Cheukting/mathqa huggingface dataset:
Question (geometry): the length and breadth of a rectangle is increased by 30 % and 45 % respectively . what is the increase in the area ?
Options: a ) 88.25 , b ) 87.5 , c ) 86.0 , d ) 88.0 , e ) 88.5
Rationale: "100 * 100 = 10000 130 * 145 = 18850 - - - - - - - - - - - 8850 10000 - - - - 8850 100 - - - - - 88.50 answer e"
Answer: e
Question (general): 8 liters of a 25 percent solution of alcohol in water are mixed with 2 liters of a 12 percent alcohol in water solution . what is the percentage of alcohol in the new solution ?
Options: a ) 21.2 % , b ) 21.6 % , c ) 22.0 % , d ) 22.4 % , e ) 22.8 %
Rationale: the total amount of alcohol is 0.25 ( 8 ) + 0.12 ( 2 ) = 2.24 liters . the percentage is 2.24 / 10 = 22.4 / 100 which is 22.4 % the answer is d .
Answer: d
Question (other): a certain university will select 1 of 6 candidates eligible to fill a position in the mathematics department and 2 of 10 candidates eligible to fill 2 identical positions in the computer science department . if none of the candidates is eligible for a position in both departments , how many different sets of 3 candidates are there to fill the 3 positions ?
Options: a ) 42 , b ) 270 , c ) 140 , d ) 165 , e ) 315
Rationale: "1 of 6 will be chosen for the math 2 of 10 will be chosen for the computer none of the 3 chosen people can be in more than one departments . we can choose any of the 6 candidates for the math dep . , which gives as 6 selections . we can choose 2 of the 10 candidates for the computer dep . , which gives us 2 selections and 8 rejections . so , the way to find how many different selections of 2 candidates we can have for the computer dep . , we do : 10 ! / 2 ! * 8 ! = ( 9 * 10 ) / 2 = 90 / 2 = 45 . we are multiplying our individual selections : 6 * 45 = 270 in the bolded part , we do n ' t have to multiply all of the numbers , as those in 8 ! are included in 10 ! , so we simplify instead . ans b"
Answer: b
Question (other): in a school 20 % of the boys are same in number as 1 / 4 th of the girls . what is the ratio of boys to the girls in the school ?
Options: a ) 5 : 4 , b ) 2 : 3 , c ) 1 : 4 , d ) 3 : 7 , e ) 2 : 5
Rationale: "20 % of b = 1 / 4 g 20 b / 100 = g / 4 b = 5 g / 4 b / g = 5 / 4 b : g = 5 : 4 answer is a"
Answer: a
Question (general): find the least number must be subtracted from 5264 so that remaining number is divisible by 17 .
Options: a ) 11 , b ) 14 , c ) 18 , d ) 20 , e ) 29
Rationale: when dividing 5264 by 17 , we get the remainder 11 , so 11 should be subtracted . the answer is a .
Answer: a
Question (general): a salesman ' s income consists of a commission and a base salary of $ 400 per week . over the past 5 weeks , his weekly income totals have been $ 406 , $ 413 , $ 420 , $ 436 and $ 395 . what must his average ( arithmetic mean ) commission be per week over the next two weeks so that his average weekly income is $ 500 over the 7 - week period ?
Options: a ) $ 150 , b ) $ 245 , c ) $ 365 , d ) $ 315 , e ) $ 730
Rationale: "total weekly income over 5 weeks = $ 406 + $ 413 + $ 420 + $ 436 + $ 395 = $ 2070 for avg weekly income to be $ 500 over 7 weeks , we need total weekly income over 7 weeks = $ 3500 now , $ 3500 - $ 2070 = $ 1430 from this , we subtract base salary for 2 weeks i . e $ 350 * 2 = $ 700 therefore , commission = $ 1430 - $ 800 = $ 630 for 2 weeks avg weekly commission = $ 315 answer d"
Answer: d
Question (physics): a car travels at a speed of 65 miles per hour . how far will it travel in 4 hours ?
