Cheukting/mathqa huggingface dataset:
Question (general): what is 3 / 4 of 4 / 5 of 2 / 3 ?
Options: a ) 1 / 4 , b ) 2 / 5 , c ) 9 / 16 , d ) 5 / 8 , e ) 16 / 9
Rationale: "3 / 4 * 4 / 5 * 2 / 3 = 2 / 5 answer : b"
Answer: b
Question (general): if the numerator of a fraction is increased by 20 % and its denominator is diminished by 25 % value of the fraction is 2 / 15 . find the original fraction ?
Options: a ) 1 / 12 , b ) 1 / 16 , c ) 1 / 19 , d ) 1 / 14 , e ) 1 / 13
Rationale: "x * ( 120 / 100 ) - - - - - - - - - - - - - - - - = 2 / 15 y * ( 75 / 100 ) x / y = 1 / 12 answer : a"
Answer: a
Question (general): when w is divided by 13 , the reminder is 0 . if w is 3 more than it value and when divided by 11 its remainder is 0 . what is the value of w ?
Options: a ) 13 , b ) 52 , c ) 39 , d ) 26 , e ) 35
Rationale: w is divided by 13 so that is multiple of 14 as 13 , 26,39 . . . w + 3 is divided by 11 the remainder is 0 so it is divisible by 11 . consider from option let us take the number is 13 it is divisible by 14 but 13 + 3 is not divisible by 11 so it is not answers so let us take 2 nd option 52 which is divisible by 13 and 52 + 3 = 55 is divisible by 11 so ans is b
Answer: b
Question (general): which is the least number that must be subtracted from 1828 so that the remainder when divided by 8 , 12 , 16 is 4 ?
Options: a ) 0 , b ) 4 , c ) 8 , d ) 6 , e ) 2
Rationale: "first we need to figure out what numbers are exactly divisible by 8 , 12,16 . this will be the set { lcm , lcmx 2 , lcmx 3 , . . . } lcm ( 8 , 12,16 ) = 48 = 48 number is to be subtracted is 0 the largest such number less than or equal to 1828 is 48 * 38 + 4 a"
Answer: a
Question (general): a high school has 400 students 1 / 2 attend the airthmetic club , 5 / 8 attend the biology club and 3 / 4 attend the chemistry club . 1 / 8 attend all 3 clubs . if every student attends at least one club how many students attend exactly 2 clubs .
Options: a ) 300 , b ) 200 , c ) 250 , d ) 150 , e ) 160
Rationale: basically , this question is asking you to figure out how many students are being double - counted . a - club has 200 members ( 1 / 2 of 400 ) b - club has 250 members ( 5 / 8 of 400 ) c - club has 300 members ( 3 / 4 of 400 ) we can create an equation to solve this : 200 + 250 + 300 = n + x + 2 y where n is the number of students , x is the number of students in two clubs , and y is the number of students in three clubs . the question provides y for us ( 50 ) . 750 = 400 + x + 100 x = 250 c
Answer: c
Question (general): the difference between the place values of two eights in the numerical 38140482 is
Options: a ) 7999920 , b ) 799920 , c ) 7920 , d ) 79920 , e ) none of them
Rationale: "required difference = ( 8000000 - 80 ) = 7999920 . 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 nd c be 27 , then how old is b ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: "solution 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 = 27 ⇔ 5 x = 25 ⇔ x = 5 . hence , b ' s age = 2 x = 10 years . answer d"
Answer: d
Question (gain): last year elaine spent 20 % of her annual earnings on rent . this year she earned 35 % more than last year and she spent 30 % of her annual earnings on rent . the amount she spent on rent this year is what percent of the amount spent on rent last year ?
Options: a ) 202.5 , b ) 194.5 , c ) 197.5 , d ) 182.5 , e ) 177.5
Rationale: "for this it is easiest to use simple numbers . let ' s assume that elaine ' s annual earnings last year were $ 100 . she would ' ve spent $ 20 of this on rent . this year she earned 15 % more , or $ 135 . she would ' ve spent 30 % of this on rent , or $ 40.5 do $ 40.5 / $ 20 this will give you 202.5 % a is the correct answer ."
Answer: a
Question (general): i chose a number and divide it by 4 . then i subtracted 24 from the result and got 10 . what was the number i chose ?
