Cheukting/mathqa huggingface dataset:
Question (geometry): the ratio between the perimeter and the width of a rectangle is 5 : 1 . if the area of the rectangle is 150 sq . cm , what is the width of the rectangle ?
Options: a ) 10 cm , b ) 12 cm , c ) 14 cm , d ) 16 cm , e ) 18 cm
Rationale: "2 l + 2 w = 5 w l = 3 w / 2 w * l = 150 3 w ^ 2 / 2 = 150 w ^ 2 = 100 w = 10 the answer is a ."
Answer: a
Question (physics): working at a constant rate , p can finish a job in 3 hours . q , also working at a constant rate , can finish the same job in 15 hours . if they work together for 2 hours , how many more minutes will it take p to finish the job , working alone at his constant rate ?
Options: a ) 30 , b ) 36 , c ) 40 , d ) 45 , e ) 48
Rationale: each hour they complete 1 / 3 + 1 / 15 = 2 / 5 of the job . in 2 hours , they complete 2 ( 2 / 5 ) = 4 / 5 of the job . the time for p to finish is ( 1 / 5 ) / ( 1 / 3 ) = ( 3 / 5 ) hour = 36 minutes the answer is b .
Answer: b
Question (general): what is the sum of the digits of integer k , if k = ( 10 ^ 30 - 54 )
Options: a ) 251 , b ) 261 , c ) 262 , d ) 269 , e ) 278
Rationale: "there are 31 digits in 10 ^ 30 when we subtract 54 from it , there will be 30 digits left . 10 ^ 30 can be written as 9999999 . . . . ( 30 times ) + 1 so , 10 ^ 30 - 54 = 9999999 . . . . ( 30 times ) + 1 - 54 = 9999999 . . . . ( 30 times ) - 53 consider the last 2 digits , 99 - 53 = 46 the last 2 digits will be 46 . and our number would be 99999 . . . . . . 99946 with 2 less 9 s after subtraction . number of 9 s left are 28 and the last two digits are 46 the sum of the digits will be ( 28 * 9 ) + 4 + 6 = 262 answer : - c"
Answer: c
Question (physics): a room of 6 m 20 cm long and 5 m 74 cm broad is to be paved with square tiles . find the least number of square tiles required to cover the floor .
Options: a ) 88900 , b ) 87700 , c ) 88970 , d ) 88000 , e ) 89000
Rationale: "explanation : area of the room = 620 * 574 sq cm size of largest square tile = h . c . f of 620 cm and 574 cm = 2 cm area of 1 tile = 2 * 2 sq cm no . of tiles required = ( 620 * 574 ) / ( 2 * 2 ) = 88970 answer : c ) 88970"
Answer: c
Question (gain): a sum of money at simple interest amounts to rs . 815 in 3 years and to rs . 854 in 4 years . the sum is ?
Options: a ) 287 , b ) 278 , c ) 698 , d ) 279 , e ) 275
Rationale: "s . i . for 1 year = ( 854 - 815 ) = rs . 39 s . i . for 3 years = 39 * 3 = rs . 117 principal = ( 815 - 117 ) = rs . 698 . answer : c"
Answer: c
Question (gain): a football team lost 5 yards and then gained 7 . what is the team ' s progress ?
Options: a ) 2 , b ) 4 , c ) 5 , d ) 6 , e ) 8
Rationale: for lost , use negative . for gain , use positive . progress = - 5 + 7 = 2 yards a
Answer: a
Question (physics): the sum of four consecutive numbers is 102 . the greatest among these three number is :
Options: a ) 26 , b ) 28 , c ) 29 , d ) 30 , e ) 27
Rationale: "let the numbers be x , x + 1 , x + 2 and x + 3 then , x + ( x + 1 ) + ( x + 2 ) + ( x + 3 ) = 102 4 x = 96 x = 24 greatest number , ( x + 3 ) = 27 answer : e"
Answer: e
Question (general): what is the least common multiple of 12 , 18 , and 24 ?