Options: a ) 125 miles , b ) 225 miles , c ) 260 miles , d ) 425 miles , e ) 525 miles
Rationale: during each hour , the car travels 65 miles . for 4 hours it will travel 65 + 65 + 65 + 65 = 4 × 65 = 260 miles correct answer is c ) 260 miles
Answer: c
Question (physics): a can give b 150 meters start and c 300 meters start in a kilometer race . how much start can b give c in a kilometer race ?
Options: a ) 111.12 , b ) 111.67 , c ) 111.64 , d ) 111.11 , e ) 176.47
Rationale: "a runs 1000 m while b runs 850 m and c runs 700 m . the number of meters that c runs when b runs 1000 m , = ( 1000 * 700 ) / 850 = 823.53 m . b can give c = 1000 - 823.53 = 176.47 m . answer : e"
Answer: e
Question (general): for the past n days , the average ( arithmetic mean ) daily production at a company was 50 units . if today ' s production of 100 units raises the average to 55 units per day , what is the value of n ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "the daily production was raised by 5 units for n days , which has a weighting of 5 n . 5 n = 100 - 55 = 45 n = 9 the answer is d ."
Answer: d
Question (general): 5 is added to a certain number , the sum is multiplied by 5 , the product is divided by 5 and 5 is subtracted from the quotient . the remainder left is half of 60 . what is the number ?
Options: a ) 21 , b ) 20 , c ) 2 , d ) 30 , e ) 45
Rationale: "let number is x . when 5 added to it , = ( x + 5 ) 5 multiplied to sum , = 5 * ( x + 5 ) now , = [ { 5 * ( x + 5 ) } / 5 ] and , = [ { 5 * ( x + 5 ) } / 5 ] - 5 according to question , [ { 5 * ( x + 5 ) } / 5 ] - 5 = half of 60 [ ( 5 x + 25 ) / 5 ) = 30 + 5 5 x + 25 = 35 * 5 x + 5 = 7 * 1 x + 5 = 7 x = 7 - 5 x = 2 so , required number is : 2 . answer : c"
Answer: c
Question (general): how many points ( x , y ) lie on the line segment between ( 32 , 12 2 / 3 ) and ( 7 , 17 2 / 3 ) such that x and y are both integers ?
Options: a ) one , b ) 4 , c ) 5 , d ) 8 , e ) 9
Rationale: "slope = ( 17 2 / 3 - 12 2 / 3 ) / ( 7 - 32 ) = - 1 / 5 y = mx + b = > 12 2 / 3 = - 22 / 3 + b = > b = 19 y = - x / 5 + 19 only integer values work , and the only multiples of 5 between 7 and 32 for x values are 10 , 15 , 20 , 25 and 30 , thus 5 points . c"
Answer: c
Question (physics): a train 250 m long running at 72 kmph crosses a platform in 15 sec . what is the length of the platform ?
Options: a ) 50 m , b ) 200 m , c ) 250 m , d ) 270 m , e ) 300 m
Rationale: "d = 72 * 5 / 18 = 15 = 300 â € “ 250 = 50 m answer : a"
Answer: a
Question (other): a bag holds 2 red marbles and 3 green marbles . if you removed two randomly selected marbles from the bag , without replacement , what is the probability that both would be green ?
Options: a ) 1 / 10 , b ) 1 / 5 , c ) 3 / 10 , d ) 2 / 5 , e ) 1 / 2
Rationale: "given : 2 r and 3 g marbles required : probability that 2 marbles removed without replacement are both red initially we have to pick one red from a total of 2 red and 3 green marbles after one red has been picked , we need to pick 1 green from a total of 2 green and 2 red marbles . p ( both green ) = ( 3 / 5 ) * ( 2 / 4 ) = 3 / 10 option c"
Answer: c
Question (gain): a baseball card decreased in value 20 % in its first year and 30 % in its second year . what was the total percent decrease of the card ' s value over the two years ?
Options: a ) 28 % , b ) 30 % , c ) 32 % , d ) 36 % , e ) 44 %
Rationale: "consider the initial value of the baseball card as $ 100 after first year price = 100 * 0.8 = 80 after second year price = 80 * 0.7 = 56 final decrease = [ ( 100 - 56 ) / 100 ] * 100 = 44 % correct answer - e"
Answer: e
Question (general): a batsman makes a score of 300 runs in the 17 th inning and thus increases his averages by 10 . what is his average after 17 th inning ?
