 . no . of 50 rupees note = 97 . answer : option e"
Answer: e
Problem: a hiker walked for 3 days . she walked 18 miles on the first day , walking 3 miles per hour . on the second day she walked for one less hour but she walked one mile per hour , faster than on the first day . on the third day 5 miles per hour for 6 hours . how many miles in total did she walk ?
Options: a ) 68 , b ) 44 , c ) 58 , d ) 60 , e ) 62
Rationale: first day - 18 miles with 3 miles per hours then total - 6 hours for that day second day - 4 miles per hour and 5 hours - 20 miles third day - 5 miles per hour and 6 hours - 30 miles total 18 + 20 + 30 = 68 answer : option a .
Answer: a
Problem: a sum of money at simple interest amounts to rs . 815 in 3 years and to rs . 878 in 4 years . the sum is :
Options: a ) 500 , b ) 698 , c ) 626 , d ) 910 , e ) none
Rationale: "sol . s . i . for 1 year = rs . ( 878 - 815 ) = rs . 63 . s . i . for 3 years = rs . ( 63 * 3 ) = rs . 189 . â ˆ ´ principal = rs . ( 815 - 189 ) = rs . 626 answer c"
Answer: c
Problem: after a storm deposits 120 billion gallons of water into the city reservoir , the reservoir is 85 % full . if the original contents of the reservoir totaled 220 billion gallons , the reservoir was approximately what percentage full before the storm ?
Options: a ) 45 % , b ) 48 % , c ) 55 % , d ) 58 % , e ) 65 %
Rationale: "when the storm deposited 120 billion gallons , volume of water in the reservoir = 220 + 120 = 340 billion gallons if this is only 85 % of the capacity of the reservoir , the total capacity of the reservoir = 340 / 0.85 = 400 billion gallons therefore percentage of reservoir that was full before the storm = ( 220 / 400 ) * 100 = 55 % option c"
Answer: c
Problem: find the value of 72517 x 9999 = m ?
Options: a ) 345434667 , b ) 246465757 , c ) 465767867 , d ) 725097483 , e ) 645354643
Rationale: "72518 x 9999 = 72517 x ( 10000 - 1 ) = 72517 x 10000 - 72517 x 1 = 725170000 - 72517 = 725097483 d"
Answer: d
Problem: 10 % people of a village in sri lanka died by bombardment , 15 % of the remainder left the village on account of fear . if now the population is reduced to 2907 , how much was it in the beginning ?
Options: a ) a ) 3800 , b ) b ) 4200 , c ) c ) 4400 , d ) d ) 4500 , e ) e ) 4600
Rationale: "x * ( 90 / 100 ) * ( 85 / 100 ) = 2907 x = 3800 answer : a"
Answer: a
Problem: average of 5 numbers is 20 , and the sum of 3 of the numbers is 48 , what is the average of the other 2 numbers ?
Options: a ) 24 , b ) 34 , c ) 29 , d ) 35 , e ) 26
Rationale: let the five numbers be a , b , c , d , e . then their average is ( a + b + c + d + e ) / 5 = 20 a + b + c = 48 ( 48 + d + e ) / 5 = 20 48 + d + e = 100 d + e = 52 average = 52 / 2 = 26 ans e
Answer: e
Problem: the population of a city increases by 4 % per year but due to migration it decrease by 1 % per years . what will be the percentage increase in population in 3 years ?
Options: a ) 9 % , b ) 9.27 % , c ) 27 % , d ) 12 % , e ) none of these
Rationale: "actual increase in population = 3 % let , earlier population = 100 then the population after 3 years = 100 ( 1 + 3 / 100 ) ^ 3 = 109.2727 ∴ required percentage = 9.27 % answer : b"
Answer: b
Problem: a rectangle measures 8 cm on length and its diagonal measures 17 cm . what is the perimeter of the rectangle ?
Options: a ) 44 cm
b ) 42 cm
c ) 46 cm
d ) 49 cm
e ) 41 cm
Rationale: second side = √ 17 power 2 - 8 power 2 = √ 289 - 64 = 15 cm perimeter = 2 ( l + b ) = 2 ( 8 + 5 ) cm = 2 ( 23 ) = 46 cm answer is c .
Answer: c
Problem: $ 6,000 is deposited in a savings account that pays 10 % annual interest compounded semiannually . to the nearest dollar , how much is in the account at the end of the year ?
Options: a ) $ 6615.15 , b ) $ 6615.00 , c ) $ 6714.10 , d ) $ 6655.55 , e ) $ 6698.20
Rationale: "this is the case of semi - annual compoundingso , multiply time period by 2 and divide rate by 2 so , new time = 2 periods and new rate = 10 / 2 = 5 % now , ca = 6000 ( 1 + 5 / 100 ) ^ 2 = $ 6615.00 hence answer is b"
Answer: b
Problem: a person spends 40 % of his salary on food , 25 % on house rent , 15 % on entertainment and 5 % on conveyance . if his savings at the end of the month is rs . 1200 , then his salary per month in rupees is :
Options: a ) 4000 , b ) 6000 , c ) 8000 , d ) 10000 , e ) none of these
Rationale: "total expenditure = 40 + 25 + 15 + 5 = 85 % saving = ( 100 - 85 ) = 15 % 15 / 100 × salary = 1200 , salary = 8000 rs . answer : c ."
