Cheukting/mathqa huggingface dataset:
Question (other): the sum of 3 numbers is 98 . if the ratio of the first to the second is 2 : 3 and that of the second to the third is 5 : 8 , then the second number is :
Options: a ) 20 , b ) 30 , c ) 38 , d ) 48 , e ) none of these
Rationale: a : b = 2 : 3 = 2 × 5 : 3 × 5 = 10 : 15 and b : c = 5 : 8 = 5 × 3 : 8 × 3 = 15 : 24 therefore , a : b : c = 10 : 15 : 24 ∴ a : b : c = 10 : 15 : 24 let the number be 10 x , 15 x and 24 x . then , 10 x + 15 x + 24 x = 98 or 49 x = 98 or x = 2 ⇒ second number = 15 x = 15 × 2 = 30 answer b
Answer: b
Question (physics): if 20 men can build a water fountain 56 metres long in 42 days , what length of a similar water fountain can be built by 35 men in 3 days ?
Options: a ) 3 m , b ) 4 m , c ) 7 m , d ) 9 m , e ) 10 m
Rationale: "explanation : let the required length be x metres more men , more length built ( direct proportion ) less days , less length built ( direct proportion ) men 20 : 35 days 42 : 3 : : 56 : x therefore ( 20 x 42 x x ) = ( 35 x 3 x 56 ) x = ( 35 x 3 x 56 ) / 840 = 7 hence , the required length is 7 m . answer : c"
Answer: c
Question (general): find large number from below question the difference of two numbers is 1500 . on dividing the larger number by the smaller , we get 6 as quotient and the 15 as remainder
Options: a ) 1234 , b ) 1345 , c ) 1456 , d ) 1797 , e ) 1635
Rationale: "let the smaller number be x . then larger number = ( x + 1500 ) . x + 1500 = 6 x + 15 5 x = 1485 x = 297 large number = 297 + 1500 = 1797 d"
Answer: d
Question (general): from below option 27 is divisible by which one ?
Options: a ) a ) 4 , b ) b ) 8 , c ) c ) 9 , d ) d ) 10 , e ) e ) 911
Rationale: "27 / 9 = 3 c"
Answer: c
Question (physics): the amounts of time that three secretaries worked on a special project are in the ratio of 2 to 3 to 5 . if they worked a combined total of 80 hours , how many hours did the secretary who worked the longest spend on the project ?
Options: a ) 80 , b ) 70 , c ) 56 , d ) 16 , e ) 40
Rationale: "10 x = 80 = > x = 8 therefore the secretary who worked the longest spent 8 x 5 = 40 hours on the project option ( e )"
Answer: e
Question (general): the ratio of number of boys and girls in a class is 3 : 2 . in the 1 st semester exam 20 % of boys and 25 % of girls get more than or equal to 90 % marks . what percentage of students get less than 90 % marks ?
Options: a ) 56 , b ) 70 , c ) 78 , d ) 80 , e ) 85
Rationale: let boys = 3 x and girls = 2 x . number of those who get less than 90 % mark = ( 80 % of 3 x ) + ( 75 % of 2 x ) = ( 80 / 100 ) * 3 x + ( 75 / 100 * 2 x ) = 39 x / 10 required percentage = ( 39 x / 10 * 1 / 5 x * 100 ) % = 78 % . answer : c
Answer: c
Question (general): if x = 4 and y = − 2 , what is the value of ( x − 2 y ) ^ y ?
Options: a ) − 100 , b ) 0.015 , c ) 0.25 , d ) 4 , e ) 8
Rationale: "quickly we can spot that answer is neither integer nor negative . eliminate a , de by inversing and squaring 0.015 answer : b"
Answer: b
Question (probability): an urn contains 5 red , 6 blue and 8 green balls . 4 balls are randomly selected from the urn , find the probability that the drawn ball are 1 blue and 2 red and 1 green balls ?
Options: a ) 20 / 323 , b ) 40 / 323 , c ) 60 / 273 , d ) 50 / 373 , e ) 40 / 373
Rationale: "sample space = no . of ways 4 balls were drawn from urn = 19 c 4 = 3876 no . ways 1 blue and 2 red and 1 green balls were drawn from bag = 6 c 1 * 5 c 2 * 8 c 1 = 480 probability = 480 / 3876 = 40 / 323 ans - b"
Answer: b
Question (physics): a car takes 6 hours to cover a distance of 504 km . how much should the speed in kmph be maintained to cover the same direction in 3 / 2 th of the previous time ?