Options: a ) 39 , b ) 140 , c ) 42 , d ) 40.5 , e ) 41.5
Rationale: "let the average after 16 th inning = x then total run after 16 th inning = 16 x then total run after 17 th inning = 16 x + 300 then average run after 17 th inning = ( 16 x + 300 ) / 17 ( 16 x + 300 ) / 17 = x + 10 = > 16 x + 300 = 17 x + 170 x = 130 average after 17 th inning = 130 + 10 = 140 answer : b"
Answer: b
Question (general): solve : 0.6 * 0.6 + 0.6 * 0.6
Options: a ) 0.46 , b ) 0.56 , c ) 0.64 , d ) 0.65 , e ) none of them
Rationale: "= 0.6 * 0.6 + ( 0.6 * 6 ) = 0.36 + 0.1 = 0.46 answer is a ."
Answer: a
Question (general): in a division sum , the remainder is 6 and the divisor is 5 times the quotient and is obtained by adding 12 to the thrice of the remainder . the dividend is
Options: a ) 74 , b ) 78 , c ) 86 , d ) 126 , e ) 98
Rationale: "divisor = ( 6 * 3 ) + 12 = 30 5 * quotient = 30 quotient = 6 . dividend = ( divisor * quotient ) + remainder dividend = ( 20 * 6 ) + 6 = 126 . d )"
Answer: d
Question (physics): a can do a piece of work 30 days . b can do work in 55 days . in how many days they will complete the work together ?
Options: a ) 15 days , b ) 16 days , c ) 19.4 days , d ) 17.2 days , e ) 18 days
Rationale: "lcm = 330 , ratio = 30 : 45 = 6 : 11 no of days = 330 / ( 6 + 11 ) = 330 / 17 = 19.4 days answer : c"
Answer: c
Question (physics): the diameter of a garden roller is 1.2 m and it is 2 m long . how much area will it cover in 5 revolutions ? ( use ï € = 22 â  „ 7 )
Options: a ) 40 m 2
b ) 44 m 2
c ) 48 m 2
d ) 37.7 m 2
e ) none of these
Rationale: required area covered in 5 revolutions = 5 ã — 2 ï € rh = 5 ã — 2 ã — 22 â  „ 7 ã — 0.6 ã — 2 = 37.7 m 2 answer d
Answer: d
Question (general): rs . 2080 is divided so that 3 times the first share , thrice the 2 nd share and four times the third share amount to the same . what is the value of the second share ?
Options: a ) s 802 , b ) s 208 , c ) s 960 , d ) s 690 , e ) s 906
Rationale: "a + b + c = 2080 3 a = 2 b = 4 c = x a : b : c = 1 / 3 : 1 / 2 : 1 / 4 = 4 : 6 : 3 6 / 13 * 2080 = rs 960 answer : c"
Answer: c
Question (physics): two trains running in opposite directions cross a man standing on the platform in 67 seconds and 17 seconds respectively and they cross each other in 73 seconds . the ratio of their speeds is :
Options: a ) 3 / 2 , b ) 3 / 9 , c ) 3 / 6 , d ) 3 / 1 , e ) 3 / 5
Rationale: "let the speeds of the two trains be x m / sec and y m / sec respectively . then , length of the first train = 27 x meters , and length of the second train = 17 y meters . ( 27 x + 17 y ) / ( x + y ) = 23 = = > 27 x + 17 y = 23 x + 23 y = = > 4 x = 6 y = = > x / y = 3 / 2 . answer : a"
Answer: a
Question (general): you make a cube that is made of 10 x 10 x 10 smaller cubes which sums up to a total of 1000 smaller cubes . now , if someone takes one layer of cubes , how many will remain ?
Options: a ) 357 , b ) 834 , c ) 500 , d ) 512 , e ) 216
Rationale: d 512 the cube that remains will be 8 x 8 x 8 . this will make a total of 512 . this is because , when a layer is taken , it will be taken from all sides of the cube which will reduce the dimension be two and not one .
Answer: d
Question (general): if a - b = 4 and a 2 + b 2 = 30 , find the value of ab .