Answer: c
Problem: in 1982 and 1983 , company b ’ s operating expenses were $ 10.0 million and $ 12.0 million , respectively , and its revenues were $ 15.6 million and $ 18.8 million , respectively . what was the percent increase in company b ’ s profit ( revenues minus operating expenses ) from 1982 to 1983 ?
Options: a ) 3 % , b ) 16 2 / 3 % , c ) 25 % , d ) 21 3 / 7 % , e ) 60 %
Rationale: "profit in 1982 = 15.6 - 10 = 5.6 million $ profit in 1983 = 18.8 - 12 = 6.8 million $ percentage increase in profit = ( 6.8 - 5.6 ) / 5.6 * 100 % = 21 3 / 7 % answer d"
Answer: d
Problem: a train running at the speed of 48 km / hr crosses a pole in 9 seconds . what is the length of the train ?
Options: a ) 140 , b ) 130 , c ) 120 , d ) 170 , e ) 160
Rationale: "speed = ( 48 x 5 / 18 ) m / sec = ( 40 / 3 ) m / sec . length of the train = ( speed x time ) . length of the train = ( 40 / 3 x 9 ) m = 120 m . answer is c ."
Answer: c
Problem: a , b , k start from the same place and travel in the same direction at speeds of 30 km / hr , 40 km / hr , 60 km / hr respectively . b starts seven hours after a . if b and k overtake a at the same instant , how many hours after a did k start ?
Options: a ) 3 , b ) 4.5 , c ) 4 , d ) d ) 5.5 , e ) e ) 14
Rationale: "the table you made does n ' t make sense to me . all three meet at the same point means the distance they cover is the same . we know their rates are 30 , 40 and 60 . say the time taken by b is t hrs . then a takes 7 + t hrs . and we need to find the time taken by k . distance covered by a = distance covered by b 30 * ( 7 + t ) = 40 * t t = 21 hrs distance covered by b = distance covered by k 40 * t = 60 * time taken by k time taken by k = 40 * 21 / 60 = 14 hrs time taken by a = 7 + t = 7 + 21 = 28 hrs time taken by k = 14 hrs so k starts 28 - 14 = 14 hrs after a . ( answer e )"
Answer: e
Problem: the average height of 35 boys in a class was calculated as 185 cm . it has later found that the height of one of the boys in the class was wrongly written as 166 cm whereas his actual height was 106 cm . find the actual average height of the boys in the class ( round off your answer to two decimal places ) . ?
Options: a ) 178.27 cm , b ) 183.29 cm , c ) 978.29 cm , d ) 178.89 cm , e ) 176.29 cm
Rationale: "calculated average height of 35 boys = 185 cm . wrong total height of 35 boys = 185 * 35 cm . this was as a result of an actual height of 106 cm being wrongly written as 166 cm . correct total height of 35 boys = 185 cm - ( 166 cm - 106 cm ) / 35 = 185 cm - 60 / 35 cm = 185 cm - 1.71 cm = 183.29 cm . answer : b"
Answer: b
Problem: the cost to park a car in a certain parking garage is $ 10.00 for up to 2 hours of parking and $ 1.75 for each hour in excess of 2 hours . what is the average ( arithmetic mean ) cost per hour to park a car in the parking garage for 9 hours ?
Options: a ) $ 1.09 , b ) $ 1.67 , c ) $ 2.225 , d ) $ 2.47 , e ) $ 2.50
Rationale: "total cost of parking for 10 hours = 10 $ for the first 2 hours and then 1.75 for ( 9 - 2 ) hours = 10 + 7 * 1.75 = 22.25 thus the average parking price = 22.25 / 9 = 2.47 $ d is the correct answer ."
Answer: d
Problem: at the wholesale store you can buy an 8 - pack of hot dogs for $ 1.55 , a 20 - pack for $ 3.05 , and a 250 - pack for $ 22.95 . what is the greatest number of hot dogs you can buy at this store with $ 205 ?
Options: a ) 1,108 , b ) 2,100 , c ) 2,140 , d ) 2,124 , e ) 2,256
Rationale: "i think it should be c . i can buy 8 250 - pack for rs 22.95 * 8 = $ 183.60 now , i can buy 7 20 - pack for 3.05 * 7 = $ 21.35 now , i am left with only $ 1.15 . i can not but anything with this . hence total hotdogs = 250 * 8 + 20 * 7 = 2140"
Answer: c
Problem: a train which has 410 m long , is running 45 kmph . in what time will it cross a person moving at 9 kmph in same direction ?
Options: a ) 56 sec , b ) 41 sec , c ) 36 sec , d ) 29 sec . , e ) 19 sec .
Rationale: "time taken to cross a moving person = length of train / relative speed time taken = 410 / ( ( 45 - 9 ) ( 5 / 18 ) = 410 / 36 * ( 5 / 18 ) = 410 / 10 = 41 sec answer : b"
Answer: b
Problem: the ratio of males to females in a class is 2 : 3 . the career preferences of the students in the class are represented in a circle graph . if the area of the graph allocated to each career preference is proportional to the number of students who have that career preference , how many degrees of the circle should be used to represent a career that is preferred by one - half of the males and three - fourths of the females in the class ?
