Cheukting/mathqa huggingface dataset:
Question (probability): a bag contains 10 red jellybeans and 10 blue jellybeans . if 3 jellybeans are removed one at a time , at random and are not replaced , what is the probability q that all 3 jellybeans removed from the bag are blue ?
Options: a ) 9 / 100 , b ) 2 / 19 , c ) 1 / 8 , d ) 3 / 20 , e ) 3 / 10
Rationale: "method - 1 10 red jellybeans and 10 blue jellybeans total outcomes = no . of ways to choose 3 jelly bean at random out of a total 20 jellybeans = 20 c 3 = 1140 favourable outcomes = no . of ways to choose 3 jelly bean such that they are all blue out of 10 blue = 10 c 3 = 120 probability = favourable outcomes / total outcomes = 10 c 3 / 20 c 3 probability q = 120 / 1140 = 2 / 19 answer : option b method - 2 probability of first jelly bean to be blue = 10 / 20 [ total 10 blue out of total 20 jellybeans ] probability of second jelly bean to be blue = 9 / 19 [ total 9 blue remaining out of total 19 jellybeans remaining ] probability of third jelly bean to be blue = 8 / 18 [ total 8 blue remaining out of total 18 jellybeans remaining ] required probability = ( 10 / 20 ) * ( 9 / 19 ) * ( 8 / 18 ) = 2 / 19 answer : option b"
Answer: b
Question (general): find the value of x from this equation ? 7 ( x - 1 ) = 21
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10
Rationale: 1 . divide both sides by 7 : 2 . simplify both sides : x - 1 = 3 3 . add 1 to both sides : x - 1 + 1 = 3 + 1 4 . simplify both sides : x = 4 b
Answer: b
Question (gain): a person incurs 10 % loss by selling a watch for $ 100 . at what price should the watch be sold to earn 10 % profit ?
Options: a ) $ 100 , b ) $ 122 , c ) $ 150 , d ) $ 210 , e ) $ 170
Rationale: "let the new selling price be $ x ( 100 - loss % ) : ( 1 st s . p . ) = ( 100 + gain % ) : ( 2 nd s . p . ) ( 100 - 10 ) / 100 = ( 100 + 10 ) / x x = 110 * 100 / 90 = 122 approximately answer is b"
Answer: b
Question (general): a sun is divided among x , y and z in such a way that for each rupee x gets , y gets 45 paisa and z gets 30 paisa . if the share of y is rs . 27 , what is the total amount ?
Options: a ) 388 , b ) 105 , c ) 288 , d ) 266 , e ) 281
Rationale: x : y : z = 100 : 45 : 30 20 : 9 : 6 9 - - - 27 35 - - - ? = > 105 answer : b
Answer: b
Question (gain): an association of mathematics teachers has 1,500 members . only 525 of these members cast votes in the election for president of the association . what percent of the total membership voted for the winning candidate if the winning candidate received 40 percent of the votes cast ?
Options: a ) 75 % , b ) 58 % , c ) 42 % , d ) 34 % , e ) 14 %
Rationale: "total umber of members = 1500 number of members that cast votes = 525 since , winning candidate received 40 percent of the votes cast number of votes for winning candidate = ( 40 / 100 ) * 525 = 210 percent of total membership that voted for winning candidate = ( 210 / 1500 ) * 100 = 14 % answer e"
Answer: e
Question (physics): to fill a tank , 25 buckets of water is required . how many buckets of water will be required to fill the same tank if the capacity of the bucket is reduced to 3 / 5 of its present ?
Options: a ) 41.66667 , b ) 60.5 , c ) 63.5 , d ) 62.5 , e ) 64.5
Rationale: "let capacity of 1 bucket = x capacity of the tank = 25 x new capacity of the bucket = 3 x / 5 hence , number of buckets needed = 25 x / ( 3 x / 5 ) = ( 25 × 5 ) / 3 = 41.66667 answer is a ."