Options: a ) a ) 7 , b ) b ) 12 , c ) c ) 15 , d ) d ) 18 , e ) e ) 20
Rationale: "explanation : 2 ab = ( a 2 + b 2 ) - ( a - b ) 2 = 30 - 16 = 14 ab = 7 answer : a"
Answer: a
Question (physics): in a regular week , there are 5 working days and for each day , the working hours are 8 . a man gets rs . 2.40 per hour for regular work and rs . 3.20 per hours for overtime . if he earns rs . 432 in 4 weeks , then how many hours does he work for ? a . 160 b . 175 c . 180 d . 195 explanation :
Options: a ) 160 , b ) 175 , c ) 180 , d ) 185 , e ) 195
Rationale: suppose the man works overtime for x hours . now , working hours in 4 weeks = ( 5 x 8 x 4 ) = 160 . 160 x 2.40 + x x 3.20 = 432 3.20 x = 432 - 384 = 48 x = 15 . hence , total hours of work = ( 160 + 15 ) = 175 . answer : option b
Answer: b
Question (other): of the 200 stamps in a collection , 90 are foreign and 60 are more than 10 years old . if 20 stamps are both foreign and more than 10 years old , how many stamps are neither foreign nor more than 10 years old ?
Options: a ) 50 , b ) 70 , c ) 100 , d ) 130 , e ) 150
Rationale: "20 stamps are both foreign and more than 10 years old . 70 stamps are foreign only . 40 stamps are 10 years old only . the number of remaining stamps is 200 - ( 20 + 70 + 40 ) = 70 the answer is b ."
Answer: b
Question (geometry): a cylindrical cube of radius 12 cm contains water upto a depth of 20 cm . a spherical iron ball is dropped into the tub and thus the level of water is raised by 6.75 cm . the radius of the ball is :
Options: a ) 7 cm
b ) 8.5 cm
c ) 9 cm
d ) 9.5 cm
e ) none
Rationale: sol . let the radius of the ball be r cm . volume of ball = volume of water displaced by it . ∴ 4 / 3 ∏ r ³ = ∏ * 12 * 12 * 6.75 ⇒ r ³ = 9 * 9 * 9 ⇒ r = 9 cm . answer c
Answer: c
Question (general): a batsman in his 12 th innings makes a score of 92 and thereby increases his average by 2 runs . what is his average after the 12 th innings if he had never been ‘ not out ’ ?
Options: a ) 42 , b ) 43 , c ) 70 , d ) 45 , e ) 46
Rationale: "let ‘ x ’ be the average score after 12 th innings ⇒ 12 x = 11 × ( x – 2 ) + 92 ∴ x = 70 answer c"
Answer: c
Question (physics): a snail , climbing a 36 feet high wall , climbs up 8 feet on the first day but slides down 4 feet on the second . it climbs 8 feet on the third day and slides down again 4 feet on the fourth day . if this pattern continues , how many days will it take the snail to reach the top of the wall ?
Options: a ) 12 , b ) 14 , c ) 15 , d ) 20 , e ) 21
Rationale: "total transaction in two days = 8 - 4 = 4 feet in 15 days it will climb 36 feet thus reaching the top therefore , total no of days required = 15 c"
Answer: c
Question (general): what is the least number by which 16800 must be divided to get a number perfect square
Options: a ) 21 , b ) 42 , c ) 24 , d ) 40 , e ) 45
Rationale: 16,800 / 42 = 400 400 = ( 20 ) ^ 2 ans - 42 answer : b
Answer: b
Question (general): addison high school ’ s senior class has 300 boys and 240 girls . if 30 % of the boys did not attend the college then 70 % of the total class attended college , what percentage of the girls class did not attend college ?
Options: a ) 70 , b ) 45 , c ) 50 , d ) 46 , e ) 30
Rationale: "% of boy attending the college = 100 - 30 = 70 % number of boys attending the college : 0.70 * 300 = 210 total people = 300 + 240 = 540 total number of students attending the college : 0.70 * 540 = 378 number of girls attending the college = 378 - 210 = 168 number of girls not attending the college = 240 - 168 = 72 % of girls not attending = 72 / 240 = 30 % . e is the correct answer"
Answer: e
Question (general): if the average ( arithmetic mean ) of a and b is 140 , and the average of b and c is 100 , what is the value of a − c ?