Options: a ) 72 , b ) 120 , c ) 240 , d ) 360 , e ) 720
Rationale: "let us first write the numbers in the form of prime factors : 12 = 2 ^ 2 * 3 ^ 1 18 = 2 ^ 1 * 3 ^ 2 24 = 2 * 17 ^ 1 the lcm would be the largest powers of the prime numbers from all these three numbers . hence lcm = 72 option a"
Answer: a
Question (general): a batsman makes a score of 90 runs in the 11 th inning and thus increases his average by 5 . find his average after 11 th inning .
Options: a ) 40 , b ) 50 , c ) 62 , d ) 45 , e ) 56
Rationale: "let the average after 11 th inning = x then , average after 10 th inning = x - 5 10 ( x - 5 ) + 90 = 11 x x = 90 - 50 = 40 answer is a"
Answer: a
Question (general): a is two years older than b who is twice as old as c . if the total of the ages of a , b and c be 72 , then how old is b ?
Options: a ) 28 years , b ) 19 years , c ) 29 years , d ) 10 years , e ) 12 years
Rationale: "let c ' s age be x years . then , b ' s age = 2 x years . a ' s age = ( 2 x + 2 ) years . ( 2 x + 2 ) + 2 x + x = 72 5 x = 70 = > x = 14 hence , b ' s age = 2 x = 28 years . answer : a"
Answer: a
Question (gain): there is 60 % increase in an amount in 6 years at si . what will be the ci of rs . 14,000 after 3 years at the same rate ?
Options: a ) 2372 , b ) 4634 , c ) 4542 , d ) 2343 , e ) 3972
Rationale: "let p = rs . 100 . then , s . i . rs . 60 and t = 6 years . r = 100 x 60 = 10 % p . a . 100 x 6 now , p = rs . 14000 . t = 3 years and r = 10 % p . a . c . i . = rs . 14000 x 1 + 10 3 - 1 100 = rs . 14000 x 331 1000 = 4634 . b"
Answer: b
Question (general): dick and jane each saved $ 1,000 in 1989 . in 1990 dick saved 15 percent more than in 1989 , and together he and jane saved a total of $ 2,000 . approximately what percent less did jane save in 1990 than in 1989 ?
Options: a ) 3 % , b ) 5 % , c ) 10 % , d ) 15 % , e ) 18 %
Rationale: 1990 dick saved = $ 1150 jane saved = $ 850 ( jane saved $ 150 less than she did the prior year ) jane saved approximately $ 150 / 1000 $ ( 15 % ) less in 1990 answer : d
Answer: d
Question (physics): worker a takes 10 hours to do a job . worker b takes 15 hours to do the same job . how long it take both a & b , working together but independently , to do the same job ?
Options: a ) 40 days , b ) 40 / 9 days , c ) 39 / 9 days , d ) 6 days , e ) 60 / 9 days
Rationale: "a ' s one hour work = 1 / 10 . b ' s one hour work = 1 / 15 . ( a + b ) ' s one hour work = 1 / 10 + 1 / 15 = 5 / 30 = 1 / 6 . both a & b can finish the work in 6 days d"
Answer: d
Question (probability): a , b , c , d , e sitting in a row what is the probability that a & b sitting adjacent .
Options: a ) 1 / 5 , b ) 2 / 5 , c ) 3 / 5 , d ) 4 / 5 , e ) 6 / 5
Rationale: total number of arrangement is = 5 ! = 120 favorable event i . e a and b can be arranged in 2 ! and the remaining can be arranged in 4 ! since ab can be in any of the four positions . so 4 ! * 2 ! / 5 ! = 2 / 5 answer : b
Answer: b
Question (physics): how many seconds will a 620 metre long train take to cross a man running with a speed of 8 km / hr in the direction of the moving train if the speed of the train is 80 km / hr ?
Options: a ) 25 , b ) 30 , c ) 31 , d ) 45 , e ) 60
Rationale: "explanation : speed of train relatively to man = ( 80 - 8 ) km / hr = 72 km / hr = ( 72 x 5 / 18 ) m / sec = 20 m / sec time taken to pass the man = ( 620 / 20 ) sec = 31 sec . answer : c"
Answer: c
Question (gain): in an election a candidate who gets 60 % of the votes is elected by a majority of 1040 votes . what is the total number of votes polled ?
