Cheukting/mathqa huggingface dataset:
Question (gain): in a recent election , geoff received 0.5 percent of the 6000 votes cast . to win the election , a candidate needed to receive more than x % of the vote . if geoff needed exactly 3000 more votes to win the election , what is the value of x ?
Options: a ) 50 , b ) 50.5 , c ) 56 , d ) 60 , e ) 63
Rationale: word problems are tricky in somehow more than other problem because you have the additional step to translate . breaking the problem : geoff how many votes he receives ? ? 30 votes he needs 3571 more votes so : 30 + 3000 = 3030 now what ' s the problem wants ? ? a x % . . . . . . . . 3030 is what % of total votes 6000 . . . . . . . . translating : 3030 = x / 100 * 6000 - - - x = 50.5 % . . . . . . . . . . b
Answer: b
Question (physics): a certain electric - company plan offers customers reduced rates for electricity used between 8 p . m . and 8 a . m . weekdays and 24 hours a day saturdays and sundays . under this plan , the reduced rates w apply to what fraction of a week ?
Options: a ) 1 / 2 , b ) 5 / 8 , c ) 9 / 14 , d ) 16 / 21 , e ) 9 / 10
Rationale: "number of hours between 8 pm to 8 am = 12 number of hours with reduced rates = ( 12 * 5 ) + ( 24 * 2 ) hours with reduced rates w / total number of hours in a week = ( 12 * 5 ) + ( 24 * 2 ) / ( 24 * 7 ) = 108 / ( 24 * 7 ) = 9 / 14 answer : c"
Answer: c
Question (physics): the sum of two consecutive number is 115 . which is the larger number ?
Options: a ) 42 , b ) 58 , c ) 44 , d ) 45 , e ) 46
Rationale: "let consecutive number be x , x + 1 therefore sum of the consecutive number is x + x + 1 = 115 2 x + 1 = 115 2 x = 114 x = 57 therefore larger number is x + 1 = 58 answer : b"
Answer: b
Question (physics): three pipes a , b and c can fill a tank from empty to full in 20 minutes , 20 minutes and 30 minutes respectively . when the tank is empty , all the three pipes are opened . a , b and c discharge chemical solutions p , q and r respectively . what is the proportion of solution p in the liquid in the tank after 3 minutes ?
Options: a ) 3 / 8 , b ) 2 / 8 , c ) 6 / 7 , d ) 3 / 5 , e ) 2 / 5
Rationale: "part filled by ( a + b + c ) in 3 minutes = 3 ( 1 / 20 + 1 / 20 + 1 / 30 ) = 6 / 15 part filled by a in 3 minutes = 3 / 20 required ratio = 3 / 20 * 15 / 6 = 3 / 8 answer : a"
Answer: a
Question (gain): if difference between compound interest and simple interest on a sum at 10 % p . a . for 2 years is rs . 36 then sum is
Options: a ) s . 5000 , b ) s . 5100 , c ) s . 5800 , d ) s . 6000 , e ) s . 3600
Rationale: "p ( r / 100 ) ^ 2 = c . i - s . i p ( 10 / 100 ) ^ 2 = 36 3600 answer : e"
Answer: e
Question (general): the ratio of ducks and frogs in a pond is 31 : 39 respectively . the average number of ducks and frogs in the pond is 152 . what is the number of frogs in the pond ?
Options: a ) 148 , b ) 152 , c ) 156 , d ) 169 , e ) none
Rationale: "solution : ratio of ducks and frogs in pond , = 31 : 39 . average of ducks and frogs in pond , = 152 . so , total number of ducks and frogs in the pond , = 2 * 152 = 304 . therefore , number of frogs , = ( 304 * 39 ) / 70 = 169 . answer : option d"
Answer: d
Question (general): x is a positive number which when increased by 17 is equal to 60 times the reciprocal of the number . find value of x ?