Answer: a
Question (general): salesperson a ' s compensation for any week is $ 300 plus 6 percent of the portion of a ' s total sales above $ 1,000 for that week . salesperson b ' s compensation for any week is 8 percent of b ' s total sales for that week . for what amount of total weekly sales would both salepeople earn the same compensation ?
Options: a ) $ 21,000 , b ) $ 12,000 , c ) $ 15,000 , d ) $ 4,500 , e ) $ 4,000
Rationale: "sometime , setting up an equation is an easy way to go with : 300 + 0.06 ( x - 1000 ) = 0.08 x x = 12,000 ans : b"
Answer: b
Question (gain): ritesh and co . generated revenue of rs . 1,800 in 2006 . this was 12.5 % of its gross revenue . in 2007 , the gross revenue grew by rs . 2,500 . what is the percentage increase in the revenue in 2007 ?
Options: a ) 17.36 % , b ) 20 % , c ) 25 % , d ) 50 % , e ) none of these
Rationale: "explanation : given , ritesh and co . generated revenue of rs . 1,800 in 2006 and that this was 12.5 % of the gross revenue . hence , if 1800 is 12.5 % of the revenue , then 100 % ( gross revenue ) is : = > ( 100 / 12.5 ) × 1800 . = > 14,400 . hence , the total revenue by end of 2007 is rs . 14,400 . in 2006 , revenue grew by rs . 2500 . this is a growth of : = > ( 2500 / 14400 ) × 100 . = > 17.36 % . answer : a"
Answer: a
Question (physics): there are 28 stations between kolkatta and chennai . how many second class tickets have to be printed , so that a passenger can travel from any station to any other station ?
Options: a ) 870 , b ) 970 , c ) 1070 , d ) 1000 , e ) 800
Rationale: the total number of stations = 30 from 30 stations we have to choose any two stations and the direction of travel ( i . e . , kolkatta to chennai is different from chennai to kolkatta ) in 30 p 2 ways . 30 p 2 = 30 * 29 = 870 answer : a
Answer: a
Question (physics): a contractor is engaged for 30 days on the condition that he receives rs . 25 for each day he works & is fined rs . 7.50 for each day is absent . he gets rs . 490 in all . for how many days was he absent ?
Options: a ) 8 , b ) 10 , c ) 15 , d ) 17 , e ) 19
Rationale: 30 * 25 = 750 490 - - - - - - - - - - - 260 25 + 7.50 = 32.5 260 / 32.5 = 8 a
Answer: a
Question (geometry): what is the area of a rectangle whose length is twice its width and whose perimeter is equal to that of a square whose area is 1 ?
Options: a ) 1 / 9 sq units .
b ) 4 / 9 sq units .
c ) 8 / 9 sq units .
d ) 7 / 9 sq units .
e ) 6 / 9 sq units .
Rationale: area will be 2 / 3 * 4 / 3 = 8 / 9 sq units . answer : c
Answer: c
Question (general): albert is 2 times mary ’ s age and 4 times as old as betty . mary is 10 years younger than albert . how old is betty ?
Options: a ) 5 , b ) 8 , c ) 10 , d ) 12 , e ) 15
Rationale: "a = 2 m = m + 10 m = 10 a = 20 a = 4 b , and so b = 5 the answer is a ."
Answer: a
Question (general): a worker is paid rs . 20 / - for a full days work . he works 11 / 32 / 31 / 8.3 / 4 days in a week . what is the total amount paid for that worker ?
Options: a ) 56.5 rupees , b ) 58.5 rupees , c ) 57.5 rupees , d ) 59.5 rupees , e ) 55.5 rupees
Rationale: the total days worked = 1 + 0.333 + 0.667 + 0.125 + 0.75 = 2.875 days amount for 2.875 days is ( 2.875 * 20 ) 57.5 rupees answer : c
Answer: c
Question (other): how many odd factors does 270 have ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 8
Rationale: "start with the prime factorization : 270 = 2 * 3 * 5 for odd factors , we put aside the factor of two , and look at the other prime factors . set of exponents = { 1 , 1 } plus 1 to each = { 2 , 2 } product = 2 * 2 = 4 therefore , there are 4 odd factors of 270 . answer : b ."