Options: a ) 170 , b ) 700 , c ) 800 , d ) 900 , e ) none
Rationale: "solution : let x be the number i chose , then x / 4 â ˆ ’ 24 = 10 x / 5 = 34 x = 170 answer : a"
Answer: a
Question (gain): an agent , gets a commission of 2.5 % on the sales of cloth . if on a certain day , he gets rs . 21 as commission , the cloth sold through him on that day is worth
Options: a ) 333 , b ) 500 , c ) 840 , d ) 299 , e ) 132
Rationale: "explanation : let the total sale be rs . x . then , 2.5 % . of x = 21 < = > ( 25 / 10 * 1 / 100 * x ) = 21 < = > x = 840 . answer : c"
Answer: c
Question (physics): the average temperature for tuesday , wednesday and thursday was 32 ° c . the average temperature for wednesday , thursday and friday was 34 ° c . if the temperature on friday be 44 ° c , what was the temperature on tuesday ?
Options: a ) 39 ° c , b ) 44 ° c , c ) 38 ° c , d ) 42 ° c , e ) none of these
Rationale: "explanation : t + w + t = 32 × 3 = 96 ° c w + t + f = 34 × 3 = 102 ° c also , temperature on friday = 44 ° c temperature on tuesday = 96 + 44 - 102 = 38 ° c answer : option c"
Answer: c
Question (physics): a cyclist bikes x distance at 10 miles per hour and returns over the same path at 9 miles per hour . what is the cyclist ' s average rate for the round trip in miles per hour ?
Options: a ) 8.1 , b ) 8.3 , c ) 8.6 , d ) 8.9 , e ) 9.5
Rationale: "distance = d 1 = x miles speed = s 1 = 10 miles per hour time = t 1 = distance / speed = x / 10 2 . going from b to a distance = d 2 = x miles speed = s 2 = 9 miles per hour time = t 2 = distance / speed = x / 9 3 . average speed = total distance / total time total distance = x + x = 2 x total time = x / 10 + x / 9 = x ( 1 / 10 + 1 / 9 ) = x ( 4 + 5 ) / 40 = 19 x / 90 speed = 2 x / ( 19 x / 90 ) = ( 2 x * 90 ) / 9 x = 180 x / 19 x = 180 / 19 = 9.5 answer : e"
Answer: e
Question (geometry): the diagonal of a cube is 8 √ 3 . find its volume and surface area .
Options: a ) 354
b ) 384
c ) 324
d ) 344
e ) 364
Rationale: √ 3 . a = 8 √ 3 = > a = 8 volume = a ( power ) 3 = > ( 8 × 8 × 8 ) cm ( power ) 3 = > 512 cm ( power ) 3 surface area = > 6 a ( power ) 2 = > ( 6 × 8 × 8 ) cm ( power ) 2 = > 384 cm ( power ) 2 answer is b .
Answer: b
Question (geometry): a certain rectangular crate measures 8 feet by 14 feet by 16 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: "ans is ` ` b ' ' . 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 14 x 20 i . e . of radius 12 / 2 = 6 c"
Answer: c
Question (gain): a group of boy scouts and girls scouts is going on a rafting trip . 70 % of the scouts arrived with signed permission slips . if 60 % of the scouts were boy scouts and 75 % of the boy scouts arrived with signed permission slips , then what percentage of the girl scouts arrived with signed permission slips ? round to the nearest percent .
Options: a ) 50 % , b ) 60 % , c ) 63 % , d ) 66 % , e ) 70 %
Rationale: 60 % were boy scouts so 40 % ( 100 - 60 = 40 ) were girl scouts . # of boy scouts with permission slips signed + # of girl scouts with permission slips signed = total # with permission slip signed ( 75 % of 60 % of the total going ) + ( ? % of 40 % of the total going ) = 70 % of the total going we can let the ` ` total going ' ' = 1,000 arbitrarily since we only care about the percent ( of girl scouts w / permission signed ) . 75 * . 60 * 1,000 + x * . 40 * 1,000 = . 70 * 1,000 450 + x * 400 = 700 400 x = 250 x = 250 / 400 x = . 625 converting this to a percent , we have 62.5 % . rounding , we have 63 % . c
Answer: c
Question (physics): the megatek corporation is displaying its distribution of employees by department in a circle graph . the size of each sector of the graph representing a department is proportional to the percentage of total employees in that department . if the section of the circle graph representing the manufacturing department takes up 216 ° of the circle , what percentage of megatek employees are in manufacturing ?
Options: a ) 20 % , b ) 25 % , c ) 30 % , d ) 35 % , e ) 60 %
Rationale: "answer : e 216 ° divided by 360 ° equals 0.6 , therefore the sector is equal to 60 % of the total"
Answer: e
Question (gain): in a school of 850 boys , 34 % of muslims , 28 % hindus , 10 % sikhs and the remaining of other communities . how many belonged to the other communities ?
