Cheukting/mathqa huggingface dataset:
Question (general): a , b and c invest in the ratio of 3 : 4 : 5 . the percentage of return on their investments are in the ratio of 6 : 5 : 4 . find the total earnings , if b earns rs . 200 more than a :
Options: a ) 2348 , b ) 7250 , c ) 2767 , d ) 1998 , e ) 5800
Rationale: explanation : a b c investment 3 x 4 x 5 x rate of return 6 y % 5 y % 4 y % return \ inline \ frac { 18 xy } { 100 } \ inline \ frac { 20 xy } { 100 } \ inline \ frac { 20 xy } { 100 } total = ( 18 + 20 + 20 ) = \ inline \ frac { 58 xy } { 100 } b ' s earnings - a ' s earnings = \ inline \ frac { 2 xy } { 100 } = 200 total earning = \ inline \ frac { 58 xy } { 100 } = 5800 answer : e ) rs . 5800
Answer: e
Question (general): the average of first 14 even numbers is ?
Options: a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 15
Rationale: "sum of 14 even numbers = 14 * 15 = 210 average = 210 / 14 = 15 answer : e"
Answer: e
Question (geometry): a certain rectangular crate measures 12 feet by 16 feet by 18 feet . a cylindrical gas tank is to be made for shipment in the crate and will stand upright when the crate is placed on one of its six faces . what should the radius of the tank be if it is to be of the largest possible volume ?
Options: a ) 4
b ) 5
c ) 6
d ) 8
e ) 10
Rationale: for max volume of cylinder ( pi * r ^ 2 * h ) we need to max out r ^ 2 * h . we do n ' t know what the dimensions of the crate refer to . . therefore for max vol base should be 18 x 16 i . e . of radius 16 / 2 = 8 d
Answer: d
Question (general): for what values of k will the pair of equations 4 ( 3 x + 4 y ) = 48 and kx + 12 y = 30 does not have a unique solution ?
Options: a ) 12 , b ) 9 , c ) 3 , d ) 7.5 , e ) 2.5
Rationale: we have 2 equations 1 . 4 ( 3 x + 4 y ) = 48 - - > 3 x + 4 y = 12 - - > 9 x + 12 y = 36 2 . kx + 12 y = 30 substract 1 - 2 , we get ( 9 - k ) x = 6 i . e . x = 6 / ( 9 - k ) then , by looking at options , we get some value of x except for b . when we put k = 9 , x becomes 6 / 0 and hence answer is b
Answer: b
Question (physics): the sector of a circle has radius of 21 cm and central angle 120 o . find its perimeter ?
Options: a ) 91.5 cm , b ) 11.5 cm , c ) 91.8 cm , d ) 86 cm , e ) 99.5 cm
Rationale: "perimeter of the sector = length of the arc + 2 ( radius ) = ( 120 / 360 * 2 * 22 / 7 * 21 ) + 2 ( 21 ) = 44 + 42 = 86 cm answer : d"
Answer: d
Question (other): how many different positive integers are factors of 40 ?
Options: a ) 3 , b ) 2 , c ) 1 , d ) 6 , e ) 4
Rationale: 2 * 20 4 * 10 8 * 5 answer : d
Answer: d
Question (general): a couple married in 1980 had two children , one in 1982 and the other in 1984 . their combined ages will equal the years of the marriage in ?
Options: a ) 1986 , b ) 1985 , c ) 1987 , d ) 1988 , e ) 1989
Rationale: sum of year = 1 + 9 + 8 + 0 = ( 18 ) 1 + 8 = 9 1 + 9 + 8 + 2 = ( 20 ) 2 + 0 = 2 1 + 9 + 8 + 4 = ( 13 ) 1 + 3 = 4 now 9 + 2 + 4 = ( 15 ) 1 + 5 = 6 nd option a 1 + 9 + 8 + 6 = 24 ( 2 + 4 ) = 6 answer : a
Answer: a
Question (physics): find the expenditure on digging a well 14 m deep and of 3 m diameter at rs . 19 per cubic meter ?