Options: a ) 218 , b ) 226 , c ) 234 , d ) 242 , e ) 250
Rationale: "1 / 2 * 2 / 5 + 3 / 4 * 3 / 5 = 4 / 20 + 9 / 20 = 13 / 20 the number of degrees is 13 / 20 * 360 = 234 degrees the answer is c ."
Answer: c
Problem: a man can row upstream at 25 kmph and downstream at 45 kmph , and then find the speed of the man in still water ?
Options: a ) 11 , b ) 77 , c ) 30 , d ) 88 , e ) 35
Rationale: "us = 25 ds = 45 m = ( 45 + 25 ) / 2 = 35 answer : e"
Answer: e
Problem: the least number which when divided by 5 , 6 , 7 and 8 leaves a remainder 3 , but when divided by 9 leaves no remainder , is :
Options: a ) 2377 , b ) 1683 , c ) 2677 , d ) 9972 , e ) 1611
Rationale: "explanation : l . c . m . of 5 , 6 , 7 , 8 = 840 . { \ color { blue } \ therefore } required number is of the form 840 k + 3 least value of k for which ( 840 k + 3 ) is divisible by 9 is k = 2 . { \ color { blue } \ therefore } required number = ( 840 x 2 + 3 ) = 1683 . answer : b ) 1683"
Answer: b
Problem: 1 men takes 37 $ to eat a pizza in restaurant such that it have discount multiple of 4 if u eat more pizza . discount increase by multiple of 4 every pizza u eat . for 1 pizza 0 % off . for 2 pizza % off for 3 pizza 8 % off . pizza without discount is 10 $ . how much that man eats the pizza .
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: solution : b . for 1 pizza 10 $ . for 2 pizza 10 $ + 9.6 $ ( 4 % off ) = 19.6 , for 3 pizza 19.6 + 9.2 ( 8 % off ) = 28.8 , for 4 pizza 28.8 + 8.8 ( 12 % off ) = 37.6 . so he have 37 so he cant eat 4 th pizza .
Answer: b
Problem: 5 people can write 25 book in 20 days working 8 hour a day . then in how many day 125 can be written by 75 people ?
Options: a ) 25 / 3 , b ) 19 / 3 , c ) 20 / 3 , d ) 25 / 3 , e ) 22 / 3
Rationale: "work per day epr hour per person = 25 / ( 20 * 8 * 5 ) / / eq - 1 people = 75 ; let suppose day = p ; per day work for 8 hours acc . to condition work per day epr hour per person = 125 / ( p * 8 * 75 ) / / eq - 2 eq - 1 = = eq - 2 ; p = 20 / 3 answer : c"
Answer: c
Problem: if there are only 2 wheelers and 4 wheelers parked in a school located at the heart of the city , find the number of 4 wheelers parked there if the total number of wheels is 46 ?
Options: a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 15
Rationale: "four wheeler = 11 * 4 = 44 ( max ) 2 wheel = 1 so no of 4 wheeler = 11 answer : a"
Answer: a
Problem: three 6 faced dice are thrown together . the probability that exactly two dice show the same number on them is
Options: a ) 5 / 15 , b ) 5 / 12 , c ) 5 / 19 , d ) 5 / 12 , e ) 5 / 11
Rationale: "using question number 11 and 12 , we get the probability as 1 - ( 1 / 36 + 5 / 9 ) = 5 / 12 answer : b"
Answer: b
Problem: a train 250 m long running at 72 kmph crosses a platform in 25 sec . what is the length of the platform ?
Options: a ) 150 m , b ) 200 m , c ) 250 m , d ) 270 m , e ) 300 m
Rationale: "d = 72 * 5 / 18 = 25 = 500 – 250 = 250 m answer : c"
Answer: c
Problem: a 9 % stock yields 8 % . the market value of the stock is :
Options: a ) rs . 72 , b ) rs . 92 , c ) rs . 112.50 , d ) rs . 116.50 , e ) none of these
Rationale: "solution to obtain rs . 8 , investment = rs . 100 . to obtain rs . 9 , investment = rs . ( 100 / 8 x 9 ) = rs . 112.50 ∴ market value of rs . 100 stock = rs . 112.50 answer c"
Answer: c
Problem: one side of a rectangular field is 15 m and one of its diagonal is 18 m . find the area of the field .
Options: a ) 100 , b ) 120 , c ) 150 , d ) 148.5 , e ) none
Rationale: "solution other side = √ ( 18 ) 2 - ( 15 ) 2 = √ 324 - 225 = √ 99 = 9.9 m . ∴ area = ( 15 x 9.9 ) m 2 = 148.5 m 2 . answer d"
Answer: d
Problem: in one hour , a boat goes 19 km / hr along the stream and 9 km / hr against the stream . the speed of the boat in still water ( in km / hr ) is :
Options: a ) 12 kmph , b ) 13 kmph , c ) 14 kmph , d ) 15 kmph , e ) 16 kmph
Rationale: explanation : let the speed downstream be a km / hr and the speed upstream be b km / hr , then speed in still water = 1 / 2 ( a + b ) km / hr rate of stream = 1 / 2 ( a − b ) km / hr speed in still water = 1 / 2 ( 19 + 9 ) kmph = 14 kmph . answer : option c
Answer: c
Problem: the average of temperatures at noontime from monday to friday is 60 ; the lowest one is 40 , what is the possible maximum range of the temperatures ?
