Cheukting/mathqa huggingface dataset:
Question (general): if greg buys 5 shirts , 4 trousers and 2 ties , the total cost is $ 80 . if greg buys 7 shirts , 4 trousers and 2 ties , the total cost is $ 70 . how much will it cost him to buy 2 trousers , 3 shirts and 1 ties ?
Options: a ) $ 37.5 , b ) $ 64 , c ) $ 75 , d ) $ 96 , e ) can not be determined
Rationale: "solution : 5 x + 4 y + 2 z = 80 7 x + 4 y + 2 z = 70 adding both the equations = 12 x + 8 y + 4 z = 150 3 x + 2 y + 1 z = 37.5 ans a"
Answer: a
Question (general): what is the sum of all the numbers between 1 and 16 , inclusive ?
Options: a ) 190 , b ) 200 , c ) 185 , d ) 166 , e ) 213
Rationale: "all you have to do is add 1 + 2 + 3 + 4 . . . + 14 + 15 + 16 , which is 190 . final answer : a"
Answer: a
Question (gain): ramesh purchased a refrigerator for rs . 12500 after getting a discount of 20 % on the labelled price . he spent rs . 125 on transport and rs . 250 on installation . at what price should it be sold so that the profit earned would be 20 % if no discount was offered ?
Options: a ) 19200 , b ) 17606 , c ) 17604 , d ) 17600 , e ) 117601
Rationale: "price at which the tv set is bought = rs . 12,500 discount offered = 20 % marked price = 12500 * 100 / 80 = rs . 15625 the total amount spent on transport and installation = 125 + 250 = rs . 375 \ total price of tv set = 15625 + 375 = rs . 16000 the price at which the tv should be sold to get a profit of 20 % if no discount was offered = 16000 * 120 / 100 = rs . 19200 . answer : a"
Answer: a
Question (physics): the distance between delhi and mathura is 100 kms . a starts from delhi with a speed of 50 kmph at 7 a . m . for mathura and b starts from mathura with a speed of 45 kmph at 8 p . m . from delhi . when will they meet ?
Options: a ) 11 , b ) 77 , c ) 8 3 / 4 , d ) 8 1 / 2 , e ) 8
Rationale: "d = 100 – 50 = 50 rs = 45 + 50 = 95 t = 90 / 45 = 0.5 hours 8 a . m . + 0.5 = 8 1 / 2 a . m . . answer : d"
Answer: d
Question (geometry): the length and breadth of a rectangular floor are 16.25 metre and 12.75 metre respectively . find how many minimum number of square tiles would be required to cover it completely ?
Options: a ) 375
b ) 2570
c ) 2800
d ) 3315
e ) none of these
Rationale: explanation : since we require minimum number of square tiles , the size of the tile is given as the h . c . f . of two sides of the room . the h . c . f . of 1625 cm & 1275 cm . is 25 cm . hence , we get , required number = ( 1625 * 1275 ) / ( 25 * 25 ) = 3315 answer : d
Answer: d
Question (physics): a man can row upstream at 25 kmph and downstream at 37 kmph , and then find the speed of the man in still water ?
Options: a ) 86 , b ) 67 , c ) 31 , d ) 15 , e ) 17
Rationale: "us = 25 ds = 37 m = ( 37 + 25 ) / 2 = 31 answer : c"
Answer: c
Question (physics): walking at 50 % of his usual speed a man takes 24 minutes more to cover a distance . what is his usual time to cover this distance ?
Options: a ) 24 , b ) 36 , c ) 42 , d ) 48 , e ) 54
Rationale: "speed is inversly proprtional to time walking at 50 % of speed meand 1 / 2 s takes 2 t . it takes 24 minutes extra to cover the distance . then 2 t = t + 24 t = 24 . option a is correct"
Answer: a
Question (general): 80 % of the population of a village is 32000 . the total population of the village is ?