Options: a ) 2998 , b ) 1881 , c ) 2890 , d ) 1485 , e ) 2780
Rationale: "22 / 7 * 14 * 3 / 2 * 3 / 2 = 99 m 2 99 * 19 = 1881 answer : b"
Answer: b
Question (gain): at an election 2 candidates are participated and a candidate got 45 % of votes and defeated by 9000 . and 83 votes are invalid . find the total polled votes ?
Options: a ) 84512 , b ) 78452 , c ) 65893 , d ) 90083 , e ) 74502
Rationale: winner votes = 100 - 45 = 55 polled votes = [ ( 100 * 9000 ) / 2 * 55 - 100 ] + 83 = 90083 answer is d
Answer: d
Question (physics): after working for 6 days , david was joined by moore . together they completed the remaining job in 3 days . how many days will it take both of them to complete the entire job , given that it would have taken david 12 days to complete the job alone ?
Options: a ) 7 , b ) 4 , c ) 6 , d ) 2 , e ) 7
Rationale: explanation : david and moore complete half work in 3 days = > they can complete whole work in 6 days answer : option c
Answer: c
Question (physics): how long does a train 110 m long running at the speed of 54 km / hr takes to cross a bridge 132 m length ?
Options: a ) 12.9 sec , b ) 12.1 sec , c ) 17.9 sec , d ) 16.13 sec , e ) 14.9 sec
Rationale: "speed = 54 * 5 / 18 = 15 m / sec total distance covered = 110 + 132 = 242 m . required time = 242 / 15 = 16.13 sec . answer : d"
Answer: d
Question (gain): by selling an article at rs . 800 , a shopkeeper makes a profit of 25 % . at what price should he sell the article so as to make a loss of 35 % ?
Options: a ) 228 , b ) 480 , c ) 267 , d ) 416 , e ) 276
Rationale: "sp = 800 profit = 25 % cp = ( sp ) * [ 100 / ( 100 + p ) ] = 800 * [ 100 / 125 ] = 640 loss = 25 % = 25 % of 640 = rs . 224 sp = cp - loss = 640 - 224 = rs . 416 answer : d"
Answer: d
Question (general): the average weight of 8 people increases by 2.5 kg when a new person comes in place of one of them weighing 55 kg . what is the weight of the new person ?
Options: a ) 75 kg , b ) 85 kg , c ) 95 kg , d ) 65 kg , e ) 55 kg
Rationale: "the total weight increase = ( 8 x 2.5 ) kg = 20 kg weight of new person = ( 55 + 20 ) kg = 75 kg the answer is a ."
Answer: a
Question (geometry): the length of a rectangular plot is 10 mtr more than its width . the cost of fencing the plot along its perimeter at the rate of rs . 6.5 mtr is rs . 910 . the perimeter of the plot is ?
Options: a ) 126 , b ) 156 , c ) 190 , d ) 140 , e ) 260
Rationale: "sol . let width = x , length = ( 10 + x ) perimeter = 2 ( x + ( 10 + x ) ) = 2 ( 2 x = 10 ) & 2 ( 2 x + 10 ) * 6.5 = 910 x = 30 required perimeter = 2 ( 30 + 40 ) = 140 d"
Answer: d
Question (general): what is the least number which should be added to 5432 so that the sum is exactly divisible by 5 , 6 , 4 , and 3 ?
Options: a ) 16 , b ) 22 , c ) 28 , d ) 34 , e ) 40
Rationale: l . c . m . of 5 , 6 , 4 and 3 = 60 . when dividing 5432 by 60 , the remainder is 32 . the number to be added = 60 - 32 = 28 . the answer is c .
Answer: c
Question (physics): two airplanes take off from one airfield at noon . one flies due east at 203 miles per hour while the other flies directly northeast at 283 miles per hour . approximately how many miles apart are the airplanes at 2 p . m . ?
Options: a ) 166 , b ) 332 , c ) 406 , d ) 483 , e ) 566
Rationale: "c in two hours : the plane flying east will be 406 miles away from airport . the other plane will be 566 miles away from airport . 566 / 406 = ~ 1.4 = ~ sqrt ( 2 ) this means that planes formed a right isocheles triangle = > sides of such triangles relate as 1 : 1 : sqrt ( 2 ) = > the planes are 406 miles apart . c"
Answer: c
Question (general): a man can swim in still water at 6 km / h , but takes twice as long to swim upstream than downstream . the speed of the stream is ?