Options: a ) a ) 125 , b ) b ) 627 , c ) c ) 153 , d ) d ) 238 , e ) e ) 159
Rationale: "34 + 28 + 10 = 72 % 100 – 72 = 28 % 850 * 28 / 100 = 238 answer : d"
Answer: d
Question (geometry): if anangletis defined as 1 percent of 1 degree , then how many anglets are there in a third circle ?
Options: a ) 0.36 , b ) 3.6 , c ) 12,000 , d ) 3,600 , e ) 36,000
Rationale: "1 degree * 1 / 100 = 1 anglet so 1 degree = 100 anglets = > 120 degrees = 12000 anglets answer - c"
Answer: c
Question (general): 2 ^ 46655 mod 9 = ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: by remainder theorem remainder = { [ ( 2 ^ 3 ) ^ 1551 * 2 ^ 2 ] / 9 } = [ { ( - 1 ) ^ 1551 * 4 } / 9 ] = 5 answer : b
Answer: b
Question (geometry): a cube has five of its faces painted half red and half white . the other face is completely painted white . what is the ratio between the red painted areas and the white painted areas of the cube ?
Options: a ) 6 : 11
b ) 2 : 5
c ) 3 : 4
d ) 5 : 7
e ) 2 : 3
Rationale: let x be the area of each face of the cube . the area painted red is 5 ( x / 2 ) = 5 x / 2 the area painted white is 5 ( x / 2 ) + x = 7 x / 2 x the ratio of red to white is 5 x / 2 : 7 x / 2 which is 5 : 7 . the answer is d .
Answer: d
Question (other): the h . c . f . of two numbers is 25 and the other two factors of their l . c . m . are 13 and 14 . the larger of the two numbers is :
Options: a ) 276 , b ) 299 , c ) 322 , d ) 345 , e ) 350
Rationale: "clearly , the numbers are ( 25 x 13 ) and ( 25 x 14 ) . larger number = ( 25 x 14 ) = 350 . answer : option e"
Answer: e
Question (gain): increasing the original price of a certain item by 25 percent and then increasing the new price by 30 percent is equivalent to increasing the original price by what percent ?
Options: a ) 31.25 , b ) 37.5 , c ) 50.0 , d ) 52.5 , e ) 62.5
Rationale: we ' re told that the original price of an item is increased by 25 % and then that price is increased by 30 % . . . . if . . . . starting value = $ 100 + 25 % = 100 + . 25 ( 100 ) = 125 + 30 % = 125 + . 30 ( 125 ) = 125 + 37.5 = 162.5 the question asks how the final price relates to the original price . this is essentially about percentage change , which means we should use the percentage change formula : percentage change = ( new - old ) / old = difference / original doing either calculation will yield the same result : 62.5 / 100 = 62.50 % final answer : e
Answer: e
Question (physics): the population of a bacteria colony doubles every day . if it was started 10 days ago with 2 bacteria and each bacteria lives for 12 days , how large is the colony today ?
Options: a ) 512 , b ) 768 , c ) 1024 , d ) 2048 , e ) 4096
Rationale: "2 ^ 10 ( 2 ) = 2 ^ 11 = 2048 the answer is d ."
Answer: d
Question (general): a computer manufacturer produces a certain electronic component at a cost of $ 80 per component . shipping costs for delivering the components are $ 2 per unit . further , the manufacturer has costs of $ 16,200 a month related to the electronic component regardless of how many it produces . if the manufacturer produces and sells 150 components a month , what is the lowest price it can sell them for such that the costs do n ' t exceed the revenues ?
Options: a ) $ 28 , b ) $ 82 , c ) $ 110 , d ) $ 190 , e ) $ 192
Rationale: "this question can be solved easily using a equation model . 150 * p = 16200 ( fixed cost ) + 150 * 80 + 150 * 2 . = 16200 + 12000 + 300 = 28500 p = $ 190 . d"
Answer: d
Question (general): a certain list consists of 21 different numbers . if n is in the list and n is 6 times the average ( arithmetic mean ) of the other 20 numbers in the list , then n is what fraction of the sum of the 21 numbers in the list ?