Options: a ) 48 kmph , b ) 50 kmph , c ) 52 kmph , d ) 56 kmph , e ) 60 kmph
Rationale: time = 6 distence = 504 3 / 2 of 6 hours = 6 * 3 / 2 = 9 hours required speed = 504 / 9 = 56 kmph d
Answer: d
Question (general): one - seventh of the light switches produced by a certain factory are defective . 4 - fifths of the defective switches are rejected and 1 / 15 of the non defective switches are rejected by mistake . if all the switches not rejected are sold , what percent of the switches sold by the factory are defective ?
Options: a ) 2.3 % , b ) 3.4 % , c ) 4.5 % , d ) 5.6 % , e ) 6.7 %
Rationale: 1 / 7 of the switches are defective . the defective switches that are not rejected are 1 / 5 * 1 / 7 = 1 / 35 = 3 / 105 of all switches . the non defective switches that are sold are 6 / 7 * 14 / 15 = 84 / 105 of all switches . the percent of switches sold that are defective is 3 / 87 which is about 3.4 % . the answer is b .
Answer: b
Question (general): the average of 10 numbers is calculated as 23 . it is discovered later on that while calculating the average , one number namely 36 was wrongly read as 26 . the correct average is ?
Options: a ) a ) 16 , b ) b ) 18 , c ) c ) 19 , d ) d ) 22 , e ) e ) 24
Rationale: "explanation : 10 * 23 + 36 – 26 = 240 = > 240 / 10 = 24 e )"
Answer: e
Question (gain): a survey was sent to 80 customers , 7 of whom responded . then the survey was redesigned and sent to another 63 customers , 9 of whom responded . by approximately what percent did the response rate increase from the original survey to the redesigned survey ?
Options: a ) 2 % , b ) 5 % , c ) 14 % , d ) 28 % , e ) 63 %
Rationale: "case 1 : ( 7 / 80 ) = x / 100 x = 9 % case 2 : ( 9 / 63 ) = y / 100 y = 14 % so percent increase is = ( y - x ) = ( 14 - 9 ) % = 5 % answer is b"
Answer: b
Question (general): average age of students of an adult school is 42 years . 120 new students whose average age is 32 years joined the school . as a result the average age is decreased by 4 years . find the number of students of the school after joining of the new students .
Options: a ) 1200 , b ) 120 , c ) 360 , d ) 200 , e ) none of these
Rationale: "explanation : let the original no . of students be x . according to situation , 42 x + 120 * 32 = ( x + 120 ) 36 ⇒ x = 80 so , required no . of students after joining the new students = x + 120 = 200 . answer : d"
Answer: d
Question (general): you have been given a physical balance and 7 weights of 45 , 50 , 53 , 46 , 52 , 46 and 80 kgs . keeping weights on one pan and object on the other , what is the maximum you can weigh less than 188 kgs .
Options: a ) 183 , b ) 185 , c ) 182 , d ) 184 , e ) 181
Rationale: "80 + 52 + 53 = 185 answer : b"
Answer: b
Question (physics): a person has to make 146 pieces of long bar . he take $ seconds to cut piece . what is total time taken by him to make 146 pieces ?
Options: a ) 580 seconds , b ) 680 seconds , c ) 500 seconds , d ) 540 seconds , e ) 560 seconds
Rationale: if it is 4 seconds , as u have mistaken with shift key , then . . . . we ' ll have to make 145 cuts for 146 pieces . so 145 * 5 = 580 seconds answer : a
Answer: a
Question (physics): a tank can supply water to a village for 60 days . if a leak at the bottom of the tank drains out 10 liters per day , the supply lasts for 45 days only . for how many days will the supply last if the leak drains out 20 liters per day ?
Options: a ) 15 , b ) 18 , c ) 20 , d ) 24 , e ) 36
Rationale: losing 10 liters per day results in a loss of 450 liters in 45 days . so , those 450 liters were for 15 days , making daily consumption of the village 30 liters per day . thus the capacity of the tank is 30 * 60 = 1800 liters . losing 20 liters plus 30 liters gives 50 liters per day . at this rate the supply will last 1800 / 50 = 36 days . the answer is e .
Answer: e
Question (physics): how many plants will be there in a circular bed whose outer edge measure 32 cms , allowing 4 cm 2 for each plant ?