Options: a ) 3 , b ) 4 , c ) 6 , d ) 7 , e ) 8
Rationale: let the number be x . then , x + 17 = 60 x x 2 + 17 x - 60 = 0 ( x + 20 ) ( x - 3 ) = 0 x = 3 a
Answer: a
Question (gain): a man invests rs . 6,000 at the rate of 5 % per annum . how much more should he invest at the rate of 8 % , so that he can earn a total of 6 % per annum ?
Options: a ) rs . 1200 , b ) rs . 1300 , c ) rs . 1500 , d ) rs . 3000 , e ) none of these
Rationale: "explanation : interest on rs . 6000 at 5 % per annum = ( 6000 × 5 × 1 ) / 100 = rs . 300 let his additional investment at 8 % = x interest on rs . x at 8 % per annum = ( x × 8 × 1 ) / 100 = 2 x / 25 . to earn 6 % per annum for the total , interest = ( 6000 + x ) × 6 × 1 / 100 . = > 300 + 2 x / 25 = ( 6000 + x ) × 6 × 1 / 100 . = > 30000 + 8 x = ( 6000 + x ) × 6 . = > 30000 + 8 x = 36000 + 6 x . = > 2 x = 6000 . = > x = 3000 . answer : d"
Answer: d
Question (physics): the lcm of two numbers is 2310 and hcf is 47 . if one of the numbers is 210 . then what is the other number ?
Options: a ) 715 , b ) 825 , c ) 330 , d ) 582 , e ) 517
Rationale: first number * second number = lcm * hcf other number = 2310 * 47 / 210 = 11 * 47 = 517 answer : e
Answer: e
Question (gain): a retailer purchases shirts from a wholesaler and then sells the shirts in her store at a retail price that is 70 percent greater than the wholesale price . if the retailer decreases the retail price by 30 percent this will have the same effect as increasing the wholesale price by what percent ?
Options: a ) 26 , b ) 37.5 , c ) 42 , d ) 19 , e ) 50
Rationale: "answer : d = 19 . assume rs . 100 to be the price at which the retailer buys from wholesaler . 70 % increase makes retail price = 170 . now 30 % decrease - > ( 1 - 30 / 100 ) * 170 = 119 . now compared to the wholesale price of 100 , 19 % increase is what will have the same effect as increasing the wholesale price ."
Answer: d
Question (gain): machine p and machine q are each used to manufacture 220 sprockets . it takes machine p 10 hours longer to produce 220 sprockets than machine q . machine q produces 10 % more sprockets per hour than machine a . how many sprockets per hour does machine a produce ?
Options: a ) 5 , b ) 2 , c ) 55 , d ) 95 , e ) 125
Rationale: "p makes x sprockets per hour . then q makes 1.1 x sprockets per hour . 220 / x = 220 / 1.1 x + 10 1.1 ( 220 ) = 220 + 11 x 11 x = 22 x = 2 the answer is b ."
Answer: b
Question (geometry): the diagonal of a square is twice the side of equilateral triangle then the ratio of area of the triangle to the area of square is ?
Options: a ) 3 √ 9
b ) 3 √ 8
c ) 3 √ 7
d ) 3 √ 5
e ) 3 √ 1
Rationale: let the side of equilateral triangle = 1 unit . we know that area of an equilateral triangle = 3 – √ 4 a 234 a 2 as side = 1 unit area of the equilateral triangle = 3 – √ 434 now diagonal of the square = 2 ( side of the equilateral triangle ) = 2 we know that area of the square = 12 d 212 d 2 where d = diagonal so area of the square = 12 ( 22 ) = 212 ( 22 ) = 2 ratio of the areas of equilateral triangle and square = 3 – √ 434 : 2 ⇒ ⇒ 3 √ 8 answer : b
Answer: b
Question (general): the average mark of the students of a class in a particular exam is 65 . if 5 students whose average mark in that exam is 20 are excluded , the average mark of the remaining will be 90 . find the number of students who wrote the exam .