Options: a ) 3 , b ) 7.5 , c ) 2.25 , d ) 2 , e ) 4
Rationale: "m = 6 s = x ds = 6 + x us = 6 - x 6 + x = ( 6 - x ) 2 6 + x = 12 - 2 x 3 x = 6 x = 2 answer : d"
Answer: d
Question (gain): the population of a town is 10000 . it increases annually at the rate of 20 % p . a . what will be its population after 4 years ?
Options: a ) 20300 , b ) 20400 , c ) 20730 , d ) 20500 , e ) 20600
Rationale: "formula : ( after = 100 denominator ago = 100 numerator ) 10000 ã — 120 / 100 ã — 120 / 100 ã — 120 / 100 ã — 120 / 100 = 20730 c"
Answer: c
Question (general): a certain roller coaster has 4 cars , and a passenger is equally likely to ride in any 1 of the 4 cars each time that passenger rides the roller coaster . if a certain passenger is to ride the roller coaster 4 times , what is the probability that the passenger will ride in each of the 4 cars ?
Options: a ) 0 , b ) 1 / 9 , c ) 2 / 9 , d ) 3 / 32 , e ) 1
Rationale: "if he is to ride 4 times and since he can choose any of the 4 cars each time , total number of ways is = 4 * 4 * 4 * 4 = 256 now the number of ways if he is to choose a different car each time is = 4 * 3 * 2 * 1 = 24 so the probability is = 24 / 256 = 6 / 64 = 3 / 32 = 3 / 32 answer : d"
Answer: d
Question (geometry): what will be the ratio between the area of a rectangle and the area of a triangle with one of the sides of rectangle as base and a vertex on the opposite side of rectangle .
Options: a ) 1 : 2 , b ) 2 : 1 , c ) 3 : 1 , d ) data inadequate , e ) none of these
Rationale: "area of δ ebc = 1 ⁄ 2 × bc × ef = 1 ⁄ 2 × bc × ab [ since , ef = ab ] area of δ ebc = 1 ⁄ 2 × area of δ abcd \ required ratio = 2 : 1 . answer b"
Answer: b
Question (general): the average age of a , b and c is 25 years . if the average age of a and c is 29 years , what is the age of b in years ?
Options: a ) 17 , b ) 35 , c ) 20 , d ) 32 , e ) 21
Rationale: "age of b = age of ( a + b + c ) â € “ age of ( a + c ) = 25 ã — 3 â € “ 29 ã — 2 = 75 â € “ 58 = 17 years a"
Answer: a
Question (geometry): a man walking at the rate of 6 km per hour crosses a square field diagonally in 9 seconds the area of the field is
Options: a ) 110 sq . m
b ) 111.5 aq . m
c ) 112.5 sq . m
d ) 114 sq . m
e ) none of these
Rationale: explanation : distance covered in 9 seconds = ( 6 × 1000 / 3600 ) × 9 = 15 m diagonal of square field = 15 m side of square = a then diagonal of that square = √ 2 a hence area of the square = a 2 = ( 152 ) / 2 = 112.5 sq . m answer : option c
Answer: c
Question (other): in a college the ratio of the numbers of boys to the girls is 8 : 5 . if there are 175 girls , the total number of students in the college is ?
Options: a ) 562 , b ) 356 , c ) 455 , d ) 416 , e ) 512
Rationale: "let the number of boys and girls be 8 x and 5 x then , 5 x = 175 x = 35 total number of students = 13 x = 13 * 35 = 455 answer is c"
Answer: c
Question (physics): i spend 40 hours a week ( 5 days ) at work and like to organize my time so that i spend an equal number of hours on the two tasks i currently have . currently , i am spending 5 hours a day on task 1 and 3 on task 2 . how many hours a week less do i need to spend on task 1 in order to evenly distribute my time ?
Options: a ) 5 , b ) 3 , c ) 7 , d ) 1 , e ) 6
Rationale: 5 x 5 = 25 25 - 5 = 20 the answer is a .