Options: a ) 18 , b ) 750 , c ) 24 , d ) 20 , e ) none of these
Rationale: "circumference of circular bed = 32 cm area of circular bed = ( 32 ) 2 â  „ 4 ï € space for each plant = 4 cm 2 â ˆ ´ required number of plants = ( 32 ) 2 â  „ 4 ï € ã · 4 = 20.36 = 20 ( approx ) answer d"
Answer: d
Question (general): he average weight of 8 persons increases by 2.5 kg when a new person comes in place of one of them weighing 60 kg . what might be the weight of the new person ?
Options: a ) 75 kg , b ) 55 kg , c ) 80 kg , d ) 85 kg , e ) 25 kg
Rationale: "explanation : total weight increased = ( 8 x 2.5 ) kg = 20 kg . weight of new person = ( 60 + 20 ) kg = 80 kg . answer : c"
Answer: c
Question (gain): a started a business with an investment of rs . 70000 and after 6 months b joined him investing rs . 120000 . if the profit at the end of a year is rs . 65000 , then the share of b is ?
Options: a ) a ) 30000 , b ) b ) 34000 , c ) c ) 34098 , d ) d ) 33007 , e ) e ) 44098
Rationale: "ratio of investments of a and b is ( 70000 * 12 ) : ( 120000 * 6 ) = 7 : 6 total profit = rs . 65000 share of b = 6 / 13 ( 65000 ) = rs . 30000 answer : a"
Answer: a
Question (geometry): if the radius of a circle is decreased 10 % , what happens to the area ?
Options: a ) 10 % decrease , b ) 19 % decrease , c ) 36 % decrease , d ) 40 % decrease , e ) 50 % decrease
Rationale: "area of square = pi * radius ^ 2 new radius = 0.9 * old radius so new area = ( 0.9 ) ^ 2 old area = > 0.81 of old area = > 81 % old area ans : b"
Answer: b
Question (general): average age of students of an adult school is 44 years . 120 new students whose average age is 32 years joined the school . as a result the average age is decreased by 4 years . find the number of students of the school after joining of the new students .
Options: a ) 1200 , b ) 180 , c ) 360 , d ) 240 , e ) none of these
Rationale: "explanation : let the original no . of students be x . according to situation , 44 x + 120 * 32 = ( x + 120 ) 36 ⇒ x = 60 so , required no . of students after joining the new students = x + 120 = 180 answer : b"
Answer: b
Question (general): a batsman makes a score of 87 runs in the 17 th inning and thus increases his average by 2 . find his average after 17 th inning .
Options: a ) 36 , b ) 39 , c ) 42 , d ) 45 , e ) none of the above
Rationale: "let the average after 17 th inning = x . then , average after 16 th inning = ( x – 2 ) . ∴ 16 ( x – 2 ) + 87 = 17 x or x = ( 87 – 32 ) = 55 . answer e"
Answer: e
Question (other): 24 oz of juice p and 25 oz of juice v are mixed to make smothies a and y . the ratio of p to v in smothie a is 4 is to 1 and that in y is 1 is to 5 . how many ounces of juice p are contained in the smothie a ?
Options: a ) 5 , b ) 10 , c ) 15 , d ) 20 , e ) 25
Rationale: the ratio of p to v in smothie x is 4 is to 1 and that in y is 1 is to 5 . p 1 + p 2 = 24 v 1 + v 2 = 25 p 1 = 4 v 1 p 2 = v 2 / 5 4 v 1 + v 2 / 5 = 24 v 1 + v 2 = 25 4 v 2 - v 2 / 5 = 76 19 v 2 / 5 = 76 = > v 2 = 20 = > v 1 = 5 = > p 1 = 20 answer - d
Answer: d
Question (gain): during a certain season , a team won 60 percent of its first 100 games and 50 percent of its remaining games . if the team won 70 percent of its games for the entire season , what was the total number of games that the team played ?
Options: a ) 80 , b ) 70 , c ) 56 , d ) 50 , e ) 105
Rationale: "we are first given that a team won 60 percent of its first 100 games . this means the team won 0.6 x 100 = 60 games out of its first 100 games . we are next given that the team won 50 percent of its remaining games . if we use variable t to represent the total number of games in the season , then we can say t – 100 equals the number of remaining games in the season . thus we can say : 0.5 ( t – 100 ) = number of wins for remaining games 0.5 t – 50 = number of wins for remaining games lastly , we are given that team won 70 percent of all games played in the season . that is , they won 0.7 t games in the entire season . with this we can set up the equation : number of first 100 games won + number of games won for remaining games = total number of games won in the entire season 60 + 0.5 t – 50 = 0.7 t 10 = 0.2 t 100 = 2 t 50 = t answer is d ."