Options: a ) 14 , b ) 25 , c ) 35 , d ) 45 , e ) 55
Rationale: "let the number of students who wrote the exam be x . total marks of students = 75 x . total marks of ( x - 5 ) students = 90 ( x - 5 ) 65 x - ( 5 * 20 ) = 90 ( x - 5 ) 350 = 25 x = > x = 14 answer : a"
Answer: a
Question (probability): there are 24 students in a class . in how many different ways can a committee of 3 students be formed ?
Options: a ) 1250 , b ) 1800 , c ) 2024 , d ) 3256 , e ) 2864
Rationale: "24 c 3 = 24 * 23 * 22 / 6 = 2024 the answer is c ."
Answer: c
Question (physics): fred and sam are standing 35 miles apart and they start walking in a straight line toward each other at the same time . if fred walks at a constant speed of 2 miles per hour and sam walks at a constant speed of 5 miles per hour , how many miles has sam walked when they meet ?
Options: a ) 5 , b ) 9 , c ) 25 , d ) 30 , e ) 45
Rationale: relative distance = 35 miles relative speed = 2 + 5 = 7 miles per hour time taken = 35 / 7 = 5 hours distance travelled by sam = 5 * 5 = 25 miles = c
Answer: c
Question (general): a camera lens filter kit containing 5 filters sells for $ 72.50 . if the filters are purchased individually , 2 of them are priced at $ 12.45 each , 2 at $ 14.05 each , 1 at $ 11.50 . the amount saved by purchasing the kit is what percent of the total price of the 5 filters purchased individually ?
Options: a ) 10.03 % , b ) 11.03 % , c ) 12.03 % , d ) 13.03 % , e ) 11 %
Rationale: cost of kit = $ 72.50 if filters are purchased individually - $ 12.45 * 2 + $ 14.05 * 2 + $ 11.50 = $ 64.50 amount saved = $ 72.50 - $ 64.50 = $ 8 required % age = ( $ 8 / $ 72.50 ) * 100 = 11.03 % so , the correct answer is b .
Answer: b
Question (general): every student in a room is either a junior or a senior . there is at least one junior and at least one senior in the room . if 1 / 2 of the juniors is equal to 2 / 3 of the seniors , what fraction of the students in the room are juniors ?
Options: a ) 4 / 7 , b ) 1 / 3 , c ) 5 / 3 , d ) 12 / 7 , e ) 17 / 20
Rationale: let total number of juniors = j total number of seniors = s ( 1 / 2 ) j = ( 2 / 3 ) s = > s = 3 / 4 j total number of students = j + s = ( 7 / 4 ) j fraction of the students in the room are juniors = j / ( j + s ) = j / [ ( 7 / 4 ) j ] = 4 / 7 answer a
Answer: a
Question (other): in a certain alphabet , 10 letters contain a dot and a straight line . 24 letters contain a straight line but do not contain a dot . if that alphabet has 40 letters , all of which contain either a dot or a straight line or both , how many letters contain a dot but do not contain a straight line ?
Options: a ) 6 , b ) 8 , c ) 14 , d ) 20 , e ) 28
Rationale: we are told that all of the letters contain either a dot or a straight line or both , which implies that there are no letters without a dot and a line ( no line / no dot box = 0 ) . first we find the total # of letters with lines : 10 + 24 = 34 ; next , we find the total # of letters without line : 40 - 34 = 6 ; finally , we find the # of letters that contain a dot but do not contain a straight line : 6 - 0 = 6 . a
Answer: a
Question (gain): a certain manufacturer increased its gross profit on a product from 10 percent of the cost of the product to 15 percent of the cost by changing the selling price . if the new selling price was $ 92.00 and the cost of the product remained the same , what was the old selling price ?
Options: a ) $ 77.40 , b ) $ 80.00 , c ) $ 83.64 , d ) $ 87.40 , e ) $ 88.00
Rationale: given that { cost of the product } * 1.15 = $ 92 - - > { cost of the product } = $ 80 . the old price was $ 80 * 1.1 = $ 88 . answer : e .