Answer: a
Question (physics): what is the greatest of 3 consecutive integers whose sum is 27 ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 11
Rationale: "the sum of three consecutive integers can be written as n + ( n + 1 ) + ( n + 2 ) = 3 n + 3 if the sum is 24 , we need to solve the equation 3 n + 3 = 27 ; = > 3 n = 27 ; = > n = 9 the greatest of the three numbers is therefore 9 + 2 = 11 answer : e"
Answer: e
Question (geometry): the area of a triangle is with base 4 m and height 5 m ?
Options: a ) 11
b ) 10
c ) 99
d ) 17
e ) 12
Rationale: 1 / 2 * 4 * 5 = 10 m 2 answer : b
Answer: b
Question (general): a pharmaceutical company received $ 5 million in royalties on the first $ 20 million in sales of and then $ 10 million in royalties on the next $ 108 million in sales . by approximately what percentage did the ratio of royalties to sales decrease from the first $ 20 million in sales to the next $ 108 million in sales ?
Options: a ) 8 % , b ) 26 % , c ) 45 % , d ) 52 % , e ) 56 %
Rationale: ( 10 / 108 ) / ( 5 / 20 ) = 20 / 27 = 74 % it means that 10 / 108 represents only 74 % . therefore a decrease of 26 % . answer b
Answer: b
Question (gain): peter brought a scooter for a certain sum of money . he spent 10 % of the cost on repairs and sold the scooter for a profit of $ 1100 . how much did he spend on repairs if he made a profit of 20 % ?
Options: a ) 100 , b ) 200 , c ) 300 , d ) 400 , e ) 500
Rationale: e 500 let the c . p . be $ x . then , 20 % of x = 1100 20 / 100 * x = 1100 = > x = 5500 c . p . = $ 5500 , expenditure on repairs = 10 % actual price = $ ( 100 * 5500 ) / 110 = $ 5000 expenditures on repairs = ( 5500 - 5000 ) = $ 500 .
Answer: e
Question (physics): 10 people can write 55 book in 12 days working 8 hour a day . then in how many day 198 can be written by 48 people ?
Options: a ) 9 , b ) 13 , c ) 21 , d ) 24 , e ) 23
Rationale: "work per day epr hour per person = 55 / ( 12 * 8 * 10 ) / / eq - 1 people = 48 ; let suppose day = p ; per day work for 8 hours acc . to condition work per day epr hour per person = 198 / ( p * 8 * 48 ) / / eq - 2 eq - 1 = = eq - 2 ; p = 9 answer : a"
Answer: a
Question (physics): the current of a stream runs at the rate of 4 kmph . a boat goes 12 km and back to the starting point in 2 hours , then find the speed of the boat in still water ?
Options: a ) a ) 17.33 , b ) b ) 2 , c ) c ) 18 , d ) d ) 16 , e ) e ) 13.21
Rationale: "s = 4 m = x ds = x + 4 us = x - 4 12 / ( x + 4 ) + 12 / ( x - 4 ) = 2 x = 13.21 answer : e"
Answer: e
Question (physics): a train 200 m long passes a man , running at 5 km / hr in the same direction in which the train is going , in 10 seconds . the speed of the train is :
Options: a ) 45 km / hr , b ) 50 km / hr , c ) 77 km / hr , d ) 55 km / hr , e ) 56 km / hr
Rationale: "speed of the train relative to man = ( 200 / 10 ) m / sec = 20 m / sec . [ 20 * ( 18 / 5 ) ] km / hr = 72 km / hr . let the speed of the train be x km / hr . then , relative speed = ( x - 5 ) km / hr . x - 5 = 72 = = > x = 77 km / hr . answer : c"
Answer: c
Question (physics): to fill a tank , 200 buckets of water is required . how many buckets of water will be required to fill the same tank if the capacity of the bucket is reduced to four - fifths of its present ?
Options: a ) 50 , b ) 100 , c ) 150 , d ) 200 , e ) 250
Rationale: "let the capacity of 1 bucket = x . then , the capacity of tank = 200 x . new capacity of bucket = 4 / 5 x therefore , required number of buckets = ( 200 x ) / ( 4 x / 5 ) = ( 200 x ) x 5 / 4 x = 1000 / 4 = 250 answer is e ."
Answer: e
Question (gain): if the cost price of 19 articles is equal to the selling price of 16 articles , what is the percentage of profit or loss that the merchant makes ?
