Cheukting/mathqa huggingface dataset:
Question (physics): 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
Question (general): 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
Question (general): 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
Question (general): 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
Question (general): 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
Question (general): 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
Question (physics): 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
Question (geometry): 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
Question (gain): 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
Question (general): 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
Question (general): 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
Question (general): 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
Question (general): 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
Question (physics): 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
Question (gain): 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
Question (other): 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
Question (physics): 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
Question (general): 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
Question (general): 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
Question (physics): 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
Question (general): 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
Question (general): 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
Question (gain): 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
Question (general): 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
Question (physics): 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
Question (gain): 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
Question (general): 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
Question (general): 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
Question (general): 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
Question (general): 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
Question (general): 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
Question (geometry): 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
Question (gain): $ 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
Question (gain): 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
Question (general): 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
Question (physics): 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
Question (physics): 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
Question (general): 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
Question (general): 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
Question (general): 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
Question (physics): 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
Question (geometry): 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
Question (physics): 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
Question (general): 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
Question (general): 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
Question (physics): 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
Question (general): 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
Question (probability): 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
Question (physics): 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
Question (gain): 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
Question (geometry): 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
Question (physics): 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
Question (general): 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
Question (general): 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