Answer: d
Question (gain): in a certain pond , 20 fish were caught , tagged , and returned to the pond . a few days later , 20 fish were caught again , of which 2 were found to have been tagged . if the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond , what ` s the approximate number of fish in the pond ?
Options: a ) 400 , b ) 625 , c ) 1250 , d ) 2500 , e ) 500
Rationale: "if x is total number of fish in the pond : 4 = 20 / x * 100 = > x = 500 so answer is e"
Answer: e
Question (general): a certain bus driver is paid a regular rate of $ 18 per hour for any number of hours that does not exceed 40 hours per week . for any overtime hours worked in excess of 40 hours per week , the bus driver is paid a rate that is 75 % higher than his regular rate . if last week the bus driver earned $ 976 in total compensation , how many total hours did he work that week ?
Options: a ) 36 , b ) 40 , c ) 44 , d ) 48 , e ) 52
Rationale: "for 40 hrs = 40 * 18 = 720 excess = 976 - 720 = 252 for extra hours = . 75 ( 18 ) = 13.5 + 18 = 31.5 number of extra hrs = 252 / 31.5 = 8 total hrs = 40 + 8 = 48 answer d 48"
Answer: d
Question (gain): a shopkeeper buys two articles for rs . 1000 each and then sells them , making 75 % profit on the first article and 75 % loss on second article . find the net profit or loss percent ?
Options: a ) 200 , b ) 768 , c ) 276 , d ) 750 , e ) 279
Rationale: "profit on first article = 75 % of 1000 = 750 . this is equal to the loss he makes on the second article . that , is he makes neither profit nor loss . answer : d"
Answer: d
Question (geometry): a spirit and water solution is sold in a market . the cost per liter of the solution is directly proportional to the part ( fraction ) of spirit ( by volume ) the solution has . a solution of 1 liter of spirit and 1 liter of water costs 50 cents . how many cents does a solution of 1 liter of spirit and 2 liters of water cost ?
Options: a ) 13 , b ) 33 , c ) 50 , d ) 51 , e ) 52
Rationale: "the cost per liter of the solution is directly proportional to the part ( fraction ) of spirit ( by volume ) the solution has . it means there is no effect of change in volume of water to the costing of the solution so a solution of 1 liter of spirit and 2 liters of water will cost 50 cents answer = 50 answer : c"
Answer: c
Question (geometry): in a company of 180 employees , 110 are females . a total of 90 employees have advanced degrees and the rest have a college degree only . if 35 employees are males with a college degree only , how many employees are females with advanced degrees ?
Options: a ) 50 , b ) 55 , c ) 60 , d ) 65 , e ) 70
Rationale: "the number of males is 180 - 110 = 70 . the number of males with advanced degrees is 70 - 35 = 35 . the number of females with advanced degrees is 90 - 35 = 55 . the answer is b ."
Answer: b
Question (general): how many positive integers less than 8,000 are there in which the sum of the digits equals 5 ?
Options: a ) 57 , b ) 56 , c ) 55 , d ) 54 , e ) 53
Rationale: "basically , the question asks how many 4 digit numbers ( including those in the form 0 xxx , 00 xx , and 000 x ) have digits which add up to 5 . think about the question this way : we know that there is a total of 5 to be spread among the 4 digits , we just have to determine the number of ways it can be spread . let x represent a sum of 1 , and | represent a seperator between two digits . as a result , we will have 5 x ' s ( digits add up to the 5 ) , and 3 | ' s ( 3 digit seperators ) . so , for example : xx | x | x | x = 2111 | | xxx | xx = 0032 etc . there are 8 c 3 ways to determine where to place the separators . hence , the answer is 8 c 3 = 56 . b"
Answer: b
Question (general): c and d started a business by investing rs . 1000 / - and rs . 1500 / - respectively . find the d ’ s share out of a total profit of rs . 500 :
Options: a ) 400 , b ) 300 , c ) 200 , d ) 100 , e ) 150
Rationale: c = rs . 1000 / - d = rs . 1500 / - c share 2 parts & d share 3 parts total 5 parts - - - - - > rs . 500 / - - - - - > 1 part - - - - - - - > rs . 100 / - d share = 3 parts - - - - - > rs . 300 / - d
Answer: d
Question (physics): a train 400 meters long completely crosses a 300 meters long bridge in 45 seconds . what is the speed of the train is ?