Options: a ) 40000 , b ) 24000 , c ) 26682 , d ) 29973 , e ) 12312
Rationale: "x * ( 80 / 100 ) = 32000 x = 400 * 100 x = 40000 answer : a"
Answer: a
Question (general): a number x is 4 times another number y . the percentage that y is less than x is
Options: a ) 12.5 % , b ) 75 % , c ) 80 % , d ) 11 % , e ) 1 %
Rationale: "say y = 1 and x = 4 . then y = 1 is less than x = 4 by ( 4 - 1 ) / 4 * 100 = 3 / 4 * 100 = 75 % . answer : b ."
Answer: b
Question (gain): a trader has 1600 kg of sugar . he sells a part at 8 % profit and the rest at 12 % profit . if he gains 11 % on the whole , find the quantity sold at 12 % ?
Options: a ) 1000 , b ) 1200 , c ) 1400 , d ) 1450 , e ) 1500
Rationale: by rule of alligation , % profit by selling part 1 % profit by selling part 2 8 12 net % profit 11 12 - 11 = 1 11 - 8 = 3 = > quantity of part 1 : quantity of part 2 = 1 : 3 given that total quantity = 1600 kg hence , quantity of part 2 ( quantity sold at 12 % profit ) = 1600 × 3 4 = 1200 b )
Answer: b
Question (gain): john spent 40 percent of his earning last month on rent and 30 percent less than what he spent on rent to purchase a new dishwasher . what percent of last month ' s earning did john have left over ?
Options: a ) 30 % , b ) 32 % , c ) 45 % , d ) 68 % , e ) 70 %
Rationale: say john ' s earning last month was $ 100 . john spent 40 percent of his earning last month on rent - - > $ 40 on rent ; 30 percent less than what he spent on rent to purchase a new dishwasher - - > $ 40 * 0.7 = $ 28 on the dishwasher . left over amount 100 - ( 40 + 28 ) = $ 32 . answer : b .
Answer: b
Question (physics): 10 women can complete a work in 7 days and 10 children take 14 days to complete the work . how many days will 5 women and 4 children take to complete the work ?
Options: a ) 4 , b ) 5 , c ) 7 , d ) 8 , e ) 10
Rationale: "1 women ' s 1 day work = 1 / 70 1 child ' s 1 day work = 1 / 140 ( 5 women + 4 children ) ' s 1 day work = ( 5 / 10 + 4 / 140 ) = 1 / 10 5 women and 4 children will complete the work in 10 days . e"
Answer: e
Question (physics): lloyd normally works 7.5 hours per day and earns $ 4.50 per hour . for each hour he works in excess of 7.5 hours on a given day , he is paid 2.0 times his regular rate . if lloyd works 10.5 hours on a given day , how much does he earn for that day ?
Options: a ) $ 33.75 , b ) $ 47.25 , c ) $ 60.75 , d ) $ 54.00 , e ) $ 70.00
Rationale: "daily working hour * regular rate + overtime * increased rate 7.5 * 4.5 + 3 * 4.5 * 2.0 = 60.75 answer c"
Answer: c
Question (gain): on a certain road , 20 % of the motorists exceed the posted speed limit and receive speeding tickets , but 20 % of the motorists who exceed the posted speed limit do not receive speeding tickets . what percent of the motorists on that road exceed the posted speed limit ?
Options: a ) 10.5 % , b ) 12.5 % , c ) 15 % , d ) 25 % , e ) 30 %
Rationale: "suppose there are x motorists . 20 % of them exceeded the speed limit and received the ticket , i . e . x / 5 . again , suppose total no . of motorists who exceeded the speed limit are y . 20 % of y exceeded the speed limit but did n ' t received the ticket , i . e . y / 5 . it means 4 y / 5 received the ticket . hence , 4 y / 5 = x / 5 or y / x = 1 / 4 or y / x * 100 = 1 / 4 * 100 = 25 % d"
Answer: d
Question (general): if the remainder is 16 when the integer n is divided by 30 , what is the remainder when 2 n is divided by 15 ?
Options: a ) 0 , b ) 2 , c ) 4 , d ) 6 , e ) 8
Rationale: n = 30 k + 16 2 n = 2 ( 30 k + 16 ) = 4 k * 15 + 32 = 4 k * 15 + 2 * 15 + 2 = 15 j + 2 the answer is b .