Options: a ) 100 , b ) 25 , c ) 40 , d ) 45 , e ) 75
Rationale: "average = 60 , sum of temperatures = 60 * 5 = 300 as the min temperature is 40 , max would be 300 - 4 * 40 = 140 - - > the range = 140 ( max ) - 40 ( min ) = 100 answer : a"
Answer: a
Problem: find out the square of a number which when doubled exceeds its one sixth by 11 ?
Options: a ) 36 , b ) 25 , c ) 19 , d ) 26 , e ) 17
Rationale: "a let the number be p , then the square will be p ^ 2 according to question : 2 p = ( p / 6 ) + 11 = > 12 p = p + 66 = > p = 6 p ^ 2 = 6 ^ 2 = 36 . answer : a"
Answer: a
Problem: a train overtakes two persons who are walking in the same direction in which the train is going , at the rate of 2 kmph and 4 kmph and passes them completely in 9 and 10 seconds respectively . find the length of train ?
Options: a ) 45 m , b ) 50 m , c ) 55 m , d ) 60 m , e ) 65 m
Rationale: "explanation : first person speed = 2 * ( 5 / 18 ) = 5 / 9 m / sec second person speed = 4 * ( 5 / 18 ) = 10 / 9 m / sec let the length of train is x metre and speed is y m / sec then , x / y − 5 / 9 = 9 = > 9 y − 5 = x = > 9 y − x = 5 . . . . . ( i ) also , x / y − 10 / 9 = 10 90 y − 9 x = 100 . . . . . ( ii ) from ( i ) and ( ii ) , we get , x = 50 so length of train is 50 metre option b"
Answer: b
Problem: a number is doubled and 9 is added . if resultant is trebled , it becomes 63 . what is that number
Options: a ) 6 , b ) 10 , c ) 12 , d ) 14 , e ) 15
Rationale: "explanation : = > 3 ( 2 x + 9 ) = 63 = > 2 x + 9 = 21 = > x = 6 answer : option a"
Answer: a
Problem: a = 5 ^ 10 - 625 ^ 2 and a / x is an integer , where x is a positive integer greater than 1 , such that it does not have a factor p such that 1 < p < x , then how many different values for x are possible ?
Options: a ) none , b ) one , c ) two , d ) three , e ) four
Rationale: this is a tricky worded question and i think the answer is should be d not c . . . here is my reason : the stem says that x is a positive integer such that has no factor grater than 2 and less than x itself . the stem wants to say that x is a prime number . because any prime number has no factor grater than 1 and itself . on the other hand the stem says that x could get how many different number not must get different number ( this is very important issue ) as our friends say , if we simplify numerator more we can obtain : 5 ^ 12 ( 5 ^ 3 - 1 ) = 5 ^ 12 ( 124 ) = 5 ^ 12 ( 31 * 2 * 2 ) divided by x and we are told that this fraction is an integer . so , x could be ( not must be ) 5 , 31 , or 2 ! ! ! so , x could get 2 different values and answer is c . . . .
Answer: c
Problem: a 80 cm long wire is to be cut into two pieces so that one piece will be 3 / 5 th of the other , how many centimeters will the shorter piece be ?
Options: a ) a ) 30 , b ) b ) 20 , c ) c ) 83 , d ) d ) 21 , e ) e ) 52
Rationale: "explanation : 1 : 3 / 5 = 5 : 3 3 / 8 * 80 = 30 answer : option a"
Answer: a
Problem: a library has an average of 510 visitors on sundays and 240 on other day . the average number of visitors in a month of 25 days starting with sunday is
Options: a ) 342 , b ) 285 , c ) 290 , d ) 295 , e ) 275
Rationale: "explanation : as the month begin with sunday , so there will be five sundays in the month . so result will be : = ( 510 × 5 + 240 × 25 / 30 ) = ( 8550 / 25 ) = 342 answer : option a"
Answer: a
Problem: a total of $ 20,000 was invested in two certificates of deposit at simple annual interest rates of 6 percent and 12 percent , respectively . if the total interest on the two certificates was $ 1,440 at the end of one year , what fractional part of the $ 20.000 was invested at the higher rate ?
Options: a ) 3 / 8 , b ) 2 / 5 , c ) 1 / 5 , d ) 3 / 5 , e ) 3 / 4
Rationale: "x * 6 / 100 * 1 + ( 20000 - x ) * 12 / 100 * 1 = 1440 6 x - 12 x = 144000 - 240000 = > - 6 x = - 96000 = > x = 16000 so 4000 / 20000 = 1 / 5 answer - c"
Answer: c
Problem: the ratio , by volume , of soap to alcohol to water in a certain solution is 6 : 30 : 90 . the solution will be altered so that the ratio of soap to alcohol is doubled while the ratio of soap to water is halved . if the altered solution will contain 150 cubic centimeters of alcohol , how many cubic centimeters of water will it contain ?