Options: a ) 32 , b ) 56 , c ) 29 , d ) 27 , e ) 21
Rationale: "s = ( 400 + 300 ) / 45 = 700 / 45 * 18 / 5 = 56 answer : b"
Answer: b
Question (general): q and r are two - digit positive integers that have the same digits but in reverse order . if the positive difference between q and r is less than 70 , what is the greatest possible value of q minus r ?
Options: a ) 63 , b ) 64 , c ) 65 , d ) 66 , e ) 67
Rationale: "a two - digit integer ` ` ab ' ' can be expressed algebraically as 10 a + b . q - r = ( 10 a + b ) - ( 10 b + a ) = 9 ( a - b ) < 70 . the greatest multiple of 9 which is less than 70 is 63 . the answer is a ."
Answer: a
Question (general): at a certain paint store forest green is made by mixing 4 parts blue paint with 3 parts yellow paint . verdant green is made by mixing 4 parts yellow paint with 3 parts blue paint . how many liters of yellow paint must be added to 7 liters of forest green to change it to verdant green ?
Options: a ) 5 / 3 , b ) 2 / 7 , c ) 7 / 3 , d ) 1 / 7 , e ) 1 / 4
Rationale: 7 liter of forset green have 4 liter of blue and 3 liter of yellow suppose we add x liter of yellow to make it a verdant green so the ratio of blue to yellow in verdant green is ¾ so the equation is blue / yellow = 4 / ( 3 + x ) = ¾ 9 + 3 x = 16 = > x = 7 / 3 answer : c
Answer: c
Question (general): the sum of three consecutive multiples of 3 is 90 . what is the largest number ?
Options: a ) 30 , b ) 33 , c ) 36 , d ) 39 , e ) 42
Rationale: "let the numbers be 3 x , 3 x + 3 and 3 x + 6 . then , 3 x + ( 3 x + 3 ) + ( 3 x + 6 ) = 90 9 x = 81 x = 9 largest number = 3 x + 6 = 33 answer : b"
Answer: b
Question (gain): what will be the difference between simple and compound interest @ 25 % per annum on a sum of $ 3600 after 2 years ?
Options: a ) $ 150 , b ) $ 220 , c ) $ 225 , d ) $ 182 , e ) $ 189
Rationale: "s . i . = 3600 * 25 * 2 / 100 = $ 1800 c . i . = 3600 * ( 1 + 25 / 100 ) ^ 2 - 3600 = $ 2025 difference = 2025 - 1800 = $ 225 answer is c"
Answer: c
Question (physics): if 3 people can do 3 times of a particular work in 3 days , then how many days would it take 8 people to do 8 times of that particular work ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 8 , e ) 11
Rationale: "3 people can do the work one time in one day . 1 person can do 1 / 3 of the work in one day . 8 people can do 8 / 3 of the work in one day . 8 people can do 8 times the work in 3 days . the answer is c ."
Answer: c
Question (physics): a is half good a work man as b and together they finish a job in 32 days . in how many days working alone b finish the job ?
Options: a ) 98 days , b ) 21 days , c ) 48 days , d ) 18 days , e ) 19 days
Rationale: "wc = 1 : 2 2 x + x = 1 / 32 = > x = 1 / 96 2 x = 1 / 96 = > 48 days answer : c"
Answer: c
Question (geometry): the measurement of a rectangular box with lid is 25 cmx 24 cmx 18 cm . find the volume of the largest sphere that can be inscribed in the box ( in terms of π cm 3 ) . ( hint : the lowest measure of rectangular box represents the diameter of the largest sphere )
Options: a ) 288 , b ) 2302 , c ) 2304 , d ) 8640 , e ) 964
Rationale: "d = 24 , r = 12 ; volume of the largest sphere = 4 / 3 π r 3 = 4 / 3 * π * 12 * 12 * 12 = 2304 π cm 3 answer : c"
Answer: c
Question (geometry): if the sides of a square are multiplied by 10 , the area of the original square is how many times as large as the area of the resultant square ?
Options: a ) 1 %
b ) 10 %
c ) 100 %
d ) 500 %
e ) 1000 %
Rationale: let x be the original length of one side . then the original area is x ^ 2 . the new square has sides of length 10 x , so the area is 100 x ^ 2 . the area of the original square is 1 / 100 = 1 % times the area of the new square . the answer is a .
Answer: a
Question (physics): machine t takes 2 more hours than machine b to make 20 widgets . if working together , the machines can make 25 widgets in 3 hours , how long will it take machine t to make 40 widgets ?