Answer: b
Question (physics): to apply for the position of photographer at a local magazine , a photographer needs to include 4 or 5 photos in an envelope accompanying the application . if the photographer has pre - selected 7 photos representative of her work , how many choices does she have to provide the photos for the magazine ?
Options: a ) 48 , b ) 50 , c ) 52 , d ) 54 , e ) 56
Rationale: 7 c 4 + 7 c 5 = 35 + 21 = 56 the answer is e .
Answer: e
Question (physics): at 6 ′ o a clock ticks 6 times . the time between first and last ticks is 30 seconds . how long does it tick at 12 ′ o clock
Options: a ) 47 , b ) 76 , c ) 28 , d ) 66 , e ) 11
Rationale: explanation : for ticking 6 times , there are 5 intervals . each interval has time duration of 30 / 5 = 6 secs at 12 o ' clock , there are 11 intervals , so total time for 11 intervals = 11 × 6 = 66 secs . answer : d
Answer: d
Question (general): john purchased some shirts and trousers for $ 1100 . he paid $ 550 less for the shirts than he did for the trousers . if he bought 5 shirts and the cost of a shirt is $ 20 less than that of a trouser , how many trousers did he buy ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 11
Rationale: "given that the total purchase of two items cost 1100 . so the average purchase of one item will cost 1100 / 2 = 550 . its given as total shirt cost 100 $ less . hence total shirt cost = 550 - 275 and total trouser cost = 300 + 275 5 shirts = 275 $ = = > one shirt = 55 $ one trouser = 55 + 20 = 75 $ total trousers = 825 / 75 = 11 . e"
Answer: e
Question (general): a case of 12 rolls of paper towels sells for $ 9 . the cost of one roll sold individually is $ 1 . what is the percent t of savings per roll for the 12 - roll package over the cost of 12 rolls purchased individually ?
Options: a ) 9 % , b ) 11 % , c ) 15 % , d ) 25 % , e ) 90 %
Rationale: "cost of 12 paper towels individually = 1 * 12 = 12 cost of a set of 12 paper towels = 9 cost of one roll = 9 / 12 = 3 / 4 = 0.75 savings per roll = 1 - . 75 = 0.25 % of savings is t = . 25 / 1 * 100 = 25 % d is the answer ."
Answer: d
Question (probability): in a throw of a coin find the probability of getting a head ?
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 2 / 3 , e ) 2 / 5
Rationale: s = { h , t } e = { h } p ( e ) = 1 / 2 answer is a
Answer: a
Question (physics): a can do a piece of work in 15 days . a does the work for 5 days only and leaves the job . b does the remaining work in 12 days . in how many days b alone can do the work ?
Options: a ) 5 days , b ) 7 days , c ) 12 days , d ) 9 days , e ) 18 days
Rationale: explanation : a ’ s 5 day work = 5 * 1 / 15 = 1 / 3 remaining work = 1 - 1 / 3 = 2 / 3 b completes 2 / 3 work in 6 days b alone can do in x days 2 / 3 * x = 12 x = 18 days answer : option e
Answer: e
Question (general): evaluate : 460 - 12 * 3 * 2 = ?
Options: a ) 878 , b ) 545 , c ) 434 , d ) 442 , e ) 452
Rationale: "according to order of operations , 12 ? 3 ? 2 ( division and multiplication ) is done first from left to right 12 * * 2 = 4 * 2 = 8 hence 460 - 12 * 3 * 2 = 460 - 8 = 452 correct answer e"
Answer: e
Question (physics): in a km race , a beats bby 28 metres or 7 seconds . find a ' s timeoverthe course
Options: a ) 4 min , b ) 3 min 3 sec , c ) 4 min 4 sec , d ) 5 min 3 sec , e ) 4 min 3 sec
Rationale: clearly , b covers 28 m in 7 seconds . : . b ' s time over the course = ( 278 x 1000 ) sec = 250 seconds . : . a ' s time over the course = ( 250 - 7 - ) sec = 243 sec = 4 min . 3 sec . answer e 4 min 3 sec
Answer: e
Question (physics): a thief is spotted by a policeman from a distance of 200 meters . when the policeman starts the chase , the thief also starts running . if the speed of the thief be 8 km / hr and that of the policeman 10 km / hr , how far the thief will have run before he is overtaken ?