Options: a ) 1200 , b ) 1300 , c ) 1500 , d ) 1800 , e ) 1900
Rationale: "soap : alcohol initial ratio soap : alcohol : water - - > 6 : 30 : 90 initial soap : alcohol = 6 / 30 = 6 : 30 after doubled soap : alcohol = 2 * 6 / 30 = 12 / 30 = 12 : 30 initial soap : water = 6 / 90 = 6 : 90 after halved soap : water : 1 / 2 * 6 / 90 = 3 / 90 = 3 : 90 = 12 : 360 after soap : alcohol : water - - > 12 : 30 : 360 given alcohol 150 cubic centimeter . ratio is 60 : 150 : 1800 ( 12 : 30 : 360 ) for 150 cubic centimeter of alcohol - - - 1800 cu cm water is required . answer - d"
Answer: d
Problem: a waiter ' s salary consists of his salary and tips . during one week his tips were 7 / 4 of his salary . what fraction of his income came from tips ?
Options: a ) 4 / 9 , b ) 5 / 4 , c ) 5 / 8 , d ) 5 / 9 , e ) 7 / 11
Rationale: "income = salary ( s ) + tips = s + s * 7 / 4 = s * 11 / 4 tips = s * 7 / 4 fraction of his income came from tips = ( s * 7 / 4 ) / ( s * 11 / 4 ) = 7 / 11 answer : e"
Answer: e
Problem: the total age of a and b is 15 years more than the total age of b and c . c is how many year younger than
Options: a ) 14 years , b ) 12 years , c ) 56 years , d ) 66 years , e ) 15 years
Rationale: "given that a + b = 15 + b + c = > a â € “ c = 15 + b â € “ b = 15 = > c is younger than a by 15 years answer : e"
Answer: e
Problem: three numbers are in the ratio 4 : 5 : 6 and their product is 76680 . the largest number is
Options: a ) 30 , b ) 24 , c ) 26 , d ) 28 , e ) 22
Rationale: "explanation : let the number be 4 x , 5 x and 6 x . then , ( 4 x ) ( 5 x ) ( 6 x ) = 2880 = > 120 x 3 = 7680 = > x 3 = 64 = > x = 4 so , largest number is 6 x = 24 answer : option b"
Answer: b
Problem: a bag has 9 green balls and 23 pink balls . how many green balls should be added to the bag so that the ratio of green balls and pink balls in the bag becomes 1 : 1 ?
Options: a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14
Rationale: suppose x green balls need to be added . then , the number of green balls becomes 9 + x , and the number of pink balls remains the same , 23 . but now the ratio of green and pink balls is 1 : 1 this means , ( 9 + x ) / 23 = 1 / 1 solving this we get x = 14 . ans e
Answer: e
Problem: what is the value of 100 p 2 ?
Options: a ) 9801 , b ) 12000 , c ) 5600 , d ) 9900 , e ) none of these
Rationale: "explanation : 100 p 2 = 100 x 99 = 9900 . answer : option d"
Answer: d
Problem: convert 2 / 5 to a decimal
Options: a ) 0.1 , b ) 0.2 , c ) 0.3 , d ) 0.4 , e ) 0.5
Rationale: "divide 2 by 5 : 2 / 5 = 0.4 answer : 2 / 5 = 0.4 ( d )"
Answer: d
Problem: what is remainder of the division ( 1625 * 1627 * 1629 ) / 12 ?
Options: a ) 3 , b ) 2 , c ) 1 , d ) 0 , e ) 4
Rationale: remainder will be number / 100 here as the divisor is two digit number = 12 . hence checking for the last two digits = 5 * 7 * 9 = 15 thus remainder = 3 . answer : a
Answer: a
Problem: if henry were to add 8 gallons of water to a tank that is already 3 / 4 full of water , the tank would be 7 / 8 full . how many gallons of water would the tank hold if it were full ?
Options: a ) 25 , b ) 40 , c ) 64 , d ) 80 , e ) 96
Rationale: "7 / 8 x - 3 / 4 x = 8 galls 1 / 8 * x = 8 gallons x = 64 gallons answer c"
Answer: c
Problem: find compound interest on $ 4000 at 15 % per annum for 2 years 4 months , compounded annually .
Options: a ) 1554.5 , b ) 1509.5 , c ) 1108.5 , d ) 1107.5 , e ) 1100.5
Rationale: "time = 2 years 4 months = 2 ( 4 / 12 ) years = 2 ( 1 / 3 ) years . amount = $ [ 4000 x ( 1 + ­ ( 15 / 100 ) ) 2 x ( 1 + ( ( 1 / 3 ) * 15 ) / 100 ) ] = $ [ 4000 * ( 23 / 20 ) * ( 23 / 20 ) * ( 21 / 20 ) ] = $ 5554.50 . : . c . i . = rs . ( 5554.50 - 4000 ) = $ 1554.50 answer a ."
Answer: a
Problem: if x = 1 + √ 2 , then what is the value of x 4 - 4 x 3 + 4 x 2 + 3 ?