Options: a ) 5 , b ) 6 , c ) 8 , d ) 10 , e ) 12
Rationale: i approached this one by plugging in numbers . . . started with c . if 40 are made in 8 hours , then 20 are made in 4 hours . so time of t is 4 , and time of b is 2 . rate together : 20 / 4 + 20 / 2 = 5 + 10 = 15 . so in 1 hour , together make 15 widgets . in 3 hours = 45 . way too much . we can eliminate right away c , b , and a - because b and t reduces the time - the total # of widgets made will be even higher . now between d and e - > try only one . . if it does n ' t work , then the other one is the answer . i picked e : 12 h to make 40 widgets , and 6 hours to make 20 . this is the time of t . time of b = 4 hours . 20 / 6 + 20 / 4 = 10 / 3 + 20 / 4 find lcm of 3 and 4 = 12 . multiply first by 4 , and second by 3 : 40 + 60 / 12 = 100 / 12 divide by 4 : 25 / 3 so this is the rate given . e is the correct answer
Answer: e
Question (general): seller selling an apple for rs . 16 , a seller loses 1 / 6 th of what it costs him . the cp of the apple is ?
Options: a ) 10 , b ) 12 , c ) 17 , d ) 18 , e ) 20
Rationale: "sp = 16 loss = cp 17 loss = cp − sp = cp − 16 ⇒ cp 17 = cp − 16 ⇒ 16 cp 17 = 16 ⇒ cp 17 = 1 ⇒ cp = 17 c"
Answer: c
Question (general): what is the smallest number which when increased by 3 is divisible by 9 , 70 , 25 and 21 ?
Options: a ) 2927 , b ) 3147 , c ) 3387 , d ) 3567 , e ) 3797
Rationale: "when increased by 3 , the number must include at least 2 * 3 ^ 2 * 5 ^ 2 * 7 = 3150 the answer is b ."
Answer: b
Question (geometry): carmen made a sculpture from small pieces of wood . the sculpture is 2 feet 10 inches tall . carmen places her sculpture on a base that is 8 inches tall . how tall are the sculpture andbase together ?
Options: a ) 3.1 feet , b ) 3.2 feet , c ) 3.3 feet , d ) 3.4 feet , e ) 3.5 feet
Rationale: "we know 1 feet = 12 inch then 2 feet = 24 inch 24 + 10 = 34 then 34 + 8 = 42 42 / 12 = 3.5 feet answer : e"
Answer: e
Question (general): an employee whose hourly wage was increased by 25 percent decided to reduce the number of hours worked per week so that the employee ' s total weekly income would remain unchanged . by what percent should the number of hours worked be reduced ?
Options: a ) 9 , b ) 13 , c ) 16 , d ) 20 , e ) 25
Rationale: let original hourly wage be x and let the no of hours worked be y total wage will be = x * y after the increment the wage will be = 1.25 x now we need to find number of hours worked so that x * y = 1.25 x * z i . e z = 4 / 5 y % decrease = ( y - 4 / 5 y ) / y * 100 = 100 / 5 = 20 % . thus my answer is d
Answer: d
Question (physics): 45 men working 8 hours per day dig 40 m deep . how many extra men should be put to dig to a depth of 50 m working 6 hours per day ?
Options: a ) 10 , b ) 20 , c ) 30 , d ) 40 , e ) 50
Rationale: "( 45 * 8 ) / 40 = ( x * 6 ) / 50 = > x = 75 75 – 45 = 30 answer : c"
Answer: c
Question (general): there are 150 ' zeroes ' and 151 ' ones ' written on a black board . a step involves choosing 3 digits and replacing them with a single digit . if all the 3 digits are identical , they are replaced with the same digit . otherwise , the digit that appears twice replaces the 3 chosen digits . what is the minimum number of steps after which there will be no zero written on the blackboard ?
Options: a ) 11 , b ) 37 , c ) 36 , d ) 76 , e ) 33
Rationale: if we strike out 3 zeros , we are in effect reducing two zeroes . so we need 74 steps to reduce 148 zeroes . there are 2 zeroes and 151 ones left now . the remaining zeroes can be reduced in 2 steps . hence the answer is 76 . answer : d
Answer: d
Question (physics): a and b complete a work in 9 days . a alone can do it in 18 days . if both together can do the work in how many days ?
Options: a ) 6 days , b ) 8 days , c ) 5 days , d ) 7 days , e ) 15 days
Rationale: "1 / 9 + 1 / 18 = 1 / 6 6 / 1 = 6 days answer : a"
Answer: a