Options: a ) − 220 , b ) − 100 , c ) 100 , d ) 135 , e ) 80
Rationale: "a + b = 280 b + c = 200 a - c = 80 . imo option e ."
Answer: e
Question (general): on dividing 95 by a number , the quotient is 6 and the remainder is 5 . find the divisor .
Options: a ) 14 , b ) 15 , c ) 16 , d ) 17 , e ) 18
Rationale: "d = ( d - r ) / q = ( 95 - 5 ) / 6 = 90 / 6 = 15 b"
Answer: b
Question (general): if money is invested at r percent interest , compounded annually , the amount of the investment will double in approximately 54 / r years . if joe ' s parents invested $ 5,000 in a long - term bond that pays 6 percent interest , compounded annually , what will be the approximate total amount of the investment 18 years later , when joe is ready for college ?
Options: a ) $ 20000 , b ) $ 15000 , c ) $ 12000 , d ) $ 10000 , e ) $ 9000
Rationale: "since investment doubles in 54 / r years , then for r = 6 it ' ll double in 54 / 6 = ~ 9 years ( we are not asked about the exact amount so such an approximation will do ) . thus after 18 years investment will become $ 5,000 * 2 = $ 10,000 . answer : d ."
Answer: d
Question (general): find out the square of a number which when doubled exceeds its one nineth by 17 ?
Options: a ) 16 , b ) 25 , c ) 81 , d ) 26 , e ) 17
Rationale: "let the number be p , then the square will be p ^ 2 according to question : 2 p = ( p / 9 ) + 17 = > 18 p = p + 153 = > p = 9 p ^ 2 = 9 ^ 2 = 81 answer : c"
Answer: c
Question (physics): the inner circumference of a circular race track , 25 m wide , is 880 m . find radius of the outer circle ?
Options: a ) 165 m , b ) 120 m , c ) 100 m , d ) 190 m , e ) 220 m
Rationale: "let inner radius be r metres . then , 2 π r = 880 ⇔ r = ( 880 x ( 7 / 44 ) ) = 140 m . radius of outer circle = ( 140 + 25 ) m = 165 m . hence a"
Answer: a
Question (gain): find the compound interest on $ 800 for 1 year at 10 % p . a . if ci is component yearly ?
Options: a ) $ 40 , b ) $ 400 , c ) $ 840 , d ) $ 800 , e ) $ 80
Rationale: "a = p ( 1 + r / 100 ) ^ t = 800 ( 1 + 10 / 100 ) ^ 1 = 800 * 21 / 20 = $ 840 ci = a - p = 840 - 800 = $ 40 answer is a"
Answer: a
Question (general): how many boxes do you need if you have to pack 1080 apples into cases that each hold one dozen apples ?
Options: a ) 40 , b ) 60 , c ) 70 , d ) 80 , e ) 90
Rationale: e 90 1080 apples = 90 dozens the required number of boxes = 90 . answer : e
Answer: e
Question (general): a sum of money lent out at s . i . amounts to rs . 820 after 2 years and to rs . 1020 after a further period of 4 years . the sum is ?
Options: a ) s . 440 , b ) s . 500 , c ) s . 720 , d ) s . 740 , e ) s . 840
Rationale: s . i for 5 years = ( 1020 - 820 ) = rs . 200 . s . i . for 2 years = 200 / 4 * 2 = rs . 100 . principal = ( 820 - 100 ) = rs . 720 . answer : c
Answer: c
Question (other): the weights of one liter vegetable ghee packet of two brands ‘ a ’ and ‘ b ’ are 900 gm and 750 gm respectively . if they are mixed in the ratio of 3 : 2 by volumes to form a mixture of 4 liters , what is the weight ( in kg ) of the mixture ?