Options: a ) - 1 , b ) 0 , c ) 4 , d ) 2 , e ) 3
Rationale: "answer x = 1 + √ 2 ∴ x 4 - 4 x 3 + 4 x 2 + 5 = x 2 ( x 2 - 4 x + 4 ) + 3 = x 2 ( x - 2 ) 2 + 3 = ( 1 + √ 2 ) 2 ( 1 + √ 2 - 2 ) 2 + 3 = ( √ 2 + 1 ) 2 ( √ 2 - 1 ) 2 + 3 = [ ( √ 2 ) 2 - ( 1 ) 2 ] 2 + 3 = ( 2 - 1 ) 2 = 1 + 3 = 4 correct option : c"
Answer: c
Problem: a train is 485 meter long is running at a speed of 45 km / hour . in what time will it pass a bridge of 140 meter length
Options: a ) 20 seconds , b ) 30 seconds , c ) 40 seconds , d ) 50 seconds , e ) none of these
Rationale: "explanation : speed = 45 km / hr = 45 * ( 5 / 18 ) m / sec = 25 / 2 m / sec total distance = 485 + 140 = 625 meter time = distance / speed = 625 ∗ 2 / 25 = 50 seconds option d"
Answer: d
Problem: if x gets 25 % more than y and y gets 20 % more than z , the share of z out of rs . 1110 will be :
Options: a ) rs . 300 , b ) rs . 200 , c ) rs . 240 , d ) rs . 350 , e ) none of these
Rationale: "z share = z , y = 1.2 z x = 1.25 ã — 1.2 z , x + y + z = 111 ( 1.25 ã — 1.2 + 1.2 + 1 ) z = 1110 3.7 z = 1110 , z = 300 answer : . a"
Answer: a
Problem: a train moves with a speed of 135 kmph . its speed in metres per second is
Options: a ) 10.8 , b ) 37.5 , c ) 30 , d ) 38.8 , e ) none
Rationale: "solution speed = 135 kmph = ( 135 x 5 / 18 ) m / sec = 37.5 m / sec . answer b"
Answer: b
Problem: a 50 ml after - shave lotion at 30 % alcohol is mixed with 30 ml of pure water . what is the percentage of alcohol in the new solution ?
Options: a ) 16.75 % , b ) 17.75 % , c ) 18.75 % , d ) 19.75 % , e ) none of these
Rationale: the amount of the final mixture is given by 50 ml + 30 ml = 80 ml the amount of alcohol is equal to the amount of alcohol in pure water ( which is 0 ) plus the amount of alcohol in the 30 % solution . let x be the percentage of alcohol in the final solution . hence 0 + 30 % 50 ml = x ( 80 ) solve for x x = 0.1817 = 18.75 % answer c
Answer: c
Problem: what is the remainder when 1201 × 1202 × 1205 × 1207 is divided by 6 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "the remainders when dividing each number by six are : 1 , 2 , 5 , and 1 . the product is 1 * 2 * 5 * 1 = 10 the remainder when dividing 10 by 6 is 4 . the answer is d ."
Answer: d
Problem: what is the value of 11 ^ x - 11 ^ ( x + 2 ) , where x is the largest integer such that 11 ^ x is a factor of 30030 ?
Options: a ) - 1331 , b ) - 1320 , c ) - 121 , d ) - 120 , e ) - 1
Rationale: the given expression is 11 x - 11 ( x ^ + 2 ) = 11 x ( 1 - x ) 1 x needs to be factor of 30030 and x needs to be the largest integer possible . this means 11 x needs to be the largest factor possible . the largest factor of a number is the number itself . the largest factor of 30030 is 30030 = ( 11 * 2730 ) x must be 2730 the value of 11 x ( 1 - x ) = – 1320 . answer : b
Answer: b
Problem: what percent of 7.2 kg is 18 gms ?
Options: a ) 25 , b ) 66 , c ) 288 , d ) 19 , e ) 17
Rationale: "explanation : required percentage = ( 18 / 7200 * 100 ) % = 1 / 4 % = 0.25 % answer : a ) . 25 %"
Answer: a
Problem: a ’ s speed is 17 / 14 times that of b . if a and b run a race , what part of the length of the race should a give b as a head start , so that the race ends in a dead heat ?
Options: a ) 1 / 14 , b ) 1 / 17 , c ) 3 / 14 , d ) 3 / 17 , e ) 1 / 31
Rationale: "let x be the fraction of the distance that b runs . let v be the speed at which b runs . the time should be the same for both runners . time = d / ( 17 v / 14 ) = xd / v ( 14 / 17 ) * d / v = x * d / v x = 14 / 17 b should have a head start of 3 / 17 of the full distance . the answer is d ."
Answer: d
Problem: a invested $ 100 in a business after 6 months b invested $ 200 in the business . end of the year if they got $ 100 as profit . find a shares ?
Options: a ) $ 100 , b ) $ 75 , c ) $ 20 , d ) $ 120 , e ) $ 50
Rationale: "a : b = 100 * 12 : 200 * 6 a : b = 1 : 1 a ' s share = 100 / 2 = $ 50 answer is e"
Answer: e
Problem: in a family 13 people eat only vegetarian , 8 people eat only non veg . , 6 people eat both veg and non veg . . how many people eat veg in the family ?
Options: a ) 20 , b ) 11 , c ) 19 , d ) 31 , e ) 21
Rationale: "total people eat veg = only veg + both veg and non veg total = 13 + 6 = 19 answer = c"
Answer: c
Problem: a shopkeeper labeled the price of his articles so as to earn a profit of 40 % on the cost price . he then sold the articles by offering a discount of 5 % on the labeled price . what is the actual percent profit earned in the deal ?