Options: a ) a ) 4500 , b ) b ) 5200 , c ) c ) 6900 , d ) d ) 7520 , e ) e ) 6000
Rationale: "let the total number of votes polled be x then , votes polled by other candidate = ( 100 - 60 ) % of x = 40 % of x 60 % of x - 40 % of x = 1040 20 x / 100 = 1040 x = 1040 * 100 / 20 = 5200 answer is b"
Answer: b
Question (physics): a person is traveling at 40 km / hr and reached his destiny in 6 hr then find the distance ?
Options: a ) 260 km , b ) 240 km , c ) 280 km , d ) 340 km , e ) 350 km
Rationale: "t = 6 hrs d = t * s = 40 * 6 = 240 km answer is b"
Answer: b
Question (general): a certain library assesses fines for overdue books as follows . on the first day that a book is overdue , the total fine is $ 0.07 . for each additional day that the book is overdue , the total fine is either increased by $ 0.30 or doubled , whichever results in the lesser amount . what is the total for a book on the fifth day it is overdue ?
Options: a ) $ 0.60 , b ) $ 0.70 , c ) $ 0.86 , d ) $ 0.90 , e ) $ 1.00
Rationale: "1 st day fine - 0.07 2 nd day fine - 0.07 * 2 = 0.14 ( as doubling gives lower value ) 3 rd day fine - 0.14 * 2 = 0.28 ( as doubling gives lower value ) 4 rd day fine - 0.28 * 2 = 0.56 ( as doubling gives lower value ) 5 th day fine - 0.56 + 0.3 = 0.86 ( as doubling gives higher value we add 0.3 this time ) answer : c ."
Answer: c
Question (general): 7 , 26 , 63 , 124 , ( . . . . )
Options: a ) 342 , b ) 125 , c ) 289 , d ) 564 , e ) 36
Rationale: "explanation : numbers are 2 ^ 3 - 1 = 7 3 ^ 3 - 1 = 26 4 ^ 3 - 1 = 63 5 ^ 3 - 1 = 124 6 ^ 3 - 1 = 342 answer : a"
Answer: a
Question (gain): by selling 100 pens , a trader gains the cost of 40 pens . find his gain percentage ?
Options: a ) 40 % , b ) 50 % , c ) 60 % , d ) 70 % , e ) 30 %
Rationale: "let the cp of each pen be rs . 1 . cp of 100 pens = rs . 100 profit = cost of 40 pens = rs . 40 profit % = 40 / 100 * 100 = 40 % answer : a"
Answer: a
Question (general): a sum of rs . 1870 has been divided among a , b and c such that a gets of what b gets and b gets of what c gets . b ’ s share is :
Options: a ) rs . 120 , b ) rs . 160 , c ) rs . 240 , d ) rs . 330 , e ) none
Rationale: "explanation let c ’ s share = rs . x then , b ’ s share = rs . x / 4 , a ’ s share = rs . ( 2 / 3 x x / 4 ) = rs . x / 6 = x / 6 + x / 4 + x = 1870 = > 17 x / 12 = 1870 = > 1870 x 12 / 17 = rs . 1320 hence , b ’ s share = rs . ( 1320 / 4 ) = rs . 330 . answer d"
Answer: d
Question (geometry): a circular logo is enlarged to fit the lid of a jar . the new diameter is 30 per cent larger than the original . by what percentage has the area of the logo increased ?
Options: a ) 50 , b ) 80 , c ) 69 , d ) 125 , e ) 250
Rationale: "let old diameter be 4 , so radius is 2 old area = 4 π new diameter is 5.2 , so radius is 2.6 new area = 6.76 π increase in area is 2.76 π % increase in area = 2.76 / 4 * 100 so , % increase is 69 % answer will be ( c )"
Answer: c
Question (gain): a is a working partner and b is a sleeping partner in the business . a puts in rs . 15000 and b rs . 25000 , a receives 10 % of the profit for managing the business the rest being divided in proportion of their capitals . out of a total profit of rs . 9600 , money received by a is ?