Options: a ) 18.75 % loss , b ) 18.75 % profit , c ) 33.33 % loss , d ) 30.33 % loss , e ) none of these
Rationale: "explanation : let cost price of 1 article be re . 1 . therefore , cost price of 19 articles = rs . 19 . selling price of 16 articles = rs . 19 therefore , selling price of 19 articles is : - = > 19 / 16 ã — 19 = > 22.56 . therefore , profit = selling price - cost price . = > 22.56 â ˆ ’ 19 = 3.56 . hence , the percentage of profit = profit x 100 / c . p . = > 3.56 / 19 ã — 100 . = > 18.75 % profit . answer : b"
Answer: b
Question (general): the mean of 40 observations was 100 . it was found later that an observation 50 was wrongly taken as 75 the corrected new mean is
Options: a ) 125.8 , b ) 102.8 , c ) 99.375 , d ) 100.52 , e ) 122
Rationale: "explanation : correct sum = ( 100 * 40 + 50 - 75 ) = 3975 . correct mean = = 3975 / 40 = 99.375 answer : c"
Answer: c
Question (general): the entrance fee for a fair is $ 5 for persons under the age of 18 , and 20 % more for persons older . each ride at the fair costs $ 0.50 . if joe goes with her 6 years old twin brothers , and they each took 3 rides in total . how much money does joe end up spending at the fair ?
Options: a ) 16 , b ) 20.5 , c ) 17.5 , d ) 20 , e ) 4.5
Rationale: total entrance fee is ( 2 * $ 5 ) + ( 1.20 * 5 ) = $ 16 total rides fee is ( 0.50 * 3 ) * 3 = $ 4.50 total money spent is $ 20.50 answer is b
Answer: b
Question (gain): in the manufacture of a certain product , 7 percent of the units produced are defective and 5 percent of the defective units are shipped for sale . what percent of the units produced are defective units that are shipped for sale ?
Options: a ) 0.125 % , b ) 0.35 % , c ) 0.8 % , d ) 1.25 % , e ) 2.0 %
Rationale: "0.07 * 0.05 = 0.0035 = 0.35 % the answer is b ."
Answer: b
Question (other): a bag contains 6 red , 5 blue and 2 green balls . if 2 ballsare picked at random , what is the probability that both are red ?
Options: a ) 2 / 13 , b ) 3 / 17 , c ) 5 / 26 , d ) 5 / 21 , e ) 7 / 15
Rationale: "p ( both are red ) , = 6 c 213 c 2 = 6 c 213 c 2 = 5 / 26 c"
Answer: c
Question (general): if 1488 / 1.24 = 1200 , then 148.8 / 12.4 is equal to ?
Options: a ) 17 , b ) 10 , c ) 14 , d ) 12 , e ) 11
Rationale: "answer given expression 148.8 / 12.4 = 1488 / 124 = 1488 / ( 1.24 x 100 ) = 1200 / 100 = 12 correct option : d"
Answer: d
Question (physics): the cross - section of a cannel is a trapezium in shape . if the cannel is 6 m wide at the top and 4 m wide at the bottom and the area of cross - section is 10290 sq m , the depth of cannel is ?
Options: a ) 258 , b ) 260 , c ) 262 , d ) 264 , e ) 266
Rationale: 1 / 2 * d ( 6 + 4 ) = 10290 d = 258 answer : a
Answer: a
Question (other): a girl scout was selling boxes of cookies . in a month , she sold both boxes of chocolate chip cookies ( $ 1.25 each ) and boxes of plain cookies ( $ 0.75 each ) . altogether , she sold 1,585 boxes for a combined value of $ 1 , 586.25 . how many boxes of plain cookies did she sell ?
Options: a ) 0 , b ) 233 , c ) 500 , d ) 695 , e ) 790
Rationale: let # plain cookies sold be x then # chocolate cookies = ( total cookies - x ) equating for x ( 0.75 ) * x + ( 1.25 ) * ( 1585 - x ) = 1586.25 = > x = 790 e
Answer: e
Question (general): in what ratio p : q should the mixture p of milk and water in the ratio of 5 : 4 be mixed with another mixture q of milk and water in the ratio 2 : 7 so that the resultant mixture contains equal quantities of milk and water ?