Answer: b
Question (general): find a number such that when 15 is subtracted from 7 times the number , the results is more than twice the number ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: solution let the number be x . = then , 7 x - 15 = 2 x + 10 = 5 x = 25 ‹ = › x = 5 . hence the required number is 5 . answer d
Answer: d
Question (general): having received his weekly allowance , a student spent 3 / 5 of his allowance at the arcade . the next day he spent one third of his remaining allowance at the toy store , and then spent his last $ 1.00 at the candy store . what is this student ’ s weekly allowance ?
Options: a ) $ 2.75 , b ) $ 3.25 , c ) $ 3.75 , d ) $ 4.25 , e ) $ 4.75
Rationale: "let x be the value of the weekly allowance . ( 2 / 3 ) ( 2 / 5 ) x = 100 cents ( 4 / 15 ) x = 100 x = $ 3.75 the answer is c ."
Answer: c
Question (general): if 2 | 2 – e | = 5 , what is the sum of all the possible values for e ?
Options: a ) 1 / 2 , b ) 2 , c ) 5 / 2 , d ) 4 , e ) 5
Rationale: if e < 2 , then 2 - e = 5 / 2 ; e = - 1 / 2 if e > 2 , then e - 2 = 5 / 2 ; e = 9 / 2 9 / 2 - 1 / 2 = 8 / 2 = 4 = d
Answer: d
Question (gain): the market value of a certain machine decreased by 10 percent of its purchase price each year . if the machine was purchased in 1982 for its market value of $ 8,000 , what was its market value two years later ?
Options: a ) $ 8,000 , b ) $ 5,600 , c ) $ 3,200 , d ) $ 6,400 , e ) $ 800
Rationale: d market value in 1982 = $ 8000 market value in 1983 = $ 8000 - ( $ 8000 x 10 / 100 ) = 8000 - 800 = $ 7200 market value in 1984 = market value in 1983 - ( 10 % of $ 8000 ) = 7200 - 800 = $ 6400
Answer: d
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 $ 5 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 18 percent , what is the discount rate on pony jeans ?
Options: a ) 9 % , b ) 10 % , c ) 34.4 % , d ) 12 % , e ) 15 %
Rationale: "you know that fox jeans costs $ 15 , and pony jeans costs $ 18 , you also know that 3 pairs of fox jeans and 2 pairs of pony jeans were purchased . so 3 ( 15 ) = 45 - fox 2 ( 18 ) = 36 - pony the total discount discount is $ 5 and you are asked to find the percent discount of pony jeans , so 45 ( 18 - x ) / 100 + 36 ( x ) / 100 = 5 or 45 * 18 - 45 * x + 36 * x = 5 * 100 or 9 x = - 5 * 100 + 45 * 18 x = 310 / 9 = 34.4 c"
Answer: c
Question (general): if | y + 5 | = 8 , what is the sum of all the possible values of y ?
Options: a ) - 14 , b ) - 13 , c ) - 8 , d ) - 12 , e ) - 10
Rationale: "there will be two cases y + 5 = 8 or y + 5 = - 8 = > y = 3 or y = - 13 sum of both the values will be - 13 + 3 = - 10 answer : e"
Answer: e
Question (general): let n ~ be defined for all positive integers n as the remainder when ( n - 1 ) ! is divided by n . what is the value of 30 ~ ?
Options: a ) 1 , b ) 0 , c ) 2 , d ) 8 , e ) 31
Rationale: n ~ = ( n - 1 ) ! so 30 ~ = ( 30 - 1 ) ! = 29 ! when 29 ! / 30 we have 16 * 2 inside 29 ! hence 30 gets cancelled and we get remainder as 0 b
Answer: b
Question (probability): two unbiased coins are tossed . what is the probability of getting two heads ?
Options: a ) 1 / 2 , b ) 1 / 4 , c ) 2 / 3 , d ) 1 / 5 , e ) 2 / 7
Rationale: "s = { hh , ht , th , tt } e = event of getting 2 heads e = { tt } p ( e ) = 1 / 4 answer is b"
Answer: b
Question (physics): a and b complete a work in 10 days . a alone can do it in 14 days . if both together can do the work in how many days ?