Options: a ) 1978 , b ) 2707 , c ) 7728 , d ) 4200 , e ) 7291
Rationale: "15 : 25 = > 3 : 5 9600 * 10 / 100 = 960 9600 - 960 = 8640 8640 * 3 / 8 = 3240 + 960 = 4200 answer : d"
Answer: d
Question (general): how many numbers from 19 to 79 are exactly divisible by 11 ?
Options: a ) 5 , b ) 6 , c ) 9 , d ) 11 , e ) 12
Rationale: "19 / 11 = 1 and 79 / 11 = 7 = = > 7 - 1 = 6 numbers answer : b"
Answer: b
Question (physics): two pipes can fill a tank in 10 minutes and 15 minutes . an outlet pipe can empty the tank in 30 minutes . if all the pipes are opened when the tank is empty , then how many minutes will it take to fill the tank ?
Options: a ) 7.0 , b ) 7.5 , c ) 8.0 , d ) 8.5 , e ) 9.0
Rationale: "let v be the volume of the tank . the rate per minute at which the tank is filled is : v / 10 + v / 15 - v / 30 = 2 v / 15 per minute the tank will be filled in 15 / 2 = 7.5 minutes . the answer is b ."
Answer: b
Question (geometry): the length of a rectangle is four times its width . if the area is 100 m 2 what is the length of the rectangle ?
Options: a ) 50 m , b ) 40 m , c ) 80 m , d ) 20 m , e ) 70 m
Rationale: "let l be the length and w be the width of the rectangle . hence l = 4 w we now use the area to write 100 = l ? w substitute l by 4 w in the equation above 100 = 4 w ? w = 4 w 2 solve for w and find l 4 w 2 = 100 w 2 = 25 , w = 5 and l = 4 w = 20 m correct answer d"
Answer: d
Question (gain): exactly 20 % of the reporters for a certain wire service cover local politics in country x . if 20 % of the reporters who cover politics for the wire service do not cover local politics in country x , what percent of the reporters for the wire service do not cover politics ?
Options: a ) 20 % , b ) 42 % , c ) 44 % , d ) 75 % , e ) 84 %
Rationale: "you are correct . people who cover local politics are a subset of people who cover politics . 20 % of reporters who cover politics do not cover local politics so 80 % do cover local politics . reporters covering local politics = 80 % of reporters covering politics = 20 % ofall reporters reporters covering politics / all reporters = 20 / 80 = 1 / 4 reporters not covering politics / all reporters = 3 / 4 = 75 % = d"
Answer: d
Question (gain): we had $ 840 left after spending 30 % of the money that we took for shopping . how much money did we start with ?
Options: a ) $ 1000 , b ) $ 1050 , c ) $ 1100 , d ) $ 1150 , e ) $ 1200
Rationale: let x be the amount of money we started with . 0.7 x = 840 x = 1200 the answer is e .
Answer: e
Question (general): if the sum and difference of two numbers are 10 and 8 respectively , then the difference of their square is :
Options: a ) 12 , b ) 28 , c ) 160 , d ) 180 , e ) 80
Rationale: "let the numbers be x and y . then , x + y = 10 and x - y = 8 x 2 - y 2 = ( x + y ) ( x - y ) = 10 * 8 = 80 . answer : e"
Answer: e
Question (general): how many times will the digit 5 be written when listing the integers from 1 to 1000 ?
Options: a ) 300 , b ) 380 , c ) 180 , d ) 415 , e ) 264
Rationale: "many approaches are possible . for example : consider numbers from 0 to 999 written as follows : 1 . 000 2 . 001 3 . 002 4 . 003 . . . . . . . . . 1000 . 999 we have 1000 numbers . we used 3 digits per number , hence used total of 3 * 1000 = 3000 digits . now , why should any digit have preferences over another ? we used each of 10 digits equal # of times , thus we used each digit ( including 5 ) 3000 / 10 = 300 times . answer : a ."