Answer: e
Question (gain): in a certain city , 60 percent of the registered voters are democrats and the rest are republicans . in a mayoral race , if 65 percent of the registered voters who are democrats and 20 percent of the registered voters who are republicans are expected to vote for candidate a , what percent of the registered voters are expected to vote for candidate a ?
Options: a ) 50 % , b ) 53 % , c ) 54 % , d ) 55 % , e ) 47 %
Rationale: "say there are total of 100 registered voters in that city . thus 60 are democrats and 40 are republicans . 60 * 0.65 = 39 democrats are expected to vote for candidate a ; 40 * 0.20 = 8 republicans are expected to vote for candidate a . thus total of 39 + 8 = 47 registered voters are expected to vote for candidate a , which is 47 % of the total number of registered voters . answer : e ."
Answer: e
Question (general): the smallest number when increased by ` ` 2 ` ` is exactly divisible by 12 , 30 , 48 , 74 and 100 is :
Options: a ) 14439 , b ) 44398 , c ) 44400 , d ) 44402 , e ) 15005
Rationale: "lcm = 44400 44400 - 2 = 44398 answer : b"
Answer: b
Question (general): how many integers between 1 and 1400 are divisible by 25 , and 35 ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: lcm of the given numbers = 175 therefore , number of integers = 1400 / 175 = 8 answer is option e
Answer: e
Question (geometry): a semicircular cubicle has a radius of 14 . what is the approximate perimeter of the cubicle ?
Options: a ) 55
b ) 86
c ) 25
d ) 72
e ) 35
Rationale: perimeter of a circle = 2 pi * r perimeter of a semicircle = pi * r + 2 r aprox perimiter = 3.14 * 14 + 2 * 14 = 71.96 approximately 72 answer d
Answer: d
Question (physics): a works thrice as much as b . if a takes 60 days less than b to do a work then find the number of days it would take to complete the work if both work together ?
Options: a ) 22.5 days , b ) 21.5 days , c ) 23.5 days , d ) 24.5 days , e ) 25.5 days
Rationale: if a finishes the job in x days b finishes it in 3 x days 3 x = x + 60 thus x = 30 in one hour 1 / t = 1 / 30 + 1 / 90 = 4 / 90 where t is the number of days they finish the job together . t = 90 / 4 = 22.5 days answer : a
Answer: a
Question (gain): a retailer bought a machine at a wholesale price of $ 90 and later on sold it after a 10 % discount of the retail price . if the retailer made a profit equivalent to 20 % of the whole price , what is the retail price t of the machine ?
Options: a ) 81 , b ) 100 , c ) 120 , d ) 135 , e ) 160
Rationale: "since the wholesale price was $ 90 and the profit was 20 % of the wholesale price ( [ . 2 ] [ 90 ] = $ 18 ) , the retail price would have to be above $ 108 , but not that much greater than that . let ' s start by testing answer c : $ 120 . . . . if . . . . . retail price t = $ 120 10 % discount off = $ 120 - ( . 1 ) ( 120 ) = 120 - 12 = 108 20 % profit on wholesale price = 90 + ( . 2 ) ( 90 ) = 90 + 18 = 108 these two numbers match , so this must be the answer ! final answer : [ reveal ] spoiler : c"
Answer: c
Question (gain): in a certain company , a third of the workers do not have a retirement plan . 20 % of the workers who do not have a retirement plan are women , and 40 % of the workers who do have a retirement plan are men . if 128 of the workers of that company are men , how many of the workers are women ?
Options: a ) 80 , b ) 95 , c ) 105 , d ) 112 , e ) 210
Rationale: "set up equation : x = total number of workers 128 = 0,4 * 2 / 3 * x + 0,8 * 1 / 3 * x 128 = 16 / 30 x x = 240 240 - 128 = 112 answer d"
Answer: d
Question (physics): calculate the number of urns of water needed to fill a tank of dimensions of 10 x 10 x 5 m to 90 % full , if the volume of the urn is 0.8 m 3 and can only be filled to 80 % .