Options: a ) 5.8 days , b ) 4.78 days , c ) 6.25 days , d ) 3.15 days , e ) 2.75 days
Rationale: 1 / 10 + 1 / 14 = 6 / 35 35 / 6 = 5.8 days answer : a
Answer: a
Question (general): if jake loses 33 pounds , he will weigh twice as much as his sister . together they now weigh 153 pounds . what is jake ' s present weight , in pounds ?
Options: a ) 131 , b ) 135 , c ) 113 , d ) 147 , e ) 188
Rationale: "j = jake ’ s current weight , in pounds s = sister ’ s current weight , in pounds we are told that “ if jake loses 8 pounds , he will weigh twice as much as his sister . we put this into an equation : j – 33 = 2 s j = 2 s + 33 ( equation 1 ) next , we are told that “ together they now weigh 153 pounds . ” we can also put this into an equation . j + s = 153 ( equation 2 ) to solve this equation , we can substitute 2 s + 8 from equation 1 for the variable j in equation 2 : 2 s + 33 = 153 - s 3 s = 120 s = 40 j + 40 = 153 j = 113 answer : c"
Answer: c
Question (gain): the value of a machine depreciates at 24 % per annum . if its present value is $ 1 , 50,000 , at what price should it be sold after two years such that a profit of $ 24,000 is made ?
Options: a ) $ 250640 , b ) $ 430640 , c ) $ 120640 , d ) $ 110640 , e ) $ 150640
Rationale: "the value of the machine after two years = 0.76 * 0.76 * 1 , 50,000 = $ 86,640 sp such that a profit of $ 24,000 is made = 86,640 + 24,000 = $ 1 , 10,640 d"
Answer: d
Question (general): a vendor buys 10 t - shirts at an average price of $ 14 per t - shirt . he then buys 15 more t - shirts at an average price of $ 11 per t - shirt . what is the average price v per t - shirt that the vendor paid for these purchases ?
Options: a ) $ 12.20 , b ) $ 12.50 , c ) $ 12.55 , d ) $ 12.70 , e ) $ 13.00
Rationale: "correct answer : a explanation : the relevant formula for this problem is average v = ( sum ) / ( number of terms ) . another way to look at the formula is sum = average x number of terms . for the first purchase , the vendor ' s sum ( total cost ) was $ 140 , since 14 x 10 = 140 . for the second purchase , the vendor ' s cost was $ 165 , since 11 x 15 = 165 . the grand sum is then $ 140 + $ 165 , which equals $ 305 . the total number of shirts purchased was 25 , so to get the average price per shirt , we divide 305 by 25 , which equals $ 12.20 . as a result , the correct answer is a . note : a relative understanding of weighted average offers a shortcut to this problem . because the true average of 11 and 14 is 12.5 , but the vendor sells more shirts at the lower price than at the higher price , the weighted average must be less than $ 12.50 ; only answer choice a is a possibility ."
Answer: a
Question (physics): if 5 machines can produce 20 units in 10 hours , how long would it take 20 machines to produce 120 units ?