Options: a ) 350 m , b ) 200 m , c ) 400 m , d ) 800 m , e ) none of them
Rationale: "relative speed of the policeman = ( 10 - 8 ) km / hr = 2 km / hr . time taken by police man to cover ( 200 m / 1000 ) x 1 / 2 hr = 1 / 10 hr . in 1 / 10 hrs , the thief covers a distance of 8 x 1 / 10 km = 4 / 5 km = 800 m answer is d ."
Answer: d
Question (general): set x consists of 10 integers and has median of 30 and a range of 20 . what is the value of the greatest possible integer that can be present in the set ?
Options: a ) 32 , b ) 37 , c ) c . 40 , d ) 43 , e ) 50
Rationale: note that both median and range do not restrict too many numbers in the set . range is only concerned with the smallest and greatest . median only cares about the middle . quick check of each option starting from the largest : ( e ) 50 range of 20 means the smallest integer will be 30 . so 20 can not lie in between and hence can not be the median . ( d ) 43 range of 20 means the smallest integer will be 23 . so 20 can not lie in between and hence can not be the median . ( c ) 40 range of 20 means the smallest integer will be 20 . 20 can lie in between such as : 20 , 20 , 20 , 20 , 20 , 20 , 20 , 20 , 20 , 50 this is possible . hence it is the greatest such number . answer ( e )
Answer: e
Question (physics): a cistern can be filled by a tap in 5 hours while it can be emptied by another tap in 9 hours . if both the taps are opened simultaneously , then after how much time will the cistern get filled ?
Options: a ) 4.5 hrs , b ) 5 hrs , c ) 6.5 hrs , d ) 7.25 hrs , e ) 11.25 hrs
Rationale: "net part filled in 1 hour = 1 / 5 - 1 / 9 = 4 / 45 therefore the cistern will be filled in 45 / 4 hours or 11.25 hours . answer : e"
Answer: e
Question (general): find the sum lend at c . i . at 5 p . c per annum will amount to rs . 650 in 2 years ?
Options: a ) 221 , b ) 287 , c ) 400 , d ) 589 , e ) 171
Rationale: "explanation : 650 = p ( 21 / 20 ) 2 p = 589.56 answer : d"
Answer: d
Question (other): there are 456 doctors and nurses in a hospital . if the ratio of the doctors to the nurses is 8 : 11 , then how many nurses are there in the hospital ?
Options: a ) 264 , b ) 209 , c ) 57 , d ) 171 , e ) 181
Rationale: given , the ratio of the doctors to the nurses is 8 : 11 number of nurses = 11 / 19 x 456 = 264 answer : a
Answer: a
Question (gain): find the simple interest on rs . 70,400 at 16 2 / 3 % per annum for 9 months .
Options: a ) s . 8500 , b ) s . 8000 , c ) s . 7500 , d ) s . 8800 , e ) s . 6500
Rationale: "p = rs . 70400 , r = 50 / 3 % p . a and t = 9 / 12 years = 3 / 4 years . s . i . = ( p * r * t ) / 100 = rs . ( 70,400 * ( 50 / 3 ) * ( 3 / 4 ) * ( 1 / 100 ) ) = rs . 8800 answer is d ."
Answer: d
Question (gain): the true discount on a bill due 9 months hence at 16 % per annum is rs . 153 . the amount of the bill is
Options: a ) rs . 1386 , b ) rs . 1764 , c ) rs . 1275 , d ) rs . 2268 , e ) none of these
Rationale: "solution 32.5 let p . w . be rs . x . then , s . i . on rs . x at 16 % for 9 months = rs . 153 . ∴ x 16 x 9 / 12 x 1 / 100 } = 153 or x = 1275 . ∴ p . w . = rs . 1275 . answer c"
Answer: c
Question (geometry): a voltage will influence current only if the circuit is :
Options: a ) 2
b ) 7
c ) 6
d ) 889
e ) 1
Rationale: answer : b
Answer: b
Question (gain): a watch was sold at a loss of 10 % . if it was sold for rs . 140 more , there would have been a gain of 2 % . what is the cost price ?