Options: a ) 520 , b ) 650.2 , c ) 685.5 , d ) 703.1 , e ) 712.2
Rationale: volume of the tank that needed to be filled = 10 x 10 x 5 x 0.9 = 450 volume of the urn that can be filled = 0.8 x 0.8 = 0.64 no . of urns of water needed to fill the tank = 450 / 0.64 = 703.1 answer : d
Answer: d
Question (general): a batsman makes a score of 92 runs in the 17 th inning and thus increases his average by 3 . find his average after 17 th inning .
Options: a ) 36 , b ) 39 , c ) 42 , d ) 44 , e ) none of the above
Rationale: "let the average after 17 th inning = x . then , average after 16 th inning = ( x – 3 ) . ∴ 16 ( x – 3 ) + 92 = 17 x or x = ( 92 – 48 ) = 44 . answer d"
Answer: d
Question (physics): a tank can be filled by two pipes a and b in 60 minutes and 40 minutes respectively . how many minutes will it take to fill the tank from empty state if b is used for the first half time and then a and b fill it together for the other half .
Options: a ) 15 mins , b ) 20 mins , c ) 25 mins , d ) 30 mins , e ) 35 mins
Rationale: explanation : let the total time be x mins . part filled in first half means in x / 2 = 1 / 40 part filled in second half means in x / 2 = 1 / 60 + 1 / 40 = 1 / 24 total = x / 2 x 1 / 40 + x / 2 x 1 / 24 = 1 x = 30 mins answer is d
Answer: d
Question (general): in a division sum , the quotient is 65 , the divisor 24 and the remainder 5 , find the dividend ?
Options: a ) 1595 , b ) 1569 , c ) 1265 , d ) 1555 , e ) 1565
Rationale: "explanation : 65 * 24 + 5 = 1565 answer : e"
Answer: e
Question (gain): the principal that amounts to rs . 3913 in 3 years at 6 1 / 4 % per annum c . i . compounded annually , is ?
Options: a ) s . 3096 , b ) s . 4076 , c ) s . 4085 , d ) s . 4096 , e ) s . 5096
Rationale: "principal = [ 4913 / ( 1 + 25 / ( 4 * 100 ) ) 3 ] = 3913 * 16 / 17 * 16 / 17 * 16 / 17 = rs . 3096 . answer : a"
Answer: a
Question (geometry): the length of a rectangular field is 7 / 5 its width . if the perimeter of the field is 240 meters , what is the width of the field ?
Options: a ) 50 , b ) 60 , c ) 70 , d ) 80 , e ) 90
Rationale: "let l be the length and w be the width . l = ( 7 / 5 ) w perimeter : 2 l + 2 w = 240 , 2 ( 7 / 5 ) w + 2 w = 240 solve the above equation to find : w = 50 m and l = 70 m . correct answer a ) 50"
Answer: a
Question (general): the sum of the present ages of two persons a and b is 60 . if the age of a is twice that of b , find the sum of their ages 10 years hence ?
Options: a ) 58 , b ) 59 , c ) 62 , d ) 70 , e ) 80
Rationale: "explanation : a + b = 60 , a = 2 b 2 b + b = 60 = > b = 20 then a = 40 . 10 years , their ages will be 50 and 30 . sum of their ages = 50 + 30 = 80 . e )"
Answer: e
Question (general): at a certain committee meeting only associate professors and assistant professors are present . each associate professor has brought 2 pencils and 1 chart to the meeting , while each assistant professor has brought 1 pencil and 2 charts . if a total of 10 pencils and 8 charts have been brought to the meeting , how many people are present ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "say there are ' a ' associate professors . so we have 2 a pencils and a charts . say there are ' b ' assistant professors . so we have b pencils and 2 b charts . total pencils are 10 so 2 a + b = 10 total charts are 11 so a + 2 b = 8 add both : 3 a + 3 b = 18 so a + b = 6 total number of people = 6 a"
Answer: a
Question (physics): it is the new year and mandy has made a resolution to lose weight this year . she plans to exercise and do yoga . for exercise she plans to workout at the gym and ride her bicycle in the ratio of 2 : 3 everyday . she will also do yoga in the ratio , yoga : exercise = 2 : 3 . if she rides her bike for 14 minutes , how much time will she spend doing yoga ? ( rounded to minutes )
Options: a ) 10 min . , b ) 41 min . , c ) 17 min . , d ) 23 min . , e ) 25 min .