Answer: a
Question (general): the average of first six prime numbers which are between 30 and 70 is
Options: a ) 35.4 , b ) 42 , c ) 45.7 , d ) 57 , e ) 67
Rationale: "explanation : first six prime numbers which are between 30 and 70 = 31 , 37 , 41 , 43 , 47 , 53 average = ( 31 + 37 + 41 + 43 + 47 + 53 ) / 6 = 42 answer : b"
Answer: b
Question (general): what is the units digit of ( 3 ^ 11 ) ( 4 ^ 13 ) ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 7 , e ) 8
Rationale: "- > the ones place of ( ~ 3 ) ^ n repeats after 4 times like 3  9  7  1  3 . the ones place of ( ~ 4 ) ^ n repeats after 2 times like 4  6  4 . then , 3 ^ 13 = 3 ^ 4 * 3 + 1  3 ^ 1 . , 4 ^ 13 = 4 ^ 2 * 6 + 1 = 4 ^ 1 = ~ 4 which is ( 3 ^ 13 ) ( 4 ^ 13 )  ( 3 ^ 1 ) ( ~ 4 ) = ( ~ 3 ) ( ~ 4 ) = ~ 2 . therefore , the answer is a ."
Answer: a
Question (physics): the distance from steve ' s house to work is 30 km . on the way back steve drives twice as fast as he did on the way to work . altogether , steve is spending 6 hours a day on the roads . what is steve ' s speed on the way back from work ?
Options: a ) 5 . , b ) 10 . , c ) 14 . , d ) 15 , e ) 20 .
Rationale: "time is in the ratio 2 : 1 : : to : fro office therefore , 2 x + 1 x = 6 hrs time take to come back - 2 hrs , distance travelled - 30 km = > speed = 15 kmph answer : d"
Answer: d
Question (physics): the sector of a circle has radius of 21 cm and central angle 270 o . find its perimeter ?
Options: a ) 145 cm , b ) 135 cm , c ) 121 cm , d ) 141 cm , e ) 151 cm
Rationale: "perimeter of the sector = length of the arc + 2 ( radius ) = ( 270 / 360 * 2 * 22 / 7 * 21 ) + 2 ( 21 ) = 99 + 42 = 141 cm answer : d"
Answer: d
Question (physics): how many times in a day the hands of a clock are straight ?
Options: a ) 21 , b ) 27 , c ) 24 , d ) 22 , e ) 25
Rationale: "in 12 hours , the hands coincide or are in oppesite direction 22 times . in 24 hours , they are at right angles 22 times . answer is d ."
Answer: d
Question (probability): on a ranch , a rancher can place a loop of rope , called a lasso , once in every 2 throws around a cow ’ s neck . what is the probability that the rancher will be able to place a lasso around a cow ’ s neck at least once in 3 attempts ?
Options: a ) 3 / 4 , b ) 5 / 8 , c ) 7 / 8 , d ) 9 / 16 , e ) 15 / 16
Rationale: "p ( missing all 3 ) = ( 1 / 2 ) ^ 3 = 1 / 8 p ( success on at least one attempt ) = 1 - 1 / 8 = 7 / 8 the answer is c ."
Answer: c
Question (physics): twelve machines , each working at the same constant rate , together can complete a certain job in 12 days . how many additional machines , each working at the same constant rate , will be needed to complete the job in 8 days ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 6 , e ) 8
Rationale: another solution which is faster is since each machine works at a constant rate . the time needs to bought down from 12 to 8 . so the new time is 2 / 3 of the original time . thus to achieve this we need the rate to be 3 / 2 of original . so 3 / 2 * 12 = 18 so we need 18 - 12 = 6 more machines . answer : d
Answer: d
Question (general): if 49 ( 7 ^ x ) = 1 then x =
Options: a ) – 2 , b ) – 1 , c ) 0 , d ) 1 , e ) 2
Rationale: "7 ^ x = 1 / 49 7 ^ x = 1 / 7 ^ 2 7 ^ x = 7 ^ - 2 x = - 2 a"
Answer: a
Question (general): a cab driver 5 days income was $ 200 , $ 150 , $ 750 , $ 400 , $ 500 . then his average income is ?
Options: a ) $ 420 , b ) $ 410 , c ) $ 400 , d ) $ 390 , e ) $ 380
Rationale: "avg = sum of observations / number of observations avg income = ( 200 + 150 + 750 + 400 + 500 ) / 5 = 400 answer is c"
Answer: c
Question (physics): x is able to do a piece of work in 14 days and y can do the same work in 20 days . if they can work together for 5 days , what is the fraction of work completed ?