Options: a ) s . 1000 , b ) s . 1009 , c ) s . 1166.7 , d ) s . 1006 , e ) s . 1002
Rationale: "explanation : 90 % 102 % - - - - - - - - 12 % - - - - 140 100 % - - - - ? = > rs . 1166.7 answer : c"
Answer: c
Question (general): in the junior basketball league there are 15 teams , 2 / 3 of them are bad and ½ are rich . what ca n ' t be the number of teams that are rich and bad ?
Options: a ) 4 . , b ) 6 . , c ) 7 . , d ) 9 . , e ) 5 .
Rationale: "total teams = 16 bad teams = ( 2 / 3 ) * 15 = 10 rich teams = 8 so maximum value that the both rich and bad can take will be 8 . so e = 9 can not be that value . ans d ."
Answer: d
Question (other): a movie buff buys movies on dvd and on blu - ray in a ratio of 17 : 4 . if she returns 4 blu - ray movies , that ratio would change to 9 : 2 . if she buys movies on no other medium , what was the original number of movies purchased ?
Options: a ) 22 , b ) 28 , c ) 77 , d ) 99 , e ) 378
Rationale: if u can just keep an eye on the options 99 is the only multiple of 9 in options given . . so you can mark it wid in seconds . now coming to the process m ( d ) = 17 x and b ( d ) = 4 x now from the next line the new eqn becomes 17 x / ( 4 x - 4 ) = 9 / 2 solving it 34 x = 36 x - 36 x = 18 which means m ( d ) = 306 and b ( d ) = 72 so total initially is m ( d ) + b ( d ) = 378 e
Answer: e
Question (gain): in 1998 the profits of company n were 10 percent of revenues . in 1999 , the revenues of company n fell by 20 percent , but profits were 15 percent of revenues . the profits in 1999 were what percent of the profits in 1998 ?
Options: a ) 80 % , b ) 105 % , c ) 120 % , d ) 124.2 % , e ) 138 %
Rationale: "let ' s test : 1998 revenues = $ 100 profits = $ 10 next we ' re told that , in 1999 , revenue fell by 20 % , but profits were 15 % of revenues . using the numbers from 1998 ( above ) , we end up with . . . 1999 revenues = $ 80 profits = $ 12 we ' re asked to compare the profits in 1999 to the profits in 1998 ( as a percentage ) : $ 12 / $ 10 = 1.2 = 120 % answer : c"
Answer: c
Question (geometry): a cube has two of its faces painted half red and half white . the other faces are completely painted white . what is the ratio between the red painted areas and the white painted areas of the cube ?
Options: a ) 1 : 5 , b ) 3 : 6 , c ) 1 : 2 , d ) 2 : 9 , e ) 1 : 3
Rationale: "let x be the area of each face of the cube . the area painted red is 2 ( x / 2 ) = x the area painted white is 2 ( x / 2 ) + 4 x = 5 x the ratio of red to white is x : 5 x which is 1 : 5 . the answer is a ."
Answer: a
Question (physics): if athul rows 16 km upstream and 24 km down steam taking 4 hours each , then the speed of the stream
Options: a ) 1 kmph , b ) 2 kmph , c ) 1.5 kmph , d ) 12 kmph , e ) 15 kmph
Rationale: speed upstream = 16 / 4 = 4 kmph speed down stream = 24 / 4 = 6 kmph speed of stream = ½ ( 6 - 4 ) = 1 kmph answer : a
Answer: a
Question (general): the average age of 30 students in a class is 5 years . if teacher ' s age is also included then average increases 1 year then find the teacher ' s age ?
Options: a ) 59 , b ) 55 , c ) 61 , d ) 45 , e ) 36
Rationale: "total age of 50 students = 30 * 5 = 150 total age of 51 persons = 31 * 6 = 186 age of teacher = 186 - 150 = 36 years answer is e"
Answer: e
Question (gain): a , b and c enter into a partnership . a invests 3 times as much as b invests and 2 / 3 of what c invests . at the end of the year , the profit earned is rs . 11000 . what is the share of c ?