Options: a ) 3 : 2 , b ) 2 : 1 , c ) 4 : 3 , d ) 4 : 1 , e ) 5 : 1
Rationale: ( 5 / 9 ) * p + ( 2 / 9 ) * q = ( 4 / 9 ) * p + ( 7 / 9 ) * q p = 5 q p / q = 5 / 1 the answer is e .
Answer: e
Question (general): a certain company expects quarterly earnings of $ 0.80 per share of stock , half of which will be distributed as dividends to shareholders while the rest will be used for research and development . if earnings are greater than expected , shareholders will receive an additional $ 0.04 per share for each additional $ 0.10 of per share earnings . if quarterly earnings are $ 1.10 per share , what will be the dividend paid to a person who owns 500 shares of the company ' s stock ?
Options: a ) $ 260 , b ) $ 96 , c ) $ 26 , d ) $ 120 , e ) $ 240
Rationale: "eps actual > eps expected . each gets and additional . 12 per share . thus . 52 * 500 - - > $ 260 answer is a"
Answer: a
Question (general): the positive integers s and t leave remainders of 2 and 3 , respectively , when divided by 6 . s > t . what is the remainder when s – t is divided by 6 ?
Options: a ) 3 , b ) 1 , c ) 4 , d ) 2 , e ) 5
Rationale: let ' s test out some values of p and q that satisfy the given information . s leaves are remainder of 2 when divided by 6 so , s could equal 8 t leaves are remainder of 3 when divided by 6 so , t could equal 3 what is the remainder when s – t is divided by 6 ? so , s - t = 8 - 3 = 5 , and when we divide 5 by 6 , we get 0 with remainder 5 answer : e
Answer: e
Question (general): what is the remainder when 9 ^ 381 is divided by 5 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: i also agree that the remainder is ' 4 ' ( using the last digit of the powers of 7 ) . could we have the official answer please ? e
Answer: e
Question (general): the sum of ages of 5 children born 2 years different each is 40 years . what is the age of the elder child ?
Options: a ) 12 , b ) 9 , c ) 10 , d ) 16 , e ) 17
Rationale: "let the ages of children be x , ( x + 2 ) , ( x + 4 ) , ( x + 6 ) and ( x + 8 ) years . then , x + ( x + 2 ) + ( x + 4 ) + ( x + 6 ) + ( x + 8 ) = 40 5 x = 20 x = 4 . x + 8 = 4 + 8 = 12 answer : a"
Answer: a
Question (general): find large number from below question the difference of two no . is 1365 . on dividing the larger no . by the smaller , we get 6 as quotient and the 15 as remainder ?
Options: a ) 1234 , b ) 1456 , c ) 1256 , d ) 1456 , e ) 1635
Rationale: "let the smaller number be x . then larger number = ( x + 1365 ) . x + 1365 = 6 x + 15 5 x = 1350 x = 270 large number = 270 + 1365 = 1635 e"
Answer: e
Question (gain): the compound interest earned by sunil on a certain amount at the end of two years at the rate of 4 % p . a . was rs . 326.40 . find the total amount that sunil got back at the end of two years in the form of principal plus interest earned .
Options: a ) rs . 4326.40 , b ) rs . 4236.40 , c ) rs . 4136.40 , d ) rs . 4316.40 , e ) rs . 4136.40
Rationale: "let the sum be rs . p p { [ 1 + 4 / 100 ] 2 - 1 } = 326.40 p ( 4 / 100 ) ( 2 + 4 / 100 ) = 326.40 [ a 2 - b 2 = ( a - b ) ( a + b ) ] p = 326.40 / ( 0.04 ) ( 2.04 ) = 4000 amount = 4000 + 326.40 = 4326.40 answer : a"
Answer: a
Question (geometry): if a square mirror has a 20 - inch diagonal , what is the approximate perimeter e of the mirror , in inches ?