Rationale: "the ratio is 2 : 3 = gym : ride , so ( 14 ) ( 3 / 2 ) = 21 minutes at the gym , and 21 + 14 = 35 minutes exercise , so ( 2 / 3 ) ( 35 ) = 23 minutes yoga . answer : d"
Answer: d
Question (general): jim â € ™ s taxi service charges an initial fee of $ 2.25 at the beginning of a trip and an additional charge of $ 0.4 for each 2 / 5 of a mile traveled . what is the total charge for a trip of 3.6 miles ?
Options: a ) $ 3.15 , b ) $ 4.45 , c ) $ 4.80 , d ) $ 5.05 , e ) $ 5.85
Rationale: "let the fixed charge of jim â € ™ s taxi service = 2.25 $ and charge per 2 / 5 mile ( . 4 mile ) = . 4 $ total charge for a trip of 3.6 miles = 2.25 + ( 3.6 / . 4 ) * . 4 = 2.25 + 9 * . 4 = 5.85 $ answer e"
Answer: e
Question (general): in a market , a dozen eggs cost as much as a pound of rice , and a half - liter of kerosene costs as much as 8 eggs . if the cost of each pound of rice is $ 0.33 , then how many w cents does a liter of kerosene cost ? [ one dollar has 100 cents . ]
Options: a ) 0.33 , b ) 0.44 , c ) 0.55 , d ) 44 , e ) 55
Rationale: "main thing to remember is answer is asked in cents , however when we calculate , it comes up as 0.44 $ just multiply by 100 , answer w = 44 . d"
Answer: d
Question (physics): a train requires 5 seconds to pass a pole while it requires 25 seconds to cross a stationary train which is 360 mtrs long . find the speed of the train .
Options: a ) 66.8 kmph , b ) 65.8 kmph , c ) 54.8 kmph , d ) 64.8 kmph , e ) 44.8 kmph
Rationale: "in 5 s the train crosses the pole and in 25 sec the train crosses one more stationary train in 20 sec the train travels a distance of 360 mtrs speed = 360 / 20 = 18 m / s = 18 ( 3600 / 1000 ) = 18 * 18 / 5 = 64.8 kmph answer : d"
Answer: d
Question (general): a two digit number is 18 less than the square of the sum of its digits . how many such numbers are there ?
Options: a ) 2233 , b ) 2222 , c ) 2211 , d ) 6382 , e ) 23,17
Rationale: option 2 take n = 10 a + b . given that , ( 10 a + b ) + 18 = k 2 = ( a + b ) 2 given number = k 2 - 18 = ( 10 a + b ) that means , when we add 18 to the given number it should be a perfect square . so k 2 takes the following values . 1 , 4 , 9 , 16 , 25 , 36 , 49 , 64 , 81 , 100 , 121 , . . . . 1 to 16 are ruled out as if we subtract 18 from them , the resulting number is a single digit number . now 25 - 18 = 7 36 - 18 = 18 49 - 18 = 31 64 - 18 = 46 81 - 18 = 63 100 - 18 = 82 121 - 18 = 103 now 63 , 82 satisfies . answer : d
Answer: d
Question (general): what is the average ( arithmetic mean ) of 10 , 20,30 , 40,50 , 60,70 , 80,90 ?
Options: a ) 90 , b ) 95 , c ) 70 , d ) 85 , e ) 50
Rationale: "so addition of all term - 10 , 20 , 30 , . . . . . . . 90 so average = ( 10 + 20 + 30 + 40 + 50 + 60 + 70 + 80 + 90 ) / 9 = ( 450 ) / 9 = 50 hence , the correct answer is e ."