Options: a ) 3.84
b ) 1.75
c ) 3.36
d ) 2.72
e ) none of these
Rationale: here ' s how i did it . my notes from reading the problem were : 1 l a = 900 gm 1 l b = 850 gm we are mixing five parts ( 3 parts a plus 2 parts b , 5 parts total ) to get 4 l , so 5 x = 4 - - - > x = 4 / 5 . eachpartis 4 / 5 of a liter . so if we have 3 parts a , we have 900 * 3 * ( 4 / 5 ) = 2160 if we have 2 parts b , we have 750 * 2 * ( 4 / 5 ) = 1200 2160 + 1200 = 3360 solving for units gives us 3.36 so the answer is c
Answer: c
Question (physics): a train 800 m long is running at a speed of 78 km / hr . if it crosses a tunnel in 1 min , then the length of the tunnel is ?
Options: a ) 288 , b ) 660 , c ) 500 , d ) 267 , e ) 298
Rationale: "speed = 78 * 5 / 18 = 65 / 3 m / sec . time = 1 min = 60 sec . let the length of the train be x meters . then , ( 800 + x ) / 60 = 65 / 3 x = 500 m . answer : c"
Answer: c
Question (physics): the sector of a circle has radius of 42 cm and central angle 135 o . find its perimeter ?
Options: a ) 91.5 cm , b ) 92.2 cm , c ) 28.9 cm , d ) 29.2 cm , e ) 183 cm
Rationale: "perimeter of the sector = length of the arc + 2 ( radius ) = ( 135 / 360 * 2 * 22 / 7 * 42 ) + 2 ( 42 ) = 99 + 84 = 183 cm answer : e"
Answer: e
Question (physics): car x began traveling at an average speed of 35 miles per hour . after 72 minutes , car y began traveling at an average speed of 42 miles per hour . when both cars had traveled the same distance , both cars stopped . how many miles did car x travel from the time car y began traveling until both cars stopped ?
Options: a ) 105 , b ) 140 , c ) 175 , d ) 210 , e ) 245
Rationale: "in 72 minutes , car x travels 42 miles . car y gains 7 miles each hour , so it takes 6 hours to catch car x . in 6 hours , car x travels 210 miles . the answer is d ."
Answer: d
Question (general): there are 4 more women than there are men on a local co - ed softball team . if there are a total of 18 players on the team , what is the ratio of men to women ?
Options: a ) 10 / 16 , b ) 6 / 16 , c ) 7 / 11 , d ) 6 / 10 , e ) 4 / 10
Rationale: "w = m + 4 w + m = 18 m + 4 + m = 18 2 m = 14 m = 7 w = 11 ratio : 7 : 11 ans : c"
Answer: c
Question (gain): a student gets 50 % in one subject , 60 % in the other . to get an overall of 60 % how much should get in third subject .
Options: a ) 75 % , b ) 70 % , c ) 45 % , d ) 55 % , e ) 65 %
Rationale: "let the 3 rd subject % = x 50 + 60 + x = 3 * 60 110 + x = 180 x = 180 - 110 = 70 answer : b"
Answer: b
Question (physics): one pump drains one - half of a pond in 6 hours , and then a second pump starts draining the pond . the two pumps working together finish emptying the pond in one - half hour . how long would it take the second pump to drain the pond if it had to do the job alone ?
Options: a ) 1 hour , b ) 1.1 hour , c ) 3 hours , d ) 5 hours , e ) 6 hours
Rationale: "first pump drains 1 / 2 of the tank in 6 hours so 12 hours it will take to drain the full tank . let , 2 nd pump drains the full tank in a hours so both together can drain ( 1 / 12 + 1 / a ) part in 1 hour son in 1 / 2 hour they drain 1 / 2 * ( 1 / 12 + 1 / a ) part of the tank given that in 1 / 2 hour they drain 1 / 2 of the tank hence we can say 1 / 2 * ( 1 / 12 + 1 / a ) = 1 / 2 solving u get a = 12 / 11 = 1.1 hence answer is b"
Answer: b
Question (general): an amount of rs . 1638 was divided among a , b and c , in the ratio 1 / 2 : 1 / 3 : 1 / 4 . find the share of b ?