Options: a ) rs . 2250 , b ) rs . 3000 , c ) rs . 6750 , d ) rs . 5625 , e ) none of these
Rationale: "explanation : let the investment of c be rs . x . the inverstment of b = rs . ( 2 x / 3 ) the inverstment of a = rs . ( 3 × ( 2 / 3 ) x ) = rs . ( 2 x ) ratio of capitals of a , b and c = 2 x : 2 x / 3 : x = 6 : 2 : 3 c ' s share = rs . [ ( 3 / 11 ) × 11000 ] = rs . 3000 answer : option b"
Answer: b
Question (general): a batsman scored 120 runs which included 3 boundaries and 8 sixes . what % of his total score did he make by running between the wickets
Options: a ) 30 % , b ) 50 % , c ) 60 % , d ) 80 % , e ) 90 %
Rationale: "number of runs made by running = 110 - ( 3 x 4 + 8 x 6 ) = 120 - ( 60 ) = 60 now , we need to calculate 60 is what percent of 120 . = > 60 / 120 * 100 = 50 % b"
Answer: b
Question (physics): worker a takes 8 hours to do a job . worker b takes 10 hours to do a job . how long should it take both a and b , working together to do same job
Options: a ) 49 , b ) 249 , c ) 349 , d ) 449 , e ) none of these
Rationale: explanation : in this type of questions , first we need to calculate 1 hours work , then their collective work as a ' s 1 hour work is 1 / 8 b ' s 1 hour work is 1 / 10 ( a + b ) ' s 1 hour work = 1 / 8 + 1 / 10 = 9 / 40 so both will finish the work in 40 / 9 hours = 449 answer : d
Answer: d
Question (general): 4.036 divided by 0.04 gives :
Options: a ) 10.09 , b ) 1.06 , c ) 10.06 , d ) 100.9 , e ) 100.6
Rationale: "= 4.036 / 0.04 = 403.6 / 4 = 100.9 answer is d ."
Answer: d
Question (general): find the constant k so that : - x 2 - ( k + 7 ) x - 8 = - ( x - 2 ) ( x - 4 )
Options: a ) - 11 , b ) - 12 , c ) - 13 , d ) - 14 , e ) - 15
Rationale: "- x 2 - ( k + 7 ) x - 8 = - ( x - 2 ) ( x - 4 ) : given - x 2 - ( k + 7 ) x - 8 = - x 2 + 6 x - 8 - ( k + 7 ) = 6 : two polynomials are equal if their corresponding coefficients are equal . k = - 13 : solve the above for k correct answer c"
Answer: c
Question (physics): a car takes 4.5 hours to travel from a to b , which is 360 miles apart . what is the average speed of the car ?
Options: a ) 40 , b ) 50 , c ) 60 , d ) 80 , e ) 85
Rationale: average speed = 360 / 4.5 hours = 360 / 270 = 1.33 miles per min = 80 miles per hour answer : d
Answer: d
Question (general): there are 20 balls which are red , blue or green . if 7 balls are green and the sum of red balls and green balls is less than 13 , at most how many red balls are there ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: "explanation : given : red + green + blue = 20 green = 7 solution : r + g < 13 therefore r + 7 < 13 so r < 6 ans : at most 5 red balls b . 5 hence ( b ) is correct . answer : b"
Answer: b
Question (gain): an amount of rs . 100000 is invested in two types of shares . the first yields an interest of 9 % p . a and the second , 11 % p . a . if the total interest at the end of one year is 9 1 / 2 % , then the amount invested at 11 % was ?
Options: a ) 23777 , b ) 25000 , c ) 29977 , d ) 26777 , e ) 19871
Rationale: "let the sum invested at 9 % be rs . x and that invested at 11 % be rs . ( 100000 - x ) . then , ( x * 9 * 1 ) / 100 + [ ( 100000 - x ) * 11 * 1 ] / 100 = ( 100000 * 19 / 2 * 1 / 100 ) ( 9 x + 1100000 - 11 x ) = 950000 x = 75000 sum invested at 9 % = rs . 75000 sum invested at 11 % = rs . ( 100000 - 75000 ) = rs . 25000 . answer : b"
Answer: b
Question (gain): at what price must an book costing $ 47.50 be marked in order that after deducting 8 % from the list price . it may be sold at a profit of 25 % on the cost price ?