Options: a ) 1 / 20 , b ) 1 / 6 , c ) 1 / 5 , d ) 3 / 13 , e ) 5 / 21
Rationale: "series : a 1 , a 2 . . . . a 20 , n sum of a 1 + a 2 + . . . + a 20 = 20 * x ( x = average ) so , n = 6 * x hence , a 1 + a 2 + . . + a 20 + n = 26 x so , the fraction asked = 6 x / 26 x = 6 / 26 = 3 / 13 d"
Answer: d
Question (other): in a sports club with 42 members , 20 play badminton and 23 play tennis and 6 do not play either . how many members play both badminton and tennis ?
Options: a ) 3 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: "20 + 23 = 43 but where as total number is 42 - 6 = 36 therefore answer is 43 - 36 = 7 hence answer is d"
Answer: d
Question (physics): a tempo , while travelling at 70 kmph , uses 30 % more petrol than it uses while travelling at 50 kmph for travelling a certain distance . using one litre of petrol , it can travel 19.5 km at 50 kmph . how far can the tempo travel on 10 litres of petrol at a speed of 70 kmph ?
Options: a ) 150 kms , b ) 160 kms , c ) 170 kms , d ) 180 kms , e ) 190 kms
Rationale: @ 50 kmph , one km distance uses 1 / 19.5 ltr petrol . @ 70 kmph , one km dist . uses 1.3 / 19.5 ltr petrol distance travelled with 10 ltrs @ 70 kmph = 10 * 19.5 / 1.3 = 150 kms . answer : a
Answer: a
Question (gain): in an examination it is necessary for a candidate to get 45 % of the maximum marks to pass . a candidate who gets 180 marks , fails by 45 marks . find the maximum marks .
Options: a ) 450 , b ) 600 , c ) 500 , d ) 550 , e ) 650
Rationale: let max . mark = x pass mark = 45 x / 100 180 = 45 x / 100 - 45 x = 180 * 100 - 4500 / 45 = 500 answer : c
Answer: c
Question (general): in a box of 9 pens , a total of 3 are defective . if a customer buys 2 pens selected at random from the box , what is the probability that neither pen will be defective ?
Options: a ) 3 / 10 , b ) 4 / 11 , c ) 5 / 12 , d ) 6 / 13 , e ) 7 / 15
Rationale: p ( neither pen is defective ) = 6 / 9 * 5 / 8 = 5 / 12 the answer is c .
Answer: c
Question (general): 265.124 x 11.98 ã · 8.001 + 32.28 = ?
Options: a ) 983.578 , b ) 659.121 , c ) 781.189 , d ) 429.966 , e ) 456.512
Rationale: "explanation : ? = 265.124 x 11.98 ã · 8.001 + 32.28 â ‰ ˆ ( 265.124 x 12 / 8 ) + 32.28 â ‰ ˆ 397.686 + 32.28 â ‰ ˆ 429.966 answer : option d"
Answer: d
Question (general): find a two digit number , given that the sum of the digits is 9 and the difference of the digits is 3 . ?
Options: a ) 75 , b ) 63 , c ) 83 , d ) 94 , e ) 39
Rationale: using elimination method find which of the options fit the description of the number . . . from the option only 63 meets this description sum of digits - - - 6 + 3 = 9 difference of digits - - - 6 - 3 = 3 answer b .
Answer: b
Question (gain): fox jeans regularly sell for $ 15 a pair and pony jeans regularly sell for $ 18 a pair . during a sale these regular unit prices are discounted at different rates so that a total of $ 9 is saved by purchasing 5 pairs of jeans : 3 pairs of fox jeans and 2 pairs of pony jeans . if the sum of the two discounts rates is 25 percent , what is the discount rate on pony jeans ?
Options: a ) 9 % , b ) 10 % , c ) 11 % , d ) 12 % , e ) 25 %
Rationale: "x discount on pony jeans , ( 0.25 - x ) discount on fox jeans . set the equation : 3 * 15 ( 0.25 - x ) + 2 * 18 x = 9 - - > x = 0.25 = 25 % answer : e ."
Answer: e
Question (physics): eight identical machines can produce 360 aluminum cans per hour . if all of the machines work at the same constant rate , how many cans could 5 such machines produce in 7 hours ?
Options: a ) 675 , b ) 750 , c ) 1,800 , d ) 5,900 , e ) 1,575
Rationale: "8 machines / 360 cans = 5 machines / x cans 8 x = 1800 x = 225 ( 225 ) ( 7 hours ) = 1575 cans . the answer is e ."
Answer: e
Question (general): if x is an integer and 2.13 × 10 ^ x is less than 2100 , what is the greatest possible value for x ?