Options: a ) 360 , b ) 358 , c ) 356 , d ) 514 , e ) 504
Rationale: "let the shares of a , b and c be a , b and c respectively . a : b : c = 1 / 2 : 1 / 3 : 1 / 4 let us express each term with a common denominator which is the last number divisible by the denominators of each term i . e . , 12 . a : b : c = 6 / 12 : 4 / 12 : 3 / 12 = 6 : 4 : 3 . share of b = 4 / 13 * 1638 = rs . 504 answer : e"
Answer: e
Question (general): how much is 80 % of 40 is greater than 4 / 5 of 25 ?
Options: a ) 22 , b ) 77 , c ) 15 , d ) 12 , e ) 88
Rationale: ( 80 / 100 ) * 40 – ( 4 / 5 ) * 25 32 - 20 = 12 answer : d
Answer: d
Question (physics): light glows for every 17 seconds . how many times did it between 1 : 57 : 58 and 3 : 20 : 47 am
Options: a ) 291 , b ) 292 , c ) 293 , d ) 384 , e ) 285
Rationale: "the diff in sec between 1 : 57 : 58 and 3 : 20 : 47 is 4969 sec , 4969 / 17 = 292 . so total 293 times light ll glow answer : c"
Answer: c
Question (physics): two trains of length 100 meters and 200 meters are 660 meters apart . they are moving towards each other on parallel tracks , at speeds of 90 km / h and 108 km / h . after how many seconds will the trains meet ?
Options: a ) 12 , b ) 14 , c ) 16 , d ) 18 , e ) 20
Rationale: "the speeds are 90000 / 3600 = 25 m / s and 108000 / 3600 = 30 m / s the relative speed is 55 m / s . time = 660 / 55 = 12 seconds the answer is a ."
Answer: a
Question (general): a vessel of capacity 2 litre has 25 % of alcohol and another vessel of capacity 6 litre had 50 % alcohol . the total liquid of 8 litre was poured out in a vessel of capacity 10 litre and thus the rest part of the vessel was filled with the water . what is the new concentration of mixture ?
Options: a ) 31 % . , b ) 71 % . , c ) 49 % . , d ) 29 % . , e ) 35 % .
Rationale: "25 % of 2 litres = 0.5 litres 50 % of 6 litres = 3.0 litres therefore , total quantity of alcohol is 3.5 litres . this mixture is in a 10 litre vessel . hence , the concentration of alcohol in this 10 litre vessel is 35 % answer : e"
Answer: e
Question (gain): a , b and c enter into partnership . a invests some money at the beginning , b invests double the amount after 6 months , and c invests thrice the amount after 8 months . if the annual gain be rs . 18300 . a ' s share is ?
Options: a ) 8876 , b ) 2765 , c ) 6000 , d ) 1298 , e ) 6100
Rationale: "x * 12 : 2 x * 6 : 3 x * 4 1 : 1 : 1 1 / 3 * 18300 = 6100 answer : e"
Answer: e
Question (general): how many different positive integers exist between 10 ^ 7 and 10 ^ 8 , the sum of whose digits is equal to 2 ?
Options: a ) 6 , b ) 7 , c ) 5 , d ) 8 , e ) 18
Rationale: so , the numbers should be from 10 , 000,000 to 100 , 000,000 the following two cases are possible for the sum of the digits to be 2 : 1 . two 1 ' s and the rest are 0 ' s : 10 , 000,001 10 , 000,010 10 , 000,100 10 , 001,000 10 , 010,000 10 , 100,000 11 , 000,000 7 numbers . 2 . one 2 and the rest are 0 ' s : 20 , 000,000 1 number . total = 8 numbers . answer : d
Answer: d
Question (gain): the workforce of company x is 60 % female . the company hired 26 additional male workers , and as a result , the percent of female workers dropped to 55 % . how many employees did the company have after hiring the additional male workers ?
Options: a ) 160 , b ) 220 , c ) 312 , d ) 360 , e ) 420
Rationale: "let ' s xx be total quantity of employees 0.6 x = females before adding men 0.55 ( x + 26 ) = females after adding men as quantity of women does n ' t change we can make an equation : 0.6 x = 0.55 ( x + 26 ) 0.05 x = 14.3 x = 286 - this is quantity of employees before adding 26 men so after adding it will be 312 answer is c"
Answer: c