Answer: e
Question (general): if the average of 6 x and 8 y is greater than 100 , and x is twice y , what is the least integer value of x ?
Options: a ) 22 , b ) 20 , c ) 21 , d ) 23 , e ) 24
Rationale: "substitution can be used in the following way : always start with the equation : x = 2 y . it is more straight forward to manage as compared to the inequality . substitute y = x / 2 , not the other way because you need to find the minimum value of x . so you can get rid of y . now go on to the inequality . so 8 y = 8 x / 2 = 4 x now average of 6 x and 4 x is greater than 100 . average of 6 x and 4 x is 5 x . so , 5 x > 100 x > 20 answer : b"
Answer: b
Question (geometry): two cubes of their volumes in the ratio 343 : 729 . the ratio of their surface area is :
Options: a ) 7 : 9 , b ) 2 : 5 , c ) 3 : 5 , d ) 1 : 5 , e ) 4 : 5
Rationale: "the ratio of their surface area is 343 : 729 7 : 9 answer is a ."
Answer: a
Question (physics): two pipes p and q can fill a cistern in 12 and 14 minutes respectively . both are opened together , but at the end of 3 minutes the first is turned off . how much longer will the cistern take to fill ?
Options: a ) 11 1 / 2 min , b ) 11 1 / 4 min , c ) 11 2 / 4 min , d ) 11 1 / 5 min , e ) 10 1 / 2 min
Rationale: "3 / 12 + x / 14 = 1 x = 10 1 / 2 answer : e"
Answer: e
Question (physics): a can complete a project in 20 days and b can complete the same project in 20 days . if a and b start working on the project together and a quits 10 days before the project is completed , in how many days will the project be completed ?
Options: a ) 18 days , b ) 27 days , c ) 26.67 days , d ) 16 days , e ) 15 days
Rationale: "let x = the number of days taken to complete the project . the amount of work done by a is ( x - 10 ) * ( 1 / 20 ) . the amount of work done by b is ( x ) * ( 1 / 30 ) . ( 1 / 20 ) * ( x - 10 ) + ( 1 / 20 ) * ( x ) = 1 ( x / 20 ) + ( x / 20 ) - ( 10 / 20 ) = 1 x / 10 = 3 / 2 x = 15 therefore , the answer is e : 15 ."
Answer: e
Question (physics): a work crew of 4 men takes 5 days to complete one - half of a job . if 11 men are then added to the crew and the men continue to work at the same rate , how many days will it take the enlarged crew to do the rest of the job ?
Options: a ) 2 , b ) 3 , c ) 1 1 / 3 , d ) 4 , e ) 4 4 / 5
Rationale: "suppose 1 man can do work in x days . . so 4 men will do in . . 4 / x = 1 / 5 * 1 / 2 as half job is done x = 40 now 11 more are added then 15 / 40 = 1 / 2 * 1 / d for remaining half job d = 1 1 / 3 number of days c"
Answer: c
Question (physics): a train 120 meters long takes 6 seconds to cross a man walking at 5 kmph in the direction opposite to that of the train . find the speed of the train .
Options: a ) 67 kmph , b ) 50 kmph , c ) 55 kmph , d ) 60 kmph , e ) 70 kmph
Rationale: "explanation : let the speed of the train be x kmph . speed of the train relative to man = ( x + 5 ) kmph = ( x + 5 ) × 5 / 18 m / sec . therefore 120 / ( ( x + 5 ) × 5 / 18 ) = 6 < = > 30 ( x + 5 ) = 2160 < = > x = 67 speed of the train is 67 kmph . answer : option a"
Answer: a
Question (gain): a small company reduced its faculty by approximately 13 percent to 195 employees . what was the original number of employees ?
Options: a ) 182 , b ) 208 , c ) 220 , d ) 224 , e ) 302
Rationale: "if x is the original number of employees , then after 13 % reduction in employees number is . 87 x but we are given . 87 x = 195 x = 224 so the original number of employees is 224 correct answer - d"
Answer: d