Options: a ) 15 / 28 , b ) 17 / 28 , c ) 13 / 28 , d ) 19 / 28 , e ) 11 / 28
Rationale: explanation : amount of work x can do in 1 day = 1 / 14 amount of work y can do in 1 day = 1 / 20 amount of work x and y can do in 1 day = 1 / 14 + 1 / 20 = 17 / 140 amount of work x and y can together do in 5 days = 5 × ( 17 / 140 ) = 17 / 28 answer : option b
Answer: b
Question (geometry): a football field is 9600 square yards . if 1200 pounds of fertilizer are spread evenly across the entire field , how many pounds of fertilizer were spread over an area of the field totaling 5600 square yards ?
Options: a ) 450
b ) 600
c ) 700
d ) 2400
e ) 3200
Rationale: answer c ) 9600 yards need 1200 lbs 1 yard will need 1200 / 9600 = 1 / 8 lbs 3600 yards will need 1 / 8 * 5600 yards = 700 lbs
Answer: c
Question (gain): if a man buys 1 liter of milk for 12 rs . and mixes it with 20 % water and sells it for 15 rs then what is the % age of gain . . .
Options: a ) 30 , b ) 40 , c ) 50 , d ) 60 , e ) 70
Rationale: quantity after adding 20 % water = 1.2 liter sp of 1.2 lit . @ 15 rs . / liter = 15 * 1.2 = 18 rs cp = 12 rs / lit . % profit = 100 * ( 18 - 12 ) / 12 = 50 answer : c
Answer: c
Question (general): a tightrope approximately 320 m long is suspended between two poles . during a performance , a break occurs in the line . assume that the line has an equal chance of breaking anywhere along its length . what is the probability that the break happened in the first 50 meters of the rope ?
Options: a ) 27 / 32 , b ) 1 / 2 , c ) 5 / 32 , d ) 5 / 27 , e ) . 2 / 3
Rationale: simly 50 / 320 = 5 / 32 answer will be ( c )
Answer: c
Question (general): on thursday mabel handled 90 transactions . anthony handled 10 % more transactions than mabel , cal handled 2 / 3 rds of the transactions that anthony handled , and jade handled 18 more transactions than cal . how much transactions did jade handled ?
Options: a ) 80 , b ) 81 , c ) 82 , d ) 83 , e ) 84
Rationale: "solution : mabel handled 90 transactions anthony handled 10 % more transactions than mabel anthony = 90 + 90 × 10 % = 90 + 90 × 0.10 = 90 + 9 = 99 cal handled 2 / 3 rds of the transactions than anthony handled cal = 2 / 3 × 99 = 66 jade handled 18 more transactions than cal . jade = 66 + 18 = 84 jade handled = 84 transactions . answer : e"
Answer: e
Question (physics): while working alone at their constant rates , computer x can process 240 files in 4 hours , and computer y can process 240 files in 6 hours . if all files processed by these computers are the same size , how many hours would it take the two computers , working at the same time at their respective constant rates , to process a total of 240 files ?
Options: a ) 2 , b ) 2.2 , c ) 2.4 , d ) 2.6 , e ) 2.8
Rationale: both computers together process files at a rate of 240 / 4 + 240 / 6 = 60 + 40 = 100 files per hour . the time required to process 240 files is 240 / 100 = 2.4 hours the answer is c .
Answer: c
Question (gain): $ 2,000 is deposited in a savings account that pays 4 % annual interest compounded semiannually . to the nearest dollar , how much is in the account at the end of the year ?
Options: a ) $ 2125.15 , b ) $ 2083.12 , c ) $ 2184.22 , d ) $ 2150.84 , e ) $ 2080.80
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 = 4 / 2 = 2 % now , ca = 2000 ( 1 + 2 / 100 ) ^ 2 = $ 2080.80 hence answer is e"
Answer: e
Question (general): a , b and c rent a pasture . if a puts 10 oxen for 7 months , b puts 12 oxen for 5 months and c puts 15 oxen for 3 months for grazing and the rent of the pasture is rs . 140 , then how much amount should c pay as his share of rent ?