Options: a ) 72.5 , b ) 64.5 , c ) 62.5 , d ) 82.5 , e ) 60.5
Rationale: c $ 62.50 cp = 47.50 sp = 47.50 * ( 125 / 100 ) = 59.375 mp * ( 92 / 100 ) = 59.375 mp = 64.5 b
Answer: b
Question (gain): exactly 36 % of the numbers in set s are even multiples of 3 . if 40 % of the even integers in set s are not multiples of 3 , what percent of the numbers in set s are not even integers ?
Options: a ) 76 % , b ) 60 % , c ) 50 % , d ) 40 % , e ) 24 %
Rationale: let s be the total number of elements in set s . we know that 0.36 * s is the number of even multiples of three . let n be the number of even numbers . we know 0.40 * n are even numbers not multiple of three . this also means , 0.60 * n are even numbers that are multiples of three . therefore : 0.06 * n = 0.36 * s n = ( 0.36 / 0.60 ) * s = ( 36 / 60 ) * s = ( 6 / 10 ) * s = 0.60 * s = 60 % of s so even numbers are 60 % of s . that means , 40 % of s are not even integers . answer = d
Answer: d
Question (general): the average age of a group of 10 persons was decreased by 3 years when one person , whose age was 48 years , was replaced by a new person . find the age of the new person ?
Options: a ) 18 , b ) 56 , c ) 12 , d ) 17 , e ) 14
Rationale: "initial average age of the 10 persons be p . age of the new person q . sum of the ages of the initial 10 persons = 10 p new average = ( p - 3 ) 10 ( p - 3 ) = 10 p - 48 + q = > q = 18 answer : a"
Answer: a
Question (physics): a glucose solution contains 10 grams of glucose per 100 cubic centimeters of solution . if 45 cubic centimeters of the solution were poured into an empty container , how many grams of glucose would be in the container ?
Options: a ) 3.00 , b ) 5.00 , c ) 4.50 , d ) 5.50 , e ) 6.75
Rationale: "we are given that a glucose solution contains 10 grams of glucose per 100 cubic centimeters of solution . since we are dealing with a solution , we know that the grams of glucose is proportional to the number of cubic centimeters of solution . thus , to determine how many grams of glucose would be in the container when we have 45 cubic centimeters of solution , we can set up a proportion . we can say : “ 10 grams of glucose is to 100 cubic centimeters of solution as x grams of glucose is to 45 cubic centimeters of solution . ” let ’ s now set up the proportion and solve for x . 10 / 100 = x / 45 when we cross multiply we obtain : ( 10 ) ( 45 ) = 100 x 450 = 100 x 4.50 = x there are 4.5 grams of glucose in the solution in the container . the answer is c ."
Answer: c
Question (other): find the two digit number , such that the ratio is 7 / 4 of original number to the number formed by reversing the digits .
Options: a ) 20 , b ) 21 , c ) 22 , d ) 23 , e ) 24
Rationale: here ratio is 7 / 4 . so lets check one by one . for 1 : 7 * 1 / 4 * 1 = 7 / 4 for 2 : 7 * 2 / 4 * 2 = 14 / 8 , which does n ' t satisfy the conditions . for 3 : 7 * 3 / 4 * 3 = 21 / 12 answer : b
Answer: b
Question (gain): the owner of a furniture shop charges his customer 10 % more than the cost price . if a customer paid rs . 7350 for a computer table , then what was the cost price of the computer table ?
Options: a ) rs . 6289 , b ) rs . 6298 , c ) rs . 6681 , d ) rs . 6725 , e ) rs . 6708
Rationale: "cp = sp * ( 100 / ( 100 + profit % ) ) = 7350 ( 100 / 110 ) = rs . 6681 . answer : c"
Answer: c