Options: a ) 18 % , b ) 20 % , c ) 17 % , d ) 33 % , e ) none of these
Rationale: "explanation : let the cp of the article = rs . 100 . then labeled price = rs . 140 . sp = rs . 140 - 5 % of 140 = rs . 140 - 7 = rs . 133 . gain = rs . 133 â € “ rs . 100 = rs . 33 therefore , gain / profit percent = 33 % . answer : option d"
Answer: d
Problem: the total of 336 of 20 paise and 25 paise make a sum of rs . 71 . the no of 20 paise coins is
Options: a ) 238 , b ) 277 , c ) 278 , d ) 260 , e ) 288
Rationale: "explanation : let the number of 20 paise coins be x . then the no of 25 paise coins = ( 336 - x ) . 0.20 * ( x ) + 0.25 ( 336 - x ) = 71 = > x = 260 . . answer : d ) 260"
Answer: d
Problem: a factory produces 6400 toys per week . if the workers at this factory work 3 days a week and if these workers make the same number of toys everyday , how many toys are produced each day ?
Options: a ) 1375 toys , b ) 2133 toys , c ) 3375 toys , d ) 4375 toys , e ) 5375 toys
Rationale: "to find the number of toys produced every day , we divide the total number of toys produced in one week ( of 3 days ) by 3 . 6400 / 3 = 2133 toys correct answer b"
Answer: b
Problem: walking at 5 / 6 th of its usual speed a cab is 15 mnts late . find its usual time to cover the journey ?
Options: a ) 25 m , b ) 45 m , c ) 32 m , d ) 75 m , e ) 62 m
Rationale: new speed = 5 / 6 th of usual speed new time = 6 / 5 th of usual time 6 / 5 ut - ut = 15 m ut / 5 = 15 m ut = 75 m answer is d
Answer: d
Problem: a part - time employee whose hourly wage was increased by 20 percent decided to reduce the number of hours worked per week so that the employee ' s total weekly income would remain unchanged . by what percent should the number of hours worked be reduced ?
Options: a ) 11 , b ) 15 , c ) 16.66 , d ) 17 , e ) 18
Rationale: "let original hourly wage be x and let the no of hours worked be y total wage will be = x * y after the increment the wage will be = 1.2 x now we need to find number of hours worked so that x * y = 1.2 x * z i . e z = 1 / 1.2 y % decrease = ( y - 1 / 1.2 y ) / y * 100 = 16.66 thus my answer is c ."
Answer: c
Problem: a person purchased a tv set for rs . 16000 and a dvd player for rs . 6250 . he sold both the items together for rs . 35600 . what percentage of profit did he make ?
Options: a ) 80 % , b ) 49 % , c ) 40 % , d ) 60 % , e ) 90 %
Rationale: the total cp = rs . 16000 + rs . 6250 = rs . 22250 and sp = rs . 35600 profit ( % ) = ( 35600 - 22250 ) / 22250 * 100 = 60 % answer : d
Answer: d
Problem: two trains each 180 m in length are running on the same parallel lines in opposite directions with the speed of each 80 kmph . in what time will they cross each other completely ?
Options: a ) 7.8 sec , b ) 8.1 sec , c ) 8.3 sec , d ) 8.2 sec , e ) 8.4 sec
Rationale: d = 180 m + 180 m = 360 m * 1 / 1000 = 0.36 kms rs = 80 + 80 = 160 kmph t = ( 0.36 / 160 ) * 3600 = 8.1 sec answer : b
Answer: b
Problem: 20 buckets of water fill a tank when the capacity of each bucket is 13.5 litres . how many buckets will be required to fill the same tank if the capacity of each bucket is 9 litres ?
Options: a ) 30 , b ) 32 , c ) 60 , d ) data inadequate , e ) none of these
Rationale: "capacity of the tank = 20 × 13.5 = 270 litres when the capacity of each bucket = 9 litres , then the required no . of buckets = 270 ⁄ 9 = 30 answer a"
Answer: a
Problem: the number of the members of a club is more than 50 and less than 80 . when 4 people sit at a table , other people exactly divided to 8 - people groups ( 8 people sit at a table ) or 7 - people groups ( 7 people sit at a table ) . if the members are divided to 9 - people groups , how many people will be left ?
Options: a ) 0 , b ) 2 , c ) 4 , d ) 6 , e ) 8
Rationale: "the number of members is 7 k + 4 = 8 j + 4 the only number in this range which satisfies this is 60 . 60 / 9 = 6 ( 9 ) + 6 the answer is d ."
Answer: d
Problem: a train running at the speed of 72 km / hr crosses a pole in 9 seconds . find the length of the train .
Options: a ) 150 meter , b ) 286 meter , c ) 180 meter , d ) 288 meter , e ) 265 meter
Rationale: "speed = 72 * ( 5 / 18 ) m / sec = 20 m / sec length of train ( distance ) = speed * time ( 20 ) * 9 = 180 meter answer : c"
Answer: c
Problem: two clocks are set correctly at 1 0 ' clock in the afternoon . one keeps correct time . the other gains 5 seconds per minute . that evening , when the fast clock shows 6 : 20 , what does the correct clock show ?