Options: a ) 50 hours , b ) 40 hours , c ) 15 hours , d ) 12 hours , e ) 8 hours
Rationale: "here , we ' re told that 5 machines can produce 20 units in 10 hours . . . . that means that each machine works for 10 hours apiece . since there are 5 machines ( and we ' re meant to assume that each machine does the same amount of work ) , then the 5 machines equally created the 20 units . 20 units / 5 machines = 4 units are made by each machine every 10 hours now that we know how long it takes each machine to make 4 units , we can break this down further if we choose to . . . 10 hours / 4 units = 2.5 hours per unit when 1 machine is working . the prompt asks us how long would it take 20 machines to produce 120 units . if 20 machines each work for 2.5 hours , then we ' ll have 20 units . since 120 units is ' 6 times ' 20 , we need ' 6 times ' more time . ( 2.5 hours ) ( 6 times ) = 15 hours final answer : [ reveal ] spoiler : c"
Answer: c
Question (physics): 66 cubic centimetres of silver is drawn into a wire 1 mm in diameter . the length if the wire in meters will be :
Options: a ) 76 m
b ) 80 m
c ) 84 m
d ) 88 m
e ) none of these
Rationale: explanation : let the length of the wire be h radius = 1 / 2 mm = 120 cm π r 2 h = 66 22 / 7 ∗ 1 / 20 ∗ 1 / 20 ∗ h = 66 = > h = 66 ∗ 20 ∗ 20 ∗ 7 / 22 = 8400 cm = 84 m option c
Answer: c
Question (general): a certain sum of money is divided among a , b and c so that for each rs . a has , b has 65 paisa and c 40 paisa . if c ' s share is rs . 48 , find the sum of money ?
Options: a ) 288 , b ) 262 , c ) 246 , d ) 205 , e ) 267
Rationale: "a : b : c = 100 : 65 : 40 = 20 : 13 : 8 8 - - - - 48 41 - - - - ? = > rs . 246 answer : c"
Answer: c
Question (physics): a is four times as fast as b . if b alone can do a piece of work in 60 days , in what time can a and b together complete the work ?
Options: a ) 10 , b ) 12 , c ) 22 , d ) 28 , e ) 20
Rationale: a can do the work in 60 / 4 i . e . , 15 days . a and b ' s one day ' s work = 1 / 15 + 1 / 60 = ( 4 + 1 ) / 60 = 1 / 12 so a and b together can do the work in 12 days . answer : b
Answer: b
Question (physics): 8 men can do a piece of work in 12 days . 4 women can do it in 48 days and 10 children can do it in 24 days . in how many days can 10 men , 4 women and 10 children together complete the piece of work ?
Options: a ) 5 days , b ) 15 days , c ) 28 days , d ) 6 days , e ) 7 days
Rationale: explanation : 1 man ’ s 1 day ’ s work = 1 / 8 × 12 = 1 / 96 10 men ’ s 1 day ’ s work = 1 × 10 / 96 = 5 / 48 1 woman ’ s 1 day ’ s work = 1 / 192 4 women ’ s 1 day ’ s work = 1 / 192 × 4 = 1 / 48 1 child ’ s 1 day ’ s work = 1 / 240 10 children ’ s 1 day ’ s work = 1 / 24 therefore , ( 10 men + 4 women + 10 children ) ’ s 1 day ’ s work = 5 / 48 + 1 / 48 + 1 / 24 = 8 / 48 = 1 / 6 the required no . of days = 6 days answer : option d
Answer: d
Question (other): if a positive integer n has 211 factors , then how many prime factors does n have ?
Options: a ) 3 , b ) 2 , c ) can not be determined , d ) 4 , e ) 1
Rationale: let the factor be a ^ x * b ^ y . . . . . so ( x + 1 ) ( y + 1 ) . . . . . = 211 . . now 211 is a prime number . . . so only one variable x or y is 210 and the others are 0 . . ( 210 + 1 ) ( 0 + 1 ) . . . so the number becomes a ^ 210 . . thus only one prime factor is there .
Answer: e
Question (general): rahim bought 65 books for rs . 1150 from one shop and 50 books for rs . 920 from another . what is the average price he paid per book ?
Options: a ) rs . 17 , b ) rs . 18 , c ) rs . 12 , d ) rs . 11 , e ) rs . 10
Rationale: "average price per book = ( 1150 + 920 ) / ( 65 + 50 ) = 2070 / 115 = rs . 18 answer : b"
Answer: b
Question (physics): a cistern 10 m long and 6 m wide contains water up to a breadth of 1 m 35 cm . find the total area of the wet surface .