Options: a ) 2 , b ) 6 , c ) 5 , d ) 4 , e ) 3
Rationale: "if x = 3 2.13 × 10 ^ 3 = 2130 > 2,100 so , x = 2 answer : a"
Answer: a
Question (gain): if 5 % more is gained by selling an article for rs . 360 than by selling it for rs . 340 , the cost of the article is ?
Options: a ) 127 , b ) 688 , c ) 400 , d ) 121 , e ) 123
Rationale: "let c . p . be rs . x . then , 5 % of x = 360 - 340 = 20 x / 20 = 20 = > x = 400 answer : c"
Answer: c
Question (general): for any integer k greater than 1 , the symbol k * denotes the product of all integers between 1 and k , inclusive . if k * is a multiple of 525 what is the least possible value of k ?
Options: a ) 10 , b ) 14 , c ) 15 , d ) 21 , e ) 25
Rationale: "525 = 3 * 5 * 5 * 7 thus k must include numbers at least up to the number 10 so that there are two appearances of 5 . the answer is a ."
Answer: a
Question (physics): find the area of trapezium whose parallel sides are 28 cm and 18 cm long , and the distance between them is 15 cm .
Options: a ) 227 , b ) 299 , c ) 345 , d ) 161 , e ) 212
Rationale: "area of a trapezium = 1 / 2 ( sum of parallel sides ) * ( perpendicular distance between them ) = 1 / 2 ( 28 + 18 ) * ( 15 ) = 345 cm 2 answer : c"
Answer: c
Question (physics): joshua and jose work at an auto repair center with 4 other workers . for a survey on health care insurance , 2 of the 6 workers will be randomly chosen to be interviewed . what is the probability that joshua and jose will both be chosen ?
Options: a ) 1 / 15 , b ) 1 / 12 , c ) 1 / 9 , d ) 1 / 6 , e ) 1 / 3
Rationale: "1 ) probability of chosing josh first = 1 / 6 probability of chosing jose second = 1 / 5 total = 1 / 30 probability of chosing jose first = 1 / 6 probability of choosing josh second = 1 / 5 total = 1 / 30 final = 1 / 30 + 1 / 30 = 1 / 15 2 ) number of ways two persons can be chosen 6 c 2 = 15 number of ways josh and jose are the two persons = 1 total = 1 / 15 answer will be a ."
Answer: a
Question (gain): 3 candidates in an election and received 6136 , 7636 and 11628 votes respectively . what % of the total votes did the winning candidate got in that election ?
Options: a ) 46 % , b ) 49 % , c ) 57 % , d ) 59 % , e ) 61 %
Rationale: "total number of votes polled = ( 6136 + 7636 + 11628 ) = 25400 so , required percentage = 11628 / 25400 * 100 = 46 % a"
Answer: a
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 - fourth of the males and one - half of the females in the class ?
Options: a ) 128
b ) 136
c ) 144
d ) 152
e ) 160
Rationale: 1 / 4 * 2 / 5 + 1 / 2 * 3 / 5 = 2 / 20 + 6 / 20 = 2 / 5 the number of degrees is 2 / 5 * 360 = 144 degrees the answer is c .
Answer: c
Question (general): 4 liters of a 20 percent solution of alcohol in water are mixed with 5 liters of a 10 percent alcohol in water solution . what is the percentage of alcohol in the new solution ?
Options: a ) 14.4 % , b ) 14.8 % , c ) 15.2 % , d ) 15.6 % , e ) 16.0 %
Rationale: "the total amount of alcohol is 0.2 ( 4 ) + 0.1 ( 5 ) = 1.3 liters . the percentage is 1.3 / 9 = 13 / 90 which is about 14.4 % the answer is a ."
Answer: a
Question (general): 300 first - time customers of a fashion store were surveyed for their shopping experience right after leaving the store . 60 % of the customers in the survey had purchased clothes for less than $ 100 . 40 % of the customers in the survey reported they were overall satisfied with their purchase . 45 % of the customers that had purchased clothes for less than $ 100 reported they were overall satisfied with their purchase . what percent of the customers surveyed purchased clothes for at least $ 100 and reported that they were not overall satisfied with their purchase ?
Options: a ) 15 , b ) 25 , c ) 13 , d ) 45 , e ) 75
Rationale: "out of 300 - 180 purchased for less than 100 $ 120 for more out of 300 - 120 responded as satisfied and 180 responded disatisfied out of 180 ( purchased less than 100 $ ) - 45 % = 81 responded as satisfied , so remaining satisfied are 120 - 81 = 39 so 39 is what percentage of 300 - 13 % so the answer should be c"
Answer: c
Question (gain): a merchant sells an item at a 20 % discount , but still makes a gross profit of 20 percent of the cost . what percent of the cost would the gross profit on the item have been if it had been sold without the discount ?