Options: a ) 40
b ) 60
c ) 80
d ) 100
e ) 120
Rationale: if you draw the square and diagonal inside the square . u can see square becomes part of two triangles opposite to each other . and we know the property of the triangle , addition of two sides of triangle must be greater than its diagonal in order to complete the triangle . and each side must be less than 20 and perimeter e must be less than 80 , so we can eliminate answer choice c , d and e . so side 1 + side 2 > 20 , that means side 1 or side 2 must be > 10 . so we can eliminate the answer choice a . now we are left with is b
Answer: b
Question (physics): james and david work at a grocery shop with 6 other workers . for an internal review , 2 of the 6 workers will be randomly chosen to be interviewed . what is the probability that james and david will both be chosen ?
Options: a ) 1 / 20 , b ) 1 / 22 , c ) 1 / 23 , d ) 1 / 25 , e ) 1 / 15
Rationale: "probability that james and david will both be chosen out of 6 workers = ( 2 / 6 ) * ( 1 / 5 ) = 1 / 15 answer e"
Answer: e
Question (gain): 60 % of a number is added to 120 , the result is the same number . find the number ?
Options: a ) 300 , b ) 288 , c ) 270 , d ) 129 , e ) 281
Rationale: "( 60 / 100 ) * x + 120 = x 2 x = 600 x = 300 answer : a"
Answer: a
Question (general): in a 60 member association consisting of men and women , exactly 20 % of men and exactly 25 % women are homeowners . what is the least number of members who are homeowners ?
Options: a ) 29 , b ) 13 , c ) 25 , d ) 23 , e ) 21
Rationale: "solution simple out of 60 20 % are male i . e 12 and 25 % are female i . e 15 , so total homeowner is 27 . now min number homeowner is 12 and max is 27 so question ask us to find least and 13 has least value among all option . so ans is 13 . answer : b"
Answer: b
Question (probability): if a card is drawn from a well shuffled pack of cards , the probability of drawing a spade or a king is -
Options: a ) 8 / 13 , b ) 6 / 13 , c ) 3 / 13 , d ) 4 / 13 , e ) 1 / 13
Rationale: explanation : p ( s á ´ œ k ) = p ( s ) + p ( k ) - p ( s â ˆ © k ) , where s denotes spade and k denotes king . p ( s á ´ œ k ) = 13 / 52 + 4 / 52 - 1 / 52 = 4 / 13 answer : d
Answer: d
Question (physics): a man swims downstream 30 km and upstream 18 km taking 6 hours each time , what is the speed of the man in still water ?
Options: a ) 7 , b ) 8 , c ) 5 , d ) 2 , e ) 4
Rationale: "30 - - - 6 ds = 5 ? - - - - 1 18 - - - - 6 us = 3 ? - - - - 1 m = ? m = ( 5 + 3 ) / 2 = 4 answer : e"
Answer: e
Question (general): what is the least value of x . so that 23 x 59 is divisible by 3 .
Options: a ) 2 , b ) 0 , c ) 1 , d ) 3 , e ) 4
Rationale: "explanation : the sum of the digits of the number is divisible by 3 , then the number is divisible by 3 . 2 + 3 + x + 5 + 9 = 19 + x least value of x may be 2 therefore 19 + 2 = 21 is divisible by 3 . answer : option a"
Answer: a
Question (general): if the sum of the 4 th term and the 12 th term of an arithmetic progression is 16 , what is the sum of the first 15 terms of the progression ?
Options: a ) 80 , b ) 100 , c ) 105 , d ) 120 , e ) 110
Rationale: "4 th term + 12 th term = 16 i . e . , ( a + 3 d ) + ( a + 11 d ) = 16 now , sum of first 15 terms = ( 15 / 2 ) * [ 2 a + ( 15 - 1 ) d ] = ( 15 / 2 ) * [ 2 a + 14 d ] = ( 15 / 2 ) * 16 - - - - - - - - - - - - - - - from ( 1 ) = 120 answer : d"
Answer: d
Question (geometry): the side of a square is increased by 25 % then how much % does its area increases ?
Options: a ) 56.28 , b ) 56.25 , c ) 56.2 , d ) 56.24 , e ) 56.21
Rationale: "a = 100 a 2 = 10000 a = 125 a 2 = 15625 - - - - - - - - - - - - - - - - 10000 - - - - - - - - - 5625 100 - - - - - - - ? = > 56.25 % answer : b"
Answer: b