Options: a ) 100 m sqaure , b ) 103 m sqaure , c ) 152 m sqaure , d ) 164 m sqaure , e ) none of these
Rationale: "explanation : area of the wet surface = 2 [ lb + bh + hl ] - lb = 2 [ bh + hl ] + lb = 2 [ ( 6 * 1.35 + 10 * 1.35 ) ] + 10 * 6 = 103 m square option b"
Answer: b
Question (general): a city with a population of 173,460 is to be divided into 9 voting districts , and no district is to have a population that is more than 10 percent greater than the population of any other district . what is the minimum possible population that the least populated district could have ?
Options: a ) 17,400 , b ) 17,500 , c ) 17,600 , d ) 17,700 , e ) 17,800
Rationale: "the minimum possible population occurs when all the other districts have a population that is 10 % greater than the least populated district . let p be the population of the least populated district . then 173,460 = p + 8 ( 1.1 ) p 9.8 p = 173,460 p = 17,700 the answer is d ."
Answer: d
Question (physics): car q and car y traveled the same 80 - mile route . if car q took 2 hours and car y traveled at an average speed that was 50 percent faster than the average speed of car q , how many hours did it take car y to travel the route ?
Options: a ) 2 / 3 , b ) 1 , c ) 4 / 3 , d ) 8 / 5 , e ) 3
Rationale: the speed of car q is ( distance ) / ( time ) = 80 / 2 = 40 miles per hour . the speed of car y = 3 / 2 * 40 = 60 miles per hour - - > ( time ) = ( distance ) / ( speed ) = 80 / 60 = 4 / 3 hours . answer : c . or : to cover the same distance at 3 / 2 as fast rate 2 / 3 as much time is needed - - > ( time ) * 2 / 3 = 2 * 2 / 3 = 4 / 3 hours . answer : c .
Answer: c
Question (general): 3 pig ’ s and 10 hens are brought for rs . 1200 . if the average price of a hen be rs . 30 . what is the average price of a pig .
Options: a ) 300 , b ) 350 , c ) 400 , d ) 425 , e ) 275
Rationale: explanation : average price of a hen = rs . 30 total price of 10 hens = 10 * 30 = rs . 300 but total price of 3 pigs and 10 hens = rs . 1200 total price of 3 pigs is = 1200 - 300 = 900 average price of a pig = 900 / 3 = rs . 300 answer : a
Answer: a
Question (other): how many factors of 240 are also multiples of 3 ?
Options: a ) 5 , b ) 8 , c ) 9 , d ) 10 , e ) 20
Rationale: "take factors of 240 240 = 2 ^ 4 * 3 ^ 1 * 5 ^ 1 total factors of 240 = ( 4 + 1 ) * ( 1 + 1 ) * ( 1 + 1 ) = 5 * 2 * 2 = 20 out of total factors of 20 , half will have 0 as power of 3 and half will have 1 as power of 3 . it is because we have considered only 0 and 1 as power of 3 to compute total factors of 240 . therefore factors that are multiple of 3 = 20 / 2 = 10 ans - d"
Answer: d
Question (general): mr yadav spends 60 % of his monthly salary on consumable items and 50 % of the remaining on clothes and transport . he saves the remaining amount . if his savings at the end of the year were 46800 , how much amount per month would he have spent on clothes and transport ?
Options: a ) 4038 , b ) 8076 , c ) 9691.2 , d ) 4845.6 , e ) 3900
Rationale: "∵ amount , he have spent in 1 month on clothes transport = amount spent on saving per month ∵ amount , spent on clothes and transport = 46800 ⁄ 12 = 3900 answer e"
Answer: e
Question (physics): a train 605 m long is running with a speed of 60 km / hr . in what time will it pass a man who is running at 6 km / hr in the direction opposite to that in which the train is going ?
Options: a ) 81 , b ) 16 , c ) 33 , d ) 54 , e ) 12
Rationale: "speed of train relative to man = 60 + 6 = 66 km / hr . = 66 * 5 / 18 = 55 / 3 m / sec . time taken to pass the men = 605 * 3 / 55 = 33 sec . answer : c"
Answer: c
Question (gain): tom opened a shop investing rs . 3000 . jose joined him 2 months later , investing rs . 4500 . they earned a profit of rs . 6300 after completion of one year . what will be jose ' s share of profit ?