Options: a ) 4.0 , b ) 5.0 , c ) 6.0 , d ) 7.2 , e ) 3.5
Rationale: faster clock gains 5 seconds per minute or 5 * 60 = 300 seconds or 5 minutes per hour . both clocks are set at 1 : 00 at 2 : 00 correct clock is at 2 : 00 faster clock is at 2 : 05 : 00 ( 1 hour + gained 5 minutes ) at 3 : 00 - correct clock is at 3 : 00 faster clock is at 3 : 10 : 00 ( 2 hours + gained 10 minutes ) . in 5 hours , faster clock would gain 20 minutes . it will show 6 : 20 . at that point , the correct clock would show 6 : 00 . answer is c
Answer: c
Problem: the triplicate ratio of 1 : 3 is ?
Options: a ) 1 : 27 , b ) 1 : 8 , c ) 1 : 3 , d ) 1 : 1 , e ) 1 : 2
Rationale: "1 ^ 3 : 3 ^ 3 = 1 : 27 answer : a"
Answer: a
Problem: a shopkeeper sold an article offering a discount of 5 % and earned a profit of 22.55 % . what would have been the percentage of profit earned if no discount was offered ?
Options: a ) 60 % , b ) 29 % , c ) 39 % , d ) 56 % , e ) 73 %
Rationale: "let c . p . be rs . 100 . then , s . p . = rs . 122.55 let marked price be rs . x . then , 95 / 100 x = 122.55 x = 12255 / 95 = rs . 129 now , s . p . = rs . 129 , c . p . = rs . 100 profit % = 29 % . answer : b"
Answer: b
Problem: 5 men are equal to as many women as are equal to 8 boys . all of them earn $ 90 only . men ’ s wages are ?
Options: a ) $ 4 , b ) $ 6 , c ) $ 7 , d ) $ 9 , e ) $ 3
Rationale: "b $ 6 5 m = xw = 8 b 5 m + xw + 8 b - - - - - $ 90 rs . 5 m + 5 m + 5 m - - - - - $ 90 rs . 15 m - - - - - - $ 90 = > 1 m = $ 6 ."
Answer: b
Problem: two trains of equal are running on parallel lines in the same direction at 48 km / hr and 36 km / hr . the faster train passes the slower train in 36 sec . the length of each train is ?
Options: a ) 60 m , b ) 72 m , c ) 80 m , d ) 82 m , e ) 84 m
Rationale: "let the length of each train be x m . then , distance covered = 2 x m . relative speed = 48 - 36 = 12 km / hr . = 12 * 5 / 18 = 10 / 3 m / sec . 2 x / 36 = 10 / 3 = > x = 60 . answer : a"
Answer: a
Problem: how many positive integers less than 20 can be expressed as the sum of a positive multiple of 2 and a positive multiple of 3 ?
Options: a ) 14 , b ) 13 , c ) 12 , d ) 11 , e ) 10
Rationale: "the numbers must be of the form 2 a + 3 b , 2 a + 3 b , where aa and bb are positive integers . the smallest number is 5 = 2 ∗ 1 + 3 ∗ 1.5 = 2 ∗ 1 + 3 ∗ 1 . starting with 55 , we can get all the other numbers by adding either 22 or 33 to the already existing numbers on our list . adding either 22 or 33 to 2 a + 3 b 2 a + 3 b will give another number of the same form . so , after 55 , we get 5 + 2 = 7,5 + 3 = 8,7 + 2 = 9,8 + 2 = 10 , . . . 5 + 2 = 7,5 + 3 = 8,7 + 2 = 9,8 + 2 = 10 , . . . we will get all the numbers up to 1919 inclusive , except 1,2 , 3,4 , 1,2 , 3,4 , and 6,6 , because once we have 77 and 8,8 , by adding 22 all the time we can get any odd or even number . we get a total of 19 − 5 = 1419 − 5 = 14 numbers . answer a"
Answer: a
Problem: a number is said to be prime saturated if the product of all the different positive prime factors of t is less than the square root of t . what is the greatest two digit prime saturated integer ?
Options: a ) 99 , b ) 98 , c ) 97 , d ) 96 , e ) 95
Rationale: "t = 96 = 3 * 32 = 3 * 2 ^ 5 answer is d ."
Answer: d
Problem: a cycle is bought for rs . 1500 and sold for rs . 1620 , find the gain percent ?
Options: a ) 11 , b ) 8 , c ) 10 , d ) 20 , e ) 12
Rationale: "1500 - - - - 120 100 - - - - ? = > 8 % answer : b"
Answer: b
Problem: a teacher grades students ’ tests by subtracting twice the number of incorrect responses from the number of correct responses . if student a answers each of the 100 questions on her test and receives a score of 76 , how many questions did student a answer correctly ?
Options: a ) 92 , b ) 60 , c ) 73 , d ) 82 , e ) 91
Rationale: "let the number of correct responses be x then the number of incorrect responses = 100 - x according to question x - 2 ( 100 - x ) = 76 ( subtracting twice of incorrect from correct ) 3 x = 276 x = 92 answer : a"
Answer: a