Options: a ) 20 % , b ) 40 % , c ) 50 % , d ) 60 % , e ) 75 %
Rationale: "soln : - original sp = x cost = c current selling price = . 8 x ( 20 % discount ) . 8 x = 1.2 c ( 20 % profit ) x = 1.2 / . 8 * c x = 3 / 2 c original selling price is 1.5 c which is 50 % profit answer : c"
Answer: c
Question (other): solution a is 30 % salt and solution b is 80 % salt . if you have 30 ounces of solution a and 60 ounces of solution b , in what ratio could you mix solution a with solution b to produce 50 ounces of a 50 % salt solution ?
Options: a ) 6 : 4 , b ) 6 : 14 , c ) 4 : 4 , d ) 4 : 6 , e ) 3 : 2
Rationale: "forget the volumes for the time being . you have to mix 30 % and 80 % solutions to get 50 % . this is very straight forward since 50 is int he middle of 20 and 80 so we need both solutions in equal quantities . if this does n ' t strike , use w 1 / w 2 = ( a 2 - aavg ) / ( aavg - a 1 ) w 1 / w 2 = ( 80 - 50 ) / ( 50 - 30 ) = 3 / 2 so the volume of the two solutions will be equal . answer has to be 3 : 2 e"
Answer: e
Question (probability): a question paper has 2 parts , a & b , each containing 8 questions . if a student has to choose 8 from part a & 4 from part b , in how many ways can he choose the questions ?
Options: a ) 110 , b ) 70 , c ) 120 , d ) 130 , e ) 140
Rationale: "there 8 questions in part a out of which 8 question can be chosen as = 8 c 8 . similarly , 4 questions can be chosen from 8 questions of part b as = 8 c 4 . hence , total number of ways , = 8 c 8 * 8 c 4 = [ 8 ! / ( 0 ! 8 ! ) ] * [ 8 ! / ( 4 ! * 4 ! ) ] = { 1 } * { 8 * 7 * 6 * 5 / ( 4 ! ) } = 70 . b"
Answer: b
Question (physics): a can do a piece of work in 80 days . he works at it for 10 days b alone finishes the remaining work in 42 days . in how much time will a and b working together , finish the work ?
Options: a ) 25 , b ) 30 , c ) 20 , d ) 32 , e ) none of them
Rationale: "work done by a in 10 days = ( 1 / 80 * 10 ) = 1 / 8 remaining work = ( 1 - 1 / 8 ) = 7 / 8 now , 7 / 8 work is done by b in 42 days . whole work will be done by b in ( 42 x 8 / 7 ) = 48 days . a ’ s 1 day ' s work = 1 / 80 and b ' s 1 day ' s work = 1 / 48 ( a + b ) ' s 1 day ' s work = ( 1 / 80 + 1 / 48 ) = 8 / 240 = 1 / 30 hence , both will finish the work in 30 days . answer is b ."
Answer: b
Question (physics): working together , printer a and printer b would finish the task in 24 minutes . printer a alone would finish the task in 60 minutes . how many pages does the task contain if printer b prints 6 pages a minute more than printer a ?
Options: a ) 600 , b ) 800 , c ) 1000 , d ) 720 , e ) 1500
Rationale: answer : d .
Answer: d
Question (general): the monthly rent of a shop of dimension 18 feet × 22 feet is rs . 2244 . what is the annual rent per square foot of the shop ? ( a ) rs . 5 ( 2 / 3 )
Options: a ) 43 , b ) 56 , c ) 68 , d ) 87 , e ) 92
Rationale: "sol . monthly rent per square feet = 2244 / ( 18 * 22 ) & annual rent per square feet = 12 * ( 2244 / ( 18 * 22 ) ) = 68 c"
Answer: c
Question (general): a grocer has a sale of rs . 5255 , rs . 5840 , rs . 5921 , rs . 6022 and rs . 6499 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 5500 ?
Options: a ) 3463 , b ) 4463 , c ) 5463 , d ) 4063 , e ) 5063
Rationale: "total sale for 5 months = rs . ( 5255 + 5840 + 5921 + 6022 + 6499 ) = rs . 29537 . required sale = rs . [ ( 5500 x 6 ) - 29537 ] = rs . ( 33000 - 29537 ) = rs . 3463 . answer : b"
Answer: b