Options: a ) 35 , b ) 45 , c ) 25 , d ) 36 , e ) 55
Rationale: "a : b : c = 10 × 7 : 12 × 5 : 15 × 3 = 2 × 7 : 12 × 1 : 3 × 3 = 14 : 12 : 9 amount that c should pay = 140 × 9 / 35 = 4 × 9 = 36 answer is d"
Answer: d
Question (gain): what is the rate percent when the simple interest on rs . 1000 amount to rs . 400 in 4 years ?
Options: a ) 5 % , b ) 6 % , c ) 2 % , d ) 95 % , e ) 10 %
Rationale: "interest for 4 yrs = 400 interest for 1 yr = 100 interest rate = 100 / 1000 x 100 = 10 % answer : e"
Answer: e
Question (physics): a cistern can be filled by a tap in 4 hours while it can be emptied by another tap in 7 hours . if both the taps are opened simultaneously , then after how much time will the cistern get filled ?
Options: a ) 9.5 , b ) 9.4 , c ) 9.3 , d ) 9.2 , e ) 9.1
Rationale: "net part filled in 1 hour = ( 1 / 4 - 1 / 7 ) = 3 / 28 the cistern will be filled in 28 / 3 hrs i . e . , 9.3 hrs . answer : c"
Answer: c
Question (general): by how much is 12 % of 24.2 more than 10 % of 14.2 ?
Options: a ) 0.1484 , b ) 14.84 , c ) 1.484 , d ) 2.762 , e ) none
Rationale: "answer required difference = ( 12 x 24.2 ) / 100 - ( 10 x 14.2 ) / 100 = 2.904 - 1.42 = 1.484 . correct option : c"
Answer: c
Question (general): the jogging track in a sports complex is 627 m in circumference . deepak and his wife start from the same point and walk in opposite directions at 4.5 km / hr and 3.75 km / hr respectively . they will meet for the first time in ?
Options: a ) 4.56 min , b ) 5.28 min , c ) 5.08 min , d ) 9.28 min , e ) 5.988 min
Rationale: "clearly , the two will meet when they are 627 m apart . to be ( 4.5 + 3.75 ) = 8.25 km apart , they take 1 hour . to be 627 m apart , they take ( 100 / 825 * 627 / 1000 ) hrs = ( 627 / 8250 * 60 ) min = 4.56 min . answer : a"
Answer: a
Question (general): a jogger running at 9 km / hr along side a railway track is 240 m ahead of the engine of a 120 m long train running at 27 km / hr in the same direction . in how much time will the train pass the jogger ?
Options: a ) 76 sec , b ) 72 sec , c ) 98 sec , d ) 36 sec , e ) 23 sec
Rationale: "speed of train relative to jogger = 27 - 9 = 18 km / hr . = 18 * 5 / 18 = 5 m / sec . distance to be covered = 240 + 120 = 360 m . time taken = 360 / 5 = 72 sec . answer : b"
Answer: b
Question (general): a sun is divided among x , y and z in such a way that for each rupee x gets , y gets 45 paisa and z gets 50 paisa . if the share of y is rs . 36 , what is the total amount ?
Options: a ) 115 , b ) 116 , c ) 117 , d ) 118 , e ) 156
Rationale: "x : y : z = 100 : 45 : 50 20 : 9 : 10 9 - - - 36 39 - - - ? = > 156 answer : e"
Answer: e
Question (general): a certain company retirement plan has arule of 70 provision that allows an employee to retire when the employee ' s age plus years of employment with the company total at least 70 . in what year could a female employee hired in 1989 on her 32 nd birthday first be eligible to retire under this provision ?
Options: a ) 2008 , b ) 2004 , c ) 2005 , d ) 2006 , e ) 2007
Rationale: "she must gain at least 70 points , now she has 32 and every year gives her two more points : one for age and one for additional year of employment , so 32 + 2 * ( # of years ) = 70 - - > ( # of years ) = 19 - - > 1989 + 19 = 2008 . answer : a ."
Answer: a