Options: a ) 3500 , b ) 2800 , c ) 3251 , d ) 4251 , e ) 3508
Rationale: "sol = ~ s - so anju ’ s share = [ 5 / 9 ] x 6300 = 3500 a"
Answer: a
Question (other): the simple form of the ratio 2 / 3 : 2 / 5 is
Options: a ) 5 : 7 , b ) 5 : 2 , c ) 5 : 9 , d ) 5 : 3 , e ) 5 : 4
Rationale: "2 / 3 : 2 / 5 = 10 : 6 = 5 : 3 answer : d"
Answer: d
Question (gain): rs . 1500 is divided into two parts such that if one part is invested at 6 % and the other at 5 % the whole annual interest from both the sum is rs . 83 . how much was lent at 5 % ?
Options: a ) 299 , b ) 566 , c ) 678 , d ) 700 , e ) 8277
Rationale: "( x * 5 * 1 ) / 100 + [ ( 1500 - x ) * 6 * 1 ] / 100 = 83 5 x / 100 + 90 – 6 x / 100 = 83 x / 100 = 7 = > x = 700 answer : d"
Answer: d
Question (gain): a towel , when bleached , was found to have lost 20 % of its length and 10 % of its breadth . the percentage of decrease in area is ?
Options: a ) 25 % , b ) 26 % , c ) 27 % , d ) 28 % , e ) 29 %
Rationale: "explanation : let original length = x and original width = y decrease in area will be = xy − ( 80 x / 100 × 90 y / 100 ) = ( xy − 18 / 25 xy ) = 7 / 25 xy decrease = ( 7 xy / 25 xy × 100 ) % = 28 option d"
Answer: d
Question (general): gold is 10 times as heavy as water and copper is 5 times as heavy as water . in what ratio should these be mixed to get an alloy 6 times as heavy as water ?
Options: a ) 3 : 2 , b ) 1 : 4 , c ) 3 : 1 , d ) 5 : 2 , e ) 4 : 3
Rationale: g = 10 w c = 5 w let 1 gm of gold mixed with x gm of copper to get 1 + x gm of the alloy 1 gm gold + x gm copper = x + 1 gm of alloy 10 w + 5 wx = x + 1 * 6 w 10 + 5 x = 6 ( x + 1 ) x = 4 ratio of gold with copper = 1 : 4 = 1 : 4 answer is b
Answer: b
Question (physics): calculate how many days it will take for 8 boys to paint a 50 m long wall if 6 boys can paint a 60 m long wall in 5 days ,
Options: a ) 4.13 days , b ) 3.13 days , c ) 513 days , d ) 9.13 days , e ) 2 days
Rationale: the length of wall painted by one boy in one day = 60 / 6 * 1 / 5 = 2 m no . of days required to paint 50 m cloth by 8 boys = 50 / 8 * 1 / 2 = 3.13 days . b
Answer: b
Question (gain): a fair price shopkeeper takes 10 % profit on his goods . he lost 20 % goods during theft . his loss percent is :
Options: a ) 10 , b ) 13 , c ) 12 , d ) 18 , e ) 19
Rationale: "c 12 % suppose he has 100 items . let c . p . of each item be $ 1 . total cost = $ 100 . number of items left after theft = 80 . s . p . of each item = $ 1.10 total sale = 1.10 * 80 = $ 88 hence , loss % = 12 / 100 * 100 = 12 %"
Answer: c
Question (gain): a customer went to a shop and paid a total of $ 40 , out of which 90 cents was for sales tax on taxable purchases . if the tax rate was 6 % , then what was the cost of the tax free items ?
Options: a ) $ 22.70 , b ) $ 23.20 , c ) $ 24.10 , d ) $ 25.50 , e ) $ 26.90
Rationale: "the total cost was $ 40 . the tax was $ 0.90 let the original price of the taxable items = x given that tax rate = 6 % 0.06 x = 0.90 x = $ 15 the cost of the tax free items was $ 40 - $ 15 - $ 0.90 = $ 24.10 the answer is c ."
Answer: c